LMFDB - Embedded newform 35.10.k.a.17.33

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			17.33
Character	$\chi$	$=$	35.17
Dual form			35.10.k.a.33.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.4516 - 39.0059i) q^{2} +(-8.35771 + 2.23944i) q^{3} +(-968.820 - 559.349i) q^{4} +(1231.21 + 661.245i) q^{5} +349.406i q^{6} +(99.7449 + 6351.67i) q^{7} +(-17323.8 + 17323.8i) q^{8} +(-16981.1 + 9804.07i) q^{9} +(38660.6 - 41113.4i) q^{10} +(-36572.6 + 63345.5i) q^{11} +(9349.75 + 2505.26i) q^{12} +(83277.2 + 83277.2i) q^{13} +(248795. + 62494.4i) q^{14} +(-11770.9 - 2769.27i) q^{15} +(208283. + 360757. i) q^{16} +(54666.7 + 204019. i) q^{17} +(204936. + 764833. 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} +(-1.91865e6 - 514101. i) q^{23} +(105992. - 183583. i) q^{24} +(1.07863e6 + 1.62826e6i) q^{25} +(4.11868e6 - 2.37792e6i) q^{26} +(240394. - 240394. i) q^{27} +(3.45616e6 - 6.20941e6i) q^{28} -3.47419e6i q^{29} +(-231043. + 430192. i) q^{30} +(1.49660e6 + 864063. i) q^{31} +(4.13219e6 - 1.10722e6i) q^{32} +(163804. - 611326. i) q^{33} +8.52929e6 q^{34} +(-4.07720e6 + 7.88619e6i) q^{35} +2.19356e7 q^{36} +(-3.84196e6 + 1.43384e7i) q^{37} +(-3.66705e7 + 9.82583e6i) q^{38} +(-882501. - 509512. i) q^{39} +(-3.27846e7 + 9.87398e6i) q^{40} +1.48704e7i q^{41} +(-2.21931e6 + 34851.4i) q^{42} +(1.16590e7 - 1.16590e7i) q^{43} +(7.08645e7 - 4.09136e7i) q^{44} +(-2.73903e7 + 842174. i) q^{45} +(-4.01060e7 + 6.94656e7i) q^{46} +(5.36138e7 + 1.43658e7i) 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} +(-3.40997e7 - 1.27262e8i) q^{52} +(-679719. - 2.53675e6i) 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} +(-1.35514e8 - 3.63109e7i) q^{58} +(-2.62607e7 + 4.54848e7i) q^{59} +(9.85492e6 + 9.26697e6i) q^{60} +(-2.12248e7 + 1.22542e7i) q^{61} +(4.93454e7 - 4.93454e7i) q^{62} +(-6.39659e7 - 1.06881e8i) q^{63} +4.05301e7i q^{64} +(4.74651e7 + 1.57598e8i) q^{65} +(-2.21333e7 - 1.27787e7i) q^{66} +(-4.32701e7 + 1.15942e7i) q^{67} +(6.11554e7 - 2.28235e8i) q^{68} +1.71868e7 q^{69} +(2.64995e8 + 2.41458e8i) q^{70} +1.14914e8 q^{71} +(1.24334e8 - 4.64022e8i) q^{72} +(-2.31417e7 + 6.20080e6i) q^{73} +(5.19127e8 + 2.99718e8i) q^{74} +(-1.26613e7 - 1.11930e7i) q^{75} +1.05172e9i q^{76} +(-4.05998e8 - 2.25978e8i) q^{77} +(-2.90975e7 + 2.90975e7i) q^{78} +(-1.54149e8 + 8.89979e7i) q^{79} +(1.78916e7 + 5.81894e8i) q^{80} +(1.91503e8 - 3.31692e8i) q^{81} +(5.80033e8 + 1.55419e8i) 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} +(7.78025e6 + 2.90363e7i) q^{87} +(-4.63810e8 - 1.73096e9i) 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} +(-1.44432e7 - 3.87004e6i) q^{93} +(1.12070e9 - 1.94111e9i) q^{94} +(-4.03787e7 - 1.31325e9i) q^{95} +(-3.20561e7 + 1.85076e7i) q^{96} +(3.93410e8 - 3.93410e8i) q^{97} +(-3.72128e8 + 1.58650e9i) 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 $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

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

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 $

$2$	10.4516	−	39.0059i	0.461900	−	1.72383i	−0.205068	−	0.978748i	$-0.565742\pi$
$2$	10.4516	−	39.0059i	0.461900	−	1.72383i	0.666968	−	0.745086i	$-0.267592\pi$
$3$	−8.35771	+	2.23944i	−0.0595719	+	0.0159623i	−0.288482	−	0.957485i	$-0.593151\pi$
$3$	−8.35771	+	2.23944i	−0.0595719	+	0.0159623i	0.228910	+	0.973448i	$0.426484\pi$
$4$	−968.820	−	559.349i	−1.89223	−	1.09248i
$5$	1231.21	+	661.245i	0.880983	+	0.473149i
$5$	1231.21	+	661.245i	0.880983	+	0.473149i
$6$			349.406i			0.110065i
$7$	99.7449	+	6351.67i	0.0157018	+	0.999877i
$7$	99.7449	+	6351.67i	0.0157018	+	0.999877i
$8$	−17323.8	+	17323.8i	−1.49534	+	1.49534i
$9$	−16981.1	+	9804.07i	−0.862731	+	0.498098i
$10$	38660.6	−	41113.4i	1.22256	−	1.30012i
$11$	−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	$0.895194\pi$
$12$	9349.75	+	2505.26i	0.130162	+	0.0348768i
$13$	83277.2	+	83277.2i	0.808688	+	0.808688i	0.984435	−	0.175747i	$-0.0562341\pi$
$13$	83277.2	+	83277.2i	0.808688	+	0.808688i	−0.175747	+	0.984435i	$0.556234\pi$
$14$	248795.	+	62494.4i	1.73087	+	0.434776i
$15$	−11770.9	−	2769.27i	−0.0600344	−	0.0141239i
$16$	208283.	+	360757.i	0.794537	+	1.37618i
$17$	54666.7	+	204019.i	0.158746	+	0.592448i	0.998755	+	0.0498760i	$0.0158826\pi$
$17$	54666.7	+	204019.i	0.158746	+	0.592448i	−0.840010	+	0.542572i	$0.817451\pi$
$18$	204936.	+	764833.i	0.460143	+	1.71728i
$19$	−470064.	−	814174.i	−0.827495	−	1.43326i	−0.899997	−	0.435895i	$-0.856432\pi$
$19$	−470064.	−	814174.i	−0.827495	−	1.43326i	0.0725025	−	0.997368i	$-0.476901\pi$
$20$	−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
$23$	−1.91865e6	−	514101.i	−1.42962	−	0.383066i	−0.540735	−	0.841193i	$-0.681854\pi$
$23$	−1.91865e6	−	514101.i	−1.42962	−	0.383066i	−0.888886	+	0.458128i	$0.848520\pi$
$24$	105992.	−	183583.i	0.0652111	−	0.112949i
$25$	1.07863e6	+	1.62826e6i	0.552261	+	0.833671i
$26$	4.11868e6	−	2.37792e6i	1.76758	−	1.02051i
$27$	240394.	−	240394.i	0.0870535	−	0.0870535i
$28$	3.45616e6	−	6.20941e6i	1.06263	−	1.90915i
$29$		−	3.47419e6i		−	0.912143i	−0.889943	−	0.456072i	$-0.849256\pi$
$29$		−	3.47419e6i		−	0.912143i	0.889943	−	0.456072i	$-0.150744\pi$
$30$	−231043.	+	430192.i	−0.0520771	+	0.0969654i
$31$	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	$0.612922\pi$
$32$	4.13219e6	−	1.10722e6i	0.696634	−	0.186663i
$33$	163804.	−	611326.i	0.0240443	−	0.0897346i
$34$	8.52929e6			1.09461
$35$	−4.07720e6	+	7.88619e6i	−0.459257	+	0.888303i
$36$	2.19356e7			2.17664
$37$	−3.84196e6	+	1.43384e7i	−0.337011	+	1.25774i	0.564661	+	0.825323i	$0.309007\pi$
$37$	−3.84196e6	+	1.43384e7i	−0.337011	+	1.25774i	−0.901672	+	0.432421i	$0.857660\pi$
$38$	−3.66705e7	+	9.82583e6i	−2.85293	+	0.764440i
$39$	−882501.	−	509512.i	−0.0610836	−	0.0352666i
$40$	−3.27846e7	+	9.87398e6i	−2.02488	+	0.609849i
$41$			1.48704e7i			0.821854i	0.911668	+	0.410927i	$0.134795\pi$
$41$			1.48704e7i			0.821854i	−0.911668	+	0.410927i	$0.865205\pi$
$42$	−2.21931e6	+	34851.4i	−0.110052	+	0.00172822i
$43$	1.16590e7	−	1.16590e7i	0.520061	−	0.520061i	−0.397528	−	0.917590i	$-0.630132\pi$
$43$	1.16590e7	−	1.16590e7i	0.520061	−	0.520061i	0.917590	+	0.397528i	$0.130132\pi$
$44$	7.08645e7	−	4.09136e7i	2.85031	−	1.64563i
$45$	−2.73903e7	+	842174.i	−0.995726	+	0.0306158i
$46$	−4.01060e7	+	6.94656e7i	−1.32068	+	2.28749i
$47$	5.36138e7	+	1.43658e7i	1.60264	+	0.429426i	0.945838	−	0.324638i	$-0.105242\pi$
$47$	5.36138e7	+	1.43658e7i	1.60264	+	0.429426i	0.656801	+	0.754064i	$0.271909\pi$
$48$	−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
$52$	−3.40997e7	−	1.27262e8i	−0.646748	−	2.41370i
$53$	−679719.	−	2.53675e6i	−0.0118328	−	0.0441607i	0.959757	−	0.280832i	$-0.0906103\pi$
$53$	−679719.	−	2.53675e6i	−0.0118328	−	0.0441607i	−0.971590	+	0.236671i	$0.923944\pi$
$54$	−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
$58$	−1.35514e8	−	3.63109e7i	−1.57238	−	0.421319i
$59$	−2.62607e7	+	4.54848e7i	−0.282145	+	0.488689i	−0.971913	−	0.235342i	$-0.924379\pi$
$59$	−2.62607e7	+	4.54848e7i	−0.282145	+	0.488689i	0.689768	+	0.724030i	$0.257712\pi$
$60$	9.85492e6	+	9.26697e6i	0.0981686	+	0.0923118i
$61$	−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
$63$	−6.39659e7	−	1.06881e8i	−0.511583	−	0.854804i
$64$			4.05301e7i			0.301973i
$65$	4.74651e7	+	1.57598e8i	0.329811	+	1.09507i
$66$	−2.21333e7	−	1.27787e7i	−0.143582	−	0.0828968i
$67$	−4.32701e7	+	1.15942e7i	−0.262332	+	0.0702917i	−0.387588	−	0.921833i	$-0.626692\pi$
$67$	−4.32701e7	+	1.15942e7i	−0.262332	+	0.0702917i	0.125256	+	0.992125i	$0.460025\pi$
$68$	6.11554e7	−	2.28235e8i	0.346853	−	1.29447i
$69$	1.71868e7			0.0912799
$70$	2.64995e8	+	2.41458e8i	1.31916	+	1.20199i
$71$	1.14914e8			0.536673			0.268336	−	0.963325i	$-0.413526\pi$
$71$	1.14914e8			0.536673			0.268336	+	0.963325i	$0.413526\pi$
$72$	1.24334e8	−	4.64022e8i	0.545249	−	2.03490i
$73$	−2.31417e7	+	6.20080e6i	−0.0953767	+	0.0255561i	−0.306192	−	0.951970i	$-0.599055\pi$
$73$	−2.31417e7	+	6.20080e6i	−0.0953767	+	0.0255561i	0.210815	+	0.977526i	$0.432388\pi$
$74$	5.19127e8	+	2.99718e8i	2.01248	+	1.16190i
$75$	−1.26613e7	−	1.11930e7i	−0.0462065	−	0.0408481i
$76$			1.05172e9i			3.61608i
$77$	−4.05998e8	−	2.25978e8i	−1.31618	−	0.732586i
$78$	−2.90975e7	+	2.90975e7i	−0.0890083	+	0.0890083i
