LMFDB - Embedded newform 16.28.e.a.5.5

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			5.5
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11221.9 + 2878.54i) q^{2} +(3.13170e6 - 3.13170e6i) q^{3} +(1.17646e8 - 6.46055e7i) q^{4} +(2.99171e9 + 2.99171e9i) q^{5} +(-2.61290e10 + 4.41585e10i) q^{6} +3.77678e11i q^{7} +(-1.13424e12 + 1.06365e12i) q^{8} -1.19895e13i q^{9} +(-4.21845e13 - 2.49610e13i) q^{10} +(8.16634e13 + 8.16634e13i) q^{11} +(1.66106e14 - 5.70757e14i) q^{12} +(1.00097e15 - 1.00097e15i) q^{13} +(-1.08716e15 - 4.23828e15i) q^{14} +1.87383e16 q^{15} +(9.66665e15 - 1.52011e16i) q^{16} -4.15045e16 q^{17} +(3.45124e16 + 1.34546e17i) q^{18} +(-6.12129e16 + 6.12129e16i) q^{19} +(5.45242e17 + 1.58681e17i) q^{20} +(1.18278e18 + 1.18278e18i) q^{21} +(-1.15149e18 - 6.81350e17i) q^{22} -2.23390e18i q^{23} +(-2.21088e17 + 6.88314e18i) q^{24} +1.04500e19i q^{25} +(-8.35152e18 + 1.41142e19i) q^{26} +(-1.36666e19 - 1.36666e19i) q^{27} +(2.44001e19 + 4.44322e19i) q^{28} +(6.99374e19 - 6.99374e19i) q^{29} +(-2.10280e20 + 5.39388e19i) q^{30} +1.12013e20 q^{31} +(-6.47215e19 + 1.98412e20i) q^{32} +5.11492e20 q^{33} +(4.65760e20 - 1.19472e20i) q^{34} +(-1.12990e21 + 1.12990e21i) q^{35} +(-7.74591e20 - 1.41052e21i) q^{36} +(7.62043e20 + 7.62043e20i) q^{37} +(5.10724e20 - 8.63131e20i) q^{38} -6.26951e21i q^{39} +(-6.57544e21 - 2.11205e20i) q^{40} +4.26521e21i q^{41} +(-1.66777e22 - 9.86836e21i) q^{42} +(-5.47987e21 - 5.47987e21i) q^{43} +(1.48833e22 + 4.33145e21i) q^{44} +(3.58692e22 - 3.58692e22i) q^{45} +(6.43037e21 + 2.50687e22i) q^{46} -1.88547e22 q^{47} +(-1.73323e22 - 7.78785e22i) q^{48} -7.69282e22 q^{49} +(-3.00808e22 - 1.17269e23i) q^{50} +(-1.29980e23 + 1.29980e23i) q^{51} +(5.30919e22 - 1.82429e23i) q^{52} +(1.66919e23 + 1.66919e23i) q^{53} +(1.92706e23 + 1.14026e23i) q^{54} +4.88626e23i q^{55} +(-4.01716e23 - 4.28379e23i) q^{56} +3.83402e23i q^{57} +(-5.83515e23 + 9.86150e23i) q^{58} +(7.00589e23 + 7.00589e23i) q^{59} +(2.20448e24 - 1.21060e24i) q^{60} +(-1.14353e24 + 1.14353e24i) q^{61} +(-1.25700e24 + 3.22433e23i) q^{62} +4.52819e24 q^{63} +(1.55164e23 - 2.41287e24i) q^{64} +5.98924e24 q^{65} +(-5.73992e24 + 1.47235e24i) q^{66} +(4.64819e23 - 4.64819e23i) q^{67} +(-4.88282e24 + 2.68142e24i) q^{68} +(-6.99592e24 - 6.99592e24i) q^{69} +(9.42721e24 - 1.59321e25i) q^{70} +1.39337e25i q^{71} +(1.27526e25 + 1.35991e25i) q^{72} -1.41951e25i q^{73} +(-1.07452e25 - 6.35802e24i) q^{74} +(3.27264e25 + 3.27264e25i) q^{75} +(-3.24675e24 + 1.11561e25i) q^{76} +(-3.08425e25 + 3.08425e25i) q^{77} +(1.80470e25 + 7.03560e25i) q^{78} -2.71335e24 q^{79} +(7.43971e25 - 1.65575e25i) q^{80} +5.82794e24 q^{81} +(-1.22776e25 - 4.78639e25i) q^{82} +(5.76649e24 - 5.76649e24i) q^{83} +(2.15562e26 + 6.27347e25i) q^{84} +(-1.24169e26 - 1.24169e26i) q^{85} +(7.72688e25 + 4.57207e25i) q^{86} -4.38047e26i q^{87} +(-1.79487e26 - 5.76517e24i) q^{88} +2.71721e26i q^{89} +(-2.99271e26 + 5.05773e26i) q^{90} +(3.78046e26 + 3.78046e26i) q^{91} +(-1.44322e26 - 2.62809e26i) q^{92} +(3.50791e26 - 3.50791e26i) q^{93} +(2.11586e26 - 5.42739e25i) q^{94} -3.66262e26 q^{95} +(4.18679e26 + 8.24056e26i) q^{96} +6.54574e26 q^{97} +(8.63283e26 - 2.21441e26i) q^{98} +(9.79108e26 - 9.79108e26i) 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 $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

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

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 $

$2$	−11221.9	+	2878.54i	−0.968641	+	0.248466i
$2$	−11221.9	+	2878.54i	−0.968641	+	0.248466i
$3$	3.13170e6	−	3.13170e6i	1.13408	−	1.13408i	0.144588	−	0.989492i	$-0.453814\pi$
$3$	3.13170e6	−	3.13170e6i	1.13408	−	1.13408i	0.989492	−	0.144588i	$-0.0461858\pi$
$4$	1.17646e8	−	6.46055e7i	0.876529	−	0.481349i
$5$	2.99171e9	+	2.99171e9i	1.09603	+	1.09603i	0.994870	+	0.101164i	$0.0322565\pi$
$5$	2.99171e9	+	2.99171e9i	1.09603	+	1.09603i	0.101164	+	0.994870i	$0.467743\pi$
$6$	−2.61290e10	+	4.41585e10i	−0.816736	+	1.38030i
$7$			3.77678e11i			1.47332i	0.676262	+	0.736662i	$0.263599\pi$
$7$			3.77678e11i			1.47332i	−0.676262	+	0.736662i	$0.736401\pi$
$8$	−1.13424e12	+	1.06365e12i	−0.729443	+	0.684042i
$9$		−	1.19895e13i		−	1.57228i
$10$	−4.21845e13	−	2.49610e13i	−1.33399	−	0.789335i
$11$	8.16634e13	+	8.16634e13i	0.713225	+	0.713225i	0.967209	−	0.253984i	$-0.0817410\pi$
$11$	8.16634e13	+	8.16634e13i	0.713225	+	0.713225i	−0.253984	+	0.967209i	$0.581741\pi$
$12$	1.66106e14	−	5.70757e14i	0.448167	−	1.53994i
$13$	1.00097e15	−	1.00097e15i	0.916617	−	0.916617i	−0.0801650	−	0.996782i	$-0.525545\pi$
$13$	1.00097e15	−	1.00097e15i	0.916617	−	0.916617i	0.996782	+	0.0801650i	$0.0255447\pi$
$14$	−1.08716e15	−	4.23828e15i	−0.366071	−	1.42712i
$15$	1.87383e16			2.48598
$16$	9.66665e15	−	1.52011e16i	0.536607	−	0.843832i
$17$	−4.15045e16			−1.01633			−0.508165	−	0.861260i	$-0.669676\pi$
$17$	−4.15045e16			−1.01633			−0.508165	+	0.861260i	$0.669676\pi$
$18$	3.45124e16	+	1.34546e17i	0.390657	+	1.52297i
$19$	−6.12129e16	+	6.12129e16i	−0.333941	+	0.333941i	−0.854081	−	0.520140i	$-0.825880\pi$
$19$	−6.12129e16	+	6.12129e16i	−0.333941	+	0.333941i	0.520140	+	0.854081i	$0.325880\pi$
$20$	5.45242e17	+	1.58681e17i	1.48828	+	0.433131i
$21$	1.18278e18	+	1.18278e18i	1.67087	+	1.67087i
$22$	−1.15149e18	−	6.81350e17i	−0.868071	−	0.513646i
$23$		−	2.23390e18i		−	0.924141i	−0.886843	−	0.462071i	$-0.847107\pi$
$23$		−	2.23390e18i		−	0.924141i	0.886843	−	0.462071i	$-0.152893\pi$
$24$	−2.21088e17	+	6.88314e18i	−0.0514889	+	1.60301i
$25$			1.04500e19i			1.40258i
$26$	−8.35152e18	+	1.41142e19i	−0.660124	+	1.11562i
$27$	−1.36666e19	−	1.36666e19i	−0.649008	−	0.649008i
$28$	2.44001e19	+	4.44322e19i	0.709182	+	1.29141i
$29$	6.99374e19	−	6.99374e19i	1.26572	−	1.26572i	0.317438	−	0.948279i	$-0.397178\pi$
$29$	6.99374e19	−	6.99374e19i	1.26572	−	1.26572i	0.948279	−	0.317438i	$-0.102822\pi$
$30$	−2.10280e20	+	5.39388e19i	−2.40802	+	0.617682i
$31$	1.12013e20			0.823919			0.411960	−	0.911202i	$-0.364844\pi$
$31$	1.12013e20			0.823919			0.411960	+	0.911202i	$0.364844\pi$
$32$	−6.47215e19	+	1.98412e20i	−0.310116	+	0.950699i
$33$	5.11492e20			1.61771
$34$	4.65760e20	−	1.19472e20i	0.984458	−	0.252523i
$35$	−1.12990e21	+	1.12990e21i	−1.61481	+	1.61481i
$36$	−7.74591e20	−	1.41052e21i	−0.756813	−	1.37815i
$37$	7.62043e20	+	7.62043e20i	0.514347	+	0.514347i	0.915855	−	0.401509i	$-0.131514\pi$
$37$	7.62043e20	+	7.62043e20i	0.514347	+	0.514347i	−0.401509	+	0.915855i	$0.631514\pi$
$38$	5.10724e20	−	8.63131e20i	0.240496	−	0.406442i
$39$		−	6.26951e21i		−	2.07903i
$40$	−6.57544e21	−	2.11205e20i	−1.54923	−	0.0497615i
$41$			4.26521e21i			0.720043i	0.932944	+	0.360022i	$0.117231\pi$
$41$			4.26521e21i			0.720043i	−0.932944	+	0.360022i	$0.882769\pi$
$42$	−1.66777e22	−	9.86836e21i	−2.03362	−	1.20332i
$43$	−5.47987e21	−	5.47987e21i	−0.486347	−	0.486347i	0.420804	−	0.907151i	$-0.361748\pi$
$43$	−5.47987e21	−	5.47987e21i	−0.486347	−	0.486347i	−0.907151	+	0.420804i	$0.861748\pi$
$44$	1.48833e22	+	4.33145e21i	0.968472	+	0.281853i
$45$	3.58692e22	−	3.58692e22i	1.72327	−	1.72327i
$46$	6.43037e21	+	2.50687e22i	0.229618	+	0.895161i
$47$	−1.88547e22			−0.503614			−0.251807	−	0.967777i	$-0.581025\pi$
$47$	−1.88547e22			−0.503614			−0.251807	+	0.967777i	$0.581025\pi$
$48$	−1.73323e22	−	7.78785e22i	−0.348418	−	1.56553i
$49$	−7.69282e22			−1.17068
$50$	−3.00808e22	−	1.17269e23i	−0.348493	−	1.35859i
$51$	−1.29980e23	+	1.29980e23i	−1.15260	+	1.15260i
$52$	5.30919e22	−	1.82429e23i	0.362229	−	1.24465i
$53$	1.66919e23	+	1.66919e23i	0.880607	+	0.880607i	0.993596	−	0.112990i	$-0.0360427\pi$
$53$	1.66919e23	+	1.66919e23i	0.880607	+	0.880607i	−0.112990	+	0.993596i	$0.536043\pi$
$54$	1.92706e23	+	1.14026e23i	0.789912	+	0.467399i
$55$			4.88626e23i			1.56344i
$56$	−4.01716e23	−	4.28379e23i	−1.00781	−	1.07471i
$57$			3.83402e23i			0.757431i
$58$	−5.83515e23	+	9.86150e23i	−0.911537	+	1.54051i
$59$	7.00589e23	+	7.00589e23i	0.868882	+	0.868882i	0.992349	−	0.123467i	$-0.0394012\pi$
$59$	7.00589e23	+	7.00589e23i	0.868882	+	0.868882i	−0.123467	+	0.992349i	$0.539401\pi$
$60$	2.20448e24	−	1.21060e24i	2.17903	−	1.19662i
$61$	−1.14353e24	+	1.14353e24i	−0.904260	+	0.904260i	−0.995801	−	0.0915416i	$-0.970821\pi$
$61$	−1.14353e24	+	1.14353e24i	−0.904260	+	0.904260i	0.0915416	+	0.995801i	$0.470821\pi$
$62$	−1.25700e24	+	3.22433e23i	−0.798082	+	0.204716i
$63$	4.52819e24			2.31647
$64$	1.55164e23	−	2.41287e24i	0.0641743	−	0.997939i
$65$	5.98924e24			2.00928
$66$	−5.73992e24	+	1.47235e24i	−1.56698	+	0.401946i
$67$	4.64819e23	−	4.64819e23i	0.103580	−	0.103580i	−0.653418	−	0.756997i	$-0.726666\pi$
$67$	4.64819e23	−	4.64819e23i	0.103580	−	0.103580i	0.756997	+	0.653418i	$0.226666\pi$
$68$	−4.88282e24	+	2.68142e24i	−0.890842	+	0.489209i
$69$	−6.99592e24	−	6.99592e24i	−1.04805	−	1.04805i
$70$	9.42721e24	−	1.59321e25i	1.16295	−	1.96540i
$71$			1.39337e25i			1.41931i	0.704548	+	0.709657i	$0.251150\pi$
$71$			1.39337e25i			1.41931i	−0.704548	+	0.709657i	$0.748850\pi$
$72$	1.27526e25	+	1.35991e25i	1.07550	+	1.14689i
$73$		−	1.41951e25i		−	0.993756i	−0.867820	−	0.496878i	$-0.834480\pi$
$73$		−	1.41951e25i		−	0.993756i	0.867820	−	0.496878i	$-0.165520\pi$
$74$	−1.07452e25	−	6.35802e24i	−0.626015	−	0.370419i
