LMFDB - Embedded newform 342.2.s.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(107,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("342.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.s (of order $6$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	342.107
Dual form			342.2.s.a.179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +1.44949 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +1.44949 q^{7} +1.00000 q^{8} +(1.22474 + 0.707107i) q^{10} -0.635674i q^{11} +(5.17423 + 2.98735i) q^{13} +(-0.724745 - 1.25529i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.77526 - 1.02494i) q^{17} +(4.00000 - 1.73205i) q^{19} -1.41421i q^{20} +(-0.550510 + 0.317837i) q^{22} +(4.89898 + 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} -5.97469i q^{26} +(-0.724745 + 1.25529i) q^{28} +(1.22474 - 2.12132i) q^{29} -0.953512i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.77526 - 1.02494i) q^{34} +(-1.77526 + 1.02494i) q^{35} -2.51059i q^{37} +(-3.50000 - 2.59808i) q^{38} +(-1.22474 + 0.707107i) q^{40} +(-1.94949 - 3.37662i) q^{43} +(0.550510 + 0.317837i) q^{44} -5.65685i q^{46} +(-1.77526 - 1.02494i) q^{47} -4.89898 q^{49} +3.00000 q^{50} +(-5.17423 + 2.98735i) q^{52} +(-2.44949 + 4.24264i) q^{53} +(0.449490 + 0.778539i) q^{55} +1.44949 q^{56} -2.44949 q^{58} +(7.22474 + 12.5136i) q^{59} +(1.72474 - 2.98735i) q^{61} +(-0.825765 + 0.476756i) q^{62} +1.00000 q^{64} -8.44949 q^{65} +(-8.84847 - 5.10867i) q^{67} +2.04989i q^{68} +(1.77526 + 1.02494i) q^{70} +(3.00000 + 5.19615i) q^{71} +(1.05051 + 1.81954i) q^{73} +(-2.17423 + 1.25529i) q^{74} +(-0.500000 + 4.33013i) q^{76} -0.921404i q^{77} +(0.825765 - 0.476756i) q^{79} +(1.22474 + 0.707107i) q^{80} -11.8065i q^{83} +(-1.44949 + 2.51059i) q^{85} +(-1.94949 + 3.37662i) q^{86} -0.635674i q^{88} +(-6.12372 + 10.6066i) q^{89} +(7.50000 + 4.33013i) q^{91} +(-4.89898 + 2.82843i) q^{92} +2.04989i q^{94} +(-3.67423 + 4.94975i) q^{95} +(-16.3485 + 9.43879i) q^{97} +(2.44949 + 4.24264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 12 q^{17} + 16 q^{19} - 12 q^{22} - 6 q^{25} + 2 q^{28} - 2 q^{32} - 12 q^{34} - 12 q^{35} - 14 q^{38} + 2 q^{43} + 12 q^{44} - 12 q^{47} + 12 q^{50} - 6 q^{52} - 8 q^{55} - 4 q^{56} + 24 q^{59} + 2 q^{61} - 18 q^{62} + 4 q^{64} - 24 q^{65} - 6 q^{67} + 12 q^{70} + 12 q^{71} + 14 q^{73} + 6 q^{74} - 2 q^{76} + 18 q^{79} + 4 q^{85} + 2 q^{86} + 30 q^{91} - 36 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 12 * q^17 + 16 * q^19 - 12 * q^22 - 6 * q^25 + 2 * q^28 - 2 * q^32 - 12 * q^34 - 12 * q^35 - 14 * q^38 + 2 * q^43 + 12 * q^44 - 12 * q^47 + 12 * q^50 - 6 * q^52 - 8 * q^55 - 4 * q^56 + 24 * q^59 + 2 * q^61 - 18 * q^62 + 4 * q^64 - 24 * q^65 - 6 * q^67 + 12 * q^70 + 12 * q^71 + 14 * q^73 + 6 * q^74 - 2 * q^76 + 18 * q^79 + 4 * q^85 + 2 * q^86 + 30 * q^91 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	−0.748203	−	0.663470i	$-0.769083\pi$
$5$	−1.22474	+	0.707107i	−0.547723	+	0.316228i	0.200480	+	0.979698i	$0.435750\pi$
$6$		0			0
$7$	1.44949			0.547856			0.273928	−	0.961750i	$-0.411677\pi$
$7$	1.44949			0.547856			0.273928	+	0.961750i	$0.411677\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	1.22474	+	0.707107i	0.387298	+	0.223607i
$11$		−	0.635674i		−	0.191663i	−0.995398	−	0.0958315i	$-0.969449\pi$
$11$		−	0.635674i		−	0.191663i	0.995398	−	0.0958315i	$-0.0305510\pi$
$12$		0			0
$13$	5.17423	+	2.98735i	1.43507	+	0.828541i	0.997502	−	0.0706424i	$-0.0225049\pi$
$13$	5.17423	+	2.98735i	1.43507	+	0.828541i	0.437573	+	0.899183i	$0.355838\pi$
$14$	−0.724745	−	1.25529i	−0.193696	−	0.335492i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.77526	−	1.02494i	0.430563	−	0.248585i	−0.269024	−	0.963134i	$-0.586701\pi$
$17$	1.77526	−	1.02494i	0.430563	−	0.248585i	0.699586	+	0.714548i	$0.253368\pi$
$18$		0			0
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$20$		−	1.41421i		−	0.316228i
$21$		0			0
$22$	−0.550510	+	0.317837i	−0.117369	+	0.0677631i
$23$	4.89898	+	2.82843i	1.02151	+	0.589768i	0.914540	−	0.404495i	$-0.132553\pi$
$23$	4.89898	+	2.82843i	1.02151	+	0.589768i	0.106967	+	0.994263i	$0.465886\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		−	5.97469i		−	1.17173i
$27$		0			0
$28$	−0.724745	+	1.25529i	−0.136964	+	0.237228i
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	−0.729616	−	0.683857i	$-0.760301\pi$
$29$	1.22474	−	2.12132i	0.227429	−	0.393919i	0.957046	+	0.289938i	$0.0936346\pi$
$30$		0			0
$31$		−	0.953512i		−	0.171256i	−0.996327	−	0.0856279i	$-0.972710\pi$
$31$		−	0.953512i		−	0.171256i	0.996327	−	0.0856279i	$-0.0272896\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.77526	−	1.02494i	−0.304454	−	0.175776i
$35$	−1.77526	+	1.02494i	−0.300073	+	0.173247i
$36$		0			0
$37$		−	2.51059i		−	0.412738i	−0.978474	−	0.206369i	$-0.933835\pi$
$37$		−	2.51059i		−	0.412738i	0.978474	−	0.206369i	$-0.0661648\pi$
$38$	−3.50000	−	2.59808i	−0.567775	−	0.421464i
$39$		0			0
$40$	−1.22474	+	0.707107i	−0.193649	+	0.111803i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−1.94949	−	3.37662i	−0.297294	−	0.514929i	0.678222	−	0.734857i	$-0.262751\pi$
$43$	−1.94949	−	3.37662i	−0.297294	−	0.514929i	−0.975516	+	0.219928i	$0.929418\pi$
$44$	0.550510	+	0.317837i	0.0829925	+	0.0479158i
$45$		0			0
$46$		−	5.65685i		−	0.834058i
$47$	−1.77526	−	1.02494i	−0.258948	−	0.149503i	0.364907	−	0.931044i	$-0.381101\pi$
$47$	−1.77526	−	1.02494i	−0.258948	−	0.149503i	−0.623854	+	0.781541i	$0.714434\pi$
$48$		0			0
$49$	−4.89898			−0.699854
$50$	3.00000			0.424264
$51$		0			0
$52$	−5.17423	+	2.98735i	−0.717537	+	0.414270i
$53$	−2.44949	+	4.24264i	−0.336463	+	0.582772i	−0.983765	−	0.179463i	$-0.942564\pi$
$53$	−2.44949	+	4.24264i	−0.336463	+	0.582772i	0.647302	+	0.762234i	$0.275897\pi$
$54$		0			0
$55$	0.449490	+	0.778539i	0.0606092	+	0.104978i
$56$	1.44949			0.193696
$57$		0			0
$58$	−2.44949			−0.321634
$59$	7.22474	+	12.5136i	0.940582	+	1.62914i	0.764365	+	0.644784i	$0.223053\pi$
$59$	7.22474	+	12.5136i	0.940582	+	1.62914i	0.176217	+	0.984351i	$0.443614\pi$
$60$		0			0
$61$	1.72474	−	2.98735i	0.220831	−	0.382490i	−0.734230	−	0.678901i	$-0.762456\pi$
$61$	1.72474	−	2.98735i	0.220831	−	0.382490i	0.955061	+	0.296411i	$0.0957898\pi$
$62$	−0.825765	+	0.476756i	−0.104872	+	0.0605481i
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.44949			−1.04803
$66$		0			0
$67$	−8.84847	−	5.10867i	−1.08101	−	0.624123i	−0.149843	−	0.988710i	$-0.547877\pi$
$67$	−8.84847	−	5.10867i	−1.08101	−	0.624123i	−0.931169	+	0.364587i	$0.881210\pi$
$68$			2.04989i			0.248585i
$69$		0			0
$70$	1.77526	+	1.02494i	0.212184	+	0.122504i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	1.05051	+	1.81954i	0.122953	+	0.212961i	0.920931	−	0.389726i	$-0.127430\pi$
$73$	1.05051	+	1.81954i	0.122953	+	0.212961i	−0.797978	+	0.602687i	$0.794097\pi$
$74$	−2.17423	+	1.25529i	−0.252750	+	0.145925i
$75$		0			0
$76$	−0.500000	+	4.33013i	−0.0573539	+	0.496700i
$77$		−	0.921404i		−	0.105004i
$78$		0			0
