LMFDB - Embedded newform 8.22.b.a.5.3

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			5.3
Root			$0.500000 - 32835.5i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.22.b.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1358.45 - 501.755i) q^{2} +131342. i q^{3} +(1.59363e6 + 1.36322e6i) q^{4} -4.61121e6i q^{5} +(6.59016e7 - 1.78422e8i) q^{6} -9.67293e8 q^{7} +(-1.48087e9 - 2.65149e9i) q^{8} -6.79041e9 q^{9} +O(q^{10})$	\(q+(-1358.45 - 501.755i) q^{2} +131342. i q^{3} +(1.59363e6 + 1.36322e6i) q^{4} -4.61121e6i q^{5} +(6.59016e7 - 1.78422e8i) q^{6} -9.67293e8 q^{7} +(-1.48087e9 - 2.65149e9i) q^{8} -6.79041e9 q^{9} +(-2.31370e9 + 6.26411e9i) q^{10} +2.63123e10i q^{11} +(-1.79049e11 + 2.09311e11i) q^{12} +1.34734e11i q^{13} +(1.31402e12 + 4.85345e11i) q^{14} +6.05646e11 q^{15} +(6.81298e11 + 4.34496e12i) q^{16} -1.18091e13 q^{17} +(9.22445e12 + 3.40712e12i) q^{18} -3.07582e13i q^{19} +(6.28610e12 - 7.34858e12i) q^{20} -1.27046e14i q^{21} +(1.32023e13 - 3.57440e13i) q^{22} +5.37921e12 q^{23} +(3.48252e14 - 1.94501e14i) q^{24} +4.55574e14 q^{25} +(6.76036e13 - 1.83030e14i) q^{26} +4.82018e14i q^{27} +(-1.54151e15 - 1.31864e15i) q^{28} -2.15109e15i q^{29} +(-8.22741e14 - 3.03886e14i) q^{30} +6.82197e15 q^{31} +(1.25459e15 - 6.24426e15i) q^{32} -3.45591e15 q^{33} +(1.60421e16 + 5.92529e15i) q^{34} +4.46039e15i q^{35} +(-1.08214e16 - 9.25683e15i) q^{36} -5.49413e16i q^{37} +(-1.54331e16 + 4.17835e16i) q^{38} -1.76963e16 q^{39} +(-1.22266e16 + 6.82862e15i) q^{40} -1.39562e16 q^{41} +(-6.37462e16 + 1.72586e17i) q^{42} +2.25991e17i q^{43} +(-3.58695e16 + 4.19322e16i) q^{44} +3.13120e16i q^{45} +(-7.30740e15 - 2.69905e15i) q^{46} +5.18777e17 q^{47} +(-5.70676e17 + 8.94832e16i) q^{48} +3.77110e17 q^{49} +(-6.18876e17 - 2.28587e17i) q^{50} -1.55103e18i q^{51} +(-1.83673e17 + 2.14717e17i) q^{52} -8.95247e17i q^{53} +(2.41855e17 - 6.54799e17i) q^{54} +1.21331e17 q^{55} +(1.43244e18 + 2.56477e18i) q^{56} +4.03984e18 q^{57} +(-1.07932e18 + 2.92215e18i) q^{58} -7.68392e18i q^{59} +(9.65179e17 + 8.25630e17i) q^{60} +9.46865e16i q^{61} +(-9.26733e18 - 3.42296e18i) q^{62} +6.56832e18 q^{63} +(-4.83740e18 + 7.85304e18i) q^{64} +6.21287e17 q^{65} +(4.69469e18 + 1.73402e18i) q^{66} +8.03267e18i q^{67} +(-1.88194e19 - 1.60984e19i) q^{68} +7.06516e17i q^{69} +(2.23802e18 - 6.05923e18i) q^{70} +1.77595e19 q^{71} +(1.00557e19 + 1.80047e19i) q^{72} -2.77572e19 q^{73} +(-2.75671e19 + 7.46351e19i) q^{74} +5.98361e19i q^{75} +(4.19302e19 - 4.90173e19i) q^{76} -2.54517e19i q^{77} +(2.40395e19 + 8.87920e18i) q^{78} -6.72796e19 q^{79} +(2.00355e19 - 3.14161e18i) q^{80} -1.34339e20 q^{81} +(1.89588e19 + 7.00259e18i) q^{82} -7.06740e19i q^{83} +(1.73192e20 - 2.02466e20i) q^{84} +5.44543e19i q^{85} +(1.13392e20 - 3.06998e20i) q^{86} +2.82529e20 q^{87} +(6.97667e19 - 3.89652e19i) q^{88} -1.26350e20 q^{89} +(1.57110e19 - 4.25358e19i) q^{90} -1.30327e20i q^{91} +(8.57249e18 + 7.33305e18i) q^{92} +8.96013e20i q^{93} +(-7.04734e20 - 2.60299e20i) q^{94} -1.41832e20 q^{95} +(8.20135e20 + 1.64781e20i) q^{96} -9.20165e20 q^{97} +(-5.12286e20 - 1.89217e20i) q^{98} -1.78671e20i 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 $

$2$	−1358.45	−	501.755i	−0.938058	−	0.346479i
$2$	−1358.45	−	501.755i	−0.938058	−	0.346479i
$3$			131342.i			1.28419i	0.766623	+	0.642097i	$0.221936\pi$
$3$			131342.i			1.28419i	−0.766623	+	0.642097i	$0.778064\pi$
$4$	1.59363e6	+	1.36322e6i	0.759904	+	0.650035i
$5$		−	4.61121e6i		−	0.211169i	−0.994410	−	0.105584i	$-0.966329\pi$
$5$		−	4.61121e6i		−	0.211169i	0.994410	−	0.105584i	$-0.0336713\pi$
$6$	6.59016e7	−	1.78422e8i	0.444947	−	1.20465i
$7$	−9.67293e8			−1.29428			−0.647141	−	0.762371i	$-0.724035\pi$
$7$	−9.67293e8			−1.29428			−0.647141	+	0.762371i	$0.724035\pi$
$8$	−1.48087e9	−	2.65149e9i	−0.487611	−	0.873061i
$9$	−6.79041e9			−0.649157
$10$	−2.31370e9	+	6.26411e9i	−0.0731656	+	0.198088i
$11$			2.63123e10i			0.305869i	0.988236	+	0.152934i	$0.0488723\pi$
$11$			2.63123e10i			0.305869i	−0.988236	+	0.152934i	$0.951128\pi$
$12$	−1.79049e11	+	2.09311e11i	−0.834772	+	0.975865i
$13$			1.34734e11i			0.271064i	0.990773	+	0.135532i	$0.0432744\pi$
$13$			1.34734e11i			0.271064i	−0.990773	+	0.135532i	$0.956726\pi$
$14$	1.31402e12	+	4.85345e11i	1.21411	+	0.448442i
$15$	6.05646e11			0.271182
$16$	6.81298e11	+	4.34496e12i	0.154909	+	0.987929i
$17$	−1.18091e13			−1.42070			−0.710352	−	0.703847i	$-0.751464\pi$
$17$	−1.18091e13			−1.42070			−0.710352	+	0.703847i	$0.751464\pi$
$18$	9.22445e12	+	3.40712e12i	0.608946	+	0.224919i
$19$		−	3.07582e13i		−	1.15093i	−0.817828	−	0.575463i	$-0.804822\pi$
$19$		−	3.07582e13i		−	1.15093i	0.817828	−	0.575463i	$-0.195178\pi$
$20$	6.28610e12	−	7.34858e12i	0.137267	−	0.160468i
$21$		−	1.27046e14i		−	1.66211i
$22$	1.32023e13	−	3.57440e13i	0.105977	−	0.286923i
$23$	5.37921e12			0.0270755			0.0135377	−	0.999908i	$-0.495691\pi$
$23$	5.37921e12			0.0270755			0.0135377	+	0.999908i	$0.495691\pi$
$24$	3.48252e14	−	1.94501e14i	1.12118	−	0.626187i
$25$	4.55574e14			0.955408
$26$	6.76036e13	−	1.83030e14i	0.0939182	−	0.254274i
$27$			4.82018e14i			0.450551i
$28$	−1.54151e15	−	1.31864e15i	−0.983530	−	0.841328i
$29$		−	2.15109e15i		−	0.949466i	−0.880130	−	0.474733i	$-0.842545\pi$
$29$		−	2.15109e15i		−	0.949466i	0.880130	−	0.474733i	$-0.157455\pi$
$30$	−8.22741e14	−	3.03886e14i	−0.254384	−	0.0939589i
$31$	6.82197e15			1.49490			0.747450	−	0.664318i	$-0.231278\pi$
$31$	6.82197e15			1.49490			0.747450	+	0.664318i	$0.231278\pi$
$32$	1.25459e15	−	6.24426e15i	0.196983	−	0.980407i
$33$	−3.45591e15			−0.392795
$34$	1.60421e16	+	5.92529e15i	1.33270	+	0.492244i
$35$			4.46039e15i			0.273312i
$36$	−1.08214e16	−	9.25683e15i	−0.493297	−	0.421975i
$37$		−	5.49413e16i		−	1.87837i	−0.343414	−	0.939184i	$-0.611584\pi$
$37$		−	5.49413e16i		−	1.87837i	0.343414	−	0.939184i	$-0.388416\pi$
$38$	−1.54331e16	+	4.17835e16i	−0.398772	+	1.07964i
$39$	−1.76963e16			−0.348099
$40$	−1.22266e16	+	6.82862e15i	−0.184363	+	0.102968i
$41$	−1.39562e16			−0.162381			−0.0811906	−	0.996699i	$-0.525872\pi$
$41$	−1.39562e16			−0.162381			−0.0811906	+	0.996699i	$0.525872\pi$
$42$	−6.37462e16	+	1.72586e17i	−0.575886	+	1.55915i
$43$			2.25991e17i			1.59467i	0.603535	+	0.797337i	$0.293758\pi$
$43$			2.25991e17i			1.59467i	−0.603535	+	0.797337i	$0.706242\pi$
$44$	−3.58695e16	+	4.19322e16i	−0.198825	+	0.232431i
$45$			3.13120e16i			0.137082i
$46$	−7.30740e15	−	2.69905e15i	−0.0253983	−	0.00938108i
$47$	5.18777e17			1.43864			0.719321	−	0.694677i	$-0.244453\pi$
$47$	5.18777e17			1.43864			0.719321	+	0.694677i	$0.244453\pi$
$48$	−5.70676e17	+	8.94832e16i	−1.26869	+	0.198934i
$49$	3.77110e17			0.675164
$50$	−6.18876e17	−	2.28587e17i	−0.896228	−	0.331029i
$51$		−	1.55103e18i		−	1.82446i
$52$	−1.83673e17	+	2.14717e17i	−0.176201	+	0.205983i
$53$		−	8.95247e17i		−	0.703147i	−0.936160	−	0.351573i	$-0.885647\pi$
$53$		−	8.95247e17i		−	0.703147i	0.936160	−	0.351573i	$-0.114353\pi$
$54$	2.41855e17	−	6.54799e17i	0.156107	−	0.422643i
$55$	1.21331e17			0.0645899
$56$	1.43244e18	+	2.56477e18i	0.631105	+	1.12999i
$57$	4.03984e18			1.47801
$58$	−1.07932e18	+	2.92215e18i	−0.328970	+	0.890654i
$59$		−	7.68392e18i		−	1.95721i	−0.205757	−	0.978603i	$-0.565966\pi$
$59$		−	7.68392e18i		−	1.95721i	0.205757	−	0.978603i	$-0.434034\pi$
$60$	9.65179e17	+	8.25630e17i	0.206072	+	0.176278i
$61$			9.46865e16i			0.0169951i	0.999964	+	0.00849757i	$0.00270489\pi$
$61$			9.46865e16i			0.0169951i	−0.999964	+	0.00849757i	$0.997295\pi$
$62$	−9.26733e18	−	3.42296e18i	−1.40230	−	0.517952i
$63$	6.56832e18			0.840191
$64$	−4.83740e18	+	7.85304e18i	−0.524472	+	0.851428i
$65$	6.21287e17			0.0572403
$66$	4.69469e18	+	1.73402e18i	0.368465	+	0.136095i
$67$			8.03267e18i			0.538362i	0.963090	+	0.269181i	$0.0867531\pi$
$67$			8.03267e18i			0.538362i	−0.963090	+	0.269181i	$0.913247\pi$
$68$	−1.88194e19	−	1.60984e19i	−1.07960	−	0.923507i
$69$			7.06516e17i			0.0347702i
$70$	2.23802e18	−	6.05923e18i	0.0946968	−	0.256382i
$71$	1.77595e19			0.647469			0.323735	−	0.946148i	$-0.395061\pi$
$71$	1.77595e19			0.647469			0.323735	+	0.946148i	$0.395061\pi$
$72$	1.00557e19	+	1.80047e19i	0.316536	+	0.566754i
$73$	−2.77572e19			−0.755937			−0.377969	−	0.925818i	$-0.623377\pi$
$73$	−2.77572e19			−0.755937			−0.377969	+	0.925818i	$0.623377\pi$
$74$	−2.75671e19	+	7.46351e19i	−0.650815	+	1.76202i
