LMFDB - Embedded newform 35.10.k.a.3.2

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			3.2
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-39.0059 - 10.4516i) q^{2} +(-2.23944 - 8.35771i) q^{3} +(968.820 + 559.349i) q^{4} +(42.9502 - 1396.88i) q^{5} +349.406i q^{6} +(6351.67 - 99.7449i) q^{7} +(-17323.8 - 17323.8i) q^{8} +(16981.1 - 9804.07i) q^{9} +(-16275.0 + 54037.8i) q^{10} +(-36572.6 + 63345.5i) q^{11} +(2505.26 - 9349.75i) q^{12} +(-83277.2 + 83277.2i) q^{13} +(-248795. - 62494.4i) q^{14} +(-11770.9 + 2769.27i) q^{15} +(208283. + 360757. i) q^{16} +(204019. - 54666.7i) q^{17} +(-764833. + 204936. i) q^{18} +(470064. + 814174. i) q^{19} +(822955. - 1.32930e6i) q^{20} +(-15057.8 - 52862.0i) q^{21} +(2.08861e6 - 2.08861e6i) q^{22} +(514101. - 1.91865e6i) q^{23} +(-105992. + 183583. i) q^{24} +(-1.94944e6 - 119993. i) q^{25} +(4.11868e6 - 2.37792e6i) q^{26} +(-240394. - 240394. i) q^{27} +(6.20941e6 + 3.45616e6i) q^{28} +3.47419e6i q^{29} +(488079. + 15007.1i) q^{30} +(1.49660e6 + 864063. i) q^{31} +(-1.10722e6 - 4.13219e6i) q^{32} +(611326. + 163804. i) q^{33} -8.52929e6 q^{34} +(133474. - 8.87681e6i) q^{35} +2.19356e7 q^{36} +(1.43384e7 + 3.84196e6i) q^{37} +(-9.82583e6 - 3.66705e7i) q^{38} +(882501. + 509512. i) q^{39} +(-2.49434e7 + 2.34553e7i) q^{40} +1.48704e7i q^{41} +(34851.4 + 2.21931e6i) q^{42} +(1.16590e7 + 1.16590e7i) q^{43} +(-7.08645e7 + 4.09136e7i) q^{44} +(-1.29658e7 - 2.41417e7i) q^{45} +(-4.01060e7 + 6.94656e7i) q^{46} +(1.43658e7 - 5.36138e7i) q^{47} +(2.54866e6 - 2.54866e6i) q^{48} +(4.03337e7 - 1.26709e6i) q^{49} +(7.47854e7 + 2.50552e7i) q^{50} +(-913776. - 1.58271e6i) q^{51} +(-1.27262e8 + 3.40997e7i) q^{52} +(2.53675e6 - 679719. i) q^{53} +(6.86428e6 + 1.18893e7i) q^{54} +(8.69155e7 + 5.38083e7i) q^{55} +(-1.11763e8 - 1.08307e8i) q^{56} +(5.75195e6 - 5.75195e6i) q^{57} +(3.63109e7 - 1.35514e8i) q^{58} +(2.62607e7 - 4.54848e7i) q^{59} +(-1.29529e7 - 3.90112e6i) q^{60} +(-2.12248e7 + 1.22542e7i) q^{61} +(-4.93454e7 - 4.93454e7i) q^{62} +(1.06881e8 - 6.39659e7i) q^{63} -4.05301e7i q^{64} +(1.12752e8 + 1.19905e8i) q^{65} +(-2.21333e7 - 1.27787e7i) q^{66} +(1.15942e7 + 4.32701e7i) q^{67} +(2.28235e8 + 6.11554e7i) q^{68} -1.71868e7 q^{69} +(-9.79832e7 + 3.44853e8i) q^{70} +1.14914e8 q^{71} +(-4.64022e8 - 1.24334e8i) q^{72} +(-6.20080e6 - 2.31417e7i) q^{73} +(-5.19127e8 - 2.99718e8i) q^{74} +(3.36278e6 + 1.65615e7i) q^{75} +1.05172e9i q^{76} +(-2.25978e8 + 4.05998e8i) q^{77} +(-2.90975e7 - 2.90975e7i) q^{78} +(1.54149e8 - 8.89979e7i) q^{79} +(5.12881e8 - 2.75452e8i) q^{80} +(1.91503e8 - 3.31692e8i) q^{81} +(1.55419e8 - 5.80033e8i) q^{82} +(1.56076e8 - 1.56076e8i) q^{83} +(1.49800e7 - 5.96364e7i) q^{84} +(-6.76002e7 - 2.87338e8i) q^{85} +(-3.32916e8 - 5.76627e8i) q^{86} +(2.90363e7 - 7.78025e6i) q^{87} +(1.73096e9 - 4.63810e8i) q^{88} +(-1.36058e8 - 2.35659e8i) q^{89} +(2.53422e8 + 1.07718e9i) q^{90} +(-5.20643e8 + 5.37255e8i) q^{91} +(1.57127e9 - 1.57127e9i) q^{92} +(3.87004e6 - 1.44432e7i) q^{93} +(-1.12070e9 + 1.94111e9i) q^{94} +(1.15749e9 - 6.21655e8i) q^{95} +(-3.20561e7 + 1.85076e7i) q^{96} +(-3.93410e8 - 3.93410e8i) q^{97} +(-1.58650e9 - 3.72128e8i) q^{98} +1.43424e9i 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 $

$2$	−39.0059	−	10.4516i	−1.72383	−	0.461900i	−0.745086	−	0.666968i	$-0.767592\pi$
$2$	−39.0059	−	10.4516i	−1.72383	−	0.461900i	−0.978748	+	0.205068i	$0.934258\pi$
$3$	−2.23944	−	8.35771i	−0.0159623	−	0.0595719i	0.957485	−	0.288482i	$-0.0931505\pi$
$3$	−2.23944	−	8.35771i	−0.0159623	−	0.0595719i	−0.973448	+	0.228910i	$0.926484\pi$
$4$	968.820	+	559.349i	1.89223	+	1.09248i
$5$	42.9502	−	1396.88i	0.0307327	−	0.999528i
$5$	42.9502	−	1396.88i	0.0307327	−	0.999528i
$6$			349.406i			0.110065i
$7$	6351.67	−	99.7449i	0.999877	−	0.0157018i
$7$	6351.67	−	99.7449i	0.999877	−	0.0157018i
$8$	−17323.8	−	17323.8i	−1.49534	−	1.49534i
$9$	16981.1	−	9804.07i	0.862731	−	0.498098i
$10$	−16275.0	+	54037.8i	−0.514660	+	1.70882i
$11$	−36572.6	+	63345.5i	−0.753162	+	1.30451i	0.193121	+	0.981175i	$0.438139\pi$
$11$	−36572.6	+	63345.5i	−0.753162	+	1.30451i	−0.946283	+	0.323340i	$0.895194\pi$
$12$	2505.26	−	9349.75i	0.0348768	−	0.130162i
$13$	−83277.2	+	83277.2i	−0.808688	+	0.808688i	−0.984435	−	0.175747i	$-0.943766\pi$
$13$	−83277.2	+	83277.2i	−0.808688	+	0.808688i	0.175747	+	0.984435i	$0.443766\pi$
$14$	−248795.	−	62494.4i	−1.73087	−	0.434776i
$15$	−11770.9	+	2769.27i	−0.0600344	+	0.0141239i
$16$	208283.	+	360757.i	0.794537	+	1.37618i
$17$	204019.	−	54666.7i	0.592448	−	0.158746i	0.0498760	−	0.998755i	$-0.484117\pi$
$17$	204019.	−	54666.7i	0.592448	−	0.158746i	0.542572	+	0.840010i	$0.317451\pi$
$18$	−764833.	+	204936.i	−1.71728	+	0.460143i
$19$	470064.	+	814174.i	0.827495	+	1.43326i	0.899997	+	0.435895i	$0.143568\pi$
$19$	470064.	+	814174.i	0.827495	+	1.43326i	−0.0725025	+	0.997368i	$0.523099\pi$
$20$	822955.	−	1.32930e6i	1.15011	−	1.85776i
$21$	−15057.8	−	52862.0i	−0.0168957	−	0.0593140i
$22$	2.08861e6	−	2.08861e6i	1.90088	−	1.90088i
$23$	514101.	−	1.91865e6i	0.383066	−	1.42962i	−0.458128	−	0.888886i	$-0.651480\pi$
$23$	514101.	−	1.91865e6i	0.383066	−	1.42962i	0.841193	−	0.540735i	$-0.181854\pi$
$24$	−105992.	+	183583.i	−0.0652111	+	0.112949i
$25$	−1.94944e6	−	119993.i	−0.998111	−	0.0614363i
$26$	4.11868e6	−	2.37792e6i	1.76758	−	1.02051i
$27$	−240394.	−	240394.i	−0.0870535	−	0.0870535i
$28$	6.20941e6	+	3.45616e6i	1.90915	+	1.06263i
$29$			3.47419e6i			0.912143i	0.889943	+	0.456072i	$0.150744\pi$
$29$			3.47419e6i			0.912143i	−0.889943	+	0.456072i	$0.849256\pi$
$30$	488079.	+	15007.1i	0.110013	+	0.00338260i
$31$	1.49660e6	+	864063.i	0.291057	+	0.168042i	0.638418	−	0.769689i	$-0.279589\pi$
$31$	1.49660e6	+	864063.i	0.291057	+	0.168042i	−0.347361	+	0.937731i	$0.612922\pi$
$32$	−1.10722e6	−	4.13219e6i	−0.186663	−	0.696634i
$33$	611326.	+	163804.i	0.0897346	+	0.0240443i
$34$	−8.52929e6			−1.09461
$35$	133474.	−	8.87681e6i	0.0150345	−	0.999887i
$36$	2.19356e7			2.17664
$37$	1.43384e7	+	3.84196e6i	1.25774	+	0.337011i	0.825323	−	0.564661i	$-0.190993\pi$
$37$	1.43384e7	+	3.84196e6i	1.25774	+	0.337011i	0.432421	+	0.901672i	$0.357660\pi$
$38$	−9.82583e6	−	3.66705e7i	−0.764440	−	2.85293i
$39$	882501.	+	509512.i	0.0610836	+	0.0352666i
$40$	−2.49434e7	+	2.34553e7i	−1.54058	+	1.44867i
$41$			1.48704e7i			0.821854i	0.911668	+	0.410927i	$0.134795\pi$
$41$			1.48704e7i			0.821854i	−0.911668	+	0.410927i	$0.865205\pi$
$42$	34851.4	+	2.21931e6i	0.00172822	+	0.110052i
$43$	1.16590e7	+	1.16590e7i	0.520061	+	0.520061i	0.917590	−	0.397528i	$-0.130132\pi$
$43$	1.16590e7	+	1.16590e7i	0.520061	+	0.520061i	−0.397528	+	0.917590i	$0.630132\pi$
$44$	−7.08645e7	+	4.09136e7i	−2.85031	+	1.64563i
$45$	−1.29658e7	−	2.41417e7i	−0.471349	−	0.877632i
$46$	−4.01060e7	+	6.94656e7i	−1.32068	+	2.28749i
$47$	1.43658e7	−	5.36138e7i	0.429426	−	1.60264i	−0.324638	−	0.945838i	$-0.605242\pi$
$47$	1.43658e7	−	5.36138e7i	0.429426	−	1.60264i	0.754064	−	0.656801i	$-0.228091\pi$
$48$	2.54866e6	−	2.54866e6i	0.0692990	−	0.0692990i
$49$	4.03337e7	−	1.26709e6i	0.999507	−	0.0313997i
$50$	7.47854e7	+	2.50552e7i	1.69220	+	0.566933i
$51$	−913776.	−	1.58271e6i	−0.0189136	−	0.0327593i
$52$	−1.27262e8	+	3.40997e7i	−2.41370	+	0.646748i
$53$	2.53675e6	−	679719.i	0.0441607	−	0.0118328i	−0.236671	−	0.971590i	$-0.576056\pi$
$53$	2.53675e6	−	679719.i	0.0441607	−	0.0118328i	0.280832	+	0.959757i	$0.409390\pi$
$54$	6.86428e6	+	1.18893e7i	0.109856	+	0.190276i
$55$	8.69155e7	+	5.38083e7i	1.28075	+	0.792897i
$56$	−1.11763e8	−	1.08307e8i	−1.51863	−	1.47167i
$57$	5.75195e6	−	5.75195e6i	0.0721736	−	0.0721736i
$58$	3.63109e7	−	1.35514e8i	0.421319	−	1.57238i
$59$	2.62607e7	−	4.54848e7i	0.282145	−	0.488689i	−0.689768	−	0.724030i	$-0.742288\pi$
$59$	2.62607e7	−	4.54848e7i	0.282145	−	0.488689i	0.971913	+	0.235342i	$0.0756209\pi$
$60$	−1.29529e7	−	3.90112e6i	−0.129029	−	0.0388606i
$61$	−2.12248e7	+	1.22542e7i	−0.196273	+	0.113318i	−0.594916	−	0.803788i	$-0.702815\pi$
$61$	−2.12248e7	+	1.22542e7i	−0.196273	+	0.113318i	0.398643	+	0.917106i	$0.369481\pi$
$62$	−4.93454e7	−	4.93454e7i	−0.424116	−	0.424116i
$63$	1.06881e8	−	6.39659e7i	0.854804	−	0.511583i
$64$		−	4.05301e7i		−	0.301973i
$65$	1.12752e8	+	1.19905e8i	0.783453	+	0.833159i
$66$	−2.21333e7	−	1.27787e7i	−0.143582	−	0.0828968i
$67$	1.15942e7	+	4.32701e7i	0.0702917	+	0.262332i	0.992125	−	0.125256i	$-0.0399751\pi$
$67$	1.15942e7	+	4.32701e7i	0.0702917	+	0.262332i	−0.921833	+	0.387588i	$0.873308\pi$
$68$	2.28235e8	+	6.11554e7i	1.29447	+	0.346853i
$69$	−1.71868e7			−0.0912799
$70$	−9.79832e7	+	3.44853e8i	−0.487765	+	1.71669i
$71$	1.14914e8			0.536673			0.268336	−	0.963325i	$-0.413526\pi$
$71$	1.14914e8			0.536673			0.268336	+	0.963325i	$0.413526\pi$
$72$	−4.64022e8	−	1.24334e8i	−2.03490	−	0.545249i
$73$	−6.20080e6	−	2.31417e7i	−0.0255561	−	0.0953767i	0.951970	−	0.306192i	$-0.0990549\pi$
$73$	−6.20080e6	−	2.31417e7i	−0.0255561	−	0.0953767i	−0.977526	+	0.210815i	$0.932388\pi$
$74$	−5.19127e8	−	2.99718e8i	−2.01248	−	1.16190i
$75$	3.36278e6	+	1.65615e7i	0.0122722	+	0.0604401i
$76$			1.05172e9i			3.61608i
$77$	−2.25978e8	+	4.05998e8i	−0.732586	+	1.31618i
$78$	−2.90975e7	−	2.90975e7i	−0.0890083	−	0.0890083i
$79$	1.54149e8	−	8.89979e7i	0.445265	−	0.257074i	−0.260563	−	0.965457i	$-0.583908\pi$
$79$	1.54149e8	−	8.89979e7i	0.445265	−	0.257074i	0.705828	+	0.708383i	$0.250575\pi$
$80$	5.12881e8	−	2.75452e8i	1.39995	−	0.751868i
$81$	1.91503e8	−	3.31692e8i	0.494302	−	0.856156i
$82$	1.55419e8	−	5.80033e8i	0.379615	−	1.41674i
$83$	1.56076e8	−	1.56076e8i	0.360982	−	0.360982i	−0.503192	−	0.864175i	$-0.667841\pi$
$83$	1.56076e8	−	1.56076e8i	0.360982	−	0.360982i	0.864175	+	0.503192i	$0.167841\pi$
$84$	1.49800e7	−	5.96364e7i	0.0328287	−	0.130694i
