LMFDB - Embedded newform 507.2.k.k.80.1

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			80.1
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.668092 + 2.49335i) q^{2} +(-1.55464 - 0.763602i) q^{3} +(-4.03841 - 2.33158i) q^{4} +(0.624703 + 0.624703i) q^{5} +(2.94257 - 3.36612i) q^{6} +(1.62412 - 0.435181i) q^{7} +(4.86096 - 4.86096i) q^{8} +(1.83382 + 2.37425i) q^{9} +(-1.97496 + 1.14025i) q^{10} +(0.346022 + 0.0927163i) q^{11} +(4.49789 + 6.70851i) q^{12} +4.34024i q^{14} +(-0.494165 - 1.44821i) q^{15} +(4.20937 + 7.29084i) q^{16} +(-1.31381 + 2.27558i) q^{17} +(-7.14502 + 2.98615i) q^{18} +(1.58246 + 5.90581i) q^{19} +(-1.06626 - 3.97935i) q^{20} +(-2.85722 - 0.563628i) q^{21} +(-0.462349 + 0.800812i) q^{22} +(2.70887 + 4.69190i) q^{23} +(-11.2689 + 3.84522i) q^{24} -4.21949i q^{25} +(-1.03796 - 5.09143i) q^{27} +(-7.57351 - 2.02932i) q^{28} +(-7.24949 + 4.18549i) q^{29} +(3.94106 - 0.264589i) q^{30} +(1.27341 - 1.27341i) q^{31} +(-7.71050 + 2.06602i) q^{32} +(-0.467142 - 0.408364i) q^{33} +(-4.79608 - 4.79608i) q^{34} +(1.28645 + 0.742731i) q^{35} +(-1.86998 - 13.8639i) q^{36} +(-0.894800 + 3.33944i) q^{37} -15.7825 q^{38} +6.07331 q^{40} +(1.79217 - 6.68847i) q^{41} +(3.31421 - 6.74752i) q^{42} +(-0.825277 - 0.476474i) q^{43} +(-1.18121 - 1.18121i) q^{44} +(-0.337608 + 2.62880i) q^{45} +(-13.5083 + 3.61955i) q^{46} +(-5.33521 + 5.33521i) q^{47} +(-0.976765 - 14.5489i) q^{48} +(-3.61381 + 2.08643i) q^{49} +(10.5207 + 2.81901i) q^{50} +(3.78013 - 2.53449i) q^{51} +9.69778i q^{53} +(13.3882 + 0.813550i) q^{54} +(0.158241 + 0.274081i) q^{55} +(5.77937 - 10.0102i) q^{56} +(2.04953 - 10.3898i) q^{57} +(-5.59259 - 20.8718i) q^{58} +(2.66789 + 9.95670i) q^{59} +(-1.38098 + 7.00067i) q^{60} +(-2.43931 + 4.22500i) q^{61} +(2.32431 + 4.02583i) q^{62} +(4.01157 + 3.05802i) q^{63} -3.76781i q^{64} +(1.33029 - 0.891926i) q^{66} +(12.1619 + 3.25877i) q^{67} +(10.6114 - 6.12649i) q^{68} +(-0.628580 - 9.36272i) q^{69} +(-2.71136 + 2.71136i) q^{70} +(3.10785 - 0.832745i) q^{71} +(20.4553 + 2.62701i) q^{72} +(0.246530 + 0.246530i) q^{73} +(-7.72860 - 4.46211i) q^{74} +(-3.22201 + 6.55980i) q^{75} +(7.37925 - 27.5397i) q^{76} +0.602329 q^{77} -3.68180 q^{79} +(-1.92500 + 7.18422i) q^{80} +(-2.27417 + 8.70794i) q^{81} +(15.4794 + 8.93703i) q^{82} +(8.47001 + 8.47001i) q^{83} +(10.2245 + 8.93801i) q^{84} +(-2.24230 + 0.600822i) q^{85} +(1.73938 - 1.73938i) q^{86} +(14.4664 - 0.971224i) q^{87} +(2.13269 - 1.23131i) q^{88} +(-6.61757 - 1.77317i) q^{89} +(-6.32897 - 2.59806i) q^{90} -25.2638i q^{92} +(-2.95208 + 1.00732i) q^{93} +(-9.73816 - 16.8670i) q^{94} +(-2.70081 + 4.67794i) q^{95} +(13.5647 + 2.67583i) q^{96} +(1.36929 + 5.11027i) q^{97} +(-2.78786 - 10.4044i) q^{98} +(0.414412 + 0.991570i) 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	$0.717381\pi$
$3$	−1.55464	−	0.763602i	−0.897573	−	0.440866i
$3$	−1.55464	−	0.763602i	−0.897573	−	0.440866i
$4$	−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	$0.686702\pi$
$6$	2.94257	−	3.36612i	1.20130	−	1.37421i
$7$	1.62412	−	0.435181i	0.613858	−	0.164483i	0.0615241	−	0.998106i	$-0.480404\pi$
$7$	1.62412	−	0.435181i	0.613858	−	0.164483i	0.552334	+	0.833623i	$0.313737\pi$
$8$	4.86096	−	4.86096i	1.71861	−	1.71861i
$9$	1.83382	+	2.37425i	0.611275	+	0.791418i
$10$	−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
$15$	−0.494165	−	1.44821i	−0.127593	−	0.373927i
$16$	4.20937	+	7.29084i	1.05234	+	1.82271i
$17$	−1.31381	+	2.27558i	−0.318645	+	0.551909i	−0.980206	−	0.197983i	$-0.936561\pi$
$17$	−1.31381	+	2.27558i	−0.318645	+	0.551909i	0.661561	+	0.749892i	$0.269894\pi$
$18$	−7.14502	+	2.98615i	−1.68410	+	0.703843i
$19$	1.58246	+	5.90581i	0.363040	+	1.35488i	0.870058	+	0.492949i	$0.164081\pi$
$19$	1.58246	+	5.90581i	0.363040	+	1.35488i	−0.507018	+	0.861936i	$0.669252\pi$
$20$	−1.06626	−	3.97935i	−0.238424	−	0.889810i
$21$	−2.85722	−	0.563628i	−0.623498	−	0.122994i
$22$	−0.462349	+	0.800812i	−0.0985732	+	0.170734i
$23$	2.70887	+	4.69190i	0.564838	+	0.978328i	0.997065	+	0.0765633i	$0.0243947\pi$
$23$	2.70887	+	4.69190i	0.564838	+	0.978328i	−0.432227	+	0.901765i	$0.642272\pi$
$24$	−11.2689	+	3.84522i	−2.30025	+	0.784902i
$25$		−	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	−0.987708	−	0.156308i	$-0.950041\pi$
$29$	−7.24949	+	4.18549i	−1.34620	+	0.777227i	−0.358488	+	0.933535i	$0.616707\pi$
$30$	3.94106	−	0.264589i	0.719535	−	0.0483071i
$31$	1.27341	−	1.27341i	0.228712	−	0.228712i	−0.583443	−	0.812154i	$-0.698295\pi$
$31$	1.27341	−	1.27341i	0.228712	−	0.228712i	0.812154	+	0.583443i	$0.198295\pi$
$32$	−7.71050	+	2.06602i	−1.36304	+	0.365225i
$33$	−0.467142	−	0.408364i	−0.0813190	−	0.0710870i
$34$	−4.79608	−	4.79608i	−0.822521	−	0.822521i
$35$	1.28645	+	0.742731i	0.217449	+	0.125545i
$36$	−1.86998	−	13.8639i	−0.311663	−	2.31066i
$37$	−0.894800	+	3.33944i	−0.147104	+	0.549001i	0.852548	+	0.522648i	$0.175056\pi$
$37$	−0.894800	+	3.33944i	−0.147104	+	0.549001i	−0.999653	+	0.0263524i	$0.991611\pi$
$38$	−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	$-0.0985096\pi$
$42$	3.31421	−	6.74752i	0.511394	−	1.04116i
