LMFDB - Embedded newform 35.10.k.a.3.15

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			3.15
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.27232 - 1.68066i) q^{2} +(15.1291 + 56.4624i) q^{3} +(-406.888 - 234.917i) q^{4} +(-873.884 - 1090.62i) q^{5} -379.577i q^{6} +(259.777 - 6347.14i) q^{7} +(4508.24 + 4508.24i) q^{8} +(14086.9 - 8133.05i) q^{9} +(3648.32 + 8309.42i) q^{10} +(-44961.3 + 77875.2i) q^{11} +(7108.13 - 26527.9i) q^{12} +(60467.0 - 60467.0i) q^{13} +(-12296.8 + 39374.7i) q^{14} +(48358.0 - 65841.7i) q^{15} +(99577.0 + 172472. i) q^{16} +(-452819. + 121333. i) q^{17} +(-102026. + 27337.8i) q^{18} +(-291502. - 504896. i) q^{19} +(99368.0 + 649050. i) q^{20} +(362305. - 81358.5i) q^{21} +(412894. - 412894. i) q^{22} +(-405811. + 1.51451e6i) q^{23} +(-186341. + 322752. i) q^{24} +(-425777. + 1.90615e6i) q^{25} +(-480893. + 277644. i) q^{26} +(1.48590e6 + 1.48590e6i) q^{27} +(-1.59675e6 + 2.52154e6i) q^{28} +3.27059e6i q^{29} +(-413974. + 331706. i) q^{30} +(6.78743e6 + 3.91873e6i) q^{31} +(-1.17958e6 - 4.40225e6i) q^{32} +(-5.07724e6 - 1.36044e6i) q^{33} +3.04415e6 q^{34} +(-7.14932e6 + 5.26334e6i) q^{35} -7.64236e6 q^{36} +(-1.62853e6 - 436363. i) q^{37} +(979833. + 3.65679e6i) q^{38} +(4.32892e6 + 2.49930e6i) q^{39} +(977095. - 8.85646e6i) q^{40} -7.67652e6i q^{41} +(-2.40923e6 - 98605.4i) q^{42} +(9.94440e6 + 9.94440e6i) q^{43} +(3.65884e7 - 2.11243e7i) q^{44} +(-2.11804e7 - 8.25606e6i) q^{45} +(5.09075e6 - 8.81743e6i) q^{46} +(-1.83835e6 + 6.86081e6i) q^{47} +(-8.23170e6 + 8.23170e6i) q^{48} +(-4.02186e7 - 3.29768e6i) q^{49} +(5.87421e6 - 1.12404e7i) q^{50} +(-1.37015e7 - 2.37316e7i) q^{51} +(-3.88080e7 + 1.03986e7i) q^{52} +(5.93925e7 - 1.59142e7i) q^{53} +(-6.82273e6 - 1.18173e7i) q^{54} +(1.24223e8 - 1.90183e7i) q^{55} +(2.97856e7 - 2.74433e7i) q^{56} +(2.40975e7 - 2.40975e7i) q^{57} +(5.49676e6 - 2.05142e7i) q^{58} +(-3.15723e7 + 5.46849e7i) q^{59} +(-3.51436e7 + 1.54301e7i) q^{60} +(-2.44912e7 + 1.41400e7i) q^{61} +(-3.59869e7 - 3.59869e7i) q^{62} +(-4.79622e7 - 9.15240e7i) q^{63} -7.23721e7i q^{64} +(-1.18788e8 - 1.31053e7i) q^{65} +(2.95597e7 + 1.70663e7i) q^{66} +(-1.16951e7 - 4.36465e7i) q^{67} +(2.12750e8 + 5.70061e7i) q^{68} -9.16521e7 q^{69} +(5.36888e7 - 2.09978e7i) q^{70} -2.78044e8 q^{71} +(1.00173e8 + 2.68412e7i) q^{72} +(5.00668e7 + 1.86852e8i) q^{73} +(9.48128e6 + 5.47402e6i) q^{74} +(-1.14067e8 + 4.79786e6i) q^{75} +2.73915e8i q^{76} +(4.82605e8 + 3.05606e8i) q^{77} +(-2.29519e7 - 2.29519e7i) q^{78} +(-1.28788e8 + 7.43557e7i) q^{79} +(1.01083e8 - 2.59322e8i) q^{80} +(9.86658e7 - 1.70894e8i) q^{81} +(-1.29016e7 + 4.81496e7i) q^{82} +(-4.43112e8 + 4.43112e8i) q^{83} +(-1.66530e8 - 5.20076e7i) q^{84} +(5.28039e8 + 3.87823e8i) q^{85} +(-4.56613e7 - 7.90876e7i) q^{86} +(-1.84665e8 + 4.94809e7i) q^{87} +(-5.53777e8 + 1.48384e8i) q^{88} +(-1.22183e8 - 2.11627e8i) q^{89} +(1.18974e8 + 8.73817e7i) q^{90} +(-3.68084e8 - 3.99500e8i) q^{91} +(5.20902e8 - 5.20902e8i) q^{92} +(-1.18573e8 + 4.42521e8i) q^{93} +(2.30614e7 - 3.99436e7i) q^{94} +(-2.95911e8 + 7.59139e8i) q^{95} +(2.30715e8 - 1.33204e8i) q^{96} +(-2.41447e8 - 2.41447e8i) q^{97} +(2.46722e8 + 8.82781e7i) q^{98} +1.46269e9i 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 $

$2$	−6.27232	−	1.68066i	−0.277200	−	0.0742755i	0.117541	−	0.993068i	$-0.462499\pi$
$2$	−6.27232	−	1.68066i	−0.277200	−	0.0742755i	−0.394741	+	0.918793i	$0.629166\pi$
$3$	15.1291	+	56.4624i	0.107837	+	0.402452i	0.998652	−	0.0519147i	$-0.0165324\pi$
$3$	15.1291	+	56.4624i	0.107837	+	0.402452i	−0.890815	+	0.454366i	$0.849866\pi$
$4$	−406.888	−	234.917i	−0.794702	−	0.458822i
$5$	−873.884	−	1090.62i	−0.625301	−	0.780384i
$5$	−873.884	−	1090.62i	−0.625301	−	0.780384i
$6$		−	379.577i		−	0.119569i
$7$	259.777	−	6347.14i	0.0408940	−	0.999163i
$7$	259.777	−	6347.14i	0.0408940	−	0.999163i
$8$	4508.24	+	4508.24i	0.389137	+	0.389137i
$9$	14086.9	−	8133.05i	0.715687	−	0.413202i
$10$	3648.32	+	8309.42i	0.115370	+	0.262767i
$11$	−44961.3	+	77875.2i	−0.925916	+	1.60373i	−0.135835	+	0.990731i	$0.543372\pi$
$11$	−44961.3	+	77875.2i	−0.925916	+	1.60373i	−0.790081	+	0.613002i	$0.789962\pi$
$12$	7108.13	−	26527.9i	0.0989555	−	0.369307i
$13$	60467.0	−	60467.0i	0.587183	−	0.587183i	−0.349685	−	0.936867i	$-0.613711\pi$
$13$	60467.0	−	60467.0i	0.587183	−	0.587183i	0.936867	+	0.349685i	$0.113711\pi$
$14$	−12296.8	+	39374.7i	−0.0855492	+	0.273931i
$15$	48358.0	−	65841.7i	0.246636	−	0.335807i
$16$	99577.0	+	172472.i	0.379856	+	0.657930i
$17$	−452819.	+	121333.i	−1.31494	+	0.352336i	−0.847079	−	0.531468i	$-0.821641\pi$
$17$	−452819.	+	121333.i	−1.31494	+	0.352336i	−0.467858	+	0.883804i	$0.654974\pi$
$18$	−102026.	+	27337.8i	−0.229079	+	0.0613816i
$19$	−291502.	−	504896.i	−0.513157	−	0.888814i	−0.999884	−	0.0152598i	$-0.995142\pi$
$19$	−291502.	−	504896.i	−0.513157	−	0.888814i	0.486726	−	0.873554i	$-0.338191\pi$
$20$	99368.0	+	649050.i	0.138871	+	0.907074i
$21$	362305.	−	81358.5i	0.406525	−	0.0912885i
$22$	412894.	−	412894.i	0.375782	−	0.375782i
$23$	−405811.	+	1.51451e6i	−0.302376	+	1.12848i	0.632804	+	0.774312i	$0.281904\pi$
$23$	−405811.	+	1.51451e6i	−0.302376	+	1.12848i	−0.935180	+	0.354172i	$0.884763\pi$
$24$	−186341.	+	322752.i	−0.114646	+	0.198572i
$25$	−425777.	+	1.90615e6i	−0.217998	+	0.975949i
$26$	−480893.	+	277644.i	−0.206380	+	0.119154i
$27$	1.48590e6	+	1.48590e6i	0.538086	+	0.538086i
$28$	−1.59675e6	+	2.52154e6i	−0.490936	+	0.775275i
$29$			3.27059e6i			0.858687i	0.903141	+	0.429344i	$0.141255\pi$
$29$			3.27059e6i			0.858687i	−0.903141	+	0.429344i	$0.858745\pi$
$30$	−413974.	+	331706.i	−0.0933099	+	0.0747667i
$31$	6.78743e6	+	3.91873e6i	1.32001	+	0.762109i	0.983730	−	0.179652i	$-0.0574971\pi$
$31$	6.78743e6	+	3.91873e6i	1.32001	+	0.762109i	0.336282	+	0.941761i	$0.390830\pi$
$32$	−1.17958e6	−	4.40225e6i	−0.198862	−	0.742163i
$33$	−5.07724e6	−	1.36044e6i	−0.745273	−	0.199695i
$34$	3.04415e6			0.390670
$35$	−7.14932e6	+	5.26334e6i	−0.805302	+	0.592865i
$36$	−7.64236e6			−0.758344
$37$	−1.62853e6	−	436363.i	−0.142853	−	0.0382772i	0.186684	−	0.982420i	$-0.440226\pi$
$37$	−1.62853e6	−	436363.i	−0.142853	−	0.0382772i	−0.329537	+	0.944143i	$0.606893\pi$
$38$	979833.	+	3.65679e6i	0.0762300	+	0.284494i
$39$	4.32892e6	+	2.49930e6i	0.299632	+	0.172993i
$40$	977095.	−	8.85646e6i	0.0603485	−	0.547004i
$41$		−	7.67652e6i		−	0.424265i	−0.977241	−	0.212132i	$-0.931959\pi$
$41$		−	7.67652e6i		−	0.424265i	0.977241	−	0.212132i	$-0.0680408\pi$
$42$	−2.40923e6	−	98605.4i	−0.119469	−	0.00488966i
$43$	9.94440e6	+	9.94440e6i	0.443578	+	0.443578i	0.893213	−	0.449634i	$-0.148446\pi$
$43$	9.94440e6	+	9.94440e6i	0.443578	+	0.443578i	−0.449634	+	0.893213i	$0.648446\pi$
$44$	3.65884e7	−	2.11243e7i	1.47166	−	0.849661i
$45$	−2.11804e7	−	8.25606e6i	−0.769976	−	0.300135i
$46$	5.09075e6	−	8.81743e6i	0.167638	−	0.290357i
$47$	−1.83835e6	+	6.86081e6i	−0.0549525	+	0.205086i	−0.987944	−	0.154814i	$-0.950522\pi$
$47$	−1.83835e6	+	6.86081e6i	−0.0549525	+	0.205086i	0.932991	+	0.359899i	$0.117189\pi$
$48$	−8.23170e6	+	8.23170e6i	−0.223823	+	0.223823i
$49$	−4.02186e7	−	3.29768e6i	−0.996655	−	0.0817196i
$50$	5.87421e6	−	1.12404e7i	0.132918	−	0.254341i
$51$	−1.37015e7	−	2.37316e7i	−0.283597	−	0.491204i
$52$	−3.88080e7	+	1.03986e7i	−0.736047	+	0.197223i
$53$	5.93925e7	−	1.59142e7i	1.03393	−	0.277040i	0.298333	−	0.954462i	$-0.403569\pi$
$53$	5.93925e7	−	1.59142e7i	1.03393	−	0.277040i	0.735595	+	0.677422i	$0.236903\pi$
$54$	−6.82273e6	−	1.18173e7i	−0.109191	−	0.189124i
$55$	1.24223e8	−	1.90183e7i	1.83050	−	0.280246i
$56$	2.97856e7	−	2.74433e7i	0.404725	−	0.372898i
$57$	2.40975e7	−	2.40975e7i	0.302368	−	0.302368i
$58$	5.49676e6	−	2.05142e7i	0.0637794	−	0.238028i
$59$	−3.15723e7	+	5.46849e7i	−0.339213	+	0.587534i	−0.984285	−	0.176588i	$-0.943494\pi$
$59$	−3.15723e7	+	5.46849e7i	−0.339213	+	0.587534i	0.645072	+	0.764122i	$0.276827\pi$
$60$	−3.51436e7	+	1.54301e7i	−0.350078	+	0.153705i
$61$	−2.44912e7	+	1.41400e7i	−0.226477	+	0.130757i	−0.608946	−	0.793212i	$-0.708407\pi$
$61$	−2.44912e7	+	1.41400e7i	−0.226477	+	0.130757i	0.382468	+	0.923969i	$0.375074\pi$
$62$	−3.59869e7	−	3.59869e7i	−0.309301	−	0.309301i
$63$	−4.79622e7	−	9.15240e7i	−0.383589	−	0.731986i
$64$		−	7.23721e7i		−	0.539214i
$65$	−1.18788e8	−	1.31053e7i	−0.825393	−	0.0910621i
$66$	2.95597e7	+	1.70663e7i	0.191757	+	0.110711i
$67$	−1.16951e7	−	4.36465e7i	−0.0709032	−	0.264614i	0.921370	−	0.388687i	$-0.127071\pi$
$67$	−1.16951e7	−	4.36465e7i	−0.0709032	−	0.264614i	−0.992273	+	0.124072i	$0.960404\pi$
$68$	2.12750e8	+	5.70061e7i	1.20664	+	0.323319i
$69$	−9.16521e7			−0.486768
$70$	5.36888e7	−	2.09978e7i	0.267265	−	0.104528i
$71$	−2.78044e8			−1.29853			−0.649263	−	0.760564i	$-0.724923\pi$
$71$	−2.78044e8			−1.29853			−0.649263	+	0.760564i	$0.724923\pi$
$72$	1.00173e8	+	2.68412e7i	0.439292	+	0.117708i
$73$	5.00668e7	+	1.86852e8i	0.206347	+	0.770096i	0.989035	+	0.147682i	$0.0471813\pi$
$73$	5.00668e7	+	1.86852e8i	0.206347	+	0.770096i	−0.782688	+	0.622414i	$0.786152\pi$
$74$	9.48128e6	+	5.47402e6i	0.0367557	+	0.0212209i
$75$	−1.14067e8	+	4.79786e6i	−0.416281	+	0.0175094i
$76$			2.73915e8i			0.941791i
$77$	4.82605e8	+	3.05606e8i	1.56453	+	0.990725i
$78$	−2.29519e7	−	2.29519e7i	−0.0702090	−	0.0702090i
$79$	−1.28788e8	+	7.43557e7i	−0.372009	+	0.214779i	−0.674336	−	0.738425i	$-0.735570\pi$
$79$	−1.28788e8	+	7.43557e7i	−0.372009	+	0.214779i	0.302327	+	0.953204i	$0.402237\pi$
$80$	1.01083e8	−	2.59322e8i	0.275914	−	0.707838i
$81$	9.86658e7	−	1.70894e8i	0.254674	−	0.441108i
$82$	−1.29016e7	+	4.81496e7i	−0.0315125	+	0.117606i
$83$	−4.43112e8	+	4.43112e8i	−1.02485	+	1.02485i	−0.0251706	+	0.999683i	$0.508013\pi$
$83$	−4.43112e8	+	4.43112e8i	−1.02485	+	1.02485i	−0.999683	+	0.0251706i	$0.991987\pi$
