LMFDB - Embedded newform 76.7.l.a.23.1

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			23.1
Character	$\chi$	$=$	76.23
Dual form			76.7.l.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.99410 + 0.307308i) q^{2} +(-27.6808 + 4.88087i) q^{3} +(63.8111 - 4.91330i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(219.783 - 47.5247i) q^{6} +(-83.9559 - 48.4720i) q^{7} +(-508.602 + 58.8871i) q^{8} +(57.3665 - 20.8797i) q^{9} +O(q^{10})$	\(q+(-7.99410 + 0.307308i) q^{2} +(-27.6808 + 4.88087i) q^{3} +(63.8111 - 4.91330i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(219.783 - 47.5247i) q^{6} +(-83.9559 - 48.4720i) q^{7} +(-508.602 + 58.8871i) q^{8} +(57.3665 - 20.8797i) q^{9} +(263.858 - 239.264i) q^{10} +(-815.927 + 471.076i) q^{11} +(-1742.36 + 447.458i) q^{12} +(-755.075 + 4282.24i) q^{13} +(686.047 + 361.689i) q^{14} +(804.416 - 958.666i) q^{15} +(4047.72 - 627.047i) q^{16} +(-3638.63 - 1324.35i) q^{17} +(-452.177 + 184.544i) q^{18} +(-6812.71 - 795.568i) q^{19} +(-2035.78 + 1993.79i) q^{20} +(2560.55 + 931.964i) q^{21} +(6377.83 - 4016.57i) q^{22} +(10416.9 - 12414.4i) q^{23} +(13791.1 - 4112.46i) q^{24} +(-2369.03 + 13435.4i) q^{25} +(4720.17 - 34464.7i) q^{26} +(16259.3 - 9387.33i) q^{27} +(-5595.48 - 2680.55i) q^{28} +(36648.4 - 13338.9i) q^{29} +(-6135.97 + 7910.87i) q^{30} +(-40577.6 - 23427.5i) q^{31} +(-32165.2 + 6256.57i) q^{32} +(20286.2 - 17022.2i) q^{33} +(29494.6 + 9468.83i) q^{34} +(4250.68 - 749.510i) q^{35} +(3558.03 - 1614.22i) q^{36} +58049.8 q^{37} +(54705.9 + 4266.24i) q^{38} -122221. i q^{39} +(15661.5 - 16564.1i) q^{40} +(2165.93 + 12283.6i) q^{41} +(-20755.7 - 6663.33i) q^{42} +(11932.4 + 14220.4i) q^{43} +(-49750.7 + 34068.8i) q^{44} +(-1359.03 + 2353.91i) q^{45} +(-79458.9 + 102443. i) q^{46} +(-4562.85 - 12536.3i) q^{47} +(-108983. + 37113.5i) q^{48} +(-54125.4 - 93748.0i) q^{49} +(14809.4 - 108132. i) q^{50} +(107184. + 18899.5i) q^{51} +(-27142.2 + 276965. i) q^{52} +(48900.6 + 41032.4i) q^{53} +(-127094. + 80039.8i) q^{54} +(14346.9 - 39417.9i) q^{55} +(45554.5 + 19709.0i) q^{56} +(192464. - 11230.0i) q^{57} +(-288872. + 117895. i) q^{58} +(75569.9 - 207627. i) q^{59} +(46620.5 - 65125.9i) q^{60} +(-165600. - 138955. i) q^{61} +(331581. + 174812. i) q^{62} +(-5828.34 - 1027.69i) q^{63} +(255209. - 59900.2i) q^{64} +(-96800.3 - 167663. i) q^{65} +(-156939. + 142311. i) q^{66} +(28802.8 + 79135.0i) q^{67} +(-238692. - 66630.8i) q^{68} +(-227756. + 394485. i) q^{69} +(-33750.0 + 7297.92i) q^{70} +(32265.4 + 38452.4i) q^{71} +(-27947.2 + 13997.6i) q^{72} +(116889. + 662910. i) q^{73} +(-464056. + 17839.2i) q^{74} -383466. i q^{75} +(-438635. - 17293.2i) q^{76} +91335.9 q^{77} +(37559.6 + 977049. i) q^{78} +(388719. - 68541.7i) q^{79} +(-120109. + 137228. i) q^{80} +(-438345. + 367815. i) q^{81} +(-21089.5 - 97530.8i) q^{82} +(-564813. - 326095. i) q^{83} +(167971. + 46888.9i) q^{84} +(162004. - 58964.5i) q^{85} +(-99758.4 - 110013. i) q^{86} +(-949351. + 548108. i) q^{87} +(387242. - 287638. i) q^{88} +(150198. - 851816. i) q^{89} +(10140.8 - 19235.0i) q^{90} +(270962. - 322920. i) q^{91} +(603721. - 843360. i) q^{92} +(1.23757e6 + 450437. i) q^{93} +(40328.3 + 98814.3i) q^{94} +(255128. - 167838. i) q^{95} +(859819. - 330181. i) q^{96} +(-624554. - 227319. i) q^{97} +(461493. + 732797. i) q^{98} +(-36971.0 + 44060.3i) 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 $

$2$	−7.99410	+	0.307308i	−0.999262	+	0.0384135i
$2$	−7.99410	+	0.307308i	−0.999262	+	0.0384135i
$3$	−27.6808	+	4.88087i	−1.02521	+	0.180773i	−0.660877	−	0.750494i	$-0.729815\pi$
$3$	−27.6808	+	4.88087i	−1.02521	+	0.180773i	−0.364337	+	0.931267i	$0.618704\pi$
$4$	63.8111	−	4.91330i	0.997049	−	0.0767704i
$5$	−34.1068	+	28.6190i	−0.272854	+	0.228952i	−0.768939	−	0.639322i	$-0.779215\pi$
$5$	−34.1068	+	28.6190i	−0.272854	+	0.228952i	0.496085	+	0.868274i	$0.334771\pi$
$6$	219.783	−	47.5247i	1.01751	−	0.220022i
$7$	−83.9559	−	48.4720i	−0.244769	−	0.141318i	0.372597	−	0.927993i	$-0.378467\pi$
$7$	−83.9559	−	48.4720i	−0.244769	−	0.141318i	−0.617367	+	0.786675i	$0.711801\pi$
$8$	−508.602	+	58.8871i	−0.993364	+	0.115014i
$9$	57.3665	−	20.8797i	0.0786921	−	0.0286416i
$10$	263.858	−	239.264i	0.263858	−	0.239264i
$11$	−815.927	+	471.076i	−0.613018	+	0.353926i	−0.774146	−	0.633007i	$-0.781820\pi$
$11$	−815.927	+	471.076i	−0.613018	+	0.353926i	0.161128	+	0.986934i	$0.448487\pi$
$12$	−1742.36	+	447.458i	−1.00831	+	0.258945i
$13$	−755.075	+	4282.24i	−0.343685	+	1.94913i	−0.0301859	+	0.999544i	$0.509610\pi$
$13$	−755.075	+	4282.24i	−0.343685	+	1.94913i	−0.313499	+	0.949589i	$0.601501\pi$
$14$	686.047	+	361.689i	0.250017	+	0.131811i
$15$	804.416	−	958.666i	0.238346	−	0.284049i
$16$	4047.72	−	627.047i	0.988213	−	0.153088i
$17$	−3638.63	−	1324.35i	−0.740613	−	0.269561i	−0.0559630	−	0.998433i	$-0.517823\pi$
$17$	−3638.63	−	1324.35i	−0.740613	−	0.269561i	−0.684650	+	0.728872i	$0.740045\pi$
$18$	−452.177	+	184.544i	−0.0775338	+	0.0316433i
$19$	−6812.71	−	795.568i	−0.993251	−	0.115989i
$19$	−6812.71	−	795.568i	−0.993251	−	0.115989i
$20$	−2035.78	+	1993.79i	−0.254472	+	0.249223i
$21$	2560.55	+	931.964i	0.276487	+	0.100633i
$22$	6377.83	−	4016.57i	0.598970	−	0.377213i
$23$	10416.9	−	12414.4i	0.856163	−	1.02034i	−0.143367	−	0.989670i	$-0.545793\pi$
$23$	10416.9	−	12414.4i	0.856163	−	1.02034i	0.999530	−	0.0306658i	$-0.00976277\pi$
$24$	13791.1	−	4112.46i	0.997619	−	0.297487i
$25$	−2369.03	+	13435.4i	−0.151618	+	0.859867i
$26$	4720.17	−	34464.7i	0.268558	−	1.96090i
$27$	16259.3	−	9387.33i	0.826059	−	0.476926i
$28$	−5595.48	−	2680.55i	−0.254896	−	0.122110i
$29$	36648.4	−	13338.9i	1.50266	−	0.546924i	0.545913	−	0.837842i	$-0.316183\pi$
$29$	36648.4	−	13338.9i	1.50266	−	0.546924i	0.956748	+	0.290918i	$0.0939607\pi$
$30$	−6135.97	+	7910.87i	−0.227258	+	0.292995i
$31$	−40577.6	−	23427.5i	−1.36208	−	0.786395i	−0.372176	−	0.928162i	$-0.621388\pi$
$31$	−40577.6	−	23427.5i	−1.36208	−	0.786395i	−0.989900	+	0.141767i	$0.954722\pi$
$32$	−32165.2	+	6256.57i	−0.981603	+	0.190935i
$33$	20286.2	−	17022.2i	0.564494	−	0.473667i
$34$	29494.6	+	9468.83i	0.750422	+	0.240913i
$35$	4250.68	−	749.510i	0.0991413	−	0.0174813i
$36$	3558.03	−	1614.22i	0.0762610	−	0.0345983i
$37$	58049.8			1.14603			0.573015	−	0.819545i	$-0.305774\pi$
$37$	58049.8			1.14603			0.573015	+	0.819545i	$0.305774\pi$
$38$	54705.9	+	4266.24i	0.996973	+	0.0777490i
$39$		−	122221.i		−	2.06041i
$40$	15661.5	−	16564.1i	0.244711	−	0.258814i
$41$	2165.93	+	12283.6i	0.0314263	+	0.178227i	0.996481	−	0.0838220i	$-0.0267127\pi$
$41$	2165.93	+	12283.6i	0.0314263	+	0.178227i	−0.965054	+	0.262050i	$0.915602\pi$
$42$	−20755.7	−	6663.33i	−0.280149	−	0.0899381i
$43$	11932.4	+	14220.4i	0.150079	+	0.178858i	0.835846	−	0.548964i	$-0.184977\pi$
$43$	11932.4	+	14220.4i	0.150079	+	0.178858i	−0.685767	+	0.727821i	$0.740533\pi$
$44$	−49750.7	+	34068.8i	−0.584038	+	0.399943i
$45$	−1359.03	+	2353.91i	−0.0149139	+	0.0258317i
$46$	−79458.9	+	102443.i	−0.816337	+	1.05247i
$47$	−4562.85	−	12536.3i	−0.0439483	−	0.120747i	0.915777	−	0.401687i	$-0.131576\pi$
$47$	−4562.85	−	12536.3i	−0.0439483	−	0.120747i	−0.959725	+	0.280940i	$0.909354\pi$
$48$	−108983.	+	37113.5i	−0.985455	+	0.335590i
$49$	−54125.4	−	93748.0i	−0.460059	−	0.796845i
$50$	14809.4	−	108132.i	0.118475	−	0.865056i
$51$	107184.	+	18899.5i	0.808017	+	0.142475i
$52$	−27142.2	+	276965.i	−0.193035	+	1.96977i
$53$	48900.6	+	41032.4i	0.328463	+	0.275613i	0.792073	−	0.610426i	$-0.209002\pi$
$53$	48900.6	+	41032.4i	0.328463	+	0.275613i	−0.463610	+	0.886039i	$0.653446\pi$
$54$	−127094.	+	80039.8i	−0.807129	+	0.508305i
$55$	14346.9	−	39417.9i	0.0862325	−	0.236922i
$56$	45554.5	+	19709.0i	0.259399	+	0.112228i
$57$	192464.	−	11230.0i	1.03926	−	0.0606393i
$58$	−288872.	+	117895.i	−1.48054	+	0.604243i
$59$	75569.9	−	207627.i	0.367953	−	1.01094i	−0.608185	−	0.793795i	$-0.708102\pi$
$59$	75569.9	−	207627.i	0.367953	−	1.01094i	0.976139	−	0.217148i	$-0.0696755\pi$
$60$	46620.5	−	65125.9i	0.215836	−	0.301509i
$61$	−165600.	−	138955.i	−0.729575	−	0.612186i	0.200441	−	0.979706i	$-0.435763\pi$
$61$	−165600.	−	138955.i	−0.729575	−	0.612186i	−0.930016	+	0.367520i	$0.880207\pi$
$62$	331581.	+	174812.i	1.39128	+	0.733492i
$63$	−5828.34	−	1027.69i	−0.0233090	−	0.00411000i
$64$	255209.	−	59900.2i	0.973544	−	0.228501i
$65$	−96800.3	−	167663.i	−0.352482	−	0.610516i
$66$	−156939.	+	142311.i	−0.545883	+	0.495002i
$67$	28802.8	+	79135.0i	0.0957657	+	0.263114i	0.978321	−	0.207095i	$-0.0664008\pi$
$67$	28802.8	+	79135.0i	0.0957657	+	0.263114i	−0.882555	+	0.470209i	$0.844179\pi$
$68$	−238692.	−	66630.8i	−0.759122	−	0.211909i
$69$	−227756.	+	394485.i	−0.693301	+	1.20083i
$70$	−33750.0	+	7297.92i	−0.0983966	+	0.0212767i
$71$	32265.4	+	38452.4i	0.0901491	+	0.107436i	0.809233	−	0.587487i	$-0.199883\pi$
$71$	32265.4	+	38452.4i	0.0901491	+	0.107436i	−0.719084	+	0.694923i	$0.755438\pi$
$72$	−27947.2	+	13997.6i	−0.0748757	+	0.0375022i
$73$	116889.	+	662910.i	0.300473	+	1.70406i	0.644086	+	0.764953i	$0.277238\pi$
$73$	116889.	+	662910.i	0.300473	+	1.70406i	−0.343613	+	0.939111i	$0.611651\pi$
$74$	−464056.	+	17839.2i	−1.14518	+	0.0440230i
$75$		−	383466.i		−	0.908956i
$76$	−438635.	−	17293.2i	−0.999224	−	0.0393943i
$77$	91335.9			0.200064
$78$	37559.6	+	977049.i	0.0791475	+	2.05889i
$79$	388719.	−	68541.7i	0.788415	−	0.139019i	0.235078	−	0.971976i	$-0.424465\pi$
$79$	388719.	−	68541.7i	0.788415	−	0.139019i	0.553337	+	0.832958i	$0.313354\pi$
$80$	−120109.	+	137228.i	−0.234588	+	0.268024i
$81$	−438345.	+	367815.i	−0.824823	+	0.692108i
$82$	−21089.5	−	97530.8i	−0.0382495	−	0.176889i
$83$	−564813.	−	326095.i	−0.987802	−	0.570308i	−0.0831858	−	0.996534i	$-0.526509\pi$