$75$	3.27264e25	+	3.27264e25i	1.59064	+	1.59064i
$76$	−3.24675e24	+	1.11561e25i	−0.131967	+	0.453451i
$77$	−3.08425e25	+	3.08425e25i	−1.05081	+	1.05081i
$78$	1.80470e25	+	7.03560e25i	0.516569	+	2.01384i
$79$	−2.71335e24			−0.0653942			−0.0326971	−	0.999465i	$-0.510410\pi$
$79$	−2.71335e24			−0.0653942			−0.0326971	+	0.999465i	$0.510410\pi$
$80$	7.43971e25	−	1.65575e25i	1.51301	−	0.336729i
$81$	5.82794e24			0.100223
$82$	−1.22776e25	−	4.78639e25i	−0.178906	−	0.697463i
$83$	5.76649e24	−	5.76649e24i	0.0713440	−	0.0713440i	−0.670534	−	0.741878i	$-0.733935\pi$
$83$	5.76649e24	−	5.76649e24i	0.0713440	−	0.0713440i	0.741878	+	0.670534i	$0.233935\pi$
$84$	2.15562e26	+	6.27347e25i	2.26883	+	0.660294i
$85$	−1.24169e26	−	1.24169e26i	−1.11393	−	1.11393i
$86$	7.72688e25	+	4.57207e25i	0.591936	+	0.350255i
$87$		−	4.38047e26i		−	2.87085i
$88$	−1.79487e26	−	5.76517e24i	−1.00813	−	0.0323814i
$89$			2.71721e26i			1.31026i	0.755515	+	0.655131i	$0.227387\pi$
$89$			2.71721e26i			1.31026i	−0.755515	+	0.655131i	$0.772613\pi$
$90$	−2.99271e26	+	5.05773e26i	−1.24105	+	2.09740i
$91$	3.78046e26	+	3.78046e26i	1.35047	+	1.35047i
$92$	−1.44322e26	−	2.62809e26i	−0.444834	−	0.810037i
$93$	3.50791e26	−	3.50791e26i	0.934391	−	0.934391i
$94$	2.11586e26	−	5.42739e25i	0.487821	−	0.125131i
$95$	−3.66262e26			−0.732021
$96$	4.18679e26	+	8.24056e26i	0.726473	+	1.42986i
$97$	6.54574e26			0.987507			0.493753	−	0.869602i	$-0.335625\pi$
$97$	6.54574e26			0.987507			0.493753	+	0.869602i	$0.335625\pi$
$98$	8.63283e26	−	2.21441e26i	1.13397	−	0.290875i
$99$	9.79108e26	−	9.79108e26i	1.12139	−	1.12139i
$100$	6.75129e26	+	1.22940e27i	0.675129	+	1.22940i
$101$	8.73679e26	+	8.73679e26i	0.763859	+	0.763859i	0.977018	−	0.213158i	$-0.0683751\pi$
$101$	8.73679e26	+	8.73679e26i	0.763859	+	0.763859i	−0.213158	+	0.977018i	$0.568375\pi$
$102$	1.08447e27	−	1.83277e27i	0.830072	−	1.40284i
$103$			1.91785e27i			1.28681i	0.765528	+	0.643403i	$0.222478\pi$
$103$			1.91785e27i			1.28681i	−0.765528	+	0.643403i	$0.777522\pi$
$104$	−7.06655e25	+	2.20003e27i	−0.0416157	+	1.29562i
$105$			7.07703e27i			3.66265i
$106$	−2.35364e27	−	1.39267e27i	−1.07179	−	0.634190i
$107$	−1.51836e27	−	1.51836e27i	−0.609105	−	0.609105i	0.333607	−	0.942712i	$-0.391734\pi$
$107$	−1.51836e27	−	1.51836e27i	−0.609105	−	0.609105i	−0.942712	+	0.333607i	$0.891734\pi$
$108$	−2.49076e27	−	7.24880e26i	−0.881273	−	0.256475i
$109$	−2.68650e27	+	2.68650e27i	−0.839323	+	0.839323i	−0.988770	−	0.149447i	$-0.952251\pi$
$109$	−2.68650e27	+	2.68650e27i	−0.839323	+	0.839323i	0.149447	+	0.988770i	$0.452251\pi$
$110$	−1.40653e27	−	5.48333e27i	−0.388461	−	1.51441i
$111$	4.77298e27			1.16662
$112$	5.74113e27	+	3.65088e27i	1.24324	+	0.790596i
$113$	−3.40909e27			−0.654755			−0.327378	−	0.944894i	$-0.606165\pi$
$113$	−3.40909e27			−0.654755			−0.327378	+	0.944894i	$0.606165\pi$
$114$	−1.10364e27	−	4.30251e27i	−0.188196	−	0.733679i
$115$	6.68318e27	−	6.68318e27i	1.01289	−	1.01289i
$116$	3.70950e27	−	1.27462e28i	0.500187	−	1.71869i
$117$	−1.20012e28	−	1.20012e28i	−1.44117	−	1.44117i
$118$	−9.87863e27	−	5.84529e27i	−1.05752	−	0.625747i
$119$		−	1.56753e28i		−	1.49738i
$120$	−2.12538e28	+	1.99309e28i	−1.81338	+	1.70051i
$121$			2.27842e26i			0.0173793i
$122$	9.54088e27	−	1.61242e28i	0.651225	−	1.10058i
$123$	1.33574e28	+	1.33574e28i	0.816587	+	0.816587i
$124$	1.31778e28	−	7.23664e27i	0.722189	−	0.396592i
$125$	−8.97345e27	+	8.97345e27i	−0.441239	+	0.441239i
$126$	−5.08150e28	+	1.30346e28i	−2.24383	+	0.575565i
$127$	2.75899e28			1.09496			0.547482	−	0.836818i	$-0.315587\pi$
$127$	2.75899e28			1.09496			0.547482	+	0.836818i	$0.315587\pi$
$128$	5.20429e27	+	2.75237e28i	0.185792	+	0.982589i
$129$	−3.43227e28			−1.10311
$130$	−6.72109e28	+	1.72403e28i	−1.94627	+	0.499239i
$131$	−1.31168e28	+	1.31168e28i	−0.342504	+	0.342504i	−0.857308	−	0.514804i	$-0.827865\pi$
$131$	−1.31168e28	+	1.31168e28i	−0.342504	+	0.342504i	0.514804	+	0.857308i	$0.327865\pi$
$132$	6.01748e28	−	3.30452e28i	1.41797	−	0.778682i
$133$	−2.31188e28	−	2.31188e28i	−0.492003	−	0.492003i
$134$	−3.87817e27	+	6.55417e27i	−0.0745954	+	0.126067i
$135$		−	8.17729e28i		−	1.42267i
$136$	4.70762e28	−	4.41461e28i	0.741354	−	0.695211i
$137$		−	5.22657e26i		−	0.00745572i	−0.999993	−	0.00372786i	$-0.998813\pi$
$137$		−	5.22657e26i		−	0.00745572i	0.999993	−	0.00372786i	$-0.00118662\pi$
$138$	9.86458e28	+	5.83697e28i	1.27559	+	0.754779i
$139$	−3.85785e28	−	3.85785e28i	−0.452528	−	0.452528i	0.443665	−	0.896193i	$-0.353678\pi$
$139$	−3.85785e28	−	3.85785e28i	−0.452528	−	0.452528i	−0.896193	+	0.443665i	$0.853678\pi$
$140$	−5.99302e28	+	2.05926e29i	−0.638142	+	2.19272i
$141$	−5.90473e28	+	5.90473e28i	−0.571139	+	0.571139i
$142$	−4.01086e28	−	1.56363e29i	−0.352651	−	1.37480i
$143$	1.63486e29			1.30751
$144$	−1.82255e29	−	1.15899e29i	−1.32674	−	0.843695i
$145$	4.18464e29			2.77454
$146$	4.08611e28	+	1.59296e29i	0.246915	+	0.962593i
$147$	−2.40917e29	+	2.40917e29i	−1.32765	+	1.32765i
$148$	1.38883e29	+	4.04189e28i	0.698420	+	0.203260i
$149$	−2.13398e29	−	2.13398e29i	−0.979888	−	0.979888i	0.0199133	−	0.999802i	$-0.493661\pi$
$149$	−2.13398e29	−	2.13398e29i	−0.979888	−	0.979888i	−0.999802	+	0.0199133i	$0.993661\pi$
$150$	−4.61457e29	−	2.73049e29i	−1.93597	−	1.14554i
$151$		−	1.63581e29i		−	0.627398i	−0.949522	−	0.313699i	$-0.898432\pi$
$151$		−	1.63581e29i		−	0.627398i	0.949522	−	0.313699i	$-0.101568\pi$
$152$	4.32143e27	−	1.34539e29i	0.0151614	−	0.472020i
$153$			4.97620e29i			1.59795i
$154$	2.57331e29	−	4.34893e29i	0.756767	−	1.27895i
$155$	3.35109e29	+	3.35109e29i	0.903043	+	0.903043i
$156$	−4.05045e29	−	7.37582e29i	−1.00074	−	1.82233i
$157$	−6.63366e28	+	6.63366e28i	−0.150351	+	0.150351i	−0.778275	−	0.627924i	$-0.783905\pi$
$157$	−6.63366e28	+	6.63366e28i	−0.150351	+	0.150351i	0.627924	+	0.778275i	$0.283905\pi$
$158$	3.04490e28	−	7.81047e27i	0.0633435	−	0.0162482i
$159$	1.04548e30			1.99736
$160$	−7.87218e29	+	3.99962e29i	−1.38189	+	0.702101i
$161$	8.43696e29			1.36156
$162$	−6.54007e28	+	1.67759e28i	−0.0970800	+	0.0249020i
$163$	−7.39399e28	+	7.39399e28i	−0.101006	+	0.101006i	−0.755804	−	0.654798i	$-0.772754\pi$
$163$	−7.39399e28	+	7.39399e28i	−0.101006	+	0.101006i	0.654798	+	0.755804i	$0.272754\pi$
$164$	2.75556e29	+	5.01784e29i	0.346592	+	0.631139i
$165$	1.53023e30	+	1.53023e30i	1.77306	+	1.77306i
$166$	−4.81121e28	+	8.13103e28i	−0.0513802	+	0.0868333i
$167$			7.93389e29i			0.781293i	0.920541	+	0.390646i	$0.127748\pi$
$167$			7.93389e29i			0.781293i	−0.920541	+	0.390646i	$0.872252\pi$
$168$	−2.59961e30	−	8.35001e28i	−2.36174	−	0.0758598i
$169$		−	8.11366e29i		−	0.680372i
$170$	1.75084e30	+	1.03599e30i	1.35577	+	0.802224i
$171$	7.33915e29	+	7.33915e29i	0.525047	+	0.525047i
$172$	−9.98714e29	−	2.90654e29i	−0.660400	−	0.192195i
$173$	2.02867e30	−	2.02867e30i	1.24048	−	1.24048i	0.280679	−	0.959802i	$-0.409440\pi$
$173$	2.02867e30	−	2.02867e30i	1.24048	−	1.24048i	0.959802	−	0.280679i	$-0.0905596\pi$
$174$	1.26093e30	+	4.91573e30i	0.713309	+	2.78082i
$175$	−3.94674e30			−2.06645
$176$	2.03079e30	−	4.51965e29i	0.984564	−	0.219121i
$177$	4.38807e30			1.97076
$178$	−7.82159e29	−	3.04923e30i	−0.325556	−	1.26917i
$179$	8.39006e28	−	8.39006e28i	0.0323780	−	0.0323780i	−0.690732	−	0.723110i	$-0.742712\pi$
$179$	8.39006e28	−	8.39006e28i	0.0323780	−	0.0323780i	0.723110	+	0.690732i	$0.242712\pi$
$180$	1.90251e30	−	6.53721e30i	0.681002	−	2.33999i
$181$	−2.12428e30	−	2.12428e30i	−0.705588	−	0.705588i	0.260017	−	0.965604i	$-0.416272\pi$
$181$	−2.12428e30	−	2.12428e30i	−0.705588	−	0.705588i	−0.965604	+	0.260017i	$0.916272\pi$
$182$	−5.33062e30	−	3.15419e30i	−1.64367	−	0.972576i
$183$			7.16237e30i			2.05101i
$184$	2.37608e30	+	2.53379e30i	0.632151	+	0.674109i
$185$			4.55961e30i			1.12748i
$186$	−2.92679e30	+	4.94632e30i	−0.672924	+	1.13725i
$187$	−3.38940e30	−	3.38940e30i	−0.724871	−	0.724871i
$188$	−2.21817e30	+	1.21812e30i	−0.441433	+	0.242414i
$189$	5.16157e30	−	5.16157e30i	0.956198	−	0.956198i
$190$	4.11017e30	−	1.05430e30i	0.709065	−	0.181882i
$191$	4.37011e30			0.702331			0.351166	−	0.936313i	$-0.385785\pi$
$191$	4.37011e30			0.702331			0.351166	+	0.936313i	$0.385785\pi$
$192$	−7.07046e30	−	8.04232e30i	−1.05896	−	1.20452i
$193$	−1.93792e30			−0.270591			−0.135295	−	0.990805i	$-0.543198\pi$
$193$	−1.93792e30			−0.270591			−0.135295	+	0.990805i	$0.543198\pi$
$194$	−7.34558e30	+	1.88422e30i	−0.956539	+	0.245362i
$195$	1.87565e31	−	1.87565e31i	2.27869	−	2.27869i
$196$	−9.05028e30	+	4.96999e30i	−1.02614	+	0.563506i
$197$	−1.15203e31	−	1.15203e31i	−1.21946	−	1.21946i	−0.967821	−	0.251641i	$-0.919030\pi$
$197$	−1.15203e31	−	1.15203e31i	−1.21946	−	1.21946i	−0.251641	−	0.967821i	$-0.580970\pi$
$198$	−8.16908e30	+	1.38059e31i	−0.807594	+	1.36485i
$199$			1.51292e31i			1.39733i	0.715448	+	0.698666i	$0.246223\pi$
$199$			1.51292e31i			1.39733i	−0.715448	+	0.698666i	$0.753777\pi$
$200$	−1.11151e31	−	1.18529e31i	−0.959422	−	1.02310i
$201$		−	2.91135e30i		−	0.234935i
$202$	−1.23193e31	−	7.28945e30i	−0.929698	−	0.550112i
$203$	2.64138e31	+	2.64138e31i	1.86481	+	1.86481i
$204$	−6.89416e30	+	2.36890e31i	−0.455485	+	1.56509i
$205$	−1.27603e31	+	1.27603e31i	−0.789192	+	0.789192i
$206$	−5.52062e30	−	2.15220e31i	−0.319728	−	1.24645i
$207$	−2.67835e31			−1.45301
$208$	−5.53987e30	−	2.48920e31i	−0.281608	−	1.26533i
