LMFDB - Embedded newform 1134.2.l.h.269.5

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 796x^12 - 2228x^11 + 5254x^10 - 10232x^9 + 16903x^8 - 23292x^7 + 26994x^6 - 25716x^5 + 19962x^4 - 12096x^3 + 5454x^2 - 1620*x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.5
Root			$0.500000 - 1.97090i$ of defining polynomial
Character	$\chi$	$=$	1134.269
Dual form			1134.2.l.h.215.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-2.08560 + 3.61236i) q^{5} +(0.582206 + 2.58090i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.08560 + 3.61236i) q^{5} +(0.582206 + 2.58090i) q^{7} -1.00000i q^{8} +(-3.61236 - 2.08560i) q^{10} +(0.0814333 - 0.0470156i) q^{11} +(-3.28654 + 1.89748i) q^{13} +(-2.58090 + 0.582206i) q^{14} +1.00000 q^{16} +(-3.82627 + 6.62729i) q^{17} +(6.77624 - 3.91226i) q^{19} +(2.08560 - 3.61236i) q^{20} +(0.0470156 + 0.0814333i) q^{22} +(3.31685 + 1.91499i) q^{23} +(-6.19941 - 10.7377i) q^{25} +(-1.89748 - 3.28654i) q^{26} +(-0.582206 - 2.58090i) q^{28} +(-1.75954 - 1.01587i) q^{29} +1.68119i q^{31} +1.00000i q^{32} +(-6.62729 - 3.82627i) q^{34} +(-10.5374 - 3.27958i) q^{35} +(-2.18343 - 3.78182i) q^{37} +(3.91226 + 6.77624i) q^{38} +(3.61236 + 2.08560i) q^{40} +(-1.53573 - 2.65995i) q^{41} +(2.56395 - 4.44089i) q^{43} +(-0.0814333 + 0.0470156i) q^{44} +(-1.91499 + 3.31685i) q^{46} +5.09920 q^{47} +(-6.32207 + 3.00523i) q^{49} +(10.7377 - 6.19941i) q^{50} +(3.28654 - 1.89748i) q^{52} +(6.05506 + 3.49589i) q^{53} +0.392222i q^{55} +(2.58090 - 0.582206i) q^{56} +(1.01587 - 1.75954i) q^{58} -10.4261 q^{59} +3.11656i q^{61} -1.68119 q^{62} -1.00000 q^{64} -15.8295i q^{65} +7.53337 q^{67} +(3.82627 - 6.62729i) q^{68} +(3.27958 - 10.5374i) q^{70} -8.61322i q^{71} +(-0.129966 - 0.0750360i) q^{73} +(3.78182 - 2.18343i) q^{74} +(-6.77624 + 3.91226i) q^{76} +(0.168753 + 0.182798i) q^{77} -12.9685 q^{79} +(-2.08560 + 3.61236i) q^{80} +(2.65995 - 1.53573i) q^{82} +(-1.29420 + 2.24162i) q^{83} +(-15.9601 - 27.6437i) q^{85} +(4.44089 + 2.56395i) q^{86} +(-0.0470156 - 0.0814333i) q^{88} +(-1.37123 - 2.37504i) q^{89} +(-6.81065 - 7.37750i) q^{91} +(-3.31685 - 1.91499i) q^{92} +5.09920i q^{94} +32.6376i q^{95} +(-3.51951 - 2.03199i) q^{97} +(-3.00523 - 6.32207i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q - 16 * q^4 - 4 * q^7	$ 16 q - 16 q^{4} - 4 q^{7} + 12 q^{11} - 12 q^{13} + 16 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} - 48 q^{29} - 60 q^{35} + 4 q^{37} + 12 q^{38} - 24 q^{41} + 16 q^{43} - 12 q^{44} - 20 q^{49} + 24 q^{50} + 12 q^{52} - 12 q^{58} - 48 q^{59} + 48 q^{62} - 16 q^{64} + 8 q^{67} + 12 q^{70} + 36 q^{73} + 36 q^{74} + 48 q^{77} - 16 q^{79} - 36 q^{83} - 12 q^{85} + 24 q^{86} - 24 q^{89} - 12 q^{91} - 12 q^{92} - 12 q^{97} - 36 q^{98}+O(q^{100}) $ 16 * q - 16 * q^4 - 4 * q^7 + 12 * q^11 - 12 * q^13 + 16 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 - 48 * q^29 - 60 * q^35 + 4 * q^37 + 12 * q^38 - 24 * q^41 + 16 * q^43 - 12 * q^44 - 20 * q^49 + 24 * q^50 + 12 * q^52 - 12 * q^58 - 48 * q^59 + 48 * q^62 - 16 * q^64 + 8 * q^67 + 12 * q^70 + 36 * q^73 + 36 * q^74 + 48 * q^77 - 16 * q^79 - 36 * q^83 - 12 * q^85 + 24 * q^86 - 24 * q^89 - 12 * q^91 - 12 * q^92 - 12 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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
$5$	−2.08560	+	3.61236i	−0.932707	+	1.61550i	−0.154033	+	0.988066i	$0.549226\pi$
$5$	−2.08560	+	3.61236i	−0.932707	+	1.61550i	−0.778673	+	0.627429i	$0.784107\pi$
$6$		0			0
$7$	0.582206	+	2.58090i	0.220053	+	0.975488i
$7$	0.582206	+	2.58090i	0.220053	+	0.975488i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−3.61236	−	2.08560i	−1.14233	−	0.659523i
$11$	0.0814333	−	0.0470156i	0.0245531	−	0.0141757i	−0.487673	−	0.873026i	$-0.662154\pi$
$11$	0.0814333	−	0.0470156i	0.0245531	−	0.0141757i	0.512226	+	0.858851i	$0.328821\pi$
$12$		0			0
$13$	−3.28654	+	1.89748i	−0.911522	+	0.526267i	−0.880920	−	0.473264i	$-0.843076\pi$
$13$	−3.28654	+	1.89748i	−0.911522	+	0.526267i	−0.0306012	+	0.999532i	$0.509742\pi$
$14$	−2.58090	+	0.582206i	−0.689774	+	0.155601i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.82627	+	6.62729i	−0.928006	+	1.60735i	−0.141353	+	0.989959i	$0.545145\pi$
$17$	−3.82627	+	6.62729i	−0.928006	+	1.60735i	−0.786654	+	0.617395i	$0.788188\pi$
$18$		0			0
$19$	6.77624	−	3.91226i	1.55458	−	0.897534i	0.556815	−	0.830636i	$-0.312023\pi$
$19$	6.77624	−	3.91226i	1.55458	−	0.897534i	0.997760	−	0.0668980i	$-0.0213102\pi$
$20$	2.08560	−	3.61236i	0.466353	−	0.807748i
$21$		0			0
$22$	0.0470156	+	0.0814333i	0.0100238	+	0.0173616i
$23$	3.31685	+	1.91499i	0.691612	+	0.399302i	0.804216	−	0.594338i	$-0.202586\pi$
$23$	3.31685	+	1.91499i	0.691612	+	0.399302i	−0.112604	+	0.993640i	$0.535919\pi$
$24$		0			0
$25$	−6.19941	−	10.7377i	−1.23988	−	2.14754i
$26$	−1.89748	−	3.28654i	−0.372127	−	0.644543i
$27$		0			0
$28$	−0.582206	−	2.58090i	−0.110027	−	0.487744i
$29$	−1.75954	−	1.01587i	−0.326738	−	0.188642i	0.327654	−	0.944798i	$-0.393742\pi$
$29$	−1.75954	−	1.01587i	−0.326738	−	0.188642i	−0.654392	+	0.756155i	$0.727075\pi$
$30$		0			0
$31$			1.68119i			0.301951i	0.988537	+	0.150976i	$0.0482415\pi$
$31$			1.68119i			0.301951i	−0.988537	+	0.150976i	$0.951759\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−6.62729	−	3.82627i	−1.13657	−	0.656199i
$35$	−10.5374	−	3.27958i	−1.78114	−	0.554349i
$36$		0			0
$37$	−2.18343	−	3.78182i	−0.358954	−	0.621727i	0.628832	−	0.777541i	$-0.283533\pi$
$37$	−2.18343	−	3.78182i	−0.358954	−	0.621727i	−0.987786	+	0.155814i	$0.950200\pi$
$38$	3.91226	+	6.77624i	0.634653	+	1.09925i
$39$		0			0
$40$	3.61236	+	2.08560i	0.571164	+	0.329762i
$41$	−1.53573	−	2.65995i	−0.239840	−	0.415415i	0.720828	−	0.693114i	$-0.243762\pi$
$41$	−1.53573	−	2.65995i	−0.239840	−	0.415415i	−0.960668	+	0.277699i	$0.910428\pi$
$42$		0			0
$43$	2.56395	−	4.44089i	0.390999	−	0.677229i	−0.601583	−	0.798810i	$-0.705463\pi$
$43$	2.56395	−	4.44089i	0.390999	−	0.677229i	0.992582	+	0.121581i	$0.0387964\pi$
$44$	−0.0814333	+	0.0470156i	−0.0122765	+	0.00708786i
$45$		0			0
$46$	−1.91499	+	3.31685i	−0.282349	+	0.489044i
$47$	5.09920			0.743794			0.371897	−	0.928274i	$-0.378707\pi$
$47$	5.09920			0.743794			0.371897	+	0.928274i	$0.378707\pi$
$48$		0			0
$49$	−6.32207	+	3.00523i	−0.903153	+	0.429318i
$50$	10.7377	−	6.19941i	1.51854	−	0.876730i
$51$		0			0
$52$	3.28654	−	1.89748i	0.455761	−	0.263134i
$53$	6.05506	+	3.49589i	0.831726	+	0.480197i	0.854443	−	0.519545i	$-0.173898\pi$
$53$	6.05506	+	3.49589i	0.831726	+	0.480197i	−0.0227173	+	0.999742i	$0.507232\pi$
$54$		0			0
$55$			0.392222i			0.0528872i
$56$	2.58090	−	0.582206i	0.344887	−	0.0778005i
$57$		0			0
$58$	1.01587	−	1.75954i	0.133390	−	0.231039i
$59$	−10.4261			−1.35736			−0.678678	−	0.734436i	$-0.737447\pi$
$59$	−10.4261			−1.35736			−0.678678	+	0.734436i	$0.737447\pi$
$60$		0			0
$61$			3.11656i			0.399034i	0.979894	+	0.199517i	$0.0639374\pi$
$61$			3.11656i			0.399034i	−0.979894	+	0.199517i	$0.936063\pi$
$62$	−1.68119			−0.213512
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	15.8295i		−	1.96341i
$66$		0			0
$67$	7.53337			0.920348			0.460174	−	0.887829i	$-0.347787\pi$
$67$	7.53337			0.920348			0.460174	+	0.887829i	$0.347787\pi$
$68$	3.82627	−	6.62729i	0.464003	−	0.803677i
$69$		0			0
$70$	3.27958	−	10.5374i	0.391984	−	1.25946i
