LMFDB - Embedded newform 37.8.e.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.e (of order $6$, degree $2$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	37.11
Dual form			37.8.e.a.27.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.60443 + 4.96777i) q^{2} +(-5.90461 + 10.2271i) q^{3} +(-14.6425 + 25.3615i) q^{4} +(369.746 + 213.473i) q^{5} -117.331i q^{6} +(428.306 - 741.848i) q^{7} -1562.71i q^{8} +(1023.77 + 1773.22i) q^{9} +O(q^{10})$	\(q+(-8.60443 + 4.96777i) q^{2} +(-5.90461 + 10.2271i) q^{3} +(-14.6425 + 25.3615i) q^{4} +(369.746 + 213.473i) q^{5} -117.331i q^{6} +(428.306 - 741.848i) q^{7} -1562.71i q^{8} +(1023.77 + 1773.22i) q^{9} -4241.93 q^{10} +2172.41 q^{11} +(-172.916 - 299.500i) q^{12} +(6946.74 + 4010.70i) q^{13} +8510.90i q^{14} +(-4366.40 + 2520.95i) q^{15} +(5888.96 + 10200.0i) q^{16} +(-28137.9 + 16245.4i) q^{17} +(-17617.9 - 10171.7i) q^{18} +(3154.73 + 1821.39i) q^{19} +(-10828.0 + 6251.55i) q^{20} +(5057.96 + 8760.64i) q^{21} +(-18692.3 + 10792.0i) q^{22} +50176.5i q^{23} +(15982.0 + 9227.20i) q^{24} +(52078.7 + 90202.9i) q^{25} -79697.0 q^{26} -50006.6 q^{27} +(12542.9 + 21725.0i) q^{28} +29115.5i q^{29} +(25047.0 - 43382.6i) q^{30} -243588. i q^{31} +(71886.3 + 41503.6i) q^{32} +(-12827.2 + 22217.4i) q^{33} +(161407. - 279565. i) q^{34} +(316728. - 182863. i) q^{35} -59962.3 q^{36} +(-254919. + 173056. i) q^{37} -36192.9 q^{38} +(-82035.6 + 47363.3i) q^{39} +(333596. - 577806. i) q^{40} +(78587.8 - 136118. i) q^{41} +(-87041.7 - 50253.5i) q^{42} +85507.5i q^{43} +(-31809.5 + 55095.6i) q^{44} +874189. i q^{45} +(-249265. - 431740. i) q^{46} +638487. q^{47} -139088. q^{48} +(44879.6 + 77733.7i) q^{49} +(-896215. - 517430. i) q^{50} -383691. i q^{51} +(-203435. + 117453. i) q^{52} +(47451.4 + 82188.2i) q^{53} +(430279. - 248421. i) q^{54} +(803238. + 463750. i) q^{55} +(-1.15929e6 - 669319. i) q^{56} +(-37254.9 + 21509.1i) q^{57} +(-144639. - 250523. i) q^{58} +(-1.53057e6 + 883675. i) q^{59} -147652. i q^{60} +(1.02418e6 + 591311. i) q^{61} +(1.21009e6 + 2.09593e6i) q^{62} +1.75395e6 q^{63} -2.33229e6 q^{64} +(1.71235e6 + 2.96588e6i) q^{65} -254891. i q^{66} +(-880496. + 1.52506e6i) q^{67} -951494. i q^{68} +(-513159. - 296272. i) q^{69} +(-1.81685e6 + 3.14687e6i) q^{70} +(2.58633e6 - 4.47966e6i) q^{71} +(2.77104e6 - 1.59986e6i) q^{72} -5.67038e6 q^{73} +(1.33373e6 - 2.75543e6i) q^{74} -1.23002e6 q^{75} +(-92386.4 + 53339.3i) q^{76} +(930455. - 1.61160e6i) q^{77} +(470580. - 815068. i) q^{78} +(1.85827e6 + 1.07287e6i) q^{79} +5.02852e6i q^{80} +(-1.94372e6 + 3.36662e6i) q^{81} +1.56162e6i q^{82} +(4.53295e6 + 7.85131e6i) q^{83} -296244. q^{84} -1.38718e7 q^{85} +(-424782. - 735744. i) q^{86} +(-297767. - 171916. i) q^{87} -3.39485e6i q^{88} +(9.77201e6 - 5.64187e6i) q^{89} +(-4.34277e6 - 7.52190e6i) q^{90} +(5.95066e6 - 3.43562e6i) q^{91} +(-1.27255e6 - 734709. i) q^{92} +(2.49119e6 + 1.43829e6i) q^{93} +(-5.49382e6 + 3.17186e6i) q^{94} +(777633. + 1.34690e6i) q^{95} +(-848921. + 490125. i) q^{96} -1.50934e7i q^{97} +(-772327. - 445903. i) q^{98} +(2.22405e6 + 3.85217e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) $ 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−8.60443	+	4.96777i	−0.760532	+	0.439093i	−0.829487	−	0.558527i	$-0.811367\pi$
$2$	−8.60443	+	4.96777i	−0.760532	+	0.439093i	0.0689550	+	0.997620i	$0.478034\pi$
$3$	−5.90461	+	10.2271i	−0.126260	+	0.218689i	−0.922225	−	0.386654i	$-0.873631\pi$
$3$	−5.90461	+	10.2271i	−0.126260	+	0.218689i	0.795965	+	0.605343i	$0.206964\pi$
$4$	−14.6425	+	25.3615i	−0.114394	+	0.198137i
$5$	369.746	+	213.473i	1.32284	+	0.763743i	0.984181	−	0.177165i	$-0.0566927\pi$
$5$	369.746	+	213.473i	1.32284	+	0.763743i	0.338661	+	0.940909i	$0.390026\pi$
$6$		−	117.331i		−	0.221760i
$7$	428.306	−	741.848i	0.471966	−	0.817470i	−0.527519	−	0.849543i	$-0.676878\pi$
$7$	428.306	−	741.848i	0.471966	−	0.817470i	0.999486	+	0.0320736i	$0.0102111\pi$
$8$		−	1562.71i		−	1.07911i
$9$	1023.77	+	1773.22i	0.468117	+	0.810802i
$10$	−4241.93			−1.34142
$11$	2172.41			0.492116			0.246058	−	0.969255i	$-0.420865\pi$
$11$	2172.41			0.492116			0.246058	+	0.969255i	$0.420865\pi$
$12$	−172.916	−	299.500i	−0.0288870	−	0.0500337i
$13$	6946.74	+	4010.70i	0.876959	+	0.506313i	0.869655	−	0.493661i	$-0.164342\pi$
$13$	6946.74	+	4010.70i	0.876959	+	0.506313i	0.00730459	+	0.999973i	$0.497675\pi$
$14$			8510.90i			0.828948i
$15$	−4366.40	+	2520.95i	−0.334045	+	0.192861i
$16$	5888.96	+	10200.0i	0.359433	+	0.622557i
$17$	−28137.9	+	16245.4i	−1.38906	+	0.801973i	−0.993209	−	0.116343i	$-0.962883\pi$
$17$	−28137.9	+	16245.4i	−1.38906	+	0.801973i	−0.395849	+	0.918316i	$0.629550\pi$
$18$	−17617.9	−	10171.7i	−0.712035	−	0.411094i
$19$	3154.73	+	1821.39i	0.105518	+	0.0609206i	0.551830	−	0.833957i	$-0.313930\pi$
$19$	3154.73	+	1821.39i	0.105518	+	0.0609206i	−0.446312	+	0.894877i	$0.647263\pi$
$20$	−10828.0	+	6251.55i	−0.302652	+	0.174736i
$21$	5057.96	+	8760.64i	0.119181	+	0.206428i
$22$	−18692.3	+	10792.0i	−0.374269	+	0.216085i
$23$			50176.5i			0.859909i	0.902851	+	0.429955i	$0.141470\pi$
$23$			50176.5i			0.859909i	−0.902851	+	0.429955i	$0.858530\pi$
$24$	15982.0	+	9227.20i	0.235989	+	0.136248i
$25$	52078.7	+	90202.9i	0.666607	+	1.15460i
$26$	−79697.0			−0.889274
$27$	−50006.6			−0.488939
$28$	12542.9	+	21725.0i	0.107981	+	0.187028i
$29$			29115.5i			0.221683i	0.993838	+	0.110841i	$0.0353546\pi$
$29$			29115.5i			0.221683i	−0.993838	+	0.110841i	$0.964645\pi$
$30$	25047.0	−	43382.6i	0.169368	−	0.293353i
$31$		−	243588.i		−	1.46855i	−0.678851	−	0.734276i	$-0.737522\pi$
$31$		−	243588.i		−	1.46855i	0.678851	−	0.734276i	$-0.262478\pi$
$32$	71886.3	+	41503.6i	0.387812	+	0.223903i
$33$	−12827.2	+	22217.4i	−0.0621346	+	0.107620i
$34$	161407.	−	279565.i	0.704282	−	1.21985i
$35$	316728.	−	182863.i	1.24867	−	0.720922i
$36$	−59962.3			−0.214200
$37$	−254919.	+	173056.i	−0.827362	+	0.561669i
$37$	−254919.	+	173056.i	−0.827362	+	0.561669i
$38$	−36192.9			−0.106999
$39$	−82035.6	+	47363.3i	−0.221450	+	0.127854i
$40$	333596.	−	577806.i	0.824159	−	1.42749i
$41$	78587.8	−	136118.i	0.178079	−	0.308441i	−0.763144	−	0.646229i	$-0.776345\pi$
$41$	78587.8	−	136118.i	0.178079	−	0.308441i	0.941222	+	0.337788i	$0.109679\pi$
$42$	−87041.7	−	50253.5i	−0.181282	−	0.104663i
$43$			85507.5i			0.164008i	0.996632	+	0.0820039i	$0.0261320\pi$
$43$			85507.5i			0.164008i	−0.996632	+	0.0820039i	$0.973868\pi$
$44$	−31809.5	+	55095.6i	−0.0562953	+	0.0975063i
$45$			874189.i			1.43008i
$46$	−249265.	−	431740.i	−0.377580	−	0.653988i
$47$	638487.			0.897036			0.448518	−	0.893774i	$-0.351952\pi$
$47$	638487.			0.897036			0.448518	+	0.893774i	$0.351952\pi$
$48$	−139088.			−0.181529
$49$	44879.6	+	77733.7i	0.0544957	+	0.0943894i
$50$	−896215.	−	517430.i	−1.01395	−	0.585405i
$51$		−	383691.i		−	0.405029i
$52$	−203435.	+	117453.i	−0.200639	+	0.115839i
$53$	47451.4	+	82188.2i	0.0437808	+	0.0758305i	0.887085	−	0.461605i	$-0.152726\pi$
$53$	47451.4	+	82188.2i	0.0437808	+	0.0758305i	−0.843305	+	0.537436i	$0.819393\pi$
$54$	430279.	−	248421.i	0.371853	−	0.214690i
$55$	803238.	+	463750.i	0.650991	+	0.375850i
$56$	−1.15929e6	−	669319.i	−0.882136	−	0.509301i
$57$	−37254.9	+	21509.1i	−0.0266454	+	0.0153837i
$58$	−144639.	−	250523.i	−0.0973394	−	0.168597i
$59$	−1.53057e6	+	883675.i	−0.970222	+	0.560158i	−0.899304	−	0.437324i	$-0.855926\pi$
$59$	−1.53057e6	+	883675.i	−0.970222	+	0.560158i	−0.0709181	+	0.997482i	$0.522593\pi$
$60$		−	147652.i		−	0.0882489i
$61$	1.02418e6	+	591311.i	0.577726	+	0.333550i	0.760229	−	0.649655i	$-0.225087\pi$
$61$	1.02418e6	+	591311.i	0.577726	+	0.333550i	−0.182503	+	0.983205i	$0.558420\pi$
$62$	1.21009e6	+	2.09593e6i	0.644831	+	1.11688i
$63$	1.75395e6			0.883741
$64$	−2.33229e6			−1.11212
$65$	1.71235e6	+	2.96588e6i	0.773386	+	1.33954i
$66$		−	254891.i		−	0.109132i
$67$	−880496.	+	1.52506e6i	−0.357656	+	0.619478i	−0.987569	−	0.157188i	$-0.949757\pi$
$67$	−880496.	+	1.52506e6i	−0.357656	+	0.619478i	0.629913	+	0.776666i	$0.283091\pi$
$68$		−	951494.i		−	0.366965i
$69$	−513159.	−	296272.i	−0.188053	−	0.108572i
$70$	−1.81685e6	+	3.14687e6i	−0.633104	+	1.09657i
$71$	2.58633e6	−	4.47966e6i	0.857590	−	1.48539i	−0.0166304	−	0.999862i	$-0.505294\pi$
$71$	2.58633e6	−	4.47966e6i	0.857590	−	1.48539i	0.874221	−	0.485529i	$-0.161373\pi$
$72$	2.77104e6	−	1.59986e6i	0.874941	−	0.505147i
$73$	−5.67038e6			−1.70601			−0.853005	−	0.521902i	$-0.825223\pi$
$73$	−5.67038e6			−1.70601			−0.853005	+	0.521902i	$0.825223\pi$
$74$	1.33373e6	−	2.75543e6i	0.382610	−	0.790456i
$75$	−1.23002e6			−0.336664
$76$	−92386.4	+	53339.3i	−0.0241413	+	0.0139380i
$77$	930455.	−	1.61160e6i	0.232262	−	0.402289i
$78$	470580.	−	815068.i	0.112280	−	0.194474i
$79$	1.85827e6	+	1.07287e6i	0.424047	+	0.244824i	0.696807	−	0.717258i	$-0.254603\pi$
$79$	1.85827e6	+	1.07287e6i	0.424047	+	0.244824i	−0.272760	+	0.962082i	$0.587937\pi$
