LMFDB - Embedded newform 507.2.k.k.80.15

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			80.15
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.15

$q$-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} +(-1.54108 + 0.790622i) q^{3} +(1.22645 + 0.708090i) q^{4} +(-0.996141 - 0.996141i) q^{5} +(0.278754 + 1.29374i) q^{6} +(-2.46232 + 0.659775i) q^{7} +(1.84572 - 1.84572i) q^{8} +(1.74983 - 2.43682i) q^{9} +(-0.932193 + 0.538202i) q^{10} +(-4.58925 - 1.22969i) q^{11} +(-2.44988 - 0.121564i) q^{12} +1.94778i q^{14} +(2.32270 + 0.747558i) q^{15} +(0.418964 + 0.725666i) q^{16} +(2.90210 - 5.02659i) q^{17} +(-1.45244 - 1.77336i) q^{18} +(-0.877888 - 3.27632i) q^{19} +(-0.516358 - 1.92707i) q^{20} +(3.27298 - 2.96353i) q^{21} +(-1.81513 + 3.14390i) q^{22} +(-1.69879 - 2.94240i) q^{23} +(-1.38513 + 4.30366i) q^{24} -3.01541i q^{25} +(-0.770022 + 5.13878i) q^{27} +(-3.48708 - 0.934361i) q^{28} +(-5.69796 + 3.28972i) q^{29} +(1.01107 - 1.56642i) q^{30} +(-0.386730 + 0.386730i) q^{31} +(5.66102 - 1.51687i) q^{32} +(8.04461 - 1.73333i) q^{33} +(-3.13593 - 3.13593i) q^{34} +(3.11004 + 1.79558i) q^{35} +(3.87157 - 1.74959i) q^{36} +(2.17320 - 8.11049i) q^{37} -2.59169 q^{38} -3.67719 q^{40} +(0.268848 - 1.00336i) q^{41} +(-1.53996 - 3.00167i) q^{42} +(-6.55422 - 3.78408i) q^{43} +(-4.75775 - 4.75775i) q^{44} +(-4.17050 + 0.684336i) q^{45} +(-2.50757 + 0.671902i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(-1.21938 - 0.787065i) q^{48} +(-0.434484 + 0.250850i) q^{49} +(-2.22551 - 0.596323i) q^{50} +(-0.498228 + 10.0408i) q^{51} -2.07223i q^{53} +(3.64038 + 1.58455i) q^{54} +(3.34660 + 5.79649i) q^{55} +(-3.32698 + 5.76250i) q^{56} +(3.94323 + 4.35499i) q^{57} +(1.30114 + 4.85592i) q^{58} +(1.30332 + 4.86406i) q^{59} +(2.31933 + 2.56152i) q^{60} +(-3.52415 + 6.10401i) q^{61} +(0.208945 + 0.361904i) q^{62} +(-2.70089 + 7.15471i) q^{63} -2.80221i q^{64} +(0.311618 - 6.28007i) q^{66} +(-6.20237 - 1.66192i) q^{67} +(7.11855 - 4.10990i) q^{68} +(4.94429 + 3.19135i) q^{69} +(1.94026 - 1.94026i) q^{70} +(-9.27862 + 2.48620i) q^{71} +(-1.26798 - 7.72737i) q^{72} +(6.04700 + 6.04700i) q^{73} +(-5.55614 - 3.20784i) q^{74} +(2.38405 + 4.64697i) q^{75} +(1.24325 - 4.63986i) q^{76} +12.1115 q^{77} +8.77426 q^{79} +(0.305519 - 1.14021i) q^{80} +(-2.87617 - 8.52805i) q^{81} +(-0.687355 - 0.396845i) q^{82} +(8.31849 + 8.31849i) q^{83} +(6.11259 - 1.31704i) q^{84} +(-7.89810 + 2.11629i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(6.18006 - 9.57464i) q^{87} +(-10.7401 + 6.20081i) q^{88} +(13.1488 + 3.52321i) q^{89} +(-0.319681 + 3.21335i) q^{90} -4.81159i q^{92} +(0.290223 - 0.901738i) q^{93} +(0.131592 + 0.227923i) q^{94} +(-2.38918 + 4.13818i) q^{95} +(-7.52480 + 6.81334i) q^{96} +(0.491207 + 1.83321i) q^{97} +(0.0992154 + 0.370277i) q^{98} +(-11.0270 + 9.03143i) 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	$-0.00373778\pi$
$3$	−1.54108	+	0.790622i	−0.889741	+	0.456466i
$3$	−1.54108	+	0.790622i	−0.889741	+	0.456466i
$4$	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	$0.852007\pi$
$6$	0.278754	+	1.29374i	0.113801	+	0.528166i
$7$	−2.46232	+	0.659775i	−0.930668	+	0.249372i	−0.692139	−	0.721764i	$-0.743332\pi$
$7$	−2.46232	+	0.659775i	−0.930668	+	0.249372i	−0.238528	+	0.971136i	$0.576665\pi$
$8$	1.84572	−	1.84572i	0.652560	−	0.652560i
$9$	1.74983	−	2.43682i	0.583277	−	0.812273i
$10$	−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
$15$	2.32270	+	0.747558i	0.599719	+	0.193019i
$16$	0.418964	+	0.725666i	0.104741	+	0.181417i
$17$	2.90210	−	5.02659i	0.703863	−	1.21913i	−0.263237	−	0.964731i	$-0.584790\pi$
$17$	2.90210	−	5.02659i	0.703863	−	1.21913i	0.967100	−	0.254395i	$-0.0818765\pi$
$18$	−1.45244	−	1.77336i	−0.342343	−	0.417985i
$19$	−0.877888	−	3.27632i	−0.201401	−	0.751640i	−0.990516	−	0.137395i	$-0.956127\pi$
$19$	−0.877888	−	3.27632i	−0.201401	−	0.751640i	0.789115	−	0.614245i	$-0.210539\pi$
$20$	−0.516358	−	1.92707i	−0.115461	−	0.430907i
$21$	3.27298	−	2.96353i	0.714223	−	0.646694i
$22$	−1.81513	+	3.14390i	−0.386987	+	0.670281i
$23$	−1.69879	−	2.94240i	−0.354223	−	0.613532i	0.632762	−	0.774346i	$-0.281921\pi$
$23$	−1.69879	−	2.94240i	−0.354223	−	0.613532i	−0.986985	+	0.160815i	$0.948588\pi$
$24$	−1.38513	+	4.30366i	−0.282738	+	0.878480i
$25$		−	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	−0.924902	−	0.380206i	$-0.875853\pi$
$29$	−5.69796	+	3.28972i	−1.05808	+	0.610885i	−0.133183	+	0.991092i	$0.542520\pi$
$30$	1.01107	−	1.56642i	0.184595	−	0.285988i
$31$	−0.386730	+	0.386730i	−0.0694587	+	0.0694587i	−0.740983	−	0.671524i	$-0.765640\pi$
$31$	−0.386730	+	0.386730i	−0.0694587	+	0.0694587i	0.671524	+	0.740983i	$0.265640\pi$
$32$	5.66102	−	1.51687i	1.00074	−	0.268147i
$33$	8.04461	−	1.73333i	1.40039	−	0.301733i
$34$	−3.13593	−	3.13593i	−0.537808	−	0.537808i
$35$	3.11004	+	1.79558i	0.525693	+	0.303509i
$36$	3.87157	−	1.74959i	0.645261	−	0.291599i
$37$	2.17320	−	8.11049i	0.357272	−	1.33336i	−0.520330	−	0.853965i	$-0.674191\pi$
$37$	2.17320	−	8.11049i	0.357272	−	1.33336i	0.877602	−	0.479391i	$-0.159142\pi$
$38$	−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	$0.0574859\pi$
