LMFDB - Embedded newform 50.2.d.b.41.1

Newspace parameters

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.399252010106$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
Defining polynomial:	$x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 11 x^{4} + 5 x^{3} - 10 x^{2} - 25 x + 25$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			41.1
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	50.41
Dual form			50.2.d.b.11.1

$q$-expansion

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.720859 - 2.21858i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} +(-0.720859 + 2.21858i) q^{6} +3.77447 q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.97539 + 1.43521i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.720859 - 2.21858i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} +(-0.720859 + 2.21858i) q^{6} +3.77447 q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.97539 + 1.43521i) q^{9} +(1.07822 + 1.95894i) q^{10} +(3.05361 + 2.21858i) q^{11} +(1.88723 - 1.37116i) q^{12} +(-2.56969 + 1.86699i) q^{13} +(-3.05361 - 2.21858i) q^{14} +(-0.651166 + 5.17538i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.430307 + 1.32435i) q^{17} +2.44172 q^{18} +(1.20945 - 3.72230i) q^{19} +(0.279141 - 2.21858i) q^{20} +(-2.72086 - 8.37394i) q^{21} +(-1.16637 - 3.58973i) q^{22} +(-0.720859 - 0.523735i) q^{23} -2.33275 q^{24} +(3.19098 + 3.84937i) q^{25} +3.17632 q^{26} +(-1.05361 - 0.765491i) q^{27} +(1.16637 + 3.58973i) q^{28} +(0.0152089 + 0.0468081i) q^{29} +(3.56882 - 3.80423i) q^{30} +(-1.72466 + 5.30795i) q^{31} +1.00000 q^{32} +(2.72086 - 8.37394i) q^{33} +(1.12656 - 0.818492i) q^{34} +(-7.63851 - 3.58973i) q^{35} +(-1.97539 - 1.43521i) q^{36} +(-5.70152 + 4.14240i) q^{37} +(-3.16637 + 2.30051i) q^{38} +(5.99445 + 4.35522i) q^{39} +(-1.52988 + 1.63079i) q^{40} +(1.20477 - 0.875319i) q^{41} +(-2.72086 + 8.37394i) q^{42} +2.69767 q^{43} +(-1.16637 + 3.58973i) q^{44} +(5.36263 - 1.02576i) q^{45} +(0.275344 + 0.847421i) q^{46} +(1.16637 + 3.58973i) q^{47} +(1.88723 + 1.37116i) q^{48} +7.24660 q^{49} +(-0.318958 - 4.98982i) q^{50} +3.24836 q^{51} +(-2.56969 - 1.86699i) q^{52} +(3.58963 + 11.0477i) q^{53} +(0.402443 + 1.23859i) q^{54} +(-4.06969 - 7.39396i) q^{55} +(1.16637 - 3.58973i) q^{56} -9.13004 q^{57} +(0.0152089 - 0.0468081i) q^{58} +(0.558282 - 0.405615i) q^{59} +(-5.12330 + 0.979986i) q^{60} +(-8.38168 - 6.08965i) q^{61} +(4.51521 - 3.28049i) q^{62} +(-7.45605 + 5.41714i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(6.97599 - 1.33437i) q^{65} +(-7.12330 + 5.17538i) q^{66} +(4.73519 - 14.5734i) q^{67} -1.39250 q^{68} +(-0.642308 + 1.97682i) q^{69} +(4.06969 + 7.39396i) q^{70} +(-2.06969 - 6.36986i) q^{71} +(0.754532 + 2.32221i) q^{72} +(-4.18158 - 3.03810i) q^{73} +7.04746 q^{74} +(6.23987 - 9.85429i) q^{75} +3.91385 q^{76} +(11.5257 + 8.37394i) q^{77} +(-2.28968 - 7.04690i) q^{78} +(-0.558282 - 1.71821i) q^{79} +(2.19625 - 0.420099i) q^{80} +(-3.20239 + 9.85596i) q^{81} -1.48918 q^{82} +(-3.08023 + 9.47997i) q^{83} +(7.12330 - 5.17538i) q^{84} +(2.13035 - 2.27088i) q^{85} +(-2.18246 - 1.58565i) q^{86} +(0.0928839 - 0.0674841i) q^{87} +(3.05361 - 2.21858i) q^{88} +(-11.7390 - 8.52891i) q^{89} +(-4.94138 - 2.32221i) q^{90} +(-9.69922 + 7.04690i) q^{91} +(0.275344 - 0.847421i) q^{92} +13.0193 q^{93} +(1.16637 - 3.58973i) q^{94} +(-5.98771 + 6.38268i) q^{95} +(-0.720859 - 2.21858i) q^{96} +(-0.0278640 - 0.0857567i) q^{97} +(-5.86263 - 4.25945i) q^{98} -9.21619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q - 2q^{2} - 3q^{3} - 2q^{4} - 3q^{6} + 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) $	$ 8q - 2q^{2} - 3q^{3} - 2q^{4} - 3q^{6} + 4q^{7} - 2q^{8} - q^{9} + q^{11} + 2q^{12} - 13q^{13} - q^{14} - 10q^{15} - 2q^{16} - 11q^{17} + 14q^{18} + 20q^{19} + 5q^{20} - 19q^{21} + q^{22} - 3q^{23} + 2q^{24} + 30q^{25} + 22q^{26} + 15q^{27} - q^{28} - 15q^{29} - 10q^{30} - 9q^{31} + 8q^{32} + 19q^{33} - q^{34} - 15q^{35} - q^{36} - 6q^{37} - 15q^{38} - 12q^{39} - 5q^{40} - 9q^{41} - 19q^{42} + 12q^{43} + q^{44} + 15q^{45} + 7q^{46} - q^{47} + 2q^{48} - 4q^{49} - 5q^{50} + 26q^{51} - 13q^{52} + 7q^{53} - 25q^{54} - 25q^{55} - q^{56} - 15q^{58} + 10q^{59} - 10q^{60} + 6q^{61} + 21q^{62} - 8q^{63} - 2q^{64} - 10q^{65} - 26q^{66} - 11q^{67} + 24q^{68} + 43q^{69} + 25q^{70} - 9q^{71} - 6q^{72} - 8q^{73} + 24q^{74} + 30q^{75} - 10q^{76} + 33q^{77} + 23q^{78} - 10q^{79} - 17q^{81} + 26q^{82} + 27q^{83} + 26q^{84} + 5q^{85} - 23q^{86} + q^{88} - 15q^{89} + 20q^{90} + q^{91} + 7q^{92} - 46q^{93} - q^{94} - 30q^{95} - 3q^{96} - 36q^{97} - 19q^{98} - 42q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.720859	−	2.21858i	−0.416188	−	1.28090i	−0.911184	−	0.412000i	$-0.864830\pi$
$3$	−0.720859	−	2.21858i	−0.416188	−	1.28090i	0.494996	−	0.868895i	$-0.335170\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.02373	−	0.951057i	−0.905040	−	0.425325i
$5$	−2.02373	−	0.951057i	−0.905040	−	0.425325i
$6$	−0.720859	+	2.21858i	−0.294289	+	0.905730i
$7$	3.77447			1.42661			0.713307	−	0.700851i	$-0.247196\pi$
$7$	3.77447			1.42661			0.713307	+	0.700851i	$0.247196\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−1.97539	+	1.43521i	−0.658464	+	0.478402i
$10$	1.07822	+	1.95894i	0.340962	+	0.619471i
$11$	3.05361	+	2.21858i	0.920698	+	0.668926i	0.943698	−	0.330810i	$-0.107322\pi$
$11$	3.05361	+	2.21858i	0.920698	+	0.668926i	−0.0230000	+	0.999735i	$0.507322\pi$
$12$	1.88723	−	1.37116i	0.544797	−	0.395818i
$13$	−2.56969	+	1.86699i	−0.712705	+	0.517810i	−0.884045	−	0.467402i	$-0.845190\pi$
$13$	−2.56969	+	1.86699i	−0.712705	+	0.517810i	0.171340	+	0.985212i	$0.445190\pi$
$14$	−3.05361	−	2.21858i	−0.816111	−	0.592939i
$15$	−0.651166	+	5.17538i	−0.168130	+	1.33628i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.430307	+	1.32435i	−0.104365	+	0.321201i	−0.989581	−	0.143979i	$-0.954010\pi$
$17$	−0.430307	+	1.32435i	−0.104365	+	0.321201i	0.885216	+	0.465180i	$0.154010\pi$
$18$	2.44172			0.575519
$19$	1.20945	−	3.72230i	0.277466	−	0.853953i	−0.711090	−	0.703101i	$-0.751798\pi$
$19$	1.20945	−	3.72230i	0.277466	−	0.853953i	0.988556	−	0.150852i	$-0.0482018\pi$
$20$	0.279141	−	2.21858i	0.0624178	−	0.496089i
$21$	−2.72086	−	8.37394i	−0.593740	−	1.82734i
$22$	−1.16637	−	3.58973i	−0.248672	−	0.765333i
$23$	−0.720859	−	0.523735i	−0.150310	−	0.109206i	0.510089	−	0.860122i	$-0.329613\pi$
$23$	−0.720859	−	0.523735i	−0.150310	−	0.109206i	−0.660398	+	0.750916i	$0.729613\pi$
$24$	−2.33275			−0.476170
$25$	3.19098	+	3.84937i	0.638197	+	0.769873i
$26$	3.17632			0.622927
$27$	−1.05361	−	0.765491i	−0.202767	−	0.147319i
$28$	1.16637	+	3.58973i	0.220424	+	0.678396i
$29$	0.0152089	+	0.0468081i	0.00282422	+	0.00869205i	0.952459	−	0.304668i	$-0.0985454\pi$
$29$	0.0152089	+	0.0468081i	0.00282422	+	0.00869205i	−0.949634	+	0.313360i	$0.898545\pi$
$30$	3.56882	−	3.80423i	0.651574	−	0.694553i
$31$	−1.72466	+	5.30795i	−0.309757	+	0.953335i	0.668102	+	0.744070i	$0.267107\pi$
