LMFDB - Embedded newform 26.8.b.a.25.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,8,Mod(25,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.25"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	26.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.12201066259$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 17770x^{8} + 98320641x^{6} + 176057788072x^{4} + 109845194658832x^{2} + 14762086704451584 $ x^10 + 17770x^8 + 98320641x^6 + 176057788072x^4 + 109845194658832x^2 + 14762086704451584
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			25.9
Root			$32.3570i$ of defining polynomial
Character	$\chi$	$=$	26.25
Dual form			26.8.b.a.25.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000i q^{2} +37.3570 q^{3} -64.0000 q^{4} -477.073i q^{5} +298.856i q^{6} -855.664i q^{7} -512.000i q^{8} -791.454 q^{9} +3816.58 q^{10} +1409.60i q^{11} -2390.85 q^{12} +(5683.55 - 5517.77i) q^{13} +6845.31 q^{14} -17822.0i q^{15} +4096.00 q^{16} +24521.4 q^{17} -6331.63i q^{18} +16871.7i q^{19} +30532.6i q^{20} -31965.0i q^{21} -11276.8 q^{22} -54186.6 q^{23} -19126.8i q^{24} -149473. q^{25} +(44142.1 + 45468.4i) q^{26} -111266. q^{27} +54762.5i q^{28} +180093. q^{29} +142576. q^{30} +73073.6i q^{31} +32768.0i q^{32} +52658.4i q^{33} +196171. i q^{34} -408214. q^{35} +50653.1 q^{36} -310734. i q^{37} -134974. q^{38} +(212320. - 206127. i) q^{39} -244261. q^{40} +405360. i q^{41} +255720. q^{42} +626140. q^{43} -90214.4i q^{44} +377581. i q^{45} -433493. i q^{46} -1.19516e6i q^{47} +153014. q^{48} +91382.5 q^{49} -1.19579e6i q^{50} +916045. q^{51} +(-363747. + 353137. i) q^{52} -1.10341e6 q^{53} -890129. i q^{54} +672481. q^{55} -438100. q^{56} +630277. i q^{57} +1.44074e6i q^{58} +2.21865e6i q^{59} +1.14061e6i q^{60} +2.71355e6 q^{61} -584589. q^{62} +677219. i q^{63} -262144. q^{64} +(-2.63238e6 - 2.71147e6i) q^{65} -421267. q^{66} +2.35192e6i q^{67} -1.56937e6 q^{68} -2.02425e6 q^{69} -3.26571e6i q^{70} +2.11218e6i q^{71} +405224. i q^{72} -297647. i q^{73} +2.48587e6 q^{74} -5.58387e6 q^{75} -1.07979e6i q^{76} +1.20614e6 q^{77} +(1.64902e6 + 1.69856e6i) q^{78} +6.13466e6 q^{79} -1.95409e6i q^{80} -2.42566e6 q^{81} -3.24288e6 q^{82} +5.86853e6i q^{83} +2.04576e6i q^{84} -1.16985e7i q^{85} +5.00912e6i q^{86} +6.72773e6 q^{87} +721715. q^{88} -5.02086e6i q^{89} -3.02065e6 q^{90} +(-4.72135e6 - 4.86321e6i) q^{91} +3.46794e6 q^{92} +2.72981e6i q^{93} +9.56128e6 q^{94} +8.04904e6 q^{95} +1.22411e6i q^{96} -4.56414e6i q^{97} +731060. i q^{98} -1.11563e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 54 q^{3} - 640 q^{4} + 13960 q^{9} - 1136 q^{10} - 3456 q^{12} + 3432 q^{13} + 3792 q^{14} + 40960 q^{16} - 6918 q^{17} + 17280 q^{22} + 94164 q^{23} - 330788 q^{25} + 118896 q^{26} - 53550 q^{27}+ \cdots + 16547484 q^{95}+O(q^{100}) $ 10 * q + 54 * q^3 - 640 * q^4 + 13960 * q^9 - 1136 * q^10 - 3456 * q^12 + 3432 * q^13 + 3792 * q^14 + 40960 * q^16 - 6918 * q^17 + 17280 * q^22 + 94164 * q^23 - 330788 * q^25 + 118896 * q^26 - 53550 * q^27 - 131304 * q^29 - 434992 * q^30 + 873450 * q^35 - 893440 * q^36 + 602976 * q^38 - 1569460 * q^39 + 72704 * q^40 + 1800592 * q^42 + 2740774 * q^43 + 221184 * q^48 - 3083904 * q^49 + 1103186 * q^51 - 219648 * q^52 - 3605916 * q^53 + 3999840 * q^55 - 242688 * q^56 + 11727656 * q^61 - 4210560 * q^62 - 2621440 * q^64 - 7481034 * q^65 - 5557248 * q^66 + 442752 * q^68 + 2035796 * q^69 + 18145392 * q^74 - 32855720 * q^75 - 7147920 * q^77 - 8343632 * q^78 - 28449228 * q^79 + 49311466 * q^81 + 17868800 * q^82 + 50156320 * q^87 - 1105920 * q^88 - 23059744 * q^90 - 20225194 * q^91 - 6026496 * q^92 + 8240976 * q^94 + 16547484 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$-1$

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 $

$2$			8.00000i			0.707107i
$2$			8.00000i			0.707107i
$3$	37.3570			0.798818			0.399409	−	0.916773i	$-0.369215\pi$
$3$	37.3570			0.798818			0.399409	+	0.916773i	$0.369215\pi$
$4$	−64.0000			−0.500000
$5$		−	477.073i		−	1.70683i	−0.521235	−	0.853413i	$-0.674528\pi$
$5$		−	477.073i		−	1.70683i	0.521235	−	0.853413i	$-0.325472\pi$
$6$			298.856i			0.564849i
$7$		−	855.664i		−	0.942888i	−0.881896	−	0.471444i	$-0.843733\pi$
$7$		−	855.664i		−	0.942888i	0.881896	−	0.471444i	$-0.156267\pi$
$8$		−	512.000i		−	0.353553i
$9$	−791.454			−0.361890
$10$	3816.58			1.20691
$11$			1409.60i			0.319316i	0.987172	+	0.159658i	$0.0510392\pi$
$11$			1409.60i			0.319316i	−0.987172	+	0.159658i	$0.948961\pi$
$12$	−2390.85			−0.399409
$13$	5683.55	−	5517.77i	0.717494	−	0.696565i
$13$	5683.55	−	5517.77i	0.717494	−	0.696565i
$14$	6845.31			0.666722
$15$		−	17822.0i		−	1.36344i
$16$	4096.00			0.250000
$17$	24521.4			1.21052			0.605262	−	0.796026i	$-0.293068\pi$
$17$	24521.4			1.21052			0.605262	+	0.796026i	$0.293068\pi$
$18$		−	6331.63i		−	0.255895i
$19$			16871.7i			0.564316i	0.959368	+	0.282158i	$0.0910502\pi$
$19$			16871.7i			0.564316i	−0.959368	+	0.282158i	$0.908950\pi$
$20$			30532.6i			0.853413i
$21$		−	31965.0i		−	0.753195i
$22$	−11276.8			−0.225791
$23$	−54186.6			−0.928634			−0.464317	−	0.885669i	$-0.653700\pi$
$23$	−54186.6			−0.928634			−0.464317	+	0.885669i	$0.653700\pi$
$24$		−	19126.8i		−	0.282425i
$25$	−149473.			−1.91326
$26$	44142.1	+	45468.4i	0.492546	+	0.507345i
$27$	−111266.			−1.08790
$28$			54762.5i			0.471444i
$29$	180093.			1.37121			0.685605	−	0.727974i	$-0.259538\pi$
$29$	180093.			1.37121			0.685605	+	0.727974i	$0.259538\pi$
$30$	142576.			0.964100
$31$			73073.6i			0.440549i	0.975438	+	0.220275i	$0.0706954\pi$
$31$			73073.6i			0.440549i	−0.975438	+	0.220275i	$0.929305\pi$
$32$			32768.0i			0.176777i
$33$			52658.4i			0.255076i
$34$			196171.i			0.855970i
$35$	−408214.			−1.60935
$36$	50653.1			0.180945
$37$		−	310734.i		−	1.00851i	−0.863554	−	0.504257i	$-0.831766\pi$
$37$		−	310734.i		−	1.00851i	0.863554	−	0.504257i	$-0.168234\pi$
$38$	−134974.			−0.399031
$39$	212320.	−	206127.i	0.573147	−	0.556429i
$40$	−244261.			−0.603454
$41$			405360.i			0.918540i	0.888297	+	0.459270i	$0.151889\pi$
$41$			405360.i			0.918540i	−0.888297	+	0.459270i	$0.848111\pi$
$42$	255720.			0.532590
$43$	626140.			1.20097			0.600484	−	0.799637i	$-0.294975\pi$
$43$	626140.			1.20097			0.600484	+	0.799637i	$0.294975\pi$
$44$		−	90214.4i		−	0.159658i
$45$			377581.i			0.617684i
$46$		−	433493.i		−	0.656643i
$47$		−	1.19516e6i		−	1.67913i	−0.543261	−	0.839564i	$-0.682811\pi$
$47$		−	1.19516e6i		−	1.67913i	0.543261	−	0.839564i	$-0.317189\pi$
$48$	153014.			0.199704
$49$	91382.5			0.110963
$50$		−	1.19579e6i		−	1.35288i
$51$	916045.			0.966989
$52$	−363747.	+	353137.i	−0.358747	+	0.348283i
$53$	−1.10341e6			−1.01806			−0.509029	−	0.860749i	$-0.669996\pi$
$53$	−1.10341e6			−1.01806			−0.509029	+	0.860749i	$0.669996\pi$
$54$		−	890129.i		−	0.769263i
$55$	672481.			0.545018
$56$	−438100.			−0.333361
$57$			630277.i			0.450785i
$58$			1.44074e6i			0.969591i
$59$			2.21865e6i			1.40639i	0.710996	+	0.703196i	$0.248244\pi$
$59$			2.21865e6i			1.40639i	−0.710996	+	0.703196i	$0.751756\pi$
$60$			1.14061e6i			0.681722i
$61$	2.71355e6			1.53068			0.765339	−	0.643627i	$-0.222571\pi$