$75$			5.98361e19i			1.22693i
$76$	4.19302e19	−	4.90173e19i	0.748142	−	0.874594i
$77$		−	2.54517e19i		−	0.395880i
$78$	2.40395e19	+	8.87920e18i	0.326537	+	0.120609i
$79$	−6.72796e19			−0.799464			−0.399732	−	0.916632i	$-0.630897\pi$
$79$	−6.72796e19			−0.799464			−0.399732	+	0.916632i	$0.630897\pi$
$80$	2.00355e19	−	3.14161e18i	0.208620	−	0.0327120i
$81$	−1.34339e20			−1.22775
$82$	1.89588e19	+	7.00259e18i	0.152323	+	0.0562617i
$83$		−	7.06740e19i		−	0.499965i	−0.968250	−	0.249982i	$-0.919575\pi$
$83$		−	7.06740e19i		−	0.499965i	0.968250	−	0.249982i	$-0.0804249\pi$
$84$	1.73192e20	−	2.02466e20i	1.08043	−	1.26304i
$85$			5.44543e19i			0.300008i
$86$	1.13392e20	−	3.06998e20i	0.552521	−	1.49590i
$87$	2.82529e20			1.21930
$88$	6.97667e19	−	3.89652e19i	0.267042	−	0.149145i
$89$	−1.26350e20			−0.429515			−0.214758	−	0.976667i	$-0.568896\pi$
$89$	−1.26350e20			−0.429515			−0.214758	+	0.976667i	$0.568896\pi$
$90$	1.57110e19	−	4.25358e19i	0.0474959	−	0.128590i
$91$		−	1.30327e20i		−	0.350834i
$92$	8.57249e18	+	7.33305e18i	0.0205748	+	0.0176000i
$93$			8.96013e20i			1.91974i
$94$	−7.04734e20	−	2.60299e20i	−1.34953	−	0.498460i
$95$	−1.41832e20			−0.243040
$96$	8.20135e20	+	1.64781e20i	1.25903	+	0.252964i
$97$	−9.20165e20			−1.26696			−0.633479	−	0.773760i	$-0.718374\pi$
$97$	−9.20165e20			−1.26696			−0.633479	+	0.773760i	$0.718374\pi$
$98$	−5.12286e20	−	1.89217e20i	−0.633343	−	0.233930i
$99$		−	1.78671e20i		−	0.198557i
$100$	7.26019e20	+	6.21048e20i	0.726019	+	0.621048i
$101$			2.85486e20i			0.257164i	0.991699	+	0.128582i	$0.0410425\pi$
$101$			2.85486e20i			0.257164i	−0.991699	+	0.128582i	$0.958957\pi$
$102$	−7.78240e20	+	2.10701e21i	−0.632138	+	1.71145i
$103$	9.57325e20			0.701889			0.350945	−	0.936396i	$-0.385861\pi$
$103$	9.57325e20			0.701889			0.350945	+	0.936396i	$0.385861\pi$
$104$	3.57246e20	−	1.99524e20i	0.236656	−	0.132174i
$105$	−5.85837e20			−0.350986
$106$	−4.49195e20	+	1.21615e21i	−0.243626	+	0.659592i
$107$		−	1.81437e21i		−	0.891655i	−0.895119	−	0.445828i	$-0.852909\pi$
$107$		−	1.81437e21i		−	0.891655i	0.895119	−	0.445828i	$-0.147091\pi$
$108$	−6.57098e20	+	7.68161e20i	−0.292874	+	0.342376i
$109$		−	1.93049e21i		−	0.781070i	−0.920588	−	0.390535i	$-0.872290\pi$
$109$		−	1.93049e21i		−	0.781070i	0.920588	−	0.390535i	$-0.127710\pi$
$110$	−1.64823e20	−	6.08787e19i	−0.0605891	−	0.0223791i
$111$	7.21611e21			2.41219
$112$	−6.59015e20	−	4.20285e21i	−0.200496	−	1.27866i
$113$	−5.27661e21			−1.46228			−0.731142	−	0.682226i	$-0.761012\pi$
$113$	−5.27661e21			−1.46228			−0.731142	+	0.682226i	$0.761012\pi$
$114$	−5.48793e21	−	2.02701e21i	−1.38646	−	0.512101i
$115$		−	2.48046e19i		−	0.00571749i
$116$	2.93241e21	−	3.42805e21i	0.617186	−	0.721504i
$117$		−	9.14900e20i		−	0.175963i
$118$	−3.85545e21	+	1.04382e22i	−0.678131	+	1.83597i
$119$	1.14229e22			1.83879
$120$	−8.96885e20	−	1.60586e21i	−0.132231	−	0.236758i
$121$	6.70791e21			0.906444
$122$	4.75095e19	−	1.28627e20i	0.00588847	−	0.0159424i
$123$		−	1.83303e21i		−	0.208529i
$124$	1.08717e22	+	9.29987e21i	1.13598	+	0.971738i
$125$		−	4.29954e21i		−	0.412921i
$126$	−8.92275e21	−	3.29569e21i	−0.788148	−	0.291109i
$127$	−7.52059e21			−0.611383			−0.305691	−	0.952131i	$-0.598888\pi$
$127$	−7.52059e21			−0.611383			−0.305691	+	0.952131i	$0.598888\pi$
$128$	1.05117e22	−	8.24078e21i	0.786987	−	0.616970i
$129$	−2.96821e22			−2.04787
$130$	−8.43989e20	−	3.11734e20i	−0.0536947	−	0.0198326i
$131$		−	2.14835e22i		−	1.26112i	−0.776140	−	0.630561i	$-0.782825\pi$
$131$		−	2.14835e22i		−	1.26112i	0.776140	−	0.630561i	$-0.217175\pi$
$132$	−5.50746e21	−	4.71117e21i	−0.298487	−	0.255331i
$133$			2.97522e22i			1.48962i
$134$	4.03044e21	−	1.09120e22i	0.186531	−	0.505015i
$135$	2.22269e21			0.0951423
$136$	1.74878e22	+	3.13117e22i	0.692750	+	1.24036i
$137$	−6.74484e21			−0.247403			−0.123702	−	0.992319i	$-0.539477\pi$
$137$	−6.74484e21			−0.247403			−0.123702	+	0.992319i	$0.539477\pi$
$138$	3.54498e20	−	9.59769e20i	0.0120471	−	0.0326164i
$139$			2.39417e22i			0.754223i	0.926168	+	0.377111i	$0.123083\pi$
$139$			2.39417e22i			0.754223i	−0.926168	+	0.377111i	$0.876917\pi$
$140$	−6.08050e21	+	7.10823e21i	−0.177662	+	0.207691i
$141$			6.81373e22i			1.84750i
$142$	−2.41255e22	−	8.91095e21i	−0.607364	−	0.224335i
$143$	−3.54516e21			−0.0829101
$144$	−4.62629e21	−	2.95040e22i	−0.100560	−	0.641321i
$145$	−9.91912e21			−0.200498
$146$	3.77069e22	+	1.39273e22i	0.709113	+	0.261917i
$147$			4.95305e22i			0.867043i
$148$	7.48972e22	−	8.75563e22i	1.22100	−	1.42738i
$149$		−	7.59336e22i		−	1.15340i	−0.816958	−	0.576698i	$-0.804341\pi$
$149$		−	7.59336e22i		−	1.15340i	0.816958	−	0.576698i	$-0.195659\pi$
$150$	3.00231e22	−	8.12845e22i	0.425106	−	1.15093i
$151$	−1.01505e23			−1.34038			−0.670190	−	0.742190i	$-0.733787\pi$
$151$	−1.01505e23			−1.34038			−0.670190	+	0.742190i	$0.733787\pi$
$152$	−8.15549e22	+	4.55489e22i	−1.00483	+	0.561204i
$153$	8.01887e22			0.922259
$154$	−1.27705e22	+	3.45749e22i	−0.137164	+	0.371359i
$155$		−	3.14575e22i		−	0.315676i
$156$	−2.82014e22	−	2.41239e22i	−0.264522	−	0.226277i
$157$		−	2.20271e23i		−	1.93202i	−0.258503	−	0.966010i	$-0.583229\pi$
$157$		−	2.20271e23i		−	1.93202i	0.258503	−	0.966010i	$-0.416771\pi$
$158$	9.13961e22	+	3.37579e22i	0.749943	+	0.276998i
$159$	1.17584e23			0.902978
$160$	−2.87936e22	−	5.78519e21i	−0.207031	−	0.0415966i
$161$	−5.20327e21			−0.0350433
$162$	1.82494e23	+	6.74055e22i	1.15170	+	0.425391i
$163$			2.55961e22i			0.151427i	0.997130	+	0.0757136i	$0.0241235\pi$
$163$			2.55961e22i			0.151427i	−0.997130	+	0.0757136i	$0.975877\pi$
$164$	−2.22410e22	−	1.90254e22i	−0.123394	−	0.105553i
$165$			1.59359e22i			0.0829461i
$166$	−3.54611e22	+	9.60073e22i	−0.173227	+	0.468996i
$167$	−1.23959e23			−0.568531			−0.284265	−	0.958746i	$-0.591750\pi$
$167$	−1.23959e23			−0.568531			−0.284265	+	0.958746i	$0.591750\pi$
$168$	−3.36862e23	+	1.88140e23i	−1.45112	+	0.810462i
$169$	2.28911e23			0.926524
$170$	2.73227e22	−	7.39735e22i	0.103947	−	0.281425i
$171$			2.08860e23i			0.747131i
$172$	−3.08075e23	+	3.60147e23i	−1.03659	+	1.21180i
$173$			1.22533e23i			0.387944i	0.981007	+	0.193972i	$0.0621371\pi$
$173$			1.22533e23i			0.387944i	−0.981007	+	0.193972i	$0.937863\pi$
$174$	−3.83802e23	−	1.41760e23i	−1.14377	−	0.422462i
$175$	−4.40674e23			−1.23657
$176$	−1.14326e23	+	1.79265e22i	−0.302177	+	0.0473819i
$177$	1.00922e24			2.51343
$178$	1.71640e23	+	6.33966e22i	0.402910	+	0.148818i
$179$		−	3.43486e23i		−	0.760242i	−0.924937	−	0.380121i	$-0.875882\pi$
$179$		−	3.43486e23i		−	0.760242i	0.924937	−	0.380121i	$-0.124118\pi$
$180$	−4.26852e22	+	4.98999e22i	−0.0891078	+	0.104169i
$181$			7.33520e22i			0.144473i	0.997388	+	0.0722365i	$0.0230136\pi$
$181$			7.33520e22i			0.144473i	−0.997388	+	0.0722365i	$0.976986\pi$
$182$	−6.53925e22	+	1.77044e23i	−0.121557	+	0.329102i
$183$	−1.24363e22			−0.0218251
$184$	−7.96592e21	−	1.42629e22i	−0.0132023	−	0.0236385i
$185$	−2.53346e23			−0.396653
$186$	4.49579e23	−	1.21719e24i	0.665151	−	1.80083i
$187$		−	3.10725e23i		−	0.434549i
$188$	8.26741e23	+	7.07208e23i	1.09323	+	0.935168i
$189$		−	4.66253e23i		−	0.583140i
$190$	1.92672e23	+	7.11651e22i	0.227985	+	0.0842082i
$191$	−6.09403e23			−0.682424			−0.341212	−	0.939986i	$-0.610837\pi$
$191$	−6.09403e23			−0.682424			−0.341212	+	0.939986i	$0.610837\pi$
$192$	−1.03143e24	−	6.35354e23i	−1.09340	−	0.673524i
$193$	−4.69329e23			−0.471114			−0.235557	−	0.971861i	$-0.575691\pi$
$193$	−4.69329e23			−0.471114			−0.235557	+	0.971861i	$0.575691\pi$
$194$	1.25000e24	+	4.61698e23i	1.18848	+	0.438975i
$195$			8.16012e22i			0.0735077i
$196$	6.00976e23	+	5.14085e23i	0.513060	+	0.438880i
$197$			1.19891e22i			0.00970269i	0.999988	+	0.00485134i	$0.00154424\pi$
$197$			1.19891e22i			0.00970269i	−0.999988	+	0.00485134i	$0.998456\pi$
$198$	−8.96492e22	+	2.42716e23i	−0.0687958	+	0.186258i
$199$	4.36237e23			0.317516			0.158758	−	0.987318i	$-0.449251\pi$
$199$	4.36237e23			0.317516			0.158758	+	0.987318i	$0.449251\pi$
$200$	−6.74647e23	−	1.20795e24i	−0.465867	−	0.834129i
$201$	−1.05503e24			−0.691362
$202$	1.43244e23	−	3.87819e23i	0.0891019	−	0.241234i
$203$			2.08073e24i			1.22888i
$204$	2.11440e24	−	2.47178e24i	1.18596	−	1.38642i
$205$			6.43548e22i			0.0342898i
$206$	−1.30048e24	−	4.80343e23i	−0.658413	−	0.243190i
$207$	−3.65270e22			−0.0175762