$31$	−1.72466	+	5.30795i	−0.309757	+	0.953335i	−0.977859	+	0.209265i	$0.932893\pi$
$32$	1.00000			0.176777
$33$	2.72086	−	8.37394i	0.473641	−	1.45772i
$34$	1.12656	−	0.818492i	0.193203	−	0.140370i
$35$	−7.63851	−	3.58973i	−1.29114	−	0.606775i
$36$	−1.97539	−	1.43521i	−0.329232	−	0.239201i
$37$	−5.70152	+	4.14240i	−0.937324	+	0.681006i	−0.947775	−	0.318940i	$-0.896673\pi$
$37$	−5.70152	+	4.14240i	−0.937324	+	0.681006i	0.0104512	+	0.999945i	$0.496673\pi$
$38$	−3.16637	+	2.30051i	−0.513654	+	0.373191i
$39$	5.99445	+	4.35522i	0.959880	+	0.697394i
$40$	−1.52988	+	1.63079i	−0.241895	+	0.257851i
$41$	1.20477	−	0.875319i	0.188154	−	0.136702i	−0.489721	−	0.871879i	$-0.662901\pi$
$41$	1.20477	−	0.875319i	0.188154	−	0.136702i	0.677875	+	0.735178i	$0.262901\pi$
$42$	−2.72086	+	8.37394i	−0.419838	+	1.29213i
$43$	2.69767			0.411391			0.205695	−	0.978616i	$-0.434054\pi$
$43$	2.69767			0.411391			0.205695	+	0.978616i	$0.434054\pi$
$44$	−1.16637	+	3.58973i	−0.175838	+	0.541172i
$45$	5.36263	−	1.02576i	0.799413	−	0.152912i
$46$	0.275344	+	0.847421i	0.0405972	+	0.124945i
$47$	1.16637	+	3.58973i	0.170133	+	0.523616i	0.999378	−	0.0352696i	$-0.0112290\pi$
$47$	1.16637	+	3.58973i	0.170133	+	0.523616i	−0.829245	+	0.558886i	$0.811229\pi$
$48$	1.88723	+	1.37116i	0.272399	+	0.197909i
$49$	7.24660			1.03523
$50$	−0.318958	−	4.98982i	−0.0451075	−	0.705667i
$51$	3.24836			0.454861
$52$	−2.56969	−	1.86699i	−0.356352	−	0.258905i
$53$	3.58963	+	11.0477i	0.493073	+	1.51752i	0.819938	+	0.572453i	$0.194008\pi$
$53$	3.58963	+	11.0477i	0.493073	+	1.51752i	−0.326864	+	0.945071i	$0.605992\pi$
$54$	0.402443	+	1.23859i	0.0547655	+	0.168551i
$55$	−4.06969	−	7.39396i	−0.548757	−	0.997001i
$56$	1.16637	−	3.58973i	0.155863	−	0.479698i
$57$	−9.13004			−1.20930
$58$	0.0152089	−	0.0468081i	0.00199702	−	0.00614620i
$59$	0.558282	−	0.405615i	0.0726821	−	0.0528066i	−0.550851	−	0.834604i	$-0.685697\pi$
$59$	0.558282	−	0.405615i	0.0726821	−	0.0528066i	0.623533	+	0.781797i	$0.285697\pi$
$60$	−5.12330	+	0.979986i	−0.661415	+	0.126516i
$61$	−8.38168	−	6.08965i	−1.07316	−	0.779700i	−0.0966862	−	0.995315i	$-0.530824\pi$
$61$	−8.38168	−	6.08965i	−1.07316	−	0.779700i	−0.976478	+	0.215615i	$0.930824\pi$
$62$	4.51521	−	3.28049i	0.573432	−	0.416623i
$63$	−7.45605	+	5.41714i	−0.939374	+	0.682495i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	6.97599	−	1.33437i	0.865265	−	0.165508i
$66$	−7.12330	+	5.17538i	−0.876818	+	0.637045i
$67$	4.73519	−	14.5734i	0.578496	−	1.78043i	−0.0454589	−	0.998966i	$-0.514475\pi$
$67$	4.73519	−	14.5734i	0.578496	−	1.78043i	0.623955	−	0.781461i	$-0.285525\pi$
$68$	−1.39250			−0.168866
$69$	−0.642308	+	1.97682i	−0.0773248	+	0.237981i
$70$	4.06969	+	7.39396i	0.486421	+	0.883747i
$71$	−2.06969	−	6.36986i	−0.245627	−	0.755963i	−0.995533	−	0.0944182i	$-0.969901\pi$
$71$	−2.06969	−	6.36986i	−0.245627	−	0.755963i	0.749905	−	0.661545i	$-0.230099\pi$
$72$	0.754532	+	2.32221i	0.0889225	+	0.273675i
$73$	−4.18158	−	3.03810i	−0.489417	−	0.355582i	0.315543	−	0.948911i	$-0.397813\pi$
$73$	−4.18158	−	3.03810i	−0.489417	−	0.355582i	−0.804960	+	0.593329i	$0.797813\pi$
$74$	7.04746			0.819251
$75$	6.23987	−	9.85429i	0.720518	−	1.13788i
$76$	3.91385			0.448950
$77$	11.5257	+	8.37394i	1.31348	+	0.954299i
$78$	−2.28968	−	7.04690i	−0.259255	−	0.797904i
$79$	−0.558282	−	1.71821i	−0.0628116	−	0.193314i	0.914726	−	0.404074i	$-0.132406\pi$
$79$	−0.558282	−	1.71821i	−0.0628116	−	0.193314i	−0.977538	+	0.210760i	$0.932406\pi$
$80$	2.19625	−	0.420099i	0.245548	−	0.0469685i
$81$	−3.20239	+	9.85596i	−0.355822	+	1.09511i
$82$	−1.48918			−0.164453
$83$	−3.08023	+	9.47997i	−0.338099	+	1.04056i	0.627076	+	0.778958i	$0.284251\pi$
$83$	−3.08023	+	9.47997i	−0.338099	+	1.04056i	−0.965175	+	0.261604i	$0.915749\pi$
$84$	7.12330	−	5.17538i	0.777216	−	0.564680i
$85$	2.13035	−	2.27088i	0.231069	−	0.246311i
$86$	−2.18246	−	1.58565i	−0.235341	−	0.170985i
$87$	0.0928839	−	0.0674841i	0.00995820	−	0.00723505i
$88$	3.05361	−	2.21858i	0.325516	−	0.236501i
$89$	−11.7390	−	8.52891i	−1.24434	−	0.904063i	−0.246457	−	0.969154i	$-0.579266\pi$
$89$	−11.7390	−	8.52891i	−1.24434	−	0.904063i	−0.997879	+	0.0650909i	$0.979266\pi$
$90$	−4.94138	−	2.32221i	−0.520868	−	0.244783i
$91$	−9.69922	+	7.04690i	−1.01675	+	0.738716i
$92$	0.275344	−	0.847421i	0.0287066	−	0.0883497i
$93$	13.0193			1.35004
$94$	1.16637	−	3.58973i	0.120302	−	0.370253i
$95$	−5.98771	+	6.38268i	−0.614326	+	0.654849i
$96$	−0.720859	−	2.21858i	−0.0735724	−	0.226432i
$97$	−0.0278640	−	0.0857567i	−0.00282917	−	0.00870727i	0.949632	−	0.313367i	$-0.101457\pi$
$97$	−0.0278640	−	0.0857567i	−0.00282917	−	0.00870727i	−0.952461	+	0.304660i	$0.901457\pi$
$98$	−5.86263	−	4.25945i	−0.592215	−	0.430269i
$99$	−9.21619			−0.926261
$100$	−2.67490	+	4.22433i	−0.267490	+	0.422433i
$101$	16.3785			1.62972			0.814859	−	0.579659i	$-0.196814\pi$
$101$	16.3785			1.62972			0.814859	+	0.579659i	$0.196814\pi$
$102$	−2.62798	−	1.90934i	−0.260208	−	0.189052i
$103$	−0.375822	−	1.15666i	−0.0370308	−	0.113969i	0.930832	−	0.365446i	$-0.119084\pi$
$103$	−0.375822	−	1.15666i	−0.0370308	−	0.113969i	−0.967863	+	0.251477i	$0.919084\pi$
$104$	0.981536	+	3.02086i	0.0962475	+	0.296219i
$105$	−2.45780	+	19.5343i	−0.239857	+	1.90635i
$106$	3.58963	−	11.0477i	0.348656	−	1.07305i
$107$	−10.8125			−1.04528			−0.522641	−	0.852553i	$-0.675053\pi$
$107$	−10.8125			−1.04528			−0.522641	+	0.852553i	$0.675053\pi$
$108$	0.402443	−	1.23859i	0.0387250	−	0.119183i
$109$	−9.23519	+	6.70976i	−0.884571	+	0.642678i	−0.934457	−	0.356077i	$-0.884114\pi$
$109$	−9.23519	+	6.70976i	−0.884571	+	0.642678i	0.0498859	+	0.998755i	$0.484114\pi$
$110$	−1.05361	+	8.37394i	−0.100458	+	0.798424i
$111$	13.3002	+	9.66317i	1.26240	+	0.917187i
$112$	−3.05361	+	2.21858i	−0.288539	+	0.209636i
$113$	8.43232	−	6.12644i	0.793246	−	0.576327i	−0.115679	−	0.993287i	$-0.536904\pi$
$113$	8.43232	−	6.12644i	0.793246	−	0.576327i	0.908925	+	0.416960i	$0.136904\pi$
$114$	7.38636	+	5.36650i	0.691796	+	0.502619i
$115$	0.960724	+	1.74548i	0.0895880	+	0.162767i
$116$	−0.0398173	+	0.0289290i	−0.00369695	+	0.00268599i
$117$	2.39663	−	7.37608i	0.221569	−	0.681919i
$118$	−0.690074			−0.0635265
$119$	−1.62418	+	4.99871i	−0.148888	+	0.458231i
$120$	4.72086	+	2.21858i	0.430954	+	0.202527i
$121$	1.00326	+	3.08770i	0.0912051	+	0.280700i
$122$	3.20152	+	9.85326i	0.289852	+	0.892072i
$123$	−2.81044	−	2.04190i	−0.253408	−	0.184112i
$124$	−5.58111			−0.501198
$125$	−2.79673	−	10.8249i	−0.250147	−	0.968208i
$126$	9.21619			0.821043
$127$	2.87115	+	2.08601i	0.254773	+	0.185104i	0.707840	−	0.706373i	$-0.249670\pi$
$127$	2.87115	+	2.08601i	0.254773	+	0.185104i	−0.453066	+	0.891477i	$0.649670\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−1.94464	−	5.98498i	−0.171216	−	0.526948i
$130$	−6.42801	−	3.02086i	−0.563774	−	0.264947i
$131$	1.25252	−	3.85486i	0.109433	−	0.336801i	−0.881312	−	0.472535i	$-0.843339\pi$
$131$	1.25252	−	3.85486i	0.109433	−	0.336801i	0.990745	+	0.135734i	$0.0433392\pi$
$132$	8.80489			0.766367
$133$	4.56502	−	14.0497i	0.395837	−	1.21826i
