LMFDB - Embedded newform 190.2.k.d.81.3

Newspace parameters

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.k (of order $9$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
Defining polynomial:	$x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} - 12862 x^{9} + 77397 x^{8} - 24822 x^{7} + 178501 x^{6} - 39408 x^{5} + 132588 x^{4} + 45584 x^{3} + 50640 x^{2} + 1824 x + 64$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.3
Root			$-1.58985 + 2.75370i$ of defining polynomial
Character	$\chi$	$=$	190.81
Dual form			190.2.k.d.61.3

$q$-expansion

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.552148 - 3.13139i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-0.552148 - 3.13139i) q^{6} +(1.67305 + 2.89781i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-6.68164 - 2.43192i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.552148 - 3.13139i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-0.552148 - 3.13139i) q^{6} +(1.67305 + 2.89781i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-6.68164 - 2.43192i) q^{9} +(0.939693 + 0.342020i) q^{10} +(-3.09216 + 5.35578i) q^{11} +(-1.58985 - 2.75370i) q^{12} +(-0.128260 - 0.727397i) q^{13} +(2.56327 + 2.15083i) q^{14} +(2.43579 - 2.04387i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.815778 + 0.296919i) q^{17} -7.11045 q^{18} +(-2.59916 - 3.49919i) q^{19} +1.00000 q^{20} +(9.99794 - 3.63895i) q^{21} +(-1.07390 + 6.09037i) q^{22} +(-0.875950 + 0.735009i) q^{23} +(-2.43579 - 2.04387i) q^{24} +(0.173648 + 0.984808i) q^{25} +(-0.369309 - 0.639662i) q^{26} +(-6.53498 + 11.3189i) q^{27} +(3.14431 + 1.14444i) q^{28} +(7.32010 + 2.66430i) q^{29} +(1.58985 - 2.75370i) q^{30} +(-3.23887 - 5.60988i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(15.0637 + 12.6399i) q^{33} +(-0.665029 + 0.558025i) q^{34} +(-0.581045 + 3.29527i) q^{35} +(-6.68164 + 2.43192i) q^{36} +1.68113 q^{37} +(-3.63921 - 2.39920i) q^{38} -2.34858 q^{39} +(0.939693 - 0.342020i) q^{40} +(1.68282 - 9.54373i) q^{41} +(8.15040 - 6.83899i) q^{42} +(1.42354 + 1.19449i) q^{43} +(1.07390 + 6.09037i) q^{44} +(-3.55522 - 6.15783i) q^{45} +(-0.571736 + 0.990275i) q^{46} +(-0.311691 - 0.113446i) q^{47} +(-2.98793 - 1.08752i) q^{48} +(-2.09821 + 3.63420i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.479338 + 2.71846i) q^{51} +(-0.565815 - 0.474775i) q^{52} +(-5.44265 + 4.56693i) q^{53} +(-2.26958 + 12.8714i) q^{54} +(-5.81136 + 2.11516i) q^{55} +3.34610 q^{56} +(-12.3925 + 6.20691i) q^{57} +7.78988 q^{58} +(-4.56719 + 1.66232i) q^{59} +(0.552148 - 3.13139i) q^{60} +(5.53664 - 4.64579i) q^{61} +(-4.96223 - 4.16381i) q^{62} +(-4.13149 - 23.4308i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.369309 - 0.639662i) q^{65} +(18.4784 + 6.72557i) q^{66} +(-2.74854 - 1.00039i) q^{67} +(-0.434067 + 0.751825i) q^{68} +(1.81794 + 3.14877i) q^{69} +(0.581045 + 3.29527i) q^{70} +(-5.27849 - 4.42918i) q^{71} +(-5.44692 + 4.57051i) q^{72} +(1.35735 - 7.69790i) q^{73} +(1.57975 - 0.574982i) q^{74} +3.17969 q^{75} +(-4.24031 - 1.00983i) q^{76} -20.6934 q^{77} +(-2.20694 + 0.803262i) q^{78} +(-0.399207 + 2.26401i) q^{79} +(0.766044 - 0.642788i) q^{80} +(15.4949 + 13.0018i) q^{81} +(-1.68282 - 9.54373i) q^{82} +(5.72338 + 9.91318i) q^{83} +(5.31979 - 9.21415i) q^{84} +(-0.815778 - 0.296919i) q^{85} +(1.74623 + 0.635576i) q^{86} +(12.3847 - 21.4510i) q^{87} +(3.09216 + 5.35578i) q^{88} +(0.404290 + 2.29284i) q^{89} +(-5.44692 - 4.57051i) q^{90} +(1.89328 - 1.58865i) q^{91} +(-0.198562 + 1.12610i) q^{92} +(-19.3550 + 7.04466i) q^{93} -0.331695 q^{94} +(0.258165 - 4.35125i) q^{95} -3.17969 q^{96} +(6.43131 - 2.34081i) q^{97} +(-0.728700 + 4.13266i) q^{98} +(33.6855 - 28.2655i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18q + 9q^{8} - 18q^{9} + O(q^{10}) $	$ 18q + 9q^{8} - 18q^{9} - 12q^{11} - 6q^{13} + 6q^{14} - 42q^{18} + 18q^{20} + 12q^{21} - 3q^{22} + 9q^{23} - 9q^{26} - 18q^{27} + 3q^{28} - 6q^{29} - 6q^{31} + 66q^{33} + 18q^{34} + 3q^{35} - 18q^{36} - 12q^{37} - 6q^{38} + 48q^{39} - 21q^{41} + 42q^{42} + 18q^{43} + 3q^{44} - 21q^{45} + 18q^{46} - 54q^{47} - 39q^{49} + 9q^{50} + 42q^{51} + 12q^{52} - 24q^{53} - 54q^{54} - 6q^{55} - 18q^{57} - 30q^{59} + 48q^{61} - 30q^{62} - 57q^{63} - 9q^{64} + 9q^{65} + 24q^{66} - 6q^{67} - 6q^{68} - 30q^{69} - 3q^{70} + 30q^{71} + 6q^{73} - 3q^{74} - 21q^{76} + 30q^{77} - 24q^{78} + 30q^{79} + 18q^{81} + 21q^{82} + 6q^{83} + 6q^{84} + 36q^{86} + 24q^{87} + 12q^{88} + 30q^{89} - 60q^{91} - 18q^{92} - 12q^{93} + 6q^{94} - 12q^{95} - 12q^{97} - 18q^{98} + 171q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.552148	−	3.13139i	0.318783	−	1.80791i	−0.231396	−	0.972860i	$-0.574329\pi$
$3$	0.552148	−	3.13139i	0.318783	−	1.80791i	0.550178	−	0.835047i	$-0.314560\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$5$	0.766044	+	0.642788i	0.342585	+	0.287463i
$6$	−0.552148	−	3.13139i	−0.225413	−	1.27838i
$7$	1.67305	+	2.89781i	0.632354	+	1.09527i	0.987069	+	0.160295i	$0.0512447\pi$
$7$	1.67305	+	2.89781i	0.632354	+	1.09527i	−0.354715	+	0.934975i	$0.615422\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−6.68164	−	2.43192i	−2.22721	−	0.810639i
$10$	0.939693	+	0.342020i	0.297157	+	0.108156i
$11$	−3.09216	+	5.35578i	−0.932322	+	1.61483i	−0.152981	+	0.988229i	$0.548887\pi$
$11$	−3.09216	+	5.35578i	−0.932322	+	1.61483i	−0.779341	+	0.626600i	$0.784446\pi$
$12$	−1.58985	−	2.75370i	−0.458949	−	0.794923i
$13$	−0.128260	−	0.727397i	−0.0355729	−	0.201744i	0.961842	−	0.273607i	$-0.0882167\pi$
$13$	−0.128260	−	0.727397i	−0.0355729	−	0.201744i	−0.997415	+	0.0718630i	$0.977106\pi$
$14$	2.56327	+	2.15083i	0.685061	+	0.574835i
$15$	2.43579	−	2.04387i	0.628917	−	0.527724i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.815778	+	0.296919i	−0.197855	+	0.0720134i	−0.439047	−	0.898464i	$-0.644684\pi$
$17$	−0.815778	+	0.296919i	−0.197855	+	0.0720134i	0.241192	+	0.970477i	$0.422462\pi$
$18$	−7.11045			−1.67595
$19$	−2.59916	−	3.49919i	−0.596289	−	0.802770i
$19$	−2.59916	−	3.49919i	−0.596289	−	0.802770i
$20$	1.00000			0.223607
$21$	9.99794	−	3.63895i	2.18173	−	0.794085i
$22$	−1.07390	+	6.09037i	−0.228956	+	1.29847i
$23$	−0.875950	+	0.735009i	−0.182648	+	0.153260i	−0.729528	−	0.683951i	$-0.760260\pi$
$23$	−0.875950	+	0.735009i	−0.182648	+	0.153260i	0.546879	+	0.837211i	$0.315816\pi$
$24$	−2.43579	−	2.04387i	−0.497203	−	0.417203i
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	−0.369309	−	0.639662i	−0.0724275	−	0.125448i
$27$	−6.53498	+	11.3189i	−1.25766	+	2.17833i
$28$	3.14431	+	1.14444i	0.594219	+	0.216278i
$29$	7.32010	+	2.66430i	1.35931	+	0.494748i	0.915840	−	0.401543i	$-0.131526\pi$
$29$	7.32010	+	2.66430i	1.35931	+	0.494748i	0.443468	+	0.896290i	$0.353748\pi$
$30$	1.58985	−	2.75370i	0.290265	−	0.502754i
$31$	−3.23887	−	5.60988i	−0.581718	−	1.00756i	−0.995276	−	0.0970869i	$-0.969048\pi$
$31$	−3.23887	−	5.60988i	−0.581718	−	1.00756i	0.413558	−	0.910478i	$-0.364286\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	15.0637	+	12.6399i	2.62225	+	2.20033i
$34$	−0.665029	+	0.558025i	−0.114051	+	0.0957005i
$35$	−0.581045	+	3.29527i	−0.0982145	+	0.557002i
$36$	−6.68164	+	2.43192i	−1.11361	+	0.405319i
$37$	1.68113			0.276377			0.138188	−	0.990406i	$-0.455872\pi$
$37$	1.68113			0.276377			0.138188	+	0.990406i	$0.455872\pi$
$38$	−3.63921	−	2.39920i	−0.590357	−	0.389202i
$39$	−2.34858			−0.376074
$40$	0.939693	−	0.342020i	0.148578	−	0.0540781i