$209$	−9.99772e30			−0.476350
$210$	−2.03715e31	−	7.94180e31i	−0.910045	−	3.54779i
$211$	1.31463e31	−	1.31463e31i	0.550797	−	0.550797i	−0.375874	−	0.926671i	$-0.622657\pi$
$211$	1.31463e31	−	1.31463e31i	0.550797	−	0.550797i	0.926671	+	0.375874i	$0.122657\pi$
$212$	3.04212e31	+	8.85343e30i	1.19576	+	0.347999i
$213$	4.36362e31	+	4.36362e31i	1.60962	+	1.60962i
$214$	2.14095e31	+	1.26682e31i	0.741346	+	0.438662i
$215$		−	3.27883e31i		−	1.06611i
$216$	3.00377e31	+	9.64818e29i	0.917362	+	0.0294659i
$217$			4.23047e31i			1.21390i
$218$	2.24145e31	−	3.78809e31i	0.604459	−	1.02155i
$219$	−4.44549e31	−	4.44549e31i	−1.12700	−	1.12700i
$220$	3.15679e31	+	5.74848e31i	0.752558	+	1.37040i
$221$	−4.15449e31	+	4.15449e31i	−0.931584	+	0.931584i
$222$	−5.35621e31	+	1.37392e31i	−1.13004	+	0.289866i
$223$	−5.43366e30			−0.107889			−0.0539444	−	0.998544i	$-0.517179\pi$
$223$	−5.43366e30			−0.107889			−0.0539444	+	0.998544i	$0.517179\pi$
$224$	−7.49358e31	−	2.44439e31i	−1.40069	−	0.456901i
$225$	1.25291e32			2.20524
$226$	3.82565e31	−	9.81319e30i	0.634223	−	0.162684i
$227$	6.60671e31	−	6.60671e31i	1.03190	−	1.03190i	0.0324226	−	0.999474i	$-0.489678\pi$
$227$	6.60671e31	−	6.60671e31i	1.03190	−	1.03190i	0.999474	−	0.0324226i	$-0.0103222\pi$
$228$	2.47699e31	+	4.51056e31i	0.364589	+	0.663911i
$229$	−8.84126e31	−	8.84126e31i	−1.22669	−	1.22669i	−0.965208	−	0.261482i	$-0.915789\pi$
$229$	−8.84126e31	−	8.84126e31i	−1.22669	−	1.22669i	−0.261482	−	0.965208i	$-0.584211\pi$
$230$	−5.57604e31	+	9.42360e31i	−0.729458	+	1.23280i
$231$			1.93179e32i			2.38341i
$232$	−4.93735e30	+	1.53715e32i	−0.0574654	+	1.78907i
$233$		−	2.06242e31i		−	0.226503i	−0.993566	−	0.113251i	$-0.963873\pi$
$233$		−	2.06242e31i		−	0.226503i	0.993566	−	0.113251i	$-0.0361265\pi$
$234$	1.69223e32	+	1.00131e32i	1.75406	+	1.03790i
$235$	−5.64076e31	−	5.64076e31i	−0.551978	−	0.551978i
$236$	1.27683e32	+	3.71594e31i	1.17984	+	0.343365i
$237$	−8.49740e30	+	8.49740e30i	−0.0741623	+	0.0741623i
$238$	4.51220e31	+	1.75907e32i	0.372048	+	1.45042i
$239$	1.28995e32			1.00508			0.502542	−	0.864553i	$-0.332398\pi$
$239$	1.28995e32			1.00508			0.502542	+	0.864553i	$0.332398\pi$
$240$	1.81136e32	−	2.84843e32i	1.33399	−	2.09775i
$241$	−9.30064e31			−0.647564			−0.323782	−	0.946132i	$-0.604954\pi$
$241$	−9.30064e31			−0.647564			−0.323782	+	0.946132i	$0.604954\pi$
$242$	−6.55853e29	−	2.55683e30i	−0.00431816	−	0.0168343i
$243$	1.22467e32	−	1.22467e32i	0.762669	−	0.762669i
$244$	−6.06529e31	+	2.08409e32i	−0.357346	+	1.22787i
$245$	−2.30147e32	−	2.30147e32i	−1.28311	−	1.28311i
$246$	−1.88345e32	−	1.11446e32i	−0.993873	−	0.588085i
$247$			1.22545e32i			0.612191i
$248$	−1.27050e32	+	1.19142e32i	−0.601002	+	0.563595i
$249$		−	3.61179e31i		−	0.161820i
$250$	7.48690e31	−	1.26530e32i	0.317769	−	0.537035i
$251$	−1.02833e32	−	1.02833e32i	−0.413557	−	0.413557i	0.469419	−	0.882976i	$-0.344463\pi$
$251$	−1.02833e32	−	1.02833e32i	−0.413557	−	0.413557i	−0.882976	+	0.469419i	$0.844463\pi$
$252$	5.32722e32	−	2.92546e32i	2.03046	−	1.11503i
$253$	1.82428e32	−	1.82428e32i	0.659121	−	0.659121i
$254$	−3.09612e32	+	7.94185e31i	−1.06063	+	0.272061i
$255$	−7.77722e32			−2.52657
$256$	−1.37630e32	−	2.93888e32i	−0.424106	−	0.905613i
$257$	2.65715e31			0.0776819			0.0388409	−	0.999245i	$-0.487633\pi$
$257$	2.65715e31			0.0776819			0.0388409	+	0.999245i	$0.487633\pi$
$258$	3.85167e32	−	9.87992e31i	1.06852	−	0.274086i
$259$	−2.87807e32	+	2.87807e32i	−0.757799	+	0.757799i
$260$	7.04609e32	−	3.86938e32i	1.76120	−	0.967166i
$261$	−8.38518e32	−	8.38518e32i	−1.99006	−	1.99006i
$262$	1.09439e32	−	1.84953e32i	0.246663	−	0.416864i
$263$			4.78124e32i			1.02362i	0.859099	+	0.511809i	$0.171025\pi$
$263$			4.78124e32i			1.02362i	−0.859099	+	0.511809i	$0.828975\pi$
$264$	−5.80156e32	+	5.44046e32i	−1.18003	+	1.10658i
$265$			9.98746e32i			1.93035i
$266$	3.25986e32	+	1.92889e32i	0.598820	+	0.354328i
$267$	8.50950e32	+	8.50950e32i	1.48594	+	1.48594i
$268$	2.46541e31	−	8.47138e31i	0.0409326	−	0.140648i
$269$	3.46601e32	−	3.46601e32i	0.547235	−	0.547235i	−0.378405	−	0.925640i	$-0.623527\pi$
$269$	3.46601e32	−	3.46601e32i	0.547235	−	0.547235i	0.925640	+	0.378405i	$0.123527\pi$
$270$	2.35386e32	+	9.17650e32i	0.353485	+	1.37805i
$271$	−8.20273e32			−1.17185			−0.585926	−	0.810364i	$-0.699269\pi$
$271$	−8.20273e32			−1.17185			−0.585926	+	0.810364i	$0.699269\pi$
$272$	−4.01209e32	+	6.30915e32i	−0.545369	+	0.857611i
$273$	2.36786e33			3.06309
$274$	1.50449e30	+	5.86523e30i	0.00185249	+	0.00722191i
$275$	−8.53385e32	+	8.53385e32i	−1.00035	+	1.00035i
$276$	−1.27502e33	−	3.71065e32i	−1.42312	−	0.414169i
$277$	−7.41105e32	−	7.41105e32i	−0.787776	−	0.787776i	0.193353	−	0.981129i	$-0.438064\pi$
$277$	−7.41105e32	−	7.41105e32i	−0.787776	−	0.787776i	−0.981129	+	0.193353i	$0.938064\pi$
$278$	5.43974e32	+	3.21875e32i	0.550774	+	0.325899i
$279$		−	1.34298e33i		−	1.29543i
$280$	7.97673e31	−	2.48340e33i	0.0733148	−	2.28251i
$281$		−	1.17693e33i		−	1.03090i	−0.856920	−	0.515449i	$-0.827625\pi$
$281$		−	1.17693e33i		−	1.03090i	0.856920	−	0.515449i	$-0.172375\pi$
$282$	4.92655e32	−	8.32594e32i	0.411320	−	0.695137i
$283$	−1.40700e33	−	1.40700e33i	−1.11989	−	1.11989i	−0.991757	−	0.128136i	$-0.959101\pi$
$283$	−1.40700e33	−	1.40700e33i	−1.11989	−	1.11989i	−0.128136	−	0.991757i	$-0.540899\pi$
$284$	9.00193e32	+	1.63924e33i	0.683184	+	1.24407i
$285$	−1.14702e33	+	1.14702e33i	−0.830170	+	0.830170i
$286$	−1.83463e33	+	4.70601e32i	−1.26650	+	0.324871i
$287$	−1.61088e33			−1.06086
$288$	2.37887e33	+	7.75981e32i	1.49476	+	0.487588i
$289$	5.49090e31			0.0329248
$290$	−4.69598e33	+	1.20457e33i	−2.68753	+	0.689378i
$291$	2.04993e33	−	2.04993e33i	1.11991	−	1.11991i
$292$	−9.17082e32	−	1.66999e33i	−0.478343	−	0.871056i
$293$	−9.79971e32	−	9.79971e32i	−0.488091	−	0.488091i	0.419613	−	0.907703i	$-0.362166\pi$
$293$	−9.79971e32	−	9.79971e32i	−0.488091	−	0.488091i	−0.907703	+	0.419613i	$0.862166\pi$
$294$	2.01006e33	−	3.39704e33i	0.956137	−	1.61589i
$295$			4.19191e33i			1.90465i
$296$	−1.67489e33	−	5.37977e31i	−0.727021	−	0.0233521i
$297$		−	2.23212e33i		−	0.925777i
$298$	3.00902e33	+	1.78047e33i	1.19263	+	0.705691i
$299$	−2.23608e33	−	2.23608e33i	−0.847083	−	0.847083i
$300$	5.96443e33	+	1.73582e33i	2.15989	+	0.628589i
$301$	2.06963e33	−	2.06963e33i	0.716547	−	0.716547i
$302$	4.70873e32	+	1.83569e33i	0.155887	+	0.607723i
$303$	5.47221e33			1.73256
$304$	3.38782e32	+	1.52223e33i	0.102595	+	0.460985i
$305$	−6.84218e33			−1.98220
$306$	−1.43242e33	−	5.58425e33i	−0.397036	−	1.54784i
$307$	−2.78215e33	+	2.78215e33i	−0.737927	+	0.737927i	−0.972176	−	0.234250i	$-0.924737\pi$
$307$	−2.78215e33	+	2.78215e33i	−0.737927	+	0.737927i	0.234250	+	0.972176i	$0.424737\pi$
$308$	−1.63589e33	+	5.62108e33i	−0.415260	+	1.42687i
$309$	6.00615e33	+	6.00615e33i	1.45934	+	1.45934i
$310$	−4.72520e33	−	2.79595e33i	−1.09910	−	0.650349i
$311$		−	1.72573e33i		−	0.384332i	−0.981362	−	0.192166i	$-0.938449\pi$
$311$		−	1.72573e33i		−	0.384332i	0.981362	−	0.192166i	$-0.0615512\pi$
$312$	6.66854e33	+	7.11115e33i	1.42215	+	1.51654i
$313$		−	3.35883e33i		−	0.686024i	−0.939331	−	0.343012i	$-0.888553\pi$
$313$		−	3.35883e33i		−	0.686024i	0.939331	−	0.343012i	$-0.111447\pi$
$314$	5.53472e32	−	9.35377e32i	0.108279	−	0.182994i
$315$	1.35470e34	+	1.35470e34i	2.53893	+	2.53893i
$316$	−3.19214e32	+	1.75297e32i	−0.0573199	+	0.0314774i
$317$	9.80948e32	−	9.80948e32i	0.168790	−	0.168790i	−0.617657	−	0.786447i	$-0.711918\pi$
$317$	9.80948e32	−	9.80948e32i	0.168790	−	0.168790i	0.786447	+	0.617657i	$0.211918\pi$
$318$	−1.17323e34	+	3.00946e33i	−1.93472	+	0.496275i
$319$	1.14227e34			1.80548
$320$	7.68279e33	−	6.75439e33i	1.16411	−	1.02344i
$321$	−9.51008e33			−1.38155
$322$	−9.46789e33	+	2.42861e33i	−1.31886	+	0.338301i
$323$	2.54061e33	−	2.54061e33i	0.339394	−	0.339394i
$324$	6.85632e32	−	3.76517e32i	0.0878483	−	0.0482422i
$325$	1.04602e34	+	1.04602e34i	1.28563	+	1.28563i
$326$	6.16909e32	−	1.04259e33i	0.0727418	−	0.122935i
$327$			1.68267e34i			1.90372i
$328$	−4.53668e33	−	4.83779e33i	−0.492540	−	0.525231i
$329$		−	7.12099e33i		−	0.741986i
$330$	−2.15770e34	−	1.27673e34i	−2.15801	−	1.27691i
$331$	1.85950e33	+	1.85950e33i	0.178532	+	0.178532i	0.790716	−	0.612183i	$-0.209709\pi$
$331$	1.85950e33	+	1.85950e33i	0.178532	+	0.178532i	−0.612183	+	0.790716i	$0.709709\pi$
$332$	3.05856e32	−	1.05095e33i	0.0281938	−	0.0968765i
$333$	9.13655e33	−	9.13655e33i	0.808695	−	0.808695i
$334$	−2.28380e33	−	8.90336e33i	−0.194125	−	0.756792i
$335$	2.78120e33			0.227053
$336$	2.94130e34	−	6.54605e33i	2.30653	−	0.513333i
$337$	9.82014e33			0.739799			0.369900	−	0.929072i	$-0.379392\pi$
$337$	9.82014e33			0.739799			0.369900	+	0.929072i	$0.379392\pi$
$338$	2.33555e33	+	9.10510e33i	0.169049	+	0.659036i
$339$	−1.06763e34	+	1.06763e34i	−0.742545	+	0.742545i
$340$	−2.26300e34	−	6.58596e33i	−1.51258	−	0.440204i
$341$	9.14735e33	+	9.14735e33i	0.587640	+	0.587640i
$342$	−1.03486e34	−	6.12334e33i	−0.639039	−	0.378126i
$343$		−	4.23599e33i		−	0.251469i
$344$	1.20442e34	+	3.86861e32i	0.687444	+	0.0220809i
$345$		−	4.18595e34i		−	2.29740i
$346$	−1.69260e34	+	2.86053e34i	−0.893363	+	1.50980i
$347$	−5.31478e32	−	5.31478e32i	−0.0269797	−	0.0269797i	0.693488	−	0.720468i	$-0.256073\pi$
