LMFDB - Embedded newform 76.7.l.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(23,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	76.23
Dual form			76.7.l.a.43.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.31367 + 3.24195i) q^{2} +(23.5223 - 4.14762i) q^{3} +(42.9795 - 47.4211i) q^{4} +(104.114 - 87.3621i) q^{5} +(-158.588 + 106.593i) q^{6} +(538.554 + 310.935i) q^{7} +(-160.601 + 486.160i) q^{8} +(-148.939 + 54.2093i) q^{9} +O(q^{10})$	\(q+(-7.31367 + 3.24195i) q^{2} +(23.5223 - 4.14762i) q^{3} +(42.9795 - 47.4211i) q^{4} +(104.114 - 87.3621i) q^{5} +(-158.588 + 106.593i) q^{6} +(538.554 + 310.935i) q^{7} +(-160.601 + 486.160i) q^{8} +(-148.939 + 54.2093i) q^{9} +(-478.233 + 976.470i) q^{10} +(1275.70 - 736.525i) q^{11} +(814.294 - 1293.72i) q^{12} +(-15.6232 + 88.6038i) q^{13} +(-4946.84 - 528.106i) q^{14} +(2086.66 - 2486.79i) q^{15} +(-401.522 - 4076.27i) q^{16} +(215.983 + 78.6113i) q^{17} +(913.546 - 879.321i) q^{18} +(-6741.68 + 1263.19i) q^{19} +(331.967 - 8691.99i) q^{20} +(13957.7 + 5080.18i) q^{21} +(-6942.27 + 9522.46i) q^{22} +(3557.68 - 4239.88i) q^{23} +(-1761.31 + 12101.7i) q^{24} +(494.357 - 2803.64i) q^{25} +(-172.986 - 698.668i) q^{26} +(-18358.0 + 10599.0i) q^{27} +(37891.7 - 12175.0i) q^{28} +(23360.2 - 8502.42i) q^{29} +(-7199.11 + 24952.4i) q^{30} +(16115.7 + 9304.39i) q^{31} +(16151.7 + 28510.8i) q^{32} +(26952.6 - 22615.9i) q^{33} +(-1834.48 + 125.268i) q^{34} +(83235.0 - 14676.6i) q^{35} +(-3830.66 + 9392.74i) q^{36} +50880.1 q^{37} +(45211.2 - 31094.8i) q^{38} +2148.97i q^{39} +(25751.1 + 64646.5i) q^{40} +(9674.68 + 54867.9i) q^{41} +(-118552. + 8095.35i) q^{42} +(-84104.7 - 100232. i) q^{43} +(19902.1 - 92150.6i) q^{44} +(-10770.8 + 18655.6i) q^{45} +(-12274.2 + 42542.9i) q^{46} +(-7482.35 - 20557.6i) q^{47} +(-26351.6 - 94218.0i) q^{48} +(134536. + 233023. i) q^{49} +(5473.69 + 22107.6i) q^{50} +(5406.46 + 953.306i) q^{51} +(3530.21 + 4549.02i) q^{52} +(51686.3 + 43370.0i) q^{53} +(99903.2 - 137034. i) q^{54} +(68473.9 - 188131. i) q^{55} +(-237656. + 211887. i) q^{56} +(-153341. + 57675.2i) q^{57} +(-143284. + 137917. i) q^{58} +(59458.3 - 163360. i) q^{59} +(-28242.4 - 205833. i) q^{60} +(-293591. - 246352. i) q^{61} +(-148029. - 15803.0i) q^{62} +(-97067.2 - 17115.6i) q^{63} +(-210559. - 156156. i) q^{64} +(6114.01 + 10589.8i) q^{65} +(-123803. + 252784. i) q^{66} +(-46978.1 - 129071. i) q^{67} +(13010.7 - 6863.46i) q^{68} +(66099.5 - 114488. i) q^{69} +(-561173. + 377183. i) q^{70} +(294848. + 351386. i) q^{71} +(-2434.63 - 81114.2i) q^{72} +(-67537.2 - 383022. i) q^{73} +(-372120. + 164951. i) q^{74} -67998.5i q^{75} +(-229852. + 373989. i) q^{76} +916045. q^{77} +(-6966.84 - 15716.8i) q^{78} +(517946. - 91327.9i) q^{79} +(-397916. - 389320. i) q^{80} +(-299351. + 251185. i) q^{81} +(-248636. - 369920. i) q^{82} +(-176423. - 101858. i) q^{83} +(840803. - 443545. i) q^{84} +(29354.5 - 10684.2i) q^{85} +(940061. + 460401. i) q^{86} +(514222. - 296886. i) q^{87} +(153190. + 738481. i) q^{88} +(-186649. + 1.05854e6i) q^{89} +(18293.6 - 171359. i) q^{90} +(-35963.9 + 42860.2i) q^{91} +(-48152.3 - 350937. i) q^{92} +(417669. + 152019. i) q^{93} +(121370. + 126094. i) q^{94} +(-591549. + 720484. i) q^{95} +(498177. + 603649. i) q^{96} +(-259572. - 94476.5i) q^{97} +(-1.73940e6 - 1.26810e6i) q^{98} +(-150075. + 178852. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) $ 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−7.31367	+	3.24195i	−0.914209	+	0.405244i
$2$	−7.31367	+	3.24195i	−0.914209	+	0.405244i
$3$	23.5223	−	4.14762i	0.871197	−	0.153616i	0.279861	−	0.960041i	$-0.409712\pi$
$3$	23.5223	−	4.14762i	0.871197	−	0.153616i	0.591336	+	0.806425i	$0.298601\pi$
$4$	42.9795	−	47.4211i	0.671555	−	0.740955i
$5$	104.114	−	87.3621i	0.832913	−	0.698897i	−0.123045	−	0.992401i	$-0.539266\pi$
$5$	104.114	−	87.3621i	0.832913	−	0.698897i	0.955958	+	0.293504i	$0.0948214\pi$
$6$	−158.588	+	106.593i	−0.734204	+	0.493484i
$7$	538.554	+	310.935i	1.57013	+	0.906515i	0.996152	+	0.0876440i	$0.0279338\pi$
$7$	538.554	+	310.935i	1.57013	+	0.906515i	0.573978	+	0.818871i	$0.305400\pi$
$8$	−160.601	+	486.160i	−0.313674	+	0.949531i
$9$	−148.939	+	54.2093i	−0.204306	+	0.0743612i
$10$	−478.233	+	976.470i	−0.478233	+	0.976470i
$11$	1275.70	−	736.525i	0.958452	−	0.553362i	0.0627556	−	0.998029i	$-0.480011\pi$
$11$	1275.70	−	736.525i	0.958452	−	0.553362i	0.895696	+	0.444666i	$0.146678\pi$
$12$	814.294	−	1293.72i	0.471235	−	0.748679i
$13$	−15.6232	+	88.6038i	−0.00711117	+	0.0403294i	−0.988157	−	0.153447i	$-0.950963\pi$
$13$	−15.6232	+	88.6038i	−0.00711117	+	0.0403294i	0.981046	+	0.193776i	$0.0620737\pi$
$14$	−4946.84	−	528.106i	−1.80279	−	0.192458i
$15$	2086.66	−	2486.79i	0.618270	−	0.736826i
$16$	−401.522	−	4076.27i	−0.0980278	−	0.995184i
$17$	215.983	+	78.6113i	0.0439615	+	0.0160007i	0.363907	−	0.931435i	$-0.381442\pi$
$17$	215.983	+	78.6113i	0.0439615	+	0.0160007i	−0.319946	+	0.947436i	$0.603665\pi$
$18$	913.546	−	879.321i	0.156644	−	0.150775i
$19$	−6741.68	+	1263.19i	−0.982895	+	0.184166i
$19$	−6741.68	+	1263.19i	−0.982895	+	0.184166i
$20$	331.967	−	8691.99i	0.0414959	−	1.08650i
$21$	13957.7	+	5080.18i	1.50715	+	0.548557i
$22$	−6942.27	+	9522.46i	−0.651978	+	0.894295i
$23$	3557.68	−	4239.88i	0.292404	−	0.348474i	−0.599764	−	0.800177i	$-0.704739\pi$
$23$	3557.68	−	4239.88i	0.292404	−	0.348474i	0.892168	+	0.451703i	$0.149183\pi$
$24$	−1761.31	+	12101.7i	−0.127409	+	0.875414i
$25$	494.357	−	2803.64i	0.0316389	−	0.179433i
$26$	−172.986	−	698.668i	−0.00984216	−	0.0397513i
$27$	−18358.0	+	10599.0i	−0.932686	+	0.538486i
$28$	37891.7	−	12175.0i	1.72611	−	0.554620i
$29$	23360.2	−	8502.42i	0.957818	−	0.348617i	0.184640	−	0.982806i	$-0.440888\pi$
$29$	23360.2	−	8502.42i	0.957818	−	0.348617i	0.773178	+	0.634189i	$0.218666\pi$
$30$	−7199.11	+	24952.4i	−0.266634	+	0.924162i
$31$	16115.7	+	9304.39i	0.540958	+	0.312322i	0.745467	−	0.666543i	$-0.232227\pi$
$31$	16115.7	+	9304.39i	0.540958	+	0.312322i	−0.204509	+	0.978865i	$0.565560\pi$
$32$	16151.7	+	28510.8i	0.492910	+	0.870080i
$33$	26952.6	−	22615.9i	0.749996	−	0.629321i
$34$	−1834.48	+	125.268i	−0.0466741	+	0.00318716i
$35$	83235.0	−	14676.6i	1.94134	−	0.342311i
$36$	−3830.66	+	9392.74i	−0.0821042	+	0.201319i
$37$	50880.1			1.00448			0.502241	−	0.864728i	$-0.332509\pi$
$37$	50880.1			1.00448			0.502241	+	0.864728i	$0.332509\pi$
$38$	45211.2	−	31094.8i	0.823939	−	0.566678i
$39$			2148.97i			0.0362273i
$40$	25751.1	+	64646.5i	0.402361	+	1.01010i
$41$	9674.68	+	54867.9i	0.140374	+	0.796098i	0.970966	+	0.239217i	$0.0768908\pi$
$41$	9674.68	+	54867.9i	0.140374	+	0.796098i	−0.830593	+	0.556881i	$0.811998\pi$
$42$	−118552.	+	8095.35i	−1.60015	+	0.109267i
$43$	−84104.7	−	100232.i	−1.05783	−	1.26067i	−0.964232	−	0.265060i	$-0.914608\pi$
$43$	−84104.7	−	100232.i	−1.05783	−	1.26067i	−0.0935957	−	0.995610i	$-0.529836\pi$
$44$	19902.1	−	92150.6i	0.233637	−	1.08178i
$45$	−10770.8	+	18655.6i	−0.118198	+	0.204725i
$46$	−12274.2	+	42542.9i	−0.126102	+	0.437073i
$47$	−7482.35	−	20557.6i	−0.0720683	−	0.198006i	0.898429	−	0.439120i	$-0.144710\pi$
$47$	−7482.35	−	20557.6i	−0.0720683	−	0.198006i	−0.970497	+	0.241114i	$0.922487\pi$
$48$	−26351.6	−	94218.0i	−0.238277	−	0.851943i
$49$	134536.	+	233023.i	1.14354	+	1.98067i
$50$	5473.69	+	22107.6i	0.0437896	+	0.176861i
$51$	5406.46	+	953.306i	0.0407571	+	0.00718657i
$52$	3530.21	+	4549.02i	0.0251067	+	0.0323525i
$53$	51686.3	+	43370.0i	0.347175	+	0.291314i	0.799654	−	0.600461i	$-0.205016\pi$
$53$	51686.3	+	43370.0i	0.347175	+	0.291314i	−0.452480	+	0.891775i	$0.649460\pi$
$54$	99903.2	−	137034.i	0.634451	−	0.870254i
$55$	68473.9	−	188131.i	0.411564	−	1.13076i
$56$	−237656.	+	211887.i	−1.35327	+	1.20654i
$57$	−153341.	+	57675.2i	−0.828005	+	0.311433i
$58$	−143284.	+	137917.i	−0.734370	+	0.706858i
$59$	59458.3	−	163360.i	0.289505	−	0.795409i	−0.706631	−	0.707583i	$-0.749786\pi$
$59$	59458.3	−	163360.i	0.289505	−	0.795409i	0.996136	−	0.0878264i	$-0.0279921\pi$
$60$	−28242.4	−	205833.i	−0.130752	−	0.952929i
$61$	−293591.	−	246352.i	−1.29346	−	1.08534i	−0.991236	−	0.132105i	$-0.957826\pi$
$61$	−293591.	−	246352.i	−1.29346	−	1.08534i	−0.302224	−	0.953237i	$-0.597729\pi$
$62$	−148029.	−	15803.0i	−0.621115	−	0.0663078i
$63$	−97067.2	−	17115.6i	−0.388196	−	0.0684494i
$64$	−210559.	−	156156.i	−0.803217	−	0.595686i
$65$	6114.01	+	10589.8i	0.0222631	+	0.0385609i
$66$	−123803.	+	252784.i	−0.430624	+	0.879262i
$67$	−46978.1	−	129071.i	−0.156197	−	0.429147i	0.836768	−	0.547557i	$-0.184442\pi$
$67$	−46978.1	−	129071.i	−0.156197	−	0.429147i	−0.992965	+	0.118411i	$0.962220\pi$
$68$	13010.7	−	6863.46i	0.0413783	−	0.0218281i
$69$	66099.5	−	114488.i	0.201211	−	0.348507i
$70$	−561173.	+	377183.i	−1.63607	+	1.09966i
$71$	294848.	+	351386.i	0.823801	+	0.981768i	0.999997	−	0.00258713i	$-0.000823511\pi$
$71$	294848.	+	351386.i	0.823801	+	0.981768i	−0.176195	+	0.984355i	$0.556379\pi$
$72$	−2434.63	−	81114.2i	−0.00652283	−	0.217320i
$73$	−67537.2	−	383022.i	−0.173610	−	0.984590i	−0.939736	−	0.341900i	$-0.888930\pi$
$73$	−67537.2	−	383022.i	−0.173610	−	0.984590i	0.766127	−	0.642690i	$-0.222182\pi$
$74$	−372120.	+	164951.i	−0.918307	+	0.407060i
$75$		−	67998.5i		−	0.161182i
$76$	−229852.	+	373989.i	−0.523610	+	0.851958i
$77$	916045.			2.00653
$78$	−6966.84	−	15716.8i	−0.0146809	−	0.0331193i
$79$	517946.	−	91327.9i	1.05052	−	0.185235i	0.378372	−	0.925654i	$-0.376484\pi$
$79$	517946.	−	91327.9i	1.05052	−	0.185235i	0.672146	+	0.740419i	$0.265373\pi$
$80$	−397916.	−	389320.i	−0.777179	−	0.760390i
$81$	−299351.	+	251185.i	−0.563282	+	0.472649i
$82$	−248636.	−	369920.i	−0.450944	−	0.670914i
$83$	−176423.	−	101858.i	−0.308547	−	0.178140i	0.337729	−	0.941243i	$-0.390341\pi$
$83$	−176423.	−	101858.i	−0.308547	−	0.178140i	−0.646276	+	0.763104i	$0.723675\pi$
$84$	840803.	−	443545.i	1.41859	−	0.748342i
$85$	29354.5	−	10684.2i	0.0477989	−	0.0173974i
$86$	940061.	+	460401.i	1.47795	+	0.723837i
