LMFDB - Embedded newform 35.10.k.a.3.20

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			3.20
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.83230 + 1.02686i) q^{2} +(-48.4413 - 180.785i) q^{3} +(-429.773 - 248.130i) q^{4} +(-576.593 - 1273.05i) q^{5} -742.566i q^{6} +(-2972.03 - 5614.33i) q^{7} +(-2828.61 - 2828.61i) q^{8} +(-13290.8 + 7673.46i) q^{9} +(-902.428 - 5470.80i) q^{10} +(35259.1 - 61070.5i) q^{11} +(-24039.4 + 89716.4i) q^{12} +(-65429.6 + 65429.6i) q^{13} +(-5624.56 - 24567.6i) q^{14} +(-202219. + 165908. i) q^{15} +(119107. + 206299. i) q^{16} +(544191. - 145816. i) q^{17} +(-58814.0 + 15759.2i) q^{18} +(-53213.6 - 92168.7i) q^{19} +(-68078.0 + 690194. i) q^{20} +(-871020. + 809264. i) q^{21} +(197834. - 197834. i) q^{22} +(288387. - 1.07627e6i) q^{23} +(-374350. + 648393. i) q^{24} +(-1.28821e6 + 1.46807e6i) q^{25} +(-317933. + 183559. i) q^{26} +(-573854. - 573854. i) q^{27} +(-115784. + 3.15033e6i) q^{28} +1.13924e6i q^{29} +(-945327. + 428159. i) q^{30} +(-2.76455e6 - 1.59611e6i) q^{31} +(774708. + 2.89125e6i) q^{32} +(-1.27487e7 - 3.41599e6i) q^{33} +2.23524e6 q^{34} +(-5.43369e6 + 7.02073e6i) q^{35} +7.61605e6 q^{36} +(1.97235e7 + 5.28489e6i) q^{37} +(-109286. - 407861. i) q^{38} +(1.49982e7 + 8.65922e6i) q^{39} +(-1.97001e6 + 5.23193e6i) q^{40} -8.74475e6i q^{41} +(-4.16901e6 + 2.20693e6i) q^{42} +(-1.48042e7 - 1.48042e7i) q^{43} +(-3.03068e7 + 1.74976e7i) q^{44} +(1.74321e7 + 1.24955e7i) q^{45} +(2.21037e6 - 3.82847e6i) q^{46} +(1.08753e7 - 4.05873e7i) q^{47} +(3.15262e7 - 3.15262e7i) q^{48} +(-2.26877e7 + 3.33718e7i) q^{49} +(-6.44429e6 + 4.30327e6i) q^{50} +(-5.27227e7 - 9.13183e7i) q^{51} +(4.43549e7 - 1.18849e7i) q^{52} +(7.55777e7 - 2.02510e7i) q^{53} +(-1.60991e6 - 2.78845e6i) q^{54} +(-9.80762e7 - 9.67385e6i) q^{55} +(-7.47404e6 + 2.42874e7i) q^{56} +(-1.40850e7 + 1.40850e7i) q^{57} +(-1.16984e6 + 4.36592e6i) q^{58} +(4.14658e7 - 7.18208e7i) q^{59} +(1.28075e8 - 2.11264e7i) q^{60} +(5.36712e7 - 3.09871e7i) q^{61} +(-8.95560e6 - 8.95560e6i) q^{62} +(8.25820e7 + 5.18133e7i) q^{63} -1.10090e8i q^{64} +(1.21022e8 + 4.55691e7i) q^{65} +(-4.53489e7 - 2.61822e7i) q^{66} +(5.81183e7 + 2.16901e8i) q^{67} +(-2.70060e8 - 7.23623e7i) q^{68} -2.08544e8 q^{69} +(-2.80328e7 + 2.13259e7i) q^{70} +5.37375e7 q^{71} +(5.92997e7 + 1.58893e7i) q^{72} +(2.09181e7 + 7.80674e7i) q^{73} +(7.01594e7 + 4.05065e7i) q^{74} +(3.27808e8 + 1.61774e8i) q^{75} +5.28155e7i q^{76} +(-4.47661e8 - 1.64529e7i) q^{77} +(4.85858e7 + 4.85858e7i) q^{78} +(-4.74250e8 + 2.73808e8i) q^{79} +(1.93954e8 - 2.70580e8i) q^{80} +(-2.26983e8 + 3.93146e8i) q^{81} +(8.97965e6 - 3.35125e7i) q^{82} +(-3.04700e8 + 3.04700e8i) q^{83} +(5.75143e8 - 1.31674e8i) q^{84} +(-4.99408e8 - 6.08708e8i) q^{85} +(-4.15322e7 - 7.19359e7i) q^{86} +(2.05958e8 - 5.51864e7i) q^{87} +(-2.72479e8 + 7.30104e7i) q^{88} +(-1.16048e8 - 2.01000e8i) q^{89} +(5.39740e7 + 6.57867e7i) q^{90} +(5.61802e8 + 1.72885e8i) q^{91} +(-3.90996e8 + 3.90996e8i) q^{92} +(-1.54636e8 + 5.77108e8i) q^{93} +(8.33551e7 - 1.44375e8i) q^{94} +(-8.66530e7 + 1.20888e8i) q^{95} +(4.85168e8 - 2.80112e8i) q^{96} +(4.76658e8 + 4.76658e8i) q^{97} +(-1.21214e8 + 1.04594e8i) q^{98} +1.08224e9i 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 $

$2$	3.83230	+	1.02686i	0.169365	+	0.0453813i	0.342505	−	0.939516i	$-0.388725\pi$
$2$	3.83230	+	1.02686i	0.169365	+	0.0453813i	−0.173140	+	0.984897i	$0.555391\pi$
$3$	−48.4413	−	180.785i	−0.345279	−	1.28860i	−0.892286	−	0.451471i	$-0.850900\pi$
$3$	−48.4413	−	180.785i	−0.345279	−	1.28860i	0.547007	−	0.837128i	$-0.315767\pi$
$4$	−429.773	−	248.130i	−0.839400	−	0.484628i
$5$	−576.593	−	1273.05i	−0.412577	−	0.910923i
$5$	−576.593	−	1273.05i	−0.412577	−	0.910923i
$6$		−	742.566i		−	0.233913i
$7$	−2972.03	−	5614.33i	−0.467855	−	0.883805i
$7$	−2972.03	−	5614.33i	−0.467855	−	0.883805i
$8$	−2828.61	−	2828.61i	−0.244156	−	0.244156i
$9$	−13290.8	+	7673.46i	−0.675244	+	0.389852i
$10$	−902.428	−	5470.80i	−0.0285373	−	0.173002i
$11$	35259.1	−	61070.5i	0.726112	−	1.25766i	−0.232402	−	0.972620i	$-0.574659\pi$
$11$	35259.1	−	61070.5i	0.726112	−	1.25766i	0.958515	−	0.285044i	$-0.0920081\pi$
$12$	−24039.4	+	89716.4i	−0.334664	+	1.24898i
$13$	−65429.6	+	65429.6i	−0.635374	+	0.635374i	−0.949411	−	0.314037i	$-0.898318\pi$
$13$	−65429.6	+	65429.6i	−0.635374	+	0.635374i	0.314037	+	0.949411i	$0.398318\pi$
$14$	−5624.56	−	24567.6i	−0.0391302	−	0.170918i
$15$	−202219.	+	165908.i	−1.03136	+	0.846168i
$16$	119107.	+	206299.i	0.454356	+	0.786969i
$17$	544191.	−	145816.i	1.58027	−	0.423432i	0.641261	−	0.767323i	$-0.278412\pi$
$17$	544191.	−	145816.i	1.58027	−	0.423432i	0.939010	+	0.343891i	$0.111745\pi$
$18$	−58814.0	+	15759.2i	−0.132055	+	0.0353840i
$19$	−53213.6	−	92168.7i	−0.0936767	−	0.162253i	0.815379	−	0.578928i	$-0.196529\pi$
$19$	−53213.6	−	92168.7i	−0.0936767	−	0.162253i	−0.909056	+	0.416675i	$0.863195\pi$
$20$	−68078.0	+	690194.i	−0.0951419	+	0.964575i
$21$	−871020.	+	809264.i	−0.977330	+	0.908037i
$22$	197834.	−	197834.i	0.180053	−	0.180053i
$23$	288387.	−	1.07627e6i	0.214882	−	0.801950i	−0.771326	−	0.636440i	$-0.780406\pi$
$23$	288387.	−	1.07627e6i	0.214882	−	0.801950i	0.986208	−	0.165510i	$-0.0529270\pi$
$24$	−374350.	+	648393.i	−0.230317	+	0.398921i
$25$	−1.28821e6	+	1.46807e6i	−0.659561	+	0.751651i
$26$	−317933.	+	183559.i	−0.136444	+	0.0787762i
$27$	−573854.	−	573854.i	−0.207809	−	0.207809i
$28$	−115784.	+	3.15033e6i	−0.0355990	+	0.968602i
$29$			1.13924e6i			0.299106i	0.988754	+	0.149553i	$0.0477835\pi$
$29$			1.13924e6i			0.299106i	−0.988754	+	0.149553i	$0.952217\pi$
$30$	−945327.	+	428159.i	−0.213077	+	0.0965071i
$31$	−2.76455e6	−	1.59611e6i	−0.537647	−	0.310410i	0.206478	−	0.978451i	$-0.433800\pi$
$31$	−2.76455e6	−	1.59611e6i	−0.537647	−	0.310410i	−0.744125	+	0.668041i	$0.767133\pi$
$32$	774708.	+	2.89125e6i	0.130606	+	0.487428i
$33$	−1.27487e7	−	3.41599e6i	−1.87133	−	0.501423i
$34$	2.23524e6			0.286859
$35$	−5.43369e6	+	7.02073e6i	−0.612052	+	0.790817i
$36$	7.61605e6			0.755733
$37$	1.97235e7	+	5.28489e6i	1.73012	+	0.463583i	0.980210	−	0.197960i	$-0.0634317\pi$
$37$	1.97235e7	+	5.28489e6i	1.73012	+	0.463583i	0.749907	+	0.661544i	$0.230098\pi$
$38$	−109286.	−	407861.i	−0.00850234	−	0.0317312i
$39$	1.49982e7	+	8.65922e6i	1.03812	+	0.599361i
$40$	−1.97001e6	+	5.23193e6i	−0.121674	+	0.323141i
$41$		−	8.74475e6i		−	0.483304i	−0.970363	−	0.241652i	$-0.922311\pi$
$41$		−	8.74475e6i		−	0.483304i	0.970363	−	0.241652i	$-0.0776892\pi$
$42$	−4.16901e6	+	2.20693e6i	−0.206734	+	0.109437i
$43$	−1.48042e7	−	1.48042e7i	−0.660353	−	0.660353i	0.295110	−	0.955463i	$-0.404644\pi$
$43$	−1.48042e7	−	1.48042e7i	−0.660353	−	0.660353i	−0.955463	+	0.295110i	$0.904644\pi$
$44$	−3.03068e7	+	1.74976e7i	−1.21900	+	0.703789i
$45$	1.74321e7	+	1.24955e7i	0.633715	+	0.454251i
$46$	2.21037e6	−	3.82847e6i	0.0727871	−	0.126071i
$47$	1.08753e7	−	4.05873e7i	0.325089	−	1.21325i	−0.589133	−	0.808036i	$-0.700531\pi$
$47$	1.08753e7	−	4.05873e7i	0.325089	−	1.21325i	0.914222	−	0.405213i	$-0.132803\pi$
$48$	3.15262e7	−	3.15262e7i	0.857207	−	0.857207i
$49$	−2.26877e7	+	3.33718e7i	−0.562223	+	0.826986i
$50$	−6.44429e6	+	4.30327e6i	−0.145818	+	0.0973718i
$51$	−5.27227e7	−	9.13183e7i	−1.09127	−	1.89013i
$52$	4.43549e7	−	1.18849e7i	0.841253	−	0.225413i
$53$	7.55777e7	−	2.02510e7i	1.31569	−	0.352537i	0.468326	−	0.883556i	$-0.344857\pi$
$53$	7.55777e7	−	2.02510e7i	1.31569	−	0.352537i	0.847360	+	0.531018i	$0.178191\pi$
$54$	−1.60991e6	−	2.78845e6i	−0.0257650	−	0.0446263i
$55$	−9.80762e7	−	9.67385e6i	−1.44521	−	0.142550i
$56$	−7.47404e6	+	2.42874e7i	−0.101557	+	0.330016i
$57$	−1.40850e7	+	1.40850e7i	−0.176734	+	0.176734i
$58$	−1.16984e6	+	4.36592e6i	−0.0135738	+	0.0506582i
$59$	4.14658e7	−	7.18208e7i	0.445508	−	0.771643i	−0.552579	−	0.833460i	$-0.686356\pi$
$59$	4.14658e7	−	7.18208e7i	0.445508	−	0.771643i	0.998087	+	0.0618177i	$0.0196897\pi$
$60$	1.28075e8	−	2.11264e7i	1.27580	−	0.210448i
$61$	5.36712e7	−	3.09871e7i	0.496315	−	0.286547i	−0.230876	−	0.972983i	$-0.574159\pi$
$61$	5.36712e7	−	3.09871e7i	0.496315	−	0.286547i	0.727190	+	0.686436i	$0.240826\pi$
$62$	−8.95560e6	−	8.95560e6i	−0.0769719	−	0.0769719i
$63$	8.25820e7	+	5.18133e7i	0.660470	+	0.414390i
$64$		−	1.10090e8i		−	0.820233i
$65$	1.21022e8	+	4.55691e7i	0.840917	+	0.316636i
$66$	−4.53489e7	−	2.61822e7i	−0.294184	−	0.169847i
$67$	5.81183e7	+	2.16901e8i	0.352352	+	1.31499i	0.883784	+	0.467894i	$0.154987\pi$
$67$	5.81183e7	+	2.16901e8i	0.352352	+	1.31499i	−0.531433	+	0.847101i	$0.678346\pi$
$68$	−2.70060e8	−	7.23623e7i	−1.53169	−	0.410414i
$69$	−2.08544e8			−1.10759
$70$	−2.80328e7	+	2.13259e7i	−0.139549	+	0.106161i
$71$	5.37375e7			0.250966			0.125483	−	0.992096i	$-0.459952\pi$
$71$	5.37375e7			0.250966			0.125483	+	0.992096i	$0.459952\pi$
$72$	5.92997e7	+	1.58893e7i	0.260050	+	0.0696801i
$73$	2.09181e7	+	7.80674e7i	0.0862123	+	0.321749i	0.995541	−	0.0943298i	$-0.0300708\pi$
$73$	2.09181e7	+	7.80674e7i	0.0862123	+	0.321749i	−0.909329	+	0.416078i	$0.863404\pi$
$74$	7.01594e7	+	4.05065e7i	0.271984	+	0.157030i
$75$	3.27808e8	+	1.61774e8i	1.19631	+	0.590381i
$76$			5.28155e7i			0.181593i
$77$	−4.47661e8	−	1.64529e7i	−1.45124	−	0.0533376i
$78$	4.85858e7	+	4.85858e7i	0.148622	+	0.148622i
$79$	−4.74250e8	+	2.73808e8i	−1.36989	+	0.790905i	−0.990913	−	0.134502i	$-0.957056\pi$
$79$	−4.74250e8	+	2.73808e8i	−1.36989	+	0.790905i	−0.378974	+	0.925407i	$0.623723\pi$
$80$	1.93954e8	−	2.70580e8i	0.529411	−	0.738568i
$81$	−2.26983e8	+	3.93146e8i	−0.585883	+	1.01478i
$82$	8.97965e6	−	3.35125e7i	0.0219330	−	0.0818549i
$83$	−3.04700e8	+	3.04700e8i	−0.704727	+	0.704727i	−0.965421	−	0.260694i	$-0.916049\pi$
$83$	−3.04700e8	+	3.04700e8i	−0.704727	+	0.704727i	0.260694	+	0.965421i	$0.416049\pi$