$134$	−12.3969	+	9.00687i	−1.07093	+	0.778075i
$135$	1.40420	+	2.55119i	0.120854	+	0.219571i
$136$	1.12656	+	0.818492i	0.0966015	+	0.0701851i
$137$	2.88636	−	2.09706i	0.246598	−	0.179164i	−0.457620	−	0.889148i	$-0.651298\pi$
$137$	2.88636	−	2.09706i	0.246598	−	0.179164i	0.704218	+	0.709984i	$0.251298\pi$
$138$	1.68158	−	1.22174i	0.143146	−	0.104002i
$139$	8.04650	+	5.84613i	0.682495	+	0.495862i	0.874185	−	0.485594i	$-0.161397\pi$
$139$	8.04650	+	5.84613i	0.682495	+	0.495862i	−0.191689	+	0.981456i	$0.561397\pi$
$140$	1.05361	−	8.37394i	0.0890461	−	0.707727i
$141$	7.12330	−	5.17538i	0.599890	−	0.435846i
$142$	−2.06969	+	6.36986i	−0.173685	+	0.534547i
$143$	−11.9889			−1.00256
$144$	0.754532	−	2.32221i	0.0628777	−	0.193518i
$145$	0.0137385	−	0.109192i	0.00114092	−	0.00906786i
$146$	1.59722	+	4.91575i	0.132187	+	0.406830i
$147$	−5.22378	−	16.0771i	−0.430850	−	1.32602i
$148$	−5.70152	−	4.14240i	−0.468662	−	0.340503i
$149$	−19.5103			−1.59834			−0.799171	−	0.601104i	$-0.794728\pi$
$149$	−19.5103			−1.59834			−0.799171	+	0.601104i	$0.794728\pi$
$150$	−10.8404	+	4.30459i	−0.885112	+	0.351468i
$151$	−18.4324			−1.50001			−0.750003	−	0.661435i	$-0.769948\pi$
$151$	−18.4324			−1.50001			−0.750003	+	0.661435i	$0.769948\pi$
$152$	−3.16637	−	2.30051i	−0.256827	−	0.186596i
$153$	−1.05069	−	3.23368i	−0.0849430	−	0.261428i
$154$	−4.40244	−	13.5493i	−0.354759	−	1.09184i
$155$	8.53840	−	9.10162i	0.685821	−	0.731059i
$156$	−2.28968	+	7.04690i	−0.183321	+	0.564203i
$157$	10.1564			0.810572			0.405286	−	0.914190i	$-0.367172\pi$
$157$	10.1564			0.810572			0.405286	+	0.914190i	$0.367172\pi$
$158$	−0.558282	+	1.71821i	−0.0444145	+	0.136694i
$159$	21.9226	−	15.9277i	1.73858	−	1.26315i
$160$	−2.02373	−	0.951057i	−0.159990	−	0.0751876i
$161$	−2.72086	−	1.97682i	−0.214434	−	0.155795i
$162$	8.38398	−	6.09132i	0.658708	−	0.478579i
$163$	15.0481	−	10.9331i	1.17865	−	0.856343i	0.186636	−	0.982429i	$-0.440242\pi$
$163$	15.0481	−	10.9331i	1.17865	−	0.856343i	0.992019	+	0.126086i	$0.0402416\pi$
$164$	1.20477	+	0.875319i	0.0940770	+	0.0683510i
$165$	−13.4704	+	14.3589i	−1.04867	+	1.11784i
$166$	8.06414	−	5.85894i	0.625899	−	0.454742i
$167$	0.671048	−	2.06527i	0.0519273	−	0.159816i	−0.921730	−	0.387832i	$-0.873224\pi$
$167$	0.671048	−	2.06527i	0.0519273	−	0.159816i	0.973657	+	0.228016i	$0.0732240\pi$
$168$	−8.80489			−0.679312
$169$	−0.899554	+	2.76854i	−0.0691965	+	0.212965i
$170$	−3.05828	+	0.584988i	−0.234560	+	0.0448666i
$171$	2.95313	+	9.08880i	0.225831	+	0.695038i
$172$	0.833625	+	2.56564i	0.0635633	+	0.195628i
$173$	5.17306	+	3.75845i	0.393300	+	0.285750i	0.766807	−	0.641878i	$-0.221845\pi$
$173$	5.17306	+	3.75845i	0.393300	+	0.285750i	−0.373506	+	0.927628i	$0.621845\pi$
$174$	−0.114811			−0.00870378
$175$	12.0443	+	14.5293i	0.910461	+	1.09831i
$176$	−3.77447			−0.284511
$177$	−1.30233	−	0.946199i	−0.0978892	−	0.0711207i
$178$	4.48391	+	13.8001i	0.336084	+	1.03436i
$179$	2.47630	+	7.62127i	0.185087	+	0.569640i	0.999950	−	0.0100140i	$-0.00318759\pi$
$179$	2.47630	+	7.62127i	0.185087	+	0.569640i	−0.814862	+	0.579654i	$0.803188\pi$
$180$	2.63270	+	4.78318i	0.196230	+	0.356517i
$181$	−3.35682	+	10.3312i	−0.249510	+	0.767913i	0.745352	+	0.666671i	$0.232282\pi$
$181$	−3.35682	+	10.3312i	−0.249510	+	0.767913i	−0.994862	+	0.101242i	$0.967718\pi$
$182$	11.9889			0.888676
$183$	−7.46834	+	22.9852i	−0.552075	+	1.69911i
$184$	−0.720859	+	0.523735i	−0.0531424	+	0.0386102i
$185$	15.4780	−	2.96063i	1.13797	−	0.217670i
$186$	−10.5328	−	7.65256i	−0.772306	−	0.561113i
$187$	−4.25215	+	3.08937i	−0.310948	+	0.225917i
$188$	−3.05361	+	2.21858i	−0.222707	+	0.161806i
$189$	−3.97681	−	2.88932i	−0.289270	−	0.210167i
$190$	8.59580	−	1.64421i	0.623605	−	0.119283i
$191$	6.62243	−	4.81147i	0.479182	−	0.348146i	−0.321827	−	0.946798i	$-0.604297\pi$
$191$	6.62243	−	4.81147i	0.479182	−	0.348146i	0.801009	+	0.598652i	$0.204297\pi$
$192$	−0.720859	+	2.21858i	−0.0520235	+	0.160112i
$193$	−17.5576			−1.26382			−0.631912	−	0.775040i	$-0.717730\pi$
$193$	−17.5576			−1.26382			−0.631912	+	0.775040i	$0.717730\pi$
$194$	−0.0278640	+	0.0857567i	−0.00200052	+	0.00615697i
$195$	−7.98910	−	14.5149i	−0.572111	−	1.03943i
$196$	2.23932	+	6.89193i	0.159952	+	0.492281i
$197$	1.47012	+	4.52458i	0.104742	+	0.322363i	0.989670	−	0.143365i	$-0.0457924\pi$
$197$	1.47012	+	4.52458i	0.104742	+	0.322363i	−0.884928	+	0.465728i	$0.845792\pi$
$198$	7.45605	+	5.41714i	0.529878	+	0.384979i
$199$	14.5320			1.03015			0.515073	−	0.857146i	$-0.327765\pi$
$199$	14.5320			1.03015			0.515073	+	0.857146i	$0.327765\pi$
$200$	4.64703	−	1.84529i	0.328595	−	0.130481i
$201$	−35.7457			−2.52130
$202$	−13.2505	−	9.62702i	−0.932299	−	0.677355i
$203$	0.0574054	+	0.176676i	0.00402907	+	0.0124002i
$204$	1.00380	+	3.08937i	0.0702799	+	0.216299i
$205$	−3.27062	+	0.625604i	−0.228430	+	0.0436941i
$206$	−0.375822	+	1.15666i	−0.0261848	+	0.0805884i
$207$	2.17565			0.151218
$208$	0.981536	−	3.02086i	0.0680572	−	0.209459i
$209$	11.9514	−	8.68318i	0.826694	−	0.600628i
$210$	13.4704	−	14.3589i	0.929545	−	0.990860i
$211$	11.4362	+	8.30886i	0.787298	+	0.572006i	0.907160	−	0.420785i	$-0.138245\pi$
$211$	11.4362	+	8.30886i	0.787298	+	0.572006i	−0.119862	+	0.992791i	$0.538245\pi$
$212$	−9.39777	+	6.82788i	−0.645441	+	0.468941i
$213$	−12.6401	+	9.18355i	−0.866083	+	0.629246i
$214$	8.74748	+	6.35542i	0.597965	+	0.434447i
$215$	−5.45936	−	2.56564i	−0.372325	−	0.174975i
$216$	−1.05361	+	0.765491i	−0.0716890	+	0.0520851i
$217$	−6.50966	+	20.0347i	−0.441904	+	1.36004i
$218$	11.4153			0.773143
$219$	−3.72592	+	11.4672i	−0.251774	+	0.774882i
$220$	5.77447	−	6.15537i	0.389315	−	0.414995i
$221$	−1.36679	−	4.20655i	−0.0919402	−	0.282963i
$222$	−5.08023	−	15.6353i	−0.340963	−	1.04938i
$223$	−3.73139	−	2.71102i	−0.249873	−	0.181543i	0.455798	−	0.890083i	$-0.349354\pi$
$223$	−3.73139	−	2.71102i	−0.249873	−	0.181543i	−0.705670	+	0.708540i	$0.749354\pi$
$224$	3.77447			0.252192
$225$	−11.8281	−	3.02429i	−0.788538	−	0.201619i
$226$	−10.4229			−0.693322
$227$	5.08578	+	3.69503i	0.337555	+	0.245248i	0.743630	−	0.668592i	$-0.233103\pi$
$227$	5.08578	+	3.69503i	0.337555	+	0.245248i	−0.406075	+	0.913840i	$0.633103\pi$
$228$	−2.82134	−	8.68318i	−0.186848	−	0.575058i
$229$	5.48103	+	16.8689i	0.362196	+	1.11473i	0.951718	+	0.306973i	$0.0993163\pi$
$229$	5.48103	+	16.8689i	0.362196	+	1.11473i	−0.589522	+	0.807753i	$0.700684\pi$
$230$	0.248723	−	1.97682i	0.0164003	−	0.130348i
$231$	10.2698	−	31.6072i	0.675703	−	2.07960i
$232$	0.0492169			0.00323125
$233$	0.792338	−	2.43856i	0.0519078	−	0.159756i	−0.921742	−	0.387803i	$-0.873234\pi$
$233$	0.792338	−	2.43856i	0.0519078	−	0.159756i	0.973650	+	0.228047i	$0.0732341\pi$
$234$	−6.27447	+	4.55867i	−0.410175	+	0.298009i
$235$	1.05361	−	8.37394i	0.0687298	−	0.546256i
$236$	0.558282	+	0.405615i	0.0363410	+	0.0264033i
$237$	−3.40955	+	2.47718i	−0.221474	+	0.160910i
$238$	4.25215	−	3.08937i	0.275626	−	0.200254i
$239$	−7.63851	−	5.54970i	−0.494094	−	0.358980i	0.312662	−	0.949864i	$-0.398779\pi$
$239$	−7.63851	−	5.54970i	−0.494094	−	0.358980i	−0.806757	+	0.590884i	$0.798779\pi$
