LMFDB - Embedded newform 342.2.s.b.179.2

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			179.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	342.179
Dual form			342.2.s.b.107.2

$q$-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 $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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	$-0.230917\pi$
$5$	1.22474	+	0.707107i	0.547723	+	0.316228i	−0.200480	+	0.979698i	$0.564250\pi$
$6$		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	0.437573	−	0.899183i	$-0.355838\pi$
$13$	5.17423	−	2.98735i	1.43507	−	0.828541i	0.997502	+	0.0706424i	$0.0225049\pi$
$14$	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	$-0.413299\pi$
$17$	−1.77526	−	1.02494i	−0.430563	−	0.248585i	−0.699586	+	0.714548i	$0.746632\pi$
$18$		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	$-0.867447\pi$
$23$	−4.89898	+	2.82843i	−1.02151	+	0.589768i	−0.106967	+	0.994263i	$0.534114\pi$
$24$		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	$-0.239699\pi$
$29$	−1.22474	−	2.12132i	−0.227429	−	0.393919i	−0.957046	+	0.289938i	$0.906365\pi$
$30$		0			0
$31$			0.953512i			0.171256i	0.996327	+	0.0856279i	$0.0272896\pi$
$31$			0.953512i			0.171256i	−0.996327	+	0.0856279i	$0.972710\pi$
$32$	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	$0.0661648\pi$
$37$			2.51059i			0.412738i	−0.978474	+	0.206369i	$0.933835\pi$
$38$	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	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	−1.94949	+	3.37662i	−0.297294	+	0.514929i	−0.975516	−	0.219928i	$-0.929418\pi$
$43$	−1.94949	+	3.37662i	−0.297294	+	0.514929i	0.678222	+	0.734857i	$0.262751\pi$
$44$	−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	$-0.618899\pi$
$47$	1.77526	−	1.02494i	0.258948	−	0.149503i	0.623854	+	0.781541i	$0.285566\pi$
$48$		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	$-0.0574359\pi$
$53$	2.44949	+	4.24264i	0.336463	+	0.582772i	−0.647302	+	0.762234i	$0.724103\pi$
$54$		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	−0.176217	+	0.984351i	$0.556386\pi$
$59$	−7.22474	+	12.5136i	−0.940582	+	1.62914i	−0.764365	+	0.644784i	$0.776947\pi$
$60$		0			0
$61$	1.72474	+	2.98735i	0.220831	+	0.382490i	0.955061	−	0.296411i	$-0.0957898\pi$
$61$	1.72474	+	2.98735i	0.220831	+	0.382490i	−0.734230	+	0.678901i	$0.762456\pi$
$62$	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	−0.931169	−	0.364587i	$-0.881210\pi$
$67$	−8.84847	+	5.10867i	−1.08101	+	0.624123i	−0.149843	+	0.988710i	$0.547877\pi$
$68$			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	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	1.05051	−	1.81954i	0.122953	−	0.212961i	−0.797978	−	0.602687i	$-0.794097\pi$
$73$	1.05051	−	1.81954i	0.122953	−	0.212961i	0.920931	+	0.389726i	$0.127430\pi$
$74$	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	0.545733	−	0.837959i	$-0.316251\pi$
$79$	0.825765	+	0.476756i	0.0929059	+	0.0536392i	−0.452827	+	0.891598i	$0.649585\pi$
$80$	−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	0.983335	+	0.181803i	$0.0581933\pi$
$89$	6.12372	+	10.6066i	0.649113	+	1.12430i	−0.334221	+	0.942495i	$0.608473\pi$
$90$		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	−0.972742	−	0.231890i	$-0.925509\pi$
$97$	−16.3485	−	9.43879i	−1.65994	−	0.958364i	−0.687193	−	0.726474i	$-0.741158\pi$
$98$	−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	$-0.438172\pi$