$79$	0.825765	−	0.476756i	0.0929059	−	0.0536392i	−0.452827	−	0.891598i	$-0.649585\pi$
$79$	0.825765	−	0.476756i	0.0929059	−	0.0536392i	0.545733	+	0.837959i	$0.316251\pi$
$80$	1.22474	+	0.707107i	0.136931	+	0.0790569i
$81$		0			0
$82$		0			0
$83$		−	11.8065i		−	1.29593i	−0.761669	−	0.647967i	$-0.775620\pi$
$83$		−	11.8065i		−	1.29593i	0.761669	−	0.647967i	$-0.224380\pi$
$84$		0			0
$85$	−1.44949	+	2.51059i	−0.157219	+	0.272312i
$86$	−1.94949	+	3.37662i	−0.210219	+	0.364110i
$87$		0			0
$88$		−	0.635674i		−	0.0677631i
$89$	−6.12372	+	10.6066i	−0.649113	+	1.12430i	0.334221	+	0.942495i	$0.391527\pi$
$89$	−6.12372	+	10.6066i	−0.649113	+	1.12430i	−0.983335	+	0.181803i	$0.941807\pi$
$90$		0			0
$91$	7.50000	+	4.33013i	0.786214	+	0.453921i
$92$	−4.89898	+	2.82843i	−0.510754	+	0.294884i
$93$		0			0
$94$			2.04989i			0.211430i
$95$	−3.67423	+	4.94975i	−0.376969	+	0.507833i
$96$		0			0
$97$	−16.3485	+	9.43879i	−1.65994	+	0.958364i	−0.687193	+	0.726474i	$0.741158\pi$
$97$	−16.3485	+	9.43879i	−1.65994	+	0.958364i	−0.972742	+	0.231890i	$0.925509\pi$
$98$	2.44949	+	4.24264i	0.247436	+	0.428571i
$99$		0			0
$100$	−1.50000	−	2.59808i	−0.150000	−	0.259808i
$101$	−11.4495	−	6.61037i	−1.13927	−	0.657756i	−0.193018	−	0.981195i	$-0.561828\pi$
$101$	−11.4495	−	6.61037i	−1.13927	−	0.657756i	−0.946249	+	0.323439i	$0.895161\pi$
$102$		0			0
$103$		−	14.4600i		−	1.42478i	−0.701782	−	0.712392i	$-0.747612\pi$
$103$		−	14.4600i		−	1.42478i	0.701782	−	0.712392i	$-0.252388\pi$
$104$	5.17423	+	2.98735i	0.507375	+	0.292933i
$105$		0			0
$106$	4.89898			0.475831
$107$	15.7980			1.52725			0.763623	−	0.645662i	$-0.223419\pi$
$107$	15.7980			1.52725			0.763623	+	0.645662i	$0.223419\pi$
$108$		0			0
$109$	−14.6969	+	8.48528i	−1.40771	+	0.812743i	−0.995167	−	0.0981950i	$-0.968693\pi$
$109$	−14.6969	+	8.48528i	−1.40771	+	0.812743i	−0.412544	+	0.910938i	$0.635360\pi$
$110$	0.449490	−	0.778539i	0.0428572	−	0.0742308i
$111$		0			0
$112$	−0.724745	−	1.25529i	−0.0684820	−	0.118614i
$113$	−17.1464			−1.61300			−0.806500	−	0.591234i	$-0.798641\pi$
$113$	−17.1464			−1.61300			−0.806500	+	0.591234i	$0.798641\pi$
$114$		0			0
$115$	−8.00000			−0.746004
$116$	1.22474	+	2.12132i	0.113715	+	0.196960i
$117$		0			0
$118$	7.22474	−	12.5136i	0.665092	−	1.15197i
$119$	2.57321	−	1.48565i	0.235886	−	0.136189i
$120$		0			0
$121$	10.5959			0.963265
$122$	−3.44949			−0.312302
$123$		0			0
$124$	0.825765	+	0.476756i	0.0741559	+	0.0428139i
$125$		−	11.3137i		−	1.01193i
$126$		0			0
$127$	7.34847	+	4.24264i	0.652071	+	0.376473i	0.789249	−	0.614073i	$-0.210470\pi$
$127$	7.34847	+	4.24264i	0.652071	+	0.376473i	−0.137178	+	0.990546i	$0.543803\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	4.22474	+	7.31747i	0.370535	+	0.641785i
$131$	12.7980	−	7.38891i	1.11816	−	0.645572i	0.177232	−	0.984169i	$-0.443286\pi$
$131$	12.7980	−	7.38891i	1.11816	−	0.645572i	0.940931	+	0.338598i	$0.109953\pi$
$132$		0			0
$133$	5.79796	−	2.51059i	0.502747	−	0.217696i
$134$			10.2173i			0.882643i
$135$		0			0
$136$	1.77526	−	1.02494i	0.152227	−	0.0878882i
$137$	−5.44949	−	3.14626i	−0.465581	−	0.268804i	0.248807	−	0.968553i	$-0.419962\pi$
$137$	−5.44949	−	3.14626i	−0.465581	−	0.268804i	−0.714388	+	0.699750i	$0.753295\pi$
$138$		0			0
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$		−	2.04989i		−	0.173247i
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	1.89898	−	3.28913i	0.158801	−	0.275051i
$144$		0			0
$145$			3.46410i			0.287678i
$146$	1.05051	−	1.81954i	0.0869408	−	0.150586i
$147$		0			0
$148$	2.17423	+	1.25529i	0.178721	+	0.103185i
$149$	17.4495	−	10.0745i	1.42952	−	0.825333i	0.432435	−	0.901665i	$-0.357654\pi$
$149$	17.4495	−	10.0745i	1.42952	−	0.825333i	0.997082	+	0.0763323i	$0.0243210\pi$
$150$		0			0
$151$		−	1.55708i		−	0.126713i	−0.997991	−	0.0633566i	$-0.979819\pi$
$151$		−	1.55708i		−	0.126713i	0.997991	−	0.0633566i	$-0.0201806\pi$
$152$	4.00000	−	1.73205i	0.324443	−	0.140488i
$153$		0			0
$154$	−0.797959	+	0.460702i	−0.0643014	+	0.0371244i
$155$	0.674235	+	1.16781i	0.0541558	+	0.0938006i
$156$		0			0
$157$	−6.17423	−	10.6941i	−0.492758	−	0.853481i	0.507208	−	0.861824i	$-0.330678\pi$
$157$	−6.17423	−	10.6941i	−0.492758	−	0.853481i	−0.999965	+	0.00834275i	$0.997344\pi$
$158$	−0.825765	−	0.476756i	−0.0656944	−	0.0379287i
$159$		0			0
$160$		−	1.41421i		−	0.111803i
$161$	7.10102	+	4.09978i	0.559639	+	0.323108i
$162$		0			0
$163$	7.69694			0.602871			0.301435	−	0.953487i	$-0.402534\pi$
$163$	7.69694			0.602871			0.301435	+	0.953487i	$0.402534\pi$
$164$		0			0
$165$		0			0
$166$	−10.2247	+	5.90326i	−0.793594	+	0.458182i
$167$	4.22474	−	7.31747i	0.326921	−	0.566243i	−0.654979	−	0.755647i	$-0.727322\pi$
$167$	4.22474	−	7.31747i	0.326921	−	0.566243i	0.981899	+	0.189404i	$0.0606557\pi$
$168$		0			0
$169$	11.3485	+	19.6561i	0.872959	+	1.51201i
$170$	2.89898			0.222342
$171$		0			0
$172$	3.89898			0.297294
$173$	−6.12372	−	10.6066i	−0.465578	−	0.806405i	0.533649	−	0.845706i	$-0.320820\pi$
$173$	−6.12372	−	10.6066i	−0.465578	−	0.806405i	−0.999227	+	0.0393009i	$0.987487\pi$
$174$		0			0
$175$	−2.17423	+	3.76588i	−0.164357	+	0.284674i
$176$	−0.550510	+	0.317837i	−0.0414963	+	0.0239579i
$177$		0			0
$178$	12.2474			0.917985
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−4.65153	−	2.68556i	−0.345746	−	0.199616i	0.317064	−	0.948404i	$-0.397303\pi$
$181$	−4.65153	−	2.68556i	−0.345746	−	0.199616i	−0.662810	+	0.748788i	$0.730636\pi$
$182$		−	8.66025i		−	0.641941i
$183$		0			0
$184$	4.89898	+	2.82843i	0.361158	+	0.208514i
$185$	1.77526	+	3.07483i	0.130519	+	0.226066i
$186$		0			0
$187$	−0.651531	−	1.12848i	−0.0476446	−	0.0825230i
$188$	1.77526	−	1.02494i	0.129474	−	0.0747517i
$189$		0			0
$190$	6.12372	+	0.707107i	0.444262	+	0.0512989i
$191$		−	15.2706i		−	1.10494i	−0.833532	−	0.552472i	$-0.813685\pi$
$191$		−	15.2706i		−	1.10494i	0.833532	−	0.552472i	$-0.186315\pi$
$192$		0			0
$193$	14.8485	−	8.57277i	1.06882	−	0.617081i	0.140958	−	0.990016i	$-0.454982\pi$
$193$	14.8485	−	8.57277i	1.06882	−	0.617081i	0.927858	+	0.372934i	$0.121648\pi$
$194$	16.3485	+	9.43879i	1.17375	+	0.677666i
$195$		0			0
$196$	2.44949	−	4.24264i	0.174964	−	0.303046i
$197$		−	20.2918i		−	1.44573i	−0.690989	−	0.722865i	$-0.742825\pi$
$197$		−	20.2918i		−	1.44573i	0.690989	−	0.722865i	$-0.257175\pi$
$198$		0			0
$199$	−8.62372	+	14.9367i	−0.611320	+	1.05884i	0.379699	+	0.925110i	$0.376028\pi$
$199$	−8.62372	+	14.9367i	−0.611320	+	1.05884i	−0.991018	+	0.133726i	$0.957306\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$			13.2207i			0.930207i
$203$	1.77526	−	3.07483i	0.124598	−	0.215811i
$204$		0			0
$205$		0			0
$206$	−12.5227	+	7.22999i	−0.872498	+	0.503737i
$207$		0			0
$208$		−	5.97469i		−	0.414270i
$209$	−1.10102	−	2.54270i	−0.0761592	−	0.175882i
$210$		0			0
$211$	3.15153	−	1.81954i	0.216960	−	0.125262i	−0.387582	−	0.921835i	$-0.626689\pi$
$211$	3.15153	−	1.81954i	0.216960	−	0.125262i	0.604542	+	0.796573i	$0.293356\pi$
$212$	−2.44949	−	4.24264i	−0.168232	−	0.291386i
$213$		0			0