$61$	2.71355e6			1.53068			0.765339	+	0.643627i	$0.222571\pi$
$62$	−584589.			−0.311515
$63$			677219.i			0.341222i
$64$	−262144.			−0.125000
$65$	−2.63238e6	−	2.71147e6i	−1.18892	−	1.22464i
$66$	−421267.			−0.180366
$67$			2.35192e6i			0.955348i	0.878537	+	0.477674i	$0.158520\pi$
$67$			2.35192e6i			0.955348i	−0.878537	+	0.477674i	$0.841480\pi$
$68$	−1.56937e6			−0.605262
$69$	−2.02425e6			−0.741809
$70$		−	3.26571e6i		−	1.13798i
$71$			2.11218e6i			0.700370i	0.936681	+	0.350185i	$0.113881\pi$
$71$			2.11218e6i			0.700370i	−0.936681	+	0.350185i	$0.886119\pi$
$72$			405224.i			0.127948i
$73$		−	297647.i		−	0.0895514i	−0.998997	−	0.0447757i	$-0.985743\pi$
$73$		−	297647.i		−	0.0895514i	0.998997	−	0.0447757i	$-0.0142573\pi$
$74$	2.48587e6			0.713127
$75$	−5.58387e6			−1.52834
$76$		−	1.07979e6i		−	0.282158i
$77$	1.20614e6			0.301080
$78$	1.64902e6	+	1.69856e6i	0.393454	+	0.405276i
$79$	6.13466e6			1.39989			0.699947	−	0.714194i	$-0.253207\pi$
$79$	6.13466e6			1.39989			0.699947	+	0.714194i	$0.253207\pi$
$80$		−	1.95409e6i		−	0.426707i
$81$	−2.42566e6			−0.507145
$82$	−3.24288e6			−0.649506
$83$			5.86853e6i			1.12656i	0.826265	+	0.563282i	$0.190462\pi$
$83$			5.86853e6i			1.12656i	−0.826265	+	0.563282i	$0.809538\pi$
$84$			2.04576e6i			0.376598i
$85$		−	1.16985e7i		−	2.06616i
$86$			5.00912e6i			0.849213i
$87$	6.72773e6			1.09535
$88$	721715.			0.112895
$89$		−	5.02086e6i		−	0.754942i	−0.926021	−	0.377471i	$-0.876794\pi$
$89$		−	5.02086e6i		−	0.754942i	0.926021	−	0.377471i	$-0.123206\pi$
$90$	−3.02065e6			−0.436769
$91$	−4.72135e6	−	4.86321e6i	−0.656783	−	0.676516i
$92$	3.46794e6			0.464317
$93$			2.72981e6i			0.351919i
$94$	9.56128e6			1.18732
$95$	8.04904e6			0.963189
$96$			1.22411e6i			0.141212i
$97$		−	4.56414e6i		−	0.507759i	−0.967236	−	0.253879i	$-0.918293\pi$
$97$		−	4.56414e6i		−	0.507759i	0.967236	−	0.253879i	$-0.0817066\pi$
$98$			731060.i			0.0784624i
$99$		−	1.11563e6i		−	0.115558i
$100$	9.56629e6			0.956629
$101$	−8.13317e6			−0.785480			−0.392740	−	0.919650i	$-0.628473\pi$
$101$	−8.13317e6			−0.785480			−0.392740	+	0.919650i	$0.628473\pi$
$102$			7.32836e6i			0.683764i
$103$	−2.68747e6			−0.242333			−0.121167	−	0.992632i	$-0.538664\pi$
$103$	−2.68747e6			−0.242333			−0.121167	+	0.992632i	$0.538664\pi$
$104$	−2.82510e6	−	2.90998e6i	−0.246273	−	0.253672i
$105$	−1.52496e7			−1.28557
$106$		−	8.82731e6i		−	0.719876i
$107$	1.61235e7			1.27238			0.636188	−	0.771534i	$-0.280510\pi$
$107$	1.61235e7			1.27238			0.636188	+	0.771534i	$0.280510\pi$
$108$	7.12103e6			0.543951
$109$			3.22187e6i			0.238295i	0.992877	+	0.119148i	$0.0380162\pi$
$109$			3.22187e6i			0.238295i	−0.992877	+	0.119148i	$0.961984\pi$
$110$			5.37985e6i			0.385386i
$111$		−	1.16081e7i		−	0.805619i
$112$		−	3.50480e6i		−	0.235722i
$113$	−2.69850e7			−1.75933			−0.879667	−	0.475589i	$-0.842235\pi$
$113$	−2.69850e7			−1.75933			−0.879667	+	0.475589i	$0.842235\pi$
$114$	−5.04222e6			−0.318753
$115$			2.58510e7i			1.58502i
$116$	−1.15259e7			−0.685605
$117$	−4.49827e6	+	4.36706e6i	−0.259654	+	0.252080i
$118$	−1.77492e7			−0.994469
$119$		−	2.09821e7i		−	1.14139i
$120$	−9.12487e6			−0.482050
$121$	1.75002e7			0.898037
$122$			2.17084e7i			1.08235i
$123$			1.51431e7i			0.733746i
$124$		−	4.67671e6i		−	0.220275i
$125$			3.40383e7i			1.55877i
$126$	−5.41775e6			−0.241280
$127$	1.50820e7			0.653349			0.326675	−	0.945137i	$-0.394072\pi$
$127$	1.50820e7			0.653349			0.326675	+	0.945137i	$0.394072\pi$
$128$		−	2.09715e6i		−	0.0883883i
$129$	2.33907e7			0.959355
$130$	2.16917e7	−	2.10590e7i	0.865949	−	0.840691i
$131$	−2.27489e7			−0.884118			−0.442059	−	0.896986i	$-0.645752\pi$
$131$	−2.27489e7			−0.884118			−0.442059	+	0.896986i	$0.645752\pi$
$132$		−	3.37014e6i		−	0.127538i
$133$	1.44365e7			0.532086
$134$	−1.88154e7			−0.675533
$135$			5.30820e7i			1.85686i
$136$		−	1.25549e7i		−	0.427985i
$137$		−	1.76565e7i		−	0.586655i	−0.956012	−	0.293328i	$-0.905237\pi$
$137$		−	1.76565e7i		−	0.586655i	0.956012	−	0.293328i	$-0.0947627\pi$
$138$		−	1.61940e7i		−	0.524538i
$139$	6.41568e6			0.202624			0.101312	−	0.994855i	$-0.467696\pi$
$139$	6.41568e6			0.202624			0.101312	+	0.994855i	$0.467696\pi$
$140$	2.61257e7			0.804673
$141$		−	4.46476e7i		−	1.34132i
$142$	−1.68975e7			−0.495236
$143$	7.77784e6	+	8.01153e6i	0.222425	+	0.229108i
$144$	−3.24180e6			−0.0904726
$145$		−	8.59174e7i		−	2.34042i
$146$	2.38118e6			0.0633224
$147$	3.41378e6			0.0886389
$148$			1.98869e7i			0.504257i
$149$			4.15648e7i			1.02938i	0.857377	+	0.514688i	$0.172092\pi$
$149$			4.15648e7i			1.02938i	−0.857377	+	0.514688i	$0.827908\pi$
$150$		−	4.46710e7i		−	1.08070i
$151$			1.02268e7i			0.241725i	0.992669	+	0.120863i	$0.0385660\pi$
$151$			1.02268e7i			0.241725i	−0.992669	+	0.120863i	$0.961434\pi$
$152$	8.63833e6			0.199516
$153$	−1.94075e7			−0.438077
$154$			9.64915e6i			0.212895i
$155$	3.48614e7			0.751941
$156$	−1.35885e7	+	1.31921e7i	−0.286573	+	0.278214i
$157$	3.73815e7			0.770918			0.385459	−	0.922725i	$-0.374043\pi$
$157$	3.73815e7			0.770918			0.385459	+	0.922725i	$0.374043\pi$
$158$			4.90772e7i			0.989875i
$159$	−4.12202e7			−0.813243
$160$	1.56327e7			0.301727
$161$			4.63655e7i			0.875598i
$162$		−	1.94053e7i		−	0.358606i
$163$		−	1.04456e8i		−	1.88919i	−0.328234	−	0.944596i	$-0.606454\pi$
$163$		−	1.04456e8i		−	1.88919i	0.328234	−	0.944596i	$-0.393546\pi$
$164$		−	2.59431e7i		−	0.459270i
$165$	2.51219e7			0.435370
$166$	−4.69483e7			−0.796601
$167$		−	8.96976e6i		−	0.149030i	−0.997220	−	0.0745149i	$-0.976259\pi$
$167$		−	8.96976e6i		−	0.149030i	0.997220	−	0.0745149i	$-0.0237408\pi$
$168$	−1.63661e7			−0.266295
$169$	1.85699e6	−	6.27210e7i	0.0295942	−	0.999562i
$170$	9.35878e7			1.46099
$171$		−	1.33532e7i		−	0.204220i
$172$	−4.00729e7			−0.600484
$173$	−8.89780e7			−1.30654			−0.653268	−	0.757127i	$-0.726602\pi$
$173$	−8.89780e7			−1.30654			−0.653268	+	0.757127i	$0.726602\pi$
$174$			5.38219e7i			0.774527i
$175$			1.27899e8i			1.80399i
$176$			5.77372e6i			0.0798291i
$177$			8.28821e7i			1.12345i
$178$	4.01669e7			0.533824
$179$	6.19856e7			0.807802			0.403901	−	0.914803i	$-0.367654\pi$
$179$	6.19856e7			0.807802			0.403901	+	0.914803i	$0.367654\pi$
$180$		−	2.41652e7i		−	0.308842i
$181$	−3.19228e7			−0.400153			−0.200077	−	0.979780i	$-0.564119\pi$
$181$	−3.19228e7			−0.400153			−0.200077	+	0.979780i	$0.564119\pi$
$182$	3.89057e7	−	3.77708e7i	0.478369	−	0.464416i
$183$	1.01370e8			1.22273
$184$			2.77435e7i			0.328322i
$185$	−1.48242e8			−1.72136
$186$	−2.18385e7			−0.248844
$187$			3.45653e7i			0.386541i
$188$			7.64902e7i			0.839564i
$189$			9.52064e7i			1.02577i
$190$			6.43923e7i			0.681077i
$191$	−1.65465e8			−1.71826			−0.859129	−	0.511759i	$-0.828994\pi$
$191$	−1.65465e8			−1.71826			−0.859129	+	0.511759i	$0.828994\pi$
$192$	−9.79292e6			−0.0998522
$193$		−	2.01766e7i		−	0.202022i	−0.994885	−	0.101011i	$-0.967792\pi$
$193$		−	2.01766e7i		−	0.202022i	0.994885	−	0.101011i	$-0.0322077\pi$
$194$	3.65131e7			0.359040
$195$	−9.83377e7	−	1.01292e8i	−0.949727	−	0.978262i
$196$	−5.84848e6			−0.0554813
