LMFDB - Embedded newform 2070.2.j.g.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(323,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("2070.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.j (of order $4$, degree $2$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.4
Root			$-0.760198 - 1.19252i$ of defining polynomial
Character	$\chi$	$=$	2070.323
Dual form			2070.2.j.g.737.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.85700 + 1.24561i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.85700 + 1.24561i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.19388 - 0.432320i) q^{10} -5.31965i q^{11} +(-0.864641 - 0.864641i) q^{13} -2.82843 q^{14} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} -6.38776i q^{19} +(-1.24561 - 1.85700i) q^{20} +(3.76156 - 3.76156i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.89692 - 4.62620i) q^{25} -1.22279i q^{26} +(-2.00000 - 2.00000i) q^{28} -4.05121 q^{29} +5.52311 q^{31} +(-0.707107 - 0.707107i) q^{32} +2.00000i q^{34} +(1.22279 - 6.20522i) q^{35} +(-5.76156 + 5.76156i) q^{37} +(4.51683 - 4.51683i) q^{38} +(0.432320 - 2.19388i) q^{40} -11.6707i q^{41} +(9.01395 + 9.01395i) q^{43} +5.31965 q^{44} -1.00000 q^{46} +(-0.885578 - 0.885578i) q^{47} -1.00000i q^{49} +(4.61254 - 1.92989i) q^{50} +(0.864641 - 0.864641i) q^{52} +(6.81662 - 6.81662i) q^{53} +(6.62620 + 9.87859i) q^{55} -2.82843i q^{56} +(-2.86464 - 2.86464i) q^{58} +2.15401 q^{59} +7.91087 q^{61} +(3.90543 + 3.90543i) q^{62} -1.00000i q^{64} +(2.68264 + 0.528636i) q^{65} +(4.35548 - 4.35548i) q^{67} +(-1.41421 + 1.41421i) q^{68} +(5.25240 - 3.52311i) q^{70} -8.00229i q^{71} +(-8.25240 - 8.25240i) q^{73} -8.14807 q^{74} +6.38776 q^{76} +(10.6393 + 10.6393i) q^{77} +8.77551i q^{79} +(1.85700 - 1.24561i) q^{80} +(8.25240 - 8.25240i) q^{82} +(2.07125 - 2.07125i) q^{83} +(-4.38776 - 0.864641i) q^{85} +12.7477i q^{86} +(3.76156 + 3.76156i) q^{88} -9.32521 q^{89} +3.45856 q^{91} +(-0.707107 - 0.707107i) q^{92} -1.25240i q^{94} +(7.95665 + 11.8621i) q^{95} +(-6.38776 + 6.38776i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{7}+O(q^{10}) $ 12 * q - 24 * q^7	$ 12 q - 24 q^{7} + 4 q^{10} - 12 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{28} + 16 q^{31} - 44 q^{37} + 12 q^{43} - 12 q^{46} + 44 q^{55} - 24 q^{58} - 16 q^{61} - 4 q^{67} - 8 q^{70} - 28 q^{73} + 16 q^{76} + 28 q^{82} + 8 q^{85} + 20 q^{88} - 16 q^{97}+O(q^{100}) $ 12 * q - 24 * q^7 + 4 * q^10 - 12 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^28 + 16 * q^31 - 44 * q^37 + 12 * q^43 - 12 * q^46 + 44 * q^55 - 24 * q^58 - 16 * q^61 - 4 * q^67 - 8 * q^70 - 28 * q^73 + 16 * q^76 + 28 * q^82 + 8 * q^85 + 20 * q^88 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−1.85700	+	1.24561i	−0.830477	+	0.557053i
$5$	−1.85700	+	1.24561i	−0.830477	+	0.557053i
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.19388	−	0.432320i	−0.693765	−	0.136712i
$11$		−	5.31965i		−	1.60393i	−0.597369	−	0.801967i	$-0.703787\pi$
$11$		−	5.31965i		−	1.60393i	0.597369	−	0.801967i	$-0.296213\pi$
$12$		0			0
$13$	−0.864641	−	0.864641i	−0.239808	−	0.239808i	0.576962	−	0.816771i	$-0.304238\pi$
$13$	−0.864641	−	0.864641i	−0.239808	−	0.239808i	−0.816771	+	0.576962i	$0.804238\pi$
$14$	−2.82843			−0.755929
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	0.857493	−	0.514496i	$-0.172021\pi$
$17$	1.41421	+	1.41421i	0.342997	+	0.342997i	−0.514496	+	0.857493i	$0.672021\pi$
$18$		0			0
$19$		−	6.38776i		−	1.46545i	−0.680524	−	0.732726i	$-0.738248\pi$
$19$		−	6.38776i		−	1.46545i	0.680524	−	0.732726i	$-0.261752\pi$
$20$	−1.24561	−	1.85700i	−0.278527	−	0.415238i
$21$		0			0
$22$	3.76156	−	3.76156i	0.801967	−	0.801967i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$		0			0
$25$	1.89692	−	4.62620i	0.379383	−	0.925240i
$26$		−	1.22279i		−	0.239808i
$27$		0			0
$28$	−2.00000	−	2.00000i	−0.377964	−	0.377964i
$29$	−4.05121			−0.752292			−0.376146	−	0.926560i	$-0.622751\pi$
$29$	−4.05121			−0.752292			−0.376146	+	0.926560i	$0.622751\pi$
$30$		0			0
$31$	5.52311			0.991981			0.495990	−	0.868328i	$-0.334805\pi$
$31$	5.52311			0.991981			0.495990	+	0.868328i	$0.334805\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$			2.00000i			0.342997i
$35$	1.22279	−	6.20522i	0.206689	−	1.04887i
$36$		0			0
$37$	−5.76156	+	5.76156i	−0.947194	+	0.947194i	−0.998674	−	0.0514799i	$-0.983606\pi$
$37$	−5.76156	+	5.76156i	−0.947194	+	0.947194i	0.0514799	+	0.998674i	$0.483606\pi$
$38$	4.51683	−	4.51683i	0.732726	−	0.732726i
$39$		0			0
$40$	0.432320	−	2.19388i	0.0683559	−	0.346883i
$41$		−	11.6707i		−	1.82265i	−0.411688	−	0.911325i	$-0.635061\pi$
$41$		−	11.6707i		−	1.82265i	0.411688	−	0.911325i	$-0.364939\pi$
$42$		0			0
$43$	9.01395	+	9.01395i	1.37461	+	1.37461i	0.853465	+	0.521150i	$0.174497\pi$
$43$	9.01395	+	9.01395i	1.37461	+	1.37461i	0.521150	+	0.853465i	$0.325503\pi$
$44$	5.31965			0.801967
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−0.885578	−	0.885578i	−0.129175	−	0.129175i	0.639563	−	0.768738i	$-0.279115\pi$
$47$	−0.885578	−	0.885578i	−0.129175	−	0.129175i	−0.768738	+	0.639563i	$0.779115\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	4.61254	−	1.92989i	0.652311	−	0.272928i
$51$		0			0
$52$	0.864641	−	0.864641i	0.119904	−	0.119904i
$53$	6.81662	−	6.81662i	0.936334	−	0.936334i	−0.0617569	−	0.998091i	$-0.519670\pi$
$53$	6.81662	−	6.81662i	0.936334	−	0.936334i	0.998091	+	0.0617569i	$0.0196704\pi$
$54$		0			0
$55$	6.62620	+	9.87859i	0.893476	+	1.33203i
$56$		−	2.82843i		−	0.377964i
$57$		0			0
$58$	−2.86464	−	2.86464i	−0.376146	−	0.376146i
$59$	2.15401			0.280428			0.140214	−	0.990121i	$-0.455221\pi$
$59$	2.15401			0.280428			0.140214	+	0.990121i	$0.455221\pi$
$60$		0			0
$61$	7.91087			1.01288			0.506442	−	0.862274i	$-0.330961\pi$
$61$	7.91087			1.01288			0.506442	+	0.862274i	$0.330961\pi$
$62$	3.90543	+	3.90543i	0.495990	+	0.495990i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.68264	+	0.528636i	0.332741	+	0.0655692i
$66$		0			0
$67$	4.35548	−	4.35548i	0.532107	−	0.532107i	−0.389092	−	0.921199i	$-0.627211\pi$
$67$	4.35548	−	4.35548i	0.532107	−	0.532107i	0.921199	+	0.389092i	$0.127211\pi$
$68$	−1.41421	+	1.41421i	−0.171499	+	0.171499i
$69$		0			0
$70$	5.25240	−	3.52311i	0.627781	−	0.421093i
$71$		−	8.00229i		−	0.949697i	−0.880068	−	0.474849i	$-0.842503\pi$
$71$		−	8.00229i		−	0.949697i	0.880068	−	0.474849i	$-0.157497\pi$
$72$		0			0
$73$	−8.25240	−	8.25240i	−0.965870	−	0.965870i	0.0335666	−	0.999436i	$-0.489313\pi$
$73$	−8.25240	−	8.25240i	−0.965870	−	0.965870i	−0.999436	+	0.0335666i	$0.989313\pi$
$74$	−8.14807			−0.947194
$75$		0			0
$76$	6.38776			0.732726
$77$	10.6393	+	10.6393i	1.21246	+	1.21246i
$78$		0			0
$79$			8.77551i			0.987322i	0.869654	+	0.493661i	$0.164342\pi$
$79$			8.77551i			0.987322i	−0.869654	+	0.493661i	$0.835658\pi$