$84$	−1.66530e8	−	5.20076e7i	−0.364951	−	0.113975i
$85$	5.28039e8	+	3.87823e8i	1.09719	+	0.805839i
$86$	−4.56613e7	−	7.90876e7i	−0.0900129	−	0.155907i
$87$	−1.84665e8	+	4.94809e7i	−0.345580	+	0.0925979i
$88$	−5.53777e8	+	1.48384e8i	−0.984380	+	0.263764i
$89$	−1.22183e8	−	2.11627e8i	−0.206422	−	0.357533i	0.744163	−	0.667998i	$-0.232849\pi$
$89$	−1.22183e8	−	2.11627e8i	−0.206422	−	0.357533i	−0.950585	+	0.310465i	$0.899515\pi$
$90$	1.18974e8	+	8.73817e7i	0.191145	+	0.140388i
$91$	−3.68084e8	−	3.99500e8i	−0.562679	−	0.610704i
$92$	5.20902e8	−	5.20902e8i	0.758072	−	0.758072i
$93$	−1.18573e8	+	4.42521e8i	−0.164367	+	0.613424i
$94$	2.30614e7	−	3.99436e7i	0.0304657	−	0.0527681i
$95$	−2.95911e8	+	7.59139e8i	−0.372739	+	0.956236i
$96$	2.30715e8	−	1.33204e8i	0.277240	−	0.160065i
$97$	−2.41447e8	−	2.41447e8i	−0.276916	−	0.276916i	0.554960	−	0.831877i	$-0.312733\pi$
$97$	−2.41447e8	−	2.41447e8i	−0.276916	−	0.276916i	−0.831877	+	0.554960i	$0.812733\pi$
$98$	2.46722e8	+	8.82781e7i	0.270203	+	0.0966798i
$99$			1.46269e9i			1.53036i
$100$	6.21030e8	−	6.75567e8i	0.621030	−	0.675567i
$101$	−8.23980e8	−	4.75725e8i	−0.787898	−	0.454893i	0.0513237	−	0.998682i	$-0.483656\pi$
$101$	−8.23980e8	−	4.75725e8i	−0.787898	−	0.454893i	−0.839222	+	0.543789i	$0.816989\pi$
$102$	4.60551e7	+	1.71880e8i	0.0421286	+	0.157226i
$103$	1.62415e9	+	4.35190e8i	1.42187	+	0.380988i	0.886146	−	0.463407i	$-0.153373\pi$
$103$	1.62415e9	+	4.35190e8i	1.42187	+	0.380988i	0.535721	+	0.844395i	$0.320040\pi$
$104$	5.45199e8			0.456989
$105$	−4.05344e8	−	3.24039e8i	−0.325440	−	0.260163i
$106$	−3.99275e8			−0.307182
$107$	−7.25044e8	−	1.94275e8i	−0.534734	−	0.143281i	−0.0186604	−	0.999826i	$-0.505940\pi$
$107$	−7.25044e8	−	1.94275e8i	−0.534734	−	0.143281i	−0.516073	+	0.856544i	$0.672607\pi$
$108$	−2.55531e8	−	9.53655e8i	−0.180733	−	0.674504i
$109$	−1.54734e8	−	8.93357e7i	−0.104995	−	0.0606186i	0.446583	−	0.894742i	$-0.352641\pi$
$109$	−1.54734e8	−	8.93357e7i	−0.104995	−	0.0606186i	−0.551578	+	0.834123i	$0.685974\pi$
$110$	−8.11131e8	−	8.94886e7i	−0.528231	−	0.0582774i
$111$		−	9.85525e7i		−	0.0616189i
$112$	1.12057e9	−	5.87225e8i	0.672914	−	0.352633i
$113$	−6.04469e8	−	6.04469e8i	−0.348756	−	0.348756i	0.510890	−	0.859646i	$-0.329316\pi$
$113$	−6.04469e8	−	6.04469e8i	−0.348756	−	0.348756i	−0.859646	+	0.510890i	$0.829316\pi$
$114$	−1.91647e8	+	1.10648e8i	−0.106275	+	0.0613578i
$115$	2.00638e9	−	8.80918e8i	1.06973	−	0.469672i
$116$	7.68316e8	−	1.33076e9i	0.393984	−	0.682401i
$117$	3.60009e8	−	1.34357e9i	0.177614	−	0.662864i
$118$	2.89939e8	−	2.89939e8i	0.137669	−	0.137669i
$119$	6.52482e8	+	2.90562e9i	0.298268	+	1.32824i
$120$	5.14839e8	−	7.88207e7i	0.226650	−	0.0346996i
$121$	−2.86406e9	−	4.96070e9i	−1.21464	−	2.10382i
$122$	1.77381e8	−	4.75291e7i	0.0724916	−	0.0194241i
$123$	4.33435e8	−	1.16139e8i	0.170746	−	0.0457513i
$124$	−1.84115e9	−	3.18896e9i	−0.699345	−	1.21130i
$125$	2.45097e9	−	1.20139e9i	0.897929	−	0.440140i
$126$	1.47013e8	+	6.54676e8i	0.0519623	+	0.231398i
$127$	−1.67878e9	+	1.67878e9i	−0.572635	+	0.572635i	−0.932864	−	0.360229i	$-0.882699\pi$
$127$	−1.67878e9	+	1.67878e9i	−0.572635	+	0.572635i	0.360229	+	0.932864i	$0.382699\pi$
$128$	−7.25577e8	+	2.70789e9i	−0.238912	+	0.891633i
$129$	−4.11035e8	+	7.11934e8i	−0.130685	+	0.226353i
$130$	7.23048e8	+	2.81843e8i	0.222035	+	0.0865489i
$131$	1.07942e9	−	6.23201e8i	0.320234	−	0.184887i	−0.331263	−	0.943539i	$-0.607475\pi$
$131$	1.07942e9	−	6.23201e8i	0.320234	−	0.184887i	0.651497	+	0.758651i	$0.274141\pi$
$132$	1.74628e9	+	1.74628e9i	0.500646	+	0.500646i
$133$	−3.28037e9	+	1.71904e9i	−0.909056	+	0.476381i
$134$			2.93420e8i			0.0786174i
$135$	3.22046e8	−	2.91905e9i	0.0834480	−	0.756379i
$136$	−2.58842e9	−	1.49442e9i	−0.648797	−	0.374583i
$137$	1.55076e9	+	5.78750e9i	0.376098	+	1.40362i	0.851734	+	0.523975i	$0.175551\pi$
$137$	1.55076e9	+	5.78750e9i	0.376098	+	1.40362i	−0.475636	+	0.879642i	$0.657782\pi$
$138$	5.74872e8	+	1.54036e8i	0.134932	+	0.0361549i
$139$	−5.13206e9			−1.16607			−0.583036	−	0.812446i	$-0.698135\pi$
$139$	−5.13206e9			−1.16607			−0.583036	+	0.812446i	$0.698135\pi$
$140$	4.14542e9	−	4.62094e8i	0.911995	−	0.101661i
$141$	−4.15191e8			−0.0884629
$142$	1.74398e9	+	4.67298e8i	0.359952	+	0.0964487i
$143$	1.99021e9	+	7.42755e9i	0.398003	+	1.48537i
$144$	2.80546e9	+	1.61973e9i	0.543716	+	0.313915i
$145$	3.56697e9	−	2.85812e9i	0.670105	−	0.536938i
$146$		−	1.25614e9i		−	0.228797i
$147$	−4.22275e8	−	2.32073e9i	−0.0745877	−	0.409918i
$148$	5.60120e8	+	5.60120e8i	0.0959628	+	0.0959628i
$149$	−5.87833e9	+	3.39385e9i	−0.977047	+	0.564099i	−0.901377	−	0.433034i	$-0.857443\pi$
$149$	−5.87833e9	+	3.39385e9i	−0.977047	+	0.564099i	−0.0756699	+	0.997133i	$0.524110\pi$
$150$	7.23531e8	+	1.61615e8i	0.116693	+	0.0260658i
$151$	−5.45111e9	+	9.44160e9i	−0.853274	+	1.47791i	0.0249632	+	0.999688i	$0.492053\pi$
$151$	−5.45111e9	+	9.44160e9i	−0.853274	+	1.47791i	−0.878237	+	0.478225i	$0.841280\pi$
$152$	9.62033e8	−	3.59036e9i	0.146182	−	0.545559i
$153$	−5.39200e9	+	5.39200e9i	−0.795497	+	0.795497i
$154$	−2.51343e9	−	2.72795e9i	−0.360101	−	0.390835i
$155$	−1.65759e9	−	1.08270e10i	−0.230667	−	1.50666i
$156$	−1.17426e9	−	2.03387e9i	−0.158746	−	0.274956i
$157$	−8.07380e8	+	2.16337e8i	−0.106055	+	0.0284172i	−0.311456	−	0.950261i	$-0.600817\pi$
$157$	−8.07380e8	+	2.16337e8i	−0.106055	+	0.0284172i	0.205401	+	0.978678i	$0.434150\pi$
$158$	9.32766e8	−	2.49934e8i	0.119074	−	0.0319057i
$159$	1.79711e9	+	3.11268e9i	0.222991	+	0.386231i
$160$	−3.77036e9	+	5.13352e9i	−0.454823	+	0.619264i
$161$	9.50735e9	+	2.96917e9i	1.11518	+	0.348272i
$162$	−9.06079e8	+	9.06079e8i	−0.103359	+	0.103359i
$163$	8.17087e8	−	3.04941e9i	0.0906617	−	0.338354i	−0.905664	−	0.423996i	$-0.860627\pi$
$163$	8.17087e8	−	3.04941e9i	0.0906617	−	0.338354i	0.996326	+	0.0856413i	$0.0272939\pi$
$164$	−1.80334e9	+	3.12348e9i	−0.194662	+	0.337164i
$165$	2.95320e9	+	6.72621e9i	0.310181	+	0.706469i
$166$	3.52406e9	−	2.03462e9i	0.360211	−	0.207968i
$167$	1.08077e10	+	1.08077e10i	1.07525	+	1.07525i	0.996928	+	0.0783248i	$0.0249571\pi$
$167$	1.08077e10	+	1.08077e10i	1.07525	+	1.07525i	0.0783248	+	0.996928i	$0.475043\pi$
$168$	2.00014e9	+	1.26657e9i	0.193717	+	0.122670i
$169$			3.29199e9i			0.310433i
$170$	−2.66023e9	−	3.32001e9i	−0.244286	−	0.304873i
$171$	−8.21270e9	−	4.74160e9i	−0.734520	−	0.424075i
$172$	−1.71015e9	−	6.38236e9i	−0.148989	−	0.556036i
$173$	2.85723e8	+	7.65592e7i	0.0242514	+	0.00649815i	0.270924	−	0.962601i	$-0.412671\pi$
$173$	2.85723e8	+	7.65592e7i	0.0242514	+	0.00649815i	−0.246673	+	0.969099i	$0.579337\pi$
$174$	1.24144e9			0.102673
$175$	1.19880e10	+	3.19764e9i	0.966218	+	0.257726i
$176$	−1.79084e10			−1.40686
$177$	−3.56530e9	−	9.55319e8i	−0.273034	−	0.0731592i
$178$	4.10697e8	+	1.53274e9i	0.0306642	+	0.114440i
$179$	−4.63733e9	−	2.67737e9i	−0.337621	−	0.194926i	0.321598	−	0.946876i	$-0.395780\pi$
$179$	−4.63733e9	−	2.67737e9i	−0.337621	−	0.194926i	−0.659220	+	0.751950i	$0.729113\pi$
$180$	6.67854e9	+	8.33491e9i	0.474193	+	0.591799i
$181$		−	2.38648e10i		−	1.65274i	−0.563128	−	0.826370i	$-0.690402\pi$
$181$		−	2.38648e10i		−	1.65274i	0.563128	−	0.826370i	$-0.309598\pi$
$182$	1.63732e9	+	3.12442e9i	0.110614	+	0.211080i
$183$	−1.16890e9	−	1.16890e9i	−0.0770459	−	0.0770459i
$184$	−8.65725e9	+	4.99827e9i	−0.556801	+	0.321469i
$185$	9.47240e8	+	2.15744e9i	0.0594549	+	0.135415i
$186$	1.48746e9	−	2.57635e9i	0.0911248	−	0.157833i
$187$	1.09105e10	−	4.07187e10i	0.652467	−	2.43504i
$188$	2.35972e9	−	2.35972e9i	0.137769	−	0.137769i
$189$	9.81719e9	−	9.04519e9i	0.559640	−	0.515631i
$190$	3.13190e9	−	4.26424e9i	0.174348	−	0.237383i
$191$	−1.39276e10	−	2.41233e10i	−0.757227	−	1.31156i	−0.944259	−	0.329202i	$-0.893220\pi$
$191$	−1.39276e10	−	2.41233e10i	−0.757227	−	1.31156i	0.187032	−	0.982354i	$-0.440113\pi$
$192$	4.08630e9	−	1.09492e9i	0.217008	−	0.0581470i
$193$	−1.37773e10	+	3.69162e9i	−0.714755	+	0.191518i	−0.597830	−	0.801623i	$-0.703970\pi$
$193$	−1.37773e10	+	3.69162e9i	−0.714755	+	0.191518i	−0.116925	+	0.993141i	$0.537304\pi$
$194$	1.10864e9	+	1.92022e9i	0.0561931	+	0.0973293i
$195$	−1.05719e9	−	6.90530e9i	−0.0523595	−	0.342001i
$196$	1.55898e10	+	1.07898e10i	0.754550	+	0.522230i
$197$	−2.40693e10	+	2.40693e10i	−1.13858	+	1.13858i	−0.149878	+	0.988704i	$0.547888\pi$
$197$	−2.40693e10	+	2.40693e10i	−1.13858	+	1.13858i	−0.988704	+	0.149878i	$0.952112\pi$
$198$	2.45829e9	−	9.17446e9i	0.113668	−	0.424216i
$199$	4.43889e9	−	7.68839e9i	0.200649	−	0.347533i	−0.748089	−	0.663598i	$-0.769028\pi$
$199$	4.43889e9	−	7.68839e9i	0.200649	−	0.347533i	0.948738	+	0.316065i	$0.102362\pi$
$200$	−1.05129e10	+	6.67388e9i	−0.464609	+	0.294947i
$201$	2.28745e9	−	1.32066e9i	0.0988485	−	0.0570702i
$202$	4.36873e9	+	4.36873e9i	0.184618	+	0.184618i
$203$	2.07589e10	+	8.49624e8i	0.857969	+	0.0351152i
$204$			1.28748e10i			0.520481i
$205$	−8.37216e9	+	6.70839e9i	−0.331089	+	0.265293i
$206$	−9.45579e9	−	5.45930e9i	−0.365843	−	0.211220i
$207$	6.60096e9	+	2.46351e10i	0.249885	+	0.932584i
$208$	1.64500e10	+	4.40777e9i	0.609370	+	0.163280i
$209$	5.24252e10			1.90056
$210$	1.99784e9	+	2.71372e9i	0.0708884	+	0.0962893i
$211$	2.30423e10			0.800302			0.400151	−	0.916449i	$-0.368958\pi$
$211$	2.30423e10			0.800302			0.400151	+	0.916449i	$0.368958\pi$
$212$	−2.79046e10	−	7.47701e9i	−0.948777	−	0.254224i
$213$	−4.20654e9	−	1.56990e10i	−0.140029	−	0.522594i
$214$	4.22120e9	+	2.43711e9i	0.137586	+	0.0794353i
$215$	2.15530e9	−	1.95358e10i	0.0687915	−	0.623531i
$216$			1.33976e10i			0.418778i
$217$	2.66359e10	−	4.20628e10i	0.815452	−	1.28774i
$218$	8.20398e8	+	8.20398e8i	0.0246020	+	0.0246020i
$219$	−9.79265e9	+	5.65379e9i	−0.287675	+	0.166089i
$220$	−5.50126e10	−	2.14438e10i	−1.58329	−	0.617163i
$221$	−2.00440e10	+	3.47172e10i	−0.565222	+	0.978993i
