LMFDB - Embedded newform 8.22.b.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,22,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, 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:	$22.3581875430$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 8499037025 x^{18} - 76491332940 x^{17} + \cdots + 35\!\cdots\!00 $ x^20 - 10x^19 + 8499037025x^18 - 76491332940x^17 + 29917993634631504354x^16 - 239343947343248489484x^15 + 56735124423752018369174556138x^14 - 397145866777745056145685733776x^13 + 63238887245213577325916647519604926269x^12 - 379433318308385206734963736802075208922x^11 + 42482893644148833600712851037696291113731507797x^10 - 212414464742605426308676323132417376601509837748x^9 + 16991149511760794392812139094660185274650292829286304832x^8 - 67964596772556393289382483692574713665819457865324101248x^7 + 3856070948945815855551883712975066709737139564290759222840809728x^6 - 11568212608961359754849022371262813346960834248571059910113653760x^5 + 447495609895006687050069424346090867517835281773807292283716383294251008x^4 - 894991200509659105123235067097342555549602100555628271172491492140580864x^3 + 21617394414514960541269362233298250396222492191038308122525553887833389622886400x^2 - 21617393967019362214475233171141277620661834650156142656637432362426234096844800*x + 356285834965428012369716852146922959222876595571555882248526187687502452643625697280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.10
Root			$0.500000 + 37074.8i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.22.b.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-377.837 + 1398.00i) q^{2} -148299. i q^{3} +(-1.81163e6 - 1.05643e6i) q^{4} -2.51716e7i q^{5} +(2.07321e8 + 5.60329e7i) q^{6} +8.96078e8 q^{7} +(2.16139e9 - 2.13349e9i) q^{8} -1.15323e10 q^{9} +O(q^{10})$	\(q+(-377.837 + 1398.00i) q^{2} -148299. i q^{3} +(-1.81163e6 - 1.05643e6i) q^{4} -2.51716e7i q^{5} +(2.07321e8 + 5.60329e7i) q^{6} +8.96078e8 q^{7} +(2.16139e9 - 2.13349e9i) q^{8} -1.15323e10 q^{9} +(3.51898e10 + 9.51079e9i) q^{10} -1.46382e11i q^{11} +(-1.56668e11 + 2.68663e11i) q^{12} +4.53853e11i q^{13} +(-3.38572e11 + 1.25271e12i) q^{14} -3.73293e12 q^{15} +(2.16596e12 + 3.82772e12i) q^{16} +6.08418e11 q^{17} +(4.35732e12 - 1.61220e13i) q^{18} -3.33025e13i q^{19} +(-2.65921e13 + 4.56017e13i) q^{20} -1.32887e14i q^{21} +(2.04641e14 + 5.53085e13i) q^{22} -2.43526e14 q^{23} +(-3.16395e14 - 3.20531e14i) q^{24} -1.56774e14 q^{25} +(-6.34484e14 - 1.71483e14i) q^{26} +1.58962e14i q^{27} +(-1.62336e15 - 9.46643e14i) q^{28} +1.19290e15i q^{29} +(1.41044e15 - 5.21862e15i) q^{30} +5.18159e15 q^{31} +(-6.16951e15 + 1.58174e15i) q^{32} -2.17083e16 q^{33} +(-2.29883e14 + 8.50565e14i) q^{34} -2.25557e16i q^{35} +(2.08922e16 + 1.21830e16i) q^{36} +2.87614e15i q^{37} +(4.65567e16 + 1.25829e16i) q^{38} +6.73060e16 q^{39} +(-5.37035e16 - 5.44056e16i) q^{40} -9.95883e16 q^{41} +(1.85776e17 + 5.02099e16i) q^{42} +2.13962e17i q^{43} +(-1.54642e17 + 2.65189e17i) q^{44} +2.90286e17i q^{45} +(9.20134e16 - 3.40449e17i) q^{46} -2.65912e17 q^{47} +(5.67647e17 - 3.21210e17i) q^{48} +2.44409e17 q^{49} +(5.92352e16 - 2.19170e17i) q^{50} -9.02277e16i q^{51} +(4.79464e17 - 8.22214e17i) q^{52} -1.06698e17i q^{53} +(-2.22228e17 - 6.00618e16i) q^{54} -3.68467e18 q^{55} +(1.93677e18 - 1.91177e18i) q^{56} -4.93873e18 q^{57} +(-1.66767e18 - 4.50721e17i) q^{58} +3.03409e18i q^{59} +(6.76269e18 + 3.94358e18i) q^{60} -3.77422e18i q^{61} +(-1.95780e18 + 7.24383e18i) q^{62} -1.03338e19 q^{63} +(1.19804e17 - 9.22259e18i) q^{64} +1.14242e19 q^{65} +(8.20219e18 - 3.03480e19i) q^{66} +7.43113e18i q^{67} +(-1.10223e18 - 6.42751e17i) q^{68} +3.61147e19i q^{69} +(3.15328e19 + 8.52241e18i) q^{70} +3.77401e19 q^{71} +(-2.49257e19 + 2.46040e19i) q^{72} -3.15308e19 q^{73} +(-4.02084e18 - 1.08672e18i) q^{74} +2.32495e19i q^{75} +(-3.51817e19 + 6.03318e19i) q^{76} -1.31169e20i q^{77} +(-2.54307e19 + 9.40934e19i) q^{78} +8.13752e19 q^{79} +(9.63500e19 - 5.45207e19i) q^{80} -9.70575e19 q^{81} +(3.76282e19 - 1.39224e20i) q^{82} -1.42229e20i q^{83} +(-1.40386e20 + 2.40743e20i) q^{84} -1.53149e19i q^{85} +(-2.99117e20 - 8.08428e19i) q^{86} +1.76906e20 q^{87} +(-3.12304e20 - 3.16387e20i) q^{88} +4.63956e20 q^{89} +(-4.05818e20 - 1.09681e20i) q^{90} +4.06688e20i q^{91} +(4.41180e20 + 2.57269e20i) q^{92} -7.68424e20i q^{93} +(1.00472e20 - 3.71744e20i) q^{94} -8.38278e20 q^{95} +(2.34571e20 + 9.14933e20i) q^{96} +8.42399e20 q^{97} +(-9.23471e19 + 3.41683e20i) q^{98} +1.68811e21i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9}+O(q^{10}) $ 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9	$ 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16} + 1740714497000 q^{17} - 41325344023822 q^{18} - 78999934156016 q^{20} + 294957216952508 q^{22} + 335749622520224 q^{23} + 786737698607504 q^{24} - 16\!\cdots\!04 q^{25}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) $ 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9 - 51269339528 * q^10 + 65316900136 * q^12 - 1924309104464 * q^14 - 2285680856096 * q^15 + 7793508571920 * q^16 + 1740714497000 * q^17 - 41325344023822 * q^18 - 78999934156016 * q^20 + 294957216952508 * q^22 + 335749622520224 * q^23 + 786737698607504 * q^24 - 1665114591247004 * q^25 - 2772669922448408 * q^26 - 4284340177681888 * q^28 + 3807691030523312 * q^30 - 8989263821171840 * q^31 - 9127378177656544 * q^32 + 5359113021386256 * q^33 + 19124803780998044 * q^34 + 39378114498954828 * q^36 - 41860137429498580 * q^38 + 121743910075345312 * q^39 - 160007944946664288 * q^40 - 84626460793452344 * q^41 + 178614544452770272 * q^42 - 27785097292304568 * q^44 + 184220935820050448 * q^46 + 149908985865280320 * q^47 + 1509829480382701344 * q^48 + 477689401234988532 * q^49 - 1722157324053237098 * q^50 - 1640429312330235856 * q^52 + 785391046636854392 * q^54 - 1936239868862269088 * q^55 - 3751496032099552448 * q^56 + 409355502574547024 * q^57 + 3182351472522780872 * q^58 + 2751731248604508192 * q^60 - 13336157978726113600 * q^62 - 8780950644120846560 * q^63 - 9021637553716933568 * q^64 + 6302857570713584320 * q^65 + 5291575090585638744 * q^66 + 40891724357029299816 * q^68 + 18077776609913587392 * q^70 + 96451291685825247456 * q^71 + 49841566955976579512 * q^72 - 21461290229157072184 * q^73 - 42953490504627871688 * q^74 - 206966483397015363224 * q^76 + 163869164384378609168 * q^78 - 284214874786393231680 * q^79 - 49904712513208125120 * q^80 + 1291808332257012164 * q^81 + 112698322843931711404 * q^82 + 178681601993395676224 * q^84 - 523293212085532715396 * q^86 + 517213147301817170208 * q^87 - 124028902608265335088 * q^88 + 17316387144455013640 * q^89 + 171098967229297148360 * q^90 + 827091233447044225632 * q^92 - 165060487582514765280 * q^94 - 2333725338330109674784 * q^95 - 715448174391177540544 * q^96 + 9560220979460741928 * q^97 + 137273120368488603630 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−377.837	+	1398.00i	−0.260910	+	0.965363i
$2$	−377.837	+	1398.00i	−0.260910	+	0.965363i
$3$		−	148299.i		−	1.44999i	−0.688754	−	0.724995i	$-0.741842\pi$
$3$		−	148299.i		−	1.44999i	0.688754	−	0.724995i	$-0.258158\pi$
$4$	−1.81163e6	−	1.05643e6i	−0.863852	−	0.503745i
$5$		−	2.51716e7i		−	1.15273i	−0.817193	−	0.576363i	$-0.804471\pi$
$5$		−	2.51716e7i		−	1.15273i	0.817193	−	0.576363i	$-0.195529\pi$
$6$	2.07321e8	+	5.60329e7i	1.39977	+	0.378316i
$7$	8.96078e8			1.19899			0.599496	−	0.800378i	$-0.295368\pi$
$7$	8.96078e8			1.19899			0.599496	+	0.800378i	$0.295368\pi$
$8$	2.16139e9	−	2.13349e9i	0.711684	−	0.702499i
$9$	−1.15323e10			−1.10247
$10$	3.51898e10	+	9.51079e9i	1.11280	+	0.300758i
$11$		−	1.46382e11i		−	1.70162i	−0.525471	−	0.850812i	$-0.676111\pi$
$11$		−	1.46382e11i		−	1.70162i	0.525471	−	0.850812i	$-0.323889\pi$
$12$	−1.56668e11	+	2.68663e11i	−0.730426	+	1.25258i
$13$			4.53853e11i			0.913083i	0.889702	+	0.456541i	$0.150912\pi$
$13$			4.53853e11i			0.913083i	−0.889702	+	0.456541i	$0.849088\pi$
$14$	−3.38572e11	+	1.25271e12i	−0.312829	+	1.15746i
$15$	−3.73293e12			−1.67144
$16$	2.16596e12	+	3.82772e12i	0.492482	+	0.870323i
$17$	6.08418e11			0.0731961			0.0365981	−	0.999330i	$-0.488348\pi$
$17$	6.08418e11			0.0731961			0.0365981	+	0.999330i	$0.488348\pi$
$18$	4.35732e12	−	1.61220e13i	0.287646	−	1.06429i
$19$		−	3.33025e13i		−	1.24613i	−0.782170	−	0.623066i	$-0.785887\pi$
$19$		−	3.33025e13i		−	1.24613i	0.782170	−	0.623066i	$-0.214113\pi$
$20$	−2.65921e13	+	4.56017e13i	−0.580681	+	0.995786i
$21$		−	1.32887e14i		−	1.73853i
$22$	2.04641e14	+	5.53085e13i	1.64268	+	0.443970i
$23$	−2.43526e14			−1.22576			−0.612878	−	0.790178i	$-0.709988\pi$
$23$	−2.43526e14			−1.22576			−0.612878	+	0.790178i	$0.709988\pi$
$24$	−3.16395e14	−	3.20531e14i	−1.01862	−	1.03194i
$25$	−1.56774e14			−0.328779
$26$	−6.34484e14	−	1.71483e14i	−0.881456	−	0.238232i
$27$			1.58962e14i			0.148585i
$28$	−1.62336e15	−	9.46643e14i	−1.03575	−	0.603986i
$29$			1.19290e15i			0.526531i	0.964723	+	0.263266i	$0.0847996\pi$
$29$			1.19290e15i			0.526531i	−0.964723	+	0.263266i	$0.915200\pi$
$30$	1.41044e15	−	5.21862e15i	0.436096	−	1.61355i
