LMFDB - Embedded newform 668.2.e.a.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

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

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

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0387535 - 0.290817i) q^{3} +(-1.08122 - 0.478126i) q^{5} +(-0.661531 + 1.42256i) q^{7} +(2.81224 - 0.763053i) q^{9} +O(q^{10})$	\(q+(-0.0387535 - 0.290817i) q^{3} +(-1.08122 - 0.478126i) q^{5} +(-0.661531 + 1.42256i) q^{7} +(2.81224 - 0.763053i) q^{9} +(-1.52518 + 1.95553i) q^{11} +(1.57161 - 3.07008i) q^{13} +(-0.0971461 + 0.332967i) q^{15} +(5.30559 + 0.402408i) q^{17} +(0.514102 - 0.773362i) q^{19} +(0.439342 + 0.137255i) q^{21} +(7.30313 + 2.90431i) q^{23} +(-2.42392 - 2.66487i) q^{25} +(-0.671561 - 1.59984i) q^{27} +(0.705224 - 0.280454i) q^{29} +(4.90024 - 1.13240i) q^{31} +(0.627807 + 0.367764i) q^{33} +(1.39542 - 1.22181i) q^{35} +(-0.523913 - 0.142155i) q^{37} +(-0.953739 - 0.338075i) q^{39} +(6.73144 - 3.28665i) q^{41} +(-0.649411 + 6.84241i) q^{43} +(-3.40549 - 0.519575i) q^{45} +(-0.232797 - 12.2994i) q^{47} +(2.92473 + 3.47070i) q^{49} +(-0.0885833 - 1.55855i) q^{51} +(-0.808450 - 4.70046i) q^{53} +(2.58404 - 1.38513i) q^{55} +(-0.244830 - 0.119539i) q^{57} +(8.03690 - 0.609566i) q^{59} +(-8.00247 + 8.15537i) q^{61} +(-0.774895 + 4.50536i) q^{63} +(-3.16715 + 2.56802i) q^{65} +(2.08121 - 0.920329i) q^{67} +(0.561602 - 2.23643i) q^{69} +(-3.99676 + 0.455799i) q^{71} +(-5.25963 + 3.94438i) q^{73} +(-0.681055 + 0.808192i) q^{75} +(-1.77290 - 3.46330i) q^{77} +(-3.52765 + 9.38398i) q^{79} +(7.10364 - 4.16126i) q^{81} +(-6.17495 + 8.56709i) q^{83} +(-5.54413 - 2.97183i) q^{85} +(-0.108891 - 0.194223i) q^{87} +(-3.78095 - 12.9592i) q^{89} +(3.32771 + 4.26666i) q^{91} +(-0.519222 - 1.38119i) q^{93} +(-0.925624 + 0.590372i) q^{95} +(11.7691 + 2.71971i) q^{97} +(-2.79700 + 6.66320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) $ 1148 * q - 2 * q^5 - 14 * q^9	$ 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) $ 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0387535	−	0.290817i	−0.0223744	−	0.167903i	0.976489	−	0.215567i	$-0.0691599\pi$
$3$	−0.0387535	−	0.290817i	−0.0223744	−	0.167903i	−0.998863	+	0.0476633i	$0.984823\pi$
$4$		0			0
$5$	−1.08122	−	0.478126i	−0.483538	−	0.213824i	0.148274	−	0.988946i	$-0.452628\pi$
$5$	−1.08122	−	0.478126i	−0.483538	−	0.213824i	−0.631812	+	0.775122i	$0.717688\pi$
$6$		0			0
$7$	−0.661531	+	1.42256i	−0.250035	+	0.537677i	−0.990999	−	0.133867i	$-0.957260\pi$
$7$	−0.661531	+	1.42256i	−0.250035	+	0.537677i	0.740964	+	0.671545i	$0.234369\pi$
$8$		0			0
$9$	2.81224	−	0.763053i	0.937414	−	0.254351i
$10$		0			0
$11$	−1.52518	+	1.95553i	−0.459858	+	0.589613i	−0.961274	−	0.275593i	$-0.911126\pi$
$11$	−1.52518	+	1.95553i	−0.459858	+	0.589613i	0.501416	+	0.865206i	$0.332813\pi$
$12$		0			0
$13$	1.57161	−	3.07008i	0.435887	−	0.851488i	−0.563787	−	0.825921i	$-0.690656\pi$
$13$	1.57161	−	3.07008i	0.435887	−	0.851488i	0.999673	−	0.0255673i	$-0.00813923\pi$
$14$		0			0
$15$	−0.0971461	+	0.332967i	−0.0250830	+	0.0859718i
$16$		0			0
$17$	5.30559	+	0.402408i	1.28680	+	0.0975983i	0.701176	−	0.712988i	$-0.252659\pi$
$17$	5.30559	+	0.402408i	1.28680	+	0.0975983i	0.585619	+	0.810586i	$0.300851\pi$
$18$		0			0
$19$	0.514102	−	0.773362i	0.117943	−	0.177421i	−0.769072	−	0.639163i	$-0.779281\pi$
$19$	0.514102	−	0.773362i	0.117943	−	0.177421i	0.887015	+	0.461741i	$0.152775\pi$
$20$		0			0
$21$	0.439342	+	0.137255i	0.0958722	+	0.0299516i
$22$		0			0
$23$	7.30313	+	2.90431i	1.52281	+	0.605591i	0.973226	−	0.229849i	$-0.0738232\pi$
$23$	7.30313	+	2.90431i	1.52281	+	0.605591i	0.549582	+	0.835440i	$0.314787\pi$
$24$		0			0
$25$	−2.42392	−	2.66487i	−0.484785	−	0.532974i
$26$		0			0
$27$	−0.671561	−	1.59984i	−0.129242	−	0.307889i
$28$		0			0
$29$	0.705224	−	0.280454i	0.130957	−	0.0520790i	−0.303135	−	0.952948i	$-0.598033\pi$
$29$	0.705224	−	0.280454i	0.130957	−	0.0520790i	0.434092	+	0.900869i	$0.357069\pi$
$30$		0			0
$31$	4.90024	−	1.13240i	0.880109	−	0.203384i	0.239172	−	0.970977i	$-0.423124\pi$
$31$	4.90024	−	1.13240i	0.880109	−	0.203384i	0.640937	+	0.767593i	$0.278546\pi$
$32$		0			0
$33$	0.627807	+	0.367764i	0.109287	+	0.0640195i
$34$		0			0
$35$	1.39542	−	1.22181i	0.235870	−	0.206523i
$36$		0			0
$37$	−0.523913	−	0.142155i	−0.0861308	−	0.0233701i	0.218538	−	0.975828i	$-0.429871\pi$
$37$	−0.523913	−	0.142155i	−0.0861308	−	0.0233701i	−0.304669	+	0.952458i	$0.598546\pi$
$38$		0			0
$39$	−0.953739	−	0.338075i	−0.152720	−	0.0541354i
$40$		0			0
$41$	6.73144	−	3.28665i	1.05127	−	0.513288i	0.169780	−	0.985482i	$-0.445694\pi$
$41$	6.73144	−	3.28665i	1.05127	−	0.513288i	0.881495	+	0.472194i	$0.156538\pi$
$42$		0			0
$43$	−0.649411	+	6.84241i	−0.0990343	+	1.04346i	0.798346	+	0.602199i	$0.205709\pi$
$43$	−0.649411	+	6.84241i	−0.0990343	+	1.04346i	−0.897380	+	0.441258i	$0.854532\pi$
$44$		0			0
$45$	−3.40549	−	0.519575i	−0.507661	−	0.0774537i
$46$		0			0
$47$	−0.232797	−	12.2994i	−0.0339570	−	1.79405i	−0.458550	−	0.888669i	$-0.651631\pi$
$47$	−0.232797	−	12.2994i	−0.0339570	−	1.79405i	0.424593	−	0.905384i	$-0.360417\pi$
$48$		0			0
$49$	2.92473	+	3.47070i	0.417818	+	0.495815i
$50$		0			0
$51$	−0.0885833	−	1.55855i	−0.0124041	−	0.218241i
$52$		0			0
$53$	−0.808450	−	4.70046i	−0.111049	−	0.645658i	−0.986680	−	0.162676i	$-0.947987\pi$
$53$	−0.808450	−	4.70046i	−0.111049	−	0.645658i	0.875630	−	0.482982i	$-0.160446\pi$
$54$		0			0
$55$	2.58404	−	1.38513i	0.348432	−	0.186771i
$56$		0			0
$57$	−0.244830	−	0.119539i	−0.0324286	−	0.0158334i
$58$		0			0
$59$	8.03690	−	0.609566i	1.04631	−	0.0793588i	0.458774	−	0.888553i	$-0.348289\pi$
$59$	8.03690	−	0.609566i	1.04631	−	0.0793588i	0.587541	+	0.809194i	$0.300096\pi$
$60$		0			0
$61$	−8.00247	+	8.15537i	−1.02461	+	1.04419i	−0.0256024	+	0.999672i	$0.508150\pi$
$61$	−8.00247	+	8.15537i	−1.02461	+	1.04419i	−0.999009	+	0.0445158i	$0.985826\pi$
$62$		0			0
$63$	−0.774895	+	4.50536i	−0.0976276	+	0.567623i
$64$		0			0
$65$	−3.16715	+	2.56802i	−0.392836	+	0.318523i
$66$		0			0
$67$	2.08121	−	0.920329i	0.254260	−	0.112436i	−0.273374	−	0.961908i	$-0.588140\pi$
$67$	2.08121	−	0.920329i	0.254260	−	0.112436i	0.527634	+	0.849472i	$0.323079\pi$
$68$		0			0
$69$	0.561602	−	2.23643i	0.0676090	−	0.269234i
$70$		0			0
$71$	−3.99676	+	0.455799i	−0.474328	+	0.0540934i	−0.347196	−	0.937792i	$-0.612866\pi$
$71$	−3.99676	+	0.455799i	−0.474328	+	0.0540934i	−0.127132	+	0.991886i	$0.540577\pi$
$72$		0			0
$73$	−5.25963	+	3.94438i	−0.615594	+	0.461655i	−0.861582	−	0.507618i	$-0.830526\pi$
$73$	−5.25963	+	3.94438i	−0.615594	+	0.461655i	0.245988	+	0.969273i	$0.420887\pi$
$74$		0			0
$75$	−0.681055	+	0.808192i	−0.0786414	+	0.0933220i
$76$		0			0
$77$	−1.77290	−	3.46330i	−0.202041	−	0.394679i
$78$		0			0
$79$	−3.52765	+	9.38398i	−0.396892	+	1.05578i	0.574543	+	0.818474i	$0.305180\pi$
$79$	−3.52765	+	9.38398i	−0.396892	+	1.05578i	−0.971435	+	0.237305i	$0.923736\pi$
$80$		0			0
$81$	7.10364	−	4.16126i	0.789293	−	0.462362i
