LMFDB - Embedded newform 16.28.e.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,28,Mod(5,16)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 28, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$N$	$=$	$16 = 2^{4}$
Weight:	$k$	$=$	$28$
Character orbit:	$[\chi]$	$=$	16.e (of order $4$ , degree $2$ , 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:	$73.8968919741$
Analytic rank:	$0$
Dimension:	$106$
Relative dimension:	$53$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	16.13
Dual form			16.28.e.a.5.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10946.6 - 3793.44i) q^{2} +(2.44645e6 + 2.44645e6i) q^{3} +(1.05437e8 + 8.30503e7i) q^{4} +(-2.13207e9 + 2.13207e9i) q^{5} +(-1.74998e10 - 3.60607e10i) q^{6} +9.04455e10i q^{7} +(-8.39133e11 - 1.30909e12i) q^{8} +4.34460e12i q^{9} +(3.14268e13 - 1.52510e13i) q^{10} +(-6.81338e13 + 6.81338e13i) q^{11} +(5.47690e13 + 4.61125e14i) q^{12} +(1.50710e14 + 1.50710e14i) q^{13} +(3.43099e14 - 9.90069e14i) q^{14} -1.04320e16 q^{15} +(4.21970e15 + 1.75132e16i) q^{16} +2.51269e16 q^{17} +(1.64810e16 - 4.75585e16i) q^{18} +(-2.25187e17 - 2.25187e17i) q^{19} +(-4.01869e17 + 4.77310e16i) q^{20} +(-2.21270e17 + 2.21270e17i) q^{21} +(1.00429e18 - 4.87371e17i) q^{22} -4.22469e18i q^{23} +(1.14972e18 - 5.25550e18i) q^{24} -1.64087e18i q^{25} +(-1.07805e18 - 2.22146e18i) q^{26} +(8.02678e18 - 8.02678e18i) q^{27} +(-7.51153e18 + 9.53634e18i) q^{28} +(-9.32745e18 - 9.32745e18i) q^{29} +(1.14195e20 + 3.95731e19i) q^{30} -1.43082e20 q^{31} +(2.02439e19 - 2.07717e20i) q^{32} -3.33371e20 q^{33} +(-2.75054e20 - 9.53174e19i) q^{34} +(-1.92836e20 - 1.92836e20i) q^{35} +(-3.60820e20 + 4.58084e20i) q^{36} +(2.39977e20 - 2.39977e20i) q^{37} +(1.61080e21 + 3.31926e21i) q^{38} +7.37406e20i q^{39} +(4.58016e21 + 1.00197e21i) q^{40} +5.71746e21i q^{41} +(3.26152e21 - 1.58278e21i) q^{42} +(-7.05720e21 + 7.05720e21i) q^{43} +(-1.28424e22 + 1.52532e21i) q^{44} +(-9.26300e21 - 9.26300e21i) q^{45} +(-1.60261e22 + 4.62460e22i) q^{46} +1.95092e21 q^{47} +(-3.25219e22 + 5.31684e22i) q^{48} +5.75320e22 q^{49} +(-6.22455e21 + 1.79620e22i) q^{50} +(6.14717e22 + 6.14717e22i) q^{51} +(3.37396e21 + 2.84069e22i) q^{52} +(-2.12669e22 + 2.12669e22i) q^{53} +(-1.18315e23 + 5.74167e22i) q^{54} -2.90532e23i q^{55} +(1.18401e23 - 7.58959e22i) q^{56} -1.10182e24i q^{57} +(6.67206e22 + 1.37487e23i) q^{58} +(7.19309e23 - 7.19309e23i) q^{59} +(-1.09992e24 - 8.66380e23i) q^{60} +(-1.15821e23 - 1.15821e23i) q^{61} +(1.56626e24 + 5.42774e23i) q^{62} -3.92950e23 q^{63} +(-1.00956e24 + 2.19700e24i) q^{64} -6.42647e23 q^{65} +(3.64928e24 + 1.26462e24i) q^{66} +(-3.93728e24 - 3.93728e24i) q^{67} +(2.64932e24 + 2.08680e24i) q^{68} +(1.03355e25 - 1.03355e25i) q^{69} +(1.37939e24 + 2.84241e24i) q^{70} +1.48813e25i q^{71} +(5.68746e24 - 3.64570e24i) q^{72} -1.52409e25i q^{73} +(-3.53726e24 + 1.71659e24i) q^{74} +(4.01431e24 - 4.01431e24i) q^{75} +(-5.04130e24 - 4.24450e25i) q^{76} +(-6.16240e24 - 6.16240e24i) q^{77} +(2.79730e24 - 8.07207e24i) q^{78} -9.50108e24 q^{79} +(-4.63361e25 - 2.83427e25i) q^{80} +7.24044e25 q^{81} +(2.16888e25 - 6.25866e25i) q^{82} +(6.35431e25 + 6.35431e25i) q^{83} +(-4.17067e25 + 4.95361e24i) q^{84} +(-5.35724e25 + 5.35724e25i) q^{85} +(1.04023e26 - 5.04812e25i) q^{86} -4.56382e25i q^{87} +(1.46366e26 + 3.20197e25i) q^{88} +1.03442e26i q^{89} +(6.62596e25 + 1.36537e26i) q^{90} +(-1.36310e25 + 1.36310e25i) q^{91} +(3.50862e26 - 4.45441e26i) q^{92} +(-3.50044e26 - 3.50044e26i) q^{93} +(-2.13558e25 - 7.40067e24i) q^{94} +9.60231e26 q^{95} +(5.57694e26 - 4.58643e26i) q^{96} -4.37385e26 q^{97} +(-6.29778e26 - 2.18244e26i) q^{98} +(-2.96014e26 - 2.96014e26i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100})$ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$ .

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−10946.6	−	3793.44i	−0.944873	−	0.327437i
$2$	−10946.6	−	3793.44i	−0.944873	−	0.327437i
$3$	2.44645e6	+	2.44645e6i	0.885929	+	0.885929i	0.994129	−	0.108200i	$-0.0345088\pi$
$3$	2.44645e6	+	2.44645e6i	0.885929	+	0.885929i	−0.108200	+	0.994129i	$0.534509\pi$
$4$	1.05437e8	+	8.30503e7i	0.785570	+	0.618773i
$5$	−2.13207e9	+	2.13207e9i	−0.781100	+	0.781100i	−0.980016	−	0.198916i	$-0.936258\pi$
$5$	−2.13207e9	+	2.13207e9i	−0.781100	+	0.781100i	0.198916	+	0.980016i	$0.436258\pi$
$6$	−1.74998e10	−	3.60607e10i	−0.547004	−	1.12718i
$7$			9.04455e10i			0.352828i	0.984316	+	0.176414i	$0.0564498\pi$
$7$			9.04455e10i			0.352828i	−0.984316	+	0.176414i	$0.943550\pi$
$8$	−8.39133e11	−	1.30909e12i	−0.539655	−	0.841886i
$9$			4.34460e12i			0.569739i
$10$	3.14268e13	−	1.52510e13i	0.993801	−	0.482279i
$11$	−6.81338e13	+	6.81338e13i	−0.595061	+	0.595061i	−0.938994	−	0.343933i	$-0.888241\pi$
$11$	−6.81338e13	+	6.81338e13i	−0.595061	+	0.595061i	0.343933	+	0.938994i	$0.388241\pi$
$12$	5.47690e13	+	4.61125e14i	0.147770	+	1.24415i
$13$	1.50710e14	+	1.50710e14i	0.138008	+	0.138008i	0.772736	−	0.634728i	$-0.218888\pi$
$13$	1.50710e14	+	1.50710e14i	0.138008	+	0.138008i	−0.634728	+	0.772736i	$0.718888\pi$
$14$	3.43099e14	−	9.90069e14i	0.115529	−	0.333378i
$15$	−1.04320e16			−1.38400
$16$	4.21970e15	+	1.75132e16i	0.234241	+	0.972179i
$17$	2.51269e16			0.615289			0.307645	−	0.951501i	$-0.400459\pi$
$17$	2.51269e16			0.615289			0.307645	+	0.951501i	$0.400459\pi$
$18$	1.64810e16	−	4.75585e16i	0.186554	−	0.538331i
$19$	−2.25187e17	−	2.25187e17i	−1.22849	−	1.22849i	−0.964536	−	0.263950i	$-0.914975\pi$
$19$	−2.25187e17	−	2.25187e17i	−1.22849	−	1.22849i	−0.263950	−	0.964536i	$-0.585025\pi$
$20$	−4.01869e17	+	4.77310e16i	−1.09693	+	0.130285i
$21$	−2.21270e17	+	2.21270e17i	−0.312581	+	0.312581i
$22$	1.00429e18	−	4.87371e17i	0.757102	−	0.367412i
$23$		−	4.22469e18i		−	1.74771i	−0.486186	−	0.873855i	$-0.661612\pi$
$23$		−	4.22469e18i		−	1.74771i	0.486186	−	0.873855i	$-0.338388\pi$
$24$	1.14972e18	−	5.25550e18i	0.267756	−	1.22395i
$25$		−	1.64087e18i		−	0.220234i
$26$	−1.07805e18	−	2.22146e18i	−0.0852114	−	0.175590i
$27$	8.02678e18	−	8.02678e18i	0.381180	−	0.381180i
$28$	−7.51153e18	+	9.53634e18i	−0.218321	+	0.277171i
$29$	−9.32745e18	−	9.32745e18i	−0.168807	−	0.168807i	0.617648	−	0.786455i	$-0.288086\pi$
$29$	−9.32745e18	−	9.32745e18i	−0.168807	−	0.168807i	−0.786455	+	0.617648i	$0.788086\pi$
$30$	1.14195e20	+	3.95731e19i	1.30770	+	0.453172i
$31$	−1.43082e20			−1.05246			−0.526228	−	0.850344i	$-0.676394\pi$
$31$	−1.43082e20			−1.05246			−0.526228	+	0.850344i	$0.676394\pi$
$32$	2.02439e19	−	2.07717e20i	0.0969997	−	0.995284i
$33$	−3.33371e20			−1.05436
$34$	−2.75054e20	−	9.53174e19i	−0.581370	−	0.201468i
$35$	−1.92836e20	−	1.92836e20i	−0.275594	−	0.275594i
$36$	−3.60820e20	+	4.58084e20i	−0.352539	+	0.447570i
$37$	2.39977e20	−	2.39977e20i	0.161974	−	0.161974i	−0.621467	−	0.783441i	$-0.713463\pi$
$37$	2.39977e20	−	2.39977e20i	0.161974	−	0.161974i	0.783441	+	0.621467i	$0.213463\pi$
$38$	1.61080e21	+	3.31926e21i	0.758512	+	1.56302i
$39$			7.37406e20i			0.244531i
$40$	4.58016e21	+	1.00197e21i	1.07912	+	0.236073i
$41$			5.71746e21i			0.965208i	0.875839	+	0.482604i	$0.160309\pi$
$41$			5.71746e21i			0.965208i	−0.875839	+	0.482604i	$0.839691\pi$
$42$	3.26152e21	−	1.58278e21i	0.397700	−	0.192999i
$43$	−7.05720e21	+	7.05720e21i	−0.626338	+	0.626338i	−0.947145	−	0.320807i	$-0.896046\pi$
$43$	−7.05720e21	+	7.05720e21i	−0.626338	+	0.626338i	0.320807	+	0.947145i	$0.396046\pi$
$44$	−1.28424e22	+	1.52532e21i	−0.835669	+	0.0992545i
$45$	−9.26300e21	−	9.26300e21i	−0.445023	−	0.445023i
$46$	−1.60261e22	+	4.62460e22i	−0.572265	+	1.65136i
$47$	1.95092e21			0.0521095			0.0260548	−	0.999661i	$-0.491706\pi$
$47$	1.95092e21			0.0521095			0.0260548	+	0.999661i	$0.491706\pi$
$48$	−3.25219e22	+	5.31684e22i	−0.653760	+	1.06880i
$49$	5.75320e22			0.875512
$50$	−6.22455e21	+	1.79620e22i	−0.0721129	+	0.208094i
$51$	6.14717e22	+	6.14717e22i	0.545102	+	0.545102i
$52$	3.37396e21	+	2.84069e22i	0.0230194	+	0.193811i
$53$	−2.12669e22	+	2.12669e22i	−0.112196	+	0.112196i	−0.760976	−	0.648780i	$-0.775280\pi$
$53$	−2.12669e22	+	2.12669e22i	−0.112196	+	0.112196i	0.648780	+	0.760976i	$0.275280\pi$
$54$	−1.18315e23	+	5.74167e22i	−0.484980	+	0.235355i
$55$		−	2.90532e23i		−	0.929604i
$56$	1.18401e23	−	7.58959e22i	0.297041	−	0.190406i
$57$		−	1.10182e24i		−	2.17670i
$58$	6.67206e22	+	1.37487e23i	0.104227	+	0.214775i
$59$	7.19309e23	−	7.19309e23i	0.892100	−	0.892100i	−0.102620	−	0.994721i	$-0.532723\pi$
$59$	7.19309e23	−	7.19309e23i	0.892100	−	0.892100i	0.994721	+	0.102620i	$0.0327227\pi$
$60$	−1.09992e24	−	8.66380e23i	−1.08723	−	0.856380i
$61$	−1.15821e23	−	1.15821e23i	−0.0915873	−	0.0915873i	0.659829	−	0.751416i	$-0.270629\pi$
$61$	−1.15821e23	−	1.15821e23i	−0.0915873	−	0.0915873i	−0.751416	+	0.659829i	$0.770629\pi$
$62$	1.56626e24	+	5.42774e23i	0.994436	+	0.344613i
$63$	−3.92950e23			−0.201020
$64$	−1.00956e24	+	2.19700e24i	−0.417545	+	0.908656i
$65$	−6.42647e23			−0.215597
$66$	3.64928e24	+	1.26462e24i	0.996239	+	0.345237i