$214$	−7.89898	−	13.6814i	−0.539963	−	0.935244i
$215$	4.77526	+	2.75699i	0.325670	+	0.188025i
$216$		0			0
$217$		−	1.38211i		−	0.0938234i
$218$	14.6969	+	8.48528i	0.995402	+	0.574696i
$219$		0			0
$220$	−0.898979			−0.0606092
$221$	12.2474			0.823853
$222$		0			0
$223$	−2.17423	+	1.25529i	−0.145598	+	0.0840608i	−0.571029	−	0.820930i	$-0.693456\pi$
$223$	−2.17423	+	1.25529i	−0.145598	+	0.0840608i	0.425432	+	0.904991i	$0.360122\pi$
$224$	−0.724745	+	1.25529i	−0.0484241	+	0.0838729i
$225$		0			0
$226$	8.57321	+	14.8492i	0.570282	+	0.987757i
$227$	−23.1464			−1.53628			−0.768141	−	0.640280i	$-0.778818\pi$
$227$	−23.1464			−1.53628			−0.768141	+	0.640280i	$0.778818\pi$
$228$		0			0
$229$	−19.2474			−1.27191			−0.635954	−	0.771727i	$-0.719393\pi$
$229$	−19.2474			−1.27191			−0.635954	+	0.771727i	$0.719393\pi$
$230$	4.00000	+	6.92820i	0.263752	+	0.456832i
$231$		0			0
$232$	1.22474	−	2.12132i	0.0804084	−	0.139272i
$233$	−15.2474	+	8.80312i	−0.998894	+	0.576711i	−0.907921	−	0.419142i	$-0.862331\pi$
$233$	−15.2474	+	8.80312i	−0.998894	+	0.576711i	−0.0909728	+	0.995853i	$0.528998\pi$
$234$		0			0
$235$	2.89898			0.189109
$236$	−14.4495			−0.940582
$237$		0			0
$238$	−2.57321	−	1.48565i	−0.166797	−	0.0963001i
$239$			22.4846i			1.45440i	0.686423	+	0.727202i	$0.259180\pi$
$239$			22.4846i			1.45440i	−0.686423	+	0.727202i	$0.740820\pi$
$240$		0			0
$241$	12.1515	+	7.01569i	0.782749	+	0.451920i	0.837404	−	0.546585i	$-0.184072\pi$
$241$	12.1515	+	7.01569i	0.782749	+	0.451920i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	−5.29796	−	9.17633i	−0.340566	−	0.589877i
$243$		0			0
$244$	1.72474	+	2.98735i	0.110415	+	0.191245i
$245$	6.00000	−	3.46410i	0.383326	−	0.221313i
$246$		0			0
$247$	25.8712	+	2.98735i	1.64614	+	0.190080i
$248$		−	0.953512i		−	0.0605481i
$249$		0			0
$250$	−9.79796	+	5.65685i	−0.619677	+	0.357771i
$251$	1.22474	+	0.707107i	0.0773052	+	0.0446322i	0.538154	−	0.842846i	$-0.319122\pi$
$251$	1.22474	+	0.707107i	0.0773052	+	0.0446322i	−0.460849	+	0.887478i	$0.652455\pi$
$252$		0			0
$253$	1.79796	−	3.11416i	0.113037	−	0.195785i
$254$		−	8.48528i		−	0.532414i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$		−	3.63907i		−	0.226121i
$260$	4.22474	−	7.31747i	0.262008	−	0.453810i
$261$		0			0
$262$	−12.7980	−	7.38891i	−0.790661	−	0.456488i
$263$	0.797959	−	0.460702i	0.0492043	−	0.0284081i	−0.475196	−	0.879880i	$-0.657623\pi$
$263$	0.797959	−	0.460702i	0.0492043	−	0.0284081i	0.524400	+	0.851472i	$0.324290\pi$
$264$		0			0
$265$		−	6.92820i		−	0.425596i
$266$	−5.07321	−	3.76588i	−0.311059	−	0.230901i
$267$		0			0
$268$	8.84847	−	5.10867i	0.540506	−	0.312061i
$269$	10.2247	+	17.7098i	0.623414	+	1.07978i	0.988845	+	0.148946i	$0.0475881\pi$
$269$	10.2247	+	17.7098i	0.623414	+	1.07978i	−0.365432	+	0.930838i	$0.619079\pi$
$270$		0			0
$271$	−15.6969	−	27.1879i	−0.953521	−	1.65155i	−0.737717	−	0.675110i	$-0.764096\pi$
$271$	−15.6969	−	27.1879i	−0.953521	−	1.65155i	−0.215804	−	0.976437i	$-0.569237\pi$
$272$	−1.77526	−	1.02494i	−0.107641	−	0.0621464i
$273$		0			0
$274$			6.29253i			0.380146i
$275$	1.65153	+	0.953512i	0.0995911	+	0.0574989i
$276$		0			0
$277$	9.10102			0.546827			0.273414	−	0.961897i	$-0.411847\pi$
$277$	9.10102			0.546827			0.273414	+	0.961897i	$0.411847\pi$
$278$	−7.00000			−0.419832
$279$		0			0
$280$	−1.77526	+	1.02494i	−0.106092	+	0.0612521i
$281$	−11.5732	+	20.0454i	−0.690400	+	1.19581i	0.281307	+	0.959618i	$0.409232\pi$
$281$	−11.5732	+	20.0454i	−0.690400	+	1.19581i	−0.971707	+	0.236190i	$0.924101\pi$
$282$		0			0
$283$	7.44949	+	12.9029i	0.442826	+	0.766997i	0.997898	−	0.0648050i	$-0.0206425\pi$
$283$	7.44949	+	12.9029i	0.442826	+	0.766997i	−0.555072	+	0.831802i	$0.687309\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−3.79796			−0.224578
$287$		0			0
$288$		0			0
$289$	−6.39898	+	11.0834i	−0.376411	+	0.651962i
$290$	3.00000	−	1.73205i	0.176166	−	0.101710i
$291$		0			0
$292$	−2.10102			−0.122953
$293$	−10.6515			−0.622269			−0.311135	−	0.950366i	$-0.600709\pi$
$293$	−10.6515			−0.622269			−0.311135	+	0.950366i	$0.600709\pi$
$294$		0			0
$295$	−17.6969	−	10.2173i	−1.03036	−	0.594876i
$296$		−	2.51059i		−	0.145925i
$297$		0			0
$298$	−17.4495	−	10.0745i	−1.01082	−	0.583598i
$299$	16.8990	+	29.2699i	0.977293	+	1.69272i
$300$		0			0
$301$	−2.82577	−	4.89437i	−0.162874	−	0.282107i
$302$	−1.34847	+	0.778539i	−0.0775957	+	0.0447999i
$303$		0			0
$304$	−3.50000	−	2.59808i	−0.200739	−	0.149010i
$305$			4.87832i			0.279332i
$306$		0			0
$307$	−13.3485	+	7.70674i	−0.761837	+	0.439847i	−0.829955	−	0.557830i	$-0.811634\pi$
$307$	−13.3485	+	7.70674i	−0.761837	+	0.439847i	0.0681177	+	0.997677i	$0.478301\pi$
$308$	0.797959	+	0.460702i	0.0454679	+	0.0262509i
$309$		0			0
$310$	0.674235	−	1.16781i	0.0382940	−	0.0663271i
$311$			5.16404i			0.292826i	0.989224	+	0.146413i	$0.0467729\pi$
$311$			5.16404i			0.292826i	−0.989224	+	0.146413i	$0.953227\pi$
$312$		0			0
$313$	−11.3485	+	19.6561i	−0.641453	+	1.11103i	0.343655	+	0.939096i	$0.388335\pi$
$313$	−11.3485	+	19.6561i	−0.641453	+	1.11103i	−0.985108	+	0.171934i	$0.944998\pi$
$314$	−6.17423	+	10.6941i	−0.348432	+	0.603502i
$315$		0			0
$316$			0.953512i			0.0536392i
$317$	3.67423	−	6.36396i	0.206366	−	0.357436i	−0.744201	−	0.667955i	$-0.767170\pi$
$317$	3.67423	−	6.36396i	0.206366	−	0.357436i	0.950567	+	0.310520i	$0.100503\pi$
$318$		0			0
$319$	−1.34847	−	0.778539i	−0.0754998	−	0.0435898i
$320$	−1.22474	+	0.707107i	−0.0684653	+	0.0395285i
$321$		0			0
$322$		−	8.19955i		−	0.456943i
$323$	5.32577	−	7.17461i	0.296334	−	0.399206i
$324$		0			0
$325$	−15.5227	+	8.96204i	−0.861045	+	0.497124i
$326$	−3.84847	−	6.66574i	−0.213147	−	0.369181i
$327$		0			0
$328$		0			0
$329$	−2.57321	−	1.48565i	−0.141866	−	0.0819063i
$330$		0			0
$331$		−	18.7026i		−	1.02799i	−0.857794	−	0.513994i	$-0.828165\pi$
$331$		−	18.7026i		−	1.02799i	0.857794	−	0.513994i	$-0.171835\pi$
$332$	10.2247	+	5.90326i	0.561156	+	0.323983i
$333$		0			0
$334$	−8.44949			−0.462336
$335$	14.4495			0.789460
$336$		0			0
$337$	1.80306	−	1.04100i	0.0982190	−	0.0567068i	−0.450086	−	0.892985i	$-0.648607\pi$
$337$	1.80306	−	1.04100i	0.0982190	−	0.0567068i	0.548305	+	0.836278i	$0.315273\pi$
$338$	11.3485	−	19.6561i	0.617275	−	1.06915i
$339$		0			0
$340$	−1.44949	−	2.51059i	−0.0786096	−	0.136156i
$341$	−0.606123			−0.0328234
$342$		0			0
$343$	−17.2474			−0.931275
$344$	−1.94949	−	3.37662i	−0.105109	−	0.182055i
$345$		0			0
$346$	−6.12372	+	10.6066i	−0.329213	+	0.570214i
$347$	−28.2247	+	16.2956i	−1.51518	+	0.874792i	−0.515342	+	0.856984i	$0.672335\pi$
$347$	−28.2247	+	16.2956i	−1.51518	+	0.874792i	−0.999841	+	0.0178073i	$0.994331\pi$
$348$		0			0
$349$	23.2474			1.24441			0.622204	−	0.782855i	$-0.286238\pi$
$349$	23.2474			1.24441			0.622204	+	0.782855i	$0.286238\pi$
$350$	4.34847			0.232435
$351$		0			0
$352$	0.550510	+	0.317837i	0.0293423	+	0.0169408i
$353$		−	3.32124i		−	0.176772i	−0.996086	−	0.0883858i	$-0.971829\pi$
$353$		−	3.32124i		−	0.176772i	0.996086	−	0.0883858i	$-0.0281708\pi$