$42$	−1.53996	−	3.00167i	−0.237620	−	0.463168i
$43$	−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
$45$	−4.17050	+	0.684336i	−0.621701	+	0.102015i
$46$	−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	$0.257997\pi$
$48$	−1.21938	−	0.787065i	−0.176003	−	0.113603i
$49$	−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	$-0.954543\pi$
$53$		−	2.07223i		−	0.284642i	0.989821	−	0.142321i	$-0.0454566\pi$
$54$	3.64038	+	1.58455i	0.495392	+	0.215630i
$55$	3.34660	+	5.79649i	0.451256	+	0.781598i
$56$	−3.32698	+	5.76250i	−0.444586	+	0.770046i
$57$	3.94323	+	4.35499i	0.522293	+	0.576832i
$58$	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	$0.810362\pi$
$60$	2.31933	+	2.56152i	0.299425	+	0.330691i
$61$	−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
$63$	−2.70089	+	7.15471i	−0.340280	+	0.901409i
$64$		−	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	−0.140791	−	0.990039i	$-0.544965\pi$
$67$	−6.20237	−	1.66192i	−0.757740	−	0.203036i	−0.616948	+	0.787004i	$0.711631\pi$
$68$	7.11855	−	4.10990i	0.863252	−	0.498399i
$69$	4.94429	+	3.19135i	0.595223	+	0.384194i
$70$	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	$0.609726\pi$
$72$	−1.26798	−	7.72737i	−0.149433	−	0.910680i
$73$	6.04700	+	6.04700i	0.707748	+	0.707748i	0.966061	−	0.258313i	$-0.0831666\pi$
$73$	6.04700	+	6.04700i	0.707748	+	0.707748i	−0.258313	+	0.966061i	$0.583167\pi$
$74$	−5.55614	−	3.20784i	−0.645888	−	0.372904i
$75$	2.38405	+	4.64697i	0.275286	+	0.536586i
$76$	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
$81$	−2.87617	−	8.52805i	−0.319575	−	0.947561i
$82$	−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	$0.526591\pi$
$84$	6.11259	−	1.31704i	0.666938	−	0.143701i
$85$	−7.89810	+	2.11629i	−0.856669	+	0.229544i
$86$	−4.08898	+	4.08898i	−0.440926	+	0.440926i
$87$	6.18006	−	9.57464i	0.662572	−	1.02651i
$88$	−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
$93$	0.290223	−	0.901738i	0.0300947	−	0.0935058i
$94$	0.131592	+	0.227923i	0.0135726	+	0.0235085i
$95$	−2.38918	+	4.13818i	−0.245125	+	0.424568i
$96$	−7.52480	+	6.81334i	−0.767996	+	0.695383i
$97$	0.491207	+	1.83321i	0.0498746	+	0.186134i	0.986369	−	0.164548i	$-0.0526164\pi$
$97$	0.491207	+	1.83321i	0.0498746	+	0.186134i	−0.936495	+	0.350682i	$0.885950\pi$
$98$	0.0992154	+	0.370277i	0.0100223	+	0.0374036i
$99$	−11.0270	+	9.03143i	−1.10825	+	0.907693i
$100$	2.13518	−	3.69824i	0.213518	−	0.369824i
$101$	1.03384	+	1.79066i	0.102871	+	0.178178i	0.912866	−	0.408258i	$-0.133864\pi$
$101$	1.03384	+	1.79066i	0.102871	+	0.178178i	−0.809995	+	0.586436i	$0.800530\pi$
$102$	7.31205	+	2.35337i	0.724001	+	0.233019i
$103$		−	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	−0.150892	−	0.988550i	$-0.548215\pi$
$107$	6.51440	−	3.76109i	0.629771	−	0.363599i	0.780663	+	0.624952i	$0.214881\pi$
$108$	−4.58311	+	5.75720i	−0.441010	+	0.553987i
$109$	2.10533	−	2.10533i	0.201654	−	0.201654i	−0.599054	−	0.800709i	$-0.704457\pi$
$109$	2.10533	−	2.10533i	0.201654	−	0.201654i	0.800709	+	0.599054i	$0.204457\pi$
$110$	4.93989	−	1.32364i	0.471000	−	0.126204i
$111$	3.06327	+	14.2171i	0.290753	+	1.34942i
$112$	−1.51040	−	1.51040i	−0.142719	−	0.142719i
$113$	1.64175	+	0.947866i	0.154443	+	0.0891677i	0.575230	−	0.817992i	$-0.304913\pi$
$113$	1.64175	+	0.947866i	0.154443	+	0.0891677i	−0.420787	+	0.907160i	$0.638246\pi$
$114$	3.99398	−	2.04904i	0.374071	−	0.191911i
$115$	−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
$120$	5.66683	−	2.90727i	0.517308	−	0.265396i
$121$	10.0228	+	5.78669i	0.911168	+	0.526063i
$122$	3.80811	+	3.80811i	0.344770	+	0.344770i
$123$	0.378960	+	1.75881i	0.0341696	+	0.158586i
$124$	−0.748144	+	0.200465i	−0.0671853	+	0.0180022i
$125$	−7.98448	+	7.98448i	−0.714153	+	0.714153i
$126$	4.74638	+	3.40828i	0.422841	+	0.303634i
$127$	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	$-0.924758\pi$
$131$		−	5.36072i		−	0.468368i	0.972192	−	0.234184i	$-0.0752419\pi$
$132$	11.0936	+	3.57047i	0.965578	+	0.310770i
$133$	4.32327	+	7.48813i	0.374875	+	0.649303i
$134$	−2.45314	+	4.24897i	−0.211919	+	0.367055i
$135$	5.88600	−	4.35190i	0.506586	−	0.374552i
$136$	−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	$0.982962\pi$
$138$	3.33314	−	3.01800i	0.283736	−	0.256909i
$139$	−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
$141$	0.182780	−	0.567905i	0.0153928	−	0.0478263i
$142$			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
$147$	0.471246	−	0.730091i	0.0388677	−	0.0602169i
$148$	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	$0.507711\pi$
$150$	3.90114	−	0.840556i	0.318527	−	0.0686311i
$151$	−12.2053	−	12.2053i	−0.993251	−	0.993251i	0.00672628	−	0.999977i	$-0.497859\pi$
$151$	−12.2053	−	12.2053i	−0.993251	−	0.993251i	−0.999977	+	0.00672628i	$0.997859\pi$
$152$	−7.66750	−	4.42683i	−0.621916	−	0.359063i
$153$	−7.17069	−	15.8676i	−0.579716	−	1.28282i
$154$	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
$159$	1.63835	+	3.19346i	0.129930	+	0.253258i
$160$	−7.15019	−	4.12816i	−0.565272	−	0.326360i
$161$	6.12428	+	6.12428i	0.482661	+	0.482661i