$240$	−2.51521	−	4.56972i	−0.162356	−	0.294974i
$241$	23.8131	−	17.3012i	1.53394	−	1.11447i	0.579940	−	0.814659i	$-0.303076\pi$
$241$	23.8131	−	17.3012i	1.53394	−	1.11447i	0.953998	−	0.299812i	$-0.0969240\pi$
$242$	1.00326	−	3.08770i	0.0644917	−	0.198485i
$243$	20.2677			1.30017
$244$	3.20152	−	9.85326i	0.204956	−	0.630790i
$245$	−14.6652	−	6.89193i	−0.936924	−	0.440309i
$246$	1.07349	+	3.30386i	0.0684433	+	0.210647i
$247$	3.84159	+	11.8232i	0.244434	+	0.752292i
$248$	4.51521	+	3.28049i	0.286716	+	0.208311i
$249$	23.2524			1.47356
$250$	−4.10011	+	10.4014i	−0.259314	+	0.657842i
$251$	−6.00759			−0.379196			−0.189598	−	0.981862i	$-0.560718\pi$
$251$	−6.00759			−0.379196			−0.189598	+	0.981862i	$0.560718\pi$
$252$	−7.45605	−	5.41714i	−0.469687	−	0.341248i
$253$	−1.03928	−	3.19856i	−0.0653387	−	0.201092i
$254$	−1.09668	−	3.37524i	−0.0688119	−	0.211781i
$255$	−6.57380	−	3.08937i	−0.411667	−	0.193464i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−13.6286			−0.850127			−0.425063	−	0.905164i	$-0.639748\pi$
$257$	−13.6286			−0.850127			−0.425063	+	0.905164i	$0.639748\pi$
$258$	−1.94464	+	5.98498i	−0.121068	+	0.372609i
$259$	−21.5202	+	15.6353i	−1.33720	+	0.971533i
$260$	3.42476	+	6.22221i	0.212394	+	0.385885i
$261$	−0.0972227	−	0.0706365i	−0.00601794	−	0.00437229i
$262$	−3.27914	+	2.38244i	−0.202586	+	0.147187i
$263$	7.41298	−	5.38584i	0.457104	−	0.332105i	−0.335290	−	0.942115i	$-0.608834\pi$
$263$	7.41298	−	5.38584i	0.457104	−	0.332105i	0.792394	+	0.610010i	$0.208834\pi$
$264$	−7.12330	−	5.17538i	−0.438409	−	0.318523i
$265$	3.24258	−	25.7716i	0.199190	−	1.58314i
$266$	−11.9514	+	8.68318i	−0.732786	+	0.532400i
$267$	−10.4598	+	32.1921i	−0.640132	+	1.97012i
$268$	15.3234			0.936026
$269$	8.68419	−	26.7272i	0.529484	−	1.62959i	−0.225790	−	0.974176i	$-0.572496\pi$
$269$	8.68419	−	26.7272i	0.529484	−	1.62959i	0.755274	−	0.655409i	$-0.227504\pi$
$270$	0.363534	−	2.88932i	0.0221240	−	0.175838i
$271$	−2.81162	−	8.65329i	−0.170794	−	0.525650i	0.828623	−	0.559808i	$-0.189125\pi$
$271$	−2.81162	−	8.65329i	−0.170794	−	0.525650i	−0.999416	+	0.0341581i	$0.989125\pi$
$272$	−0.430307	−	1.32435i	−0.0260912	−	0.0803004i
$273$	22.6259	+	16.4386i	1.36938	+	0.994912i
$274$	−3.56773			−0.215535
$275$	1.20390	+	18.8339i	0.0725977	+	1.13573i
$276$	−2.07855			−0.125114
$277$	−15.2006	−	11.0439i	−0.913318	−	0.663564i	0.0285338	−	0.999593i	$-0.490916\pi$
$277$	−15.2006	−	11.0439i	−0.913318	−	0.663564i	−0.941852	+	0.336028i	$0.890916\pi$
$278$	−3.07349	−	9.45923i	−0.184336	−	0.567327i
$279$	−4.21112	−	12.9605i	−0.252113	−	0.775925i
$280$	−5.77447	+	6.15537i	−0.345090	+	0.367854i
$281$	2.43554	−	7.49583i	0.145292	−	0.447164i	−0.851756	−	0.523938i	$-0.824462\pi$
$281$	2.43554	−	7.49583i	0.145292	−	0.447164i	0.997048	+	0.0767748i	$0.0244622\pi$
$282$	−8.80489			−0.524323
$283$	−5.65496	+	17.4042i	−0.336153	+	1.03457i	0.629999	+	0.776596i	$0.283055\pi$
$283$	−5.65496	+	17.4042i	−0.336153	+	1.03457i	−0.966151	+	0.257975i	$0.916945\pi$
$284$	5.41853	−	3.93679i	0.321530	−	0.233606i
$285$	18.4768	+	8.68318i	1.09447	+	0.514347i
$286$	9.69922	+	7.04690i	0.573527	+	0.416692i
$287$	4.54738	−	3.30386i	0.268423	−	0.195021i
$288$	−1.97539	+	1.43521i	−0.116401	+	0.0845703i
$289$	12.1846	+	8.85260i	0.716739	+	0.520741i
$290$	−0.0752958	+	0.0802625i	−0.00442152	+	0.00471318i
$291$	−0.170172	+	0.123637i	−0.00997564	+	0.00724773i
$292$	1.59722	−	4.91575i	0.0934704	−	0.287672i
$293$	−29.4990			−1.72335			−0.861675	−	0.507461i	$-0.830584\pi$
$293$	−29.4990			−1.72335			−0.861675	+	0.507461i	$0.830584\pi$
$294$	−5.22378	+	16.0771i	−0.304657	+	0.937638i
$295$	−1.51558	+	0.289899i	−0.0882402	+	0.0168786i
$296$	2.17779	+	6.70254i	0.126581	+	0.389577i
$297$	−1.51901	−	4.67502i	−0.0881417	−	0.271272i
$298$	15.7841	+	11.4678i	0.914350	+	0.664314i
$299$	2.83020			0.163674
$300$	11.3002	+	2.88932i	0.652418	+	0.166815i
$301$	10.1823			0.586896
$302$	14.9121	+	10.8343i	0.858095	+	0.623443i
$303$	−11.8066	−	36.3369i	−0.678269	−	2.08750i
$304$	1.20945	+	3.72230i	0.0693666	+	0.213488i
$305$	11.1707	+	20.2953i	0.639631	+	1.16210i
$306$	−1.05069	+	3.23368i	−0.0600638	+	0.184857i
$307$	13.9131			0.794064			0.397032	−	0.917805i	$-0.370040\pi$
$307$	13.9131			0.794064			0.397032	+	0.917805i	$0.370040\pi$
$308$	−4.40244	+	13.5493i	−0.250852	+	0.772044i
$309$	−2.29523	+	1.66758i	−0.130571	+	0.0948653i
$310$	−12.2575	+	2.34462i	−0.696180	+	0.133165i
$311$	−21.0050	−	15.2610i	−1.19108	−	0.865373i	−0.197705	−	0.980262i	$-0.563349\pi$
$311$	−21.0050	−	15.2610i	−1.19108	−	0.865373i	−0.993378	+	0.114889i	$0.963349\pi$
$312$	5.99445	−	4.35522i	0.339369	−	0.246566i
$313$	−7.66454	+	5.56861i	−0.433225	+	0.314757i	−0.782937	−	0.622101i	$-0.786279\pi$
$313$	−7.66454	+	5.56861i	−0.433225	+	0.314757i	0.349712	+	0.936857i	$0.386279\pi$
$314$	−8.21673	−	5.96980i	−0.463697	−	0.336895i
$315$	20.2411	−	3.87171i	1.14045	−	0.218146i
$316$	1.46160	−	1.06192i	0.0822215	−	0.0597374i
$317$	7.57321	−	23.3079i	0.425354	−	1.30910i	−0.477301	−	0.878740i	$-0.658385\pi$
$317$	7.57321	−	23.3079i	0.425354	−	1.30910i	0.902655	−	0.430365i	$-0.141615\pi$
$318$	−27.0979			−1.51957
$319$	−0.0574054	+	0.176676i	−0.00321408	+	0.00989194i
$320$	1.07822	+	1.95894i	0.0602741	+	0.109508i
$321$	7.79427	+	23.9883i	0.435034	+	1.33890i
$322$	1.03928	+	3.19856i	0.0579166	+	0.178249i
$323$	4.40918	+	3.20346i	0.245333	+	0.178245i
$324$	−10.3632			−0.575731
$325$	−15.3866	−	3.93416i	−0.853494	−	0.218228i
$326$	−18.6004			−1.03018
$327$	21.5434	+	15.6522i	1.19135	+	0.865568i
$328$	−0.460183	−	1.41630i	−0.0254093	−	0.0782019i
$329$	4.40244	+	13.5493i	0.242715	+	0.746998i
$330$	19.3377	−	3.69892i	1.06451	−	0.203619i
$331$	−3.06247	+	9.42530i	−0.168328	+	0.518061i	−0.999266	−	0.0383039i	$-0.987804\pi$
$331$	−3.06247	+	9.42530i	−0.168328	+	0.518061i	0.830938	+	0.556365i	$0.187804\pi$
$332$	−9.96783			−0.547056
$333$	5.31754	−	16.3657i	0.291399	−	0.896835i
$334$	−1.75683	+	1.27641i	−0.0961293	+	0.0698420i
$335$	−23.4429	+	24.9893i	−1.28082	+	1.36531i
$336$	7.12330	+	5.17538i	0.388608	+	0.282340i
$337$	8.03812	−	5.84003i	0.437864	−	0.318127i	−0.346922	−	0.937894i	$-0.612773\pi$
$337$	8.03812	−	5.84003i	0.437864	−	0.318127i	0.784786	+	0.619767i	$0.212773\pi$
$338$	2.35506	−	1.71105i	0.128099	−	0.0930690i
$339$	−19.6705	−	14.2914i	−1.06835	−	0.776205i
$340$	2.81805	+	1.32435i	0.152830	+	0.0718228i
$341$	−17.0425	+	12.3821i	−0.922904	+	0.670529i
$342$	2.95313	−	9.08880i	0.159687	−	0.491466i
$343$	0.930796			0.0502583
$344$	0.833625	−	2.56564i	0.0449461	−	0.138330i
$345$	3.17993	−	3.38968i	0.171201	−	0.182494i
$346$	−1.97593	−	6.08130i	−0.106227	−	0.326933i
$347$	−6.06757	−	18.6741i	−0.325724	−	1.00248i	−0.971113	−	0.238622i	$-0.923304\pi$
$347$	−6.06757	−	18.6741i	−0.325724	−	1.00248i	0.645388	−	0.763855i	$-0.276696\pi$
$348$	0.0928839	+	0.0674841i	0.00497910	+	0.00361753i
$349$	1.48432			0.0794538			0.0397269	−	0.999211i	$-0.487351\pi$
$349$	1.48432			0.0794538			0.0397269	+	0.999211i	$0.487351\pi$