$31$	5.18159e15			1.13544			0.567721	−	0.823221i	$-0.307825\pi$
$31$	5.18159e15			1.13544			0.567721	+	0.823221i	$0.307825\pi$
$32$	−6.16951e15	+	1.58174e15i	−0.968671	+	0.248348i
$33$	−2.17083e16			−2.46734
$34$	−2.29883e14	+	8.50565e14i	−0.0190976	+	0.0706608i
$35$		−	2.25557e16i		−	1.38211i
$36$	2.08922e16	+	1.21830e16i	0.952374	+	0.555365i
$37$			2.87614e15i			0.0983315i	0.998791	+	0.0491657i	$0.0156563\pi$
$37$			2.87614e15i			0.0983315i	−0.998791	+	0.0491657i	$0.984344\pi$
$38$	4.65567e16	+	1.25829e16i	1.20297	+	0.325128i
$39$	6.73060e16			1.32396
$40$	−5.37035e16	−	5.44056e16i	−0.809790	−	0.820378i
$41$	−9.95883e16			−1.15872			−0.579359	−	0.815073i	$-0.696697\pi$
$41$	−9.95883e16			−1.15872			−0.579359	+	0.815073i	$0.696697\pi$
$42$	1.85776e17	+	5.02099e16i	1.67831	+	0.453598i
$43$			2.13962e17i			1.50979i	0.655844	+	0.754896i	$0.272313\pi$
$43$			2.13962e17i			1.50979i	−0.655844	+	0.754896i	$0.727687\pi$
$44$	−1.54642e17	+	2.65189e17i	−0.857184	+	1.46995i
$45$			2.90286e17i			1.27085i
$46$	9.20134e16	−	3.40449e17i	0.319811	−	1.18330i
$47$	−2.65912e17			−0.737412			−0.368706	−	0.929546i	$-0.620199\pi$
$47$	−2.65912e17			−0.737412			−0.368706	+	0.929546i	$0.620199\pi$
$48$	5.67647e17	−	3.21210e17i	1.26196	−	0.714094i
$49$	2.44409e17			0.437582
$50$	5.92352e16	−	2.19170e17i	0.0857817	−	0.317392i
$51$		−	9.02277e16i		−	0.106134i
$52$	4.79464e17	−	8.22214e17i	0.459961	−	0.788769i
$53$		−	1.06698e17i		−	0.0838034i	−0.999122	−	0.0419017i	$-0.986658\pi$
$53$		−	1.06698e17i		−	0.0838034i	0.999122	−	0.0419017i	$-0.0133416\pi$
$54$	−2.22228e17	−	6.00618e16i	−0.143438	−	0.0387672i
$55$	−3.68467e18			−1.96151
$56$	1.93677e18	−	1.91177e18i	0.853304	−	0.842291i
$57$	−4.93873e18			−1.80688
$58$	−1.66767e18	−	4.50721e17i	−0.508294	−	0.137377i
$59$			3.03409e18i			0.772828i	0.922325	+	0.386414i	$0.126286\pi$
$59$			3.03409e18i			0.772828i	−0.922325	+	0.386414i	$0.873714\pi$
$60$	6.76269e18	+	3.94358e18i	1.44388	+	0.841981i
$61$		−	3.77422e18i		−	0.677429i	−0.940889	−	0.338714i	$-0.890008\pi$
$61$		−	3.77422e18i		−	0.677429i	0.940889	−	0.338714i	$-0.109992\pi$
$62$	−1.95780e18	+	7.24383e18i	−0.296248	+	1.09611i
$63$	−1.03338e19			−1.32186
$64$	1.19804e17	−	9.22259e18i	0.0129892	−	0.999916i
$65$	1.14242e19			1.05253
$66$	8.20219e18	−	3.03480e19i	0.643752	−	2.38188i
$67$			7.43113e18i			0.498046i	0.968498	+	0.249023i	$0.0801095\pi$
$67$			7.43113e18i			0.498046i	−0.968498	+	0.249023i	$0.919890\pi$
$68$	−1.10223e18	−	6.42751e17i	−0.0632306	−	0.0368722i
$69$			3.61147e19i			1.77733i
$70$	3.15328e19	+	8.52241e18i	1.33424	+	0.360606i
$71$	3.77401e19			1.37591			0.687955	−	0.725753i	$-0.258509\pi$
$71$	3.77401e19			1.37591			0.687955	+	0.725753i	$0.258509\pi$
$72$	−2.49257e19	+	2.46040e19i	−0.784613	+	0.774487i
$73$	−3.15308e19			−0.858707			−0.429353	−	0.903137i	$-0.641259\pi$
$73$	−3.15308e19			−0.858707			−0.429353	+	0.903137i	$0.641259\pi$
$74$	−4.02084e18	−	1.08672e18i	−0.0949256	−	0.0256556i
$75$			2.32495e19i			0.476727i
$76$	−3.51817e19	+	6.03318e19i	−0.627732	+	1.07647i
$77$		−	1.31169e20i		−	2.04023i
$78$	−2.54307e19	+	9.40934e19i	−0.345434	+	1.27810i
$79$	8.13752e19			0.966958			0.483479	−	0.875356i	$-0.339373\pi$
$79$	8.13752e19			0.966958			0.483479	+	0.875356i	$0.339373\pi$
$80$	9.63500e19	−	5.45207e19i	1.00324	−	0.567697i
$81$	−9.70575e19			−0.887026
$82$	3.76282e19	−	1.39224e20i	0.302321	−	1.11858i
$83$		−	1.42229e20i		−	1.00616i	−0.864239	−	0.503081i	$-0.832200\pi$
$83$		−	1.42229e20i		−	1.00616i	0.864239	−	0.503081i	$-0.167800\pi$
$84$	−1.40386e20	+	2.40743e20i	−0.875774	+	1.50183i
$85$		−	1.53149e19i		−	0.0843751i
$86$	−2.99117e20	−	8.08428e19i	−1.45750	−	0.393919i
$87$	1.76906e20			0.763465
$88$	−3.12304e20	−	3.16387e20i	−1.19539	−	1.21102i
$89$	4.63956e20			1.57718			0.788591	−	0.614918i	$-0.210811\pi$
$89$	4.63956e20			1.57718			0.788591	+	0.614918i	$0.210811\pi$
$90$	−4.05818e20	−	1.09681e20i	−1.22683	−	0.331577i
$91$			4.06688e20i			1.09478i
$92$	4.41180e20	+	2.57269e20i	1.05887	+	0.617468i
$93$		−	7.68424e20i		−	1.64638i
$94$	1.00472e20	−	3.71744e20i	0.192398	−	0.711871i
$95$	−8.38278e20			−1.43645
$96$	2.34571e20	+	9.14933e20i	0.360103	+	1.40456i
$97$	8.42399e20			1.15988			0.579942	−	0.814658i	$-0.303075\pi$
$97$	8.42399e20			1.15988			0.579942	+	0.814658i	$0.303075\pi$
$98$	−9.23471e19	+	3.41683e20i	−0.114169	+	0.422425i
$99$			1.68811e21i			1.87599i
$100$	2.84017e20	+	1.65621e20i	0.284017	+	0.165621i
$101$		−	1.03579e21i		−	0.933037i	−0.884511	−	0.466519i	$-0.845508\pi$
$101$		−	1.03579e21i		−	0.933037i	0.884511	−	0.466519i	$-0.154492\pi$
$102$	1.26138e20	+	3.40914e19i	0.102458	+	0.0276913i
$103$	1.62379e21			1.19053			0.595264	−	0.803530i	$-0.297048\pi$
$103$	1.62379e21			1.19053			0.595264	+	0.803530i	$0.297048\pi$
$104$	9.68291e20	+	9.80952e20i	0.641440	+	0.649827i
$105$	−3.34500e21			−2.00405
$106$	1.49164e20	+	4.03147e19i	0.0809007	+	0.0218651i
$107$			2.50232e20i			0.122974i	0.998108	+	0.0614869i	$0.0195842\pi$
$107$			2.50232e20i			0.122974i	−0.998108	+	0.0614869i	$0.980416\pi$
$108$	1.67932e20	−	2.87980e20i	0.0748488	−	0.128355i
$109$			1.25252e20i			0.0506764i	0.999679	+	0.0253382i	$0.00806626\pi$
$109$			1.25252e20i			0.0506764i	−0.999679	+	0.0253382i	$0.991934\pi$
$110$	1.39220e21	−	5.15115e21i	0.511776	−	1.89357i
$111$	4.26529e20			0.142580
$112$	1.94087e21	+	3.42993e21i	0.590482	+	1.04351i
$113$	−3.08147e21			−0.853954			−0.426977	−	0.904263i	$-0.640421\pi$
$113$	−3.08147e21			−0.853954			−0.426977	+	0.904263i	$0.640421\pi$
$114$	1.86604e21	−	6.90432e21i	0.471432	−	1.74429i
$115$			6.12996e21i			1.41296i
$116$	1.26021e21	−	2.16109e21i	0.265238	−	0.454845i
$117$		−	5.23395e21i		−	1.00665i
$118$	−4.24165e21	−	1.14639e21i	−0.746060	−	0.201638i
$119$	5.45189e20			0.0877616
$120$	−8.06830e21	+	7.96417e21i	−1.18954	+	1.17419i
$121$	−1.40273e22			−1.89552
$122$	5.27634e21	+	1.42604e21i	0.653965	+	0.176748i
$123$			1.47688e22i			1.68013i
$124$	−9.38711e21	−	5.47398e21i	−0.980854	−	0.571973i
$125$		−	8.05651e21i		−	0.773734i
$126$	3.90450e21	−	1.44466e22i	0.344885	−	1.27607i
$127$	−6.83307e21			−0.555491			−0.277745	−	0.960655i	$-0.589587\pi$
$127$	−6.83307e21			−0.555491			−0.277745	+	0.960655i	$0.589587\pi$
$128$	1.28479e22	+	3.65213e21i	0.961893	+	0.273427i
$129$	3.17303e22			2.18919
$130$	−4.31650e21	+	1.59710e22i	−0.274616	+	1.01608i
$131$		−	1.86944e22i		−	1.09740i	−0.836020	−	0.548698i	$-0.815124\pi$
$131$		−	1.86944e22i		−	1.09740i	0.836020	−	0.548698i	$-0.184876\pi$
$132$	3.93273e22	+	2.29333e22i	2.13142	+	1.24291i
$133$		−	2.98416e22i		−	1.49410i
$134$	−1.03887e22	−	2.80776e21i	−0.480796	−	0.129945i
$135$	4.00134e21			0.171278
$136$	1.31503e21	−	1.29805e21i	0.0520925	−	0.0514202i
$137$	2.98494e21			0.109489			0.0547444	−	0.998500i	$-0.482566\pi$
$137$	2.98494e21			0.109489			0.0547444	+	0.998500i	$0.482566\pi$
$138$	−5.04882e22	−	1.36455e22i	−1.71577	−	0.463723i
$139$			4.72414e22i			1.48822i	0.668057	+	0.744110i	$0.267126\pi$
$139$			4.72414e22i			1.48822i	−0.668057	+	0.744110i	$0.732874\pi$
$140$	−2.38286e22	+	4.08627e22i	−0.696231	+	1.19394i
$141$			3.94345e22i			1.06924i
$142$	−1.42596e22	+	5.27605e22i	−0.358988	+	1.32825i
$143$	6.64358e22			1.55372
$144$	−2.49784e22	−	4.41422e22i	−0.542948	−	0.959507i
$145$	3.00272e22			0.606947
$146$	1.19135e22	−	4.40799e22i	0.224045	−	0.828964i
$147$		−	3.62457e22i		−	0.634489i
$148$	3.03844e21	−	5.21051e21i	0.0495340	−	0.0849439i
$149$		−	9.12955e21i		−	0.138674i	−0.997593	−	0.0693368i	$-0.977912\pi$
$149$		−	9.12955e21i		−	0.138674i	0.997593	−	0.0693368i	$-0.0220883\pi$
$150$	−3.25027e22	−	8.78452e21i	−0.460215	−	0.124383i
$151$	−5.75381e22			−0.759797			−0.379898	−	0.925028i	$-0.624041\pi$
$151$	−5.75381e22			−0.759797			−0.379898	+	0.925028i	$0.624041\pi$
$152$	−7.10505e22	−	7.19795e22i	−0.875406	−	0.886852i
$153$	−7.01643e21			−0.0806967
$154$	1.83374e23	+	4.95607e22i	1.96957	+	0.532316i
$155$		−	1.30429e23i		−	1.30885i
$156$	−1.21934e23	−	7.11041e22i	−1.14371	−	0.666939i
$157$		−	1.16143e23i		−	1.01870i	−0.860558	−	0.509352i	$-0.829885\pi$
$157$		−	1.16143e23i		−	1.01870i	0.860558	−	0.509352i	$-0.170115\pi$
$158$	−3.07466e22	+	1.13762e23i	−0.252289	+	0.933465i
$159$	−1.58233e22			−0.121514
$160$	3.98151e22	+	1.55297e23i	0.286278	+	1.11661i
$161$	−2.18219e23			−1.46967
$162$	3.66720e22	−	1.35686e23i	0.231434	−	0.856303i
$163$		−	2.22608e23i		−	1.31696i	−0.752600	−	0.658478i	$-0.771201\pi$
$163$		−	2.22608e23i		−	1.31696i	0.752600	−	0.658478i	$-0.228799\pi$
$164$	1.80417e23	+	1.05208e23i	1.00096	+	0.583698i
$165$			5.46433e23i			2.84417i
$166$	1.98835e23	+	5.37394e22i	0.971313	+	0.262518i
$167$	−3.76525e22			−0.172691			−0.0863457	−	0.996265i	$-0.527519\pi$
$167$	−3.76525e22			−0.172691			−0.0863457	+	0.996265i	$0.527519\pi$
$168$	−2.83514e23	−	2.87221e23i	−1.22131	−	1.23728i
$169$	4.10819e22			0.166280
$170$	2.14101e22	+	5.78653e21i	0.0814527	+	0.0220143i
$171$			3.84053e23i			1.37383i
$172$	2.26036e23	−	3.87619e23i	0.760551	−	1.30424i
$173$			3.88706e23i			1.23066i	0.788271	+	0.615328i	$0.210976\pi$
$173$			3.88706e23i			1.23066i	−0.788271	+	0.615328i	$0.789024\pi$