$101$	11.4495	−	6.61037i	1.13927	−	0.657756i	0.946249	+	0.323439i	$0.104839\pi$
$102$		0			0
$103$			14.4600i			1.42478i	0.701782	+	0.712392i	$0.252388\pi$
$103$			14.4600i			1.42478i	−0.701782	+	0.712392i	$0.747612\pi$
$104$	−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	$-0.776581\pi$
$107$	−15.7980			−1.52725			−0.763623	+	0.645662i	$0.776581\pi$
$108$		0			0
$109$	−14.6969	−	8.48528i	−1.40771	−	0.812743i	−0.412544	−	0.910938i	$-0.635360\pi$
$109$	−14.6969	−	8.48528i	−1.40771	−	0.812743i	−0.995167	+	0.0981950i	$0.968693\pi$
$110$	−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	$-0.201359\pi$
$113$	17.1464			1.61300			0.806500	+	0.591234i	$0.201359\pi$
$114$		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	−0.137178	−	0.990546i	$-0.543803\pi$
$127$	7.34847	−	4.24264i	0.652071	−	0.376473i	0.789249	+	0.614073i	$0.210470\pi$
$128$	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	$-0.556714\pi$
$131$	−12.7980	−	7.38891i	−1.11816	−	0.645572i	−0.940931	+	0.338598i	$0.890047\pi$
$132$		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	$-0.580038\pi$
$137$	5.44949	−	3.14626i	0.465581	−	0.268804i	0.714388	+	0.699750i	$0.246705\pi$
$138$		0			0
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	−0.678551	+	0.734553i	$0.737392\pi$
$140$		−	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	$-0.642346\pi$
$149$	−17.4495	−	10.0745i	−1.42952	−	0.825333i	−0.997082	+	0.0763323i	$0.975679\pi$
$150$		0			0
$151$			1.55708i			0.126713i	0.997991	+	0.0633566i	$0.0201806\pi$
$151$			1.55708i			0.126713i	−0.997991	+	0.0633566i	$0.979819\pi$
$152$	−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	−0.999965	−	0.00834275i	$-0.997344\pi$
$157$	−6.17423	+	10.6941i	−0.492758	+	0.853481i	0.507208	+	0.861824i	$0.330678\pi$
$158$	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	$-0.272678\pi$
$167$	−4.22474	−	7.31747i	−0.326921	−	0.566243i	−0.981899	+	0.189404i	$0.939344\pi$
$168$		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	$-0.679180\pi$
$173$	6.12372	−	10.6066i	0.465578	−	0.806405i	0.999227	+	0.0393009i	$0.0125131\pi$
$174$		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	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−4.65153	+	2.68556i	−0.345746	+	0.199616i	−0.662810	−	0.748788i	$-0.730636\pi$
$181$	−4.65153	+	2.68556i	−0.345746	+	0.199616i	0.317064	+	0.948404i	$0.397303\pi$
$182$		−	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	0.927858	−	0.372934i	$-0.121648\pi$
$193$	14.8485	+	8.57277i	1.06882	+	0.617081i	0.140958	+	0.990016i	$0.454982\pi$
$194$	−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	−0.991018	−	0.133726i	$-0.957306\pi$
$199$	−8.62372	−	14.9367i	−0.611320	−	1.05884i	0.379699	−	0.925110i	$-0.376028\pi$
$200$	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	0.604542	−	0.796573i	$-0.293356\pi$
$211$	3.15153	+	1.81954i	0.216960	+	0.125262i	−0.387582	+	0.921835i	$0.626689\pi$
$212$	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	0.425432	−	0.904991i	$-0.360122\pi$
$223$	−2.17423	−	1.25529i	−0.145598	−	0.0840608i	−0.571029	+	0.820930i	$0.693456\pi$
$224$	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	$-0.221182\pi$
$227$	23.1464			1.53628			0.768141	+	0.640280i	$0.221182\pi$
$228$		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	$-0.137669\pi$
$233$	15.2474	+	8.80312i	0.998894	+	0.576711i	0.0909728	+	0.995853i	$0.471002\pi$