$350$	−1.20390	−	18.8339i	−0.0643510	−	1.00671i
$351$	4.13662			0.220796
$352$	3.05361	+	2.21858i	0.162758	+	0.118251i
$353$	3.17632	+	9.77569i	0.169058	+	0.520308i	0.999312	−	0.0370772i	$-0.0118048\pi$
$353$	3.17632	+	9.77569i	0.169058	+	0.520308i	−0.830254	+	0.557385i	$0.811805\pi$
$354$	0.497446	+	1.53098i	0.0264390	+	0.0813708i
$355$	−1.86959	+	14.8593i	−0.0992277	+	0.788649i
$356$	4.48391	−	13.8001i	0.237647	−	0.731402i
$357$	12.2608			0.648911
$358$	2.47630	−	7.62127i	0.130877	−	0.402797i
$359$	8.39154	−	6.09681i	0.442889	−	0.321777i	−0.343893	−	0.939009i	$-0.611746\pi$
$359$	8.39154	−	6.09681i	0.442889	−	0.321777i	0.786782	+	0.617231i	$0.211746\pi$
$360$	0.681583	−	5.41714i	0.0359226	−	0.285508i
$361$	2.97859	+	2.16408i	0.156768	+	0.113899i
$362$	8.78826	−	6.38504i	0.461901	−	0.335590i
$363$	6.12710	−	4.45160i	0.321589	−	0.233648i
$364$	−9.69922	−	7.04690i	−0.508377	−	0.369358i
$365$	5.57300	+	10.1252i	0.291704	+	0.529978i
$366$	19.5524	−	14.2056i	1.02202	−	0.742540i
$367$	8.05741	−	24.7981i	0.420593	−	1.29445i	−0.486558	−	0.873648i	$-0.661748\pi$
$367$	8.05741	−	24.7981i	0.420593	−	1.29445i	0.907151	−	0.420804i	$-0.138252\pi$
$368$	0.891031			0.0464482
$369$	−1.12364	+	3.45820i	−0.0584942	+	0.180027i
$370$	−14.2622	−	6.70254i	−0.741455	−	0.348448i
$371$	13.5489	+	41.6993i	0.703426	+	2.16492i
$372$	4.02319	+	12.3821i	0.208593	+	0.641982i
$373$	−7.65001	−	5.55806i	−0.396102	−	0.287785i	0.371849	−	0.928293i	$-0.378724\pi$
$373$	−7.65001	−	5.55806i	−0.396102	−	0.287785i	−0.767952	+	0.640508i	$0.778724\pi$
$374$	5.25595			0.271779
$375$	−21.9998	+	14.0080i	−1.13606	+	0.723369i
$376$	3.77447			0.194653
$377$	−0.126472	−	0.0918876i	−0.00651366	−	0.00473245i
$378$	1.51901	+	4.67502i	0.0781292	+	0.240457i
$379$	−10.9163	−	33.5968i	−0.560731	−	1.72575i	−0.680307	−	0.732927i	$-0.738154\pi$
$379$	−10.9163	−	33.5968i	−0.560731	−	1.72575i	0.119576	−	0.992825i	$-0.461846\pi$
$380$	−7.92059	−	3.72230i	−0.406318	−	0.190950i
$381$	2.55828	−	7.87358i	0.131065	−	0.403376i
$382$	−8.18577			−0.418820
$383$	9.21407	−	28.3580i	0.470817	−	1.44902i	−0.380700	−	0.924698i	$-0.624317\pi$
$383$	9.21407	−	28.3580i	0.470817	−	1.44902i	0.851517	−	0.524327i	$-0.175683\pi$
$384$	1.88723	−	1.37116i	0.0963075	−	0.0699715i
$385$	−15.3609	−	27.9083i	−0.782865	−	1.42234i
$386$	14.2044	+	10.3201i	0.722985	+	0.525280i
$387$	−5.32895	+	3.87171i	−0.270886	+	0.196810i
$388$	0.0729490	−	0.0530006i	0.00370343	−	0.00269070i
$389$	17.2942	+	12.5649i	0.876848	+	0.637068i	0.932416	−	0.361387i	$-0.117697\pi$
$389$	17.2942	+	12.5649i	0.876848	+	0.637068i	−0.0555675	+	0.998455i	$0.517697\pi$
$390$	−2.06831	+	16.4386i	−0.104733	+	0.832403i
$391$	1.00380	−	0.729301i	0.0507642	−	0.0368824i
$392$	2.23932	−	6.89193i	0.113103	−	0.348095i
$393$	−9.45519			−0.476951
$394$	1.47012	−	4.52458i	0.0740638	−	0.227945i
$395$	−0.504306	+	4.00816i	−0.0253744	+	0.201673i
$396$	−2.84796	−	8.76511i	−0.143115	−	0.440464i
$397$	6.49555	+	19.9913i	0.326002	+	1.00333i	0.970986	+	0.239136i	$0.0768642\pi$
$397$	6.49555	+	19.9913i	0.326002	+	1.00333i	−0.644984	+	0.764196i	$0.723136\pi$
$398$	−11.7566	−	8.54169i	−0.589307	−	0.428156i
$399$	−34.4610			−1.72521
$400$	−4.84416	−	1.23859i	−0.242208	−	0.0619295i
$401$	16.7820			0.838053			0.419026	−	0.907974i	$-0.362371\pi$
$401$	16.7820			0.838053			0.419026	+	0.907974i	$0.362371\pi$
$402$	28.9188	+	21.0108i	1.44234	+	1.04792i
$403$	−5.47805	−	16.8597i	−0.272881	−	0.839842i
$404$	5.06122	+	15.5768i	0.251805	+	0.774977i
$405$	15.8544	−	16.9002i	0.787810	−	0.839776i
$406$	0.0574054	−	0.176676i	0.00284898	−	0.00876826i
$407$	−26.6004			−1.31853
$408$	1.00380	−	3.08937i	0.0496954	−	0.152947i
$409$	−29.4165	+	21.3723i	−1.45455	+	1.05679i	−0.469809	+	0.882768i	$0.655677\pi$
$409$	−29.4165	+	21.3723i	−1.45455	+	1.05679i	−0.984741	+	0.174025i	$0.944323\pi$
$410$	3.01371	+	1.41630i	0.148836	+	0.0699459i
$411$	−6.73315	−	4.89192i	−0.332122	−	0.241301i
$412$	0.983915	−	0.714856i	0.0484740	−	0.0352184i
$413$	2.10722	−	1.53098i	0.103689	−	0.0753347i
$414$	−1.76013	−	1.27881i	−0.0865059	−	0.0628502i
$415$	15.2495	−	16.2554i	0.748571	−	0.797948i
$416$	−2.56969	+	1.86699i	−0.125990	+	0.0915368i
$417$	7.16968	−	22.0660i	0.351101	−	1.08058i
$418$	−14.7727			−0.722557
$419$	−10.6731	+	32.8484i	−0.521415	+	1.60475i	0.249884	+	0.968276i	$0.419608\pi$
$419$	−10.6731	+	32.8484i	−0.521415	+	1.60475i	−0.771298	+	0.636474i	$0.780392\pi$
$420$	−19.3377	+	3.69892i	−0.943585	+	0.180489i
$421$	3.00798	+	9.25762i	0.146600	+	0.451189i	0.997213	−	0.0746033i	$-0.0237691\pi$
$421$	3.00798	+	9.25762i	0.146600	+	0.451189i	−0.850613	+	0.525792i	$0.823769\pi$
$422$	−4.36823	−	13.4440i	−0.212642	−	0.654445i
$423$	−7.45605	−	5.41714i	−0.362526	−	0.263390i
$424$	11.6163			0.564136
$425$	−6.47100	+	2.56956i	−0.313890	+	0.124642i
$426$	15.6240			0.756984
$427$	−31.6364	−	22.9852i	−1.53099	−	1.11233i
$428$	−3.34124	−	10.2833i	−0.161505	−	0.497061i
$429$	8.64231	+	26.5983i	0.417255	+	1.28418i
$430$	2.90867	+	5.28457i	0.140269	+	0.254845i
$431$	−0.956560	+	2.94399i	−0.0460759	+	0.141807i	−0.971448	−	0.237254i	$-0.923753\pi$
$431$	−0.956560	+	2.94399i	−0.0460759	+	0.141807i	0.925372	+	0.379061i	$0.123753\pi$
$432$	1.30233			0.0626584
$433$	−5.63542	+	17.3440i	−0.270821	+	0.833501i	0.719474	+	0.694519i	$0.244383\pi$
$433$	−5.63542	+	17.3440i	−0.270821	+	0.833501i	−0.990295	+	0.138981i	$0.955617\pi$
$434$	17.0425	−	12.3821i	0.818067	−	0.594360i
$435$	−0.252153	+	0.0482319i	−0.0120898	+	0.00231254i
$436$	−9.23519	−	6.70976i	−0.442285	−	0.321339i
$437$	−2.82134	+	2.04982i	−0.134963	+	0.0980563i
$438$	9.75458	−	7.08712i	0.466092	−	0.338636i
$439$	21.4595	+	15.5912i	1.02421	+	0.744129i	0.967141	−	0.254242i	$-0.0818259\pi$
$439$	21.4595	+	15.5912i	1.02421	+	0.744129i	0.0570645	+	0.998370i	$0.481826\pi$
$440$	−8.28968	+	1.58565i	−0.395195	+	0.0755929i
$441$	−14.3149	+	10.4004i	−0.681661	+	0.495256i
$442$	−1.36679	+	4.20655i	−0.0650115	+	0.200085i
$443$	35.5267			1.68793			0.843963	−	0.536401i	$-0.180217\pi$
$443$	35.5267			1.68793			0.843963	+	0.536401i	$0.180217\pi$
$444$	−5.08023	+	15.6353i	−0.241097	+	0.742020i
$445$	15.6452	+	28.4247i	0.741653	+	1.34746i
$446$	1.42527	+	4.38652i	0.0674883	+	0.207708i
$447$	14.0641	+	43.2850i	0.665211	+	2.04731i
$448$	−3.05361	−	2.21858i	−0.144269	−	0.104818i
$449$	16.1841			0.763776			0.381888	−	0.924209i	$-0.375274\pi$
$449$	16.1841			0.763776			0.381888	+	0.924209i	$0.375274\pi$
$450$	7.79148	+	9.39907i	0.367294	+	0.443076i
$451$	5.62087			0.264676
$452$	8.43232	+	6.12644i	0.396623	+	0.288163i
$453$	13.2871	+	40.8936i	0.624284	+	1.92135i
$454$	−1.94259	−	5.97869i	−0.0911705	−	0.280594i
$455$	26.3306	−	5.03652i	1.23440	−	0.236116i
$456$	−2.82134	+	8.68318i	−0.132121	+	0.406627i
$457$	23.7205			1.10960			0.554799	−	0.831984i	$-0.312795\pi$
$457$	23.7205			1.10960			0.554799	+	0.831984i	$0.312795\pi$
$458$	5.48103	−	16.8689i	0.256112	−	0.788230i
$459$	1.46715	−	1.06595i	0.0684807	−	0.0497542i
$460$	−1.36317	+	1.45309i	−0.0635580	+	0.0677504i