$84$	5.75143e8	−	1.31674e8i	1.26043	−	0.288565i
$85$	−4.99408e8	−	6.08708e8i	−1.03770	−	1.26481i
$86$	−4.15322e7	−	7.19359e7i	−0.0818732	−	0.141809i
$87$	2.05958e8	−	5.51864e7i	0.385428	−	0.103275i
$88$	−2.72479e8	+	7.30104e7i	−0.484351	+	0.129782i
$89$	−1.16048e8	−	2.01000e8i	−0.196056	−	0.339579i	0.751190	−	0.660086i	$-0.229480\pi$
$89$	−1.16048e8	−	2.01000e8i	−0.196056	−	0.339579i	−0.947246	+	0.320507i	$0.896147\pi$
$90$	5.39740e7	+	6.57867e7i	0.0867148	+	0.105693i
$91$	5.61802e8	+	1.72885e8i	0.858809	+	0.264284i
$92$	−3.90996e8	+	3.90996e8i	−0.569019	+	0.569019i
$93$	−1.54636e8	+	5.77108e8i	−0.214356	+	0.799989i
$94$	8.33551e7	−	1.44375e8i	0.110118	−	0.190729i
$95$	−8.66530e7	+	1.20888e8i	−0.109151	+	0.152274i
$96$	4.85168e8	−	2.80112e8i	0.583004	−	0.336597i
$97$	4.76658e8	+	4.76658e8i	0.546682	+	0.546682i	0.925479	−	0.378798i	$-0.123662\pi$
$97$	4.76658e8	+	4.76658e8i	0.546682	+	0.546682i	−0.378798	+	0.925479i	$0.623662\pi$
$98$	−1.21214e8	+	1.04594e8i	−0.132751	+	0.114548i
$99$			1.08224e9i			1.13231i
$100$	9.17907e8	−	3.11294e8i	0.917907	−	0.311294i
$101$	−7.78199e8	−	4.49293e8i	−0.744123	−	0.429619i	0.0794438	−	0.996839i	$-0.474686\pi$
$101$	−7.78199e8	−	4.49293e8i	−0.744123	−	0.429619i	−0.823566	+	0.567220i	$0.808019\pi$
$102$	−1.08278e8	−	4.04098e8i	−0.0990463	−	0.369646i
$103$	−3.57513e8	−	9.57953e7i	−0.312986	−	0.0838642i	0.0989069	−	0.995097i	$-0.468465\pi$
$103$	−3.57513e8	−	9.57953e7i	−0.312986	−	0.0838642i	−0.411892	+	0.911232i	$0.635132\pi$
$104$	3.70149e8			0.310261
$105$	1.53246e9	+	6.42238e8i	1.23037	+	0.515637i
$106$	3.10431e8			0.238830
$107$	−1.07063e9	−	2.86874e8i	−0.789608	−	0.211575i	−0.158592	−	0.987344i	$-0.550695\pi$
$107$	−1.07063e9	−	2.86874e8i	−0.789608	−	0.211575i	−0.631017	+	0.775769i	$0.717362\pi$
$108$	1.04237e8	+	3.89017e8i	0.0737249	+	0.275145i
$109$	−6.96630e8	−	4.02200e8i	−0.472697	−	0.272912i	0.244671	−	0.969606i	$-0.421320\pi$
$109$	−6.96630e8	−	4.02200e8i	−0.472697	−	0.272912i	−0.717368	+	0.696694i	$0.754653\pi$
$110$	−3.65924e8	−	1.37784e8i	−0.238300	−	0.0897286i
$111$		−	3.82172e9i		−	2.38949i
$112$	8.04242e8	−	1.28183e9i	0.482954	−	0.769750i
$113$	1.35633e9	+	1.35633e9i	0.782552	+	0.782552i	0.980261	−	0.197708i	$-0.0633499\pi$
$113$	1.35633e9	+	1.35633e9i	0.782552	+	0.782552i	−0.197708	+	0.980261i	$0.563350\pi$
$114$	−6.84413e7	+	3.95146e7i	−0.0379530	+	0.0219122i
$115$	−1.53644e9	+	2.53440e8i	−0.819170	+	0.135125i
$116$	2.82680e8	−	4.89615e8i	0.144955	−	0.251070i
$117$	3.67542e8	−	1.37168e9i	0.181330	−	0.676734i
$118$	2.32659e8	−	2.32659e8i	0.110472	−	0.110472i
$119$	−2.43601e9	−	2.62190e9i	−1.11357	−	1.19855i
$120$	1.04129e9	+	1.02708e8i	0.458410	+	0.0452158i
$121$	−1.30743e9	−	2.26454e9i	−0.554478	−	0.960384i
$122$	2.37504e8	−	6.36389e7i	0.0970624	−	0.0260078i
$123$	−1.58092e9	+	4.23607e8i	−0.622785	+	0.166875i
$124$	7.92086e8	+	1.37193e9i	0.300867	+	0.521117i
$125$	2.61170e9	+	7.93477e8i	0.956815	+	0.290696i
$126$	2.63274e8	+	2.83364e8i	0.0930551	+	0.100156i
$127$	5.25719e8	−	5.25719e8i	0.179323	−	0.179323i	−0.611738	−	0.791061i	$-0.709529\pi$
$127$	5.25719e8	−	5.25719e8i	0.179323	−	0.179323i	0.791061	+	0.611738i	$0.209529\pi$
$128$	5.09697e8	−	1.90222e9i	0.167829	−	0.626347i
$129$	−1.95925e9	+	3.39351e9i	−0.622924	+	1.07894i
$130$	4.16998e8	+	2.98907e8i	0.128053	+	0.0917891i
$131$	2.53676e9	−	1.46460e9i	0.752591	−	0.434509i	−0.0740384	−	0.997255i	$-0.523589\pi$
$131$	2.53676e9	−	1.46460e9i	0.752591	−	0.434509i	0.826629	+	0.562747i	$0.190255\pi$
$132$	4.63142e9	+	4.63142e9i	1.32780	+	1.32780i
$133$	−3.59313e8	+	5.72686e8i	−0.0995727	+	0.158703i
$134$			8.90907e8i			0.238705i
$135$	−3.99667e8	+	1.06143e9i	−0.103561	+	0.275035i
$136$	−1.95176e9	−	1.12685e9i	−0.489216	−	0.282449i
$137$	1.24132e9	+	4.63265e9i	0.301051	+	1.12354i	0.936292	+	0.351222i	$0.114234\pi$
$137$	1.24132e9	+	4.63265e9i	0.301051	+	1.12354i	−0.635241	+	0.772314i	$0.719099\pi$
$138$	−7.99204e8	−	2.14146e8i	−0.187587	−	0.0502637i
$139$	−6.85482e8			−0.155751			−0.0778753	−	0.996963i	$-0.524814\pi$
$139$	−6.85482e8			−0.155751			−0.0778753	+	0.996963i	$0.524814\pi$
$140$	4.07730e9	−	1.66906e9i	0.897009	−	0.367194i
$141$	−7.86441e9			−1.67564
$142$	2.05938e8	+	5.51809e7i	0.0425049	+	0.0113892i
$143$	1.68883e9	+	6.30281e9i	0.337734	+	1.26044i
$144$	−3.16606e9	−	1.82792e9i	−0.613603	−	0.354264i
$145$	1.45032e9	−	6.56879e8i	0.272462	−	0.123404i
$146$			3.20658e8i			0.0584055i
$147$	7.13217e9	+	2.48504e9i	1.25978	+	0.438939i
$148$	−7.16527e9	−	7.16527e9i	−1.22759	−	1.22759i
$149$	−3.17737e9	+	1.83446e9i	−0.528117	+	0.304909i	−0.740249	−	0.672332i	$-0.765293\pi$
$149$	−3.17737e9	+	1.83446e9i	−0.528117	+	0.304909i	0.212132	+	0.977241i	$0.431959\pi$
$150$	1.09014e9	+	9.56578e8i	0.175821	+	0.154280i
$151$	3.36449e9	−	5.82747e9i	0.526652	−	0.912187i	−0.472866	−	0.881134i	$-0.656781\pi$
$151$	3.36449e9	−	5.82747e9i	0.526652	−	0.912187i	0.999518	−	0.0310531i	$-0.00988610\pi$
$152$	−1.10189e8	+	4.11229e8i	−0.0167433	+	0.0624868i
$153$	−6.11384e9	+	6.11384e9i	−0.901992	+	0.901992i
$154$	−1.69867e9	−	5.22738e8i	−0.243370	−	0.0748929i
$155$	−4.37918e8	+	4.43973e9i	−0.0609396	+	0.617823i
$156$	−4.29722e9	−	7.44300e9i	−0.580934	−	1.00621i
$157$	2.88844e9	−	7.73955e8i	0.379415	−	0.101664i	−0.0640706	−	0.997945i	$-0.520408\pi$
$157$	2.88844e9	−	7.73955e8i	0.379415	−	0.101664i	0.443486	+	0.896281i	$0.353742\pi$
$158$	−2.09863e9	+	5.62326e8i	−0.267904	+	0.0717846i
$159$	−7.32217e9	−	1.26824e10i	−0.908558	−	1.57367i
$160$	3.23402e9	−	2.65332e9i	0.390124	−	0.320073i
$161$	−6.89964e9	+	1.57962e9i	−0.809301	+	0.185283i
$162$	−1.27357e9	+	1.27357e9i	−0.145280	+	0.145280i
$163$	−2.05803e9	+	7.68069e9i	−0.228354	+	0.852228i	0.752679	+	0.658387i	$0.228761\pi$
$163$	−2.05803e9	+	7.68069e9i	−0.228354	+	0.852228i	−0.981033	+	0.193841i	$0.937906\pi$
$164$	−2.16983e9	+	3.75826e9i	−0.234223	+	0.405685i
$165$	3.00205e9	+	1.81994e10i	0.315311	+	1.91152i
$166$	−1.48059e9	+	8.54817e8i	−0.151338	+	0.0873749i
$167$	−2.24044e9	−	2.24044e9i	−0.222899	−	0.222899i	0.586819	−	0.809718i	$-0.300380\pi$
$167$	−2.24044e9	−	2.24044e9i	−0.222899	−	0.222899i	−0.809718	+	0.586819i	$0.800380\pi$
$168$	4.75286e9	+	1.74682e8i	0.460324	+	0.0169183i
$169$			2.04243e9i			0.192601i
$170$	−1.28882e9	−	2.84557e9i	−0.118351	−	0.261306i
$171$	1.41451e9	+	8.16665e8i	0.126509	+	0.0730401i
$172$	2.68908e9	+	1.00358e10i	0.234275	+	0.874326i
$173$	2.01295e10	+	5.39367e9i	1.70854	+	0.457802i	0.975066	−	0.221917i	$-0.0712314\pi$
$173$	2.01295e10	+	5.39367e9i	1.70854	+	0.457802i	0.733473	+	0.679719i	$0.237898\pi$
$174$	8.45963e8			0.0699648
$175$	1.20708e10	+	2.86927e9i	0.972892	+	0.231260i
$176$	1.67984e10			1.31966
$177$	−1.49928e10	−	4.01731e9i	−1.14816	−	0.307649i
$178$	−2.38329e8	−	8.89458e8i	−0.0177946	−	0.0664103i
$179$	1.47850e10	+	8.53612e9i	1.07642	+	0.621472i	0.929929	−	0.367739i	$-0.119868\pi$
$179$	1.47850e10	+	8.53612e9i	1.07642	+	0.621472i	0.146493	+	0.989212i	$0.453201\pi$
$180$	−4.39136e9	−	9.69564e9i	−0.311798	−	0.688415i
$181$			1.34860e10i			0.933964i	0.884267	+	0.466982i	$0.154659\pi$
$181$			1.34860e10i			0.933964i	−0.884267	+	0.466982i	$0.845341\pi$
$182$	1.97546e9	+	1.23944e9i	0.133459	+	0.0837344i
$183$	−8.20192e9	−	8.20192e9i	−0.540612	−	0.540612i
$184$	−3.86009e9	+	2.22862e9i	−0.248266	+	0.143336i
$185$	−4.64447e9	−	2.81563e10i	−0.291517	−	1.76727i
$186$	−1.18522e9	+	2.05286e9i	−0.0726091	+	0.125763i
$187$	1.02826e10	−	3.83754e10i	0.614919	−	2.29491i
$188$	−1.47448e10	+	1.47448e10i	−0.860854	+	0.860854i
$189$	−1.51630e9	+	4.92732e9i	−0.0864382	+	0.280887i
$190$	−4.56215e8	+	3.74297e8i	−0.0253968	+	0.0208365i
$191$	−1.50205e10	−	2.60163e10i	−0.816648	−	1.41448i	−0.908139	−	0.418669i	$-0.862497\pi$
$191$	−1.50205e10	−	2.60163e10i	−0.816648	−	1.41448i	0.0914910	−	0.995806i	$-0.470837\pi$
$192$	−1.99026e10	+	5.33289e9i	−1.05695	+	0.283209i
$193$	3.23653e9	−	8.67225e8i	0.167908	−	0.0449908i	−0.173886	−	0.984766i	$-0.555632\pi$
$193$	3.23653e9	−	8.67225e8i	0.167908	−	0.0449908i	0.341794	+	0.939775i	$0.388966\pi$
$194$	1.33724e9	+	2.31616e9i	0.0677798	+	0.117398i
$195$	2.37579e9	−	2.40864e10i	0.117666	−	1.19293i
$196$	1.80311e10	−	8.71282e9i	0.872711	−	0.421703i
$197$	−3.26503e9	+	3.26503e9i	−0.154450	+	0.154450i	−0.780102	−	0.625652i	$-0.784833\pi$
$197$	−3.26503e9	+	3.26503e9i	−0.154450	+	0.154450i	0.625652	+	0.780102i	$0.284833\pi$
$198$	−1.11131e9	+	4.14745e9i	−0.0513855	+	0.191773i
$199$	2.03468e10	−	3.52417e10i	0.919725	−	1.59301i	0.119893	−	0.992787i	$-0.461745\pi$
$199$	2.03468e10	−	3.52417e10i	0.919725	−	1.59301i	0.799832	−	0.600223i	$-0.204922\pi$
$200$	7.79642e9	−	5.08760e8i	0.344556	−	0.0224842i
$201$	3.63971e10	−	2.10139e10i	1.57284	−	0.908080i
$202$	−2.52093e9	−	2.52093e9i	−0.106532	−	0.106532i
$203$	6.39608e9	−	3.38586e9i	0.264351	−	0.139938i
$204$			5.23282e10i			2.11544i
$205$	−1.11325e10	+	5.04217e9i	−0.440253	+	0.199400i
$206$	−1.27173e9	−	7.34233e8i	−0.0492030	−	0.0284074i
$207$	4.42585e9	+	1.65175e10i	0.167544	+	0.625284i
$208$	−2.12912e10	−	5.70495e9i	−0.788705	−	0.211333i
$209$	−7.50505e9			−0.272079
$210$	5.21336e9	+	4.03487e9i	0.184983	+	0.143167i
$211$	3.63806e9			0.126357			0.0631784	−	0.998002i	$-0.479876\pi$
$211$	3.63806e9			0.126357			0.0631784	+	0.998002i	$0.479876\pi$
$212$	−3.75061e10	−	1.00497e10i	−1.27524	−	0.341699i
$213$	−2.60311e9	−	9.71495e9i	−0.0866532	−	0.323394i
$214$	−3.80839e9	−	2.19877e9i	−0.124131	−	0.0716669i
$215$	−1.03105e10	+	2.73825e10i	−0.329085	+	0.873977i
$216$			3.24642e9i			0.101476i
$217$	−7.44791e8	+	2.02648e10i	−0.0228016	+	0.620402i
$218$	−2.25669e9	−	2.25669e9i	−0.0676734	−	0.0676734i
$219$	1.31001e10	−	7.56337e9i	0.384838	−	0.222186i
$220$	3.97501e10	+	2.84931e10i	1.14403	+	0.820046i
$221$	−2.60656e10	+	4.51469e10i	−0.735024	+	1.27310i
