LMFDB - Embedded newform 8.22.b.a.5.5

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			5.5
Root			$0.500000 + 21396.5i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.22.b.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-962.766 - 1081.77i) q^{2} -85585.8i q^{3} +(-243314. + 2.08299e6i) q^{4} +2.31314e7i q^{5} +(-9.25844e7 + 8.23991e7i) q^{6} -3.19239e8 q^{7} +(2.48758e9 - 1.74222e9i) q^{8} +3.13542e9 q^{9} +O(q^{10})$	\(q+(-962.766 - 1081.77i) q^{2} -85585.8i q^{3} +(-243314. + 2.08299e6i) q^{4} +2.31314e7i q^{5} +(-9.25844e7 + 8.23991e7i) q^{6} -3.19239e8 q^{7} +(2.48758e9 - 1.74222e9i) q^{8} +3.13542e9 q^{9} +(2.50229e10 - 2.22701e10i) q^{10} -6.15505e10i q^{11} +(1.78274e11 + 2.08242e10i) q^{12} +1.45426e11i q^{13} +(3.07353e11 + 3.45344e11i) q^{14} +1.97972e12 q^{15} +(-4.27964e12 - 1.01364e12i) q^{16} +9.09430e12 q^{17} +(-3.01868e12 - 3.39182e12i) q^{18} -2.56378e13i q^{19} +(-4.81824e13 - 5.62817e12i) q^{20} +2.73223e13i q^{21} +(-6.65837e13 + 5.92588e13i) q^{22} -3.28653e14 q^{23} +(-1.49109e14 - 2.12901e14i) q^{24} -5.82225e13 q^{25} +(1.57317e14 - 1.40011e14i) q^{26} -1.16361e15i q^{27} +(7.76752e13 - 6.64971e14i) q^{28} -6.87857e14i q^{29} +(-1.90600e15 - 2.14160e15i) q^{30} -4.52295e15 q^{31} +(3.02377e15 + 5.60550e15i) q^{32} -5.26785e15 q^{33} +(-8.75569e15 - 9.83797e15i) q^{34} -7.38443e15i q^{35} +(-7.62891e14 + 6.53105e15i) q^{36} +1.80364e15i q^{37} +(-2.77343e16 + 2.46832e16i) q^{38} +1.24464e16 q^{39} +(4.03000e16 + 5.75410e16i) q^{40} +1.56600e17 q^{41} +(2.95566e16 - 2.63050e16i) q^{42} -1.27330e17i q^{43} +(1.28209e17 + 1.49761e16i) q^{44} +7.25266e16i q^{45} +(3.16416e17 + 3.55528e17i) q^{46} -2.70417e17 q^{47} +(-8.67532e16 + 3.66277e17i) q^{48} -4.56632e17 q^{49} +(5.60547e16 + 6.29836e16i) q^{50} -7.78343e17i q^{51} +(-3.02920e17 - 3.53840e16i) q^{52} -2.47963e18i q^{53} +(-1.25876e18 + 1.12028e18i) q^{54} +1.42375e18 q^{55} +(-7.94131e17 + 5.56185e17i) q^{56} -2.19423e18 q^{57} +(-7.44105e17 + 6.62246e17i) q^{58} -2.19093e18i q^{59} +(-4.81692e17 + 4.12373e18i) q^{60} -8.68847e18i q^{61} +(4.35455e18 + 4.89281e18i) q^{62} -1.00095e18 q^{63} +(3.15270e18 - 8.66782e18i) q^{64} -3.36389e18 q^{65} +(5.07171e18 + 5.69862e18i) q^{66} -1.31826e19i q^{67} +(-2.21277e18 + 1.89433e19i) q^{68} +2.81280e19i q^{69} +(-7.98828e18 + 7.10948e18i) q^{70} -6.01424e18 q^{71} +(7.79960e18 - 5.46260e18i) q^{72} +3.87079e19 q^{73} +(1.95113e18 - 1.73649e18i) q^{74} +4.98302e18i q^{75} +(5.34033e19 + 6.23803e18i) q^{76} +1.96493e19i q^{77} +(-1.19829e19 - 1.34641e19i) q^{78} +7.07237e19 q^{79} +(2.34469e19 - 9.89940e19i) q^{80} -6.67905e19 q^{81} +(-1.50769e20 - 1.69405e20i) q^{82} +3.61780e19i q^{83} +(-5.69121e19 - 6.64789e18i) q^{84} +2.10363e20i q^{85} +(-1.37742e20 + 1.22589e20i) q^{86} -5.88708e19 q^{87} +(-1.07235e20 - 1.53112e20i) q^{88} -4.11242e20 q^{89} +(7.84573e19 - 6.98262e19i) q^{90} -4.64255e19i q^{91} +(7.99657e19 - 6.84580e20i) q^{92} +3.87101e20i q^{93} +(2.60349e20 + 2.92530e20i) q^{94} +5.93037e20 q^{95} +(4.79751e20 - 2.58792e20i) q^{96} +1.14761e20 q^{97} +(4.39630e20 + 4.93973e20i) q^{98} -1.92987e20i 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 $

$2$	−962.766	−	1081.77i	−0.664823	−	0.747001i
$2$	−962.766	−	1081.77i	−0.664823	−	0.747001i
$3$		−	85585.8i		−	0.836813i	−0.908260	−	0.418407i	$-0.862589\pi$
$3$		−	85585.8i		−	0.836813i	0.908260	−	0.418407i	$-0.137411\pi$
$4$	−243314.	+	2.08299e6i	−0.116021	+	0.993247i
$5$			2.31314e7i			1.05929i	0.848219	+	0.529646i	$0.177675\pi$
$5$			2.31314e7i			1.05929i	−0.848219	+	0.529646i	$0.822325\pi$
$6$	−9.25844e7	+	8.23991e7i	−0.625100	+	0.556333i
$7$	−3.19239e8			−0.427156			−0.213578	−	0.976926i	$-0.568512\pi$
$7$	−3.19239e8			−0.427156			−0.213578	+	0.976926i	$0.568512\pi$
$8$	2.48758e9	−	1.74222e9i	0.819090	−	0.573665i
$9$	3.13542e9			0.299744
$10$	2.50229e10	−	2.22701e10i	0.791293	−	0.704242i
$11$		−	6.15505e10i		−	0.715498i	−0.933818	−	0.357749i	$-0.883544\pi$
$11$		−	6.15505e10i		−	0.715498i	0.933818	−	0.357749i	$-0.116456\pi$
$12$	1.78274e11	+	2.08242e10i	0.831162	+	0.0970879i
$13$			1.45426e11i			0.292574i	0.989242	+	0.146287i	$0.0467323\pi$
$13$			1.45426e11i			0.292574i	−0.989242	+	0.146287i	$0.953268\pi$
$14$	3.07353e11	+	3.45344e11i	0.283983	+	0.319086i
$15$	1.97972e12			0.886430
$16$	−4.27964e12	−	1.01364e12i	−0.973078	−	0.230475i
$17$	9.09430e12			1.09410			0.547048	−	0.837101i	$-0.315751\pi$
$17$	9.09430e12			1.09410			0.547048	+	0.837101i	$0.315751\pi$
$18$	−3.01868e12	−	3.39182e12i	−0.199276	−	0.223909i
$19$		−	2.56378e13i		−	0.959330i	−0.877452	−	0.479665i	$-0.840758\pi$
$19$		−	2.56378e13i		−	0.959330i	0.877452	−	0.479665i	$-0.159242\pi$
$20$	−4.81824e13	−	5.62817e12i	−1.05214	−	0.122900i
$21$			2.73223e13i			0.357450i
$22$	−6.65837e13	+	5.92588e13i	−0.534478	+	0.475680i
$23$	−3.28653e14			−1.65423			−0.827114	−	0.562035i	$-0.810019\pi$
$23$	−3.28653e14			−1.65423			−0.827114	+	0.562035i	$0.810019\pi$
$24$	−1.49109e14	−	2.12901e14i	−0.480051	−	0.685425i
$25$	−5.82225e13			−0.122101
$26$	1.57317e14	−	1.40011e14i	0.218553	−	0.194510i
$27$		−	1.16361e15i		−	1.08764i
$28$	7.76752e13	−	6.64971e14i	0.0495591	−	0.424271i
$29$		−	6.87857e14i		−	0.303612i	−0.988410	−	0.151806i	$-0.951491\pi$
$29$		−	6.87857e14i		−	0.303612i	0.988410	−	0.151806i	$-0.0485089\pi$
$30$	−1.90600e15	−	2.14160e15i	−0.589319	−	0.662164i
$31$	−4.52295e15			−0.991116			−0.495558	−	0.868575i	$-0.665036\pi$
$31$	−4.52295e15			−0.991116			−0.495558	+	0.868575i	$0.665036\pi$
$32$	3.02377e15	+	5.60550e15i	0.474760	+	0.880115i
$33$	−5.26785e15			−0.598739
$34$	−8.75569e15	−	9.83797e15i	−0.727380	−	0.817291i
$35$		−	7.38443e15i		−	0.452483i
$36$	−7.62891e14	+	6.53105e15i	−0.0347765	+	0.297719i
$37$			1.80364e15i			0.0616642i	0.999525	+	0.0308321i	$0.00981571\pi$
$37$			1.80364e15i			0.0616642i	−0.999525	+	0.0308321i	$0.990184\pi$
$38$	−2.77343e16	+	2.46832e16i	−0.716621	+	0.637785i
$39$	1.24464e16			0.244830
$40$	4.03000e16	+	5.75410e16i	0.607680	+	0.867656i
$41$	1.56600e17			1.82205			0.911026	−	0.412350i	$-0.135292\pi$
$41$	1.56600e17			1.82205			0.911026	+	0.412350i	$0.135292\pi$
$42$	2.95566e16	−	2.63050e16i	0.267015	−	0.237641i
$43$		−	1.27330e17i		−	0.898489i	−0.893409	−	0.449244i	$-0.851693\pi$
$43$		−	1.27330e17i		−	0.898489i	0.893409	−	0.449244i	$-0.148307\pi$
$44$	1.28209e17	+	1.49761e16i	0.710667	+	0.0830128i
$45$			7.25266e16i			0.317516i
$46$	3.16416e17	+	3.55528e17i	1.09977	+	1.23571i
$47$	−2.70417e17			−0.749907			−0.374953	−	0.927044i	$-0.622341\pi$
$47$	−2.70417e17			−0.749907			−0.374953	+	0.927044i	$0.622341\pi$
$48$	−8.67532e16	+	3.66277e17i	−0.192864	+	0.814285i
$49$	−4.56632e17			−0.817538
$50$	5.60547e16	+	6.29836e16i	0.0811759	+	0.0912099i
$51$		−	7.78343e17i		−	0.915554i
$52$	−3.02920e17	−	3.53840e16i	−0.290598	−	0.0339447i
$53$		−	2.47963e18i		−	1.94756i	−0.227497	−	0.973779i	$-0.573054\pi$
$53$		−	2.47963e18i		−	1.94756i	0.227497	−	0.973779i	$-0.426946\pi$
$54$	−1.25876e18	+	1.12028e18i	−0.812470	+	0.723090i
$55$	1.42375e18			0.757922
$56$	−7.94131e17	+	5.56185e17i	−0.349879	+	0.245045i
$57$	−2.19423e18			−0.802780
$58$	−7.44105e17	+	6.62246e17i	−0.226799	+	0.201848i
$59$		−	2.19093e18i		−	0.558061i	−0.960282	−	0.279031i	$-0.909987\pi$
$59$		−	2.19093e18i		−	0.558061i	0.960282	−	0.279031i	$-0.0900131\pi$
$60$	−4.81692e17	+	4.12373e18i	−0.102845	+	0.880444i
$61$		−	8.68847e18i		−	1.55948i	−0.626103	−	0.779741i	$-0.715351\pi$
$61$		−	8.68847e18i		−	1.55948i	0.626103	−	0.779741i	$-0.284649\pi$
$62$	4.35455e18	+	4.89281e18i	0.658917	+	0.740365i
$63$	−1.00095e18			−0.128037
$64$	3.15270e18	−	8.66782e18i	0.341816	−	0.939767i
$65$	−3.36389e18			−0.309921
$66$	5.07171e18	+	5.69862e18i	0.398055	+	0.447258i
$67$		−	1.31826e19i		−	0.883517i	−0.897134	−	0.441759i	$-0.854355\pi$
$67$		−	1.31826e19i		−	0.883517i	0.897134	−	0.441759i	$-0.145645\pi$
$68$	−2.21277e18	+	1.89433e19i	−0.126938	+	1.08671i
$69$			2.81280e19i			1.38428i
$70$	−7.98828e18	+	7.10948e18i	−0.338006	+	0.300821i
$71$	−6.01424e18			−0.219264			−0.109632	−	0.993972i	$-0.534967\pi$
$71$	−6.01424e18			−0.219264			−0.109632	+	0.993972i	$0.534967\pi$
$72$	7.79960e18	−	5.46260e18i	0.245517	−	0.171952i
$73$	3.87079e19			1.05417			0.527084	−	0.849813i	$-0.323285\pi$
$73$	3.87079e19			1.05417			0.527084	+	0.849813i	$0.323285\pi$