$174$	−6.68416e22	+	2.47313e23i	−0.199195	+	0.737022i
$175$	−1.40482e23			−0.394204
$176$	5.60308e23	−	3.17057e23i	1.48096	−	0.838019i
$177$	4.49953e23			1.12059
$178$	−1.75300e23	+	6.48608e23i	−0.411502	+	1.52255i
$179$		−	4.49307e23i		−	0.994458i	−0.867619	−	0.497229i	$-0.834351\pi$
$179$		−	4.49307e23i		−	0.994458i	0.867619	−	0.497229i	$-0.165649\pi$
$180$	3.06667e23	−	5.25890e23i	0.640185	−	1.09783i
$181$		−	1.39246e23i		−	0.274257i	−0.990553	−	0.137129i	$-0.956213\pi$
$181$		−	1.39246e23i		−	0.274257i	0.990553	−	0.137129i	$-0.0437874\pi$
$182$	−5.68547e23	−	1.53662e23i	−1.05686	−	0.285638i
$183$	−5.59713e23			−0.982265
$184$	−5.26354e23	+	5.19561e23i	−0.872351	+	0.861092i
$185$	7.23973e22			0.113349
$186$	1.07425e24	+	2.90339e23i	1.58935	+	0.429556i
$187$		−	8.90612e22i		−	0.124552i
$188$	4.81734e23	+	2.80917e23i	0.637015	+	0.371468i
$189$			1.42442e23i			0.178152i
$190$	3.16733e23	−	1.17191e24i	0.374783	−	1.38670i
$191$	−8.95475e23			−1.00277			−0.501387	−	0.865223i	$-0.667177\pi$
$191$	−8.95475e23			−1.00277			−0.501387	+	0.865223i	$0.667177\pi$
$192$	−1.36770e24	−	1.77668e22i	−1.44987	−	0.0188342i
$193$	2.12695e22			0.0213504			0.0106752	−	0.999943i	$-0.496602\pi$
$193$	2.12695e22			0.0213504			0.0106752	+	0.999943i	$0.496602\pi$
$194$	−3.18290e23	+	1.17767e24i	−0.302625	+	1.11971i
$195$		−	1.69420e24i		−	1.52617i
$196$	−4.42780e23	−	2.58202e23i	−0.378006	−	0.220430i
$197$		−	1.30981e24i		−	1.06002i	−0.847991	−	0.530011i	$-0.822188\pi$
$197$		−	1.30981e24i		−	1.06002i	0.847991	−	0.530011i	$-0.177812\pi$
$198$	−2.35997e24	−	6.37831e23i	−1.81102	−	0.489465i
$199$	1.93979e24			1.41188			0.705940	−	0.708271i	$-0.250525\pi$
$199$	1.93979e24			1.41188			0.705940	+	0.708271i	$0.250525\pi$
$200$	−3.38850e23	+	3.34477e23i	−0.233987	+	0.230967i
$201$	1.10203e24			0.722162
$202$	1.44804e24	+	3.91362e23i	0.900720	+	0.243438i
$203$			1.06893e24i			0.631307i
$204$	−9.53193e22	+	1.63459e23i	−0.0534643	+	0.0916838i
$205$			2.50680e24i			1.33569i
$206$	−6.13529e23	+	2.27005e24i	−0.310620	+	1.14929i
$207$	2.80841e24			1.35136
$208$	−1.73722e24	+	9.83027e23i	−0.794677	+	0.449677i
$209$	−4.87487e24			−2.12045
$210$	1.26386e24	−	4.67629e24i	0.522875	−	1.93463i
$211$			1.29678e24i			0.510389i	0.966890	+	0.255194i	$0.0821395\pi$
$211$			1.29678e24i			0.510389i	−0.966890	+	0.255194i	$0.917861\pi$
$212$	−1.12719e23	+	1.93298e23i	−0.0422155	+	0.0723937i
$213$		−	5.59682e24i		−	1.99506i
$214$	−3.49823e23	−	9.45469e22i	−0.118714	−	0.0320850i
$215$	5.38577e24			1.74038
$216$	3.39144e23	+	3.43578e23i	0.104381	+	0.105745i
$217$	4.64310e24			1.36139
$218$	−1.75101e23	−	4.73248e22i	−0.0489211	−	0.0132220i
$219$			4.67599e24i			1.24512i
$220$	6.67525e24	+	3.89259e24i	1.69445	+	0.988100i
$221$			2.76132e23i			0.0668341i
$222$	−1.61159e23	+	5.96286e23i	−0.0372004	+	0.137641i
$223$	−6.28246e24			−1.38334			−0.691670	−	0.722214i	$-0.743125\pi$
$223$	−6.28246e24			−1.38334			−0.691670	+	0.722214i	$0.743125\pi$
$224$	−5.52836e24	+	1.41736e24i	−1.16143	+	0.297768i
$225$	1.80796e24			0.362470
$226$	1.16429e24	−	4.30788e24i	0.222805	−	0.824376i
$227$		−	2.30805e22i		−	0.00421671i	−0.999998	−	0.00210835i	$-0.999329\pi$
$227$		−	2.30805e22i		−	0.00421671i	0.999998	−	0.00210835i	$-0.000671111\pi$
$228$	8.94714e24	+	5.21742e24i	1.56088	+	0.910206i
$229$		−	9.27018e23i		−	0.154460i	−0.997013	−	0.0772299i	$-0.975392\pi$
$229$		−	9.27018e23i		−	0.154460i	0.997013	−	0.0772299i	$-0.0246076\pi$
$230$	−8.56965e24	−	2.31613e24i	−1.36402	−	0.368655i
$231$	−1.94523e25			−2.95832
$232$	2.54504e24	+	2.57831e24i	0.369888	+	0.374724i
$233$	−9.00822e24			−1.25142			−0.625708	−	0.780057i	$-0.715190\pi$
$233$	−9.00822e24			−1.25142			−0.625708	+	0.780057i	$0.715190\pi$
$234$	7.31704e24	+	1.97758e24i	0.971782	+	0.262644i
$235$			6.69344e24i			0.850035i
$236$	3.20531e24	−	5.49665e24i	0.389308	−	0.667609i
$237$		−	1.20679e25i		−	1.40208i
$238$	−2.05993e23	+	7.62172e23i	−0.0228978	+	0.0847218i
$239$	9.23555e24			0.982392			0.491196	−	0.871049i	$-0.336560\pi$
$239$	9.23555e24			0.982392			0.491196	+	0.871049i	$0.336560\pi$
$240$	−8.08537e24	−	1.42886e25i	−0.823155	−	1.45470i
$241$	6.50280e24			0.633755			0.316878	−	0.948466i	$-0.397366\pi$
$241$	6.50280e24			0.633755			0.316878	+	0.948466i	$0.397366\pi$
$242$	5.30005e24	−	1.96102e25i	0.494560	−	1.82987i
$243$			1.60563e25i			1.43476i
$244$	−3.98720e24	+	6.83748e24i	−0.341251	+	0.585198i
$245$		−	6.15219e24i		−	0.504412i
$246$	−2.06468e25	−	5.58022e24i	−1.62194	−	0.438362i
$247$	1.51144e25			1.13782
$248$	1.11994e25	−	1.10549e25i	0.808076	−	0.797647i
$249$	−2.10924e25			−1.45893
$250$	1.12630e25	+	3.04405e24i	0.746934	+	0.201875i
$251$		−	1.58273e25i		−	1.00654i	−0.864128	−	0.503272i	$-0.832129\pi$
$251$		−	1.58273e25i		−	1.00654i	0.864128	−	0.503272i	$-0.167871\pi$
$252$	1.87210e25	+	1.09169e25i	1.14189	+	0.665878i
$253$			3.56478e25i			2.08577i
$254$	2.58179e24	−	9.55260e24i	0.144933	−	0.536250i
$255$	−2.27118e24			−0.122343
$256$	−9.96007e24	+	1.65814e25i	−0.514923	+	0.857236i
$257$	5.16742e24			0.256434			0.128217	−	0.991746i	$-0.459075\pi$
$257$	5.16742e24			0.256434			0.128217	+	0.991746i	$0.459075\pi$
$258$	−1.19889e25	+	4.43588e25i	−0.571179	+	2.11336i
$259$			2.57725e24i			0.117899i
$260$	−2.06965e25	−	1.20689e25i	−0.909235	−	0.530209i
$261$		−	1.37568e25i		−	0.580486i
$262$	2.61347e25	+	7.06346e24i	1.05939	+	0.286321i
$263$	6.63930e24			0.258575			0.129288	−	0.991607i	$-0.458731\pi$
$263$	6.63930e24			0.258575			0.129288	+	0.991607i	$0.458731\pi$
$264$	−4.69199e25	+	4.63144e25i	−1.75597	+	1.73330i
$265$	−2.68577e24			−0.0966024
$266$	4.17184e25	+	1.12753e25i	1.44235	+	0.389825i
$267$		−	6.88043e25i		−	2.28690i
$268$	7.85047e24	−	1.34625e25i	0.250888	−	0.430238i
$269$			2.10873e25i			0.648070i	0.946045	+	0.324035i	$0.105040\pi$
$269$			2.10873e25i			0.648070i	−0.946045	+	0.324035i	$0.894960\pi$
$270$	−1.51185e24	+	5.59385e24i	−0.0446880	+	0.165345i
$271$	5.01746e25			1.42661			0.713307	−	0.700851i	$-0.247196\pi$
$271$	5.01746e25			1.42661			0.713307	+	0.700851i	$0.247196\pi$
$272$	1.31781e24	+	2.32885e24i	0.0360478	+	0.0637042i
$273$	6.03114e25			1.58742
$274$	−1.12782e24	+	4.17293e24i	−0.0285667	+	0.105696i
$275$			2.29489e25i			0.559459i
$276$	3.81527e25	−	6.54265e25i	0.895323	−	1.53535i
$277$		−	5.06908e25i		−	1.14523i	−0.819825	−	0.572614i	$-0.805929\pi$
$277$		−	5.06908e25i		−	1.14523i	0.819825	−	0.572614i	$-0.194071\pi$
$278$	−6.60432e25	−	1.78496e25i	−1.43667	−	0.388291i
$279$	−5.97554e25			−1.25179
$280$	−4.81225e25	−	4.87517e25i	−0.970932	−	0.983626i
$281$	5.97108e25			1.16048			0.580239	−	0.814446i	$-0.302959\pi$
$281$	5.97108e25			1.16048			0.580239	+	0.814446i	$0.302959\pi$
$282$	−5.51292e25	−	1.48998e25i	−1.03221	−	0.278975i
$283$			1.89285e25i			0.341475i	0.985317	+	0.170738i	$0.0546150\pi$
$283$			1.89285e25i			0.341475i	−0.985317	+	0.170738i	$0.945385\pi$
$284$	−6.83711e25	−	3.98698e25i	−1.18858	−	0.693108i
$285$			1.24316e26i			2.08284i
$286$	−2.51019e25	+	9.28769e25i	−0.405381	+	1.49991i
$287$	−8.92388e25			−1.38929
$288$	7.11484e25	−	1.82411e25i	1.06793	−	0.273797i
$289$	−6.87218e25			−0.994642
$290$	−1.13454e25	+	4.19779e25i	−0.158358	+	0.585924i
$291$		−	1.24927e26i		−	1.68182i
$292$	5.71221e25	+	3.33101e25i	0.741796	+	0.432569i
$293$		−	4.58459e25i		−	0.574369i	−0.957875	−	0.287184i	$-0.907281\pi$
$293$		−	4.58459e25i		−	0.574369i	0.957875	−	0.287184i	$-0.0927192\pi$
$294$	5.06713e25	+	1.36950e25i	0.612513	+	0.165544i
$295$	7.63731e25			0.890860
$296$	6.13623e24	+	6.21646e24i	0.0690778	+	0.0699810i
$297$	2.32691e25			0.252835
$298$	1.27631e25	+	3.44949e24i	0.133870	+	0.0361813i
$299$		−	1.10525e26i		−	1.11922i
$300$	2.45614e25	−	4.21194e25i	0.240149	−	0.411822i
$301$			1.91726e26i			1.81023i
$302$	2.17400e25	−	8.04380e25i	0.198238	−	0.733480i
$303$	−1.53607e26			−1.35290
$304$	1.27473e26	−	7.21318e25i	1.08454	−	0.613697i
$305$	−9.50032e25			−0.780890
$306$	2.65107e24	−	9.80893e24i	0.0210546	−	0.0779017i
$307$			1.67324e26i			1.28412i	0.766655	+	0.642059i	$0.221920\pi$
$307$			1.67324e26i			1.28412i	−0.766655	+	0.642059i	$0.778080\pi$
$308$	−1.38571e26	+	2.37630e26i	−1.02776	+	1.76246i
$309$		−	2.40807e26i		−	1.72625i
$310$	1.82339e26	+	4.92810e25i	1.26352	+	0.341493i
$311$	5.58847e25			0.374377			0.187188	−	0.982324i	$-0.440062\pi$
$311$	5.58847e25			0.374377			0.187188	+	0.982324i	$0.440062\pi$
$312$	1.45474e26	−	1.43597e26i	0.942242	−	0.930082i
$313$	−3.51318e25			−0.220032			−0.110016	−	0.993930i	$-0.535090\pi$
$313$	−3.51318e25			−0.220032			−0.110016	+	0.993930i	$0.535090\pi$
$314$	1.62368e26	+	4.38833e25i	0.983420	+	0.265790i
$315$			2.60119e26i			1.52374i
$316$	−1.47422e26	−	8.59672e25i	−0.835309	−	0.487100i
$317$			2.27250e26i			1.24561i	0.782378	+	0.622804i	$0.214007\pi$
$317$			2.27250e26i			1.24561i	−0.782378	+	0.622804i	$0.785993\pi$
$318$	5.97863e24	−	2.21209e25i	0.0317042	−	0.117305i
$319$	1.74618e26			0.895958
$320$	−2.32148e26	−	3.01566e24i	−1.15263	−	0.0149730i
$321$	3.71091e25			0.178311
$322$	8.24511e25	−	3.05069e26i	0.383451	−	1.41877i
