LMFDB - Embedded newform 507.2.k.k.80.9

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			80.9
Character	$\chi$	$=$	507.80
Dual form			507.2.k.k.488.9

$q$-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	$0.170404\pi$
$2$	−0.197759	+	0.738045i	−0.139837	+	0.521877i	−0.999931	+	0.0117423i	$0.996262\pi$
$3$	−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	0.893851	−	0.448363i	$-0.147993\pi$
$5$	0.996141	+	0.996141i	0.445488	+	0.445488i	−0.448363	+	0.893851i	$0.647993\pi$
$6$	−0.278754	−	1.29374i	−0.113801	−	0.528166i
$7$	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
$9$	1.74983	−	2.43682i	0.583277	−	0.812273i
$10$	−0.932193	+	0.538202i	−0.294785	+	0.170194i
$11$	4.58925	+	1.22969i	1.38371	+	0.370765i	0.872468	−	0.488671i	$-0.162518\pi$
$11$	4.58925	+	1.22969i	1.38371	+	0.370765i	0.511244	+	0.859436i	$0.329185\pi$
$12$	−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	$0.0438728\pi$
$19$	0.877888	+	3.27632i	0.201401	+	0.751640i	−0.789115	+	0.614245i	$0.789461\pi$
$20$	0.516358	+	1.92707i	0.115461	+	0.430907i
$21$	−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	−0.671524	−	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
$33$	−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	$0.325809\pi$
$37$	−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	−0.983737	−	0.179617i	$-0.942514\pi$
$41$	−0.268848	+	1.00336i	−0.0419871	+	0.156698i	0.941750	+	0.336315i	$0.109181\pi$
$42$	−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	−0.689120	−	0.724647i	$-0.742003\pi$
$47$	0.243559	−	0.243559i	0.0355267	−	0.0355267i	0.724647	+	0.689120i	$0.242003\pi$
$48$	−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	$-0.977029\pi$
$59$	−1.30332	−	4.86406i	−0.169678	−	0.633247i	0.827719	−	0.561143i	$-0.189638\pi$
$60$	−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	0.616948	−	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
$69$	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	0.337929	−	0.941172i	$-0.390274\pi$
$71$	9.27862	−	2.48620i	1.10117	−	0.295057i	0.763241	+	0.646114i	$0.223607\pi$
$72$	1.26798	+	7.72737i	0.149433	+	0.910680i
$73$	−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
$75$	2.38405	+	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	0.0834395	−	0.996513i	$-0.473409\pi$
$83$	−8.31849	−	8.31849i	−0.913073	−	0.913073i	−0.996513	+	0.0834395i	$0.973409\pi$
$84$	−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	−0.517667	−	0.855582i	$-0.673199\pi$
$89$	−13.1488	−	3.52321i	−1.39377	−	0.373460i	−0.876104	+	0.482123i	$0.839866\pi$
$90$	−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	0.936495	−	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
$99$	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	−0.800709	−	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
$111$	−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	0.998568	−	0.0535011i	$-0.0170381\pi$
$137$	1.25278	+	4.67544i	0.107032	+	0.399450i	−0.891536	+	0.452951i	$0.850371\pi$
$138$	−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	0.0242209	−	0.999707i	$-0.492289\pi$
$149$	6.65319	−	1.78272i	0.545050	−	0.146046i	0.520829	+	0.853661i	$0.325623\pi$
$150$	−3.90114	+	0.840556i	−0.318527	+	0.0686311i
$151$	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
$153$	−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	−0.491411	−	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
$165$	−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	0.418826	−	0.908066i	$-0.362442\pi$
$167$	4.23233	+	1.13405i	0.327507	+	0.0877553i	−0.0913190	+	0.995822i	$0.529108\pi$
$168$	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	−0.938232	−	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	$0.302773\pi$
$197$	−4.62128	+	17.2469i	−0.329253	+	1.22879i	−0.909967	+	0.414681i	$0.863893\pi$
$198$	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	−0.0921788	−	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
$225$	−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	−0.260936	−	0.965356i	$-0.584031\pi$
$227$	−0.0638035	+	0.0170961i	−0.00423478	+	0.00113471i	0.256701	+	0.966491i	$0.417364\pi$
$228$	−1.75244	−	8.13332i	−0.116058	−	0.538643i
$229$	−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
$231$	−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	$0.0781856\pi$
$239$	18.7548	+	18.7548i	1.21315	+	1.21315i	0.243165	+	0.969985i	$0.421814\pi$
$240$	−0.430650	−	1.99871i	−0.0277983	−	0.129016i
$241$	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
$243$	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	−0.887194	−	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
$276$	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	$0.505387\pi$
$281$	−17.0443	+	17.0443i	−1.01678	+	1.01678i	−0.999857	+	0.0169217i	$0.994613\pi$
$282$	−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	$0.0685497\pi$
$293$	4.06923	+	15.1866i	0.237727	+	0.887209i	−0.739174	+	0.673515i	$0.764784\pi$
$294$	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	0.652942	−	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
$309$	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	0.956219	−	0.292654i	$-0.0945383\pi$
$317$	11.8144	+	11.8144i	0.663565	+	0.663565i	−0.292654	+	0.956219i	$0.594538\pi$
$318$	−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	$0.128539\pi$
$331$	5.81579	+	21.7048i	0.319665	+	1.19300i	−0.599903	+	0.800073i	$0.704794\pi$
$332$	−4.31196	−	16.0924i	−0.236649	−	0.883188i
$333$	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	$-0.533678\pi$
$349$	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	$0.411053\pi$
$353$	−8.33550	+	31.1085i	−0.443654	+	1.65574i	−0.719466	+	0.694528i	$0.755613\pi$