$71$		−	8.61322i		−	1.02220i	−0.859521	−	0.511100i	$-0.829238\pi$
$71$		−	8.61322i		−	1.02220i	0.859521	−	0.511100i	$-0.170762\pi$
$72$		0			0
$73$	−0.129966	−	0.0750360i	−0.0152114	−	0.00878230i	0.492375	−	0.870383i	$-0.336129\pi$
$73$	−0.129966	−	0.0750360i	−0.0152114	−	0.00878230i	−0.507586	+	0.861601i	$0.669462\pi$
$74$	3.78182	−	2.18343i	0.439628	−	0.253819i
$75$		0			0
$76$	−6.77624	+	3.91226i	−0.777288	+	0.448767i
$77$	0.168753	+	0.182798i	0.0192312	+	0.0208318i
$78$		0			0
$79$	−12.9685			−1.45907			−0.729535	−	0.683943i	$-0.760264\pi$
$79$	−12.9685			−1.45907			−0.729535	+	0.683943i	$0.760264\pi$
$80$	−2.08560	+	3.61236i	−0.233177	+	0.403874i
$81$		0			0
$82$	2.65995	−	1.53573i	0.293743	−	0.169592i
$83$	−1.29420	+	2.24162i	−0.142057	+	0.246050i	−0.928271	−	0.371904i	$-0.878705\pi$
$83$	−1.29420	+	2.24162i	−0.142057	+	0.246050i	0.786214	+	0.617954i	$0.212038\pi$
$84$		0			0
$85$	−15.9601	−	27.6437i	−1.73111	−	2.99838i
$86$	4.44089	+	2.56395i	0.478873	+	0.276478i
$87$		0			0
$88$	−0.0470156	−	0.0814333i	−0.00501188	−	0.00868082i
$89$	−1.37123	−	2.37504i	−0.145350	−	0.251754i	0.784153	−	0.620567i	$-0.213098\pi$
$89$	−1.37123	−	2.37504i	−0.145350	−	0.251754i	−0.929504	+	0.368813i	$0.879764\pi$
$90$		0			0
$91$	−6.81065	−	7.37750i	−0.713950	−	0.773372i
$92$	−3.31685	−	1.91499i	−0.345806	−	0.199651i
$93$		0			0
$94$			5.09920i			0.525942i
$95$			32.6376i			3.34854i
$96$		0			0
$97$	−3.51951	−	2.03199i	−0.357352	−	0.206317i	0.310567	−	0.950552i	$-0.399481\pi$
$97$	−3.51951	−	2.03199i	−0.357352	−	0.206317i	−0.667919	+	0.744234i	$0.732815\pi$
$98$	−3.00523	−	6.32207i	−0.303574	−	0.638626i
$99$		0			0
$100$	6.19941	+	10.7377i	0.619941	+	1.07377i
$101$	6.16567	+	10.6793i	0.613507	+	1.06263i	0.990644	+	0.136468i	$0.0435751\pi$
$101$	6.16567	+	10.6793i	0.613507	+	1.06263i	−0.377137	+	0.926157i	$0.623092\pi$
$102$		0			0
$103$	1.57103	+	0.907035i	0.154798	+	0.0893728i	0.575398	−	0.817873i	$-0.304847\pi$
$103$	1.57103	+	0.907035i	0.154798	+	0.0893728i	−0.420600	+	0.907246i	$0.638180\pi$
$104$	1.89748	+	3.28654i	0.186064	+	0.322272i
$105$		0			0
$106$	−3.49589	+	6.05506i	−0.339551	+	0.588119i
$107$	−2.70445	+	1.56142i	−0.261449	+	0.150948i	−0.624996	−	0.780628i	$-0.714899\pi$
$107$	−2.70445	+	1.56142i	−0.261449	+	0.150948i	0.363546	+	0.931576i	$0.381566\pi$
$108$		0			0
$109$	1.12213	−	1.94358i	0.107480	−	0.186161i	−0.807269	−	0.590184i	$-0.799055\pi$
$109$	1.12213	−	1.94358i	0.107480	−	0.186161i	0.914749	+	0.404023i	$0.132388\pi$
$110$	−0.392222			−0.0373969
$111$		0			0
$112$	0.582206	+	2.58090i	0.0550133	+	0.243872i
$113$	−3.10165	+	1.79074i	−0.291779	+	0.168458i	−0.638744	−	0.769420i	$-0.720546\pi$
$113$	−3.10165	+	1.79074i	−0.291779	+	0.168458i	0.346965	+	0.937878i	$0.387212\pi$
$114$		0			0
$115$	−13.8352	+	7.98778i	−1.29014	+	0.744864i
$116$	1.75954	+	1.01587i	0.163369	+	0.0943212i
$117$		0			0
$118$		−	10.4261i		−	0.959796i
$119$	−19.3320	−	6.01676i	−1.77216	−	0.551556i
$120$		0			0
$121$	−5.49558	+	9.51862i	−0.499598	+	0.865329i
$122$	−3.11656			−0.282160
$123$		0			0
$124$		−	1.68119i		−	0.150976i
$125$	30.8619			2.76037
$126$		0			0
$127$	9.49968			0.842960			0.421480	−	0.906838i	$-0.361511\pi$
$127$	9.49968			0.842960			0.421480	+	0.906838i	$0.361511\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	15.8295			1.38834
$131$	−1.51601	+	2.62581i	−0.132455	+	0.229418i	−0.924622	−	0.380886i	$-0.875619\pi$
$131$	−1.51601	+	2.62581i	−0.132455	+	0.229418i	0.792168	+	0.610304i	$0.208953\pi$
$132$		0			0
$133$	14.0423	+	15.2110i	1.21762	+	1.31896i
$134$			7.53337i			0.650784i
$135$		0			0
$136$	6.62729	+	3.82627i	0.568285	+	0.328100i
$137$	−3.82389	+	2.20773i	−0.326697	+	0.188619i	−0.654374	−	0.756171i	$-0.727068\pi$
$137$	−3.82389	+	2.20773i	−0.326697	+	0.188619i	0.327677	+	0.944790i	$0.393734\pi$
$138$		0			0
$139$	−1.14947	+	0.663644i	−0.0974964	+	0.0562896i	−0.547955	−	0.836508i	$-0.684594\pi$
$139$	−1.14947	+	0.663644i	−0.0974964	+	0.0562896i	0.450459	+	0.892797i	$0.351260\pi$
$140$	10.5374	+	3.27958i	0.890570	+	0.277175i
$141$		0			0
$142$	8.61322			0.722805
$143$	−0.178423	+	0.309037i	−0.0149204	+	0.0258430i
$144$		0			0
$145$	7.33937	−	4.23739i	0.609502	−	0.351896i
$146$	0.0750360	−	0.129966i	0.00621002	−	0.0107561i
$147$		0			0
$148$	2.18343	+	3.78182i	0.179477	+	0.310864i
$149$	−9.16722	−	5.29269i	−0.751008	−	0.433594i	0.0750503	−	0.997180i	$-0.476088\pi$
$149$	−9.16722	−	5.29269i	−0.751008	−	0.433594i	−0.826058	+	0.563585i	$0.809422\pi$
$150$		0			0
$151$	3.86400	+	6.69264i	0.314448	+	0.544639i	0.979320	−	0.202318i	$-0.0648474\pi$
$151$	3.86400	+	6.69264i	0.314448	+	0.544639i	−0.664872	+	0.746957i	$0.731514\pi$
$152$	−3.91226	−	6.77624i	−0.317326	−	0.549625i
$153$		0			0
$154$	−0.182798	+	0.168753i	−0.0147303	+	0.0135985i
$155$	−6.07307	−	3.50629i	−0.487801	−	0.281632i
$156$		0			0
$157$			3.89155i			0.310580i	0.987869	+	0.155290i	$0.0496312\pi$
$157$			3.89155i			0.310580i	−0.987869	+	0.155290i	$0.950369\pi$
$158$		−	12.9685i		−	1.03172i
$159$		0			0
$160$	−3.61236	−	2.08560i	−0.285582	−	0.164881i
$161$	−3.01130	+	9.67538i	−0.237323	+	0.762527i
$162$		0			0
$163$	8.82699	+	15.2888i	0.691383	+	1.19751i	0.971385	+	0.237511i	$0.0763317\pi$
$163$	8.82699	+	15.2888i	0.691383	+	1.19751i	−0.280002	+	0.960000i	$0.590335\pi$
$164$	1.53573	+	2.65995i	0.119920	+	0.207708i
$165$		0			0
$166$	−2.24162	−	1.29420i	−0.173984	−	0.100450i
$167$	−8.19835	−	14.2000i	−0.634407	−	1.09883i	−0.986640	−	0.162914i	$-0.947911\pi$
$167$	−8.19835	−	14.2000i	−0.634407	−	1.09883i	0.352233	−	0.935912i	$-0.385422\pi$
$168$		0			0
$169$	0.700889	−	1.21398i	0.0539145	−	0.0933827i
$170$	27.6437	−	15.9601i	2.12017	−	1.22408i
$171$		0			0
$172$	−2.56395	+	4.44089i	−0.195499	+	0.338615i
$173$	7.85639			0.597310			0.298655	−	0.954361i	$-0.403462\pi$
$173$	7.85639			0.597310			0.298655	+	0.954361i	$0.403462\pi$
$174$		0			0
$175$	24.1036	−	22.2516i	1.82206	−	1.68206i
$176$	0.0814333	−	0.0470156i	0.00613827	−	0.00354393i
$177$		0			0
$178$	2.37504	−	1.37123i	0.178017	−	0.102778i
$179$	−15.7884	−	9.11541i	−1.18008	−	0.681318i	−0.224044	−	0.974579i	$-0.571926\pi$
$179$	−15.7884	−	9.11541i	−1.18008	−	0.681318i	−0.956032	+	0.293261i	$0.905259\pi$
$180$		0			0
$181$			14.2290i			1.05763i	0.848736	+	0.528817i	$0.177364\pi$
$181$			14.2290i			1.05763i	−0.848736	+	0.528817i	$0.822636\pi$
$182$	7.37750	−	6.81065i	0.546856	−	0.504839i
$183$		0			0
$184$	1.91499	−	3.31685i	0.141175	−	0.244522i
$185$	18.2150			1.33920
$186$		0			0
$187$			0.719576i			0.0526206i
$188$	−5.09920			−0.371897
$189$		0			0
$190$	−32.6376			−2.36778
$191$			19.2203i			1.39073i	0.718657	+	0.695365i	$0.244757\pi$
$191$			19.2203i			1.39073i	−0.718657	+	0.695365i	$0.755243\pi$
$192$		0			0
$193$	7.55634			0.543918			0.271959	−	0.962309i	$-0.412329\pi$
$193$	7.55634			0.543918			0.271959	+	0.962309i	$0.412329\pi$
$194$	2.03199	−	3.51951i	0.145888	−	0.252686i
$195$		0			0
$196$	6.32207	−	3.00523i	0.451577	−	0.214659i
$197$			2.10437i			0.149930i	0.997186	+	0.0749651i	$0.0238845\pi$
$197$			2.10437i			0.149930i	−0.997186	+	0.0749651i	$0.976115\pi$
$198$		0			0
$199$	1.24340	+	0.717876i	0.0881421	+	0.0508889i	0.543423	−	0.839459i	$-0.317128\pi$
$199$	1.24340	+	0.717876i	0.0881421	+	0.0508889i	−0.455281	+	0.890348i	$0.650461\pi$
$200$	−10.7377	+	6.19941i	−0.759270	+	0.438365i
$201$		0			0