$461$	6.36936	+	4.62761i	0.296651	+	0.215529i	0.726147	−	0.687539i	$-0.241309\pi$
$461$	6.36936	+	4.62761i	0.296651	+	0.215529i	−0.429497	+	0.903068i	$0.641309\pi$
$462$	−26.8867	+	19.5343i	−1.25088	+	0.908818i
$463$	−12.4775	+	9.06543i	−0.579878	+	0.421306i	−0.838680	−	0.544624i	$-0.816672\pi$
$463$	−12.4775	+	9.06543i	−0.579878	+	0.421306i	0.258802	+	0.965930i	$0.416672\pi$
$464$	−0.0398173	−	0.0289290i	−0.00184847	−	0.00134299i
$465$	−26.3476	−	12.3821i	−1.22184	−	0.574206i
$466$	−2.07437	+	1.50712i	−0.0960932	+	0.0698158i
$467$	−5.26481	+	16.2034i	−0.243626	+	0.749805i	0.752233	+	0.658897i	$0.228977\pi$
$467$	−5.26481	+	16.2034i	−0.243626	+	0.749805i	−0.995859	+	0.0909075i	$0.971023\pi$
$468$	7.75567			0.358506
$469$	17.8728	−	55.0069i	0.825290	−	2.53998i
$470$	−5.77447	+	6.15537i	−0.266356	+	0.283926i
$471$	−7.32136	−	22.5328i	−0.337350	−	1.03826i
$472$	−0.213245	−	0.656300i	−0.00981538	−	0.0302086i
$473$	8.23762	+	5.98498i	0.378766	+	0.275190i
$474$	4.21443			0.193575
$475$	18.1878	−	7.22218i	0.834514	−	0.331376i
$476$	−5.25595			−0.240906
$477$	−22.9467	−	16.6718i	−1.05066	−	0.763347i
$478$	2.91765	+	8.97961i	0.133450	+	0.410718i
$479$	−7.75544	−	23.8688i	−0.354355	−	1.09059i	−0.956382	−	0.292118i	$-0.905640\pi$
$479$	−7.75544	−	23.8688i	−0.354355	−	1.09059i	0.602027	−	0.798476i	$-0.294360\pi$
$480$	−0.651166	+	5.17538i	−0.0297215	+	0.236223i
$481$	6.91734	−	21.2894i	0.315403	−	0.970712i
$482$	−29.4346			−1.34071
$483$	−2.42437	+	7.46144i	−0.110313	+	0.339507i
$484$	−2.62656	+	1.90831i	−0.119389	+	0.0867412i
$485$	−0.0251701	+	0.200049i	−0.00114292	+	0.00908375i
$486$	−16.3969	−	11.9130i	−0.743778	−	0.540386i
$487$	11.0735	−	8.04536i	0.501788	−	0.364570i	−0.307912	−	0.951415i	$-0.599630\pi$
$487$	11.0735	−	8.04536i	0.501788	−	0.364570i	0.809699	+	0.586845i	$0.199630\pi$
$488$	−8.38168	+	6.08965i	−0.379421	+	0.275665i
$489$	−35.1033	−	25.5041i	−1.58743	−	1.15333i
$490$	7.81341	+	14.1957i	0.352974	+	0.641295i
$491$	2.08733	−	1.51654i	0.0942001	−	0.0684403i	−0.539688	−	0.841865i	$-0.681458\pi$
$491$	2.08733	−	1.51654i	0.0942001	−	0.0684403i	0.633888	+	0.773425i	$0.281458\pi$
$492$	1.07349	−	3.30386i	0.0483967	−	0.148950i
$493$	−0.0685347			−0.00308665
$494$	3.84159	−	11.8232i	0.172841	−	0.531950i
$495$	18.6511	+	8.76511i	0.838304	+	0.393963i
$496$	−1.72466	−	5.30795i	−0.0774394	−	0.238334i
$497$	−7.81199	−	24.0428i	−0.350416	−	1.07847i
$498$	−18.8116	−	13.6674i	−0.842969	−	0.612453i
$499$	−39.0539			−1.74829			−0.874146	−	0.485664i	$-0.838578\pi$
$499$	−39.0539			−1.74829			−0.874146	+	0.485664i	$0.838578\pi$
$500$	9.43085	−	6.00492i	0.421760	−	0.268548i
$501$	−5.06570			−0.226319
$502$	4.86025	+	3.53118i	0.216923	+	0.157604i
$503$	3.69387	+	11.3686i	0.164702	+	0.506899i	0.999014	−	0.0443923i	$-0.0141352\pi$
$503$	3.69387	+	11.3686i	0.164702	+	0.506899i	−0.834313	+	0.551292i	$0.814135\pi$
$504$	2.84796	+	8.76511i	0.126858	+	0.390429i
$505$	−33.1456	−	15.5768i	−1.47496	−	0.693160i
$506$	−1.03928	+	3.19856i	−0.0462014	+	0.142193i
$507$	6.79067			0.301584
$508$	−1.09668	+	3.37524i	−0.0486574	+	0.149752i
$509$	3.94254	−	2.86442i	0.174750	−	0.126963i	−0.496972	−	0.867767i	$-0.665555\pi$
$509$	3.94254	−	2.86442i	0.174750	−	0.126963i	0.671722	+	0.740803i	$0.265555\pi$
$510$	3.50243	+	6.36334i	0.155090	+	0.281773i
$511$	−15.7832	−	11.4672i	−0.698210	−	0.507279i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−4.12367	+	2.99602i	−0.182064	+	0.132278i
$514$	11.0257	+	8.01067i	0.486325	+	0.353336i
$515$	−0.339487	+	2.69820i	−0.0149596	+	0.118897i
$516$	5.09113	−	3.69892i	0.224125	−	0.162836i
$517$	−4.40244	+	13.5493i	−0.193619	+	0.595899i
$518$	26.6004			1.16876
$519$	4.60936	−	14.1861i	0.202328	−	0.622702i
$520$	0.886640	−	7.04690i	0.0388817	−	0.309027i
$521$	−2.70131	−	8.31378i	−0.118347	−	0.364233i	0.874284	−	0.485415i	$-0.161332\pi$
$521$	−2.70131	−	8.31378i	−0.118347	−	0.364233i	−0.992630	+	0.121182i	$0.961332\pi$
$522$	0.0371358	+	0.114292i	0.00162539	+	0.00500243i
$523$	17.0534	+	12.3900i	0.745694	+	0.541778i	0.894489	−	0.447090i	$-0.147540\pi$
$523$	17.0534	+	12.3900i	0.745694	+	0.541778i	−0.148795	+	0.988868i	$0.547540\pi$
$524$	4.05324			0.177067
$525$	23.5522	−	37.1947i	1.02790	−	1.62331i
$526$	−9.16294			−0.399523
$527$	−6.28743	−	4.56809i	−0.273885	−	0.198989i
$528$	2.72086	+	8.37394i	0.118410	+	0.364429i
$529$	−6.86205	−	21.1192i	−0.298350	−	0.918227i
$530$	−17.7715	+	18.9437i	−0.771943	+	0.822863i
$531$	−0.520683	+	1.60250i	−0.0225957	+	0.0695425i
$532$	14.7727			0.640478
$533$	−1.46169	+	4.49861i	−0.0633126	+	0.194856i
$534$	27.3842	−	19.8958i	1.18503	−	0.860976i
$535$	21.8816	+	10.2833i	0.946022	+	0.444585i
$536$	−12.3969	−	9.00687i	−0.535464	−	0.389038i
$537$	15.1233	−	10.9877i	0.652619	−	0.474155i
$538$	−22.7355	+	16.5183i	−0.980197	+	0.712155i
$539$	22.1283	+	16.0771i	0.953133	+	0.692492i
$540$	−1.99241	+	2.12383i	−0.0857395	+	0.0913951i
$541$	−26.5406	+	19.2829i	−1.14107	+	0.829036i	−0.987268	−	0.159066i	$-0.949152\pi$
$541$	−26.5406	+	19.2829i	−1.14107	+	0.829036i	−0.153802	+	0.988102i	$0.549152\pi$
$542$	−2.81162	+	8.65329i	−0.120770	+	0.371690i
$543$	25.3404			1.08746
$544$	−0.430307	+	1.32435i	−0.0184492	+	0.0567809i
$545$	25.0709	−	4.79557i	1.07392	−	0.205419i
$546$	−8.64231	−	26.5983i	−0.369857	−	1.13830i
$547$	−1.69044	−	5.20264i	−0.0722781	−	0.222449i	0.908391	−	0.418121i	$-0.137311\pi$
$547$	−1.69044	−	5.20264i	−0.0722781	−	0.222449i	−0.980669	+	0.195672i	$0.937311\pi$
$548$	2.88636	+	2.09706i	0.123299	+	0.0895820i
$549$	25.2970			1.07965
$550$	10.0963	−	15.9446i	0.430508	−	0.679879i
$551$	0.192628			0.00820623
$552$	1.68158	+	1.22174i	0.0715729	+	0.0520008i
$553$	−2.10722	−	6.48535i	−0.0896080	−	0.275785i
$554$	5.80613	+	17.8694i	0.246679	+	0.759199i
$555$	−17.7258	−	32.2049i	−0.752420	−	1.36702i
$556$	−3.07349	+	9.45923i	−0.130345	+	0.401161i
$557$	−5.19840			−0.220263			−0.110132	−	0.993917i	$-0.535127\pi$
$557$	−5.19840			−0.220263			−0.110132	+	0.993917i	$0.535127\pi$
$558$	−4.21112	+	12.9605i	−0.178271	+	0.548662i
$559$	−6.93218	+	5.03652i	−0.293200	+	0.213022i
$560$	8.28968	−	1.58565i	0.350303	−	0.0670059i
$561$	9.91921	+	7.20673i	0.418789	+	0.304268i
$562$	−6.37633	+	4.63268i	−0.268969	+	0.195418i
$563$	4.05741	−	2.94788i	0.170999	−	0.124238i	−0.498994	−	0.866605i	$-0.666297\pi$
$563$	4.05741	−	2.94788i	0.170999	−	0.124238i	0.669993	+	0.742367i	$0.266297\pi$
$564$	7.12330	+	5.17538i	0.299945	+	0.217923i
$565$	−22.8913	+	4.37866i	−0.963046	+	0.184212i
$566$	14.8049	−	10.7564i	0.622296	−	0.452124i
$567$	−12.0873	+	37.2010i	−0.507620	+	1.56229i
$568$	−6.69767			−0.281028
$569$	−12.9303	+	39.7952i	−0.542064	+	1.66830i	0.185805	+	0.982587i	$0.440511\pi$
$569$	−12.9303	+	39.7952i	−0.542064	+	1.66830i	−0.727869	+	0.685716i	$0.759489\pi$
$570$	−9.84416	−	17.8852i	−0.412327	−	0.749129i
$571$	−13.7723	−	42.3869i	−0.576355	−	1.77384i	−0.631519	−	0.775360i	$-0.717568\pi$
$571$	−13.7723	−	42.3869i	−0.576355	−	1.77384i	0.0551642	−	0.998477i	$-0.482432\pi$
$572$	−3.70477	−	11.4021i	−0.154904	−	0.476747i
