LMFDB - Embedded newform 507.2.k.k.80.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(80,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("507.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.2
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.668092 + 2.49335i) q^{2} +(0.116023 - 1.72816i) q^{3} +(-4.03841 - 2.33158i) q^{4} +(0.624703 + 0.624703i) q^{5} +(4.23140 + 1.44386i) q^{6} +(-1.62412 + 0.435181i) q^{7} +(4.86096 - 4.86096i) q^{8} +(-2.97308 - 0.401012i) q^{9} +(-1.97496 + 1.14025i) q^{10} +(0.346022 + 0.0927163i) q^{11} +(-4.49789 + 6.70851i) q^{12} -4.34024i q^{14} +(1.15207 - 1.00711i) q^{15} +(4.20937 + 7.29084i) q^{16} +(1.31381 - 2.27558i) q^{17} +(2.98615 - 7.14502i) q^{18} +(-1.58246 - 5.90581i) q^{19} +(-1.06626 - 3.97935i) q^{20} +(0.563628 + 2.85722i) q^{21} +(-0.462349 + 0.800812i) q^{22} +(-2.70887 - 4.69190i) q^{23} +(-7.83654 - 8.96451i) q^{24} -4.21949i q^{25} +(-1.03796 + 5.09143i) q^{27} +(7.57351 + 2.02932i) q^{28} +(7.24949 - 4.18549i) q^{29} +(1.74139 + 3.54535i) q^{30} +(-1.27341 + 1.27341i) q^{31} +(-7.71050 + 2.06602i) q^{32} +(0.200375 - 0.587225i) q^{33} +(4.79608 + 4.79608i) q^{34} +(-1.28645 - 0.742731i) q^{35} +(11.0715 + 8.55142i) q^{36} +(0.894800 - 3.33944i) q^{37} +15.7825 q^{38} +6.07331 q^{40} +(1.79217 - 6.68847i) q^{41} +(-7.50063 - 0.503566i) q^{42} +(-0.825277 - 0.476474i) q^{43} +(-1.18121 - 1.18121i) q^{44} +(-1.60678 - 2.10780i) q^{45} +(13.5083 - 3.61955i) q^{46} +(-5.33521 + 5.33521i) q^{47} +(13.0881 - 6.42856i) q^{48} +(-3.61381 + 2.08643i) q^{49} +(10.5207 + 2.81901i) q^{50} +(-3.78013 - 2.53449i) q^{51} -9.69778i q^{53} +(-12.0013 - 5.98954i) q^{54} +(0.158241 + 0.274081i) q^{55} +(-5.77937 + 10.0102i) q^{56} +(-10.3898 + 2.04953i) q^{57} +(5.59259 + 20.8718i) q^{58} +(2.66789 + 9.95670i) q^{59} +(-7.00067 + 1.38098i) q^{60} +(-2.43931 + 4.22500i) q^{61} +(-2.32431 - 4.02583i) q^{62} +(5.00314 - 0.642536i) q^{63} -3.76781i q^{64} +(1.33029 + 0.891926i) q^{66} +(-12.1619 - 3.25877i) q^{67} +(-10.6114 + 6.12649i) q^{68} +(-8.42264 + 4.13699i) q^{69} +(2.71136 - 2.71136i) q^{70} +(3.10785 - 0.832745i) q^{71} +(-16.4013 + 12.5027i) q^{72} +(-0.246530 - 0.246530i) q^{73} +(7.72860 + 4.46211i) q^{74} +(-7.29196 - 0.489557i) q^{75} +(-7.37925 + 27.5397i) q^{76} -0.602329 q^{77} -3.68180 q^{79} +(-1.92500 + 7.18422i) q^{80} +(8.67838 + 2.38448i) q^{81} +(15.4794 + 8.93703i) q^{82} +(8.47001 + 8.47001i) q^{83} +(4.38568 - 12.8528i) q^{84} +(2.24230 - 0.600822i) q^{85} +(1.73938 - 1.73938i) q^{86} +(-6.39210 - 13.0139i) q^{87} +(2.13269 - 1.23131i) q^{88} +(-6.61757 - 1.77317i) q^{89} +(6.32897 - 2.59806i) q^{90} +25.2638i q^{92} +(2.05292 + 2.34841i) q^{93} +(-9.73816 - 16.8670i) q^{94} +(2.70081 - 4.67794i) q^{95} +(2.67583 + 13.5647i) q^{96} +(-1.36929 - 5.11027i) q^{97} +(-2.78786 - 10.4044i) q^{98} +(-0.991570 - 0.414412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.668092	+	2.49335i	−0.472412	+	1.76307i	0.158650	+	0.987335i	$0.449286\pi$
$2$	−0.668092	+	2.49335i	−0.472412	+	1.76307i	−0.631062	+	0.775732i	$0.717381\pi$
$3$	0.116023	−	1.72816i	0.0669857	−	0.997754i
$3$	0.116023	−	1.72816i	0.0669857	−	0.997754i
$4$	−4.03841	−	2.33158i	−2.01921	−	1.16579i
$5$	0.624703	+	0.624703i	0.279376	+	0.279376i	0.832860	−	0.553484i	$-0.186702\pi$
$5$	0.624703	+	0.624703i	0.279376	+	0.279376i	−0.553484	+	0.832860i	$0.686702\pi$
$6$	4.23140	+	1.44386i	1.72746	+	0.589452i
$7$	−1.62412	+	0.435181i	−0.613858	+	0.164483i	−0.552334	−	0.833623i	$-0.686263\pi$
$7$	−1.62412	+	0.435181i	−0.613858	+	0.164483i	−0.0615241	+	0.998106i	$0.519596\pi$
$8$	4.86096	−	4.86096i	1.71861	−	1.71861i
$9$	−2.97308	−	0.401012i	−0.991026	−	0.133671i
$10$	−1.97496	+	1.14025i	−0.624538	+	0.360577i
$11$	0.346022	+	0.0927163i	0.104330	+	0.0279550i	0.310606	−	0.950539i	$-0.399468\pi$
$11$	0.346022	+	0.0927163i	0.104330	+	0.0279550i	−0.206277	+	0.978494i	$0.566135\pi$
$12$	−4.49789	+	6.70851i	−1.29843	+	1.93658i
$13$		0			0
$13$		0			0
$14$		−	4.34024i		−	1.15998i
$15$	1.15207	−	1.00711i	0.297462	−	0.260034i
$16$	4.20937	+	7.29084i	1.05234	+	1.82271i
$17$	1.31381	−	2.27558i	0.318645	−	0.551909i	−0.661561	−	0.749892i	$-0.730106\pi$
$17$	1.31381	−	2.27558i	0.318645	−	0.551909i	0.980206	+	0.197983i	$0.0634390\pi$
$18$	2.98615	−	7.14502i	0.703843	−	1.68410i
$19$	−1.58246	−	5.90581i	−0.363040	−	1.35488i	−0.870058	−	0.492949i	$-0.835919\pi$
$19$	−1.58246	−	5.90581i	−0.363040	−	1.35488i	0.507018	−	0.861936i	$-0.330748\pi$
$20$	−1.06626	−	3.97935i	−0.238424	−	0.889810i
$21$	0.563628	+	2.85722i	0.122994	+	0.623498i
$22$	−0.462349	+	0.800812i	−0.0985732	+	0.170734i
$23$	−2.70887	−	4.69190i	−0.564838	−	0.978328i	−0.997065	−	0.0765633i	$-0.975605\pi$
$23$	−2.70887	−	4.69190i	−0.564838	−	0.978328i	0.432227	−	0.901765i	$-0.357728\pi$
$24$	−7.83654	−	8.96451i	−1.59963	−	1.82987i
$25$		−	4.21949i		−	0.843899i
$26$		0			0
$27$	−1.03796	+	5.09143i	−0.199755	+	0.979846i
$28$	7.57351	+	2.02932i	1.43126	+	0.383505i
$29$	7.24949	−	4.18549i	1.34620	−	0.777227i	0.358488	−	0.933535i	$-0.383293\pi$
$29$	7.24949	−	4.18549i	1.34620	−	0.777227i	0.987708	+	0.156308i	$0.0499592\pi$
$30$	1.74139	+	3.54535i	0.317932	+	0.647289i
$31$	−1.27341	+	1.27341i	−0.228712	+	0.228712i	−0.812154	−	0.583443i	$-0.801705\pi$
$31$	−1.27341	+	1.27341i	−0.228712	+	0.228712i	0.583443	+	0.812154i	$0.301705\pi$
$32$	−7.71050	+	2.06602i	−1.36304	+	0.365225i
$33$	0.200375	−	0.587225i	0.0348808	−	0.102223i
$34$	4.79608	+	4.79608i	0.822521	+	0.822521i
$35$	−1.28645	−	0.742731i	−0.217449	−	0.125545i
$36$	11.0715	+	8.55142i	1.84526	+	1.42524i
$37$	0.894800	−	3.33944i	0.147104	−	0.549001i	−0.852548	−	0.522648i	$-0.824944\pi$
$37$	0.894800	−	3.33944i	0.147104	−	0.549001i	0.999653	−	0.0263524i	$-0.00838920\pi$
$38$	15.7825			2.56026
$39$		0			0
$40$	6.07331			0.960275
$41$	1.79217	−	6.68847i	0.279890	−	1.04456i	−0.672603	−	0.740004i	$-0.734824\pi$
$41$	1.79217	−	6.68847i	0.279890	−	1.04456i	0.952493	−	0.304560i	$-0.0985096\pi$
$42$	−7.50063	−	0.503566i	−1.15737	−	0.0777019i
$43$	−0.825277	−	0.476474i	−0.125854	−	0.0726616i	0.435752	−	0.900067i	$-0.356483\pi$
$43$	−0.825277	−	0.476474i	−0.125854	−	0.0726616i	−0.561605	+	0.827405i	$0.689816\pi$
$44$	−1.18121	−	1.18121i	−0.178073	−	0.178073i
$45$	−1.60678	−	2.10780i	−0.239524	−	0.314213i
$46$	13.5083	−	3.61955i	1.99170	−	0.533673i
$47$	−5.33521	+	5.33521i	−0.778220	+	0.778220i	−0.979528	−	0.201308i	$-0.935481\pi$
$47$	−5.33521	+	5.33521i	−0.778220	+	0.778220i	0.201308	+	0.979528i	$0.435481\pi$
$48$	13.0881	−	6.42856i	1.88911	−	0.927883i
$49$	−3.61381	+	2.08643i	−0.516258	+	0.298062i
$50$	10.5207	+	2.81901i	1.48785	+	0.398668i
$51$	−3.78013	−	2.53449i	−0.529325	−	0.354899i
$52$		0			0
$53$		−	9.69778i		−	1.33209i	−0.745911	−	0.666046i	$-0.767985\pi$
$53$		−	9.69778i		−	1.33209i	0.745911	−	0.666046i	$-0.232015\pi$