$82$		0			0
$83$	−6.17495	+	8.56709i	−0.677788	+	0.940360i	−0.999980	−	0.00631424i	$-0.997990\pi$
$83$	−6.17495	+	8.56709i	−0.677788	+	0.940360i	0.322192	+	0.946674i	$0.395580\pi$
$84$		0			0
$85$	−5.54413	−	2.97183i	−0.601345	−	0.322341i
$86$		0			0
$87$	−0.108891	−	0.194223i	−0.0116743	−	0.0208229i
$88$		0			0
$89$	−3.78095	−	12.9592i	−0.400780	−	1.37367i	−0.871070	−	0.491158i	$-0.836574\pi$
$89$	−3.78095	−	12.9592i	−0.400780	−	1.37367i	0.470290	−	0.882512i	$-0.344149\pi$
$90$		0			0
$91$	3.32771	+	4.26666i	0.348839	+	0.447268i
$92$		0			0
$93$	−0.519222	−	1.38119i	−0.0538408	−	0.143223i
$94$		0			0
$95$	−0.925624	+	0.590372i	−0.0949670	+	0.0605708i
$96$		0			0
$97$	11.7691	+	2.71971i	1.19497	+	0.276145i	0.775335	−	0.631550i	$-0.217581\pi$
$97$	11.7691	+	2.71971i	1.19497	+	0.276145i	0.419632	+	0.907694i	$0.362159\pi$
$98$		0			0
$99$	−2.79700	+	6.66320i	−0.281109	+	0.669677i
$100$		0			0
$101$	−0.296888	−	3.12811i	−0.0295415	−	0.311259i	−0.998057	−	0.0623059i	$-0.980155\pi$
$101$	−0.296888	−	3.12811i	−0.0295415	−	0.311259i	0.968516	−	0.248953i	$-0.0800864\pi$
$102$		0			0
$103$	−9.72112	+	6.73092i	−0.957851	+	0.663217i	−0.941629	−	0.336651i	$-0.890706\pi$
$103$	−9.72112	+	6.73092i	−0.957851	+	0.663217i	−0.0162211	+	0.999868i	$0.505164\pi$
$104$		0			0
$105$	−0.409401	−	0.358464i	−0.0399534	−	0.0349825i
$106$		0			0
$107$	11.9990	+	8.30810i	1.15998	+	0.803174i	0.983461	−	0.181122i	$-0.0579729\pi$
$107$	11.9990	+	8.30810i	1.15998	+	0.803174i	0.176523	+	0.984297i	$0.443515\pi$
$108$		0			0
$109$	−12.4546	−	7.94368i	−1.19294	−	0.760866i	−0.216418	−	0.976301i	$-0.569438\pi$
$109$	−12.4546	−	7.94368i	−1.19294	−	0.760866i	−0.976518	+	0.215434i	$0.930883\pi$
$110$		0			0
$111$	−0.0210376	+	0.157872i	−0.00199680	+	0.0149846i
$112$		0			0
$113$	5.16835	−	8.45192i	0.486197	−	0.795090i	−0.511750	−	0.859135i	$-0.671003\pi$
$113$	5.16835	−	8.45192i	0.486197	−	0.795090i	0.997947	+	0.0640449i	$0.0204001\pi$
$114$		0			0
$115$	−6.50769	−	6.63203i	−0.606845	−	0.618440i
$116$		0			0
$117$	2.07711	−	9.83304i	0.192029	−	0.909065i
$118$		0			0
$119$	−4.08226	+	7.28132i	−0.374220	+	0.667478i
$120$		0			0
$121$	1.18118	+	4.70372i	0.107380	+	0.427611i
$122$		0			0
$123$	−1.21668	−	1.83025i	−0.109704	−	0.165028i
$124$		0			0
$125$	3.21580	+	9.64807i	0.287630	+	0.862949i
$126$		0			0
$127$	−1.81226	−	0.206673i	−0.160812	−	0.0183393i	0.0325302	−	0.999471i	$-0.489643\pi$
$127$	−1.81226	−	0.206673i	−0.160812	−	0.0183393i	−0.193342	+	0.981131i	$0.561933\pi$
$128$		0			0
$129$	2.01506	−	0.0763074i	0.177416	−	0.00671850i
$130$		0			0
$131$	−0.150962	+	2.65605i	−0.0131896	+	0.232060i	0.985029	+	0.172391i	$0.0551492\pi$
$131$	−0.150962	+	2.65605i	−0.0131896	+	0.232060i	−0.998218	+	0.0596693i	$0.980995\pi$
$132$		0			0
$133$	0.760060	+	1.24294i	0.0659056	+	0.107777i
$134$		0			0
$135$	−0.0388180	+	2.05087i	−0.00334092	+	0.176511i
$136$		0			0
$137$	−14.7482	+	5.22784i	−1.26002	+	0.446645i	−0.878512	−	0.477720i	$-0.841463\pi$
$137$	−14.7482	+	5.22784i	−1.26002	+	0.446645i	−0.381510	+	0.924365i	$0.624596\pi$
$138$		0			0
$139$	−5.24139	−	4.95195i	−0.444569	−	0.420019i	0.431568	−	0.902080i	$-0.357960\pi$
$139$	−5.24139	−	4.95195i	−0.444569	−	0.420019i	−0.876137	+	0.482061i	$0.839888\pi$
$140$		0			0
$141$	−3.56786	+	0.544347i	−0.300468	+	0.0458423i
$142$		0			0
$143$	3.60664	+	7.75575i	0.301602	+	0.648568i
$144$		0			0
$145$	−0.896596	−	0.0339529i	−0.0744583	−	0.00281963i
$146$		0			0
$147$	0.895997	−	0.985063i	0.0739006	−	0.0812466i
$148$		0			0
$149$	−9.82438	−	7.96589i	−0.804845	−	0.652591i	0.136273	−	0.990671i	$-0.456488\pi$
$149$	−9.82438	−	7.96589i	−0.804845	−	0.652591i	−0.941117	+	0.338080i	$0.890223\pi$
$150$		0			0
$151$	−11.5218	−	8.64059i	−0.937632	−	0.703162i	0.0173429	−	0.999850i	$-0.494479\pi$
$151$	−11.5218	−	8.64059i	−0.937632	−	0.703162i	−0.954974	+	0.296688i	$0.904118\pi$
$152$		0			0
$153$	15.2277	−	2.91678i	1.23108	−	0.235808i
$154$		0			0
$155$	−5.83968	−	1.11856i	−0.469054	−	0.0898450i
$156$		0			0
$157$	−1.45063	−	6.86726i	−0.115773	−	0.548067i	−0.997136	−	0.0756282i	$-0.975904\pi$
$157$	−1.45063	−	6.86726i	−0.115773	−	0.548067i	0.881363	−	0.472439i	$-0.156626\pi$
$158$		0			0
$159$	−1.33565	+	0.417271i	−0.105924	+	0.0330917i
$160$		0			0
$161$	−8.96280	+	8.46785i	−0.706368	+	0.667360i
$162$		0			0
$163$	−5.18031	+	15.5420i	−0.405754	+	1.21735i	0.524811	+	0.851219i	$0.324136\pi$
$163$	−5.18031	+	15.5420i	−0.405754	+	1.21735i	−0.930565	+	0.366128i	$0.880683\pi$
$164$		0			0
$165$	−0.502961	−	0.697806i	−0.0391555	−	0.0543241i
$166$		0			0
$167$	−9.79664	+	8.42768i	−0.758087	+	0.652153i
$167$	−9.79664	+	8.42768i	−0.758087	+	0.652153i
$168$		0			0
$169$	0.645897	+	0.896114i	0.0496844	+	0.0689318i
$170$		0			0
$171$	0.855662	−	2.56717i	0.0654341	−	0.196316i
$172$		0			0
$173$	5.60127	−	5.29195i	0.425856	−	0.402339i	−0.443698	−	0.896176i	$-0.646334\pi$
$173$	5.60127	−	5.29195i	0.425856	−	0.402339i	0.869555	+	0.493837i	$0.164406\pi$
$174$		0			0
$175$	5.39444	−	1.68528i	0.407781	−	0.127395i
$176$		0			0
$177$	−0.488730	−	2.31365i	−0.0367352	−	0.173904i
$178$		0			0
$179$	−12.3176	−	2.35937i	−0.920659	−	0.176348i	−0.294148	−	0.955760i	$-0.595036\pi$
$179$	−12.3176	−	2.35937i	−0.920659	−	0.176348i	−0.626511	+	0.779412i	$0.715518\pi$
$180$		0			0
$181$	−20.2160	+	3.87227i	−1.50264	+	0.287824i	−0.872484	−	0.488642i	$-0.837492\pi$
$181$	−20.2160	+	3.87227i	−1.50264	+	0.287824i	−0.630159	+	0.776466i	$0.717010\pi$
$182$		0			0
$183$	2.68185	+	2.01121i	0.198248	+	0.148673i
$184$		0			0
$185$	0.498499	+	0.404198i	0.0366504	+	0.0297172i
$186$		0			0
$187$	−8.87889	+	9.76148i	−0.649289	+	0.713830i
$188$		0			0
$189$	2.72013	+	0.103007i	0.197860	+	0.00749268i
$190$		0			0
$191$	−4.83847	−	10.4047i	−0.350099	−	0.752856i	0.649875	−	0.760041i	$-0.274821\pi$
$191$	−4.83847	−	10.4047i	−0.350099	−	0.752856i	−0.999974	+	0.00718499i	$0.997713\pi$
$192$		0			0
$193$	−0.975189	+	0.148784i	−0.0701956	+	0.0107097i	−0.185827	−	0.982582i	$-0.559496\pi$
$193$	−0.975189	+	0.148784i	−0.0701956	+	0.0107097i	0.115631	+	0.993292i	$0.463111\pi$
$194$		0			0
$195$	0.869562	+	0.821542i	0.0622706	+	0.0588318i
$196$		0			0
$197$	11.3167	−	4.01147i	0.806281	−	0.285805i	0.101140	−	0.994872i	$-0.467751\pi$
$197$	11.3167	−	4.01147i	0.806281	−	0.285805i	0.705141	+	0.709067i	$0.250884\pi$
$198$		0			0
$199$	−0.210627	+	11.1281i	−0.0149310	+	0.788849i	0.911268	+	0.411814i	$0.135105\pi$
$199$	−0.210627	+	11.1281i	−0.0149310	+	0.788849i	−0.926199	+	0.377035i	$0.876944\pi$
$200$		0			0
$201$	−0.348302	−	0.569586i	−0.0245673	−	0.0401755i
$202$		0			0
$203$	−0.0675649	+	1.18875i	−0.00474213	+	0.0834340i
$204$		0			0
$205$	−8.84962	+	0.335123i	−0.618085	+	0.0234060i
$206$		0			0
$207$	22.7543	+	2.59495i	1.58153	+	0.180361i
$208$		0			0
$209$	0.728233	+	2.18485i	0.0503729	+	0.151130i
$210$		0			0
$211$	−8.50596	−	12.7955i	−0.585574	−	0.880878i	0.413993	−	0.910280i	$-0.364134\pi$
$211$	−8.50596	−	12.7955i	−0.585574	−	0.880878i	−0.999568	+	0.0294020i	$0.990640\pi$