$79$	−1.54149e8	+	8.89979e7i	−0.445265	+	0.257074i	−0.705828	−	0.708383i	$-0.749425\pi$
$79$	−1.54149e8	+	8.89979e7i	−0.445265	+	0.257074i	0.260563	+	0.965457i	$0.416092\pi$
$80$	1.78916e7	+	5.81894e8i	0.0488365	+	1.58832i
$81$	1.91503e8	−	3.31692e8i	0.494302	−	0.856156i
$82$	5.80033e8	+	1.55419e8i	1.41674	+	0.379615i
$83$	−1.56076e8	−	1.56076e8i	−0.360982	−	0.360982i	0.503192	−	0.864175i	$-0.332159\pi$
$83$	−1.56076e8	−	1.56076e8i	−0.360982	−	0.360982i	−0.864175	+	0.503192i	$0.832159\pi$
$84$	−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
$87$	7.78025e6	+	2.90363e7i	0.0145599	+	0.0543381i
$88$	−4.63810e8	−	1.73096e9i	−0.824457	−	3.07692i
$89$	1.36058e8	+	2.35659e8i	0.229863	+	0.398134i	0.957767	−	0.287545i	$-0.0928390\pi$
$89$	1.36058e8	+	2.35659e8i	0.229863	+	0.398134i	−0.727905	+	0.685678i	$0.759506\pi$
$90$	−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
$93$	−1.44432e7	−	3.87004e6i	−0.0200212	−	0.00536465i
$94$	1.12070e9	−	1.94111e9i	1.48052	−	2.56433i
$95$	−4.03787e7	−	1.31325e9i	−0.0508623	−	1.65421i
$96$	−3.20561e7	+	1.85076e7i	−0.0385203	+	0.0222397i
$97$	3.93410e8	−	3.93410e8i	0.451203	−	0.451203i	−0.444550	−	0.895754i	$-0.646637\pi$
$97$	3.93410e8	−	3.93410e8i	0.451203	−	0.451203i	0.895754	+	0.444550i	$0.146637\pi$
$98$	−3.72128e8	+	1.58650e9i	−0.407544	+	1.73749i
$99$		−	1.43424e9i		−	1.50059i
$100$	−1.34236e8	−	2.18083e9i	−0.134236	−	2.18083i
$101$	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	$0.468021\pi$
$102$	−7.12854e7	+	1.91009e7i	−0.0652078	+	0.0174724i
$103$	1.09874e8	−	4.10057e8i	0.0961898	−	0.358985i	−0.901007	−	0.433804i	$-0.857171\pi$
$103$	1.09874e8	−	4.10057e8i	0.0961898	−	0.358985i	0.997197	+	0.0748185i	$0.0238378\pi$
$104$	−2.88536e9			−2.41852
$105$	1.64154e7	−	7.50412e7i	0.0131795	−	0.0602487i
$106$	−1.06052e8			−0.0815912
$107$	2.97183e8	−	1.10910e9i	0.219178	−	0.817984i	−0.765476	−	0.643465i	$-0.777496\pi$
$107$	2.97183e8	−	1.10910e9i	0.219178	−	0.817984i	0.984654	−	0.174519i	$-0.0558371\pi$
$108$	−3.67362e8	+	9.84344e7i	−0.259829	+	0.0696210i
$109$	2.72971e8	+	1.57600e8i	0.185224	+	0.106939i	0.589745	−	0.807590i	$-0.299228\pi$
$109$	2.72971e8	+	1.57600e8i	0.185224	+	0.106939i	−0.404521	+	0.914529i	$0.632562\pi$
$110$	1.19043e9	+	3.95260e9i	0.775244	+	2.57404i
$111$		−	1.28440e8i		−	0.0803057i
$112$	−2.27063e9	+	1.35893e9i	−1.36353	+	0.816048i
$113$	3.68340e8	−	3.68340e8i	0.212518	−	0.212518i	−0.592818	−	0.805336i	$-0.701985\pi$
$113$	3.68340e8	−	3.68340e8i	0.212518	−	0.212518i	0.805336	+	0.592818i	$0.201985\pi$
$114$	2.84477e8	−	1.64243e8i	0.157752	−	0.0910783i
$115$	−2.02232e9	−	1.90167e9i	−1.07822	−	1.01390i
$116$	−1.94329e9	+	3.36587e9i	−0.996496	+	1.72598i
$117$	−2.23060e9	−	5.97687e8i	−1.10049	−	0.294875i
$118$	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
$122$	2.56151e8	+	9.55970e8i	0.104683	+	0.390683i
$123$	−3.33014e7	−	1.24282e8i	−0.0131186	−	0.0489595i
$124$	−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	0.933553	−	0.358441i	$-0.116691\pi$
$127$	1.68604e9	+	1.68604e9i	0.575112	+	0.575112i	−0.358441	+	0.933553i	$0.616691\pi$
$128$	3.69659e9	+	9.90499e8i	1.21719	+	0.326144i
$129$	−7.13331e7	+	1.23553e8i	−0.0226797	+	0.0392824i
$130$	6.64336e9	−	2.04265e8i	2.04006	−	0.0627261i
$131$	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
$133$	5.12447e9	−	3.06690e9i	1.42009	−	0.849898i
$134$			1.80897e9i			0.484685i
$135$	4.54935e8	−	1.37016e8i	0.117882	−	0.0355034i
$136$	−4.48142e9	−	2.58735e9i	−1.12329	−	0.648530i
$137$	−3.85200e9	+	1.03214e9i	−0.934208	+	0.250320i	−0.693648	−	0.720314i	$-0.743998\pi$
$137$	−3.85200e9	+	1.03214e9i	−0.934208	+	0.250320i	−0.240560	+	0.970634i	$0.577331\pi$
$138$	1.79630e8	−	6.70388e8i	0.0421622	−	0.157351i
$139$	−1.11876e9			−0.254198			−0.127099	−	0.991890i	$-0.540567\pi$
$139$	−1.11876e9			−0.254198			−0.127099	+	0.991890i	$0.540567\pi$
$140$	8.36121e9	−	5.35973e9i	1.83947	−	1.17914i
$141$	−4.80260e8			−0.102327
$142$	1.20103e9	−	4.48232e9i	0.247889	−	0.925134i
$143$	−8.32090e9	+	2.22958e9i	−1.66402	+	0.445872i
$144$	−7.07377e9	−	4.08404e9i	−1.37094	−	0.791515i
$145$	2.29729e9	−	4.27746e9i	0.431579	−	0.803582i
$146$			9.67471e8i			0.176218i
$147$	3.34260e8	−	1.00915e8i	0.0590413	−	0.0178249i
$148$	1.17423e10	−	1.17423e10i	2.01176	−	2.01176i
$149$	−5.12506e9	+	2.95896e9i	−0.851846	+	0.491813i	−0.861273	−	0.508142i	$-0.830332\pi$
$149$	−5.12506e9	+	2.95896e9i	−0.851846	+	0.491813i	0.00942735	+	0.999956i	$0.496999\pi$
$150$	−5.68925e8	+	3.76881e8i	−0.0917581	+	0.0607846i
$151$	−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	$0.981010\pi$
$152$	2.22479e10	+	5.96131e9i	3.38059	+	0.905827i
$153$	−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
$157$	1.26565e9	+	4.72348e9i	0.166252	+	0.620460i	0.997877	+	0.0651229i	$0.0207439\pi$
$157$	1.26565e9	+	4.72348e9i	0.166252	+	0.620460i	−0.831626	+	0.555337i	$0.812589\pi$
$158$	1.86034e9	+	6.94289e9i	0.237485	+	0.886305i
$159$	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
$163$	1.09310e10	+	2.92896e9i	1.21288	+	0.324989i	0.807890	−	0.589333i	$-0.200609\pi$
$163$	1.09310e10	+	2.92896e9i	1.21288	+	0.324989i	0.404987	+	0.914323i	$0.367276\pi$
$164$	8.31773e9	−	1.44067e10i	0.897858	−	1.55514i
$165$	6.05914e8	−	6.44356e8i	0.0636404	−	0.0676781i
$166$	−7.71915e9	+	4.45666e9i	−0.789011	+	0.455536i
$167$	2.55209e9	−	2.55209e9i	0.253905	−	0.253905i	−0.568664	−	0.822570i	$-0.692540\pi$
$167$	2.55209e9	−	2.55209e9i	0.253905	−	0.253905i	0.822570	+	0.568664i	$0.192540\pi$
$168$	1.17663e9	+	6.54913e8i	0.113959	+	0.0634296i
$169$			3.26569e9i			0.307953i
$170$	1.05014e10	+	5.63995e9i	0.964329	+	0.517911i
$171$	1.59644e10	+	9.21707e9i	1.42781	+	0.824348i
$172$	−1.78170e10	+	4.77404e9i	−1.55223	+	0.415919i
$173$	−3.97500e9	+	1.48349e10i	−0.337388	+	1.25915i	0.563868	+	0.825865i	$0.309312\pi$
$173$	−3.97500e9	+	1.48349e10i	−0.337388	+	1.25915i	−0.901257	+	0.433285i	$0.857354\pi$
$174$	1.21390e9			0.100395
$175$	−1.02346e10	+	7.01354e9i	−0.824897	+	0.565283i
$176$	−3.04698e10			−2.39366
$177$	1.17618e8	−	4.38958e8i	0.00900732	−	0.0336158i
$178$	1.06141e10	−	2.84404e9i	0.792490	−	0.212347i
$179$	−7.27026e9	−	4.19749e9i	−0.529312	−	0.305598i	0.211424	−	0.977394i	$-0.432190\pi$
$179$	−7.27026e9	−	4.19749e9i	−0.529312	−	0.305598i	−0.740736	+	0.671796i	$0.765523\pi$
$180$	2.70073e10	+	1.45048e10i	1.91759	+	1.02988i
$181$			6.25708e9i			0.433330i	0.976246	+	0.216665i	$0.0695179\pi$
$181$			6.25708e9i			0.433330i	−0.976246	+	0.216665i	$0.930482\pi$
$182$	1.55146e10	+	2.59233e10i	1.04814	+	1.75134i
$183$	1.49949e8	−	1.49949e8i	0.00988354	−	0.00988354i
$184$	4.21446e10	−	2.43322e10i	2.71057	−	1.56495i
$185$	−1.42114e10	+	1.51131e10i	−0.892001	+	0.948594i
$186$	−3.01909e8	+	5.22921e8i	−0.0184955	+	0.0320352i
$187$	−1.49230e10	−	3.99860e9i	−0.892418	−	0.239123i
$188$	−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	$0.776610\pi$
$192$	−9.07649e7	−	3.38739e8i	−0.00482017	−	0.0179891i
$193$	−3.97996e9	−	1.48534e10i	−0.206476	−	0.770580i	−0.988994	−	0.147952i	$-0.952732\pi$
$193$	−3.97996e9	−	1.48534e10i	−0.206476	−	0.770580i	0.782518	−	0.622628i	$-0.213935\pi$
$194$	−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	0.442860	−	0.896591i	$-0.353964\pi$
$197$	−9.59171e9	−	9.59171e9i	−0.453731	−	0.453731i	−0.896591	+	0.442860i	$0.853964\pi$
$198$	−5.59438e10	−	1.49901e10i	−2.58678	−	0.693124i
$199$	2.01507e9	−	3.49020e9i	0.0910858	−	0.157765i	−0.816882	−	0.576804i	$-0.804300\pi$
$199$	2.01507e9	−	3.49020e9i	0.0910858	−	0.157765i	0.907968	+	0.419039i	$0.137633\pi$
$200$	−4.68938e10	−	9.52168e9i	−2.07243	−	0.420803i
$201$	3.35675e8	−	1.93802e8i	0.0145056	−	0.00837483i
$202$	3.48989e10	−	3.48989e10i	1.47479	−	1.47479i
$203$	2.20669e10	−	3.46533e8i	0.912031	−	0.0143223i
$204$			2.04448e9i			0.0826507i
$205$	−9.83297e9	+	1.83086e10i	−0.388859	+	0.724040i
$206$	−1.48463e10	−	8.57150e9i	−0.574401	−	0.331631i
$207$	3.76212e10	−	1.00806e10i	1.42418	−	0.381609i
$208$	−1.26976e10	+	4.73881e10i	−0.470367	+	1.75543i
$209$	6.87657e10			2.49295
$210$	−2.75548e9	−	1.42460e9i	−0.0977712	−	0.0505482i
$211$	−1.00183e10			−0.347955			−0.173977	−	0.984750i	$-0.555662\pi$
$211$	−1.00183e10			−0.347955			−0.173977	+	0.984750i	$0.555662\pi$
$212$	−7.60400e8	+	2.83785e9i	−0.0258542	+	0.0964891i
$213$	−9.60416e8	+	2.57343e8i	−0.0319706	+	0.00856650i