$54$	−12.0013	−	5.98954i	−1.63317	−	0.815073i
$55$	0.158241	+	0.274081i	0.0213372	+	0.0369571i
$56$	−5.77937	+	10.0102i	−0.772301	+	1.33766i
$57$	−10.3898	+	2.04953i	−1.37616	+	0.271467i
$58$	5.59259	+	20.8718i	0.734343	+	2.74061i
$59$	2.66789	+	9.95670i	0.347330	+	1.29625i	0.889867	+	0.456220i	$0.150797\pi$
$59$	2.66789	+	9.95670i	0.347330	+	1.29625i	−0.542538	+	0.840032i	$0.682536\pi$
$60$	−7.00067	+	1.38098i	−0.903783	+	0.178284i
$61$	−2.43931	+	4.22500i	−0.312321	+	0.540956i	−0.978864	−	0.204510i	$-0.934440\pi$
$61$	−2.43931	+	4.22500i	−0.312321	+	0.540956i	0.666543	+	0.745466i	$0.267773\pi$
$62$	−2.32431	−	4.02583i	−0.295188	−	0.511281i
$63$	5.00314	−	0.642536i	0.630336	−	0.0809520i
$64$		−	3.76781i		−	0.470977i
$65$		0			0
$66$	1.33029	+	0.891926i	0.163747	+	0.109789i
$67$	−12.1619	−	3.25877i	−1.48581	−	0.398122i	−0.577491	−	0.816397i	$-0.695968\pi$
$67$	−12.1619	−	3.25877i	−1.48581	−	0.398122i	−0.908320	+	0.418275i	$0.862635\pi$
$68$	−10.6114	+	6.12649i	−1.28682	+	0.742946i
$69$	−8.42264	+	4.13699i	−1.01397	+	0.498035i
$70$	2.71136	−	2.71136i	0.324069	−	0.324069i
$71$	3.10785	−	0.832745i	0.368834	−	0.0988287i	−0.0696413	−	0.997572i	$-0.522185\pi$
$71$	3.10785	−	0.832745i	0.368834	−	0.0988287i	0.438475	+	0.898743i	$0.355519\pi$
$72$	−16.4013	+	12.5027i	−1.93291	+	1.47346i
$73$	−0.246530	−	0.246530i	−0.0288542	−	0.0288542i	0.692532	−	0.721387i	$-0.256495\pi$
$73$	−0.246530	−	0.246530i	−0.0288542	−	0.0288542i	−0.721387	+	0.692532i	$0.756495\pi$
$74$	7.72860	+	4.46211i	0.898431	+	0.518709i
$75$	−7.29196	−	0.489557i	−0.842003	−	0.0565291i
$76$	−7.37925	+	27.5397i	−0.846457	+	3.15902i
$77$	−0.602329			−0.0686417
$78$		0			0
$79$	−3.68180			−0.414235			−0.207118	−	0.978316i	$-0.566408\pi$
$79$	−3.68180			−0.414235			−0.207118	+	0.978316i	$0.566408\pi$
$80$	−1.92500	+	7.18422i	−0.215222	+	0.803220i
$81$	8.67838	+	2.38448i	0.964264	+	0.264942i
$82$	15.4794	+	8.93703i	1.70941	+	0.986930i
$83$	8.47001	+	8.47001i	0.929705	+	0.929705i	0.997687	−	0.0679819i	$-0.0216560\pi$
$83$	8.47001	+	8.47001i	0.929705	+	0.929705i	−0.0679819	+	0.997687i	$0.521656\pi$
$84$	4.38568	−	12.8528i	0.478517	−	1.40236i
$85$	2.24230	−	0.600822i	0.243211	−	0.0651683i
$86$	1.73938	−	1.73938i	0.187562	−	0.187562i
$87$	−6.39210	−	13.0139i	−0.685305	−	1.39524i
$88$	2.13269	−	1.23131i	0.227346	−	0.131258i
$89$	−6.61757	−	1.77317i	−0.701461	−	0.187956i	−0.109576	−	0.993978i	$-0.534949\pi$
$89$	−6.61757	−	1.77317i	−0.701461	−	0.187956i	−0.591885	+	0.806022i	$0.701616\pi$
$90$	6.32897	−	2.59806i	0.667132	−	0.273859i
$91$		0			0
$92$			25.2638i			2.63393i
$93$	2.05292	+	2.34841i	0.212878	+	0.243519i
$94$	−9.73816	−	16.8670i	−1.00441	−	1.73970i
$95$	2.70081	−	4.67794i	0.277097	−	0.479946i
$96$	2.67583	+	13.5647i	0.273100	+	1.38444i
$97$	−1.36929	−	5.11027i	−0.139031	−	0.518870i	−0.999949	−	0.0101260i	$-0.996777\pi$
$97$	−1.36929	−	5.11027i	−0.139031	−	0.518870i	0.860918	−	0.508744i	$-0.169890\pi$
$98$	−2.78786	−	10.4044i	−0.281616	−	1.05101i
$99$	−0.991570	−	0.414412i	−0.0996566	−	0.0416499i
$100$	−9.83809	+	17.0401i	−0.983809	+	1.70401i
$101$	4.24104	+	7.34570i	0.421999	+	0.730924i	0.996135	−	0.0878358i	$-0.0279951\pi$
$101$	4.24104	+	7.34570i	0.421999	+	0.730924i	−0.574136	+	0.818760i	$0.694662\pi$
$102$	8.84485	−	7.73194i	0.875770	−	0.765576i
$103$		−	0.554855i		−	0.0546714i	−0.999626	−	0.0273357i	$-0.991298\pi$
$103$		−	0.554855i		−	0.0546714i	0.999626	−	0.0273357i	$-0.00870232\pi$
$104$		0			0
$105$	−1.43282	+	2.13702i	−0.139829	+	0.208551i
$106$	24.1800	+	6.47901i	2.34857	+	0.629297i
$107$	−2.87486	+	1.65980i	−0.277923	+	0.160459i	−0.632483	−	0.774574i	$-0.717964\pi$
$107$	−2.87486	+	1.65980i	−0.277923	+	0.160459i	0.354560	+	0.935033i	$0.384631\pi$
$108$	16.0628	−	18.1412i	1.54564	−	1.74564i
$109$	1.95379	−	1.95379i	0.187139	−	0.187139i	−0.607319	−	0.794458i	$-0.707755\pi$
$109$	1.95379	−	1.95379i	0.187139	−	0.187139i	0.794458	+	0.607319i	$0.207755\pi$
$110$	−0.789101	+	0.211439i	−0.0752378	+	0.0201599i
$111$	−5.66727	−	1.93381i	−0.537914	−	0.183549i
$112$	−10.0093	−	10.0093i	−0.945794	−	0.945794i
$113$	4.96947	+	2.86913i	0.467489	+	0.269905i	0.715188	−	0.698932i	$-0.246341\pi$
$113$	4.96947	+	2.86913i	0.467489	+	0.269905i	−0.247699	+	0.968837i	$0.579674\pi$
$114$	1.83113	−	27.2747i	0.171501	−	2.55451i
$115$	1.23880	−	4.62328i	0.115519	−	0.431123i
$116$	−39.0352			−3.62433
$117$		0			0
$118$	−26.6080			−2.44946
$119$	−1.14349	+	4.26755i	−0.104823	+	0.391205i
$120$	0.704642	−	10.4957i	0.0643247	−	0.958119i
$121$	−9.41514	−	5.43584i	−0.855922	−	0.494167i
$122$	−8.90475	−	8.90475i	−0.806198	−	0.806198i
$123$	−11.3508	−	3.87317i	−1.02347	−	0.349232i
$124$	8.11164	−	2.17351i	0.728447	−	0.195187i
$125$	5.75944	−	5.75944i	0.515140	−	0.515140i
$126$	−1.74049	+	12.9039i	−0.155055	+	1.14957i
$127$	11.7986	−	6.81191i	1.04695	−	0.604459i	0.125159	−	0.992137i	$-0.460056\pi$
$127$	11.7986	−	6.81191i	1.04695	−	0.604459i	0.921795	+	0.387678i	$0.126723\pi$
$128$	−6.02651	−	1.61480i	−0.532673	−	0.142729i
$129$	−0.919175	+	1.37093i	−0.0809288	+	0.120704i
$130$		0			0
$131$		−	6.35913i		−	0.555599i	−0.960639	−	0.277800i	$-0.910395\pi$
$131$		−	6.35913i		−	0.555599i	0.960639	−	0.277800i	$-0.0896052\pi$
$132$	−2.17836	+	1.90427i	−0.189602	+	0.165745i
$133$	5.14019	+	8.90306i	0.445711	+	0.771993i
$134$	16.2505	−	28.1467i	1.40383	−	2.43151i
$135$	−3.82904	+	2.53222i	−0.329552	+	0.217938i
$136$	−4.67514	−	17.4479i	−0.400890	−	1.49614i
$137$	0.528741	+	1.97329i	0.0451734	+	0.168589i	0.984827	−	0.173537i	$-0.0555196\pi$
$137$	0.528741	+	1.97329i	0.0451734	+	0.168589i	−0.939654	+	0.342126i	$0.888853\pi$
$138$	−4.68789	−	23.7645i	−0.399059	−	2.02297i
$139$	2.55676	−	4.42843i	0.216861	−	0.375615i	−0.736986	−	0.675908i	$-0.763751\pi$
$139$	2.55676	−	4.42843i	0.216861	−	0.375615i	0.953847	+	0.300294i	$0.0970848\pi$
$140$	3.46348	+	5.99892i	0.292717	+	0.507001i
$141$	8.60110	+	9.83911i	0.724343	+	0.828602i
$142$			8.30531i			0.696966i
$143$		0			0
$144$	−9.59107	−	23.3642i	−0.799256	−	1.94702i
$145$	7.14346	+	1.91409i	0.593232	+	0.158956i
$146$	0.779393	−	0.449983i	0.0645030	−	0.0372408i
$147$	3.18641	+	6.48731i	0.262810	+	0.535064i
$148$	−11.3997	+	11.3997i	−0.937053	+	0.937053i
$149$	10.2394	−	2.74363i	0.838841	−	0.224767i	0.186274	−	0.982498i	$-0.440359\pi$
$149$	10.2394	−	2.74363i	0.838841	−	0.224767i	0.652567	+	0.757731i	$0.273692\pi$
$150$	6.09234	−	17.8544i	0.497437	−	1.45780i
$151$	−6.62875	−	6.62875i	−0.539440	−	0.539440i	0.383925	−	0.923364i	$-0.374572\pi$
$151$	−6.62875	−	6.62875i	−0.539440	−	0.539440i	−0.923364	+	0.383925i	$0.874572\pi$
$152$	−36.4002	−	21.0156i	−2.95244	−	1.70459i
$153$	−4.81858	+	6.23862i	−0.389559	+	0.504362i
$154$	0.402411	−	1.50182i	0.0324272	−	0.121020i
$155$	−1.59101			−0.127793
$156$		0			0
$157$	21.9960			1.75547			0.877735	−	0.479147i	$-0.159054\pi$
$157$	21.9960			1.75547			0.877735	+	0.479147i	$0.159054\pi$