$80$			5.02852e6i			1.09806i
$81$	−1.94372e6	+	3.36662e6i	−0.406383	+	0.703876i
$82$			1.56162e6i			0.312772i
$83$	4.53295e6	+	7.85131e6i	0.870178	+	1.50719i	0.861812	+	0.507227i	$0.169329\pi$
$83$	4.53295e6	+	7.85131e6i	0.870178	+	1.50719i	0.00836523	+	0.999965i	$0.497337\pi$
$84$	−296244.			−0.0545347
$85$	−1.38718e7			−2.45001
$86$	−424782.	−	735744.i	−0.0720147	−	0.124733i
$87$	−297767.	−	171916.i	−0.0484796	−	0.0279897i
$88$		−	3.39485e6i		−	0.531045i
$89$	9.77201e6	−	5.64187e6i	1.46933	−	0.848317i	0.469920	−	0.882709i	$-0.344283\pi$
$89$	9.77201e6	−	5.64187e6i	1.46933	−	0.848317i	0.999408	+	0.0343919i	$0.0109494\pi$
$90$	−4.34277e6	−	7.52190e6i	−0.627940	−	1.08762i
$91$	5.95066e6	−	3.43562e6i	0.827790	−	0.477925i
$92$	−1.27255e6	−	734709.i	−0.170380	−	0.0983689i
$93$	2.49119e6	+	1.43829e6i	0.321157	+	0.185420i
$94$	−5.49382e6	+	3.17186e6i	−0.682224	+	0.393882i
$95$	777633.	+	1.34690e6i	0.0930555	+	0.161177i
$96$	−848921.	+	490125.i	−0.0979305	+	0.0565402i
$97$		−	1.50934e7i		−	1.67914i	−0.543252	−	0.839570i	$-0.682807\pi$
$97$		−	1.50934e7i		−	1.67914i	0.543252	−	0.839570i	$-0.317193\pi$
$98$	−772327.	−	445903.i	−0.0828915	−	0.0478574i
$99$	2.22405e6	+	3.85217e6i	0.230368	+	0.399008i
$100$	−3.05025e6			−0.305025
$101$	1.28897e7			1.24485			0.622424	−	0.782680i	$-0.286148\pi$
$101$	1.28897e7			1.24485			0.622424	+	0.782680i	$0.286148\pi$
$102$	1.90609e6	+	3.30145e6i	0.177846	+	0.308037i
$103$		−	1.23149e7i		−	1.11045i	−0.831700	−	0.555225i	$-0.812632\pi$
$103$		−	1.23149e7i		−	1.11045i	0.831700	−	0.555225i	$-0.187368\pi$
$104$	6.26757e6	−	1.08558e7i	0.546365	−	0.946332i
$105$			4.31894e6i			0.364095i
$106$	−816585.	−	471455.i	−0.0665933	−	0.0384477i
$107$	3.26822e6	−	5.66073e6i	0.257910	−	0.446714i	−0.707772	−	0.706441i	$-0.750299\pi$
$107$	3.26822e6	−	5.66073e6i	0.257910	−	0.446714i	0.965682	+	0.259728i	$0.0836328\pi$
$108$	732222.	−	1.26825e6i	0.0559319	−	0.0968769i
$109$	7.09419e6	−	4.09583e6i	0.524699	−	0.302935i	−0.214156	−	0.976799i	$-0.568700\pi$
$109$	7.09419e6	−	4.09583e6i	0.524699	−	0.302935i	0.738855	+	0.673865i	$0.235367\pi$
$110$	−9.21521e6			−0.660132
$111$	−264661.	−	3.62890e6i	−0.0183679	−	0.251852i
$112$	1.00891e7			0.678562
$113$	−208905.	+	120612.i	−0.0136199	+	0.00786347i	−0.506795	−	0.862067i	$-0.669170\pi$
$113$	−208905.	+	120612.i	−0.0136199	+	0.00786347i	0.493175	+	0.869930i	$0.335836\pi$
$114$	213705.	−	370148.i	0.0135098	−	0.0233996i
$115$	−1.07113e7	+	1.85525e7i	−0.656750	+	1.13752i
$116$	−738415.	−	426324.i	−0.0439236	−	0.0253593i
$117$			1.64242e7i			0.948054i
$118$	8.77979e6	−	1.52070e7i	0.491923	−	0.852036i
$119$			2.78320e7i			1.51402i
$120$	3.93951e6	+	6.82343e6i	0.208117	+	0.360469i
$121$	−1.47678e7			−0.757822
$122$	−1.17500e7			−0.585839
$123$	928060.	+	1.60745e6i	0.0449685	+	0.0778877i
$124$	6.17776e6	+	3.56673e6i	0.290975	+	0.167994i
$125$			1.11144e7i			0.508981i
$126$	−1.50917e7	+	8.71322e6i	−0.672113	+	0.388045i
$127$	−2.59285e6	−	4.49095e6i	−0.112322	−	0.194547i	0.804384	−	0.594110i	$-0.202495\pi$
$127$	−2.59285e6	−	4.49095e6i	−0.112322	−	0.194547i	−0.916706	+	0.399562i	$0.869162\pi$
$128$	1.08666e7	−	6.27384e6i	0.457994	−	0.264423i
$129$	−874492.	−	504888.i	−0.0358667	−	0.0207077i
$130$	−2.94676e7	−	1.70131e7i	−1.17637	−	0.679177i
$131$	−2.92941e7	+	1.69130e7i	−1.13849	+	0.657310i	−0.946057	−	0.323999i	$-0.894973\pi$
$131$	−2.92941e7	+	1.69130e7i	−1.13849	+	0.657310i	−0.192437	+	0.981309i	$0.561639\pi$
$132$	−375645.	−	650636.i	−0.0142157	−	0.0246223i
$133$	2.70238e6	−	1.56022e6i	0.0996015	−	0.0575050i
$134$		−	1.74964e7i		−	0.628177i
$135$	−1.84897e7	−	1.06750e7i	−0.646789	−	0.373424i
$136$	2.53869e7	+	4.39714e7i	0.865413	+	1.49894i
$137$	−1.12528e7			−0.373885			−0.186943	−	0.982371i	$-0.559858\pi$
$137$	−1.12528e7			−0.373885			−0.186943	+	0.982371i	$0.559858\pi$
$138$	5.88725e6			0.190693
$139$	−943987.	−	1.63503e6i	−0.0298136	−	0.0516386i	0.850734	−	0.525597i	$-0.176158\pi$
$139$	−943987.	−	1.63503e6i	−0.0298136	−	0.0516386i	−0.880547	+	0.473958i	$0.842825\pi$
$140$			1.07103e7i			0.329878i
$141$	−3.77002e6	+	6.52986e6i	−0.113260	+	0.196172i
$142$			5.13932e7i			1.50625i
$143$	1.50912e7	+	8.71289e6i	0.431565	+	0.249164i
$144$	−1.20579e7	+	2.08849e7i	−0.336513	+	0.582858i
$145$	−6.21537e6	+	1.07653e7i	−0.169309	+	0.293251i
$146$	4.87904e7	−	2.81691e7i	1.29748	−	0.749098i
$147$	−1.05999e6			−0.0275226
$148$	−656317.	−	8.99910e6i	−0.0166417	−	0.228183i
$149$	6.52343e7			1.61556			0.807782	−	0.589482i	$-0.200668\pi$
$149$	6.52343e7			1.61556			0.807782	+	0.589482i	$0.200668\pi$
$150$	1.05836e7	−	6.11044e6i	0.256044	−	0.147827i
$151$	−9.90549e6	+	1.71568e7i	−0.234130	+	0.405524i	−0.959019	−	0.283340i	$-0.908557\pi$
$151$	−9.90549e6	+	1.71568e7i	−0.234130	+	0.405524i	0.724890	+	0.688865i	$0.241891\pi$
$152$	2.84630e6	−	4.92994e6i	0.0657398	−	0.113865i
$153$	−5.76135e7	−	3.32632e7i	−1.30048	−	0.750834i
$154$			1.84892e7i			0.407938i
$155$	5.19993e7	−	9.00655e7i	1.12160	−	1.94266i
$156$		−	2.77406e6i		−	0.0585033i
$157$	−4.73194e7	−	8.19596e7i	−0.975867	−	1.69025i	−0.677045	−	0.735941i	$-0.736740\pi$
$157$	−4.73194e7	−	8.19596e7i	−0.975867	−	1.69025i	−0.298821	−	0.954309i	$-0.596593\pi$
$158$	−2.13192e7			−0.430002
$159$	−1.12073e6			−0.0221111
$160$	1.77198e7	+	3.06915e7i	0.342009	+	0.592378i
$161$	3.72233e7	+	2.14909e7i	0.702950	+	0.405848i
$162$		−	3.86238e7i		−	0.713760i
$163$	5.86621e6	−	3.38686e6i	0.106097	−	0.0612549i	−0.446013	−	0.895027i	$-0.647156\pi$
$163$	5.86621e6	−	3.38686e6i	0.106097	−	0.0612549i	0.552109	+	0.833772i	$0.313823\pi$
$164$	2.30144e6	+	3.98622e6i	0.0407424	+	0.0705679i
$165$	−9.48562e6	+	5.47652e6i	−0.164389	+	0.0949098i
$166$	−7.80070e7	−	4.50374e7i	−1.32360	−	0.764178i
$167$	−2.06678e7	−	1.19325e7i	−0.343389	−	0.198255i	0.318381	−	0.947963i	$-0.396861\pi$
$167$	−2.06678e7	−	1.19325e7i	−0.343389	−	0.198255i	−0.661769	+	0.749707i	$0.730194\pi$
$168$	1.36904e7	−	7.90413e6i	0.222757	−	0.128609i
$169$	797216.	+	1.38082e6i	0.0127049	+	0.0220056i
$170$	1.19359e8	−	6.89120e7i	1.86331	−	1.07578i
$171$			7.45873e6i			0.114072i
$172$	−2.16860e6	−	1.25204e6i	−0.0324960	−	0.0187616i
$173$	4.04179e6	+	7.00059e6i	0.0593489	+	0.102795i	0.894173	−	0.447721i	$-0.147764\pi$
$173$	4.04179e6	+	7.00059e6i	0.0593489	+	0.102795i	−0.834824	+	0.550516i	$0.814431\pi$
$174$	3.41615e6			0.0491604
$175$	8.92224e7			1.25846
$176$	1.27932e7	+	2.21585e7i	0.176883	+	0.306370i
$177$		−	2.08710e7i		−	0.282903i
$178$	−5.60551e7	+	9.70902e7i	−0.744980	+	1.29034i
$179$		−	1.02140e7i		−	0.133110i	−0.997783	−	0.0665548i	$-0.978799\pi$
$179$		−	1.02140e7i		−	0.133110i	0.997783	−	0.0665548i	$-0.0212007\pi$
$180$	−2.21708e7	−	1.28003e7i	−0.283353	−	0.163594i
$181$	3.99533e7	−	6.92012e7i	0.500816	−	0.867438i	−0.499184	−	0.866496i	$-0.666367\pi$
$181$	3.99533e7	−	6.92012e7i	0.500816	−	0.867438i	1.00000		0.000941928i	$-0.000299825\pi$
$182$	−3.41347e7	+	5.91230e7i	−0.419707	+	0.726954i
$183$	−1.20948e7	+	6.98292e6i	−0.145888	+	0.0842283i
$184$	7.84113e7			0.927933
$185$	−1.31198e8	+	9.56844e6i	−1.52344	+	0.111107i
$186$	−2.85804e7			−0.325666
$187$	−6.11270e7	+	3.52917e7i	−0.683577	+	0.394663i
$188$	−9.34905e6	+	1.61930e7i	−0.102616	+	0.177736i
$189$	−2.14181e7	+	3.70973e7i	−0.230763	+	0.399692i
$190$	−1.33822e7	−	7.72620e6i	−0.141543	−	0.0817200i
$191$		−	1.11670e8i		−	1.15964i	−0.814746	−	0.579818i	$-0.803124\pi$
$191$		−	1.11670e8i		−	1.15964i	0.814746	−	0.579818i	$-0.196876\pi$
$192$	1.37713e7	−	2.38526e7i	0.140417	−	0.243210i
$193$			1.11466e8i			1.11607i	0.829816	+	0.558037i	$0.188445\pi$
$193$			1.11466e8i			1.11607i	−0.829816	+	0.558037i	$0.811555\pi$
$194$	7.49807e7	+	1.29870e8i	0.737299	+	1.27704i
$195$	−4.04430e7			−0.390591
$196$	−2.62860e6			−0.0249360
$197$	−2.20003e7	−	3.81057e7i	−0.205020	−	0.355106i	0.745119	−	0.666932i	$-0.232393\pi$
$197$	−2.20003e7	−	3.81057e7i	−0.205020	−	0.355106i	−0.950139	+	0.311826i	$0.899059\pi$
$198$	−3.82734e7	−	2.20971e7i	−0.350404	−	0.202306i
$199$		−	1.41123e8i		−	1.26944i	−0.772741	−	0.634722i	$-0.781115\pi$
$199$		−	1.41123e8i		−	1.26944i	0.772741	−	0.634722i	$-0.218885\pi$
$200$	1.40961e8	−	8.13840e7i	1.24593	−	0.719340i
$201$	−1.03980e7	−	1.80098e7i	−0.0903154	−	0.156431i
$202$	−1.10908e8	+	6.40329e7i	−0.946747	+	0.546604i
$203$	2.15993e7	+	1.24704e7i	0.181219	+	0.104627i
$204$	9.73100e6	+	5.61820e6i	0.0802513	+	0.0463331i
$205$	5.81150e7	−	3.35527e7i	0.471140	−	0.272013i
$206$	6.11774e7	+	1.05962e8i	0.487591	+	0.844533i
$207$	−8.89741e7	+	5.13692e7i	−0.697216	+	0.402538i
$208$			9.44754e7i			0.727942i
$209$	6.85337e6	+	3.95680e6i	0.0519269	+	0.0299800i
$210$	−2.14555e7	−	3.71621e7i	−0.159872	−	0.276906i
$211$	1.52394e8			1.11681			0.558406	−	0.829568i	$-0.311413\pi$
$211$	1.52394e8			1.11681			0.558406	+	0.829568i	$0.311413\pi$
$212$	−2.77923e6			−0.0200331
$213$	3.05425e7	+	5.29012e7i	0.216559	+	0.375091i