$212$		0			0
$213$	0.287443	+	1.14466i	0.0196953	+	0.0784310i
$214$		0			0
$215$	3.97369	−	7.08767i	0.271004	−	0.483375i
$216$		0			0
$217$	−1.63076	+	7.72000i	−0.110703	+	0.524068i
$218$		0			0
$219$	1.35092	+	1.37673i	0.0912869	+	0.0930311i
$220$		0			0
$221$	9.57376	−	15.6562i	0.644001	−	1.05315i
$222$		0			0
$223$	2.10496	−	15.7962i	0.140958	−	1.05779i	−0.767865	−	0.640612i	$-0.778681\pi$
$223$	2.10496	−	15.7962i	0.140958	−	1.05779i	0.908824	−	0.417181i	$-0.136982\pi$
$224$		0			0
$225$	−8.85010	−	5.64468i	−0.590006	−	0.376312i
$226$		0			0
$227$	23.2731	+	16.1143i	1.54469	+	1.06955i	0.967479	+	0.252951i	$0.0814011\pi$
$227$	23.2731	+	16.1143i	1.54469	+	1.06955i	0.577211	+	0.816595i	$0.304141\pi$
$228$		0			0
$229$	21.7396	+	19.0348i	1.43659	+	1.25786i	0.914268	+	0.405110i	$0.132767\pi$
$229$	21.7396	+	19.0348i	1.43659	+	1.25786i	0.522326	+	0.852746i	$0.325064\pi$
$230$		0			0
$231$	−0.938480	+	0.649805i	−0.0617474	+	0.0427540i
$232$		0			0
$233$	−0.238496	−	2.51287i	−0.0156244	−	0.164624i	0.984305	−	0.176473i	$-0.0564690\pi$
$233$	−0.238496	−	2.51287i	−0.0156244	−	0.164624i	−0.999930	+	0.0118498i	$0.996228\pi$
$234$		0			0
$235$	−5.62896	+	13.4097i	−0.367193	+	0.874753i
$236$		0			0
$237$	2.86573	+	0.662241i	0.186149	+	0.0430172i
$238$		0			0
$239$	1.91779	−	1.22319i	0.124052	−	0.0791213i	−0.474260	−	0.880385i	$-0.657284\pi$
$239$	1.91779	−	1.22319i	0.124052	−	0.0791213i	0.598312	+	0.801264i	$0.295839\pi$
$240$		0			0
$241$	−6.16860	−	16.4092i	−0.397354	−	1.05701i	−0.971246	−	0.238078i	$-0.923483\pi$
$241$	−6.16860	−	16.4092i	−0.397354	−	1.05701i	0.573892	−	0.818931i	$-0.305433\pi$
$242$		0			0
$243$	−4.68666	−	6.00906i	−0.300649	−	0.385482i
$244$		0			0
$245$	−1.50285	−	5.15099i	−0.0960133	−	0.329085i
$246$		0			0
$247$	−1.56632	−	2.79376i	−0.0996624	−	0.177763i
$248$		0			0
$249$	2.73076	+	1.46378i	0.173055	+	0.0927631i
$250$		0			0
$251$	−9.47076	+	13.1397i	−0.597789	+	0.829370i	−0.996132	−	0.0878669i	$-0.971995\pi$
$251$	−9.47076	+	13.1397i	−0.597789	+	0.829370i	0.398343	+	0.917236i	$0.369585\pi$
$252$		0			0
$253$	−16.8180	+	9.85187i	−1.05734	+	0.619382i
$254$		0			0
$255$	−0.649406	+	1.72750i	−0.0406674	+	0.108180i
$256$		0			0
$257$	12.9482	+	25.2939i	0.807689	+	1.57779i	0.816160	+	0.577825i	$0.196099\pi$
$257$	12.9482	+	25.2939i	0.807689	+	1.57779i	−0.00847155	+	0.999964i	$0.502697\pi$
$258$		0			0
$259$	0.548809	−	0.651258i	0.0341013	−	0.0404672i
$260$		0			0
$261$	1.76926	−	1.32683i	0.109514	−	0.0821285i
$262$		0			0
$263$	13.7733	−	1.57074i	0.849298	−	0.0968557i	0.322212	−	0.946668i	$-0.395574\pi$
$263$	13.7733	−	1.57074i	0.849298	−	0.0968557i	0.527086	+	0.849812i	$0.323285\pi$
$264$		0			0
$265$	−1.37330	+	5.46879i	−0.0843610	+	0.335945i
$266$		0			0
$267$	−3.62223	+	1.60178i	−0.221677	+	0.0980273i
$268$		0			0
$269$	3.10007	−	2.51362i	0.189014	−	0.153258i	−0.530624	−	0.847607i	$-0.678042\pi$
$269$	3.10007	−	2.51362i	0.189014	−	0.153258i	0.719639	+	0.694349i	$0.244308\pi$
$270$		0			0
$271$	2.55941	−	14.8809i	0.155473	−	0.903947i	−0.798042	−	0.602602i	$-0.794131\pi$
$271$	2.55941	−	14.8809i	0.155473	−	0.903947i	0.953515	−	0.301345i	$-0.0974357\pi$
$272$		0			0
$273$	1.11186	−	1.13310i	0.0672928	−	0.0685785i
$274$		0			0
$275$	8.90814	−	0.675646i	0.537181	−	0.0407430i
$276$		0			0
$277$	−13.9240	−	6.79845i	−0.836613	−	0.408479i	−0.0299934	−	0.999550i	$-0.509549\pi$
$277$	−13.9240	−	6.79845i	−0.836613	−	0.408479i	−0.806619	+	0.591071i	$0.798705\pi$
$278$		0			0
$279$	12.9166	−	6.92371i	0.773295	−	0.414512i
$280$		0			0
$281$	−4.15417	−	24.1530i	−0.247817	−	1.44085i	−0.796409	−	0.604758i	$-0.793270\pi$
$281$	−4.15417	−	24.1530i	−0.247817	−	1.44085i	0.548592	−	0.836090i	$-0.315164\pi$
$282$		0			0
$283$	−0.465963	−	8.19825i	−0.0276986	−	0.487335i	−0.982047	−	0.188638i	$-0.939593\pi$
$283$	−0.465963	−	8.19825i	−0.0276986	−	0.487335i	0.954348	−	0.298697i	$-0.0965519\pi$
$284$		0			0
$285$	0.207561	+	0.246308i	0.0122949	+	0.0145900i
$286$		0			0
$287$	0.222400	+	11.7501i	0.0131279	+	0.693587i
$288$		0			0
$289$	11.1819	+	1.70601i	0.657757	+	0.100354i
$290$		0			0
$291$	0.334846	−	3.52805i	0.0196290	−	0.206818i
$292$		0			0
$293$	5.35528	−	2.61473i	0.312859	−	0.152754i	−0.275621	−	0.961266i	$-0.588883\pi$
$293$	5.35528	−	2.61473i	0.312859	−	0.152754i	0.588480	+	0.808512i	$0.299727\pi$
$294$		0			0
$295$	−8.98113	−	3.18357i	−0.522901	−	0.185355i
$296$		0			0
$297$	4.15278	+	1.12678i	0.240969	+	0.0653827i
$298$		0			0
$299$	20.3942	−	17.8568i	1.17942	−	1.03268i
$300$		0			0
$301$	−9.30413	−	5.45029i	−0.536281	−	0.314150i
$302$		0			0
$303$	−0.898203	+	0.207566i	−0.0516004	+	0.0119243i
$304$		0			0
$305$	12.5517	−	4.99158i	0.718711	−	0.285817i
$306$		0			0
$307$	−5.05314	−	12.0379i	−0.288398	−	0.687041i	0.711480	−	0.702707i	$-0.248025\pi$
$307$	−5.05314	−	12.0379i	−0.288398	−	0.687041i	−0.999877	+	0.0156653i	$0.995013\pi$
$308$		0			0
$309$	2.33420	+	2.56622i	0.132788	+	0.145987i
$310$		0			0
$311$	−12.2474	−	4.87055i	−0.694486	−	0.276183i	−0.00448272	−	0.999990i	$-0.501427\pi$
$311$	−12.2474	−	4.87055i	−0.694486	−	0.276183i	−0.690003	+	0.723807i	$0.742391\pi$
$312$		0			0
$313$	25.7486	+	8.04414i	1.45539	+	0.454682i	0.920669	−	0.390344i	$-0.127644\pi$
$313$	25.7486	+	8.04414i	1.45539	+	0.454682i	0.534725	+	0.845026i	$0.320415\pi$
$314$		0			0
$315$	2.99197	−	4.50081i	0.168578	−	0.253592i
$316$		0			0
$317$	7.73712	+	0.586830i	0.434560	+	0.0329596i	0.291091	−	0.956695i	$-0.405982\pi$
$317$	7.73712	+	0.586830i	0.434560	+	0.0329596i	0.143469	+	0.989655i	$0.454174\pi$
$318$		0			0
$319$	−0.527157	+	1.80682i	−0.0295151	+	0.101163i
$320$		0			0
$321$	1.95114	−	3.81147i	0.108902	−	0.212736i
$322$		0			0
$323$	3.03882	−	3.89627i	0.169085	−	0.216794i
$324$		0			0
$325$	−11.9908	+	3.25351i	−0.665132	+	0.180472i
$326$		0			0
$327$	−1.82750	+	3.92987i	−0.101061	+	0.217322i
$328$		0			0
$329$	17.6506	+	7.80527i	0.973112	+	0.430318i
$330$		0			0
$331$	−2.17672	−	16.3347i	−0.119643	−	0.897837i	−0.943578	−	0.331152i	$-0.892563\pi$
$331$	−2.17672	−	16.3347i	−0.119643	−	0.897837i	0.823934	−	0.566686i	$-0.191775\pi$
$332$		0			0
$333$	−1.58184			−0.0866844
$334$		0			0
$335$	−2.69028			−0.146986
$336$		0			0
$337$	3.77217	+	28.3074i	0.205483	+	1.54200i	0.725725	+	0.687985i	$0.241504\pi$
$337$	3.77217	+	28.3074i	0.205483	+	1.54200i	−0.520242	+	0.854019i	$0.674158\pi$
$338$		0			0
$339$	−2.65826	−	1.17550i	−0.144377	−	0.0638446i
$340$		0			0
$341$	−5.25931	+	11.3096i	−0.284807	+	0.612452i
$342$		0			0
$343$	−17.4708	+	4.74041i	−0.943336	+	0.255958i
$344$		0			0
$345$	−1.67651	+	2.14956i	−0.0902604	+	0.115729i
$346$		0			0
$347$	9.72301	−	18.9935i	0.521958	−	1.01963i	−0.468713	−	0.883351i	$-0.655282\pi$
$347$	9.72301	−	18.9935i	0.521958	−	1.01963i	0.990671	−	0.136275i	$-0.0435132\pi$
$348$		0			0
$349$	−1.98459	+	6.80215i	−0.106232	+	0.364111i	−0.995671	−	0.0929433i	$-0.970372\pi$
$349$	−1.98459	+	6.80215i	−0.106232	+	0.364111i	0.889439	+	0.457054i	$0.151095\pi$
$350$		0			0