$80$	1.85700	−	1.24561i	0.207619	−	0.139263i
$81$		0			0
$82$	8.25240	−	8.25240i	0.911325	−	0.911325i
$83$	2.07125	−	2.07125i	0.227349	−	0.227349i	−0.584235	−	0.811584i	$-0.698605\pi$
$83$	2.07125	−	2.07125i	0.227349	−	0.227349i	0.811584	+	0.584235i	$0.198605\pi$
$84$		0			0
$85$	−4.38776	−	0.864641i	−0.475919	−	0.0937835i
$86$			12.7477i			1.37461i
$87$		0			0
$88$	3.76156	+	3.76156i	0.400983	+	0.400983i
$89$	−9.32521			−0.988471			−0.494235	−	0.869328i	$-0.664552\pi$
$89$	−9.32521			−0.988471			−0.494235	+	0.869328i	$0.664552\pi$
$90$		0			0
$91$	3.45856			0.362556
$92$	−0.707107	−	0.707107i	−0.0737210	−	0.0737210i
$93$		0			0
$94$		−	1.25240i		−	0.129175i
$95$	7.95665	+	11.8621i	0.816335	+	1.21702i
$96$		0			0
$97$	−6.38776	+	6.38776i	−0.648578	+	0.648578i	−0.952649	−	0.304071i	$-0.901654\pi$
$97$	−6.38776	+	6.38776i	−0.648578	+	0.648578i	0.304071	+	0.952649i	$0.401654\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$		0			0
$100$	4.62620	+	1.89692i	0.462620	+	0.189692i
$101$		−	9.41650i		−	0.936977i	−0.883470	−	0.468489i	$-0.844799\pi$
$101$		−	9.41650i		−	0.936977i	0.883470	−	0.468489i	$-0.155201\pi$
$102$		0			0
$103$	6.98168	+	6.98168i	0.687925	+	0.687925i	0.961773	−	0.273848i	$-0.0882965\pi$
$103$	6.98168	+	6.98168i	0.687925	+	0.687925i	−0.273848	+	0.961773i	$0.588296\pi$
$104$	1.22279			0.119904
$105$		0			0
$106$	9.64015			0.936334
$107$	−11.6076	−	11.6076i	−1.12215	−	1.12215i	−0.991417	−	0.130734i	$-0.958267\pi$
$107$	−11.6076	−	11.6076i	−1.12215	−	1.12215i	−0.130734	−	0.991417i	$-0.541733\pi$
$108$		0			0
$109$		−	15.8463i		−	1.51780i	−0.651206	−	0.758901i	$-0.725737\pi$
$109$		−	15.8463i		−	1.51780i	0.651206	−	0.758901i	$-0.274263\pi$
$110$	−2.29979	+	11.6707i	−0.219277	+	1.11275i
$111$		0			0
$112$	2.00000	−	2.00000i	0.188982	−	0.188982i
$113$	8.84222	−	8.84222i	0.831806	−	0.831806i	−0.155957	−	0.987764i	$-0.549846\pi$
$113$	8.84222	−	8.84222i	0.831806	−	0.831806i	0.987764	+	0.155957i	$0.0498463\pi$
$114$		0			0
$115$	0.432320	−	2.19388i	0.0403141	−	0.204580i
$116$		−	4.05121i		−	0.376146i
$117$		0			0
$118$	1.52311	+	1.52311i	0.140214	+	0.140214i
$119$	−5.65685			−0.518563
$120$		0			0
$121$	−17.2986			−1.57260
$122$	5.59383	+	5.59383i	0.506442	+	0.506442i
$123$		0			0
$124$			5.52311i			0.495990i
$125$	2.23986	+	10.9537i	0.200339	+	0.979727i
$126$		0			0
$127$	1.86464	−	1.86464i	0.165460	−	0.165460i	−0.619520	−	0.784981i	$-0.712673\pi$
$127$	1.86464	−	1.86464i	0.165460	−	0.165460i	0.784981	+	0.619520i	$0.212673\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	1.52311	+	2.27072i	0.133586	+	0.199155i
$131$		−	15.5304i		−	1.35690i	−0.734646	−	0.678450i	$-0.762652\pi$
$131$		−	15.5304i		−	1.35690i	0.734646	−	0.678450i	$-0.237348\pi$
$132$		0			0
$133$	12.7755	+	12.7755i	1.10778	+	1.10778i
$134$	6.15958			0.532107
$135$		0			0
$136$	−2.00000			−0.171499
$137$	−1.96258	−	1.96258i	−0.167675	−	0.167675i	0.618282	−	0.785957i	$-0.287829\pi$
$137$	−1.96258	−	1.96258i	−0.167675	−	0.167675i	−0.785957	+	0.618282i	$0.787829\pi$
$138$		0			0
$139$			16.2341i			1.37696i	0.725257	+	0.688478i	$0.241721\pi$
$139$			16.2341i			1.37696i	−0.725257	+	0.688478i	$0.758279\pi$
$140$	6.20522	+	1.22279i	0.524437	+	0.103344i
$141$		0			0
$142$	5.65847	−	5.65847i	0.474849	−	0.474849i
$143$	−4.59958	+	4.59958i	−0.384636	+	0.384636i
$144$		0			0
$145$	7.52311	−	5.04623i	0.624761	−	0.419066i
$146$		−	11.6707i		−	0.965870i
$147$		0			0
$148$	−5.76156	−	5.76156i	−0.473597	−	0.473597i
$149$	−1.39448			−0.114240			−0.0571202	−	0.998367i	$-0.518192\pi$
$149$	−1.39448			−0.114240			−0.0571202	+	0.998367i	$0.518192\pi$
$150$		0			0
$151$	−2.20617			−0.179535			−0.0897677	−	0.995963i	$-0.528612\pi$
$151$	−2.20617			−0.179535			−0.0897677	+	0.995963i	$0.528612\pi$
$152$	4.51683	+	4.51683i	0.366363	+	0.366363i
$153$		0			0
$154$			15.0462i			1.21246i
$155$	−10.2564	+	6.87964i	−0.823817	+	0.552586i
$156$		0			0
$157$	11.5554	−	11.5554i	0.922221	−	0.922221i	−0.0749656	−	0.997186i	$-0.523885\pi$
$157$	11.5554	−	11.5554i	0.922221	−	0.922221i	0.997186	+	0.0749656i	$0.0238847\pi$
$158$	−6.20522	+	6.20522i	−0.493661	+	0.493661i
$159$		0			0
$160$	2.19388	+	0.432320i	0.173441	+	0.0341779i
$161$		−	2.82843i		−	0.222911i
$162$		0			0
$163$	−14.7755	−	14.7755i	−1.15731	−	1.15731i	−0.985052	−	0.172255i	$-0.944895\pi$
$163$	−14.7755	−	14.7755i	−1.15731	−	1.15731i	−0.172255	−	0.985052i	$-0.555105\pi$
$164$	11.6707			0.911325
$165$		0			0
$166$	2.92919			0.227349
$167$	−11.7163	−	11.7163i	−0.906634	−	0.906634i	0.0893648	−	0.995999i	$-0.471516\pi$
$167$	−11.7163	−	11.7163i	−0.906634	−	0.906634i	−0.995999	+	0.0893648i	$0.971516\pi$
$168$		0			0
$169$		−	11.5048i		−	0.884984i
$170$	−2.49122	−	3.71400i	−0.191068	−	0.284851i
$171$		0			0
$172$	−9.01395	+	9.01395i	−0.687307	+	0.687307i
$173$	4.62549	−	4.62549i	0.351670	−	0.351670i	−0.509061	−	0.860731i	$-0.670007\pi$
$173$	4.62549	−	4.62549i	0.351670	−	0.351670i	0.860731	+	0.509061i	$0.170007\pi$
$174$		0			0
$175$	5.45856	+	13.0462i	0.412629	+	0.986202i
$176$			5.31965i			0.400983i
$177$		0			0
$178$	−6.59392	−	6.59392i	−0.494235	−	0.494235i
$179$	−24.8209			−1.85520			−0.927600	−	0.373574i	$-0.878132\pi$
$179$	−24.8209			−1.85520			−0.927600	+	0.373574i	$0.878132\pi$
$180$		0			0
$181$	−14.1816			−1.05411			−0.527055	−	0.849831i	$-0.676704\pi$
$181$	−14.1816			−1.05411			−0.527055	+	0.849831i	$0.676704\pi$
$182$	2.44557	+	2.44557i	0.181278	+	0.181278i
$183$		0			0
$184$		−	1.00000i		−	0.0737210i
$185$	3.52258	−	17.8759i	0.258985	−	1.31426i
$186$		0			0
$187$	7.52311	−	7.52311i	0.550145	−	0.550145i
$188$	0.885578	−	0.885578i	0.0645874	−	0.0645874i
$189$		0			0
$190$	−2.76156	+	14.0140i	−0.200344	+	1.01668i
$191$			2.15401i			0.155859i	0.996959	+	0.0779293i	$0.0248308\pi$
$191$			2.15401i			0.155859i	−0.996959	+	0.0779293i	$0.975169\pi$
$192$		0			0
$193$	−10.7938	−	10.7938i	−0.776957	−	0.776957i	0.202355	−	0.979312i	$-0.435140\pi$
$193$	−10.7938	−	10.7938i	−0.776957	−	0.776957i	−0.979312	+	0.202355i	$0.935140\pi$
$194$	−9.03365			−0.648578
$195$		0			0
$196$	1.00000			0.0714286
$197$	−1.03136	−	1.03136i	−0.0734814	−	0.0734814i	0.669411	−	0.742892i	$-0.266547\pi$
$197$	−1.03136	−	1.03136i	−0.0734814	−	0.0734814i	−0.742892	+	0.669411i	$0.766547\pi$
$198$		0			0
$199$			7.04623i			0.499494i	0.968311	+	0.249747i	$0.0803474\pi$
$199$			7.04623i			0.499494i	−0.968311	+	0.249747i	$0.919653\pi$
$200$	1.92989	+	4.61254i	0.136464	+	0.326156i
$201$		0			0
$202$	6.65847	−	6.65847i	0.468489	−	0.468489i
$203$	8.10243	−	8.10243i	0.568679	−	0.568679i
$204$		0			0
$205$	14.5371	+	21.6724i	1.01531	+	1.51367i
$206$			9.87358i			0.687925i
$207$		0			0
$208$	0.864641	+	0.864641i	0.0599521	+	0.0599521i
$209$	−33.9806			−2.35049
$210$		0			0
$211$	10.2707			0.707065			0.353533	−	0.935422i	$-0.384980\pi$