$41$	1.68282	−	9.54373i	0.262812	−	1.49048i	−0.512383	−	0.858757i	$-0.671237\pi$
$41$	1.68282	−	9.54373i	0.262812	−	1.49048i	0.775194	−	0.631723i	$-0.217652\pi$
$42$	8.15040	−	6.83899i	1.25763	−	1.05528i
$43$	1.42354	+	1.19449i	0.217088	+	0.182158i	0.744846	−	0.667236i	$-0.232523\pi$
$43$	1.42354	+	1.19449i	0.217088	+	0.182158i	−0.527758	+	0.849395i	$0.676967\pi$
$44$	1.07390	+	6.09037i	0.161896	+	0.918158i
$45$	−3.55522	−	6.15783i	−0.529982	−	0.917955i
$46$	−0.571736	+	0.990275i	−0.0842978	+	0.146008i
$47$	−0.311691	−	0.113446i	−0.0454649	−	0.0165479i	0.319188	−	0.947692i	$-0.396590\pi$
$47$	−0.311691	−	0.113446i	−0.0454649	−	0.0165479i	−0.364652	+	0.931144i	$0.618812\pi$
$48$	−2.98793	−	1.08752i	−0.431271	−	0.156970i
$49$	−2.09821	+	3.63420i	−0.299744	+	0.519172i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.479338	+	2.71846i	0.0671207	+	0.380661i
$52$	−0.565815	−	0.474775i	−0.0784644	−	0.0658394i
$53$	−5.44265	+	4.56693i	−0.747606	+	0.627316i	−0.934868	−	0.354994i	$-0.884483\pi$
$53$	−5.44265	+	4.56693i	−0.747606	+	0.627316i	0.187263	+	0.982310i	$0.440038\pi$
$54$	−2.26958	+	12.8714i	−0.308850	+	1.75158i
$55$	−5.81136	+	2.11516i	−0.783604	+	0.285209i
$56$	3.34610			0.447142
$57$	−12.3925	+	6.20691i	−1.64142	+	0.822125i
$58$	7.78988			1.02286
$59$	−4.56719	+	1.66232i	−0.594597	+	0.216416i	−0.621750	−	0.783216i	$-0.713578\pi$
$59$	−4.56719	+	1.66232i	−0.594597	+	0.216416i	0.0271531	+	0.999631i	$0.491356\pi$
$60$	0.552148	−	3.13139i	0.0712820	−	0.404260i
$61$	5.53664	−	4.64579i	0.708894	−	0.594833i	−0.215394	−	0.976527i	$-0.569104\pi$
$61$	5.53664	−	4.64579i	0.708894	−	0.594833i	0.924289	+	0.381694i	$0.124659\pi$
$62$	−4.96223	−	4.16381i	−0.630204	−	0.528804i
$63$	−4.13149	−	23.4308i	−0.520519	−	2.95201i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.369309	−	0.639662i	0.0458072	−	0.0793404i
$66$	18.4784	+	6.72557i	2.27453	+	0.827861i
$67$	−2.74854	−	1.00039i	−0.335787	−	0.122217i	0.168623	−	0.985681i	$-0.446068\pi$
$67$	−2.74854	−	1.00039i	−0.335787	−	0.122217i	−0.504410	+	0.863464i	$0.668290\pi$
$68$	−0.434067	+	0.751825i	−0.0526383	+	0.0911722i
$69$	1.81794	+	3.14877i	0.218855	+	0.379068i
$70$	0.581045	+	3.29527i	0.0694482	+	0.393860i
$71$	−5.27849	−	4.42918i	−0.626442	−	0.525647i	0.273379	−	0.961906i	$-0.411859\pi$
$71$	−5.27849	−	4.42918i	−0.626442	−	0.525647i	−0.899821	+	0.436259i	$0.856303\pi$
$72$	−5.44692	+	4.57051i	−0.641926	+	0.538640i
$73$	1.35735	−	7.69790i	0.158866	−	0.900972i	−0.796301	−	0.604901i	$-0.793213\pi$
$73$	1.35735	−	7.69790i	0.158866	−	0.900972i	0.955166	−	0.296070i	$-0.0956763\pi$
$74$	1.57975	−	0.574982i	0.183642	−	0.0668403i
$75$	3.17969			0.367159
$76$	−4.24031	−	1.00983i	−0.486397	−	0.115835i
$77$	−20.6934			−2.35823
$78$	−2.20694	+	0.803262i	−0.249887	+	0.0909515i
$79$	−0.399207	+	2.26401i	−0.0449143	+	0.254721i	−0.998995	−	0.0448292i	$-0.985726\pi$
$79$	−0.399207	+	2.26401i	−0.0449143	+	0.254721i	0.954080	+	0.299551i	$0.0968368\pi$
$80$	0.766044	−	0.642788i	0.0856464	−	0.0718658i
$81$	15.4949	+	13.0018i	1.72165	+	1.44464i
$82$	−1.68282	−	9.54373i	−0.185836	−	1.05393i
$83$	5.72338	+	9.91318i	0.628223	+	1.08811i	0.987908	+	0.155040i	$0.0495506\pi$
$83$	5.72338	+	9.91318i	0.628223	+	1.08811i	−0.359686	+	0.933074i	$0.617116\pi$
$84$	5.31979	−	9.21415i	0.580437	−	1.00535i
$85$	−0.815778	−	0.296919i	−0.0884836	−	0.0322054i
$86$	1.74623	+	0.635576i	0.188301	+	0.0685359i
$87$	12.3847	−	21.4510i	1.32778	−	2.29978i
$88$	3.09216	+	5.35578i	0.329626	+	0.570928i
$89$	0.404290	+	2.29284i	0.0428546	+	0.243041i	0.998709	−	0.0508007i	$-0.0161773\pi$
$89$	0.404290	+	2.29284i	0.0428546	+	0.243041i	−0.955854	+	0.293841i	$0.905066\pi$
$90$	−5.44692	−	4.57051i	−0.574156	−	0.481774i
$91$	1.89328	−	1.58865i	0.198469	−	0.166535i
$92$	−0.198562	+	1.12610i	−0.0207015	+	0.117404i
$93$	−19.3550	+	7.04466i	−2.00702	+	0.730497i
$94$	−0.331695			−0.0342117
$95$	0.258165	−	4.35125i	0.0264872	−	0.446429i
$96$	−3.17969			−0.324526
$97$	6.43131	−	2.34081i	0.653000	−	0.237673i	0.00578901	−	0.999983i	$-0.498157\pi$
$97$	6.43131	−	2.34081i	0.653000	−	0.237673i	0.647211	+	0.762311i	$0.275935\pi$
$98$	−0.728700	+	4.13266i	−0.0736098	+	0.417462i
$99$	33.6855	−	28.2655i	3.38552	−	2.84079i
$100$	0.766044	+	0.642788i	0.0766044	+	0.0642788i
$101$	1.76892	+	10.0321i	0.176015	+	0.998228i	0.936966	+	0.349420i	$0.113621\pi$
$101$	1.76892	+	10.0321i	0.176015	+	0.998228i	−0.760952	+	0.648809i	$0.775268\pi$
$102$	1.38020	+	2.39057i	0.136660	+	0.236702i
$103$	−1.03525	+	1.79310i	−0.102006	+	0.176680i	−0.912511	−	0.409052i	$-0.865859\pi$
$103$	−1.03525	+	1.79310i	−0.102006	+	0.176680i	0.810505	+	0.585732i	$0.199193\pi$
$104$	−0.694074	−	0.252622i	−0.0680596	−	0.0247717i
$105$	9.99794	+	3.63895i	0.975699	+	0.355125i
$106$	−3.55244	+	6.15300i	−0.345043	+	0.597632i
$107$	7.31857	+	12.6761i	0.707513	+	1.22545i	0.965777	+	0.259374i	$0.0835164\pi$
$107$	7.31857	+	12.6761i	0.707513	+	1.22545i	−0.258264	+	0.966075i	$0.583150\pi$
$108$	2.26958	+	12.8714i	0.218390	+	1.23855i
$109$	−6.66091	−	5.58917i	−0.637999	−	0.535345i	0.265404	−	0.964137i	$-0.414495\pi$
$109$	−6.66091	−	5.58917i	−0.637999	−	0.535345i	−0.903403	+	0.428792i	$0.858939\pi$
$110$	−4.73747	+	3.97521i	−0.451700	+	0.379021i
$111$	0.928235	−	5.26428i	0.0881041	−	0.499663i
$112$	3.14431	−	1.14444i	0.297109	−	0.108139i
$113$	10.8308			1.01888			0.509439	−	0.860507i	$-0.329853\pi$
$113$	10.8308			1.01888			0.509439	+	0.860507i	$0.329853\pi$
$114$	−9.52221	+	10.0711i	−0.891836	+	0.943240i
$115$	−1.14347			−0.106629
$116$	7.32010	−	2.66430i	0.679654	−	0.247374i
$117$	−0.911985	+	5.17212i	−0.0843130	+	0.478163i
$118$	−3.72320	+	3.12414i	−0.342749	+	0.287600i
$119$	−2.22526	−	1.86721i	−0.203989	−	0.171167i
$120$	−0.552148	−	3.13139i	−0.0504040	−	0.285855i
$121$	−13.6229	−	23.5956i	−1.23845	−	2.14506i
$122$	3.61379	−	6.25926i	0.327177	−	0.566687i
$123$	−28.9559	−	10.5391i	−2.61087	−	0.950279i
$124$	−6.08708	−	2.21552i	−0.546636	−	0.198959i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	−11.8962	−	20.6047i	−1.05979	−	1.83562i
$127$	−1.94911	−	11.0540i	−0.172956	−	0.980880i	−0.940477	−	0.339857i	$-0.889621\pi$
$127$	−1.94911	−	11.0540i	−0.172956	−	0.980880i	0.767522	−	0.641023i	$-0.221490\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	4.52642	−	3.79812i	0.398529	−	0.334406i
$130$	0.128260	−	0.727397i	0.0112491	−	0.0637970i
$131$	−14.2703	+	5.19396i	−1.24680	+	0.453798i	−0.879319	−	0.476233i	$-0.842002\pi$
$131$	−14.2703	+	5.19396i	−1.24680	+	0.453798i	−0.367481	+	0.930031i	$0.619780\pi$
$132$	19.6643			1.71155
$133$	5.79147	−	13.3862i	0.502184	−	1.16073i
$134$	−2.92493			−0.252676
$135$	−12.2818	+	4.47019i	−1.05704	+	0.384733i
$136$	−0.150750	+	0.854944i	−0.0129267	+	0.0733109i
$137$	−6.54988	+	5.49600i	−0.559594	+	0.469555i	−0.878174	−	0.478341i	$-0.841238\pi$
$137$	−6.54988	+	5.49600i	−0.559594	+	0.469555i	0.318580	+	0.947896i	$0.396794\pi$
$138$	2.78525	+	2.33710i	0.237096	+	0.198948i
$139$	1.52883	+	8.67044i	0.129674	+	0.735417i	0.978421	+	0.206619i	$0.0662460\pi$
$139$	1.52883	+	8.67044i	0.129674	+	0.735417i	−0.848748	+	0.528798i	$0.822643\pi$
$140$	1.67305	+	2.89781i	0.141399	+	0.244910i
$141$	−0.527344	+	0.913387i	−0.0444104	+	0.0769210i
$142$	−6.47503	−	2.35672i	−0.543372	−	0.197771i
$143$	4.29238	+	1.56230i	0.358947	+	0.130646i
$144$	−3.55522	+	6.15783i	−0.296269	+	0.513152i
$145$	3.89494	+	6.74624i	0.323457	+	0.560245i
$146$	−1.35735	−	7.69790i	−0.112335	−	0.637083i
$147$	10.2216	+	8.57692i	0.843061	+	0.707413i