$351$	−5.96708	−	0.452579i	−0.318499	−	0.0241569i
$352$		0			0
$353$	4.52715	−	6.81019i	0.240956	−	0.362470i	−0.692344	−	0.721568i	$-0.743422\pi$
$353$	4.52715	−	6.81019i	0.240956	−	0.362470i	0.933300	+	0.359098i	$0.116916\pi$
$354$		0			0
$355$	4.53932	+	1.41813i	0.240922	+	0.0752668i
$356$		0			0
$357$	2.27574	+	0.905016i	0.120445	+	0.0478985i
$358$		0			0
$359$	8.87690	+	9.75930i	0.468505	+	0.515076i	0.927734	−	0.373242i	$-0.121754\pi$
$359$	8.87690	+	9.75930i	0.468505	+	0.515076i	−0.459229	+	0.888318i	$0.651874\pi$
$360$		0			0
$361$	7.02017	+	16.7239i	0.369482	+	0.880207i
$362$		0			0
$363$	1.32215	−	0.525792i	0.0693947	−	0.0275969i
$364$		0			0
$365$	7.57275	−	1.74998i	0.396376	−	0.0915983i
$366$		0			0
$367$	5.45278	+	3.19420i	0.284633	+	0.166736i	0.640847	−	0.767669i	$-0.278583\pi$
$367$	5.45278	+	3.19420i	0.284633	+	0.166736i	−0.356214	+	0.934404i	$0.615933\pi$
$368$		0			0
$369$	16.4226	−	14.3793i	0.854924	−	0.748556i
$370$		0			0
$371$	7.22150	+	1.95943i	0.374922	+	0.101729i
$372$		0			0
$373$	20.0244	+	7.09813i	1.03682	+	0.367527i	0.797440	−	0.603398i	$-0.206187\pi$
$373$	20.0244	+	7.09813i	1.03682	+	0.367527i	0.239385	+	0.970925i	$0.423054\pi$
$374$		0			0
$375$	2.68120	−	1.30911i	0.138457	−	0.0676019i
$376$		0			0
$377$	0.247322	−	2.60586i	0.0127377	−	0.134209i
$378$		0			0
$379$	17.2331	+	2.62925i	0.885206	+	0.135055i	0.577466	−	0.816415i	$-0.304042\pi$
$379$	17.2331	+	2.62925i	0.885206	+	0.135055i	0.307740	+	0.951470i	$0.400427\pi$
$380$		0			0
$381$	0.0101271	+	0.535045i	0.000518825	+	0.0274112i
$382$		0			0
$383$	8.70213	+	10.3266i	0.444658	+	0.527666i	0.940065	−	0.340995i	$-0.110764\pi$
$383$	8.70213	+	10.3266i	0.444658	+	0.527666i	−0.495407	+	0.868661i	$0.664981\pi$
$384$		0			0
$385$	0.261010	+	4.59226i	0.0133023	+	0.234043i
$386$		0			0
$387$	3.39482	+	19.7380i	0.172568	+	1.00334i
$388$		0			0
$389$	−26.3902	+	14.1460i	−1.33803	+	0.717231i	−0.976579	−	0.215159i	$-0.930973\pi$
$389$	−26.3902	+	14.1460i	−1.33803	+	0.717231i	−0.361456	+	0.932389i	$0.617720\pi$
$390$		0			0
$391$	37.5787	+	18.3479i	1.90044	+	0.927895i
$392$		0			0
$393$	0.778276	−	0.0590291i	0.0392588	−	0.00297762i
$394$		0			0
$395$	8.30090	−	8.45951i	0.417664	−	0.425644i
$396$		0			0
$397$	4.43279	−	25.7729i	0.222475	−	1.29351i	−0.632387	−	0.774652i	$-0.717925\pi$
$397$	4.43279	−	25.7729i	0.222475	−	1.29351i	0.854862	−	0.518855i	$-0.173641\pi$
$398$		0			0
$399$	0.332015	−	0.269207i	0.0166215	−	0.0134772i
$400$		0			0
$401$	8.24562	−	3.64628i	0.411767	−	0.182087i	−0.188166	−	0.982137i	$-0.560254\pi$
$401$	8.24562	−	3.64628i	0.411767	−	0.182087i	0.599933	+	0.800051i	$0.295194\pi$
$402$		0			0
$403$	4.22473	−	16.8238i	0.210449	−	0.838055i
$404$		0			0
$405$	−9.67022	+	1.10281i	−0.480517	+	0.0547992i
$406$		0			0
$407$	1.07705	−	0.807715i	0.0533873	−	0.0400369i
$408$		0			0
$409$	−12.2890	+	14.5831i	−0.607652	+	0.721086i	−0.978186	−	0.207733i	$-0.933392\pi$
$409$	−12.2890	+	14.5831i	−0.607652	+	0.721086i	0.370534	+	0.928819i	$0.379175\pi$
$410$		0			0
$411$	2.09189	+	4.08643i	0.103185	+	0.201569i
$412$		0			0
$413$	−4.44951	+	11.8362i	−0.218946	+	0.582422i
$414$		0			0
$415$	10.7726	−	6.31053i	0.528808	−	0.309772i
$416$		0			0
$417$	−1.23699	+	1.71619i	−0.0605757	+	0.0840424i
$418$		0			0
$419$	−3.36845	−	1.80560i	−0.164560	−	0.0882094i	0.388096	−	0.921619i	$-0.373133\pi$
$419$	−3.36845	−	1.80560i	−0.164560	−	0.0882094i	−0.552656	+	0.833409i	$0.686386\pi$
$420$		0			0
$421$	−12.7997	−	22.8302i	−0.623821	−	1.11268i	−0.983724	−	0.179687i	$-0.942491\pi$
$421$	−12.7997	−	22.8302i	−0.623821	−	1.11268i	0.359903	−	0.932990i	$-0.382810\pi$
$422$		0			0
$423$	−10.0398	−	34.4113i	−0.488151	−	1.67313i
$424$		0			0
$425$	−11.7880	−	15.1141i	−0.571802	−	0.733143i
$426$		0			0
$427$	−6.30762	−	16.7790i	−0.305247	−	0.811994i
$428$		0			0
$429$	2.11573	−	1.34944i	0.102149	−	0.0651514i
$430$		0			0
$431$	−28.1126	−	6.49654i	−1.35414	−	0.312927i	−0.515160	−	0.857094i	$-0.672268\pi$
$431$	−28.1126	−	6.49654i	−1.35414	−	0.312927i	−0.838977	+	0.544167i	$0.816846\pi$
$432$		0			0
$433$	1.19288	−	2.84177i	0.0573264	−	0.136567i	−0.890864	−	0.454271i	$-0.849900\pi$
$433$	1.19288	−	2.84177i	0.0573264	−	0.136567i	0.948190	+	0.317704i	$0.102912\pi$
$434$		0			0
$435$	0.0248722	+	0.262062i	0.00119253	+	0.0125649i
$436$		0			0
$437$	6.00064	−	4.15485i	0.287050	−	0.198754i
$438$		0			0
$439$	28.3578	+	24.8296i	1.35344	+	1.18505i	0.964591	+	0.263751i	$0.0849597\pi$
$439$	28.3578	+	24.8296i	1.35344	+	1.18505i	0.388852	+	0.921300i	$0.372872\pi$
$440$		0			0
$441$	10.8734	+	7.52874i	0.517779	+	0.358511i
$442$		0			0
$443$	−9.25699	−	5.90420i	−0.439813	−	0.280517i	0.299223	−	0.954183i	$-0.403273\pi$
$443$	−9.25699	−	5.90420i	−0.439813	−	0.280517i	−0.739036	+	0.673666i	$0.764718\pi$
$444$		0			0
$445$	−2.10807	+	15.8195i	−0.0999320	+	0.749918i
$446$		0			0
$447$	−1.93589	+	3.16581i	−0.0915645	+	0.149737i
$448$		0			0
$449$	−7.23565	−	7.37390i	−0.341471	−	0.347996i	0.521497	−	0.853253i	$-0.325374\pi$
$449$	−7.23565	−	7.37390i	−0.341471	−	0.347996i	−0.862969	+	0.505257i	$0.831398\pi$
$450$		0			0
$451$	−3.83951	+	18.1762i	−0.180796	+	0.855885i
$452$		0			0
$453$	−2.06632	+	3.68559i	−0.0970844	+	0.173164i
$454$		0			0
$455$	−1.55799	−	6.20428i	−0.0730398	−	0.290861i
$456$		0			0
$457$	−5.92741	−	8.91658i	−0.277272	−	0.417100i	0.667609	−	0.744512i	$-0.267318\pi$
$457$	−5.92741	−	8.91658i	−0.277272	−	0.417100i	−0.944882	+	0.327411i	$0.893824\pi$
$458$		0			0
$459$	−2.91924	−	8.75834i	−0.136259	−	0.408804i
$460$		0			0
$461$	−34.2345	−	3.90418i	−1.59446	−	0.181836i	−0.729609	−	0.683864i	$-0.760298\pi$
$461$	−34.2345	−	3.90418i	−1.59446	−	0.181836i	−0.864851	+	0.502029i	$0.832587\pi$
$462$		0			0
$463$	−36.9238	+	1.39825i	−1.71600	+	0.0649824i	−0.877397	−	0.479766i	$-0.840722\pi$
$463$	−36.9238	+	1.39825i	−1.71600	+	0.0649824i	−0.838600	+	0.544748i	$0.816625\pi$
$464$		0			0
$465$	−0.0989887	+	1.74163i	−0.00459049	+	0.0807661i
$466$		0			0
$467$	14.1226	+	23.0950i	0.653516	+	1.06871i	0.991817	+	0.127671i	$0.0407503\pi$
$467$	14.1226	+	23.0950i	0.653516	+	1.06871i	−0.338301	+	0.941038i	$0.609852\pi$
$468$		0			0
$469$	−0.0675612	+	3.56947i	−0.00311969	+	0.164823i
$470$		0			0
$471$	−1.94090	+	0.687998i	−0.0894320	+	0.0317013i
$472$		0			0
$473$	−12.3900	−	11.7058i	−0.569695	−	0.538234i
$474$		0			0
$475$	−3.30706	+	0.504556i	−0.151738	+	0.0231506i
$476$		0			0
$477$	−5.86026	−	12.6019i	−0.268323	−	0.577003i
$478$		0			0
$479$	−7.30589	−	0.276664i	−0.333814	−	0.0126411i	−0.129597	−	0.991567i	$-0.541368\pi$
$479$	−7.30589	−	0.276664i	−0.333814	−	0.0126411i	−0.204217	+	0.978926i	$0.565465\pi$
$480$		0			0
$481$	−1.25982	+	1.38505i	−0.0574426	+	0.0631526i
$482$		0			0
$483$	2.80994	+	2.27838i	0.127857	+	0.103670i
$484$		0			0
$485$	−11.4246	−	8.56771i	−0.518765	−	0.389040i
$486$		0			0
$487$	−10.7237	+	2.05408i	−0.485939	+	0.0930791i	−0.425247	−	0.905077i	$-0.639813\pi$
$487$	−10.7237	+	2.05408i	−0.485939	+	0.0930791i	−0.0606920	+	0.998157i	$0.519331\pi$