$74$	1.95113e18	−	1.73649e18i	0.0460632	−	0.0409958i
$75$			4.98302e18i			0.102176i
$76$	5.34033e19	+	6.23803e18i	0.952852	+	0.111302i
$77$			1.96493e19i			0.305629i
$78$	−1.19829e19	−	1.34641e19i	−0.162768	−	0.182888i
$79$	7.07237e19			0.840390			0.420195	−	0.907434i	$-0.361962\pi$
$79$	7.07237e19			0.840390			0.420195	+	0.907434i	$0.361962\pi$
$80$	2.34469e19	−	9.89940e19i	0.244140	−	1.03077i
$81$	−6.67905e19			−0.610410
$82$	−1.50769e20	−	1.69405e20i	−1.21134	−	1.36107i
$83$			3.61780e19i			0.255932i	0.991779	+	0.127966i	$0.0408449\pi$
$83$			3.61780e19i			0.255932i	−0.991779	+	0.127966i	$0.959155\pi$
$84$	−5.69121e19	−	6.64789e18i	−0.355036	−	0.0414717i
$85$			2.10363e20i			1.15897i
$86$	−1.37742e20	+	1.22589e20i	−0.671172	+	0.597336i
$87$	−5.88708e19			−0.254067
$88$	−1.07235e20	−	1.53112e20i	−0.410457	−	0.586057i
$89$	−4.11242e20			−1.39799			−0.698993	−	0.715129i	$-0.746368\pi$
$89$	−4.11242e20			−1.39799			−0.698993	+	0.715129i	$0.746368\pi$
$90$	7.84573e19	−	6.98262e19i	0.237185	−	0.211092i
$91$		−	4.64255e19i		−	0.124975i
$92$	7.99657e19	−	6.84580e20i	0.191925	−	1.64306i
$93$			3.87101e20i			0.829379i
$94$	2.60349e20	+	2.92530e20i	0.498555	+	0.560181i
$95$	5.93037e20			1.01621
$96$	4.79751e20	−	2.58792e20i	0.736492	−	0.397285i
$97$	1.14761e20			0.158013			0.0790065	−	0.996874i	$-0.474825\pi$
$97$	1.14761e20			0.158013			0.0790065	+	0.996874i	$0.474825\pi$
$98$	4.39630e20	+	4.93973e20i	0.543518	+	0.610702i
$99$		−	1.92987e20i		−	0.214466i
$100$	1.41663e19	−	1.21277e20i	0.0141663	−	0.121277i
$101$			6.94108e20i			0.625249i	0.949877	+	0.312624i	$0.101208\pi$
$101$			6.94108e20i			0.625249i	−0.949877	+	0.312624i	$0.898792\pi$
$102$	−8.41990e20	+	7.49362e20i	−0.683920	+	0.608682i
$103$	2.01390e21			1.47654			0.738271	−	0.674504i	$-0.235642\pi$
$103$	2.01390e21			1.47654			0.738271	+	0.674504i	$0.235642\pi$
$104$	2.53364e20	+	3.61757e20i	0.167840	+	0.239644i
$105$	−6.32003e20			−0.378644
$106$	−2.68240e21	+	2.38730e21i	−1.45483	+	1.29478i
$107$		−	2.98308e21i		−	1.46600i	−0.680226	−	0.733002i	$-0.738118\pi$
$107$		−	2.98308e21i		−	1.46600i	0.680226	−	0.733002i	$-0.261882\pi$
$108$	2.42378e21	+	2.83121e20i	1.08030	+	0.126189i
$109$			5.86573e20i			0.237325i	0.992935	+	0.118663i	$0.0378607\pi$
$109$			5.86573e20i			0.237325i	−0.992935	+	0.118663i	$0.962139\pi$
$110$	−1.37074e21	−	1.54017e21i	−0.503884	−	0.566169i
$111$	1.54366e20			0.0516014
$112$	1.36623e21	+	3.23593e20i	0.415656	+	0.0984488i
$113$	−6.67964e21			−1.85110			−0.925549	−	0.378627i	$-0.876396\pi$
$113$	−6.67964e21			−1.85110			−0.925549	+	0.378627i	$0.876396\pi$
$114$	2.11253e21	+	2.37366e21i	0.533707	+	0.599678i
$115$		−	7.60219e21i		−	1.75231i
$116$	1.43280e21	+	1.67365e20i	0.301562	+	0.0352254i
$117$			4.55971e20i			0.0876971i
$118$	−2.37009e21	+	2.10935e21i	−0.416872	+	0.371012i
$119$	−2.90325e21			−0.467350
$120$	4.92469e21	−	3.44910e21i	0.726066	−	0.508514i
$121$	3.61178e21			0.488062
$122$	−9.39895e21	+	8.36497e21i	−1.16493	+	1.03678i
$123$		−	1.34027e22i		−	1.52472i
$124$	1.10050e21	−	9.42127e21i	0.114990	−	0.984423i
$125$			9.68312e21i			0.929952i
$126$	9.63680e20	+	1.08280e21i	0.0851221	+	0.0956439i
$127$	1.32002e22			1.07310			0.536551	−	0.843868i	$-0.319727\pi$
$127$	1.32002e22			1.07310			0.536551	+	0.843868i	$0.319727\pi$
$128$	−1.24119e22	+	4.93458e21i	−0.929254	+	0.369442i
$129$	−1.08977e22			−0.751867
$130$	3.23864e21	+	3.63897e21i	0.206043	+	0.231512i
$131$			1.63529e22i			0.959942i	0.877284	+	0.479971i	$0.159353\pi$
$131$			1.63529e22i			0.959942i	−0.877284	+	0.479971i	$0.840647\pi$
$132$	1.28174e21	−	1.09729e22i	0.0694662	−	0.594695i
$133$			8.18459e21i			0.409784i
$134$	−1.42606e22	+	1.26917e22i	−0.659988	+	0.587382i
$135$	2.69158e22			1.15213
$136$	2.26228e22	−	1.58443e22i	0.896163	−	0.627645i
$137$	−1.45685e22			−0.534379			−0.267190	−	0.963644i	$-0.586095\pi$
$137$	−1.45685e22			−0.534379			−0.267190	+	0.963644i	$0.586095\pi$
$138$	3.04281e22	−	2.70807e22i	1.03406	−	0.920301i
$139$			2.57291e22i			0.810531i	0.914199	+	0.405265i	$0.132821\pi$
$139$			2.57291e22i			0.810531i	−0.914199	+	0.405265i	$0.867179\pi$
$140$	1.53817e22	+	1.79673e21i	0.449428	+	0.0524976i
$141$			2.31439e22i			0.627532i
$142$	5.79031e21	+	6.50604e21i	0.145772	+	0.163791i
$143$	8.95102e21			0.209336
$144$	−1.34185e22	−	3.17819e21i	−0.291674	−	0.0690834i
$145$	1.59111e22			0.321614
$146$	−3.72667e22	−	4.18732e22i	−0.700835	−	0.787465i
$147$			3.90812e22i			0.684126i
$148$	−3.75697e21	−	4.38851e20i	−0.0612477	−	0.00715434i
$149$			2.18678e21i			0.0332161i	0.999862	+	0.0166081i	$0.00528675\pi$
$149$			2.18678e21i			0.0332161i	−0.999862	+	0.0166081i	$0.994713\pi$
$150$	5.39050e21	−	4.79749e21i	0.0763257	−	0.0679290i
$151$	−7.75304e22			−1.02380			−0.511899	−	0.859046i	$-0.671058\pi$
$151$	−7.75304e22			−1.02380			−0.511899	+	0.859046i	$0.671058\pi$
$152$	−4.46668e22	−	6.37760e22i	−0.550335	−	0.785778i
$153$	2.85145e22			0.327948
$154$	2.12561e22	−	1.89177e22i	0.228306	−	0.203189i
$155$		−	1.04622e23i		−	1.04988i
$156$	−3.02837e21	+	2.59256e22i	−0.0284054	+	0.243176i
$157$		−	4.72811e22i		−	0.414707i	−0.978266	−	0.207353i	$-0.933515\pi$
$157$		−	4.72811e22i		−	0.414707i	0.978266	−	0.207353i	$-0.0664850\pi$
$158$	−6.80904e22	−	7.65070e22i	−0.558710	−	0.627772i
$159$	−2.12221e23			−1.62974
$160$	−1.29663e23	+	6.99439e22i	−0.932300	+	0.502910i
$161$	1.04919e23			0.706613
$162$	6.43036e22	+	7.22521e22i	0.405815	+	0.455977i
$163$			1.19323e23i			0.705919i	0.935639	+	0.352959i	$0.114825\pi$
$163$			1.19323e23i			0.705919i	−0.935639	+	0.352959i	$0.885175\pi$
$164$	−3.81029e22	+	3.26196e23i	−0.211396	+	1.80975i
$165$		−	1.21853e23i		−	0.634240i
$166$	3.91364e22	−	3.48310e22i	0.191182	−	0.170150i
$167$	1.59868e23			0.733225			0.366613	−	0.930374i	$-0.380517\pi$
$167$	1.59868e23			0.733225			0.366613	+	0.930374i	$0.380517\pi$
$168$	4.76016e22	+	6.79664e22i	0.205057	+	0.292783i
$169$	2.25916e23			0.914401
$170$	2.27566e23	−	2.02531e23i	0.865751	−	0.770509i
$171$		−	8.03854e22i		−	0.287553i
$172$	2.65227e23	+	3.09812e22i	0.892421	+	0.104244i
$173$		−	6.05098e23i		−	1.91576i	−0.287162	−	0.957882i	$-0.592712\pi$
$173$		−	6.05098e23i		−	1.91576i	0.287162	−	0.957882i	$-0.407288\pi$
$174$	5.66788e22	+	6.36849e22i	0.168909	+	0.189788i
$175$	1.85869e22			0.0521564
$176$	−6.23901e22	+	2.63414e23i	−0.164904	+	0.696236i
$177$	−1.87512e23			−0.466993
$178$	3.95930e23	+	4.44871e23i	0.929413	+	1.04430i
$179$			8.43189e23i			1.86624i	0.359562	+	0.933121i	$0.382926\pi$
$179$			8.43189e23i			1.86624i	−0.359562	+	0.933121i	$0.617074\pi$
$180$	−1.51072e23	−	1.76467e22i	−0.315372	−	0.0368385i
$181$		−	2.75450e23i		−	0.542523i	−0.962506	−	0.271261i	$-0.912559\pi$
$181$		−	2.75450e23i		−	0.542523i	0.962506	−	0.271261i	$-0.0874408\pi$
$182$	−5.02219e22	+	4.46969e22i	−0.0933562	+	0.0830860i
$183$	−7.43610e23			−1.30499
$184$	−8.17549e23	+	5.72586e23i	−1.35496	+	0.948973i
$185$	−4.17207e22			−0.0653204
$186$	4.18755e23	−	3.72688e23i	0.619547	−	0.551390i
$187$		−	5.59759e23i		−	0.782824i
$188$	6.57963e22	−	5.63277e23i	0.0870049	−	0.744842i
$189$			3.71468e23i			0.464593i
$190$	−5.70957e23	−	6.41532e23i	−0.675601	−	0.759111i
$191$	4.33862e23			0.485849			0.242924	−	0.970045i	$-0.421893\pi$
$191$	4.33862e23			0.485849			0.242924	+	0.970045i	$0.421893\pi$
$192$	−7.41842e23	−	2.69826e23i	−0.786409	−	0.286036i
$193$	1.33285e24			1.33792			0.668960	−	0.743299i	$-0.266740\pi$
$193$	1.33285e24			1.33792			0.668960	+	0.743299i	$0.266740\pi$
$194$	−1.10488e23	−	1.24146e23i	−0.105051	−	0.118036i
$195$			2.87901e23i			0.259346i
$196$	1.11105e23	−	9.51160e23i	0.0948515	−	0.812017i
$197$		−	4.36913e23i		−	0.353590i	−0.984248	−	0.176795i	$-0.943427\pi$
$197$		−	4.36913e23i		−	0.353590i	0.984248	−	0.176795i	$-0.0565730\pi$
$198$	−2.08768e23	+	1.85801e23i	−0.160206	+	0.142582i
$199$	−1.90595e23			−0.138725			−0.0693624	−	0.997592i	$-0.522096\pi$
$199$	−1.90595e23			−0.138725			−0.0693624	+	0.997592i	$0.522096\pi$
$200$	−1.44833e23	+	1.01437e23i	−0.100012	+	0.0700454i
$201$	−1.12824e24			−0.739339
$202$	7.50868e23	−	6.68264e23i	0.467061	−	0.415680i
$203$			2.19591e23i			0.129690i
$204$	1.62128e24	+	1.89381e23i	0.909371	+	0.106224i
$205$			3.62237e24i			1.93009i
$206$	−1.93891e24	−	2.17858e24i	−0.981640	−	1.10298i
$207$	−1.03047e24			−0.495844
$208$	1.47409e23	−	6.22370e23i	0.0674310	−	0.284697i
