LMFDB - Embedded newform 35.10.k.a.3.8

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			3.8
Character	$\chi$	$=$	35.3
Dual form			35.10.k.a.12.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-26.6836 - 7.14985i) q^{2} +(-65.2186 - 243.399i) q^{3} +(217.489 + 125.567i) q^{4} +(1313.38 - 477.656i) q^{5} +6961.07i q^{6} +(-2565.03 - 5811.56i) q^{7} +(5095.68 + 5095.68i) q^{8} +(-37943.7 + 21906.8i) q^{9} +(-38460.9 + 3355.11i) q^{10} +(-32759.3 + 56740.8i) q^{11} +(16378.6 - 61125.9i) q^{12} +(8546.45 - 8546.45i) q^{13} +(26892.3 + 173413. i) q^{14} +(-201918. - 288524. i) q^{15} +(-163828. - 283759. i) q^{16} +(-108837. + 29162.7i) q^{17} +(1.16910e6 - 313260. i) q^{18} +(456807. + 791214. i) q^{19} +(345624. + 61032.8i) q^{20} +(-1.24724e6 + 1.00335e6i) q^{21} +(1.27983e6 - 1.27983e6i) q^{22} +(-348891. + 1.30208e6i) q^{23} +(907950. - 1.57262e6i) q^{24} +(1.49681e6 - 1.25469e6i) q^{25} +(-289156. + 166944. i) q^{26} +(4.29960e6 + 4.29960e6i) q^{27} +(171877. - 1.58603e6i) q^{28} +507962. i q^{29} +(3.32499e6 + 9.14253e6i) q^{30} +(-4.07425e6 - 2.35227e6i) q^{31} +(1.38774e6 + 5.17911e6i) q^{32} +(1.59472e7 + 4.27304e6i) q^{33} +3.11267e6 q^{34} +(-6.14478e6 - 6.40760e6i) q^{35} -1.10031e7 q^{36} +(111026. + 29749.2i) q^{37} +(-6.53221e6 - 2.43785e7i) q^{38} +(-2.63758e6 - 1.52281e6i) q^{39} +(9.12655e6 + 4.25859e6i) q^{40} -2.01255e7i q^{41} +(4.04547e7 - 1.78553e7i) q^{42} +(-1.84133e7 - 1.84133e7i) q^{43} +(-1.42496e7 + 8.22701e6i) q^{44} +(-3.93706e7 + 4.68960e7i) q^{45} +(1.86193e7 - 3.22497e7i) q^{46} +(-8.72742e6 + 3.25712e7i) q^{47} +(-5.83820e7 + 5.83820e7i) q^{48} +(-2.71949e7 + 2.98136e7i) q^{49} +(-4.89112e7 + 2.27776e7i) q^{50} +(1.41964e7 + 2.45888e7i) q^{51} +(2.93191e6 - 785604. i) q^{52} +(3.88889e7 - 1.04202e7i) q^{53} +(-8.39872e7 - 1.45470e8i) q^{54} +(-1.59229e7 + 9.01700e7i) q^{55} +(1.65433e7 - 4.26844e7i) q^{56} +(1.62788e8 - 1.62788e8i) q^{57} +(3.63185e6 - 1.35543e7i) q^{58} +(8.88903e6 - 1.53962e7i) q^{59} +(-7.68577e6 - 8.81050e7i) q^{60} +(-1.30067e8 + 7.50944e7i) q^{61} +(9.18973e7 + 9.18973e7i) q^{62} +(2.24639e8 + 1.64320e8i) q^{63} +1.96407e7i q^{64} +(7.14248e6 - 1.53070e7i) q^{65} +(-3.94977e8 - 2.28040e8i) q^{66} +(-4.55098e7 - 1.69845e8i) q^{67} +(-2.73327e7 - 7.32378e6i) q^{68} +3.39679e8 q^{69} +(1.18152e8 + 2.14912e8i) q^{70} +1.11742e7 q^{71} +(-3.04979e8 - 8.17188e7i) q^{72} +(1.12759e8 + 4.20822e8i) q^{73} +(-2.74986e6 - 1.58763e6i) q^{74} +(-4.03010e8 - 2.82494e8i) q^{75} +2.29440e8i q^{76} +(4.13781e8 + 4.48412e7i) q^{77} +(5.94924e7 + 5.94924e7i) q^{78} +(-2.56198e7 + 1.47916e7i) q^{79} +(-3.50708e8 - 2.94430e8i) q^{80} +(3.34913e8 - 5.80086e8i) q^{81} +(-1.43895e8 + 5.37022e8i) q^{82} +(-3.31641e7 + 3.31641e7i) q^{83} +(-3.97249e8 + 6.16041e7i) q^{84} +(-1.29014e8 + 9.02884e7i) q^{85} +(3.59681e8 + 6.22985e8i) q^{86} +(1.23638e8 - 3.31286e7i) q^{87} +(-4.56064e8 + 1.22202e8i) q^{88} +(4.64190e8 + 8.04001e8i) q^{89} +(1.38585e9 - 9.69859e8i) q^{90} +(-7.15901e7 - 2.77464e7i) q^{91} +(-2.39379e8 + 2.39379e8i) q^{92} +(-3.06824e8 + 1.14508e9i) q^{93} +(4.65758e8 - 8.06717e8i) q^{94} +(9.77890e8 + 8.20968e8i) q^{95} +(1.17008e9 - 6.75548e8i) q^{96} +(1.86590e8 + 1.86590e8i) q^{97} +(9.38820e8 - 6.01095e8i) q^{98} -2.87061e9i 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 $

$2$	−26.6836	−	7.14985i	−1.17926	−	0.315982i	−0.384627	−	0.923072i	$-0.625670\pi$
$2$	−26.6836	−	7.14985i	−1.17926	−	0.315982i	−0.794633	+	0.607091i	$0.792337\pi$
$3$	−65.2186	−	243.399i	−0.464864	−	1.73490i	−0.657341	−	0.753594i	$-0.728319\pi$
$3$	−65.2186	−	243.399i	−0.464864	−	1.73490i	0.192477	−	0.981302i	$-0.438348\pi$
$4$	217.489	+	125.567i	0.424783	+	0.245249i
$5$	1313.38	−	477.656i	0.939779	−	0.341783i
$5$	1313.38	−	477.656i	0.939779	−	0.341783i
$6$			6961.07i			2.19278i
$7$	−2565.03	−	5811.56i	−0.403785	−	0.914854i
$7$	−2565.03	−	5811.56i	−0.403785	−	0.914854i
$8$	5095.68	+	5095.68i	0.439842	+	0.439842i
$9$	−37943.7	+	21906.8i	−1.92774	+	1.11298i
$10$	−38460.9	+	3355.11i	−1.21624	+	0.106098i
$11$	−32759.3	+	56740.8i	−0.674634	+	1.16850i	0.301942	+	0.953326i	$0.402365\pi$
$11$	−32759.3	+	56740.8i	−0.674634	+	1.16850i	−0.976576	+	0.215174i	$0.930968\pi$
$12$	16378.6	−	61125.9i	0.228014	−	0.850962i
$13$	8546.45	−	8546.45i	0.0829928	−	0.0829928i	−0.664392	−	0.747385i	$-0.731309\pi$
$13$	8546.45	−	8546.45i	0.0829928	−	0.0829928i	0.747385	+	0.664392i	$0.231309\pi$
$14$	26892.3	+	173413.i	0.187091	+	1.20644i
$15$	−201918.	−	288524.i	−1.02983	−	1.47154i
$16$	−163828.	−	283759.i	−0.624955	−	1.08245i
$17$	−108837.	+	29162.7i	−0.316050	+	0.0846853i	−0.413357	−	0.910569i	$-0.635644\pi$
$17$	−108837.	+	29162.7i	−0.316050	+	0.0846853i	0.0973070	+	0.995254i	$0.468977\pi$
$18$	1.16910e6	−	313260.i	2.62498	−	0.703362i
$19$	456807.	+	791214.i	0.804159	+	1.39284i	0.916857	+	0.399215i	$0.130717\pi$
$19$	456807.	+	791214.i	0.804159	+	1.39284i	−0.112699	+	0.993629i	$0.535949\pi$
$20$	345624.	+	61032.8i	0.483024	+	0.0852960i
$21$	−1.24724e6	+	1.00335e6i	−1.39947	+	1.12581i
$22$	1.27983e6	−	1.27983e6i	1.16479	−	1.16479i
$23$	−348891.	+	1.30208e6i	−0.259965	+	0.970203i	0.705296	+	0.708913i	$0.250814\pi$
$23$	−348891.	+	1.30208e6i	−0.259965	+	0.970203i	−0.965261	+	0.261289i	$0.915852\pi$
$24$	907950.	−	1.57262e6i	0.558614	−	0.967547i
$25$	1.49681e6	−	1.25469e6i	0.766369	−	0.642401i
$26$	−289156.	+	166944.i	−0.124094	+	0.0716459i
$27$	4.29960e6	+	4.29960e6i	1.55701	+	1.55701i
$28$	171877.	−	1.58603e6i	0.0528455	−	0.487642i
$29$			507962.i			0.133365i	0.997774	+	0.0666823i	$0.0212414\pi$
$29$			507962.i			0.133365i	−0.997774	+	0.0666823i	$0.978759\pi$
$30$	3.32499e6	+	9.14253e6i	0.749455	+	2.06073i
$31$	−4.07425e6	−	2.35227e6i	−0.792356	−	0.457467i	0.0484354	−	0.998826i	$-0.484577\pi$
$31$	−4.07425e6	−	2.35227e6i	−0.792356	−	0.457467i	−0.840791	+	0.541359i	$0.817910\pi$
$32$	1.38774e6	+	5.17911e6i	0.233955	+	0.873132i
$33$	1.59472e7	+	4.27304e6i	2.34084	+	0.627226i
$34$	3.11267e6			0.399464
$35$	−6.14478e6	−	6.40760e6i	−0.692150	−	0.721753i
$36$	−1.10031e7			−1.09183
$37$	111026.	+	29749.2i	0.00973902	+	0.00260956i	0.263685	−	0.964609i	$-0.415062\pi$
$37$	111026.	+	29749.2i	0.00973902	+	0.00260956i	−0.253946	+	0.967218i	$0.581729\pi$
$38$	−6.53221e6	−	2.43785e7i	−0.508199	−	1.89662i
$39$	−2.63758e6	−	1.52281e6i	−0.182564	−	0.105404i
$40$	9.12655e6	+	4.25859e6i	0.563685	+	0.263024i
$41$		−	2.01255e7i		−	1.11230i	−0.831084	−	0.556148i	$-0.812279\pi$
$41$		−	2.01255e7i		−	1.11230i	0.831084	−	0.556148i	$-0.187721\pi$
$42$	4.04547e7	−	1.78553e7i	2.00607	−	0.885412i
$43$	−1.84133e7	−	1.84133e7i	−0.821341	−	0.821341i	0.164959	−	0.986300i	$-0.447251\pi$
$43$	−1.84133e7	−	1.84133e7i	−0.821341	−	0.821341i	−0.986300	+	0.164959i	$0.947251\pi$
$44$	−1.42496e7	+	8.22701e6i	−0.573146	+	0.330906i
$45$	−3.93706e7	+	4.68960e7i	−1.43125	+	1.70482i
$46$	1.86193e7	−	3.22497e7i	0.613132	−	1.06198i
$47$	−8.72742e6	+	3.25712e7i	−0.260883	+	0.973628i	0.703840	+	0.710359i	$0.251467\pi$
$47$	−8.72742e6	+	3.25712e7i	−0.260883	+	0.973628i	−0.964722	+	0.263269i	$0.915199\pi$
$48$	−5.83820e7	+	5.83820e7i	−1.58742	+	1.58742i
$49$	−2.71949e7	+	2.98136e7i	−0.673915	+	0.738809i
$50$	−4.89112e7	+	2.27776e7i	−1.10673	+	0.515398i
$51$	1.41964e7	+	2.45888e7i	0.293840	+	0.508946i
$52$	2.93191e6	−	785604.i	0.0556079	−	0.0149001i
$53$	3.88889e7	−	1.04202e7i	0.676993	−	0.181400i	0.0960902	−	0.995373i	$-0.469366\pi$
$53$	3.88889e7	−	1.04202e7i	0.676993	−	0.181400i	0.580903	+	0.813973i	$0.302700\pi$
$54$	−8.39872e7	−	1.45470e8i	−1.34413	−	2.32810i
$55$	−1.59229e7	+	9.01700e7i	−0.234633	+	1.32871i
$56$	1.65433e7	−	4.26844e7i	0.224790	−	0.579993i
$57$	1.62788e8	−	1.62788e8i	2.04261	−	2.04261i
$58$	3.63185e6	−	1.35543e7i	0.0421408	−	0.157271i
$59$	8.88903e6	−	1.53962e7i	0.0955037	−	0.165417i	−0.814315	−	0.580423i	$-0.802887\pi$
$59$	8.88903e6	−	1.53962e7i	0.0955037	−	0.165417i	0.909819	+	0.415006i	$0.136220\pi$
$60$	−7.68577e6	−	8.81050e7i	−0.0765609	−	0.877647i
$61$	−1.30067e8	+	7.50944e7i	−1.20277	+	0.694422i	−0.961171	−	0.275953i	$-0.911006\pi$
$61$	−1.30067e8	+	7.50944e7i	−1.20277	+	0.694422i	−0.241603	+	0.970375i	$0.577673\pi$
$62$	9.18973e7	+	9.18973e7i	0.789842	+	0.789842i
$63$	2.24639e8	+	1.64320e8i	1.79661	+	1.31419i
$64$			1.96407e7i			0.146335i
$65$	7.14248e6	−	1.53070e7i	0.0496294	−	0.106360i
$66$	−3.94977e8	−	2.28040e8i	−2.56226	−	1.47932i
$67$	−4.55098e7	−	1.69845e8i	−0.275910	−	1.02971i	−0.955229	−	0.295868i	$-0.904391\pi$
$67$	−4.55098e7	−	1.69845e8i	−0.275910	−	1.02971i	0.679318	−	0.733844i	$-0.262276\pi$
$68$	−2.73327e7	−	7.32378e6i	−0.155022	−	0.0415379i
$69$	3.39679e8			1.80405
$70$	1.18152e8	+	2.14912e8i	0.588164	+	1.06984i
$71$	1.11742e7			0.0521858			0.0260929	−	0.999660i	$-0.491693\pi$
$71$	1.11742e7			0.0521858			0.0260929	+	0.999660i	$0.491693\pi$
$72$	−3.04979e8	−	8.17188e7i	−1.33744	−	0.358365i
$73$	1.12759e8	+	4.20822e8i	0.464727	+	1.73438i	0.657793	+	0.753198i	$0.271490\pi$
$73$	1.12759e8	+	4.20822e8i	0.464727	+	1.73438i	−0.193067	+	0.981186i	$0.561843\pi$
$74$	−2.74986e6	−	1.58763e6i	−0.0106603	−	0.00615470i
$75$	−4.03010e8	−	2.82494e8i	−1.47075	−	1.03094i
$76$			2.29440e8i			0.788876i
$77$	4.13781e8	+	4.48412e7i	1.34141	+	0.145368i
$78$	5.94924e7	+	5.94924e7i	0.181985	+	0.181985i
$79$	−2.56198e7	+	1.47916e7i	−0.0740039	+	0.0427262i	−0.536545	−	0.843871i	$-0.680271\pi$
$79$	−2.56198e7	+	1.47916e7i	−0.0740039	+	0.0427262i	0.462541	+	0.886598i	$0.346938\pi$
$80$	−3.50708e8	−	2.94430e8i	−0.957283	−	0.803668i
$81$	3.34913e8	−	5.80086e8i	0.864468	−	1.49730i
$82$	−1.43895e8	+	5.37022e8i	−0.351465	+	1.31168i
$83$	−3.31641e7	+	3.31641e7i	−0.0767039	+	0.0767039i	−0.744418	−	0.667714i	$-0.767273\pi$
$83$	−3.31641e7	+	3.31641e7i	−0.0767039	+	0.0767039i	0.667714	+	0.744418i	$0.267273\pi$
$84$	−3.97249e8	+	6.16041e7i	−0.870574	+	0.135006i
$85$	−1.29014e8	+	9.02884e7i	−0.268073	+	0.187606i