$83$	−564813.	−	326095.i	−0.987802	−	0.570308i	−0.904617	+	0.426226i	$0.859843\pi$
$84$	167971.	+	46888.9i	0.283397	+	0.0791102i
$85$	162004.	−	58964.5i	0.263796	−	0.0960139i
$86$	−99758.4	−	110013.i	−0.156839	−	0.172960i
$87$	−949351.	+	548108.i	−1.44168	+	0.832354i
$88$	387242.	−	287638.i	0.568244	−	0.422083i
$89$	150198.	−	851816.i	0.213056	−	1.20830i	−0.671191	−	0.741284i	$-0.734217\pi$
$89$	150198.	−	851816.i	0.213056	−	1.20830i	0.884248	−	0.467018i	$-0.154672\pi$
$90$	10140.8	−	19235.0i	0.0139106	−	0.0263855i
$91$	270962.	−	322920.i	0.359570	−	0.428519i
$92$	603721.	−	843360.i	0.775305	−	1.08305i
$93$	1.23757e6	+	450437.i	1.53858	+	0.559997i
$94$	40328.3	+	98814.3i	0.0485542	+	0.118970i
$95$	255128.	−	167838.i	0.297568	−	0.195758i
$96$	859819.	−	330181.i	0.971837	−	0.373197i
$97$	−624554.	−	227319.i	−0.684313	−	0.249070i	−0.0236148	−	0.999721i	$-0.507518\pi$
$97$	−624554.	−	227319.i	−0.684313	−	0.249070i	−0.660698	+	0.750652i	$0.729740\pi$
$98$	461493.	+	732797.i	0.490329	+	0.778584i
$99$	−36971.0	+	44060.3i	−0.0381027	+	0.0454090i
$100$	−85158.0	+	868969.i	−0.0851580	+	0.868969i
$101$	258546.	−	1.46629e6i	0.250942	−	1.42316i	−0.555336	−	0.831626i	$-0.687410\pi$
$101$	258546.	−	1.46629e6i	0.250942	−	1.42316i	0.806278	−	0.591537i	$-0.201479\pi$
$102$	−862649.	−	118146.i	−0.812893	−	0.111331i
$103$	1.37130e6	−	791721.i	1.25493	−	0.724537i	0.282850	−	0.959164i	$-0.408720\pi$
$103$	1.37130e6	−	791721.i	1.25493	−	0.724537i	0.972085	+	0.234627i	$0.0753870\pi$
$104$	131864.	−	2.22242e6i	0.117227	−	1.97573i
$105$	−114004.	+	41494.0i	−0.0984809	+	0.0358441i
$106$	−403525.	−	312990.i	−0.338808	−	0.262792i
$107$	896424.	+	517551.i	0.731749	+	0.422475i	0.819062	−	0.573706i	$-0.194495\pi$
$107$	896424.	+	517551.i	0.731749	+	0.422475i	−0.0873128	+	0.996181i	$0.527828\pi$
$108$	991403.	−	678903.i	0.787008	−	0.538935i
$109$	−245244.	+	205784.i	−0.189373	+	0.158903i	−0.732545	−	0.680719i	$-0.761668\pi$
$109$	−245244.	+	205784.i	−0.189373	+	0.158903i	0.543172	+	0.839622i	$0.317223\pi$
$110$	−102577.	+	319519.i	−0.0770678	+	0.240059i
$111$	−1.60686e6	+	283333.i	−1.17492	+	0.207171i
$112$	−370224.	−	143557.i	−0.263518	−	0.102181i
$113$	853052.			0.591208			0.295604	−	0.955311i	$-0.404479\pi$
$113$	853052.			0.591208			0.295604	+	0.955311i	$0.404479\pi$
$114$	−1.53512e6	+	148919.i	−1.03617	+	0.100516i
$115$			721538.i			0.474423i
$116$	2.27304e6	−	1.03124e6i	1.45624	−	0.660670i
$117$	46096.0	+	261423.i	0.0287810	+	0.163225i
$118$	−540307.	+	1.68301e6i	−0.328848	+	1.02433i
$119$	241291.	+	287559.i	0.143186	+	0.170642i
$120$	−352675.	+	534949.i	−0.204094	+	0.309577i
$121$	−441956.	+	765490.i	−0.249473	+	0.432099i
$122$	1.36652e6	+	1.05993e6i	0.752552	+	0.583708i
$123$	−119909.	−	329448.i	−0.0644374	−	0.177040i
$124$	−2.70441e6	−	1.29556e6i	−1.41843	−	0.679507i
$125$	−651546.	−	1.12851e6i	−0.333591	−	0.577797i
$126$	46908.1	+	6424.38i	0.0234497	+	0.00321159i
$127$	−134671.	−	23746.1i	−0.0657449	−	0.0115926i	0.140679	−	0.990055i	$-0.455071\pi$
$127$	−134671.	−	23746.1i	−0.0657449	−	0.0115926i	−0.206424	+	0.978463i	$0.566183\pi$
$128$	−2.02175e6	+	557276.i	−0.964048	+	0.265730i
$129$	−399705.	−	335392.i	−0.186196	−	0.156237i
$130$	825355.	+	1.31057e6i	0.375674	+	0.596526i
$131$	−915764.	+	2.51604e6i	−0.407352	+	1.11919i	0.551225	+	0.834357i	$0.314161\pi$
$131$	−915764.	+	2.51604e6i	−0.407352	+	1.11919i	−0.958577	+	0.284834i	$0.908062\pi$
$132$	1.21085e6	−	1.18588e6i	0.526465	−	0.515606i
$133$	533404.	+	397018.i	0.226726	+	0.168754i
$134$	−254571.	−	623761.i	−0.105802	−	0.259241i
$135$	−285897.	+	785497.i	−0.116201	+	0.319259i
$136$	1.92861e6	+	459301.i	0.766702	+	0.182592i
$137$	−778809.	−	653499.i	−0.302879	−	0.254146i	0.478662	−	0.877999i	$-0.341122\pi$
$137$	−778809.	−	653499.i	−0.302879	−	0.254146i	−0.781541	+	0.623853i	$0.785566\pi$
$138$	1.69947e6	−	3.22354e6i	0.646661	−	1.22658i
$139$	−158465.	−	27941.7i	−0.0590051	−	0.0104042i	0.144068	−	0.989568i	$-0.453982\pi$
$139$	−158465.	−	27941.7i	−0.0590051	−	0.0104042i	−0.203073	+	0.979164i	$0.565093\pi$
$140$	267558.	−	68712.0i	0.0975067	−	0.0250408i
$141$	187491.	+	324744.i	0.0668842	+	0.115847i
$142$	−269749.	−	297477.i	−0.0942096	−	0.103893i
$143$	−1.40118e6	−	3.84970e6i	−0.479164	−	1.31649i
$144$	219111.	−	120487.i	0.0733798	−	0.0403508i
$145$	−868212.	+	1.50379e6i	−0.284788	+	0.493267i
$146$	−1.13814e6	−	5.26345e6i	−0.365710	−	1.69126i
$147$	1.95581e6	+	2.33084e6i	0.615706	+	0.733770i
$148$	3.70422e6	−	285216.i	1.14265	−	0.0879811i
$149$	155722.	+	883144.i	0.0470751	+	0.266976i	0.999256	−	0.0385573i	$-0.0122762\pi$
$149$	155722.	+	883144.i	0.0470751	+	0.266976i	−0.952181	+	0.305534i	$0.901165\pi$
$150$	117842.	+	3.06546e6i	0.0349162	+	0.908285i
$151$			5.64567e6i			1.63978i	0.572524	+	0.819888i	$0.305964\pi$
$151$			5.64567e6i			1.63978i	−0.572524	+	0.819888i	$0.694036\pi$
$152$	3.51181e6	+	3447.00i	1.00000	+	0.000981544i
$153$	−236388.			−0.0660011
$154$	−730148.	+	28068.3i	−0.199916	+	0.00768517i
$155$	2.05444e6	−	362253.i	0.551695	−	0.0972786i
$156$	−600510.	−	7.79908e6i	−0.158178	−	2.05433i
$157$	2.82818e6	−	2.37312e6i	0.730816	−	0.613227i	−0.199538	−	0.979890i	$-0.563944\pi$
$157$	2.82818e6	−	2.37312e6i	0.730816	−	0.613227i	0.930354	+	0.366663i	$0.119500\pi$
$158$	−3.08640e6	+	667386.i	−0.782493	+	0.169202i
$159$	−1.55388e6	−	897133.i	−0.386568	−	0.223185i
$160$	917993.	−	1.13393e6i	0.224119	−	0.276837i
$161$	−1.47631e6	+	537335.i	−0.353754	+	0.128756i
$162$	3.39114e6	−	3.07505e6i	0.797628	−	0.723282i
$163$	−3.22508e6	+	1.86200e6i	−0.744693	+	0.429949i	−0.823773	−	0.566920i	$-0.808135\pi$
$163$	−3.22508e6	+	1.86200e6i	−0.744693	+	0.429949i	0.0790802	+	0.996868i	$0.474802\pi$
$164$	198564.	+	773190.i	0.0450162	+	0.175289i
$165$	−204741.	+	1.16114e6i	−0.0455777	+	0.258484i
$166$	4.61538e6	+	2.43326e6i	1.00898	+	0.531942i
$167$	−4.89733e6	+	5.83641e6i	−1.05150	+	1.25313i	−0.0850243	+	0.996379i	$0.527097\pi$
$167$	−4.89733e6	+	5.83641e6i	−1.05150	+	1.25313i	−0.966477	+	0.256752i	$0.917348\pi$
$168$	−1.35718e6	−	323216.i	−0.286227	−	0.0681655i
$169$	−1.32318e7	−	4.81597e6i	−2.74131	−	0.997754i
$170$	−1.27695e6	+	521153.i	−0.259913	+	0.106076i
$171$	−407432.	+	96608.3i	−0.0814831	+	0.0193209i
$172$	831286.	+	848794.i	0.163367	+	0.166808i
$173$	5.46995e6	+	1.99090e6i	1.05644	+	0.384513i	0.811090	−	0.584922i	$-0.198875\pi$
$173$	5.46995e6	+	1.99090e6i	1.05644	+	0.384513i	0.245351	+	0.969434i	$0.421097\pi$
$174$	7.42076e6	−	4.67337e6i	1.40864	−	0.887120i
$175$	850135.	−	1.01315e6i	0.158626	−	0.189043i
$176$	−3.00726e6	+	2.41841e6i	−0.551611	+	0.443600i
$177$	−1.07844e6	+	6.11611e6i	−0.194480	+	1.10295i
$178$	−938928.	+	6.85566e6i	−0.166484	+	1.21560i
$179$	1.99030e6	−	1.14910e6i	0.347024	−	0.200355i	−0.316350	−	0.948643i	$-0.602457\pi$
$179$	1.99030e6	−	1.14910e6i	0.347024	−	0.200355i	0.663374	+	0.748288i	$0.269124\pi$
$180$	−75155.8	+	156883.i	−0.0128868	+	0.0269004i
$181$	1.57770e6	−	574237.i	0.266066	−	0.0968401i	−0.205542	−	0.978648i	$-0.565896\pi$
$181$	1.57770e6	−	574237.i	0.266066	−	0.0968401i	0.471608	+	0.881808i	$0.343674\pi$
$182$	−2.06686e6	+	2.66472e6i	−0.342844	+	0.442015i
$183$	5.26214e6	+	3.03810e6i	0.858637	+	0.495734i
$184$	−4.56703e6	+	6.92743e6i	−0.733129	+	1.11204i
$185$	−1.97989e6	+	1.66133e6i	−0.312699	+	0.262385i
$186$	−1.00316e7	−	3.22052e6i	−1.55895	−	0.500481i
$187$	3.59273e6	−	633495.i	0.549414	−	0.0968766i
$188$	−352755.	−	777538.i	−0.0530884	−	0.117017i
$189$	−1.82009e6			−0.269592
$190$	−1.98794e6	+	1.42012e6i	−0.289829	+	0.207045i
$191$		−	3.23808e6i		−	0.464716i	−0.972630	−	0.232358i	$-0.925356\pi$
$191$		−	3.23808e6i		−	0.464716i	0.972630	−	0.232358i	$-0.0746441\pi$
$192$	−6.77201e6	+	2.90372e6i	−0.956784	+	0.410253i
$193$	220758.	+	1.25198e6i	0.0307075	+	0.174151i	0.996304	−	0.0858925i	$-0.0273742\pi$
$193$	220758.	+	1.25198e6i	0.0307075	+	0.174151i	−0.965597	+	0.260044i	$0.916263\pi$
$194$	5.06260e6	+	1.62528e6i	0.693376	+	0.222599i
$195$	3.49785e6	+	4.16857e6i	0.471734	+	0.562191i
$196$	−3.91442e6	−	5.71623e6i	−0.519875	−	0.759174i
$197$	390604.	−	676546.i	0.0510902	−	0.0884909i	−0.839349	−	0.543592i	$-0.817064\pi$
$197$	390604.	−	676546.i	0.0510902	−	0.0884909i	0.890440	+	0.455102i	$0.150397\pi$
$198$	282009.	−	363584.i	0.0363302	−	0.0468391i
$199$	−1.75097e6	−	4.81076e6i	−0.222188	−	0.610456i	0.777646	−	0.628703i	$-0.216414\pi$
$199$	−1.75097e6	−	4.81076e6i	−0.222188	−	0.610456i	−0.999834	+	0.0182467i	$0.994192\pi$
$200$	413719.	−	6.97279e6i	0.0517149	−	0.871599i
$201$	−1.18353e6	−	2.04994e6i	−0.145744	−	0.252436i
$202$	−1.61624e6	+	1.18011e7i	−0.196088	+	1.43175i
$203$	−3.72341e6	−	656538.i	−0.445095	−	0.0784823i
$204$	6.93240e6	+	679368.i	0.816570	+	0.0800229i
$205$	−425418.	−	356968.i	−0.0493803	−	0.0414350i
$206$	−1.07190e7	+	6.75051e6i	−1.22618	+	0.772209i
$207$	338374.	−	929675.i	0.0381492	−	0.104814i
$208$	−371164.	+	1.78068e7i	−0.0412454	+	1.97877i
$209$	5.93344e6	−	2.56017e6i	0.649932	−	0.280434i
$210$	898607.	−	366742.i	0.0970313	−	0.0396007i
$211$	−169690.	+	466221.i	−0.0180638	+	0.0496300i	−0.948397	−	0.317086i	$-0.897296\pi$
$211$	−169690.	+	466221.i	−0.0180638	+	0.0496300i	0.930333	+	0.366716i	$0.119518\pi$
$212$	3.32200e6	+	2.37806e6i	0.348652	+	0.249583i
$213$	−1.08081e6	−	906908.i	−0.111844	−	0.0938479i
$214$	−7.32515e6	−	3.86187e6i	−0.747438	−	0.394055i
$215$	−813948.	−	143521.i	−0.0818995	−	0.0144411i
$216$	−7.71674e6	+	5.73188e6i	−0.765724	+	0.568769i
$217$	2.27115e6	+	3.93375e6i	0.222263	+	0.384971i
$218$	1.89726e6	−	1.72042e6i	0.183129	−	0.166060i
$219$	−6.47115e6	−	1.77793e7i	−0.616097	−	1.69271i
$220$	721822.	−	2.58579e6i	0.0677894	−	0.242843i
