LMFDB - Embedded newform 8.21.d.b.3.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,21,Mod(3,8)]

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([1, 1]))

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$20.2811012082$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 $ x^18 + 66008406614424x^16 - 170362825164232872x^15 + 1756210031321623676418457398x^14 - 8143876994687623666322842711032x^13 + 24350477750271510634494454384791667990404x^12 - 150098892256302975432925342820456817156772440x^11 + 191202710428210659782696002203561503780870353303759377x^10 - 1295069212697340229160215370735662134952032297259046562056x^9 + 870944882856087336674875277000277878990405713083632292121165358076x^8 - 4812915841402167440171875831348280575634953635256498021616060003579520x^7 + 2268474737024234177226752378807914883078144887754356976399017987196241603311520x^6 - 4757172104321022064833287336478952531807855909655138781977813255912131556348455680x^5 + 3199222078336759259493497095495346495581808310744107378246303720899215796326992176238102400x^4 + 8929774272757329376425833321340788600302219356646171490279817057245825930569313705998374604800x^3 + 2186805491439153577309421324561832859804177633153493793273223699303415894069647268007263015677943481600x^2 + 13250359115341501288916746421398415873922554950681918855831714718905060696192946493864164248007740533504000x + 531754461748673811827664952573861209640978431708236170453755006606958174478016712983511620954972201107600928640000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.14
Root			$7663.46 + 3.49192e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(607.571 + 824.278i) q^{2} +24307.8 q^{3} +(-310291. + 1.00161e6i) q^{4} -1.39677e7i q^{5} +(1.47687e7 + 2.00364e7i) q^{6} +2.84328e8i q^{7} +(-1.01413e9 + 3.52785e8i) q^{8} -2.89591e9 q^{9} +O(q^{10})$	\(q+(607.571 + 824.278i) q^{2} +24307.8 q^{3} +(-310291. + 1.00161e6i) q^{4} -1.39677e7i q^{5} +(1.47687e7 + 2.00364e7i) q^{6} +2.84328e8i q^{7} +(-1.01413e9 + 3.52785e8i) q^{8} -2.89591e9 q^{9} +(1.15133e10 - 8.48636e9i) q^{10} -4.00855e10 q^{11} +(-7.54252e9 + 2.43471e10i) q^{12} +2.05883e11i q^{13} +(-2.34365e11 + 1.72749e11i) q^{14} -3.39524e11i q^{15} +(-9.06950e11 - 6.21585e11i) q^{16} +2.13586e12 q^{17} +(-1.75947e12 - 2.38704e12i) q^{18} -8.51094e12 q^{19} +(1.39902e13 + 4.33406e12i) q^{20} +6.91139e12i q^{21} +(-2.43548e13 - 3.30416e13i) q^{22} -3.75944e13i q^{23} +(-2.46514e13 + 8.57545e12i) q^{24} -9.97290e13 q^{25} +(-1.69705e14 + 1.25088e14i) q^{26} -1.55150e14 q^{27} +(-2.84787e14 - 8.82244e13i) q^{28} -8.26668e13i q^{29} +(2.79862e14 - 2.06285e14i) q^{30} +1.32448e14i q^{31} +(-3.86781e13 - 1.12524e15i) q^{32} -9.74392e14 q^{33} +(1.29769e15 + 1.76055e15i) q^{34} +3.97140e15 q^{35} +(8.98577e14 - 2.90059e15i) q^{36} +5.16964e15i q^{37} +(-5.17100e15 - 7.01537e15i) q^{38} +5.00457e15i q^{39} +(4.92760e15 + 1.41651e16i) q^{40} +1.72416e16 q^{41} +(-5.69691e15 + 4.19916e15i) q^{42} -7.35091e15 q^{43} +(1.24382e16 - 4.01502e16i) q^{44} +4.04492e16i q^{45} +(3.09882e16 - 2.28412e16i) q^{46} +2.83483e16i q^{47} +(-2.20460e16 - 1.51094e16i) q^{48} -1.04993e15 q^{49} +(-6.05924e16 - 8.22044e16i) q^{50} +5.19183e16 q^{51} +(-2.06215e17 - 6.38836e16i) q^{52} -2.16094e16i q^{53} +(-9.42644e16 - 1.27886e17i) q^{54} +5.59902e17i q^{55} +(-1.00307e17 - 2.88346e17i) q^{56} -2.06883e17 q^{57} +(6.81404e16 - 5.02259e16i) q^{58} -2.04432e17 q^{59} +(3.40073e17 + 1.05352e17i) q^{60} +6.34107e17i q^{61} +(-1.09174e17 + 8.04713e16i) q^{62} -8.23388e17i q^{63} +(9.04007e17 - 7.15542e17i) q^{64} +2.87571e18 q^{65} +(-5.92012e17 - 8.03169e17i) q^{66} +5.81095e17 q^{67} +(-6.62740e17 + 2.13931e18i) q^{68} -9.13838e17i q^{69} +(2.41291e18 + 3.27354e18i) q^{70} +1.90384e18i q^{71} +(2.93684e18 - 1.02164e18i) q^{72} -6.95411e18 q^{73} +(-4.26122e18 + 3.14092e18i) q^{74} -2.42420e18 q^{75} +(2.64087e18 - 8.52467e18i) q^{76} -1.13974e19i q^{77} +(-4.12515e18 + 3.04063e18i) q^{78} -3.49017e18i q^{79} +(-8.68210e18 + 1.26680e19i) q^{80} +6.32607e18 q^{81} +(1.04755e19 + 1.42119e19i) q^{82} -1.42925e19 q^{83} +(-6.92255e18 - 2.14455e18i) q^{84} -2.98331e19i q^{85} +(-4.46620e18 - 6.05919e18i) q^{86} -2.00945e18i q^{87} +(4.06520e19 - 1.41416e19i) q^{88} +2.96835e19 q^{89} +(-3.33414e19 + 2.45758e19i) q^{90} -5.85381e19 q^{91} +(3.76551e19 + 1.16652e19i) q^{92} +3.21952e18i q^{93} +(-2.33669e19 + 1.72236e19i) q^{94} +1.18878e20i q^{95} +(-9.40182e17 - 2.73520e19i) q^{96} +6.85825e19 q^{97} +(-6.37905e17 - 8.65431e17i) q^{98} +1.16084e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

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 $

$2$	607.571	+	824.278i	0.593331	+	0.804959i
$2$	607.571	+	824.278i	0.593331	+	0.804959i
$3$	24307.8			0.411655			0.205828	−	0.978588i	$-0.434011\pi$
$3$	24307.8			0.411655			0.205828	+	0.978588i	$0.434011\pi$
$4$	−310291.	+	1.00161e6i	−0.295917	+	0.955214i
$5$		−	1.39677e7i		−	1.43029i	−0.698975	−	0.715146i	$-0.746360\pi$
$5$		−	1.39677e7i		−	1.43029i	0.698975	−	0.715146i	$-0.253640\pi$
$6$	1.47687e7	+	2.00364e7i	0.244248	+	0.331366i
$7$			2.84328e8i			1.00656i	0.864124	+	0.503279i	$0.167873\pi$
$7$			2.84328e8i			1.00656i	−0.864124	+	0.503279i	$0.832127\pi$
$8$	−1.01413e9	+	3.52785e8i	−0.944484	+	0.328557i
$9$	−2.89591e9			−0.830540
$10$	1.15133e10	−	8.48636e9i	1.15133	−	0.848636i
$11$	−4.00855e10			−1.54547			−0.772734	−	0.634730i	$-0.781111\pi$
$11$	−4.00855e10			−1.54547			−0.772734	+	0.634730i	$0.781111\pi$
$12$	−7.54252e9	+	2.43471e10i	−0.121816	+	0.393219i
$13$			2.05883e11i			1.49344i	0.665141	+	0.746718i	$0.268371\pi$
$13$			2.05883e11i			1.49344i	−0.665141	+	0.746718i	$0.731629\pi$
$14$	−2.34365e11	+	1.72749e11i	−0.810237	+	0.597222i
$15$		−	3.39524e11i		−	0.588787i
$16$	−9.06950e11	−	6.21585e11i	−0.824866	−	0.565328i
$17$	2.13586e12			1.05946			0.529730	−	0.848166i	$-0.322293\pi$
$17$	2.13586e12			1.05946			0.529730	+	0.848166i	$0.322293\pi$
$18$	−1.75947e12	−	2.38704e12i	−0.492785	−	0.668550i
$19$	−8.51094e12			−1.38817			−0.694083	−	0.719895i	$-0.744190\pi$
$19$	−8.51094e12			−1.38817			−0.694083	+	0.719895i	$0.744190\pi$
$20$	1.39902e13	+	4.33406e12i	1.36623	+	0.423248i
$21$			6.91139e12i			0.414355i
$22$	−2.43548e13	−	3.30416e13i	−0.916974	−	1.24404i
$23$		−	3.75944e13i		−	0.907496i	−0.891130	−	0.453748i	$-0.850087\pi$
$23$		−	3.75944e13i		−	0.907496i	0.891130	−	0.453748i	$-0.149913\pi$
$24$	−2.46514e13	+	8.57545e12i	−0.388802	+	0.135252i
$25$	−9.97290e13			−1.04573
$26$	−1.69705e14	+	1.25088e14i	−1.20215	+	0.886101i
$27$	−1.55150e14			−0.753552
$28$	−2.84787e14	−	8.82244e13i	−0.961478	−	0.297857i
$29$		−	8.26668e13i		−	0.196495i	−0.995162	−	0.0982474i	$-0.968676\pi$
$29$		−	8.26668e13i		−	0.196495i	0.995162	−	0.0982474i	$-0.0313237\pi$
$30$	2.79862e14	−	2.06285e14i	0.473950	−	0.349346i
$31$			1.32448e14i			0.161595i	0.996731	+	0.0807974i	$0.0257467\pi$
$31$			1.32448e14i			0.161595i	−0.996731	+	0.0807974i	$0.974253\pi$
$32$	−3.86781e13	−	1.12524e15i	−0.0343531	−	0.999410i
$33$	−9.74392e14			−0.636201
$34$	1.29769e15	+	1.76055e15i	0.628610	+	0.852821i
$35$	3.97140e15			1.43967
$36$	8.98577e14	−	2.90059e15i	0.245771	−	0.793343i
$37$			5.16964e15i			1.07509i	0.843236	+	0.537543i	$0.180647\pi$
$37$			5.16964e15i			1.07509i	−0.843236	+	0.537543i	$0.819353\pi$
$38$	−5.17100e15	−	7.01537e15i	−0.823642	−	1.11742i
$39$			5.00457e15i			0.614781i
$40$	4.92760e15	+	1.41651e16i	0.469932	+	1.35089i
$41$	1.72416e16			1.28452			0.642258	−	0.766489i	$-0.277998\pi$
$41$	1.72416e16			1.28452			0.642258	+	0.766489i	$0.277998\pi$
$42$	−5.69691e15	+	4.19916e15i	−0.333539	+	0.245850i
$43$	−7.35091e15			−0.340139			−0.170069	−	0.985432i	$-0.554399\pi$
$43$	−7.35091e15			−0.340139			−0.170069	+	0.985432i	$0.554399\pi$
$44$	1.24382e16	−	4.01502e16i	0.457330	−	1.47625i
$45$			4.04492e16i			1.18791i
$46$	3.09882e16	−	2.28412e16i	0.730497	−	0.538445i
$47$			2.83483e16i			0.538950i	0.963007	+	0.269475i	$0.0868501\pi$
$47$			2.83483e16i			0.538950i	−0.963007	+	0.269475i	$0.913150\pi$
$48$	−2.20460e16	−	1.51094e16i	−0.339561	−	0.232720i
$49$	−1.04993e15			−0.0131583
$50$	−6.05924e16	−	8.22044e16i	−0.620466	−	0.841773i
$51$	5.19183e16			0.436132
$52$	−2.06215e17	−	6.38836e16i	−1.42655	−	0.441933i
$53$		−	2.16094e16i		−	0.123562i	−0.998090	−	0.0617810i	$-0.980322\pi$
$53$		−	2.16094e16i		−	0.123562i	0.998090	−	0.0617810i	$-0.0196780\pi$
$54$	−9.42644e16	−	1.27886e17i	−0.447106	−	0.606578i
$55$			5.59902e17i			2.21047i
$56$	−1.00307e17	−	2.88346e17i	−0.330711	−	0.950678i