$209$	−1.57802e24			−0.686399
$210$	6.08471e23	+	6.83683e23i	0.251731	+	0.282847i
$211$			1.64897e24i			0.649002i	0.945885	+	0.324501i	$0.105196\pi$
$211$			1.64897e24i			0.649002i	−0.945885	+	0.324501i	$0.894804\pi$
$212$	5.16504e24	+	6.03328e23i	1.93441	+	0.225958i
$213$			5.14734e23i			0.183483i
$214$	−3.22702e24	+	2.87201e24i	−1.09511	+	0.974633i
$215$	2.94532e24			0.951763
$216$	−2.02726e24	−	2.89456e24i	−0.623943	−	0.890877i
$217$	1.44390e24			0.423361
$218$	6.34539e23	−	5.64733e23i	0.177282	−	0.157779i
$219$		−	3.31285e24i		−	0.882142i
$220$	−3.46417e23	+	2.96565e24i	−0.0879349	+	0.752804i
$221$			1.32254e24i			0.320104i
$222$	−1.48619e23	−	1.66989e23i	−0.0343058	−	0.0385463i
$223$	6.12693e24			1.34909			0.674546	−	0.738232i	$-0.264339\pi$
$223$	6.12693e24			1.34909			0.674546	+	0.738232i	$0.264339\pi$
$224$	−9.65305e23	−	1.78949e24i	−0.202796	−	0.375947i
$225$	−1.82552e23			−0.0365991
$226$	6.43094e24	+	7.22586e24i	1.23065	+	1.38277i
$227$		−	6.30984e24i		−	1.15278i	−0.817174	−	0.576390i	$-0.804461\pi$
$227$		−	6.30984e24i		−	1.15278i	0.817174	−	0.576390i	$-0.195539\pi$
$228$	5.33887e23	−	4.57056e24i	0.0931394	−	0.797359i
$229$			1.77844e24i			0.296324i	0.988963	+	0.148162i	$0.0473356\pi$
$229$			1.77844e24i			0.296324i	−0.988963	+	0.148162i	$0.952664\pi$
$230$	−8.22384e24	+	7.31913e24i	−1.30898	+	1.16498i
$231$	1.68170e24			0.255755
$232$	−1.19840e24	−	1.71110e24i	−0.174172	−	0.248686i
$233$	−1.03763e25			−1.44147			−0.720736	−	0.693210i	$-0.756196\pi$
$233$	−1.03763e25			−1.44147			−0.720736	+	0.693210i	$0.756196\pi$
$234$	4.93257e23	−	4.38993e23i	0.0655098	−	0.0583031i
$235$		−	6.25512e24i		−	0.794371i
$236$	4.56368e24	+	5.33083e23i	0.554293	+	0.0647468i
$237$		−	6.05295e24i		−	0.703249i
$238$	2.79516e24	+	3.14066e24i	0.310705	+	0.349111i
$239$	−9.41422e24			−1.00140			−0.500699	−	0.865622i	$-0.666924\pi$
$239$	−9.41422e24			−1.00140			−0.500699	+	0.865622i	$0.666924\pi$
$240$	−8.47248e24	−	2.00672e24i	−0.862566	−	0.204300i
$241$	−8.85778e24			−0.863269			−0.431634	−	0.902049i	$-0.642063\pi$
$241$	−8.85778e24			−0.863269			−0.431634	+	0.902049i	$0.642063\pi$
$242$	−3.47730e24	−	3.90713e24i	−0.324475	−	0.364583i
$243$		−	6.45541e24i		−	0.576843i
$244$	1.80980e25	+	2.11402e24i	1.54895	+	0.180933i
$245$		−	1.05625e25i		−	0.866012i
$246$	−1.44987e25	+	1.29037e25i	−1.13897	+	1.01367i
$247$	3.72839e24			0.280675
$248$	−1.12512e25	+	7.87999e24i	−0.811813	+	0.568569i
$249$	3.09633e24			0.214168
$250$	1.04749e25	−	9.32259e24i	0.694675	−	0.618253i
$251$			7.73500e24i			0.491911i	0.969281	+	0.245955i	$0.0791017\pi$
$251$			7.73500e24i			0.491911i	−0.969281	+	0.245955i	$0.920898\pi$
$252$	2.43545e23	−	2.08497e24i	0.0148550	−	0.127173i
$253$			2.02288e25i			1.18360i
$254$	−1.27087e25	−	1.42796e25i	−0.713423	−	0.801609i
$255$	1.80041e25			0.969840
$256$	1.72879e25	+	8.67603e24i	0.893763	+	0.448540i
$257$	6.43055e24			0.319117			0.159559	−	0.987188i	$-0.448993\pi$
$257$	6.43055e24			0.319117			0.159559	+	0.987188i	$0.448993\pi$
$258$	1.04919e25	+	1.17888e25i	0.499859	+	0.561646i
$259$		−	5.75794e23i		−	0.0263402i
$260$	8.18481e23	−	7.00695e24i	0.0359574	−	0.307828i
$261$		−	2.15672e24i		−	0.0910058i
$262$	1.76901e25	−	1.57440e25i	0.717078	−	0.638191i
$263$	−1.78031e25			−0.693360			−0.346680	−	0.937983i	$-0.612691\pi$
$263$	−1.78031e25			−0.693360			−0.346680	+	0.937983i	$0.612691\pi$
$264$	−1.31042e25	+	9.17777e24i	−0.490421	+	0.343476i
$265$	5.73572e25			2.06303
$266$	8.85387e24	−	7.87985e24i	0.306109	−	0.272434i
$267$			3.51965e25i			1.16985i
$268$	2.74592e25	+	3.20750e24i	0.877551	+	0.102507i
$269$			3.84283e25i			1.18101i	0.807035	+	0.590503i	$0.201071\pi$
$269$			3.84283e25i			1.18101i	−0.807035	+	0.590503i	$0.798929\pi$
$270$	−2.59136e25	−	2.91168e25i	−0.765964	−	0.860644i
$271$	−2.68472e25			−0.763345			−0.381673	−	0.924298i	$-0.624652\pi$
$271$	−2.68472e25			−0.763345			−0.381673	+	0.924298i	$0.624652\pi$
$272$	−3.89204e25	−	9.21834e24i	−1.06464	−	0.252162i
$273$	−3.97337e24			−0.104580
$274$	1.40261e25	+	1.57598e25i	0.355267	+	0.399182i
$275$			3.58363e24i			0.0873634i
$276$	−5.85904e25	−	6.84393e24i	−1.37493	−	0.160605i
$277$		−	4.18944e25i		−	0.946495i	−0.880929	−	0.473248i	$-0.843082\pi$
$277$		−	4.18944e25i		−	0.946495i	0.880929	−	0.473248i	$-0.156918\pi$
$278$	2.78331e25	−	2.47711e25i	0.605467	−	0.538859i
$279$	−1.41814e25			−0.297081
$280$	−1.28653e25	−	1.83693e25i	−0.259574	−	0.370624i
$281$	−3.19530e25			−0.621005			−0.310503	−	0.950573i	$-0.600497\pi$
$281$	−3.19530e25			−0.621005			−0.310503	+	0.950573i	$0.600497\pi$
$282$	2.50364e25	−	2.22822e25i	0.468767	−	0.417198i
$283$			1.00824e26i			1.81889i	0.415822	+	0.909446i	$0.363494\pi$
$283$			1.00824e26i			1.81889i	−0.415822	+	0.909446i	$0.636506\pi$
$284$	1.46335e24	−	1.25276e25i	0.0254393	−	0.217784i
$285$		−	5.07556e25i		−	0.850380i
$286$	−8.61774e24	−	9.68298e24i	−0.139171	−	0.156374i
$287$	−4.99928e25			−0.778300
$288$	9.48080e24	+	1.75756e25i	0.142306	+	0.263809i
$289$	1.36143e25			0.197047
$290$	−1.53186e25	−	1.72122e25i	−0.213817	−	0.240246i
$291$		−	9.82195e24i		−	0.132227i
$292$	−9.41817e24	+	8.06282e25i	−0.122306	+	1.04705i
$293$		−	1.04014e26i		−	1.30311i	−0.758600	−	0.651557i	$-0.774116\pi$
$293$		−	1.04014e26i		−	1.30311i	0.758600	−	0.651557i	$-0.225884\pi$
$294$	4.22770e25	−	3.76261e25i	0.511043	−	0.454823i
$295$	5.06791e25			0.591151
$296$	3.14235e24	+	4.48670e24i	0.0353746	+	0.0505085i
$297$	−7.16206e25			−0.778207
$298$	2.36560e24	−	2.10536e24i	0.0248125	−	0.0220828i
$299$		−	4.77945e25i		−	0.483984i
$300$	−1.03796e25	−	1.21244e24i	−0.101486	−	0.0118546i
$301$			4.06488e25i			0.383795i
$302$	7.46437e25	+	8.38703e25i	0.680644	+	0.764778i
$303$	5.94058e25			0.523216
$304$	−2.59875e25	+	1.09721e26i	−0.221102	+	0.933504i
$305$	2.00976e26			1.65195
$306$	−2.74528e25	−	3.08462e25i	−0.218028	−	0.244978i
$307$		−	3.87077e25i		−	0.297060i	−0.988908	−	0.148530i	$-0.952546\pi$
$307$		−	3.87077e25i		−	0.297060i	0.988908	−	0.148530i	$-0.0474542\pi$
$308$	−4.09294e25	−	4.78095e24i	−0.303565	−	0.0354594i
$309$		−	1.72361e26i		−	1.23559i
$310$	−1.13177e26	+	1.00727e26i	−0.784263	+	0.697986i
$311$	−1.49312e26			−1.00025			−0.500127	−	0.865952i	$-0.666713\pi$
$311$	−1.49312e26			−1.00025			−0.500127	+	0.865952i	$0.666713\pi$
$312$	3.09613e25	−	2.16843e25i	0.200538	−	0.140450i
$313$	9.54625e25			0.597885			0.298942	−	0.954271i	$-0.403366\pi$
$313$	9.54625e25			0.597885			0.298942	+	0.954271i	$0.403366\pi$
$314$	−5.11474e25	+	4.55207e25i	−0.309786	+	0.275707i
$315$		−	2.31533e25i		−	0.135629i
$316$	−1.72081e25	+	1.47317e26i	−0.0975028	+	0.834714i
$317$			3.28521e26i			1.80070i	0.435170	+	0.900348i	$0.356688\pi$
$317$			3.28521e26i			1.80070i	−0.435170	+	0.900348i	$0.643312\pi$
$318$	2.04319e26	+	2.29575e26i	1.08349	+	1.21742i
$319$	−4.23380e25			−0.217234
$320$	2.00498e26	+	7.29261e25i	0.995488	+	0.362083i
$321$	−2.55309e26			−1.22677
$322$	−1.01012e26	−	1.13498e26i	−0.469773	−	0.527841i
$323$		−	2.33158e26i		−	1.04960i
$324$	1.62510e25	−	1.39124e26i	0.0708204	−	0.606288i
$325$		−	8.46704e24i		−	0.0357237i
$326$	1.29081e26	−	1.14880e26i	0.527322	−	0.469311i
$327$	5.02023e25			0.198597
$328$	3.89554e26	−	2.72832e26i	1.49242	−	1.04525i
$329$	8.63278e25			0.320327
$330$	−1.31817e26	+	1.17316e26i	−0.473778	+	0.421657i
$331$		−	3.04633e26i		−	1.06068i	−0.847786	−	0.530338i	$-0.822065\pi$
$331$		−	3.04633e26i		−	1.06068i	0.847786	−	0.530338i	$-0.177935\pi$
$332$	−7.53585e25	−	8.80261e24i	−0.254204	−	0.0296935i
$333$			5.65519e24i			0.0184834i
$334$	−1.53915e26	−	1.72940e26i	−0.487465	−	0.547720i
$335$	3.04931e26			0.935903
$336$	2.76950e25	−	1.16930e26i	0.0823832	−	0.347827i
$337$	−3.57096e26			−1.02961			−0.514804	−	0.857308i	$-0.672135\pi$
$337$	−3.57096e26			−1.02961			−0.514804	+	0.857308i	$0.672135\pi$
$338$	−2.17504e26	−	2.44390e26i	−0.607914	−	0.683058i
$339$			5.71683e26i			1.54902i
$340$	−4.38185e26	−	5.11843e25i	−1.15114	−	0.134465i
$341$			2.78390e26i			0.709142i
$342$	−8.69588e25	+	7.73924e25i	−0.214802	+	0.191172i
$343$	3.24084e26			0.776372
$344$	−2.21837e26	−	3.16744e26i	−0.515432	−	0.735943i
$345$	−6.50639e26			−1.46636
$346$	−6.54579e26	+	5.82568e26i	−1.43108	+	1.27364i
$347$		−	4.44596e24i		−	0.00942988i	−0.999989	−	0.00471494i	$-0.998499\pi$
$347$		−	4.44596e24i		−	0.00942988i	0.999989	−	0.00471494i	$-0.00150082\pi$