$148$	1.28782	−	1.08061i	0.105858	−	0.0888258i
$149$	0.132240	−	0.749969i	0.0108335	−	0.0614398i	−0.978912	−	0.204284i	$-0.934514\pi$
$149$	0.132240	−	0.749969i	0.0108335	−	0.0614398i	0.989745	+	0.142844i	$0.0456246\pi$
$150$	2.98793	−	1.08752i	0.243964	−	0.0887956i
$151$	−6.08784			−0.495421			−0.247711	−	0.968834i	$-0.579678\pi$
$151$	−6.08784			−0.495421			−0.247711	+	0.968834i	$0.579678\pi$
$152$	−4.32997	+	0.501343i	−0.351207	+	0.0406643i
$153$	6.17282			0.499043
$154$	−19.4454	+	7.07756i	−1.56696	+	0.570326i
$155$	1.12485	−	6.37932i	0.0903499	−	0.512400i
$156$	−1.79912	+	1.50964i	−0.144045	+	0.120868i
$157$	18.6728	+	15.6683i	1.49025	+	1.25047i	0.894317	+	0.447434i	$0.147662\pi$
$157$	18.6728	+	15.6683i	1.49025	+	1.25047i	0.595933	+	0.803034i	$0.296782\pi$
$158$	0.399207	+	2.26401i	0.0317592	+	0.180115i
$159$	11.2957	+	19.5647i	0.895804	+	1.55158i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−3.59543	−	1.30863i	−0.283360	−	0.103134i
$162$	19.0073	+	6.91809i	1.49335	+	0.543536i
$163$	2.15496	−	3.73250i	0.168789	−	0.292352i	−0.769205	−	0.639002i	$-0.779348\pi$
$163$	2.15496	−	3.73250i	0.168789	−	0.292352i	0.937994	+	0.346650i	$0.112681\pi$
$164$	−4.84548	−	8.39261i	−0.378368	−	0.655353i
$165$	3.41466	+	19.3655i	0.265831	+	1.50760i
$166$	8.76873	+	7.35783i	0.680585	+	0.571079i
$167$	3.99229	−	3.34993i	0.308933	−	0.259225i	−0.475118	−	0.879922i	$-0.657595\pi$
$167$	3.99229	−	3.34993i	0.308933	−	0.259225i	0.784051	+	0.620697i	$0.213150\pi$
$168$	1.84754	−	10.4779i	0.142541	−	0.808391i
$169$	11.7033	−	4.25967i	0.900258	−	0.327667i
$170$	−0.868133			−0.0665828
$171$	8.85690	+	29.7013i	0.677304	+	2.27131i
$172$	1.85830			0.141694
$173$	−6.61144	+	2.40637i	−0.502658	+	0.182953i	−0.580889	−	0.813983i	$-0.697295\pi$
$173$	−6.61144	+	2.40637i	−0.502658	+	0.182953i	0.0782309	+	0.996935i	$0.475073\pi$
$174$	4.30117	−	24.3931i	0.326071	−	1.84924i
$175$	−2.56327	+	2.15083i	−0.193765	+	0.162588i
$176$	4.73747	+	3.97521i	0.357100	+	0.299642i
$177$	2.68360	+	15.2195i	0.201712	+	1.14397i
$178$	1.16411	+	2.01629i	0.0872534	+	0.151127i
$179$	−1.59972	+	2.77080i	−0.119569	+	0.207099i	−0.919597	−	0.392863i	$-0.871485\pi$
$179$	−1.59972	+	2.77080i	−0.119569	+	0.207099i	0.800028	+	0.599963i	$0.204818\pi$
$180$	−6.68164	−	2.43192i	−0.498020	−	0.181264i
$181$	4.44963	+	1.61953i	0.330738	+	0.120379i	0.502052	−	0.864838i	$-0.332579\pi$
$181$	4.44963	+	1.61953i	0.330738	+	0.120379i	−0.171313	+	0.985217i	$0.554801\pi$
$182$	1.23575	−	2.14038i	0.0915997	−	0.158655i
$183$	−11.4907	−	19.9025i	−0.849419	−	1.47124i
$184$	0.198562	+	1.12610i	0.0146382	+	0.0830172i
$185$	1.28782	+	1.08061i	0.0946826	+	0.0794482i
$186$	−15.7784	+	13.2396i	−1.15693	+	0.970777i
$187$	0.932285	−	5.28725i	0.0681754	−	0.386642i
$188$	−0.311691	+	0.113446i	−0.0227324	+	0.00827393i
$189$	−43.7335			−3.18114
$190$	−1.24562	−	4.17713i	−0.0903666	−	0.303041i
$191$	−18.4307			−1.33360			−0.666800	−	0.745237i	$-0.732336\pi$
$191$	−18.4307			−1.33360			−0.666800	+	0.745237i	$0.732336\pi$
$192$	−2.98793	+	1.08752i	−0.215636	+	0.0784849i
$193$	−2.35285	+	13.3437i	−0.169362	+	0.960501i	0.775090	+	0.631851i	$0.217705\pi$
$193$	−2.35285	+	13.3437i	−0.169362	+	0.960501i	−0.944452	+	0.328649i	$0.893407\pi$
$194$	5.24285	−	4.39927i	0.376415	−	0.315849i
$195$	−1.79912	−	1.50964i	−0.128837	−	0.108107i
$196$	0.728700	+	4.13266i	0.0520500	+	0.295190i
$197$	−4.09550	−	7.09361i	−0.291792	−	0.505399i	0.682441	−	0.730940i	$-0.260918\pi$
$197$	−4.09550	−	7.09361i	−0.291792	−	0.505399i	−0.974234	+	0.225541i	$0.927585\pi$
$198$	21.9867	−	38.0820i	1.56252	−	2.70637i
$199$	−5.58408	−	2.03244i	−0.395845	−	0.144076i	0.136425	−	0.990650i	$-0.456439\pi$
$199$	−5.58408	−	2.03244i	−0.395845	−	0.144076i	−0.532270	+	0.846575i	$0.678661\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	−4.65019	+	8.05437i	−0.327999	+	0.568112i
$202$	5.09342	+	8.82205i	0.358371	+	0.620718i
$203$	4.52627	+	25.6698i	0.317682	+	1.80166i
$204$	2.11459	+	1.77435i	0.148051	+	0.124229i
$205$	7.42370	−	6.22923i	0.518494	−	0.435068i
$206$	−0.359538	+	2.03904i	−0.0250502	+	0.142067i
$207$	7.64026	−	2.78083i	0.531035	−	0.193281i
$208$	−0.738619			−0.0512140
$209$	26.7779	−	3.10047i	1.85227	−	0.214464i
$210$	10.6396			0.734201
$211$	1.63846	−	0.596352i	0.112796	−	0.0410545i	−0.285005	−	0.958526i	$-0.591995\pi$
$211$	1.63846	−	0.596352i	0.112796	−	0.0410545i	0.397802	+	0.917471i	$0.369773\pi$
$212$	−1.23375	+	6.99694i	−0.0847342	+	0.480552i
$213$	−16.7840	+	14.0834i	−1.15002	+	0.964981i
$214$	11.2127	+	9.40858i	0.766485	+	0.643157i
$215$	0.322690	+	1.83007i	0.0220073	+	0.124810i
$216$	6.53498	+	11.3189i	0.444649	+	0.770155i
$217$	10.8376	−	18.7713i	0.735703	−	1.27428i
$218$	−8.17082	−	2.97393i	−0.553397	−	0.201420i
$219$	−23.3557	−	8.50076i	−1.57823	−	0.574428i
$220$	−3.09216	+	5.35578i	−0.208474	+	0.361087i
$221$	0.320610	+	0.555312i	0.0215665	+	0.0373543i
$222$	−0.928235	−	5.26428i	−0.0622990	−	0.353315i
$223$	20.2549	+	16.9959i	1.35637	+	1.13813i	0.977085	+	0.212848i	$0.0682739\pi$
$223$	20.2549	+	16.9959i	1.35637	+	1.13813i	0.379283	+	0.925281i	$0.376171\pi$
$224$	2.56327	−	2.15083i	0.171265	−	0.143709i
$225$	1.23472	−	7.00242i	0.0823144	−	0.466828i
$226$	10.1777	−	3.70436i	0.677007	−	0.246411i
$227$	−27.4472			−1.82174			−0.910869	−	0.412697i	$-0.864587\pi$
$227$	−27.4472			−1.82174			−0.910869	+	0.412697i	$0.864587\pi$
$228$	−5.50345	+	12.7205i	−0.364475	+	0.842434i
$229$	−11.5722			−0.764711			−0.382355	−	0.924015i	$-0.624887\pi$
$229$	−11.5722			−0.764711			−0.382355	+	0.924015i	$0.624887\pi$
$230$	−1.07451	+	0.391090i	−0.0708512	+	0.0257877i
$231$	−11.4258	+	64.7990i	−0.751764	+	4.26346i
$232$	5.96740	−	5.00724i	0.391779	−	0.328741i
$233$	9.84970	+	8.26488i	0.645275	+	0.541450i	0.905633	−	0.424062i	$-0.139396\pi$
$233$	9.84970	+	8.26488i	0.645275	+	0.541450i	−0.260358	+	0.965512i	$0.583841\pi$
$234$	0.911985	+	5.17212i	0.0596183	+	0.338112i
$235$	−0.165847	−	0.287256i	−0.0108187	−	0.0187385i
$236$	−2.43015	+	4.20914i	−0.158189	+	0.273992i
$237$	6.86908	+	2.50014i	0.446195	+	0.162402i
$238$	−2.72968	−	0.993522i	−0.176939	−	0.0644005i
$239$	5.65708	−	9.79836i	0.365926	−	0.633803i	−0.622998	−	0.782223i	$-0.714086\pi$
$239$	5.65708	−	9.79836i	0.365926	−	0.633803i	0.988924	+	0.148420i	$0.0474189\pi$
$240$	−1.58985	−	2.75370i	−0.102624	−	0.177750i
$241$	−4.13196	−	23.4335i	−0.266163	−	1.50948i	−0.765704	−	0.643193i	$-0.777609\pi$
$241$	−4.13196	−	23.4335i	−0.266163	−	1.50948i	0.499541	−	0.866290i	$-0.333502\pi$
$242$	−20.8715	−	17.5133i	−1.34167	−	1.12580i
$243$	19.2325	−	16.1379i	1.23376	−	1.03525i
$244$	1.25506	−	7.11777i	0.0803467	−	0.455669i
$245$	−3.94334	+	1.43526i	−0.251931	+	0.0916954i
$246$	−30.8143			−1.96465
$247$	−2.21194	+	2.33943i	−0.140742	+	0.148854i
$248$	−6.47773			−0.411337
$249$	34.2022	−	12.4486i	2.16747	−	0.788896i
$250$	−0.173648	+	0.984808i	−0.0109825	+	0.0622847i
$251$	19.9736	−	16.7599i	1.26072	−	1.05787i	0.265120	−	0.964215i	$-0.414588\pi$
$251$	19.9736	−	16.7599i	1.26072	−	1.05787i	0.995604	−	0.0936578i	$-0.0298560\pi$
$252$	−18.2260	−	15.2934i	−1.14813	−	0.963394i
$253$	−1.22797	−	6.96417i	−0.0772018	−	0.437833i
$254$	−5.61224	−	9.72069i	−0.352143	−	0.609930i
$255$	−1.38020	+	2.39057i	−0.0864314	+	0.149704i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	9.54054	+	3.47247i	0.595122	+	0.216607i	0.621981	−	0.783032i	$-0.286328\pi$
$257$	9.54054	+	3.47247i	0.595122	+	0.216607i	−0.0268585	+	0.999639i	$0.508550\pi$