$573$	−15.4485	−	11.2240i	−0.645369	−	0.468888i
$574$	−5.62087			−0.234611
$575$	−0.284202	−	4.44608i	−0.0118520	−	0.185414i
$576$	2.44172			0.101738
$577$	20.3401	+	14.7779i	0.846769	+	0.615213i	0.924253	−	0.381780i	$-0.124689\pi$
$577$	20.3401	+	14.7779i	0.846769	+	0.615213i	−0.0774845	+	0.996994i	$0.524689\pi$
$578$	−4.65409	−	14.3238i	−0.193584	−	0.595792i
$579$	12.6566	+	38.9529i	0.525989	+	1.61883i
$580$	0.108093	−	0.0206760i	0.00448831	−	0.000858524i
$581$	−11.6262	+	35.7818i	−0.482337	+	1.48448i
$582$	0.210344			0.00871903
$583$	−13.5489	+	41.6993i	−0.561140	+	1.72701i
$584$	−4.18158	+	3.03810i	−0.173035	+	0.125717i
$585$	−11.8652	+	12.6479i	−0.490566	+	0.522925i
$586$	23.8652	+	17.3391i	0.985861	+	0.716270i
$587$	−17.2770	+	12.5525i	−0.713099	+	0.518097i	−0.884172	−	0.467162i	$-0.845277\pi$
$587$	−17.2770	+	12.5525i	−0.713099	+	0.518097i	0.171073	+	0.985258i	$0.445277\pi$
$588$	13.6760	−	9.93622i	0.563990	−	0.409763i
$589$	17.6719	+	12.8394i	0.728157	+	0.529037i
$590$	1.39653	+	0.656300i	0.0574940	+	0.0270194i
$591$	8.97836	−	6.52316i	0.369321	−	0.268327i
$592$	2.17779	−	6.70254i	0.0895065	−	0.275473i
$593$	−33.4430			−1.37334			−0.686669	−	0.726970i	$-0.740928\pi$
$593$	−33.4430			−1.37334			−0.686669	+	0.726970i	$0.740928\pi$
$594$	−1.51901	+	4.67502i	−0.0623256	+	0.191818i
$595$	8.04095	−	8.57136i	0.329647	−	0.351391i
$596$	−6.02900	−	18.5554i	−0.246957	−	0.760057i
$597$	−10.4755	−	32.2403i	−0.428734	−	1.31951i
$598$	−2.28968	−	1.66355i	−0.0936318	−	0.0680275i
$599$	26.3174			1.07530			0.537650	−	0.843168i	$-0.319312\pi$
$599$	26.3174			1.07530			0.537650	+	0.843168i	$0.319312\pi$
$600$	−7.44376	−	8.97961i	−0.303890	−	0.366591i
$601$	20.9964			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$601$	20.9964			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$602$	−8.23762	−	5.98498i	−0.335740	−	0.243930i
$603$	11.5620	+	35.5842i	0.470841	+	1.44910i
$604$	−5.69592	−	17.5302i	−0.231764	−	0.713295i
$605$	0.906260	−	7.20284i	0.0368447	−	0.292837i
$606$	−11.8066	+	36.3369i	−0.479609	+	1.47608i
$607$	9.32822			0.378621			0.189310	−	0.981917i	$-0.439375\pi$
$607$	9.32822			0.378621			0.189310	+	0.981917i	$0.439375\pi$
$608$	1.20945	−	3.72230i	0.0490496	−	0.150959i
$609$	0.350587	−	0.254716i	0.0142065	−	0.0103216i
$610$	2.89199	−	22.9852i	0.117093	−	0.930643i
$611$	−9.69922	−	7.04690i	−0.392389	−	0.285087i
$612$	2.75074	−	1.99853i	0.111192	−	0.0807856i
$613$	25.9724	−	18.8700i	1.04902	−	0.762154i	0.0769902	−	0.997032i	$-0.475469\pi$
$613$	25.9724	−	18.8700i	1.04902	−	0.762154i	0.972025	+	0.234878i	$0.0754690\pi$
$614$	−11.2560	−	8.17793i	−0.454253	−	0.330034i
$615$	3.74560	+	6.80514i	0.151037	+	0.274410i
$616$	11.5257	−	8.37394i	0.464385	−	0.337396i
$617$	−9.86557	+	30.3631i	−0.397173	+	1.22237i	0.530084	+	0.847945i	$0.322160\pi$
$617$	−9.86557	+	30.3631i	−0.397173	+	1.22237i	−0.927257	+	0.374427i	$0.877840\pi$
$618$	2.83706			0.114123
$619$	−1.40420	+	4.32167i	−0.0564394	+	0.173703i	−0.975302	−	0.220875i	$-0.929109\pi$
$619$	−1.40420	+	4.32167i	−0.0564394	+	0.173703i	0.918863	+	0.394577i	$0.129109\pi$
$620$	11.2947	+	5.30795i	0.453605	+	0.213172i
$621$	0.358589	+	1.10362i	0.0143897	+	0.0442868i
$622$	8.02319	+	24.6928i	0.321701	+	0.990093i
$623$	−44.3086	−	32.1921i	−1.77519	−	1.28975i
$624$	−7.40955			−0.296619
$625$	−4.63525	+	24.5665i	−0.185410	+	0.982661i
$626$	9.47389			0.378653
$627$	−27.8796	−	20.2557i	−1.11340	−	0.808934i
$628$	3.13851	+	9.65934i	0.125240	+	0.385450i
$629$	−3.03257	−	9.33329i	−0.120916	−	0.372143i
$630$	−18.6511	−	8.76511i	−0.743077	−	0.349210i
$631$	−8.31756	+	25.5988i	−0.331117	+	1.01907i	0.637486	+	0.770462i	$0.279974\pi$
$631$	−8.31756	+	25.5988i	−0.331117	+	1.01907i	−0.968603	+	0.248611i	$0.920026\pi$
$632$	−1.80664			−0.0718642
$633$	10.1900	−	31.3615i	0.405015	−	1.24651i
$634$	−19.8269	+	14.4051i	−0.787427	+	0.572100i
$635$	−3.82652	−	6.95215i	−0.151851	−	0.275888i
$636$	21.9226	+	15.9277i	0.869289	+	0.631575i
$637$	−18.6215	+	13.5293i	−0.737813	+	0.536052i
$638$	0.150289	−	0.109192i	0.00595001	−	0.00432293i
$639$	13.2305	+	9.61253i	0.523391	+	0.380266i
$640$	0.279141	−	2.21858i	0.0110340	−	0.0876969i
$641$	−28.9303	+	21.0191i	−1.14268	+	0.830205i	−0.987490	−	0.157679i	$-0.949599\pi$
$641$	−28.9303	+	21.0191i	−1.14268	+	0.830205i	−0.155189	+	0.987885i	$0.549599\pi$
$642$	7.79427	−	23.9883i	0.307615	−	0.946743i
$643$	28.2255			1.11311			0.556553	−	0.830812i	$-0.312124\pi$
$643$	28.2255			1.11311			0.556553	+	0.830812i	$0.312124\pi$
$644$	1.03928	−	3.19856i	0.0409532	−	0.126041i
$645$	−1.75663	+	13.9615i	−0.0691672	+	0.549732i
$646$	−1.68416	−	5.18330i	−0.0662623	−	0.203934i
$647$	0.394848	+	1.21522i	0.0155231	+	0.0477751i	0.958518	−	0.285032i	$-0.0920042\pi$
$647$	0.394848	+	1.21522i	0.0155231	+	0.0477751i	−0.942995	+	0.332807i	$0.892004\pi$
$648$	8.38398	+	6.09132i	0.329354	+	0.239290i
$649$	2.60466			0.102242
$650$	10.1356	+	12.2268i	0.397550	+	0.479575i
$651$	49.1410			1.92599
$652$	15.0481	+	10.9331i	0.589327	+	0.428171i
$653$	−8.47040	−	26.0692i	−0.331472	−	1.02017i	−0.968434	−	0.249272i	$-0.919809\pi$
$653$	−8.47040	−	26.0692i	−0.331472	−	1.02017i	0.636961	−	0.770896i	$-0.280191\pi$
$654$	−8.22884	−	25.3258i	−0.321773	−	0.990316i
$655$	−6.20096	+	6.60999i	−0.242291	+	0.258274i
$656$	−0.460183	+	1.41630i	−0.0179671	+	0.0552971i
$657$	12.6206			0.492375
$658$	4.40244	−	13.5493i	0.171625	−	0.528208i
$659$	33.3535	−	24.2327i	1.29927	−	0.943972i	0.299318	−	0.954153i	$-0.403241\pi$
$659$	33.3535	−	24.2327i	1.29927	−	0.943972i	0.999948	+	0.0101814i	$0.00324090\pi$
$660$	−17.8187	−	8.37394i	−0.693593	−	0.325955i
$661$	21.4653	+	15.5955i	0.834904	+	0.606593i	0.920942	−	0.389699i	$-0.127421\pi$
$661$	21.4653	+	15.5955i	0.834904	+	0.606593i	−0.0860388	+	0.996292i	$0.527421\pi$
$662$	8.01764	−	5.82516i	0.311614	−	0.226401i
$663$	−8.34728	+	6.06465i	−0.324181	+	0.235532i
$664$	8.06414	+	5.85894i	0.312949	+	0.227371i
$665$	−22.6004	+	24.0912i	−0.876407	+	0.934217i
$666$	−13.9215	+	10.1146i	−0.539447	+	0.391931i
$667$	0.0135516	−	0.0417075i	0.000524719	−	0.00161492i
$668$	2.17156			0.0840201
$669$	−3.32479	+	10.2326i	−0.128544	+	0.395617i
$670$	33.6540	−	6.43735i	1.30017	−	0.248696i
$671$	−12.0840	−	37.1908i	−0.466499	−	1.43574i
$672$	−2.72086	−	8.37394i	−0.104959	−	0.323032i
$673$	6.42142	+	4.66543i	0.247527	+	0.179839i	0.704630	−	0.709575i	$-0.251113\pi$
$673$	6.42142	+	4.66543i	0.247527	+	0.179839i	−0.457103	+	0.889414i	$0.651113\pi$
$674$	−9.93566			−0.382707
$675$	−0.415389	−	6.49839i	−0.0159883	−	0.250123i
$676$	−2.91102			−0.111962
$677$	−23.8667	−	17.3402i	−0.917271	−	0.666436i	0.0255722	−	0.999673i	$-0.491859\pi$
$677$	−23.8667	−	17.3402i	−0.917271	−	0.666436i	−0.942843	+	0.333237i	$0.891859\pi$
$678$	7.51346	+	23.1240i	0.288553	+	0.888073i
$679$	−0.105172	−	0.323686i	−0.00403613	−	0.0124219i
$680$	−1.50142	−	2.72783i	−0.0575768	−	0.104607i
$681$	4.53159	−	13.9468i	0.173651	−	0.534442i
$682$	21.0657			0.806647
$683$	11.6650	−	35.9012i	0.446349	−	1.37372i	−0.434648	−	0.900600i	$-0.643127\pi$