$211$	10.2707			0.707065			0.353533	+	0.935422i	$0.384980\pi$
$212$	6.81662	+	6.81662i	0.468167	+	0.468167i
$213$		0			0
$214$		−	16.4157i		−	1.12215i
$215$	−27.9668	−	5.51107i	−1.90732	−	0.375852i
$216$		0			0
$217$	−11.0462	+	11.0462i	−0.749867	+	0.749867i
$218$	11.2050	−	11.2050i	0.758901	−	0.758901i
$219$		0			0
$220$	−9.87859	+	6.62620i	−0.666015	+	0.446738i
$221$		−	2.44557i		−	0.164507i
$222$		0			0
$223$	−17.1170	−	17.1170i	−1.14624	−	1.14624i	−0.987286	−	0.158956i	$-0.949187\pi$
$223$	−17.1170	−	17.1170i	−1.14624	−	1.14624i	−0.158956	−	0.987286i	$-0.550813\pi$
$224$	2.82843			0.188982
$225$		0			0
$226$	12.5048			0.831806
$227$	1.47724	+	1.47724i	0.0980477	+	0.0980477i	0.754429	−	0.656381i	$-0.227914\pi$
$227$	1.47724	+	1.47724i	0.0980477	+	0.0980477i	−0.656381	+	0.754429i	$0.727914\pi$
$228$		0			0
$229$			24.6864i			1.63132i	0.578530	+	0.815661i	$0.303626\pi$
$229$			24.6864i			1.63132i	−0.578530	+	0.815661i	$0.696374\pi$
$230$	1.85700	−	1.24561i	0.122447	−	0.0821330i
$231$		0			0
$232$	2.86464	−	2.86464i	0.188073	−	0.188073i
$233$	−8.69644	+	8.69644i	−0.569723	+	0.569723i	−0.932051	−	0.362328i	$-0.881982\pi$
$233$	−8.69644	+	8.69644i	−0.569723	+	0.569723i	0.362328	+	0.932051i	$0.381982\pi$
$234$		0			0
$235$	2.74760	+	0.541436i	0.179234	+	0.0353194i
$236$			2.15401i			0.140214i
$237$		0			0
$238$	−4.00000	−	4.00000i	−0.259281	−	0.259281i
$239$	5.75699			0.372389			0.186194	−	0.982513i	$-0.440385\pi$
$239$	5.75699			0.372389			0.186194	+	0.982513i	$0.440385\pi$
$240$		0			0
$241$	15.1878			0.978335			0.489168	−	0.872190i	$-0.337301\pi$
$241$	15.1878			0.978335			0.489168	+	0.872190i	$0.337301\pi$
$242$	−12.2320	−	12.2320i	−0.786301	−	0.786301i
$243$		0			0
$244$			7.91087i			0.506442i
$245$	1.24561	+	1.85700i	0.0795790	+	0.118640i
$246$		0			0
$247$	−5.52311	+	5.52311i	−0.351427	+	0.351427i
$248$	−3.90543	+	3.90543i	−0.247995	+	0.247995i
$249$		0			0
$250$	−6.16160	+	9.32924i	−0.389694	+	0.590033i
$251$		−	2.87407i		−	0.181410i	−0.995878	−	0.0907049i	$-0.971088\pi$
$251$		−	2.87407i		−	0.181410i	0.995878	−	0.0907049i	$-0.0289120\pi$
$252$		0			0
$253$	3.76156	+	3.76156i	0.236487	+	0.236487i
$254$	2.63700			0.165460
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.4677	+	13.4677i	0.840093	+	0.840093i	0.988871	−	0.148778i	$-0.0475338\pi$
$257$	13.4677	+	13.4677i	0.840093	+	0.840093i	−0.148778	+	0.988871i	$0.547534\pi$
$258$		0			0
$259$		−	23.0462i		−	1.43202i
$260$	−0.528636	+	2.68264i	−0.0327846	+	0.166371i
$261$		0			0
$262$	10.9817	−	10.9817i	0.678450	−	0.678450i
$263$	−16.4617	+	16.4617i	−1.01507	+	1.01507i	−0.0151847	+	0.999885i	$0.504834\pi$
$263$	−16.4617	+	16.4617i	−1.01507	+	1.01507i	−0.999885	+	0.0151847i	$0.995166\pi$
$264$		0			0
$265$	−4.16763	+	21.1493i	−0.256016	+	1.29919i
$266$			18.0673i			1.10778i
$267$		0			0
$268$	4.35548	+	4.35548i	0.266053	+	0.266053i
$269$	23.5981			1.43880			0.719401	−	0.694595i	$-0.244416\pi$
$269$	23.5981			1.43880			0.719401	+	0.694595i	$0.244416\pi$
$270$		0			0
$271$	17.5510			1.06615			0.533074	−	0.846068i	$-0.321037\pi$
$271$	17.5510			1.06615			0.533074	+	0.846068i	$0.321037\pi$
$272$	−1.41421	−	1.41421i	−0.0857493	−	0.0857493i
$273$		0			0
$274$		−	2.77551i		−	0.167675i
$275$	−24.6097	−	10.0909i	−1.48402	−	0.608505i
$276$		0			0
$277$	15.1633	−	15.1633i	0.911072	−	0.911072i	−0.0852843	−	0.996357i	$-0.527180\pi$
$277$	15.1633	−	15.1633i	0.911072	−	0.911072i	0.996357	+	0.0852843i	$0.0271799\pi$
$278$	−11.4792	+	11.4792i	−0.688478	+	0.688478i
$279$		0			0
$280$	3.52311	+	5.25240i	0.210546	+	0.313891i
$281$			14.3989i			0.858969i	0.903074	+	0.429484i	$0.141305\pi$
$281$			14.3989i			0.858969i	−0.903074	+	0.429484i	$0.858695\pi$
$282$		0			0
$283$	6.14931	+	6.14931i	0.365539	+	0.365539i	0.865847	−	0.500309i	$-0.166780\pi$
$283$	6.14931	+	6.14931i	0.365539	+	0.365539i	−0.500309	+	0.865847i	$0.666780\pi$
$284$	8.00229			0.474849
$285$		0			0
$286$	−6.50479			−0.384636
$287$	23.3413	+	23.3413i	1.37779	+	1.37779i
$288$		0			0
$289$		−	13.0000i		−	0.764706i
$290$	8.88787	+	1.75142i	0.521914	+	0.102847i
$291$		0			0
$292$	8.25240	−	8.25240i	0.482935	−	0.482935i
$293$	6.31389	−	6.31389i	0.368862	−	0.368862i	−0.498200	−	0.867062i	$-0.666006\pi$
$293$	6.31389	−	6.31389i	0.368862	−	0.368862i	0.867062	+	0.498200i	$0.166006\pi$
$294$		0			0
$295$	−4.00000	+	2.68305i	−0.232889	+	0.156213i
$296$		−	8.14807i		−	0.473597i
$297$		0			0
$298$	−0.986047	−	0.986047i	−0.0571202	−	0.0571202i
$299$	1.22279			0.0707156
$300$		0			0
$301$	−36.0558			−2.07822
$302$	−1.56000	−	1.56000i	−0.0897677	−	0.0897677i
$303$		0			0
$304$			6.38776i			0.366363i
$305$	−14.6905	+	9.85385i	−0.841176	+	0.564230i
$306$		0			0
$307$	−9.72928	+	9.72928i	−0.555279	+	0.555279i	−0.927960	−	0.372680i	$-0.878439\pi$
$307$	−9.72928	+	9.72928i	−0.555279	+	0.555279i	0.372680	+	0.927960i	$0.378439\pi$
$308$	−10.6393	+	10.6393i	−0.606230	+	0.606230i
$309$		0			0
$310$	−12.1170	−	2.38776i	−0.688201	−	0.135615i
$311$			23.1499i			1.31271i	0.754453	+	0.656354i	$0.227902\pi$
$311$			23.1499i			1.31271i	−0.754453	+	0.656354i	$0.772098\pi$
$312$		0			0
$313$	6.65847	+	6.65847i	0.376359	+	0.376359i	0.869787	−	0.493428i	$-0.164256\pi$
$313$	6.65847	+	6.65847i	0.376359	+	0.376359i	−0.493428	+	0.869787i	$0.664256\pi$
$314$	16.3418			0.922221
$315$		0			0
$316$	−8.77551			−0.493661
$317$	0.100138	+	0.100138i	0.00562431	+	0.00562431i	0.709913	−	0.704289i	$-0.248734\pi$
$317$	0.100138	+	0.100138i	0.00562431	+	0.00562431i	−0.704289	+	0.709913i	$0.748734\pi$
$318$		0			0
$319$			21.5510i			1.20663i
$320$	1.24561	+	1.85700i	0.0696317	+	0.103810i
$321$		0			0
$322$	2.00000	−	2.00000i	0.111456	−	0.111456i
$323$	9.03365	−	9.03365i	0.502646	−	0.502646i
$324$		0			0
$325$	−5.64015	+	2.35985i	−0.312859	+	0.130901i
$326$		−	20.8957i		−	1.15731i
$327$		0			0
$328$	8.25240	+	8.25240i	0.455662	+	0.455662i
$329$	3.54231			0.195294
$330$		0			0
$331$	20.7755			1.14193			0.570963	−	0.820976i	$-0.306570\pi$
$331$	20.7755			1.14193			0.570963	+	0.820976i	$0.306570\pi$
$332$	2.07125	+	2.07125i	0.113675	+	0.113675i
$333$		0			0
$334$		−	16.5693i		−	0.906634i
$335$	−2.66291	+	13.5134i	−0.145490	+	0.738314i
$336$		0			0
$337$	−7.64015	+	7.64015i	−0.416186	+	0.416186i	−0.883887	−	0.467701i	$-0.845082\pi$
$337$	−7.64015	+	7.64015i	−0.416186	+	0.416186i	0.467701	+	0.883887i	$0.345082\pi$
$338$	8.13512	−	8.13512i	0.442492	−	0.442492i
$339$		0			0
$340$	0.864641	−	4.38776i	0.0468917	−	0.237959i
$341$		−	29.3810i		−	1.59107i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−12.7477			−0.687307
$345$		0			0
$346$	6.54144			0.351670
$347$	6.87964	+	6.87964i	0.369318	+	0.369318i	0.867229	−	0.497910i	$-0.165899\pi$
$347$	6.87964	+	6.87964i	0.369318	+	0.369318i	−0.497910	+	0.867229i	$0.665899\pi$
$348$		0			0
