LMFDB - Embedded newform 1134.2.l.e.215.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(215,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1134.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.l (of order $6$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			215.3
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1134.215
Dual form			1134.2.l.e.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000i q^{8} +(2.12132 - 1.22474i) q^{10} +(3.67423 + 2.12132i) q^{11} +(-0.621320 - 0.358719i) q^{13} +(-2.09077 - 1.62132i) q^{14} +1.00000 q^{16} +(-1.22474 - 2.12132i) q^{17} +(-4.24264 - 2.44949i) q^{19} +(1.22474 + 2.12132i) q^{20} +(-2.12132 + 3.67423i) q^{22} +(5.19615 - 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.358719 - 0.621320i) q^{26} +(1.62132 - 2.09077i) q^{28} +(-1.52192 + 0.878680i) q^{29} -9.08052i q^{31} +1.00000i q^{32} +(2.12132 - 1.22474i) q^{34} +(6.42090 + 0.878680i) q^{35} +(-2.62132 + 4.54026i) q^{37} +(2.44949 - 4.24264i) q^{38} +(-2.12132 + 1.22474i) q^{40} +(1.22474 - 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-3.67423 - 2.12132i) q^{44} +(3.00000 + 5.19615i) q^{46} +12.8418 q^{47} +(-1.74264 - 6.77962i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(0.621320 + 0.358719i) q^{52} +(12.5446 - 7.24264i) q^{53} -10.3923i q^{55} +(2.09077 + 1.62132i) q^{56} +(-0.878680 - 1.52192i) q^{58} -2.44949 q^{59} -4.18154i q^{61} +9.08052 q^{62} -1.00000 q^{64} +1.75736i q^{65} +13.4853 q^{67} +(1.22474 + 2.12132i) q^{68} +(-0.878680 + 6.42090i) q^{70} -12.7279i q^{71} +(-4.75736 + 2.74666i) q^{73} +(-4.54026 - 2.62132i) q^{74} +(4.24264 + 2.44949i) q^{76} +(-10.3923 + 4.24264i) q^{77} +0.757359 q^{79} +(-1.22474 - 2.12132i) q^{80} +(2.12132 + 1.22474i) q^{82} +(-7.64564 - 13.2426i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(6.06218 - 3.50000i) q^{86} +(2.12132 - 3.67423i) q^{88} +(-1.52192 + 2.63604i) q^{89} +(1.75736 - 0.717439i) q^{91} +(-5.19615 + 3.00000i) q^{92} +12.8418i q^{94} +12.0000i q^{95} +(-2.74264 + 1.58346i) q^{97} +(6.77962 - 1.74264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 + 4 * q^7	$ 8 q - 8 q^{4} + 4 q^{7} + 12 q^{13} + 8 q^{16} - 4 q^{25} - 4 q^{28} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} - 12 q^{52} - 24 q^{58} - 8 q^{64} + 40 q^{67} - 24 q^{70} - 72 q^{73} + 40 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^13 + 8 * q^16 - 4 * q^25 - 4 * q^28 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 - 12 * q^52 - 24 * q^58 - 8 * q^64 + 40 * q^67 - 24 * q^70 - 72 * q^73 + 40 * q^79 - 24 * q^85 + 48 * q^91 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	−0.998430	−	0.0560116i	$-0.982162\pi$
$5$	−1.22474	−	2.12132i	−0.547723	−	0.948683i	0.450708	−	0.892672i	$-0.351172\pi$
$6$		0			0
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$7$	−1.62132	+	2.09077i	−0.612801	+	0.790237i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.12132	−	1.22474i	0.670820	−	0.387298i
$11$	3.67423	+	2.12132i	1.10782	+	0.639602i	0.938265	−	0.345918i	$-0.112432\pi$
$11$	3.67423	+	2.12132i	1.10782	+	0.639602i	0.169559	+	0.985520i	$0.445766\pi$
$12$		0			0
$13$	−0.621320	−	0.358719i	−0.172323	−	0.0994909i	0.411358	−	0.911474i	$-0.365055\pi$
$13$	−0.621320	−	0.358719i	−0.172323	−	0.0994909i	−0.583681	+	0.811983i	$0.698388\pi$
$14$	−2.09077	−	1.62132i	−0.558782	−	0.433316i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.22474	−	2.12132i	−0.297044	−	0.514496i	0.678414	−	0.734680i	$-0.262668\pi$
$17$	−1.22474	−	2.12132i	−0.297044	−	0.514496i	−0.975458	+	0.220184i	$0.929334\pi$
$18$		0			0
$19$	−4.24264	−	2.44949i	−0.973329	−	0.561951i	−0.0730792	−	0.997326i	$-0.523283\pi$
$19$	−4.24264	−	2.44949i	−0.973329	−	0.561951i	−0.900249	+	0.435375i	$0.856616\pi$
$20$	1.22474	+	2.12132i	0.273861	+	0.474342i
$21$		0			0
$22$	−2.12132	+	3.67423i	−0.452267	+	0.783349i
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.358719	−	0.621320i	0.0703507	−	0.121851i
$27$		0			0
$28$	1.62132	−	2.09077i	0.306401	−	0.395118i
$29$	−1.52192	+	0.878680i	−0.282613	+	0.163167i	−0.634606	−	0.772836i	$-0.718838\pi$
$29$	−1.52192	+	0.878680i	−0.282613	+	0.163167i	0.351993	+	0.936003i	$0.385504\pi$
$30$		0			0
$31$		−	9.08052i		−	1.63091i	−0.578821	−	0.815455i	$-0.696487\pi$
$31$		−	9.08052i		−	1.63091i	0.578821	−	0.815455i	$-0.303513\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	2.12132	−	1.22474i	0.363803	−	0.210042i
$35$	6.42090	+	0.878680i	1.08533	+	0.148524i
$36$		0			0
$37$	−2.62132	+	4.54026i	−0.430942	+	0.746414i	−0.996955	−	0.0779826i	$-0.975152\pi$
$37$	−2.62132	+	4.54026i	−0.430942	+	0.746414i	0.566012	+	0.824397i	$0.308485\pi$
$38$	2.44949	−	4.24264i	0.397360	−	0.688247i
$39$		0			0
$40$	−2.12132	+	1.22474i	−0.335410	+	0.193649i
$41$	1.22474	−	2.12132i	0.191273	−	0.331295i	−0.754399	−	0.656416i	$-0.772072\pi$
$41$	1.22474	−	2.12132i	0.191273	−	0.331295i	0.945672	+	0.325121i	$0.105405\pi$
$42$		0			0
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	−0.999223	−	0.0394140i	$-0.987451\pi$
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	0.465478	−	0.885059i	$-0.345882\pi$
$44$	−3.67423	−	2.12132i	−0.553912	−	0.319801i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	12.8418			1.87317			0.936584	−	0.350443i	$-0.113969\pi$
$47$	12.8418			1.87317			0.936584	+	0.350443i	$0.113969\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$		0			0
$52$	0.621320	+	0.358719i	0.0861616	+	0.0497454i
$53$	12.5446	−	7.24264i	1.72314	−	0.994853i	0.810905	−	0.585178i	$-0.198975\pi$
$53$	12.5446	−	7.24264i	1.72314	−	0.994853i	0.912231	−	0.409675i	$-0.134358\pi$
$54$		0			0
$55$		−	10.3923i		−	1.40130i
$56$	2.09077	+	1.62132i	0.279391	+	0.216658i
$57$		0			0
$58$	−0.878680	−	1.52192i	−0.115376	−	0.199838i
$59$	−2.44949			−0.318896			−0.159448	−	0.987206i	$-0.550971\pi$
$59$	−2.44949			−0.318896			−0.159448	+	0.987206i	$0.550971\pi$
$60$		0			0
$61$		−	4.18154i		−	0.535391i	−0.963504	−	0.267696i	$-0.913738\pi$
$61$		−	4.18154i		−	0.535391i	0.963504	−	0.267696i	$-0.0862622\pi$
$62$	9.08052			1.15323
$63$		0			0
$64$	−1.00000			−0.125000
$65$			1.75736i			0.217974i
$66$		0			0
$67$	13.4853			1.64749			0.823745	−	0.566961i	$-0.191881\pi$
$67$	13.4853			1.64749			0.823745	+	0.566961i	$0.191881\pi$
$68$	1.22474	+	2.12132i	0.148522	+	0.257248i
$69$		0			0
$70$	−0.878680	+	6.42090i	−0.105022	+	0.767444i
$71$		−	12.7279i		−	1.51053i	−0.655422	−	0.755263i	$-0.727509\pi$
$71$		−	12.7279i		−	1.51053i	0.655422	−	0.755263i	$-0.272491\pi$
$72$		0			0
$73$	−4.75736	+	2.74666i	−0.556807	+	0.321473i	−0.751863	−	0.659320i	$-0.770844\pi$
$73$	−4.75736	+	2.74666i	−0.556807	+	0.321473i	0.195056	+	0.980792i	$0.437511\pi$
$74$	−4.54026	−	2.62132i	−0.527795	−	0.304722i
$75$		0			0
$76$	4.24264	+	2.44949i	0.486664	+	0.280976i
$77$	−10.3923	+	4.24264i	−1.18431	+	0.483494i
$78$		0			0
$79$	0.757359			0.0852096			0.0426048	−	0.999092i	$-0.486434\pi$
$79$	0.757359			0.0852096			0.0426048	+	0.999092i	$0.486434\pi$
$80$	−1.22474	−	2.12132i	−0.136931	−	0.237171i
$81$		0			0
$82$	2.12132	+	1.22474i	0.234261	+	0.135250i