$323$		−	2.02618e25i		−	0.0912120i
$324$	1.75832e26	+	1.02534e26i	0.766260	+	0.446835i
$325$		−	7.11525e25i		−	0.300203i
$326$	3.11205e26	+	8.41097e25i	1.27134	+	0.343606i
$327$	1.85747e25			0.0734803
$328$	−2.15249e26	+	2.12471e26i	−0.824641	+	0.813999i
$329$	−2.38278e26			−0.884152
$330$	−7.63910e26	−	2.06463e26i	−2.74565	−	0.742071i
$331$		−	2.84106e26i		−	0.989205i	−0.869119	−	0.494602i	$-0.835314\pi$
$331$		−	2.84106e26i		−	0.989205i	0.869119	−	0.494602i	$-0.164686\pi$
$332$	−1.50255e26	+	2.57666e26i	−0.506850	+	0.869176i
$333$		−	3.31684e25i		−	0.108408i
$334$	1.42265e25	−	5.26380e25i	0.0450568	−	0.166710i
$335$	1.87054e26			0.574111
$336$	5.08656e26	−	2.87829e26i	1.51308	−	0.856193i
$337$	−2.89525e26			−0.834780			−0.417390	−	0.908727i	$-0.637055\pi$
$337$	−2.89525e26			−0.834780			−0.417390	+	0.908727i	$0.637055\pi$
$338$	−1.55223e25	+	5.74323e25i	−0.0433841	+	0.160521i
$339$			4.56979e26i			1.23822i
$340$	−1.61791e25	+	2.77449e25i	−0.0425036	+	0.0728877i
$341$		−	7.58489e26i		−	1.93209i
$342$	−5.36904e26	−	1.45109e26i	−1.32624	−	0.358444i
$343$	−2.81491e26			−0.674335
$344$	4.56485e26	+	4.62454e26i	1.06063	+	1.07450i
$345$	9.09067e26			2.04878
$346$	−5.43409e26	−	1.46868e26i	−1.18803	−	0.321090i
$347$			2.79843e26i			0.593546i	0.954948	+	0.296773i	$0.0959104\pi$
$347$			2.79843e26i			0.593546i	−0.954948	+	0.296773i	$0.904090\pi$
$348$	−3.20487e26	−	1.86888e26i	−0.659521	−	0.384592i
$349$		−	8.76564e26i		−	1.75032i	−0.483837	−	0.875158i	$-0.660757\pi$
$349$		−	8.76564e26i		−	1.75032i	0.483837	−	0.875158i	$-0.339243\pi$
$350$	5.30793e25	−	1.96393e26i	0.102852	−	0.380550i
$351$	−7.21454e25			−0.135670
$352$	2.31538e26	+	9.03104e26i	0.422595	+	1.64831i
$353$	2.35539e26			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$353$	2.35539e26			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$354$	−1.70009e26	+	6.29032e26i	−0.292374	+	1.08178i
$355$		−	9.49980e26i		−	1.58605i
$356$	−8.40517e26	−	4.90137e26i	−1.36245	−	0.794498i
$357$		−	8.08511e25i		−	0.127253i
$358$	6.28129e26	+	1.69765e26i	0.960014	+	0.259464i
$359$	6.42377e26			0.953451			0.476726	−	0.879052i	$-0.341823\pi$
$359$	6.42377e26			0.953451			0.476726	+	0.879052i	$0.341823\pi$
$360$	6.19322e26	+	6.27420e26i	0.892772	+	0.904444i
$361$	−3.94846e26			−0.552843
$362$	1.94665e26	+	5.26124e25i	0.264758	+	0.0715564i
$363$			2.08024e27i			2.74849i
$364$	4.29637e26	−	7.36767e26i	0.551489	−	0.945727i
$365$			7.93682e26i			0.989855i
$366$	2.11480e26	−	7.82476e26i	0.256282	−	0.948243i
$367$	4.19084e25			0.0493522			0.0246761	−	0.999695i	$-0.492145\pi$
$367$	4.19084e25			0.0493522			0.0246761	+	0.999695i	$0.492145\pi$
$368$	−5.27468e26	−	9.32151e26i	−0.603662	−	1.06680i
$369$	1.14848e27			1.27745
$370$	−2.73544e25	+	1.01211e26i	−0.0295739	+	0.109423i
$371$		−	9.56101e25i		−	0.100480i
$372$	−8.11786e26	+	1.39210e27i	−0.829356	+	1.42223i
$373$			9.82973e26i			0.976335i	0.872750	+	0.488168i	$0.162335\pi$
$373$			9.82973e26i			0.976335i	−0.872750	+	0.488168i	$0.837665\pi$
$374$	1.24507e26	+	3.36506e25i	0.120238	+	0.0324969i
$375$	−1.19477e27			−1.12191
$376$	−5.74738e26	+	5.67321e26i	−0.524805	+	0.518032i
$377$	−5.41400e26			−0.480767
$378$	−1.99134e26	−	5.38201e25i	−0.171981	−	0.0464815i
$379$		−	4.71820e26i		−	0.396337i	−0.980168	−	0.198168i	$-0.936501\pi$
$379$		−	4.71820e26i		−	0.396337i	0.980168	−	0.198168i	$-0.0634993\pi$
$380$	1.51865e27	+	8.85582e26i	1.24088	+	0.723604i
$381$			1.01334e27i			0.805456i
$382$	3.38344e26	−	1.25187e27i	0.261633	−	0.968041i
$383$	2.20926e27			1.66211			0.831055	−	0.556190i	$-0.187737\pi$
$383$	2.20926e27			1.66211			0.831055	+	0.556190i	$0.187737\pi$
$384$	5.41607e26	−	1.90533e27i	0.396466	−	1.39474i
$385$	−3.30175e27			−2.35183
$386$	−8.03641e24	+	2.97346e25i	−0.00557051	+	0.0206109i
$387$		−	2.46746e27i		−	1.66451i
$388$	−1.52612e27	−	8.89936e26i	−1.00197	−	0.584286i
$389$		−	1.89014e27i		−	1.20788i	−0.797030	−	0.603939i	$-0.793597\pi$
$389$		−	1.89014e27i		−	1.20788i	0.797030	−	0.603939i	$-0.206403\pi$
$390$	2.36849e27	+	6.40133e26i	1.47330	+	0.398191i
$391$	−1.48166e26			−0.0897205
$392$	5.28263e26	−	5.21445e26i	0.311420	−	0.307401i
$393$	−2.77237e27			−1.59122
$394$	1.83112e27	+	4.94897e26i	1.02331	+	0.276570i
$395$		−	2.04835e27i		−	1.11464i
$396$	1.78337e27	−	3.05823e27i	0.945023	−	1.62058i
$397$			1.30987e27i			0.675968i	0.941152	+	0.337984i	$0.109745\pi$
$397$			1.30987e27i			0.675968i	−0.941152	+	0.337984i	$0.890255\pi$
$398$	−7.32926e26	+	2.71182e27i	−0.368373	+	1.36298i
$399$	−4.42548e27			−2.16643
$400$	−3.39567e26	−	6.00088e26i	−0.161918	−	0.286144i
$401$	2.88034e27			1.33791			0.668957	−	0.743301i	$-0.266741\pi$
$401$	2.88034e27			1.33791			0.668957	+	0.743301i	$0.266741\pi$
$402$	−4.16388e26	+	1.54063e27i	−0.188419	+	0.697149i
$403$			2.35168e27i			1.03675i
$404$	−1.09424e27	+	1.87648e27i	−0.470013	+	0.806006i
$405$			2.44310e27i			1.02250i
$406$	−1.49436e27	−	4.03881e26i	−0.609440	−	0.164714i
$407$	4.21015e26			0.167323
$408$	−1.92500e26	−	1.95017e26i	−0.0745589	−	0.0755337i
$409$	3.18034e27			1.20055			0.600273	−	0.799795i	$-0.295059\pi$
$409$	3.18034e27			1.20055			0.600273	+	0.799795i	$0.295059\pi$
$410$	−3.50449e27	−	9.47163e26i	−1.28942	−	0.348493i
$411$		−	4.42664e26i		−	0.158758i
$412$	−2.94171e27	−	1.71542e27i	−1.02844	−	0.599723i
$413$			2.71878e27i			0.926614i
$414$	−1.06112e27	+	3.92614e27i	−0.352583	+	1.30455i
$415$	−3.58014e27			−1.15983
$416$	−7.17879e26	−	2.80005e27i	−0.226763	−	0.884476i
$417$	7.00585e27			2.15790
$418$	1.84191e27	−	6.81505e27i	0.553245	−	2.04700i
$419$			1.61453e26i			0.0472933i	0.999720	+	0.0236466i	$0.00752766\pi$
$419$			1.61453e26i			0.0472933i	−0.999720	+	0.0236466i	$0.992472\pi$
$420$	6.05989e27	+	3.53375e27i	1.73120	+	1.00953i
$421$			2.50436e27i			0.697806i	0.937159	+	0.348903i	$0.113446\pi$
$421$			2.50436e27i			0.697806i	−0.937159	+	0.348903i	$0.886554\pi$
$422$	−1.81290e27	−	4.89973e26i	−0.492711	−	0.133165i
$423$	3.06657e27			0.812977
$424$	−2.27640e26	−	2.30616e26i	−0.0588718	−	0.0596415i
$425$	−9.53842e25			−0.0240654
$426$	7.82433e27	+	2.11469e27i	1.92595	+	0.520530i
$427$		−	3.38199e27i		−	0.812232i
$428$	2.64352e26	−	4.53327e26i	0.0619474	−	0.106231i
$429$		−	9.85236e27i		−	2.25288i
$430$	−2.03494e27	+	7.52928e27i	−0.454082	+	1.68010i
$431$	7.09541e27			1.54513			0.772567	−	0.634934i	$-0.218973\pi$
$431$	7.09541e27			1.54513			0.772567	+	0.634934i	$0.218973\pi$
$432$	−6.08462e26	+	3.44305e26i	−0.129317	+	0.0731753i
$433$	−1.11944e27			−0.232208			−0.116104	−	0.993237i	$-0.537041\pi$
$433$	−1.11944e27			−0.232208			−0.116104	+	0.993237i	$0.537041\pi$
$434$	−1.75434e27	+	6.49104e27i	−0.355199	+	1.31423i
$435$		−	4.45300e27i		−	0.880067i
$436$	1.32320e26	−	2.26910e26i	0.0255280	−	0.0437769i
$437$			8.11003e27i			1.52745i
$438$	−6.53701e27	−	1.76676e27i	−1.20199	−	0.324863i
$439$	−1.40907e27			−0.252962			−0.126481	−	0.991969i	$-0.540368\pi$
$439$	−1.40907e27			−0.252962			−0.126481	+	0.991969i	$0.540368\pi$
$440$	−7.96399e27	+	7.86120e27i	−1.39597	+	1.37796i
$441$	−2.81859e27			−0.482422
$442$	−3.86031e26	−	1.04333e26i	−0.0645192	−	0.0174377i
$443$		−	2.66928e27i		−	0.435667i	−0.975986	−	0.217833i	$-0.930101\pi$
$443$		−	2.66928e27i		−	0.435667i	0.975986	−	0.217833i	$-0.0698989\pi$
$444$	−7.72713e26	−	4.50599e26i	−0.123168	−	0.0718238i
$445$		−	1.16785e28i		−	1.81806i
$446$	2.37375e27	−	8.78285e27i	0.360927	−	1.33542i
$447$	−1.35390e27			−0.201075
$448$	1.07354e26	−	8.26416e27i	0.0155739	−	1.19889i
$449$	−1.06055e28			−1.50296			−0.751478	−	0.659758i	$-0.770659\pi$
$449$	−1.06055e28			−1.50296			−0.751478	+	0.659758i	$0.770659\pi$
$450$	−6.83115e26	+	2.52752e27i	−0.0945720	+	0.349916i
$451$			1.45779e28i			1.97170i
$452$	5.58248e27	+	3.25536e27i	0.737690	+	0.430175i
$453$			8.53284e27i			1.10170i
$454$	3.22664e25	+	8.72068e24i	0.00407066	+	0.00110018i
$455$	1.02370e28			1.26198
$456$	−1.06745e28	+	1.05367e28i	−1.28593	+	1.26933i
$457$	2.89399e27			0.340704			0.170352	−	0.985383i	$-0.445510\pi$
$457$	2.89399e27			0.340704			0.170352	+	0.985383i	$0.445510\pi$
$458$	1.29597e27	+	3.50262e26i	0.149110	+	0.0403001i
$459$			9.67153e25i			0.0108758i
$460$	6.47587e27	−	1.11052e28i	0.711772	−	1.22059i
$461$		−	1.47793e28i		−	1.58780i	−0.608050	−	0.793899i	$-0.708048\pi$
$461$		−	1.47793e28i		−	1.58780i	0.608050	−	0.793899i	$-0.291952\pi$
$462$	7.34980e27	−	2.71942e28i	0.771854	−	2.85585i
$463$	4.49400e27			0.461353			0.230676	−	0.973031i	$-0.425906\pi$
$463$	4.49400e27			0.461353			0.230676	+	0.973031i	$0.425906\pi$
$464$	−4.56608e27	+	2.58377e27i	−0.458252	+	0.259307i
$465$	−1.93425e28			−1.89783
$466$	3.40364e27	−	1.25935e28i	0.326507	−	1.20807i
$467$		−	5.56958e25i		−	0.00522390i	−0.999997	−	0.00261195i	$-0.999169\pi$
$467$		−	5.56958e25i		−	0.00522390i	0.999997	−	0.00261195i	$-0.000831410\pi$
$468$	−5.52930e27	+	9.48198e27i	−0.507094	+	0.869596i
$469$			6.65887e27i			0.597153i
$470$	−9.35740e27	−	2.52903e27i	−0.820593	−	0.221782i
$471$	−1.72240e28			−1.47711
$472$	6.47321e27	+	6.55785e27i	0.542911	+	0.550009i
$473$	3.13201e28			2.56910
$474$	1.68708e28	+	4.55969e27i	1.35352	+	0.365816i