$87$	514222.	−	296886.i	0.780895	−	0.450850i
$88$	153190.	+	738481.i	0.224793	+	1.08365i
$89$	−186649.	+	1.05854e6i	−0.264762	+	1.50154i	0.504952	+	0.863147i	$0.331510\pi$
$89$	−186649.	+	1.05854e6i	−0.264762	+	1.50154i	−0.769713	+	0.638390i	$0.779601\pi$
$90$	18293.6	−	171359.i	0.0250941	−	0.235060i
$91$	−35963.9	+	42860.2i	−0.0477247	+	0.0568761i
$92$	−48152.3	−	350937.i	−0.0618377	−	0.450677i
$93$	417669.	+	152019.i	0.519258	+	0.188995i
$94$	121370.	+	126094.i	0.146126	+	0.151814i
$95$	−591549.	+	720484.i	−0.689953	+	0.840337i
$96$	498177.	+	603649.i	0.563080	+	0.682293i
$97$	−259572.	−	94476.5i	−0.284409	−	0.103516i	0.195877	−	0.980628i	$-0.437245\pi$
$97$	−259572.	−	94476.5i	−0.284409	−	0.103516i	−0.480285	+	0.877112i	$0.659467\pi$
$98$	−1.73940e6	−	1.26810e6i	−1.84809	−	1.34733i
$99$	−150075.	+	178852.i	−0.154668	+	0.184327i
$100$	−111704.	−	143942.i	−0.111704	−	0.143942i
$101$	151937.	−	861675.i	0.147468	−	0.836333i	−0.817884	−	0.575383i	$-0.804853\pi$
$101$	151937.	−	861675.i	0.147468	−	0.836333i	0.965352	−	0.260950i	$-0.0840359\pi$
$102$	−42631.7	+	10555.3i	−0.0401728	+	0.00994652i
$103$	−81911.2	+	47291.4i	−0.0749603	+	0.0432784i	−0.537012	−	0.843575i	$-0.680447\pi$
$103$	−81911.2	+	47291.4i	−0.0749603	+	0.0432784i	0.462051	+	0.886853i	$0.347114\pi$
$104$	−40566.5	−	21825.3i	−0.0360634	−	0.0194026i
$105$	1.89701e6	−	690455.i	1.63871	−	0.596441i
$106$	−518620.	−	149629.i	−0.435443	−	0.125632i
$107$	−1.06935e6	−	617387.i	−0.872905	−	0.503972i	−0.00459245	−	0.999989i	$-0.501462\pi$
$107$	−1.06935e6	−	617387.i	−0.872905	−	0.503972i	−0.868312	+	0.496018i	$0.834795\pi$
$108$	−286403.	+	1.32610e6i	−0.227356	+	1.05270i
$109$	−1.27849e6	+	1.07278e6i	−0.987226	+	0.828381i	−0.985164	−	0.171617i	$-0.945101\pi$
$109$	−1.27849e6	+	1.07278e6i	−0.987226	+	0.828381i	−0.00206252	+	0.999998i	$0.500657\pi$
$110$	109114.	+	1.59791e6i	0.0819791	+	1.20054i
$111$	1.19682e6	−	211031.i	0.875102	−	0.154304i
$112$	1.05121e6	−	2.32014e6i	0.748232	−	1.65143i
$113$	−800114.			−0.554519			−0.277260	−	0.960795i	$-0.589426\pi$
$113$	−800114.			−0.554519			−0.277260	+	0.960795i	$0.589426\pi$
$114$	934503.	−	918940.i	0.630763	−	0.620258i
$115$		−	752238.i		−	0.494609i
$116$	600817.	−	1.47320e6i	0.384918	−	0.943815i
$117$	−2476.24	−	14043.5i	−0.00154609	−	0.00876833i
$118$	94747.7	+	1.38752e6i	0.0576664	+	0.844490i
$119$	91875.5	+	109493.i	0.0545204	+	0.0649748i
$120$	873855.	+	1.41383e6i	0.505703	+	0.818189i
$121$	199159.	−	344953.i	0.112420	−	0.194717i
$122$	2.94589e6	+	849930.i	1.62232	+	0.468062i
$123$	455142.	+	1.25049e6i	0.244586	+	0.671995i
$124$	1.13387e6	−	364325.i	0.594699	−	0.191084i
$125$	868345.	+	1.50402e6i	0.444593	+	0.770057i
$126$	765406.	−	189510.i	0.382631	−	0.0947369i
$127$	−3.01710e6	−	531995.i	−1.47292	−	0.259715i	−0.621172	−	0.783674i	$-0.713343\pi$
$127$	−3.01710e6	−	531995.i	−1.47292	−	0.259715i	−0.851743	+	0.523959i	$0.824454\pi$
$128$	2.04620e6	+	459450.i	0.975706	+	0.219083i
$129$	−2.39406e6	−	2.00886e6i	−1.11524	−	0.935793i
$130$	−79047.4	−	57628.8i	−0.0359797	−	0.0262307i
$131$	413212.	−	1.13529e6i	0.183806	−	0.505002i	−0.813230	−	0.581942i	$-0.802293\pi$
$131$	413212.	−	1.13529e6i	0.183806	−	0.505002i	0.997036	+	0.0769404i	$0.0245151\pi$
$132$	85938.1	−	2.25014e6i	0.0373649	−	0.978336i
$133$	−4.02353e6	−	1.41592e6i	−1.71022	−	0.601845i
$134$	762026.	+	791685.i	0.316705	+	0.329032i
$135$	−985379.	+	2.70731e6i	−0.400499	+	1.10036i
$136$	−72904.7	+	92377.0i	−0.0289827	+	0.0367238i
$137$	3.06559e6	+	2.57233e6i	1.19221	+	1.00038i	0.999818	+	0.0190627i	$0.00606820\pi$
$137$	3.06559e6	+	2.57233e6i	1.19221	+	1.00038i	0.192390	+	0.981319i	$0.438376\pi$
$138$	−112267.	+	1.05162e6i	−0.0427182	+	0.400148i
$139$	−4.44811e6	−	784322.i	−1.65627	−	0.292045i	−0.734161	−	0.678976i	$-0.762424\pi$
$139$	−4.44811e6	−	784322.i	−1.65627	−	0.292045i	−0.922109	+	0.386931i	$0.873535\pi$
$140$	2.88142e6	−	4.57789e6i	1.05008	−	1.66833i
$141$	−261267.	−	452528.i	−0.0932025	−	0.161431i
$142$	−3.29559e6	−	1.61404e6i	−1.15098	−	0.563701i
$143$	45328.4	+	124539.i	0.0155011	+	0.0425889i
$144$	280774.	+	585349.i	0.0940307	+	0.196032i
$145$	1.68934e6	−	2.92602e6i	0.554131	−	0.959784i
$146$	1.73568e6	+	2.58235e6i	0.557714	+	0.829766i
$147$	4.13110e6	+	4.92325e6i	1.30051	+	1.54989i
$148$	2.18680e6	−	2.41279e6i	0.674565	−	0.744276i
$149$	−239618.	−	1.35894e6i	−0.0724370	−	0.410810i	−0.999367	−	0.0355762i	$-0.988673\pi$
$149$	−239618.	−	1.35894e6i	−0.0724370	−	0.410810i	0.926930	−	0.375234i	$-0.122438\pi$
$150$	220448.	+	497319.i	0.0653179	+	0.147354i
$151$			5.27029e6i			1.53075i	0.643585	+	0.765374i	$0.277446\pi$
$151$			5.27029e6i			1.53075i	−0.643585	+	0.765374i	$0.722554\pi$
$152$	468608.	−	3.48040e6i	0.133438	−	0.991057i
$153$	−36429.7			−0.0101714
$154$	−6.69965e6	+	2.96977e6i	−1.83438	+	0.813132i
$155$	2.49072e6	−	439181.i	0.668852	−	0.117937i
$156$	101906.	+	92361.5i	0.0268428	+	0.0243286i
$157$	−5.84995e6	+	4.90869e6i	−1.51166	+	1.26843i	−0.651198	+	0.758908i	$0.725733\pi$
$157$	−5.84995e6	+	4.90869e6i	−1.51166	+	1.26843i	−0.860458	+	0.509522i	$0.829822\pi$
$158$	−3.49201e6	+	2.34710e6i	−0.885327	+	0.595059i
$159$	1.39566e6	+	805788.i	0.347208	+	0.200461i
$160$	4.17238e6	+	1.55733e6i	1.01865	+	0.380208i
$161$	3.23433e6	−	1.17720e6i	0.775009	−	0.282080i
$162$	1.37502e6	−	2.80757e6i	0.323419	−	0.660367i
$163$	34735.8	−	20054.7i	0.00802074	−	0.00463078i	−0.495984	−	0.868332i	$-0.665193\pi$
$163$	34735.8	−	20054.7i	0.00802074	−	0.00463078i	0.504005	+	0.863701i	$0.331859\pi$
$164$	3.01771e6	+	1.89941e6i	0.684141	+	0.430613i
$165$	830372.	−	4.70927e6i	0.184850	−	1.04834i
$166$	1.62052e6	+	173000.i	0.354266	+	0.0378201i
$167$	3.54812e6	−	4.22848e6i	0.761813	−	0.907893i	−0.236148	−	0.971717i	$-0.575885\pi$
$167$	3.54812e6	−	4.22848e6i	0.761813	−	0.907893i	0.997961	+	0.0638237i	$0.0203295\pi$
$168$	−4.71140e6	+	5.96978e6i	−0.993625	+	1.25901i
$169$	4.52811e6	+	1.64810e6i	0.938117	+	0.341447i
$170$	−180052.	+	173306.i	−0.0366480	+	0.0352750i
$171$	935621.	−	553600.i	0.187116	−	0.110715i
$172$	−8.36790e6	−	319589.i	−1.64449	−	0.0628068i
$173$	−7.24147e6	−	2.63568e6i	−1.39858	−	0.509043i	−0.470826	−	0.882226i	$-0.656044\pi$
$173$	−7.24147e6	−	2.63568e6i	−1.39858	−	0.509043i	−0.927758	+	0.373183i	$0.878266\pi$
$174$	−2.79836e6	+	3.83841e6i	−0.531197	+	0.728624i
$175$	1.13799e6	−	1.35620e6i	0.212336	−	0.253052i
$176$	−3.51450e6	−	4.90437e6i	−0.644652	−	0.899591i
$177$	721041.	−	4.08922e6i	0.130029	−	0.737431i
$178$	−2.06664e6	−	8.34690e6i	−0.366441	−	1.48001i
$179$	−8.24891e6	+	4.76251e6i	−1.43826	+	0.830380i	−0.997729	−	0.0673571i	$-0.978543\pi$
$179$	−8.24891e6	+	4.76251e6i	−1.43826	+	0.830380i	−0.440531	+	0.897737i	$0.645210\pi$
$180$	421744.	+	1.31257e6i	0.0723155	+	0.225064i
$181$	−9.28907e6	+	3.38094e6i	−1.56652	+	0.570167i	−0.972219	−	0.234074i	$-0.924794\pi$
$181$	−9.28907e6	+	3.38094e6i	−1.56652	+	0.570167i	−0.594303	+	0.804241i	$0.702572\pi$
$182$	124078.	−	430058.i	0.0205816	−	0.0713367i
$183$	−7.92771e6	−	4.57707e6i	−1.29358	−	0.746851i
$184$	1.48989e6	+	2.41053e6i	0.239167	+	0.386954i
$185$	5.29733e6	−	4.44499e6i	0.836647	−	0.702030i
$186$	−3.54753e6	+	242245.i	−0.551299	+	0.0376457i
$187$	333428.	−	58792.4i	0.0509891	−	0.00899076i
$188$	−1.29645e6	−	528734.i	−0.195111	−	0.0795726i
$189$	−1.31824e7			−1.95258
$190$	1.99062e6	−	7.18715e6i	0.290220	−	1.04784i
$191$		−	311805.i		−	0.0447489i	−0.999750	−	0.0223745i	$-0.992877\pi$
$191$		−	311805.i		−	0.0447489i	0.999750	−	0.0223745i	$-0.00712261\pi$
$192$	−5.60050e6	−	2.79983e6i	−0.791267	−	0.395574i
$193$	1.79761e6	+	1.01948e7i	0.250048	+	1.41809i	0.808470	+	0.588537i	$0.200296\pi$
$193$	1.79761e6	+	1.01948e7i	0.250048	+	1.41809i	−0.558422	+	0.829557i	$0.688593\pi$
$194$	2.20471e6	−	150550.i	0.301958	−	0.0206193i
$195$	187738.	+	223738.i	0.0253191	+	0.0301742i
$196$	1.68325e7	+	3.63538e6i	2.23553	+	0.482816i
$197$	4.08986e6	−	7.08385e6i	0.534946	−	0.926553i	−0.464220	−	0.885720i	$-0.653665\pi$
$197$	4.08986e6	−	7.08385e6i	0.534946	−	0.926553i	0.999166	−	0.0408335i	$-0.0130013\pi$
$198$	517767.	−	1.79460e6i	0.0667020	−	0.231192i
$199$	525473.	+	1.44373e6i	0.0666793	+	0.183200i	0.968557	−	0.248791i	$-0.0800333\pi$
$199$	525473.	+	1.44373e6i	0.0666793	+	0.183200i	−0.901878	+	0.431991i	$0.857811\pi$
$200$	1.28362e6	+	690605.i	0.160453	+	0.0863256i
$201$	−1.64037e6	−	2.84121e6i	−0.202002	−	0.349877i
$202$	1.68229e6	+	6.79458e6i	0.204102	+	0.824344i
$203$	1.52244e7	+	2.68448e6i	1.81992	+	0.320902i
$204$	277574.	−	215408.i	0.0326955	−	0.0253730i
$205$	5.80064e6	+	4.86732e6i	0.673309	+	0.564974i
$206$	445755.	−	611426.i	0.0509911	−	0.0699427i
$207$	−300036.	+	824342.i	−0.0338269	+	0.0929387i
$208$	367446.	+	28108.2i	0.0408323	+	0.00312351i
$209$	−7.66998e6	+	6.57687e6i	−0.840147	+	0.720411i
$210$	−1.16357e7	+	1.11998e7i	−1.25642	+	1.20935i
$211$	5.23226e6	−	1.43755e7i	0.556983	−	1.53030i	−0.267008	−	0.963694i	$-0.586035\pi$
$211$	5.23226e6	−	1.43755e7i	0.556983	−	1.53030i	0.823991	−	0.566603i	$-0.191743\pi$
$212$	4.27811e6	−	587002.i	0.448998	−	0.0616073i
$213$	8.39291e6	+	7.04249e6i	0.868508	+	0.728765i
$214$	9.82238e6	+	1.04860e6i	1.00225	+	0.106996i
$215$	−1.75130e7	−	3.08801e6i	−1.76216	−	0.310716i
$216$	−2.20450e6	−	1.06272e7i	−0.218750	−	1.05452i
$217$	5.78611e6	+	1.00218e7i	0.566249	+	0.980772i
$218$	5.87254e6	−	1.19907e7i	0.566835	−	1.15738i
$219$	−3.17726e6	−	8.72945e6i	−0.302497	−	0.831103i
$220$	−5.97838e6	−	1.13329e7i	−0.561456	−	1.06432i
$221$	−10339.6	+	17908.7i	−0.000957915	+	0.00165916i
$222$	−8.06897e6	+	5.42343e6i	−0.737495	+	0.495696i
$223$	−8.65128e6	−	1.03102e7i	−0.780128	−	0.929721i	0.218811	−	0.975767i	$-0.429782\pi$
$223$	−8.65128e6	−	1.03102e7i	−0.780128	−	0.929721i	−0.998939	+	0.0460466i	$0.985338\pi$
$224$	−166438.	+	2.03767e7i	−0.0148084	+	1.81297i
$225$	78354.4	+	444370.i	0.00687885	+	0.0390119i
$226$	5.85177e6	−	2.59393e6i	0.506946	−	0.224715i
$227$			1.70779e7i			1.46001i	0.683440	+	0.730006i	$0.260483\pi$