$83$	−7.64564	−	13.2426i	−0.839218	−	1.45357i	−0.890549	−	0.454887i	$-0.849680\pi$
$83$	−7.64564	−	13.2426i	−0.839218	−	1.45357i	0.0513309	−	0.998682i	$-0.483654\pi$
$84$		0			0
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$	6.06218	−	3.50000i	0.653701	−	0.377415i
$87$		0			0
$88$	2.12132	−	3.67423i	0.226134	−	0.391675i
$89$	−1.52192	+	2.63604i	−0.161323	+	0.279420i	−0.935343	−	0.353741i	$-0.884909\pi$
$89$	−1.52192	+	2.63604i	−0.161323	+	0.279420i	0.774020	+	0.633161i	$0.218243\pi$
$90$		0			0
$91$	1.75736	−	0.717439i	0.184221	−	0.0752080i
$92$	−5.19615	+	3.00000i	−0.541736	+	0.312772i
$93$		0			0
$94$			12.8418i			1.32453i
$95$			12.0000i			1.23117i
$96$		0			0
$97$	−2.74264	+	1.58346i	−0.278473	+	0.160776i	−0.632732	−	0.774371i	$-0.718066\pi$
$97$	−2.74264	+	1.58346i	−0.278473	+	0.160776i	0.354259	+	0.935147i	$0.384733\pi$
$98$	6.77962	−	1.74264i	0.684845	−	0.176033i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−3.67423	+	6.36396i	−0.365600	+	0.633238i	−0.988872	−	0.148767i	$-0.952470\pi$
$101$	−3.67423	+	6.36396i	−0.365600	+	0.633238i	0.623272	+	0.782005i	$0.285803\pi$
$102$		0			0
$103$	−9.62132	+	5.55487i	−0.948017	+	0.547338i	−0.892464	−	0.451118i	$-0.851025\pi$
$103$	−9.62132	+	5.55487i	−0.948017	+	0.547338i	−0.0555525	+	0.998456i	$0.517692\pi$
$104$	−0.358719	+	0.621320i	−0.0351753	+	0.0609255i
$105$		0			0
$106$	7.24264	+	12.5446i	0.703467	+	1.21844i
$107$	2.15232	+	1.24264i	0.208072	+	0.120131i	0.600415	−	0.799688i	$-0.295002\pi$
$107$	2.15232	+	1.24264i	0.208072	+	0.120131i	−0.392343	+	0.919819i	$0.628335\pi$
$108$		0			0
$109$	8.86396	+	15.3528i	0.849013	+	1.47053i	0.882090	+	0.471082i	$0.156136\pi$
$109$	8.86396	+	15.3528i	0.849013	+	1.47053i	−0.0330761	+	0.999453i	$0.510530\pi$
$110$	10.3923			0.990867
$111$		0			0
$112$	−1.62132	+	2.09077i	−0.153200	+	0.197559i
$113$	−8.87039	−	5.12132i	−0.834456	−	0.481773i	0.0209200	−	0.999781i	$-0.493340\pi$
$113$	−8.87039	−	5.12132i	−0.834456	−	0.481773i	−0.855376	+	0.518008i	$0.826674\pi$
$114$		0			0
$115$	−12.7279	−	7.34847i	−1.18688	−	0.685248i
$116$	1.52192	−	0.878680i	0.141307	−	0.0815834i
$117$		0			0
$118$		−	2.44949i		−	0.225494i
$119$	6.42090	+	0.878680i	0.588603	+	0.0805484i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	4.18154			0.378579
$123$		0			0
$124$			9.08052i			0.815455i
$125$	−9.79796			−0.876356
$126$		0			0
$127$	−7.72792			−0.685742			−0.342871	−	0.939382i	$-0.611399\pi$
$127$	−7.72792			−0.685742			−0.342871	+	0.939382i	$0.611399\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−1.75736			−0.154131
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	12.0000	−	4.89898i	1.04053	−	0.424795i
$134$			13.4853i			1.16495i
$135$		0			0
$136$	−2.12132	+	1.22474i	−0.181902	+	0.105021i
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	0.261329	−	0.965250i	$-0.415839\pi$
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	−0.705266	+	0.708942i	$0.749173\pi$
$138$		0			0
$139$	6.98528	+	4.03295i	0.592484	+	0.342071i	0.766079	−	0.642746i	$-0.222205\pi$
$139$	6.98528	+	4.03295i	0.592484	+	0.342071i	−0.173595	+	0.984817i	$0.555538\pi$
$140$	−6.42090	−	0.878680i	−0.542665	−	0.0742620i
$141$		0			0
$142$	12.7279			1.06810
$143$	−1.52192	−	2.63604i	−0.127269	−	0.220437i
$144$		0			0
$145$	3.72792	+	2.15232i	0.309587	+	0.178740i
$146$	−2.74666	−	4.75736i	−0.227315	−	0.393722i
$147$		0			0
$148$	2.62132	−	4.54026i	0.215471	−	0.373207i
$149$	14.0665	−	8.12132i	1.15238	−	0.665324i	0.202911	−	0.979197i	$-0.434960\pi$
$149$	14.0665	−	8.12132i	1.15238	−	0.665324i	0.949465	+	0.313873i	$0.101627\pi$
$150$		0			0
$151$	−4.37868	+	7.58410i	−0.356332	+	0.617185i	−0.987345	−	0.158587i	$-0.949306\pi$
$151$	−4.37868	+	7.58410i	−0.356332	+	0.617185i	0.631013	+	0.775772i	$0.282639\pi$
$152$	−2.44949	+	4.24264i	−0.198680	+	0.344124i
$153$		0			0
$154$	−4.24264	−	10.3923i	−0.341882	−	0.837436i
$155$	−19.2627	+	11.1213i	−1.54722	+	0.893286i
$156$		0			0
$157$		−	10.3923i		−	0.829396i	−0.909959	−	0.414698i	$-0.863887\pi$
$157$		−	10.3923i		−	0.829396i	0.909959	−	0.414698i	$-0.136113\pi$
$158$			0.757359i			0.0602523i
$159$		0			0
$160$	2.12132	−	1.22474i	0.167705	−	0.0968246i
$161$	−2.15232	+	15.7279i	−0.169626	+	1.23953i
$162$		0			0
$163$	4.74264	−	8.21449i	0.371472	−	0.643409i	−0.618320	−	0.785926i	$-0.712186\pi$
$163$	4.74264	−	8.21449i	0.371472	−	0.643409i	0.989792	+	0.142518i	$0.0455197\pi$
$164$	−1.22474	+	2.12132i	−0.0956365	+	0.165647i
$165$		0			0
$166$	13.2426	−	7.64564i	1.02783	−	0.593417i
$167$	0.297173	−	0.514719i	0.0229959	−	0.0398301i	−0.854298	−	0.519783i	$-0.826013\pi$
$167$	0.297173	−	0.514719i	0.0229959	−	0.0398301i	0.877294	+	0.479953i	$0.159346\pi$
$168$		0			0
$169$	−6.24264	−	10.8126i	−0.480203	−	0.831736i
$170$	−5.19615	−	3.00000i	−0.398527	−	0.230089i
$171$		0			0
$172$	3.50000	+	6.06218i	0.266872	+	0.462237i
$173$	20.7846			1.58022			0.790112	−	0.612962i	$-0.210022\pi$
$173$	20.7846			1.58022			0.790112	+	0.612962i	$0.210022\pi$
$174$		0			0
$175$	−1.00000	−	2.44949i	−0.0755929	−	0.185164i
$176$	3.67423	+	2.12132i	0.276956	+	0.159901i
$177$		0			0
$178$	−2.63604	−	1.52192i	−0.197579	−	0.114073i
$179$	−5.82655	+	3.36396i	−0.435497	+	0.251434i	−0.701686	−	0.712487i	$-0.747569\pi$
$179$	−5.82655	+	3.36396i	−0.435497	+	0.251434i	0.266189	+	0.963921i	$0.414236\pi$
$180$		0			0
$181$			9.79796i			0.728277i	0.931345	+	0.364138i	$0.118636\pi$
$181$			9.79796i			0.728277i	−0.931345	+	0.364138i	$0.881364\pi$
$182$	0.717439	+	1.75736i	0.0531801	+	0.130264i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	12.8418			0.944148
$186$		0			0
$187$		−	10.3923i		−	0.759961i
$188$	−12.8418			−0.936584
$189$		0			0
$190$	−12.0000			−0.870572
$191$			21.2132i			1.53493i	0.641089	+	0.767467i	$0.278483\pi$
$191$			21.2132i			1.53493i	−0.641089	+	0.767467i	$0.721517\pi$
$192$		0			0
$193$	−1.48528			−0.106913			−0.0534564	−	0.998570i	$-0.517024\pi$
$193$	−1.48528			−0.106913			−0.0534564	+	0.998570i	$0.517024\pi$
$194$	−1.58346	−	2.74264i	−0.113686	−	0.196910i
$195$		0			0
$196$	1.74264	+	6.77962i	0.124474	+	0.484258i
$197$			16.9706i			1.20910i	0.796566	+	0.604551i	$0.206648\pi$
$197$			16.9706i			1.20910i	−0.796566	+	0.604551i	$0.793352\pi$
$198$		0			0
$199$	−18.1066	+	10.4539i	−1.28354	+	0.741054i	−0.977494	−	0.210962i	$-0.932340\pi$
$199$	−18.1066	+	10.4539i	−1.28354	+	0.741054i	−0.306049	+	0.952016i	$0.599007\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$		0			0
$202$	−6.36396	−	3.67423i	−0.447767	−	0.258518i
$203$	0.630399	−	4.60660i	0.0442453	−	0.323320i
$204$		0			0
$205$	−6.00000			−0.419058
$206$	−5.55487	−	9.62132i	−0.387026	−	0.670349i
$207$		0			0
$208$	−0.621320	−	0.358719i	−0.0430808	−	0.0248727i
$209$	−10.3923	−	18.0000i	−0.718851	−	1.24509i
$210$		0			0
$211$	−1.74264	+	3.01834i	−0.119968	+	0.207791i	−0.919755	−	0.392493i	$-0.871613\pi$
$211$	−1.74264	+	3.01834i	−0.119968	+	0.207791i	0.799787	+	0.600284i	$0.204946\pi$
$212$	−12.5446	+	7.24264i	−0.861568	+	0.497427i
$213$		0			0
$214$	−1.24264	+	2.15232i	−0.0849452	+	0.147129i
$215$	−8.57321	+	14.8492i	−0.584688	+	1.01271i
$216$		0			0