$197$		−	1.42398e8i		−	1.32700i	−0.748175	−	0.663502i	$-0.769070\pi$
$197$		−	1.42398e8i		−	1.32700i	0.748175	−	0.663502i	$-0.230930\pi$
$198$	8.92507e6			0.0817115
$199$	−1.04834e8			−0.943014			−0.471507	−	0.881862i	$-0.656290\pi$
$199$	−1.04834e8			−0.943014			−0.471507	+	0.881862i	$0.656290\pi$
$200$			7.65303e7i			0.676439i
$201$			8.78609e7i			0.763149i
$202$		−	6.50654e7i		−	0.555418i
$203$		−	1.54099e8i		−	1.29290i
$204$	−5.86269e7			−0.483494
$205$	1.93386e8			1.56779
$206$		−	2.14997e7i		−	0.171355i
$207$	4.28862e7			0.336064
$208$	2.32798e7	−	2.26008e7i	0.179373	−	0.174141i
$209$	−2.37824e7			−0.180195
$210$		−	1.21997e8i		−	0.909038i
$211$	1.69773e8			1.24417			0.622085	−	0.782950i	$-0.286286\pi$
$211$	1.69773e8			1.24417			0.622085	+	0.782950i	$0.286286\pi$
$212$	7.06185e7			0.509029
$213$			7.89049e7i			0.559468i
$214$			1.28988e8i			0.899705i
$215$		−	2.98714e8i		−	2.04985i
$216$			5.69683e7i			0.384631i
$217$	6.25264e7			0.415389
$218$	−2.57750e7			−0.168500
$219$		−	1.11192e7i		−	0.0715352i
$220$	−4.30388e7			−0.272509
$221$	1.39369e8	−	1.35303e8i	0.868544	−	0.843209i
$222$	9.28646e7			0.569659
$223$			2.62885e8i			1.58745i	0.608278	+	0.793724i	$0.291861\pi$
$223$			2.62885e8i			1.58745i	−0.608278	+	0.793724i	$0.708139\pi$
$224$	2.80384e7			0.166681
$225$	1.18301e8			0.692389
$226$		−	2.15880e8i		−	1.24404i
$227$			6.27164e7i			0.355869i	0.984042	+	0.177935i	$0.0569415\pi$
$227$			6.27164e7i			0.355869i	−0.984042	+	0.177935i	$0.943058\pi$
$228$		−	4.03378e7i		−	0.225393i
$229$			3.15618e8i			1.73675i	0.495905	+	0.868377i	$0.334836\pi$
$229$			3.15618e8i			1.73675i	−0.495905	+	0.868377i	$0.665164\pi$
$230$	−2.06808e8			−1.12078
$231$	4.50579e7			0.240508
$232$		−	9.22076e7i		−	0.484796i
$233$	1.06060e8			0.549297			0.274648	−	0.961545i	$-0.411439\pi$
$233$	1.06060e8			0.549297			0.274648	+	0.961545i	$0.411439\pi$
$234$	−3.49365e7	−	3.59862e7i	−0.178248	−	0.183603i
$235$	−5.70178e8			−2.86598
$236$		−	1.41993e8i		−	0.703196i
$237$	2.29172e8			1.11826
$238$	1.67856e8			0.807084
$239$			1.00469e8i			0.476035i	0.971261	+	0.238018i	$0.0764976\pi$
$239$			1.00469e8i			0.476035i	−0.971261	+	0.238018i	$0.923502\pi$
$240$		−	7.29989e7i		−	0.340861i
$241$		−	6.84416e7i		−	0.314964i	−0.987522	−	0.157482i	$-0.949662\pi$
$241$		−	6.84416e7i		−	0.314964i	0.987522	−	0.157482i	$-0.0503376\pi$
$242$			1.40002e8i			0.635008i
$243$	1.52724e8			0.682786
$244$	−1.73667e8			−0.765339
$245$		−	4.35961e7i		−	0.189394i
$246$	−1.21144e8			−0.518837
$247$	9.30943e7	+	9.58913e7i	0.393083	+	0.404893i
$248$	3.74137e7			0.155758
$249$			2.19231e8i			0.899920i
$250$	−2.72306e8			−1.10222
$251$	−3.83227e7			−0.152967			−0.0764835	−	0.997071i	$-0.524369\pi$
$251$	−3.83227e7			−0.152967			−0.0764835	+	0.997071i	$0.524369\pi$
$252$		−	4.33420e7i		−	0.170611i
$253$		−	7.63814e7i		−	0.296528i
$254$			1.20656e8i			0.461988i
$255$		−	4.37020e8i		−	1.65048i
$256$	1.67772e7			0.0625000
$257$	3.94016e8			1.44793			0.723965	−	0.689837i	$-0.242318\pi$
$257$	3.94016e8			1.44793			0.723965	+	0.689837i	$0.242318\pi$
$258$			1.87126e8i			0.678366i
$259$	−2.65883e8			−0.950916
$260$	1.68472e8	+	1.73534e8i	0.594458	+	0.612319i
$261$	−1.42535e8			−0.496227
$262$		−	1.81991e8i		−	0.625166i
$263$	−1.69352e8			−0.574044			−0.287022	−	0.957924i	$-0.592665\pi$
$263$	−1.69352e8			−0.574044			−0.287022	+	0.957924i	$0.592665\pi$
$264$	2.69611e7			0.0901829
$265$			5.26408e8i			1.73765i
$266$			1.15492e8i			0.376242i
$267$		−	1.87564e8i		−	0.603061i
$268$		−	1.50523e8i		−	0.477674i
$269$	−4.28499e8			−1.34220			−0.671099	−	0.741368i	$-0.734177\pi$
$269$	−4.28499e8			−1.34220			−0.671099	+	0.741368i	$0.734177\pi$
$270$	−4.24656e8			−1.31300
$271$			2.68069e8i			0.818189i	0.912492	+	0.409094i	$0.134155\pi$
$271$			2.68069e8i			0.818189i	−0.912492	+	0.409094i	$0.865845\pi$
$272$	1.00440e8			0.302631
$273$	−1.76376e8	−	1.81675e8i	−0.524650	−	0.540413i
$274$	1.41252e8			0.414828
$275$		−	2.10697e8i		−	0.610935i
$276$	1.29552e8			0.370905
$277$	−2.29029e8			−0.647457			−0.323728	−	0.946150i	$-0.604936\pi$
$277$	−2.29029e8			−0.647457			−0.323728	+	0.946150i	$0.604936\pi$
$278$			5.13254e7i			0.143277i
$279$		−	5.78344e7i		−	0.159431i
$280$			2.09005e8i			0.568990i
$281$			4.22322e8i			1.13546i	0.823215	+	0.567730i	$0.192178\pi$
$281$			4.22322e8i			1.13546i	−0.823215	+	0.567730i	$0.807822\pi$
$282$	3.57181e8			0.948454
$283$	−4.65403e8			−1.22061			−0.610305	−	0.792167i	$-0.708953\pi$
$283$	−4.65403e8			−1.22061			−0.610305	+	0.792167i	$0.708953\pi$
$284$		−	1.35180e8i		−	0.350185i
$285$	3.00688e8			0.769412
$286$	−6.40922e7	+	6.22227e7i	−0.162003	+	0.157278i
$287$	3.46852e8			0.866080
$288$		−	2.59344e7i		−	0.0639738i
$289$	1.90959e8			0.465370
$290$	6.87339e8			1.65492
$291$		−	1.70502e8i		−	0.405607i
$292$			1.90494e7i			0.0447757i
$293$			4.57814e8i			1.06329i	0.846967	+	0.531646i	$0.178426\pi$
$293$			4.57814e8i			1.06329i	−0.846967	+	0.531646i	$0.821574\pi$
$294$			2.73102e7i			0.0626772i
$295$	1.05846e9			2.40047
$296$	−1.59096e8			−0.356564
$297$		−	1.56841e8i		−	0.347385i
$298$	−3.32519e8			−0.727879
$299$	−3.07972e8	+	2.98989e8i	−0.666289	+	0.646854i
$300$	3.57368e8			0.764172
$301$		−	5.35765e8i		−	1.13238i
$302$	−8.18147e7			−0.170925
$303$	−3.03831e8			−0.627455
$304$			6.91066e7i			0.141079i
$305$		−	1.29456e9i		−	2.61260i
$306$		−	1.55260e8i		−	0.309767i
$307$		−	8.26875e8i		−	1.63101i	−0.578753	−	0.815503i	$-0.696460\pi$
$307$		−	8.26875e8i		−	1.63101i	0.578753	−	0.815503i	$-0.303540\pi$
$308$	−7.71932e7			−0.150540
$309$	−1.00396e8			−0.193580
$310$			2.78891e8i			0.531703i
$311$	3.14108e8			0.592130			0.296065	−	0.955168i	$-0.404325\pi$
$311$	3.14108e8			0.592130			0.296065	+	0.955168i	$0.404325\pi$
$312$	−1.05537e8	−	1.08708e8i	−0.196727	−	0.202638i
$313$	−3.13248e8			−0.577408			−0.288704	−	0.957418i	$-0.593224\pi$
$313$	−3.13248e8			−0.577408			−0.288704	+	0.957418i	$0.593224\pi$
$314$			2.99052e8i			0.545121i
$315$	3.23082e8			0.582407
$316$	−3.92618e8			−0.699947
$317$		−	9.62760e8i		−	1.69750i	−0.528792	−	0.848751i	$-0.677355\pi$
$317$		−	9.62760e8i		−	1.69750i	0.528792	−	0.848751i	$-0.322645\pi$
$318$		−	3.29762e8i		−	0.575050i
$319$			2.53859e8i			0.437850i
$320$			1.25062e8i			0.213353i
$321$	6.02325e8			1.01640
$322$	−3.70924e8			−0.619141
$323$			4.13718e8i			0.683118i
$324$	1.55242e8			0.253573
$325$	−8.49539e8	+	8.24759e8i	−1.37275	+	1.33271i
$326$	8.35647e8			1.33586
$327$			1.20359e8i			0.190354i
$328$	2.07545e8			0.324753
$329$	−1.02266e9			−1.58323
$330$			2.00975e8i			0.307853i
$331$			1.03693e9i			1.57163i	0.618462	+	0.785815i	$0.287756\pi$
$331$			1.03693e9i			1.57163i	−0.618462	+	0.785815i	$0.712244\pi$
$332$		−	3.75586e8i		−	0.563282i
$333$			2.45931e8i			0.364972i
$334$	7.17581e7			0.105380
$335$	1.12204e9			1.63061
$336$		−	1.30929e8i		−	0.188299i
$337$	3.19276e8			0.454425			0.227213	−	0.973845i	$-0.427039\pi$
$337$	3.19276e8			0.454425			0.227213	+	0.973845i	$0.427039\pi$
$338$	5.01768e8	+	1.48559e7i	0.706797	+	0.0209262i
$339$	−1.00808e9			−1.40539
$340$			7.48703e8i			1.03308i
$341$	−1.03004e8			−0.140675