$158$	2.45978	−	9.18004i	0.195690	−	0.730325i
$159$	−16.7593	−	1.12516i	−1.32910	−	0.0892311i
$160$	−6.10742	−	3.52612i	−0.482834	−	0.278764i
$161$	6.44134	+	6.44134i	0.507649	+	0.507649i
$162$	−11.7433	+	20.0452i	−0.922641	+	1.57490i
$163$	−19.8654	+	5.32291i	−1.55598	+	0.416923i	−0.931387	−	0.364030i	$-0.881400\pi$
$163$	−19.8654	+	5.32291i	−1.55598	+	0.416923i	−0.624590	+	0.780953i	$0.714734\pi$
$164$	−22.8322	+	22.8322i	−1.78290	+	1.78290i
$165$	0.492016	−	0.241666i	0.0383034	−	0.0188137i
$166$	−26.7775	+	15.4600i	−2.07834	+	1.19993i
$167$	−9.68331	−	2.59464i	−0.749317	−	0.200779i	−0.136102	−	0.990695i	$-0.543458\pi$
$167$	−9.68331	−	2.59464i	−0.749317	−	0.200779i	−0.613215	+	0.789916i	$0.710124\pi$
$168$	16.6286	+	11.1491i	1.28293	+	0.860171i
$169$		0			0
$170$			5.99225i			0.459584i
$171$	2.33647	+	18.1930i	0.178674	+	1.39125i
$172$	2.22188	+	3.84840i	0.169416	+	0.293438i
$173$	−5.88220	+	10.1883i	−0.447215	+	0.774599i	−0.998204	−	0.0599136i	$-0.980917\pi$
$173$	−5.88220	+	10.1883i	−0.447215	+	0.774599i	0.550988	+	0.834513i	$0.314251\pi$
$174$	36.7187	−	7.24329i	2.78364	−	0.549112i
$175$	1.83624	+	6.85295i	0.138807	+	0.518034i
$176$	0.780555	+	2.91307i	0.0588365	+	0.219581i
$177$	17.5163	−	3.45534i	1.31661	−	0.259719i
$178$	8.84230	−	15.3153i	0.662758	−	1.14793i
$179$	5.90594	+	10.2294i	0.441431	+	0.764580i	0.997796	−	0.0663576i	$-0.0211378\pi$
$179$	5.90594	+	10.2294i	0.441431	+	0.764580i	−0.556365	+	0.830938i	$0.687804\pi$
$180$	1.57432	+	12.2585i	0.117343	+	0.913695i
$181$		−	20.0999i		−	1.49402i	−0.664815	−	0.747008i	$-0.731490\pi$
$181$		−	20.0999i		−	1.49402i	0.664815	−	0.747008i	$-0.268510\pi$
$182$		0			0
$183$	7.01847	+	4.70571i	0.518820	+	0.347856i
$184$	−35.9749	−	9.63943i	−2.65210	−	0.710628i
$185$	2.64514	−	1.52717i	0.194475	−	0.112280i
$186$	−7.22695	+	3.54970i	−0.529906	+	0.260277i
$187$	0.665589	−	0.665589i	0.0486727	−	0.0486727i
$188$	33.9853	−	9.10632i	2.47863	−	0.664147i
$189$	−0.529929	−	8.72077i	−0.0385467	−	0.634343i
$190$	9.85936	+	9.85936i	0.715274	+	0.715274i
$191$	14.6715	+	8.47057i	1.06159	+	0.612909i	0.925871	−	0.377839i	$-0.123333\pi$
$191$	14.6715	+	8.47057i	1.06159	+	0.612909i	0.135718	+	0.990748i	$0.456666\pi$
$192$	−6.51139	−	0.437152i	−0.469919	−	0.0315487i
$193$	−4.33031	+	16.1609i	−0.311702	+	1.16329i	0.615318	+	0.788279i	$0.289027\pi$
$193$	−4.33031	+	16.1609i	−0.311702	+	1.16329i	−0.927021	+	0.375010i	$0.877639\pi$
$194$	13.6565			0.980482
$195$		0			0
$196$	19.4587			1.38991
$197$	−3.78551	+	14.1277i	−0.269706	+	1.00656i	0.689600	+	0.724190i	$0.257786\pi$
$197$	−3.78551	+	14.1277i	−0.269706	+	1.00656i	−0.959306	+	0.282367i	$0.908880\pi$
$198$	1.69574	−	2.19547i	0.120511	−	0.156025i
$199$	0.289508	+	0.167148i	0.0205227	+	0.0118488i	0.510226	−	0.860040i	$-0.329562\pi$
$199$	0.289508	+	0.167148i	0.0205227	+	0.0118488i	−0.489704	+	0.871889i	$0.662895\pi$
$200$	−20.5108	−	20.5108i	−1.45033	−	1.45033i
$201$	−7.04273	+	20.6396i	−0.496756	+	1.45581i
$202$	−21.1488	+	5.66681i	−1.48803	+	0.398716i
$203$	−9.95256	+	9.95256i	−0.698533	+	0.698533i
$204$	9.35639	+	19.0490i	0.655078	+	1.33370i
$205$	5.29788	−	3.05873i	0.370020	−	0.213631i
$206$	1.38345	+	0.370694i	0.0963894	+	0.0258275i
$207$	6.17217	+	15.0357i	0.428996	+	1.04505i
$208$		0			0
$209$		−	2.19026i		−	0.151503i
$210$	−4.37108	−	5.00024i	−0.301633	−	0.345049i
$211$	1.34455	+	2.32883i	0.0925626	+	0.160323i	0.908589	−	0.417692i	$-0.137161\pi$
$211$	1.34455	+	2.32883i	0.0925626	+	0.160323i	−0.816026	+	0.578015i	$0.803828\pi$
$212$	−22.6111	+	39.1636i	−1.55294	+	2.68977i
$213$	−1.07854	−	5.46748i	−0.0739001	−	0.374625i
$214$	−2.21780	−	8.27694i	−0.151606	−	0.565800i
$215$	−0.217898	−	0.813208i	−0.0148605	−	0.0554603i
$216$	19.7038	+	29.7947i	1.34067	+	2.02727i
$217$	1.51401	−	2.62234i	0.102778	−	0.178016i
$218$	3.56617	+	6.17679i	0.241532	+	0.418345i
$219$	−0.454647	+	0.397441i	−0.0307222	+	0.0268566i
$220$		−	1.47580i		−	0.0994987i
$221$		0			0
$222$	8.60793	−	12.8386i	0.577726	−	0.861667i
$223$	−7.48636	−	2.00597i	−0.501324	−	0.134329i	−0.000709598	−	1.00000i	$-0.500226\pi$
$223$	−7.48636	−	2.00597i	−0.501324	−	0.134329i	−0.500614	+	0.865670i	$0.666893\pi$
$224$	11.6237	−	6.71092i	0.776638	−	0.448392i
$225$	−1.69207	+	12.5449i	−0.112804	+	0.836325i
$226$	−10.4738	+	10.4738i	−0.696708	+	0.696708i
$227$	−18.1111	+	4.85285i	−1.20207	+	0.322095i	−0.803648	−	0.595105i	$-0.797110\pi$
$227$	−18.1111	+	4.85285i	−1.20207	+	0.322095i	−0.398427	+	0.917200i	$0.630444\pi$
$228$	46.7369	+	15.9478i	3.09523	+	1.05617i
$229$	−8.11488	−	8.11488i	−0.536246	−	0.536246i	0.386178	−	0.922424i	$-0.373795\pi$
$229$	−8.11488	−	8.11488i	−0.536246	−	0.536246i	−0.922424	+	0.386178i	$0.873795\pi$
$230$	10.6998	+	6.17755i	0.705526	+	0.407336i
$231$	−0.0698838	+	1.04092i	−0.00459801	+	0.0684875i
$232$	14.8940	−	55.5850i	0.977837	−	3.64934i
$233$	−11.2799			−0.738973			−0.369486	−	0.929236i	$-0.620466\pi$
$233$	−11.2799			−0.738973			−0.369486	+	0.929236i	$0.620466\pi$
$234$		0			0
$235$	−6.66584			−0.434832
$236$	12.4408	−	46.4297i	0.809827	−	3.02231i
$237$	−0.427173	+	6.36275i	−0.0277478	+	0.413305i
$238$	−9.87655	−	5.70223i	−0.640202	−	0.369621i
$239$	−1.32193	−	1.32193i	−0.0855084	−	0.0855084i	0.663059	−	0.748567i	$-0.269258\pi$
$239$	−1.32193	−	1.32193i	−0.0855084	−	0.0855084i	−0.748567	+	0.663059i	$0.769258\pi$
$240$	12.1921	+	4.16025i	0.786999	+	0.268543i
$241$	22.4684	−	6.02040i	1.44732	−	0.387808i	0.552228	−	0.833693i	$-0.313778\pi$
$241$	22.4684	−	6.02040i	1.44732	−	0.387808i	0.895090	+	0.445885i	$0.147111\pi$
$242$	19.8436	−	19.8436i	1.27560	−	1.27560i
$243$	5.12765	−	14.7210i	0.328939	−	0.944351i
$244$	19.7019	−	11.3749i	1.26128	−	0.728202i
$245$	−3.56095	−	0.954155i	−0.227501	−	0.0609587i
$246$	17.2406	−	25.7140i	1.09922	−	1.63946i
$247$		0			0
$248$			12.3800i			0.786133i
$249$	15.6203	−	13.6548i	0.989893	−	0.865340i
$250$	10.5125	+	18.2082i	0.664868	+	1.15159i
$251$	5.39681	−	9.34756i	0.340644	−	0.590013i	−0.643909	−	0.765102i	$-0.722688\pi$
$251$	5.39681	−	9.34756i	0.340644	−	0.590013i	0.984552	+	0.175090i	$0.0560216\pi$
$252$	−21.7029	−	9.07038i	−1.36715	−	0.571380i
$253$	−0.502313	−	1.87466i	−0.0315801	−	0.117859i
$254$	9.10196	+	33.9690i	0.571108	+	2.13140i
$255$	−0.778159	−	3.94476i	−0.0487302	−	0.247030i
$256$	11.8203	−	20.4734i	0.738771	−	1.27959i
$257$	2.12801	+	3.68582i	0.132741	+	0.229915i	0.924732	−	0.380618i	$-0.124289\pi$
$257$	2.12801	+	3.68582i	0.132741	+	0.229915i	−0.791991	+	0.610533i	$0.790955\pi$
$258$	−2.80412	−	3.20773i	−0.174577	−	0.199705i
$259$			5.81304i			0.361205i
$260$		0			0
$261$	−23.2317	+	9.53667i	−1.43801	+	0.590305i
$262$	15.8555	+	4.24848i	0.979559	+	0.262472i
$263$	−21.9508	+	12.6733i	−1.35355	+	0.781470i	−0.988744	−	0.149615i	$-0.952196\pi$
$263$	−21.9508	+	12.6733i	−1.35355	+	0.781470i	−0.364801	+	0.931085i	$0.618863\pi$