$214$			6.49431e7i			0.452986i
$215$	−1.82535e7	+	3.16160e7i	−0.125260	+	0.216956i
$216$			7.81459e7i			0.527616i
$217$	−1.80705e8	−	1.04330e8i	−1.20050	−	0.693107i
$218$	−4.06943e7	+	7.04846e7i	−0.266033	+	0.460783i
$219$	3.34813e7	−	5.79914e7i	0.215401	−	0.373086i
$220$	−2.35228e7	+	1.35809e7i	−0.148940	+	0.0859903i
$221$	−2.60622e8			−1.62420
$222$	2.03048e7	+	2.99099e7i	0.124556	+	0.183476i
$223$	1.65684e8			1.00049			0.500247	−	0.865883i	$-0.333243\pi$
$223$	1.65684e8			1.00049			0.500247	+	0.865883i	$0.333243\pi$
$224$	6.15787e7	−	3.55525e7i	0.366068	−	0.211350i
$225$	−1.06633e8	+	1.84694e8i	−0.624100	+	1.08097i
$226$	1.19834e6	−	2.07559e6i	0.00690559	−	0.0119608i
$227$	1.41080e8	+	8.14523e7i	0.800522	+	0.462182i	0.843654	−	0.536888i	$-0.180400\pi$
$227$	1.41080e8	+	8.14523e7i	0.800522	+	0.462182i	−0.0431314	+	0.999069i	$0.513733\pi$
$228$		−	1.25979e6i		−	0.00703925i
$229$	−1.07971e8	+	1.87011e8i	−0.594130	+	1.02906i	0.399538	+	0.916716i	$0.369170\pi$
$229$	−1.07971e8	+	1.87011e8i	−0.594130	+	1.02906i	−0.993669	+	0.112348i	$0.964163\pi$
$230$		−	2.12845e8i		−	1.15350i
$231$	1.09879e7	+	1.90317e7i	0.0586509	+	0.101586i
$232$	4.54992e7			0.239219
$233$	1.91376e8			0.991153			0.495577	−	0.868564i	$-0.334957\pi$
$233$	1.91376e8			0.991153			0.495577	+	0.868564i	$0.334957\pi$
$234$	−8.15915e7	−	1.41321e8i	−0.416284	−	0.721025i
$235$	2.36078e8	+	1.36300e8i	1.18664	+	0.685105i
$236$		−	5.17568e7i		−	0.256316i
$237$	−2.19447e7	+	1.26698e7i	−0.107081	+	0.0618230i
$238$	−1.38263e8	−	2.39479e8i	−0.664794	−	1.15146i
$239$	2.37658e8	−	1.37212e8i	1.12606	−	0.650129i	0.183116	−	0.983091i	$-0.441382\pi$
$239$	2.37658e8	−	1.37212e8i	1.12606	−	0.650129i	0.942940	+	0.332963i	$0.108048\pi$
$240$	−5.14271e7	−	2.96915e7i	−0.240134	−	0.138641i
$241$	−8.11767e7	−	4.68674e7i	−0.373570	−	0.215681i	0.301447	−	0.953483i	$-0.402530\pi$
$241$	−8.11767e7	−	4.68674e7i	−0.373570	−	0.215681i	−0.675017	+	0.737802i	$0.735864\pi$
$242$	1.27069e8	−	7.33631e7i	0.576348	−	0.332755i
$243$	−7.76360e7	−	1.34470e8i	−0.347089	−	0.601176i
$244$	−2.99931e7	+	1.73165e7i	−0.132177	+	0.0763126i
$245$			3.83223e7i			0.166483i
$246$	−1.59709e7	−	9.22078e6i	−0.0683999	−	0.0394907i
$247$	1.46101e7	+	2.53054e7i	0.0616898	+	0.106850i
$248$	−3.80657e8			−1.58472
$249$	−1.07061e8			−0.439475
$250$	−5.52138e7	−	9.56332e7i	−0.223490	−	0.387096i
$251$			3.64757e8i			1.45595i	0.685605	+	0.727974i	$0.259538\pi$
$251$			3.64757e8i			1.45595i	−0.685605	+	0.727974i	$0.740462\pi$
$252$	−2.56822e7	+	4.44829e7i	−0.101095	+	0.175102i
$253$			1.09004e8i			0.423175i
$254$	4.46200e7	+	2.57614e7i	0.170849	+	0.0986396i
$255$	8.19076e7	−	1.41868e8i	0.309338	−	0.535790i
$256$	8.69328e7	−	1.50572e8i	0.323850	−	0.560924i
$257$	−2.53272e8	+	1.46226e8i	−0.930723	+	0.537353i	−0.887040	−	0.461692i	$-0.847242\pi$
$257$	−2.53272e8	+	1.46226e8i	−0.930723	+	0.537353i	−0.0436828	+	0.999045i	$0.513909\pi$
$258$	1.00327e7			0.0363704
$259$	1.91979e7	+	2.63232e8i	0.0686600	+	0.941432i
$260$	−1.00292e8			−0.353884
$261$	−5.16284e7	+	2.98077e7i	−0.179741	+	0.103773i
$262$	1.68040e8	−	2.91053e8i	0.577241	−	0.999811i
$263$	2.93182e8	−	5.07805e8i	0.993783	−	1.72128i	0.400474	−	0.916308i	$-0.368846\pi$
$263$	2.93182e8	−	5.07805e8i	0.993783	−	1.72128i	0.593309	−	0.804974i	$-0.297821\pi$
$264$	3.47194e7	+	2.00452e7i	0.116134	+	0.0670498i
$265$			4.05183e7i			0.133749i
$266$	−1.55016e7	+	2.68496e7i	−0.0505001	+	0.0874687i
$267$			1.33252e8i			0.428435i
$268$	−2.57853e7	−	4.46615e7i	−0.0818277	−	0.141730i
$269$	3.92348e8			1.22896			0.614482	−	0.788931i	$-0.289365\pi$
$269$	3.92348e8			1.22896			0.614482	+	0.788931i	$0.289365\pi$
$270$	2.12125e8			0.655871
$271$	−1.32525e8	−	2.29540e8i	−0.404488	−	0.700594i	0.589773	−	0.807569i	$-0.299217\pi$
$271$	−1.32525e8	−	2.29540e8i	−0.404488	−	0.700594i	−0.994262	+	0.106974i	$0.965884\pi$
$272$	−3.31406e8	−	1.91337e8i	−0.998547	−	0.576512i
$273$			8.11438e7i			0.241372i
$274$	9.68238e7	−	5.59013e7i	0.284351	−	0.164170i
$275$	1.13136e8	+	1.95958e8i	0.328048	+	0.568195i
$276$	1.50278e7	−	8.67633e6i	0.0430244	−	0.0248402i
$277$	9.54447e7	+	5.51050e7i	0.269819	+	0.155780i	0.628805	−	0.777563i	$-0.283544\pi$
$277$	9.54447e7	+	5.51050e7i	0.269819	+	0.155780i	−0.358986	+	0.933343i	$0.616878\pi$
$278$	1.62449e7	+	9.37902e6i	0.0453483	+	0.0261819i
$279$	4.31936e8	−	2.49378e8i	1.19071	−	0.687454i
$280$	−2.85763e8	−	4.94955e8i	−0.777951	−	1.34745i
$281$	−2.54405e8	+	1.46881e8i	−0.683995	+	0.394905i	−0.801359	−	0.598184i	$-0.795889\pi$
$281$	−2.54405e8	+	1.46881e8i	−0.683995	+	0.394905i	0.117363	+	0.993089i	$0.462556\pi$
$282$		−	7.49143e7i		−	0.198927i
$283$	2.35368e8	+	1.35890e8i	0.617298	+	0.356397i	0.775816	−	0.630959i	$-0.217338\pi$
$283$	2.35368e8	+	1.35890e8i	0.617298	+	0.356397i	−0.158518	+	0.987356i	$0.550672\pi$
$284$	7.57407e7	+	1.31187e8i	0.196207	+	0.339841i
$285$	−1.83665e7			−0.0469968
$286$	−1.73134e8			−0.437625
$287$	−6.73192e7	−	1.16600e8i	−0.168094	−	0.291148i
$288$			1.69961e8i			0.419252i
$289$	3.22658e8	−	5.58860e8i	0.786321	−	1.36195i
$290$		−	1.23506e8i		−	0.297369i
$291$	1.54362e8	+	8.91208e7i	0.367210	+	0.212009i
$292$	8.30284e7	−	1.43809e8i	0.195158	−	0.338024i
$293$	1.40348e8	−	2.43090e8i	0.325964	−	0.564586i	−0.655743	−	0.754984i	$-0.727645\pi$
$293$	1.40348e8	−	2.43090e8i	0.325964	−	0.564586i	0.981707	+	0.190398i	$0.0609779\pi$
$294$	9.12057e6	−	5.26576e6i	0.0209318	−	0.0120850i
$295$	−7.54562e8			−1.71127
$296$	2.70436e8	+	3.98364e8i	0.606100	+	0.892811i
$297$	−1.08635e8			−0.240614
$298$	−5.61304e8	+	3.24069e8i	−1.22869	+	0.709383i
$299$	−2.01243e8	+	3.48563e8i	−0.435383	+	0.754105i
$300$	1.80105e7	−	3.11951e7i	0.0385125	−	0.0667056i
$301$	6.34335e7	+	3.66234e7i	0.134071	+	0.0774062i
$302$		−	1.96833e8i		−	0.411219i
$303$	−7.61084e7	+	1.31824e8i	−0.157175	+	0.272235i
$304$			4.29043e7i			0.0875876i
$305$	2.52457e8	+	4.37269e8i	0.509494	+	0.882469i
$306$	6.60976e8			1.31874
$307$	−4.77802e8			−0.942462			−0.471231	−	0.882010i	$-0.656190\pi$
$307$	−4.77802e8			−0.942462			−0.471231	+	0.882010i	$0.656190\pi$
$308$	2.72484e7	+	4.71956e7i	0.0531390	+	0.0920394i
$309$	1.25945e8	+	7.27144e7i	0.242843	+	0.140206i
$310$			1.03328e9i			1.96994i
$311$	−3.10762e8	+	1.79418e8i	−0.585823	+	0.338225i	−0.763444	−	0.645874i	$-0.776493\pi$
$311$	−3.10762e8	+	1.79418e8i	−0.585823	+	0.338225i	0.177621	+	0.984099i	$0.443160\pi$
$312$	7.40151e7	+	1.28198e8i	0.137968	+	0.238968i
$313$	−4.03408e8	+	2.32908e8i	−0.743600	+	0.429318i	−0.823377	−	0.567495i	$-0.807913\pi$
$313$	−4.03408e8	+	2.32908e8i	−0.743600	+	0.429318i	0.0797766	+	0.996813i	$0.474579\pi$
$314$	8.14313e8	+	4.70144e8i	1.48435	+	0.856993i
$315$	6.48515e8	+	3.74420e8i	1.16905	+	0.674951i
$316$	−5.44195e7	+	3.14191e7i	−0.0970174	+	0.0560130i
$317$	−4.34767e8	−	7.53038e8i	−0.766565	−	1.32773i	−0.939415	−	0.342782i	$-0.888631\pi$
$317$	−4.34767e8	−	7.53038e8i	−0.766565	−	1.32773i	0.172850	−	0.984948i	$-0.444702\pi$
$318$	9.64322e6	−	5.56752e6i	0.0168162	−	0.00970882i
$319$			6.32509e7i			0.109094i
$320$	−8.62355e8	−	4.97881e8i	−1.47116	−	0.849377i
$321$	3.85952e7	+	6.68488e7i	0.0651276	+	0.112804i
$322$	−4.27047e8			−0.712820
$323$	−1.18357e8			−0.195427
$324$	−5.69218e7	−	9.85914e7i	−0.0929760	−	0.161039i
$325$			8.35489e8i			1.35005i
$326$	−3.36503e7	+	5.82840e7i	−0.0537932	+	0.0931725i
$327$			9.67371e7i			0.152995i
$328$	−2.12713e8	−	1.22810e8i	−0.332841	−	0.192166i
$329$	2.73468e8	−	4.73660e8i	0.423371	−	0.733300i
$330$	5.44122e7	−	9.42447e7i	0.0833485	−	0.144364i
$331$	−2.04963e7	+	1.18335e7i	−0.0310654	+	0.0179356i	−0.515452	−	0.856918i	$-0.672376\pi$
$331$	−2.04963e7	+	1.18335e7i	−0.0310654	+	0.0179356i	0.484387	+	0.874854i	$0.339043\pi$
$332$	−2.65495e8			−0.398174
$333$	−5.67845e8	−	2.74858e8i	−0.842704	−	0.407900i
$334$	2.37113e8			0.348210
$335$	−6.51119e8	+	3.75924e8i	−0.946245	+	0.546315i
$336$	−5.95722e7	+	1.03182e8i	−0.0856753	+	0.148394i
$337$	−3.56960e7	+	6.18274e7i	−0.0508061	+	0.0879987i	−0.890310	−	0.455355i	$-0.849512\pi$
$337$	−3.56960e7	+	6.18274e7i	−0.0508061	+	0.0879987i	0.839504	+	0.543354i	$0.182846\pi$
$338$	−1.37192e7	−	7.92078e6i	−0.0193250	−	0.0111573i
$339$		−	2.84865e6i		−	0.00397137i
$340$	2.03118e8	−	3.51811e8i	0.280267	−	0.485437i
$341$		−	5.29172e8i		−	0.722698i
$342$	−3.70533e7	−	6.41782e7i	−0.0500882	−	0.0867553i
$343$	7.82345e8			1.04681
$344$	1.33624e8			0.176982
$345$	−1.26492e8	−	2.19091e8i	−0.165843	−	0.287248i
$346$	−6.95547e7	−	4.01574e7i	−0.0902734	−	0.0521194i
$347$			2.10920e8i			0.270997i	0.990778	+	0.135498i	$0.0432636\pi$
$347$			2.10920e8i			0.270997i	−0.990778	+	0.135498i	$0.956736\pi$
$348$	8.72010e6	−	5.03455e6i	0.0110916	−	0.00640374i
$349$	2.77648e8	+	4.80900e8i	0.349627	+	0.605572i	0.986183	−	0.165659i	$-0.0529749\pi$
$349$	2.77648e8	+	4.80900e8i	0.349627	+	0.605572i	−0.636556	+	0.771230i	$0.719642\pi$
$350$	−7.67709e8	+	4.43237e8i	−0.957102	+	0.552583i