$347$	−5.31478e32	−	5.31478e32i	−0.0269797	−	0.0269797i	−0.720468	+	0.693488i	$0.756073\pi$
$348$	−2.83002e34	−	5.15343e34i	−1.38188	−	2.51638i
$349$	−2.18417e33	+	2.18417e33i	−0.102599	+	0.102599i	−0.756543	−	0.653944i	$-0.773113\pi$
$349$	−2.18417e33	+	2.18417e33i	−0.102599	+	0.102599i	0.653944	+	0.756543i	$0.273113\pi$
$350$	4.42901e34	−	1.13609e34i	2.00165	−	0.513443i
$351$	−2.73598e34			−1.18978
$352$	−2.14884e34	+	1.09176e34i	−0.899244	+	0.456880i
$353$	2.47069e33			0.0995084			0.0497542	−	0.998761i	$-0.484156\pi$
$353$	2.47069e33			0.0995084			0.0497542	+	0.998761i	$0.484156\pi$
$354$	−4.92427e34	+	1.26312e34i	−1.90896	+	0.489668i
$355$	−4.16855e34	+	4.16855e34i	−1.55561	+	1.55561i
$356$	1.75547e34	+	3.19668e34i	0.630693	+	1.14848i
$357$	−4.90905e34	−	4.90905e34i	−1.69815	−	1.69815i
$358$	−7.00016e32	+	1.18304e33i	−0.0233178	+	0.0394074i
$359$		−	4.81366e34i		−	1.54419i	−0.635508	−	0.772094i	$-0.719209\pi$
$359$		−	4.81366e34i		−	1.54419i	0.635508	−	0.772094i	$-0.280791\pi$
$360$	−2.53225e33	+	7.88365e34i	−0.0782389	+	2.43581i
$361$			2.61066e34i			0.776967i
$362$	2.99533e34	+	1.77237e34i	0.858775	+	0.508146i
$363$	7.13535e32	+	7.13535e32i	0.0197095	+	0.0197095i
$364$	6.88994e34	+	2.00516e34i	1.83378	+	0.533681i
$365$	4.24676e34	−	4.24676e34i	1.08919	−	1.08919i
$366$	−2.06172e34	−	8.03756e34i	−0.509605	−	1.98669i
$367$	−1.49278e34			−0.355634			−0.177817	−	0.984064i	$-0.556903\pi$
$367$	−1.49278e34			−0.355634			−0.177817	+	0.984064i	$0.556903\pi$
$368$	−3.39578e34	−	2.15944e34i	−0.779820	−	0.495901i
$369$	5.11380e34			1.13211
$370$	−1.31250e34	−	5.11677e34i	−0.280141	−	1.09213i
$371$	−6.30417e34	+	6.30417e34i	−1.29742	+	1.29742i
$372$	1.86060e34	−	6.39321e34i	0.369253	−	1.26879i
$373$	2.02249e34	+	2.02249e34i	0.387095	+	0.387095i	0.873650	−	0.486555i	$-0.161747\pi$
$373$	2.02249e34	+	2.02249e34i	0.387095	+	0.387095i	−0.486555	+	0.873650i	$0.661747\pi$
$374$	4.77921e34	+	2.82791e34i	0.882245	+	0.522034i
$375$			5.62044e34i			1.00080i
$376$	2.13858e34	−	2.00547e34i	0.367358	−	0.344493i
$377$		−	1.40011e35i		−	2.32035i
$378$	−4.30650e34	+	7.27806e34i	−0.688629	+	1.16379i
$379$	6.53646e34	+	6.53646e34i	1.00859	+	1.00859i	0.999963	+	0.00862339i	$0.00274494\pi$
$379$	6.53646e34	+	6.53646e34i	1.00859	+	1.00859i	0.00862339	+	0.999963i	$0.497255\pi$
$380$	−4.30892e34	+	2.36626e34i	−0.641637	+	0.352357i
$381$	8.64034e34	−	8.64034e34i	1.24178	−	1.24178i
$382$	−4.90411e34	+	1.25795e34i	−0.680307	+	0.174505i
$383$	1.12805e35			1.51058			0.755292	−	0.655389i	$-0.227495\pi$
$383$	1.12805e35			1.51058			0.755292	+	0.655389i	$0.227495\pi$
$384$	1.02494e35	+	6.98977e34i	1.32504	+	0.903632i
$385$	−1.84543e35			−2.30345
$386$	2.17472e34	−	5.57838e33i	0.262105	−	0.0672326i
$387$	−6.57012e34	+	6.57012e34i	−0.764672	+	0.764672i
$388$	7.70078e34	−	4.22891e34i	0.865579	−	0.475335i
$389$	−8.87777e34	−	8.87777e34i	−0.963794	−	0.963794i	0.0355729	−	0.999367i	$-0.488674\pi$
$389$	−8.87777e34	−	8.87777e34i	−0.963794	−	0.963794i	−0.999367	+	0.0355729i	$0.988674\pi$
$390$	−1.56493e35	+	2.64476e35i	−1.64105	+	2.77341i
$391$			9.27169e34i			0.939232i
$392$	8.72553e34	−	8.18245e34i	0.853945	−	0.800795i
$393$			8.21559e34i			0.776854i
$394$	1.62441e35	+	9.61180e34i	1.48421	+	0.878225i
$395$	−8.11753e33	−	8.11753e33i	−0.0716742	−	0.0716742i
$396$	5.19321e34	−	1.78444e35i	0.443150	−	1.52271i
$397$	−9.59636e34	+	9.59636e34i	−0.791470	+	0.791470i	−0.981733	−	0.190263i	$-0.939066\pi$
$397$	−9.59636e34	+	9.59636e34i	−0.791470	+	0.791470i	0.190263	+	0.981733i	$0.439066\pi$
$398$	−4.35500e34	−	1.69779e35i	−0.347190	−	1.35351i
$399$	−1.44802e35			−1.11594
$400$	1.58852e35	+	1.01017e35i	1.18354	+	0.752633i
$401$	2.64669e35			1.90657			0.953287	−	0.302066i	$-0.0976764\pi$
$401$	2.64669e35			1.90657			0.953287	+	0.302066i	$0.0976764\pi$
$402$	8.38044e33	+	3.26710e34i	0.0583734	+	0.227568i
$403$	1.12122e35	−	1.12122e35i	0.755218	−	0.755218i
$404$	1.59229e35	+	4.63401e34i	1.03723	+	0.301862i
$405$	1.74355e34	+	1.74355e34i	0.109848	+	0.109848i
$406$	−3.72447e35	−	2.20381e35i	−2.26967	−	1.34299i
$407$			1.24462e35i			0.733690i
$408$	9.17614e33	−	2.85681e35i	0.0523297	−	1.62918i
$409$		−	7.01740e34i		−	0.387179i	−0.981083	−	0.193589i	$-0.937987\pi$
$409$		−	7.01740e34i		−	0.387179i	0.981083	−	0.193589i	$-0.0620130\pi$
$410$	1.06464e35	−	1.79926e35i	0.568356	−	0.960530i
$411$	−1.63681e33	−	1.63681e33i	−0.00845538	−	0.00845538i
$412$	1.23904e35	+	2.25627e35i	0.619402	+	1.12792i
$413$	−2.64597e35	+	2.64597e35i	−1.28014	+	1.28014i
$414$	3.00562e35	−	7.70973e34i	1.40744	−	0.361023i
$415$	3.45033e34			0.156391
$416$	1.33821e35	+	2.63390e35i	0.587169	+	1.15568i
$417$	−2.41633e35			−1.02641
$418$	1.12194e35	−	2.87788e34i	0.461412	−	0.118357i
$419$	−1.69063e35	+	1.69063e35i	−0.673222	+	0.673222i	−0.958457	−	0.285236i	$-0.907928\pi$
$419$	−1.69063e35	+	1.69063e35i	−0.673222	+	0.673222i	0.285236	+	0.958457i	$0.407928\pi$
$420$	4.57215e35	+	8.32583e35i	1.76301	+	3.21042i
$421$	−2.38107e35	−	2.38107e35i	−0.889127	−	0.889127i	0.105312	−	0.994439i	$-0.466416\pi$
$421$	−2.38107e35	−	2.38107e35i	−0.889127	−	0.889127i	−0.994439	+	0.105312i	$0.966416\pi$
$422$	−1.09685e35	+	1.85369e35i	−0.396670	+	0.670378i
$423$			2.26059e35i			0.791821i
$424$	−3.66870e35	−	1.17839e34i	−1.24472	−	0.0399808i
$425$		−	4.33723e35i		−	1.42548i
$426$	−6.15291e35	−	3.64074e35i	−1.95907	−	1.15920i
$427$	−4.31884e35	−	4.31884e35i	−1.33227	−	1.33227i
$428$	−2.76722e35	−	8.05340e34i	−0.827091	−	0.240707i
$429$	5.11990e35	−	5.11990e35i	1.48282	−	1.48282i
$430$	9.43825e34	+	3.67948e35i	0.264891	+	1.03267i
$431$	−4.80569e34			−0.130711			−0.0653556	−	0.997862i	$-0.520818\pi$
$431$	−4.80569e34			−0.130711			−0.0653556	+	0.997862i	$0.520818\pi$
$432$	−3.39858e35	+	7.56375e34i	−0.895916	+	0.199392i
$433$	−3.31020e34			−0.0845799			−0.0422900	−	0.999105i	$-0.513465\pi$
$433$	−3.31020e34			−0.0845799			−0.0422900	+	0.999105i	$0.513465\pi$
$434$	−1.21776e35	−	4.74741e35i	−0.301613	−	1.17583i
$435$	1.31051e36	−	1.31051e36i	3.14655	−	3.14655i
$436$	−1.42493e35	+	4.89618e35i	−0.331684	+	1.13970i
$437$	1.36744e35	+	1.36744e35i	0.308609	+	0.308609i
$438$	6.26834e35	+	3.70904e35i	1.37168	+	0.811636i
$439$		−	7.92134e35i		−	1.68084i	−0.541932	−	0.840422i	$-0.682307\pi$
$439$		−	7.92134e35i		−	1.68084i	0.541932	−	0.840422i	$-0.317693\pi$
$440$	−5.19725e35	−	5.54221e35i	−1.06946	−	1.14044i
$441$			9.22335e35i			1.84063i
$442$	3.46625e35	−	5.85803e35i	0.670903	−	1.13384i
$443$	4.84742e35	+	4.84742e35i	0.910040	+	0.910040i	0.996275	−	0.0862350i	$-0.0274836\pi$
$443$	4.84742e35	+	4.84742e35i	0.910040	+	0.910040i	−0.0862350	+	0.996275i	$0.527484\pi$
$444$	5.61521e35	−	3.08361e35i	1.02258	−	0.561551i
$445$	−8.12909e35	+	8.12909e35i	−1.43609	+	1.43609i
$446$	6.09761e34	−	1.56410e34i	0.104506	−	0.0268067i
$447$	−1.33660e36			−2.22254
$448$	9.11287e35	+	5.86019e34i	1.47029	+	0.0945494i
$449$	9.85150e34			0.154233			0.0771164	−	0.997022i	$-0.475429\pi$
$449$	9.85150e34			0.154233			0.0771164	+	0.997022i	$0.475429\pi$
$450$	−1.40601e36	+	3.60655e35i	−2.13609	+	0.547928i
$451$	−3.48312e35	+	3.48312e35i	−0.513553	+	0.513553i
$452$	−4.01065e35	+	2.20246e35i	−0.573912	+	0.315166i
$453$	−5.12286e35	−	5.12286e35i	−0.711520	−	0.711520i
$454$	−5.51224e35	+	9.31577e35i	−0.743146	+	1.25593i
$455$			2.26200e36i			2.96033i
$456$	−4.07804e35	−	4.34871e35i	−0.518115	−	0.552503i
$457$			4.84383e35i			0.597476i	0.954335	+	0.298738i	$0.0965657\pi$
$457$			4.84383e35i			0.597476i	−0.954335	+	0.298738i	$0.903434\pi$
$458$	1.24666e36	+	7.37661e35i	1.49301	+	0.883431i
$459$	5.67225e35	+	5.67225e35i	0.659605	+	0.659605i
$460$	3.54477e35	−	1.21802e36i	0.400274	−	1.37538i
$461$	4.63789e35	−	4.63789e35i	0.508579	−	0.508579i	−0.405511	−	0.914090i	$-0.632906\pi$
$461$	4.63789e35	−	4.63789e35i	0.508579	−	0.508579i	0.914090	+	0.405511i	$0.132906\pi$
$462$	−5.56073e35	−	2.16784e36i	−0.592196	−	2.30867i
$463$	3.00115e34			0.0310416			0.0155208	−	0.999880i	$-0.495059\pi$
$463$	3.00115e34			0.0310416			0.0155208	+	0.999880i	$0.495059\pi$
$464$	−3.87067e35	−	1.73919e36i	−0.388860	−	1.74725i
$465$	2.09893e36			2.04825
$466$	5.93677e34	+	2.31444e35i	0.0562782	+	0.219400i
$467$	−1.91323e35	+	1.91323e35i	−0.176193	+	0.176193i	−0.789694	−	0.613501i	$-0.789761\pi$
$467$	−1.91323e35	+	1.91323e35i	−0.176193	+	0.176193i	0.613501	+	0.789694i	$0.289761\pi$
$468$	−2.18724e36	−	6.36548e35i	−1.95694	−	0.569524i
$469$	1.75552e35	+	1.75552e35i	0.152606	+	0.152606i
$470$	7.95374e35	+	4.70631e35i	0.671816	+	0.397520i
$471$			4.15493e35i			0.341021i
$472$	−1.53982e36	−	4.94593e34i	−1.22815	−	0.0394485i
$473$		−	8.95011e35i		−	0.693750i
$474$	7.08971e34	−	1.19817e35i	0.0534098	−	0.0902634i
$475$	−6.39676e35	−	6.39676e35i	−0.468378	−	0.468378i
$476$	−1.01271e36	−	1.84413e36i	−0.720762	−	1.31250i
$477$	2.00129e36	−	2.00129e36i	1.38456	−	1.38456i
$478$	−1.44758e36	+	3.71318e35i	−0.973564	+	0.249729i
$479$	−1.37145e36			−0.896704			−0.448352	−	0.893857i	$-0.647989\pi$
$479$	−1.37145e36			−0.896704			−0.448352	+	0.893857i	$0.647989\pi$
$480$	−1.21277e36	+	3.71790e36i	−0.770941	+	2.36342i
$481$	1.52557e36			0.942917
$482$	1.04371e36	−	2.67723e35i	0.627257	−	0.160898i
$483$	2.64221e36	−	2.64221e36i	1.54412	−	1.54412i