$234$		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	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	12.1515	−	7.01569i	0.782749	−	0.451920i	0.837404	+	0.546585i	$0.184072\pi$
$242$	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	$-0.680878\pi$
$251$	−1.22474	+	0.707107i	−0.0773052	+	0.0446322i	0.460849	+	0.887478i	$0.347545\pi$
$252$		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	$-0.0445601\pi$
$257$	6.00000	+	10.3923i	0.374270	+	0.648254i	−0.615948	+	0.787787i	$0.711227\pi$
$258$		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	$-0.342377\pi$
$263$	−0.797959	−	0.460702i	−0.0492043	−	0.0284081i	−0.524400	+	0.851472i	$0.675710\pi$
$264$		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	0.365432	+	0.930838i	$0.380921\pi$
$269$	−10.2247	+	17.7098i	−0.623414	+	1.07978i	−0.988845	+	0.148946i	$0.952412\pi$
$270$		0			0
$271$	−15.6969	+	27.1879i	−0.953521	+	1.65155i	−0.215804	+	0.976437i	$0.569237\pi$
$271$	−15.6969	+	27.1879i	−0.953521	+	1.65155i	−0.737717	+	0.675110i	$0.764096\pi$
$272$	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	0.971707	+	0.236190i	$0.0758988\pi$
$281$	11.5732	+	20.0454i	0.690400	+	1.19581i	−0.281307	+	0.959618i	$0.590768\pi$
$282$		0			0
$283$	7.44949	−	12.9029i	0.442826	−	0.766997i	−0.555072	−	0.831802i	$-0.687309\pi$
$283$	7.44949	−	12.9029i	0.442826	−	0.766997i	0.997898	+	0.0648050i	$0.0206425\pi$
$284$	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	$-0.399291\pi$
$293$	10.6515			0.622269			0.311135	+	0.950366i	$0.399291\pi$
$294$		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	0.0681177	−	0.997677i	$-0.478301\pi$
$307$	−13.3485	−	7.70674i	−0.761837	−	0.439847i	−0.829955	+	0.557830i	$0.811634\pi$
$308$	−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	−0.985108	−	0.171934i	$-0.944998\pi$
$313$	−11.3485	−	19.6561i	−0.641453	−	1.11103i	0.343655	−	0.939096i	$-0.388335\pi$
$314$	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	$-0.232830\pi$
$317$	−3.67423	−	6.36396i	−0.206366	−	0.357436i	−0.950567	+	0.310520i	$0.899497\pi$
$318$		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	$0.171835\pi$
$331$			18.7026i			1.02799i	−0.857794	+	0.513994i	$0.828165\pi$
$332$	−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	0.548305	−	0.836278i	$-0.315273\pi$
$337$	1.80306	+	1.04100i	0.0982190	+	0.0567068i	−0.450086	+	0.892985i	$0.648607\pi$
$338$	−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	0.999841	+	0.0178073i	$0.00566852\pi$
$347$	28.2247	+	16.2956i	1.51518	+	0.874792i	0.515342	+	0.856984i	$0.327665\pi$
$348$		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	$-0.429839\pi$
$359$	−9.79796	−	5.65685i	−0.517116	−	0.298557i	−0.735754	+	0.677249i	$0.763172\pi$
$360$		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	0.990251	−	0.139295i	$-0.0444838\pi$
$367$	7.17423	+	12.4261i	0.374492	+	0.648639i	−0.615759	+	0.787935i	$0.711150\pi$
$368$		−	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	$0.103151\pi$
$373$			12.2993i			0.636835i	−0.947951	+	0.318418i	$0.896849\pi$
$374$	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	$-0.837241\pi$
$379$		−	19.0526i		−	0.978664i	0.872098	−	0.489332i	$-0.162759\pi$
$380$	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	$-0.743511\pi$
$383$	5.44949	−	9.43879i	0.278456	−	0.482300i	0.971001	+	0.239075i	$0.0768441\pi$