$351$	−3.47383e8	−	2.00562e8i	−0.428779	−	0.247556i
$352$	1.56166e8	+	9.01627e7i	0.190848	+	0.110186i
$353$	−9.41950e7	+	5.43835e7i	−0.113977	+	0.0658045i	−0.555905	−	0.831246i	$-0.687628\pi$
$353$	−9.41950e7	+	5.43835e7i	−0.113977	+	0.0658045i	0.441928	+	0.897051i	$0.354295\pi$
$354$	1.03682e8	+	1.79583e8i	0.124221	+	0.215156i
$355$	1.91257e9	−	1.10422e9i	2.26891	−	1.30996i
$356$			3.30444e8i			0.388171i
$357$	−2.84640e8	−	1.64337e8i	−0.331099	−	0.191160i
$358$	5.07407e7	+	8.78855e7i	0.0584475	+	0.101234i
$359$	1.66288e9			1.89684			0.948420	−	0.317017i	$-0.102681\pi$
$359$	1.66288e9			1.89684			0.948420	+	0.317017i	$0.102681\pi$
$360$	1.36611e9			1.54321
$361$	−4.40301e8	−	7.62624e8i	−0.492577	−	0.853169i
$362$			7.93916e8i			0.879619i
$363$	8.71981e7	−	1.51032e8i	0.0956828	−	0.165728i
$364$			2.01224e8i			0.218688i
$365$	−2.09660e9	−	1.21047e9i	−2.25678	−	1.30295i
$366$	6.93791e7	−	1.20168e8i	0.0739681	−	0.128117i
$367$	8.51314e8	−	1.47452e9i	0.898997	−	1.55711i	0.0702194	−	0.997532i	$-0.477630\pi$
$367$	8.51314e8	−	1.47452e9i	0.898997	−	1.55711i	0.828778	−	0.559578i	$-0.189037\pi$
$368$	−5.11798e8	+	2.95487e8i	−0.535342	+	0.309080i
$369$	3.21824e8			0.333446
$370$	1.08135e9	−	7.34091e8i	1.10984	−	0.753432i
$371$	8.12948e7			0.0826522
$372$	−7.29545e7	+	4.21203e7i	−0.0734771	+	0.0424220i
$373$	−7.26354e8	+	1.25808e9i	−0.724715	+	1.25524i	0.234376	+	0.972146i	$0.424695\pi$
$373$	−7.26354e8	+	1.25808e9i	−0.724715	+	1.25524i	−0.959091	+	0.283097i	$0.908638\pi$
$374$	3.50642e8	−	6.07330e8i	0.346588	−	0.600308i
$375$	−1.13668e8	−	6.56262e7i	−0.111309	−	0.0642640i
$376$		−	9.97772e8i		−	0.967996i
$377$	−1.16774e8	+	2.02258e8i	−0.112241	+	0.194407i
$378$		−	4.25602e8i		−	0.405305i
$379$	−1.80221e8	−	3.12151e8i	−0.170046	−	0.294529i	0.768390	−	0.639982i	$-0.221058\pi$
$379$	−1.80221e8	−	3.12151e8i	−0.170046	−	0.294529i	−0.938436	+	0.345454i	$0.887725\pi$
$380$	−4.55459e7			−0.0425801
$381$	6.12391e7			0.0567272
$382$	5.54753e8	+	9.60861e8i	0.509188	+	0.881939i
$383$	−6.03762e8	−	3.48582e8i	−0.549124	−	0.317037i	0.199645	−	0.979868i	$-0.436021\pi$
$383$	−6.03762e8	−	3.48582e8i	−0.549124	−	0.317037i	−0.748769	+	0.662831i	$0.769355\pi$
$384$			1.48178e8i			0.133544i
$385$	6.88064e8	−	3.97254e8i	0.614492	−	0.354777i
$386$	−5.53739e8	−	9.59104e8i	−0.490061	−	0.848810i
$387$	−1.51624e8	+	8.75401e7i	−0.132978	+	0.0767748i
$388$	3.82793e8	+	2.21005e8i	0.332700	+	0.192084i
$389$	−1.08196e9	−	6.24668e8i	−0.931936	−	0.538053i	−0.0445125	−	0.999009i	$-0.514173\pi$
$389$	−1.08196e9	−	6.24668e8i	−0.931936	−	0.538053i	−0.887423	+	0.460955i	$0.847507\pi$
$390$	3.47989e8	−	2.00912e8i	0.297057	−	0.171506i
$391$	−8.15138e8	−	1.41186e9i	−0.689624	−	1.19446i
$392$	1.21475e8	−	7.01338e7i	0.101856	−	0.0588066i
$393$		−	3.99458e8i		−	0.331969i
$394$	3.78601e8	+	2.18585e8i	0.311849	+	0.180046i
$395$	4.58058e8	+	7.93381e8i	0.373965	+	0.647727i
$396$	−1.30263e8			−0.105411
$397$	3.71492e8			0.297977			0.148988	−	0.988839i	$-0.452398\pi$
$397$	3.71492e8			0.297977			0.148988	+	0.988839i	$0.452398\pi$
$398$	7.01069e8	+	1.21429e9i	0.557404	+	0.965452i
$399$			3.68500e7i			0.0290424i
$400$	−6.13378e8	+	1.06240e9i	−0.479202	+	0.830002i
$401$			1.21835e9i			0.943554i	0.881718	+	0.471777i	$0.156387\pi$
$401$			1.21835e9i			0.943554i	−0.881718	+	0.471777i	$0.843613\pi$
$402$	1.78937e8	+	1.03309e8i	0.137375	+	0.0793138i
$403$	9.76958e8	−	1.69214e9i	0.743547	−	1.28786i
$404$	−1.88737e8	+	3.26902e8i	−0.142404	+	0.246651i
$405$	−1.43736e9	+	8.29862e8i	−1.07516	+	0.620745i
$406$	−2.47800e8			−0.183764
$407$	−5.53788e8	+	3.75948e8i	−0.407158	+	0.276406i
$408$	−5.99599e8			−0.437069
$409$	−4.85090e8	+	2.80067e8i	−0.350583	+	0.202409i	−0.664942	−	0.746895i	$-0.731544\pi$
$409$	−4.85090e8	+	2.80067e8i	−0.350583	+	0.202409i	0.314359	+	0.949304i	$0.398210\pi$
$410$	−3.33364e8	+	5.77404e8i	−0.238878	+	0.413748i
$411$	6.64433e7	−	1.15083e8i	0.0472068	−	0.0817646i
$412$	3.12324e8	+	1.80320e8i	0.220021	+	0.127029i
$413$			1.51393e9i			1.05750i
$414$	5.10381e8	−	8.84006e8i	0.353503	−	0.612286i
$415$			3.87065e9i			2.65837i
$416$	3.32917e8	+	5.76629e8i	0.226730	+	0.392708i
$417$	2.22955e7			0.0150571
$418$	−7.86258e7			−0.0526560
$419$	−7.30864e8	−	1.26589e9i	−0.485387	−	0.840714i	0.514472	−	0.857507i	$-0.327988\pi$
$419$	−7.30864e8	−	1.26589e9i	−0.485387	−	0.840714i	−0.999859	+	0.0167928i	$0.994654\pi$
$420$	−1.09535e8	−	6.32401e7i	−0.0721407	−	0.0416505i
$421$		−	7.02997e7i		−	0.0459162i	−0.999736	−	0.0229581i	$-0.992692\pi$
$421$		−	7.02997e7i		−	0.0459162i	0.999736	−	0.0229581i	$-0.00730843\pi$
$422$	−1.31127e9	+	7.57059e8i	−0.849370	+	0.490384i
$423$	6.53665e8	+	1.13218e9i	0.419918	+	0.727318i
$424$	1.28436e8	−	7.41528e7i	0.0818291	−	0.0472441i
$425$	−2.93077e9	−	1.69208e9i	−1.85191	−	1.06920i
$426$	−5.25602e8	−	3.03457e8i	−0.329400	−	0.190179i
$427$	8.77325e8	−	5.06524e8i	0.545334	−	0.314849i
$428$	9.57099e7	+	1.65774e8i	0.0590070	+	0.102203i
$429$	−1.78215e8	+	1.02892e8i	−0.108979	+	0.0629191i
$430$		−	3.62717e8i		−	0.220003i
$431$	1.11695e9	+	6.44870e8i	0.671989	+	0.387973i	0.796830	−	0.604204i	$-0.206509\pi$
$431$	1.11695e9	+	6.44870e8i	0.671989	+	0.387973i	−0.124841	+	0.992177i	$0.539842\pi$
$432$	−2.94487e8	−	5.10066e8i	−0.175741	−	0.304392i
$433$	−1.87043e9			−1.10722			−0.553611	−	0.832775i	$-0.686750\pi$
$433$	−1.87043e9			−1.10722			−0.553611	+	0.832775i	$0.686750\pi$
$434$	2.07315e9			1.21735
$435$	−7.33987e7	−	1.27130e8i	−0.0427539	−	0.0740519i
$436$			2.39893e8i			0.138616i
$437$	−9.13907e7	+	1.58293e8i	−0.0523862	+	0.0907356i
$438$			6.65311e8i			0.378325i
$439$	5.40294e8	+	3.11939e8i	0.304793	+	0.175972i	0.644594	−	0.764525i	$-0.277026\pi$
$439$	5.40294e8	+	3.11939e8i	0.304793	+	0.175972i	−0.339801	+	0.940497i	$0.610360\pi$
$440$	7.24707e8	−	1.25523e9i	0.405582	−	0.702488i
$441$	−9.18928e7	+	1.59163e8i	−0.0510207	+	0.0883705i
$442$	2.24251e9	−	1.29471e9i	1.23525	−	0.713173i
$443$	−2.36581e9			−1.29291			−0.646454	−	0.762953i	$-0.723749\pi$
$443$	−2.36581e9			−1.29291			−0.646454	+	0.762953i	$0.723749\pi$
$444$	9.59098e7	+	4.64240e7i	0.0520023	+	0.0251711i
$445$	4.81754e9			2.59159
$446$	−1.42562e9	+	8.23082e8i	−0.760907	+	0.439310i
$447$	−3.85183e8	+	6.67156e8i	−0.203981	+	0.353306i
$448$	−9.98935e8	+	1.73021e9i	−0.524885	+	0.909128i
$449$	1.31917e9	+	7.61620e8i	0.687760	+	0.397078i	0.802772	−	0.596286i	$-0.203357\pi$
$449$	1.31917e9	+	7.61620e8i	0.687760	+	0.397078i	−0.115012	+	0.993364i	$0.536691\pi$
$450$		−	2.11892e9i		−	1.09615i
$451$	1.70725e8	−	2.95704e8i	0.0876352	−	0.151789i
$452$		−	7.06421e6i		−	0.00359815i
$453$	−1.16976e8	−	2.02608e8i	−0.0591225	−	0.102403i
$454$	−1.61855e9			−0.811763
$455$	2.93364e9			1.46005
$456$	3.36126e7	+	5.82187e7i	0.0166006	+	0.0287532i
$457$	1.60492e9	+	9.26601e8i	0.786587	+	0.454136i	0.838759	−	0.544502i	$-0.183281\pi$
$457$	1.60492e9	+	9.26601e8i	0.786587	+	0.454136i	−0.0521729	+	0.998638i	$0.516615\pi$
$458$		−	2.14550e9i		−	1.04351i
$459$	1.40708e9	−	8.12379e8i	0.679164	−	0.392116i
$460$	−3.13680e8	−	5.43310e8i	−0.150257	−	0.260253i
$461$	−1.94844e9	+	1.12493e9i	−0.926263	+	0.534778i	−0.885628	−	0.464396i	$-0.846272\pi$
$461$	−1.94844e9	+	1.12493e9i	−0.926263	+	0.534778i	−0.0406354	+	0.999174i	$0.512938\pi$
$462$	−1.89090e8	−	1.09171e8i	−0.0892117	−	0.0515064i
$463$	−3.68359e9	−	2.12672e9i	−1.72480	−	0.995812i	−0.908109	−	0.418734i	$-0.862474\pi$
$463$	−3.68359e9	−	2.12672e9i	−1.72480	−	0.995812i	−0.816689	−	0.577078i	$-0.804193\pi$
$464$	−2.96978e8	+	1.71460e8i	−0.138010	+	0.0796802i
$465$	6.14071e8	+	1.06360e9i	0.283226	+	0.490562i
$466$	−1.64668e9	+	9.50710e8i	−0.753803	+	0.435208i
$467$			1.02705e9i			0.466640i	0.972400	+	0.233320i	$0.0749590\pi$
$467$			1.02705e9i			0.466640i	−0.972400	+	0.233320i	$0.925041\pi$
$468$	−4.16542e8	−	2.40491e8i	−0.187845	−	0.108452i
$469$	7.54243e8	+	1.30639e9i	0.337603	+	0.584746i
$470$	−2.70842e9			−1.20330
$471$	1.11761e9			0.492853
$472$	1.38093e9	+	2.39184e9i	0.604470	+	1.04697i
$473$			1.85757e8i			0.0807108i
$474$	1.25881e8	−	2.18033e8i	0.0542921	−	0.0940367i
$475$			3.79422e8i			0.162441i
$476$	−7.05863e8	−	4.07530e8i	−0.299983	−	0.173195i
$477$	−9.71587e7	+	1.68284e8i	−0.0409890	+	0.0709951i
$478$	−1.36328e9	+	2.36126e9i	−0.570934	+	0.988887i
$479$	3.95329e9	−	2.28243e9i	1.64356	−	0.948908i	0.664002	−	0.747731i	$-0.268857\pi$
$479$	3.95329e9	−	2.28243e9i	1.64356	−	0.948908i	0.979555	−	0.201177i	$-0.0644766\pi$
$480$	−4.18513e8			−0.172729
$481$	−2.46493e9	+	1.79771e8i	−1.00994	+	0.0736565i
$482$	9.31306e8			0.378815
$483$	−4.39578e8	+	2.53790e8i	−0.177509	+	0.102485i
$484$	2.16238e8	−	3.74535e8i	0.0866907	−	0.150153i
$485$	3.22204e9	−	5.58073e9i	1.28243	−	2.22124i
$486$	1.33603e9	+	7.71356e8i	0.527945	+	0.304809i
$487$			1.37185e8i			0.0538213i	0.999638	+	0.0269107i	$0.00856697\pi$
$487$			1.37185e8i			0.0538213i	−0.999638	+	0.0269107i	$0.991433\pi$