$85$	−6.76002e7	−	2.87338e8i	−0.140463	−	0.597047i
$86$	−3.32916e8	−	5.76627e8i	−0.656283	−	1.13672i
$87$	2.90363e7	−	7.78025e6i	0.0543381	−	0.0145599i
$88$	1.73096e9	−	4.63810e8i	3.07692	−	0.824457i
$89$	−1.36058e8	−	2.35659e8i	−0.229863	−	0.398134i	0.727905	−	0.685678i	$-0.240494\pi$
$89$	−1.36058e8	−	2.35659e8i	−0.229863	−	0.398134i	−0.957767	+	0.287545i	$0.907161\pi$
$90$	2.53422e8	+	1.07718e9i	0.407149	+	1.73061i
$91$	−5.20643e8	+	5.37255e8i	−0.795891	+	0.821286i
$92$	1.57127e9	−	1.57127e9i	2.28668	−	2.28668i
$93$	3.87004e6	−	1.44432e7i	0.00536465	−	0.0200212i
$94$	−1.12070e9	+	1.94111e9i	−1.48052	+	2.56433i
$95$	1.15749e9	−	6.21655e8i	1.45802	−	0.783056i
$96$	−3.20561e7	+	1.85076e7i	−0.0385203	+	0.0222397i
$97$	−3.93410e8	−	3.93410e8i	−0.451203	−	0.451203i	0.444550	−	0.895754i	$-0.353363\pi$
$97$	−3.93410e8	−	3.93410e8i	−0.451203	−	0.451203i	−0.895754	+	0.444550i	$0.853363\pi$
$98$	−1.58650e9	−	3.72128e8i	−1.73749	−	0.407544i
$99$			1.43424e9i			1.50059i
$100$	−1.82153e9	−	1.20667e9i	−1.82153	−	1.20667i
$101$	1.05845e9	+	6.11096e8i	1.01210	+	0.584337i	0.911806	−	0.410620i	$-0.134688\pi$
$101$	1.05845e9	+	6.11096e8i	1.01210	+	0.584337i	0.100295	+	0.994958i	$0.468021\pi$
$102$	1.91009e7	+	7.12854e7i	0.0174724	+	0.0652078i
$103$	4.10057e8	+	1.09874e8i	0.358985	+	0.0961898i	0.433804	−	0.901007i	$-0.357171\pi$
$103$	4.10057e8	+	1.09874e8i	0.358985	+	0.0961898i	−0.0748185	+	0.997197i	$0.523838\pi$
$104$	2.88536e9			2.41852
$105$	−7.44887e7	+	1.87636e7i	−0.0598052	+	0.0150648i
$106$	−1.06052e8			−0.0815912
$107$	−1.10910e9	−	2.97183e8i	−0.817984	−	0.219178i	−0.174519	−	0.984654i	$-0.555837\pi$
$107$	−1.10910e9	−	2.97183e8i	−0.817984	−	0.219178i	−0.643465	+	0.765476i	$0.722504\pi$
$108$	−9.84344e7	−	3.67362e8i	−0.0696210	−	0.259829i
$109$	−2.72971e8	−	1.57600e8i	−0.185224	−	0.106939i	0.404521	−	0.914529i	$-0.367438\pi$
$109$	−2.72971e8	−	1.57600e8i	−0.185224	−	0.106939i	−0.589745	+	0.807590i	$0.700772\pi$
$110$	−2.82783e9	−	3.00725e9i	−1.84156	−	1.95840i
$111$		−	1.28440e8i		−	0.0803057i
$112$	1.35893e9	+	2.27063e9i	0.816048	+	1.36353i
$113$	3.68340e8	+	3.68340e8i	0.212518	+	0.212518i	0.805336	−	0.592818i	$-0.201985\pi$
$113$	3.68340e8	+	3.68340e8i	0.212518	+	0.212518i	−0.592818	+	0.805336i	$0.701985\pi$
$114$	−2.84477e8	+	1.64243e8i	−0.157752	+	0.0910783i
$115$	−2.65805e9	−	8.00545e8i	−1.41717	−	0.426821i
$116$	−1.94329e9	+	3.36587e9i	−0.996496	+	1.72598i
$117$	−5.97687e8	+	2.23060e9i	−0.294875	+	1.10049i
$118$	−1.49971e9	+	1.49971e9i	−0.712096	+	0.712096i
$119$	1.29041e9	−	3.67574e8i	0.589882	−	0.168029i
$120$	2.51892e8	+	1.55943e8i	0.110891	+	0.0686515i
$121$	−1.49613e9	−	2.59138e9i	−0.634506	−	1.09900i
$122$	9.55970e8	−	2.56151e8i	0.390683	−	0.104683i
$123$	1.24282e8	−	3.33014e7i	0.0489595	−	0.0131186i
$124$	9.66624e8	+	1.67424e9i	0.367164	+	0.635947i
$125$	−2.51345e8	+	2.71798e9i	−0.0920820	+	0.995751i
$126$	−4.83752e9	+	1.37798e9i	−1.70984	+	0.487051i
$127$	1.68604e9	−	1.68604e9i	0.575112	−	0.575112i	−0.358441	−	0.933553i	$-0.616691\pi$
$127$	1.68604e9	−	1.68604e9i	0.575112	−	0.575112i	0.933553	+	0.358441i	$0.116691\pi$
$128$	−9.90499e8	+	3.69659e9i	−0.326144	+	1.21719i
$129$	7.13331e7	−	1.23553e8i	0.0226797	−	0.0392824i
$130$	−3.14478e9	−	5.85545e9i	−0.965707	−	1.79811i
$131$	2.20166e9	−	1.27113e9i	0.653174	−	0.377110i	−0.136497	−	0.990640i	$-0.543584\pi$
$131$	2.20166e9	−	1.27113e9i	0.653174	−	0.377110i	0.789671	+	0.613530i	$0.210251\pi$
$132$	5.00641e8	+	5.00641e8i	0.143530	+	0.143530i
$133$	3.06690e9	+	5.12447e9i	0.849898	+	1.42009i
$134$		−	1.80897e9i		−	0.484685i
$135$	−3.46127e8	+	3.25477e8i	−0.0896878	+	0.0843370i
$136$	−4.48142e9	−	2.58735e9i	−1.12329	−	0.648530i
$137$	1.03214e9	+	3.85200e9i	0.250320	+	0.934208i	0.970634	+	0.240560i	$0.0773310\pi$
$137$	1.03214e9	+	3.85200e9i	0.250320	+	0.934208i	−0.720314	+	0.693648i	$0.756002\pi$
$138$	6.70388e8	+	1.79630e8i	0.157351	+	0.0421622i
$139$	1.11876e9			0.254198			0.127099	−	0.991890i	$-0.459433\pi$
$139$	1.11876e9			0.254198			0.127099	+	0.991890i	$0.459433\pi$
$140$	5.09455e9	−	8.52538e9i	1.12080	−	1.87559i
$141$	−4.80260e8			−0.102327
$142$	−4.48232e9	−	1.20103e9i	−0.925134	−	0.247889i
$143$	−2.22958e9	−	8.32090e9i	−0.445872	−	1.66402i
$144$	7.07377e9	+	4.08404e9i	1.37094	+	0.791515i
$145$	4.85304e9	+	1.49217e8i	0.911712	+	0.0280326i
$146$			9.67471e8i			0.176218i
$147$	−1.00915e8	−	3.34260e8i	−0.0178249	−	0.0590413i
$148$	1.17423e10	+	1.17423e10i	2.01176	+	2.01176i
$149$	5.12506e9	−	2.95896e9i	0.851846	−	0.491813i	−0.00942735	−	0.999956i	$-0.503001\pi$
$149$	5.12506e9	−	2.95896e9i	0.851846	−	0.491813i	0.861273	+	0.508142i	$0.169668\pi$
$150$	4.19262e7	−	6.81144e8i	0.00676200	−	0.109857i
$151$	−3.51842e9	+	6.09408e9i	−0.550746	+	0.953920i	0.447475	+	0.894296i	$0.352323\pi$
$151$	−3.51842e9	+	6.09408e9i	−0.550746	+	0.953920i	−0.998221	+	0.0596234i	$0.981010\pi$
$152$	5.96131e9	−	2.22479e10i	0.905827	−	3.38059i
$153$	2.92852e9	−	2.92852e9i	0.432052	−	0.432052i
$154$	1.30578e10	−	1.34745e10i	1.87080	−	1.93049i
$155$	1.27127e9	−	2.05346e9i	0.176907	−	0.285755i
$156$	5.69990e8	+	9.87252e8i	0.0770560	+	0.133465i
$157$	4.72348e9	−	1.26565e9i	0.620460	−	0.166252i	0.0651229	−	0.997877i	$-0.479256\pi$
$157$	4.72348e9	−	1.26565e9i	0.620460	−	0.166252i	0.555337	+	0.831626i	$0.312589\pi$
$158$	−6.94289e9	+	1.86034e9i	−0.886305	+	0.237485i
$159$	−1.13618e7	−	1.96792e7i	−0.00140981	−	0.00244186i
$160$	−5.81973e9	+	1.36917e9i	−0.702042	+	0.165165i
$161$	3.07402e9	−	1.22379e10i	0.360571	−	1.43546i
$162$	−1.09365e10	+	1.09365e10i	−1.24755	+	1.24755i
$163$	−2.92896e9	+	1.09310e10i	−0.324989	+	1.21288i	0.589333	+	0.807890i	$0.299391\pi$
$163$	−2.92896e9	+	1.09310e10i	−0.324989	+	1.21288i	−0.914323	+	0.404987i	$0.867276\pi$
$164$	−8.31773e9	+	1.44067e10i	−0.897858	+	1.55514i
$165$	2.55072e8	−	8.46915e8i	0.0267907	−	0.0889533i
$166$	−7.71915e9	+	4.45666e9i	−0.789011	+	0.455536i
$167$	−2.55209e9	−	2.55209e9i	−0.253905	−	0.253905i	0.568664	−	0.822570i	$-0.307460\pi$
$167$	−2.55209e9	−	2.55209e9i	−0.253905	−	0.253905i	−0.822570	+	0.568664i	$0.807460\pi$
$168$	−6.54913e8	+	1.17663e9i	−0.0634296	+	0.113959i
$169$		−	3.26569e9i		−	0.307953i
$170$	−3.66335e8	+	1.19144e10i	−0.0336402	+	1.09409i
$171$	1.59644e10	+	9.21707e9i	1.42781	+	0.824348i
$172$	4.77404e9	+	1.78170e10i	0.415919	+	1.55223i
$173$	−1.48349e10	−	3.97500e9i	−1.25915	−	0.337388i	−0.433285	−	0.901257i	$-0.642646\pi$
$173$	−1.48349e10	−	3.97500e9i	−1.25915	−	0.337388i	−0.825865	+	0.563868i	$0.809312\pi$
$174$	−1.21390e9			−0.100395
$175$	−1.23941e10	−	5.67708e8i	−0.998953	−	0.0457566i
$176$	−3.04698e10			−2.39366
$177$	−4.38958e8	−	1.17618e8i	−0.0336158	−	0.00900732i
$178$	2.84404e9	+	1.06141e10i	0.212347	+	0.792490i
$179$	7.27026e9	+	4.19749e9i	0.529312	+	0.305598i	0.740736	−	0.671796i	$-0.234477\pi$
$179$	7.27026e9	+	4.19749e9i	0.529312	+	0.305598i	−0.211424	+	0.977394i	$0.567810\pi$
$180$	9.42138e8	−	3.06414e10i	0.0668941	−	2.17562i
$181$			6.25708e9i			0.433330i	0.976246	+	0.216665i	$0.0695179\pi$
$181$			6.25708e9i			0.433330i	−0.976246	+	0.216665i	$0.930482\pi$
$182$	2.59233e10	−	1.55146e10i	1.75134	−	1.04814i
$183$	1.49949e8	+	1.49949e8i	0.00988354	+	0.00988354i
$184$	−4.21446e10	+	2.43322e10i	−2.71057	+	1.56495i
$185$	5.98260e9	−	1.98640e10i	0.375506	−	1.24679i
$186$	−3.01909e8	+	5.22921e8i	−0.0184955	+	0.0320352i
$187$	−3.99860e9	+	1.49230e10i	−0.239123	+	0.892418i
$188$	4.39066e10	−	4.39066e10i	2.56342	−	2.56342i
$189$	−1.55088e9	−	1.50292e9i	−0.0884097	−	0.0856759i
$190$	−5.16464e10	+	1.21505e10i	−2.87507	+	0.676401i
$191$	3.26030e9	+	5.64701e9i	0.177259	+	0.307021i	0.940941	−	0.338571i	$-0.109944\pi$
$191$	3.26030e9	+	5.64701e9i	0.177259	+	0.307021i	−0.763682	+	0.645593i	$0.776610\pi$
$192$	−3.38739e8	+	9.07649e7i	−0.0179891	+	0.00482017i
$193$	1.48534e10	−	3.97996e9i	0.770580	−	0.206476i	0.147952	−	0.988994i	$-0.452732\pi$
$193$	1.48534e10	−	3.97996e9i	0.770580	−	0.206476i	0.622628	+	0.782518i	$0.286065\pi$
$194$	1.12335e10	+	1.94571e10i	0.569389	+	0.986211i
$195$	7.49632e8	−	1.21087e9i	0.0371272	−	0.0599709i
$196$	3.97849e10	+	2.13330e10i	1.92560	+	1.03252i
$197$	−9.59171e9	+	9.59171e9i	−0.453731	+	0.453731i	−0.896591	−	0.442860i	$-0.853964\pi$
$197$	−9.59171e9	+	9.59171e9i	−0.453731	+	0.453731i	0.442860	+	0.896591i	$0.353964\pi$
$198$	1.49901e10	−	5.59438e10i	0.693124	−	2.58678i
$199$	−2.01507e9	+	3.49020e9i	−0.0910858	+	0.157765i	−0.907968	−	0.419039i	$-0.862367\pi$
$199$	−2.01507e9	+	3.49020e9i	−0.0910858	+	0.157765i	0.816882	+	0.576804i	$0.195700\pi$
$200$	3.16929e10	+	3.58504e10i	1.40064	+	1.58438i
$201$	3.35675e8	−	1.93802e8i	0.0145056	−	0.00837483i
$202$	−3.48989e10	−	3.48989e10i	−1.47479	−	1.47479i
$203$	3.46533e8	+	2.20669e10i	0.0143223	+	0.912031i
$204$		−	2.04448e9i		−	0.0826507i
$205$	2.07722e10	+	6.38687e8i	0.821466	+	0.0252578i
$206$	−1.48463e10	−	8.57150e9i	−0.574401	−	0.331631i
$207$	−1.00806e10	−	3.76212e10i	−0.381609	−	1.42418i
$208$	−4.73881e10	−	1.26976e10i	−1.75543	−	0.470367i
$209$	−6.87657e10			−2.49295
$210$	3.10161e9	+	4.66365e7i	0.110053	+	0.00165478i
$211$	−1.00183e10			−0.347955			−0.173977	−	0.984750i	$-0.555662\pi$
$211$	−1.00183e10			−0.347955			−0.173977	+	0.984750i	$0.555662\pi$
$212$	2.83785e9	+	7.60400e8i	0.0964891	+	0.0258542i
$213$	−2.57343e8	−	9.60416e8i	−0.00856650	−	0.0319706i
$214$	4.01555e10	+	2.31838e10i	1.30883	+	0.755654i
$215$	1.67871e10	−	1.57855e10i	0.535799	−	0.503833i
$216$			8.32907e9i			0.260348i
$217$	9.59209e9	+	5.33896e9i	0.293660	+	0.163451i
$218$	9.00031e9	+	9.00031e9i	0.269900	+	0.269900i
$219$	−1.79525e8	+	1.03649e8i	−0.00527384	+	0.00304485i
$220$	5.41079e10	+	1.00747e11i	1.55725	+	2.89953i
$221$	−1.24376e10	+	2.15426e10i	−0.350730	+	0.607481i