$264$	−1.88046	−	3.82849i	−0.115734	−	0.235627i
$265$	6.05823	−	6.05823i	0.372154	−	0.372154i
$266$	−25.6326	+	6.86823i	−1.57164	+	0.421118i
$267$	−3.83212	+	11.2305i	−0.234522	+	0.687295i
$268$	41.5167	+	41.5167i	2.53604	+	2.53604i
$269$	19.6286	+	11.3326i	1.19677	+	0.690958i	0.959835	−	0.280566i	$-0.0905222\pi$
$269$	19.6286	+	11.3326i	1.19677	+	0.690958i	0.236940	+	0.971524i	$0.423855\pi$
$270$	−3.75555	−	11.2389i	−0.228556	−	0.683979i
$271$	5.51672	−	20.5887i	0.335117	−	1.25067i	−0.568625	−	0.822597i	$-0.692524\pi$
$271$	5.51672	−	20.5887i	0.335117	−	1.25067i	0.903742	−	0.428077i	$-0.140809\pi$
$272$	22.1212			1.34129
$273$		0			0
$274$	−5.27335			−0.318575
$275$	0.391216	−	1.46004i	0.0235912	−	0.0880436i
$276$	43.6599	+	2.93117i	2.62801	+	0.176436i
$277$	9.25074	+	5.34092i	0.555823	+	0.320905i	0.751467	−	0.659770i	$-0.229346\pi$
$277$	9.25074	+	5.34092i	0.555823	+	0.320905i	−0.195644	+	0.980675i	$0.562680\pi$
$278$	9.33349	+	9.33349i	0.559786	+	0.559786i
$279$	4.29661	−	3.27530i	0.257231	−	0.196087i
$280$	−9.86377	+	2.64299i	−0.589473	+	0.157949i
$281$	9.84122	−	9.84122i	0.587078	−	0.587078i	−0.349761	−	0.936839i	$-0.613737\pi$
$281$	9.84122	−	9.84122i	0.587078	−	0.587078i	0.936839	+	0.349761i	$0.113737\pi$
$282$	−30.2787	+	14.8721i	−1.80307	+	0.885623i
$283$	14.1131	−	8.14822i	0.838938	−	0.484361i	−0.0179649	−	0.999839i	$-0.505719\pi$
$283$	14.1131	−	8.14822i	0.838938	−	0.484361i	0.856903	+	0.515477i	$0.172385\pi$
$284$	−14.4924	−	3.88322i	−0.859965	−	0.230427i
$285$	−7.77087	−	5.21018i	−0.460307	−	0.308624i
$286$		0			0
$287$			11.6428i			0.687251i
$288$	23.7524	−	3.05044i	1.39962	−	0.179749i
$289$	5.04783	+	8.74310i	0.296931	+	0.514300i
$290$	−9.54498	+	16.5324i	−0.560501	+	0.970816i
$291$	−8.99024	+	1.77345i	−0.527017	+	0.103962i
$292$	0.420787	+	1.57040i	0.0246247	+	0.0919006i
$293$	−4.25757	−	15.8895i	−0.248730	−	0.928272i	−0.971472	−	0.237154i	$-0.923785\pi$
$293$	−4.25757	−	15.8895i	−0.248730	−	0.928272i	0.722742	−	0.691117i	$-0.242881\pi$
$294$	−18.3040	+	3.61072i	−1.06751	+	0.210581i
$295$	−4.55334	+	7.88661i	−0.265106	+	0.459176i
$296$	−11.8833	−	20.5825i	−0.690703	−	1.19633i
$297$	−0.831215	+	1.66551i	−0.0482320	+	0.0966428i
$298$			27.3633i			1.58512i
$299$		0			0
$300$	28.3065	+	18.9788i	1.63428	+	1.09574i
$301$	1.54770	+	0.414705i	0.0892079	+	0.0239032i
$302$	20.9564	−	12.0992i	1.20591	−	0.696231i
$303$	13.1866	−	6.47693i	0.757551	−	0.372090i
$304$	36.3972	−	36.3972i	2.08752	−	2.08752i
$305$	−4.16321	+	1.11553i	−0.238385	+	0.0638750i
$306$	−12.3358	−	16.1824i	−0.705192	−	0.925086i
$307$	−5.70702	−	5.70702i	−0.325717	−	0.325717i	0.525238	−	0.850955i	$-0.323976\pi$
$307$	−5.70702	−	5.70702i	−0.325717	−	0.325717i	−0.850955	+	0.525238i	$0.823976\pi$
$308$	2.43245	+	1.40438i	0.138602	+	0.0800218i
$309$	−0.958878	−	0.0643757i	−0.0545487	−	0.00366221i
$310$	1.06294	−	3.96695i	0.0603710	−	0.225308i
$311$	25.3416			1.43699			0.718496	−	0.695531i	$-0.244831\pi$
$311$	25.3416			1.43699			0.718496	+	0.695531i	$0.244831\pi$
$312$		0			0
$313$	−3.49487			−0.197542			−0.0987709	−	0.995110i	$-0.531491\pi$
$313$	−3.49487			−0.197542			−0.0987709	+	0.995110i	$0.531491\pi$
$314$	−14.6953	+	54.8437i	−0.829306	+	3.09501i
$315$	3.52687	+	2.72408i	0.198716	+	0.153484i
$316$	14.8687	+	8.58442i	0.836427	+	0.482911i
$317$	−5.25697	−	5.25697i	−0.295261	−	0.295261i	0.543893	−	0.839154i	$-0.316950\pi$
$317$	−5.25697	−	5.25697i	−0.295261	−	0.295261i	−0.839154	+	0.543893i	$0.816950\pi$
$318$	14.0022	−	41.0352i	0.785204	−	2.30114i
$319$	2.89655	−	0.776127i	0.162175	−	0.0434548i
$320$	2.35376	−	2.35376i	0.131579	−	0.131579i
$321$	2.53485	+	5.16080i	0.141482	+	0.288048i
$322$	−20.3640	+	11.7571i	−1.13484	+	0.655199i
$323$	−15.5182	−	4.15808i	−0.863454	−	0.231362i
$324$	−29.4873	−	29.8638i	−1.63818	−	1.65910i
$325$		0			0
$326$		−	53.0876i		−	2.94025i
$327$	−3.14977	−	3.60314i	−0.174183	−	0.199254i
$328$	−23.8007	−	41.2241i	−1.31418	−	2.27622i
$329$	6.34322	−	10.9868i	0.349713	−	0.605721i
$330$	0.273847	+	1.38822i	0.0150748	+	0.0764192i
$331$	4.65404	+	17.3691i	0.255809	+	0.954693i	0.967638	+	0.252341i	$0.0812004\pi$
$331$	4.65404	+	17.3691i	0.255809	+	0.954693i	−0.711829	+	0.702353i	$0.752133\pi$
$332$	−14.4569	−	53.9539i	−0.793426	−	2.96111i
$333$	−3.99946	+	9.56959i	−0.219169	+	0.524410i
$334$	12.9387	−	22.4105i	0.707974	−	1.22625i
$335$	−5.56180	−	9.63333i	−0.303874	−	0.526325i
$336$	−18.4591	+	16.1364i	−1.00702	+	0.880315i
$337$			16.3852i			0.892558i	0.894894	+	0.446279i	$0.147251\pi$
$337$			16.3852i			0.892558i	−0.894894	+	0.446279i	$0.852749\pi$
$338$		0			0
$339$	5.53488	−	8.25516i	0.300614	−	0.448359i
$340$	−10.4562	−	2.80173i	−0.567067	−	0.151945i
$341$	−0.558696	+	0.322563i	−0.0302551	+	0.0174678i
$342$	−46.9226	−	6.32896i	−2.53728	−	0.342231i
$343$	13.2838	−	13.2838i	0.717259	−	0.717259i
$344$	−6.32777	+	1.69552i	−0.341170	+	0.0914163i
$345$	−7.84604	−	2.67726i	−0.422417	−	0.144139i
$346$	−21.4731	−	21.4731i	−1.15440	−	1.15440i
$347$	−20.8470	−	12.0360i	−1.11912	−	0.646126i	−0.177946	−	0.984040i	$-0.556945\pi$
$347$	−20.8470	−	12.0360i	−1.11912	−	0.646126i	−0.941177	+	0.337914i	$0.890279\pi$
$348$	−4.52897	+	67.4592i	−0.242778	+	3.61619i
$349$	−4.47957	+	16.7180i	−0.239786	+	0.894894i	0.736147	+	0.676822i	$0.236643\pi$
$349$	−4.47957	+	16.7180i	−0.239786	+	0.894894i	−0.975933	+	0.218072i	$0.930023\pi$
$350$	−18.3136			−0.978903
$351$		0			0
$352$	−2.85956			−0.152415
$353$	5.48522	−	20.4711i	0.291949	−	1.08957i	−0.651662	−	0.758510i	$-0.725928\pi$
$353$	5.48522	−	20.4711i	0.291949	−	1.08957i	0.943611	−	0.331058i	$-0.107405\pi$
$354$	−3.08713	+	45.9828i	−0.164079	+	2.44396i
$355$	2.46170	+	1.42126i	0.130653	+	0.0754328i
$356$	22.5902	+	22.5902i	1.19728	+	1.19728i
$357$	7.24234	+	2.47126i	0.383305	+	0.130793i
$358$	−29.4512	+	7.89142i	−1.55654	+	0.417075i
$359$	18.7493	−	18.7493i	0.989548	−	0.989548i	−0.0103977	−	0.999946i	$-0.503310\pi$
$359$	18.7493	−	18.7493i	0.989548	−	0.989548i	0.999946	+	0.0103977i	$0.00330975\pi$
$360$	−18.0564	−	2.43547i	−0.951658	−	0.128361i
$361$	−15.9199	+	9.19136i	−0.837889	+	0.483756i
$362$	50.1162	+	13.4286i	2.63405	+	0.705792i
$363$	−10.4864	+	15.6402i	−0.550392	+	0.820898i
$364$		0			0
$365$		−	0.308016i		−	0.0161223i
$366$	−16.4220	+	14.3557i	−0.858391	+	0.750383i
$367$	−10.1653	−	17.6069i	−0.530626	−	0.919072i	−0.999361	−	0.0357329i	$-0.988623\pi$
$367$	−10.1653	−	17.6069i	−0.530626	−	0.919072i	0.468735	−	0.883339i	$-0.344710\pi$
$368$	22.8053	−	39.4999i	1.18881	−	2.05907i
$369$	−8.01042	+	19.1667i	−0.417006	+	0.997777i
$370$	2.04058	+	7.61557i	0.106085	+	0.395914i
$371$	4.22028	+	15.7503i	0.219106	+	0.817716i
$372$	−2.81504	−	14.2704i	−0.145953	−	0.739885i
$373$	−16.0055	+	27.7224i	−0.828735	+	1.43541i	0.0702957	+	0.997526i	$0.477606\pi$
$373$	−16.0055	+	27.7224i	−0.828735	+	1.43541i	−0.899031	+	0.437885i	$0.855728\pi$