$348$	1.43241e25	−	1.22627e26i	0.0294771	−	0.252351i
$349$			2.40437e26i			0.480103i	0.970760	+	0.240052i	$0.0771644\pi$
$349$			2.40437e26i			0.480103i	−0.970760	+	0.240052i	$0.922836\pi$
$350$	−1.78948e25	−	2.01068e25i	−0.0346748	−	0.0389609i
$351$	1.69218e26			0.318216
$352$	3.45022e26	−	1.86115e26i	0.629721	−	0.339690i
$353$	3.42158e26			0.606167			0.303084	−	0.952964i	$-0.401984\pi$
$353$	3.42158e26			0.606167			0.303084	+	0.952964i	$0.401984\pi$
$354$	1.80531e26	+	2.02846e26i	0.310468	+	0.348844i
$355$		−	1.39118e26i		−	0.232265i
$356$	1.00061e26	−	8.56613e26i	0.162196	−	1.38854i
$357$			2.48477e26i			0.391085i
$358$	9.12139e26	−	8.11794e26i	1.39408	−	1.24072i
$359$	2.30610e26			0.342284			0.171142	−	0.985246i	$-0.445254\pi$
$359$	2.30610e26			0.342284			0.171142	+	0.985246i	$0.445254\pi$
$360$	1.26357e26	+	1.80415e26i	0.182148	+	0.260074i
$361$	5.69119e25			0.0796851
$362$	−2.97975e26	+	2.65194e26i	−0.405265	+	0.360682i
$363$		−	3.09117e26i		−	0.408417i
$364$	9.67039e25	+	1.12960e25i	0.124131	+	0.0144997i
$365$			8.95367e26i			1.11667i
$366$	7.15923e26	+	8.04417e26i	0.867590	+	0.974832i
$367$	−6.62349e26			−0.779997			−0.389999	−	0.920815i	$-0.627525\pi$
$367$	−6.62349e26			−0.779997			−0.389999	+	0.920815i	$0.627525\pi$
$368$	1.40652e27	+	3.33136e26i	1.60969	+	0.381258i
$369$	4.91007e26			0.546148
$370$	4.01673e25	+	4.51324e25i	0.0434265	+	0.0487944i
$371$			7.91595e26i			0.831911i
$372$	−8.06327e26	−	9.41869e25i	−0.823778	−	0.0962254i
$373$		−	3.93880e26i		−	0.391220i	−0.980682	−	0.195610i	$-0.937331\pi$
$373$		−	3.93880e26i		−	0.391220i	0.980682	−	0.195610i	$-0.0626687\pi$
$374$	−6.05532e26	+	5.38917e26i	−0.584770	+	0.520440i
$375$	8.28738e26			0.778196
$376$	−6.72684e26	+	4.71127e26i	−0.614241	+	0.430196i
$377$	1.00032e26			0.0888290
$378$	4.01844e26	−	3.57637e26i	0.347052	−	0.308872i
$379$		−	1.61789e27i		−	1.35906i	−0.733648	−	0.679529i	$-0.762184\pi$
$379$		−	1.61789e27i		−	1.35906i	0.733648	−	0.679529i	$-0.237816\pi$
$380$	−1.44294e26	+	1.23529e27i	−0.117902	+	1.00935i
$381$		−	1.12975e27i		−	0.897987i
$382$	−4.17708e26	−	4.69340e26i	−0.323004	−	0.362930i
$383$	−5.52449e26			−0.415628			−0.207814	−	0.978168i	$-0.566635\pi$
$383$	−5.52449e26			−0.415628			−0.207814	+	0.978168i	$0.566635\pi$
$384$	4.22330e26	+	1.06228e27i	0.309154	+	0.777612i
$385$	−4.54516e26			−0.323751
$386$	−1.28322e27	−	1.44184e27i	−0.889480	−	0.999427i
$387$		−	3.99234e26i		−	0.269316i
$388$	−2.79230e25	+	2.39047e26i	−0.0183328	+	0.156946i
$389$		−	1.52238e27i		−	0.972864i	−0.873718	−	0.486432i	$-0.838298\pi$
$389$		−	1.52238e27i		−	0.972864i	0.873718	−	0.486432i	$-0.161702\pi$
$390$	3.11444e26	−	2.77182e26i	0.193732	−	0.172419i
$391$	−2.98887e27			−1.80988
$392$	−1.13591e27	+	7.95555e26i	−0.669637	+	0.468993i
$393$	1.39957e27			0.803292
$394$	−4.72641e26	+	4.20646e26i	−0.264132	+	0.235075i
$395$			1.63594e27i			0.890219i
$396$	4.01990e26	+	4.69564e25i	0.213018	+	0.0248826i
$397$		−	1.82841e27i		−	0.943569i	−0.881714	−	0.471784i	$-0.843610\pi$
$397$		−	1.82841e27i		−	0.943569i	0.881714	−	0.471784i	$-0.156390\pi$
$398$	1.83498e26	+	2.06181e26i	0.0922274	+	0.103628i
$399$	7.00485e26			0.342912
$400$	2.49172e26	+	5.90167e25i	0.118814	+	0.0281413i
$401$	−1.20301e27			−0.558795			−0.279398	−	0.960175i	$-0.590135\pi$
$401$	−1.20301e27			−0.558795			−0.279398	+	0.960175i	$0.590135\pi$
$402$	1.08623e27	+	1.22050e27i	0.491529	+	0.552287i
$403$		−	6.57753e26i		−	0.289975i
$404$	−1.44582e27	−	1.68886e26i	−0.621026	−	0.0725420i
$405$		−	1.54495e27i		−	0.646603i
$406$	2.37547e26	−	2.11415e26i	0.0968784	−	0.0862208i
$407$	1.11015e26			0.0441206
$408$	−1.35605e27	−	1.93619e27i	−0.525222	−	0.749921i
$409$	1.95526e27			0.738090			0.369045	−	0.929412i	$-0.379685\pi$
$409$	1.95526e27			0.738090			0.369045	+	0.929412i	$0.379685\pi$
$410$	3.91858e27	−	3.48749e27i	1.44178	−	1.28317i
$411$			1.24686e27i			0.447176i
$412$	−4.90008e26	+	4.19492e27i	−0.171310	+	1.46657i
$413$			6.99430e26i			0.238379i
$414$	9.92098e26	+	1.11473e27i	0.329648	+	0.370396i
$415$	−8.36847e26			−0.271107
$416$	−8.15183e26	+	4.39733e26i	−0.257499	+	0.138902i
$417$	2.20205e27			0.678263
$418$	1.51927e27	+	1.70706e27i	0.456334	+	0.512741i
$419$			4.94852e27i			1.44953i	0.688994	+	0.724767i	$0.258053\pi$
$419$			4.94852e27i			1.44953i	−0.688994	+	0.724767i	$0.741947\pi$
$420$	1.53775e26	−	1.31645e27i	0.0439307	−	0.376087i
$421$			1.93164e27i			0.538225i	0.963109	+	0.269113i	$0.0867304\pi$
$421$			1.93164e27i			0.538225i	−0.963109	+	0.269113i	$0.913270\pi$
$422$	1.78381e27	−	1.58757e27i	0.484806	−	0.431472i
$423$	−8.47873e26			−0.224780
$424$	−4.32007e27	−	6.16827e27i	−1.11725	−	1.59522i
$425$	−5.29493e26			−0.133591
$426$	5.56825e26	−	4.95568e26i	0.137062	−	0.121984i
$427$			2.77370e27i			0.666142i
$428$	6.21372e27	+	7.25824e26i	1.45610	+	0.170087i
$429$		−	7.66081e26i		−	0.175175i
$430$	−2.83566e27	−	3.18617e27i	−0.632754	−	0.710968i
$431$	8.53161e26			0.185789			0.0928945	−	0.995676i	$-0.470388\pi$
$431$	8.53161e26			0.185789			0.0928945	+	0.995676i	$0.470388\pi$
$432$	−1.17948e27	+	4.97982e27i	−0.250674	+	1.05836i
$433$	−3.38217e26			−0.0701572			−0.0350786	−	0.999385i	$-0.511168\pi$
$433$	−3.38217e26			−0.0701572			−0.0350786	+	0.999385i	$0.511168\pi$
$434$	−1.39014e27	−	1.56198e27i	−0.281460	−	0.316251i
$435$		−	1.36176e27i		−	0.269131i
$436$	−1.22183e27	−	1.42721e26i	−0.235723	−	0.0275347i
$437$			8.42594e27i			1.58695i
$438$	−3.58375e27	+	3.18950e27i	−0.658961	+	0.586468i
$439$	3.73815e27			0.671087			0.335544	−	0.942025i	$-0.391080\pi$
$439$	3.73815e27			0.671087			0.335544	+	0.942025i	$0.391080\pi$
$440$	3.54168e27	−	2.48048e27i	0.620807	−	0.434794i
$441$	−1.43174e27			−0.245052
$442$	1.43069e27	−	1.27330e27i	0.239118	−	0.212813i
$443$			5.68467e27i			0.927825i	0.885881	+	0.463913i	$0.153555\pi$
$443$			5.68467e27i			0.927825i	−0.885881	+	0.463913i	$0.846445\pi$
$444$	−3.75594e25	+	3.21544e26i	−0.00598684	+	0.0512529i
$445$		−	9.51259e27i		−	1.48088i
$446$	−5.89880e27	−	6.62795e27i	−0.896908	−	1.00777i
$447$	1.87157e26			0.0277957
$448$	−1.00646e27	+	2.76711e27i	−0.146009	+	0.401427i
$449$	4.91257e27			0.696180			0.348090	−	0.937461i	$-0.386830\pi$
$449$	4.91257e27			0.696180			0.348090	+	0.937461i	$0.386830\pi$
$450$	1.75755e26	+	1.97480e26i	0.0243319	+	0.0273396i
$451$		−	9.63880e27i		−	1.30368i
$452$	1.62525e27	−	1.39136e28i	0.214766	−	1.83860i
$453$			6.63551e27i			0.856728i
$454$	−6.82581e27	+	6.07490e27i	−0.861128	+	0.766395i
$455$	1.07389e27			0.132385
$456$	−5.45832e27	+	3.82284e27i	−0.657549	+	0.460527i
$457$	−6.21823e27			−0.732060			−0.366030	−	0.930603i	$-0.619283\pi$
$457$	−6.21823e27			−0.732060			−0.366030	+	0.930603i	$0.619283\pi$
$458$	1.92387e27	−	1.71222e27i	0.221354	−	0.197003i
$459$		−	1.05822e28i		−	1.18999i
$460$	1.58353e28	+	1.84972e27i	1.74048	+	0.203305i
$461$			5.41641e27i			0.581905i	0.956738	+	0.290952i	$0.0939721\pi$
$461$			5.41641e27i			0.581905i	−0.956738	+	0.290952i	$0.906028\pi$
$462$	−1.61909e27	−	1.81922e27i	−0.170032	−	0.191049i
$463$	−1.01152e28			−1.03842			−0.519211	−	0.854646i	$-0.673774\pi$
$463$	−1.01152e28			−1.03842			−0.519211	+	0.854646i	$0.673774\pi$
$464$	−6.97239e26	+	2.94378e27i	−0.0699750	+	0.295439i
$465$	−8.95417e27			−0.878555
$466$	9.98997e27	+	1.12248e28i	0.958323	+	1.07678i
$467$		−	1.29588e28i		−	1.21545i	−0.794148	−	0.607724i	$-0.792083\pi$
$467$		−	1.29588e28i		−	1.21545i	0.794148	−	0.607724i	$-0.207917\pi$
$468$	−9.49782e26	−	1.10944e26i	−0.0871049	−	0.0101747i
$469$			4.20839e27i			0.377400i
$470$	−6.76662e27	+	6.02222e27i	−0.593396	+	0.528116i
$471$	−4.04659e27			−0.347032
$472$	−3.81708e27	−	5.45010e27i	−0.320141	−	0.457102i
$473$	−7.83724e27			−0.642867
$474$	−6.54792e27	+	5.82758e27i	−0.525328	+	0.467536i
$475$			1.49270e27i			0.117136i
$476$	7.06402e26	−	6.04745e27i	0.0542224	−	0.464194i
$477$		−	7.77469e27i		−	0.583768i
$478$	9.06370e27	+	1.01840e28i	0.665752	+	0.748045i
$479$	2.04998e28			1.47308			0.736539	−	0.676395i	$-0.236459\pi$
$479$	2.04998e28			1.47308			0.736539	+	0.676395i	$0.236459\pi$
$480$	5.98620e27	+	1.10973e28i	0.420841	+	0.780161i
$481$	−2.62296e26			−0.0180413
$482$	8.52797e27	+	9.58211e27i	0.573921	+	0.644863i
$483$		−	8.97956e27i		−	0.591303i
$484$	−8.78795e26	+	7.52330e27i	−0.0566254	+	0.484766i
$485$			2.65459e27i			0.167382i