$488$		0			0
$489$	4.72065	+	0.904216i	0.213475	+	0.0408901i
$490$		0			0
$491$	4.18092	+	19.7924i	0.188682	+	0.893220i	0.964872	+	0.262720i	$0.0846197\pi$
$491$	4.18092	+	19.7924i	0.188682	+	0.893220i	−0.776190	+	0.630499i	$0.782850\pi$
$492$		0			0
$493$	3.85449	−	1.20419i	0.173597	−	0.0542338i
$494$		0			0
$495$	6.21002	−	5.86709i	0.279120	−	0.263706i
$496$		0			0
$497$	1.99558	−	5.98716i	0.0895139	−	0.268561i
$498$		0			0
$499$	−16.5613	−	22.9771i	−0.741387	−	1.02860i	−0.998070	−	0.0621003i	$-0.980220\pi$
$499$	−16.5613	−	22.9771i	−0.741387	−	1.02860i	0.256683	−	0.966496i	$-0.417370\pi$
$500$		0			0
$501$	2.83057	+	2.52243i	0.126460	+	0.112694i
$502$		0			0
$503$	−0.232796	−	0.322980i	−0.0103799	−	0.0144010i	0.806014	−	0.591896i	$-0.201621\pi$
$503$	−0.232796	−	0.322980i	−0.0103799	−	0.0144010i	−0.816394	+	0.577495i	$0.804030\pi$
$504$		0			0
$505$	−1.17463	+	3.52414i	−0.0522703	+	0.156822i
$506$		0			0
$507$	0.235575	−	0.222566i	0.0104622	−	0.00988448i
$508$		0			0
$509$	14.9790	−	4.67962i	0.663935	−	0.207421i	0.0523851	−	0.998627i	$-0.483318\pi$
$509$	14.9790	−	4.67962i	0.663935	−	0.207421i	0.611549	+	0.791206i	$0.290547\pi$
$510$		0			0
$511$	−2.13170	−	10.0915i	−0.0943011	−	0.446420i
$512$		0			0
$513$	−1.58251	−	0.303121i	−0.0698694	−	0.0133831i
$514$		0			0
$515$	13.7289	−	2.62971i	0.604969	−	0.115879i
$516$		0			0
$517$	24.4069	+	18.3035i	1.07341	+	0.804988i
$518$		0			0
$519$	−1.75606	−	1.42386i	−0.0770824	−	0.0625007i
$520$		0			0
$521$	3.02147	−	3.32181i	0.132373	−	0.145531i	−0.669985	−	0.742375i	$-0.733699\pi$
$521$	3.02147	−	3.32181i	0.132373	−	0.145531i	0.802357	+	0.596844i	$0.203579\pi$
$522$		0			0
$523$	1.77142	+	0.0670813i	0.0774589	+	0.00293326i	0.0765425	−	0.997066i	$-0.475612\pi$
$523$	1.77142	+	0.0670813i	0.0774589	+	0.00293326i	0.000916395		1.00000i	$0.499708\pi$
$524$		0			0
$525$	−0.699163	−	1.50349i	−0.0305140	−	0.0656175i
$526$		0			0
$527$	26.4544	−	4.03613i	1.15237	−	0.175817i
$528$		0			0
$529$	28.1822	+	26.6259i	1.22531	+	1.15765i
$530$		0			0
$531$	22.1366	−	7.84683i	0.960645	−	0.340523i
$532$		0			0
$533$	0.488925	−	25.8314i	0.0211777	−	1.11888i
$534$		0			0
$535$	−9.00123	−	14.7199i	−0.389157	−	0.636398i
$536$		0			0
$537$	−0.208796	+	3.67360i	−0.00901020	+	0.158527i
$538$		0			0
$539$	−11.2478	+	0.425937i	−0.484476	+	0.0183464i
$540$		0			0
$541$	6.87453	+	0.783986i	0.295559	+	0.0337062i	0.259827	−	0.965655i	$-0.416335\pi$
$541$	6.87453	+	0.783986i	0.295559	+	0.0337062i	0.0357322	+	0.999361i	$0.488624\pi$
$542$		0			0
$543$	1.90956	+	5.72910i	0.0819472	+	0.245859i
$544$		0			0
$545$	9.66815	+	14.5438i	0.414138	+	0.622987i
$546$		0			0
$547$	−1.06569	−	4.24383i	−0.0455656	−	0.181453i	0.942852	−	0.333212i	$-0.108133\pi$
$547$	−1.06569	−	4.24383i	−0.0455656	−	0.181453i	−0.988417	+	0.151759i	$0.951506\pi$
$548$		0			0
$549$	−16.2819	+	29.0412i	−0.694894	+	1.23945i
$550$		0			0
$551$	0.145665	−	0.689576i	0.00620553	−	0.0293769i
$552$		0			0
$553$	−11.0156	−	11.2261i	−0.468432	−	0.477382i
$554$		0			0
$555$	0.0982291	−	0.160636i	0.00416959	−	0.00681863i
$556$		0			0
$557$	−4.21395	+	31.6226i	−0.178551	+	1.33989i	0.641288	+	0.767300i	$0.278400\pi$
$557$	−4.21395	+	31.6226i	−0.178551	+	1.33989i	−0.819839	+	0.572594i	$0.805937\pi$
$558$		0			0
$559$	19.9861	+	12.7474i	0.845324	+	0.539156i
$560$		0			0
$561$	3.18290	+	2.20384i	0.134382	+	0.0930463i
$562$		0			0
$563$	−3.30506	−	2.89385i	−0.139292	−	0.121961i	0.586278	−	0.810110i	$-0.300592\pi$
$563$	−3.30506	−	2.89385i	−0.139292	−	0.121961i	−0.725570	+	0.688148i	$0.758424\pi$
$564$		0			0
$565$	−9.62922	+	6.66729i	−0.405104	+	0.280495i
$566$		0			0
$567$	1.22036	+	12.8581i	0.0512504	+	0.539991i
$568$		0			0
$569$	−7.94024	+	18.9158i	−0.332872	+	0.792991i	0.666020	+	0.745934i	$0.267996\pi$
$569$	−7.94024	+	18.9158i	−0.332872	+	0.792991i	−0.998892	+	0.0470576i	$0.985016\pi$
$570$		0			0
$571$	−44.9720	−	10.3926i	−1.88202	−	0.434915i	−0.882637	−	0.470056i	$-0.844234\pi$
$571$	−44.9720	−	10.3926i	−1.88202	−	0.434915i	−0.999382	+	0.0351407i	$0.988812\pi$
$572$		0			0
$573$	−2.83835	+	1.81033i	−0.118574	+	0.0756276i
$574$		0			0
$575$	−9.96262	−	26.5017i	−0.415470	−	1.10520i
$576$		0			0
$577$	10.8035	+	13.8519i	0.449757	+	0.576661i	0.958801	−	0.284079i	$-0.0916878\pi$
$577$	10.8035	+	13.8519i	0.449757	+	0.576661i	−0.509044	+	0.860740i	$0.670001\pi$
$578$		0			0
$579$	0.0810610	+	0.277836i	0.00336878	+	0.0115465i
$580$		0			0
$581$	−8.10228	−	14.4516i	−0.336139	−	0.599554i
$582$		0			0
$583$	10.4249	+	5.58809i	0.431755	+	0.231435i
$584$		0			0
$585$	−6.94725	+	9.63858i	−0.287234	+	0.398506i
$586$		0			0
$587$	−6.82577	+	3.99849i	−0.281730	+	0.165035i	−0.639537	−	0.768760i	$-0.720874\pi$
$587$	−6.82577	+	3.99849i	−0.281730	+	0.165035i	0.357807	+	0.933795i	$0.383525\pi$
$588$		0			0
$589$	1.64347	−	4.37183i	0.0677181	−	0.180138i
$590$		0			0
$591$	−1.60517	−	3.13563i	−0.0660277	−	0.128983i
$592$		0			0
$593$	−5.75298	+	6.82692i	−0.236246	+	0.280348i	−0.869857	−	0.493304i	$-0.835789\pi$
$593$	−5.75298	+	6.82692i	−0.236246	+	0.280348i	0.633611	+	0.773652i	$0.281572\pi$
$594$		0			0
$595$	7.89522	−	5.92089i	0.323673	−	0.242733i
$596$		0			0
$597$	3.24440	−	0.369998i	0.132785	−	0.0151430i
$598$		0			0
$599$	3.96986	−	15.8089i	0.162204	−	0.645934i	−0.833433	−	0.552621i	$-0.813628\pi$
$599$	3.96986	−	15.8089i	0.162204	−	0.645934i	0.995637	−	0.0933129i	$-0.0297457\pi$
$600$		0			0
$601$	−39.3184	+	17.3869i	−1.60383	+	0.709228i	−0.996371	−	0.0851206i	$-0.972872\pi$
$601$	−39.3184	+	17.3869i	−1.60383	+	0.709228i	−0.607462	+	0.794349i	$0.707812\pi$
$602$		0			0
$603$	5.15060	−	4.17626i	0.209749	−	0.170070i
$604$		0			0
$605$	0.971854	−	5.65052i	0.0395115	−	0.229726i
$606$		0			0
$607$	−20.8847	+	21.2838i	−0.847684	+	0.863881i	−0.992076	−	0.125640i	$-0.959902\pi$
$607$	−20.8847	+	21.2838i	−0.847684	+	0.863881i	0.144392	+	0.989521i	$0.453878\pi$
$608$		0			0
$609$	0.348328	−	0.0264193i	0.0141150	−	0.00107056i
$610$		0			0
$611$	−38.1261	−	18.6152i	−1.54242	−	0.753090i
$612$		0			0
$613$	−32.3697	+	17.3512i	−1.30740	+	0.700809i	−0.970584	−	0.240761i	$-0.922603\pi$
$613$	−32.3697	+	17.3512i	−1.30740	+	0.700809i	−0.336815	+	0.941571i	$0.609350\pi$
$614$		0			0
$615$	0.440414	+	2.56064i	0.0177592	+	0.103255i
$616$		0			0
$617$	−0.154406	−	2.71666i	−0.00621616	−	0.109368i	0.993782	−	0.111344i	$-0.0355156\pi$
$617$	−0.154406	−	2.71666i	−0.00621616	−	0.109368i	−0.999998	+	0.00197587i	$0.999371\pi$
$618$		0			0
$619$	−12.3874	−	14.6998i	−0.497890	−	0.590834i	0.456379	−	0.889786i	$-0.349146\pi$
$619$	−12.3874	−	14.6998i	−0.497890	−	0.590834i	−0.954268	+	0.298951i	$0.903363\pi$
$620$		0			0
$621$	−0.258063	−	13.6343i	−0.0103557	−	0.547124i
$622$		0			0
$623$	20.9364	+	3.19426i	0.838800	+	0.127975i
$624$		0			0
$625$	−0.565844	+	5.96192i	−0.0226338	+	0.238477i
$626$		0			0
$627$	0.607172	−	0.296454i	0.0242481	−	0.0118392i
$628$		0			0
$629$	−2.72247	−	0.965043i	−0.108552	−	0.0384788i
$630$		0			0