$214$	−4.01555e10	−	2.31838e10i	−1.30883	−	0.755654i
$215$	2.20642e10	−	6.64525e9i	0.704231	−	0.212099i
$216$			8.32907e9i			0.260348i
$217$	−5.33896e9	+	9.59209e9i	−0.163451	+	0.293660i
$218$	9.00031e9	−	9.00031e9i	0.269900	−	0.269900i
$219$	1.79525e8	−	1.03649e8i	0.00527384	−	0.00304485i
$220$	1.14303e11	−	3.51450e9i	3.28970	−	0.101149i
$221$	−1.24376e10	+	2.15426e10i	−0.350730	+	0.607481i
$222$	−5.00991e9	−	1.34240e9i	−0.138434	−	0.0370932i
$223$	−2.76355e10	−	2.76355e10i	−0.748333	−	0.748333i	0.225833	−	0.974166i	$-0.427490\pi$
$223$	−2.76355e10	−	2.76355e10i	−0.748333	−	0.748333i	−0.974166	+	0.225833i	$0.927490\pi$
$224$	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
$227$	−1.97010e10	−	7.35250e10i	−0.492460	−	1.83789i	−0.543812	−	0.839207i	$-0.683020\pi$
$227$	−1.97010e10	−	7.35250e10i	−0.492460	−	1.83789i	0.0513520	−	0.998681i	$-0.483647\pi$
$228$	−2.35526e9	−	8.78995e9i	−0.0577208	−	0.215417i
$229$	2.52046e10	+	4.36556e10i	0.605647	+	1.04901i	0.991949	+	0.126639i	$0.0404190\pi$
$229$	2.52046e10	+	4.36556e10i	0.605647	+	1.04901i	−0.386302	+	0.922372i	$0.626248\pi$
$230$	−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
$233$	6.02615e10	+	1.61470e10i	1.33949	+	0.358914i	0.856243	−	0.516573i	$-0.172792\pi$
$233$	6.02615e10	+	1.61470e10i	1.33949	+	0.358914i	0.483242	+	0.875487i	$0.339459\pi$
$234$	−4.66266e10	+	8.07597e10i	−1.01663	+	1.76085i
$235$	5.65105e10	+	5.31391e10i	1.20872	+	1.13660i
$236$	5.08837e10	−	2.93777e10i	1.06776	−	0.616473i
$237$	1.08903e9	−	1.08903e9i	0.0224218	−	0.0224218i
$238$	8.50753e8	+	5.41752e10i	0.0171873	+	1.09447i
$239$			3.18362e10i			0.631147i	0.948901	+	0.315574i	$0.102197\pi$
$239$			3.18362e10i			0.631147i	−0.948901	+	0.315574i	$0.897803\pi$
$240$	−1.45265e9	−	4.82324e9i	−0.0282625	−	0.0938400i
$241$	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	$0.596372\pi$
$242$	−1.16716e11	+	3.12739e10i	−2.18757	+	0.586156i
$243$	−2.58963e9	+	9.66463e9i	−0.0476441	+	0.177810i
$244$	2.74174e10			0.495190
$245$	−5.04972e10	−	2.51104e10i	−0.895405	−	0.445253i
$246$	−5.19580e9			−0.0904575
$247$	2.86566e10	−	1.06948e11i	0.489878	−	1.82825i
$248$	−4.08957e10	+	1.09580e10i	−0.686507	+	0.183949i
$249$	1.65397e9	+	9.54918e8i	0.0272665	+	0.0157423i
$250$	1.08644e11	+	1.86033e10i	1.75904	+	0.301204i
$251$			6.67930e9i			0.106218i	0.998589	+	0.0531091i	$0.0169131\pi$
$251$			6.67930e9i			0.106218i	−0.998589	+	0.0531091i	$0.983087\pi$
$252$	2.18796e9	+	1.39327e11i	0.0341772	+	2.17638i
$253$	1.02736e11	−	1.02736e11i	1.57645	−	1.57645i
$254$	8.33876e10	−	4.81438e10i	1.25704	−	0.725753i
$255$	−7.84938e7	−	2.55288e9i	−0.00116253	−	0.0378093i
$256$	6.68949e10	−	1.15865e11i	0.973450	−	1.68606i
$257$	−7.74933e10	−	2.07643e10i	−1.10807	−	0.296905i	−0.342020	−	0.939692i	$-0.611111\pi$
$257$	−7.74933e10	−	2.07643e10i	−1.10807	−	0.296905i	−0.766045	+	0.642787i	$0.777778\pi$
$258$	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
$262$	−2.65707e10	−	9.91630e10i	−0.348375	−	1.30015i
$263$	3.14557e10	+	1.17394e11i	0.405414	+	1.51303i	0.803290	+	0.595588i	$0.203081\pi$
$263$	3.14557e10	+	1.17394e11i	0.405414	+	1.51303i	−0.397876	+	0.917439i	$0.630253\pi$
$264$	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
$268$	4.84062e10	+	1.29704e10i	0.573184	+	0.153584i
$269$	−4.77454e10	+	8.26975e10i	−0.555964	+	0.962958i	0.441864	+	0.897082i	$0.354317\pi$
$269$	−4.77454e10	+	8.26975e10i	−0.555964	+	0.962958i	−0.997828	+	0.0658756i	$0.979016\pi$
$270$	−5.89645e8	−	1.91772e10i	−0.00675233	−	0.219608i
$271$	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
$273$	3.14823e9	−	5.65617e9i	0.0343032	−	0.0616298i
$274$			1.61038e11i			1.72604i
$275$	−1.42592e11	+	8.77689e9i	−1.50348	+	0.0925430i
$276$	−1.66510e10	−	9.61343e9i	−0.172722	−	0.0997212i
$277$	5.06945e10	−	1.35836e10i	0.517371	−	0.138629i	0.00932078	−	0.999957i	$-0.497033\pi$
$277$	5.06945e10	−	1.35836e10i	0.517371	−	0.138629i	0.508050	+	0.861327i	$0.330366\pi$
$278$	−1.16929e10	+	4.36384e10i	−0.117414	+	0.438195i
$279$	−3.38853e10			−0.334805
$280$	−6.59863e10	−	2.07252e11i	−0.641568	−	2.01506i
$281$	6.33592e10			0.606222			0.303111	−	0.952955i	$-0.401975\pi$
$281$	6.33592e10			0.606222			0.303111	+	0.952955i	$0.401975\pi$
$282$	−5.01948e9	+	1.87330e10i	−0.0472648	+	0.176395i
$283$	−1.76785e11	+	4.73693e10i	−1.63835	+	0.438994i	−0.956317	−	0.292331i	$-0.905569\pi$
$283$	−1.76785e11	+	4.73693e10i	−1.63835	+	0.438994i	−0.682029	+	0.731325i	$0.738902\pi$
$284$	−1.11331e11	−	6.42768e10i	−1.01551	−	0.586303i
$285$	3.27841e9	+	1.08853e10i	0.0294349	+	0.0977325i
$286$			3.47867e11i			3.07444i
$287$	−9.44517e10	+	1.48324e9i	−0.821753	+	0.0129046i
$288$	−5.93140e10	+	5.93140e10i	−0.508032	+	0.508032i
$289$	6.40649e10	−	3.69879e10i	0.540231	−	0.311903i
$290$	−1.42836e11	−	1.34314e11i	−1.18590	−	1.11515i
$291$	−2.40699e9	+	4.16902e9i	−0.0196768	+	0.0340813i
$292$	2.58886e10	+	6.93682e9i	0.208394	+	0.0558390i
$293$	5.78945e10	+	5.78945e10i	0.458916	+	0.458916i	0.898300	−	0.439384i	$-0.144803\pi$
$293$	5.78945e10	+	5.78945e10i	0.458916	+	0.458916i	−0.439384	+	0.898300i	$0.644803\pi$
$294$	−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
$297$	6.43606e9	+	2.40197e10i	0.0479972	+	0.179128i
$298$	6.18517e10	+	2.30834e11i	0.454337	+	1.69561i
$299$	−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
$303$	−1.02147e10	−	2.73703e9i	−0.0696202	−	0.0186547i
$304$	1.95813e11	−	3.39157e11i	1.31495	−	2.27756i
$305$	−3.42353e10	+	1.05264e9i	−0.226529	+	0.00696514i
$306$	−1.44837e11	+	8.36218e10i	−0.944351	+	0.545221i
$307$	−1.12857e11	+	1.12857e11i	−0.725110	+	0.725110i	−0.969641	−	0.244531i	$-0.921366\pi$
$307$	−1.12857e11	+	1.12857e11i	−0.725110	+	0.725110i	0.244531	+	0.969641i	$0.421366\pi$
$308$	2.66938e11	+	4.46027e11i	1.69018	+	2.82412i
$309$			3.67319e9i			0.0229209i
$310$	9.33840e10	−	2.81252e10i	0.574308	−	0.172969i
$311$	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	$0.524983\pi$
$312$	2.41150e10	−	6.46159e9i	0.144076	−	0.0386050i
$313$	2.18507e10	−	8.15479e10i	0.128681	−	0.480245i	−0.871263	−	0.490817i	$-0.836698\pi$
$313$	2.18507e10	−	8.15479e10i	0.128681	−	0.480245i	0.999944	+	0.0105716i	$0.00336511\pi$
$314$	1.97472e11			1.14636
$315$	−8.08125e9	−	1.73890e11i	−0.0462467	−	0.995122i
$316$	1.99123e11			1.12339
$317$	−5.34600e10	+	1.99515e11i	−0.297346	+	1.10971i	0.641990	+	0.766713i	$0.278109\pi$
$317$	−5.34600e10	+	1.99515e11i	−0.297346	+	1.10971i	−0.939336	+	0.342998i	$0.888558\pi$
$318$	8.86354e8	−	2.37498e8i	0.00486055	−	0.00130238i
$319$	2.20075e11	+	1.27060e11i	1.18990	+	0.686991i
$320$	−2.68004e10	+	4.99011e10i	−0.142878	+	0.266033i
$321$			9.93509e9i			0.0522275i
$322$	−4.45223e11	−	2.47811e11i	−2.30795	−	1.28460i
$323$	1.40410e11	−	1.40410e11i	0.717772	−	0.717772i
$324$	−3.71063e11	+	2.14233e11i	−1.87066	+	1.08003i
$325$	−4.57716e10	+	2.25423e11i	−0.227573	+	1.12079i
$326$	2.28493e11	−	3.95762e11i	1.12046	−	1.94069i
$327$	−2.63435e9	−	7.05871e8i	−0.0127411	−	0.00341398i
$328$	−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	$-0.410061\pi$
$332$	6.39089e10	+	2.38511e11i	0.288695	+	1.07743i
$333$	−7.53336e10	−	2.81149e11i	−0.335730	−	1.25296i
$334$	−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	0.300807	−	0.953685i	$-0.402744\pi$
$337$	−1.54585e11	−	1.54585e11i	−0.652878	−	0.652878i	−0.953685	+	0.300807i	$0.902744\pi$
$338$	1.27381e11	+	3.41317e10i	0.530860	+	0.142244i
$339$	−2.25360e9	+	3.90336e9i	−0.00926785	+	0.0160524i
$340$	2.26215e11	−	2.40567e11i	0.918049	−	0.976294i
$341$	−1.09469e11	+	6.32020e10i	−0.438426	+	0.253126i
$342$	5.26374e11	−	5.26374e11i	2.08054	−	2.08054i
$343$	−1.20712e10	−	2.56060e11i	−0.0470899	−	0.998891i
$344$			4.03958e11i			1.55533i
$345$	2.11606e10	+	1.13647e10i	0.0804160	+	0.0431889i
$346$	5.37104e11	+	3.10097e11i	2.01473	+	1.16320i
$347$	6.04683e10	−	1.62024e10i	0.223895	−	0.0599926i	−0.145127	−	0.989413i	$-0.546359\pi$
$347$	6.04683e10	−	1.62024e10i	0.223895	−	0.0599926i	0.369023	+	0.929420i	$0.379692\pi$
$348$	8.70375e9	−	3.24828e10i	0.0318126	−	0.118726i
$349$	−5.17296e11			−1.86649			−0.933243	−	0.359245i	$-0.883034\pi$
$349$	−5.17296e11			−1.86649			−0.933243	+	0.359245i	$0.883034\pi$
$350$	1.66601e11	+	4.72513e11i	0.593434	+	1.68309i
$351$	4.00386e10			0.140798
$352$	−8.09874e10	+	3.02249e11i	−0.281174	+	1.04936i