$486$	−6.98329e27	+	6.21505e27i	−0.430902	+	0.383499i
$487$	3.13071e28			1.89055			0.945277	−	0.326268i	$-0.105791\pi$
$487$	3.13071e28			1.89055			0.945277	+	0.326268i	$0.105791\pi$
$488$	−1.51372e28	−	2.16132e28i	−0.894620	−	1.27736i
$489$	1.02124e28			0.590722
$490$	−1.14263e28	+	1.01692e28i	−0.646912	+	0.575745i
$491$			1.20085e28i			0.665477i	0.943019	+	0.332739i	$0.107973\pi$
$491$			1.20085e28i			0.665477i	−0.943019	+	0.332739i	$0.892027\pi$
$492$	2.79177e28	+	3.26106e27i	1.51442	+	0.176899i
$493$		−	6.25558e27i		−	0.332181i
$494$	−3.58957e27	−	4.03328e27i	−0.186599	−	0.209665i
$495$	4.46405e27			0.227182
$496$	1.93566e28	+	4.58465e27i	0.964433	+	0.228427i
$497$	1.91998e27			0.0936601
$498$	−2.98104e27	−	3.34952e27i	−0.142383	−	0.159983i
$499$			4.32273e27i			0.202163i	0.994878	+	0.101082i	$0.0322304\pi$
$499$			4.32273e27i			0.202163i	−0.994878	+	0.101082i	$0.967770\pi$
$500$	−2.01698e28	−	2.35604e27i	−0.923671	−	0.107894i
$501$		−	1.36824e28i		−	0.613573i
$502$	8.36752e27	−	7.44700e27i	0.367458	−	0.327034i
$503$	−1.46505e28			−0.630071			−0.315036	−	0.949080i	$-0.602016\pi$
$503$	−1.46505e28			−0.630071			−0.315036	+	0.949080i	$0.602016\pi$
$504$	−2.48994e27	+	1.74388e27i	−0.104874	+	0.0734505i
$505$	−1.60557e28			−0.662322
$506$	2.18829e28	−	1.94756e28i	0.884148	−	0.786882i
$507$		−	1.93352e28i		−	0.765183i
$508$	−3.21179e27	+	2.74959e28i	−0.124502	+	1.06586i
$509$			2.35798e28i			0.895373i	0.894191	+	0.447687i	$0.147752\pi$
$509$			2.35798e28i			0.895373i	−0.894191	+	0.447687i	$0.852248\pi$
$510$	−1.73338e28	−	1.94764e28i	−0.644772	−	0.724472i
$511$	−1.23571e28			−0.450294
$512$	−7.25870e27	−	2.70546e28i	−0.259134	−	0.965841i
$513$	−2.98323e28			−1.04341
$514$	−6.19112e27	−	6.95640e27i	−0.212157	−	0.238381i
$515$			4.65841e28i			1.56409i
$516$	2.65155e27	−	2.26997e28i	0.0872324	−	0.746790i
$517$			1.66443e28i			0.536557i
$518$	−6.22878e26	+	5.54355e26i	−0.0196762	+	0.0175116i
$519$	−5.17878e28			−1.60314
$520$	−8.36793e27	+	5.86065e27i	−0.253853	+	0.177791i
$521$	1.58835e28			0.472227			0.236114	−	0.971725i	$-0.424126\pi$
$521$	1.58835e28			0.472227			0.236114	+	0.971725i	$0.424126\pi$
$522$	−2.33309e27	+	2.07642e27i	−0.0679814	+	0.0605027i
$523$		−	7.21649e27i		−	0.206091i	−0.994677	−	0.103045i	$-0.967141\pi$
$523$		−	7.21649e27i		−	0.206091i	0.994677	−	0.103045i	$-0.0328587\pi$
$524$	−3.40628e28	−	3.97887e27i	−0.953459	−	0.111373i
$525$		−	1.59077e27i		−	0.0436452i
$526$	1.71402e28	+	1.92589e28i	0.460962	+	0.517941i
$527$	−4.11331e28			−1.08438
$528$	2.25445e28	+	5.33970e27i	0.582620	+	0.137994i
$529$	6.85411e28			1.73647
$530$	−5.52216e28	−	6.20475e28i	−1.37155	−	1.54109i
$531$		−	6.86949e27i		−	0.167275i
$532$	−1.70484e28	−	1.99142e27i	−0.407016	−	0.0475435i
$533$			2.27736e28i			0.533085i
$534$	3.80746e28	−	3.38860e28i	0.873881	−	0.777745i
$535$	6.90027e28			1.55293
$536$	−2.29670e28	−	3.27927e28i	−0.506843	−	0.723680i
$537$	7.21650e28			1.56170
$538$	4.15707e28	−	3.69975e28i	0.882213	−	0.785160i
$539$			2.81060e28i			0.584947i
$540$	−6.54897e27	+	5.60653e28i	−0.133672	+	1.14435i
$541$		−	6.44139e28i		−	1.28946i	−0.764410	−	0.644730i	$-0.776970\pi$
$541$		−	6.44139e28i		−	1.28946i	0.764410	−	0.644730i	$-0.223030\pi$
$542$	2.58476e28	+	2.90425e28i	0.507489	+	0.570220i
$543$	−2.35746e28			−0.453990
$544$	2.74991e28	+	5.09781e28i	0.519433	+	0.962931i
$545$	−1.35682e28			−0.251397
$546$	3.82542e27	+	4.29828e27i	0.0695275	+	0.0781217i
$547$			7.92936e28i			1.41375i	0.707341	+	0.706873i	$0.249895\pi$
$547$			7.92936e28i			1.41375i	−0.707341	+	0.706873i	$0.750105\pi$
$548$	3.54472e27	−	3.03461e28i	0.0619992	−	0.530770i
$549$		−	2.72420e28i		−	0.467444i
$550$	3.87667e27	−	3.45020e27i	0.0652606	−	0.0580812i
$551$	−1.76352e28			−0.291264
$552$	4.90053e28	+	6.99706e28i	0.794113	+	1.13385i
$553$	−2.25778e28			−0.358978
$554$	−4.53202e28	+	4.03345e28i	−0.707033	+	0.629252i
$555$			3.57070e27i			0.0546610i
$556$	−5.35935e28	−	6.26024e27i	−0.805057	−	0.0940386i
$557$			3.80649e28i			0.561106i	0.959839	+	0.280553i	$0.0905178\pi$
$557$			3.80649e28i			0.561106i	−0.959839	+	0.280553i	$0.909482\pi$
$558$	1.36534e28	+	1.53410e28i	0.197506	+	0.221919i
$559$	1.85171e28			0.262874
$560$	−7.48515e27	+	3.16027e28i	−0.104286	+	0.440302i
$561$	−4.79074e28			−0.655078
$562$	3.07633e28	+	3.45659e28i	0.412858	+	0.463891i
$563$			5.24146e28i			0.690421i	0.938525	+	0.345211i	$0.112193\pi$
$563$			5.24146e28i			0.690421i	−0.938525	+	0.345211i	$0.887807\pi$
$564$	−4.82085e28	−	5.63123e27i	−0.623294	−	0.0728069i
$565$		−	1.54509e29i		−	1.96086i
$566$	1.09069e29	−	9.70701e28i	1.35871	−	1.20924i
$567$	2.13221e28			0.260740
$568$	−1.49609e28	+	1.04781e28i	−0.179597	+	0.125784i
$569$	−3.41201e28			−0.402097			−0.201049	−	0.979581i	$-0.564435\pi$
$569$	−3.41201e28			−0.402097			−0.201049	+	0.979581i	$0.564435\pi$
$570$	−5.49060e28	+	4.88658e28i	−0.635234	+	0.565352i
$571$		−	1.10667e29i		−	1.25702i	−0.777803	−	0.628508i	$-0.783666\pi$
$571$		−	1.10667e29i		−	1.25702i	0.777803	−	0.628508i	$-0.216334\pi$
$572$	−2.17791e27	+	1.86449e28i	−0.0242874	+	0.207922i
$573$		−	3.71324e28i		−	0.406565i
$574$	4.81313e28	+	5.40808e28i	0.517432	+	0.581391i
$575$	1.91350e28			0.201984
$576$	9.88504e27	−	2.71773e28i	0.102457	−	0.281689i
$577$	3.69871e28			0.376448			0.188224	−	0.982126i	$-0.439727\pi$
$577$	3.69871e28			0.376448			0.188224	+	0.982126i	$0.439727\pi$
$578$	−1.31074e28	−	1.47276e28i	−0.131001	−	0.147194i
$579$		−	1.14073e29i		−	1.11959i
$580$	−3.87138e27	+	3.31426e28i	−0.0373140	+	0.319442i
$581$		−	1.15494e28i		−	0.109323i
$582$	−1.06251e28	+	9.45624e27i	−0.0987740	+	0.0879078i
$583$	−1.52623e29			−1.39347
$584$	9.62889e28	−	6.74378e28i	0.863458	−	0.604740i
$585$	−1.05472e28			−0.0928969
$586$	−1.12520e29	+	1.00141e29i	−0.973427	+	0.866339i
$587$			8.55853e27i			0.0727276i	0.999339	+	0.0363638i	$0.0115775\pi$
$587$			8.55853e27i			0.0727276i	−0.999339	+	0.0363638i	$0.988422\pi$
$588$	−8.14058e28	−	9.50900e27i	−0.679506	−	0.0793730i
$589$			1.15959e29i			0.950808i
$590$	−4.87922e28	−	5.48233e28i	−0.393010	−	0.441590i
$591$	−3.73936e28			−0.295889
$592$	1.82825e27	−	7.71896e27i	0.0142120	−	0.0600041i
$593$	3.35903e28			0.256531			0.128265	−	0.991740i	$-0.459059\pi$
$593$	3.35903e28			0.256531			0.128265	+	0.991740i	$0.459059\pi$
$594$	6.89539e28	+	7.74772e28i	0.517370	+	0.581321i
$595$		−	6.71562e28i		−	0.495060i
$596$	−4.55504e27	−	5.32073e26i	−0.0329918	−	0.00385377i
$597$			1.63122e28i			0.116087i
$598$	−5.17028e28	+	4.60150e28i	−0.361536	+	0.321763i
$599$	2.07004e29			1.42232			0.711159	−	0.703031i	$-0.248170\pi$
$599$	2.07004e29			1.42232			0.711159	+	0.703031i	$0.248170\pi$
$600$	8.68153e27	+	1.23956e28i	0.0586149	+	0.0836914i
$601$	−7.69663e28			−0.510645			−0.255322	−	0.966856i	$-0.582182\pi$
$601$	−7.69663e28			−0.510645			−0.255322	+	0.966856i	$0.582182\pi$
$602$	4.39727e28	−	3.91353e28i	0.286695	−	0.255156i
$603$		−	4.13330e28i		−	0.264829i
$604$	1.88642e28	−	1.61495e29i	0.118782	−	1.01688i
$605$			8.35454e28i			0.517001i
$606$	−5.71939e28	−	6.42636e28i	−0.347846	−	0.390843i
$607$	−1.13092e29			−0.676008			−0.338004	−	0.941145i	$-0.609752\pi$
$607$	−1.13092e29			−0.676008			−0.338004	+	0.941145i	$0.609752\pi$
$608$	1.43713e29	−	7.75228e28i	0.844322	−	0.455451i
$609$	1.87939e28			0.108526
$610$	−1.93493e29	−	2.17411e29i	−1.09825	−	1.23401i
$611$		−	3.93256e28i		−	0.219403i
$612$	−6.93796e27	+	5.93953e28i	−0.0380489	+	0.325734i
$613$			1.65636e29i			0.892935i	0.894800	+	0.446468i	$0.147318\pi$
$613$			1.65636e29i			0.892935i	−0.894800	+	0.446468i	$0.852682\pi$
$614$	−4.18729e28	+	3.72665e28i	−0.221904	+	0.197492i
$615$	3.10023e29			1.61512
$616$	3.42335e28	+	4.88792e28i	0.175329	+	0.250338i
$617$	−2.73372e28			−0.137645			−0.0688224	−	0.997629i	$-0.521924\pi$
$617$	−2.73372e28			−0.137645			−0.0688224	+	0.997629i	$0.521924\pi$
$618$	−1.86455e29	+	1.65943e29i	−0.922987	+	0.821449i
$619$			4.99662e28i			0.243178i	0.992581	+	0.121589i	$0.0387990\pi$
$619$			4.99662e28i			0.243178i	−0.992581	+	0.121589i	$0.961201\pi$
$620$	2.17927e29	+	2.54560e28i	1.04279	+	0.121808i
$621$			3.82422e29i			1.79921i
$622$	1.43752e29	+	1.61522e29i	0.664992	+	0.747191i
$623$	1.31285e29			0.597158
$624$	−5.32660e28	−	1.26161e28i	−0.238238	−	0.0564271i
$625$	−2.51746e29			−1.10719
$626$	−9.19081e28	−	1.03269e29i	−0.397487	−	0.446620i