$202$	−10.6793	+	6.16567i	−0.751390	+	0.433815i
$203$	1.59745	−	5.13264i	0.112119	−	0.360241i
$204$		0			0
$205$	12.8116			0.894801
$206$	−0.907035	+	1.57103i	−0.0631961	+	0.109459i
$207$		0			0
$208$	−3.28654	+	1.89748i	−0.227880	+	0.131567i
$209$	0.367874	−	0.637177i	0.0254464	−	0.0440745i
$210$		0			0
$211$	2.18400	+	3.78280i	0.150353	+	0.260419i	0.931357	−	0.364107i	$-0.118626\pi$
$211$	2.18400	+	3.78280i	0.150353	+	0.260419i	−0.781004	+	0.624526i	$0.785292\pi$
$212$	−6.05506	−	3.49589i	−0.415863	−	0.240099i
$213$		0			0
$214$	−1.56142	−	2.70445i	−0.106736	−	0.184873i
$215$	10.6947	+	18.5238i	0.729374	+	1.26331i
$216$		0			0
$217$	−4.33899	+	0.978800i	−0.294550	+	0.0664452i
$218$	1.94358	+	1.12213i	0.131636	+	0.0760000i
$219$		0			0
$220$		−	0.392222i		−	0.0264436i
$221$		−	29.0411i		−	1.95352i
$222$		0			0
$223$	14.9763	+	8.64657i	1.00289	+	0.579017i	0.909101	−	0.416575i	$-0.136770\pi$
$223$	14.9763	+	8.64657i	1.00289	+	0.579017i	0.0937859	+	0.995592i	$0.470103\pi$
$224$	−2.58090	+	0.582206i	−0.172444	+	0.0389002i
$225$		0			0
$226$	−1.79074	−	3.10165i	−0.119118	−	0.206319i
$227$	4.25063	+	7.36231i	0.282124	+	0.488653i	0.971908	−	0.235362i	$-0.0756277\pi$
$227$	4.25063	+	7.36231i	0.282124	+	0.488653i	−0.689784	+	0.724016i	$0.742294\pi$
$228$		0			0
$229$	21.0383	+	12.1465i	1.39025	+	0.802662i	0.993343	−	0.115196i	$-0.0367496\pi$
$229$	21.0383	+	12.1465i	1.39025	+	0.802662i	0.396909	+	0.917858i	$0.370083\pi$
$230$	−7.98778	−	13.8352i	−0.526698	−	0.912268i
$231$		0			0
$232$	−1.01587	+	1.75954i	−0.0666952	+	0.115519i
$233$	−14.2442	+	8.22389i	−0.933168	+	0.538765i	−0.887812	−	0.460206i	$-0.847776\pi$
$233$	−14.2442	+	8.22389i	−0.933168	+	0.538765i	−0.0453562	+	0.998971i	$0.514442\pi$
$234$		0			0
$235$	−10.6349	+	18.4201i	−0.693742	+	1.20160i
$236$	10.4261			0.678678
$237$		0			0
$238$	6.01676	−	19.3320i	0.390009	−	1.25311i
$239$	15.4650	−	8.92870i	1.00034	−	0.577549i	0.0919945	−	0.995760i	$-0.470676\pi$
$239$	15.4650	−	8.92870i	1.00034	−	0.577549i	0.908350	+	0.418210i	$0.137342\pi$
$240$		0			0
$241$	−7.27380	+	4.19953i	−0.468546	+	0.270515i	−0.715631	−	0.698479i	$-0.753861\pi$
$241$	−7.27380	+	4.19953i	−0.468546	+	0.270515i	0.247085	+	0.968994i	$0.420527\pi$
$242$	−9.51862	−	5.49558i	−0.611880	−	0.353269i
$243$		0			0
$244$		−	3.11656i		−	0.199517i
$245$	2.32933	−	29.1053i	0.148816	−	1.85947i
$246$		0			0
$247$	−14.8469	+	25.7156i	−0.944686	+	1.63624i
$248$	1.68119			0.106756
$249$		0			0
$250$			30.8619i			1.95188i
$251$	12.3552			0.779850			0.389925	−	0.920847i	$-0.372501\pi$
$251$	12.3552			0.779850			0.389925	+	0.920847i	$0.372501\pi$
$252$		0			0
$253$	0.360137			0.0226416
$254$			9.49968i			0.596063i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−6.94605	+	12.0309i	−0.433283	+	0.750468i	−0.997154	−	0.0753950i	$-0.975978\pi$
$257$	−6.94605	+	12.0309i	−0.433283	+	0.750468i	0.563871	+	0.825863i	$0.309312\pi$
$258$		0			0
$259$	8.48928	−	7.83702i	0.527498	−	0.486969i
$260$			15.8295i			0.981706i
$261$		0			0
$262$	−2.62581	−	1.51601i	−0.162223	−	0.0936595i
$263$	−9.51479	+	5.49337i	−0.586707	+	0.338736i	−0.763794	−	0.645460i	$-0.776666\pi$
$263$	−9.51479	+	5.49337i	−0.586707	+	0.338736i	0.177087	+	0.984195i	$0.443333\pi$
$264$		0			0
$265$	−25.2568	+	14.5820i	−1.55151	+	0.895766i
$266$	−15.2110	+	14.0423i	−0.932648	+	0.860989i
$267$		0			0
$268$	−7.53337			−0.460174
$269$	10.0800	−	17.4590i	0.614585	−	1.06449i	−0.375872	−	0.926672i	$-0.622657\pi$
$269$	10.0800	−	17.4590i	0.614585	−	1.06449i	0.990457	−	0.137821i	$-0.0440100\pi$
$270$		0			0
$271$	−12.1106	+	6.99205i	−0.735666	+	0.424737i	−0.820491	−	0.571659i	$-0.806300\pi$
$271$	−12.1106	+	6.99205i	−0.735666	+	0.424737i	0.0848253	+	0.996396i	$0.472967\pi$
$272$	−3.82627	+	6.62729i	−0.232002	+	0.401838i
$273$		0			0
$274$	−2.20773	−	3.82389i	−0.133374	−	0.231010i
$275$	−1.00968	−	0.582938i	−0.0608859	−	0.0351525i
$276$		0			0
$277$	9.47254	+	16.4069i	0.569150	+	0.985796i	0.996650	+	0.0817810i	$0.0260608\pi$
$277$	9.47254	+	16.4069i	0.569150	+	0.985796i	−0.427501	+	0.904015i	$0.640606\pi$
$278$	−0.663644	−	1.14947i	−0.0398028	−	0.0689404i
$279$		0			0
$280$	−3.27958	+	10.5374i	−0.195992	+	0.629728i
$281$	−5.30142	−	3.06078i	−0.316256	−	0.182591i	0.333466	−	0.942762i	$-0.391782\pi$
$281$	−5.30142	−	3.06078i	−0.316256	−	0.182591i	−0.649723	+	0.760171i	$0.725115\pi$
$282$		0			0
$283$		−	27.3084i		−	1.62331i	−0.584134	−	0.811657i	$-0.698566\pi$
$283$		−	27.3084i		−	1.62331i	0.584134	−	0.811657i	$-0.301434\pi$
$284$			8.61322i			0.511100i
$285$		0			0
$286$	−0.309037	−	0.178423i	−0.0182737	−	0.0105503i
$287$	5.97096	−	5.51219i	0.352455	−	0.325374i
$288$		0			0
$289$	−20.7806	−	35.9931i	−1.22239	−	2.11724i
$290$	4.23739	+	7.33937i	0.248828	+	0.430983i
$291$		0			0
$292$	0.129966	+	0.0750360i	0.00760569	+	0.00439115i
$293$	−7.63564	−	13.2253i	−0.446079	−	0.772631i	0.552048	−	0.833813i	$-0.313847\pi$
$293$	−7.63564	−	13.2253i	−0.446079	−	0.772631i	−0.998127	+	0.0611811i	$0.980513\pi$
$294$		0			0
$295$	21.7445	−	37.6626i	1.26601	−	2.19280i
$296$	−3.78182	+	2.18343i	−0.219814	+	0.126910i
$297$		0			0
$298$	5.29269	−	9.16722i	0.306598	−	0.531043i
$299$	−14.5346			−0.840559
$300$		0			0
$301$	12.9542	+	4.03178i	0.746670	+	0.232388i
$302$	−6.69264	+	3.86400i	−0.385118	+	0.222348i
$303$		0			0
$304$	6.77624	−	3.91226i	0.388644	−	0.224384i
$305$	−11.2581	−	6.49988i	−0.644638	−	0.372182i
$306$		0			0
$307$			28.9407i			1.65173i	0.563866	+	0.825866i	$0.309313\pi$
$307$			28.9407i			1.65173i	−0.563866	+	0.825866i	$0.690687\pi$
$308$	−0.168753	−	0.182798i	−0.00961561	−	0.0104159i
$309$		0			0
$310$	3.50629	−	6.07307i	0.199144	−	0.344927i
$311$	−6.45823			−0.366213			−0.183106	−	0.983093i	$-0.558615\pi$
$311$	−6.45823			−0.366213			−0.183106	+	0.983093i	$0.558615\pi$
$312$		0			0
$313$			27.3991i			1.54869i	0.632764	+	0.774344i	$0.281920\pi$
$313$			27.3991i			1.54869i	−0.632764	+	0.774344i	$0.718080\pi$
$314$	−3.89155			−0.219613
$315$		0			0
$316$	12.9685			0.729535
$317$			19.4183i			1.09064i	0.838228	+	0.545320i	$0.183592\pi$
$317$			19.4183i			1.09064i	−0.838228	+	0.545320i	$0.816408\pi$
$318$		0			0
$319$	−0.191047			−0.0106966
$320$	2.08560	−	3.61236i	0.116588	−	0.201937i
$321$		0			0
$322$	−9.67538	−	3.01130i	−0.539188	−	0.167813i
$323$			59.8774i			3.33167i
$324$		0			0
$325$	40.7492	+	23.5266i	2.26036	+	1.30502i
$326$	−15.2888	+	8.82699i	−0.846768	+	0.488882i
$327$		0			0
$328$	−2.65995	+	1.53573i	−0.146871	+	0.0847962i
$329$	2.96878	+	13.1605i	0.163674	+	0.725562i
$330$		0			0
$331$	13.1186			0.721064			0.360532	−	0.932747i	$-0.382595\pi$
$331$	13.1186			0.721064			0.360532	+	0.932747i	$0.382595\pi$
$332$	1.29420	−	2.24162i	0.0710286	−	0.123025i
$333$		0			0
$334$	14.2000	−	8.19835i	0.776987	−	0.448594i
$335$	−15.7116	+	27.2132i	−0.858415	+	1.48682i
$336$		0			0
$337$	−11.8656	−	20.5518i	−0.646359	−	1.11953i	−0.983986	−	0.178246i	$-0.942958\pi$
$337$	−11.8656	−	20.5518i	−0.646359	−	1.11953i	0.337627	−	0.941280i	$-0.390376\pi$
$338$	1.21398	+	0.700889i	0.0660315	+	0.0381233i
$339$		0			0
$340$	15.9601	+	27.6437i	0.865557	+	1.49919i
$341$	0.0790422	+	0.136905i	0.00428038	+	0.00741383i
$342$		0			0
$343$	−11.4369	−	14.5670i	−0.617536	−	0.786542i
$344$	−4.44089	−	2.56395i	−0.239437	−	0.138239i
$345$		0			0
$346$			7.85639i			0.422362i