$222$	−1.65633e8	+	6.18153e8i	−0.00457678	+	0.0170808i
$223$	−3.11011e10	+	3.11011e10i	−0.842179	+	0.842179i	−0.989142	−	0.146963i	$-0.953050\pi$
$223$	−3.11011e10	+	3.11011e10i	−0.842179	+	0.842179i	0.146963	+	0.989142i	$0.453050\pi$
$224$	−2.82481e10	+	6.34334e9i	−0.749674	+	0.168346i
$225$	9.50496e9	+	3.03146e10i	0.247246	+	0.788551i
$226$	2.77552e9	+	4.80733e9i	0.0707711	+	0.122579i
$227$	2.56966e10	−	6.88539e9i	0.642332	−	0.172112i	0.0770725	−	0.997025i	$-0.475443\pi$
$227$	2.56966e10	−	6.88539e9i	0.642332	−	0.172112i	0.565259	+	0.824913i	$0.308776\pi$
$228$	−1.54659e10	+	4.14407e9i	−0.379025	+	0.101559i
$229$	−3.09771e10	−	5.36539e10i	−0.744356	−	1.28926i	−0.950495	−	0.310740i	$-0.899423\pi$
$229$	−3.09771e10	−	5.36539e10i	−0.744356	−	1.28926i	0.206139	−	0.978523i	$-0.433910\pi$
$230$	−1.40652e10	+	2.15335e9i	−0.331414	+	0.0507387i
$231$	−9.95387e9	+	3.18725e10i	−0.230005	+	0.736483i
$232$	−1.47446e10	+	1.47446e10i	−0.334147	+	0.334147i
$233$	6.68212e9	−	2.49380e10i	0.148529	−	0.554319i	−0.851044	−	0.525095i	$-0.824030\pi$
$233$	6.68212e9	−	2.49380e10i	0.148529	−	0.554319i	0.999573	−	0.0292240i	$-0.00930361\pi$
$234$	−4.51618e9	+	7.82225e9i	−0.0984691	+	0.170553i
$235$	9.08904e9	−	3.99062e9i	0.194407	−	0.0853561i
$236$	2.56928e10	−	1.48337e10i	0.539147	−	0.311277i
$237$	−6.14674e9	−	6.14674e9i	−0.126554	−	0.126554i
$238$	7.90799e8	−	1.93216e10i	0.0159761	−	0.390344i
$239$		−	1.20764e10i		−	0.239412i	−0.992809	−	0.119706i	$-0.961805\pi$
$239$		−	1.20764e10i		−	0.239412i	0.992809	−	0.119706i	$-0.0381952\pi$
$240$	1.61712e10	+	1.78410e9i	0.314624	+	0.0347111i
$241$	5.71490e10	+	3.29950e10i	1.09127	+	0.630044i	0.933914	−	0.357498i	$-0.116370\pi$
$241$	5.71490e10	+	3.29950e10i	1.09127	+	0.630044i	0.157355	+	0.987542i	$0.449703\pi$
$242$	9.62704e9	+	3.59286e10i	0.180436	+	0.673397i
$243$	5.10938e10	+	1.36906e10i	0.940027	+	0.251879i
$244$	1.32869e10			0.239976
$245$	3.15499e10	+	4.67450e10i	0.559437	+	0.828873i
$246$	−2.91383e9			−0.0507290
$247$	−4.81558e10	−	1.29033e10i	−0.823213	−	0.220579i
$248$	1.29328e10	+	4.82660e10i	0.217101	+	0.810230i
$249$	−3.17230e10	−	1.83153e10i	−0.522971	−	0.301937i
$250$	−1.73924e10	+	3.41628e9i	−0.281598	+	0.0553126i
$251$			7.86729e10i			1.25110i	0.780183	+	0.625552i	$0.215126\pi$
$251$			7.86729e10i			1.25110i	−0.780183	+	0.625552i	$0.784874\pi$
$252$	−1.98531e9	+	4.85071e10i	−0.0310117	+	0.757710i
$253$	−9.96967e10	−	9.96967e10i	−1.52981	−	1.52981i
$254$	1.33513e10	−	7.70840e9i	0.201267	−	0.116202i
$255$	−1.39087e10	+	3.56818e10i	−0.205994	+	0.528464i
$256$	−9.42516e9	+	1.63249e10i	−0.137154	+	0.237558i
$257$	−1.23835e10	+	4.62160e10i	−0.177070	+	0.660835i	0.819119	+	0.573623i	$0.194463\pi$
$257$	−1.23835e10	+	4.62160e10i	−0.177070	+	0.660835i	−0.996190	+	0.0872124i	$0.972204\pi$
$258$	3.77467e9	−	3.77467e9i	0.0530383	−	0.0530383i
$259$	−3.19271e9	+	1.02231e10i	−0.0440870	+	0.141168i
$260$	4.52546e10	+	3.32376e10i	0.614161	+	0.451076i
$261$	2.65999e10	+	4.60723e10i	0.354811	+	0.614551i
$262$	−7.81783e9	+	2.09478e9i	−0.102502	+	0.0274652i
$263$	1.14245e11	−	3.06118e10i	1.47243	−	0.394538i	0.568670	−	0.822566i	$-0.307458\pi$
$263$	1.14245e11	−	3.06118e10i	1.47243	−	0.394538i	0.903765	+	0.428028i	$0.140792\pi$
$264$	−1.67562e10	−	2.90227e10i	−0.212304	−	0.367722i
$265$	−6.92585e10	−	5.08675e10i	−0.862714	−	0.633627i
$266$	2.34647e10	−	5.26919e9i	0.287374	−	0.0645321i
$267$	1.01005e10	−	1.01005e10i	0.121630	−	0.121630i
$268$	−5.49473e9	+	2.05066e10i	−0.0650638	+	0.242821i
$269$	6.61492e9	−	1.14574e10i	0.0770263	−	0.133414i	−0.824939	−	0.565221i	$-0.808791\pi$
$269$	6.61492e9	−	1.14574e10i	0.0770263	−	0.133414i	0.901966	+	0.431808i	$0.142124\pi$
$270$	−6.92592e9	+	1.77680e10i	−0.0793123	+	0.203470i
$271$	3.16240e10	−	1.82581e10i	0.356168	−	0.205634i	−0.311230	−	0.950335i	$-0.600741\pi$
$271$	3.16240e10	−	1.82581e10i	0.356168	−	0.205634i	0.667399	+	0.744701i	$0.267408\pi$
$272$	−6.60169e10	−	6.60169e10i	−0.731299	−	0.731299i
$273$	1.69880e10	−	2.68270e10i	0.185101	−	0.292307i
$274$		−	3.89074e10i		−	0.417018i
$275$	−1.29298e11	−	1.18860e11i	−1.36332	−	1.25326i
$276$	3.72921e10	+	2.15306e10i	0.386835	+	0.223340i
$277$	−3.00342e9	−	1.12089e10i	−0.0306519	−	0.114394i	0.948905	−	0.315562i	$-0.102193\pi$
$277$	−3.00342e9	−	1.12089e10i	−0.0306519	−	0.114394i	−0.979557	+	0.201168i	$0.935526\pi$
$278$	3.21900e10	+	8.62527e9i	0.323235	+	0.0866106i
$279$	1.27485e11			1.25962
$280$	−5.59593e10	−	8.50246e9i	−0.544078	−	0.0826672i
$281$	−6.83073e9			−0.0653565			−0.0326782	−	0.999466i	$-0.510404\pi$
$281$	−6.83073e9			−0.0653565			−0.0326782	+	0.999466i	$0.510404\pi$
$282$	2.60421e9	+	6.97795e8i	0.0245219	+	0.00657063i
$283$	−3.08835e10	−	1.15259e11i	−0.286212	−	1.06816i	−0.947949	−	0.318421i	$-0.896847\pi$
$283$	−3.08835e10	−	1.15259e11i	−0.286212	−	1.06816i	0.661738	−	0.749735i	$-0.269819\pi$
$284$	1.13133e11	+	6.53172e10i	1.03194	+	0.595792i
$285$	−4.73397e10	−	5.22278e9i	−0.425034	−	0.0468921i
$286$		−	4.99329e10i		−	0.441305i
$287$	−4.87239e10	−	1.99418e9i	−0.423910	−	0.0173499i
$288$	−5.24203e10	−	5.24203e10i	−0.448986	−	0.448986i
$289$	8.76236e10	−	5.05895e10i	0.738891	−	0.426599i
$290$	−2.71767e10	+	1.19321e10i	−0.225635	+	0.0990667i
$291$	9.97980e9	−	1.72855e10i	0.0815837	−	0.141307i
$292$	2.35231e10	−	8.77893e10i	0.189353	−	0.706674i
$293$	−1.00166e11	+	1.00166e11i	−0.793991	+	0.793991i	−0.982140	−	0.188149i	$-0.939751\pi$
$293$	−1.00166e11	+	1.00166e11i	−0.793991	+	0.793991i	0.188149	+	0.982140i	$0.439751\pi$
$294$	−1.25172e9	+	1.52661e10i	−0.00977115	+	0.119169i
$295$	8.72310e10	−	1.33549e10i	0.670613	−	0.102669i
$296$	−5.37457e9	−	9.30904e9i	−0.0406941	−	0.0704842i
$297$	−1.82522e11	+	4.89067e10i	−1.36117	+	0.364724i
$298$	4.25747e10	−	1.14079e10i	0.312736	−	0.0837974i
$299$	6.70394e10	+	1.16116e11i	0.485076	+	0.840177i
$300$	4.75397e10	+	2.48442e10i	0.338853	+	0.177084i
$301$	6.57018e10	−	6.05351e10i	0.461347	−	0.425068i
$302$	5.00592e10	−	5.00592e10i	0.346300	−	0.346300i
$303$	1.43945e10	−	5.37211e10i	0.0981083	−	0.366145i
$304$	5.80538e10	−	1.00552e11i	0.389852	−	0.675243i
$305$	3.68238e10	+	1.43538e10i	0.243657	+	0.0949770i
$306$	4.28825e10	−	2.47582e10i	0.279598	−	0.161426i
$307$	−8.10579e9	−	8.10579e9i	−0.0520802	−	0.0520802i	0.680587	−	0.732667i	$-0.261725\pi$
$307$	−8.10579e9	−	8.10579e9i	−0.0520802	−	0.0520802i	−0.732667	+	0.680587i	$0.761725\pi$
$308$	−1.24574e11	−	2.37719e11i	−0.788768	−	1.50517i
$309$			9.82875e10i			0.613317i
$310$	−7.79963e9	+	7.06964e10i	−0.0479674	+	0.434780i
$311$	−5.74237e9	−	3.31536e9i	−0.0348073	−	0.0200960i	0.482495	−	0.875899i	$-0.339731\pi$
$311$	−5.74237e9	−	3.31536e9i	−0.0348073	−	0.0200960i	−0.517303	+	0.855803i	$0.673064\pi$
$312$	8.24835e9	+	3.07833e10i	0.0492801	+	0.183916i
$313$	−4.91256e10	−	1.31632e10i	−0.289307	−	0.0775195i	0.111247	−	0.993793i	$-0.464516\pi$
$313$	−4.91256e10	−	1.31632e10i	−0.289307	−	0.0775195i	−0.400554	+	0.916273i	$0.631182\pi$
$314$	5.42773e9			0.0315090
$315$	−5.79045e10	+	1.32290e11i	−0.331371	+	0.757058i
$316$	6.98696e10			0.394182
$317$	1.50628e11	+	4.03608e10i	0.837800	+	0.224488i	0.652114	−	0.758121i	$-0.273883\pi$
$317$	1.50628e11	+	4.03608e10i	0.837800	+	0.224488i	0.185686	+	0.982609i	$0.440549\pi$
$318$	−6.04066e9	−	2.25440e10i	−0.0331255	−	0.123626i
$319$	−2.54698e11	−	1.47050e11i	−1.37711	−	0.795072i
$320$	−7.89305e10	+	6.32449e10i	−0.420794	+	0.337171i
$321$		−	4.38769e10i		−	0.230655i
$322$	−5.46430e10	−	3.46022e10i	−0.283258	−	0.179371i
$323$	1.93258e11	+	1.93258e11i	0.987930	+	0.987930i
$324$	−8.02918e10	+	4.63565e10i	−0.404780	+	0.233700i
$325$	8.95137e10	+	1.41005e11i	0.445056	+	0.701065i
$326$	−1.02501e10	+	1.77536e10i	−0.0502629	+	0.0870578i
$327$	2.70313e9	−	1.00882e10i	0.0130738	−	0.0487921i
$328$	3.46076e10	−	3.46076e10i	0.165097	−	0.165097i
$329$	4.30689e10	+	1.34505e10i	0.202667	+	0.0632933i
$330$	−7.21891e9	−	4.71523e10i	−0.0335088	−	0.218872i
$331$	8.82408e10	+	1.52838e11i	0.404058	+	0.699848i	0.994211	−	0.107443i	$-0.0342662\pi$
$331$	8.82408e10	+	1.52838e11i	0.404058	+	0.699848i	−0.590154	+	0.807291i	$0.700933\pi$
$332$	2.84391e11	−	7.62024e10i	1.28468	−	0.344229i
$333$	−2.64898e10	+	7.09793e9i	−0.118054	+	0.0316324i
$334$	−4.96254e10	−	8.59537e10i	−0.218195	−	0.377925i
$335$	−3.73816e10	+	5.08969e10i	−0.162165	+	0.220795i
$336$	5.01093e10	+	5.43862e10i	0.214483	+	0.232789i
$337$	−2.86251e11	+	2.86251e11i	−1.20896	+	1.20896i	−0.237595	+	0.971364i	$0.576359\pi$
$337$	−2.86251e11	+	2.86251e11i	−1.20896	+	1.20896i	−0.971364	+	0.237595i	$0.923641\pi$
$338$	5.53273e9	−	2.06484e10i	0.0230576	−	0.0860521i
$339$	2.49847e10	−	4.32748e10i	0.102749	−	0.177966i
$340$	−1.23747e11	−	2.81846e11i	−0.502202	−	1.14382i
$341$	−6.10343e11	+	3.52382e11i	−2.44444	+	1.41130i
$342$	4.35436e10	+	4.35436e10i	0.172110	+	0.172110i
$343$	−3.13787e10	+	2.54416e11i	−0.122408	+	0.992480i
$344$			8.96635e10i			0.345225i
$345$	8.00934e10	+	9.99576e10i	0.304376	+	0.379866i
$346$	−1.66347e9	−	9.60407e8i	−0.00623984	−	0.00360257i
$347$	−1.17798e11	−	4.39629e11i	−0.436170	−	1.62781i	−0.738251	−	0.674527i	$-0.764348\pi$
$347$	−1.17798e11	−	4.39629e11i	−0.436170	−	1.62781i	0.302080	−	0.953282i	$-0.402319\pi$
$348$	8.67619e10	+	2.32478e10i	0.317119	+	0.0849718i
$349$	−8.78400e10			−0.316941			−0.158470	−	0.987364i	$-0.550656\pi$
$349$	−8.78400e10			−0.316941			−0.158470	+	0.987364i	$0.550656\pi$
$350$	−6.98184e10	−	4.02044e10i	−0.248693	−	0.143208i
$351$	1.79695e11			0.631910
$352$	3.95861e11	+	1.06071e11i	1.37436	+	0.368259i
$353$	−1.49320e10	−	5.57270e10i	−0.0511838	−	0.191020i	0.935600	−	0.353061i	$-0.114859\pi$
$353$	−1.49320e10	−	5.57270e10i	−0.0511838	−	0.191020i	−0.986784	+	0.162040i	$0.948192\pi$
$354$	2.07571e10	+	1.19841e10i	0.0702510	+	0.0405594i