$627$			1.35056e29i			0.574388i
$628$	9.84860e28	+	1.15041e28i	0.411906	+	0.0481147i
$629$			1.64029e28i			0.0674665i
$630$	−2.50466e28	+	2.22912e28i	−0.101315	+	0.0901692i
$631$	−9.88004e28			−0.393052			−0.196526	−	0.980499i	$-0.562966\pi$
$631$	−9.88004e28			−0.393052			−0.196526	+	0.980499i	$0.562966\pi$
$632$	1.75931e29	−	1.23216e29i	0.688355	−	0.482103i
$633$	1.41128e29			0.543094
$634$	3.55385e29	−	3.16289e29i	1.34512	−	1.19714i
$635$			3.05338e29i			1.13673i
$636$	5.16363e28	−	4.42054e29i	0.189084	−	1.61874i
$637$		−	6.64060e28i		−	0.239190i
$638$	4.07616e28	+	4.58001e28i	0.144422	+	0.162274i
$639$	−1.88572e28			−0.0657231
$640$	−1.14144e29	−	2.87105e29i	−0.391347	−	0.984352i
$641$	−7.20323e28			−0.242951			−0.121475	−	0.992594i	$-0.538763\pi$
$641$	−7.20323e28			−0.242951			−0.121475	+	0.992594i	$0.538763\pi$
$642$	2.45803e29	+	2.76187e29i	0.815586	+	0.916400i
$643$		−	3.59862e29i		−	1.17468i	−0.809339	−	0.587342i	$-0.800174\pi$
$643$		−	3.59862e29i		−	1.17468i	0.809339	−	0.587342i	$-0.199826\pi$
$644$	−2.55282e28	+	2.18545e29i	−0.0819819	+	0.701841i
$645$		−	2.52078e29i		−	0.796448i
$646$	−2.52224e29	+	2.24477e29i	−0.784052	+	0.697798i
$647$	3.09691e29			0.947183			0.473592	−	0.880745i	$-0.342957\pi$
$647$	3.09691e29			0.947183			0.473592	+	0.880745i	$0.342957\pi$
$648$	−1.66146e29	+	1.16364e29i	−0.499981	+	0.350171i
$649$	−1.34853e29			−0.399292
$650$	−9.15942e27	+	8.15179e27i	−0.0266856	+	0.0237499i
$651$		−	1.23578e29i		−	0.354274i
$652$	−2.48549e29	−	2.90329e28i	−0.701152	−	0.0819014i
$653$			3.33990e29i			0.927140i	0.886060	+	0.463570i	$0.153432\pi$
$653$			3.33990e29i			0.927140i	−0.886060	+	0.463570i	$0.846568\pi$
$654$	−4.83331e28	−	5.43075e28i	−0.132032	−	0.148352i
$655$	−3.78264e29			−1.01686
$656$	−6.70191e29	−	1.58736e29i	−1.77300	−	0.419937i
$657$	1.21366e29			0.315980
$658$	−8.31135e28	−	9.33871e28i	−0.212961	−	0.239285i
$659$		−	2.48515e29i		−	0.626693i	−0.949639	−	0.313347i	$-0.898550\pi$
$659$		−	2.48515e29i		−	0.626693i	0.949639	−	0.313347i	$-0.101450\pi$
$660$	2.53818e29	+	2.96484e28i	0.629956	+	0.0735851i
$661$		−	4.90992e29i		−	1.19939i	−0.800230	−	0.599693i	$-0.795289\pi$
$661$		−	4.90992e29i		−	1.19939i	0.800230	−	0.599693i	$-0.204711\pi$
$662$	−3.29543e29	+	2.93290e29i	−0.792326	+	0.705162i
$663$	1.13191e29			0.267867
$664$	6.30302e28	+	8.99956e28i	0.146819	+	0.209631i
$665$	−1.89321e29			−0.434081
$666$	6.11763e27	−	5.44463e27i	0.0138071	−	0.0122882i
$667$			2.26066e29i			0.502244i
$668$	−3.88980e28	+	3.33003e29i	−0.0850695	+	0.728274i
$669$		−	5.24378e29i		−	1.12894i
$670$	−2.93577e29	−	3.29866e29i	−0.622210	−	0.699121i
$671$	−5.34780e29			−1.11581
$672$	−1.53155e29	+	8.26164e28i	−0.314597	+	0.169703i
$673$	5.41718e29			1.09551			0.547753	−	0.836640i	$-0.315483\pi$
$673$	5.41718e29			1.09551			0.547753	+	0.836640i	$0.315483\pi$
$674$	3.43800e29	+	3.86297e29i	0.684506	+	0.769118i
$675$			6.77480e28i			0.132803i
$676$	−5.49684e28	+	4.70580e29i	−0.106090	+	0.908225i
$677$			2.63315e28i			0.0500374i	0.999687	+	0.0250187i	$0.00796452\pi$
$677$			2.63315e28i			0.0500374i	−0.999687	+	0.0250187i	$0.992035\pi$
$678$	6.18431e29	−	5.50397e29i	1.15712	−	1.02983i
$679$	−3.66363e28			−0.0674962
$680$	3.66500e29	+	5.23295e29i	0.664860	+	0.949299i
$681$	−5.40033e29			−0.964662
$682$	3.01155e29	−	2.68025e29i	0.529730	−	0.471454i
$683$		−	3.19607e29i		−	0.553603i	−0.960927	−	0.276801i	$-0.910726\pi$
$683$		−	3.19607e29i		−	0.553603i	0.960927	−	0.276801i	$-0.0892744\pi$
$684$	1.67442e29	+	1.95589e28i	0.285611	+	0.0333622i
$685$		−	3.36990e29i		−	0.566064i
$686$	−3.12018e29	−	3.50586e29i	−0.516150	−	0.579951i
$687$	1.52209e29			0.247968
$688$	−1.29067e29	+	5.44928e29i	−0.207079	+	0.874300i
$689$	3.60602e29			0.569804
$690$	6.26414e29	+	7.03844e29i	0.974868	+	1.09537i
$691$			3.11843e29i			0.477988i	0.971021	+	0.238994i	$0.0768176\pi$
$691$			3.11843e29i			0.477988i	−0.971021	+	0.238994i	$0.923182\pi$
$692$	1.26041e30	+	1.47229e29i	1.90283	+	0.222269i
$693$			6.16090e28i			0.0916105i
$694$	−4.80952e27	+	4.28042e27i	−0.00704413	+	0.00626920i
$695$	−5.95149e29			−0.858589
$696$	−1.46446e29	+	1.02566e29i	−0.208103	+	0.145749i
$697$	1.42417e30			1.99350
$698$	2.60098e29	−	2.31485e29i	0.358638	−	0.319184i
$699$			8.88066e29i			1.20624i
$700$	−4.52245e27	+	3.87163e28i	−0.00605123	+	0.0518042i
$701$		−	1.24991e30i		−	1.64755i	−0.566916	−	0.823775i	$-0.691864\pi$
$701$		−	1.24991e30i		−	1.64755i	0.566916	−	0.823775i	$-0.308136\pi$
$702$	−1.62917e29	−	1.83055e29i	−0.211557	−	0.237708i
$703$	4.62415e28			0.0591563
$704$	−5.33509e29	−	1.94050e29i	−0.672402	−	0.244569i
$705$	−5.35350e29			−0.664740
$706$	−3.29418e29	−	3.70138e29i	−0.402994	−	0.452808i
$707$		−	2.21586e29i		−	0.267079i
$708$	4.56243e28	−	3.90586e29i	0.0541810	−	0.463840i
$709$			1.22731e30i			1.43605i	0.696019	+	0.718024i	$0.254953\pi$
$709$			1.22731e30i			1.43605i	−0.696019	+	0.718024i	$0.745047\pi$
$710$	−1.50494e29	+	1.33938e29i	−0.173502	+	0.154415i
$711$	2.21749e29			0.251901
$712$	−1.02300e30	+	7.16475e29i	−1.14508	+	0.801976i
$713$	1.48648e30			1.63953
$714$	2.68796e29	−	2.39226e29i	0.292141	−	0.260002i
$715$			2.07049e29i			0.221748i
$716$	−1.75635e30	−	2.05159e29i	−1.85364	−	0.216523i
$717$			8.05724e29i			0.837983i
$718$	−2.22023e29	−	2.49468e29i	−0.227558	−	0.255686i
$719$	−1.53244e30			−1.54785			−0.773925	−	0.633277i	$-0.781709\pi$
$719$	−1.53244e30			−1.54785			−0.773925	+	0.633277i	$0.781709\pi$
$720$	7.35158e28	−	3.10388e29i	0.0731795	−	0.308968i
$721$	−6.42914e29			−0.630714
$722$	−5.47928e28	−	6.15657e28i	−0.0529765	−	0.0595249i
$723$			7.58100e29i			0.722395i
$724$	5.73760e29	+	6.70208e28i	0.538859	+	0.0629440i
$725$			4.00488e28i			0.0370715i
$726$	−3.34395e29	+	2.97608e29i	−0.305088	+	0.271525i
$727$	1.43067e30			1.28655			0.643276	−	0.765634i	$-0.277575\pi$
$727$	1.43067e30			1.28655			0.643276	+	0.765634i	$0.277575\pi$
$728$	−8.08836e28	−	1.15487e29i	−0.0716937	−	0.102365i
$729$	−1.25114e30			−1.09312
$730$	9.68584e29	−	8.62029e29i	0.834156	−	0.742390i
$731$		−	1.15798e30i		−	0.983033i
$732$	1.80930e29	−	1.54893e30i	0.151407	−	1.29618i
$733$		−	1.04481e30i		−	0.861882i	−0.902380	−	0.430941i	$-0.858182\pi$
$733$		−	1.04481e30i		−	0.861882i	0.902380	−	0.430941i	$-0.141818\pi$
$734$	6.37687e29	+	7.16511e29i	0.518560	+	0.582659i
$735$	−9.04002e29			−0.724690
$736$	−9.93770e29	−	1.84226e30i	−0.785360	−	1.45591i
$737$	−8.11395e29			−0.632155
$738$	−4.72725e29	−	5.31158e29i	−0.363092	−	0.407973i
$739$			2.40655e30i			1.82233i	0.412037	+	0.911167i	$0.364818\pi$
$739$			2.40655e30i			1.82233i	−0.412037	+	0.911167i	$0.635182\pi$
$740$	1.01512e28	−	8.69039e28i	0.00757854	−	0.0648793i
$741$		−	3.19098e29i		−	0.234873i
$742$	8.56326e29	−	7.62121e29i	0.621438	−	0.553073i
$743$	1.99367e30			1.42650			0.713249	−	0.700911i	$-0.247223\pi$
$743$	1.99367e30			1.42650			0.713249	+	0.700911i	$0.247223\pi$
$744$	6.74415e29	+	9.62942e29i	0.475786	+	0.679336i
$745$	−5.05831e28			−0.0351856
$746$	−4.26089e29	+	3.79214e29i	−0.292242	+	0.260092i
$747$			1.13433e29i			0.0767140i
$748$	1.16597e30	+	1.36197e29i	0.777538	+	0.0908240i
$749$			9.52316e29i			0.626213i
$750$	−7.97881e29	−	8.96506e29i	−0.517362	−	0.581313i
$751$	−1.01146e30			−0.646738			−0.323369	−	0.946273i	$-0.604816\pi$
$751$	−1.01146e30			−0.646738			−0.323369	+	0.946273i	$0.604816\pi$
$752$	1.15729e30	+	2.74106e29i	0.729718	+	0.172835i
$753$	6.62007e29			0.411638
$754$	−9.63075e28	−	1.08212e29i	−0.0590556	−	0.0663554i
$755$		−	1.79338e30i		−	1.08450i
$756$	−7.73764e29	−	9.03833e28i	−0.461456	−	0.0539025i
$757$			8.41731e29i			0.495070i	0.968879	+	0.247535i	$0.0796205\pi$
$757$			8.41731e29i			0.495070i	−0.968879	+	0.247535i	$0.920380\pi$
$758$	−1.75019e30	+	1.55765e30i	−1.01522	+	0.903533i
$759$	1.73129e30			0.990450
$760$	1.47523e30	−	1.03320e30i	0.832369	−	0.582966i
$761$	−2.60924e30			−1.45203			−0.726015	−	0.687679i	$-0.758630\pi$
$761$	−2.60924e30			−1.45203			−0.726015	+	0.687679i	$0.758630\pi$
$762$	−1.22213e30	+	1.08768e30i	−0.670797	+	0.597002i
$763$		−	1.87257e29i		−	0.101375i
$764$	−1.05565e29	+	9.03730e29i	−0.0563687	+	0.482568i
$765$			6.59578e29i			0.347393i
$766$	5.31879e29	+	5.97624e29i	0.276319	+	0.310475i
$767$	3.18617e29			0.163274
$768$	7.42545e29	−	1.47960e30i	0.375344	−	0.747912i
$769$	1.25464e30			0.625594			0.312797	−	0.949820i	$-0.398734\pi$