$217$	18.9853	+	14.7224i	1.28880	+	0.999424i
$218$	−15.3528	+	8.86396i	−1.03982	+	0.600343i
$219$		0			0
$220$			10.3923i			0.700649i
$221$			1.75736i			0.118213i
$222$		0			0
$223$	9.00000	−	5.19615i	0.602685	−	0.347960i	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	9.00000	−	5.19615i	0.602685	−	0.347960i	0.770097	+	0.637927i	$0.220208\pi$
$224$	−2.09077	−	1.62132i	−0.139695	−	0.108329i
$225$		0			0
$226$	5.12132	−	8.87039i	0.340665	−	0.590049i
$227$	12.5446	−	21.7279i	0.832616	−	1.44213i	−0.0633412	−	0.997992i	$-0.520176\pi$
$227$	12.5446	−	21.7279i	0.832616	−	1.44213i	0.895957	−	0.444141i	$-0.146491\pi$
$228$		0			0
$229$	4.86396	−	2.80821i	0.321420	−	0.185572i	−0.330606	−	0.943769i	$-0.607253\pi$
$229$	4.86396	−	2.80821i	0.321420	−	0.185572i	0.652025	+	0.758197i	$0.273920\pi$
$230$	7.34847	−	12.7279i	0.484544	−	0.839254i
$231$		0			0
$232$	0.878680	+	1.52192i	0.0576881	+	0.0999188i
$233$	−17.7408	−	10.2426i	−1.16224	−	0.671018i	−0.210398	−	0.977616i	$-0.567476\pi$
$233$	−17.7408	−	10.2426i	−1.16224	−	0.671018i	−0.951839	+	0.306598i	$0.900809\pi$
$234$		0			0
$235$	−15.7279	−	27.2416i	−1.02598	−	1.77704i
$236$	2.44949			0.159448
$237$		0			0
$238$	−0.878680	+	6.42090i	−0.0569563	+	0.416205i
$239$	−14.0665	−	8.12132i	−0.909889	−	0.525325i	−0.0294934	−	0.999565i	$-0.509389\pi$
$239$	−14.0665	−	8.12132i	−0.909889	−	0.525325i	−0.880395	+	0.474240i	$0.842723\pi$
$240$		0			0
$241$	0.985281	+	0.568852i	0.0634676	+	0.0366430i	0.531398	−	0.847122i	$-0.321667\pi$
$241$	0.985281	+	0.568852i	0.0634676	+	0.0366430i	−0.467930	+	0.883765i	$0.655000\pi$
$242$	−6.06218	+	3.50000i	−0.389692	+	0.224989i
$243$		0			0
$244$			4.18154i			0.267696i
$245$	−12.2474	+	12.0000i	−0.782461	+	0.766652i
$246$		0			0
$247$	1.75736	+	3.04384i	0.111818	+	0.193675i
$248$	−9.08052			−0.576614
$249$		0			0
$250$		−	9.79796i		−	0.619677i
$251$	−15.2913			−0.965177			−0.482589	−	0.875847i	$-0.660303\pi$
$251$	−15.2913			−0.965177			−0.482589	+	0.875847i	$0.660303\pi$
$252$		0			0
$253$	25.4558			1.60040
$254$		−	7.72792i		−	0.484893i
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	0.930474	+	0.366358i	$0.119395\pi$
$257$	12.5446	+	21.7279i	0.782512	+	1.35535i	−0.147962	+	0.988993i	$0.547271\pi$
$258$		0			0
$259$	−5.24264	−	12.8418i	−0.325762	−	0.797950i
$260$		−	1.75736i		−	0.108987i
$261$		0			0
$262$		0			0
$263$	−5.82655	−	3.36396i	−0.359281	−	0.207431i	0.309485	−	0.950904i	$-0.399843\pi$
$263$	−5.82655	−	3.36396i	−0.359281	−	0.207431i	−0.668765	+	0.743474i	$0.733177\pi$
$264$		0			0
$265$	−30.7279	−	17.7408i	−1.88760	−	1.08981i
$266$	4.89898	+	12.0000i	0.300376	+	0.735767i
$267$		0			0
$268$	−13.4853			−0.823745
$269$	4.89898	+	8.48528i	0.298696	+	0.517357i	0.975838	−	0.218496i	$-0.0701150\pi$
$269$	4.89898	+	8.48528i	0.298696	+	0.517357i	−0.677142	+	0.735853i	$0.736782\pi$
$270$		0			0
$271$	−16.3492	−	9.43924i	−0.993146	−	0.573393i	−0.0869326	−	0.996214i	$-0.527706\pi$
$271$	−16.3492	−	9.43924i	−0.993146	−	0.573393i	−0.906213	+	0.422821i	$0.861040\pi$
$272$	−1.22474	−	2.12132i	−0.0742611	−	0.128624i
$273$		0			0
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$	−3.67423	+	2.12132i	−0.221565	+	0.127920i
$276$		0			0
$277$	−11.8640	+	20.5490i	−0.712836	+	1.23467i	0.250952	+	0.968000i	$0.419256\pi$
$277$	−11.8640	+	20.5490i	−0.712836	+	1.23467i	−0.963788	+	0.266669i	$0.914077\pi$
$278$	−4.03295	+	6.98528i	−0.241881	+	0.418949i
$279$		0			0
$280$	0.878680	−	6.42090i	0.0525112	−	0.383722i
$281$	−11.9142	+	6.87868i	−0.710743	+	0.410348i	−0.811336	−	0.584580i	$-0.801259\pi$
$281$	−11.9142	+	6.87868i	−0.710743	+	0.410348i	0.100593	+	0.994928i	$0.467926\pi$
$282$		0			0
$283$			6.03668i			0.358844i	0.983772	+	0.179422i	$0.0574227\pi$
$283$			6.03668i			0.358844i	−0.983772	+	0.179422i	$0.942577\pi$
$284$			12.7279i			0.755263i
$285$		0			0
$286$	2.63604	−	1.52192i	0.155872	−	0.0899929i
$287$	2.44949	+	6.00000i	0.144589	+	0.354169i
$288$		0			0
$289$	5.50000	−	9.52628i	0.323529	−	0.560369i
$290$	−2.15232	+	3.72792i	−0.126388	+	0.218911i
$291$		0			0
$292$	4.75736	−	2.74666i	0.278403	−	0.160736i
$293$	6.42090	−	11.1213i	0.375113	−	0.649714i	−0.615231	−	0.788347i	$-0.710937\pi$
$293$	6.42090	−	11.1213i	0.375113	−	0.649714i	0.990344	+	0.138632i	$0.0442706\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$	4.54026	+	2.62132i	0.263897	+	0.152361i
$297$		0			0
$298$	8.12132	+	14.0665i	0.470455	+	0.814853i
$299$	−4.30463			−0.248943
$300$		0			0
$301$	18.3492	+	2.51104i	1.05763	+	0.144734i
$302$	−7.58410	−	4.37868i	−0.436416	−	0.251965i
$303$		0			0
$304$	−4.24264	−	2.44949i	−0.243332	−	0.140488i
$305$	−8.87039	+	5.12132i	−0.507917	+	0.293246i
$306$		0			0
$307$		−	26.8213i		−	1.53077i	−0.643571	−	0.765386i	$-0.722548\pi$
$307$		−	26.8213i		−	1.53077i	0.643571	−	0.765386i	$-0.277452\pi$
$308$	10.3923	−	4.24264i	0.592157	−	0.241747i
$309$		0			0
$310$	−11.1213	−	19.2627i	−0.631649	−	1.09405i
$311$	17.1464			0.972285			0.486142	−	0.873880i	$-0.338404\pi$
$311$	17.1464			0.972285			0.486142	+	0.873880i	$0.338404\pi$
$312$		0			0
$313$			20.1903i			1.14122i	0.821221	+	0.570611i	$0.193293\pi$
$313$			20.1903i			1.14122i	−0.821221	+	0.570611i	$0.806707\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	−0.757359			−0.0426048
$317$		−	22.2426i		−	1.24927i	−0.780916	−	0.624636i	$-0.785248\pi$
$317$		−	22.2426i		−	1.24927i	0.780916	−	0.624636i	$-0.214752\pi$
$318$		0			0
$319$	−7.45584			−0.417447
$320$	1.22474	+	2.12132i	0.0684653	+	0.118585i
$321$		0			0
$322$	−15.7279	−	2.15232i	−0.876483	−	0.119944i
$323$			12.0000i			0.667698i
$324$		0			0
$325$	0.621320	−	0.358719i	0.0344647	−	0.0198982i
$326$	8.21449	+	4.74264i	0.454959	+	0.262671i
$327$		0			0
$328$	−2.12132	−	1.22474i	−0.117130	−	0.0676252i
$329$	−20.8207	+	26.8492i	−1.14788	+	1.48025i
$330$		0			0
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$	7.64564	+	13.2426i	0.419609	+	0.726784i
$333$		0			0
$334$	0.514719	+	0.297173i	0.0281642	+	0.0162606i
$335$	−16.5160	−	28.6066i	−0.902367	−	1.56295i
$336$		0			0
$337$	10.7279	−	18.5813i	0.584387	−	1.01219i	−0.410564	−	0.911832i	$-0.634668\pi$
$337$	10.7279	−	18.5813i	0.584387	−	1.01219i	0.994952	−	0.100357i	$-0.0319984\pi$
$338$	10.8126	−	6.24264i	0.588126	−	0.339555i
$339$		0			0
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$	19.2627	−	33.3640i	1.04313	−	1.80676i
$342$		0			0
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$	−6.06218	+	3.50000i	−0.326851	+	0.188707i
$345$		0			0
$346$			20.7846i			1.11739i
$347$			4.97056i			0.266834i	0.991060	+	0.133417i	$0.0425949\pi$
$347$			4.97056i			0.266834i	−0.991060	+	0.133417i	$0.957405\pi$
$348$		0			0
$349$	0.106602	−	0.0615465i	0.00570626	−	0.00329451i	−0.497144	−	0.867668i	$-0.665618\pi$
$349$	0.106602	−	0.0615465i	0.00570626	−	0.00329451i	0.502850	+	0.864373i	$0.332285\pi$
$350$	2.44949	−	1.00000i	0.130931	−	0.0534522i
$351$		0			0
$352$	−2.12132	+	3.67423i	−0.113067	+	0.195837i
$353$	5.49333	−	9.51472i	0.292380	−	0.506417i	−0.681992	−	0.731360i	$-0.738886\pi$
$353$	5.49333	−	9.51472i	0.292380	−	0.506417i	0.974372	+	0.224942i	$0.0722194\pi$