$488$	9.24048e8	−	1.60050e9i	0.359936	−	0.623427i
$489$			7.99923e7i			0.0309362i
$490$	−1.90376e8	−	3.29741e8i	−0.0731015	−	0.126616i
$491$	−1.28464e9			−0.489773			−0.244887	−	0.969552i	$-0.578751\pi$
$491$	−1.28464e9			−0.489773			−0.244887	+	0.969552i	$0.578751\pi$
$492$	−5.43565e7			−0.0205766
$493$	−4.72994e8	−	8.19250e8i	−0.177784	−	0.307930i
$494$	−2.51423e8	−	1.45159e8i	−0.0938341	−	0.0541751i
$495$			1.89910e9i			0.703766i
$496$	2.48459e9	−	1.43448e9i	0.914257	−	0.527847i
$497$	−2.21548e9	−	3.83733e9i	−0.809507	−	1.40211i
$498$	9.21201e8	−	5.31856e8i	0.334235	−	0.192971i
$499$	−2.70401e9	−	1.56116e9i	−0.974218	−	0.562465i	−0.0736988	−	0.997281i	$-0.523480\pi$
$499$	−2.70401e9	−	1.56116e9i	−0.974218	−	0.562465i	−0.900520	+	0.434815i	$0.856814\pi$
$500$	−2.81879e8	−	1.62743e8i	−0.100848	−	0.0582246i
$501$	2.44070e8	−	1.40914e8i	0.0867127	−	0.0500636i
$502$	−1.81203e9	−	3.13853e9i	−0.639297	−	1.10729i
$503$	−4.58931e9	+	2.64964e9i	−1.60790	+	0.928322i	−0.618063	+	0.786129i	$0.712082\pi$
$503$	−4.58931e9	+	2.64964e9i	−1.60790	+	0.928322i	−0.989839	+	0.142194i	$0.954584\pi$
$504$		−	2.74092e9i		−	0.953650i
$505$	4.76589e9	+	2.75159e9i	1.64674	+	0.950745i
$506$	−5.41506e8	−	9.37916e8i	−0.185813	−	0.321838i
$507$	−1.88290e7			−0.00641652
$508$	1.51863e8			0.0513960
$509$	9.95512e8	+	1.72428e9i	0.334606	+	0.579555i	0.983409	−	0.181401i	$-0.0580633\pi$
$509$	9.95512e8	+	1.72428e9i	0.334606	+	0.579555i	−0.648803	+	0.760957i	$0.724730\pi$
$510$			1.62759e9i			0.543313i
$511$	−2.42866e9	+	4.20655e9i	−0.805180	+	1.39461i
$512$			3.33355e9i			1.09765i
$513$	−1.57758e8	−	9.10814e7i	−0.0515917	−	0.0297865i
$514$	1.45284e9	−	2.51639e9i	0.471896	−	0.817348i
$515$	2.62889e9	−	4.55336e9i	0.848099	−	1.46895i
$516$	2.56095e7	−	1.47856e7i	0.00820592	−	0.00473769i
$517$	1.38706e9			0.441445
$518$	−1.47286e9	−	2.16959e9i	−0.465594	−	0.685841i
$519$	−9.54608e7			−0.0299736
$520$	4.63481e9	−	2.67591e9i	1.44551	−	0.834565i
$521$	−1.43873e8	+	2.49195e8i	−0.0445705	+	0.0771983i	−0.887450	−	0.460904i	$-0.847525\pi$
$521$	−1.43873e8	+	2.49195e8i	−0.0445705	+	0.0771983i	0.842880	+	0.538102i	$0.180859\pi$
$522$	2.96155e8	−	5.12956e8i	0.0911324	−	0.157846i
$523$	−4.89259e9	−	2.82474e9i	−1.49549	−	0.863421i	−0.495502	−	0.868607i	$-0.665016\pi$
$523$	−4.89259e9	−	2.82474e9i	−1.49549	−	0.863421i	−0.999987	+	0.00518609i	$0.998349\pi$
$524$		−	9.90593e8i		−	0.300771i
$525$	−5.26824e8	+	9.12485e8i	−0.158894	+	0.275213i
$526$			5.82584e9i			1.74545i
$527$	3.95719e9	+	6.85405e9i	1.17774	+	2.03990i
$528$	−3.02156e8			−0.0893330
$529$	8.87148e8			0.260556
$530$	−2.01286e8	−	3.48637e8i	−0.0587283	−	0.101720i
$531$	−3.13391e9	−	1.80936e9i	−0.908354	−	0.524439i
$532$			9.13821e7i			0.0263130i
$533$	1.09186e9	−	6.30385e8i	0.312335	−	0.180327i
$534$	−6.61966e8	−	1.14656e9i	−0.188123	−	0.325838i
$535$	2.41682e9	−	1.39535e9i	0.682349	−	0.393954i
$536$	2.38323e9	+	1.37596e9i	0.668482	+	0.385948i
$537$	1.04459e8	+	6.03096e7i	0.0291096	+	0.0168065i
$538$	−3.37593e9	+	1.94910e9i	−0.934665	+	0.539629i
$539$	9.74968e7	+	1.68869e8i	0.0268182	+	0.0464505i
$540$	5.41471e8	−	3.12619e8i	0.147978	−	0.0854352i
$541$		−	1.92536e9i		−	0.522782i	−0.965233	−	0.261391i	$-0.915819\pi$
$541$		−	1.92536e9i		−	0.522782i	0.965233	−	0.261391i	$-0.0841812\pi$
$542$	2.28061e9	+	1.31671e9i	0.615252	+	0.355216i
$543$	4.71817e8	+	8.17211e8i	0.126466	+	0.219046i
$544$	−2.69697e9			−0.718258
$545$	3.49739e9			0.925458
$546$	−4.03104e8	−	6.98197e8i	−0.105985	−	0.183571i
$547$		−	1.57259e9i		−	0.410827i	−0.978675	−	0.205414i	$-0.934146\pi$
$547$		−	1.57259e9i		−	0.410827i	0.978675	−	0.205414i	$-0.0658540\pi$
$548$	1.64769e8	−	2.85388e8i	0.0427704	−	0.0740805i
$549$			2.42147e9i			0.624562i
$550$	−1.94695e9	−	1.12407e9i	−0.498981	−	0.288087i
$551$	−5.30307e7	+	9.18518e7i	−0.0135051	+	0.0233914i
$552$	−4.62988e8	+	8.01919e8i	−0.117161	+	0.202929i
$553$	1.59182e9	−	9.19036e8i	0.400272	−	0.231097i
$554$	−1.09500e9			−0.273608
$555$	6.76814e8	−	1.39827e9i	0.168052	−	0.347188i
$556$	5.52893e7			0.0136420
$557$	−2.93805e9	+	1.69628e9i	−0.720387	+	0.415915i	−0.814895	−	0.579609i	$-0.803205\pi$
$557$	−2.93805e9	+	1.69628e9i	−0.720387	+	0.415915i	0.0945084	+	0.995524i	$0.469872\pi$
$558$	−2.47771e9	+	4.29152e9i	−0.603713	+	1.04566i
$559$	−3.42945e8	+	5.93999e8i	−0.0830392	+	0.143828i
$560$	3.73040e9	+	2.15375e9i	0.897630	+	0.518247i
$561$		−	8.33534e8i		−	0.199321i
$562$	1.45934e9	−	2.52765e9i	0.346800	−	0.600675i
$563$		−	5.83188e9i		−	1.37730i	−0.725093	−	0.688651i	$-0.758203\pi$
$563$		−	5.83188e9i		−	1.37730i	0.725093	−	0.688651i	$-0.241797\pi$
$564$	−1.10405e8	−	1.91227e8i	−0.0259126	−	0.0448820i
$565$	−1.02989e8			−0.0240227
$566$	−2.70028e9			−0.625966
$567$	1.66501e9	+	2.88389e9i	0.383598	+	0.664412i
$568$	−7.00041e9	−	4.04169e9i	−1.60289	−	0.925431i
$569$			3.21632e9i			0.731925i	0.930630	+	0.365962i	$0.119260\pi$
$569$			3.21632e9i			0.731925i	−0.930630	+	0.365962i	$0.880740\pi$
$570$	1.58033e8	−	9.12404e7i	0.0357426	−	0.0206360i
$571$	−1.92142e9	−	3.32799e9i	−0.431912	−	0.748094i	0.565126	−	0.825005i	$-0.308828\pi$
$571$	−1.92142e9	−	3.32799e9i	−0.431912	−	0.748094i	−0.997038	+	0.0769108i	$0.975494\pi$
$572$	−4.41944e8	+	2.55157e8i	−0.0987374	+	0.0570061i
$573$	1.14206e9	+	6.59370e8i	0.253600	+	0.146416i
$574$	1.15849e9	+	6.68853e8i	0.255682	+	0.147618i
$575$	−4.52606e9	+	2.61312e9i	−0.992849	+	0.573222i
$576$	−2.38774e9	−	4.13568e9i	−0.520604	−	0.901713i
$577$	1.30959e9	−	7.56094e8i	0.283806	−	0.163855i	−0.351339	−	0.936248i	$-0.614274\pi$
$577$	1.30959e9	−	7.56094e8i	0.283806	−	0.163855i	0.635145	+	0.772393i	$0.280940\pi$
$578$			6.41156e9i			1.38107i
$579$	−1.13997e9	−	6.58165e8i	−0.244073	−	0.140916i
$580$	−1.82017e8	−	3.15263e8i	−0.0387360	−	0.0670927i
$581$	7.76596e9			1.64278
$582$	−1.77093e9			−0.372366
$583$	1.03084e8	+	1.78546e8i	0.0215452	+	0.0373174i
$584$			8.86116e9i			1.84097i
$585$	−3.50611e9	+	6.07276e9i	−0.724069	+	1.25413i
$586$			2.78887e9i			0.572514i
$587$	6.92411e9	+	3.99763e9i	1.41296	+	0.815774i	0.995666	−	0.0929971i	$-0.0296447\pi$
$587$	6.92411e9	+	3.99763e9i	1.41296	+	0.815774i	0.417295	+	0.908771i	$0.362978\pi$
$588$	1.55208e7	−	2.68829e7i	0.00314843	−	0.00545324i
$589$	4.43668e8	−	7.68455e8i	0.0894652	−	0.154958i
$590$	6.49258e9	−	3.74849e9i	1.30147	−	0.751406i
$591$	5.19613e8			0.103544
$592$	−3.26637e9	−	1.58105e9i	−0.647052	−	0.313198i
$593$	5.16589e9			1.01731			0.508656	−	0.860970i	$-0.330143\pi$
$593$	5.16589e9			1.01731			0.508656	+	0.860970i	$0.330143\pi$
$594$	9.34741e8	−	5.39673e8i	0.182995	−	0.105652i
$595$	−5.94138e9	+	1.02908e10i	−1.15632	+	2.00280i
$596$	−9.55193e8	+	1.65444e9i	−0.184812	+	0.320103i
$597$	1.44328e9	+	8.33278e8i	0.277613	+	0.160280i
$598$		−	3.99891e9i		−	0.764694i
$599$	−2.16043e9	+	3.74198e9i	−0.410721	+	0.711389i	−0.994969	−	0.100186i	$-0.968056\pi$
$599$	−2.16043e9	+	3.74198e9i	−0.410721	+	0.711389i	0.584248	+	0.811575i	$0.301390\pi$
$600$			1.92216e9i			0.363296i
$601$	−5.60704e8	−	9.71168e8i	−0.105359	−	0.182488i	0.808526	−	0.588461i	$-0.200266\pi$
$601$	−5.60704e8	−	9.71168e8i	−0.105359	−	0.182488i	−0.913885	+	0.405973i	$0.866933\pi$
$602$	−7.27746e8			−0.135954
$603$	−3.60570e9			−0.669699
$604$	−2.90082e8	−	5.02437e8i	−0.0535663	−	0.0927795i
$605$	−5.46033e9	−	3.15252e9i	−1.00248	−	0.578782i
$606$		−	1.51236e9i		−	0.276058i
$607$	−6.51099e9	+	3.75912e9i	−1.18164	+	0.682223i	−0.956394	−	0.292078i	$-0.905653\pi$
$607$	−6.51099e9	+	3.75912e9i	−1.18164	+	0.682223i	−0.225250	+	0.974301i	$0.572320\pi$
$608$	1.51188e8	+	2.61866e8i	0.0272807	+	0.0472515i
$609$	−2.55071e8	+	1.47265e8i	−0.0457615	+	0.0264204i
$610$	−4.34451e9	−	2.50830e9i	−0.774972	−	0.447430i
$611$	4.43541e9	+	2.56078e9i	0.786664	+	0.454181i
$612$	1.68721e9	−	9.74112e8i	0.297536	−	0.171783i
$613$	−4.92296e8	−	8.52681e8i	−0.0863206	−	0.149512i	0.819633	−	0.572890i	$-0.194178\pi$
$613$	−4.92296e8	−	8.52681e8i	−0.0863206	−	0.149512i	−0.905953	+	0.423378i	$0.860844\pi$
$614$	4.11122e9	−	2.37361e9i	0.716772	−	0.413829i
$615$			7.92462e8i			0.137377i
$616$	−2.51846e9	−	1.45403e9i	−0.434113	−	0.250635i
$617$	−3.86682e9	−	6.69753e9i	−0.662760	−	1.14793i	−0.979888	−	0.199550i	$-0.936052\pi$
$617$	−3.86682e9	−	6.69753e9i	−0.662760	−	1.14793i	0.317128	−	0.948383i	$-0.397282\pi$
$618$	−1.44491e9			−0.246253
$619$	5.18368e9			0.878458			0.439229	−	0.898375i	$-0.355252\pi$
$619$	5.18368e9			0.878458			0.439229	+	0.898375i	$0.355252\pi$
$620$	1.52280e9	+	2.63757e9i	0.256609	+	0.444460i
$621$		−	2.50916e9i		−	0.420443i
$622$	1.78262e9	−	3.08759e9i	0.297025	−	0.514462i
$623$		−	9.66579e9i		−	1.60151i
$624$	−9.66207e8	−	5.57840e8i	−0.159193	−	0.0919102i
$625$	1.69603e9	−	2.93760e9i	0.277877	−	0.481297i
$626$	2.31407e9	−	4.00808e9i	0.377021	−	0.653020i
$627$	−8.09329e7	+	4.67266e7i	−0.0131126	+	0.00757056i
$628$	2.77150e9			0.446535