$222$	−1.34240e9	+	5.00991e9i	−0.0370932	+	0.138434i
$223$	2.76355e10	−	2.76355e10i	0.748333	−	0.748333i	−0.225833	−	0.974166i	$-0.572510\pi$
$223$	2.76355e10	−	2.76355e10i	0.748333	−	0.748333i	0.974166	+	0.225833i	$0.0725105\pi$
$224$	−7.44483e9	−	2.61358e10i	−0.197578	−	0.693618i
$225$	−3.42801e10	+	1.70748e10i	−0.891703	+	0.444154i
$226$	−1.05177e10	−	1.82172e10i	−0.268184	−	0.464508i
$227$	−7.35250e10	+	1.97010e10i	−1.83789	+	0.492460i	−0.998681	−	0.0513520i	$-0.983647\pi$
$227$	−7.35250e10	+	1.97010e10i	−1.83789	+	0.492460i	−0.839207	+	0.543812i	$0.816980\pi$
$228$	8.78995e9	−	2.35526e9i	0.215417	−	0.0577208i
$229$	−2.52046e10	−	4.36556e10i	−0.605647	−	1.04901i	−0.991949	−	0.126639i	$-0.959581\pi$
$229$	−2.52046e10	−	4.36556e10i	−0.605647	−	1.04901i	0.386302	−	0.922372i	$-0.373752\pi$
$230$	9.53127e10	+	5.90069e10i	2.24582	+	1.39036i
$231$	3.89928e9	+	9.79453e8i	0.0901011	+	0.0226324i
$232$	6.01863e10	−	6.01863e10i	1.36396	−	1.36396i
$233$	−1.61470e10	+	6.02615e10i	−0.358914	+	1.33949i	0.516573	+	0.856243i	$0.327208\pi$
$233$	−1.61470e10	+	6.02615e10i	−0.358914	+	1.33949i	−0.875487	+	0.483242i	$0.839459\pi$
$234$	4.66266e10	−	8.07597e10i	1.01663	−	1.76085i
$235$	−7.42751e10	−	2.23700e10i	−1.58869	−	0.478477i
$236$	5.08837e10	−	2.93777e10i	1.06776	−	0.616473i
$237$	−1.08903e9	−	1.08903e9i	−0.0224218	−	0.0224218i
$238$	−5.41752e10	+	8.50753e8i	−1.09447	+	0.0171873i
$239$		−	3.18362e10i		−	0.631147i	−0.948901	−	0.315574i	$-0.897803\pi$
$239$		−	3.18362e10i		−	0.631147i	0.948901	−	0.315574i	$-0.102197\pi$
$240$	−3.45072e9	−	3.66965e9i	−0.0671366	−	0.0713960i
$241$	1.98688e10	+	1.14713e10i	0.379398	+	0.219045i	0.677556	−	0.735471i	$-0.263039\pi$
$241$	1.98688e10	+	1.14713e10i	0.379398	+	0.219045i	−0.298158	+	0.954516i	$0.596372\pi$
$242$	3.12739e10	+	1.16716e11i	0.586156	+	2.18757i
$243$	−9.66463e9	−	2.58963e9i	−0.177810	−	0.0476441i
$244$	−2.74174e10			−0.495190
$245$	−3.76365e7	−	5.63959e10i	−0.000667363	−	1.00000i
$246$	−5.19580e9			−0.0904575
$247$	−1.06948e11	−	2.86566e10i	−1.82825	−	0.489878i
$248$	−1.09580e10	−	4.08957e10i	−0.183949	−	0.686507i
$249$	−1.65397e9	−	9.54918e8i	−0.0272665	−	0.0157423i
$250$	3.82112e10	−	1.03390e11i	0.618672	−	1.67398i
$251$			6.67930e9i			0.106218i	0.998589	+	0.0531091i	$0.0169131\pi$
$251$			6.67930e9i			0.106218i	−0.998589	+	0.0531091i	$0.983087\pi$
$252$	1.39327e11	−	2.18796e9i	2.17638	−	0.0341772i
$253$	1.02736e11	+	1.02736e11i	1.57645	+	1.57645i
$254$	−8.33876e10	+	4.81438e10i	−1.25704	+	0.725753i
$255$	−2.25010e9	+	1.20846e9i	−0.0333251	+	0.0178979i
$256$	6.68949e10	−	1.15865e11i	0.973450	−	1.68606i
$257$	−2.07643e10	+	7.74933e10i	−0.296905	+	1.10807i	0.642787	+	0.766045i	$0.277778\pi$
$257$	−2.07643e10	+	7.74933e10i	−0.296905	+	1.10807i	−0.939692	+	0.342020i	$0.888889\pi$
$258$	−4.07374e9	+	4.07374e9i	−0.0572406	+	0.0572406i
$259$	9.14558e10	+	2.29726e10i	1.26288	+	0.317221i
$260$	4.21673e10	+	1.79234e11i	0.572263	+	2.43243i
$261$	3.40612e10	+	5.89958e10i	0.454337	+	0.786934i
$262$	−9.91630e10	+	2.65707e10i	−1.30015	+	0.348375i
$263$	−1.17394e11	+	3.14557e10i	−1.51303	+	0.405414i	−0.917439	−	0.397876i	$-0.869747\pi$
$263$	−1.17394e11	+	3.14557e10i	−1.51303	+	0.405414i	−0.595588	+	0.803290i	$0.703081\pi$
$264$	−7.75278e9	−	1.34282e10i	−0.0982290	−	0.170138i
$265$	−8.40534e8	−	3.57273e9i	−0.0104701	−	0.0445035i
$266$	−6.60681e10	−	2.31939e11i	−0.809142	−	2.84057i
$267$	−1.66488e9	+	1.66488e9i	−0.0200485	+	0.0200485i
$268$	−1.29704e10	+	4.84062e10i	−0.153584	+	0.573184i
$269$	4.77454e10	−	8.26975e10i	0.555964	−	0.962958i	−0.441864	−	0.897082i	$-0.645683\pi$
$269$	4.77454e10	−	8.26975e10i	0.555964	−	0.962958i	0.997828	−	0.0658756i	$-0.0209840\pi$
$270$	1.69027e10	−	9.07794e9i	0.193562	−	0.103956i
$271$	9.81082e10	−	5.66428e10i	1.10495	−	0.637944i	0.167435	−	0.985883i	$-0.446452\pi$
$271$	9.81082e10	−	5.66428e10i	1.10495	−	0.637944i	0.937517	+	0.347939i	$0.113118\pi$
$272$	6.22151e10	+	6.22151e10i	0.689184	+	0.689184i
$273$	5.65617e9	+	3.14823e9i	0.0616298	+	0.0343032i
$274$		−	1.61038e11i		−	1.72604i
$275$	7.88969e10	−	1.19100e11i	0.831884	−	1.25578i
$276$	−1.66510e10	−	9.61343e9i	−0.172722	−	0.0997212i
$277$	−1.35836e10	−	5.06945e10i	−0.138629	−	0.517371i	−0.999957	−	0.00932078i	$-0.997033\pi$
$277$	−1.35836e10	−	5.06945e10i	−0.138629	−	0.517371i	0.861327	−	0.508050i	$-0.169634\pi$
$278$	−4.36384e10	−	1.16929e10i	−0.438195	−	0.117414i
$279$	3.38853e10			0.334805
$280$	−1.56093e11	+	1.51468e11i	−1.51765	+	1.47268i
$281$	6.33592e10			0.606222			0.303111	−	0.952955i	$-0.401975\pi$
$281$	6.33592e10			0.606222			0.303111	+	0.952955i	$0.401975\pi$
$282$	1.87330e10	+	5.01948e9i	0.176395	+	0.0472648i
$283$	−4.73693e10	−	1.76785e11i	−0.438994	−	1.63835i	−0.731325	−	0.682029i	$-0.761098\pi$
$283$	−4.73693e10	−	1.76785e11i	−0.438994	−	1.63835i	0.292331	−	0.956317i	$-0.405569\pi$
$284$	1.11331e11	+	6.42768e10i	1.01551	+	0.586303i
$285$	−7.78775e9	−	8.28185e9i	−0.0699214	−	0.0743576i
$286$			3.47867e11i			3.07444i
$287$	1.48324e9	+	9.44517e10i	0.0129046	+	0.821753i
$288$	−5.93140e10	−	5.93140e10i	−0.508032	−	0.508032i
$289$	−6.40649e10	+	3.69879e10i	−0.540231	+	0.311903i
$290$	−1.87738e11	−	5.65424e10i	−1.55869	−	0.469443i
$291$	−2.40699e9	+	4.16902e9i	−0.0196768	+	0.0340813i
$292$	6.93682e9	−	2.58886e10i	0.0558390	−	0.208394i
$293$	−5.78945e10	+	5.78945e10i	−0.458916	+	0.458916i	−0.898300	−	0.439384i	$-0.855197\pi$
$293$	−5.78945e10	+	5.78945e10i	−0.458916	+	0.458916i	0.439384	+	0.898300i	$0.355197\pi$
$294$	4.42729e8	+	1.40928e10i	0.00345601	+	0.110011i
$295$	−6.24090e10	−	3.86366e10i	−0.479787	−	0.297030i
$296$	−1.81838e11	−	3.14953e11i	−1.37680	−	2.38469i
$297$	2.40197e10	−	6.43606e9i	0.179128	−	0.0479972i
$298$	−2.30834e11	+	6.18517e10i	−1.69561	+	0.454337i
$299$	1.16967e11	+	2.02593e11i	0.846337	+	1.46590i
$300$	−6.00574e9	+	1.79261e10i	−0.0428076	+	0.127773i
$301$	7.52172e10	+	7.28914e10i	0.528163	+	0.511831i
$302$	2.00932e11	−	2.00932e11i	1.39001	−	1.39001i
$303$	2.73703e9	−	1.02147e10i	0.0186547	−	0.0696202i
$304$	−1.95813e11	+	3.39157e11i	−1.31495	+	2.27756i
$305$	1.62060e10	+	3.01749e10i	0.107233	+	0.199663i
$306$	−1.44837e11	+	8.36218e10i	−0.944351	+	0.545221i
$307$	1.12857e11	+	1.12857e11i	0.725110	+	0.725110i	0.969641	−	0.244531i	$-0.0786340\pi$
$307$	1.12857e11	+	1.12857e11i	0.725110	+	0.725110i	−0.244531	+	0.969641i	$0.578634\pi$
$308$	−4.46027e11	+	2.66938e11i	−2.82412	+	1.69018i
$309$		−	3.67319e9i		−	0.0229209i
$310$	−7.10491e10	+	6.68103e10i	−0.436949	+	0.410881i
$311$	1.23031e11	+	7.10320e10i	0.745749	+	0.430559i	0.824156	−	0.566363i	$-0.191650\pi$
$311$	1.23031e11	+	7.10320e10i	0.745749	+	0.430559i	−0.0784067	+	0.996921i	$0.524983\pi$
$312$	−6.46159e9	−	2.41150e10i	−0.0386050	−	0.144076i
$313$	8.15479e10	+	2.18507e10i	0.480245	+	0.128681i	0.490817	−	0.871263i	$-0.336698\pi$
$313$	8.15479e10	+	2.18507e10i	0.480245	+	0.128681i	−0.0105716	+	0.999944i	$0.503365\pi$
$314$	−1.97472e11			−1.14636
$315$	−8.47623e10	−	1.52047e11i	−0.485071	−	0.870123i
$316$	1.99123e11			1.12339
$317$	1.99515e11	+	5.34600e10i	1.10971	+	0.297346i	0.766713	−	0.641990i	$-0.221891\pi$
$317$	1.99515e11	+	5.34600e10i	1.10971	+	0.297346i	0.342998	+	0.939336i	$0.388558\pi$
$318$	2.37498e8	+	8.86354e8i	0.00130238	+	0.00486055i
$319$	−2.20075e11	−	1.27060e11i	−1.18990	−	0.686991i
$320$	−5.66158e10	−	1.74078e9i	−0.301830	−	0.00928044i
$321$			9.93509e9i			0.0522275i
$322$	−2.47811e11	+	4.45223e11i	−1.28460	+	2.30795i
$323$	1.40410e11	+	1.40410e11i	0.717772	+	0.717772i
$324$	3.71063e11	−	2.14233e11i	1.87066	−	1.08003i
$325$	1.72336e11	−	1.52351e11i	0.856843	−	0.757478i
$326$	2.28493e11	−	3.95762e11i	1.12046	−	1.94069i
$327$	−7.05871e8	+	2.63435e9i	−0.00341398	+	0.0127411i
$328$	2.57612e11	−	2.57612e11i	1.22895	−	1.22895i
$329$	8.58988e10	−	3.41970e11i	0.404209	−	1.60918i
$330$	−1.88009e10	+	3.03688e10i	−0.0872703	+	0.140966i
$331$	−1.51185e11	−	2.61860e11i	−0.692281	−	1.19907i	−0.971089	−	0.238719i	$-0.923273\pi$
$331$	−1.51185e11	−	2.61860e11i	−0.692281	−	1.19907i	0.278808	−	0.960347i	$-0.410061\pi$
$332$	2.38511e11	−	6.39089e10i	1.07743	−	0.288695i
$333$	2.81149e11	−	7.53336e10i	1.25296	−	0.335730i
$334$	7.28731e10	+	1.26220e11i	0.320411	+	0.554969i
$335$	6.09413e10	−	1.43373e10i	0.264369	−	0.0621963i
$336$	1.59341e10	−	1.64425e10i	0.0682024	−	0.0703786i
$337$	−1.54585e11	+	1.54585e11i	−0.652878	+	0.652878i	−0.953685	−	0.300807i	$-0.902744\pi$
$337$	−1.54585e11	+	1.54585e11i	−0.652878	+	0.652878i	0.300807	+	0.953685i	$0.402744\pi$
$338$	−3.41317e10	+	1.27381e11i	−0.142244	+	0.530860i
$339$	2.25360e9	−	3.90336e9i	0.00926785	−	0.0160524i
$340$	9.52297e10	−	3.16191e11i	0.386471	−	1.28320i
$341$	−1.09469e11	+	6.32020e10i	−0.438426	+	0.253126i
$342$	−5.26374e11	−	5.26374e11i	−2.08054	−	2.08054i
$343$	2.56060e11	−	1.20712e10i	0.998891	−	0.0470899i
$344$		−	4.03958e11i		−	1.55533i
$345$	−7.38179e8	+	2.40080e10i	−0.00280528	+	0.0912368i
$346$	5.37104e11	+	3.10097e11i	2.01473	+	1.16320i
$347$	−1.62024e10	−	6.04683e10i	−0.0599926	−	0.223895i	0.929420	−	0.369023i	$-0.120308\pi$
$347$	−1.62024e10	−	6.04683e10i	−0.0599926	−	0.223895i	−0.989413	+	0.145127i	$0.953641\pi$
$348$	3.24828e10	+	8.70375e9i	0.118726	+	0.0318126i
$349$	5.17296e11			1.86649			0.933243	−	0.359245i	$-0.116966\pi$
$349$	5.17296e11			1.86649			0.933243	+	0.359245i	$0.116966\pi$
$350$	4.77511e11	+	1.51683e11i	1.70089	+	0.540293i
$351$	4.00386e10			0.140798
$352$	3.02249e11	+	8.09874e10i	1.04936	+	0.281174i
$353$	−8.21978e9	−	3.06766e10i	−0.0281757	−	0.105153i	0.950406	−	0.311012i	$-0.100668\pi$
$353$	−8.21978e9	−	3.06766e10i	−0.0281757	−	0.105153i	−0.978582	+	0.205859i	$0.934001\pi$
$354$	1.58927e10	+	9.17563e9i	0.0537876	+	0.0310543i
