LMFDB - Embedded newform 507.2.k.k.80.16

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			80.16
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.197759 - 0.738045i) q^{2} +(1.45524 - 0.939300i) q^{3} +(1.22645 + 0.708090i) q^{4} +(-0.996141 - 0.996141i) q^{5} +(-0.405460 - 1.25979i) q^{6} +(2.46232 - 0.659775i) q^{7} +(1.84572 - 1.84572i) q^{8} +(1.23543 - 2.73381i) q^{9} +(-0.932193 + 0.538202i) q^{10} +(-4.58925 - 1.22969i) q^{11} +(2.44988 - 0.121564i) q^{12} -1.94778i q^{14} +(-2.38530 - 0.513946i) q^{15} +(0.418964 + 0.725666i) q^{16} +(-2.90210 + 5.02659i) q^{17} +(-1.77336 - 1.45244i) q^{18} +(0.877888 + 3.27632i) q^{19} +(-0.516358 - 1.92707i) q^{20} +(2.96353 - 3.27298i) q^{21} +(-1.81513 + 3.14390i) q^{22} +(1.69879 + 2.94240i) q^{23} +(0.952274 - 4.41964i) q^{24} -3.01541i q^{25} +(-0.770022 - 5.13878i) q^{27} +(3.48708 + 0.934361i) q^{28} +(5.69796 - 3.28972i) q^{29} +(-0.851029 + 1.65882i) q^{30} +(0.386730 - 0.386730i) q^{31} +(5.66102 - 1.51687i) q^{32} +(-7.83350 + 2.52120i) q^{33} +(3.13593 + 3.13593i) q^{34} +(-3.11004 - 1.79558i) q^{35} +(3.45098 - 2.47808i) q^{36} +(-2.17320 + 8.11049i) q^{37} +2.59169 q^{38} -3.67719 q^{40} +(0.268848 - 1.00336i) q^{41} +(-1.82955 - 2.83448i) q^{42} +(-6.55422 - 3.78408i) q^{43} +(-4.75775 - 4.75775i) q^{44} +(-3.95392 + 1.49260i) q^{45} +(2.50757 - 0.671902i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(1.29131 + 0.662484i) q^{48} +(-0.434484 + 0.250850i) q^{49} +(-2.22551 - 0.596323i) q^{50} +(0.498228 + 10.0408i) q^{51} +2.07223i q^{53} +(-3.94493 - 0.447927i) q^{54} +(3.34660 + 5.79649i) q^{55} +(3.32698 - 5.76250i) q^{56} +(4.35499 + 3.94323i) q^{57} +(-1.30114 - 4.85592i) q^{58} +(1.30332 + 4.86406i) q^{59} +(-2.56152 - 2.31933i) q^{60} +(-3.52415 + 6.10401i) q^{61} +(-0.208945 - 0.361904i) q^{62} +(1.23832 - 7.54661i) q^{63} -2.80221i q^{64} +(0.311618 + 6.28007i) q^{66} +(6.20237 + 1.66192i) q^{67} +(-7.11855 + 4.10990i) q^{68} +(5.23594 + 2.68621i) q^{69} +(-1.94026 + 1.94026i) q^{70} +(-9.27862 + 2.48620i) q^{71} +(-2.76558 - 7.32609i) q^{72} +(-6.04700 - 6.04700i) q^{73} +(5.55614 + 3.20784i) q^{74} +(-2.83237 - 4.38813i) q^{75} +(-1.24325 + 4.63986i) q^{76} -12.1115 q^{77} +8.77426 q^{79} +(0.305519 - 1.14021i) q^{80} +(-5.94742 - 6.75486i) q^{81} +(-0.687355 - 0.396845i) q^{82} +(8.31849 + 8.31849i) q^{83} +(5.95218 - 1.91570i) q^{84} +(7.89810 - 2.11629i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(5.20185 - 10.1394i) q^{87} +(-10.7401 + 6.20081i) q^{88} +(13.1488 + 3.52321i) q^{89} +(0.319681 + 3.21335i) q^{90} +4.81159i q^{92} +(0.199528 - 0.926039i) q^{93} +(0.131592 + 0.227923i) q^{94} +(2.38918 - 4.13818i) q^{95} +(6.81334 - 7.52480i) q^{96} +(-0.491207 - 1.83321i) q^{97} +(0.0992154 + 0.370277i) q^{98} +(-9.03143 + 11.0270i) 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 $

$2$	0.197759	−	0.738045i	0.139837	−	0.521877i	−0.860095	−	0.510135i	$-0.829596\pi$
$2$	0.197759	−	0.738045i	0.139837	−	0.521877i	0.999931	−	0.0117423i	$-0.00373778\pi$
$3$	1.45524	−	0.939300i	0.840182	−	0.542305i
$3$	1.45524	−	0.939300i	0.840182	−	0.542305i
$4$	1.22645	+	0.708090i	0.613224	+	0.354045i
$5$	−0.996141	−	0.996141i	−0.445488	−	0.445488i	0.448363	−	0.893851i	$-0.352007\pi$
$5$	−0.996141	−	0.996141i	−0.445488	−	0.445488i	−0.893851	+	0.448363i	$0.852007\pi$
$6$	−0.405460	−	1.25979i	−0.165528	−	0.514305i
$7$	2.46232	−	0.659775i	0.930668	−	0.249372i	0.238528	−	0.971136i	$-0.423335\pi$
$7$	2.46232	−	0.659775i	0.930668	−	0.249372i	0.692139	+	0.721764i	$0.256668\pi$
$8$	1.84572	−	1.84572i	0.652560	−	0.652560i
$9$	1.23543	−	2.73381i	0.411810	−	0.911270i
$10$	−0.932193	+	0.538202i	−0.294785	+	0.170194i
$11$	−4.58925	−	1.22969i	−1.38371	−	0.370765i	−0.511244	−	0.859436i	$-0.670815\pi$
$11$	−4.58925	−	1.22969i	−1.38371	−	0.370765i	−0.872468	+	0.488671i	$0.837482\pi$
$12$	2.44988	−	0.121564i	0.707220	−	0.0350924i
$13$		0			0
$13$		0			0
$14$		−	1.94778i		−	0.520565i
$15$	−2.38530	−	0.513946i	−0.615881	−	0.132700i
$16$	0.418964	+	0.725666i	0.104741	+	0.181417i
$17$	−2.90210	+	5.02659i	−0.703863	+	1.21913i	0.263237	+	0.964731i	$0.415210\pi$
$17$	−2.90210	+	5.02659i	−0.703863	+	1.21913i	−0.967100	+	0.254395i	$0.918124\pi$
$18$	−1.77336	−	1.45244i	−0.417985	−	0.342343i
$19$	0.877888	+	3.27632i	0.201401	+	0.751640i	0.990516	+	0.137395i	$0.0438728\pi$
$19$	0.877888	+	3.27632i	0.201401	+	0.751640i	−0.789115	+	0.614245i	$0.789461\pi$
$20$	−0.516358	−	1.92707i	−0.115461	−	0.430907i
$21$	2.96353	−	3.27298i	0.646694	−	0.714223i
$22$	−1.81513	+	3.14390i	−0.386987	+	0.670281i
$23$	1.69879	+	2.94240i	0.354223	+	0.613532i	0.986985	−	0.160815i	$-0.0514121\pi$
$23$	1.69879	+	2.94240i	0.354223	+	0.613532i	−0.632762	+	0.774346i	$0.718079\pi$
$24$	0.952274	−	4.41964i	0.194382	−	0.902155i
$25$		−	3.01541i		−	0.603081i
$26$		0			0
$27$	−0.770022	−	5.13878i	−0.148191	−	0.988959i
$28$	3.48708	+	0.934361i	0.658997	+	0.176578i
$29$	5.69796	−	3.28972i	1.05808	−	0.610885i	0.133183	−	0.991092i	$-0.457480\pi$
$29$	5.69796	−	3.28972i	1.05808	−	0.610885i	0.924902	+	0.380206i	$0.124147\pi$
$30$	−0.851029	+	1.65882i	−0.155376	+	0.302858i
$31$	0.386730	−	0.386730i	0.0694587	−	0.0694587i	−0.671524	−	0.740983i	$-0.734360\pi$
$31$	0.386730	−	0.386730i	0.0694587	−	0.0694587i	0.740983	+	0.671524i	$0.234360\pi$
$32$	5.66102	−	1.51687i	1.00074	−	0.268147i
$33$	−7.83350	+	2.52120i	−1.36364	+	0.438885i
$34$	3.13593	+	3.13593i	0.537808	+	0.537808i
$35$	−3.11004	−	1.79558i	−0.525693	−	0.303509i
$36$	3.45098	−	2.47808i	0.575163	−	0.413013i
$37$	−2.17320	+	8.11049i	−0.357272	+	1.33336i	0.520330	+	0.853965i	$0.325809\pi$
$37$	−2.17320	+	8.11049i	−0.357272	+	1.33336i	−0.877602	+	0.479391i	$0.840858\pi$
$38$	2.59169			0.420427
$39$		0			0
$40$	−3.67719			−0.581415
$41$	0.268848	−	1.00336i	0.0419871	−	0.156698i	−0.941750	−	0.336315i	$-0.890819\pi$
$41$	0.268848	−	1.00336i	0.0419871	−	0.156698i	0.983737	+	0.179617i	$0.0574859\pi$
$42$	−1.82955	−	2.83448i	−0.282305	−	0.437369i
$43$	−6.55422	−	3.78408i	−0.999509	−	0.577067i	−0.0914058	−	0.995814i	$-0.529136\pi$
$43$	−6.55422	−	3.78408i	−0.999509	−	0.577067i	−0.908103	+	0.418747i	$0.862469\pi$
$44$	−4.75775	−	4.75775i	−0.717258	−	0.717258i
$45$	−3.95392	+	1.49260i	−0.589416	+	0.222503i
$46$	2.50757	−	0.671902i	0.369721	−	0.0990666i
$47$	−0.243559	+	0.243559i	−0.0355267	+	0.0355267i	−0.724647	−	0.689120i	$-0.757997\pi$
$47$	−0.243559	+	0.243559i	−0.0355267	+	0.0355267i	0.689120	+	0.724647i	$0.257997\pi$
$48$	1.29131	+	0.662484i	0.186385	+	0.0956214i
$49$	−0.434484	+	0.250850i	−0.0620692	+	0.0358357i
$50$	−2.22551	−	0.596323i	−0.314734	−	0.0843327i
$51$	0.498228	+	10.0408i	0.0697658	+	1.40600i
$52$		0			0
$53$			2.07223i			0.284642i	0.989821	+	0.142321i	$0.0454566\pi$
$53$			2.07223i			0.284642i	−0.989821	+	0.142321i	$0.954543\pi$
$54$	−3.94493	−	0.447927i	−0.536837	−	0.0609552i
$55$	3.34660	+	5.79649i	0.451256	+	0.781598i