$222$	3.92438e9	−	1.46460e10i	0.108438	−	0.404697i
$223$	2.71598e10	−	2.71598e10i	0.735452	−	0.735452i	−0.236242	−	0.971694i	$-0.575916\pi$
$223$	2.71598e10	−	2.71598e10i	0.735452	−	0.735452i	0.971694	+	0.236242i	$0.0759159\pi$
$224$	1.39300e10	−	1.29423e10i	0.369687	−	0.343476i
$225$	5.85615e9	−	2.93968e10i	0.152332	−	0.764679i
$226$	3.80511e9	+	6.59064e9i	0.0970240	+	0.168050i
$227$	−4.82770e8	+	1.29358e8i	−0.0120677	+	0.00323352i	−0.264848	−	0.964290i	$-0.585322\pi$
$227$	−4.82770e8	+	1.29358e8i	−0.0120677	+	0.00323352i	0.252780	+	0.967524i	$0.418655\pi$
$228$	9.54826e9	−	2.55845e9i	0.234001	−	0.0627004i
$229$	−3.97633e10	−	6.88720e10i	−0.955481	−	1.65494i	−0.733263	−	0.679945i	$-0.762003\pi$
$229$	−3.97633e10	−	6.88720e10i	−0.955481	−	1.65494i	−0.222219	−	0.974997i	$-0.571330\pi$
$230$	−6.14833e9	−	6.06447e8i	−0.144871	−	0.0142895i
$231$	1.87108e10	+	8.17275e10i	0.432354	+	1.88849i
$232$	3.22247e9	−	3.22247e9i	0.0730286	−	0.0730286i
$233$	−6.90199e9	+	2.57586e10i	−0.153417	+	0.572559i	0.845819	+	0.533470i	$0.179112\pi$
$233$	−6.90199e9	+	2.57586e10i	−0.153417	+	0.572559i	−0.999236	+	0.0390891i	$0.987554\pi$
$234$	2.81706e9	−	4.87929e9i	0.0614221	−	0.106386i
$235$	−5.79405e10	+	9.55748e9i	−1.23930	+	0.204427i
$236$	−3.56417e10	+	2.05778e10i	−0.747919	+	0.431811i
$237$	7.24738e10	+	7.24738e10i	1.49215	+	1.49215i
$238$	−6.64318e9	−	1.25493e10i	−0.134208	−	0.253527i
$239$			5.90627e10i			1.17091i	0.810706	+	0.585454i	$0.199084\pi$
$239$			5.90627e10i			1.17091i	−0.810706	+	0.585454i	$0.800916\pi$
$240$	−5.83123e10	−	2.19567e10i	−1.13451	−	0.427186i
$241$	−6.06419e10	−	3.50116e10i	−1.15797	−	0.668553i	−0.207151	−	0.978309i	$-0.566419\pi$
$241$	−6.06419e10	−	3.50116e10i	−1.15797	−	0.668553i	−0.950816	+	0.309756i	$0.899753\pi$
$242$	−2.68510e9	−	1.00209e10i	−0.0503259	−	0.187819i
$243$	6.66409e10	+	1.78564e10i	1.22606	+	0.328523i
$244$	−3.07553e10			−0.555476
$245$	5.55657e10	+	9.64072e9i	0.985280	+	0.170947i
$246$	−6.49356e9			−0.113051
$247$	9.51230e9	+	2.54881e9i	0.162611	+	0.0435714i
$248$	3.30505e9	+	1.23346e10i	0.0554811	+	0.207058i
$249$	6.98454e10	+	4.03253e10i	1.15144	+	0.664783i
$250$	9.19402e9	+	5.72269e9i	0.148859	+	0.0926553i
$251$			3.54285e10i			0.563405i	0.959502	+	0.281703i	$0.0908992\pi$
$251$			3.54285e10i			0.563405i	−0.959502	+	0.281703i	$0.909101\pi$
$252$	−2.26351e10	−	4.27590e10i	−0.353574	−	0.667921i
$253$	−5.55603e10	−	5.55603e10i	−0.852555	−	0.852555i
$254$	2.55455e9	−	1.47487e9i	0.0385091	−	0.0222332i
$255$	−8.58536e10	+	1.19772e11i	−1.27153	+	1.77389i
$256$	−2.42763e10	+	4.20479e10i	−0.353267	+	0.611877i
$257$	1.23316e10	−	4.60222e10i	0.176328	−	0.658064i	−0.819994	−	0.572372i	$-0.806023\pi$
$257$	1.23316e10	−	4.60222e10i	0.176328	−	0.658064i	0.996322	−	0.0856918i	$-0.0273100\pi$
$258$	−1.09931e10	+	1.09931e10i	−0.154465	+	0.154465i
$259$	−2.89476e10	−	1.26441e11i	−0.399727	−	1.74598i
$260$	−4.07048e10	−	4.96134e10i	−0.552415	−	0.673316i
$261$	−8.74193e9	−	1.51415e10i	−0.116607	−	0.201969i
$262$	1.12256e10	−	3.00788e9i	0.147181	−	0.0394371i
$263$	4.80652e10	−	1.28790e10i	0.619483	−	0.165990i	0.0645904	−	0.997912i	$-0.479426\pi$
$263$	4.80652e10	−	1.28790e10i	0.619483	−	0.165990i	0.554893	+	0.831922i	$0.312759\pi$
$264$	2.63984e10	+	4.57234e10i	0.334473	+	0.579324i
$265$	−6.93582e10	−	8.45379e10i	−0.863956	−	1.05304i
$266$	−1.96506e9	+	1.82574e9i	−0.0240663	+	0.0223600i
$267$	−3.07164e10	+	3.07164e10i	−0.369888	+	0.369888i
$268$	2.88417e10	−	1.07639e11i	0.341519	−	1.27457i
$269$	−3.00578e10	+	5.20617e10i	−0.350004	+	0.606224i	−0.986250	−	0.165262i	$-0.947153\pi$
$269$	−3.00578e10	+	5.20617e10i	−0.350004	+	0.606224i	0.636246	+	0.771486i	$0.280486\pi$
$270$	−2.62158e9	+	3.65731e9i	−0.0300211	+	0.0418817i
$271$	2.88301e10	−	1.66450e10i	0.324701	−	0.187466i	−0.328785	−	0.944405i	$-0.606639\pi$
$271$	2.88301e10	−	1.66450e10i	0.324701	−	0.187466i	0.653486	+	0.756939i	$0.273306\pi$
$272$	9.48985e10	+	9.48985e10i	1.05123	+	1.05123i
$273$	4.04064e9	−	1.09940e11i	0.0440269	−	1.19791i
$274$			1.90284e10i			0.203950i
$275$	4.42347e10	+	1.30434e11i	0.466408	+	1.37529i
$276$	8.96267e10	+	5.17460e10i	0.929708	+	0.536767i
$277$	−4.08700e10	−	1.52529e11i	−0.417105	−	1.55666i	−0.780581	−	0.625055i	$-0.785077\pi$
$277$	−4.08700e10	−	1.52529e11i	−0.417105	−	1.55666i	0.363476	−	0.931604i	$-0.381590\pi$
$278$	−2.62697e9	−	7.03895e8i	−0.0263787	−	0.00706816i
$279$	4.89909e10			0.484057
$280$	3.52287e10	−	4.48912e9i	0.342519	−	0.0436465i
$281$	7.54000e10			0.721428			0.360714	−	0.932677i	$-0.382533\pi$
$281$	7.54000e10			0.721428			0.360714	+	0.932677i	$0.382533\pi$
$282$	−3.01388e10	−	8.07566e9i	−0.283795	−	0.0760426i
$283$	2.00613e10	+	7.48696e10i	0.185917	+	0.693852i	0.994432	+	0.105377i	$0.0336048\pi$
$283$	2.00613e10	+	7.48696e10i	0.185917	+	0.693852i	−0.808515	+	0.588475i	$0.799729\pi$
$284$	−2.30949e10	−	1.33338e10i	−0.210661	−	0.121625i
$285$	2.60523e10	+	9.80965e9i	0.233907	+	0.0880748i
$286$			2.58884e10i			0.228801i
$287$	−4.90959e10	+	2.59896e10i	−0.427146	+	0.226116i
$288$	−3.24824e10	−	3.24824e10i	−0.278216	−	0.278216i
$289$	1.72182e11	−	9.94092e10i	1.45193	−	0.838274i
$290$	6.23257e9	−	1.02808e9i	0.0517459	−	0.00853567i
$291$	6.30829e10	−	1.09263e11i	0.515696	−	0.893211i
$292$	1.03808e10	−	3.87416e10i	0.0835618	−	0.311857i
$293$	1.09965e11	−	1.09965e11i	0.871666	−	0.871666i	−0.120988	−	0.992654i	$-0.538606\pi$
$293$	1.09965e11	−	1.09965e11i	0.871666	−	0.871666i	0.992654	+	0.120988i	$0.0386063\pi$
$294$	2.47808e10	+	1.68471e10i	0.193443	+	0.131511i
$295$	−1.15341e11	−	1.13767e10i	−0.886713	−	0.0874619i
$296$	−4.08411e10	−	7.07388e10i	−0.309232	−	0.535606i
$297$	−5.52791e10	+	1.48120e10i	−0.412247	+	0.110461i
$298$	−1.40604e10	+	3.76747e9i	−0.103282	+	0.0276743i
$299$	5.15511e10	+	8.92891e10i	0.373008	+	0.646068i
$300$	−1.00742e11	−	1.50865e11i	−0.718067	−	1.07533i
$301$	−3.91171e10	+	1.27114e11i	−0.274674	+	0.892573i
$302$	1.88778e10	−	1.88778e10i	0.130593	−	0.130593i
$303$	−4.35287e10	+	1.62451e11i	−0.296677	+	1.10721i
$304$	1.26762e10	−	2.19558e10i	0.0851252	−	0.147441i
$305$	−7.03947e10	−	5.04594e10i	−0.465790	−	0.333882i
$306$	−2.97081e10	+	1.71520e10i	−0.193700	+	0.111833i
$307$	−8.94110e10	−	8.94110e10i	−0.574471	−	0.574471i	0.358904	−	0.933375i	$-0.383151\pi$
$307$	−8.94110e10	−	8.94110e10i	−0.574471	−	0.574471i	−0.933375	+	0.358904i	$0.883151\pi$
$308$	1.88310e11	+	1.18149e11i	1.19233	+	0.748085i
$309$			6.92736e10i			0.432269i
$310$	−6.23722e9	+	1.65647e10i	−0.0383587	+	0.101872i
$311$	−1.08263e11	−	6.25056e10i	−0.656233	−	0.378876i	0.134607	−	0.990899i	$-0.457023\pi$
$311$	−1.08263e11	−	6.25056e10i	−0.656233	−	0.378876i	−0.790840	+	0.612023i	$0.790356\pi$
$312$	−1.79305e10	−	6.69176e10i	−0.107127	−	0.399802i
$313$	−3.30447e10	−	8.85430e9i	−0.194604	−	0.0521441i	0.160200	−	0.987085i	$-0.448786\pi$
$313$	−3.30447e10	−	8.85430e9i	−0.194604	−	0.0521441i	−0.354805	+	0.934940i	$0.615453\pi$
$314$	1.18641e10			0.0688734
$315$	1.83449e10	−	1.35007e11i	0.104983	−	0.772604i
$316$	2.71759e11			1.53318
$317$	−2.75564e11	−	7.38372e10i	−1.53270	−	0.410685i	−0.608799	−	0.793324i	$-0.708349\pi$
$317$	−2.75564e11	−	7.38372e10i	−1.53270	−	0.410685i	−0.923898	+	0.382639i	$0.875015\pi$
$318$	−1.50377e10	−	5.61215e10i	−0.0824631	−	0.307756i
$319$	6.95741e10	+	4.01686e10i	0.376175	+	0.217185i
$320$	−1.40150e11	+	6.34770e10i	−0.747169	+	0.338409i
$321$			2.07451e11i			1.09054i
$322$	−2.80635e10	−	1.03142e9i	−0.145476	−	0.00534667i
$323$	−4.23980e10	−	4.23980e10i	−0.216737	−	0.216737i
$324$	1.95102e11	−	1.12642e11i	0.983580	−	0.567870i
$325$	−1.17683e10	−	1.80342e11i	−0.0585113	−	0.896647i
$326$	−1.57740e10	+	2.73214e10i	−0.0773504	+	0.133975i
$327$	−3.89661e10	+	1.45424e11i	−0.188461	+	0.703348i
$328$	−2.47355e10	+	2.47355e10i	−0.118002	+	0.118002i
$329$	−2.60192e11	+	5.95688e10i	−1.22437	+	0.280309i
$330$	−7.18347e9	+	7.28281e10i	−0.0333443	+	0.338054i
$331$	2.01555e11	+	3.49103e11i	0.922926	+	1.59856i	0.794863	+	0.606789i	$0.207543\pi$
$331$	2.01555e11	+	3.49103e11i	0.922926	+	1.59856i	0.128064	+	0.991766i	$0.459124\pi$
$332$	2.06557e11	−	5.53468e10i	0.933079	−	0.250018i
$333$	−3.02694e11	+	8.11067e10i	−1.34898	+	0.361458i
$334$	−6.28541e9	−	1.08866e10i	−0.0276359	−	0.0478669i
$335$	2.42615e11	−	1.99051e11i	1.05249	−	0.863501i
$336$	−2.70695e11	−	8.33017e10i	−1.15865	−	0.356555i
$337$	9.17254e10	−	9.17254e10i	0.387396	−	0.387396i	−0.486362	−	0.873758i	$-0.661676\pi$
$337$	9.17254e10	−	9.17254e10i	0.387396	−	0.387396i	0.873758	+	0.486362i	$0.161676\pi$
$338$	−2.09730e9	+	7.82722e9i	−0.00874047	+	0.0326199i
$339$	1.79503e11	−	3.10908e11i	0.738197	−	1.27860i
$340$	6.35936e10	+	3.85524e11i	0.258082	+	1.56458i
$341$	−1.94951e11	+	1.12555e11i	−0.780784	+	0.450786i
$342$	4.58221e9	+	4.58221e9i	0.0181116	+	0.0181116i
$343$	2.54789e11	+	2.81944e10i	0.993933	+	0.109986i
$344$			8.37504e10i			0.322459i
$345$	1.20245e11	+	2.65488e11i	0.456964	+	1.00893i
$346$	7.16036e10	+	4.13403e10i	0.268592	+	0.155071i
$347$	3.62393e10	+	1.35247e11i	0.134183	+	0.500778i	1.00000		0.000416964i	$0.000132724\pi$
$347$	3.62393e10	+	1.35247e11i	0.134183	+	0.500778i	−0.865817	+	0.500361i	$0.833201\pi$
$348$	−1.02209e11	−	2.73867e10i	−0.373578	−	0.100100i
$349$	−3.99493e11			−1.44143			−0.720717	−	0.693230i	$-0.756187\pi$
$349$	−3.99493e11			−1.44143			−0.720717	+	0.693230i	$0.756187\pi$
$350$	4.33126e10	+	2.33909e10i	0.154279	+	0.0833185i
$351$	7.50941e10			0.264073
$352$	2.03885e11	+	5.46310e10i	0.707855	+	0.189669i
$353$	2.72821e10	+	1.01818e11i	0.0935174	+	0.349012i	0.996790	−	0.0800545i	$-0.0255094\pi$
$353$	2.72821e10	+	1.01818e11i	0.0935174	+	0.349012i	−0.903273	+	0.429066i	$0.858843\pi$
$354$	−5.33317e10	−	3.07911e10i	−0.180497	−	0.104210i