$631$	−25.1091	−	6.81293i	−0.999579	−	0.271218i	−0.275773	−	0.961223i	$-0.588934\pi$
$631$	−25.1091	−	6.81293i	−0.999579	−	0.271218i	−0.723805	+	0.690004i	$0.757609\pi$
$632$		0			0
$633$	−3.39151	+	2.96955i	−0.134801	+	0.118029i
$634$		0			0
$635$	1.86064	+	1.08995i	0.0738371	+	0.0432532i
$636$		0			0
$637$	15.2519	−	3.52455i	0.604302	−	0.139648i
$638$		0			0
$639$	−10.8921	+	4.33156i	−0.430883	+	0.171354i
$640$		0			0
$641$	10.4844	+	24.9766i	0.414107	+	0.986516i	0.986084	+	0.166246i	$0.0531646\pi$
$641$	10.4844	+	24.9766i	0.414107	+	0.986516i	−0.571977	+	0.820270i	$0.693823\pi$
$642$		0			0
$643$	−17.5217	−	19.2635i	−0.690990	−	0.759677i	0.289300	−	0.957238i	$-0.406577\pi$
$643$	−17.5217	−	19.2635i	−0.690990	−	0.759677i	−0.980291	+	0.197561i	$0.936698\pi$
$644$		0			0
$645$	−2.21521	−	0.880946i	−0.0872239	−	0.0346872i
$646$		0			0
$647$	−11.2656	−	3.51949i	−0.442896	−	0.138366i	0.0686138	−	0.997643i	$-0.478142\pi$
$647$	−11.2656	−	3.51949i	−0.442896	−	0.138366i	−0.511509	+	0.859278i	$0.670913\pi$
$648$		0			0
$649$	−11.0657	+	16.6461i	−0.434365	+	0.653415i
$650$		0			0
$651$	2.30831	+	0.175076i	0.0904697	+	0.00686176i
$652$		0			0
$653$	−1.13985	+	3.90682i	−0.0446057	+	0.152886i	−0.979231	−	0.202749i	$-0.935012\pi$
$653$	−1.13985	+	3.90682i	−0.0446057	+	0.152886i	0.934625	+	0.355635i	$0.115735\pi$
$654$		0			0
$655$	1.43315	−	2.79960i	0.0559978	−	0.109390i
$656$		0			0
$657$	−11.7816	+	15.1059i	−0.459644	+	0.589338i
$658$		0			0
$659$	−9.47888	+	2.57193i	−0.369245	+	0.100188i	−0.441651	−	0.897187i	$-0.645607\pi$
$659$	−9.47888	+	2.57193i	−0.369245	+	0.100188i	0.0724060	+	0.997375i	$0.476932\pi$
$660$		0			0
$661$	−10.3604	+	22.2790i	−0.402972	+	0.866554i	0.595050	+	0.803689i	$0.297132\pi$
$661$	−10.3604	+	22.2790i	−0.402972	+	0.866554i	−0.998022	+	0.0628650i	$0.979976\pi$
$662$		0			0
$663$	−4.92411	−	2.17748i	−0.191236	−	0.0845664i
$664$		0			0
$665$	−0.227511	−	1.70730i	−0.00882248	−	0.0662064i
$666$		0			0
$667$	5.96487			0.230961
$668$		0			0
$669$	−4.67538			−0.180761
$670$		0			0
$671$	−3.74285	−	28.0874i	−0.144491	−	1.08430i
$672$		0			0
$673$	−14.6331	−	6.47089i	−0.564065	−	0.249435i	0.102687	−	0.994714i	$-0.467256\pi$
$673$	−14.6331	−	6.47089i	−0.564065	−	0.249435i	−0.666753	+	0.745279i	$0.732316\pi$
$674$		0			0
$675$	−2.63555	+	5.66751i	−0.101443	+	0.218143i
$676$		0			0
$677$	2.80459	−	0.760977i	0.107789	−	0.0292467i	−0.207561	−	0.978222i	$-0.566553\pi$
$677$	2.80459	−	0.760977i	0.107789	−	0.0292467i	0.315350	+	0.948975i	$0.397878\pi$
$678$		0			0
$679$	−11.6545	+	14.9430i	−0.447260	+	0.573461i
$680$		0			0
$681$	3.78441	−	7.39271i	0.145019	−	0.283289i
$682$		0			0
$683$	−3.42351	+	11.7341i	−0.130997	+	0.448991i	−0.998856	−	0.0478194i	$-0.984773\pi$
$683$	−3.42351	+	11.7341i	−0.130997	+	0.448991i	0.867859	+	0.496811i	$0.165496\pi$
$684$		0			0
$685$	18.4456	+	1.39903i	0.704772	+	0.0534541i
$686$		0			0
$687$	4.69317	−	7.05992i	0.179056	−	0.269353i
$688$		0			0
$689$	−15.7014	−	4.90529i	−0.598175	−	0.186877i
$690$		0			0
$691$	−26.7306	−	10.6302i	−1.01688	−	0.404393i	−0.199134	−	0.979972i	$-0.563813\pi$
$691$	−26.7306	−	10.6302i	−1.01688	−	0.404393i	−0.817746	+	0.575579i	$0.804777\pi$
$692$		0			0
$693$	−7.62850	−	8.38680i	−0.289783	−	0.318588i
$694$		0			0
$695$	3.29946	+	7.86021i	0.125156	+	0.298155i
$696$		0			0
$697$	37.0369	−	14.7288i	1.40287	−	0.557895i
$698$		0			0
$699$	−0.721544	+	0.166741i	−0.0272913	+	0.00630674i
$700$		0			0
$701$	−16.7806	−	9.82997i	−0.633796	−	0.371273i	0.153232	−	0.988190i	$-0.451032\pi$
$701$	−16.7806	−	9.82997i	−0.633796	−	0.371273i	−0.787028	+	0.616918i	$0.788381\pi$
$702$		0			0
$703$	−0.379282	+	0.332093i	−0.0143049	+	0.0125251i
$704$		0			0
$705$	4.11792	+	1.11733i	0.155090	+	0.0420809i
$706$		0			0
$707$	4.64633	+	1.64700i	0.174743	+	0.0619418i
$708$		0			0
$709$	−22.0329	+	10.7577i	−0.827464	+	0.404012i	−0.803212	−	0.595694i	$-0.796877\pi$
$709$	−22.0329	+	10.7577i	−0.827464	+	0.404012i	−0.0242526	+	0.999706i	$0.507721\pi$
$710$		0			0
$711$	−2.76014	+	29.0818i	−0.103514	+	1.09065i
$712$		0			0
$713$	39.0759	+	5.96180i	1.46341	+	0.223271i
$714$		0			0
$715$	−0.191359	−	10.1101i	−0.00715644	−	0.378097i
$716$		0			0
$717$	−0.430045	−	0.510324i	−0.0160603	−	0.0190584i
$718$		0			0
$719$	0.458211	+	8.06186i	0.0170884	+	0.300657i	0.995550	+	0.0942300i	$0.0300389\pi$
$719$	0.458211	+	8.06186i	0.0170884	+	0.300657i	−0.978462	+	0.206427i	$0.933817\pi$
$720$		0			0
$721$	−3.14432	−	18.2816i	−0.117101	−	0.680842i
$722$		0			0
$723$	−4.53302	+	2.42985i	−0.168585	+	0.0903670i
$724$		0			0
$725$	−2.45678	−	1.19953i	−0.0912426	−	0.0445495i
$726$		0			0
$727$	19.6141	−	1.48765i	0.727445	−	0.0551738i	0.293305	−	0.956019i	$-0.405245\pi$
$727$	19.6141	−	1.48765i	0.727445	−	0.0551738i	0.434140	+	0.900845i	$0.357052\pi$
$728$		0			0
$729$	15.7323	−	16.0329i	0.582677	−	0.593810i
$730$		0			0
$731$	−6.19895	+	36.0417i	−0.229277	+	1.33305i
$732$		0			0
$733$	−13.1171	+	10.6357i	−0.484490	+	0.392839i	−0.840644	−	0.541589i	$-0.817823\pi$
$733$	−13.1171	+	10.6357i	−0.484490	+	0.392839i	0.356153	+	0.934427i	$0.384088\pi$
$734$		0			0
$735$	−1.43976	+	0.636673i	−0.0531062	+	0.0234840i
$736$		0			0
$737$	−1.37449	+	5.47352i	−0.0506299	+	0.201620i
$738$		0			0
$739$	46.1363	−	5.26148i	1.69715	−	0.193547i	0.789638	−	0.613573i	$-0.210268\pi$
$739$	46.1363	−	5.26148i	1.69715	−	0.193547i	0.907512	+	0.420027i	$0.137979\pi$
$740$		0			0
$741$	−0.751774	+	0.563780i	−0.0276171	+	0.0207110i
$742$		0			0
$743$	−21.1796	+	25.1334i	−0.777005	+	0.922053i	−0.998590	−	0.0530877i	$-0.983094\pi$
$743$	−21.1796	+	25.1334i	−0.777005	+	0.922053i	0.221585	+	0.975141i	$0.428877\pi$
$744$		0			0
$745$	6.81364	+	13.3102i	0.249633	+	0.487648i
$746$		0			0
$747$	−10.8283	+	28.8045i	−0.396187	+	1.05390i
$748$		0			0
$749$	−19.7565	+	11.5732i	−0.721885	+	0.422875i
$750$		0			0
$751$	16.9242	−	23.4805i	0.617572	−	0.856816i	−0.380105	−	0.924943i	$-0.624112\pi$
$751$	16.9242	−	23.4805i	0.617572	−	0.856816i	0.997677	+	0.0681276i	$0.0217025\pi$
$752$		0			0
$753$	4.18827	+	2.24505i	0.152629	+	0.0818142i
$754$		0			0
$755$	8.32635	+	14.8513i	0.303027	+	0.540494i
$756$		0			0
$757$	−11.8844	−	40.7338i	−0.431947	−	1.48049i	−0.827192	−	0.561919i	$-0.810063\pi$
$757$	−11.8844	−	40.7338i	−0.431947	−	1.48049i	0.395245	−	0.918576i	$-0.370660\pi$
$758$		0			0
$759$	3.51685	+	4.50918i	0.127654	+	0.163673i
$760$		0			0
$761$	12.8942	+	34.3000i	0.467414	+	1.24337i	0.933481	+	0.358626i	$0.116755\pi$
$761$	12.8942	+	34.3000i	0.467414	+	1.24337i	−0.466068	+	0.884749i	$0.654330\pi$
$762$		0			0
$763$	19.5395	−	12.4625i	0.707376	−	0.451171i
$764$		0			0
$765$	−17.8591	−	4.12705i	−0.645697	−	0.149214i
$766$		0			0
$767$	10.7595	−	25.6319i	0.388501	−	0.925516i
$768$		0			0
$769$	0.0230929	+	0.243314i	0.000832750	+	0.00877413i	0.995933	−	0.0900971i	$-0.0287178\pi$
$769$	0.0230929	+	0.243314i	0.000832750	+	0.00877413i	−0.995100	+	0.0988713i	$0.968477\pi$
$770$		0			0
$771$	6.85411	−	4.74580i	0.246845	−	0.170916i
$772$		0			0