$355$	2.42978e11	+	3.03240e11i	0.811970	+	1.01335i
$356$			1.14811e11i			0.378843i
$357$	−1.54187e11	+	8.08001e10i	−0.502390	+	0.263272i
$358$	2.45871e10	+	2.45871e10i	0.0791104	+	0.0791104i
$359$	−1.66527e11	+	9.61446e10i	−0.529128	+	0.305492i	−0.740661	−	0.671879i	$-0.765488\pi$
$359$	−1.66527e11	+	9.61446e10i	−0.529128	+	0.305492i	0.211534	+	0.977371i	$0.432154\pi$
$360$	−5.82659e10	−	1.32706e11i	−0.182832	−	0.416419i
$361$	−8.60305e9	+	1.49009e10i	−0.0266606	+	0.0461775i
$362$	−4.01087e10	+	1.49688e11i	−0.122758	+	0.458139i
$363$	2.36762e11	−	2.36762e11i	0.715703	−	0.715703i
$364$	5.59197e10	+	2.49021e11i	0.166958	+	0.743497i
$365$	1.60032e11	−	2.17891e11i	0.471942	−	0.642571i
$366$	5.36721e9	+	9.29628e9i	0.0156345	+	0.0270797i
$367$	3.14651e9	−	8.43105e8i	0.00905382	−	0.00242596i	−0.254289	−	0.967128i	$-0.581842\pi$
$367$	3.14651e9	−	8.43105e8i	0.00905382	−	0.00242596i	0.263343	+	0.964702i	$0.415175\pi$
$368$	−3.01620e11	+	8.08188e10i	−0.857324	+	0.229719i
$369$	−6.24336e10	−	1.08138e11i	−0.175307	−	0.303641i
$370$	−2.31547e9	−	1.51241e10i	−0.00642290	−	0.0419530i
$371$	−8.55806e10	−	3.81106e11i	−0.234527	−	1.04439i
$372$	1.52202e11	−	1.52202e11i	0.412075	−	0.412075i
$373$	−1.65534e11	+	6.17782e11i	−0.442790	+	1.65251i	0.278916	+	0.960315i	$0.410025\pi$
$373$	−1.65534e11	+	6.17782e11i	−0.442790	+	1.65251i	−0.721706	+	0.692200i	$0.756642\pi$
$374$	−1.36869e11	+	2.37064e11i	−0.361728	+	0.626531i
$375$	1.04914e11	+	1.20211e11i	0.273965	+	0.313910i
$376$	−3.92179e10	+	2.26425e10i	−0.101190	+	0.0584223i
$377$	1.97763e11	+	1.97763e11i	0.504206	+	0.504206i
$378$	−7.67785e10	+	4.02349e10i	−0.193431	+	0.101365i
$379$		−	6.26332e11i		−	1.55929i	−0.626219	−	0.779647i	$-0.715399\pi$
$379$		−	6.26332e11i		−	1.55929i	0.626219	−	0.779647i	$-0.284601\pi$
$380$	2.98737e11	−	2.39370e11i	0.734958	−	0.588902i
$381$	−1.20187e11	−	6.93897e10i	−0.292209	−	0.168707i
$382$	4.68152e10	+	1.74717e11i	0.112487	+	0.419807i
$383$	−6.64395e10	−	1.78024e10i	−0.157773	−	0.0422751i	0.179068	−	0.983837i	$-0.442692\pi$
$383$	−6.64395e10	−	1.78024e10i	−0.157773	−	0.0422751i	−0.336841	+	0.941562i	$0.609358\pi$
$384$	−1.63871e11			−0.384603
$385$	−8.84413e10	−	7.93402e11i	−0.205155	−	1.84043i
$386$	9.26202e10			0.212355
$387$	2.20964e11	+	5.92071e10i	0.500751	+	0.134176i
$388$	4.15218e10	+	1.54962e11i	0.0930109	+	0.347121i
$389$	1.56904e10	+	9.05888e9i	0.0347426	+	0.0200586i	0.517271	−	0.855822i	$-0.326948\pi$
$389$	1.56904e10	+	9.05888e9i	0.0347426	+	0.0200586i	−0.482528	+	0.875880i	$0.660281\pi$
$390$	−4.97448e9	+	4.50891e10i	−0.0108882	+	0.0986916i
$391$		−	7.35035e11i		−	1.59042i
$392$	−1.66449e11	−	1.96182e11i	−0.356035	−	0.419635i
$393$	5.15180e10	+	5.15180e10i	0.108941	+	0.108941i
$394$	1.91422e11	−	1.10518e11i	0.400184	−	0.231046i
$395$	1.93640e11	+	7.54803e10i	0.400228	+	0.156008i
$396$	3.43610e11	−	5.95151e11i	0.702163	−	1.21618i
$397$	−6.92405e10	+	2.58409e11i	−0.139895	+	0.522096i	0.860034	+	0.510236i	$0.170442\pi$
$397$	−6.92405e10	+	2.58409e11i	−0.139895	+	0.522096i	−0.999930	+	0.0118601i	$0.996225\pi$
$398$	−4.07638e10	+	4.07638e10i	−0.0814330	+	0.0814330i
$399$	−1.46690e11	−	1.59210e11i	−0.289750	−	0.314480i
$400$	−3.71156e11	+	1.16374e11i	−0.724915	+	0.227293i
$401$	−9.05200e10	−	1.56785e11i	−0.174821	−	0.302800i	0.765278	−	0.643700i	$-0.222602\pi$
$401$	−9.05200e10	−	1.56785e11i	−0.174821	−	0.302800i	−0.940099	+	0.340900i	$0.889268\pi$
$402$	−1.65672e10	+	4.43917e9i	−0.0316397	+	0.00847784i
$403$	6.47369e11	−	1.73462e11i	1.22259	−	0.327591i
$404$	2.23511e11	+	3.87133e11i	0.417430	+	0.723010i
$405$	−2.72603e11	+	4.17349e10i	−0.503481	+	0.0770818i
$406$	−1.28778e11	−	4.02178e10i	−0.235221	−	0.0734600i
$407$	1.07203e11	−	1.07203e11i	0.193656	−	0.193656i
$408$	4.52184e10	−	1.68757e11i	0.0807875	−	0.301503i
$409$	−1.96145e11	+	3.39733e11i	−0.346595	+	0.600320i	−0.985642	−	0.168847i	$-0.945996\pi$
$409$	−1.96145e11	+	3.39733e11i	−0.346595	+	0.600320i	0.639047	+	0.769168i	$0.279329\pi$
$410$	6.37874e10	−	2.80064e10i	0.111483	−	0.0489474i
$411$	−3.03315e11	+	1.75119e11i	−0.524331	+	0.302723i
$412$	−5.58614e11	−	5.58614e11i	−0.955156	−	0.955156i
$413$	3.38891e11	+	2.14600e11i	0.573171	+	0.362956i
$414$		−	1.65613e11i		−	0.277073i
$415$	8.70495e11	+	9.60379e10i	1.44062	+	0.158937i
$416$	−3.37516e11	−	1.94865e11i	−0.552553	−	0.319017i
$417$	−7.76433e10	−	2.89769e11i	−0.125745	−	0.469288i
$418$	−3.28828e11	−	8.81092e10i	−0.526836	−	0.141165i
$419$	1.16519e11			0.184687			0.0923433	−	0.995727i	$-0.470564\pi$
$419$	1.16519e11			0.184687			0.0923433	+	0.995727i	$0.470564\pi$
$420$	8.88072e10	+	2.27069e11i	0.139260	+	0.356071i
$421$	−9.23539e11			−1.43280			−0.716401	−	0.697689i	$-0.754212\pi$
$421$	−9.23539e11			−1.43280			−0.716401	+	0.697689i	$0.754212\pi$
$422$	−1.44528e11	−	3.87263e10i	−0.221844	−	0.0594428i
$423$	2.99028e10	+	1.11599e11i	0.0454130	+	0.169484i
$424$	3.39501e11	+	1.96011e11i	0.510146	+	0.294533i
$425$	−3.84781e10	−	9.14802e11i	−0.0572088	−	1.36012i
$426$			1.05539e11i			0.155264i
$427$	8.33861e10	+	1.59122e11i	0.121386	+	0.231635i
$428$	2.49373e11	+	2.49373e11i	0.359214	+	0.359214i
$429$	−3.89268e11	+	2.24744e11i	−0.554869	+	0.320354i
$430$	−4.63519e10	+	1.18913e11i	−0.0653821	+	0.167733i
$431$	3.05580e11	−	5.29280e11i	0.426557	−	0.738819i	−0.570007	−	0.821640i	$-0.693060\pi$
$431$	3.05580e11	−	5.29280e11i	0.426557	−	0.738819i	0.996564	+	0.0828210i	$0.0263930\pi$
$432$	−1.08315e11	+	4.04238e11i	−0.149628	+	0.558419i
$433$	−3.66141e9	+	3.66141e9i	−0.00500556	+	0.00500556i	−0.709605	−	0.704600i	$-0.751127\pi$
$433$	−3.66141e9	+	3.66141e9i	−0.00500556	+	0.00500556i	0.704600	+	0.709605i	$0.251127\pi$
$434$	−2.37762e11	+	2.19065e11i	−0.321691	+	0.296394i
$435$	2.15341e11	+	1.58159e11i	0.288353	+	0.211784i
$436$	4.19729e10	+	7.26992e10i	0.0556263	+	0.0963475i
$437$	8.82963e11	−	2.36589e11i	1.15818	−	0.310333i
$438$	7.09248e10	−	1.90042e10i	0.0920798	−	0.0246727i
$439$	5.74101e11	+	9.94372e11i	0.737731	+	1.27779i	0.953515	+	0.301346i	$0.0974360\pi$
$439$	5.74101e11	+	9.94372e11i	0.737731	+	1.27779i	−0.215784	+	0.976441i	$0.569231\pi$
$440$	6.45767e11	+	4.74289e11i	0.821370	+	0.603262i
$441$	−5.93375e11	+	2.80646e11i	−0.747060	+	0.353334i
$442$	1.84070e11	−	1.84070e11i	0.229395	−	0.229395i
$443$	−1.26836e11	+	4.73357e11i	−0.156468	+	0.583945i	0.842508	+	0.538684i	$0.181078\pi$
$443$	−1.26836e11	+	4.73357e11i	−0.156468	+	0.583945i	−0.998975	+	0.0452605i	$0.985588\pi$
$444$	−2.31516e10	+	4.00998e10i	−0.0282721	+	0.0489687i
$445$	−1.24031e11	+	3.18193e11i	−0.149937	+	0.384654i
$446$	2.47347e11	−	1.42806e11i	0.296005	−	0.170899i
$447$	−2.80559e11	−	2.80559e11i	−0.332384	−	0.332384i
$448$	−4.59356e11	−	1.88006e10i	−0.538763	−	0.0220506i
$449$		−	1.17618e12i		−	1.36573i	−0.730545	−	0.682865i	$-0.760734\pi$
$449$		−	1.17618e12i		−	1.36573i	0.730545	−	0.682865i	$-0.239266\pi$
$450$	−8.66962e9	−	2.06117e11i	−0.00996653	−	0.236951i
$451$	5.97811e11	+	3.45146e11i	0.680408	+	0.392834i
$452$	1.03951e11	+	3.87951e11i	0.117140	+	0.437174i
$453$	−6.15565e11	−	1.64940e11i	−0.686803	−	0.184028i
$454$	−1.72749e11			−0.190838
$455$	−1.14040e11	+	7.50557e11i	−0.124740	+	0.820979i
$456$	2.17275e11			0.235325
$457$	6.07755e11	+	1.62847e11i	0.651787	+	0.174646i	0.569537	−	0.821966i	$-0.307123\pi$
$457$	6.07755e11	+	1.62847e11i	0.651787	+	0.174646i	0.0822503	+	0.996612i	$0.473789\pi$
$458$	1.04124e11	+	3.88596e11i	0.110575	+	0.412671i
$459$	−8.53130e11	−	4.92555e11i	−0.897136	−	0.517962i
$460$	−1.02331e12	−	1.12898e11i	−1.06561	−	0.117564i
$461$			6.73735e10i			0.0694761i	0.999396	+	0.0347380i	$0.0110597\pi$
$461$			6.73735e10i			0.0694761i	−0.999396	+	0.0347380i	$0.988940\pi$
$462$	1.16001e11	−	1.83186e11i	0.118460	−	0.187069i
$463$	2.82268e11	+	2.82268e11i	0.285461	+	0.285461i	0.835282	−	0.549821i	$-0.185304\pi$
$463$	2.82268e11	+	2.82268e11i	0.285461	+	0.285461i	−0.549821	+	0.835282i	$0.685304\pi$
$464$	−5.64087e11	+	3.25676e11i	−0.564956	+	0.326178i
$465$	5.86242e11	−	2.57394e11i	0.581485	−	0.255306i
$466$	−8.38247e10	+	1.45189e11i	−0.0823447	+	0.142625i
$467$	−5.28219e10	+	1.97134e11i	−0.0513911	+	0.191794i	−0.986849	−	0.161643i	$-0.948321\pi$
$467$	−5.28219e10	+	1.97134e11i	−0.0513911	+	0.191794i	0.935458	+	0.353438i	$0.114987\pi$
$468$	−4.62110e11	+	4.62110e11i	−0.445286	+	0.445286i
$469$	−2.80069e11	+	6.28917e10i	−0.267292	+	0.0600227i
$470$	−6.37163e10	+	9.75481e9i	−0.0602296	+	0.00922101i
$471$	−2.44298e10	−	4.23136e10i	−0.0228731	−	0.0396174i
$472$	−3.88868e11	+	1.04197e11i	−0.360632	+	0.0966309i
$473$	−1.22154e12	+	3.27309e11i	−1.12210	+	0.300665i
$474$	2.82237e10	+	4.88849e10i	0.0256810	+	0.0444808i
$475$	1.08652e12	−	3.40674e11i	0.979305	−	0.307056i
$476$	4.17093e11	−	1.33554e12i	0.372393	−	1.19241i
$477$	7.07223e11	−	7.07223e11i	0.625495	−	0.625495i
$478$	−2.02963e10	+	7.57468e10i	−0.0177824	+	0.0663649i
$479$	2.79003e11	−	4.83248e11i	0.242159	−	0.419431i	−0.719170	−	0.694834i	$-0.755478\pi$
$479$	2.79003e11	−	4.83248e11i	0.242159	−	0.419431i	0.961329	+	0.275403i	$0.0888113\pi$
$480$	−3.46893e11	−	1.35218e11i	−0.298270	−	0.116265i
$481$	−1.24858e11	+	7.20867e10i	−0.106356	+	0.0614048i
$482$	−3.03003e11	−	3.03003e11i	−0.255703	−	0.255703i
$483$	−2.38091e10	+	5.81729e11i	−0.0199059	+	0.486360i
$484$			2.69126e12i			2.22922i
$485$	−5.23300e10	+	4.74323e11i	−0.0429450	+	0.389257i
$486$	−2.97468e11	−	1.71743e11i	−0.241867	−	0.139642i
$487$	5.20830e11	+	1.94376e12i	0.419581	+	1.56590i	0.775479	+	0.631373i	$0.217508\pi$
$487$	5.20830e11	+	1.94376e12i	0.419581	+	1.56590i	−0.355898	+	0.934525i	$0.615825\pi$
$488$	−1.74158e11	−	4.66656e10i	−0.139013	−	0.0372484i
$489$	1.84539e11			0.145948
$490$	−1.19329e11	−	3.46225e11i	−0.0935109	−	0.271316i
$491$	−8.65785e11			−0.672269			−0.336135	−	0.941814i	$-0.609120\pi$