$355$	−3.09846e10	−	6.84107e10i	−0.103543	−	0.228610i
$356$			1.15179e11i			0.380057i
$357$	−3.55998e11	+	5.67403e11i	−1.15995	+	1.84878i
$358$	4.78951e10	+	4.78951e10i	0.154105	+	0.154105i
$359$	−2.86018e10	+	1.65133e10i	−0.0908801	+	0.0524696i	−0.544751	−	0.838598i	$-0.683376\pi$
$359$	−2.86018e10	+	1.65133e10i	−0.0908801	+	0.0524696i	0.453871	+	0.891067i	$0.350043\pi$
$360$	−1.39639e10	−	8.46534e10i	−0.0438172	−	0.265634i
$361$	1.55680e11	−	2.69646e11i	0.482449	−	0.835627i
$362$	−1.38483e10	+	5.16824e10i	−0.0423845	+	0.158181i
$363$	−3.46061e11	+	3.46061e11i	−1.04610	+	1.04610i
$364$	−1.98549e11	−	2.13701e11i	−0.592805	−	0.638043i
$365$	8.73227e10	−	7.16430e10i	0.257519	−	0.211279i
$366$	−2.30100e10	−	3.98544e10i	−0.0670272	−	0.116095i
$367$	−4.89552e10	+	1.31175e10i	−0.140864	+	0.0377445i	−0.328562	−	0.944482i	$-0.606564\pi$
$367$	−4.89552e10	+	1.31175e10i	−0.140864	+	0.0377445i	0.187698	+	0.982227i	$0.439897\pi$
$368$	2.56383e11	−	6.86976e10i	0.728742	−	0.195266i
$369$	6.71025e10	+	1.16225e11i	0.188417	+	0.326348i
$370$	1.11136e10	−	1.12672e11i	0.0308280	−	0.312543i
$371$	−3.38315e11	−	3.64132e11i	−0.927125	−	0.997874i
$372$	2.09656e11	−	2.09656e11i	0.567628	−	0.567628i
$373$	4.12708e10	−	1.54025e11i	0.110396	−	0.412003i	−0.888505	−	0.458866i	$-0.848256\pi$
$373$	4.12708e10	−	1.54025e11i	0.110396	−	0.412003i	0.998901	+	0.0468631i	$0.0149225\pi$
$374$	7.88123e10	−	1.36507e11i	0.208292	−	0.360772i
$375$	1.69348e10	−	5.10594e11i	0.0442222	−	1.33332i
$376$	−1.45568e11	+	8.40436e10i	−0.375595	+	0.216850i
$377$	−7.45402e10	−	7.45402e10i	−0.190044	−	0.190044i
$378$	−1.08706e10	+	1.73259e10i	−0.0273867	+	0.0436499i
$379$			4.56016e11i			1.13528i	0.823276	+	0.567641i	$0.192144\pi$
$379$			4.56016e11i			1.13528i	−0.823276	+	0.567641i	$0.807856\pi$
$380$	6.72369e10	−	3.04530e10i	0.165418	−	0.0749211i
$381$	−1.20509e11	−	6.95758e10i	−0.292992	−	0.169159i
$382$	−3.08480e10	−	1.15126e11i	−0.0741211	−	0.276624i
$383$	−4.03658e9	−	1.08160e9i	−0.00958559	−	0.00256845i	0.254023	−	0.967198i	$-0.418246\pi$
$383$	−4.03658e9	−	1.08160e9i	−0.00958559	−	0.00256845i	−0.263609	+	0.964630i	$0.584913\pi$
$384$	−3.68583e11			−0.865058
$385$	2.37173e11	+	5.79383e11i	0.550163	+	1.34398i
$386$	1.32939e10			0.0304795
$387$	3.10359e11	+	8.31605e10i	0.703340	+	0.188459i
$388$	−8.65819e10	−	3.23128e11i	−0.193947	−	0.723822i
$389$	−8.97253e10	−	5.18029e10i	−0.198674	−	0.114705i	0.397363	−	0.917662i	$-0.369926\pi$
$389$	−8.97253e10	−	5.18029e10i	−0.198674	−	0.114705i	−0.596037	+	0.802957i	$0.703259\pi$
$390$	3.38381e10	−	8.98666e10i	0.0740654	−	0.196701i
$391$		−	6.27750e11i		−	1.35829i
$392$	1.58571e11	−	3.02212e10i	0.339184	−	0.0646434i
$393$	−3.87662e11	−	3.87662e11i	−0.819761	−	0.819761i
$394$	−1.58653e10	+	9.15983e9i	−0.0331677	+	0.0191494i
$395$	6.22021e11	+	4.45869e11i	1.28564	+	0.921553i
$396$	2.68535e11	−	4.65116e11i	0.548747	−	0.950458i
$397$	−1.95069e11	+	7.28008e11i	−0.394123	+	1.47089i	0.429147	+	0.903235i	$0.358814\pi$
$397$	−1.95069e11	+	7.28008e11i	−0.394123	+	1.47089i	−0.823269	+	0.567651i	$0.807852\pi$
$398$	1.14164e11	−	1.14164e11i	0.228062	−	0.228062i
$399$	1.20939e11	+	3.72168e10i	0.238884	+	0.0735126i
$400$	−4.56295e11	−	9.08987e10i	−0.891201	−	0.177537i
$401$	−2.76199e11	−	4.78390e11i	−0.533423	−	0.923916i	−0.999238	−	0.0390337i	$-0.987572\pi$
$401$	−2.76199e11	−	4.78390e11i	−0.533423	−	0.923916i	0.465815	−	0.884882i	$-0.345761\pi$
$402$	1.61063e11	−	4.31567e10i	0.307595	−	0.0824197i
$403$	2.85317e11	−	7.64503e10i	0.538833	−	0.144380i
$404$	2.22966e11	+	3.86188e11i	0.416411	+	0.721245i
$405$	6.31373e11	+	6.22761e10i	1.16611	+	0.115020i
$406$	2.79885e10	−	6.40773e9i	0.0511225	−	0.0117041i
$407$	1.01818e12	−	1.01818e12i	1.83929	−	1.83929i
$408$	−1.09172e11	+	4.07435e11i	−0.195048	+	0.727927i
$409$	−2.00539e11	+	3.47344e11i	−0.354359	+	0.613768i	−0.987008	−	0.160671i	$-0.948634\pi$
$409$	−2.00539e11	+	3.47344e11i	−0.354359	+	0.613768i	0.632649	+	0.774439i	$0.281968\pi$
$410$	−4.78408e10	+	7.89151e9i	−0.0836125	+	0.0137922i
$411$	7.77385e11	−	4.48823e11i	1.34384	−	0.775867i
$412$	1.29880e11	+	1.29880e11i	0.222077	+	0.222077i
$413$	−5.26463e11	−	1.93491e10i	−0.890415	−	0.0327254i
$414$			6.78447e10i			0.113505i
$415$	5.63588e11	+	2.12212e11i	0.932706	+	0.351198i
$416$	−2.39862e11	−	1.38484e11i	−0.392683	−	0.226715i
$417$	3.32056e10	+	1.23925e11i	0.0537774	+	0.200700i
$418$	−2.87616e10	−	7.70664e9i	−0.0460808	−	0.0123473i
$419$	−8.52216e11			−1.35079			−0.675393	−	0.737458i	$-0.736026\pi$
$419$	−8.52216e11			−1.35079			−0.675393	+	0.737458i	$0.736026\pi$
$420$	−4.99252e11	−	6.56265e11i	−0.782885	−	1.02910i
$421$	−6.21862e11			−0.964772			−0.482386	−	0.875959i	$-0.660230\pi$
$421$	−6.21862e11			−0.964772			−0.482386	+	0.875959i	$0.660230\pi$
$422$	1.39421e10	+	3.73578e9i	0.0214005	+	0.00573424i
$423$	1.66903e11	+	6.22890e11i	0.253473	+	0.945976i
$424$	−2.71062e11	−	1.56498e11i	−0.407307	−	0.235159i
$425$	−4.86963e11	+	9.86750e11i	−0.724012	+	1.46709i
$426$		−	3.99036e10i		−	0.0587042i
$427$	−3.33484e11	−	2.09233e11i	−0.485456	−	0.304583i
$428$	3.88945e11	+	3.88945e11i	0.560262	+	0.560262i
$429$	1.05765e12	−	6.10632e11i	1.50759	−	0.870406i
$430$	−6.76311e10	+	9.43505e10i	−0.0953977	+	0.133087i
$431$	2.21739e11	−	3.84063e11i	0.309524	−	0.536111i	−0.668735	−	0.743501i	$-0.733164\pi$
$431$	2.21739e11	−	3.84063e11i	0.309524	−	0.536111i	0.978258	+	0.207391i	$0.0664971\pi$
$432$	5.00356e10	−	1.86736e11i	0.0691198	−	0.257959i
$433$	6.21920e11	−	6.21920e11i	0.850235	−	0.850235i	−0.139927	−	0.990162i	$-0.544687\pi$
$433$	6.21920e11	−	6.21920e11i	0.850235	−	0.850235i	0.990162	+	0.139927i	$0.0446867\pi$
$434$	−2.36634e10	+	7.68959e10i	−0.0320165	+	0.104040i
$435$	−1.89009e11	−	2.30376e11i	−0.253094	−	0.308486i
$436$	1.99595e11	+	3.45709e11i	0.264521	+	0.458165i
$437$	−1.14545e11	+	3.06922e10i	−0.150248	+	0.0402588i
$438$	5.79702e10	−	1.55331e10i	0.0752612	−	0.0201662i
$439$	−1.38581e11	−	2.40030e11i	−0.178079	−	0.308443i	0.763143	−	0.646229i	$-0.223655\pi$
$439$	−1.38581e11	−	2.40030e11i	−0.178079	−	0.308443i	−0.941223	+	0.337787i	$0.890322\pi$
$440$	2.50055e11	+	3.04783e11i	0.318053	+	0.387662i
$441$	4.54611e10	−	6.17633e11i	0.0572356	−	0.777601i
$442$	−1.46251e11	+	1.46251e11i	−0.182263	+	0.182263i
$443$	−1.30257e11	+	4.86126e11i	−0.160688	+	0.599697i	0.837863	+	0.545881i	$0.183805\pi$
$443$	−1.30257e11	+	4.86126e11i	−0.160688	+	0.599697i	−0.998551	+	0.0538158i	$0.982862\pi$
$444$	−9.48282e11	+	1.64247e12i	−1.15801	+	2.00574i
$445$	−1.88972e11	+	2.63630e11i	−0.228443	+	0.318695i
$446$	1.31974e11	−	7.61951e10i	0.157936	−	0.0911843i
$447$	4.85559e11	+	4.85559e11i	0.575252	+	0.575252i
$448$	−6.18080e11	+	3.27190e11i	−0.724926	+	0.383750i
$449$		−	6.46661e11i		−	0.750876i	−0.926848	−	0.375438i	$-0.877492\pi$
$449$		−	6.46661e11i		−	0.750876i	0.926848	−	0.375438i	$-0.122508\pi$
$450$	5.26290e10	−	1.06644e11i	0.0605019	−	0.122597i
$451$	−5.34047e11	−	3.08332e11i	−0.607834	−	0.350933i
$452$	−2.46369e11	−	9.19462e11i	−0.277628	−	1.03612i
$453$	−1.21650e12	−	3.25961e11i	−1.35729	−	0.363684i
$454$	−1.98295e9			−0.00219059
$455$	−1.03839e11	−	8.14888e11i	−0.113582	−	0.891346i
$456$	7.96820e10			0.0863015
$457$	−5.29314e10	−	1.41829e10i	−0.0567663	−	0.0152105i	0.230324	−	0.973114i	$-0.426021\pi$
$457$	−5.29314e10	−	1.41829e10i	−0.0567663	−	0.0152105i	−0.287090	+	0.957903i	$0.592688\pi$
$458$	−8.16627e10	−	3.04769e11i	−0.0867220	−	0.323651i
$459$	−3.95963e11	−	2.28610e11i	−0.416388	−	0.240402i
$460$	7.23204e11	+	2.72313e11i	0.753097	+	0.283569i
$461$			1.23936e12i			1.27804i	0.769191	+	0.639019i	$0.220660\pi$
$461$			1.23936e12i			1.27804i	−0.769191	+	0.639019i	$0.779340\pi$
$462$	−1.22173e10	+	3.32418e11i	−0.0124764	+	0.339465i
$463$	7.60993e11	+	7.60993e11i	0.769602	+	0.769602i	0.978036	−	0.208435i	$-0.0668369\pi$
$463$	7.60993e11	+	7.60993e11i	0.769602	+	0.769602i	−0.208435	+	0.978036i	$0.566837\pi$
$464$	−2.35025e11	+	1.35692e11i	−0.235387	+	0.135901i
$465$	8.23852e11	−	1.35897e11i	0.817167	−	0.134795i
$466$	−5.29010e10	+	9.16272e10i	−0.0519669	+	0.0900094i
$467$	−9.38892e10	+	3.50399e11i	−0.0913460	+	0.340908i	−0.996440	−	0.0843033i	$-0.973134\pi$
$467$	−9.38892e10	+	3.50399e11i	−0.0913460	+	0.340908i	0.905094	+	0.425211i	$0.139800\pi$
$468$	−4.98315e11	+	4.98315e11i	−0.480173	+	0.480173i
$469$	1.04502e12	−	9.70929e11i	0.997350	−	0.926637i
$470$	−2.31859e11	−	2.28697e10i	−0.219172	−	0.0216182i
$471$	−2.79840e11	−	4.84696e11i	−0.262008	−	0.453812i
$472$	−3.20443e11	+	8.58625e10i	−0.297175	+	0.0796278i
$473$	−1.42608e12	+	3.82117e11i	−1.30999	+	0.351011i
$474$	2.03321e11	+	3.52162e11i	0.185003	+	0.320435i
$475$	2.03860e11	+	4.06110e10i	0.183743	+	0.0366035i
$476$	3.96359e11	+	1.73127e12i	0.353881	+	1.54573i
$477$	−8.49095e11	+	8.49095e11i	−0.750972	+	0.750972i
$478$	−6.06492e10	+	2.26346e11i	−0.0531373	+	0.198311i
$479$	7.11490e11	−	1.23234e12i	0.617531	−	1.06960i	−0.372404	−	0.928071i	$-0.621466\pi$
$479$	7.11490e11	−	1.23234e12i	0.617531	−	1.06960i	0.989935	−	0.141524i	$-0.0452003\pi$
$480$	−6.36342e11	−	4.56134e11i	−0.547148	−	0.392199i
$481$	−1.63629e12	+	9.44710e11i	−1.39382	+	0.804722i
$482$	−1.96446e11	−	1.96446e11i	−0.165780	−	0.165780i
$483$	6.19799e11	+	1.17084e12i	0.518190	+	0.978890i
$484$			1.29765e12i			1.07486i
$485$	3.31974e11	−	8.81650e11i	0.272437	−	0.723533i
$486$	2.37052e11	+	1.36862e11i	0.192744	+	0.111281i
$487$	3.48121e11	+	1.29920e12i	0.280446	+	1.04664i	0.952103	+	0.305777i	$0.0989163\pi$
$487$	3.48121e11	+	1.29920e12i	0.280446	+	1.04664i	−0.671657	+	0.740862i	$0.734417\pi$
$488$	−2.39465e11	−	6.41645e10i	−0.191141	−	0.0512160i
$489$	1.48825e12			1.17703
$490$	2.03045e11	+	9.40044e10i	0.159114	+	0.0736658i
$491$	1.38512e12			1.07552			0.537762	−	0.843097i	$-0.319270\pi$