$162$	−6.86288	+	0.436250i	−0.539199	+	0.0342751i
$163$	6.14766	−	1.64726i	0.481522	−	0.129023i	−0.00988942	−	0.999951i	$-0.503148\pi$
$163$	6.14766	−	1.64726i	0.481522	−	0.129023i	0.491411	+	0.870928i	$0.336481\pi$
$164$	1.04019	−	1.04019i	0.0812256	−	0.0812256i
$165$	−9.74020	−	6.28693i	−0.758274	−	0.489437i
$166$	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
$171$	−9.51996	−	3.59376i	−0.728010	−	0.274822i
$172$	−5.35894	−	9.28195i	−0.408615	−	0.707742i
$173$	2.16677	−	3.75296i	0.164737	−	0.285332i	−0.771825	−	0.635835i	$-0.780656\pi$
$173$	2.16677	−	3.75296i	0.164737	−	0.285332i	0.936562	+	0.350503i	$0.113989\pi$
$174$	−5.84436	−	6.45464i	−0.443060	−	0.489325i
$175$	1.98949	+	7.42488i	0.150391	+	0.561268i
$176$	−1.03039	−	3.84546i	−0.0776685	−	0.289863i
$177$	−5.85416	−	6.46546i	−0.440025	−	0.485974i
$178$	5.20058	−	9.00767i	0.389800	−	0.675153i
$179$	6.99613	+	12.1177i	0.522916	+	0.905716i	0.999644	+	0.0266660i	$0.00848906\pi$
$179$	6.99613	+	12.1177i	0.522916	+	0.905716i	−0.476729	+	0.879050i	$0.658178\pi$
$180$	−5.59947	−	2.11379i	−0.417360	−	0.157552i
$181$			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
$186$	−0.608129	−	0.392524i	−0.0445902	−	0.0287813i
$187$	−19.4996	+	19.4996i	−1.42595	+	1.42595i
$188$	−0.471174	+	0.126251i	−0.0343639	+	0.00920777i
$189$	−1.49440	−	13.1613i	−0.108702	−	0.957347i
$190$	2.58168	+	2.58168i	0.187295	+	0.187295i
$191$	14.8153	+	8.55364i	1.07200	+	0.618920i	0.928727	−	0.370763i	$-0.120904\pi$
$191$	14.8153	+	8.55364i	1.07200	+	0.618920i	0.143273	+	0.989683i	$0.454237\pi$
$192$	2.21549	+	4.31842i	0.159889	+	0.311655i
$193$	−0.657172	+	2.45260i	−0.0473043	+	0.176542i	−0.985536	−	0.169465i	$-0.945796\pi$
$193$	−0.657172	+	2.45260i	−0.0473043	+	0.176542i	0.938232	+	0.346007i	$0.112463\pi$
$194$	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	$-0.136107\pi$
$198$	4.48493	+	9.92444i	0.318730	+	0.705299i
$199$	−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
$201$	10.8723	−	2.34259i	0.766871	−	0.165233i
$202$	1.52604	−	0.408902i	0.107372	−	0.0287702i
$203$	11.8597	−	11.8597i	0.832387	−	0.832387i
$204$	−7.72086	+	11.9618i	−0.540568	+	0.837491i
$205$	−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
$210$	−1.45608	+	4.52410i	−0.100479	+	0.312193i
$211$	−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
$213$	12.3334	−	11.1673i	0.845072	−	0.765171i
$214$	−1.48758	−	5.55172i	−0.101689	−	0.379507i
$215$	2.75945	+	10.2984i	0.188193	+	0.702345i
$216$	8.06349	+	10.9060i	0.548651	+	0.742058i
$217$	0.697096	−	1.20741i	0.0473220	−	0.0819641i
$218$	−1.13748	−	1.97018i	−0.0770402	−	0.133437i
$219$	−14.0998	−	4.53800i	−0.952776	−	0.306650i
$220$			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	0.577700	−	0.816249i	$-0.303950\pi$
$223$	10.0034	+	2.68041i	0.669879	+	0.179494i	0.0921788	+	0.995742i	$0.470617\pi$
$224$	−12.9384	+	7.47001i	−0.864485	+	0.499111i
$225$	−7.34800	−	5.27645i	−0.489866	−	0.351764i
$226$	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	$0.415969\pi$
$228$	1.75244	+	8.13332i	0.116058	+	0.538643i
$229$	19.2246	+	19.2246i	1.27040	+	1.27040i	0.945880	+	0.324517i	$0.105202\pi$
$229$	19.2246	+	19.2246i	1.27040	+	1.27040i	0.324517	+	0.945880i	$0.394798\pi$
$230$	3.16721	+	1.82859i	0.208839	+	0.120573i
$231$	−18.6648	+	9.57563i	−1.22805	+	0.630030i
$232$	−4.44493	+	16.5887i	−0.291824	+	1.08910i
$233$	−16.5148			−1.08192			−0.540961	−	0.841047i	$-0.681939\pi$
$233$	−16.5148			−1.08192			−0.540961	+	0.841047i	$0.681939\pi$
$234$		0			0
$235$	0.485238			0.0316534
$236$	−1.84574	+	6.88839i	−0.120147	+	0.448396i
$237$	−13.5218	+	6.93713i	−0.878336	+	0.450615i
$238$	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	$-0.578186\pi$
$240$	0.430650	+	1.99871i	0.0277983	+	0.129016i
$241$	−4.55333	+	1.22006i	−0.293306	+	0.0785911i	−0.402472	−	0.915432i	$-0.631849\pi$
$241$	−4.55333	+	1.22006i	−0.293306	+	0.0785911i	0.109166	+	0.994024i	$0.465182\pi$
$242$	6.25295	−	6.25295i	0.401955	−	0.401955i
$243$	11.1749	+	10.8684i	0.716868	+	0.697209i
$244$	−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
$249$	−19.3962	−	6.24265i	−1.22919	−	0.395612i
$250$	4.31391	+	7.47191i	0.272835	+	0.472565i
$251$	7.02308	−	12.1643i	0.443293	−	0.767806i	−0.554638	−	0.832091i	$-0.687143\pi$
$251$	7.02308	−	12.1643i	0.443293	−	0.767806i	0.997932	+	0.0642852i	$0.0204767\pi$
$252$	−8.37868	+	6.86241i	−0.527807	+	0.432291i
$253$	4.17797	+	15.5924i	0.262666	+	0.980285i
$254$	−1.40700	−	5.25100i	−0.0882831	−	0.329477i
$255$	10.4984	−	9.50577i	0.657434	−	0.595275i
$256$	6.46228	−	11.1930i	0.403893	−	0.699563i
$257$	−9.76740	−	16.9176i	−0.609274	−	1.05529i	−0.991360	−	0.131167i	$-0.958128\pi$
$257$	−9.76740	−	16.9176i	−0.609274	−	1.05529i	0.382087	−	0.924127i	$-0.375206\pi$
$258$	3.06859	−	9.53426i	0.191042	−	0.593577i
$259$			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	−0.464650	−	0.885494i	$-0.653820\pi$
$263$	1.13335	−	0.654340i	0.0698854	−	0.0403484i	0.534536	+	0.845146i	$0.320487\pi$
$264$	11.6488	−	18.0473i	0.716937	−	1.11073i
$265$	−2.06423	+	2.06423i	−0.126805	+	0.126805i
$266$	6.38155	−	1.70993i	0.391278	−	0.104843i