$484$	1.47199e34	+	2.68047e34i	0.00836550	+	0.0152335i
$485$	1.95829e36	+	1.95829e36i	1.08234	+	1.08234i
$486$	−1.02179e36	+	1.72685e36i	−0.549254	+	0.928249i
$487$		−	7.45130e35i		−	0.389575i	−0.980845	−	0.194787i	$-0.937598\pi$
$487$		−	7.45130e35i		−	0.389575i	0.980845	−	0.194787i	$-0.0624017\pi$
$488$	8.07292e34	−	2.51334e36i	0.0410547	−	1.27816i
$489$			4.63116e35i			0.229097i
$490$	3.24518e36	+	1.92020e36i	1.56168	+	0.924060i
$491$	1.35757e36	+	1.35757e36i	0.635566	+	0.635566i	0.949458	−	0.313893i	$-0.101633\pi$
$491$	1.35757e36	+	1.35757e36i	0.635566	+	0.635566i	−0.313893	+	0.949458i	$0.601633\pi$
$492$	2.43440e36	+	7.08479e35i	1.10883	+	0.322699i
$493$	−2.90271e36	+	2.90271e36i	−1.28638	+	1.28638i
$494$	−3.52751e35	−	1.37519e36i	−0.152109	−	0.592993i
$495$	5.85840e36			2.45815
$496$	1.08279e36	−	1.70272e36i	0.442121	−	0.695250i
$497$	−5.26244e36			−2.09111
$498$	1.03967e35	+	4.05313e35i	0.0402067	+	0.156745i
$499$	−3.19342e36	+	3.19342e36i	−1.20199	+	1.20199i	−0.228423	+	0.973562i	$0.573357\pi$
$499$	−3.19342e36	+	3.19342e36i	−1.20199	+	1.20199i	−0.973562	+	0.228423i	$0.926643\pi$
$500$	−4.75954e35	+	1.63542e36i	−0.174369	+	0.599149i
$501$	2.48466e36	+	2.48466e36i	0.886049	+	0.886049i
$502$	1.44999e36	+	8.57972e35i	0.503343	+	0.297833i
$503$		−	4.92464e36i		−	1.66420i	−0.554622	−	0.832102i	$-0.687137\pi$
$503$		−	4.92464e36i		−	1.66420i	0.554622	−	0.832102i	$-0.312863\pi$
$504$	−5.13607e36	+	4.81639e36i	−1.68973	+	1.58456i
$505$			5.22758e36i			1.67443i
$506$	−1.52207e36	+	2.57232e36i	−0.474682	+	0.802220i
$507$	−2.54096e36	−	2.54096e36i	−0.771596	−	0.771596i
$508$	3.24583e36	−	1.78246e36i	0.959768	−	0.527059i
$509$	6.62858e35	−	6.62858e35i	0.190867	−	0.190867i	−0.605204	−	0.796071i	$-0.706908\pi$
$509$	6.62858e35	−	6.62858e35i	0.190867	−	0.190867i	0.796071	+	0.605204i	$0.206908\pi$
$510$	8.72754e36	−	2.23870e36i	2.44734	−	0.627768i
$511$	5.36118e36			1.46412
$512$	2.39044e36	+	2.90182e36i	0.635820	+	0.771837i
$513$	1.67315e36			0.433460
$514$	−2.98184e35	+	7.64872e34i	−0.0752458	+	0.0193013i
$515$	−5.73765e36	+	5.73765e36i	−1.41038	+	1.41038i
$516$	−4.03792e36	+	2.21744e36i	−0.966911	+	0.530982i
$517$	−1.53974e36	−	1.53974e36i	−0.359190	−	0.359190i
$518$	2.40128e36	−	4.05821e36i	0.545747	−	0.922322i
$519$		−	1.27064e37i		−	2.81361i
$520$	−6.79326e36	+	6.37044e36i	−1.46566	+	1.37443i
$521$		−	7.74557e36i		−	1.62834i	−0.580629	−	0.814169i	$-0.697193\pi$
$521$		−	7.74557e36i		−	1.62834i	0.580629	−	0.814169i	$-0.302807\pi$
$522$	1.18235e37	+	6.99608e36i	2.42211	+	1.43319i
$523$	−9.70340e35	−	9.70340e35i	−0.193710	−	0.193710i	0.603587	−	0.797297i	$-0.293737\pi$
$523$	−9.70340e35	−	9.70340e35i	−0.193710	−	0.193710i	−0.797297	+	0.603587i	$0.793737\pi$
$524$	−6.95719e35	+	2.39055e36i	−0.135351	+	0.465079i
$525$	−1.23600e37	+	1.23600e37i	−2.34352	+	2.34352i
$526$	−1.37630e36	−	5.36548e36i	−0.254334	−	0.991519i
$527$	−4.64903e36			−0.837373
$528$	4.94441e36	−	7.77525e36i	0.868074	−	1.36507i
$529$	8.52890e35			0.145963
$530$	−2.87493e36	−	1.12079e37i	−0.479626	−	1.86981i
$531$	8.39974e36	−	8.39974e36i	1.36612	−	1.36612i
$532$	−4.21343e36	−	1.22623e36i	−0.668080	−	0.194430i
$533$	4.26937e36	+	4.26937e36i	0.660004	+	0.660004i
$534$	−1.19988e37	−	7.09981e36i	−1.80855	−	1.07014i
$535$		−	9.08495e36i		−	1.33520i
$536$	−3.28147e34	+	1.02162e36i	−0.00470266	+	0.146408i
$537$		−	5.25504e35i		−	0.0734384i
$538$	−2.89183e36	+	4.88723e36i	−0.394105	+	0.666043i
$539$	−6.28222e36	−	6.28222e36i	−0.834959	−	0.834959i
$540$	−5.28298e36	−	9.62024e36i	−0.684799	−	1.24701i
$541$	−1.75599e36	+	1.75599e36i	−0.222003	+	0.222003i	−0.809341	−	0.587339i	$-0.800176\pi$
$541$	−1.75599e36	+	1.75599e36i	−0.222003	+	0.222003i	0.587339	+	0.809341i	$0.300176\pi$
$542$	9.20505e36	−	2.36119e36i	1.13510	−	0.291166i
$543$	−1.33052e37			−1.60039
$544$	2.68623e36	−	8.23498e36i	0.315180	−	0.966223i
$545$	−1.60744e37			−1.83985
$546$	−2.65719e37	+	6.81596e36i	−2.96703	+	0.761074i
$547$	5.24181e36	−	5.24181e36i	0.571021	−	0.571021i	−0.361392	−	0.932414i	$-0.617699\pi$
$547$	5.24181e36	−	5.24181e36i	0.571021	−	0.571021i	0.932414	+	0.361392i	$0.117699\pi$
$548$	−3.37666e34	−	6.14884e34i	−0.00358880	−	0.00653515i
$549$	1.37104e37	+	1.37104e37i	1.42175	+	1.42175i
$550$	7.12013e36	−	1.20331e37i	0.720429	−	1.21754i
$551$			8.56215e36i			0.845349i
$552$	1.53763e37	+	4.93889e35i	1.48140	+	0.0475830i
$553$		−	1.02477e36i		−	0.0963468i
$554$	1.04499e37	+	6.18333e36i	0.958808	+	0.567337i
$555$	1.42794e37	+	1.42794e37i	1.27866	+	1.27866i
$556$	−7.03097e36	−	2.04621e36i	−0.614477	−	0.178830i
$557$	4.03049e36	−	4.03049e36i	0.343805	−	0.343805i	−0.513991	−	0.857796i	$-0.671833\pi$
$557$	4.03049e36	−	4.03049e36i	0.343805	−	0.343805i	0.857796	+	0.513991i	$0.171833\pi$
$558$	3.86583e36	+	1.50709e37i	0.321870	+	1.25481i
$559$	−1.09704e37			−0.891588
$560$	6.25341e36	+	2.80981e37i	0.496111	+	2.22915i
$561$	−2.12292e37			−1.64412
$562$	3.38784e36	+	1.32074e37i	0.256143	+	0.998569i
$563$	4.13227e36	−	4.13227e36i	0.305018	−	0.305018i	−0.537955	−	0.842973i	$-0.680803\pi$
$563$	4.13227e36	−	4.13227e36i	0.305018	−	0.305018i	0.842973	+	0.537955i	$0.180803\pi$
$564$	−3.13188e36	+	1.07614e37i	−0.225703	+	0.775537i
$565$	−1.01990e37	−	1.01990e37i	−0.717634	−	0.717634i
$566$	1.98393e37	+	1.17391e37i	1.36303	+	0.806518i
$567$			2.20108e36i			0.147661i
$568$	−1.48205e37	−	1.58042e37i	−0.970869	−	1.03531i
$569$			1.26345e37i			0.808245i	0.914705	+	0.404123i	$0.132423\pi$
$569$			1.26345e37i			0.808245i	−0.914705	+	0.404123i	$0.867577\pi$
$570$	9.57008e36	−	1.61736e37i	0.597867	−	1.01041i
$571$	5.83670e36	+	5.83670e36i	0.356107	+	0.356107i	0.862376	−	0.506269i	$-0.168976\pi$
$571$	5.83670e36	+	5.83670e36i	0.356107	+	0.356107i	−0.506269	+	0.862376i	$0.668976\pi$
$572$	1.92334e37	−	1.05621e37i	1.14607	−	0.629367i
$573$	1.36859e37	−	1.36859e37i	0.796500	−	0.796500i
$574$	1.80771e37	−	4.63697e36i	1.02759	−	0.263587i
$575$	2.33443e37			1.29618
$576$	−2.89292e37	−	1.86034e36i	−1.56904	−	0.100900i
$577$	−2.58987e37			−1.37216			−0.686080	−	0.727526i	$-0.740670\pi$
$577$	−2.58987e37			−1.37216			−0.686080	+	0.727526i	$0.740670\pi$
$578$	−6.16185e35	+	1.58058e35i	−0.0318923	+	0.00818069i
$579$	−6.06900e36	+	6.06900e36i	−0.306872	+	0.306872i
$580$	4.92305e37	−	2.70351e37i	2.43196	−	1.33552i
$581$	2.17788e36	+	2.17788e36i	0.105113	+	0.105113i
$582$	−1.71034e37	+	2.89050e37i	−0.806532	+	1.36305i
$583$			2.72624e37i			1.25614i
$584$	1.50986e37	+	1.61007e37i	0.679771	+	0.724889i
$585$		−	7.18083e37i		−	3.15915i
$586$	1.38181e37	+	8.17629e36i	0.594058	+	0.351511i
$587$	−2.30752e37	−	2.30752e37i	−0.969464	−	0.969464i	0.0300831	−	0.999547i	$-0.490423\pi$
$587$	−2.30752e37	−	2.30752e37i	−0.969464	−	0.969464i	−0.999547	+	0.0300831i	$0.990423\pi$
$588$	−1.27783e37	+	4.39073e37i	−0.524660	+	1.80278i
$589$	−6.85663e36	+	6.85663e36i	−0.275140	+	0.275140i
$590$	−1.20666e37	−	4.70413e37i	−0.473240	−	1.84492i
$591$	−7.21561e37			−2.76593
$592$	1.89503e37	−	4.21751e36i	0.710024	−	0.158020i
$593$	2.88143e37			1.05528			0.527642	−	0.849467i	$-0.323076\pi$
$593$	2.88143e37			1.05528			0.527642	+	0.849467i	$0.323076\pi$
$594$	6.42525e36	+	2.50487e37i	0.230024	+	0.896745i
$595$	4.68959e37	−	4.68959e37i	1.64118	−	1.64118i
$596$	−3.88921e37	−	1.13187e37i	−1.33057	−	0.387233i
$597$	4.73802e37	+	4.73802e37i	1.58469	+	1.58469i
$598$	3.15298e37	+	1.86565e37i	1.03099	+	0.610048i
$599$			2.55414e36i			0.0816551i	0.999166	+	0.0408275i	$0.0129994\pi$
$599$			2.55414e36i			0.0816551i	−0.999166	+	0.0408275i	$0.987001\pi$
$600$	−7.19290e37	−	2.31038e36i	−2.24834	−	0.0722172i
$601$			2.21970e37i			0.678404i	0.940714	+	0.339202i	$0.110157\pi$
$601$			2.21970e37i			0.678404i	−0.940714	+	0.339202i	$0.889843\pi$
$602$	−1.72677e37	+	2.91827e37i	−0.516039	+	0.872114i
$603$	−5.57297e36	−	5.57297e36i	−0.162856	−	0.162856i
$604$	−1.05682e37	−	1.92446e37i	−0.301997	−	0.549933i
$605$	−6.81638e35	+	6.81638e35i	−0.0190483	+	0.0190483i
$606$	−6.14087e37	+	1.57520e37i	−1.67822	+	0.430481i
$607$	1.12387e37			0.300379			0.150189	−	0.988657i	$-0.452012\pi$
$607$	1.12387e37			0.300379			0.150189	+	0.988657i	$0.452012\pi$
$608$	−8.18358e36	−	1.61072e37i	−0.213917	−	0.421037i
$609$	1.65441e38			4.22969
$610$	7.67825e37	−	1.96955e37i	1.92004	−	0.492509i
$611$	−1.88730e37	+	1.88730e37i	−0.461621	+	0.461621i
$612$	3.21490e37	+	5.85429e37i	0.769171	+	1.40065i
$613$	−9.54654e36	−	9.54654e36i	−0.223424	−	0.223424i	0.586515	−	0.809939i	$-0.300500\pi$
$613$	−9.54654e36	−	9.54654e36i	−0.223424	−	0.223424i	−0.809939	+	0.586515i	$0.800500\pi$
$614$	2.32126e37	−	3.92297e37i	0.531436	−	0.898135i
$615$			7.99227e37i			1.79001i
$616$	2.17738e36	−	6.77884e37i	0.0477083	−	1.48530i
$617$		−	1.88273e37i		−	0.403587i	−0.979428	−	0.201794i	$-0.935323\pi$
$617$		−	1.88273e37i		−	0.403587i	0.979428	−	0.201794i	$-0.0646770\pi$
$618$	−8.46896e37	−	5.01117e37i	−1.77617	−	1.05098i
$619$	5.64391e37	+	5.64391e37i	1.15813	+	1.15813i	0.984878	+	0.173250i	$0.0554269\pi$
$619$	5.64391e37	+	5.64391e37i	1.15813	+	1.15813i	0.173250	+	0.984878i	$0.444573\pi$
$620$	6.10741e37	+	1.77743e37i	1.22622	+	0.356865i
$621$	−3.05299e37	+	3.05299e37i	−0.599775	+	0.599775i
$622$	4.96757e36	+	1.93660e37i	0.0954934	+	0.372279i
$623$	−1.02623e38			−1.93044