$86$	3.59681e8	+	6.22985e8i	0.709046	+	1.22810i
$87$	1.23638e8	−	3.31286e7i	0.231374	−	0.0619964i
$88$	−4.56064e8	+	1.22202e8i	−0.810688	+	0.217223i
$89$	4.64190e8	+	8.04001e8i	0.784226	+	1.35832i	0.929461	+	0.368922i	$0.120273\pi$
$89$	4.64190e8	+	8.04001e8i	0.784226	+	1.35832i	−0.145235	+	0.989397i	$0.546394\pi$
$90$	1.38585e9	−	9.69859e8i	2.22651	−	1.55818i
$91$	−7.15901e7	−	2.77464e7i	−0.109438	−	0.0424150i
$92$	−2.39379e8	+	2.39379e8i	−0.348370	+	0.348370i
$93$	−3.06824e8	+	1.14508e9i	−0.425320	+	1.58731i
$94$	4.65758e8	−	8.06717e8i	0.615297	−	1.06573i
$95$	9.77890e8	+	8.20968e8i	1.23178	+	1.03412i
$96$	1.17008e9	−	6.75548e8i	1.40604	−	0.811775i
$97$	1.86590e8	+	1.86590e8i	0.214001	+	0.214001i	0.805965	−	0.591964i	$-0.201647\pi$
$97$	1.86590e8	+	1.86590e8i	0.214001	+	0.214001i	−0.591964	+	0.805965i	$0.701647\pi$
$98$	9.38820e8	−	6.01095e8i	1.02817	−	0.658303i
$99$		−	2.87061e9i		−	3.00342i
$100$	4.83089e8	−	8.49300e7i	0.483089	−	0.0849300i
$101$	−1.39376e8	−	8.04685e7i	−0.133272	−	0.0769449i	0.431881	−	0.901930i	$-0.357850\pi$
$101$	−1.39376e8	−	8.04685e7i	−0.133272	−	0.0769449i	−0.565154	+	0.824986i	$0.691183\pi$
$102$	−2.03004e8	−	7.57620e8i	−0.185696	−	0.693028i
$103$	−1.44706e9	−	3.87738e8i	−1.26683	−	0.339446i	−0.438014	−	0.898968i	$-0.644318\pi$
$103$	−1.44706e9	−	3.87738e8i	−1.26683	−	0.339446i	−0.828815	+	0.559522i	$0.810985\pi$
$104$	8.70999e7			0.0730075
$105$	−1.15885e9	+	1.91353e9i	−0.930411	+	1.53633i
$106$	−1.11220e9			−0.855670
$107$	−1.75819e9	−	4.71105e8i	−1.29670	−	0.347449i	−0.456497	−	0.889725i	$-0.650896\pi$
$107$	−1.75819e9	−	4.71105e8i	−1.29670	−	0.347449i	−0.840201	+	0.542276i	$0.817563\pi$
$108$	3.95226e8	+	1.47500e9i	0.279537	+	1.04324i
$109$	−5.80722e8	−	3.35280e8i	−0.394048	−	0.227504i	0.289864	−	0.957068i	$-0.406390\pi$
$109$	−5.80722e8	−	3.35280e8i	−0.394048	−	0.227504i	−0.683913	+	0.729564i	$0.739723\pi$
$110$	1.06958e9	−	2.29221e9i	0.696542	−	1.49275i
$111$		−	2.89637e7i		−	0.0181093i
$112$	−1.22886e9	+	1.67995e9i	−0.737939	+	1.00882i
$113$	1.07609e9	+	1.07609e9i	0.620861	+	0.620861i	0.945751	−	0.324891i	$-0.105328\pi$
$113$	1.07609e9	+	1.07609e9i	0.620861	+	0.620861i	−0.324891	+	0.945751i	$0.605328\pi$
$114$	−5.50769e9	+	3.17987e9i	−3.05420	+	1.76334i
$115$	1.63719e8	+	1.87678e9i	0.0872889	+	1.00063i
$116$	−6.37835e7	+	1.10476e8i	−0.0327075	+	0.0566510i
$117$	−1.37058e8	+	5.11509e8i	−0.0676191	+	0.252358i
$118$	−3.47272e8	+	3.47272e8i	−0.164892	+	0.164892i
$119$	4.48650e8	+	5.57709e8i	0.205091	+	0.254945i
$120$	4.41315e8	−	2.49913e9i	0.194282	−	1.10020i
$121$	−9.67375e8	−	1.67554e9i	−0.410262	−	0.710594i
$122$	4.00758e9	−	1.07383e9i	1.63781	−	0.438849i
$123$	−4.89854e9	+	1.31256e9i	−1.92972	+	0.517066i
$124$	−5.90737e8	−	1.02319e9i	−0.224386	−	0.388649i
$125$	1.36658e9	−	2.36285e9i	0.500656	−	0.865646i
$126$	−4.81931e9	−	5.99080e9i	−1.70340	−	2.11747i
$127$	1.82219e9	−	1.82219e9i	0.621553	−	0.621553i	−0.324376	−	0.945928i	$-0.605154\pi$
$127$	1.82219e9	−	1.82219e9i	0.621553	−	0.621553i	0.945928	+	0.324376i	$0.105154\pi$
$128$	8.50950e8	−	3.17579e9i	0.280194	−	1.04570i
$129$	−3.28089e9	+	5.68267e9i	−1.04313	+	1.80675i
$130$	−3.00030e8	+	3.57378e8i	−0.0921339	+	0.109745i
$131$	1.03974e7	−	6.00294e6i	0.00308464	−	0.00178092i	−0.498457	−	0.866914i	$-0.666100\pi$
$131$	1.03974e7	−	6.00294e6i	0.00308464	−	0.00178092i	0.501542	+	0.865134i	$0.332766\pi$
$132$	2.93178e9	+	2.93178e9i	0.840522	+	0.840522i
$133$	3.42646e9	−	4.68425e9i	0.949541	−	1.29810i
$134$			4.85746e9i			1.30148i
$135$	7.70073e9	+	3.59328e9i	1.99540	+	0.931084i
$136$	−7.03201e8	−	4.05993e8i	−0.176260	−	0.101764i
$137$	−5.28415e8	−	1.97207e9i	−0.128154	−	0.478278i	0.871778	−	0.489900i	$-0.162967\pi$
$137$	−5.28415e8	−	1.97207e9i	−0.128154	−	0.478278i	−0.999932	+	0.0116230i	$0.996300\pi$
$138$	−9.06386e9	−	2.42866e9i	−2.12744	−	0.570046i
$139$	−3.53556e9			−0.803326			−0.401663	−	0.915788i	$-0.631568\pi$
$139$	−3.53556e9			−0.803326			−0.401663	+	0.915788i	$0.631568\pi$
$140$	−5.31838e8	−	2.16517e9i	−0.117005	−	0.476338i
$141$	8.49699e9			1.81042
$142$	−2.98167e8	−	7.98935e7i	−0.0615406	−	0.0164897i
$143$	2.04957e8	+	7.64909e8i	0.0409874	+	0.152967i
$144$	1.24325e10	+	7.17790e9i	2.40950	+	1.39112i
$145$	2.42631e8	+	6.67148e8i	0.0455817	+	0.125333i
$146$		−	1.20352e10i		−	2.19213i
$147$	9.03022e9	+	4.67481e9i	1.59503	+	0.825726i
$148$	2.04113e7	+	2.04113e7i	0.00349698	+	0.00349698i
$149$	2.21471e9	−	1.27866e9i	0.368110	−	0.212529i	−0.304522	−	0.952505i	$-0.598497\pi$
$149$	2.21471e9	−	1.27866e9i	0.368110	−	0.212529i	0.672633	+	0.739977i	$0.265163\pi$
$150$	8.73397e9	+	1.04194e10i	1.40864	+	1.68048i
$151$	−3.95036e9	+	6.84222e9i	−0.618358	+	1.07103i	0.371427	+	0.928462i	$0.378868\pi$
$151$	−3.95036e9	+	6.84222e9i	−0.618358	+	1.07103i	−0.989785	+	0.142565i	$0.954465\pi$
$152$	−1.70403e9	+	6.35951e9i	−0.258929	+	0.966335i
$153$	3.49081e9	−	3.49081e9i	0.515008	−	0.515008i
$154$	−1.07206e10	−	4.15500e9i	−1.53594	−	0.595289i
$155$	−6.47462e9	−	1.14334e9i	−0.900994	−	0.159104i
$156$	−3.82431e8	−	6.62389e8i	−0.0517002	−	0.0895473i
$157$	8.14416e9	−	2.18222e9i	1.06979	−	0.286649i	0.319382	−	0.947626i	$-0.396525\pi$
$157$	8.14416e9	−	2.18222e9i	1.06979	−	0.286649i	0.750406	+	0.660977i	$0.229858\pi$
$158$	7.89387e8	−	2.11516e8i	0.100770	−	0.0270014i
$159$	−5.07256e9	−	8.78593e9i	−0.629419	−	1.09019i
$160$	4.29646e9	+	6.13928e9i	0.518288	+	0.740589i
$161$	8.46203e9	−	1.31227e9i	0.992563	−	0.153924i
$162$	−1.30842e10	+	1.30842e10i	−1.49255	+	1.49255i
$163$	−4.37098e9	+	1.63127e10i	−0.484991	+	1.81001i	0.0951077	+	0.995467i	$0.469680\pi$
$163$	−4.37098e9	+	1.63127e10i	−0.484991	+	1.81001i	−0.580099	+	0.814546i	$0.696986\pi$
$164$	2.52711e9	−	4.37708e9i	0.272789	−	0.472484i
$165$	2.29858e10	−	2.00515e9i	2.41425	−	0.210605i
$166$	1.12206e9	−	6.47820e8i	0.114691	−	0.0662167i
$167$	−5.47333e9	−	5.47333e9i	−0.544538	−	0.544538i	0.380318	−	0.924856i	$-0.375815\pi$
$167$	−5.47333e9	−	5.47333e9i	−0.544538	−	0.544538i	−0.924856	+	0.380318i	$0.875815\pi$
$168$	−1.14683e10	−	1.24281e9i	−1.11072	−	0.120368i
$169$			1.04584e10i			0.986224i
$170$	4.08812e9	−	1.48678e9i	0.375408	−	0.136530i
$171$	−3.46659e10	−	2.00144e10i	−3.10041	−	1.79003i
$172$	−1.69258e9	−	6.31680e9i	−0.147459	−	0.550325i
$173$	4.56454e9	+	1.22306e9i	0.387427	+	0.103811i	0.447274	−	0.894397i	$-0.352395\pi$
$173$	4.56454e9	+	1.22306e9i	0.387427	+	0.103811i	−0.0598476	+	0.998208i	$0.519061\pi$
$174$	−3.53596e9			−0.292439
$175$	−1.11311e10	−	5.48052e9i	−0.897151	−	0.441724i
$176$	2.14676e10			1.68646
$177$	−4.32716e9	−	1.15946e9i	−0.331378	−	0.0887924i
$178$	−6.63778e9	−	2.47725e10i	−0.495602	−	1.84961i
$179$	−3.45357e9	−	1.99392e9i	−0.251437	−	0.145167i	0.368985	−	0.929435i	$-0.379705\pi$
$179$	−3.45357e9	−	1.99392e9i	−0.251437	−	0.145167i	−0.620422	+	0.784268i	$0.713039\pi$
$180$	−1.44513e10	+	5.25570e9i	−1.02608	+	0.373168i
$181$			1.66496e10i			1.15306i	0.817076	+	0.576529i	$0.195593\pi$
$181$			1.66496e10i			1.15306i	−0.817076	+	0.576529i	$0.804407\pi$
$182$	1.71190e9	+	1.25223e9i	0.115653	+	0.0845986i
$183$	2.67607e10	+	2.67607e10i	1.76388	+	1.76388i
$184$	−8.41282e9	+	4.85714e9i	−0.541080	+	0.312393i
$185$	1.60029e8	−	1.39600e7i	0.0100444	−	0.000876217i
$186$	1.63743e10	−	2.83611e10i	1.00312	−	1.73746i
$187$	1.91070e9	−	7.13085e9i	0.114263	−	0.426436i
$188$	−5.98800e9	+	5.98800e9i	−0.349600	+	0.349600i
$189$	1.39588e10	−	3.60159e10i	0.795737	−	2.05313i
$190$	−2.02238e10	−	2.88981e10i	−1.12583	−	1.60871i
$191$	1.11883e10	+	1.93787e10i	0.608295	+	1.05360i	0.991521	+	0.129943i	$0.0414796\pi$
$191$	1.11883e10	+	1.93787e10i	0.608295	+	1.05360i	−0.383226	+	0.923654i	$0.625187\pi$
$192$	4.78053e9	−	1.28094e9i	0.253875	−	0.0680257i
$193$	1.00201e10	−	2.68487e9i	0.519832	−	0.139288i	0.0106429	−	0.999943i	$-0.496612\pi$
$193$	1.00201e10	−	2.68487e9i	0.519832	−	0.139288i	0.509189	+	0.860655i	$0.329946\pi$
$194$	−3.64480e9	−	6.31298e9i	−0.184742	−	0.319983i
$195$	−4.19153e9	−	7.40172e8i	−0.207595	−	0.0366587i
$196$	−9.65821e9	+	3.06934e9i	−0.467460	+	0.148557i
$197$	−1.33184e9	+	1.33184e9i	−0.0630018	+	0.0630018i	−0.737906	−	0.674904i	$-0.764185\pi$
$197$	−1.33184e9	+	1.33184e9i	−0.0630018	+	0.0630018i	0.674904	+	0.737906i	$0.264185\pi$
$198$	−2.05244e10	+	7.65981e10i	−0.949024	+	3.54181i
$199$	−1.12074e10	+	1.94118e10i	−0.506603	+	0.877461i	0.493368	+	0.869821i	$0.335765\pi$
$199$	−1.12074e10	+	1.94118e10i	−0.506603	+	0.877461i	−0.999971	+	0.00764077i	$0.997568\pi$
$200$	1.40208e10	+	1.23379e9i	0.619636	+	0.0545265i
$201$	−3.83720e10	+	2.21541e10i	−1.65818	+	0.957351i
$202$	3.14370e9	+	3.14370e9i	0.132850	+	0.132850i
$203$	2.95205e9	−	1.30294e9i	0.122009	−	0.0538507i
$204$			7.13040e9i			0.288256i
$205$	−9.61308e9	−	2.64325e10i	−0.380163	−	1.04531i
$206$	3.58404e10	+	2.06925e10i	1.38666	+	0.800590i
$207$	−1.52862e10	−	5.70488e10i	−0.578672	−	2.15963i
$208$	−3.82528e9	−	1.02498e9i	−0.141703	−	0.0379691i
$209$	−5.98588e10			−2.17005
$210$	4.46037e10	−	4.27742e10i	1.58265	−	1.51773i
$211$	−4.07738e10			−1.41615			−0.708077	−	0.706135i	$-0.750437\pi$
$211$	−4.07738e10			−1.41615			−0.708077	+	0.706135i	$0.750437\pi$
$212$	9.76635e9	+	2.61689e9i	0.332063	+	0.0889761i
$213$	−7.28762e8	−	2.71978e9i	−0.0242593	−	0.0905368i
$214$	4.35465e10	+	2.51416e10i	1.41936	+	0.819465i
$215$	−3.29789e10	−	1.53885e10i	−1.05260	−	0.491159i
$216$			4.38187e10i			1.36968i
$217$	−3.21980e9	+	2.97114e10i	−0.0985736	+	0.909608i
$218$	1.30986e10	+	1.30986e10i	0.392798	+	0.392798i
$219$	9.50736e10	−	5.48908e10i	2.79294	−	1.61250i
$220$	−1.47855e10	+	1.76116e10i	−0.425533	+	0.506870i
$221$	−6.80931e8	+	1.17941e9i	−0.0192016	+	0.0332582i
$222$	−2.07086e8	+	7.72856e8i	−0.00572220	+	0.0213555i
$223$	1.94989e10	−	1.94989e10i	0.528006	−	0.528006i	−0.391972	−	0.919977i	$-0.628207\pi$
$223$	1.94989e10	−	1.94989e10i	0.528006	−	0.528006i	0.919977	+	0.391972i	$0.128207\pi$