$227$			1.70779e7i			1.46001i	−0.683440	+	0.730006i	$0.739517\pi$
$228$	−3.85549e6	+	9.75044e6i	−0.325293	+	0.822658i
$229$	1.02791e7			0.855951			0.427975	−	0.903790i	$-0.359227\pi$
$229$	1.02791e7			0.855951			0.427975	+	0.903790i	$0.359227\pi$
$230$	2.43872e6	+	5.50162e6i	0.200437	+	0.452175i
$231$	2.15475e7	−	3.79941e6i	1.74808	−	0.308234i
$232$	381858.	+	1.27223e7i	0.0305800	+	1.01883i
$233$	5.70716e6	−	4.78887e6i	0.451182	−	0.378587i	−0.388692	−	0.921368i	$-0.627073\pi$
$233$	5.70716e6	−	4.78887e6i	0.451182	−	0.378587i	0.839874	+	0.542781i	$0.182629\pi$
$234$	63638.6	+	94681.4i	0.00496676	+	0.00738954i
$235$	−2.57497e6	−	1.48666e6i	−0.198412	−	0.114553i
$236$	−5.19124e6	−	9.84073e6i	−0.394943	−	0.748671i
$237$	1.18045e7	−	4.29649e6i	0.886753	−	0.322752i
$238$	−1.02692e6	−	502939.i	−0.0761736	−	0.0373065i
$239$	1.39076e6	−	802956.i	0.101873	−	0.0588164i	−0.448198	−	0.893934i	$-0.647934\pi$
$239$	1.39076e6	−	802956.i	0.101873	−	0.0588164i	0.550071	+	0.835118i	$0.314601\pi$
$240$	−1.09747e7	−	7.50730e6i	−0.793884	−	0.543063i
$241$	803998.	−	4.55970e6i	0.0574386	−	0.325750i	−0.942526	−	0.334132i	$-0.891557\pi$
$241$	803998.	−	4.55970e6i	0.0574386	−	0.325750i	0.999965	+	0.00838159i	$0.00266798\pi$
$242$	−338261.	+	3.16854e6i	−0.0238674	+	0.223570i
$243$	3.93363e6	−	4.68792e6i	0.274141	−	0.326709i
$244$	−2.43007e7	+	3.33431e6i	−1.67282	+	0.229529i
$245$	3.43645e7	+	1.25077e7i	2.33675	+	0.850507i
$246$	−7.38279e6	−	7.67014e6i	−0.495924	−	0.515226i
$247$	−6596.87	−	617073.i	−0.000437771	−	0.0409492i
$248$	−7.11161e6	+	6.34049e6i	−0.466244	+	0.415689i
$249$	−4.57235e6	−	1.66420e6i	−0.296170	−	0.107797i
$250$	−1.12267e7	−	8.18476e6i	−0.718511	−	0.523824i
$251$	1.96988e7	−	2.34762e7i	1.24572	−	1.48459i	0.433588	−	0.901111i	$-0.357247\pi$
$251$	1.96988e7	−	2.34762e7i	1.24572	−	1.48459i	0.812130	−	0.583477i	$-0.198308\pi$
$252$	−4.98354e6	+	3.86742e6i	−0.311413	+	0.241668i
$253$	1.41575e6	−	8.02913e6i	0.0874230	−	0.495801i
$254$	2.37907e7	−	5.89044e6i	1.45180	−	0.359456i
$255$	646172.	−	373068.i	0.0389698	−	0.0224992i
$256$	−1.64548e7	+	3.27342e6i	−0.980781	+	0.195111i
$257$	1.61343e6	−	587242.i	0.0950499	−	0.0345953i	−0.294058	−	0.955788i	$-0.595006\pi$
$257$	1.61343e6	−	587242.i	0.0950499	−	0.0345953i	0.389107	+	0.921192i	$0.372783\pi$
$258$	2.40220e7	+	6.93069e6i	1.39878	+	0.403568i
$259$	2.74017e7	+	1.58204e7i	1.57717	+	0.910578i
$260$	764956.	+	165210.i	0.0435228	+	0.00939978i
$261$	−3.01833e6	+	2.53268e6i	−0.169764	+	0.142449i
$262$	658459.	+	9.64275e6i	0.0366121	+	0.536163i
$263$	−2.29637e7	+	4.04911e6i	−1.26233	+	0.222583i	−0.764462	−	0.644668i	$-0.776996\pi$
$263$	−2.29637e7	+	4.04911e6i	−1.26233	+	0.222583i	−0.497870	+	0.867252i	$0.665884\pi$
$264$	6.66633e6	+	1.67354e7i	0.362305	+	0.909546i
$265$	9.17017e6			0.492765
$266$	3.40171e7	−	2.68850e6i	1.80739	−	0.142845i
$267$			2.56734e7i			1.34881i
$268$	−8.13981e6	−	3.31967e6i	−0.422873	−	0.172461i
$269$	−2.08990e6	−	1.18524e7i	−0.107366	−	0.608904i	−0.990249	−	0.139310i	$-0.955511\pi$
$269$	−2.08990e6	−	1.18524e7i	−0.107366	−	0.608904i	0.882883	−	0.469594i	$-0.155600\pi$
$270$	−1.57022e6	−	2.29949e7i	−0.0797753	−	1.16826i
$271$	−6.33654e6	−	7.55159e6i	−0.318379	−	0.379429i	0.582991	−	0.812478i	$-0.301882\pi$
$271$	−6.33654e6	−	7.55159e6i	−0.318379	−	0.379429i	−0.901370	+	0.433049i	$0.857438\pi$
$272$	233719.	−	911968.i	0.0116142	−	0.0453182i
$273$	−668188.	+	1.15734e6i	−0.0328406	+	0.0568815i
$274$	−3.07601e7	−	8.87471e6i	−1.49533	−	0.431422i
$275$	−1.43430e6	−	3.94071e6i	−0.0689671	−	0.189486i
$276$	−2.58821e6	−	8.05514e6i	−0.123104	−	0.383130i
$277$	9.36633e6	+	1.62230e7i	0.440687	+	0.763292i	0.997741	−	0.0671845i	$-0.0214016\pi$
$277$	9.36633e6	+	1.62230e7i	0.440687	+	0.763292i	−0.557054	+	0.830476i	$0.688068\pi$
$278$	3.50747e7	−	8.68428e6i	1.63253	−	0.404203i
$279$	−2.90463e6	−	512165.i	−0.133745	−	0.0235829i
$280$	−6.23248e6	+	4.28226e7i	−0.283914	+	1.95074i
$281$	8.72234e6	+	7.31891e6i	0.393110	+	0.329858i	0.817823	−	0.575469i	$-0.195181\pi$
$281$	8.72234e6	+	7.31891e6i	0.393110	+	0.329858i	−0.424713	+	0.905328i	$0.639625\pi$
$282$	3.37790e6	+	2.46263e6i	0.150626	+	0.109812i
$283$	2.37160e6	−	6.51590e6i	0.104636	−	0.287485i	−0.876316	−	0.481738i	$-0.840006\pi$
$283$	2.37160e6	−	6.51590e6i	0.104636	−	0.287485i	0.980952	+	0.194252i	$0.0622281\pi$
$284$	2.93355e7	+	1.12039e6i	1.28067	+	0.0489118i
$285$	−1.09263e7	+	1.94010e7i	−0.471997	+	0.838086i
$286$	−735265.	−	763882.i	−0.0314301	−	0.0326534i
$287$	−1.18500e7	+	3.25575e7i	−0.501270	+	1.37723i
$288$	−3.95116e6	−	3.37079e6i	−0.165405	−	0.141109i
$289$	−1.84500e7	−	1.54814e7i	−0.764368	−	0.641381i
$290$	−2.86925e6	+	2.68767e7i	−0.117645	+	1.10200i
$291$	−6.49759e6	−	1.14570e6i	−0.263678	−	0.0464935i
$292$	−2.10661e7	−	1.32594e7i	−0.846125	−	0.532569i
$293$	−2.00534e6	−	3.47335e6i	−0.0797232	−	0.138085i	0.823407	−	0.567451i	$-0.192070\pi$
$293$	−2.00534e6	−	3.47335e6i	−0.0797232	−	0.138085i	−0.903130	+	0.429366i	$0.858737\pi$
$294$	−4.61744e7	−	2.26142e7i	−1.81702	−	0.889896i
$295$	−8.08106e6	−	2.22025e7i	−0.314776	−	0.864841i
$296$	−8.17140e6	+	2.47358e7i	−0.315080	+	0.953787i
$297$	−1.56129e7	+	2.70423e7i	−0.595956	+	1.03223i
$298$	6.15810e6	+	9.16201e6i	0.232701	+	0.346212i
$299$	320087.	+	381464.i	0.0119744	+	0.0142705i
$300$	−3.22457e6	−	2.92254e6i	−0.119428	−	0.108242i
$301$	−1.41293e7	−	8.01315e7i	−0.518111	−	2.93835i
$302$	−1.70860e7	−	3.85452e7i	−0.620326	−	1.39942i
$303$		−	2.08988e7i		−	0.751265i
$304$	7.85605e6	+	2.69737e7i	0.279630	+	0.960108i
$305$	−5.20888e7			−1.83588
$306$	266435.	−	118103.i	0.00929879	−	0.00412190i
$307$	1.04979e7	−	1.85107e6i	0.362818	−	0.0639746i	0.0107325	−	0.999942i	$-0.496584\pi$
$307$	1.04979e7	−	1.85107e6i	0.362818	−	0.0639746i	0.352086	+	0.935968i	$0.385473\pi$
$308$	3.93712e7	−	4.34399e7i	1.34749	−	1.48674i
$309$	−1.73059e6	+	1.45214e6i	−0.0586570	+	0.0492191i
$310$	−1.67925e7	+	1.12868e7i	−0.563677	+	0.378867i
$311$	3.26007e6	+	1.88220e6i	0.108379	+	0.0625727i	0.553210	−	0.833042i	$-0.313403\pi$
$311$	3.26007e6	+	1.88220e6i	0.108379	+	0.0625727i	−0.444831	+	0.895615i	$0.646736\pi$
$312$	−1.04474e6	−	345126.i	−0.0343989	−	0.0113636i
$313$	−1.78069e7	+	6.48117e6i	−0.580703	+	0.211359i	−0.615636	−	0.788031i	$-0.711101\pi$
$313$	−1.78069e7	+	6.48117e6i	−0.580703	+	0.211359i	0.0349324	+	0.999390i	$0.488878\pi$
$314$	2.68708e7	−	5.48657e7i	0.867945	−	1.77220i
$315$	−1.16013e7	+	6.69803e6i	−0.371173	+	0.214297i
$316$	1.79302e7	−	2.84868e7i	0.568230	−	0.902781i
$317$	−2.52676e6	+	1.43300e7i	−0.0793206	+	0.449849i	0.919118	+	0.393983i	$0.128903\pi$
$317$	−2.52676e6	+	1.43300e7i	−0.0793206	+	0.449849i	−0.998438	+	0.0558662i	$0.982208\pi$
$318$	−1.28198e7	−	1.36859e6i	−0.398656	−	0.0425590i
$319$	2.35384e7	−	2.80519e7i	0.725111	−	0.864153i
$320$	−3.55642e7	+	2.13684e6i	−1.08533	+	0.0652110i
$321$	−2.77142e7	−	1.00871e7i	−0.837890	−	0.304967i
$322$	−1.98384e7	+	1.90952e7i	−0.594209	+	0.571948i
$323$	−1.55539e6	−	257144.i	−0.0461563	−	0.00763078i
$324$	−954478.	+	2.49914e7i	−0.0280628	+	0.734776i
$325$	240690.	+	87603.9i	0.00701144	+	0.00255196i
$326$	−189030.	+	259285.i	−0.00545604	+	0.00748386i
$327$	−2.56235e7	+	3.05369e7i	−0.732817	+	0.873337i
$328$	−2.82283e7	−	4.10840e6i	−0.799951	−	0.116426i
$329$	2.36241e6	−	1.33979e7i	0.0663388	−	0.376226i
$330$	9.19416e6	+	3.71341e7i	0.255841	+	1.03331i
$331$	−6.75298e6	+	3.89884e6i	−0.186214	+	0.107511i	−0.590209	−	0.807251i	$-0.700955\pi$
$331$	−6.75298e6	+	3.89884e6i	−0.186214	+	0.107511i	0.403995	+	0.914761i	$0.367621\pi$
$332$	−1.24128e7	+	3.98838e6i	−0.339200	+	0.108989i
$333$	−7.57802e6	+	2.75817e6i	−0.205222	+	0.0746945i
$334$	−1.22412e7	+	4.24285e7i	−0.328538	+	1.13872i
$335$	−1.61670e7	−	9.33404e6i	−0.430027	−	0.248276i
$336$	1.51039e7	−	5.89352e7i	0.398172	−	1.55366i
$337$	−1.68318e7	+	1.41236e7i	−0.439786	+	0.369025i	−0.835629	−	0.549294i	$-0.814897\pi$
$337$	−1.68318e7	+	1.41236e7i	−0.439786	+	0.369025i	0.395843	+	0.918318i	$0.370452\pi$
$338$	−3.84602e7	+	2.62627e6i	−0.996004	+	0.0680125i
$339$	−1.88205e7	+	3.31857e6i	−0.483095	+	0.0851828i
$340$	754987.	−	1.85122e6i	0.0192089	−	0.0471001i
$341$	2.74117e7			0.691309
$342$	−5.04808e6	+	7.08209e6i	−0.126197	+	0.177045i
$343$			9.41654e7i			2.33351i
$344$	6.22361e7	−	2.47909e7i	1.52886	−	0.609000i
$345$	−3.12000e6	−	1.76944e7i	−0.0759796	−	0.430902i
$346$	6.15065e7	−	4.20000e6i	1.48488	−	0.101396i
$347$	−2.46778e7	−	2.94098e7i	−0.590633	−	0.703889i	0.385095	−	0.922877i	$-0.374169\pi$
$347$	−2.46778e7	−	2.94098e7i	−0.590633	−	0.703889i	−0.975727	+	0.218988i	$0.929724\pi$
$348$	8.02234e6	−	3.71450e7i	0.190355	−	0.881379i
$349$	−2.92983e7	+	5.07462e7i	−0.689233	+	1.19379i	0.282853	+	0.959163i	$0.408719\pi$
$349$	−2.92983e7	+	5.07462e7i	−0.689233	+	1.19379i	−0.972086	+	0.234624i	$0.924614\pi$
$350$	−3.92613e6	+	1.36081e7i	−0.0915715	+	0.317390i
$351$	−652301.	−	1.79218e6i	−0.0150844	−	0.0414439i
$352$	4.16036e7	+	2.44751e7i	0.953900	+	0.561172i
$353$	2.25155e7	+	3.89979e7i	0.511866	+	0.886579i	0.999905	+	0.0137568i	$0.00437905\pi$
$353$	2.25155e7	+	3.89979e7i	0.511866	+	0.886579i	−0.488039	+	0.872822i	$0.662288\pi$
$354$	7.98361e6	+	3.22448e7i	0.179966	+	0.726859i
$355$	6.13956e7	+	1.08257e7i	1.37231	+	0.241975i
$356$	4.21749e7	+	5.43465e7i	0.934769	+	1.20454i
$357$	2.61526e6	+	2.19446e6i	0.0574791	+	0.0482307i
$358$	4.48900e7	−	6.15740e7i	0.978364	−	1.34199i
$359$	−1.16239e7	+	3.19365e7i	−0.251229	+	0.690246i	0.748406	+	0.663241i	$0.230819\pi$
$359$	−1.16239e7	+	3.19365e7i	−0.251229	+	0.690246i	−0.999635	+	0.0270054i	$0.991403\pi$
$360$	−7.33978e6	−	8.23243e6i	−0.157317	−	0.176450i
$361$	4.38546e7	−	1.70321e7i	0.932166	−	0.362031i
$362$	5.69763e7	−	5.48418e7i	1.20107	−	1.15608i
$363$	3.25394e6	−	8.94014e6i	0.0680284	−	0.186907i
$364$	486763.	+	3.54756e6i	0.0100928	+	0.0735572i
$365$	−4.04932e7	−	3.39778e7i	−0.832729	−	0.698742i
$366$	7.28193e7	+	7.77391e6i	1.48526	+	0.158561i
$367$	−4.64758e7	−	8.19494e6i	−0.940219	−	0.165786i	−0.317523	−	0.948250i	$-0.602851\pi$