$355$	4.93557e9	−	1.60521e11i	0.0164934	−	0.536419i
$356$		−	3.04415e11i		−	1.00448i
$357$	−5.96187e9	−	9.96168e9i	−0.0194256	−	0.0324583i
$358$	−2.39713e11	−	2.39713e11i	−0.771290	−	0.771290i
$359$	−5.12777e11	+	2.96052e11i	−1.62931	+	0.940682i	−0.645010	+	0.764174i	$0.723147\pi$
$359$	−5.12777e11	+	2.96052e11i	−1.62931	+	0.940682i	−0.984299	+	0.176507i	$0.943520\pi$
$360$	−1.93610e11	+	6.42844e11i	−0.607529	+	2.01718i
$361$	−2.80576e11	+	4.85971e11i	−0.869496	+	1.50601i
$362$	6.53965e10	−	2.44063e11i	0.200155	−	0.746988i
$363$	−1.83075e10	+	1.83075e10i	−0.0553412	+	0.0553412i
$364$	−8.04922e11	+	2.29283e11i	−2.40324	+	0.684567i
$365$	−3.25926e10	+	7.66785e9i	−0.0961171	+	0.0226129i
$366$	−4.28168e9	−	7.41608e9i	−0.0124724	−	0.0216028i
$367$	−3.71699e11	+	9.95965e10i	−1.06953	+	0.286580i	−0.750301	−	0.661096i	$-0.770091\pi$
$367$	−3.71699e11	+	9.95965e10i	−1.06953	+	0.286580i	−0.319232	+	0.947677i	$0.603425\pi$
$368$	7.99246e11	−	2.14157e11i	2.27177	−	0.608720i
$369$	1.45790e11	+	2.52516e11i	0.409364	+	0.709040i
$370$	−4.40967e11	+	7.12286e11i	−1.22320	+	1.97582i
$371$	1.60448e10	−	4.57038e9i	0.0439694	−	0.0125248i
$372$	1.18281e10	−	1.18281e10i	0.0320238	−	0.0320238i
$373$	−7.32956e10	+	2.73543e11i	−0.196060	+	0.731705i	0.795930	+	0.605388i	$0.206982\pi$
$373$	−7.32956e10	+	2.73543e11i	−0.196060	+	0.731705i	−0.991990	+	0.126316i	$0.959685\pi$
$374$	3.11938e11	−	5.40293e11i	0.824416	−	1.42793i
$375$	2.32789e10	−	3.98609e9i	0.0607887	−	0.0104089i
$376$	−1.17766e12	+	6.79925e11i	−3.03862	+	1.75435i
$377$	−2.89321e11	−	2.89321e11i	−0.737639	−	0.737639i
$378$	4.47855e10	+	7.48320e10i	0.112830	+	0.188527i
$379$			1.05524e11i			0.262708i	0.991336	+	0.131354i	$0.0419324\pi$
$379$			1.05524e11i			0.262708i	−0.991336	+	0.131354i	$0.958068\pi$
$380$	1.46913e12	+	4.51715e10i	3.61437	+	0.111132i
$381$	−1.78673e10	−	1.03157e10i	−0.0434406	−	0.0250804i
$382$	−6.81508e10	−	2.54342e11i	−0.163752	−	0.611130i
$383$	−4.11220e10	−	1.10186e10i	−0.0976517	−	0.0261657i	0.209662	−	0.977774i	$-0.432764\pi$
$383$	−4.11220e10	−	1.10186e10i	−0.0976517	−	0.0261657i	−0.307314	+	0.951608i	$0.599430\pi$
$384$	3.31132e10			0.0777161
$385$	5.57425e11	+	3.33103e11i	1.29304	+	0.772690i
$386$	−6.20967e11			−1.42372
$387$	3.12290e11	+	8.36778e10i	0.707715	+	0.189632i
$388$	−1.61090e11	−	6.01197e11i	−0.360850	−	1.34671i
$389$	−7.14031e11	−	4.12246e11i	−1.58104	−	0.912816i	−0.994708	−	0.102747i	$-0.967237\pi$
$389$	−7.14031e11	−	4.12246e11i	−1.58104	−	0.912816i	−0.586335	−	0.810068i	$-0.699430\pi$
$390$	−4.18956e10	+	3.93961e10i	−0.0917018	+	0.0862308i
$391$		−	4.19545e11i		−	0.907786i
$392$	−7.20685e11	−	6.76783e11i	−1.54155	−	1.44765i
$393$	−1.55542e10	−	1.55542e10i	−0.0328913	−	0.0328913i
$394$	4.74382e11	−	2.73885e11i	0.991734	−	0.572578i
$395$	−1.17699e11	−	2.19150e11i	−0.243268	−	0.452955i
$396$	−8.02240e11	+	1.38952e12i	−1.63937	+	2.83946i
$397$	3.92796e10	−	1.46593e11i	0.0793614	−	0.296181i	−0.914825	−	0.403850i	$-0.867672\pi$
$397$	3.92796e10	−	1.46593e11i	0.0793614	−	0.296181i	0.994187	+	0.107669i	$0.0343386\pi$
$398$	1.15078e11	−	1.15078e11i	0.229889	−	0.229889i
$399$	3.59607e10	−	3.71082e10i	0.0710314	−	0.0732979i
$400$	−3.62746e11	−	7.28265e11i	−0.708489	−	1.42239i
$401$	2.57062e11	+	4.45244e11i	0.496464	+	0.859901i	0.999992	−	0.00407832i	$-0.00129817\pi$
$401$	2.57062e11	+	4.45244e11i	0.496464	+	0.859901i	−0.503528	+	0.863979i	$0.667965\pi$
$402$	−1.51188e10	+	4.05108e9i	−0.0288736	+	0.00773666i
$403$	−1.96589e11	+	5.26760e10i	−0.371268	+	0.0994809i
$404$	6.83632e11	+	1.18409e12i	1.27675	+	2.21140i
$405$	−4.55110e11	−	2.81753e11i	−0.840560	−	0.520380i
$406$	2.17118e11	−	8.64362e11i	0.396578	−	1.57880i
$407$	−7.67762e11	+	7.67762e11i	−1.38692	+	1.38692i
$408$	−1.15884e10	+	4.32486e10i	−0.0207040	+	0.0772683i
$409$	−2.64051e10	+	4.57350e10i	−0.0466587	+	0.0808153i	−0.888412	−	0.459048i	$-0.848191\pi$
$409$	−2.64051e10	+	4.57350e10i	−0.0466587	+	0.0808153i	0.841753	+	0.539863i	$0.181524\pi$
$410$	−8.03563e11	−	2.42015e11i	−1.40440	−	0.422975i
$411$	2.98825e10	−	1.72527e10i	0.0516569	−	0.0298241i
$412$	3.35813e11	+	3.35813e11i	0.574196	+	0.574196i
$413$	1.62262e11	−	2.91524e11i	0.274436	−	0.493059i
$414$			1.57281e12i			2.63132i
$415$	−2.11317e11	−	2.24724e11i	−0.349718	−	0.371906i
$416$	4.36323e11	+	2.51911e11i	0.714312	+	0.412408i
$417$	−2.50541e9	−	9.35030e9i	−0.00405757	−	0.0151430i
$418$	2.68227e12	+	7.18712e11i	4.29743	+	1.15149i
$419$	−1.00043e12			−1.58572			−0.792858	−	0.609407i	$-0.791408\pi$
$419$	−1.00043e12			−1.58572			−0.792858	+	0.609407i	$0.791408\pi$
$420$	−8.26616e10	−	2.34866e10i	−0.129623	−	0.0368298i
$421$	1.25128e12			1.94126			0.970632	−	0.240569i	$-0.0773340\pi$
$421$	1.25128e12			1.94126			0.970632	+	0.240569i	$0.0773340\pi$
$422$	3.90773e11	+	1.04707e11i	0.599816	+	0.160720i
$423$	−2.81686e11	−	1.05127e12i	−0.427793	−	1.59654i
$424$	−5.57215e10	−	3.21708e10i	−0.0837291	−	0.0483410i
$425$	−4.04281e11	+	8.20884e10i	−0.601081	+	0.122048i
$426$			4.01515e10i			0.0590689i
$427$	−1.33591e11	+	7.99514e10i	−0.194469	+	0.116386i
$428$	−9.08292e11	−	9.08292e11i	−1.30836	−	1.30836i
$429$	−6.45507e10	+	3.72683e10i	−0.0920117	+	0.0531230i
$430$	−8.19779e11	+	4.40278e11i	−1.15635	+	0.621039i
$431$	−3.38727e10	+	5.86692e10i	−0.0472826	+	0.0818959i	−0.888698	−	0.458493i	$-0.848389\pi$
$431$	−3.38727e10	+	5.86692e10i	−0.0472826	+	0.0818959i	0.841415	+	0.540389i	$0.181723\pi$
$432$	3.66538e10	−	1.36794e11i	0.0506339	−	0.188968i
$433$	1.32923e11	−	1.32923e11i	0.181721	−	0.181721i	−0.610384	−	0.792105i	$-0.708985\pi$
$433$	1.32923e11	−	1.32923e11i	0.181721	−	0.181721i	0.792105	+	0.610384i	$0.208985\pi$
$434$	−3.18348e11	−	3.08504e11i	−0.430723	−	0.417404i
$435$	−9.62098e9	−	4.08945e10i	−0.0128830	−	0.0547599i
$436$	−1.76306e11	−	3.05372e11i	−0.233657	−	0.404706i
$437$	1.80378e12	−	4.83320e11i	2.36601	−	0.633970i
$438$	8.08585e9	−	2.16660e9i	0.0104976	−	0.00281284i
$439$	−1.54008e11	−	2.66750e11i	−0.197903	−	0.342779i	0.749945	−	0.661500i	$-0.230080\pi$
$439$	−1.54008e11	−	2.66750e11i	−0.197903	−	0.342779i	−0.947848	+	0.318721i	$0.896747\pi$
$440$	−5.73543e11	−	2.43787e12i	−0.729506	−	3.10080i
$441$	6.72490e11	−	4.16951e11i	0.846666	−	0.524942i
$442$	7.10296e11	−	7.10296e11i	0.885195	−	0.885195i
$443$	−2.22734e11	+	8.31256e11i	−0.274771	+	1.02546i	0.681224	+	0.732075i	$0.261448\pi$
$443$	−2.22734e11	+	8.31256e11i	−0.274771	+	1.02546i	−0.955995	+	0.293383i	$0.905219\pi$
$444$	7.18426e10	−	1.24435e11i	0.0877322	−	0.151957i
$445$	−3.35032e11	+	1.79935e11i	−0.405010	+	0.217518i
$446$	−1.36678e12	+	7.89111e11i	−1.63566	+	0.944346i
$447$	−3.62074e10	−	3.62074e10i	−0.0428957	−	0.0428957i
$448$	−4.04267e9	−	2.57434e11i	−0.00474152	−	0.301936i
$449$			9.98153e11i			1.15901i	0.814967	+	0.579507i	$0.196755\pi$
$449$			9.98153e11i			1.15901i	−0.814967	+	0.579507i	$0.803245\pi$
$450$	1.51558e12	−	3.07736e11i	1.74230	−	0.353771i
$451$	−9.41973e11	−	5.43848e11i	−1.07212	−	0.618989i
$452$	1.50825e11	+	5.62886e11i	0.169961	+	0.634304i
$453$	5.88118e10	+	1.57586e10i	0.0656180	+	0.0175823i
$454$	3.07382e12			3.39568
$455$	7.28121e11	+	7.50352e11i	0.796439	+	0.820755i
$456$	−1.99291e11			−0.215847
$457$	6.57872e11	+	1.76276e11i	0.705535	+	0.189047i	0.593708	−	0.804680i	$-0.297663\pi$
$457$	6.57872e11	+	1.76276e11i	0.705535	+	0.189047i	0.111826	+	0.993728i	$0.464330\pi$
$458$	5.26856e11	+	1.96625e12i	0.559497	+	2.08807i
$459$	−6.21864e10	−	3.59033e10i	−0.0653940	−	0.0377553i
$460$	−2.12739e12	−	2.26236e12i	−2.21532	−	2.35587i
$461$			1.79010e12i			1.84596i	0.384846	+	0.922981i	$0.374255\pi$
$461$			1.79010e12i			1.84596i	−0.384846	+	0.922981i	$0.625745\pi$
$462$	−1.41858e11	−	7.89582e10i	−0.144865	−	0.0806321i
$463$	−5.36805e11	−	5.36805e11i	−0.542877	−	0.542877i	0.381494	−	0.924371i	$-0.375410\pi$
$463$	−5.36805e11	−	5.36805e11i	−0.542877	−	0.542877i	−0.924371	+	0.381494i	$0.875410\pi$
$464$	−1.25334e12	+	7.23616e11i	−1.25527	+	0.724732i
$465$	−2.00092e10	−	6.02632e9i	−0.0198468	−	0.00597742i
$466$	1.25966e12	−	2.18179e12i	1.23742	−	2.14327i
$467$	2.31286e11	−	8.63172e11i	0.225021	−	0.839791i	−0.757375	−	0.652981i	$-0.773518\pi$
$467$	2.31286e11	−	8.63172e11i	0.225021	−	0.839791i	0.982396	−	0.186811i	$-0.0598151\pi$
$468$	−1.82673e12	+	1.82673e12i	−1.76023	+	1.76023i
$469$	7.79585e10	+	2.73681e11i	0.0744021	+	0.261196i
$470$	2.66337e12	+	1.64886e12i	2.51762	+	1.55863i
$471$	−2.11559e10	−	3.66431e10i	−0.0198079	−	0.0343082i
$472$	−1.24291e12	+	3.33035e11i	−1.15265	+	0.308853i
$473$	−1.16495e12	+	3.12147e11i	−1.07012	+	0.286737i
$474$	3.10964e10	+	5.38605e10i	0.0282949	+	0.0490081i
$475$	−8.18664e11	−	1.64358e12i	−0.737877	−	1.48139i
$476$	1.45577e12	+	3.65674e11i	1.29976	+	0.326484i
$477$	3.64128e10	−	3.64128e10i	0.0322049	−	0.0322049i
$478$	−3.32739e11	+	1.24180e12i	−0.291527	+	1.08799i
$479$	8.34044e11	−	1.44461e12i	0.723901	−	1.25383i	−0.235523	−	0.971869i	$-0.575680\pi$
$479$	8.34044e11	−	1.44461e12i	0.723901	−	1.25383i	0.959425	−	0.281965i	$-0.0909862\pi$
$480$	2.44761e10	+	4.55735e10i	0.0210454	+	0.0391856i
$481$	−1.51401e12	+	8.74112e11i	−1.28966	+	0.744585i
$482$	−6.55108e11	−	6.55108e11i	−0.552842	−	0.552842i
$483$	−1.09165e11	+	1.71430e9i	−0.0912686	+	0.00143326i
$484$		−	3.34744e12i		−	2.77273i
$485$	−5.66444e11	+	5.32650e11i	−0.464857	+	0.437124i
$486$	3.49912e11	+	2.02022e11i	0.284509	+	0.164261i
$487$	−7.20374e10	−	2.68847e11i	−0.0580334	−	0.216584i	0.930820	−	0.365479i	$-0.119095\pi$
$487$	−7.20374e10	−	2.68847e11i	−0.0580334	−	0.216584i	−0.988853	+	0.148896i	$0.952428\pi$
$488$	5.79984e11	+	1.55406e11i	0.462942	+	0.124045i
$489$	9.79176e10			0.0774410
$490$	−5.87959e11	+	2.20017e12i	−0.460749	+	1.72414i
$491$	−1.73175e12			−1.34468			−0.672339	−	0.740244i	$-0.734710\pi$