$354$		0			0
$355$	−7.34847	−	4.24264i	−0.390016	−	0.225176i
$356$	−6.12372	−	10.6066i	−0.324557	−	0.562149i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	9.79796	−	5.65685i	0.517116	−	0.298557i	−0.218638	−	0.975806i	$-0.570161\pi$
$359$	9.79796	−	5.65685i	0.517116	−	0.298557i	0.735754	+	0.677249i	$0.236828\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$			5.37113i			0.282300i
$363$		0			0
$364$	−7.50000	+	4.33013i	−0.393107	+	0.226960i
$365$	−2.57321	−	1.48565i	−0.134688	−	0.0777623i
$366$		0			0
$367$	7.17423	−	12.4261i	0.374492	−	0.648639i	−0.615759	−	0.787935i	$-0.711150\pi$
$367$	7.17423	−	12.4261i	0.374492	−	0.648639i	0.990251	+	0.139295i	$0.0444838\pi$
$368$		−	5.65685i		−	0.294884i
$369$		0			0
$370$	1.77526	−	3.07483i	0.0922911	−	0.159853i
$371$	−3.55051	+	6.14966i	−0.184333	+	0.319275i
$372$		0			0
$373$		−	12.2993i		−	0.636835i	−0.947951	−	0.318418i	$-0.896849\pi$
$373$		−	12.2993i		−	0.636835i	0.947951	−	0.318418i	$-0.103151\pi$
$374$	−0.651531	+	1.12848i	−0.0336899	+	0.0583525i
$375$		0			0
$376$	−1.77526	−	1.02494i	−0.0915518	−	0.0528575i
$377$	12.6742	−	7.31747i	0.652756	−	0.376869i
$378$		0			0
$379$			19.0526i			0.978664i	0.872098	+	0.489332i	$0.162759\pi$
$379$			19.0526i			0.978664i	−0.872098	+	0.489332i	$0.837241\pi$
$380$	−2.44949	−	5.65685i	−0.125656	−	0.290191i
$381$		0			0
$382$	−13.2247	+	7.63531i	−0.676637	+	0.390656i
$383$	−5.44949	−	9.43879i	−0.278456	−	0.482300i	0.692545	−	0.721374i	$-0.256489\pi$
$383$	−5.44949	−	9.43879i	−0.278456	−	0.482300i	−0.971001	+	0.239075i	$0.923156\pi$
$384$		0			0
$385$	0.651531	+	1.12848i	0.0332051	+	0.0575129i
$386$	−14.8485	−	8.57277i	−0.755767	−	0.436342i
$387$		0			0
$388$		−	18.8776i		−	0.958364i
$389$	22.8990	+	13.2207i	1.16102	+	0.670318i	0.951549	−	0.307496i	$-0.0994912\pi$
$389$	22.8990	+	13.2207i	1.16102	+	0.670318i	0.209475	+	0.977814i	$0.432824\pi$
$390$		0			0
$391$	11.5959			0.586431
$392$	−4.89898			−0.247436
$393$		0			0
$394$	−17.5732	+	10.1459i	−0.885326	+	0.511143i
$395$	−0.674235	+	1.16781i	−0.0339244	+	0.0587588i
$396$		0			0
$397$	−10.8258	−	18.7508i	−0.543330	−	0.941074i	−0.998710	−	0.0507775i	$-0.983830\pi$
$397$	−10.8258	−	18.7508i	−0.543330	−	0.941074i	0.455380	−	0.890297i	$-0.349503\pi$
$398$	17.2474			0.864536
$399$		0			0
$400$	3.00000			0.150000
$401$	0.123724	+	0.214297i	0.00617850	+	0.0107015i	0.869098	−	0.494640i	$-0.164700\pi$
$401$	0.123724	+	0.214297i	0.00617850	+	0.0107015i	−0.862920	+	0.505341i	$0.831367\pi$
$402$		0			0
$403$	2.84847	−	4.93369i	0.141892	−	0.245765i
$404$	11.4495	−	6.61037i	0.569633	−	0.328878i
$405$		0			0
$406$	−3.55051			−0.176209
$407$	−1.59592			−0.0791067
$408$		0			0
$409$	−25.0454	−	14.4600i	−1.23842	−	0.715000i	−0.269645	−	0.962960i	$-0.586906\pi$
$409$	−25.0454	−	14.4600i	−1.23842	−	0.715000i	−0.968770	+	0.247960i	$0.920240\pi$
$410$		0			0
$411$		0			0
$412$	12.5227	+	7.22999i	0.616949	+	0.356196i
$413$	10.4722	+	18.1384i	0.515303	+	0.892531i
$414$		0			0
$415$	8.34847	+	14.4600i	0.409810	+	0.709812i
$416$	−5.17423	+	2.98735i	−0.253688	+	0.146467i
$417$		0			0
$418$	−1.65153	+	2.22486i	−0.0807790	+	0.108821i
$419$		−	3.74983i		−	0.183191i	−0.995796	−	0.0915956i	$-0.970803\pi$
$419$		−	3.74983i		−	0.183191i	0.995796	−	0.0915956i	$-0.0291967\pi$
$420$		0			0
$421$	1.34847	−	0.778539i	0.0657204	−	0.0379437i	−0.466780	−	0.884374i	$-0.654586\pi$
$421$	1.34847	−	0.778539i	0.0657204	−	0.0379437i	0.532500	+	0.846430i	$0.321253\pi$
$422$	−3.15153	−	1.81954i	−0.153414	−	0.0885737i
$423$		0			0
$424$	−2.44949	+	4.24264i	−0.118958	+	0.206041i
$425$			6.14966i			0.298303i
$426$		0			0
$427$	2.50000	−	4.33013i	0.120983	−	0.209550i
$428$	−7.89898	+	13.6814i	−0.381812	+	0.661317i
$429$		0			0
$430$		−	5.51399i		−	0.265908i
$431$	−8.02270	+	13.8957i	−0.386440	+	0.669334i	−0.991968	−	0.126490i	$-0.959629\pi$
$431$	−8.02270	+	13.8957i	−0.386440	+	0.669334i	0.605528	+	0.795824i	$0.292962\pi$
$432$		0			0
$433$	25.1969	+	14.5475i	1.21089	+	0.699106i	0.962953	−	0.269670i	$-0.0869148\pi$
$433$	25.1969	+	14.5475i	1.21089	+	0.699106i	0.247935	+	0.968777i	$0.420248\pi$
$434$	−1.19694	+	0.691053i	−0.0574549	+	0.0331716i
$435$		0			0
$436$		−	16.9706i		−	0.812743i
$437$	24.4949	+	2.82843i	1.17175	+	0.135302i
$438$		0			0
$439$	−12.5227	+	7.22999i	−0.597676	+	0.345068i	−0.768127	−	0.640298i	$-0.778811\pi$
$439$	−12.5227	+	7.22999i	−0.597676	+	0.345068i	0.170451	+	0.985366i	$0.445478\pi$
$440$	0.449490	+	0.778539i	0.0214286	+	0.0371154i
$441$		0			0
$442$	−6.12372	−	10.6066i	−0.291276	−	0.504505i
$443$	−25.7753	−	14.8814i	−1.22462	−	0.707034i	−0.258720	−	0.965952i	$-0.583301\pi$
$443$	−25.7753	−	14.8814i	−1.22462	−	0.707034i	−0.965899	+	0.258918i	$0.916634\pi$
$444$		0			0
$445$		−	17.3205i		−	0.821071i
$446$	2.17423	+	1.25529i	0.102953	+	0.0594399i
$447$		0			0
$448$	1.44949			0.0684820
$449$	−18.2474			−0.861150			−0.430575	−	0.902555i	$-0.641689\pi$
$449$	−18.2474			−0.861150			−0.430575	+	0.902555i	$0.641689\pi$
$450$		0			0
$451$		0			0
$452$	8.57321	−	14.8492i	0.403250	−	0.698450i
$453$		0			0
$454$	11.5732	+	20.0454i	0.543158	+	0.940777i
$455$	−12.2474			−0.574169
$456$		0			0
$457$	19.6969			0.921384			0.460692	−	0.887560i	$-0.347601\pi$
$457$	19.6969			0.921384			0.460692	+	0.887560i	$0.347601\pi$
$458$	9.62372	+	16.6688i	0.449687	+	0.778881i
$459$		0			0
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	9.12372	−	5.26758i	0.424934	−	0.245336i	−0.272252	−	0.962226i	$-0.587768\pi$
$461$	9.12372	−	5.26758i	0.424934	−	0.245336i	0.697186	+	0.716890i	$0.254435\pi$
$462$		0			0
$463$	40.1464			1.86576			0.932881	−	0.360184i	$-0.117286\pi$
$463$	40.1464			1.86576			0.932881	+	0.360184i	$0.117286\pi$
$464$	−2.44949			−0.113715
$465$		0			0
$466$	15.2474	+	8.80312i	0.706324	+	0.407797i
$467$		−	21.0703i		−	0.975019i	−0.873118	−	0.487510i	$-0.837905\pi$
$467$		−	21.0703i		−	0.975019i	0.873118	−	0.487510i	$-0.162095\pi$
$468$		0			0
$469$	−12.8258	−	7.40496i	−0.592239	−	0.341929i
$470$	−1.44949	−	2.51059i	−0.0668600	−	0.115805i
$471$		0			0
$472$	7.22474	+	12.5136i	0.332546	+	0.575986i
$473$	−2.14643	+	1.23924i	−0.0986929	+	0.0569804i
$474$		0			0
$475$	−1.50000	+	12.9904i	−0.0688247	+	0.596040i
$476$			2.97129i			0.136189i
$477$		0			0
$478$	19.4722	−	11.2423i	0.890637	−	0.514210i
$479$	−8.14643	−	4.70334i	−0.372220	−	0.214901i	0.302208	−	0.953242i	$-0.402276\pi$
$479$	−8.14643	−	4.70334i	−0.372220	−	0.214901i	−0.674428	+	0.738341i	$0.735610\pi$
$480$		0			0
$481$	7.50000	−	12.9904i	0.341971	−	0.592310i
$482$		−	14.0314i		−	0.639112i
$483$		0			0
$484$	−5.29796	+	9.17633i	−0.240816	+	0.417106i
$485$	13.3485	−	23.1202i	0.606123	−	1.04984i
$486$		0			0
$487$			39.6622i			1.79727i	0.438702	+	0.898633i	$0.355439\pi$
$487$			39.6622i			1.79727i	−0.438702	+	0.898633i	$0.644561\pi$
$488$	1.72474	−	2.98735i	0.0780755	−	0.135231i
$489$		0			0
$490$	−6.00000	−	3.46410i	−0.271052	−	0.156492i
$491$	26.1464	−	15.0956i	1.17997	−	0.681257i	0.223964	−	0.974597i	$-0.428100\pi$