$267$	−23.0488	+	4.96620i	−1.41057	+	0.303927i
$268$	−6.43009	−	6.43009i	−0.392780	−	0.392780i
$269$	−24.4901	−	14.1394i	−1.49319	−	0.862093i	−0.493219	−	0.869905i	$-0.664180\pi$
$269$	−24.4901	−	14.1394i	−1.49319	−	0.862093i	−0.999969	+	0.00781215i	$0.997513\pi$
$270$	−2.04789	−	5.20476i	−0.124631	−	0.316752i
$271$	−1.84107	+	6.87097i	−0.111837	+	0.417382i	−0.999031	−	0.0440153i	$-0.985985\pi$
$271$	−1.84107	+	6.87097i	−0.111837	+	0.417382i	0.887194	+	0.461397i	$0.152652\pi$
$272$	4.86350			0.294893
$273$		0			0
$274$	−3.69843			−0.223431
$275$	−3.70800	+	13.8385i	−0.223601	+	0.834491i
$276$	3.80415	+	7.41503i	0.228983	+	0.446333i
$277$	−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
$279$	0.265678	+	1.61910i	0.0159057	+	0.0969332i
$280$	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	$-0.00538659\pi$
$282$	−0.382994	−	0.247208i	−0.0228070	−	0.0147210i
$283$	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
$288$	6.20951	−	16.4491i	0.365899	−	0.969275i
$289$	−8.34439	−	14.4529i	−0.490846	−	0.850171i
$290$	3.54107	−	6.13331i	0.207939	−	0.360160i
$291$	−2.20637	−	2.43676i	−0.129339	−	0.142845i
$292$	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	$-0.235216\pi$
$294$	−0.445648	−	0.492183i	−0.0259907	−	0.0287047i
$295$	3.54700	−	6.14359i	0.206514	−	0.357693i
$296$	−10.9586	−	18.9808i	−0.636953	−	1.10324i
$297$	9.85292	−	22.6363i	0.571724	−	1.31349i
$298$			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
$303$	−3.00897	−	1.94217i	−0.172861	−	0.111575i
$304$	2.00971	−	2.00971i	0.115265	−	0.115265i
$305$	9.59101	−	2.56990i	0.549180	−	0.147152i
$306$	−13.1291	+	2.15434i	−0.750539	+	0.123156i
$307$	1.83038	+	1.83038i	0.104465	+	0.104465i	0.757408	−	0.652942i	$-0.226466\pi$
$307$	1.83038	+	1.83038i	0.104465	+	0.104465i	−0.652942	+	0.757408i	$0.726466\pi$
$308$	14.8541	+	8.57604i	0.846393	+	0.488665i
$309$	10.5799	+	20.6223i	0.601870	+	1.17316i
$310$	0.152368	−	0.568646i	0.00865393	−	0.0322969i
$311$	−15.2844			−0.866701			−0.433350	−	0.901226i	$-0.642669\pi$
$311$	−15.2844			−0.866701			−0.433350	+	0.901226i	$0.642669\pi$
$312$		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
$315$	9.81757	−	4.43664i	0.553157	−	0.249976i
$316$	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	$0.905462\pi$
$318$	2.68092	−	0.577642i	0.150338	−	0.0323925i
$319$	30.1947	−	8.09065i	1.69058	−	0.452989i
$320$	−2.79140	+	2.79140i	−0.156044	+	0.156044i
$321$	−7.06559	+	10.9466i	−0.394363	+	0.610978i
$322$	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
$327$	−1.57996	+	4.90901i	−0.0873718	+	0.271469i
$328$	−1.35569	−	2.34813i	−0.0748556	−	0.129654i
$329$	0.439024	−	0.760412i	0.0242042	−	0.0419229i
$330$	−6.56625	+	5.94542i	−0.361460	+	0.327285i
$331$	−5.81579	−	21.7048i	−0.319665	−	1.19300i	−0.919568	−	0.392932i	$-0.871461\pi$
$331$	−5.81579	−	21.7048i	−0.319665	−	1.19300i	0.599903	−	0.800073i	$-0.295206\pi$
$332$	4.31196	+	16.0924i	0.236649	+	0.883188i
$333$	−15.9611	−	19.4877i	−0.874660	−	1.06792i
$334$	−1.67396	+	2.89938i	−0.0915949	+	0.158647i
$335$	4.52293	+	7.83394i	0.247114	+	0.428014i
$336$	3.52179	+	1.13348i	0.192130	+	0.0618366i
$337$		−	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
$342$	−4.53501	+	6.31547i	−0.245226	+	0.341501i
$343$	13.5221	−	13.5221i	0.730125	−	0.730125i
$344$	−19.0816	+	5.11289i	−1.02881	+	0.275669i
$345$	−1.74618	−	8.10425i	−0.0940110	−	0.436318i
$346$	−2.34136	−	2.34136i	−0.125872	−	0.125872i
$347$	9.72982	+	5.61751i	0.522324	+	0.301564i	0.737885	−	0.674926i	$-0.235825\pi$
$347$	9.72982	+	5.61751i	0.522324	+	0.301564i	−0.215561	+	0.976490i	$0.569158\pi$
$348$	14.3592	−	7.36676i	0.769736	−	0.394900i
$349$	−9.02423	+	33.6789i	−0.483056	+	1.80279i	0.105605	+	0.994408i	$0.466322\pi$
$349$	−9.02423	+	33.6789i	−0.483056	+	1.80279i	−0.588660	+	0.808380i	$0.700344\pi$
$350$	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	$-0.244387\pi$
$354$	−5.92951	+	3.04203i	−0.315150	+	0.161682i
$355$	11.7194	+	6.76621i	0.622002	+	0.359113i
$356$	13.6316	+	13.6316i	0.722472	+	0.722472i
$357$	−5.39789	−	25.0524i	−0.285687	−	1.32591i
$358$	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	$0.966175\pi$
$360$	−6.43447	+	8.96065i	−0.339126	+	0.472268i
$361$	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
$366$	−8.87936	−	2.85781i	−0.464131	−	0.149380i
$367$	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
$369$	−1.97456	−	2.41084i	−0.102791	−	0.125503i
$370$	2.33924	+	8.73016i	0.121611	+	0.453859i
$371$	1.36720	+	5.10248i	0.0709817	+	0.264907i
$372$	0.994455	−	0.900431i	0.0515601	−	0.0466851i
$373$	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
$375$	5.99198	−	18.6174i	0.309425	−	0.961398i
$376$			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	0.979001	−	0.203855i	$-0.0653471\pi$
$379$	33.5805	+	8.99786i	1.72491	+	0.462189i	0.745912	+	0.666044i	$0.232014\pi$
$380$	−5.86041	+	3.38351i	−0.300633	+	0.173570i
$381$	−6.68287	+	10.3536i	−0.342374	+	0.530432i
$382$	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	$0.274809\pi$
$384$	−16.2213	+	3.49512i	−0.827792	+	0.178360i
$385$	−12.0648	−	12.0648i	−0.614878	−	0.614878i
