LMFDB - Embedded newform 35.10.k.a.3.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,10,Mod(3,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("35.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.k (of order $12$, degree $4$, 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:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.11
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-21.6149 - 5.79170i) q^{2} +(-55.2156 - 206.067i) q^{3} +(-9.74350 - 5.62541i) q^{4} +(-1252.88 - 619.202i) q^{5} +4773.93i q^{6} +(2224.73 + 5950.14i) q^{7} +(8279.52 + 8279.52i) q^{8} +(-22369.0 + 12914.8i) q^{9} +(23494.7 + 20640.3i) q^{10} +(2156.53 - 3735.22i) q^{11} +(-621.221 + 2318.43i) q^{12} +(-19867.8 + 19867.8i) q^{13} +(-13625.8 - 141497. i) q^{14} +(-58418.7 + 292368. i) q^{15} +(-128128. - 221925. i) q^{16} +(-351000. + 94050.1i) q^{17} +(558304. - 149597. i) q^{18} +(-18871.3 - 32686.0i) q^{19} +(8724.19 + 13081.2i) q^{20} +(1.10329e6 - 786984. i) q^{21} +(-68246.5 + 68246.5i) q^{22} +(375491. - 1.40135e6i) q^{23} +(1.24898e6 - 2.16330e6i) q^{24} +(1.18630e6 + 1.55157e6i) q^{25} +(544510. - 314373. i) q^{26} +(927216. + 927216. i) q^{27} +(11795.4 - 70490.2i) q^{28} +3.26780e6i q^{29} +(2.95602e6 - 5.98117e6i) q^{30} +(7.12679e6 + 4.11466e6i) q^{31} +(-67458.4 - 251758. i) q^{32} +(-888781. - 238148. i) q^{33} +8.13155e6 q^{34} +(897021. - 8.83238e6i) q^{35} +290604. q^{36} +(-2.14396e7 - 5.74472e6i) q^{37} +(218594. + 815803. i) q^{38} +(5.19113e6 + 2.99710e6i) q^{39} +(-5.24657e6 - 1.55000e7i) q^{40} -1.18297e7i q^{41} +(-2.84055e7 + 1.06207e7i) q^{42} +(1.24637e7 + 1.24637e7i) q^{43} +(-42024.3 + 24262.7i) q^{44} +(3.60226e7 - 2.32973e6i) q^{45} +(-1.62324e7 + 2.81154e7i) q^{46} +(-3.74838e6 + 1.39891e7i) q^{47} +(-3.86568e7 + 3.86568e7i) q^{48} +(-3.04548e7 + 2.64749e7i) q^{49} +(-1.66556e7 - 4.04079e7i) q^{50} +(3.87613e7 + 6.71366e7i) q^{51} +(305347. - 81817.4i) q^{52} +(-7.17470e6 + 1.92246e6i) q^{53} +(-1.46715e7 - 2.54119e7i) q^{54} +(-5.01473e6 + 3.34446e6i) q^{55} +(-3.08447e7 + 6.76840e7i) q^{56} +(-5.69353e6 + 5.69353e6i) q^{57} +(1.89261e7 - 7.06332e7i) q^{58} +(5.79832e7 - 1.00430e8i) q^{59} +(2.21389e6 - 2.52006e6i) q^{60} +(1.17851e8 - 6.80411e7i) q^{61} +(-1.30214e8 - 1.30214e8i) q^{62} +(-1.26610e8 - 1.04367e8i) q^{63} +1.37036e8i q^{64} +(3.71943e7 - 1.25898e7i) q^{65} +(1.78317e7 + 1.02951e7i) q^{66} +(6.38260e7 + 2.38202e8i) q^{67} +(3.94904e6 + 1.05814e6i) q^{68} -3.09506e8 q^{69} +(-7.05436e7 + 1.85716e8i) q^{70} +2.77462e8 q^{71} +(-2.92133e8 - 7.82768e7i) q^{72} +(-5.94096e7 - 2.21720e8i) q^{73} +(4.30144e8 + 2.48344e8i) q^{74} +(2.54227e8 - 3.30129e8i) q^{75} +424635. i q^{76} +(2.70228e7 + 4.52182e6i) q^{77} +(-9.48475e7 - 9.48475e7i) q^{78} +(2.51568e7 - 1.45243e7i) q^{79} +(2.31135e7 + 3.57383e8i) q^{80} +(-1.14329e8 + 1.98024e8i) q^{81} +(-6.85143e7 + 2.55699e8i) q^{82} +(1.61041e8 - 1.61041e8i) q^{83} +(-1.51770e7 + 1.46151e6i) q^{84} +(4.97997e8 + 9.95061e7i) q^{85} +(-1.97216e8 - 3.41588e8i) q^{86} +(6.73387e8 - 1.80433e8i) q^{87} +(4.87808e7 - 1.30708e7i) q^{88} +(3.08261e8 + 5.33923e8i) q^{89} +(-7.92120e8 - 1.58275e8i) q^{90} +(-1.62417e8 - 7.40159e7i) q^{91} +(-1.15418e7 + 1.15418e7i) q^{92} +(4.54386e8 - 1.69579e9i) q^{93} +(1.62042e8 - 2.80665e8i) q^{94} +(3.40424e6 + 5.26369e7i) q^{95} +(-4.81544e7 + 2.78020e7i) q^{96} +(8.19315e8 + 8.19315e8i) q^{97} +(8.11613e8 - 3.95868e8i) q^{98} +1.11404e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) $ 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−21.6149	−	5.79170i	−0.955254	−	0.255960i	−0.252664	−	0.967554i	$-0.581307\pi$
$2$	−21.6149	−	5.79170i	−0.955254	−	0.255960i	−0.702590	+	0.711595i	$0.747973\pi$
$3$	−55.2156	−	206.067i	−0.393565	−	1.46880i	−0.824211	−	0.566283i	$-0.808381\pi$
$3$	−55.2156	−	206.067i	−0.393565	−	1.46880i	0.430646	−	0.902521i	$-0.358286\pi$
$4$	−9.74350	−	5.62541i	−0.0190303	−	0.0109871i
$5$	−1252.88	−	619.202i	−0.896490	−	0.443065i
$5$	−1252.88	−	619.202i	−0.896490	−	0.443065i
$6$			4773.93i			1.50382i
$7$	2224.73	+	5950.14i	0.350216	+	0.936669i
$7$	2224.73	+	5950.14i	0.350216	+	0.936669i
$8$	8279.52	+	8279.52i	0.714661	+	0.714661i
$9$	−22369.0	+	12914.8i	−1.13646	+	0.656138i
$10$	23494.7	+	20640.3i	0.742969	+	0.652705i
$11$	2156.53	−	3735.22i	0.0444108	−	0.0769217i	−0.842966	−	0.537968i	$-0.819192\pi$
$11$	2156.53	−	3735.22i	0.0444108	−	0.0769217i	0.887376	+	0.461046i	$0.152526\pi$
$12$	−621.221	+	2318.43i	−0.00864829	+	0.0322759i
$13$	−19867.8	+	19867.8i	−0.192932	+	0.192932i	−0.796962	−	0.604029i	$-0.793561\pi$
$13$	−19867.8	+	19867.8i	−0.192932	+	0.192932i	0.604029	+	0.796962i	$0.293561\pi$
$14$	−13625.8	−	141497.i	−0.0947954	−	0.984398i
$15$	−58418.7	+	292368.i	−0.297949	+	1.49114i
$16$	−128128.	−	221925.i	−0.488771	−	0.846577i
$17$	−351000.	+	94050.1i	−1.01926	+	0.273111i	−0.729495	−	0.683986i	$-0.760245\pi$
$17$	−351000.	+	94050.1i	−1.01926	+	0.273111i	−0.289769	+	0.957097i	$0.593578\pi$
$18$	558304.	−	149597.i	1.25356	−	0.335890i
$19$	−18871.3	−	32686.0i	−0.0332208	−	0.0575401i	0.848937	−	0.528494i	$-0.177243\pi$
$19$	−18871.3	−	32686.0i	−0.0332208	−	0.0575401i	−0.882158	+	0.470954i	$0.843910\pi$
$20$	8724.19	+	13081.2i	0.0121924	+	0.0182815i
$21$	1.10329e6	−	786984.i	1.23795	−	0.883038i
$22$	−68246.5	+	68246.5i	−0.0621124	+	0.0621124i
$23$	375491.	−	1.40135e6i	0.279785	−	1.04417i	−0.672782	−	0.739841i	$-0.734901\pi$
$23$	375491.	−	1.40135e6i	0.279785	−	1.04417i	0.952567	−	0.304330i	$-0.0984325\pi$
$24$	1.24898e6	−	2.16330e6i	0.768431	−	1.33096i
$25$	1.18630e6	+	1.55157e6i	0.607387	+	0.794406i
$26$	544510.	−	314373.i	0.233682	−	0.134917i
$27$	927216.	+	927216.i	0.335772	+	0.335772i
$28$	11795.4	−	70490.2i	0.00362661	−	0.0216729i
$29$			3.26780e6i			0.857954i	0.903315	+	0.428977i	$0.141126\pi$
$29$			3.26780e6i			0.857954i	−0.903315	+	0.428977i	$0.858874\pi$
$30$	2.95602e6	−	5.98117e6i	0.666289	−	1.34816i
$31$	7.12679e6	+	4.11466e6i	1.38601	+	0.800214i	0.992863	−	0.119262i	$-0.0380528\pi$
$31$	7.12679e6	+	4.11466e6i	1.38601	+	0.800214i	0.393148	+	0.919475i	$0.371386\pi$
$32$	−67458.4	−	251758.i	−0.0113726	−	0.0424433i
$33$	−888781.	−	238148.i	−0.130461	−	0.0349570i
$34$	8.13155e6			1.04356
$35$	897021.	−	8.83238e6i	0.101041	−	0.994882i
$36$	290604.			0.0288363
$37$	−2.14396e7	−	5.74472e6i	−1.88065	−	0.503920i	−0.999518	−	0.0310561i	$-0.990113\pi$
$37$	−2.14396e7	−	5.74472e6i	−1.88065	−	0.503920i	−0.881136	−	0.472863i	$-0.843220\pi$
$38$	218594.	+	815803.i	0.0170064	+	0.0634686i
$39$	5.19113e6	+	2.99710e6i	0.359311	+	0.207448i
$40$	−5.24657e6	−	1.55000e7i	−0.324045	−	0.957327i
$41$		−	1.18297e7i		−	0.653804i	−0.945058	−	0.326902i	$-0.893995\pi$
$41$		−	1.18297e7i		−	0.653804i	0.945058	−	0.326902i	$-0.106005\pi$
$42$	−2.84055e7	+	1.06207e7i	−1.40858	+	0.526660i
$43$	1.24637e7	+	1.24637e7i	0.555953	+	0.555953i	0.928153	−	0.372199i	$-0.121396\pi$
$43$	1.24637e7	+	1.24637e7i	0.555953	+	0.555953i	−0.372199	+	0.928153i	$0.621396\pi$
$44$	−42024.3	+	24262.7i	−0.00169030	+	0.000975894i
$45$	3.60226e7	−	2.32973e6i	1.30954	−	0.0846934i
$46$	−1.62324e7	+	2.81154e7i	−0.534531	+	0.925835i
$47$	−3.74838e6	+	1.39891e7i	−0.112048	+	0.418168i	−0.999049	−	0.0435989i	$-0.986118\pi$
$47$	−3.74838e6	+	1.39891e7i	−0.112048	+	0.418168i	0.887001	+	0.461767i	$0.152784\pi$
$48$	−3.86568e7	+	3.86568e7i	−1.05109	+	1.05109i
$49$	−3.04548e7	+	2.64749e7i	−0.754698	+	0.656072i
$50$	−1.66556e7	−	4.04079e7i	−0.376873	−	0.914326i
$51$	3.87613e7	+	6.71366e7i	0.802293	+	1.38961i
$52$	305347.	−	81817.4i	0.00579133	−	0.00155178i
$53$	−7.17470e6	+	1.92246e6i	−0.124900	+	0.0334669i	−0.320728	−	0.947171i	$-0.603927\pi$
$53$	−7.17470e6	+	1.92246e6i	−0.124900	+	0.0334669i	0.195828	+	0.980638i	$0.437261\pi$
$54$	−1.46715e7	−	2.54119e7i	−0.234803	−	0.406691i
$55$	−5.01473e6	+	3.34446e6i	−0.0738951	+	0.0492827i
$56$	−3.08447e7	+	6.76840e7i	−0.419116	+	0.919686i
$57$	−5.69353e6	+	5.69353e6i	−0.0714406	+	0.0714406i
$58$	1.89261e7	−	7.06332e7i	0.219602	−	0.819565i
$59$	5.79832e7	−	1.00430e8i	0.622971	−	1.07902i	−0.365958	−	0.930631i	$-0.619259\pi$
$59$	5.79832e7	−	1.00430e8i	0.622971	−	1.07902i	0.988929	−	0.148387i	$-0.0474081\pi$
$60$	2.21389e6	−	2.52006e6i	0.0220534	−	0.0251032i
$61$	1.17851e8	−	6.80411e7i	1.08980	−	0.629198i	0.156279	−	0.987713i	$-0.450050\pi$
$61$	1.17851e8	−	6.80411e7i	1.08980	−	0.629198i	0.933524	+	0.358515i	$0.116717\pi$
$62$	−1.30214e8	−	1.30214e8i	−1.11917	−	1.11917i
$63$	−1.26610e8	−	1.04367e8i	−1.01259	−	0.834702i
$64$			1.37036e8i			1.02100i
$65$	3.71943e7	−	1.25898e7i	0.258444	−	0.0874803i
$66$	1.78317e7	+	1.02951e7i	0.115676	+	0.0667857i
$67$	6.38260e7	+	2.38202e8i	0.386955	+	1.44414i	0.835061	+	0.550157i	$0.185432\pi$
$67$	6.38260e7	+	2.38202e8i	0.386955	+	1.44414i	−0.448106	+	0.893980i	$0.647901\pi$
$68$	3.94904e6	+	1.05814e6i	0.0223976	+	0.00600141i
$69$	−3.09506e8			−1.64379
$70$	−7.05436e7	+	1.85716e8i	−0.351169	+	0.924503i
$71$	2.77462e8			1.29581			0.647905	−	0.761721i	$-0.275645\pi$
$71$	2.77462e8			1.29581			0.647905	+	0.761721i	$0.275645\pi$
$72$	−2.92133e8	−	7.82768e7i	−1.28110	−	0.343271i
$73$	−5.94096e7	−	2.21720e8i	−0.244852	−	0.913800i	−0.973458	−	0.228867i	$-0.926498\pi$
$73$	−5.94096e7	−	2.21720e8i	−0.244852	−	0.913800i	0.728606	−	0.684933i	$-0.240169\pi$
$74$	4.30144e8	+	2.48344e8i	1.66752	+	0.962742i
$75$	2.54227e8	−	3.30129e8i	0.927780	−	1.20478i
$76$			424635.i			0.00146001i
$77$	2.70228e7	+	4.52182e6i	0.0876036	+	0.0146590i
$78$	−9.48475e7	−	9.48475e7i	−0.290135	−	0.290135i
$79$	2.51568e7	−	1.45243e7i	0.0726664	−	0.0419540i	−0.463227	−	0.886240i	$-0.653308\pi$
$79$	2.51568e7	−	1.45243e7i	0.0726664	−	0.0419540i	0.535893	+	0.844286i	$0.319975\pi$
$80$	2.31135e7	+	3.57383e8i	0.0630899	+	0.975505i
$81$	−1.14329e8	+	1.98024e8i	−0.295104	+	0.511134i