$349$		−	16.0925i		−	0.861409i	−0.902493	−	0.430705i	$-0.858265\pi$
$349$		−	16.0925i		−	0.861409i	0.902493	−	0.430705i	$-0.141735\pi$
$350$	−5.36529	+	13.0849i	−0.286787	+	0.699415i
$351$		0			0
$352$	−3.76156	+	3.76156i	−0.200492	+	0.200492i
$353$	5.12822	−	5.12822i	0.272948	−	0.272948i	−0.557338	−	0.830286i	$-0.688177\pi$
$353$	5.12822	−	5.12822i	0.272948	−	0.272948i	0.830286	+	0.557338i	$0.188177\pi$
$354$		0			0
$355$	9.96772	+	14.8603i	0.529032	+	0.788701i
$356$		−	9.32521i		−	0.494235i
$357$		0			0
$358$	−17.5510	−	17.5510i	−0.927600	−	0.927600i
$359$	−2.15401			−0.113684			−0.0568421	−	0.998383i	$-0.518103\pi$
$359$	−2.15401			−0.113684			−0.0568421	+	0.998383i	$0.518103\pi$
$360$		0			0
$361$	−21.8034			−1.14755
$362$	−10.0279	−	10.0279i	−0.527055	−	0.527055i
$363$		0			0
$364$			3.45856i			0.181278i
$365$	25.6040	+	5.04546i	1.34017	+	0.264091i
$366$		0			0
$367$	−11.5510	+	11.5510i	−0.602958	+	0.602958i	−0.941096	−	0.338138i	$-0.890203\pi$
$367$	−11.5510	+	11.5510i	−0.602958	+	0.602958i	0.338138	+	0.941096i	$0.390203\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$		0			0
$370$	15.1310	−	10.1493i	0.786623	−	0.527638i
$371$			27.2665i			1.41560i
$372$		0			0
$373$	−19.5554	−	19.5554i	−1.01254	−	1.01254i	−0.999920	−	0.0126193i	$-0.995983\pi$
$373$	−19.5554	−	19.5554i	−1.01254	−	1.01254i	−0.0126193	−	0.999920i	$-0.504017\pi$
$374$	10.6393			0.550145
$375$		0			0
$376$	1.25240			0.0645874
$377$	3.50285	+	3.50285i	0.180406	+	0.180406i
$378$		0			0
$379$		−	28.9571i		−	1.48743i	−0.668499	−	0.743713i	$-0.733063\pi$
$379$		−	28.9571i		−	1.48743i	0.668499	−	0.743713i	$-0.266937\pi$
$380$	−11.8621	+	7.95665i	−0.608512	+	0.408167i
$381$		0			0
$382$	−1.52311	+	1.52311i	−0.0779293	+	0.0779293i
$383$	−14.0161	+	14.0161i	−0.716189	+	0.716189i	−0.967822	−	0.251634i	$-0.919032\pi$
$383$	−14.0161	+	14.0161i	−0.716189	+	0.716189i	0.251634	+	0.967822i	$0.419032\pi$
$384$		0			0
$385$	−33.0096	−	6.50479i	−1.68232	−	0.331515i
$386$		−	15.2648i		−	0.776957i
$387$		0			0
$388$	−6.38776	−	6.38776i	−0.324289	−	0.324289i
$389$	−3.03959			−0.154113			−0.0770566	−	0.997027i	$-0.524552\pi$
$389$	−3.03959			−0.154113			−0.0770566	+	0.997027i	$0.524552\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$		0			0
$394$		−	1.45856i		−	0.0734814i
$395$	−10.9309	−	16.2961i	−0.549991	−	0.819948i
$396$		0			0
$397$	−10.0525	+	10.0525i	−0.504520	+	0.504520i	−0.912839	−	0.408319i	$-0.866115\pi$
$397$	−10.0525	+	10.0525i	−0.504520	+	0.504520i	0.408319	+	0.912839i	$0.366115\pi$
$398$	−4.98244	+	4.98244i	−0.249747	+	0.249747i
$399$		0			0
$400$	−1.89692	+	4.62620i	−0.0948458	+	0.231310i
$401$		−	4.52536i		−	0.225985i	−0.993596	−	0.112993i	$-0.963956\pi$
$401$		−	4.52536i		−	0.225985i	0.993596	−	0.112993i	$-0.0360437\pi$
$402$		0			0
$403$	−4.77551	−	4.77551i	−0.237885	−	0.237885i
$404$	9.41650			0.468489
$405$		0			0
$406$	11.4586			0.568679
$407$	30.6494	+	30.6494i	1.51924	+	1.51924i
$408$		0			0
$409$			0.917127i			0.0453490i	0.999743	+	0.0226745i	$0.00721814\pi$
$409$			0.917127i			0.0453490i	−0.999743	+	0.0226745i	$0.992782\pi$
$410$	−5.04546	+	25.6040i	−0.249178	+	1.26449i
$411$		0			0
$412$	−6.98168	+	6.98168i	−0.343963	+	0.343963i
$413$	−4.30802	+	4.30802i	−0.211984	+	0.211984i
$414$		0			0
$415$	−1.26635	+	6.42629i	−0.0621626	+	0.315454i
$416$			1.22279i			0.0599521i
$417$		0			0
$418$	−24.0279	−	24.0279i	−1.17524	−	1.17524i
$419$	3.80529			0.185901			0.0929504	−	0.995671i	$-0.470370\pi$
$419$	3.80529			0.185901			0.0929504	+	0.995671i	$0.470370\pi$
$420$		0			0
$421$	−4.80009			−0.233942			−0.116971	−	0.993135i	$-0.537318\pi$
$421$	−4.80009			−0.233942			−0.116971	+	0.993135i	$0.537318\pi$
$422$	7.26249	+	7.26249i	0.353533	+	0.353533i
$423$		0			0
$424$			9.64015i			0.468167i
$425$	9.22508	−	3.85979i	0.447482	−	0.187227i
$426$		0			0
$427$	−15.8217	+	15.8217i	−0.765668	+	0.765668i
$428$	11.6076	−	11.6076i	0.561076	−	0.561076i
$429$		0			0
$430$	−15.8786	−	23.6724i	−0.765734	−	1.14159i
$431$		−	11.0221i		−	0.530918i	−0.964122	−	0.265459i	$-0.914477\pi$
$431$		−	11.0221i		−	0.530918i	0.964122	−	0.265459i	$-0.0855235\pi$
$432$		0			0
$433$	15.3415	+	15.3415i	0.737267	+	0.737267i	0.972048	−	0.234781i	$-0.0754375\pi$
$433$	15.3415	+	15.3415i	0.737267	+	0.737267i	−0.234781	+	0.972048i	$0.575437\pi$
$434$	−15.6217			−0.749867
$435$		0			0
$436$	15.8463			0.758901
$437$	4.51683	+	4.51683i	0.216069	+	0.216069i
$438$		0			0
$439$			5.22449i			0.249351i	0.992198	+	0.124676i	$0.0397890\pi$
$439$			5.22449i			0.249351i	−0.992198	+	0.124676i	$0.960211\pi$
$440$	−11.6707	−	2.29979i	−0.556376	−	0.109638i
$441$		0			0
$442$	1.72928	−	1.72928i	0.0822535	−	0.0822535i
$443$	14.7818	−	14.7818i	0.702304	−	0.702304i	−0.262600	−	0.964905i	$-0.584580\pi$
$443$	14.7818	−	14.7818i	0.702304	−	0.702304i	0.964905	+	0.262600i	$0.0845801\pi$
$444$		0			0
$445$	17.3169	−	11.6156i	0.820902	−	0.550631i
$446$		−	24.2071i		−	1.14624i
$447$		0			0
$448$	2.00000	+	2.00000i	0.0944911	+	0.0944911i
$449$	−40.3772			−1.90552			−0.952760	−	0.303724i	$-0.901770\pi$
$449$	−40.3772			−1.90552			−0.952760	+	0.303724i	$0.901770\pi$
$450$		0			0
$451$	−62.0837			−2.92341
$452$	8.84222	+	8.84222i	0.415903	+	0.415903i
$453$		0			0
$454$			2.08913i			0.0980477i
$455$	−6.42256	+	4.30802i	−0.301094	+	0.201963i
$456$		0			0
$457$	21.8463	−	21.8463i	1.02193	−	1.02193i	0.0221736	−	0.999754i	$-0.492941\pi$
$457$	21.8463	−	21.8463i	1.02193	−	1.02193i	0.999754	−	0.0221736i	$-0.00705864\pi$
$458$	−17.4559	+	17.4559i	−0.815661	+	0.815661i
$459$		0			0
$460$	2.19388	+	0.432320i	0.102290	+	0.0201570i
$461$		−	22.1185i		−	1.03016i	−0.857142	−	0.515081i	$-0.827762\pi$
$461$		−	22.1185i		−	1.03016i	0.857142	−	0.515081i	$-0.172238\pi$
$462$		0			0
$463$	−11.3878	−	11.3878i	−0.529234	−	0.529234i	0.391110	−	0.920344i	$-0.372091\pi$
$463$	−11.3878	−	11.3878i	−0.529234	−	0.529234i	−0.920344	+	0.391110i	$0.872091\pi$
$464$	4.05121			0.188073
$465$		0			0
$466$	−12.2986			−0.569723
$467$	16.7618	+	16.7618i	0.775642	+	0.775642i	0.979086	−	0.203445i	$-0.0652138\pi$
$467$	16.7618	+	16.7618i	0.775642	+	0.775642i	−0.203445	+	0.979086i	$0.565214\pi$
$468$		0			0
$469$			17.4219i			0.804469i
$470$	1.56000	+	2.32570i	0.0719572	+	0.107277i
$471$		0			0
$472$	−1.52311	+	1.52311i	−0.0701070	+	0.0701070i
$473$	47.9510	−	47.9510i	2.20479	−	2.20479i
$474$		0			0
$475$	−29.5510	−	12.1170i	−1.35589	−	0.555968i
$476$		−	5.65685i		−	0.259281i
$477$		0			0
$478$	4.07081	+	4.07081i	0.186194	+	0.186194i
$479$	−13.1762			−0.602034			−0.301017	−	0.953619i	$-0.597326\pi$
$479$	−13.1762			−0.602034			−0.301017	+	0.953619i	$0.597326\pi$
$480$		0			0
$481$	9.96336			0.454290
$482$	10.7394	+	10.7394i	0.489168	+	0.489168i
$483$		0			0
$484$		−	17.2986i		−	0.786301i
$485$	3.90543	−	19.8187i	0.177337	−	0.899922i
$486$		0			0