$354$		0			0
$355$	−27.0000	+	15.5885i	−1.43301	+	0.827349i
$356$	1.52192	−	2.63604i	0.0806615	−	0.139710i
$357$		0			0
$358$	−3.36396	−	5.82655i	−0.177791	−	0.307943i
$359$	12.5446	+	7.24264i	0.662080	+	0.382252i	0.793069	−	0.609132i	$-0.208482\pi$
$359$	12.5446	+	7.24264i	0.662080	+	0.382252i	−0.130989	+	0.991384i	$0.541815\pi$
$360$		0			0
$361$	2.50000	+	4.33013i	0.131579	+	0.227901i
$362$	−9.79796			−0.514969
$363$		0			0
$364$	−1.75736	+	0.717439i	−0.0921107	+	0.0376040i
$365$	11.6531	+	6.72792i	0.609951	+	0.352156i
$366$		0			0
$367$	25.9706	+	14.9941i	1.35565	+	0.782686i	0.989034	−	0.147685i	$-0.0471823\pi$
$367$	25.9706	+	14.9941i	1.35565	+	0.782686i	0.366618	+	0.930372i	$0.380516\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$		0			0
$370$			12.8418i			0.667613i
$371$	−5.19615	+	37.9706i	−0.269771	+	1.97133i
$372$		0			0
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	0.996610	+	0.0822766i	$0.0262191\pi$
$373$	11.0000	+	19.0526i	0.569558	+	0.986504i	−0.427051	+	0.904227i	$0.640448\pi$
$374$	10.3923			0.537373
$375$		0			0
$376$		−	12.8418i		−	0.662265i
$377$	1.26080			0.0649344
$378$		0			0
$379$	−7.48528			−0.384493			−0.192247	−	0.981347i	$-0.561577\pi$
$379$	−7.48528			−0.384493			−0.192247	+	0.981347i	$0.561577\pi$
$380$		−	12.0000i		−	0.615587i
$381$		0			0
$382$	−21.2132			−1.08536
$383$	2.74666	+	4.75736i	0.140348	+	0.243090i	0.927628	−	0.373506i	$-0.121845\pi$
$383$	2.74666	+	4.75736i	0.140348	+	0.243090i	−0.787280	+	0.616596i	$0.788511\pi$
$384$		0			0
$385$	21.7279	+	16.8493i	1.10736	+	0.858718i
$386$		−	1.48528i		−	0.0755988i
$387$		0			0
$388$	2.74264	−	1.58346i	0.139236	−	0.0803882i
$389$	13.4361	+	7.75736i	0.681239	+	0.393314i	0.800322	−	0.599571i	$-0.204662\pi$
$389$	13.4361	+	7.75736i	0.681239	+	0.393314i	−0.119082	+	0.992884i	$0.537995\pi$
$390$		0			0
$391$	−12.7279	−	7.34847i	−0.643679	−	0.371628i
$392$	−6.77962	+	1.74264i	−0.342422	+	0.0880166i
$393$		0			0
$394$	−16.9706			−0.854965
$395$	−0.927572	−	1.60660i	−0.0466712	−	0.0808369i
$396$		0			0
$397$	−13.1360	−	7.58410i	−0.659279	−	0.380635i	0.132723	−	0.991153i	$-0.457628\pi$
$397$	−13.1360	−	7.58410i	−0.659279	−	0.380635i	−0.792002	+	0.610518i	$0.790961\pi$
$398$	−10.4539	−	18.1066i	−0.524004	−	0.907602i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−17.1104	+	9.87868i	−0.854451	+	0.493318i	−0.862150	−	0.506653i	$-0.830883\pi$
$401$	−17.1104	+	9.87868i	−0.854451	+	0.493318i	0.00769892	+	0.999970i	$0.497549\pi$
$402$		0			0
$403$	−3.25736	+	5.64191i	−0.162261	+	0.281044i
$404$	3.67423	−	6.36396i	0.182800	−	0.316619i
$405$		0			0
$406$	4.60660	+	0.630399i	0.228622	+	0.0312862i
$407$	−19.2627	+	11.1213i	−0.954816	+	0.551263i
$408$		0			0
$409$		−	3.76127i		−	0.185983i	−0.995667	−	0.0929915i	$-0.970357\pi$
$409$		−	3.76127i		−	0.185983i	0.995667	−	0.0929915i	$-0.0296430\pi$
$410$		−	6.00000i		−	0.296319i
$411$		0			0
$412$	9.62132	−	5.55487i	0.474008	−	0.273669i
$413$	3.97141	−	5.12132i	0.195420	−	0.252004i
$414$		0			0
$415$	−18.7279	+	32.4377i	−0.919318	+	1.59230i
$416$	0.358719	−	0.621320i	0.0175877	−	0.0304627i
$417$		0			0
$418$	18.0000	−	10.3923i	0.880409	−	0.508304i
$419$	3.97141	−	6.87868i	0.194016	−	0.336045i	−0.752562	−	0.658522i	$-0.771182\pi$
$419$	3.97141	−	6.87868i	0.194016	−	0.336045i	0.946577	+	0.322476i	$0.104515\pi$
$420$		0			0
$421$	11.7279	+	20.3134i	0.571584	+	0.990012i	0.996404	+	0.0847344i	$0.0270042\pi$
$421$	11.7279	+	20.3134i	0.571584	+	0.990012i	−0.424820	+	0.905278i	$0.639662\pi$
$422$	−3.01834	−	1.74264i	−0.146931	−	0.0848304i
$423$		0			0
$424$	−7.24264	−	12.5446i	−0.351734	−	0.609221i
$425$	2.44949			0.118818
$426$		0			0
$427$	8.74264	+	6.77962i	0.423086	+	0.328089i
$428$	−2.15232	−	1.24264i	−0.104036	−	0.0600653i
$429$		0			0
$430$	−14.8492	−	8.57321i	−0.716094	−	0.413437i
$431$	−1.52192	+	0.878680i	−0.0733082	+	0.0423245i	−0.536206	−	0.844087i	$-0.680143\pi$
$431$	−1.52192	+	0.878680i	−0.0733082	+	0.0423245i	0.462898	+	0.886412i	$0.346810\pi$
$432$		0			0
$433$		−	2.57258i		−	0.123630i	−0.998088	−	0.0618152i	$-0.980311\pi$
$433$		−	2.57258i		−	0.123630i	0.998088	−	0.0618152i	$-0.0196889\pi$
$434$	−14.7224	+	18.9853i	−0.706699	+	0.911323i
$435$		0			0
$436$	−8.86396	−	15.3528i	−0.424507	−	0.735267i
$437$	−29.3939			−1.40610
$438$		0			0
$439$		−	4.30463i		−	0.205449i	−0.994710	−	0.102724i	$-0.967244\pi$
$439$		−	4.30463i		−	0.205449i	0.994710	−	0.102724i	$-0.0327560\pi$
$440$	−10.3923			−0.495434
$441$		0			0
$442$	−1.75736			−0.0835891
$443$		−	25.4558i		−	1.20944i	−0.796437	−	0.604722i	$-0.793284\pi$
$443$		−	25.4558i		−	1.20944i	0.796437	−	0.604722i	$-0.206716\pi$
$444$		0			0
$445$	7.45584			0.353441
$446$	5.19615	+	9.00000i	0.246045	+	0.426162i
$447$		0			0
$448$	1.62132	−	2.09077i	0.0766002	−	0.0987796i
$449$			5.27208i			0.248805i	0.992232	+	0.124402i	$0.0397014\pi$
$449$			5.27208i			0.248805i	−0.992232	+	0.124402i	$0.960299\pi$
$450$		0			0
$451$	9.00000	−	5.19615i	0.423793	−	0.244677i
$452$	8.87039	+	5.12132i	0.417228	+	0.240887i
$453$		0			0
$454$	21.7279	+	12.5446i	1.01974	+	0.588748i
$455$	−3.67423	−	2.84924i	−0.172251	−	0.133575i
$456$		0			0
$457$	−23.0000			−1.07589			−0.537947	−	0.842978i	$-0.680800\pi$
$457$	−23.0000			−1.07589			−0.537947	+	0.842978i	$0.680800\pi$
$458$	2.80821	+	4.86396i	0.131219	+	0.227278i
$459$		0			0
$460$	12.7279	+	7.34847i	0.593442	+	0.342624i
$461$	10.7255	+	18.5772i	0.499538	+	0.865225i	1.00000		0.000533648i	$-0.000169865\pi$
$461$	10.7255	+	18.5772i	0.499538	+	0.865225i	−0.500462	+	0.865758i	$0.666837\pi$
$462$		0			0
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	−0.488702	−	0.872451i	$-0.662530\pi$
$463$	11.0000	−	19.0526i	0.511213	−	0.885448i	0.999916	−	0.0129968i	$-0.00413714\pi$
$464$	−1.52192	+	0.878680i	−0.0706533	+	0.0407917i
$465$		0			0
$466$	10.2426	−	17.7408i	0.474481	−	0.821825i
$467$	8.87039	−	15.3640i	0.410473	−	0.710959i	−0.584469	−	0.811416i	$-0.698697\pi$
$467$	8.87039	−	15.3640i	0.410473	−	0.710959i	0.994941	+	0.100457i	$0.0320304\pi$
$468$		0			0
$469$	−21.8640	+	28.1946i	−1.00958	+	1.30191i
$470$	27.2416	−	15.7279i	1.25656	−	0.725475i
$471$		0			0
$472$			2.44949i			0.112747i
$473$		−	29.6985i		−	1.36554i
$474$		0			0
$475$	4.24264	−	2.44949i	0.194666	−	0.112390i
$476$	−6.42090	−	0.878680i	−0.294301	−	0.0402742i
$477$		0			0
$478$	8.12132	−	14.0665i	0.371461	−	0.643389i
$479$	1.22474	−	2.12132i	0.0559600	−	0.0969256i	−0.836688	−	0.547679i	$-0.815511\pi$
$479$	1.22474	−	2.12132i	0.0559600	−	0.0969256i	0.892648	+	0.450754i	$0.148845\pi$
$480$		0			0
$481$	3.25736	−	1.88064i	0.148523	−	0.0857497i
$482$	−0.568852	+	0.985281i	−0.0259105	+	0.0448783i
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	6.71807	+	3.87868i	0.305052	+	0.176122i
$486$		0			0
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	0.501541	−	0.865134i	$-0.332767\pi$
$487$	−11.0000	−	19.0526i	−0.498458	−	0.863354i	−0.999998	+	0.00178012i	$0.999433\pi$
$488$	−4.18154			−0.189289
$489$		0			0
$490$	−12.0000	−	12.2474i	−0.542105	−	0.553283i
$491$	−30.2854	−	17.4853i	−1.36676	−	0.789100i	−0.376248	−	0.926519i	$-0.622786\pi$