$769$	1.25464e30			0.625594			0.312797	+	0.949820i	$0.398734\pi$
$770$	4.37593e29	+	4.91683e29i	0.215237	+	0.241842i
$771$		−	5.50364e29i		−	0.267042i
$772$	−3.24301e29	+	2.77632e30i	−0.155227	+	1.32888i
$773$			1.04829e30i			0.494989i	0.968889	+	0.247494i	$0.0796072\pi$
$773$			1.04829e30i			0.494989i	−0.968889	+	0.247494i	$0.920393\pi$
$774$	−4.31881e29	+	3.84369e29i	−0.201179	+	0.179048i
$775$	2.63338e29			0.121017
$776$	2.85478e29	−	1.99940e29i	0.129427	−	0.0906466i
$777$	−4.92798e28			−0.0220418
$778$	−1.64687e30	+	1.46570e30i	−0.726731	+	0.646783i
$779$		−	4.01488e30i		−	1.74795i
$780$	−5.99695e29	−	7.00503e28i	−0.257595	−	0.0300896i
$781$			3.70180e29i			0.156883i
$782$	2.87758e30	+	3.23328e30i	1.20325	+	1.35199i
$783$	−8.00394e29			−0.330222
$784$	1.95422e30	+	4.62861e29i	0.795528	+	0.188422i
$785$	1.09368e30			0.439296
$786$	−1.34746e30	−	1.51402e30i	−0.534047	−	0.600060i
$787$			3.92755e29i			0.153599i	0.997047	+	0.0767993i	$0.0244701\pi$
$787$			3.92755e29i			0.153599i	−0.997047	+	0.0767993i	$0.975530\pi$
$788$	9.10086e29	+	1.06307e29i	0.351202	+	0.0410239i
$789$			1.52369e30i			0.580213i
$790$	1.76971e30	−	1.57502e30i	0.664994	−	0.591838i
$791$	2.13240e30			0.790708
$792$	−3.36226e29	−	4.80070e29i	−0.123032	−	0.175667i
$793$	1.26353e30			0.456264
$794$	−1.97793e30	+	1.76033e30i	−0.704847	+	0.627306i
$795$		−	4.90896e30i		−	1.72637i
$796$	4.63744e28	−	3.97007e29i	0.0160950	−	0.137788i
$797$		−	4.13816e30i		−	1.41741i	−0.705507	−	0.708703i	$-0.749281\pi$
$797$		−	4.13816e30i		−	1.41741i	0.705507	−	0.708703i	$-0.250719\pi$
$798$	−6.74403e29	−	7.57766e29i	−0.227976	−	0.256156i
$799$	−2.45926e30			−0.820470
$800$	−1.76051e29	−	3.26366e29i	−0.0579689	−	0.107463i
$801$	−1.28942e30			−0.419037
$802$	1.15822e30	+	1.30138e30i	0.371500	+	0.417421i
$803$		−	2.38249e30i		−	0.754256i
$804$	2.74517e29	−	2.35012e30i	0.0857788	−	0.734346i
$805$			2.42691e30i			0.748510i
$806$	−7.11540e29	+	6.33263e29i	−0.216611	+	0.192782i
$807$	3.28892e30			0.988282
$808$	1.20929e30	+	1.72665e30i	0.358684	+	0.512135i
$809$	−2.92470e30			−0.856293			−0.428147	−	0.903709i	$-0.640833\pi$
$809$	−2.92470e30			−0.856293			−0.428147	+	0.903709i	$0.640833\pi$
$810$	−1.67129e30	+	1.48743e30i	−0.483013	+	0.429877i
$811$			4.63718e30i			1.32292i	0.749979	+	0.661462i	$0.230064\pi$
$811$			4.63718e30i			1.32292i	−0.749979	+	0.661462i	$0.769936\pi$
$812$	−4.57405e29	−	5.34294e28i	−0.128814	−	0.0150467i
$813$			2.29774e30i			0.638777i
$814$	−1.06882e29	−	1.20093e29i	−0.0293324	−	0.0329581i
$815$	−2.76011e30			−0.747775
$816$	−7.88959e29	+	3.33103e30i	−0.211012	+	0.890906i
$817$	−3.26447e30			−0.861948
$818$	−1.88246e30	−	2.11515e30i	−0.490699	−	0.551354i
$819$		−	1.45564e29i		−	0.0374604i
$820$	−7.54535e30	−	8.81371e29i	−1.91705	−	0.223930i
$821$		−	6.33160e30i		−	1.58822i	−0.607775	−	0.794110i	$-0.707938\pi$
$821$		−	6.33160e30i		−	1.58822i	0.607775	−	0.794110i	$-0.292062\pi$
$822$	1.34882e30	−	1.20043e30i	0.334041	−	0.297293i
$823$	−1.21628e30			−0.297396			−0.148698	−	0.988883i	$-0.547508\pi$
$823$	−1.21628e30			−0.297396			−0.148698	+	0.988883i	$0.547508\pi$
$824$	5.00972e30	−	3.50865e30i	1.20942	−	0.847042i
$825$	3.06708e29			0.0731069
$826$	7.56624e29	−	6.73387e29i	0.178070	−	0.158480i
$827$			5.80379e30i			1.34866i	0.738428	+	0.674332i	$0.235568\pi$
$827$			5.80379e30i			1.34866i	−0.738428	+	0.674332i	$0.764432\pi$
$828$	2.50726e29	−	2.14645e30i	0.0575283	−	0.492495i
$829$		−	6.09051e30i		−	1.37985i	−0.723882	−	0.689924i	$-0.757644\pi$
$829$		−	6.09051e30i		−	1.37985i	0.723882	−	0.689924i	$-0.242356\pi$
$830$	8.05688e29	+	9.05279e29i	0.180238	+	0.202517i
$831$	−3.58557e30			−0.792040
$832$	1.26052e30	+	4.58483e29i	0.274951	+	0.100006i
$833$	−4.15275e30			−0.894465
$834$	−2.12006e30	−	2.38211e30i	−0.450925	−	0.506663i
$835$			3.69795e30i			0.776700i
$836$	3.83954e29	−	3.28700e30i	0.0796367	−	0.681764i
$837$			5.26293e30i			1.07798i
$838$	5.35318e30	−	4.76427e30i	1.08280	−	0.963683i
$839$	9.23520e30			1.84479			0.922393	−	0.386253i	$-0.126231\pi$
$839$	9.23520e30			1.84479			0.922393	+	0.386253i	$0.126231\pi$
$840$	−1.57215e30	+	1.10109e30i	−0.310143	+	0.217215i
$841$	4.65970e30			0.907820
$842$	2.08960e30	−	1.85972e30i	0.402055	−	0.357825i
$843$			2.73472e30i			0.519665i
$844$	−3.43478e30	−	4.01216e29i	−0.644620	−	0.0752979i
$845$			5.22574e30i			0.968618i
$846$	8.16304e29	+	9.17206e29i	0.149439	+	0.167911i
$847$	−1.15302e30			−0.208479
$848$	−2.51345e30	+	1.06119e31i	−0.448863	+	1.89513i
$849$	8.62911e30			1.52207
$850$	5.09778e29	+	5.72791e29i	0.0888142	+	0.0997925i
$851$		−	5.92773e29i		−	0.102007i
$852$	−1.07218e30	−	1.25242e29i	−0.182244	−	0.0212879i
$853$		−	7.11400e28i		−	0.0119440i	−0.999982	−	0.00597199i	$-0.998099\pi$
$853$		−	7.11400e28i		−	0.0119440i	0.999982	−	0.00597199i	$-0.00190096\pi$
$854$	3.00051e30	−	2.67042e30i	0.497609	−	0.442866i
$855$	1.85942e30			0.304603
$856$	−5.19719e30	−	7.42064e30i	−0.840996	−	1.20079i
$857$	4.06153e30			0.649219			0.324610	−	0.945848i	$-0.394767\pi$
$857$	4.06153e30			0.649219			0.324610	+	0.945848i	$0.394767\pi$
$858$	−8.28725e29	+	7.37557e29i	−0.130856	+	0.116461i
$859$			8.57477e30i			1.33750i	0.743487	+	0.668751i	$0.233171\pi$
$859$			8.57477e30i			1.33750i	−0.743487	+	0.668751i	$0.766829\pi$
$860$	−7.16637e29	+	6.13507e30i	−0.110424	+	0.945335i
$861$			4.27867e30i			0.651292i
$862$	−8.21395e29	−	9.22927e29i	−0.123517	−	0.138785i
$863$	−1.23197e31			−1.83014			−0.915072	−	0.403290i	$-0.867867\pi$
$863$	−1.23197e31			−1.83014			−0.915072	+	0.403290i	$0.867867\pi$
$864$	6.52259e30	−	3.51847e30i	0.957251	−	0.516369i
$865$	1.39967e31			2.02936
$866$	3.25624e29	+	3.65874e29i	0.0466421	+	0.0524075i
$867$		−	1.16519e30i		−	0.164891i
$868$	−3.51321e29	+	3.00764e30i	−0.0491188	+	0.420502i
$869$		−	4.35308e30i		−	0.601298i
$870$	−1.47312e30	+	1.31106e30i	−0.201041	+	0.178925i
$871$	1.91708e30			0.258494
$872$	1.02194e30	+	1.45915e30i	0.136145	+	0.194391i
$873$	3.59826e29			0.0473634
$874$	9.11496e30	−	8.11221e30i	1.18545	−	1.05504i
$875$		−	3.09123e30i		−	0.397234i
$876$	6.90063e30	+	8.06061e29i	0.876185	+	0.102347i
$877$		−	5.52645e30i		−	0.693347i	−0.937986	−	0.346673i	$-0.887311\pi$
$877$		−	5.52645e30i		−	0.693347i	0.937986	−	0.346673i	$-0.112689\pi$
$878$	−3.59896e30	−	4.04383e30i	−0.446154	−	0.501303i
$879$	−8.90213e30			−1.09046
$880$	−6.09313e30	−	1.44317e30i	−0.737518	−	0.174682i
$881$	−1.49606e31			−1.78938			−0.894689	−	0.446691i	$-0.852602\pi$
$881$	−1.49606e31			−1.78938			−0.894689	+	0.446691i	$0.852602\pi$
$882$	1.37843e30	+	1.54881e30i	0.162916	+	0.183054i
$883$		−	3.92373e30i		−	0.458260i	−0.973396	−	0.229130i	$-0.926412\pi$
$883$		−	3.92373e30i		−	0.458260i	0.973396	−	0.229130i	$-0.0735881\pi$
$884$	−2.75484e30	−	3.21793e29i	−0.317942	−	0.0371388i
$885$		−	4.33742e30i		−	0.494683i
$886$	6.14952e30	−	5.47301e30i	0.693086	−	0.616839i
$887$	3.38103e30			0.376575			0.188288	−	0.982114i	$-0.439706\pi$
$887$	3.38103e30			0.376575			0.188288	+	0.982114i	$0.439706\pi$
$888$	3.83998e29	−	2.68941e29i	0.0422662	−	0.0296019i
$889$	−4.21402e30			−0.458382
$890$	−1.02905e31	+	9.15840e30i	−1.10622	+	0.984520i
$891$			4.11099e30i			0.436748i
$892$	−1.49077e30	+	1.27623e31i	−0.156523	+	1.33998i
$893$			6.93291e30i			0.719408i
$894$	−1.80189e29	−	2.02462e29i	−0.0184792	−	0.0207634i
$895$	−1.95041e31			−1.97690
$896$	3.96237e30	−	1.57531e30i	0.396936	−	0.157809i
$897$	−4.09053e30			−0.405004
$898$	−4.72965e30	−	5.31428e30i	−0.462837	−	0.520047i
$899$			3.11115e30i			0.300915i
$900$	4.44175e28	−	3.80254e29i	0.00424627	−	0.0363520i
$901$		−	2.25505e31i		−	2.13082i
$902$	−1.04270e31	+	9.27991e30i	−0.973847	+	0.866713i
$903$	3.47896e30			0.321165
$904$	−1.66161e31	+	1.16374e31i	−1.51622	+	1.06191i
$905$	6.37154e30			0.574691
$906$	7.17811e30	−	6.38844e30i	0.639977	−	0.569572i
$907$		−	9.95299e30i		−	0.877156i	−0.898693	−	0.438578i	$-0.855482\pi$
$907$		−	9.95299e30i		−	0.877156i	0.898693	−	0.438578i	$-0.144518\pi$
$908$	1.31433e31	+	1.53527e30i	1.14500	+	0.133747i
$909$			2.17632e30i			0.187414i
$910$	−1.03390e30	−	1.16170e30i	−0.0880125	−	0.0988916i
$911$	1.72059e31			1.44788			0.723942	−	0.689861i	$-0.242329\pi$
$911$	1.72059e31			1.44788			0.723942	+	0.689861i	$0.242329\pi$
$912$	9.39054e30	+	2.22416e30i	0.781168	+	0.185021i
$913$	2.22678e30			0.183119