$487$	11.6864	−	11.6864i	0.529560	−	0.529560i	−0.390881	−	0.920441i	$-0.627830\pi$
$487$	11.6864	−	11.6864i	0.529560	−	0.529560i	0.920441	+	0.390881i	$0.127830\pi$
$488$	−5.59383	+	5.59383i	−0.253221	+	0.253221i
$489$		0			0
$490$	−0.432320	+	2.19388i	−0.0195302	+	0.0991093i
$491$			33.3062i			1.50309i	0.659684	+	0.751543i	$0.270690\pi$
$491$			33.3062i			1.50309i	−0.659684	+	0.751543i	$0.729310\pi$
$492$		0			0
$493$	−5.72928	−	5.72928i	−0.258034	−	0.258034i
$494$	−7.81086			−0.351427
$495$		0			0
$496$	−5.52311			−0.247995
$497$	16.0046	+	16.0046i	0.717904	+	0.717904i
$498$		0			0
$499$			35.0462i			1.56888i	0.620202	+	0.784442i	$0.287051\pi$
$499$			35.0462i			1.56888i	−0.620202	+	0.784442i	$0.712949\pi$
$500$	−10.9537	+	2.23986i	−0.489863	+	0.100169i
$501$		0			0
$502$	2.03228	−	2.03228i	0.0907049	−	0.0907049i
$503$	−18.9072	+	18.9072i	−0.843032	+	0.843032i	−0.989252	−	0.146220i	$-0.953289\pi$
$503$	−18.9072	+	18.9072i	−0.843032	+	0.843032i	0.146220	+	0.989252i	$0.453289\pi$
$504$		0			0
$505$	11.7293	+	17.4865i	0.521946	+	0.778138i
$506$			5.31965i			0.236487i
$507$		0			0
$508$	1.86464	+	1.86464i	0.0827301	+	0.0827301i
$509$	−16.1306			−0.714978			−0.357489	−	0.933917i	$-0.616367\pi$
$509$	−16.1306			−0.714978			−0.357489	+	0.933917i	$0.616367\pi$
$510$		0			0
$511$	33.0096			1.46026
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			19.0462i			0.840093i
$515$	−21.6614	−	4.26855i	−0.954517	−	0.188095i
$516$		0			0
$517$	−4.71096	+	4.71096i	−0.207188	+	0.207188i
$518$	16.2961	−	16.2961i	0.716011	−	0.716011i
$519$		0			0
$520$	−2.27072	+	1.52311i	−0.0995776	+	0.0667930i
$521$		−	35.2034i		−	1.54229i	−0.636661	−	0.771144i	$-0.719685\pi$
$521$		−	35.2034i		−	1.54229i	0.636661	−	0.771144i	$-0.280315\pi$
$522$		0			0
$523$	0.302994	+	0.302994i	0.0132490	+	0.0132490i	0.713700	−	0.700451i	$-0.247018\pi$
$523$	0.302994	+	0.302994i	0.0132490	+	0.0132490i	−0.700451	+	0.713700i	$0.747018\pi$
$524$	15.5304			0.678450
$525$		0			0
$526$	−23.2803			−1.01507
$527$	7.81086	+	7.81086i	0.340247	+	0.340247i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	−17.9018	+	12.0079i	−0.777604	+	0.521588i
$531$		0			0
$532$	−12.7755	+	12.7755i	−0.553889	+	0.553889i
$533$	−10.0909	+	10.0909i	−0.437086	+	0.437086i
$534$		0			0
$535$	36.0140	+	7.09683i	1.55702	+	0.306823i
$536$			6.15958i			0.266053i
$537$		0			0
$538$	16.6864	+	16.6864i	0.719401	+	0.719401i
$539$	−5.31965			−0.229133
$540$		0			0
$541$	−12.9171			−0.555351			−0.277675	−	0.960675i	$-0.589564\pi$
$541$	−12.9171			−0.555351			−0.277675	+	0.960675i	$0.589564\pi$
$542$	12.4104	+	12.4104i	0.533074	+	0.533074i
$543$		0			0
$544$		−	2.00000i		−	0.0857493i
$545$	19.7383	+	29.4267i	0.845497	+	1.26050i
$546$		0			0
$547$	20.0279	−	20.0279i	0.856331	−	0.856331i	−0.134572	−	0.990904i	$-0.542966\pi$
$547$	20.0279	−	20.0279i	0.856331	−	0.856331i	0.990904	+	0.134572i	$0.0429661\pi$
$548$	1.96258	−	1.96258i	0.0838374	−	0.0838374i
$549$		0			0
$550$	−10.2663	−	24.5371i	−0.437759	−	1.04626i
$551$			25.8782i			1.10245i
$552$		0			0
$553$	−17.5510	−	17.5510i	−0.746345	−	0.746345i
$554$	21.4441			0.911072
$555$		0			0
$556$	−16.2341			−0.688478
$557$	29.5639	+	29.5639i	1.25266	+	1.25266i	0.954522	+	0.298141i	$0.0963666\pi$
$557$	29.5639	+	29.5639i	1.25266	+	1.25266i	0.298141	+	0.954522i	$0.403633\pi$
$558$		0			0
$559$		−	15.5877i		−	0.659288i
$560$	−1.22279	+	6.20522i	−0.0516722	+	0.262219i
$561$		0			0
$562$	−10.1816	+	10.1816i	−0.429484	+	0.429484i
$563$	21.8184	−	21.8184i	0.919537	−	0.919537i	−0.0774588	−	0.996996i	$-0.524681\pi$
$563$	21.8184	−	21.8184i	0.919537	−	0.919537i	0.996996	+	0.0774588i	$0.0246806\pi$
$564$		0			0
$565$	−5.40608	+	27.4340i	−0.227435	+	1.15416i
$566$			8.69644i			0.365539i
$567$		0			0
$568$	5.65847	+	5.65847i	0.237424	+	0.237424i
$569$	−22.4101			−0.939479			−0.469740	−	0.882805i	$-0.655652\pi$
$569$	−22.4101			−0.939479			−0.469740	+	0.882805i	$0.655652\pi$
$570$		0			0
$571$	−37.9109			−1.58652			−0.793260	−	0.608883i	$-0.791618\pi$
$571$	−37.9109			−1.58652			−0.793260	+	0.608883i	$0.791618\pi$
$572$	−4.59958	−	4.59958i	−0.192318	−	0.192318i
$573$		0			0
$574$			33.0096i			1.37779i
$575$	1.92989	+	4.61254i	0.0804821	+	0.192356i
$576$		0			0
$577$	−10.9634	+	10.9634i	−0.456410	+	0.456410i	−0.897475	−	0.441065i	$-0.854601\pi$
$577$	−10.9634	+	10.9634i	−0.456410	+	0.456410i	0.441065	+	0.897475i	$0.354601\pi$
$578$	9.19239	−	9.19239i	0.382353	−	0.382353i
$579$		0			0
$580$	5.04623	+	7.52311i	0.209533	+	0.312380i
$581$			8.28501i			0.343720i
$582$		0			0
$583$	−36.2620	−	36.2620i	−1.50182	−	1.50182i
$584$	11.6707			0.482935
$585$		0			0
$586$	8.92919			0.368862
$587$	5.65685	+	5.65685i	0.233483	+	0.233483i	0.814145	−	0.580662i	$-0.197206\pi$
$587$	5.65685	+	5.65685i	0.233483	+	0.233483i	−0.580662	+	0.814145i	$0.697206\pi$
$588$		0			0
$589$		−	35.2803i		−	1.45370i
$590$	−4.72563	−	0.931222i	−0.194551	−	0.0383378i
$591$		0			0
$592$	5.76156	−	5.76156i	0.236799	−	0.236799i
$593$	−7.81086	+	7.81086i	−0.320754	+	0.320754i	−0.849056	−	0.528303i	$-0.822829\pi$
$593$	−7.81086	+	7.81086i	−0.320754	+	0.320754i	0.528303	+	0.849056i	$0.322829\pi$
$594$		0			0
$595$	10.5048	−	7.04623i	0.430654	−	0.288867i
$596$		−	1.39448i		−	0.0571202i
$597$		0			0
$598$	0.864641	+	0.864641i	0.0353578	+	0.0353578i
$599$	45.6165			1.86384			0.931919	−	0.362665i	$-0.118133\pi$
$599$	45.6165			1.86384			0.931919	+	0.362665i	$0.118133\pi$
$600$		0			0
$601$	4.29862			0.175345			0.0876723	−	0.996149i	$-0.472057\pi$
$601$	4.29862			0.175345			0.0876723	+	0.996149i	$0.472057\pi$
$602$	−25.4953	−	25.4953i	−1.03911	−	1.03911i
$603$		0			0
$604$		−	2.20617i		−	0.0897677i
$605$	32.1236	−	21.5473i	1.30601	−	0.876023i
$606$		0			0
$607$	1.08913	−	1.08913i	0.0442064	−	0.0442064i	−0.684658	−	0.728864i	$-0.740048\pi$
$607$	1.08913	−	1.08913i	0.0442064	−	0.0442064i	0.728864	+	0.684658i	$0.240048\pi$
$608$	−4.51683	+	4.51683i	−0.183181	+	0.183181i
$609$		0			0
$610$	−17.3555	−	3.42003i	−0.702703	−	0.138473i
$611$			1.53141i			0.0619544i
$612$		0			0
$613$	−4.17722	−	4.17722i	−0.168716	−	0.168716i	0.617699	−	0.786415i	$-0.288065\pi$
$613$	−4.17722	−	4.17722i	−0.168716	−	0.168716i	−0.786415	+	0.617699i	$0.788065\pi$
$614$	−13.7593			−0.555279
$615$		0			0
$616$	−15.0462			−0.606230
$617$	−12.8934	−	12.8934i	−0.519070	−	0.519070i	0.398220	−	0.917290i	$-0.369628\pi$
$617$	−12.8934	−	12.8934i	−0.519070	−	0.519070i	−0.917290	+	0.398220i	$0.869628\pi$
$618$		0			0
$619$			21.5631i			0.866694i	0.901227	+	0.433347i	$0.142667\pi$
$619$			21.5631i			0.866694i	−0.901227	+	0.433347i	$0.857333\pi$
$620$	−6.87964	−	10.2564i	−0.276293	−	0.411908i
$621$		0			0
$622$	−16.3694	+	16.3694i	−0.656354	+	0.656354i
$623$	18.6504	−	18.6504i	0.747214	−	0.747214i
$624$		0			0
$625$	−17.8034	−	17.5510i	−0.712137	−	0.702041i
$626$			9.41650i			0.376359i