$43$	−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
$45$	−0.337608	+	2.62880i	−0.0503276	+	0.391878i
$46$	−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	$0.435481\pi$
$48$	−0.976765	−	14.5489i	−0.140984	−	2.09996i
$49$	−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	$0.232015\pi$
$53$			9.69778i			1.33209i	−0.745911	+	0.666046i	$0.767985\pi$
$54$	13.3882	+	0.813550i	1.82190	+	0.110710i
$55$	0.158241	+	0.274081i	0.0213372	+	0.0369571i
$56$	5.77937	−	10.0102i	0.772301	−	1.33766i
$57$	2.04953	−	10.3898i	0.271467	−	1.37616i
$58$	−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	$0.682536\pi$
$60$	−1.38098	+	7.00067i	−0.178284	+	0.903783i
$61$	−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
$63$	4.01157	+	3.05802i	0.505411	+	0.385274i
$64$		−	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	0.908320	−	0.418275i	$-0.137365\pi$
$67$	12.1619	+	3.25877i	1.48581	+	0.398122i	0.577491	+	0.816397i	$0.304032\pi$
$68$	10.6114	−	6.12649i	1.28682	−	0.742946i
$69$	−0.628580	−	9.36272i	−0.0756722	−	1.12714i
$70$	−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	$0.355519\pi$
$72$	20.4553	+	2.62701i	2.41068	+	0.309596i
$73$	0.246530	+	0.246530i	0.0288542	+	0.0288542i	0.721387	−	0.692532i	$-0.243505\pi$
$73$	0.246530	+	0.246530i	0.0288542	+	0.0288542i	−0.692532	+	0.721387i	$0.743505\pi$
$74$	−7.72860	−	4.46211i	−0.898431	−	0.518709i
$75$	−3.22201	+	6.55980i	−0.372046	+	0.757461i
$76$	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
$81$	−2.27417	+	8.70794i	−0.252686	+	0.967548i
$82$	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	$0.521656\pi$
$84$	10.2245	+	8.93801i	1.11559	+	0.975217i
$85$	−2.24230	+	0.600822i	−0.243211	+	0.0651683i
$86$	1.73938	−	1.73938i	0.187562	−	0.187562i
$87$	14.4664	−	0.971224i	1.55096	−	0.104126i
$88$	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
$93$	−2.95208	+	1.00732i	−0.306117	+	0.104454i
$94$	−9.73816	−	16.8670i	−1.00441	−	1.73970i
$95$	−2.70081	+	4.67794i	−0.277097	+	0.479946i
$96$	13.5647	+	2.67583i	1.38444	+	0.273100i
$97$	1.36929	+	5.11027i	0.139031	+	0.518870i	0.999949	+	0.0101260i	$0.00322327\pi$
$97$	1.36929	+	5.11027i	0.139031	+	0.518870i	−0.860918	+	0.508744i	$0.830110\pi$
$98$	−2.78786	−	10.4044i	−0.281616	−	1.05101i
$99$	0.414412	+	0.991570i	0.0416499	+	0.0996566i
$100$	−9.83809	+	17.0401i	−0.983809	+	1.70401i
$101$	−4.24104	−	7.34570i	−0.421999	−	0.730924i	0.574136	−	0.818760i	$-0.305338\pi$
$101$	−4.24104	−	7.34570i	−0.421999	−	0.730924i	−0.996135	+	0.0878358i	$0.972005\pi$
$102$	3.79389	+	11.1185i	0.375651	+	1.10089i
$103$		−	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	−0.354560	−	0.935033i	$-0.615369\pi$
$107$	2.87486	−	1.65980i	0.277923	−	0.160459i	0.632483	+	0.774574i	$0.282036\pi$
$108$	−7.67937	+	22.9814i	−0.738948	+	2.21138i
$109$	−1.95379	+	1.95379i	−0.187139	+	0.187139i	−0.794458	−	0.607319i	$-0.792245\pi$
$109$	−1.95379	+	1.95379i	−0.187139	+	0.187139i	0.607319	+	0.794458i	$0.292245\pi$
$110$	−0.789101	+	0.211439i	−0.0752378	+	0.0201599i
$111$	3.94110	−	4.50836i	0.374072	−	0.427915i
$112$	10.0093	+	10.0093i	0.945794	+	0.945794i
$113$	−4.96947	−	2.86913i	−0.467489	−	0.269905i	0.247699	−	0.968837i	$-0.420326\pi$
$113$	−4.96947	−	2.86913i	−0.467489	−	0.269905i	−0.715188	+	0.698932i	$0.753659\pi$
$114$	24.5361	+	12.0515i	2.29802	+	1.12873i
$115$	−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
$120$	−9.44183	−	4.63759i	−0.861917	−	0.423352i
$121$	−9.41514	−	5.43584i	−0.855922	−	0.494167i
$122$	−8.90475	−	8.90475i	−0.806198	−	0.806198i
$123$	−7.89351	+	9.02968i	−0.711734	+	0.814179i
$124$	−8.11164	+	2.17351i	−0.728447	+	0.195187i
$125$	5.75944	−	5.75944i	0.515140	−	0.515140i
$126$	−10.3048	+	7.95924i	−0.918027	+	0.709065i
$127$	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	$0.0896052\pi$
$131$			6.35913i			0.555599i	−0.960639	+	0.277800i	$0.910395\pi$
$132$	0.934381	+	2.73832i	0.0813275	+	0.238340i
$133$	5.14019	+	8.90306i	0.445711	+	0.771993i
$134$	−16.2505	+	28.1467i	−1.40383	+	2.43151i
$135$	2.53222	−	3.82904i	0.217938	−	0.329552i
$136$	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	$0.888853\pi$
$138$	23.7645	+	4.68789i	2.02297	+	0.399059i
$139$	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
$141$	12.3683	−	4.22037i	1.04160	−	0.355419i
$142$			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
$147$	7.21138	−	0.484147i	0.594784	−	0.0399317i
$148$	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	$0.273692\pi$
$150$	−14.2033	−	12.4162i	−1.15970	−	1.01378i
$151$	6.62875	+	6.62875i	0.539440	+	0.539440i	0.923364	−	0.383925i	$-0.125428\pi$
$151$	6.62875	+	6.62875i	0.539440	+	0.539440i	−0.383925	+	0.923364i	$0.625428\pi$
$152$	36.4002	+	21.0156i	2.95244	+	1.70459i
$153$	−7.81209	+	1.05370i	−0.631570	+	0.0851868i
$154$	−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
$159$	7.40524	−	15.0766i	0.587274	−	1.19565i
$160$	−6.10742	−	3.52612i	−0.482834	−	0.278764i
$161$	6.44134	+	6.44134i	0.507649	+	0.507649i
$162$	−20.1926	−	11.4880i	−1.58648	−	0.902584i