$258$	2.95441	−	5.11719i	0.183934	−	0.318582i
$259$	2.81263	+	4.87161i	0.174768	+	0.302707i
$260$	−0.128260	−	0.727397i	−0.00795433	−	0.0451113i
$261$	−42.4309	−	35.6037i	−2.62641	−	2.20382i
$262$	−11.6332	+	9.76144i	−0.718704	+	0.603064i
$263$	2.97399	−	16.8663i	0.183384	−	1.04002i	−0.744630	−	0.667477i	$-0.767374\pi$
$263$	2.97399	−	16.8663i	0.183384	−	1.04002i	0.928014	−	0.372545i	$-0.121515\pi$
$264$	18.4784	−	6.72557i	1.13726	−	0.413930i
$265$	−7.10488			−0.436449
$266$	0.863848	−	14.5597i	0.0529659	−	0.892714i
$267$	7.40300			0.453056
$268$	−2.74854	+	1.00039i	−0.167894	+	0.0611083i
$269$	3.96080	−	22.4628i	0.241495	−	1.36958i	−0.587000	−	0.809587i	$-0.699691\pi$
$269$	3.96080	−	22.4628i	0.241495	−	1.36958i	0.828495	−	0.559997i	$-0.189198\pi$
$270$	−10.0122	+	8.40121i	−0.609322	+	0.511281i
$271$	13.6282	+	11.4354i	0.827852	+	0.694650i	0.954797	−	0.297260i	$-0.0960727\pi$
$271$	13.6282	+	11.4354i	0.827852	+	0.694650i	−0.126945	+	0.991910i	$0.540517\pi$
$272$	0.150750	+	0.854944i	0.00914054	+	0.0518386i
$273$	−3.92930	−	6.80574i	−0.237812	−	0.411902i
$274$	−4.27513	+	7.40475i	−0.258270	+	0.447337i
$275$	−5.81136	−	2.11516i	−0.350438	−	0.127549i
$276$	3.41662	+	1.24355i	0.205656	+	0.0748527i
$277$	10.4365	−	18.0765i	0.627066	−	1.08611i	−0.361071	−	0.932538i	$-0.617589\pi$
$277$	10.4365	−	18.0765i	0.627066	−	1.08611i	0.988137	−	0.153572i	$-0.0490777\pi$
$278$	4.40210	+	7.62466i	0.264020	+	0.457296i
$279$	7.99817	+	45.3598i	0.478838	+	2.71562i
$280$	2.56327	+	2.15083i	0.153184	+	0.128537i
$281$	−20.8354	+	17.4830i	−1.24294	+	1.04295i	−0.245650	+	0.969359i	$0.579001\pi$
$281$	−20.8354	+	17.4830i	−1.24294	+	1.04295i	−0.997289	+	0.0735907i	$0.976554\pi$
$282$	−0.183145	+	1.03867i	−0.0109061	+	0.0618516i
$283$	18.5060	−	6.73563i	1.10007	−	0.400392i	0.272726	−	0.962092i	$-0.412075\pi$
$283$	18.5060	−	6.73563i	1.10007	−	0.400392i	0.827341	+	0.561700i	$0.189852\pi$
$284$	−6.89058			−0.408881
$285$	−13.4829	−	3.21095i	−0.798658	−	0.190200i
$286$	4.56786			0.270103
$287$	30.4714	−	11.0907i	1.79867	−	0.654662i
$288$	−1.23472	+	7.00242i	−0.0727564	+	0.412622i
$289$	−12.4454	+	10.4429i	−0.732084	+	0.614291i
$290$	5.96740	+	5.00724i	0.350418	+	0.294035i
$291$	−3.77893	−	21.4314i	−0.221525	−	1.25633i
$292$	−3.90833	−	6.76942i	−0.228718	−	0.396151i
$293$	7.38854	−	12.7973i	0.431643	−	0.747628i	−0.565372	−	0.824836i	$-0.691267\pi$
$293$	7.38854	−	12.7973i	0.431643	−	0.747628i	0.997015	+	0.0772085i	$0.0246007\pi$
$294$	12.5386	+	4.56368i	0.731267	+	0.266159i
$295$	−4.56719	−	1.66232i	−0.265912	−	0.0967840i
$296$	0.840567	−	1.45590i	0.0488570	−	0.0846227i
$297$	−40.4145	−	69.9999i	−2.34508	−	4.06181i
$298$	−0.132240	−	0.749969i	−0.00766044	−	0.0434445i
$299$	0.646993	+	0.542892i	0.0374166	+	0.0313962i
$300$	2.43579	−	2.04387i	0.140630	−	0.118003i
$301$	−1.07976	+	6.12360i	−0.0622361	+	0.352958i
$302$	−5.72070	+	2.08216i	−0.329189	+	0.119815i
$303$	32.3910			1.86081
$304$	−3.89737	+	1.95205i	−0.223530	+	0.111958i
$305$	7.22757			0.413850
$306$	5.80055	−	2.11123i	0.331595	−	0.120691i
$307$	−0.736086	+	4.17455i	−0.0420106	+	0.238254i	−0.998581	−	0.0532459i	$-0.983043\pi$
$307$	−0.736086	+	4.17455i	−0.0420106	+	0.238254i	0.956571	+	0.291500i	$0.0941544\pi$
$308$	−15.8521	+	13.3015i	−0.903255	+	0.757921i
$309$	5.04328	+	4.23182i	0.286902	+	0.240740i
$310$	−1.12485	−	6.37932i	−0.0638870	−	0.362321i
$311$	3.49343	+	6.05079i	0.198094	+	0.343109i	0.947910	−	0.318537i	$-0.103192\pi$
$311$	3.49343	+	6.05079i	0.198094	+	0.343109i	−0.749816	+	0.661646i	$0.769858\pi$
$312$	−1.17429	+	2.03393i	−0.0664811	+	0.115149i
$313$	7.16016	+	2.60608i	0.404716	+	0.147305i	0.536354	−	0.843993i	$-0.319801\pi$
$313$	7.16016	+	2.60608i	0.404716	+	0.147305i	−0.131638	+	0.991298i	$0.542024\pi$
$314$	22.9056	+	8.33694i	1.29264	+	0.470481i
$315$	11.8962	−	20.6047i	0.670272	−	1.16095i
$316$	1.14947	+	1.99094i	0.0646627	+	0.111999i
$317$	2.38566	+	13.5297i	0.133992	+	0.759905i	0.975557	+	0.219749i	$0.0705237\pi$
$317$	2.38566	+	13.5297i	0.133992	+	0.759905i	−0.841565	+	0.540156i	$0.818365\pi$
$318$	17.3060	+	14.5214i	0.970470	+	0.814321i
$319$	−36.9043	+	30.9664i	−2.06625	+	1.73379i
$320$	0.173648	−	0.984808i	0.00970723	−	0.0550524i
$321$	43.7348	−	15.9182i	2.44104	−	0.888466i
$322$	−3.82618			−0.213224
$323$	3.15932	+	2.08283i	0.175789	+	0.115892i
$324$	20.2271			1.12373
$325$	0.694074	−	0.252622i	0.0385003	−	0.0140130i
$326$	0.748409	−	4.24444i	0.0414506	−	0.235078i
$327$	−21.1796	+	17.7718i	−1.17124	+	0.982785i
$328$	−7.42370	−	6.22923i	−0.409905	−	0.343952i
$329$	−0.192730	−	1.09302i	−0.0106255	−	0.0602604i
$330$	9.83213	+	17.0297i	0.541241	+	0.937456i
$331$	3.32212	−	5.75409i	0.182600	−	0.316273i	−0.760165	−	0.649730i	$-0.774882\pi$
$331$	3.32212	−	5.75409i	0.182600	−	0.316273i	0.942765	+	0.333457i	$0.108215\pi$
$332$	10.7564	+	3.91502i	0.590336	+	0.214865i
$333$	−11.2327	−	4.08838i	−0.615550	−	0.224042i
$334$	2.60578	−	4.51335i	0.142582	−	0.246959i
$335$	−1.46247	−	2.53307i	−0.0799031	−	0.138396i
$336$	−1.84754	−	10.4779i	−0.100792	−	0.571619i
$337$	−14.1012	−	11.8323i	−0.768139	−	0.644545i	0.172093	−	0.985081i	$-0.444947\pi$
$337$	−14.1012	−	11.8323i	−0.768139	−	0.644545i	−0.940232	+	0.340536i	$0.889392\pi$
$338$	9.54066	−	8.00556i	0.518943	−	0.435445i
$339$	5.98022	−	33.9155i	0.324801	−	1.84204i
$340$	−0.815778	+	0.296919i	−0.0442418	+	0.0161027i
$341$	40.0604			2.16939
$342$	18.4812	+	24.8808i	0.999349	+	1.34540i
$343$	9.38108			0.506531
$344$	1.74623	−	0.635576i	0.0941504	−	0.0342680i
$345$	−0.631365	+	3.58065i	−0.0339916	+	0.192776i
$346$	−5.38969	+	4.52249i	−0.289752	+	0.243131i
$347$	5.68212	+	4.76787i	0.305032	+	0.255952i	0.782435	−	0.622732i	$-0.213977\pi$
$347$	5.68212	+	4.76787i	0.305032	+	0.255952i	−0.477403	+	0.878684i	$0.658422\pi$
$348$	−4.30117	−	24.3931i	−0.230567	−	1.30761i
$349$	−9.57581	−	16.5858i	−0.512581	−	0.887817i	−0.999894	−	0.0145891i	$-0.995356\pi$
$349$	−9.57581	−	16.5858i	−0.512581	−	0.887817i	0.487312	−	0.873228i	$-0.337977\pi$
$350$	−1.67305	+	2.89781i	−0.0894284	+	0.154895i
$351$	9.07153	+	3.30177i	0.484202	+	0.176235i
$352$	5.81136	+	2.11516i	0.309747	+	0.112739i
$353$	0.801691	−	1.38857i	0.0426697	−	0.0739061i	−0.843902	−	0.536498i	$-0.819747\pi$
$353$	0.801691	−	1.38857i	0.0426697	−	0.0739061i	0.886572	+	0.462592i	$0.153080\pi$
$354$	7.72713	+	13.3838i	0.410692	+	0.711340i
$355$	−1.19654	−	6.78590i	−0.0635056	−	0.360158i
$356$	1.78351	+	1.49655i	0.0945261	+	0.0793168i
$357$	−7.07563	+	5.93716i	−0.374482	+	0.314228i
$358$	−0.555577	+	3.15084i	−0.0293632	+	0.166527i
$359$	20.2961	−	7.38717i	1.07119	−	0.389880i	0.254566	−	0.967055i	$-0.418067\pi$
$359$	20.2961	−	7.38717i	1.07119	−	0.389880i	0.816620	+	0.577175i	$0.195845\pi$
$360$	−7.11045			−0.374754
$361$	−5.48872	+	18.1899i	−0.288880	+	0.957365i
$362$	4.73520			0.248876
$363$	−81.4089	+	29.6304i	−4.27286	+	1.55519i
$364$	0.429171	−	2.43395i	0.0224947	−	0.127574i
$365$	5.98791	−	5.02445i	0.313421	−	0.262992i
$366$	−17.6048	−	14.7722i	−0.920219	−	0.772155i
$367$	3.42815	+	19.4420i	0.178948	+	1.01486i	0.933488	+	0.358610i	$0.116749\pi$
$367$	3.42815	+	19.4420i	0.178948	+	1.01486i	−0.754540	+	0.656255i	$0.772140\pi$
$368$	0.571736	+	0.990275i	0.0298038	+	0.0516217i
$369$	−34.4535	+	59.6753i	−1.79358	+	3.10657i
$370$	1.57975	+	0.574982i	0.0821272	+	0.0298919i
$371$	−22.3399	−	8.13107i	−1.15983	−	0.422144i
$372$	−10.2986	+	17.8377i	−0.533958	+	0.924842i
$373$	11.5800	+	20.0572i	0.599592	+	1.03852i	0.992881	+	0.119109i	$0.0380037\pi$