$208$	−5.85414e23	+	9.17941e22i	−0.267792	+	0.0419904i
$209$	8.09317e23			0.352032
$210$	7.95832e23	+	2.93947e23i	0.329245	+	0.121609i
$211$			2.63965e24i			1.03892i	0.854495	+	0.519459i	$0.173867\pi$
$211$			2.63965e24i			1.03892i	−0.854495	+	0.519459i	$0.826133\pi$
$212$	1.22042e24	−	1.42670e24i	0.457070	−	0.534324i
$213$			2.33258e24i			0.831477i
$214$	−9.10372e23	+	2.46474e24i	−0.308940	+	0.836424i
$215$	1.04209e24			0.336745
$216$	1.27807e24	−	7.13808e23i	0.393359	−	0.219694i
$217$	−6.59885e24			−1.93482
$218$	−9.68635e23	+	2.62248e24i	−0.270625	+	0.732689i
$219$		−	3.64569e24i		−	0.970771i
$220$	1.93358e23	+	1.65402e23i	0.0490822	+	0.0419857i
$221$		−	1.59109e24i		−	0.385102i
$222$	−9.80274e24	−	3.62072e24i	−2.26277	−	0.835774i
$223$	4.35564e24			0.959072			0.479536	−	0.877522i	$-0.340805\pi$
$223$	4.35564e24			0.959072			0.479536	+	0.877522i	$0.340805\pi$
$224$	−1.21356e24	+	6.04003e24i	−0.254951	+	1.26892i
$225$	−3.09353e24			−0.620209
$226$	7.16803e24	+	2.64757e24i	1.37171	+	0.506651i
$227$		−	7.88616e24i		−	1.44077i	−0.693575	−	0.720384i	$-0.743965\pi$
$227$		−	7.88616e24i		−	1.44077i	0.693575	−	0.720384i	$-0.256035\pi$
$228$	6.43803e24	+	5.50720e24i	1.12315	+	0.960760i
$229$			8.16351e24i			1.36020i	0.733117	+	0.680102i	$0.238065\pi$
$229$			8.16351e24i			1.36020i	−0.733117	+	0.680102i	$0.761935\pi$
$230$	−1.24459e22	+	3.36959e22i	−0.00198099	+	0.00536334i
$231$	3.34288e24			0.508388
$232$	−5.70359e24	+	3.18549e24i	−0.828942	+	0.462970i
$233$	7.57552e24			1.05239			0.526193	−	0.850365i	$-0.323619\pi$
$233$	7.57552e24			1.05239			0.526193	+	0.850365i	$0.323619\pi$
$234$	−4.59056e23	+	1.24285e24i	−0.0609676	+	0.165064i
$235$		−	2.39219e24i		−	0.303796i
$236$	1.04749e25	−	1.22454e25i	1.27225	−	1.48729i
$237$		−	8.83664e24i		−	1.02667i
$238$	−1.55174e25	−	5.73149e24i	−1.72489	−	0.637103i
$239$	1.08243e25			1.15139			0.575695	−	0.817665i	$-0.304732\pi$
$239$	1.08243e25			1.15139			0.575695	+	0.817665i	$0.304732\pi$
$240$	4.12626e23	+	2.63151e24i	0.0420086	+	0.267908i
$241$	−1.11526e24			−0.108692			−0.0543461	−	0.998522i	$-0.517307\pi$
$241$	−1.11526e24			−0.108692			−0.0543461	+	0.998522i	$0.517307\pi$
$242$	−9.11238e24	−	3.36573e24i	−0.850297	−	0.314064i
$243$		−	1.26023e25i		−	1.12612i
$244$	−1.29079e23	+	1.50896e23i	−0.0110474	+	0.0129147i
$245$		−	1.73893e24i		−	0.142574i
$246$	−9.19735e23	+	2.49009e24i	−0.0722510	+	0.195612i
$247$	4.14417e24			0.311975
$248$	−1.01025e25	−	1.80884e25i	−0.728929	−	1.30514i
$249$	9.28247e24			0.642052
$250$	−2.15732e24	+	5.84072e24i	−0.143069	+	0.387344i
$251$			5.91114e24i			0.375922i	0.982177	+	0.187961i	$0.0601878\pi$
$251$			5.91114e24i			0.375922i	−0.982177	+	0.187961i	$0.939812\pi$
$252$	1.04675e25	+	8.95407e24i	0.638465	+	0.546154i
$253$			1.41539e23i			0.00828154i
$254$	1.02164e25	+	3.77350e24i	0.573512	+	0.211831i
$255$	−7.15214e24			−0.385269
$256$	−1.84145e25	+	5.92042e24i	−0.952006	+	0.306079i
$257$	−3.01957e25			−1.49847			−0.749233	−	0.662306i	$-0.769578\pi$
$257$	−3.01957e25			−1.49847			−0.749233	+	0.662306i	$0.769578\pi$
$258$	4.03217e25	+	1.48932e25i	1.92102	+	0.709545i
$259$			5.31443e25i			2.43114i
$260$	9.90105e23	+	8.46952e23i	0.0434972	+	0.0372082i
$261$			1.46068e25i			0.616352i
$262$	−1.07795e25	+	2.91844e25i	−0.436953	+	1.18301i
$263$	−1.44398e25			−0.562375			−0.281188	−	0.959653i	$-0.590728\pi$
$263$	−1.44398e25			−0.562375			−0.281188	+	0.959653i	$0.590728\pi$
$264$	5.11777e24	+	9.16330e24i	0.191531	+	0.342934i
$265$	−4.12817e24			−0.148483
$266$	1.49283e25	−	4.04169e25i	0.516123	−	1.39735i
$267$		−	1.65950e25i		−	0.551582i
$268$	−1.09503e25	+	1.28012e25i	−0.349954	+	0.409104i
$269$		−	5.11331e25i		−	1.57146i	−0.618571	−	0.785729i	$-0.712288\pi$
$269$		−	5.11331e25i		−	1.57146i	0.618571	−	0.785729i	$-0.287712\pi$
$270$	−3.01942e24	−	1.11525e24i	−0.0892490	−	0.0329648i
$271$	−4.56245e25			−1.29724			−0.648620	−	0.761112i	$-0.724654\pi$
$271$	−4.56245e25			−1.29724			−0.648620	+	0.761112i	$0.724654\pi$
$272$	−8.04553e24	−	5.13101e25i	−0.220080	−	1.40355i
$273$	1.71175e25			0.450539
$274$	9.16254e24	+	3.38426e24i	0.232079	+	0.0857201i
$275$			1.19872e25i			0.292229i
$276$	−9.63139e23	+	1.12593e24i	−0.0226018	+	0.0264220i
$277$			5.99999e25i			1.35554i	0.735273	+	0.677771i	$0.237054\pi$
$277$			5.99999e25i			1.35554i	−0.735273	+	0.677771i	$0.762946\pi$
$278$	1.20129e25	−	3.25237e25i	0.261322	−	0.707504i
$279$	−4.63240e25			−0.970425
$280$	1.18267e25	−	6.60527e24i	0.238618	−	0.133270i
$281$	7.22423e25			1.40403			0.702013	−	0.712164i	$-0.252285\pi$
$281$	7.22423e25			1.40403			0.702013	+	0.712164i	$0.252285\pi$
$282$	3.41882e25	−	9.25612e25i	0.640120	−	1.73306i
$283$			3.77936e25i			0.681806i	0.940099	+	0.340903i	$0.110733\pi$
$283$			3.77936e25i			0.681806i	−0.940099	+	0.340903i	$0.889267\pi$
$284$	2.83022e25	+	2.42102e25i	0.492015	+	0.420878i
$285$		−	1.86286e25i		−	0.312110i
$286$	4.81593e24	+	1.77880e24i	0.0777745	+	0.0287266i
$287$	1.34997e25			0.210167
$288$	−8.51921e24	+	4.24011e25i	−0.127873	+	0.636438i
$289$	7.03632e25			1.01840
$290$	1.34747e25	+	4.97697e24i	0.188078	+	0.0694682i
$291$		−	1.20856e26i		−	1.62702i
$292$	−4.42349e25	−	3.78392e25i	−0.574440	−	0.491386i
$293$			7.56075e25i			0.947229i	0.880732	+	0.473614i	$0.157051\pi$
$293$			7.56075e25i			0.947229i	−0.880732	+	0.473614i	$0.842949\pi$
$294$	2.48522e25	−	6.72848e25i	0.300412	−	0.813336i
$295$	−3.54321e25			−0.413301
$296$	−1.45676e26	+	8.13611e25i	−1.63993	+	0.915912i
$297$	−1.26830e25			−0.137810
$298$	−3.81001e25	+	1.03152e26i	−0.399628	+	1.08195i
$299$			7.24763e23i			0.00733919i
$300$	−8.15698e25	+	9.53568e25i	−0.797547	+	0.932349i
$301$		−	2.18599e26i		−	2.06396i
$302$	1.37889e26	+	5.09305e25i	1.25735	+	0.464414i
$303$	−3.74963e25			−0.330248
$304$	1.33643e26	−	2.09555e25i	1.13703	−	0.178289i
$305$	4.36619e23			0.00358884
$306$	−1.08933e26	−	4.02351e25i	−0.865132	−	0.319544i
$307$			5.24145e25i			0.402252i	0.979565	+	0.201126i	$0.0644601\pi$
$307$			5.24145e25i			0.402252i	−0.979565	+	0.201126i	$0.935540\pi$
$308$	3.46963e25	−	4.05607e25i	0.257336	−	0.300831i
$309$			1.25737e26i			0.901363i
$310$	−1.57840e25	+	4.27336e25i	−0.109375	+	0.296123i
$311$	1.19975e26			0.803726			0.401863	−	0.915700i	$-0.368363\pi$
$311$	1.19975e26			0.803726			0.401863	+	0.915700i	$0.368363\pi$
$312$	2.62059e25	+	4.69214e25i	0.169737	+	0.303912i
$313$	−2.62450e25			−0.164373			−0.0821866	−	0.996617i	$-0.526190\pi$
$313$	−2.62450e25			−0.164373			−0.0821866	+	0.996617i	$0.526190\pi$
$314$	−1.10522e26	+	2.99228e26i	−0.669405	+	1.81235i
$315$		−	3.02879e25i		−	0.177422i
$316$	−1.07219e26	−	9.17170e25i	−0.607516	−	0.519679i
$317$		−	2.60275e26i		−	1.42663i	−0.700845	−	0.713314i	$-0.747193\pi$
$317$		−	2.60275e26i		−	1.42663i	0.700845	−	0.713314i	$-0.252807\pi$
$318$	−1.59732e26	−	5.89982e25i	−0.847045	−	0.312863i
$319$	5.66001e25			0.290412
$320$	3.62120e25	+	2.23063e25i	0.179795	+	0.110752i
$321$	2.38304e26			1.14506
$322$	7.06839e24	+	2.61077e24i	0.0328726	+	0.0121418i
$323$			3.63226e26i			1.63513i
$324$	−2.14088e26	−	1.83134e26i	−0.932974	−	0.798082i
$325$			6.13814e25i			0.258977i
$326$	1.28430e25	−	3.47711e25i	0.0524664	−	0.142047i
$327$	2.53555e26			1.00305
$328$	2.06673e25	+	3.70046e25i	0.0791788	+	0.141769i
$329$	−5.01809e26			−1.86201
$330$	7.99594e24	−	2.16482e25i	0.0287391	−	0.0778082i
$331$		−	1.42594e26i		−	0.496488i	−0.968698	−	0.248244i	$-0.920147\pi$
$331$		−	1.42594e26i		−	0.496488i	0.968698	−	0.248244i	$-0.0798534\pi$
$332$	9.63443e25	−	1.12629e26i	0.324995	−	0.379926i
$333$			3.73074e26i			1.21936i
$334$	1.68392e26	+	6.21970e25i	0.533315	+	0.196984i
$335$	3.70403e25			0.113685
$336$	5.52011e26	−	8.65565e25i	1.64205	−	0.257476i
$337$	−3.51069e26			−1.01223			−0.506115	−	0.862466i	$-0.668919\pi$
$337$	−3.51069e26			−1.01223			−0.506115	+	0.862466i	$0.668919\pi$
$338$	−3.10965e26	−	1.14857e26i	−0.869133	−	0.321021i
$339$		−	6.93042e26i		−	1.87786i
$340$	−7.42332e25	+	8.67802e25i	−0.195016	+	0.227978i
$341$			1.79502e26i			0.457243i
$342$	1.04797e26	−	2.83727e26i	0.258865	−	0.700852i
$343$	1.75501e26			0.420429
$344$	5.99211e26	−	3.34664e26i	1.39225	−	0.777579i
$345$	3.25789e24			0.00734237
$346$	6.14817e25	−	1.66455e26i	0.134415	−	0.363914i
$347$		−	9.52863e25i		−	0.202102i	−0.994881	−	0.101051i	$-0.967779\pi$
$347$		−	9.52863e25i		−	0.202102i	0.994881	−	0.101051i	$-0.0322206\pi$