$353$	−3.06766e10	+	8.21978e9i	−0.105153	+	0.0281757i	−0.311012	−	0.950406i	$-0.600668\pi$
$353$	−3.06766e10	+	8.21978e9i	−0.105153	+	0.0281757i	0.205859	+	0.978582i	$0.434001\pi$
$354$	−1.58927e10	−	9.17563e9i	−0.0537876	−	0.0310543i
$355$	1.41483e11	+	7.59862e10i	0.472799	+	0.253926i
$356$		−	3.04415e11i		−	1.00448i
$357$	9.96168e9	−	5.96187e9i	0.0324583	−	0.0194256i
$358$	−2.39713e11	+	2.39713e11i	−0.771290	+	0.771290i
$359$	5.12777e11	−	2.96052e11i	1.62931	−	0.940682i	0.645010	−	0.764174i	$-0.276853\pi$
$359$	5.12777e11	−	2.96052e11i	1.62931	−	0.940682i	0.984299	−	0.176507i	$-0.0564800\pi$
$360$	4.59914e11	−	4.89093e11i	1.44316	−	1.53473i
$361$	−2.80576e11	+	4.85971e11i	−0.869496	+	1.50601i
$362$	2.44063e11	+	6.53965e10i	0.746988	+	0.200155i
$363$	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
$367$	−9.95965e10	−	3.71699e11i	−0.286580	−	1.06953i	−0.947677	−	0.319232i	$-0.896575\pi$
$367$	−9.95965e10	−	3.71699e11i	−0.286580	−	1.06953i	0.661096	−	0.750301i	$-0.270091\pi$
$368$	−2.14157e11	−	7.99246e11i	−0.608720	−	2.27177i
$369$	−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
$373$	2.73543e11	+	7.32956e10i	0.731705	+	0.196060i	0.605388	−	0.795930i	$-0.293018\pi$
$373$	2.73543e11	+	7.32956e10i	0.731705	+	0.196060i	0.126316	+	0.991990i	$0.459685\pi$
$374$	−3.11938e11	+	5.40293e11i	−0.824416	+	1.42793i
$375$	−8.18742e9	−	2.21532e10i	−0.0213799	−	0.0578490i
$376$	−1.17766e12	+	6.79925e11i	−3.03862	+	1.75435i
$377$	2.89321e11	−	2.89321e11i	0.737639	−	0.737639i
$378$	7.48320e10	−	4.47855e10i	0.188527	−	0.112830i
$379$		−	1.05524e11i		−	0.262708i	−0.991336	−	0.131354i	$-0.958068\pi$
$379$		−	1.05524e11i		−	0.262708i	0.991336	−	0.131354i	$-0.0419324\pi$
$380$	−6.95443e11	+	1.29489e12i	−1.71094	+	3.18570i
$381$	−1.78673e10	−	1.03157e10i	−0.0434406	−	0.0250804i
$382$	2.54342e11	−	6.81508e10i	0.611130	−	0.163752i
$383$	−1.10186e10	+	4.11220e10i	−0.0261657	+	0.0976517i	−0.977774	−	0.209662i	$-0.932764\pi$
$383$	−1.10186e10	+	4.11220e10i	−0.0261657	+	0.0976517i	0.951608	+	0.307314i	$0.0994302\pi$
$384$	−3.31132e10			−0.0777161
$385$	−3.50442e11	−	5.46691e11i	−0.812910	−	1.26814i
$386$	−6.20967e11			−1.42372
$387$	−8.36778e10	+	3.12290e11i	−0.189632	+	0.707715i
$388$	−6.01197e11	+	1.61090e11i	−1.34671	+	0.360850i
$389$	7.14031e11	+	4.12246e11i	1.58104	+	0.912816i	0.994708	+	0.102747i	$0.0327633\pi$
$389$	7.14031e11	+	4.12246e11i	1.58104	+	0.912816i	0.586335	+	0.810068i	$0.300570\pi$
$390$	−5.50658e10	+	1.65846e10i	−0.120529	+	0.0363006i
$391$		−	4.19545e11i		−	0.907786i
$392$	6.76783e11	−	7.20685e11i	1.44765	−	1.54155i
$393$	−1.55542e10	+	1.55542e10i	−0.0328913	+	0.0328913i
$394$	−4.74382e11	+	2.73885e11i	−0.991734	+	0.572578i
$395$	−2.48639e11	+	7.64496e9i	−0.513905	+	0.0158011i
$396$	−8.02240e11	+	1.38952e12i	−1.63937	+	2.83946i
$397$	1.46593e11	+	3.92796e10i	0.296181	+	0.0793614i	0.403850	−	0.914825i	$-0.367672\pi$
$397$	1.46593e11	+	3.92796e10i	0.296181	+	0.0793614i	−0.107669	+	0.994187i	$0.534339\pi$
$398$	−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	$0.667965\pi$
$402$	−4.05108e9	−	1.51188e10i	−0.00773666	−	0.0288736i
$403$	5.26760e10	+	1.96589e11i	0.0994809	+	0.371268i
$404$	−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
$408$	4.32486e10	+	1.15884e10i	0.0772683	+	0.0207040i
$409$	2.64051e10	−	4.57350e10i	0.0466587	−	0.0808153i	−0.841753	−	0.539863i	$-0.818476\pi$
$409$	2.64051e10	−	4.57350e10i	0.0466587	−	0.0808153i	0.888412	+	0.459048i	$0.151809\pi$
$410$	6.11373e11	+	5.74898e11i	1.06851	+	1.00476i
$411$	2.98825e10	−	1.72527e10i	0.0516569	−	0.0298241i
$412$	−3.35813e11	+	3.35813e11i	−0.574196	+	0.574196i
$413$	−2.91524e11	−	1.62262e11i	−0.493059	−	0.274436i
$414$		−	1.57281e12i		−	2.63132i
$415$	−8.89582e10	−	2.95368e11i	−0.147221	−	0.488818i
$416$	4.36323e11	+	2.51911e11i	0.714312	+	0.412408i
$417$	9.35030e9	−	2.50541e9i	0.0151430	−	0.00405757i
$418$	7.18712e11	−	2.68227e12i	1.15149	−	4.29743i
$419$	1.00043e12			1.58572			0.792858	−	0.609407i	$-0.208592\pi$
$419$	1.00043e12			1.58572			0.792858	+	0.609407i	$0.208592\pi$
$420$	−5.78777e10	+	6.35195e10i	−0.0907590	+	0.0996059i
$421$	1.25128e12			1.94126			0.970632	−	0.240569i	$-0.0773340\pi$
$421$	1.25128e12			1.94126			0.970632	+	0.240569i	$0.0773340\pi$
$422$	−1.04707e11	+	3.90773e11i	−0.160720	+	0.599816i
$423$	−1.05127e12	+	2.81686e11i	−1.59654	+	0.427793i
$424$	5.57215e10	+	3.21708e10i	0.0837291	+	0.0483410i
$425$	−2.73231e11	+	3.09074e11i	−0.406237	+	0.459528i
$426$			4.01515e10i			0.0590689i
$427$	−7.99514e10	−	1.33591e11i	−0.116386	−	0.194469i
$428$	−9.08292e11	+	9.08292e11i	−1.30836	+	1.30836i
$429$	6.45507e10	−	3.72683e10i	0.0920117	−	0.0531230i
$430$	−2.85976e10	−	9.30088e11i	−0.0403387	−	1.31195i
$431$	−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	$0.181723\pi$
$432$	1.36794e11	+	3.66538e10i	0.188968	+	0.0506339i
$433$	−1.32923e11	−	1.32923e11i	−0.181721	−	0.181721i	0.610384	−	0.792105i	$-0.291015\pi$
$433$	−1.32923e11	−	1.32923e11i	−0.181721	−	0.181721i	−0.792105	+	0.610384i	$0.791015\pi$
$434$	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
$437$	4.83320e11	+	1.80378e12i	0.633970	+	2.36601i
$438$	−2.16660e9	−	8.08585e9i	−0.00281284	−	0.0104976i
$439$	1.54008e11	+	2.66750e11i	0.197903	+	0.342779i	0.947848	−	0.318721i	$-0.103253\pi$
$439$	1.54008e11	+	2.66750e11i	0.197903	+	0.342779i	−0.749945	+	0.661500i	$0.769920\pi$
$440$	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
$443$	8.31256e11	+	2.22734e11i	1.02546	+	0.274771i	0.732075	−	0.681224i	$-0.238552\pi$
$443$	8.31256e11	+	2.22734e11i	1.02546	+	0.274771i	0.293383	+	0.955995i	$0.405219\pi$
$444$	−7.18426e10	+	1.24435e11i	−0.0877322	+	0.151957i
$445$	1.16874e10	+	3.80113e11i	0.0141286	+	0.459508i
$446$	−1.36678e12	+	7.89111e11i	−1.63566	+	0.944346i
$447$	3.62074e10	−	3.62074e10i	0.0428957	−	0.0428957i
$448$	−2.57434e11	+	4.04267e9i	−0.301936	+	0.00474152i
$449$		−	9.98153e11i		−	1.15901i	−0.814967	−	0.579507i	$-0.803245\pi$
$449$		−	9.98153e11i		−	1.15901i	0.814967	−	0.579507i	$-0.196755\pi$
$450$	−1.02430e12	+	1.15867e12i	−1.17753	+	1.33199i
$451$	−9.41973e11	−	5.43848e11i	−1.07212	−	0.618989i
$452$	−5.62886e11	+	1.50825e11i	−0.634304	+	0.169961i
$453$	1.57586e10	−	5.88118e10i	0.0175823	−	0.0656180i
$454$	−3.07382e12			−3.39568
$455$	−9.96278e11	+	3.17202e11i	−1.08976	+	0.346965i
$456$	−1.99291e11			−0.215847
$457$	−1.76276e11	+	6.57872e11i	−0.189047	+	0.705535i	0.804680	+	0.593708i	$0.202337\pi$
$457$	−1.76276e11	+	6.57872e11i	−0.189047	+	0.705535i	−0.993728	+	0.111826i	$0.964330\pi$
$458$	1.96625e12	−	5.26856e11i	2.08807	−	0.559497i
$459$	6.21864e10	+	3.59033e10i	0.0653940	+	0.0377553i
$460$	8.95568e11	+	2.97355e12i	0.932585	+	3.09646i
$461$			1.79010e12i			1.84596i	0.384846	+	0.922981i	$0.374255\pi$
$461$			1.79010e12i			1.84596i	−0.384846	+	0.922981i	$0.625745\pi$
$462$	7.89582e10	−	1.41858e11i	0.0806321	−	0.144865i
$463$	−5.36805e11	+	5.36805e11i	−0.542877	+	0.542877i	−0.924371	−	0.381494i	$-0.875410\pi$
$463$	−5.36805e11	+	5.36805e11i	−0.542877	+	0.542877i	0.381494	+	0.924371i	$0.375410\pi$
$464$	1.25334e12	−	7.23616e11i	1.25527	−	0.724732i
$465$	−1.52235e10	−	1.43153e10i	−0.0151000	−	0.0141991i
$466$	1.25966e12	−	2.18179e12i	1.23742	−	2.14327i
$467$	8.63172e11	+	2.31286e11i	0.839791	+	0.225021i	0.652981	−	0.757375i	$-0.273518\pi$
$467$	8.63172e11	+	2.31286e11i	0.839791	+	0.225021i	0.186811	+	0.982396i	$0.440185\pi$
$468$	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
$472$	−3.33035e11	−	1.24291e12i	−0.308853	−	1.15265i
$473$	3.12147e11	+	1.16495e12i	0.286737	+	1.07012i
$474$	−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
$478$	1.24180e12	+	3.32739e11i	1.08799	+	0.291527i
$479$	−8.34044e11	+	1.44461e12i	−0.723901	+	1.25383i	0.235523	+	0.971869i	$0.424320\pi$
$479$	−8.34044e11	+	1.44461e12i	−0.723901	+	1.25383i	−0.959425	+	0.281965i	$0.909014\pi$
$480$	−5.17058e10	+	1.58981e9i	−0.0444584	+	0.00136697i
$481$	−1.51401e12	+	8.74112e11i	−1.28966	+	0.744585i
$482$	6.55108e11	−	6.55108e11i	0.552842	−	0.552842i
$483$	1.71430e9	+	1.09165e11i	0.00143326	+	0.0912686i
$484$			3.34744e12i			2.77273i
$485$	7.44511e11	−	2.24230e11i	0.610989	−	0.184016i
$486$	3.49912e11	+	2.02022e11i	0.284509	+	0.164261i
$487$	2.68847e11	−	7.20374e10i	0.216584	−	0.0580334i	−0.148896	−	0.988853i	$-0.547572\pi$