$491$	−30.2854	−	17.4853i	−1.36676	−	0.789100i	−0.990513	+	0.137419i	$0.956119\pi$
$492$		0			0
$493$	3.72792	+	2.15232i	0.167897	+	0.0969355i
$494$	−3.04384	+	1.75736i	−0.136949	+	0.0790673i
$495$		0			0
$496$		−	9.08052i		−	0.407727i
$497$	26.6112	+	20.6360i	1.19367	+	0.925653i
$498$		0			0
$499$	12.2279	+	21.1794i	0.547397	+	0.948119i	0.998452	+	0.0556231i	$0.0177145\pi$
$499$	12.2279	+	21.1794i	0.547397	+	0.948119i	−0.451055	+	0.892496i	$0.648952\pi$
$500$	9.79796			0.438178
$501$		0			0
$502$		−	15.2913i		−	0.682483i
$503$	0.594346			0.0265006			0.0132503	−	0.999912i	$-0.495782\pi$
$503$	0.594346			0.0265006			0.0132503	+	0.999912i	$0.495782\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$			25.4558i			1.13165i
$507$		0			0
$508$	7.72792			0.342871
$509$	−4.60181	−	7.97056i	−0.203971	−	0.353289i	0.745833	−	0.666133i	$-0.232052\pi$
$509$	−4.60181	−	7.97056i	−0.203971	−	0.353289i	−0.949805	+	0.312844i	$0.898718\pi$
$510$		0			0
$511$	1.97056	−	14.3998i	0.0871726	−	0.637008i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−21.7279	+	12.5446i	−0.958378	+	0.553320i
$515$	23.5673	+	13.6066i	1.03850	+	0.599579i
$516$		0			0
$517$	47.1838	+	27.2416i	2.07514	+	1.19808i
$518$	12.8418	−	5.24264i	0.564236	−	0.230348i
$519$		0			0
$520$	1.75736			0.0770653
$521$	−14.9941	−	25.9706i	−0.656904	−	1.13779i	−0.981413	−	0.191908i	$-0.938532\pi$
$521$	−14.9941	−	25.9706i	−0.656904	−	1.13779i	0.324509	−	0.945883i	$-0.394801\pi$
$522$		0			0
$523$	23.7426	+	13.7078i	1.03819	+	0.599401i	0.919321	−	0.393508i	$-0.128739\pi$
$523$	23.7426	+	13.7078i	1.03819	+	0.599401i	0.118872	+	0.992910i	$0.462072\pi$
$524$		0			0
$525$		0			0
$526$	3.36396	−	5.82655i	0.146676	−	0.254050i
$527$	−19.2627	+	11.1213i	−0.839096	+	0.484452i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	17.7408	−	30.7279i	0.770610	−	1.33474i
$531$		0			0
$532$	−12.0000	+	4.89898i	−0.520266	+	0.212398i
$533$	−1.52192	+	0.878680i	−0.0659216	+	0.0380598i
$534$		0			0
$535$		−	6.08767i		−	0.263193i
$536$		−	13.4853i		−	0.582475i
$537$		0			0
$538$	−8.48528	+	4.89898i	−0.365826	+	0.211210i
$539$	7.97887	−	28.6066i	0.343674	−	1.23217i
$540$		0			0
$541$	2.72792	−	4.72490i	0.117283	−	0.203139i	−0.801407	−	0.598119i	$-0.795915\pi$
$541$	2.72792	−	4.72490i	0.117283	−	0.203139i	0.918690	+	0.394980i	$0.129248\pi$
$542$	9.43924	−	16.3492i	0.405450	−	0.702260i
$543$		0			0
$544$	2.12132	−	1.22474i	0.0909509	−	0.0525105i
$545$	21.7122	−	37.6066i	0.930048	−	1.61089i
$546$		0			0
$547$	−19.9853	−	34.6155i	−0.854509	−	1.48005i	−0.877100	−	0.480308i	$-0.840525\pi$
$547$	−19.9853	−	34.6155i	−0.854509	−	1.48005i	0.0225909	−	0.999745i	$-0.492808\pi$
$548$	5.19615	+	3.00000i	0.221969	+	0.128154i
$549$		0			0
$550$	−2.12132	−	3.67423i	−0.0904534	−	0.156670i
$551$	8.60927			0.366767
$552$		0			0
$553$	−1.22792	+	1.58346i	−0.0522166	+	0.0673358i
$554$	−20.5490	−	11.8640i	−0.873043	−	0.504051i
$555$		0			0
$556$	−6.98528	−	4.03295i	−0.296242	−	0.171035i
$557$	18.3712	−	10.6066i	0.778412	−	0.449416i	−0.0574555	−	0.998348i	$-0.518299\pi$
$557$	18.3712	−	10.6066i	0.778412	−	0.449416i	0.835867	+	0.548932i	$0.184965\pi$
$558$		0			0
$559$			5.02207i			0.212411i
$560$	6.42090	+	0.878680i	0.271332	+	0.0371310i
$561$		0			0
$562$	−6.87868	−	11.9142i	−0.290160	−	0.502571i
$563$	45.8739			1.93335			0.966676	−	0.256002i	$-0.0824054\pi$
$563$	45.8739			1.93335			0.966676	+	0.256002i	$0.0824054\pi$
$564$		0			0
$565$			25.0892i			1.05551i
$566$	−6.03668			−0.253741
$567$		0			0
$568$	−12.7279			−0.534052
$569$		−	10.2426i		−	0.429394i	−0.976681	−	0.214697i	$-0.931124\pi$
$569$		−	10.2426i		−	0.429394i	0.976681	−	0.214697i	$-0.0688764\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	1.52192	+	2.63604i	0.0636346	+	0.110218i
$573$		0			0
$574$	−6.00000	+	2.44949i	−0.250435	+	0.102240i
$575$			6.00000i			0.250217i
$576$		0			0
$577$	23.7426	−	13.7078i	0.988419	−	0.570664i	0.0836177	−	0.996498i	$-0.473353\pi$
$577$	23.7426	−	13.7078i	0.988419	−	0.570664i	0.904801	+	0.425834i	$0.140019\pi$
$578$	9.52628	+	5.50000i	0.396241	+	0.228770i
$579$		0			0
$580$	−3.72792	−	2.15232i	−0.154794	−	0.0893701i
$581$	40.0834	+	5.48528i	1.66294	+	0.227568i
$582$		0			0
$583$	61.4558			2.54524
$584$	2.74666	+	4.75736i	0.113658	+	0.196861i
$585$		0			0
$586$	11.1213	+	6.42090i	0.459418	+	0.265245i
$587$	16.2189	+	28.0919i	0.669424	+	1.15948i	0.978065	+	0.208298i	$0.0667923\pi$
$587$	16.2189	+	28.0919i	0.669424	+	1.15948i	−0.308642	+	0.951178i	$0.599874\pi$
$588$		0			0
$589$	−22.2426	+	38.5254i	−0.916492	+	1.58741i
$590$	−5.19615	+	3.00000i	−0.213922	+	0.123508i
$591$		0			0
$592$	−2.62132	+	4.54026i	−0.107736	+	0.186604i
$593$	−0.927572	+	1.60660i	−0.0380908	+	0.0659752i	−0.884442	−	0.466650i	$-0.845461\pi$
$593$	−0.927572	+	1.60660i	−0.0380908	+	0.0659752i	0.846352	+	0.532625i	$0.178794\pi$
$594$		0			0
$595$	−6.00000	−	14.6969i	−0.245976	−	0.602516i
$596$	−14.0665	+	8.12132i	−0.576188	+	0.332662i
$597$		0			0
$598$		−	4.30463i		−	0.176030i
$599$		−	3.51472i		−	0.143608i	−0.997419	−	0.0718038i	$-0.977124\pi$
$599$		−	3.51472i		−	0.143608i	0.997419	−	0.0718038i	$-0.0228755\pi$
$600$		0			0
$601$	−35.9558	+	20.7591i	−1.46667	+	0.846782i	−0.999305	−	0.0372826i	$-0.988130\pi$
$601$	−35.9558	+	20.7591i	−1.46667	+	0.846782i	−0.467365	+	0.884065i	$0.654796\pi$
$602$	−2.51104	+	18.3492i	−0.102342	+	0.747859i
$603$		0			0
$604$	4.37868	−	7.58410i	0.178166	−	0.308592i
$605$	8.57321	−	14.8492i	0.348551	−	0.603708i
$606$		0			0
$607$	−31.2426	+	18.0379i	−1.26810	+	0.732138i	−0.974628	−	0.223830i	$-0.928144\pi$
$607$	−31.2426	+	18.0379i	−1.26810	+	0.732138i	−0.293471	+	0.955968i	$0.594811\pi$
$608$	2.44949	−	4.24264i	0.0993399	−	0.172062i
$609$		0			0
$610$	−5.12132	−	8.87039i	−0.207356	−	0.359151i
$611$	−7.97887	−	4.60660i	−0.322790	−	0.186363i
$612$		0			0
$613$	14.1066	+	24.4334i	0.569760	+	0.986854i	0.996589	+	0.0825214i	$0.0262973\pi$
$613$	14.1066	+	24.4334i	0.569760	+	0.986854i	−0.426829	+	0.904332i	$0.640369\pi$
$614$	26.8213			1.08242
$615$		0			0
$616$	4.24264	+	10.3923i	0.170941	+	0.418718i
$617$	−3.67423	−	2.12132i	−0.147919	−	0.0854011i	0.424214	−	0.905562i	$-0.360551\pi$
$617$	−3.67423	−	2.12132i	−0.147919	−	0.0854011i	−0.572133	+	0.820161i	$0.693884\pi$
$618$		0			0
$619$	11.0147	+	6.35935i	0.442719	+	0.255604i	0.704750	−	0.709455i	$-0.251059\pi$
$619$	11.0147	+	6.35935i	0.442719	+	0.255604i	−0.262031	+	0.965059i	$0.584392\pi$
$620$	19.2627	−	11.1213i	0.773608	−	0.446643i
$621$		0			0
$622$			17.1464i			0.687509i
$623$	−3.04384	−	7.45584i	−0.121949	−	0.298712i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	−20.1903			−0.806965
$627$		0			0
$628$			10.3923i			0.414698i
$629$	12.8418			0.512036
$630$		0			0
$631$	−14.7574			−0.587481			−0.293741	−	0.955885i	$-0.594900\pi$
$631$	−14.7574			−0.587481			−0.293741	+	0.955885i	$0.594900\pi$
$632$		−	0.757359i		−	0.0301261i
$633$		0			0
$634$	22.2426			0.883368
$635$	9.46473	+	16.3934i	0.375596	+	0.650552i
$636$		0			0
$637$	−1.34924	+	4.83743i	−0.0534589	+	0.191666i
$638$		−	7.45584i		−	0.295180i
$639$		0			0