$348$	4.50248e26	+	3.85149e26i	0.926551	+	0.792587i
$349$		−	5.04209e26i		−	1.00680i	−0.864053	−	0.503401i	$-0.832082\pi$
$349$		−	5.04209e26i		−	1.00680i	0.864053	−	0.503401i	$-0.167918\pi$
$350$	5.98634e26	+	2.21110e26i	1.15997	+	0.428445i
$351$	−6.49443e25			−0.122128
$352$	1.64301e26	+	3.30112e25i	0.299876	+	0.0602509i
$353$	−3.84348e26			−0.680910			−0.340455	−	0.940261i	$-0.610581\pi$
$353$	−3.84348e26			−0.680910			−0.340455	+	0.940261i	$0.610581\pi$
$354$	−1.37098e27	−	5.06383e26i	−2.35775	−	0.870853i
$355$		−	8.18930e25i		−	0.136725i
$356$	−2.01355e26	−	1.72243e26i	−0.326391	−	0.279200i
$357$			1.50030e27i			2.36137i
$358$	−1.72346e26	+	4.66609e26i	−0.263408	+	0.713150i
$359$	−1.10054e27			−1.63348			−0.816740	−	0.577006i	$-0.804221\pi$
$359$	−1.10054e27			−1.63348			−0.816740	+	0.577006i	$0.804221\pi$
$360$	8.30233e25	−	4.63691e25i	0.119681	−	0.0668424i
$361$	−2.31855e26			−0.324631
$362$	3.68048e25	−	9.96452e25i	0.0500569	−	0.135524i
$363$			8.81032e26i			1.16405i
$364$	1.77665e26	−	2.07694e26i	0.228054	−	0.266600i
$365$			1.27994e26i			0.159630i
$366$	1.68942e25	+	6.24000e24i	0.0204732	+	0.00756194i
$367$	1.42924e27			1.68310			0.841552	−	0.540175i	$-0.181642\pi$
$367$	1.42924e27			1.68310			0.841552	+	0.540175i	$0.181642\pi$
$368$	3.66484e24	+	2.33724e25i	0.00419424	+	0.0267486i
$369$	9.47681e25			0.105411
$370$	3.44158e26	+	1.27118e26i	0.372083	+	0.137432i
$371$			8.65966e26i			0.910070i
$372$	−1.22146e27	+	1.42792e27i	−1.24790	+	1.45882i
$373$		−	6.22058e26i		−	0.617858i	−0.951085	−	0.308929i	$-0.900030\pi$
$373$		−	6.22058e26i		−	0.617858i	0.951085	−	0.308929i	$-0.0999705\pi$
$374$	−1.55908e26	+	4.22105e26i	−0.150562	+	0.407632i
$375$	5.64711e26			0.530271
$376$	−7.68243e26	−	1.37553e27i	−0.701497	−	1.25602i
$377$	2.89825e26			0.257366
$378$	−2.33945e26	+	6.33383e26i	−0.202046	+	0.547019i
$379$		−	5.80604e26i		−	0.487717i	−0.969811	−	0.243859i	$-0.921587\pi$
$379$		−	5.80604e26i		−	0.487717i	0.969811	−	0.243859i	$-0.0784133\pi$
$380$	−2.26029e26	−	1.93349e26i	−0.184687	−	0.157984i
$381$		−	9.87771e26i		−	0.785134i
$382$	8.27845e26	+	3.05771e26i	0.640153	+	0.236446i
$383$	−7.77927e25			−0.0585264			−0.0292632	−	0.999572i	$-0.509316\pi$
$383$	−7.77927e25			−0.0585264			−0.0292632	+	0.999572i	$0.509316\pi$
$384$	1.08236e27	+	1.38063e27i	0.792309	+	1.01064i
$385$	−1.17363e26			−0.0835976
$386$	6.37561e26	+	2.35488e26i	0.441932	+	0.163231i
$387$		−	1.53457e27i		−	1.03519i
$388$	−1.46641e27	−	1.25439e27i	−0.962767	−	0.823567i
$389$		−	2.68862e27i		−	1.71814i	−0.511858	−	0.859070i	$-0.671043\pi$
$389$		−	2.68862e27i		−	1.71814i	0.511858	−	0.859070i	$-0.328957\pi$
$390$	4.09438e25	−	1.10851e26i	0.0254689	−	0.0689545i
$391$	−6.35236e25			−0.0384662
$392$	−5.58453e26	−	9.99903e26i	−0.329217	−	0.589460i
$393$	2.82169e27			1.61953
$394$	6.01561e24	−	1.62867e25i	0.00336178	−	0.00910168i
$395$			3.10240e26i			0.168822i
$396$	2.43568e26	−	2.84737e26i	0.129069	−	0.150884i
$397$		−	1.63947e27i		−	0.846063i	−0.906115	−	0.423032i	$-0.860966\pi$
$397$		−	1.63947e27i		−	0.846063i	0.906115	−	0.423032i	$-0.139034\pi$
$398$	−5.92607e26	−	2.18884e26i	−0.297848	−	0.110013i
$399$	−3.90771e27			−1.91297
$400$	3.10382e26	+	1.97945e27i	0.148002	+	0.943875i
$401$	1.32965e27			0.617618			0.308809	−	0.951124i	$-0.400070\pi$
$401$	1.32965e27			0.617618			0.308809	+	0.951124i	$0.400070\pi$
$402$	1.43321e27	+	5.29366e26i	0.648538	+	0.239543i
$403$			9.19153e26i			0.405214i
$404$	−3.89180e26	+	4.54960e26i	−0.167165	+	0.195420i
$405$			6.19467e26i			0.259263i
$406$	1.04402e27	−	2.82658e27i	0.425780	−	1.15276i
$407$	1.44563e27			0.574534
$408$	−4.11255e27	+	2.29689e27i	−1.59287	+	0.889626i
$409$	4.35693e27			1.64470			0.822348	−	0.568984i	$-0.192664\pi$
$409$	4.35693e27			1.64470			0.822348	+	0.568984i	$0.192664\pi$
$410$	3.22904e25	−	8.74230e25i	0.0118807	−	0.0321658i
$411$		−	8.85881e26i		−	0.317714i
$412$	1.52563e27	+	1.30505e27i	0.533369	+	0.456253i
$413$			7.43260e27i			2.53318i
$414$	4.96202e25	+	1.83276e25i	0.0164875	+	0.00608979i
$415$	−3.25892e26			−0.105577
$416$	8.41315e26	+	1.69037e26i	0.265753	+	0.0533950i
$417$	−3.14455e27			−0.968569
$418$	−1.09942e27	−	4.06079e26i	−0.330227	−	0.121972i
$419$			2.64636e27i			0.775179i	0.921832	+	0.387589i	$0.126692\pi$
$419$			2.64636e27i			0.775179i	−0.921832	+	0.387589i	$0.873308\pi$
$420$	−9.33611e26	−	7.98626e26i	−0.266716	−	0.228153i
$421$		−	1.20674e27i		−	0.336241i	−0.985766	−	0.168120i	$-0.946230\pi$
$421$		−	1.20674e27i		−	0.336241i	0.985766	−	0.168120i	$-0.0537697\pi$
$422$	1.32446e27	−	3.58585e27i	0.359964	−	0.974565i
$423$	−3.52271e27			−0.933905
$424$	−2.37373e27	+	1.32575e27i	−0.613890	+	0.342862i
$425$	−5.37992e27			−1.35735
$426$	1.17038e27	−	3.16870e27i	0.288089	−	0.779973i
$427$		−	9.15897e25i		−	0.0219965i
$428$	2.47339e27	−	2.89145e27i	0.579607	−	0.677573i
$429$		−	4.65629e26i		−	0.106473i
$430$	−1.41563e27	−	5.22874e26i	−0.315886	−	0.116675i
$431$	−5.84901e27			−1.27371			−0.636856	−	0.770983i	$-0.719765\pi$
$431$	−5.84901e27			−1.27371			−0.636856	+	0.770983i	$0.719765\pi$
$432$	−2.09435e27	+	3.28398e26i	−0.445112	+	0.0697946i
$433$	5.61825e27			1.16541			0.582704	−	0.812685i	$-0.301995\pi$
$433$	5.61825e27			1.16541			0.582704	+	0.812685i	$0.301995\pi$
$434$	8.96422e27	+	3.31101e27i	1.81497	+	0.670376i
$435$		−	1.30280e27i		−	0.257478i
$436$	2.63169e27	−	3.07650e27i	0.507723	−	0.593539i
$437$		−	1.65454e26i		−	0.0311619i
$438$	−1.82925e27	+	4.95250e27i	−0.336352	+	0.910639i
$439$	−1.35712e27			−0.243636			−0.121818	−	0.992552i	$-0.538872\pi$
$439$	−1.35712e27			−0.243636			−0.121818	+	0.992552i	$0.538872\pi$
$440$	−1.79676e26	−	3.21709e26i	−0.0314947	−	0.0563910i
$441$	−2.56073e27			−0.438288
$442$	−7.98338e26	+	2.16142e27i	−0.133430	+	0.361248i
$443$			6.78078e27i			1.10673i	0.832940	+	0.553363i	$0.186656\pi$
$443$			6.78078e27i			1.10673i	−0.832940	+	0.553363i	$0.813344\pi$
$444$	1.14998e28	+	9.83715e27i	1.83303	+	1.56801i
$445$			5.82624e26i			0.0907002i
$446$	−5.91693e27	−	2.18547e27i	−0.899665	−	0.332298i
$447$	9.97328e27			1.48118
$448$	4.67918e27	−	7.59619e27i	0.678814	−	1.10199i
$449$	−4.56086e27			−0.646338			−0.323169	−	0.946341i	$-0.604748\pi$
$449$	−4.56086e27			−0.646338			−0.323169	+	0.946341i	$0.604748\pi$
$450$	4.20242e27	+	1.55220e27i	0.581792	+	0.214890i
$451$		−	3.67219e26i		−	0.0496674i
$452$	−8.40900e27	−	7.19320e27i	−1.11120	−	0.950535i
$453$		−	1.33318e28i		−	1.72131i
$454$	−3.95693e27	+	1.07130e28i	−0.499196	+	1.35152i
$455$	−6.00967e26			−0.0740851
$456$	−5.98250e27	−	1.07116e28i	−0.720695	−	1.29040i
$457$	−7.39549e27			−0.870657			−0.435328	−	0.900272i	$-0.643368\pi$
$457$	−7.39549e27			−0.870657			−0.435328	+	0.900272i	$0.643368\pi$
$458$	4.09609e27	−	1.10897e28i	0.471283	−	1.27595i
$459$		−	5.69221e27i		−	0.640100i
$460$	3.38142e25	−	3.95295e25i	0.00371657	−	0.00434475i
$461$			1.27772e28i			1.37270i	0.727272	+	0.686349i	$0.240788\pi$
$461$			1.27772e28i			1.37270i	−0.727272	+	0.686349i	$0.759212\pi$
$462$	−4.54114e27	−	1.67731e27i	−0.476897	−	0.176146i
$463$	1.27718e28			1.31115			0.655576	−	0.755129i	$-0.272426\pi$
$463$	1.27718e28			1.31115			0.655576	+	0.755129i	$0.272426\pi$
$464$	9.34639e27	−	1.46553e27i	0.938005	−	0.147081i
$465$	4.13170e27			0.405390
$466$	−1.02910e28	−	3.80106e27i	−0.987199	−	0.364630i
$467$		−	2.14873e26i		−	0.0201536i	−0.999949	−	0.0100768i	$-0.996792\pi$
$467$		−	2.14873e26i		−	0.0201536i	0.999949	−	0.0100768i	$-0.00320761\pi$
$468$	1.24721e27	−	1.45802e27i	0.114382	−	0.133715i
$469$		−	7.76995e27i		−	0.696792i
$470$	−1.20029e27	+	3.24967e27i	−0.105259	+	0.284979i
$471$	2.89309e28			2.48109
$472$	−2.03738e28	+	1.13789e28i	−1.70876	+	0.954354i
$473$	−5.94633e27			−0.487761
$474$	−4.43383e27	+	1.20042e28i	−0.355719	+	0.963073i
$475$		−	1.40126e28i		−	1.09960i
$476$	1.82039e28	+	1.55719e28i	1.39730	+	1.19528i
$477$			6.07909e27i			0.456452i
$478$	−1.47043e28	−	5.43116e27i	−1.08007	−	0.398933i
$479$	−9.96855e27			−0.716323			−0.358162	−	0.933660i	$-0.616596\pi$
$479$	−9.96855e27			−0.716323			−0.358162	+	0.933660i	$0.616596\pi$
$480$	7.59840e26	−	3.78181e27i	0.0534182	−	0.265869i
$481$	7.40247e27			0.509159
$482$	1.51503e27	+	5.59589e26i	0.101959	+	0.0376596i
$483$		−	6.83409e26i		−	0.0450024i
$484$	1.06900e28	+	9.14438e27i	0.688811	+	0.589220i
$485$			4.24307e27i			0.267542i