$163$	19.8654	−	5.32291i	1.55598	−	0.416923i	0.624590	−	0.780953i	$-0.285266\pi$
$163$	19.8654	−	5.32291i	1.55598	−	0.416923i	0.931387	+	0.364030i	$0.118600\pi$
$164$	−22.8322	+	22.8322i	−1.78290	+	1.78290i
$165$	−0.0367190	−	0.546931i	−0.00285857	−	0.0425785i
$166$	−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
$171$	−11.1199	+	14.5874i	−0.850363	+	1.11552i
$172$	2.22188	+	3.84840i	0.169416	+	0.293438i
$173$	5.88220	−	10.1883i	0.447215	−	0.774599i	−0.550988	−	0.834513i	$-0.685749\pi$
$173$	5.88220	−	10.1883i	0.447215	−	0.774599i	0.998204	+	0.0599136i	$0.0190825\pi$
$174$	−7.24329	+	36.7187i	−0.549112	+	2.78364i
$175$	−1.83624	−	6.85295i	−0.138807	−	0.518034i
$176$	0.780555	+	2.91307i	0.0588365	+	0.219581i
$177$	3.45534	−	17.5163i	0.259719	−	1.31661i
$178$	8.84230	−	15.3153i	0.662758	−	1.14793i
$179$	−5.90594	−	10.2294i	−0.441431	−	0.764580i	0.556365	−	0.830938i	$-0.312196\pi$
$179$	−5.90594	−	10.2294i	−0.441431	−	0.764580i	−0.997796	+	0.0663576i	$0.978862\pi$
$180$	7.49266	−	9.82902i	0.558470	−	0.732612i
$181$		−	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
$186$	−0.539346	−	8.03357i	−0.0395468	−	0.589050i
$187$	−0.665589	+	0.665589i	−0.0486727	+	0.0486727i
$188$	33.9853	−	9.10632i	2.47863	−	0.664147i
$189$	−3.90145	−	7.81737i	−0.283789	−	0.568630i
$190$	−9.85936	−	9.85936i	−0.715274	−	0.715274i
$191$	−14.6715	−	8.47057i	−1.06159	−	0.612909i	−0.135718	−	0.990748i	$-0.543334\pi$
$191$	−14.6715	−	8.47057i	−1.06159	−	0.612909i	−0.925871	+	0.377839i	$0.876667\pi$
$192$	−2.87711	+	5.85760i	−0.207637	+	0.422736i
$193$	4.33031	−	16.1609i	0.311702	−	1.16329i	−0.615318	−	0.788279i	$-0.710973\pi$
$193$	4.33031	−	16.1609i	0.311702	−	1.16329i	0.927021	−	0.375010i	$-0.122361\pi$
$194$	−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	$0.908880\pi$
$198$	−2.74920	+	0.370815i	−0.195377	+	0.0263527i
$199$	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
$201$	−16.4190	−	14.3531i	−1.15811	−	1.01239i
$202$	21.1488	−	5.66681i	1.48803	−	0.398716i
$203$	−9.95256	+	9.95256i	−0.698533	+	0.698533i
$204$	−21.1751	+	1.42162i	−1.48255	+	0.0995335i
$205$	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
$210$	6.28559	−	2.14479i	0.433747	−	0.148005i
$211$	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
$213$	−5.46748	−	1.07854i	−0.374625	−	0.0739001i
$214$	2.21780	+	8.27694i	0.151606	+	0.565800i
$215$	−0.217898	−	0.813208i	−0.0148605	−	0.0554603i
$216$	−29.7947	−	19.7038i	−2.02727	−	1.34067i
$217$	1.51401	−	2.62234i	0.102778	−	0.178016i
$218$	−3.56617	−	6.17679i	−0.241532	−	0.418345i
$219$	−0.195016	−	0.571518i	−0.0131779	−	0.0386196i
$220$		−	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	0.500614	−	0.865670i	$-0.333107\pi$
$223$	7.48636	+	2.00597i	0.501324	+	0.134329i	0.000709598		1.00000i	$0.499774\pi$
$224$	−11.6237	+	6.71092i	−0.776638	+	0.448392i
$225$	10.0182	−	7.73781i	0.667877	−	0.515854i
$226$	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	$0.630444\pi$
$228$	−32.5015	+	37.1796i	−2.15246	+	2.46228i
$229$	8.11488	+	8.11488i	0.536246	+	0.536246i	0.922424	−	0.386178i	$-0.126205\pi$
$229$	8.11488	+	8.11488i	0.536246	+	0.536246i	−0.386178	+	0.922424i	$0.626205\pi$
$230$	−10.6998	−	6.17755i	−0.705526	−	0.407336i
$231$	−0.936405	−	0.459939i	−0.0616110	−	0.0302618i
$232$	−14.8940	+	55.5850i	−0.977837	+	3.64934i
$233$	11.2799			0.738973			0.369486	−	0.929236i	$-0.379534\pi$
$233$	11.2799			0.738973			0.369486	+	0.929236i	$0.379534\pi$
$234$		0			0
$235$	−6.66584			−0.434832
$236$	12.4408	−	46.4297i	0.809827	−	3.02231i
$237$	5.72389	+	2.81143i	0.371806	+	0.182622i
$238$	−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	$0.769258\pi$
$240$	8.47857	−	9.69895i	0.547289	−	0.626064i
$241$	−22.4684	+	6.02040i	−1.44732	+	0.387808i	−0.895090	−	0.445885i	$-0.852889\pi$
$241$	−22.4684	+	6.02040i	−1.44732	+	0.387808i	−0.552228	+	0.833693i	$0.686222\pi$
$242$	19.8436	−	19.8436i	1.27560	−	1.27560i
$243$	10.1849	−	11.8012i	0.653363	−	0.757045i
$244$	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
$249$	−6.70012	−	19.6356i	−0.424603	−	1.24435i
$250$	10.5125	+	18.2082i	0.664868	+	1.15159i
$251$	−5.39681	+	9.34756i	−0.340644	+	0.590013i	−0.984552	−	0.175090i	$-0.943978\pi$
$251$	−5.39681	+	9.34756i	−0.340644	+	0.590013i	0.643909	+	0.765102i	$0.277312\pi$
$252$	−9.07038	−	21.7029i	−0.571380	−	1.36715i
$253$	0.502313	+	1.87466i	0.0315801	+	0.117859i
$254$	9.10196	+	33.9690i	0.571108	+	2.13140i
$255$	3.94476	+	0.778159i	0.247030	+	0.0487302i
$256$	11.8203	−	20.4734i	0.738771	−	1.27959i
$257$	−2.12801	−	3.68582i	−0.132741	−	0.229915i	0.791991	−	0.610533i	$-0.209045\pi$
$257$	−2.12801	−	3.68582i	−0.132741	−	0.229915i	−0.924732	+	0.380618i	$0.875711\pi$
$258$	−4.03231	+	1.37592i	−0.251040	+	0.0856610i
$259$			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	0.364801	−	0.931085i	$-0.381137\pi$
$263$	21.9508	−	12.6733i	1.35355	−	0.781470i	0.988744	+	0.149615i	$0.0478036\pi$
$264$	−4.25580	+	0.285720i	−0.261927	+	0.0175848i
$265$	−6.05823	+	6.05823i	−0.372154	+	0.372154i
$266$	−25.6326	+	6.86823i	−1.57164	+	0.421118i
$267$	8.93396	+	7.80984i	0.546749	+	0.477954i