$475$			5.22097e27i			0.409702i
$476$	−9.87681e26	−	5.75954e26i	−0.0758130	−	0.0442095i
$477$			1.23047e27i			0.0923909i
$478$	−3.48954e27	+	1.29113e28i	−0.256315	+	0.948365i
$479$	−2.10943e28			−1.51580			−0.757902	−	0.652369i	$-0.773775\pi$
$479$	−2.10943e28			−1.51580			−0.757902	+	0.652369i	$0.773775\pi$
$480$	2.30304e28	−	5.90454e27i	1.61908	−	0.415100i
$481$	−1.30535e27			−0.0897848
$482$	−2.45700e27	+	9.09089e27i	−0.165353	+	0.611804i
$483$			3.23616e28i			2.13101i
$484$	2.54123e28	+	1.48189e28i	1.63745	+	0.954860i
$485$		−	2.12046e28i		−	1.33703i
$486$	−2.24467e28	−	6.06669e27i	−1.38507	−	0.374344i
$487$	−3.98240e27			−0.240486			−0.120243	−	0.992744i	$-0.538367\pi$
$487$	−3.98240e27			−0.240486			−0.120243	+	0.992744i	$0.538367\pi$
$488$	−8.05226e27	−	8.15754e27i	−0.475893	−	0.482115i
$489$	−3.30126e28			−1.90957
$490$	8.60073e27	+	2.32453e27i	0.486941	+	0.131606i
$491$			1.33854e28i			0.741781i	0.928677	+	0.370890i	$0.120947\pi$
$491$			1.33854e28i			0.741781i	−0.928677	+	0.370890i	$0.879053\pi$
$492$	1.56023e28	−	2.67557e28i	0.846357	−	1.45138i
$493$			7.25780e26i			0.0385401i
$494$	−5.71080e27	+	2.11299e28i	−0.296868	+	1.09841i
$495$	4.24925e28			2.16251
$496$	1.12231e28	+	1.98337e28i	0.559184	+	0.988201i
$497$	3.38180e28			1.64971
$498$	7.96951e27	−	2.94871e28i	0.380648	−	1.40839i
$499$		−	2.25670e28i		−	1.05540i	−0.849430	−	0.527701i	$-0.823054\pi$
$499$		−	2.25670e28i		−	1.05540i	0.849430	−	0.527701i	$-0.176946\pi$
$500$	−8.51114e27	+	1.45954e28i	−0.389765	+	0.668392i
$501$			5.58383e27i			0.250401i
$502$	2.21265e28	+	5.98015e27i	0.971681	+	0.262617i
$503$	−1.46446e28			−0.629817			−0.314908	−	0.949122i	$-0.601974\pi$
$503$	−1.46446e28			−0.629817			−0.314908	+	0.949122i	$0.601974\pi$
$504$	−2.23353e28	+	2.20471e28i	−0.940744	+	0.928603i
$505$	−2.60726e28			−1.07554
$506$	−4.98354e28	−	1.34691e28i	−2.01353	−	0.544198i
$507$		−	6.09241e27i		−	0.241105i
$508$	1.23790e28	+	7.21866e27i	0.479862	+	0.279826i
$509$		−	1.67624e28i		−	0.636500i	−0.948007	−	0.318250i	$-0.896905\pi$
$509$		−	1.67624e28i		−	0.636500i	0.948007	−	0.318250i	$-0.103095\pi$
$510$	8.58137e26	−	3.17510e27i	0.0319205	−	0.118106i
$511$	−2.82540e28			−1.02958
$512$	−1.94174e28	−	2.01892e28i	−0.693196	−	0.720749i
$513$	5.29383e27			0.185156
$514$	−1.95244e27	+	7.22403e27i	−0.0669061	+	0.247552i
$515$		−	4.08735e28i		−	1.37235i
$516$	−5.74836e28	−	3.35209e28i	−1.89113	−	1.10279i
$517$			3.89246e28i			1.25480i
$518$	−3.60298e27	−	9.73781e26i	−0.113815	−	0.0307609i
$519$	5.76447e28			1.78444
$520$	2.46922e28	−	2.43735e28i	0.749073	−	0.739405i
$521$	3.72501e28			1.10747			0.553734	−	0.832694i	$-0.313203\pi$
$521$	3.72501e28			1.10747			0.553734	+	0.832694i	$0.313203\pi$
$522$	1.92319e28	+	5.19783e27i	0.560380	+	0.151454i
$523$			1.32871e27i			0.0379458i	0.999820	+	0.0189729i	$0.00603963\pi$
$523$			1.32871e27i			0.0379458i	−0.999820	+	0.0189729i	$0.993960\pi$
$524$	−1.97494e28	+	3.38674e28i	−0.552808	+	0.947989i
$525$			2.08333e28i			0.571592i
$526$	−2.50858e27	+	9.28171e27i	−0.0674648	+	0.249619i
$527$	3.15257e27			0.0831099
$528$	−4.70192e28	−	8.30931e28i	−1.21512	−	2.14738i
$529$	1.98335e28			0.502476
$530$	1.01479e27	−	3.75470e27i	0.0252045	−	0.0932564i
$531$		−	3.49899e28i		−	0.852022i
$532$	−3.15256e28	+	5.40620e28i	−0.752646	+	1.29068i
$533$		−	4.51984e28i		−	1.05801i
$534$	9.61880e28	+	2.59968e28i	2.20769	+	0.596674i
$535$	6.29874e27			0.141755
$536$	1.58543e28	+	1.60615e28i	0.349877	+	0.354452i
$537$	−6.66318e28			−1.44196
$538$	−2.94799e28	−	7.96757e27i	−0.625623	−	0.169088i
$539$		−	3.57771e28i		−	0.744599i
$540$	−7.24894e27	−	4.22713e27i	−0.147959	−	0.0862802i
$541$			4.04278e28i			0.809299i	0.914472	+	0.404649i	$0.132606\pi$
$541$			4.04278e28i			0.809299i	−0.914472	+	0.404649i	$0.867394\pi$
$542$	−1.89579e28	+	7.01439e28i	−0.372217	+	1.37720i
$543$	−2.06501e28			−0.397671
$544$	−3.75364e27	+	9.62360e26i	−0.0709029	+	0.0181781i
$545$	3.15279e27			0.0584160
$546$	−2.27879e28	+	8.43150e28i	−0.414173	+	1.53244i
$547$			2.51386e28i			0.448202i	0.974566	+	0.224101i	$0.0719445\pi$
$547$			2.51386e28i			0.448202i	−0.974566	+	0.224101i	$0.928055\pi$
$548$	−5.40761e27	−	3.15338e27i	−0.0945822	−	0.0551544i
$549$			4.35252e28i			0.746847i
$550$	−3.20824e28	−	8.67095e27i	−0.540081	−	0.145968i
$551$	3.97265e28			0.656127
$552$	7.70505e28	+	7.80579e28i	1.24858	+	1.26490i
$553$	7.29185e28			1.15937
$554$	7.08655e28	+	1.91529e28i	1.10556	+	0.298801i
$555$		−	1.07364e28i		−	0.164355i
$556$	4.99072e28	−	8.55839e28i	0.749683	−	1.28560i
$557$			4.95837e27i			0.0730903i	0.999332	+	0.0365451i	$0.0116353\pi$
$557$			4.95837e27i			0.0730903i	−0.999332	+	0.0365451i	$0.988365\pi$
$558$	2.25778e28	−	8.35377e28i	0.326605	−	1.20844i
$559$	−9.71072e28			−1.37857
$560$	8.63371e28	−	4.88548e28i	1.20288	−	0.680664i
$561$	−1.32077e28			−0.180600
$562$	−2.25610e28	+	8.34755e28i	−0.302780	+	1.12028i
$563$		−	6.59568e28i		−	0.868803i	−0.900719	−	0.434401i	$-0.856960\pi$
$563$		−	6.59568e28i		−	0.868803i	0.900719	−	0.434401i	$-0.143040\pi$
$564$	4.16598e28	−	7.14407e28i	0.538625	−	0.923666i
$565$			7.75657e28i			0.984376i
$566$	−2.64620e28	−	7.15190e27i	−0.329647	−	0.0890941i
$567$	−8.69711e28			−1.06354
$568$	8.15709e28	−	8.05181e28i	0.979214	−	0.966576i
$569$	5.81145e28			0.684866			0.342433	−	0.939542i	$-0.388749\pi$
$569$	5.81145e28			0.684866			0.342433	+	0.939542i	$0.388749\pi$
$570$	−1.73793e29	−	4.69712e28i	−2.01069	−	0.543432i
$571$			7.57765e28i			0.860707i	0.902660	+	0.430354i	$0.141611\pi$
$571$			7.57765e28i			0.860707i	−0.902660	+	0.430354i	$0.858389\pi$
$572$	−1.20357e29	−	7.01847e28i	−1.34219	−	0.782680i
$573$			1.32798e29i			1.45401i
$574$	3.37178e28	−	1.24755e29i	0.362480	−	1.34117i
$575$	3.81787e28			0.403003
$576$	−1.38161e27	+	1.06357e29i	−0.0143202	+	1.10238i
$577$	1.62995e28			0.165893			0.0829464	−	0.996554i	$-0.473567\pi$
$577$	1.62995e28			0.165893			0.0829464	+	0.996554i	$0.473567\pi$
$578$	2.59657e28	−	9.60727e28i	0.259512	−	0.960191i
$579$		−	3.15424e27i		−	0.0309578i
$580$	−5.43981e28	−	3.17216e28i	−0.524312	−	0.305746i
$581$		−	1.27448e29i		−	1.20638i
$582$	1.74647e29	+	4.72021e28i	1.62357	+	0.438803i
$583$	−1.56187e28			−0.142602
$584$	−6.81502e28	+	6.72707e28i	−0.611128	+	0.603241i
$585$	−1.31747e29			−1.16039
$586$	6.40924e28	+	1.73223e28i	0.554474	+	0.149858i
$587$			1.78494e29i			1.51678i	0.651801	+	0.758390i	$0.274014\pi$
$587$			1.78494e29i			1.51678i	−0.651801	+	0.758390i	$0.725986\pi$
$588$	−3.82910e28	+	6.56638e28i	−0.319621	+	0.548105i
$589$		−	1.72560e29i		−	1.41491i
$590$	−2.88566e28	+	1.06769e29i	−0.232434	+	0.860003i
$591$	−1.94244e29			−1.53702
$592$	−1.10091e28	+	6.22961e27i	−0.0855801	+	0.0484265i
$593$	−1.26328e29			−0.964776			−0.482388	−	0.875958i	$-0.660230\pi$
$593$	−1.26328e29			−0.964776			−0.482388	+	0.875958i	$0.660230\pi$
$594$	−8.79195e27	+	3.25301e28i	−0.0659671	+	0.244078i
$595$		−	1.37233e28i		−	0.101165i
$596$	−9.64473e27	+	1.65394e28i	−0.0698561	+	0.119793i
$597$		−	2.87669e29i		−	2.04721i
$598$	1.54514e29	+	4.17606e28i	1.08045	+	0.292014i
$599$	8.54065e28			0.586826			0.293413	−	0.955986i	$-0.405209\pi$
$599$	8.54065e28			0.586826			0.293413	+	0.955986i	$0.405209\pi$
$600$	4.96026e28	+	5.02511e28i	0.334901	+	0.339279i
$601$	−1.52766e29			−1.01355			−0.506775	−	0.862079i	$-0.669162\pi$
$601$	−1.52766e29			−1.01355			−0.506775	+	0.862079i	$0.669162\pi$
$602$	−2.68033e29	−	7.24414e28i	−1.74753	−	0.472306i
$603$		−	8.56977e28i		−	0.549082i
$604$	1.04238e29	+	6.07850e28i	0.656352	+	0.382744i
$605$			3.53091e29i			2.18502i
$606$	5.80386e28	−	2.14742e29i	0.352983	−	1.30604i
$607$	2.39633e29			1.43240			0.716200	−	0.697895i	$-0.245880\pi$
$607$	2.39633e29			1.43240			0.716200	+	0.697895i	$0.245880\pi$
$608$	5.26760e28	+	2.05460e29i	0.309475	+	1.20709i
$609$	1.58521e29			0.915389
$610$	3.58958e28	−	1.32814e29i	0.203742	−	0.753843i
$611$		−	1.20685e29i		−	0.673318i
$612$	1.27112e28	+	7.41236e27i	0.0697101	+	0.0406506i
$613$		−	1.83479e29i		−	0.989124i	−0.869142	−	0.494562i	$-0.835329\pi$
$613$		−	1.83479e29i		−	0.989124i	0.869142	−	0.494562i	$-0.164671\pi$
$614$	−2.33918e29	−	6.32212e28i	−1.23964	−	0.335039i
$615$	3.71756e29			1.93673
$616$	−2.79849e29	−	2.83508e29i	−1.43326	−	1.45200i
$617$	2.40146e29			1.20915			0.604575	−	0.796548i	$-0.293343\pi$
$617$	2.40146e29			1.20915			0.604575	+	0.796548i	$0.293343\pi$
$618$	3.36647e29	+	9.09858e28i	1.66646	+	0.450396i
$619$		−	8.90433e28i		−	0.433360i	−0.976243	−	0.216680i	$-0.930477\pi$
$619$		−	8.90433e28i		−	0.433360i	0.976243	−	0.216680i	$-0.0695229\pi$
$620$	−1.37789e29	+	2.36289e29i	−0.659329	+	1.13066i
$621$		−	3.87115e28i		−	0.182128i
$622$	−2.11153e28	+	7.81266e28i	−0.0976785	+	0.361410i
$623$	4.15741e29			1.89103
$624$	1.45782e29	+	2.57628e29i	0.652027	+	1.15227i
$625$	−2.77551e29			−1.22068
$626$	1.32741e28	−	4.91141e28i	0.0574084	−	0.212410i
$627$			7.22939e29i			3.07463i
$628$	−1.22697e29	+	2.10409e29i	−0.513167	+	0.880010i
$629$			1.74990e27i			0.00719748i
$630$	−3.63645e29	−	9.82826e28i	−1.47096	−	0.397558i