$342$	1.06826e8			0.144406
$343$		−	7.82869e8i		−	1.04751i
$344$		−	3.20584e8i		−	0.424607i
$345$			9.65714e8i			1.26614i
$346$		−	7.11824e8i		−	0.923860i
$347$	−1.04362e9			−1.34088			−0.670442	−	0.741962i	$-0.733895\pi$
$347$	−1.04362e9			−1.34088			−0.670442	+	0.741962i	$0.733895\pi$
$348$	−4.30575e8			−0.547673
$349$		−	8.79993e8i		−	1.10813i	−0.832474	−	0.554064i	$-0.813076\pi$
$349$		−	8.79993e8i		−	1.10813i	0.832474	−	0.554064i	$-0.186924\pi$
$350$	−1.02319e9			−1.27561
$351$	−6.32387e8	+	6.13941e8i	−0.780563	+	0.757795i
$352$	−4.61898e7			−0.0564477
$353$			8.23795e8i			0.996799i	0.866948	+	0.498399i	$0.166079\pi$
$353$			8.23795e8i			0.996799i	−0.866948	+	0.498399i	$0.833921\pi$
$354$	−6.63056e8			−0.794400
$355$	1.00767e9			1.19541
$356$			3.21335e8i			0.377471i
$357$		−	7.83827e8i		−	0.911762i
$358$			4.95885e8i			0.571203i
$359$			9.21279e8i			1.05090i	0.850825	+	0.525449i	$0.176103\pi$
$359$			9.21279e8i			1.05090i	−0.850825	+	0.525449i	$0.823897\pi$
$360$	1.93321e8			0.218384
$361$	6.09216e8			0.681548
$362$		−	2.55383e8i		−	0.282951i
$363$	6.53755e8			0.717368
$364$	3.02167e8	+	3.11245e8i	0.328391	+	0.338258i
$365$	−1.41999e8			−0.152849
$366$			8.10962e8i			0.864603i
$367$	1.43004e9			1.51014			0.755072	−	0.655642i	$-0.227602\pi$
$367$	1.43004e9			1.51014			0.755072	+	0.655642i	$0.227602\pi$
$368$	−2.21948e8			−0.232159
$369$		−	3.20824e8i		−	0.332411i
$370$		−	1.18594e9i		−	1.21718i
$371$			9.44151e8i			0.959915i
$372$		−	1.74708e8i		−	0.175959i
$373$	−7.93446e8			−0.791656			−0.395828	−	0.918325i	$-0.629542\pi$
$373$	−7.93446e8			−0.791656			−0.395828	+	0.918325i	$0.629542\pi$
$374$	−2.76523e8			−0.273325
$375$			1.27157e9i			1.24518i
$376$	−6.11922e8			−0.593661
$377$	1.02357e9	−	9.93711e8i	0.983834	−	0.955136i
$378$	−7.61651e8			−0.725329
$379$		−	3.49684e8i		−	0.329942i	−0.986298	−	0.164971i	$-0.947247\pi$
$379$		−	3.49684e8i		−	0.329942i	0.986298	−	0.164971i	$-0.0527531\pi$
$380$	−5.15139e8			−0.481594
$381$	5.63418e8			0.521907
$382$		−	1.32372e9i		−	1.21499i
$383$			7.07518e8i			0.643490i	0.946826	+	0.321745i	$0.104269\pi$
$383$			7.07518e8i			0.643490i	−0.946826	+	0.321745i	$0.895731\pi$
$384$		−	7.83433e7i		−	0.0706062i
$385$		−	5.75418e8i		−	0.513891i
$386$	1.61413e8			0.142851
$387$	−4.95561e8			−0.434619
$388$			2.92105e8i			0.253879i
$389$	−3.66545e8			−0.315721			−0.157860	−	0.987461i	$-0.550460\pi$
$389$	−3.66545e8			−0.315721			−0.157860	+	0.987461i	$0.550460\pi$
$390$	8.10338e8	−	7.86701e8i	0.691736	−	0.671558i
$391$	−1.32873e9			−1.12413
$392$		−	4.67878e7i		−	0.0392312i
$393$	−8.49830e8			−0.706249
$394$	1.13918e9			0.938333
$395$		−	2.92668e9i		−	2.38938i
$396$			7.14005e7i			0.0577788i
$397$			2.77347e8i			0.222463i	0.993795	+	0.111231i	$0.0354794\pi$
$397$			2.77347e8i			0.222463i	−0.993795	+	0.111231i	$0.964521\pi$
$398$		−	8.38675e8i		−	0.666811i
$399$	5.39306e8			0.425040
$400$	−6.12242e8			−0.478314
$401$		−	3.07048e7i		−	0.0237794i	−0.999929	−	0.0118897i	$-0.996215\pi$
$401$		−	3.07048e7i		−	0.0237794i	0.999929	−	0.0118897i	$-0.00378470\pi$
$402$	−7.02887e8			−0.539628
$403$	4.03203e8	+	4.15317e8i	0.306871	+	0.316091i
$404$	5.20523e8			0.392740
$405$			1.15722e9i			0.865609i
$406$	1.23279e9			0.914216
$407$	4.38010e8			0.322035
$408$		−	4.69015e8i		−	0.341882i
$409$		−	4.23466e7i		−	0.0306046i	−0.999883	−	0.0153023i	$-0.995129\pi$
$409$		−	4.23466e7i		−	0.0306046i	0.999883	−	0.0153023i	$-0.00487107\pi$
$410$			1.54709e9i			1.10859i
$411$		−	6.59595e8i		−	0.468631i
$412$	1.71998e8			0.121167
$413$	1.89842e9			1.32607
$414$			3.43090e8i			0.237633i
$415$	2.79972e9			1.92285
$416$	1.80806e8	+	1.86239e8i	0.123136	+	0.126836i
$417$	2.39671e8			0.161860
$418$		−	1.90259e8i		−	0.127417i
$419$	−1.33683e8			−0.0887824			−0.0443912	−	0.999014i	$-0.514135\pi$
$419$	−1.33683e8			−0.0887824			−0.0443912	+	0.999014i	$0.514135\pi$
$420$	9.75977e8			0.642787
$421$		−	9.79644e8i		−	0.639854i	−0.947442	−	0.319927i	$-0.896342\pi$
$421$		−	9.79644e8i		−	0.639854i	0.947442	−	0.319927i	$-0.103658\pi$
$422$			1.35818e9i			0.879761i
$423$			9.45914e8i			0.607660i
$424$			5.64948e8i			0.359938i
$425$	−3.66529e9			−2.31605
$426$	−6.31239e8			−0.395604
$427$		−	2.32189e9i		−	1.44326i
$428$	−1.03190e9			−0.636188
$429$	2.90557e8	+	2.99287e8i	0.177677	+	0.183015i
$430$	2.38971e9			1.44946
$431$			1.66486e9i			1.00163i	0.865554	+	0.500816i	$0.166967\pi$
$431$			1.66486e9i			1.00163i	−0.865554	+	0.500816i	$0.833033\pi$
$432$	−4.55746e8			−0.271976
$433$	−9.13220e8			−0.540589			−0.270295	−	0.962778i	$-0.587121\pi$
$433$	−9.13220e8			−0.540589			−0.270295	+	0.962778i	$0.587121\pi$
$434$			5.00211e8i			0.293724i
$435$		−	3.20962e9i		−	1.86957i
$436$		−	2.06200e8i		−	0.119148i
$437$		−	9.14222e8i		−	0.524043i
$438$	8.89538e7			0.0505830
$439$	−5.44736e8			−0.307299			−0.153649	−	0.988125i	$-0.549103\pi$
$439$	−5.44736e8			−0.307299			−0.153649	+	0.988125i	$0.549103\pi$
$440$		−	3.44310e8i		−	0.192693i
$441$	−7.23250e7			−0.0401563
$442$	1.08243e9	+	1.11495e9i	0.596239	+	0.614153i
$443$	1.84491e8			0.100823			0.0504117	−	0.998729i	$-0.483947\pi$
$443$	1.84491e8			0.100823			0.0504117	+	0.998729i	$0.483947\pi$
$444$			7.42917e8i			0.402810i
$445$	−2.39532e9			−1.28855
$446$	−2.10308e9			−1.12250
$447$			1.55274e9i			0.822284i
$448$			2.24307e8i			0.117861i
$449$			7.85913e8i			0.409744i	0.978789	+	0.204872i	$0.0656778\pi$
$449$			7.85913e8i			0.409744i	−0.978789	+	0.204872i	$0.934322\pi$
$450$			9.46410e8i			0.489593i
$451$	−5.71396e8			−0.293305
$452$	1.72704e9			0.879667
$453$			3.82044e8i			0.193094i
$454$	−5.01731e8			−0.251637
$455$	−2.32010e9	+	2.25243e9i	−1.15470	+	1.12101i
$456$	3.22702e8			0.159377
$457$			1.23679e9i			0.606162i	0.952965	+	0.303081i	$0.0980152\pi$
$457$			1.23679e9i			0.606162i	−0.952965	+	0.303081i	$0.901985\pi$
$458$	−2.52495e9			−1.22807
$459$	−2.72840e9			−1.31693
$460$		−	1.65446e9i		−	0.792509i
$461$			5.60686e7i			0.0266542i	0.999911	+	0.0133271i	$0.00424228\pi$
$461$			5.60686e7i			0.0266542i	−0.999911	+	0.0133271i	$0.995758\pi$
$462$			3.60463e8i			0.170065i
$463$			1.12359e9i			0.526109i	0.964781	+	0.263055i	$0.0847299\pi$
$463$			1.12359e9i			0.526109i	−0.964781	+	0.263055i	$0.915270\pi$
$464$	7.37661e8			0.342802
$465$	1.30232e9			0.600664
$466$			8.48482e8i			0.388411i
$467$	−1.26480e9			−0.574664			−0.287332	−	0.957831i	$-0.592768\pi$
$467$	−1.26480e9			−0.574664			−0.287332	+	0.957831i	$0.592768\pi$
$468$	2.87889e8	−	2.79492e8i	0.129827	−	0.126040i
$469$	2.01246e9			0.900786
$470$		−	4.56142e9i		−	2.02655i
$471$	1.39646e9			0.615823
$472$	1.13595e9			0.497235
$473$			8.82606e8i			0.383489i
$474$			1.83338e9i			0.790730i
$475$		−	2.52187e9i		−	1.07968i
$476$			1.34285e9i			0.570695i
$477$	8.73301e8			0.368426
$478$	−8.03751e8			−0.336608
$479$			1.89708e8i			0.0788701i	0.999222	+	0.0394350i	$0.0125558\pi$
$479$			1.89708e8i			0.0788701i	−0.999222	+	0.0394350i	$0.987444\pi$
$480$	5.83991e8			0.241025
$481$	−1.71456e9	−	1.76607e9i	−0.702496	−	0.723603i
$482$	5.47533e8			0.222713
$483$			1.73208e9i			0.699443i
$484$	−1.12001e9			−0.449018