$67$	−3.93728e24	−	3.93728e24i	−0.877377	−	0.877377i	0.115886	−	0.993263i	$-0.463029\pi$
$67$	−3.93728e24	−	3.93728e24i	−0.877377	−	0.877377i	−0.993263	+	0.115886i	$0.963029\pi$
$68$	2.64932e24	+	2.08680e24i	0.483353	+	0.380724i
$69$	1.03355e25	−	1.03355e25i	1.54835	−	1.54835i
$70$	1.37939e24	+	2.84241e24i	0.170162	+	0.350641i
$71$			1.48813e25i			1.51584i	0.652347	+	0.757920i	$0.273784\pi$
$71$			1.48813e25i			1.51584i	−0.652347	+	0.757920i	$0.726216\pi$
$72$	5.68746e24	−	3.64570e24i	0.479656	−	0.307462i
$73$		−	1.52409e25i		−	1.06697i	−0.845810	−	0.533484i	$-0.820882\pi$
$73$		−	1.52409e25i		−	1.06697i	0.845810	−	0.533484i	$-0.179118\pi$
$74$	−3.53726e24	+	1.71659e24i	−0.206081	+	0.100009i
$75$	4.01431e24	−	4.01431e24i	0.195112	−	0.195112i
$76$	−5.04130e24	−	4.24450e25i	−0.204908	−	1.72522i
$77$	−6.16240e24	−	6.16240e24i	−0.209954	−	0.209954i
$78$	2.79730e24	−	8.07207e24i	0.0800686	−	0.231051i
$79$	−9.50108e24			−0.228985			−0.114493	−	0.993424i	$-0.536524\pi$
$79$	−9.50108e24			−0.228985			−0.114493	+	0.993424i	$0.536524\pi$
$80$	−4.63361e25	−	2.83427e25i	−0.942334	−	0.576403i
$81$	7.24044e25			1.24514
$82$	2.16888e25	−	6.25866e25i	0.316045	−	0.911999i
$83$	6.35431e25	+	6.35431e25i	0.786166	+	0.786166i	0.980863	−	0.194697i	$-0.0623725\pi$
$83$	6.35431e25	+	6.35431e25i	0.786166	+	0.786166i	−0.194697	+	0.980863i	$0.562372\pi$
$84$	−4.17067e25	+	4.95361e24i	−0.438971	+	0.0521376i
$85$	−5.35724e25	+	5.35724e25i	−0.480602	+	0.480602i
$86$	1.04023e26	−	5.04812e25i	0.796896	−	0.386723i
$87$		−	4.56382e25i		−	0.299102i
$88$	1.46366e26	+	3.20197e25i	0.822101	+	0.179846i
$89$			1.03442e26i			0.498806i	0.968400	+	0.249403i	$0.0802344\pi$
$89$			1.03442e26i			0.498806i	−0.968400	+	0.249403i	$0.919766\pi$
$90$	6.62596e25	+	1.36537e26i	0.274773	+	0.566207i
$91$	−1.36310e25	+	1.36310e25i	−0.0486933	+	0.0486933i
$92$	3.50862e26	−	4.45441e26i	1.08144	−	1.37295i
$93$	−3.50044e26	−	3.50044e26i	−0.932400	−	0.932400i
$94$	−2.13558e25	−	7.40067e24i	−0.0492369	−	0.0170626i
$95$	9.60231e26			1.91914
$96$	5.57694e26	−	4.58643e26i	0.967686	−	0.795816i
$97$	−4.37385e26			−0.659850			−0.329925	−	0.944007i	$-0.607024\pi$
$97$	−4.37385e26			−0.659850			−0.329925	+	0.944007i	$0.607024\pi$
$98$	−6.29778e26	−	2.18244e26i	−0.827248	−	0.286675i
$99$	−2.96014e26	−	2.96014e26i	−0.339029	−	0.339029i
$100$	1.36275e26	−	1.73010e26i	0.136275	−	0.173010i
$101$	1.06158e27	−	1.06158e27i	0.928143	−	0.928143i	−0.0694431	−	0.997586i	$-0.522122\pi$
$101$	1.06158e27	−	1.06158e27i	0.928143	−	0.928143i	0.997586	+	0.0694431i	$0.0221222\pi$
$102$	−4.39716e26	−	9.06094e26i	−0.336566	−	0.693539i
$103$		−	1.38431e27i		−	0.928816i	−0.885621	−	0.464408i	$-0.846267\pi$
$103$		−	1.38431e27i		−	0.928816i	0.885621	−	0.464408i	$-0.153733\pi$
$104$	7.08265e25	−	3.23757e26i	0.0417105	−	0.190664i
$105$		−	9.43527e26i		−	0.488314i
$106$	3.13474e26	−	1.52125e26i	0.142749	−	0.0692741i
$107$	2.76343e27	−	2.76343e27i	1.10858	−	1.10858i	0.115244	−	0.993337i	$-0.463235\pi$
$107$	2.76343e27	−	2.76343e27i	1.10858	−	1.10858i	0.993337	−	0.115244i	$-0.0367650\pi$
$108$	1.51295e27	−	1.79697e26i	0.535308	−	0.0635799i
$109$	−3.86883e26	−	3.86883e26i	−0.120871	−	0.120871i	0.644084	−	0.764955i	$-0.277239\pi$
$109$	−3.86883e26	−	3.86883e26i	−0.120871	−	0.120871i	−0.764955	+	0.644084i	$0.777239\pi$
$110$	−1.10212e27	+	3.18033e27i	−0.304387	+	0.878358i
$111$	1.17418e27			0.286995
$112$	−1.58399e27	+	3.81653e26i	−0.343012	+	0.0826467i
$113$	−7.13896e27			−1.37112			−0.685560	−	0.728016i	$-0.740443\pi$
$113$	−7.13896e27			−1.37112			−0.685560	+	0.728016i	$0.740443\pi$
$114$	−4.17967e27	+	1.20611e28i	−0.712733	+	2.05671i
$115$	9.00735e27	+	9.00735e27i	1.36514	+	1.36514i
$116$	−2.08815e26	−	1.75811e27i	−0.0281565	−	0.237063i
$117$	−6.54773e26	+	6.54773e26i	−0.0786288	+	0.0786288i
$118$	−1.06026e28	+	5.14532e27i	−1.13503	+	0.550815i
$119$			2.27262e27i			0.217091i
$120$	8.75383e27	+	1.36564e28i	0.746881	+	1.16517i
$121$			3.82556e27i			0.291805i
$122$	8.28486e26	+	1.70721e27i	0.0565493	+	0.116527i
$123$	−1.39875e28	+	1.39875e28i	−0.855106	+	0.855106i
$124$	−1.50862e28	−	1.18830e28i	−0.826777	−	0.651230i
$125$	−1.23867e28	−	1.23867e28i	−0.609075	−	0.609075i
$126$	4.30146e27	+	1.49063e27i	0.189939	+	0.0658214i
$127$	−1.72307e27			−0.0683836			−0.0341918	−	0.999415i	$-0.510886\pi$
$127$	−1.72307e27			−0.0683836			−0.0341918	+	0.999415i	$0.510886\pi$
$128$	1.93854e28	−	2.02199e28i	0.692055	−	0.721845i
$129$	−3.45301e28			−1.10978
$130$	7.03479e27	+	2.43784e27i	0.203712	+	0.0705944i
$131$	3.78519e28	+	3.78519e28i	0.988383	+	0.988383i	0.999933	−	0.0115501i	$-0.00367659\pi$
$131$	3.78519e28	+	3.78519e28i	0.988383	+	0.988383i	−0.0115501	+	0.999933i	$0.503677\pi$
$132$	−3.51498e28	−	2.76866e28i	−0.828276	−	0.652411i
$133$	2.03672e28	−	2.03672e28i	0.433445	−	0.433445i
$134$	2.81639e28	+	5.80355e28i	0.541724	+	1.11630i
$135$			3.42273e28i			0.595480i
$136$	−2.10848e28	−	3.28933e28i	−0.332044	−	0.518003i
$137$		−	4.55358e27i		−	0.0649569i	−0.999472	−	0.0324785i	$-0.989660\pi$
$137$		−	4.55358e27i		−	0.0649569i	0.999472	−	0.0324785i	$-0.0103400\pi$
$138$	−1.52345e29	+	7.39312e28i	−1.96998	+	0.956005i
$139$	2.46287e28	−	2.46287e28i	0.288896	−	0.288896i	−0.547747	−	0.836644i	$-0.684515\pi$
$139$	2.46287e28	−	2.46287e28i	0.288896	−	0.288896i	0.836644	+	0.547747i	$0.184515\pi$
$140$	−4.31706e27	−	3.63473e28i	−0.0459684	−	0.387029i
$141$	4.77281e27	+	4.77281e27i	0.0461653	+	0.0461653i
$142$	5.64513e28	−	1.62899e29i	0.496342	−	1.43228i
$143$	−2.05368e28			−0.164247
$144$	−7.60879e28	+	1.83329e28i	−0.553888	+	0.133456i
$145$	3.97736e28			0.263710
$146$	−5.78153e28	+	1.66836e29i	−0.349365	+	1.00815i
$147$	1.40749e29	+	1.40749e29i	0.775641	+	0.775641i
$148$	4.52327e28	−	5.37240e27i	0.227467	−	0.0270169i
$149$	1.45579e29	−	1.45579e29i	0.668474	−	0.668474i	−0.288889	−	0.957363i	$-0.593286\pi$
$149$	1.45579e29	−	1.45579e29i	0.668474	−	0.668474i	0.957363	+	0.288889i	$0.0932857\pi$
$150$	−5.91710e28	+	2.87149e28i	−0.248243	+	0.120469i
$151$		−	4.61625e29i		−	1.77052i	−0.465096	−	0.885260i	$-0.653980\pi$
$151$		−	4.61625e29i		−	1.77052i	0.465096	−	0.885260i	$-0.346020\pi$
$152$	−1.05827e29	+	4.83752e29i	−0.371287	+	1.69720i
$153$			1.09167e29i			0.350554i
$154$	4.40805e28	+	9.08338e28i	0.129633	+	0.267127i
$155$	3.05062e29	−	3.05062e29i	0.822073	−	0.822073i
$156$	−6.12418e28	+	7.77502e28i	−0.151309	+	0.192096i
$157$	3.64400e28	+	3.64400e28i	0.0825912	+	0.0825912i	0.747195	−	0.664604i	$-0.231400\pi$
$157$	3.64400e28	+	3.64400e28i	0.0825912	+	0.0825912i	−0.664604	+	0.747195i	$0.731400\pi$
$158$	1.04004e29	+	3.60417e28i	0.216362	+	0.0749782i
$159$	−1.04056e29			−0.198796
$160$	3.99706e29	+	4.86029e29i	0.701650	+	0.853183i
$161$	3.82105e29			0.616642
$162$	−7.92580e29	−	2.74661e29i	−1.17650	−	0.407704i
$163$	−2.55994e29	−	2.55994e29i	−0.349701	−	0.349701i	0.510297	−	0.859998i	$-0.329535\pi$
$163$	−2.55994e29	−	2.55994e29i	−0.349701	−	0.349701i	−0.859998	+	0.510297i	$0.829535\pi$
$164$	−4.74837e29	+	6.02834e29i	−0.597245	+	0.758239i
$165$	7.10771e29	−	7.10771e29i	0.823563	−	0.823563i
$166$	−4.54533e29	−	9.36626e29i	−0.485407	−	1.00025i
$167$		−	1.73129e30i		−	1.70490i	−0.522811	−	0.852449i	$-0.675117\pi$
$167$		−	1.73129e30i		−	1.70490i	0.522811	−	0.852449i	$-0.324883\pi$
$168$	4.75337e29	+	1.03987e29i	0.431843	+	0.0944718i
$169$		−	1.14711e30i		−	0.961907i
$170$	7.89658e29	−	3.83211e29i	0.611475	−	0.296741i
$171$	9.78349e29	−	9.78349e29i	0.699917	−	0.699917i
$172$	−1.33020e30	+	1.57991e29i	−0.879593	+	0.104471i
$173$	1.45239e30	+	1.45239e30i	0.888101	+	0.888101i	0.994341	−	0.106240i	$-0.0338811\pi$
$173$	1.45239e30	+	1.45239e30i	0.888101	+	0.888101i	−0.106240	+	0.994341i	$0.533881\pi$
$174$	−1.73126e29	+	4.99583e29i	−0.0979370	+	0.282613i
$175$	1.48410e29			0.0777050
$176$	−1.48075e30	−	9.05737e29i	−0.717893	−	0.439118i
$177$	3.51950e30			1.58067
$178$	3.92401e29	−	1.13234e30i	0.163328	−	0.471309i
$179$	1.26846e30	+	1.26846e30i	0.489509	+	0.489509i	0.908151	−	0.418642i	$-0.137494\pi$
$179$	1.26846e30	+	1.26846e30i	0.489509	+	0.489509i	−0.418642	+	0.908151i	$0.637494\pi$
$180$	−2.07372e29	−	1.74596e30i	−0.0742287	−	0.624965i
$181$	1.08560e30	−	1.08560e30i	0.360588	−	0.360588i	−0.503442	−	0.864029i	$-0.667933\pi$
$181$	1.08560e30	−	1.08560e30i	0.360588	−	0.360588i	0.864029	+	0.503442i	$0.167933\pi$
$182$	2.00921e29	−	9.75046e28i	0.0619530	−	0.0300650i
$183$		−	5.66701e29i		−	0.162280i
$184$	−5.53049e30	+	3.54508e30i	−1.47137	+	0.943161i
$185$			1.02330e30i			0.253036i
$186$	2.50391e30	+	5.15965e30i	0.575697	+	1.18630i
$187$	−1.71199e30	+	1.71199e30i	−0.366134	+	0.366134i
$188$	2.05699e29	+	1.62024e29i	0.0409357	+	0.0322440i
$189$	7.25987e29	+	7.25987e29i	0.134491	+	0.134491i
$190$	−1.05112e31	−	3.64257e30i	−1.81334	−	0.628398i
$191$	−1.09631e30			−0.176191			−0.0880956	−	0.996112i	$-0.528078\pi$
$191$	−1.09631e30			−0.176191			−0.0880956	+	0.996112i	$0.528078\pi$
$192$	−7.84467e30	+	2.90499e30i	−1.17492	+	0.435089i