$374$	1.21487	+	2.10422i	0.0628197	+	0.108807i
$375$	−9.28502	−	10.6215i	−0.479476	−	0.548490i
$376$			51.8685i			2.67492i
$377$		0			0
$378$	22.0980	+	4.50498i	1.13660	+	0.231711i
$379$	−16.8350	−	4.51091i	−0.864754	−	0.231710i	−0.200936	−	0.979604i	$-0.564398\pi$
$379$	−16.8350	−	4.51091i	−0.864754	−	0.231710i	−0.663818	+	0.747894i	$0.731065\pi$
$380$	−21.8140	+	12.5943i	−1.11903	+	0.646074i
$381$	−10.4032	−	21.1802i	−0.532970	−	1.08509i
$382$	−30.9220	+	30.9220i	−1.58211	+	1.58211i
$383$	20.9622	−	5.61681i	1.07112	−	0.287005i	0.320166	−	0.947361i	$-0.396261\pi$
$383$	20.9622	−	5.61681i	1.07112	−	0.287005i	0.750953	+	0.660356i	$0.229595\pi$
$384$	−3.48984	+	10.2274i	−0.178090	+	0.521916i
$385$	−0.376276	−	0.376276i	−0.0191768	−	0.0191768i
$386$	−37.4019	−	21.5940i	−1.90370	−	1.09910i
$387$	2.26254	+	1.74754i	0.115011	+	0.0888325i
$388$	−6.38524	+	23.8300i	−0.324161	+	1.20979i
$389$	−3.24468			−0.164512			−0.0822559	−	0.996611i	$-0.526212\pi$
$389$	−3.24468			−0.164512			−0.0822559	+	0.996611i	$0.526212\pi$
$390$		0			0
$391$	−14.2357			−0.719931
$392$	−7.42451	+	27.7086i	−0.374994	+	1.39950i
$393$	−10.9896	−	0.737803i	−0.554351	−	0.0372172i
$394$	−32.6963	−	18.8772i	−1.64722	−	0.951020i
$395$	−2.30003	−	2.30003i	−0.115727	−	0.115727i
$396$	3.03814	+	3.98549i	0.152672	+	0.200279i
$397$	30.7348	−	8.23536i	1.54253	−	0.413321i	0.615451	−	0.788175i	$-0.288974\pi$
$397$	30.7348	−	8.23536i	1.54253	−	0.413321i	0.927084	+	0.374855i	$0.122307\pi$
$398$	−0.610176	+	0.610176i	−0.0305854	+	0.0305854i
$399$	15.9823	−	7.85011i	0.800116	−	0.392997i
$400$	30.7637	−	17.7614i	1.53818	−	0.888070i
$401$	36.5184	+	9.78507i	1.82364	+	0.488643i	0.997227	−	0.0744193i	$-0.0237103\pi$
$401$	36.5184	+	9.78507i	1.82364	+	0.488643i	0.826414	+	0.563062i	$0.190377\pi$
$402$	−46.7567	−	31.3492i	−2.33201	−	1.56355i
$403$		0			0
$404$		−	39.5533i		−	1.96785i
$405$	3.93182	+	6.91100i	0.195374	+	0.343410i
$406$	−18.1660	−	31.4645i	−0.901565	−	1.56156i
$407$	0.619241	−	1.07256i	0.0306947	−	0.0531647i
$408$	−30.6951	+	6.05505i	−1.51964	+	0.299770i
$409$	−0.785323	−	2.93087i	−0.0388317	−	0.144922i	0.943788	−	0.330551i	$-0.107234\pi$
$409$	−0.785323	−	2.93087i	−0.0388317	−	0.144922i	−0.982620	+	0.185629i	$0.940568\pi$
$410$	4.08703	+	15.2530i	0.201844	+	0.753292i
$411$	3.47151	−	0.684803i	0.171237	−	0.0337789i
$412$	−1.29369	+	2.24073i	−0.0637354	+	0.110393i
$413$	−8.66592	−	15.0098i	−0.426422	−	0.738585i
$414$	−41.6128	+	5.34420i	−2.04516	+	0.262653i
$415$			10.5825i			0.519474i
$416$		0			0
$417$	−7.35640	−	4.93228i	−0.360244	−	0.241535i
$418$	5.46109	+	1.46329i	0.267111	+	0.0715721i
$419$	32.1726	−	18.5749i	1.57173	−	0.907442i	0.575778	−	0.817606i	$-0.304699\pi$
$419$	32.1726	−	18.5749i	1.57173	−	0.907442i	0.995957	−	0.0898356i	$-0.0286342\pi$
$420$	10.7689	−	5.28943i	0.525470	−	0.258098i
$421$	18.7201	−	18.7201i	0.912361	−	0.912361i	−0.0840970	−	0.996458i	$-0.526801\pi$
$421$	18.7201	−	18.7201i	0.912361	−	0.912361i	0.996458	+	0.0840970i	$0.0268006\pi$
$422$	−6.70488	+	1.79657i	−0.326388	+	0.0874555i
$423$	18.0015	−	13.7225i	0.875262	−	0.667211i
$424$	−47.1405	−	47.1405i	−2.28935	−	2.28935i
$425$	−9.60179	−	5.54359i	−0.465755	−	0.268904i
$426$	14.3529	+	0.963604i	0.695401	+	0.0466868i
$427$	2.12308	−	7.92344i	0.102743	−	0.383442i
$428$	15.4798			0.748246
$429$		0			0
$430$	2.17319			0.104801
$431$	−1.87956	+	7.01461i	−0.0905352	+	0.337882i	−0.996305	−	0.0858886i	$-0.972627\pi$
$431$	−1.87956	+	7.01461i	−0.0905352	+	0.337882i	0.905770	+	0.423771i	$0.139294\pi$
$432$	−41.4900	+	13.8641i	−1.99619	+	0.667038i
$433$	5.89093	+	3.40113i	0.283100	+	0.163448i	0.634826	−	0.772655i	$-0.281072\pi$
$433$	5.89093	+	3.40113i	0.283100	+	0.163448i	−0.351726	+	0.936103i	$0.614405\pi$
$434$	5.52692	+	5.52692i	0.265301	+	0.265301i
$435$	4.13665	−	12.1230i	0.198337	−	0.581252i
$436$	−12.4456	+	3.33479i	−0.596037	+	0.159708i
$437$	−23.4228	+	23.4228i	−1.12046	+	1.12046i
$438$	−0.687215	−	1.39912i	−0.0328364	−	0.0668527i
$439$	14.0407	−	8.10639i	0.670125	−	0.386897i	−0.125999	−	0.992030i	$-0.540214\pi$
$439$	14.0407	−	8.10639i	0.670125	−	0.386897i	0.796124	+	0.605134i	$0.206880\pi$
$440$	2.10150	+	0.563096i	0.100185	+	0.0268445i
$441$	11.5808	−	4.75395i	0.551467	−	0.226378i
$442$		0			0
$443$			6.09878i			0.289762i	0.989449	+	0.144881i	$0.0462799\pi$
$443$			6.09878i			0.289762i	−0.989449	+	0.144881i	$0.953720\pi$
$444$	18.3780	+	21.0232i	0.872180	+	0.997718i
$445$	−3.02631	−	5.24172i	−0.143461	−	0.248481i
$446$	10.0032	−	17.3260i	0.473663	−	0.820409i
$447$	−3.55343	−	18.0136i	−0.168072	−	0.852013i
$448$	1.63968	+	6.11937i	0.0774676	+	0.289113i
$449$	−6.93935	−	25.8980i	−0.327488	−	1.22220i	−0.911787	−	0.410663i	$-0.865297\pi$
$449$	−6.93935	−	25.8980i	−0.327488	−	1.22220i	0.584299	−	0.811538i	$-0.301370\pi$
$450$	−30.1484	−	12.6001i	−1.42121	−	0.593972i
$451$	1.24026	−	2.14820i	0.0584016	−	0.101155i
$452$	−13.3792	−	23.1734i	−0.629304	−	1.08999i
$453$	−12.2246	+	10.6865i	−0.574363	+	0.502094i
$454$		−	48.3995i		−	2.27150i
$455$		0			0
$456$	−40.5417	+	60.4670i	−1.89854	+	2.83163i
$457$	18.5062	+	4.95873i	0.865686	+	0.231960i	0.664221	−	0.747536i	$-0.268763\pi$
$457$	18.5062	+	4.95873i	0.865686	+	0.231960i	0.201464	+	0.979496i	$0.435430\pi$
$458$	25.6547	−	14.8118i	1.19877	−	0.692109i
$459$	10.2223	+	9.05110i	0.477135	+	0.422469i
$460$	−15.7823	+	15.7823i	−0.735856	+	0.735856i
$461$	−4.31989	+	1.15751i	−0.201197	+	0.0539106i	−0.358010	−	0.933718i	$-0.616545\pi$
$461$	−4.31989	+	1.15751i	−0.201197	+	0.0539106i	0.156813	+	0.987628i	$0.449878\pi$
$462$	−2.54869	−	0.869676i	−0.118576	−	0.0404610i
$463$	25.0898	+	25.0898i	1.16602	+	1.16602i	0.983134	+	0.182885i	$0.0585437\pi$
$463$	25.0898	+	25.0898i	1.16602	+	1.16602i	0.182885	+	0.983134i	$0.441456\pi$
$464$	61.0316	+	35.2366i	2.83332	+	1.63582i
$465$	−0.184593	+	2.74952i	−0.00856031	+	0.127506i
$466$	7.53603	−	28.1249i	0.349100	−	1.30286i
$467$	10.0568			0.465374			0.232687	−	0.972552i	$-0.425248\pi$
$467$	10.0568			0.465374			0.232687	+	0.972552i	$0.425248\pi$
$468$		0			0
$469$	21.1705			0.977562
$470$	4.45340	−	16.6203i	0.205420	−	0.766637i
$471$	2.55203	−	38.0126i	0.117591	−	1.75153i
$472$	61.3676	+	35.4306i	2.82467	+	1.63083i
$473$	−0.241387	−	0.241387i	−0.0110990	−	0.0110990i
$474$	−15.5792	−	5.31599i	−0.715576	−	0.244172i
$475$	−24.9195	+	6.67716i	−1.14339	+	0.306369i
$476$	14.5680	−	14.5680i	0.667723	−	0.667723i
$477$	−3.88892	+	28.8322i	−0.178061	+	1.32014i
$478$	4.17920	−	2.41286i	0.191152	−	0.110362i
$479$	5.71284	+	1.53075i	0.261026	+	0.0699418i	0.386959	−	0.922097i	$-0.373526\pi$
$479$	5.71284	+	1.53075i	0.261026	+	0.0699418i	−0.125932	+	0.992039i	$0.540192\pi$
$480$	−6.80230	+	10.1455i	−0.310481	+	0.463076i
$481$		0			0
$482$			60.0439i			2.73493i
$483$	11.8790	−	10.3843i	0.540514	−	0.472503i