$491$	−8.65785e11			−0.672269			−0.336135	+	0.941814i	$0.609120\pi$
$492$	−2.03642e11	−	5.45657e10i	−0.156684	−	0.0419834i
$493$	−3.96829e11	−	1.48099e12i	−0.302546	−	1.12912i
$494$	2.80362e11	+	1.61867e11i	0.211811	+	0.122289i
$495$	1.59524e12	−	1.27822e12i	1.19427	−	0.956936i
$496$			1.56086e12i			1.15797i
$497$	−7.22294e10	+	1.76478e12i	−0.0531019	+	1.29744i
$498$	1.68195e11	+	1.68195e11i	0.122541	+	0.122541i
$499$	5.39904e11	−	3.11714e11i	0.389820	−	0.225063i	−0.292262	−	0.956338i	$-0.594408\pi$
$499$	5.39904e11	−	3.11714e11i	0.389820	−	0.225063i	0.682082	+	0.731276i	$0.261075\pi$
$500$	−1.27950e12	−	8.69401e10i	−0.915532	−	0.0622093i
$501$	−4.46720e11	+	7.73741e11i	−0.316786	+	0.548689i
$502$	1.32223e11	−	4.93461e11i	0.0929264	−	0.346806i
$503$	4.23651e11	−	4.23651e11i	0.295088	−	0.295088i	−0.543998	−	0.839086i	$-0.683090\pi$
$503$	4.23651e11	−	4.23651e11i	0.295088	−	0.295088i	0.839086	+	0.543998i	$0.183090\pi$
$504$	1.96387e11	−	6.28837e11i	0.135574	−	0.434111i
$505$	2.01228e11	+	1.31438e12i	0.137682	+	0.899308i
$506$	4.57773e11	+	7.92886e11i	0.310437	+	0.537692i
$507$	−1.85874e11	+	4.98047e10i	−0.124934	+	0.0334761i
$508$	1.07745e12	−	2.88702e11i	0.717812	−	0.192337i
$509$	−7.92976e11	−	1.37347e12i	−0.523636	−	0.906965i	−0.999621	−	0.0275114i	$-0.991242\pi$
$509$	−7.92976e11	−	1.37347e12i	−0.523636	−	0.906965i	0.475985	−	0.879453i	$-0.342092\pi$
$510$	1.47209e11	−	2.00432e11i	0.0963535	−	0.131190i
$511$	1.19898e12	−	2.69241e11i	0.777890	−	0.174682i
$512$	1.10150e12	−	1.10150e12i	0.708385	−	0.708385i
$513$	3.17082e11	−	1.18337e12i	0.202136	−	0.754381i
$514$	1.55347e11	−	2.69069e11i	0.0981678	−	0.170032i
$515$	−9.44694e11	−	2.15164e12i	−0.591778	−	1.34783i
$516$	3.34490e11	−	1.93118e11i	0.207711	−	0.119922i
$517$	−4.51633e11	−	4.51633e11i	−0.278021	−	0.278021i
$518$	3.72074e10	−	5.87569e10i	0.0227062	−	0.0358571i
$519$			1.72909e10i			0.0104608i
$520$	−4.76441e11	−	5.94605e11i	−0.285755	−	0.356627i
$521$	−1.47798e11	−	8.53312e10i	−0.0878817	−	0.0507385i	0.455415	−	0.890279i	$-0.349491\pi$
$521$	−1.47798e11	−	8.53312e10i	−0.0878817	−	0.0507385i	−0.543297	+	0.839541i	$0.682824\pi$
$522$	−8.94109e10	−	3.33686e11i	−0.0527076	−	0.196707i
$523$	1.46303e12	+	3.92018e11i	0.855058	+	0.229112i	0.659616	−	0.751603i	$-0.270719\pi$
$523$	1.46303e12	+	3.92018e11i	0.855058	+	0.229112i	0.195442	+	0.980715i	$0.437386\pi$
$524$	−5.85601e11			−0.339321
$525$	8.20554e8	+	7.25248e11i	0.000471401	+	0.416648i
$526$	−7.68029e11			−0.437463
$527$	−3.54895e12	−	9.50938e11i	−2.00425	−	0.537037i
$528$	−2.70938e11	−	1.01115e12i	−0.151711	−	0.566193i
$529$	−5.69201e11	−	3.28628e11i	−0.316020	−	0.182454i
$530$	3.48920e11	+	4.35457e11i	0.192081	+	0.239720i
$531$			1.02712e12i			0.560654i
$532$	1.73857e12	+	7.11568e10i	0.941003	+	0.0385136i
$533$	−4.64176e11	−	4.64176e11i	−0.249121	−	0.249121i
$534$	−8.03288e10	+	4.63779e10i	−0.0427500	+	0.0246817i
$535$	4.21725e11	+	9.60522e11i	0.222555	+	0.506892i
$536$	1.44045e11	−	2.49493e11i	0.0753801	−	0.130562i
$537$	8.10120e10	−	3.02341e11i	0.0420402	−	0.156896i
$538$	−6.07469e10	+	6.07469e10i	−0.0312611	+	0.0312611i
$539$	2.06509e12	−	2.98377e12i	1.05388	−	1.52270i
$540$	−8.16770e11	+	1.11207e12i	−0.413360	+	0.562809i
$541$	−1.46186e12	−	2.53201e12i	−0.733697	−	1.27080i	−0.955293	−	0.295662i	$-0.904460\pi$
$541$	−1.46186e12	−	2.53201e12i	−0.733697	−	1.27080i	0.221596	−	0.975139i	$-0.428873\pi$
$542$	−2.29042e11	+	6.13716e10i	−0.114003	+	0.0305471i
$543$	1.34746e12	−	3.61052e11i	0.665148	−	0.178226i
$544$	1.06827e12	+	1.85030e12i	0.522982	+	0.905831i
$545$	3.77884e10	+	2.46825e11i	0.0183474	+	0.119841i
$546$	−1.51641e11	+	1.39716e11i	−0.0730214	+	0.0672791i
$547$	−1.38972e12	+	1.38972e12i	−0.663719	+	0.663719i	−0.956255	−	0.292536i	$-0.905501\pi$
$547$	−1.38972e12	+	1.38972e12i	−0.663719	+	0.663719i	0.292536	+	0.956255i	$0.405501\pi$
$548$	7.28597e11	−	2.71916e12i	0.345124	−	1.28802i
$549$	−2.30002e11	+	3.98376e11i	−0.108058	+	0.187162i
$550$	6.11237e11	+	9.62838e11i	0.284825	+	0.448664i
$551$	1.65131e12	−	9.53383e11i	0.763213	−	0.440641i
$552$	−4.13190e11	−	4.13190e11i	−0.189419	−	0.189419i
$553$	4.38490e11	+	8.36750e11i	0.199387	+	0.380481i
$554$			7.53536e10i			0.0339868i
$555$	−1.07483e11	+	8.61235e10i	−0.0480864	+	0.0385304i
$556$	2.08817e12	+	1.20561e12i	0.926681	+	0.535019i
$557$	4.72757e11	+	1.76435e12i	0.208109	+	0.776672i	0.988480	+	0.151355i	$0.0483636\pi$
$557$	4.72757e11	+	1.76435e12i	0.208109	+	0.776672i	−0.780371	+	0.625317i	$0.784970\pi$
$558$	−7.99626e11	−	2.14259e11i	−0.349167	−	0.0935590i
$559$	1.20262e12			0.520923
$560$	−1.61969e12	−	7.08954e11i	−0.695963	−	0.304629i
$561$	2.46414e12			1.05035
$562$	4.28445e10	+	1.14802e10i	0.0181168	+	0.00485439i
$563$	−3.52630e11	−	1.31603e12i	−0.147921	−	0.552050i	−0.999608	−	0.0279988i	$-0.991087\pi$
$563$	−3.52630e11	−	1.31603e12i	−0.147921	−	0.552050i	0.851686	−	0.524052i	$-0.175580\pi$
$564$	1.68936e11	+	9.75352e10i	0.0703017	+	0.0405887i
$565$	−1.31010e11	+	1.18748e12i	−0.0540861	+	0.490241i
$566$			7.74844e11i			0.317351i
$567$	−1.05906e12	−	6.70640e11i	−0.430324	−	0.272499i
$568$	−1.25349e12	−	1.25349e12i	−0.505304	−	0.505304i
$569$	−7.70812e11	+	4.45028e11i	−0.308278	+	0.177985i	−0.646156	−	0.763205i	$-0.723624\pi$
$569$	−7.70812e11	+	4.45028e11i	−0.308278	+	0.177985i	0.337877	+	0.941190i	$0.390291\pi$
$570$	2.88152e11	+	1.12321e11i	0.114336	+	0.0445681i
$571$	−9.51420e11	+	1.64791e12i	−0.374550	+	0.648739i	−0.990260	−	0.139234i	$-0.955536\pi$
$571$	−9.51420e11	+	1.64791e12i	−0.374550	+	0.648739i	0.615710	+	0.787973i	$0.288869\pi$
$572$	9.35066e11	−	3.48971e12i	0.365225	−	1.36304i
$573$	1.15135e12	−	1.15135e12i	0.446181	−	0.446181i
$574$	3.02260e11	+	9.43966e10i	0.116219	+	0.0362955i
$575$	−2.71409e12	−	1.41838e12i	−1.03543	−	0.541111i
$576$	−5.88606e11	−	1.01950e12i	−0.222804	−	0.385909i
$577$	−3.42904e12	+	9.18808e11i	−1.28790	+	0.345091i	−0.836862	−	0.547415i	$-0.815612\pi$
$577$	−3.42904e12	+	9.18808e11i	−1.28790	+	0.345091i	−0.451036	+	0.892506i	$0.648945\pi$
$578$	−6.34627e11	+	1.70048e11i	−0.236507	+	0.0633717i
$579$	−4.16876e11	−	7.22050e11i	−0.154153	−	0.267002i
$580$	−2.12277e12	+	3.24992e11i	−0.778893	+	0.119247i
$581$	2.69738e12	+	2.92760e12i	0.982086	+	1.06591i
$582$	−9.16477e10	+	9.16477e10i	−0.0331107	+	0.0331107i
$583$	−1.43104e12	+	5.34073e12i	−0.513032	+	1.91466i
$584$	−6.16661e11	+	1.06809e12i	−0.219376	+	0.379970i
$585$	−1.77993e12	+	7.81493e11i	−0.628350	+	0.275882i
$586$	7.96618e11	−	4.59928e11i	0.279069	−	0.161120i
$587$	3.16164e11	+	3.16164e11i	0.109911	+	0.109911i	0.759923	−	0.650013i	$-0.225236\pi$
$587$	3.16164e11	+	3.16164e11i	0.109911	+	0.109911i	−0.650013	+	0.759923i	$0.725236\pi$
$588$	−3.73360e11	+	1.04348e12i	−0.128804	+	0.359985i
$589$		−	4.56927e12i		−	1.56433i
$590$	−5.69586e11	−	6.28399e10i	−0.193520	−	0.0213502i
$591$	−1.72315e12	−	9.94863e11i	−0.581005	−	0.335444i
$592$	−8.69035e10	−	3.24328e11i	−0.0290797	−	0.108527i
$593$	1.26302e12	+	3.38426e11i	0.419436	+	0.112388i	0.462363	−	0.886691i	$-0.347002\pi$
$593$	1.26302e12	+	3.38426e11i	0.419436	+	0.112388i	−0.0429271	+	0.999078i	$0.513668\pi$
$594$	1.22703e12			0.404406
$595$	2.59874e12	−	3.25079e12i	0.850033	−	1.06332i
$596$	3.18909e12			1.03528
$597$	5.01261e11	+	1.34313e11i	0.161503	+	0.0432745i
$598$	−2.25341e11	−	8.40985e11i	−0.0720586	−	0.268926i
$599$	2.94190e12	+	1.69851e12i	0.933701	+	0.539072i	0.887980	−	0.459882i	$-0.152108\pi$
$599$	2.94190e12	+	1.69851e12i	0.933701	+	0.539072i	0.0457205	+	0.998954i	$0.485442\pi$
$600$	−5.35874e11	−	4.92614e11i	−0.168804	−	0.155177i
$601$			5.86013e12i			1.83220i	0.400954	+	0.916098i	$0.368679\pi$
$601$			5.86013e12i			1.83220i	−0.400954	+	0.916098i	$0.631321\pi$
$602$	−5.13842e11	+	2.69273e11i	−0.159458	+	0.0835620i
$603$	−5.19726e11	−	5.19726e11i	−0.160084	−	0.160084i
$604$	4.43598e12	−	2.56111e12i	1.35620	−	0.783001i
$605$	−2.90738e12	+	7.45868e12i	−0.882271	+	2.26341i
$606$	−1.80574e11	+	3.12764e11i	−0.0543912	+	0.0942084i
$607$	9.99843e11	−	3.73146e12i	0.298939	−	1.11566i	−0.639099	−	0.769124i	$-0.720693\pi$
$607$	9.99843e11	−	3.73146e12i	0.298939	−	1.11566i	0.938038	−	0.346532i	$-0.112641\pi$
$608$	−1.87883e12	+	1.87883e12i	−0.557598	+	0.557598i
$609$	2.66090e11	+	1.18495e12i	0.0783883	+	0.349078i
$610$	−2.06847e11	−	1.51920e11i	−0.0604873	−	0.0444254i
$611$	3.03693e11	+	5.26012e11i	0.0881555	+	0.152690i
$612$	3.46061e12	−	9.27267e11i	0.997174	−	0.267192i
$613$	−7.47647e10	+	2.00332e10i	−0.0213858	+	0.00573030i	−0.269496	−	0.963001i	$-0.586857\pi$
$613$	−7.47647e10	+	2.00332e10i	−0.0213858	+	0.00573030i	0.248110	+	0.968732i	$0.420190\pi$
$614$	3.72190e10	+	6.44652e10i	0.0105684	+	0.0183049i
$615$	−5.05435e11	−	3.71221e11i	−0.142471	−	0.104639i
$616$	7.97955e11	+	3.55344e12i	0.223288	+	0.994343i
$617$	−3.09216e12	+	3.09216e12i	−0.858971	+	0.858971i	−0.991217	−	0.132246i	$-0.957781\pi$
$617$	−3.09216e12	+	3.09216e12i	−0.858971	+	0.858971i	0.132246	+	0.991217i	$0.457781\pi$
$618$	1.65188e11	−	6.16491e11i	0.0455545	−	0.170012i
$619$	4.24866e9	−	7.35889e9i	0.00116317	−	0.00201467i	−0.865443	−	0.501007i	$-0.832963\pi$
$619$	4.24866e9	−	7.35889e9i	0.00116317	−	0.00201467i	0.866606	+	0.498992i	$0.166296\pi$
$620$	−1.86899e12	+	4.79478e12i	−0.507979	+	1.30318i
$621$	−2.85339e12	+	1.64741e12i	−0.769926	+	0.444517i
$622$	3.04460e10	+	3.04460e10i	0.00815593	+	0.00815593i
$623$	−1.37497e12	+	7.20536e11i	−0.365676	+	0.191628i
$624$			9.95493e11i			0.262850i
$625$	−3.45212e12	−	1.62319e12i	−0.904954	−	0.425510i
$626$	2.86009e11	+	1.65127e11i	0.0744380	+	0.0429768i
$627$	7.93144e11	+	2.96005e12i	0.204950	+	0.764884i
$628$	3.79334e11	+	1.01642e11i	0.0973203	+	0.0260769i
$629$	7.90375e11			0.201328
$630$	5.85530e11	−	7.32446e11i	0.148087	−	0.185244i