$221$	8.41865e6	−	1.45815e7i	0.779948	−	1.35091i
$222$	1.27584e7	−	2.75880e6i	1.16610	−	0.252151i
$223$	1.00649e7	+	1.19949e7i	0.907603	+	1.08164i	0.996331	+	0.0855830i	$0.0272753\pi$
$223$	1.00649e7	+	1.19949e7i	0.907603	+	1.08164i	−0.0887282	+	0.996056i	$0.528280\pi$
$224$	3.00372e6	+	1.03383e6i	0.267249	+	0.0919827i
$225$	144625.	+	820208.i	0.0126968	+	0.0720073i
$226$	−6.81938e6	+	262150.i	−0.590771	+	0.0227104i
$227$		−	2.21790e7i		−	1.89611i	−0.318101	−	0.948057i	$-0.603045\pi$
$227$		−	2.21790e7i		−	1.89611i	0.318101	−	0.948057i	$-0.396955\pi$
$228$	1.22262e7	−	1.66223e6i	1.03154	−	0.140245i
$229$	1.52160e7			1.26705			0.633524	−	0.773723i	$-0.281608\pi$
$229$	1.52160e7			1.26705			0.633524	+	0.773723i	$0.281608\pi$
$230$	−221735.	−	5.76804e6i	−0.0182243	−	0.474073i
$231$	−2.52825e6	+	445798.i	−0.205109	+	0.0361662i
$232$	−1.78540e7	+	8.94233e6i	−1.42979	+	0.716121i
$233$	6.36996e6	−	5.34503e6i	0.503580	−	0.422554i	−0.355283	−	0.934759i	$-0.615616\pi$
$233$	6.36996e6	−	5.34503e6i	0.503580	−	0.422554i	0.858863	+	0.512205i	$0.171171\pi$
$234$	−448833.	−	2.07568e6i	−0.0350298	−	0.161999i
$235$	514400.	+	296989.i	0.0396367	+	0.0228843i
$236$	3.80207e6	−	1.36202e7i	0.289257	−	1.03621i
$237$	−1.04255e7	+	3.79458e6i	−0.783163	+	0.285048i
$238$	−2.01727e6	−	2.22462e6i	−0.149635	−	0.165016i
$239$	7.53006e6	−	4.34748e6i	0.551575	−	0.318452i	−0.198182	−	0.980165i	$-0.563504\pi$
$239$	7.53006e6	−	4.34748e6i	0.551575	−	0.318452i	0.749757	+	0.661713i	$0.230170\pi$
$240$	2.65492e6	−	4.38482e6i	0.192052	−	0.317189i
$241$	1.05937e6	−	6.00800e6i	0.0756828	−	0.429219i	−0.923298	−	0.384084i	$-0.874517\pi$
$241$	1.05937e6	−	6.00800e6i	0.0756828	−	0.429219i	0.998981	−	0.0451345i	$-0.0143716\pi$
$242$	3.29780e6	−	6.25522e6i	0.232690	−	0.441363i
$243$	1.54081e6	−	1.83626e6i	0.107382	−	0.127972i
$244$	−1.12498e7	−	8.05320e6i	−0.774419	−	0.554369i
$245$	4.52902e6	+	1.64843e6i	0.307968	+	0.112091i
$246$	1.05981e6	+	2.59679e6i	0.0711906	+	0.174434i
$247$	8.55092e6	−	2.85730e7i	0.567443	−	1.89611i
$248$	2.20174e7	+	9.52578e6i	1.44348	+	0.624519i
$249$	1.72261e7	+	6.26978e6i	1.11581	+	0.406120i
$250$	5.55532e6	+	8.82119e6i	0.355540	+	0.564556i
$251$	1.01292e7	−	1.20715e7i	0.640549	−	0.763377i	−0.343907	−	0.939004i	$-0.611751\pi$
$251$	1.01292e7	−	1.20715e7i	0.640549	−	0.763377i	0.984457	+	0.175627i	$0.0561951\pi$
$252$	−376962.	−	36941.9i	−0.0235557	−	0.00230843i
$253$	−2.65133e6	+	1.50364e7i	−0.163720	+	0.928503i
$254$	1.08387e6	+	148443.i	0.0661416	+	0.00905854i
$255$	−4.19659e6	+	2.42290e6i	−0.253091	+	0.146122i
$256$	1.59908e7	−	5.07622e6i	0.953128	−	0.302566i
$257$	4.49976e6	−	1.63778e6i	0.265088	−	0.0964840i	−0.206057	−	0.978540i	$-0.566063\pi$
$257$	4.49976e6	−	1.63778e6i	0.265088	−	0.0964840i	0.471145	+	0.882056i	$0.343841\pi$
$258$	3.29835e6	+	2.55832e6i	0.192060	+	0.148969i
$259$	−4.87362e6	−	2.81379e6i	−0.280513	−	0.161954i
$260$	−7.00071e6	−	1.02232e7i	−0.398311	−	0.581654i
$261$	1.82388e6	−	1.53042e6i	0.102583	−	0.0860772i
$262$	6.54751e6	−	2.03949e7i	0.364059	−	1.13401i
$263$	−3.27786e7	+	5.77975e6i	−1.80187	+	0.317718i	−0.971059	−	0.238838i	$-0.923233\pi$
$263$	−3.27786e7	+	5.77975e6i	−1.80187	+	0.317718i	−0.830810	+	0.556556i	$0.812122\pi$
$264$	−9.31524e6	+	9.85211e6i	−0.506270	+	0.535448i
$265$	−2.84215e6			−0.152725
$266$	−4.38609e6	−	3.00988e6i	−0.233041	−	0.159920i
$267$			2.43120e7i			1.27728i
$268$	2.22675e6	+	4.90818e6i	0.115682	+	0.254986i
$269$	1.42001e6	+	8.05325e6i	0.0729513	+	0.413728i	0.999312	+	0.0370898i	$0.0118087\pi$
$269$	1.42001e6	+	8.05325e6i	0.0729513	+	0.413728i	−0.926361	+	0.376638i	$0.877080\pi$
$270$	2.04410e6	−	6.36719e6i	0.103851	−	0.323487i
$271$	−1.33872e7	−	1.59543e7i	−0.672640	−	0.801621i	0.316501	−	0.948592i	$-0.397492\pi$
$271$	−1.33872e7	−	1.59543e7i	−0.672640	−	0.801621i	−0.989141	+	0.146971i	$0.953048\pi$
$272$	−1.55586e7	−	3.07902e6i	−0.773150	−	0.153005i
$273$	−5.92431e6	+	1.02612e7i	−0.291172	+	0.504325i
$274$	6.42670e6	+	4.98480e6i	0.312418	+	0.242324i
$275$	−4.39615e6	−	1.20783e7i	−0.211385	−	0.580775i
$276$	−1.25951e7	+	2.62915e7i	−0.599067	+	1.25051i
$277$	4.93973e6	+	8.55586e6i	0.232415	+	0.402554i	0.958518	−	0.285031i	$-0.0920040\pi$
$277$	4.93973e6	+	8.55586e6i	0.232415	+	0.402554i	−0.726103	+	0.687585i	$0.758671\pi$
$278$	1.27537e6	+	174671.i	0.0593612	+	0.00812992i
$279$	−2.81696e6	−	496705.i	−0.129708	−	0.0228711i
$280$	−2.11777e6	+	631513.i	−0.0964728	+	0.0287679i
$281$	−6.34693e6	−	5.32571e6i	−0.286052	−	0.240026i	0.488459	−	0.872587i	$-0.337559\pi$
$281$	−6.34693e6	−	5.32571e6i	−0.286052	−	0.240026i	−0.774511	+	0.632561i	$0.782004\pi$
$282$	−1.59862e6	−	2.53842e6i	−0.0712849	−	0.113192i
$283$	4.87259e6	−	1.33873e7i	0.214981	−	0.590656i	−0.784588	−	0.620018i	$-0.787125\pi$
$283$	4.87259e6	−	1.33873e7i	0.214981	−	0.590656i	0.999569	+	0.0293618i	$0.00934749\pi$
$284$	2.24782e6	+	2.29516e6i	0.0981310	+	0.100198i
$285$	−6.24293e6	+	5.89114e6i	−0.269683	+	0.254487i
$286$	1.23842e7	+	3.03443e7i	0.529382	+	1.29711i
$287$	413568.	−	1.13627e6i	0.0174945	−	0.0480657i
$288$	−1.71457e6	+	1.03052e6i	−0.0717757	+	0.0431397i
$289$	−7.00471e6	−	5.87765e6i	−0.290199	−	0.243506i
$290$	6.47844e6	−	1.22882e7i	0.265630	−	0.503843i
$291$	1.83977e7	+	3.24400e6i	0.746592	+	0.131644i
$292$	1.07159e7	+	4.17267e7i	0.430408	+	1.67597i
$293$	−1.53775e7	−	2.66346e7i	−0.611341	−	1.05887i	−0.991015	−	0.133753i	$-0.957297\pi$
$293$	−1.53775e7	−	2.66346e7i	−0.611341	−	1.05887i	0.379674	−	0.925120i	$-0.376036\pi$
$294$	−1.63512e7	−	1.80319e7i	−0.643439	−	0.709577i
$295$	3.36461e6	+	9.24420e6i	0.131060	+	0.360084i
$296$	−2.95243e7	+	3.41839e6i	−1.13842	+	0.131809i
$297$	−8.84428e6	+	1.53187e7i	−0.337593	+	0.584728i
$298$	−1.51626e6	−	7.01209e6i	−0.0572959	−	0.264971i
$299$	4.52960e7	+	5.39817e7i	1.69452	+	2.01945i
$300$	−1.88408e6	−	2.44694e7i	−0.0697809	−	0.906273i
$301$	−312500.	−	1.77227e6i	−0.0114591	−	0.0649877i
$302$	−1.73496e6	−	4.51320e7i	−0.0629896	−	1.63857i
$303$			4.18499e7i			1.50441i
$304$	−2.80748e7	+	1.05165e6i	−0.999299	+	0.0374327i
$305$	9.62480e6			0.339228
$306$	1.88971e6	−	72644.0i	0.0659524	−	0.00253534i
$307$	1.97832e7	−	3.48831e6i	0.683725	−	0.120559i	0.179013	−	0.983847i	$-0.442710\pi$
$307$	1.97832e7	−	3.48831e6i	0.683725	−	0.120559i	0.504712	+	0.863288i	$0.331599\pi$
$308$	5.82824e6	−	448761.i	0.199474	−	0.0153590i
$309$	−3.40944e7	+	2.86086e7i	−1.15560	+	0.969664i
$310$	−1.63121e7	+	3.52724e6i	−0.547551	+	0.118399i
$311$	−3.49481e7	−	2.01773e7i	−1.16183	−	0.670782i	−0.210087	−	0.977683i	$-0.567375\pi$
$311$	−3.49481e7	−	2.01773e7i	−1.16183	−	0.670782i	−0.951742	+	0.306901i	$0.900708\pi$
$312$	7.19726e6	+	6.21620e7i	0.236975	+	2.04673i
$313$	1.22985e7	−	4.47628e6i	0.401068	−	0.145977i	−0.133607	−	0.991034i	$-0.542656\pi$
$313$	1.22985e7	−	4.47628e6i	0.401068	−	0.145977i	0.534675	+	0.845058i	$0.320434\pi$
$314$	−2.18794e7	+	1.98401e7i	−0.706720	+	0.640848i
$315$	228197.	−	131750.i	0.00730094	−	0.00421520i
$316$	2.44679e7	−	6.28362e6i	0.775416	−	0.199136i
$317$	−636734.	+	3.61110e6i	−0.0199885	+	0.113360i	−0.993170	−	0.116680i	$-0.962775\pi$
$317$	−636734.	+	3.61110e6i	−0.0199885	+	0.113360i	0.973181	+	0.230041i	$0.0738859\pi$
$318$	1.26976e7	+	6.69424e6i	0.394856	+	0.208171i
$319$	−2.36188e7	+	2.81478e7i	−0.727588	+	0.867105i
$320$	−6.99006e6	+	9.34681e6i	−0.213320	+	0.285242i
$321$	−2.73398e7	−	9.95087e6i	−0.826571	−	0.300847i
$322$	1.16367e7	−	4.74919e6i	0.348547	−	0.142250i
$323$	2.37353e7	+	1.19172e7i	0.704349	+	0.353645i
$324$	−2.61641e7	+	2.56244e7i	−0.769255	+	0.753388i
$325$	−5.57450e7	−	2.02895e7i	−1.62389	−	0.591046i
$326$	2.52094e7	−	1.58761e7i	0.727627	−	0.458238i
$327$	5.78413e6	−	6.89326e6i	0.165423	−	0.197143i
$328$	−1.82495e6	−	6.11993e6i	−0.0517164	−	0.173430i
$329$	−224582.	+	1.27367e6i	−0.00630648	+	0.0357658i
$330$	1.27989e6	−	9.34520e6i	0.0356148	−	0.260044i
$331$	−3.89402e7	+	2.24821e7i	−1.07378	+	0.619946i	−0.929211	−	0.369549i	$-0.879512\pi$
$331$	−3.89402e7	+	2.24821e7i	−1.07378	+	0.619946i	−0.144566	+	0.989495i	$0.546179\pi$
$332$	−3.76435e7	−	1.80334e7i	−1.02867	−	0.492791i
$333$	3.33012e6	−	1.21206e6i	0.0901834	−	0.0328241i
$334$	3.73561e7	−	4.81618e7i	1.00259	−	1.29260i
$335$	−3.24713e6	−	1.87473e6i	−0.0863705	−	0.0498661i
$336$	1.09488e7	+	2.16674e6i	0.288634	+	0.0571202i
$337$	2.94971e7	−	2.47510e7i	0.770708	−	0.646701i	−0.170182	−	0.985413i	$-0.554436\pi$
$337$	2.94971e7	−	2.47510e7i	0.770708	−	0.646701i	0.940890	+	0.338712i	$0.109991\pi$
$338$	1.07256e8	+	3.44331e7i	2.77761	+	0.891714i
$339$	−2.36131e7	+	4.16363e6i	−0.606114	+	0.106874i
$340$	1.00479e7	−	4.55857e6i	0.255646	−	0.115982i
$341$	4.41445e7			1.11330
$342$	3.22737e6	−	897504.i	0.0806807	−	0.0224366i
$343$			2.18996e7i			0.542693i
$344$	−6.90622e6	−	6.52988e6i	−0.169654	−	0.160409i
$345$	−3.52173e6	−	1.99727e7i	−0.0857628	−	0.486385i
$346$	−4.43391e7	−	1.42345e7i	−1.07043	−	0.343647i
$347$	2.25791e7	+	2.69088e7i	0.540405	+	0.644029i	0.965278	−	0.261223i	$-0.0841259\pi$
$347$	2.25791e7	+	2.69088e7i	0.540405	+	0.644029i	−0.424874	+	0.905253i	$0.639682\pi$
$348$	−5.78861e7	+	3.96398e7i	−1.37353	+	0.940576i
$349$	2.48944e7	−	4.31184e7i	0.585633	−	1.01435i	−0.409163	−	0.912461i	$-0.634179\pi$
$349$	2.48944e7	−	4.31184e7i	0.585633	−	1.01435i	0.994796	−	0.101885i	$-0.0324874\pi$
$350$	−6.48471e6	+	8.36048e6i	−0.151247	+	0.194997i
$351$	2.79218e7	+	7.67146e7i	0.645687	+	1.77401i
$352$	2.32971e7	−	2.02571e7i	0.534163	−	0.464462i
$353$	−2.29711e7	−	3.97871e7i	−0.522225	−	0.904520i	−0.999666	−	0.0258558i	$-0.991769\pi$
$353$	−2.29711e7	−	3.97871e7i	−0.522225	−	0.904520i	0.477441	−	0.878664i	$-0.341564\pi$
$354$	6.74158e6	−	4.92242e7i	0.151968	−	1.10961i