$914$	5.98670e30	+	6.72671e30i	0.486690	+	0.546850i
$915$		−	1.72007e31i		−	1.38237i
$916$	−3.70447e30	−	4.32718e29i	−0.294322	−	0.0343798i
$917$		−	5.22047e30i		−	0.410045i
$918$	−1.14475e31	+	1.01882e31i	−0.888921	+	0.791130i
$919$	1.98440e31			1.52341			0.761704	−	0.647925i	$-0.224363\pi$
$919$	1.98440e31			1.52341			0.761704	+	0.647925i	$0.224363\pi$
$920$	−1.32447e31	−	1.89110e31i	−1.00524	−	1.43530i
$921$	−3.31283e30			−0.248584
$922$	5.85933e30	−	5.21474e30i	0.434683	−	0.386864i
$923$		−	8.74624e29i		−	0.0641510i
$924$	−4.09182e29	+	3.50297e30i	−0.0296729	+	0.254028i
$925$		−	1.05013e29i		−	0.00752929i
$926$	9.73857e30	+	1.09423e31i	0.690366	+	0.775702i
$927$	6.31441e30			0.442584
$928$	3.85578e30	−	2.07992e30i	0.267214	−	0.144143i
$929$	7.54923e29			0.0517294			0.0258647	−	0.999665i	$-0.491766\pi$
$929$	7.54923e29			0.0517294			0.0258647	+	0.999665i	$0.491766\pi$
$930$	8.62077e30	+	9.68637e30i	0.584084	+	0.656282i
$931$			1.17071e31i			0.784289i
$932$	2.52470e30	−	2.16138e31i	0.167241	−	1.43174i
$933$			1.27790e31i			0.837026i
$934$	−1.40184e31	+	1.24763e31i	−0.907941	+	0.808058i
$935$	1.29480e31			0.829240
$936$	7.94402e29	+	1.13426e30i	0.0503088	+	0.0718318i
$937$	−1.46929e31			−0.920111			−0.460056	−	0.887890i	$-0.652171\pi$
$937$	−1.46929e31			−0.920111			−0.460056	+	0.887890i	$0.652171\pi$
$938$	4.55253e30	−	4.05170e30i	0.281918	−	0.250904i
$939$		−	8.17024e30i		−	0.500318i
$940$	1.30294e31	+	1.52196e30i	0.789006	+	0.0921637i
$941$			2.23754e31i			1.33993i	0.742395	+	0.669963i	$0.233690\pi$
$941$			2.23754e31i			1.33993i	−0.742395	+	0.669963i	$0.766310\pi$
$942$	3.89592e30	+	4.37749e30i	0.230715	+	0.259233i
$943$	−5.14670e31			−3.01409
$944$	−2.22081e30	+	9.37639e30i	−0.128619	+	0.543037i
$945$	−8.59256e30			−0.492140
$946$	7.54543e30	+	8.47812e30i	0.427393	+	0.480223i
$947$			1.27373e30i			0.0713515i	0.999363	+	0.0356758i	$0.0113584\pi$
$947$			1.27373e30i			0.0713515i	−0.999363	+	0.0356758i	$0.988642\pi$
$948$	1.26082e31	+	1.47276e30i	0.698500	+	0.0815917i
$949$			5.62912e30i			0.308422i
$950$	1.61476e30	−	1.43712e30i	0.0875005	−	0.0778745i
$951$	2.81167e31			1.50685
$952$	−7.22207e30	+	5.05812e30i	−0.382801	+	0.268102i
$953$	1.12362e31			0.589038			0.294519	−	0.955646i	$-0.404841\pi$
$953$	1.12362e31			0.589038			0.294519	+	0.955646i	$0.404841\pi$
$954$	−8.41045e30	+	7.48521e30i	−0.436075	+	0.388102i
$955$			1.00358e31i			0.514656i
$956$	2.29061e30	−	1.96097e31i	0.116183	−	0.994635i
$957$			3.62353e30i			0.181784i
$958$	−1.97365e31	−	2.21761e31i	−0.979336	−	1.10039i
$959$	4.65084e30			0.228263
$960$	6.24144e30	−	1.71598e31i	0.302996	−	0.833038i
$961$	−3.68387e29			−0.0176892
$962$	2.52530e29	+	2.83745e29i	0.0119943	+	0.0134769i
$963$		−	9.35322e30i		−	0.439425i
$964$	2.15522e30	−	1.84507e31i	0.100157	−	0.857439i
$965$			3.08307e31i			1.41725i
$966$	−9.71385e30	+	8.64522e30i	−0.441704	+	0.393112i
$967$	1.46347e31			0.658275			0.329137	−	0.944282i	$-0.393242\pi$
$967$	1.46347e31			0.658275			0.329137	+	0.944282i	$0.393242\pi$
$968$	8.98458e30	−	6.29252e30i	0.399767	−	0.279984i
$969$	−1.99550e31			−0.878319
$970$	2.87166e30	−	2.55575e30i	0.125035	−	0.111279i
$971$		−	2.15109e31i		−	0.926525i	−0.886221	−	0.463262i	$-0.846679\pi$
$971$		−	2.15109e31i		−	0.926525i	0.886221	−	0.463262i	$-0.153321\pi$
$972$	1.34465e31	+	1.57069e30i	0.572948	+	0.0669259i
$973$		−	8.21374e30i		−	0.346223i
$974$	−3.01415e31	−	3.38672e31i	−1.25688	−	1.41225i
$975$	−7.24659e29			−0.0298941
$976$	−8.80698e30	+	3.71836e31i	−0.359421	+	1.51750i
$977$	6.93004e30			0.279797			0.139898	−	0.990166i	$-0.455322\pi$
$977$	6.93004e30			0.279797			0.139898	+	0.990166i	$0.455322\pi$
$978$	−9.83212e30	−	1.10475e31i	−0.392726	−	0.441270i
$979$			2.53122e31i			1.00026i
$980$	2.20016e31	+	2.57001e30i	0.860164	+	0.100476i
$981$			1.83915e30i			0.0711367i
$982$	1.29905e31	−	1.15614e31i	0.497112	−	0.442424i
$983$	2.43435e31			0.921659			0.460830	−	0.887489i	$-0.347552\pi$
$983$	2.43435e31			0.921659			0.460830	+	0.887489i	$0.347552\pi$
$984$	−2.33505e31	−	3.33403e31i	−0.874677	−	1.24888i
$985$	1.01064e31			0.374555
$986$	−6.76712e30	+	6.02266e30i	−0.248140	+	0.220842i
$987$		−	7.38844e30i		−	0.268054i
$988$	−9.07169e29	+	7.76621e30i	−0.0325642	+	0.278780i
$989$			4.18474e31i			1.48630i
$990$	−4.29784e30	−	4.82909e30i	−0.151036	−	0.169705i
$991$	−1.97734e31			−0.687555			−0.343777	−	0.939051i	$-0.611707\pi$
$991$	−1.97734e31			−0.687555			−0.343777	+	0.939051i	$0.611707\pi$
$992$	−1.36764e31	−	2.53534e31i	−0.470542	−	0.872296i
$993$	−2.60722e31			−0.887588
$994$	−1.84849e30	−	2.07698e30i	−0.0622674	−	0.0699642i
$995$		−	4.40872e30i		−	0.146950i
$996$	−7.53378e29	+	6.44962e30i	−0.0248479	+	0.212721i
$997$		−	5.62726e31i		−	1.83653i	−0.395969	−	0.918264i	$-0.629591\pi$
$997$		−	5.62726e31i		−	1.83653i	0.395969	−	0.918264i	$-0.370409\pi$
$998$	4.67621e30	−	4.16178e30i	0.151016	−	0.134403i
$999$	2.09873e30			0.0670686

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.22.b.a.5.5	✓	20
4.3	odd	2		32.22.b.a.17.15		20
8.3	odd	2		32.22.b.a.17.6		20
8.5	even	2	inner	8.22.b.a.5.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.22.b.a.5.5	✓	20	1.1	even	1	trivial
8.22.b.a.5.6	yes	20	8.5	even	2	inner
32.22.b.a.17.6		20	8.3	odd	2
32.22.b.a.17.15		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)

\(f(q)\)	\(=\)	\(q+(-962.766 - 1081.77i) q^{2} -85585.8i q^{3} +(-243314. + 2.08299e6i) q^{4} +2.31314e7i q^{5} +(-9.25844e7 + 8.23991e7i) q^{6} -3.19239e8 q^{7} +(2.48758e9 - 1.74222e9i) q^{8} +3.13542e9 q^{9} +O(q^{10})\)	\(q+(-962.766 - 1081.77i) q^{2} -85585.8i q^{3} +(-243314. + 2.08299e6i) q^{4} +2.31314e7i q^{5} +(-9.25844e7 + 8.23991e7i) q^{6} -3.19239e8 q^{7} +(2.48758e9 - 1.74222e9i) q^{8} +3.13542e9 q^{9} +(2.50229e10 - 2.22701e10i) q^{10} -6.15505e10i q^{11} +(1.78274e11 + 2.08242e10i) q^{12} +1.45426e11i q^{13} +(3.07353e11 + 3.45344e11i) q^{14} +1.97972e12 q^{15} +(-4.27964e12 - 1.01364e12i) q^{16} +9.09430e12 q^{17} +(-3.01868e12 - 3.39182e12i) q^{18} -2.56378e13i q^{19} +(-4.81824e13 - 5.62817e12i) q^{20} +2.73223e13i q^{21} +(-6.65837e13 + 5.92588e13i) q^{22} -3.28653e14 q^{23} +(-1.49109e14 - 2.12901e14i) q^{24} -5.82225e13 q^{25} +(1.57317e14 - 1.40011e14i) q^{26} -1.16361e15i q^{27} +(7.76752e13 - 6.64971e14i) q^{28} -6.87857e14i q^{29} +(-1.90600e15 - 2.14160e15i) q^{30} -4.52295e15 q^{31} +(3.02377e15 + 5.60550e15i) q^{32} -5.26785e15 q^{33} +(-8.75569e15 - 9.83797e15i) q^{34} -7.38443e15i q^{35} +(-7.62891e14 + 6.53105e15i) q^{36} +1.80364e15i q^{37} +(-2.77343e16 + 2.46832e16i) q^{38} +1.24464e16 q^{39} +(4.03000e16 + 5.75410e16i) q^{40} +1.56600e17 q^{41} +(2.95566e16 - 2.63050e16i) q^{42} -1.27330e17i q^{43} +(1.28209e17 + 1.49761e16i) q^{44} +7.25266e16i q^{45} +(3.16416e17 + 3.55528e17i) q^{46} -2.70417e17 q^{47} +(-8.67532e16 + 3.66277e17i) q^{48} -4.56632e17 q^{49} +(5.60547e16 + 6.29836e16i) q^{50} -7.78343e17i q^{51} +(-3.02920e17 - 3.53840e16i) q^{52} -2.47963e18i q^{53} +(-1.25876e18 + 1.12028e18i) q^{54} +1.42375e18 q^{55} +(-7.94131e17 + 5.56185e17i) q^{56} -2.19423e18 q^{57} +(-7.44105e17 + 6.62246e17i) q^{58} -2.19093e18i q^{59} +(-4.81692e17 + 4.12373e18i) q^{60} -8.68847e18i q^{61} +(4.35455e18 + 4.89281e18i) q^{62} -1.00095e18 q^{63} +(3.15270e18 - 8.66782e18i) q^{64} -3.36389e18 q^{65} +(5.07171e18 + 5.69862e18i) q^{66} -1.31826e19i q^{67} +(-2.21277e18 + 1.89433e19i) q^{68} +2.81280e19i q^{69} +(-7.98828e18 + 7.10948e18i) q^{70} -6.01424e18 q^{71} +(7.79960e18 - 5.46260e18i) q^{72} +3.87079e19 q^{73} +(1.95113e18 - 1.73649e18i) q^{74} +4.98302e18i q^{75} +(5.34033e19 + 6.23803e18i) q^{76} +1.96493e19i q^{77} +(-1.19829e19 - 1.34641e19i) q^{78} +7.07237e19 q^{79} +(2.34469e19 - 9.89940e19i) q^{80} -6.67905e19 q^{81} +(-1.50769e20 - 1.69405e20i) q^{82} +3.61780e19i q^{83} +(-5.69121e19 - 6.64789e18i) q^{84} +2.10363e20i q^{85} +(-1.37742e20 + 1.22589e20i) q^{86} -5.88708e19 q^{87} +(-1.07235e20 - 1.53112e20i) q^{88} -4.11242e20 q^{89} +(7.84573e19 - 6.98262e19i) q^{90} -4.64255e19i q^{91} +(7.99657e19 - 6.84580e20i) q^{92} +3.87101e20i q^{93} +(2.60349e20 + 2.92530e20i) q^{94} +5.93037e20 q^{95} +(4.79751e20 - 2.58792e20i) q^{96} +1.14761e20 q^{97} +(4.39630e20 + 4.93973e20i) q^{98} -1.92987e20i 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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