$631$	−2.06194e12			−0.517778			−0.258889	−	0.965907i	$-0.583356\pi$
$631$	−2.06194e12			−0.517778			−0.258889	+	0.965907i	$0.583356\pi$
$632$	−9.15821e11	−	2.45393e11i	−0.228341	−	0.0611837i
$633$	3.48608e11	+	1.30102e12i	0.0863018	+	0.322083i
$634$	−8.76957e11	−	5.06311e11i	−0.215564	−	0.124456i
$635$	3.29798e12	+	3.63851e11i	0.804944	+	0.0888060i
$636$		−	1.68868e12i		−	0.409252i
$637$	−2.63130e12	+	2.23250e12i	−0.633203	+	0.537234i
$638$	1.35041e12	+	1.35041e12i	0.322679	+	0.322679i
$639$	−3.91677e12	+	2.26135e12i	−0.929338	+	0.536554i
$640$	3.58735e12	−	1.57505e12i	0.845208	−	0.371096i
$641$	1.86433e12	−	3.22912e12i	0.436176	−	0.755479i	−0.561215	−	0.827670i	$-0.689666\pi$
$641$	1.86433e12	−	3.22912e12i	0.436176	−	0.755479i	0.997391	+	0.0721909i	$0.0229991\pi$
$642$	−7.37424e10	+	2.75210e11i	−0.0171321	+	0.0639377i
$643$	5.07481e12	−	5.07481e12i	1.17077	−	1.17077i	0.188741	−	0.982027i	$-0.439559\pi$
$643$	5.07481e12	−	5.07481e12i	1.17077	−	1.17077i	0.982027	−	0.188741i	$-0.0604405\pi$
$644$	−3.17092e12	−	3.44155e12i	−0.726438	−	0.788439i
$645$	1.13565e12	−	1.73865e11i	0.258360	−	0.0395542i
$646$	−8.87375e11	−	1.53698e12i	−0.200475	−	0.347233i
$647$	5.42252e12	−	1.45296e12i	1.21655	−	0.325975i	0.407224	−	0.913328i	$-0.366497\pi$
$647$	5.42252e12	−	1.45296e12i	1.21655	−	0.325975i	0.809331	+	0.587353i	$0.199830\pi$
$648$	1.21524e12	−	3.25623e11i	0.270754	−	0.0725484i
$649$	−2.83907e12	−	4.91741e12i	−0.628166	−	1.08802i
$650$	−3.24477e11	−	1.03487e12i	−0.0712975	−	0.227392i
$651$	2.77794e12	+	8.67557e11i	0.606190	+	0.189314i
$652$	−1.04882e12	+	1.04882e12i	−0.227293	+	0.227293i
$653$	7.50260e11	−	2.80001e12i	0.161474	−	0.602629i	−0.836990	−	0.547219i	$-0.815687\pi$
$653$	7.50260e11	−	2.80001e12i	0.161474	−	0.602629i	0.998464	−	0.0554104i	$-0.0176467\pi$
$654$	−3.39098e10	+	5.87335e10i	−0.00724812	+	0.0125541i
$655$	−1.62296e12	−	6.32626e11i	−0.344526	−	0.134295i
$656$	1.32399e12	−	7.64405e11i	0.279137	−	0.161160i
$657$	2.22496e12	+	2.22496e12i	0.465885	+	0.465885i
$658$	−2.47536e11	−	1.56750e11i	−0.0514781	−	0.0325981i
$659$			5.11092e12i			1.05564i	0.849357	+	0.527819i	$0.176990\pi$
$659$			5.11092e12i			1.05564i	−0.849357	+	0.527819i	$0.823010\pi$
$660$	3.78480e11	−	3.43057e12i	0.0776417	−	0.703750i
$661$	−4.61705e12	−	2.66566e12i	−0.940715	−	0.543122i	−0.0505308	−	0.998723i	$-0.516091\pi$
$661$	−4.61705e12	−	2.66566e12i	−0.940715	−	0.543122i	−0.890184	+	0.455600i	$0.849425\pi$
$662$	−2.96606e11	−	1.10695e12i	−0.0600232	−	0.224010i
$663$	−2.26346e12	−	6.06493e11i	−0.454949	−	0.121903i
$664$	−3.99531e12			−0.797617
$665$	4.74149e12	+	2.07539e12i	0.940193	+	0.411531i
$666$	1.78082e11			0.0350741
$667$	−4.95332e12	−	1.32724e12i	−0.969015	−	0.259647i
$668$	−1.85862e12	−	6.93645e12i	−0.361157	−	1.34786i
$669$	−2.22657e12	−	1.28551e12i	−0.429754	−	0.248118i
$670$	3.20010e11	−	2.56416e11i	0.0613518	−	0.0491595i
$671$		−	2.54301e12i		−	0.484279i
$672$	−7.85527e11	−	1.49899e12i	−0.148593	−	0.283554i
$673$	−2.87257e12	−	2.87257e12i	−0.539763	−	0.539763i	0.383696	−	0.923459i	$-0.374651\pi$
$673$	−2.87257e12	−	2.87257e12i	−0.539763	−	0.539763i	−0.923459	+	0.383696i	$0.874651\pi$
$674$	2.27655e12	−	1.31436e12i	0.424920	−	0.245327i
$675$	−3.46500e12	+	2.19968e12i	−0.642446	+	0.407843i
$676$	7.73343e11	−	1.33947e12i	0.142434	−	0.246702i
$677$	9.31586e11	−	3.47673e12i	0.170441	−	0.636094i	−0.826842	−	0.562434i	$-0.809865\pi$
$677$	9.31586e11	−	3.47673e12i	0.170441	−	0.636094i	0.997283	−	0.0736605i	$-0.0234681\pi$
$678$	−2.29443e11	+	2.29443e11i	−0.0417004	+	0.0417004i
$679$	−1.59522e12	+	1.46977e12i	−0.288009	+	0.265361i
$680$	6.32130e11	+	4.12893e12i	0.113375	+	0.740538i
$681$	7.77531e11	+	1.34672e12i	0.138534	+	0.239948i
$682$	4.42051e12	−	1.18447e12i	0.782424	−	0.209650i
$683$	1.49400e12	−	4.00316e11i	0.262698	−	0.0703897i	−0.125066	−	0.992148i	$-0.539914\pi$
$683$	1.49400e12	−	4.00316e11i	0.262698	−	0.0703897i	0.387764	+	0.921759i	$0.373248\pi$
$684$	2.22776e12	+	3.85860e12i	0.389150	+	0.674027i
$685$	4.95678e12	−	6.74889e12i	0.860186	−	1.17118i
$686$	6.24406e11	−	1.54304e12i	0.107649	−	0.266023i
$687$	2.56077e12	−	2.56077e12i	0.438597	−	0.438597i
$688$	−7.24901e11	+	2.70537e12i	−0.123348	+	0.460340i
$689$	2.62900e12	−	4.55357e12i	0.444431	−	0.769778i
$690$	−3.34376e11	−	7.61576e11i	−0.0561584	−	0.127906i
$691$	−3.23684e12	+	1.86879e12i	−0.540095	+	0.311824i	−0.745117	−	0.666933i	$-0.767607\pi$
$691$	−3.23684e12	+	1.86879e12i	−0.540095	+	0.311824i	0.205023	+	0.978757i	$0.434273\pi$
$692$	−9.82720e10	−	9.82720e10i	−0.0162912	−	0.0162912i
$693$	9.28389e12	+	3.79973e11i	1.52908	+	0.0625826i
$694$			2.95547e12i			0.483625i
$695$	4.48483e12	+	5.59713e12i	0.729146	+	0.909984i
$696$	−1.05559e12	−	6.09444e11i	−0.170511	−	0.0984446i
$697$	9.31412e11	+	3.47608e12i	0.149484	+	0.557881i
$698$	5.50960e11	+	1.47629e11i	0.0878559	+	0.0235409i
$699$	1.50915e12			0.239104
$700$	−4.12659e12	−	4.11726e12i	−0.649606	−	0.648137i
$701$	−6.73685e12			−1.05372			−0.526860	−	0.849952i	$-0.676631\pi$
$701$	−6.73685e12			−1.05372			−0.526860	+	0.849952i	$0.676631\pi$
$702$	−1.12711e12	−	3.02007e11i	−0.175165	−	0.0469354i
$703$	2.54402e11	+	9.49439e11i	0.0392845	+	0.146612i
$704$	5.63600e12	+	3.25394e12i	0.864756	+	0.499267i
$705$	3.62828e11	+	4.52815e11i	0.0553159	+	0.0690351i
$706$			3.74633e11i			0.0567526i
$707$	−3.23354e12	+	5.10633e12i	−0.486733	+	0.768637i
$708$	1.22626e12	+	1.22626e12i	0.183414	+	0.183414i
$709$	2.63583e12	−	1.52180e12i	0.391750	−	0.226177i	−0.291168	−	0.956672i	$-0.594044\pi$
$709$	2.63583e12	−	1.52180e12i	0.391750	−	0.226177i	0.682918	+	0.730495i	$0.260711\pi$
$710$	−1.01439e12	−	2.31038e12i	−0.149811	−	0.341210i
$711$	−1.20948e12	+	2.09488e12i	−0.177495	+	0.307430i
$712$	4.03236e11	−	1.50490e12i	0.0588030	−	0.219456i
$713$	−8.68934e12	+	8.68934e12i	−1.25917	+	1.25917i
$714$	1.10291e12	−	2.47667e11i	0.158817	−	0.0356637i
$715$	6.36142e12	−	8.66138e12i	0.910284	−	1.23940i
$716$	1.25792e12	+	2.17877e12i	0.178872	+	0.309816i
$717$	6.81860e11	−	1.82704e11i	0.0963516	−	0.0258173i
$718$	1.20610e12	−	3.23173e11i	0.169365	−	0.0453811i
$719$	1.18211e12	+	2.04747e12i	0.164959	+	0.285718i	0.936641	−	0.350291i	$-0.113917\pi$
$719$	1.18211e12	+	2.04747e12i	0.164959	+	0.285718i	−0.771681	+	0.636009i	$0.780584\pi$
$720$	−6.85134e11	−	4.47514e12i	−0.0950122	−	0.620598i
$721$	3.18413e12	−	1.01957e13i	0.438815	−	1.40510i
$722$	7.90045e10	−	7.90045e10i	0.0108202	−	0.0108202i
$723$	−9.98366e11	+	3.72595e12i	−0.135884	+	0.507125i
$724$	−5.60624e12	+	9.71030e12i	−0.758313	+	1.31344i
$725$	−6.23423e12	−	1.39254e12i	−0.838035	−	0.187192i
$726$	−1.88297e12	+	1.08713e12i	−0.251552	+	0.145234i
$727$	−4.39801e12	−	4.39801e12i	−0.583917	−	0.583917i	0.352060	−	0.935977i	$-0.385481\pi$
$727$	−4.39801e12	−	4.39801e12i	−0.583917	−	0.583917i	−0.935977	+	0.352060i	$0.885481\pi$
$728$	1.41630e11	−	3.46045e12i	0.0186881	−	0.456606i
$729$		−	7.92072e11i		−	0.103870i
$730$	−1.36997e12	+	1.09772e12i	−0.178550	+	0.143067i
$731$	−5.70959e12	−	3.29644e12i	−0.739566	−	0.426989i
$732$	2.01018e11	+	7.50208e11i	0.0258782	+	0.0965788i
$733$	7.58215e12	+	2.03163e12i	0.970118	+	0.259942i	0.708878	−	0.705331i	$-0.249202\pi$
$733$	7.58215e12	+	2.03163e12i	0.970118	+	0.259942i	0.261240	+	0.965274i	$0.415868\pi$
$734$	−2.11529e10			−0.00268991
$735$	−2.16202e12	+	2.48859e12i	−0.273254	+	0.314529i
$736$	7.14591e12			0.897651
$737$	3.92481e12	+	1.05165e12i	0.490021	+	0.131301i
$738$	2.09860e11	+	7.83207e11i	0.0260420	+	0.0971902i
$739$	−1.17477e13	−	6.78251e12i	−1.44894	−	0.836548i	−0.450525	−	0.892764i	$-0.648763\pi$
$739$	−1.17477e13	−	6.78251e12i	−1.44894	−	0.836548i	−0.998419	+	0.0562162i	$0.982096\pi$
$740$	1.21398e11	−	1.10036e12i	0.0148822	−	0.134893i
$741$		−	2.91421e12i		−	0.355090i
$742$	−1.03723e11	+	2.53425e12i	−0.0125619	+	0.306925i
$743$	−7.53425e12	−	7.53425e12i	−0.906965	−	0.906965i	0.0890612	−	0.996026i	$-0.471613\pi$
$743$	−7.53425e12	−	7.53425e12i	−0.906965	−	0.906965i	−0.996026	+	0.0890612i	$0.971613\pi$
$744$	−2.52955e12	+	1.46044e12i	−0.302667	+	0.174745i
$745$	8.83838e12	+	3.44518e12i	1.05116	+	0.409741i
$746$	2.07657e12	−	3.59672e12i	0.245483	−	0.425189i
$747$	−2.63820e12	+	9.84591e12i	−0.310003	+	1.15695i
$748$	−1.40049e13	+	1.40049e13i	−1.63577	+	1.63577i
$749$	−1.42144e12	+	4.55149e12i	−0.165029	+	0.528427i
$750$	−4.56022e11	−	9.30330e11i	−0.0526272	−	0.107365i
$751$	1.29672e12	+	2.24599e12i	0.148754	+	0.257649i	0.930767	−	0.365613i	$-0.119141\pi$
$751$	1.29672e12	+	2.24599e12i	0.148754	+	0.257649i	−0.782013	+	0.623262i	$0.785807\pi$
$752$	−1.36636e12	+	3.66115e11i	−0.155806	+	0.0417481i
$753$	−4.44206e12	+	1.19025e12i	−0.503509	+	0.134915i
$754$	−9.08058e11	−	1.57280e12i	−0.102316	−	0.177216i
$755$	1.50608e13	−	2.30578e12i	1.68689	−	0.258259i
$756$	−6.11936e12	+	1.37415e12i	−0.681331	+	0.152998i
$757$	1.03813e13	−	1.03813e13i	1.14900	−	1.14900i	0.162248	−	0.986750i	$-0.448125\pi$
$757$	1.03813e13	−	1.03813e13i	1.14900	−	1.14900i	0.986750	−	0.162248i	$-0.0518746\pi$
$758$	−1.05265e12	+	3.92855e12i	−0.115817	+	0.432236i
$759$	4.12080e12	−	7.13743e12i	0.450706	−	0.780646i
$760$	−4.75642e12	+	2.08834e12i	−0.517153	+	0.227060i
$761$	−5.08472e12	+	2.93567e12i	−0.549587	+	0.317304i	−0.748955	−	0.662621i	$-0.769444\pi$
$761$	−5.08472e12	+	2.93567e12i	−0.549587	+	0.317304i	0.199369	+	0.979925i	$0.436111\pi$
$762$	6.37228e11	+	6.37228e11i	0.0684695	+	0.0684695i
$763$	−6.07222e11	+	9.58910e11i	−0.0648616	+	0.102428i
$764$			1.30873e13i			1.38973i
$765$	1.05926e13	+	1.16864e12i	1.11822	+	0.123368i
$766$	3.86810e11	+	2.23325e11i	0.0405946	+	0.0234373i
$767$	1.39755e12	+	5.21571e12i	0.145810	+	0.544170i
$768$	−1.06433e12	−	2.85188e11i	−0.110396	−	0.0295805i