$224$	2.65391e10	−	2.13495e10i	0.704321	−	0.566593i
$225$	−2.93084e10	+	8.03979e10i	−0.762379	+	2.09133i
$226$	−2.10200e10	−	3.64077e10i	−0.535975	−	0.928336i
$227$	−1.66581e10	+	4.46353e9i	−0.416399	+	0.111574i	−0.460935	−	0.887434i	$-0.652486\pi$
$227$	−1.66581e10	+	4.46353e9i	−0.416399	+	0.111574i	0.0445359	+	0.999008i	$0.485819\pi$
$228$	5.58456e10	−	1.49638e10i	1.36862	−	0.366720i
$229$	−1.02899e10	−	1.78227e10i	−0.247260	−	0.428266i	0.715505	−	0.698608i	$-0.246197\pi$
$229$	−1.02899e10	−	1.78227e10i	−0.247260	−	0.428266i	−0.962764	+	0.270342i	$0.912863\pi$
$230$	9.05006e9	−	5.12497e10i	0.213244	−	1.20758i
$231$	−1.60719e10	−	1.03639e11i	−0.371376	−	2.39479i
$232$	−2.58841e9	+	2.58841e9i	−0.0586594	+	0.0586594i
$233$	3.77249e9	−	1.40791e10i	0.0838544	−	0.312949i	−0.911240	−	0.411875i	$-0.864874\pi$
$233$	3.77249e9	−	1.40791e10i	0.0838544	−	0.312949i	0.995095	+	0.0989260i	$0.0315407\pi$
$234$	7.31442e9	−	1.26689e10i	0.159481	−	0.276229i
$235$	4.09539e9	+	4.69471e10i	0.0875971	+	1.00416i
$236$	3.86653e9	−	2.23234e9i	0.0811367	−	0.0468443i
$237$	5.27116e9	+	5.27116e9i	0.108527	+	0.108527i
$238$	−7.98407e9	−	1.80895e10i	−0.161298	−	0.365451i
$239$			1.41955e10i			0.281424i	0.990051	+	0.140712i	$0.0449392\pi$
$239$			1.41955e10i			0.281424i	−0.990051	+	0.140712i	$0.955061\pi$
$240$	−4.87913e10	+	1.04564e11i	−0.949274	+	2.03438i
$241$	4.44284e10	+	2.56508e10i	0.848368	+	0.489805i	0.860100	−	0.510126i	$-0.170401\pi$
$241$	4.44284e10	+	2.56508e10i	0.848368	+	0.489805i	−0.0117319	+	0.999931i	$0.503734\pi$
$242$	1.38332e10	+	5.16261e10i	0.259270	+	0.967610i
$243$	−4.74296e10	−	1.27087e10i	−0.872613	−	0.233816i
$244$	−3.77176e10			−0.681224
$245$	−2.14766e10	+	5.21464e10i	−0.380819	+	0.924650i
$246$	1.40095e11			2.43902
$247$	1.06661e10	+	2.85799e9i	0.182336	+	0.0488567i
$248$	−8.77466e9	−	3.27475e10i	−0.147298	−	0.549725i
$249$	1.02350e10	+	5.90920e9i	0.168730	+	0.0974163i
$250$	−5.33592e10	+	5.32784e10i	−0.863932	+	0.862624i
$251$			5.01153e10i			0.796963i	0.917176	+	0.398482i	$0.130463\pi$
$251$			5.01153e10i			0.796963i	−0.917176	+	0.398482i	$0.869537\pi$
$252$	2.82232e10	+	6.39452e10i	0.440864	+	0.998863i
$253$	−6.24517e10	−	6.24517e10i	−0.958301	−	0.958301i
$254$	−6.16511e10	+	3.55943e10i	−0.929371	+	0.536573i
$255$	3.03902e10	+	2.55135e10i	0.450094	+	0.377868i
$256$	−4.03848e10	+	6.99485e10i	−0.587676	+	1.01788i
$257$	3.50523e10	−	1.30817e11i	0.501207	−	1.87053i	0.00916855	−	0.999958i	$-0.497082\pi$
$257$	3.50523e10	−	1.30817e11i	0.501207	−	1.87053i	0.492039	−	0.870573i	$-0.336252\pi$
$258$	1.28176e11	−	1.28176e11i	1.80102	−	1.80102i
$259$	−1.11894e8	−	7.21539e8i	−0.00154510	−	0.00996348i
$260$	3.47547e9	−	2.43224e9i	0.0471665	−	0.0330086i
$261$	−1.11278e10	−	1.92739e10i	−0.148432	−	0.257092i
$262$	−3.20360e8	+	8.58403e7i	−0.00420033	+	0.00112547i
$263$	−4.11356e10	+	1.10223e10i	−0.530172	+	0.142059i	−0.513968	−	0.857809i	$-0.671825\pi$
$263$	−4.11356e10	+	1.10223e10i	−0.530172	+	0.142059i	−0.0162044	+	0.999869i	$0.505158\pi$
$264$	5.94877e10	+	1.03036e11i	0.753719	+	1.30548i
$265$	4.60986e10	−	3.22613e10i	0.574225	−	0.401860i
$266$	−1.24922e11	+	1.00494e11i	−1.52993	+	1.23076i
$267$	1.65419e11	−	1.65419e11i	1.99198	−	1.99198i
$268$	1.14291e10	−	4.26539e10i	0.135333	−	0.505071i
$269$	−7.11681e9	+	1.23267e10i	−0.0828705	+	0.143536i	−0.904482	−	0.426512i	$-0.859742\pi$
$269$	−7.11681e9	+	1.23267e10i	−0.0828705	+	0.143536i	0.821611	+	0.570048i	$0.193075\pi$
$270$	−1.79792e11	−	1.50941e11i	−2.05889	−	1.72850i
$271$	−4.77569e8	+	2.75724e8i	−0.00537866	+	0.00310537i	−0.502687	−	0.864469i	$-0.667655\pi$
$271$	−4.77569e8	+	2.75724e8i	−0.00537866	+	0.00310537i	0.497308	+	0.867574i	$0.334322\pi$
$272$	2.61057e10	+	2.61057e10i	0.289185	+	0.289185i
$273$	−2.08443e9	+	1.92345e10i	−0.0227120	+	0.209580i
$274$			5.64000e10i			0.604508i
$275$	2.21574e10	+	1.26033e11i	0.233627	+	1.32889i
$276$	7.38765e10	+	4.26526e10i	0.766329	+	0.442440i
$277$	3.36110e10	+	1.25438e11i	0.343022	+	1.28018i	0.894906	+	0.446256i	$0.147243\pi$
$277$	3.36110e10	+	1.25438e11i	0.343022	+	1.28018i	−0.551883	+	0.833921i	$0.686091\pi$
$278$	9.43415e10	+	2.52787e10i	0.947330	+	0.253836i
$279$	2.06123e11			2.03661
$280$	1.33920e9	−	6.39629e10i	0.0130207	−	0.621895i
$281$	−1.59741e10			−0.152841			−0.0764203	−	0.997076i	$-0.524349\pi$
$281$	−1.59741e10			−0.152841			−0.0764203	+	0.997076i	$0.524349\pi$
$282$	−2.26730e11	−	6.07522e10i	−2.13495	−	0.572059i
$283$	9.07921e9	+	3.38841e10i	0.0841413	+	0.314019i	0.995150	−	0.0983672i	$-0.0313620\pi$
$283$	9.07921e9	+	3.38841e10i	0.0841413	+	0.314019i	−0.911009	+	0.412387i	$0.864695\pi$
$284$	2.43026e9	+	1.40311e9i	0.0221676	+	0.0127985i
$285$	1.36046e11	−	2.91560e11i	1.22148	−	2.61774i
$286$		−	2.18759e10i		−	0.193339i
$287$	−1.16961e11	+	5.16225e10i	−1.01759	+	0.449128i
$288$	−1.66113e11	−	1.66113e11i	−1.42278	−	1.42278i
$289$	−9.17051e10	+	5.29460e10i	−0.773309	+	0.446470i
$290$	−1.70427e9	−	1.95367e10i	−0.0141497	−	0.162203i
$291$	3.32467e10	−	5.75849e10i	0.271788	−	0.470750i
$292$	−2.83177e10	+	1.05683e11i	−0.227947	+	0.850711i
$293$	4.50664e10	−	4.50664e10i	0.357231	−	0.357231i	−0.505560	−	0.862791i	$-0.668714\pi$
$293$	4.50664e10	−	4.50664e10i	0.357231	−	0.357231i	0.862791	+	0.505560i	$0.168714\pi$
$294$	−2.07534e11	−	1.89305e11i	−1.62005	−	1.47775i
$295$	4.32057e9	−	2.44670e10i	0.0332156	−	0.188097i
$296$	4.14158e8	+	7.17343e8i	0.00313584	+	0.00543143i
$297$	−3.84815e11	+	1.03111e11i	−2.86977	+	0.768953i
$298$	−6.82386e10	+	1.82845e10i	−0.501253	+	0.134310i
$299$	8.14638e9	+	1.41099e10i	0.0589446	+	0.102095i
$300$	−5.21782e10	−	1.12044e11i	−0.371915	−	0.798627i
$301$	−5.97794e10	+	1.54241e11i	−0.419761	+	1.08305i
$302$	1.54331e11	−	1.54331e11i	1.06763	−	1.06763i
$303$	−1.04961e10	+	3.91719e10i	−0.0715378	+	0.266983i
$304$	1.49676e11	−	2.59246e11i	1.00513	−	1.74093i
$305$	−1.34959e11	+	1.60755e11i	−0.893000	+	1.06369i
$306$	−1.18106e11	+	6.81885e10i	−0.770062	+	0.444595i
$307$	−1.66726e11	−	1.66726e11i	−1.07122	−	1.07122i	−0.997261	−	0.0739607i	$-0.976436\pi$
$307$	−1.66726e11	−	1.66726e11i	−1.07122	−	1.07122i	−0.0739607	−	0.997261i	$-0.523564\pi$
$308$	8.43623e10	+	6.17099e10i	0.534159	+	0.390730i
$309$			3.77500e11i			2.35561i
$310$	1.64592e11	+	7.68009e10i	1.01223	+	0.472323i
$311$	1.73426e11	+	1.00128e11i	1.05122	+	0.606921i	0.922990	−	0.384823i	$-0.125738\pi$
$311$	1.73426e11	+	1.00128e11i	1.05122	+	0.606921i	0.128228	+	0.991745i	$0.459071\pi$
$312$	−5.68053e9	−	2.12000e10i	−0.0339386	−	0.126660i
$313$	−1.67833e11	−	4.49706e10i	−0.988387	−	0.264837i	−0.271814	−	0.962350i	$-0.587624\pi$
$313$	−1.67833e11	−	4.49706e10i	−0.988387	−	0.264837i	−0.716573	+	0.697512i	$0.754290\pi$
$314$	−2.32918e11			−1.35213
$315$	3.73525e11	+	1.08515e11i	2.13758	+	0.621002i
$316$	−7.42938e9			−0.0419141
$317$	−1.23940e10	−	3.32095e9i	−0.0689356	−	0.0184712i	0.224186	−	0.974546i	$-0.428028\pi$
$317$	−1.23940e10	−	3.32095e9i	−0.0689356	−	0.0184712i	−0.293122	+	0.956075i	$0.594694\pi$
$318$	7.25360e10	+	2.70708e11i	0.397770	+	1.48450i
$319$	−2.88222e10	−	1.66405e10i	−0.155836	−	0.0899722i
$320$	9.38151e9	+	2.57957e10i	0.0500147	+	0.137522i
$321$			4.58667e11i			2.41115i
$322$	−2.35180e11	−	2.54863e10i	−1.21913	−	0.132116i
$323$	−7.27914e10	−	7.27914e10i	−0.372108	−	0.372108i
$324$	1.45680e11	−	8.41082e10i	0.734423	−	0.424020i
$325$	2.06932e9	−	2.35156e10i	0.0102885	−	0.116918i
$326$	2.33267e11	−	4.04030e11i	1.14386	−	1.98123i
$327$	−4.37330e10	+	1.63214e11i	−0.211517	+	0.789391i
$328$	1.02553e11	−	1.02553e11i	0.489234	−	0.489234i
$329$	2.11675e11	−	3.28260e10i	0.996068	−	0.154467i
$330$	−6.27680e11	−	1.10840e11i	−2.91357	−	0.514500i
$331$	−6.06009e10	−	1.04964e11i	−0.277494	−	0.480634i	0.693267	−	0.720680i	$-0.256170\pi$
$331$	−6.06009e10	−	1.04964e11i	−0.277494	−	0.480634i	−0.970761	+	0.240047i	$0.922837\pi$
$332$	−1.13772e10	+	3.04850e9i	−0.0513940	+	0.0137710i
$333$	−4.86442e9	+	1.30342e9i	−0.0216787	+	0.00580878i
$334$	1.06915e11	+	1.85182e11i	0.470087	+	0.814215i
$335$	−1.40899e11	−	2.01333e11i	−0.611233	−	0.873400i
$336$	4.89042e11	+	1.89539e11i	2.09324	+	0.811283i
$337$	1.80071e11	−	1.80071e11i	0.760518	−	0.760518i	−0.215898	−	0.976416i	$-0.569268\pi$
$337$	1.80071e11	−	1.80071e11i	0.760518	−	0.760518i	0.976416	+	0.215898i	$0.0692680\pi$
$338$	7.47761e10	−	2.79068e11i	0.311629	−	1.16301i
$339$	1.91738e11	−	3.32099e11i	0.788512	−	1.36574i
$340$	−3.93965e10	+	3.43672e9i	−0.159883	+	0.0139473i
$341$	2.66940e11	−	1.54118e11i	1.06910	−	0.617245i
$342$	7.81911e11	+	7.81911e11i	3.09058	+	3.09058i
$343$	2.43019e11	+	8.15721e10i	0.948019	+	0.318213i
$344$		−	1.87656e11i		−	0.722521i
$345$	4.46128e11	−	1.62250e11i	1.69541	−	0.616593i
$346$	−1.13054e11	−	6.52715e10i	−0.424074	−	0.244839i
$347$	−2.42112e10	−	9.03575e10i	−0.0896466	−	0.334566i	0.906507	−	0.422191i	$-0.138739\pi$
$347$	−2.42112e10	−	9.03575e10i	−0.0896466	−	0.334566i	−0.996154	+	0.0876253i	$0.972072\pi$
$348$	3.10497e10	+	8.31973e9i	0.113488	+	0.0304091i
$349$	−3.59092e11			−1.29566			−0.647830	−	0.761785i	$-0.724323\pi$
$349$	−3.59092e11			−1.29566			−0.647830	+	0.761785i	$0.724323\pi$
$350$	2.57832e11	+	2.25825e11i	0.918398	+	0.804390i
$351$	7.34925e10			0.258441
$352$	−3.39328e11	−	9.09227e10i	−1.17809	−	0.315668i
$353$	−4.77393e10	−	1.78165e11i	−0.163640	−	0.610713i	−0.998210	−	0.0598105i	$-0.980950\pi$
$353$	−4.77393e10	−	1.78165e11i	−0.163640	−	0.610713i	0.834570	−	0.550902i	$-0.185716\pi$
$354$	1.07174e11	+	6.18771e10i	0.362724	+	0.209419i
$355$	1.46759e10	−	5.33740e9i	0.0490431	−	0.0178362i
$356$			2.33149e11i			0.769321i
$357$	1.06485e11	−	1.45574e11i	0.346963	−	0.474326i
$358$	7.78974e10	+	7.78974e10i	0.250639	+	0.250639i
$359$	2.81848e11	−	1.62725e11i	0.895552	−	0.517047i	0.0197973	−	0.999804i	$-0.493698\pi$
$359$	2.81848e11	−	1.62725e11i	0.895552	−	0.517047i	0.875754	+	0.482757i	$0.160365\pi$
$360$	−4.39586e11	+	3.83470e10i	−1.37938	+	0.120329i