$631$	−3.00155e29			−1.19409			−0.597046	−	0.802207i	$-0.703659\pi$
$631$	−3.00155e29			−1.19409			−0.597046	+	0.802207i	$0.703659\pi$
$632$	1.75883e29	−	1.73613e29i	0.688169	−	0.679287i
$633$	1.92312e29			0.740059
$634$	−3.17694e29	−	8.58636e28i	−1.20246	−	0.324991i
$635$			1.72000e29i			0.640329i
$636$	2.86659e28	+	1.67162e28i	0.104970	+	0.0612121i
$637$			1.10926e29i			0.399548i
$638$	−6.59773e28	+	2.44116e29i	−0.233764	+	0.864925i
$639$	−4.35228e29			−1.51690
$640$	9.19300e28	−	3.23402e29i	0.315187	−	1.10880i
$641$	1.00517e28			0.0339025			0.0169513	−	0.999856i	$-0.494604\pi$
$641$	1.00517e28			0.0339025			0.0169513	+	0.999856i	$0.494604\pi$
$642$	−1.40212e28	+	5.18784e28i	−0.0465230	+	0.172135i
$643$		−	1.20968e28i		−	0.0394871i	−0.999805	−	0.0197435i	$-0.993715\pi$
$643$		−	1.20968e28i		−	0.0394871i	0.999805	−	0.0197435i	$-0.00628497\pi$
$644$	3.95331e29	+	2.30533e29i	1.26958	+	0.740339i
$645$		−	7.98704e29i		−	2.52353i
$646$	2.83259e28	+	7.65567e27i	0.0880527	+	0.0237981i
$647$	−3.73180e28			−0.114136			−0.0570680	−	0.998370i	$-0.518175\pi$
$647$	−3.73180e28			−0.114136			−0.0570680	+	0.998370i	$0.518175\pi$
$648$	−2.09779e29	+	2.07071e29i	−0.631283	+	0.623136i
$649$	4.44136e29			1.31506
$650$	9.94708e28	+	2.68841e28i	0.289805	+	0.0783258i
$651$		−	6.88568e29i		−	1.97400i
$652$	−2.35170e29	+	4.03283e29i	−0.663410	+	1.13766i
$653$		−	2.06395e29i		−	0.572941i	−0.958089	−	0.286470i	$-0.907518\pi$
$653$		−	2.06395e29i		−	0.572941i	0.958089	−	0.286470i	$-0.0924820\pi$
$654$	−7.01822e27	+	2.59674e28i	−0.0191717	+	0.0709352i
$655$	−4.70570e29			−1.26500
$656$	−2.15704e29	−	3.81196e29i	−0.570647	−	1.00846i
$657$	3.63621e29			0.946701
$658$	9.00303e28	−	3.33111e29i	0.230684	−	0.853527i
$659$			1.87417e29i			0.472621i	0.971678	+	0.236310i	$0.0759382\pi$
$659$			1.87417e29i			0.472621i	−0.971678	+	0.236310i	$0.924062\pi$
$660$	5.77268e29	−	9.89933e29i	1.43274	−	2.45694i
$661$			2.63521e29i			0.643724i	0.946787	+	0.321862i	$0.104309\pi$
$661$			2.63521e29i			0.643724i	−0.946787	+	0.321862i	$0.895691\pi$
$662$	3.97179e29	+	1.07346e29i	0.954942	+	0.258093i
$663$	4.09501e28			0.0969088
$664$	−3.03444e29	−	3.07412e29i	−0.706829	−	0.716070i
$665$	−7.51162e29			−1.72229
$666$	4.63693e28	+	1.25323e28i	0.104653	+	0.0282846i
$667$		−	2.90502e29i		−	0.645398i
$668$	6.82124e28	+	3.97772e28i	0.149180	+	0.0869925i
$669$			9.31683e29i			2.00583i
$670$	−7.06759e28	+	2.61500e29i	−0.149791	+	0.554226i
$671$	−5.52476e29			−1.15273
$672$	2.10194e29	+	8.19851e29i	0.431760	+	1.68406i
$673$	−7.87039e29			−1.59161			−0.795807	−	0.605550i	$-0.792953\pi$
$673$	−7.87039e29			−1.59161			−0.795807	+	0.605550i	$0.792953\pi$
$674$	1.09393e29	−	4.04754e29i	0.217802	−	0.805866i
$675$		−	2.49212e28i		−	0.0488516i
$676$	−7.44252e28	−	4.34002e28i	−0.143641	−	0.0837628i
$677$			4.18898e29i			0.796025i	0.917380	+	0.398013i	$0.130300\pi$
$677$			4.18898e29i			0.796025i	−0.917380	+	0.398013i	$0.869700\pi$
$678$	−6.38855e29	−	1.72664e29i	−1.19534	−	0.323065i
$679$	7.54855e29			1.39069
$680$	−3.26741e28	−	3.31013e28i	−0.0592735	−	0.0600485i
$681$	−3.42282e27			−0.00611419
$682$	1.06036e30	+	2.86586e29i	1.86517	+	0.504102i
$683$			2.99571e28i			0.0518898i	0.999663	+	0.0259449i	$0.00825944\pi$
$683$			2.99571e28i			0.0518898i	−0.999663	+	0.0259449i	$0.991741\pi$
$684$	4.05725e29	−	6.95761e29i	0.692058	−	1.18678i
$685$		−	7.51358e28i		−	0.126211i
$686$	1.06358e29	−	3.93523e29i	0.175940	−	0.650978i
$687$	−1.37476e29			−0.223965
$688$	−8.18986e29	+	4.63432e29i	−1.31401	+	0.743545i
$689$	4.84254e28			0.0765194
$690$	−3.43480e29	+	1.27087e30i	−0.534546	+	1.97782i
$691$		−	5.44845e29i		−	0.835128i	−0.908647	−	0.417564i	$-0.862884\pi$
$691$		−	5.44845e29i		−	0.835128i	0.908647	−	0.417564i	$-0.137116\pi$
$692$	4.10640e29	−	7.04191e29i	0.619937	−	1.06311i
$693$			1.51268e30i			2.24930i
$694$	−3.91219e29	−	1.05735e29i	−0.572987	−	0.154862i
$695$	1.18914e30			1.71551
$696$	3.82361e29	−	3.77426e29i	0.543346	−	0.536334i
$697$	−6.05913e28			−0.0848136
$698$	1.22543e30	+	3.31199e29i	1.68969	+	0.456674i
$699$			1.33591e30i			1.81454i
$700$	2.54501e29	+	1.48409e29i	0.340534	+	0.198578i
$701$		−	9.74969e29i		−	1.28514i	−0.766226	−	0.642572i	$-0.777867\pi$
$701$		−	9.74969e29i		−	1.28514i	0.766226	−	0.642572i	$-0.222133\pi$
$702$	2.72592e28	−	1.00859e29i	0.0353976	−	0.130971i
$703$	9.57827e28			0.122534
$704$	−1.35002e30	−	1.75371e28i	−1.70148	−	0.0221027i
$705$	9.92631e29			1.23254
$706$	−8.89954e28	+	3.29282e29i	−0.108873	+	0.402828i
$707$		−	9.28152e29i		−	1.11870i
$708$	−8.15148e29	−	4.75344e29i	−0.968027	−	0.564493i
$709$			1.42226e30i			1.66416i	0.554657	+	0.832079i	$0.312849\pi$
$709$			1.42226e30i			1.66416i	−0.554657	+	0.832079i	$0.687151\pi$
$710$	1.32807e30	+	3.58938e29i	1.53111	+	0.413815i
$711$	−9.38439e29			−1.06604
$712$	1.00279e30	−	9.89846e29i	1.12246	−	1.10797i
$713$	−1.26185e30			−1.39177
$714$	1.13029e29	+	3.05486e28i	0.122846	+	0.0332016i
$715$		−	1.67230e30i		−	1.79102i
$716$	−4.74662e29	+	8.13978e29i	−0.500953	+	0.859065i
$717$		−	1.36962e30i		−	1.42446i
$718$	−2.42714e29	+	8.98041e29i	−0.248765	+	0.920427i
$719$	−1.33357e30			−1.34698			−0.673490	−	0.739197i	$-0.735205\pi$
$719$	−1.33357e30			−1.34698			−0.673490	+	0.739197i	$0.735205\pi$
$720$	−1.11113e30	+	6.28747e29i	−1.10605	+	0.625871i
$721$	1.45504e30			1.42743
$722$	1.49187e29	−	5.51992e29i	0.144242	−	0.533694i
$723$		−	9.64360e29i		−	0.918939i
$724$	−1.47104e29	+	2.52263e29i	−0.138156	+	0.236918i
$725$		−	1.87016e29i		−	0.173113i
$726$	−2.90817e30	−	7.85993e29i	−2.65329	−	0.717107i
$727$	1.13248e30			1.01840			0.509201	−	0.860648i	$-0.329941\pi$
$727$	1.13248e30			1.01840			0.509201	+	0.860648i	$0.329941\pi$
$728$	8.67664e29	+	8.79009e29i	0.769081	+	0.779137i
$729$	1.36588e30			1.19337
$730$	−1.10956e30	−	2.99883e29i	−0.955569	−	0.258263i
$731$			1.30178e29i			0.110511i
$732$	1.01399e30	+	5.91297e29i	0.848532	+	0.494811i
$733$		−	2.85479e29i		−	0.235495i	−0.993044	−	0.117748i	$-0.962433\pi$
$733$		−	2.85479e29i		−	0.235495i	0.993044	−	0.117748i	$-0.0375674\pi$
$734$	−1.58345e28	+	5.85877e28i	−0.0128765	+	0.0476428i
$735$	−9.12364e29			−0.731393
$736$	1.50244e30	−	3.85196e29i	1.18735	−	0.304414i
$737$	1.08778e30			0.847487
$738$	−4.33938e29	+	1.60557e30i	−0.333300	+	1.23321i
$739$			8.37054e29i			0.633851i	0.948450	+	0.316925i	$0.102650\pi$
$739$			8.37054e29i			0.633851i	−0.948450	+	0.316925i	$0.897350\pi$
$740$	−1.31157e29	−	7.64826e28i	−0.0979171	−	0.0570992i
$741$		−	2.24146e30i		−	1.64983i
$742$	1.33662e29	+	3.61251e28i	0.0969993	+	0.0262161i
$743$	−9.64894e29			−0.690394			−0.345197	−	0.938530i	$-0.612188\pi$
$743$	−9.64894e29			−0.690394			−0.345197	+	0.938530i	$0.612188\pi$
$744$	−1.63943e30	−	1.66086e30i	−1.15658	−	1.17170i
$745$	−2.29806e29			−0.159853
$746$	−1.37419e30	−	3.71404e29i	−0.942518	−	0.254735i
$747$			1.64022e30i			1.10927i
$748$	−9.40869e28	+	1.61346e29i	−0.0627426	+	0.107595i
$749$			2.24227e29i			0.147445i
$750$	4.51430e29	−	1.67029e30i	0.292716	−	1.08305i
$751$	7.09757e29			0.453827			0.226914	−	0.973915i	$-0.427137\pi$
$751$	7.09757e29			0.453827			0.226914	+	0.973915i	$0.427137\pi$
$752$	−5.75954e29	−	1.01784e30i	−0.363162	−	0.641787i
$753$	−2.34718e30			−1.45948
$754$	2.04561e29	−	7.56875e29i	0.125437	−	0.464114i
$755$			1.44833e30i			0.875838i
$756$	1.50480e29	−	2.58053e29i	0.0897431	−	0.153897i
$757$			2.32050e30i			1.36482i	0.730972	+	0.682408i	$0.239067\pi$
$757$			2.32050e30i			1.36482i	−0.730972	+	0.682408i	$0.760933\pi$
$758$	6.59602e29	+	1.78271e29i	0.382609	+	0.103408i
$759$	5.28653e30			3.02435
$760$	−1.81184e30	+	1.78846e30i	−1.02230	+	1.00910i
$761$	−1.27435e28			−0.00709170			−0.00354585	−	0.999994i	$-0.501129\pi$
$761$	−1.27435e28			−0.00709170			−0.00354585	+	0.999994i	$0.501129\pi$
$762$	−1.41664e30	−	3.82877e29i	−0.777558	−	0.210151i
$763$			1.12235e29i			0.0607606i
$764$	1.62227e30	+	9.46007e29i	0.866249	+	0.505143i
$765$			1.76615e29i			0.0930213i
$766$	−8.34741e29	+	3.08854e30i	−0.433660	+	1.60454i
$767$	−1.37703e30			−0.705656
$768$	2.45900e30	+	1.47707e30i	1.24298	+	0.746634i
$769$	−1.03254e30			−0.514847			−0.257424	−	0.966299i	$-0.582874\pi$
$769$	−1.03254e30			−0.514847			−0.257424	+	0.966299i	$0.582874\pi$
$770$	1.24752e30	−	4.61583e30i	0.613615	−	2.27037i
$771$		−	7.66323e29i		−	0.371827i
$772$	−3.85324e28	−	2.24697e28i	−0.0184436	−	0.0107551i
$773$		−	1.06430e30i		−	0.502549i	−0.967916	−	0.251274i	$-0.919150\pi$
$773$		−	1.06430e30i		−	0.502549i	0.967916	−	0.251274i	$-0.0808496\pi$
$774$	3.44950e30	+	9.32299e29i	1.60685	+	0.434285i
$775$	−8.12339e29			−0.373310
$776$	1.82075e30	−	1.79725e30i	0.825472	−	0.814818i
$777$	3.82204e29			0.170952
$778$	2.64241e30	+	7.14166e29i	1.16604	+	0.315147i
$779$			3.31654e30i			1.44391i
$780$	−1.78981e30	+	3.06927e30i	−0.768799	+	1.31838i
$781$		−	5.52446e30i		−	2.34128i
$782$	5.59826e28	−	2.07135e29i	0.0234089	−	0.0866129i
$783$	−1.89626e29			−0.0782345
$784$	5.29381e29	+	9.35531e29i	0.215501	+	0.380837i
$785$	−2.92352e30			−1.17429
$786$	1.04750e30	−	3.87576e30i	0.415163	−	1.53610i
$787$		−	1.57804e30i		−	0.617141i	−0.951201	−	0.308571i	$-0.900149\pi$