$484$	25.3482	+	43.9043i	1.15219	+	1.99565i
$485$	2.33700	−	4.04780i	0.106118	−	0.183801i
$486$	33.2789	+	22.6200i	1.50956	+	1.02606i
$487$	−2.43194	−	9.07613i	−0.110202	−	0.411279i	0.888681	−	0.458525i	$-0.151622\pi$
$487$	−2.43194	−	9.07613i	−0.110202	−	0.411279i	−0.998883	+	0.0472463i	$0.984955\pi$
$488$	8.68021	+	32.3950i	0.392934	+	1.46645i
$489$	6.89401	+	34.9481i	0.311758	+	1.58041i
$490$	4.75809	−	8.24126i	0.214949	−	0.372302i
$491$	−12.1772	−	21.0915i	−0.549548	−	0.951845i	−0.998305	−	0.0581914i	$-0.981467\pi$
$491$	−12.1772	−	21.0915i	−0.549548	−	0.951845i	0.448758	−	0.893654i	$-0.351867\pi$
$492$	36.8087	+	42.1068i	1.65947	+	1.89832i
$493$		−	21.9957i		−	0.990637i
$494$		0			0
$495$	−0.360552	−	0.878321i	−0.0162056	−	0.0394776i
$496$	−14.6445	−	3.92399i	−0.657559	−	0.176192i
$497$	−4.68511	+	2.70495i	−0.210156	+	0.121334i
$498$	23.6105	+	48.0695i	1.05801	+	2.15405i
$499$	6.97195	−	6.97195i	0.312107	−	0.312107i	−0.533618	−	0.845725i	$-0.679168\pi$
$499$	6.97195	−	6.97195i	0.312107	−	0.312107i	0.845725	+	0.533618i	$0.179168\pi$
$500$	−36.6876	+	9.83042i	−1.64072	+	0.439630i
$501$	−5.60743	+	16.4333i	−0.250522	+	0.734185i
$502$	19.7012	+	19.7012i	0.879307	+	0.879307i
$503$	−11.3931	−	6.57779i	−0.507992	−	0.293289i	0.224016	−	0.974586i	$-0.428083\pi$
$503$	−11.3931	−	6.57779i	−0.507992	−	0.293289i	−0.732008	+	0.681296i	$0.761417\pi$
$504$	21.1967	−	27.4434i	0.944177	−	1.22243i
$505$	−1.93949	+	7.23827i	−0.0863061	+	0.322099i
$506$	5.00977			0.222712
$507$		0			0
$508$	−63.5300			−2.81869
$509$	5.15115	−	19.2244i	0.228321	−	0.852105i	−0.752726	−	0.658334i	$-0.771261\pi$
$509$	5.15115	−	19.2244i	0.228321	−	0.852105i	0.981047	−	0.193771i	$-0.0620718\pi$
$510$	10.3556	+	0.695236i	0.458552	+	0.0307856i
$511$	0.507679	+	0.293109i	0.0224584	+	0.0129664i
$512$	34.3270	+	34.3270i	1.51705	+	1.51705i
$513$	31.7115	−	1.92699i	1.40010	−	0.0850787i
$514$	−10.6117	+	2.84341i	−0.468064	+	0.125417i
$515$	0.346619	−	0.346619i	0.0152739	−	0.0152739i
$516$	6.90844	−	3.39326i	0.304127	−	0.149380i
$517$	−2.34076	+	1.35144i	−0.102947	+	0.0594362i
$518$	−14.4940	−	3.88365i	−0.636828	−	0.170638i
$519$	16.9245	+	11.3474i	0.742902	+	0.498098i
$520$		0			0
$521$			12.9958i			0.569355i	0.958623	+	0.284678i	$0.0918865\pi$
$521$			12.9958i			0.569355i	−0.958623	+	0.284678i	$0.908113\pi$
$522$	−8.25736	−	64.2963i	−0.361415	−	2.81417i
$523$	−3.05976	−	5.29966i	−0.133794	−	0.231738i	0.791342	−	0.611374i	$-0.209383\pi$
$523$	−3.05976	−	5.29966i	−0.133794	−	0.231738i	−0.925136	+	0.379636i	$0.876049\pi$
$524$	−14.8268	+	25.6808i	−0.647712	+	1.12187i
$525$	12.0560	−	2.37822i	0.526169	−	0.103794i
$526$	−16.9339	−	63.1981i	−0.738352	−	2.75557i
$527$	1.22473	+	4.57077i	0.0533503	+	0.199106i
$528$	5.12482	−	1.01094i	0.223029	−	0.0439956i
$529$	−3.17594	+	5.50088i	−0.138084	+	0.239169i
$530$	11.0578	+	19.1528i	0.480322	+	0.831943i
$531$	−3.93909	−	30.6719i	−0.170942	−	1.33105i
$532$		−	47.9390i		−	2.07842i
$533$		0			0
$534$	−25.4414	−	17.0578i	−1.10096	−	0.738164i
$535$	−2.83282	−	0.759051i	−0.122473	−	0.0328166i
$536$	−74.9593	+	43.2778i	−3.23775	+	1.86931i
$537$	18.3632	−	9.01957i	0.792432	−	0.389223i
$538$	−41.3698	+	41.3698i	−1.78358	+	1.78358i
$539$	−1.44390	+	0.386893i	−0.0621933	+	0.0166646i
$540$	21.3673	−	1.29841i	0.919503	−	0.0558748i
$541$	−9.48746	−	9.48746i	−0.407898	−	0.407898i	0.473107	−	0.881005i	$-0.343132\pi$
$541$	−9.48746	−	9.48746i	−0.407898	−	0.407898i	−0.881005	+	0.473107i	$0.843132\pi$
$542$	47.6492	+	27.5103i	2.04671	+	1.18167i
$543$	−34.7359	−	2.33205i	−1.49066	−	0.100078i
$544$	−5.42870	+	20.2602i	−0.232754	+	0.868649i
$545$	2.44107			0.104564
$546$		0			0
$547$	8.20259			0.350717			0.175359	−	0.984505i	$-0.443892\pi$
$547$	8.20259			0.350717			0.175359	+	0.984505i	$0.443892\pi$
$548$	2.46560	−	9.20176i	0.105325	−	0.393080i
$549$	8.94652	−	11.5831i	0.381828	−	0.494354i
$550$	3.37902	+	1.95088i	0.144082	+	0.0831858i
$551$	−36.1907	−	36.1907i	−1.54178	−	1.54178i
$552$	−20.8324	+	61.0519i	−0.886685	+	2.59854i
$553$	5.97968	−	1.60225i	0.254282	−	0.0681346i
$554$	−19.4971	+	19.4971i	−0.828354	+	0.828354i
$555$	−2.33230	−	4.74842i	−0.0990008	−	0.201559i
$556$	−20.6505	+	11.9226i	−0.875775	+	0.505629i
$557$	21.3067	+	5.70912i	0.902795	+	0.241903i	0.680216	−	0.733012i	$-0.261886\pi$
$557$	21.3067	+	5.70912i	0.902795	+	0.241903i	0.222579	+	0.974915i	$0.428553\pi$
$558$	5.29596	+	12.9012i	0.224196	+	0.546150i
$559$		0			0
$560$		−	12.5057i		−	0.528463i
$561$	−1.07302	−	1.22747i	−0.0453030	−	0.0518238i
$562$	17.9628	+	31.1125i	0.757715	+	1.31240i
$563$	−19.7230	+	34.1613i	−0.831227	+	1.43973i	0.0658393	+	0.997830i	$0.479028\pi$
$563$	−19.7230	+	34.1613i	−0.831227	+	1.43973i	−0.897066	+	0.441897i	$0.854306\pi$
$564$	−11.7941	−	59.7885i	−0.496622	−	2.51755i
$565$	1.31209	+	4.89679i	0.0552001	+	0.206010i
$566$	10.8875	+	40.6328i	0.457637	+	1.70792i
$567$	−15.1324	−	0.0960047i	−0.635500	−	0.00403182i
$568$	11.0592	−	19.1551i	0.464033	−	0.803729i
$569$	7.67489	+	13.2933i	0.321748	+	0.557284i	0.980849	−	0.194771i	$-0.0623962\pi$
$569$	7.67489	+	13.2933i	0.321748	+	0.557284i	−0.659101	+	0.752055i	$0.729063\pi$
$570$	18.1825	−	15.8947i	0.761580	−	0.665754i
$571$		−	4.70947i		−	0.197085i	−0.995133	−	0.0985425i	$-0.968582\pi$
$571$		−	4.70947i		−	0.197085i	0.995133	−	0.0985425i	$-0.0314181\pi$
$572$		0			0
$573$	16.3407	−	24.3718i	0.682643	−	1.01815i
$574$	−29.0296	−	7.77845i	−1.21167	−	0.324666i
$575$	−19.7974	+	11.4301i	−0.825610	+	0.476666i
$576$	−1.51094	+	11.2020i	−0.0629557	+	0.466750i
$577$	−25.1056	+	25.1056i	−1.04516	+	1.04516i	−0.0462290	+	0.998931i	$0.514720\pi$
$577$	−25.1056	+	25.1056i	−1.04516	+	1.04516i	−0.998931	+	0.0462290i	$0.985280\pi$
$578$	−25.1720	+	6.74483i	−1.04702	+	0.280548i
$579$	27.4263	+	9.35850i	1.13980	+	0.388926i
$580$	−24.3854	−	24.3854i	−1.01255	−	1.01255i
$581$	−17.4423	−	10.0703i	−0.723627	−	0.417786i
$582$	1.58447	−	23.6007i	0.0656783	−	0.978280i
$583$	0.899142	−	3.35564i	0.0372387	−	0.138977i
$584$	−2.39675			−0.0991783
$585$		0			0
$586$	42.4625			1.75411
$587$	−4.49920	+	16.7912i	−0.185702	+	0.693049i	0.808777	+	0.588115i	$0.200130\pi$
$587$	−4.49920	+	16.7912i	−0.185702	+	0.693049i	−0.994479	+	0.104934i	$0.966537\pi$
$588$	2.25765	−	33.6278i	0.0931041	−	1.38679i
$589$	9.53566	+	5.50541i	0.392910	+	0.226847i
$590$	−16.6221	−	16.6221i	−0.684320	−	0.684320i
$591$	23.9757	+	8.18110i	0.986230	+	0.336525i
$592$	28.1139	−	7.53309i	1.15547	−	0.309608i
$593$	−3.78428	+	3.78428i	−0.155402	+	0.155402i	−0.780526	−	0.625124i	$-0.785048\pi$
$593$	−3.78428	+	3.78428i	−0.155402	+	0.155402i	0.625124	+	0.780526i	$0.285048\pi$
$594$	−3.59738	−	3.18523i	−0.147602	−	0.130691i
$595$	−3.38029	+	1.95161i	−0.138578	+	0.0800082i
$596$	−47.7478	−	12.7940i	−1.95582	−	0.524062i
$597$	0.322448	−	0.480924i	0.0131969	−	0.0196829i
$598$		0			0
$599$		−	6.35465i		−	0.259644i	−0.991537	−	0.129822i	$-0.958559\pi$