$491$	1.38512e12			1.07552			0.537762	+	0.843097i	$0.319270\pi$
$492$	7.84548e11	+	2.10219e11i	0.603638	+	0.161744i
$493$	1.66119e11	+	6.19966e11i	0.126651	+	0.472668i
$494$	3.38367e10	+	1.95356e10i	0.0255633	+	0.0147590i
$495$	1.37774e12	−	6.24010e11i	1.03144	−	0.467163i
$496$		−	7.60432e11i		−	0.564148i
$497$	−1.59709e11	−	3.01700e11i	−0.117416	−	0.221805i
$498$	2.26260e11	+	2.26260e11i	0.164845	+	0.164845i
$499$	−1.77477e12	+	1.02466e12i	−1.28141	+	0.739823i	−0.977106	−	0.212752i	$-0.931757\pi$
$499$	−1.77477e12	+	1.02466e12i	−1.28141	+	0.739823i	−0.304305	+	0.952575i	$0.598424\pi$
$500$	−9.25553e11	−	9.89055e11i	−0.662272	−	0.707710i
$501$	−2.96509e11	+	5.13568e11i	−0.210265	+	0.364190i
$502$	−3.63802e10	+	1.35773e11i	−0.0255681	+	0.0954213i
$503$	1.89072e12	−	1.89072e12i	1.31696	−	1.31696i	0.400786	−	0.916172i	$-0.368737\pi$
$503$	1.89072e12	−	1.89072e12i	1.31696	−	1.31696i	0.916172	−	0.400786i	$-0.131263\pi$
$504$	−8.70325e10	−	3.80152e11i	−0.0600820	−	0.262434i
$505$	−1.23270e11	+	1.24975e12i	−0.0843426	+	0.855089i
$506$	−1.55871e11	−	2.69976e11i	−0.105703	−	0.183083i
$507$	3.69242e11	−	9.89381e10i	0.248185	−	0.0665010i
$508$	−3.56386e11	+	9.54933e10i	−0.237429	+	0.0636189i
$509$	−7.18794e11	−	1.24499e12i	−0.474651	−	0.822119i	0.524928	−	0.851147i	$-0.324092\pi$
$509$	−7.18794e11	−	1.24499e12i	−0.474651	−	0.822119i	−0.999579	+	0.0290275i	$0.990759\pi$
$510$	−4.52006e11	+	3.70844e11i	−0.295855	+	0.242731i
$511$	3.76127e11	−	3.49459e11i	0.244028	−	0.226727i
$512$	−8.49181e11	+	8.49181e11i	−0.546117	+	0.546117i
$513$	−2.23545e10	+	8.34282e10i	−0.0142507	+	0.0531845i
$514$	9.45168e10	−	1.63708e11i	0.0597276	−	0.103451i
$515$	8.41870e10	+	5.10368e11i	0.0527366	+	0.319706i
$516$	1.68406e12	−	9.72293e11i	1.04577	−	0.603773i
$517$	−2.09523e12	−	2.09523e12i	−1.28981	−	1.28981i
$518$	1.89015e10	−	5.14284e11i	0.0115348	−	0.313848i
$519$		−	3.90039e12i		−	2.35969i
$520$	−2.13426e11	−	4.71220e11i	−0.128006	−	0.282624i
$521$	−1.85981e11	−	1.07376e11i	−0.110586	−	0.0638467i	0.443687	−	0.896182i	$-0.353670\pi$
$521$	−1.85981e11	−	1.07376e11i	−0.110586	−	0.0638467i	−0.554273	+	0.832335i	$0.687004\pi$
$522$	−1.79535e10	−	6.70034e10i	−0.0105836	−	0.0394984i
$523$	5.54547e11	+	1.48591e11i	0.324101	+	0.0868427i	0.417201	−	0.908814i	$-0.363011\pi$
$523$	5.54547e11	+	1.48591e11i	0.324101	+	0.0868427i	−0.0931000	+	0.995657i	$0.529678\pi$
$524$	−1.45364e12			−0.842300
$525$	−6.60025e10	−	2.32121e12i	−0.0379179	−	1.33352i
$526$	1.97425e11			0.112452
$527$	−1.73718e12	−	4.65477e11i	−0.981065	−	0.262875i
$528$	−8.13736e11	−	3.03690e12i	−0.455649	−	1.70051i
$529$	4.84647e11	+	2.79811e11i	0.269076	+	0.155351i
$530$	−1.78993e11	−	3.95196e11i	−0.0985358	−	0.217556i
$531$			1.27274e12i			0.694729i
$532$	2.96523e11	−	1.56969e11i	0.160493	−	0.0849594i
$533$	5.72166e11	+	5.72166e11i	0.307079	+	0.307079i
$534$	−1.49256e11	+	8.61730e10i	−0.0794321	+	0.0458601i
$535$	2.52111e11	+	1.52838e12i	0.133045	+	0.806563i
$536$	4.49133e11	−	7.77921e11i	0.235035	−	0.407093i
$537$	8.27001e11	−	3.08641e12i	0.429163	−	1.60166i
$538$	−1.68651e11	+	1.68651e11i	−0.0867897	+	0.0867897i
$539$	1.23809e12	+	2.56221e12i	0.631832	+	1.30757i
$540$	4.35137e11	−	3.57004e11i	0.220219	−	0.180676i
$541$	7.65030e11	+	1.32507e12i	0.383964	+	0.665046i	0.991625	−	0.129151i	$-0.0412252\pi$
$541$	7.65030e11	+	1.32507e12i	0.383964	+	0.665046i	−0.607661	+	0.794197i	$0.707892\pi$
$542$	1.27578e11	−	3.41843e10i	0.0635005	−	0.0170149i
$543$	2.43807e12	−	6.53280e11i	1.20350	−	0.322478i
$544$	8.43178e11	+	1.46043e12i	0.412785	+	0.714965i
$545$	−1.10349e11	+	1.11875e12i	−0.0535779	+	0.543188i
$546$	1.28378e11	−	4.17175e11i	0.0618194	−	0.200887i
$547$	3.49210e11	−	3.49210e11i	0.166780	−	0.166780i	−0.618782	−	0.785562i	$-0.712374\pi$
$547$	3.49210e11	−	3.49210e11i	0.166780	−	0.166780i	0.785562	+	0.618782i	$0.212374\pi$
$548$	6.16014e11	−	2.29899e12i	0.291795	−	1.08899i
$549$	−4.75557e11	+	8.23688e11i	−0.223422	+	0.386979i
$550$	3.55830e10	+	5.45285e11i	0.0165810	+	0.254092i
$551$	1.05002e11	−	6.06232e10i	0.0485308	−	0.0280192i
$552$	5.89890e11	+	5.89890e11i	0.270424	+	0.270424i
$553$	2.94673e12	+	1.84883e12i	1.33991	+	0.840685i
$554$		−	6.26504e11i		−	0.282573i
$555$	−4.86526e12	+	2.20358e12i	−2.17664	+	0.985848i
$556$	2.94602e11	+	1.70088e11i	0.130737	+	0.0754811i
$557$	8.25646e11	+	3.08135e12i	0.363451	+	1.35642i	0.869509	+	0.493917i	$0.164435\pi$
$557$	8.25646e11	+	3.08135e12i	0.363451	+	1.35642i	−0.506058	+	0.862499i	$0.668898\pi$
$558$	1.87748e11	+	5.03068e10i	0.0819824	+	0.0219671i
$559$	1.93726e12			0.839142
$560$	−2.09556e12	−	2.84748e11i	−0.900438	−	0.122353i
$561$	−7.43581e12			−3.16953
$562$	2.88955e11	+	7.74253e10i	0.122185	+	0.0327393i
$563$	−1.65047e11	−	6.15962e11i	−0.0692339	−	0.258384i	0.922630	−	0.385686i	$-0.126035\pi$
$563$	−1.65047e11	−	6.15962e11i	−0.0692339	−	0.258384i	−0.991864	+	0.127301i	$0.959368\pi$
$564$	3.37991e12	+	1.95139e12i	1.40653	+	0.812061i
$565$	9.44632e11	−	2.50874e12i	0.389982	−	1.03571i
$566$			3.07523e11i			0.125952i
$567$	2.88185e12	+	1.05917e11i	1.17097	+	0.0430368i
$568$	−1.52002e11	−	1.52002e11i	−0.0612749	−	0.0612749i
$569$	1.09443e12	−	6.31867e11i	0.437704	−	0.252709i	−0.264919	−	0.964271i	$-0.585345\pi$
$569$	1.09443e12	−	6.31867e11i	0.437704	−	0.252709i	0.702623	+	0.711562i	$0.252012\pi$
$570$	8.97670e10	+	6.43456e10i	0.0356189	+	0.0255318i
$571$	−7.39172e11	+	1.28028e12i	−0.290993	+	0.504015i	−0.974045	−	0.226355i	$-0.927319\pi$
$571$	−7.39172e11	+	1.28028e12i	−0.290993	+	0.504015i	0.683051	+	0.730370i	$0.260652\pi$
$572$	8.38098e11	−	3.12782e12i	0.327350	−	1.22169i
$573$	−3.97575e12	+	3.97575e12i	−1.54072	+	1.54072i
$574$	−2.14838e11	+	4.91853e10i	−0.0826052	+	0.0189118i
$575$	1.20854e12	+	1.80983e12i	0.461059	+	0.690451i
$576$	8.44769e11	+	1.46318e12i	0.319769	+	0.553857i
$577$	2.33760e12	−	6.26357e11i	0.877967	−	0.235251i	0.208437	−	0.978036i	$-0.433162\pi$
$577$	2.33760e12	−	6.26357e11i	0.877967	−	0.235251i	0.669530	+	0.742785i	$0.266496\pi$
$578$	7.61931e11	−	2.04159e11i	0.283949	−	0.0760840i
$579$	−3.13563e11	−	5.43107e11i	−0.115950	−	0.200832i
$580$	−7.86298e11	−	7.75573e10i	−0.288510	−	0.0284575i
$581$	2.61626e12	+	8.05110e11i	0.952552	+	0.293131i
$582$	3.53950e11	−	3.53950e11i	0.127876	−	0.127876i
$583$	1.42806e12	−	5.32960e12i	0.511963	−	1.91067i
$584$	1.61653e11	−	2.79991e11i	0.0575077	−	0.0996062i
$585$	−1.95815e12	+	3.23004e11i	−0.691265	+	0.114027i
$586$	5.34337e11	−	3.08500e11i	0.187187	−	0.108073i
$587$	−2.43965e12	−	2.43965e12i	−0.848116	−	0.848116i	0.141782	−	0.989898i	$-0.454717\pi$
$587$	−2.43965e12	−	2.43965e12i	−0.848116	−	0.848116i	−0.989898	+	0.141782i	$0.954717\pi$
$588$	−2.44860e12	−	2.83770e12i	−0.844734	−	0.978969i
$589$			3.39740e11i			0.116313i
$590$	−4.30337e11	−	1.62038e11i	−0.146209	−	0.0550532i
$591$	7.48431e11	+	4.32107e11i	0.252353	+	0.145696i
$592$	1.25893e12	+	4.69840e12i	0.421264	+	1.57218i
$593$	−1.35344e12	−	3.62654e11i	−0.449463	−	0.120433i	0.0269853	−	0.999636i	$-0.491409\pi$
$593$	−1.35344e12	−	3.62654e11i	−0.449463	−	0.120433i	−0.476448	+	0.879203i	$0.658076\pi$
$594$	−2.27056e11			−0.0748332
$595$	−1.93323e12	+	4.61294e12i	−0.632351	+	1.50887i
$596$	1.82073e12			0.591069
$597$	−7.35682e12	−	1.97125e12i	−2.37031	−	0.635123i
$598$	1.05872e11	+	3.95119e11i	0.0338551	+	0.126349i
$599$	−2.25216e12	−	1.30028e12i	−0.714790	−	0.412684i	0.0980422	−	0.995182i	$-0.468742\pi$
$599$	−2.25216e12	−	1.30028e12i	−0.714790	−	0.412684i	−0.812832	+	0.582498i	$0.802075\pi$
$600$	−4.69645e11	−	1.38483e12i	−0.147941	−	0.436231i
$601$		−	2.95541e12i		−	0.924023i	−0.886874	−	0.462012i	$-0.847128\pi$
$601$		−	2.95541e12i		−	0.924023i	0.886874	−	0.462012i	$-0.152872\pi$
$602$	−2.80437e11	+	4.46971e11i	−0.0870264	+	0.138706i
$603$	−2.43682e12	−	2.43682e12i	−0.750577	−	0.750577i
$604$	−2.89194e12	+	1.66966e12i	−0.884143	+	0.510460i
$605$	−2.12902e12	+	2.97014e12i	−0.646071	+	0.901319i
$606$	−3.33630e11	+	5.77864e11i	−0.100494	+	0.174060i
$607$	−1.01019e12	+	3.77009e12i	−0.302033	+	1.12720i	0.633436	+	0.773795i	$0.281644\pi$
$607$	−1.01019e12	+	3.77009e12i	−0.302033	+	1.12720i	−0.935469	+	0.353409i	$0.885023\pi$
$608$	2.25258e11	−	2.25258e11i	0.0668518	−	0.0668518i
$609$	−9.21948e11	−	9.92302e11i	−0.271599	−	0.292325i
$610$	−2.17959e11	−	2.65661e11i	−0.0637368	−	0.0776862i
$611$	1.94404e12	+	3.36718e12i	0.564314	+	0.977420i
$612$	4.14459e12	−	1.11054e12i	1.19426	−	0.320002i
$613$	3.18601e12	−	8.53688e11i	0.911328	−	0.244190i	0.227453	−	0.973789i	$-0.426960\pi$
$613$	3.18601e12	−	8.53688e11i	0.911328	−	0.244190i	0.683875	+	0.729599i	$0.260293\pi$
$614$	−2.50837e11	−	4.34462e11i	−0.0712252	−	0.123366i
$615$	1.45082e12	+	1.76835e12i	0.408956	+	0.498460i
$616$	1.21972e12	+	1.31280e12i	0.341308	+	0.367353i
$617$	−1.15409e12	+	1.15409e12i	−0.320594	+	0.320594i	−0.848995	−	0.528401i	$-0.822792\pi$
$617$	−1.15409e12	+	1.15409e12i	−0.320594	+	0.320594i	0.528401	+	0.848995i	$0.322792\pi$
$618$	−7.11344e10	+	2.65477e11i	−0.0196169	+	0.0732114i
$619$	−6.91455e11	+	1.19764e12i	−0.189302	+	0.327881i	−0.945018	−	0.327019i	$-0.893956\pi$
$619$	−6.91455e11	+	1.19764e12i	−0.189302	+	0.327881i	0.755715	+	0.654900i	$0.227289\pi$
$620$	1.28983e12	−	1.79942e12i	0.350567	−	0.489067i
$621$	−7.83116e11	+	4.52132e11i	−0.211307	+	0.121998i
$622$	−3.50711e11	−	3.50711e11i	−0.0939492	−	0.0939492i
$623$	−7.83585e11	+	1.24891e12i	−0.208396	+	0.332150i
$624$			4.12549e12i			1.08929i
$625$	−4.95750e11	−	3.78235e12i	−0.129958	−	0.991520i
$626$	−1.17545e11	−	6.78647e10i	−0.0305929	−	0.0176628i
$627$	3.63554e11	+	1.35680e12i	0.0939432	+	0.350601i
$628$	−1.43341e12	−	3.84082e11i	−0.367751	−	0.0985385i
$629$	1.15040e13			2.93035
$630$	2.08936e11	−	4.98548e11i	0.0528422	−	0.126088i