$491$	−1.73175e12			−1.34468			−0.672339	+	0.740244i	$0.734710\pi$
$492$	1.39034e11	+	3.72541e10i	0.106974	+	0.0286637i
$493$	1.89923e11	+	7.08801e11i	0.144799	+	0.540397i
$494$	3.87209e12	+	2.23555e12i	2.92532	+	1.68894i
$495$	2.00346e12	+	6.16009e10i	1.49989	+	0.0461173i
$496$			7.19879e11i			0.534062i
$497$	7.29894e11	−	1.14621e10i	0.536606	−	0.00842672i
$498$	5.45340e10	+	5.45340e10i	0.0397316	+	0.0397316i
$499$	−5.23630e11	+	3.02318e11i	−0.378070	+	0.218279i	−0.676978	−	0.736003i	$-0.736711\pi$
$499$	−5.23630e11	+	3.02318e11i	−0.378070	+	0.218279i	0.298908	+	0.954282i	$0.403378\pi$
$500$	−1.76381e12	+	2.49264e12i	−1.26208	+	1.78359i
$501$	−1.56144e10	+	2.70449e10i	−0.0110727	+	0.0191785i
$502$	6.98094e10	−	2.60532e11i	0.0490622	−	0.183103i
$503$	8.52175e11	−	8.52175e11i	0.593572	−	0.593572i	−0.345023	−	0.938594i	$-0.612129\pi$
$503$	8.52175e11	−	8.52175e11i	0.593572	−	0.593572i	0.938594	+	0.345023i	$0.112129\pi$
$504$	−2.95971e12	−	7.43446e11i	−2.04321	−	0.513230i
$505$	8.99090e11	−	1.45228e12i	0.615166	−	0.993665i
$506$	−2.93356e12	−	5.08107e12i	−1.98938	−	3.44570i
$507$	−2.72937e10	+	7.31332e9i	−0.0183454	+	0.00491562i
$508$	2.57656e12	−	6.90387e11i	1.71654	−	0.459945i
$509$	−2.85483e11	−	4.94471e11i	−0.188517	−	0.326521i	0.756239	−	0.654296i	$-0.227035\pi$
$509$	−2.85483e11	−	4.94471e11i	−0.188517	−	0.326521i	−0.944756	+	0.327774i	$0.893701\pi$
$510$	1.00398e11	−	2.36199e10i	0.0657140	−	0.0154601i
$511$	−4.16937e10	−	1.46370e11i	−0.0270506	−	0.0949637i
$512$	−2.43476e12	+	2.43476e12i	−1.56582	+	1.56582i
$513$	8.27220e10	−	3.08723e11i	0.0527343	−	0.196807i
$514$	1.61986e12	−	2.80568e12i	1.02363	−	1.77298i
$515$	1.71094e11	−	5.68082e11i	0.107177	−	0.355860i
$516$	1.38218e11	−	7.98002e10i	0.0858303	−	0.0495542i
$517$	2.87080e12	+	2.87080e12i	1.76724	+	1.76724i
$518$	−3.32721e12	−	1.85193e12i	−2.03047	−	1.13016i
$519$			1.32888e11i			0.0803955i
$520$	1.23927e11	−	4.03051e12i	0.0743276	−	2.41738i
$521$	1.76380e12	+	1.01833e12i	1.04877	+	0.605506i	0.922304	−	0.386466i	$-0.126304\pi$
$521$	1.76380e12	+	1.01833e12i	1.04877	+	0.605506i	0.126463	+	0.991971i	$0.459638\pi$
$522$	−7.11989e11	−	2.65718e12i	−0.419716	−	1.56640i
$523$	1.94222e12	+	5.20417e11i	1.13512	+	0.304154i	0.776987	−	0.629517i	$-0.216747\pi$
$523$	1.94222e12	+	5.20417e11i	1.13512	+	0.304154i	0.358132	+	0.933671i	$0.383414\pi$
$524$	2.84402e12			1.64794
$525$	2.30112e10	+	1.04858e11i	0.0132197	+	0.0602399i
$526$	4.90784e12			2.79547
$527$	3.52570e11	+	9.44708e10i	0.199112	+	0.0533519i
$528$	6.82353e10	+	2.54658e11i	0.0382082	+	0.142595i
$529$	−1.85708e12	−	1.07219e12i	−1.03105	−	0.595278i
$530$	−4.55497e9	+	1.48143e11i	−0.00250752	+	0.0815527i
$531$		−	1.02985e12i		−	0.562143i
$532$	1.04903e11	+	6.68016e12i	0.0567789	+	3.61563i
$533$	−1.23836e12	−	1.23836e12i	−0.664624	−	0.664624i
$534$	8.23406e10	−	4.75394e10i	0.0438206	−	0.0252999i
$535$	−4.62766e11	+	1.53652e12i	−0.244213	+	0.810862i
$536$	5.48748e11	−	9.50460e11i	0.287165	−	0.497384i
$537$	1.88001e10	−	7.01628e10i	0.00975607	−	0.0364102i
$538$	−2.72668e12	+	2.72668e12i	−1.40318	+	1.40318i
$539$	−1.39484e12	+	2.60130e12i	−0.711829	+	1.32752i
$540$	−5.17389e11	+	1.21723e11i	−0.261846	+	0.0616028i
$541$	−1.59265e12	−	2.75855e12i	−0.799343	−	1.38450i	−0.920045	−	0.391813i	$-0.871848\pi$
$541$	−1.59265e12	−	2.75855e12i	−0.799343	−	1.38450i	0.120702	−	0.992689i	$-0.461485\pi$
$542$	−4.41881e12	+	1.18402e12i	−2.19942	+	0.589333i
$543$	5.22949e10	−	1.40124e10i	0.0258143	−	0.00691692i
$544$	−4.51786e11	−	7.82516e11i	−0.221176	−	0.383087i
$545$	−2.31873e11	+	3.74539e11i	−0.112581	+	0.181850i
$546$	−1.87720e11	−	1.81916e11i	−0.0903950	−	0.0875998i
$547$	9.09916e11	−	9.09916e11i	0.434569	−	0.434569i	−0.455611	−	0.890179i	$-0.650579\pi$
$547$	9.09916e11	−	9.09916e11i	0.434569	−	0.434569i	0.890179	+	0.455611i	$0.150579\pi$
$548$	−1.15465e12	+	4.30922e12i	−0.546939	+	2.04120i
$549$	−2.40281e11	+	4.16179e11i	−0.112887	+	0.195526i
$550$	−4.32223e12	+	3.82099e12i	−2.01407	+	1.78051i
$551$	−2.82860e12	+	1.63309e12i	−1.30734	+	0.754794i
$552$	2.97742e11	+	2.97742e11i	0.136494	+	0.136494i
$553$	9.70225e11	−	5.80661e11i	0.441174	−	0.264034i
$554$			2.11936e12i			0.955895i
$555$	−1.79415e11	−	5.51652e9i	−0.0802677	−	0.00246801i
$556$	1.08388e12	+	6.25779e11i	0.481000	+	0.277705i
$557$	1.68036e11	+	6.27117e11i	0.0739695	+	0.276058i	0.992998	−	0.118134i	$-0.0376912\pi$
$557$	1.68036e11	+	6.27117e11i	0.0739695	+	0.276058i	−0.919028	+	0.394192i	$0.871025\pi$
$558$	−1.32173e12	−	3.54156e11i	−0.577149	−	0.154647i
$559$	−1.94186e12			−0.841135
$560$	3.23017e12	−	1.80074e12i	1.38797	−	0.773757i
$561$	1.33677e11			0.0569800
$562$	−2.47138e12	−	6.62205e11i	−1.04503	−	0.280014i
$563$	−1.06421e12	−	3.97167e12i	−0.446414	−	1.66604i	−0.712177	−	0.702000i	$-0.752290\pi$
$563$	−1.06421e12	−	3.97167e12i	−0.446414	−	1.66604i	0.265763	−	0.964038i	$-0.414376\pi$
$564$	−4.65285e11	−	2.68633e11i	−0.193626	−	0.111790i
$565$	5.30348e11	−	4.98708e11i	0.218949	−	0.205887i
$566$			7.39073e12i			3.02701i
$567$	1.18328e12	−	2.12590e12i	0.480798	−	0.863812i
$568$	−1.99074e12	−	1.99074e12i	−0.802506	−	0.802506i
$569$	−3.08914e12	+	1.78351e12i	−1.23547	+	0.713299i	−0.968165	−	0.250314i	$-0.919466\pi$
$569$	−3.08914e12	+	1.78351e12i	−1.23547	+	0.713299i	−0.267304	+	0.963612i	$0.586133\pi$
$570$	2.17210e11	+	4.04435e11i	0.0861871	+	0.160477i
$571$	−3.87173e11	+	6.70603e11i	−0.152420	+	0.263999i	−0.932117	−	0.362158i	$-0.882040\pi$
$571$	−3.87173e11	+	6.70603e11i	−0.152420	+	0.263999i	0.779697	+	0.626158i	$0.215373\pi$
$572$	2.49422e12	−	9.30857e12i	0.974211	−	3.63581i
$573$	3.98948e10	−	3.98948e10i	0.0154604	−	0.0154604i
$574$	9.29317e11	−	3.69968e12i	0.357322	−	1.42253i
$575$	−1.23243e12	+	3.67860e12i	−0.470173	+	1.40339i
$576$	−3.97360e11	−	6.88248e11i	−0.150412	−	0.260522i
$577$	1.59356e12	−	4.26993e11i	0.598518	−	0.160372i	0.0531745	−	0.998585i	$-0.483066\pi$
$577$	1.59356e12	−	4.26993e11i	0.598518	−	0.160372i	0.545343	+	0.838213i	$0.316399\pi$
$578$	2.88549e12	−	7.73165e11i	1.07534	−	0.288136i
$579$	−6.65266e10	−	1.15228e11i	−0.0246004	−	0.0426091i
$580$	4.61826e12	+	2.85911e12i	1.69454	+	1.04907i
$581$	9.75778e11	−	1.00691e12i	0.355270	−	0.366606i
$582$	1.37460e11	−	1.37460e11i	0.0496617	−	0.0496617i
$583$	−4.97182e10	+	1.85551e11i	−0.0178241	+	0.0665203i
$584$	−2.93481e11	+	5.08324e11i	−0.104405	+	0.180835i
$585$	3.09021e12	+	9.30703e11i	1.09090	+	0.328556i
$586$	2.86332e12	−	1.65314e12i	1.00307	−	0.579122i
$587$	−6.29587e11	−	6.29587e11i	−0.218869	−	0.218869i	0.589153	−	0.808022i	$-0.299462\pi$
$587$	−6.29587e11	−	6.29587e11i	−0.218869	−	0.218869i	−0.808022	+	0.589153i	$0.799462\pi$
$588$	8.91993e10	−	3.80284e11i	0.0307726	−	0.131193i
$589$			1.62466e12i			0.556215i
$590$	2.03051e12	+	2.15933e12i	0.689875	+	0.733644i
$591$	1.01645e11	+	5.86847e10i	0.0342722	+	0.0197870i
$592$	1.60043e12	+	5.97288e12i	0.535536	+	1.99865i
$593$	6.03000e10	+	1.61573e10i	0.0200249	+	0.00536567i	0.268818	−	0.963191i	$-0.413367\pi$
$593$	6.03000e10	+	1.61573e10i	0.0200249	+	0.00536567i	−0.248793	+	0.968557i	$0.580034\pi$
$594$	−1.00418e12			−0.330957
$595$	−4.58035e11	−	1.81833e12i	−0.149821	−	0.594767i
$596$	6.62035e12			2.14918
$597$	3.36827e10	+	9.02525e9i	0.0108523	+	0.00290787i
$598$	−2.44499e12	−	9.12481e12i	−0.781846	−	2.91789i
$599$	1.08217e12	+	6.24793e11i	0.343460	+	0.198297i	0.661801	−	0.749680i	$-0.269792\pi$
$599$	1.08217e12	+	6.24793e11i	0.343460	+	0.198297i	−0.318341	+	0.947976i	$0.603126\pi$
$600$	2.28653e11	−	3.45165e11i	0.0720271	−	0.108729i
$601$		−	4.60882e12i		−	1.44097i	−0.693471	−	0.720485i	$-0.743919\pi$
$601$		−	4.60882e12i		−	1.44097i	0.693471	−	0.720485i	$-0.256081\pi$
$602$	−2.17208e12	−	3.62933e12i	−0.674051	−	1.12627i
$603$	6.21106e11	+	6.21106e11i	0.191310	+	0.191310i
$604$	−6.81743e12	+	3.93604e12i	−2.08427	+	1.20336i
$605$	−3.68411e12	+	1.97862e12i	−1.11798	+	0.600431i
$606$	−2.13521e11	+	3.69829e11i	−0.0643151	+	0.111397i
$607$	−4.71608e11	+	1.76007e12i	−0.141004	+	0.526235i	0.858897	+	0.512149i	$0.171150\pi$
$607$	−4.71608e11	+	1.76007e12i	−0.141004	+	0.526235i	−0.999901	+	0.0140858i	$0.995516\pi$
$608$	2.84386e12	−	2.84386e12i	0.843998	−	0.843998i
$609$	1.83653e11	−	5.23138e10i	0.0541028	−	0.0154113i
$610$	−3.16754e11	−	1.34638e12i	−0.0926271	−	0.393716i
$611$	3.26846e12	+	5.66115e12i	0.948764	+	1.64331i
$612$	4.47527e12	−	1.19914e12i	1.28955	−	0.345533i
$613$	2.09070e12	−	5.60200e11i	0.598024	−	0.160240i	0.0529062	−	0.998599i	$-0.483152\pi$
$613$	2.09070e12	−	5.60200e11i	0.598024	−	0.160240i	0.545118	+	0.838359i	$0.316485\pi$
$614$	−3.22254e12	−	5.58161e12i	−0.915042	−	1.58490i
$615$	−4.11801e10	−	1.75038e11i	−0.0116078	−	0.0493395i
$616$	1.09482e13	−	3.11862e12i	3.06359	−	0.872669i
$617$	2.58514e12	−	2.58514e12i	0.718127	−	0.718127i	−0.250095	−	0.968221i	$-0.580462\pi$
$617$	2.58514e12	−	2.58514e12i	0.718127	−	0.718127i	0.968221	+	0.250095i	$0.0804617\pi$
$618$	−3.83908e10	+	1.43276e11i	−0.0105871	+	0.0395117i
$619$	−3.13270e12	+	5.42599e12i	−0.857651	+	1.48550i	0.0165122	+	0.999864i	$0.494744\pi$
$619$	−3.13270e12	+	5.42599e12i	−0.857651	+	1.48550i	−0.874163	+	0.485632i	$0.838590\pi$
$620$	2.38024e12	−	1.27835e12i	0.646930	−	0.347446i
$621$	−5.84819e11	+	3.37645e11i	−0.157801	+	0.0911063i
$622$	−4.05654e12	−	4.05654e12i	−1.08667	−	1.08667i
$623$	−8.87699e11	−	1.48326e12i	−0.236086	−	0.394475i
$624$			4.24491e11i			0.112083i
$625$	3.78590e12	+	4.67837e11i	0.992451	+	0.122641i
$626$	−2.95247e12	−	1.70461e12i	−0.768425	−	0.443650i
$627$	1.53997e11	+	5.74724e11i	0.0397931	+	0.148510i
$628$	5.28414e12	+	1.41588e12i	1.35568	+	0.363252i
$629$	3.13532e12			0.798646
$630$	1.71710e12	+	6.81663e12i	0.434273	+	1.72400i