$627$		0			0
$628$	11.5554	+	11.5554i	0.461110	+	0.461110i
$629$	−16.2961			−0.649770
$630$		0			0
$631$	−23.5877			−0.939010			−0.469505	−	0.882930i	$-0.655568\pi$
$631$	−23.5877			−0.939010			−0.469505	+	0.882930i	$0.655568\pi$
$632$	−6.20522	−	6.20522i	−0.246831	−	0.246831i
$633$		0			0
$634$			0.141617i			0.00562431i
$635$	−1.14003	+	5.78526i	−0.0452407	+	0.229581i
$636$		0			0
$637$	−0.864641	+	0.864641i	−0.0342583	+	0.0342583i
$638$	−15.2389	+	15.2389i	−0.603313	+	0.603313i
$639$		0			0
$640$	−0.432320	+	2.19388i	−0.0170890	+	0.0867206i
$641$		−	22.9755i		−	0.907478i	−0.891135	−	0.453739i	$-0.850090\pi$
$641$		−	22.9755i		−	0.907478i	0.891135	−	0.453739i	$-0.149910\pi$
$642$		0			0
$643$	25.3651	+	25.3651i	1.00030	+	1.00030i	1.00000		0.000300538i	$9.56641e-5\pi$
$643$	25.3651	+	25.3651i	1.00030	+	1.00030i	0.000300538		1.00000i	$0.499904\pi$
$644$	2.82843			0.111456
$645$		0			0
$646$	12.7755			0.502646
$647$	−8.09358	−	8.09358i	−0.318191	−	0.318191i	0.529881	−	0.848072i	$-0.322237\pi$
$647$	−8.09358	−	8.09358i	−0.318191	−	0.318191i	−0.848072	+	0.529881i	$0.822237\pi$
$648$		0			0
$649$		−	11.4586i		−	0.449788i
$650$	−5.65685	−	2.31952i	−0.221880	−	0.0909792i
$651$		0			0
$652$	14.7755	−	14.7755i	0.578654	−	0.578654i
$653$	−9.13379	+	9.13379i	−0.357433	+	0.357433i	−0.862866	−	0.505433i	$-0.831333\pi$
$653$	−9.13379	+	9.13379i	−0.357433	+	0.357433i	0.505433	+	0.862866i	$0.331333\pi$
$654$		0			0
$655$	19.3449	+	28.8401i	0.755866	+	1.12687i
$656$			11.6707i			0.455662i
$657$		0			0
$658$	2.50479	+	2.50479i	0.0976470	+	0.0976470i
$659$	2.27388			0.0885778			0.0442889	−	0.999019i	$-0.485898\pi$
$659$	2.27388			0.0885778			0.0442889	+	0.999019i	$0.485898\pi$
$660$		0			0
$661$	20.9850			0.816222			0.408111	−	0.912932i	$-0.366188\pi$
$661$	20.9850			0.816222			0.408111	+	0.912932i	$0.366188\pi$
$662$	14.6905	+	14.6905i	0.570963	+	0.570963i
$663$		0			0
$664$			2.92919i			0.113675i
$665$	−39.6374	−	7.81086i	−1.53707	−	0.302892i
$666$		0			0
$667$	2.86464	−	2.86464i	0.110919	−	0.110919i
$668$	11.7163	−	11.7163i	0.453317	−	0.453317i
$669$		0			0
$670$	−11.4384	+	7.67243i	−0.441902	+	0.296412i
$671$		−	42.0830i		−	1.62460i
$672$		0			0
$673$	−10.5877	−	10.5877i	−0.408125	−	0.408125i	0.472960	−	0.881084i	$-0.343186\pi$
$673$	−10.5877	−	10.5877i	−0.408125	−	0.408125i	−0.881084	+	0.472960i	$0.843186\pi$
$674$	−10.8048			−0.416186
$675$		0			0
$676$	11.5048			0.442492
$677$	−14.8734	−	14.8734i	−0.571631	−	0.571631i	0.360953	−	0.932584i	$-0.382452\pi$
$677$	−14.8734	−	14.8734i	−0.571631	−	0.571631i	−0.932584	+	0.360953i	$0.882452\pi$
$678$		0			0
$679$		−	25.5510i		−	0.980558i
$680$	3.71400	−	2.49122i	0.142426	−	0.0955339i
$681$		0			0
$682$	20.7755	−	20.7755i	0.795535	−	0.795535i
$683$	12.4104	−	12.4104i	0.474873	−	0.474873i	−0.428615	−	0.903487i	$-0.640998\pi$
$683$	12.4104	−	12.4104i	0.474873	−	0.474873i	0.903487	+	0.428615i	$0.140998\pi$
$684$		0			0
$685$	6.08913	+	1.19991i	0.232654	+	0.0458462i
$686$		−	16.9706i		−	0.647939i
$687$		0			0
$688$	−9.01395	−	9.01395i	−0.343654	−	0.343654i
$689$	−11.7879			−0.449081
$690$		0			0
$691$	−14.9171			−0.567474			−0.283737	−	0.958902i	$-0.591574\pi$
$691$	−14.9171			−0.567474			−0.283737	+	0.958902i	$0.591574\pi$
$692$	4.62549	+	4.62549i	0.175835	+	0.175835i
$693$		0			0
$694$			9.72928i			0.369318i
$695$	−20.2213	−	30.1467i	−0.767038	−	1.14353i
$696$		0			0
$697$	16.5048	−	16.5048i	0.625164	−	0.625164i
$698$	11.3791	−	11.3791i	0.430705	−	0.430705i
$699$		0			0
$700$	−13.0462	+	5.45856i	−0.493101	+	0.206314i
$701$		−	4.84550i		−	0.183012i	−0.995805	−	0.0915061i	$-0.970832\pi$
$701$		−	4.84550i		−	0.183012i	0.995805	−	0.0915061i	$-0.0291681\pi$
$702$		0			0
$703$	36.8034	+	36.8034i	1.38807	+	1.38807i
$704$	−5.31965			−0.200492
$705$		0			0
$706$	7.25240			0.272948
$707$	18.8330	+	18.8330i	0.708288	+	0.708288i
$708$		0			0
$709$		−	40.3232i		−	1.51437i	−0.653201	−	0.757185i	$-0.726574\pi$
$709$		−	40.3232i		−	1.51437i	0.653201	−	0.757185i	$-0.273426\pi$
$710$	−3.45955	+	17.5560i	−0.129835	+	0.658867i
$711$		0			0
$712$	6.59392	−	6.59392i	0.247118	−	0.247118i
$713$	−3.90543	+	3.90543i	−0.146260	+	0.146260i
$714$		0			0
$715$	2.81215	−	14.2707i	0.105169	−	0.533695i
$716$		−	24.8209i		−	0.927600i
$717$		0			0
$718$	−1.52311	−	1.52311i	−0.0568421	−	0.0568421i
$719$	17.8364			0.665186			0.332593	−	0.943071i	$-0.392077\pi$
$719$	17.8364			0.665186			0.332593	+	0.943071i	$0.392077\pi$
$720$		0			0
$721$	−27.9267			−1.04005
$722$	−15.4173	−	15.4173i	−0.573774	−	0.573774i
$723$		0			0
$724$		−	14.1816i		−	0.527055i
$725$	−7.68481	+	18.7417i	−0.285407	+	0.696050i
$726$		0			0
$727$	−25.1387	+	25.1387i	−0.932342	+	0.932342i	−0.997852	−	0.0655097i	$-0.979133\pi$
$727$	−25.1387	+	25.1387i	−0.932342	+	0.932342i	0.0655097	+	0.997852i	$0.479133\pi$
$728$	−2.44557	+	2.44557i	−0.0906390	+	0.0906390i
$729$		0			0
$730$	14.5371	+	21.6724i	0.538041	+	0.802133i
$731$			25.4953i			0.942978i
$732$		0			0
$733$	25.7370	+	25.7370i	0.950617	+	0.950617i	0.998837	−	0.0482198i	$-0.0153548\pi$
$733$	25.7370	+	25.7370i	0.950617	+	0.950617i	−0.0482198	+	0.998837i	$0.515355\pi$
$734$	−16.3356			−0.602958
$735$		0			0
$736$	1.00000			0.0368605
$737$	−23.1696	−	23.1696i	−0.853463	−	0.853463i
$738$		0			0
$739$			9.31695i			0.342729i	0.985208	+	0.171365i	$0.0548176\pi$
$739$			9.31695i			0.342729i	−0.985208	+	0.171365i	$0.945182\pi$
$740$	17.8759	+	3.52258i	0.657130	+	0.129493i
$741$		0			0
$742$	−19.2803	+	19.2803i	−0.707802	+	0.707802i
$743$	−14.0161	+	14.0161i	−0.514200	+	0.514200i	−0.915811	−	0.401610i	$-0.868451\pi$
$743$	−14.0161	+	14.0161i	−0.514200	+	0.514200i	0.401610	+	0.915811i	$0.368451\pi$
$744$		0			0
$745$	2.58955	−	1.73698i	0.0948739	−	0.0636379i
$746$		−	27.6555i		−	1.01254i
$747$		0			0
$748$	7.52311	+	7.52311i	0.275072	+	0.275072i
$749$	46.4305			1.69653
$750$		0			0
$751$	−33.7293			−1.23080			−0.615399	−	0.788215i	$-0.711005\pi$
$751$	−33.7293			−1.23080			−0.615399	+	0.788215i	$0.711005\pi$
$752$	0.885578	+	0.885578i	0.0322937	+	0.0322937i
$753$		0			0
$754$			4.95377i			0.180406i
$755$	4.09686	−	2.74802i	0.149100	−	0.100011i
$756$		0			0
$757$	−21.1310	+	21.1310i	−0.768019	+	0.768019i	−0.977757	−	0.209739i	$-0.932739\pi$
$757$	−21.1310	+	21.1310i	−0.768019	+	0.768019i	0.209739	+	0.977757i	$0.432739\pi$
$758$	20.4758	−	20.4758i	0.743713	−	0.743713i
$759$		0			0
$760$	−14.0140	−	2.76156i	−0.508340	−	0.100172i
$761$		−	2.41966i		−	0.0877127i	−0.999038	−	0.0438563i	$-0.986036\pi$
$761$		−	2.41966i		−	0.0877127i	0.999038	−	0.0438563i	$-0.0139644\pi$
$762$		0			0
$763$	31.6926	+	31.6926i	1.14735	+	1.14735i
$764$	−2.15401			−0.0779293
$765$		0			0
$766$	−19.8217			−0.716189
$767$	−1.86244	−	1.86244i	−0.0672490	−	0.0672490i
$768$		0			0
$769$			2.12910i			0.0767774i	0.999263	+	0.0383887i	$0.0122225\pi$