$640$	−2.12132	+	1.22474i	−0.0838525	+	0.0484123i
$641$	28.7635	+	16.6066i	1.13609	+	0.655921i	0.945459	−	0.325741i	$-0.105614\pi$
$641$	28.7635	+	16.6066i	1.13609	+	0.655921i	0.190630	+	0.981662i	$0.438947\pi$
$642$		0			0
$643$	−1.50000	−	0.866025i	−0.0591542	−	0.0341527i	0.470131	−	0.882597i	$-0.344207\pi$
$643$	−1.50000	−	0.866025i	−0.0591542	−	0.0341527i	−0.529285	+	0.848444i	$0.677540\pi$
$644$	2.15232	−	15.7279i	0.0848132	−	0.619767i
$645$		0			0
$646$	−12.0000			−0.472134
$647$	10.3923	+	18.0000i	0.408564	+	0.707653i	0.994729	−	0.102538i	$-0.0326965\pi$
$647$	10.3923	+	18.0000i	0.408564	+	0.707653i	−0.586165	+	0.810191i	$0.699363\pi$
$648$		0			0
$649$	−9.00000	−	5.19615i	−0.353281	−	0.203967i
$650$	0.358719	+	0.621320i	0.0140701	+	0.0243702i
$651$		0			0
$652$	−4.74264	+	8.21449i	−0.185736	+	0.321704i
$653$	−2.15232	+	1.24264i	−0.0842267	+	0.0486283i	−0.541522	−	0.840687i	$-0.682152\pi$
$653$	−2.15232	+	1.24264i	−0.0842267	+	0.0486283i	0.457295	+	0.889315i	$0.348818\pi$
$654$		0			0
$655$		0			0
$656$	1.22474	−	2.12132i	0.0478183	−	0.0828236i
$657$		0			0
$658$	−26.8492	−	20.8207i	−1.04669	−	0.811674i
$659$	19.2627	−	11.1213i	0.750368	−	0.433225i	−0.0754589	−	0.997149i	$-0.524042\pi$
$659$	19.2627	−	11.1213i	0.750368	−	0.433225i	0.825827	+	0.563924i	$0.190709\pi$
$660$		0			0
$661$		−	4.89898i		−	0.190548i	−0.995451	−	0.0952741i	$-0.969627\pi$
$661$		−	4.89898i		−	0.190548i	0.995451	−	0.0952741i	$-0.0303728\pi$
$662$			10.0000i			0.388661i
$663$		0			0
$664$	−13.2426	+	7.64564i	−0.513914	+	0.296708i
$665$	−25.0892	−	19.4558i	−0.972919	−	0.754465i
$666$		0			0
$667$	−5.27208	+	9.13151i	−0.204136	+	0.353573i
$668$	−0.297173	+	0.514719i	−0.0114980	+	0.0199151i
$669$		0			0
$670$	28.6066	−	16.5160i	1.10517	−	0.638070i
$671$	8.87039	−	15.3640i	0.342437	−	0.593119i
$672$		0			0
$673$	22.7279	+	39.3659i	0.876097	+	1.51744i	0.855590	+	0.517655i	$0.173195\pi$
$673$	22.7279	+	39.3659i	0.876097	+	1.51744i	0.0205075	+	0.999790i	$0.493472\pi$
$674$	18.5813	+	10.7279i	0.715725	+	0.413224i
$675$		0			0
$676$	6.24264	+	10.8126i	0.240102	+	0.415868i
$677$	14.6969			0.564849			0.282425	−	0.959289i	$-0.408861\pi$
$677$	14.6969			0.564849			0.282425	+	0.959289i	$0.408861\pi$
$678$		0			0
$679$	1.13604	−	8.30153i	0.0435972	−	0.318584i
$680$	5.19615	+	3.00000i	0.199263	+	0.115045i
$681$		0			0
$682$	33.3640	+	19.2627i	1.27757	+	0.737607i
$683$	−8.87039	+	5.12132i	−0.339416	+	0.195962i	−0.660014	−	0.751254i	$-0.729450\pi$
$683$	−8.87039	+	5.12132i	−0.339416	+	0.195962i	0.320598	+	0.947215i	$0.396116\pi$
$684$		0			0
$685$			14.6969i			0.561541i
$686$	−7.34847	+	17.0000i	−0.280566	+	0.649063i
$687$		0			0
$688$	−3.50000	−	6.06218i	−0.133436	−	0.231118i
$689$	−10.3923			−0.395915
$690$		0			0
$691$		−	2.57258i		−	0.0978657i	−0.998802	−	0.0489328i	$-0.984418\pi$
$691$		−	2.57258i		−	0.0978657i	0.998802	−	0.0489328i	$-0.0155820\pi$
$692$	−20.7846			−0.790112
$693$		0			0
$694$	−4.97056			−0.188680
$695$		−	19.7574i		−	0.749439i
$696$		0			0
$697$	−6.00000			−0.227266
$698$	0.0615465	+	0.106602i	0.00232957	+	0.00403493i
$699$		0			0
$700$	1.00000	+	2.44949i	0.0377964	+	0.0925820i
$701$			20.4853i			0.773718i	0.922139	+	0.386859i	$0.126440\pi$
$701$			20.4853i			0.773718i	−0.922139	+	0.386859i	$0.873560\pi$
$702$		0			0
$703$	22.2426	−	12.8418i	0.838897	−	0.484337i
$704$	−3.67423	−	2.12132i	−0.138478	−	0.0799503i
$705$		0			0
$706$	9.51472	+	5.49333i	0.358091	+	0.206744i
$707$	−7.34847	−	18.0000i	−0.276368	−	0.676960i
$708$		0			0
$709$	16.2132			0.608900			0.304450	−	0.952528i	$-0.401527\pi$
$709$	16.2132			0.608900			0.304450	+	0.952528i	$0.401527\pi$
$710$	−15.5885	−	27.0000i	−0.585024	−	1.01329i
$711$		0			0
$712$	2.63604	+	1.52192i	0.0987897	+	0.0570363i
$713$	−27.2416	−	47.1838i	−1.02020	−	1.76705i
$714$		0			0
$715$	−3.72792	+	6.45695i	−0.139416	+	0.241476i
$716$	5.82655	−	3.36396i	0.217748	−	0.125717i
$717$		0			0
$718$	−7.24264	+	12.5446i	−0.270293	+	0.468161i
$719$	26.3140	−	45.5772i	0.981346	−	1.69974i	0.324181	−	0.945995i	$-0.394911\pi$
$719$	26.3140	−	45.5772i	0.981346	−	1.69974i	0.657166	−	0.753746i	$-0.271755\pi$
$720$		0			0
$721$	3.98528	−	29.1222i	0.148420	−	1.08457i
$722$	−4.33013	+	2.50000i	−0.161151	+	0.0930404i
$723$		0			0
$724$		−	9.79796i		−	0.364138i
$725$		−	1.75736i		−	0.0652667i
$726$		0			0
$727$	24.3198	−	14.0410i	0.901972	−	0.520754i	0.0241323	−	0.999709i	$-0.492318\pi$
$727$	24.3198	−	14.0410i	0.901972	−	0.520754i	0.877839	+	0.478955i	$0.158984\pi$
$728$	−0.717439	−	1.75736i	−0.0265901	−	0.0651321i
$729$		0			0
$730$	−6.72792	+	11.6531i	−0.249012	+	0.431301i
$731$	−8.57321	+	14.8492i	−0.317092	+	0.549219i
$732$		0			0
$733$	−1.13604	+	0.655892i	−0.0419606	+	0.0242259i	−0.520834	−	0.853658i	$-0.674379\pi$
$733$	−1.13604	+	0.655892i	−0.0419606	+	0.0242259i	0.478873	+	0.877884i	$0.341045\pi$
$734$	−14.9941	+	25.9706i	−0.553443	+	0.958591i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	49.5481	+	28.6066i	1.82513	+	1.05374i
$738$		0			0
$739$	4.22792	+	7.32298i	0.155527	+	0.269380i	0.933251	−	0.359226i	$-0.116959\pi$
$739$	4.22792	+	7.32298i	0.155527	+	0.269380i	−0.777724	+	0.628606i	$0.783626\pi$
$740$	−12.8418			−0.472074
$741$		0			0
$742$	−37.9706	−	5.19615i	−1.39394	−	0.190757i
$743$	−16.2189	−	9.36396i	−0.595012	−	0.343530i	0.172065	−	0.985086i	$-0.444956\pi$
$743$	−16.2189	−	9.36396i	−0.595012	−	0.343530i	−0.767077	+	0.641555i	$0.778290\pi$
$744$		0			0
$745$	−34.4558	−	19.8931i	−1.26236	−	0.728826i
$746$	−19.0526	+	11.0000i	−0.697564	+	0.402739i
$747$		0			0
$748$			10.3923i			0.379980i
$749$	−6.08767	+	2.48528i	−0.222439	+	0.0908102i
$750$		0			0
$751$	−26.7279	−	46.2941i	−0.975316	−	1.68930i	−0.678889	−	0.734241i	$-0.737538\pi$
$751$	−26.7279	−	46.2941i	−0.975316	−	1.68930i	−0.296427	−	0.955056i	$-0.595795\pi$
$752$	12.8418			0.468292
$753$		0			0
$754$			1.26080i			0.0459156i
$755$	21.4511			0.780684
$756$		0			0
$757$	32.7574			1.19059			0.595293	−	0.803509i	$-0.297036\pi$
$757$	32.7574			1.19059			0.595293	+	0.803509i	$0.297036\pi$
$758$		−	7.48528i		−	0.271878i
$759$		0			0
$760$	12.0000			0.435286
$761$	12.2474	+	21.2132i	0.443970	+	0.768978i	0.997980	−	0.0635319i	$-0.0202365\pi$
$761$	12.2474	+	21.2132i	0.443970	+	0.768978i	−0.554010	+	0.832510i	$0.686903\pi$
$762$		0			0
$763$	−46.4706	−	6.35935i	−1.68235	−	0.230224i
$764$		−	21.2132i		−	0.767467i
$765$		0			0
$766$	−4.75736	+	2.74666i	−0.171890	+	0.0992410i
$767$	1.52192	+	0.878680i	0.0549533	+	0.0317273i
$768$		0			0
$769$	−34.9706	−	20.1903i	−1.26107	−	0.728080i	−0.287789	−	0.957694i	$-0.592920\pi$
$769$	−34.9706	−	20.1903i	−1.26107	−	0.728080i	−0.973282	+	0.229614i	$0.926254\pi$
$770$	−16.8493	+	21.7279i	−0.607205	+	0.783020i
$771$		0			0
$772$	1.48528			0.0534564
$773$	−4.89898	−	8.48528i	−0.176204	−	0.305194i	0.764373	−	0.644774i	$-0.223049\pi$
$773$	−4.89898	−	8.48528i	−0.176204	−	0.305194i	−0.940577	+	0.339580i	$0.889715\pi$
$774$		0			0
$775$	7.86396	+	4.54026i	0.282482	+	0.163091i
$776$	1.58346	+	2.74264i	0.0568431	+	0.0984551i
$777$		0			0
$778$	−7.75736	+	13.4361i	−0.278115	+	0.481709i