$57$	−2.06883e17			−0.571446
$58$	6.81404e16	−	5.02259e16i	0.158170	−	0.116586i
$59$	−2.04432e17			−0.399970			−0.199985	−	0.979799i	$-0.564089\pi$
$59$	−2.04432e17			−0.399970			−0.199985	+	0.979799i	$0.564089\pi$
$60$	3.40073e17	+	1.05352e17i	0.562418	+	0.174232i
$61$			6.34107e17i			0.888923i	0.895798	+	0.444462i	$0.146605\pi$
$61$			6.34107e17i			0.888923i	−0.895798	+	0.444462i	$0.853395\pi$
$62$	−1.09174e17	+	8.04713e16i	−0.130077	+	0.0958792i
$63$		−	8.23388e17i		−	0.835986i
$64$	9.04007e17	−	7.15542e17i	0.784101	−	0.620633i
$65$	2.87571e18			2.13605
$66$	−5.92012e17	−	8.03169e17i	−0.377477	−	0.512115i
$67$	5.81095e17			0.318786			0.159393	−	0.987215i	$-0.449046\pi$
$67$	5.81095e17			0.318786			0.159393	+	0.987215i	$0.449046\pi$
$68$	−6.62740e17	+	2.13931e18i	−0.313512	+	1.01201i
$69$		−	9.13838e17i		−	0.373576i
$70$	2.41291e18	+	3.27354e18i	0.854201	+	1.15888i
$71$			1.90384e18i			0.584852i	0.956288	+	0.292426i	$0.0944625\pi$
$71$			1.90384e18i			0.584852i	−0.956288	+	0.292426i	$0.905537\pi$
$72$	2.93684e18	−	1.02164e18i	0.784432	−	0.272880i
$73$	−6.95411e18			−1.61813			−0.809064	−	0.587720i	$-0.800025\pi$
$73$	−6.95411e18			−1.61813			−0.809064	+	0.587720i	$0.800025\pi$
$74$	−4.26122e18	+	3.14092e18i	−0.865399	+	0.637881i
$75$	−2.42420e18			−0.430482
$76$	2.64087e18	−	8.52467e18i	0.410782	−	1.32599i
$77$		−	1.13974e19i		−	1.55560i
$78$	−4.12515e18	+	3.04063e18i	−0.494873	+	0.364768i
$79$		−	3.49017e18i		−	0.368617i	−0.982868	−	0.184309i	$-0.940995\pi$
$79$		−	3.49017e18i		−	0.368617i	0.982868	−	0.184309i	$-0.0590046\pi$
$80$	−8.68210e18	+	1.26680e19i	−0.808584	+	1.17980i
$81$	6.32607e18			0.520336
$82$	1.04755e19	+	1.42119e19i	0.762143	+	1.03398i
$83$	−1.42925e19			−0.921144			−0.460572	−	0.887622i	$-0.652356\pi$
$83$	−1.42925e19			−0.921144			−0.460572	+	0.887622i	$0.652356\pi$
$84$	−6.92255e18	−	2.14455e18i	−0.395798	−	0.122615i
$85$		−	2.98331e19i		−	1.51534i
$86$	−4.46620e18	−	6.05919e18i	−0.201815	−	0.273798i
$87$		−	2.00945e18i		−	0.0808882i
$88$	4.06520e19	−	1.41416e19i	1.45967	−	0.507774i
$89$	2.96835e19			0.951953			0.475976	−	0.879458i	$-0.342095\pi$
$89$	2.96835e19			0.951953			0.475976	+	0.879458i	$0.342095\pi$
$90$	−3.33414e19	+	2.45758e19i	−0.956222	+	0.704826i
$91$	−5.85381e19			−1.50323
$92$	3.76551e19	+	1.16652e19i	0.866852	+	0.268543i
$93$			3.21952e18i			0.0665214i
$94$	−2.33669e19	+	1.72236e19i	−0.433832	+	0.319776i
$95$			1.18878e20i			1.98548i
$96$	−9.40182e17	−	2.73520e19i	−0.0141416	−	0.411413i
$97$	6.85825e19			0.930028			0.465014	−	0.885303i	$-0.346049\pi$
$97$	6.85825e19			0.930028			0.465014	+	0.885303i	$0.346049\pi$
$98$	−6.37905e17	−	8.65431e17i	−0.00780720	−	0.0105918i
$99$	1.16084e20			1.28357
$100$	3.09451e19	−	9.98900e19i	0.309451	−	0.998900i
$101$		−	1.09960e20i		−	0.995451i	−0.867335	−	0.497726i	$-0.834169\pi$
$101$		−	1.09960e20i		−	0.995451i	0.867335	−	0.497726i	$-0.165831\pi$
$102$	3.15440e19	+	4.27951e19i	0.258771	+	0.351069i
$103$			1.81814e20i			1.35287i	0.736502	+	0.676435i	$0.236476\pi$
$103$			1.81814e20i			1.35287i	−0.736502	+	0.676435i	$0.763524\pi$
$104$	−7.26324e19	−	2.08792e20i	−0.490678	−	1.41053i
$105$	9.65362e19			0.592648
$106$	1.78122e19	−	1.31293e19i	0.0994623	−	0.0733131i
$107$	−2.14467e20			−1.09024			−0.545121	−	0.838357i	$-0.683516\pi$
$107$	−2.14467e20			−1.09024			−0.545121	+	0.838357i	$0.683516\pi$
$108$	4.81416e19	−	1.55400e20i	0.222989	−	0.719803i
$109$			1.20761e20i			0.510109i	0.966927	+	0.255054i	$0.0820933\pi$
$109$			1.20761e20i			0.510109i	−0.966927	+	0.255054i	$0.917907\pi$
$110$	−4.61514e20	+	3.40180e20i	−1.77934	+	1.31154i
$111$			1.25663e20i			0.442565i
$112$	1.76734e20	−	2.57871e20i	0.569035	−	0.830275i
$113$	−1.03816e20			−0.305830			−0.152915	−	0.988239i	$-0.548866\pi$
$113$	−1.03816e20			−0.305830			−0.152915	+	0.988239i	$0.548866\pi$
$114$	−1.25696e20	−	1.70529e20i	−0.339057	−	0.459990i
$115$	−5.25107e20			−1.29798
$116$	8.28002e19	+	2.56508e19i	0.187695	+	0.0581462i
$117$		−	5.96218e20i		−	1.24036i
$118$	−1.24207e20	−	1.68508e20i	−0.237315	−	0.321960i
$119$			6.07285e20i			1.06641i
$120$	1.19779e20	+	3.44323e20i	0.193450	+	0.556100i
$121$	9.34095e20			1.38847
$122$	−5.22680e20	+	3.85265e20i	−0.715547	+	0.527426i
$123$	4.19106e20			0.528778
$124$	−1.32661e20	−	4.10974e19i	−0.154358	−	0.0478186i
$125$			6.09209e19i			0.0654134i
$126$	6.78700e20	−	5.00267e20i	0.672934	−	0.496016i
$127$		−	1.27937e21i		−	1.17208i	−0.810282	−	0.586040i	$-0.800686\pi$
$127$		−	1.27937e21i		−	1.17208i	0.810282	−	0.586040i	$-0.199314\pi$
$128$	1.13905e21	+	3.10410e20i	0.964816	+	0.262928i
$129$	−1.78685e20			−0.140020
$130$	1.74720e21	+	2.37038e21i	1.26738	+	1.71943i
$131$	−4.67394e20			−0.314029			−0.157015	−	0.987596i	$-0.550187\pi$
$131$	−4.67394e20			−0.314029			−0.157015	+	0.987596i	$0.550187\pi$
$132$	3.02345e20	−	9.75964e20i	0.188263	−	0.607708i
$133$		−	2.41989e21i		−	1.39727i
$134$	3.53056e20	+	4.78984e20i	0.189145	+	0.256609i
$135$			2.16708e21i			1.07780i
$136$	−2.16605e21	+	7.53501e20i	−1.00064	+	0.348093i
$137$	−1.74801e21			−0.750479			−0.375239	−	0.926928i	$-0.622440\pi$
$137$	−1.74801e21			−0.750479			−0.375239	+	0.926928i	$0.622440\pi$
$138$	7.53257e20	−	5.55222e20i	0.300713	−	0.221654i
$139$	9.57638e20			0.355675			0.177837	−	0.984060i	$-0.443090\pi$
$139$	9.57638e20			0.355675			0.177837	+	0.984060i	$0.443090\pi$
$140$	−1.23229e21	+	3.97781e21i	−0.426023	+	1.37519i
$141$			6.89086e20i			0.221862i
$142$	−1.56929e21	+	1.15672e21i	−0.470782	+	0.347011i
$143$		−	8.25291e21i		−	2.30806i
$144$	2.62645e21	+	1.80005e21i	0.685084	+	0.469527i
$145$	−1.15466e21			−0.281045
$146$	−4.22511e21	−	5.73212e21i	−0.960085	−	1.30253i
$147$	−2.55215e19			−0.00541667
$148$	−5.17798e21	−	1.60409e21i	−1.02694	−	0.318136i
$149$			8.57844e21i			1.59054i	0.606252	+	0.795272i	$0.292672\pi$
$149$			8.57844e21i			1.59054i	−0.606252	+	0.795272i	$0.707328\pi$
$150$	−1.47287e21	−	1.99821e21i	−0.255418	−	0.346520i
$151$		−	6.24048e18i		−	0.00101262i	−1.00000		0.000506312i	$-0.999839\pi$
$151$		−	6.24048e18i		−	0.00101262i	1.00000		0.000506312i	$-0.000161164\pi$
$152$	8.63121e21	−	3.00253e21i	1.31110	−	0.456091i
$153$	−6.18528e21			−0.879923
$154$	9.39463e21	−	6.92473e21i	1.25220	−	0.922987i
$155$	1.84999e21			0.231128
$156$	−5.01264e21	−	1.55287e21i	−0.587247	−	0.181924i
$157$			8.84474e21i			0.972050i	0.873945	+	0.486025i	$0.161554\pi$
$157$			8.84474e21i			0.972050i	−0.873945	+	0.486025i	$0.838446\pi$
$158$	2.87687e21	−	2.12053e21i	0.296722	−	0.218712i
$159$		−	5.25279e20i		−	0.0508650i
$160$	−1.57169e22	+	5.40244e20i	−1.42945	+	0.0491349i
$161$	1.06891e22			0.913447
$162$	3.84354e21	+	5.21444e21i	0.308731	+	0.418849i
$163$	1.69388e22			1.27940			0.639701	−	0.768624i	$-0.279058\pi$
$163$	1.69388e22			1.27940			0.639701	+	0.768624i	$0.279058\pi$
$164$	−5.34992e21	+	1.72694e22i	−0.380110	+	1.22699i
$165$			1.36100e22i			0.909952i
$166$	−8.68371e21	−	1.17810e22i	−0.546543	−	0.741483i
$167$			1.22986e22i			0.728940i	0.931215	+	0.364470i	$0.118750\pi$
$167$			1.22986e22i			0.728940i	−0.931215	+	0.364470i	$0.881250\pi$
$168$	−2.43824e21	−	7.00906e21i	−0.136139	−	0.391352i
$169$	−2.33827e22			−1.23035
$170$	2.45908e22	−	1.81257e22i	1.21978	−	0.899096i
$171$	2.46469e22			1.15293
$172$	2.28092e21	−	7.36277e21i	0.100653	−	0.324905i
$173$		−	2.44986e21i		−	0.102019i	−0.998698	−	0.0510093i	$-0.983756\pi$
$173$		−	2.44986e21i		−	0.102019i	0.998698	−	0.0510093i	$-0.0162438\pi$
$174$	1.65635e21	−	1.22088e21i	0.0651116	−	0.0479935i
$175$		−	2.83557e22i		−	1.05259i
$176$	3.63555e22	+	2.49165e22i	1.27480	+	0.873696i
$177$	−4.96929e21			−0.164650
$178$	1.80348e22	+	2.44675e22i	0.564823	+	0.766283i
$179$	−3.04158e22			−0.900675			−0.450338	−	0.892858i	$-0.648696\pi$
$179$	−3.04158e22			−0.900675			−0.450338	+	0.892858i	$0.648696\pi$
$180$	−4.05145e22	−	1.25510e22i	−1.13471	−	0.351524i
$181$			2.35703e21i			0.0624566i	0.999512	+	0.0312283i	$0.00994190\pi$
$181$			2.35703e21i			0.0624566i	−0.999512	+	0.0312283i	$0.990058\pi$
$182$	−3.55661e22	−	4.82517e22i	−0.891912	−	1.21004i
$183$			1.54138e22i			0.365930i
$184$	1.32627e22	+	3.81257e22i	0.298164	+	0.857115i
$185$	7.22079e22			1.53769
$186$	−2.65378e21	+	1.95609e21i	−0.0535470	+	0.0394692i
$187$	−8.56171e22			−1.63736
$188$	−2.83941e22	−	8.79623e21i	−0.514812	−	0.159484i
$189$		−	4.41133e22i		−	0.758493i
$190$	−9.79886e22	+	7.22269e22i	−1.59823	+	1.17805i
$191$		−	1.20961e23i		−	1.87203i	−0.351966	−	0.936013i	$-0.614487\pi$
$191$		−	1.20961e23i		−	1.87203i	0.351966	−	0.936013i	$-0.385513\pi$