$373$	11.5800	+	20.0572i	0.599592	+	1.03852i	−0.393289	+	0.919415i	$0.628663\pi$
$374$	−0.932285	−	5.28725i	−0.0482073	−	0.273397i
$375$	2.43579	+	2.04387i	0.125783	+	0.105545i
$376$	−0.254093	+	0.213209i	−0.0131039	+	0.0109954i
$377$	0.999129	−	5.66634i	0.0514578	−	0.291831i
$378$	−41.0960	+	14.9577i	−2.11375	+	0.769343i
$379$	−3.52957			−0.181302			−0.0906508	−	0.995883i	$-0.528895\pi$
$379$	−3.52957			−0.181302			−0.0906508	+	0.995883i	$0.528895\pi$
$380$	−2.59916	−	3.49919i	−0.133334	−	0.179505i
$381$	−35.6904			−1.82847
$382$	−17.3192	+	6.30368i	−0.886128	+	0.322524i
$383$	6.36973	−	36.1246i	0.325478	−	1.84588i	−0.180815	−	0.983517i	$-0.557873\pi$
$383$	6.36973	−	36.1246i	0.325478	−	1.84588i	0.506293	−	0.862362i	$-0.331015\pi$
$384$	−2.43579	+	2.04387i	−0.124301	+	0.104301i
$385$	−15.8521	−	13.3015i	−0.807896	−	0.677905i
$386$	2.35285	+	13.3437i	0.119757	+	0.679176i
$387$	−6.60667	−	11.4431i	−0.335836	−	0.581685i
$388$	3.42203	−	5.92713i	0.173727	−	0.300904i
$389$	23.1021	+	8.40847i	1.17132	+	0.426327i	0.853129	−	0.521699i	$-0.174702\pi$
$389$	23.1021	+	8.40847i	1.17132	+	0.426327i	0.318193	+	0.948026i	$0.396924\pi$
$390$	−2.20694	−	0.803262i	−0.111753	−	0.0406747i
$391$	0.496343	−	0.859691i	0.0251011	−	0.0434764i
$392$	2.09821	+	3.63420i	0.105976	+	0.183555i
$393$	8.38498	+	47.5536i	0.422966	+	2.39876i
$394$	−6.27467	−	5.26507i	−0.316113	−	0.265251i
$395$	−1.76109	+	1.47773i	−0.0886101	+	0.0743527i
$396$	7.63589	−	43.3053i	0.383718	−	2.17617i
$397$	−19.1282	+	6.96208i	−0.960015	+	0.349417i	−0.774039	−	0.633137i	$-0.781767\pi$
$397$	−19.1282	+	6.96208i	−0.960015	+	0.349417i	−0.185976	+	0.982554i	$0.559545\pi$
$398$	−5.94246			−0.297868
$399$	−38.7197	−	25.5265i	−1.93841	−	1.27792i
$400$	1.00000			0.0500000
$401$	−18.9313	+	6.89045i	−0.945386	+	0.344092i	−0.768291	−	0.640101i	$-0.778892\pi$
$401$	−18.9313	+	6.89045i	−0.945386	+	0.344092i	−0.177096	+	0.984194i	$0.556670\pi$
$402$	−1.61500	+	9.15910i	−0.0805487	+	0.456814i
$403$	−3.66520	+	3.07547i	−0.182576	+	0.153200i
$404$	7.80356	+	6.54797i	0.388242	+	0.325774i
$405$	3.51240	+	19.9198i	0.174533	+	0.989825i
$406$	13.0329	+	22.5736i	0.646811	+	1.12031i
$407$	−5.19834	+	9.00379i	−0.257672	+	0.446301i
$408$	2.59392	+	0.944111i	0.128418	+	0.0467405i
$409$	−12.1073	−	4.40670i	−0.598668	−	0.217897i	0.0248698	−	0.999691i	$-0.492083\pi$
$409$	−12.1073	−	4.40670i	−0.598668	−	0.217897i	−0.623537	+	0.781794i	$0.714305\pi$
$410$	4.84548	−	8.39261i	0.239301	−	0.414482i
$411$	13.5936	+	23.5448i	0.670523	+	1.16138i
$412$	0.359538	+	2.03904i	0.0177132	+	0.100456i
$413$	−12.4582	−	10.4537i	−0.613030	−	0.514393i
$414$	6.22840	−	5.22625i	0.306109	−	0.256856i
$415$	−1.98771	+	11.2729i	−0.0975728	+	0.553363i
$416$	−0.694074	+	0.252622i	−0.0340298	+	0.0123858i
$417$	27.9946			1.37090
$418$	24.1026	−	12.0721i	1.17890	−	0.590465i
$419$	20.0166			0.977876			0.488938	−	0.872319i	$-0.337384\pi$
$419$	20.0166			0.977876			0.488938	+	0.872319i	$0.337384\pi$
$420$	9.99794	−	3.63895i	0.487850	−	0.177563i
$421$	1.16311	−	6.59634i	0.0566867	−	0.321486i	−0.943257	−	0.332062i	$-0.892256\pi$
$421$	1.16311	−	6.59634i	0.0566867	−	0.321486i	0.999944	+	0.0105764i	$0.00336662\pi$
$422$	1.33569	−	1.12077i	0.0650202	−	0.0545585i
$423$	1.80672	+	1.51601i	0.0878455	+	0.0737112i
$424$	1.23375	+	6.99694i	0.0599161	+	0.339801i
$425$	−0.434067	−	0.751825i	−0.0210553	−	0.0364689i
$426$	−10.9550	+	18.9746i	−0.530770	+	0.919321i
$427$	22.7257	+	8.27149i	1.09978	+	0.400285i
$428$	13.7544	+	5.00620i	0.664845	+	0.241984i
$429$	7.26219	−	12.5785i	0.350622	−	0.607295i
$430$	0.929150	+	1.60933i	0.0448076	+	0.0776090i
$431$	−4.86528	−	27.5924i	−0.234352	−	1.32908i	−0.843974	−	0.536385i	$-0.819790\pi$
$431$	−4.86528	−	27.5924i	−0.234352	−	1.32908i	0.609621	−	0.792693i	$-0.291321\pi$
$432$	10.0122	+	8.40121i	0.481711	+	0.404203i
$433$	−17.3262	+	14.5384i	−0.832646	+	0.698673i	−0.955897	−	0.293702i	$-0.905113\pi$
$433$	−17.3262	+	14.5384i	−0.832646	+	0.698673i	0.123251	+	0.992376i	$0.460668\pi$
$434$	3.76386	−	21.3459i	0.180671	−	1.02464i
$435$	23.2757	−	8.47165i	1.11598	−	0.406184i
$436$	−8.69520			−0.416425
$437$	4.84868	+	1.15471i	0.231944	+	0.0552373i
$438$	−24.8546			−1.18760
$439$	3.88563	−	1.41425i	0.185451	−	0.0674986i	−0.247626	−	0.968856i	$-0.579650\pi$
$439$	3.88563	−	1.41425i	0.185451	−	0.0674986i	0.433076	+	0.901357i	$0.357428\pi$
$440$	−1.07390	+	6.09037i	−0.0511960	+	0.290347i
$441$	22.8575	−	19.1798i	1.08845	−	0.913322i
$442$	0.491202	+	0.412168i	0.0233641	+	0.0196048i
$443$	−5.02534	−	28.5001i	−0.238761	−	1.35408i	−0.834547	−	0.550937i	$-0.814270\pi$
$443$	−5.02534	−	28.5001i	−0.238761	−	1.35408i	0.595786	−	0.803144i	$-0.296841\pi$
$444$	−2.67274	−	4.62933i	−0.126843	−	0.219698i
$445$	−1.16411	+	2.01629i	−0.0551839	+	0.0955814i
$446$	24.8463	+	9.04332i	1.17651	+	0.428214i
$447$	−2.27543	−	0.828187i	−0.107624	−	0.0391719i
$448$	1.67305	−	2.89781i	0.0790443	−	0.136909i
$449$	2.78070	+	4.81632i	0.131229	+	0.227296i	0.924151	−	0.382028i	$-0.124774\pi$
$449$	2.78070	+	4.81632i	0.131229	+	0.227296i	−0.792921	+	0.609324i	$0.791441\pi$
$450$	−1.23472	−	7.00242i	−0.0582051	−	0.330097i
$451$	45.9106	+	38.5236i	2.16185	+	1.81400i
$452$	8.29690	−	6.96192i	0.390253	−	0.327461i
$453$	−3.36139	+	19.0634i	−0.157932	+	0.895676i
$454$	−25.7920	+	9.38751i	−1.21048	+	0.440578i
$455$	2.47150			0.115865
$456$	−0.820886	+	13.8356i	−0.0384415	+	0.647913i
$457$	−3.44090			−0.160959			−0.0804793	−	0.996756i	$-0.525645\pi$
$457$	−3.44090			−0.160959			−0.0804793	+	0.996756i	$0.525645\pi$
$458$	−10.8743	+	3.95792i	−0.508122	+	0.184941i
$459$	1.97029	−	11.1741i	0.0919654	−	0.521562i
$460$	−0.875950	+	0.735009i	−0.0408414	+	0.0342700i
$461$	−3.88985	−	3.26397i	−0.181169	−	0.152018i	0.547693	−	0.836679i	$-0.315506\pi$
$461$	−3.88985	−	3.26397i	−0.181169	−	0.152018i	−0.728862	+	0.684661i	$0.759950\pi$
$462$	11.4258	+	64.7990i	0.531577	+	3.01472i
$463$	2.56405	+	4.44107i	0.119162	+	0.206394i	0.919436	−	0.393240i	$-0.128646\pi$
$463$	2.56405	+	4.44107i	0.119162	+	0.206394i	−0.800274	+	0.599634i	$0.795313\pi$
$464$	3.89494	−	6.74624i	0.180818	−	0.313186i
$465$	−19.3550	−	7.04466i	−0.897569	−	0.326688i
$466$	12.0824	+	4.39765i	0.559708	+	0.203717i
$467$	−14.8110	+	25.6535i	−0.685373	+	1.18710i	0.287947	+	0.957646i	$0.407027\pi$
$467$	−14.8110	+	25.6535i	−0.685373	+	1.18710i	−0.973320	+	0.229454i	$0.926306\pi$
$468$	2.62595	+	4.54829i	0.121385	+	0.210245i
$469$	−1.69952	−	9.63844i	−0.0784764	−	0.445062i
$470$	−0.254093	−	0.213209i	−0.0117204	−	0.00983462i
$471$	59.3737	−	49.8205i	2.73580	−	2.29561i
$472$	−0.843982	+	4.78646i	−0.0388474	+	0.220315i
$473$	−10.7993	+	3.93061i	−0.496550	+	0.180729i
$474$	7.30992			0.335756
$475$	2.99469	−	3.16730i	0.137406	−	0.145326i
$476$	−2.90486			−0.133144
$477$	47.4722	−	17.2785i	2.17360	−	0.791127i
$478$	1.96468	−	11.1423i	0.0898626	−	0.509636i
$479$	−28.8677	+	24.2229i	−1.31900	+	1.10677i	−0.332485	+	0.943109i	$0.607887\pi$
$479$	−28.8677	+	24.2229i	−1.31900	+	1.10677i	−0.986516	+	0.163664i	$0.947669\pi$
$480$	−2.43579	−	2.04387i	−0.111178	−	0.0932894i
$481$	−0.215622	−	1.22285i	−0.00983151	−	0.0557573i
$482$	−11.8975	−	20.6071i	−0.541916	−	0.938626i
$483$	−6.08303	+	10.5361i	−0.276788	+	0.479410i
$484$	−25.6027	−	9.31863i	−1.16376	−	0.423574i
$485$	6.43131	+	2.34081i	0.292031	+	0.106290i
$486$	12.5531	−	21.7426i	0.569420	−	0.986264i
$487$	8.87714	+	15.3757i	0.402262	+	0.696738i	0.993999	−	0.109393i	$-0.0348909\pi$