$193$	4.17074e30			0.582358			0.291179	−	0.956669i	$-0.405953\pi$
$193$	4.17074e30			0.582358			0.291179	+	0.956669i	$0.405953\pi$
$194$	4.78787e30	+	1.65919e30i	0.623475	+	0.216059i
$195$	−1.57220e30	−	1.57220e30i	−0.191003	−	0.191003i
$196$	6.06602e30	+	4.77805e30i	0.687776	+	0.541743i
$197$	−5.20097e30	+	5.20097e30i	−0.550542	+	0.550542i	−0.926597	−	0.376055i	$-0.877280\pi$
$197$	−5.20097e30	+	5.20097e30i	−0.550542	+	0.550542i	0.376055	+	0.926597i	$0.377280\pi$
$198$	2.11743e30	+	4.36325e30i	0.209329	+	0.431351i
$199$			4.25153e30i			0.392671i	0.980537	+	0.196336i	$0.0629042\pi$
$199$			4.25153e30i			0.392671i	−0.980537	+	0.196336i	$0.937096\pi$
$200$	−2.14805e30	+	1.37691e30i	−0.185412	+	0.118851i
$201$		−	1.92647e31i		−	1.55459i
$202$	−1.56477e31	+	7.59364e30i	−1.18089	+	0.573069i
$203$	8.43627e29	−	8.43627e29i	0.0595599	−	0.0595599i
$204$	1.37618e30	+	1.15867e31i	0.0909216	+	0.765510i
$205$	−1.21900e31	−	1.21900e31i	−0.753924	−	0.753924i
$206$	−5.25128e30	+	1.51534e31i	−0.304129	+	0.877613i
$207$	1.83546e31			0.995739
$208$	−2.00346e30	+	3.27536e30i	−0.101842	+	0.166496i
$209$	3.06857e31			1.46205
$210$	−3.57921e30	+	1.03284e31i	−0.159892	+	0.461394i
$211$	1.00443e31	+	1.00443e31i	0.420829	+	0.420829i	0.885489	−	0.464660i	$-0.153823\pi$
$211$	1.00443e31	+	1.00443e31i	0.420829	+	0.420829i	−0.464660	+	0.885489i	$0.653823\pi$
$212$	−4.00854e30	+	4.76104e29i	−0.157562	+	0.0187141i
$213$	−3.64063e31	+	3.64063e31i	−1.34293	+	1.34293i
$214$	−4.07330e31	+	1.97672e31i	−1.41046	+	0.684478i
$215$		−	3.00929e31i		−	0.978465i
$216$	−1.72433e31	−	3.77221e30i	−0.526617	−	0.115205i
$217$		−	1.29412e31i		−	0.371336i
$218$	2.76743e30	+	5.70266e30i	0.0746300	+	0.153785i
$219$	3.72860e31	−	3.72860e31i	0.945258	−	0.945258i
$220$	2.41288e31	−	3.06330e31i	0.575214	−	0.730269i
$221$	3.78687e30	+	3.78687e30i	0.0849151	+	0.0849151i
$222$	−1.28533e31	−	4.45418e30i	−0.271174	−	0.0939728i
$223$	−6.41269e30			−0.127328			−0.0636641	−	0.997971i	$-0.520279\pi$
$223$	−6.41269e30			−0.127328			−0.0636641	+	0.997971i	$0.520279\pi$
$224$	1.87871e31	+	1.83097e30i	0.351165	+	0.0342242i
$225$	7.12894e30			0.125476
$226$	7.81471e31	+	2.70812e31i	1.29554	+	0.448956i
$227$	5.54347e31	+	5.54347e31i	0.865830	+	0.865830i	0.992008	−	0.126177i	$-0.0402708\pi$
$227$	5.54347e31	+	5.54347e31i	0.865830	+	0.865830i	−0.126177	+	0.992008i	$0.540271\pi$
$228$	9.15062e31	−	1.16173e32i	1.34688	−	1.70995i
$229$	−4.63121e31	+	4.63121e31i	−0.642563	+	0.642563i	−0.951185	−	0.308622i	$-0.900132\pi$
$229$	−4.63121e31	+	4.63121e31i	−0.642563	+	0.642563i	0.308622	+	0.951185i	$0.400132\pi$
$230$	−6.44309e31	−	1.32768e32i	−0.842885	−	1.73688i
$231$		−	3.01520e31i		−	0.372009i
$232$	−4.38347e30	+	2.00374e31i	−0.0510188	+	0.233214i
$233$		−	1.48678e32i		−	1.63284i	−0.577460	−	0.816419i	$-0.695956\pi$
$233$		−	1.48678e32i		−	1.63284i	0.577460	−	0.816419i	$-0.304044\pi$
$234$	9.65137e30	−	4.68369e30i	0.100040	−	0.0485483i
$235$	−4.15949e30	+	4.15949e30i	−0.0407028	+	0.0407028i
$236$	1.35581e32	−	1.61033e31i	1.25281	−	0.148800i
$237$	−2.32439e31	−	2.32439e31i	−0.202864	−	0.202864i
$238$	8.62103e30	−	2.48774e31i	0.0710838	−	0.205124i
$239$	−2.04461e32			−1.59308			−0.796542	−	0.604584i	$-0.793339\pi$
$239$	−2.04461e32			−1.59308			−0.796542	+	0.604584i	$0.793339\pi$
$240$	−4.40199e31	−	1.82698e32i	−0.324188	−	1.34549i
$241$	−7.63534e31			−0.531616			−0.265808	−	0.964026i	$-0.585639\pi$
$241$	−7.63534e31			−0.531616			−0.265808	+	0.964026i	$0.585639\pi$
$242$	1.45120e31	−	4.18768e31i	0.0955478	−	0.275719i
$243$	1.15924e32	+	1.15924e32i	0.721922	+	0.721922i
$244$	−2.59291e30	−	2.18309e31i	−0.0152765	−	0.128620i
$245$	−1.22662e32	+	1.22662e32i	−0.683862	+	0.683862i
$246$	2.06175e32	−	1.00054e32i	1.08796	−	0.527973i
$247$		−	6.78758e31i		−	0.339083i
$248$	1.20065e32	+	1.87307e32i	0.567962	+	0.886048i
$249$			3.10910e32i			1.39297i
$250$	8.86039e31	+	1.82580e32i	0.376065	+	0.774932i
$251$	−2.75496e32	+	2.75496e32i	−1.10795	+	1.10795i	−0.114529	+	0.993420i	$0.536536\pi$
$251$	−2.75496e32	+	2.75496e32i	−1.10795	+	1.10795i	−0.993420	+	0.114529i	$0.963464\pi$
$252$	−4.14316e31	−	3.26346e31i	−0.157915	−	0.124386i
$253$	2.87845e32	+	2.87845e32i	1.03999	+	1.03999i
$254$	1.88617e31	+	6.53634e30i	0.0646138	+	0.0223913i
$255$	−2.62124e32			−0.851559
$256$	−2.88907e32	+	1.47801e32i	−0.890263	+	0.455447i
$257$	4.66283e32			1.36318			0.681589	−	0.731735i	$-0.261289\pi$
$257$	4.66283e32			1.36318			0.681589	+	0.731735i	$0.261289\pi$
$258$	3.77987e32	+	1.30988e32i	1.04860	+	0.363383i
$259$	2.17048e31	+	2.17048e31i	0.0571491	+	0.0571491i
$260$	−6.77591e31	−	5.33720e31i	−0.169366	−	0.133405i
$261$	4.05241e31	−	4.05241e31i	0.0961759	−	0.0961759i
$262$	−2.70760e32	−	5.57938e32i	−0.610263	−	1.25753i
$263$		−	9.02584e32i		−	1.93235i	−0.257893	−	0.966173i	$-0.583028\pi$
$263$		−	9.02584e32i		−	1.93235i	0.257893	−	0.966173i	$-0.416972\pi$
$264$	2.79743e32	+	4.36412e32i	0.568992	+	0.887654i
$265$		−	9.06849e31i		−	0.175273i
$266$	−3.00213e32	+	1.45689e32i	−0.551476	+	0.267624i
$267$	−2.53065e32	+	2.53065e32i	−0.441907	+	0.441907i
$268$	−8.81444e31	−	7.42128e32i	−0.146344	−	1.23214i
$269$	−7.45421e32	−	7.45421e32i	−1.17692	−	1.17692i	−0.980526	−	0.196392i	$-0.937078\pi$
$269$	−7.45421e32	−	7.45421e32i	−1.17692	−	1.17692i	−0.196392	−	0.980526i	$-0.562922\pi$
$270$	1.29839e32	−	3.74672e32i	0.194982	−	0.562653i
$271$	−1.36537e33			−1.95059			−0.975295	−	0.220906i	$-0.929099\pi$
$271$	−1.36537e33			−1.95059			−0.975295	+	0.220906i	$0.929099\pi$
$272$	1.06028e32	+	4.40053e32i	0.144126	+	0.598171i
$273$	−6.66951e31			−0.0862776
$274$	−1.72737e31	+	4.98462e31i	−0.0212693	+	0.0613761i
$275$	1.11799e32	+	1.11799e32i	0.131053	+	0.131053i
$276$	1.94811e33	−	2.31382e32i	2.17441	−	0.258260i
$277$	−9.62619e32	+	9.62619e32i	−1.02324	+	1.02324i	−0.0235168	+	0.999723i	$0.507486\pi$
$277$	−9.62619e32	+	9.62619e32i	−1.02324	+	1.02324i	−0.999723	+	0.0235168i	$0.992514\pi$
$278$	−3.63028e32	+	1.76173e32i	−0.367566	+	0.178375i
$279$		−	6.21636e32i		−	0.599625i
$280$	−9.06240e31	+	4.14255e32i	−0.0832933	+	0.380745i
$281$			1.65071e33i			1.44589i	0.690904	+	0.722947i	$0.257213\pi$
$281$			1.65071e33i			1.44589i	−0.690904	+	0.722947i	$0.742787\pi$
$282$	−3.41406e31	−	7.03513e31i	−0.0285041	−	0.0587366i
$283$	7.85724e32	−	7.85724e32i	0.625393	−	0.625393i	−0.321512	−	0.946905i	$-0.604191\pi$
$283$	7.85724e32	−	7.85724e32i	0.625393	−	0.625393i	0.946905	+	0.321512i	$0.104191\pi$
$284$	−1.23590e33	+	1.56905e33i	−0.937961	+	1.19080i
$285$	2.34915e33	+	2.34915e33i	1.70022	+	1.70022i
$286$	2.24808e32	+	7.79052e31i	0.155192	+	0.0537805i
$287$	−5.17119e32			−0.340553
$288$	9.02447e32	+	8.79518e31i	0.567052	+	0.0552645i
$289$	−1.03635e33			−0.621419
$290$	−4.35385e32	−	1.50879e32i	−0.249173	−	0.0863485i
$291$	−1.07004e33	−	1.07004e33i	−0.584580	−	0.584580i
$292$	1.26576e33	−	1.60696e33i	0.660211	−	0.838179i
$293$	−1.31438e33	+	1.31438e33i	−0.654646	+	0.654646i	−0.954108	−	0.299462i	$-0.903193\pi$
$293$	−1.31438e33	+	1.31438e33i	−0.654646	+	0.654646i	0.299462	+	0.954108i	$0.403193\pi$
$294$	−1.00680e33	−	2.07464e33i	−0.478909	−	0.986856i
$295$			3.06724e33i			1.39364i
$296$	−5.15523e32	−	1.12778e32i	−0.223774	−	0.0489537i
$297$			1.09379e33i			0.453651i
$298$	−2.14584e33	+	1.04135e33i	−0.850506	+	0.412740i
$299$	6.36702e32	−	6.36702e32i	0.241199	−	0.241199i
$300$	7.56648e32	−	8.98690e31i	0.274004	−	0.0325441i
$301$	−6.38293e32	−	6.38293e32i	−0.220990	−	0.220990i
$302$	−1.75115e33	+	5.05322e33i	−0.579734	+	1.67292i
$303$	5.19420e33			1.64454
$304$	2.99353e33	−	4.89398e33i	0.906547	−	1.48207i
$305$	4.93878e32			0.143078
$306$	4.14116e32	−	1.19500e33i	0.114784	−	0.331229i
$307$	−2.48834e31	−	2.48834e31i	−0.00659995	−	0.00659995i	0.703799	−	0.710399i	$-0.251486\pi$
$307$	−2.48834e31	−	2.48834e31i	−0.00659995	−	0.00659995i	−0.710399	+	0.703799i	$0.751486\pi$
$308$	−1.37959e32	−	1.16154e33i	−0.0350198	−	0.294848i
$309$	3.38663e33	−	3.38663e33i	0.822865	−	0.822865i
$310$	−4.49662e33	+	2.18215e33i	−1.04593	+	0.507577i
$311$		−	7.75721e33i		−	1.72759i	−0.503845	−	0.863794i	$-0.668082\pi$
$311$		−	7.75721e33i		−	1.72759i	0.503845	−	0.863794i	$-0.331918\pi$
$312$	9.65328e32	−	6.18782e32i	0.205868	−	0.131963i
$313$		−	5.82845e33i		−	1.19043i	−0.803566	−	0.595216i	$-0.797067\pi$
$313$		−	5.82845e33i		−	1.19043i	0.803566	−	0.595216i	$-0.202933\pi$
$314$	−2.60661e32	−	5.37127e32i	−0.0509948	−	0.105082i
$315$	8.37797e32	−	8.37797e32i	0.157017	−	0.157017i
$316$	−1.00177e33	−	7.89067e32i	−0.179884	−	0.141690i
$317$	−5.36256e32	−	5.36256e32i	−0.0922725	−	0.0922725i	0.659464	−	0.751736i	$-0.270783\pi$
$317$	−5.36256e32	−	5.36256e32i	−0.0922725	−	0.0922725i	−0.751736	+	0.659464i	$0.770783\pi$
$318$	1.13906e33	+	3.94731e32i	0.187837	+	0.0650932i
$319$	1.27103e33			0.200901
$320$	−2.53169e33	−	6.83661e33i	−0.383607	−	1.03590i
$321$	1.35212e34			1.96425
$322$	−4.18274e33	−	1.44949e33i	−0.582648	−	0.201911i
$323$	−5.65827e33	−	5.65827e33i	−0.755874	−	0.755874i