$268$	−41.5167	−	41.5167i	−2.53604	−	2.53604i
$269$	−19.6286	−	11.3326i	−1.19677	−	0.690958i	−0.236940	−	0.971524i	$-0.576145\pi$
$269$	−19.6286	−	11.3326i	−1.19677	−	0.690958i	−0.959835	+	0.280566i	$0.909478\pi$
$270$	7.85541	+	8.87186i	0.478065	+	0.539924i
$271$	−5.51672	+	20.5887i	−0.335117	+	1.25067i	0.568625	+	0.822597i	$0.307476\pi$
$271$	−5.51672	+	20.5887i	−0.335117	+	1.25067i	−0.903742	+	0.428077i	$0.859191\pi$
$272$	−22.1212			−1.34129
$273$		0			0
$274$	−5.27335			−0.318575
$275$	0.391216	−	1.46004i	0.0235912	−	0.0880436i
$276$	−19.2915	+	39.2761i	−1.16121	+	2.36415i
$277$	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
$279$	5.35863	+	0.688191i	0.320813	+	0.0412009i
$280$	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	$0.113737\pi$
$282$	2.25969	+	33.6582i	0.134563	+	2.00432i
$283$	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
$288$	−19.0450	−	14.5180i	−1.12224	−	0.855479i
$289$	5.04783	+	8.74310i	0.296931	+	0.514300i
$290$	9.54498	−	16.5324i	0.560501	−	0.970816i
$291$	1.77345	−	8.99024i	0.103962	−	0.527017i
$292$	−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	$-0.242881\pi$
$294$	−3.61072	+	18.3040i	−0.210581	+	1.06751i
$295$	−4.55334	+	7.88661i	−0.265106	+	0.459176i
$296$	11.8833	+	20.5825i	0.690703	+	1.19633i
$297$	0.112903	−	1.85798i	0.00655128	−	0.107811i
$298$			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
$303$	0.984114	+	14.6584i	0.0565359	+	0.842103i
$304$	−36.3972	+	36.3972i	−2.08752	+	2.08752i
$305$	−4.16321	+	1.11553i	−0.238385	+	0.0638750i
$306$	2.59194	−	20.1823i	0.148172	−	1.15374i
$307$	5.70702	+	5.70702i	0.325717	+	0.325717i	0.850955	−	0.525238i	$-0.176024\pi$
$307$	5.70702	+	5.70702i	0.325717	+	0.325717i	−0.525238	+	0.850955i	$0.676024\pi$
$308$	−2.43245	−	1.40438i	−0.138602	−	0.0800218i
$309$	−0.423688	+	0.862600i	−0.0241028	+	0.0490716i
$310$	−1.06294	+	3.96695i	−0.0603710	+	0.225308i
$311$	−25.3416			−1.43699			−0.718496	−	0.695531i	$-0.755169\pi$
$311$	−25.3416			−1.43699			−0.718496	+	0.695531i	$0.755169\pi$
$312$		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
$315$	0.595688	+	4.41640i	0.0335632	+	0.248836i
$316$	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	$0.816950\pi$
$318$	32.6438	+	28.5364i	1.83058	+	1.60024i
$319$	−2.89655	+	0.776127i	−0.162175	+	0.0434548i
$320$	2.35376	−	2.35376i	0.131579	−	0.131579i
$321$	−5.73681	+	0.385149i	−0.320197	+	0.0214969i
$322$	−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
$327$	4.52935	−	1.54552i	0.250474	−	0.0854677i
$328$	−23.8007	−	41.2241i	−1.31418	−	2.27622i
$329$	−6.34322	+	10.9868i	−0.349713	+	0.605721i
$330$	1.38822	+	0.273847i	0.0764192	+	0.0150748i
$331$	−4.65404	−	17.3691i	−0.255809	−	0.954693i	−0.967638	−	0.252341i	$-0.918800\pi$
$331$	−4.65404	−	17.3691i	−0.255809	−	0.954693i	0.711829	−	0.702353i	$-0.247867\pi$
$332$	−14.4569	−	53.9539i	−0.793426	−	2.96111i
$333$	−9.56959	+	3.99946i	−0.524410	+	0.219169i
$334$	12.9387	−	22.4105i	0.707974	−	1.22625i
$335$	5.56180	+	9.63333i	0.303874	+	0.526325i
$336$	−7.91779	−	23.2041i	−0.431951	−	1.26589i
$337$			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
$342$	−28.9423	−	37.4717i	−1.56502	−	2.02623i
$343$	−13.2838	+	13.2838i	−0.717259	+	0.717259i
$344$	−6.32777	+	1.69552i	−0.341170	+	0.0914163i
$345$	5.45624	−	6.24159i	0.293754	−	0.336036i
$346$	21.4731	+	21.4731i	1.15440	+	1.15440i
$347$	20.8470	+	12.0360i	1.11912	+	0.646126i	0.941177	−	0.337914i	$-0.109721\pi$
$347$	20.8470	+	12.0360i	1.11912	+	0.646126i	0.177946	+	0.984040i	$0.443055\pi$
$348$	−60.6858	−	29.8074i	−3.25310	−	1.59784i
$349$	4.47957	−	16.7180i	0.239786	−	0.894894i	−0.736147	−	0.676822i	$-0.763357\pi$
$349$	4.47957	−	16.7180i	0.239786	−	0.894894i	0.975933	−	0.218072i	$-0.0699767\pi$
$350$	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	$-0.107405\pi$
$354$	41.3659	+	20.3179i	2.19857	+	1.07988i
$355$	2.46170	+	1.42126i	0.130653	+	0.0754328i
$356$	22.5902	+	22.5902i	1.19728	+	1.19728i
$357$	5.03642	−	5.76134i	0.266555	−	0.304922i
$358$	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	$0.00330975\pi$
$360$	11.1374	+	14.4196i	0.586992	+	0.759979i
$361$	−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
$366$	7.04402	+	20.6434i	0.368197	+	1.07905i
$367$	−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
$369$	19.1667	−	8.01042i	0.997777	−	0.417006i
$370$	−2.04058	−	7.61557i	−0.106085	−	0.395914i
$371$	4.22028	+	15.7503i	0.219106	+	0.817716i
$372$	14.2704	+	2.81504i	0.739885	+	0.145953i
$373$	−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
$375$	−13.3518	+	4.55595i	−0.689484	+	0.235268i
$376$			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	0.663818	−	0.747894i	$-0.268935\pi$
$379$	16.8350	+	4.51091i	0.864754	+	0.231710i	0.200936	+	0.979604i	$0.435602\pi$
$380$	21.8140	−	12.5943i	1.11903	−	0.646074i
$381$	−23.5441	+	1.58067i	−1.20620	+	0.0809802i
$382$	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	$0.229595\pi$
$384$	8.13600	+	7.11228i	0.415188	+	0.362947i
$385$	0.376276	+	0.376276i	0.0191768	+	0.0191768i
$386$	37.4019	+	21.5940i	1.90370	+	1.09910i