$367$	−4.64758e7	−	8.19494e6i	−0.940219	−	0.165786i	−0.622695	+	0.782464i	$0.713962\pi$
$368$	−1.87114e7	−	1.27997e7i	−0.375459	−	0.256836i
$369$	−4.41528e6	−	7.64750e6i	−0.0878779	−	0.152209i
$370$	−2.43325e7	+	4.96829e7i	−0.480376	+	0.980848i
$371$	1.43507e7	+	3.94282e7i	0.281029	+	0.772120i
$372$	2.51601e7	−	1.32726e7i	0.488747	−	0.257827i
$373$	−5.67462e6	+	9.82872e6i	−0.109348	+	0.189396i	−0.915506	−	0.402304i	$-0.868210\pi$
$373$	−5.67462e6	+	9.82872e6i	−0.109348	+	0.189396i	0.806158	+	0.591700i	$0.201543\pi$
$374$	−2.24798e6	+	1.51095e6i	−0.0429712	+	0.0288824i
$375$	2.66636e7	+	3.17764e7i	0.505621	+	0.602575i
$376$	1.11959e7	−	336045.i	0.210619	−	0.00632170i
$377$	388385.	+	2.20264e6i	0.00724833	+	0.0411073i
$378$	9.64118e7	−	4.27367e7i	1.78507	−	0.791272i
$379$			1.66630e6i			0.0306080i	0.999883	+	0.0153040i	$0.00487161\pi$
$379$			1.66630e6i			0.0306080i	−0.999883	+	0.0153040i	$0.995128\pi$
$380$	8.74165e6	+	5.90179e7i	0.159310	+	1.07556i
$381$	−7.31756e7			−1.32310
$382$	1.01086e6	+	2.28044e6i	0.0181342	+	0.0409099i
$383$	−4.72262e7	+	8.32725e6i	−0.840595	+	0.148220i	−0.577337	−	0.816506i	$-0.695908\pi$
$383$	−4.72262e7	+	8.32725e6i	−0.840595	+	0.148220i	−0.263258	+	0.964726i	$0.584797\pi$
$384$	5.00371e7	+	2.32046e6i	0.883687	+	0.0409808i
$385$	9.53732e7	−	8.00276e7i	1.67126	−	1.40235i
$386$	−4.61980e7	−	6.87333e7i	−0.803270	−	1.19510i
$387$	1.79600e7	+	1.03692e7i	0.309865	+	0.178901i
$388$	−1.56365e7	+	8.24864e6i	−0.267697	+	0.141217i
$389$	9.58120e7	−	3.48727e7i	1.62769	−	0.592430i	0.642862	−	0.765982i	$-0.277747\pi$
$389$	9.58120e7	−	3.48727e7i	1.62769	−	0.592430i	0.984825	+	0.173552i	$0.0555244\pi$
$390$	−2.09840e6	−	1.02771e6i	−0.0353749	−	0.0173251i
$391$	1.10170e6	−	636066.i	0.0184303	−	0.0106408i
$392$	−1.34893e8	+	2.79822e7i	−2.23940	+	0.464541i
$393$	5.01095e6	−	2.84185e7i	0.0825548	−	0.468192i
$394$	−6.94641e6	+	6.50680e7i	−0.113572	+	1.06385i
$395$	4.59469e7	−	5.47574e7i	0.745530	−	0.888488i
$396$	2.03122e6	+	1.48037e7i	0.0327094	+	0.238388i
$397$	−2.29525e7	−	8.35404e6i	−0.366825	−	0.133513i	0.152029	−	0.988376i	$-0.451419\pi$
$397$	−2.29525e7	−	8.35404e6i	−0.366825	−	0.133513i	−0.518855	+	0.854863i	$0.673641\pi$
$398$	−8.52362e6	−	8.85538e6i	−0.135200	−	0.140462i
$399$	−1.00516e8	−	1.66177e7i	−1.58239	−	0.261609i
$400$	−1.16269e7	−	889413.i	−0.181670	−	0.0138971i
$401$	−3.94755e7	−	1.43679e7i	−0.612201	−	0.222823i	0.0172648	−	0.999851i	$-0.494504\pi$
$401$	−3.94755e7	−	1.43679e7i	−0.612201	−	0.222823i	−0.629466	+	0.777028i	$0.716726\pi$
$402$	2.12082e7	+	1.54617e7i	0.326457	+	0.238001i
$403$	−1.07618e6	+	1.28254e6i	−0.0164426	+	0.0195955i
$404$	−3.43314e7	−	4.42394e7i	−0.520652	−	0.670911i
$405$	−9.22258e6	+	5.23039e7i	−0.138831	+	0.787352i
$406$	−1.20050e8	+	2.97235e7i	−1.79383	+	0.444142i
$407$	6.49077e7	−	3.74745e7i	0.962748	−	0.555843i
$408$	−1.33174e6	+	2.47530e6i	−0.0196083	+	0.0364458i
$409$	4.47254e7	−	1.62787e7i	0.653709	−	0.237931i	0.00619117	−	0.999981i	$-0.498029\pi$
$409$	4.47254e7	−	1.62787e7i	0.653709	−	0.237931i	0.647518	+	0.762050i	$0.275807\pi$
$410$	−5.82036e7	−	1.67926e7i	−0.844497	−	0.243649i
$411$	8.27788e7	+	4.77924e7i	1.19232	+	0.688388i
$412$	−1.27789e6	+	5.91688e6i	−0.0182727	+	0.0846060i
$413$	8.28159e7	−	6.94908e7i	1.17561	−	0.986455i
$414$	−478112.	−	7.00167e6i	−0.00673796	−	0.0986735i
$415$	−2.72667e7	+	4.80785e6i	−0.381494	+	0.0672677i
$416$	−2.77851e6	+	985668.i	−0.0385950	+	0.0136915i
$417$	−1.07883e8			−1.48780
$418$	3.47738e7	−	7.29668e7i	0.476128	−	0.999071i
$419$			1.27367e8i			1.73147i	0.500504	+	0.865734i	$0.333148\pi$
$419$			1.27367e8i			1.73147i	−0.500504	+	0.865734i	$0.666852\pi$
$420$	4.87904e7	−	1.19634e8i	0.658547	−	1.61475i
$421$	1.16604e7	+	6.61293e7i	0.156267	+	0.886233i	0.957619	+	0.288039i	$0.0930034\pi$
$421$	1.16604e7	+	6.61293e7i	0.156267	+	0.886233i	−0.801352	+	0.598193i	$0.795885\pi$
$422$	8.33768e6	+	1.22100e8i	0.110945	+	1.62473i
$423$	2.22882e6	+	2.65621e6i	0.0294479	+	0.0350947i
$424$	−2.93856e7	+	1.81625e7i	−0.385511	+	0.238275i
$425$	327170.	−	566676.i	0.00426194	−	0.00738189i
$426$	−8.42144e7	−	2.42970e7i	−1.08933	−	0.314286i
$427$	−8.15153e7	−	2.23962e8i	−1.04702	−	2.87667i
$428$	−7.52372e7	+	2.41746e7i	−0.959624	+	0.308338i
$429$	1.58277e6	+	2.74143e6i	0.0200468	+	0.0347221i
$430$	1.38095e8	−	3.41915e7i	1.73689	−	0.430044i
$431$	2.76490e7	+	4.87526e6i	0.345340	+	0.0608928i	0.343628	−	0.939106i	$-0.388344\pi$
$431$	2.76490e7	+	4.87526e6i	0.345340	+	0.0608928i	0.00171182	+	0.999999i	$0.499455\pi$
$432$	5.05757e7	+	7.05767e7i	0.627322	+	0.875407i
$433$	9.33031e7	+	7.82906e7i	1.14930	+	0.964375i	0.999703	−	0.0243730i	$-0.00775892\pi$
$433$	9.33031e7	+	7.82906e7i	1.14930	+	0.964375i	0.149594	+	0.988748i	$0.452203\pi$
$434$	−7.48080e7	−	5.45381e7i	−0.915122	−	0.667162i
$435$	2.76012e7	−	7.58335e7i	0.335320	−	0.921284i
$436$	−4.07644e6	+	1.06735e8i	−0.0491838	+	1.28779i
$437$	−1.86289e7	+	3.30779e7i	−0.223226	+	0.396364i
$438$	5.15379e7	+	5.35438e7i	0.613344	+	0.637217i
$439$	2.26856e7	−	6.23282e7i	0.268137	−	0.736701i	−0.730420	−	0.682998i	$-0.760676\pi$
$439$	2.26856e7	−	6.23282e7i	0.268137	−	0.736701i	0.998557	−	0.0537022i	$-0.0171022\pi$
$440$	8.04645e7	+	6.35032e7i	0.944596	+	0.745483i
$441$	−3.26697e7	−	2.74131e7i	−0.380916	−	0.319627i
$442$	17561.3	−	164499.i	0.000203371	−	0.00190501i
$443$	−1.37968e7	−	2.43276e6i	−0.158697	−	0.0279826i	0.0937351	−	0.995597i	$-0.470119\pi$
$443$	−1.37968e7	−	2.43276e6i	−0.158697	−	0.0279826i	−0.252432	+	0.967615i	$0.581230\pi$
$444$	4.14313e7	−	6.58244e7i	0.473347	−	0.752035i
$445$	7.30433e7	+	1.26515e8i	0.828896	+	1.43569i
$446$	9.66978e7	+	4.73584e7i	1.08996	+	0.533817i
$447$	−1.12727e7	−	3.09716e7i	−0.126214	−	0.346770i
$448$	−6.48431e7	−	1.49568e8i	−0.721156	−	1.66343i
$449$	−2.09043e7	+	3.62073e7i	−0.230939	+	0.399998i	−0.958085	−	0.286485i	$-0.907513\pi$
$449$	−2.09043e7	+	3.62073e7i	−0.230939	+	0.399998i	0.727146	+	0.686483i	$0.240846\pi$
$450$	−2.01368e6	−	2.99595e6i	−0.0220980	−	0.0328774i
$451$	5.27536e7	+	6.28692e7i	0.575072	+	0.685344i
$452$	−3.43885e7	+	3.79423e7i	−0.372390	+	0.410874i
$453$	2.18592e7	+	1.23970e8i	0.235147	+	1.33358i
$454$	−5.53657e7	−	1.24902e8i	−0.591661	−	1.33476i
$455$			7.60423e6i			0.0807274i
$456$	−3.41265e6	−	8.38108e7i	−0.0359913	−	0.883904i
$457$	7.78623e6			0.0815790			0.0407895	−	0.999168i	$-0.487013\pi$
$457$	7.78623e6			0.0815790			0.0407895	+	0.999168i	$0.487013\pi$
$458$	−7.51780e7	+	3.33243e7i	−0.782518	+	0.346869i
$459$	−4.79822e6	+	846056.i	−0.0496184	+	0.00874906i
$460$	−3.56719e7	−	3.23308e7i	−0.366483	−	0.332157i
$461$	3.41246e7	−	2.86339e7i	0.348309	−	0.292266i	−0.451802	−	0.892118i	$-0.649219\pi$
$461$	3.41246e7	−	2.86339e7i	0.348309	−	0.292266i	0.800110	+	0.599853i	$0.204774\pi$
$462$	−1.45274e8	+	9.76435e7i	−1.47320	+	0.990188i
$463$	1.72299e7	+	9.94768e6i	0.173596	+	0.100226i	0.584280	−	0.811552i	$-0.301377\pi$
$463$	1.72299e7	+	9.94768e6i	0.173596	+	0.100226i	−0.410684	+	0.911778i	$0.634710\pi$
$464$	−4.40378e7	−	9.18087e7i	−0.440831	−	0.919030i
$465$	5.67660e7	−	2.06611e7i	0.564585	−	0.205492i
$466$	−2.62150e7	+	5.35265e7i	−0.259055	+	0.528946i
$467$	6.13134e7	−	3.53993e7i	0.602011	−	0.347571i	−0.167821	−	0.985817i	$-0.553673\pi$
$467$	6.13134e7	−	3.53993e7i	0.602011	−	0.347571i	0.769832	+	0.638246i	$0.220340\pi$
$468$	−772384.	−	486155.i	−0.00753522	−	0.00474283i
$469$	1.48325e7	−	8.41191e7i	0.143779	−	0.815410i
$470$	2.36522e7	+	2.52501e6i	0.227812	+	0.0243204i
$471$	−1.17245e8	+	1.39727e8i	−1.12210	+	1.33727i
$472$	6.98701e7	+	5.51421e7i	0.664455	+	0.524393i
$473$	−1.81116e8	−	6.59208e7i	−1.71148	−	0.622929i
$474$	−7.24053e7	+	6.96927e7i	−0.679884	+	0.654414i
$475$	208741.	+	1.95257e7i	0.00194772	+	0.182191i
$476$	9.14104e6	+	349117.i	0.0847568	+	0.00323706i
$477$	−1.00492e7	−	3.65760e6i	−0.0925922	−	0.0337008i
$478$	−7.56842e6	+	1.03813e7i	−0.0692982	+	0.0950538i
$479$	2.90773e7	−	3.46530e7i	0.264574	−	0.315307i	−0.617359	−	0.786681i	$-0.711797\pi$
$479$	2.90773e7	−	3.46530e7i	0.264574	−	0.315307i	0.881933	+	0.471374i	$0.156242\pi$
$480$	1.04603e8	+	1.93266e7i	0.945849	+	0.174756i
$481$	−794911.	+	4.50816e6i	−0.00714304	+	0.0405102i
$482$	8.90214e6	+	3.59546e7i	0.0794975	+	0.321080i
$483$	7.11964e7	−	4.11052e7i	0.631854	−	0.364801i
$484$	−7.79831e6	−	2.42703e7i	−0.0687804	−	0.214061i
$485$	−3.52788e7	+	1.28404e7i	−0.309235	+	0.112552i
$486$	−1.35713e7	+	4.70385e7i	−0.118226	+	0.409774i
$487$	−5.71287e7	−	3.29833e7i	−0.494615	−	0.285566i	0.231872	−	0.972746i	$-0.425515\pi$
$487$	−5.71287e7	−	3.29833e7i	−0.494615	−	0.285566i	−0.726487	+	0.687180i	$0.758848\pi$
$488$	1.66917e8	−	1.03168e8i	1.43629	−	0.887736i
$489$	733888.	−	615805.i	0.00627629	−	0.00526643i
$490$	−2.91880e8	+	1.99312e7i	−2.48094	+	0.169412i
$491$	5.58774e7	−	9.85269e6i	0.472054	−	0.0832359i	0.0674399	−	0.997723i	$-0.478517\pi$
$491$	5.58774e7	−	9.85269e6i	0.472054	−	0.0832359i	0.404614	+	0.914487i	$0.367406\pi$
$492$	7.88615e7	+	3.21622e7i	0.662171	+	0.270054i
$493$	5.71379e6			0.0476852
$494$	2.04877e6	+	4.49168e6i	0.0169946	+	0.0372587i
$495$			3.17319e7i			0.261625i
$496$	3.14564e7	−	6.94278e7i	0.257789	−	0.568969i
$497$	4.95335e7	+	2.80919e8i	0.403487	+	2.28829i
$498$	3.88359e7	−	2.65193e6i	0.314446	−	0.0214721i
$499$	−5.57219e7	−	6.64068e7i	−0.448461	−	0.534455i	0.493693	−	0.869636i	$-0.335647\pi$
$499$	−5.57219e7	−	6.64068e7i	−0.448461	−	0.534455i	−0.942153	+	0.335182i	$0.891202\pi$
$500$	1.08643e8	+	2.34641e7i	0.869146	+	0.187713i
$501$	6.59218e7	−	1.14180e8i	0.524223	−	0.907981i
$502$	−6.79623e7	+	2.35560e8i	−0.537226	+	1.86204i
$503$	−5.70287e7	−	1.56685e8i	−0.448115	−	1.23119i	−0.934035	−	0.357183i	$-0.883737\pi$
$503$	−5.70287e7	−	1.56685e8i	−0.448115	−	1.23119i	0.485919	−	0.874004i	$-0.338485\pi$
$504$	2.39100e7	−	4.44414e7i	0.186762	−	0.347133i
$505$	−5.94590e7	−	1.02986e8i	−0.461683	−	0.799658i
$506$	1.56757e7	+	6.33122e7i	0.120997	+	0.488693i
$507$	1.13347e8	+	1.99862e7i	0.869736	+	0.153358i