$355$	−2.20093e6	−	388084.i	−0.0491951	−	0.00867443i
$356$	5.39908e6	−	5.50933e7i	0.119666	−	1.22109i
$357$	−8.08265e6	−	6.78215e6i	−0.177643	−	0.149061i
$358$	−1.55575e7	+	9.79766e6i	−0.339072	+	0.213537i
$359$	1.81318e7	−	4.98168e7i	0.391885	−	1.07670i	−0.574255	−	0.818677i	$-0.694708\pi$
$359$	1.81318e7	−	4.98168e7i	0.391885	−	1.07670i	0.966140	−	0.258019i	$-0.0830696\pi$
$360$	552591.	−	1.27723e6i	0.0118439	−	0.0273756i
$361$	4.57800e7	+	1.08399e7i	0.973093	+	0.230412i
$362$	−1.24358e7	+	5.07534e6i	−0.262150	+	0.106989i
$363$	8.49742e6	−	2.33465e7i	0.177651	−	0.488092i
$364$	1.57038e7	−	2.19372e7i	0.325612	−	0.454859i
$365$	−2.29585e7	−	1.92645e7i	−0.472134	−	0.396167i
$366$	−4.29997e7	−	2.26698e7i	−0.877046	−	0.462385i
$367$	−3.30606e7	−	5.82948e6i	−0.668826	−	0.117932i	−0.171083	−	0.985257i	$-0.554727\pi$
$367$	−3.30606e7	−	5.82948e6i	−0.668826	−	0.117932i	−0.497743	+	0.867325i	$0.665838\pi$
$368$	3.43804e7	−	5.67820e7i	0.689870	−	1.13938i
$369$	380730.	+	659444.i	0.00757772	+	0.0131250i
$370$	1.53169e7	−	1.38892e7i	0.302389	−	0.274204i
$371$	−2.11657e6	−	5.81522e6i	−0.0414487	−	0.113879i
$372$	8.11836e7	+	2.26624e7i	1.57703	+	0.440227i
$373$	−1.99706e7	+	3.45901e7i	−0.384826	+	0.666538i	−0.991745	−	0.128226i	$-0.959072\pi$
$373$	−1.99706e7	+	3.45901e7i	−0.384826	+	0.666538i	0.606919	+	0.794764i	$0.292405\pi$
$374$	−2.85260e7	+	6.16830e6i	−0.545287	+	0.117910i
$375$	2.35434e7	+	2.80579e7i	0.446453	+	0.532062i
$376$	3.05890e6	+	6.10731e6i	0.0575442	+	0.114891i
$377$	2.94482e7	+	1.67009e8i	0.549586	+	3.11686i
$378$	1.45500e7	−	559328.i	0.269393	−	0.0103560i
$379$		−	6.02246e7i		−	1.10626i	−0.833095	−	0.553129i	$-0.813434\pi$
$379$		−	6.02246e7i		−	1.10626i	0.833095	−	0.553129i	$-0.186566\pi$
$380$	1.54553e7	−	1.19635e7i	0.281662	−	0.218025i
$381$	3.84369e6			0.0694982
$382$	995090.	+	2.58855e7i	0.0178514	+	0.464373i
$383$	−1.07398e8	+	1.89371e7i	−1.91161	+	0.337068i	−0.997636	−	0.0687146i	$-0.978110\pi$
$383$	−1.07398e8	+	1.89371e7i	−1.91161	+	0.337068i	−0.913970	+	0.405782i	$0.866999\pi$
$384$	5.32437e7	−	2.52937e7i	0.940318	−	0.446704i
$385$	−3.11517e6	+	2.61394e6i	−0.0545883	+	0.0458050i
$386$	−2.14951e6	−	9.94063e6i	−0.0373746	−	0.172843i
$387$	981436.	+	566632.i	0.0169328	+	0.00977616i
$388$	−4.09704e7	−	1.14369e7i	−0.701415	−	0.195800i
$389$	−9.08694e7	+	3.30738e7i	−1.54372	+	0.561868i	−0.966934	−	0.255026i	$-0.917916\pi$
$389$	−9.08694e7	+	3.30738e7i	−1.54372	+	0.561868i	−0.576787	+	0.816895i	$0.695694\pi$
$390$	−2.92432e7	−	3.22490e7i	−0.492981	−	0.543655i
$391$	−5.43445e7	+	3.13758e7i	−0.909129	+	0.524886i
$392$	3.30489e7	+	4.44932e7i	0.548654	+	0.738644i
$393$	1.30686e7	−	7.41157e7i	0.215304	−	1.22105i
$394$	−2.91462e6	+	5.52841e6i	−0.0476533	+	0.0903881i
$395$	−1.12964e7	+	1.34625e7i	−0.183294	+	0.218441i
$396$	−2.14268e6	+	2.99319e6i	−0.0345042	+	0.0482001i
$397$	6.40818e7	+	2.33239e7i	1.02415	+	0.372760i	0.798850	−	0.601530i	$-0.205442\pi$
$397$	6.40818e7	+	2.33239e7i	1.02415	+	0.372760i	0.225299	+	0.974290i	$0.427664\pi$
$398$	1.54758e7	+	3.79196e7i	0.245474	+	0.601470i
$399$	−1.67028e7	−	8.38629e6i	−0.262949	−	0.132023i
$400$	−1.16452e6	+	5.58683e7i	−0.0181956	+	0.872942i
$401$	1.81977e7	+	6.62341e6i	0.282217	+	0.102718i	0.479250	−	0.877678i	$-0.340909\pi$
$401$	1.81977e7	+	6.62341e6i	0.282217	+	0.102718i	−0.197034	+	0.980397i	$0.563131\pi$
$402$	1.00912e7	+	1.60237e7i	0.155334	+	0.246652i
$403$	1.30961e8	−	1.56074e8i	2.00091	−	2.38459i
$404$	9.29379e6	−	9.48357e7i	0.140945	−	1.43823i
$405$	4.42403e6	−	2.50899e7i	0.0665968	−	0.377689i
$406$	2.99671e7	+	4.10419e6i	0.447782	+	0.0613267i
$407$	−4.73644e7	+	2.73459e7i	−0.702537	+	0.405610i
$408$	−5.56271e7	−	3.30054e6i	−0.819041	−	0.0485965i
$409$	−4.33522e7	+	1.57789e7i	−0.633638	+	0.230626i	−0.638814	−	0.769361i	$-0.720575\pi$
$409$	−4.33522e7	+	1.57789e7i	−0.633638	+	0.230626i	0.00517574	+	0.999987i	$0.498353\pi$
$410$	3.51053e6	+	2.72290e6i	0.0509355	+	0.0395075i
$411$	2.47477e7	+	1.42881e7i	0.356459	+	0.205801i
$412$	8.36143e7	−	5.72582e7i	1.19561	−	0.818741i
$413$	−1.64086e7	+	1.37685e7i	−0.232928	+	0.195450i
$414$	−2.41930e6	+	7.53590e6i	−0.0340948	+	0.106202i
$415$	2.85964e7	−	5.04232e6i	0.400099	−	0.0705483i
$416$	−2.50506e6	−	1.42463e8i	−0.0347966	−	1.97890i
$417$	4.52282e6			0.0623737
$418$	−4.66457e7	+	2.22897e7i	−0.638680	+	0.305193i
$419$			5.30039e7i			0.720553i	0.932846	+	0.360276i	$0.117318\pi$
$419$			5.30039e7i			0.720553i	−0.932846	+	0.360276i	$0.882682\pi$
$420$	−7.07085e6	+	3.20792e6i	−0.0954385	+	0.0432987i
$421$	−6.67046e6	−	3.78300e7i	−0.0893942	−	0.506980i	−0.996322	−	0.0856928i	$-0.972690\pi$
$421$	−6.67046e6	−	3.78300e7i	−0.0893942	−	0.506980i	0.906927	−	0.421287i	$-0.138421\pi$
$422$	1.21325e6	−	3.77916e6i	0.0161440	−	0.0502872i
$423$	−523509.	−	623894.i	−0.00691677	−	0.00824308i
$424$	−2.72872e7	−	1.79896e7i	−0.357982	−	0.236006i
$425$	2.64133e7	−	4.57491e7i	0.344077	−	0.595959i
$426$	8.91881e6	+	6.91777e6i	0.115366	+	0.0894823i
$427$	7.16766e6	+	1.96930e7i	0.0920649	+	0.252946i
$428$	5.97447e7	+	2.86211e7i	0.762023	+	0.365052i
$429$	5.75755e7	+	9.97237e7i	0.729232	+	1.26307i
$430$	6.55088e6	+	897187.i	0.0823938	+	0.0112844i
$431$	−7.22175e6	−	1.27339e6i	−0.0902009	−	0.0159048i	0.128366	−	0.991727i	$-0.459027\pi$
$431$	−7.22175e6	−	1.27339e6i	−0.0902009	−	0.0159048i	−0.218566	+	0.975822i	$0.570138\pi$
$432$	5.99269e7	−	4.81926e7i	0.743311	−	0.597763i
$433$	−3.14065e7	−	2.63532e7i	−0.386862	−	0.324615i	0.428527	−	0.903529i	$-0.359033\pi$
$433$	−3.14065e7	−	2.63532e7i	−0.386862	−	0.324615i	−0.815389	+	0.578913i	$0.803477\pi$
$434$	−1.93647e7	−	3.07488e7i	−0.236887	−	0.376149i
$435$	1.66930e7	−	4.58636e7i	0.202799	−	0.557186i
$436$	−1.46382e7	+	1.43363e7i	−0.176615	+	0.172972i
$437$	−8.08440e7	+	7.62884e7i	−0.968732	+	0.914143i
$438$	5.71948e7	+	1.40141e8i	0.680666	+	1.66780i
$439$	3.35142e7	−	9.20795e7i	0.396128	−	1.08835i	−0.568026	−	0.823010i	$-0.692293\pi$
$439$	3.35142e7	−	9.20795e7i	0.396128	−	1.08835i	0.964154	−	0.265342i	$-0.0854849\pi$
$440$	−4.97568e6	+	2.08929e7i	−0.0584109	+	0.245268i
$441$	−5.06242e6	−	4.24787e6i	−0.0590259	−	0.0495286i
$442$	−6.28185e7	+	1.19153e8i	−0.727479	+	1.37987i
$443$	9.09025e7	+	1.60286e7i	1.04560	+	0.184367i	0.669958	−	0.742399i	$-0.266312\pi$
$443$	9.09025e7	+	1.60286e7i	1.04560	+	0.184367i	0.375640	+	0.926766i	$0.377423\pi$
$444$	−1.01144e8	+	2.59748e7i	−1.15555	+	0.296759i
$445$	1.92553e7	+	3.33512e7i	0.218510	+	0.378470i
$446$	−8.41461e7	−	9.27954e7i	−0.948483	−	1.04598i
$447$	−8.62102e6	−	2.36861e7i	−0.0965242	−	0.265198i
$448$	−2.43298e7	−	7.34148e6i	−0.270585	−	0.0816488i
$449$	7.98830e7	−	1.38361e8i	0.882502	−	1.52854i	0.0339512	−	0.999423i	$-0.489191\pi$
$449$	7.98830e7	−	1.38361e8i	0.882502	−	1.52854i	0.848551	−	0.529114i	$-0.177476\pi$
$450$	−1.40820e6	−	6.51238e6i	−0.0154535	−	0.0714664i
$451$	−7.55376e6	−	9.00222e6i	−0.0823443	−	0.0981341i
$452$	5.44342e7	−	4.19130e6i	0.589463	−	0.0453873i
$453$	−2.75558e7	−	1.56276e8i	−0.296427	−	1.68112i
$454$	6.81579e6	+	1.77301e8i	0.0728364	+	1.89471i
$455$			1.87684e7i			0.199248i
$456$	−9.72263e7	+	1.70452e7i	−1.02539	+	0.179766i
$457$	1.71819e8			1.80021			0.900103	−	0.435677i	$-0.143491\pi$
$457$	1.71819e8			1.80021			0.900103	+	0.435677i	$0.143491\pi$
$458$	−1.21638e8	+	4.67599e6i	−1.26611	+	0.0486718i
$459$	−7.15939e7	+	1.26239e7i	−0.740351	+	0.130544i
$460$	3.54514e6	+	4.60421e7i	0.0364216	+	0.473023i
$461$	1.75734e7	−	1.47458e7i	0.179371	−	0.150510i	−0.548682	−	0.836031i	$-0.684870\pi$
$461$	1.75734e7	−	1.47458e7i	0.179371	−	0.150510i	0.728053	+	0.685521i	$0.240426\pi$
$462$	2.00741e7	−	4.34071e6i	0.203568	−	0.0440184i
$463$	−1.21404e8	−	7.00929e7i	−1.22318	−	0.706205i	−0.257588	−	0.966255i	$-0.582928\pi$
$463$	−1.21404e8	−	7.00929e7i	−1.22318	−	0.706205i	−0.965595	+	0.260050i	$0.916261\pi$
$464$	1.39978e8	−	7.69725e7i	1.40122	−	0.770516i
$465$	−5.51004e7	+	2.00549e7i	−0.548020	+	0.199463i
$466$	−4.92795e7	+	4.46862e7i	−0.486977	+	0.441587i
$467$	4.18701e7	−	2.41737e7i	0.411105	−	0.237352i	−0.280159	−	0.959954i	$-0.590387\pi$
$467$	4.18701e7	−	2.41737e7i	0.411105	−	0.237352i	0.691265	+	0.722602i	$0.257054\pi$
$468$	4.22589e6	+	1.64552e7i	0.0412269	+	0.160534i
$469$	1.41767e6	−	8.03998e6i	0.0137422	−	0.0779357i
$470$	−4.20343e6	−	2.21608e6i	−0.0404865	−	0.0213448i
$471$	−6.67033e7	+	7.94939e7i	−0.638388	+	0.760801i
$472$	−2.62085e7	+	1.10049e8i	−0.249239	+	1.04655i
$473$	−1.64348e7	−	5.98179e6i	−0.155304	−	0.0565259i
$474$	8.21764e7	−	3.35380e7i	0.771636	−	0.314922i
$475$	2.68283e7	−	8.96468e7i	0.250329	−	0.836477i
$476$	1.68099e7	+	1.71639e7i	0.155863	+	0.159146i
$477$	3.66200e6	+	1.33286e6i	0.0337414	+	0.0122809i
$478$	−5.88600e7	+	3.70682e7i	−0.538935	+	0.339405i
$479$	8.53463e6	−	1.01712e7i	0.0776566	−	0.0925475i	−0.725817	−	0.687888i	$-0.758538\pi$
$479$	8.53463e6	−	1.01712e7i	0.0776566	−	0.0925475i	0.803474	+	0.595340i	$0.202983\pi$
$480$	−1.98762e7	+	3.58685e7i	−0.179726	+	0.324332i
$481$	−4.38320e7	+	2.48583e8i	−0.393873	+	2.23376i
$482$	−6.62241e6	+	4.83541e7i	−0.0591392	+	0.431809i
$483$	3.82429e7	−	2.20795e7i	0.339398	−	0.195951i
$484$	−2.44406e7	+	5.10182e7i	−0.215564	+	0.449976i
$485$	2.78072e7	−	1.01210e7i	0.243743	−	0.0887151i
$486$	−1.17531e7	+	1.51528e7i	−0.102386	+	0.132003i
$487$	7.97039e6	+	4.60171e6i	0.0690070	+	0.0398412i	0.534106	−	0.845417i	$-0.320648\pi$
$487$	7.97039e6	+	4.60171e6i	0.0690070	+	0.0398412i	−0.465100	+	0.885258i	$0.653981\pi$
$488$	9.24070e7	+	6.09209e7i	0.795143	+	0.524212i
$489$	8.01844e7	−	6.72827e7i	0.685746	−	0.575410i
$490$	−3.67120e7	−	1.17859e7i	−0.312046	−	0.100178i
$491$	1.13195e6	−	199593.i	0.00956273	−	0.00168617i	−0.168865	−	0.985639i	$-0.554010\pi$