$487$	8.87714	+	15.3757i	0.402262	+	0.696738i	−0.591737	+	0.806131i	$0.701558\pi$
$488$	−1.25506	−	7.11777i	−0.0568137	−	0.322206i
$489$	−10.4980	−	8.80890i	−0.474738	−	0.398352i
$490$	−3.21464	+	2.69741i	−0.145223	+	0.121856i
$491$	−3.87201	+	21.9592i	−0.174741	+	0.991006i	0.763701	+	0.645570i	$0.223380\pi$
$491$	−3.87201	+	21.9592i	−0.174741	+	0.991006i	−0.938442	+	0.345436i	$0.887731\pi$
$492$	−28.9559	+	10.5391i	−1.30543	+	0.475139i
$493$	−6.76266			−0.304575
$494$	−1.27841	+	2.95487i	−0.0575183	+	0.132946i
$495$	43.9733			1.97645
$496$	−6.08708	+	2.21552i	−0.273318	+	0.0994796i
$497$	4.00374	−	22.7063i	0.179592	−	1.01852i
$498$	27.8819	−	23.3957i	1.24942	−	1.04838i
$499$	−14.4603	−	12.1337i	−0.647334	−	0.543177i	0.258927	−	0.965897i	$-0.416631\pi$
$499$	−14.4603	−	12.1337i	−0.647334	−	0.543177i	−0.906261	+	0.422719i	$0.861076\pi$
$500$	0.173648	+	0.984808i	0.00776578	+	0.0440419i
$501$	−8.28559	−	14.3511i	−0.370173	−	0.641158i
$502$	13.0369	−	22.5805i	0.581864	−	1.00782i
$503$	−38.3963	−	13.9751i	−1.71201	−	0.623119i	−0.714905	−	0.699221i	$-0.753530\pi$
$503$	−38.3963	−	13.9751i	−1.71201	−	0.623119i	−0.997100	+	0.0761023i	$0.975752\pi$
$504$	−22.3575	−	8.13745i	−0.995880	−	0.362471i
$505$	−5.09342	+	8.82205i	−0.226654	+	0.392576i
$506$	−3.53580	−	6.12418i	−0.157185	−	0.272253i
$507$	−6.87669	−	38.9997i	−0.305405	−	1.73204i
$508$	−8.59845	−	7.21496i	−0.381495	−	0.320112i
$509$	−10.1977	+	8.55692i	−0.452007	+	0.379279i	−0.840180	−	0.542308i	$-0.817551\pi$
$509$	−10.1977	+	8.55692i	−0.452007	+	0.379279i	0.388173	+	0.921586i	$0.373106\pi$
$510$	−0.479338	+	2.71846i	−0.0212254	+	0.120375i
$511$	24.5780	−	8.94566i	1.08727	−	0.395733i
$512$	−1.00000			−0.0441942
$513$	56.5926	−	6.55254i	2.49862	−	0.289302i
$514$	10.1528			0.447822
$515$	−1.94563	+	0.708151i	−0.0857347	+	0.0312049i
$516$	1.02606	−	5.81905i	0.0451696	−	0.256170i
$517$	1.57139	−	1.31856i	0.0691098	−	0.0579900i
$518$	4.30919	+	3.61584i	0.189335	+	0.158871i
$519$	3.88477	+	22.0316i	0.170523	+	0.967082i
$520$	−0.369309	−	0.639662i	−0.0161953	−	0.0280511i
$521$	13.8343	−	23.9617i	0.606091	−	1.04978i	−0.385787	−	0.922588i	$-0.626070\pi$
$521$	13.8343	−	23.9617i	0.606091	−	1.04978i	0.991878	−	0.127193i	$-0.0405968\pi$
$522$	−52.0492	−	18.9443i	−2.27813	−	0.829172i
$523$	1.00974	+	0.367514i	0.0441527	+	0.0160703i	0.364002	−	0.931398i	$-0.381410\pi$
$523$	1.00974	+	0.367514i	0.0441527	+	0.0160703i	−0.319849	+	0.947468i	$0.603632\pi$
$524$	−7.59305	+	13.1516i	−0.331704	+	0.574528i
$525$	5.31979	+	9.21415i	0.232175	+	0.402139i
$526$	−2.97399	−	16.8663i	−0.129672	−	0.735407i
$527$	4.30788	+	3.61474i	0.187654	+	0.157460i
$528$	15.0637	−	12.6399i	0.655563	−	0.550083i
$529$	−3.76686	+	21.3629i	−0.163776	+	0.928822i
$530$	−6.67640	+	2.43001i	−0.290004	+	0.105553i
$531$	34.5589			1.49973
$532$	−4.16797	−	13.9771i	−0.180704	−	0.605985i
$533$	−7.15792			−0.310044
$534$	6.95655	−	2.53198i	0.301039	−	0.109569i
$535$	−2.54171	+	14.4148i	−0.109888	+	0.623205i
$536$	−2.24063	+	1.88011i	−0.0967804	+	0.0812084i
$537$	7.79316	+	6.53924i	0.336300	+	0.282189i
$538$	−3.96080	−	22.4628i	−0.170762	−	0.968442i
$539$	−12.9760	−	22.4751i	−0.558916	−	0.968071i
$540$	−6.53498	+	11.3189i	−0.281221	+	0.487089i
$541$	−14.5180	−	5.28411i	−0.624177	−	0.227182i	0.0105181	−	0.999945i	$-0.496652\pi$
$541$	−14.5180	−	5.28411i	−0.624177	−	0.227182i	−0.634695	+	0.772763i	$0.718874\pi$
$542$	16.7174	+	6.08464i	0.718074	+	0.261358i
$543$	7.52824	−	13.0393i	0.323068	−	0.559569i
$544$	0.434067	+	0.751825i	0.0186104	+	0.0322342i
$545$	−1.50991	−	8.56310i	−0.0646772	−	0.366803i
$546$	−6.02003	−	5.05141i	−0.257634	−	0.216180i
$547$	−25.7407	+	21.5990i	−1.10059	+	0.923508i	−0.997465	−	0.0711601i	$-0.977330\pi$
$547$	−25.7407	+	21.5990i	−1.10059	+	0.923508i	−0.103129	+	0.994668i	$0.532885\pi$
$548$	−1.48474	+	8.42037i	−0.0634248	+	0.359700i
$549$	−48.2920	+	17.5769i	−2.06105	+	0.750162i
$550$	−6.18432			−0.263700
$551$	−9.70322	−	32.5394i	−0.413371	−	1.38622i
$552$	3.63589			0.154754
$553$	−7.22858	+	2.63099i	−0.307391	+	0.111881i
$554$	3.62454	−	20.5558i	0.153992	−	0.873333i
$555$	4.09488	−	3.43601i	0.173818	−	0.145851i
$556$	6.74440	+	5.65923i	0.286026	+	0.240005i
$557$	−2.47429	−	14.0324i	−0.104839	−	0.594571i	−0.991285	−	0.131739i	$-0.957944\pi$
$557$	−2.47429	−	14.0324i	−0.104839	−	0.594571i	0.886446	−	0.462833i	$-0.153167\pi$
$558$	23.0298	+	39.8888i	0.974929	+	1.68863i
$559$	0.686287	−	1.18868i	0.0290269	−	0.0502760i
$560$	3.14431	+	1.14444i	0.132871	+	0.0483612i
$561$	−16.0417	−	5.83869i	−0.677280	−	0.246510i
$562$	−13.5994	+	23.5548i	−0.573655	+	0.993599i
$563$	−7.38607	−	12.7930i	−0.311286	−	0.539163i	0.667355	−	0.744740i	$-0.267426\pi$
$563$	−7.38607	−	12.7930i	−0.311286	−	0.539163i	−0.978641	+	0.205577i	$0.934093\pi$
$564$	0.183145	+	1.03867i	0.00771178	+	0.0437357i
$565$	8.29690	+	6.96192i	0.349053	+	0.292890i
$566$	15.0862	−	12.6588i	0.634122	−	0.532091i
$567$	−11.7529	+	66.6539i	−0.493574	+	2.79920i
$568$	−6.47503	+	2.35672i	−0.271686	+	0.0988857i
$569$	19.4550			0.815598			0.407799	−	0.913072i	$-0.366296\pi$
$569$	19.4550			0.815598			0.407799	+	0.913072i	$0.366296\pi$
$570$	−13.7680	+	1.59412i	−0.576677	+	0.0667702i
$571$	−39.3956			−1.64866			−0.824328	−	0.566112i	$-0.808447\pi$
$571$	−39.3956			−1.64866			−0.824328	+	0.566112i	$0.808447\pi$
$572$	4.29238	−	1.56230i	0.179473	−	0.0653230i
$573$	−10.1765	+	57.7137i	−0.425129	+	2.41102i
$574$	24.8405	−	20.8436i	1.03682	−	0.869997i
$575$	−0.875950	−	0.735009i	−0.0365296	−	0.0306520i
$576$	1.23472	+	7.00242i	0.0514465	+	0.291768i
$577$	7.94763	+	13.7657i	0.330864	+	0.573073i	0.982682	−	0.185303i	$-0.0593265\pi$
$577$	7.94763	+	13.7657i	0.330864	+	0.573073i	−0.651818	+	0.758376i	$0.725993\pi$
$578$	−8.12317	+	14.0697i	−0.337879	+	0.585224i
$579$	40.4852	+	14.7354i	1.68251	+	0.612382i
$580$	7.32010	+	2.66430i	0.303950	+	0.110629i
$581$	−19.1510	+	33.1706i	−0.794519	+	1.37615i
$582$	−10.8810	−	18.8464i	−0.451032	−	0.781210i
$583$	−7.62990	−	43.2713i	−0.315998	−	1.79212i
$584$	−5.98791	−	5.02445i	−0.247781	−	0.207913i
$585$	−4.02320	+	3.37586i	−0.166339	+	0.139575i
$586$	2.56601	−	14.5526i	0.106001	−	0.601161i
$587$	12.0891	−	4.40009i	0.498973	−	0.181611i	−0.0802592	−	0.996774i	$-0.525575\pi$
$587$	12.0891	−	4.40009i	0.498973	−	0.181611i	0.579232	+	0.815163i	$0.303353\pi$
$588$	13.3433			0.550269
$589$	−11.2117	+	25.9144i	−0.461971	+	1.06778i
$590$	−4.86030			−0.200095
$591$	−24.4742	+	8.90787i	−1.00673	+	0.366421i
$592$	0.291926	−	1.65559i	0.0119981	−	0.0680445i
$593$	1.66829	−	1.39986i	0.0685086	−	0.0574855i	−0.607890	−	0.794021i	$-0.707984\pi$
$593$	1.66829	−	1.39986i	0.0685086	−	0.0574855i	0.676399	+	0.736535i	$0.263540\pi$
$594$	−61.9185	−	51.9558i	−2.54055	−	2.13177i
$595$	−0.504424	−	2.86073i	−0.0206794	−	0.117279i
$596$	−0.380769	−	0.659512i	−0.0155969	−	0.0270146i
$597$	−9.44759	+	16.3637i	−0.386664	+	0.669722i
$598$	0.793654	+	0.288867i	0.0324549	+	0.0118126i
$599$	−3.32108	−	1.20877i	−0.135696	−	0.0493891i	0.273280	−	0.961935i	$-0.411892\pi$
$599$	−3.32108	−	1.20877i	−0.135696	−	0.0493891i	−0.408975	+	0.912545i	$0.634114\pi$
$600$	1.58985	−	2.75370i	0.0649052	−	0.112419i
$601$	−11.2019	−	19.4022i	−0.456935	−	0.791434i	0.541863	−	0.840467i	$-0.317719\pi$
$601$	−11.2019	−	19.4022i	−0.456935	−	0.791434i	−0.998797	+	0.0490333i	$0.984386\pi$
$602$	1.07976	+	6.12360i	0.0440076	+	0.249579i
$603$	15.9319	+	13.3684i	0.648796	+	0.544405i
$604$	−4.66356	+	3.91319i	−0.189757	+	0.159225i