$508$	−1.54901e8	+	1.20209e8i	−1.18158	+	0.916951i
$509$	−3.63256e7	−	3.04808e7i	−0.275461	−	0.231139i	0.494583	−	0.869131i	$-0.335321\pi$
$509$	−3.63256e7	−	3.04808e7i	−0.275461	−	0.231139i	−0.770043	+	0.637992i	$0.779765\pi$
$510$	−3.51642e6	+	4.82335e6i	−0.0265088	+	0.0363612i
$511$	8.27224e7	−	2.27278e8i	0.619955	−	1.70331i
$512$	1.09733e8	−	7.72863e7i	0.817571	−	0.575828i
$513$	1.10375e8	−	9.46450e7i	0.817561	−	0.701044i
$514$	−9.89631e6	+	9.52556e6i	−0.0728759	+	0.0701457i
$515$	−4.39663e6	+	1.20796e7i	−0.0321883	+	0.0884367i
$516$	−1.98158e8	+	2.71894e7i	−1.44232	+	0.197902i
$517$	−2.46864e7	−	2.07144e7i	−0.178643	−	0.149899i
$518$	−2.51696e8	−	2.68701e7i	−1.81087	−	0.193321i
$519$	−1.81268e8	−	3.19624e7i	−1.29664	−	0.228632i
$520$	−6.13024e6	+	1.27166e6i	−0.0435981	+	0.00904398i
$521$	−1.21928e8	−	2.11185e8i	−0.862162	−	1.49331i	−0.869838	−	0.493337i	$-0.835777\pi$
$521$	−1.21928e8	−	2.11185e8i	−0.862162	−	1.49331i	0.00767659	−	0.999971i	$-0.497556\pi$
$522$	1.38643e7	−	2.83085e7i	0.0974732	−	0.199024i
$523$	6.63718e7	+	1.82355e8i	0.463958	+	1.27471i	0.922485	+	0.386033i	$0.126155\pi$
$523$	6.63718e7	+	1.82355e8i	0.463958	+	1.27471i	−0.458528	+	0.888680i	$0.651623\pi$
$524$	−3.60771e7	−	6.83892e7i	−0.250748	−	0.475328i
$525$	2.11431e7	−	3.66209e7i	0.146114	−	0.253076i
$526$	1.54822e8	−	1.04061e8i	1.06383	−	0.715040i
$527$	2.74928e6	+	3.27646e6i	0.0187839	+	0.0223858i
$528$	−1.03011e8	−	1.00785e8i	−0.699810	−	0.684692i
$529$	2.03867e7	+	1.15619e8i	0.137714	+	0.781018i
$530$	−6.70676e7	+	2.97292e7i	−0.450490	+	0.199690i
$531$			2.75539e7i			0.184035i
$532$	−2.40074e8	+	1.29945e8i	−1.59445	+	0.863025i
$533$	−5.01265e6			−0.0331044
$534$	−8.32319e7	−	1.87767e8i	−0.546595	−	1.23309i
$535$	−1.65270e8	+	2.91416e7i	−1.07928	+	0.190306i
$536$	7.02941e7	−	2.10987e6i	0.456483	−	0.0137013i
$537$	−1.74280e8	+	1.46239e8i	−1.12545	+	0.944364i
$538$	5.37097e7	+	7.99091e7i	0.344910	+	0.513156i
$539$	3.43255e8	+	1.98179e8i	2.19205	+	1.26558i
$540$	8.60323e7	+	1.63086e8i	0.546362	+	1.03571i
$541$	3.62327e7	−	1.31876e7i	0.228828	−	0.0832865i	−0.225062	−	0.974345i	$-0.572258\pi$
$541$	3.62327e7	−	1.31876e7i	0.228828	−	0.0832865i	0.453889	+	0.891058i	$0.350036\pi$
$542$	7.08252e7	+	3.46871e7i	0.444826	+	0.217856i
$543$	−2.04478e8	+	1.18055e8i	−1.27716	+	0.737370i
$544$	1.24721e6	+	7.42754e6i	0.00774717	+	0.0461369i
$545$	−3.93884e7	+	2.23383e8i	−0.243320	+	1.37994i
$546$	1.13488e6	−	1.06306e7i	0.00697225	−	0.0653100i
$547$	1.43150e8	−	1.70599e8i	0.874637	−	1.04235i	−0.124108	−	0.992269i	$-0.539607\pi$
$547$	1.43150e8	−	1.70599e8i	0.874637	−	1.04235i	0.998745	−	0.0500834i	$-0.0159487\pi$
$548$	2.53740e8	−	3.48159e7i	1.54187	−	0.211561i
$549$	5.70817e7	+	2.07760e7i	0.344969	+	0.125558i
$550$	2.32656e7	+	2.41711e7i	0.139838	+	0.145281i
$551$	−1.46747e8	+	8.68291e7i	−0.877231	+	0.519051i
$552$	4.50437e7	+	5.05218e7i	0.267804	+	0.300373i
$553$	3.07339e8	+	1.11862e8i	1.81737	+	0.661467i
$554$	−1.21096e8	−	8.82842e7i	−0.712199	−	0.519223i
$555$	1.06169e8	−	1.26528e8i	0.621041	−	0.740128i
$556$	−2.28371e8	+	1.77224e8i	−1.32867	+	1.03110i
$557$	3.14991e7	−	1.78640e8i	0.182277	−	1.03375i	−0.747126	−	0.664682i	$-0.768567\pi$
$557$	3.14991e7	−	1.78640e8i	0.182277	−	1.03375i	0.929404	−	0.369065i	$-0.120322\pi$
$558$	2.29039e7	−	5.67087e6i	0.131828	−	0.0326398i
$559$	1.01949e7	−	5.88604e6i	0.0583645	−	0.0336968i
$560$	−9.32464e7	−	3.33396e8i	−0.530968	−	1.89844i
$561$	7.59916e6	−	2.76587e6i	0.0430405	−	0.0156654i
$562$	−8.75199e7	−	2.52507e7i	−0.493058	−	0.142254i
$563$	1.02286e8	+	5.90548e7i	0.573180	+	0.330925i	0.758418	−	0.651768i	$-0.225972\pi$
$563$	1.02286e8	+	5.90548e7i	0.573180	+	0.330925i	−0.185239	+	0.982694i	$0.559306\pi$
$564$	−3.26885e7	−	7.05986e6i	−0.182204	−	0.0393513i
$565$	−8.33032e7	+	6.98996e7i	−0.461866	+	0.387552i
$566$	3.77917e6	+	5.53438e7i	0.0208424	+	0.305225i
$567$	−2.39319e8	+	4.21984e7i	−1.31289	+	0.231498i
$568$	−2.18182e8	+	8.69101e7i	−1.19062	+	0.474269i
$569$	1.83440e7			0.0995764			0.0497882	−	0.998760i	$-0.484145\pi$
$569$	1.83440e7			0.0995764			0.0497882	+	0.998760i	$0.484145\pi$
$570$	1.70144e7	−	1.77315e8i	0.0918740	−	0.957460i
$571$		−	3.34531e8i		−	1.79691i	−0.439061	−	0.898457i	$-0.644689\pi$
$571$		−	3.34531e8i		−	1.79691i	0.439061	−	0.898457i	$-0.355311\pi$
$572$	7.85395e6	+	3.20309e6i	0.0419663	+	0.0171152i
$573$	−1.29325e6	−	7.33437e6i	−0.00687413	−	0.0389852i
$574$	−1.88831e7	−	2.76532e8i	−0.0998476	−	1.46221i
$575$	−1.01283e7	−	1.20705e7i	−0.0532763	−	0.0634922i
$576$	3.98254e7	+	1.18434e7i	0.208398	+	0.0619740i
$577$	3.55978e7	−	6.16573e7i	0.185309	−	0.320964i	−0.758372	−	0.651822i	$-0.774005\pi$
$577$	3.55978e7	−	6.16573e7i	0.185309	−	0.320964i	0.943681	+	0.330858i	$0.107338\pi$
$578$	1.85127e8	+	5.34117e7i	0.958707	+	0.276601i
$579$	8.45680e7	+	2.32349e8i	0.435683	+	1.19703i
$580$	−6.61481e7	−	2.05869e8i	−0.339027	−	1.05513i
$581$	−6.33423e7	−	1.09712e8i	−0.322973	−	0.559405i
$582$	5.12355e7	−	1.26856e7i	0.259898	−	0.0643490i
$583$	9.78793e7	+	1.72588e7i	0.493953	+	0.0870972i
$584$	1.97057e8	+	2.86800e7i	0.989355	+	0.143993i
$585$	−1.48468e6	−	1.24579e6i	−0.00741592	−	0.00622269i
$586$	2.59268e7	+	1.89017e7i	0.128842	+	0.0939309i
$587$	−5.38147e7	+	1.47855e8i	−0.266065	+	0.731006i	0.732664	+	0.680591i	$0.238277\pi$
$587$	−5.38147e7	+	1.47855e8i	−0.266065	+	0.731006i	−0.998728	+	0.0504155i	$0.983945\pi$
$588$	4.11018e8	+	1.56977e7i	2.02176	+	0.0772156i
$589$	−1.20400e8	−	4.23700e7i	−0.589224	−	0.207354i
$590$	1.31082e8	+	1.36183e8i	0.638243	+	0.663084i
$591$	6.68219e7	−	1.83592e8i	0.323710	−	0.889387i
$592$	−2.04295e7	−	2.07401e8i	−0.0984672	−	0.999645i
$593$	−3.78967e7	−	3.17991e7i	−0.181735	−	0.152493i	0.547382	−	0.836883i	$-0.315624\pi$
$593$	−3.78967e7	−	3.17991e7i	−0.181735	−	0.152493i	−0.729117	+	0.684389i	$0.760069\pi$
$594$	2.65177e7	−	2.48395e8i	0.126525	−	1.18518i
$595$	1.91311e7	+	3.37332e6i	0.0908214	+	0.0160143i
$596$	−7.47411e7	−	4.70437e7i	−0.353037	−	0.222209i
$597$	1.83484e7	+	3.17803e7i	0.0862332	+	0.149360i
$598$	−3.57770e6	−	1.75220e6i	−0.0167302	−	0.00819370i
$599$	3.45141e6	+	9.48268e6i	0.0160589	+	0.0441215i	0.947463	−	0.319865i	$-0.103638\pi$
$599$	3.45141e6	+	9.48268e6i	0.0160589	+	0.0441215i	−0.931404	+	0.363987i	$0.881415\pi$
$600$	3.30582e7	+	1.09206e7i	0.153047	+	0.0505585i
$601$	3.63906e7	−	6.30304e7i	0.167635	−	0.290353i	−0.769953	−	0.638101i	$-0.779720\pi$
$601$	3.63906e7	−	6.30304e7i	0.167635	−	0.290353i	0.937588	+	0.347748i	$0.113054\pi$
$602$	3.63120e8	+	5.40249e8i	1.66441	+	2.47631i
$603$	1.39937e7	+	1.66771e7i	0.0638237	+	0.0760621i
$604$	2.49923e8	+	2.26515e8i	1.13422	+	1.02798i
$605$	−9.40060e6	−	5.33135e7i	−0.0424511	−	0.240752i
$606$	6.77528e7	+	1.52847e8i	0.304445	+	0.686813i
$607$			1.56622e7i			0.0700306i	0.999387	+	0.0350153i	$0.0111480\pi$
$607$			1.56622e7i			0.0700306i	−0.999387	+	0.0350153i	$0.988852\pi$
$608$	−1.44904e8	−	1.71808e8i	−0.644718	−	0.764421i
$609$	3.69249e8			1.63481
$610$	3.80960e8	−	1.68869e8i	1.67838	−	0.743980i
$611$	1.93838e6	−	341788.i	0.00849796	−	0.00149842i
$612$	−1.56573e6	+	1.72754e6i	−0.00683066	+	0.00753655i
$613$	9.18930e7	−	7.71074e7i	0.398934	−	0.334745i	−0.421147	−	0.906992i	$-0.638373\pi$
$613$	9.18930e7	−	7.71074e7i	0.398934	−	0.334745i	0.820081	+	0.572247i	$0.193928\pi$
$614$	−7.07774e7	+	4.75719e7i	−0.305766	+	0.205516i
$615$	1.56632e8	+	9.04318e7i	0.673374	+	0.388773i
$616$	−1.47118e8	+	4.45344e8i	−0.629395	+	1.90526i
$617$	−4.20822e8	+	1.53167e8i	−1.79161	+	0.652092i	−0.792499	+	0.609873i	$0.791220\pi$
$617$	−4.20822e8	+	1.53167e8i	−1.79161	+	0.652092i	−0.999108	+	0.0422182i	$0.986558\pi$
$618$	7.94923e6	−	1.62310e7i	0.0336790	−	0.0687669i
$619$	−3.01024e7	+	1.73796e7i	−0.126920	+	0.0732771i	−0.562116	−	0.827059i	$-0.690012\pi$
$619$	−3.01024e7	+	1.73796e7i	−0.126920	+	0.0732771i	0.435196	+	0.900336i	$0.356679\pi$
$620$	8.62235e7	−	1.36988e8i	0.361785	−	0.574790i
$621$	−2.03735e7	+	1.15544e8i	−0.0850728	+	0.482472i
$622$	−2.99451e7	−	3.19682e6i	−0.124438	−	0.0132846i
$623$	−4.29656e8	+	5.12044e8i	−1.77688	+	2.11760i
$624$	8.75977e6	−	862857.i	0.0360528	−	0.00355128i
$625$	2.63601e8	+	9.59430e7i	1.07971	+	0.392982i
$626$	1.09222e8	−	1.05130e8i	0.445232	−	0.428552i
$627$	−1.53137e8	+	1.86516e8i	−0.621268	+	0.756680i
$628$	−1.86525e7	+	4.88384e8i	−0.0753109	+	1.97189i
$629$	1.09892e7	+	3.99975e6i	0.0441585	+	0.0160724i
$630$	6.31336e7	−	8.65981e7i	0.252487	−	0.346327i
$631$	3.20210e8	−	3.81611e8i	1.27452	−	1.51891i	0.537015	−	0.843573i	$-0.319552\pi$
$631$	3.20210e8	−	3.81611e8i	1.27452	−	1.51891i	0.737505	−	0.675342i	$-0.236004\pi$
$632$	−3.87828e7	+	2.66472e8i	−0.153634	+	1.05560i
$633$	6.34507e7	−	3.59847e8i	0.250164	−	1.41875i
$634$	−2.79771e7	−	1.12996e8i	−0.109783	−	0.443400i
$635$	−3.60599e8	+	2.08192e8i	−1.40832	+	0.813097i
$636$	9.81963e7	−	3.15516e7i	0.381702	−	0.122645i
$637$	−2.27486e7	+	8.27983e6i	−0.0880110	+	0.0320334i
$638$	−8.12089e7	+	2.81473e8i	−0.312710	+	1.08386i
$639$	−6.29626e7	−	3.63515e7i	−0.241313	−	0.139322i
$640$	2.53177e8	−	1.30925e8i	0.965795	−	0.499441i
$641$	2.66507e8	−	2.23626e8i	1.01189	−	0.849079i	0.0233055	−	0.999728i	$-0.492581\pi$
$641$	2.66507e8	−	2.23626e8i	1.01189	−	0.849079i	0.988587	+	0.150650i	$0.0481365\pi$
$642$	2.35394e8	−	1.60740e7i	0.889593	−	0.0607462i
$643$	−1.51506e8	+	2.67146e7i	−0.569898	+	0.100488i	−0.451169	−	0.892438i	$-0.648993\pi$
$643$	−1.51506e8	+	2.67146e7i	−0.569898	+	0.100488i	−0.118729	+	0.992927i	$0.537882\pi$
$644$	8.31858e7	−	2.03971e8i	0.311452	−	0.763679i
$645$	−4.24754e8			−1.58292
$646$	1.22092e7	−	3.16182e6i	0.0452888	−	0.0117284i
$647$			2.62996e8i			0.971038i	0.874226	+	0.485519i	$0.161369\pi$
$647$			2.62996e8i			0.971038i	−0.874226	+	0.485519i	$0.838631\pi$
$648$	−7.40401e7	−	1.85873e8i	−0.272108	−	0.683111i
$649$	−4.44681e7	−	2.52191e8i	−0.162673	−	0.922563i
$650$	−2.04433e6	+	139598.i	−0.00744408	+	0.000508323i
$651$	1.77670e8	+	2.11738e8i	0.643977	+	0.767461i