$347$		−	8.33530i		−	0.447463i	−0.974651	−	0.223731i	$-0.928176\pi$
$347$		−	8.33530i		−	0.447463i	0.974651	−	0.223731i	$-0.0718238\pi$
$348$		0			0
$349$	16.2367	+	9.37428i	0.869132	+	0.501794i	0.867060	−	0.498204i	$-0.166007\pi$
$349$	16.2367	+	9.37428i	0.869132	+	0.501794i	0.00207250	+	0.999998i	$0.499340\pi$
$350$	22.2516	+	24.1036i	1.18940	+	1.28839i
$351$		0			0
$352$	0.0470156	+	0.0814333i	0.00250594	+	0.00434041i
$353$	−9.76869	−	16.9199i	−0.519935	−	0.900554i	−0.999731	−	0.0231739i	$-0.992623\pi$
$353$	−9.76869	−	16.9199i	−0.519935	−	0.900554i	0.479797	−	0.877380i	$-0.340710\pi$
$354$		0			0
$355$	31.1140	+	17.9637i	1.65136	+	0.953413i
$356$	1.37123	+	2.37504i	0.0726752	+	0.125877i
$357$		0			0
$358$	9.11541	−	15.7884i	0.481764	−	0.834440i
$359$	−14.3290	+	8.27288i	−0.756258	+	0.436626i	−0.827951	−	0.560801i	$-0.810493\pi$
$359$	−14.3290	+	8.27288i	−0.756258	+	0.436626i	0.0716925	+	0.997427i	$0.477160\pi$
$360$		0			0
$361$	21.1116	−	36.5663i	1.11114	−	1.92454i
$362$	−14.2290			−0.747860
$363$		0			0
$364$	6.81065	+	7.37750i	0.356975	+	0.386686i
$365$	0.542113	−	0.312989i	0.0283755	−	0.0163826i
$366$		0			0
$367$	−27.8308	+	16.0681i	−1.45276	+	0.838749i	−0.998637	−	0.0521924i	$-0.983379\pi$
$367$	−27.8308	+	16.0681i	−1.45276	+	0.838749i	−0.454119	+	0.890941i	$0.650046\pi$
$368$	3.31685	+	1.91499i	0.172903	+	0.0998256i
$369$		0			0
$370$			18.2150i			0.946955i
$371$	−5.49725	+	17.6628i	−0.285403	+	0.917007i
$372$		0			0
$373$	12.8677	−	22.2875i	0.666264	−	1.15400i	−0.312677	−	0.949860i	$-0.601226\pi$
$373$	12.8677	−	22.2875i	0.666264	−	1.15400i	0.978941	−	0.204144i	$-0.0654410\pi$
$374$	−0.719576			−0.0372084
$375$		0			0
$376$		−	5.09920i		−	0.262971i
$377$	7.71039			0.397105
$378$		0			0
$379$	−36.3772			−1.86857			−0.934285	−	0.356527i	$-0.883961\pi$
$379$	−36.3772			−1.86857			−0.934285	+	0.356527i	$0.883961\pi$
$380$		−	32.6376i		−	1.67427i
$381$		0			0
$382$	−19.2203			−0.983395
$383$	−12.5773	+	21.7845i	−0.642670	+	1.11314i	0.342165	+	0.939640i	$0.388840\pi$
$383$	−12.5773	+	21.7845i	−0.642670	+	1.11314i	−0.984834	+	0.173497i	$0.944493\pi$
$384$		0			0
$385$	−1.01228	+	0.228354i	−0.0515908	+	0.0116380i
$386$			7.55634i			0.384608i
$387$		0			0
$388$	3.51951	+	2.03199i	0.178676	+	0.103159i
$389$	8.39614	−	4.84752i	0.425701	−	0.245779i	−0.271812	−	0.962350i	$-0.587623\pi$
$389$	8.39614	−	4.84752i	0.425701	−	0.245779i	0.697514	+	0.716571i	$0.254290\pi$
$390$		0			0
$391$	−25.3823	+	14.6545i	−1.28364	+	0.741110i
$392$	3.00523	+	6.32207i	0.151787	+	0.319313i
$393$		0			0
$394$	−2.10437			−0.106017
$395$	27.0471	−	46.8469i	1.36088	−	2.35712i
$396$		0			0
$397$	−11.1844	+	6.45731i	−0.561329	+	0.324083i	−0.753679	−	0.657243i	$-0.771722\pi$
$397$	−11.1844	+	6.45731i	−0.561329	+	0.324083i	0.192350	+	0.981326i	$0.438389\pi$
$398$	−0.717876	+	1.24340i	−0.0359839	+	0.0623259i
$399$		0			0
$400$	−6.19941	−	10.7377i	−0.309971	−	0.536885i
$401$	−24.9194	−	14.3872i	−1.24442	−	0.718464i	−0.274427	−	0.961608i	$-0.588488\pi$
$401$	−24.9194	−	14.3872i	−1.24442	−	0.718464i	−0.969990	+	0.243144i	$0.921821\pi$
$402$		0			0
$403$	−3.19004	−	5.52530i	−0.158907	−	0.275235i
$404$	−6.16567	−	10.6793i	−0.306754	−	0.531313i
$405$		0			0
$406$	5.13264	+	1.59745i	0.254729	+	0.0792799i
$407$	−0.355609	−	0.205311i	−0.0176269	−	0.0101769i
$408$		0			0
$409$			33.2333i			1.64328i	0.570006	+	0.821641i	$0.306941\pi$
$409$			33.2333i			1.64328i	−0.570006	+	0.821641i	$0.693059\pi$
$410$			12.8116i			0.632720i
$411$		0			0
$412$	−1.57103	−	0.907035i	−0.0773991	−	0.0446864i
$413$	−6.07010	−	26.9086i	−0.298690	−	1.32408i
$414$		0			0
$415$	−5.39836	−	9.35024i	−0.264995	−	0.458985i
$416$	−1.89748	−	3.28654i	−0.0930318	−	0.161136i
$417$		0			0
$418$	0.637177	+	0.367874i	0.0311653	+	0.0179933i
$419$	1.08302	+	1.87584i	0.0529090	+	0.0916410i	0.891267	−	0.453479i	$-0.149817\pi$
$419$	1.08302	+	1.87584i	0.0529090	+	0.0916410i	−0.838358	+	0.545120i	$0.816484\pi$
$420$		0			0
$421$	−6.19326	+	10.7270i	−0.301841	+	0.522804i	−0.976553	−	0.215277i	$-0.930934\pi$
$421$	−6.19326	+	10.7270i	−0.301841	+	0.522804i	0.674712	+	0.738081i	$0.264268\pi$
$422$	−3.78280	+	2.18400i	−0.184144	+	0.106316i
$423$		0			0
$424$	3.49589	−	6.05506i	0.169775	−	0.294060i
$425$	94.8825			4.60248
$426$		0			0
$427$	−8.04352	+	1.81448i	−0.389253	+	0.0878087i
$428$	2.70445	−	1.56142i	0.130725	−	0.0754739i
$429$		0			0
$430$	−18.5238	+	10.6947i	−0.893297	+	0.515745i
$431$	−20.2513	−	11.6921i	−0.975468	−	0.563187i	−0.0745695	−	0.997216i	$-0.523758\pi$
$431$	−20.2513	−	11.6921i	−0.975468	−	0.563187i	−0.900899	+	0.434029i	$0.857092\pi$
$432$		0			0
$433$		−	30.6220i		−	1.47160i	−0.677199	−	0.735800i	$-0.736806\pi$
$433$		−	30.6220i		−	1.47160i	0.677199	−	0.735800i	$-0.263194\pi$
$434$	−0.978800	−	4.33899i	−0.0469839	−	0.208278i
$435$		0			0
$436$	−1.12213	+	1.94358i	−0.0537401	+	0.0930807i
$437$	29.9677			1.43355
$438$		0			0
$439$		−	30.9972i		−	1.47941i	−0.672929	−	0.739707i	$-0.734964\pi$
$439$		−	30.9972i		−	1.47941i	0.672929	−	0.739707i	$-0.265036\pi$
$440$	0.392222			0.0186984
$441$		0			0
$442$	29.0411			1.38135
$443$		−	10.0489i		−	0.477436i	−0.971089	−	0.238718i	$-0.923273\pi$
$443$		−	10.0489i		−	0.477436i	0.971089	−	0.238718i	$-0.0767271\pi$
$444$		0			0
$445$	11.4393			0.542277
$446$	−8.64657	+	14.9763i	−0.409427	+	0.709148i
$447$		0			0
$448$	−0.582206	−	2.58090i	−0.0275066	−	0.121936i
$449$			3.58784i			0.169320i	0.996410	+	0.0846602i	$0.0269805\pi$
$449$			3.58784i			0.169320i	−0.996410	+	0.0846602i	$0.973020\pi$
$450$		0			0
$451$	−0.250118	−	0.144406i	−0.0117776	−	0.00679981i
$452$	3.10165	−	1.79074i	0.145889	−	0.0842292i
$453$		0			0
$454$	−7.36231	+	4.25063i	−0.345530	+	0.199492i
$455$	40.8544	−	9.21604i	1.91528	−	0.432055i
$456$		0			0
$457$	2.57354			0.120385			0.0601926	−	0.998187i	$-0.480829\pi$
$457$	2.57354			0.120385			0.0601926	+	0.998187i	$0.480829\pi$
$458$	−12.1465	+	21.0383i	−0.567568	+	0.983056i
$459$		0			0
$460$	13.8352	−	7.98778i	0.645071	−	0.372432i
$461$	8.70540	−	15.0782i	0.405451	−	0.702262i	−0.588923	−	0.808189i	$-0.700448\pi$
$461$	8.70540	−	15.0782i	0.405451	−	0.702262i	0.994374	+	0.105927i	$0.0337811\pi$
$462$		0			0
$463$	−7.94124	−	13.7546i	−0.369061	−	0.639232i	0.620358	−	0.784319i	$-0.286987\pi$
$463$	−7.94124	−	13.7546i	−0.369061	−	0.639232i	−0.989419	+	0.145087i	$0.953654\pi$
$464$	−1.75954	−	1.01587i	−0.0816846	−	0.0471606i
$465$		0			0
$466$	−8.22389	−	14.2442i	−0.380964	−	0.659850i
$467$	−16.3177	−	28.2631i	−0.755093	−	1.30786i	−0.945328	−	0.326121i	$-0.894258\pi$
$467$	−16.3177	−	28.2631i	−0.755093	−	1.30786i	0.190235	−	0.981739i	$-0.439075\pi$
$468$		0			0
$469$	4.38597	+	19.4429i	0.202525	+	0.897788i
$470$	−18.4201	−	10.6349i	−0.849657	−	0.490550i
$471$		0			0
$472$			10.4261i			0.479898i
$473$		−	0.482182i		−	0.0221708i
$474$		0			0
$475$	−84.0174	−	48.5075i	−3.85498	−	2.22567i
$476$	19.3320	+	6.01676i	0.886082	+	0.275778i
$477$		0			0
$478$	8.92870	+	15.4650i	0.408389	+	0.707351i
$479$	5.58651	+	9.67613i	0.255254	+	0.442113i	0.964965	−	0.262380i	$-0.0845075\pi$
$479$	5.58651	+	9.67613i	0.255254	+	0.442113i	−0.709710	+	0.704494i	$0.751174\pi$
$480$		0			0
$481$	14.3519	+	8.28606i	0.654389	+	0.377812i
$482$	−4.19953	−	7.27380i	−0.191283	−	0.331312i
$483$		0			0
$484$	5.49558	−	9.51862i	0.249799	−	0.432665i
$485$	14.6805	−	8.47581i	0.666609	−	0.384867i