$486$	−6.32329e27	+	1.71197e28i	−0.390178	+	1.05637i
$487$	−2.28763e28			−1.38144			−0.690719	−	0.723123i	$-0.742706\pi$
$487$	−2.28763e28			−1.38144			−0.690719	+	0.723123i	$0.742706\pi$
$488$	2.51060e26	−	1.40219e26i	0.0148378	−	0.00828701i
$489$	−3.36185e27			−0.194462
$490$	−8.72520e26	+	2.36226e27i	−0.0493988	+	0.133742i
$491$		−	1.10634e28i		−	0.613100i	−0.951855	−	0.306550i	$-0.900825\pi$
$491$		−	1.10634e28i		−	0.613100i	0.951855	−	0.306550i	$-0.0991747\pi$
$492$	2.49883e27	−	2.92119e27i	0.135551	−	0.158462i
$493$			2.54025e28i			1.34891i
$494$	−5.62966e27	−	2.07936e27i	−0.292651	−	0.108093i
$495$	−8.23890e26			−0.0419290
$496$	4.64780e27	+	2.96412e28i	0.231574	+	1.47686i
$497$	−1.71787e28			−0.838008
$498$	−1.26098e28	−	4.65753e27i	−0.602282	−	0.222458i
$499$		−	1.24056e28i		−	0.580178i	−0.957000	−	0.290089i	$-0.906315\pi$
$499$		−	1.24056e28i		−	0.580178i	0.957000	−	0.290089i	$-0.0936849\pi$
$500$	5.86123e27	−	6.85190e27i	0.268413	−	0.313780i
$501$		−	1.62810e28i		−	0.730104i
$502$	2.96595e27	−	8.03000e27i	0.130249	−	0.352636i
$503$	1.66783e28			0.717279			0.358640	−	0.933476i	$-0.383241\pi$
$503$	1.66783e28			0.717279			0.358640	+	0.933476i	$0.383241\pi$
$504$	−9.72685e27	−	1.74158e28i	−0.409686	−	0.733539i
$505$	1.31643e27			0.0543050
$506$	7.10180e25	−	1.92274e26i	0.00286938	−	0.00776856i
$507$			3.00657e28i			1.18984i
$508$	−1.19851e28	−	1.02522e28i	−0.464592	−	0.397420i
$509$		−	3.10881e27i		−	0.118048i	−0.998257	−	0.0590239i	$-0.981201\pi$
$509$		−	3.10881e27i		−	0.118048i	0.998257	−	0.0590239i	$-0.0187988\pi$
$510$	9.71584e27	+	3.58863e27i	0.361405	+	0.133488i
$511$	2.68494e28			0.978396
$512$	2.79858e28	+	1.19695e27i	0.999087	+	0.0427309i
$513$	1.48260e28			0.518551
$514$	4.10194e28	+	1.51508e28i	1.40565	+	0.519187i
$515$		−	4.41443e27i		−	0.148217i
$516$	−4.73024e28	−	4.04633e28i	−1.55619	−	1.33119i
$517$			1.36502e28i			0.440036i
$518$	2.66655e28	−	7.21941e28i	0.842338	−	2.28055i
$519$	−1.60938e28			−0.498196
$520$	−9.20048e26	−	1.64733e27i	−0.0279110	−	0.0499743i
$521$	1.68751e28			0.501706			0.250853	−	0.968025i	$-0.419289\pi$
$521$	1.68751e28			0.501706			0.250853	+	0.968025i	$0.419289\pi$
$522$	7.32903e27	−	1.98426e28i	0.213553	−	0.578174i
$523$			2.56228e28i			0.731744i	0.930665	+	0.365872i	$0.119229\pi$
$523$			2.56228e28i			0.731744i	−0.930665	+	0.365872i	$0.880771\pi$
$524$	2.92868e28	−	3.42369e28i	0.819774	−	0.958332i
$525$		−	5.78790e28i		−	1.58799i
$526$	1.96158e28	+	7.24525e27i	0.527540	+	0.194851i
$527$	−8.05615e28			−2.12381
$528$	−2.35451e27	−	1.50158e28i	−0.0608476	−	0.388054i
$529$	−3.94426e28			−0.999267
$530$	5.60792e27	+	2.07133e27i	0.139285	+	0.0514461i
$531$			5.21769e28i			1.27053i
$532$	−4.05588e28	+	4.74141e28i	−0.968307	+	1.13197i
$533$		−	1.88037e27i		−	0.0440158i
$534$	−8.32665e27	+	2.25436e28i	−0.191112	+	0.517415i
$535$	−8.36645e27			−0.188290
$536$	2.12985e28	−	1.18954e28i	0.470023	−	0.262511i
$537$	4.51141e28			0.976298
$538$	−2.56563e28	+	6.94619e28i	−0.544478	+	1.47412i
$539$			9.92263e27i			0.206512i
$540$	3.54215e27	+	3.03002e27i	0.0722991	+	0.0618458i
$541$			5.67117e27i			0.113528i	0.998388	+	0.0567638i	$0.0180782\pi$
$541$			5.67117e27i			0.113528i	−0.998388	+	0.0567638i	$0.981922\pi$
$542$	6.19787e28	+	2.28923e28i	1.21689	+	0.449467i
$543$	−9.63421e27			−0.185532
$544$	−1.48156e28	+	7.37392e28i	−0.279854	+	1.39287i
$545$	−8.90190e27			−0.164938
$546$	−2.32533e28	−	8.58879e27i	−0.422631	−	0.156102i
$547$		−	5.58678e27i		−	0.0996081i	−0.998759	−	0.0498041i	$-0.984140\pi$
$547$		−	5.58678e27i		−	0.0996081i	0.998759	−	0.0498041i	$-0.0158597\pi$
$548$	−1.07488e28	−	9.19471e27i	−0.188003	−	0.160821i
$549$		−	6.42960e26i		−	0.0110325i
$550$	6.01464e27	−	1.62840e28i	0.101251	−	0.274128i
$551$	−6.61636e28			−1.09277
$552$	1.87332e27	−	1.04626e27i	0.0303565	−	0.0169543i
$553$	6.50791e28			1.03473
$554$	3.01053e28	−	8.15071e28i	0.469667	−	1.27158i
$555$		−	3.32750e28i		−	0.509379i
$556$	−3.26378e28	+	3.81543e28i	−0.490271	+	0.573137i
$557$			5.59258e28i			0.824390i	0.911096	+	0.412195i	$0.135238\pi$
$557$			5.59258e28i			0.824390i	−0.911096	+	0.412195i	$0.864762\pi$
$558$	6.29289e28	+	2.32433e28i	0.910314	+	0.336232i
$559$	−3.04487e28			−0.432259
$560$	−1.93802e28	+	3.03886e27i	−0.270013	+	0.0423385i
$561$	4.08112e28			0.558046
$562$	−9.81377e28	−	3.62480e28i	−1.31706	−	0.486466i
$563$		−	1.87963e28i		−	0.247590i	−0.992308	−	0.123795i	$-0.960493\pi$
$563$		−	1.87963e28i		−	0.247590i	0.992308	−	0.123795i	$-0.0395065\pi$
$564$	−9.28862e28	+	1.08586e29i	−1.20094	+	1.40392i
$565$			2.43316e28i			0.308789i
$566$	1.89631e28	−	5.13408e28i	0.236231	−	0.639573i
$567$	1.29946e29			1.58906
$568$	−2.62996e28	−	4.70892e28i	−0.315713	−	0.565280i
$569$	−1.83407e28			−0.216141			−0.108070	−	0.994143i	$-0.534467\pi$
$569$	−1.83407e28			−0.216141			−0.108070	+	0.994143i	$0.534467\pi$
$570$	−9.34698e27	+	2.53060e28i	−0.108140	+	0.292777i
$571$		−	9.30834e28i		−	1.05729i	−0.848844	−	0.528644i	$-0.822701\pi$
$571$		−	9.30834e28i		−	1.05729i	0.848844	−	0.528644i	$-0.177299\pi$
$572$	−5.64969e27	−	4.83284e27i	−0.0630038	−	0.0538945i
$573$		−	8.00403e28i		−	0.876366i
$574$	−1.83387e28	−	6.77355e27i	−0.197149	−	0.0728185i
$575$	2.45063e27			0.0258681
$576$	3.28479e28	−	5.33253e28i	0.340464	−	0.552710i
$577$	1.40638e29			1.43139			0.715693	−	0.698415i	$-0.246111\pi$
$577$	1.40638e29			1.43139			0.715693	+	0.698415i	$0.246111\pi$
$578$	−9.55850e28	−	3.53051e28i	−0.955317	−	0.352854i
$579$		−	6.16427e28i		−	0.605002i
$580$	−1.58075e28	−	1.35220e28i	−0.152359	−	0.130330i
$581$			6.83625e28i			0.647095i
$582$	−6.06404e28	+	1.64178e29i	−0.563729	+	1.52624i
$583$	2.35560e28			0.215071
$584$	4.11049e28	+	7.35979e28i	0.368603	+	0.659980i
$585$	−4.21879e27			−0.0371579
$586$	3.79365e28	−	1.02709e29i	0.328195	−	0.888555i
$587$			1.42052e29i			1.20711i	0.797321	+	0.603555i	$0.206250\pi$
$587$			1.42052e29i			1.20711i	−0.797321	+	0.603555i	$0.793750\pi$
$588$	−6.75210e28	+	7.89335e28i	−0.563608	+	0.658870i
$589$		−	2.09831e29i		−	1.72052i
$590$	4.81329e28	+	1.77783e28i	0.387700	+	0.143200i
$591$	−1.57468e27			−0.0124601
$592$	2.38717e29	−	3.74314e28i	1.85569	−	0.290977i
$593$	−1.08043e29			−0.825130			−0.412565	−	0.910928i	$-0.635367\pi$
$593$	−1.08043e29			−0.825130			−0.412565	+	0.910928i	$0.635367\pi$
$594$	1.72293e28	+	6.36377e27i	0.129273	+	0.0477481i
$595$		−	5.26732e28i		−	0.388295i
$596$	1.03514e29	−	1.21010e29i	0.749747	−	0.876470i
$597$			5.72963e28i			0.407752i
$598$	3.63654e26	−	9.84556e26i	0.00254288	−	0.00688459i
$599$	1.28909e29			0.885731			0.442865	−	0.896588i	$-0.353962\pi$
$599$	1.28909e29			0.885731			0.442865	+	0.896588i	$0.353962\pi$
$600$	1.58655e29	−	8.86096e28i	1.07118	−	0.598264i
$601$	−9.93244e28			−0.658982			−0.329491	−	0.944159i	$-0.606877\pi$
$601$	−9.93244e28			−0.658982			−0.329491	+	0.944159i	$0.606877\pi$
$602$	−1.09683e29	+	2.96957e29i	−0.715118	+	1.93611i
$603$		−	5.45451e28i		−	0.349482i
$604$	−1.61761e29	−	1.38373e29i	−1.01856	−	0.871294i
$605$		−	3.09316e28i		−	0.191413i
$606$	5.09369e28	+	1.88140e28i	0.309792	+	0.114424i
$607$	1.20903e28			0.0722698			0.0361349	−	0.999347i	$-0.488495\pi$
$607$	1.20903e28			0.0722698			0.0361349	+	0.999347i	$0.488495\pi$
$608$	−1.92062e29	−	3.85890e28i	−1.12838	−	0.226713i
$609$	−2.73288e29			−1.57812
$610$	−5.93127e26	−	2.19076e26i	−0.00336654	−	0.00124346i
$611$			6.98969e28i			0.389965i
$612$	1.27791e29	+	1.09315e29i	0.700829	+	0.599501i
$613$			5.11741e28i			0.275877i	0.990441	+	0.137939i	$0.0440476\pi$
$613$			5.11741e28i			0.275877i	−0.990441	+	0.137939i	$0.955952\pi$
$614$	2.62992e28	−	7.12025e28i	0.139372	−	0.377335i
$615$	−8.45250e27			−0.0440348
$616$	−6.74848e28	+	3.76907e28i	−0.345628	+	0.193035i
$617$	−2.59475e29			−1.30647			−0.653237	−	0.757153i	$-0.726590\pi$
$617$	−2.59475e29			−1.30647			−0.653237	+	0.757153i	$0.726590\pi$
$618$	6.30893e28	−	1.70808e29i	0.312303	−	0.845530i
$619$			1.51206e29i			0.735897i	0.929846	+	0.367948i	$0.119940\pi$
$619$			1.51206e29i			0.735897i	−0.929846	+	0.367948i	$0.880060\pi$
$620$	4.28836e28	−	5.01318e28i	0.205201	−	0.239884i
$621$			2.59288e27i			0.0121989i
$622$	−1.62981e29	−	6.01983e28i	−0.753941	−	0.278474i
$623$	1.22217e29			0.555914
$624$	−1.20564e28	−	7.68895e28i	−0.0539238	−	0.343897i
$625$	1.97408e29			0.868212
$626$	3.56526e28	+	1.31686e28i	0.154192	+	0.0569519i