$787$		−	1.57804e30i		−	0.617141i	0.951201	−	0.308571i	$-0.0998506\pi$
$788$	−1.38373e30	+	2.37290e30i	−0.533980	+	0.915702i
$789$		−	9.84602e29i		−	0.374932i
$790$	2.86358e30	+	7.73942e29i	1.07603	+	0.290820i
$791$	−2.76124e30			−1.02388
$792$	3.60157e30	+	3.64866e30i	1.31788	+	1.33512i
$793$	1.71294e30			0.618548
$794$	−1.83119e30	−	4.94916e29i	−0.652555	−	0.176367i
$795$			3.98298e29i			0.140073i
$796$	−3.51419e30	−	2.04926e30i	−1.21966	−	0.711228i
$797$			5.04618e30i			1.72842i	0.503129	+	0.864212i	$0.332182\pi$
$797$			5.04618e30i			1.72842i	−0.503129	+	0.864212i	$0.667818\pi$
$798$	1.67211e30	−	6.18680e30i	0.565243	−	2.09139i
$799$	−1.61786e29			−0.0539757
$800$	9.67221e29	−	2.47977e29i	0.318479	−	0.0816518i
$801$	−5.35046e30			−1.73880
$802$	−1.08830e30	+	4.02671e30i	−0.349075	+	1.29157i
$803$			4.61553e30i			1.46120i
$804$	−1.99647e30	−	1.16422e30i	−0.623842	−	0.363786i
$805$			5.49292e30i			1.69413i
$806$	−3.28764e30	−	8.88552e29i	−1.00084	−	0.270499i
$807$	3.12722e30			0.939695
$808$	−2.20986e30	−	2.23875e30i	−0.655458	−	0.664028i
$809$	−2.38668e30			−0.698772			−0.349386	−	0.936979i	$-0.613610\pi$
$809$	−2.38668e30			−0.698772			−0.349386	+	0.936979i	$0.613610\pi$
$810$	−3.41544e30	−	9.23094e29i	−0.987083	−	0.266780i
$811$			1.81967e30i			0.519127i	0.965726	+	0.259563i	$0.0835786\pi$
$811$			1.81967e30i			0.519127i	−0.965726	+	0.259563i	$0.916421\pi$
$812$	1.12925e30	−	1.93650e30i	0.318018	−	0.545356i
$813$		−	7.44085e30i		−	2.06858i
$814$	−1.59075e29	+	5.88577e29i	−0.0436562	+	0.161528i
$815$	−5.60341e30			−1.51809
$816$	3.45367e29	−	1.95430e29i	0.0923706	−	0.0522689i
$817$	7.12546e30			1.88140
$818$	−1.20165e30	+	4.44610e30i	−0.313234	+	1.15896i
$819$		−	4.69003e30i		−	1.20696i
$820$	2.64826e30	−	4.54139e30i	0.672845	−	1.15383i
$821$		−	9.92204e29i		−	0.248885i	−0.992227	−	0.124442i	$-0.960286\pi$
$821$		−	9.92204e29i		−	0.248885i	0.992227	−	0.124442i	$-0.0397142\pi$
$822$	6.18842e29	+	1.67255e29i	0.153259	+	0.0414214i
$823$	7.58169e30			1.85382			0.926910	−	0.375283i	$-0.122454\pi$
$823$	7.58169e30			1.85382			0.926910	+	0.375283i	$0.122454\pi$
$824$	3.50964e30	−	3.46435e30i	0.847280	−	0.836345i
$825$	3.40330e30			0.811210
$826$	−3.80085e30	−	1.02726e30i	−0.894519	−	0.241763i
$827$		−	1.94050e30i		−	0.450926i	−0.974252	−	0.225463i	$-0.927610\pi$
$827$		−	1.94050e30i		−	0.450926i	0.974252	−	0.225463i	$-0.0723895\pi$
$828$	−5.08780e30	−	2.96689e30i	−1.16738	−	0.680742i
$829$		−	1.79220e30i		−	0.406034i	−0.979175	−	0.203017i	$-0.934925\pi$
$829$		−	1.79220e30i		−	0.406034i	0.979175	−	0.203017i	$-0.0650748\pi$
$830$	1.35271e30	−	5.00502e30i	0.302611	−	1.11966i
$831$	−7.51740e30			−1.66057
$832$	4.18570e30	+	5.43734e28i	0.913006	+	0.0118602i
$833$	1.48703e29			0.0320293
$834$	−2.64707e30	+	9.79415e30i	−0.563018	+	2.08316i
$835$			9.47775e29i			0.199066i
$836$	8.83146e30	+	5.14996e30i	1.83175	+	1.06816i
$837$			8.23676e29i			0.168709i
$838$	−2.25711e29	−	6.10031e28i	−0.0456552	−	0.0123393i
$839$	5.57748e30			1.11413			0.557067	−	0.830468i	$-0.311927\pi$
$839$	5.57748e30			1.11413			0.557067	+	0.830468i	$0.311927\pi$
$840$	−7.22983e30	+	7.13652e30i	−1.42625	+	1.40784i
$841$	3.70984e30			0.722765
$842$	−3.50108e30	−	9.46241e29i	−0.673636	−	0.182064i
$843$		−	8.85506e30i		−	1.68268i
$844$	1.36996e30	−	2.34929e30i	0.257106	−	0.440901i
$845$		−	1.03410e30i		−	0.191676i
$846$	−1.15866e30	+	4.28704e30i	−0.212114	+	0.784818i
$847$	−1.25696e31			−2.27272
$848$	4.08412e29	−	2.31104e29i	0.0729360	−	0.0412716i
$849$	2.80708e30			0.495136
$850$	3.60397e28	−	1.33347e29i	0.00627889	−	0.0232318i
$851$		−	7.00417e29i		−	0.120530i
$852$	−5.91265e30	+	1.01394e31i	−1.00500	+	1.72343i
$853$			9.45023e30i			1.58664i	0.608807	+	0.793319i	$0.291649\pi$
$853$			9.45023e30i			1.58664i	−0.608807	+	0.793319i	$0.708351\pi$
$854$	4.72801e30	+	1.27784e30i	0.784099	+	0.211919i
$855$	9.66724e30			1.58365
$856$	5.33867e29	+	5.40847e29i	0.0863890	+	0.0875185i
$857$	−2.83338e30			−0.452903			−0.226452	−	0.974022i	$-0.572713\pi$
$857$	−2.83338e30			−0.452903			−0.226452	+	0.974022i	$0.572713\pi$
$858$	1.37736e31	+	3.72259e30i	2.17485	+	0.587799i
$859$		−	5.97912e30i		−	0.932629i	−0.884619	−	0.466314i	$-0.845582\pi$
$859$		−	5.97912e30i		−	0.932629i	0.884619	−	0.466314i	$-0.154418\pi$
$860$	−9.75702e30	−	5.68969e30i	−1.50343	−	0.876707i
$861$			1.32340e31i			2.01446i
$862$	−2.68091e30	+	9.91935e30i	−0.403140	+	1.49161i
$863$	1.19155e31			1.77010			0.885049	−	0.465497i	$-0.154125\pi$
$863$	1.19155e31			1.77010			0.885049	+	0.465497i	$0.154125\pi$
$864$	−2.51437e29	−	9.80719e29i	−0.0369008	−	0.143930i
$865$	9.78436e30			1.41861
$866$	4.22966e29	−	1.56497e30i	0.0605853	−	0.224165i
$867$			1.01914e31i			1.44222i
$868$	−8.41158e30	−	4.90511e30i	−1.17604	−	0.685791i
$869$		−	1.19118e31i		−	1.64540i
$870$	6.22528e30	+	1.68251e30i	0.849585	+	0.229618i
$871$	−3.37264e30			−0.454757
$872$	2.67224e29	+	2.70717e29i	0.0356001	+	0.0360656i
$873$	−9.71476e30			−1.27874
$874$	−1.13378e31	−	3.06427e30i	−1.47455	−	0.398527i
$875$		−	7.21926e30i		−	0.927701i
$876$	4.93985e30	−	8.47116e30i	0.627221	−	1.07560i
$877$			1.16672e31i			1.46377i	0.681429	+	0.731885i	$0.261359\pi$
$877$			1.16672e31i			1.46377i	−0.681429	+	0.731885i	$0.738641\pi$
$878$	5.32400e29	−	1.96988e30i	0.0660003	−	0.244201i
$879$	−6.79891e30			−0.832829
$880$	−7.98083e30	−	1.41039e31i	−0.966007	−	1.70714i
$881$	4.77006e30			0.570528			0.285264	−	0.958449i	$-0.407919\pi$
$881$	4.77006e30			0.570528			0.285264	+	0.958449i	$0.407919\pi$
$882$	1.06497e30	−	3.94038e30i	0.125869	−	0.465713i
$883$		−	1.56775e31i		−	1.83101i	−0.402308	−	0.915504i	$-0.631792\pi$
$883$		−	1.56775e31i		−	1.83101i	0.402308	−	0.915504i	$-0.368208\pi$
$884$	2.91714e29	−	5.00249e29i	0.0336674	−	0.0577348i
$885$		−	1.13261e31i		−	1.29174i
$886$	3.73163e30	+	1.00855e30i	0.420577	+	0.113670i
$887$	3.82440e30			0.425957			0.212978	−	0.977057i	$-0.431684\pi$
$887$	3.82440e30			0.425957			0.212978	+	0.977057i	$0.431684\pi$
$888$	9.21895e29	−	9.09997e29i	0.101472	−	0.100162i
$889$	−6.12296e30			−0.666029
$890$	1.63265e31	+	4.41259e30i	1.75509	+	0.474349i
$891$			1.42074e31i			1.50939i
$892$	1.13815e31	+	6.63698e30i	1.19500	+	0.696850i
$893$			8.85553e30i			0.918913i
$894$	5.11556e29	−	1.89275e30i	0.0524625	−	0.194111i
$895$	−1.13098e31			−1.14634
$896$	1.15127e31	+	3.27259e30i	1.15330	+	0.327837i
$897$	−1.63908e31			−1.62285
$898$	4.00717e30	−	1.48265e31i	0.392136	−	1.45090i
$899$			6.18110e30i			0.597846i
$900$	−3.27536e30	−	1.90998e30i	−0.313121	−	0.182593i
$901$		−	6.49172e28i		−	0.00613408i
$902$	−2.03798e31	−	5.50807e30i	−1.90341	−	0.514436i
$903$	2.84328e31			2.62482
$904$	−6.66025e30	+	6.57429e30i	−0.607746	+	0.599902i
$905$	−3.50505e30			−0.316144
$906$	−1.19289e31	−	3.22403e30i	−1.06354	−	0.287444i
$907$		−	2.09565e31i		−	1.84690i	−0.383719	−	0.923450i	$-0.625357\pi$
$907$		−	2.09565e31i		−	1.84690i	0.383719	−	0.923450i	$-0.374643\pi$
$908$	−2.43829e28	+	4.18133e28i	−0.00212415	+	0.00364261i
$909$			1.19450e31i			1.02865i
$910$	−3.86792e30	+	1.43113e31i	−0.329263	+	1.21827i
$911$	−2.16429e31			−1.82126			−0.910632	−	0.413217i	$-0.864405\pi$
$911$	−2.16429e31			−1.82126			−0.910632	+	0.413217i	$0.864405\pi$
$912$	−1.06971e31	−	1.89041e31i	−0.889855	−	1.57257i
$913$	−2.08197e31			−1.71211
$914$	−1.09346e30	+	4.04578e30i	−0.0888928	+	0.328903i
$915$			1.40889e31i			1.13228i
$916$	−9.79330e29	+	1.67941e30i	−0.0778084	+	0.133431i
$917$		−	1.67517e31i		−	1.31577i
$918$	−1.35208e29	−	3.65427e28i	−0.0104991	−	0.00283761i
$919$	−2.29685e31			−1.76327			−0.881637	−	0.471928i	$-0.843558\pi$
$919$	−2.29685e31			−1.76327			−0.881637	+	0.471928i	$0.843558\pi$
$920$	1.30782e31	+	1.32492e31i	0.992604	+	1.00558i
$921$	2.48140e31			1.86196
$922$	2.06614e31	+	5.58419e30i	1.53280	+	0.414272i
$923$			1.71285e31i			1.25632i
$924$	3.52403e31	+	2.05500e31i	2.55555	+	1.49024i
$925$		−	4.50905e29i		−	0.0323294i
$926$	−1.69800e30	+	6.28260e30i	−0.120371	+	0.445373i
$927$	−1.87260e31			−1.31252
$928$	−1.88686e30	−	7.35960e30i	−0.130763	−	0.510036i
$929$	2.65004e31			1.81588			0.907941	−	0.419099i	$-0.137654\pi$
$929$	2.65004e31			1.81588			0.907941	+	0.419099i	$0.137654\pi$
$930$	7.30832e30	−	2.70407e31i	0.495161	−	1.83209i
$931$		−	8.13944e30i		−	0.545284i
$932$	1.63196e31	+	9.51656e30i	1.08104	+	0.630395i
$933$		−	8.28765e30i		−	0.542843i
$934$	7.78624e28	+	2.10439e28i	0.00504296	+	0.00136297i
$935$	−2.24182e30			−0.143575
$936$	−1.11666e31	−	1.13126e31i	−0.707170	−	0.716416i
$937$	9.36798e30			0.586652			0.293326	−	0.956013i	$-0.405238\pi$
$937$	9.36798e30			0.586652			0.293326	+	0.956013i	$0.405238\pi$
$938$	−9.30907e30	−	2.51597e30i	−0.576470	−	0.155803i
$939$			5.21001e30i			0.319044i
$940$	7.07115e30	−	1.21260e31i	0.428201	−	0.734305i
$941$		−	5.08613e30i		−	0.304576i	−0.988336	−	0.152288i	$-0.951336\pi$
$941$		−	5.08613e30i		−	0.304576i	0.988336	−	0.152288i	$-0.0486642\pi$
$942$	6.50786e30	−	2.40790e31i	0.385393	−	1.42595i
$943$	2.42524e31			1.42030
$944$	−1.16137e31	+	6.57172e30i	−0.672610	+	0.380604i
$945$	3.58551e30			0.205360