$599$		−	6.35465i		−	0.259644i	0.991537	−	0.129822i	$-0.0414406\pi$
$600$	−37.8257	+	33.0662i	−1.54423	+	1.34992i
$601$	−12.4761	−	21.6093i	−0.508912	−	0.881461i	−0.999947	−	0.0103212i	$-0.996715\pi$
$601$	−12.4761	−	21.6093i	−0.508912	−	0.881461i	0.491035	−	0.871140i	$-0.336619\pi$
$602$	−2.06801	+	3.58190i	−0.0842858	+	0.145987i
$603$	34.8514	+	14.5656i	1.41926	+	0.593158i
$604$	11.3142	+	42.2251i	0.460367	+	1.71811i
$605$	−2.48588	−	9.27745i	−0.101066	−	0.377182i
$606$	7.33942	+	37.2061i	0.298143	+	1.51139i
$607$	−2.11757	+	3.66773i	−0.0859494	+	0.148869i	−0.905795	−	0.423715i	$-0.860726\pi$
$607$	−2.11757	+	3.66773i	−0.0859494	+	0.148869i	0.819846	+	0.572584i	$0.194059\pi$
$608$	24.4031	+	42.2673i	0.989674	+	1.71417i
$609$	16.0449	+	18.3544i	0.650172	+	0.743756i
$610$		−	11.1256i		−	0.450464i
$611$		0			0
$612$	34.0053	−	13.9592i	1.37458	−	0.564268i
$613$	−35.4117	−	9.48855i	−1.43027	−	0.383239i	−0.541153	−	0.840924i	$-0.682012\pi$
$613$	−35.4117	−	9.48855i	−1.43027	−	0.383239i	−0.889114	+	0.457686i	$0.848679\pi$
$614$	18.0424	−	10.4168i	0.728134	−	0.420388i
$615$	−4.67131	−	9.51047i	−0.188365	−	0.383499i
$616$	−2.92790	+	2.92790i	−0.117968	+	0.117968i
$617$	29.4981	−	7.90398i	1.18755	−	0.318202i	0.389631	−	0.920971i	$-0.372602\pi$
$617$	29.4981	−	7.90398i	1.18755	−	0.318202i	0.797916	+	0.602769i	$0.205936\pi$
$618$	0.801130	−	2.34781i	0.0322262	−	0.0944429i
$619$	11.8576	+	11.8576i	0.476599	+	0.476599i	0.904042	−	0.427443i	$-0.140586\pi$
$619$	11.8576	+	11.8576i	0.476599	+	0.476599i	−0.427443	+	0.904042i	$0.640586\pi$
$620$	6.42516	+	3.70957i	0.258041	+	0.148980i
$621$	26.7002	−	8.92202i	1.07144	−	0.358028i
$622$	−16.9306	+	63.1857i	−0.678853	+	2.53352i
$623$	11.5194			0.461513
$624$		0			0
$625$	−13.9016			−0.556063
$626$	2.33490	−	8.71395i	0.0933212	−	0.348279i
$627$	−3.78512	−	0.254120i	−0.151163	−	0.0101486i
$628$	−88.8289	−	51.2854i	−3.54466	−	2.04651i
$629$	−6.42356	−	6.42356i	−0.256124	−	0.256124i
$630$	−9.14836	+	6.97379i	−0.364480	+	0.277843i
$631$	−26.8433	+	7.19263i	−1.06861	+	0.286334i	−0.749923	−	0.661525i	$-0.769910\pi$
$631$	−26.8433	+	7.19263i	−1.06861	+	0.286334i	−0.318690	+	0.947859i	$0.603243\pi$
$632$	−17.8971	+	17.8971i	−0.711909	+	0.711909i
$633$	4.18059	−	2.05340i	0.166163	−	0.0816154i
$634$	16.6196	−	9.59535i	0.660050	−	0.381080i
$635$	11.6260	+	3.11518i	0.461364	+	0.123622i
$636$	65.0577	+	43.6195i	2.57970	+	1.72963i
$637$		0			0
$638$			7.74064i			0.306455i
$639$	−9.57381	+	1.22953i	−0.378734	+	0.0486396i
$640$	−2.75601	−	4.77354i	−0.108941	−	0.188691i
$641$	−4.28764	+	7.42640i	−0.169351	+	0.293325i	−0.938192	−	0.346115i	$-0.887501\pi$
$641$	−4.28764	+	7.42640i	−0.169351	+	0.293325i	0.768841	+	0.639440i	$0.220834\pi$
$642$	−14.5612	+	2.87240i	−0.574685	+	0.113365i
$643$	−0.583059	−	2.17600i	−0.0229936	−	0.0858132i	0.953476	−	0.301470i	$-0.0974774\pi$
$643$	−0.583059	−	2.17600i	−0.0229936	−	0.0858132i	−0.976469	+	0.215657i	$0.930811\pi$
$644$	−10.9943	−	41.0313i	−0.433236	−	1.61686i
$645$	−1.43063	+	0.282213i	−0.0563312	+	0.0111121i
$646$	20.7351	−	35.9143i	0.815813	−	1.41303i
$647$	12.2169	+	21.1603i	0.480296	+	0.831897i	0.999744	−	0.0226045i	$-0.00719585\pi$
$647$	12.2169	+	21.1603i	0.480296	+	0.831897i	−0.519448	+	0.854502i	$0.673863\pi$
$648$	53.7761	−	30.5944i	2.11253	−	1.20186i
$649$			3.69259i			0.144947i
$650$		0			0
$651$	−4.35616	−	2.92070i	−0.170731	−	0.114471i
$652$	92.6355	+	24.8216i	3.62788	+	0.972089i
$653$	11.0765	−	6.39504i	0.433458	−	0.250257i	−0.267361	−	0.963597i	$-0.586151\pi$
$653$	11.0765	−	6.39504i	0.433458	−	0.250257i	0.700819	+	0.713339i	$0.252818\pi$
$654$	11.0882	−	5.44627i	0.433585	−	0.212966i
$655$	3.97256	−	3.97256i	0.155221	−	0.155221i
$656$	56.3085	−	15.0878i	2.19848	−	0.589081i
$657$	0.634093	+	0.831816i	0.0247383	+	0.0324522i
$658$	23.1561	+	23.1561i	0.902718	+	0.902718i
$659$	−26.1230	−	15.0821i	−1.01761	−	0.587515i	−0.104197	−	0.994557i	$-0.533227\pi$
$659$	−26.1230	−	15.0821i	−1.01761	−	0.587515i	−0.913410	+	0.407041i	$0.866561\pi$
$660$	−2.55043	−	0.171227i	−0.0992752	−	0.00666499i
$661$	6.48058	−	24.1859i	0.252065	−	0.940721i	−0.717634	−	0.696420i	$-0.754775\pi$
$661$	6.48058	−	24.1859i	0.252065	−	0.940721i	0.969700	−	0.244301i	$-0.0785584\pi$
$662$	−46.4167			−1.80404
$663$		0			0
$664$	82.3448			3.19560
$665$	−2.35068	+	8.77286i	−0.0911554	+	0.340197i
$666$	−21.1884	−	16.3654i	−0.821032	−	0.634148i
$667$	−39.2758	−	22.6759i	−1.52077	−	0.878014i
$668$	33.0556	+	33.0556i	1.27896	+	1.27896i
$669$	−4.33522	+	12.7049i	−0.167609	+	0.491200i
$670$	27.7351	−	7.43160i	1.07150	−	0.287108i
$671$	−1.23578	+	1.23578i	−0.0477068	+	0.0477068i
$672$	−10.2489	−	20.8662i	−0.395361	−	0.804930i
$673$	−36.1567	+	20.8751i	−1.39374	+	0.804674i	−0.993727	−	0.111836i	$-0.964327\pi$
$673$	−36.1567	+	20.8751i	−1.39374	+	0.804674i	−0.400010	+	0.916511i	$0.630993\pi$
$674$	−40.8541	−	10.9468i	−1.57364	−	0.421656i
$675$	21.4832	+	4.37965i	0.826891	+	0.168573i
$676$		0			0
$677$			23.6516i			0.909004i	0.890746	+	0.454502i	$0.150183\pi$
$677$			23.6516i			0.909004i	−0.890746	+	0.454502i	$0.849817\pi$
$678$	16.8852	+	19.3156i	0.648473	+	0.741812i
$679$	4.44779	+	7.70379i	0.170690	+	0.295644i
$680$	7.97916	−	13.8203i	0.305987	−	0.529984i
$681$	6.28521	+	31.8619i	0.240850	+	1.22095i
$682$	−0.431004	−	1.60853i	−0.0165040	−	0.0615937i
$683$	−2.11591	−	7.89669i	−0.0809631	−	0.302158i	0.913556	−	0.406713i	$-0.133325\pi$
$683$	−2.11591	−	7.89669i	−0.0809631	−	0.302158i	−0.994519	+	0.104554i	$0.966658\pi$
$684$	32.9828	−	78.9186i	1.26113	−	3.01753i
$685$	−0.902413	+	1.56302i	−0.0344794	+	0.0597201i
$686$	24.2464	+	41.9961i	0.925733	+	1.60342i
$687$	−14.9653	+	13.0823i	−0.570963	+	0.499121i
$688$		−	8.02262i		−	0.305860i
$689$		0			0
$690$	11.9172	−	17.7743i	0.453681	−	0.676656i
$691$	−14.4779	−	3.87934i	−0.550764	−	0.147577i	−0.0273044	−	0.999627i	$-0.508692\pi$
$691$	−14.4779	−	3.87934i	−0.550764	−	0.147577i	−0.523460	+	0.852050i	$0.675359\pi$
$692$	47.5095	−	27.4296i	1.80604	−	1.04272i
$693$	1.79077	+	0.241541i	0.0680257	+	0.00917537i
$694$	43.9377	−	43.9377i	1.66785	−	1.66785i
$695$	4.36366	−	1.16924i	0.165523	−	0.0443518i
$696$	−94.3318	−	32.1883i	−3.57564	−	1.22009i
$697$	−12.8656	−	12.8656i	−0.487319	−	0.487319i
$698$	−38.6911	−	22.3383i	−1.46448	−	0.845518i
$699$	−1.30873	+	19.4935i	−0.0495006	+	0.737313i
$700$	8.56269	−	31.9564i	0.323639	−	1.20784i
$701$	−38.5186			−1.45483			−0.727414	−	0.686199i	$-0.759278\pi$
$701$	−38.5186			−1.45483			−0.727414	+	0.686199i	$0.759278\pi$
$702$		0			0
$703$	−21.1381			−0.797237
$704$	0.349338	−	1.30375i	0.0131662	−	0.0491368i
$705$	−0.773389	+	11.5196i	−0.0291275	+	0.433855i
$706$	47.3771	+	27.3532i	1.78306	+	1.02945i
$707$	−10.0847	−	10.0847i	−0.379272	−	0.379272i
$708$	−78.7945	−	26.8866i	−2.96128	−	1.01046i