$627$			1.06297e29i			0.452078i
$628$	3.00279e29	−	3.51032e29i	1.25588	−	1.46815i
$629$			6.48808e29i			2.66860i
$630$	−1.51971e28	+	4.11446e28i	−0.0614731	+	0.166432i
$631$	9.55177e28			0.379993			0.189997	−	0.981785i	$-0.439152\pi$
$631$	9.55177e28			0.379993			0.189997	+	0.981785i	$0.439152\pi$
$632$	9.96325e28	+	1.78391e29i	0.389827	+	0.697981i
$633$	−3.46698e29			−1.33417
$634$	−1.30595e29	+	3.53572e29i	−0.494297	+	1.33826i
$635$			3.46790e28i			0.129105i
$636$	1.87385e29	+	1.60293e29i	0.686177	+	0.586967i
$637$			5.08096e28i			0.183013i
$638$	−7.68885e28	−	2.83994e28i	−0.272423	−	0.100622i
$639$	−1.20595e29			−0.420309
$640$	−3.80000e28	−	4.84715e28i	−0.130285	−	0.166187i
$641$	1.23787e29			0.417510			0.208755	−	0.977968i	$-0.433059\pi$
$641$	1.23787e29			0.417510			0.208755	+	0.977968i	$0.433059\pi$
$642$	−3.23724e29	−	1.19570e29i	−1.07413	−	0.396739i
$643$			4.84294e28i			0.158086i	0.996871	+	0.0790430i	$0.0251865\pi$
$643$			4.84294e28i			0.158086i	−0.996871	+	0.0790430i	$0.974814\pi$
$644$	−8.29211e27	−	7.09321e27i	−0.0266295	−	0.0227793i
$645$			1.36870e29i			0.432446i
$646$	1.82251e29	−	4.93426e29i	0.566537	−	1.53384i
$647$	−1.90340e29			−0.582151			−0.291075	−	0.956700i	$-0.594013\pi$
$647$	−1.90340e29			−0.582151			−0.291075	+	0.956700i	$0.594013\pi$
$648$	1.98940e29	+	3.56199e29i	0.598665	+	1.07190i
$649$	2.02181e29			0.598648
$650$	3.07984e28	−	8.33837e28i	0.0897301	−	0.242935i
$651$		−	8.66707e29i		−	2.48469i
$652$	−3.48932e28	+	4.07908e28i	−0.0984330	+	0.115070i
$653$		−	5.45871e29i		−	1.51531i	−0.652656	−	0.757655i	$-0.726345\pi$
$653$		−	5.45871e29i		−	1.51531i	0.652656	−	0.757655i	$-0.273655\pi$
$654$	−3.44443e29	−	1.27223e29i	−0.940915	−	0.347535i
$655$	−9.90651e28			−0.266310
$656$	−9.50832e27	−	6.06390e28i	−0.0251544	−	0.160421i
$657$	1.88483e29			0.490722
$658$	6.81684e29	+	2.51786e29i	1.74667	+	0.645147i
$659$		−	2.14166e29i		−	0.540075i	−0.962850	−	0.270038i	$-0.912964\pi$
$659$		−	2.14166e29i		−	0.540075i	0.962850	−	0.270038i	$-0.0870361\pi$
$660$	−2.17242e28	+	2.53960e28i	−0.0539178	+	0.0630311i
$661$		−	7.24474e29i		−	1.76973i	−0.465846	−	0.884866i	$-0.654250\pi$
$661$		−	7.24474e29i		−	1.76973i	0.465846	−	0.884866i	$-0.345750\pi$
$662$	−7.15475e28	+	1.93708e29i	−0.172023	+	0.465734i
$663$	2.08977e29			0.494546
$664$	−1.87391e29	+	1.04659e29i	−0.436500	+	0.243788i
$665$	1.37193e29			0.314562
$666$	1.87192e29	−	5.06803e29i	0.422481	−	1.14383i
$667$		−	1.15712e28i		−	0.0257072i
$668$	−1.97545e29	−	1.68983e29i	−0.432029	−	0.369565i
$669$			5.72079e29i			1.23164i
$670$	−5.03175e28	−	1.85852e28i	−0.106643	−	0.0393896i
$671$	−2.49142e27			−0.00519829
$672$	−7.93311e29	−	1.59392e29i	−1.62954	−	0.327407i
$673$	−2.43245e29			−0.491910			−0.245955	−	0.969281i	$-0.579101\pi$
$673$	−2.43245e29			−0.491910			−0.245955	+	0.969281i	$0.579101\pi$
$674$	4.76911e29	+	1.76151e29i	0.949530	+	0.350716i
$675$			2.19595e29i			0.430460i
$676$	3.64801e29	+	3.12057e29i	0.704070	+	0.602273i
$677$		−	3.49827e29i		−	0.664771i	−0.943144	−	0.332386i	$-0.892146\pi$
$677$		−	3.49827e29i		−	0.664771i	0.943144	−	0.332386i	$-0.107854\pi$
$678$	−3.47737e29	+	9.41464e29i	−0.650638	+	1.76154i
$679$	8.90069e29			1.63980
$680$	1.44385e29	−	8.06399e28i	0.261926	−	0.146287i
$681$	1.03579e30			1.85023
$682$	9.00659e28	−	2.43845e29i	0.158425	−	0.428921i
$683$			8.72945e29i			1.51206i	0.654536	+	0.756030i	$0.272864\pi$
$683$			8.72945e29i			1.51206i	−0.654536	+	0.756030i	$0.727136\pi$
$684$	−2.84723e29	+	3.32847e29i	−0.485662	+	0.567748i
$685$			3.11018e28i			0.0522438i
$686$	−2.38410e29	−	8.80588e28i	−0.394386	−	0.145670i
$687$	−1.07221e30			−1.74677
$688$	−9.81920e29	+	1.53967e29i	−1.57542	+	0.247030i
$689$	1.20620e29			0.190598
$690$	−4.42569e27	−	1.63467e27i	−0.00688757	−	0.00254398i
$691$			3.57836e28i			0.0548484i	0.999624	+	0.0274242i	$0.00873050\pi$
$691$			3.57836e28i			0.0548484i	−0.999624	+	0.0274242i	$0.991270\pi$
$692$	−1.67040e29	+	1.95273e29i	−0.252177	+	0.294801i
$693$			1.72827e29i			0.256988i
$694$	−4.78104e28	+	1.29442e29i	−0.0700242	+	0.189583i
$695$	1.10400e29			0.159268
$696$	−4.18389e29	−	7.49121e29i	−0.594543	−	1.06452i
$697$	1.64810e29			0.230696
$698$	−2.52990e29	+	6.84944e29i	−0.348836	+	0.944438i
$699$			9.94984e29i			1.35147i
$700$	−7.02273e29	−	6.00736e29i	−0.939672	−	0.803811i
$701$		−	1.12962e30i		−	1.48900i	−0.667623	−	0.744500i	$-0.732688\pi$
$701$		−	1.12962e30i		−	1.48900i	0.667623	−	0.744500i	$-0.267312\pi$
$702$	8.82238e28	+	3.25862e28i	0.114563	+	0.0423149i
$703$	−1.68989e30			−2.16186
$704$	−2.06631e29	−	1.27283e29i	−0.260425	−	0.160420i
$705$	3.14195e29			0.390134
$706$	5.22118e29	+	1.92849e29i	0.638733	+	0.235921i
$707$		−	2.76148e29i		−	0.332842i
$708$	1.60833e30	+	1.37579e30i	1.90997	+	1.63382i
$709$		−	3.22850e29i		−	0.377760i	−0.982000	−	0.188880i	$-0.939514\pi$
$709$		−	3.22850e29i		−	0.377760i	0.982000	−	0.188880i	$-0.0604857\pi$
$710$	−4.10902e28	+	1.11248e29i	−0.0473725	+	0.128256i
$711$	4.56856e29			0.518977
$712$	1.87108e29	+	3.35014e29i	0.209436	+	0.374993i
$713$	3.66968e28			0.0404751
$714$	7.52786e29	−	2.03809e30i	0.818164	−	2.21510i
$715$			1.63475e28i			0.0175080i
$716$	4.68247e29	−	5.47391e29i	0.494184	−	0.577711i
$717$			1.42169e30i			1.47861i
$718$	1.49503e30	+	5.52202e29i	1.53230	+	0.565967i
$719$	1.11477e29			0.112598			0.0562989	−	0.998414i	$-0.482070\pi$
$719$	1.11477e29			0.112598			0.0562989	+	0.998414i	$0.482070\pi$
$720$	−1.36049e29	+	2.13328e28i	−0.135427	+	0.0212352i
$721$	−9.26014e29			−0.908442
$722$	3.14964e29	+	1.16334e29i	0.304523	+	0.112478i
$723$		−	1.46481e29i		−	0.139582i
$724$	−9.99950e28	+	1.16896e29i	−0.0939125	+	0.109786i
$725$		−	9.79980e29i		−	0.907127i
$726$	4.42063e29	−	1.19684e30i	0.403319	−	1.09195i
$727$	−1.23195e30			−1.10785			−0.553925	−	0.832567i	$-0.686870\pi$
$727$	−1.23195e30			−1.10785			−0.553925	+	0.832567i	$0.686870\pi$
$728$	−3.45562e29	+	1.92998e29i	−0.306299	+	0.171070i
$729$	2.49981e29			0.218408
$730$	6.42218e28	−	1.73874e29i	0.0553086	−	0.149742i
$731$		−	2.66875e30i		−	2.26556i
$732$	−1.98190e28	−	1.69535e28i	−0.0165850	−	0.0141871i
$733$			1.26642e30i			1.04469i	0.852735	+	0.522343i	$0.174942\pi$
$733$			1.26642e30i			1.04469i	−0.852735	+	0.522343i	$0.825058\pi$
$734$	−1.94155e30	−	7.17128e29i	−1.57885	−	0.583161i
$735$	2.28395e29			0.183092
$736$	6.74872e27	−	3.35892e28i	0.00533340	−	0.0265450i
$737$	−2.11358e29			−0.164668
$738$	−1.28738e29	−	4.75504e28i	−0.0988815	−	0.0365227i
$739$			1.28809e30i			0.975391i	0.873014	+	0.487696i	$0.162162\pi$
$739$			1.28809e30i			0.975391i	−0.873014	+	0.487696i	$0.837838\pi$
$740$	−4.03740e29	−	3.45366e29i	−0.301418	−	0.257838i
$741$			5.44305e29i			0.400637i
$742$	4.34503e29	−	1.17637e30i	0.315320	−	0.853698i
$743$	1.70077e30			1.21692			0.608461	−	0.793584i	$-0.291787\pi$
$743$	1.70077e30			1.21692			0.608461	+	0.793584i	$0.291787\pi$
$744$	2.37577e30	−	1.32688e30i	1.67605	−	0.936087i
$745$	−3.50146e29			−0.243561
$746$	−3.12121e29	+	8.45037e29i	−0.214075	+	0.579586i
$747$			4.79905e29i			0.324556i
$748$	4.23587e29	−	4.95182e29i	0.282472	−	0.330216i
$749$			1.75503e30i			1.15405i
$750$	−7.67133e29	−	2.83347e29i	−0.497425	−	0.183728i
$751$	−1.13206e30			−0.723853			−0.361926	−	0.932207i	$-0.617881\pi$
$751$	−1.13206e30			−0.723853			−0.361926	+	0.932207i	$0.617881\pi$
$752$	3.53442e29	+	2.25406e30i	0.222859	+	1.42128i
$753$	−7.76382e29			−0.482757
$754$	−3.93714e29	−	1.45421e29i	−0.241425	−	0.0891721i
$755$			4.68059e29i			0.283046i
$756$	6.35607e29	−	7.43037e29i	0.379061	−	0.443131i
$757$			2.49281e29i			0.146616i	0.997309	+	0.0733081i	$0.0233556\pi$
$757$			2.49281e29i			0.146616i	−0.997309	+	0.0733081i	$0.976644\pi$
$758$	−2.91321e29	+	7.88723e29i	−0.168984	+	0.457507i
$759$	−1.85901e28			−0.0106351
$760$	2.10036e29	+	3.76066e29i	0.118509	+	0.212188i
$761$	1.24410e30			0.692336			0.346168	−	0.938173i	$-0.387483\pi$
$761$	1.24410e30			0.692336			0.346168	+	0.938173i	$0.387483\pi$
$762$	−4.95619e29	+	1.34184e30i	−0.272033	+	0.736501i
$763$			1.86735e30i			1.01092i
$764$	−9.71166e29	−	8.30752e29i	−0.518577	−	0.443599i
$765$		−	3.69767e29i		−	0.194752i
$766$	1.05678e29	+	3.90329e28i	0.0549011	+	0.0202782i
$767$	1.03529e30			0.530529
$768$	−7.77601e29	−	2.41860e30i	−0.393065	−	1.22256i
$769$	1.40070e30			0.698423			0.349211	−	0.937044i	$-0.386449\pi$