$387$	−0.382143	−	2.83319i	−0.0194254	−	0.144019i
$388$	6.38524	−	23.8300i	0.324161	−	1.20979i
$389$	3.24468			0.164512			0.0822559	−	0.996611i	$-0.473788\pi$
$389$	3.24468			0.164512			0.0822559	+	0.996611i	$0.473788\pi$
$390$		0			0
$391$	−14.2357			−0.719931
$392$	−7.42451	+	27.7086i	−0.374994	+	1.39950i
$393$	4.85584	−	9.88617i	0.244945	−	0.498691i
$394$	−32.6963	−	18.8772i	−1.64722	−	0.951020i
$395$	−2.30003	−	2.30003i	−0.115727	−	0.115727i
$396$	0.638359	−	4.97061i	0.0320787	−	0.249782i
$397$	−30.7348	+	8.23536i	−1.54253	+	0.413321i	−0.927084	−	0.374855i	$-0.877693\pi$
$397$	−30.7348	+	8.23536i	−1.54253	+	0.413321i	−0.615451	+	0.788175i	$0.711026\pi$
$398$	−0.610176	+	0.610176i	−0.0305854	+	0.0305854i
$399$	−1.19276	−	17.7661i	−0.0597125	−	0.889419i
$400$	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
$405$	−6.86055	+	4.01919i	−0.340904	+	0.199715i
$406$	−18.1660	−	31.4645i	−0.901565	−	1.56156i
$407$	−0.619241	+	1.07256i	−0.0306947	+	0.0531647i
$408$	6.05505	−	30.6951i	0.299770	−	1.51964i
$409$	0.785323	+	2.93087i	0.0388317	+	0.144922i	0.982620	−	0.185629i	$-0.0594322\pi$
$409$	0.785323	+	2.93087i	0.0388317	+	0.144922i	−0.943788	+	0.330551i	$0.892766\pi$
$410$	4.08703	+	15.2530i	0.201844	+	0.753292i
$411$	0.684803	−	3.47151i	0.0337789	−	0.171237i
$412$	−1.29369	+	2.24073i	−0.0637354	+	0.110393i
$413$	8.66592	+	15.0098i	0.426422	+	0.738585i
$414$	−33.3656	−	25.4346i	−1.63983	−	1.25004i
$415$			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	$0.695301\pi$
$419$	−32.1726	+	18.5749i	−1.57173	+	0.907442i	−0.995957	+	0.0898356i	$0.971366\pi$
$420$	0.803683	+	11.9709i	0.0392157	+	0.584119i
$421$	−18.7201	+	18.7201i	−0.912361	+	0.912361i	−0.996458	−	0.0840970i	$-0.973199\pi$
$421$	−18.7201	+	18.7201i	−0.912361	+	0.912361i	0.0840970	+	0.996458i	$0.473199\pi$
$422$	−6.70488	+	1.79657i	−0.326388	+	0.0874555i
$423$	−22.4510	−	2.88331i	−1.09160	−	0.140191i
$424$	47.1405	+	47.1405i	2.28935	+	2.28935i
$425$	9.60179	+	5.54359i	0.465755	+	0.268904i
$426$	6.34195	−	12.9118i	0.307269	−	0.625578i
$427$	−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	$0.139294\pi$
$432$	32.7517	−	28.9993i	1.57577	−	1.39523i
$433$	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
$435$	9.64393	+	8.43048i	0.462391	+	0.404211i
$436$	12.4456	−	3.33479i	0.596037	−	0.159708i
$437$	−23.4228	+	23.4228i	−1.12046	+	1.12046i
$438$	1.55528	−	0.104416i	0.0743144	−	0.00498921i
$439$	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	$-0.953720\pi$
$443$		−	6.09878i		−	0.289762i	0.989449	−	0.144881i	$-0.0462799\pi$
$444$	−26.4274	+	9.01766i	−1.25419	+	0.427959i
$445$	−3.02631	−	5.24172i	−0.143461	−	0.248481i
$446$	−10.0032	+	17.3260i	−0.473663	+	0.820409i
$447$	−18.0136	−	3.55343i	−0.852013	−	0.168072i
$448$	−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	$-0.301370\pi$
$450$	12.6001	+	30.1484i	0.593972	+	1.42121i
$451$	1.24026	−	2.14820i	0.0584016	−	0.101155i
$452$	13.3792	+	23.1734i	0.629304	+	1.08999i
$453$	−5.24361	−	15.3671i	−0.246366	−	0.722007i
$454$		−	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	−0.201464	−	0.979496i	$-0.564570\pi$
$457$	−18.5062	−	4.95873i	−0.865686	−	0.231960i	−0.664221	+	0.747536i	$0.731237\pi$
$458$	−25.6547	+	14.8118i	−1.19877	+	0.692109i
$459$	12.9496	+	4.32720i	0.604436	+	0.201976i
$460$	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	$0.449878\pi$
$462$	1.77240	−	2.02751i	0.0824593	−	0.0943282i
$463$	−25.0898	−	25.0898i	−1.16602	−	1.16602i	−0.983134	−	0.182885i	$-0.941456\pi$
$463$	−25.0898	−	25.0898i	−1.16602	−	1.16602i	−0.182885	−	0.983134i	$-0.558544\pi$
$464$	−61.0316	−	35.2366i	−2.83332	−	1.63582i
$465$	−2.47345	−	1.21490i	−0.114704	−	0.0563395i
$466$	−7.53603	+	28.1249i	−0.349100	+	1.30286i
$467$	−10.0568			−0.465374			−0.232687	−	0.972552i	$-0.574752\pi$
$467$	−10.0568			−0.465374			−0.232687	+	0.972552i	$0.574752\pi$
$468$		0			0
$469$	21.1705			0.977562
$470$	4.45340	−	16.6203i	0.205420	−	0.766637i
$471$	−34.1959	−	16.7962i	−1.57566	−	0.773926i
$472$	61.3676	+	35.4306i	2.82467	+	1.63083i
$473$	−0.241387	−	0.241387i	−0.0110990	−	0.0110990i
$474$	−10.8340	+	12.3934i	−0.497621	+	0.569247i
$475$	24.9195	−	6.67716i	1.14339	−	0.306369i
$476$	14.5680	−	14.5680i	0.667723	−	0.667723i
$477$	−23.0250	+	17.7840i	−1.05424	+	0.814274i
$478$	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
$483$	−5.09536	−	14.9326i	−0.231847	−	0.679457i
$484$	25.3482	+	43.9043i	1.15219	+	1.99565i
$485$	−2.33700	+	4.04780i	−0.106118	+	0.183801i
$486$	22.6200	+	33.2789i	1.02606	+	1.50956i
$487$	2.43194	+	9.07613i	0.110202	+	0.411279i	0.998883	−	0.0472463i	$-0.0150446\pi$
$487$	2.43194	+	9.07613i	0.110202	+	0.411279i	−0.888681	+	0.458525i	$0.848378\pi$
$488$	8.68021	+	32.3950i	0.392934	+	1.46645i
$489$	−34.9481	−	6.89401i	−1.58041	−	0.311758i
$490$	4.75809	−	8.24126i	0.214949	−	0.372302i
$491$	12.1772	+	21.0915i	0.549548	+	0.951845i	0.998305	+	0.0581914i	$0.0185334\pi$
$491$	12.1772	+	21.0915i	0.549548	+	0.951845i	−0.448758	+	0.893654i	$0.648133\pi$
$492$	52.9307	−	18.0612i	2.38630	−	0.814263i
$493$		−	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