$631$	−1.59457e12			−0.400416			−0.200208	−	0.979753i	$-0.564162\pi$
$631$	−1.59457e12			−0.400416			−0.200208	+	0.979753i	$0.564162\pi$
$632$	−4.21223e12	−	1.12866e12i	−1.05023	−	0.281409i
$633$	2.24354e10	+	8.37300e10i	0.00555414	+	0.0207283i
$634$	−7.22354e12	−	4.17051e12i	−1.77561	−	1.02515i
$635$	−2.28279e12	−	2.42762e12i	−0.557165	−	0.592515i
$636$		−	2.54208e10i		−	0.00616073i
$637$	−3.25336e12	+	3.46440e12i	−0.782897	+	0.833682i
$638$	7.25623e12	+	7.25623e12i	1.73388	+	1.73388i
$639$	1.95137e12	−	1.12662e12i	0.463004	−	0.267316i
$640$	5.12116e12	+	1.54238e12i	1.20659	+	0.363397i
$641$	−2.50749e12	+	4.34310e12i	−0.586649	+	1.01611i	0.408019	+	0.912974i	$0.366220\pi$
$641$	−2.50749e12	+	4.34310e12i	−0.586649	+	1.01611i	−0.994668	+	0.103132i	$0.967114\pi$
$642$	1.03838e11	−	3.87527e11i	0.0241239	−	0.0900315i
$643$	5.83268e12	−	5.83268e12i	1.34561	−	1.34561i	0.455242	−	0.890368i	$-0.349553\pi$
$643$	5.83268e12	−	5.83268e12i	1.34561	−	1.34561i	0.890368	−	0.455242i	$-0.150447\pi$
$644$	9.82344e12	−	1.01369e13i	2.25049	−	2.32230i
$645$	−1.69525e11	−	1.04951e11i	−0.0385668	−	0.0238763i
$646$	−4.00931e12	−	6.94433e12i	−0.905781	−	1.56886i
$647$	−1.57287e12	+	4.21451e11i	−0.352878	+	0.0945534i	−0.430904	−	0.902398i	$-0.641805\pi$
$647$	−1.57287e12	+	4.21451e11i	−0.352878	+	0.0945534i	0.0780254	+	0.996951i	$0.475138\pi$
$648$	−9.06373e12	+	2.42862e12i	−2.01939	+	0.541093i
$649$	1.92084e12	+	3.32699e12i	0.425001	+	0.736123i
$650$	−8.31444e12	+	4.14140e12i	−1.82693	+	0.909990i
$651$	2.31405e10	−	9.21242e10i	0.00504962	−	0.0201029i
$652$	−8.95189e12	+	8.95189e12i	−1.93999	+	1.93999i
$653$	1.70246e11	−	6.35366e11i	0.0366410	−	0.136746i	−0.945182	−	0.326543i	$-0.894116\pi$
$653$	1.70246e11	−	6.35366e11i	0.0366410	−	0.136746i	0.981823	+	0.189797i	$0.0607829\pi$
$654$	5.50663e10	−	9.53776e10i	0.0117703	−	0.0203867i
$655$	−1.68105e12	−	3.13005e12i	−0.356859	−	0.664456i
$656$	−5.36460e12	+	3.09725e12i	−1.13102	+	0.652994i
$657$	−3.32179e11	−	3.32179e11i	−0.0695550	−	0.0695550i
$658$	−6.92469e12	+	1.24411e13i	−1.44007	+	2.58726i
$659$		−	7.89734e12i		−	1.63116i	−0.578645	−	0.815580i	$-0.696418\pi$
$659$		−	7.89734e12i		−	1.63116i	0.578645	−	0.815580i	$-0.303582\pi$
$660$	7.20839e11	−	6.77834e11i	0.147874	−	0.139052i
$661$	4.54671e12	+	2.62505e12i	0.926384	+	0.534848i	0.885666	−	0.464323i	$-0.153702\pi$
$661$	4.54671e12	+	2.62505e12i	0.926384	+	0.534848i	0.0407179	+	0.999171i	$0.487036\pi$
$662$	3.16025e12	+	1.17942e13i	0.639529	+	2.38675i
$663$	2.07900e11	+	5.57067e10i	0.0417873	+	0.0111969i
$664$	−5.40768e12			−1.07958
$665$	7.29001e12	−	4.06400e12i	1.44554	−	0.805853i
$666$	−1.17538e13			−2.31497
$667$	6.66577e12	+	1.78609e12i	1.30402	+	0.349411i
$668$	−1.04501e12	−	3.90002e12i	−0.203060	−	0.757832i
$669$	−2.92857e11	−	1.69081e11i	−0.0565247	−	0.0326345i
$670$	−2.52692e12	−	7.76957e10i	−0.484456	−	0.0148957i
$671$		−	1.79267e12i		−	0.341388i
$672$	−2.01763e11	+	1.20751e11i	−0.0381663	+	0.0228418i
$673$	−5.79849e12	−	5.79849e12i	−1.08955	−	1.08955i	−0.995574	−	0.0939762i	$-0.970042\pi$
$673$	−5.79849e12	−	5.79849e12i	−1.08955	−	1.08955i	−0.0939762	−	0.995574i	$-0.529958\pi$
$674$	7.64537e12	−	4.41406e12i	1.42702	−	0.823889i
$675$	4.39787e11	+	4.97478e11i	0.0815408	+	0.0922373i
$676$	1.82666e12	−	3.16386e12i	0.336432	−	0.582717i
$677$	4.11666e11	−	1.53636e12i	0.0753176	−	0.281089i	−0.917988	−	0.396609i	$-0.870187\pi$
$677$	4.11666e11	−	1.53636e12i	0.0753176	−	0.281089i	0.993305	+	0.115520i	$0.0368535\pi$
$678$	−1.28700e11	+	1.28700e11i	−0.0233908	+	0.0233908i
$679$	−2.53805e12	−	2.45957e12i	−0.458232	−	0.444063i
$680$	−3.80670e12	+	6.14889e12i	−0.682745	+	1.10282i
$681$	3.29310e11	+	5.70382e11i	0.0586736	+	0.101626i
$682$	4.93050e12	−	1.32112e12i	0.872693	−	0.233837i
$683$	−6.60965e11	+	1.77105e11i	−0.116221	+	0.0311414i	−0.316461	−	0.948606i	$-0.602495\pi$
$683$	−6.60965e11	+	1.77105e11i	−0.116221	+	0.0311414i	0.200240	+	0.979747i	$0.435828\pi$
$684$	1.03111e13	+	1.78594e13i	1.80116	+	3.11970i
$685$	5.42512e12	−	1.27633e12i	0.941460	−	0.221491i
$686$	−1.01140e13	−	2.20539e12i	−1.74367	−	0.380212i
$687$	−3.08417e11	+	3.08417e11i	−0.0528242	+	0.0528242i
$688$	−1.77770e12	+	6.63446e12i	−0.302489	+	1.12891i
$689$	−1.54648e11	+	2.67858e11i	−0.0261432	+	0.0452813i
$690$	2.79715e11	−	9.28738e11i	0.0469781	−	0.155981i
$691$	2.42587e12	−	1.40058e12i	0.404777	−	0.233698i	−0.283766	−	0.958894i	$-0.591584\pi$
$691$	2.42587e12	−	1.40058e12i	0.404777	−	0.233698i	0.688543	+	0.725195i	$0.258251\pi$
$692$	−1.21489e13	−	1.21489e13i	−2.01401	−	2.01401i
$693$	1.43058e11	+	9.10981e12i	0.0235620	+	1.50041i
$694$			2.52796e12i			0.413669i
$695$	4.80511e10	−	1.56278e12i	0.00781218	−	0.254078i
$696$	−6.37803e11	−	3.68236e11i	−0.103026	−	0.0594819i
$697$	8.12915e11	+	3.03384e12i	0.130466	+	0.486906i
$698$	−2.01776e13	−	5.40657e12i	−3.21751	−	0.862130i
$699$	5.39808e11			0.0855248
$700$	−1.16901e13	−	7.48265e12i	−1.84026	−	1.17792i
$701$	−7.79044e12			−1.21851			−0.609257	−	0.792973i	$-0.708532\pi$
$701$	−7.79044e12			−1.21851			−0.609257	+	0.792973i	$0.708532\pi$
$702$	−1.56174e12	−	4.18468e11i	−0.242713	−	0.0650347i
$703$	3.61193e12	+	1.34799e13i	0.557750	+	2.08155i
$704$	2.56740e12	+	1.48229e12i	0.393928	+	0.227435i
$705$	−2.06273e10	+	6.70866e11i	−0.00314478	+	0.102279i
$706$			1.28248e12i			0.194281i
$707$	6.78387e12	+	3.77591e12i	1.02115	+	0.568373i
$708$	−3.59482e11	−	3.59482e11i	−0.0537684	−	0.0537684i
$709$	1.81400e12	−	1.04731e12i	0.269605	−	0.155657i	−0.359103	−	0.933298i	$-0.616917\pi$
$709$	1.81400e12	−	1.04731e12i	0.269605	−	0.155657i	0.628708	+	0.777641i	$0.283584\pi$
$710$	−1.87022e12	+	6.20968e12i	−0.276204	+	0.917079i
$711$	1.74508e12	−	3.02257e12i	0.256096	−	0.443571i
$712$	−1.72547e12	+	6.43955e12i	−0.251622	+	0.939065i
$713$	2.42724e12	−	2.42724e12i	0.351730	−	0.351730i
$714$	1.28433e11	+	4.50876e11i	0.0184941	+	0.0649254i
$715$	−1.17191e13	+	2.75707e12i	−1.67694	+	0.394522i
$716$	4.69572e12	+	8.13322e12i	0.667719	+	1.15652i
$717$	−2.66078e11	+	7.12953e10i	−0.0375986	+	0.0100745i
$718$	2.30955e13	−	6.18843e12i	3.24316	−	0.869002i
$719$	−2.32097e12	−	4.02003e12i	−0.323883	−	0.560983i	0.657402	−	0.753540i	$-0.271655\pi$
$719$	−2.32097e12	−	4.02003e12i	−0.323883	−	0.560983i	−0.981286	+	0.192557i	$0.938322\pi$
$720$	6.00875e12	−	9.70582e12i	0.833274	−	1.34597i
$721$	2.61550e12	+	6.56985e11i	0.360451	+	0.0905412i
$722$	1.60233e13	−	1.60233e13i	2.19449	−	2.19449i
$723$	5.13784e10	−	1.91747e11i	0.00699292	−	0.0260979i
$724$	−3.49989e12	+	6.06199e12i	−0.473403	+	0.819958i
$725$	4.16878e11	−	6.77272e12i	0.0560387	−	0.910420i
$726$	9.05442e11	−	5.22757e11i	0.120961	−	0.0698369i
$727$	−2.54474e12	−	2.54474e12i	−0.337862	−	0.337862i	0.517700	−	0.855562i	$-0.326788\pi$
$727$	−2.54474e12	−	2.54474e12i	−0.337862	−	0.337862i	−0.855562	+	0.517700i	$0.826788\pi$
$728$	1.83268e13	−	2.87800e11i	2.41822	−	0.0379751i
$729$		−	7.45212e12i		−	0.977251i
$730$	1.35144e12	+	4.15531e10i	0.176135	+	0.00541565i
$731$	3.01602e12	+	1.74130e12i	0.390667	+	0.225552i
$732$	6.13997e10	+	2.29147e11i	0.00790435	+	0.0294994i
$733$	−9.21754e12	−	2.46983e12i	−1.17936	−	0.316009i	−0.384689	−	0.923046i	$-0.625691\pi$
$733$	−9.21754e12	−	2.46983e12i	−1.17936	−	0.316009i	−0.794674	+	0.607037i	$0.792358\pi$
$734$	1.55394e13			1.97607
$735$	−4.71256e11	+	1.26610e11i	−0.0595613	+	0.0160020i
$736$	−8.49745e12			−1.06743
$737$	−3.16500e12	−	8.48059e11i	−0.395157	−	0.105882i
$738$	−3.04748e12	−	1.13734e13i	−0.378171	−	1.41135i
$739$	9.24985e12	+	5.34040e12i	1.14087	+	0.658679i	0.946645	−	0.322278i	$-0.104449\pi$
$739$	9.24985e12	+	5.34040e12i	1.14087	+	0.658679i	0.194221	+	0.980958i	$0.437782\pi$
$740$	1.69070e13	−	1.58983e13i	2.07264	−	1.94898i
$741$			9.58013e11i			0.116732i
$742$	−6.73609e11	+	1.05782e10i	−0.0815812	+	0.00128113i
$743$	7.33647e11	+	7.33647e11i	0.0883156	+	0.0883156i	0.749884	−	0.661569i	$-0.230109\pi$
$743$	7.33647e11	+	7.33647e11i	0.0883156	+	0.0883156i	−0.661569	+	0.749884i	$0.730109\pi$
$744$	−3.17255e11	+	1.83167e11i	−0.0379603	+	0.0219164i
$745$	−3.91319e12	−	7.28620e12i	−0.465402	−	0.866558i
$746$	5.71793e12	−	9.90374e12i	0.675949	−	1.17078i
$747$	1.12017e12	−	4.18054e12i	0.131626	−	0.491236i
$748$	−1.22211e13	+	1.22211e13i	−1.42742	+	1.42742i
$749$	−7.07429e12	−	1.77698e12i	−0.821325	−	0.206307i
$750$	−9.49678e11	−	8.78213e10i	−0.109597	−	0.0101350i
$751$	3.29206e12	+	5.70202e12i	0.377649	+	0.654107i	0.990720	−	0.135921i	$-0.0433993\pi$
$751$	3.29206e12	+	5.70202e12i	0.377649	+	0.654107i	−0.613071	+	0.790028i	$0.710066\pi$
$752$	2.23337e13	−	5.98429e12i	2.54671	−	0.682390i
$753$	5.58237e10	−	1.49579e10i	0.00632763	−	0.00169548i
$754$	8.26136e12	+	1.43091e13i	0.930852	+	1.61228i
$755$	8.36160e12	+	5.17656e12i	0.936543	+	0.579802i
$756$	−6.61865e11	−	2.32354e12i	−0.0736922	−	0.258704i
$757$	−6.82321e12	+	6.82321e12i	−0.755192	+	0.755192i	−0.975443	−	0.220251i	$-0.929312\pi$
$757$	−6.82321e12	+	6.82321e12i	−0.755192	+	0.755192i	0.220251	+	0.975443i	$0.429312\pi$
$758$	1.10289e12	−	4.11604e12i	0.121345	−	0.452865i
$759$	6.28567e11	−	1.08871e12i	0.0687485	−	0.119076i
$760$	−3.08217e13	−	9.28280e12i	−3.35116	−	1.00929i
$761$	4.18775e12	−	2.41780e12i	0.452637	−	0.261330i	−0.256306	−	0.966596i	$-0.582506\pi$
$761$	4.18775e12	−	2.41780e12i	0.452637	−	0.261330i	0.708943	+	0.705265i	$0.249172\pi$
$762$	5.89114e11	+	5.89114e11i	0.0632997	+	0.0632997i
$763$	−1.74954e12	−	9.73794e11i	−0.186880	−	0.104018i
$764$			7.29459e12i			0.774605i
$765$	−3.96501e12	−	4.21657e12i	−0.418570	−	0.445126i
$766$	1.48884e12	+	8.59582e11i	0.156249	+	0.0902106i
$767$	1.60093e12	+	5.97476e12i	0.167030	+	0.623364i
$768$	−1.11818e12	−	2.99615e11i	−0.115981	−	0.0310769i
$769$	−1.70913e13			−1.76241			−0.881205	−	0.472734i	$-0.843267\pi$