$487$	2.68847e11	−	7.20374e10i	0.216584	−	0.0580334i	0.365479	+	0.930820i	$0.380905\pi$
$488$	1.55406e11	−	5.79984e11i	0.124045	−	0.462942i
$489$	−9.79176e10			−0.0774410
$490$	−1.50723e12	+	1.70724e12i	−1.18113	+	1.33787i
$491$	−1.73175e12			−1.34468			−0.672339	−	0.740244i	$-0.734710\pi$
$491$	−1.73175e12			−1.34468			−0.672339	+	0.740244i	$0.734710\pi$
$492$	−3.72541e10	+	1.39034e11i	−0.0286637	+	0.106974i
$493$	7.08801e11	−	1.89923e11i	0.540397	−	0.144799i
$494$	−3.87209e12	−	2.23555e12i	−2.92532	−	1.68894i
$495$	9.48384e11	−	1.76585e12i	0.710004	−	1.32200i
$496$			7.19879e11i			0.534062i
$497$	1.14621e10	+	7.29894e11i	0.00842672	+	0.536606i
$498$	5.45340e10	−	5.45340e10i	0.0397316	−	0.0397316i
$499$	5.23630e11	−	3.02318e11i	0.378070	−	0.218279i	−0.298908	−	0.954282i	$-0.596622\pi$
$499$	5.23630e11	−	3.02318e11i	0.378070	−	0.218279i	0.676978	+	0.736003i	$0.263289\pi$
$500$	1.27679e12	−	2.77382e12i	0.913596	−	1.98479i
$501$	−1.56144e10	+	2.70449e10i	−0.0110727	+	0.0191785i
$502$	2.60532e11	+	6.98094e10i	0.183103	+	0.0490622i
$503$	−8.52175e11	−	8.52175e11i	−0.593572	−	0.593572i	0.345023	−	0.938594i	$-0.387871\pi$
$503$	−8.52175e11	−	8.52175e11i	−0.593572	−	0.593572i	−0.938594	+	0.345023i	$0.887871\pi$
$504$	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
$507$	−7.31332e9	−	2.72937e10i	−0.00491562	−	0.0183454i
$508$	−6.90387e11	−	2.57656e12i	−0.459945	−	1.71654i
$509$	2.85483e11	+	4.94471e11i	0.188517	+	0.326521i	0.944756	−	0.327774i	$-0.106299\pi$
$509$	2.85483e11	+	4.94471e11i	0.188517	+	0.326521i	−0.756239	+	0.654296i	$0.772965\pi$
$510$	−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
$513$	−3.08723e11	−	8.27220e10i	−0.196807	−	0.0527343i
$514$	−1.61986e12	+	2.80568e12i	−1.02363	+	1.77298i
$515$	4.06427e11	−	4.32213e11i	0.254595	−	0.270748i
$516$	1.38218e11	−	7.98002e10i	0.0858303	−	0.0495542i
$517$	−2.87080e12	+	2.87080e12i	−1.76724	+	1.76724i
$518$	−1.85193e12	+	3.32721e12i	−1.13016	+	2.03047i
$519$		−	1.32888e11i		−	0.0803955i
$520$	−3.55248e12	−	1.90793e12i	−2.13067	−	1.14432i
$521$	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	$0.459638\pi$
$522$	2.65718e12	−	7.11989e11i	1.56640	−	0.419716i
$523$	5.20417e11	−	1.94222e12i	0.304154	−	1.13512i	−0.629517	−	0.776987i	$-0.716747\pi$
$523$	5.20417e11	−	1.94222e12i	0.304154	−	1.13512i	0.933671	−	0.358132i	$-0.116586\pi$
$524$	−2.84402e12			−1.64794
$525$	6.98314e10	−	8.15369e10i	0.0401175	−	0.0468422i
$526$	4.90784e12			2.79547
$527$	−9.44708e10	+	3.52570e11i	−0.0533519	+	0.199112i
$528$	2.54658e11	−	6.82353e10i	0.142595	−	0.0382082i
$529$	1.85708e12	+	1.07219e12i	1.03105	+	0.595278i
$530$	−1.30573e11	−	7.01266e10i	−0.0718805	−	0.0386048i
$531$		−	1.02985e12i		−	0.562143i
$532$	−6.68016e12	+	1.04903e11i	−3.61563	+	0.0567789i
$533$	−1.23836e12	+	1.23836e12i	−0.664624	+	0.664624i
$534$	−8.23406e10	+	4.75394e10i	−0.0438206	+	0.0252999i
$535$	1.09928e12	−	1.16903e12i	0.580120	−	0.616926i
$536$	5.48748e11	−	9.50460e11i	0.287165	−	0.497384i
$537$	7.01628e10	+	1.88001e10i	0.0364102	+	0.00975607i
$538$	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	$-0.461485\pi$
$542$	−1.18402e12	−	4.41881e12i	−0.589333	−	2.19942i
$543$	−1.40124e10	−	5.22949e10i	−0.00691692	−	0.0258143i
$544$	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	0.890179	−	0.455611i	$-0.150579\pi$
$547$	9.09916e11	+	9.09916e11i	0.434569	+	0.434569i	−0.455611	+	0.890179i	$0.650579\pi$
$548$	4.30922e12	+	1.15465e12i	2.04120	+	0.546939i
$549$	2.40281e11	−	4.16179e11i	0.112887	−	0.195526i
$550$	−1.14796e12	+	5.65365e12i	−0.534928	+	2.63449i
$551$	−2.82860e12	+	1.63309e12i	−1.30734	+	0.754794i
$552$	−2.97742e11	+	2.97742e11i	−0.136494	+	0.136494i
$553$	−5.80661e11	−	9.70225e11i	−0.264034	−	0.441174i
$554$		−	2.11936e12i		−	0.955895i
$555$	8.49302e10	−	1.58136e11i	0.0379965	−	0.0707479i
$556$	1.08388e12	+	6.25779e11i	0.481000	+	0.277705i
$557$	−6.27117e11	+	1.68036e11i	−0.276058	+	0.0739695i	−0.394192	−	0.919028i	$-0.628975\pi$
$557$	−6.27117e11	+	1.68036e11i	−0.276058	+	0.0739695i	0.118134	+	0.992998i	$0.462309\pi$
$558$	−3.54156e11	+	1.32173e12i	−0.154647	+	0.577149i
$559$	1.94186e12			0.841135
$560$	−3.69421e12	+	1.71683e11i	−1.58736	+	0.0737701i
$561$	1.33677e11			0.0569800
$562$	6.62205e11	−	2.47138e12i	0.280014	−	1.04503i
$563$	−3.97167e12	+	1.06421e12i	−1.66604	+	0.446414i	−0.964038	−	0.265763i	$-0.914376\pi$
$563$	−3.97167e12	+	1.06421e12i	−1.66604	+	0.446414i	−0.702000	+	0.712177i	$0.747710\pi$
$564$	4.65285e11	+	2.68633e11i	0.193626	+	0.111790i
$565$	6.97068e11	−	2.09941e11i	0.287778	−	0.0866722i
$566$			7.39073e12i			3.02701i
$567$	2.12590e12	+	1.18328e12i	0.863812	+	0.480798i
$568$	−1.99074e12	+	1.99074e12i	−0.802506	+	0.802506i
$569$	3.08914e12	−	1.78351e12i	1.23547	−	0.713299i	0.267304	−	0.963612i	$-0.413867\pi$
$569$	3.08914e12	−	1.78351e12i	1.23547	−	0.713299i	0.968165	+	0.250314i	$0.0805337\pi$
$570$	4.58856e11	−	1.41085e10i	0.182071	−	0.00559816i
$571$	−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	$0.215373\pi$
$572$	9.30857e12	+	2.49422e12i	3.63581	+	0.974211i
$573$	−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
$577$	4.26993e11	+	1.59356e12i	0.160372	+	0.598518i	0.998585	+	0.0531745i	$0.0169340\pi$
$577$	4.26993e11	+	1.59356e12i	0.160372	+	0.598518i	−0.838213	+	0.545343i	$0.816399\pi$
$578$	−7.73165e11	−	2.88549e12i	−0.288136	−	1.07534i
$579$	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
$583$	1.85551e11	+	4.97182e10i	0.0665203	+	0.0178241i
$584$	2.93481e11	−	5.08324e11i	0.104405	−	0.180835i
$585$	−2.35112e12	−	2.21085e12i	−0.829990	−	0.780473i
$586$	2.86332e12	−	1.65314e12i	1.00307	−	0.579122i
$587$	6.29587e11	−	6.29587e11i	0.218869	−	0.218869i	−0.589153	−	0.808022i	$-0.700538\pi$
$587$	6.29587e11	−	6.29587e11i	0.218869	−	0.218869i	0.808022	+	0.589153i	$0.200538\pi$
$588$	−3.80284e11	−	8.91993e10i	−0.131193	−	0.0307726i
$589$		−	1.62466e12i		−	0.556215i
$590$	8.54783e11	+	2.83814e12i	0.290417	+	0.964271i
$591$	1.01645e11	+	5.86847e10i	0.0342722	+	0.0197870i
$592$	−5.97288e12	+	1.60043e12i	−1.99865	+	0.535536i
$593$	1.61573e10	−	6.03000e10i	0.00536567	−	0.0200249i	−0.963191	−	0.268818i	$-0.913367\pi$
$593$	1.61573e10	−	6.03000e10i	0.00536567	−	0.0200249i	0.968557	+	0.248793i	$0.0800338\pi$
$594$	1.00418e12			0.330957
$595$	−1.83182e12	−	4.00714e11i	−0.599178	−	0.131071i
$596$	6.62035e12			2.14918
$597$	−9.02525e9	+	3.36827e10i	−0.00290787	+	0.0108523i
$598$	−9.12481e12	+	2.44499e12i	−2.91789	+	0.781846i
$599$	−1.08217e12	−	6.24793e11i	−0.343460	−	0.198297i	0.318341	−	0.947976i	$-0.396874\pi$
$599$	−1.08217e12	−	6.24793e11i	−0.343460	−	0.198297i	−0.661801	+	0.749680i	$0.730208\pi$
$600$	4.13248e11	−	2.54365e10i	0.130176	−	0.00801266i
$601$		−	4.60882e12i		−	1.44097i	−0.693471	−	0.720485i	$-0.743919\pi$
$601$		−	4.60882e12i		−	1.44097i	0.693471	−	0.720485i	$-0.256081\pi$
$602$	3.62933e12	−	2.17208e12i	1.12627	−	0.674051i
$603$	6.21106e11	−	6.21106e11i	0.191310	−	0.191310i
$604$	6.81743e12	−	3.93604e12i	2.08427	−	1.20336i
$605$	−1.28518e11	−	4.17984e12i	−0.0390001	−	1.26841i
$606$	−2.13521e11	+	3.69829e11i	−0.0643151	+	0.111397i
$607$	−1.76007e12	−	4.71608e11i	−0.526235	−	0.141004i	−0.0140858	−	0.999901i	$-0.504484\pi$
$607$	−1.76007e12	−	4.71608e11i	−0.526235	−	0.141004i	−0.512149	+	0.858897i	$0.671150\pi$
$608$	−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
$612$	1.19914e12	+	4.47527e12i	0.345533	+	1.28955i
$613$	−5.60200e11	−	2.09070e12i	−0.160240	−	0.598024i	−0.998599	−	0.0529062i	$-0.983152\pi$
$613$	−5.60200e11	−	2.09070e12i	−0.160240	−	0.598024i	0.838359	−	0.545118i	$-0.183515\pi$
$614$	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	0.968221	−	0.250095i	$-0.0804617\pi$
$617$	2.58514e12	+	2.58514e12i	0.718127	+	0.718127i	−0.250095	+	0.968221i	$0.580462\pi$
$618$	1.43276e11	+	3.83908e10i	0.0395117	+	0.0105871i
$619$	3.13270e12	−	5.42599e12i	0.857651	−	1.48550i	−0.0165122	−	0.999864i	$-0.505256\pi$
$619$	3.13270e12	−	5.42599e12i	0.857651	−	1.48550i	0.874163	−	0.485632i	$-0.161410\pi$
$620$	−8.30335e10	−	2.70052e12i	−0.0225679	−	0.733981i
$621$	−5.84819e11	+	3.37645e11i	−0.157801	+	0.0911063i
$622$	4.05654e12	−	4.05654e12i	1.08667	−	1.08667i
$623$	−1.48326e12	+	8.87699e11i	−0.394475	+	0.236086i
$624$		−	4.24491e11i		−	0.112083i