$769$			2.12910i			0.0767774i	−0.999263	+	0.0383887i	$0.987777\pi$
$770$	−18.7417	−	27.9409i	−0.675405	−	1.00692i
$771$		0			0
$772$	10.7938	−	10.7938i	0.388479	−	0.388479i
$773$	−11.5075	+	11.5075i	−0.413896	+	0.413896i	−0.883093	−	0.469198i	$-0.844543\pi$
$773$	−11.5075	+	11.5075i	−0.413896	+	0.413896i	0.469198	+	0.883093i	$0.344543\pi$
$774$		0			0
$775$	10.4769	−	25.5510i	0.376341	−	0.917820i
$776$		−	9.03365i		−	0.324289i
$777$		0			0
$778$	−2.14931	−	2.14931i	−0.0770566	−	0.0770566i
$779$	−74.5493			−2.67100
$780$		0			0
$781$	−42.5693			−1.52325
$782$	−1.41421	−	1.41421i	−0.0505722	−	0.0505722i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	−7.06489	+	35.8519i	−0.252157	+	1.27961i
$786$		0			0
$787$	1.60788	−	1.60788i	0.0573146	−	0.0573146i	−0.677869	−	0.735183i	$-0.737096\pi$
$787$	1.60788	−	1.60788i	0.0573146	−	0.0573146i	0.735183	+	0.677869i	$0.237096\pi$
$788$	1.03136	−	1.03136i	0.0367407	−	0.0367407i
$789$		0			0
$790$	3.79383	−	19.2524i	0.134979	−	0.684970i
$791$			35.3689i			1.25757i
$792$		0			0
$793$	−6.84006	−	6.84006i	−0.242898	−	0.242898i
$794$	−14.2164			−0.504520
$795$		0			0
$796$	−7.04623			−0.249747
$797$	16.9470	+	16.9470i	0.600294	+	0.600294i	0.940390	−	0.340097i	$-0.110460\pi$
$797$	16.9470	+	16.9470i	0.600294	+	0.600294i	−0.340097	+	0.940390i	$0.610460\pi$
$798$		0			0
$799$		−	2.50479i		−	0.0886132i
$800$	−4.61254	+	1.92989i	−0.163078	+	0.0682320i
$801$		0			0
$802$	3.19991	−	3.19991i	0.112993	−	0.112993i
$803$	−43.8998	+	43.8998i	−1.54919	+	1.54919i
$804$		0			0
$805$	3.52311	+	5.25240i	0.124173	+	0.185123i
$806$		−	6.75359i		−	0.237885i
$807$		0			0
$808$	6.65847	+	6.65847i	0.234244	+	0.234244i
$809$	38.6061			1.35732			0.678659	−	0.734454i	$-0.262562\pi$
$809$	38.6061			1.35732			0.678659	+	0.734454i	$0.262562\pi$
$810$		0			0
$811$	27.1020			0.951681			0.475841	−	0.879531i	$-0.342144\pi$
$811$	27.1020			0.951681			0.475841	+	0.879531i	$0.342144\pi$
$812$	8.10243	+	8.10243i	0.284339	+	0.284339i
$813$		0			0
$814$			43.3449i			1.51924i
$815$	45.8427	+	9.03365i	1.60580	+	0.316435i
$816$		0			0
$817$	57.5789	−	57.5789i	2.01443	−	2.01443i
$818$	−0.648507	+	0.648507i	−0.0226745	+	0.0226745i
$819$		0			0
$820$	−21.6724	+	14.5371i	−0.756834	+	0.507656i
$821$		−	29.2155i		−	1.01963i	−0.860285	−	0.509814i	$-0.829714\pi$
$821$		−	29.2155i		−	1.01963i	0.860285	−	0.509814i	$-0.170286\pi$
$822$		0			0
$823$	−9.80009	−	9.80009i	−0.341610	−	0.341610i	0.515363	−	0.856972i	$-0.327657\pi$
$823$	−9.80009	−	9.80009i	−0.341610	−	0.341610i	−0.856972	+	0.515363i	$0.827657\pi$
$824$	−9.87358			−0.343963
$825$		0			0
$826$	−6.09246			−0.211984
$827$	1.64275	+	1.64275i	0.0571241	+	0.0571241i	0.735092	−	0.677968i	$-0.237139\pi$
$827$	1.64275	+	1.64275i	0.0571241	+	0.0571241i	−0.677968	+	0.735092i	$0.737139\pi$
$828$		0			0
$829$		−	55.7359i		−	1.93579i	−0.251357	−	0.967895i	$-0.580877\pi$
$829$		−	55.7359i		−	1.93579i	0.251357	−	0.967895i	$-0.419123\pi$
$830$	−5.43952	+	3.64863i	−0.188808	+	0.126646i
$831$		0			0
$832$	−0.864641	+	0.864641i	−0.0299760	+	0.0299760i
$833$	1.41421	−	1.41421i	0.0489996	−	0.0489996i
$834$		0			0
$835$	36.3511	+	7.16327i	1.25798	+	0.247895i
$836$		−	33.9806i		−	1.17524i
$837$		0			0
$838$	2.69075	+	2.69075i	0.0929504	+	0.0929504i
$839$	30.2775			1.04529			0.522647	−	0.852549i	$-0.324945\pi$
$839$	30.2775			1.04529			0.522647	+	0.852549i	$0.324945\pi$
$840$		0			0
$841$	−12.5877			−0.434057
$842$	−3.39418	−	3.39418i	−0.116971	−	0.116971i
$843$		0			0
$844$			10.2707i			0.353533i
$845$	14.3305	+	21.3644i	0.492983	+	0.734959i
$846$		0			0
$847$	34.5972	−	34.5972i	1.18878	−	1.18878i
$848$	−6.81662	+	6.81662i	−0.234084	+	0.234084i
$849$		0			0
$850$	9.25240	+	3.79383i	0.317355	+	0.130127i
$851$		−	8.14807i		−	0.279312i
$852$		0			0
$853$	22.1816	+	22.1816i	0.759483	+	0.759483i	0.976228	−	0.216745i	$-0.0695441\pi$
$853$	22.1816	+	22.1816i	0.759483	+	0.759483i	−0.216745	+	0.976228i	$0.569544\pi$
$854$	−22.3753			−0.765668
$855$		0			0
$856$	16.4157			0.561076
$857$	13.9964	+	13.9964i	0.478106	+	0.478106i	0.904526	−	0.426419i	$-0.140225\pi$
$857$	13.9964	+	13.9964i	0.478106	+	0.478106i	−0.426419	+	0.904526i	$0.640225\pi$
$858$		0			0
$859$		−	15.2803i		−	0.521357i	−0.965426	−	0.260679i	$-0.916054\pi$
$859$		−	15.2803i		−	0.521357i	0.965426	−	0.260679i	$-0.0839463\pi$
$860$	5.51107	−	27.9668i	0.187926	−	0.953660i
$861$		0			0
$862$	7.79383	−	7.79383i	0.265459	−	0.265459i
$863$	−9.00774	+	9.00774i	−0.306627	+	0.306627i	−0.843600	−	0.536973i	$-0.819568\pi$
$863$	−9.00774	+	9.00774i	−0.306627	+	0.306627i	0.536973	+	0.843600i	$0.319568\pi$
$864$		0			0
$865$	−2.82800	+	14.3511i	−0.0961548	+	0.487952i
$866$			21.6962i			0.737267i
$867$		0			0
$868$	−11.0462	−	11.0462i	−0.374933	−	0.374933i
$869$	46.6826			1.58360
$870$		0			0
$871$	−7.53185			−0.255207
$872$	11.2050	+	11.2050i	0.379451	+	0.379451i
$873$		0			0
$874$			6.38776i			0.216069i
$875$	−26.3871	−	17.4276i	−0.892046	−	0.589162i
$876$		0			0
$877$	31.9388	−	31.9388i	1.07850	−	1.07850i	0.0818513	−	0.996645i	$-0.473917\pi$
$877$	31.9388	−	31.9388i	1.07850	−	1.07850i	0.996645	−	0.0818513i	$-0.0260833\pi$
$878$	−3.69427	+	3.69427i	−0.124676	+	0.124676i
$879$		0			0
$880$	−6.62620	−	9.87859i	−0.223369	−	0.333007i
$881$		−	4.43407i		−	0.149388i	−0.997207	−	0.0746938i	$-0.976202\pi$
$881$		−	4.43407i		−	0.149388i	0.997207	−	0.0746938i	$-0.0237979\pi$
$882$		0			0
$883$	9.25240	+	9.25240i	0.311368	+	0.311368i	0.845439	−	0.534071i	$-0.179339\pi$
$883$	9.25240	+	9.25240i	0.311368	+	0.311368i	−0.534071	+	0.845439i	$0.679339\pi$
$884$	2.44557			0.0822535
$885$		0			0
$886$	20.9046			0.702304
$887$	−23.5130	−	23.5130i	−0.789489	−	0.789489i	0.191921	−	0.981410i	$-0.438528\pi$
$887$	−23.5130	−	23.5130i	−0.789489	−	0.789489i	−0.981410	+	0.191921i	$0.938528\pi$
$888$		0			0
$889$			7.45856i			0.250152i
$890$	20.4584	+	4.03148i	0.685766	+	0.135136i
$891$		0			0
$892$	17.1170	−	17.1170i	0.573121	−	0.573121i
$893$	−5.65685	+	5.65685i	−0.189299	+	0.189299i
$894$		0			0
$895$	46.0925	−	30.9171i	1.54070	−	1.03345i
$896$			2.82843i			0.0944911i
$897$		0			0
$898$	−28.5510	−	28.5510i	−0.952760	−	0.952760i
$899$	−22.3753			−0.746259
$900$		0			0
$901$	19.2803			0.642320
$902$	−43.8998	−	43.8998i	−1.46170	−	1.46170i
$903$		0			0
$904$			12.5048i			0.415903i
$905$	26.3352	−	17.6647i	0.875413	−	0.587195i
$906$		0			0
$907$	9.72491	−	9.72491i	0.322910	−	0.322910i	−0.526972	−	0.849883i	$-0.676673\pi$
$907$	9.72491	−	9.72491i	0.322910	−	0.322910i	0.849883	+	0.526972i	$0.176673\pi$
$908$	−1.47724	+	1.47724i	−0.0490239	+	0.0490239i
$909$		0			0
$910$	−7.58767	−	1.49521i	−0.251529	−	0.0495657i
$911$			47.3570i			1.56901i	0.620124	+	0.784504i	$0.287082\pi$
$911$			47.3570i			1.56901i	−0.620124	+	0.784504i	$0.712918\pi$
$912$		0			0