$192$	2.19745e22	−	1.73933e22i	0.322779	−	0.255487i
$193$	−1.36921e23			−1.90940			−0.954702	−	0.297564i	$-0.903826\pi$
$193$	−1.36921e23			−1.90940			−0.954702	+	0.297564i	$0.903826\pi$
$194$	4.16687e22	+	5.65310e22i	0.551814	+	0.748634i
$195$	6.99022e22			0.879316
$196$	3.25783e20	−	1.05162e21i	0.00389375	−	0.0125689i
$197$		−	2.38694e22i		−	0.271131i	−0.990768	−	0.135566i	$-0.956715\pi$
$197$		−	2.38694e22i		−	0.271131i	0.990768	−	0.135566i	$-0.0432851\pi$
$198$	7.05293e22	+	9.56855e22i	0.761584	+	1.03322i
$199$			1.43271e23i			1.47105i	0.677497	+	0.735526i	$0.263065\pi$
$199$			1.43271e23i			1.47105i	−0.677497	+	0.735526i	$0.736935\pi$
$200$	1.01138e23	−	3.51829e22i	0.987680	−	0.343583i
$201$	1.41252e22			0.131230
$202$	9.06374e22	−	6.68083e22i	0.801297	−	0.590632i
$203$	2.35045e22			0.197783
$204$	−1.61098e22	+	5.20021e22i	−0.129059	+	0.416600i
$205$		−	2.40826e23i		−	1.83723i
$206$	−1.49866e23	+	1.10465e23i	−1.08900	+	0.802700i
$207$			1.08870e23i			0.753711i
$208$	1.27974e23	−	1.86725e23i	0.844280	−	1.23188i
$209$	3.41165e23			2.14537
$210$	5.86526e22	+	7.95726e22i	0.351637	+	0.477058i
$211$	−7.39581e22			−0.422826			−0.211413	−	0.977397i	$-0.567806\pi$
$211$	−7.39581e22			−0.422826			−0.211413	+	0.977397i	$0.567806\pi$
$212$	2.16443e22	+	6.70522e21i	0.118028	+	0.0365641i
$213$			4.62781e22i			0.240758i
$214$	−1.30304e23	−	1.76781e23i	−0.646875	−	0.877601i
$215$			1.02675e23i			0.486498i
$216$	1.57342e23	−	5.47345e22i	0.711718	−	0.247585i
$217$	−3.76585e22			−0.162655
$218$	−9.95408e22	+	7.33710e22i	−0.410616	+	0.302663i
$219$	−1.69039e23			−0.666111
$220$	−5.60805e23	−	1.73733e23i	−2.11147	−	0.654116i
$221$			4.39737e23i			1.58223i
$222$	−1.03581e23	+	7.63491e22i	−0.356246	+	0.262587i
$223$			3.94167e23i			1.29608i	0.761606	+	0.648040i	$0.224411\pi$
$223$			3.94167e23i			1.29608i	−0.761606	+	0.648040i	$0.775589\pi$
$224$	3.19935e23	−	1.09973e22i	1.00596	−	0.0345784i
$225$	2.88806e23			0.868524
$226$	−6.30755e22	−	8.55731e22i	−0.181458	−	0.246180i
$227$	−4.13516e23			−1.13824			−0.569119	−	0.822255i	$-0.692716\pi$
$227$	−4.13516e23			−1.13824			−0.569119	+	0.822255i	$0.692716\pi$
$228$	6.41939e22	−	2.07216e23i	0.169101	−	0.545853i
$229$		−	5.15394e23i		−	1.29953i	−0.760137	−	0.649763i	$-0.774868\pi$
$229$		−	5.15394e23i		−	1.29953i	0.760137	−	0.649763i	$-0.225132\pi$
$230$	−3.19040e23	−	4.32834e23i	−0.770134	−	1.04482i
$231$		−	2.77046e23i		−	0.640373i
$232$	2.91636e22	+	8.38351e22i	0.0645597	+	0.185586i
$233$	−4.42845e23			−0.939058			−0.469529	−	0.882917i	$-0.655576\pi$
$233$	−4.42845e23			−0.939058			−0.469529	+	0.882917i	$0.655576\pi$
$234$	4.91450e23	−	3.62245e23i	0.998436	−	0.735942i
$235$	3.95960e23			0.770855
$236$	6.34334e22	−	2.04762e23i	0.118358	−	0.382057i
$237$		−	8.48386e22i		−	0.151743i
$238$	−5.00572e23	+	3.68969e23i	−0.858414	+	0.632732i
$239$			8.87412e23i			1.45931i	0.683818	+	0.729653i	$0.260318\pi$
$239$			8.87412e23i			1.45931i	−0.683818	+	0.729653i	$0.739682\pi$
$240$	−2.11043e23	+	3.07932e23i	−0.332858	+	0.485671i
$241$	−5.69966e22			−0.0862340			−0.0431170	−	0.999070i	$-0.513729\pi$
$241$	−5.69966e22			−0.0862340			−0.0431170	+	0.999070i	$0.513729\pi$
$242$	5.67529e23	+	7.69954e23i	0.823824	+	1.11766i
$243$	6.94746e23			0.967751
$244$	−6.35131e23	−	1.96758e23i	−0.849112	−	0.263048i
$245$			1.46651e22i			0.0188201i
$246$	2.54637e23	+	3.45460e23i	0.313740	+	0.425644i
$247$		−	1.75225e24i		−	2.07314i
$248$	−4.67256e22	−	1.34319e23i	−0.0530931	−	0.152624i
$249$	−3.47420e23			−0.379194
$250$	−5.02158e22	+	3.70138e22i	−0.0526551	+	0.0388118i
$251$	5.20650e23			0.524576			0.262288	−	0.964990i	$-0.415523\pi$
$251$	5.20650e23			0.524576			0.262288	+	0.964990i	$0.415523\pi$
$252$	8.24717e23	+	2.55490e23i	0.798545	+	0.247382i
$253$			1.50699e24i			1.40251i
$254$	1.05455e24	−	7.77305e23i	0.943476	−	0.695431i
$255$		−	7.25178e23i		−	0.623796i
$256$	4.36191e23	+	1.12749e24i	0.360809	+	0.932640i
$257$	6.80863e22			0.0541662			0.0270831	−	0.999633i	$-0.491378\pi$
$257$	6.80863e22			0.0541662			0.0270831	+	0.999633i	$0.491378\pi$
$258$	−1.08564e23	−	1.47286e23i	−0.0830782	−	0.112710i
$259$	−1.46987e24			−1.08214
$260$	−8.92307e23	+	2.88035e24i	−0.632093	+	2.04038i
$261$			2.39396e23i			0.163197i
$262$	−2.83975e23	−	3.85263e23i	−0.186323	−	0.252781i
$263$		−	1.19590e24i		−	0.755333i	−0.925942	−	0.377666i	$-0.876727\pi$
$263$		−	1.19590e24i		−	0.755333i	0.925942	−	0.377666i	$-0.123273\pi$
$264$	9.88162e23	−	3.43751e23i	0.600881	−	0.209028i
$265$	−3.01834e23			−0.176730
$266$	1.99466e24	−	1.47026e24i	1.12474	−	0.829043i
$267$	7.21543e23			0.391877
$268$	−1.80309e23	+	5.82033e23i	−0.0943341	+	0.304509i
$269$		−	2.10757e24i		−	1.06233i	−0.847269	−	0.531165i	$-0.821755\pi$
$269$		−	2.10757e24i		−	1.06233i	0.847269	−	0.531165i	$-0.178245\pi$
$270$	−1.78628e24	+	1.31666e24i	−0.867583	+	0.639491i
$271$		−	1.72548e24i		−	0.807640i	−0.914839	−	0.403820i	$-0.867682\pi$
$271$		−	1.72548e24i		−	0.807640i	0.914839	−	0.403820i	$-0.132318\pi$
$272$	−1.93712e24	−	1.32762e24i	−0.873913	−	0.598942i
$273$	−1.42294e24			−0.618812
$274$	−1.06204e24	−	1.44085e24i	−0.445282	−	0.604105i
$275$	3.99768e24			1.61615
$276$	9.15313e23	+	2.83556e23i	0.356844	+	0.110547i
$277$			1.47149e24i			0.553299i	0.960971	+	0.276649i	$0.0892240\pi$
$277$			1.47149e24i			0.553299i	−0.960971	+	0.276649i	$0.910776\pi$
$278$	5.81833e23	+	7.89360e23i	0.211033	+	0.286304i
$279$		−	3.83557e23i		−	0.134211i
$280$	−4.02753e24	+	1.40105e24i	−1.35975	+	0.473014i
$281$	−3.14997e24			−1.02623			−0.513113	−	0.858321i	$-0.671508\pi$
$281$	−3.14997e24			−1.02623			−0.513113	+	0.858321i	$0.671508\pi$
$282$	−5.67998e23	+	4.18669e23i	−0.178589	+	0.131637i
$283$	−5.42512e24			−1.64644			−0.823218	−	0.567725i	$-0.807824\pi$
$283$	−5.42512e24			−1.64644			−0.823218	+	0.567725i	$0.807824\pi$
$284$	−1.90691e24	−	5.90744e23i	−0.558659	−	0.173068i
$285$			2.88967e24i			0.817334i
$286$	6.80269e24	−	5.01422e24i	1.85789	−	1.36944i
$287$			4.90227e24i			1.29294i
$288$	1.12009e23	+	3.25858e24i	0.0285316	+	0.830050i
$289$	4.97684e23			0.122455
$290$	−7.01540e23	−	9.51764e23i	−0.166753	−	0.226230i
$291$	1.66709e24			0.382851
$292$	2.15780e24	−	6.96533e24i	0.478832	−	1.54566i
$293$			2.74098e24i			0.587800i	0.955836	+	0.293900i	$0.0949532\pi$
$293$			2.74098e24i			0.587800i	−0.955836	+	0.293900i	$0.905047\pi$
$294$	−1.55061e22	−	2.10368e22i	−0.00321388	−	0.00436019i
$295$			2.85544e24i			0.572074i
$296$	−1.82377e24	−	5.24270e24i	−0.353227	−	1.01540i
$297$	6.21925e24			1.16459
$298$	−7.07102e24	+	5.21201e24i	−1.28032	+	0.943719i
$299$	7.74003e24			1.35529
$300$	7.52208e23	−	2.42811e24i	0.127387	−	0.411203i
$301$		−	2.09007e24i		−	0.342369i
$302$	5.14389e21	−	3.79153e21i	0.000815121	−	0.000600821i
$303$		−	2.67288e24i		−	0.409783i
$304$	7.71899e24	+	5.29027e24i	1.14505	+	0.784769i
$305$	8.85701e24			1.27142
$306$	−3.75799e24	−	5.09839e24i	−0.522086	−	0.708302i
$307$	−2.09763e24			−0.282062			−0.141031	−	0.990005i	$-0.545042\pi$
$307$	−2.09763e24			−0.282062			−0.141031	+	0.990005i	$0.545042\pi$
$308$	1.14158e25	+	3.53652e24i	1.48593	+	0.460329i
$309$			4.41952e24i			0.556916i
$310$	1.12400e24	+	1.52490e24i	0.137135	+	0.186048i
$311$			4.77389e24i			0.563986i	0.959417	+	0.281993i	$0.0909955\pi$
$311$			4.77389e24i			0.563986i	−0.959417	+	0.281993i	$0.909005\pi$
$312$	−1.76554e24	−	5.07529e24i	−0.201990	−	0.580651i
$313$	−4.62194e24			−0.512130			−0.256065	−	0.966660i	$-0.582426\pi$
$313$	−4.62194e24			−0.512130			−0.256065	+	0.966660i	$0.582426\pi$
$314$	−7.29052e24	+	5.37380e24i	−0.782460	+	0.576747i
$315$	−1.15008e25			−1.19570
$316$	3.49581e24	+	1.08297e24i	0.352108	+	0.109080i
$317$		−	1.06496e25i		−	1.03929i	−0.854381	−	0.519647i	$-0.826063\pi$
$317$		−	1.06496e25i		−	1.03929i	0.854381	−	0.519647i	$-0.173937\pi$
$318$	4.32976e23	−	3.19144e23i	0.0409442	−	0.0301798i
$319$			3.31374e24i			0.303677i
$320$	−9.99447e24	−	1.26269e25i	−0.887687	−	1.12149i
$321$	−5.21324e24			−0.448805
$322$	6.49440e24	+	8.81080e24i	0.541976	+	0.735287i
$323$	−1.81782e25			−1.47071
$324$	−1.96293e24	+	6.33628e24i	−0.153976	+	0.497032i
$325$		−	2.05325e25i		−	1.56174i
$326$	1.02915e25	+	1.39623e25i	0.759108	+	1.02987i
$327$			2.93545e24i			0.209989i
$328$	−1.74853e25	+	6.08259e24i	−1.21320	+	0.422036i
$329$	−8.06020e24			−0.542484
$330$	−1.12184e25	+	8.26904e24i	−0.732474	+	0.539903i
$331$	1.49182e25			0.945011			0.472506	−	0.881328i	$-0.343350\pi$
$331$	1.49182e25			0.945011			0.472506	+	0.881328i	$0.343350\pi$