$625$	−1.48779e12	+	3.51260e12i	−0.390016	+	0.920808i
$626$	−2.95247e12	−	1.70461e12i	−0.768425	−	0.443650i
$627$	−5.74724e11	+	1.53997e11i	−0.148510	+	0.0397931i
$628$	1.41588e12	−	5.28414e12i	0.363252	−	1.35568i
$629$	−3.13532e12			−0.798646
$630$	−6.86719e12	−	1.50221e12i	−1.73679	−	0.379925i
$631$	−1.59457e12			−0.400416			−0.200208	−	0.979753i	$-0.564162\pi$
$631$	−1.59457e12			−0.400416			−0.200208	+	0.979753i	$0.564162\pi$
$632$	1.12866e12	−	4.21223e12i	0.281409	−	1.05023i
$633$	8.37300e10	−	2.24354e10i	0.0207283	−	0.00555414i
$634$	7.22354e12	+	4.17051e12i	1.77561	+	1.02515i
$635$	9.60987e11	+	3.19077e12i	0.234550	+	0.778777i
$636$		−	2.54208e10i		−	0.00616073i
$637$	−3.46440e12	−	3.25336e12i	−0.833682	−	0.782897i
$638$	7.25623e12	−	7.25623e12i	1.73388	−	1.73388i
$639$	−1.95137e12	+	1.12662e12i	−0.463004	+	0.267316i
$640$	3.89632e12	+	3.66387e12i	0.918005	+	0.863237i
$641$	−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	$0.967114\pi$
$642$	3.87527e11	+	1.03838e11i	0.0900315	+	0.0241239i
$643$	−5.83268e12	−	5.83268e12i	−1.34561	−	1.34561i	−0.890368	−	0.455242i	$-0.849553\pi$
$643$	−5.83268e12	−	5.83268e12i	−1.34561	−	1.34561i	−0.455242	−	0.890368i	$-0.650447\pi$
$644$	−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
$647$	−4.21451e11	−	1.57287e12i	−0.0945534	−	0.352878i	0.902398	−	0.430904i	$-0.141805\pi$
$647$	−4.21451e11	−	1.57287e12i	−0.0945534	−	0.352878i	−0.996951	+	0.0780254i	$0.975138\pi$
$648$	2.42862e12	+	9.06373e12i	0.541093	+	2.01939i
$649$	−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
$653$	−6.35366e11	−	1.70246e11i	−0.136746	−	0.0366410i	0.189797	−	0.981823i	$-0.439217\pi$
$653$	−6.35366e11	−	1.70246e11i	−0.136746	−	0.0366410i	−0.326543	+	0.945182i	$0.605884\pi$
$654$	−5.50663e10	+	9.53776e10i	−0.0117703	+	0.0203867i
$655$	3.55123e12	−	1.09191e11i	0.753865	−	0.0231792i
$656$	−5.36460e12	+	3.09725e12i	−1.13102	+	0.652994i
$657$	3.32179e11	−	3.32179e11i	0.0695550	−	0.0695550i
$658$	1.24411e13	+	6.92469e12i	2.58726	+	1.44007i
$659$			7.89734e12i			1.63116i	0.578645	+	0.815580i	$0.303582\pi$
$659$			7.89734e12i			1.63116i	−0.578645	+	0.815580i	$0.696418\pi$
$660$	−9.47441e11	+	2.85348e11i	−0.194359	+	0.0585366i
$661$	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	$0.487036\pi$
$662$	−1.17942e13	+	3.16025e12i	−2.38675	+	0.639529i
$663$	5.57067e10	−	2.07900e11i	0.0111969	−	0.0417873i
$664$	5.40768e12			1.07958
$665$	8.33728e12	−	3.87462e11i	1.65321	−	0.0768301i
$666$	−1.17538e13			−2.31497
$667$	−1.78609e12	+	6.66577e12i	−0.349411	+	1.30402i
$668$	−3.90002e12	+	1.04501e12i	−0.757832	+	0.203060i
$669$	2.92857e11	+	1.69081e11i	0.0565247	+	0.0326345i
$670$	−1.19617e12	+	2.22722e12i	−0.229328	+	0.426999i
$671$		−	1.79267e12i		−	0.341388i
$672$	−1.20751e11	−	2.01763e11i	−0.0228418	−	0.0381663i
$673$	−5.79849e12	+	5.79849e12i	−1.08955	+	1.08955i	−0.0939762	+	0.995574i	$0.529958\pi$
$673$	−5.79849e12	+	5.79849e12i	−1.08955	+	1.08955i	−0.995574	+	0.0939762i	$0.970042\pi$
$674$	−7.64537e12	+	4.41406e12i	−1.42702	+	0.823889i
$675$	6.50722e11	+	1.32128e11i	0.120650	+	0.0244978i
$676$	1.82666e12	−	3.16386e12i	0.336432	−	0.582717i
$677$	1.53636e12	+	4.11666e11i	0.281089	+	0.0753176i	0.396609	−	0.917988i	$-0.370187\pi$
$677$	1.53636e12	+	4.11666e11i	0.281089	+	0.0753176i	−0.115520	+	0.993305i	$0.536853\pi$
$678$	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
$682$	1.32112e12	+	4.93050e12i	0.233837	+	0.872693i
$683$	1.77105e11	+	6.60965e11i	0.0311414	+	0.116221i	0.979747	−	0.200240i	$-0.0641721\pi$
$683$	1.77105e11	+	6.60965e11i	0.0311414	+	0.116221i	−0.948606	+	0.316461i	$0.897505\pi$
$684$	−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
$688$	6.63446e12	+	1.77770e12i	1.12891	+	0.302489i
$689$	1.54648e11	−	2.67858e11i	0.0261432	−	0.0452813i
$690$	6.64453e11	−	7.06610e11i	0.111595	−	0.118675i
$691$	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
$693$	9.10981e12	−	1.43058e11i	1.50041	−	0.0235620i
$694$		−	2.52796e12i		−	0.413669i
$695$	−1.37743e12	−	7.39777e11i	−0.223944	−	0.120273i
$696$	−6.37803e11	−	3.68236e11i	−0.103026	−	0.0594819i
$697$	−3.03384e12	+	8.12915e11i	−0.486906	+	0.130466i
$698$	−5.40657e12	+	2.01776e13i	−0.862130	+	3.21751i
$699$	−5.39808e11			−0.0855248
$700$	1.38385e13	−	1.07015e12i	2.17845	−	0.168462i
$701$	−7.79044e12			−1.21851			−0.609257	−	0.792973i	$-0.708532\pi$
$701$	−7.79044e12			−1.21851			−0.609257	+	0.792973i	$0.708532\pi$
$702$	4.18468e11	−	1.56174e12i	0.0650347	−	0.242713i
$703$	1.34799e13	−	3.61193e12i	2.08155	−	0.557750i
$704$	−2.56740e12	−	1.48229e12i	−0.393928	−	0.227435i
$705$	−5.91301e11	−	3.17569e11i	−0.0901483	−	0.0484158i
$706$			1.28248e12i			0.194281i
$707$	−3.77591e12	+	6.78387e12i	−0.568373	+	1.02115i
$708$	−3.59482e11	+	3.59482e11i	−0.0537684	+	0.0537684i
$709$	−1.81400e12	+	1.04731e12i	−0.269605	+	0.155657i	−0.628708	−	0.777641i	$-0.716416\pi$
$709$	−1.81400e12	+	1.04731e12i	−0.269605	+	0.155657i	0.359103	+	0.933298i	$0.383083\pi$
$710$	4.44263e12	−	4.72450e12i	0.656112	−	0.697739i
$711$	1.74508e12	−	3.02257e12i	0.256096	−	0.443571i
$712$	−6.43955e12	−	1.72547e12i	−0.939065	−	0.251622i
$713$	−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
$717$	−7.12953e10	−	2.66078e11i	−0.0100745	−	0.0375986i
$718$	−6.18843e12	−	2.30955e13i	−0.869002	−	3.24316i
$719$	2.32097e12	+	4.02003e12i	0.323883	+	0.560983i	0.981286	−	0.192557i	$-0.0616781\pi$
$719$	2.32097e12	+	4.02003e12i	0.323883	+	0.560983i	−0.657402	+	0.753540i	$0.728345\pi$
$720$	−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
$723$	−1.91747e11	−	5.13784e10i	−0.0260979	−	0.00699292i
$724$	3.49989e12	−	6.06199e12i	0.473403	−	0.819958i
$725$	5.65690e12	−	3.74739e12i	0.760428	−	0.503741i
$726$	9.05442e11	−	5.22757e11i	0.120961	−	0.0698369i
$727$	2.54474e12	−	2.54474e12i	0.337862	−	0.337862i	−0.517700	−	0.855562i	$-0.673212\pi$
$727$	2.54474e12	−	2.54474e12i	0.337862	−	0.337862i	0.855562	+	0.517700i	$0.173212\pi$
$728$	−2.87800e11	−	1.83268e13i	−0.0379751	−	2.41822i
$729$			7.45212e12i			0.977251i
$730$	−6.39736e11	+	1.19116e12i	−0.0833773	+	0.155245i
$731$	3.01602e12	+	1.74130e12i	0.390667	+	0.225552i
$732$	−2.29147e11	+	6.13997e10i	−0.0294994	+	0.00790435i
$733$	−2.46983e12	+	9.21754e12i	−0.316009	+	1.17936i	0.607037	+	0.794674i	$0.292358\pi$
$733$	−2.46983e12	+	9.21754e12i	−0.316009	+	1.17936i	−0.923046	+	0.384689i	$0.874309\pi$
$734$	−1.55394e13			−1.97607
$735$	4.78274e11	+	9.67801e10i	0.0604482	+	0.0122319i
$736$	−8.49745e12			−1.06743
$737$	8.48059e11	−	3.16500e12i	0.105882	−	0.395157i
$738$	−1.13734e13	+	3.04748e12i	−1.41135	+	0.378171i
$739$	−9.24985e12	−	5.34040e12i	−1.14087	−	0.658679i	−0.194221	−	0.980958i	$-0.562218\pi$
$739$	−9.24985e12	−	5.34040e12i	−1.14087	−	0.658679i	−0.946645	+	0.322278i	$0.895551\pi$
$740$	2.22218e13	−	6.69271e12i	2.72419	−	0.820464i
$741$			9.58013e11i			0.116732i
$742$	−1.05782e10	−	6.73609e11i	−0.00128113	−	0.0815812i
$743$	7.33647e11	−	7.33647e11i	0.0883156	−	0.0883156i	−0.661569	−	0.749884i	$-0.730109\pi$
$743$	7.33647e11	−	7.33647e11i	0.0883156	−	0.0883156i	0.749884	+	0.661569i	$0.230109\pi$
$744$	3.17255e11	−	1.83167e11i	0.0379603	−	0.0219164i
$745$	−8.26663e12	+	2.54176e11i	−0.983162	+	0.0302295i
$746$	5.71793e12	−	9.90374e12i	0.675949	−	1.17078i
$747$	4.18054e12	+	1.12017e12i	0.491236	+	0.131626i
$748$	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	$0.710066\pi$
$752$	5.98429e12	+	2.23337e13i	0.682390	+	2.54671i
$753$	−1.49579e10	−	5.58237e10i	−0.00169548	−	0.00632763i
$754$	−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	0.220251	−	0.975443i	$-0.429312\pi$
$757$	−6.82321e12	−	6.82321e12i	−0.755192	−	0.755192i	−0.975443	+	0.220251i	$0.929312\pi$
$758$	−4.11604e12	−	1.10289e12i	−0.452865	−	0.121345i
$759$	−6.28567e11	+	1.08871e12i	−0.0687485	+	0.119076i
$760$	2.34500e13	+	2.20509e13i	2.54965	+	2.39754i
$761$	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
$763$	−9.73794e11	+	1.74954e12i	−0.104018	+	0.186880i
$764$		−	7.29459e12i		−	0.774605i
$765$	−1.66915e12	−	5.54209e12i	−0.176206	−	0.585055i
$766$	1.48884e12	+	8.59582e11i	0.156249	+	0.0902106i
$767$	−5.97476e12	+	1.60093e12i	−0.623364	+	0.167030i
$768$	−2.99615e11	+	1.11818e12i	−0.0310769	+	0.115981i
$769$	1.70913e13			1.76241			0.881205	−	0.472734i	$-0.156733\pi$