$491$	26.1464	−	15.0956i	1.17997	−	0.681257i	0.956008	+	0.293340i	$0.0947669\pi$
$492$		0			0
$493$		−	5.02118i		−	0.226143i
$494$	−10.3485	−	23.8988i	−0.465600	−	1.07526i
$495$		0			0
$496$	−0.825765	+	0.476756i	−0.0370780	+	0.0214070i
$497$	4.34847	+	7.53177i	0.195056	+	0.337846i
$498$		0			0
$499$	21.7474	+	37.6677i	0.973550	+	1.68624i	0.684641	+	0.728881i	$0.259959\pi$
$499$	21.7474	+	37.6677i	0.973550	+	1.68624i	0.288909	+	0.957357i	$0.406708\pi$
$500$	9.79796	+	5.65685i	0.438178	+	0.252982i
$501$		0			0
$502$		−	1.41421i		−	0.0631194i
$503$	−35.5176	−	20.5061i	−1.58365	−	0.914322i	−0.994320	−	0.106430i	$-0.966058\pi$
$503$	−35.5176	−	20.5061i	−1.58365	−	0.914322i	−0.589331	−	0.807891i	$-0.700609\pi$
$504$		0			0
$505$	18.6969			0.832003
$506$	−3.59592			−0.159858
$507$		0			0
$508$	−7.34847	+	4.24264i	−0.326036	+	0.188237i
$509$	−6.67423	+	11.5601i	−0.295830	+	0.512393i	−0.975178	−	0.221424i	$-0.928930\pi$
$509$	−6.67423	+	11.5601i	−0.295830	+	0.512393i	0.679347	+	0.733817i	$0.262263\pi$
$510$		0			0
$511$	1.52270	+	2.63740i	0.0673605	+	0.116672i
$512$	1.00000			0.0441942
$513$		0			0
$514$	12.0000			0.529297
$515$	10.2247	+	17.7098i	0.450556	+	0.780386i
$516$		0			0
$517$	−0.651531	+	1.12848i	−0.0286543	+	0.0496307i
$518$	−3.15153	+	1.81954i	−0.138470	+	0.0799459i
$519$		0			0
$520$	−8.44949			−0.370535
$521$	−8.20204			−0.359338			−0.179669	−	0.983727i	$-0.557503\pi$
$521$	−8.20204			−0.359338			−0.179669	+	0.983727i	$0.557503\pi$
$522$		0			0
$523$	13.5000	+	7.79423i	0.590314	+	0.340818i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	13.5000	+	7.79423i	0.590314	+	0.340818i	−0.174908	+	0.984585i	$0.555963\pi$
$524$			14.7778i			0.645572i
$525$		0			0
$526$	−0.797959	−	0.460702i	−0.0347927	−	0.0200876i
$527$	−0.977296	−	1.69273i	−0.0425717	−	0.0737363i
$528$		0			0
$529$	4.50000	+	7.79423i	0.195652	+	0.338880i
$530$	−6.00000	+	3.46410i	−0.260623	+	0.150471i
$531$		0			0
$532$	−0.724745	+	6.27647i	−0.0314217	+	0.272120i
$533$		0			0
$534$		0			0
$535$	−19.3485	+	11.1708i	−0.836507	+	0.482958i
$536$	−8.84847	−	5.10867i	−0.382196	−	0.220661i
$537$		0			0
$538$	10.2247	−	17.7098i	0.440820	−	0.763523i
$539$			3.11416i			0.134136i
$540$		0			0
$541$	−15.1742	+	26.2825i	−0.652391	+	1.12997i	0.330150	+	0.943929i	$0.392901\pi$
$541$	−15.1742	+	26.2825i	−0.652391	+	1.12997i	−0.982541	+	0.186046i	$0.940433\pi$
$542$	−15.6969	+	27.1879i	−0.674241	+	1.16782i
$543$		0			0
$544$			2.04989i			0.0878882i
$545$	12.0000	−	20.7846i	0.514024	−	0.890315i
$546$		0			0
$547$	−1.80306	−	1.04100i	−0.0770933	−	0.0445099i	0.460958	−	0.887422i	$-0.347506\pi$
$547$	−1.80306	−	1.04100i	−0.0770933	−	0.0445099i	−0.538051	+	0.842912i	$0.680839\pi$
$548$	5.44949	−	3.14626i	0.232791	−	0.134402i
$549$		0			0
$550$		−	1.90702i		−	0.0813158i
$551$	1.22474	−	10.6066i	0.0521759	−	0.451856i
$552$		0			0
$553$	1.19694	−	0.691053i	0.0508990	−	0.0293866i
$554$	−4.55051	−	7.88171i	−0.193333	−	0.334862i
$555$		0			0
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	22.5959	+	13.0458i	0.957420	+	0.552767i	0.895378	−	0.445307i	$-0.146905\pi$
$557$	22.5959	+	13.0458i	0.957420	+	0.552767i	0.0620418	+	0.998074i	$0.480239\pi$
$558$		0			0
$559$		−	23.2952i		−	0.985282i
$560$	1.77526	+	1.02494i	0.0750182	+	0.0433118i
$561$		0			0
$562$	23.1464			0.976373
$563$	−25.5959			−1.07874			−0.539370	−	0.842069i	$-0.681337\pi$
$563$	−25.5959			−1.07874			−0.539370	+	0.842069i	$0.681337\pi$
$564$		0			0
$565$	21.0000	−	12.1244i	0.883477	−	0.510075i
$566$	7.44949	−	12.9029i	0.313125	−	0.542349i
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	31.1010			1.30382			0.651911	−	0.758295i	$-0.273967\pi$
$569$	31.1010			1.30382			0.651911	+	0.758295i	$0.273967\pi$
$570$		0			0
$571$	−3.69694			−0.154712			−0.0773560	−	0.997004i	$-0.524648\pi$
$571$	−3.69694			−0.154712			−0.0773560	+	0.997004i	$0.524648\pi$
$572$	1.89898	+	3.28913i	0.0794003	+	0.137525i
$573$		0			0
$574$		0			0
$575$	−14.6969	+	8.48528i	−0.612905	+	0.353861i
$576$		0			0
$577$	5.79796			0.241372			0.120686	−	0.992691i	$-0.461491\pi$
$577$	5.79796			0.241372			0.120686	+	0.992691i	$0.461491\pi$
$578$	12.7980			0.532325
$579$		0			0
$580$	−3.00000	−	1.73205i	−0.124568	−	0.0719195i
$581$		−	17.1134i		−	0.709985i
$582$		0			0
$583$	2.69694	+	1.55708i	0.111696	+	0.0644876i
$584$	1.05051	+	1.81954i	0.0434704	+	0.0752930i
$585$		0			0
$586$	5.32577	+	9.22450i	0.220005	+	0.381060i
$587$	24.1237	−	13.9278i	0.995693	−	0.574863i	0.0887216	−	0.996056i	$-0.471722\pi$
$587$	24.1237	−	13.9278i	0.995693	−	0.574863i	0.906971	+	0.421193i	$0.138389\pi$
$588$		0			0
$589$	−1.65153	−	3.81405i	−0.0680501	−	0.157155i
$590$			20.4347i			0.841282i
$591$		0			0
$592$	−2.17423	+	1.25529i	−0.0893605	+	0.0515923i
$593$	−13.4722	−	7.77817i	−0.553237	−	0.319411i	0.197190	−	0.980365i	$-0.436818\pi$
$593$	−13.4722	−	7.77817i	−0.553237	−	0.319411i	−0.750426	+	0.660954i	$0.770152\pi$
$594$		0			0
$595$	−2.10102	+	3.63907i	−0.0861334	+	0.149188i
$596$			20.1489i			0.825333i
$597$		0			0
$598$	16.8990	−	29.2699i	0.691051	−	1.19693i
$599$	18.7980	−	32.5590i	0.768064	−	1.33033i	−0.170548	−	0.985349i	$-0.554554\pi$
$599$	18.7980	−	32.5590i	0.768064	−	1.33033i	0.938611	−	0.344976i	$-0.112113\pi$
$600$		0			0
$601$		−	10.2173i		−	0.416774i	−0.978046	−	0.208387i	$-0.933179\pi$
$601$		−	10.2173i		−	0.416774i	0.978046	−	0.208387i	$-0.0668213\pi$
$602$	−2.82577	+	4.89437i	−0.115170	+	0.199480i
$603$		0			0
$604$	1.34847	+	0.778539i	0.0548684	+	0.0316783i
$605$	−12.9773	+	7.49245i	−0.527602	+	0.304611i
$606$		0			0
$607$		−	2.16064i		−	0.0876979i	−0.999038	−	0.0438489i	$-0.986038\pi$
$607$		−	2.16064i		−	0.0876979i	0.999038	−	0.0438489i	$-0.0139620\pi$
$608$	−0.500000	+	4.33013i	−0.0202777	+	0.175610i
$609$		0			0
$610$	4.22474	−	2.43916i	0.171055	−	0.0987586i
$611$	−6.12372	−	10.6066i	−0.247739	−	0.429097i
$612$		0			0
$613$	−9.44949	−	16.3670i	−0.381661	−	0.661057i	0.609639	−	0.792680i	$-0.291315\pi$
$613$	−9.44949	−	16.3670i	−0.381661	−	0.661057i	−0.991300	+	0.131623i	$0.957981\pi$
$614$	13.3485	+	7.70674i	0.538700	+	0.311019i
$615$		0			0
$616$		−	0.921404i		−	0.0371244i
$617$	−28.1010	−	16.2241i	−1.13130	−	0.653159i	−0.187042	−	0.982352i	$-0.559890\pi$
$617$	−28.1010	−	16.2241i	−1.13130	−	0.653159i	−0.944263	+	0.329193i	$0.893223\pi$
$618$		0			0
$619$	−36.3939			−1.46279			−0.731397	−	0.681952i	$-0.761131\pi$
$619$	−36.3939			−1.46279			−0.731397	+	0.681952i	$0.761131\pi$
$620$	−1.34847			−0.0541558
$621$		0			0
$622$	4.47219	−	2.58202i	0.179319	−	0.103530i
$623$	−8.87628	+	15.3742i	−0.355620	+	0.615953i
$624$		0			0
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	22.6969			0.907152
$627$		0			0
$628$	12.3485			0.492758
$629$	−2.57321	−	4.45694i	−0.102601	−	0.177710i
$630$		0			0
$631$	−7.27526	+	12.6011i	−0.289623	+	0.501642i	−0.973720	−	0.227749i	$-0.926863\pi$
$631$	−7.27526	+	12.6011i	−0.289623	+	0.501642i	0.684096	+	0.729392i	$0.260197\pi$
$632$	0.825765	−	0.476756i	0.0328472	−	0.0189643i