$332$	4.43484e24	−	1.43156e25i	0.272582	−	0.879889i
$333$		−	1.49708e25i		−	0.892901i
$334$	−1.01375e25	+	7.47229e24i	−0.586767	+	0.432503i
$335$		−	8.11655e24i		−	0.455957i
$336$	4.29601e24	−	6.26829e24i	0.234246	−	0.341787i
$337$	3.10066e25			1.64118			0.820588	−	0.571520i	$-0.193646\pi$
$337$	3.10066e25			1.64118			0.820588	+	0.571520i	$0.193646\pi$
$338$	−1.42067e25	−	1.92739e25i	−0.730004	−	0.990380i
$339$	−2.52354e24			−0.125896
$340$	2.98812e25	+	9.25695e24i	1.44747	+	0.448414i
$341$		−	5.30923e24i		−	0.249740i
$342$	1.49748e25	+	2.03159e25i	0.684067	+	0.928058i
$343$			2.23886e25i			0.993313i
$344$	7.45479e24	−	2.59329e24i	0.321256	−	0.111755i
$345$	−1.27642e25			−0.534322
$346$	2.01936e24	−	1.48846e24i	0.0821208	−	0.0605308i
$347$	−2.79742e25			−1.10526			−0.552628	−	0.833428i	$-0.686375\pi$
$347$	−2.79742e25			−1.10526			−0.552628	+	0.833428i	$0.686375\pi$
$348$	2.01270e24	+	6.23516e23i	0.0772655	+	0.0239362i
$349$			2.94131e24i			0.109720i	0.998494	+	0.0548601i	$0.0174713\pi$
$349$			2.94131e24i			0.109720i	−0.998494	+	0.0548601i	$0.982529\pi$
$350$	2.33730e25	−	1.72281e25i	0.847293	−	0.624535i
$351$		−	3.19426e25i		−	1.12538i
$352$	1.55043e24	+	4.51056e25i	0.0530916	+	1.54456i
$353$	−1.82153e24			−0.0606302			−0.0303151	−	0.999540i	$-0.509651\pi$
$353$	−1.82153e24			−0.0606302			−0.0303151	+	0.999540i	$0.509651\pi$
$354$	−3.01920e24	−	4.09608e24i	−0.0976919	−	0.132536i
$355$	2.65922e25			0.836509
$356$	−9.21054e24	+	2.97314e25i	−0.281699	+	0.909318i
$357$			1.47618e25i			0.438992i
$358$	−1.84797e25	−	2.50710e25i	−0.534398	−	0.725006i
$359$			3.11321e25i			0.875517i	0.899093	+	0.437758i	$0.144227\pi$
$359$			3.11321e25i			0.875517i	−0.899093	+	0.437758i	$0.855773\pi$
$360$	−1.42699e25	−	4.10209e25i	−0.390297	−	1.12197i
$361$	3.48461e25			0.927004
$362$	−1.94284e24	+	1.43206e24i	−0.0502750	+	0.0370574i
$363$	2.27058e25			0.571573
$364$	1.81639e25	−	5.86326e25i	0.444831	−	1.43590i
$365$			9.71329e25i			2.31440i
$366$	−1.27052e25	+	9.36496e24i	−0.294559	+	0.217118i
$367$		−	4.62723e25i		−	1.04390i	−0.852975	−	0.521952i	$-0.825204\pi$
$367$		−	4.62723e25i		−	1.04390i	0.852975	−	0.521952i	$-0.174796\pi$
$368$	−2.33681e25	+	3.40962e25i	−0.513033	+	0.748563i
$369$	−4.99302e25			−1.06684
$370$	4.38714e25	+	5.95194e25i	0.912357	+	1.23777i
$371$	6.14416e24			0.124372
$372$	−3.22471e24	−	9.98989e23i	−0.0635421	−	0.0196848i
$373$		−	7.18562e24i		−	0.137840i	−0.997622	−	0.0689201i	$-0.978045\pi$
$373$		−	7.18562e24i		−	0.137840i	0.997622	−	0.0689201i	$-0.0219554\pi$
$374$	−5.20185e25	−	7.05723e25i	−0.971497	−	1.31801i
$375$			1.48086e24i			0.0269278i
$376$	−1.00009e25	−	2.87489e25i	−0.177076	−	0.509030i
$377$	1.70197e25			0.293452
$378$	3.63616e25	−	2.68020e25i	0.610556	−	0.450037i
$379$	5.99644e25			0.980621			0.490311	−	0.871548i	$-0.336883\pi$
$379$	5.99644e25			0.980621			0.490311	+	0.871548i	$0.336883\pi$
$380$	−1.19070e26	−	3.68869e25i	−1.89656	−	0.587538i
$381$		−	3.10986e25i		−	0.482493i
$382$	9.97055e25	−	7.34924e25i	1.50690	−	1.11073i
$383$			6.57084e25i			0.967460i	0.875217	+	0.483730i	$0.160718\pi$
$383$			6.57084e25i			0.967460i	−0.875217	+	0.483730i	$0.839282\pi$
$384$	2.76879e25	+	7.54541e24i	0.397172	+	0.108236i
$385$	−1.59195e26			−2.22497
$386$	−8.31893e25	−	1.12861e26i	−1.13291	−	1.53699i
$387$	2.12876e25			0.282499
$388$	−2.12806e25	+	6.86932e25i	−0.275211	+	0.888376i
$389$			7.85873e25i			0.990504i	0.868749	+	0.495252i	$0.164924\pi$
$389$			7.85873e25i			0.990504i	−0.868749	+	0.495252i	$0.835076\pi$
$390$	4.24706e25	+	5.76188e25i	0.521725	+	0.707813i
$391$		−	8.02965e25i		−	0.961455i
$392$	1.06476e24	−	3.70399e23i	0.0124278	−	0.00432323i
$393$	−1.13613e25			−0.129272
$394$	1.96750e25	−	1.45024e25i	0.218249	−	0.160870i
$395$	−4.87496e25			−0.527231
$396$	−3.60199e25	+	1.16271e26i	−0.379831	+	1.22609i
$397$			7.66767e25i			0.788421i	0.919020	+	0.394211i	$0.128982\pi$
$397$			7.66767e25i			0.788421i	−0.919020	+	0.394211i	$0.871018\pi$
$398$	−1.18095e26	+	8.70473e25i	−1.18414	+	0.872820i
$399$		−	5.88224e25i		−	0.575193i
$400$	9.04492e25	+	6.19900e25i	0.862591	+	0.591183i
$401$	1.45021e26			1.34892			0.674462	−	0.738310i	$-0.264376\pi$
$401$	1.45021e26			1.34892			0.674462	+	0.738310i	$0.264376\pi$
$402$	8.58204e24	+	1.16431e25i	0.0778628	+	0.105635i
$403$	−2.72687e25			−0.241331
$404$	1.10137e26	+	3.41196e25i	0.950869	+	0.294571i
$405$		−	8.83606e25i		−	0.744232i
$406$	1.42806e25	+	1.93742e25i	0.117351	+	0.159207i
$407$		−	2.07227e26i		−	1.66151i
$408$	−5.26520e25	+	1.83160e25i	−0.411920	+	0.143294i
$409$	7.43957e25			0.567956			0.283978	−	0.958831i	$-0.408346\pi$
$409$	7.43957e25			0.567956			0.283978	+	0.958831i	$0.408346\pi$
$410$	1.98507e26	−	1.46319e26i	1.47890	−	1.09009i
$411$	−4.24904e25			−0.308939
$412$	−1.82108e26	−	5.64155e25i	−1.29228	−	0.400337i
$413$		−	5.81255e25i		−	0.402593i
$414$	−8.97392e25	+	6.61463e25i	−0.606706	+	0.447200i
$415$			1.99633e26i			1.31750i
$416$	2.31667e26	−	7.96316e24i	1.49255	−	0.0513041i
$417$	2.32781e25			0.146416
$418$	2.07282e26	+	2.81215e26i	1.27291	+	1.72693i
$419$	1.90766e26			1.14383			0.571914	−	0.820314i	$-0.306201\pi$
$419$	1.90766e26			1.14383			0.571914	+	0.820314i	$0.306201\pi$
$420$	−2.99544e25	+	9.66920e25i	−0.175375	+	0.566106i
$421$		−	1.28355e26i		−	0.733827i	−0.930255	−	0.366913i	$-0.880415\pi$
$421$		−	1.28355e26i		−	0.733827i	0.930255	−	0.366913i	$-0.119585\pi$
$422$	−4.49348e25	−	6.09620e25i	−0.250876	−	0.340357i
$423$		−	8.20942e25i		−	0.447619i
$424$	7.62349e24	+	2.19148e25i	0.0405971	+	0.116702i
$425$	−2.13008e26			−1.10791
$426$	−3.81460e25	+	2.81173e25i	−0.193800	+	0.142849i
$427$	−1.80294e26			−0.894753
$428$	6.65474e25	−	2.14813e26i	0.322621	−	1.04141i
$429$		−	2.00610e26i		−	0.950124i
$430$	−8.46329e25	+	6.23825e25i	−0.391611	+	0.288654i
$431$			2.45768e26i			1.11110i	0.831484	+	0.555549i	$0.187492\pi$
$431$			2.45768e26i			1.11110i	−0.831484	+	0.555549i	$0.812508\pi$
$432$	1.40713e26	+	9.64386e25i	0.621579	+	0.426004i
$433$	−7.14228e25			−0.308289			−0.154145	−	0.988048i	$-0.549262\pi$
$433$	−7.14228e25			−0.308289			−0.154145	+	0.988048i	$0.549262\pi$
$434$	−2.28802e25	−	3.10411e25i	−0.0965079	−	0.130930i
$435$	−2.80674e25			−0.115694
$436$	−1.20956e26	−	3.74712e25i	−0.487263	−	0.150950i
$437$			3.19963e26i			1.25975i
$438$	−1.02703e26	−	1.39335e26i	−0.395224	−	0.536192i
$439$		−	1.50251e26i		−	0.565162i	−0.959243	−	0.282581i	$-0.908809\pi$
$439$		−	1.50251e26i		−	0.565162i	0.959243	−	0.282581i	$-0.0911907\pi$
$440$	−1.97525e26	−	5.67814e26i	−0.726265	−	2.08775i
$441$	3.04050e24			0.0109285
$442$	−3.62466e26	+	2.67172e26i	−1.27363	+	0.938788i
$443$	1.83787e26			0.631361			0.315680	−	0.948866i	$-0.397767\pi$
$443$	1.83787e26			0.631361			0.315680	+	0.948866i	$0.397767\pi$
$444$	−1.25866e26	−	3.89921e25i	−0.422744	−	0.130962i
$445$		−	4.14610e26i		−	1.36157i
$446$	−3.24903e26	+	2.39485e26i	−1.04329	+	0.769004i
$447$			2.08523e26i			0.654756i
$448$	2.03448e26	+	2.57034e26i	0.624703	+	0.789243i
$449$	2.83524e26			0.851386			0.425693	−	0.904868i	$-0.360030\pi$
$449$	2.83524e26			0.851386			0.425693	+	0.904868i	$0.360030\pi$
$450$	1.75470e26	+	2.38057e26i	0.515322	+	0.699126i
$451$	−6.91138e26			−1.98518
$452$	3.22132e25	−	1.03983e26i	0.0905001	−	0.292133i
$453$		−	1.51693e23i		−	0.000416852i
$454$	−2.51240e26	−	3.40852e26i	−0.675352	−	0.916235i
$455$			8.17643e26i			2.15006i
$456$	2.09806e26	−	7.29851e25i	0.539722	−	0.187752i
$457$	6.33685e26			1.59482			0.797409	−	0.603439i	$-0.206203\pi$
$457$	6.33685e26			1.59482			0.797409	+	0.603439i	$0.206203\pi$
$458$	4.24828e26	−	3.13139e26i	1.04606	−	0.771049i
$459$	−3.31379e26			−0.798358
$460$	1.62936e26	−	5.25954e26i	0.384095	−	1.23985i
$461$			3.19396e26i			0.736750i	0.929677	+	0.368375i	$0.120086\pi$
$461$			3.19396e26i			0.736750i	−0.929677	+	0.368375i	$0.879914\pi$
$462$	2.28363e26	−	1.68325e26i	0.515473	−	0.379953i
$463$		−	6.34081e26i		−	1.40067i	−0.713816	−	0.700333i	$-0.753035\pi$
$463$		−	6.34081e26i		−	1.40067i	0.713816	−	0.700333i	$-0.246965\pi$
$464$	−5.13844e25	+	7.49747e25i	−0.111084	+	0.162082i
$465$	4.49692e25			0.0951450
$466$	−2.69059e26	−	3.65027e26i	−0.557172	−	0.755903i
$467$	4.04419e26			0.819716			0.409858	−	0.912149i	$-0.365578\pi$
$467$	4.04419e26			0.819716			0.409858	+	0.912149i	$0.365578\pi$
$468$	5.97181e26	+	1.85001e26i	1.18481	+	0.367043i
$469$			1.65221e26i			0.320876i
$470$	2.40574e26	+	3.26381e26i	0.457372	+	0.620507i
$471$			2.14997e26i			0.400150i
$472$	2.07321e26	−	7.21204e25i	0.377766	−	0.131413i