$386$	1.68017	+	0.970045i	0.0855183	+	0.0493740i
$387$	−20.6899	+	9.34994i	−1.05173	+	0.475284i
$388$	−0.695638	+	2.59616i	−0.0353157	+	0.131800i
$389$	35.0012			1.77463			0.887315	−	0.461164i	$-0.152568\pi$
$389$	35.0012			1.77463			0.887315	+	0.461164i	$0.152568\pi$
$390$		0			0
$391$	−19.7203			−0.997297
$392$	−0.338938	+	1.26493i	−0.0171189	+	0.0638887i
$393$	4.23831	+	8.26128i	0.213794	+	0.416727i
$394$	−11.8151	−	6.82144i	−0.595235	−	0.343659i
$395$	−8.74040	−	8.74040i	−0.439777	−	0.439777i
$396$	−19.9191	+	3.26851i	−1.00097	+	0.164249i
$397$	−1.28080	+	0.343188i	−0.0642813	+	0.0172241i	−0.290816	−	0.956779i	$-0.593927\pi$
$397$	−1.28080	+	0.343188i	−0.0642813	+	0.0172241i	0.226535	+	0.974003i	$0.427260\pi$
$398$	−1.41001	+	1.41001i	−0.0706776	+	0.0706776i
$399$	−12.5828	−	8.12170i	−0.629927	−	0.406594i
$400$	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
$405$	−5.63007	+	11.3602i	−0.279760	+	0.564494i
$406$	−6.40764	−	11.0984i	−0.318006	−	0.550802i
$407$	−19.9467	+	34.5487i	−0.988722	+	1.71252i
$408$	17.6129	+	19.4521i	0.871970	+	0.963023i
$409$	−2.43275	−	9.07916i	−0.120292	−	0.448936i	0.879336	−	0.476201i	$-0.157987\pi$
$409$	−2.43275	−	9.07916i	−0.120292	−	0.448936i	−0.999628	+	0.0272657i	$0.991320\pi$
$410$	0.289389	+	1.08002i	0.0142919	+	0.0533382i
$411$	5.62713	+	6.21473i	0.277566	+	0.306550i
$412$	9.47549	−	16.4120i	0.466824	−	0.808563i
$413$	−6.41838	−	11.1170i	−0.315828	−	0.547030i
$414$	−2.75053	+	7.28622i	−0.135181	+	0.358098i
$415$		−	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	0.360664	−	0.932696i	$-0.382550\pi$
$419$	27.6079	−	15.9394i	1.34873	−	0.778692i	0.988070	+	0.154003i	$0.0492166\pi$
$420$	−7.40096	−	4.77704i	−0.361130	−	0.233096i
$421$	−19.6414	+	19.6414i	−0.957263	+	0.957263i	−0.999123	−	0.0418609i	$-0.986671\pi$
$421$	−19.6414	+	19.6414i	−0.957263	+	0.957263i	0.0418609	+	0.999123i	$0.486671\pi$
$422$	−9.99628	+	2.67850i	−0.486612	+	0.130387i
$423$	0.167322	+	1.01970i	0.00813545	+	0.0495793i
$424$	−3.82475	−	3.82475i	−0.185746	−	0.185746i
$425$	−15.1572	−	8.75101i	−0.735232	−	0.424486i
$426$	−5.80294	−	11.3111i	−0.281153	−	0.548022i
$427$	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	$0.0468202\pi$
$432$	−4.05165	+	1.59418i	−0.194935	+	0.0767002i
$433$	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
$435$	−15.6939	+	3.38148i	−0.752465	+	0.162129i
$436$	4.07285	−	1.09132i	0.195054	−	0.0522646i
$437$	−8.14889	+	8.14889i	−0.389814	+	0.389814i
$438$	−6.13761	+	9.50886i	−0.293266	+	0.454351i
$439$	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	$-0.888820\pi$
$443$		−	14.4060i		−	0.684449i	0.939618	−	0.342224i	$-0.111180\pi$
$444$	−6.31002	+	19.6056i	−0.299460	+	0.930438i
$445$	−9.58845	−	16.6077i	−0.454536	−	0.787280i
$446$	3.95653	−	6.85291i	0.187347	−	0.324495i
$447$	8.84361	−	8.00746i	0.418288	−	0.378740i
$448$	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	$-0.209909\pi$
$450$	−5.34739	+	4.37969i	−0.252079	+	0.206461i
$451$	−2.46763	+	4.27406i	−0.116196	+	0.201257i
$452$	1.34235	+	2.32502i	0.0631388	+	0.109360i
$453$	28.4590	+	9.15950i	1.33712	+	0.430351i
$454$		−	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	−0.296411	−	0.955061i	$-0.595790\pi$
$457$	−22.0326	−	5.90361i	−1.03064	−	0.276159i	−0.734230	+	0.678901i	$0.762456\pi$
$458$	17.9905	−	10.3868i	0.840639	−	0.485343i
$459$	23.5959	+	18.7838i	1.10136	+	0.876755i
$460$	−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	$0.175372\pi$
$462$	3.37613	+	15.6691i	0.157072	+	0.728993i
$463$	25.6118	+	25.6118i	1.19028	+	1.19028i	0.976988	+	0.213295i	$0.0684197\pi$
$463$	25.6118	+	25.6118i	1.19028	+	1.19028i	0.213295	+	0.976988i	$0.431580\pi$
$464$	−4.77448	−	2.75654i	−0.221649	−	0.127969i
$465$	−1.18736	+	0.609155i	−0.0550626	+	0.0282489i
$466$	−3.26595	+	12.1887i	−0.151292	+	0.564631i
$467$	−14.0544			−0.650361			−0.325180	−	0.945652i	$-0.605425\pi$
$467$	−14.0544			−0.650361			−0.325180	+	0.945652i	$0.605425\pi$
$468$		0			0
$469$	16.3687			0.755835
$470$	0.0959600	−	0.358128i	0.00442630	−	0.0165192i
$471$	20.7136	−	10.6268i	0.954434	−	0.489656i
$472$	11.3832	+	6.57212i	0.523956	+	0.302506i
$473$	25.4257	+	25.4257i	1.16908	+	1.16908i
$474$	2.44586	+	11.3516i	0.112342	+	0.521396i
$475$	−9.87944	+	2.64719i	−0.453300	+	0.121461i
$476$	−14.8165	+	14.8165i	−0.679114	+	0.679114i
$477$	−5.04964	−	3.62605i	−0.231207	−	0.166025i
$478$	−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
$483$	−14.2800	−	4.59599i	−0.649762	−	0.209125i
$484$	8.19500	+	14.1942i	0.372500	+	0.645189i
$485$	1.33683	−	2.31545i	0.0607021	−	0.105139i
$486$	10.2313	−	6.09824i	0.464102	−	0.276622i
$487$	7.01541	+	26.1819i	0.317898	+	1.18641i	0.921261	+	0.388946i	$0.127161\pi$
$487$	7.01541	+	26.1819i	0.317898	+	1.18641i	−0.603362	+	0.797467i	$0.706173\pi$
$488$	4.76169	+	17.7709i	0.215552	+	0.804449i
$489$	−8.17165	+	7.39903i	−0.369535	+	0.334596i
$490$	0.270016	−	0.467681i	0.0121981	−	0.0211277i
$491$	6.27068	+	10.8611i	0.282992	+	0.490156i	0.972120	−	0.234483i	$-0.0753398\pi$
$491$	6.27068	+	10.8611i	0.282992	+	0.490156i	−0.689128	+	0.724639i	$0.742006\pi$