$82$	−6.85143e7	+	2.55699e8i	−0.167347	+	0.624549i
$83$	1.61041e8	−	1.61041e8i	0.372465	−	0.372465i	−0.495910	−	0.868374i	$-0.665165\pi$
$83$	1.61041e8	−	1.61041e8i	0.372465	−	0.372465i	0.868374	+	0.495910i	$0.165165\pi$
$84$	−1.51770e7	+	1.46151e6i	−0.0332606	+	0.00320292i
$85$	4.97997e8	+	9.95061e7i	1.03477	+	0.206759i
$86$	−1.97216e8	−	3.41588e8i	−0.388775	−	0.673378i
$87$	6.73387e8	−	1.80433e8i	1.26017	−	0.337661i
$88$	4.87808e7	−	1.30708e7i	0.0867116	−	0.0232343i
$89$	3.08261e8	+	5.33923e8i	0.520791	+	0.902036i	0.999708	+	0.0241757i	$0.00769610\pi$
$89$	3.08261e8	+	5.33923e8i	0.520791	+	0.902036i	−0.478917	+	0.877860i	$0.658971\pi$
$90$	−7.92120e8	−	1.58275e8i	−1.27262	−	0.254286i
$91$	−1.62417e8	−	7.40159e7i	−0.248282	−	0.113146i
$92$	−1.15418e7	+	1.15418e7i	−0.0167968	+	0.0167968i
$93$	4.54386e8	−	1.69579e9i	0.629872	−	2.35071i
$94$	1.62042e8	−	2.80665e8i	0.214068	−	0.370777i
$95$	3.40424e6	+	5.26369e7i	0.00428810	+	0.0663031i
$96$	−4.81544e7	+	2.78020e7i	−0.0578649	+	0.0334083i
$97$	8.19315e8	+	8.19315e8i	0.939676	+	0.939676i	0.998281	−	0.0586050i	$-0.0186652\pi$
$97$	8.19315e8	+	8.19315e8i	0.939676	+	0.939676i	−0.0586050	+	0.998281i	$0.518665\pi$
$98$	8.11613e8	−	3.95868e8i	0.888856	−	0.433543i
$99$			1.11404e8i			0.116558i
$100$	−2.83049e6	−	2.17912e7i	−0.00283049	−	0.0217912i
$101$	−7.02818e8	−	4.05772e8i	−0.672043	−	0.388004i	0.124808	−	0.992181i	$-0.460169\pi$
$101$	−7.02818e8	−	4.05772e8i	−0.672043	−	0.388004i	−0.796850	+	0.604177i	$0.793502\pi$
$102$	−4.48988e8	−	1.67565e9i	−0.410709	−	1.53279i
$103$	−8.03216e8	−	2.15221e8i	−0.703178	−	0.188416i	−0.110524	−	0.993873i	$-0.535253\pi$
$103$	−8.03216e8	−	2.15221e8i	−0.703178	−	0.188416i	−0.592653	+	0.805458i	$0.701920\pi$
$104$	−3.28992e8			−0.275763
$105$	−1.86960e9	+	3.02839e8i	−1.50105	+	0.243142i
$106$	1.66215e8			0.127877
$107$	−2.35660e8	−	6.31449e7i	−0.173804	−	0.0465705i	0.170868	−	0.985294i	$-0.445343\pi$
$107$	−2.35660e8	−	6.31449e7i	−0.173804	−	0.0465705i	−0.344671	+	0.938723i	$0.612010\pi$
$108$	−3.81836e6	−	1.42503e7i	−0.00270066	−	0.0100790i
$109$	5.53452e8	+	3.19535e8i	0.375544	+	0.216820i	0.675878	−	0.737014i	$-0.263765\pi$
$109$	5.53452e8	+	3.19535e8i	0.375544	+	0.216820i	−0.300334	+	0.953834i	$0.597098\pi$
$110$	1.27763e8	−	4.32465e7i	0.0832030	−	0.0281633i
$111$			4.73520e9i			2.96063i
$112$	1.03544e9	−	1.25611e9i	0.621787	−	0.754302i
$113$	2.09631e9	+	2.09631e9i	1.20949	+	1.20949i	0.971191	+	0.238301i	$0.0765905\pi$
$113$	2.09631e9	+	2.09631e9i	1.20949	+	1.20949i	0.238301	+	0.971191i	$0.423410\pi$
$114$	1.56041e8	−	9.00901e7i	0.0865298	−	0.0499580i
$115$	−1.33816e9	+	1.52322e9i	−0.713459	+	0.812125i
$116$	1.83827e7	−	3.18398e7i	0.00942646	−	0.0163271i
$117$	1.87836e8	−	7.01013e8i	0.0926706	−	0.345851i
$118$	−1.83496e9	+	1.83496e9i	−0.871281	+	0.871281i
$119$	−1.34049e9	−	1.87926e9i	−0.612777	−	0.859065i
$120$	−2.90434e9	+	1.93699e9i	−1.27859	+	0.852728i
$121$	1.16967e9	+	2.02593e9i	0.496055	+	0.859193i
$122$	−2.94141e9	+	7.88148e8i	−1.20209	+	0.322099i
$123$	−2.43772e9	+	6.53185e8i	−0.960309	+	0.257314i
$124$	−4.62933e7	−	8.01823e7i	−0.0175841	−	0.0304566i
$125$	−5.25559e8	−	2.67850e9i	−0.192543	−	0.981289i
$126$	2.13220e9	+	2.98917e9i	0.753633	+	1.05653i
$127$	−3.92669e9	+	3.92669e9i	−1.33940	+	1.33940i	−0.442757	+	0.896642i	$0.646000\pi$
$127$	−3.92669e9	+	3.92669e9i	−1.33940	+	1.33940i	−0.896642	+	0.442757i	$0.854000\pi$
$128$	7.59133e8	−	2.83312e9i	0.249962	−	0.932869i
$129$	1.88017e9	−	3.25655e9i	0.597782	−	1.03539i
$130$	−8.76868e8	+	5.67107e7i	−0.269271	+	0.0174148i
$131$	3.62416e9	−	2.09241e9i	1.07519	−	0.620762i	0.145596	−	0.989344i	$-0.453490\pi$
$131$	3.62416e9	−	2.09241e9i	1.07519	−	0.620762i	0.929595	+	0.368582i	$0.120157\pi$
$132$	7.32016e6	+	7.32016e6i	0.00209864	+	0.00209864i
$133$	1.52503e8	−	1.85004e8i	0.0422616	−	0.0512684i
$134$		−	5.51838e9i		−	1.47856i
$135$	−5.87558e8	−	1.73583e9i	−0.152247	−	0.449784i
$136$	−3.68480e9	−	2.12742e9i	−0.923610	−	0.533247i
$137$	−1.74429e9	−	6.50978e9i	−0.423035	−	1.57879i	−0.768177	−	0.640237i	$-0.778836\pi$
$137$	−1.74429e9	−	6.50978e9i	−0.423035	−	1.57879i	0.345143	−	0.938550i	$-0.387831\pi$
$138$	6.68994e9	+	1.79256e9i	1.57024	+	0.420745i
$139$	6.56570e9			1.49181			0.745907	−	0.666050i	$-0.232016\pi$
$139$	6.56570e9			1.49181			0.745907	+	0.666050i	$0.232016\pi$
$140$	−5.84259e7	+	8.10122e7i	−0.0128537	+	0.0178227i
$141$	3.08967e9			0.658304
$142$	−5.99733e9	−	1.60698e9i	−1.23783	−	0.331675i
$143$	3.13651e7	+	1.17056e8i	0.00627242	+	0.0234090i
$144$	5.73222e9	+	3.30950e9i	1.11094	+	0.641403i
$145$	2.02343e9	−	4.09417e9i	0.380130	−	0.769147i
$146$			5.13654e9i			0.935584i
$147$	7.13719e9	+	4.81391e9i	1.26066	+	0.850296i
$148$	1.76580e8	+	1.76580e8i	0.0302527	+	0.0302527i
$149$	5.24129e9	−	3.02606e9i	0.871164	−	0.502967i	0.00342910	−	0.999994i	$-0.498908\pi$
$149$	5.24129e9	−	3.02606e9i	0.871164	−	0.502967i	0.867735	+	0.497027i	$0.165575\pi$
$150$	−7.40710e9	+	5.66332e9i	−1.19464	+	0.913399i
$151$	−4.59846e9	+	7.96477e9i	−0.719808	+	1.24674i	0.241268	+	0.970458i	$0.422437\pi$
$151$	−4.59846e9	+	7.96477e9i	−0.719808	+	1.24674i	−0.961076	+	0.276285i	$0.910897\pi$
$152$	1.14379e8	−	4.26870e8i	0.0173801	−	0.0648633i
$153$	6.63689e9	−	6.63689e9i	0.979159	−	0.979159i
$154$	−5.57907e8	−	2.54247e8i	−0.0799315	−	0.0364261i
$155$	−6.38123e9	−	9.56810e9i	−0.887997	−	1.33148i
$156$	−3.37198e7	−	5.84044e7i	−0.00455853	−	0.00789560i
$157$	3.66407e9	−	9.81784e8i	0.481299	−	0.128964i	−0.0100083	−	0.999950i	$-0.503186\pi$
$157$	3.66407e9	−	9.81784e8i	0.481299	−	0.128964i	0.491308	+	0.870986i	$0.336519\pi$
$158$	−6.27883e8	+	1.68241e8i	−0.0801534	+	0.0214770i
$159$	7.92311e8	+	1.37232e9i	0.0983125	+	0.170282i
$160$	−7.13718e7	+	3.57194e8i	−0.00860967	+	0.0430888i
$161$	9.17360e9	−	8.83397e8i	1.07603	−	0.103619i
$162$	3.61811e9	−	3.61811e9i	0.412729	−	0.412729i
$163$	−5.87357e8	+	2.19205e9i	−0.0651716	+	0.243224i	−0.990825	−	0.135148i	$-0.956849\pi$
$163$	−5.87357e8	+	2.19205e9i	−0.0651716	+	0.243224i	0.925654	+	0.378371i	$0.123516\pi$
$164$	−6.65471e7	+	1.15263e8i	−0.00718343	+	0.0124421i
$165$	9.66076e8	+	8.48707e8i	0.101469	+	0.0891415i
$166$	−4.41359e9	+	2.54819e9i	−0.451134	+	0.260462i
$167$	−3.34283e9	−	3.34283e9i	−0.332575	−	0.332575i	0.520988	−	0.853564i	$-0.325563\pi$
$167$	−3.34283e9	−	3.34283e9i	−0.332575	−	0.332575i	−0.853564	+	0.520988i	$0.825563\pi$
$168$	1.56506e10	+	2.61887e9i	1.51579	+	0.253642i
$169$			9.81504e9i			0.925554i
$170$	−1.01879e10	−	5.03507e9i	−0.935542	−	0.462366i
$171$	8.44265e8	+	4.87436e8i	0.0755085	+	0.0435949i
$172$	−5.13265e7	−	1.91553e8i	−0.00447161	−	0.0166883i
$173$	9.49109e9	+	2.54313e9i	0.805580	+	0.215854i	0.638032	−	0.770010i	$-0.279749\pi$
$173$	9.49109e9	+	2.54313e9i	0.805580	+	0.215854i	0.167547	+	0.985864i	$0.446415\pi$
$174$	−1.56002e10			−1.29021
$175$	−6.59289e9	+	1.05105e10i	−0.531379	+	0.847134i
$176$	−1.10525e9			−0.0868269
$177$	−2.38969e10	−	6.40315e9i	−1.83005	−	0.490359i
$178$	−3.57071e9	−	1.33261e10i	−0.266603	−	0.994975i
$179$	4.00647e9	+	2.31314e9i	0.291691	+	0.168408i	0.638704	−	0.769452i	$-0.279471\pi$
$179$	4.00647e9	+	2.31314e9i	0.291691	+	0.168408i	−0.347013	+	0.937860i	$0.612804\pi$
$180$	−3.64092e8	−	1.79942e8i	−0.0258514	−	0.0127764i
$181$		−	5.43135e9i		−	0.376144i	−0.982155	−	0.188072i	$-0.939776\pi$
$181$		−	5.43135e9i		−	0.376144i	0.982155	−	0.188072i	$-0.0602239\pi$
$182$	3.08195e9	+	2.54052e9i	0.208211	+	0.171633i
$183$	−2.05283e10	−	2.05283e10i	−1.35308	−	1.35308i
$184$	1.47114e10	−	8.49362e9i	0.946179	−	0.546277i
$185$	2.33041e10	+	2.04729e10i	1.46272	+	1.28501i
$186$	−1.96431e10	+	3.40228e10i	−1.20337	+	2.08431i
$187$	−4.05644e8	+	1.51388e9i	−0.0242581	+	0.0905326i
$188$	1.15217e8	−	1.15217e8i	0.00672676	−	0.00672676i
$189$	−3.45427e9	+	7.57987e9i	−0.196914	+	0.432099i
$190$	2.31275e8	−	1.15746e9i	0.0128747	−	0.0644339i
$191$	−8.15095e9	−	1.41179e10i	−0.443157	−	0.767571i	0.554764	−	0.832008i	$-0.312808\pi$
$191$	−8.15095e9	−	1.41179e10i	−0.443157	−	0.767571i	−0.997922	+	0.0644363i	$0.979475\pi$
$192$	2.82387e10	−	7.56653e9i	1.49965	−	0.401829i
$193$	−3.31045e10	+	8.87033e9i	−1.71743	+	0.460185i	−0.977227	−	0.212197i	$-0.931938\pi$
$193$	−3.31045e10	+	8.87033e9i	−1.71743	+	0.460185i	−0.740205	+	0.672381i	$0.765272\pi$
$194$	−1.29642e10	−	2.24547e10i	−0.657110	−	1.13815i
$195$	−4.64806e9	−	6.96937e9i	−0.230206	−	0.345174i
$196$	4.45668e8	−	8.66372e7i	0.0215705	−	0.00419326i
$197$	−6.47748e9	+	6.47748e9i	−0.306414	+	0.306414i	−0.843517	−	0.537103i	$-0.819519\pi$
$197$	−6.47748e9	+	6.47748e9i	−0.306414	+	0.306414i	0.537103	+	0.843517i	$0.319519\pi$
$198$	6.45221e8	−	2.40800e9i	0.0298342	−	0.111343i
$199$	−8.68902e9	+	1.50498e10i	−0.392764	+	0.680288i	−0.992813	−	0.119676i	$-0.961814\pi$
$199$	−8.68902e9	+	1.50498e10i	−0.392764	+	0.680288i	0.600049	+	0.799963i	$0.295148\pi$
$200$	−3.02427e9	+	2.26683e10i	−0.133655	+	1.00181i
$201$	4.55614e10	−	2.63049e10i	1.96886	−	1.13672i
$202$	1.28413e10	+	1.28413e10i	0.542658	+	0.542658i
$203$	−1.94439e10	+	7.26996e9i	−0.803619	+	0.300469i
$204$		−	8.72194e8i		−	0.0352596i
$205$	−7.32499e9	+	1.48213e10i	−0.289678	+	0.586128i
$206$	1.61150e10	+	9.30398e9i	0.623486	+	0.359970i
$207$	9.69875e9	+	3.61962e10i	0.367155	+	1.37024i
$208$	6.95480e9	+	1.86353e9i	0.257632	+	0.0690323i
$209$	−1.62786e8			−0.00590145
$210$	4.21651e10	+	4.28231e9i	1.49612	+	0.151947i
$211$	−9.24386e9			−0.321057			−0.160529	−	0.987031i	$-0.551320\pi$
$211$	−9.24386e9			−0.321057			−0.160529	+	0.987031i	$0.551320\pi$
$212$	8.07213e7	+	2.16292e7i	0.00274459	+	0.000735410i
$213$	−1.53202e10	−	5.71759e10i	−0.509985	−	1.90329i
$214$	4.72806e9	+	2.72974e9i	0.154106	+	0.0889734i
$215$	−7.89799e9	−	2.33331e10i	−0.252083	−	0.744730i
$216$			1.53538e10i			0.479926i
$217$	−8.62763e9	+	5.15594e10i	−0.264133	+	1.57848i