$473$	2.94665e26			0.525674
$474$	6.99305e25	−	5.15454e25i	0.122147	−	0.0900340i
$475$	8.48787e26			1.45165
$476$	−6.08265e26	−	1.88435e26i	−1.01865	−	0.315568i
$477$			6.25791e25i			0.102623i
$478$	−7.31474e26	+	5.39166e26i	−1.17468	+	0.865851i
$479$			1.19581e27i			1.88064i	0.340293	+	0.940319i	$0.389474\pi$
$479$			1.19581e27i			1.88064i	−0.340293	+	0.940319i	$0.610526\pi$
$480$	−3.82045e26	+	1.31322e25i	−0.588440	+	0.0202267i
$481$	−1.06434e27			−1.60557
$482$	−3.46295e25	−	4.69810e25i	−0.0511653	−	0.0694148i
$483$	2.59829e26			0.376025
$484$	−2.89842e26	+	9.35603e26i	−0.410873	+	1.32629i
$485$		−	9.57940e26i		−	1.33021i
$486$	4.22108e26	+	5.72664e26i	0.574197	+	0.779000i
$487$		−	8.77926e25i		−	0.116995i	−0.998288	−	0.0584976i	$-0.981369\pi$
$487$		−	8.77926e25i		−	0.116995i	0.998288	−	0.0584976i	$-0.0186310\pi$
$488$	−2.23704e26	−	6.43069e26i	−0.292062	−	0.839574i
$489$	4.11746e26			0.526673
$490$	−1.20881e25	+	8.91006e24i	−0.0151494	+	0.0111666i
$491$	−6.94416e26			−0.852717			−0.426359	−	0.904554i	$-0.640204\pi$
$491$	−6.94416e26			−0.852717			−0.426359	+	0.904554i	$0.640204\pi$
$492$	−1.30045e26	+	4.19783e26i	−0.156474	+	0.505096i
$493$		−	1.76565e26i		−	0.208178i
$494$	1.44434e27	−	1.06462e27i	1.66879	−	1.23006i
$495$		−	1.62143e27i		−	1.83588i
$496$	8.23274e25	−	1.20123e26i	0.0913541	−	0.133294i
$497$	−5.41313e26			−0.588687
$498$	−2.11082e26	−	2.86371e26i	−0.224987	−	0.305235i
$499$	−6.25596e26			−0.653565			−0.326782	−	0.945100i	$-0.605964\pi$
$499$	−6.25596e26			−0.653565			−0.326782	+	0.945100i	$0.605964\pi$
$500$	−6.10193e25	−	1.89032e25i	−0.0624837	−	0.0193569i
$501$			2.98953e26i			0.300072i
$502$	3.16331e26	+	4.29160e26i	0.311247	+	0.422262i
$503$		−	1.46764e27i		−	1.41560i	−0.706415	−	0.707798i	$-0.749689\pi$
$503$		−	1.46764e27i		−	1.41560i	0.706415	−	0.707798i	$-0.250311\pi$
$504$	2.90479e26	+	8.35024e26i	0.274669	+	0.789576i
$505$	−1.53588e27			−1.42379
$506$	−1.24218e27	+	9.15602e26i	−1.12896	+	0.832150i
$507$	−5.68384e26			−0.506480
$508$	1.28143e27	+	3.96976e26i	1.11959	+	0.346838i
$509$			2.17480e27i			1.86313i	0.363579	+	0.931563i	$0.381555\pi$
$509$			2.17480e27i			1.86313i	−0.363579	+	0.931563i	$0.618445\pi$
$510$	5.97748e26	−	4.40597e26i	0.502130	−	0.370118i
$511$		−	1.97725e27i		−	1.62874i
$512$	−6.64350e26	+	1.04457e27i	−0.536657	+	0.843800i
$513$	1.32047e27			1.04605
$514$	4.13673e25	+	5.61220e25i	0.0321385	+	0.0436016i
$515$	2.53953e27			1.93500
$516$	5.54443e25	−	1.78973e26i	0.0414343	−	0.133749i
$517$		−	1.13635e27i		−	0.832930i
$518$	−8.93051e26	−	1.21158e27i	−0.642064	−	0.871074i
$519$		−	5.95507e25i		−	0.0419965i
$520$	−2.91635e27	+	1.01451e27i	−2.01746	+	0.701813i
$521$	−1.42093e27			−0.964266			−0.482133	−	0.876098i	$-0.660138\pi$
$521$	−1.42093e27			−0.964266			−0.482133	+	0.876098i	$0.660138\pi$
$522$	−1.97329e26	+	1.45450e26i	−0.131367	+	0.0968297i
$523$	−5.60940e26			−0.366353			−0.183176	−	0.983080i	$-0.558638\pi$
$523$	−5.60940e26			−0.366353			−0.183176	+	0.983080i	$0.558638\pi$
$524$	1.45028e26	−	4.68149e26i	0.0929267	−	0.299965i
$525$		−	6.89266e26i		−	0.433305i
$526$	9.85756e26	−	7.26596e26i	0.608012	−	0.448162i
$527$			2.82890e26i			0.171203i
$528$	8.83724e26	+	6.05667e26i	0.524780	+	0.359662i
$529$	3.02818e26			0.176452
$530$	−1.83386e26	−	2.48795e26i	−0.104859	−	0.142260i
$531$	5.92016e26			0.332191
$532$	2.42380e27	+	7.50872e26i	1.33469	+	0.413476i
$533$			3.54975e27i			1.91834i
$534$	4.38388e26	+	5.94751e26i	0.232512	+	0.315444i
$535$			2.99561e27i			1.55937i
$536$	−5.89307e26	+	2.05002e26i	−0.301088	+	0.104739i
$537$	−7.39341e26			−0.370768
$538$	1.73722e27	−	1.28050e27i	0.855131	−	0.630313i
$539$	4.20868e25			0.0203357
$540$	−2.17058e27	−	6.72427e26i	−1.02953	−	0.318939i
$541$		−	9.48899e25i		−	0.0441822i	−0.999756	−	0.0220911i	$-0.992968\pi$
$541$		−	9.48899e25i		−	0.0441822i	0.999756	−	0.0220911i	$-0.00703239\pi$
$542$	1.42228e27	−	1.04835e27i	0.650117	−	0.479198i
$543$			5.72942e25i			0.0257106i
$544$	−8.26112e25	−	2.40335e27i	−0.0363957	−	1.05883i
$545$	1.68676e27			0.729604
$546$	−8.64534e26	−	1.17289e27i	−0.367160	−	0.498118i
$547$	2.21993e27			0.925692			0.462846	−	0.886439i	$-0.346828\pi$
$547$	2.21993e27			0.925692			0.462846	+	0.886439i	$0.346828\pi$
$548$	5.42393e26	−	1.75083e27i	0.222079	−	0.716868i
$549$		−	1.83632e27i		−	0.738286i
$550$	2.42888e27	+	3.29520e27i	0.958911	+	1.30093i
$551$			7.03572e26i			0.272767i
$552$	3.22389e26	+	9.26753e26i	0.122741	+	0.352836i
$553$	9.92352e26			0.371035
$554$	−1.21292e27	+	8.94034e26i	−0.445383	+	0.328289i
$555$	1.75522e27			0.632997
$556$	−2.97147e26	+	9.59184e26i	−0.105250	+	0.339746i
$557$			1.37717e27i			0.479111i	0.970883	+	0.239556i	$0.0770017\pi$
$557$			1.37717e27i			0.479111i	−0.970883	+	0.239556i	$0.922998\pi$
$558$	3.16157e26	−	2.33038e26i	0.108034	−	0.0796315i
$559$		−	1.51342e27i		−	0.507975i
$560$	−3.60186e27	−	2.46856e27i	−1.18754	−	0.813886i
$561$	−2.08117e27			−0.674029
$562$	−1.91383e27	−	2.59645e27i	−0.608892	−	0.826070i
$563$	−3.26206e27			−1.01955			−0.509774	−	0.860308i	$-0.670271\pi$
$563$	−3.26206e27			−1.01955			−0.509774	+	0.860308i	$0.670271\pi$
$564$	−6.90198e26	−	2.13817e26i	−0.211925	−	0.0656526i
$565$			1.45007e27i			0.437425i
$566$	−3.29614e27	−	4.47181e27i	−0.976882	−	1.32531i
$567$			1.79868e27i			0.523748i
$568$	−6.71645e26	−	1.93074e27i	−0.192157	−	0.552383i
$569$	2.95455e27			0.830556			0.415278	−	0.909695i	$-0.363684\pi$
$569$	2.95455e27			0.830556			0.415278	+	0.909695i	$0.363684\pi$
$570$	−2.38189e27	+	1.75568e27i	−0.657920	+	0.484950i
$571$	−6.52375e27			−1.77066			−0.885332	−	0.464960i	$-0.846069\pi$
$571$	−6.52375e27			−1.77066			−0.885332	+	0.464960i	$0.846069\pi$
$572$	8.26623e27	+	2.56081e27i	2.20469	+	0.682993i
$573$		−	2.94030e27i		−	0.770630i
$574$	−4.04083e27	+	2.97847e27i	−1.04076	+	0.767141i
$575$			3.74925e27i			0.948999i
$576$	−2.61792e27	+	2.07215e27i	−0.651227	+	0.515461i
$577$	4.43876e27			1.08519			0.542593	−	0.839996i	$-0.317443\pi$
$577$	4.43876e27			1.08519			0.542593	+	0.839996i	$0.317443\pi$
$578$	3.02378e26	+	4.10230e26i	0.0726561	+	0.0985709i
$579$	−3.32826e27			−0.786016
$580$	3.58282e26	−	1.15653e27i	0.0831660	−	0.268458i
$581$		−	4.06375e27i		−	0.927185i
$582$	1.01288e27	+	1.37415e27i	0.227157	+	0.308179i
$583$			8.66225e26i			0.190961i
$584$	7.05239e27	−	2.45331e27i	1.52830	−	0.531647i
$585$	−8.32780e27			−1.77407
$586$	−2.25933e27	+	1.66534e27i	−0.473154	+	0.348760i
$587$	1.40751e27			0.289782			0.144891	−	0.989448i	$-0.453717\pi$
$587$	1.40751e27			0.289782			0.144891	+	0.989448i	$0.453717\pi$
$588$	7.91909e24	−	2.55627e25i	0.00160288	−	0.00517407i
$589$		−	1.12725e27i		−	0.224320i
$590$	−2.35367e27	+	1.73488e27i	−0.460496	+	0.339429i
$591$		−	5.80214e26i		−	0.111613i
$592$	3.21337e27	−	4.68861e27i	0.607776	−	0.886802i
$593$	1.04753e27			0.194814			0.0974072	−	0.995245i	$-0.468945\pi$
$593$	1.04753e27			0.194814			0.0974072	+	0.995245i	$0.468945\pi$
$594$	3.77863e27	+	5.12639e27i	0.690988	+	0.937447i
$595$	8.48237e27			1.52527
$596$	−8.59229e27	−	2.66182e27i	−1.51931	−	0.470669i
$597$			3.48261e27i			0.605566i
$598$	4.70262e27	+	6.37994e27i	0.804133	+	1.09095i
$599$		−	9.04310e27i		−	1.52072i	−0.649502	−	0.760360i	$-0.725022\pi$
$599$		−	9.04310e27i		−	1.52072i	0.649502	−	0.760360i	$-0.274978\pi$
$600$	2.45846e27	−	8.55221e26i	0.406584	−	0.141438i
$601$	8.61316e27			1.40093			0.700467	−	0.713685i	$-0.252975\pi$
$601$	8.61316e27			1.40093			0.700467	+	0.713685i	$0.252975\pi$
$602$	1.72279e27	−	1.26986e27i	0.275593	−	0.203138i
$603$	−1.68280e27			−0.264764
$604$	6.25055e24	+	1.93637e24i	0.000967273	+	0.000299653i
$605$		−	1.30472e28i		−	1.98592i
$606$	2.20320e27	−	1.62397e27i	0.329858	−	0.243137i
$607$			1.08110e28i			1.59213i	0.605214	+	0.796063i	$0.293088\pi$
$607$			1.08110e28i			1.59213i	−0.605214	+	0.796063i	$0.706912\pi$
$608$	3.29187e26	+	9.57681e27i	0.0476878	+	1.38735i
$609$	5.71343e26			0.0814186
$610$	5.38126e27	+	7.30064e27i	0.754373	+	1.02344i
$611$	−5.83642e27			−0.804887
$612$	1.91924e27	−	6.19526e27i	0.260384	−	0.840515i
$613$		−	8.75826e27i		−	1.16900i	−0.811395	−	0.584498i	$-0.801291\pi$
$613$		−	8.75826e27i		−	1.16900i	0.811395	−	0.584498i	$-0.198709\pi$
$614$	−1.27446e27	−	1.72903e27i	−0.167356	−	0.227049i
$615$		−	5.85395e27i		−	0.756307i
$616$	4.02084e27	+	1.15585e28i	0.511104	+	1.46924i
$617$	2.57137e27			0.321598			0.160799	−	0.986987i	$-0.448593\pi$
$617$	2.57137e27			0.321598			0.160799	+	0.986987i	$0.448593\pi$
$618$	−3.64291e27	+	2.68517e27i	−0.448295	+	0.330436i