$486$		0			0
$487$	−16.1951	+	28.0507i	−0.733868	+	1.27110i	0.221350	+	0.975194i	$0.428954\pi$
$487$	−16.1951	+	28.0507i	−0.733868	+	1.27110i	−0.955218	+	0.295902i	$0.904380\pi$
$488$	3.11656			0.141080
$489$		0			0
$490$	29.1053	+	2.32933i	1.31484	+	0.105229i
$491$	28.6950	−	16.5671i	1.29499	−	0.747661i	0.315453	−	0.948941i	$-0.397844\pi$
$491$	28.6950	−	16.5671i	1.29499	−	0.747661i	0.979534	+	0.201281i	$0.0645104\pi$
$492$		0			0
$493$	13.4649	−	7.77399i	0.606430	−	0.350123i
$494$	−25.7156	−	14.8469i	−1.15700	−	0.667994i
$495$		0			0
$496$			1.68119i			0.0754878i
$497$	22.2298	−	5.01466i	0.997144	−	0.224938i
$498$		0			0
$499$	12.0418	−	20.8569i	0.539063	−	0.933685i	−0.459892	−	0.887975i	$-0.652112\pi$
$499$	12.0418	−	20.8569i	0.539063	−	0.933685i	0.998955	−	0.0457097i	$-0.0145549\pi$
$500$	−30.8619			−1.38019
$501$		0			0
$502$			12.3552i			0.551438i
$503$	−30.1146			−1.34274			−0.671372	−	0.741121i	$-0.734295\pi$
$503$	−30.1146			−1.34274			−0.671372	+	0.741121i	$0.734295\pi$
$504$		0			0
$505$	−51.4364			−2.28889
$506$			0.360137i			0.0160100i
$507$		0			0
$508$	−9.49968			−0.421480
$509$	4.94736	−	8.56907i	0.219288	−	0.379817i	−0.735303	−	0.677739i	$-0.762960\pi$
$509$	4.94736	−	8.56907i	0.219288	−	0.379817i	0.954590	+	0.297921i	$0.0962933\pi$
$510$		0			0
$511$	0.117993	−	0.379116i	0.00521971	−	0.0167711i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.0309	−	6.94605i	−0.530661	−	0.306377i
$515$	−6.55307	+	3.78341i	−0.288763	+	0.166717i
$516$		0			0
$517$	0.415245	−	0.239742i	0.0182624	−	0.0105438i
$518$	7.83702	+	8.48928i	0.344339	+	0.372998i
$519$		0			0
$520$	−15.8295			−0.694171
$521$	−0.0257283	+	0.0445628i	−0.00112718	+	0.00195233i	−0.866588	−	0.499024i	$-0.833692\pi$
$521$	−0.0257283	+	0.0445628i	−0.00112718	+	0.00195233i	0.865461	+	0.500976i	$0.167025\pi$
$522$		0			0
$523$	−3.58537	+	2.07001i	−0.156777	+	0.0905154i	−0.576336	−	0.817213i	$-0.695518\pi$
$523$	−3.58537	+	2.07001i	−0.156777	+	0.0905154i	0.419559	+	0.907728i	$0.362185\pi$
$524$	1.51601	−	2.62581i	0.0662273	−	0.114709i
$525$		0			0
$526$	−5.49337	−	9.51479i	−0.239522	−	0.414865i
$527$	−11.1418	−	6.43269i	−0.485342	−	0.280212i
$528$		0			0
$529$	−4.16565	−	7.21512i	−0.181115	−	0.313701i
$530$	−14.5820	−	25.2568i	−0.633402	−	1.09708i
$531$		0			0
$532$	−14.0423	−	15.2110i	−0.608811	−	0.659482i
$533$	10.0944	+	5.82803i	0.437239	+	0.252440i
$534$		0			0
$535$		−	13.0259i		−	0.563160i
$536$		−	7.53337i		−	0.325392i
$537$		0			0
$538$	17.4590	+	10.0800i	0.752710	+	0.434578i
$539$	−0.373535	+	0.541961i	−0.0160893	+	0.0233439i
$540$		0			0
$541$	9.98675	+	17.2976i	0.429364	+	0.743680i	0.996817	−	0.0797258i	$-0.0254045\pi$
$541$	9.98675	+	17.2976i	0.429364	+	0.743680i	−0.567453	+	0.823406i	$0.692071\pi$
$542$	−6.99205	−	12.1106i	−0.300334	−	0.520194i
$543$		0			0
$544$	−6.62729	−	3.82627i	−0.284143	−	0.164050i
$545$	4.68061	+	8.10705i	0.200495	+	0.347268i
$546$		0			0
$547$	3.95703	−	6.85377i	0.169190	−	0.293046i	−0.768945	−	0.639315i	$-0.779218\pi$
$547$	3.95703	−	6.85377i	0.169190	−	0.293046i	0.938135	+	0.346269i	$0.112551\pi$
$548$	3.82389	−	2.20773i	0.163349	−	0.0943094i
$549$		0			0
$550$	0.582938	−	1.00968i	0.0248566	−	0.0430528i
$551$	−15.8974			−0.677252
$552$		0			0
$553$	−7.55034	−	33.4704i	−0.321073	−	1.42331i
$554$	−16.4069	+	9.47254i	−0.697063	+	0.402450i
$555$		0			0
$556$	1.14947	−	0.663644i	0.0487482	−	0.0281448i
$557$	30.5833	+	17.6573i	1.29586	+	0.748163i	0.979686	−	0.200539i	$-0.0642694\pi$
$557$	30.5833	+	17.6573i	1.29586	+	0.748163i	0.316171	+	0.948702i	$0.397603\pi$
$558$		0			0
$559$			19.4602i			0.823079i
$560$	−10.5374	−	3.27958i	−0.445285	−	0.138587i
$561$		0			0
$562$	3.06078	−	5.30142i	0.129111	−	0.223627i
$563$	36.1965			1.52550			0.762751	−	0.646693i	$-0.223848\pi$
$563$	36.1965			1.52550			0.762751	+	0.646693i	$0.223848\pi$
$564$		0			0
$565$		−	14.9390i		−	0.628489i
$566$	27.3084			1.14786
$567$		0			0
$568$	−8.61322			−0.361403
$569$			22.1243i			0.927500i	0.885966	+	0.463750i	$0.153496\pi$
$569$			22.1243i			0.927500i	−0.885966	+	0.463750i	$0.846504\pi$
$570$		0			0
$571$	−24.1041			−1.00873			−0.504363	−	0.863492i	$-0.668273\pi$
$571$	−24.1041			−1.00873			−0.504363	+	0.863492i	$0.668273\pi$
$572$	0.178423	−	0.309037i	0.00746022	−	0.0129215i
$573$		0			0
$574$	5.51219	+	5.97096i	0.230074	+	0.249223i
$575$		−	47.4872i		−	1.98035i
$576$		0			0
$577$	9.03494	+	5.21633i	0.376129	+	0.217158i	0.676133	−	0.736780i	$-0.263654\pi$
$577$	9.03494	+	5.21633i	0.376129	+	0.217158i	−0.300003	+	0.953938i	$0.596988\pi$
$578$	35.9931	−	20.7806i	1.49712	−	0.864361i
$579$		0			0
$580$	−7.33937	+	4.23739i	−0.304751	+	0.175948i
$581$	−6.53889	−	2.03512i	−0.271279	−	0.0844309i
$582$		0			0
$583$	0.657445			0.0272286
$584$	−0.0750360	+	0.129966i	−0.00310501	+	0.00537804i
$585$		0			0
$586$	13.2253	−	7.63564i	0.546333	−	0.315425i
$587$	10.0723	−	17.4458i	0.415730	−	0.720066i	−0.579775	−	0.814777i	$-0.696859\pi$
$587$	10.0723	−	17.4458i	0.415730	−	0.720066i	0.995505	+	0.0947111i	$0.0301927\pi$
$588$		0			0
$589$	6.57727	+	11.3922i	0.271011	+	0.469406i
$590$	37.6626	+	21.7445i	1.55055	+	0.895208i
$591$		0			0
$592$	−2.18343	−	3.78182i	−0.0897386	−	0.155432i
$593$	9.16661	+	15.8770i	0.376428	+	0.651992i	0.990540	−	0.137227i	$-0.0438190\pi$
$593$	9.16661	+	15.8770i	0.376428	+	0.651992i	−0.614112	+	0.789219i	$0.710486\pi$
$594$		0			0
$595$	62.0535	−	57.2857i	2.54395	−	2.34848i
$596$	9.16722	+	5.29269i	0.375504	+	0.216797i
$597$		0			0
$598$		−	14.5346i		−	0.594365i
$599$			15.8902i			0.649255i	0.945842	+	0.324628i	$0.105239\pi$
$599$			15.8902i			0.649255i	−0.945842	+	0.324628i	$0.894761\pi$
$600$		0			0
$601$	−34.8624	−	20.1278i	−1.42207	−	0.821030i	−0.425591	−	0.904916i	$-0.639934\pi$
$601$	−34.8624	−	20.1278i	−1.42207	−	0.821030i	−0.996475	+	0.0838852i	$0.973267\pi$
$602$	−4.03178	+	12.9542i	−0.164323	+	0.527975i
$603$		0			0
$604$	−3.86400	−	6.69264i	−0.157224	−	0.272320i
$605$	−22.9231	−	39.7040i	−0.931957	−	1.61420i
$606$		0			0
$607$	6.94932	+	4.01219i	0.282064	+	0.162850i	0.634358	−	0.773040i	$-0.281265\pi$
$607$	6.94932	+	4.01219i	0.282064	+	0.162850i	−0.352293	+	0.935890i	$0.614598\pi$
$608$	3.91226	+	6.77624i	0.158663	+	0.274813i
$609$		0			0
$610$	6.49988	−	11.2581i	0.263172	−	0.455828i
$611$	−16.7587	+	9.67564i	−0.677985	+	0.391435i
$612$		0			0
$613$	20.4658	−	35.4478i	0.826606	−	1.43172i	−0.0740802	−	0.997252i	$-0.523602\pi$
$613$	20.4658	−	35.4478i	0.826606	−	1.43172i	0.900686	−	0.434471i	$-0.143065\pi$
$614$	−28.9407			−1.16795
$615$		0			0
$616$	0.182798	−	0.168753i	0.00736516	−	0.00679926i
$617$	5.18641	−	2.99438i	0.208797	−	0.120549i	−0.391955	−	0.919984i	$-0.628201\pi$
$617$	5.18641	−	2.99438i	0.208797	−	0.120549i	0.600752	+	0.799435i	$0.294868\pi$
$618$		0			0
$619$	16.5700	−	9.56672i	0.666006	−	0.384519i	−0.128556	−	0.991702i	$-0.541034\pi$
$619$	16.5700	−	9.56672i	0.666006	−	0.384519i	0.794562	+	0.607183i	$0.207701\pi$
$620$	6.07307	+	3.50629i	0.243900	+	0.140816i
$621$		0			0
$622$		−	6.45823i		−	0.258951i
$623$	5.33141	−	4.92178i	0.213598	−	0.197187i
$624$		0			0
$625$	−33.3684	+	57.7958i	−1.33474	+	2.31183i
$626$	−27.3991			−1.09509
$627$		0			0
$628$		−	3.89155i		−	0.155290i
$629$	33.4176			1.33245
$630$		0			0
$631$	44.6986			1.77942			0.889712	−	0.456522i	$-0.150905\pi$