$769$	1.70913e13			1.76241			0.881205	+	0.472734i	$0.156733\pi$
$770$	−2.49869e13	+	7.95550e12i	−2.56155	+	0.815566i
$771$	6.94167e11			0.0707489
$772$	−4.45237e12	+	1.66165e13i	−0.451142	+	1.68368i
$773$	1.26585e13	−	3.39183e12i	1.27519	−	0.341685i	0.443170	−	0.896437i	$-0.353854\pi$
$773$	1.26585e13	−	3.39183e12i	1.27519	−	0.341685i	0.832016	+	0.554752i	$0.187187\pi$
$774$	1.13066e13	+	6.52786e12i	1.13239	+	0.653787i
$775$	2.07363e11	+	3.36887e12i	0.0206478	+	0.335449i
$776$			1.36307e13i			1.34940i
$777$	8.15807e11	−	1.28112e10i	0.0802958	−	0.00126094i
$778$	2.35428e13	−	2.35428e13i	2.30383	−	2.30383i
$779$	1.21071e13	−	6.99003e12i	1.17793	−	0.680080i
$780$	4.89624e10	+	1.59242e12i	0.00473628	+	0.154039i
$781$	−4.20269e12	+	7.27927e12i	−0.404201	+	0.700097i
$782$	−1.63647e13	−	4.38492e12i	−1.56487	−	0.419306i
$783$	−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
$787$	−2.35525e12	−	8.78992e12i	−0.218852	−	0.816768i	−0.984775	−	0.173835i	$-0.944384\pi$
$787$	−2.35525e12	−	8.78992e12i	−0.218852	−	0.816768i	0.765922	−	0.642933i	$-0.222283\pi$
$788$	3.92753e12	+	1.46578e13i	0.362871	+	1.35425i
$789$	−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
$793$	−2.78804e12	−	7.47053e11i	−0.250363	−	0.0670844i
$794$	3.06427e12	−	5.30747e12i	0.273612	−	0.473910i
$795$	9.75983e8	+	3.17422e10i	8.66543e−5	+	0.00281828i
$796$	−3.90447e12	+	2.25425e12i	−0.344710	+	0.199018i
$797$	1.32697e13	−	1.32697e13i	1.16493	−	1.16493i	0.181547	−	0.983382i	$-0.441890\pi$
$797$	1.32697e13	−	1.32697e13i	1.16493	−	1.16493i	0.983382	−	0.181547i	$-0.0581103\pi$
$798$	1.07159e12	+	1.79052e12i	0.0935441	+	0.156303i
$799$			1.17235e13i			1.01765i
$800$	6.25996e12	+	5.53401e12i	0.540339	+	0.477678i
$801$	−4.62083e12	−	2.66784e12i	−0.396619	−	0.228988i
$802$	2.00539e13	−	5.37341e12i	1.71164	−	0.458633i
$803$	4.53558e11	−	1.69270e12i	0.0384958	−	0.143668i
$804$	−4.33611e11			−0.0365972
$805$	1.18770e13	−	1.30348e13i	0.996842	−	1.09401i
$806$	8.21870e12			0.685954
$807$	2.13846e11	−	7.98085e11i	0.0177489	−	0.0662397i
$808$	−2.89229e13	+	7.74987e12i	−2.38721	+	0.639652i
$809$	−1.81753e12	−	1.04935e12i	−0.149181	−	0.0861295i	0.423552	−	0.905872i	$-0.360783\pi$
$809$	−1.81753e12	−	1.04935e12i	−0.149181	−	0.0861295i	−0.572732	+	0.819742i	$0.694117\pi$
$810$	−6.23340e12	−	2.06968e13i	−0.508795	−	1.68935i
$811$			4.28385e12i			0.347728i	0.984770	+	0.173864i	$0.0556254\pi$
$811$			4.28385e12i			0.347728i	−0.984770	+	0.173864i	$0.944375\pi$
$812$	−2.15727e13	−	1.20074e13i	−1.74142	−	0.969272i
$813$	−6.93111e11	+	6.93111e11i	−0.0556411	+	0.0556411i
$814$	−3.79716e13	+	2.19229e13i	−3.03144	+	1.75020i
$815$	1.15216e13	+	1.08343e13i	0.914755	+	0.860181i
$816$	3.80648e11	−	6.59303e11i	0.0300551	−	0.0520570i
$817$	−1.49730e13	−	4.01200e12i	−1.17573	−	0.315037i
$818$	−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	$0.878341\pi$
$822$	−3.60636e11	−	1.34591e12i	−0.0275515	−	0.102824i
$823$	5.15318e12	+	1.92319e13i	0.391540	+	1.46125i	0.827594	+	0.561327i	$0.189709\pi$
$823$	5.15318e12	+	1.92319e13i	0.391540	+	1.46125i	−0.436054	+	0.899920i	$0.643624\pi$
$824$	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	0.912239	−	0.409658i	$-0.134352\pi$
$827$	6.76053e12	+	6.76053e12i	0.502581	+	0.502581i	−0.409658	+	0.912239i	$0.634352\pi$
$828$	−4.20867e13	−	1.12771e13i	−3.11178	−	0.833798i
$829$	−3.77372e11	+	6.53627e11i	−0.0277507	+	0.0480656i	−0.879567	−	0.475775i	$-0.842168\pi$
$829$	−3.77372e11	+	6.53627e11i	−0.0277507	+	0.0480656i	0.851817	+	0.523840i	$0.175501\pi$
$830$	−1.24508e13	+	3.82829e11i	−0.910642	+	0.0279997i
$831$	−3.93271e11	+	2.27055e11i	−0.0286080	+	0.0165168i
$832$	−3.37524e12	+	3.37524e12i	−0.244202	+	0.244202i
$833$	−2.46342e12	−	8.15957e12i	−0.177270	−	0.587171i
$834$		−	3.90902e11i		−	0.0279783i
$835$	4.82971e12	−	1.45460e12i	0.343821	−	0.103551i
$836$	−6.66216e13	−	3.84640e13i	−4.71723	−	2.72349i
$837$	5.67489e11	−	1.52058e11i	0.0399662	−	0.0107089i
$838$	1.04561e13	−	3.90228e13i	0.732442	−	2.73351i
$839$	−2.14353e13			−1.49348			−0.746742	−	0.665114i	$-0.768383\pi$
$839$	−2.14353e13			−1.49348			−0.746742	+	0.665114i	$0.768383\pi$
$840$	1.01562e12	+	1.58438e12i	0.0703843	+	0.109800i
$841$	2.43713e12			0.167995
$842$	1.30779e13	−	4.88073e13i	0.896670	−	3.34642i
$843$	−5.29538e11	+	1.41889e11i	−0.0361138	+	0.00967666i
$844$	9.70593e12	+	5.60372e12i	0.658410	+	0.380133i
$845$	−2.15942e12	+	4.02075e12i	−0.145708	+	0.271301i
$846$			4.39496e13i			2.94977i
$847$	1.63103e13	−	9.76140e12i	1.08890	−	0.651684i
$848$	7.73575e11	−	7.73575e11i	0.0513714	−	0.0513714i
$849$	1.37143e12	−	7.91798e11i	0.0905921	−	0.0523034i
$850$	9.19999e12	+	1.38879e13i	0.604508	+	0.912542i
$851$	1.47428e13	−	2.55352e13i	0.963597	−	1.66900i
$852$	1.07441e12	+	2.87888e11i	0.0698544	+	0.0187174i
$853$	−7.77297e12	−	7.77297e12i	−0.502708	−	0.502708i	0.409570	−	0.912279i	$-0.365679\pi$
$853$	−7.77297e12	−	7.77297e12i	−0.502708	−	0.502708i	−0.912279	+	0.409570i	$0.865679\pi$
$854$	−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
$857$	−3.83724e12	−	1.43208e13i	−0.243000	−	0.906887i	−0.974378	−	0.224915i	$-0.927790\pi$
$857$	−3.83724e12	−	1.43208e13i	−0.243000	−	0.906887i	0.731379	−	0.681971i	$-0.238877\pi$
$858$	−7.79028e11	−	2.90737e12i	−0.0490750	−	0.183150i
$859$	8.45434e12	+	1.46433e13i	0.529798	+	0.917637i	0.999396	+	0.0347567i	$0.0110656\pi$
$859$	8.45434e12	+	1.46433e13i	0.529798	+	0.917637i	−0.469598	+	0.882880i	$0.655601\pi$
$860$	−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
$863$	2.27711e13	+	6.10149e12i	1.39744	+	0.374444i	0.877426	−	0.479711i	$-0.159259\pi$
$863$	2.27711e13	+	6.10149e12i	1.39744	+	0.374444i	0.520018	+	0.854155i	$0.325925\pi$
$864$	7.27184e11	−	1.25952e12i	0.0443948	−	0.0768941i
$865$	−1.47036e13	+	1.56365e13i	−0.892998	+	0.949655i
$866$	−6.57404e12	+	3.79553e12i	−0.397193	+	0.229320i
$867$	−4.52604e11	+	4.52604e11i	−0.0272040	+	0.0272040i
$868$	1.05378e13	−	6.30667e12i	0.630103	−	0.377104i
$869$		−	1.30195e13i		−	0.774473i
$870$	1.49457e12	+	8.02688e11i	0.0884464	+	0.0475018i
$871$	−4.56895e12	−	2.63788e12i	−0.268989	−	0.155301i
$872$	−7.45913e12	+	1.99867e12i	−0.436882	+	0.117062i
$873$	−2.82353e12	+	1.05376e13i	−0.164524	+	0.614011i
$874$	7.54094e13			4.37144
$875$	−1.72386e13	+	1.86756e12i	−0.994183	+	0.107706i
$876$	−2.31904e11			−0.0133057
$877$	2.62541e12	−	9.79815e12i	0.149864	−	0.559301i	−0.849626	−	0.527385i	$-0.823172\pi$
$877$	2.62541e12	−	9.79815e12i	0.149864	−	0.559301i	0.999491	−	0.0319160i	$-0.0101609\pi$
$878$	1.20145e13	−	3.21926e12i	0.682306	−	0.182823i
$879$	−6.13517e11	−	3.54214e11i	−0.0346638	−	0.0200132i
$880$	−3.75147e13	−	2.01480e13i	−2.10877	−	1.13256i
$881$		−	2.13671e12i		−	0.119496i	−0.998213	−	0.0597481i	$-0.980970\pi$
$881$		−	2.13671e12i		−	0.119496i	0.998213	−	0.0597481i	$-0.0190298\pi$
$882$	−9.23496e12	−	3.05889e13i	−0.513838	−	1.70198i
$883$	−1.02436e13	+	1.02436e13i	−0.567062	+	0.567062i	−0.931304	−	0.364242i	$-0.881328\pi$
$883$	−1.02436e13	+	1.02436e13i	−0.567062	+	0.567062i	0.364242	+	0.931304i	$0.381328\pi$
$884$	2.40996e13	−	1.39139e13i	1.32732	−	0.766328i
$885$	4.35072e11	−	4.62675e11i	0.0238406	−	0.0253531i
$886$	1.73759e13	−	3.00960e13i	0.947318	−	1.64080i
$887$	−1.71491e13	−	4.59508e12i	−0.930217	−	0.249251i	−0.238270	−	0.971199i	$-0.576580\pi$
$887$	−1.71491e13	−	4.59508e12i	−0.930217	−	0.249251i	−0.691947	+	0.721948i	$0.743247\pi$
$888$	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
$892$	1.13159e13	+	4.22316e13i	0.598478	+	2.23355i
$893$	−1.35056e13	−	5.04037e13i	−0.710696	−	2.65235i
$894$	−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
$898$	−3.89339e13	−	1.04323e13i	−1.99795	−	0.535349i
$899$	3.00192e12	−	5.19948e12i	0.153278	−	0.265486i
$900$	2.36605e13	+	3.57169e13i	1.20208	+	1.81461i
$901$	4.80386e11	−	2.77351e11i	0.0242845	−	0.0140206i
$902$	−3.10584e13	+	3.10584e13i	−1.56225	+	1.56225i
$903$	−7.91880e11	−	4.40760e11i	−0.0396337	−	0.0220601i
$904$			1.27621e13i			0.635572i
$905$	−4.13747e12	+	7.70379e12i	−0.205029	+	0.381756i
$906$	−2.12931e12	−	1.22936e12i	−0.104993	−	0.0606179i
$907$	−2.20268e13	+	5.90207e12i	−1.08074	+	0.289582i	−0.754897	−	0.655843i	$-0.772313\pi$
$907$	−2.20268e13	+	5.90207e12i	−1.08074	+	0.289582i	−0.325838	+	0.945425i	$0.605647\pi$
$908$	−2.20394e13	+	8.22522e13i	−1.07600	+	4.01570i