$218$	−1.01122e10	−	1.01122e10i	−0.303242	−	0.303242i
$219$	−4.24089e10	+	2.44848e10i	−1.24583	+	0.719279i
$220$	6.76750e7	−	4.37682e6i	0.00194772	−	0.000125967i
$221$	5.10503e9	−	8.84218e9i	0.143957	−	0.249341i
$222$	2.74249e10	−	1.02351e11i	0.757803	−	2.82816i
$223$	3.05014e10	−	3.05014e10i	0.825939	−	0.825939i	−0.161013	−	0.986952i	$-0.551476\pi$
$223$	3.05014e10	−	3.05014e10i	0.825939	−	0.825939i	0.986952	+	0.161013i	$0.0514762\pi$
$224$	1.34792e9	−	9.61481e8i	0.0357724	−	0.0255167i
$225$	−4.65747e10	−	1.93864e10i	−1.21151	−	0.504285i
$226$	−3.31704e10	−	5.74529e10i	−0.845791	−	1.46495i
$227$	−3.29486e10	+	8.82855e9i	−0.823608	+	0.220685i	−0.645923	−	0.763402i	$-0.723527\pi$
$227$	−3.29486e10	+	8.82855e9i	−0.823608	+	0.220685i	−0.177685	+	0.984087i	$0.556861\pi$
$228$	8.75034e7	−	2.34465e7i	0.00214446	−	0.000574607i
$229$	3.63221e10	+	6.29117e10i	0.872793	+	1.51172i	0.859095	+	0.511816i	$0.171027\pi$
$229$	3.63221e10	+	6.29117e10i	0.872793	+	1.51172i	0.0136977	+	0.999906i	$0.495640\pi$
$230$	3.77464e10	−	2.51741e10i	0.889406	−	0.593169i
$231$	−5.60279e8	−	5.81819e9i	−0.0129464	−	0.134442i
$232$	−2.70558e10	+	2.70558e10i	−0.613147	+	0.613147i
$233$	−1.07471e10	+	4.01089e10i	−0.238886	+	0.891536i	0.737472	+	0.675378i	$0.236019\pi$
$233$	−1.07471e10	+	4.01089e10i	−0.238886	+	0.891536i	−0.976358	+	0.216159i	$0.930647\pi$
$234$	−8.12011e9	+	1.40645e10i	−0.177048	+	0.306656i
$235$	1.33584e10	−	1.52057e10i	0.285725	−	0.325239i
$236$	−1.12992e9	+	6.52359e8i	−0.0237106	+	0.0136893i
$237$	−4.38203e9	−	4.38203e9i	−0.0902211	−	0.0902211i
$238$	1.80905e10	+	4.83839e10i	0.365471	+	0.977472i
$239$			2.22045e10i			0.440200i	0.975477	+	0.220100i	$0.0706383\pi$
$239$			2.22045e10i			0.440200i	−0.975477	+	0.220100i	$0.929362\pi$
$240$	7.23688e10	−	2.44961e10i	1.40799	−	0.476591i
$241$	−4.64931e10	−	2.68428e10i	−0.887793	−	0.512568i	−0.0145730	−	0.999894i	$-0.504639\pi$
$241$	−4.64931e10	−	2.68428e10i	−0.887793	−	0.512568i	−0.873220	+	0.487326i	$0.837972\pi$
$242$	−1.35488e10	−	5.05648e10i	−0.253940	−	0.947718i
$243$	7.20495e10	+	1.93056e10i	1.32557	+	0.355186i
$244$	−1.53104e9			−0.0276523
$245$	5.45496e10	−	1.43122e10i	0.967262	−	0.253782i
$246$	5.64742e10			0.983201
$247$	1.02433e9	+	2.74469e8i	0.0175107	+	0.00469199i
$248$	2.49390e10	+	9.30738e10i	0.418646	+	1.56241i
$249$	−4.20773e10	−	2.42933e10i	−0.693666	−	0.400488i
$250$	−4.15315e9	+	6.09395e10i	−0.0672431	+	0.986663i
$251$			6.36684e10i			1.01249i	0.862389	+	0.506247i	$0.168968\pi$
$251$			6.36684e10i			1.01249i	−0.862389	+	0.506247i	$0.831032\pi$
$252$	6.46513e8	+	1.72913e9i	0.0100989	+	0.0270101i
$253$	−4.42459e9	−	4.42459e9i	−0.0678939	−	0.0678939i
$254$	1.07617e11	−	6.21329e10i	1.62230	−	0.936634i
$255$	−6.99226e9	−	1.08115e11i	−0.103559	−	1.60124i
$256$	2.26399e9	−	3.92134e9i	0.0329454	−	0.0570630i
$257$	−1.91532e10	+	7.14807e10i	−0.273868	+	1.02209i	0.682727	+	0.730673i	$0.260794\pi$
$257$	−1.91532e10	+	7.14807e10i	−0.273868	+	1.02209i	−0.956596	+	0.291418i	$0.905873\pi$
$258$	−5.95007e10	+	5.95007e10i	−0.836052	+	0.836052i
$259$	−1.35153e10	−	1.40349e11i	−0.186628	−	1.93803i
$260$	−4.33225e8	−	8.65638e7i	−0.00587941	−	0.00117478i
$261$	−4.22029e10	−	7.30975e10i	−0.562937	−	0.975035i
$262$	−9.04545e10	+	2.42372e10i	−1.18597	+	0.317780i
$263$	2.76771e10	−	7.41605e9i	0.356713	−	0.0955810i	−0.0760119	−	0.997107i	$-0.524219\pi$
$263$	2.76771e10	−	7.41605e9i	0.356713	−	0.0955810i	0.432725	+	0.901526i	$0.357552\pi$
$264$	−5.38693e9	−	9.33043e9i	−0.0682533	−	0.118218i
$265$	1.01794e10	+	2.03398e9i	0.126800	+	0.0253361i
$266$	−4.36783e9	+	3.11560e9i	−0.0534932	+	0.0381570i
$267$	9.30034e10	−	9.30034e10i	1.11995	−	1.11995i
$268$	7.18095e8	−	2.67997e9i	0.00850306	−	0.0317338i
$269$	2.45175e10	−	4.24656e10i	0.285490	−	0.494483i	−0.687238	−	0.726432i	$-0.741177\pi$
$269$	2.45175e10	−	4.24656e10i	0.285490	−	0.494483i	0.972728	+	0.231949i	$0.0745103\pi$
$270$	2.64664e9	+	4.09227e10i	0.0303081	+	0.468627i
$271$	−9.10580e9	+	5.25724e9i	−0.102555	+	0.0592101i	−0.550400	−	0.834901i	$-0.685525\pi$
$271$	−9.10580e9	+	5.25724e9i	−0.102555	+	0.0592101i	0.447845	+	0.894111i	$0.352192\pi$
$272$	6.58452e10	+	6.58452e10i	0.729397	+	0.729397i
$273$	−6.28433e9	+	3.75557e10i	−0.0684742	+	0.409207i
$274$			1.50811e11i			1.61642i
$275$	8.35377e9	−	1.08508e9i	0.0880816	−	0.0114411i
$276$	3.01567e9	+	1.74110e9i	0.0312818	+	0.0180606i
$277$	1.37014e10	+	5.11342e10i	0.139831	+	0.521858i	0.999931	+	0.0117320i	$0.00373450\pi$
$277$	1.37014e10	+	5.11342e10i	0.139831	+	0.521858i	−0.860100	+	0.510126i	$0.829599\pi$
$278$	−1.41917e11	−	3.80266e10i	−1.42506	−	0.381844i
$279$	−2.12559e11			−2.10020
$280$	8.05548e10	−	6.57010e10i	0.783213	−	0.638794i
$281$	4.16733e10			0.398731			0.199365	−	0.979925i	$-0.436112\pi$
$281$	4.16733e10			0.398731			0.199365	+	0.979925i	$0.436112\pi$
$282$	−6.67831e10	−	1.78945e10i	−0.628848	−	0.168499i
$283$	2.09230e10	+	7.80859e10i	0.193904	+	0.723658i	0.992548	+	0.121855i	$0.0388842\pi$
$283$	2.09230e10	+	7.80859e10i	0.193904	+	0.723658i	−0.798644	+	0.601803i	$0.794449\pi$
$284$	−2.70345e9	−	1.56084e9i	−0.0246596	−	0.0142372i
$285$	1.06588e10	−	3.60788e9i	0.0956986	−	0.0323929i
$286$		−	2.71182e9i		−	0.0239670i
$287$	7.03886e10	−	2.63179e10i	0.612398	−	0.228972i
$288$	4.76038e9	+	4.76038e9i	0.0407733	+	0.0407733i
$289$	1.16553e10	−	6.72920e9i	0.0982842	−	0.0567444i
$290$	−6.74484e10	+	7.67760e10i	−0.559991	+	0.637433i
$291$	1.23595e11	−	2.14073e11i	1.01038	−	1.75002i
$292$	−6.68407e8	+	2.49453e9i	−0.00538044	+	0.0200801i
$293$	−5.56854e10	+	5.56854e10i	−0.441405	+	0.441405i	−0.892484	−	0.451079i	$-0.851039\pi$
$293$	−5.56854e10	+	5.56854e10i	−0.441405	+	0.441405i	0.451079	+	0.892484i	$0.351039\pi$
$294$	−1.26389e11	−	1.45389e11i	−0.986612	−	1.13493i
$295$	−1.34832e11	+	8.99235e10i	−1.03656	+	0.691312i
$296$	−1.29946e11	−	2.25073e11i	−0.983898	−	1.70416i
$297$	5.46292e9	−	1.46379e9i	0.0407400	−	0.0109163i
$298$	−1.30816e11	+	3.50521e10i	−0.960922	+	0.257478i
$299$	2.03816e10	+	3.53020e10i	0.147475	+	0.255434i
$300$	−4.33417e9	+	1.78649e9i	−0.0308930	+	0.0127337i
$301$	−4.64324e10	+	1.01889e11i	−0.326041	+	0.715448i
$302$	1.45525e11	−	1.45525e11i	1.00671	−	1.00671i
$303$	−4.48099e10	+	1.67233e11i	−0.305409	+	1.13980i
$304$	−4.83590e9	+	8.37602e9i	−0.0324748	+	0.0562479i
$305$	−1.89784e11	+	1.22741e10i	−1.25577	+	0.0812160i
$306$	−1.81895e11	+	1.05017e11i	−1.18597	+	0.684721i
$307$	1.66404e11	+	1.66404e11i	1.06915	+	1.06915i	0.997424	+	0.0717296i	$0.0228519\pi$
$307$	1.66404e11	+	1.66404e11i	1.06915	+	1.06915i	0.0717296	+	0.997424i	$0.477148\pi$
$308$	−2.37859e8	−	1.96073e8i	−0.00150606	−	0.00124148i
$309$			1.77400e11i			1.10698i
$310$	8.25142e10	+	2.43772e11i	0.507459	+	1.49919i
$311$	4.18124e10	+	2.41404e10i	0.253445	+	0.146327i	0.621341	−	0.783541i	$-0.286588\pi$
$311$	4.18124e10	+	2.41404e10i	0.253445	+	0.146327i	−0.367896	+	0.929867i	$0.619922\pi$
$312$	1.81655e10	+	6.77945e10i	0.108530	+	0.405041i
$313$	1.08287e11	+	2.90154e10i	0.637715	+	0.170875i	0.563168	−	0.826342i	$-0.309582\pi$
$313$	1.08287e11	+	2.90154e10i	0.637715	+	0.170875i	0.0745468	+	0.997218i	$0.476249\pi$
$314$	−8.48848e10			−0.492773
$315$	9.40027e10	+	2.09157e11i	0.537951	+	1.19695i
$316$	−3.26821e8			−0.00184382
$317$	1.70215e11	+	4.56088e10i	0.946738	+	0.253678i	0.698978	−	0.715144i	$-0.253639\pi$
$317$	1.70215e11	+	4.56088e10i	0.946738	+	0.253678i	0.247761	+	0.968821i	$0.420305\pi$
$318$	−9.17766e9	−	3.42515e10i	−0.0503280	−	0.187827i
$319$	1.22059e10	+	7.04711e9i	0.0659953	+	0.0381024i
$320$	8.48530e10	−	1.71690e11i	0.452368	−	0.915314i
$321$			5.20484e10i			0.273612i
$322$	−2.03403e11	−	3.40362e10i	−1.05440	−	0.176437i
$323$	9.69794e9	+	9.69794e9i	0.0495756	+	0.0495756i
$324$	2.22793e9	−	1.28630e9i	0.0112318	−	0.00648468i
$325$	−5.43957e10	−	7.25716e9i	−0.270451	−	0.0360821i
$326$	2.53914e10	−	4.39792e10i	0.124511	−	0.215659i
$327$	3.52867e10	−	1.31692e11i	0.170666	−	0.636932i
$328$	9.79445e10	−	9.79445e10i	0.467248	−	0.467248i
$329$	−9.15765e10	+	8.81862e9i	−0.430926	+	0.0414972i
$330$	−1.59662e10	−	2.39400e10i	−0.0741121	−	0.111125i
$331$	−2.51758e10	−	4.36058e10i	−0.115281	−	0.199673i	0.802611	−	0.596503i	$-0.203444\pi$
$331$	−2.51758e10	−	4.36058e10i	−0.115281	−	0.199673i	−0.917892	+	0.396830i	$0.870110\pi$
$332$	−2.47502e9	+	6.63181e8i	−0.0111804	+	0.00299578i
$333$	5.53775e11	−	1.48383e11i	2.46794	−	0.661282i
$334$	5.28943e10	+	9.16157e10i	0.232568	+	0.402820i
$335$	6.75286e10	−	3.37960e11i	0.292945	−	1.46610i
$336$	−3.16015e11	−	1.44013e11i	−1.35263	−	0.616417i
$337$	2.06483e11	−	2.06483e11i	0.872068	−	0.872068i	−0.120630	−	0.992698i	$-0.538491\pi$
$337$	2.06483e11	−	2.06483e11i	0.872068	−	0.872068i	0.992698	+	0.120630i	$0.0384915\pi$
$338$	5.68458e10	−	2.12151e11i	0.236904	−	0.884139i
$339$	3.16233e11	−	5.47731e11i	1.30049	−	2.25252i
$340$	−4.29247e9	−	3.77098e9i	−0.0174202	−	0.0153038i
$341$	3.07383e10	−	1.77468e10i	0.123108	−	0.0710762i
$342$	−1.54256e10	−	1.54256e10i	−0.0609713	−	0.0609713i
$343$	−2.25283e11	−	1.22311e11i	−0.878830	−	0.477136i
$344$			2.06387e11i			0.794636i
$345$	3.87774e11	+	1.91646e11i	1.47364	+	0.728308i
$346$	−1.90420e11	−	1.09939e11i	−0.714283	−	0.412392i
$347$	−4.83280e10	−	1.80362e11i	−0.178944	−	0.667826i	−0.995846	−	0.0910508i	$-0.970977\pi$
$347$	−4.83280e10	−	1.80362e11i	−0.178944	−	0.667826i	0.816903	−	0.576775i	$-0.195689\pi$
$348$	−7.57615e9	−	2.03002e9i	−0.0276912	−	0.00741984i
$349$	−1.09365e11			−0.394606			−0.197303	−	0.980343i	$-0.563218\pi$
$349$	−1.09365e11			−0.394606			−0.197303	+	0.980343i	$0.563218\pi$
$350$	2.03379e11	−	1.89000e11i	0.724434	−	0.673217i
$351$	−3.68435e10			−0.129562
$352$	−1.08585e9	−	2.90952e8i	−0.00376988	−	0.00101014i
$353$	2.03949e10	+	7.61149e10i	0.0699095	+	0.260906i	0.992031	−	0.125995i	$-0.0402123\pi$