$485$	−2.17742e9			−0.866656
$486$			1.22179e9i			0.482802i
$487$		−	1.76109e8i		−	0.0690925i	−0.999403	−	0.0345463i	$-0.989001\pi$
$487$		−	1.76109e8i		−	0.0690925i	0.999403	−	0.0345463i	$-0.0109986\pi$
$488$		−	1.38934e9i		−	0.541176i
$489$		−	3.90216e9i		−	1.50912i
$490$	3.48769e8			0.133922
$491$	2.15724e9			0.822456			0.411228	−	0.911533i	$-0.365100\pi$
$491$	2.15724e9			0.822456			0.411228	+	0.911533i	$0.365100\pi$
$492$		−	9.69155e8i		−	0.366873i
$493$	4.41613e9			1.65988
$494$	−7.67131e8	+	7.44754e8i	−0.286302	+	0.277951i
$495$	−5.32238e8			−0.197237
$496$			2.99309e8i			0.110137i
$497$	1.80732e9			0.660370
$498$	−1.75385e9			−0.636339
$499$			2.05373e9i			0.739930i	0.929046	+	0.369965i	$0.120630\pi$
$499$			2.05373e9i			0.739930i	−0.929046	+	0.369965i	$0.879370\pi$
$500$		−	2.17845e9i		−	0.779386i
$501$		−	3.35084e8i		−	0.119048i
$502$		−	3.06581e8i		−	0.108164i
$503$	5.06626e9			1.77500			0.887502	−	0.460803i	$-0.152439\pi$
$503$	5.06626e9			1.77500			0.887502	+	0.460803i	$0.152439\pi$
$504$	3.46736e8			0.120640
$505$			3.88011e9i			1.34068i
$506$	6.11051e8			0.209677
$507$	6.93716e7	−	2.34307e9i	0.0236403	−	0.798468i
$508$	−9.65247e8			−0.326675
$509$		−	2.26125e9i		−	0.760040i	−0.924978	−	0.380020i	$-0.875917\pi$
$509$		−	2.26125e9i		−	0.760040i	0.924978	−	0.380020i	$-0.124083\pi$
$510$	3.49616e9			1.16707
$511$	−2.54686e8			−0.0844369
$512$			1.34218e8i			0.0441942i
$513$		−	1.87725e9i		−	0.613920i
$514$			3.15213e9i			1.02384i
$515$			1.28212e9i			0.413621i
$516$	−1.49701e9			−0.479677
$517$	1.68470e9			0.536173
$518$		−	2.12707e9i		−	0.672399i
$519$	−3.32395e9			−1.04368
$520$	−1.38827e9	+	1.34778e9i	−0.432975	+	0.420345i
$521$	1.92865e9			0.597477			0.298739	−	0.954335i	$-0.403434\pi$
$521$	1.92865e9			0.597477			0.298739	+	0.954335i	$0.403434\pi$
$522$		−	1.14028e9i		−	0.350886i
$523$	−2.29757e9			−0.702285			−0.351142	−	0.936322i	$-0.614207\pi$
$523$	−2.29757e9			−0.702285			−0.351142	+	0.936322i	$0.614207\pi$
$524$	1.45593e9			0.442059
$525$			4.77792e9i			1.44106i
$526$		−	1.35482e9i		−	0.405910i
$527$			1.79187e9i			0.533296i
$528$			2.15689e8i			0.0637689i
$529$	−4.68636e8			−0.137639
$530$	−4.21127e9			−1.22870
$531$		−	1.75596e9i		−	0.508960i
$532$	−9.23938e8			−0.266043
$533$	2.23669e9	+	2.30389e9i	0.639823	+	0.659046i
$534$	1.50052e9			0.426428
$535$		−	7.69206e9i		−	2.17172i
$536$	1.20419e9			0.337767
$537$	2.31560e9			0.645287
$538$		−	3.42799e9i		−	0.949077i
$539$			1.28813e8i			0.0354322i
$540$		−	3.39725e9i		−	0.928430i
$541$		−	5.72111e8i		−	0.155342i	−0.996979	−	0.0776712i	$-0.975252\pi$
$541$		−	5.72111e8i		−	0.155342i	0.996979	−	0.0776712i	$-0.0247484\pi$
$542$	−2.14455e9			−0.578547
$543$	−1.19254e9			−0.319650
$544$			8.03517e8i			0.213993i
$545$	1.53707e9			0.406729
$546$	1.45340e9	−	1.41101e9i	0.382130	−	0.370983i
$547$	−3.34561e9			−0.874018			−0.437009	−	0.899457i	$-0.643962\pi$
$547$	−3.34561e9			−0.874018			−0.437009	+	0.899457i	$0.643962\pi$
$548$			1.13002e9i			0.293328i
$549$	−2.14765e9			−0.553938
$550$	1.68558e9			0.431996
$551$			3.03848e9i			0.773795i
$552$			1.03642e9i			0.262269i
$553$		−	5.24920e9i		−	1.31994i
$554$		−	1.83223e9i		−	0.457821i
$555$	−5.53789e9			−1.37505
$556$	−4.10604e8			−0.101312
$557$			4.94218e9i			1.21178i	0.795547	+	0.605892i	$0.207184\pi$
$557$			4.94218e9i			1.21178i	−0.795547	+	0.605892i	$0.792816\pi$
$558$	4.62675e8			0.112734
$559$	3.55870e9	−	3.45489e9i	0.861687	−	0.836553i
$560$	−1.67204e9			−0.402337
$561$			1.29126e9i			0.308775i
$562$	−3.37858e9			−0.802891
$563$	5.69292e9			1.34448			0.672242	−	0.740332i	$-0.265332\pi$
$563$	5.69292e9			1.34448			0.672242	+	0.740332i	$0.265332\pi$
$564$			2.85745e9i			0.670658i
$565$			1.28738e10i			3.00288i
$566$		−	3.72323e9i		−	0.863102i
$567$			2.07555e9i			0.478181i
$568$	1.08144e9			0.247618
$569$	−3.35746e9			−0.764044			−0.382022	−	0.924153i	$-0.624772\pi$
$569$	−3.35746e9			−0.764044			−0.382022	+	0.924153i	$0.624772\pi$
$570$			2.40550e9i			0.544057i
$571$	−5.43730e9			−1.22224			−0.611120	−	0.791538i	$-0.709281\pi$
$571$	−5.43730e9			−1.22224			−0.611120	+	0.791538i	$0.709281\pi$
$572$	−4.97782e8	−	5.12738e8i	−0.111212	−	0.114554i
$573$	−6.18126e9			−1.37257
$574$			2.77482e9i			0.612411i
$575$	8.09945e9			1.77672
$576$	2.07475e8			0.0452363
$577$		−	5.94360e7i		−	0.0128805i	−0.999979	−	0.00644027i	$-0.997950\pi$
$577$		−	5.94360e7i		−	0.0128805i	0.999979	−	0.00644027i	$-0.00205002\pi$
$578$			1.52768e9i			0.329067i
$579$		−	7.53739e8i		−	0.161379i
$580$			5.49871e9i			1.17021i
$581$	5.02149e9			1.06222
$582$	1.36402e9			0.286807
$583$		−	1.55537e9i		−	0.325083i
$584$	−1.52396e8			−0.0316612
$585$	2.08340e9	+	2.14600e9i	0.430257	+	0.443184i
$586$	−3.66251e9			−0.751860
$587$		−	2.94167e9i		−	0.600290i	−0.953894	−	0.300145i	$-0.902965\pi$
$587$		−	2.94167e9i		−	0.600290i	0.953894	−	0.300145i	$-0.0970351\pi$
$588$	−2.18482e8			−0.0443194
$589$	−1.23288e9			−0.248609
$590$			8.46765e9i			1.69739i
$591$		−	5.31956e9i		−	1.06003i
$592$		−	1.27276e9i		−	0.252129i
$593$			8.23762e9i			1.62222i	0.584892	+	0.811111i	$0.301137\pi$
$593$			8.23762e9i			1.62222i	−0.584892	+	0.811111i	$0.698863\pi$
$594$	1.25473e9			0.245638
$595$	−1.00100e10			−1.94815
$596$		−	2.66015e9i		−	0.514688i
$597$	−3.91630e9			−0.753296
$598$	−2.39191e9	−	2.46378e9i	−0.457395	−	0.471138i
$599$	−3.51762e9			−0.668737			−0.334368	−	0.942442i	$-0.608523\pi$
$599$	−3.51762e9			−0.668737			−0.334368	+	0.942442i	$0.608523\pi$
$600$			2.85894e9i			0.540351i
$601$	6.64097e8			0.124787			0.0623937	−	0.998052i	$-0.480127\pi$
$601$	6.64097e8			0.124787			0.0623937	+	0.998052i	$0.480127\pi$
$602$	4.28612e9			0.800713
$603$		−	1.86144e9i		−	0.345731i
$604$		−	6.54517e8i		−	0.120863i
$605$		−	8.34887e9i		−	1.53279i
$606$		−	2.43065e9i		−	0.443678i
$607$	1.57643e9			0.286097			0.143049	−	0.989716i	$-0.454309\pi$
$607$	1.57643e9			0.286097			0.143049	+	0.989716i	$0.454309\pi$
$608$	−5.52853e8			−0.0997578
$609$		−	5.75668e9i		−	1.03279i
$610$	1.03565e10			1.84739
$611$	−6.59462e9	−	6.79275e9i	−1.16962	−	1.20476i
$612$	1.24208e9			0.219039
$613$		−	2.49714e9i		−	0.437856i	−0.975741	−	0.218928i	$-0.929744\pi$
$613$		−	2.49714e9i		−	0.437856i	0.975741	−	0.218928i	$-0.0702560\pi$
$614$	6.61500e9			1.15330
$615$	7.22434e9			1.25238
$616$		−	6.17545e8i		−	0.106448i
$617$			2.59765e9i			0.445228i	0.974907	+	0.222614i	$0.0714590\pi$
$617$			2.59765e9i			0.445228i	−0.974907	+	0.222614i	$0.928541\pi$
$618$		−	8.03165e8i		−	0.136882i
$619$			8.01395e9i			1.35809i	0.734096	+	0.679046i	$0.237606\pi$
$619$			8.01395e9i			1.35809i	−0.734096	+	0.679046i	$0.762394\pi$
$620$	−2.23113e9			−0.375971
$621$	6.02914e9			1.01026
$622$			2.51286e9i			0.418699i
$623$	−4.29617e9			−0.711825
$624$	8.69665e8	−	8.44297e8i	0.143287	−	0.139107i
$625$	4.56114e9			0.747297
$626$		−	2.50598e9i		−	0.408289i
$627$	−8.88439e8			−0.143943
$628$	−2.39242e9			−0.385459
$629$		−	7.61961e9i		−	1.22083i
$630$			2.58466e9i			0.411824i
$631$		−	3.75388e8i		−	0.0594809i	−0.999558	−	0.0297405i	$-0.990532\pi$