$624$	−9.53037e37	−	6.06052e37i	−1.75436	−	1.11562i
$625$	2.41669e37			0.435352
$626$	9.66851e36	+	3.76925e37i	0.170454	+	0.664510i
$627$	−3.13099e37	+	3.13099e37i	−0.540219	+	0.540219i
$628$	−3.51851e36	+	1.20899e37i	−0.0594160	+	0.204159i
$629$	−3.16282e37	−	3.16282e37i	−0.522745	−	0.522745i
$630$	−1.91019e38	−	1.13028e38i	−3.09015	−	1.82847i
$631$		−	3.51996e37i		−	0.557368i	−0.960383	−	0.278684i	$-0.910102\pi$
$631$		−	3.51996e37i		−	0.557368i	0.960383	−	0.278684i	$-0.0898982\pi$
$632$	3.07759e36	−	2.88604e36i	0.0477014	−	0.0447324i
$633$		−	8.23408e37i		−	1.24930i
$634$	−8.18444e36	+	1.38318e37i	−0.121558	+	0.205435i
$635$	8.25408e37	+	8.25408e37i	1.20012	+	1.20012i
$636$	1.22997e38	−	6.75440e37i	1.75074	−	0.961425i
$637$	−7.70032e37	+	7.70032e37i	−1.07307	+	1.07307i
$638$	−1.28184e38	+	3.28806e37i	−1.74886	+	0.448601i
$639$	1.67059e38			2.23155
$640$	−6.67730e37	+	9.79125e37i	−0.873316	+	1.28058i
$641$	−6.31267e37			−0.808407			−0.404203	−	0.914669i	$-0.632451\pi$
$641$	−6.31267e37			−0.808407			−0.404203	+	0.914669i	$0.632451\pi$
$642$	1.06721e38	−	2.73751e37i	1.33822	−	0.343268i
$643$	4.84842e37	−	4.84842e37i	0.595323	−	0.595323i	−0.343742	−	0.939064i	$-0.611694\pi$
$643$	4.84842e37	−	4.84842e37i	0.595323	−	0.595323i	0.939064	+	0.343742i	$0.111694\pi$
$644$	9.92572e37	−	5.45074e37i	1.19345	−	0.655385i
$645$	−1.02683e38	−	1.02683e38i	−1.20905	−	1.20905i
$646$	−2.11973e37	+	3.58238e37i	−0.244423	+	0.413078i
$647$		−	6.88709e37i		−	0.777728i	−0.921295	−	0.388864i	$-0.872868\pi$
$647$		−	6.88709e37i		−	0.777728i	0.921295	−	0.388864i	$-0.127132\pi$
$648$	−6.61030e36	+	6.19887e36i	−0.0731069	+	0.0685567i
$649$			1.14425e38i			1.23942i
$650$	−1.47494e38	−	8.72736e37i	−1.56474	−	0.925876i
$651$	1.32486e38	+	1.32486e38i	1.37666	+	1.37666i
$652$	−3.92179e36	+	1.34756e37i	−0.0399155	+	0.137153i
$653$	1.13996e38	−	1.13996e38i	1.13648	−	1.13648i	0.147404	−	0.989076i	$-0.452908\pi$
$653$	1.13996e38	−	1.13996e38i	1.13648	−	1.13648i	0.989076	−	0.147404i	$-0.0470919\pi$
$654$	−4.84362e37	−	1.88828e38i	−0.473010	−	1.84402i
$655$	−7.84832e37			−0.750791
$656$	6.48361e37	+	4.12303e37i	0.607596	+	0.386380i
$657$	−1.70193e38			−1.56246
$658$	2.04981e37	+	7.99113e37i	0.184358	+	0.718718i
$659$	1.21592e38	−	1.21592e38i	1.07140	−	1.07140i	0.0741496	−	0.997247i	$-0.476376\pi$
$659$	1.21592e38	−	1.21592e38i	1.07140	−	1.07140i	0.997247	−	0.0741496i	$-0.0236242\pi$
$660$	2.78887e38	+	8.11639e37i	2.40760	+	0.700680i
$661$	−3.46152e37	−	3.46152e37i	−0.292783	−	0.292783i	0.545395	−	0.838179i	$-0.316380\pi$
$661$	−3.46152e37	−	3.46152e37i	−0.292783	−	0.292783i	−0.838179	+	0.545395i	$0.816380\pi$
$662$	−2.62198e37	−	1.55145e37i	−0.217293	−	0.128575i
$663$			2.60213e38i			2.11298i
$664$	−4.07096e35	+	1.26741e37i	−0.00323912	+	0.100844i
$665$		−	1.38329e38i		−	1.07850i
$666$	−7.62298e37	+	1.28830e38i	−0.582402	+	0.984268i
$667$	−1.56233e38	−	1.56233e38i	−1.16970	−	1.16970i
$668$	5.12573e37	+	9.33388e37i	0.376074	+	0.684826i
$669$	−1.70166e37	+	1.70166e37i	−0.122355	+	0.122355i
$670$	−3.12105e37	+	8.00580e36i	−0.219933	+	0.0564150i
$671$	−1.86769e38			−1.28988
$672$	−3.11228e38	+	1.58126e38i	−2.10665	+	1.07033i
$673$	5.66114e36			0.0375578			0.0187789	−	0.999824i	$-0.494022\pi$
$673$	5.66114e36			0.0375578			0.0187789	+	0.999824i	$0.494022\pi$
$674$	−1.10201e38	+	2.82676e37i	−0.716600	+	0.183815i
$675$	1.42816e38	−	1.42816e38i	0.910284	−	0.910284i
$676$	−5.24187e37	−	9.54538e37i	−0.327496	−	0.596366i
$677$	4.22629e37	+	4.22629e37i	0.258829	+	0.258829i	0.824578	−	0.565749i	$-0.191413\pi$
$677$	4.22629e37	+	4.22629e37i	0.258829	+	0.258829i	−0.565749	+	0.824578i	$0.691413\pi$
$678$	8.90762e37	−	1.50540e38i	0.534762	−	0.903757i
$679$			2.47218e38i			1.45492i
$680$	2.72910e38	+	8.76593e36i	1.57452	+	0.0505741i
$681$		−	4.13805e38i		−	2.34051i
$682$	−1.28982e38	−	7.63199e37i	−0.715220	−	0.423203i
$683$	7.37223e37	+	7.37223e37i	0.400792	+	0.400792i	0.878512	−	0.477720i	$-0.158537\pi$
$683$	7.37223e37	+	7.37223e37i	0.400792	+	0.400792i	−0.477720	+	0.878512i	$0.658537\pi$
$684$	1.33757e38	+	3.89270e37i	0.712950	+	0.207489i
$685$	1.56364e36	−	1.56364e36i	0.00817172	−	0.00817172i
$686$	1.21935e37	+	4.75360e37i	0.0624815	+	0.243583i
$687$	−5.53764e38			−2.78233
$688$	−1.36272e38	+	3.03282e37i	−0.671373	+	0.149418i
$689$	3.34164e38			1.61436
$690$	1.20494e38	+	4.69744e38i	0.570825	+	2.22535i
$691$	1.10919e38	−	1.10919e38i	0.515289	−	0.515289i	−0.400853	−	0.916142i	$-0.631286\pi$
$691$	1.10919e38	−	1.10919e38i	0.515289	−	0.515289i	0.916142	+	0.400853i	$0.131286\pi$
$692$	1.07601e38	−	3.69729e38i	0.490214	−	1.68442i
$693$	3.69787e38	+	3.69787e38i	1.65217	+	1.65217i
$694$	7.49408e36	+	4.43433e36i	0.0328372	+	0.0194301i
$695$		−	2.30831e38i		−	0.991971i
$696$	4.65927e38	+	4.96851e38i	1.96378	+	2.09412i
$697$		−	1.77025e38i		−	0.731801i
$698$	1.82234e37	−	3.07978e37i	0.0738892	−	0.124874i
$699$	−6.45890e37	−	6.45890e37i	−0.256872	−	0.256872i
$700$	−4.64318e38	+	2.54981e38i	−1.81130	+	0.994683i
$701$	−3.32141e38	+	3.32141e38i	−1.27095	+	1.27095i	−0.325365	+	0.945588i	$0.605487\pi$
$701$	−3.32141e38	+	3.32141e38i	−1.27095	+	1.27095i	−0.945588	+	0.325365i	$0.894513\pi$
$702$	3.07030e38	−	7.87563e37i	1.15247	−	0.295621i
$703$	−9.32937e37			−0.343523
$704$	2.09714e38	−	1.84372e38i	0.757525	−	0.665984i
$705$	−3.53304e38			−1.25197
$706$	−2.77259e37	+	7.11198e36i	−0.0963879	+	0.0247245i
$707$	−3.29969e38	+	3.29969e38i	−1.12541	+	1.12541i
$708$	5.16238e38	−	2.83494e38i	1.72743	−	0.948625i
$709$	9.28028e37	+	9.28028e37i	0.304675	+	0.304675i	0.842840	−	0.538165i	$-0.180882\pi$
$709$	9.28028e37	+	9.28028e37i	0.304675	+	0.304675i	−0.538165	+	0.842840i	$0.680882\pi$
$710$	3.47798e38	−	5.87785e38i	1.12031	−	1.89335i
$711$			3.25318e37i			0.102818i
$712$	−2.89015e38	−	3.08198e38i	−0.896274	−	0.955761i
$713$		−	2.50226e38i		−	0.761418i
$714$	6.92199e38	+	4.09581e38i	2.06683	+	1.22296i
$715$	4.89102e38	+	4.89102e38i	1.43307	+	1.43307i
$716$	4.45011e36	−	1.52910e37i	0.0127951	−	0.0439653i
$717$	4.03975e38	−	4.03975e38i	1.13985	−	1.13985i
$718$	1.38563e38	+	5.40185e38i	0.383678	+	1.49576i
$719$	3.56905e38			0.969869			0.484934	−	0.874551i	$-0.338843\pi$
$719$	3.56905e38			0.969869			0.484934	+	0.874551i	$0.338843\pi$
$720$	−1.98517e38	−	8.91987e38i	−0.529431	−	2.37887i
$721$	−7.24331e38			−1.89588
$722$	−7.51488e37	−	2.92966e38i	−0.193050	−	0.752602i
$723$	−2.91269e38	+	2.91269e38i	−0.734390	+	0.734390i
$724$	−3.87153e38	−	1.12672e38i	−0.958102	−	0.278835i
$725$	7.30847e38	+	7.30847e38i	1.77527	+	1.77527i
$726$	−1.00612e37	−	5.95331e36i	−0.0239886	−	0.0141943i
$727$			3.75790e37i			0.0879491i	0.999033	+	0.0439745i	$0.0140020\pi$
$727$			3.75790e37i			0.0879491i	−0.999033	+	0.0439745i	$0.985998\pi$
$728$	−8.30903e38	−	2.66888e37i	−1.90887	−	0.0613134i
$729$		−	7.22622e38i		−	1.62963i
$730$	−3.54324e38	+	5.98813e38i	−0.784407	+	1.32566i
$731$	2.27439e38	+	2.27439e38i	0.494289	+	0.494289i
$732$	4.62729e38	+	8.42622e38i	0.987249	+	1.79777i
$733$	−5.63729e38	+	5.63729e38i	−1.18077	+	1.18077i	−0.201229	+	0.979544i	$0.564494\pi$
$733$	−5.63729e38	+	5.63729e38i	−1.18077	+	1.18077i	−0.979544	+	0.201229i	$0.935506\pi$
$734$	1.67518e38	−	4.29702e37i	0.344481	−	0.0883629i
$735$	−1.44150e39			−2.91029
$736$	4.43233e38	+	1.44581e38i	0.878580	+	0.286591i
$737$	7.59174e37			0.147751
$738$	−5.73867e38	+	1.47203e38i	−1.09661	+	0.281290i
$739$	1.78384e38	−	1.78384e38i	0.334699	−	0.334699i	−0.519669	−	0.854368i	$-0.673945\pi$
$739$	1.78384e38	−	1.78384e38i	0.334699	−	0.334699i	0.854368	+	0.519669i	$0.173945\pi$
$740$	2.94576e38	+	5.36419e38i	0.542712	+	0.988271i
$741$	3.83775e38	+	3.83775e38i	0.694274	+	0.694274i
$742$	5.25981e38	−	8.88917e38i	0.934367	−	1.57910i
$743$		−	4.99178e38i		−	0.870777i	−0.900243	−	0.435388i	$-0.856611\pi$
$743$		−	4.99178e38i		−	0.870777i	0.900243	−	0.435388i	$-0.143389\pi$
$744$	−2.47647e37	+	7.71000e38i	−0.0424227	+	1.32075i
$745$		−	1.27685e39i		−	2.14798i
$746$	−2.85181e38	−	1.68744e38i	−0.471135	−	0.278776i
$747$	−6.91377e37	−	6.91377e37i	−0.112173	−	0.112173i
$748$	−6.17722e38	−	1.79774e38i	−0.984286	−	0.286455i
$749$	5.73449e38	−	5.73449e38i	0.897409	−	0.897409i
$750$	−1.61786e38	−	6.30722e38i	−0.248665	−	0.969417i
$751$	3.65700e38			0.552059			0.276029	−	0.961149i	$-0.410981\pi$
$751$	3.65700e38			0.552059			0.276029	+	0.961149i	$0.410981\pi$
$752$	−1.82262e38	+	2.86612e38i	−0.270243	+	0.424966i
$753$	−6.44082e38			−0.938014
$754$	4.03027e38	+	1.57119e39i	0.576529	+	2.24759i
$755$	4.89385e38	−	4.89385e38i	0.687649	−	0.687649i
$756$	2.73771e38	−	9.40704e38i	0.377871	−	1.29840i
$757$	−5.97752e37	−	5.97752e37i	−0.0810451	−	0.0810451i	0.665422	−	0.746467i	$-0.268252\pi$
$757$	−5.97752e37	−	5.97752e37i	−0.0810451	−	0.0810451i	−0.746467	+	0.665422i	$0.768252\pi$
$758$	−9.21671e38	−	5.45362e38i	−1.22756	−	0.726358i
$759$		−	1.14262e39i		−	1.49499i
$760$	4.15430e38	−	3.89573e38i	0.533967	−	0.500733i
$761$		−	8.10363e38i		−	1.02326i	−0.859205	−	0.511631i	$-0.829042\pi$
$761$		−	8.10363e38i		−	1.02326i	0.859205	−	0.511631i	$-0.170958\pi$
$762$	−7.20897e38	+	1.21833e39i	−0.894296	+	1.51137i
$763$	−1.01463e39	−	1.01463e39i	−1.23659	−	1.23659i
$764$	5.14125e38	−	2.82333e38i	0.615614	−	0.338066i
$765$	−1.48873e39	+	1.48873e39i	−1.75141	+	1.75141i