$619$	−2.27538e27			−0.275516			−0.137758	−	0.990466i	$-0.543990\pi$
$619$	−2.27538e27			−0.275516			−0.137758	+	0.990466i	$0.543990\pi$
$620$	−5.74036e26	+	1.85297e27i	−0.0683946	+	0.220776i
$621$			5.83275e27i			0.683845i
$622$	−3.93501e27	+	2.90047e27i	−0.453985	+	0.334630i
$623$			8.43985e27i			0.958195i
$624$	3.11076e27	−	4.53889e27i	0.347553	−	0.507112i
$625$	−8.65997e27			−0.952174
$626$	−2.80815e27	−	3.80976e27i	−0.303863	−	0.412244i
$627$	8.29298e27			0.883152
$628$	−8.85901e27	−	2.74445e27i	−0.928515	−	0.287646i
$629$			1.10416e28i			1.13901i
$630$	−6.98757e27	−	9.47988e27i	−0.709448	−	0.962492i
$631$		−	2.15086e27i		−	0.214941i	−0.994208	−	0.107470i	$-0.965725\pi$
$631$		−	2.15086e27i		−	0.214941i	0.994208	−	0.107470i	$-0.0342751\pi$
$632$	1.23128e27	+	3.53950e27i	0.121112	+	0.348153i
$633$	−1.79776e27			−0.174059
$634$	8.77819e27	−	6.47036e27i	0.836589	−	0.616646i
$635$	−1.78698e28			−1.67642
$636$	5.26127e26	+	1.62990e26i	0.0485869	+	0.0150518i
$637$		−	2.16162e26i		−	0.0196510i
$638$	−2.73144e27	+	2.01333e27i	−0.244447	+	0.180181i
$639$		−	5.51334e27i		−	0.485743i
$640$	4.33572e27	−	1.59099e28i	0.376063	−	1.37997i
$641$	−6.68225e27			−0.570614			−0.285307	−	0.958436i	$-0.592096\pi$
$641$	−6.68225e27			−0.570614			−0.285307	+	0.958436i	$0.592096\pi$
$642$	−3.16741e27	−	4.29716e27i	−0.266290	−	0.361269i
$643$	9.21310e27			0.762599			0.381299	−	0.924452i	$-0.375477\pi$
$643$	9.21310e27			0.762599			0.381299	+	0.924452i	$0.375477\pi$
$644$	−3.31674e27	+	1.07064e28i	−0.270304	+	0.872537i
$645$			2.49581e27i			0.200270i
$646$	−1.10445e28	−	1.49839e28i	−0.872615	−	1.18386i
$647$		−	1.05751e28i		−	0.822701i	−0.911477	−	0.411351i	$-0.865057\pi$
$647$		−	1.05751e28i		−	0.822701i	0.911477	−	0.411351i	$-0.134943\pi$
$648$	−6.41547e27	+	2.23174e27i	−0.491449	+	0.170960i
$649$	8.19474e27			0.618142
$650$	1.69245e28	−	1.24749e28i	1.25713	−	0.926626i
$651$	−9.15398e26			−0.0669576
$652$	−5.25597e27	+	1.69662e28i	−0.378597	+	1.22210i
$653$			2.34679e28i			1.66472i	0.554232	+	0.832362i	$0.313012\pi$
$653$			2.34679e28i			1.66472i	−0.554232	+	0.832362i	$0.686988\pi$
$654$	−2.41962e27	+	1.78349e27i	−0.169032	+	0.124593i
$655$			6.52842e27i			0.449154i
$656$	−1.56373e28	−	1.07171e28i	−1.05955	−	0.726172i
$657$	2.01385e28			1.34392
$658$	−4.89714e27	−	6.64385e27i	−0.321873	−	0.436677i
$659$	2.82917e28			1.83149			0.915745	−	0.401760i	$-0.131601\pi$
$659$	2.82917e28			1.83149			0.915745	+	0.401760i	$0.131601\pi$
$660$	−1.36320e28	−	4.22307e27i	−0.869199	−	0.269270i
$661$			7.66843e27i			0.481606i	0.970574	+	0.240803i	$0.0774107\pi$
$661$			7.66843e27i			0.481606i	−0.970574	+	0.240803i	$0.922589\pi$
$662$	9.06387e27	+	1.22968e28i	0.560704	+	0.760695i
$663$			1.06891e28i			0.651335i
$664$	1.44945e28	−	5.04219e27i	0.870006	−	0.302648i
$665$	−3.38003e28			−1.99850
$666$	1.23401e28	−	9.09584e27i	0.718749	−	0.529786i
$667$	−3.10781e27			−0.178318
$668$	−1.23185e28	−	3.81616e27i	−0.696294	−	0.215706i
$669$			9.58136e27i			0.533539i
$670$	6.69029e27	−	4.93138e27i	0.367026	−	0.270533i
$671$		−	2.54185e28i		−	1.37380i
$672$	7.77694e27	−	2.67320e26i	0.414110	−	0.0142344i
$673$	−1.51939e28			−0.797108			−0.398554	−	0.917145i	$-0.630488\pi$
$673$	−1.51939e28			−0.797108			−0.398554	+	0.917145i	$0.630488\pi$
$674$	1.88387e28	+	2.55581e28i	0.973761	+	1.32108i
$675$	1.54729e28			0.788015
$676$	7.25546e27	−	2.34205e28i	0.364081	−	1.17525i
$677$		−	2.48298e28i		−	1.22769i	−0.789428	−	0.613843i	$-0.789623\pi$
$677$		−	2.48298e28i		−	1.22769i	0.789428	−	0.613843i	$-0.210377\pi$
$678$	−1.53323e27	−	2.08010e27i	−0.0746982	−	0.101341i
$679$			1.94999e28i			0.936127i
$680$	1.05247e28	+	3.02547e28i	0.497874	+	1.43121i
$681$	−1.00517e28			−0.468562
$682$	4.37628e27	−	3.22573e27i	0.201030	−	0.148178i
$683$	9.69721e27			0.438975			0.219488	−	0.975615i	$-0.429561\pi$
$683$	9.69721e27			0.438975			0.219488	+	0.975615i	$0.429561\pi$
$684$	−7.64773e27	+	2.46867e28i	−0.341171	+	1.10129i
$685$			2.44157e28i			1.07340i
$686$	−1.84544e28	+	1.36027e28i	−0.799576	+	0.589363i
$687$		−	1.25281e28i		−	0.534957i
$688$	6.66691e27	+	4.56921e27i	0.280569	+	0.192290i
$689$	4.44901e27			0.184532
$690$	−7.75516e27	−	1.05213e28i	−0.317030	−	0.430107i
$691$	−9.52315e27			−0.383707			−0.191854	−	0.981424i	$-0.561450\pi$
$691$	−9.52315e27			−0.383707			−0.191854	+	0.981424i	$0.561450\pi$
$692$	2.45381e27	+	7.60169e26i	0.0974496	+	0.0301890i
$693$			3.30059e28i			1.29199i
$694$	−1.69963e28	−	2.30585e28i	−0.655782	−	0.889685i
$695$		−	1.33760e28i		−	0.508719i
$696$	7.08905e26	+	2.03785e27i	0.0265764	+	0.0763976i
$697$	3.68257e28			1.36089
$698$	−2.42445e27	+	1.78705e27i	−0.0883202	+	0.0651003i
$699$	−1.07646e28			−0.386568
$700$	2.84015e28	+	8.79853e27i	1.00545	+	0.311480i
$701$		−	5.09671e28i		−	1.77873i	−0.457199	−	0.889365i	$-0.651147\pi$
$701$		−	5.09671e28i		−	1.77873i	0.457199	−	0.889365i	$-0.348853\pi$
$702$	2.63296e28	−	1.94074e28i	0.905885	−	0.667723i
$703$		−	4.39985e28i		−	1.49240i
$704$	−3.62375e28	+	2.86828e28i	−1.21180	+	0.959170i
$705$	9.62494e27			0.317327
$706$	−1.10671e27	−	1.50144e27i	−0.0359737	−	0.0488048i
$707$	3.12646e28			1.00198
$708$	1.54193e27	−	4.97731e27i	0.0487227	−	0.157276i
$709$		−	5.45169e28i		−	1.69851i	−0.527981	−	0.849256i	$-0.677051\pi$
$709$		−	5.45169e28i		−	1.69851i	0.527981	−	0.849256i	$-0.322949\pi$
$710$	1.61566e28	+	2.19194e28i	0.496327	+	0.673355i
$711$			1.01072e28i			0.306151i
$712$	−3.01030e28	+	1.04719e28i	−0.899104	+	0.312771i
$713$	4.97929e27			0.146647
$714$	−1.21678e28	+	8.96883e27i	−0.353371	+	0.260468i
$715$	−1.15274e29			−3.30119
$716$	9.43775e27	−	3.04648e28i	0.266525	−	0.860337i
$717$			2.15711e28i			0.600731i
$718$	−2.56615e28	+	1.89150e28i	−0.704755	+	0.519471i
$719$			9.63091e27i			0.260843i	0.991459	+	0.130421i	$0.0416330\pi$
$719$			9.63091e27i			0.260843i	−0.991459	+	0.130421i	$0.958367\pi$
$720$	2.51426e28	−	3.66854e28i	0.671561	−	0.979870i
$721$	−5.16949e28			−1.36174
$722$	2.11714e28	+	2.87228e28i	0.550020	+	0.746200i
$723$	−1.38547e27			−0.0354987
$724$	−2.36083e27	−	7.31365e26i	−0.0596594	−	0.0184820i
$725$			8.24428e27i			0.205481i
$726$	1.37954e28	+	1.87159e28i	0.339132	+	0.460092i
$727$			5.73358e28i			1.39021i	0.718906	+	0.695107i	$0.244643\pi$
$727$			5.73358e28i			1.39021i	−0.718906	+	0.695107i	$0.755357\pi$
$728$	5.93654e28	−	2.06514e28i	1.41978	−	0.493896i
$729$	−5.16986e27			−0.121956
$730$	−8.00644e28	+	5.90151e28i	−1.86299	+	1.37320i
$731$	−1.57005e28			−0.360363
$732$	−1.54387e28	−	4.78276e27i	−0.349542	−	0.108285i
$733$		−	4.62077e28i		−	1.03199i	−0.856593	−	0.515993i	$-0.827423\pi$
$733$		−	4.62077e28i		−	1.03199i	0.856593	−	0.515993i	$-0.172577\pi$
$734$	3.81413e28	−	2.81137e28i	0.840300	−	0.619381i
$735$			3.56476e26i			0.00774741i
$736$	−4.23025e28	+	1.45408e27i	−0.906960	+	0.0311753i
$737$	−2.32935e28			−0.492673
$738$	−3.03361e28	−	4.11564e28i	−0.632990	−	0.858763i
$739$	6.84208e28			1.40846			0.704229	−	0.709973i	$-0.251293\pi$
$739$	6.84208e28			1.40846			0.704229	+	0.709973i	$0.251293\pi$
$740$	−2.24055e28	+	7.23245e28i	−0.455027	+	1.46882i
$741$		−	4.25935e28i		−	0.853418i
$742$	3.73301e27	+	5.06449e27i	0.0737939	+	0.100115i
$743$		−	8.05426e27i		−	0.157086i	−0.996911	−	0.0785430i	$-0.974973\pi$
$743$		−	8.05426e27i		−	0.157086i	0.996911	−	0.0785430i	$-0.0250268\pi$
$744$	−1.13580e27	−	3.26502e27i	−0.0218561	−	0.0628284i
$745$	1.19821e29			2.27494
$746$	5.92295e27	−	4.36577e27i	0.110956	−	0.0817849i
$747$	4.13899e28			0.765047
$748$	2.65663e28	−	8.57553e28i	0.484523	−	1.56403i
$749$		−	6.09790e28i		−	1.09739i
$750$	−1.22064e27	+	8.99725e26i	−0.0216757	+	0.0159771i
$751$			1.10694e29i			1.93965i	0.243792	+	0.969827i	$0.421608\pi$
$751$			1.10694e29i			1.93965i	−0.243792	+	0.969827i	$0.578392\pi$
$752$	1.76209e28	−	2.57105e28i	0.304683	−	0.444562i
$753$	1.26559e28			0.215945
$754$	1.03407e28	+	1.40289e28i	0.174114	+	0.236217i
$755$	−8.71651e25			−0.00144835
$756$	4.41845e28	+	1.36880e28i	0.724523	+	0.224451i
$757$			1.05202e29i			1.70242i	0.524827	+	0.851209i	$0.324130\pi$
$757$			1.05202e29i			1.70242i	−0.524827	+	0.851209i	$0.675870\pi$
$758$	3.64326e28	+	4.94273e28i	0.581833	+	0.789360i
$759$			3.66316e28i			0.577349i
$760$	−4.19384e28	−	1.20558e29i	−0.652344	−	1.87526i
$761$	1.48008e28			0.227216			0.113608	−	0.993526i	$-0.463759\pi$
$761$	1.48008e28			0.227216			0.113608	+	0.993526i	$0.463759\pi$
$762$	2.56339e28	−	1.88946e28i	0.388387	−	0.286278i
$763$	−3.43358e28			−0.513454
$764$	1.21156e29	+	3.75332e28i	1.78818	+	0.553964i