$491$	1.13195e6	−	199593.i	0.00956273	−	0.00168617i	0.178427	+	0.983953i	$0.442899\pi$
$492$	−9.27024e6	−	2.04333e7i	−0.0778387	−	0.171571i
$493$	−1.51016e8			−1.26032
$494$	−5.95762e7	+	2.31043e8i	−0.494187	+	1.91651i
$495$		−	2.56083e6i		−	0.0211137i
$496$	−1.78937e8	−	6.93838e7i	−1.46641	−	0.568608i
$497$	−845006.	−	4.79227e6i	−0.00688321	−	0.0390366i
$498$	−1.39634e8	−	4.48275e7i	−1.13058	−	0.362958i
$499$	4.14447e7	+	4.93918e7i	0.333555	+	0.397515i	0.906588	−	0.422017i	$-0.138678\pi$
$499$	4.14447e7	+	4.93918e7i	0.333555	+	0.397515i	−0.573033	+	0.819532i	$0.694233\pi$
$500$	−4.71206e7	−	6.88103e7i	−0.376965	−	0.550482i
$501$	1.07075e8	−	1.85460e8i	0.851482	−	1.47481i
$502$	−7.72639e7	+	9.96133e7i	−0.610753	+	0.787419i
$503$	−4.31101e7	−	1.18444e8i	−0.338747	−	0.930699i	−0.985751	−	0.168212i	$-0.946201\pi$
$503$	−4.31101e7	−	1.18444e8i	−0.338747	−	0.930699i	0.647004	−	0.762487i	$-0.276022\pi$
$504$	3.02482e6	+	179473.i	0.0236270	+	0.00140187i
$505$	3.31455e7	+	5.74096e7i	0.257365	+	0.445770i
$506$	1.65742e7	−	1.21017e8i	0.127932	−	0.934106i
$507$	3.89772e8	+	6.87273e7i	2.99079	+	0.527358i
$508$	−8.71016e6	−	853585.i	−0.0664408	−	0.00651112i
$509$	5.56331e7	+	4.66817e7i	0.421872	+	0.353992i	0.828874	−	0.559435i	$-0.188982\pi$
$509$	5.56331e7	+	4.66817e7i	0.421872	+	0.353992i	−0.407003	+	0.913427i	$0.633426\pi$
$510$	3.28034e7	−	2.06586e7i	0.247291	−	0.155736i
$511$	2.23190e7	−	6.13211e7i	0.167268	−	0.459565i
$512$	−1.26272e8	+	4.54939e7i	−0.940802	+	0.338956i
$513$	−1.18238e8	+	5.10177e7i	−0.875802	+	0.377893i
$514$	−3.54682e7	+	1.44754e7i	−0.261186	+	0.106596i
$515$	−2.41124e7	+	6.62483e7i	−0.176530	+	0.485013i
$516$	−2.71535e7	−	1.94379e7i	−0.197641	−	0.141482i
$517$	9.62850e6	+	8.07927e6i	0.0696766	+	0.0584656i
$518$	3.98249e7	+	2.09960e7i	0.286527	+	0.151059i
$519$	−1.61130e8	−	2.84115e7i	−1.15259	−	0.203232i
$520$	5.91060e7	+	7.95735e7i	0.420360	+	0.565924i
$521$	68636.4	+	118882.i	0.000485334	+	0.000840624i	0.866268	−	0.499580i	$-0.166512\pi$
$521$	68636.4	+	118882.i	0.000485334	+	0.000840624i	−0.865783	+	0.500420i	$0.833179\pi$
$522$	−1.41099e7	+	1.27948e7i	−0.0992005	+	0.0899542i
$523$	−7.29630e7	−	2.00464e8i	−0.510032	−	1.40130i	−0.881203	−	0.472738i	$-0.843266\pi$
$523$	−7.29630e7	−	2.00464e8i	−0.510032	−	1.40130i	0.371171	−	0.928565i	$-0.378956\pi$
$524$	−4.60739e7	+	1.65051e8i	−0.320229	+	1.14716i
$525$	−1.85873e7	+	3.21942e7i	−0.128452	+	0.222485i
$526$	2.60259e8	−	5.62770e7i	1.78833	−	0.386700i
$527$	1.16621e8	+	1.38983e8i	0.796790	+	0.949578i
$528$	7.14393e7	−	8.16214e7i	0.485328	−	0.554501i
$529$	−1.98991e7	−	1.12854e8i	−0.134421	−	0.762340i
$530$	2.27204e7	−	873415.i	0.152612	−	0.00586669i
$531$		−	1.34887e7i		−	0.0900920i
$532$	3.59878e7	+	2.27134e7i	0.239012	+	0.150851i
$533$	−5.42369e7			−0.358190
$534$	−7.47129e6	−	1.94353e8i	−0.0490650	−	1.27634i
$535$	−4.53859e7	+	8.00276e6i	−0.296387	+	0.0522611i
$536$	−1.93092e7	−	3.85521e7i	−0.125392	−	0.250354i
$537$	−4.94845e7	+	4.15224e7i	−0.319556	+	0.268139i
$538$	−1.38265e7	−	6.39421e7i	−0.0887902	−	0.410620i
$539$	8.83248e7	+	5.09944e7i	0.564049	+	0.325654i
$540$	−1.43840e7	+	5.15281e7i	−0.0913482	+	0.327237i
$541$	8.77581e7	−	3.19413e7i	0.554237	−	0.201726i	−0.0496911	−	0.998765i	$-0.515824\pi$
$541$	8.77581e7	−	3.19413e7i	0.554237	−	0.201726i	0.603928	+	0.797039i	$0.293601\pi$
$542$	1.11922e8	+	1.23426e8i	0.702937	+	0.775191i
$543$	−4.08692e7	+	2.35959e7i	−0.255268	+	0.147379i
$544$	1.25323e8	+	1.98327e7i	0.778457	+	0.123193i
$545$	2.47514e6	−	1.40372e7i	0.0152901	−	0.0867146i
$546$	4.42061e7	−	8.38496e7i	0.271584	−	0.515137i
$547$	−5.97037e7	+	7.11521e7i	−0.364787	+	0.434736i	−0.916951	−	0.398999i	$-0.869358\pi$
$547$	−5.97037e7	+	7.11521e7i	−0.364787	+	0.434736i	0.552164	+	0.833735i	$0.313802\pi$
$548$	−5.29075e7	−	3.78740e7i	−0.321496	−	0.230144i
$549$	−1.24012e7	−	4.51367e6i	−0.0749457	−	0.0272780i
$550$	3.88550e7	+	9.52042e7i	0.233539	+	0.572227i
$551$	−2.60287e8	+	6.17179e7i	−1.55596	+	0.368940i
$552$	9.26070e7	−	2.14048e8i	0.550588	−	1.27260i
$553$	−3.59576e7	−	1.30875e7i	−0.212626	−	0.0773894i
$554$	−4.21179e7	−	6.68783e7i	−0.247707	−	0.393329i
$555$	4.66962e7	−	5.56504e7i	0.273151	−	0.325529i
$556$	−1.02491e7	−	1.00440e6i	−0.0596297	−	0.00584364i
$557$	−3.45731e7	+	1.96074e8i	−0.200066	+	1.13463i	0.704952	+	0.709255i	$0.250969\pi$
$557$	−3.45731e7	+	1.96074e8i	−0.200066	+	1.13463i	−0.905017	+	0.425374i	$0.860142\pi$
$558$	2.26717e7	+	3.10504e6i	0.130491	+	0.0178716i
$559$	−6.99052e7	+	4.03598e7i	−0.400197	+	0.231054i
$560$	1.67356e7	−	5.69918e6i	0.0952965	−	0.0324525i
$561$	−9.63576e7	+	3.50713e7i	−0.545754	+	0.198638i
$562$	5.23746e7	+	4.06238e7i	0.295061	+	0.228861i
$563$	−7.49485e7	−	4.32716e7i	−0.419989	−	0.242481i	0.275084	−	0.961420i	$-0.411294\pi$
$563$	−7.49485e7	−	4.32716e7i	−0.419989	−	0.242481i	−0.695073	+	0.718940i	$0.744628\pi$
$564$	1.35596e7	+	1.98011e7i	0.0755804	+	0.110370i
$565$	−2.90948e7	+	2.44135e7i	−0.161313	+	0.135358i
$566$	−3.48379e7	+	1.08517e8i	−0.192133	+	0.598479i
$567$	5.46303e7	−	9.63280e6i	0.299699	−	0.0528449i
$568$	−1.86746e7	−	1.76569e7i	−0.101907	−	0.0963542i
$569$	−5.10585e7			−0.277160			−0.138580	−	0.990351i	$-0.544254\pi$
$569$	−5.10585e7			−0.277160			−0.138580	+	0.990351i	$0.544254\pi$
$570$	4.80962e7	−	4.90129e7i	0.259709	−	0.264658i
$571$		−	2.00473e8i		−	1.07683i	−0.842679	−	0.538416i	$-0.819023\pi$
$571$		−	2.00473e8i		−	1.07683i	0.842679	−	0.538416i	$-0.180977\pi$
$572$	−1.08325e8	−	2.38769e8i	−0.578818	−	1.27582i
$573$	1.58047e7	+	8.96326e7i	0.0840081	+	0.476433i
$574$	−2.95692e6	+	9.21054e6i	−0.0156352	+	0.0487023i
$575$	1.42115e8	+	1.69366e8i	0.747543	+	0.890887i
$576$	1.33897e7	−	8.76495e6i	0.0700655	−	0.0458651i
$577$	−3.10826e7	+	5.38367e7i	−0.161804	+	0.280253i	−0.935516	−	0.353285i	$-0.885065\pi$
$577$	−3.10826e7	+	5.38367e7i	−0.161804	+	0.280253i	0.773711	+	0.633538i	$0.218398\pi$
$578$	5.78026e7	+	4.48339e7i	0.299339	+	0.232179i
$579$	−1.22215e7	−	3.35783e7i	−0.0629636	−	0.172991i
$580$	−4.80130e7	+	1.00224e8i	−0.246079	+	0.513675i
$581$	3.16129e7	+	5.47552e7i	0.161189	+	0.279188i
$582$	−1.48070e8	−	2.02791e7i	−0.751098	−	0.102868i
$583$	−5.92287e7	−	1.04436e7i	−0.298900	−	0.0527042i
$584$	−9.84868e7	−	3.30274e8i	−0.494470	−	1.65820i
$585$	−9.05385e6	−	7.59708e6i	−0.0452237	−	0.0379472i
$586$	1.31114e8	+	2.08194e8i	0.651565	+	1.03461i
$587$	4.51651e6	−	1.24090e7i	0.0223300	−	0.0613512i	−0.928027	−	0.372513i	$-0.878496\pi$
$587$	4.51651e6	−	1.24090e7i	0.0223300	−	0.0613512i	0.950357	+	0.311162i	$0.100718\pi$
$588$	1.36254e8	+	1.39124e8i	0.670221	+	0.684337i
$589$	2.57805e8	+	1.91887e8i	1.26167	+	0.939073i
$590$	−2.97379e7	−	7.28651e7i	−0.144795	−	0.354783i
$591$	−7.51009e6	+	2.06338e7i	−0.0363817	+	0.0999578i
$592$	2.34969e8	−	3.64000e7i	1.13252	−	0.175443i
$593$	−2.31207e8	−	1.94006e8i	−1.10876	−	0.930358i	−0.110775	−	0.993846i	$-0.535333\pi$
$593$	−2.31207e8	−	1.94006e8i	−1.10876	−	0.930358i	−0.997983	+	0.0634878i	$0.979778\pi$
$594$	6.59945e7	−	1.25177e8i	0.314882	−	0.597265i
$595$	−1.64593e7	−	2.90222e6i	−0.0781376	−	0.0137778i
$596$	1.42760e7	+	5.55893e7i	0.0674321	+	0.262575i
$597$	7.19490e7	+	1.24619e8i	0.338144	+	0.585683i
$598$	−3.78690e8	−	4.17615e8i	−1.77084	−	1.95287i
$599$	9.35359e7	+	2.56988e8i	0.435209	+	1.19573i	0.942575	+	0.333996i	$0.108397\pi$
$599$	9.35359e7	+	2.56988e8i	0.435209	+	1.19573i	−0.507366	+	0.861731i	$0.669381\pi$
$600$	2.25812e7	+	1.95032e8i	0.104543	+	0.902924i
$601$	3.05727e7	−	5.29534e7i	0.140835	−	0.243933i	−0.786976	−	0.616983i	$-0.788355\pi$
$601$	3.05727e7	−	5.29534e7i	0.140835	−	0.243933i	0.927811	+	0.373050i	$0.121688\pi$
$602$	3.04279e6	+	1.40717e7i	0.0139470	+	0.0644996i
$603$	3.30463e6	+	3.93831e6i	0.0150720	+	0.0179621i
$604$	2.77389e7	+	3.60256e8i	0.125886	+	1.63494i
$605$	−6.83385e6	−	3.87567e7i	−0.0308603	−	0.175017i
$606$	−1.28608e7	−	3.34552e8i	−0.0577897	−	1.50330i
$607$		−	2.53022e8i		−	1.13134i	−0.824633	−	0.565668i	$-0.808618\pi$
$607$		−	2.53022e8i		−	1.13134i	0.824633	−	0.565668i	$-0.191382\pi$
$608$	2.24109e8	−	1.70346e7i	0.997124	−	0.0757917i
$609$	1.06271e8			0.470506
$610$	−7.69416e7	+	2.95778e6i	−0.338978	+	0.0130310i
$611$	5.71289e7	−	1.00734e7i	0.250456	−	0.0441622i
$612$	−1.50842e7	+	1.16145e6i	−0.0658063	+	0.00506693i
$613$	1.87006e8	−	1.56916e8i	0.811846	−	0.681219i	−0.139202	−	0.990264i	$-0.544454\pi$
$613$	1.87006e8	−	1.56916e8i	0.811846	−	0.681219i	0.951048	+	0.309045i	$0.100009\pi$
$614$	−1.57077e8	+	3.39655e7i	−0.678589	+	0.146735i
$615$	1.35182e7	+	7.80474e6i	0.0581157	+	0.0335531i
$616$	−4.64536e7	+	5.37851e6i	−0.198736	+	0.0230102i
$617$	−3.98931e7	+	1.45199e7i	−0.169841	+	0.0618170i	−0.425541	−	0.904939i	$-0.639916\pi$
$617$	−3.98931e7	+	1.45199e7i	−0.169841	+	0.0618170i	0.255700	+	0.966756i	$0.417694\pi$
$618$	2.63762e8	−	2.39177e8i	1.11750	−	1.01334i
$619$	−3.38699e8	+	1.95548e8i	−1.42805	+	0.824482i	−0.996966	−	0.0778319i	$-0.975200\pi$
$619$	−3.38699e8	+	1.95548e8i	−1.42805	+	0.824482i	−0.431079	+	0.902314i	$0.641867\pi$
$620$	1.29316e8	−	3.32099e7i	0.542598	−	0.139345i
$621$	5.28341e7	−	2.99637e8i	0.220617	−	1.25118i
$622$	2.85579e8	+	1.50559e8i	1.18674	+	0.625657i
$623$	−5.38992e7	+	6.42346e7i	−0.222904	+	0.265647i
$624$	−7.66385e7	−	4.94717e8i	−0.315423	−	2.03612i
$625$	−1.45792e8	−	5.30641e7i	−0.597166	−	0.217351i
$626$	−9.69395e7	+	3.95632e7i	−0.395164	+	0.161275i
$627$	−1.51746e8	+	9.98280e7i	−0.615624	+	0.404995i
$628$	1.68809e8	−	1.65327e8i	0.681581	−	0.667522i
$629$	−2.11222e8	−	7.68785e7i	−0.848765	−	0.308925i
$630$	−1.78374e6	+	1.12335e6i	−0.00713363	+	0.00449255i
$631$	−7.07629e7	+	8.43319e7i	−0.281655	+	0.335663i	−0.888261	−	0.459339i	$-0.848086\pi$