$909$	−2.39649e13			−1.16423
$910$	1.96006e12	+	4.21760e13i	0.0947510	+	2.03882i
$911$	−1.69330e13			−0.814521			−0.407260	−	0.913312i	$-0.633516\pi$
$911$	−1.69330e13			−0.814521			−0.407260	+	0.913312i	$0.633516\pi$
$912$	−8.77022e11	+	3.27309e12i	−0.0419792	+	0.156668i
$913$	1.55949e13	−	4.17863e12i	0.742785	−	0.199029i
$914$	2.38185e13	+	1.37516e13i	1.12890	+	0.651773i
$915$	2.83771e11	−	8.54655e10i	0.0133836	−	0.00403084i
$916$		−	5.63926e13i		−	2.64662i
$917$	8.29339e12	+	1.38574e13i	0.387320	+	0.647173i
$918$	2.05039e12	−	2.05039e12i	0.0952893	−	0.0952893i
$919$	−3.17278e13	+	1.83181e13i	−1.46731	+	0.847150i	−0.999330	−	0.0365918i	$-0.988350\pi$
$919$	−3.17278e13	+	1.83181e13i	−1.46731	+	0.847150i	−0.467976	+	0.883741i	$0.655017\pi$
$920$	6.79784e13	−	2.09015e12i	3.12842	−	0.0961903i
$921$	6.90487e11	−	1.19596e12i	0.0316218	−	0.0547706i
$922$	6.98244e13	+	1.87094e13i	3.18213	+	0.852650i
$923$	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
$927$	2.15443e12	+	8.04045e12i	0.0958239	+	0.357620i
$928$	−3.84668e12	−	1.43560e13i	−0.170263	−	0.635430i
$929$	1.69569e13	+	2.93703e13i	0.746925	+	1.29371i	0.949290	+	0.314402i	$0.101804\pi$
$929$	1.69569e13	+	2.93703e13i	0.746925	+	1.29371i	−0.202365	+	0.979310i	$0.564863\pi$
$930$	−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
$933$	−1.18733e12	−	3.18144e11i	−0.0512984	−	0.0137454i
$934$	1.80431e13	−	3.12515e13i	0.775799	−	1.34372i
$935$	−1.57293e13	−	1.47909e13i	−0.673064	−	0.632909i
$936$	4.89967e13	−	2.82882e13i	2.08653	−	1.20466i
$937$	7.02099e12	−	7.02099e12i	0.297557	−	0.297557i	−0.542499	−	0.840056i	$-0.682522\pi$
$937$	7.02099e12	−	7.02099e12i	0.297557	−	0.297557i	0.840056	+	0.542499i	$0.182522\pi$
$938$	−1.14900e13	+	1.80435e11i	−0.484625	+	0.00761043i
$939$			7.30487e11i			0.0306632i
$940$	−2.50253e13	−	8.30913e13i	−1.04545	−	3.47121i
$941$	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	$0.558265\pi$
$942$	−1.65041e12	+	4.42226e11i	−0.0682909	+	0.0182985i
$943$	7.64488e12	−	2.85311e13i	0.314824	−	1.17494i
$944$	−2.18786e13			−0.896697
$945$	9.15658e11	+	2.87593e12i	0.0373500	+	0.117310i
$946$	4.87023e13			1.97715
$947$	−1.15819e12	+	4.32244e12i	−0.0467958	+	0.174644i	−0.985369	−	0.170437i	$-0.945482\pi$
$947$	−1.15819e12	+	4.32244e12i	−0.0467958	+	0.174644i	0.938573	+	0.345081i	$0.112149\pi$
$948$	−1.66422e12	+	4.45925e11i	−0.0669225	+	0.0179318i
$949$	−2.44356e12	−	1.41079e12i	−0.0977970	−	0.0564631i
$950$	−5.55531e13	−	4.91108e13i	−2.21285	−	1.95623i
$951$		−	1.78721e12i		−	0.0708539i
$952$	1.59870e13	−	2.87226e13i	0.630812	−	1.13333i
$953$	−3.36282e12	+	3.36282e12i	−0.132064	+	0.132064i	−0.770049	−	0.637985i	$-0.779768\pi$
$953$	−3.36282e12	+	3.36282e12i	−0.132064	+	0.132064i	0.637985	+	0.770049i	$0.279768\pi$
$954$	1.80089e12	−	1.03974e12i	0.0703913	−	0.0406405i
$955$	2.80062e11	+	9.10852e12i	0.0108953	+	0.354350i
$956$	1.78075e13	−	3.08435e13i	0.689514	−	1.19427i
$957$	−2.12386e12	−	5.69088e11i	−0.0818508	−	0.0219319i
$958$	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
$962$	1.82718e13	+	6.81911e13i	0.687848	+	2.56708i
$963$	5.82721e12	+	2.17474e13i	0.218345	+	0.814873i
$964$	−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	0.630855	−	0.775901i	$-0.282704\pi$
$967$	−3.94387e12	−	3.94387e12i	−0.145045	−	0.145045i	−0.775901	+	0.630855i	$0.782704\pi$
$968$	7.08112e13	+	1.89738e13i	2.59217	+	0.694569i
$969$	−8.59066e11	+	1.48795e12i	−0.0313018	+	0.0542163i
$970$	−9.64967e11	−	3.13839e13i	−0.0349977	−	1.13824i
$971$	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
$973$	−1.11591e11	−	7.10601e12i	−0.00399136	−	0.254166i
$974$		−	1.12395e13i		−	0.400160i
$975$	−1.22276e11	−	1.98652e12i	−0.00433331	−	0.0704000i
$976$	−8.84155e12	−	5.10467e12i	−0.311892	−	0.180071i
$977$	2.85366e13	−	7.64637e12i	1.00202	−	0.268491i	0.279730	−	0.960079i	$-0.409755\pi$
$977$	2.85366e13	−	7.64637e12i	1.00202	−	0.268491i	0.722293	+	0.691588i	$0.243088\pi$
$978$	−1.02340e12	+	3.81936e12i	−0.0357700	+	0.133495i
$979$	−1.99039e13			−0.692495
$980$	3.48772e13	+	5.25730e13i	1.20788	+	1.82073i
$981$	−6.18048e12			−0.213065
$982$	−1.80995e13	+	6.75484e13i	−0.621106	+	2.31800i
$983$	−1.68029e13	+	4.50234e12i	−0.573977	+	0.153797i	−0.534120	−	0.845409i	$-0.679357\pi$
$983$	−1.68029e13	+	4.50234e12i	−0.573977	+	0.153797i	−0.0398572	+	0.999205i	$0.512690\pi$
$984$	2.72995e12	+	1.57614e12i	0.0928276	+	0.0535940i
$985$	−5.46694e12	−	1.81519e13i	−0.185047	−	0.614411i
$986$		−	2.96324e13i		−	0.998437i
$987$	−4.79034e10	−	3.05045e12i	−0.00160672	−	0.102314i
$988$	−8.75841e13	+	8.75841e13i	−2.92428	+	2.92428i
$989$	−2.83636e13	+	1.63757e13i	−0.942708	+	0.544273i
$990$	−5.89665e13	−	5.54486e13i	−1.95095	−	1.83456i
$991$	−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	$0.917731\pi$
$992$	7.14093e12	+	1.91341e12i	0.234128	+	0.0627343i
$993$	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
$997$	−1.36297e12	−	5.08668e12i	−0.0436877	−	0.163045i	0.940636	−	0.339418i	$-0.110230\pi$
$997$	−1.36297e12	−	5.08668e12i	−0.0436877	−	0.163045i	−0.984323	+	0.176373i	$0.943563\pi$
$998$	−6.31941e12	−	2.35844e13i	−0.201646	−	0.752553i
$999$	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.17.33	yes	136
5.3	odd	4	inner	35.10.k.a.3.2	✓	136
7.5	odd	6	inner	35.10.k.a.12.2	yes	136
35.33	even	12	inner	35.10.k.a.33.33	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.2	✓	136	5.3	odd	4	inner
35.10.k.a.12.2	yes	136	7.5	odd	6	inner
35.10.k.a.17.33	yes	136	1.1	even	1	trivial
35.10.k.a.33.33	yes	136	35.33	even	12	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+(10.4516 - 39.0059i) q^{2} +(-8.35771 + 2.23944i) q^{3} +(-968.820 - 559.349i) q^{4} +(1231.21 + 661.245i) q^{5} +349.406i q^{6} +(99.7449 + 6351.67i) q^{7} +(-17323.8 + 17323.8i) q^{8} +(-16981.1 + 9804.07i) q^{9} +(38660.6 - 41113.4i) q^{10} +(-36572.6 + 63345.5i) q^{11} +(9349.75 + 2505.26i) q^{12} +(83277.2 + 83277.2i) q^{13} +(248795. + 62494.4i) q^{14} +(-11770.9 - 2769.27i) q^{15} +(208283. + 360757. i) q^{16} +(54666.7 + 204019. i) q^{17} +(204936. + 764833. 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} +(-1.91865e6 - 514101. i) q^{23} +(105992. - 183583. i) q^{24} +(1.07863e6 + 1.62826e6i) q^{25} +(4.11868e6 - 2.37792e6i) q^{26} +(240394. - 240394. i) q^{27} +(3.45616e6 - 6.20941e6i) q^{28} -3.47419e6i q^{29} +(-231043. + 430192. i) q^{30} +(1.49660e6 + 864063. i) q^{31} +(4.13219e6 - 1.10722e6i) q^{32} +(163804. - 611326. i) q^{33} +8.52929e6 q^{34} +(-4.07720e6 + 7.88619e6i) q^{35} +2.19356e7 q^{36} +(-3.84196e6 + 1.43384e7i) q^{37} +(-3.66705e7 + 9.82583e6i) q^{38} +(-882501. - 509512. i) q^{39} +(-3.27846e7 + 9.87398e6i) q^{40} +1.48704e7i q^{41} +(-2.21931e6 + 34851.4i) q^{42} +(1.16590e7 - 1.16590e7i) q^{43} +(7.08645e7 - 4.09136e7i) q^{44} +(-2.73903e7 + 842174. i) q^{45} +(-4.01060e7 + 6.94656e7i) q^{46} +(5.36138e7 + 1.43658e7i) 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} +(-3.40997e7 - 1.27262e8i) q^{52} +(-679719. - 2.53675e6i) 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} +(-1.35514e8 - 3.63109e7i) q^{58} +(-2.62607e7 + 4.54848e7i) q^{59} +(9.85492e6 + 9.26697e6i) q^{60} +(-2.12248e7 + 1.22542e7i) q^{61} +(4.93454e7 - 4.93454e7i) q^{62} +(-6.39659e7 - 1.06881e8i) q^{63} +4.05301e7i q^{64} +(4.74651e7 + 1.57598e8i) q^{65} +(-2.21333e7 - 1.27787e7i) q^{66} +(-4.32701e7 + 1.15942e7i) q^{67} +(6.11554e7 - 2.28235e8i) q^{68} +1.71868e7 q^{69} +(2.64995e8 + 2.41458e8i) q^{70} +1.14914e8 q^{71} +(1.24334e8 - 4.64022e8i) q^{72} +(-2.31417e7 + 6.20080e6i) q^{73} +(5.19127e8 + 2.99718e8i) q^{74} +(-1.26613e7 - 1.11930e7i) q^{75} +1.05172e9i q^{76} +(-4.05998e8 - 2.25978e8i) q^{77} +(-2.90975e7 + 2.90975e7i) q^{78} +(-1.54149e8 + 8.89979e7i) q^{79} +(1.78916e7 + 5.81894e8i) q^{80} +(1.91503e8 - 3.31692e8i) q^{81} +(5.80033e8 + 1.55419e8i) 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} +(7.78025e6 + 2.90363e7i) q^{87} +(-4.63810e8 - 1.73096e9i) 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} +(-1.44432e7 - 3.87004e6i) q^{93} +(1.12070e9 - 1.94111e9i) q^{94} +(-4.03787e7 - 1.31325e9i) q^{95} +(-3.20561e7 + 1.85076e7i) q^{96} +(3.93410e8 - 3.93410e8i) q^{97} +(-3.72128e8 + 1.58650e9i) 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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