$769$	−1.70913e13			−1.76241			−0.881205	+	0.472734i	$0.843267\pi$
$770$	−1.82614e13	−	1.88190e13i	−1.87209	−	1.92925i
$771$	6.94167e11			0.0707489
$772$	1.66165e13	+	4.45237e12i	1.68368	+	0.451142i
$773$	3.39183e12	+	1.26585e13i	0.341685	+	1.27519i	0.896437	+	0.443170i	$0.146146\pi$
$773$	3.39183e12	+	1.26585e13i	0.341685	+	1.27519i	−0.554752	+	0.832016i	$0.687187\pi$
$774$	−1.13066e13	−	6.52786e12i	−1.13239	−	0.653787i
$775$	−2.81384e12	−	1.86402e12i	−0.280183	−	0.185606i
$776$			1.36307e13i			1.34940i
$777$	−1.28112e10	−	8.15807e11i	−0.00126094	−	0.0802958i
$778$	2.35428e13	+	2.35428e13i	2.30383	+	2.30383i
$779$	−1.21071e13	+	6.99003e12i	−1.17793	+	0.680080i
$780$	1.40356e12	−	7.53806e11i	0.135770	−	0.0729179i
$781$	−4.20269e12	+	7.27927e12i	−0.404201	+	0.700097i
$782$	−4.38492e12	+	1.63647e13i	−0.419306	+	1.56487i
$783$	8.35174e11	−	8.35174e11i	0.0794052	−	0.0794052i
$784$	8.85795e12	+	1.42868e13i	0.837357	+	1.35055i
$785$	−1.56509e12	−	6.65250e12i	−0.147105	−	0.625276i
$786$	4.44140e11	+	7.69273e11i	0.0415067	+	0.0718917i
$787$	−8.78992e12	+	2.35525e12i	−0.816768	+	0.218852i	−0.642933	−	0.765922i	$-0.722283\pi$
$787$	−8.78992e12	+	2.35525e12i	−0.816768	+	0.218852i	−0.173835	+	0.984775i	$0.555616\pi$
$788$	−1.46578e13	+	3.92753e12i	−1.35425	+	0.362871i
$789$	5.25796e11	+	9.10705e11i	0.0483026	+	0.0836626i
$790$	2.30048e12	+	9.77830e12i	0.210134	+	0.893185i
$791$	2.37631e12	+	2.30283e12i	0.215829	+	0.209155i
$792$	2.48465e13	−	2.48465e13i	2.24389	−	2.24389i
$793$	7.47053e11	−	2.78804e12i	0.0670844	−	0.250363i
$794$	−3.06427e12	+	5.30747e12i	−0.273612	+	0.473910i
$795$	−2.79775e10	+	1.50259e10i	−0.00248403	+	0.00133410i
$796$	−3.90447e12	+	2.25425e12i	−0.344710	+	0.199018i
$797$	−1.32697e13	−	1.32697e13i	−1.16493	−	1.16493i	−0.983382	−	0.181547i	$-0.941890\pi$
$797$	−1.32697e13	−	1.32697e13i	−1.16493	−	1.16493i	−0.181547	−	0.983382i	$-0.558110\pi$
$798$	−1.79052e12	+	1.07159e12i	−0.156303	+	0.0935441i
$799$		−	1.17235e13i		−	1.01765i
$800$	1.66261e12	+	8.18829e12i	0.143511	+	0.706786i
$801$	−4.62083e12	−	2.66784e12i	−0.396619	−	0.228988i
$802$	−5.37341e12	−	2.00539e13i	−0.458633	−	1.71164i
$803$	1.69270e12	+	4.53558e11i	0.143668	+	0.0384958i
$804$	4.33611e11			0.0365972
$805$	−1.69629e13	−	4.81967e12i	−1.42370	−	0.404516i
$806$	8.21870e12			0.685954
$807$	−7.98085e11	−	2.13846e11i	−0.0662397	−	0.0177489i
$808$	−7.74987e12	−	2.89229e13i	−0.639652	−	2.38721i
$809$	1.81753e12	+	1.04935e12i	0.149181	+	0.0861295i	0.572732	−	0.819742i	$-0.305883\pi$
$809$	1.81753e12	+	1.04935e12i	0.149181	+	0.0861295i	−0.423552	+	0.905872i	$0.639217\pi$
$810$	1.48072e13	+	1.57467e13i	1.20862	+	1.28530i
$811$			4.28385e12i			0.347728i	0.984770	+	0.173864i	$0.0556254\pi$
$811$			4.28385e12i			0.347728i	−0.984770	+	0.173864i	$0.944375\pi$
$812$	−1.20074e13	+	2.15727e13i	−0.969272	+	1.74142i
$813$	−6.93111e11	−	6.93111e11i	−0.0556411	−	0.0556411i
$814$	3.79716e13	−	2.19229e13i	3.03144	−	1.75020i
$815$	1.51436e13	+	4.56090e12i	1.20232	+	0.362111i
$816$	3.80648e11	−	6.59303e11i	0.0300551	−	0.0520570i
$817$	−4.01200e12	+	1.49730e13i	−0.315037	+	1.17573i
$818$	1.50796e12	−	1.50796e12i	0.117761	−	0.117761i
$819$	−3.57382e12	+	1.42276e13i	−0.277559	+	1.10498i
$820$	1.97673e13	+	1.22377e13i	1.52681	+	0.945227i
$821$	−1.83457e12	−	3.17757e12i	−0.140926	−	0.244091i	0.786920	−	0.617055i	$-0.211675\pi$
$821$	−1.83457e12	−	3.17757e12i	−0.140926	−	0.244091i	−0.927846	+	0.372965i	$0.878341\pi$
$822$	−1.34591e12	+	3.60636e11i	−0.102824	+	0.0275515i
$823$	−1.92319e13	+	5.15318e12i	−1.46125	+	0.391540i	−0.899920	−	0.436054i	$-0.856376\pi$
$823$	−1.92319e13	+	5.15318e12i	−1.46125	+	0.391540i	−0.561327	+	0.827594i	$0.689709\pi$
$824$	−5.20031e12	−	9.00720e12i	−0.392967	−	0.680639i
$825$	−1.17209e12	−	3.92681e11i	−0.0880879	−	0.0295119i
$826$	−9.37607e12	+	9.67525e12i	−0.700827	+	0.723189i
$827$	6.76053e12	−	6.76053e12i	0.502581	−	0.502581i	−0.409658	−	0.912239i	$-0.634352\pi$
$827$	6.76053e12	−	6.76053e12i	0.502581	−	0.502581i	0.912239	+	0.409658i	$0.134352\pi$
$828$	1.12771e13	−	4.20867e13i	0.833798	−	3.11178i
$829$	3.77372e11	−	6.53627e11i	0.0277507	−	0.0480656i	−0.851817	−	0.523840i	$-0.824499\pi$
$829$	3.77372e11	−	6.53627e11i	0.0277507	−	0.0480656i	0.879567	+	0.475775i	$0.157832\pi$
$830$	5.89388e12	+	1.09742e13i	0.431072	+	0.802639i
$831$	−3.93271e11	+	2.27055e11i	−0.0286080	+	0.0165168i
$832$	3.37524e12	+	3.37524e12i	0.244202	+	0.244202i
$833$	8.15957e12	−	2.46342e12i	0.587171	−	0.177270i
$834$			3.90902e11i			0.0279783i
$835$	−3.67458e12	+	3.45535e12i	−0.261588	+	0.245982i
$836$	−6.66216e13	−	3.84640e13i	−4.71723	−	2.72349i
$837$	−1.52058e11	−	5.67489e11i	−0.0107089	−	0.0399662i
$838$	3.90228e13	+	1.04561e13i	2.73351	+	0.732442i
$839$	2.14353e13			1.49348			0.746742	−	0.665114i	$-0.231617\pi$
$839$	2.14353e13			1.49348			0.746742	+	0.665114i	$0.231617\pi$
$840$	1.61549e12	+	9.65373e11i	0.111956	+	0.0669019i
$841$	2.43713e12			0.167995
$842$	−4.88073e13	−	1.30779e13i	−3.34642	−	0.896670i
$843$	−1.41889e11	−	5.29538e11i	−0.00967666	−	0.0361138i
$844$	−9.70593e12	−	5.60372e12i	−0.658410	−	0.380133i
$845$	−4.56178e12	−	1.40262e11i	−0.307808	−	0.00946423i
$846$			4.39496e13i			2.94977i
$847$	−9.76140e12	−	1.63103e13i	−0.651684	−	1.08890i
$848$	7.73575e11	+	7.73575e11i	0.0513714	+	0.0513714i
$849$	−1.37143e12	+	7.91798e11i	−0.0905921	+	0.0523034i
$850$	1.66273e13	+	1.02345e12i	1.09254	+	0.0672486i
$851$	1.47428e13	−	2.55352e13i	0.963597	−	1.66900i
$852$	2.87888e11	−	1.07441e12i	0.0187174	−	0.0698544i
$853$	7.77297e12	−	7.77297e12i	0.502708	−	0.502708i	−0.409570	−	0.912279i	$-0.634321\pi$
$853$	7.77297e12	−	7.77297e12i	0.502708	−	0.502708i	0.912279	+	0.409570i	$0.134321\pi$
$854$	6.04645e12	−	1.72234e12i	0.388992	−	0.110805i
$855$	1.35608e13	−	2.19046e13i	0.867839	−	1.40180i
$856$	1.40655e13	+	2.43622e13i	0.895416	+	1.55091i
$857$	−1.43208e13	+	3.83724e12i	−0.906887	+	0.243000i	−0.681971	−	0.731379i	$-0.738877\pi$
$857$	−1.43208e13	+	3.83724e12i	−0.906887	+	0.243000i	−0.224915	+	0.974378i	$0.572210\pi$
$858$	2.90737e12	−	7.79028e11i	0.183150	−	0.0490750i
$859$	−8.45434e12	−	1.46433e13i	−0.529798	−	0.917637i	−0.999396	−	0.0347567i	$-0.988934\pi$
$859$	−8.45434e12	−	1.46433e13i	−0.529798	−	0.917637i	0.469598	−	0.882880i	$-0.344399\pi$
$860$	2.50933e13	−	5.90353e12i	1.56428	−	0.368018i
$861$	7.86079e11	−	2.23916e11i	0.0487474	−	0.0138858i
$862$	1.93442e12	−	1.93442e12i	0.119335	−	0.119335i
$863$	−6.10149e12	+	2.27711e13i	−0.374444	+	1.39744i	0.479711	+	0.877426i	$0.340741\pi$
$863$	−6.10149e12	+	2.27711e13i	−0.374444	+	1.39744i	−0.854155	+	0.520018i	$0.825925\pi$
$864$	−7.27184e11	+	1.25952e12i	−0.0443948	+	0.0768941i
$865$	−6.18977e12	+	2.05519e13i	−0.375926	+	1.24819i
$866$	−6.57404e12	+	3.79553e12i	−0.397193	+	0.229320i
$867$	4.52604e11	+	4.52604e11i	0.0272040	+	0.0272040i
$868$	6.30667e12	+	1.05378e13i	0.377104	+	0.630103i
$869$			1.30195e13i			0.774473i
$870$	−5.21374e10	+	1.69568e12i	−0.00308541	+	0.100348i
$871$	−4.56895e12	−	2.63788e12i	−0.268989	−	0.155301i
$872$	1.99867e12	+	7.45913e12i	0.117062	+	0.436882i
$873$	−1.05376e13	−	2.82353e12i	−0.614011	−	0.164524i
$874$	−7.54094e13			−4.37144
$875$	−1.32535e12	+	1.72888e13i	−0.0764355	+	0.997075i
$876$	−2.31904e11			−0.0133057
$877$	−9.79815e12	−	2.62541e12i	−0.559301	−	0.149864i	−0.0319160	−	0.999491i	$-0.510161\pi$
$877$	−9.79815e12	−	2.62541e12i	−0.559301	−	0.149864i	−0.527385	+	0.849626i	$0.676828\pi$
$878$	3.21926e12	+	1.20145e13i	0.182823	+	0.682306i
$879$	6.13517e11	+	3.54214e11i	0.0346638	+	0.0200132i
$880$	−1.30869e12	+	4.25627e13i	−0.0735636	+	2.39253i
$881$		−	2.13671e12i		−	0.119496i	−0.998213	−	0.0597481i	$-0.980970\pi$
$881$		−	2.13671e12i		−	0.119496i	0.998213	−	0.0597481i	$-0.0190298\pi$
$882$	−3.05889e13	+	9.23496e12i	−1.70198	+	0.513838i
$883$	−1.02436e13	−	1.02436e13i	−0.567062	−	0.567062i	0.364242	−	0.931304i	$-0.381328\pi$
$883$	−1.02436e13	−	1.02436e13i	−0.567062	−	0.567062i	−0.931304	+	0.364242i	$0.881328\pi$
$884$	−2.40996e13	+	1.39139e13i	−1.32732	+	0.766328i
$885$	−1.83153e11	+	6.08121e11i	−0.0100362	+	0.0333231i
$886$	1.73759e13	−	3.00960e13i	0.947318	−	1.64080i
$887$	−4.59508e12	+	1.71491e13i	−0.249251	+	0.930217i	0.721948	+	0.691947i	$0.243247\pi$
$887$	−4.59508e12	+	1.71491e13i	−0.249251	+	0.930217i	−0.971199	+	0.238270i	$0.923420\pi$
$888$	−2.22507e12	+	2.22507e12i	−0.120084	+	0.120084i
$889$	1.05410e13	−	1.08774e13i	0.566011	−	0.584071i
$890$	1.49488e13	−	3.51692e12i	0.798642	−	0.187891i
$891$	1.40075e13	+	2.42617e13i	0.744579	+	1.28965i
$892$	4.22316e13	−	1.13159e13i	2.23355	−	0.598478i
$893$	5.04037e13	−	1.35056e13i	2.65235	−	0.710696i
$894$	1.03388e12	+	1.79073e12i	0.0541315	+	0.0937585i
$895$	6.17566e12	−	9.97542e12i	0.321721	−	0.519670i
$896$	−5.92260e12	+	2.35783e13i	−0.306992	+	1.22216i
$897$	1.43127e12	−	1.43127e12i	0.0738170	−	0.0738170i
$898$	1.04323e13	−	3.89339e13i	0.535349	−	1.99795i
$899$	−3.00192e12	+	5.19948e12i	−0.153278	+	0.265486i
$900$	−4.27620e13	−	2.63211e12i	−2.17253	−	0.133725i
$901$	4.80386e11	−	2.77351e11i	0.0242845	−	0.0140206i
$902$	3.10584e13	+	3.10584e13i	1.56225	+	1.56225i
$903$	4.40760e11	−	7.91880e11i	0.0220601	−	0.0396337i
$904$		−	1.27621e13i		−	0.635572i
$905$	8.74041e12	+	2.68743e11i	0.433125	+	0.0133174i
$906$	−2.12931e12	−	1.22936e12i	−0.104993	−	0.0606179i
$907$	5.90207e12	+	2.20268e13i	0.289582	+	1.08074i	0.945425	+	0.325838i	$0.105647\pi$
$907$	5.90207e12	+	2.20268e13i	0.289582	+	1.08074i	−0.655843	+	0.754897i	$0.727687\pi$
$908$	−8.22522e13	−	2.20394e13i	−4.01570	−	1.07600i
$909$	2.39649e13			1.16423
$910$	−2.05586e13	−	3.68782e13i	−0.993821	−	1.78272i
$911$	−1.69330e13			−0.814521			−0.407260	−	0.913312i	$-0.633516\pi$