$353$	2.03949e10	+	7.61149e10i	0.0699095	+	0.260906i	−0.922121	+	0.386901i	$0.873546\pi$
$354$	4.79445e11	+	2.76807e11i	1.62265	+	0.936835i
$355$	−3.47627e11	−	1.71805e11i	−1.16168	−	0.574128i
$356$		−	6.93637e9i		−	0.0228880i
$357$	−3.13239e11	+	3.79996e11i	−1.02063	+	1.23815i
$358$	−7.32025e10	−	7.32025e10i	−0.235533	−	0.235533i
$359$	−1.99861e11	+	1.15390e11i	−0.635042	+	0.366642i	−0.782702	−	0.622396i	$-0.786159\pi$
$359$	−1.99861e11	+	1.15390e11i	−0.635042	+	0.366642i	0.147660	+	0.989038i	$0.452826\pi$
$360$	3.17539e11	+	2.78961e11i	0.996405	+	0.875350i
$361$	1.60632e11	−	2.78222e11i	0.497793	−	0.862202i
$362$	−3.14568e10	+	1.17398e11i	−0.0962777	+	0.359313i
$363$	3.52894e11	−	3.52894e11i	1.06676	−	1.06676i
$364$	1.16614e9	+	1.63484e9i	0.00348172	+	0.00488110i
$365$	−6.28560e10	+	3.14575e11i	−0.185366	+	0.927698i
$366$	3.24823e11	+	5.62611e11i	0.946199	+	1.63886i
$367$	1.20727e11	−	3.23487e10i	0.347381	−	0.0930806i	−0.0809096	−	0.996721i	$-0.525782\pi$
$367$	1.20727e11	−	3.23487e10i	0.347381	−	0.0930806i	0.428291	+	0.903641i	$0.359116\pi$
$368$	−3.59106e11	+	9.62221e10i	−1.02072	+	0.273501i
$369$	1.52778e11	+	2.64620e11i	0.428986	+	0.743025i
$370$	−3.85144e11	−	5.77491e11i	−1.06836	−	1.60191i
$371$	−2.74006e10	−	3.84136e10i	−0.0750893	−	0.105269i
$372$	−1.39668e10	+	1.39668e10i	−0.0378142	+	0.0378142i
$373$	−9.93725e10	+	3.70863e11i	−0.265813	+	0.992029i	0.695937	+	0.718102i	$0.254989\pi$
$373$	−9.93725e10	+	3.70863e11i	−0.265813	+	0.992029i	−0.961751	+	0.273926i	$0.911678\pi$
$374$	1.75359e10	−	3.03731e10i	0.0463454	−	0.0802726i
$375$	−5.22933e11	+	2.56196e11i	−1.36554	+	0.669008i
$376$	−1.46858e11	+	8.47886e10i	−0.378924	+	0.218772i
$377$	−6.49241e10	−	6.49241e10i	−0.165527	−	0.165527i
$378$	1.18564e11	−	1.43832e11i	0.298703	−	0.362362i
$379$		−	3.24907e10i		−	0.0808877i	−0.999182	−	0.0404439i	$-0.987123\pi$
$379$		−	3.24907e10i		−	0.0808877i	0.999182	−	0.0404439i	$-0.0128772\pi$
$380$	2.62935e8	−	5.32017e8i	0.000646877	−	0.00130888i
$381$	1.02598e12	+	5.92348e11i	2.49445	+	1.44017i
$382$	9.44158e10	+	3.52364e11i	0.226861	+	0.846656i
$383$	−6.60111e11	−	1.76876e11i	−1.56755	−	0.420025i	−0.632508	−	0.774554i	$-0.717975\pi$
$383$	−6.60111e11	−	1.76876e11i	−1.56755	−	0.420025i	−0.935045	+	0.354529i	$0.884641\pi$
$384$	−6.25731e11			−1.46858
$385$	−3.10564e10	−	2.23979e10i	−0.0720408	−	0.0519557i
$386$	7.66927e11			1.75837
$387$	−4.39766e11	−	1.17835e11i	−0.996603	−	0.267039i
$388$	−3.37401e9	−	1.25920e10i	−0.00755795	−	0.0282066i
$389$	9.36124e10	+	5.40471e10i	0.207281	+	0.119674i	0.600047	−	0.799965i	$-0.295148\pi$
$389$	9.36124e10	+	5.40471e10i	0.207281	+	0.119674i	−0.392766	+	0.919638i	$0.628482\pi$
$390$	6.01030e10	+	1.77563e11i	0.131554	+	0.388652i
$391$			5.27189e11i			1.14070i
$392$	−4.71350e11	−	3.29518e10i	−1.00822	−	0.0704842i
$393$	−6.31287e11	−	6.31287e11i	−1.33494	−	1.33494i
$394$	1.77526e11	−	1.02495e11i	0.371133	−	0.214274i
$395$	−4.05120e10	+	2.62008e9i	−0.0837330	+	0.00541536i
$396$	6.26695e8	−	1.08547e9i	0.00128064	−	0.00221814i
$397$	−4.43424e10	+	1.65488e11i	−0.0895906	+	0.334357i	−0.996144	−	0.0877348i	$-0.972037\pi$
$397$	−4.43424e10	+	1.65488e11i	−0.0895906	+	0.334357i	0.906553	+	0.422091i	$0.138704\pi$
$398$	2.74977e11	−	2.74977e11i	0.549316	−	0.549316i
$399$	−4.65439e10	−	2.12108e10i	−0.0919358	−	0.0418966i
$400$	1.92334e11	−	4.62071e11i	0.375653	−	0.902483i
$401$	−1.66493e11	−	2.88375e11i	−0.321549	−	0.556939i	0.659259	−	0.751916i	$-0.270870\pi$
$401$	−1.66493e11	−	2.88375e11i	−0.321549	−	0.556939i	−0.980808	+	0.194977i	$0.937537\pi$
$402$	−1.13716e12	+	3.04700e11i	−2.17172	+	0.581910i
$403$	−2.23343e11	+	5.98446e10i	−0.421794	+	0.113019i
$404$	4.56527e9	+	7.90728e9i	0.00852610	+	0.0147676i
$405$	2.65858e11	−	1.77308e11i	0.491023	−	0.327477i
$406$	4.62383e11	−	4.45265e10i	0.844569	−	0.0813301i
$407$	−6.76929e10	+	6.76929e10i	−0.122284	+	0.122284i
$408$	−2.34933e11	+	8.76784e11i	−0.419734	+	1.56647i
$409$	−1.58449e10	+	2.74443e10i	−0.0279986	+	0.0484950i	−0.879685	−	0.475557i	$-0.842247\pi$
$409$	−1.58449e10	+	2.74443e10i	−0.0279986	+	0.0484950i	0.851687	+	0.524051i	$0.175580\pi$
$410$	2.44170e11	−	2.77936e11i	0.426741	−	0.485756i
$411$	−1.24514e12	+	7.18883e11i	−2.15244	+	1.24271i
$412$	6.61543e9	+	6.61543e9i	0.0113115	+	0.0113115i
$413$	7.26569e11	+	1.21579e11i	1.22886	+	0.205629i
$414$		−	8.38551e11i		−	1.40290i
$415$	−3.01482e11	+	1.02048e11i	−0.498937	+	0.168885i
$416$	6.34214e9	+	3.66164e9i	0.0103828	+	0.00599453i
$417$	−3.62529e11	−	1.35298e12i	−0.587125	−	2.19118i
$418$	3.51861e9	+	9.42808e8i	0.00563738	+	0.00151053i
$419$	8.95942e11			1.42009			0.710046	−	0.704155i	$-0.248674\pi$
$419$	8.95942e11			1.42009			0.710046	+	0.704155i	$0.248674\pi$
$420$	1.99200e10	+	7.56654e9i	0.0312369	+	0.0118652i
$421$	6.10979e11			0.947887			0.473944	−	0.880555i	$-0.342830\pi$
$421$	6.10979e11			0.947887			0.473944	+	0.880555i	$0.342830\pi$
$422$	1.99805e11	+	5.35377e10i	0.306691	+	0.0821777i
$423$	−9.68189e10	−	3.61333e11i	−0.147038	−	0.548752i
$424$	−7.53201e10	−	4.34861e10i	−0.113179	−	0.0653437i
$425$	−5.62318e11	−	4.33030e11i	−0.836049	−	0.643826i
$426$			1.32458e12i			1.94866i
$427$	6.67040e11	+	5.49856e11i	0.971016	+	0.800430i
$428$	1.94094e9	+	1.94094e9i	0.00279585	+	0.00279585i
$429$	2.23896e10	−	1.29267e10i	0.0319146	−	0.0184259i
$430$	3.55763e10	+	5.50085e11i	0.0501825	+	0.775929i
$431$	−3.63250e11	+	6.29168e11i	−0.507059	+	0.878252i	0.492908	+	0.870082i	$0.335934\pi$
$431$	−3.63250e11	+	6.29168e11i	−0.507059	+	0.878252i	−0.999967	+	0.00817005i	$0.997399\pi$
$432$	8.69697e10	−	3.24575e11i	0.120141	−	0.448372i
$433$	7.29647e11	−	7.29647e11i	0.997510	−	0.997510i	−0.00248729	−	0.999997i	$-0.500792\pi$
$433$	7.29647e11	−	7.29647e11i	0.997510	−	0.997510i	0.999997	+	0.00248729i	$0.000791731\pi$
$434$	4.85102e11	−	1.06448e12i	0.656341	−	1.44024i
$435$	−9.55399e11	−	1.90901e11i	−1.27933	−	0.255626i
$436$	−3.59504e9	−	6.22679e9i	−0.00476446	−	0.00825229i
$437$	−5.28905e10	+	1.41720e10i	−0.0693764	+	0.0185893i
$438$	1.05847e12	−	2.83617e11i	1.37419	−	0.368213i
$439$	1.40237e11	+	2.42898e11i	0.180208	+	0.312129i	0.941951	−	0.335750i	$-0.108990\pi$
$439$	1.40237e11	+	2.42898e11i	0.180208	+	0.312129i	−0.761743	+	0.647879i	$0.775656\pi$
$440$	−6.92101e10	−	1.38290e10i	−0.0880304	−	0.0175896i
$441$	3.39327e11	−	9.85534e11i	0.427214	−	1.24079i
$442$	−1.61556e11	+	1.61556e11i	−0.201337	+	0.201337i
$443$	−3.02153e11	+	1.12765e12i	−0.372743	+	1.39110i	0.483871	+	0.875140i	$0.339231\pi$
$443$	−3.02153e11	+	1.12765e12i	−0.372743	+	1.39110i	−0.856614	+	0.515958i	$0.827436\pi$
$444$	2.66374e10	−	4.61374e10i	0.0325289	−	0.0563417i
$445$	−5.56080e10	−	8.59819e11i	−0.0672229	−	1.03941i
$446$	−8.35941e11	+	4.82631e11i	−1.00039	+	0.577575i
$447$	−9.12973e11	−	9.12973e11i	−1.08162	−	1.08162i
$448$	−8.15384e11	+	3.04868e11i	−0.956337	+	0.357569i
$449$			1.40240e12i			1.62841i	0.580580	+	0.814203i	$0.302826\pi$
$449$			1.40240e12i			1.62841i	−0.580580	+	0.814203i	$0.697174\pi$
$450$	8.94428e11	+	6.88782e11i	1.02823	+	0.791819i
$451$	−4.41866e10	−	2.55112e10i	−0.0502917	−	0.0290359i
$452$	−8.63280e9	−	3.22180e10i	−0.00972811	−	0.0363058i
$453$	1.89519e12	+	5.07814e11i	2.11451	+	0.566582i
$454$	7.63314e11			0.843241
$455$	1.57658e11	+	1.93302e11i	0.172451	+	0.211439i
$456$	−9.42794e10			−0.102112
$457$	1.57453e12	+	4.21894e11i	1.68861	+	0.452461i	0.970030	−	0.242987i	$-0.0781272\pi$
$457$	1.57453e12	+	4.21894e11i	1.68861	+	0.452461i	0.718577	+	0.695448i	$0.244794\pi$
$458$	−4.20734e11	−	1.57020e12i	−0.446799	−	1.66748i
$459$	−4.12657e11	−	2.38248e11i	−0.433943	−	0.250537i
$460$	2.16072e10	−	7.31379e9i	0.0225002	−	0.00761609i
$461$			1.07850e11i			0.111215i	0.998453	+	0.0556077i	$0.0177096\pi$
$461$			1.07850e11i			0.111215i	−0.998453	+	0.0556077i	$0.982290\pi$
$462$	−2.15868e10	+	1.29005e11i	−0.0220445	+	0.131740i
$463$	2.10897e11	+	2.10897e11i	0.213283	+	0.213283i	0.805661	−	0.592377i	$-0.201811\pi$
$463$	2.10897e11	+	2.10897e11i	0.213283	+	0.213283i	−0.592377	+	0.805661i	$0.701811\pi$
$464$	7.25206e11	−	4.18698e11i	0.726324	−	0.419344i
$465$	−1.61933e12	+	1.84327e12i	−1.60619	+	1.82832i
$466$	4.64598e11	−	8.04707e11i	0.456395	−	0.790499i
$467$	3.17037e10	−	1.18320e11i	0.0308449	−	0.115115i	−0.948787	−	0.315917i	$-0.897688\pi$
$467$	3.17037e10	−	1.18320e11i	0.0308449	−	0.115115i	0.979632	+	0.200802i	$0.0643547\pi$
$468$	−5.77366e9	+	5.77366e9i	−0.00556346	+	0.00556346i
$469$	−1.27534e12	+	9.09707e11i	−1.21716	+	0.868208i
$470$	−3.76808e11	+	2.51303e11i	−0.356188	+	0.237551i
$471$	−4.04627e11	−	7.00835e11i	−0.378845	−	0.656178i
$472$	1.31158e12	−	3.51438e11i	1.21635	−	0.325919i
$473$	7.34329e10	−	1.96763e10i	0.0674552	−	0.0180746i
$474$	6.93379e10	+	1.20097e11i	0.0630911	+	0.109277i
$475$	2.83277e10	−	6.80557e10i	0.0255323	−	0.0613399i
$476$	2.48943e9	+	2.58514e10i	0.00222264	+	0.0230809i
$477$	1.35663e11	−	1.35663e11i	0.119986	−	0.119986i
$478$	1.28602e11	−	4.79948e11i	0.112673	−	0.420503i
$479$	−6.01127e11	+	1.04118e12i	−0.521743	+	0.903685i	0.477938	+	0.878394i	$0.341384\pi$
$479$	−6.01127e11	+	1.04118e12i	−0.521743	+	0.903685i	−0.999680	+	0.0252908i	$0.991949\pi$
$480$	7.75468e10	−	5.01527e9i	0.0666774	−	0.00431230i
$481$	5.40093e11	−	3.11823e11i	0.460062	−	0.265617i
$482$	8.49479e11	+	8.49479e11i	0.716871	+	0.716871i
$483$	−6.88565e11	−	1.84160e12i	−0.575682	−	1.53969i
$484$		−	2.63196e10i		−	0.0218009i
$485$	−5.19184e11	−	1.53383e12i	−0.426072	−	1.25875i
$486$	−1.44553e12	−	8.34579e11i	−1.17534	−	0.678585i
$487$	−2.37044e11	−	8.84659e11i	−0.190963	−	0.712682i	−0.993275	−	0.115778i	$-0.963064\pi$
$487$	−2.37044e11	−	8.84659e11i	−0.190963	−	0.712682i	0.802313	−	0.596904i	$-0.203603\pi$
$488$	1.53910e12	+	4.12399e11i	1.22850	+	0.329176i
$489$	4.84141e11			0.382897