$384$		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	$-0.900509\pi$
$389$	−22.8990	+	13.2207i	−1.16102	+	0.670318i	−0.209475	+	0.977814i	$0.567176\pi$
$390$		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	0.455380	+	0.890297i	$0.349503\pi$
$397$	−10.8258	+	18.7508i	−0.543330	+	0.941074i	−0.998710	+	0.0507775i	$0.983830\pi$
$398$	−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	$-0.835300\pi$
$401$	−0.123724	+	0.214297i	−0.00617850	+	0.0107015i	0.862920	+	0.505341i	$0.168633\pi$
$402$		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	−0.968770	−	0.247960i	$-0.920240\pi$
$409$	−25.0454	+	14.4600i	−1.23842	+	0.715000i	−0.269645	+	0.962960i	$0.586906\pi$
$410$		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	0.532500	−	0.846430i	$-0.321253\pi$
$421$	1.34847	+	0.778539i	0.0657204	+	0.0379437i	−0.466780	+	0.884374i	$0.654586\pi$
$422$	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	$-0.0403713\pi$
$431$	8.02270	+	13.8957i	0.386440	+	0.669334i	−0.605528	+	0.795824i	$0.707038\pi$
$432$		0			0
$433$	25.1969	−	14.5475i	1.21089	−	0.699106i	0.247935	−	0.968777i	$-0.420248\pi$
$433$	25.1969	−	14.5475i	1.21089	−	0.699106i	0.962953	+	0.269670i	$0.0869148\pi$
$434$	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	0.170451	−	0.985366i	$-0.445478\pi$
$439$	−12.5227	−	7.22999i	−0.597676	−	0.345068i	−0.768127	+	0.640298i	$0.778811\pi$
$440$	−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	$-0.416699\pi$
$443$	25.7753	−	14.8814i	1.22462	−	0.707034i	0.965899	+	0.258918i	$0.0833660\pi$
$444$		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	$-0.358311\pi$
$449$	18.2474			0.861150			0.430575	+	0.902555i	$0.358311\pi$
$450$		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	$-0.412232\pi$
$461$	−9.12372	−	5.26758i	−0.424934	−	0.245336i	−0.697186	+	0.716890i	$0.745565\pi$
$462$		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	$-0.597724\pi$
$479$	8.14643	−	4.70334i	0.372220	−	0.214901i	0.674428	+	0.738341i	$0.264390\pi$
$480$		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	$-0.644561\pi$
$487$		−	39.6622i		−	1.79727i	0.438702	−	0.898633i	$-0.355439\pi$
$488$	−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	$-0.571900\pi$
$491$	−26.1464	−	15.0956i	−1.17997	−	0.681257i	−0.956008	+	0.293340i	$0.905233\pi$
$492$		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	0.288909	−	0.957357i	$-0.406708\pi$
$499$	21.7474	−	37.6677i	0.973550	−	1.68624i	0.684641	−	0.728881i	$-0.259959\pi$
$500$	−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	0.589331	−	0.807891i	$-0.299391\pi$
$503$	35.5176	−	20.5061i	1.58365	−	0.914322i	0.994320	−	0.106430i	$-0.0339421\pi$
$504$		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	$-0.0710704\pi$
$509$	6.67423	+	11.5601i	0.295830	+	0.512393i	−0.679347	+	0.733817i	$0.737737\pi$
$510$		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	$-0.442497\pi$
$521$	8.20204			0.359338			0.179669	+	0.983727i	$0.442497\pi$
$522$		0			0
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	−0.174908	−	0.984585i	$-0.555963\pi$
$523$	13.5000	−	7.79423i	0.590314	−	0.340818i	0.765222	+	0.643767i	$0.222629\pi$
$524$			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	−0.982541	−	0.186046i	$-0.940433\pi$
$541$	−15.1742	−	26.2825i	−0.652391	−	1.12997i	0.330150	−	0.943929i	$-0.392901\pi$
$542$	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	−0.538051	−	0.842912i	$-0.680839\pi$