$631$	44.6986			1.77942			0.889712	+	0.456522i	$0.150905\pi$
$632$			12.9685i			0.515859i
$633$		0			0
$634$	−19.4183			−0.771199
$635$	−19.8125	+	34.3162i	−0.786235	+	1.36180i
$636$		0			0
$637$	15.0754	−	21.8728i	0.597308	−	0.866633i
$638$		−	0.191047i		−	0.00756362i
$639$		0			0
$640$	3.61236	+	2.08560i	0.142791	+	0.0824404i
$641$	23.6804	−	13.6719i	0.935321	−	0.540008i	0.0468305	−	0.998903i	$-0.485088\pi$
$641$	23.6804	−	13.6719i	0.935321	−	0.540008i	0.888490	+	0.458895i	$0.151755\pi$
$642$		0			0
$643$	−0.619011	+	0.357386i	−0.0244114	+	0.0140939i	−0.512156	−	0.858892i	$-0.671153\pi$
$643$	−0.619011	+	0.357386i	−0.0244114	+	0.0140939i	0.487745	+	0.872986i	$0.337820\pi$
$644$	3.01130	−	9.67538i	0.118662	−	0.381263i
$645$		0			0
$646$	−59.8774			−2.35585
$647$	−6.33080	+	10.9653i	−0.248889	+	0.431089i	−0.963218	−	0.268722i	$-0.913399\pi$
$647$	−6.33080	+	10.9653i	−0.248889	+	0.431089i	0.714329	+	0.699810i	$0.246732\pi$
$648$		0			0
$649$	−0.849028	+	0.490187i	−0.0333273	+	0.0192415i
$650$	−23.5266	+	40.7492i	−0.922788	+	1.59832i
$651$		0			0
$652$	−8.82699	−	15.2888i	−0.345692	−	0.598755i
$653$	32.8218	+	18.9497i	1.28442	+	0.741558i	0.977652	−	0.210228i	$-0.0674206\pi$
$653$	32.8218	+	18.9497i	1.28442	+	0.741558i	0.306764	+	0.951786i	$0.400754\pi$
$654$		0			0
$655$	−6.32357	−	10.9528i	−0.247083	−	0.427959i
$656$	−1.53573	−	2.65995i	−0.0599600	−	0.103854i
$657$		0			0
$658$	−13.1605	+	2.96878i	−0.513050	+	0.115735i
$659$	−40.8745	−	23.5989i	−1.59225	−	0.919284i	−0.992921	−	0.118779i	$-0.962102\pi$
$659$	−40.8745	−	23.5989i	−1.59225	−	0.919284i	−0.599326	−	0.800505i	$-0.704565\pi$
$660$		0			0
$661$			25.4156i			0.988553i	0.869305	+	0.494276i	$0.164567\pi$
$661$			25.4156i			0.988553i	−0.869305	+	0.494276i	$0.835433\pi$
$662$			13.1186i			0.509869i
$663$		0			0
$664$	2.24162	+	1.29420i	0.0869919	+	0.0502248i
$665$	−84.2343	+	19.0018i	−3.26646	+	0.736857i
$666$		0			0
$667$	−3.89076	−	6.73899i	−0.150651	−	0.260935i
$668$	8.19835	+	14.2000i	0.317204	+	0.549413i
$669$		0			0
$670$	−27.2132	−	15.7116i	−1.05134	−	0.606991i
$671$	0.146527	+	0.253792i	0.00565660	+	0.00979752i
$672$		0			0
$673$	−1.78998	+	3.10034i	−0.0689987	+	0.119509i	−0.898461	−	0.439054i	$-0.855314\pi$
$673$	−1.78998	+	3.10034i	−0.0689987	+	0.119509i	0.829462	+	0.558563i	$0.188647\pi$
$674$	20.5518	−	11.8656i	0.791624	−	0.457045i
$675$		0			0
$676$	−0.700889	+	1.21398i	−0.0269573	+	0.0466914i
$677$	−24.1259			−0.927233			−0.463617	−	0.886036i	$-0.653448\pi$
$677$	−24.1259			−0.927233			−0.463617	+	0.886036i	$0.653448\pi$
$678$		0			0
$679$	3.19528	−	10.2665i	0.122624	−	0.393993i
$680$	−27.6437	+	15.9601i	−1.06009	+	0.612042i
$681$		0			0
$682$	−0.136905	+	0.0790422i	−0.00524237	+	0.00302668i
$683$	12.8920	+	7.44319i	0.493298	+	0.284806i	0.725942	−	0.687756i	$-0.241404\pi$
$683$	12.8920	+	7.44319i	0.493298	+	0.284806i	−0.232644	+	0.972562i	$0.574738\pi$
$684$		0			0
$685$		−	18.4177i		−	0.703704i
$686$	14.5670	−	11.4369i	0.556169	−	0.436664i
$687$		0			0
$688$	2.56395	−	4.44089i	0.0977496	−	0.169307i
$689$	−26.5336			−1.01085
$690$		0			0
$691$			36.1757i			1.37619i	0.725621	+	0.688095i	$0.241553\pi$
$691$			36.1757i			1.37619i	−0.725621	+	0.688095i	$0.758447\pi$
$692$	−7.85639			−0.298655
$693$		0			0
$694$	8.33530			0.316404
$695$		−	5.53637i		−	0.210007i
$696$		0			0
$697$	23.5044			0.890292
$698$	−9.37428	+	16.2367i	−0.354822	+	0.614569i
$699$		0			0
$700$	−24.1036	+	22.2516i	−0.911030	+	0.841032i
$701$		−	23.4537i		−	0.885834i	−0.896563	−	0.442917i	$-0.853944\pi$
$701$		−	23.4537i		−	0.885834i	0.896563	−	0.442917i	$-0.146056\pi$
$702$		0			0
$703$	−29.5909	−	17.0843i	−1.11604	−	0.644348i
$704$	−0.0814333	+	0.0470156i	−0.00306913	+	0.00177197i
$705$		0			0
$706$	16.9199	−	9.76869i	0.636788	−	0.367650i
$707$	−23.9724	+	22.1305i	−0.901574	+	0.832303i
$708$		0			0
$709$	−18.1342			−0.681043			−0.340521	−	0.940237i	$-0.610604\pi$
$709$	−18.1342			−0.681043			−0.340521	+	0.940237i	$0.610604\pi$
$710$	−17.9637	+	31.1140i	−0.674165	+	1.16769i
$711$		0			0
$712$	−2.37504	+	1.37123i	−0.0890085	+	0.0513891i
$713$	−3.21946	+	5.57627i	−0.120570	+	0.208833i
$714$		0			0
$715$	−0.744234	−	1.28905i	−0.0278328	−	0.0482078i
$716$	15.7884	+	9.11541i	0.590038	+	0.340659i
$717$		0			0
$718$	−8.27288	−	14.3290i	−0.308741	−	0.534755i
$719$	16.4312	+	28.4597i	0.612781	+	1.06137i	0.990769	+	0.135558i	$0.0432826\pi$
$719$	16.4312	+	28.4597i	0.612781	+	1.06137i	−0.377988	+	0.925810i	$0.623384\pi$
$720$		0			0
$721$	−1.42630	+	4.58275i	−0.0531183	+	0.170671i
$722$	36.5663	+	21.1116i	1.36086	+	0.785692i
$723$		0			0
$724$		−	14.2290i		−	0.528817i
$725$			25.1912i			0.935578i
$726$		0			0
$727$	6.27758	+	3.62436i	0.232823	+	0.134420i	0.611874	−	0.790956i	$-0.290416\pi$
$727$	6.27758	+	3.62436i	0.232823	+	0.134420i	−0.379051	+	0.925376i	$0.623749\pi$
$728$	−7.37750	+	6.81065i	−0.273428	+	0.252420i
$729$		0			0
$730$	0.312989	+	0.542113i	0.0115843	+	0.0200645i
$731$	19.6207	+	33.9841i	0.725698	+	1.25695i
$732$		0			0
$733$	−29.5250	−	17.0463i	−1.09053	−	0.629619i	−0.156814	−	0.987628i	$-0.550122\pi$
$733$	−29.5250	−	17.0463i	−1.09053	−	0.629619i	−0.933718	+	0.358010i	$0.883456\pi$
$734$	−16.0681	−	27.8308i	−0.593085	−	1.02725i
$735$		0			0
$736$	−1.91499	+	3.31685i	−0.0705874	+	0.122261i
$737$	0.613468	−	0.354186i	0.0225974	−	0.0130466i
$738$		0			0
$739$	−17.4439	+	30.2137i	−0.641683	+	1.11143i	0.343373	+	0.939199i	$0.388430\pi$
$739$	−17.4439	+	30.2137i	−0.641683	+	1.11143i	−0.985057	+	0.172229i	$0.944903\pi$
$740$	−18.2150			−0.669598
$741$		0			0
$742$	−17.6628	−	5.49725i	−0.648422	−	0.201810i
$743$	39.6692	−	22.9030i	1.45532	−	0.840230i	0.456545	−	0.889700i	$-0.349087\pi$
$743$	39.6692	−	22.9030i	1.45532	−	0.840230i	0.998776	+	0.0494704i	$0.0157533\pi$
$744$		0			0
$745$	38.2382	−	22.0768i	1.40094	−	0.808833i
$746$	22.2875	+	12.8677i	0.816004	+	0.471120i
$747$		0			0
$748$		−	0.719576i		−	0.0263103i
$749$	−5.60440	−	6.07085i	−0.204780	−	0.221824i
$750$		0			0
$751$	−15.7630	+	27.3024i	−0.575201	+	0.996277i	0.420819	+	0.907145i	$0.361743\pi$
$751$	−15.7630	+	27.3024i	−0.575201	+	0.996277i	−0.996020	+	0.0891324i	$0.971591\pi$
$752$	5.09920			0.185949
$753$		0			0
$754$			7.71039i			0.280796i
$755$	−32.2349			−1.17315
$756$		0			0
$757$	−0.176603			−0.00641874			−0.00320937	−	0.999995i	$-0.501022\pi$
$757$	−0.176603			−0.00641874			−0.00320937	+	0.999995i	$0.501022\pi$
$758$		−	36.3772i		−	1.32128i
$759$		0			0
$760$	32.6376			1.18389
$761$	19.0504	−	32.9963i	0.690576	−	1.19611i	−0.281073	−	0.959686i	$-0.590690\pi$
$761$	19.0504	−	32.9963i	0.690576	−	1.19611i	0.971649	−	0.236427i	$-0.0759764\pi$
$762$		0			0
$763$	5.66949	+	1.76453i	0.205249	+	0.0638804i
$764$		−	19.2203i		−	0.695365i
$765$		0			0
$766$	−21.7845	−	12.5773i	−0.787107	−	0.454436i
$767$	34.2656	−	19.7833i	1.23726	−	0.714332i
$768$		0			0
$769$	−15.3223	+	8.84636i	−0.552538	+	0.319008i	−0.750145	−	0.661274i	$-0.770016\pi$
$769$	−15.3223	+	8.84636i	−0.552538	+	0.319008i	0.197607	+	0.980281i	$0.436683\pi$
$770$	−0.228354	−	1.01228i	−0.00822929	−	0.0364802i
$771$		0			0
$772$	−7.55634			−0.271959
$773$	5.67628	−	9.83160i	0.204162	−	0.353618i	−0.745704	−	0.666278i	$-0.767887\pi$
$773$	5.67628	−	9.83160i	0.204162	−	0.353618i	0.949865	+	0.312659i	$0.101220\pi$
$774$		0			0
$775$	18.0521	−	10.4224i	0.648452	−	0.374384i