$779$	−10.3923	+	6.00000i	−0.372343	+	0.214972i
$780$		0			0
$781$	27.0000	−	46.7654i	0.966136	−	1.67340i
$782$	7.34847	−	12.7279i	0.262781	−	0.455150i
$783$		0			0
$784$	−1.74264	−	6.77962i	−0.0622372	−	0.242129i
$785$	−22.0454	+	12.7279i	−0.786834	+	0.454279i
$786$		0			0
$787$		−	28.2562i		−	1.00722i	−0.863930	−	0.503612i	$-0.832004\pi$
$787$		−	28.2562i		−	1.00722i	0.863930	−	0.503612i	$-0.167996\pi$
$788$		−	16.9706i		−	0.604551i
$789$		0			0
$790$	1.60660	−	0.927572i	0.0571603	−	0.0330015i
$791$	25.0892	−	10.2426i	0.892071	−	0.364186i
$792$		0			0
$793$	−1.50000	+	2.59808i	−0.0532666	+	0.0922604i
$794$	7.58410	−	13.1360i	0.269149	−	0.466181i
$795$		0			0
$796$	18.1066	−	10.4539i	0.641771	−	0.370527i
$797$	−8.87039	+	15.3640i	−0.314205	+	0.544219i	−0.979268	−	0.202568i	$-0.935071\pi$
$797$	−8.87039	+	15.3640i	−0.314205	+	0.544219i	0.665063	+	0.746787i	$0.268405\pi$
$798$		0			0
$799$	−15.7279	−	27.2416i	−0.556414	−	0.963737i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	−9.87868	−	17.1104i	−0.348828	−	0.604188i
$803$	−23.3062			−0.822458
$804$		0			0
$805$	36.0000	−	14.6969i	1.26883	−	0.517999i
$806$	−5.64191	−	3.25736i	−0.198728	−	0.114736i
$807$		0			0
$808$	6.36396	+	3.67423i	0.223883	+	0.129259i
$809$	−12.5446	+	7.24264i	−0.441045	+	0.254638i	−0.704041	−	0.710159i	$-0.748623\pi$
$809$	−12.5446	+	7.24264i	−0.441045	+	0.254638i	0.262996	+	0.964797i	$0.415290\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−0.630399	+	4.60660i	−0.0221227	+	0.161660i
$813$		0			0
$814$	−11.1213	−	19.2627i	−0.389802	−	0.675157i
$815$	−23.2341			−0.813855
$816$		0			0
$817$			34.2929i			1.19976i
$818$	3.76127			0.131510
$819$		0			0
$820$	6.00000			0.209529
$821$			22.9706i			0.801678i	0.916148	+	0.400839i	$0.131281\pi$
$821$			22.9706i			0.801678i	−0.916148	+	0.400839i	$0.868719\pi$
$822$		0			0
$823$	−2.75736			−0.0961155			−0.0480578	−	0.998845i	$-0.515303\pi$
$823$	−2.75736			−0.0961155			−0.0480578	+	0.998845i	$0.515303\pi$
$824$	5.55487	+	9.62132i	0.193513	+	0.335175i
$825$		0			0
$826$	5.12132	+	3.97141i	0.178194	+	0.138183i
$827$		−	3.51472i		−	0.122219i	−0.998131	−	0.0611094i	$-0.980536\pi$
$827$		−	3.51472i		−	0.122219i	0.998131	−	0.0611094i	$-0.0194638\pi$
$828$		0			0
$829$	8.48528	−	4.89898i	0.294706	−	0.170149i	−0.345356	−	0.938472i	$-0.612242\pi$
$829$	8.48528	−	4.89898i	0.294706	−	0.170149i	0.640062	+	0.768323i	$0.278909\pi$
$830$	−32.4377	−	18.7279i	−1.12593	−	0.650056i
$831$		0			0
$832$	0.621320	+	0.358719i	0.0215404	+	0.0124364i
$833$	−12.2474	+	12.0000i	−0.424349	+	0.415775i
$834$		0			0
$835$	−1.45584			−0.0503816
$836$	10.3923	+	18.0000i	0.359425	+	0.622543i
$837$		0			0
$838$	6.87868	+	3.97141i	0.237620	+	0.137190i
$839$	7.64564	+	13.2426i	0.263957	+	0.457187i	0.967290	−	0.253674i	$-0.0816390\pi$
$839$	7.64564	+	13.2426i	0.263957	+	0.457187i	−0.703333	+	0.710861i	$0.748306\pi$
$840$		0			0
$841$	−12.9558	+	22.4402i	−0.446753	+	0.773799i
$842$	−20.3134	+	11.7279i	−0.700045	+	0.404171i
$843$		0			0
$844$	1.74264	−	3.01834i	0.0599842	−	0.103896i
$845$	−15.2913	+	26.4853i	−0.526036	+	0.911121i
$846$		0			0
$847$	−18.3492	−	2.51104i	−0.630487	−	0.0862802i
$848$	12.5446	−	7.24264i	0.430784	−	0.248713i
$849$		0			0
$850$			2.44949i			0.0840168i
$851$			31.4558i			1.07829i
$852$		0			0
$853$	−27.5147	+	15.8856i	−0.942086	+	0.543914i	−0.890614	−	0.454761i	$-0.849725\pi$
$853$	−27.5147	+	15.8856i	−0.942086	+	0.543914i	−0.0514724	+	0.998674i	$0.516391\pi$
$854$	−6.77962	+	8.74264i	−0.231994	+	0.299167i
$855$		0			0
$856$	1.24264	−	2.15232i	0.0424726	−	0.0735647i
$857$	−13.7694	+	23.8492i	−0.470353	+	0.814675i	−0.999425	−	0.0339020i	$-0.989207\pi$
$857$	−13.7694	+	23.8492i	−0.470353	+	0.814675i	0.529073	+	0.848577i	$0.322540\pi$
$858$		0			0
$859$	−24.4706	+	14.1281i	−0.834925	+	0.482044i	−0.855536	−	0.517743i	$-0.826772\pi$
$859$	−24.4706	+	14.1281i	−0.834925	+	0.482044i	0.0206111	+	0.999788i	$0.493439\pi$
$860$	8.57321	−	14.8492i	0.292344	−	0.506355i
$861$		0			0
$862$	−0.878680	−	1.52192i	−0.0299279	−	0.0518367i
$863$	−32.4377	−	18.7279i	−1.10419	−	0.637506i	−0.166874	−	0.985978i	$-0.553367\pi$
$863$	−32.4377	−	18.7279i	−1.10419	−	0.637506i	−0.937319	+	0.348472i	$0.886700\pi$
$864$		0			0
$865$	−25.4558	−	44.0908i	−0.865525	−	1.49913i
$866$	2.57258			0.0874199
$867$		0			0
$868$	−18.9853	−	14.7224i	−0.644402	−	0.499712i
$869$	2.78272	+	1.60660i	0.0943972	+	0.0545002i
$870$		0			0
$871$	−8.37868	−	4.83743i	−0.283901	−	0.163910i
$872$	15.3528	−	8.86396i	0.519912	−	0.300172i
$873$		0			0
$874$		−	29.3939i		−	0.994263i
$875$	15.8856	−	20.4853i	0.537032	−	0.692529i
$876$		0			0
$877$	23.1066	+	40.0218i	0.780254	+	1.35144i	0.931793	+	0.362989i	$0.118244\pi$
$877$	23.1066	+	40.0218i	0.780254	+	1.35144i	−0.151539	+	0.988451i	$0.548423\pi$
$878$	4.30463			0.145274
$879$		0			0
$880$		−	10.3923i		−	0.350325i
$881$	25.0892			0.845278			0.422639	−	0.906298i	$-0.361104\pi$
$881$	25.0892			0.845278			0.422639	+	0.906298i	$0.361104\pi$
$882$		0			0
$883$	−2.00000			−0.0673054			−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000			−0.0673054			−0.0336527	+	0.999434i	$0.510714\pi$
$884$		−	1.75736i		−	0.0591064i
$885$		0			0
$886$	25.4558			0.855206
$887$	4.60181	+	7.97056i	0.154514	+	0.267625i	0.932882	−	0.360183i	$-0.117286\pi$
$887$	4.60181	+	7.97056i	0.154514	+	0.267625i	−0.778368	+	0.627808i	$0.783952\pi$
$888$		0			0
$889$	12.5294	−	16.1573i	0.420224	−	0.541899i
$890$			7.45584i			0.249920i
$891$		0			0
$892$	−9.00000	+	5.19615i	−0.301342	+	0.173980i
$893$	−54.4831	−	31.4558i	−1.82321	−	1.05263i
$894$		0			0
$895$	14.2721	+	8.23999i	0.477063	+	0.275432i
$896$	2.09077	+	1.62132i	0.0698477	+	0.0541645i
$897$		0			0
$898$	−5.27208			−0.175932
$899$	7.97887	+	13.8198i	0.266110	+	0.460916i
$900$		0			0
$901$	−30.7279	−	17.7408i	−1.02370	−	0.591031i
$902$	5.19615	+	9.00000i	0.173013	+	0.299667i
$903$		0			0
$904$	−5.12132	+	8.87039i	−0.170333	+	0.295025i
$905$	20.7846	−	12.0000i	0.690904	−	0.398893i
$906$		0			0
$907$	6.74264	−	11.6786i	0.223886	−	0.387781i	−0.732099	−	0.681198i	$-0.761459\pi$
$907$	6.74264	−	11.6786i	0.223886	−	0.387781i	0.955985	+	0.293417i	$0.0947924\pi$
$908$	−12.5446	+	21.7279i	−0.416308	+	0.721066i
$909$		0			0
$910$	2.84924	−	3.67423i	0.0944515	−	0.121800i
$911$	−8.87039	+	5.12132i	−0.293889	+	0.169677i	−0.639694	−	0.768629i	$-0.720939\pi$
$911$	−8.87039	+	5.12132i	−0.293889	+	0.169677i	0.345805	+	0.938306i	$0.387606\pi$
$912$		0			0
$913$		−	64.8754i		−	2.14706i
$914$		−	23.0000i		−	0.760772i
$915$		0			0
$916$	−4.86396	+	2.80821i	−0.160710	+	0.0927858i
$917$		0			0
$918$		0			0
$919$	−12.8640	+	22.2810i	−0.424343	+	0.734983i	−0.996359	−	0.0852590i	$-0.972828\pi$
$919$	−12.8640	+	22.2810i	−0.424343	+	0.734983i	0.572016	+	0.820243i	$0.306162\pi$
$920$	−7.34847	+	12.7279i	−0.242272	+	0.419627i
$921$		0			0
$922$	−18.5772	+	10.7255i	−0.611806	+	0.353227i
$923$	−4.56575	+	7.90812i	−0.150284	+	0.260299i
$924$		0			0
$925$	−2.62132	−	4.54026i	−0.0861885	−	0.149283i
$926$	19.0526	+	11.0000i	0.626106	+	0.361482i
$927$		0			0
$928$	−0.878680	−	1.52192i	−0.0288441	−	0.0499594i