$631$	−2.21509e12			−0.556236			−0.278118	−	0.960547i	$-0.589711\pi$
$631$	−2.21509e12			−0.556236			−0.278118	+	0.960547i	$0.589711\pi$
$632$	2.11596e12	+	5.66970e11i	0.527571	+	0.141362i
$633$	−1.76232e11	−	6.57708e11i	−0.0436284	−	0.162823i
$634$	−9.80224e11	−	5.65933e11i	−0.240948	−	0.139112i
$635$	−9.72394e11	−	3.66142e11i	−0.237334	−	0.0893651i
$636$			7.26738e12i			1.76125i
$637$	−6.99057e11	−	3.66796e12i	−0.168223	−	0.882667i
$638$	2.25381e11	+	2.25381e11i	0.0538548	+	0.0538548i
$639$	−7.14215e11	+	4.12352e11i	−0.169463	+	0.0978396i
$640$	−2.71551e12	+	4.47933e11i	−0.639796	+	0.105537i
$641$	−1.92295e12	+	3.33065e12i	−0.449890	+	0.779233i	−0.998378	−	0.0569255i	$-0.981870\pi$
$641$	−1.92295e12	+	3.33065e12i	−0.449890	+	0.779233i	0.548488	+	0.836158i	$0.315204\pi$
$642$	−2.13023e11	+	7.95013e11i	−0.0494902	+	0.184700i
$643$	−1.74831e12	+	1.74831e12i	−0.403338	+	0.403338i	−0.879407	−	0.476070i	$-0.842061\pi$
$643$	−1.74831e12	+	1.74831e12i	−0.403338	+	0.403338i	0.476070	+	0.879407i	$0.342061\pi$
$644$	3.35723e12	+	1.03313e12i	0.769121	+	0.236684i
$645$	5.44981e12	+	5.37548e11i	1.23983	+	0.122292i
$646$	−1.18945e11	−	2.06019e11i	−0.0268720	−	0.0465436i
$647$	−4.61930e12	+	1.23774e12i	−1.03635	+	0.277690i	−0.736601	−	0.676328i	$-0.763570\pi$
$647$	−4.61930e12	+	1.23774e12i	−1.03635	+	0.277690i	−0.299751	+	0.954017i	$0.596904\pi$
$648$	1.75410e12	−	4.70010e11i	0.390811	−	0.104718i
$649$	−2.92409e12	−	5.06467e12i	−0.646978	−	1.12060i
$650$	1.40086e11	−	7.03209e11i	0.0307812	−	0.154516i
$651$	3.69966e12	−	8.47005e11i	0.807322	−	0.184830i
$652$	2.79029e12	−	2.79029e12i	0.604694	−	0.604694i
$653$	−1.46379e12	+	5.46293e12i	−0.315042	+	1.17575i	0.608908	+	0.793241i	$0.291608\pi$
$653$	−1.46379e12	+	5.46293e12i	−0.315042	+	1.17575i	−0.923950	+	0.382513i	$0.875059\pi$
$654$	−2.98660e11	+	5.17294e11i	−0.0638377	+	0.110570i
$655$	−3.32719e12	−	2.38496e12i	−0.706305	−	0.506284i
$656$	1.80403e12	−	1.04156e12i	0.380345	−	0.219592i
$657$	−8.77066e11	−	8.77066e11i	−0.183649	−	0.183649i
$658$	−1.05830e12	−	3.88958e10i	−0.220087	−	0.00808885i
$659$		−	5.41088e12i		−	1.11759i	−0.829305	−	0.558796i	$-0.811263\pi$
$659$		−	5.41088e12i		−	1.11759i	0.829305	−	0.558796i	$-0.188737\pi$
$660$	3.22560e12	−	8.56649e12i	0.661702	−	1.75734i
$661$	−3.90480e12	−	2.25444e12i	−0.795596	−	0.459337i	0.0463332	−	0.998926i	$-0.485246\pi$
$661$	−3.90480e12	−	2.25444e12i	−0.795596	−	0.459337i	−0.841929	+	0.539589i	$0.818580\pi$
$662$	4.13938e11	+	1.54484e12i	0.0837672	+	0.312623i
$663$	9.42454e12	+	2.52530e12i	1.89430	+	0.507577i
$664$	1.72375e12			0.344127
$665$	9.36237e11	+	1.27218e11i	0.185647	+	0.0252261i
$666$	−1.24330e12			−0.244874
$667$	1.22614e12	+	3.28542e11i	0.239868	+	0.0642724i
$668$	4.06961e11	+	1.51880e12i	0.0790785	+	0.295125i
$669$	−6.22575e12	−	3.59444e12i	−1.20164	−	0.693766i
$670$	1.13417e12	−	5.13691e11i	0.217442	−	0.0984840i
$671$		−	4.37030e12i		−	0.832263i
$672$	−3.01457e12	−	1.89139e12i	−0.570248	−	0.357783i
$673$	2.26375e12	+	2.26375e12i	0.425363	+	0.425363i	0.887045	−	0.461682i	$-0.152754\pi$
$673$	2.26375e12	+	2.26375e12i	0.425363	+	0.425363i	−0.461682	+	0.887045i	$0.652754\pi$
$674$	4.45709e11	−	2.57330e11i	0.0831920	−	0.0480309i
$675$	1.58170e12	−	1.03215e11i	0.293263	−	0.0191371i
$676$	5.06788e11	−	8.77783e11i	0.0933397	−	0.161669i
$677$	1.04930e12	−	3.91605e12i	0.191978	−	0.716472i	−0.801050	−	0.598597i	$-0.795725\pi$
$677$	1.04930e12	−	3.91605e12i	0.191978	−	0.716472i	0.993028	−	0.117875i	$-0.0376082\pi$
$678$	1.00717e12	−	1.00717e12i	0.183049	−	0.183049i
$679$	1.25948e12	−	4.09276e12i	0.227392	−	0.738928i
$680$	−3.09168e11	+	3.13443e12i	−0.0554503	+	0.562170i
$681$	4.67720e10	+	8.10115e10i	0.00833343	+	0.0144339i
$682$	−8.62689e11	+	2.31157e11i	−0.152695	+	0.0409145i
$683$	−2.28105e12	+	6.11207e11i	−0.401091	+	0.107472i	−0.453725	−	0.891142i	$-0.649905\pi$
$683$	−2.28105e12	+	6.11207e11i	−0.401091	+	0.107472i	0.0526339	+	0.998614i	$0.483238\pi$
$684$	−4.05277e11	−	7.01961e11i	−0.0707946	−	0.122620i
$685$	5.18188e12	−	4.25142e12i	0.899248	−	0.737779i
$686$	9.47476e11	+	3.69682e11i	0.163346	+	0.0637339i
$687$	−1.05249e13	+	1.05249e13i	−1.80265	+	1.80265i
$688$	1.29081e12	−	4.81737e12i	0.219641	−	0.819713i
$689$	−3.62001e12	+	6.27004e12i	−0.611960	+	1.05995i
$690$	1.88196e11	+	1.14090e12i	0.0316075	+	0.191615i
$691$	5.52571e11	−	3.19027e11i	0.0922012	−	0.0532324i	−0.453190	−	0.891414i	$-0.649714\pi$
$691$	5.52571e11	−	3.19027e11i	0.0922012	−	0.0532324i	0.545392	+	0.838181i	$0.316381\pi$
$692$	−7.31277e12	−	7.31277e12i	−1.21228	−	1.21228i
$693$	6.07603e12	−	3.21643e12i	1.00074	−	0.529755i
$694$			5.55520e11i			0.0909038i
$695$	3.95244e11	+	8.72655e11i	0.0642590	+	0.141877i
$696$	−7.38676e11	−	4.26475e11i	−0.119320	−	0.0688893i
$697$	−1.27512e12	−	4.75882e12i	−0.204646	−	0.763751i
$698$	−1.53098e12	−	4.10224e11i	−0.244129	−	0.0654141i
$699$	4.99112e12			0.790770
$700$	−4.47575e12	−	4.22826e12i	−0.704571	−	0.665610i
$701$	5.89589e12			0.922186			0.461093	−	0.887352i	$-0.347458\pi$
$701$	5.89589e12			0.922186			0.461093	+	0.887352i	$0.347458\pi$
$702$	2.87783e11	+	7.71113e10i	0.0447248	+	0.0119840i
$703$	−5.62456e11	−	2.09911e12i	−0.0868539	−	0.324143i
$704$	−6.72324e12	−	3.88166e12i	−1.03158	−	0.595581i
$705$	4.53457e12	+	1.00118e13i	0.691329	+	1.52638i
$706$			4.18213e11i			0.0633544i
$707$	−2.09653e11	+	5.70438e12i	−0.0315583	+	0.858659i
$708$	5.44669e12	+	5.44669e12i	0.814672	+	0.814672i
$709$	−4.60998e12	+	2.66158e12i	−0.685159	+	0.395577i	−0.801796	−	0.597598i	$-0.796122\pi$
$709$	−4.60998e12	+	2.66158e12i	−0.685159	+	0.395577i	0.116637	+	0.993175i	$0.462789\pi$
$710$	−4.84942e10	−	2.93987e11i	−0.00716188	−	0.0434176i
$711$	4.20211e12	−	7.27827e12i	0.616672	−	1.06811i
$712$	−2.40298e11	+	8.96804e11i	−0.0350421	+	0.130779i
$713$	−2.51511e12	+	2.51511e12i	−0.364464	+	0.364464i
$714$	−1.94693e12	+	1.80890e12i	−0.280356	+	0.260478i
$715$	7.05004e12	−	5.78413e12i	1.00882	−	0.827677i
$716$	−4.23613e12	−	7.33719e12i	−0.602366	−	1.04333i
$717$	1.06777e13	−	2.86107e12i	1.50883	−	0.404290i
$718$	−1.26568e11	+	3.39137e10i	−0.0177731	+	0.00476228i
$719$	4.34326e12	+	7.52275e12i	0.606088	+	1.04978i	0.991878	+	0.127189i	$0.0405955\pi$
$719$	4.34326e12	+	7.52275e12i	0.606088	+	1.04978i	−0.385790	+	0.922587i	$0.626071\pi$
$720$	−5.01518e11	+	5.08453e12i	−0.0695489	+	0.705106i
$721$	5.24712e11	+	2.29190e12i	0.0723123	+	0.315855i
$722$	8.73504e11	−	8.73504e11i	0.119632	−	0.119632i
$723$	−3.39202e12	+	1.26592e13i	−0.461674	+	1.72299i
$724$	3.34628e12	−	5.79592e12i	0.452625	−	0.783969i
$725$	−1.67249e12	−	1.46758e12i	−0.224823	−	0.197279i
$726$	−1.68157e12	+	9.70854e11i	−0.224646	+	0.129700i
$727$	5.39022e12	+	5.39022e12i	0.715651	+	0.715651i	0.967712	−	0.252060i	$-0.0811081\pi$
$727$	5.39022e12	+	5.39022e12i	0.715651	+	0.715651i	−0.252060	+	0.967712i	$0.581108\pi$
$728$	−1.10009e12	−	2.07814e12i	−0.145157	−	0.274210i
$729$		−	3.97728e12i		−	0.521570i
$730$	4.08214e11	−	1.84889e11i	0.0532029	−	0.0240967i
$731$	−1.02150e13	−	5.89762e12i	−1.32315	−	0.763922i
$732$	1.48982e12	+	5.56010e12i	0.191794	+	0.715785i
$733$	−1.45834e13	−	3.90761e12i	−1.86591	−	0.499970i	−0.865912	−	0.500197i	$-0.833261\pi$
$733$	−1.45834e13	−	3.90761e12i	−1.86591	−	0.499970i	−1.00000		0.000227323i	$0.999928\pi$
$734$	−2.01081e11			−0.0255705
$735$	−9.48776e11	−	1.05125e13i	−0.119914	−	1.32866i
$736$	3.33519e12			0.418958
$737$	1.52954e13	+	4.09840e12i	1.90967	+	0.511694i
$738$	1.37810e11	+	5.14314e11i	0.0171012	+	0.0638226i
$739$	−1.39728e12	−	8.06722e11i	−0.172339	−	0.0995001i	0.411349	−	0.911478i	$-0.365058\pi$
$739$	−1.39728e12	−	8.06722e11i	−0.172339	−	0.0995001i	−0.583688	+	0.811978i	$0.698391\pi$
$740$	−4.99033e12	+	1.32532e13i	−0.611768	+	1.62472i
$741$		−	1.84315e12i		−	0.224584i
$742$	−9.22610e11	−	1.74286e12i	−0.111738	−	0.211079i
$743$	−1.16529e13	−	1.16529e13i	−1.40277	−	1.40277i	−0.791162	−	0.611607i	$-0.790523\pi$
$743$	−1.16529e13	−	1.16529e13i	−1.40277	−	1.40277i	−0.611607	−	0.791162i	$-0.709477\pi$
$744$	2.06982e12	−	1.19501e12i	0.247659	−	0.142986i
$745$	4.16742e12	+	2.98723e12i	0.495637	+	0.355276i
$746$	3.16324e11	−	5.47889e11i	0.0373945	−	0.0647691i
$747$	1.71161e12	−	6.38782e12i	0.201123	−	0.750602i
$748$	−1.39413e13	+	1.39413e13i	−1.62834	+	1.62834i
$749$	1.57133e12	+	6.86346e12i	0.182431	+	0.796847i
$750$	5.89209e11	−	1.93936e12i	0.0679976	−	0.223812i
$751$	1.34517e12	+	2.32991e12i	0.154311	+	0.267275i	0.932808	−	0.360373i	$-0.117351\pi$
$751$	1.34517e12	+	2.32991e12i	0.154311	+	0.267275i	−0.778497	+	0.627649i	$0.784017\pi$
$752$	9.66845e12	−	2.59065e12i	1.10250	−	0.295413i
$753$	6.40496e12	−	1.71620e12i	0.726004	−	0.194532i
$754$	−2.09118e11	−	3.62203e11i	−0.0235624	−	0.0408113i
$755$	−9.35863e12	−	9.23099e11i	−1.04822	−	0.103392i
$756$	1.87428e12	−	1.74139e12i	0.208682	−	0.193887i
$757$	1.54193e12	−	1.54193e12i	0.170661	−	0.170661i	−0.616609	−	0.787270i	$-0.711494\pi$
$757$	1.54193e12	−	1.54193e12i	0.170661	−	0.170661i	0.787270	+	0.616609i	$0.211494\pi$
$758$	−4.68265e11	+	1.74759e12i	−0.0515206	+	0.192277i
$759$	−7.35308e12	+	1.27359e13i	−0.804232	+	1.39297i
$760$	5.87051e11	−	9.68361e10i	0.0638285	−	0.0105287i
$761$	−2.36905e12	+	1.36777e12i	−0.256061	+	0.147837i	−0.622536	−	0.782591i	$-0.713898\pi$
$761$	−2.36905e12	+	1.36777e12i	−0.256061	+	0.147837i	0.366476	+	0.930428i	$0.380564\pi$
$762$	−3.90381e11	−	3.90381e11i	−0.0419461	−	0.0419461i
$763$	−1.87678e11	+	5.10646e12i	−0.0200471	+	0.545455i
$764$			1.49081e13i			1.58308i
$765$	1.13084e13	+	4.25805e12i	1.19379	+	0.449504i
$766$	−1.43587e10	−	8.29001e9i	−0.00150691	−	0.000870013i
$767$	1.98612e12	+	7.41229e12i	0.207217	+	0.773345i
$768$	8.77762e12	+	2.35196e12i	0.910440	+	0.243952i