$324$	7.63413e33	+	6.01320e33i	0.978142	+	0.770457i
$325$	2.47296e32	−	2.47296e32i	0.0303942	−	0.0303942i
$326$	1.83116e33	+	3.77335e33i	0.215918	+	0.444928i
$327$		−	1.89298e33i		−	0.214166i
$328$	7.48465e33	−	4.79771e33i	0.812596	−	0.520879i
$329$			1.76452e32i			0.0183857i
$330$	−1.04768e34	+	5.08425e33i	−1.04783	+	0.508497i
$331$	1.29741e34	−	1.29741e34i	1.24566	−	1.24566i	0.288038	−	0.957619i	$-0.406997\pi$
$331$	1.29741e34	−	1.29741e34i	1.24566	−	1.24566i	0.957619	−	0.288038i	$-0.0930030\pi$
$332$	1.42255e33	+	1.19771e34i	0.131130	+	1.10405i
$333$	1.04260e33	+	1.04260e33i	0.0922830	+	0.0922830i
$334$	−6.56755e33	+	1.89517e34i	−0.558247	+	1.61091i
$335$	1.67891e34			1.37064
$336$	−4.80885e33	−	2.94146e33i	−0.377104	−	0.230665i
$337$	−2.57281e34			−1.93822			−0.969112	−	0.246619i	$-0.920680\pi$
$337$	−2.57281e34			−1.93822			−0.969112	+	0.246619i	$0.920680\pi$
$338$	−4.35147e33	+	1.25569e34i	−0.314964	+	0.908880i
$339$	−1.74651e34	−	1.74651e34i	−1.21472	−	1.21472i
$340$	−1.00977e34	+	1.19933e33i	−0.674930	+	0.0801632i
$341$	9.74875e33	−	9.74875e33i	0.626275	−	0.626275i
$342$	−1.44209e34	+	6.99827e33i	−0.890511	+	0.432154i
$343$			1.11469e34i			0.661734i
$344$	1.51604e34	+	3.31655e33i	0.865311	+	0.189299i
$345$			4.40720e34i			2.41883i
$346$	−1.03892e34	−	2.14083e34i	−0.548345	−	1.12994i
$347$	4.34341e33	−	4.34341e33i	0.220487	−	0.220487i	−0.588216	−	0.808704i	$-0.700170\pi$
$347$	4.34341e33	−	4.34341e33i	0.220487	−	0.220487i	0.808704	+	0.588216i	$0.200170\pi$
$348$	3.79027e33	−	4.81198e33i	0.185076	−	0.234965i
$349$	2.71559e34	+	2.71559e34i	1.27562	+	1.27562i	0.943096	+	0.332521i	$0.107899\pi$
$349$	2.71559e34	+	2.71559e34i	1.27562	+	1.27562i	0.332521	+	0.943096i	$0.392101\pi$
$350$	−1.62458e33	−	5.62983e32i	−0.0734213	−	0.0254435i
$351$	2.41943e33			0.105212
$352$	1.27732e34	+	1.55318e34i	0.534534	+	0.649976i
$353$	2.08703e34			0.840564			0.420282	−	0.907394i	$-0.361931\pi$
$353$	2.08703e34			0.840564			0.420282	+	0.907394i	$0.361931\pi$
$354$	−3.85265e34	−	1.33510e34i	−1.49354	−	0.517571i
$355$	−3.17280e34	−	3.17280e34i	−1.18402	−	1.18402i
$356$	−8.59089e33	+	1.09067e34i	−0.308648	+	0.391847i
$357$	−5.55984e33	+	5.55984e33i	−0.192328	+	0.192328i
$358$	−9.07347e33	−	1.86971e34i	−0.302240	−	0.622807i
$359$		−	1.99561e34i		−	0.640178i	−0.947387	−	0.320089i	$-0.896287\pi$
$359$		−	1.99561e34i		−	0.640178i	0.947387	−	0.320089i	$-0.103713\pi$
$360$	−4.35318e33	+	1.98990e34i	−0.134500	+	0.614818i
$361$			6.78180e34i			2.01836i
$362$	−1.60018e34	+	7.76548e33i	−0.458779	+	0.222640i
$363$	−9.35904e33	+	9.35904e33i	−0.258519	+	0.258519i
$364$	−2.56928e33	+	3.05160e32i	−0.0683821	+	0.00812191i
$365$	3.24947e34	+	3.24947e34i	0.833409	+	0.833409i
$366$	−2.14974e33	+	6.20344e33i	−0.0531364	+	0.153334i
$367$	−6.79042e34			−1.61773			−0.808863	−	0.587997i	$-0.799917\pi$
$367$	−6.79042e34			−1.61773			−0.808863	+	0.587997i	$0.799917\pi$
$368$	7.39880e34	−	1.78270e34i	1.69909	−	0.409385i
$369$	−2.48401e34			−0.549917
$370$	3.88180e33	−	1.12016e34i	0.0828534	−	0.239087i
$371$	−1.92349e33	−	1.92349e33i	−0.0395861	−	0.0395861i
$372$	−7.83648e33	−	6.59789e34i	−0.155522	−	1.30941i
$373$	−2.16747e34	+	2.16747e34i	−0.414843	+	0.414843i	−0.883422	−	0.468578i	$-0.844766\pi$
$373$	−2.16747e34	+	2.16747e34i	−0.414843	+	0.414843i	0.468578	+	0.883422i	$0.344766\pi$
$374$	2.52348e34	−	1.22461e34i	0.465836	−	0.226065i
$375$		−	6.06068e34i		−	1.07919i
$376$	−1.63708e33	−	2.55392e33i	−0.0281212	−	0.0438703i
$377$		−	2.81147e33i		−	0.0465936i
$378$	−5.19309e33	−	1.07011e34i	−0.0830398	−	0.171115i
$379$	−3.04447e33	+	3.04447e33i	−0.0469766	+	0.0469766i	−0.730205	−	0.683228i	$-0.760575\pi$
$379$	−3.04447e33	+	3.04447e33i	−0.0469766	+	0.0469766i	0.683228	+	0.730205i	$0.260575\pi$
$380$	1.01244e35	+	7.97474e34i	1.50762	+	1.18751i
$381$	−4.21539e33	−	4.21539e33i	−0.0605830	−	0.0605830i
$382$	1.20009e34	+	4.15879e33i	0.166478	+	0.0576915i
$383$	−4.89902e34			−0.656034			−0.328017	−	0.944672i	$-0.606380\pi$
$383$	−4.89902e34			−0.656034			−0.328017	+	0.944672i	$0.606380\pi$
$384$	9.68922e34	−	2.04146e33i	1.25261	−	0.0263918i
$385$	2.62773e34			0.327991
$386$	−4.56554e34	−	1.58214e34i	−0.550254	−	0.190685i
$387$	−3.06607e34	−	3.06607e34i	−0.356849	−	0.356849i
$388$	−4.61168e34	−	3.63249e34i	−0.518359	−	0.408297i
$389$	1.11106e35	−	1.11106e35i	1.20620	−	1.20620i	0.233946	−	0.972250i	$-0.424836\pi$
$389$	1.11106e35	−	1.11106e35i	1.20620	−	1.20620i	0.972250	−	0.233946i	$-0.0751638\pi$
$390$	1.12462e34	+	2.31743e34i	0.117932	+	0.243016i
$391$		−	1.06154e35i		−	1.07535i
$392$	−4.82770e34	−	7.53143e34i	−0.472474	−	0.737082i
$393$			1.85205e35i			1.75127i
$394$	7.66624e34	−	3.72033e34i	0.700460	−	0.339924i
$395$	2.02570e34	−	2.02570e34i	0.178860	−	0.178860i
$396$	−6.62692e33	−	5.57950e34i	−0.0565492	−	0.476114i
$397$	−5.22244e33	−	5.22244e33i	−0.0430727	−	0.0430727i	0.685242	−	0.728315i	$-0.259696\pi$
$397$	−5.22244e33	−	5.22244e33i	−0.0430727	−	0.0430727i	−0.728315	+	0.685242i	$0.759696\pi$
$398$	1.61279e34	−	4.65397e34i	0.128575	−	0.371024i
$399$	9.96544e34			0.768002
$400$	2.87370e34	−	6.92400e33i	0.214107	−	0.0515878i
$401$	−1.37044e35			−0.987216			−0.493608	−	0.869685i	$-0.664322\pi$
$401$	−1.37044e35			−0.987216			−0.493608	+	0.869685i	$0.664322\pi$
$402$	−7.30793e34	+	2.10882e35i	−0.509029	+	1.46889i
$403$	−2.15639e34	−	2.15639e34i	−0.145248	−	0.145248i
$404$	2.00095e35	−	2.37658e34i	1.30343	−	0.154812i
$405$	−1.54371e35	+	1.54371e35i	−0.972576	+	0.972576i
$406$	−1.24351e34	+	6.03458e33i	−0.0757786	+	0.0367744i
$407$			3.27011e34i			0.192769i
$408$	2.88888e34	−	1.32055e35i	0.164747	−	0.753081i
$409$		−	2.45311e35i		−	1.35348i	−0.736220	−	0.676742i	$-0.763391\pi$
$409$		−	2.45311e35i		−	1.35348i	0.736220	−	0.676742i	$-0.236609\pi$
$410$	8.71970e34	+	1.79681e35i	0.465500	+	0.959225i
$411$	1.11401e34	−	1.11401e34i	0.0575472	−	0.0575472i
$412$	1.14967e35	−	1.45958e35i	0.574726	−	0.729650i
$413$	6.50583e34	+	6.50583e34i	0.314758	+	0.314758i
$414$	−2.00920e35	−	6.96270e34i	−0.940847	−	0.326042i
$415$	−2.70957e35			−1.22815
$416$	3.43559e34	−	2.82540e34i	0.150744	−	0.123971i
$417$	1.20506e35			0.511883
$418$	−3.35904e35	−	1.16404e35i	−1.38145	−	0.478729i
$419$	2.20917e35	+	2.20917e35i	0.879712	+	0.879712i	0.993505	−	0.113792i	$-0.0362999\pi$
$419$	2.20917e35	+	2.20917e35i	0.879712	+	0.879712i	−0.113792	+	0.993505i	$0.536300\pi$
$420$	7.83602e34	−	9.94831e34i	0.302155	−	0.383605i
$421$	−2.58148e35	+	2.58148e35i	−0.963963	+	0.963963i	−0.999373	−	0.0354102i	$-0.988726\pi$
$421$	−2.58148e35	+	2.58148e35i	−0.963963	+	0.963963i	0.0354102	+	0.999373i	$0.488726\pi$
$422$	−7.18482e34	−	1.48053e35i	−0.259835	−	0.535425i
$423$			8.47595e33i			0.0296888i
$424$	4.56859e34	+	9.99442e33i	0.155004	+	0.0339093i
$425$		−	4.12301e34i		−	0.135508i
$426$	5.36630e35	−	2.60420e35i	1.70862	−	0.829171i
$427$	1.04755e34	−	1.04755e34i	0.0323146	−	0.0323146i
$428$	5.20873e35	−	6.18653e34i	1.55683	−	0.184908i
$429$	−5.02423e34	−	5.02423e34i	−0.145511	−	0.145511i
$430$	−1.14156e35	+	3.29414e35i	−0.320385	+	0.924525i
$431$	−1.80848e35			−0.491892			−0.245946	−	0.969284i	$-0.579099\pi$
$431$	−1.80848e35			−0.491892			−0.245946	+	0.969284i	$0.579099\pi$
$432$	1.74445e35	+	1.06704e35i	0.459863	+	0.281288i
$433$	3.04798e35			0.778800			0.389400	−	0.921069i	$-0.372682\pi$
$433$	3.04798e35			0.778800			0.389400	+	0.921069i	$0.372682\pi$
$434$	−4.90915e34	+	1.41662e35i	−0.121589	+	0.350865i
$435$	9.73040e34	+	9.73040e34i	0.233628	+	0.233628i
$436$	−8.66120e33	−	7.29226e34i	−0.0201609	−	0.169744i
$437$	−9.51348e35	+	9.51348e35i	−2.14704	+	2.14704i
$438$	−5.49596e35	+	2.66712e35i	−1.20266	+	0.583636i
$439$		−	1.64470e35i		−	0.348993i	−0.984658	−	0.174496i	$-0.944170\pi$
$439$		−	1.64470e35i		−	0.348993i	0.984658	−	0.174496i	$-0.0558298\pi$
$440$	−3.80332e35	+	2.43795e35i	−0.782621	+	0.501665i
$441$			2.49953e35i			0.498813i
$442$	−2.70880e34	−	5.58185e34i	−0.0524296	−	0.108038i
$443$	6.87224e34	−	6.87224e34i	0.129017	−	0.129017i	−0.639649	−	0.768667i	$-0.720920\pi$
$443$	6.87224e34	−	6.87224e34i	0.129017	−	0.129017i	0.768667	+	0.639649i	$0.220920\pi$
$444$	1.23803e35	+	9.75160e34i	0.225455	+	0.177585i
$445$	−2.20546e35	−	2.20546e35i	−0.389618	−	0.389618i
$446$	7.01970e34	+	2.43261e34i	0.120309	+	0.0416920i
$447$	7.12303e35			1.18444
$448$	−1.98708e35	−	9.13104e34i	−0.320600	−	0.147322i
$449$	7.80125e34			0.122135			0.0610673	−	0.998134i	$-0.480550\pi$
$449$	7.80125e34			0.122135			0.0610673	+	0.998134i	$0.480550\pi$
$450$	−7.80375e34	−	2.70432e34i	−0.118559	−	0.0410855i
$451$	−3.89552e35	−	3.89552e35i	−0.574358	−	0.574358i
$452$	−7.52713e35	−	5.92892e35i	−1.07711	−	0.848412i
$453$	1.12934e36	−	1.12934e36i	1.56855	−	1.56855i
$454$	−3.96533e35	−	8.17109e35i	−0.534595	−	1.10160i
$455$		−	5.81246e34i		−	0.0760687i
$456$	−1.44237e36	+	9.24571e35i	−1.83254	+	1.17467i
$457$		−	6.04604e35i		−	0.745765i	−0.927879	−	0.372882i	$-0.878369\pi$