$709$	35.5833	−	9.53453i	1.33636	−	0.358077i	0.481278	−	0.876568i	$-0.340173\pi$
$709$	35.5833	−	9.53453i	1.33636	−	0.358077i	0.855083	+	0.518492i	$0.173506\pi$
$710$	−5.18835	+	5.18835i	−0.194715	+	0.194715i
$711$	10.9463	+	1.47645i	0.410518	+	0.0553710i
$712$	−40.7871	+	23.5484i	−1.52856	+	0.882515i
$713$	9.42424	+	2.52522i	0.352940	+	0.0945701i
$714$	−11.0003	+	16.4067i	−0.411675	+	0.614004i
$715$		0			0
$716$		−	55.0807i		−	2.05846i
$717$	−2.43788	+	2.13113i	−0.0910442	+	0.0795885i
$718$	34.2223	+	59.2748i	1.27717	+	2.21212i
$719$	−2.38818	+	4.13644i	−0.0890640	+	0.154263i	−0.907116	−	0.420881i	$-0.861721\pi$
$719$	−2.38818	+	4.13644i	−0.0890640	+	0.154263i	0.818052	+	0.575145i	$0.195054\pi$
$720$	8.60414	−	20.5873i	0.320657	−	0.767243i
$721$	0.241462	+	0.901148i	0.00899251	+	0.0335605i
$722$	−12.2813	−	45.8346i	−0.457064	−	1.70579i
$723$	−7.79737	−	39.5276i	−0.289987	−	1.47005i
$724$	−46.8646	+	81.1718i	−1.74171	+	3.01673i
$725$	−17.6607	−	30.5892i	−0.655900	−	1.13605i
$726$	−31.9907	−	36.5953i	−1.18729	−	1.35818i
$727$			26.2267i			0.972694i	0.873766	+	0.486347i	$0.161671\pi$
$727$			26.2267i			0.972694i	−0.873766	+	0.486347i	$0.838329\pi$
$728$		0			0
$729$	−24.8453	−	10.5694i	−0.920196	−	0.391458i
$730$	0.767994	+	0.205783i	0.0284247	+	0.00761638i
$731$	−2.16851	+	1.25199i	−0.0802052	+	0.0463065i
$732$	−17.3718	−	35.3677i	−0.642078	−	1.30723i
$733$	9.54380	−	9.54380i	0.352508	−	0.352508i	−0.508534	−	0.861042i	$-0.669812\pi$
$733$	9.54380	−	9.54380i	0.352508	−	0.352508i	0.861042	+	0.508534i	$0.169812\pi$
$734$	50.6916	−	13.5828i	1.87106	−	0.501349i
$735$	−2.06208	+	6.04320i	−0.0760611	+	0.222907i
$736$	30.5803	+	30.5803i	1.12720	+	1.12720i
$737$	−3.90614	−	2.25521i	−0.143885	−	0.0830718i
$738$	−42.4376	−	32.7779i	−1.56215	−	1.20657i
$739$	−3.11949	+	11.6421i	−0.114752	+	0.428261i	−0.999268	−	0.0382487i	$-0.987822\pi$
$739$	−3.11949	+	11.6421i	−0.114752	+	0.428261i	0.884516	+	0.466510i	$0.154489\pi$
$740$	−14.2429			−0.523580
$741$		0			0
$742$	−42.0906			−1.54520
$743$	5.75322	−	21.4713i	0.211065	−	0.787706i	−0.776450	−	0.630179i	$-0.782981\pi$
$743$	5.75322	−	21.4713i	0.211065	−	0.787706i	0.987515	−	0.157526i	$-0.0503519\pi$
$744$	21.3947	+	1.43636i	0.784367	+	0.0526597i
$745$	8.11051	+	4.68260i	0.297146	+	0.171557i
$746$	−58.4286	−	58.4286i	−2.13922	−	2.13922i
$747$	−21.7854	−	28.5786i	−0.797087	−	1.04564i
$748$	−4.23980	+	1.13605i	−0.155022	+	0.0415381i
$749$	3.94679	−	3.94679i	0.144213	−	0.144213i
$750$	32.6863	−	16.0547i	1.19354	−	0.586235i
$751$	32.4803	−	18.7525i	1.18522	−	0.684288i	0.228005	−	0.973660i	$-0.426780\pi$
$751$	32.4803	−	18.7525i	1.18522	−	0.684288i	0.957217	+	0.289372i	$0.0934465\pi$
$752$	−61.3561	−	16.4403i	−2.23743	−	0.599516i
$753$	−15.5279	−	10.4111i	−0.565869	−	0.379401i
$754$		0			0
$755$		−	8.28200i		−	0.301413i
$756$	−18.1931	+	36.4537i	−0.661677	+	1.32581i
$757$	10.6958	+	18.5257i	0.388747	+	0.673329i	0.992281	−	0.124008i	$-0.0395747\pi$
$757$	10.6958	+	18.5257i	0.388747	+	0.673329i	−0.603534	+	0.797337i	$0.706241\pi$
$758$	22.4946	−	38.9618i	0.817041	−	1.41516i
$759$	−3.29799	+	0.650574i	−0.119709	+	0.0236144i
$760$	−9.61075	−	35.8678i	−0.348619	−	1.30106i
$761$	13.2143	+	49.3165i	0.479018	+	1.78772i	0.605606	+	0.795765i	$0.292931\pi$
$761$	13.2143	+	49.3165i	0.479018	+	1.78772i	−0.126587	+	0.991955i	$0.540402\pi$
$762$	59.7599	−	11.7885i	2.16487	−	0.427051i
$763$	−2.32293	+	4.02343i	−0.0840956	+	0.145658i
$764$	−39.4996	−	68.4153i	−1.42905	−	2.47518i
$765$	−6.90746	+	0.887103i	−0.249740	+	0.0320733i
$766$			56.0187i			2.02404i
$767$		0			0
$768$	−34.0099	−	22.8028i	−1.22723	−	0.822826i
$769$	43.8009	+	11.7364i	1.57950	+	0.423226i	0.938771	−	0.344541i	$-0.111965\pi$
$769$	43.8009	+	11.7364i	1.57950	+	0.423226i	0.640729	+	0.767767i	$0.278632\pi$
$770$	1.18958	−	0.686803i	0.0428694	−	0.0247507i
$771$	6.61658	−	3.24990i	0.238290	−	0.117042i
$772$	55.1681	−	55.1681i	1.98554	−	1.98554i
$773$	−39.4237	+	10.5635i	−1.41797	+	0.379944i	−0.884763	−	0.466040i	$-0.845680\pi$
$773$	−39.4237	+	10.5635i	−1.41797	+	0.379944i	−0.533207	+	0.845985i	\(0.679013\pi\

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.668092 + 2.49335i) q^{2} +(0.116023 - 1.72816i) q^{3} +(-4.03841 - 2.33158i) q^{4} +(0.624703 + 0.624703i) q^{5} +(4.23140 + 1.44386i) q^{6} +(-1.62412 + 0.435181i) q^{7} +(4.86096 - 4.86096i) q^{8} +(-2.97308 - 0.401012i) q^{9} +(-1.97496 + 1.14025i) q^{10} +(0.346022 + 0.0927163i) q^{11} +(-4.49789 + 6.70851i) q^{12} -4.34024i q^{14} +(1.15207 - 1.00711i) q^{15} +(4.20937 + 7.29084i) q^{16} +(1.31381 - 2.27558i) q^{17} +(2.98615 - 7.14502i) q^{18} +(-1.58246 - 5.90581i) q^{19} +(-1.06626 - 3.97935i) q^{20} +(0.563628 + 2.85722i) q^{21} +(-0.462349 + 0.800812i) q^{22} +(-2.70887 - 4.69190i) q^{23} +(-7.83654 - 8.96451i) q^{24} -4.21949i q^{25} +(-1.03796 + 5.09143i) q^{27} +(7.57351 + 2.02932i) q^{28} +(7.24949 - 4.18549i) q^{29} +(1.74139 + 3.54535i) q^{30} +(-1.27341 + 1.27341i) q^{31} +(-7.71050 + 2.06602i) q^{32} +(0.200375 - 0.587225i) q^{33} +(4.79608 + 4.79608i) q^{34} +(-1.28645 - 0.742731i) q^{35} +(11.0715 + 8.55142i) q^{36} +(0.894800 - 3.33944i) q^{37} +15.7825 q^{38} +6.07331 q^{40} +(1.79217 - 6.68847i) q^{41} +(-7.50063 - 0.503566i) q^{42} +(-0.825277 - 0.476474i) q^{43} +(-1.18121 - 1.18121i) q^{44} +(-1.60678 - 2.10780i) q^{45} +(13.5083 - 3.61955i) q^{46} +(-5.33521 + 5.33521i) q^{47} +(13.0881 - 6.42856i) q^{48} +(-3.61381 + 2.08643i) q^{49} +(10.5207 + 2.81901i) q^{50} +(-3.78013 - 2.53449i) q^{51} -9.69778i q^{53} +(-12.0013 - 5.98954i) q^{54} +(0.158241 + 0.274081i) q^{55} +(-5.77937 + 10.0102i) q^{56} +(-10.3898 + 2.04953i) q^{57} +(5.59259 + 20.8718i) q^{58} +(2.66789 + 9.95670i) q^{59} +(-7.00067 + 1.38098i) q^{60} +(-2.43931 + 4.22500i) q^{61} +(-2.32431 - 4.02583i) q^{62} +(5.00314 - 0.642536i) q^{63} -3.76781i q^{64} +(1.33029 + 0.891926i) q^{66} +(-12.1619 - 3.25877i) q^{67} +(-10.6114 + 6.12649i) q^{68} +(-8.42264 + 4.13699i) q^{69} +(2.71136 - 2.71136i) q^{70} +(3.10785 - 0.832745i) q^{71} +(-16.4013 + 12.5027i) q^{72} +(-0.246530 - 0.246530i) q^{73} +(7.72860 + 4.46211i) q^{74} +(-7.29196 - 0.489557i) q^{75} +(-7.37925 + 27.5397i) q^{76} -0.602329 q^{77} -3.68180 q^{79} +(-1.92500 + 7.18422i) q^{80} +(8.67838 + 2.38448i) q^{81} +(15.4794 + 8.93703i) q^{82} +(8.47001 + 8.47001i) q^{83} +(4.38568 - 12.8528i) q^{84} +(2.24230 - 0.600822i) q^{85} +(1.73938 - 1.73938i) q^{86} +(-6.39210 - 13.0139i) q^{87} +(2.13269 - 1.23131i) q^{88} +(-6.61757 - 1.77317i) q^{89} +(6.32897 - 2.59806i) q^{90} +25.2638i q^{92} +(2.05292 + 2.34841i) q^{93} +(-9.73816 - 16.8670i) q^{94} +(2.70081 - 4.67794i) q^{95} +(2.67583 + 13.5647i) q^{96} +(-1.36929 - 5.11027i) q^{97} +(-2.78786 - 10.4044i) q^{98} +(-0.991570 - 0.414412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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