$946$	−1.18339e31	+	4.37853e31i	−0.670302	+	2.48011i
$947$			3.38102e31i			1.89397i	0.321280	+	0.946984i	$0.395887\pi$
$947$			3.38102e31i			1.89397i	−0.321280	+	0.946984i	$0.604113\pi$
$948$	−1.27488e31	+	2.18625e31i	−0.706291	+	1.21119i
$949$		−	1.43103e31i		−	0.784070i
$950$	−7.29889e30	−	1.97268e30i	−0.395512	−	0.106895i
$951$	3.37010e31			1.80612
$952$	1.17836e30	−	1.16316e30i	0.0624585	−	0.0616524i
$953$	−2.83165e31			−1.48445			−0.742223	−	0.670153i	$-0.766228\pi$
$953$	−2.83165e31			−1.48445			−0.742223	+	0.670153i	$0.766228\pi$
$954$	−1.72020e30	−	4.64919e29i	−0.0891908	−	0.0241057i
$955$			2.25406e31i			1.15592i
$956$	−1.67314e31	−	9.75671e30i	−0.848642	−	0.494875i
$957$		−	2.58957e31i		−	1.29913i
$958$	7.97023e30	−	2.94898e31i	0.395488	−	1.46330i
$959$	2.67474e30			0.131276
$960$	−4.47220e29	+	3.44273e31i	−0.0217107	+	1.67130i
$961$	6.02332e30			0.289228
$962$	4.93209e29	−	1.82487e30i	0.0234257	−	0.0866749i
$963$		−	2.88573e30i		−	0.135575i
$964$	−1.17807e31	−	6.86976e30i	−0.547471	−	0.319251i
$965$		−	5.35388e29i		−	0.0246111i
$966$	−4.52414e31	−	1.22274e31i	−2.05720	−	0.556001i
$967$	2.31354e31			1.04064			0.520318	−	0.853972i	$-0.325813\pi$
$967$	2.31354e31			1.04064			0.520318	+	0.853972i	$0.325813\pi$
$968$	−3.03185e31	+	2.99272e31i	−1.34901	+	1.33160i
$969$	−3.00481e30			−0.132257
$970$	2.96439e31	+	8.01188e30i	1.29072	+	0.348844i
$971$		−	1.00801e31i		−	0.434172i	−0.976152	−	0.217086i	$-0.930345\pi$
$971$		−	1.00801e31i		−	0.434172i	0.976152	−	0.217086i	$-0.0696552\pi$
$972$	1.69624e31	−	2.90881e31i	0.722756	−	1.23942i
$973$			4.23319e31i			1.78436i
$974$	1.50470e30	−	5.56737e30i	0.0627452	−	0.232157i
$975$	−1.05518e31			−0.435291
$976$	1.44466e31	−	8.17480e30i	0.589582	−	0.333621i
$977$	1.99499e30			0.0805468			0.0402734	−	0.999189i	$-0.487177\pi$
$977$	1.99499e30			0.0805468			0.0402734	+	0.999189i	$0.487177\pi$
$978$	1.24734e31	−	4.61514e31i	0.498226	−	1.84343i
$979$		−	6.79147e31i		−	2.68377i
$980$	−6.49936e30	+	1.11455e31i	−0.254095	+	0.435738i
$981$		−	1.44444e30i		−	0.0558693i
$982$	−1.87127e31	−	5.05751e30i	−0.716088	−	0.193538i
$983$	4.84717e31			1.83517			0.917584	−	0.397541i	$-0.130136\pi$
$983$	4.84717e31			1.83517			0.917584	+	0.397541i	$0.130136\pi$
$984$	3.15092e31	+	3.19212e31i	1.18029	+	1.19572i
$985$	−3.29702e31			−1.22192
$986$	−1.01464e30	−	2.74227e29i	−0.0372051	−	0.0100555i
$987$			3.53364e31i			1.28201i
$988$	−2.73818e31	−	1.59673e31i	−0.982909	−	0.573172i
$989$		−	5.21053e31i		−	1.85064i
$990$	−1.60553e31	+	5.94043e31i	−0.564219	+	2.08761i
$991$	−4.86084e31			−1.69020			−0.845100	−	0.534608i	$-0.820459\pi$
$991$	−4.86084e31			−1.69020			−0.845100	+	0.534608i	$0.820459\pi$
$992$	−3.19679e31	+	8.19594e30i	−1.09987	+	0.281985i
$993$	−4.21326e31			−1.43434
$994$	−1.27777e31	+	4.72775e31i	−0.430424	+	1.59257i
$995$		−	4.88278e31i		−	1.62751i
$996$	3.82117e31	+	2.22827e31i	1.26030	+	0.734927i
$997$		−	5.40626e30i		−	0.176440i	−0.996101	−	0.0882201i	$-0.971882\pi$
$997$		−	5.40626e30i		−	0.176440i	0.996101	−	0.0882201i	$-0.0281179\pi$
$998$	3.15485e31	+	8.52665e30i	1.01885	+	0.275364i
$999$	−4.57198e29			−0.0146106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.22.b.a.5.10	yes	20
4.3	odd	2		32.22.b.a.17.18		20
8.3	odd	2		32.22.b.a.17.3		20
8.5	even	2	inner	8.22.b.a.5.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.22.b.a.5.9	✓	20	8.5	even	2	inner
8.22.b.a.5.10	yes	20	1.1	even	1	trivial
32.22.b.a.17.3		20	8.3	odd	2
32.22.b.a.17.18		20	4.3	odd	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-377.837 + 1398.00i) q^{2} -148299. i q^{3} +(-1.81163e6 - 1.05643e6i) q^{4} -2.51716e7i q^{5} +(2.07321e8 + 5.60329e7i) q^{6} +8.96078e8 q^{7} +(2.16139e9 - 2.13349e9i) q^{8} -1.15323e10 q^{9} +O(q^{10})\)	\(q+(-377.837 + 1398.00i) q^{2} -148299. i q^{3} +(-1.81163e6 - 1.05643e6i) q^{4} -2.51716e7i q^{5} +(2.07321e8 + 5.60329e7i) q^{6} +8.96078e8 q^{7} +(2.16139e9 - 2.13349e9i) q^{8} -1.15323e10 q^{9} +(3.51898e10 + 9.51079e9i) q^{10} -1.46382e11i q^{11} +(-1.56668e11 + 2.68663e11i) q^{12} +4.53853e11i q^{13} +(-3.38572e11 + 1.25271e12i) q^{14} -3.73293e12 q^{15} +(2.16596e12 + 3.82772e12i) q^{16} +6.08418e11 q^{17} +(4.35732e12 - 1.61220e13i) q^{18} -3.33025e13i q^{19} +(-2.65921e13 + 4.56017e13i) q^{20} -1.32887e14i q^{21} +(2.04641e14 + 5.53085e13i) q^{22} -2.43526e14 q^{23} +(-3.16395e14 - 3.20531e14i) q^{24} -1.56774e14 q^{25} +(-6.34484e14 - 1.71483e14i) q^{26} +1.58962e14i q^{27} +(-1.62336e15 - 9.46643e14i) q^{28} +1.19290e15i q^{29} +(1.41044e15 - 5.21862e15i) q^{30} +5.18159e15 q^{31} +(-6.16951e15 + 1.58174e15i) q^{32} -2.17083e16 q^{33} +(-2.29883e14 + 8.50565e14i) q^{34} -2.25557e16i q^{35} +(2.08922e16 + 1.21830e16i) q^{36} +2.87614e15i q^{37} +(4.65567e16 + 1.25829e16i) q^{38} +6.73060e16 q^{39} +(-5.37035e16 - 5.44056e16i) q^{40} -9.95883e16 q^{41} +(1.85776e17 + 5.02099e16i) q^{42} +2.13962e17i q^{43} +(-1.54642e17 + 2.65189e17i) q^{44} +2.90286e17i q^{45} +(9.20134e16 - 3.40449e17i) q^{46} -2.65912e17 q^{47} +(5.67647e17 - 3.21210e17i) q^{48} +2.44409e17 q^{49} +(5.92352e16 - 2.19170e17i) q^{50} -9.02277e16i q^{51} +(4.79464e17 - 8.22214e17i) q^{52} -1.06698e17i q^{53} +(-2.22228e17 - 6.00618e16i) q^{54} -3.68467e18 q^{55} +(1.93677e18 - 1.91177e18i) q^{56} -4.93873e18 q^{57} +(-1.66767e18 - 4.50721e17i) q^{58} +3.03409e18i q^{59} +(6.76269e18 + 3.94358e18i) q^{60} -3.77422e18i q^{61} +(-1.95780e18 + 7.24383e18i) q^{62} -1.03338e19 q^{63} +(1.19804e17 - 9.22259e18i) q^{64} +1.14242e19 q^{65} +(8.20219e18 - 3.03480e19i) q^{66} +7.43113e18i q^{67} +(-1.10223e18 - 6.42751e17i) q^{68} +3.61147e19i q^{69} +(3.15328e19 + 8.52241e18i) q^{70} +3.77401e19 q^{71} +(-2.49257e19 + 2.46040e19i) q^{72} -3.15308e19 q^{73} +(-4.02084e18 - 1.08672e18i) q^{74} +2.32495e19i q^{75} +(-3.51817e19 + 6.03318e19i) q^{76} -1.31169e20i q^{77} +(-2.54307e19 + 9.40934e19i) q^{78} +8.13752e19 q^{79} +(9.63500e19 - 5.45207e19i) q^{80} -9.70575e19 q^{81} +(3.76282e19 - 1.39224e20i) q^{82} -1.42229e20i q^{83} +(-1.40386e20 + 2.40743e20i) q^{84} -1.53149e19i q^{85} +(-2.99117e20 - 8.08428e19i) q^{86} +1.76906e20 q^{87} +(-3.12304e20 - 3.16387e20i) q^{88} +4.63956e20 q^{89} +(-4.05818e20 - 1.09681e20i) q^{90} +4.06688e20i q^{91} +(4.41180e20 + 2.57269e20i) q^{92} -7.68424e20i q^{93} +(1.00472e20 - 3.71744e20i) q^{94} -8.38278e20 q^{95} +(2.34571e20 + 9.14933e20i) q^{96} +8.42399e20 q^{97} +(-9.23471e19 + 3.41683e20i) q^{98} +1.68811e21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9}+O(q^{10}) \) 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9	\( 20 q + 286 q^{2} + 409876 q^{4} + 118236748 q^{6} + 564950496 q^{7} + 3649699336 q^{8} - 62762119220 q^{9} - 51269339528 q^{10} + 65316900136 q^{12} - 1924309104464 q^{14} - 2285680856096 q^{15} + 7793508571920 q^{16} + 1740714497000 q^{17} - 41325344023822 q^{18} - 78999934156016 q^{20} + 294957216952508 q^{22} + 335749622520224 q^{23} + 786737698607504 q^{24} - 16\!\cdots\!04 q^{25}+ \cdots + 13\!\cdots\!30 q^{98}+O(q^{100}) \) 20 * q + 286 * q^2 + 409876 * q^4 + 118236748 * q^6 + 564950496 * q^7 + 3649699336 * q^8 - 62762119220 * q^9 - 51269339528 * q^10 + 65316900136 * q^12 - 1924309104464 * q^14 - 2285680856096 * q^15 + 7793508571920 * q^16 + 1740714497000 * q^17 - 41325344023822 * q^18 - 78999934156016 * q^20 + 294957216952508 * q^22 + 335749622520224 * q^23 + 786737698607504 * q^24 - 1665114591247004 * q^25 - 2772669922448408 * q^26 - 4284340177681888 * q^28 + 3807691030523312 * q^30 - 8989263821171840 * q^31 - 9127378177656544 * q^32 + 5359113021386256 * q^33 + 19124803780998044 * q^34 + 39378114498954828 * q^36 - 41860137429498580 * q^38 + 121743910075345312 * q^39 - 160007944946664288 * q^40 - 84626460793452344 * q^41 + 178614544452770272 * q^42 - 27785097292304568 * q^44 + 184220935820050448 * q^46 + 149908985865280320 * q^47 + 1509829480382701344 * q^48 + 477689401234988532 * q^49 - 1722157324053237098 * q^50 - 1640429312330235856 * q^52 + 785391046636854392 * q^54 - 1936239868862269088 * q^55 - 3751496032099552448 * q^56 + 409355502574547024 * q^57 + 3182351472522780872 * q^58 + 2751731248604508192 * q^60 - 13336157978726113600 * q^62 - 8780950644120846560 * q^63 - 9021637553716933568 * q^64 + 6302857570713584320 * q^65 + 5291575090585638744 * q^66 + 40891724357029299816 * q^68 + 18077776609913587392 * q^70 + 96451291685825247456 * q^71 + 49841566955976579512 * q^72 - 21461290229157072184 * q^73 - 42953490504627871688 * q^74 - 206966483397015363224 * q^76 + 163869164384378609168 * q^78 - 284214874786393231680 * q^79 - 49904712513208125120 * q^80 + 1291808332257012164 * q^81 + 112698322843931711404 * q^82 + 178681601993395676224 * q^84 - 523293212085532715396 * q^86 + 517213147301817170208 * q^87 - 124028902608265335088 * q^88 + 17316387144455013640 * q^89 + 171098967229297148360 * q^90 + 827091233447044225632 * q^92 - 165060487582514765280 * q^94 - 2333725338330109674784 * q^95 - 715448174391177540544 * q^96 + 9560220979460741928 * q^97 + 137273120368488603630 * q^98

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