$56$	3.32698	−	5.76250i	0.444586	−	0.770046i
$57$	4.35499	+	3.94323i	0.576832	+	0.522293i
$58$	−1.30114	−	4.85592i	−0.170848	−	0.637614i
$59$	1.30332	+	4.86406i	0.169678	+	0.633247i	0.997397	+	0.0721043i	$0.0229715\pi$
$59$	1.30332	+	4.86406i	0.169678	+	0.633247i	−0.827719	+	0.561143i	$0.810362\pi$
$60$	−2.56152	−	2.31933i	−0.330691	−	0.299425i
$61$	−3.52415	+	6.10401i	−0.451222	+	0.781539i	−0.998462	−	0.0554367i	$-0.982345\pi$
$61$	−3.52415	+	6.10401i	−0.451222	+	0.781539i	0.547241	+	0.836975i	$0.315678\pi$
$62$	−0.208945	−	0.361904i	−0.0265361	−	0.0459618i
$63$	1.23832	−	7.54661i	0.156014	−	0.950783i
$64$		−	2.80221i		−	0.350276i
$65$		0			0
$66$	0.311618	+	6.28007i	0.0383575	+	0.773023i
$67$	6.20237	+	1.66192i	0.757740	+	0.203036i	0.616948	−	0.787004i	$-0.288369\pi$
$67$	6.20237	+	1.66192i	0.757740	+	0.203036i	0.140791	+	0.990039i	$0.455035\pi$
$68$	−7.11855	+	4.10990i	−0.863252	+	0.498399i
$69$	5.23594	+	2.68621i	0.630333	+	0.323381i
$70$	−1.94026	+	1.94026i	−0.231906	+	0.231906i
$71$	−9.27862	+	2.48620i	−1.10117	+	0.295057i	−0.763241	−	0.646114i	$-0.776393\pi$
$71$	−9.27862	+	2.48620i	−1.10117	+	0.295057i	−0.337929	+	0.941172i	$0.609726\pi$
$72$	−2.76558	−	7.32609i	−0.325927	−	0.863388i
$73$	−6.04700	−	6.04700i	−0.707748	−	0.707748i	0.258313	−	0.966061i	$-0.416833\pi$
$73$	−6.04700	−	6.04700i	−0.707748	−	0.707748i	−0.966061	+	0.258313i	$0.916833\pi$
$74$	5.55614	+	3.20784i	0.645888	+	0.372904i
$75$	−2.83237	−	4.38813i	−0.327054	−	0.506698i
$76$	−1.24325	+	4.63986i	−0.142610	+	0.532229i
$77$	−12.1115			−1.38023
$78$		0			0
$79$	8.77426			0.987182			0.493591	−	0.869694i	$-0.335684\pi$
$79$	8.77426			0.987182			0.493591	+	0.869694i	$0.335684\pi$
$80$	0.305519	−	1.14021i	0.0341581	−	0.127480i
$81$	−5.94742	−	6.75486i	−0.660825	−	0.750540i
$82$	−0.687355	−	0.396845i	−0.0759057	−	0.0438242i
$83$	8.31849	+	8.31849i	0.913073	+	0.913073i	0.996513	−	0.0834395i	$-0.0265905\pi$
$83$	8.31849	+	8.31849i	0.913073	+	0.913073i	−0.0834395	+	0.996513i	$0.526591\pi$
$84$	5.95218	−	1.91570i	0.649436	−	0.209020i
$85$	7.89810	−	2.11629i	0.856669	−	0.229544i
$86$	−4.08898	+	4.08898i	−0.440926	+	0.440926i
$87$	5.20185	−	10.1394i	0.557697	−	1.08706i
$88$	−10.7401	+	6.20081i	−1.14490	+	0.661009i
$89$	13.1488	+	3.52321i	1.39377	+	0.373460i	0.876104	−	0.482123i	$-0.160134\pi$
$89$	13.1488	+	3.52321i	1.39377	+	0.373460i	0.517667	+	0.855582i	$0.326801\pi$
$90$	0.319681	+	3.21335i	0.0336974	+	0.338717i
$91$		0			0
$92$			4.81159i			0.501643i
$93$	0.199528	−	0.926039i	0.0206901	−	0.0960258i
$94$	0.131592	+	0.227923i	0.0135726	+	0.0235085i
$95$	2.38918	−	4.13818i	0.245125	−	0.424568i
$96$	6.81334	−	7.52480i	0.695383	−	0.767996i
$97$	−0.491207	−	1.83321i	−0.0498746	−	0.186134i	0.936495	−	0.350682i	$-0.114050\pi$
$97$	−0.491207	−	1.83321i	−0.0498746	−	0.186134i	−0.986369	+	0.164548i	$0.947384\pi$
$98$	0.0992154	+	0.370277i	0.0100223	+	0.0374036i
$99$	−9.03143	+	11.0270i	−0.907693	+	1.10825i
$100$	2.13518	−	3.69824i	0.213518	−	0.369824i
$101$	−1.03384	−	1.79066i	−0.102871	−	0.178178i	0.809995	−	0.586436i	$-0.199470\pi$
$101$	−1.03384	−	1.79066i	−0.102871	−	0.178178i	−0.912866	+	0.408258i	$0.866136\pi$
$102$	7.50911	+	1.61795i	0.743513	+	0.160200i
$103$		−	13.3818i		−	1.31854i	−0.751905	−	0.659272i	$-0.770865\pi$
$103$		−	13.3818i		−	1.31854i	0.751905	−	0.659272i	$-0.229135\pi$
$104$		0			0
$105$	−6.21244	+	0.308263i	−0.606272	+	0.0300834i
$106$	1.52940	+	0.409801i	0.148548	+	0.0398034i
$107$	−6.51440	+	3.76109i	−0.629771	+	0.363599i	−0.780663	−	0.624952i	$-0.785119\pi$
$107$	−6.51440	+	3.76109i	−0.629771	+	0.363599i	0.150892	+	0.988550i	$0.451785\pi$
$108$	2.69433	−	6.84769i	0.259262	−	0.658920i
$109$	−2.10533	+	2.10533i	−0.201654	+	0.201654i	−0.800709	−	0.599054i	$-0.795543\pi$
$109$	−2.10533	+	2.10533i	−0.201654	+	0.201654i	0.599054	+	0.800709i	$0.295543\pi$
$110$	4.93989	−	1.32364i	0.471000	−	0.126204i
$111$	4.45566	+	13.8440i	0.422913	+	1.31401i
$112$	1.51040	+	1.51040i	0.142719	+	0.142719i
$113$	−1.64175	−	0.947866i	−0.154443	−	0.0891677i	0.420787	−	0.907160i	$-0.361754\pi$
$113$	−1.64175	−	0.947866i	−0.154443	−	0.0891677i	−0.575230	+	0.817992i	$0.695087\pi$
$114$	3.77152	−	2.43437i	0.353235	−	0.228000i
$115$	1.23880	−	4.62328i	0.115519	−	0.431123i
$116$	9.31767			0.865124
$117$		0			0
$118$	3.84764			0.354204
$119$	−3.82947	+	14.2918i	−0.351047	+	1.31013i
$120$	−5.35118	+	3.45398i	−0.488494	+	0.315304i
$121$	10.0228	+	5.78669i	0.911168	+	0.526063i
$122$	3.80811	+	3.80811i	0.344770	+	0.344770i
$123$	−0.551214	−	1.71265i	−0.0497013	−	0.154424i
$124$	0.748144	−	0.200465i	0.0671853	−	0.0180022i
$125$	−7.98448	+	7.98448i	−0.714153	+	0.714153i
$126$	−5.32485	−	2.40634i	−0.474375	−	0.214374i
$127$	6.16154	−	3.55737i	0.546748	−	0.315665i	−0.201061	−	0.979579i	$-0.564439\pi$
$127$	6.16154	−	3.55737i	0.546748	−	0.315665i	0.747810	+	0.663913i	$0.231106\pi$
$128$	9.25388	+	2.47957i	0.817936	+	0.219165i
$129$	−13.0923	+	0.649644i	−1.15272	+	0.0571980i
$130$		0			0
$131$			5.36072i			0.468368i	0.972192	+	0.234184i	$0.0752419\pi$
$131$			5.36072i			0.468368i	−0.972192	+	0.234184i	$0.924758\pi$
$132$	−11.3926	−	2.45470i	−0.991600	−	0.213654i
$133$	4.32327	+	7.48813i	0.374875	+	0.649303i
$134$	2.45314	−	4.24897i	0.211919	−	0.367055i
$135$	−4.35190	+	5.88600i	−0.374552	+	0.506586i
$136$	3.92120	+	14.6341i	0.336240	+	1.25487i
$137$	−1.25278	−	4.67544i	−0.107032	−	0.399450i	0.891536	−	0.452951i	$-0.149629\pi$
$137$	−1.25278	−	4.67544i	−0.107032	−	0.399450i	−0.998568	+	0.0535011i	$0.982962\pi$
$138$	3.01800	−	3.33314i	0.256909	−	0.283736i
$139$	−5.89404	+	10.2088i	−0.499926	+	0.865897i	−1.00000		8.58189e-5i	$-0.999973\pi$
$139$	−5.89404	+	10.2088i	−0.499926	+	0.865897i	0.500074	+	0.865982i	$0.333306\pi$
$140$	−2.54287	−	4.40438i	−0.214912	−	0.372238i
$141$	−0.125661	+	0.583210i	−0.0105826	+	0.0491152i
$142$			7.33971i			0.615935i
$143$		0			0
$144$	2.50143	−	0.248856i	0.208453	−	0.0207380i
$145$	−8.95300	−	2.39895i	−0.743506	−	0.199222i
$146$	−5.65881	+	3.26712i	−0.468327	+	0.270389i
$147$	−0.396655	+	0.773157i	−0.0327155	+	0.0637689i
$148$	−8.40827	+	8.40827i	−0.691156	+	0.691156i
$149$	−6.65319	+	1.78272i	−0.545050	+	0.146046i	−0.520829	−	0.853661i	$-0.674377\pi$
$149$	−6.65319	+	1.78272i	−0.545050	+	0.146046i	−0.0242209	+	0.999707i	$0.507711\pi$
$150$	−3.79877	+	1.22263i	−0.310168	+	0.0998271i
$151$	12.2053	+	12.2053i	0.993251	+	0.993251i	0.999977	−	0.00672628i	$-0.00214106\pi$
$151$	12.2053	+	12.2053i	0.993251	+	0.993251i	−0.00672628	+	0.999977i	$0.502141\pi$
$152$	7.66750	+	4.42683i	0.621916	+	0.359063i
$153$	10.1564	+	14.1438i	0.821095	+	1.14346i
$154$	−2.39516	+	8.93884i	−0.193007	+	0.720313i
$155$	−0.770475			−0.0618861
$156$		0			0
$157$	−13.4410			−1.07271			−0.536355	−	0.843993i	$-0.680199\pi$
$157$	−13.4410			−1.07271			−0.536355	+	0.843993i	$0.680199\pi$
$158$	1.73519	−	6.47580i	0.138044	−	0.515187i