$776$	−2.03199	+	3.51951i	−0.0729442	+	0.126343i
$777$		0			0
$778$	4.84752	+	8.39614i	0.173792	+	0.301016i
$779$	−20.8129	−	12.0163i	−0.745699	−	0.430529i
$780$		0			0
$781$	−0.404955	−	0.701403i	−0.0144904	−	0.0250982i
$782$	−14.6545	−	25.3823i	−0.524044	−	0.907671i
$783$		0			0
$784$	−6.32207	+	3.00523i	−0.225788	+	0.107330i
$785$	−14.0577	−	8.11621i	−0.501740	−	0.289680i
$786$		0			0
$787$			28.3356i			1.01006i	0.863103	+	0.505028i	$0.168518\pi$
$787$			28.3356i			1.01006i	−0.863103	+	0.505028i	$0.831482\pi$
$788$		−	2.10437i		−	0.0749651i
$789$		0			0
$790$	46.8469	+	27.0471i	1.66674	+	0.962291i
$791$	−6.42751	−	6.96246i	−0.228536	−	0.247557i
$792$		0			0
$793$	−5.91362	−	10.2427i	−0.209999	−	0.363729i
$794$	−6.45731	−	11.1844i	−0.229161	−	0.396919i
$795$		0			0
$796$	−1.24340	−	0.717876i	−0.0440710	−	0.0254444i
$797$	23.9709	+	41.5187i	0.849091	+	1.47067i	0.882020	+	0.471212i	$0.156183\pi$
$797$	23.9709	+	41.5187i	0.849091	+	1.47067i	−0.0329287	+	0.999458i	$0.510483\pi$
$798$		0			0
$799$	−19.5109	+	33.7939i	−0.690246	+	1.19554i
$800$	10.7377	−	6.19941i	0.379635	−	0.219182i
$801$		0			0
$802$	14.3872	−	24.9194i	0.508031	−	0.879936i
$803$	−0.0141114			−0.000497982
$804$		0			0
$805$	−28.6706	−	31.0568i	−1.01051	−	1.09461i
$806$	5.52530	−	3.19004i	0.194621	−	0.112364i
$807$		0			0
$808$	10.6793	−	6.16567i	0.375695	−	0.216908i
$809$	29.3232	+	16.9297i	1.03095	+	0.595218i	0.917256	−	0.398298i	$-0.130399\pi$
$809$	29.3232	+	16.9297i	1.03095	+	0.595218i	0.113692	+	0.993516i	$0.463732\pi$
$810$		0			0
$811$			32.8364i			1.15304i	0.817082	+	0.576521i	$0.195590\pi$
$811$			32.8364i			1.15304i	−0.817082	+	0.576521i	$0.804410\pi$
$812$	−1.59745	+	5.13264i	−0.0560593	+	0.180120i
$813$		0			0
$814$	0.205311	−	0.355609i	0.00719614	−	0.0124641i
$815$	−73.6381			−2.57943
$816$		0			0
$817$		−	40.1234i		−	1.40374i
$818$	−33.2333			−1.16198
$819$		0			0
$820$	−12.8116			−0.447401
$821$			34.7480i			1.21271i	0.795193	+	0.606357i	$0.207370\pi$
$821$			34.7480i			1.21271i	−0.795193	+	0.606357i	$0.792630\pi$
$822$		0			0
$823$	44.3897			1.54733			0.773663	−	0.633597i	$-0.218422\pi$
$823$	44.3897			1.54733			0.773663	+	0.633597i	$0.218422\pi$
$824$	0.907035	−	1.57103i	0.0315981	−	0.0547294i
$825$		0			0
$826$	26.9086	−	6.07010i	0.936269	−	0.211206i
$827$		−	13.2991i		−	0.462456i	−0.972900	−	0.231228i	$-0.925726\pi$
$827$		−	13.2991i		−	0.462456i	0.972900	−	0.231228i	$-0.0742743\pi$
$828$		0			0
$829$	1.16441	+	0.672270i	0.0404415	+	0.0233489i	0.520084	−	0.854115i	$-0.325900\pi$
$829$	1.16441	+	0.672270i	0.0404415	+	0.0233489i	−0.479643	+	0.877464i	$0.659234\pi$
$830$	9.35024	−	5.39836i	0.324552	−	0.187380i
$831$		0			0
$832$	3.28654	−	1.89748i	0.113940	−	0.0657834i
$833$	4.27344	−	53.3970i	0.148066	−	1.85010i
$834$		0			0
$835$	68.3938			2.36686
$836$	−0.367874	+	0.637177i	−0.0127232	+	0.0220372i
$837$		0			0
$838$	−1.87584	+	1.08302i	−0.0648000	+	0.0374123i
$839$	1.55022	−	2.68507i	0.0535196	−	0.0926987i	−0.838024	−	0.545633i	$-0.816289\pi$
$839$	1.55022	−	2.68507i	0.0535196	−	0.0926987i	0.891544	+	0.452934i	$0.149623\pi$
$840$		0			0
$841$	−12.4360	−	21.5398i	−0.428828	−	0.742752i
$842$	−10.7270	−	6.19326i	−0.369678	−	0.213434i
$843$		0			0
$844$	−2.18400	−	3.78280i	−0.0751764	−	0.130209i
$845$	2.92354	+	5.06372i	0.100573	+	0.174197i
$846$		0			0
$847$	−27.7662	−	8.64174i	−0.954056	−	0.296934i
$848$	6.05506	+	3.49589i	0.207931	+	0.120049i
$849$		0			0
$850$			94.8825i			3.25444i
$851$		−	16.7250i		−	0.573325i
$852$		0			0
$853$	−25.2032	−	14.5511i	−0.862941	−	0.498219i	0.00205494	−	0.999998i	$-0.499346\pi$
$853$	−25.2032	−	14.5511i	−0.862941	−	0.498219i	−0.864996	+	0.501779i	$0.832679\pi$
$854$	−1.81448	−	8.04352i	−0.0620902	−	0.275244i
$855$		0			0
$856$	1.56142	+	2.70445i	0.0533681	+	0.0924363i
$857$	−2.37441	−	4.11260i	−0.0811084	−	0.140484i	0.822618	−	0.568595i	$-0.192513\pi$
$857$	−2.37441	−	4.11260i	−0.0811084	−	0.140484i	−0.903726	+	0.428111i	$0.859179\pi$
$858$		0			0
$859$	31.2496	+	18.0419i	1.06622	+	0.615583i	0.927147	−	0.374699i	$-0.122254\pi$
$859$	31.2496	+	18.0419i	1.06622	+	0.615583i	0.139075	+	0.990282i	$0.455587\pi$
$860$	−10.6947	−	18.5238i	−0.364687	−	0.631656i
$861$		0			0
$862$	11.6921	−	20.2513i	0.398233	−	0.689760i
$863$	−10.3650	+	5.98423i	−0.352829	+	0.203706i	−0.665930	−	0.746014i	$-0.731965\pi$
$863$	−10.3650	+	5.98423i	−0.352829	+	0.203706i	0.313102	+	0.949720i	$0.398632\pi$
$864$		0			0
$865$	−16.3852	+	28.3801i	−0.557115	+	0.964952i
$866$	30.6220			1.04058
$867$		0			0
$868$	4.33899	−	0.978800i	0.147275	−	0.0332226i
$869$	−1.05607	+	0.609722i	−0.0358247	+	0.0206834i
$870$		0			0
$871$	−24.7587	+	14.2945i	−0.838917	+	0.484349i
$872$	−1.94358	−	1.12213i	−0.0658180	−	0.0380000i
$873$		0			0
$874$			29.9677i			1.01367i
$875$	17.9680	+	79.6515i	0.607429	+	2.69271i
$876$		0			0
$877$	12.0096	−	20.8013i	0.405537	−	0.702410i	−0.588847	−	0.808244i	$-0.700418\pi$
$877$	12.0096	−	20.8013i	0.405537	−	0.702410i	0.994384	+	0.105834i	$0.0337514\pi$
$878$	30.9972			1.04610
$879$		0			0
$880$			0.392222i			0.0132218i
$881$	−13.4264			−0.452348			−0.226174	−	0.974087i	$-0.572622\pi$
$881$	−13.4264			−0.452348			−0.226174	+	0.974087i	$0.572622\pi$
$882$		0			0
$883$	27.1649			0.914172			0.457086	−	0.889423i	$-0.348893\pi$
$883$	27.1649			0.914172			0.457086	+	0.889423i	$0.348893\pi$
$884$			29.0411i			0.976759i
$885$		0			0
$886$	10.0489			0.337598
$887$	4.12273	−	7.14078i	0.138428	−	0.239764i	−0.788474	−	0.615068i	$-0.789128\pi$
$887$	4.12273	−	7.14078i	0.138428	−	0.239764i	0.926902	+	0.375304i	$0.122462\pi$
$888$		0			0
$889$	5.53077	+	24.5177i	0.185496	+	0.822298i
$890$			11.4393i			0.383448i
$891$		0			0
$892$	−14.9763	−	8.64657i	−0.501444	−	0.289509i
$893$	34.5534	−	19.9494i	1.15628	−	0.667581i
$894$		0			0
$895$	65.8562	−	38.0221i	2.20133	−	1.27094i
$896$	2.58090	−	0.582206i	0.0862218	−	0.0194501i
$897$		0			0
$898$	−3.58784			−0.119728
$899$	1.70787	−	2.95813i	0.0569608	−	0.0986590i
$900$		0			0
$901$	−46.3365	+	26.7524i	−1.54369	+	0.891252i
$902$	0.144406	−	0.250118i	0.00480819	−	0.00832803i
$903$		0			0
$904$	1.79074	+	3.10165i	0.0595590	+	0.103159i
$905$	−51.4002	−	29.6759i	−1.70860	−	0.986461i
$906$		0			0
$907$	18.6275	+	32.2638i	0.618517	+	1.07130i	0.989756	+	0.142766i	$0.0455997\pi$
$907$	18.6275	+	32.2638i	0.618517	+	1.07130i	−0.371239	+	0.928537i	$0.621067\pi$
$908$	−4.25063	−	7.36231i	−0.141062	−	0.244327i
$909$		0			0
$910$	9.21604	+	40.8544i	0.305509	+	1.35431i
$911$	−13.3220	−	7.69143i	−0.441376	−	0.254829i	0.262805	−	0.964849i	$-0.415352\pi$
$911$	−13.3220	−	7.69143i	−0.441376	−	0.254829i	−0.704181	+	0.710020i	$0.748686\pi$
$912$		0			0
$913$			0.243391i			0.00805505i
$914$			2.57354i			0.0851252i
$915$		0			0
$916$	−21.0383	−	12.1465i	−0.695126	−	0.401331i
$917$	−7.65958	−	2.38391i	−0.252942	−	0.0787237i
$918$		0			0
$919$	25.3211	+	43.8575i	0.835267	+	1.44673i	0.893812	+	0.448441i	$0.148021\pi$
$919$	25.3211	+	43.8575i	0.835267	+	1.44673i	−0.0585450	+	0.998285i	$0.518646\pi$
$920$	7.98778	+	13.8352i	0.263349	+	0.456134i
$921$		0			0
$922$	15.0782	+	8.70540i	0.496574	+	0.286697i
$923$	16.3434	+	28.3077i	0.537951	+	0.931758i
$924$		0			0
$925$	−27.0720	+	46.8901i	−0.890123	+	1.54174i
$926$	13.7546	−	7.94124i	0.452005	−	0.260965i
$927$		0			0
$928$	1.01587	−	1.75954i	0.0333476	−	0.0577597i