$457$		−	6.04604e35i		−	0.745765i	0.927879	−	0.372882i	$-0.121631\pi$
$458$	6.82641e35	−	3.31277e35i	0.817539	−	0.396741i
$459$	2.01688e35	−	2.01688e35i	0.234536	−	0.234536i
$460$	2.01649e35	+	1.69777e36i	0.227701	+	1.91712i
$461$	1.46049e35	+	1.46049e35i	0.160154	+	0.160154i	0.782635	−	0.622481i	$-0.213875\pi$
$461$	1.46049e35	+	1.46049e35i	0.160154	+	0.160154i	−0.622481	+	0.782635i	$0.713875\pi$
$462$	−1.14379e35	+	3.30061e35i	−0.121810	+	0.351501i
$463$	−7.05519e35			−0.729735			−0.364868	−	0.931059i	$-0.618886\pi$
$463$	−7.05519e35			−0.729735			−0.364868	+	0.931059i	$0.618886\pi$
$464$	1.23995e35	−	2.02713e35i	0.124569	−	0.203652i
$465$	1.49264e36			1.45660
$466$	−5.64002e35	+	1.62752e36i	−0.534651	+	1.54282i
$467$	7.15340e35	+	7.15340e35i	0.658771	+	0.658771i	0.955089	−	0.296318i	$-0.0957589\pi$
$467$	7.15340e35	+	7.15340e35i	0.658771	+	0.658771i	−0.296318	+	0.955089i	$0.595759\pi$
$468$	−1.23417e35	+	1.46585e34i	−0.110422	+	0.0131151i
$469$	3.56109e35	−	3.56109e35i	0.309563	−	0.309563i
$470$	6.13109e34	−	2.97534e34i	0.0517865	−	0.0251314i
$471$			1.78297e35i			0.146340i
$472$	−1.54523e36	−	3.38042e35i	−1.23247	−	0.269621i
$473$		−	9.61668e35i		−	0.745418i
$474$	1.66267e35	+	3.42615e35i	0.125256	+	0.258106i
$475$	−3.69504e35	+	3.69504e35i	−0.270555	+	0.270555i
$476$	−1.88742e35	+	2.39619e35i	−0.134330	+	0.170541i
$477$	−9.23960e34	−	9.23960e34i	−0.0639227	−	0.0639227i
$478$	2.23815e36	+	7.75609e35i	1.50526	+	0.521634i
$479$	−9.79626e35			−0.640518			−0.320259	−	0.947330i	$-0.603770\pi$
$479$	−9.79626e35			−0.640518			−0.320259	+	0.947330i	$0.603770\pi$
$480$	−2.11185e35	+	2.16690e36i	−0.134247	+	1.37747i
$481$	7.23336e34			0.0447076
$482$	8.35808e35	+	2.89642e35i	0.502310	+	0.174071i
$483$	9.34799e35	+	9.34799e35i	0.546301	+	0.546301i
$484$	−3.17714e35	+	4.03358e35i	−0.180561	+	0.229233i
$485$	9.32536e35	−	9.32536e35i	0.515409	−	0.515409i
$486$	−8.29224e35	−	1.70873e36i	−0.445740	−	0.918508i
$487$		−	1.97640e36i		−	1.03332i	−0.856191	−	0.516660i	$-0.827175\pi$
$487$		−	1.97640e36i		−	1.03332i	0.856191	−	0.516660i	$-0.172825\pi$
$488$	−5.44306e34	+	2.48809e35i	−0.0276806	+	0.126532i
$489$		−	1.25255e36i		−	0.619620i
$490$	1.80804e36	−	8.77421e35i	0.870085	−	0.422241i
$491$	−3.21210e35	+	3.21210e35i	−0.150380	+	0.150380i	−0.778288	−	0.627908i	$-0.783911\pi$
$491$	−3.21210e35	+	3.21210e35i	−0.150380	+	0.150380i	0.627908	+	0.778288i	$0.283911\pi$
$492$	−2.63646e36	+	3.13139e35i	−1.20086	+	0.142629i
$493$	−2.34370e35	−	2.34370e35i	−0.103865	−	0.103865i
$494$	−2.57482e35	+	7.43008e35i	−0.111028	+	0.320390i
$495$	1.26225e36			0.529632
$496$	−6.03766e35	−	2.50583e36i	−0.246528	−	1.02317i
$497$	−1.34595e36			−0.534832
$498$	1.17942e36	−	3.40340e36i	0.456111	−	1.31618i
$499$	2.95768e35	+	2.95768e35i	0.111325	+	0.111325i	0.760575	−	0.649250i	$-0.224917\pi$
$499$	2.95768e35	+	2.95768e35i	0.111325	+	0.111325i	−0.649250	+	0.760575i	$0.724917\pi$
$500$	−2.77303e35	−	2.33474e36i	−0.101592	−	0.855350i
$501$	4.23552e36	−	4.23552e36i	1.51042	−	1.51042i
$502$	4.06081e36	−	1.97066e36i	1.40965	−	0.684088i
$503$			1.72042e36i			0.581389i	0.956816	+	0.290695i	$0.0938864\pi$
$503$			1.72042e36i			0.581389i	−0.956816	+	0.290695i	$0.906114\pi$
$504$	3.29737e35	+	5.14405e35i	0.108482	+	0.169236i
$505$			4.52673e36i			1.44994i
$506$	−2.05899e36	−	4.24283e36i	−0.642130	−	1.32320i
$507$	2.80633e36	−	2.80633e36i	0.852181	−	0.852181i
$508$	−1.81676e35	−	1.43101e35i	−0.0537201	−	0.0423139i
$509$	−3.05138e36	−	3.05138e36i	−0.878630	−	0.878630i	0.114763	−	0.993393i	$-0.463389\pi$
$509$	−3.05138e36	−	3.05138e36i	−0.878630	−	0.878630i	−0.993393	+	0.114763i	$0.963389\pi$
$510$	2.86936e36	+	9.94351e35i	0.804615	+	0.278832i
$511$	1.37847e36			0.376457
$512$	3.72321e36	−	5.21967e35i	0.990316	−	0.138835i
$513$	−3.61506e36			−0.936550
$514$	−5.10420e36	−	1.76881e36i	−1.28803	−	0.446355i
$515$	2.95144e36	+	2.95144e36i	0.725498	+	0.725498i
$516$	−3.64077e36	−	2.86774e36i	−0.871811	−	0.686702i
$517$	−1.32923e35	+	1.32923e35i	−0.0310084	+	0.0310084i
$518$	−1.55258e35	−	3.19929e35i	−0.0352859	−	0.0727114i
$519$			7.10641e36i			1.57359i
$520$	5.39267e35	+	8.41281e35i	0.116348	+	0.181508i
$521$		−	3.55687e36i		−	0.747754i	−0.927478	−	0.373877i	$-0.878028\pi$
$521$		−	3.55687e36i		−	0.747754i	0.927478	−	0.373877i	$-0.121972\pi$
$522$	−5.97325e35	+	2.89874e35i	−0.122366	+	0.0593825i
$523$	−1.42730e36	+	1.42730e36i	−0.284933	+	0.284933i	−0.835073	−	0.550140i	$-0.814574\pi$
$523$	−1.42730e36	+	1.42730e36i	−0.284933	+	0.284933i	0.550140	+	0.835073i	$0.314574\pi$
$524$	8.47397e35	+	7.13462e36i	0.164860	+	1.38803i
$525$	3.63076e35	+	3.63076e35i	0.0688410	+	0.0688410i
$526$	−3.42389e36	+	9.88021e36i	−0.632722	+	1.82582i
$527$	−3.59522e36			−0.647564
$528$	−1.40673e36	−	5.83840e36i	−0.246975	−	1.02503i
$529$	−1.20048e37			−2.05449
$530$	−3.44007e35	+	9.92689e35i	−0.0573909	+	0.165611i
$531$	3.12511e36	+	3.12511e36i	0.508264	+	0.508264i
$532$	3.83896e36	−	4.55963e35i	0.608705	−	0.0722974i
$533$	−8.61676e35	+	8.61676e35i	−0.133207	+	0.133207i
$534$	3.73019e36	−	1.81021e36i	0.562242	−	0.272849i
$535$			1.17837e37i			1.73183i
$536$	−1.85034e36	+	8.45813e36i	−0.265171	+	1.21213i
$537$			6.20644e36i			0.867340i
$538$	5.33210e36	+	1.09875e37i	0.726671	+	1.49740i
$539$	−3.91987e36	+	3.91987e36i	−0.520983	+	0.520983i
$540$	−2.84259e36	+	3.60884e36i	−0.368467	+	0.467791i
$541$	−8.54713e36	−	8.54713e36i	−1.08058	−	1.08058i	−0.996455	−	0.0841260i	$-0.973190\pi$
$541$	−8.54713e36	−	8.54713e36i	−1.08058	−	1.08058i	−0.0841260	−	0.996455i	$-0.526810\pi$
$542$	1.49462e37	+	5.17946e36i	1.84306	+	0.638695i
$543$	5.31175e36			0.638910
$544$	5.08668e35	−	5.21929e36i	0.0596828	−	0.612388i
$545$	1.64972e36			0.188824
$546$	7.30083e35	+	2.53003e35i	0.0815214	+	0.0282505i
$547$	−7.42613e36	−	7.42613e36i	−0.808972	−	0.808972i	0.175506	−	0.984478i	$-0.443844\pi$
$547$	−7.42613e36	−	7.42613e36i	−0.808972	−	0.808972i	−0.984478	+	0.175506i	$0.943844\pi$
$548$	3.78176e35	−	4.80118e35i	0.0401936	−	0.0510282i
$549$	5.03197e35	−	5.03197e35i	0.0521809	−	0.0521809i
$550$	−7.99714e35	−	1.64792e36i	−0.0809168	−	0.166740i
$551$			4.20085e36i			0.414754i
$552$	−2.22029e37	−	4.85720e36i	−2.13911	−	0.467959i
$553$		−	8.59330e35i		−	0.0807924i
$554$	1.41890e37	−	6.88575e36i	1.30188	−	0.631785i
$555$	−2.50344e36	+	2.50344e36i	−0.224172	+	0.224172i
$556$	4.64221e36	−	5.51367e35i	0.405709	−	0.0481871i
$557$	−9.73993e36	−	9.73993e36i	−0.830827	−	0.830827i	0.156803	−	0.987630i	$-0.449881\pi$
$557$	−9.73993e36	−	9.73993e36i	−0.830827	−	0.830827i	−0.987630	+	0.156803i	$0.949881\pi$
$558$	−2.35814e36	+	6.80479e36i	−0.196339	+	0.566569i
$559$	−2.12718e36			−0.172880
$560$	2.56347e36	−	4.19090e36i	0.203372	−	0.332482i
$561$	−8.37660e36			−0.648738
$562$	6.26187e36	−	1.80697e37i	0.473439	−	1.36619i
$563$	5.56246e35	+	5.56246e35i	0.0410586	+	0.0410586i	0.727338	−	0.686279i	$-0.240757\pi$
$563$	5.56246e35	+	5.56246e35i	0.0410586	+	0.0410586i	−0.686279	+	0.727338i	$0.740757\pi$
$564$	1.06850e35	+	8.99616e35i	0.00770025	+	0.0648320i
$565$	1.52208e37	−	1.52208e37i	1.07098	−	1.07098i
$566$	−1.15816e37	+	5.62039e36i	−0.795694	+	0.386140i
$567$			6.54865e36i			0.439320i
$568$	1.94809e37	−	1.24874e37i	1.27617	−	0.818031i
$569$			9.11310e36i			0.582976i	0.956575	+	0.291488i	$0.0941503\pi$
$569$			9.11310e36i			0.582976i	−0.956575	+	0.291488i	$0.905850\pi$
$570$	−1.68038e37	−	3.46265e37i	−1.04978	−	2.16321i
$571$	−7.67475e36	+	7.67475e36i	−0.468249	+	0.468249i	−0.901347	−	0.433098i	$-0.857420\pi$
$571$	−7.67475e36	+	7.67475e36i	−0.468249	+	0.468249i	0.433098	+	0.901347i	$0.357420\pi$
$572$	−2.16535e36	−	1.70559e36i	−0.129027	−	0.101632i
$573$	−2.68207e36	−	2.68207e36i	−0.156093	−	0.156093i
$574$	5.66068e36	+	1.96166e36i	0.321779	+	0.111510i
$575$	−6.93219e36			−0.384906
$576$	−9.54507e36	−	4.38615e36i	−0.517697	−	0.237892i
$577$	2.31629e37			1.22721			0.613606	−	0.789612i	$-0.289718\pi$
$577$	2.31629e37			1.22721			0.613606	+	0.789612i	$0.289718\pi$
$578$	1.13445e37	+	3.93132e36i	0.587162	+	0.203476i
$579$	1.02035e37	+	1.02035e37i	0.515927	+	0.515927i
$580$	4.19363e36	+	3.30321e36i	0.207163	+	0.163177i
$581$	−5.74719e36	+	5.74719e36i	−0.277382	+	0.277382i
$582$	7.65414e36	+	1.57724e37i	0.360941	+	0.743768i
$583$		−	2.89798e36i		−	0.133527i
$584$	−1.99516e37	+	1.27891e37i	−0.898267	+	0.575795i
$585$		−	2.79205e36i		−	0.122834i
$586$	1.93739e37	−	9.40192e36i	0.832913	−	0.404202i
$587$	1.95986e37	−	1.95986e37i	0.823399	−	0.823399i	−0.163195	−	0.986594i	$-0.552180\pi$
$587$	1.95986e37	−	1.95986e37i	0.823399	−	0.823399i	0.986594	+	0.163195i	$0.0521799\pi$
$588$	3.15097e36	+	2.65294e37i	0.129375	+	1.08927i
$589$	3.22204e37	+	3.22204e37i	1.29293	+	1.29293i
$590$	1.16354e37	−	3.35758e37i	0.456329	−	1.31681i
$591$	−2.54478e37			−0.975481
$592$	5.21539e36	+	3.19013e36i	0.195409	+	0.119527i
$593$	9.63227e36			0.352769			0.176384	−	0.984321i	$-0.443560\pi$
$593$	9.63227e36			0.352769			0.176384	+	0.984321i	$0.443560\pi$