$159$	1.94644	+	3.01558i	0.154363	+	0.239151i
$160$	−7.15019	−	4.12816i	−0.565272	−	0.326360i
$161$	6.12428	+	6.12428i	0.482661	+	0.482661i
$162$	−6.16155	+	3.05363i	−0.484097	+	0.239916i
$163$	−6.14766	+	1.64726i	−0.481522	+	0.129023i	−0.491411	−	0.870928i	$-0.663519\pi$
$163$	−6.14766	+	1.64726i	−0.481522	+	0.129023i	0.00988942	+	0.999951i	$0.496852\pi$
$164$	1.04019	−	1.04019i	0.0812256	−	0.0812256i
$165$	10.3147	+	5.29180i	0.803002	+	0.411966i
$166$	7.78448	−	4.49437i	0.604193	−	0.348831i
$167$	−4.23233	−	1.13405i	−0.327507	−	0.0877553i	0.0913190	−	0.995822i	$-0.470892\pi$
$167$	−4.23233	−	1.13405i	−0.327507	−	0.0877553i	−0.418826	+	0.908066i	$0.637558\pi$
$168$	−0.571170	−	11.5108i	−0.0440667	−	0.888080i
$169$		0			0
$170$		−	6.24767i		−	0.479174i
$171$	10.0414	+	1.64769i	0.767886	+	0.126002i
$172$	−5.35894	−	9.28195i	−0.408615	−	0.707742i
$173$	−2.16677	+	3.75296i	−0.164737	+	0.285332i	−0.936562	−	0.350503i	$-0.886011\pi$
$173$	−2.16677	+	3.75296i	−0.164737	+	0.285332i	0.771825	+	0.635835i	$0.219344\pi$
$174$	−6.45464	−	5.84436i	−0.489325	−	0.443060i
$175$	−1.98949	−	7.42488i	−0.150391	−	0.561268i
$176$	−1.03039	−	3.84546i	−0.0776685	−	0.289863i
$177$	6.46546	+	5.85416i	0.485974	+	0.440025i
$178$	5.20058	−	9.00767i	0.389800	−	0.675153i
$179$	−6.99613	−	12.1177i	−0.522916	−	0.905716i	−0.999644	−	0.0266660i	$-0.991511\pi$
$179$	−6.99613	−	12.1177i	−0.522916	−	0.905716i	0.476729	−	0.879050i	$-0.341822\pi$
$180$	−5.90617	−	0.969142i	−0.440220	−	0.0722356i
$181$			0.976007i			0.0725460i	0.999342	+	0.0362730i	$0.0115486\pi$
$181$			0.976007i			0.0725460i	−0.999342	+	0.0362730i	$0.988451\pi$
$182$		0			0
$183$	0.605020	+	12.1930i	0.0447244	+	0.901334i
$184$	8.56632	+	2.29534i	0.631518	+	0.169215i
$185$	10.2440	−	5.91438i	0.753154	−	0.434834i
$186$	−0.644001	−	0.330393i	−0.0472204	−	0.0242256i
$187$	19.4996	−	19.4996i	1.42595	−	1.42595i
$188$	−0.471174	+	0.126251i	−0.0343639	+	0.00920777i
$189$	−5.28648	−	12.1453i	−0.384535	−	0.883437i
$190$	−2.58168	−	2.58168i	−0.187295	−	0.187295i
$191$	−14.8153	−	8.55364i	−1.07200	−	0.618920i	−0.143273	−	0.989683i	$-0.545763\pi$
$191$	−14.8153	−	8.55364i	−1.07200	−	0.618920i	−0.928727	+	0.370763i	$0.879096\pi$
$192$	−2.63212	−	4.07788i	−0.189957	−	0.294296i
$193$	0.657172	−	2.45260i	0.0473043	−	0.176542i	−0.938232	−	0.346007i	$-0.887537\pi$
$193$	0.657172	−	2.45260i	0.0473043	−	0.176542i	0.985536	+	0.169465i	$0.0542040\pi$
$194$	−1.45013			−0.104114
$195$		0			0
$196$	−0.710497			−0.0507498
$197$	4.62128	−	17.2469i	0.329253	−	1.22879i	−0.580714	−	0.814108i	$-0.697227\pi$
$197$	4.62128	−	17.2469i	0.329253	−	1.22879i	0.909967	−	0.414681i	$-0.136107\pi$
$198$	6.35235	+	8.84628i	0.451442	+	0.628678i
$199$	−2.26011	−	1.30487i	−0.160215	−	0.0925001i	0.417749	−	0.908563i	$-0.362819\pi$
$199$	−2.26011	−	1.30487i	−0.160215	−	0.0925001i	−0.577964	+	0.816062i	$0.696153\pi$
$200$	−5.56558	−	5.56558i	−0.393546	−	0.393546i
$201$	10.5870	−	3.40740i	0.746746	−	0.240339i
$202$	−1.52604	+	0.408902i	−0.107372	+	0.0287702i
$203$	11.8597	−	11.8597i	0.832387	−	0.832387i
$204$	−6.49876	+	12.6673i	−0.455004	+	0.886891i
$205$	−1.26730	+	0.731673i	−0.0885117	+	0.0511023i
$206$	−9.87634	−	2.64636i	−0.688117	−	0.184381i
$207$	10.1427	−	1.00905i	0.704965	−	0.0701337i
$208$		0			0
$209$		−	16.1154i		−	1.11473i
$210$	−1.00105	+	4.64603i	−0.0690792	+	0.320606i
$211$	−6.77213	−	11.7297i	−0.466213	−	0.807504i	0.533042	−	0.846088i	$-0.321049\pi$
$211$	−6.77213	−	11.7297i	−0.466213	−	0.807504i	−0.999255	+	0.0385841i	$0.987715\pi$
$212$	−1.46732	+	2.54148i	−0.100776	+	0.174550i
$213$	−11.1673	+	12.3334i	−0.765171	+	0.845072i
$214$	1.48758	+	5.55172i	0.101689	+	0.379507i
$215$	2.75945	+	10.2984i	0.188193	+	0.702345i
$216$	−10.9060	−	8.06349i	−0.742058	−	0.548651i
$217$	0.697096	−	1.20741i	0.0473220	−	0.0819641i
$218$	1.13748	+	1.97018i	0.0770402	+	0.133437i
$219$	−14.4798	−	3.11987i	−0.978453	−	0.210822i
$220$			9.47879i			0.639060i
$221$		0			0
$222$	11.0986	−	0.550716i	0.744891	−	0.0369616i
$223$	−10.0034	−	2.68041i	−0.669879	−	0.179494i	−0.0921788	−	0.995742i	$-0.529383\pi$
$223$	−10.0034	−	2.68041i	−0.669879	−	0.179494i	−0.577700	+	0.816249i	$0.696050\pi$
$224$	12.9384	−	7.47001i	0.864485	−	0.499111i
$225$	−8.24354	−	3.72532i	−0.549569	−	0.248355i
$226$	−1.02424	+	1.02424i	−0.0681314	+	0.0681314i
$227$	0.0638035	−	0.0170961i	0.00423478	−	0.00113471i	−0.256701	−	0.966491i	$-0.582636\pi$
$227$	0.0638035	−	0.0170961i	0.00423478	−	0.00113471i	0.260936	+	0.965356i	$0.415969\pi$
$228$	2.54900	+	7.91989i	0.168812	+	0.524507i
$229$	−19.2246	−	19.2246i	−1.27040	−	1.27040i	−0.945880	−	0.324517i	$-0.894798\pi$
$229$	−19.2246	−	19.2246i	−1.27040	−	1.27040i	−0.324517	−	0.945880i	$-0.605202\pi$
$230$	−3.16721	−	1.82859i	−0.208839	−	0.120573i
$231$	−17.6251	+	11.3763i	−1.15965	+	0.748508i
$232$	4.44493	−	16.5887i	0.291824	−	1.08910i
$233$	16.5148			1.08192			0.540961	−	0.841047i	$-0.318061\pi$
$233$	16.5148			1.08192			0.540961	+	0.841047i	$0.318061\pi$
$234$		0			0
$235$	0.485238			0.0316534
$236$	−1.84574	+	6.88839i	−0.120147	+	0.448396i
$237$	12.7686	−	8.24166i	0.829412	−	0.535354i
$238$	9.79067	+	5.65265i	0.634635	+	0.366407i
$239$	−18.7548	−	18.7548i	−1.21315	−	1.21315i	−0.969985	−	0.243165i	$-0.921814\pi$
$239$	−18.7548	−	18.7548i	−1.21315	−	1.21315i	−0.243165	−	0.969985i	$-0.578186\pi$
$240$	−0.626400	−	1.94626i	−0.0404339	−	0.125630i
$241$	4.55333	−	1.22006i	0.293306	−	0.0785911i	−0.109166	−	0.994024i	$-0.534818\pi$
$241$	4.55333	−	1.22006i	0.293306	−	0.0785911i	0.402472	+	0.915432i	$0.368151\pi$
$242$	6.25295	−	6.25295i	0.401955	−	0.401955i
$243$	−14.9998	−	4.24352i	−0.962235	−	0.272222i
$244$	−8.64438	+	4.99084i	−0.553400	+	0.319506i
$245$	0.682689	+	0.182926i	0.0436154	+	0.0116867i
$246$	−1.37302	+	0.0681296i	−0.0875406	+	0.00434378i
$247$		0			0
$248$		−	1.42759i		−	0.0906519i
$249$	19.9189	+	4.29182i	1.26231	+	0.271983i
$250$	4.31391	+	7.47191i	0.272835	+	0.472565i
$251$	−7.02308	+	12.1643i	−0.443293	+	0.767806i	−0.997932	−	0.0642852i	$-0.979523\pi$
$251$	−7.02308	+	12.1643i	−0.443293	+	0.767806i	0.554638	+	0.832091i	$0.312857\pi$
$252$	6.86241	−	8.37868i	0.432291	−	0.527807i
$253$	−4.17797	−	15.5924i	−0.262666	−	0.980285i
$254$	−1.40700	−	5.25100i	−0.0882831	−	0.329477i
$255$	9.50577	−	10.4984i	0.595275	−	0.657434i
$256$	6.46228	−	11.1930i	0.403893	−	0.699563i
$257$	9.76740	+	16.9176i	0.609274	+	1.05529i	0.991360	+	0.131167i	$0.0418723\pi$
$257$	9.76740	+	16.9176i	0.609274	+	1.05529i	−0.382087	+	0.924127i	$0.624794\pi$
$258$	−2.10965	+	9.79121i	−0.131341	+	0.609574i
$259$			21.4044i			1.33000i
$260$		0			0
$261$	−1.95403	−	19.6413i	−0.120951	−	1.21577i
$262$	3.95646	+	1.06013i	0.244431	+	0.0654950i
$263$	−1.13335	+	0.654340i	−0.0698854	+	0.0403484i	−0.534536	−	0.845146i	$-0.679513\pi$
$263$	−1.13335	+	0.654340i	−0.0698854	+	0.0403484i	0.464650	+	0.885494i	$0.346180\pi$