$361$	−2.56002e11	+	4.43409e11i	−0.793343	+	1.37411i
$362$	1.19042e11	−	4.44272e11i	0.364345	−	1.35976i
$363$	−3.44735e11	+	3.44735e11i	−1.04209	+	1.04209i
$364$	−1.20860e10	−	1.50239e10i	−0.0360850	−	0.0448566i
$365$	3.49103e11	+	4.98839e11i	1.02952	+	1.47110i
$366$	−5.22737e11	−	9.05407e11i	−1.52271	−	2.63742i
$367$	−2.42823e11	+	6.50641e10i	−0.698702	+	0.187217i	−0.590649	−	0.806929i	$-0.701128\pi$
$367$	−2.42823e11	+	6.50641e10i	−0.698702	+	0.187217i	−0.108053	+	0.994145i	$0.534462\pi$
$368$	4.26635e11	−	1.14316e11i	1.21267	−	0.324933i
$369$	4.40886e11	+	7.63636e11i	1.23796	+	2.14421i
$370$	−4.36995e9	−	7.71679e8i	−0.0121219	−	0.00214057i
$371$	−1.60309e11	−	1.99277e11i	−0.439314	−	0.546103i
$372$	−2.10516e11	+	2.10516e11i	−0.569955	+	0.569955i
$373$	−1.51456e11	+	5.65242e11i	−0.405132	+	1.51197i	0.398679	+	0.917090i	$0.369469\pi$
$373$	−1.51456e11	+	5.65242e11i	−0.405132	+	1.51197i	−0.803811	+	0.594884i	$0.797198\pi$
$374$	−1.01969e11	+	1.76615e11i	−0.269492	+	0.466774i
$375$	−6.64241e11	−	1.78522e11i	−1.73454	−	0.466178i
$376$	−2.10444e11	+	1.21500e11i	−0.542990	+	0.313496i
$377$	4.34127e9	+	4.34127e9i	0.0110683	+	0.0110683i
$378$	−6.29979e11	+	8.61232e11i	−1.58713	+	2.16974i
$379$		−	4.92224e11i		−	1.22542i	−0.790307	−	0.612712i	$-0.790079\pi$
$379$		−	4.92224e11i		−	1.22542i	0.790307	−	0.612712i	$-0.209921\pi$
$380$	1.09594e11	+	3.01343e11i	0.269624	+	0.741369i
$381$	−5.62361e11	−	3.24679e11i	−1.36727	−	0.789391i
$382$	−1.59989e11	−	5.97089e11i	−0.384420	−	1.43468i
$383$	7.33659e10	+	1.96583e10i	0.174221	+	0.0466823i	0.344875	−	0.938649i	$-0.387921\pi$
$383$	7.33659e10	+	1.96583e10i	0.174221	+	0.0466823i	−0.170654	+	0.985331i	$0.554588\pi$
$384$	−8.28482e11			−1.94443
$385$	5.64871e11	−	1.38752e11i	1.31032	−	0.321858i
$386$	−2.86568e11			−0.657029
$387$	1.10204e12	+	2.95292e11i	2.49747	+	0.669194i
$388$	1.71517e10	+	6.40109e10i	0.0384205	+	0.143387i
$389$	−5.49324e8	−	3.17152e8i	−0.00121634	−	0.000702255i	0.499392	−	0.866376i	$-0.333557\pi$
$389$	−5.49324e8	−	3.17152e8i	−0.00121634	−	0.000702255i	−0.500608	+	0.865674i	$0.666890\pi$
$390$	1.06553e11	+	4.97193e10i	0.233225	+	0.108826i
$391$		−	1.51889e11i		−	0.328648i
$392$	−2.90497e11	+	1.33441e10i	−0.621376	+	0.0285432i
$393$	−2.13922e9	−	2.13922e9i	−0.00452364	−	0.00452364i
$394$	4.50606e10	−	2.60158e10i	0.0942029	−	0.0543881i
$395$	−2.65833e10	+	3.16645e10i	−0.0549442	+	0.0654464i
$396$	3.60455e11	−	6.24326e11i	0.736584	−	1.27580i
$397$	−8.45393e9	+	3.15505e10i	−0.0170805	+	0.0637454i	−0.973940	−	0.226805i	$-0.927172\pi$
$397$	−8.45393e9	+	3.15505e10i	−0.0170805	+	0.0637454i	0.956860	+	0.290551i	$0.0938385\pi$
$398$	4.37846e11	−	4.37846e11i	0.874677	−	0.874677i
$399$	−1.36361e12	−	5.28498e11i	−2.69347	−	1.04392i
$400$	−6.01249e11	−	2.19181e11i	−1.17431	−	0.428087i
$401$	−4.34662e11	−	7.52857e11i	−0.839464	−	1.45399i	−0.890344	−	0.455289i	$-0.849536\pi$
$401$	−4.34662e11	−	7.52857e11i	−0.839464	−	1.45399i	0.0508796	−	0.998705i	$-0.483798\pi$
$402$	1.18230e12	−	3.16797e11i	2.25793	−	0.605011i
$403$	−5.49240e10	+	1.47168e10i	−0.103726	+	0.0277934i
$404$	−2.02084e10	−	3.50020e10i	−0.0377413	−	0.0653698i
$405$	1.62787e11	−	9.21847e11i	0.300657	−	1.70259i
$406$	−8.80872e10	+	1.36603e10i	−0.160896	+	0.0249513i
$407$	−5.32512e9	+	5.32512e9i	−0.00961954	+	0.00961954i
$408$	−5.29566e10	+	1.97637e11i	−0.0946127	+	0.353100i
$409$	2.90819e11	−	5.03713e11i	0.513887	−	0.890078i	−0.485983	−	0.873968i	$-0.661538\pi$
$409$	2.90819e11	−	5.03713e11i	0.513887	−	0.890078i	0.999870	−	0.0161101i	$-0.00512822\pi$
$410$	6.75233e10	+	7.74046e11i	0.118012	+	1.35282i
$411$	−4.45538e11	+	2.57231e11i	−0.770187	+	0.444668i
$412$	−2.66032e11	−	2.66032e11i	−0.454879	−	0.454879i
$413$	−1.12277e11	−	1.21674e10i	−0.189896	−	0.0205789i
$414$			1.63156e12i			2.72962i
$415$	−2.77161e10	+	5.93982e10i	−0.0458686	+	0.0983007i
$416$	5.61232e10	+	3.24027e10i	0.0918803	+	0.0530471i
$417$	2.30584e11	+	8.60553e11i	0.373437	+	1.39369i
$418$	1.59725e12	+	4.27982e11i	2.55905	+	0.685696i
$419$	−8.22645e11			−1.30392			−0.651958	−	0.758255i	$-0.726052\pi$
$419$	−8.22645e11			−1.30392			−0.651958	+	0.758255i	$0.726052\pi$
$420$	−4.92314e11	+	2.70658e11i	−0.772005	+	0.424423i
$421$	7.81385e11			1.21226			0.606130	−	0.795366i	$-0.292721\pi$
$421$	7.81385e11			1.21226			0.606130	+	0.795366i	$0.292721\pi$
$422$	1.08799e12	+	2.91527e11i	1.67001	+	0.447479i
$423$	−3.82379e11	−	1.42706e12i	−0.580715	−	2.16726i
$424$	2.51264e11	+	1.45067e11i	0.377557	+	0.217983i
$425$	−1.26318e11	+	1.80208e11i	−0.187809	+	0.267931i
$426$			7.77840e10i			0.114432i
$427$	7.70042e11	+	5.63275e11i	1.12096	+	0.819965i
$428$	−3.23231e11	−	3.23231e11i	−0.465604	−	0.465604i
$429$	1.72811e11	−	9.97725e10i	0.246328	−	0.142218i
$430$	7.69970e11	+	6.46413e11i	1.08609	+	0.911806i
$431$	−3.28104e11	+	5.68293e11i	−0.457998	+	0.793277i	−0.998855	−	0.0478382i	$-0.984767\pi$
$431$	−3.28104e11	+	5.68293e11i	−0.457998	+	0.793277i	0.540857	+	0.841115i	$0.318100\pi$
$432$	5.15653e11	−	1.92444e12i	0.712329	−	2.65845i
$433$	−3.32470e11	+	3.32470e11i	−0.454524	+	0.454524i	−0.896853	−	0.442329i	$-0.854152\pi$
$433$	−3.32470e11	+	3.32470e11i	−0.454524	+	0.454524i	0.442329	+	0.896853i	$0.354152\pi$
$434$	2.98348e11	−	7.69786e11i	0.403663	−	1.04152i
$435$	1.46559e11	−	1.02567e11i	0.196251	−	0.137342i
$436$	−8.42005e10	−	1.45840e11i	−0.111590	−	0.193280i
$437$	−1.18960e12	+	3.18752e11i	−1.56039	+	0.418106i
$438$	−2.92937e12	+	7.84922e11i	−3.80312	+	1.01904i
$439$	−2.37117e11	−	4.10698e11i	−0.304700	−	0.527755i	0.672495	−	0.740102i	$-0.265223\pi$
$439$	−2.37117e11	−	4.10698e11i	−0.304700	−	0.527755i	−0.977194	+	0.212347i	$0.931889\pi$
$440$	−5.40615e11	+	3.78340e11i	−0.687625	+	0.481221i
$441$	3.78754e11	−	1.72699e12i	0.476851	−	2.17428i
$442$	2.66023e10	−	2.66023e10i	0.0331526	−	0.0331526i
$443$	−1.25173e11	+	4.67153e11i	−0.154417	+	0.576291i	0.844738	+	0.535180i	$0.179756\pi$
$443$	−1.25173e11	+	4.67153e11i	−0.154417	+	0.576291i	−0.999155	+	0.0411109i	$0.986910\pi$
$444$	3.63690e9	−	6.29929e9i	0.00444127	−	0.00769251i
$445$	9.93695e11	+	8.34237e11i	1.20125	+	1.00848i
$446$	−6.59715e11	+	3.80887e11i	−0.789496	+	0.455816i
$447$	−4.55665e11	−	4.55665e11i	−0.539836	−	0.539836i
$448$	1.14143e11	−	5.03789e10i	0.133875	−	0.0590878i
$449$			3.09578e11i			0.359470i	0.983715	+	0.179735i	$0.0575240\pi$
$449$			3.09578e11i			0.359470i	−0.983715	+	0.179735i	$0.942476\pi$
$450$	1.35689e12	−	1.93575e12i	1.55987	−	2.22533i
$451$	1.14194e12	+	6.59299e11i	1.29972	+	0.750392i
$452$	9.89157e10	+	3.69158e11i	0.111466	+	0.415996i
$453$	1.92303e12	+	5.15273e11i	2.14557	+	0.574904i
$454$	4.76412e11			0.526297
$455$	−1.07278e11	−	2.24611e9i	−0.117344	−	0.00245685i
$456$	1.65903e12			1.79686
$457$	−1.70051e12	−	4.55650e11i	−1.82371	−	0.488662i	−0.826478	−	0.562970i	$-0.809659\pi$
$457$	−1.70051e12	−	4.55650e11i	−1.82371	−	0.488662i	−0.997235	+	0.0743072i	$0.976325\pi$
$458$	1.47143e11	+	5.49145e11i	0.156259	+	0.583166i
$459$	−5.93342e11	−	3.42566e11i	−0.623948	−	0.360236i
$460$	−2.00055e11	+	4.28736e11i	−0.208324	+	0.446457i
$461$		−	2.10247e11i		−	0.216808i	−0.994107	−	0.108404i	$-0.965426\pi$
$461$		−	2.10247e11i		−	0.216808i	0.994107	−	0.108404i	$-0.0345741\pi$
$462$	−3.12143e11	+	2.88036e12i	−0.318760	+	2.94143i
$463$	−5.77746e11	−	5.77746e11i	−0.584282	−	0.584282i	0.351795	−	0.936077i	$-0.385571\pi$
$463$	−5.77746e11	−	5.77746e11i	−0.584282	−	0.584282i	−0.936077	+	0.351795i	$0.885571\pi$
$464$	1.44139e11	−	8.32185e10i	0.144361	−	0.0833468i
$465$	1.43979e11	+	1.65048e12i	0.142810	+	1.63709i
$466$	−2.01327e11	+	3.48709e11i	−0.197772	+	0.342552i
$467$	−5.17701e11	+	1.93209e12i	−0.503678	+	1.87975i	−0.0290241	+	0.999579i	$0.509240\pi$
$467$	−5.17701e11	+	1.93209e12i	−0.503678	+	1.87975i	−0.474654	+	0.880173i	$0.657427\pi$
$468$	−9.40375e10	+	9.40375e10i	−0.0906139	+	0.0906139i
$469$	−8.70330e11	+	7.00139e11i	−0.830627	+	0.668200i
$470$	2.26385e11	−	1.28200e12i	0.213997	−	1.21185i
$471$	−1.06230e12	−	1.83996e12i	−0.994612	−	1.72272i
$472$	1.23750e11	−	3.31587e10i	0.114764	−	0.0307509i
$473$	1.64799e12	−	4.41579e11i	1.51384	−	0.405633i
$474$	−1.02965e11	−	1.78341e11i	−0.0936891	−	0.162274i
$475$	1.67648e12	+	6.11149e11i	1.51105	+	0.550840i
$476$	2.75465e10	+	1.77631e11i	0.0245943	+	0.158595i
$477$	−1.24731e12	+	1.24731e12i	−1.10317	+	1.10317i
$478$	1.01496e11	−	3.78788e11i	0.0889249	−	0.331872i
$479$	−4.57496e11	+	7.92407e11i	−0.397080	+	0.687762i	−0.993364	−	0.115011i	$-0.963310\pi$
$479$	−4.57496e11	+	7.92407e11i	−0.397080	+	0.687762i	0.596285	+	0.802773i	$0.296643\pi$
$480$	1.21409e12	−	1.44615e12i	1.04391	−	1.24345i
$481$	1.20312e9	−	6.94624e8i	0.00102484	−	0.000591694i
$482$	−1.00211e12	−	1.00211e12i	−0.845676	−	0.845676i
$483$	−8.71286e11	−	1.97407e12i	−0.728448	−	1.65044i
$484$		−	4.85883e11i		−	0.402464i
$485$	3.34189e11	+	1.55938e11i	0.274255	+	0.127972i
$486$	1.17473e12	+	6.78229e11i	0.955155	+	0.551459i
$487$	−4.17718e11	−	1.55894e12i	−0.336513	−	1.25589i	−0.902219	−	0.431278i	$-0.858063\pi$
$487$	−4.17718e11	−	1.55894e12i	−0.336513	−	1.25589i	0.565706	−	0.824607i	$-0.308604\pi$
$488$	−1.04544e12	−	2.80124e11i	−0.834467	−	0.223595i
$489$	4.25556e12			3.36564
$490$	9.45912e11	−	1.23790e12i	0.741256	−	0.970070i
$491$	−7.42610e11			−0.576625			−0.288313	−	0.957536i	$-0.593094\pi$
$491$	−7.42610e11			−0.576625			−0.288313	+	0.957536i	$0.593094\pi$
$492$	−1.23019e12	−	3.29629e11i	−0.946521	−	0.253619i
$493$	−1.48136e10	−	5.52850e10i	−0.0112940	−	0.0421499i
$494$	−2.64177e11	−	1.52523e11i	−0.199583	−	0.115229i
$495$	−1.37116e12	−	3.77020e12i	−1.02652	−	2.82255i
$496$			1.54147e12i			1.14358i
$497$	−2.86620e10	−	6.49393e10i	−0.0210718	−	0.0477423i
$498$	−2.30858e11	−	2.30858e11i	−0.168195	−	0.168195i
$499$	1.28528e12	−	7.42055e11i	0.927992	−	0.535777i	0.0418161	−	0.999125i	$-0.486686\pi$