$490$	−1.26198e12	−	6.57698e9i	−0.988938	−	0.00515400i
$491$	−1.19543e11			−0.0928232			−0.0464116	−	0.998922i	$-0.514779\pi$
$491$	−1.19543e11			−0.0928232			−0.0464116	+	0.998922i	$0.514779\pi$
$492$	2.74264e10	+	7.34887e9i	0.0211021	+	0.00565429i
$493$	−3.07337e11	−	1.14700e12i	−0.234317	−	0.874482i
$494$	−2.05512e10	−	1.18653e10i	−0.0155262	−	0.00896408i
$495$	6.89818e10	−	1.39577e11i	0.0516430	−	0.104493i
$496$		−	2.10882e12i		−	1.56449i
$497$	6.17277e11	+	1.65094e12i	0.453813	+	1.21374i
$498$	7.68798e11	+	7.68798e11i	0.560119	+	0.560119i
$499$	3.66492e11	−	2.11594e11i	0.264614	−	0.152775i	−0.361824	−	0.932247i	$-0.617846\pi$
$499$	3.66492e11	−	2.11594e11i	0.264614	−	0.152775i	0.626437	+	0.779472i	$0.284512\pi$
$500$	−9.94688e9	+	2.90545e10i	−0.00711741	+	0.0207897i
$501$	−5.04272e11	+	8.73424e11i	−0.357598	+	0.619378i
$502$	3.68749e11	−	1.37619e12i	0.259158	−	0.967189i
$503$	−1.72809e12	+	1.72809e12i	−1.20368	+	1.20368i	−0.230643	+	0.973038i	$0.574083\pi$
$503$	−1.72809e12	+	1.72809e12i	−1.20368	+	1.20368i	−0.973038	+	0.230643i	$0.925917\pi$
$504$	−1.84158e11	−	1.91238e12i	−0.127131	−	1.32019i
$505$	6.29293e11	+	9.43571e11i	0.430568	+	0.645600i
$506$	7.00114e10	+	1.21263e11i	0.0474779	+	0.0822341i
$507$	2.02256e12	−	5.41943e11i	1.35946	−	0.364265i
$508$	6.03489e10	−	1.61705e10i	0.0402053	−	0.0107730i
$509$	−2.20320e11	−	3.81606e11i	−0.145487	−	0.251991i	0.784067	−	0.620676i	$-0.213142\pi$
$509$	−2.20320e11	−	3.81606e11i	−0.145487	−	0.251991i	−0.929555	+	0.368684i	$0.879808\pi$
$510$	−4.75035e11	+	2.37740e12i	−0.310928	+	1.55610i
$511$	1.18709e12	−	8.46761e11i	0.770177	−	0.549372i
$512$	−1.13353e12	+	1.13353e12i	−0.728985	+	0.728985i
$513$	1.28092e10	−	4.78047e10i	0.00816574	−	0.0304749i
$514$	8.27990e11	−	1.43412e12i	0.523228	−	0.906257i
$515$	8.73070e11	+	7.67000e11i	0.546911	+	0.480466i
$516$	−3.66388e10	+	2.11534e10i	−0.0227519	+	0.0131358i
$517$	4.41690e10	+	4.41690e10i	0.0271901	+	0.0271901i
$518$	−5.20728e11	+	3.11191e12i	−0.317780	+	1.89908i
$519$		−	2.09622e12i		−	1.26819i
$520$	4.12188e11	+	2.03713e11i	0.247218	+	0.122181i
$521$	1.38182e12	+	7.97795e11i	0.821641	+	0.474375i	0.850982	−	0.525195i	$-0.176008\pi$
$521$	1.38182e12	+	7.97795e11i	0.821641	+	0.474375i	−0.0293412	+	0.999569i	$0.509341\pi$
$522$	4.88853e11	+	1.82442e12i	0.288178	+	1.07550i
$523$	−2.67741e12	−	7.17409e11i	−1.56479	−	0.419285i	−0.630615	−	0.776095i	$-0.717197\pi$
$523$	−2.67741e12	−	7.17409e11i	−1.56479	−	0.419285i	−0.934177	+	0.356811i	$0.883864\pi$
$524$	−4.70826e10			−0.0272816
$525$	2.52990e12	+	7.78236e11i	1.45341	+	0.447090i
$526$	−6.41190e11			−0.365217
$527$	−2.88849e12	−	7.73968e11i	−1.63126	−	0.437094i
$528$	6.10271e10	+	2.27756e11i	0.0341720	+	0.127532i
$529$	−2.62945e11	−	1.51811e11i	−0.145987	−	0.0842857i
$530$	−2.08248e11	−	1.02921e11i	−0.114641	−	0.0566580i
$531$			2.99536e12i			1.63502i
$532$	−2.52664e9	+	9.44696e8i	−0.00136754	+	0.000511317i
$533$	2.35031e11	+	2.35031e11i	0.126140	+	0.126140i
$534$	−2.54891e12	+	1.47161e12i	−1.35650	+	0.783174i
$535$	2.56155e11	+	2.25034e11i	0.135179	+	0.118756i
$536$	−1.44375e12	+	2.50064e12i	−0.755527	+	1.30861i
$537$	2.55442e11	−	9.53324e11i	0.132559	−	0.494716i
$538$	−7.75892e11	+	7.75892e11i	−0.399283	+	0.399283i
$539$	3.32128e10	+	1.70849e11i	0.0169495	+	0.0871894i
$540$	−4.03986e9	+	2.02183e10i	−0.00204454	+	0.0102323i
$541$	−1.65493e12	−	2.86642e12i	−0.830600	−	1.43864i	−0.897563	−	0.440886i	$-0.854664\pi$
$541$	−1.65493e12	−	2.86642e12i	−0.830600	−	1.43864i	0.0669630	−	0.997755i	$-0.478669\pi$
$542$	2.27270e11	−	6.08967e10i	0.113121	−	0.0303108i
$543$	−1.11922e12	+	2.99895e11i	−0.552482	+	0.148037i
$544$	4.73558e10	+	8.20226e10i	0.0231834	+	0.0401549i
$545$	−4.95553e11	−	7.43039e11i	−0.240605	−	0.360767i
$546$	3.53347e11	−	7.75366e11i	0.170151	−	0.373370i
$547$	1.35641e12	−	1.35641e12i	0.647812	−	0.647812i	−0.304652	−	0.952464i	$-0.598540\pi$
$547$	1.35641e12	−	1.35641e12i	0.647812	−	0.647812i	0.952464	+	0.304652i	$0.0985401\pi$
$548$	−1.96247e10	+	7.32404e10i	−0.00929588	+	0.0346927i
$549$	−1.75747e12	+	3.04403e12i	−0.825682	+	1.43012i
$550$	−1.86851e11	−	2.49285e10i	−0.0870688	−	0.0116162i
$551$	1.06811e11	−	6.16675e10i	0.0493668	−	0.0285019i
$552$	−2.56256e12	−	2.56256e12i	−1.17476	−	1.17476i
$553$	1.42389e11	+	1.17374e11i	0.0647459	+	0.0533715i
$554$		−	1.18462e12i		−	0.534298i
$555$	2.93204e12	−	5.93265e12i	1.31175	−	2.65418i
$556$	−6.39729e10	−	3.69348e10i	−0.0283896	−	0.0163908i
$557$	8.11216e11	+	3.02750e12i	0.357098	+	1.33271i	0.877823	+	0.478985i	$0.158995\pi$
$557$	8.11216e11	+	3.02750e12i	0.357098	+	1.33271i	−0.520725	+	0.853725i	$0.674338\pi$
$558$	4.59446e12	+	1.23108e12i	2.00623	+	0.537567i
$559$	−4.95253e11			−0.214523
$560$	−2.07506e12	+	9.32609e11i	−0.891630	+	0.400731i
$561$	3.34360e11			0.142522
$562$	−9.00766e11	−	2.41360e11i	−0.380889	−	0.102059i
$563$	−3.61002e11	−	1.34728e12i	−0.151433	−	0.565157i	−0.999384	−	0.0350824i	$-0.988831\pi$
$563$	−3.61002e11	−	1.34728e12i	−0.151433	−	0.565157i	0.847951	−	0.530074i	$-0.177836\pi$
$564$	−3.01042e10	−	1.73807e10i	−0.0125277	−	0.00723288i
$565$	−1.32839e12	−	3.92447e12i	−0.548414	−	1.62018i
$566$		−	1.80900e12i		−	0.740909i
$567$	−1.43262e12	−	2.39726e11i	−0.582114	−	0.0974072i
$568$	2.29725e12	+	2.29725e12i	0.926065	+	0.926065i
$569$	−2.60459e12	+	1.50376e12i	−1.04168	+	0.601415i	−0.920309	−	0.391192i	$-0.872063\pi$
$569$	−2.60459e12	+	1.50376e12i	−1.04168	+	0.601415i	−0.121372	+	0.992607i	$0.538729\pi$
$570$	−2.51284e11	+	1.62516e10i	−0.0997077	+	0.00644851i
$571$	−9.79630e10	+	1.69677e11i	−0.0385655	+	0.0667975i	−0.884664	−	0.466229i	$-0.845612\pi$
$571$	−9.79630e10	+	1.69677e11i	−0.0385655	+	0.0667975i	0.846098	+	0.533027i	$0.178946\pi$
$572$	3.52884e8	−	1.31698e9i	0.000137832	−	0.000514395i
$573$	−2.45917e12	+	2.45917e12i	−0.953000	+	0.953000i
$574$	−1.67387e12	+	1.61190e11i	−0.643603	+	0.0619776i
$575$	2.61974e12	−	1.07982e12i	0.999433	−	0.411953i
$576$	−1.76979e12	−	3.06536e12i	−0.669916	−	1.16033i
$577$	2.32772e12	−	6.23712e11i	0.874260	−	0.234257i	0.206331	−	0.978482i	$-0.433848\pi$
$577$	2.32772e12	−	6.23712e11i	0.874260	−	0.234257i	0.667929	+	0.744225i	$0.267181\pi$
$578$	−2.90902e11	+	7.79471e10i	−0.108411	+	0.0290485i
$579$	3.65577e12	+	6.33198e12i	1.35184	+	2.34146i
$580$	−4.27466e10	+	2.85089e10i	−0.0156847	+	0.0104605i
$581$	1.31649e12	+	5.99945e11i	0.479319	+	0.218433i
$582$	−3.91135e12	+	3.91135e12i	−1.41310	+	1.41310i
$583$	−8.29167e9	+	3.09449e10i	−0.00297258	+	0.0110938i
$584$	1.34385e12	−	2.32761e12i	0.478071	−	0.828044i
$585$	−6.69404e11	+	7.61978e11i	−0.236313	+	0.268993i
$586$	1.52615e12	−	8.81123e11i	0.534636	−	0.308672i
$587$	−2.71256e12	−	2.71256e12i	−0.942992	−	0.942992i	0.0554685	−	0.998460i	$-0.482335\pi$
$587$	−2.71256e12	−	2.71256e12i	−0.942992	−	0.942992i	−0.998460	+	0.0554685i	$0.982335\pi$
$588$	−4.24609e10	−	8.70540e10i	−0.0146484	−	0.0300324i
$589$		−	3.10595e11i		−	0.106335i
$590$	3.43521e12	−	1.16278e12i	1.16713	−	0.395060i
$591$	1.69246e12	+	9.77140e11i	0.570655	+	0.329468i
$592$	1.47213e12	+	5.49405e12i	0.492603	+	1.83842i
$593$	−1.90773e12	−	5.11174e11i	−0.633535	−	0.169755i	−0.0722615	−	0.997386i	$-0.523022\pi$
$593$	−1.90773e12	−	5.11174e11i	−0.633535	−	0.169755i	−0.561273	+	0.827631i	$0.689688\pi$
$594$	−1.26559e11			−0.0417112
$595$	5.15833e11	+	3.18453e12i	0.168726	+	1.04164i
$596$	−6.80913e10			−0.0221046
$597$	3.58105e12	+	9.59539e11i	1.15379	+	0.309156i
$598$	−2.36088e11	−	8.81094e11i	−0.0754952	−	0.281752i
$599$	5.50671e11	+	3.17930e11i	0.174772	+	0.100905i	0.584834	−	0.811153i	$-0.301160\pi$
$599$	5.50671e11	+	3.17930e11i	0.174772	+	0.100905i	−0.410062	+	0.912058i	$0.634493\pi$
$600$	4.83819e12	−	6.28439e11i	1.52406	−	0.197962i
$601$		−	7.70771e10i		−	0.0240985i	−0.999927	−	0.0120493i	$-0.996165\pi$
$601$		−	7.70771e10i		−	0.0240985i	0.999927	−	0.0120493i	$-0.00383549\pi$
$602$	1.59374e12	−	1.93340e12i	0.494578	−	0.599981i
$603$	−4.50405e12	−	4.50405e12i	−1.38731	−	1.38731i
$604$	8.96102e10	−	5.17365e10i	0.0273963	−	0.0158172i
$605$	−2.11001e11	−	3.26252e12i	−0.0640301	−	0.990042i
$606$	1.93713e12	−	3.35520e12i	0.583487	−	1.01063i
$607$	−2.29628e10	+	8.56985e10i	−0.00686557	+	0.0256226i	−0.969274	−	0.245985i	$-0.920889\pi$
$607$	−2.29628e10	+	8.56985e10i	−0.00686557	+	0.0256226i	0.962408	+	0.271608i	$0.0875553\pi$
$608$	−6.95595e9	+	6.95595e9i	−0.00206438	+	0.00206438i
$609$	2.57171e12	+	3.60533e12i	0.757606	+	1.06210i
$610$	4.17326e12	+	8.33870e11i	1.22037	+	0.243845i
$611$	−2.03462e11	−	3.52406e11i	−0.0590605	−	0.102296i
$612$	−1.02002e11	+	2.73313e10i	−0.0293918	+	0.00787551i
$613$	1.48524e12	−	3.97968e11i	0.424838	−	0.113835i	−0.0400642	−	0.999197i	$-0.512756\pi$
$613$	1.48524e12	−	3.97968e11i	0.424838	−	0.113835i	0.464902	+	0.885362i	$0.346090\pi$
$614$	−2.63304e12	−	4.56056e12i	−0.747653	−	1.29497i
$615$	3.45863e12	+	6.91078e11i	0.974914	+	0.194800i
$616$	1.86297e11	+	2.61174e11i	0.0521306	+	0.0730831i
$617$	−1.68286e12	+	1.68286e12i	−0.467483	+	0.467483i	−0.901098	−	0.433615i	$-0.857238\pi$
$617$	−1.68286e12	+	1.68286e12i	−0.467483	+	0.467483i	0.433615	+	0.901098i	$0.357238\pi$
$618$	1.02745e12	−	3.83450e12i	0.283343	−	1.05745i
$619$	4.02187e11	−	6.96608e11i	0.110108	−	0.190713i	−0.805706	−	0.592316i	$-0.798214\pi$
$619$	4.02187e11	−	6.96608e11i	0.110108	−	0.190713i	0.915814	+	0.401603i	$0.131547\pi$
$620$	8.35097e9	+	1.29124e11i	0.00226973	+	0.0350949i
$621$	1.64751e12	−	9.51193e11i	0.444546	−	0.256659i
$622$	−7.63959e11	−	7.63959e11i	−0.204651	−	0.204651i
$623$	−2.49112e12	+	3.02203e12i	−0.662520	+	0.803715i
$624$		−	1.53605e12i		−	0.405580i
$625$	−1.00007e12	+	3.68127e12i	−0.262162	+	0.965024i
$626$	−2.17257e12	−	1.25433e12i	−0.565443	−	0.326459i
$627$	8.98832e9	+	3.35449e10i	0.00232260	+	0.00866807i
$628$	−4.12238e10	−	1.10459e10i	−0.0105762	−	0.00283388i