$264$	−9.80500	+	19.1118i	−0.603456	+	1.17625i
$265$	2.06423	−	2.06423i	0.126805	−	0.126805i
$266$	6.38155	−	1.70993i	0.391278	−	0.104843i
$267$	22.4440	−	7.22356i	1.37355	−	0.442075i
$268$	6.43009	+	6.43009i	0.392780	+	0.392780i
$269$	24.4901	+	14.1394i	1.49319	+	0.862093i	0.999969	−	0.00781215i	$-0.00248671\pi$
$269$	24.4901	+	14.1394i	1.49319	+	0.862093i	0.493219	+	0.869905i	$0.335820\pi$
$270$	3.48351	+	4.37591i	0.212000	+	0.266309i
$271$	1.84107	−	6.87097i	0.111837	−	0.417382i	−0.887194	−	0.461397i	$-0.847348\pi$
$271$	1.84107	−	6.87097i	0.111837	−	0.417382i	0.999031	+	0.0440153i	$0.0140150\pi$
$272$	−4.86350			−0.294893
$273$		0			0
$274$	−3.69843			−0.223431
$275$	−3.70800	+	13.8385i	−0.223601	+	0.834491i
$276$	4.51953	+	7.00201i	0.272044	+	0.421471i
$277$	−10.6104	−	6.12593i	−0.637518	−	0.368071i	0.146140	−	0.989264i	$-0.453315\pi$
$277$	−10.6104	−	6.12593i	−0.637518	−	0.368071i	−0.783658	+	0.621193i	$0.786648\pi$
$278$	6.36894	+	6.36894i	0.381984	+	0.381984i
$279$	−0.579468	−	1.53502i	−0.0346918	−	0.0918995i
$280$	−9.05440	+	2.42612i	−0.541104	+	0.144988i
$281$	17.0443	−	17.0443i	1.01678	−	1.01678i	0.0169217	−	0.999857i	$-0.494613\pi$
$281$	17.0443	−	17.0443i	1.01678	−	1.01678i	0.999857	−	0.0169217i	$-0.00538659\pi$
$282$	0.405585	+	0.208078i	0.0241522	+	0.0123909i
$283$	10.6763	−	6.16394i	0.634638	−	0.366408i	−0.147908	−	0.989001i	$-0.547254\pi$
$283$	10.6763	−	6.16394i	0.634638	−	0.366408i	0.782546	+	0.622593i	$0.213921\pi$
$284$	−13.1402	−	3.52091i	−0.779727	−	0.208927i
$285$	−0.410170	−	8.26619i	−0.0242964	−	0.489647i
$286$		0			0
$287$		−	2.64796i		−	0.156304i
$288$	2.84698	−	17.3501i	0.167760	−	1.02237i
$289$	−8.34439	−	14.4529i	−0.490846	−	0.850171i
$290$	−3.54107	+	6.13331i	−0.207939	+	0.360160i
$291$	−2.43676	−	2.20637i	−0.142845	−	0.129339i
$292$	−3.13451	−	11.6982i	−0.183434	−	0.684583i
$293$	−4.06923	−	15.1866i	−0.237727	−	0.887209i	−0.976901	−	0.213694i	$-0.931450\pi$
$293$	−4.06923	−	15.1866i	−0.237727	−	0.887209i	0.739174	−	0.673515i	$-0.235216\pi$
$294$	0.492183	+	0.445648i	0.0287047	+	0.0259907i
$295$	3.54700	−	6.14359i	0.206514	−	0.357693i
$296$	10.9586	+	18.9808i	0.636953	+	1.10324i
$297$	−2.78527	+	24.5301i	−0.161617	+	1.42338i
$298$			5.26290i			0.304872i
$299$		0			0
$300$	−0.366564	−	7.38739i	−0.0211636	−	0.426511i
$301$	−18.6352	−	4.99328i	−1.07411	−	0.287808i
$302$	11.4217	−	6.59435i	0.657248	−	0.379462i
$303$	−3.18646	−	1.63476i	−0.183057	−	0.0939142i
$304$	−2.00971	+	2.00971i	−0.115265	+	0.115265i
$305$	9.59101	−	2.56990i	0.549180	−	0.147152i
$306$	12.4473	−	4.69882i	0.711563	−	0.268613i
$307$	−1.83038	−	1.83038i	−0.104465	−	0.104465i	0.652942	−	0.757408i	$-0.273534\pi$
$307$	−1.83038	−	1.83038i	−0.104465	−	0.104465i	−0.757408	+	0.652942i	$0.773534\pi$
$308$	−14.8541	−	8.57604i	−0.846393	−	0.488665i
$309$	−12.5695	−	19.4736i	−0.715053	−	1.10782i
$310$	−0.152368	+	0.568646i	−0.00865393	+	0.0322969i
$311$	15.2844			0.866701			0.433350	−	0.901226i	$-0.357331\pi$
$311$	15.2844			0.866701			0.433350	+	0.901226i	$0.357331\pi$
$312$		0			0
$313$	31.4063			1.77519			0.887593	−	0.460628i	$-0.152376\pi$
$313$	31.4063			1.77519			0.887593	+	0.460628i	$0.152376\pi$
$314$	−2.65808	+	9.92008i	−0.150004	+	0.559823i
$315$	−8.75103	+	6.28394i	−0.493065	+	0.354060i
$316$	10.7612	+	6.21297i	0.605364	+	0.349507i
$317$	−11.8144	−	11.8144i	−0.663565	−	0.663565i	0.292654	−	0.956219i	$-0.405462\pi$
$317$	−11.8144	−	11.8144i	−0.663565	−	0.663565i	−0.956219	+	0.292654i	$0.905462\pi$
$318$	2.61056	−	0.840206i	0.146393	−	0.0471164i
$319$	−30.1947	+	8.09065i	−1.69058	+	0.452989i
$320$	−2.79140	+	2.79140i	−0.156044	+	0.156044i
$321$	−5.94721	+	11.5923i	−0.331941	+	0.647017i
$322$	5.73113	−	3.30887i	0.319383	−	0.184396i
$323$	−19.0164	−	5.09544i	−1.05810	−	0.283518i
$324$	−2.51115	−	12.4958i	−0.139508	−	0.694211i
$325$		0			0
$326$			4.86301i			0.269337i
$327$	−1.08622	+	5.04130i	−0.0600681	+	0.278785i
$328$	−1.35569	−	2.34813i	−0.0748556	−	0.129654i
$329$	−0.439024	+	0.760412i	−0.0242042	+	0.0419229i
$330$	5.94542	−	6.56625i	0.327285	−	0.361460i
$331$	5.81579	+	21.7048i	0.319665	+	1.19300i	0.919568	+	0.392932i	$0.128539\pi$
$331$	5.81579	+	21.7048i	0.319665	+	1.19300i	−0.599903	+	0.800073i	$0.704794\pi$
$332$	4.31196	+	16.0924i	0.236649	+	0.883188i
$333$	19.4877	+	15.9611i	1.06792	+	0.874660i
$334$	−1.67396	+	2.89938i	−0.0915949	+	0.158647i
$335$	−4.52293	−	7.83394i	−0.247114	−	0.428014i
$336$	3.61670	+	0.779270i	0.197307	+	0.0425127i
$337$		−	9.19516i		−	0.500892i	−0.968131	−	0.250446i	$-0.919423\pi$
$337$		−	9.19516i		−	0.500892i	0.968131	−	0.250446i	$-0.0805773\pi$
$338$		0			0
$339$	−3.27947	+	0.162728i	−0.178116	+	0.00883817i
$340$	11.1851	+	2.99705i	0.606599	+	0.162538i
$341$	−2.25036	+	1.29925i	−0.121864	+	0.0703581i
$342$	3.20185	−	7.08517i	0.173136	−	0.383122i
$343$	−13.5221	+	13.5221i	−0.730125	+	0.730125i
$344$	−19.0816	+	5.11289i	−1.02881	+	0.275669i
$345$	−2.53989	−	7.89158i	−0.136743	−	0.424868i
$346$	2.34136	+	2.34136i	0.125872	+	0.125872i
$347$	−9.72982	−	5.61751i	−0.522324	−	0.301564i	0.215561	−	0.976490i	$-0.430842\pi$
$347$	−9.72982	−	5.61751i	−0.522324	−	0.301564i	−0.737885	+	0.674926i	$0.764175\pi$
$348$	13.5594	−	8.75209i	0.726861	−	0.469161i
$349$	9.02423	−	33.6789i	0.483056	−	1.80279i	−0.105605	−	0.994408i	$-0.533678\pi$
$349$	9.02423	−	33.6789i	0.483056	−	1.80279i	0.588660	−	0.808380i	$-0.299656\pi$
$350$	−5.87334			−0.313943
$351$		0			0
$352$	−27.8451			−1.48415
$353$	8.33550	−	31.1085i	0.443654	−	1.65574i	−0.275812	−	0.961212i	$-0.588947\pi$
$353$	8.33550	−	31.1085i	0.443654	−	1.65574i	0.719466	−	0.694528i	$-0.244387\pi$
$354$	5.59923	−	3.61409i	0.297596	−	0.192087i
$355$	11.7194	+	6.76621i	0.622002	+	0.359113i
$356$	13.6316	+	13.6316i	0.722472	+	0.722472i
$357$	7.85148	+	24.3950i	0.415544	+	1.29112i
$358$	−10.3269	+	2.76709i	−0.545795	+	0.146245i
$359$	−20.8500	+	20.8500i	−1.10042	+	1.10042i	−0.106064	+	0.994359i	$0.533825\pi$
$359$	−20.8500	+	20.8500i	−1.10042	+	1.10042i	−0.994359	+	0.106064i	$0.966175\pi$
$360$	−4.54291	+	10.0527i	−0.239433	+	0.529826i
$361$	6.49088	−	3.74751i	0.341625	−	0.197237i
$362$	0.720338	+	0.193014i	0.0378601	+	0.0101446i
$363$	20.0211	−	0.993449i	1.05083	−	0.0521425i
$364$		0			0
$365$			12.0473i			0.630587i
$366$	9.11865	+	1.96474i	0.476640	+	0.102699i
$367$	10.6590	+	18.4619i	0.556395	+	0.963705i	0.997794	+	0.0663937i	$0.0211493\pi$
$367$	10.6590	+	18.4619i	0.556395	+	0.963705i	−0.441398	+	0.897311i	$0.645517\pi$
$368$	−1.42347	+	2.46551i	−0.0742032	+	0.128524i
$369$	−2.41084	−	1.97456i	−0.125503	−	0.102791i
$370$	−2.33924	−	8.73016i	−0.121611	−	0.453859i
$371$	1.36720	+	5.10248i	0.0709817	+	0.264907i
$372$	0.900431	−	0.994455i	0.0466851	−	0.0515601i
$373$	6.95177	−	12.0408i	0.359949	−	0.623450i	−0.628003	−	0.778211i	$-0.716127\pi$
$373$	6.95177	−	12.0408i	0.359949	−	0.623450i	0.987952	+	0.154761i	$0.0494607\pi$