$766$	−1.26589e39	+	3.24713e38i	−1.46321	+	0.375329i
$767$	1.40254e39			1.59286
$768$	−1.35139e39	−	4.89354e38i	−1.50801	−	0.546067i
$769$	8.22357e37			0.0901685			0.0450843	−	0.998983i	$-0.485644\pi$
$769$	8.22357e37			0.0901685			0.0450843	+	0.998983i	$0.485644\pi$
$770$	2.07093e39	−	5.31215e38i	2.23121	−	0.572328i
$771$	8.32142e37	−	8.32142e37i	0.0880975	−	0.0880975i
$772$	−2.27988e38	+	1.25200e38i	−0.237181	+	0.130248i
$773$	−8.52119e38	−	8.52119e38i	−0.871118	−	0.871118i	0.121476	−	0.992594i	$-0.461237\pi$
$773$	−8.52119e38	−	8.52119e38i	−0.871118	−	0.871118i	−0.992594	+	0.121476i	$0.961237\pi$
$774$	5.48171e38	−	9.26418e38i	0.550698	−	0.930688i
$775$			1.17054e39i			1.15561i
$776$	−7.42446e38	+	6.96235e38i	−0.720330	+	0.675496i
$777$			1.80265e39i			1.71881i
$778$	1.25181e39	+	7.40707e38i	1.17304	+	0.694100i
$779$	−2.61086e38	−	2.61086e38i	−0.240452	−	0.240452i
$780$	9.94851e38	−	3.41840e39i	0.900494	−	3.09418i
$781$	−1.13787e39	+	1.13787e39i	−1.01229	+	1.01229i
$782$	−2.66889e38	−	1.04046e39i	−0.233367	−	0.909778i
$783$	−1.91161e39			−1.64292
$784$	−7.43639e38	+	1.16940e39i	−0.628196	+	0.987859i
$785$	−3.96919e38			−0.329580
$786$	−2.36489e38	−	9.21948e38i	−0.193022	−	0.752492i
$787$	1.44742e39	−	1.44742e39i	1.16128	−	1.16128i	0.177085	−	0.984196i	$-0.443333\pi$
$787$	1.44742e39	−	1.44742e39i	1.16128	−	1.16128i	0.984196	−	0.177085i	$-0.0566666\pi$
$788$	−2.09958e39	−	6.11037e38i	−1.65588	−	0.481907i
$789$	1.49734e39	+	1.49734e39i	1.16087	+	1.16087i
$790$	1.14461e38	+	6.77277e37i	0.0872352	+	0.0516180i
$791$		−	1.28754e39i		−	0.964666i
$792$	−6.91218e37	+	2.15197e39i	−0.0509126	+	1.58506i
$793$			2.28928e39i			1.65772i
$794$	8.00662e38	−	1.35313e39i	0.569997	−	0.963304i
$795$	3.12778e39	+	3.12778e39i	2.18917	+	2.18917i
$796$	9.77430e38	+	1.77989e39i	0.672604	+	1.22480i
$797$	1.35920e39	−	1.35920e39i	0.919592	−	0.919592i	−0.0774077	−	0.997000i	$-0.524664\pi$
$797$	1.35920e39	−	1.35920e39i	0.919592	−	0.919592i	0.997000	+	0.0774077i	$0.0246643\pi$
$798$	1.62496e39	−	4.16819e38i	1.08095	−	0.277274i
$799$	7.82553e38			0.511838
$800$	−2.07341e39	−	6.76341e38i	−1.33343	−	0.434962i
$801$	3.25781e39			2.06009
$802$	−2.97009e39	+	7.61859e38i	−1.84678	+	0.473719i
$803$	1.15922e39	−	1.15922e39i	0.708772	−	0.708772i
$804$	−1.88089e38	−	3.42508e38i	−0.113086	−	0.205927i
$805$	2.52409e39	+	2.52409e39i	1.49231	+	1.49231i
$806$	−9.35477e38	+	1.58097e39i	−0.543889	+	0.919181i
$807$		−	2.17090e39i		−	1.24122i
$808$	−1.92025e39	−	6.16789e37i	−1.07970	−	0.0346803i
$809$			6.84163e38i			0.378316i	0.981947	+	0.189158i	$0.0605758\pi$
$809$			6.84163e38i			0.378316i	−0.981947	+	0.189158i	$0.939424\pi$
$810$	−2.45848e38	−	1.45471e38i	−0.133696	−	0.0791095i
$811$	−1.72726e38	−	1.72726e38i	−0.0923799	−	0.0923799i	0.659407	−	0.751786i	$-0.270808\pi$
$811$	−1.72726e38	−	1.72726e38i	−0.0923799	−	0.0923799i	−0.751786	+	0.659407i	$0.770808\pi$
$812$	4.81395e39	+	1.40100e39i	2.53218	+	0.736937i
$813$	−2.56885e39	+	2.56885e39i	−1.32898	+	1.32898i
$814$	−3.58269e38	−	1.39670e39i	−0.182297	−	0.710682i
$815$	−4.42413e38			−0.221411
$816$	7.19370e38	+	3.23231e39i	0.354107	+	1.59109i
$817$	6.70878e38			0.324822
$818$	2.01999e38	+	7.87488e38i	0.0962008	+	0.375037i
$819$	4.53260e39	−	4.53260e39i	2.12332	−	2.12332i
$820$	−6.76807e38	+	2.32557e39i	−0.311873	+	1.07163i
$821$	−7.50458e38	−	7.50458e38i	−0.340168	−	0.340168i	0.516262	−	0.856430i	$-0.327323\pi$
$821$	−7.50458e38	−	7.50458e38i	−0.340168	−	0.340168i	−0.856430	+	0.516262i	$0.827323\pi$
$822$	2.30798e37	+	1.36565e37i	0.0102911	+	0.00608935i
$823$			2.38558e39i			1.04639i	0.852211	+	0.523197i	$0.175261\pi$
$823$			2.38558e39i			1.04639i	−0.852211	+	0.523197i	$0.824739\pi$
$824$	−2.03992e39	−	2.17531e39i	−0.880229	−	0.938651i
$825$			5.34510e39i			2.26896i
$826$	2.20764e39	−	3.73094e39i	0.921927	−	1.55807i
$827$	1.96419e39	+	1.96419e39i	0.806974	+	0.806974i	0.984175	−	0.177200i	$-0.0567041\pi$
$827$	1.96419e39	+	1.96419e39i	0.806974	+	0.806974i	−0.177200	+	0.984175i	$0.556704\pi$
$828$	−3.15096e39	+	1.73036e39i	−1.27360	+	0.699402i
$829$	−1.00514e38	+	1.00514e38i	−0.0399708	+	0.0399708i	−0.726810	−	0.686839i	$-0.758998\pi$
$829$	−1.00514e38	+	1.00514e38i	−0.0399708	+	0.0399708i	0.686839	+	0.726810i	$0.258998\pi$
$830$	−3.87194e38	+	9.93191e37i	−0.151487	+	0.0388578i
$831$	−4.64185e39			−1.78680
$832$	−2.25990e39	−	2.57053e39i	−0.855904	−	0.973550i
$833$	3.19287e39			1.18980
$834$	2.71159e39	−	6.95549e38i	0.994218	−	0.255027i
$835$	−2.37359e39	+	2.37359e39i	−0.856323	+	0.856323i
$836$	−1.17619e39	+	6.45908e38i	−0.417535	+	0.229290i
$837$	−1.53083e39	−	1.53083e39i	−0.534730	−	0.534730i
$838$	1.41056e39	−	2.38386e39i	0.484837	−	0.819383i
$839$			1.48802e39i			0.503294i	0.967819	+	0.251647i	$0.0809721\pi$
$839$			1.48802e39i			0.503294i	−0.967819	+	0.251647i	$0.919028\pi$
$840$	−7.52746e39	−	8.02708e39i	−2.50541	−	2.67170i
$841$		−	6.72935e39i		−	2.20408i
$842$	3.35742e39	+	1.98662e39i	1.08216	+	0.640327i
$843$	−3.68580e39	−	3.68580e39i	−1.16912	−	1.16912i
$844$	6.97285e38	−	2.39594e39i	0.217664	−	0.747915i
$845$	2.42737e39	−	2.42737e39i	0.745710	−	0.745710i
$846$	−6.50719e38	−	2.53682e39i	−0.196741	−	0.766990i
$847$	−8.60511e37			−0.0256053
$848$	4.15091e39	−	9.23810e38i	1.21562	−	0.270545i
$849$	−8.81260e39			−2.54010
$850$	1.24849e39	+	4.86721e39i	0.354184	+	1.38078i
$851$	1.70233e39	−	1.70233e39i	0.475329	−	0.475329i
$852$	7.95275e39	+	2.31447e39i	2.18566	+	0.636089i
$853$	−4.07176e39	−	4.07176e39i	−1.10146	−	1.10146i	−0.994234	−	0.107229i	$-0.965802\pi$
$853$	−4.07176e39	−	4.07176e39i	−1.10146	−	1.10146i	−0.107229	−	0.994234i	$-0.534198\pi$
$854$	6.08977e39	+	3.60338e39i	1.62151	+	0.959465i
$855$			4.39132e39i			1.15094i
$856$	3.33718e39	+	1.07191e38i	0.860961	+	0.0276543i
$857$		−	6.84887e39i		−	1.73931i	−0.493657	−	0.869657i	$-0.664340\pi$
$857$		−	6.84887e39i		−	1.73931i	0.493657	−	0.869657i	$-0.335660\pi$
$858$	−4.27173e39	+	7.21930e39i	−1.06789	+	1.80475i
$859$	−1.18832e39	−	1.18832e39i	−0.292432	−	0.292432i	0.545608	−	0.838040i	$-0.316299\pi$
$859$	−1.18832e39	−	1.18832e39i	−0.292432	−	0.292432i	−0.838040	+	0.545608i	$0.816299\pi$
$860$	−2.11831e39	−	3.85741e39i	−0.513168	−	0.934473i
$861$	−5.04479e39	+	5.04479e39i	−1.20310	+	1.20310i
$862$	5.39292e38	−	1.38334e38i	0.126612	−	0.0324773i
$863$	−3.08008e39			−0.711896			−0.355948	−	0.934506i	$-0.615842\pi$
$863$	−3.08008e39			−0.711896			−0.355948	+	0.934506i	$0.615842\pi$
$864$	3.59614e39	−	1.82709e39i	0.818278	−	0.415743i
$865$	1.21384e40			2.71922
$866$	3.71468e38	−	9.52853e37i	0.0819275	−	0.0210152i
$867$	1.71959e38	−	1.71959e38i	0.0373393	−	0.0373393i
$868$	2.73312e39	+	4.97697e39i	0.584309	+	1.06402i
$869$	−2.21581e38	−	2.21581e38i	−0.0466408	−	0.0466408i
$870$	−1.09341e40	+	1.84788e40i	−2.26606	+	3.82968i
$871$		−	9.30544e38i		−	0.189885i
$872$	1.89658e38	−	5.90463e39i	0.0381065	−	1.18637i
$873$		−	7.84804e39i		−	1.55263i
$874$	−1.92815e39	−	1.14091e39i	−0.375610	−	0.222252i
$875$	−3.38907e39	−	3.38907e39i	−0.650088	−	0.650088i
$876$	−8.10196e39	−	2.35790e39i	−1.53033	−	0.445368i
$877$	2.46391e39	−	2.46391e39i	0.458279	−	0.458279i	−0.439811	−	0.898090i	$-0.644955\pi$
$877$	2.46391e39	−	2.46391e39i	0.458279	−	0.458279i	0.898090	+	0.439811i	$0.144955\pi$
$878$	2.28019e39	+	8.88927e39i	0.417633	+	1.62813i
$879$	−6.13796e39			−1.10707
$880$	7.42767e39	+	4.72338e39i	1.31928	+	0.838951i
$881$	−7.60892e39			−1.33091			−0.665454	−	0.746439i	$-0.731762\pi$
$881$	−7.60892e39			−1.33091			−0.665454	+	0.746439i	$0.731762\pi$
$882$	−2.65498e39	−	1.03504e40i	−0.457335	−	1.78291i
$883$	−2.99752e39	+	2.99752e39i	−0.508502	+	0.508502i	−0.914067	−	0.405564i	$-0.867075\pi$
$883$	−2.99752e39	+	2.99752e39i	−0.508502	+	0.508502i	0.405564	+	0.914067i	$0.367075\pi$
$884$	−2.20355e39	+	7.57161e39i	−0.368144	+	1.26498i
$885$	1.31278e40	+	1.31278e40i	2.16002	+	2.16002i
$886$	−6.83509e39	−	4.04439e39i	−1.10762	−	0.655388i
$887$			1.12894e40i			1.80179i	0.434041	+	0.900893i	$0.357087\pi$
$887$			1.12894e40i			1.80179i	−0.434041	+	0.900893i	$0.642913\pi$
$888$	−5.41372e39	+	5.07677e39i	−0.850984	+	0.798017i
$889$			1.04201e40i			1.61324i
$890$	6.78242e39	−	1.14624e40i	1.03424	−	1.74788i
$891$	4.75929e38	+	4.75929e38i	0.0714815	+	0.0714815i
$892$	−6.39247e38	+	3.51044e38i	−0.0945677	+	0.0519321i
$893$	1.15415e39	−	1.15415e39i	0.168177	−	0.168177i
$894$	1.49993e40	−	3.84746e39i	2.15285	−	0.552227i
$895$	5.02012e38			0.0709746
$896$	−1.03951e40	+	1.96555e39i	−1.44767	+	0.273732i
$897$	−1.40055e40			−1.92132
$898$	−1.10553e39	+	2.83579e38i	−0.149396	+	0.0383216i
$899$	7.83388e39	−	7.83388e39i	1.04285	−	1.04285i
$900$	1.47400e40	−	8.09449e39i	1.93296	−	1.06149i
$901$	−6.92789e39	−	6.92789e39i	−0.894986	−	0.894986i
$902$	2.90610e39	−	4.91136e39i	0.369848	−	0.625049i
$903$		−	1.29629e40i		−	1.62524i
$904$	3.86673e39	−	3.62606e39i	0.477607	−	0.447880i
$905$		−	1.27104e40i		−	1.54670i
$906$	7.22348e39	+	4.27420e39i	0.865995	+	0.512418i
$907$	−1.78164e39	−	1.78164e39i	−0.210437	−	0.210437i	0.594016	−	0.804453i	$-0.297542\pi$
$907$	−1.78164e39	−	1.78164e39i	−0.210437	−	0.210437i	−0.804453	+	0.594016i	$0.797542\pi$
$908$	3.50422e39	−	1.20408e40i	0.407786	−	1.40119i
$909$	1.04750e40	−	1.04750e40i	1.20100	−	1.20100i