$629$	8.06558e12			2.05451
$630$	−8.20488e11	−	5.06534e12i	−0.207510	−	1.28108i
$631$	−2.17208e12			−0.545436			−0.272718	−	0.962094i	$-0.587923\pi$
$631$	−2.17208e12			−0.545436			−0.272718	+	0.962094i	$0.587923\pi$
$632$	3.28540e11	+	8.80322e10i	0.0819147	+	0.0219490i
$633$	5.10405e11	+	1.90486e12i	0.126357	+	0.471570i
$634$	−3.41502e12	−	1.97166e12i	−0.839444	−	0.484653i
$635$	7.35109e12	−	2.48827e12i	1.79420	−	0.607316i
$636$		−	1.78283e10i		−	0.00432069i
$637$	7.90723e10	−	1.13107e12i	0.0190282	−	0.272183i
$638$	−2.23016e11	−	2.23016e11i	−0.0532896	−	0.0532896i
$639$	−6.20656e12	+	3.58336e12i	−1.47264	+	0.850230i
$640$	−2.70538e12	+	3.07951e12i	−0.637410	+	0.725558i
$641$	1.34695e12	−	2.33299e12i	0.315130	−	0.545822i	−0.664335	−	0.747435i	$-0.731285\pi$
$641$	1.34695e12	−	2.33299e12i	0.315130	−	0.545822i	0.979465	+	0.201613i	$0.0646184\pi$
$642$	3.01449e11	−	1.12502e12i	0.0700335	−	0.261369i
$643$	4.23017e12	−	4.23017e12i	0.975908	−	0.975908i	−0.0238084	−	0.999717i	$-0.507579\pi$
$643$	4.23017e12	−	4.23017e12i	0.975908	−	0.975908i	0.999717	+	0.0238084i	$0.00757916\pi$
$644$	−9.43524e10	−	4.29979e10i	−0.0216156	−	0.00985055i
$645$	−4.37209e12	+	2.91587e12i	−0.994651	+	0.663360i
$646$	−1.53453e11	−	2.65788e11i	−0.0346680	−	0.0600467i
$647$	−5.76567e12	+	1.54491e12i	−1.29354	+	0.346604i	−0.839005	−	0.544124i	$-0.816862\pi$
$647$	−5.76567e12	+	1.54491e12i	−1.29354	+	0.346604i	−0.454538	+	0.890727i	$0.650196\pi$
$648$	−2.58613e12	+	6.92952e11i	−0.576187	+	0.154389i
$649$	−2.50085e11	−	4.33160e11i	−0.0553333	−	0.0958401i
$650$	1.13373e12	+	4.71907e11i	0.249114	+	0.103692i
$651$	1.11011e13	−	1.06901e12i	2.42243	−	0.233275i
$652$	1.80541e10	−	1.80541e10i	0.00391256	−	0.00391256i
$653$	−2.70167e11	+	1.00828e12i	−0.0581465	+	0.217006i	−0.988886	−	0.148678i	$-0.952498\pi$
$653$	−2.70167e11	+	1.00828e12i	−0.0581465	+	0.217006i	0.930739	+	0.365684i	$0.119165\pi$
$654$	−1.52544e12	+	2.64214e12i	−0.326058	+	0.564749i
$655$	−5.83626e12	+	3.77455e11i	−1.23894	+	0.0801271i
$656$	−2.62531e12	+	1.51573e12i	−0.553495	+	0.319561i
$657$	4.19239e12	+	4.19239e12i	0.877845	+	0.877845i
$658$	2.03049e12	+	3.39770e11i	0.422265	+	0.0706592i
$659$		−	3.46938e12i		−	0.716584i	−0.933610	−	0.358292i	$-0.883359\pi$
$659$		−	3.46938e12i		−	0.716584i	0.933610	−	0.358292i	$-0.116641\pi$
$660$	−4.63864e9	−	1.37039e10i	−0.000951574	−	0.00281124i
$661$	−5.52510e12	−	3.18992e12i	−1.12573	−	0.649940i	−0.182871	−	0.983137i	$-0.558539\pi$
$661$	−5.52510e12	−	3.18992e12i	−1.12573	−	0.649940i	−0.942857	+	0.333197i	$0.891873\pi$
$662$	2.91622e11	+	1.08835e12i	0.0590145	+	0.220245i
$663$	−2.10396e12	−	5.63755e11i	−0.422890	−	0.113313i
$664$	2.66668e12			0.532372
$665$	−3.05623e11	+	1.37358e11i	−0.0606023	+	0.0272369i
$666$	−1.28292e13			−2.52677
$667$	4.57933e12	+	1.22703e12i	0.895851	+	0.240042i
$668$	1.37661e10	+	5.13756e10i	0.00267495	+	0.00998305i
$669$	−7.96950e12	−	4.60119e12i	−1.53820	−	0.888082i
$670$	−3.41699e12	+	6.91388e12i	−0.655099	+	1.32552i
$671$		−	5.86931e11i		−	0.111773i
$672$	−2.72556e11	−	2.24674e11i	−0.0515578	−	0.0425002i
$673$	−1.08159e12	−	1.08159e12i	−0.203233	−	0.203233i	0.598150	−	0.801384i	$-0.295903\pi$
$673$	−1.08159e12	−	1.08159e12i	−0.203233	−	0.203233i	−0.801384	+	0.598150i	$0.795903\pi$
$674$	−5.65901e12	+	3.26723e12i	−1.05626	+	0.609832i
$675$	−3.38686e11	+	2.53860e12i	−0.0627957	+	0.470682i
$676$	5.52136e10	−	9.56328e10i	0.0101692	−	0.0176135i
$677$	2.40414e12	−	8.97238e12i	0.439857	−	1.64157i	−0.289313	−	0.957235i	$-0.593427\pi$
$677$	2.40414e12	−	8.97238e12i	0.439857	−	1.64157i	0.729170	−	0.684333i	$-0.239907\pi$
$678$	−1.00076e13	+	1.00076e13i	−1.81886	+	1.81886i
$679$	−3.05229e12	+	6.69780e12i	−0.551077	+	1.20925i
$680$	3.29932e12	+	4.94704e12i	0.591744	+	0.887269i
$681$	3.63855e12	+	6.30216e12i	0.648286	+	1.12286i
$682$	−7.67190e11	+	2.05568e11i	−0.135792	+	0.0363853i
$683$	6.39218e12	−	1.71278e12i	1.12397	−	0.301168i	0.351483	−	0.936194i	$-0.385678\pi$
$683$	6.39218e12	−	1.71278e12i	1.12397	−	0.301168i	0.772490	+	0.635027i	$0.219011\pi$
$684$	−5.48406e9	−	9.49867e9i	−0.000957965	−	0.00165924i
$685$	−1.84548e12	+	9.23605e12i	−0.320259	+	1.60280i
$686$	4.16109e12	+	3.94852e12i	0.717378	+	0.680731i
$687$	1.09585e13	−	1.09585e13i	1.87692	−	1.87692i
$688$	1.16905e12	−	4.36296e12i	0.198923	−	0.742391i
$689$	1.04351e11	−	1.80741e11i	0.0176404	−	0.0305541i
$690$	−7.27175e12	−	6.38830e12i	−1.22129	−	1.07291i
$691$	−8.96329e12	+	5.17496e12i	−1.49560	+	0.863487i	−0.999987	−	0.00505532i	$-0.998391\pi$
$691$	−8.96329e12	+	5.17496e12i	−1.49560	+	0.863487i	−0.495616	+	0.868542i	$0.665057\pi$
$692$	−7.81702e10	−	7.81702e10i	−0.0129588	−	0.0129588i
$693$	−6.62872e11	+	2.47844e11i	−0.109177	+	0.0408206i
$694$			4.17842e12i			0.683746i
$695$	−8.22605e12	−	4.06550e12i	−1.33740	−	0.660971i
$696$	7.06922e12	+	4.08142e12i	1.14190	+	0.659279i
$697$	1.11259e12	+	4.15223e12i	0.178561	+	0.666399i
$698$	2.36391e12	+	6.33409e11i	0.376949	+	0.101003i
$699$	8.85855e12			1.40351
$700$	1.23364e11	−	6.53213e10i	0.0194199	−	0.0102829i
$701$	−2.76352e12			−0.432246			−0.216123	−	0.976366i	$-0.569341\pi$
$701$	−2.76352e12			−0.432246			−0.216123	+	0.976366i	$0.569341\pi$
$702$	7.96371e11	+	2.13387e11i	0.123765	+	0.0331628i
$703$	2.16821e11	+	8.09185e11i	0.0334812	+	0.124954i
$704$	5.11860e11	+	2.95522e11i	0.0785369	+	0.0453433i
$705$	−3.87100e12	−	1.91313e12i	−0.590163	−	0.291672i
$706$		−	1.76334e12i		−	0.267125i
$707$	8.50825e11	−	5.08460e12i	0.128072	−	0.765367i
$708$	1.96819e11	+	1.96819e11i	0.0294386	+	0.0294386i
$709$	9.20289e11	−	5.31329e11i	0.136778	−	0.0789688i	−0.430050	−	0.902805i	$-0.641504\pi$
$709$	9.20289e11	−	5.31329e11i	0.136778	−	0.0789688i	0.566828	+	0.823836i	$0.308171\pi$
$710$	6.51890e12	+	5.72691e12i	0.962746	+	0.845781i
$711$	−3.75156e11	+	6.49789e11i	−0.0550552	+	0.0953584i
$712$	−1.86838e12	+	6.97288e12i	−0.272461	+	1.01684i
$713$	8.44212e12	−	8.44212e12i	1.22334	−	1.22334i
$714$	8.97146e12	−	6.39940e12i	1.29188	−	0.921504i
$715$	3.31847e10	−	1.66079e11i	0.00474854	−	0.0237650i
$716$	−2.60247e10	−	4.50761e10i	−0.00370064	−	0.00640969i
$717$	4.57562e12	−	1.22603e12i	0.646567	−	0.173247i
$718$	4.98828e12	−	1.33661e12i	0.700472	−	0.187691i
$719$	1.86160e11	+	3.22438e11i	0.0259780	+	0.0449952i	0.878722	−	0.477334i	$-0.158397\pi$
$719$	1.86160e11	+	3.22438e11i	0.0259780	+	0.0449952i	−0.852744	+	0.522329i	$0.825063\pi$
$720$	−5.13255e12	−	7.69582e12i	−0.711765	−	1.06723i
$721$	−5.06340e11	−	5.25806e12i	−0.0697804	−	0.724631i
$722$	−5.08342e12	+	5.08342e12i	−0.696208	+	0.696208i
$723$	−2.96428e12	+	1.10629e13i	−0.403457	+	1.50572i
$724$	−3.05536e10	+	5.29204e10i	−0.00413275	+	0.00715813i
$725$	−5.07023e12	+	3.87660e12i	−0.681564	+	0.521110i
$726$	−9.67165e12	+	5.58393e12i	−1.29207	+	0.745977i
$727$	−4.05800e12	−	4.05800e12i	−0.538775	−	0.538775i	0.384394	−	0.923169i	$-0.374410\pi$
$727$	−4.05800e12	−	4.05800e12i	−0.538775	−	0.538775i	−0.923169	+	0.384394i	$0.874410\pi$
$728$	−7.31917e11	−	1.95755e12i	−0.0965764	−	0.258298i
$729$		−	1.14123e13i		−	1.49658i
$730$	3.18055e12	−	6.43548e12i	0.414524	−	0.838741i
$731$	−5.54696e12	−	3.20254e12i	−0.718500	−	0.414826i
$732$	8.45372e10	+	3.15497e11i	0.0108830	+	0.0406158i
$733$	1.43490e12	+	3.84480e11i	0.183592	+	0.0491933i	0.349444	−	0.936957i	$-0.386371\pi$
$733$	1.43490e12	+	3.84480e11i	0.183592	+	0.0491933i	−0.165852	+	0.986151i	$0.553037\pi$
$734$	−2.79686e12			−0.355662
$735$	−5.96127e12	−	1.04506e13i	−0.753435	−	1.32084i
$736$	−3.78131e11			−0.0474999
$737$	1.02738e12	+	2.75285e11i	0.128271	+	0.0343700i
$738$	−1.76969e12	−	6.60458e12i	−0.219606	−	0.819581i
$739$	3.82071e11	+	2.20589e11i	0.0471242	+	0.0272072i	0.523377	−	0.852101i	$-0.324672\pi$
$739$	3.82071e11	+	2.20589e11i	0.0471242	+	0.0272072i	−0.476253	+	0.879308i	$0.658005\pi$
$740$	−1.11895e11	−	3.30573e11i	−0.0137173	−	0.0405252i
$741$		−	2.26236e11i		−	0.0275664i
$742$	3.69783e11	+	9.89003e11i	0.0447847	+	0.119779i
$743$	4.07079e12	+	4.07079e12i	0.490037	+	0.490037i	0.908318	−	0.418281i	$-0.137367\pi$
$743$	4.07079e12	+	4.07079e12i	0.490037	+	0.490037i	−0.418281	+	0.908318i	$0.637367\pi$
$744$	1.78024e13	−	1.02782e13i	2.13011	−	1.22982i
$745$	−8.44046e12	+	5.45879e11i	−1.00384	+	0.0649222i
$746$	4.29586e12	−	7.44065e12i	0.507838	−	0.879602i
$747$	−1.52252e12	+	5.68214e12i	−0.178905	+	0.667681i
$748$	1.24686e10	−	1.24686e10i	0.00145633	−	0.00145633i
$749$	−1.48558e11	−	1.54269e12i	−0.0172475	−	0.179106i
$750$	1.27870e13	−	2.50898e12i	1.47568	−	0.289549i
$751$	4.25324e12	+	7.36684e12i	0.487911	+	0.845087i	0.999903	−	0.0139033i	$-0.00442570\pi$
$751$	4.25324e12	+	7.36684e12i	0.487911	+	0.845087i	−0.511992	+	0.858990i	$0.671092\pi$
$752$	3.58481e12	−	9.60548e11i	0.408777	−	0.109531i
$753$	1.31200e13	−	3.51549e12i	1.48715	−	0.398482i
$754$	1.02731e12	+	1.77935e12i	0.115752	+	0.200489i
$755$	1.06931e13	−	7.13154e12i	1.19769	−	0.798771i
$756$	7.62965e10	−	5.44228e10i	0.00849487	−	0.00605944i
$757$	−3.29028e12	+	3.29028e12i	−0.364168	+	0.364168i	−0.865345	−	0.501177i	$-0.832901\pi$
$757$	−3.29028e12	+	3.29028e12i	−0.364168	+	0.364168i	0.501177	+	0.865345i	$0.332901\pi$
$758$	−1.88176e11	+	7.02284e11i	−0.0207040	+	0.0772683i
$759$	−6.67458e11	+	1.15607e12i	−0.0730022	+	0.126444i
$760$	−4.07622e11	+	4.63993e11i	−0.0443197	+	0.0504488i
$761$	7.88322e12	−	4.55138e12i	0.852065	−	0.491940i	−0.00928211	−	0.999957i	$-0.502955\pi$
$761$	7.88322e12	−	4.55138e12i	0.852065	−	0.491940i	0.861347	+	0.508017i	$0.169621\pi$
$762$	−1.87457e13	−	1.87457e13i	−2.01421	−	2.01421i
$763$	−6.70003e11	+	4.00399e12i	−0.0715676	+	0.427694i
$764$			1.83410e11i			0.0194761i
$765$	−1.24248e13	+	4.20567e12i	−1.31164	+	0.443975i
$766$	1.32438e13	+	7.64633e12i	1.38990	+	0.802460i
$767$	8.43323e11	+	3.14732e12i	0.0879862	+	0.328369i