$913$	−11.0183	−	11.0183i	−0.364653	−	0.364653i
$914$	30.8954			1.02193
$915$		0			0
$916$	−24.6864			−0.815661
$917$	31.0609	+	31.0609i	1.02572	+	1.02572i
$918$		0			0
$919$			37.1387i			1.22509i	0.790435	+	0.612546i	$0.209855\pi$
$919$			37.1387i			1.22509i	−0.790435	+	0.612546i	$0.790145\pi$
$920$	1.24561	+	1.85700i	0.0410665	+	0.0612236i
$921$		0			0
$922$	15.6402	−	15.6402i	0.515081	−	0.515081i
$923$	−6.91911	+	6.91911i	−0.227745	+	0.227745i
$924$		0			0
$925$	15.7249	+	37.5833i	0.517032	+	1.23573i
$926$		−	16.1047i		−	0.529234i
$927$		0			0
$928$	2.86464	+	2.86464i	0.0940364	+	0.0940364i
$929$	−33.9547			−1.11402			−0.557008	−	0.830507i	$-0.688051\pi$
$929$	−33.9547			−1.11402			−0.557008	+	0.830507i	$0.688051\pi$
$930$		0			0
$931$	−6.38776			−0.209350
$932$	−8.69644	−	8.69644i	−0.284861	−	0.284861i
$933$		0			0
$934$			23.7047i			0.775642i
$935$	−4.59958	+	23.3413i	−0.150422	+	0.763342i
$936$		0			0
$937$	27.9667	−	27.9667i	0.913632	−	0.913632i	−0.0829242	−	0.996556i	$-0.526426\pi$
$937$	27.9667	−	27.9667i	0.913632	−	0.913632i	0.996556	+	0.0829242i	$0.0264259\pi$
$938$	−12.3192	+	12.3192i	−0.402235	+	0.402235i
$939$		0			0
$940$	−0.541436	+	2.74760i	−0.0176597	+	0.0896170i
$941$			44.1566i			1.43946i	0.694252	+	0.719732i	$0.255736\pi$
$941$			44.1566i			1.43946i	−0.694252	+	0.719732i	$0.744264\pi$
$942$		0			0
$943$	8.25240	+	8.25240i	0.268735	+	0.268735i
$944$	−2.15401			−0.0701070
$945$		0			0
$946$	67.8130			2.20479
$947$	20.4734	+	20.4734i	0.665296	+	0.665296i	0.956623	−	0.291327i	$-0.0940968\pi$
$947$	20.4734	+	20.4734i	0.665296	+	0.665296i	−0.291327	+	0.956623i	$0.594097\pi$
$948$		0			0
$949$			14.2707i			0.463247i
$950$	−12.3277	−	29.4638i	−0.399963	−	0.955931i
$951$		0			0
$952$	4.00000	−	4.00000i	0.129641	−	0.129641i
$953$	0.905311	−	0.905311i	0.0293259	−	0.0293259i	−0.692292	−	0.721618i	$-0.743399\pi$
$953$	0.905311	−	0.905311i	0.0293259	−	0.0293259i	0.721618	+	0.692292i	$0.243399\pi$
$954$		0			0
$955$	−2.68305	−	4.00000i	−0.0868216	−	0.129437i
$956$			5.75699i			0.186194i
$957$		0			0
$958$	−9.31695	−	9.31695i	−0.301017	−	0.301017i
$959$	7.85033			0.253500
$960$		0			0
$961$	−0.495208			−0.0159744
$962$	7.04516	+	7.04516i	0.227145	+	0.227145i
$963$		0			0
$964$			15.1878i			0.489168i
$965$	33.4891	+	6.59928i	1.07805	+	0.212438i
$966$		0			0
$967$	4.27698	−	4.27698i	0.137538	−	0.137538i	−0.634986	−	0.772524i	$-0.718994\pi$
$967$	4.27698	−	4.27698i	0.137538	−	0.137538i	0.772524	+	0.634986i	$0.218994\pi$
$968$	12.2320	−	12.2320i	0.393151	−	0.393151i
$969$		0			0
$970$	16.7755	−	11.2524i	0.538629	−	0.361293i
$971$			44.6485i			1.43284i	0.697671	+	0.716419i	$0.254220\pi$
$971$			44.6485i			1.43284i	−0.697671	+	0.716419i	$0.745780\pi$
$972$		0			0
$973$	−32.4681	−	32.4681i	−1.04088	−	1.04088i
$974$	16.5270			0.529560
$975$		0			0
$976$	−7.91087			−0.253221
$977$	8.25909	+	8.25909i	0.264232	+	0.264232i	0.826771	−	0.562539i	$-0.190175\pi$
$977$	8.25909	+	8.25909i	0.264232	+	0.264232i	−0.562539	+	0.826771i	$0.690175\pi$
$978$		0			0
$979$			49.6068i			1.58544i
$980$	−1.85700	+	1.24561i	−0.0593198	+	0.0397895i
$981$		0			0
$982$	−23.5510	+	23.5510i	−0.751543	+	0.751543i
$983$	22.2840	−	22.2840i	0.710750	−	0.710750i	−0.255942	−	0.966692i	$-0.582386\pi$
$983$	22.2840	−	22.2840i	0.710750	−	0.710750i	0.966692	+	0.255942i	$0.0823856\pi$
$984$		0			0
$985$	3.19991	+	0.630567i	0.101958	+	0.0200915i
$986$		−	8.10243i		−	0.258034i
$987$		0			0
$988$	−5.52311	−	5.52311i	−0.175714	−	0.175714i
$989$	−12.7477			−0.405352
$990$		0			0
$991$	6.26198			0.198918			0.0994592	−	0.995042i	$-0.468289\pi$
$991$	6.26198			0.198918			0.0994592	+	0.995042i	$0.468289\pi$
$992$	−3.90543	−	3.90543i	−0.123998	−	0.123998i
$993$		0			0
$994$			22.6339i			0.717904i
$995$	−8.77685	−	13.0849i	−0.278245	−	0.414818i
$996$		0			0
$997$	4.11704	−	4.11704i	0.130388	−	0.130388i	−0.638901	−	0.769289i	$-0.720611\pi$
$997$	4.11704	−	4.11704i	0.130388	−	0.130388i	0.769289	+	0.638901i	$0.220611\pi$
$998$	−24.7814	+	24.7814i	−0.784442	+	0.784442i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.j.g.323.4	yes	12
3.2	odd	2	inner	2070.2.j.g.323.3	✓	12
5.2	odd	4	inner	2070.2.j.g.737.3	yes	12
15.2	even	4	inner	2070.2.j.g.737.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.j.g.323.3	✓	12	3.2	odd	2	inner
2070.2.j.g.323.4	yes	12	1.1	even	1	trivial
2070.2.j.g.737.3	yes	12	5.2	odd	4	inner
2070.2.j.g.737.4	yes	12	15.2	even	4	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.85700 + 1.24561i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.85700 + 1.24561i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.19388 - 0.432320i) q^{10} -5.31965i q^{11} +(-0.864641 - 0.864641i) q^{13} -2.82843 q^{14} -1.00000 q^{16} +(1.41421 + 1.41421i) q^{17} -6.38776i q^{19} +(-1.24561 - 1.85700i) q^{20} +(3.76156 - 3.76156i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(1.89692 - 4.62620i) q^{25} -1.22279i q^{26} +(-2.00000 - 2.00000i) q^{28} -4.05121 q^{29} +5.52311 q^{31} +(-0.707107 - 0.707107i) q^{32} +2.00000i q^{34} +(1.22279 - 6.20522i) q^{35} +(-5.76156 + 5.76156i) q^{37} +(4.51683 - 4.51683i) q^{38} +(0.432320 - 2.19388i) q^{40} -11.6707i q^{41} +(9.01395 + 9.01395i) q^{43} +5.31965 q^{44} -1.00000 q^{46} +(-0.885578 - 0.885578i) q^{47} -1.00000i q^{49} +(4.61254 - 1.92989i) q^{50} +(0.864641 - 0.864641i) q^{52} +(6.81662 - 6.81662i) q^{53} +(6.62620 + 9.87859i) q^{55} -2.82843i q^{56} +(-2.86464 - 2.86464i) q^{58} +2.15401 q^{59} +7.91087 q^{61} +(3.90543 + 3.90543i) q^{62} -1.00000i q^{64} +(2.68264 + 0.528636i) q^{65} +(4.35548 - 4.35548i) q^{67} +(-1.41421 + 1.41421i) q^{68} +(5.25240 - 3.52311i) q^{70} -8.00229i q^{71} +(-8.25240 - 8.25240i) q^{73} -8.14807 q^{74} +6.38776 q^{76} +(10.6393 + 10.6393i) q^{77} +8.77551i q^{79} +(1.85700 - 1.24561i) q^{80} +(8.25240 - 8.25240i) q^{82} +(2.07125 - 2.07125i) q^{83} +(-4.38776 - 0.864641i) q^{85} +12.7477i q^{86} +(3.76156 + 3.76156i) q^{88} -9.32521 q^{89} +3.45856 q^{91} +(-0.707107 - 0.707107i) q^{92} -1.25240i q^{94} +(7.95665 + 11.8621i) q^{95} +(-6.38776 + 6.38776i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{7}+O(q^{10}) \) 12 * q - 24 * q^7	\( 12 q - 24 q^{7} + 4 q^{10} - 12 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{28} + 16 q^{31} - 44 q^{37} + 12 q^{43} - 12 q^{46} + 44 q^{55} - 24 q^{58} - 16 q^{61} - 4 q^{67} - 8 q^{70} - 28 q^{73} + 16 q^{76} + 28 q^{82} + 8 q^{85} + 20 q^{88} - 16 q^{97}+O(q^{100}) \) 12 * q - 24 * q^7 + 4 * q^10 - 12 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^28 + 16 * q^31 - 44 * q^37 + 12 * q^43 - 12 * q^46 + 44 * q^55 - 24 * q^58 - 16 * q^61 - 4 * q^67 - 8 * q^70 - 28 * q^73 + 16 * q^76 + 28 * q^82 + 8 * q^85 + 20 * q^88 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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