$498$	53.4347	−	3.58742i	2.39447	−	0.160756i
$499$	−6.97195	+	6.97195i	−0.312107	+	0.312107i	−0.845725	−	0.533618i	$-0.820832\pi$
$499$	−6.97195	+	6.97195i	−0.312107	+	0.312107i	0.533618	+	0.845725i	$0.320832\pi$
$500$	−36.6876	+	9.83042i	−1.64072	+	0.439630i
$501$	13.0728	+	11.4279i	0.584051	+	0.510562i
$502$	−19.7012	−	19.7012i	−0.879307	−	0.879307i
$503$	11.3931	+	6.57779i	0.507992	+	0.293289i	0.732008	−	0.681296i	$-0.238583\pi$
$503$	11.3931	+	6.57779i	0.507992	+	0.293289i	−0.224016	+	0.974586i	$0.571917\pi$
$504$	34.3650	−	4.63519i	1.53074	−	0.206468i
$505$	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	$-0.0620718\pi$
$510$	−4.57569	+	9.31580i	−0.202615	+	0.412511i
$511$	0.507679	+	0.293109i	0.0224584	+	0.0129664i
$512$	34.3270	+	34.3270i	1.51705	+	1.51705i
$513$	28.4265	−	14.1869i	1.25506	−	0.626368i
$514$	10.6117	−	2.84341i	0.468064	−	0.125417i
$515$	0.346619	−	0.346619i	0.0152739	−	0.0152739i
$516$	−0.515576	−	7.67951i	−0.0226970	−	0.338072i
$517$	−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	$-0.908113\pi$
$521$		−	12.9958i		−	0.569355i	0.958623	−	0.284678i	$-0.0918865\pi$
$522$	39.2992	−	51.5535i	1.72008	−	2.25644i
$523$	−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
$525$	−2.37822	+	12.0560i	−0.103794	+	0.526169i
$526$	16.9339	+	63.1981i	0.738352	+	2.75557i
$527$	1.22473	+	4.57077i	0.0533503	+	0.199106i
$528$	1.01094	−	5.12482i	0.0439956	−	0.223029i
$529$	−3.17594	+	5.50088i	−0.138084	+	0.239169i
$530$	−11.0578	−	19.1528i	−0.480322	−	0.831943i
$531$	−18.7473	+	24.5931i	−0.813563	+	1.06725i
$532$		−	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
$537$	1.37045	+	20.4128i	0.0591391	+	0.880878i
$538$	41.3698	−	41.3698i	1.78358	−	1.78358i
$539$	−1.44390	+	0.386893i	−0.0621933	+	0.0166646i
$540$	−19.1539	+	9.55921i	−0.824251	+	0.411363i
$541$	9.48746	+	9.48746i	0.407898	+	0.407898i	0.881005	−	0.473107i	$-0.156868\pi$
$541$	9.48746	+	9.48746i	0.407898	+	0.407898i	−0.473107	+	0.881005i	$0.656868\pi$
$542$	−47.6492	−	27.5103i	−2.04671	−	1.18167i
$543$	−15.3483	+	31.2482i	−0.658660	+	1.34099i
$544$	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
$549$	−14.5045	+	1.95638i	−0.619037	+	0.0834963i
$550$	3.37902	+	1.95088i	0.144082	+	0.0831858i
$551$	−36.1907	−	36.1907i	−1.54178	−	1.54178i
$552$	−48.5673	−	42.4563i	−2.06716	−	1.80706i
$553$	−5.97968	+	1.60225i	−0.254282	+	0.0681346i
$554$	−19.4971	+	19.4971i	−0.828354	+	0.828354i
$555$	5.27840	−	0.354373i	0.224056	−	0.0150423i
$556$	−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
$561$	1.54300	−	0.526508i	0.0651454	−	0.0222292i
$562$	17.9628	+	31.1125i	0.757715	+	1.31240i
$563$	19.7230	−	34.1613i	0.831227	−	1.43973i	−0.0658393	−	0.997830i	$-0.520972\pi$
$563$	19.7230	−	34.1613i	0.831227	−	1.43973i	0.897066	−	0.441897i	$-0.145694\pi$
$564$	−59.7885	−	11.7941i	−2.51755	−	0.496622i
$565$	−1.31209	−	4.89679i	−0.0552001	−	0.206010i
$566$	10.8875	+	40.6328i	0.457637	+	1.70792i
$567$	0.0960047	+	15.1324i	0.00403182	+	0.635500i
$568$	11.0592	−	19.1551i	0.464033	−	0.803729i
$569$	−7.67489	−	13.2933i	−0.321748	−	0.557284i	0.659101	−	0.752055i	$-0.270937\pi$
$569$	−7.67489	−	13.2933i	−0.321748	−	0.557284i	−0.980849	+	0.194771i	$0.937604\pi$
$570$	7.79916	+	22.8564i	0.326671	+	0.957350i
$571$		−	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
$576$	8.94575	−	6.90951i	0.372740	−	0.287896i
$577$	25.1056	−	25.1056i	1.04516	−	1.04516i	0.0462290	−	0.998931i	$-0.485280\pi$
$577$	25.1056	−	25.1056i	1.04516	−	1.04516i	0.998931	−	0.0462290i	$-0.0147204\pi$
$578$	−25.1720	+	6.74483i	−1.04702	+	0.280548i
$579$	−19.0726	+	21.8178i	−0.792630	+	0.906718i
$580$	24.3854	+	24.3854i	1.01255	+	1.01255i
$581$	17.4423	+	10.0703i	0.723627	+	0.417786i
$582$	21.2310	+	10.4282i	0.880055	+	0.432261i
$583$	−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	$0.966537\pi$
$588$	−30.2514	−	14.8587i	−1.24755	−	0.612763i
$589$	9.53566	+	5.50541i	0.392910	+	0.226847i
$590$	−16.6221	−	16.6221i	−0.684320	−	0.684320i
$591$	16.6730	−	19.0729i	0.685838	−	0.784555i
$592$	−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	$0.285048\pi$
$594$	4.55718	+	1.52281i	0.186983	+	0.0624816i
$595$	−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	$0.0414406\pi$
$599$			6.35465i			0.259644i	−0.991537	+	0.129822i	$0.958559\pi$
$600$	16.2249	+	47.5490i	0.662378	+	1.94118i
$601$	−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
$603$	14.5656	+	34.8514i	0.593158	+	1.41926i
$604$	−11.3142	−	42.2251i	−0.460367	−	1.71811i
$605$	−2.48588	−	9.27745i	−0.101066	−	0.377182i
$606$	−37.2061	−	7.33942i	−1.51139	−	0.298143i
$607$	−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
$609$	23.0725	−	7.87288i	0.934944	−	0.319025i
$610$		−	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	0.889114	−	0.457686i	$-0.151321\pi$
$613$	35.4117	+	9.48855i	1.43027	+	0.383239i	0.541153	+	0.840924i	$0.317988\pi$
$614$	−18.0424	+	10.4168i	−0.728134	+	0.420388i
$615$	−10.5720	+	0.709765i	−0.426303	+	0.0286205i
$616$	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	$0.205936\pi$