$765$			8.63940e28i			1.25855i
$766$	−5.41620e28	+	3.99225e28i	−0.778765	+	0.574024i
$767$		−	4.20889e28i		−	0.597330i
$768$	1.06029e28	+	2.74069e28i	0.148529	+	0.383926i
$769$	2.64757e28			0.366087			0.183044	−	0.983105i	$-0.441405\pi$
$769$	2.64757e28			0.366087			0.183044	+	0.983105i	$0.441405\pi$
$770$	−9.67225e28	−	1.31221e29i	−1.32014	−	1.79101i
$771$	1.65503e27			0.0222978
$772$	4.24855e28	−	1.37142e29i	0.565025	−	1.82389i
$773$			6.20389e28i			0.814459i	0.913326	+	0.407229i	$0.133505\pi$
$773$			6.20389e28i			0.814459i	−0.913326	+	0.407229i	$0.866495\pi$
$774$	1.29337e28	+	1.75469e28i	0.167615	+	0.227400i
$775$		−	1.32089e28i		−	0.168985i
$776$	−6.95517e28	+	2.41949e28i	−0.878397	+	0.305567i
$777$	−3.57294e28			−0.445467
$778$	−6.47777e28	+	4.77473e28i	−0.797315	+	0.587697i
$779$	−1.46742e29			−1.78312
$780$	−2.16901e28	+	7.00151e28i	−0.260204	+	0.839934i
$781$		−	7.63162e28i		−	0.903870i
$782$	6.61866e28	−	4.87858e28i	0.773932	−	0.570461i
$783$			1.28257e28i			0.148069i
$784$	9.52231e26	+	6.52618e26i	0.0108538	+	0.00743873i
$785$	1.23541e29			1.39031
$786$	−6.90282e27	−	9.36491e27i	−0.0767010	−	0.104059i
$787$	2.28741e28			0.250956			0.125478	−	0.992096i	$-0.459954\pi$
$787$	2.28741e28			0.250956			0.125478	+	0.992096i	$0.459954\pi$
$788$	2.39079e28	+	7.40647e27i	0.258988	+	0.0802323i
$789$		−	2.90698e28i		−	0.310937i
$790$	−2.96189e28	−	4.01832e28i	−0.312822	−	0.424399i
$791$		−	2.95177e28i		−	0.307835i
$792$	−1.17725e29	+	4.09527e28i	−1.21231	+	0.421727i
$793$	−1.30552e29			−1.32755
$794$	−6.32029e28	+	4.65865e28i	−0.634646	+	0.467795i
$795$	−7.33693e27			−0.0727517
$796$	−1.43502e29	−	4.44558e28i	−1.40517	−	0.435309i
$797$			2.62443e28i			0.253777i	0.991917	+	0.126888i	$0.0404990\pi$
$797$			2.62443e28i			0.253777i	−0.991917	+	0.126888i	$0.959501\pi$
$798$	4.84860e28	−	3.57388e28i	0.463007	−	0.341280i
$799$			6.05481e28i			0.570996i
$800$	3.85733e27	+	1.12219e29i	0.0359242	+	1.04512i
$801$	−8.59609e28			−0.790635
$802$	8.81106e28	+	1.19538e29i	0.800358	+	1.08583i
$803$	2.78759e29			2.50077
$804$	−4.38292e27	+	1.41480e28i	−0.0388332	+	0.125353i
$805$		−	1.49302e29i		−	1.30650i
$806$	−1.65677e28	−	2.24770e28i	−0.143189	−	0.194262i
$807$		−	5.12305e28i		−	0.437314i
$808$	3.87922e28	+	1.11514e29i	0.327062	+	0.940188i
$809$	−2.30994e29			−1.92361			−0.961803	−	0.273741i	$-0.911739\pi$
$809$	−2.30994e29			−1.92361			−0.961803	+	0.273741i	$0.911739\pi$
$810$	7.28337e28	−	5.36853e28i	0.599076	−	0.441576i
$811$	−1.54510e29			−1.25531			−0.627653	−	0.778494i	$-0.715984\pi$
$811$	−1.54510e29			−1.25531			−0.627653	+	0.778494i	$0.715984\pi$
$812$	−7.29323e27	+	2.35424e28i	−0.0585275	+	0.188925i
$813$		−	4.19428e28i		−	0.332469i
$814$	1.70813e29	−	1.25905e29i	1.33745	−	0.985826i
$815$		−	2.36596e29i		−	1.82992i
$816$	−4.70873e28	−	3.22716e28i	−0.359751	−	0.246558i
$817$	6.25631e28			0.472169
$818$	4.52006e28	+	6.13227e28i	0.336986	+	0.457181i
$819$	1.69521e29			1.24849
$820$	2.41214e29	+	7.47261e28i	1.75495	+	0.543668i
$821$			1.26136e29i			0.906581i	0.891363	+	0.453290i	$0.149750\pi$
$821$			1.26136e29i			0.906581i	−0.891363	+	0.453290i	$0.850250\pi$
$822$	−2.58159e28	−	3.50239e28i	−0.183303	−	0.248683i
$823$		−	6.26104e28i		−	0.439186i	−0.975592	−	0.219593i	$-0.929527\pi$
$823$		−	6.26104e28i		−	0.439186i	0.975592	−	0.219593i	$-0.0704729\pi$
$824$	−6.41414e28	−	1.84384e29i	−0.444495	−	1.27776i
$825$	9.71751e28			0.665297
$826$	4.79116e28	−	3.53154e28i	0.324071	−	0.238871i
$827$	−2.24910e29			−1.50298			−0.751491	−	0.659743i	$-0.770665\pi$
$827$	−2.24910e29			−1.50298			−0.751491	+	0.659743i	$0.770665\pi$
$828$	−1.09046e29	−	3.37814e28i	−0.719955	−	0.223036i
$829$			8.89643e28i			0.580324i	0.956978	+	0.290162i	$0.0937092\pi$
$829$			8.89643e28i			0.580324i	−0.956978	+	0.290162i	$0.906291\pi$
$830$	−1.64553e29	+	1.21291e29i	−1.06054	+	0.781716i
$831$			3.57687e28i			0.227768i
$832$	1.47318e29	+	1.86119e29i	0.926876	+	1.17100i
$833$	−2.24250e27			−0.0139406
$834$	1.41431e28	+	1.91876e28i	0.0868729	+	0.117858i
$835$	1.71783e29			1.04260
$836$	−1.05861e29	+	3.41716e29i	−0.634850	+	2.04928i
$837$		−	2.05492e28i		−	0.121770i
$838$	1.15904e29	+	1.57244e29i	0.678668	+	0.920734i
$839$		−	2.30769e29i		−	1.33523i	−0.744505	−	0.667617i	$-0.767315\pi$
$839$		−	2.30769e29i		−	1.33523i	0.744505	−	0.667617i	$-0.232685\pi$
$840$	−9.79005e28	+	3.40565e28i	−0.559747	+	0.194719i
$841$	1.70161e29			0.961390
$842$	1.05801e29	−	7.79850e28i	0.590700	−	0.435402i
$843$	−7.65690e28			−0.422452
$844$	2.29486e28	−	7.40775e28i	0.125121	−	0.403889i
$845$			3.26603e29i			1.75976i
$846$	6.76684e28	−	4.98780e28i	0.360315	−	0.265586i
$847$			2.65589e29i			1.39758i
$848$	−1.34321e28	+	1.95987e28i	−0.0698530	+	0.101922i
$849$	−1.31873e29			−0.677765
$850$	−1.29417e29	−	1.75577e29i	−0.657359	−	0.891824i
$851$	1.94349e29			0.975636
$852$	−4.63528e28	−	1.43597e28i	−0.229975	−	0.0712442i
$853$		−	1.64058e29i		−	0.804463i	−0.915538	−	0.402232i	$-0.868235\pi$
$853$		−	1.64058e29i		−	0.804463i	0.915538	−	0.402232i	$-0.131765\pi$
$854$	−1.09541e29	−	1.48612e29i	−0.530884	−	0.720239i
$855$		−	3.44261e29i		−	1.64902i
$856$	2.17498e29	−	7.56609e28i	1.02972	−	0.358207i
$857$	−8.34337e28			−0.390421			−0.195211	−	0.980761i	$-0.562539\pi$
$857$	−8.34337e28			−0.390421			−0.195211	+	0.980761i	$0.562539\pi$
$858$	1.65359e29	−	1.21885e29i	0.764811	−	0.563738i
$859$	−5.92383e27			−0.0270814			−0.0135407	−	0.999908i	$-0.504310\pi$
$859$	−5.92383e27			−0.0270814			−0.0135407	+	0.999908i	$0.504310\pi$
$860$	−1.02841e29	−	3.18592e28i	−0.464709	−	0.143963i
$861$			1.19164e29i			0.532245i
$862$	−2.02581e29	+	1.49321e29i	−0.894388	+	0.659249i
$863$			2.50392e28i			0.109273i	0.998506	+	0.0546364i	$0.0174000\pi$
$863$			2.50392e28i			0.109273i	−0.998506	+	0.0546364i	$0.982600\pi$
$864$	6.00090e27	+	1.74580e29i	0.0258868	+	0.753107i
$865$	−3.42188e28			−0.145916
$866$	−4.33944e28	−	5.88723e28i	−0.182917	−	0.248160i
$867$	1.20976e28			0.0504091
$868$	1.16851e28	−	3.77193e28i	0.0481322	−	0.155370i
$869$			1.39905e29i			0.569687i
$870$	−1.70529e28	−	2.31353e28i	−0.0686446	−	0.0931286i
$871$			1.19637e29i			0.476086i
$872$	−4.26028e28	−	1.22468e29i	−0.167600	−	0.481789i
$873$	−1.98609e29			−0.772425
$874$	−2.63739e29	+	1.94400e29i	−1.01405	+	0.747451i
$875$	−1.73215e28			−0.0658423
$876$	5.24515e28	−	1.69312e29i	0.197114	−	0.636279i
$877$		−	3.01387e29i		−	1.11977i	−0.828570	−	0.559885i	$-0.810845\pi$
$877$		−	3.01387e29i		−	1.11977i	0.828570	−	0.559885i	$-0.189155\pi$
$878$	1.23849e29	−	9.12883e28i	0.454932	−	0.335328i
$879$			6.66273e28i			0.241971i
$880$	3.48026e29	−	5.07803e29i	1.24964	−	1.82334i
$881$	−1.20836e29			−0.428981			−0.214490	−	0.976726i	$-0.568809\pi$
$881$	−1.20836e29			−0.428981			−0.214490	+	0.976726i	$0.568809\pi$
$882$	1.84732e27	+	2.50621e27i	0.00648419	+	0.00879695i
$883$	3.02684e28			0.105047			0.0525233	−	0.998620i	$-0.483274\pi$
$883$	3.02684e28			0.105047			0.0525233	+	0.998620i	$0.483274\pi$
$884$	−4.40447e29	−	1.36447e29i	−1.51137	−	0.468210i
$885$			6.94095e28i			0.235498i
$886$	1.11664e29	+	1.51492e29i	0.374606	+	0.508219i
$887$			5.85909e29i			1.94354i	0.235927	+	0.971771i	$0.424188\pi$
$887$			5.85909e29i			1.94354i	−0.235927	+	0.971771i	$0.575812\pi$
$888$	−4.43320e28	−	1.27439e29i	−0.145408	−	0.417996i
$889$	3.63759e29			1.17977
$890$	3.41754e29	−	2.51905e29i	1.09601	−	0.807862i
$891$	−2.53584e29			−0.804163
$892$	−3.94803e29	−	1.22307e29i	−1.23803	−	0.383532i
$893$		−	2.41271e29i		−	0.748152i
$894$	−1.71881e29	+	1.26693e29i	−0.527052	+	0.388487i
$895$			4.24838e29i			1.28823i
$896$	−8.82582e28	+	3.23864e29i	−0.264652	+	0.971142i
$897$	1.88144e29			0.557911
$898$	1.72261e29	+	2.33703e29i	0.505154	+	0.685331i
$899$	1.09490e28			0.0317525
$900$	−8.96142e28	+	2.89273e29i	−0.257011	+	0.829626i
$901$		−	4.61548e28i		−	0.130909i
$902$	−4.19915e29	−	5.69690e29i	−1.17787	−	1.59799i
$903$		−	5.08050e28i		−	0.140938i
$904$	1.05283e29	−	3.66247e28i	0.288851	−	0.100482i
$905$	3.29222e28			0.0893312
$906$	1.25037e26	−	9.21640e25i	0.000335549	−	0.000247331i
$907$	−3.06710e29			−0.814058			−0.407029	−	0.913415i	$-0.633435\pi$
$907$	−3.06710e29			−0.814058			−0.407029	+	0.913415i	$0.633435\pi$
$908$	1.28310e29	−	4.14183e29i	0.336824	−	1.08726i
$909$			3.18434e29i			0.826762i
$910$	−6.73965e29	+	4.96776e29i	−1.73071	+	1.27569i
$911$		−	2.79180e29i		−	0.709088i	−0.935039	−	0.354544i	$-0.884636\pi$
$911$		−	2.79180e29i		−	0.709088i	0.935039	−	0.354544i	$-0.115364\pi$
$912$	1.87632e29	+	1.28595e29i	0.471367	+	0.323054i