$547$	−1.80306	+	1.04100i	−0.0770933	+	0.0445099i	0.460958	+	0.887422i	$0.347506\pi$
$548$	−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	$-0.853095\pi$
$557$	−22.5959	+	13.0458i	−0.957420	+	0.552767i	−0.0620418	+	0.998074i	$0.519761\pi$
$558$		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	$-0.318663\pi$
$563$	25.5959			1.07874			0.539370	+	0.842069i	$0.318663\pi$
$564$		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	$-0.726033\pi$
$569$	−31.1010			−1.30382			−0.651911	+	0.758295i	$0.726033\pi$
$570$		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	$-0.528278\pi$
$587$	−24.1237	−	13.9278i	−0.995693	−	0.574863i	−0.906971	+	0.421193i	$0.861611\pi$
$588$		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	$-0.563182\pi$
$593$	13.4722	−	7.77817i	0.553237	−	0.319411i	0.750426	+	0.660954i	$0.229848\pi$
$594$		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	−0.938611	−	0.344976i	$-0.887887\pi$
$599$	−18.7980	−	32.5590i	−0.768064	−	1.33033i	0.170548	−	0.985349i	$-0.445446\pi$
$600$		0			0
$601$			10.2173i			0.416774i	0.978046	+	0.208387i	$0.0668213\pi$
$601$			10.2173i			0.416774i	−0.978046	+	0.208387i	$0.933179\pi$
$602$	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	$0.0139620\pi$
$607$			2.16064i			0.0876979i	−0.999038	+	0.0438489i	$0.986038\pi$
$608$	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	−0.991300	−	0.131623i	$-0.957981\pi$
$613$	−9.44949	+	16.3670i	−0.381661	+	0.661057i	0.609639	+	0.792680i	$0.291315\pi$
$614$	−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	$-0.440110\pi$
$617$	28.1010	−	16.2241i	1.13130	−	0.653159i	0.944263	+	0.329193i	$0.106777\pi$
$618$		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	0.684096	−	0.729392i	$-0.260197\pi$
$631$	−7.27526	−	12.6011i	−0.289623	−	0.501642i	−0.973720	+	0.227749i	$0.926863\pi$
$632$	−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	−0.0943619	+	0.995538i	$0.530081\pi$
$641$	−23.0227	+	39.8765i	−0.909342	+	1.57503i	−0.814980	+	0.579489i	$0.803252\pi$
$642$		0			0
$643$	−21.2980	+	36.8891i	−0.839910	+	1.45477i	0.0500601	+	0.998746i	$0.484059\pi$
$643$	−21.2980	+	36.8891i	−0.839910	+	1.45477i	−0.889970	+	0.456020i	$0.849275\pi$
$644$	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	$-0.237899\pi$
$659$	−5.69694	−	9.86739i	−0.221921	−	0.384379i	−0.955391	+	0.295343i	$0.904566\pi$
$660$		0			0
$661$	−23.6969	+	13.6814i	−0.921704	+	0.532146i	−0.884178	−	0.467150i	$-0.845281\pi$
$661$	−23.6969	+	13.6814i	−0.921704	+	0.532146i	−0.0375258	+	0.999296i	$0.511948\pi$
$662$	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	$-0.880313\pi$
$673$		−	19.0526i		−	0.734422i	0.930138	−	0.367211i	$-0.119687\pi$
$674$	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	$-0.754809\pi$
$677$	−37.3485			−1.43542			−0.717709	+	0.696343i	$0.754809\pi$
$678$		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	$-0.319722\pi$
$683$	28.0454			1.07313			0.536564	+	0.843860i	$0.319722\pi$
$684$		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	$-0.428246\pi$
$701$	−13.4722	−	7.77817i	−0.508838	−	0.293778i	−0.732356	+	0.680922i	$0.761579\pi$
$702$		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	0.800244	−	0.599674i	$-0.204703\pi$
$709$	−3.17423	−	5.49794i	−0.119211	−	0.206479i	−0.919455	+	0.393195i	$0.871370\pi$
$710$			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	$-0.453698\pi$