$499$	1.28528e12	−	7.42055e11i	0.927992	−	0.535777i	0.886176	+	0.463349i	$0.153352\pi$
$500$	5.93912e11	−	3.42296e11i	0.424969	−	0.244927i
$501$	−9.75241e11	+	1.68917e12i	−0.691580	+	1.19785i
$502$	3.58317e11	−	1.33726e12i	0.251826	−	0.939827i
$503$	−8.09255e11	+	8.09255e11i	−0.563676	+	0.563676i	−0.930350	−	0.366674i	$-0.880497\pi$
$503$	−8.09255e11	+	8.09255e11i	−0.563676	+	0.563676i	0.366674	+	0.930350i	$0.380497\pi$
$504$	3.07364e11	+	1.98201e12i	0.212186	+	1.36826i
$505$	−2.21489e11	−	3.91122e10i	−0.151545	−	0.0267609i
$506$	1.21992e12	+	2.11296e12i	0.827280	+	1.43289i
$507$	2.54557e12	−	6.82083e11i	1.71100	−	0.458460i
$508$	6.25115e11	−	1.67499e11i	0.416460	−	0.111590i
$509$	6.88887e11	+	1.19319e12i	0.454902	+	0.787913i	0.998683	−	0.0513140i	$-0.0163409\pi$
$509$	6.88887e11	+	1.19319e12i	0.454902	+	0.787913i	−0.543781	+	0.839227i	$0.683008\pi$
$510$	−6.28503e11	−	8.98078e11i	−0.411379	−	0.587825i
$511$	2.15640e12	−	1.73472e12i	1.39906	−	1.12548i
$512$	3.87415e11	−	3.87415e11i	0.249151	−	0.249151i
$513$	−1.43781e12	+	5.36598e12i	−0.916587	+	3.42075i
$514$	−1.87064e12	+	3.24005e12i	−1.18211	+	2.04747i
$515$	−2.08574e12	+	1.81948e11i	−1.30656	+	0.113976i
$516$	−1.42712e12	+	8.23945e11i	−0.886207	+	0.511652i
$517$	−1.56221e12	−	1.56221e12i	−0.961684	−	0.961684i
$518$	−2.17316e9	+	2.00533e10i	−0.00132620	+	0.0122378i
$519$		−	1.19077e12i		−	0.720402i
$520$	1.14395e11	−	4.16038e10i	0.0686109	−	0.0249527i
$521$	−1.57138e12	−	9.07237e11i	−0.934354	−	0.539450i	−0.0461681	−	0.998934i	$-0.514701\pi$
$521$	−1.57138e12	−	9.07237e11i	−0.934354	−	0.539450i	−0.888186	+	0.459484i	$0.848034\pi$
$522$	1.59124e11	+	5.93860e11i	0.0938036	+	0.350080i
$523$	2.33772e12	+	6.26391e11i	1.36627	+	0.366090i	0.866114	−	0.499847i	$-0.166610\pi$
$523$	2.33772e12	+	6.26391e11i	1.36627	+	0.366090i	0.500153	+	0.865937i	$0.333277\pi$
$524$	3.01510e9			0.00174707
$525$	−6.08001e11	+	3.06672e12i	−0.349291	+	1.76180i
$526$	1.17645e12			0.670099
$527$	5.12027e11	+	1.37197e11i	0.289165	+	0.0774815i
$528$	−1.40009e12	−	5.22520e12i	−0.783975	−	2.92584i
$529$	−1.38432e10	−	7.99240e9i	−0.00768577	−	0.00443738i
$530$	−1.46074e12	+	5.31248e11i	−0.804140	+	0.292453i
$531$			7.78920e11i			0.425175i
$532$	1.33341e12	−	5.88520e11i	0.721706	−	0.318536i
$533$	−1.72002e11	−	1.72002e11i	−0.0923125	−	0.0923125i
$534$	−5.59671e12	+	3.23126e12i	−2.97849	+	1.71963i
$535$	−2.53420e12	+	2.21069e11i	−1.33736	+	0.116664i
$536$	6.33571e11	−	1.09738e12i	0.331554	−	0.574268i
$537$	−2.60081e11	+	9.70636e11i	−0.134966	+	0.503700i
$538$	2.78036e11	−	2.78036e11i	0.143081	−	0.143081i
$539$	−8.00763e11	−	2.51974e12i	−0.408653	−	1.28590i
$540$	1.22363e12	+	1.74846e12i	0.619266	+	0.884879i
$541$	9.62586e11	+	1.66725e12i	0.483116	+	0.836782i	0.999812	−	0.0193870i	$-0.00617146\pi$
$541$	9.62586e11	+	1.66725e12i	0.483116	+	0.836782i	−0.516696	+	0.856169i	$0.672838\pi$
$542$	1.47146e10	−	3.94278e9i	0.00732408	−	0.00196248i
$543$	4.05251e12	−	1.08587e12i	2.00044	−	0.536015i
$544$	−3.02074e11	−	5.23207e11i	−0.147883	−	0.256141i
$545$	−9.22858e11	−	1.62965e11i	−0.448075	−	0.0791244i
$546$	1.93144e11	−	4.98343e11i	0.0930068	−	0.239973i
$547$	−4.72783e11	+	4.72783e11i	−0.225797	+	0.225797i	−0.810934	−	0.585137i	$-0.801041\pi$
$547$	−4.72783e11	+	4.72783e11i	−0.225797	+	0.225797i	0.585137	+	0.810934i	$0.301041\pi$
$548$	1.32703e11	−	4.95255e11i	0.0628592	−	0.234594i
$549$	3.29015e12	−	5.69871e12i	1.54576	−	2.67733i
$550$	3.09879e11	−	3.52144e12i	0.144398	−	1.64092i
$551$	−4.01907e11	+	2.32041e11i	−0.185756	+	0.107246i
$552$	1.73090e12	+	1.73090e12i	0.793497	+	0.793497i
$553$	1.51678e11	+	1.10950e11i	0.0689699	+	0.0504505i
$554$		−	3.58745e12i		−	1.61805i
$555$	−1.38347e10	−	3.80404e10i	−0.00618944	−	0.0170187i
$556$	−7.68946e11	−	4.43951e11i	−0.341239	−	0.197015i
$557$	−8.47359e11	−	3.16239e12i	−0.373009	−	1.39209i	−0.856232	−	0.516591i	$-0.827201\pi$
$557$	−8.47359e11	−	3.16239e12i	−0.373009	−	1.39209i	0.483223	−	0.875497i	$-0.339466\pi$
$558$	−5.50010e12	−	1.47375e12i	−2.40169	−	0.643530i
$559$	−3.14737e11			−0.136331
$560$	−8.11522e11	+	2.79338e12i	−0.348702	+	1.20028i
$561$	−1.86025e12			−0.792939
$562$	4.26247e11	+	1.14213e11i	0.180239	+	0.0482948i
$563$	−1.39113e11	−	5.19176e11i	−0.0583552	−	0.217785i	0.930591	−	0.366061i	$-0.119294\pi$
$563$	−1.39113e11	−	5.19176e11i	−0.0583552	−	0.217785i	−0.988946	+	0.148277i	$0.952627\pi$
$564$	1.84800e12	+	1.06694e12i	0.769035	+	0.444003i
$565$	1.92731e12	+	8.99312e11i	0.795671	+	0.371272i
$566$		−	9.69064e11i		−	0.396897i
$567$	−4.23027e12	−	4.58431e11i	−1.71887	−	0.186273i
$568$	5.69399e10	+	5.69399e10i	0.0229535	+	0.0229535i
$569$	−3.32499e12	+	1.91968e12i	−1.32979	+	0.767757i	−0.985268	−	0.171019i	$-0.945294\pi$
$569$	−3.32499e12	+	1.91968e12i	−1.32979	+	0.767757i	−0.344527	+	0.938776i	$0.611961\pi$
$570$	−5.71481e12	+	6.80716e12i	−2.26759	+	2.70103i
$571$	2.99744e11	−	5.19172e11i	0.118002	−	0.204385i	−0.800974	−	0.598699i	$-0.795685\pi$
$571$	2.99744e11	−	5.19172e11i	0.118002	−	0.204385i	0.918976	+	0.394314i	$0.129018\pi$
$572$	−5.14717e10	+	1.92095e11i	−0.0201042	+	0.0750299i
$573$	3.98708e12	−	3.98708e12i	1.54511	−	1.54511i
$574$	3.49003e12	−	5.41222e11i	1.34192	−	0.208100i
$575$	1.11148e12	+	2.38672e12i	0.424030	+	0.910535i
$576$	−4.30265e11	−	7.45241e11i	−0.162868	−	0.282095i
$577$	3.43924e11	−	9.21541e10i	0.129173	−	0.0346117i	−0.193653	−	0.981070i	$-0.562034\pi$
$577$	3.43924e11	−	9.21541e10i	0.129173	−	0.0346117i	0.322826	+	0.946458i	$0.395367\pi$
$578$	2.82558e12	−	7.57111e11i	1.05301	−	0.282153i
$579$	−1.30699e12	−	2.26377e12i	−0.483302	−	0.837103i
$580$	−3.10024e10	+	1.75564e11i	−0.0113755	+	0.0644183i
$581$	2.77802e11	+	1.07669e11i	0.101145	+	0.0392009i
$582$	−1.29886e12	+	1.29886e12i	−0.469257	+	0.469257i
$583$	−6.82721e11	+	2.54795e12i	−0.244757	+	0.913445i
$584$	−1.56979e12	+	2.71895e12i	−0.558449	+	0.967262i
$585$	6.43154e10	+	7.37273e11i	0.0227046	+	0.260272i
$586$	−1.52475e12	+	8.80317e11i	−0.534146	+	0.308390i
$587$	3.00548e12	+	3.00548e12i	1.04482	+	1.04482i	0.998947	+	0.0458757i	$0.0146078\pi$
$587$	3.00548e12	+	3.00548e12i	1.04482	+	1.04482i	0.0458757	+	0.998947i	$0.485392\pi$
$588$	1.37697e12	+	2.15062e12i	0.475036	+	0.741935i
$589$		−	4.29814e12i		−	1.47150i
$590$	−2.90224e11	+	6.21977e11i	−0.0986051	+	0.211320i
$591$	4.11028e11	+	2.37307e11i	0.138589	+	0.0800143i
$592$	−9.74752e9	−	3.63782e10i	−0.00326172	−	0.0121729i
$593$	−3.80389e12	−	1.01925e12i	−1.26323	−	0.338481i	−0.435796	−	0.900045i	$-0.643533\pi$
$593$	−3.80389e12	−	1.01925e12i	−1.26323	−	0.338481i	−0.827433	+	0.561564i	$0.810200\pi$
$594$	1.10055e13			3.62718
$595$	8.55642e11	+	5.18184e11i	0.279876	+	0.169495i
$596$	6.42233e11			0.208489
$597$	5.45576e12	+	1.46187e12i	1.75780	+	0.471002i
$598$	−1.16491e11	−	4.34749e11i	−0.0372508	−	0.139022i
$599$	−3.57690e11	−	2.06513e11i	−0.113524	−	0.0655429i	0.442163	−	0.896935i	$-0.354211\pi$
$599$	−3.57690e11	−	2.06513e11i	−0.113524	−	0.0655429i	−0.555687	+	0.831392i	$0.687545\pi$
$600$	−6.14110e11	−	3.49311e12i	−0.193449	−	1.10035i
$601$			3.97014e12i			1.24128i	0.784094	+	0.620642i	$0.213128\pi$
$601$			3.97014e12i			1.24128i	−0.784094	+	0.620642i	$0.786872\pi$
$602$	2.69793e12	−	3.68828e12i	0.837232	−	1.14456i
$603$	5.44756e12	+	5.44756e12i	1.67793	+	1.67793i
$604$	−1.71832e12	+	9.92071e11i	−0.525336	+	0.303303i
$605$	−2.07087e12	−	1.73855e12i	−0.628424	−	0.527581i
$606$	5.60146e11	−	9.70202e11i	0.168723	−	0.292237i
$607$	3.49599e11	−	1.30472e12i	0.104525	−	0.390093i	−0.893766	−	0.448534i	$-0.851946\pi$
$607$	3.49599e11	−	1.30472e12i	0.104525	−	0.390093i	0.998291	+	0.0584409i	$0.0186129\pi$
$608$	−3.46385e12	+	3.46385e12i	−1.02800	+	1.02800i
$609$	−5.09662e11	−	6.33551e11i	−0.150143	−	0.186640i
$610$	4.75056e12	−	3.32459e12i	1.38919	−	0.972196i
$611$	2.03779e11	+	3.52956e11i	0.0591528	+	0.102456i
$612$	1.19754e12	−	3.20881e11i	0.345072	−	0.0924618i
$613$	−1.61154e12	+	4.31812e11i	−0.460967	+	0.123516i	−0.481826	−	0.876267i	$-0.660026\pi$
$613$	−1.61154e12	+	4.31812e11i	−0.460967	+	0.123516i	0.0208594	+	0.999782i	$0.493360\pi$
$614$	3.25677e12	+	5.64090e12i	0.924762	+	1.60174i
$615$	−5.80669e12	+	4.06370e12i	−1.63678	+	1.14547i
$616$	1.88000e12	+	2.33699e12i	0.526072	+	0.653950i
$617$	1.57053e12	−	1.57053e12i	0.436278	−	0.436278i	−0.454479	−	0.890757i	$-0.650175\pi$
$617$	1.57053e12	−	1.57053e12i	0.436278	−	0.436278i	0.890757	+	0.454479i	$0.150175\pi$
$618$	2.69907e12	−	1.00731e13i	0.744330	−	2.77788i
$619$	2.97671e11	−	5.15581e11i	0.0814946	−	0.141153i	−0.822398	−	0.568913i	$-0.807364\pi$
$619$	2.97671e11	−	5.15581e11i	0.0814946	−	0.141153i	0.903892	+	0.427761i	$0.140697\pi$
$620$	−1.26459e12	−	1.06166e12i	−0.343707	−	0.288552i
$621$	−7.09851e12	+	4.09833e12i	−1.91538	+	1.10585i
$622$	−3.91174e12	−	3.91174e12i	−1.04788	−	1.04788i
$623$	3.48184e12	−	4.75995e12i	0.926004	−	1.26592i
$624$			9.97917e11i			0.263490i
$625$	6.66210e11	−	3.75607e12i	0.174643	−	0.984632i
$626$	4.15685e12	+	2.39996e12i	1.08188	+	0.624624i
$627$	3.90391e12	+	1.45696e13i	1.00878	+	3.76481i
$628$	2.04528e12	+	5.48031e11i	0.524729	+	0.140601i
$629$	−1.29512e10			−0.00329901
$630$	−9.19113e12	−	5.56622e12i	−2.32454	−	1.40776i
$631$	−6.75384e12			−1.69597			−0.847986	−	0.530018i	$-0.822185\pi$
$631$	−6.75384e12			−1.69597			−0.847986	+	0.530018i	$0.822185\pi$
$632$	−2.05924e11	−	5.51771e10i	−0.0513428	−	0.0137573i
$633$	2.65921e12	+	9.92431e12i	0.658319	+	2.45688i
$634$	3.06971e11	+	1.77230e11i	0.0754564	+	0.0435647i
$635$	1.52285e12	−	3.26362e12i	0.371686	−	0.796558i
$636$		−	2.54779e12i		−	0.617457i
$637$	2.23807e10	+	4.87220e11i	0.00538576	+	0.117246i
$638$	6.50103e11	+	6.50103e11i	0.155342	+	0.155342i
$639$	−4.23988e11	+	2.44790e11i	−0.100600	+	0.0580817i
$640$	−3.99313e11	−	4.57748e12i	−0.0940813	−	1.07849i
$641$	1.91135e12	−	3.31056e12i	0.447177	−	0.774534i	−0.551024	−	0.834490i	$-0.685763\pi$