$618$	−1.86771	−	1.63270i	−0.0751301	−	0.0656768i
$619$	−11.8576	−	11.8576i	−0.476599	−	0.476599i	0.427443	−	0.904042i	$-0.359414\pi$
$619$	−11.8576	−	11.8576i	−0.476599	−	0.476599i	−0.904042	+	0.427443i	$0.859414\pi$
$620$	−6.42516	−	3.70957i	−0.258041	−	0.148980i
$621$	21.0768	−	18.6620i	0.845782	−	0.748880i
$622$	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
$627$	1.67249	−	3.40507i	0.0667926	−	0.135985i
$628$	−88.8289	−	51.2854i	−3.54466	−	2.04651i
$629$	−6.42356	−	6.42356i	−0.256124	−	0.256124i
$630$	−11.4096	−	1.46530i	−0.454570	−	0.0583789i
$631$	26.8433	−	7.19263i	1.06861	−	0.286334i	0.318690	−	0.947859i	$-0.396757\pi$
$631$	26.8433	−	7.19263i	1.06861	−	0.286334i	0.749923	+	0.661525i	$0.230090\pi$
$632$	−17.8971	+	17.8971i	−0.711909	+	0.711909i
$633$	−0.311996	−	4.64720i	−0.0124007	−	0.184709i
$634$	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
$639$	7.67640	+	5.85171i	0.303674	+	0.231490i
$640$	−2.75601	−	4.77354i	−0.108941	−	0.188691i
$641$	4.28764	−	7.42640i	0.169351	−	0.293325i	−0.768841	−	0.639440i	$-0.779166\pi$
$641$	4.28764	−	7.42640i	0.169351	−	0.293325i	0.938192	+	0.346115i	$0.112499\pi$
$642$	2.87240	−	14.5612i	0.113365	−	0.574685i
$643$	0.583059	+	2.17600i	0.0229936	+	0.0858132i	0.976469	−	0.215657i	$-0.0691893\pi$
$643$	0.583059	+	2.17600i	0.0229936	+	0.0858132i	−0.953476	+	0.301470i	$0.902523\pi$
$644$	−10.9943	−	41.0313i	−0.433236	−	1.61686i
$645$	−0.282213	+	1.43063i	−0.0111121	+	0.0563312i
$646$	20.7351	−	35.9143i	0.815813	−	1.41303i
$647$	−12.2169	−	21.1603i	−0.480296	−	0.831897i	0.519448	−	0.854502i	$-0.326137\pi$
$647$	−12.2169	−	21.1603i	−0.480296	−	0.831897i	−0.999744	+	0.0226045i	$0.992804\pi$
$648$	31.2743	+	53.3836i	1.22857	+	2.09711i
$649$			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	−0.700819	−	0.713339i	$-0.747182\pi$
$653$	−11.0765	+	6.39504i	−0.433458	+	0.250257i	0.267361	+	0.963597i	$0.413849\pi$
$654$	0.827513	+	12.3258i	0.0323583	+	0.481978i
$655$	−3.97256	+	3.97256i	−0.155221	+	0.155221i
$656$	56.3085	−	15.0878i	2.19848	−	0.589081i
$657$	−0.133232	+	1.03742i	−0.00519789	+	0.0404736i
$658$	−23.1561	−	23.1561i	−0.902718	−	0.902718i
$659$	26.1230	+	15.0821i	1.01761	+	0.587515i	0.913410	−	0.407041i	$-0.133439\pi$
$659$	26.1230	+	15.0821i	1.01761	+	0.587515i	0.104197	+	0.994557i	$0.466773\pi$
$660$	−1.12693	+	2.29435i	−0.0438656	+	0.0893074i
$661$	−6.48058	+	24.1859i	−0.252065	+	0.940721i	0.717634	+	0.696420i	$0.245225\pi$
$661$	−6.48058	+	24.1859i	−0.252065	+	0.940721i	−0.969700	+	0.244301i	$0.921442\pi$
$662$	46.4167			1.80404
$663$		0			0
$664$	82.3448			3.19560
$665$	−2.35068	+	8.77286i	−0.0911554	+	0.340197i
$666$	−3.57871	−	26.5324i	−0.138672	−	1.02811i
$667$	−39.2758	−	22.6759i	−1.52077	−	0.878014i
$668$	33.0556	+	33.0556i	1.27896	+	1.27896i
$669$	−10.1069	−	8.83516i	−0.390754	−	0.341587i
$670$	−27.7351	+	7.43160i	−1.07150	+	0.287108i
$671$	−1.23578	+	1.23578i	−0.0477068	+	0.0477068i
$672$	23.1951	−	1.55724i	0.894770	−	0.0600717i
$673$	−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	$-0.849817\pi$
$677$		−	23.6516i		−	0.909004i	0.890746	−	0.454502i	$-0.150183\pi$
$678$	−24.2809	+	8.28521i	−0.932501	+	0.318192i
$679$	4.44779	+	7.70379i	0.170690	+	0.295644i
$680$	−7.97916	+	13.8203i	−0.305987	+	0.529984i
$681$	31.8619	+	6.28521i	1.22095	+	0.240850i
$682$	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	$0.966658\pi$
$684$	78.9186	−	32.9828i	3.01753	−	1.26113i
$685$	−0.902413	+	1.56302i	−0.0344794	+	0.0597201i
$686$	−24.2464	−	41.9961i	−0.925733	−	1.60342i
$687$	−6.41920	−	18.8123i	−0.244908	−	0.717733i
$688$		−	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	0.523460	−	0.852050i	$-0.324641\pi$
$691$	14.4779	+	3.87934i	0.550764	+	0.147577i	0.0273044	+	0.999627i	$0.491308\pi$
$692$	−47.5095	+	27.4296i	−1.80604	+	1.04272i
$693$	1.10457	+	1.43008i	0.0419590	+	0.0543243i
$694$	−43.9377	+	43.9377i	−1.66785	+	1.66785i
$695$	4.36366	−	1.16924i	0.165523	−	0.0443518i
$696$	65.5996	−	75.0418i	2.48655	−	2.84445i
$697$	12.8656	+	12.8656i	0.487319	+	0.487319i
$698$	38.6911	+	22.3383i	1.46448	+	0.845518i
$699$	−17.5363	−	8.61337i	−0.663282	−	0.325788i
$700$	−8.56269	+	31.9564i	−0.323639	+	1.20784i
$701$	38.5186			1.45483			0.727414	−	0.686199i	$-0.240722\pi$
$701$	38.5186			1.45483			0.727414	+	0.686199i	$0.240722\pi$
$702$		0			0
$703$	−21.1381			−0.797237
$704$	0.349338	−	1.30375i	0.0131662	−	0.0491368i
$705$	10.3630	+	5.09005i	0.390293	+	0.191702i
$706$	47.3771	+	27.3532i	1.78306	+	1.02945i
$707$	−10.0847	−	10.0847i	−0.379272	−	0.379272i
$708$	−54.7947	+	62.6817i	−2.05931	+	2.35572i
$709$	−35.5833	+	9.53453i	−1.33636	+	0.358077i	−0.855083	−	0.518492i	$-0.826494\pi$
$709$	−35.5833	+	9.53453i	−1.33636	+	0.358077i	−0.481278	+	0.876568i	$0.659827\pi$
$710$	−5.18835	+	5.18835i	−0.194715	+	0.194715i
$711$	−6.75178	−	8.74154i	−0.253212	−	0.327833i
$712$	−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
$717$	1.04570	+	3.06455i	0.0390523	+	0.114448i
$718$	34.2223	+	59.2748i	1.27717	+	2.21212i
$719$	2.38818	−	4.13644i	0.0890640	−	0.154263i	−0.818052	−	0.575145i	$-0.804946\pi$