$768$	−9.33068e11	−	2.50015e11i	−0.0967805	−	0.0259323i
$769$	−6.43965e11			−0.0664039			−0.0332019	−	0.999449i	$-0.510570\pi$
$769$	−6.43965e11			−0.0664039			−0.0332019	+	0.999449i	$0.510570\pi$
$770$	5.41561e11	+	6.63998e11i	0.0555187	+	0.0680704i
$771$	1.57874e13			1.60904
$772$	3.72453e11	+	9.97985e10i	0.0377393	+	0.0101122i
$773$	−5.82123e11	−	2.17251e12i	−0.0586417	−	0.218854i	0.930387	−	0.366580i	$-0.119471\pi$
$773$	−5.82123e11	−	2.17251e12i	−0.0586417	−	0.218854i	−0.989028	+	0.147726i	$0.952805\pi$
$774$	8.82305e12	+	5.09399e12i	0.883658	+	0.510180i
$775$	2.07034e12	+	1.59390e13i	0.206150	+	1.58709i
$776$			1.35671e13i			1.34310i
$777$	−2.81751e13	+	1.05345e13i	−2.77314	+	1.03686i
$778$	−1.71040e12	−	1.71040e12i	−0.167375	−	0.167375i
$779$	−3.86667e11	+	2.23242e11i	−0.0376200	+	0.0217199i
$780$	6.08281e9	+	9.40533e10i	0.000588408	+	0.00909805i
$781$	5.98355e11	−	1.03638e12i	0.0575479	−	0.0996759i
$782$	3.05332e12	−	1.13951e13i	0.291972	−	1.08966i
$783$	−3.02995e12	+	3.02995e12i	−0.288077	+	0.288077i
$784$	9.77757e12	+	3.36650e12i	0.924290	+	0.318241i
$785$	−5.19857e12	−	1.03874e12i	−0.488619	−	0.0976322i
$786$	9.98899e12	+	1.73014e13i	0.933513	+	1.61689i
$787$	8.51496e10	−	2.28158e10i	0.00791218	−	0.00212006i	−0.254861	−	0.966978i	$-0.582030\pi$
$787$	8.51496e10	−	2.28158e10i	0.00791218	−	0.00212006i	0.262773	+	0.964858i	$0.415363\pi$
$788$	9.95519e10	−	2.66748e10i	0.00919775	−	0.00246453i
$789$	−3.05641e12	−	5.29386e12i	−0.280780	−	0.486324i
$790$	8.90839e11	+	1.78001e11i	0.0813724	+	0.0162592i
$791$	−7.80964e12	+	1.71371e13i	−0.709311	+	1.55648i
$792$	−9.22374e11	+	9.22374e11i	−0.0832998	+	0.0832998i
$793$	−9.89608e11	+	3.69327e12i	−0.0888657	+	0.331651i
$794$	1.91692e12	−	3.32020e12i	0.171164	−	0.296464i
$795$	−1.42927e11	−	2.20996e12i	−0.0126900	−	0.196215i
$796$	1.69323e11	−	9.77586e10i	0.0149488	−	0.00863070i
$797$	−3.28029e11	−	3.28029e11i	−0.0287972	−	0.0287972i	0.692562	−	0.721359i	$-0.256482\pi$
$797$	−3.28029e11	−	3.28029e11i	−0.0287972	−	0.0287972i	−0.721359	+	0.692562i	$0.756482\pi$
$798$	8.83197e11	+	7.28038e11i	0.0770982	+	0.0635537i
$799$		−	5.26272e12i		−	0.456825i
$800$	3.10596e11	−	4.03328e11i	0.0268096	−	0.0348140i
$801$	−1.37910e13	−	7.96223e12i	−1.18372	−	0.683421i
$802$	1.92856e12	+	7.19748e12i	0.164607	+	0.614322i
$803$	−9.56290e11	−	2.56237e11i	−0.0811652	−	0.0217481i
$804$	−5.91904e11			−0.0499573
$805$	−1.20404e13	−	4.57352e12i	−1.01056	−	0.383856i
$806$	5.17415e12			0.431848
$807$	−1.01045e13	−	2.70750e12i	−0.838657	−	0.224718i
$808$	−2.45940e12	−	9.17859e12i	−0.202991	−	0.757574i
$809$	−9.93352e12	−	5.73512e12i	−0.815332	−	0.470732i	0.0334719	−	0.999440i	$-0.489344\pi$
$809$	−9.93352e12	−	5.73512e12i	−0.815332	−	0.470732i	−0.848804	+	0.528707i	$0.822677\pi$
$810$	−6.77341e12	+	2.29273e12i	−0.552873	+	0.187141i
$811$			1.26106e12i			0.102363i	0.998689	+	0.0511816i	$0.0162987\pi$
$811$			1.26106e12i			0.102363i	−0.998689	+	0.0511816i	$0.983701\pi$
$812$	2.30348e11	+	3.85449e10i	0.0185944	+	0.00311147i
$813$	1.58613e12	+	1.58613e12i	0.127330	+	0.127330i
$814$	1.85524e12	−	1.07112e12i	0.148112	−	0.0855123i
$815$	2.09321e12	−	2.38268e12i	0.166190	−	0.189172i
$816$	9.93286e12	−	1.72042e13i	0.784275	−	1.35840i
$817$	1.72182e11	−	6.42594e11i	0.0135204	−	0.0504588i
$818$	5.01437e11	−	5.01437e11i	0.0391585	−	0.0391585i
$819$	4.58901e12	−	4.41911e11i	0.356403	−	0.0343208i
$820$	1.54747e11	−	1.03205e11i	0.0119525	−	0.00797145i
$821$	2.59733e12	+	4.49872e12i	0.199519	+	0.345577i	0.948372	−	0.317159i	$-0.102729\pi$
$821$	2.59733e12	+	4.49872e12i	0.199519	+	0.345577i	−0.748854	+	0.662735i	$0.769395\pi$
$822$	3.10772e13	−	8.32711e12i	2.37421	−	0.636167i
$823$	7.56970e12	−	2.02829e12i	0.575148	−	0.154110i	0.0404913	−	0.999180i	$-0.487108\pi$
$823$	7.56970e12	−	2.02829e12i	0.575148	−	0.154110i	0.534656	+	0.845070i	$0.320441\pi$
$824$	−4.86832e12	−	8.43217e12i	−0.367880	−	0.637187i
$825$	−6.84859e11	−	1.66153e12i	−0.0514705	−	0.124872i
$826$	−1.50006e13	−	6.83600e12i	−1.12124	−	0.510966i
$827$	−6.86450e11	+	6.86450e11i	−0.0510310	+	0.0510310i	−0.732162	−	0.681131i	$-0.761489\pi$
$827$	−6.86450e11	+	6.86450e11i	−0.0510310	+	0.0510310i	0.681131	+	0.732162i	$0.261489\pi$
$828$	1.09119e11	−	4.07237e11i	0.00806795	−	0.0301100i
$829$	−1.12151e13	+	1.94251e13i	−0.824723	+	1.42846i	0.0774082	+	0.996999i	$0.475336\pi$
$829$	−1.12151e13	+	1.94251e13i	−0.824723	+	1.42846i	−0.902131	+	0.431462i	$0.857998\pi$
$830$	7.10755e12	−	4.59675e11i	0.519839	−	0.0336201i
$831$	9.78056e12	−	5.64681e12i	0.711474	−	0.410770i
$832$	−2.72261e12	−	2.72261e12i	−0.196984	−	0.196984i
$833$	8.19966e12	−	1.21570e13i	0.590056	−	0.874827i
$834$			3.13442e13i			2.24342i
$835$	2.11828e12	+	6.25806e12i	0.150798	+	0.445503i
$836$	1.58610e9	+	9.15738e8i	0.000112306	+	6.48400e-5i
$837$	2.79290e12	+	1.04233e13i	0.196694	+	0.734072i
$838$	−1.93657e13	−	5.18903e12i	−1.35655	−	0.363486i
$839$	−1.19326e13			−0.831394			−0.415697	−	0.909503i	$-0.636462\pi$
$839$	−1.19326e13			−0.831394			−0.415697	+	0.909503i	$0.636462\pi$
$840$	−1.79867e13	−	1.29720e13i	−1.24651	−	0.898980i
$841$	3.82864e12			0.263914
$842$	−1.32063e13	−	3.53861e12i	−0.905473	−	0.242621i
$843$	−2.30102e12	−	8.58751e12i	−0.156926	−	0.585657i
$844$	9.00676e10	+	5.20005e10i	0.00610981	+	0.00352750i
$845$	6.07749e12	−	1.22971e13i	0.410081	−	0.829750i
$846$			8.37093e12i			0.561833i
$847$	−9.45239e12	+	1.14669e13i	−0.631053	+	0.765543i
$848$	1.34593e12	+	1.34593e12i	0.0893799	+	0.0893799i
$849$	1.49357e13	−	8.62312e12i	0.986598	−	0.569613i
$850$	9.64648e12	+	1.26167e13i	0.633846	+	0.829012i
$851$	−1.61007e13	+	2.78873e13i	−1.05236	+	1.82273i
$852$	−1.72365e11	+	6.43276e11i	−0.0112065	+	0.0418234i
$853$	5.48270e12	−	5.48270e12i	0.354588	−	0.354588i	−0.507226	−	0.861813i	$-0.669329\pi$
$853$	5.48270e12	−	5.48270e12i	0.354588	−	0.354588i	0.861813	+	0.507226i	$0.169329\pi$
$854$	−1.12334e13	−	1.57484e13i	−0.722690	−	1.01315i
$855$	−7.55943e11	−	1.13347e12i	−0.0483773	−	0.0725375i
$856$	−1.42834e12	−	2.47396e12i	−0.0909285	−	0.157493i
$857$	2.41199e13	−	6.46290e12i	1.52743	−	0.409274i	0.605250	−	0.796035i	$-0.293073\pi$
$857$	2.41199e13	−	6.46290e12i	1.52743	−	0.409274i	0.922180	+	0.386761i	$0.126406\pi$
$858$	−5.58818e11	+	1.49735e11i	−0.0352028	+	0.00943257i
$859$	2.54897e12	+	4.41495e12i	0.159733	+	0.276667i	0.934773	−	0.355247i	$-0.115603\pi$
$859$	2.54897e12	+	4.41495e12i	0.159733	+	0.276667i	−0.775039	+	0.631913i	$0.782270\pi$
$860$	−5.43040e10	+	2.71775e11i	−0.00338524	+	0.0169421i
$861$	−9.30981e12	−	1.30516e13i	−0.577333	−	0.809377i
$862$	1.14956e13	−	1.14956e13i	0.709167	−	0.709167i
$863$	−1.12780e12	+	4.20902e12i	−0.0692125	+	0.258304i	−0.991859	−	0.127343i	$-0.959355\pi$
$863$	−1.12780e12	+	4.20902e12i	−0.0692125	+	0.258304i	0.922646	+	0.385647i	$0.126022\pi$
$864$	1.70886e11	−	2.95983e11i	0.0104326	−	0.0180699i
$865$	−1.03165e13	−	9.06314e12i	−0.626556	−	0.550435i
$866$	−1.99972e13	+	1.15454e13i	−1.20820	+	0.697553i
$867$	−2.03022e12	−	2.03022e12i	−0.122028	−	0.122028i
$868$	3.74106e11	−	4.53835e11i	0.0223695	−	0.0271368i
$869$		−	1.25288e11i		−	0.00745284i
$870$	1.95452e13	+	9.65969e12i	1.15666	+	0.571645i
$871$	−6.00064e12	−	3.46447e12i	−0.353277	−	0.203965i
$872$	1.93671e12	+	7.22791e12i	0.113433	+	0.423339i
$873$	−2.89086e13	−	7.74602e12i	−1.68447	−	0.451351i
$874$	1.22531e12			0.0710302
$875$	1.47682e13	−	9.08609e12i	0.851711	−	0.524011i
$876$	5.50947e11			0.0316112
$877$	7.44379e11	+	1.99456e11i	0.0424909	+	0.0113854i	0.280002	−	0.959999i	$-0.409665\pi$
$877$	7.44379e11	+	1.99456e11i	0.0424909	+	0.0113854i	−0.237511	+	0.971385i	$0.576332\pi$
$878$	−1.62443e12	−	6.06245e12i	−0.0922519	−	0.344289i
$879$	1.45497e13	+	8.40025e12i	0.822058	+	0.474616i
$880$	1.38475e12	+	6.84374e11i	0.0778394	+	0.0384699i
$881$			1.05988e13i			0.592741i	0.955073	+	0.296370i	$0.0957762\pi$
$881$			1.05988e13i			0.592741i	−0.955073	+	0.296370i	$0.904224\pi$
$882$	−1.30425e13	+	1.93370e13i	−0.725690	+	1.07592i
$883$	3.47670e12	+	3.47670e12i	0.192462	+	0.192462i	0.796759	−	0.604297i	$-0.206546\pi$
$883$	3.47670e12	+	3.47670e12i	0.192462	+	0.192462i	−0.604297	+	0.796759i	$0.706546\pi$
$884$	−9.94817e10	+	5.74358e10i	−0.00547909	+	0.00316335i
$885$	2.59751e13	+	2.28194e13i	1.42336	+	1.25043i
$886$	1.30620e13	−	2.26241e13i	0.712129	−	1.23344i
$887$	−5.54103e12	+	2.06794e13i	−0.300562	+	1.12171i	0.636136	+	0.771577i	$0.280532\pi$
$887$	−5.54103e12	+	2.06794e13i	−0.300562	+	1.12171i	−0.936699	+	0.350137i	$0.886135\pi$
$888$	−3.92052e13	+	3.92052e13i	−2.11585	+	2.11585i
$889$	−3.21002e13	−	1.46286e13i	−1.72365	−	0.785495i
$890$	−3.77785e12	+	1.89070e13i	−0.201832	+	1.01011i
$891$	4.93109e11	+	8.54089e11i	0.0262116	+	0.0453998i
$892$	−4.68773e11	+	1.25607e11i	−0.0247925	+	0.00664314i
$893$	5.27986e11	−	1.41473e11i	0.0277837	−	0.00744463i
$894$	1.44462e13	+	2.50215e13i	0.756370	+	1.31007i
$895$	−3.58733e12	−	5.37890e12i	−0.186882	−	0.280214i
$896$	1.85464e13	−	1.78597e12i	0.961330	−	0.0925740i
$897$	6.14920e12	−	6.14920e12i	0.317141	−	0.317141i
$898$	8.12227e12	−	3.03127e13i	0.416806	−	1.55554i
$899$	−1.34459e13	+	2.32889e13i	−0.686547	+	1.18913i
$900$	3.44744e11	+	4.50893e11i	0.0175148	+	0.0229077i
$901$	2.33751e12	−	1.34956e12i	0.118166	−	0.0682231i
$902$	8.07338e11	+	8.07338e11i	0.0406093	+	0.0406093i
$903$	2.35598e13	+	3.94235e12i	1.17917	+	0.197315i
$904$			3.47129e13i			1.72875i
$905$	−3.36311e12	+	6.80485e12i	−0.166656	+	0.337209i
$906$	−3.80232e13	−	2.19527e13i	−1.87487	−	1.08246i
$907$	−1.01630e13	−	3.79290e13i	−0.498644	−	1.86097i	−0.508581	−	0.861014i	$-0.669830\pi$
$907$	−1.01630e13	−	3.79290e13i	−0.498644	−	1.86097i	0.00993646	−	0.999951i	$-0.496837\pi$
$908$	3.70699e11	+	9.93284e10i	0.0180982	+	0.00484939i
$909$	2.09618e13			1.01834
$910$	−2.28823e12	−	5.09132e12i	−0.110615	−	0.246119i