$719$	−17.1464	−	9.89949i	−0.639454	−	0.369189i	−0.784404	+	0.620250i	$0.787031\pi$
$720$		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	−0.941531	−	0.336927i	$-0.890612\pi$
$727$	−4.82577	+	8.35847i	−0.178978	+	0.309999i	0.762553	+	0.646926i	$0.223946\pi$
$728$	−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	0.0248879	+	0.999690i	$0.492077\pi$
$739$	−23.1969	+	40.1783i	−0.853313	+	1.47798i	−0.878201	+	0.478292i	$0.841256\pi$
$740$	3.55051			0.130519
$741$		0			0
$742$	7.10102			0.260687
$743$	23.6969	−	41.0443i	0.869356	−	1.50577i	0.00670079	−	0.999978i	$-0.497867\pi$
$743$	23.6969	−	41.0443i	0.869356	−	1.50577i	0.862656	−	0.505792i	$-0.168800\pi$
$744$		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	0.0118820	−	0.999929i	$-0.496218\pi$
$751$	24.2196	−	13.9832i	0.883787	−	0.510255i	0.871905	+	0.489675i	$0.162884\pi$
$752$			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	−0.997873	−	0.0651902i	$-0.979235\pi$
$757$	−12.1742	+	21.0864i	−0.442480	+	0.766398i	0.555393	+	0.831588i	$0.312568\pi$
$758$	−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	0.888479	−	0.458917i	$-0.151763\pi$
$769$	1.29796	+	2.24813i	0.0468056	+	0.0810697i	−0.841673	+	0.539987i	$0.818429\pi$
$770$	−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	$-0.218091\pi$
$773$	−4.47219	−	7.74607i	−0.160854	−	0.278607i	−0.935175	+	0.354186i	$0.884758\pi$
$774$		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	$-0.858842\pi$
$787$		−	24.0737i		−	0.858136i	0.903272	−	0.429068i	$-0.141158\pi$
$788$	−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	$-0.735694\pi$
$797$	−38.0908			−1.34925			−0.674623	+	0.738162i	$0.735694\pi$
$798$		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	−0.155999	−	0.987757i	$-0.549860\pi$
$811$	17.6969	−	10.2173i	0.621424	−	0.358779i	0.777423	+	0.628978i	$0.216526\pi$
$812$	−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	$-0.424938\pi$
$821$	34.1691	−	19.7276i	1.19251	−	0.688497i	0.958875	+	0.283828i	$0.0916044\pi$
$822$		0			0
$823$	−17.3485	−	30.0484i	−0.604730	−	1.04742i	−0.992094	−	0.125496i	$-0.959948\pi$
$823$	−17.3485	−	30.0484i	−0.604730	−	1.04742i	0.387365	−	0.921927i	$-0.373385\pi$
$824$		−	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	0.899351	+	0.437228i	$0.144040\pi$
$827$	23.8207	+	41.2586i	0.828326	+	1.43470i	−0.0710253	+	0.997475i	$0.522627\pi$
$828$		0			0
$829$			10.9959i			0.381902i	0.981600	+	0.190951i	$0.0611572\pi$
$829$			10.9959i			0.381902i	−0.981600	+	0.190951i	$0.938843\pi$
$830$	−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	$-0.777857\pi$
$839$	5.02270	−	8.69958i	0.173403	−	0.300343i	0.939607	+	0.342254i	$0.111190\pi$
$840$		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	−0.492337	−	0.870405i	$-0.663857\pi$
$853$	14.8258	−	25.6790i	0.507625	−	0.879231i	0.999961	−	0.00882655i	$-0.00280961\pi$
$854$	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	$-0.870679\pi$
$857$	−3.42679	+	5.93537i	−0.117057	+	0.202748i	0.801543	+	0.597937i	$0.204013\pi$
$858$		0			0
$859$	−1.94949	−	3.37662i	−0.0665157	−	0.115209i	0.830850	−	0.556497i	$-0.187855\pi$
$859$	−1.94949	−	3.37662i	−0.0665157	−	0.115209i	−0.897365	+	0.441288i	$0.854522\pi$
$860$	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	$-0.719280\pi$
$863$	−37.3485			−1.27136			−0.635678	+	0.771954i	$0.719280\pi$