$605$	4.73119	−	26.8319i	0.192350	−	1.09087i
$606$	30.4376	−	11.0784i	1.23644	−	0.450028i
$607$	−12.5717			−0.510269			−0.255134	−	0.966906i	$-0.582120\pi$
$607$	−12.5717			−0.510269			−0.255134	+	0.966906i	$0.582120\pi$
$608$	−2.99469	+	3.16730i	−0.121451	+	0.128451i
$609$	82.8812			3.35851
$610$	6.79170	−	2.47198i	0.274988	−	0.100087i
$611$	−0.0425431	+	0.241274i	−0.00172111	+	0.00976090i
$612$	4.72865	−	3.96781i	0.191144	−	0.160389i
$613$	−35.9199	−	30.1404i	−1.45079	−	1.21736i	−0.932000	−	0.362458i	$-0.881938\pi$
$613$	−35.9199	−	30.1404i	−1.45079	−	1.21736i	−0.518791	−	0.854901i	$-0.673618\pi$
$614$	0.736086	+	4.17455i	0.0297060	+	0.168471i
$615$	−15.4071	−	26.6859i	−0.621276	−	1.07608i
$616$	−10.3467	+	17.9210i	−0.416880	+	0.722058i
$617$	−0.496525	−	0.180720i	−0.0199893	−	0.00727553i	0.332006	−	0.943277i	$-0.392275\pi$
$617$	−0.496525	−	0.180720i	−0.0199893	−	0.00727553i	−0.351995	+	0.936002i	$0.614497\pi$
$618$	6.18650	+	2.25170i	0.248858	+	0.0905768i
$619$	−10.9317	+	18.9343i	−0.439383	+	0.761034i	−0.997642	−	0.0686330i	$-0.978136\pi$
$619$	−10.9317	+	18.9343i	−0.439383	+	0.761034i	0.558259	+	0.829667i	$0.311470\pi$
$620$	−3.23887	−	5.60988i	−0.130076	−	0.225298i
$621$	−2.59520	−	14.7181i	−0.104142	−	0.590616i
$622$	5.35224	+	4.49106i	0.214605	+	0.180075i
$623$	−5.96783	+	5.00760i	−0.239096	+	0.200625i
$624$	−0.407827	+	2.31290i	−0.0163261	+	0.0925901i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	7.61968			0.304544
$627$	5.07663	−	85.5640i	0.202741	−	3.41710i
$628$	24.3756			0.972692
$629$	−1.37143	+	0.499161i	−0.0546826	+	0.0199028i
$630$	4.13149	−	23.4308i	0.164603	−	0.933507i
$631$	23.0776	−	19.3644i	0.918705	−	0.770885i	−0.0550497	−	0.998484i	$-0.517532\pi$
$631$	23.0776	−	19.3644i	0.918705	−	0.770885i	0.973755	+	0.227598i	$0.0730873\pi$
$632$	1.76109	+	1.47773i	0.0700524	+	0.0587810i
$633$	−0.962734	−	5.45993i	−0.0382652	−	0.217013i
$634$	6.86922	+	11.8978i	0.272812	+	0.472524i
$635$	5.61224	−	9.72069i	0.222715	−	0.385754i
$636$	21.2289	+	7.72669i	0.841781	+	0.306383i
$637$	2.91263	+	1.06011i	0.115402	+	0.0420031i
$638$	−24.0876	+	41.7209i	−0.953637	+	1.65175i
$639$	24.4976	+	42.4310i	0.969109	+	1.67855i
$640$	−0.173648	−	0.984808i	−0.00686405	−	0.0389279i
$641$	24.6653	+	20.6967i	0.974223	+	0.817470i	0.983208	−	0.182490i	$-0.0584156\pi$
$641$	24.6653	+	20.6967i	0.974223	+	0.817470i	−0.00898505	+	0.999960i	$0.502860\pi$
$642$	35.6530	−	29.9164i	1.40711	−	1.18071i
$643$	−4.44391	+	25.2027i	−0.175251	+	0.993896i	0.762604	+	0.646866i	$0.223921\pi$
$643$	−4.44391	+	25.2027i	−0.175251	+	0.993896i	−0.937854	+	0.347030i	$0.887190\pi$
$644$	−3.59543	+	1.30863i	−0.141680	+	0.0515672i
$645$	5.90882			0.232660
$646$	3.68115	+	0.876666i	0.144833	+	0.0344920i
$647$	−18.8860			−0.742483			−0.371242	−	0.928536i	$-0.621068\pi$
$647$	−18.8860			−0.742483			−0.371242	+	0.928536i	$0.621068\pi$
$648$	19.0073	−	6.91809i	0.746677	−	0.271768i
$649$	5.21946	−	29.6010i	0.204882	−	1.16194i
$650$	0.565815	−	0.474775i	0.0221931	−	0.0186222i
$651$	−52.7961	−	44.3012i	−2.06924	−	1.73630i
$652$	−0.748409	−	4.24444i	−0.0293100	−	0.166225i
$653$	−12.4152	−	21.5038i	−0.485846	−	0.841510i	0.514022	−	0.857777i	$-0.328155\pi$
$653$	−12.4152	−	21.5038i	−0.485846	−	0.841510i	−0.999868	+	0.0162674i	$0.994822\pi$
$654$	−13.8240	+	23.9439i	−0.540562	+	0.936282i
$655$	−14.2703	−	5.19396i	−0.557586	−	0.202945i
$656$	−9.10652	−	3.31450i	−0.355550	−	0.129410i
$657$	−27.7900	+	48.1336i	−1.08419	+	1.87787i
$658$	−0.554943	−	0.961190i	−0.0216339	−	0.0374711i
$659$	5.44946	+	30.9054i	0.212281	+	1.20391i	0.885563	+	0.464519i	$0.153773\pi$
$659$	5.44946	+	30.9054i	0.212281	+	1.20391i	−0.673282	+	0.739386i	$0.735116\pi$
$660$	15.0637	+	12.6399i	0.586353	+	0.492009i
$661$	−14.2738	+	11.9771i	−0.555186	+	0.465857i	−0.876693	−	0.481051i	$-0.840255\pi$
$661$	−14.2738	+	11.9771i	−0.555186	+	0.465857i	0.321506	+	0.946907i	$0.395811\pi$
$662$	1.15376	−	6.54331i	0.0448422	−	0.254313i
$663$	1.91592	−	0.697338i	0.0744082	−	0.0270824i
$664$	11.4468			0.444220
$665$	13.0410	−	6.53175i	0.505709	−	0.253290i
$666$	−11.9536			−0.463193
$667$	−8.37032	+	3.04655i	−0.324100	+	0.117963i
$668$	0.904979	−	5.13239i	0.0350147	−	0.198578i
$669$	64.4044	−	54.0417i	2.49002	−	2.08937i
$670$	−2.24063	−	1.88011i	−0.0865630	−	0.0726350i
$671$	7.76167	+	44.0186i	0.299636	+	1.69932i
$672$	−5.31979	−	9.21415i	−0.205215	−	0.355444i
$673$	7.28810	−	12.6234i	0.280935	−	0.486594i	−0.690680	−	0.723161i	$-0.742689\pi$
$673$	7.28810	−	12.6234i	0.280935	−	0.486594i	0.971615	+	0.236566i	$0.0760220\pi$
$674$	−17.2976	−	6.29582i	−0.666280	−	0.242506i
$675$	−12.2818	−	4.47019i	−0.472725	−	0.172058i
$676$	6.22722	−	10.7859i	0.239509	−	0.414841i
$677$	−1.21821	−	2.11001i	−0.0468197	−	0.0810941i	0.841666	−	0.539999i	$-0.181575\pi$
$677$	−1.21821	−	2.11001i	−0.0468197	−	0.0810941i	−0.888486	+	0.458905i	$0.848242\pi$
$678$	−5.98022	−	33.9155i	−0.229669	−	1.30252i
$679$	17.5431	+	14.7204i	0.673244	+	0.564918i
$680$	−0.665029	+	0.558025i	−0.0255027	+	0.0213993i
$681$	−15.1549	+	85.9479i	−0.580738	+	3.29353i
$682$	37.6445	−	13.7015i	1.44148	−	0.524656i
$683$	15.0962			0.577639			0.288820	−	0.957384i	$-0.406737\pi$
$683$	15.0962			0.577639			0.288820	+	0.957384i	$0.406737\pi$
$684$	25.8764	+	17.0594i	0.989409	+	0.652282i
$685$	−8.55026			−0.326689
$686$	8.81533	−	3.20852i	0.336571	−	0.122502i
$687$	−6.38955	+	36.2370i	−0.243777	+	1.38253i
$688$	1.42354	−	1.19449i	0.0542720	−	0.0455396i
$689$	4.02004	+	3.37322i	0.153151	+	0.128509i
$690$	0.631365	+	3.58065i	0.0240357	+	0.136313i
$691$	6.12019	+	10.6005i	0.232823	+	0.403261i	0.958638	−	0.284629i	$-0.0918704\pi$
$691$	6.12019	+	10.6005i	0.232823	+	0.403261i	−0.725815	+	0.687890i	$0.758537\pi$
$692$	−3.51787	+	6.09314i	−0.133729	+	0.231626i
$693$	138.266	+	50.3246i	5.25228	+	1.91167i
$694$	6.97015	+	2.53693i	0.264583	+	0.0963005i
$695$	−4.40210	+	7.62466i	−0.166981	+	0.289220i
$696$	−12.3847	−	21.4510i	−0.469442	−	0.813097i
$697$	1.46091	+	8.28523i	0.0553359	+	0.313825i
$698$	−14.6710	−	12.3104i	−0.555305	−	0.465956i
$699$	31.3190	−	26.2798i	1.18459	−	0.993992i
$700$	−0.581045	+	3.29527i	−0.0219614	+	0.124549i
$701$	−41.9967	+	15.2856i	−1.58620	+	0.577328i	−0.976539	−	0.215339i	$-0.930914\pi$
$701$	−41.9967	+	15.2856i	−1.58620	+	0.577328i	−0.609656	+	0.792666i	$0.708692\pi$
$702$	9.65372			0.364356
$703$	−4.36954	−	5.88261i	−0.164800	−	0.221867i
$704$	6.18432			0.233080
$705$	−0.991083	+	0.360725i	−0.0373263	+	0.0135857i
$706$	0.278424	−	1.57902i	0.0104786	−	0.0594273i
$707$	−26.1115	+	21.9102i	−0.982026	+	0.824017i
$708$	11.8386	+	9.93381i	0.444924	+	0.373335i
$709$	−2.78707	−	15.8063i	−0.104671	−	0.593617i	−0.991351	−	0.131235i	$-0.958106\pi$
$709$	−2.78707	−	15.8063i	−0.104671	−	0.593617i	0.886681	−	0.462382i	$-0.153005\pi$
$710$	−3.44529	−	5.96742i	−0.129299	−	0.223953i
$711$	8.17325	−	14.1565i	0.306521	−	0.530910i
$712$	2.18780	+	0.796295i	0.0819914	+	0.0298424i
$713$	6.96040	+	2.53338i	0.260669	+	0.0948758i
$714$	−4.61829	+	7.99911i	−0.172835	+	0.299359i
$715$	2.28393	+	3.95588i	0.0854141	+	0.147942i
$716$	0.555577	+	3.15084i	0.0207629	+	0.117752i
$717$	−27.5589	−	23.1247i	−1.02921	−	0.863606i
$718$	16.5455	−	13.8833i	0.617474	−	0.518122i
$719$	−0.265213	+	1.50410i	−0.00989079	+	0.0560934i	−0.989354	−	0.145531i	$-0.953511\pi$
$719$	−0.265213	+	1.50410i	−0.00989079	+	0.0560934i	0.979463	+	0.201624i	$0.0646221\pi$
$720$	−6.68164	+	2.43192i	−0.249010	+	0.0906322i