$631$		−	3.75388e8i		−	0.0594809i	0.999558	−	0.0297405i	$-0.00946808\pi$
$632$		−	3.14094e9i		−	0.494937i
$633$	6.34220e9			0.993865
$634$	7.70208e9			1.20032
$635$		−	7.19520e9i		−	1.11515i
$636$	2.63810e9			0.406622
$637$	5.19377e8	−	5.04227e8i	0.0796150	−	0.0772927i
$638$	−2.03087e9			−0.309606
$639$		−	1.67170e9i		−	0.253457i
$640$	−1.00049e9			−0.150864
$641$	−8.82161e9			−1.32295			−0.661477	−	0.749965i	$-0.730070\pi$
$641$	−8.82161e9			−1.32295			−0.661477	+	0.749965i	$0.730070\pi$
$642$			4.81860e9i			0.718700i
$643$			1.10280e10i			1.63591i	0.575285	+	0.817953i	$0.304891\pi$
$643$			1.10280e10i			1.63591i	−0.575285	+	0.817953i	$0.695109\pi$
$644$		−	2.96739e9i		−	0.437799i
$645$		−	1.11591e10i		−	1.63745i
$646$	−3.30975e9			−0.483037
$647$	−5.88926e9			−0.854861			−0.427430	−	0.904048i	$-0.640581\pi$
$647$	−5.88926e9			−0.854861			−0.427430	+	0.904048i	$0.640581\pi$
$648$			1.24194e9i			0.179303i
$649$	−3.12741e9			−0.449084
$650$	−6.59807e9	−	6.79631e9i	−0.942367	−	0.970681i
$651$	2.33580e9			0.331820
$652$			6.68518e9i			0.944596i
$653$	3.58689e9			0.504106			0.252053	−	0.967713i	$-0.418894\pi$
$653$	3.58689e9			0.504106			0.252053	+	0.967713i	$0.418894\pi$
$654$	−9.62875e8			−0.134601
$655$			1.08529e10i			1.50904i
$656$			1.66036e9i			0.229635i
$657$			2.35574e8i			0.0324078i
$658$		−	8.18124e9i		−	1.11951i
$659$	9.75238e9			1.32743			0.663715	−	0.747986i	$-0.268979\pi$
$659$	9.75238e9			1.32743			0.663715	+	0.747986i	$0.268979\pi$
$660$	−1.60780e9			−0.217685
$661$		−	4.28515e9i		−	0.577113i	−0.957463	−	0.288556i	$-0.906825\pi$
$661$		−	4.28515e9i		−	0.577113i	0.957463	−	0.288556i	$-0.0931753\pi$
$662$	−8.29542e9			−1.11131
$663$	5.20639e9	−	5.05453e9i	0.693808	−	0.673571i
$664$	3.00469e9			0.398301
$665$		−	6.88727e9i		−	0.908179i
$666$	−1.96745e9			−0.258074
$667$	−9.75863e9			−1.27335
$668$			5.74065e8i			0.0745149i
$669$			9.82061e9i			1.26808i
$670$			8.97631e9i			1.15302i
$671$			3.82502e9i			0.488771i
$672$	1.04743e9			0.133147
$673$	3.75536e9			0.474897			0.237448	−	0.971400i	$-0.423689\pi$
$673$	3.75536e9			0.474897			0.237448	+	0.971400i	$0.423689\pi$
$674$			2.55421e9i			0.321327i
$675$	1.66313e10			2.08144
$676$	−1.18847e8	+	4.01415e9i	−0.0147971	+	0.499781i
$677$	1.35417e10			1.67731			0.838654	−	0.544664i	$-0.183343\pi$
$677$	1.35417e10			1.67731			0.838654	+	0.544664i	$0.183343\pi$
$678$		−	8.06464e9i		−	0.993759i
$679$	−3.90537e9			−0.478760
$680$	−5.98962e9			−0.730497
$681$			2.34290e9i			0.284275i
$682$		−	8.24036e8i		−	0.0994720i
$683$			4.91290e9i			0.590019i	0.955494	+	0.295009i	$0.0953227\pi$
$683$			4.91290e9i			0.590019i	−0.955494	+	0.295009i	$0.904677\pi$
$684$			8.54605e8i			0.102110i
$685$	−8.42344e9			−1.00132
$686$	6.26295e9			0.740704
$687$			1.17906e10i			1.38735i
$688$	2.56467e9			0.300242
$689$	−6.27131e9	+	6.08838e9i	−0.730451	+	0.709144i
$690$	−7.72571e9			−0.895296
$691$			7.93688e9i			0.915117i	0.889180	+	0.457558i	$0.151276\pi$
$691$			7.93688e9i			0.915117i	−0.889180	+	0.457558i	$0.848724\pi$
$692$	5.69459e9			0.653268
$693$	−9.54607e8			−0.108958
$694$		−	8.34900e9i		−	0.948148i
$695$		−	3.06075e9i		−	0.345844i
$696$		−	3.44460e9i		−	0.387263i
$697$			9.94000e9i			1.11192i
$698$	7.03994e9			0.783565
$699$	3.96209e9			0.438788
$700$		−	8.18553e9i		−	0.901994i
$701$	−8.76538e9			−0.961076			−0.480538	−	0.876974i	$-0.659559\pi$
$701$	−8.76538e9			−0.961076			−0.480538	+	0.876974i	$0.659559\pi$
$702$	−4.91153e9	−	5.05909e9i	−0.535842	−	0.551941i
$703$	5.24261e9			0.569120
$704$		−	3.69518e8i		−	0.0399146i
$705$	−2.13001e10			−2.28939
$706$	−6.59036e9			−0.704843
$707$			6.95926e9i			0.740619i
$708$		−	5.30445e9i		−	0.561725i
$709$		−	1.60949e10i		−	1.69600i	−0.529995	−	0.848001i	$-0.677806\pi$
$709$		−	1.60949e10i		−	1.69600i	0.529995	−	0.848001i	$-0.322194\pi$
$710$			8.06132e9i			0.845283i
$711$	−4.85530e9			−0.506608
$712$	−2.57068e9			−0.266912
$713$		−	3.95961e9i		−	0.409109i
$714$	6.27062e9			0.644713
$715$	3.82208e9	−	3.71060e9i	0.391047	−	0.379640i
$716$	−3.96708e9			−0.403901
$717$			3.75322e9i			0.380265i
$718$	−7.37023e9			−0.743097
$719$	7.66897e9			0.769460			0.384730	−	0.923029i	$-0.374295\pi$
$719$	7.66897e9			0.769460			0.384730	+	0.923029i	$0.374295\pi$
$720$			1.54657e9i			0.154421i
$721$			2.29957e9i			0.228493i
$722$			4.87373e9i			0.481927i
$723$		−	2.55677e9i		−	0.251599i
$724$	2.04306e9			0.200077
$725$	−2.69191e10			−2.62348
$726$			5.23004e9i			0.507256i
$727$	−1.05757e10			−1.02080			−0.510398	−	0.859938i	$-0.670502\pi$
$727$	−1.05757e10			−1.02080			−0.510398	+	0.859938i	$0.670502\pi$
$728$	−2.48996e9	+	2.41733e9i	−0.239185	+	0.232208i
$729$	1.10102e10			1.05257
$730$		−	1.13600e9i		−	0.108080i
$731$	1.53538e10			1.45380
$732$	−6.48769e9			−0.611366
$733$			1.15268e10i			1.08104i	0.841330	+	0.540522i	$0.181773\pi$
$733$			1.15268e10i			1.08104i	−0.841330	+	0.540522i	$0.818227\pi$
$734$			1.14404e10i			1.06783i
$735$		−	1.62862e9i		−	0.151291i
$736$		−	1.77559e9i		−	0.164161i
$737$	−3.31527e9			−0.305058
$738$	2.56659e9			0.235050
$739$		−	1.69679e10i		−	1.54658i	−0.634051	−	0.773291i	$-0.718609\pi$
$739$		−	1.69679e10i		−	1.54658i	0.634051	−	0.773291i	$-0.281391\pi$
$740$	9.48752e9			0.860680
$741$	3.47772e9	+	3.58221e9i	0.314001	+	0.323436i
$742$	−7.55321e9			−0.678763
$743$			5.71581e9i			0.511231i	0.966779	+	0.255615i	$0.0822780\pi$
$743$			5.71581e9i			0.511231i	−0.966779	+	0.255615i	$0.917722\pi$
$744$	1.39766e9			0.124422
$745$	1.98294e10			1.75697
$746$		−	6.34757e9i		−	0.559785i
$747$		−	4.64467e9i		−	0.407693i
$748$		−	2.21218e9i		−	0.193270i
$749$		−	1.37963e10i		−	1.19971i
$750$	−1.01726e10			−0.880472
$751$	1.36628e10			1.17707			0.588534	−	0.808473i	$-0.299705\pi$
$751$	1.36628e10			1.17707			0.588534	+	0.808473i	$0.299705\pi$
$752$		−	4.89538e9i		−	0.419782i
$753$	−1.43162e9			−0.122193
$754$	7.94969e9	+	8.18854e9i	0.675383	+	0.695675i
$755$	4.87894e9			0.412583
$756$		−	6.09321e9i		−	0.512885i
$757$	−6.72435e9			−0.563397			−0.281699	−	0.959503i	$-0.590898\pi$
$757$	−6.72435e9			−0.563397			−0.281699	+	0.959503i	$0.590898\pi$
$758$	2.79747e9			0.233304
$759$		−	2.85338e9i		−	0.236872i
$760$		−	4.12111e9i		−	0.340539i
$761$			8.09445e9i			0.665796i	0.942963	+	0.332898i	$0.108026\pi$
$761$			8.09445e9i			0.665796i	−0.942963	+	0.332898i	$0.891974\pi$
$762$			4.50734e9i			0.369044i
$763$	2.75684e9			0.224686
$764$	1.05897e10			0.859129
$765$			9.25881e9i			0.747722i
$766$	−5.66014e9			−0.455016
$767$	1.22420e10	+	1.26098e10i	0.979644	+	1.00908i
$768$	6.26747e8			0.0499261
$769$		−	1.30012e10i		−	1.03096i	−0.856901	−	0.515481i	$-0.827613\pi$
$769$		−	1.30012e10i		−	1.03096i	0.856901	−	0.515481i	$-0.172387\pi$
$770$	4.60334e9			0.363376
$771$	1.47192e10			1.15663
$772$			1.29131e9i			0.101011i
$773$		−	2.12901e10i		−	1.65786i	−0.559349	−	0.828932i	$-0.688949\pi$
$773$		−	2.12901e10i		−	1.65786i	0.559349	−	0.828932i	$-0.311051\pi$
$774$		−	3.96449e9i		−	0.307322i
$775$		−	1.09225e10i		−	0.842884i
$776$	−2.33684e9			−0.179520
$777$	−9.93261e9			−0.759608
$778$		−	2.93236e9i		−	0.223248i
$779$	−6.83913e9			−0.518346