$864$		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	0.853192	−	0.521596i	$-0.174663\pi$
$877$	24.5227	+	14.1582i	0.828073	+	0.478088i	−0.0251195	+	0.999684i	$0.507997\pi$
$878$	−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	0.911378	−	0.411571i	$-0.135020\pi$
$883$	2.94949	+	5.10867i	0.0992582	+	0.171920i	−0.812120	+	0.583491i	$0.801686\pi$
$884$	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	$-0.0424936\pi$
$887$	11.3258	+	19.6168i	0.380282	+	0.658668i	−0.610820	+	0.791769i	$0.709160\pi$
$888$		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	0.957234	−	0.289315i	$-0.0934274\pi$
$907$	35.6969	+	20.6096i	1.18530	+	0.684332i	0.228063	+	0.973646i	$0.426761\pi$
$908$	−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	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		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	$-0.0979785\pi$
$929$	35.5732	+	20.5382i	1.16712	+	0.673837i	0.214119	+	0.976807i	$0.431312\pi$
$930$		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	0.700507	−	0.713646i	$-0.252957\pi$
$937$	−8.19694	−	14.1975i	−0.267782	−	0.463813i	−0.968289	+	0.249833i	$0.919624\pi$
$938$			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	−0.978839	−	0.204630i	$-0.934401\pi$
$941$	−20.4495	−	35.4196i	−0.666634	−	1.15464i	0.312205	−	0.950015i	$-0.398932\pi$
$942$		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	$-0.549627\pi$
$947$	−33.4949	−	19.3383i	−1.08844	−	0.628410i	−0.933160	+	0.359461i	$0.882961\pi$
$948$		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	$-0.827657\pi$
$953$	0.550510	−	0.953512i	0.0178328	−	0.0308873i	0.874804	+	0.484477i	$0.160990\pi$
$954$		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	−0.948058	−	0.318096i	$-0.896957\pi$
$967$	−6.17423	+	10.6941i	−0.198550	+	0.343899i	0.749508	+	0.661995i	$0.230290\pi$
$968$	−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	$-0.991109\pi$
$971$	−14.8207	+	25.6701i	−0.475618	+	0.823794i	0.523992	+	0.851723i	$0.324442\pi$
$972$		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	$-0.498740\pi$
$977$	0.247449			0.00791659			0.00395829	+	0.999992i	$0.498740\pi$
$978$		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	$-0.738031\pi$
$983$	9.24745	−	16.0171i	0.294948	−	0.510865i	0.974973	+	0.222324i	$0.0713644\pi$
$984$		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	0.961974	+	0.273141i	$0.0880626\pi$
$991$	52.8712	+	30.5252i	1.67951	+	0.969664i	0.717534	+	0.696523i	$0.245271\pi$
$992$	−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	0.983132	+	0.182898i	$0.0585479\pi$
$997$	20.5227	+	35.5464i	0.649961	+	1.12576i	−0.333171	+	0.942866i	$0.608119\pi$
$998$	−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.b.179.2	yes	4
3.2	odd	2		342.2.s.a.179.1	yes	4
4.3	odd	2		2736.2.dc.a.1889.2		4
12.11	even	2		2736.2.dc.b.1889.1		4
19.12	odd	6		342.2.s.a.107.1	✓	4
57.50	even	6	inner	342.2.s.b.107.2	yes	4
76.31	even	6		2736.2.dc.b.449.1		4
228.107	odd	6		2736.2.dc.a.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.s.a.107.1	✓	4	19.12	odd	6
342.2.s.a.179.1	yes	4	3.2	odd	2
342.2.s.b.107.2	yes	4	57.50	even	6	inner
342.2.s.b.179.2	yes	4	1.1	even	1	trivial
2736.2.dc.a.449.2		4	228.107	odd	6
2736.2.dc.a.1889.2		4	4.3	odd	2
2736.2.dc.b.449.1		4	76.31	even	6
2736.2.dc.b.1889.1		4	12.11	even	2

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

Introduction

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