$769$	1.40070e30			0.698423			0.349211	+	0.937044i	$0.386449\pi$
$770$	1.59432e29	+	5.88875e28i	0.0784193	+	0.0289648i
$771$		−	3.96596e30i		−	1.92432i
$772$	−7.47939e29	−	6.39800e29i	−0.358001	−	0.306240i
$773$		−	3.83467e30i		−	1.81068i	−0.424682	−	0.905342i	$-0.639614\pi$
$773$		−	3.83467e30i		−	1.81068i	0.424682	−	0.905342i	$-0.360386\pi$
$774$	−7.69978e29	+	2.08464e30i	−0.358673	+	0.971071i
$775$	3.10791e30			1.42824
$776$	1.36265e30	+	2.43981e30i	0.617782	+	1.10613i
$777$	−6.98009e30			−3.12205
$778$	−1.34903e30	+	3.65236e30i	−0.595300	+	1.61171i
$779$			4.29266e29i			0.186889i
$780$	−1.11241e29	+	1.30042e29i	−0.0477826	+	0.0558588i
$781$			4.67294e29i			0.198041i
$782$	8.62938e28	+	3.18733e28i	0.0360835	+	0.0133277i
$783$	1.03686e30			0.427783
$784$	2.56925e29	+	1.63853e30i	0.104589	+	0.667014i
$785$	−1.01572e30			−0.407982
$786$	−3.83314e30	−	1.41580e30i	−1.51921	−	0.561132i
$787$			1.20183e30i			0.470011i	0.971994	+	0.235005i	$0.0755108\pi$
$787$			1.20183e30i			0.470011i	−0.971994	+	0.235005i	$0.924489\pi$
$788$	−1.63438e28	+	1.91063e28i	−0.00630709	+	0.00737312i
$789$		−	1.89656e30i		−	0.722199i
$790$	1.55665e29	−	4.21446e29i	0.0584932	−	0.158365i
$791$	5.10403e30			1.89261
$792$	−4.73744e29	+	2.64589e29i	−0.173352	+	0.0968184i
$793$	−1.27575e28			−0.00460678
$794$	−8.22613e29	+	2.22714e30i	−0.293143	+	0.793656i
$795$		−	5.42202e29i		−	0.190681i
$796$	6.95202e29	+	5.94688e29i	0.241281	+	0.206396i
$797$			3.83121e30i			1.31227i	0.754643	+	0.656135i	$0.227810\pi$
$797$			3.83121e30i			1.31227i	−0.754643	+	0.656135i	$0.772190\pi$
$798$	5.30844e30	+	1.96072e30i	1.79447	+	0.662803i
$799$	−6.12629e30			−2.04389
$800$	5.71560e29	−	2.84472e30i	0.188199	−	0.936688i
$801$	8.57965e29			0.278823
$802$	−1.80626e30	−	6.67157e29i	−0.579361	−	0.213992i
$803$		−	7.30355e29i		−	0.231218i
$804$	−1.68133e30	−	1.43824e30i	−0.525369	−	0.449410i
$805$			2.39934e28i			0.00740004i
$806$	4.61190e29	−	1.24863e30i	0.140398	−	0.380114i
$807$	6.71593e30			2.01806
$808$	7.56962e29	−	4.22768e29i	0.224520	−	0.125396i
$809$	3.06168e30			0.896396			0.448198	−	0.893934i	$-0.352066\pi$
$809$	3.06168e30			0.896396			0.448198	+	0.893934i	$0.352066\pi$
$810$	3.10821e29	−	8.41516e29i	0.0898292	−	0.243204i
$811$		−	8.37976e29i		−	0.239063i	−0.992830	−	0.119532i	$-0.961861\pi$
$811$		−	8.37976e29i		−	0.239063i	0.992830	−	0.119532i	$-0.0381393\pi$
$812$	−2.83650e30	+	3.31593e30i	−0.798813	+	0.933829i
$813$		−	5.99242e30i		−	1.66591i
$814$	−1.96382e30	−	7.25353e29i	−0.538946	−	0.199064i
$815$	1.18029e29			0.0319767
$816$	6.73918e30	−	1.05672e30i	1.80244	−	0.282626i
$817$	6.95106e30			1.83535
$818$	−5.91868e30	−	2.18611e30i	−1.54282	−	0.569853i
$819$			8.84976e29i			0.227746i
$820$	−8.77299e28	+	1.02558e29i	−0.0222896	+	0.0260570i
$821$			4.01385e30i			1.00683i	0.864044	+	0.503417i	$0.167924\pi$
$821$			4.01385e30i			1.00683i	−0.864044	+	0.503417i	$0.832076\pi$
$822$	−4.44496e29	+	1.20343e30i	−0.110081	+	0.298034i
$823$	−4.33335e30			−1.05956			−0.529780	−	0.848135i	$-0.677726\pi$
$823$	−4.33335e30			−1.05956			−0.529780	+	0.848135i	$0.677726\pi$
$824$	−1.41768e30	−	2.53834e30i	−0.342249	−	0.612792i
$825$	−1.57442e30			−0.375280
$826$	3.72935e30	−	1.00968e31i	0.877693	−	2.37626i
$827$		−	7.73034e30i		−	1.79635i	−0.439638	−	0.898175i	$-0.644893\pi$
$827$		−	7.73034e30i		−	1.79635i	0.439638	−	0.898175i	$-0.355107\pi$
$828$	−5.82107e28	−	4.97944e28i	−0.0133562	−	0.0114252i
$829$			4.10451e30i			0.929906i	0.885335	+	0.464953i	$0.153929\pi$
$829$			4.10451e30i			0.929906i	−0.885335	+	0.464953i	$0.846071\pi$
$830$	4.42709e29	+	1.63518e29i	0.0990373	+	0.0365802i
$831$	−7.88052e30			−1.74078
$832$	−1.05807e30	−	6.51763e29i	−0.230792	−	0.142166i
$833$	−4.45334e30			−0.959209
$834$	4.27173e30	+	1.57780e30i	0.908573	+	0.335589i
$835$			5.71599e29i			0.120056i
$836$	1.28976e30	+	1.10328e30i	0.267511	+	0.228833i
$837$			3.28832e30i			0.673529i
$838$	1.32783e30	−	3.59496e30i	0.268583	−	0.727163i
$839$	1.74902e30			0.349377			0.174689	−	0.984624i	$-0.444108\pi$
$839$	1.74902e30			0.349377			0.174689	+	0.984624i	$0.444108\pi$
$840$	8.67551e29	+	1.55334e30i	0.171144	+	0.306432i
$841$	5.05656e29			0.0985138
$842$	−6.05487e29	+	1.63929e30i	−0.116500	+	0.315413i
$843$			9.48846e30i			1.80304i
$844$	−3.59844e30	+	4.20665e30i	−0.675333	+	0.789478i
$845$		−	1.05556e30i		−	0.195653i
$846$	4.78543e30	+	1.76754e30i	0.876056	+	0.323579i
$847$	−6.48852e30			−1.17319
$848$	3.88981e30	−	6.09930e29i	0.694659	−	0.108924i
$849$	−4.96389e30			−0.875571
$850$	7.30837e30	+	2.69941e30i	1.27327	+	0.470294i
$851$		−	2.95540e29i		−	0.0508577i
$852$	−3.17982e30	+	3.71728e30i	−0.540489	+	0.631843i
$853$		−	1.82486e30i		−	0.306383i	−0.988197	−	0.153191i	$-0.951045\pi$
$853$		−	1.82486e30i		−	0.306383i	0.988197	−	0.153191i	$-0.0489551\pi$
$854$	−4.59556e28	+	1.24420e29i	−0.00762133	+	0.0206340i
$855$	9.63099e29			0.157771
$856$	−4.81079e30	+	2.68686e30i	−0.778470	+	0.434781i
$857$	3.41116e30			0.545260			0.272630	−	0.962119i	$-0.412106\pi$
$857$	3.41116e30			0.545260			0.272630	+	0.962119i	$0.412106\pi$
$858$	−2.33632e29	+	6.32535e29i	−0.0368906	+	0.0998776i
$859$			2.05786e30i			0.320987i	0.987037	+	0.160494i	$0.0513086\pi$
$859$			2.05786e30i			0.320987i	−0.987037	+	0.160494i	$0.948691\pi$
$860$	1.66071e30	+	1.42060e30i	0.255894	+	0.218896i
$861$			1.77308e30i			0.269895i
$862$	7.94561e30	+	2.93477e30i	1.19482	+	0.441315i
$863$	−6.05899e30			−0.900093			−0.450046	−	0.893005i	$-0.648593\pi$
$863$	−6.05899e30			−0.900093			−0.450046	+	0.893005i	$0.648593\pi$
$864$	3.00985e30	+	6.04738e29i	0.441724	+	0.0887509i
$865$	5.65026e29			0.0819217
$866$	−7.63212e30	−	2.81899e30i	−1.09322	−	0.403790i
$867$			9.24165e30i			1.30782i
$868$	−1.05162e31	−	8.99570e30i	−1.47028	−	1.25770i
$869$		−	1.77028e30i		−	0.244531i
$870$	−6.53686e29	+	1.76979e30i	−0.0892108	+	0.241529i
$871$	−1.08228e30			−0.145931
$872$	−5.11868e30	+	2.85882e30i	−0.681922	+	0.380858i
$873$	6.24829e30			0.822455
$874$	−8.30177e28	+	2.24762e29i	−0.0107969	+	0.0292316i
$875$			4.15892e30i			0.534436i
$876$	4.96989e30	−	5.80990e30i	0.631035	−	0.737693i
$877$		−	6.94443e30i		−	0.871246i	−0.900129	−	0.435623i	$-0.856528\pi$
$877$		−	6.94443e30i		−	0.871246i	0.900129	−	0.435623i	$-0.143472\pi$
$878$	1.84359e30	+	6.80944e29i	0.228545	+	0.0844149i
$879$	−9.93045e30			−1.21643
$880$	8.26628e28	+	5.27180e29i	0.0100056	+	0.0638103i
$881$	5.74177e30			0.686750			0.343375	−	0.939198i	$-0.388430\pi$
$881$	5.74177e30			0.686750			0.343375	+	0.939198i	$0.388430\pi$
$882$	3.47863e30	+	1.28486e30i	0.411139	+	0.151858i
$883$			3.80196e30i			0.444038i	0.975042	+	0.222019i	$0.0712647\pi$
$883$			3.80196e30i			0.444038i	−0.975042	+	0.222019i	$0.928735\pi$
$884$	2.16901e30	−	2.53562e30i	0.250330	−	0.292641i
$885$		−	4.65373e30i		−	0.530759i
$886$	3.40229e30	−	9.21137e30i	0.383458	−	1.03817i
$887$	1.13040e31			1.25903			0.629513	−	0.776990i	$-0.283254\pi$
$887$	1.13040e31			1.25903			0.629513	+	0.776990i	$0.283254\pi$
$888$	−1.06861e31	−	1.91334e31i	−1.17621	−	2.10599i
$889$	7.27462e30			0.791301
$890$	2.92335e29	−	7.91467e29i	0.0314257	−	0.0850821i
$891$		−	3.53478e30i		−	0.375531i
$892$	6.94130e30	+	5.93771e30i	0.728803	+	0.623430i
$893$		−	1.59566e31i		−	1.65577i
$894$	−1.35482e31	−	5.00415e30i	−1.38944	−	0.513200i
$895$	−1.58388e30			−0.160539
$896$	−1.01679e31	+	7.97125e30i	−1.01858	+	0.798533i
$897$	−9.51919e28			−0.00942495
$898$	6.19571e30	+	2.28843e30i	0.606302	+	0.223943i
$899$		−	1.46747e31i		−	1.41936i
$900$	−4.92996e30	−	4.21717e30i	−0.471300	−	0.403158i
$901$			1.05721e31i			0.998963i
$902$	−1.84254e29	+	4.98849e29i	−0.0172087	+	0.0465908i
$903$	2.87113e31			2.65052
$904$	7.81400e30	+	1.39909e31i	0.713025	+	1.27666i
$905$	3.38241e29			0.0305082
$906$	−6.68932e30	+	1.81107e31i	−0.596398	+	1.61469i
$907$		−	1.35749e31i		−	1.19636i	−0.801363	−	0.598179i	$-0.795891\pi$
$907$		−	1.35749e31i		−	1.19636i	0.801363	−	0.598179i	$-0.204109\pi$
$908$	1.07506e31	−	1.25677e31i	0.936550	−	1.09485i
$909$		−	1.93856e30i		−	0.166940i
$910$	8.16385e29	+	3.01538e29i	0.0694961	+	0.0256689i
$911$	−1.26019e31			−1.06046			−0.530228	−	0.847855i	$-0.677894\pi$
$911$	−1.26019e31			−1.06046			−0.530228	+	0.847855i	$0.677894\pi$
$912$	2.75234e30	+	1.75529e31i	0.228958	+	1.46017i
$913$	1.85959e30			0.152924