$633$		0			0
$634$	−7.34847			−0.291845
$635$	−12.0000			−0.476205
$636$		0			0
$637$	−25.3485	−	14.6349i	−1.00434	−	0.579858i
$638$			1.55708i			0.0616453i
$639$		0			0
$640$	1.22474	+	0.707107i	0.0484123	+	0.0279508i
$641$	23.0227	+	39.8765i	0.909342	+	1.57503i	0.814980	+	0.579489i	$0.196748\pi$
$641$	23.0227	+	39.8765i	0.909342	+	1.57503i	0.0943619	+	0.995538i	$0.469919\pi$
$642$		0			0
$643$	−21.2980	−	36.8891i	−0.839910	−	1.45477i	−0.889970	−	0.456020i	$-0.849275\pi$
$643$	−21.2980	−	36.8891i	−0.839910	−	1.45477i	0.0500601	−	0.998746i	$-0.484059\pi$
$644$	−7.10102	+	4.09978i	−0.279819	+	0.161554i
$645$		0			0
$646$	−8.87628	−	1.02494i	−0.349232	−	0.0403259i
$647$		−	2.97129i		−	0.116814i	−0.998293	−	0.0584068i	$-0.981398\pi$
$647$		−	2.97129i		−	0.116814i	0.998293	−	0.0584068i	$-0.0186020\pi$
$648$		0			0
$649$	7.95459	−	4.59259i	0.312245	−	0.180275i
$650$	15.5227	+	8.96204i	0.608851	+	0.351520i
$651$		0			0
$652$	−3.84847	+	6.66574i	−0.150718	+	0.261051i
$653$		−	38.3908i		−	1.50235i	−0.660103	−	0.751175i	$-0.729487\pi$
$653$		−	38.3908i		−	1.50235i	0.660103	−	0.751175i	$-0.270513\pi$
$654$		0			0
$655$	−10.4495	+	18.0990i	−0.408295	+	0.707188i
$656$		0			0
$657$		0			0
$658$			2.97129i			0.115833i
$659$	5.69694	−	9.86739i	0.221921	−	0.384379i	−0.733470	−	0.679722i	$-0.762101\pi$
$659$	5.69694	−	9.86739i	0.221921	−	0.384379i	0.955391	+	0.295343i	$0.0954339\pi$
$660$		0			0
$661$	−23.6969	−	13.6814i	−0.921704	−	0.532146i	−0.0375258	−	0.999296i	$-0.511948\pi$
$661$	−23.6969	−	13.6814i	−0.921704	−	0.532146i	−0.884178	+	0.467150i	$0.845281\pi$
$662$	−16.1969	+	9.35131i	−0.629512	+	0.363449i
$663$		0			0
$664$		−	11.8065i		−	0.458182i
$665$	−5.32577	+	7.17461i	−0.206524	+	0.278219i
$666$		0			0
$667$	12.0000	−	6.92820i	0.464642	−	0.268261i
$668$	4.22474	+	7.31747i	0.163460	+	0.283122i
$669$		0			0
$670$	−7.22474	−	12.5136i	−0.279116	−	0.483444i
$671$	−1.89898	−	1.09638i	−0.0733093	−	0.0423251i
$672$		0			0
$673$			19.0526i			0.734422i	0.930138	+	0.367211i	$0.119687\pi$
$673$			19.0526i			0.734422i	−0.930138	+	0.367211i	$0.880313\pi$
$674$	−1.80306	−	1.04100i	−0.0694513	−	0.0400977i
$675$		0			0
$676$	−22.6969			−0.872959
$677$	37.3485			1.43542			0.717709	−	0.696343i	$-0.245191\pi$
$677$	37.3485			1.43542			0.717709	+	0.696343i	$0.245191\pi$
$678$		0			0
$679$	−23.6969	+	13.6814i	−0.909405	+	0.525045i
$680$	−1.44949	+	2.51059i	−0.0555854	+	0.0962767i
$681$		0			0
$682$	0.303062	+	0.524918i	0.0116048	+	0.0201001i
$683$	−28.0454			−1.07313			−0.536564	−	0.843860i	$-0.680278\pi$
$683$	−28.0454			−1.07313			−0.536564	+	0.843860i	$0.680278\pi$
$684$		0			0
$685$	8.89898			0.340013
$686$	8.62372	+	14.9367i	0.329255	+	0.570287i
$687$		0			0
$688$	−1.94949	+	3.37662i	−0.0743236	+	0.128732i
$689$	−25.3485	+	14.6349i	−0.965700	+	0.557547i
$690$		0			0
$691$	−0.696938			−0.0265128			−0.0132564	−	0.999912i	$-0.504220\pi$
$691$	−0.696938			−0.0265128			−0.0132564	+	0.999912i	$0.504220\pi$
$692$	12.2474			0.465578
$693$		0			0
$694$	28.2247	+	16.2956i	1.07140	+	0.618571i
$695$			9.89949i			0.375509i
$696$		0			0
$697$		0			0
$698$	−11.6237	−	20.1329i	−0.439964	−	0.762041i
$699$		0			0
$700$	−2.17423	−	3.76588i	−0.0821783	−	0.142337i
$701$	13.4722	−	7.77817i	0.508838	−	0.293778i	−0.223518	−	0.974700i	$-0.571754\pi$
$701$	13.4722	−	7.77817i	0.508838	−	0.293778i	0.732356	+	0.680922i	$0.238421\pi$
$702$		0			0
$703$	−4.34847	−	10.0424i	−0.164006	−	0.378755i
$704$		−	0.635674i		−	0.0239579i
$705$		0			0
$706$	−2.87628	+	1.66062i	−0.108250	+	0.0624982i
$707$	−16.5959	−	9.58166i	−0.624154	−	0.360355i
$708$		0			0
$709$	−3.17423	+	5.49794i	−0.119211	+	0.206479i	−0.919455	−	0.393195i	$-0.871370\pi$
$709$	−3.17423	+	5.49794i	−0.119211	+	0.206479i	0.800244	+	0.599674i	$0.204703\pi$
$710$			8.48528i			0.318447i
$711$		0			0
$712$	−6.12372	+	10.6066i	−0.229496	+	0.397499i
$713$	2.69694	−	4.67123i	0.101001	−	0.174939i
$714$		0			0
$715$			5.37113i			0.200869i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	−9.79796	−	5.65685i	−0.365657	−	0.211112i
$719$	17.1464	−	9.89949i	0.639454	−	0.369189i	−0.144950	−	0.989439i	$-0.546302\pi$
$719$	17.1464	−	9.89949i	0.639454	−	0.369189i	0.784404	+	0.620250i	$0.212969\pi$
$720$		0			0
$721$		−	20.9596i		−	0.780576i
$722$	−18.5000	−	4.33013i	−0.688499	−	0.161151i
$723$		0			0
$724$	4.65153	−	2.68556i	0.172873	−	0.0998081i
$725$	3.67423	+	6.36396i	0.136458	+	0.236352i
$726$		0			0
$727$	−4.82577	−	8.35847i	−0.178978	−	0.309999i	0.762553	−	0.646926i	$-0.223946\pi$
$727$	−4.82577	−	8.35847i	−0.178978	−	0.309999i	−0.941531	+	0.336927i	$0.890612\pi$
$728$	7.50000	+	4.33013i	0.277968	+	0.160485i
$729$		0			0
$730$			2.97129i			0.109972i
$731$	−6.92168	−	3.99624i	−0.256008	−	0.147806i
$732$		0			0
$733$	−30.6969			−1.13382			−0.566909	−	0.823781i	$-0.691861\pi$
$733$	−30.6969			−1.13382			−0.566909	+	0.823781i	$0.691861\pi$
$734$	−14.3485			−0.529612
$735$		0			0
$736$	−4.89898	+	2.82843i	−0.180579	+	0.104257i
$737$	−3.24745	+	5.62475i	−0.119621	+	0.207190i
$738$		0			0
$739$	−23.1969	−	40.1783i	−0.853313	−	1.47798i	−0.878201	−	0.478292i	$-0.841256\pi$
$739$	−23.1969	−	40.1783i	−0.853313	−	1.47798i	0.0248879	−	0.999690i	$-0.492077\pi$
$740$	−3.55051			−0.130519
$741$		0			0
$742$	7.10102			0.260687
$743$	−23.6969	−	41.0443i	−0.869356	−	1.50577i	−0.862656	−	0.505792i	$-0.831200\pi$
$743$	−23.6969	−	41.0443i	−0.869356	−	1.50577i	−0.00670079	−	0.999978i	$-0.502133\pi$
$744$		0			0
$745$	−14.2474	+	24.6773i	−0.521986	+	0.904107i
$746$	−10.6515	+	6.14966i	−0.389980	+	0.225155i
$747$		0			0
$748$	1.30306			0.0476446
$749$	22.8990			0.836711
$750$		0			0
$751$	24.2196	+	13.9832i	0.883787	+	0.510255i	0.871905	−	0.489675i	$-0.162884\pi$
$751$	24.2196	+	13.9832i	0.883787	+	0.510255i	0.0118820	+	0.999929i	$0.496218\pi$
$752$			2.04989i			0.0747517i
$753$		0			0
$754$	−12.6742	−	7.31747i	−0.461568	−	0.266487i
$755$	1.10102	+	1.90702i	0.0400702	+	0.0694037i
$756$		0			0
$757$	−12.1742	−	21.0864i	−0.442480	−	0.766398i	0.555393	−	0.831588i	$-0.312568\pi$
$757$	−12.1742	−	21.0864i	−0.442480	−	0.766398i	−0.997873	+	0.0651902i	$0.979235\pi$
$758$	16.5000	−	9.52628i	0.599307	−	0.346010i
$759$		0			0
$760$	−3.67423	+	4.94975i	−0.133278	+	0.179546i
$761$			44.8262i			1.62495i	0.582996	+	0.812475i	$0.301880\pi$
$761$			44.8262i			1.62495i	−0.582996	+	0.812475i	$0.698120\pi$
$762$		0			0
$763$	−21.3031	+	12.2993i	−0.771223	+	0.445266i
$764$	13.2247	+	7.63531i	0.478454	+	0.276236i
$765$		0			0
$766$	−5.44949	+	9.43879i	−0.196898	+	0.341037i
$767$			86.3312i			3.11724i
$768$		0			0
$769$	1.29796	−	2.24813i	0.0468056	−	0.0810697i	−0.841673	−	0.539987i	$-0.818429\pi$
$769$	1.29796	−	2.24813i	0.0468056	−	0.0810697i	0.888479	+	0.458917i	$0.151763\pi$
$770$	0.651531	−	1.12848i	0.0234795	−	0.0406678i
$771$		0			0
$772$			17.1455i			0.617081i
$773$	4.47219	−	7.74607i	0.160854	−	0.278607i	−0.774321	−	0.632792i	$-0.781909\pi$
$773$	4.47219	−	7.74607i	0.160854	−	0.278607i	0.935175	+	0.354186i	$0.115242\pi$