$354$	−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	$-0.466175\pi$
$359$	20.8500	−	20.8500i	1.10042	−	1.10042i	0.994359	−	0.106064i	$-0.0338248\pi$
$360$	−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	−0.745912	−	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
$381$	−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	−0.649904	−	0.760016i	$-0.725191\pi$
$383$	−16.2968	+	4.36672i	−0.832729	+	0.223129i	−0.182825	+	0.983145i	$0.558524\pi$
$384$	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	−0.226535	−	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
$399$	−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	−0.447502	−	0.894283i	$-0.647686\pi$
$401$	−25.6759	−	6.87983i	−1.28219	−	0.343562i	−0.834689	+	0.550721i	$0.814353\pi$
$402$	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	0.999628	−	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
$411$	−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	−0.0418609	−	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
$423$	−0.167322	−	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	−0.989202	−	0.146560i	$-0.953180\pi$
$431$	−1.23002	+	4.59049i	−0.0592479	+	0.221116i	0.929954	+	0.367676i	$0.119846\pi$
$432$	−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	$0.0432423\pi$
$449$	4.24760	+	15.8522i	0.200456	+	0.748113i	−0.790330	+	0.612681i	$0.790091\pi$
$450$	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	0.734230	−	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
$459$	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	−0.852030	−	0.523494i	$-0.824628\pi$
$461$	−28.5168	+	7.64107i	−1.32816	+	0.355880i	−0.476132	+	0.879374i	$0.657962\pi$
$462$	−3.37613	−	15.6691i	−0.157072	−	0.728993i
$463$	−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
$465$	−1.18736	+	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	0.531099	−	0.847310i	$-0.321779\pi$
$479$	12.4179	+	3.32737i	0.567389	+	0.152031i	0.0362900	+	0.999341i	$0.488446\pi$
$480$	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	$-0.872839\pi$
$487$	−7.01541	−	26.1819i	−0.317898	−	1.18641i	0.603362	−	0.797467i	$-0.293827\pi$
$488$	−4.76169	−	17.7709i	−0.215552	−	0.804449i
$489$	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	−0.828180	−	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
$501$	−7.41894	+	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	$-0.615541\pi$
$509$	9.47229	−	35.3511i	0.419852	−	1.56691i	0.774915	−	0.632066i	$-0.217793\pi$
$510$	−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	0.447017	−	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
$543$	−0.771653	−	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	−0.0143553	−	0.999897i	$-0.504570\pi$
$557$	−12.4314	−	3.33099i	−0.526736	−	0.141138i	−0.512381	+	0.858759i	$0.671236\pi$
$558$	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	−0.660372	−	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
$579$	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	$-0.816061\pi$
$587$	3.89820	−	14.5483i	0.160896	−	0.600472i	0.998528	−	0.0542369i	$-0.0172726\pi$
$588$	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	−0.973568	−	0.228397i	$-0.926652\pi$
$593$	−18.1461	+	18.1461i	−0.745171	+	0.745171i	0.228397	+	0.973568i	$0.426652\pi$
$594$	−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	0.803640	−	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
$615$	1.37452	−	2.12952i	0.0554260	−	0.0858704i
$616$	−22.3544	+	22.3544i	−0.900685	+	0.900685i
$617$	28.0366	−	7.51239i	1.12871	−	0.302437i	0.354308	−	0.935129i	$-0.384717\pi$
$617$	28.0366	−	7.51239i	1.12871	−	0.302437i	0.774404	+	0.632691i	$0.218050\pi$
$618$	−17.3125	+	3.73022i	−0.696410	+	0.150051i
$619$	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
$621$	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	−0.693449	−	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
$633$	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	$0.274533\pi$
$643$	11.8390	+	44.1838i	0.466885	+	1.74244i	−0.183677	+	0.982987i	$0.558800\pi$
$644$	−3.17457	−	11.8477i	−0.125096	−	0.466863i
$645$	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	$0.268719\pi$
$661$	−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
$666$	−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	$-0.969337\pi$
$683$	−4.74192	−	17.6971i	−0.181445	−	0.677161i	0.813919	−	0.580978i	$-0.197330\pi$
$684$	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	0.443805	−	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
$693$	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	0.267343	−	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
$711$	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	−0.702650	−	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
$735$	1.19670	−	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	$0.297462\pi$
$739$	−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	$0.290943\pi$
$743$	−8.56404	+	31.9614i	−0.314184	+	1.17255i	−0.924747	+	0.380583i	$0.875723\pi$
$744$	−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	0.990493	−	0.137566i	$-0.0439280\pi$
$761$	1.76325	+	6.58054i	0.0639177	+	0.238544i	−0.926575	+	0.376110i	$0.877261\pi$
$762$	−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	−0.136765	−	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
$771$	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	−0.209516	−	0.977805i	$-0.567189\pi$
$773$	2.72302	−	0.729632i	0.0979403	−	0.0262430i	0.307456	+	0.951562i	$0.400522\pi$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.197759 + 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

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