$719$	2.38818	−	4.13644i	0.0890640	−	0.154263i	0.907116	+	0.420881i	$0.138279\pi$
$720$	−20.5873	+	8.60414i	−0.767243	+	0.320657i
$721$	−0.241462	−	0.901148i	−0.00899251	−	0.0335605i
$722$	−12.2813	−	45.8346i	−0.457064	−	1.70579i
$723$	39.5276	+	7.79737i	1.47005	+	0.289987i
$724$	−46.8646	+	81.1718i	−1.74171	+	3.01673i
$725$	17.6607	+	30.5892i	0.655900	+	1.13605i
$726$	−46.0024	+	15.6971i	−1.70731	+	0.582575i
$727$			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
$732$	−39.3152	+	2.63949i	−1.45313	+	0.0975583i
$733$	−9.54380	+	9.54380i	−0.352508	+	0.352508i	−0.861042	−	0.508534i	$-0.830188\pi$
$733$	−9.54380	+	9.54380i	−0.352508	+	0.352508i	0.508534	+	0.861042i	$0.330188\pi$
$734$	50.6916	−	13.5828i	1.87106	−	0.501349i
$735$	4.80742	+	4.20252i	0.177324	+	0.155012i
$736$	−30.5803	−	30.5803i	−1.12720	−	1.12720i
$737$	3.90614	+	2.25521i	0.143885	+	0.0830718i
$738$	7.16771	+	53.1410i	0.263847	+	1.95615i
$739$	3.11949	−	11.6421i	0.114752	−	0.428261i	−0.884516	−	0.466510i	$-0.845511\pi$
$739$	3.11949	−	11.6421i	0.114752	−	0.428261i	0.999268	+	0.0382487i	$0.0121779\pi$
$740$	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	$-0.0503519\pi$
$744$	−9.45342	+	19.2465i	−0.346579	+	0.705612i
$745$	8.11051	+	4.68260i	0.297146	+	0.171557i
$746$	−58.4286	−	58.4286i	−2.13922	−	2.13922i
$747$	−4.57745	+	35.6425i	−0.167480	+	1.30409i
$748$	4.23980	−	1.13605i	0.155022	−	0.0415381i
$749$	3.94679	−	3.94679i	0.144213	−	0.144213i
$750$	−2.43937	−	36.3345i	−0.0890733	−	1.32675i
$751$	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
$756$	−2.47114	+	40.6664i	−0.0898746	+	1.47902i
$757$	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
$759$	0.650574	−	3.29799i	0.0236144	−	0.119709i
$760$	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	$0.540402\pi$
$762$	11.7885	−	59.7599i	0.427051	−	2.16487i
$763$	−2.32293	+	4.02343i	−0.0840956	+	0.145658i
$764$	39.4996	+	68.4153i	1.42905	+	2.47518i
$765$	−5.53849	−	4.22198i	−0.200244	−	0.152646i
$766$			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	−0.640729	−	0.767767i	$-0.721368\pi$
$769$	−43.8009	−	11.7364i	−1.57950	−	0.423226i	−0.938771	+	0.344541i	$0.888035\pi$
$770$	−1.18958	+	0.686803i	−0.0428694	+	0.0247507i
$771$	0.493794	+	7.35507i	0.0177836	+	0.264886i
$772$	−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	$0.679013\pi$
$774$

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} +(-1.55464 - 0.763602i) q^{3} +(-4.03841 - 2.33158i) q^{4} +(0.624703 + 0.624703i) q^{5} +(2.94257 - 3.36612i) q^{6} +(1.62412 - 0.435181i) q^{7} +(4.86096 - 4.86096i) q^{8} +(1.83382 + 2.37425i) q^{9} +(-1.97496 + 1.14025i) q^{10} +(0.346022 + 0.0927163i) q^{11} +(4.49789 + 6.70851i) q^{12} +4.34024i q^{14} +(-0.494165 - 1.44821i) q^{15} +(4.20937 + 7.29084i) q^{16} +(-1.31381 + 2.27558i) q^{17} +(-7.14502 + 2.98615i) q^{18} +(1.58246 + 5.90581i) q^{19} +(-1.06626 - 3.97935i) q^{20} +(-2.85722 - 0.563628i) q^{21} +(-0.462349 + 0.800812i) q^{22} +(2.70887 + 4.69190i) q^{23} +(-11.2689 + 3.84522i) q^{24} -4.21949i q^{25} +(-1.03796 - 5.09143i) q^{27} +(-7.57351 - 2.02932i) q^{28} +(-7.24949 + 4.18549i) q^{29} +(3.94106 - 0.264589i) q^{30} +(1.27341 - 1.27341i) q^{31} +(-7.71050 + 2.06602i) q^{32} +(-0.467142 - 0.408364i) q^{33} +(-4.79608 - 4.79608i) q^{34} +(1.28645 + 0.742731i) q^{35} +(-1.86998 - 13.8639i) q^{36} +(-0.894800 + 3.33944i) q^{37} -15.7825 q^{38} +6.07331 q^{40} +(1.79217 - 6.68847i) q^{41} +(3.31421 - 6.74752i) q^{42} +(-0.825277 - 0.476474i) q^{43} +(-1.18121 - 1.18121i) q^{44} +(-0.337608 + 2.62880i) q^{45} +(-13.5083 + 3.61955i) q^{46} +(-5.33521 + 5.33521i) q^{47} +(-0.976765 - 14.5489i) q^{48} +(-3.61381 + 2.08643i) q^{49} +(10.5207 + 2.81901i) q^{50} +(3.78013 - 2.53449i) q^{51} +9.69778i q^{53} +(13.3882 + 0.813550i) q^{54} +(0.158241 + 0.274081i) q^{55} +(5.77937 - 10.0102i) q^{56} +(2.04953 - 10.3898i) q^{57} +(-5.59259 - 20.8718i) q^{58} +(2.66789 + 9.95670i) q^{59} +(-1.38098 + 7.00067i) q^{60} +(-2.43931 + 4.22500i) q^{61} +(2.32431 + 4.02583i) q^{62} +(4.01157 + 3.05802i) q^{63} -3.76781i q^{64} +(1.33029 - 0.891926i) q^{66} +(12.1619 + 3.25877i) q^{67} +(10.6114 - 6.12649i) q^{68} +(-0.628580 - 9.36272i) q^{69} +(-2.71136 + 2.71136i) q^{70} +(3.10785 - 0.832745i) q^{71} +(20.4553 + 2.62701i) q^{72} +(0.246530 + 0.246530i) q^{73} +(-7.72860 - 4.46211i) q^{74} +(-3.22201 + 6.55980i) q^{75} +(7.37925 - 27.5397i) q^{76} +0.602329 q^{77} -3.68180 q^{79} +(-1.92500 + 7.18422i) q^{80} +(-2.27417 + 8.70794i) q^{81} +(15.4794 + 8.93703i) q^{82} +(8.47001 + 8.47001i) q^{83} +(10.2245 + 8.93801i) q^{84} +(-2.24230 + 0.600822i) q^{85} +(1.73938 - 1.73938i) q^{86} +(14.4664 - 0.971224i) q^{87} +(2.13269 - 1.23131i) q^{88} +(-6.61757 - 1.77317i) q^{89} +(-6.32897 - 2.59806i) q^{90} -25.2638i q^{92} +(-2.95208 + 1.00732i) q^{93} +(-9.73816 - 16.8670i) q^{94} +(-2.70081 + 4.67794i) q^{95} +(13.5647 + 2.67583i) q^{96} +(1.36929 + 5.11027i) q^{97} +(-2.78786 - 10.4044i) q^{98} +(0.414412 + 0.991570i) 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

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