$774$		0			0
$775$	2.47730	+	1.43027i	0.0889871	+	0.0513767i
$776$	−16.3485	+	9.43879i	−0.586876	+	0.338833i
$777$		0			0
$778$		−	26.4415i		−	0.947972i
$779$		0			0
$780$		0			0
$781$	3.30306	−	1.90702i	0.118193	−	0.0682387i
$782$	−5.79796	−	10.0424i	−0.207335	−	0.359114i
$783$		0			0
$784$	2.44949	+	4.24264i	0.0874818	+	0.151523i
$785$	15.1237	+	8.73169i	0.539789	+	0.311647i
$786$		0			0
$787$			24.0737i			0.858136i	0.903272	+	0.429068i	$0.141158\pi$
$787$			24.0737i			0.858136i	−0.903272	+	0.429068i	$0.858842\pi$
$788$	17.5732	+	10.1459i	0.626020	+	0.361433i
$789$		0			0
$790$	1.34847			0.0479764
$791$	−24.8536			−0.883691
$792$		0			0
$793$	17.8485	−	10.3048i	0.633818	−	0.365935i
$794$	−10.8258	+	18.7508i	−0.384192	+	0.665440i
$795$		0			0
$796$	−8.62372	−	14.9367i	−0.305660	−	0.529418i
$797$	38.0908			1.34925			0.674623	−	0.738162i	$-0.264306\pi$
$797$	38.0908			1.34925			0.674623	+	0.738162i	$0.264306\pi$
$798$		0			0
$799$	−4.20204			−0.148658
$800$	−1.50000	−	2.59808i	−0.0530330	−	0.0918559i
$801$		0			0
$802$	0.123724	−	0.214297i	0.00436886	−	0.00756709i
$803$	1.15663	−	0.667783i	0.0408167	−	0.0235655i
$804$		0			0
$805$	−11.5959			−0.408702
$806$	−5.69694			−0.200666
$807$		0			0
$808$	−11.4495	−	6.61037i	−0.402792	−	0.232552i
$809$			5.16404i			0.181558i	0.995871	+	0.0907791i	$0.0289357\pi$
$809$			5.16404i			0.181558i	−0.995871	+	0.0907791i	$0.971064\pi$
$810$		0			0
$811$	17.6969	+	10.2173i	0.621424	+	0.358779i	0.777423	−	0.628978i	$-0.216526\pi$
$811$	17.6969	+	10.2173i	0.621424	+	0.358779i	−0.155999	+	0.987757i	$0.549860\pi$
$812$	1.77526	+	3.07483i	0.0622992	+	0.107905i
$813$		0			0
$814$	0.797959	+	1.38211i	0.0279684	+	0.0484428i
$815$	−9.42679	+	5.44256i	−0.330206	+	0.190644i
$816$		0			0
$817$	−13.6464	−	10.1298i	−0.477428	−	0.354398i
$818$			28.9199i			1.01116i
$819$		0			0
$820$		0			0
$821$	−34.1691	−	19.7276i	−1.19251	−	0.688497i	−0.233636	−	0.972324i	$-0.575062\pi$
$821$	−34.1691	−	19.7276i	−1.19251	−	0.688497i	−0.958875	+	0.283828i	$0.908396\pi$
$822$		0			0
$823$	−17.3485	+	30.0484i	−0.604730	+	1.04742i	0.387365	+	0.921927i	$0.373385\pi$
$823$	−17.3485	+	30.0484i	−0.604730	+	1.04742i	−0.992094	+	0.125496i	$0.959948\pi$
$824$		−	14.4600i		−	0.503737i
$825$		0			0
$826$	10.4722	−	18.1384i	0.364374	−	0.631115i
$827$	−23.8207	+	41.2586i	−0.828326	+	1.43470i	0.0710253	+	0.997475i	$0.477373\pi$
$827$	−23.8207	+	41.2586i	−0.828326	+	1.43470i	−0.899351	+	0.437228i	$0.855960\pi$
$828$		0			0
$829$		−	10.9959i		−	0.381902i	−0.981600	−	0.190951i	$-0.938843\pi$
$829$		−	10.9959i		−	0.381902i	0.981600	−	0.190951i	$-0.0611572\pi$
$830$	8.34847	−	14.4600i	0.289780	−	0.501913i
$831$		0			0
$832$	5.17423	+	2.98735i	0.179384	+	0.103568i
$833$	−8.69694	+	5.02118i	−0.301331	+	0.173974i
$834$		0			0
$835$			11.9494i			0.413525i
$836$	2.75255	+	0.317837i	0.0951990	+	0.0109926i
$837$		0			0
$838$	−3.24745	+	1.87492i	−0.112181	+	0.0647679i
$839$	−5.02270	−	8.69958i	−0.173403	−	0.300343i	0.766204	−	0.642597i	$-0.222143\pi$
$839$	−5.02270	−	8.69958i	−0.173403	−	0.300343i	−0.939607	+	0.342254i	$0.888810\pi$
$840$		0			0
$841$	11.5000	+	19.9186i	0.396552	+	0.686848i
$842$	−1.34847	−	0.778539i	−0.0464713	−	0.0268302i
$843$		0			0
$844$			3.63907i			0.125262i
$845$	−27.7980	−	16.0492i	−0.956279	−	0.552108i
$846$		0			0
$847$	15.3587			0.527730
$848$	4.89898			0.168232
$849$		0			0
$850$	5.32577	−	3.07483i	0.182672	−	0.105466i
$851$	7.10102	−	12.2993i	0.243420	−	0.421616i
$852$		0			0
$853$	14.8258	+	25.6790i	0.507625	+	0.879231i	0.999961	+	0.00882655i	$0.00280961\pi$
$853$	14.8258	+	25.6790i	0.507625	+	0.879231i	−0.492337	+	0.870405i	$0.663857\pi$
$854$	−5.00000			−0.171096
$855$		0			0
$856$	15.7980			0.539963
$857$	3.42679	+	5.93537i	0.117057	+	0.202748i	0.918600	−	0.395188i	$-0.129321\pi$
$857$	3.42679	+	5.93537i	0.117057	+	0.202748i	−0.801543	+	0.597937i	$0.795987\pi$
$858$		0			0
$859$	−1.94949	+	3.37662i	−0.0665157	+	0.115209i	−0.897365	−	0.441288i	$-0.854522\pi$
$859$	−1.94949	+	3.37662i	−0.0665157	+	0.115209i	0.830850	+	0.556497i	$0.187855\pi$
$860$	−4.77526	+	2.75699i	−0.162835	+	0.0940127i
$861$		0			0
$862$	16.0454			0.546509
$863$	37.3485			1.27136			0.635678	−	0.771954i	$-0.280720\pi$
$863$	37.3485			1.27136			0.635678	+	0.771954i	$0.280720\pi$
$864$		0			0
$865$	15.0000	+	8.66025i	0.510015	+	0.294457i
$866$		−	29.0949i		−	0.988686i
$867$		0			0
$868$	1.19694	+	0.691053i	0.0406267	+	0.0234559i
$869$	−0.303062	−	0.524918i	−0.0102807	−	0.0178066i
$870$		0			0
$871$	−30.5227	−	52.8669i	−1.03422	−	1.79133i
$872$	−14.6969	+	8.48528i	−0.497701	+	0.287348i
$873$		0			0
$874$	−9.79796	−	22.6274i	−0.331421	−	0.765384i
$875$		−	16.3991i		−	0.554391i
$876$		0			0
$877$	24.5227	−	14.1582i	0.828073	−	0.478088i	−0.0251195	−	0.999684i	$-0.507997\pi$
$877$	24.5227	−	14.1582i	0.828073	−	0.478088i	0.853192	+	0.521596i	$0.174663\pi$
$878$	12.5227	+	7.22999i	0.422621	+	0.244000i
$879$		0			0
$880$	0.449490	−	0.778539i	0.0151523	−	0.0262445i
$881$			2.04989i			0.0690625i	0.999404	+	0.0345312i	$0.0109938\pi$
$881$			2.04989i			0.0690625i	−0.999404	+	0.0345312i	$0.989006\pi$
$882$		0			0
$883$	2.94949	−	5.10867i	0.0992582	−	0.171920i	−0.812120	−	0.583491i	$-0.801686\pi$
$883$	2.94949	−	5.10867i	0.0992582	−	0.171920i	0.911378	+	0.411571i	$0.135020\pi$
$884$	−6.12372	+	10.6066i	−0.205963	+	0.356739i
$885$		0			0
$886$			29.7627i			0.999897i
$887$	−11.3258	+	19.6168i	−0.380282	+	0.658668i	−0.991102	−	0.133101i	$-0.957506\pi$
$887$	−11.3258	+	19.6168i	−0.380282	+	0.658668i	0.610820	+	0.791769i	$0.290840\pi$
$888$		0			0
$889$	10.6515	+	6.14966i	0.357241	+	0.206253i
$890$	−15.0000	+	8.66025i	−0.502801	+	0.290292i
$891$		0			0
$892$		−	2.51059i		−	0.0840608i
$893$	−8.87628	−	1.02494i	−0.297033	−	0.0342984i
$894$		0			0
$895$	14.6969	−	8.48528i	0.491264	−	0.283632i
$896$	−0.724745	−	1.25529i	−0.0242120	−	0.0419365i
$897$		0			0
$898$	9.12372	+	15.8028i	0.304463	+	0.527345i
$899$	−2.02270	−	1.16781i	−0.0674610	−	0.0389486i
$900$		0			0
$901$			10.0424i			0.334560i
$902$		0			0
$903$		0			0
$904$	−17.1464			−0.570282
$905$	7.59592			0.252497
$906$		0			0
$907$	35.6969	−	20.6096i	1.18530	−	0.684332i	0.228063	−	0.973646i	$-0.426761\pi$
$907$	35.6969	−	20.6096i	1.18530	−	0.684332i	0.957234	+	0.289315i	$0.0934274\pi$
$908$	11.5732	−	20.0454i	0.384071	−	0.665230i
$909$		0			0
$910$	6.12372	+	10.6066i	0.202999	+	0.351605i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−7.50510			−0.248383
$914$	−9.84847	−	17.0580i	−0.325758	−	0.564230i
$915$		0			0
$916$	9.62372	−	16.6688i	0.317977	−	0.550752i
$917$	18.5505	−	10.7101i	0.612592	−	0.353680i
$918$		0			0
$919$	9.04541			0.298380			0.149190	−	0.988809i	$-0.452333\pi$
$919$	9.04541			0.298380			0.149190	+	0.988809i	$0.452333\pi$
$920$	−8.00000			−0.263752
$921$		0			0
$922$	−9.12372	−	5.26758i	−0.300474	−	0.173479i
$923$			35.8481i			1.17996i
$924$		0			0
$925$	6.52270	+	3.76588i	0.214465	+	0.123822i
$926$	−20.0732	−	34.7678i	−0.659647	−	1.14254i
$927$		0			0