$910$	−6.51127e39	−	2.53841e40i	−0.735540	−	2.86749i
$911$	−6.41458e37			−0.00713954			−0.00356977	−	0.999994i	$-0.501136\pi$
$911$	−6.41458e37			−0.00713954			−0.00356977	+	0.999994i	$0.501136\pi$
$912$	5.82814e39	+	3.70621e39i	0.639145	+	0.406443i
$913$	9.41824e38			0.101769
$914$	−1.39432e39	−	5.43572e39i	−0.148453	−	0.578740i
$915$	−2.14277e40	+	2.14277e40i	−2.24797	+	2.24797i
$916$	−1.61133e40	−	4.68943e39i	−1.66570	−	0.484764i
$917$	−4.95393e39	−	4.95393e39i	−0.504619	−	0.504619i
$918$	−7.99814e39	−	4.73258e39i	−0.802810	−	0.475031i
$919$			4.36685e39i			0.431926i	0.976402	+	0.215963i	$0.0692890\pi$
$919$			4.36685e39i			0.431926i	−0.976402	+	0.215963i	$0.930711\pi$
$920$	−4.71811e38	+	1.46889e40i	−0.0459867	+	1.43170i
$921$			1.74258e40i			1.67374i
$922$	−3.86958e39	+	6.53965e39i	−0.366266	+	0.618995i
$923$	1.39473e40	+	1.39473e40i	1.30097	+	1.30097i
$924$	1.24804e40	+	2.27267e40i	1.14725	+	2.08913i
$925$	−7.96336e39	+	7.96336e39i	−0.721412	+	0.721412i
$926$	−3.36787e38	+	8.63893e37i	−0.0300682	+	0.00771279i
$927$	2.29942e40			2.02321
$928$	9.34996e39	+	1.84029e40i	0.810797	+	1.59583i
$929$	−6.42627e39			−0.549220			−0.274610	−	0.961556i	$-0.588549\pi$
$929$	−6.42627e39			−0.549220			−0.274610	+	0.961556i	$0.588549\pi$
$930$	−2.35540e40	+	6.04184e39i	−1.98401	+	0.508920i
$931$	4.70900e39	−	4.70900e39i	0.390938	−	0.390938i
$932$	−1.33244e39	−	2.42636e39i	−0.109027	−	0.198536i
$933$	−5.40446e39	−	5.40446e39i	−0.435863	−	0.435863i
$934$	1.59628e39	−	2.69774e39i	0.126890	−	0.214446i
$935$		−	2.02802e40i		−	1.58897i
$936$	2.63774e40	+	8.47248e38i	2.03708	+	0.0654314i
$937$			1.05925e40i			0.806331i	0.915127	+	0.403165i	$0.132090\pi$
$937$			1.05925e40i			0.806331i	−0.915127	+	0.403165i	$0.867910\pi$
$938$	−2.47536e39	−	1.46470e39i	−0.185738	−	0.109903i
$939$	−1.05189e40	−	1.05189e40i	−0.778006	−	0.778006i
$940$	−1.02804e40	−	2.99187e39i	−0.749519	−	0.218131i
$941$	−1.24631e40	+	1.24631e40i	−0.895705	+	0.895705i	−0.995053	−	0.0993476i	$-0.968324\pi$
$941$	−1.24631e40	+	1.24631e40i	−0.895705	+	0.895705i	0.0993476	+	0.995053i	$0.468324\pi$
$942$	−1.19601e39	−	4.66263e39i	−0.0847322	−	0.330327i
$943$	9.52807e39			0.665422
$944$	1.74221e40	−	3.87739e39i	1.19944	−	0.266943i
$945$	3.08838e40			2.09605
$946$	2.57632e39	+	1.00437e40i	0.172373	+	0.671994i
$947$	−8.94676e39	+	8.94676e39i	−0.590121	+	0.590121i	−0.937664	−	0.347543i	$-0.887016\pi$
$947$	−8.94676e39	+	8.94676e39i	−0.590121	+	0.590121i	0.347543	+	0.937664i	$0.387016\pi$
$948$	−4.50704e38	+	1.54866e39i	−0.0293075	+	0.100703i
$949$	−1.42089e40	−	1.42089e40i	−0.910893	−	0.910893i
$950$	9.01974e39	+	5.33707e39i	0.570066	+	0.337314i
$951$		−	6.14408e39i		−	0.382842i
$952$	1.66730e40	+	1.77796e40i	1.02427	+	1.09225i
$953$			6.79190e39i			0.411374i	0.978618	+	0.205687i	$0.0659429\pi$
$953$			6.79190e39i			0.411374i	−0.978618	+	0.205687i	$0.934057\pi$
$954$	−1.66975e40	+	2.82191e40i	−0.997123	+	1.68515i
$955$	1.30741e40	+	1.30741e40i	0.769779	+	0.769779i
$956$	1.51757e40	−	8.33380e39i	0.880985	−	0.483795i
$957$	3.57724e40	−	3.57724e40i	2.04756	−	2.04756i
$958$	1.53903e40	−	3.94776e39i	0.868584	−	0.222800i
$959$	1.97396e38			0.0109847
$960$	2.90750e39	−	4.52130e40i	0.159536	−	2.48086i
$961$	−5.93585e39			−0.321157
$962$	−1.71198e40	+	4.39141e39i	−0.913348	+	0.234283i
$963$	−1.82044e40	+	1.82044e40i	−0.957682	+	0.957682i
$964$	−1.09418e40	+	6.00873e39i	−0.567609	+	0.311704i
$965$	−5.79769e39	−	5.79769e39i	−0.296576	−	0.296576i
$966$	−2.20450e40	+	3.72563e40i	−1.11203	+	1.87936i
$967$			2.57677e40i			1.28180i	0.767626	+	0.640898i	$0.221438\pi$
$967$			2.57677e40i			1.28180i	−0.767626	+	0.640898i	$0.778562\pi$
$968$	−2.42344e38	−	2.58429e38i	−0.0118882	−	0.0126772i
$969$		−	1.59129e40i		−	0.769800i
$970$	−2.76128e40	−	1.63388e40i	−1.31732	−	0.779474i
$971$	2.57003e40	+	2.57003e40i	1.20914	+	1.20914i	0.971305	+	0.237839i	$0.0764390\pi$
$971$	2.57003e40	+	2.57003e40i	1.20914	+	1.20914i	0.237839	+	0.971305i	$0.423561\pi$
$972$	6.49570e39	−	2.23198e40i	0.301392	−	1.03561i
$973$	1.45702e40	−	1.45702e40i	0.666719	−	0.666719i
$974$	2.14488e39	+	8.36179e39i	0.0967961	+	0.377358i
$975$	6.55165e40			2.91601
$976$	6.32882e39	+	2.84370e40i	0.277811	+	1.24828i
$977$	−1.07502e40			−0.465412			−0.232706	−	0.972547i	$-0.574758\pi$
$977$	−1.07502e40			−0.465412			−0.232706	+	0.972547i	$0.574758\pi$
$978$	−1.33310e39	−	5.19705e39i	−0.0569229	−	0.221913i
$979$	−2.21897e40	+	2.21897e40i	−0.934511	+	0.934511i
$980$	−4.19445e40	−	1.22070e40i	−1.74230	−	0.507059i
$981$	3.22099e40	+	3.22099e40i	1.31965	+	1.31965i
$982$	−1.91423e40	−	1.13267e40i	−0.773551	−	0.457718i
$983$		−	3.32264e40i		−	1.32437i	−0.749338	−	0.662187i	$-0.769628\pi$
$983$		−	3.32264e40i		−	1.32437i	0.749338	−	0.662187i	$-0.230372\pi$
$984$	−2.93581e40	−	9.42988e38i	−1.15423	−	0.0370742i
$985$		−	6.89304e40i		−	2.67314i
$986$	2.42185e40	−	4.09296e40i	0.926422	−	1.56567i
$987$	−2.23008e40	−	2.23008e40i	−0.841472	−	0.841472i
$988$	7.91709e39	+	1.44169e40i	0.294677	+	0.536604i
$989$	−1.22415e40	+	1.22415e40i	−0.449454	+	0.449454i
$990$	−6.57426e40	+	1.68636e40i	−2.38107	+	0.610768i
$991$	−6.66843e39			−0.238248			−0.119124	−	0.992879i	$-0.538009\pi$
$991$	−6.66843e39			−0.238248			−0.119124	+	0.992879i	$0.538009\pi$
$992$	−7.24963e39	+	2.22247e40i	−0.255510	+	0.783299i
$993$	1.16468e40			0.404940
$994$	5.90548e40	−	1.51481e40i	2.02553	−	0.519569i
$995$	−4.52621e40	+	4.52621e40i	−1.53152	+	1.53152i
$996$	−2.33342e39	−	4.24912e39i	−0.0778917	−	0.141840i
$997$	−2.83764e40	−	2.83764e40i	−0.934486	−	0.934486i	0.0634965	−	0.997982i	$-0.479775\pi$
$997$	−2.83764e40	−	2.83764e40i	−0.934486	−	0.934486i	−0.997982	+	0.0634965i	$0.979775\pi$
$998$	2.66440e40	−	4.50288e40i	0.865639	−	1.46294i
$999$		−	2.08291e40i		−	0.667630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.5.5	✓	106
16.13	even	4	inner	16.28.e.a.13.5	yes	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.5	✓	106	1.1	even	1	trivial
16.28.e.a.13.5	yes	106	16.13	even	4	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11221.9 + 2878.54i) q^{2} +(3.13170e6 - 3.13170e6i) q^{3} +(1.17646e8 - 6.46055e7i) q^{4} +(2.99171e9 + 2.99171e9i) q^{5} +(-2.61290e10 + 4.41585e10i) q^{6} +3.77678e11i q^{7} +(-1.13424e12 + 1.06365e12i) q^{8} -1.19895e13i q^{9} +(-4.21845e13 - 2.49610e13i) q^{10} +(8.16634e13 + 8.16634e13i) q^{11} +(1.66106e14 - 5.70757e14i) q^{12} +(1.00097e15 - 1.00097e15i) q^{13} +(-1.08716e15 - 4.23828e15i) q^{14} +1.87383e16 q^{15} +(9.66665e15 - 1.52011e16i) q^{16} -4.15045e16 q^{17} +(3.45124e16 + 1.34546e17i) q^{18} +(-6.12129e16 + 6.12129e16i) q^{19} +(5.45242e17 + 1.58681e17i) q^{20} +(1.18278e18 + 1.18278e18i) q^{21} +(-1.15149e18 - 6.81350e17i) q^{22} -2.23390e18i q^{23} +(-2.21088e17 + 6.88314e18i) q^{24} +1.04500e19i q^{25} +(-8.35152e18 + 1.41142e19i) q^{26} +(-1.36666e19 - 1.36666e19i) q^{27} +(2.44001e19 + 4.44322e19i) q^{28} +(6.99374e19 - 6.99374e19i) q^{29} +(-2.10280e20 + 5.39388e19i) q^{30} +1.12013e20 q^{31} +(-6.47215e19 + 1.98412e20i) q^{32} +5.11492e20 q^{33} +(4.65760e20 - 1.19472e20i) q^{34} +(-1.12990e21 + 1.12990e21i) q^{35} +(-7.74591e20 - 1.41052e21i) q^{36} +(7.62043e20 + 7.62043e20i) q^{37} +(5.10724e20 - 8.63131e20i) q^{38} -6.26951e21i q^{39} +(-6.57544e21 - 2.11205e20i) q^{40} +4.26521e21i q^{41} +(-1.66777e22 - 9.86836e21i) q^{42} +(-5.47987e21 - 5.47987e21i) q^{43} +(1.48833e22 + 4.33145e21i) q^{44} +(3.58692e22 - 3.58692e22i) q^{45} +(6.43037e21 + 2.50687e22i) q^{46} -1.88547e22 q^{47} +(-1.73323e22 - 7.78785e22i) q^{48} -7.69282e22 q^{49} +(-3.00808e22 - 1.17269e23i) q^{50} +(-1.29980e23 + 1.29980e23i) q^{51} +(5.30919e22 - 1.82429e23i) q^{52} +(1.66919e23 + 1.66919e23i) q^{53} +(1.92706e23 + 1.14026e23i) q^{54} +4.88626e23i q^{55} +(-4.01716e23 - 4.28379e23i) q^{56} +3.83402e23i q^{57} +(-5.83515e23 + 9.86150e23i) q^{58} +(7.00589e23 + 7.00589e23i) q^{59} +(2.20448e24 - 1.21060e24i) q^{60} +(-1.14353e24 + 1.14353e24i) q^{61} +(-1.25700e24 + 3.22433e23i) q^{62} +4.52819e24 q^{63} +(1.55164e23 - 2.41287e24i) q^{64} +5.98924e24 q^{65} +(-5.73992e24 + 1.47235e24i) q^{66} +(4.64819e23 - 4.64819e23i) q^{67} +(-4.88282e24 + 2.68142e24i) q^{68} +(-6.99592e24 - 6.99592e24i) q^{69} +(9.42721e24 - 1.59321e25i) q^{70} +1.39337e25i q^{71} +(1.27526e25 + 1.35991e25i) q^{72} -1.41951e25i q^{73} +(-1.07452e25 - 6.35802e24i) q^{74} +(3.27264e25 + 3.27264e25i) q^{75} +(-3.24675e24 + 1.11561e25i) q^{76} +(-3.08425e25 + 3.08425e25i) q^{77} +(1.80470e25 + 7.03560e25i) q^{78} -2.71335e24 q^{79} +(7.43971e25 - 1.65575e25i) q^{80} +5.82794e24 q^{81} +(-1.22776e25 - 4.78639e25i) q^{82} +(5.76649e24 - 5.76649e24i) q^{83} +(2.15562e26 + 6.27347e25i) q^{84} +(-1.24169e26 - 1.24169e26i) q^{85} +(7.72688e25 + 4.57207e25i) q^{86} -4.38047e26i q^{87} +(-1.79487e26 - 5.76517e24i) q^{88} +2.71721e26i q^{89} +(-2.99271e26 + 5.05773e26i) q^{90} +(3.78046e26 + 3.78046e26i) q^{91} +(-1.44322e26 - 2.62809e26i) q^{92} +(3.50791e26 - 3.50791e26i) q^{93} +(2.11586e26 - 5.42739e25i) q^{94} -3.66262e26 q^{95} +(4.18679e26 + 8.24056e26i) q^{96} +6.54574e26 q^{97} +(8.63283e26 - 2.21441e26i) q^{98} +(9.79108e26 - 9.79108e26i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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