$911$	2.08375e13			1.00233			0.501167	−	0.865351i	$-0.332904\pi$
$911$	2.08375e13			1.00233			0.501167	+	0.865351i	$0.332904\pi$
$912$	1.99304e12	+	5.34034e11i	0.0953981	+	0.0255618i
$913$	−2.54234e11	−	9.48813e11i	−0.0121092	−	0.0451921i
$914$	−3.15899e13	−	1.82384e13i	−1.49724	−	0.864430i
$915$	1.30084e13	+	3.84306e13i	0.613518	+	1.81252i
$916$		−	8.17307e11i		−	0.0383580i
$917$	2.05129e13	+	1.69092e13i	0.957998	+	0.789698i
$918$	7.53970e12	+	7.53970e12i	0.350398	+	0.350398i
$919$	7.91094e12	−	4.56738e12i	0.365854	−	0.211226i	−0.305791	−	0.952099i	$-0.598921\pi$
$919$	7.91094e12	−	4.56738e12i	0.365854	−	0.211226i	0.671646	+	0.740872i	$0.265588\pi$
$920$	−2.36909e13	+	1.53219e12i	−1.09028	+	0.0705126i
$921$	2.51023e13	−	4.34784e13i	1.14960	−	1.99116i
$922$	6.24634e11	−	2.33117e12i	0.0284667	−	0.106239i
$923$	−5.51257e12	+	5.51257e12i	−0.250004	+	0.250004i
$924$	−2.72706e10	+	5.98413e10i	−0.00123075	+	0.00270071i
$925$	−1.65205e13	−	4.00801e13i	−0.741968	−	1.80008i
$926$	−3.33708e12	−	5.77999e12i	−0.149148	−	0.258332i
$927$	2.07467e13	−	5.55906e12i	0.922763	−	0.247254i
$928$	8.22695e11	−	2.20441e11i	0.0364144	−	0.00975721i
$929$	−1.83106e12	−	3.17150e12i	−0.0806553	−	0.139699i	0.822876	−	0.568221i	$-0.192368\pi$
$929$	−1.83106e12	−	3.17150e12i	−0.0806553	−	0.139699i	−0.903532	+	0.428522i	$0.859035\pi$
$930$	4.56774e13	−	3.04635e13i	2.00230	−	1.33539i
$931$	1.44008e12	+	4.95831e11i	0.0628222	+	0.0216302i
$932$	3.30344e11	−	3.30344e11i	0.0143415	−	0.0143415i
$933$	2.66586e12	−	9.94911e12i	0.115178	−	0.429850i
$934$	−1.37054e12	+	2.37385e12i	−0.0589294	+	0.102069i
$935$	1.44562e12	−	1.64554e12i	0.0618590	−	0.0704136i
$936$	7.35924e12	−	4.24886e12i	0.313394	−	0.180938i
$937$	2.01517e13	+	2.01517e13i	0.854050	+	0.854050i	0.990629	−	0.136579i	$-0.0436108\pi$
$937$	2.01517e13	+	2.01517e13i	0.854050	+	0.854050i	−0.136579	+	0.990629i	$0.543611\pi$
$938$	3.28351e13	−	1.22769e13i	1.38492	−	0.517816i
$939$		−	2.39165e13i		−	1.00393i
$940$	−2.15696e11	+	7.30107e10i	−0.00901087	+	0.00305008i
$941$	−4.13579e13	−	2.38780e13i	−1.71951	−	0.992760i	−0.919813	−	0.392356i	$-0.871660\pi$
$941$	−4.13579e13	−	2.38780e13i	−1.71951	−	0.992760i	−0.799697	−	0.600404i	$-0.795007\pi$
$942$	4.68697e12	+	1.74920e13i	0.193938	+	0.723786i
$943$	−1.65776e13	−	4.44195e12i	−0.682683	−	0.182924i
$944$	−2.97172e13			−1.21796
$945$	9.02126e12	−	7.35779e12i	0.367980	−	0.300127i
$946$	−1.70121e12			−0.0690632
$947$	−3.54302e13	−	9.49350e12i	−1.43152	−	0.383576i	−0.541967	−	0.840400i	$-0.682320\pi$
$947$	−3.54302e13	−	9.49350e12i	−1.43152	−	0.383576i	−0.889557	+	0.456824i	$0.848987\pi$
$948$	1.80456e10	+	6.73471e10i	0.000725661	+	0.00270820i
$949$	5.58543e12	+	3.22475e12i	0.223542	+	0.129062i
$950$	−1.00646e12	+	1.30695e12i	−0.0400904	+	0.0520600i
$951$		−	3.75940e13i		−	1.49041i
$952$	4.46078e12	−	2.66580e13i	0.176013	−	1.05187i
$953$	−1.66961e13	−	1.66961e13i	−0.655688	−	0.655688i	0.298669	−	0.954357i	$-0.403457\pi$
$953$	−1.66961e13	−	1.66961e13i	−0.655688	−	0.655688i	−0.954357	+	0.298669i	$0.903457\pi$
$954$	−3.71807e12	+	2.14663e12i	−0.145328	+	0.0839053i
$955$	1.47037e12	+	2.27351e13i	0.0572021	+	0.884467i
$956$	1.24909e11	−	2.16349e11i	0.00483653	−	0.00837712i
$957$	7.78220e11	−	2.90436e12i	0.0299915	−	0.111930i
$958$	1.90235e13	−	1.90235e13i	0.729703	−	0.729703i
$959$	3.48535e13	−	2.48612e13i	1.33065	−	0.949160i
$960$	−4.00649e13	−	8.00547e12i	−1.52245	−	0.304205i
$961$	2.06410e13	+	3.57512e13i	0.780683	+	1.35218i
$962$	−1.34801e13	+	3.61197e12i	−0.507463	+	0.135974i
$963$	6.08698e12	−	1.63100e12i	0.228078	−	0.0611134i
$964$	3.02004e11	+	5.23085e11i	0.0112633	+	0.0195086i
$965$	4.69686e13	+	9.38491e12i	1.74355	+	0.348383i
$966$	4.21727e12	+	4.37941e13i	0.155824	+	1.61815i
$967$	1.65795e13	−	1.65795e13i	0.609750	−	0.609750i	−0.333131	−	0.942881i	$-0.608105\pi$
$967$	1.65795e13	−	1.65795e13i	0.609750	−	0.609750i	0.942881	+	0.333131i	$0.108105\pi$
$968$	−7.08942e12	+	2.64581e13i	−0.259520	+	0.968543i
$969$	1.46295e12	−	2.53391e12i	0.0533056	−	0.0923280i
$970$	2.33865e12	+	3.61605e13i	0.0848189	+	1.31148i
$971$	3.82706e13	−	2.20956e13i	1.38159	−	0.797662i	0.389242	−	0.921135i	$-0.372737\pi$
$971$	3.82706e13	−	2.20956e13i	1.38159	−	0.797662i	0.992348	+	0.123474i	$0.0394035\pi$
$972$	−5.93412e11	−	5.93412e11i	−0.0213235	−	0.0213235i
$973$	1.46069e13	+	3.90669e13i	0.522457	+	1.39734i
$974$			2.04947e13i			0.729671i
$975$	1.50803e12	+	1.16099e13i	0.0534427	+	0.411441i
$976$	−3.02001e13	−	1.74360e13i	−1.06533	−	0.615068i
$977$	1.04632e13	+	3.90492e13i	0.367400	+	1.37116i	0.864138	+	0.503256i	$0.167865\pi$
$977$	1.04632e13	+	3.90492e13i	0.367400	+	1.37116i	−0.496737	+	0.867901i	$0.665469\pi$
$978$	−1.04647e13	−	2.80400e12i	−0.365764	−	0.0980061i
$979$	2.65909e12			0.0925149
$980$	−6.12016e11	−	1.67413e11i	−0.0211956	−	0.00579790i
$981$	−1.65069e13			−0.569056
$982$	2.58391e12	+	6.92356e11i	0.0886697	+	0.0237590i
$983$	1.30422e13	+	4.86741e13i	0.445512	+	1.66267i	0.714582	+	0.699552i	$0.246617\pi$
$983$	1.30422e13	+	4.86741e13i	0.445512	+	1.66267i	−0.269070	+	0.963121i	$0.586716\pi$
$984$	−2.55912e13	−	1.47751e13i	−0.870188	−	0.502403i
$985$	1.21264e13	−	4.10465e12i	0.410458	−	0.138936i
$986$			2.65723e13i			0.895328i
$987$	6.87368e12	+	1.83840e13i	0.230548	+	0.616613i
$988$	−8.43657e9	−	8.43657e9i	−0.000281682	−	0.000281682i
$989$	2.21460e13	−	1.27860e13i	0.736057	−	0.424963i
$990$	−2.29942e12	+	2.61741e12i	−0.0760782	+	0.0865993i
$991$	6.92493e12	−	1.19943e13i	0.228078	−	0.395043i	−0.729160	−	0.684343i	$-0.760089\pi$
$991$	6.92493e12	−	1.19943e13i	0.228078	−	0.395043i	0.957238	+	0.289300i	$0.0934225\pi$
$992$	5.55136e11	−	2.07180e12i	0.0182011	−	0.0679274i
$993$	−7.59564e12	+	7.59564e12i	−0.247909	+	0.247909i
$994$	−3.78066e12	−	3.92600e13i	−0.122837	−	1.27559i
$995$	2.02052e13	−	1.34754e13i	0.653521	−	0.435851i
$996$	2.73320e11	+	4.73404e11i	0.00880043	+	0.0152428i
$997$	2.48499e13	−	6.65851e12i	0.796520	−	0.213427i	0.162464	−	0.986714i	$-0.448056\pi$
$997$	2.48499e13	−	6.65851e12i	0.796520	−	0.213427i	0.634056	+	0.773288i	$0.281389\pi$
$998$	−9.14720e12	+	2.45098e12i	−0.291877	+	0.0782083i
$999$	−1.45525e13	−	2.52057e13i	−0.462268	−	0.800672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.11	✓	136
5.2	odd	4	inner	35.10.k.a.17.24	yes	136
7.5	odd	6	inner	35.10.k.a.33.24	yes	136
35.12	even	12	inner	35.10.k.a.12.11	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.11	✓	136	1.1	even	1	trivial
35.10.k.a.12.11	yes	136	35.12	even	12	inner
35.10.k.a.17.24	yes	136	5.2	odd	4	inner
35.10.k.a.33.24	yes	136	7.5	odd	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.6149 - 5.79170i) q^{2} +(-55.2156 - 206.067i) q^{3} +(-9.74350 - 5.62541i) q^{4} +(-1252.88 - 619.202i) q^{5} +4773.93i q^{6} +(2224.73 + 5950.14i) q^{7} +(8279.52 + 8279.52i) q^{8} +(-22369.0 + 12914.8i) q^{9} +(23494.7 + 20640.3i) q^{10} +(2156.53 - 3735.22i) q^{11} +(-621.221 + 2318.43i) q^{12} +(-19867.8 + 19867.8i) q^{13} +(-13625.8 - 141497. i) q^{14} +(-58418.7 + 292368. i) q^{15} +(-128128. - 221925. i) q^{16} +(-351000. + 94050.1i) q^{17} +(558304. - 149597. i) q^{18} +(-18871.3 - 32686.0i) q^{19} +(8724.19 + 13081.2i) q^{20} +(1.10329e6 - 786984. i) q^{21} +(-68246.5 + 68246.5i) q^{22} +(375491. - 1.40135e6i) q^{23} +(1.24898e6 - 2.16330e6i) q^{24} +(1.18630e6 + 1.55157e6i) q^{25} +(544510. - 314373. i) q^{26} +(927216. + 927216. i) q^{27} +(11795.4 - 70490.2i) q^{28} +3.26780e6i q^{29} +(2.95602e6 - 5.98117e6i) q^{30} +(7.12679e6 + 4.11466e6i) q^{31} +(-67458.4 - 251758. i) q^{32} +(-888781. - 238148. i) q^{33} +8.13155e6 q^{34} +(897021. - 8.83238e6i) q^{35} +290604. q^{36} +(-2.14396e7 - 5.74472e6i) q^{37} +(218594. + 815803. i) q^{38} +(5.19113e6 + 2.99710e6i) q^{39} +(-5.24657e6 - 1.55000e7i) q^{40} -1.18297e7i q^{41} +(-2.84055e7 + 1.06207e7i) q^{42} +(1.24637e7 + 1.24637e7i) q^{43} +(-42024.3 + 24262.7i) q^{44} +(3.60226e7 - 2.32973e6i) q^{45} +(-1.62324e7 + 2.81154e7i) q^{46} +(-3.74838e6 + 1.39891e7i) q^{47} +(-3.86568e7 + 3.86568e7i) q^{48} +(-3.04548e7 + 2.64749e7i) q^{49} +(-1.66556e7 - 4.04079e7i) q^{50} +(3.87613e7 + 6.71366e7i) q^{51} +(305347. - 81817.4i) q^{52} +(-7.17470e6 + 1.92246e6i) q^{53} +(-1.46715e7 - 2.54119e7i) q^{54} +(-5.01473e6 + 3.34446e6i) q^{55} +(-3.08447e7 + 6.76840e7i) q^{56} +(-5.69353e6 + 5.69353e6i) q^{57} +(1.89261e7 - 7.06332e7i) q^{58} +(5.79832e7 - 1.00430e8i) q^{59} +(2.21389e6 - 2.52006e6i) q^{60} +(1.17851e8 - 6.80411e7i) q^{61} +(-1.30214e8 - 1.30214e8i) q^{62} +(-1.26610e8 - 1.04367e8i) q^{63} +1.37036e8i q^{64} +(3.71943e7 - 1.25898e7i) q^{65} +(1.78317e7 + 1.02951e7i) q^{66} +(6.38260e7 + 2.38202e8i) q^{67} +(3.94904e6 + 1.05814e6i) q^{68} -3.09506e8 q^{69} +(-7.05436e7 + 1.85716e8i) q^{70} +2.77462e8 q^{71} +(-2.92133e8 - 7.82768e7i) q^{72} +(-5.94096e7 - 2.21720e8i) q^{73} +(4.30144e8 + 2.48344e8i) q^{74} +(2.54227e8 - 3.30129e8i) q^{75} +424635. i q^{76} +(2.70228e7 + 4.52182e6i) q^{77} +(-9.48475e7 - 9.48475e7i) q^{78} +(2.51568e7 - 1.45243e7i) q^{79} +(2.31135e7 + 3.57383e8i) q^{80} +(-1.14329e8 + 1.98024e8i) q^{81} +(-6.85143e7 + 2.55699e8i) q^{82} +(1.61041e8 - 1.61041e8i) q^{83} +(-1.51770e7 + 1.46151e6i) q^{84} +(4.97997e8 + 9.95061e7i) q^{85} +(-1.97216e8 - 3.41588e8i) q^{86} +(6.73387e8 - 1.80433e8i) q^{87} +(4.87808e7 - 1.30708e7i) q^{88} +(3.08261e8 + 5.33923e8i) q^{89} +(-7.92120e8 - 1.58275e8i) q^{90} +(-1.62417e8 - 7.40159e7i) q^{91} +(-1.15418e7 + 1.15418e7i) q^{92} +(4.54386e8 - 1.69579e9i) q^{93} +(1.62042e8 - 2.80665e8i) q^{94} +(3.40424e6 + 5.26369e7i) q^{95} +(-4.81544e7 + 2.78020e7i) q^{96} +(8.19315e8 + 8.19315e8i) q^{97} +(8.11613e8 - 3.95868e8i) q^{98} +1.11404e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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