$929$	−30.3962			−0.997268			−0.498634	−	0.866813i	$-0.666165\pi$
$929$	−30.3962			−0.997268			−0.498634	+	0.866813i	$0.666165\pi$
$930$		0			0
$931$	−31.0826	+	45.0977i	−1.01869	+	1.47802i
$932$	14.2442	−	8.22389i	0.466584	−	0.269383i
$933$		0			0
$934$	28.2631	−	16.3177i	0.924796	−	0.533931i
$935$	−2.59937	−	1.50075i	−0.0850084	−	0.0490796i
$936$		0			0
$937$		−	13.7262i		−	0.448416i	−0.974541	−	0.224208i	$-0.928020\pi$
$937$		−	13.7262i		−	0.448416i	0.974541	−	0.224208i	$-0.0719796\pi$
$938$	−19.4429	+	4.38597i	−0.634832	+	0.143207i
$939$		0			0
$940$	10.6349	−	18.4201i	0.346871	−	0.600798i
$941$	−31.4438			−1.02504			−0.512520	−	0.858676i	$-0.671288\pi$
$941$	−31.4438			−1.02504			−0.512520	+	0.858676i	$0.671288\pi$
$942$		0			0
$943$		−	11.7636i		−	0.383075i
$944$	−10.4261			−0.339339
$945$		0			0
$946$	0.482182			0.0156771
$947$			0.839464i			0.0272789i	0.999907	+	0.0136395i	$0.00434171\pi$
$947$			0.839464i			0.0272789i	−0.999907	+	0.0136395i	$0.995658\pi$
$948$		0			0
$949$	0.569518			0.0184873
$950$	48.5075	−	84.0174i	1.57379	−	2.72588i
$951$		0			0
$952$	−6.01676	+	19.3320i	−0.195004	+	0.626555i
$953$			41.8952i			1.35712i	0.734545	+	0.678560i	$0.237396\pi$
$953$			41.8952i			1.35712i	−0.734545	+	0.678560i	$0.762604\pi$
$954$		0			0
$955$	−69.4305	−	40.0857i	−2.24672	−	1.29714i
$956$	−15.4650	+	8.92870i	−0.500172	+	0.288775i
$957$		0			0
$958$	−9.67613	+	5.58651i	−0.312621	+	0.180492i
$959$	−7.92421	−	8.58373i	−0.255886	−	0.277183i
$960$		0			0
$961$	28.1736			0.908826
$962$	−8.28606	+	14.3519i	−0.267153	+	0.462723i
$963$		0			0
$964$	7.27380	−	4.19953i	0.234273	−	0.135258i
$965$	−15.7595	+	27.2962i	−0.507315	+	0.878696i
$966$		0			0
$967$	23.3435	+	40.4321i	0.750676	+	1.30021i	0.947496	+	0.319769i	$0.103605\pi$
$967$	23.3435	+	40.4321i	0.750676	+	1.30021i	−0.196820	+	0.980440i	$0.563061\pi$
$968$	9.51862	+	5.49558i	0.305940	+	0.176635i
$969$		0			0
$970$	8.47581	+	14.6805i	0.272142	+	0.471364i
$971$	−11.6725	−	20.2173i	−0.374587	−	0.648804i	0.615678	−	0.787998i	$-0.288882\pi$
$971$	−11.6725	−	20.2173i	−0.374587	−	0.648804i	−0.990265	+	0.139194i	$0.955549\pi$
$972$		0			0
$973$	−2.38202	−	2.58028i	−0.0763642	−	0.0827199i
$974$	−28.0507	−	16.1951i	−0.898801	−	0.518923i
$975$		0			0
$976$			3.11656i			0.0997586i
$977$		−	31.2051i		−	0.998341i	−0.866504	−	0.499171i	$-0.833638\pi$
$977$		−	31.2051i		−	0.998341i	0.866504	−	0.499171i	$-0.166362\pi$
$978$		0			0
$979$	−0.223328	−	0.128939i	−0.00713760	−	0.00412089i
$980$	−2.32933	+	29.1053i	−0.0744079	+	0.929734i
$981$		0			0
$982$	16.5671	+	28.6950i	0.528676	+	0.915693i
$983$	−1.41367	−	2.44856i	−0.0450892	−	0.0780968i	0.842600	−	0.538540i	$-0.181024\pi$
$983$	−1.41367	−	2.44856i	−0.0450892	−	0.0780968i	−0.887689	+	0.460443i	$0.847691\pi$
$984$		0			0
$985$	−7.60174	−	4.38887i	−0.242211	−	0.139841i
$986$	7.77399	+	13.4649i	0.247574	+	0.428811i
$987$		0			0
$988$	14.8469	−	25.7156i	0.472343	−	0.818122i
$989$	17.0085	−	9.81986i	0.540839	−	0.312253i
$990$		0			0
$991$	14.4402	−	25.0111i	0.458708	−	0.794505i	−0.540185	−	0.841546i	$-0.681646\pi$
$991$	14.4402	−	25.0111i	0.458708	−	0.794505i	0.998893	+	0.0470409i	$0.0149791\pi$
$992$	−1.68119			−0.0533779
$993$		0			0
$994$	5.01466	+	22.2298i	0.159055	+	0.705088i
$995$	−5.18645	+	2.99440i	−0.164421	+	0.0949287i
$996$		0			0
$997$	−29.6911	+	17.1421i	−0.940326	+	0.542897i	−0.890062	−	0.455839i	$-0.849339\pi$
$997$	−29.6911	+	17.1421i	−0.940326	+	0.542897i	−0.0502633	+	0.998736i	$0.516006\pi$
$998$	20.8569	+	12.0418i	0.660215	+	0.381175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.l.h.269.5		16
3.2	odd	2		1134.2.l.g.269.4		16
7.5	odd	6		1134.2.t.g.593.5		16
9.2	odd	6		1134.2.k.d.647.4	yes	16
9.4	even	3		1134.2.t.h.1025.4		16
9.5	odd	6		1134.2.t.g.1025.5		16
9.7	even	3		1134.2.k.c.647.5	✓	16
21.5	even	6		1134.2.t.h.593.4		16
63.5	even	6	inner	1134.2.l.h.215.1		16
63.40	odd	6		1134.2.l.g.215.8		16
63.47	even	6		1134.2.k.c.971.5	yes	16
63.61	odd	6		1134.2.k.d.971.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.k.c.647.5	✓	16	9.7	even	3
1134.2.k.c.971.5	yes	16	63.47	even	6
1134.2.k.d.647.4	yes	16	9.2	odd	6
1134.2.k.d.971.4	yes	16	63.61	odd	6
1134.2.l.g.215.8		16	63.40	odd	6
1134.2.l.g.269.4		16	3.2	odd	2
1134.2.l.h.215.1		16	63.5	even	6	inner
1134.2.l.h.269.5		16	1.1	even	1	trivial
1134.2.t.g.593.5		16	7.5	odd	6
1134.2.t.g.1025.5		16	9.5	odd	6
1134.2.t.h.593.4		16	21.5	even	6
1134.2.t.h.1025.4		16	9.4	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.08560 + 3.61236i) q^{5} +(0.582206 + 2.58090i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-2.08560 + 3.61236i) q^{5} +(0.582206 + 2.58090i) q^{7} -1.00000i q^{8} +(-3.61236 - 2.08560i) q^{10} +(0.0814333 - 0.0470156i) q^{11} +(-3.28654 + 1.89748i) q^{13} +(-2.58090 + 0.582206i) q^{14} +1.00000 q^{16} +(-3.82627 + 6.62729i) q^{17} +(6.77624 - 3.91226i) q^{19} +(2.08560 - 3.61236i) q^{20} +(0.0470156 + 0.0814333i) q^{22} +(3.31685 + 1.91499i) q^{23} +(-6.19941 - 10.7377i) q^{25} +(-1.89748 - 3.28654i) q^{26} +(-0.582206 - 2.58090i) q^{28} +(-1.75954 - 1.01587i) q^{29} +1.68119i q^{31} +1.00000i q^{32} +(-6.62729 - 3.82627i) q^{34} +(-10.5374 - 3.27958i) q^{35} +(-2.18343 - 3.78182i) q^{37} +(3.91226 + 6.77624i) q^{38} +(3.61236 + 2.08560i) q^{40} +(-1.53573 - 2.65995i) q^{41} +(2.56395 - 4.44089i) q^{43} +(-0.0814333 + 0.0470156i) q^{44} +(-1.91499 + 3.31685i) q^{46} +5.09920 q^{47} +(-6.32207 + 3.00523i) q^{49} +(10.7377 - 6.19941i) q^{50} +(3.28654 - 1.89748i) q^{52} +(6.05506 + 3.49589i) q^{53} +0.392222i q^{55} +(2.58090 - 0.582206i) q^{56} +(1.01587 - 1.75954i) q^{58} -10.4261 q^{59} +3.11656i q^{61} -1.68119 q^{62} -1.00000 q^{64} -15.8295i q^{65} +7.53337 q^{67} +(3.82627 - 6.62729i) q^{68} +(3.27958 - 10.5374i) q^{70} -8.61322i q^{71} +(-0.129966 - 0.0750360i) q^{73} +(3.78182 - 2.18343i) q^{74} +(-6.77624 + 3.91226i) q^{76} +(0.168753 + 0.182798i) q^{77} -12.9685 q^{79} +(-2.08560 + 3.61236i) q^{80} +(2.65995 - 1.53573i) q^{82} +(-1.29420 + 2.24162i) q^{83} +(-15.9601 - 27.6437i) q^{85} +(4.44089 + 2.56395i) q^{86} +(-0.0470156 - 0.0814333i) q^{88} +(-1.37123 - 2.37504i) q^{89} +(-6.81065 - 7.37750i) q^{91} +(-3.31685 - 1.91499i) q^{92} +5.09920i q^{94} +32.6376i q^{95} +(-3.51951 - 2.03199i) q^{97} +(-3.00523 - 6.32207i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q - 16 * q^4 - 4 * q^7	\( 16 q - 16 q^{4} - 4 q^{7} + 12 q^{11} - 12 q^{13} + 16 q^{16} + 12 q^{23} - 8 q^{25} + 4 q^{28} - 48 q^{29} - 60 q^{35} + 4 q^{37} + 12 q^{38} - 24 q^{41} + 16 q^{43} - 12 q^{44} - 20 q^{49} + 24 q^{50} + 12 q^{52} - 12 q^{58} - 48 q^{59} + 48 q^{62} - 16 q^{64} + 8 q^{67} + 12 q^{70} + 36 q^{73} + 36 q^{74} + 48 q^{77} - 16 q^{79} - 36 q^{83} - 12 q^{85} + 24 q^{86} - 24 q^{89} - 12 q^{91} - 12 q^{92} - 12 q^{97} - 36 q^{98}+O(q^{100}) \) 16 * q - 16 * q^4 - 4 * q^7 + 12 * q^11 - 12 * q^13 + 16 * q^16 + 12 * q^23 - 8 * q^25 + 4 * q^28 - 48 * q^29 - 60 * q^35 + 4 * q^37 + 12 * q^38 - 24 * q^41 + 16 * q^43 - 12 * q^44 - 20 * q^49 + 24 * q^50 + 12 * q^52 - 12 * q^58 - 48 * q^59 + 48 * q^62 - 16 * q^64 + 8 * q^67 + 12 * q^70 + 36 * q^73 + 36 * q^74 + 48 * q^77 - 16 * q^79 - 36 * q^83 - 12 * q^85 + 24 * q^86 - 24 * q^89 - 12 * q^91 - 12 * q^92 - 12 * q^97 - 36 * q^98

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