$629$	4.36151e9	−	9.01069e9i	0.698811	−	1.44371i
$630$	−7.44014e9			−1.18547
$631$	−7.07233e9	+	4.08321e9i	−1.12062	+	0.646992i	−0.941560	−	0.336845i	$-0.890640\pi$
$631$	−7.07233e9	+	4.08321e9i	−1.12062	+	0.646992i	−0.179064	+	0.983837i	$0.557307\pi$
$632$	1.67659e9	−	2.90394e9i	0.264191	−	0.457592i
$633$	−8.99828e8	+	1.55855e9i	−0.141009	+	0.244234i
$634$	7.48184e9	+	4.31964e9i	1.16599	+	0.673187i
$635$		−	2.21401e9i		−	0.343140i
$636$	1.64102e7	−	2.84234e7i	0.00252939	−	0.00438103i
$637$			7.19995e8i			0.110368i
$638$	−3.14216e8	−	5.44238e8i	−0.0479022	−	0.0829691i
$639$	1.05912e10			1.60581
$640$	5.35718e9			0.807804
$641$	3.10515e8	+	5.37827e8i	0.0465671	+	0.0806565i	0.888369	−	0.459129i	$-0.151839\pi$
$641$	3.10515e8	+	5.37827e8i	0.0465671	+	0.0806565i	−0.841802	+	0.539786i	$0.818505\pi$
$642$	−6.64179e8	−	3.83464e8i	−0.0990632	−	0.0571942i
$643$			9.71474e9i			1.44110i	0.693405	+	0.720548i	$0.256110\pi$
$643$			9.71474e9i			1.44110i	−0.693405	+	0.720548i	$0.743890\pi$
$644$	−1.09008e9	+	6.29360e8i	−0.160827	+	0.0928536i
$645$	−2.15560e8	−	3.73360e8i	−0.0316307	−	0.0547860i
$646$	1.01839e9	−	5.87969e8i	0.148628	−	0.0858106i
$647$	−5.79554e9	−	3.34606e9i	−0.841257	−	0.485700i	0.0164342	−	0.999865i	$-0.494769\pi$
$647$	−5.79554e9	−	3.34606e9i	−0.841257	−	0.485700i	−0.857691	+	0.514165i	$0.828102\pi$
$648$	5.26105e9	+	3.03747e9i	0.759557	+	0.438530i
$649$	−3.32502e9	+	1.91970e9i	−0.477461	+	0.275662i
$650$	−4.15052e9	−	7.18891e9i	−0.592796	−	1.02675i
$651$	2.13398e9	−	1.23206e9i	0.303150	−	0.175024i
$652$			1.98368e8i			0.0280289i
$653$	3.92957e9	+	2.26874e9i	0.552266	+	0.318851i	0.750036	−	0.661398i	$-0.230036\pi$
$653$	3.92957e9	+	2.26874e9i	0.552266	+	0.318851i	−0.197769	+	0.980249i	$0.563370\pi$
$654$	−4.80568e8	−	8.32368e8i	−0.0671788	−	0.116357i
$655$	−1.44418e10			−2.00807
$656$	1.85120e9			0.256029
$657$	−5.80517e9	−	1.00548e10i	−0.798612	−	1.38324i
$658$			5.43411e9i			0.743597i
$659$	6.87855e9	−	1.19140e10i	0.936263	−	1.62165i	0.163897	−	0.986478i	$-0.447594\pi$
$659$	6.87855e9	−	1.19140e10i	0.936263	−	1.62165i	0.772366	−	0.635177i	$-0.219073\pi$
$660$		−	3.20760e8i		−	0.0434286i
$661$	6.80379e9	+	3.92817e9i	0.916318	+	0.529036i	0.882458	−	0.470390i	$-0.155887\pi$
$661$	6.80379e9	+	3.92817e9i	0.916318	+	0.529036i	0.0338593	+	0.999427i	$0.489220\pi$
$662$	1.17573e8	−	2.03642e8i	0.0157508	−	0.0272812i
$663$	1.53887e9	−	2.66540e9i	0.205071	−	0.355194i
$664$	1.22693e10	−	7.08370e9i	1.62642	−	0.939014i
$665$	1.33226e9			0.175676
$666$	6.25142e9	−	4.55925e8i	0.820009	−	0.0598044i
$667$	−1.46091e9			−0.190627
$668$	6.05255e8	−	3.49444e8i	0.0785635	−	0.0453587i
$669$	−9.78301e8	+	1.69447e9i	−0.126323	+	0.218797i
$670$	3.73500e9	−	6.46922e9i	0.479766	−	0.830979i
$671$	2.22494e9	+	1.28457e9i	0.284308	+	0.164145i
$672$			8.39693e8i			0.106740i
$673$	−1.25441e9	+	2.17270e9i	−0.158631	+	0.274756i	−0.934375	−	0.356291i	$-0.884041\pi$
$673$	−1.25441e9	+	2.17270e9i	−0.158631	+	0.274756i	0.775745	+	0.631047i	$0.217375\pi$
$674$		−	7.09319e8i		−	0.0892344i
$675$	−2.60428e9	−	4.51074e9i	−0.325930	−	0.564527i
$676$	−4.66929e7			−0.00581350
$677$	1.15940e10			1.43606			0.718031	−	0.696011i	$-0.245043\pi$
$677$	1.15940e10			1.43606			0.718031	+	0.696011i	$0.245043\pi$
$678$	1.41515e7	+	2.45111e7i	0.00174380	+	0.00302036i
$679$	−1.11970e10	−	6.46461e9i	−1.37265	−	0.792497i
$680$			2.16776e10i			2.64381i
$681$	−1.66604e9	+	9.61888e8i	−0.202148	+	0.116710i
$682$	2.62881e9	+	4.55323e9i	0.317332	+	0.549634i
$683$	−2.76871e9	+	1.59852e9i	−0.332510	+	0.191975i	−0.656955	−	0.753930i	$-0.728156\pi$
$683$	−2.76871e9	+	1.59852e9i	−0.332510	+	0.191975i	0.324445	+	0.945905i	$0.394823\pi$
$684$	−1.89165e8	−	1.09214e8i	−0.0226019	−	0.0130492i
$685$	−4.16067e9	−	2.40216e9i	−0.494591	−	0.285552i
$686$	−6.73164e9	+	3.88651e9i	−0.796134	+	0.459648i
$687$	−1.27505e9	−	2.20845e9i	−0.150030	−	0.259860i
$688$	−8.72174e8	+	5.03550e8i	−0.102104	+	0.0589499i
$689$			7.61254e8i			0.0886670i
$690$	2.17679e9	+	1.25677e9i	0.252257	+	0.145641i
$691$	−3.67876e9	−	6.37180e9i	−0.424159	−	0.734665i	0.572183	−	0.820126i	$-0.306097\pi$
$691$	−3.67876e9	−	6.37180e9i	−0.424159	−	0.734665i	−0.996341	+	0.0854616i	$0.972763\pi$
$692$	−2.36728e8			−0.0271568
$693$	3.81029e9			0.434903
$694$	−1.04780e9	−	1.81484e9i	−0.118993	−	0.206102i
$695$		−	8.06062e8i		−	0.0910797i
$696$	−2.68655e8	+	4.65324e8i	−0.0302039	+	0.0523146i
$697$			5.10677e9i			0.571257i
$698$	−4.77800e9	−	2.75858e9i	−0.531805	−	0.307038i
$699$	−1.13000e9	+	1.95721e9i	−0.125143	+	0.216754i
$700$	−1.30644e9	+	2.26282e9i	−0.143961	+	0.249348i
$701$	−3.42977e9	+	1.98018e9i	−0.376055	+	0.217116i	−0.676101	−	0.736809i	$-0.736332\pi$
$701$	−3.42977e9	+	1.98018e9i	−0.376055	+	0.217116i	0.300045	+	0.953925i	$0.402998\pi$
$702$	3.98538e9			0.434800
$703$	−1.11940e9	+	8.16396e7i	−0.121519	+	0.00886252i
$704$	−5.06670e9			−0.547294
$705$	−2.78789e9	+	1.60959e9i	−0.299650	+	0.173003i
$706$	5.40329e8	−	9.35878e8i	0.0577886	−	0.100093i
$707$	5.52072e9	−	9.56216e9i	0.587526	−	1.01763i
$708$	5.29321e8	+	3.05604e8i	0.0560535	+	0.0323625i
$709$			3.77318e9i			0.397600i	0.980040	+	0.198800i	$0.0637044\pi$
$709$			3.77318e9i			0.397600i	−0.980040	+	0.198800i	$0.936296\pi$
$710$	−1.09710e10	+	1.90024e10i	−1.15039	+	1.99253i
$711$			4.39351e9i			0.458425i
$712$	−8.81662e9	−	1.52708e10i	−0.915424	−	1.58556i
$713$	1.22224e10			1.26282
$714$	3.26556e9			0.335748
$715$	3.71993e9	+	6.44310e9i	0.380595	+	0.659210i
$716$	2.59042e8	+	1.49558e8i	0.0263740	+	0.0152270i
$717$			3.24073e9i			0.328342i
$718$	−1.43081e10	+	8.26081e9i	−1.44261	+	0.832889i
$719$	−1.21964e9	−	2.11248e9i	−0.122372	−	0.211954i	0.798331	−	0.602219i	$-0.205717\pi$
$719$	−1.21964e9	−	2.11248e9i	−0.122372	−	0.211954i	−0.920703	+	0.390265i	$0.872383\pi$
$720$	−8.91670e9	+	5.14806e9i	−0.890308	+	0.514020i
$721$	−9.13575e9	−	5.27453e9i	−0.907759	−	0.524095i
$722$	7.57708e9	+	4.37463e9i	0.749241	+	0.432575i
$723$	9.58633e8	−	5.53467e8i	0.0943340	−	0.0544638i
$724$	1.17003e9	+	2.02656e9i	0.114581	+	0.198460i
$725$	−2.62631e9	+	1.51630e9i	−0.255954	+	0.147775i
$726$			1.73272e9i			0.168055i
$727$	2.58726e9	+	1.49376e9i	0.249730	+	0.144181i	0.619640	−	0.784886i	$-0.287278\pi$
$727$	2.58726e9	+	1.49376e9i	0.249730	+	0.144181i	−0.369911	+	0.929067i	$0.620612\pi$
$728$	−5.36888e9	−	9.29917e9i	−0.515731	−	0.893273i
$729$	−6.66818e9			−0.637472
$730$	2.40534e10			2.28847
$731$	−1.38911e9	−	2.40600e9i	−0.131530	−	0.227816i
$732$		−	4.08989e8i		−	0.0385410i
$733$	−8.92463e9	+	1.54579e10i	−0.837001	+	1.44973i	0.0553890	+	0.998465i	$0.482360\pi$
$733$	−8.92463e9	+	1.54579e10i	−0.837001	+	1.44973i	−0.892390	+	0.451264i	$0.850973\pi$
$734$			1.69165e10i			1.57897i
$735$	−3.91925e8	−	2.26278e8i	−0.0364080	−	0.0210202i
$736$	−2.08250e9	+	3.60700e9i	−0.192537	+	0.333483i
$737$	−1.91280e9	+	3.31306e9i	−0.176008	+	0.304855i
$738$	−2.76911e9	+	1.59875e9i	−0.253596	+	0.146414i
$739$	4.30817e9			0.392679			0.196339	−	0.980536i	$-0.437095\pi$
$739$	4.30817e9			0.392679			0.196339	+	0.980536i	$0.437095\pi$
$740$	1.67839e9	−	3.46748e9i	0.152259	−	0.314560i
$741$	−3.45067e8			−0.0311559
$742$	−6.99496e8	+	4.03854e8i	−0.0628596	+	0.0362920i
$743$	−6.34856e8	+	1.09960e9i	−0.0567825	+	0.0983501i	−0.893019	−	0.450018i	$-0.851417\pi$
$743$	−6.34856e8	+	1.09960e9i	−0.0567825	+	0.0983501i	0.836237	+	0.548368i	$0.184751\pi$
$744$	2.24763e9	−	3.89301e9i	0.200088	−	0.346562i
$745$	2.41201e10	+	1.39257e10i	2.13714	+	1.23388i
$746$		−	1.44334e10i		−	1.27287i
$747$	−9.28142e9	+	1.60759e10i	−0.814689	+	1.41108i
$748$		−	2.06703e9i		−	0.180589i
$749$	−2.79960e9	−	4.84905e9i	−0.243450	−	0.421667i
$750$	1.30406e9			0.112872
$751$	3.37234e9			0.290531			0.145265	−	0.989393i	$-0.453596\pi$
$751$	3.37234e9			0.290531			0.145265	+	0.989393i	$0.453596\pi$
$752$	3.76002e9	+	6.51255e9i	0.322425	+	0.558456i
$753$	−3.73040e9	−	2.15375e9i	−0.318400	−	0.183828i
$754$		−	2.32042e9i		−	0.197137i
$755$	−7.32502e9	+	4.22910e9i	−0.619433	+	0.357630i
$756$	−6.27230e8	−	1.08639e9i	−0.0527959	−	0.0914452i
$757$	3.70418e9	−	2.13861e9i	0.310353	−	0.179182i	−0.336731	−	0.941601i	$-0.609321\pi$
$757$	3.70418e9	−	2.13861e9i	0.310353	−	0.179182i	0.647084	+	0.762418i	$0.275988\pi$
$758$	3.10139e9	+	1.79059e9i	0.258651	+	0.149332i
$759$	−1.11479e9	−	6.43624e8i	−0.0925437	−	0.0534301i
$760$	2.10482e9	−	1.21522e9i	0.173927	−	0.100417i
$761$	2.88613e9	+	4.99893e9i	0.237394	+	0.411178i	0.959966	−	0.280117i	$-0.0903734\pi$
$761$	2.88613e9	+	4.99893e9i	0.237394	+	0.411178i	−0.722572	+	0.691296i	$0.757040\pi$
$762$	−5.26928e8	+	3.04222e8i	−0.0431428	+	0.0249085i
$763$		−	7.01707e9i		−	0.571900i
$764$	2.83213e9	+	1.63513e9i	0.229767	+	0.132656i
$765$	−1.42016e10	−	2.45978e10i	−1.14689	−	1.98647i
$766$	6.92671e9			0.556835
$767$	−1.41766e10			−1.13446
$768$	1.02661e9	+	1.77814e9i	0.0817787	+	0.141645i