$769$	7.42780e12			0.765934			0.382967	−	0.923762i	$-0.374902\pi$
$769$	7.42780e12			0.765934			0.382967	+	0.923762i	$0.374902\pi$
$770$	−7.78709e11	+	5.12511e12i	−0.0798302	+	0.525406i
$771$	−2.79682e12			−0.285049
$772$	6.47305e12	+	1.73445e12i	0.655890	+	0.175745i
$773$	4.82352e12	+	1.80016e13i	0.485911	+	1.81344i	0.575925	+	0.817503i	$0.304642\pi$
$773$	4.82352e12	+	1.80016e13i	0.485911	+	1.81344i	−0.0900138	+	0.995941i	$0.528691\pi$
$774$	−1.28645e12	−	7.42731e11i	−0.128842	−	0.0743870i
$775$	−1.03596e13	+	1.12694e13i	−1.03154	+	1.12213i
$776$		−	2.17700e12i		−	0.215517i
$777$	−6.25526e11	−	2.56017e10i	−0.0615674	−	0.00251984i
$778$	−8.31905e10	−	8.31905e10i	−0.00814077	−	0.00814077i
$779$	−3.87585e12	+	2.23772e12i	−0.377093	+	0.217715i
$780$	−1.19202e12	+	3.05803e12i	−0.115307	+	0.295813i
$781$	1.25012e13	−	2.16527e13i	1.20233	−	2.08249i
$782$	−1.23535e12	+	4.61038e12i	−0.118130	+	0.440865i
$783$	−4.85976e12	+	4.85976e12i	−0.462048	+	0.462048i
$784$	−3.43609e12	−	7.26498e12i	−0.324820	−	0.686772i
$785$	9.41498e11	+	6.91491e11i	0.0884924	+	0.0649940i
$786$	−2.36553e11	−	4.09722e11i	−0.0221068	−	0.0382902i
$787$	1.22263e13	−	3.27604e12i	1.13608	−	0.304412i	0.358708	−	0.933450i	$-0.383217\pi$
$787$	1.22263e13	−	3.27604e12i	1.13608	−	0.304412i	0.777375	+	0.629038i	$0.216551\pi$
$788$	1.54478e13	−	4.13921e12i	1.42724	−	0.382428i
$789$	3.45684e12	+	5.98742e12i	0.317565	+	0.550038i
$790$	−1.08771e12	−	7.98879e11i	−0.0993556	−	0.0729725i
$791$	−3.99368e12	+	3.67962e12i	−0.362726	+	0.334202i
$792$	−6.59416e12	+	6.59416e12i	−0.595520	+	0.595520i
$793$	−6.25905e11	+	2.33591e12i	−0.0562055	+	0.209762i
$794$	8.68597e11	−	1.50445e12i	0.0775579	−	0.134334i
$795$	1.82428e12	−	4.68008e12i	0.161972	−	0.415529i
$796$	−3.61226e12	+	2.08554e12i	−0.318912	+	0.184124i
$797$	−1.26672e13	−	1.26672e13i	−1.11204	−	1.11204i	−0.992875	−	0.119162i	$-0.961979\pi$
$797$	−1.26672e13	−	1.26672e13i	−1.11204	−	1.11204i	−0.119162	−	0.992875i	$-0.538021\pi$
$798$	6.52509e11	+	1.24515e12i	0.0569605	+	0.108695i
$799$		−	3.32976e12i		−	0.289036i
$800$	8.89358e12	−	3.74078e11i	0.767665	−	0.0322892i
$801$	−3.44235e12	−	1.98744e12i	−0.295467	−	0.170588i
$802$	3.04267e11	+	1.13554e12i	0.0259699	+	0.0969210i
$803$	−1.68022e13	−	4.50214e12i	−1.42609	−	0.382119i
$804$	−1.24098e12			−0.104740
$805$	−5.07009e12	−	1.29636e13i	−0.425534	−	1.08804i
$806$	−4.35204e12			−0.363233
$807$	7.46988e11	+	2.00155e11i	0.0619987	+	0.0166125i
$808$	−1.57002e12	−	5.85938e12i	−0.129585	−	0.483616i
$809$	−7.69845e12	−	4.44470e12i	−0.631880	−	0.364816i	0.149600	−	0.988747i	$-0.452202\pi$
$809$	−7.69845e12	−	4.44470e12i	−0.631880	−	0.364816i	−0.781480	+	0.623930i	$0.785535\pi$
$810$	1.78000e12	+	1.96379e11i	0.145290	+	0.0160292i
$811$			1.87779e13i			1.52424i	0.647435	+	0.762121i	$0.275842\pi$
$811$			1.87779e13i			1.52424i	−0.647435	+	0.762121i	$0.724158\pi$
$812$	−8.24694e12	−	5.22231e12i	−0.665718	−	0.421561i
$813$	1.50934e12	+	1.50934e12i	0.121166	+	0.121166i
$814$	−8.52581e11	+	4.92238e11i	−0.0680653	+	0.0392975i
$815$	−4.03979e12	+	1.77370e12i	−0.320737	+	0.140822i
$816$	2.72870e12	−	4.72625e12i	0.215452	−	0.373174i
$817$	2.12208e12	−	7.91970e12i	0.166633	−	0.621884i
$818$	1.80126e12	−	1.80126e12i	0.140665	−	0.140665i
$819$	−8.43431e12	−	2.63405e12i	−0.655046	−	0.204572i
$820$	4.98244e12	−	7.62801e11i	0.384840	−	0.0589181i
$821$	4.66957e12	+	8.08794e12i	0.358701	+	0.621289i	0.987744	−	0.156082i	$-0.0498863\pi$
$821$	4.66957e12	+	8.08794e12i	0.358701	+	0.621289i	−0.629043	+	0.777371i	$0.716553\pi$
$822$	2.19680e12	−	5.88632e11i	0.167829	−	0.0449698i
$823$	1.30472e13	−	3.49600e12i	0.991332	−	0.265627i	0.273522	−	0.961866i	$-0.411811\pi$
$823$	1.30472e13	−	3.49600e12i	0.991332	−	0.265627i	0.717810	+	0.696239i	$0.245145\pi$
$824$	5.36013e12	+	9.28401e12i	0.405044	+	0.701557i
$825$	4.75499e12	−	9.09875e12i	0.357360	−	0.683815i
$826$	−1.76496e12	−	1.91560e12i	−0.131924	−	0.143184i
$827$	1.44832e13	−	1.44832e13i	1.07668	−	1.07668i	0.0798805	−	0.996804i	$-0.474546\pi$
$827$	1.44832e13	−	1.44832e13i	1.07668	−	1.07668i	0.996804	−	0.0798805i	$-0.0254539\pi$
$828$	3.10135e12	−	1.15744e13i	0.229305	−	0.855779i
$829$	−1.25767e13	+	2.17835e13i	−0.924851	+	1.60189i	−0.133050	+	0.991109i	$0.542477\pi$
$829$	−1.25767e13	+	2.17835e13i	−0.924851	+	1.60189i	−0.791801	+	0.610779i	$0.790856\pi$
$830$	−5.29862e12	−	2.06539e12i	−0.387535	−	0.151060i
$831$	5.87443e11	−	3.39161e11i	0.0427328	−	0.0246718i
$832$	−4.37612e12	−	4.37612e12i	−0.316617	−	0.316617i
$833$	1.86119e13	−	3.38658e12i	1.33933	−	0.243702i
$834$			1.94801e12i			0.139426i
$835$	2.34242e12	−	2.12318e13i	0.166754	−	1.51147i
$836$	−2.13312e13	−	1.23156e13i	−1.51038	−	0.872019i
$837$	4.26260e12	+	1.59083e13i	0.300200	+	1.12036i
$838$	−7.30847e11	−	1.95830e11i	−0.0511951	−	0.0137177i
$839$	2.35415e13			1.64024			0.820118	−	0.572195i	$-0.193908\pi$
$839$	2.35415e13			1.64024			0.820118	+	0.572195i	$0.193908\pi$
$840$	−3.66542e11	−	3.28823e12i	−0.0254020	−	0.227880i
$841$	3.81040e12			0.262657
$842$	5.79273e12	+	1.55216e12i	0.397173	+	0.106422i
$843$	−1.03342e11	−	3.85679e11i	−0.00704782	−	0.0263028i
$844$	−9.37561e12	−	5.41301e12i	−0.636002	−	0.367196i
$845$	3.59031e12	−	2.87682e12i	0.242257	−	0.194114i
$846$		−	7.50240e11i		−	0.0503539i
$847$	−3.22302e13	+	1.68899e13i	−2.15173	+	1.12759i
$848$	8.65889e12	+	8.65889e12i	0.575017	+	0.575017i
$849$	6.04055e12	−	3.48751e12i	0.399017	−	0.230373i
$850$	−1.29613e12	+	5.80260e12i	−0.0851653	+	0.381274i
$851$	1.32175e12	−	2.28934e12i	0.0863905	−	0.149633i
$852$	−1.97637e12	+	7.37593e12i	−0.128496	+	0.479555i
$853$	1.53128e13	−	1.53128e13i	0.990342	−	0.990342i	−0.00961185	−	0.999954i	$-0.503060\pi$
$853$	1.53128e13	−	1.53128e13i	0.990342	−	0.990342i	0.999954	+	0.00961185i	$0.00305959\pi$
$854$	−2.55594e11	−	1.13821e12i	−0.0164433	−	0.0732253i
$855$	2.00566e12	+	1.31005e13i	0.128354	+	0.838382i
$856$	−2.39284e12	−	4.14451e12i	−0.152328	−	0.263841i
$857$	1.56156e13	−	4.18419e12i	0.988884	−	0.264971i	0.272103	−	0.962268i	$-0.412281\pi$
$857$	1.56156e13	−	4.18419e12i	0.988884	−	0.264971i	0.716782	+	0.697297i	$0.245614\pi$
$858$	2.81933e12	−	7.55437e11i	0.177604	−	0.0475889i
$859$	−1.13702e13	−	1.96938e13i	−0.712525	−	1.23413i	−0.963906	−	0.266241i	$-0.914218\pi$
$859$	−1.13702e13	−	1.96938e13i	−0.712525	−	1.23413i	0.251381	−	0.967888i	$-0.419115\pi$
$860$	−5.46625e12	+	7.44256e12i	−0.340759	+	0.463959i
$861$	−6.24550e11	−	2.78124e12i	−0.0387305	−	0.172474i
$862$	−2.80624e12	+	2.80624e12i	−0.173118	+	0.173118i
$863$	−5.82787e12	+	2.17499e13i	−0.357652	+	1.33478i	0.519461	+	0.854494i	$0.326133\pi$
$863$	−5.82787e12	+	2.17499e13i	−0.357652	+	1.33478i	−0.877114	+	0.480283i	$0.840534\pi$
$864$	4.78855e12	−	8.29401e12i	0.292343	−	0.506352i
$865$	−1.66192e11	−	3.78519e11i	−0.0100934	−	0.0229887i
$866$	2.91191e10	−	1.68119e10i	0.00175933	−	0.00101575i
$867$	4.18207e12	+	4.18207e12i	0.251365	+	0.251365i
$868$	−2.07191e13	+	1.08576e13i	−1.23889	+	0.649225i
$869$		−	1.33725e13i		−	0.795471i
$870$	−1.08488e12	−	1.35394e12i	−0.0642012	−	0.0801240i
$871$	−3.34634e12	−	1.93201e12i	−0.197010	−	0.113744i
$872$	−2.94831e11	−	1.10033e12i	−0.0172683	−	0.0644462i
$873$	−5.36493e12	−	1.43753e12i	−0.312608	−	0.0837630i
$874$	−5.93585e12			−0.344098
$875$	−6.98871e12	−	1.58687e13i	−0.403052	−	0.915177i
$876$	5.31268e12			0.304821
$877$	5.35580e11	+	1.43508e11i	0.0305722	+	0.00819179i	0.274073	−	0.961709i	$-0.411629\pi$
$877$	5.35580e11	+	1.43508e11i	0.0305722	+	0.00819179i	−0.243501	+	0.969901i	$0.578296\pi$
$878$	−1.92974e12	−	7.20189e12i	−0.109591	−	0.408998i
$879$	−7.17103e12	−	4.14019e12i	−0.405164	−	0.233922i
$880$	1.56499e13	+	1.95313e13i	0.879711	+	1.09789i
$881$		−	2.76382e13i		−	1.54568i	−0.634603	−	0.772839i	$-0.718836\pi$
$881$		−	2.76382e13i		−	1.54568i	0.634603	−	0.772839i	$-0.281164\pi$
$882$	4.19351e12	−	7.63041e11i	0.233329	−	0.0424560i
$883$	−4.14609e12	−	4.14609e12i	−0.229518	−	0.229518i	0.582974	−	0.812491i	$-0.301889\pi$
$883$	−4.14609e12	−	4.14609e12i	−0.229518	−	0.229518i	−0.812491	+	0.582974i	$0.801889\pi$
$884$	1.63113e13	−	9.41734e12i	0.898367	−	0.518672i
$885$	2.07377e12	+	4.72322e12i	0.113636	+	0.258818i
$886$	1.59111e12	−	2.75588e12i	0.0867456	−	0.150248i
$887$	1.77130e12	−	6.61057e12i	0.0960804	−	0.358577i	−0.901101	−	0.433610i	$-0.857240\pi$
$887$	1.77130e12	−	6.61057e12i	0.0960804	−	0.358577i	0.997181	+	0.0750330i	$0.0239062\pi$
$888$	4.44298e11	−	4.44298e11i	0.0239782	−	0.0239782i
$889$	1.02194e13	+	1.10916e13i	0.548739	+	0.595573i
$890$	1.31274e12	−	1.78735e12i	0.0701330	−	0.0954895i
$891$	8.87228e12	+	1.53672e13i	0.471613	+	0.816858i
$892$	1.99608e13	−	5.34849e12i	1.05569	−	0.282872i
$893$	3.99988e12	−	1.07177e12i	0.210482	−	0.0563986i
$894$	1.28823e12	+	2.23128e12i	0.0674488	+	0.116825i
$895$	1.13251e12	+	7.39727e12i	0.0589979	+	0.385361i
$896$	1.69989e13	+	5.30878e12i	0.881117	+	0.275175i
$897$	−5.54193e12	+	5.54193e12i	−0.285821	+	0.285821i
$898$	−1.97676e12	+	7.37737e12i	−0.101440	+	0.378580i
$899$	−1.28165e13	+	2.21989e13i	−0.654413	+	1.13348i
$900$	3.25394e12	−	1.45675e13i	0.165317	−	0.740105i
$901$	−2.49632e13	+	1.44125e13i	−1.26194	+	0.728580i
$902$	−3.16959e12	−	3.16959e12i	−0.159431	−	0.159431i
$903$	4.41196e12	+	2.79384e12i	0.220819	+	0.139832i
$904$		−	5.45019e12i		−	0.271427i
$905$	−2.60274e13	+	2.08551e13i	−1.28977	+	1.03346i
$906$	3.58381e12	+	2.06912e12i	0.176713	+	0.102025i
$907$	−6.33622e11	−	2.36471e12i	−0.0310883	−	0.116023i	0.948638	−	0.316363i	$-0.102462\pi$
$907$	−6.33622e11	−	2.36471e12i	−0.0310883	−	0.116023i	−0.979726	+	0.200340i	$0.935795\pi$
$908$	−1.20731e13	−	3.23498e12i	−0.589432	−	0.157938i
$909$	−1.54764e13			−0.751851
$910$	1.97673e12	−	4.51607e12i	0.0955565	−	0.218310i
$911$	−6.50713e12			−0.313009			−0.156505	−	0.987677i	$-0.550023\pi$