$769$	3.46070e12			0.356858			0.178429	−	0.983953i	$-0.442899\pi$
$769$	3.46070e12			0.356858			0.178429	+	0.983953i	$0.442899\pi$
$770$	3.13971e11	+	2.46391e12i	0.0321871	+	0.252590i
$771$	−8.91750e12			−0.908863
$772$	−1.60616e12	−	4.30368e11i	−0.162746	−	0.0436076i
$773$	−2.88792e12	−	1.07779e13i	−0.290922	−	1.08574i	−0.944402	−	0.328793i	$-0.893358\pi$
$773$	−2.88792e12	−	1.07779e13i	−0.290922	−	1.08574i	0.653480	−	0.756944i	$-0.273308\pi$
$774$	1.10399e12	+	6.37392e11i	0.110569	+	0.0638369i
$775$	5.90451e12	−	2.00243e12i	0.587931	−	0.199388i
$776$		−	2.69656e12i		−	0.266951i
$777$	−2.14564e13	+	1.13583e13i	−2.11185	+	1.11794i
$778$	−2.90660e11	−	2.90660e11i	−0.0284431	−	0.0284431i
$779$	−8.05992e11	+	4.65340e11i	−0.0784174	+	0.0452743i
$780$	−6.99759e12	+	9.76217e12i	−0.676897	+	0.944323i
$781$	1.89473e12	−	3.28177e12i	0.182229	−	0.315630i
$782$	6.44612e11	−	2.40572e12i	0.0616408	−	0.230046i
$783$	6.53759e11	−	6.53759e11i	0.0621570	−	0.0621570i
$784$	−9.58685e12	−	7.05644e11i	−0.906261	−	0.0667057i
$785$	−2.65074e12	−	3.23088e12i	−0.249146	−	0.303674i
$786$	−1.08756e12	−	1.88371e12i	−0.101637	−	0.176041i
$787$	1.58681e13	−	4.25184e12i	1.47448	−	0.395085i	0.570013	−	0.821635i	$-0.306938\pi$
$787$	1.58681e13	−	4.25184e12i	1.47448	−	0.395085i	0.904464	+	0.426550i	$0.140271\pi$
$788$	2.21337e12	−	5.93071e11i	0.204497	−	0.0547947i
$789$	−4.65668e12	−	8.06560e12i	−0.427789	−	0.740952i
$790$	1.92593e12	+	2.34743e12i	0.175921	+	0.214423i
$791$	3.58384e12	−	1.16460e13i	0.325503	−	1.05775i
$792$	3.06122e12	−	3.06122e12i	0.276460	−	0.276460i
$793$	−1.48421e12	+	5.53916e12i	−0.133281	+	0.497410i
$794$	−1.49513e12	+	2.58964e12i	−0.133501	+	0.231231i
$795$	−1.19234e13	+	1.66341e13i	−1.05864	+	1.47688i
$796$	−1.74890e13	+	1.00973e13i	−1.54403	+	0.891449i
$797$	−4.24368e12	−	4.24368e12i	−0.372546	−	0.372546i	0.495858	−	0.868404i	$-0.334854\pi$
$797$	−4.24368e12	−	4.24368e12i	−0.372546	−	0.372546i	−0.868404	+	0.495858i	$0.834854\pi$
$798$	4.25257e11	+	2.66814e11i	0.0371226	+	0.0232914i
$799$		−	2.36731e13i		−	2.05491i
$800$	−5.24253e12	−	2.58720e12i	−0.452518	−	0.223319i
$801$	3.08473e12	+	1.78097e12i	0.264772	+	0.152866i
$802$	−5.67235e11	−	2.11695e12i	−0.0484149	−	0.180687i
$803$	5.50517e12	+	1.47510e12i	0.467251	+	0.125200i
$804$	−2.08567e13			−1.76032
$805$	5.98922e12	+	7.87282e12i	0.502677	+	0.660768i
$806$	1.17192e12			0.0978118
$807$	1.08680e13	+	2.91208e12i	0.902029	+	0.241698i
$808$	9.30345e11	+	3.47209e12i	0.0767879	+	0.286576i
$809$	6.90858e12	+	3.98867e12i	0.567049	+	0.327386i	0.755970	−	0.654607i	$-0.227166\pi$
$809$	6.90858e12	+	3.98867e12i	0.567049	+	0.327386i	−0.188921	+	0.981992i	$0.560499\pi$
$810$	2.35566e12	+	8.86993e11i	0.192278	+	0.0723999i
$811$		−	2.05142e13i		−	1.66518i	−0.553893	−	0.832588i	$-0.686858\pi$
$811$		−	2.05142e13i		−	1.66518i	0.553893	−	0.832588i	$-0.313142\pi$
$812$	−3.58899e12	−	1.31906e11i	−0.289715	−	0.0106479i
$813$	−4.40575e12	−	4.40575e12i	−0.353681	−	0.353681i
$814$	4.94751e12	−	2.85645e12i	0.394981	−	0.228043i
$815$	1.09646e13	−	1.80864e12i	0.870528	−	0.143597i
$816$	1.25593e13	−	2.17533e13i	0.991650	−	1.71759i
$817$	−5.76698e11	+	2.15226e12i	−0.0452844	+	0.169004i
$818$	−1.12520e12	+	1.12520e12i	−0.0878697	+	0.0878697i
$819$	−8.79343e12	+	2.01318e12i	−0.682937	+	0.156353i
$820$	6.03557e12	+	5.95325e11i	0.466183	+	0.0459824i
$821$	3.96473e12	+	6.86712e12i	0.304558	+	0.527510i	0.977163	−	0.212492i	$-0.0681580\pi$
$821$	3.96473e12	+	6.86712e12i	0.304558	+	0.527510i	−0.672605	+	0.740002i	$0.734825\pi$
$822$	3.44005e12	−	9.21759e11i	0.262810	−	0.0704197i
$823$	1.08526e13	−	2.90795e12i	0.824586	−	0.220947i	0.178235	−	0.983988i	$-0.442961\pi$
$823$	1.08526e13	−	2.90795e12i	0.824586	−	0.220947i	0.646350	+	0.763041i	$0.276294\pi$
$824$	7.40297e11	+	1.28223e12i	0.0559414	+	0.0968934i
$825$	2.14378e13	−	1.43154e13i	1.61115	−	1.07587i
$826$	−1.99769e12	−	6.14756e11i	−0.149320	−	0.0459507i
$827$	3.57731e12	−	3.57731e12i	0.265939	−	0.265939i	−0.561523	−	0.827461i	$-0.689784\pi$
$827$	3.57731e12	−	3.57731e12i	0.265939	−	0.265939i	0.827461	+	0.561523i	$0.189784\pi$
$828$	2.19637e12	−	8.19695e12i	0.162393	−	0.606060i
$829$	6.43104e12	−	1.11389e13i	0.472918	−	0.819118i	−0.526601	−	0.850112i	$-0.676534\pi$
$829$	6.43104e12	−	1.11389e13i	0.472918	−	0.819118i	0.999520	+	0.0309940i	$0.00986728\pi$
$830$	1.94192e12	+	1.39198e12i	0.142030	+	0.101808i
$831$	−2.55952e13	+	1.47774e13i	−1.86189	+	1.07496i
$832$	7.20313e12	+	7.20313e12i	0.521154	+	0.521154i
$833$	−7.48033e12	+	2.14689e13i	−0.538292	+	1.54492i
$834$			5.09016e11i			0.0364321i
$835$	−1.56038e12	+	4.14402e12i	−0.111081	+	0.295007i
$836$	3.22547e12	+	1.86222e12i	0.228383	+	0.131857i
$837$	6.70512e11	+	2.50239e12i	0.0472218	+	0.176234i
$838$	−3.26595e12	−	8.75108e11i	−0.228776	−	0.0613004i
$839$	−4.45086e12			−0.310110			−0.155055	−	0.987906i	$-0.549555\pi$
$839$	−4.45086e12			−0.310110			−0.155055	+	0.987906i	$0.549555\pi$
$840$	−2.51809e12	−	6.15137e12i	−0.174508	−	0.426300i
$841$	1.32093e13			0.910536
$842$	−2.38316e12	−	6.38566e11i	−0.163399	−	0.0437826i
$843$	−3.65247e12	−	1.36312e13i	−0.249094	−	0.929631i
$844$	−1.56354e12	−	9.02710e11i	−0.106064	−	0.0612361i
$845$	2.60013e12	−	1.17765e12i	0.175444	−	0.0794625i
$846$			2.55849e12i			0.171718i
$847$	−8.82813e12	+	1.40706e13i	−0.589377	+	0.939371i
$848$	1.31796e13	+	1.31796e13i	0.875226	+	0.875226i
$849$	1.25635e13	−	7.25356e12i	0.829903	−	0.479145i
$850$	−2.87944e12	+	3.28148e12i	−0.189201	+	0.215618i
$851$	1.13760e13	−	1.97037e13i	0.743541	−	1.28785i
$852$	−1.29182e12	+	4.82113e12i	−0.0839891	+	0.313452i
$853$	9.85593e12	−	9.85593e12i	0.637422	−	0.637422i	−0.312497	−	0.949919i	$-0.601165\pi$
$853$	9.85593e12	−	9.85593e12i	0.637422	−	0.637422i	0.949919	+	0.312497i	$0.101165\pi$
$854$	−1.06316e12	−	1.14429e12i	−0.0683970	−	0.0736164i
$855$	2.24064e11	−	2.27162e12i	0.0143392	−	0.145375i
$856$	2.21693e12	+	3.83984e12i	0.141130	+	0.244445i
$857$	6.47175e12	−	1.73410e12i	0.409834	−	0.109815i	−0.0480107	−	0.998847i	$-0.515288\pi$
$857$	6.47175e12	−	1.73410e12i	0.409834	−	0.109815i	0.457845	+	0.889032i	$0.348622\pi$
$858$	4.68025e12	−	1.25407e12i	0.294833	−	0.0790003i
$859$	1.10266e13	+	1.90986e13i	0.690988	+	1.19683i	0.971514	+	0.236980i	$0.0761577\pi$
$859$	1.10266e13	+	1.90986e13i	0.690988	+	1.19683i	−0.280526	+	0.959846i	$0.590509\pi$
$860$	1.12256e13	−	9.20991e12i	0.699788	−	0.574133i
$861$	7.07682e12	+	7.61685e12i	0.438858	+	0.472347i
$862$	1.24415e12	−	1.24415e12i	0.0767520	−	0.0767520i
$863$	−8.30903e11	+	3.10097e12i	−0.0509919	+	0.190305i	−0.986724	−	0.162408i	$-0.948074\pi$
$863$	−8.30903e11	+	3.10097e12i	−0.0509919	+	0.190305i	0.935732	+	0.352712i	$0.114741\pi$
$864$	1.21459e12	−	2.10372e12i	0.0741509	−	0.128433i
$865$	−4.74008e12	−	2.87358e13i	−0.287881	−	1.74523i
$866$	3.02201e12	−	1.74476e12i	0.182585	−	0.105416i
$867$	−2.63124e13	−	2.63124e13i	−1.58152	−	1.58152i
$868$	5.34838e12	−	8.52445e12i	0.319804	−	0.509715i
$869$			3.86169e13i			2.29714i
$870$	−4.87776e11	−	1.07696e12i	−0.0288658	−	0.0637326i
$871$	−1.79944e13	−	1.03891e13i	−1.05939	−	0.611638i
$872$	8.32829e11	+	3.10816e12i	0.0487788	+	0.182045i
$873$	−9.99280e12	−	2.67756e12i	−0.582268	−	0.156018i
$874$	−4.70486e11			−0.0272738
$875$	−3.30720e12	−	1.70212e13i	−0.190732	−	0.981642i
$876$	−7.50678e12			−0.430710
$877$	−3.27988e13	−	8.78841e12i	−1.87223	−	0.501663i	−0.999919	−	0.0127167i	$-0.995952\pi$
$877$	−3.27988e13	−	8.78841e12i	−1.87223	−	0.501663i	−0.872314	−	0.488947i	$-0.837381\pi$
$878$	−2.84607e11	−	1.06217e12i	−0.0161629	−	0.0603209i
$879$	−2.52069e13	−	1.45532e13i	−1.42420	−	0.822260i
$880$	−9.68583e12	−	2.13852e13i	−0.544459	−	1.20210i
$881$			2.79362e13i			1.56234i	0.624317	+	0.781171i	$0.285377\pi$
$881$			2.79362e13i			1.56234i	−0.624317	+	0.781171i	$0.714623\pi$
$882$	8.08444e11	−	2.32027e12i	0.0449823	−	0.129101i
$883$	−1.25841e13	−	1.25841e13i	−0.696624	−	0.696624i	0.267057	−	0.963681i	$-0.413949\pi$
$883$	−1.25841e13	−	1.25841e13i	−0.696624	−	0.696624i	−0.963681	+	0.267057i	$0.913949\pi$
$884$	2.24045e13	−	1.29353e13i	1.23396	−	0.712427i
$885$	3.53050e12	+	2.14030e13i	0.193460	+	1.17282i
$886$	−9.98368e11	+	1.72922e12i	−0.0544301	+	0.0942756i
$887$	−1.84077e12	+	6.86985e12i	−0.0998490	+	0.372642i	−0.997710	−	0.0676376i	$-0.978454\pi$
$887$	−1.84077e12	+	6.86985e12i	−0.0998490	+	0.372642i	0.897861	+	0.440279i	$0.145121\pi$
$888$	−1.08102e13	+	1.08102e13i	−0.583409	+	0.583409i
$889$	−4.51401e12	−	1.38911e12i	−0.242384	−	0.0745895i
$890$	−9.94908e11	+	8.16261e11i	−0.0531530	+	0.0436088i
$891$	1.60064e13	+	2.77239e13i	0.850833	+	1.47369i
$892$	−1.84117e13	+	4.93339e12i	−0.973759	+	0.260918i
$893$	−4.31959e12	+	1.15743e12i	−0.227306	+	0.0609065i
$894$	1.36221e12	+	2.35941e12i	0.0713221	+	0.123534i
$895$	2.34201e12	−	2.37440e13i	0.122007	−	1.23694i
$896$	−1.21945e13	+	2.79183e12i	−0.632088	+	0.144711i
$897$	1.36450e13	−	1.36450e13i	0.703731	−	0.703731i
$898$	6.64031e11	−	2.47820e12i	0.0340757	−	0.127172i
$899$	1.81836e12	−	3.14949e12i	0.0928456	−	0.160813i
$900$	−9.81104e12	+	1.11809e13i	−0.498452	+	0.568047i
$901$	3.81758e13	−	2.20408e13i	1.92986	−	1.11421i
$902$	−1.73001e12	−	1.73001e12i	−0.0870201	−	0.0870201i
$903$	2.48752e13	+	9.14239e11i	1.24501	+	0.0457578i
$904$		−	7.67307e12i		−	0.382130i
$905$	1.71684e13	−	7.77594e12i	0.850769	−	0.385331i
$906$	−4.32729e12	−	2.49836e12i	−0.213373	−	0.123191i
$907$	8.24730e12	+	3.07793e13i	0.404650	+	1.51017i	0.804701	+	0.593680i	$0.202326\pi$
$907$	8.24730e12	+	3.07793e13i	0.404650	+	1.51017i	−0.400052	+	0.916493i	$0.631008\pi$
$908$	2.39579e11	+	6.41950e10i	0.0116967	+	0.00313411i
$909$	1.37905e13			0.669952
$910$	4.38833e11	−	3.22952e12i	0.0212135	−	0.156118i
$911$	7.07685e12			0.340414			0.170207	−	0.985408i	$-0.445556\pi$