$641$	1.91135e12	−	3.31056e12i	0.447177	−	0.774534i	0.998201	+	0.0599558i	$0.0190960\pi$
$642$	3.27940e12	−	1.22389e13i	0.761879	−	2.84337i
$643$	−5.09764e11	+	5.09764e11i	−0.117603	+	0.117603i	−0.763459	−	0.645856i	$-0.776501\pi$
$643$	−5.09764e11	+	5.09764e11i	−0.117603	+	0.117603i	0.645856	+	0.763459i	$0.276501\pi$
$644$	2.00518e12	+	7.77152e11i	0.459374	+	0.178041i
$645$	−1.59470e12	+	9.03065e12i	−0.362794	+	2.05447i
$646$	1.42189e12	+	2.46278e12i	0.321232	+	0.556391i
$647$	1.35920e12	−	3.64196e11i	0.304939	−	0.0817082i	−0.103105	−	0.994671i	$-0.532878\pi$
$647$	1.35920e12	−	3.64196e11i	0.304939	−	0.0817082i	0.408044	+	0.912962i	$0.366211\pi$
$648$	4.66254e12	−	1.24932e12i	1.03881	−	0.278348i
$649$	5.82397e11	+	1.00874e12i	0.128860	+	0.223192i
$650$	−2.23350e11	+	6.12685e11i	−0.0490767	+	0.134625i
$651$	7.44172e12	−	1.15404e12i	1.62390	−	0.251829i
$652$	−2.99898e12	+	2.99898e12i	−0.649920	+	0.649920i
$653$	1.17701e11	−	4.39268e11i	0.0253322	−	0.0945410i	−0.952102	−	0.305779i	$-0.901083\pi$
$653$	1.17701e11	−	4.39268e11i	0.0253322	−	0.0945410i	0.977435	+	0.211238i	$0.0677497\pi$
$654$	2.33391e12	−	4.04245e12i	0.498866	−	0.864061i
$655$	1.07884e10	−	1.28505e10i	0.00229019	−	0.00272794i
$656$	−5.71080e12	+	3.29713e12i	−1.20401	+	0.695134i
$657$	−1.34973e13	−	1.34973e13i	−2.82621	−	2.82621i
$658$	−5.88296e12	−	6.37533e11i	−1.22343	−	0.132582i
$659$			3.66191e11i			0.0756350i	0.999285	+	0.0378175i	$0.0120406\pi$
$659$			3.66191e11i			0.0756350i	−0.999285	+	0.0378175i	$0.987959\pi$
$660$	5.25093e12	+	2.45017e12i	1.07718	+	0.502629i
$661$	2.90907e12	+	1.67955e12i	0.592717	+	0.342205i	0.766171	−	0.642637i	$-0.222159\pi$
$661$	2.90907e12	+	1.67955e12i	0.592717	+	0.342205i	−0.173454	+	0.984842i	$0.555493\pi$
$662$	8.66575e11	+	3.23410e12i	0.175366	+	0.654475i
$663$	3.31476e11	+	8.88186e10i	0.0666256	+	0.0178523i
$664$	−3.37987e11			−0.0674752
$665$	2.26279e12	−	7.78887e12i	0.448691	−	1.54446i
$666$	1.39120e11			0.0274002
$667$	−6.61407e11	−	1.77224e11i	−0.129391	−	0.0346701i
$668$	−5.03118e11	−	1.87766e12i	−0.0977633	−	0.364858i
$669$	−6.01771e12	−	3.47433e12i	−1.16148	−	0.670584i
$670$	2.32019e12	+	6.37969e12i	0.444823	+	1.22310i
$671$		−	9.84017e12i		−	1.87392i
$672$	−6.92728e12	−	5.06721e12i	−1.31039	−	0.958534i
$673$	−2.59124e12	−	2.59124e12i	−0.486900	−	0.486900i	0.420426	−	0.907327i	$-0.361881\pi$
$673$	−2.59124e12	−	2.59124e12i	−0.486900	−	0.486900i	−0.907327	+	0.420426i	$0.861881\pi$
$674$	−6.09242e12	+	3.51746e12i	−1.13716	+	0.656538i
$675$	1.18304e13	+	1.04104e12i	2.19346	+	0.193020i
$676$	−1.31324e12	+	2.27459e12i	−0.241870	+	0.418932i
$677$	−2.04220e12	+	7.62159e12i	−0.373636	+	1.39443i	0.481691	+	0.876341i	$0.340023\pi$
$677$	−2.04220e12	+	7.62159e12i	−0.373636	+	1.39443i	−0.855327	+	0.518088i	$0.826644\pi$
$678$	−7.49071e12	+	7.49071e12i	−1.36141	+	1.36141i
$679$	6.05771e11	−	1.56299e12i	0.109369	−	0.282190i
$680$	−1.11750e12	−	1.97336e11i	−0.200427	−	0.0353929i
$681$	2.17284e12	+	3.76346e12i	0.387137	+	0.670542i
$682$	−8.22483e12	+	2.20384e12i	−1.45578	+	0.390076i
$683$	4.73950e12	−	1.26994e12i	0.833373	−	0.223302i	0.183188	−	0.983078i	$-0.441358\pi$
$683$	4.73950e12	−	1.26994e12i	0.833373	−	0.223302i	0.650185	+	0.759776i	$0.274692\pi$
$684$	−5.02630e12	−	8.70581e12i	−0.878003	−	1.52075i
$685$	−1.63598e12	−	2.33768e12i	−0.283904	−	0.405674i
$686$	−5.90140e12	−	3.91419e12i	−1.01741	−	0.674813i
$687$	−3.66693e12	+	3.66693e12i	−0.628055	+	0.628055i
$688$	−2.20832e12	+	8.24155e12i	−0.375762	+	1.40236i
$689$	2.43306e11	−	4.21418e11i	0.0411307	−	0.0712405i
$690$	−1.30644e13	+	1.13966e12i	−2.19416	+	0.191405i
$691$	4.35750e12	−	2.51580e12i	0.727087	−	0.419784i	−0.0902689	−	0.995917i	$-0.528773\pi$
$691$	4.35750e12	−	2.51580e12i	0.727087	−	0.419784i	0.817355	+	0.576134i	$0.195439\pi$
$692$	8.39160e11	+	8.39160e11i	0.139113	+	0.139113i
$693$	−1.66827e13	+	7.36318e12i	−2.74769	+	1.21274i
$694$			2.58417e12i			0.422867i
$695$	−4.64354e12	+	1.68878e12i	−0.754949	+	0.274563i
$696$	7.98830e11	+	4.61204e11i	0.129036	+	0.0744992i
$697$	5.86916e11	+	2.19040e12i	0.0941951	+	0.351541i
$698$	9.58186e12	+	2.56745e12i	1.52792	+	0.409405i
$699$	−3.67288e12			−0.581915
$700$	−1.73271e12	−	2.58965e12i	−0.272763	−	0.407662i
$701$	8.18508e12			1.28024			0.640120	−	0.768275i	$-0.278884\pi$
$701$	8.18508e12			1.28024			0.640120	+	0.768275i	$0.278884\pi$
$702$	−1.96105e12	−	5.25461e11i	−0.304769	−	0.0816626i
$703$	2.71793e10	+	1.01435e11i	0.00419700	+	0.0156634i
$704$	−1.11443e12	−	6.43417e11i	−0.170992	−	0.0987224i
$705$	1.11598e13	−	4.05864e12i	1.70139	−	0.618770i
$706$			5.09542e12i			0.771896i
$707$	−1.10146e11	+	1.01639e12i	−0.0165799	+	0.152994i
$708$	−7.95520e11	−	7.95520e11i	−0.118988	−	0.118988i
$709$	9.68063e12	−	5.58912e12i	1.43878	−	0.830682i	0.441019	−	0.897498i	$-0.354617\pi$
$709$	9.68063e12	−	5.58912e12i	1.43878	−	0.830682i	0.997765	+	0.0668155i	$0.0212839\pi$
$710$	−4.29768e11	+	3.74905e10i	−0.0634704	+	0.00553679i
$711$	6.48074e11	−	1.12250e12i	0.0951067	−	0.164730i
$712$	−1.73157e12	+	6.46230e12i	−0.252510	+	0.942382i
$713$	4.48432e12	−	4.48432e12i	0.649820	−	0.649820i
$714$	−3.88225e12	+	3.12308e12i	−0.559038	+	0.449720i
$715$	6.34550e11	+	9.06718e11i	0.0908005	+	0.129746i
$716$	−5.00742e11	−	8.67311e11i	−0.0712042	−	0.123329i
$717$	3.45518e12	−	9.25813e11i	0.488241	−	0.130824i
$718$	−8.68419e12	+	2.32692e12i	−1.21947	+	0.326755i
$719$	3.84045e12	+	6.65186e12i	0.535923	+	0.928246i	0.999118	+	0.0419899i	$0.0133697\pi$
$719$	3.84045e12	+	6.65186e12i	0.535923	+	0.928246i	−0.463195	+	0.886257i	$0.653297\pi$
$720$	1.97571e13	+	3.48886e12i	2.73986	+	0.483824i
$721$	1.45838e12	+	9.40422e12i	0.200984	+	1.29603i
$722$	1.00014e13	−	1.00014e13i	1.36975	−	1.36975i
$723$	3.34581e12	−	1.24867e13i	0.455386	−	1.69952i
$724$	−2.09065e12	+	3.62111e12i	−0.282786	+	0.489800i
$725$	6.37334e11	+	7.60325e11i	0.0856735	+	0.102206i
$726$	1.16636e13	−	6.73396e12i	1.55818	−	0.899613i
$727$	−5.73679e12	−	5.73679e12i	−0.761665	−	0.761665i	0.214959	−	0.976623i	$-0.431038\pi$
$727$	−5.73679e12	−	5.73679e12i	−0.761665	−	0.761665i	−0.976623	+	0.214959i	$0.931038\pi$
$728$	−2.23413e11	−	5.06186e11i	−0.0294794	−	0.0667912i
$729$		−	8.11004e11i		−	0.106353i
$730$	−5.74871e12	−	1.58069e13i	−0.749234	−	2.06012i
$731$	2.54103e12	+	1.46706e12i	0.329140	+	0.190029i
$732$	2.45989e12	+	9.18043e12i	0.316676	+	1.18185i
$733$	−1.36910e13	−	3.66849e12i	−1.75173	−	0.469374i	−0.766734	−	0.641965i	$-0.778119\pi$
$733$	−1.36910e13	−	3.66849e12i	−1.75173	−	0.469374i	−0.984994	+	0.172591i	$0.944786\pi$
$734$	6.94458e12			0.883108
$735$	1.40931e13	+	1.82647e12i	1.78120	+	0.230844i
$736$	−7.22778e12			−0.907935
$737$	1.11280e13	+	2.98174e12i	1.38936	+	0.372277i
$738$	−6.30453e12	−	2.35288e13i	−0.782347	−	2.91976i
$739$	2.60260e12	+	1.50261e12i	0.321002	+	0.185331i	0.651839	−	0.758357i	$-0.273998\pi$
$739$	2.60260e12	+	1.50261e12i	0.321002	+	0.185331i	−0.330837	+	0.943688i	$0.607331\pi$
$740$	3.65574e10	+	1.70582e10i	0.00448160	+	0.00209118i
$741$		−	2.78252e12i		−	0.339045i
$742$	2.85282e12	+	6.46361e12i	0.345507	+	0.782812i
$743$	−2.84528e12	−	2.84528e12i	−0.342512	−	0.342512i	0.514799	−	0.857311i	$-0.327866\pi$
$743$	−2.84528e12	−	2.84528e12i	−0.342512	−	0.342512i	−0.857311	+	0.514799i	$0.827866\pi$
$744$	−7.39844e12	+	4.27149e12i	−0.885241	+	0.511094i
$745$	2.29799e12	−	2.73724e12i	0.273304	−	0.325544i
$746$	8.08279e12	−	1.39998e13i	0.955512	−	1.65500i
$747$	5.31849e11	−	1.98489e12i	0.0624951	−	0.233235i
$748$	1.31096e12	−	1.31096e12i	0.153120	−	0.153120i
$749$	1.77194e12	+	1.14262e13i	0.205722	+	1.32658i
$750$	1.64479e13	+	9.51284e12i	1.89817	+	1.09783i
$751$	−7.09675e12	−	1.22919e13i	−0.814104	−	1.41007i	−0.909969	−	0.414676i	$-0.863895\pi$
$751$	−7.09675e12	−	1.22919e13i	−0.814104	−	1.41007i	0.0958650	−	0.995394i	$-0.469438\pi$
$752$	1.06722e13	−	2.85960e12i	1.21695	−	0.326080i
$753$	1.21980e13	−	3.26845e12i	1.38265	−	0.370479i
$754$	−8.48013e10	−	1.46880e11i	−0.00955502	−	0.0165498i
$755$	−1.92010e12	+	1.08733e13i	−0.215061	+	1.21787i
$756$	7.55831e12	−	6.08030e12i	0.841544	−	0.676982i
$757$	−6.28975e12	+	6.28975e12i	−0.696149	+	0.696149i	−0.963578	−	0.267429i	$-0.913826\pi$
$757$	−6.28975e12	+	6.28975e12i	−0.696149	+	0.696149i	0.267429	+	0.963578i	$0.413826\pi$
$758$	−3.51932e12	+	1.31343e13i	−0.387211	+	1.44509i
$759$	−1.11277e13	+	1.92737e13i	−1.21707	+	2.10803i
$760$	7.99624e11	+	9.16640e12i	0.0869410	+	0.996638i
$761$	−7.21097e12	+	4.16325e12i	−0.779404	+	0.449989i	−0.836219	−	0.548396i	$-0.815239\pi$
$761$	−7.21097e12	+	4.16325e12i	−0.779404	+	0.449989i	0.0568152	+	0.998385i	$0.481905\pi$
$762$	1.26844e13	+	1.26844e13i	1.36293	+	1.36293i
$763$	−4.58934e11	+	4.23491e12i	−0.0490219	+	0.452359i
$764$			5.61954e12i			0.596734i
$765$	2.91735e12	−	6.25216e12i	0.307973	−	0.660015i
$766$	−1.81711e12	−	1.04911e12i	−0.190701	−	0.110101i
$767$	−5.56136e10	−	2.07553e11i	−0.00580232	−	0.0216546i
$768$	1.96592e13	+	5.26768e12i	2.03911	+	0.546378i
$769$	−1.59724e13			−1.64703			−0.823517	−	0.567291i	$-0.807991\pi$
$769$	−1.59724e13			−1.64703			−0.823517	+	0.567291i	$0.807991\pi$
$770$	−1.60649e13	−	3.36353e11i	−1.64690	−	0.0344816i
$771$	−3.41268e13			−3.47817
$772$	2.51639e12	+	6.74264e11i	0.254976	+	0.0683206i
$773$	−4.99016e11	−	1.86235e12i	−0.0502698	−	0.187609i	0.936225	−	0.351400i	$-0.114294\pi$
$773$	−4.99016e11	−	1.86235e12i	−0.0502698	−	0.187609i	−0.986495	+	0.163791i	$0.947628\pi$
$774$	−2.72952e13	−	1.57589e13i	−2.73371	−	1.57831i
$775$	−9.04977e12	+	1.59101e12i	−0.901114	+	0.158421i
$776$			1.90160e12i			0.188253i
$777$	−1.68324e11	+	7.42927e10i	−0.0165673	+	0.00731226i
$778$	1.23904e10	+	1.23904e10i	0.00121248	+	0.00121248i
$779$	1.59236e13	−	9.19349e12i	1.54925	−	0.894462i
$780$	−8.18671e11	−	6.87299e11i	−0.0791924	−	0.0664844i
$781$	−3.66058e11	+	6.34031e11i	−0.0352063	+	0.0609791i
$782$	−1.08598e12	+	4.05294e12i	−0.103847	+	0.387561i