$769$		−	1.06914e10i		−	0.847796i	−0.905710	−	0.423898i	$-0.860661\pi$
$769$		−	1.06914e10i		−	0.847796i	0.905710	−	0.423898i	$-0.139339\pi$
$770$	−3.94693e9	+	6.83628e9i	−0.311560	+	0.539638i
$771$		−	3.45364e9i		−	0.271385i
$772$	−2.82696e9	−	1.63215e9i	−0.221136	−	0.127673i
$773$	8.31348e9	−	1.43994e10i	0.647373	−	1.12128i	−0.336375	−	0.941728i	$-0.609201\pi$
$773$	8.31348e9	−	1.43994e10i	0.647373	−	1.12128i	0.983748	−	0.179555i	$-0.0574656\pi$
$774$	8.69759e8	−	1.50647e9i	0.0674226	−	0.116779i
$775$	2.19723e10	−	1.26857e10i	1.69559	−	0.978948i
$776$	−2.35867e10			−1.81197
$777$	−2.80545e9	−	1.35794e9i	−0.214550	−	0.103850i
$778$	1.24128e10			0.945022
$779$	4.95847e8	−	2.86278e8i	0.0375809	−	0.0216973i
$780$	5.92187e8	−	1.02570e9i	0.0446815	−	0.0773906i
$781$	5.61857e9	−	9.73165e9i	0.422034	−	0.730984i
$782$	1.40276e10	+	8.09884e9i	1.04896	+	0.605618i
$783$		−	1.45597e9i		−	0.108389i
$784$	−5.28588e8	+	9.15541e8i	−0.0391752	+	0.0678534i
$785$		−	4.04056e10i		−	2.98125i
$786$	1.98442e9	+	3.43711e9i	0.145765	+	0.252473i
$787$	1.47290e10			1.07712			0.538558	−	0.842588i	$-0.318969\pi$
$787$	1.47290e10			1.07712			0.538558	+	0.842588i	$0.318969\pi$
$788$	1.28856e9			0.0938129
$789$	3.46224e9	+	5.99678e9i	0.250951	+	0.434659i
$790$	−7.88267e9	−	4.55106e9i	−0.568825	−	0.328411i
$791$			2.06634e8i			0.0148452i
$792$	6.01983e9	−	3.47555e9i	0.430572	−	0.248591i
$793$	4.74314e9	+	8.21537e9i	0.337761	+	0.585020i
$794$	−3.19648e9	+	1.84549e9i	−0.226621	+	0.130840i
$795$	−4.14384e8	−	2.39245e8i	−0.0292495	−	0.0168872i
$796$	3.57911e9	+	2.06640e9i	0.251524	+	0.145217i
$797$	−1.65425e10	+	9.55082e9i	−1.15744	+	0.668246i	−0.950688	−	0.310148i	$-0.899621\pi$
$797$	−1.65425e10	+	9.55082e9i	−1.15744	+	0.668246i	−0.206748	+	0.978394i	$0.566288\pi$
$798$	−1.83062e8	−	3.17073e8i	−0.0127523	−	0.0220876i
$799$	−1.79657e10	+	1.03725e10i	−1.24603	+	0.719399i
$800$			8.64581e9i			0.597023i
$801$	2.00086e10	+	1.15520e10i	1.37563	+	0.794223i
$802$	−6.05249e9	−	1.04832e10i	−0.414308	−	0.717603i
$803$	−1.23184e10			−0.839555
$804$	6.09008e8			0.0413264
$805$	9.17543e9	+	1.58923e10i	0.619927	+	1.07375i
$806$			1.94132e10i			1.30595i
$807$	−2.31666e9	+	4.01258e9i	−0.155169	+	0.268761i
$808$		−	2.01428e10i		−	1.34332i
$809$	8.90155e9	+	5.13931e9i	0.591079	+	0.341260i	0.765524	−	0.643407i	$-0.222480\pi$
$809$	8.90155e9	+	5.13931e9i	0.591079	+	0.341260i	−0.174445	+	0.984667i	$0.555813\pi$
$810$	8.24513e9	−	1.42810e10i	0.545129	−	0.944192i
$811$	−2.98282e9	+	5.16640e9i	−0.196361	+	0.340107i	−0.947346	−	0.320213i	$-0.896246\pi$
$811$	−2.98282e9	+	5.16640e9i	−0.196361	+	0.340107i	0.750985	+	0.660319i	$0.229579\pi$
$812$	−6.32535e8	+	3.65194e8i	−0.0414609	+	0.0239375i
$813$	3.13004e9			0.204283
$814$	2.89740e9	−	5.98591e9i	0.188288	−	0.388996i
$815$	2.89201e9			0.187132
$816$	3.91364e9	−	2.25954e9i	0.252154	−	0.145581i
$817$	−1.55742e8	+	2.69753e8i	−0.00999146	+	0.0173057i
$818$	2.78262e9	−	4.81964e9i	0.177753	−	0.307877i
$819$	1.21842e10	+	7.03457e9i	0.775005	+	0.447449i
$820$			1.96518e9i			0.124467i
$821$	−5.06415e9	+	8.77136e9i	−0.319378	+	0.553179i	−0.980358	−	0.197224i	$-0.936807\pi$
$821$	−5.06415e9	+	8.77136e9i	−0.319378	+	0.553179i	0.660980	+	0.750403i	$0.270141\pi$
$822$			1.32030e9i			0.0829127i
$823$	4.43583e9	+	7.68308e9i	0.277380	+	0.480436i	0.970733	−	0.240162i	$-0.0772006\pi$
$823$	4.43583e9	+	7.68308e9i	0.277380	+	0.480436i	−0.693353	+	0.720598i	$0.743867\pi$
$824$	−1.92446e10			−1.19829
$825$	−2.67210e9			−0.165678
$826$	−7.52087e9	−	1.30265e10i	−0.464342	−	0.804264i
$827$	−2.18353e10	−	1.26066e10i	−1.34242	−	0.775048i	−0.355260	−	0.934768i	$-0.615608\pi$
$827$	−2.18353e10	−	1.26066e10i	−1.34242	−	0.775048i	−0.987162	+	0.159720i	$0.948941\pi$
$828$		−	3.00869e9i		−	0.184192i
$829$	8.36739e9	−	4.83091e9i	0.510093	−	0.294502i	−0.222779	−	0.974869i	$-0.571513\pi$
$829$	8.36739e9	−	4.83091e9i	0.510093	−	0.294502i	0.732872	+	0.680367i	$0.238180\pi$
$830$	−1.92285e10	−	3.33047e10i	−1.16727	−	2.02177i
$831$	−1.12713e9	+	6.50747e8i	−0.0681348	+	0.0393377i
$832$	−1.62018e10	−	9.35414e9i	−0.975288	−	0.563083i
$833$	−2.52563e9	−	1.45818e9i	−0.151395	−	0.0874082i
$834$	−1.91840e8	+	1.10759e8i	−0.0114514	+	0.00661146i
$835$	−5.09454e9	−	8.82401e9i	−0.302833	−	0.524521i
$836$	−2.00701e8	+	1.15875e8i	−0.0118803	+	0.00685909i
$837$			1.21810e10i			0.718032i
$838$	1.25773e10	+	7.26153e9i	0.738304	+	0.426260i
$839$	−2.83180e9	−	4.90482e9i	−0.165537	−	0.286719i	0.771309	−	0.636461i	$-0.219602\pi$
$839$	−2.83180e9	−	4.90482e9i	−0.165537	−	0.286719i	−0.936846	+	0.349742i	$0.886269\pi$
$840$	6.74926e9			0.392897
$841$	1.64022e10			0.950857
$842$	3.49233e8	+	6.04889e8i	0.0201615	+	0.0349207i
$843$		−	3.46909e9i		−	0.199443i
$844$	−2.23143e9	+	3.86495e9i	−0.127757	+	0.221282i
$845$			6.80736e8i			0.0388132i
$846$	−1.12488e10	−	6.49452e9i	−0.638721	−	0.368766i
$847$	−6.32514e9	+	1.09555e10i	−0.357667	+	0.619497i
$848$	−5.58878e8	+	9.68005e8i	−0.0314725	+	0.0545120i
$849$	−2.77951e9	+	1.60475e9i	−0.155880	+	0.0899976i
$850$	3.36235e10			1.87792
$851$	−8.68333e9	−	1.27909e10i	−0.482984	−	0.711456i
$852$	−1.78888e9			−0.0990927
$853$	1.17567e10	−	6.78772e9i	0.648579	−	0.374457i	−0.139332	−	0.990246i	$-0.544496\pi$
$853$	1.17567e10	−	6.78772e9i	0.648579	−	0.374457i	0.787912	+	0.615788i	$0.211162\pi$
$854$	−5.03259e9	+	8.71670e9i	−0.276496	+	0.478905i
$855$	−1.59224e9	+	2.75783e9i	−0.0871216	+	0.150899i
$856$	−8.84609e9	−	5.10729e9i	−0.482051	−	0.278312i
$857$		−	1.02044e10i		−	0.553801i	−0.960899	−	0.276900i	$-0.910693\pi$
$857$		−	1.02044e10i		−	0.553801i	0.960899	−	0.276900i	$-0.0893072\pi$
$858$	1.02229e9	−	1.77066e9i	0.0552547	−	0.0957039i
$859$			3.25675e10i			1.75311i	0.481304	+	0.876554i	$0.340163\pi$
$859$			3.25675e10i			1.75311i	−0.481304	+	0.876554i	$0.659837\pi$
$860$	−5.34554e8	−	9.25875e8i	−0.0286581	−	0.0496373i
$861$	1.58997e9			0.0848944
$862$	−1.28143e10			−0.681426
$863$	1.52341e10	+	2.63863e10i	0.806826	+	1.39746i	0.915051	+	0.403338i	$0.132150\pi$
$863$	1.52341e10	+	2.63863e10i	0.806826	+	1.39746i	−0.108225	+	0.994126i	$0.534517\pi$
$864$	−3.59479e9	−	2.07545e9i	−0.189616	−	0.109475i
$865$			3.45125e9i			0.181309i
$866$	1.60940e10	−	9.29189e9i	0.842077	−	0.486173i
$867$	3.81034e9	+	6.59970e9i	0.198562	+	0.343920i
$868$	5.29194e9	−	3.05531e9i	0.274661	−	0.158575i
$869$	4.03692e9	+	2.33072e9i	0.208680	+	0.120482i
$870$	1.26311e9	+	7.29256e8i	0.0650314	+	0.0375459i
$871$	−1.22332e10	+	7.06281e9i	−0.627299	+	0.362171i
$872$	−6.40060e9	−	1.10862e10i	−0.326899	−	0.566205i
$873$	2.67640e10	−	1.54522e10i	1.36145	−	0.786033i
$874$		−	1.81603e9i		−	0.0920097i
$875$	8.24520e9	+	4.76037e9i	0.416076	+	0.240222i
$876$	9.80501e8	+	1.69828e9i	0.0492815	+	0.0853580i
$877$	−3.44352e10			−1.72387			−0.861933	−	0.507022i	$-0.830746\pi$
$877$	−3.44352e10			−1.72387			−0.861933	+	0.507022i	$0.830746\pi$
$878$	−6.19857e9			−0.309073
$879$	1.65740e9	+	2.87070e9i	0.0823125	+	0.142569i
$880$			1.09240e10i			0.540372i
$881$	−1.62732e10	+	2.81860e10i	−0.801785	+	1.38873i	0.116656	+	0.993172i	$0.462783\pi$
$881$	−1.62732e10	+	2.81860e10i	−0.801785	+	1.38873i	−0.918440	+	0.395559i	$0.870551\pi$
$882$		−	1.82601e9i		−	0.0896114i
$883$	1.55889e10	+	9.00026e9i	0.761997	+	0.439939i	0.830012	−	0.557745i	$-0.188333\pi$
$883$	1.55889e10	+	9.00026e9i	0.761997	+	0.439939i	−0.0680154	+	0.997684i	$0.521667\pi$
$884$	3.81616e9	−	6.60978e9i	0.185799	−	0.321813i
$885$	4.45539e9	−	7.71696e9i	0.216065	−	0.374236i
$886$	2.03565e10	−	1.17528e10i	0.983297	−	0.567707i
$887$	2.59491e10			1.24850			0.624252	−	0.781223i	$-0.285404\pi$
$887$	2.59491e10			1.24850			0.624252	+	0.781223i	$0.285404\pi$
$888$	−5.67093e9	+	4.13589e8i	−0.271774	+	0.0198209i
$889$	−4.44213e9			−0.212049
$890$	−4.14522e10	+	2.39325e10i	−1.97098	+	1.13795i
$891$	−4.22255e9	+	7.31367e9i	−0.199987	+	0.346388i
$892$	−2.42603e9	+	4.20201e9i	−0.114451	+	0.198235i
$893$	2.01426e9	+	1.16293e9i	0.0946531	+	0.0546480i
$894$		−	7.65400e9i		−	0.358267i
$895$	2.18041e9	−	3.77658e9i	0.101662	−	0.176083i
$896$		−	1.07485e10i		−	0.499194i
$897$	−2.37652e9	−	4.11625e9i	−0.109943	−	0.190427i
$898$	−1.51342e10			−0.697418
$899$	7.09219e9			0.325553
$900$	−3.12276e9	−	5.40877e9i	−0.142787	−	0.247315i
$901$	−2.67036e9	−	1.54174e9i	−0.121628	−	0.0702220i
$902$			3.39249e9i			0.153920i
$903$	−7.49100e8	+	4.32493e8i	−0.0338558	+	0.0195466i
$904$	1.88481e8	+	3.26459e8i	0.00848551	+	0.0146973i
$905$	2.95451e10	−	1.70579e10i	1.32500	−	0.764989i
$906$	2.01302e9	+	1.16222e9i	0.0899291	+	0.0519206i
$907$	−1.38407e10	−	7.99096e9i	−0.615934	−	0.355609i	0.159351	−	0.987222i	$-0.449060\pi$
$907$	−1.38407e10	−	7.99096e9i	−0.615934	−	0.355609i	−0.775284	+	0.631613i	$0.782393\pi$
$908$	−4.13151e9	+	2.38533e9i	−0.183151	+	0.105742i
$909$	1.31961e10	+	2.28562e10i	0.582734	+	1.00933i
$910$	−2.52423e10	+	1.45737e10i	−1.11041	+	0.641097i