$911$	7.07685e12			0.340414			0.170207	+	0.985408i	$0.445556\pi$
$912$	−4.58335e12	−	1.22810e12i	−0.219384	−	0.0587839i
$913$	7.86475e12	+	2.93516e13i	0.374599	+	1.39802i
$914$	−1.88285e11	−	1.08707e11i	−0.00892397	−	0.00515226i
$915$	−5.71231e12	+	1.51707e13i	−0.269412	+	0.715499i
$916$			3.94657e13i			1.85221i
$917$	−1.57621e13	−	9.88938e12i	−0.736124	−	0.461857i
$918$	−1.28270e12	−	1.28270e12i	−0.0596119	−	0.0596119i
$919$	−5.40145e12	+	3.11853e12i	−0.249799	+	0.144221i	−0.619672	−	0.784861i	$-0.712734\pi$
$919$	−5.40145e12	+	3.11853e12i	−0.249799	+	0.144221i	0.369873	+	0.929082i	$0.379401\pi$
$920$	5.06286e12	+	3.62909e12i	0.232997	+	0.167014i
$921$	−1.18330e13	+	2.04954e13i	−0.541910	+	0.938616i
$922$	−1.27265e12	+	4.74960e12i	−0.0579990	+	0.216455i
$923$	−3.51602e12	+	3.51602e12i	−0.159457	+	0.159457i
$924$	1.22376e13	−	3.97670e13i	0.552297	−	1.79473i
$925$	−3.31664e13	+	2.21474e13i	−1.48957	+	0.994682i
$926$	2.13492e12	+	3.69779e12i	0.0954183	+	0.165269i
$927$	5.48672e12	−	1.47016e12i	0.244036	−	0.0653893i
$928$	−3.29383e12	+	8.82580e11i	−0.145793	+	0.0390650i
$929$	7.79795e12	+	1.35064e13i	0.343486	+	0.594936i	0.985078	−	0.172111i	$-0.0550587\pi$
$929$	7.79795e12	+	1.35064e13i	0.343486	+	0.594936i	−0.641591	+	0.767047i	$0.721725\pi$
$930$	3.29679e12	+	3.25183e11i	0.144517	+	0.0142546i
$931$	4.28313e12	+	3.15262e11i	0.186848	+	0.0137530i
$932$	9.35775e12	−	9.35775e12i	0.406256	−	0.406256i
$933$	−6.05571e12	+	2.26002e13i	−0.261636	+	0.976439i
$934$	−7.19623e11	+	1.24642e12i	−0.0309417	+	0.0535926i
$935$	−5.47828e13	+	9.03661e12i	−2.34418	+	0.386681i
$936$	−4.91959e12	+	2.84033e12i	−0.209502	+	0.120956i
$937$	1.34156e13	+	1.34156e13i	0.568567	+	0.568567i	0.931727	−	0.363160i	$-0.118302\pi$
$937$	1.34156e13	+	1.34156e13i	0.568567	+	0.568567i	−0.363160	+	0.931727i	$0.618302\pi$
$938$	5.00185e12	−	2.64780e12i	0.210968	−	0.111679i
$939$			6.40292e12i			0.268771i
$940$	2.72727e13	+	1.02692e13i	1.13934	+	0.429004i
$941$	−8.66245e12	−	5.00127e12i	−0.360153	−	0.207935i	0.308995	−	0.951064i	$-0.400007\pi$
$941$	−8.66245e12	−	5.00127e12i	−0.360153	−	0.207935i	−0.669148	+	0.743129i	$0.733341\pi$
$942$	−5.74713e11	−	2.14486e12i	−0.0237805	−	0.0887502i
$943$	−9.41174e12	−	2.52187e12i	−0.387585	−	0.103853i
$944$	1.97554e13			0.809678
$945$	7.14702e12	−	9.10730e11i	0.291529	−	0.0371490i
$946$	−5.85755e12			−0.237797
$947$	−7.24352e12	−	1.94090e12i	−0.292668	−	0.0784201i	0.109498	−	0.993987i	$-0.465076\pi$
$947$	−7.24352e12	−	1.94090e12i	−0.292668	−	0.0784201i	−0.402166	+	0.915567i	$0.631742\pi$
$948$	−1.31644e13	−	4.91301e13i	−0.529374	−	1.97565i
$949$	−6.47658e12	−	3.73926e12i	−0.259208	−	0.149654i
$950$	7.39550e11	+	3.64969e11i	0.0294586	+	0.0145378i
$951$			5.33948e13i			2.11683i
$952$	−5.25819e11	+	1.43068e13i	−0.0207477	+	0.564517i
$953$	−1.74448e13	−	1.74448e13i	−0.685092	−	0.685092i	0.276051	−	0.961143i	$-0.410974\pi$
$953$	−1.74448e13	−	1.74448e13i	−0.685092	−	0.685092i	−0.961143	+	0.276051i	$0.910974\pi$
$954$	−4.12589e12	+	2.38208e12i	−0.161269	+	0.0931085i
$955$	−2.44594e13	+	3.41227e13i	−0.951548	+	1.32748i
$956$	1.46552e13	−	2.53835e13i	0.567455	−	0.982860i
$957$	3.89164e12	−	1.45238e13i	0.149979	−	0.559727i
$958$	3.99208e12	−	3.99208e12i	0.153128	−	0.153128i
$959$	2.23200e13	−	2.07375e13i	0.852139	−	0.791722i
$960$	1.82648e13	+	2.22622e13i	0.694055	+	0.845955i
$961$	−8.12465e12	−	1.40723e13i	−0.307291	−	0.532243i
$962$	−7.24083e12	+	1.94017e12i	−0.272584	+	0.0730386i
$963$	1.64309e13	−	4.40263e12i	0.615661	−	0.164966i
$964$	1.73748e13	+	3.00941e13i	0.647999	+	1.12237i
$965$	−2.97018e12	−	3.62024e12i	−0.110258	−	0.134389i
$966$	1.17297e12	+	5.12344e12i	0.0433401	+	0.189306i
$967$	2.34227e13	−	2.34227e13i	0.861426	−	0.861426i	−0.130078	−	0.991504i	$-0.541523\pi$
$967$	2.34227e13	−	2.34227e13i	0.861426	−	0.861426i	0.991504	+	0.130078i	$0.0415228\pi$
$968$	−2.70728e12	+	1.01037e13i	−0.0991045	+	0.369863i
$969$	−5.61112e12	+	9.71875e12i	−0.204453	+	0.354123i
$970$	2.17755e12	−	3.03785e12i	0.0789762	−	0.110178i
$971$	−2.42646e13	+	1.40092e13i	−0.875965	+	0.505739i	−0.869326	−	0.494239i	$-0.835447\pi$
$971$	−2.42646e13	+	1.40092e13i	−0.875965	+	0.505739i	−0.00663912	+	0.999978i	$0.502113\pi$
$972$	−2.42098e13	−	2.42098e13i	−0.869946	−	0.869946i
$973$	2.03727e12	+	3.84852e12i	0.0728687	+	0.137653i
$974$			5.33641e12i			0.189991i
$975$	−3.20331e13	+	1.08635e13i	−1.13522	+	0.384991i
$976$	1.27852e13	+	7.38155e12i	0.451008	+	0.260389i
$977$	−7.30977e12	−	2.72804e13i	−0.256672	−	0.957912i	−0.967153	−	0.254196i	$-0.918189\pi$
$977$	−7.30977e12	−	2.72804e13i	−0.256672	−	0.957912i	0.710481	−	0.703716i	$-0.248477\pi$
$978$	5.70342e12	+	1.52823e12i	0.199347	+	0.0534150i
$979$	−1.63669e13			−0.569436
$980$	−2.14885e13	−	1.79308e13i	−0.744199	−	0.620987i
$981$	1.23451e13			0.425581
$982$	5.30819e12	+	1.42233e12i	0.182157	+	0.0488087i
$983$	1.67136e12	+	6.23761e12i	0.0570926	+	0.213072i	0.988579	−	0.150704i	$-0.0481540\pi$
$983$	1.67136e12	+	6.23761e12i	0.0570926	+	0.213072i	−0.931486	+	0.363776i	$0.881487\pi$
$984$	5.67003e12	+	3.27360e12i	0.192800	+	0.111313i
$985$	6.03915e12	+	2.27396e12i	0.204415	+	0.0769697i
$986$			2.54648e12i			0.0858012i
$987$	2.33732e13	+	4.41534e13i	0.783956	+	1.48094i
$988$	−3.45569e12	−	3.45569e12i	−0.115380	−	0.115380i
$989$	−2.02027e13	+	1.16640e13i	−0.671468	+	0.387672i
$990$	5.92070e12	−	9.76641e11i	0.195891	−	0.0323129i
$991$	7.67269e11	−	1.32895e12i	0.0252706	−	0.0437700i	−0.853114	−	0.521725i	$-0.825289\pi$
$991$	7.67269e11	−	1.32895e12i	0.0252706	−	0.0437700i	0.878384	+	0.477955i	$0.158622\pi$
$992$	2.47304e12	−	9.22953e12i	0.0810829	−	0.302606i
$993$	5.33492e13	−	5.33492e13i	1.74123	−	1.74123i
$994$	−3.02249e11	−	1.32020e12i	−0.00982034	−	0.0428945i
$995$	−5.65965e13	−	5.58245e12i	−1.83057	−	0.180560i
$996$	−2.00118e13	−	3.46614e13i	−0.644345	−	1.11604i
$997$	2.40019e13	−	6.43128e12i	0.769337	−	0.206143i	0.147258	−	0.989098i	$-0.452955\pi$
$997$	2.40019e13	−	6.43128e12i	0.769337	−	0.206143i	0.622079	+	0.782955i	$0.286288\pi$
$998$	−7.85362e12	+	2.10437e12i	−0.250601	+	0.0671483i
$999$	−8.28564e12	−	1.43511e13i	−0.263197	−	0.455871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.20	✓	136
5.2	odd	4	inner	35.10.k.a.17.15	yes	136
7.5	odd	6	inner	35.10.k.a.33.15	yes	136
35.12	even	12	inner	35.10.k.a.12.20	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.20	✓	136	1.1	even	1	trivial
35.10.k.a.12.20	yes	136	35.12	even	12	inner
35.10.k.a.17.15	yes	136	5.2	odd	4	inner
35.10.k.a.33.15	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+(3.83230 + 1.02686i) q^{2} +(-48.4413 - 180.785i) q^{3} +(-429.773 - 248.130i) q^{4} +(-576.593 - 1273.05i) q^{5} -742.566i q^{6} +(-2972.03 - 5614.33i) q^{7} +(-2828.61 - 2828.61i) q^{8} +(-13290.8 + 7673.46i) q^{9} +(-902.428 - 5470.80i) q^{10} +(35259.1 - 61070.5i) q^{11} +(-24039.4 + 89716.4i) q^{12} +(-65429.6 + 65429.6i) q^{13} +(-5624.56 - 24567.6i) q^{14} +(-202219. + 165908. i) q^{15} +(119107. + 206299. i) q^{16} +(544191. - 145816. i) q^{17} +(-58814.0 + 15759.2i) q^{18} +(-53213.6 - 92168.7i) q^{19} +(-68078.0 + 690194. i) q^{20} +(-871020. + 809264. i) q^{21} +(197834. - 197834. i) q^{22} +(288387. - 1.07627e6i) q^{23} +(-374350. + 648393. i) q^{24} +(-1.28821e6 + 1.46807e6i) q^{25} +(-317933. + 183559. i) q^{26} +(-573854. - 573854. i) q^{27} +(-115784. + 3.15033e6i) q^{28} +1.13924e6i q^{29} +(-945327. + 428159. i) q^{30} +(-2.76455e6 - 1.59611e6i) q^{31} +(774708. + 2.89125e6i) q^{32} +(-1.27487e7 - 3.41599e6i) q^{33} +2.23524e6 q^{34} +(-5.43369e6 + 7.02073e6i) q^{35} +7.61605e6 q^{36} +(1.97235e7 + 5.28489e6i) q^{37} +(-109286. - 407861. i) q^{38} +(1.49982e7 + 8.65922e6i) q^{39} +(-1.97001e6 + 5.23193e6i) q^{40} -8.74475e6i q^{41} +(-4.16901e6 + 2.20693e6i) q^{42} +(-1.48042e7 - 1.48042e7i) q^{43} +(-3.03068e7 + 1.74976e7i) q^{44} +(1.74321e7 + 1.24955e7i) q^{45} +(2.21037e6 - 3.82847e6i) q^{46} +(1.08753e7 - 4.05873e7i) q^{47} +(3.15262e7 - 3.15262e7i) q^{48} +(-2.26877e7 + 3.33718e7i) q^{49} +(-6.44429e6 + 4.30327e6i) q^{50} +(-5.27227e7 - 9.13183e7i) q^{51} +(4.43549e7 - 1.18849e7i) q^{52} +(7.55777e7 - 2.02510e7i) q^{53} +(-1.60991e6 - 2.78845e6i) q^{54} +(-9.80762e7 - 9.67385e6i) q^{55} +(-7.47404e6 + 2.42874e7i) q^{56} +(-1.40850e7 + 1.40850e7i) q^{57} +(-1.16984e6 + 4.36592e6i) q^{58} +(4.14658e7 - 7.18208e7i) q^{59} +(1.28075e8 - 2.11264e7i) q^{60} +(5.36712e7 - 3.09871e7i) q^{61} +(-8.95560e6 - 8.95560e6i) q^{62} +(8.25820e7 + 5.18133e7i) q^{63} -1.10090e8i q^{64} +(1.21022e8 + 4.55691e7i) q^{65} +(-4.53489e7 - 2.61822e7i) q^{66} +(5.81183e7 + 2.16901e8i) q^{67} +(-2.70060e8 - 7.23623e7i) q^{68} -2.08544e8 q^{69} +(-2.80328e7 + 2.13259e7i) q^{70} +5.37375e7 q^{71} +(5.92997e7 + 1.58893e7i) q^{72} +(2.09181e7 + 7.80674e7i) q^{73} +(7.01594e7 + 4.05065e7i) q^{74} +(3.27808e8 + 1.61774e8i) q^{75} +5.28155e7i q^{76} +(-4.47661e8 - 1.64529e7i) q^{77} +(4.85858e7 + 4.85858e7i) q^{78} +(-4.74250e8 + 2.73808e8i) q^{79} +(1.93954e8 - 2.70580e8i) q^{80} +(-2.26983e8 + 3.93146e8i) q^{81} +(8.97965e6 - 3.35125e7i) q^{82} +(-3.04700e8 + 3.04700e8i) q^{83} +(5.75143e8 - 1.31674e8i) q^{84} +(-4.99408e8 - 6.08708e8i) q^{85} +(-4.15322e7 - 7.19359e7i) q^{86} +(2.05958e8 - 5.51864e7i) q^{87} +(-2.72479e8 + 7.30104e7i) q^{88} +(-1.16048e8 - 2.01000e8i) q^{89} +(5.39740e7 + 6.57867e7i) q^{90} +(5.61802e8 + 1.72885e8i) q^{91} +(-3.90996e8 + 3.90996e8i) q^{92} +(-1.54636e8 + 5.77108e8i) q^{93} +(8.33551e7 - 1.44375e8i) q^{94} +(-8.66530e7 + 1.20888e8i) q^{95} +(4.85168e8 - 2.80112e8i) q^{96} +(4.76658e8 + 4.76658e8i) q^{97} +(-1.21214e8 + 1.04594e8i) q^{98} +1.08224e9i 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

Related objects

Downloads

Learn more