$780$	6.29361e9	+	6.48271e9i	0.474864	+	0.489131i
$781$	−2.97733e9			−0.223640
$782$		−	1.06298e10i		−	0.794883i
$783$	−2.00382e10			−1.49174
$784$	3.74303e8			0.0277407
$785$		−	1.78337e10i		−	1.31582i
$786$		−	6.79864e9i		−	0.499394i
$787$			1.73104e10i			1.26589i	0.774198	+	0.632943i	$0.218153\pi$
$787$			1.73104e10i			1.26589i	−0.774198	+	0.632943i	$0.781847\pi$
$788$			9.11347e9i			0.663502i
$789$	−6.32648e9			−0.458556
$790$	2.34134e10			1.68955
$791$			2.30901e10i			1.65886i
$792$	−5.71204e8			−0.0408558
$793$	1.54226e10	−	1.49728e10i	1.09825	−	1.06622i
$794$	−2.21878e9			−0.157305
$795$			1.96650e10i			1.38807i
$796$	6.70940e9			0.471507
$797$	−2.31694e9			−0.162110			−0.0810551	−	0.996710i	$-0.525829\pi$
$797$	−2.31694e9			−0.162110			−0.0810551	+	0.996710i	$0.525829\pi$
$798$			4.31444e9i			0.300549i
$799$		−	2.93070e10i		−	2.03263i
$800$		−	4.89794e9i		−	0.338219i
$801$			3.97378e9i			0.273206i
$802$	2.45639e8			0.0168146
$803$	4.19564e8			0.0285952
$804$		−	5.62310e9i		−	0.381574i
$805$	2.21197e10			1.49449
$806$	−3.32254e9	+	3.22562e9i	−0.223510	+	0.216991i
$807$	−1.60074e10			−1.07217
$808$			4.16418e9i			0.277709i
$809$	8.62119e9			0.572463			0.286232	−	0.958160i	$-0.407597\pi$
$809$	8.62119e9			0.572463			0.286232	+	0.958160i	$0.407597\pi$
$810$	−9.25773e9			−0.612078
$811$		−	8.00455e9i		−	0.526943i	−0.964667	−	0.263472i	$-0.915132\pi$
$811$		−	8.00455e9i		−	0.526943i	0.964667	−	0.263472i	$-0.0848675\pi$
$812$			9.86234e9i			0.646448i
$813$			1.00142e10i			0.653584i
$814$			3.50408e9i			0.227713i
$815$	−4.98330e10			−3.22452
$816$	3.75212e9			0.241747
$817$			1.05641e10i			0.677725i
$818$	3.38773e8			0.0216408
$819$	3.73673e9	+	3.84901e9i	0.237683	+	0.244825i
$820$	−1.23767e10			−0.783894
$821$			7.27959e9i			0.459099i	0.973297	+	0.229549i	$0.0737252\pi$
$821$			7.27959e9i			0.459099i	−0.973297	+	0.229549i	$0.926275\pi$
$822$	5.27676e9			0.331372
$823$	−8.53877e8			−0.0533944			−0.0266972	−	0.999644i	$-0.508499\pi$
$823$	−8.53877e8			−0.0533944			−0.0266972	+	0.999644i	$0.508499\pi$
$824$			1.37598e9i			0.0856777i
$825$		−	7.87103e9i		−	0.488025i
$826$			1.51873e10i			0.937673i
$827$		−	2.01479e10i		−	1.23868i	−0.785122	−	0.619342i	$-0.787400\pi$
$827$		−	2.01479e10i		−	1.23868i	0.785122	−	0.619342i	$-0.212600\pi$
$828$	−2.74472e9			−0.168032
$829$	1.50140e9			0.0915284			0.0457642	−	0.998952i	$-0.485428\pi$
$829$	1.50140e9			0.0915284			0.0457642	+	0.998952i	$0.485428\pi$
$830$			2.23977e10i			1.35966i
$831$	−8.55582e9			−0.517200
$832$	−1.48991e9	+	1.44645e9i	−0.0896867	+	0.0870706i
$833$	2.24082e9			0.134323
$834$			1.91737e9i			0.114452i
$835$	−4.27923e9			−0.254368
$836$	1.52207e9			0.0900976
$837$		−	8.13062e9i		−	0.479274i
$838$		−	1.06946e9i		−	0.0627787i
$839$		−	1.78226e10i		−	1.04185i	−0.853603	−	0.520925i	$-0.825587\pi$
$839$		−	1.78226e10i		−	1.04185i	0.853603	−	0.520925i	$-0.174413\pi$
$840$			7.80782e9i			0.454519i
$841$	1.51836e10			0.880214
$842$	7.83715e9			0.452445
$843$			1.57767e10i			0.907025i
$844$	−1.08655e10			−0.622085
$845$	−2.99225e10	−	8.85919e8i	−1.70608	−	0.0505121i
$846$	−7.56731e9			−0.429680
$847$		−	1.49743e10i		−	0.846748i
$848$	−4.51958e9			−0.254515
$849$	−1.73861e10			−0.975045
$850$		−	2.93223e10i		−	1.63769i
$851$			1.68376e10i			0.936541i
$852$		−	5.04991e9i		−	0.279734i
$853$		−	5.18447e9i		−	0.286011i	−0.989722	−	0.143005i	$-0.954323\pi$
$853$		−	5.18447e9i		−	0.286011i	0.989722	−	0.143005i	$-0.0456766\pi$
$854$	1.85751e10			1.02054
$855$	−6.37045e9			−0.348569
$856$		−	8.25522e9i		−	0.449853i
$857$	−2.11545e10			−1.14807			−0.574037	−	0.818829i	$-0.694623\pi$
$857$	−2.11545e10			−1.14807			−0.574037	+	0.818829i	$0.694623\pi$
$858$	−2.39429e9	+	2.32446e9i	−0.129411	+	0.125636i
$859$	6.22064e9			0.334856			0.167428	−	0.985884i	$-0.446454\pi$
$859$	6.22064e9			0.334856			0.167428	+	0.985884i	$0.446454\pi$
$860$			1.91177e10i			1.02492i
$861$	1.29574e10			0.691840
$862$	−1.33189e10			−0.708261
$863$			7.78903e9i			0.412521i	0.978497	+	0.206260i	$0.0661294\pi$
$863$			7.78903e9i			0.412521i	−0.978497	+	0.206260i	$0.933871\pi$
$864$		−	3.64597e9i		−	0.192316i
$865$			4.24490e10i			2.23003i
$866$		−	7.30576e9i		−	0.382254i
$867$	7.13367e9			0.371746
$868$	−4.00169e9			−0.207694
$869$			8.64741e9i			0.447009i
$870$	2.56769e10			1.32198
$871$	1.29774e10	+	1.33673e10i	0.665462	+	0.685456i
$872$	1.64960e9			0.0842501
$873$			3.61230e9i			0.183753i
$874$	7.31378e9			0.370554
$875$	2.91253e10			1.46975
$876$			7.11630e8i			0.0357676i
$877$			5.19360e8i			0.0259998i	0.999915	+	0.0129999i	$0.00413811\pi$
$877$			5.19360e8i			0.0259998i	−0.999915	+	0.0129999i	$0.995862\pi$
$878$		−	4.35789e9i		−	0.217293i
$879$			1.71026e10i			0.849376i
$880$	2.75448e9			0.136254
$881$	3.70780e9			0.182684			0.0913420	−	0.995820i	$-0.470884\pi$
$881$	3.70780e9			0.182684			0.0913420	+	0.995820i	$0.470884\pi$
$882$		−	5.78600e8i		−	0.0283948i
$883$	1.10427e9			0.0539774			0.0269887	−	0.999636i	$-0.491408\pi$
$883$	1.10427e9			0.0539774			0.0269887	+	0.999636i	$0.491408\pi$
$884$	−8.91959e9	+	8.65941e9i	−0.434272	+	0.421605i
$885$	3.95408e10			1.91754
$886$			1.47593e9i			0.0712930i
$887$	4.25547e9			0.204746			0.102373	−	0.994746i	$-0.467356\pi$
$887$	4.25547e9			0.204746			0.102373	+	0.994746i	$0.467356\pi$
$888$	−5.94333e9			−0.284829
$889$		−	1.29051e10i		−	0.616035i
$890$		−	1.91625e10i		−	0.911146i
$891$		−	3.41921e9i		−	0.161940i
$892$		−	1.68247e10i		−	0.793724i
$893$	2.01644e10			0.947558
$894$	−1.24219e10			−0.581443
$895$		−	2.95716e10i		−	1.37878i
$896$	−1.79446e9			−0.0833403
$897$	−1.15049e10	+	1.11693e10i	−0.532243	+	0.516718i
$898$	−6.28730e9			−0.289733
$899$			1.31600e10i			0.604085i
$900$	−7.57128e9			−0.346195
$901$	−2.70572e10			−1.23239
$902$		−	4.57117e9i		−	0.207398i
$903$		−	2.00146e10i		−	0.904564i
$904$			1.38163e10i			0.622019i
$905$			1.52295e10i			0.682992i
$906$	−3.05635e9			−0.136538
$907$	−2.01728e10			−0.897719			−0.448859	−	0.893602i	$-0.648170\pi$
$907$	−2.01728e10			−0.897719			−0.448859	+	0.893602i	$0.648170\pi$
$908$		−	4.01385e9i		−	0.177935i
$909$	6.43703e9			0.284258
$910$	−1.80194e10	−	1.85608e10i	−0.792677	−	0.816493i
$911$	1.56380e10			0.685280			0.342640	−	0.939467i	$-0.388679\pi$
$911$	1.56380e10			0.685280			0.342640	+	0.939467i	$0.388679\pi$
$912$			2.58162e9i			0.112696i
$913$	−8.27228e9			−0.359731
$914$	−9.89430e9			−0.428621
$915$		−	4.83609e10i		−	2.08699i
$916$		−	2.01996e10i		−	0.868377i
$917$			1.94654e10i			0.833624i
$918$		−	2.18272e10i		−	0.931212i
$919$	1.23405e10			0.524481			0.262240	−	0.965003i	$-0.415539\pi$
$919$	1.23405e10			0.524481			0.262240	+	0.965003i	$0.415539\pi$
$920$	1.32357e10			0.560388
$921$		−	3.08896e10i		−	1.30288i
$922$	−4.48548e8			−0.0188474
$923$	1.16545e10	+	1.20047e10i	0.487853	+	0.502511i
$924$	−2.88371e9			−0.120254
$925$			4.64463e10i			1.92955i
$926$	−8.98875e9			−0.372015
$927$	2.12701e9			0.0876980
$928$			5.90128e9i			0.242398i
$929$		−	3.16207e10i		−	1.29395i	−0.762512	−	0.646974i	$-0.776034\pi$
$929$		−	3.16207e10i		−	1.29395i	0.762512	−	0.646974i	$-0.223966\pi$