$631$	−7.07629e7	+	8.43319e7i	−0.281655	+	0.335663i	0.606606	+	0.795003i	$0.292531\pi$
$632$	−1.93667e8	+	5.77510e7i	−0.767194	+	0.228775i
$633$	2.42160e6	−	1.37336e7i	0.00954754	−	0.0541468i
$634$	3.98039e6	−	2.90631e7i	0.0156192	−	0.114045i
$635$	5.27277e6	−	3.04423e6i	0.0205929	−	0.0118893i
$636$	−1.03563e8	−	4.96124e7i	−0.402561	−	0.192849i
$637$	4.42321e8	−	1.60992e8i	1.71127	−	0.622852i
$638$	1.80161e8	−	2.32274e8i	0.693742	−	0.894414i
$639$	2.65383e6	+	1.53219e6i	0.0101711	+	0.00587231i
$640$	5.30068e7	−	7.68674e7i	0.202205	−	0.293226i
$641$	1.88736e8	−	1.58368e8i	0.716607	−	0.601304i	−0.209838	−	0.977736i	$-0.567294\pi$
$641$	1.88736e8	−	1.58368e8i	0.716607	−	0.601304i	0.926444	+	0.376432i	$0.122849\pi$
$642$	2.21615e8	+	7.11465e7i	0.837518	+	0.268874i
$643$	3.45531e8	−	6.09265e7i	1.29973	−	0.229178i	0.519394	−	0.854535i	$-0.326158\pi$
$643$	3.45531e8	−	6.09265e7i	1.29973	−	0.229178i	0.780339	+	0.625357i	$0.215047\pi$
$644$	−9.15652e7	+	4.15415e7i	−0.342825	+	0.155534i
$645$	2.32312e7			0.0865751
$646$	−1.93405e8	−	8.79733e7i	−0.717413	−	0.326327i
$647$			2.31151e8i			0.853460i	0.904379	+	0.426730i	$0.140334\pi$
$647$			2.31151e8i			0.853460i	−0.904379	+	0.426730i	$0.859666\pi$
$648$	2.01284e8	−	2.12884e8i	0.739747	−	0.782382i
$649$	3.61483e7	+	2.05007e8i	0.132237	+	0.749955i
$650$	4.51866e8	+	1.45065e8i	1.64539	+	0.528231i
$651$	−8.20674e7	−	9.78041e7i	−0.297459	−	0.354498i
$652$	−1.96647e8	+	1.34662e8i	−0.709488	+	0.485850i
$653$	1.07959e8	−	1.86990e8i	0.387720	−	0.671551i	−0.604423	−	0.796664i	$-0.706596\pi$
$653$	1.07959e8	−	1.86990e8i	0.387720	−	0.671551i	0.992142	+	0.125113i	$0.0399295\pi$
$654$	−4.41205e7	+	5.68829e7i	−0.157728	+	0.203352i
$655$	−4.07728e7	−	1.12022e8i	−0.145093	−	0.398640i
$656$	1.64695e7	+	4.83625e7i	0.0583403	+	0.171316i
$657$	2.05469e7	+	3.55882e7i	0.0724519	+	0.125490i
$658$	1.40392e6	−	1.02508e7i	0.00492794	−	0.0359817i
$659$	3.81280e8	+	6.72300e7i	1.33226	+	0.234913i	0.794026	−	0.607884i	$-0.207981\pi$
$659$	3.81280e8	+	6.72300e7i	1.33226	+	0.234913i	0.538232	+	0.842797i	$0.319092\pi$
$660$	−7.35969e6	+	7.50998e7i	−0.0255993	+	0.261220i
$661$	−1.60832e8	−	1.34954e8i	−0.556889	−	0.467285i	0.320377	−	0.947290i	$-0.396190\pi$
$661$	−1.60832e8	−	1.34954e8i	−0.556889	−	0.467285i	−0.877266	+	0.480005i	$0.840635\pi$
$662$	3.04383e8	−	1.91691e8i	1.04917	−	0.660736i
$663$	−1.61864e8	+	4.44719e8i	−0.555406	+	1.52597i
$664$	3.06468e8	+	1.32592e8i	1.04684	+	0.452912i
$665$	−2.95549e7	+	1.72449e6i	−0.100500	+	0.00586401i
$666$	−2.62488e7	+	1.07127e7i	−0.0888560	+	0.0362641i
$667$	2.16169e8	−	5.93919e8i	0.728477	−	2.00147i
$668$	−2.83828e8	+	3.96490e8i	−0.952195	+	1.33016i
$669$	−3.37150e8	−	2.82903e8i	−1.12602	−	0.944841i
$670$	2.65340e7	+	1.39889e7i	0.0882223	+	0.0465114i
$671$	2.00575e8	+	3.53668e7i	0.663911	+	0.117065i
$672$	−8.81914e7	−	1.39565e7i	−0.290615	−	0.0459906i
$673$	−2.24263e8	−	3.88434e8i	−0.735718	−	1.27430i	−0.954407	−	0.298507i	$-0.903511\pi$
$673$	−2.24263e8	−	3.88434e8i	−0.735718	−	1.27430i	0.218689	−	0.975795i	$-0.429822\pi$
$674$	−2.28197e8	+	2.06927e8i	−0.745297	+	0.675829i
$675$	8.76039e7	+	2.40690e8i	0.284847	+	0.782611i
$676$	−8.67996e8	−	2.42301e8i	−2.80982	−	0.784358i
$677$	−2.10207e8	+	3.64089e8i	−0.677456	+	1.17339i	0.298289	+	0.954476i	$0.403584\pi$
$677$	−2.10207e8	+	3.64089e8i	−0.677456	+	1.17339i	−0.975745	+	0.218912i	$0.929749\pi$
$678$	1.87486e8	−	4.05410e7i	0.601562	−	0.130078i
$679$	4.14164e7	+	4.93581e7i	0.132301	+	0.157670i
$680$	−7.89232e7	+	3.95294e7i	−0.251002	+	0.125717i
$681$	1.08253e8	+	6.13932e8i	0.342766	+	1.94392i
$682$	−3.52895e8	+	1.35660e7i	−1.11248	+	0.0427659i
$683$			2.66091e8i			0.835157i	0.908641	+	0.417578i	$0.137121\pi$
$683$			2.66091e8i			0.835157i	−0.908641	+	0.417578i	$0.862879\pi$
$684$	−2.55241e7	+	8.16653e6i	−0.0797593	+	0.0255193i
$685$	4.52651e7			0.140829
$686$	−6.72994e6	−	1.75068e8i	−0.0208468	−	0.542293i
$687$	−4.21190e8	+	7.42671e7i	−1.29900	+	0.229048i
$688$	5.72157e7	+	5.00781e7i	0.175691	+	0.153774i
$689$	−2.12635e8	+	1.78422e8i	−0.650094	+	0.545494i
$690$	3.42908e7	+	1.58582e8i	0.104383	+	0.482731i
$691$	4.39501e8	+	2.53746e8i	1.33207	+	0.769069i	0.985616	−	0.168999i	$-0.0540534\pi$
$691$	4.39501e8	+	2.53746e8i	1.33207	+	0.769069i	0.346451	+	0.938068i	$0.387387\pi$
$692$	3.58826e8	+	1.00166e8i	1.08284	+	0.302275i
$693$	5.23962e6	−	1.90707e6i	0.0157435	−	0.00573015i
$694$	−1.88769e8	−	2.08173e8i	−0.564745	−	0.622795i
$695$	6.20440e6	−	3.58211e6i	0.0184818	−	0.0106705i
$696$	4.50565e8	−	3.34673e8i	1.33638	−	0.992644i
$697$	8.38683e6	−	4.75641e7i	0.0247685	−	0.140469i
$698$	−1.85758e8	+	3.52343e8i	−0.546236	+	1.03609i
$699$	−1.50237e8	+	1.79045e8i	−0.439891	+	0.524242i
$700$	4.92701e7	−	6.88273e7i	0.143645	−	0.200663i
$701$	−7.79272e7	−	2.83632e7i	−0.226222	−	0.0823381i	0.226422	−	0.974029i	$-0.427297\pi$
$701$	−7.79272e7	−	2.83632e7i	−0.226222	−	0.0823381i	−0.452644	+	0.891691i	$0.649519\pi$
$702$	−2.46785e8	−	6.04683e8i	−0.713357	−	1.74790i
$703$	−3.95476e8	−	4.61826e7i	−1.13829	−	0.132927i
$704$	−1.80014e8	+	1.69097e8i	−0.515927	+	0.484638i
$705$	−1.56886e7	−	5.71017e6i	−0.0447730	−	0.0162960i
$706$	1.95860e8	+	3.11003e8i	0.556585	+	0.883792i
$707$	−9.27803e7	+	1.10571e8i	−0.262541	+	0.312884i
$708$	−3.87658e7	+	3.95574e8i	−0.109232	+	1.11462i
$709$	5.58796e7	−	3.16909e8i	0.156789	−	0.889193i	−0.800343	−	0.599542i	$-0.795350\pi$
$709$	5.58796e7	−	3.16909e8i	0.156789	−	0.889193i	0.957132	−	0.289651i	$-0.0935394\pi$
$710$	1.77137e7	+	2.42602e6i	0.0494920	+	0.00677827i
$711$	2.08684e7	−	1.20483e7i	0.0580603	−	0.0335211i
$712$	−2.62301e7	+	4.42080e8i	−0.0726709	+	1.22479i
$713$	−7.13533e8	+	2.59705e8i	−1.96855	+	0.716492i
$714$	6.66977e7	+	5.17333e7i	0.183238	+	0.142127i
$715$	1.57964e8	+	9.12005e7i	0.432155	+	0.249505i
$716$	1.21358e8	−	8.31044e7i	0.330619	−	0.226405i
$717$	−1.87218e8	+	1.57095e8i	−0.507915	+	0.426191i
$718$	−1.29639e8	+	4.03813e8i	−0.350236	+	1.09095i
$719$	−2.83310e8	+	4.99552e7i	−0.762211	+	0.134398i	−0.541224	−	0.840878i	$-0.682039\pi$
$719$	−2.83310e8	+	4.99552e7i	−0.762211	+	0.134398i	−0.220987	+	0.975277i	$0.570928\pi$
$720$	−4.02496e6	+	1.03801e7i	−0.0107836	+	0.0278103i
$721$	−1.53505e8			−0.409560
$722$	−3.69301e8	−	7.25869e7i	−0.981226	−	0.192862i
$723$			1.71477e8i			0.453722i
$724$	9.78535e7	−	4.43944e7i	0.257846	−	0.116980i
$725$	9.23930e7	+	5.23987e8i	0.242452	+	1.37501i
$726$	−6.07547e7	+	1.89245e8i	−0.158770	+	0.494556i
$727$	−3.06132e8	−	3.64834e8i	−0.796719	−	0.949493i	0.202839	−	0.979212i	$-0.434983\pi$
$727$	−3.06132e8	−	3.64834e8i	−0.796719	−	0.949493i	−0.999558	+	0.0297192i	$0.990539\pi$
$728$	−1.18796e8	+	1.80194e8i	−0.307899	+	0.467031i
$729$	1.74885e8	−	3.02910e8i	0.451410	−	0.781864i
$730$	1.89453e8	+	1.46947e8i	0.487004	+	0.377739i
$731$	−2.45846e7	−	6.75456e7i	−0.0629377	−	0.172920i
$732$	3.50710e8	+	1.68010e8i	0.894160	+	0.428353i
$733$	2.32593e8	+	4.02862e8i	0.590587	+	1.02293i	0.994153	+	0.107977i	$0.0344372\pi$
$733$	2.32593e8	+	4.02862e8i	0.590587	+	1.02293i	−0.403566	+	0.914950i	$0.632229\pi$
$734$	2.66081e8	+	3.64416e7i	0.672863	+	0.0921531i
$735$	−1.33412e8	−	2.35242e7i	−0.335996	−	0.0592452i
$736$	−2.57391e8	+	4.64486e8i	−0.645594	+	1.16504i
$737$	−6.07796e7	−	5.10001e7i	−0.151829	−	0.127400i
$738$	−3.24625e6	−	5.15466e6i	−0.00807630	−	0.0128242i
$739$	3.04297e7	−	8.36049e7i	0.0753988	−	0.207156i	−0.896267	−	0.443514i	$-0.853732\pi$
$739$	3.04297e7	−	8.36049e7i	0.0753988	−	0.207156i	0.971666	+	0.236358i	$0.0759538\pi$
$740$	−1.18176e8	+	1.15739e8i	−0.291632	+	0.285617i
$741$	−9.72353e7	+	8.32658e8i	−0.238984	+	2.04650i
$742$	1.87071e7	+	4.58370e7i	0.0457926	+	0.112203i
$743$	4.13319e7	−	1.13558e8i	0.100767	−	0.276855i	−0.879057	−	0.476716i	$-0.841827\pi$
$743$	4.13319e7	−	1.13558e8i	0.100767	−	0.276855i	0.979824	+	0.199861i	$0.0640491\pi$
$744$	−6.55954e8	−	1.56217e8i	−1.59278	−	0.379323i
$745$	−3.05859e7	−	2.56646e7i	−0.0739694	−	0.0620677i
$746$	1.49017e8	−	2.82653e8i	0.358938	−	0.680829i
$747$	−3.92101e7	−	6.91380e6i	−0.0940668	−	0.0165865i
$748$	2.26144e8	−	5.80762e7i	0.540356	−	0.138769i
$749$	−5.01734e7	−	8.69029e7i	−0.119406	−	0.206818i
$750$	−1.96831e8	−	2.17063e8i	−0.466561	−	0.514519i
$751$	−4.02773e7	−	1.10661e8i	−0.0950913	−	0.261261i	0.883023	−	0.469330i	$-0.155504\pi$
$751$	−4.02773e7	−	1.10661e8i	−0.0950913	−	0.261261i	−0.978114	+	0.208069i	$0.933282\pi$
$752$	−2.63300e7	−	4.78824e7i	−0.0619151	−	0.112596i
$753$	−2.21464e8	+	3.83587e8i	−0.518702	+	0.898419i
$754$	−2.86735e8	−	1.32604e9i	−0.668909	−	3.09344i
$755$	−1.61573e8	−	1.92556e8i	−0.375430	−	0.447420i
$756$	−1.16142e8	+	8.94265e6i	−0.268796	+	0.0206967i
$757$	−5.53688e7	−	3.14012e8i	−0.127637	−	0.723867i	−0.979706	−	0.200438i	$-0.935764\pi$
$757$	−5.53688e7	−	3.14012e8i	−0.127637	−	0.723867i	0.852069	−	0.523429i	$-0.175348\pi$
$758$	1.85075e7	+	4.81442e8i	0.0424953	+	1.10544i
$759$		−	4.29161e8i		−	0.981510i
$760$	−1.19875e8	+	1.00387e8i	−0.273079	+	0.228684i
$761$	4.46350e8			1.01280			0.506398	−	0.862300i	$-0.330977\pi$
$761$	4.46350e8			1.01280			0.506398	+	0.862300i	$0.330977\pi$
$762$	−3.07268e7	+	1.18120e6i	−0.0694469	+	0.00266967i
$763$	3.05644e7	−	5.38933e6i	0.0688085	−	0.0121328i
$764$	−1.59097e7	−	2.06626e8i	−0.0356764	−	0.463345i
$765$	8.06243e6	−	6.76518e6i	0.0180087	−	0.0151111i
$766$	8.52727e8	−	1.84389e8i	1.89725	−	0.410251i
$767$	8.32047e8	+	4.80382e8i	1.84400	+	1.06464i
$768$	−4.17862e8	+	2.18563e8i	−0.922465	+	0.482495i
$769$	3.49074e8	−	1.27053e8i	0.767607	−	0.279386i	0.0716117	−	0.997433i	$-0.477186\pi$
$769$	3.49074e8	−	1.27053e8i	0.767607	−	0.279386i	0.695995	+	0.718047i	$0.254964\pi$