$911$	−6.50713e12			−0.313009			−0.156505	+	0.987677i	$0.550023\pi$
$912$	6.55572e12	+	1.75660e12i	0.313793	+	0.0840806i
$913$	−1.45846e13	−	5.44303e13i	−0.694664	−	2.59252i
$914$	−3.53834e12	−	2.04286e12i	−0.167703	−	0.0968236i
$915$	−2.53343e11	+	2.29632e12i	−0.0119485	+	0.108302i
$916$			2.91081e13i			1.36611i
$917$	−3.67513e12	−	7.01309e12i	−0.171637	−	0.327527i
$918$	4.52329e12	+	4.52329e12i	0.210214	+	0.210214i
$919$	1.31374e13	−	7.58490e12i	0.607562	−	0.350776i	−0.164449	−	0.986386i	$-0.552584\pi$
$919$	1.31374e13	−	7.58490e12i	0.607562	−	0.350776i	0.772011	+	0.635609i	$0.219251\pi$
$920$	1.30166e13	+	5.07386e12i	0.599037	+	0.233503i
$921$	3.35040e11	−	5.80306e11i	0.0153436	−	0.0265759i
$922$	1.13232e11	−	4.22588e11i	0.00516037	−	0.0192588i
$923$	−1.68125e13	+	1.68125e13i	−0.762472	+	0.762472i
$924$	1.15375e13	−	1.06302e13i	0.520700	−	0.479753i
$925$	1.52516e12	−	2.91843e12i	0.0684982	−	0.131072i
$926$	−1.29608e12	−	2.24487e12i	−0.0579270	−	0.100333i
$927$	2.64186e13	−	7.07885e12i	1.17504	−	0.314850i
$928$	1.43979e13	−	3.85791e12i	0.637286	−	0.170760i
$929$	1.98471e13	+	3.43762e13i	0.874233	+	1.51422i	0.857578	+	0.514354i	$0.171968\pi$
$929$	1.98471e13	+	3.43762e13i	0.874233	+	1.51422i	0.0166544	+	0.999861i	$0.494698\pi$
$930$	−4.10969e12	+	6.29184e11i	−0.180151	+	0.0275806i
$931$	1.00588e13	+	2.12675e13i	0.438807	+	0.927777i
$932$	−8.57722e12	+	8.57722e12i	−0.372370	+	0.372370i
$933$	1.00317e11	−	3.74387e11i	0.00433416	−	0.0161753i
$934$	6.62632e11	−	1.14771e12i	0.0284912	−	0.0493483i
$935$	−5.39431e13	+	2.36842e13i	−2.30826	+	1.01346i
$936$	7.68015e12	−	4.43414e12i	0.327061	−	0.188829i
$937$	−1.34462e13	−	1.34462e13i	−0.569863	−	0.569863i	0.362227	−	0.932090i	$-0.382016\pi$
$937$	−1.34462e13	−	1.34462e13i	−0.569863	−	0.569863i	−0.932090	+	0.362227i	$0.882016\pi$
$938$	1.86238e12	+	7.62239e10i	0.0785517	+	0.00321498i
$939$		−	2.97290e12i		−	0.124791i
$940$	−4.63568e12	−	5.11435e11i	−0.193659	−	0.0213656i
$941$	2.17510e13	+	1.25579e13i	0.904326	+	0.522113i	0.878601	−	0.477556i	$-0.158477\pi$
$941$	2.17510e13	+	1.25579e13i	0.904326	+	0.522113i	0.0257249	+	0.999669i	$0.491811\pi$
$942$	8.21165e10	+	3.06463e11i	0.00339783	+	0.0126809i
$943$	1.16261e13	+	3.11521e12i	0.478776	+	0.128288i
$944$	−1.25755e13			−0.515409
$945$	−1.84439e13	−	2.80237e12i	−0.752334	−	0.114310i
$946$	8.21196e12			0.333378
$947$	−4.49201e13	−	1.20363e13i	−1.81495	−	0.486315i	−0.818811	−	0.574063i	$-0.805366\pi$
$947$	−4.49201e13	−	1.20363e13i	−1.81495	−	0.486315i	−0.996143	+	0.0877476i	$0.972033\pi$
$948$	1.05706e12	+	3.94501e12i	0.0425072	+	0.158639i
$949$	1.43258e13	+	8.27099e12i	0.573350	+	0.331024i
$950$	−7.38758e12	+	3.10733e11i	−0.294270	+	0.0123775i
$951$			9.11546e12i			0.361382i
$952$	−1.01577e13	+	1.60408e13i	−0.400802	+	0.632936i
$953$	4.90434e12	+	4.90434e12i	0.192603	+	0.192603i	0.796820	−	0.604217i	$-0.206514\pi$
$953$	4.90434e12	+	4.90434e12i	0.192603	+	0.192603i	−0.604217	+	0.796820i	$0.706514\pi$
$954$	−5.62454e12	+	3.24733e12i	−0.219846	+	0.126928i
$955$	−1.41382e13	+	3.62707e13i	−0.550022	+	1.41104i
$956$	−2.83694e12	+	4.91372e12i	−0.109847	+	0.190261i
$957$	4.44945e12	−	1.66056e13i	0.171476	−	0.639956i
$958$	−2.56218e12	+	2.56218e12i	−0.0982798	+	0.0982798i
$959$	3.71369e13	−	8.33940e12i	1.41782	−	0.318384i
$960$	−4.76510e12	−	3.49977e12i	−0.181072	−	0.132990i
$961$	1.74930e13	+	3.02988e13i	0.661622	+	1.14596i
$962$	9.04302e11	−	2.42307e11i	0.0340428	−	0.00912175i
$963$	−1.17937e13	+	3.16010e12i	−0.441906	+	0.118408i
$964$	−1.55021e13	−	2.68505e13i	−0.578156	−	1.00140i
$965$	1.60659e13	+	1.17998e13i	0.596394	+	0.438027i
$966$	1.12703e12	−	3.60877e12i	0.0416426	−	0.133341i
$967$	−8.16941e12	+	8.16941e12i	−0.300450	+	0.300450i	−0.841190	−	0.540740i	$-0.818144\pi$
$967$	−8.16941e12	+	8.16941e12i	−0.300450	+	0.300450i	0.540740	+	0.841190i	$0.318144\pi$
$968$	9.45215e12	−	3.52759e13i	0.346012	−	1.29134i
$969$	−7.98800e12	+	1.38356e13i	−0.291059	+	0.504129i
$970$	1.12541e12	−	2.88716e12i	0.0408166	−	0.104712i
$971$	1.42976e13	−	8.25474e12i	0.516152	−	0.298000i	−0.219207	−	0.975678i	$-0.570347\pi$
$971$	1.42976e13	−	8.25474e12i	0.516152	−	0.298000i	0.735359	+	0.677678i	$0.237014\pi$
$972$	−1.75733e13	−	1.75733e13i	−0.631474	−	0.631474i
$973$	−1.33319e12	+	3.25739e13i	−0.0476854	+	1.16510i
$974$		−	1.30673e13i		−	0.465231i
$975$	−6.60720e12	+	7.18743e12i	−0.234151	+	0.254714i
$976$	−4.87751e12	−	2.81603e12i	−0.172058	−	0.0993376i
$977$	1.15642e13	+	4.31580e13i	0.406058	+	1.51543i	0.802096	+	0.597195i	$0.203718\pi$
$977$	1.15642e13	+	4.31580e13i	0.406058	+	1.51543i	−0.396038	+	0.918234i	$0.629615\pi$
$978$	−1.15749e12	−	3.10148e11i	−0.0404568	−	0.0108404i
$979$	2.19740e13			0.764518
$980$	−1.85609e12	−	2.64316e13i	−0.0642808	−	0.915389i
$981$	−2.90629e12			−0.100191
$982$	5.43048e12	+	1.45509e12i	0.186353	+	0.0499332i
$983$	−9.34229e12	−	3.48659e13i	−0.319126	−	1.19099i	−0.920086	−	0.391716i	$-0.871882\pi$
$983$	−9.34229e12	−	3.48659e13i	−0.319126	−	1.19099i	0.600960	−	0.799279i	$-0.294785\pi$
$984$	2.47761e12	+	1.43045e12i	0.0842471	+	0.0486401i
$985$	4.72841e13	+	5.21665e12i	1.60049	+	0.176575i
$986$			9.95615e12i			0.335464i
$987$	−1.07857e11	+	2.63527e12i	−0.00361760	+	0.0883889i
$988$	1.65628e13	+	1.65628e13i	0.553003	+	0.553003i
$989$	−1.90964e13	+	1.10253e13i	−0.634699	+	0.366444i
$990$	−1.21541e13	+	5.33636e12i	−0.402128	+	0.176558i
$991$	1.04843e13	−	1.81594e13i	0.345311	−	0.598096i	−0.640099	−	0.768292i	$-0.721107\pi$
$991$	1.04843e13	−	1.81594e13i	0.345311	−	0.598096i	0.985410	+	0.170196i	$0.0544402\pi$
$992$	9.24489e12	−	3.45024e13i	0.303109	−	1.13122i
$993$	−7.29457e12	+	7.29457e12i	−0.238083	+	0.238083i
$994$	3.41905e12	−	1.09479e13i	0.111088	−	0.355706i
$995$	−1.22642e13	+	1.87762e12i	−0.396675	+	0.0607301i
$996$	8.60514e12	+	1.49045e13i	0.277071	+	0.479901i
$997$	−2.68293e13	+	7.18889e12i	−0.859966	+	0.230427i	−0.661744	−	0.749730i	$-0.730183\pi$
$997$	−2.68293e13	+	7.18889e12i	−0.859966	+	0.230427i	−0.198222	+	0.980157i	$0.563517\pi$
$998$	−3.91033e12	+	1.04777e12i	−0.124775	+	0.0334333i
$999$	−1.77144e12	−	3.06822e12i	−0.0562705	−	0.0974634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.15	✓	136
5.2	odd	4	inner	35.10.k.a.17.20	yes	136
7.5	odd	6	inner	35.10.k.a.33.20	yes	136
35.12	even	12	inner	35.10.k.a.12.15	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.15	✓	136	1.1	even	1	trivial
35.10.k.a.12.15	yes	136	35.12	even	12	inner
35.10.k.a.17.20	yes	136	5.2	odd	4	inner
35.10.k.a.33.20	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+(-6.27232 - 1.68066i) q^{2} +(15.1291 + 56.4624i) q^{3} +(-406.888 - 234.917i) q^{4} +(-873.884 - 1090.62i) q^{5} -379.577i q^{6} +(259.777 - 6347.14i) q^{7} +(4508.24 + 4508.24i) q^{8} +(14086.9 - 8133.05i) q^{9} +(3648.32 + 8309.42i) q^{10} +(-44961.3 + 77875.2i) q^{11} +(7108.13 - 26527.9i) q^{12} +(60467.0 - 60467.0i) q^{13} +(-12296.8 + 39374.7i) q^{14} +(48358.0 - 65841.7i) q^{15} +(99577.0 + 172472. i) q^{16} +(-452819. + 121333. i) q^{17} +(-102026. + 27337.8i) q^{18} +(-291502. - 504896. i) q^{19} +(99368.0 + 649050. i) q^{20} +(362305. - 81358.5i) q^{21} +(412894. - 412894. i) q^{22} +(-405811. + 1.51451e6i) q^{23} +(-186341. + 322752. i) q^{24} +(-425777. + 1.90615e6i) q^{25} +(-480893. + 277644. i) q^{26} +(1.48590e6 + 1.48590e6i) q^{27} +(-1.59675e6 + 2.52154e6i) q^{28} +3.27059e6i q^{29} +(-413974. + 331706. i) q^{30} +(6.78743e6 + 3.91873e6i) q^{31} +(-1.17958e6 - 4.40225e6i) q^{32} +(-5.07724e6 - 1.36044e6i) q^{33} +3.04415e6 q^{34} +(-7.14932e6 + 5.26334e6i) q^{35} -7.64236e6 q^{36} +(-1.62853e6 - 436363. i) q^{37} +(979833. + 3.65679e6i) q^{38} +(4.32892e6 + 2.49930e6i) q^{39} +(977095. - 8.85646e6i) q^{40} -7.67652e6i q^{41} +(-2.40923e6 - 98605.4i) q^{42} +(9.94440e6 + 9.94440e6i) q^{43} +(3.65884e7 - 2.11243e7i) q^{44} +(-2.11804e7 - 8.25606e6i) q^{45} +(5.09075e6 - 8.81743e6i) q^{46} +(-1.83835e6 + 6.86081e6i) q^{47} +(-8.23170e6 + 8.23170e6i) q^{48} +(-4.02186e7 - 3.29768e6i) q^{49} +(5.87421e6 - 1.12404e7i) q^{50} +(-1.37015e7 - 2.37316e7i) q^{51} +(-3.88080e7 + 1.03986e7i) q^{52} +(5.93925e7 - 1.59142e7i) q^{53} +(-6.82273e6 - 1.18173e7i) q^{54} +(1.24223e8 - 1.90183e7i) q^{55} +(2.97856e7 - 2.74433e7i) q^{56} +(2.40975e7 - 2.40975e7i) q^{57} +(5.49676e6 - 2.05142e7i) q^{58} +(-3.15723e7 + 5.46849e7i) q^{59} +(-3.51436e7 + 1.54301e7i) q^{60} +(-2.44912e7 + 1.41400e7i) q^{61} +(-3.59869e7 - 3.59869e7i) q^{62} +(-4.79622e7 - 9.15240e7i) q^{63} -7.23721e7i q^{64} +(-1.18788e8 - 1.31053e7i) q^{65} +(2.95597e7 + 1.70663e7i) q^{66} +(-1.16951e7 - 4.36465e7i) q^{67} +(2.12750e8 + 5.70061e7i) q^{68} -9.16521e7 q^{69} +(5.36888e7 - 2.09978e7i) q^{70} -2.78044e8 q^{71} +(1.00173e8 + 2.68412e7i) q^{72} +(5.00668e7 + 1.86852e8i) q^{73} +(9.48128e6 + 5.47402e6i) q^{74} +(-1.14067e8 + 4.79786e6i) q^{75} +2.73915e8i q^{76} +(4.82605e8 + 3.05606e8i) q^{77} +(-2.29519e7 - 2.29519e7i) q^{78} +(-1.28788e8 + 7.43557e7i) q^{79} +(1.01083e8 - 2.59322e8i) q^{80} +(9.86658e7 - 1.70894e8i) q^{81} +(-1.29016e7 + 4.81496e7i) q^{82} +(-4.43112e8 + 4.43112e8i) q^{83} +(-1.66530e8 - 5.20076e7i) q^{84} +(5.28039e8 + 3.87823e8i) q^{85} +(-4.56613e7 - 7.90876e7i) q^{86} +(-1.84665e8 + 4.94809e7i) q^{87} +(-5.53777e8 + 1.48384e8i) q^{88} +(-1.22183e8 - 2.11627e8i) q^{89} +(1.18974e8 + 8.73817e7i) q^{90} +(-3.68084e8 - 3.99500e8i) q^{91} +(5.20902e8 - 5.20902e8i) q^{92} +(-1.18573e8 + 4.42521e8i) q^{93} +(2.30614e7 - 3.99436e7i) q^{94} +(-2.95911e8 + 7.59139e8i) q^{95} +(2.30715e8 - 1.33204e8i) q^{96} +(-2.41447e8 - 2.41447e8i) q^{97} +(2.46722e8 + 8.82781e7i) q^{98} +1.46269e9i 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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