$492$	−0.780618	+	2.42542i	−0.0351930	+	0.109346i
$493$			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
$498$	−8.44313	+	13.0808i	−0.378346	+	0.586163i
$499$	5.98039	−	5.98039i	0.267719	−	0.267719i	−0.560461	−	0.828180i	$-0.689376\pi$
$499$	5.98039	−	5.98039i	0.267719	−	0.267719i	0.828180	+	0.560461i	$0.189376\pi$
$500$	−15.4463	+	4.13882i	−0.690778	+	0.185094i
$501$	7.41894	−	1.59852i	0.331454	−	0.0714165i
$502$	−7.58896	−	7.58896i	−0.338712	−	0.338712i
$503$	16.0716	+	9.27897i	0.716599	+	0.413729i	0.813500	−	0.581565i	$-0.197560\pi$
$503$	16.0716	+	9.27897i	0.716599	+	0.413729i	−0.0969004	+	0.995294i	$0.530893\pi$
$504$	8.22050	+	18.1906i	0.366170	+	0.810276i
$505$	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	$0.782207\pi$
$510$	−4.93955	−	9.62813i	−0.218727	−	0.426341i
$511$	−18.8793	−	10.9000i	−0.835171	−	0.482186i
$512$	6.56566	+	6.56566i	0.290164	+	0.290164i
$513$	17.5123	−	1.98843i	0.773187	−	0.0877915i
$514$	−14.4176	+	3.86318i	−0.635932	+	0.170397i
$515$	−13.3301	+	13.3301i	−0.587395	+	0.587395i
$516$	15.5971	+	10.0673i	0.686622	+	0.443188i
$517$	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	$-0.752485\pi$
$521$		−	32.0270i		−	1.40313i	0.712605	−	0.701565i	$-0.247515\pi$
$522$	14.1098	+	5.32641i	0.617568	+	0.233131i
$523$	−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
$525$	−8.93623	−	9.86937i	−0.390009	−	0.430735i
$526$	−0.258803	−	0.965866i	−0.0112843	−	0.0421138i
$527$	0.821602	+	3.06626i	0.0357896	+	0.133568i
$528$	4.62822	+	5.11150i	0.201417	+	0.222450i
$529$	5.72821	−	9.92154i	0.249052	−	0.431372i
$530$	1.11528	+	1.93172i	0.0484445	+	0.0839084i
$531$	14.1334	+	5.33534i	0.613339	+	0.231534i
$532$			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
$537$	−20.3621	−	13.1429i	−0.878688	−	0.567160i
$538$	−15.2786	+	15.2786i	−0.658709	+	0.658709i
$539$	2.30243	−	0.616933i	0.0991725	−	0.0265732i
$540$	10.3004	−	1.16956i	0.443259	−	0.0503299i
$541$	10.4088	+	10.4088i	0.447508	+	0.447508i	0.894525	−	0.447017i	$-0.147514\pi$
$541$	10.4088	+	10.4088i	0.447508	+	0.447508i	−0.447017	+	0.894525i	$0.647514\pi$
$542$	4.70700	+	2.71759i	0.202183	+	0.116730i
$543$	−0.771653	−	1.50410i	−0.0331148	−	0.0645472i
$544$	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
$549$	8.70769	+	19.2687i	0.371635	+	0.822369i
$550$	9.48012	+	5.47335i	0.404234	+	0.233384i
$551$	15.7803	+	15.7803i	0.672265	+	0.672265i
$552$	15.0161	−	3.23543i	0.639128	−	0.137709i
$553$	−21.6050	+	5.78904i	−0.918738	+	0.246175i
$554$	−6.61952	+	6.61952i	−0.281236	+	0.281236i
$555$	11.1108	−	17.2136i	0.471625	−	0.730679i
$556$	−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
$561$	14.6336	−	45.4672i	0.617829	−	1.91963i
$562$	−9.20882	−	15.9501i	−0.388451	−	0.672816i
$563$	−13.9437	+	24.1513i	−0.587659	+	1.01785i	0.406880	+	0.913482i	$0.366617\pi$
$563$	−13.9437	+	24.1513i	−0.587659	+	1.01785i	−0.994538	+	0.104373i	$0.966716\pi$
$564$	0.626298	−	0.567082i	0.0263719	−	0.0238785i
$565$	−0.691209	−	2.57963i	−0.0290794	−	0.108526i
$566$	−2.43795	−	9.09854i	−0.102475	−	0.382440i
$567$	12.7086	+	19.1011i	0.533713	+	0.802172i
$568$	−12.5369	+	21.7145i	−0.526036	+	0.911121i
$569$	0.877082	+	1.51915i	0.0367692	+	0.0636861i	0.883824	−	0.467819i	$-0.154960\pi$
$569$	0.877082	+	1.51915i	0.0367692	+	0.0636861i	−0.847055	+	0.531505i	$0.821627\pi$
$570$	−6.01971	−	1.93744i	−0.252138	−	0.0811502i
$571$		−	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
$576$	−6.82848	−	4.90340i	−0.284520	−	0.204308i
$577$	−2.17547	+	2.17547i	−0.0905662	+	0.0905662i	−0.750938	−	0.660372i	$-0.770399\pi$
$577$	−2.17547	+	2.17547i	−0.0905662	+	0.0905662i	0.660372	+	0.750938i	$0.270399\pi$
$578$	−12.3171	+	3.30035i	−0.512323	+	0.137277i
$579$	−0.926327	−	4.29922i	−0.0384969	−	0.178669i
$580$	9.28171	+	9.28171i	0.385402	+	0.385402i
$581$	−25.9711	−	14.9944i	−1.07746	−	0.622073i
$582$	−2.23477	+	1.14651i	−0.0926341	+	0.0475243i
$583$	−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	$0.982727\pi$
$588$	1.09493	−	0.561735i	0.0451541	−	0.0231655i
$589$	1.60656	+	0.927547i	0.0661971	+	0.0382189i
$590$	−3.83280	−	3.83280i	−0.157794	−	0.157794i
$591$	6.51401	+	30.2324i	0.267950	+	1.24360i
$592$	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	$0.0733483\pi$
$594$	−14.7581	−	11.7484i	−0.605532	−	0.482044i
$595$	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	$0.133679\pi$
$599$			19.9578i			0.815455i	−0.913104	+	0.407728i	$0.866321\pi$
$600$	12.9773	+	4.17672i	0.529795	+	0.170514i
$601$	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
$603$	−14.9029	+	12.2060i	−0.606893	+	0.497065i
$604$	−6.32670	−	23.6116i	−0.257430	−	0.960741i
$605$	−4.21981	−	15.7485i	−0.171560	−	0.640269i
$606$	−2.02846	+	1.83667i	−0.0824006	+	0.0746097i
$607$	−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
$609$	−8.90016	+	27.6532i	−0.360653	+	1.12057i
$610$		−	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	−0.398415	−	0.917205i	$-0.630440\pi$
$613$	−29.7615	−	7.97457i	−1.20206	−	0.322090i	−0.803640	+	0.595115i	$0.797106\pi$
$614$	1.71288	−	0.988929i	0.0691261	−	0.0399099i
$615$	1.37452	−	2.12952i	0.0554260	−	0.0858704i