$773$	−8.48903	−	7.43285i	−0.305329	−	0.267341i	0.492384	−	0.870378i	$-0.336126\pi$
$773$	−8.48903	−	7.43285i	−0.305329	−	0.267341i	−0.797713	+	0.603037i	$0.793957\pi$
$774$		0			0
$775$	−14.8955	−	10.3137i	−0.535062	−	0.370478i
$776$		0			0
$777$	−0.210665	−	0.134364i	−0.00755758	−	0.00482030i
$778$		0			0
$779$	0.918878	−	6.89552i	0.0329222	−	0.247058i
$780$		0			0
$781$	5.20444	−	8.51094i	0.186230	−	0.304545i
$782$		0			0
$783$	−0.922282	−	0.939904i	−0.0329597	−	0.0335894i
$784$		0			0
$785$	−1.71496	+	8.11863i	−0.0612097	+	0.289766i
$786$		0			0
$787$	5.80745	−	10.3584i	0.207013	−	0.369239i	−0.748997	−	0.662574i	$-0.769464\pi$
$787$	5.80745	−	10.3584i	0.207013	−	0.369239i	0.956010	+	0.293335i	$0.0947653\pi$
$788$		0			0
$789$	−0.990561	−	3.94464i	−0.0352649	−	0.140433i
$790$		0			0
$791$	8.60434	+	12.9435i	0.305935	+	0.460217i
$792$		0			0
$793$	12.4609	+	37.3853i	0.442499	+	1.32759i
$794$		0			0
$795$	1.64364	+	0.187444i	0.0582939	+	0.00664795i
$796$		0			0
$797$	2.09033	−	0.0791580i	0.0740434	−	0.00280392i	−0.000793806	−	1.00000i	$-0.500253\pi$
$797$	2.09033	−	0.0791580i	0.0740434	−	0.00280392i	0.0748372	+	0.997196i	$0.476156\pi$
$798$		0			0
$799$	3.71425	−	65.3493i	0.131401	−	2.31189i
$800$		0			0
$801$	−20.5215	−	33.5593i	−0.725091	−	1.18576i
$802$		0			0
$803$	0.308542	−	16.3012i	0.0108882	−	0.575258i
$804$		0			0
$805$	13.7395	−	4.87029i	0.484253	−	0.171655i
$806$		0			0
$807$	−0.851144	−	0.804141i	−0.0299617	−	0.0283071i
$808$		0			0
$809$	−29.2048	+	4.45576i	−1.02678	+	0.156656i	−0.642283	−	0.766468i	$-0.722012\pi$
$809$	−29.2048	+	4.45576i	−1.02678	+	0.156656i	−0.384502	+	0.923124i	$0.625627\pi$
$810$		0			0
$811$	−5.61863	−	12.0823i	−0.197297	−	0.424269i	0.782940	−	0.622098i	$-0.213719\pi$
$811$	−5.61863	−	12.0823i	−0.197297	−	0.424269i	−0.980237	+	0.197829i	$0.936611\pi$
$812$		0			0
$813$	−4.42679	−	0.167637i	−0.155254	−	0.00587927i
$814$		0			0
$815$	13.0321	−	14.3276i	0.456496	−	0.501873i
$816$		0			0
$817$	4.95780	+	4.01993i	0.173451	+	0.140639i
$818$		0			0
$819$	12.6140	+	9.45967i	0.440769	+	0.330548i
$820$		0			0
$821$	33.1283	−	6.34556i	1.15619	−	0.221462i	0.426009	−	0.904719i	$-0.359919\pi$
$821$	33.1283	−	6.34556i	1.15619	−	0.221462i	0.730178	+	0.683257i	$0.239437\pi$
$822$		0			0
$823$	−31.9434	−	6.11860i	−1.11348	−	0.213281i	−0.401759	−	0.915745i	$-0.631601\pi$
$823$	−31.9434	−	6.11860i	−1.11348	−	0.213281i	−0.711719	+	0.702464i	$0.752083\pi$
$824$		0			0
$825$	−0.541711	−	2.56446i	−0.0188600	−	0.0892829i
$826$		0			0
$827$	22.1634	−	6.92411i	0.770698	−	0.240775i	0.112532	−	0.993648i	$-0.464104\pi$
$827$	22.1634	−	6.92411i	0.770698	−	0.240775i	0.658165	+	0.752873i	$0.271333\pi$
$828$		0			0
$829$	−3.64894	+	3.44743i	−0.126733	+	0.119734i	−0.747503	−	0.664258i	$-0.768748\pi$
$829$	−3.64894	+	3.44743i	−0.126733	+	0.119734i	0.620770	+	0.783992i	$0.286820\pi$
$830$		0			0
$831$	−1.43750	+	4.31281i	−0.0498664	+	0.149610i
$832$		0			0
$833$	14.1208	+	19.5911i	0.489256	+	0.678791i
$834$		0			0
$835$	14.6218	−	4.42817i	0.506010	−	0.153243i
$836$		0			0
$837$	−5.10246	−	7.07913i	−0.176367	−	0.244690i
$838$		0			0
$839$	2.30606	−	6.91867i	0.0796140	−	0.238859i	−0.901336	−	0.433122i	$-0.857412\pi$
$839$	2.30606	−	6.91867i	0.0796140	−	0.238859i	0.980950	+	0.194263i	$0.0622314\pi$
$840$		0			0
$841$	−20.6612	+	19.5202i	−0.712455	+	0.673111i
$842$		0			0
$843$	−6.86313	+	2.14412i	−0.236379	+	0.0738474i
$844$		0			0
$845$	−0.269903	−	1.27772i	−0.00928495	−	0.0439549i
$846$		0			0
$847$	−7.47270	−	1.43136i	−0.256765	−	0.0491820i
$848$		0			0
$849$	−2.36613	+	0.453221i	−0.0812055	+	0.0155545i
$850$		0			0
$851$	−3.41335	−	2.55978i	−0.117008	−	0.0877483i
$852$		0			0
$853$	35.5190	+	28.7999i	1.21615	+	0.986089i	0.999953	+	0.00973883i	$0.00310002\pi$
$853$	35.5190	+	28.7999i	1.21615	+	0.986089i	0.216196	+	0.976350i	$0.430635\pi$
$854$		0			0
$855$	−2.15259	+	2.36657i	−0.0736171	+	0.0809349i
$856$		0			0
$857$	49.6993	+	1.88204i	1.69769	+	0.0642893i	0.868815	−	0.495137i	$-0.164882\pi$
$857$	49.6993	+	1.88204i	1.69769	+	0.0642893i	0.828880	+	0.559427i	$0.188979\pi$
$858$		0			0
$859$	11.9582	+	25.7151i	0.408010	+	0.877387i	0.997571	+	0.0696632i	$0.0221925\pi$
$859$	11.9582	+	25.7151i	0.408010	+	0.877387i	−0.589561	+	0.807724i	$0.700699\pi$
$860$		0			0
$861$	3.40851	−	0.520036i	0.116162	−	0.0177228i
$862$		0			0
$863$	9.39267	+	8.87398i	0.319730	+	0.302074i	0.829802	−	0.558058i	$-0.188453\pi$
$863$	9.39267	+	8.87398i	0.319730	+	0.302074i	−0.510072	+	0.860132i	$0.670381\pi$
$864$		0			0
$865$	−8.58644	+	3.04366i	−0.291948	+	0.103488i
$866$		0			0
$867$	0.0628014	−	3.31799i	0.00213285	−	0.112685i
$868$		0			0
$869$	−12.9703	−	21.2106i	−0.439987	−	0.719522i
$870$		0			0
$871$	0.445367	−	7.83589i	0.0150907	−	0.265509i
$872$		0			0
$873$	35.1727	−	1.33194i	1.19042	−	0.0450794i
$874$		0			0
$875$	−15.8523	−	1.80783i	−0.535906	−	0.0611158i
$876$		0			0
$877$	−1.08031	−	3.24116i	−0.0364795	−	0.109446i	0.928871	−	0.370404i	$-0.120781\pi$
$877$	−1.08031	−	3.24116i	−0.0364795	−	0.109446i	−0.965350	+	0.260958i	$0.915962\pi$
$878$		0			0
$879$	−0.967946	−	1.45608i	−0.0326480	−	0.0491123i
$880$		0			0
$881$	2.14252	+	8.53202i	0.0721834	+	0.287451i	0.995271	−	0.0971393i	$-0.0309692\pi$
$881$	2.14252	+	8.53202i	0.0721834	+	0.287451i	−0.923087	+	0.384590i	$0.874343\pi$
$882$		0			0
$883$	−4.51312	+	8.04982i	−0.151879	+	0.270898i	−0.937623	−	0.347653i	$-0.886979\pi$
$883$	−4.51312	+	8.04982i	−0.151879	+	0.270898i	0.785745	+	0.618551i	$0.212280\pi$
$884$		0			0
$885$	−0.577787	+	2.73524i	−0.0194221	+	0.0919441i
$886$		0			0
$887$	−13.3931	−	13.6490i	−0.449698	−	0.458290i	0.451135	−	0.892455i	$-0.351019\pi$
$887$	−13.3931	−	13.6490i	−0.449698	−	0.458290i	−0.900833	+	0.434166i	$0.857043\pi$
$888$		0			0
$889$	1.49287	−	2.44132i	0.0500692	−	0.0818793i
$890$		0			0
$891$	−2.69686	+	20.2380i	−0.0903482	+	0.677998i
$892$		0			0
$893$	−9.63158	−	6.14311i	−0.322309	−	0.205571i
$894$		0			0
$895$	12.1900	+	8.44036i	0.407466	+	0.282130i
$896$		0			0
$897$	−5.98340	−	5.23896i	−0.199780	−	0.174924i
$898$		0			0
$899$	3.13818	−	2.17288i	0.104664	−	0.0724697i
$900$		0			0
$901$	−2.39781	−	25.2641i	−0.0798825	−	0.841668i
$902$		0			0
$903$	−1.22447	+	2.91702i	−0.0407478	+	0.0970724i
$904$		0			0
$905$	23.7094	+	5.47901i	0.788128	+	0.182128i
$906$		0			0
$907$	−33.1921	+	21.1702i	−1.10212	+	0.702945i	−0.958044	−	0.286621i	$-0.907468\pi$
$907$	−33.1921	+	21.1702i	−1.10212	+	0.702945i	−0.144080	+	0.989566i	$0.546022\pi$
$908$		0			0
$909$	−3.22184	−	8.57046i	−0.106862	−	0.284264i
$910$		0			0
$911$	−11.5040	−	14.7501i	−0.381146	−	0.488691i	0.559142	−	0.829072i	$-0.311131\pi$
$911$	−11.5040	−	14.7501i	−0.381146	−	0.488691i	−0.940288	+	0.340381i	$0.889444\pi$
$912$		0			0
$913$	−7.33528	−	25.1416i	−0.242762	−	0.832065i
$914$		0			0
$915$	−1.93806	−	3.45682i	−0.0640704	−	0.114279i
$916$		0			0
$917$	−3.67852	−	1.97181i	−0.121476	−	0.0651149i
$918$		0			0
$919$	9.94108	−	13.7922i	0.327926	−	0.454963i	−0.614726	−	0.788741i	$-0.710733\pi$