$770$	2.40997e7	−	2.18534e7i	0.0527885	−	0.0478682i
$771$	−1.16563e8	+	6.72977e7i	−0.254330	+	0.146837i
$772$	2.02382e7	+	7.88057e7i	0.0439866	+	0.171280i
$773$	1.54732e8	−	8.77531e8i	0.334999	−	1.89987i	−0.0922484	−	0.995736i	$-0.529405\pi$
$773$	1.54732e8	−	8.77531e8i	0.334999	−	1.89987i	0.427247	−	0.904135i	$-0.359483\pi$
$774$	−8.01982e6	−	4.22811e6i	−0.0172959	−	0.00911850i
$775$	4.10888e8	−	4.89677e8i	0.882710	−	1.05197i
$776$	3.31036e8	+	7.88368e7i	0.708418	+	0.168711i
$777$	1.48639e8	+	5.41003e7i	0.316863	+	0.115329i
$778$	7.16255e8	−	2.92320e8i	1.52100	−	0.620754i
$779$	−4.98342e6	−	8.54078e7i	−0.0105418	−	0.180670i
$780$	2.43683e8	+	2.48815e8i	0.513501	+	0.524316i
$781$	−4.44402e7	−	1.61749e7i	−0.0932873	−	0.0339538i
$782$	4.24793e8	−	2.67522e8i	0.888295	−	0.559421i
$783$	4.70661e8	−	5.60912e8i	0.980445	−	1.16845i
$784$	−2.77869e8	−	3.45526e8i	−0.576623	−	0.717023i
$785$	−2.85437e7	+	1.61879e8i	−0.0590066	+	0.334643i
$786$	−8.16952e7	+	5.96504e8i	−0.168240	+	1.22842i
$787$	6.04619e8	−	3.49077e8i	1.24039	−	0.716138i	0.271215	−	0.962519i	$-0.412575\pi$
$787$	6.04619e8	−	3.49077e8i	1.24039	−	0.716138i	0.969173	+	0.246380i	$0.0792413\pi$
$788$	2.16008e7	−	4.50903e7i	0.0441460	−	0.0921520i
$789$	8.79127e8	−	3.19976e8i	1.78987	−	0.651458i
$790$	8.61671e7	−	1.11092e8i	0.174767	−	0.225321i
$791$	−7.16188e7	−	4.13491e7i	−0.144710	−	0.0835481i
$792$	1.62089e7	−	2.45863e7i	0.0326271	−	0.0494900i
$793$	7.20078e8	−	6.04217e8i	1.44398	−	1.21164i
$794$	−5.19444e8	−	1.66760e8i	−1.03771	−	0.333144i
$795$	7.86728e7	−	1.38721e7i	0.156575	−	0.0276085i
$796$	−1.35368e8	−	2.98377e8i	−0.268397	−	0.591597i
$797$	−2.87770e8			−0.568422			−0.284211	−	0.958762i	$-0.591732\pi$
$797$	−2.87770e8			−0.568422			−0.284211	+	0.958762i	$0.591732\pi$
$798$	1.36101e8	+	6.19079e7i	0.267826	+	0.121825i
$799$			5.16579e7i			0.101274i
$800$	−7.85954e6	−	4.46974e8i	−0.0153507	−	0.872997i
$801$	−9.16932e6	−	5.20018e7i	−0.0178418	−	0.101186i
$802$	−1.47509e8	−	4.73559e7i	−0.285954	−	0.0918017i
$803$	−4.07654e8	−	4.85823e8i	−0.787308	−	0.938277i
$804$	−8.55944e7	−	1.24994e8i	−0.164694	−	0.240503i
$805$	3.49744e7	−	6.05774e7i	0.0670443	−	0.116124i
$806$	−9.98955e8	+	1.28791e9i	−1.90784	+	2.45970i
$807$	−7.86137e7	−	2.15989e8i	−0.149581	−	0.410972i
$808$	−4.51517e7	+	7.60982e8i	−0.0855933	+	1.44258i
$809$	−1.39905e8	−	2.42322e8i	−0.264233	−	0.457664i	0.703130	−	0.711062i	$-0.251785\pi$
$809$	−1.39905e8	−	2.42322e8i	−0.264233	−	0.457664i	−0.967362	+	0.253397i	$0.918452\pi$
$810$	−2.76558e7	+	2.01931e8i	−0.0520393	+	0.379969i
$811$	−7.43419e8	−	1.31085e8i	−1.39371	−	0.245748i	−0.574151	−	0.818750i	$-0.694668\pi$
$811$	−7.43419e8	−	1.31085e8i	−1.39371	−	0.245748i	−0.819554	+	0.573002i	$0.805779\pi$
$812$	−2.40821e8	−	2.36002e7i	−0.449807	−	0.0440806i
$813$	4.48440e8	+	3.76286e8i	0.834512	+	0.700238i
$814$	3.70232e8	−	2.33161e8i	0.686437	−	0.432297i
$815$	5.67084e7	−	1.55805e8i	0.104755	−	0.287812i
$816$	4.45702e8	+	9.29020e6i	0.820303	+	0.0170984i
$817$	−6.99783e7	−	1.06373e8i	−0.128321	−	0.195058i
$818$	3.41713e8	−	1.39461e8i	0.624312	−	0.254796i
$819$	8.80167e6	−	2.41824e7i	0.0160219	−	0.0440197i
$820$	−2.89003e7	−	2.06883e7i	−0.0524156	−	0.0375218i
$821$	−2.19183e8	−	1.83916e8i	−0.396075	−	0.332346i	0.422899	−	0.906177i	$-0.361012\pi$
$821$	−2.19183e8	−	1.83916e8i	−0.396075	−	0.332346i	−0.818974	+	0.573831i	$0.805457\pi$
$822$	−2.02226e8	−	1.06615e8i	−0.364101	−	0.191957i
$823$	−9.57765e8	−	1.68880e8i	−1.71814	−	0.302955i	−0.774170	−	0.632977i	$-0.781833\pi$
$823$	−9.57765e8	−	1.68880e8i	−1.71814	−	0.302955i	−0.943973	+	0.330022i	$0.892944\pi$
$824$	−6.50825e8	+	4.83423e8i	−1.16328	+	0.864064i
$825$	1.80641e8	+	3.12880e8i	0.321703	+	0.557206i
$826$	1.26941e8	−	1.15109e8i	0.225248	−	0.204253i
$827$	1.35041e8	+	3.71022e8i	0.238753	+	0.655969i	0.999972	+	0.00747417i	$0.00237912\pi$
$827$	1.35041e8	+	3.71022e8i	0.238753	+	0.655969i	−0.761219	+	0.648495i	$0.775399\pi$
$828$	1.70242e7	−	6.09861e7i	0.0299900	−	0.107434i
$829$	1.87637e7	−	3.24996e7i	0.0329347	−	0.0570447i	−0.849088	−	0.528251i	$-0.822848\pi$
$829$	1.87637e7	−	3.24996e7i	0.0329347	−	0.0570447i	0.882023	+	0.471206i	$0.156181\pi$
$830$	−2.27053e8	+	4.90967e7i	−0.397094	+	0.0858654i
$831$	−1.78495e8	−	2.12723e8i	−0.311046	−	0.370690i
$832$	6.38058e7	+	1.13810e9i	0.110787	+	1.97610i
$833$	7.27871e7	+	4.12796e8i	0.125927	+	0.714168i
$834$	−3.61559e7	+	1.38990e6i	−0.0623276	+	0.00239599i
$835$		−	3.39218e8i		−	0.582665i
$836$	3.66041e8	−	1.92520e8i	0.626485	−	0.329502i
$837$	−8.79686e8			−1.50021
$838$	−1.62885e7	−	4.23718e8i	−0.0276790	−	0.720021i
$839$	6.94236e8	−	1.22412e8i	1.17550	−	0.207272i	0.448416	−	0.893825i	$-0.351988\pi$
$839$	6.94236e8	−	1.22412e8i	1.17550	−	0.207272i	0.727080	+	0.686553i	$0.240877\pi$
$840$	5.55392e7	−	2.78173e7i	0.0937048	−	0.0469329i
$841$	7.09517e8	−	5.95355e8i	1.19282	−	1.00089i
$842$	6.49498e7	+	3.00367e8i	0.108803	+	0.503172i
$843$	2.01682e8	+	1.16441e8i	0.336655	+	0.194368i
$844$	−8.53745e6	+	3.05838e7i	−0.0142004	+	0.0508703i
$845$	5.89121e8	−	2.14422e8i	0.976415	−	0.355386i
$846$	4.37671e6	+	4.82659e6i	0.00722831	+	0.00797130i
$847$	7.42096e7	−	4.28449e7i	0.122126	−	0.0705098i
$848$	2.23665e8	+	1.35425e8i	0.366784	+	0.222081i
$849$	−6.95353e7	+	3.94354e8i	−0.113627	+	0.644412i
$850$	−1.97091e8	+	3.73840e8i	−0.320930	+	0.608736i
$851$	6.04701e8	−	7.20655e8i	0.981188	−	1.16933i
$852$	−7.34237e7	−	5.25605e7i	−0.118718	−	0.0849847i
$853$	−4.51735e8	−	1.64418e8i	−0.727841	−	0.264912i	−0.0485901	−	0.998819i	$-0.515473\pi$
$853$	−4.51735e8	−	1.64418e8i	−0.727841	−	0.264912i	−0.679251	+	0.733906i	$0.737695\pi$
$854$	−6.33508e7	−	1.55225e8i	−0.101713	−	0.249223i
$855$	1.11314e7	−	1.49553e7i	0.0178094	−	0.0239275i
$856$	−4.86400e8	−	2.10440e8i	−0.775483	−	0.335511i
$857$	9.87605e8	+	3.59459e8i	1.56906	+	0.571093i	0.972790	−	0.231688i	$-0.0744248\pi$
$857$	9.87605e8	+	3.59459e8i	1.56906	+	0.571093i	0.596274	+	0.802781i	$0.296647\pi$
$858$	−4.90910e8	−	7.79507e8i	−0.777213	−	1.23412i
$859$	−1.39273e8	+	1.65979e8i	−0.219730	+	0.261863i	−0.864637	−	0.502397i	$-0.832451\pi$
$859$	−1.39273e8	+	1.65979e8i	−0.219730	+	0.261863i	0.644907	+	0.764261i	$0.276896\pi$
$860$	−5.26441e7	−	5.15906e6i	−0.0827664	−	0.00811102i
$861$	−5.90191e6	+	3.34714e7i	−0.00924662	+	0.0524402i
$862$	5.81227e7	+	7.96029e6i	0.0907452	+	0.0124282i
$863$	−4.05820e8	+	2.34300e8i	−0.631394	+	0.364536i	−0.781292	−	0.624166i	$-0.785439\pi$
$863$	−4.05820e8	+	2.34300e8i	−0.631394	+	0.364536i	0.149898	+	0.988702i	$0.452106\pi$
$864$	−4.64251e8	+	4.03672e8i	−0.719800	+	0.625875i
$865$	−2.43540e8	+	8.86412e7i	−0.376289	+	0.136958i
$866$	2.59165e8	+	2.01018e8i	0.399046	+	0.309515i
$867$	2.22584e8	+	1.28509e8i	0.341536	+	0.197186i
$868$	1.64253e8	+	2.39858e8i	0.251161	+	0.366771i
$869$	−2.84878e8	+	2.39041e8i	−0.434110	+	0.364262i
$870$	−1.19351e8	+	3.71768e8i	−0.181246	+	0.564565i
$871$	−3.60624e8	+	6.35877e7i	−0.545758	+	0.0962318i
$872$	1.12613e8	−	1.19104e8i	0.169840	−	0.179629i
$873$	−4.05749e7			−0.0609838
$874$	6.22831e8	−	6.34701e8i	0.932902	−	0.950681i
$875$			1.26327e8i			0.188569i
$876$	−5.00287e8	−	1.10273e9i	−0.744229	−	1.64042i
$877$	1.80370e8	+	1.02293e9i	0.267403	+	1.51652i	0.762105	+	0.647454i	$0.224166\pi$
$877$	1.80370e8	+	1.02293e9i	0.267403	+	1.51652i	−0.494702	+	0.869063i	$0.664723\pi$
$878$	−2.39619e8	+	7.46392e8i	−0.354028	+	1.10277i
$879$	5.55662e8	+	6.62212e8i	0.818171	+	0.975058i
$880$	3.33555e7	−	1.68549e8i	0.0489462	−	0.247330i
$881$	3.50498e8	−	6.07080e8i	0.512575	−	0.887806i	−0.487319	−	0.873224i	$-0.662025\pi$
$881$	3.50498e8	−	6.07080e8i	0.512575	−	0.887806i	0.999894	−	0.0145819i	$-0.00464174\pi$
$882$	4.17749e7	+	3.24022e7i	0.0608849	+	0.0472246i
$883$	−6.42534e7	−	1.76535e8i	−0.0933285	−	0.256418i	0.884241	−	0.467031i	$-0.154676\pi$
$883$	−6.42534e7	−	1.76535e8i	−0.0933285	−	0.256418i	−0.977570	+	0.210613i	$0.932454\pi$
$884$	4.65560e8	−	9.71828e8i	0.673937	−	1.40680i
$885$	−1.38255e8	−	2.39464e8i	−0.199458	−	0.345471i
$886$	−7.31609e8	−	1.00199e8i	−1.05191	−	0.144066i
$887$	6.90726e8	+	1.21794e8i	0.989772	+	0.174524i	0.645016	−	0.764169i	$-0.276851\pi$
$887$	6.90726e8	+	1.21794e8i	0.989772	+	0.174524i	0.344756	+	0.938692i	$0.387962\pi$
$888$	8.00570e8	−	2.38728e8i	1.14330	−	0.340929i
$889$	1.01554e7	+	8.52137e6i	0.0144541	+	0.0121284i
$890$	−1.64178e8	−	2.60695e8i	−0.232887	−	0.369797i
$891$	1.84389e8	−	5.06604e8i	0.260676	−	0.716201i
$892$	7.01189e8	+	7.15956e8i	0.987962	+	1.00877i
$893$	2.11118e7	+	8.90363e7i	0.0296464	+	0.125030i
$894$	7.61962e7	+	1.86699e8i	0.106640	+	0.261294i
$895$	−3.49967e7	+	9.61526e7i	−0.0488155	+	0.134119i
$896$	1.96750e8	+	5.12118e7i	0.273522	+	0.0711944i
$897$	−1.51731e9	−	1.27317e9i	−2.10231	−	1.76404i
$898$	−5.96073e8	+	1.13062e9i	−0.823134	+	1.56131i
$899$	−1.79960e9	−	3.17318e8i	−2.47684	−	0.436733i
$900$	1.32586e7	+	5.16278e7i	0.0181874	+	0.0708200i
$901$	−1.23590e8	−	2.14064e8i	−0.168969	−	0.292664i
$902$	6.31519e7	+	6.96433e7i	0.0860532	+	0.0948985i
$903$	1.73005e7	+	4.75326e7i	0.0234960	+	0.0645548i
$904$	−4.33864e8	+	5.02338e7i	−0.587285	+	0.0679971i
$905$	−3.73763e7	+	6.47376e7i	−0.0504255	+	0.0873395i
$906$	2.68308e8	+	1.24082e9i	0.360786	+	1.66849i
$907$	3.28838e7	+	3.91894e7i	0.0440718	+	0.0525227i	0.787630	−	0.616148i	$-0.211308\pi$
$907$	3.28838e7	+	3.91894e7i	0.0440718	+	0.0525227i	−0.743558	+	0.668671i	$0.766863\pi$
$908$	−1.08972e8	−	1.41527e9i	−0.145565	−	1.89052i
$909$	−1.57838e7	−	8.95142e7i	−0.0210145	−	0.119179i
$910$	−5.76769e6	−	1.50036e8i	−0.00765381	−	0.199101i
$911$			6.69661e8i			0.885727i	0.896589	+	0.442863i	$0.146037\pi$
$911$			6.69661e8i			0.885727i	−0.896589	+	0.442863i	$0.853963\pi$