$374$	−10.5354	−	18.2478i	−0.544772	−	0.943572i
$375$	−4.11949	+	19.1191i	−0.212729	+	0.987307i
$376$			0.899081i			0.0463666i
$377$		0			0
$378$	−10.0092	+	1.49983i	−0.514818	+	0.0771430i
$379$	−33.5805	−	8.99786i	−1.72491	−	0.462189i	−0.745912	−	0.666044i	$-0.767986\pi$
$379$	−33.5805	−	8.99786i	−1.72491	−	0.462189i	−0.979001	+	0.203855i	$0.934653\pi$
$380$	5.86041	−	3.38351i	0.300633	−	0.173570i
$381$	5.62507	−	10.9644i	0.288181	−	0.561721i
$382$	−9.24284	+	9.24284i	−0.472905	+	0.472905i
$383$	16.2968	−	4.36672i	0.832729	−	0.223129i	0.182825	−	0.983145i	$-0.441476\pi$
$383$	16.2968	−	4.36672i	0.832729	−	0.223129i	0.649904	+	0.760016i	$0.274809\pi$
$384$	15.7957	−	5.08381i	0.806069	−	0.259432i
$385$	12.0648	+	12.0648i	0.614878	+	0.614878i
$386$	−1.68017	−	0.970045i	−0.0855183	−	0.0493740i
$387$	−18.4422	+	13.2430i	−0.937471	+	0.673180i
$388$	0.695638	−	2.59616i	0.0353157	−	0.131800i
$389$	−35.0012			−1.77463			−0.887315	−	0.461164i	$-0.847432\pi$
$389$	−35.0012			−1.77463			−0.887315	+	0.461164i	$0.847432\pi$
$390$		0			0
$391$	−19.7203			−0.997297
$392$	−0.338938	+	1.26493i	−0.0171189	+	0.0638887i
$393$	5.03533	+	7.80112i	0.253999	+	0.393515i
$394$	−11.8151	−	6.82144i	−0.595235	−	0.343659i
$395$	−8.74040	−	8.74040i	−0.439777	−	0.439777i
$396$	−18.8847	+	7.12891i	−0.948990	+	0.358241i
$397$	1.28080	−	0.343188i	0.0642813	−	0.0172241i	−0.226535	−	0.974003i	$-0.572740\pi$
$397$	1.28080	−	0.343188i	0.0642813	−	0.0172241i	0.290816	+	0.956779i	$0.406073\pi$
$398$	−1.41001	+	1.41001i	−0.0706776	+	0.0706776i
$399$	13.3250	+	6.83616i	0.667084	+	0.342236i
$400$	2.18818	−	1.26335i	0.109409	−	0.0631673i
$401$	25.6759	+	6.87983i	1.28219	+	0.343562i	0.834689	−	0.550721i	$-0.185647\pi$
$401$	25.6759	+	6.87983i	1.28219	+	0.343562i	0.447502	+	0.894283i	$0.352314\pi$
$402$	−0.421151	−	8.48750i	−0.0210051	−	0.423318i
$403$		0			0
$404$		−	2.92821i		−	0.145684i
$405$	−0.804326	+	12.6533i	−0.0399673	+	0.628746i
$406$	−6.40764	−	11.0984i	−0.318006	−	0.550802i
$407$	19.9467	−	34.5487i	0.988722	−	1.71252i
$408$	19.4521	+	17.6129i	0.963023	+	0.871970i
$409$	2.43275	+	9.07916i	0.120292	+	0.448936i	0.999628	−	0.0272657i	$-0.00868002\pi$
$409$	2.43275	+	9.07916i	0.120292	+	0.448936i	−0.879336	+	0.476201i	$0.842013\pi$
$410$	0.289389	+	1.08002i	0.0142919	+	0.0533382i
$411$	−6.21473	−	5.62713i	−0.306550	−	0.277566i
$412$	9.47549	−	16.4120i	0.466824	−	0.808563i
$413$	6.41838	+	11.1170i	0.315828	+	0.547030i
$414$	1.26108	−	7.68531i	0.0619787	−	0.377713i
$415$		−	16.5728i		−	0.813526i
$416$		0			0
$417$	1.01188	+	20.3925i	0.0495519	+	0.998623i
$418$	−11.8939	−	3.18696i	−0.581750	−	0.155879i
$419$	−27.6079	+	15.9394i	−1.34873	+	0.778692i	−0.988070	−	0.154003i	$-0.950783\pi$
$419$	−27.6079	+	15.9394i	−1.34873	+	0.778692i	−0.360664	+	0.932696i	$0.617450\pi$
$420$	−7.83752	−	4.02090i	−0.382432	−	0.196200i
$421$	19.6414	−	19.6414i	0.957263	−	0.957263i	−0.0418609	−	0.999123i	$-0.513329\pi$
$421$	19.6414	−	19.6414i	0.957263	−	0.957263i	0.999123	+	0.0418609i	$0.0133286\pi$
$422$	−9.99628	+	2.67850i	−0.486612	+	0.130387i
$423$	0.364943	+	0.966743i	0.0177441	+	0.0470046i
$424$	3.82475	+	3.82475i	0.185746	+	0.185746i
$425$	15.1572	+	8.75101i	0.735232	+	0.424486i
$426$	6.89419	+	10.6810i	0.334025	+	0.517497i
$427$	−4.65030	+	17.3552i	−0.225044	+	0.839875i
$428$	−10.6528			−0.514921
$429$		0			0
$430$	8.14640			0.392854
$431$	1.23002	−	4.59049i	0.0592479	−	0.221116i	−0.929954	−	0.367676i	$-0.880154\pi$
$431$	1.23002	−	4.59049i	0.0592479	−	0.221116i	0.989202	+	0.146560i	$0.0468202\pi$
$432$	3.40643	−	2.71174i	0.163892	−	0.130469i
$433$	1.78345	+	1.02968i	0.0857072	+	0.0494831i	0.542241	−	0.840223i	$-0.317576\pi$
$433$	1.78345	+	1.02968i	0.0857072	+	0.0494831i	−0.456534	+	0.889706i	$0.650909\pi$
$434$	−0.753264	−	0.753264i	−0.0361578	−	0.0361578i
$435$	−15.2821	+	4.91851i	−0.732719	+	0.235825i
$436$	−4.07285	+	1.09132i	−0.195054	+	0.0522646i
$437$	−8.14889	+	8.14889i	−0.389814	+	0.389814i
$438$	−5.16611	+	10.0698i	−0.246846	+	0.481151i
$439$	11.1416	−	6.43260i	0.531759	−	0.307011i	−0.209973	−	0.977707i	$-0.567338\pi$
$439$	11.1416	−	6.43260i	0.531759	−	0.307011i	0.741733	+	0.670696i	$0.234004\pi$
$440$	16.8756	+	4.52179i	0.804511	+	0.215568i
$441$	0.149000	+	1.49770i	0.00709522	+	0.0713193i
$442$		0			0
$443$			14.4060i			0.684449i	0.939618	+	0.342224i	$0.111180\pi$
$443$			14.4060i			0.684449i	−0.939618	+	0.342224i	$0.888820\pi$
$444$	−4.33814	+	20.1339i	−0.205879	+	0.955514i
$445$	−9.58845	−	16.6077i	−0.454536	−	0.787280i
$446$	−3.95653	+	6.85291i	−0.187347	+	0.324495i
$447$	−8.00746	+	8.84361i	−0.378740	+	0.418288i
$448$	−1.84883	−	6.89992i	−0.0873490	−	0.325991i
$449$	−4.24760	−	15.8522i	−0.200456	−	0.748113i	−0.990787	−	0.135432i	$-0.956758\pi$
$449$	−4.24760	−	15.8522i	−0.200456	−	0.748113i	0.790330	−	0.612681i	$-0.209909\pi$
$450$	−4.37969	+	5.34739i	−0.206461	+	0.252079i
$451$	−2.46763	+	4.27406i	−0.116196	+	0.201257i
$452$	−1.34235	−	2.32502i	−0.0631388	−	0.109360i
$453$	29.2260	+	6.29715i	1.37316	+	0.295866i
$454$		−	0.0504707i		−	0.00236871i
$455$		0			0
$456$	15.3162	−	0.759991i	0.717245	−	0.0355898i
$457$	22.0326	+	5.90361i	1.03064	+	0.276159i	0.734230	−	0.678901i	$-0.237544\pi$
$457$	22.0326	+	5.90361i	1.03064	+	0.276159i	0.296411	+	0.955061i	$0.404210\pi$
$458$	−17.9905	+	10.3868i	−0.840639	+	0.485343i
$459$	28.0652	+	11.0427i	1.30997	+	0.515428i
$460$	4.79303	−	4.79303i	0.223476	−	0.223476i
$461$	28.5168	−	7.64107i	1.32816	−	0.355880i	0.476132	−	0.879374i	$-0.342038\pi$
$461$	28.5168	−	7.64107i	1.32816	−	0.355880i	0.852030	+	0.523494i	$0.175372\pi$
$462$	4.91074	+	15.2579i	0.228468	+	0.709862i
$463$	−25.6118	−	25.6118i	−1.19028	−	1.19028i	−0.976988	−	0.213295i	$-0.931580\pi$
$463$	−25.6118	−	25.6118i	−1.19028	−	1.19028i	−0.213295	−	0.976988i	$-0.568420\pi$
$464$	4.77448	+	2.75654i	0.221649	+	0.127969i
$465$	−1.12122	+	0.723708i	−0.0519955	+	0.0335611i
$466$	3.26595	−	12.1887i	0.151292	−	0.564631i
$467$	14.0544			0.650361			0.325180	−	0.945652i	$-0.394575\pi$
$467$	14.0544			0.650361			0.325180	+	0.945652i	$0.394575\pi$
$468$		0			0
$469$	16.3687			0.755835
$470$	0.0959600	−	0.358128i	0.00442630	−	0.0165192i
$471$	−19.5599	+	12.6251i	−0.901271	+	0.581736i
$472$	11.3832	+	6.57212i	0.523956	+	0.302506i
$473$	25.4257	+	25.4257i	1.16908	+	1.16908i
$474$	−3.55762	−	11.0537i	−0.163407	−	0.507713i
$475$	9.87944	−	2.64719i	0.453300	−	0.121461i
$476$	−14.8165	+	14.8165i	−0.679114	+	0.679114i
$477$	5.66507	+	2.56009i	0.259386	+	0.117219i
$478$	−17.5509	+	10.1330i	−0.802758	+	0.463472i
$479$	−12.4179	−	3.32737i	−0.567389	−	0.152031i	−0.0362900	−	0.999341i	$-0.511554\pi$
$479$	−12.4179	−	3.32737i	−0.567389	−	0.152031i	−0.531099	+	0.847310i	$0.678221\pi$
$480$	−14.2828	+	0.708716i	−0.651918	+	0.0323483i
$481$		0			0
$482$		−	3.60185i		−	0.164060i
$483$	14.6648	+	3.15975i	0.667273	+	0.143773i
$484$	8.19500	+	14.1942i	0.372500	+	0.645189i