$594$	4.14922e36	−	1.19733e37i	0.148542	−	0.428643i
$595$	−4.84539e36	−	4.84539e36i	−0.169570	−	0.169570i
$596$	2.74399e37	−	3.25910e36i	0.938767	−	0.111500i
$597$	−1.04011e37	+	1.04011e37i	−0.347879	+	0.347879i
$598$	−9.38500e36	+	4.55442e36i	−0.306880	+	0.148925i
$599$		−	2.95423e37i		−	0.944457i	−0.881476	−	0.472228i	$-0.843450\pi$
$599$		−	2.95423e37i		−	0.944457i	0.881476	−	0.472228i	$-0.156550\pi$
$600$	−8.62362e36	−	1.88654e36i	−0.269555	−	0.0589690i
$601$			3.07165e37i			0.938784i	0.882990	+	0.469392i	$0.155527\pi$
$601$			3.07165e37i			0.938784i	−0.882990	+	0.469392i	$0.844473\pi$
$602$	4.56580e36	+	9.40844e36i	0.136447	+	0.281167i
$603$	1.71059e37	−	1.71059e37i	0.499876	−	0.499876i
$604$	3.83381e37	−	4.86726e37i	1.09555	−	1.39087i
$605$	−8.15637e36	−	8.15637e36i	−0.227929	−	0.227929i
$606$	−5.68588e37	−	1.97039e37i	−1.55388	−	0.538482i
$607$	−4.82172e37			−1.28871			−0.644354	−	0.764727i	$-0.722874\pi$
$607$	−4.82172e37			−1.28871			−0.644354	+	0.764727i	$0.722874\pi$
$608$	−5.13339e37	+	4.22165e37i	−1.34186	+	1.10353i
$609$	4.12777e36			0.105532
$610$	−5.40628e36	−	1.87350e36i	−0.135190	−	0.0468489i
$611$	2.94022e35	+	2.94022e35i	0.00719156	+	0.00719156i
$612$	−9.06631e36	+	1.15102e37i	−0.216913	+	0.275385i
$613$	1.59987e37	−	1.59987e37i	0.374427	−	0.374427i	−0.494660	−	0.869087i	$-0.664707\pi$
$613$	1.59987e37	−	1.59987e37i	0.374427	−	0.374427i	0.869087	+	0.494660i	$0.164707\pi$
$614$	1.77994e35	+	3.66781e35i	0.00407505	+	0.00839719i
$615$		−	5.96445e37i		−	1.33585i
$616$	−2.89604e36	+	1.32382e37i	−0.0634548	+	0.290061i
$617$			7.27017e36i			0.155846i	0.996959	+	0.0779229i	$0.0248288\pi$
$617$			7.27017e36i			0.155846i	−0.996959	+	0.0779229i	$0.975171\pi$
$618$	−4.99190e37	+	2.42251e37i	−1.04694	+	0.508066i
$619$	6.65683e37	−	6.65683e37i	1.36598	−	1.36598i	0.499886	−	0.866091i	$-0.333375\pi$
$619$	6.65683e37	−	6.65683e37i	1.36598	−	1.36598i	0.866091	−	0.499886i	$-0.166625\pi$
$620$	5.75004e37	−	6.82947e36i	1.15447	−	0.137119i
$621$	−3.39107e37	−	3.39107e37i	−0.666193	−	0.666193i
$622$	−2.94265e37	+	8.49149e37i	−0.565676	+	1.63235i
$623$	−9.35587e36			−0.175993
$624$	−1.29144e37	+	3.11163e36i	−0.237728	+	0.0572792i
$625$	6.50441e37			1.17173
$626$	−2.21098e37	+	6.38016e37i	−0.389791	+	1.12481i
$627$	7.50710e37	+	7.50710e37i	1.29527	+	1.29527i
$628$	8.15789e35	+	6.86850e36i	0.0137760	+	0.115986i
$629$	6.02988e36	−	6.02988e36i	0.0996610	−	0.0996610i
$630$	−1.23491e37	+	5.99288e36i	−0.199774	+	0.0969479i
$631$		−	6.86584e37i		−	1.08717i	−0.839354	−	0.543585i	$-0.817067\pi$
$631$		−	6.86584e37i		−	1.08717i	0.839354	−	0.543585i	$-0.182933\pi$
$632$	7.97267e36	+	1.24377e37i	0.123573	+	0.192779i
$633$			4.91456e37i			0.745649i
$634$	3.83592e36	+	7.90442e36i	0.0569723	+	0.117399i
$635$	3.67370e36	−	3.67370e36i	0.0534144	−	0.0534144i
$636$	−1.09714e37	−	8.64191e36i	−0.156168	−	0.123010i
$637$	8.67062e36	+	8.67062e36i	0.120828	+	0.120828i
$638$	−1.39134e37	−	4.82157e36i	−0.189826	−	0.0657823i
$639$	−6.46534e37			−0.863634
$640$	1.77913e36	+	8.44413e37i	0.0232690	+	1.10440i
$641$	−2.51544e37			−0.322130			−0.161065	−	0.986944i	$-0.551493\pi$
$641$	−2.51544e37			−0.322130			−0.161065	+	0.986944i	$0.551493\pi$
$642$	−1.48011e38	−	5.12917e37i	−1.85596	−	0.643167i
$643$	3.57241e37	+	3.57241e37i	0.438645	+	0.438645i	0.891556	−	0.452911i	$-0.149615\pi$
$643$	3.57241e37	+	3.57241e37i	0.438645	+	0.438645i	−0.452911	+	0.891556i	$0.649615\pi$
$644$	4.02881e37	+	3.17339e37i	0.484416	+	0.381561i
$645$	7.36207e37	−	7.36207e37i	0.866850	−	0.866850i
$646$	4.04744e37	+	8.34029e37i	0.466704	+	0.961706i
$647$		−	7.42221e37i		−	0.838158i	−0.907950	−	0.419079i	$-0.862353\pi$
$647$		−	7.42221e37i		−	0.838158i	0.907950	−	0.419079i	$-0.137647\pi$
$648$	−6.07569e37	−	9.47836e37i	−0.671944	−	1.04826i
$649$			9.80186e37i			1.06171i
$650$	−3.64514e36	+	1.76894e36i	−0.0386709	+	0.0187665i
$651$	3.16599e37	−	3.16599e37i	0.328977	−	0.328977i
$652$	−5.73097e36	−	4.82516e37i	−0.0583291	−	0.491100i
$653$	−4.69291e37	−	4.69291e37i	−0.467859	−	0.467859i	0.433362	−	0.901220i	$-0.357327\pi$
$653$	−4.69291e37	−	4.69291e37i	−0.467859	−	0.467859i	−0.901220	+	0.433362i	$0.857327\pi$
$654$	−7.18088e36	+	2.07216e37i	−0.0701258	+	0.202360i
$655$	−1.61406e38			−1.54405
$656$	−1.00131e38	+	2.41260e37i	−0.938355	+	0.226091i
$657$	6.62156e37			0.607894
$658$	6.69358e35	−	1.93154e36i	0.00602017	−	0.0173722i
$659$	1.42339e38	+	1.42339e38i	1.25421	+	1.25421i	0.953816	+	0.300392i	$0.0971176\pi$
$659$	1.42339e38	+	1.42339e38i	1.25421	+	1.25421i	0.300392	+	0.953816i	$0.402882\pi$
$660$	1.33972e38	−	1.59122e37i	1.15656	−	0.137368i
$661$	−6.61027e37	+	6.61027e37i	−0.559113	+	0.559113i	−0.929055	−	0.369942i	$-0.879377\pi$
$661$	−6.61027e37	+	6.61027e37i	−0.559113	+	0.559113i	0.369942	+	0.929055i	$0.379377\pi$
$662$	−1.91238e38	+	9.28054e37i	−1.58486	+	0.769114i
$663$			1.85288e37i			0.150457i
$664$	2.98623e37	−	1.36505e38i	0.237604	−	1.08612i
$665$			8.68486e37i			0.677128i
$666$	−7.45789e36	−	1.53680e37i	−0.0569789	−	0.117413i
$667$	−3.94057e37	+	3.94057e37i	−0.295026	+	0.295026i
$668$	1.43784e38	−	1.82543e38i	1.05494	−	1.33932i
$669$	−1.56883e37	−	1.56883e37i	−0.112804	−	0.112804i
$670$	−1.83783e38	−	6.36884e37i	−1.29508	−	0.448798i
$671$	1.57827e37			0.109000
$672$	4.14822e37	+	5.04409e37i	0.280787	+	0.341427i
$673$	−1.88688e38			−1.25182			−0.625909	−	0.779896i	$-0.715272\pi$
$673$	−1.88688e38			−1.25182			−0.625909	+	0.779896i	$0.715272\pi$
$674$	2.81635e38	+	9.75979e37i	1.83138	+	0.634646i
$675$	−1.31709e37	−	1.31709e37i	−0.0839490	−	0.0839490i
$676$	9.52675e37	−	1.20948e38i	0.595202	−	0.755646i
$677$	1.38990e37	−	1.38990e37i	0.0851212	−	0.0851212i	−0.663264	−	0.748385i	$-0.730829\pi$
$677$	1.38990e37	−	1.38990e37i	0.0851212	−	0.0851212i	0.748385	+	0.663264i	$0.230829\pi$
$678$	1.24930e38	+	2.57435e38i	0.750009	+	1.54549i
$679$		−	3.95595e37i		−	0.232814i
$680$	1.15085e38	+	2.51765e37i	0.663972	+	0.145253i
$681$			2.71236e38i			1.53413i
$682$	−1.43697e38	+	6.97342e37i	−0.796816	+	0.386685i
$683$	8.82968e37	−	8.82968e37i	0.480027	−	0.480027i	−0.425113	−	0.905140i	$-0.639766\pi$
$683$	8.82968e37	−	8.82968e37i	0.480027	−	0.480027i	0.905140	+	0.425113i	$0.139766\pi$
$684$	1.84407e38	−	2.19024e37i	0.982923	−	0.116744i
$685$	9.70856e36	+	9.70856e36i	0.0507379	+	0.0507379i
$686$	4.22850e37	−	1.22020e38i	0.216676	−	0.625255i
$687$	−2.26600e38			−1.13853
$688$	−1.53374e38	−	9.38150e37i	−0.755626	−	0.462198i
$689$	−6.41024e36			−0.0309681
$690$	1.67184e38	−	4.82438e38i	0.792014	−	2.28549i
$691$	−2.78304e38	−	2.78304e38i	−1.29290	−	1.29290i	−0.932983	−	0.359920i	$-0.882804\pi$
$691$	−2.78304e38	−	2.78304e38i	−1.29290	−	1.29290i	−0.359920	−	0.932983i	$-0.617196\pi$
$692$	3.25150e37	+	2.73759e38i	0.148133	+	1.24720i
$693$	2.67732e37	−	2.67732e37i	0.119619	−	0.119619i
$694$	−6.40220e37	+	3.10691e37i	−0.280528	+	0.136137i
$695$			1.05020e38i			0.451314i
$696$	−5.97444e37	+	3.82966e37i	−0.251810	+	0.161412i
$697$			1.43662e38i			0.593882i
$698$	−1.94250e38	−	4.00278e38i	−0.787612	−	1.62298i
$699$	3.63734e38	−	3.63734e38i	1.44658	−	1.44658i
$700$	1.56479e37	+	1.23255e37i	0.0610427	+	0.0480817i
$701$	1.89915e38	+	1.89915e38i	0.726717	+	0.726717i	0.969964	−	0.243248i	$-0.0782128\pi$
$701$	1.89915e38	+	1.89915e38i	0.726717	+	0.726717i	−0.243248	+	0.969964i	$0.578213\pi$
$702$	−2.64844e37	−	9.17794e36i	−0.0994122	−	0.0344504i
$703$	−1.08079e38			−0.397966
$704$	−8.09043e37	−	2.18475e38i	−0.292241	−	0.789171i
$705$	−2.03519e37			−0.0721195
$706$	−2.28459e38	−	7.91702e37i	−0.794226	−	0.275232i
$707$	9.60153e37	+	9.60153e37i	0.327475	+	0.327475i
$708$	3.71087e38	+	2.92296e38i	1.24173	+	0.978078i
$709$	3.20737e38	−	3.20737e38i	1.05299	−	1.05299i	0.0544760	−	0.998515i	$-0.482651\pi$
$709$	3.20737e38	−	3.20737e38i	1.05299	−	1.05299i	0.998515	−	0.0544760i	$-0.0173488\pi$
$710$	2.26955e38	+	4.67671e38i	0.731059	+	1.50644i
$711$		−	4.12784e37i		−	0.130462i
$712$	1.35415e38	−	8.68016e37i	0.419938	−	0.269183i
$713$			6.04480e38i			1.83939i
$714$	8.19521e37	−	3.97703e37i	0.244700	−	0.118750i
$715$	4.37860e37	−	4.37860e37i	0.128293	−	0.128293i
$716$	2.83972e37	+	2.39089e38i	0.0816488	+	0.687438i
$717$	−5.00202e38	−	5.00202e38i	−1.41136	−	1.41136i
$718$	−7.57022e37	+	2.18451e38i	−0.209618	+	0.604887i
$719$	−2.05371e37			−0.0558084			−0.0279042	−	0.999611i	$-0.508883\pi$
$719$	−2.05371e37			−0.0558084			−0.0279042	+	0.999611i	$0.508883\pi$
$720$	1.23138e38	−	2.01312e38i	0.328400	−	0.536885i
$721$	1.25204e38			0.327713
$722$	2.57263e38	−	7.42375e38i	0.660885	−	1.90709i
$723$	−1.86794e38	−	1.86794e38i	−0.470974	−	0.470974i
$724$	2.04623e38	−	2.43036e37i	0.506389	−	0.0601450i
$725$	−1.53052e37	+	1.53052e37i	−0.0371771	+	0.0371771i
$726$	1.37952e38	−	6.69465e37i	0.328916	−	0.159619i
$727$		−	8.37859e37i		−	0.196090i	−0.995182	−	0.0980452i	$-0.968741\pi$
$727$		−	8.37859e37i		−	0.196090i	0.995182	−	0.0980452i	$-0.0312590\pi$
$728$	2.92824e37	+	6.40594e36i	0.0672718	+	0.0147167i
$729$			1.50790e37i			0.0340055i