$914$	1.00464e31	+	3.71073e30i	0.816726	+	0.301664i
$915$			5.73465e28i			0.00460878i
$916$	−1.11287e31	+	1.30097e31i	−0.884181	+	1.03363i
$917$			2.07809e31i			1.63225i
$918$	−2.85610e30	+	7.73260e30i	−0.221781	+	0.600451i
$919$	8.20060e29			0.0629554			0.0314777	−	0.999504i	$-0.489979\pi$
$919$	8.20060e29			0.0629554			0.0314777	+	0.999504i	$0.489979\pi$
$920$	−6.57692e28	+	3.67325e28i	−0.00499172	+	0.00278791i
$921$	−6.88423e30			−0.516570
$922$	6.41102e30	−	1.73572e31i	0.475611	−	1.28767i
$923$			2.39282e30i			0.175506i
$924$	5.32733e30	+	4.55709e30i	0.386326	+	0.330470i
$925$		−	2.50298e31i		−	1.79461i
$926$	−1.73499e31	−	6.40834e30i	−1.22994	−	0.454287i
$927$	−6.50063e30			−0.455636
$928$	−1.34320e31	−	2.69874e30i	−0.930863	−	0.187029i
$929$	−2.25997e31			−1.54859			−0.774296	−	0.632824i	$-0.781896\pi$
$929$	−2.25997e31			−1.54859			−0.774296	+	0.632824i	$0.781896\pi$
$930$	−5.61272e30	−	2.07310e30i	−0.380279	−	0.140459i
$931$		−	1.15992e31i		−	0.777064i
$932$	1.20726e31	+	1.03271e31i	0.799713	+	0.684088i
$933$			1.57578e31i			1.03214i
$934$	−1.07813e29	+	2.91894e29i	−0.00698282	+	0.0189053i
$935$	−1.43282e30			−0.0917632
$936$	−2.42585e30	+	1.35485e30i	−0.153627	+	0.0858015i
$937$	1.94712e31			1.21935			0.609674	−	0.792652i	$-0.291300\pi$
$937$	1.94712e31			1.21935			0.609674	+	0.792652i	$0.291300\pi$
$938$	−3.89862e30	+	1.05551e31i	−0.241424	+	0.653632i
$939$		−	3.44708e30i		−	0.211087i
$940$	3.26108e30	−	3.81227e30i	0.197478	−	0.230856i
$941$			2.75852e31i			1.65191i	0.563739	+	0.825953i	$0.309362\pi$
$941$			2.75852e31i			1.65191i	−0.563739	+	0.825953i	$0.690638\pi$
$942$	−3.93013e31	−	1.45162e31i	−2.32741	−	0.859646i
$943$	−7.50731e28			−0.00439655
$944$	3.33863e31	−	5.23504e30i	1.93358	−	0.303189i
$945$	−2.14999e30			−0.123141
$946$	8.07781e30	+	2.98360e30i	0.457548	+	0.168999i
$947$			1.25436e31i			0.702664i	0.936251	+	0.351332i	$0.114271\pi$
$947$			1.25436e31i			0.702664i	−0.936251	+	0.351332i	$0.885729\pi$
$948$	1.20463e31	−	1.40824e31i	0.667369	−	0.780169i
$949$		−	3.73984e30i		−	0.204908i
$950$	−7.03091e30	+	1.90355e31i	−0.380990	+	1.03149i
$951$	3.41851e31			1.83207
$952$	−1.69158e31	−	3.02876e31i	−0.896614	−	1.60538i
$953$	−3.13809e31			−1.64509			−0.822546	−	0.568699i	$-0.807447\pi$
$953$	−3.13809e31			−1.64509			−0.822546	+	0.568699i	$0.807447\pi$
$954$	3.05022e30	−	8.25815e30i	0.158151	−	0.428179i
$955$			2.81008e30i			0.144107i
$956$	1.72500e31	+	1.47559e31i	0.874946	+	0.748444i
$957$			7.43397e30i			0.372946i
$958$	1.35418e31	+	5.00177e30i	0.671952	+	0.248191i
$959$	6.52423e30			0.320209
$960$	−2.92975e30	+	4.75616e30i	−0.142227	+	0.230892i
$961$	2.57138e31			1.23473
$962$	−1.00559e31	−	3.71423e30i	−0.477620	−	0.176413i
$963$			1.23203e31i			0.578824i
$964$	−1.77732e30	−	1.52035e30i	−0.0825956	−	0.0706537i
$965$			2.16417e30i			0.0994845i
$966$	−3.42904e29	+	9.28378e29i	−0.0155924	+	0.0422148i
$967$	−1.64628e31			−0.740499			−0.370250	−	0.928932i	$-0.620728\pi$
$967$	−1.64628e31			−0.740499			−0.370250	+	0.928932i	$0.620728\pi$
$968$	−9.93357e30	−	1.77859e31i	−0.441992	−	0.791381i
$969$	−4.77069e31			−2.09982
$970$	2.12898e30	−	5.76401e30i	0.0926977	−	0.250970i
$971$			3.20354e31i			1.37984i	0.723887	+	0.689918i	$0.242354\pi$
$971$			3.20354e31i			1.37984i	−0.723887	+	0.689918i	$0.757646\pi$
$972$	1.71798e31	−	2.00835e31i	0.732019	−	0.855745i
$973$		−	2.31586e31i		−	0.976176i
$974$	3.10764e31	+	1.14783e31i	1.29587	+	0.478640i
$975$	−8.06196e30			−0.332577
$976$	−4.11409e29	+	6.45098e28i	−0.0167900	+	0.00263271i
$977$	−3.74614e31			−1.51249			−0.756243	−	0.654291i	$-0.772967\pi$
$977$	−3.74614e31			−1.51249			−0.756243	+	0.654291i	$0.772967\pi$
$978$	4.56691e30	+	1.68683e30i	0.182417	+	0.0673771i
$979$		−	3.32455e30i		−	0.131375i
$980$	2.37055e30	−	2.77123e30i	0.0926778	−	0.108342i
$981$			1.31088e31i			0.507037i
$982$	−5.55110e30	+	1.50290e31i	−0.212426	+	0.575123i
$983$	4.49119e31			1.70039			0.850197	−	0.526465i	$-0.176483\pi$
$983$	4.49119e31			1.70039			0.850197	+	0.526465i	$0.176483\pi$
$984$	−4.86027e30	+	2.71449e30i	−0.182059	+	0.101681i
$985$	5.52843e28			0.00204890
$986$	1.27458e31	−	3.45080e31i	0.467369	−	1.26536i
$987$		−	6.59087e31i		−	2.39118i
$988$	6.60430e30	+	5.64943e30i	0.237071	+	0.202795i
$989$			1.21565e30i			0.0431765i
$990$	1.11921e30	+	4.13391e29i	0.0393318	+	0.0145275i
$991$	−4.53920e31			−1.57836			−0.789179	−	0.614163i	$-0.789494\pi$
$991$	−4.53920e31			−1.57836			−0.789179	+	0.614163i	$0.789494\pi$
$992$	8.55881e30	−	4.25982e31i	0.294470	−	1.46561i
$993$	1.87286e31			0.637587
$994$	2.33364e31	+	8.61950e30i	0.786099	+	0.290352i
$995$		−	2.01158e30i		−	0.0670494i
$996$	1.47929e31	+	1.26541e31i	0.487898	+	0.417357i
$997$		−	4.79551e31i		−	1.56508i	−0.622603	−	0.782538i	$-0.713925\pi$
$997$		−	4.79551e31i		−	1.56508i	0.622603	−	0.782538i	$-0.286075\pi$
$998$	−6.22457e30	+	1.68524e31i	−0.201020	+	0.544241i
$999$	2.64827e31			0.846301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.22.b.a.5.3	✓	20
4.3	odd	2		32.22.b.a.17.4		20
8.3	odd	2		32.22.b.a.17.17		20
8.5	even	2	inner	8.22.b.a.5.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.22.b.a.5.3	✓	20	1.1	even	1	trivial
8.22.b.a.5.4	yes	20	8.5	even	2	inner
32.22.b.a.17.4		20	4.3	odd	2
32.22.b.a.17.17		20	8.3	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)

\(f(q)\)	\(=\)	\(q+(-1358.45 - 501.755i) q^{2} +131342. i q^{3} +(1.59363e6 + 1.36322e6i) q^{4} -4.61121e6i q^{5} +(6.59016e7 - 1.78422e8i) q^{6} -9.67293e8 q^{7} +(-1.48087e9 - 2.65149e9i) q^{8} -6.79041e9 q^{9} +O(q^{10})\)	\(q+(-1358.45 - 501.755i) q^{2} +131342. i q^{3} +(1.59363e6 + 1.36322e6i) q^{4} -4.61121e6i q^{5} +(6.59016e7 - 1.78422e8i) q^{6} -9.67293e8 q^{7} +(-1.48087e9 - 2.65149e9i) q^{8} -6.79041e9 q^{9} +(-2.31370e9 + 6.26411e9i) q^{10} +2.63123e10i q^{11} +(-1.79049e11 + 2.09311e11i) q^{12} +1.34734e11i q^{13} +(1.31402e12 + 4.85345e11i) q^{14} +6.05646e11 q^{15} +(6.81298e11 + 4.34496e12i) q^{16} -1.18091e13 q^{17} +(9.22445e12 + 3.40712e12i) q^{18} -3.07582e13i q^{19} +(6.28610e12 - 7.34858e12i) q^{20} -1.27046e14i q^{21} +(1.32023e13 - 3.57440e13i) q^{22} +5.37921e12 q^{23} +(3.48252e14 - 1.94501e14i) q^{24} +4.55574e14 q^{25} +(6.76036e13 - 1.83030e14i) q^{26} +4.82018e14i q^{27} +(-1.54151e15 - 1.31864e15i) q^{28} -2.15109e15i q^{29} +(-8.22741e14 - 3.03886e14i) q^{30} +6.82197e15 q^{31} +(1.25459e15 - 6.24426e15i) q^{32} -3.45591e15 q^{33} +(1.60421e16 + 5.92529e15i) q^{34} +4.46039e15i q^{35} +(-1.08214e16 - 9.25683e15i) q^{36} -5.49413e16i q^{37} +(-1.54331e16 + 4.17835e16i) q^{38} -1.76963e16 q^{39} +(-1.22266e16 + 6.82862e15i) q^{40} -1.39562e16 q^{41} +(-6.37462e16 + 1.72586e17i) q^{42} +2.25991e17i q^{43} +(-3.58695e16 + 4.19322e16i) q^{44} +3.13120e16i q^{45} +(-7.30740e15 - 2.69905e15i) q^{46} +5.18777e17 q^{47} +(-5.70676e17 + 8.94832e16i) q^{48} +3.77110e17 q^{49} +(-6.18876e17 - 2.28587e17i) q^{50} -1.55103e18i q^{51} +(-1.83673e17 + 2.14717e17i) q^{52} -8.95247e17i q^{53} +(2.41855e17 - 6.54799e17i) q^{54} +1.21331e17 q^{55} +(1.43244e18 + 2.56477e18i) q^{56} +4.03984e18 q^{57} +(-1.07932e18 + 2.92215e18i) q^{58} -7.68392e18i q^{59} +(9.65179e17 + 8.25630e17i) q^{60} +9.46865e16i q^{61} +(-9.26733e18 - 3.42296e18i) q^{62} +6.56832e18 q^{63} +(-4.83740e18 + 7.85304e18i) q^{64} +6.21287e17 q^{65} +(4.69469e18 + 1.73402e18i) q^{66} +8.03267e18i q^{67} +(-1.88194e19 - 1.60984e19i) q^{68} +7.06516e17i q^{69} +(2.23802e18 - 6.05923e18i) q^{70} +1.77595e19 q^{71} +(1.00557e19 + 1.80047e19i) q^{72} -2.77572e19 q^{73} +(-2.75671e19 + 7.46351e19i) q^{74} +5.98361e19i q^{75} +(4.19302e19 - 4.90173e19i) q^{76} -2.54517e19i q^{77} +(2.40395e19 + 8.87920e18i) q^{78} -6.72796e19 q^{79} +(2.00355e19 - 3.14161e18i) q^{80} -1.34339e20 q^{81} +(1.89588e19 + 7.00259e18i) q^{82} -7.06740e19i q^{83} +(1.73192e20 - 2.02466e20i) q^{84} +5.44543e19i q^{85} +(1.13392e20 - 3.06998e20i) q^{86} +2.82529e20 q^{87} +(6.97667e19 - 3.89652e19i) q^{88} -1.26350e20 q^{89} +(1.57110e19 - 4.25358e19i) q^{90} -1.30327e20i q^{91} +(8.57249e18 + 7.33305e18i) q^{92} +8.96013e20i q^{93} +(-7.04734e20 - 2.60299e20i) q^{94} -1.41832e20 q^{95} +(8.20135e20 + 1.64781e20i) q^{96} -9.20165e20 q^{97} +(-5.12286e20 - 1.89217e20i) q^{98} -1.78671e20i 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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