$652$	541911.	−	2.50915e6i	0.00195517	−	0.00905283i
$653$	−9.42973e7	+	1.63328e8i	−0.338657	+	0.586571i	−0.984180	−	0.177170i	$-0.943306\pi$
$653$	−9.42973e7	+	1.63328e8i	−0.338657	+	0.586571i	0.645524	+	0.763740i	$0.276639\pi$
$654$	8.84027e7	−	3.06407e8i	0.316033	−	1.09538i
$655$	−5.61602e7	−	1.54299e8i	−0.199850	−	0.549084i
$656$	2.19772e8	−	6.14673e7i	0.778503	−	0.217737i
$657$	3.08223e7	+	5.33858e7i	0.108685	+	0.188248i
$658$	2.61574e7	+	1.05647e8i	0.0918158	+	0.370833i
$659$	4.35774e7	+	7.68388e6i	0.152267	+	0.0268488i	0.249262	−	0.968436i	$-0.419812\pi$
$659$	4.35774e7	+	7.68388e6i	0.152267	+	0.0268488i	−0.0969950	+	0.995285i	$0.530923\pi$
$660$	−1.87630e8	−	2.41779e8i	−0.652635	−	0.840983i
$661$	−9.84635e7	−	8.26207e7i	−0.340934	−	0.286078i	0.456203	−	0.889876i	$-0.349209\pi$
$661$	−9.84635e7	−	8.26207e7i	−0.340934	−	0.286078i	−0.797138	+	0.603798i	$0.793653\pi$
$662$	3.67492e7	−	5.04076e7i	0.126670	−	0.173749i
$663$	−168933.	+	464139.i	−0.000579660	+	0.00159260i
$664$	7.78530e7	−	6.94113e7i	0.265932	−	0.237097i
$665$	−5.42604e8	+	2.04087e8i	−1.84509	+	0.693985i
$666$	4.64813e7	−	4.47399e7i	0.157346	−	0.151451i
$667$	4.70589e7	−	1.29293e8i	0.158586	−	0.435711i
$668$	−4.80229e7	−	3.49994e8i	−0.161109	−	1.17417i
$669$	−2.46261e8	−	2.06638e8i	−0.822465	−	0.690130i
$670$	1.48501e8	+	1.58534e7i	0.493747	+	0.0527105i
$671$	−5.55978e8	−	9.80340e7i	−1.84031	−	0.324496i
$672$	8.05999e7	+	4.79998e8i	0.265599	+	1.58173i
$673$	−7.02708e7	−	1.21713e8i	−0.230531	−	0.399292i	0.727433	−	0.686178i	$-0.240713\pi$
$673$	−7.02708e7	−	1.21713e8i	−0.230531	−	0.399292i	−0.957965	+	0.286887i	$0.907380\pi$
$674$	7.73145e7	−	1.57863e8i	0.252512	−	0.515586i
$675$	2.06404e7	+	5.67091e7i	0.0671131	+	0.184392i
$676$	2.72771e8	−	1.43894e8i	0.882993	−	0.465802i
$677$	−2.04547e8	+	3.54286e8i	−0.659215	+	1.14179i	0.321604	+	0.946874i	$0.395778\pi$
$677$	−2.04547e8	+	3.54286e8i	−0.659215	+	1.14179i	−0.980819	+	0.194920i	$0.937555\pi$
$678$	1.26889e8	−	8.52862e7i	0.407130	−	0.273646i
$679$	−1.10418e8	−	1.31591e8i	−0.352719	−	0.420355i
$680$	479844.	+	1.59869e7i	0.00152607	+	0.0508436i
$681$	7.08326e7	+	4.01712e8i	0.224281	+	1.27196i
$682$	−2.00480e8	+	8.88673e7i	−0.632001	+	0.280149i
$683$		−	3.43483e8i		−	1.07806i	−0.842287	−	0.539030i	$-0.818791\pi$
$683$		−	3.43483e8i		−	1.07806i	0.842287	−	0.539030i	$-0.181209\pi$
$684$	1.39602e7	−	6.81617e7i	0.0436238	−	0.212996i
$685$	5.43895e8			1.69217
$686$	−3.05280e8	−	6.88695e8i	−0.945639	−	2.13331i
$687$	2.41788e8	−	4.26338e7i	0.745702	−	0.131487i
$688$	−3.74803e8	+	3.83079e8i	−1.15090	+	1.17631i
$689$	−4.65025e6	+	3.90202e6i	−0.0142174	+	0.0119298i
$690$	8.01829e7	+	1.19296e8i	0.244081	+	0.363144i
$691$	2.35013e8	+	1.35685e8i	0.712293	+	0.411243i	0.811909	−	0.583783i	$-0.198428\pi$
$691$	2.35013e8	+	1.35685e8i	0.712293	+	0.411243i	−0.0996165	+	0.995026i	$0.531762\pi$
$692$	−4.36222e8	+	2.30118e8i	−1.31640	+	0.694437i
$693$	−1.36435e8	+	4.96582e7i	−0.409945	+	0.149208i
$694$	2.75830e8	+	1.35090e8i	0.825208	+	0.404151i
$695$	−5.31631e8	+	3.06937e8i	−1.58364	+	0.914314i
$696$	6.17494e7	+	2.97674e8i	0.183149	+	0.882904i
$697$	−2.22367e6	+	1.26110e7i	−0.00656707	+	0.0372437i
$698$	4.97616e7	−	4.66124e8i	0.146328	−	1.37068i
$699$	1.14383e8	−	1.36317e8i	0.334912	−	0.399132i
$700$	−1.54024e7	−	1.12253e8i	−0.0449049	−	0.327269i
$701$	−4.92291e8	−	1.79179e8i	−1.42912	−	0.520156i	−0.492439	−	0.870347i	$-0.663894\pi$
$701$	−4.92291e8	−	1.79179e8i	−1.42912	−	0.520156i	−0.936678	+	0.350191i	$0.886117\pi$
$702$	1.05809e7	+	1.09927e7i	0.0305852	+	0.0317756i
$703$	−3.43017e8	+	6.42713e7i	−0.987301	+	0.184991i
$704$	−3.83622e8	−	4.41259e7i	−1.09948	−	0.126467i
$705$	−6.67354e7	−	2.42897e7i	−0.190454	−	0.0693194i
$706$	−2.91100e8	−	2.12224e8i	−0.827233	−	0.603087i
$707$	3.49751e8	−	4.16817e8i	0.989693	−	1.17947i
$708$	−1.62926e8	−	2.09945e8i	−0.459081	−	0.591571i
$709$	−4.83494e7	+	2.74203e8i	−0.135660	+	0.769367i	0.838738	+	0.544536i	$0.183294\pi$
$709$	−4.83494e7	+	2.74203e8i	−0.135660	+	0.769367i	−0.974398	+	0.224831i	$0.927817\pi$
$710$	−4.84123e8	+	1.19866e8i	−1.35264	+	0.334904i
$711$	−7.21915e7	+	4.16798e7i	−0.200853	+	0.115962i
$712$	−4.84642e8	−	2.60743e8i	−1.34271	−	0.722393i
$713$	9.67839e7	−	3.52264e7i	0.267014	−	0.0971852i
$714$	−2.62415e7	−	7.57104e6i	−0.0720931	−	0.0207999i
$715$	1.55993e7	+	9.00625e6i	0.0426763	+	0.0246392i
$716$	−1.28691e8	+	5.95863e8i	−0.350597	+	1.62333i
$717$	2.93836e7	−	2.46558e7i	0.0797163	−	0.0668899i
$718$	−1.85229e7	−	2.71257e8i	−0.0500422	−	0.732838i
$719$	4.50959e8	−	7.95162e7i	1.21325	−	0.213929i	0.469832	−	0.882756i	$-0.344314\pi$
$719$	4.50959e8	−	7.95162e7i	1.21325	−	0.213929i	0.743418	+	0.668827i	$0.233203\pi$
$720$	8.03699e7	+	3.64141e7i	0.215326	+	0.0975600i
$721$	−5.88182e7			−0.156930
$722$	−2.65521e8	+	2.66741e8i	−0.705483	+	0.708727i
$723$		−	1.10589e8i		−	0.292616i
$724$	−2.38912e8	+	5.85809e8i	−0.629537	+	1.54362i
$725$	−1.22894e7	−	6.96969e7i	−0.0322491	−	0.182894i
$726$	5.18521e6	+	7.59343e7i	0.0135505	+	0.198440i
$727$	4.07444e8	+	4.85573e8i	1.06039	+	1.26372i	0.963295	+	0.268445i	$0.0865099\pi$
$727$	4.07444e8	+	4.85573e8i	1.06039	+	1.26372i	0.0970928	+	0.995275i	$0.469046\pi$
$728$	−1.50610e7	−	2.43676e7i	−0.0390356	−	0.0631566i
$729$	2.15522e8	−	3.73295e8i	0.556300	−	0.963539i
$730$	4.06308e8	+	1.17226e8i	1.04445	+	0.301338i
$731$	−1.02858e7	−	2.82600e7i	−0.0263321	−	0.0723468i
$732$	−5.57779e8	+	1.79221e8i	−1.42210	+	0.456936i
$733$	3.41177e8	+	5.90936e8i	0.866299	+	1.50047i	0.865752	+	0.500474i	$0.166841\pi$
$733$	3.41177e8	+	5.90936e8i	0.866299	+	1.50047i	0.000547014		1.00000i	$0.499826\pi$
$734$	3.66476e8	−	9.07372e7i	0.926740	−	0.229455i
$735$	8.60211e8	+	1.51678e8i	2.16642	+	0.381998i
$736$	1.78345e8	+	3.29512e7i	0.447329	+	0.0826490i
$737$	−1.54994e8	−	1.30056e8i	−0.387180	−	0.324883i
$738$	5.70847e7	+	4.16171e7i	0.142020	+	0.103539i
$739$	1.06622e8	−	2.92940e8i	0.264187	−	0.725848i	−0.734687	−	0.678406i	$-0.762671\pi$
$739$	1.06622e8	−	2.92940e8i	0.264187	−	0.725848i	0.998874	−	0.0474417i	$-0.0151068\pi$
$740$	1.68905e7	−	4.42249e8i	0.0416819	−	1.09137i
$741$	−2.71456e6	−	1.44876e7i	−0.00667183	−	0.0356076i
$742$	−2.32780e8	−	2.41840e8i	−0.569816	−	0.591994i
$743$	2.33820e8	−	6.42415e8i	0.570053	−	1.56621i	−0.234369	−	0.972148i	$-0.575302\pi$
$743$	2.33820e8	−	6.42415e8i	0.570053	−	1.56621i	0.804421	−	0.594059i	$-0.202476\pi$
$744$	−1.40984e8	+	1.78639e8i	−0.342334	+	0.433769i
$745$	−1.43667e8	−	1.20551e8i	−0.347448	−	0.291543i
$746$	9.63804e6	−	9.02809e7i	0.0232152	−	0.217460i
$747$	3.17979e7	+	5.60683e6i	0.0762846	+	0.0134510i
$748$	1.15426e7	−	1.83384e7i	0.0275802	−	0.0438184i
$749$	−3.83934e8	−	6.64993e8i	−0.913716	−	1.58260i
$750$	−2.98026e8	−	1.45960e8i	−0.706433	−	0.345980i
$751$	7.00624e7	+	1.92495e8i	0.165411	+	0.454464i	0.994510	−	0.104638i	$-0.0333683\pi$
$751$	7.00624e7	+	1.92495e8i	0.165411	+	0.454464i	−0.829099	+	0.559102i	$0.811146\pi$
$752$	−8.07940e7	+	3.87544e7i	−0.189988	+	0.0911313i
$753$	3.65992e8	−	6.33917e8i	0.857210	−	1.48473i
$754$	−9.98136e6	−	1.48502e7i	−0.0232850	−	0.0346433i
$755$	4.60424e8	+	5.48712e8i	1.06984	+	1.27498i
$756$	−5.66574e8	+	6.25125e8i	−1.31127	+	1.44678i
$757$	2.62240e7	+	1.48724e8i	0.0604521	+	0.342841i	1.00000		0.000423169i	$0.000134699\pi$
$757$	2.62240e7	+	1.48724e8i	0.0604521	+	0.342841i	−0.939548	+	0.342418i	$0.888754\pi$
$758$	−5.40206e6	−	1.21868e7i	−0.0124037	−	0.0279821i
$759$		−	1.94736e8i		−	0.445370i
$760$	−2.55267e8	−	4.03298e8i	−0.581505	−	0.918724i
$761$	−2.95952e8			−0.671532			−0.335766	−	0.941945i	$-0.608995\pi$
$761$	−2.95952e8			−0.671532			−0.335766	+	0.941945i	$0.608995\pi$
$762$	5.35182e8	−	2.37232e8i	1.20959	−	0.536177i
$763$	−1.02210e9	+	1.80224e8i	−2.30101	+	0.405731i
$764$	−1.47861e7	−	1.34012e7i	−0.0331569	−	0.0300514i
$765$	−3.79284e6	+	3.18257e6i	−0.00847190	+	0.00710877i
$766$	3.18400e8	−	2.14008e8i	0.708414	−	0.476149i
$767$	1.35454e7	+	7.82044e6i	0.0300197	+	0.0173319i
$768$	−3.73478e8	+	1.45247e8i	−0.824482	+	0.320644i
$769$	6.25110e8	−	2.27521e8i	1.37460	−	0.500315i	0.454065	−	0.890968i	$-0.349973\pi$
$769$	6.25110e8	−	2.27521e8i	1.37460	−	0.500315i	0.920538	+	0.390654i	$0.127751\pi$
$770$	−4.38083e8	+	8.94491e8i	−0.959586	+	1.95931i
$771$	3.55160e7	−	2.05052e7i	0.0774928	−	0.0447405i
$772$	5.60707e8	+	3.52921e8i	1.21866	+	0.767054i
$773$	2.97473e7	−	1.68705e8i	0.0644033	−	0.365249i	−0.935525	−	0.353261i	$-0.885073\pi$
$773$	2.97473e7	−	1.68705e8i	0.0644033	−	0.365249i	0.999928	−	0.0119885i	$-0.00381614\pi$
$774$	−1.64970e8	−	1.76115e7i	−0.355780	−	0.0379817i
$775$	3.40531e7	−	4.05828e7i	0.0731562	−	0.0871841i
$776$	8.76182e7	−	1.11020e8i	0.187503	−	0.237584i
$777$	7.10168e8	+	2.58480e8i	1.51390	+	0.551016i
$778$	−5.87681e8	+	5.65665e8i	−1.24797	+	1.20121i
$779$	−1.34532e8	−	3.57680e8i	−0.284586	−	0.756629i
$780$	1.86788e7	+	713385.i	0.0393609	+	0.00150328i
$781$	6.34941e8	+	2.31100e8i	1.33285	+	0.485117i
$782$	−5.99537e6	+	8.22363e6i	−0.0125371	+	0.0171966i
$783$	−3.38731e8	+	4.03683e8i	−0.705617	+	0.840922i
$784$	8.95848e8	−	6.41970e8i	1.85903	−	1.33219i
$785$	−1.80229e8	+	1.02213e9i	−0.372576	+	2.11298i
$786$	5.54830e7	+	2.24089e8i	0.114259	+	0.461480i
$787$	−2.30157e8	+	1.32881e8i	−0.472172	+	0.272609i	−0.717149	−	0.696920i	$-0.754553\pi$
$787$	−2.30157e8	+	1.32881e8i	−0.472172	+	0.272609i	0.244976	+	0.969529i	$0.421220\pi$
$788$	−1.60144e8	−	4.98406e8i	−0.327289	−	1.01860i
$789$	−5.23364e8	+	1.90489e8i	−1.06555	+	0.387828i
$790$	−1.58520e8	+	5.49435e8i	−0.321516	+	1.11438i
$791$	−4.30905e8	−	2.48783e8i	−0.870667	−	0.502680i
$792$	−6.28485e7	−	1.01684e8i	−0.126508	−	0.204681i
$793$	2.64146e7	−	2.21644e7i	0.0529692	−	0.0444465i
$794$	1.94951e8	−	1.33123e7i	0.389460	−	0.0265945i
$795$	2.15704e8	−	3.80344e7i	0.429295	−	0.0756964i
$796$	9.10477e7	+	3.71321e7i	0.180522	+	0.0736225i
$797$	1.33267e8			0.263238			0.131619	−	0.991300i	$-0.457982\pi$
$797$	1.33267e8			0.263238			0.131619	+	0.991300i	$0.457982\pi$