$485$	−1.33683	+	2.31545i	−0.0607021	+	0.105139i
$486$	−6.09824	+	10.2313i	−0.276622	+	0.464102i
$487$	−7.01541	−	26.1819i	−0.317898	−	1.18641i	−0.921261	−	0.388946i	$-0.872839\pi$
$487$	−7.01541	−	26.1819i	−0.317898	−	1.18641i	0.603362	−	0.797467i	$-0.293827\pi$
$488$	4.76169	+	17.7709i	0.215552	+	0.804449i
$489$	−7.39903	+	8.17165i	−0.334596	+	0.369535i
$490$	0.270016	−	0.467681i	0.0121981	−	0.0211277i
$491$	−6.27068	−	10.8611i	−0.282992	−	0.490156i	0.689128	−	0.724639i	$-0.257994\pi$
$491$	−6.27068	−	10.8611i	−0.282992	−	0.490156i	−0.972120	+	0.234483i	$0.924660\pi$
$492$	0.536675	−	2.49079i	0.0241952	−	0.112293i
$493$			38.1884i			1.71992i
$494$		0			0
$495$	19.9810	−	1.98782i	0.898079	−	0.0893457i
$496$	0.442663	+	0.118611i	0.0198761	+	0.00532580i
$497$	−21.2066	+	12.2436i	−0.951244	+	0.549201i
$498$	7.10670	−	13.8523i	0.318459	−	0.620738i
$499$	−5.98039	+	5.98039i	−0.267719	+	0.267719i	−0.828180	−	0.560461i	$-0.810624\pi$
$499$	−5.98039	+	5.98039i	−0.267719	+	0.267719i	0.560461	+	0.828180i	$0.310624\pi$
$500$	−15.4463	+	4.13882i	−0.690778	+	0.185094i
$501$	−7.22425	+	2.32511i	−0.322756	+	0.103878i
$502$	7.58896	+	7.58896i	0.338712	+	0.338712i
$503$	−16.0716	−	9.27897i	−0.716599	−	0.413729i	0.0969004	−	0.995294i	$-0.469107\pi$
$503$	−16.0716	−	9.27897i	−0.716599	−	0.413729i	−0.813500	+	0.581565i	$0.802440\pi$
$504$	−11.6433	−	16.2145i	−0.518634	−	0.722251i
$505$	−0.753904	+	2.81361i	−0.0335483	+	0.125204i
$506$	−12.3341			−0.548318
$507$		0			0
$508$	10.0757			0.447039
$509$	−9.47229	+	35.3511i	−0.419852	+	1.56691i	0.355063	+	0.934842i	$0.384459\pi$
$509$	−9.47229	+	35.3511i	−0.419852	+	1.56691i	−0.774915	+	0.632066i	$0.782207\pi$
$510$	−5.86843	−	9.09184i	−0.259859	−	0.402593i
$511$	−18.8793	−	10.9000i	−0.835171	−	0.482186i
$512$	6.56566	+	6.56566i	0.290164	+	0.290164i
$513$	16.1603	−	7.03411i	0.713495	−	0.310564i
$514$	14.4176	−	3.86318i	0.635932	−	0.170397i
$515$	−13.3301	+	13.3301i	−0.587395	+	0.587395i
$516$	−16.5171	−	8.47379i	−0.727123	−	0.373038i
$517$	1.41725	−	0.818252i	0.0623307	−	0.0359867i
$518$	15.7974	+	4.23291i	0.694099	+	0.185983i
$519$	0.371988	+	7.49670i	0.0163285	+	0.329069i
$520$		0			0
$521$			32.0270i			1.40313i	0.712605	+	0.701565i	$0.247515\pi$
$521$			32.0270i			1.40313i	−0.712605	+	0.701565i	$0.752485\pi$
$522$	−14.8826	−	2.44209i	−0.651395	−	0.106887i
$523$	−8.20295	−	14.2079i	−0.358690	−	0.621269i	0.629052	−	0.777363i	$-0.283443\pi$
$523$	−8.20295	−	14.2079i	−0.358690	−	0.621269i	−0.987742	+	0.156094i	$0.950110\pi$
$524$	−3.79587	+	6.57465i	−0.165824	+	0.287215i
$525$	−9.86937	−	8.93623i	−0.430735	−	0.390009i
$526$	0.258803	+	0.965866i	0.0112843	+	0.0421138i
$527$	0.821602	+	3.06626i	0.0357896	+	0.133568i
$528$	−5.11150	−	4.62822i	−0.222450	−	0.201417i
$529$	5.72821	−	9.92154i	0.249052	−	0.431372i
$530$	−1.11528	−	1.93172i	−0.0484445	−	0.0839084i
$531$	14.9076	+	2.44618i	0.646934	+	0.106155i
$532$			12.2451i			0.530891i
$533$		0			0
$534$	−0.892826	−	17.9932i	−0.0386364	−	0.778642i
$535$	10.2358	+	2.74269i	0.442534	+	0.118577i
$536$	14.5152	−	8.38038i	0.626963	−	0.361977i
$537$	−21.5632	−	11.0626i	−0.930519	−	0.477386i
$538$	15.2786	−	15.2786i	0.658709	−	0.658709i
$539$	2.30243	−	0.616933i	0.0991725	−	0.0265732i
$540$	−9.50520	+	4.13734i	−0.409039	+	0.178043i
$541$	−10.4088	−	10.4088i	−0.447508	−	0.447508i	0.447017	−	0.894525i	$-0.352486\pi$
$541$	−10.4088	−	10.4088i	−0.447508	−	0.447508i	−0.894525	+	0.447017i	$0.852486\pi$
$542$	−4.70700	−	2.71759i	−0.202183	−	0.116730i
$543$	0.916763	+	1.42032i	0.0393421	+	0.0609518i
$544$	−8.80420	+	32.8577i	−0.377477	+	1.40876i
$545$	4.19442			0.179669
$546$		0			0
$547$	−18.0787			−0.772988			−0.386494	−	0.922292i	$-0.626314\pi$
$547$	−18.0787			−0.772988			−0.386494	+	0.922292i	$0.626314\pi$
$548$	1.77416	−	6.62126i	0.0757884	−	0.282846i
$549$	12.3334	+	17.1754i	0.526375	+	0.733030i
$550$	9.48012	+	5.47335i	0.404234	+	0.233384i
$551$	15.7803	+	15.7803i	0.672265	+	0.672265i
$552$	14.6220	−	4.70608i	0.622355	−	0.200304i
$553$	21.6050	−	5.78904i	0.918738	−	0.246175i
$554$	−6.61952	+	6.61952i	−0.281236	+	0.281236i
$555$	9.35208	−	18.2290i	0.396974	−	0.773779i
$556$	−14.4575	+	8.34702i	−0.613133	+	0.353992i
$557$	12.4314	+	3.33099i	0.526736	+	0.141138i	0.512381	−	0.858759i	$-0.328764\pi$
$557$	12.4314	+	3.33099i	0.526736	+	0.141138i	0.0143553	+	0.999897i	$0.495430\pi$
$558$	−1.24751	+	0.124109i	−0.0528114	+	0.00525396i
$559$		0			0
$560$		−	3.00914i		−	0.127159i
$561$	10.0606	−	46.6925i	0.424758	−	1.97136i
$562$	−9.20882	−	15.9501i	−0.388451	−	0.672816i
$563$	13.9437	−	24.1513i	0.587659	−	1.01785i	−0.406880	−	0.913482i	$-0.633383\pi$
$563$	13.9437	−	24.1513i	0.587659	−	1.01785i	0.994538	−	0.104373i	$-0.0332835\pi$
$564$	−0.567082	+	0.626298i	−0.0238785	+	0.0263719i
$565$	0.691209	+	2.57963i	0.0290794	+	0.108526i
$566$	−2.43795	−	9.09854i	−0.102475	−	0.382440i
$567$	−19.1011	−	12.7086i	−0.802172	−	0.533713i
$568$	−12.5369	+	21.7145i	−0.526036	+	0.911121i
$569$	−0.877082	−	1.51915i	−0.0367692	−	0.0636861i	0.847055	−	0.531505i	$-0.178373\pi$
$569$	−0.877082	−	1.51915i	−0.0367692	−	0.0636861i	−0.883824	+	0.467819i	$0.845040\pi$
$570$	−6.18194	−	1.33199i	−0.258933	−	0.0557908i
$571$		−	13.1497i		−	0.550300i	−0.961401	−	0.275150i	$-0.911273\pi$
$571$		−	13.1497i		−	0.550300i	0.961401	−	0.275150i	$-0.0887275\pi$
$572$		0			0
$573$	−29.5943	+	1.46847i	−1.23632	+	0.0613464i
$574$	−1.95431	−	0.523657i	−0.0815715	−	0.0218570i
$575$	8.87251	−	5.12255i	0.370009	−	0.213625i
$576$	−7.66071	−	3.46194i	−0.319196	−	0.144247i
$577$	2.17547	−	2.17547i	0.0905662	−	0.0905662i	−0.660372	−	0.750938i	$-0.729601\pi$
$577$	2.17547	−	2.17547i	0.0905662	−	0.0905662i	0.750938	+	0.660372i	$0.229601\pi$
$578$	−12.3171	+	3.30035i	−0.512323	+	0.137277i
$579$	−1.34739	−	4.18639i	−0.0559954	−	0.173981i
$580$	−9.28171	−	9.28171i	−0.385402	−	0.385402i
$581$	25.9711	+	14.9944i	1.07746	+	0.622073i
$582$	−2.11029	+	1.36211i	−0.0874743	+	0.0564613i
$583$	2.54819	−	9.50998i	0.105535	−	0.393863i
$584$	−22.3221			−0.923696
$585$		0			0
$586$	−12.0131			−0.496257
$587$	−3.89820	+	14.5483i	−0.160896	+	0.600472i	0.837632	+	0.546235i	$0.183939\pi$
$587$	−3.89820	+	14.5483i	−0.160896	+	0.600472i	−0.998528	+	0.0542369i	$0.982727\pi$
$588$	−1.03394	+	0.667370i	−0.0426390	+	0.0275219i
$589$	1.60656	+	0.927547i	0.0661971	+	0.0382189i
$590$	−3.83280	−	3.83280i	−0.157794	−	0.157794i
$591$	−9.47492	−	29.4391i	−0.389746	−	1.21096i
$592$	−6.79600	+	1.82098i	−0.279314	+	0.0748419i
$593$	18.1461	−	18.1461i	0.745171	−	0.745171i	−0.228397	−	0.973568i	$-0.573348\pi$
$593$	18.1461	−	18.1461i	0.745171	−	0.745171i	0.973568	+	0.228397i	$0.0733483\pi$
$594$	17.5535	+	6.90668i	0.720228	+	0.283385i
$595$	18.0513	−	10.4219i	0.740032	−	0.427258i
$596$	−9.42211	−	2.52465i	−0.385945	−	0.103414i
$597$	−4.51467	+	0.224019i	−0.184773	+	0.00916847i
$598$		0			0