$913$	5.72922e29			1.42360
$914$	3.85008e29	+	5.22332e29i	0.946255	+	1.28376i
$915$	2.15295e29			0.523387
$916$	5.16226e29	+	1.59922e29i	1.24132	+	0.384552i
$917$		−	1.32893e29i		−	0.316089i
$918$	−2.01336e29	−	2.73148e29i	−0.473690	−	0.642645i
$919$			6.39509e28i			0.148830i	0.997227	+	0.0744151i	$0.0237090\pi$
$919$			6.39509e28i			0.148830i	−0.997227	+	0.0744151i	$0.976291\pi$
$920$	5.32528e29	−	1.85250e29i	1.22592	−	0.426461i
$921$	−5.09889e28			−0.116113
$922$	−2.63271e29	+	1.94056e29i	−0.593053	+	0.437136i
$923$	−3.91967e29			−0.873439
$924$	2.77494e29	+	8.59651e28i	0.611693	+	0.189497i
$925$		−	5.15563e29i		−	1.12425i
$926$	5.22659e29	−	3.85249e29i	1.12748	−	0.831059i
$927$		−	5.26519e29i		−	1.12361i
$928$	−9.30196e28	+	3.19740e27i	−0.196379	+	0.00675020i
$929$	2.77307e29			0.579166			0.289583	−	0.957153i	$-0.406483\pi$
$929$	2.77307e29			0.579166			0.289583	+	0.957153i	$0.406483\pi$
$930$	2.73220e28	+	3.70671e28i	0.0564525	+	0.0765878i
$931$	8.93586e27			0.0182658
$932$	1.37411e29	−	4.43559e29i	0.277883	−	0.897001i
$933$			1.16043e29i			0.232168i
$934$	2.45713e29	+	3.33354e29i	0.486363	+	0.659837i
$935$			1.19587e30i			2.34190i
$936$	2.10337e29	+	6.04644e29i	0.407528	+	1.17150i
$937$	2.62562e27			0.00503310			0.00251655	−	0.999997i	$-0.499199\pi$
$937$	2.62562e27			0.00503310			0.00251655	+	0.999997i	$0.499199\pi$
$938$	−1.36188e29	+	1.00384e29i	−0.258292	+	0.190386i
$939$	−1.12349e29			−0.210821
$940$	−1.22863e29	+	3.96599e29i	−0.228109	+	0.736332i
$941$		−	5.28984e29i		−	0.971732i	−0.874033	−	0.485866i	$-0.838504\pi$
$941$		−	5.28984e29i		−	0.971732i	0.874033	−	0.485866i	$-0.161496\pi$
$942$	−1.77217e29	+	1.30626e29i	−0.322104	+	0.237421i
$943$		−	6.48188e29i		−	1.16569i
$944$	1.85409e29	+	1.27072e29i	0.329922	+	0.226114i
$945$	−6.16161e29			−1.08487
$946$	1.79030e29	+	2.42885e29i	0.311899	+	0.423146i
$947$	9.11095e29			1.57059			0.785297	−	0.619120i	$-0.212510\pi$
$947$	9.11095e29			1.57059			0.785297	+	0.619120i	$0.212510\pi$
$948$	8.49755e28	+	2.63247e28i	0.144947	+	0.0449034i
$949$		−	1.43173e30i		−	2.41657i
$950$	5.15698e29	+	6.99636e29i	0.861310	+	1.16852i
$951$		−	2.58868e29i		−	0.427831i
$952$	−2.14241e29	−	6.15867e29i	−0.350375	−	1.00720i
$953$	−3.76652e29			−0.609552			−0.304776	−	0.952424i	$-0.598582\pi$
$953$	−3.76652e29			−0.609552			−0.304776	+	0.952424i	$0.598582\pi$
$954$	−5.15825e28	+	3.80212e28i	−0.0826074	+	0.0608895i
$955$	−1.68955e30			−2.67754
$956$	−8.88844e29	−	2.75356e29i	−1.39395	−	0.431833i
$957$			8.05498e28i			0.125010i
$958$	−9.85676e29	+	7.26537e29i	−1.51384	+	1.11584i
$959$		−	4.97008e29i		−	0.755400i
$960$	−2.42944e29	−	3.06932e29i	−0.365421	−	0.461669i
$961$	6.54248e29			0.973887
$962$	−6.46662e29	−	8.77311e29i	−0.952635	−	1.29242i
$963$	6.21079e29			0.905490
$964$	1.76856e28	−	5.70886e28i	0.0255181	−	0.0823719i
$965$			1.91247e30i			2.73100i
$966$	1.57865e29	+	2.14172e29i	0.223107	+	0.302685i
$967$			3.11403e29i			0.435571i	0.975997	+	0.217785i	$0.0698833\pi$
$967$			3.11403e29i			0.435571i	−0.975997	+	0.217785i	$0.930117\pi$
$968$	−9.47296e29	+	3.29535e29i	−1.31139	+	0.456192i
$969$	−4.41873e29			−0.605424
$970$	7.89608e29	−	5.82016e29i	1.07077	−	0.789256i
$971$	1.12701e30			1.51263			0.756317	−	0.654206i	$-0.226997\pi$
$971$	1.12701e30			1.51263			0.756317	+	0.654206i	$0.226997\pi$
$972$	−2.15574e29	+	6.95868e29i	−0.286374	+	0.924409i
$973$			2.72283e29i			0.358007i
$974$	7.23655e28	−	5.33402e28i	0.0941764	−	0.0694169i
$975$		−	4.99100e29i		−	0.642897i
$976$	3.94151e29	−	5.75104e29i	0.502533	−	0.733243i
$977$	−1.35380e30			−1.70847			−0.854235	−	0.519887i	$-0.825974\pi$
$977$	−1.35380e30			−1.70847			−0.854235	+	0.519887i	$0.825974\pi$
$978$	2.50165e29	+	3.39393e29i	0.312491	+	0.423950i
$979$	−1.18988e30			−1.47121
$980$	−1.46887e28	−	4.55044e27i	−0.0179773	−	0.00556920i
$981$		−	3.49714e29i		−	0.423665i
$982$	−4.21907e29	−	5.72392e29i	−0.505943	−	0.686402i
$983$		−	5.32011e29i		−	0.631517i	−0.948840	−	0.315759i	$-0.897741\pi$
$983$		−	5.32011e29i		−	0.631517i	0.948840	−	0.315759i	$-0.102259\pi$
$984$	−4.25029e29	+	1.47855e29i	−0.499422	+	0.173734i
$985$	−3.33400e29			−0.387797
$986$	1.45539e29	−	1.07276e29i	0.167575	−	0.123519i
$987$	−1.95926e29			−0.223317
$988$	1.75508e30	+	5.43710e29i	1.98029	+	0.613476i
$989$			2.76353e29i			0.308675i
$990$	1.33651e30	−	9.85131e29i	1.47781	−	1.08929i
$991$			1.58702e30i			1.73719i	0.495525	+	0.868594i	$0.334976\pi$
$991$			1.58702e30i			1.73719i	−0.495525	+	0.868594i	$0.665024\pi$
$992$	1.49035e29	−	5.12283e27i	0.161499	−	0.00555128i
$993$	3.62630e29			0.389019
$994$	−3.28886e29	−	4.46192e29i	−0.349286	−	0.473869i
$995$	2.00117e30			2.10403
$996$	1.07801e29	−	3.47981e29i	0.112210	−	0.362211i
$997$			5.62022e29i			0.579164i	0.957153	+	0.289582i	$0.0935163\pi$
$997$			5.62022e29i			0.579164i	−0.957153	+	0.289582i	$0.906484\pi$
$998$	−3.80094e29	−	5.15665e29i	−0.387780	−	0.526092i
$999$		−	8.02068e29i		−	0.810133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.14	yes	18
3.2	odd	2		72.21.b.b.19.5		18
4.3	odd	2		32.21.d.b.15.7		18
8.3	odd	2	inner	8.21.d.b.3.13	✓	18
8.5	even	2		32.21.d.b.15.8		18
24.11	even	2		72.21.b.b.19.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.13	✓	18	8.3	odd	2	inner
8.21.d.b.3.14	yes	18	1.1	even	1	trivial
32.21.d.b.15.7		18	4.3	odd	2
32.21.d.b.15.8		18	8.5	even	2
72.21.b.b.19.5		18	3.2	odd	2
72.21.b.b.19.6		18	24.11	even	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:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(607.571 + 824.278i) q^{2} +24307.8 q^{3} +(-310291. + 1.00161e6i) q^{4} -1.39677e7i q^{5} +(1.47687e7 + 2.00364e7i) q^{6} +2.84328e8i q^{7} +(-1.01413e9 + 3.52785e8i) q^{8} -2.89591e9 q^{9} +O(q^{10})\)	\(q+(607.571 + 824.278i) q^{2} +24307.8 q^{3} +(-310291. + 1.00161e6i) q^{4} -1.39677e7i q^{5} +(1.47687e7 + 2.00364e7i) q^{6} +2.84328e8i q^{7} +(-1.01413e9 + 3.52785e8i) q^{8} -2.89591e9 q^{9} +(1.15133e10 - 8.48636e9i) q^{10} -4.00855e10 q^{11} +(-7.54252e9 + 2.43471e10i) q^{12} +2.05883e11i q^{13} +(-2.34365e11 + 1.72749e11i) q^{14} -3.39524e11i q^{15} +(-9.06950e11 - 6.21585e11i) q^{16} +2.13586e12 q^{17} +(-1.75947e12 - 2.38704e12i) q^{18} -8.51094e12 q^{19} +(1.39902e13 + 4.33406e12i) q^{20} +6.91139e12i q^{21} +(-2.43548e13 - 3.30416e13i) q^{22} -3.75944e13i q^{23} +(-2.46514e13 + 8.57545e12i) q^{24} -9.97290e13 q^{25} +(-1.69705e14 + 1.25088e14i) q^{26} -1.55150e14 q^{27} +(-2.84787e14 - 8.82244e13i) q^{28} -8.26668e13i q^{29} +(2.79862e14 - 2.06285e14i) q^{30} +1.32448e14i q^{31} +(-3.86781e13 - 1.12524e15i) q^{32} -9.74392e14 q^{33} +(1.29769e15 + 1.76055e15i) q^{34} +3.97140e15 q^{35} +(8.98577e14 - 2.90059e15i) q^{36} +5.16964e15i q^{37} +(-5.17100e15 - 7.01537e15i) q^{38} +5.00457e15i q^{39} +(4.92760e15 + 1.41651e16i) q^{40} +1.72416e16 q^{41} +(-5.69691e15 + 4.19916e15i) q^{42} -7.35091e15 q^{43} +(1.24382e16 - 4.01502e16i) q^{44} +4.04492e16i q^{45} +(3.09882e16 - 2.28412e16i) q^{46} +2.83483e16i q^{47} +(-2.20460e16 - 1.51094e16i) q^{48} -1.04993e15 q^{49} +(-6.05924e16 - 8.22044e16i) q^{50} +5.19183e16 q^{51} +(-2.06215e17 - 6.38836e16i) q^{52} -2.16094e16i q^{53} +(-9.42644e16 - 1.27886e17i) q^{54} +5.59902e17i q^{55} +(-1.00307e17 - 2.88346e17i) q^{56} -2.06883e17 q^{57} +(6.81404e16 - 5.02259e16i) q^{58} -2.04432e17 q^{59} +(3.40073e17 + 1.05352e17i) q^{60} +6.34107e17i q^{61} +(-1.09174e17 + 8.04713e16i) q^{62} -8.23388e17i q^{63} +(9.04007e17 - 7.15542e17i) q^{64} +2.87571e18 q^{65} +(-5.92012e17 - 8.03169e17i) q^{66} +5.81095e17 q^{67} +(-6.62740e17 + 2.13931e18i) q^{68} -9.13838e17i q^{69} +(2.41291e18 + 3.27354e18i) q^{70} +1.90384e18i q^{71} +(2.93684e18 - 1.02164e18i) q^{72} -6.95411e18 q^{73} +(-4.26122e18 + 3.14092e18i) q^{74} -2.42420e18 q^{75} +(2.64087e18 - 8.52467e18i) q^{76} -1.13974e19i q^{77} +(-4.12515e18 + 3.04063e18i) q^{78} -3.49017e18i q^{79} +(-8.68210e18 + 1.26680e19i) q^{80} +6.32607e18 q^{81} +(1.04755e19 + 1.42119e19i) q^{82} -1.42925e19 q^{83} +(-6.92255e18 - 2.14455e18i) q^{84} -2.98331e19i q^{85} +(-4.46620e18 - 6.05919e18i) q^{86} -2.00945e18i q^{87} +(4.06520e19 - 1.41416e19i) q^{88} +2.96835e19 q^{89} +(-3.33414e19 + 2.45758e19i) q^{90} -5.85381e19 q^{91} +(3.76551e19 + 1.16652e19i) q^{92} +3.21952e18i q^{93} +(-2.33669e19 + 1.72236e19i) q^{94} +1.18878e20i q^{95} +(-9.40182e17 - 2.73520e19i) q^{96} +6.85825e19 q^{97} +(-6.37905e17 - 8.65431e17i) q^{98} +1.16084e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

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