$798$	7.89011e8	−	2.04330e8i	1.55265	−	0.402090i
$799$		−	5.02828e6i		−	0.00985777i
$800$	8.79187e7	−	3.11889e7i	0.171716	−	0.0609159i
$801$	−2.95833e7	−	1.67775e8i	−0.0575638	−	0.326461i
$802$	3.35291e8	−	2.28955e7i	0.649978	−	0.0443840i
$803$	−3.68263e8	−	4.38878e8i	−0.711232	−	0.847613i
$804$	−2.05236e8	−	4.43256e7i	−0.394898	−	0.0852876i
$805$	2.33897e8	−	4.05121e8i	0.448370	−	0.776600i
$806$	3.71290e6	−	1.28690e7i	0.00709101	−	0.0245777i
$807$	−9.83184e7	−	2.70128e8i	−0.187074	−	0.513983i
$808$	3.94511e8	+	2.12251e8i	0.747867	+	0.402362i
$809$	2.93677e8	+	5.08664e8i	0.554658	+	0.960695i	0.997930	+	0.0643084i	$0.0204841\pi$
$809$	2.93677e8	+	5.08664e8i	0.554658	+	0.960695i	−0.443272	+	0.896387i	$0.646183\pi$
$810$	−1.02116e8	−	4.12432e8i	−0.192149	−	0.776064i
$811$	−4.81517e8	−	8.49044e7i	−0.902711	−	0.159172i	−0.297019	−	0.954871i	$-0.595993\pi$
$811$	−4.81517e8	−	8.49044e7i	−0.902711	−	0.159172i	−0.605692	+	0.795699i	$0.707104\pi$
$812$	7.81640e8	−	6.06582e8i	1.45995	−	1.13298i
$813$	−1.80371e8	−	1.51349e8i	−0.335657	−	0.281650i
$814$	−3.53223e8	+	4.84503e8i	−0.654901	+	0.898304i
$815$	1.86447e6	−	5.12258e6i	0.00344414	−	0.00946271i
$816$	1.71512e6	−	2.24210e7i	0.00315663	−	0.0412652i
$817$	6.93619e8	+	5.69492e8i	1.27191	+	1.04429i
$818$	−2.74332e8	+	2.64055e8i	−0.501207	+	0.482430i
$819$	3.03301e6	−	8.33312e6i	0.00552105	−	0.0151690i
$820$	4.80122e8	−	6.58779e7i	0.870784	−	0.119481i
$821$	7.42294e8	+	6.22859e8i	1.34136	+	1.12554i	0.981273	+	0.192621i	$0.0616987\pi$
$821$	7.42294e8	+	6.22859e8i	1.34136	+	1.12554i	0.360091	+	0.932917i	$0.382746\pi$
$822$	−7.60357e8	−	8.11728e7i	−1.36900	−	0.146149i
$823$	3.39107e8	+	5.97936e7i	0.608326	+	0.107264i	0.469322	−	0.883027i	$-0.344499\pi$
$823$	3.39107e8	+	5.97936e7i	0.608326	+	0.107264i	0.139005	+	0.990292i	$0.455610\pi$
$824$	−9.83616e6	−	4.74170e7i	−0.0175810	−	0.0847524i
$825$	−5.00827e7	−	8.67457e7i	−0.0891919	−	0.154485i
$826$	−3.80402e8	+	7.76718e8i	−0.674999	+	1.37823i
$827$	−4.40094e7	−	1.20915e8i	−0.0778089	−	0.213778i	0.894689	−	0.446689i	$-0.147397\pi$
$827$	−4.40094e7	−	1.20915e8i	−0.0778089	−	0.213778i	−0.972498	+	0.232911i	$0.925175\pi$
$828$	2.61958e7	+	4.96579e7i	0.0461467	+	0.0874776i
$829$	−6.54441e7	+	1.13353e8i	−0.114870	+	0.198961i	−0.917728	−	0.397210i	$-0.869979\pi$
$829$	−6.54441e7	+	1.13353e8i	−0.114870	+	0.198961i	0.802858	+	0.596171i	$0.203312\pi$
$830$	1.83833e8	−	1.23560e8i	0.321505	−	0.216095i
$831$	2.87605e8	+	3.42754e8i	0.501179	+	0.597282i
$832$	1.71256e7	−	1.62166e7i	0.0297355	−	0.0281573i
$833$	1.07392e7	+	6.09051e7i	0.0185796	+	0.105370i
$834$	7.89020e8	−	3.49751e8i	1.36016	−	0.602922i
$835$		−	7.50215e8i		−	1.28862i
$836$	−1.77696e7	+	6.46390e8i	−0.0304129	+	1.10631i
$837$	−3.94470e8			−0.672725
$838$	−4.12917e8	−	9.31520e8i	−0.701667	−	1.58292i
$839$	2.90180e8	−	5.11666e7i	0.491340	−	0.0866365i	0.0775118	−	0.996991i	$-0.475302\pi$
$839$	2.90180e8	−	5.11666e7i	0.491340	−	0.0866365i	0.413828	+	0.910355i	$0.364191\pi$
$840$	3.10095e7	+	1.03314e9i	0.0523187	+	1.74309i
$841$	1.77474e7	−	1.48918e7i	0.0298364	−	0.0250357i
$842$	−2.99668e8	−	4.45846e8i	−0.502001	−	0.746876i
$843$	2.35526e8	+	1.35981e8i	0.393148	+	0.226984i
$844$	−4.56823e8	−	8.65972e8i	−0.759837	−	1.44038i
$845$	6.15422e8	−	2.23995e8i	1.02001	−	0.371252i
$846$	−2.49122e7	−	1.22009e7i	−0.0411435	−	0.0201503i
$847$	2.14516e8	−	1.23851e8i	0.353028	−	0.203821i
$848$	1.56035e8	−	2.28102e8i	0.255878	−	0.374059i
$849$	2.87599e7	−	1.63106e8i	0.0469964	−	0.266530i
$850$	−555682.	+	5.20515e6i	−0.000904835	+	0.00847571i
$851$	1.81015e8	−	2.15725e8i	0.293715	−	0.350036i
$852$	6.94686e8	−	9.53183e7i	1.12323	−	0.154120i
$853$	7.32754e8	+	2.66701e8i	1.18062	+	0.429712i	0.856422	−	0.516277i	$-0.172682\pi$
$853$	7.32754e8	+	2.66701e8i	1.18062	+	0.429712i	0.324201	+	0.945988i	$0.394905\pi$
$854$	1.32225e9	+	1.37371e9i	2.12295	+	2.20558i
$855$	4.90477e7	−	1.39375e8i	0.0784729	−	0.222991i
$856$	4.71887e8	−	4.20720e8i	0.752344	−	0.670767i
$857$	−5.23060e7	−	1.90378e7i	−0.0831015	−	0.0302465i	0.300135	−	0.953897i	$-0.402968\pi$
$857$	−5.23060e7	−	1.90378e7i	−0.0831015	−	0.0302465i	−0.383236	+	0.923650i	$0.625191\pi$
$858$	−2.04634e7	−	1.49187e7i	−0.0323979	−	0.0236194i
$859$	7.37240e8	−	8.78608e8i	1.16313	−	1.38617i	0.255286	−	0.966866i	$-0.417831\pi$
$859$	7.37240e8	−	8.78608e8i	1.16313	−	1.38617i	0.907847	−	0.419302i	$-0.137725\pi$
$860$	−8.99136e8	+	6.97763e8i	−1.41361	+	1.09702i
$861$	−1.43703e8	+	8.14978e8i	−0.225141	+	1.27684i
$862$	−2.18021e8	+	5.39805e7i	−0.340389	+	0.0842782i
$863$	9.69860e8	−	5.59949e8i	1.50896	−	0.871196i	0.509011	−	0.860760i	$-0.330011\pi$
$863$	9.69860e8	−	5.59949e8i	1.50896	−	0.871196i	0.999946	−	0.0104361i	$-0.00332196\pi$
$864$	−5.98700e8	−	3.52211e8i	−0.928256	−	0.546086i
$865$	−9.84198e8	+	3.58219e8i	−1.52067	+	0.553478i
$866$	−9.36202e8	−	2.70107e8i	−1.44150	−	0.415894i
$867$	−4.98197e8	−	2.87634e8i	−0.764441	−	0.441350i
$868$	7.23931e8	+	1.56350e8i	1.10698	+	0.239078i
$869$	5.93478e8	−	4.97987e8i	0.904369	−	0.758856i
$870$	4.39829e7	+	6.44103e8i	0.0667922	+	0.978132i
$871$	1.21702e7	−	2.14593e6i	0.0184180	−	0.00324759i
$872$	−3.16215e8	−	7.93838e8i	−0.476906	−	1.19724i
$873$	4.37819e7			0.0658039
$874$	2.90090e7	−	3.02315e8i	0.0434508	−	0.452820i
$875$			1.07999e9i			1.61212i
$876$	−5.50518e8	−	2.24519e8i	−0.818953	−	0.333995i
$877$	−3.02825e7	−	1.71741e8i	−0.0448945	−	0.254610i	0.954098	−	0.299496i	$-0.0968185\pi$
$877$	−3.02825e7	−	1.71741e8i	−0.0448945	−	0.254610i	−0.998992	+	0.0448864i	$0.985707\pi$
$878$	3.61499e7	+	5.29393e8i	0.0534101	+	0.782159i
$879$	−6.15764e7	−	7.33838e7i	−0.0906666	−	0.108052i
$880$	−7.94365e8	−	2.03580e8i	−1.16566	−	0.298735i
$881$	2.35097e8	−	4.07199e8i	0.343810	−	0.595496i	−0.641327	−	0.767268i	$-0.721616\pi$
$881$	2.35097e8	−	4.07199e8i	0.343810	−	0.595496i	0.985137	+	0.171771i	$0.0549490\pi$
$882$	3.27807e8	+	9.45770e7i	0.477763	+	0.137841i
$883$	3.17183e8	+	8.71453e8i	0.460710	+	1.26579i	0.924953	+	0.380083i	$0.124104\pi$
$883$	3.17183e8	+	8.71453e8i	0.460710	+	1.26579i	−0.464242	+	0.885708i	$0.653673\pi$
$884$	404860.	+	1.26002e6i	0.000586068	+	0.00182399i
$885$	−2.82173e8	−	4.88738e8i	−0.407085	−	0.705092i
$886$	1.08792e8	−	2.69363e7i	0.156422	−	0.0387291i
$887$	−1.00289e7	−	1.76837e6i	−0.0143709	−	0.00253397i	0.166458	−	0.986049i	$-0.446767\pi$
$887$	−1.00289e7	−	1.76837e6i	−0.0143709	−	0.00253397i	−0.180829	+	0.983515i	$0.557878\pi$
$888$	−8.96154e7	+	6.15736e8i	−0.127980	+	0.879338i
$889$	−1.45945e9	−	1.22463e9i	−2.07723	−	1.74301i
$890$	−9.44369e8	−	6.88484e8i	−1.33959	−	0.976616i
$891$	−1.96878e8	+	5.40917e8i	−0.278332	+	0.764711i
$892$	−8.60749e8	−	3.28740e7i	−1.21278	−	0.0463188i
$893$	7.64118e7	+	1.29141e8i	0.107302	+	0.181347i
$894$	1.82853e8	+	1.89970e8i	0.255912	+	0.265872i
$895$	−4.42765e8	+	1.21649e9i	−0.617596	+	1.69683i
$896$	9.59134e8	+	8.83675e8i	1.33338	+	1.22848i
$897$	9.11135e6	+	7.64533e6i	0.0126242	+	0.0105930i
$898$	3.55049e7	−	3.32579e8i	0.0490296	−	0.459268i
$899$	4.55575e8	+	8.03302e7i	0.627020	+	0.110560i
$900$	2.44401e7	+	1.53831e7i	0.0335256	+	0.0211017i
$901$	7.75398e6	+	1.34303e7i	0.0106011	+	0.0183616i
$902$	−5.89641e8	−	2.88780e8i	−0.803467	−	0.393503i
$903$	−6.64710e8	−	1.82628e9i	−0.902753	−	2.48029i
$904$	1.28499e8	−	3.88983e8i	0.173938	−	0.526533i
$905$	−6.71757e8	+	1.16352e9i	−0.906288	+	1.56974i
$906$	−5.61774e8	−	8.35806e8i	−0.755400	−	1.12388i
$907$	4.84563e8	+	5.77480e8i	0.649424	+	0.773953i	0.985827	−	0.167765i	$-0.0536549\pi$
$907$	4.84563e8	+	5.77480e8i	0.649424	+	0.773953i	−0.336403	+	0.941718i	$0.609210\pi$
$908$	8.09852e8	+	7.34000e8i	1.08180	+	0.980479i
$909$	2.40816e7	+	1.36573e8i	0.0320622	+	0.181834i
$910$	−2.46525e7	−	5.56148e7i	−0.0327143	−	0.0738017i
$911$		−	2.45233e7i		−	0.0324357i	−0.999868	−	0.0162178i	$-0.994837\pi$
$911$		−	2.45233e7i		−	0.0324357i	0.999868	−	0.0162178i	$-0.00516253\pi$
$912$	2.96669e8	+	6.01901e8i	0.391100	+	0.793488i
$913$	−3.00084e8			−0.394303
$914$	−5.69459e7	+	2.52426e7i	−0.0745803	+	0.0330594i
$915$	−1.22525e9	+	2.16045e8i	−1.59942	+	0.282020i
$916$	4.41791e8	−	4.87446e8i	0.574818	−	0.634221i
$917$	5.75538e8	−	4.82934e8i	0.746391	−	0.626296i
$918$	3.23497e7	−	2.17434e7i	0.0418160	−	0.0281060i
$919$	−2.80614e8	−	1.62013e8i	−0.361546	−	0.208738i	0.308213	−	0.951317i	$-0.400269\pi$
$919$	−2.80614e8	−	1.62013e8i	−0.361546	−	0.208738i	−0.669759	+	0.742579i	$0.733602\pi$
$920$	3.65708e8	+	1.20810e8i	0.469646	+	0.155146i
$921$	2.39258e8	−	8.70829e7i	0.306259	−	0.111469i
$922$	−1.56746e8	+	3.20049e8i	−0.199988	+	0.408342i
$923$	−3.57406e7	+	2.06348e7i	−0.0454523	+	0.0262419i
$924$	7.45929e8	−	1.18510e9i	0.945544	−	1.50224i
$925$	2.51529e7	−	1.42649e8i	0.0317807	−	0.180237i
$926$	−1.58264e8	−	1.68956e7i	−0.199319	−	0.0212785i
$927$	9.63612e6	−	1.14839e7i	0.0120966	−	0.0144162i
$928$	6.19717e8	+	5.28690e8i	0.775443	+	0.661542i
$929$	−5.24253e8	−	1.90813e8i	−0.653874	−	0.237991i	−0.00628454	−	0.999980i	$-0.502000\pi$
$929$	−5.24253e8	−	1.90813e8i	−0.653874	−	0.237991i	−0.647589	+	0.761990i	$0.724223\pi$
$930$	−3.48185e8	+	3.35141e8i	−0.432874	+	0.416657i
$931$	−1.20135e9	−	1.40102e9i	−1.48875	−	1.73619i
$932$	1.81972e7	−	4.76463e8i	0.0224780	−	0.588547i
$933$	8.44910e7	+	3.07522e7i	0.104032	+	0.0378644i
$934$	−3.33663e8	+	4.57674e8i	−0.409513	+	0.561714i
$935$	2.95784e7	−	3.52501e7i	0.0361859	−	0.0431247i
$936$	7.22506e6	+	1.05155e6i	0.00881077	+	0.00128234i
$937$	−1.54035e8	+	8.73574e8i	−0.187240	+	1.06189i	0.735802	+	0.677196i	$0.236805\pi$
$937$	−1.54035e8	+	8.73574e8i	−0.187240	+	1.06189i	−0.923043	+	0.384697i	$0.874306\pi$
$938$	1.64230e8	+	6.63306e8i	0.198996	+	0.803721i
$939$	−3.91977e8	+	2.26308e8i	−0.473439	+	0.273340i
$940$	−1.81170e8	+	5.82120e7i	−0.218124	+	0.0700857i
$941$	5.68692e8	−	2.06987e8i	0.682509	−	0.248413i	0.0225845	−	0.999745i	$-0.492811\pi$
$941$	5.68692e8	−	2.06987e8i	0.682509	−	0.248413i	0.659924	+	0.751332i	$0.270588\pi$
$942$	4.04503e8	−	1.40202e9i	0.483914	−	1.67726i