$912$	7.71999e8	−	1.66140e8i	1.01773	−	0.219023i
$913$	6.14461e8			0.807388
$914$	−1.37354e9	+	5.28014e7i	−1.79888	+	0.0691523i
$915$	−2.66422e8	+	4.69774e7i	−0.347782	+	0.0613233i
$916$	9.70948e8	−	7.47607e7i	1.26331	−	0.0972718i
$917$	1.98841e8	−	1.66848e8i	0.257869	−	0.216378i
$918$	5.68449e8	−	1.22918e8i	0.734790	−	0.158887i
$919$	7.86336e8	+	4.53991e8i	1.01312	+	0.584926i	0.912104	−	0.409959i	$-0.134457\pi$
$919$	7.86336e8	+	4.53991e8i	1.01312	+	0.584926i	0.101017	+	0.994885i	$0.467790\pi$
$920$	−4.24893e7	−	3.66976e8i	−0.0545652	−	0.471275i
$921$	−5.30589e8	+	1.93118e8i	−0.679171	+	0.247198i
$922$	−1.35952e8	+	1.23280e8i	−0.173457	+	0.157289i
$923$	−1.89025e8	+	1.09134e8i	−0.240389	+	0.138789i
$924$	−1.59140e8	+	4.08689e7i	−0.201727	+	0.0518057i
$925$	−1.37522e8	+	7.79924e8i	−0.173758	+	0.985432i
$926$	9.92059e8	+	5.23021e8i	1.24941	+	0.658697i
$927$	6.21359e7	−	7.40507e7i	0.0780016	−	0.0929586i
$928$	−1.09535e9	+	6.58342e8i	−1.37059	+	0.823773i
$929$	−1.77113e7	−	6.44638e6i	−0.0220904	−	0.00804023i	0.330951	−	0.943648i	$-0.392630\pi$
$929$	−1.77113e7	−	6.44638e6i	−0.0220904	−	0.00804023i	−0.353042	+	0.935608i	$0.614853\pi$
$930$	4.34315e8	−	1.77254e8i	0.539953	−	0.220367i
$931$	2.94158e8	+	6.81738e8i	0.364528	+	0.844828i
$932$	3.80212e8	−	3.72370e8i	0.469655	−	0.459967i
$933$	1.06587e9	+	3.87946e8i	1.31238	+	0.477668i
$934$	−3.27285e8	+	2.06114e8i	−0.401684	+	0.252969i
$935$	−1.04406e8	+	1.24427e8i	−0.127730	+	0.152223i
$936$	−3.88390e7	−	1.30246e8i	−0.0473631	−	0.158832i
$937$	−1.77872e8	+	1.00876e9i	−0.216217	+	1.22623i	0.662565	+	0.749004i	$0.269468\pi$
$937$	−1.77872e8	+	1.00876e9i	−0.216217	+	1.22623i	−0.878782	+	0.477223i	$0.841643\pi$
$938$	−8.86220e6	+	6.47080e7i	−0.0107382	+	0.0784061i
$939$	−3.18583e8	+	1.83934e8i	−0.384792	+	0.222160i
$940$	3.42837e7	+	1.64238e7i	0.0412766	+	0.0197738i
$941$	−1.09172e9	+	3.97355e8i	−1.31022	+	0.476881i	−0.900312	−	0.435246i	$-0.856661\pi$
$941$	−1.09172e9	+	3.97355e8i	−1.31022	+	0.476881i	−0.409908	+	0.912127i	$0.634439\pi$
$942$	5.08803e8	−	6.55980e8i	0.608691	−	0.784762i
$943$	1.75056e8	+	1.01069e8i	0.208758	+	0.120526i
$944$	1.75694e8	−	8.87800e8i	0.208853	−	1.05536i
$945$	6.20773e7	−	5.20891e7i	0.0735593	−	0.0617236i
$946$	1.33220e8	+	4.27684e7i	0.157360	+	0.0505184i
$947$	−4.13944e8	+	7.29895e7i	−0.487407	+	0.0859429i	−0.411951	−	0.911206i	$-0.635152\pi$
$947$	−4.13944e8	+	7.29895e7i	−0.487407	+	0.0859429i	−0.0754561	+	0.997149i	$0.524041\pi$
$948$	−6.46620e8	+	2.93360e8i	−0.758969	+	0.344331i
$949$	−2.92700e9			−3.42472
$950$	−1.86919e8	+	7.24890e8i	−0.218013	+	0.845476i
$951$		−	1.03066e8i		−	0.119832i
$952$	−1.39655e8	−	1.32044e8i	−0.161862	−	0.153041i
$953$	−2.40217e7	−	1.36234e8i	−0.0277539	−	0.157400i	0.967781	−	0.251793i	$-0.0810202\pi$
$953$	−2.40217e7	−	1.36234e8i	−0.0277539	−	0.157400i	−0.995535	+	0.0943926i	$0.969909\pi$
$954$	−2.96840e7	−	9.52964e6i	−0.0341883	−	0.0109757i
$955$	9.26706e7	+	1.10441e8i	0.106398	+	0.126800i
$956$	4.59141e8	−	3.14415e8i	0.525499	−	0.359857i
$957$	5.16401e8	−	8.94432e8i	0.589184	−	1.02050i
$958$	−6.51010e7	+	8.39321e7i	−0.0740442	+	0.0954623i
$959$	3.37093e7	+	9.26155e7i	0.0382203	+	0.105009i
$960$	1.47870e8	−	2.92845e8i	0.167134	−	0.330997i
$961$	6.53943e8	+	1.13266e9i	0.736834	+	1.27623i
$962$	2.74005e8	−	2.00067e9i	0.307775	−	2.24724i
$963$	6.22310e7	+	1.09730e7i	0.0696832	+	0.0122870i
$964$	3.80806e7	−	3.88582e8i	0.0425082	−	0.433762i
$965$	−4.33598e7	−	3.63832e7i	−0.0482509	−	0.0404873i
$966$	−2.98932e8	+	1.88258e8i	−0.331620	+	0.208844i
$967$	−2.45420e8	+	6.74285e8i	−0.271413	+	0.745700i	0.726851	+	0.686795i	$0.240983\pi$
$967$	−2.45420e8	+	6.74285e8i	−0.271413	+	0.745700i	−0.998264	+	0.0589048i	$0.981239\pi$
$968$	1.79702e8	−	4.15355e8i	0.198120	−	0.457924i
$969$	−7.15179e8	−	2.14029e8i	−0.786037	−	0.235234i
$970$	−2.19183e8	+	8.94534e7i	−0.240155	+	0.0980126i
$971$	−5.27449e8	+	1.44915e9i	−0.576133	+	1.58291i	0.218510	+	0.975835i	$0.429880\pi$
$971$	−5.27449e8	+	1.44915e9i	−0.576133	+	1.58291i	−0.794643	+	0.607078i	$0.792342\pi$
$972$	8.92986e7	−	1.24744e8i	0.0972402	−	0.135838i
$973$	1.19497e7	+	1.00270e7i	0.0129723	+	0.0108851i
$974$	−6.51302e7	−	3.43371e7i	−0.0704865	−	0.0371610i
$975$	1.64209e9	+	2.89546e8i	1.77168	+	0.312394i
$976$	−7.57432e8	−	4.58610e8i	−0.814693	−	0.493281i
$977$	−2.19626e8	−	3.80404e8i	−0.235505	−	0.407907i	0.723914	−	0.689890i	$-0.242341\pi$
$977$	−2.19626e8	−	3.80404e8i	−0.235505	−	0.407907i	−0.959419	+	0.281983i	$0.909008\pi$
$978$	−6.20326e8	+	5.62506e8i	−0.663137	+	0.601327i
$979$	2.78719e8	+	7.65774e8i	0.297043	+	0.816118i
$980$	2.97101e8	+	8.29355e7i	0.315664	+	0.0881176i
$981$	−9.77207e6	+	1.69257e7i	−0.0103509	+	0.0179283i
$982$	−8.98757e6	+	1.94342e6i	−0.00949090	+	0.00205226i
$983$	−8.41469e8	−	1.00282e9i	−0.885886	−	1.05576i	−0.998072	−	0.0620703i	$-0.980230\pi$
$983$	−8.41469e8	−	1.00282e9i	−0.885886	−	1.05576i	0.112186	−	0.993687i	$-0.464215\pi$
$984$	8.03865e7	+	1.60497e8i	0.0843719	+	0.168454i
$985$	6.03981e6	+	3.42535e7i	0.00631997	+	0.0358423i
$986$	1.20723e9	−	4.64083e7i	1.25939	−	0.0484134i
$987$		−	3.63523e7i		−	0.0378077i
$988$	4.05256e8	−	1.86529e9i	0.420203	−	1.93408i
$989$	3.00837e8			0.310987
$990$	786963.	+	2.04715e7i	0.000811052	+	0.0210981i
$991$	2.18583e8	−	3.85421e7i	0.224593	−	0.0396017i	−0.0602192	−	0.998185i	$-0.519180\pi$
$991$	2.18583e8	−	3.85421e7i	0.224593	−	0.0396017i	0.284812	+	0.958583i	$0.408069\pi$
$992$	1.45176e9	+	4.99672e8i	1.48717	+	0.511859i
$993$	9.68163e8	−	8.12385e8i	0.988782	−	0.829687i
$994$	8.22777e6	+	3.80502e7i	0.00837766	+	0.0387434i
$995$	1.97399e8	+	1.13968e8i	0.200390	+	0.115695i
$996$	1.13002e9	+	3.15445e8i	1.14369	+	0.319260i
$997$	−2.74726e8	+	9.99921e7i	−0.277214	+	0.100898i	−0.476886	−	0.878965i	$-0.658234\pi$
$997$	−2.74726e8	+	9.99921e7i	−0.277214	+	0.100898i	0.199672	+	0.979863i	$0.436012\pi$
$998$	−3.46491e8	−	3.82107e8i	−0.348578	−	0.384409i
$999$	9.43851e8	−	5.44933e8i	0.946688	−	0.546571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.l.a.23.1	✓	348
4.3	odd	2	inner	76.7.l.a.23.14	yes	348
19.5	even	9	inner	76.7.l.a.43.14	yes	348
76.43	odd	18	inner	76.7.l.a.43.1	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.l.a.23.1	✓	348	1.1	even	1	trivial
76.7.l.a.23.14	yes	348	4.3	odd	2	inner
76.7.l.a.43.1	yes	348	76.43	odd	18	inner
76.7.l.a.43.14	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)

\(f(q)\)	\(=\)	\(q+(-7.99410 + 0.307308i) q^{2} +(-27.6808 + 4.88087i) q^{3} +(63.8111 - 4.91330i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(219.783 - 47.5247i) q^{6} +(-83.9559 - 48.4720i) q^{7} +(-508.602 + 58.8871i) q^{8} +(57.3665 - 20.8797i) q^{9} +O(q^{10})\)	\(q+(-7.99410 + 0.307308i) q^{2} +(-27.6808 + 4.88087i) q^{3} +(63.8111 - 4.91330i) q^{4} +(-34.1068 + 28.6190i) q^{5} +(219.783 - 47.5247i) q^{6} +(-83.9559 - 48.4720i) q^{7} +(-508.602 + 58.8871i) q^{8} +(57.3665 - 20.8797i) q^{9} +(263.858 - 239.264i) q^{10} +(-815.927 + 471.076i) q^{11} +(-1742.36 + 447.458i) q^{12} +(-755.075 + 4282.24i) q^{13} +(686.047 + 361.689i) q^{14} +(804.416 - 958.666i) q^{15} +(4047.72 - 627.047i) q^{16} +(-3638.63 - 1324.35i) q^{17} +(-452.177 + 184.544i) q^{18} +(-6812.71 - 795.568i) q^{19} +(-2035.78 + 1993.79i) q^{20} +(2560.55 + 931.964i) q^{21} +(6377.83 - 4016.57i) q^{22} +(10416.9 - 12414.4i) q^{23} +(13791.1 - 4112.46i) q^{24} +(-2369.03 + 13435.4i) q^{25} +(4720.17 - 34464.7i) q^{26} +(16259.3 - 9387.33i) q^{27} +(-5595.48 - 2680.55i) q^{28} +(36648.4 - 13338.9i) q^{29} +(-6135.97 + 7910.87i) q^{30} +(-40577.6 - 23427.5i) q^{31} +(-32165.2 + 6256.57i) q^{32} +(20286.2 - 17022.2i) q^{33} +(29494.6 + 9468.83i) q^{34} +(4250.68 - 749.510i) q^{35} +(3558.03 - 1614.22i) q^{36} +58049.8 q^{37} +(54705.9 + 4266.24i) q^{38} -122221. i q^{39} +(15661.5 - 16564.1i) q^{40} +(2165.93 + 12283.6i) q^{41} +(-20755.7 - 6663.33i) q^{42} +(11932.4 + 14220.4i) q^{43} +(-49750.7 + 34068.8i) q^{44} +(-1359.03 + 2353.91i) q^{45} +(-79458.9 + 102443. i) q^{46} +(-4562.85 - 12536.3i) q^{47} +(-108983. + 37113.5i) q^{48} +(-54125.4 - 93748.0i) q^{49} +(14809.4 - 108132. i) q^{50} +(107184. + 18899.5i) q^{51} +(-27142.2 + 276965. i) q^{52} +(48900.6 + 41032.4i) q^{53} +(-127094. + 80039.8i) q^{54} +(14346.9 - 39417.9i) q^{55} +(45554.5 + 19709.0i) q^{56} +(192464. - 11230.0i) q^{57} +(-288872. + 117895. i) q^{58} +(75569.9 - 207627. i) q^{59} +(46620.5 - 65125.9i) q^{60} +(-165600. - 138955. i) q^{61} +(331581. + 174812. i) q^{62} +(-5828.34 - 1027.69i) q^{63} +(255209. - 59900.2i) q^{64} +(-96800.3 - 167663. i) q^{65} +(-156939. + 142311. i) q^{66} +(28802.8 + 79135.0i) q^{67} +(-238692. - 66630.8i) q^{68} +(-227756. + 394485. i) q^{69} +(-33750.0 + 7297.92i) q^{70} +(32265.4 + 38452.4i) q^{71} +(-27947.2 + 13997.6i) q^{72} +(116889. + 662910. i) q^{73} +(-464056. + 17839.2i) q^{74} -383466. i q^{75} +(-438635. - 17293.2i) q^{76} +91335.9 q^{77} +(37559.6 + 977049. i) q^{78} +(388719. - 68541.7i) q^{79} +(-120109. + 137228. i) q^{80} +(-438345. + 367815. i) q^{81} +(-21089.5 - 97530.8i) q^{82} +(-564813. - 326095. i) q^{83} +(167971. + 46888.9i) q^{84} +(162004. - 58964.5i) q^{85} +(-99758.4 - 110013. i) q^{86} +(-949351. + 548108. i) q^{87} +(387242. - 287638. i) q^{88} +(150198. - 851816. i) q^{89} +(10140.8 - 19235.0i) q^{90} +(270962. - 322920. i) q^{91} +(603721. - 843360. i) q^{92} +(1.23757e6 + 450437. i) q^{93} +(40328.3 + 98814.3i) q^{94} +(255128. - 167838. i) q^{95} +(859819. - 330181. i) q^{96} +(-624554. - 227319. i) q^{97} +(461493. + 732797. i) q^{98} +(-36971.0 + 44060.3i) 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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