$616$	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	$0.615283\pi$
$618$	17.3125	−	3.73022i	0.696410	−	0.150051i
$619$	−28.5202	−	28.5202i	−1.14633	−	1.14633i	−0.987270	−	0.159056i	$-0.949155\pi$
$619$	−28.5202	−	28.5202i	−1.14633	−	1.14633i	−0.159056	−	0.987270i	$-0.550845\pi$
$620$	0.944948	+	0.545566i	0.0379500	+	0.0219105i
$621$	16.4284	−	6.46401i	0.659250	−	0.259392i
$622$	−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
$627$	−12.7412	−	24.8351i	−0.508835	−	0.991817i
$628$	−16.4847	−	9.51745i	−0.657812	−	0.379788i
$629$	−34.4612	−	34.4612i	−1.37406	−	1.37406i
$630$	−1.33293	−	8.12320i	−0.0531053	−	0.323636i
$631$	23.4553	−	6.28482i	0.933740	−	0.250195i	0.240291	−	0.970701i	$-0.422757\pi$
$631$	23.4553	−	6.28482i	0.933740	−	0.250195i	0.693449	+	0.720506i	$0.256090\pi$
$632$	16.1948	−	16.1948i	0.644195	−	0.644195i
$633$	19.7101	+	12.7221i	0.783407	+	0.505659i
$634$	−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
$639$	−10.1776	+	26.9607i	−0.402620	+	1.06655i
$640$	−6.74817	−	11.6882i	−0.266745	−	0.462016i
$641$	−4.70367	+	8.14700i	−0.185784	+	0.321787i	−0.943840	−	0.330402i	$-0.892816\pi$
$641$	−4.70367	+	8.14700i	−0.185784	+	0.321787i	0.758056	+	0.652189i	$0.226149\pi$
$642$	6.68178	+	7.37951i	0.263709	+	0.291246i
$643$	−11.8390	−	44.1838i	−0.466885	−	1.74244i	−0.650563	−	0.759453i	$-0.725467\pi$
$643$	−11.8390	−	44.1838i	−0.466885	−	1.74244i	0.183677	−	0.982987i	$-0.441200\pi$
$644$	3.17457	+	11.8477i	0.125096	+	0.466863i
$645$	−12.3947	−	13.6889i	−0.488040	−	0.539002i
$646$	−7.52133	+	13.0273i	−0.295923	+	0.512554i
$647$	4.40379	+	7.62760i	0.173131	+	0.299872i	0.939513	−	0.342514i	$-0.111278\pi$
$647$	4.40379	+	7.62760i	0.173131	+	0.299872i	−0.766382	+	0.642385i	$0.777945\pi$
$648$	−21.0490	−	10.4318i	−0.826882	−	0.409798i
$649$		−	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	−0.749164	−	0.662384i	$-0.769545\pi$
$653$	−14.0573	+	8.11599i	−0.550105	+	0.317603i	0.199059	+	0.979987i	$0.436211\pi$
$654$	3.31062	+	2.13688i	0.129455	+	0.0835586i
$655$	−5.34004	+	5.34004i	−0.208653	+	0.208653i
$656$	0.840739	−	0.225275i	0.0328254	−	0.00879553i
$657$	25.3167	−	4.15421i	0.987699	−	0.162071i
$658$	−0.474398	−	0.474398i	−0.0184940	−	0.0184940i
$659$	−16.1496	−	9.32398i	−0.629099	−	0.363211i	0.151304	−	0.988487i	$-0.451653\pi$
$659$	−16.1496	−	9.32398i	−0.629099	−	0.363211i	−0.780403	+	0.625277i	$0.784986\pi$
$660$	−7.49414	−	14.6075i	−0.291709	−	0.568598i
$661$	7.32011	−	27.3190i	0.284719	−	1.06259i	−0.664325	−	0.747444i	$-0.731281\pi$
$661$	7.32011	−	27.3190i	0.284719	−	1.06259i	0.949044	−	0.315143i	$-0.102052\pi$
$662$	−17.1693			−0.667303
$663$		0			0
$664$	30.7072			1.19167
$665$	3.15264	−	11.7658i	0.122254	−	0.456259i
$666$	−17.5392	+	7.92613i	−0.679632	+	0.307131i
$667$	19.3593	+	11.1771i	0.749595	+	0.432779i
$668$	−4.38772	−	4.38772i	−0.169766	−	0.169766i
$669$	−17.5352	+	3.77822i	−0.677952	+	0.146074i
$670$	6.67625	−	1.78890i	0.257926	−	0.0691111i
$671$	23.6793	−	23.6793i	0.914128	−	0.914128i
$672$	14.0332	−	21.7413i	0.541341	−	0.838687i
$673$	−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	$0.381162\pi$
$677$			48.4537i			1.86223i	−0.364727	+	0.931114i	$0.618838\pi$
$678$	−0.768644	+	2.38822i	−0.0295196	+	0.0917189i
$679$	−2.41902	−	4.18986i	−0.0928333	−	0.160792i
$680$	−10.6716	+	18.4837i	−0.409236	+	0.708818i
$681$	−0.0848094	+	0.0767908i	−0.00324990	+	0.00294263i
$682$	−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	$0.802670\pi$
$684$	−9.13103	−	11.1486i	−0.349134	−	0.426276i
$685$	−3.40945	+	5.90534i	−0.130268	+	0.225632i
$686$	−7.30582	−	12.6540i	−0.278937	−	0.483134i
$687$	−44.8260	−	14.4272i	−1.71022	−	0.550431i
$688$		−	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	0.0637158	−	0.997968i	$-0.479705\pi$
$691$	−9.99134	−	2.67717i	−0.380089	−	0.101844i	−0.443805	+	0.896124i	$0.646372\pi$
$692$	5.31487	−	3.06854i	0.202041	−	0.116648i
$693$	21.1931	−	29.5136i	0.805060	−	1.12113i
$694$	6.07014	−	6.07014i	0.230419	−	0.230419i
$695$	16.0407	−	4.29809i	0.608457	−	0.163036i
$696$	−6.26543	−	29.0787i	−0.237490	−	1.10223i
$697$	−4.26323	−	4.26323i	−0.161481	−	0.161481i
$698$	23.0719	+	13.3206i	0.873285	+	0.504191i
$699$	25.4506	−	13.0570i	0.962631	−	0.493861i
$700$	−2.81748	+	10.5150i	−0.106491	+	0.397428i
$701$	−1.23945			−0.0468132			−0.0234066	−	0.999726i	$-0.507451\pi$
$701$	−1.23945			−0.0468132			−0.0234066	+	0.999726i	$0.507451\pi$
$702$		0			0
$703$	−28.4804			−1.07416
$704$	−3.44584	+	12.8601i	−0.129870	+	0.484682i
$705$	−0.747788	+	0.383640i	−0.0281633	+	0.0144487i
$706$	−21.3111	−	12.3040i	−0.802053	−	0.463066i
$707$	−3.72708	−	3.72708i	−0.140171	−	0.140171i
$708$	−2.60169	−	12.0748i	−0.0977776	−	0.453799i
$709$	−26.1123	+	6.99678i	−0.980670	+	0.262770i	−0.713327	−	0.700832i	$-0.752812\pi$
$709$	−26.1123	+	6.99678i	−0.980670	+	0.262770i	−0.267343	+	0.963601i	$0.586146\pi$
$710$	7.31139	−	7.31139i	0.274392	−	0.274392i
$711$	15.3535	−	21.3813i	0.575801	−	0.801861i
$712$	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
$717$	43.7306	+	14.0746i	1.63315	+	0.525627i