$943$	2.67052e8	+	1.54183e8i	0.318465	+	0.183866i
$944$	−6.89775e8	−	1.76775e8i	−0.819958	−	0.210139i
$945$	−1.37248e9	+	1.15164e9i	−1.62633	+	1.36465i
$946$	1.53833e9	−	1.05046e8i	1.81709	−	0.124081i
$947$	−6.30242e7	+	1.11129e7i	−0.0742091	+	0.0130851i	−0.210629	−	0.977566i	$-0.567551\pi$
$947$	−6.30242e7	+	1.11129e7i	−0.0742091	+	0.0130851i	0.136420	+	0.990651i	$0.456440\pi$
$948$	3.03608e8	−	7.44444e8i	0.356359	−	0.873790i
$949$	3.49924e7			0.0409425
$950$	−6.48280e7	−	1.42128e8i	−0.0756122	−	0.165771i
$951$			3.47554e8i			0.404092i
$952$	−6.79864e7	+	2.70815e7i	−0.0787972	+	0.0313878i
$953$	−2.28949e8	−	1.29843e9i	−0.264521	−	1.50017i	−0.770396	−	0.637565i	$-0.779942\pi$
$953$	−2.28949e8	−	1.29843e9i	−0.264521	−	1.50017i	0.505875	−	0.862607i	$-0.331170\pi$
$954$	8.53540e7	−	5.82843e6i	0.0983057	−	0.00671285i
$955$	−2.72399e7	−	3.24633e7i	−0.0312749	−	0.0372720i
$956$	2.16972e7	−	1.00462e8i	0.0248330	−	0.114982i
$957$	4.37328e8	−	7.57475e8i	0.498967	−	0.864236i
$958$	−1.00319e8	+	3.47708e8i	−0.114100	+	0.395474i
$959$	8.51159e8	+	2.33854e9i	0.965061	+	2.65148i
$960$	−8.27690e8	+	1.97770e8i	−0.935522	+	0.223536i
$961$	−2.70609e8	−	4.68708e8i	−0.304910	−	0.528119i
$962$	−8.80153e6	−	3.55483e7i	−0.00988628	−	0.0399295i
$963$	1.92735e8	+	3.39844e7i	0.215815	+	0.0380541i
$964$	−1.81670e8	−	2.34100e8i	−0.202793	−	0.261319i
$965$	1.07779e9	+	9.04375e8i	1.19937	+	1.00639i
$966$	−3.87446e8	+	5.31445e8i	−0.429813	+	0.589559i
$967$	−2.42199e8	+	6.65438e8i	−0.267851	+	0.735915i	0.730730	+	0.682667i	$0.239180\pi$
$967$	−2.42199e8	+	6.65438e8i	−0.267851	+	0.735915i	−0.998581	+	0.0532488i	$0.983042\pi$
$968$	1.35717e8	+	1.52223e8i	0.149627	+	0.167824i
$969$	−3.76529e7	+	402531.i	−0.0413834	+	0.000442413i
$970$	2.16389e8	−	2.08283e8i	0.237094	−	0.228212i
$971$	−2.42308e8	+	6.65736e8i	−0.264673	+	0.727184i	0.734164	+	0.678972i	$0.237574\pi$
$971$	−2.42308e8	+	6.65736e8i	−0.264673	+	0.727184i	−0.998837	+	0.0482116i	$0.984648\pi$
$972$	−5.32407e7	−	3.88022e8i	−0.0579756	−	0.422530i
$973$	−2.15168e9	−	1.80547e9i	−2.33581	−	1.95998i
$974$	5.24751e8	+	5.60203e7i	0.567905	+	0.0606274i
$975$	6.02493e6	+	1.06236e6i	0.00650037	+	0.00114619i
$976$	−8.86315e8	+	1.29567e9i	−0.953319	+	1.39362i
$977$	6.95779e7	+	1.20512e8i	0.0746083	+	0.129225i	0.900916	−	0.433994i	$-0.142896\pi$
$977$	6.95779e7	+	1.20512e8i	0.0746083	+	0.129225i	−0.826308	+	0.563219i	$0.809563\pi$
$978$	−3.37100e6	+	6.88302e6i	−0.00360365	+	0.00735805i
$979$	5.41532e8	+	1.48785e9i	0.577133	+	1.58566i
$980$	2.07010e9	−	1.09203e9i	2.19944	−	1.16026i
$981$	1.32262e8	−	2.29084e8i	0.140097	−	0.242654i
$982$	−3.76727e8	+	2.53211e8i	−0.397825	+	0.267392i
$983$	−6.79030e8	−	8.09236e8i	−0.714872	−	0.851951i	0.279250	−	0.960218i	$-0.409914\pi$
$983$	−6.79030e8	−	8.09236e8i	−0.714872	−	0.851951i	−0.994122	+	0.108267i	$0.965470\pi$
$984$	−6.81035e8	+	2.04412e7i	−0.714800	+	0.0214546i
$985$	−1.93048e8	−	1.09483e9i	−0.202002	−	1.14561i
$986$	−4.17888e7	+	1.85238e7i	−0.0435942	+	0.0193241i
$987$		−	3.24948e8i		−	0.337958i
$988$	−2.95458e7	−	2.62087e7i	−0.0306355	−	0.0271753i
$989$	−7.24190e8			−0.748623
$990$	−1.02873e8	−	2.32076e8i	−0.106022	−	0.239180i
$991$	2.13759e8	−	3.76914e7i	0.219635	−	0.0387277i	−0.0627474	−	0.998029i	$-0.519986\pi$
$991$	2.13759e8	−	3.76914e7i	0.219635	−	0.0387277i	0.282383	+	0.959302i	$0.408875\pi$
$992$	−4.98048e6	+	6.09752e8i	−0.00510195	+	0.624623i
$993$	−1.42675e8	+	1.19718e8i	−0.145714	+	0.122268i
$994$	−1.27300e9	−	1.89396e9i	−1.29619	−	1.92846i
$995$	1.80836e8	+	1.04406e8i	0.183576	+	0.105988i
$996$	−2.75436e8	+	1.45299e8i	−0.278768	+	0.147057i
$997$	1.16184e8	−	4.22875e7i	0.117236	−	0.0426704i	−0.282736	−	0.959198i	$-0.591242\pi$
$997$	1.16184e8	−	4.22875e7i	0.117236	−	0.0426704i	0.399972	+	0.916527i	$0.369020\pi$
$998$	6.22819e8	+	3.05030e8i	0.626571	+	0.306867i
$999$	−9.34059e8	+	5.39279e8i	−0.936866	+	0.540900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.l.a.23.7	✓	348
4.3	odd	2	inner	76.7.l.a.23.21	yes	348
19.5	even	9	inner	76.7.l.a.43.21	yes	348
76.43	odd	18	inner	76.7.l.a.43.7	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.l.a.23.7	✓	348	1.1	even	1	trivial
76.7.l.a.23.21	yes	348	4.3	odd	2	inner
76.7.l.a.43.7	yes	348	76.43	odd	18	inner
76.7.l.a.43.21	yes	348	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.31367 + 3.24195i) q^{2} +(23.5223 - 4.14762i) q^{3} +(42.9795 - 47.4211i) q^{4} +(104.114 - 87.3621i) q^{5} +(-158.588 + 106.593i) q^{6} +(538.554 + 310.935i) q^{7} +(-160.601 + 486.160i) q^{8} +(-148.939 + 54.2093i) q^{9} +O(q^{10})\)	\(q+(-7.31367 + 3.24195i) q^{2} +(23.5223 - 4.14762i) q^{3} +(42.9795 - 47.4211i) q^{4} +(104.114 - 87.3621i) q^{5} +(-158.588 + 106.593i) q^{6} +(538.554 + 310.935i) q^{7} +(-160.601 + 486.160i) q^{8} +(-148.939 + 54.2093i) q^{9} +(-478.233 + 976.470i) q^{10} +(1275.70 - 736.525i) q^{11} +(814.294 - 1293.72i) q^{12} +(-15.6232 + 88.6038i) q^{13} +(-4946.84 - 528.106i) q^{14} +(2086.66 - 2486.79i) q^{15} +(-401.522 - 4076.27i) q^{16} +(215.983 + 78.6113i) q^{17} +(913.546 - 879.321i) q^{18} +(-6741.68 + 1263.19i) q^{19} +(331.967 - 8691.99i) q^{20} +(13957.7 + 5080.18i) q^{21} +(-6942.27 + 9522.46i) q^{22} +(3557.68 - 4239.88i) q^{23} +(-1761.31 + 12101.7i) q^{24} +(494.357 - 2803.64i) q^{25} +(-172.986 - 698.668i) q^{26} +(-18358.0 + 10599.0i) q^{27} +(37891.7 - 12175.0i) q^{28} +(23360.2 - 8502.42i) q^{29} +(-7199.11 + 24952.4i) q^{30} +(16115.7 + 9304.39i) q^{31} +(16151.7 + 28510.8i) q^{32} +(26952.6 - 22615.9i) q^{33} +(-1834.48 + 125.268i) q^{34} +(83235.0 - 14676.6i) q^{35} +(-3830.66 + 9392.74i) q^{36} +50880.1 q^{37} +(45211.2 - 31094.8i) q^{38} +2148.97i q^{39} +(25751.1 + 64646.5i) q^{40} +(9674.68 + 54867.9i) q^{41} +(-118552. + 8095.35i) q^{42} +(-84104.7 - 100232. i) q^{43} +(19902.1 - 92150.6i) q^{44} +(-10770.8 + 18655.6i) q^{45} +(-12274.2 + 42542.9i) q^{46} +(-7482.35 - 20557.6i) q^{47} +(-26351.6 - 94218.0i) q^{48} +(134536. + 233023. i) q^{49} +(5473.69 + 22107.6i) q^{50} +(5406.46 + 953.306i) q^{51} +(3530.21 + 4549.02i) q^{52} +(51686.3 + 43370.0i) q^{53} +(99903.2 - 137034. i) q^{54} +(68473.9 - 188131. i) q^{55} +(-237656. + 211887. i) q^{56} +(-153341. + 57675.2i) q^{57} +(-143284. + 137917. i) q^{58} +(59458.3 - 163360. i) q^{59} +(-28242.4 - 205833. i) q^{60} +(-293591. - 246352. i) q^{61} +(-148029. - 15803.0i) q^{62} +(-97067.2 - 17115.6i) q^{63} +(-210559. - 156156. i) q^{64} +(6114.01 + 10589.8i) q^{65} +(-123803. + 252784. i) q^{66} +(-46978.1 - 129071. i) q^{67} +(13010.7 - 6863.46i) q^{68} +(66099.5 - 114488. i) q^{69} +(-561173. + 377183. i) q^{70} +(294848. + 351386. i) q^{71} +(-2434.63 - 81114.2i) q^{72} +(-67537.2 - 383022. i) q^{73} +(-372120. + 164951. i) q^{74} -67998.5i q^{75} +(-229852. + 373989. i) q^{76} +916045. q^{77} +(-6966.84 - 15716.8i) q^{78} +(517946. - 91327.9i) q^{79} +(-397916. - 389320. i) q^{80} +(-299351. + 251185. i) q^{81} +(-248636. - 369920. i) q^{82} +(-176423. - 101858. i) q^{83} +(840803. - 443545. i) q^{84} +(29354.5 - 10684.2i) q^{85} +(940061. + 460401. i) q^{86} +(514222. - 296886. i) q^{87} +(153190. + 738481. i) q^{88} +(-186649. + 1.05854e6i) q^{89} +(18293.6 - 171359. i) q^{90} +(-35963.9 + 42860.2i) q^{91} +(-48152.3 - 350937. i) q^{92} +(417669. + 152019. i) q^{93} +(121370. + 126094. i) q^{94} +(-591549. + 720484. i) q^{95} +(498177. + 603649. i) q^{96} +(-259572. - 94476.5i) q^{97} +(-1.73940e6 - 1.26810e6i) q^{98} +(-150075. + 178852. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9}+O(q^{10}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9	\( 348 q - 6 q^{2} + 192 q^{4} - 12 q^{5} - 492 q^{6} - 3 q^{8} + 1368 q^{9} + 2811 q^{10} - 3 q^{12} - 7572 q^{13} + 8217 q^{14} - 1392 q^{16} - 12 q^{17} - 12 q^{18} + 33618 q^{20} - 33546 q^{21} - 198 q^{22} - 7128 q^{24} - 12 q^{25} + 84453 q^{26} + 13464 q^{28} - 12 q^{29} + 75510 q^{30} + 9339 q^{32} - 366 q^{33} - 289248 q^{34} - 419349 q^{36} - 24 q^{37} + 158040 q^{38} + 264570 q^{40} + 27360 q^{41} + 206001 q^{42} - 525639 q^{44} - 6 q^{45} - 269328 q^{46} - 703179 q^{48} + 2319360 q^{49} + 264534 q^{50} + 130809 q^{52} - 182292 q^{53} + 607083 q^{54} - 705906 q^{56} - 12 q^{57} - 710004 q^{58} + 1060416 q^{60} - 325092 q^{61} - 1967868 q^{62} - 1611921 q^{64} + 398994 q^{65} - 2295684 q^{66} + 1125642 q^{68} - 1625190 q^{69} + 3496059 q^{70} + 4948626 q^{72} - 2224812 q^{73} + 2661159 q^{74} - 968262 q^{76} + 974412 q^{77} - 340743 q^{78} - 3996663 q^{80} + 4277754 q^{81} - 3214221 q^{82} - 872109 q^{84} - 3207900 q^{85} + 3189360 q^{86} + 827973 q^{88} - 2016084 q^{89} - 710406 q^{90} - 2545116 q^{92} + 4486254 q^{93} - 14322630 q^{94} + 2623530 q^{96} - 1223112 q^{97} + 10989009 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 192 * q^4 - 12 * q^5 - 492 * q^6 - 3 * q^8 + 1368 * q^9 + 2811 * q^10 - 3 * q^12 - 7572 * q^13 + 8217 * q^14 - 1392 * q^16 - 12 * q^17 - 12 * q^18 + 33618 * q^20 - 33546 * q^21 - 198 * q^22 - 7128 * q^24 - 12 * q^25 + 84453 * q^26 + 13464 * q^28 - 12 * q^29 + 75510 * q^30 + 9339 * q^32 - 366 * q^33 - 289248 * q^34 - 419349 * q^36 - 24 * q^37 + 158040 * q^38 + 264570 * q^40 + 27360 * q^41 + 206001 * q^42 - 525639 * q^44 - 6 * q^45 - 269328 * q^46 - 703179 * q^48 + 2319360 * q^49 + 264534 * q^50 + 130809 * q^52 - 182292 * q^53 + 607083 * q^54 - 705906 * q^56 - 12 * q^57 - 710004 * q^58 + 1060416 * q^60 - 325092 * q^61 - 1967868 * q^62 - 1611921 * q^64 + 398994 * q^65 - 2295684 * q^66 + 1125642 * q^68 - 1625190 * q^69 + 3496059 * q^70 + 4948626 * q^72 - 2224812 * q^73 + 2661159 * q^74 - 968262 * q^76 + 974412 * q^77 - 340743 * q^78 - 3996663 * q^80 + 4277754 * q^81 - 3214221 * q^82 - 872109 * q^84 - 3207900 * q^85 + 3189360 * q^86 + 827973 * q^88 - 2016084 * q^89 - 710406 * q^90 - 2545116 * q^92 + 4486254 * q^93 - 14322630 * q^94 + 2623530 * q^96 - 1223112 * q^97 + 10989009 * q^98

Introduction

L-functions

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