$930$			1.04185e10i			0.424734i
$931$			1.54178e9i			0.0626179i
$932$	−6.78786e9			−0.274648
$933$	1.17341e10			0.473004
$934$		−	1.01184e10i		−	0.406349i
$935$	1.64902e10			0.659758
$936$	2.23593e9	+	2.30311e9i	0.0891238	+	0.0918015i
$937$	1.10850e10			0.440196			0.220098	−	0.975478i	$-0.429362\pi$
$937$	1.10850e10			0.440196			0.220098	+	0.975478i	$0.429362\pi$
$938$			1.60997e10i			0.636952i
$939$	−1.17020e10			−0.461244
$940$	3.64914e10			1.43299
$941$		−	1.36475e10i		−	0.533937i	−0.963705	−	0.266969i	$-0.913978\pi$
$941$		−	1.36475e10i		−	0.533937i	0.963705	−	0.266969i	$-0.0860220\pi$
$942$			1.11717e10i			0.435453i
$943$		−	2.19651e10i		−	0.852987i
$944$			9.08758e9i			0.351598i
$945$	4.54204e10			1.75081
$946$	−7.06085e9			−0.271168
$947$		−	4.34410e9i		−	0.166217i	−0.996541	−	0.0831083i	$-0.973515\pi$
$947$		−	4.34410e9i		−	0.166217i	0.996541	−	0.0831083i	$-0.0264848\pi$
$948$	−1.46670e10			−0.559130
$949$	−1.64235e9	−	1.69169e9i	−0.0623784	−	0.0642525i
$950$	2.01750e10			0.763450
$951$		−	3.59658e10i		−	1.35600i
$952$	−1.07428e10			−0.403542
$953$	−8.40733e9			−0.314654			−0.157327	−	0.987547i	$-0.550288\pi$
$953$	−8.40733e9			−0.314654			−0.157327	+	0.987547i	$0.550288\pi$
$954$			6.98641e9i			0.260516i
$955$			7.89386e10i			2.93277i
$956$		−	6.43001e9i		−	0.238018i
$957$			9.48341e9i			0.349762i
$958$	−1.51767e9			−0.0557696
$959$	−1.51080e10			−0.553150
$960$			4.67193e9i			0.170430i
$961$	2.21729e10			0.805916
$962$	1.41286e10	−	1.37164e10i	0.511664	−	0.496740i
$963$	−1.27610e10			−0.460460
$964$			4.38026e9i			0.157482i
$965$	−9.62572e9			−0.344816
$966$	−1.38566e10			−0.494581
$967$		−	4.83860e10i		−	1.72079i	−0.509629	−	0.860394i	$-0.670217\pi$
$967$		−	4.83860e10i		−	1.72079i	0.509629	−	0.860394i	$-0.329783\pi$
$968$		−	8.96010e9i		−	0.317504i
$969$			1.54553e10i			0.545687i
$970$		−	1.74194e10i		−	0.612819i
$971$	−2.60955e10			−0.914740			−0.457370	−	0.889276i	$-0.651209\pi$
$971$	−2.60955e10			−0.914740			−0.457370	+	0.889276i	$0.651209\pi$
$972$	−9.77431e9			−0.341393
$973$		−	5.48967e9i		−	0.191052i
$974$	1.40887e9			0.0488558
$975$	−3.17362e10	+	3.08105e10i	−1.09658	+	1.06459i
$976$	1.11147e10			0.382670
$977$		−	8.92873e9i		−	0.306308i	−0.988202	−	0.153154i	$-0.951057\pi$
$977$		−	8.92873e9i		−	0.306308i	0.988202	−	0.153154i	$-0.0489431\pi$
$978$	3.12173e10			1.06711
$979$	7.07741e9			0.241065
$980$			2.79015e9i			0.0946970i
$981$		−	2.54996e9i		−	0.0862367i
$982$			1.72579e10i			0.581564i
$983$		−	4.62667e10i		−	1.55357i	−0.629765	−	0.776786i	$-0.716849\pi$
$983$		−	4.62667e10i		−	1.55357i	0.629765	−	0.776786i	$-0.283151\pi$
$984$	7.75324e9			0.259418
$985$	−6.79342e10			−2.26496
$986$			3.53290e10i			1.17371i
$987$	−3.82033e10			−1.26471
$988$	−5.95803e9	−	6.13705e9i	−0.196541	−	0.202446i
$989$	−3.39284e10			−1.11526
$990$		−	4.25790e9i		−	0.139467i
$991$	2.15714e10			0.704079			0.352040	−	0.935985i	$-0.385488\pi$
$991$	2.15714e10			0.704079			0.352040	+	0.935985i	$0.385488\pi$
$992$	−2.39448e9			−0.0778788
$993$			3.87365e10i			1.25545i
$994$			1.44586e10i			0.466952i
$995$			5.00136e10i			1.60956i
$996$		−	1.40308e10i		−	0.449960i
$997$	4.72486e10			1.50993			0.754963	−	0.655767i	$-0.227655\pi$
$997$	4.72486e10			1.50993			0.754963	+	0.655767i	$0.227655\pi$
$998$	−1.64298e10			−0.523209
$999$			3.45741e10i			1.09716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.b.a.25.9	yes	10
3.2	odd	2		234.8.b.c.181.5		10
4.3	odd	2		208.8.f.c.129.3		10
13.5	odd	4		338.8.a.l.1.4		5
13.8	odd	4		338.8.a.k.1.4		5
13.12	even	2	inner	26.8.b.a.25.4	✓	10
39.38	odd	2		234.8.b.c.181.6		10
52.51	odd	2		208.8.f.c.129.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.b.a.25.4	✓	10	13.12	even	2	inner
26.8.b.a.25.9	yes	10	1.1	even	1	trivial
208.8.f.c.129.3		10	4.3	odd	2
208.8.f.c.129.4		10	52.51	odd	2
234.8.b.c.181.5		10	3.2	odd	2
234.8.b.c.181.6		10	39.38	odd	2
338.8.a.k.1.4		5	13.8	odd	4
338.8.a.l.1.4		5	13.5	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	26.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.00000i q^{2} +37.3570 q^{3} -64.0000 q^{4} -477.073i q^{5} +298.856i q^{6} -855.664i q^{7} -512.000i q^{8} -791.454 q^{9} +3816.58 q^{10} +1409.60i q^{11} -2390.85 q^{12} +(5683.55 - 5517.77i) q^{13} +6845.31 q^{14} -17822.0i q^{15} +4096.00 q^{16} +24521.4 q^{17} -6331.63i q^{18} +16871.7i q^{19} +30532.6i q^{20} -31965.0i q^{21} -11276.8 q^{22} -54186.6 q^{23} -19126.8i q^{24} -149473. q^{25} +(44142.1 + 45468.4i) q^{26} -111266. q^{27} +54762.5i q^{28} +180093. q^{29} +142576. q^{30} +73073.6i q^{31} +32768.0i q^{32} +52658.4i q^{33} +196171. i q^{34} -408214. q^{35} +50653.1 q^{36} -310734. i q^{37} -134974. q^{38} +(212320. - 206127. i) q^{39} -244261. q^{40} +405360. i q^{41} +255720. q^{42} +626140. q^{43} -90214.4i q^{44} +377581. i q^{45} -433493. i q^{46} -1.19516e6i q^{47} +153014. q^{48} +91382.5 q^{49} -1.19579e6i q^{50} +916045. q^{51} +(-363747. + 353137. i) q^{52} -1.10341e6 q^{53} -890129. i q^{54} +672481. q^{55} -438100. q^{56} +630277. i q^{57} +1.44074e6i q^{58} +2.21865e6i q^{59} +1.14061e6i q^{60} +2.71355e6 q^{61} -584589. q^{62} +677219. i q^{63} -262144. q^{64} +(-2.63238e6 - 2.71147e6i) q^{65} -421267. q^{66} +2.35192e6i q^{67} -1.56937e6 q^{68} -2.02425e6 q^{69} -3.26571e6i q^{70} +2.11218e6i q^{71} +405224. i q^{72} -297647. i q^{73} +2.48587e6 q^{74} -5.58387e6 q^{75} -1.07979e6i q^{76} +1.20614e6 q^{77} +(1.64902e6 + 1.69856e6i) q^{78} +6.13466e6 q^{79} -1.95409e6i q^{80} -2.42566e6 q^{81} -3.24288e6 q^{82} +5.86853e6i q^{83} +2.04576e6i q^{84} -1.16985e7i q^{85} +5.00912e6i q^{86} +6.72773e6 q^{87} +721715. q^{88} -5.02086e6i q^{89} -3.02065e6 q^{90} +(-4.72135e6 - 4.86321e6i) q^{91} +3.46794e6 q^{92} +2.72981e6i q^{93} +9.56128e6 q^{94} +8.04904e6 q^{95} +1.22411e6i q^{96} -4.56414e6i q^{97} +731060. i q^{98} -1.11563e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 54 q^{3} - 640 q^{4} + 13960 q^{9} - 1136 q^{10} - 3456 q^{12} + 3432 q^{13} + 3792 q^{14} + 40960 q^{16} - 6918 q^{17} + 17280 q^{22} + 94164 q^{23} - 330788 q^{25} + 118896 q^{26} - 53550 q^{27}+ \cdots + 16547484 q^{95}+O(q^{100}) \) 10 * q + 54 * q^3 - 640 * q^4 + 13960 * q^9 - 1136 * q^10 - 3456 * q^12 + 3432 * q^13 + 3792 * q^14 + 40960 * q^16 - 6918 * q^17 + 17280 * q^22 + 94164 * q^23 - 330788 * q^25 + 118896 * q^26 - 53550 * q^27 - 131304 * q^29 - 434992 * q^30 + 873450 * q^35 - 893440 * q^36 + 602976 * q^38 - 1569460 * q^39 + 72704 * q^40 + 1800592 * q^42 + 2740774 * q^43 + 221184 * q^48 - 3083904 * q^49 + 1103186 * q^51 - 219648 * q^52 - 3605916 * q^53 + 3999840 * q^55 - 242688 * q^56 + 11727656 * q^61 - 4210560 * q^62 - 2621440 * q^64 - 7481034 * q^65 - 5557248 * q^66 + 442752 * q^68 + 2035796 * q^69 + 18145392 * q^74 - 32855720 * q^75 - 7147920 * q^77 - 8343632 * q^78 - 28449228 * q^79 + 49311466 * q^81 + 17868800 * q^82 + 50156320 * q^87 - 1105920 * q^88 - 23059744 * q^90 - 20225194 * q^91 - 6026496 * q^92 + 8240976 * q^94 + 16547484 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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