$730$	−2.32439e38	−	4.78972e38i	−0.514577	−	1.06036i
$731$	−1.77326e38	+	1.77326e38i	−0.385379	+	0.385379i
$732$	4.70647e37	−	5.97515e37i	0.100414	−	0.127482i
$733$	−2.95415e38	−	2.95415e38i	−0.618770	−	0.618770i	0.326446	−	0.945216i	$-0.394149\pi$
$733$	−2.95415e38	−	2.95415e38i	−0.618770	−	0.618770i	−0.945216	+	0.326446i	$0.894149\pi$
$734$	7.43319e38	+	2.57590e38i	1.52855	+	0.529703i
$735$	−6.00173e38			−1.21171
$736$	−8.77541e38	−	8.55244e37i	−1.73947	−	0.169527i
$737$	5.36523e38			1.04419
$738$	2.71914e38	+	9.42292e37i	0.519602	+	0.180063i
$739$	−3.46258e38	−	3.46258e38i	−0.649681	−	0.649681i	0.303235	−	0.952916i	$-0.401933\pi$
$739$	−3.46258e38	−	3.46258e38i	−0.649681	−	0.649681i	−0.952916	+	0.303235i	$0.901933\pi$
$740$	−8.49849e37	+	1.07894e38i	−0.156572	+	0.198778i
$741$	1.66054e38	−	1.66054e38i	0.300403	−	0.300403i
$742$	1.37590e37	+	2.83523e37i	0.0244419	+	0.0503658i
$743$			4.88275e38i			0.851757i	0.904780	+	0.425878i	$0.140035\pi$
$743$			4.88275e38i			0.851757i	−0.904780	+	0.425878i	$0.859965\pi$
$744$	−1.64504e38	+	7.51970e38i	−0.281801	+	1.28815i
$745$			6.20770e38i			1.04429i
$746$	3.19486e38	−	1.55042e38i	0.527809	−	0.256139i
$747$	−2.76069e38	+	2.76069e38i	−0.447909	+	0.447909i
$748$	−3.22690e38	+	3.83267e37i	−0.514178	+	0.0610702i
$749$	2.49940e38	+	2.49940e38i	0.391139	+	0.391139i
$750$	−2.29908e38	+	6.63437e38i	−0.353368	+	1.01970i
$751$	−8.04259e38			−1.21411			−0.607053	−	0.794661i	$-0.707648\pi$
$751$	−8.04259e38			−1.21411			−0.607053	+	0.794661i	$0.707648\pi$
$752$	8.23228e36	+	3.41668e37i	0.0122062	+	0.0506598i
$753$	−1.34797e39			−1.96313
$754$	−1.06651e37	+	3.07760e37i	−0.0152565	+	0.0440250i
$755$	9.84218e38	+	9.84218e38i	1.38295	+	1.38295i
$756$	1.62528e37	+	1.36840e38i	0.0224328	+	0.188872i
$757$	6.52114e38	−	6.52114e38i	0.884157	−	0.884157i	−0.109797	−	0.993954i	$-0.535020\pi$
$757$	6.52114e38	−	6.52114e38i	0.884157	−	0.884157i	0.993954	+	0.109797i	$0.0350202\pi$
$758$	4.48755e37	−	2.17775e37i	0.0597688	−	0.0290051i
$759$			1.40839e39i			1.84272i
$760$	−8.05761e38	−	1.25702e39i	−1.03567	−	1.61570i
$761$			5.37444e38i			0.678642i	0.940671	+	0.339321i	$0.110197\pi$
$761$			5.37444e38i			0.678642i	−0.940671	+	0.339321i	$0.889803\pi$
$762$	3.01533e37	+	6.21349e37i	0.0374061	+	0.0770803i
$763$	3.49918e37	−	3.49918e37i	0.0426467	−	0.0426467i
$764$	−1.15592e38	−	9.10491e37i	−0.138410	−	0.109022i
$765$	−2.32751e38	−	2.32751e38i	−0.273818	−	0.273818i
$766$	5.36275e38	+	1.85841e38i	0.619868	+	0.214810i
$767$	2.16814e38			0.246235
$768$	−1.06838e39	−	3.45207e38i	−1.19220	−	0.385215i
$769$	−8.44277e38			−0.925720			−0.462860	−	0.886431i	$-0.653177\pi$
$769$	−8.44277e38			−0.925720			−0.462860	+	0.886431i	$0.653177\pi$
$770$	−2.87647e38	−	9.96814e37i	−0.309910	−	0.107396i
$771$	1.14074e39	+	1.14074e39i	1.20768	+	1.20768i
$772$	4.39753e38	+	3.46381e38i	0.457483	+	0.360347i
$773$	5.45390e38	−	5.45390e38i	0.557550	−	0.557550i	−0.371059	−	0.928609i	$-0.621005\pi$
$773$	5.45390e38	−	5.45390e38i	0.557550	−	0.557550i	0.928609	+	0.371059i	$0.121005\pi$
$774$	2.19321e38	+	4.51940e38i	0.220331	+	0.454023i
$775$			2.34780e38i			0.231787i
$776$	3.67024e38	+	5.72575e38i	0.356092	+	0.555519i
$777$			1.06199e38i			0.101260i
$778$	−1.63770e39	+	7.94757e38i	−1.53465	+	0.744749i
$779$	1.28750e39	−	1.28750e39i	1.18575	−	1.18575i
$780$	−3.51971e37	−	2.96341e38i	−0.0318589	−	0.268234i
$781$	−1.01392e39	−	1.01392e39i	−0.902017	−	0.902017i
$782$	−4.02687e38	+	1.16202e39i	−0.352108	+	1.01607i
$783$	−1.49739e38			−0.128692
$784$	2.42768e38	+	1.00757e39i	0.205080	+	0.851154i
$785$	−1.55386e38			−0.129024
$786$	7.02564e38	−	2.02736e39i	0.573432	−	1.65473i
$787$	1.35956e39	+	1.35956e39i	1.09079	+	1.09079i	0.995445	+	0.0953418i	$0.0303944\pi$
$787$	1.35956e39	+	1.35956e39i	1.09079	+	1.09079i	0.0953418	+	0.995445i	$0.469606\pi$
$788$	−9.80319e38	+	1.16435e38i	−0.773149	+	0.0918289i
$789$	2.20812e39	−	2.20812e39i	1.71192	−	1.71192i
$790$	−2.98588e38	+	1.44901e38i	−0.227566	+	0.110435i
$791$		−	6.45687e38i		−	0.483770i
$792$	−1.39113e38	+	6.35903e38i	−0.102465	+	0.468383i
$793$		−	3.49108e37i		−	0.0252797i
$794$	3.73569e37	+	7.69789e37i	0.0265946	+	0.0548018i
$795$	2.21856e38	−	2.21856e38i	0.155280	−	0.155280i
$796$	−3.53091e38	+	4.48271e38i	−0.242974	+	0.308471i
$797$	−6.50414e38	−	6.50414e38i	−0.440051	−	0.440051i	0.451978	−	0.892029i	$-0.350718\pi$
$797$	−6.50414e38	−	6.50414e38i	−0.440051	−	0.440051i	−0.892029	+	0.451978i	$0.850718\pi$
$798$	−1.09088e39	−	3.78033e38i	−0.725665	−	0.251472i
$799$	4.90205e37			0.0320624
$800$	−3.40837e38	−	3.32177e37i	−0.219196	−	0.0213627i
$801$	−4.49414e38			−0.284189
$802$	1.50017e39	+	5.19869e38i	0.932794	+	0.323251i
$803$	1.03842e39	+	1.03842e39i	0.634911	+	0.634911i
$804$	1.59994e39	−	2.03122e39i	0.961936	−	1.22124i
$805$	−8.14675e38	+	8.14675e38i	−0.481659	+	0.481659i
$806$	1.54250e38	+	3.17852e38i	0.0896812	+	0.184800i
$807$		−	3.64727e39i		−	2.08533i
$808$	−2.28051e39	−	4.98894e38i	−1.28227	−	0.280514i
$809$		−	2.18187e39i		−	1.20649i	−0.797555	−	0.603246i	$-0.793874\pi$
$809$		−	2.18187e39i		−	1.20649i	0.797555	−	0.603246i	$-0.206126\pi$
$810$	2.27543e39	−	1.10424e39i	1.23742	−	0.600504i
$811$	1.55694e39	−	1.55694e39i	0.832704	−	0.832704i	−0.155182	−	0.987886i	$-0.549596\pi$
$811$	1.55694e39	−	1.55694e39i	0.832704	−	0.832704i	0.987886	+	0.155182i	$0.0495963\pi$
$812$	1.59013e38	−	1.88864e37i	0.0836425	−	0.00993443i
$813$	−3.34031e39	−	3.34031e39i	−1.72808	−	1.72808i
$814$	1.24049e38	−	3.57965e38i	0.0631197	−	0.182142i
$815$	1.09159e39			0.546302
$816$	−8.17175e38	+	1.33596e39i	−0.402252	+	0.657622i
$817$	3.17839e39			1.53889
$818$	−9.30573e38	+	2.68532e39i	−0.443181	+	1.27887i
$819$	−5.92213e37	−	5.92213e37i	−0.0277425	−	0.0277425i
$820$	−2.72900e38	−	2.29767e39i	−0.125753	−	1.05877i
$821$	1.13841e39	−	1.13841e39i	0.516020	−	0.516020i	−0.400344	−	0.916365i	$-0.631110\pi$
$821$	1.13841e39	−	1.13841e39i	0.516020	−	0.516020i	0.916365	+	0.400344i	$0.131110\pi$
$822$	−1.64205e38	+	7.96867e37i	−0.0732179	+	0.0355317i
$823$		−	1.07639e39i		−	0.472143i	−0.971736	−	0.236071i	$-0.924140\pi$
$823$		−	1.07639e39i		−	0.472143i	0.971736	−	0.236071i	$-0.0758600\pi$
$824$	−1.81218e39	+	1.16162e39i	−0.781958	+	0.501240i
$825$			5.47020e38i			0.232207i
$826$	−4.65372e38	−	9.58961e38i	−0.194343	−	0.400470i
$827$	2.69050e38	−	2.69050e38i	0.110537	−	0.110537i	−0.649675	−	0.760212i	$-0.725095\pi$
$827$	2.69050e38	−	2.69050e38i	0.110537	−	0.110537i	0.760212	+	0.649675i	$0.225095\pi$
$828$	1.93526e39	+	1.52436e39i	0.782223	+	0.616136i
$829$	9.35957e38	+	9.35957e38i	0.372194	+	0.372194i	0.868276	−	0.496081i	$-0.165228\pi$
$829$	9.35957e38	+	9.35957e38i	0.372194	+	0.372194i	−0.496081	+	0.868276i	$0.665228\pi$
$830$	2.96605e39	+	1.02786e39i	1.16044	+	0.402141i
$831$	−4.70999e39			−1.81304
$832$	−4.83259e38	+	1.78958e38i	−0.183027	+	0.0677775i
$833$	1.44560e39			0.538693
$834$	−1.31912e39	−	4.57130e38i	−0.483664	−	0.167609i
$835$	3.69124e39	+	3.69124e39i	1.33170	+	1.33170i
$836$	3.23542e39	+	2.54846e39i	1.14854	+	0.904676i
$837$	−1.14849e39	+	1.14849e39i	−0.401175	+	0.401175i
$838$	−1.58025e39	−	3.25633e39i	−0.543166	−	1.11927i
$839$			4.83984e39i			1.63698i	0.574518	+	0.818492i	$0.305190\pi$
$839$			4.83984e39i			1.63698i	−0.574518	+	0.818492i	$0.694810\pi$
$840$	−1.23516e39	+	7.91745e38i	−0.411105	+	0.263521i
$841$		−	2.87913e39i		−	0.943008i
$842$	3.80510e39	−	1.84657e39i	1.22646	−	0.595185i
$843$	−4.03838e39	+	4.03838e39i	−1.28096	+	1.28096i
$844$	2.24863e38	+	1.89322e39i	0.0701932	+	0.590988i
$845$	2.44571e39	+	2.44571e39i	0.751346	+	0.751346i
$846$	3.21530e37	−	9.27826e37i	0.00972123	−	0.0280522i
$847$	−3.46005e38			−0.102957
$848$	−4.62191e38	−	2.82711e38i	−0.135356	−	0.0827940i
$849$	3.84446e39			1.10811
$850$	−1.56404e38	+	4.51329e38i	−0.0443703	+	0.128038i
$851$	−1.01383e39	−	1.01383e39i	−0.283084	−	0.283084i
$852$	−6.86215e39	+	8.15034e38i	−1.88593	+	0.223997i
$853$	−2.32984e39	+	2.32984e39i	−0.630252	+	0.630252i	−0.948131	−	0.317880i	$-0.897029\pi$
$853$	−2.32984e39	+	2.32984e39i	−0.630252	+	0.630252i	0.317880	+	0.948131i	$0.397029\pi$
$854$	−1.54409e38	+	7.49328e37i	−0.0411142	+	0.0199522i
$855$			4.17182e39i			1.09341i
$856$	−5.93645e39	−	1.29868e39i	−1.53155	−	0.335048i
$857$			5.29398e39i			1.34444i	0.740351	+	0.672220i	$0.234659\pi$
$857$			5.29398e39i			1.34444i	−0.740351	+	0.672220i	$0.765341\pi$
$858$	3.59390e38	+	7.40572e38i	0.0898438	+	0.185135i
$859$	1.52750e39	−	1.52750e39i	0.375902	−	0.375902i	−0.493720	−	0.869621i	$-0.664363\pi$
$859$	1.52750e39	−	1.52750e39i	0.375902	−	0.375902i	0.869621	+	0.493720i	$0.164363\pi$
$860$	2.49923e39	−	3.17292e39i	0.605447	−	0.768652i
$861$	−1.26510e39	−	1.26510e39i	−0.301706	−	0.301706i
$862$	1.97966e39	+	6.86034e38i	0.464775	+	0.161064i
$863$	−1.36004e39			−0.314344			−0.157172	−	0.987571i	$-0.550238\pi$
$863$	−1.36004e39			−0.314344			−0.157172	+	0.987571i	$0.550238\pi$
$864$	−1.50480e39	−	1.82979e39i	−0.342409	−	0.416357i