$783$	−2.18403e12	+	2.18403e12i	−0.207650	+	0.207650i
$784$	1.29152e13	+	2.83248e12i	1.22089	+	0.267759i
$785$	9.65404e12	−	6.75620e12i	0.907393	−	0.635022i
$786$	4.17869e10	+	7.23770e10i	0.00390516	+	0.00676393i
$787$	−5.09867e12	+	1.36619e12i	−0.473774	+	0.126947i	−0.487802	−	0.872954i	$-0.662201\pi$
$787$	−5.09867e12	+	1.36619e12i	−0.473774	+	0.126947i	0.0140283	+	0.999902i	$0.495534\pi$
$788$	−4.56895e11	+	1.22425e11i	−0.0422132	+	0.0113110i
$789$	5.36561e12	+	9.29351e12i	0.492916	+	0.853755i
$790$	9.35734e11	−	6.54856e11i	0.0854733	−	0.0598169i
$791$	3.49355e12	−	9.01393e12i	0.317302	−	0.818691i
$792$	1.46277e13	−	1.46277e13i	1.32103	−	1.32103i
$793$	−4.69823e11	+	1.75340e12i	−0.0421896	+	0.157454i
$794$	4.51163e11	−	7.81436e11i	0.0402848	−	0.0697753i
$795$	−1.08589e13	−	9.11633e12i	−0.964122	−	0.809409i
$796$	−4.87499e12	+	2.81458e12i	−0.430393	+	0.248487i
$797$	−1.17156e13	−	1.17156e13i	−1.02850	−	1.02850i	−0.999582	−	0.0289150i	$-0.990795\pi$
$797$	−1.17156e13	−	1.17156e13i	−1.02850	−	1.02850i	−0.0289150	−	0.999582i	$-0.509205\pi$
$798$	3.26073e13	+	2.38518e13i	2.84644	+	2.08213i
$799$		−	3.79946e12i		−	0.329808i
$800$	8.57535e12	+	6.01098e12i	0.740197	+	0.518849i
$801$	−3.52262e13	−	2.03378e13i	−3.02356	−	1.74565i
$802$	6.21554e12	+	2.31967e13i	0.530510	+	1.97989i
$803$	−2.75717e13	−	7.38781e12i	−2.34015	−	0.627041i
$804$	−1.11273e13			−0.939157
$805$	1.04871e13	−	5.76545e12i	0.880182	−	0.483895i
$806$	1.57079e12			0.131102
$807$	3.46445e12	+	9.28296e11i	0.287543	+	0.0770470i
$808$	−3.00171e11	−	1.12025e12i	−0.0247752	−	0.0924625i
$809$	1.05323e13	+	6.08081e12i	0.864478	+	0.499107i	0.865509	−	0.500893i	$-0.166995\pi$
$809$	1.05323e13	+	6.08081e12i	0.864478	+	0.499107i	−0.00103132	+	0.999999i	$0.500328\pi$
$810$	−1.09348e13	+	2.34343e13i	−0.892541	+	1.91280i
$811$			1.13315e13i			0.919802i	0.887970	+	0.459901i	$0.152115\pi$
$811$			1.13315e13i			0.919802i	−0.887970	+	0.459901i	$0.847885\pi$
$812$	8.05646e11	+	8.73073e10i	0.0650342	+	0.00704771i
$813$	9.82574e10	+	9.82574e10i	0.00788784	+	0.00788784i
$814$	1.80167e11	−	1.04020e11i	0.0143835	−	0.00830434i
$815$	2.05110e12	+	2.35126e13i	0.162846	+	1.86677i
$816$	4.65153e12	−	8.05669e12i	0.367274	−	0.636137i
$817$	6.15752e12	−	2.29802e13i	0.483511	−	1.80449i
$818$	−1.13616e13	+	1.13616e13i	−0.887254	+	0.887254i
$819$	3.32422e12	−	5.15510e11i	0.258174	−	0.0400368i
$820$	1.22832e12	−	6.95587e12i	0.0948743	−	0.537265i
$821$	2.34601e12	+	4.06342e12i	0.180213	+	0.312138i	0.941953	−	0.335745i	$-0.108988\pi$
$821$	2.34601e12	+	4.06342e12i	0.180213	+	0.312138i	−0.761740	+	0.647883i	$0.775655\pi$
$822$	1.37277e13	−	3.67833e12i	1.04876	−	0.281014i
$823$	−6.44133e12	+	1.72595e12i	−0.489414	+	0.131138i	−0.495083	−	0.868846i	$-0.664862\pi$
$823$	−6.44133e12	+	1.72595e12i	−0.489414	+	0.131138i	0.00566879	+	0.999984i	$0.498196\pi$
$824$	−5.39795e12	−	9.34952e12i	−0.407902	−	0.706508i
$825$	2.92313e13	−	1.36128e13i	2.19688	−	1.02307i
$826$	2.90895e12	+	1.12743e12i	0.217434	+	0.0842713i
$827$	−1.05407e13	+	1.05407e13i	−0.783598	+	0.783598i	−0.980436	−	0.196838i	$-0.936933\pi$
$827$	−1.05407e13	+	1.05407e13i	−0.783598	+	0.783598i	0.196838	+	0.980436i	$0.436933\pi$
$828$	3.83889e12	−	1.43269e13i	0.283837	−	1.05929i
$829$	4.55725e11	−	7.89339e11i	0.0335125	−	0.0580454i	−0.848783	−	0.528742i	$-0.822664\pi$
$829$	4.55725e11	−	7.89339e11i	0.0335125	−	0.0580454i	0.882295	+	0.470696i	$0.155997\pi$
$830$	1.16425e12	−	1.38679e12i	0.0851522	−	0.101428i
$831$	2.83394e13	−	1.63618e13i	2.06151	−	1.19022i
$832$	1.67858e11	+	1.67858e11i	0.0121447	+	0.0121447i
$833$	2.09036e12	−	4.03790e12i	0.150424	−	0.290571i
$834$		−	2.46113e13i		−	1.76152i
$835$	−9.80295e12	−	4.57420e12i	−0.697859	−	0.325631i
$836$	−1.30186e13	−	7.51631e12i	−0.921801	−	0.532202i
$837$	−7.40382e12	−	2.76314e13i	−0.521425	−	1.94598i
$838$	2.19511e13	+	5.88179e12i	1.53765	+	0.412013i
$839$	1.03641e13			0.722106			0.361053	−	0.932545i	$-0.382417\pi$
$839$	1.03641e13			0.722106			0.361053	+	0.932545i	$0.382417\pi$
$840$	−1.56558e13	+	3.84561e12i	−1.08497	+	0.266507i
$841$	1.42491e13			0.982214
$842$	−2.08502e13	−	5.58678e12i	−1.42957	−	0.383052i
$843$	1.04181e12	+	3.88809e12i	0.0710501	+	0.265162i
$844$	−8.86786e12	−	5.11986e12i	−0.601558	−	0.347310i
$845$	4.99553e12	+	1.37359e13i	0.337075	+	0.926833i
$846$			4.08130e13i			2.73925i
$847$	−7.25618e12	+	9.91977e12i	−0.484432	+	0.662257i
$848$	−9.32793e12	−	9.32793e12i	−0.619447	−	0.619447i
$849$	7.65522e12	−	4.41974e12i	0.505677	−	0.291953i
$850$	4.65909e12	−	3.90543e12i	0.306137	−	0.256616i
$851$	−7.74717e10	+	1.34185e11i	−0.00506361	+	0.00877042i
$852$	1.83018e11	−	6.83031e11i	0.0118991	−	0.0444081i
$853$	−1.01038e13	+	1.01038e13i	−0.653450	+	0.653450i	−0.953822	−	0.300372i	$-0.902889\pi$
$853$	−1.01038e13	+	1.01038e13i	−0.653450	+	0.653450i	0.300372	+	0.953822i	$0.402889\pi$
$854$	−1.65202e13	−	2.05359e13i	−1.06281	−	1.32115i
$855$	−5.50895e13	−	9.72811e12i	−3.52550	−	0.622560i
$856$	−6.55857e12	−	1.13598e13i	−0.417520	−	0.723165i
$857$	2.43877e13	−	6.53466e12i	1.54439	−	0.413818i	0.616708	−	0.787192i	$-0.288466\pi$
$857$	2.43877e13	−	6.53466e12i	1.54439	−	0.413818i	0.927681	+	0.373374i	$0.121799\pi$
$858$	−5.32458e12	+	1.42672e12i	−0.335423	+	0.0898763i
$859$	−3.20319e12	−	5.54809e12i	−0.200731	−	0.347676i	0.748033	−	0.663661i	$-0.230998\pi$
$859$	−3.20319e12	−	5.54809e12i	−0.200731	−	0.347676i	−0.948764	+	0.315985i	$0.897665\pi$
$860$	−5.24026e12	−	7.48789e12i	−0.326670	−	0.466785i
$861$	2.01929e13	+	2.51014e13i	1.25223	+	1.55662i
$862$	1.28182e13	−	1.28182e13i	0.790760	−	0.790760i
$863$	−6.10544e12	+	2.27858e13i	−0.374687	+	1.39835i	0.479114	+	0.877752i	$0.340958\pi$
$863$	−6.10544e12	+	2.27858e13i	−0.374687	+	1.39835i	−0.853801	+	0.520599i	$0.825709\pi$
$864$	−1.63014e13	+	2.82348e13i	−0.995203	+	1.72374i
$865$	6.57918e12	−	5.73930e11i	0.399576	−	0.0348567i
$866$	1.12486e13	−	6.49438e12i	0.679622	−	0.392380i
$867$	1.88679e13	+	1.88679e13i	1.13406	+	1.13406i
$868$	−4.43105e12	+	6.05760e12i	−0.264953	+	0.362211i
$869$		−	1.93825e12i		−	0.115298i
$870$	−4.64406e12	+	1.68897e12i	−0.274828	+	0.0999507i
$871$	−1.84052e12	−	1.06262e12i	−0.108357	−	0.0625601i
$872$	−1.25069e12	−	4.66765e12i	−0.0732533	−	0.273385i
$873$	−1.11675e13	−	2.99232e12i	−0.650716	−	0.174359i
$874$	3.40218e13			1.97222
$875$	−1.72371e13	−	1.88119e12i	−0.994097	−	0.108492i
$876$	2.75700e13			1.58186
$877$	−2.35913e13	−	6.32126e12i	−1.34664	−	0.360832i	−0.487749	−	0.872984i	$-0.662182\pi$
$877$	−2.35913e13	−	6.32126e12i	−1.34664	−	0.360832i	−0.858895	+	0.512151i	$0.828849\pi$
$878$	3.39070e12	+	1.26543e13i	0.192559	+	0.718640i
$879$	−1.39083e13	−	8.02996e12i	−0.785822	−	0.453694i
$880$	2.81952e13	−	1.02541e13i	1.58490	−	0.576404i
$881$		−	2.77532e13i		−	1.55211i	−0.630668	−	0.776053i	$-0.717219\pi$
$881$		−	2.77532e13i		−	1.55211i	0.630668	−	0.776053i	$-0.282781\pi$
$882$	−2.24542e13	+	4.33743e13i	−1.24937	+	2.41337i
$883$	2.19556e12	+	2.19556e12i	0.121541	+	0.121541i	0.765261	−	0.643720i	$-0.222610\pi$
$883$	2.19556e12	+	2.19556e12i	0.121541	+	0.121541i	−0.643720	+	0.765261i	$0.722610\pi$
$884$	−2.96190e11	+	1.71005e11i	−0.0163130	+	0.00941834i
$885$	−6.23703e12	+	5.44083e11i	−0.341770	+	0.0298140i
$886$	6.68014e12	−	1.15703e13i	0.364195	−	0.630804i
$887$	−4.35833e12	+	1.62655e13i	−0.236409	+	0.882291i	0.741100	+	0.671395i	$0.234305\pi$
$887$	−4.35833e12	+	1.62655e13i	−0.236409	+	0.882291i	−0.977509	+	0.210895i	$0.932362\pi$
$888$	1.47590e11	−	1.47590e11i	0.00796522	−	0.00796522i
$889$	−1.52638e13	−	5.91582e12i	−0.819604	−	0.317656i
$890$	−2.05507e13	−	2.93652e13i	−1.09792	−	1.56884i
$891$	2.19430e13	+	3.80065e13i	1.16640	+	2.02026i
$892$	6.68923e12	−	1.79237e12i	0.353781	−	0.0947952i
$893$	−2.97575e13	+	7.97350e12i	−1.56590	+	0.419583i
$894$	8.90085e12	+	1.54167e13i	0.466029	+	0.807185i
$895$	−5.48826e12	−	9.69157e11i	−0.285911	−	0.0504883i
$896$	−2.06390e13	+	3.20063e12i	−1.06980	+	0.165901i
$897$	2.90305e12	−	2.90305e12i	0.149723	−	0.149723i
$898$	2.21344e12	−	8.26067e12i	0.113586	−	0.423908i
$899$	1.19486e12	−	2.06957e12i	0.0610099	−	0.105672i
$900$	−1.64696e13	+	1.38055e13i	−0.836743	+	0.701391i
$901$	−3.92866e12	+	2.26821e12i	−0.198602	+	0.114663i
$902$	−2.57572e13	−	2.57572e13i	−1.29559	−	1.29559i
$903$	4.14407e13	+	4.49090e12i	2.07411	+	0.224770i
$904$			1.09668e13i			0.546161i
$905$	7.95280e12	+	2.18673e13i	0.394096	+	1.08362i
$906$	−4.76291e13	−	2.74987e13i	−2.34853	−	1.35592i
$907$	−5.03647e12	−	1.87964e13i	−0.247112	−	0.922233i	−0.972310	−	0.233694i	$-0.924919\pi$
$907$	−5.03647e12	−	1.87964e13i	−0.247112	−	0.922233i	0.725199	−	0.688540i	$-0.241748\pi$
$908$	−4.18343e12	−	1.12095e12i	−0.204243	−	0.0547266i
$909$	7.05122e12			0.342552
$910$	2.84651e12	+	8.26958e11i	0.137603	+	0.0399758i
$911$	3.54027e13			1.70296			0.851478	−	0.524391i	$-0.175707\pi$
$911$	3.54027e13			1.70296			0.851478	+	0.524391i	$0.175707\pi$
$912$	−7.28619e13	−	1.95233e13i	−3.48758	−	0.934493i
$913$	−7.95326e11	−	2.96820e12i	−0.0378814	−	0.141375i
$914$	4.21179e13	+	2.43168e13i	1.99622	+	1.15252i
$915$	4.79294e13	+	2.23646e13i	2.26052	+	1.05479i
$916$		−	5.16832e12i		−	0.242560i
$917$	−6.15561e10	−	4.50275e10i	−0.00287481	−	0.00210288i
$918$	1.33832e13	+	1.33832e13i	0.621968	+	0.621968i
$919$	1.65755e13	−	9.56984e12i	0.766559	−	0.442573i	−0.0650868	−	0.997880i	$-0.520732\pi$
$919$	1.65755e13	−	9.56984e12i	0.766559	−	0.442573i	0.831646	+	0.555307i	$0.187399\pi$
$920$	−8.72919e12	+	1.03977e13i	−0.401725	+	0.478512i
$921$	−2.97072e13	+	5.14544e13i	−1.36049	+	2.35643i
$922$	−1.50323e12	+	5.61015e12i	−0.0685074	+	0.255673i
$923$	9.54993e10	−	9.54993e10i	0.00433105	−	0.00433105i
$924$	9.51814e12	−	2.45583e13i	0.429564	−	1.10835i
$925$	2.03511e11	−	9.47735e10i	0.00914007	−	0.00425646i
$926$	1.12855e13	+	1.95471e13i	0.504398	+	0.873642i
$927$	6.34007e13	−	1.69882e13i	2.81991	−	0.755593i