$928$	1.22474	+	2.12132i	0.0402042	+	0.0696358i
$929$	−35.5732	+	20.5382i	−1.16712	+	0.673837i	−0.953000	−	0.302971i	$-0.902022\pi$
$929$	−35.5732	+	20.5382i	−1.16712	+	0.673837i	−0.214119	+	0.976807i	$0.568688\pi$
$930$		0			0
$931$	−19.5959	+	8.48528i	−0.642230	+	0.278094i
$932$		−	17.6062i		−	0.576711i
$933$		0			0
$934$	−18.2474	+	10.5352i	−0.597075	+	0.344721i
$935$	1.59592	+	0.921404i	0.0521921	+	0.0301331i
$936$		0			0
$937$	−8.19694	+	14.1975i	−0.267782	+	0.463813i	−0.968289	−	0.249833i	$-0.919624\pi$
$937$	−8.19694	+	14.1975i	−0.267782	+	0.463813i	0.700507	+	0.713646i	$0.252957\pi$
$938$			14.8099i			0.483561i
$939$		0			0
$940$	−1.44949	+	2.51059i	−0.0472771	+	0.0818864i
$941$	20.4495	−	35.4196i	0.666634	−	1.15464i	−0.312205	−	0.950015i	$-0.601068\pi$
$941$	20.4495	−	35.4196i	0.666634	−	1.15464i	0.978839	−	0.204630i	$-0.0655990\pi$
$942$		0			0
$943$		0			0
$944$	7.22474	−	12.5136i	0.235145	−	0.407284i
$945$		0			0
$946$	2.14643	+	1.23924i	0.0697864	+	0.0402912i
$947$	33.4949	−	19.3383i	1.08844	−	0.628410i	0.155278	−	0.987871i	$-0.450373\pi$
$947$	33.4949	−	19.3383i	1.08844	−	0.628410i	0.933160	+	0.359461i	$0.117039\pi$
$948$		0			0
$949$			12.5529i			0.407486i
$950$	12.0000	−	5.19615i	0.389331	−	0.168585i
$951$		0			0
$952$	2.57321	−	1.48565i	0.0833983	−	0.0481501i
$953$	−0.550510	−	0.953512i	−0.0178328	−	0.0308873i	0.856971	−	0.515364i	$-0.172343\pi$
$953$	−0.550510	−	0.953512i	−0.0178328	−	0.0308873i	−0.874804	+	0.484477i	$0.839010\pi$
$954$		0			0
$955$	10.7980	+	18.7026i	0.349414	+	0.605202i
$956$	−19.4722	−	11.2423i	−0.629776	−	0.363601i
$957$		0			0
$958$			9.40669i			0.303916i
$959$	−7.89898	−	4.56048i	−0.255071	−	0.147266i
$960$		0			0
$961$	30.0908			0.970671
$962$	−15.0000			−0.483619
$963$		0			0
$964$	−12.1515	+	7.01569i	−0.391374	+	0.225960i
$965$	−12.1237	+	20.9989i	−0.390276	+	0.675979i
$966$		0			0
$967$	−6.17423	−	10.6941i	−0.198550	−	0.343899i	0.749508	−	0.661995i	$-0.230290\pi$
$967$	−6.17423	−	10.6941i	−0.198550	−	0.343899i	−0.948058	+	0.318096i	$0.896957\pi$
$968$	10.5959			0.340566
$969$		0			0
$970$	−26.6969			−0.857187
$971$	14.8207	+	25.6701i	0.475618	+	0.823794i	0.999610	−	0.0279290i	$-0.00889124\pi$
$971$	14.8207	+	25.6701i	0.475618	+	0.823794i	−0.523992	+	0.851723i	$0.675558\pi$
$972$		0			0
$973$	5.07321	−	8.78706i	0.162640	−	0.281700i
$974$	34.3485	−	19.8311i	1.10060	−	0.635429i
$975$		0			0
$976$	−3.44949			−0.110415
$977$	−0.247449			−0.00791659			−0.00395829	−	0.999992i	$-0.501260\pi$
$977$	−0.247449			−0.00791659			−0.00395829	+	0.999992i	$0.501260\pi$
$978$		0			0
$979$	6.74235	+	3.89270i	0.215486	+	0.124411i
$980$			6.92820i			0.221313i
$981$		0			0
$982$	−26.1464	−	15.0956i	−0.834366	−	0.481721i
$983$	−9.24745	−	16.0171i	−0.294948	−	0.510865i	0.680025	−	0.733189i	$-0.261969\pi$
$983$	−9.24745	−	16.0171i	−0.294948	−	0.510865i	−0.974973	+	0.222324i	$0.928636\pi$
$984$		0			0
$985$	14.3485	+	24.8523i	0.457180	+	0.791859i
$986$	−4.34847	+	2.51059i	−0.138483	+	0.0799535i
$987$		0			0
$988$	−15.5227	+	20.9114i	−0.493843	+	0.665281i
$989$		−	22.0560i		−	0.701339i
$990$		0			0
$991$	52.8712	−	30.5252i	1.67951	−	0.969664i	0.717534	−	0.696523i	$-0.245271\pi$
$991$	52.8712	−	30.5252i	1.67951	−	0.969664i	0.961974	−	0.273141i	$-0.0880626\pi$
$992$	0.825765	+	0.476756i	0.0262181	+	0.0151370i
$993$		0			0
$994$	4.34847	−	7.53177i	0.137925	−	0.238893i
$995$		−	24.3916i		−	0.773265i
$996$		0			0
$997$	20.5227	−	35.5464i	0.649961	−	1.12576i	−0.333171	−	0.942866i	$-0.608119\pi$
$997$	20.5227	−	35.5464i	0.649961	−	1.12576i	0.983132	−	0.182898i	$-0.0585479\pi$
$998$	21.7474	−	37.6677i	0.688403	−	1.19235i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.s.a.107.1	✓	4
3.2	odd	2		342.2.s.b.107.2	yes	4
4.3	odd	2		2736.2.dc.b.449.1		4
12.11	even	2		2736.2.dc.a.449.2		4
19.8	odd	6		342.2.s.b.179.2	yes	4
57.8	even	6	inner	342.2.s.a.179.1	yes	4
76.27	even	6		2736.2.dc.a.1889.2		4
228.179	odd	6		2736.2.dc.b.1889.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.s.a.107.1	✓	4	1.1	even	1	trivial
342.2.s.a.179.1	yes	4	57.8	even	6	inner
342.2.s.b.107.2	yes	4	3.2	odd	2
342.2.s.b.179.2	yes	4	19.8	odd	6
2736.2.dc.a.449.2		4	12.11	even	2
2736.2.dc.a.1889.2		4	76.27	even	6
2736.2.dc.b.449.1		4	4.3	odd	2
2736.2.dc.b.1889.1		4	228.179	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +1.44949 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 + 0.707107i) q^{5} +1.44949 q^{7} +1.00000 q^{8} +(1.22474 + 0.707107i) q^{10} -0.635674i q^{11} +(5.17423 + 2.98735i) q^{13} +(-0.724745 - 1.25529i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.77526 - 1.02494i) q^{17} +(4.00000 - 1.73205i) q^{19} -1.41421i q^{20} +(-0.550510 + 0.317837i) q^{22} +(4.89898 + 2.82843i) q^{23} +(-1.50000 + 2.59808i) q^{25} -5.97469i q^{26} +(-0.724745 + 1.25529i) q^{28} +(1.22474 - 2.12132i) q^{29} -0.953512i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.77526 - 1.02494i) q^{34} +(-1.77526 + 1.02494i) q^{35} -2.51059i q^{37} +(-3.50000 - 2.59808i) q^{38} +(-1.22474 + 0.707107i) q^{40} +(-1.94949 - 3.37662i) q^{43} +(0.550510 + 0.317837i) q^{44} -5.65685i q^{46} +(-1.77526 - 1.02494i) q^{47} -4.89898 q^{49} +3.00000 q^{50} +(-5.17423 + 2.98735i) q^{52} +(-2.44949 + 4.24264i) q^{53} +(0.449490 + 0.778539i) q^{55} +1.44949 q^{56} -2.44949 q^{58} +(7.22474 + 12.5136i) q^{59} +(1.72474 - 2.98735i) q^{61} +(-0.825765 + 0.476756i) q^{62} +1.00000 q^{64} -8.44949 q^{65} +(-8.84847 - 5.10867i) q^{67} +2.04989i q^{68} +(1.77526 + 1.02494i) q^{70} +(3.00000 + 5.19615i) q^{71} +(1.05051 + 1.81954i) q^{73} +(-2.17423 + 1.25529i) q^{74} +(-0.500000 + 4.33013i) q^{76} -0.921404i q^{77} +(0.825765 - 0.476756i) q^{79} +(1.22474 + 0.707107i) q^{80} -11.8065i q^{83} +(-1.44949 + 2.51059i) q^{85} +(-1.94949 + 3.37662i) q^{86} -0.635674i q^{88} +(-6.12372 + 10.6066i) q^{89} +(7.50000 + 4.33013i) q^{91} +(-4.89898 + 2.82843i) q^{92} +2.04989i q^{94} +(-3.67423 + 4.94975i) q^{95} +(-16.3485 + 9.43879i) q^{97} +(2.44949 + 4.24264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{7} + 4 q^{8} + 6 q^{13} + 2 q^{14} - 2 q^{16} + 12 q^{17} + 16 q^{19} - 12 q^{22} - 6 q^{25} + 2 q^{28} - 2 q^{32} - 12 q^{34} - 12 q^{35} - 14 q^{38} + 2 q^{43} + 12 q^{44} - 12 q^{47} + 12 q^{50} - 6 q^{52} - 8 q^{55} - 4 q^{56} + 24 q^{59} + 2 q^{61} - 18 q^{62} + 4 q^{64} - 24 q^{65} - 6 q^{67} + 12 q^{70} + 12 q^{71} + 14 q^{73} + 6 q^{74} - 2 q^{76} + 18 q^{79} + 4 q^{85} + 2 q^{86} + 30 q^{91} - 36 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 + 4 * q^8 + 6 * q^13 + 2 * q^14 - 2 * q^16 + 12 * q^17 + 16 * q^19 - 12 * q^22 - 6 * q^25 + 2 * q^28 - 2 * q^32 - 12 * q^34 - 12 * q^35 - 14 * q^38 + 2 * q^43 + 12 * q^44 - 12 * q^47 + 12 * q^50 - 6 * q^52 - 8 * q^55 - 4 * q^56 + 24 * q^59 + 2 * q^61 - 18 * q^62 + 4 * q^64 - 24 * q^65 - 6 * q^67 + 12 * q^70 + 12 * q^71 + 14 * q^73 + 6 * q^74 - 2 * q^76 + 18 * q^79 + 4 * q^85 + 2 * q^86 + 30 * q^91 - 36 * q^97

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