$599$		−	19.9578i		−	0.815455i	−0.913104	−	0.407728i	$-0.866321\pi$
$599$		−	19.9578i		−	0.815455i	0.913104	−	0.407728i	$-0.133679\pi$
$600$	−13.3270	−	2.87149i	−0.544073	−	0.117228i
$601$	23.4640	+	40.6409i	0.957118	+	1.65778i	0.729444	+	0.684040i	$0.239779\pi$
$601$	23.4640	+	40.6409i	0.957118	+	1.65778i	0.227674	+	0.973737i	$0.426888\pi$
$602$	−7.37054	+	12.7662i	−0.300401	+	0.520310i
$603$	12.2060	−	14.9029i	0.497065	−	0.606893i
$604$	6.32670	+	23.6116i	0.257430	+	0.960741i
$605$	−4.21981	−	15.7485i	−0.171560	−	0.640269i
$606$	−1.83667	+	2.02846i	−0.0746097	+	0.0824006i
$607$	−16.7800	+	29.0639i	−0.681081	+	1.17967i	0.293570	+	0.955938i	$0.405157\pi$
$607$	−16.7800	+	29.0639i	−0.681081	+	1.17967i	−0.974651	+	0.223730i	$0.928177\pi$
$608$	9.93949	+	17.2157i	0.403099	+	0.698189i
$609$	6.11886	−	28.3985i	0.247949	−	1.15076i
$610$		−	7.58682i		−	0.307182i
$611$		0			0
$612$	2.44120	+	24.5383i	0.0986796	+	0.991901i
$613$	29.7615	+	7.97457i	1.20206	+	0.322090i	0.803640	−	0.595115i	$-0.202894\pi$
$613$	29.7615	+	7.97457i	1.20206	+	0.322090i	0.398415	+	0.917205i	$0.369560\pi$
$614$	−1.71288	+	0.988929i	−0.0691261	+	0.0399099i
$615$	−1.15695	+	2.25513i	−0.0466529	+	0.0909356i
$616$	−22.3544	+	22.3544i	−0.900685	+	0.900685i
$617$	−28.0366	+	7.51239i	−1.12871	+	0.302437i	−0.774404	−	0.632691i	$-0.781950\pi$
$617$	−28.0366	+	7.51239i	−1.12871	+	0.302437i	−0.354308	+	0.935129i	$0.615283\pi$
$618$	−16.8581	+	5.42577i	−0.678134	+	0.218257i
$619$	28.5202	+	28.5202i	1.14633	+	1.14633i	0.987270	+	0.159056i	$0.0508449\pi$
$619$	28.5202	+	28.5202i	1.14633	+	1.14633i	0.159056	+	0.987270i	$0.449155\pi$
$620$	−0.944948	−	0.545566i	−0.0379500	−	0.0219105i
$621$	13.8122	−	10.9954i	0.554265	−	0.441231i
$622$	3.02263	−	11.2806i	0.121196	−	0.452311i
$623$	34.7010			1.39027
$624$		0			0
$625$	0.830307			0.0332123
$626$	6.21086	−	23.1792i	0.248236	−	0.926429i
$627$	−15.1372	−	23.4517i	−0.604522	−	0.936572i
$628$	−16.4847	−	9.51745i	−0.657812	−	0.379788i
$629$	−34.4612	−	34.4612i	−1.37406	−	1.37406i
$630$	2.90724	+	7.70136i	0.115827	+	0.306830i
$631$	−23.4553	+	6.28482i	−0.933740	+	0.250195i	−0.693449	−	0.720506i	$-0.743910\pi$
$631$	−23.4553	+	6.28482i	−0.933740	+	0.250195i	−0.240291	+	0.970701i	$0.577243\pi$
$632$	16.1948	−	16.1948i	0.644195	−	0.644195i
$633$	−20.8727	−	10.7084i	−0.829617	−	0.425621i
$634$	−11.0560	+	6.38318i	−0.439090	+	0.253509i
$635$	−9.68141	−	2.59413i	−0.384195	−	0.102945i
$636$	0.251907	+	5.07671i	0.00998878	+	0.201305i
$637$		0			0
$638$			23.8851i			0.945619i
$639$	−4.66630	+	28.4375i	−0.184596	+	1.12497i
$640$	−6.74817	−	11.6882i	−0.266745	−	0.462016i
$641$	4.70367	−	8.14700i	0.185784	−	0.321787i	−0.758056	−	0.652189i	$-0.773851\pi$
$641$	4.70367	−	8.14700i	0.185784	−	0.321787i	0.943840	+	0.330402i	$0.107184\pi$
$642$	7.37951	+	6.68178i	0.291246	+	0.263709i
$643$	11.8390	+	44.1838i	0.466885	+	1.74244i	0.650563	+	0.759453i	$0.274533\pi$
$643$	11.8390	+	44.1838i	0.466885	+	1.74244i	−0.183677	+	0.982987i	$0.558800\pi$
$644$	3.17457	+	11.8477i	0.125096	+	0.466863i
$645$	13.6889	+	12.3947i	0.539002	+	0.488040i
$646$	−7.52133	+	13.0273i	−0.295923	+	0.512554i
$647$	−4.40379	−	7.62760i	−0.173131	−	0.299872i	0.766382	−	0.642385i	$-0.222055\pi$
$647$	−4.40379	−	7.62760i	−0.173131	−	0.299872i	−0.939513	+	0.342514i	$0.888722\pi$
$648$	−23.4448	−	1.49031i	−0.921000	−	0.0585449i
$649$		−	23.9251i		−	0.939142i
$650$		0			0
$651$	−0.119676	−	2.41184i	−0.00469048	−	0.0945276i
$652$	−8.70619	−	2.33282i	−0.340961	−	0.0913602i
$653$	14.0573	−	8.11599i	0.550105	−	0.317603i	−0.199059	−	0.979987i	$-0.563789\pi$
$653$	14.0573	−	8.11599i	0.550105	−	0.317603i	0.749164	+	0.662384i	$0.230455\pi$
$654$	3.50590	+	1.79864i	0.137092	+	0.0703324i
$655$	5.34004	−	5.34004i	0.208653	−	0.208653i
$656$	0.840739	−	0.225275i	0.0328254	−	0.00879553i
$657$	−24.0020	+	9.06070i	−0.936408	+	0.353492i
$658$	0.474398	+	0.474398i	0.0184940	+	0.0184940i
$659$	16.1496	+	9.32398i	0.629099	+	0.363211i	0.780403	−	0.625277i	$-0.215014\pi$
$659$	16.1496	+	9.32398i	0.629099	+	0.363211i	−0.151304	+	0.988487i	$0.548347\pi$
$660$	8.90343	+	13.7939i	0.346565	+	0.536926i
$661$	−7.32011	+	27.3190i	−0.284719	+	1.06259i	0.664325	+	0.747444i	$0.268719\pi$
$661$	−7.32011	+	27.3190i	−0.284719	+	1.06259i	−0.949044	+	0.315143i	$0.897948\pi$
$662$	17.1693			0.667303
$663$		0			0
$664$	30.7072			1.19167
$665$	3.15264	−	11.7658i	0.122254	−	0.456259i
$666$	15.6338	−	11.2264i	0.605799	−	0.435013i
$667$	19.3593	+	11.1771i	0.749595	+	0.432779i
$668$	−4.38772	−	4.38772i	−0.169766	−	0.169766i
$669$	−17.0751	+	5.49559i	−0.660161	+	0.212472i
$670$	−6.67625	+	1.78890i	−0.257926	+	0.0691111i
$671$	23.6793	−	23.6793i	0.914128	−	0.914128i
$672$	11.8119	−	23.0237i	0.455654	−	0.888158i
$673$	−21.3639	+	12.3345i	−0.823519	+	0.475459i	−0.851629	−	0.524146i	$-0.824385\pi$
$673$	−21.3639	+	12.3345i	−0.823519	+	0.475459i	0.0281092	+	0.999605i	$0.491051\pi$
$674$	−6.78645	−	1.81842i	−0.261404	−	0.0700430i
$675$	−15.4955	+	2.32193i	−0.596422	+	0.0893710i
$676$		0			0
$677$		−	48.4537i		−	1.86223i	−0.364727	−	0.931114i	$-0.618838\pi$
$677$		−	48.4537i		−	1.86223i	0.364727	−	0.931114i	$-0.381162\pi$
$678$	−0.528443	+	2.45258i	−0.0202947	+	0.0941907i
$679$	−2.41902	−	4.18986i	−0.0928333	−	0.160792i
$680$	10.6716	−	18.4837i	0.409236	−	0.708818i
$681$	0.0767908	−	0.0848094i	0.00294263	−	0.00324990i
$682$	0.513874	+	1.91780i	0.0196773	+	0.0734365i
$683$	4.74192	+	17.6971i	0.181445	+	0.677161i	0.995364	+	0.0961824i	$0.0306632\pi$
$683$	4.74192	+	17.6971i	0.181445	+	0.677161i	−0.813919	+	0.580978i	$0.802670\pi$
$684$	11.1486	+	9.13103i	0.426276	+	0.349134i
$685$	−3.40945	+	5.90534i	−0.130268	+	0.225632i
$686$	7.30582	+	12.6540i	0.278937	+	0.483134i
$687$	−46.0340	−	9.91868i	−1.75631	−	0.378421i
$688$		−	6.34157i		−	0.241770i
$689$		0			0
$690$	−6.32663	+	0.313929i	−0.240851	+	0.0119511i
$691$	9.99134	+	2.67717i	0.380089	+	0.101844i	0.443805	−	0.896124i	$-0.353628\pi$
$691$	9.99134	+	2.67717i	0.380089	+	0.101844i	−0.0637158	+	0.997968i	$0.520295\pi$
$692$	−5.31487	+	3.06854i	−0.202041	+	0.116648i
$693$	−14.9629	+	33.1105i	−0.568395	+	1.25777i
$694$	−6.07014	+	6.07014i	−0.230419	+	0.230419i
$695$	16.0407	−	4.29809i	0.608457	−	0.163036i
$696$	−9.11335	−	28.3156i	−0.345440	−	1.07330i
$697$	4.26323	+	4.26323i	0.161481	+	0.161481i
$698$	−23.0719	−	13.3206i	−0.873285	−	0.504191i
$699$	24.0330	−	15.5124i	0.909012	−	0.586732i
$700$	2.81748	−	10.5150i	0.106491	−	0.397428i
$701$	1.23945			0.0468132			0.0234066	−	0.999726i	$-0.492549\pi$
$701$	1.23945			0.0468132			0.0234066	+	0.999726i	$0.492549\pi$
$702$		0			0
$703$	−28.4804			−1.07416
$704$	−3.44584	+	12.8601i	−0.129870	+	0.484682i
$705$	0.706136	−	0.455784i	0.0265946	−	0.0171658i
$706$	−21.3111	−	12.3040i	−0.802053	−	0.463066i
$707$	−3.72708	−	3.72708i	−0.140171	−	0.140171i
$708$	3.78428	+	11.7579i	0.142222	+	0.441891i
$709$	26.1123	−	6.99678i	0.980670	−	0.262770i	0.267343	−	0.963601i	$-0.413854\pi$