$865$	−6.19322e39			−1.38739
$866$	−3.33650e39	−	1.15623e39i	−0.735867	−	0.255008i
$867$	−2.53537e39	−	2.53537e39i	−0.550533	−	0.550533i
$868$	1.07477e39	−	1.36448e39i	0.229773	−	0.291710i
$869$	6.47345e38	−	6.47345e38i	0.136260	−	0.136260i
$870$	−6.96029e38	−	1.43426e39i	−0.144251	−	0.297248i
$871$		−	1.18677e39i		−	0.242171i
$872$	−1.81817e38	+	8.31109e38i	−0.0365310	+	0.166988i
$873$		−	1.90026e39i		−	0.375943i
$874$	1.40229e40	−	6.80513e39i	2.73170	−	1.32566i
$875$	1.12032e39	−	1.12032e39i	0.214899	−	0.214899i
$876$	7.02796e39	−	8.34728e38i	1.32747	−	0.157667i
$877$	1.10931e39	+	1.10931e39i	0.206328	+	0.206328i	0.802705	−	0.596377i	$-0.203393\pi$
$877$	1.10931e39	+	1.10931e39i	0.206328	+	0.206328i	−0.596377	+	0.802705i	$0.703393\pi$
$878$	−6.23908e38	+	1.80039e39i	−0.114273	+	0.329754i
$879$	−6.43110e39			−1.15994
$880$	5.08815e39	−	1.22596e39i	0.903741	−	0.217751i
$881$	2.73515e39			0.478416			0.239208	−	0.970968i	$-0.423112\pi$
$881$	2.73515e39			0.478416			0.239208	+	0.970968i	$0.423112\pi$
$882$	9.48182e38	−	2.73613e39i	0.163330	−	0.471315i
$883$	−3.07635e39	−	3.07635e39i	−0.521875	−	0.521875i	0.396262	−	0.918137i	$-0.370307\pi$
$883$	−3.07635e39	−	3.07635e39i	−0.521875	−	0.521875i	−0.918137	+	0.396262i	$0.870307\pi$
$884$	8.47773e37	+	7.13779e38i	0.0141636	+	0.119250i
$885$	−7.50383e39	+	7.50383e39i	−1.23466	+	1.23466i
$886$	−1.01297e39	+	4.91581e38i	−0.164150	+	0.0796599i
$887$		−	6.19651e39i		−	0.988959i	−0.869189	−	0.494480i	$-0.835359\pi$
$887$		−	6.19651e39i		−	0.988959i	0.869189	−	0.494480i	$-0.164641\pi$
$888$	−9.85294e38	−	1.53710e39i	−0.154878	−	0.241617i
$889$		−	1.55844e38i		−	0.0241277i
$890$	1.57760e39	+	3.25085e39i	0.240564	+	0.495714i
$891$	−4.93318e39	+	4.93318e39i	−0.740932	+	0.740932i
$892$	−6.76138e38	−	5.32576e38i	−0.100025	−	0.0787872i
$893$	−4.39321e38	−	4.39321e38i	−0.0640159	−	0.0640159i
$894$	−7.79728e39	−	2.70208e39i	−1.11915	−	0.387830i
$895$	−5.40889e39			−0.764711
$896$	1.82880e39	+	1.75332e39i	0.254687	+	0.244177i
$897$	3.11532e39			0.427370
$898$	−8.53970e38	−	2.95935e38i	−0.115402	−	0.0399914i
$899$	1.33460e39	+	1.33460e39i	0.177662	+	0.177662i
$900$	7.51657e38	+	5.92061e38i	0.0985703	+	0.0776412i
$901$	−5.34371e38	+	5.34371e38i	−0.0690332	+	0.0690332i
$902$	2.78652e39	+	5.74201e39i	0.354629	+	0.730761i
$903$		−	3.12310e39i		−	0.391562i
$904$	5.99054e39	+	9.34551e39i	0.739932	+	1.15433i
$905$			4.62917e39i			0.563310i
$906$	−1.66465e40	+	8.07834e39i	−1.99569	+	0.968482i
$907$	1.26283e39	−	1.26283e39i	0.149158	−	0.149158i	−0.628584	−	0.777742i	$-0.716365\pi$
$907$	1.26283e39	−	1.26283e39i	0.149158	−	0.149158i	0.777742	+	0.628584i	$0.216365\pi$
$908$	1.24103e39	+	1.04488e40i	0.144418	+	1.21592i
$909$	4.61215e39	+	4.61215e39i	0.528799	+	0.528799i
$910$	−2.20492e38	+	6.36265e38i	−0.0249077	+	0.0718753i
$911$	1.48301e40			1.65062			0.825310	−	0.564680i	$-0.191000\pi$
$911$	1.48301e40			1.65062			0.825310	+	0.564680i	$0.191000\pi$
$912$	1.92964e40	−	4.64934e39i	2.11614	−	0.509872i
$913$	−8.65887e39			−0.935633
$914$	−2.29352e39	+	6.61834e39i	−0.244191	+	0.704653i
$915$	1.20825e39	+	1.20825e39i	0.126757	+	0.126757i
$916$	−8.72926e39	+	1.03680e39i	−0.902378	+	0.107178i
$917$	−3.42354e39	+	3.42354e39i	−0.348730	+	0.348730i
$918$	−2.97289e39	+	1.44271e39i	−0.298403	+	0.144811i
$919$			5.74195e39i			0.567937i	0.958834	+	0.283968i	$0.0916511\pi$
$919$			5.74195e39i			0.567937i	−0.958834	+	0.283968i	$0.908349\pi$
$920$	4.23303e39	−	1.93498e40i	0.412587	−	1.88599i
$921$		−	1.21752e38i		−	0.0116942i
$922$	−1.04471e39	−	2.15277e39i	−0.0988847	−	0.203765i
$923$	−2.24276e39	+	2.24276e39i	−0.209199	+	0.209199i
$924$	2.50413e39	−	3.17914e39i	0.230189	−	0.292239i
$925$	−3.93772e38	−	3.93772e38i	−0.0356723	−	0.0356723i
$926$	7.72302e39	+	2.67634e39i	0.689507	+	0.238942i
$927$	6.01426e39			0.529183
$928$	−2.12629e39	+	1.74865e39i	−0.184385	+	0.151637i
$929$	−1.30348e40			−1.11402			−0.557010	−	0.830506i	$-0.688052\pi$
$929$	−1.30348e40			−1.11402			−0.557010	+	0.830506i	$0.688052\pi$
$930$	−1.63393e40	−	5.66222e39i	−1.37630	−	0.476943i
$931$	−1.29555e40	−	1.29555e40i	−1.07555	−	1.07555i
$932$	1.23478e40	−	1.56763e40i	1.01036	−	1.28271i
$933$	1.89776e40	−	1.89776e40i	1.53052	−	1.53052i
$934$	−5.11693e39	−	1.05441e40i	−0.406749	−	0.838161i
$935$		−	7.30019e39i		−	0.571975i
$936$	1.40660e39	+	3.07713e38i	0.108629	+	0.0237641i
$937$			1.86880e40i			1.42259i	0.702895	+	0.711294i	$0.251890\pi$
$937$			1.86880e40i			1.42259i	−0.702895	+	0.711294i	$0.748110\pi$
$938$	−5.24905e39	+	2.54730e39i	−0.393861	+	0.191136i
$939$	1.42590e40	−	1.42590e40i	1.05464	−	1.05464i
$940$	−7.84013e38	+	9.31191e37i	−0.0571606	+	0.00678911i
$941$	3.76603e39	+	3.76603e39i	0.270660	+	0.270660i	0.829366	−	0.558706i	$-0.188702\pi$
$941$	3.76603e39	+	3.76603e39i	0.270660	+	0.270660i	−0.558706	+	0.829366i	$0.688702\pi$
$942$	6.76359e38	−	1.95174e39i	0.0479170	−	0.138272i
$943$	2.41545e40			1.68691
$944$	1.56327e40	+	9.56215e39i	1.07625	+	0.658315i
$945$	−3.09571e39			−0.210102
$946$	−3.64803e39	+	1.05270e40i	−0.244077	+	0.704325i
$947$	−1.82297e40	−	1.82297e40i	−1.20241	−	1.20241i	−0.973430	−	0.228983i	$-0.926460\pi$
$947$	−1.82297e40	−	1.82297e40i	−1.20241	−	1.20241i	−0.228983	−	0.973430i	$-0.573540\pi$
$948$	−5.20364e38	−	4.38119e39i	−0.0338372	−	0.284891i
$949$	2.29695e39	−	2.29695e39i	0.147251	−	0.147251i
$950$	5.44649e39	−	2.64311e39i	0.344230	−	0.167050i
$951$		−	2.62384e39i		−	0.163494i
$952$	2.97506e39	−	1.90703e39i	0.182766	−	0.117154i
$953$			9.78269e39i			0.592522i	0.955107	+	0.296261i	$0.0957397\pi$
$953$			9.78269e39i			0.592522i	−0.955107	+	0.296261i	$0.904260\pi$
$954$	6.60922e38	+	1.36192e39i	0.0394682	+	0.0813295i
$955$	2.33742e39	−	2.33742e39i	0.137623	−	0.137623i
$956$	−2.15578e40	−	1.69805e40i	−1.25148	−	0.985756i
$957$	3.10951e39	+	3.10951e39i	0.177984	+	0.177984i
$958$	1.07236e40	+	3.71615e39i	0.605208	+	0.209729i
$959$	4.11851e38			0.0229187
$960$	1.05318e40	−	2.29190e40i	0.577882	−	1.25758i
$961$	1.98988e39			0.107662
$962$	−7.91806e38	−	2.74393e38i	−0.0422430	−	0.0146389i
$963$	1.20060e40	+	1.20060e40i	0.631602	+	0.631602i
$964$	−8.05050e39	−	6.34117e39i	−0.417622	−	0.328950i
$965$	−8.89232e39	+	8.89232e39i	−0.454880	+	0.454880i
$966$	−6.68675e39	−	1.37789e40i	−0.337306	−	0.695064i
$967$			1.06933e40i			0.531929i	0.963983	+	0.265965i	$0.0856904\pi$
$967$			1.06933e40i			0.531929i	−0.963983	+	0.265965i	$0.914310\pi$
$968$	5.00799e39	−	3.21016e39i	0.245667	−	0.157474i
$969$		−	2.76853e40i		−	1.33930i
$970$	−1.37456e40	+	6.67056e39i	−0.655760	+	0.318232i
$971$	−1.95101e40	+	1.95101e40i	−0.917910	+	0.917910i	−0.996877	−	0.0789675i	$-0.974838\pi$
$971$	−1.95101e40	+	1.95101e40i	−0.917910	+	0.917910i	0.0789675	+	0.996877i	$0.474838\pi$
$972$	2.59522e39	+	2.18503e40i	0.120415	+	1.01383i
$973$	2.22756e39	+	2.22756e39i	0.101931	+	0.101931i
$974$	−7.49736e39	+	2.16349e40i	−0.338347	+	0.976356i
$975$	1.20999e39			0.0538542
$976$	1.53967e39	−	2.51713e39i	0.0675858	−	0.110493i
$977$	3.94627e39			0.170848			0.0854240	−	0.996345i	$-0.472776\pi$
$977$	3.94627e39			0.170848			0.0854240	+	0.996345i	$0.472776\pi$
$978$	−4.75146e39	+	1.37111e40i	−0.202886	+	0.585462i
$979$	−7.04790e39	−	7.04790e39i	−0.296820	−	0.296820i
$980$	−2.31203e40	+	2.74606e39i	−0.960377	+	0.114066i
$981$	1.68085e39	−	1.68085e39i	0.0688649	−	0.0688649i
$982$	4.73464e39	−	2.29766e39i	0.191330	−	0.0928499i
$983$		−	2.15265e40i		−	0.858026i	−0.903298	−	0.429013i	$-0.858861\pi$
$983$		−	2.15265e40i		−	0.858026i	0.903298	−	0.429013i	$-0.141139\pi$
$984$	3.00481e40	+	6.57345e39i	1.18136	+	0.258440i
$985$		−	2.21777e40i		−	0.860056i
$986$	1.67649e39	+	3.45462e39i	0.0641300	+	0.132149i
$987$	−4.31679e38	+	4.31679e38i	−0.0162884	+	0.0162884i
$988$	5.63710e39	−	7.15665e39i	0.209815	−	0.266373i
$989$	2.98145e40	+	2.98145e40i	1.09466	+	1.09466i
$990$	−1.38173e40	−	4.78825e39i	−0.500435	−	0.173421i
$991$	1.95120e39			0.0697121			0.0348561	−	0.999392i	$-0.488903\pi$
$991$	1.95120e39			0.0697121			0.0348561	+	0.999392i	$0.488903\pi$
$992$	−2.89655e39	+	2.97207e40i	−0.102088	+	1.04749i
$993$	6.34808e40			2.20713
$994$	1.47335e40	+	5.10577e39i	0.505348	+	0.175124i
$995$	−9.06457e39	−	9.06457e39i	−0.306715	−	0.306715i
$996$	−2.58211e40	+	3.27815e40i	−0.861934	+	1.09428i
$997$	−5.62643e39	+	5.62643e39i	−0.185288	+	0.185288i	−0.793656	−	0.608367i	$-0.791825\pi$
$997$	−5.62643e39	+	5.62643e39i	−0.185288	+	0.185288i	0.608367	+	0.793656i	$0.291825\pi$
$998$	−2.11567e39	−	4.35962e39i	−0.0687363	−	0.141640i
$999$		−	3.85248e39i		−	0.123483i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.13.6	yes	106
16.5	even	4	inner	16.28.e.a.5.6	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.6	✓	106	16.5	even	4	inner
16.28.e.a.13.6	yes	106	1.1	even	1	trivial

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	16.28.e.a.13.6

Level	$16$
Weight	$28$
Character	16.13
Analytic conductor	$73.897$
Analytic rank	$0$
Dimension	$106$
Inner twists	$2$