$919$	9.94108	−	13.7922i	0.327926	−	0.454963i	0.942652	+	0.333778i	$0.108324\pi$
$920$		0			0
$921$	−3.30501	+	1.93605i	−0.108904	+	0.0637951i
$922$		0			0
$923$	−4.88201	+	12.9867i	−0.160693	+	0.427463i
$924$		0			0
$925$	0.891102	+	1.74073i	0.0292993	+	0.0572350i
$926$		0			0
$927$	−22.2021	+	26.3467i	−0.729212	+	0.865339i
$928$		0			0
$929$	25.0082	−	18.7545i	0.820494	−	0.615316i	−0.104832	−	0.994490i	$-0.533430\pi$
$929$	25.0082	−	18.7545i	0.820494	−	0.615316i	0.925325	+	0.379174i	$0.123792\pi$
$930$		0			0
$931$	4.18772	−	0.477576i	0.137247	−	0.0156519i
$932$		0			0
$933$	−0.941810	+	3.75050i	−0.0308335	+	0.122786i
$934$		0			0
$935$	14.2673	−	6.30911i	0.466590	−	0.206330i
$936$		0			0
$937$	28.4140	−	23.0389i	0.928244	−	0.752647i	−0.0408948	−	0.999163i	$-0.513021\pi$
$937$	28.4140	−	23.0389i	0.928244	−	0.752647i	0.969139	+	0.246516i	$0.0792859\pi$
$938$		0			0
$939$	1.34153	−	7.79986i	0.0437791	−	0.254539i
$940$		0			0
$941$	−0.0308108	+	0.0313995i	−0.00100440	+	0.00102359i	−0.714268	−	0.699872i	$-0.753240\pi$
$941$	−0.0308108	+	0.0313995i	−0.00100440	+	0.00102359i	0.713264	+	0.700896i	$0.247216\pi$
$942$		0			0
$943$	58.7061	−	4.45262i	1.91173	−	0.144997i
$944$		0			0
$945$	−2.89181	−	1.41194i	−0.0940707	−	0.0459303i
$946$		0			0
$947$	47.2976	−	25.3531i	1.53697	−	0.823865i	0.537159	−	0.843481i	$-0.319497\pi$
$947$	47.2976	−	25.3531i	1.53697	−	0.823865i	0.999808	+	0.0196161i	$0.00624441\pi$
$948$		0			0
$949$	3.84347	+	22.3465i	0.124764	+	0.725400i
$950$		0			0
$951$	−0.129181	−	2.27283i	−0.00418897	−	0.0737016i
$952$		0			0
$953$	22.9000	+	27.1749i	0.741803	+	0.880280i	0.996225	−	0.0868131i	$-0.0276683\pi$
$953$	22.9000	+	27.1749i	0.741803	+	0.880280i	−0.254422	+	0.967093i	$0.581885\pi$
$954$		0			0
$955$	0.256717	+	13.5632i	0.00830718	+	0.438894i
$956$		0			0
$957$	0.545885	+	0.0832855i	0.0176460	+	0.00269224i
$958$		0			0
$959$	2.31946	−	24.4386i	0.0748992	−	0.789162i
$960$		0			0
$961$	−5.12686	+	2.50321i	−0.165383	+	0.0807486i
$962$		0			0
$963$	40.0835	+	14.2085i	1.29167	+	0.457864i
$964$		0			0
$965$	1.12553	+	0.305394i	0.0362322	+	0.00983099i
$966$		0			0
$967$	−14.2381	+	12.4666i	−0.457865	+	0.400899i	−0.856448	−	0.516234i	$-0.827334\pi$
$967$	−14.2381	+	12.4666i	−0.457865	+	0.400899i	0.398583	+	0.917132i	$0.369502\pi$
$968$		0			0
$969$	−1.25087	−	0.732748i	−0.0401836	−	0.0235393i
$970$		0			0
$971$	−46.7352	+	10.8000i	−1.49980	+	0.346589i	−0.893653	−	0.448759i	$-0.851866\pi$
$971$	−46.7352	+	10.8000i	−1.49980	+	0.346589i	−0.606152	+	0.795349i	$0.707288\pi$
$972$		0			0
$973$	10.5118	−	4.18033i	0.336992	−	0.134015i
$974$		0			0
$975$	1.41086	+	3.36106i	0.0451838	+	0.107640i
$976$		0			0
$977$	13.5323	+	14.8775i	0.432938	+	0.475974i	0.916901	−	0.399115i	$-0.130683\pi$
$977$	13.5323	+	14.8775i	0.432938	+	0.475974i	−0.483963	+	0.875089i	$0.660803\pi$
$978$		0			0
$979$	31.1086	+	12.3713i	0.994236	+	0.395388i
$980$		0			0
$981$	−41.0869	−	12.8360i	−1.31180	−	0.409822i
$982$		0			0
$983$	−8.48044	+	12.7571i	−0.270484	+	0.406889i	−0.942791	−	0.333384i	$-0.891810\pi$
$983$	−8.48044	+	12.7571i	−0.270484	+	0.406889i	0.672307	+	0.740272i	$0.265303\pi$
$984$		0			0
$985$	−14.1539	−	1.07351i	−0.450979	−	0.0342050i
$986$		0			0
$987$	1.58588	−	5.43559i	0.0504792	−	0.173017i
$988$		0			0
$989$	−24.6152	+	48.0849i	−0.782719	+	1.52901i
$990$		0			0
$991$	20.5592	−	26.3602i	0.653083	−	0.837360i	−0.341653	−	0.939826i	$-0.610987\pi$
$991$	20.5592	−	26.3602i	0.653083	−	0.837360i	0.994736	+	0.102467i	$0.0326735\pi$
$992$		0			0
$993$	−4.66606	+	1.26606i	−0.148073	+	0.0401771i
$994$		0			0
$995$	5.54836	−	11.9312i	0.175895	−	0.378246i
$996$		0			0
$997$	1.67197	+	0.739359i	0.0529518	+	0.0234157i	0.430737	−	0.902478i	$-0.358254\pi$
$997$	1.67197	+	0.739359i	0.0529518	+	0.0234157i	−0.377785	+	0.925893i	$0.623314\pi$
$998$		0			0
$999$	0.124415	+	0.933643i	0.00393631	+	0.0295392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.6	✓	1148
167.130	even	83	inner	668.2.e.a.297.6	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.6	✓	1148	1.1	even	1	trivial
668.2.e.a.297.6	yes	1148	167.130	even	83	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0387535 - 0.290817i) q^{3} +(-1.08122 - 0.478126i) q^{5} +(-0.661531 + 1.42256i) q^{7} +(2.81224 - 0.763053i) q^{9} +O(q^{10})\)	\(q+(-0.0387535 - 0.290817i) q^{3} +(-1.08122 - 0.478126i) q^{5} +(-0.661531 + 1.42256i) q^{7} +(2.81224 - 0.763053i) q^{9} +(-1.52518 + 1.95553i) q^{11} +(1.57161 - 3.07008i) q^{13} +(-0.0971461 + 0.332967i) q^{15} +(5.30559 + 0.402408i) q^{17} +(0.514102 - 0.773362i) q^{19} +(0.439342 + 0.137255i) q^{21} +(7.30313 + 2.90431i) q^{23} +(-2.42392 - 2.66487i) q^{25} +(-0.671561 - 1.59984i) q^{27} +(0.705224 - 0.280454i) q^{29} +(4.90024 - 1.13240i) q^{31} +(0.627807 + 0.367764i) q^{33} +(1.39542 - 1.22181i) q^{35} +(-0.523913 - 0.142155i) q^{37} +(-0.953739 - 0.338075i) q^{39} +(6.73144 - 3.28665i) q^{41} +(-0.649411 + 6.84241i) q^{43} +(-3.40549 - 0.519575i) q^{45} +(-0.232797 - 12.2994i) q^{47} +(2.92473 + 3.47070i) q^{49} +(-0.0885833 - 1.55855i) q^{51} +(-0.808450 - 4.70046i) q^{53} +(2.58404 - 1.38513i) q^{55} +(-0.244830 - 0.119539i) q^{57} +(8.03690 - 0.609566i) q^{59} +(-8.00247 + 8.15537i) q^{61} +(-0.774895 + 4.50536i) q^{63} +(-3.16715 + 2.56802i) q^{65} +(2.08121 - 0.920329i) q^{67} +(0.561602 - 2.23643i) q^{69} +(-3.99676 + 0.455799i) q^{71} +(-5.25963 + 3.94438i) q^{73} +(-0.681055 + 0.808192i) q^{75} +(-1.77290 - 3.46330i) q^{77} +(-3.52765 + 9.38398i) q^{79} +(7.10364 - 4.16126i) q^{81} +(-6.17495 + 8.56709i) q^{83} +(-5.54413 - 2.97183i) q^{85} +(-0.108891 - 0.194223i) q^{87} +(-3.78095 - 12.9592i) q^{89} +(3.32771 + 4.26666i) q^{91} +(-0.519222 - 1.38119i) q^{93} +(-0.925624 + 0.590372i) q^{95} +(11.7691 + 2.71971i) q^{97} +(-2.79700 + 6.66320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 1148 * q - 2 * q^5 - 14 * q^9	\( 1148 q - 2 q^{5} - 14 q^{9} + 2 q^{11} + 4 q^{13} + 14 q^{15} + 2 q^{17} + 2 q^{19} + 14 q^{23} - 6 q^{25} + 2 q^{29} - 2 q^{31} + 16 q^{33} - 2 q^{35} + 10 q^{37} + 6 q^{39} + 4 q^{41} + 4 q^{43} - 2 q^{45} + 2 q^{47} - 30 q^{49} - 2 q^{51} - 6 q^{55} - 4 q^{57} + 6 q^{59} + 2 q^{61} + 14 q^{63} + 22 q^{65} + 12 q^{67} - 14 q^{69} - 8 q^{71} - 18 q^{73} - 26 q^{75} - 2 q^{79} - 6 q^{81} - 22 q^{83} + 34 q^{85} + 2 q^{87} + 14 q^{89} - 6 q^{91} + 32 q^{93} - 8 q^{95} + 44 q^{97} + 2 q^{99}+O(q^{100}) \) 1148 * q - 2 * q^5 - 14 * q^9 + 2 * q^11 + 4 * q^13 + 14 * q^15 + 2 * q^17 + 2 * q^19 + 14 * q^23 - 6 * q^25 + 2 * q^29 - 2 * q^31 + 16 * q^33 - 2 * q^35 + 10 * q^37 + 6 * q^39 + 4 * q^41 + 4 * q^43 - 2 * q^45 + 2 * q^47 - 30 * q^49 - 2 * q^51 - 6 * q^55 - 4 * q^57 + 6 * q^59 + 2 * q^61 + 14 * q^63 + 22 * q^65 + 12 * q^67 - 14 * q^69 - 8 * q^71 - 18 * q^73 - 26 * q^75 - 2 * q^79 - 6 * q^81 - 22 * q^83 + 34 * q^85 + 2 * q^87 + 14 * q^89 - 6 * q^91 + 32 * q^93 - 8 * q^95 + 44 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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