$929$	−28.7274			−0.942516			−0.471258	−	0.881995i	$-0.656200\pi$
$929$	−28.7274			−0.942516			−0.471258	+	0.881995i	$0.656200\pi$
$930$		0			0
$931$	−9.21320	+	33.0321i	−0.301951	+	1.08258i
$932$	17.7408	+	10.2426i	0.581118	+	0.335509i
$933$		0			0
$934$	15.3640	+	8.87039i	0.502724	+	0.290248i
$935$	−22.0454	+	12.7279i	−0.720962	+	0.416248i
$936$		0			0
$937$			33.5033i			1.09451i	0.836967	+	0.547253i	$0.184326\pi$
$937$			33.5033i			1.09451i	−0.836967	+	0.547253i	$0.815674\pi$
$938$	−28.1946	−	21.8640i	−0.920587	−	0.713884i
$939$		0			0
$940$	15.7279	+	27.2416i	0.512988	+	0.888522i
$941$	−42.2357			−1.37684			−0.688422	−	0.725311i	$-0.741696\pi$
$941$	−42.2357			−1.37684			−0.688422	+	0.725311i	$0.741696\pi$
$942$		0			0
$943$		−	14.6969i		−	0.478598i
$944$	−2.44949			−0.0797241
$945$		0			0
$946$	29.6985			0.965581
$947$		−	16.2426i		−	0.527815i	−0.964548	−	0.263907i	$-0.914989\pi$
$947$		−	16.2426i		−	0.527815i	0.964548	−	0.263907i	$-0.0850114\pi$
$948$		0			0
$949$	3.94113			0.127934
$950$	2.44949	+	4.24264i	0.0794719	+	0.137649i
$951$		0			0
$952$	0.878680	−	6.42090i	0.0284782	−	0.208102i
$953$		−	1.02944i		−	0.0333467i	−0.999861	−	0.0166734i	$-0.994692\pi$
$953$		−	1.02944i		−	0.0333467i	0.999861	−	0.0166734i	$-0.00530755\pi$
$954$		0			0
$955$	45.0000	−	25.9808i	1.45617	−	0.840718i
$956$	14.0665	+	8.12132i	0.454944	+	0.262662i
$957$		0			0
$958$	2.12132	+	1.22474i	0.0685367	+	0.0395697i
$959$	14.6969	−	6.00000i	0.474589	−	0.193750i
$960$		0			0
$961$	−51.4558			−1.65987
$962$	1.88064	+	3.25736i	0.0606342	+	0.105021i
$963$		0			0
$964$	−0.985281	−	0.568852i	−0.0317338	−	0.0183215i
$965$	1.81909	+	3.15076i	0.0585586	+	0.101426i
$966$		0			0
$967$	21.3492	−	36.9780i	0.686545	−	1.18913i	−0.286403	−	0.958109i	$-0.592460\pi$
$967$	21.3492	−	36.9780i	0.686545	−	1.18913i	0.972948	−	0.231022i	$-0.0742070\pi$
$968$	6.06218	−	3.50000i	0.194846	−	0.112494i
$969$		0			0
$970$	−3.87868	+	6.71807i	−0.124537	+	0.215704i
$971$	−20.1903	+	34.9706i	−0.647936	+	1.12226i	0.335679	+	0.941977i	$0.391034\pi$
$971$	−20.1903	+	34.9706i	−0.647936	+	1.12226i	−0.983615	+	0.180282i	$0.942299\pi$
$972$		0			0
$973$	−19.7574	+	8.06591i	−0.633392	+	0.258581i
$974$	19.0526	−	11.0000i	0.610483	−	0.352463i
$975$		0			0
$976$		−	4.18154i		−	0.133848i
$977$			6.00000i			0.191957i	0.995383	+	0.0959785i	$0.0305980\pi$
$977$			6.00000i			0.191957i	−0.995383	+	0.0959785i	$0.969402\pi$
$978$		0			0
$979$	−11.1838	+	6.45695i	−0.357435	+	0.206365i
$980$	12.2474	−	12.0000i	0.391230	−	0.383326i
$981$		0			0
$982$	17.4853	−	30.2854i	0.557978	−	0.966446i
$983$	11.6170	−	20.1213i	0.370526	−	0.641770i	−0.619120	−	0.785296i	$-0.712511\pi$
$983$	11.6170	−	20.1213i	0.370526	−	0.641770i	0.989647	+	0.143526i	$0.0458440\pi$
$984$		0			0
$985$	36.0000	−	20.7846i	1.14706	−	0.662253i
$986$	−2.15232	+	3.72792i	−0.0685437	+	0.118721i
$987$		0			0
$988$	−1.75736	−	3.04384i	−0.0559090	−	0.0968373i
$989$	−36.3731	−	21.0000i	−1.15660	−	0.667761i
$990$		0			0
$991$	10.1066	+	17.5051i	0.321047	+	0.556069i	0.980704	−	0.195497i	$-0.0626320\pi$
$991$	10.1066	+	17.5051i	0.321047	+	0.556069i	−0.659658	+	0.751566i	$0.729299\pi$
$992$	9.08052			0.288307
$993$		0			0
$994$	−20.6360	+	26.6112i	−0.654535	+	0.844055i
$995$	44.3519	+	25.6066i	1.40605	+	0.811784i
$996$		0			0
$997$	−16.8640	−	9.73641i	−0.534087	−	0.308355i	0.208592	−	0.978003i	$-0.433112\pi$
$997$	−16.8640	−	9.73641i	−0.534087	−	0.308355i	−0.742679	+	0.669647i	$0.766445\pi$
$998$	−21.1794	+	12.2279i	−0.670422	+	0.387068i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.l.e.215.3		8
3.2	odd	2	inner	1134.2.l.e.215.2		8
7.3	odd	6		1134.2.t.f.1025.1		8
9.2	odd	6		1134.2.t.f.593.1		8
9.4	even	3		378.2.k.d.215.1	✓	8
9.5	odd	6		378.2.k.d.215.4	yes	8
9.7	even	3		1134.2.t.f.593.4		8
21.17	even	6		1134.2.t.f.1025.4		8
63.5	even	6		2646.2.d.d.2645.4		8
63.23	odd	6		2646.2.d.d.2645.2		8
63.31	odd	6		378.2.k.d.269.4	yes	8
63.38	even	6	inner	1134.2.l.e.269.1		8
63.40	odd	6		2646.2.d.d.2645.5		8
63.52	odd	6	inner	1134.2.l.e.269.4		8
63.58	even	3		2646.2.d.d.2645.7		8
63.59	even	6		378.2.k.d.269.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.k.d.215.1	✓	8	9.4	even	3
378.2.k.d.215.4	yes	8	9.5	odd	6
378.2.k.d.269.1	yes	8	63.59	even	6
378.2.k.d.269.4	yes	8	63.31	odd	6
1134.2.l.e.215.2		8	3.2	odd	2	inner
1134.2.l.e.215.3		8	1.1	even	1	trivial
1134.2.l.e.269.1		8	63.38	even	6	inner
1134.2.l.e.269.4		8	63.52	odd	6	inner
1134.2.t.f.593.1		8	9.2	odd	6
1134.2.t.f.593.4		8	9.7	even	3
1134.2.t.f.1025.1		8	7.3	odd	6
1134.2.t.f.1025.4		8	21.17	even	6
2646.2.d.d.2645.2		8	63.23	odd	6
2646.2.d.d.2645.4		8	63.5	even	6
2646.2.d.d.2645.5		8	63.40	odd	6
2646.2.d.d.2645.7		8	63.58	even	3

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.22474 - 2.12132i) q^{5} +(-1.62132 + 2.09077i) q^{7} -1.00000i q^{8} +(2.12132 - 1.22474i) q^{10} +(3.67423 + 2.12132i) q^{11} +(-0.621320 - 0.358719i) q^{13} +(-2.09077 - 1.62132i) q^{14} +1.00000 q^{16} +(-1.22474 - 2.12132i) q^{17} +(-4.24264 - 2.44949i) q^{19} +(1.22474 + 2.12132i) q^{20} +(-2.12132 + 3.67423i) q^{22} +(5.19615 - 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(0.358719 - 0.621320i) q^{26} +(1.62132 - 2.09077i) q^{28} +(-1.52192 + 0.878680i) q^{29} -9.08052i q^{31} +1.00000i q^{32} +(2.12132 - 1.22474i) q^{34} +(6.42090 + 0.878680i) q^{35} +(-2.62132 + 4.54026i) q^{37} +(2.44949 - 4.24264i) q^{38} +(-2.12132 + 1.22474i) q^{40} +(1.22474 - 2.12132i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(-3.67423 - 2.12132i) q^{44} +(3.00000 + 5.19615i) q^{46} +12.8418 q^{47} +(-1.74264 - 6.77962i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(0.621320 + 0.358719i) q^{52} +(12.5446 - 7.24264i) q^{53} -10.3923i q^{55} +(2.09077 + 1.62132i) q^{56} +(-0.878680 - 1.52192i) q^{58} -2.44949 q^{59} -4.18154i q^{61} +9.08052 q^{62} -1.00000 q^{64} +1.75736i q^{65} +13.4853 q^{67} +(1.22474 + 2.12132i) q^{68} +(-0.878680 + 6.42090i) q^{70} -12.7279i q^{71} +(-4.75736 + 2.74666i) q^{73} +(-4.54026 - 2.62132i) q^{74} +(4.24264 + 2.44949i) q^{76} +(-10.3923 + 4.24264i) q^{77} +0.757359 q^{79} +(-1.22474 - 2.12132i) q^{80} +(2.12132 + 1.22474i) q^{82} +(-7.64564 - 13.2426i) q^{83} +(-3.00000 + 5.19615i) q^{85} +(6.06218 - 3.50000i) q^{86} +(2.12132 - 3.67423i) q^{88} +(-1.52192 + 2.63604i) q^{89} +(1.75736 - 0.717439i) q^{91} +(-5.19615 + 3.00000i) q^{92} +12.8418i q^{94} +12.0000i q^{95} +(-2.74264 + 1.58346i) q^{97} +(6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 + 4 * q^7	\( 8 q - 8 q^{4} + 4 q^{7} + 12 q^{13} + 8 q^{16} - 4 q^{25} - 4 q^{28} - 4 q^{37} - 28 q^{43} + 24 q^{46} + 20 q^{49} - 12 q^{52} - 24 q^{58} - 8 q^{64} + 40 q^{67} - 24 q^{70} - 72 q^{73} + 40 q^{79} - 24 q^{85} + 48 q^{91} + 12 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^7 + 12 * q^13 + 8 * q^16 - 4 * q^25 - 4 * q^28 - 4 * q^37 - 28 * q^43 + 24 * q^46 + 20 * q^49 - 12 * q^52 - 24 * q^58 - 8 * q^64 + 40 * q^67 - 24 * q^70 - 72 * q^73 + 40 * q^79 - 24 * q^85 + 48 * q^91 + 12 * q^97

Introduction

L-functions

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