$911$	−1.69330e13			−0.814521			−0.407260	+	0.913312i	$0.633516\pi$
$912$	3.27309e12	+	8.77022e11i	0.156668	+	0.0419792i
$913$	4.17863e12	+	1.55949e13i	0.199029	+	0.742785i
$914$	−2.38185e13	−	1.37516e13i	−1.12890	−	0.651773i
$915$	2.15901e11	−	2.03020e11i	0.0101826	−	0.00957512i
$916$		−	5.63926e13i		−	2.64662i
$917$	1.38574e13	−	8.29339e12i	0.647173	−	0.387320i
$918$	2.05039e12	+	2.05039e12i	0.0952893	+	0.0952893i
$919$	3.17278e13	−	1.83181e13i	1.46731	−	0.847150i	0.467976	−	0.883741i	$-0.344983\pi$
$919$	3.17278e13	−	1.83181e13i	1.46731	−	0.847150i	0.999330	+	0.0365918i	$0.0116501\pi$
$920$	3.21791e13	+	5.99161e13i	1.48091	+	2.75739i
$921$	6.90487e11	−	1.19596e12i	0.0316218	−	0.0547706i
$922$	1.87094e13	−	6.98244e13i	0.852650	−	3.18213i
$923$	−9.56970e12	+	9.56970e12i	−0.434001	+	0.434001i
$924$	3.22984e12	+	3.12997e12i	0.145766	+	0.141259i
$925$	−2.74907e13	−	9.21015e12i	−1.23466	−	0.413646i
$926$	1.53281e13	+	2.65490e13i	0.685075	+	1.18659i
$927$	8.04045e12	−	2.15443e12i	0.357620	−	0.0958239i
$928$	1.43560e13	−	3.84668e12i	0.635430	−	0.170263i
$929$	−1.69569e13	−	2.93703e13i	−0.746925	−	1.29371i	−0.949290	−	0.314402i	$-0.898196\pi$
$929$	−1.69569e13	−	2.93703e13i	−0.746925	−	1.29371i	0.202365	−	0.979310i	$-0.435137\pi$
$930$	7.17492e11	+	4.44190e11i	0.0314517	+	0.0194713i
$931$	1.99910e13	+	3.22430e13i	0.872091	+	1.40657i
$932$	−4.93507e13	+	4.93507e13i	−2.14250	+	2.14250i
$933$	3.18144e11	−	1.18733e12i	0.0137454	−	0.0512984i
$934$	−1.80431e13	+	3.12515e13i	−0.775799	+	1.34372i
$935$	2.06739e13	+	6.22652e12i	0.884648	+	0.266436i
$936$	4.89967e13	−	2.82882e13i	2.08653	−	1.20466i
$937$	−7.02099e12	−	7.02099e12i	−0.297557	−	0.297557i	0.542499	−	0.840056i	$-0.317478\pi$
$937$	−7.02099e12	−	7.02099e12i	−0.297557	−	0.297557i	−0.840056	+	0.542499i	$0.817478\pi$
$938$	−1.80435e11	−	1.14900e13i	−0.00761043	−	0.484625i
$939$		−	7.30487e11i		−	0.0306632i
$940$	−5.94466e13	−	6.32182e13i	−2.48343	−	2.64099i
$941$	1.39146e13	+	8.03361e12i	0.578519	+	0.334008i	0.760545	−	0.649286i	$-0.224932\pi$
$941$	1.39146e13	+	8.03361e12i	0.578519	+	0.334008i	−0.182025	+	0.983294i	$0.558265\pi$
$942$	4.42226e11	+	1.65041e12i	0.0182985	+	0.0682909i
$943$	2.85311e13	+	7.64488e12i	1.17494	+	0.314824i
$944$	2.18786e13			0.896697
$945$	−2.16602e12	+	2.10184e12i	−0.0883525	+	0.0857348i
$946$	4.87023e13			1.97715
$947$	4.32244e12	+	1.15819e12i	0.174644	+	0.0467958i	0.345081	−	0.938573i	$-0.387851\pi$
$947$	4.32244e12	+	1.15819e12i	0.174644	+	0.0467958i	−0.170437	+	0.985369i	$0.554518\pi$
$948$	−4.45925e11	−	1.66422e12i	−0.0179318	−	0.0669225i
$949$	2.44356e12	+	1.41079e12i	0.0977970	+	0.0564631i
$950$	1.47546e13	+	7.26658e13i	0.587722	+	2.89450i
$951$		−	1.78721e12i		−	0.0708539i
$952$	−2.87226e13	−	1.59870e13i	−1.13333	−	0.630812i
$953$	−3.36282e12	−	3.36282e12i	−0.132064	−	0.132064i	0.637985	−	0.770049i	$-0.279768\pi$
$953$	−3.36282e12	−	3.36282e12i	−0.132064	−	0.132064i	−0.770049	+	0.637985i	$0.779768\pi$
$954$	−1.80089e12	+	1.03974e12i	−0.0703913	+	0.0406405i
$955$	8.02824e12	−	4.31172e12i	0.312324	−	0.167740i
$956$	1.78075e13	−	3.08435e13i	0.689514	−	1.19427i
$957$	−5.69088e11	+	2.12386e12i	−0.0219319	+	0.0818508i
$958$	−4.76311e13	+	4.76311e13i	−1.82703	+	1.82703i
$959$	6.94002e12	+	2.43637e13i	0.264958	+	0.930162i
$960$	1.12239e11	+	4.77077e11i	0.00426504	+	0.0181288i
$961$	−1.17266e13	−	2.03111e13i	−0.443524	−	0.768206i
$962$	6.81911e13	−	1.82718e13i	2.56708	−	0.687848i
$963$	−2.17474e13	+	5.82721e12i	−0.814873	+	0.218345i
$964$	1.28329e13	+	2.22272e13i	0.478605	+	0.828968i
$965$	−4.92157e12	−	2.09194e13i	−0.182697	−	0.776562i
$966$	4.27600e12	+	1.07408e12i	0.157994	+	0.0396863i
$967$	−3.94387e12	+	3.94387e12i	−0.145045	+	0.145045i	−0.775901	−	0.630855i	$-0.782704\pi$
$967$	−3.94387e12	+	3.94387e12i	−0.145045	+	0.145045i	0.630855	+	0.775901i	$0.282704\pi$
$968$	−1.89738e13	+	7.08112e13i	−0.694569	+	2.59217i
$969$	8.59066e11	−	1.48795e12i	0.0313018	−	0.0542163i
$970$	2.76617e13	−	1.48563e13i	1.00324	−	0.538811i
$971$	3.40006e13	−	1.96303e13i	1.22744	−	0.708663i	0.260946	−	0.965353i	$-0.415965\pi$
$971$	3.40006e13	−	1.96303e13i	1.22744	−	0.708663i	0.966494	+	0.256691i	$0.0826321\pi$
$972$	−7.91478e12	−	7.91478e12i	−0.284407	−	0.284407i
$973$	7.10601e12	−	1.11591e11i	0.254166	−	0.00399136i
$974$			1.12395e13i			0.400160i
$975$	−1.65924e12	−	1.09916e12i	−0.0588016	−	0.0389528i
$976$	−8.84155e12	−	5.10467e12i	−0.311892	−	0.180071i
$977$	−7.64637e12	−	2.85366e13i	−0.268491	−	1.00202i	−0.960079	−	0.279730i	$-0.909755\pi$
$977$	−7.64637e12	−	2.85366e13i	−0.268491	−	1.00202i	0.691588	−	0.722293i	$-0.256912\pi$
$978$	−3.81936e12	−	1.02340e12i	−0.133495	−	0.0357700i
$979$	1.99039e13			0.692495
$980$	3.15085e13	−	5.46585e13i	1.09121	−	1.89296i
$981$	−6.18048e12			−0.213065
$982$	6.75484e13	+	1.80995e13i	2.31800	+	0.621106i
$983$	−4.50234e12	−	1.68029e13i	−0.153797	−	0.573977i	−0.999205	−	0.0398572i	$-0.987310\pi$
$983$	−4.50234e12	−	1.68029e13i	−0.153797	−	0.573977i	0.845409	−	0.534120i	$-0.179357\pi$
$984$	−2.72995e12	−	1.57614e12i	−0.0928276	−	0.0535940i
$985$	1.29865e13	+	1.38105e13i	0.439572	+	0.467461i
$986$		−	2.96324e13i		−	0.998437i
$987$	−3.05045e12	+	4.79034e10i	−0.102314	+	0.00160672i
$988$	−8.75841e13	−	8.75841e13i	−2.92428	−	2.92428i
$989$	2.83636e13	−	1.63757e13i	0.942708	−	0.544273i
$990$	−7.75031e13	−	2.33422e13i	−2.56425	−	0.772296i
$991$	−2.13973e13	+	3.70613e13i	−0.704739	+	1.22064i	0.262047	+	0.965055i	$0.415602\pi$
$991$	−2.13973e13	+	3.70613e13i	−0.704739	+	1.22064i	−0.966786	+	0.255588i	$0.917731\pi$
$992$	1.91341e12	−	7.14093e12i	0.0627343	−	0.234128i
$993$	−1.84998e12	+	1.84998e12i	−0.0603803	+	0.0603803i
$994$	−2.85900e13	−	7.18147e12i	−0.928913	−	0.233332i
$995$	4.78885e12	+	2.96472e12i	0.154891	+	0.0958913i
$996$	−1.06826e12	−	1.85029e12i	−0.0343963	−	0.0595761i
$997$	−5.08668e12	+	1.36297e12i	−0.163045	+	0.0436877i	−0.339418	−	0.940636i	$-0.610230\pi$
$997$	−5.08668e12	+	1.36297e12i	−0.163045	+	0.0436877i	0.176373	+	0.984323i	$0.443563\pi$
$998$	2.35844e13	−	6.31941e12i	0.752553	−	0.201646i
$999$	−2.52327e12	−	4.37044e12i	−0.0801530	−	0.138829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.2	✓	136
5.2	odd	4	inner	35.10.k.a.17.33	yes	136
7.5	odd	6	inner	35.10.k.a.33.33	yes	136
35.12	even	12	inner	35.10.k.a.12.2	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.2	✓	136	1.1	even	1	trivial
35.10.k.a.12.2	yes	136	35.12	even	12	inner
35.10.k.a.17.33	yes	136	5.2	odd	4	inner
35.10.k.a.33.33	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+(-39.0059 - 10.4516i) q^{2} +(-2.23944 - 8.35771i) q^{3} +(968.820 + 559.349i) q^{4} +(42.9502 - 1396.88i) q^{5} +349.406i q^{6} +(6351.67 - 99.7449i) q^{7} +(-17323.8 - 17323.8i) q^{8} +(16981.1 - 9804.07i) q^{9} +(-16275.0 + 54037.8i) q^{10} +(-36572.6 + 63345.5i) q^{11} +(2505.26 - 9349.75i) q^{12} +(-83277.2 + 83277.2i) q^{13} +(-248795. - 62494.4i) q^{14} +(-11770.9 + 2769.27i) q^{15} +(208283. + 360757. i) q^{16} +(204019. - 54666.7i) q^{17} +(-764833. + 204936. i) q^{18} +(470064. + 814174. i) q^{19} +(822955. - 1.32930e6i) q^{20} +(-15057.8 - 52862.0i) q^{21} +(2.08861e6 - 2.08861e6i) q^{22} +(514101. - 1.91865e6i) q^{23} +(-105992. + 183583. i) q^{24} +(-1.94944e6 - 119993. i) q^{25} +(4.11868e6 - 2.37792e6i) q^{26} +(-240394. - 240394. i) q^{27} +(6.20941e6 + 3.45616e6i) q^{28} +3.47419e6i q^{29} +(488079. + 15007.1i) q^{30} +(1.49660e6 + 864063. i) q^{31} +(-1.10722e6 - 4.13219e6i) q^{32} +(611326. + 163804. i) q^{33} -8.52929e6 q^{34} +(133474. - 8.87681e6i) q^{35} +2.19356e7 q^{36} +(1.43384e7 + 3.84196e6i) q^{37} +(-9.82583e6 - 3.66705e7i) q^{38} +(882501. + 509512. i) q^{39} +(-2.49434e7 + 2.34553e7i) q^{40} +1.48704e7i q^{41} +(34851.4 + 2.21931e6i) q^{42} +(1.16590e7 + 1.16590e7i) q^{43} +(-7.08645e7 + 4.09136e7i) q^{44} +(-1.29658e7 - 2.41417e7i) q^{45} +(-4.01060e7 + 6.94656e7i) q^{46} +(1.43658e7 - 5.36138e7i) q^{47} +(2.54866e6 - 2.54866e6i) q^{48} +(4.03337e7 - 1.26709e6i) q^{49} +(7.47854e7 + 2.50552e7i) q^{50} +(-913776. - 1.58271e6i) q^{51} +(-1.27262e8 + 3.40997e7i) q^{52} +(2.53675e6 - 679719. i) q^{53} +(6.86428e6 + 1.18893e7i) q^{54} +(8.69155e7 + 5.38083e7i) q^{55} +(-1.11763e8 - 1.08307e8i) q^{56} +(5.75195e6 - 5.75195e6i) q^{57} +(3.63109e7 - 1.35514e8i) q^{58} +(2.62607e7 - 4.54848e7i) q^{59} +(-1.29529e7 - 3.90112e6i) q^{60} +(-2.12248e7 + 1.22542e7i) q^{61} +(-4.93454e7 - 4.93454e7i) q^{62} +(1.06881e8 - 6.39659e7i) q^{63} -4.05301e7i q^{64} +(1.12752e8 + 1.19905e8i) q^{65} +(-2.21333e7 - 1.27787e7i) q^{66} +(1.15942e7 + 4.32701e7i) q^{67} +(2.28235e8 + 6.11554e7i) q^{68} -1.71868e7 q^{69} +(-9.79832e7 + 3.44853e8i) q^{70} +1.14914e8 q^{71} +(-4.64022e8 - 1.24334e8i) q^{72} +(-6.20080e6 - 2.31417e7i) q^{73} +(-5.19127e8 - 2.99718e8i) q^{74} +(3.36278e6 + 1.65615e7i) q^{75} +1.05172e9i q^{76} +(-2.25978e8 + 4.05998e8i) q^{77} +(-2.90975e7 - 2.90975e7i) q^{78} +(1.54149e8 - 8.89979e7i) q^{79} +(5.12881e8 - 2.75452e8i) q^{80} +(1.91503e8 - 3.31692e8i) q^{81} +(1.55419e8 - 5.80033e8i) q^{82} +(1.56076e8 - 1.56076e8i) q^{83} +(1.49800e7 - 5.96364e7i) q^{84} +(-6.76002e7 - 2.87338e8i) q^{85} +(-3.32916e8 - 5.76627e8i) q^{86} +(2.90363e7 - 7.78025e6i) q^{87} +(1.73096e9 - 4.63810e8i) q^{88} +(-1.36058e8 - 2.35659e8i) q^{89} +(2.53422e8 + 1.07718e9i) q^{90} +(-5.20643e8 + 5.37255e8i) q^{91} +(1.57127e9 - 1.57127e9i) q^{92} +(3.87004e6 - 1.44432e7i) q^{93} +(-1.12070e9 + 1.94111e9i) q^{94} +(1.15749e9 - 6.21655e8i) q^{95} +(-3.20561e7 + 1.85076e7i) q^{96} +(-3.93410e8 - 3.93410e8i) q^{97} +(-1.58650e9 - 3.72128e8i) q^{98} +1.43424e9i 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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