$911$			1.10481e10i			0.484143i	0.970258	+	0.242071i	$0.0778268\pi$
$911$			1.10481e10i			0.484143i	−0.970258	+	0.242071i	$0.922173\pi$
$912$	−4.38785e8	−	2.53333e8i	−0.0191545	−	0.0110588i
$913$	9.84743e9	+	1.70562e10i	0.428228	+	0.741713i
$914$	−1.84126e10			−0.797632
$915$	−5.96265e9			−0.257315
$916$	−3.16192e9	−	5.47661e9i	−0.135931	−	0.235439i
$917$			2.89757e10i			1.24091i
$918$	−8.07142e9	+	1.39801e10i	−0.344350	+	0.596432i
$919$			2.20180e10i			0.935778i	0.883787	+	0.467889i	$0.154985\pi$
$919$			2.20180e10i			0.935778i	−0.883787	+	0.467889i	$0.845015\pi$
$920$	2.89922e10	+	1.67387e10i	1.22751	+	0.708702i
$921$	2.82123e9	−	4.88652e9i	0.118995	−	0.206106i
$922$	1.11768e10	−	1.93588e10i	0.469635	−	0.813432i
$923$	3.59331e10	−	2.07460e10i	1.50414	−	0.868418i
$924$	−6.43564e8			−0.0268374
$925$	−2.88860e10	−	1.39819e10i	−1.20003	−	0.580858i
$926$	4.22603e10			1.74902
$927$	2.18370e10	−	1.26076e10i	0.900355	−	0.519820i
$928$	−1.20840e9	+	2.09301e9i	−0.0496355	+	0.0859712i
$929$	−9.93078e9	+	1.72006e10i	−0.406376	+	0.703864i	−0.994481	−	0.104921i	$-0.966541\pi$
$929$	−9.93078e9	+	1.72006e10i	−0.406376	+	0.703864i	0.588104	+	0.808785i	$0.299874\pi$
$930$	−1.05675e10	−	6.10113e9i	−0.430805	−	0.248725i
$931$			3.26972e8i			0.0132797i
$932$	−2.80222e9	+	4.85358e9i	−0.113382	+	0.196384i
$933$		−	4.23758e9i		−	0.170818i
$934$	−5.10214e9	−	8.83717e9i	−0.204898	−	0.354895i
$935$	−3.01352e10			−1.20569
$936$	2.56662e10			1.02305
$937$	−5.06278e9	−	8.76900e9i	−0.201048	−	0.348226i	0.747818	−	0.663904i	$-0.231102\pi$
$937$	−5.06278e9	−	8.76900e9i	−0.201048	−	0.348226i	−0.948867	+	0.315678i	$0.897768\pi$
$938$	−1.29797e10	−	7.49381e9i	−0.513516	−	0.296478i
$939$		−	5.50092e9i		−	0.216823i
$940$	−6.91354e9	+	3.99153e9i	−0.271489	+	0.156744i
$941$	−1.66908e10	−	2.89092e10i	−0.652999	−	1.13103i	−0.982391	−	0.186834i	$-0.940177\pi$
$941$	−1.66908e10	−	2.89092e10i	−0.652999	−	1.13103i	0.329392	−	0.944193i	$-0.393156\pi$
$942$	−9.61640e9	+	5.55203e9i	−0.374830	+	0.216408i
$943$	6.82992e9	+	3.94326e9i	0.265231	+	0.153131i
$944$	−1.80269e10	−	1.04078e10i	−0.697460	−	0.402679i
$945$	−1.58385e10	+	9.14437e9i	−0.610525	+	0.352487i
$946$	−9.22799e8	−	1.59834e9i	−0.0354396	−	0.0613831i
$947$	−1.40999e10	+	8.14057e9i	−0.539499	+	0.311480i	−0.744876	−	0.667203i	$-0.767491\pi$
$947$	−1.40999e10	+	8.14057e9i	−0.539499	+	0.311480i	0.205377	+	0.978683i	$0.434158\pi$
$948$		−	7.42070e8i		−	0.0282889i
$949$	−3.93906e10	−	2.27422e10i	−1.49610	−	0.863775i
$950$	−1.88488e9	−	3.26471e9i	−0.0713265	−	0.123541i
$951$	1.02685e10			0.387147
$952$	4.34935e10			1.63378
$953$	5.70488e9	+	9.88113e9i	0.213511	+	0.369813i	0.952811	−	0.303564i	$-0.0981766\pi$
$953$	5.70488e9	+	9.88113e9i	0.213511	+	0.369813i	−0.739300	+	0.673377i	$0.764843\pi$
$954$		−	1.93065e9i		−	0.0719920i
$955$	2.38386e10	−	4.12896e10i	0.885664	−	1.53401i
$956$			8.03650e9i			0.297485i
$957$	−6.46872e8	−	3.73471e8i	−0.0238576	−	0.0137742i
$958$	−2.26772e10	+	3.92781e10i	−0.833318	+	1.44335i
$959$	−4.81963e9	+	8.34785e9i	−0.176461	+	0.305640i
$960$	1.01837e10	−	5.87958e9i	0.371499	−	0.214485i
$961$	−3.18224e10			−1.15665
$962$	2.03163e10	−	1.37920e10i	0.735751	−	0.499477i
$963$	1.33837e10			0.482928
$964$	2.37726e9	−	1.37251e9i	0.0854686	−	0.0493453i
$965$	−2.37950e10	+	4.12142e10i	−0.852394	+	1.47639i
$966$	2.52155e9	−	4.36744e9i	0.0900009	−	0.155886i
$967$	−3.68533e10	−	2.12773e10i	−1.31064	−	0.756699i	−0.328439	−	0.944525i	$-0.606523\pi$
$967$	−3.68533e10	−	2.12773e10i	−1.31064	−	0.756699i	−0.982202	+	0.187826i	$0.939856\pi$
$968$			2.30778e10i			0.817770i
$969$	6.98850e8	−	1.21044e9i	0.0246746	−	0.0427377i
$970$			6.40253e10i			2.25243i
$971$	7.60281e9	+	1.31685e10i	0.266506	+	0.461602i	0.967957	−	0.251116i	$-0.0807975\pi$
$971$	7.60281e9	+	1.31685e10i	0.266506	+	0.461602i	−0.701451	+	0.712718i	$0.747464\pi$
$972$	4.54714e9			0.158820
$973$	−1.61726e9			−0.0562840
$974$	−6.81503e8	−	1.18040e9i	−0.0236326	−	0.0409328i
$975$	−8.54461e9	−	4.93323e9i	−0.295241	−	0.170457i
$976$			1.39288e10i			0.479556i
$977$	−2.98711e10	+	1.72461e10i	−1.02476	+	0.591644i	−0.915478	−	0.402367i	$-0.868187\pi$
$977$	−2.98711e10	+	1.72461e10i	−1.02476	+	0.591644i	−0.109279	+	0.994011i	$0.534854\pi$
$978$	−3.97384e8	−	6.88289e8i	−0.0135839	−	0.0235280i
$979$	2.12288e10	−	1.22565e10i	0.723079	−	0.417470i
$980$	−9.71912e8	−	5.61134e8i	−0.0329864	−	0.0190447i
$981$	1.45257e10	+	8.38639e9i	0.491240	+	0.283618i
$982$	1.10536e10	−	6.38178e9i	0.372488	−	0.215056i
$983$	−1.92524e10	−	3.33461e10i	−0.646469	−	1.11972i	−0.983960	−	0.178388i	$-0.942912\pi$
$983$	−1.92524e10	−	3.33461e10i	−0.646469	−	1.11972i	0.337492	−	0.941329i	$-0.390422\pi$
$984$	2.51198e9	−	1.45029e9i	0.0840490	−	0.0485257i
$985$		−	1.87859e10i		−	0.626332i
$986$	8.13969e9	+	4.69945e9i	0.270420	+	0.156127i
$987$	3.22944e9	+	5.59356e9i	0.106910	+	0.185173i
$988$	−8.55712e8			−0.0282279
$989$	−4.29046e9			−0.141032
$990$	−9.43427e9	−	1.63406e10i	−0.309019	−	0.535237i
$991$		−	1.17434e10i		−	0.383296i	−0.981464	−	0.191648i	$-0.938617\pi$
$991$		−	1.17434e10i		−	0.383296i	0.981464	−	0.191648i	$-0.0613833\pi$
$992$	1.01098e10	−	1.75106e10i	0.328814	−	0.569522i
$993$		−	2.79489e8i		−	0.00905822i
$994$	3.81259e10	+	2.20120e10i	1.23131	+	0.710898i
$995$	3.01260e10	−	5.21798e10i	0.969529	−	1.67927i
$996$	1.56764e9	−	2.71524e9i	0.0502736	−	0.0870764i
$997$	4.92724e10	−	2.84475e10i	1.57460	−	0.909097i	0.579009	−	0.815321i	$-0.303439\pi$
$997$	4.92724e10	−	2.84475e10i	1.57460	−	0.909097i	0.995593	−	0.0937765i	$-0.0298939\pi$
$998$	3.10220e10			0.987899
$999$	1.27476e10	−	8.65394e9i	0.404529	−	0.274622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.e.a.11.6	✓	40
37.27	even	6	inner	37.8.e.a.27.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.e.a.11.6	✓	40	1.1	even	1	trivial
37.8.e.a.27.6	yes	40	37.27	even	6	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.60443 + 4.96777i) q^{2} +(-5.90461 + 10.2271i) q^{3} +(-14.6425 + 25.3615i) q^{4} +(369.746 + 213.473i) q^{5} -117.331i q^{6} +(428.306 - 741.848i) q^{7} -1562.71i q^{8} +(1023.77 + 1773.22i) q^{9} +O(q^{10})\)	\(q+(-8.60443 + 4.96777i) q^{2} +(-5.90461 + 10.2271i) q^{3} +(-14.6425 + 25.3615i) q^{4} +(369.746 + 213.473i) q^{5} -117.331i q^{6} +(428.306 - 741.848i) q^{7} -1562.71i q^{8} +(1023.77 + 1773.22i) q^{9} -4241.93 q^{10} +2172.41 q^{11} +(-172.916 - 299.500i) q^{12} +(6946.74 + 4010.70i) q^{13} +8510.90i q^{14} +(-4366.40 + 2520.95i) q^{15} +(5888.96 + 10200.0i) q^{16} +(-28137.9 + 16245.4i) q^{17} +(-17617.9 - 10171.7i) q^{18} +(3154.73 + 1821.39i) q^{19} +(-10828.0 + 6251.55i) q^{20} +(5057.96 + 8760.64i) q^{21} +(-18692.3 + 10792.0i) q^{22} +50176.5i q^{23} +(15982.0 + 9227.20i) q^{24} +(52078.7 + 90202.9i) q^{25} -79697.0 q^{26} -50006.6 q^{27} +(12542.9 + 21725.0i) q^{28} +29115.5i q^{29} +(25047.0 - 43382.6i) q^{30} -243588. i q^{31} +(71886.3 + 41503.6i) q^{32} +(-12827.2 + 22217.4i) q^{33} +(161407. - 279565. i) q^{34} +(316728. - 182863. i) q^{35} -59962.3 q^{36} +(-254919. + 173056. i) q^{37} -36192.9 q^{38} +(-82035.6 + 47363.3i) q^{39} +(333596. - 577806. i) q^{40} +(78587.8 - 136118. i) q^{41} +(-87041.7 - 50253.5i) q^{42} +85507.5i q^{43} +(-31809.5 + 55095.6i) q^{44} +874189. i q^{45} +(-249265. - 431740. i) q^{46} +638487. q^{47} -139088. q^{48} +(44879.6 + 77733.7i) q^{49} +(-896215. - 517430. i) q^{50} -383691. i q^{51} +(-203435. + 117453. i) q^{52} +(47451.4 + 82188.2i) q^{53} +(430279. - 248421. i) q^{54} +(803238. + 463750. i) q^{55} +(-1.15929e6 - 669319. i) q^{56} +(-37254.9 + 21509.1i) q^{57} +(-144639. - 250523. i) q^{58} +(-1.53057e6 + 883675. i) q^{59} -147652. i q^{60} +(1.02418e6 + 591311. i) q^{61} +(1.21009e6 + 2.09593e6i) q^{62} +1.75395e6 q^{63} -2.33229e6 q^{64} +(1.71235e6 + 2.96588e6i) q^{65} -254891. i q^{66} +(-880496. + 1.52506e6i) q^{67} -951494. i q^{68} +(-513159. - 296272. i) q^{69} +(-1.81685e6 + 3.14687e6i) q^{70} +(2.58633e6 - 4.47966e6i) q^{71} +(2.77104e6 - 1.59986e6i) q^{72} -5.67038e6 q^{73} +(1.33373e6 - 2.75543e6i) q^{74} -1.23002e6 q^{75} +(-92386.4 + 53339.3i) q^{76} +(930455. - 1.61160e6i) q^{77} +(470580. - 815068. i) q^{78} +(1.85827e6 + 1.07287e6i) q^{79} +5.02852e6i q^{80} +(-1.94372e6 + 3.36662e6i) q^{81} +1.56162e6i q^{82} +(4.53295e6 + 7.85131e6i) q^{83} -296244. q^{84} -1.38718e7 q^{85} +(-424782. - 735744. i) q^{86} +(-297767. - 171916. i) q^{87} -3.39485e6i q^{88} +(9.77201e6 - 5.64187e6i) q^{89} +(-4.34277e6 - 7.52190e6i) q^{90} +(5.95066e6 - 3.43562e6i) q^{91} +(-1.27255e6 - 734709. i) q^{92} +(2.49119e6 + 1.43829e6i) q^{93} +(-5.49382e6 + 3.17186e6i) q^{94} +(777633. + 1.34690e6i) q^{95} +(-848921. + 490125. i) q^{96} -1.50934e7i q^{97} +(-772327. - 445903. i) q^{98} +(2.22405e6 + 3.85217e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Introduction

L-functions

Modular forms

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