$709$	26.1123	−	6.99678i	0.980670	−	0.262770i	0.713327	+	0.700832i	$0.247188\pi$
$710$	7.31139	−	7.31139i	0.274392	−	0.274392i
$711$	10.8400	−	23.9872i	0.406532	−	0.899589i
$712$	30.7718	−	17.7661i	1.15322	−	0.665814i
$713$	1.79489	+	0.480938i	0.0672190	+	0.0180113i
$714$	19.5573	−	0.970436i	0.731913	−	0.0363177i
$715$		0			0
$716$		−	19.8156i		−	0.740543i
$717$	−44.9092	−	9.67632i	−1.67716	−	0.361369i
$718$	11.2650	+	19.5116i	0.420406	+	0.728165i
$719$	−19.0678	+	33.0264i	−0.711109	+	1.23168i	0.253332	+	0.967379i	$0.418473\pi$
$719$	−19.0678	+	33.0264i	−0.711109	+	1.23168i	−0.964441	+	0.264298i	$0.914860\pi$
$720$	−2.73968	−	2.24389i	−0.102102	−	0.0836247i
$721$	−8.82895	−	32.9501i	−0.328807	−	1.22713i
$722$	−1.48221	−	5.53167i	−0.0551620	−	0.205867i
$723$	5.48018	−	6.05243i	0.203810	−	0.225092i
$724$	−0.691101	+	1.19702i	−0.0256846	+	0.0444870i
$725$	−9.91983	−	17.1817i	−0.368413	−	0.638111i
$726$	3.22613	−	14.9729i	0.119733	−	0.555697i
$727$		−	15.5870i		−	0.578091i	−0.957315	−	0.289046i	$-0.906662\pi$
$727$		−	15.5870i		−	0.578091i	0.957315	−	0.289046i	$-0.0933379\pi$
$728$		0			0
$729$	−25.8141	+	7.91395i	−0.956079	+	0.293109i
$730$	8.89149	+	2.38247i	0.329089	+	0.0881791i
$731$	38.0420	−	21.9636i	1.40703	−	0.812352i
$732$	−7.89173	+	15.3825i	−0.291687	+	0.568554i
$733$	0.240557	−	0.240557i	0.00888518	−	0.00888518i	−0.702650	−	0.711535i	$-0.748000\pi$
$733$	0.240557	−	0.240557i	0.00888518	−	0.00888518i	0.711535	+	0.702650i	$0.248000\pi$
$734$	15.7337	−	4.21582i	0.580740	−	0.155609i
$735$	1.16530	−	0.375049i	0.0429827	−	0.0138339i
$736$	14.0801	+	14.0801i	0.519000	+	0.519000i
$737$	−26.4206	−	15.2539i	−0.973215	−	0.561886i
$738$	−1.93408	+	1.38882i	−0.0711944	+	0.0511233i
$739$	−8.76818	+	32.7233i	−0.322543	+	1.20375i	0.594216	+	0.804305i	$0.297462\pi$
$739$	−8.76818	+	32.7233i	−0.322543	+	1.20375i	−0.916759	+	0.399441i	$0.869204\pi$
$740$	16.7517			0.615803
$741$		0			0
$742$	4.03624			0.148175
$743$	8.56404	−	31.9614i	0.314184	−	1.17255i	−0.610563	−	0.791968i	$-0.709057\pi$
$743$	8.56404	−	31.9614i	0.314184	−	1.17255i	0.924747	−	0.380583i	$-0.124277\pi$
$744$	−1.34093	−	2.07748i	−0.0491610	−	0.0761641i
$745$	8.40335	+	4.85168i	0.307875	+	0.177752i
$746$	−7.51190	−	7.51190i	−0.275030	−	0.275030i
$747$	33.0181	−	12.4642i	1.20807	−	0.456043i
$748$	37.7227	−	10.1078i	1.37928	−	0.369577i
$749$	−13.5590	+	13.5590i	−0.495437	+	0.495437i
$750$	13.2961	+	6.82134i	0.485506	+	0.249080i
$751$	−4.65403	+	2.68701i	−0.169828	+	0.0980503i	−0.582505	−	0.812827i	$-0.697927\pi$
$751$	−4.65403	+	2.68701i	−0.169828	+	0.0980503i	0.412677	+	0.910878i	$0.364594\pi$
$752$	−0.278785	−	0.0747001i	−0.0101662	−	0.00272403i
$753$	1.20571	+	24.2988i	0.0439385	+	0.885497i
$754$		0			0
$755$		−	24.3164i		−	0.884963i
$756$	2.11635	−	18.6388i	0.0769708	−	0.677888i
$757$	20.8335	+	36.0847i	0.757207	+	1.31152i	0.944270	+	0.329173i	$0.106770\pi$
$757$	20.8335	+	36.0847i	0.757207	+	1.31152i	−0.187062	+	0.982348i	$0.559897\pi$
$758$	−13.2817	+	23.0045i	−0.482412	+	0.835562i
$759$	−20.7259	−	18.7663i	−0.752301	−	0.681172i
$760$	−3.22816	−	12.0477i	−0.117098	−	0.437015i
$761$	−1.76325	−	6.58054i	−0.0639177	−	0.238544i	0.926575	−	0.376110i	$-0.122739\pi$
$761$	−1.76325	−	6.58054i	−0.0639177	−	0.238544i	−0.990493	+	0.137566i	$0.956072\pi$
$762$	−6.97978	−	6.31985i	−0.252851	−	0.228944i
$763$	−3.79495	+	6.57305i	−0.137386	+	0.237960i
$764$	−12.1135	−	20.9812i	−0.438251	−	0.759073i
$765$	3.97202	−	24.2064i	0.143609	−	0.875185i
$766$		−	12.8914i		−	0.465784i
$767$		0			0
$768$	−1.10943	−	22.3585i	−0.0400332	−	0.806793i
$769$	−20.8122	−	5.57662i	−0.750508	−	0.201098i	−0.136765	−	0.990604i	$-0.543670\pi$
$769$	−20.8122	−	5.57662i	−0.750508	−	0.201098i	−0.613744	+	0.789505i	$0.710337\pi$
$770$	11.2903	−	6.51844i	0.406873	−	0.234908i
$771$	30.1046	+	15.4447i	1.08419	+	0.556226i
$772$	2.54265	−	2.54265i	0.0915119	−	0.0915119i
$773$	−2.72302	+	0.729632i	−0.0979403	+	0.0262430i	−0.307456	−	0.951562i	$-0.599478\pi$
$773$	−2.72302	+	0.729632i	−0.0979403	+	0.0262430i

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+(0.197759 - 0.738045i) q^{2} +(1.45524 - 0.939300i) q^{3} +(1.22645 + 0.708090i) q^{4} +(-0.996141 - 0.996141i) q^{5} +(-0.405460 - 1.25979i) q^{6} +(2.46232 - 0.659775i) q^{7} +(1.84572 - 1.84572i) q^{8} +(1.23543 - 2.73381i) q^{9} +(-0.932193 + 0.538202i) q^{10} +(-4.58925 - 1.22969i) q^{11} +(2.44988 - 0.121564i) q^{12} -1.94778i q^{14} +(-2.38530 - 0.513946i) q^{15} +(0.418964 + 0.725666i) q^{16} +(-2.90210 + 5.02659i) q^{17} +(-1.77336 - 1.45244i) q^{18} +(0.877888 + 3.27632i) q^{19} +(-0.516358 - 1.92707i) q^{20} +(2.96353 - 3.27298i) q^{21} +(-1.81513 + 3.14390i) q^{22} +(1.69879 + 2.94240i) q^{23} +(0.952274 - 4.41964i) q^{24} -3.01541i q^{25} +(-0.770022 - 5.13878i) q^{27} +(3.48708 + 0.934361i) q^{28} +(5.69796 - 3.28972i) q^{29} +(-0.851029 + 1.65882i) q^{30} +(0.386730 - 0.386730i) q^{31} +(5.66102 - 1.51687i) q^{32} +(-7.83350 + 2.52120i) q^{33} +(3.13593 + 3.13593i) q^{34} +(-3.11004 - 1.79558i) q^{35} +(3.45098 - 2.47808i) q^{36} +(-2.17320 + 8.11049i) q^{37} +2.59169 q^{38} -3.67719 q^{40} +(0.268848 - 1.00336i) q^{41} +(-1.82955 - 2.83448i) q^{42} +(-6.55422 - 3.78408i) q^{43} +(-4.75775 - 4.75775i) q^{44} +(-3.95392 + 1.49260i) q^{45} +(2.50757 - 0.671902i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(1.29131 + 0.662484i) q^{48} +(-0.434484 + 0.250850i) q^{49} +(-2.22551 - 0.596323i) q^{50} +(0.498228 + 10.0408i) q^{51} +2.07223i q^{53} +(-3.94493 - 0.447927i) q^{54} +(3.34660 + 5.79649i) q^{55} +(3.32698 - 5.76250i) q^{56} +(4.35499 + 3.94323i) q^{57} +(-1.30114 - 4.85592i) q^{58} +(1.30332 + 4.86406i) q^{59} +(-2.56152 - 2.31933i) q^{60} +(-3.52415 + 6.10401i) q^{61} +(-0.208945 - 0.361904i) q^{62} +(1.23832 - 7.54661i) q^{63} -2.80221i q^{64} +(0.311618 + 6.28007i) q^{66} +(6.20237 + 1.66192i) q^{67} +(-7.11855 + 4.10990i) q^{68} +(5.23594 + 2.68621i) q^{69} +(-1.94026 + 1.94026i) q^{70} +(-9.27862 + 2.48620i) q^{71} +(-2.76558 - 7.32609i) q^{72} +(-6.04700 - 6.04700i) q^{73} +(5.55614 + 3.20784i) q^{74} +(-2.83237 - 4.38813i) q^{75} +(-1.24325 + 4.63986i) q^{76} -12.1115 q^{77} +8.77426 q^{79} +(0.305519 - 1.14021i) q^{80} +(-5.94742 - 6.75486i) q^{81} +(-0.687355 - 0.396845i) q^{82} +(8.31849 + 8.31849i) q^{83} +(5.95218 - 1.91570i) q^{84} +(7.89810 - 2.11629i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(5.20185 - 10.1394i) q^{87} +(-10.7401 + 6.20081i) q^{88} +(13.1488 + 3.52321i) q^{89} +(0.319681 + 3.21335i) q^{90} +4.81159i q^{92} +(0.199528 - 0.926039i) q^{93} +(0.131592 + 0.227923i) q^{94} +(2.38918 - 4.13818i) q^{95} +(6.81334 - 7.52480i) q^{96} +(-0.491207 - 1.83321i) q^{97} +(0.0992154 + 0.370277i) q^{98} +(-9.03143 + 11.0270i) 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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