$928$	−2.63079e12	+	7.04918e11i	−0.116445	+	0.0312013i
$929$	−1.01830e13	−	1.76375e13i	−0.448544	−	0.776901i	0.549748	−	0.835331i	$-0.314724\pi$
$929$	−1.01830e13	−	1.76375e13i	−0.448544	−	0.776901i	−0.998292	+	0.0584301i	$0.981391\pi$
$930$	7.95884e12	−	4.50703e13i	0.348880	−	1.97568i
$931$	−3.60118e13	−	7.89789e12i	−1.57098	−	0.344538i
$932$	2.58835e12	−	2.58835e12i	0.112370	−	0.112370i
$933$	1.30604e13	−	4.87420e13i	0.564272	−	2.10589i
$934$	2.76282e13	−	4.78535e13i	1.18793	−	2.05756i
$935$	−8.96608e11	−	1.02782e13i	−0.0383664	−	0.439809i
$936$	−3.30489e12	+	1.90808e12i	−0.140739	+	0.0812559i
$937$	−1.32739e12	−	1.32739e12i	−0.0562561	−	0.0562561i	0.678419	−	0.734675i	$-0.262665\pi$
$937$	−1.32739e12	−	1.32739e12i	−0.0562561	−	0.0562561i	−0.734675	+	0.678419i	$0.762665\pi$
$938$	2.82294e13	−	1.24595e13i	1.19066	−	0.525518i
$939$			4.37832e13i			1.83786i
$940$	−5.00432e12	+	1.07247e13i	−0.209059	+	0.448034i
$941$	1.35281e13	+	7.81045e12i	0.562449	+	0.324730i	0.754128	−	0.656727i	$-0.228060\pi$
$941$	1.35281e13	+	7.81045e12i	0.562449	+	0.324730i	−0.191679	+	0.981458i	$0.561393\pi$
$942$	1.51906e13	+	5.66920e13i	0.628558	+	2.34581i
$943$	2.62051e13	+	7.02162e12i	1.07915	+	0.289158i
$944$	−5.82509e12			−0.238742
$945$	1.12998e12	−	5.39701e13i	0.0460924	−	2.20146i
$946$	−4.71316e13			−1.91338
$947$	1.94176e13	+	5.20292e12i	0.784549	+	0.210219i	0.628789	−	0.777576i	$-0.283551\pi$
$947$	1.94176e13	+	5.20292e12i	0.784549	+	0.210219i	0.155760	+	0.987795i	$0.450217\pi$
$948$	4.84533e11	+	1.80830e12i	0.0194844	+	0.0727166i
$949$	4.56022e12	+	2.63284e12i	0.182510	+	0.105372i
$950$	−4.03650e13	−	2.82942e13i	−1.60786	−	1.12705i
$951$			3.23327e12i			0.128183i
$952$	−5.55727e11	+	5.12808e12i	−0.0219278	+	0.202343i
$953$	1.42393e13	+	1.42393e13i	0.559203	+	0.559203i	0.929081	−	0.369877i	$-0.120600\pi$
$953$	1.42393e13	+	1.42393e13i	0.559203	+	0.559203i	−0.369877	+	0.929081i	$0.620600\pi$
$954$	4.22009e13	−	2.43647e13i	1.64951	−	0.952343i
$955$	2.39509e13	+	2.01075e13i	0.931764	+	0.782244i
$956$	−1.78250e12	+	3.08737e12i	−0.0690189	+	0.119544i
$957$	−2.17054e12	+	8.10057e12i	−0.0836497	+	0.312185i
$958$	1.78732e13	−	1.78732e13i	0.685580	−	0.685580i
$959$	−1.01054e13	+	8.12933e12i	−0.385807	+	0.310364i
$960$	5.66681e12	−	3.96581e12i	0.215337	−	0.150699i
$961$	−2.15346e12	−	3.72990e12i	−0.0814481	−	0.141072i
$962$	−3.70701e10	+	9.93291e9i	−0.00139552	+	0.000373929i
$963$	7.70325e13	−	2.06408e13i	2.88640	−	0.773408i
$964$	6.44180e12	+	1.11575e13i	0.240248	+	0.416122i
$965$	1.18777e13	−	8.31240e12i	0.440920	−	0.308570i
$966$	9.13477e12	+	5.89048e13i	0.337521	+	2.17647i
$967$	−3.17352e13	+	3.17352e13i	−1.16714	+	1.16714i	−0.184259	+	0.982878i	$0.558988\pi$
$967$	−3.17352e13	+	3.17352e13i	−1.16714	+	1.16714i	−0.982878	+	0.184259i	$0.941012\pi$
$968$	3.60859e12	−	1.34675e13i	0.132099	−	0.493000i
$969$	−1.29700e13	+	2.24647e13i	−0.472589	+	0.818548i
$970$	−7.80244e12	−	6.55039e12i	−0.282981	−	0.237571i
$971$	−8.52507e11	+	4.92195e11i	−0.0307760	+	0.0177685i	−0.515309	−	0.857004i	$-0.672323\pi$
$971$	−8.52507e11	+	4.92195e11i	−0.0307760	+	0.0177685i	0.484533	+	0.874773i	$0.338990\pi$
$972$	−8.71962e12	−	8.71962e12i	−0.313328	−	0.313328i
$973$	9.06881e12	+	2.05471e13i	0.324371	+	0.734926i
$974$			4.45848e13i			1.58735i
$975$	−5.85863e12	+	1.02998e12i	−0.207623	+	0.0365014i
$976$	4.26174e13	+	2.46052e13i	1.50336	+	0.867965i
$977$	3.99203e11	+	1.48984e12i	0.0140174	+	0.0523137i	0.972580	−	0.232567i	$-0.0747126\pi$
$977$	3.99203e11	+	1.48984e12i	0.0140174	+	0.0523137i	−0.958563	+	0.284881i	$0.908046\pi$
$978$	−1.13554e14	−	3.04266e13i	−3.96896	−	1.06348i
$979$	−6.08263e13			−2.11626
$980$	−1.12188e13	+	8.64452e12i	−0.388535	+	0.299380i
$981$	2.93796e13			1.01283
$982$	1.98155e13	+	5.30955e12i	0.679991	+	0.182203i
$983$	−6.83314e11	−	2.55016e12i	−0.0233415	−	0.0871118i	0.953273	−	0.302112i	$-0.0976915\pi$
$983$	−6.83314e11	−	2.55016e12i	−0.0233415	−	0.0871118i	−0.976614	+	0.215000i	$0.931025\pi$
$984$	−3.16497e13	−	1.82730e13i	−1.07620	−	0.621343i
$985$	−1.11305e12	+	2.38537e12i	−0.0376748	+	0.0807407i
$986$			1.58112e12i			0.0532743i
$987$	−2.17950e13	−	4.93808e13i	−0.731020	−	1.65627i
$988$	1.96090e12	+	1.96090e12i	0.0654710	+	0.0654710i
$989$	3.03998e13	−	1.75513e13i	1.01039	−	0.583347i
$990$	9.63119e12	+	1.10406e14i	0.318656	+	3.65287i
$991$	3.23609e12	−	5.60507e12i	0.106583	−	0.184608i	−0.807801	−	0.589456i	$-0.799342\pi$
$991$	3.23609e12	−	5.60507e12i	0.106583	−	0.184608i	0.914384	+	0.404848i	$0.132676\pi$
$992$	6.52867e12	−	2.43653e13i	0.214053	−	0.798858i
$993$	−2.15958e13	+	2.15958e13i	−0.704852	+	0.704852i
$994$	3.00499e11	+	1.93774e12i	0.00976347	+	0.0629589i
$995$	−5.44745e12	+	3.08484e13i	−0.176193	+	0.997768i
$996$	1.48401e12	+	2.57037e12i	0.0477825	+	0.0827616i
$997$	5.30560e13	−	1.42163e13i	1.70061	−	0.455678i	0.727521	−	0.686086i	$-0.240673\pi$
$997$	5.30560e13	−	1.42163e13i	1.70061	−	0.455678i	0.973094	+	0.230407i	$0.0740059\pi$
$998$	−3.96014e13	+	1.06112e13i	−1.26364	+	0.338591i
$999$	3.49455e11	+	6.05274e11i	0.0111006	+	0.0192268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.k.a.3.8	✓	136
5.2	odd	4	inner	35.10.k.a.17.27	yes	136
7.5	odd	6	inner	35.10.k.a.33.27	yes	136
35.12	even	12	inner	35.10.k.a.12.8	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.k.a.3.8	✓	136	1.1	even	1	trivial
35.10.k.a.12.8	yes	136	35.12	even	12	inner
35.10.k.a.17.27	yes	136	5.2	odd	4	inner
35.10.k.a.33.27	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+(-26.6836 - 7.14985i) q^{2} +(-65.2186 - 243.399i) q^{3} +(217.489 + 125.567i) q^{4} +(1313.38 - 477.656i) q^{5} +6961.07i q^{6} +(-2565.03 - 5811.56i) q^{7} +(5095.68 + 5095.68i) q^{8} +(-37943.7 + 21906.8i) q^{9} +(-38460.9 + 3355.11i) q^{10} +(-32759.3 + 56740.8i) q^{11} +(16378.6 - 61125.9i) q^{12} +(8546.45 - 8546.45i) q^{13} +(26892.3 + 173413. i) q^{14} +(-201918. - 288524. i) q^{15} +(-163828. - 283759. i) q^{16} +(-108837. + 29162.7i) q^{17} +(1.16910e6 - 313260. i) q^{18} +(456807. + 791214. i) q^{19} +(345624. + 61032.8i) q^{20} +(-1.24724e6 + 1.00335e6i) q^{21} +(1.27983e6 - 1.27983e6i) q^{22} +(-348891. + 1.30208e6i) q^{23} +(907950. - 1.57262e6i) q^{24} +(1.49681e6 - 1.25469e6i) q^{25} +(-289156. + 166944. i) q^{26} +(4.29960e6 + 4.29960e6i) q^{27} +(171877. - 1.58603e6i) q^{28} +507962. i q^{29} +(3.32499e6 + 9.14253e6i) q^{30} +(-4.07425e6 - 2.35227e6i) q^{31} +(1.38774e6 + 5.17911e6i) q^{32} +(1.59472e7 + 4.27304e6i) q^{33} +3.11267e6 q^{34} +(-6.14478e6 - 6.40760e6i) q^{35} -1.10031e7 q^{36} +(111026. + 29749.2i) q^{37} +(-6.53221e6 - 2.43785e7i) q^{38} +(-2.63758e6 - 1.52281e6i) q^{39} +(9.12655e6 + 4.25859e6i) q^{40} -2.01255e7i q^{41} +(4.04547e7 - 1.78553e7i) q^{42} +(-1.84133e7 - 1.84133e7i) q^{43} +(-1.42496e7 + 8.22701e6i) q^{44} +(-3.93706e7 + 4.68960e7i) q^{45} +(1.86193e7 - 3.22497e7i) q^{46} +(-8.72742e6 + 3.25712e7i) q^{47} +(-5.83820e7 + 5.83820e7i) q^{48} +(-2.71949e7 + 2.98136e7i) q^{49} +(-4.89112e7 + 2.27776e7i) q^{50} +(1.41964e7 + 2.45888e7i) q^{51} +(2.93191e6 - 785604. i) q^{52} +(3.88889e7 - 1.04202e7i) q^{53} +(-8.39872e7 - 1.45470e8i) q^{54} +(-1.59229e7 + 9.01700e7i) q^{55} +(1.65433e7 - 4.26844e7i) q^{56} +(1.62788e8 - 1.62788e8i) q^{57} +(3.63185e6 - 1.35543e7i) q^{58} +(8.88903e6 - 1.53962e7i) q^{59} +(-7.68577e6 - 8.81050e7i) q^{60} +(-1.30067e8 + 7.50944e7i) q^{61} +(9.18973e7 + 9.18973e7i) q^{62} +(2.24639e8 + 1.64320e8i) q^{63} +1.96407e7i q^{64} +(7.14248e6 - 1.53070e7i) q^{65} +(-3.94977e8 - 2.28040e8i) q^{66} +(-4.55098e7 - 1.69845e8i) q^{67} +(-2.73327e7 - 7.32378e6i) q^{68} +3.39679e8 q^{69} +(1.18152e8 + 2.14912e8i) q^{70} +1.11742e7 q^{71} +(-3.04979e8 - 8.17188e7i) q^{72} +(1.12759e8 + 4.20822e8i) q^{73} +(-2.74986e6 - 1.58763e6i) q^{74} +(-4.03010e8 - 2.82494e8i) q^{75} +2.29440e8i q^{76} +(4.13781e8 + 4.48412e7i) q^{77} +(5.94924e7 + 5.94924e7i) q^{78} +(-2.56198e7 + 1.47916e7i) q^{79} +(-3.50708e8 - 2.94430e8i) q^{80} +(3.34913e8 - 5.80086e8i) q^{81} +(-1.43895e8 + 5.37022e8i) q^{82} +(-3.31641e7 + 3.31641e7i) q^{83} +(-3.97249e8 + 6.16041e7i) q^{84} +(-1.29014e8 + 9.02884e7i) q^{85} +(3.59681e8 + 6.22985e8i) q^{86} +(1.23638e8 - 3.31286e7i) q^{87} +(-4.56064e8 + 1.22202e8i) q^{88} +(4.64190e8 + 8.04001e8i) q^{89} +(1.38585e9 - 9.69859e8i) q^{90} +(-7.15901e7 - 2.77464e7i) q^{91} +(-2.39379e8 + 2.39379e8i) q^{92} +(-3.06824e8 + 1.14508e9i) q^{93} +(4.65758e8 - 8.06717e8i) q^{94} +(9.77890e8 + 8.20968e8i) q^{95} +(1.17008e9 - 6.75548e8i) q^{96} +(1.86590e8 + 1.86590e8i) q^{97} +(9.38820e8 - 6.01095e8i) q^{98} -2.87061e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) 136 * q - 2 * q^2 - 6 * q^3 - 1710 * q^5 + 5940 * q^7 - 3484 * q^8 + 153786 * q^10 - 87752 * q^11 + 3066 * q^12 - 318872 * q^15 + 3132804 * q^16 - 1578678 * q^17 - 239036 * q^18 - 5745396 * q^21 + 2132088 * q^22 + 312550 * q^23 + 4308518 * q^25 + 2294580 * q^26 - 9559382 * q^28 + 21412708 * q^30 + 8900220 * q^31 + 17154282 * q^32 - 13729410 * q^33 + 6034552 * q^35 - 114903056 * q^36 + 26817310 * q^37 - 20958672 * q^38 + 143985558 * q^40 - 38052106 * q^42 + 46427728 * q^43 - 96332286 * q^45 + 2421124 * q^46 + 147698754 * q^47 - 11742092 * q^50 - 138178540 * q^51 - 126665976 * q^52 - 16288570 * q^53 + 501495076 * q^56 - 71567164 * q^57 - 681848346 * q^58 + 254653694 * q^60 - 575844240 * q^61 + 491512776 * q^63 + 833960586 * q^65 + 260439612 * q^66 + 22092746 * q^67 - 2824755312 * q^68 - 1044240840 * q^70 + 355056144 * q^71 + 98662792 * q^72 + 1852831146 * q^73 + 2937834474 * q^75 + 1226263510 * q^77 + 2595615712 * q^78 - 3778385244 * q^80 + 1504403888 * q^81 - 3707543946 * q^82 - 1726556112 * q^85 + 1771746456 * q^86 + 30331668 * q^87 - 1182712628 * q^88 - 4378590056 * q^91 + 2593806924 * q^92 - 4305536726 * q^93 + 861804818 * q^95 + 15624596040 * q^96 + 5117393178 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more