$718$	11.2650	+	19.5116i	0.420406	+	0.728165i
$719$	19.0678	−	33.0264i	0.711109	−	1.23168i	−0.253332	−	0.967379i	$-0.581527\pi$
$719$	19.0678	−	33.0264i	0.711109	−	1.23168i	0.964441	−	0.264298i	$-0.0851401\pi$
$720$	−2.24389	−	2.73968i	−0.0836247	−	0.102102i
$721$	8.82895	+	32.9501i	0.328807	+	1.22713i
$722$	−1.48221	−	5.53167i	−0.0551620	−	0.205867i
$723$	6.05243	−	5.48018i	0.225092	−	0.203810i
$724$	−0.691101	+	1.19702i	−0.0256846	+	0.0444870i
$725$	9.91983	+	17.1817i	0.368413	+	0.638111i
$726$	−4.69255	+	14.5800i	−0.174157	+	0.541114i
$727$		−	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
$732$	9.37578	−	14.5257i	0.346539	−	0.536885i
$733$	−0.240557	+	0.240557i	−0.00888518	+	0.00888518i	−0.711535	−	0.702650i	$-0.752000\pi$
$733$	−0.240557	+	0.240557i	−0.00888518	+	0.00888518i	0.702650	+	0.711535i	$0.252000\pi$
$734$	15.7337	−	4.21582i	0.580740	−	0.155609i
$735$	−1.19670	+	0.257847i	−0.0441410	+	0.00951081i
$736$	−14.0801	−	14.0801i	−0.519000	−	0.519000i
$737$	26.4206	+	15.2539i	0.973215	+	0.561886i
$738$	−2.16979	+	0.980548i	−0.0798713	+	0.0360945i
$739$	8.76818	−	32.7233i	0.322543	−	1.20375i	−0.594216	−	0.804305i	$-0.702538\pi$
$739$	8.76818	−	32.7233i	0.322543	−	1.20375i	0.916759	−	0.399441i	$-0.130796\pi$
$740$	−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	$-0.124277\pi$
$744$	−1.12868	−	2.20002i	−0.0413795	−	0.0806567i
$745$	8.40335	+	4.85168i	0.307875	+	0.177752i
$746$	−7.51190	−	7.51190i	−0.275030	−	0.275030i
$747$	34.8266	−	5.71469i	1.27424	−	0.209090i
$748$	−37.7227	+	10.1078i	−1.37928	+	0.369577i
$749$	−13.5590	+	13.5590i	−0.495437	+	0.495437i
$750$	−12.5555	−	8.10411i	−0.458463	−	0.295920i
$751$	−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
$756$	7.48661	−	17.1999i	0.272285	−	0.625553i
$757$	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
$759$	−18.7663	−	20.7259i	−0.681172	−	0.752301i
$760$	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	$0.956072\pi$
$762$	6.31985	+	6.97978i	0.228944	+	0.252851i
$763$	−3.79495	+	6.57305i	−0.137386	+	0.237960i
$764$	12.1135	+	20.9812i	0.438251	+	0.759073i
$765$	−8.66333	+	22.9494i	−0.313223	+	0.829736i
$766$		−	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	0.613744	−	0.789505i	$-0.289663\pi$
$769$	20.8122	+	5.57662i	0.750508	+	0.201098i	0.136765	+	0.990604i	$0.456330\pi$
$770$	−11.2903	+	6.51844i	−0.406873	+	0.234908i
$771$	28.4278	+	18.3490i	1.02380	+	0.660825i
$772$	−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} +(-1.54108 + 0.790622i) q^{3} +(1.22645 + 0.708090i) q^{4} +(-0.996141 - 0.996141i) q^{5} +(0.278754 + 1.29374i) q^{6} +(-2.46232 + 0.659775i) q^{7} +(1.84572 - 1.84572i) q^{8} +(1.74983 - 2.43682i) q^{9} +(-0.932193 + 0.538202i) q^{10} +(-4.58925 - 1.22969i) q^{11} +(-2.44988 - 0.121564i) q^{12} +1.94778i q^{14} +(2.32270 + 0.747558i) q^{15} +(0.418964 + 0.725666i) q^{16} +(2.90210 - 5.02659i) q^{17} +(-1.45244 - 1.77336i) q^{18} +(-0.877888 - 3.27632i) q^{19} +(-0.516358 - 1.92707i) q^{20} +(3.27298 - 2.96353i) q^{21} +(-1.81513 + 3.14390i) q^{22} +(-1.69879 - 2.94240i) q^{23} +(-1.38513 + 4.30366i) q^{24} -3.01541i q^{25} +(-0.770022 + 5.13878i) q^{27} +(-3.48708 - 0.934361i) q^{28} +(-5.69796 + 3.28972i) q^{29} +(1.01107 - 1.56642i) q^{30} +(-0.386730 + 0.386730i) q^{31} +(5.66102 - 1.51687i) q^{32} +(8.04461 - 1.73333i) q^{33} +(-3.13593 - 3.13593i) q^{34} +(3.11004 + 1.79558i) q^{35} +(3.87157 - 1.74959i) q^{36} +(2.17320 - 8.11049i) q^{37} -2.59169 q^{38} -3.67719 q^{40} +(0.268848 - 1.00336i) q^{41} +(-1.53996 - 3.00167i) q^{42} +(-6.55422 - 3.78408i) q^{43} +(-4.75775 - 4.75775i) q^{44} +(-4.17050 + 0.684336i) q^{45} +(-2.50757 + 0.671902i) q^{46} +(-0.243559 + 0.243559i) q^{47} +(-1.21938 - 0.787065i) q^{48} +(-0.434484 + 0.250850i) q^{49} +(-2.22551 - 0.596323i) q^{50} +(-0.498228 + 10.0408i) q^{51} -2.07223i q^{53} +(3.64038 + 1.58455i) q^{54} +(3.34660 + 5.79649i) q^{55} +(-3.32698 + 5.76250i) q^{56} +(3.94323 + 4.35499i) q^{57} +(1.30114 + 4.85592i) q^{58} +(1.30332 + 4.86406i) q^{59} +(2.31933 + 2.56152i) q^{60} +(-3.52415 + 6.10401i) q^{61} +(0.208945 + 0.361904i) q^{62} +(-2.70089 + 7.15471i) q^{63} -2.80221i q^{64} +(0.311618 - 6.28007i) q^{66} +(-6.20237 - 1.66192i) q^{67} +(7.11855 - 4.10990i) q^{68} +(4.94429 + 3.19135i) q^{69} +(1.94026 - 1.94026i) q^{70} +(-9.27862 + 2.48620i) q^{71} +(-1.26798 - 7.72737i) q^{72} +(6.04700 + 6.04700i) q^{73} +(-5.55614 - 3.20784i) q^{74} +(2.38405 + 4.64697i) q^{75} +(1.24325 - 4.63986i) q^{76} +12.1115 q^{77} +8.77426 q^{79} +(0.305519 - 1.14021i) q^{80} +(-2.87617 - 8.52805i) q^{81} +(-0.687355 - 0.396845i) q^{82} +(8.31849 + 8.31849i) q^{83} +(6.11259 - 1.31704i) q^{84} +(-7.89810 + 2.11629i) q^{85} +(-4.08898 + 4.08898i) q^{86} +(6.18006 - 9.57464i) q^{87} +(-10.7401 + 6.20081i) q^{88} +(13.1488 + 3.52321i) q^{89} +(-0.319681 + 3.21335i) q^{90} -4.81159i q^{92} +(0.290223 - 0.901738i) q^{93} +(0.131592 + 0.227923i) q^{94} +(-2.38918 + 4.13818i) q^{95} +(-7.52480 + 6.81334i) q^{96} +(0.491207 + 1.83321i) q^{97} +(0.0992154 + 0.370277i) q^{98} +(-11.0270 + 9.03143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more