$721$	−6.92809			−0.258016
$722$	1.06362	+	18.9702i	0.0395838	+	0.705998i
$723$	−75.6608			−2.81385
$724$	4.44963	−	1.61953i	0.165369	−	0.0601894i
$725$	−1.35270	+	7.67154i	−0.0502380	+	0.284914i
$726$	−66.3651	+	55.6869i	−2.46304	+	2.06674i
$727$	−29.0850	−	24.4052i	−1.07870	−	0.905139i	−0.0828900	−	0.996559i	$-0.526415\pi$
$727$	−29.0850	−	24.4052i	−1.07870	−	0.905139i	−0.995812	+	0.0914199i	$0.970859\pi$
$728$	−0.429171	−	2.43395i	−0.0159061	−	0.0902081i
$729$	−9.57428	−	16.5831i	−0.354603	−	0.614190i
$730$	3.90833	−	6.76942i	0.144654	−	0.250548i
$731$	−1.51596	−	0.551764i	−0.0560698	−	0.0204077i
$732$	−21.5955	−	7.86012i	−0.798193	−	0.290519i
$733$	16.0110	−	27.7319i	0.591381	−	1.02430i	−0.402666	−	0.915347i	$-0.631916\pi$
$733$	16.0110	−	27.7319i	0.591381	−	1.02430i	0.994047	−	0.108955i	$-0.0347504\pi$
$734$	9.87097	+	17.0970i	0.364344	+	0.631062i
$735$	2.31704	+	13.1406i	0.0854654	+	0.484699i
$736$	0.875950	+	0.735009i	0.0322879	+	0.0270928i
$737$	13.8568	−	11.6272i	0.510421	−	0.428294i
$738$	−11.9656	+	67.8602i	−0.440459	+	2.49797i
$739$	36.3892	−	13.2446i	1.33860	−	0.487210i	0.429228	−	0.903196i	$-0.358786\pi$
$739$	36.3892	−	13.2446i	1.33860	−	0.487210i	0.909371	+	0.415986i	$0.136564\pi$
$740$	1.68113			0.0617997
$741$	6.10434	+	8.21814i	0.224249	+	0.301901i
$742$	−23.7737			−0.872758
$743$	29.3436	−	10.6802i	1.07651	−	0.391819i	0.257905	−	0.966170i	$-0.416968\pi$
$743$	29.3436	−	10.6802i	1.07651	−	0.391819i	0.818609	+	0.574351i	$0.194746\pi$
$744$	−3.57667	+	20.2843i	−0.131127	+	0.743658i
$745$	0.583372	−	0.489507i	0.0213731	−	0.0179342i
$746$	17.7417	+	14.8870i	0.649568	+	0.545052i
$747$	−14.1335	−	80.1551i	−0.517118	−	2.93272i
$748$	−2.68441	−	4.64953i	−0.0981517	−	0.170004i
$749$	−24.4887	+	42.4157i	−0.894798	+	1.54984i
$750$	2.98793	+	1.08752i	0.109104	+	0.0397106i
$751$	32.3847	+	11.7871i	1.18173	+	0.430116i	0.856814	−	0.515625i	$-0.172440\pi$
$751$	32.3847	+	11.7871i	1.18173	+	0.430116i	0.324920	+	0.945741i	$0.394663\pi$
$752$	−0.165847	+	0.287256i	−0.00604784	+	0.0104752i
$753$	−41.4532	−	71.7991i	−1.51064	−	2.61650i
$754$	−0.999129	−	5.66634i	−0.0363861	−	0.206356i
$755$	−4.66356	−	3.91319i	−0.169724	−	0.142416i
$756$	−33.5018	+	28.1113i	−1.21845	+	1.02240i
$757$	−0.469366	+	2.66191i	−0.0170594	+	0.0967487i	−0.992149	−	0.125064i	$-0.960086\pi$
$757$	−0.469366	+	2.66191i	−0.0170594	+	0.0967487i	0.975089	+	0.221813i	$0.0711974\pi$
$758$	−3.31671	+	1.20718i	−0.120468	+	0.0438468i
$759$	−22.4855			−0.816173
$760$	−3.63921	−	2.39920i	−0.132008	−	0.0870282i
$761$	9.19327			0.333256			0.166628	−	0.986020i	$-0.446712\pi$
$761$	9.19327			0.333256			0.166628	+	0.986020i	$0.446712\pi$
$762$	−33.5380	+	12.2068i	−1.21495	+	0.442207i
$763$	5.05230	−	28.6530i	0.182906	−	1.03731i
$764$	−14.1187	+	11.8470i	−0.510798	+	0.428611i
$765$	4.72865	+	3.96781i	0.170965	+	0.143456i
$766$	−6.36973	−	36.1246i	−0.230148	−	1.30523i
$767$	1.79495	+	3.10895i	0.0648120	+	0.112258i
$768$	−1.58985	+	2.75370i	−0.0573686	+	0.0993654i
$769$	−0.0570740	−	0.0207732i	−0.00205814	−	0.000749102i	0.340991	−	0.940067i	$-0.389237\pi$
$769$	−0.0570740	−	0.0207732i	−0.00205814	−	0.000749102i	−0.343049	+	0.939318i	$0.611460\pi$
$770$	−19.4454	−	7.07756i	−0.700765	−	0.255058i
$771$	16.1414	−	27.9578i	0.581320	−	1.00688i
$772$	6.77477	+	11.7343i	0.243829	+	0.422325i

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.552148 - 3.13139i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-0.552148 - 3.13139i) q^{6} +(1.67305 + 2.89781i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-6.68164 - 2.43192i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.552148 - 3.13139i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.766044 + 0.642788i) q^{5} +(-0.552148 - 3.13139i) q^{6} +(1.67305 + 2.89781i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-6.68164 - 2.43192i) q^{9} +(0.939693 + 0.342020i) q^{10} +(-3.09216 + 5.35578i) q^{11} +(-1.58985 - 2.75370i) q^{12} +(-0.128260 - 0.727397i) q^{13} +(2.56327 + 2.15083i) q^{14} +(2.43579 - 2.04387i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.815778 + 0.296919i) q^{17} -7.11045 q^{18} +(-2.59916 - 3.49919i) q^{19} +1.00000 q^{20} +(9.99794 - 3.63895i) q^{21} +(-1.07390 + 6.09037i) q^{22} +(-0.875950 + 0.735009i) q^{23} +(-2.43579 - 2.04387i) q^{24} +(0.173648 + 0.984808i) q^{25} +(-0.369309 - 0.639662i) q^{26} +(-6.53498 + 11.3189i) q^{27} +(3.14431 + 1.14444i) q^{28} +(7.32010 + 2.66430i) q^{29} +(1.58985 - 2.75370i) q^{30} +(-3.23887 - 5.60988i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(15.0637 + 12.6399i) q^{33} +(-0.665029 + 0.558025i) q^{34} +(-0.581045 + 3.29527i) q^{35} +(-6.68164 + 2.43192i) q^{36} +1.68113 q^{37} +(-3.63921 - 2.39920i) q^{38} -2.34858 q^{39} +(0.939693 - 0.342020i) q^{40} +(1.68282 - 9.54373i) q^{41} +(8.15040 - 6.83899i) q^{42} +(1.42354 + 1.19449i) q^{43} +(1.07390 + 6.09037i) q^{44} +(-3.55522 - 6.15783i) q^{45} +(-0.571736 + 0.990275i) q^{46} +(-0.311691 - 0.113446i) q^{47} +(-2.98793 - 1.08752i) q^{48} +(-2.09821 + 3.63420i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.479338 + 2.71846i) q^{51} +(-0.565815 - 0.474775i) q^{52} +(-5.44265 + 4.56693i) q^{53} +(-2.26958 + 12.8714i) q^{54} +(-5.81136 + 2.11516i) q^{55} +3.34610 q^{56} +(-12.3925 + 6.20691i) q^{57} +7.78988 q^{58} +(-4.56719 + 1.66232i) q^{59} +(0.552148 - 3.13139i) q^{60} +(5.53664 - 4.64579i) q^{61} +(-4.96223 - 4.16381i) q^{62} +(-4.13149 - 23.4308i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.369309 - 0.639662i) q^{65} +(18.4784 + 6.72557i) q^{66} +(-2.74854 - 1.00039i) q^{67} +(-0.434067 + 0.751825i) q^{68} +(1.81794 + 3.14877i) q^{69} +(0.581045 + 3.29527i) q^{70} +(-5.27849 - 4.42918i) q^{71} +(-5.44692 + 4.57051i) q^{72} +(1.35735 - 7.69790i) q^{73} +(1.57975 - 0.574982i) q^{74} +3.17969 q^{75} +(-4.24031 - 1.00983i) q^{76} -20.6934 q^{77} +(-2.20694 + 0.803262i) q^{78} +(-0.399207 + 2.26401i) q^{79} +(0.766044 - 0.642788i) q^{80} +(15.4949 + 13.0018i) q^{81} +(-1.68282 - 9.54373i) q^{82} +(5.72338 + 9.91318i) q^{83} +(5.31979 - 9.21415i) q^{84} +(-0.815778 - 0.296919i) q^{85} +(1.74623 + 0.635576i) q^{86} +(12.3847 - 21.4510i) q^{87} +(3.09216 + 5.35578i) q^{88} +(0.404290 + 2.29284i) q^{89} +(-5.44692 - 4.57051i) q^{90} +(1.89328 - 1.58865i) q^{91} +(-0.198562 + 1.12610i) q^{92} +(-19.3550 + 7.04466i) q^{93} -0.331695 q^{94} +(0.258165 - 4.35125i) q^{95} -3.17969 q^{96} +(6.43131 - 2.34081i) q^{97} +(-0.728700 + 4.13266i) q^{98} +(33.6855 - 28.2655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18q + 9q^{8} - 18q^{9} + O(q^{10}) \)	\( 18q + 9q^{8} - 18q^{9} - 12q^{11} - 6q^{13} + 6q^{14} - 42q^{18} + 18q^{20} + 12q^{21} - 3q^{22} + 9q^{23} - 9q^{26} - 18q^{27} + 3q^{28} - 6q^{29} - 6q^{31} + 66q^{33} + 18q^{34} + 3q^{35} - 18q^{36} - 12q^{37} - 6q^{38} + 48q^{39} - 21q^{41} + 42q^{42} + 18q^{43} + 3q^{44} - 21q^{45} + 18q^{46} - 54q^{47} - 39q^{49} + 9q^{50} + 42q^{51} + 12q^{52} - 24q^{53} - 54q^{54} - 6q^{55} - 18q^{57} - 30q^{59} + 48q^{61} - 30q^{62} - 57q^{63} - 9q^{64} + 9q^{65} + 24q^{66} - 6q^{67} - 6q^{68} - 30q^{69} - 3q^{70} + 30q^{71} + 6q^{73} - 3q^{74} - 21q^{76} + 30q^{77} - 24q^{78} + 30q^{79} + 18q^{81} + 21q^{82} + 6q^{83} + 6q^{84} + 36q^{86} + 24q^{87} + 12q^{88} + 30q^{89} - 60q^{91} - 18q^{92} - 12q^{93} + 6q^{94} - 12q^{95} - 12q^{97} - 18q^{98} + 171q^{99} + O(q^{100}) \)

Introduction

L-functions

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