$683$	11.6650	−	35.9012i	0.446349	−	1.37372i	0.880997	−	0.473121i	$-0.156873\pi$
$684$	−7.73139	+	5.61719i	−0.295617	+	0.214779i
$685$	−7.83564	+	1.49880i	−0.299384	+	0.0572663i
$686$	−0.753030	−	0.547108i	−0.0287508	−	0.0208887i
$687$	33.4738	−	24.3201i	1.27711	−	0.927872i
$688$	−2.18246	+	1.58565i	−0.0832055	+	0.0604523i
$689$	−29.8503	−	21.6875i	−1.13721	−	0.826228i
$690$	−4.56502	+	0.873197i	−0.173787	+	0.0332421i
$691$	−14.2843	+	10.3782i	−0.543401	+	0.394804i	−0.825347	−	0.564626i	$-0.809020\pi$
$691$	−14.2843	+	10.3782i	−0.543401	+	0.394804i	0.281945	+	0.959430i	$0.409020\pi$
$692$	−1.97593	+	6.08130i	−0.0751137	+	0.231176i
$693$	−34.7862			−1.32142
$694$	−6.06757	+	18.6741i	−0.230322	+	0.708858i
$695$	−10.7240	−	19.4837i	−0.406783	−	0.739058i
$696$	−0.0354785	−	0.109192i	−0.00134481	−	0.00413889i
$697$	0.640805	+	1.97219i	0.0242722	+	0.0747022i
$698$	−1.20084	−	0.872461i	−0.0454524	−	0.0330231i
$699$	−5.98131			−0.226234
$700$	−10.0963	+	15.9446i	−0.381605	+	0.602648i
$701$	−16.8372			−0.635931			−0.317965	−	0.948102i	$-0.603000\pi$
$701$	−16.8372			−0.635931			−0.317965	+	0.948102i	$0.603000\pi$
$702$	−3.34659	−	2.43144i	−0.126309	−	0.0917688i
$703$	8.52354	+	26.2328i	0.321471	+	0.989387i
$704$	−1.16637	−	3.58973i	−0.0439594	−	0.135293i
$705$	−19.3377	+	3.69892i	−0.728301	+	0.139310i
$706$	3.17632	−	9.77569i	0.119542	−	0.367913i
$707$	61.8200			2.32498
$708$	0.497446	−	1.53098i	0.0186952	−	0.0575378i
$709$	23.1615	−	16.8278i	0.869849	−	0.631982i	−0.0606978	−	0.998156i	$-0.519333\pi$
$709$	23.1615	−	16.8278i	0.869849	−	0.631982i	0.930546	+	0.366174i	$0.119333\pi$
$710$	10.2466	−	10.9225i	0.384548	−	0.409914i
$711$	3.56882	+	2.59290i	0.133841	+	0.0972412i
$712$	−11.7390	+	8.52891i	−0.439939	+	0.319635i
$713$	4.02319	−	2.92302i	0.150670	−	0.109468i
$714$	−9.91921	−	7.20673i	−0.371217	−	0.269705i
$715$	24.2623	+	11.4021i	0.907359	+	0.426415i
$716$	−6.48304	+	4.71020i	−0.242283	+	0.176029i
$717$	−6.80615	+	20.9472i	−0.254180	+	0.782286i
$718$	−10.3725			−0.387099
$719$	−2.54857	+	7.84368i	−0.0950455	+	0.292520i	−0.987266	−	0.159081i	$-0.949147\pi$
$719$	−2.54857	+	7.84368i	−0.0950455	+	0.292520i	0.892220	+	0.451601i	$0.149147\pi$
$720$	−3.73553	+	3.98193i	−0.139215	+	0.148398i
$721$	−1.41853	−	4.36578i	−0.0528287	−	0.162590i
$722$	−1.13772	−	3.50155i	−0.0423416	−	0.130314i
$723$	−55.5500	−	40.3595i	−2.06593	−	1.50098i
$724$	−10.8629			−0.403716
$725$	−0.131650	+	0.207908i	−0.00488937	+	0.00772152i
$726$	−7.57351			−0.281079
$727$	1.71013	+	1.24248i	0.0634251	+	0.0460810i	0.619046	−	0.785355i	$-0.287519\pi$
$727$	1.71013	+	1.24248i	0.0634251	+	0.0460810i	−0.555621	+	0.831436i	$0.687519\pi$
$728$	3.70477	+	11.4021i	0.137308	+	0.422591i
$729$	−5.00295	−	15.3975i	−0.185295	−	0.570278i
$730$	1.44280	−	11.4672i	0.0534005	−	0.424420i
$731$	−1.16082	+	3.57265i	−0.0429346	+	0.132139i
$732$	−24.1681			−0.893277
$733$	13.9537	−	42.9451i	0.515393	−	1.58622i	−0.267174	−	0.963648i	$-0.586090\pi$
$733$	13.9537	−	42.9451i	0.515393	−	1.58622i	0.782567	−	0.622567i	$-0.213910\pi$
$734$	−21.0946	+	15.3261i	−0.778614	+	0.565697i
$735$	−4.71874	+	37.5039i	−0.174053	+	1.38335i
$736$	−0.720859	−	0.523735i	−0.0265712	−	0.0193051i
$737$	46.7917	−	33.9961i	1.72359	−	1.25226i
$738$	2.94172	−	2.13728i	0.108286	−	0.0786745i
$739$	−24.2478	−	17.6171i	−0.891969	−	0.648054i	0.0444213	−	0.999013i	$-0.485856\pi$
$739$	−24.2478	−	17.6171i	−0.891969	−	0.648054i	−0.936391	+	0.350959i	$0.885856\pi$
$740$	7.59869	+	13.8056i	0.279334	+	0.507503i
$741$	23.4614	−	17.0457i	0.861876	−	0.626190i
$742$	13.5489	−	41.6993i	0.497397	−	1.53083i
$743$	17.6562			0.647741			0.323871	−	0.946101i	$-0.395016\pi$
$743$	17.6562			0.647741			0.323871	+	0.946101i	$0.395016\pi$
$744$	4.02319	−	12.3821i	0.147497	−	0.453950i
$745$	39.4835	+	18.5554i	1.44656	+	0.679816i
$746$	2.92204	+	8.99312i	0.106984	+	0.329262i
$747$	−7.52105	−	23.1474i	−0.275181	−	0.846920i
$748$	−4.25215	−	3.08937i	−0.155474	−	0.112959i
$749$	−40.8113			−1.49121
$750$	26.0319	+	1.59847i	0.950550	+	0.0583677i
$751$	30.1342			1.09961			0.549806	−	0.835293i	$-0.314702\pi$
$751$	30.1342			1.09961			0.549806	+	0.835293i	$0.314702\pi$
$752$	−3.05361	−	2.21858i	−0.111354	−	0.0809031i
$753$	4.33063	+	13.3283i	0.157817	+	0.485710i
$754$	0.0483082	+	0.148677i	0.00175928	+	0.00541451i
$755$	37.3022	+	17.5302i	1.35757	+	0.637990i
$756$	1.51901	−	4.67502i	0.0552457	−	0.170029i
$757$	−4.90706			−0.178350			−0.0891750	−	0.996016i	$-0.528423\pi$
$757$	−4.90706			−0.178350			−0.0891750	+	0.996016i	$0.528423\pi$
$758$	−10.9163	+	33.5968i	−0.396497	+	1.22029i
$759$	−6.34708	+	4.61142i	−0.230384	+	0.167384i
$760$	4.21998	+	7.66701i	0.153075	+	0.278112i
$761$	−10.7466	−	7.80786i	−0.389564	−	0.283035i	0.375713	−	0.926736i	$-0.377398\pi$
$761$	−10.7466	−	7.80786i	−0.389564	−	0.283035i	−0.765277	+	0.643701i	$0.777398\pi$
$762$	−6.69767	+	4.86614i	−0.242631	+	0.176282i
$763$	−34.8579	+	25.3258i	−1.26194	+	0.916854i
$764$	6.62243	+	4.81147i	0.239591	+	0.174073i
$765$	−0.949106	+	7.54337i	−0.0343150	+	0.272731i
$766$	−24.1227	+	17.5262i	−0.871590	+	0.633247i
$767$	−0.677332	+	2.08461i	−0.0244571	+	0.0752711i
$768$	−2.33275			−0.0841758
$769$	−8.83716	+	27.1980i	−0.318676	+	0.980784i	0.655539	+	0.755162i	$0.272442\pi$
$769$	−8.83716	+	27.1980i	−0.318676	+	0.980784i	−0.974215	+	0.225623i	$0.927558\pi$
$770$	−3.97681	+	31.6072i	−0.143314	+	1.13904i
$771$	9.82428	+	30.2360i	0.353813	+	1.08892i
$772$	−5.42560	−	16.6983i	−0.195272	−	0.600984i
$773$	36.4564	+	26.4871i	1.31124	+	0.952675i	0.999997	+	0.00234562i	$0.000746636\pi$

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.720859 - 2.21858i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} +(-0.720859 + 2.21858i) q^{6} +3.77447 q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.97539 + 1.43521i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.720859 - 2.21858i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} +(-0.720859 + 2.21858i) q^{6} +3.77447 q^{7} +(0.309017 - 0.951057i) q^{8} +(-1.97539 + 1.43521i) q^{9} +(1.07822 + 1.95894i) q^{10} +(3.05361 + 2.21858i) q^{11} +(1.88723 - 1.37116i) q^{12} +(-2.56969 + 1.86699i) q^{13} +(-3.05361 - 2.21858i) q^{14} +(-0.651166 + 5.17538i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.430307 + 1.32435i) q^{17} +2.44172 q^{18} +(1.20945 - 3.72230i) q^{19} +(0.279141 - 2.21858i) q^{20} +(-2.72086 - 8.37394i) q^{21} +(-1.16637 - 3.58973i) q^{22} +(-0.720859 - 0.523735i) q^{23} -2.33275 q^{24} +(3.19098 + 3.84937i) q^{25} +3.17632 q^{26} +(-1.05361 - 0.765491i) q^{27} +(1.16637 + 3.58973i) q^{28} +(0.0152089 + 0.0468081i) q^{29} +(3.56882 - 3.80423i) q^{30} +(-1.72466 + 5.30795i) q^{31} +1.00000 q^{32} +(2.72086 - 8.37394i) q^{33} +(1.12656 - 0.818492i) q^{34} +(-7.63851 - 3.58973i) q^{35} +(-1.97539 - 1.43521i) q^{36} +(-5.70152 + 4.14240i) q^{37} +(-3.16637 + 2.30051i) q^{38} +(5.99445 + 4.35522i) q^{39} +(-1.52988 + 1.63079i) q^{40} +(1.20477 - 0.875319i) q^{41} +(-2.72086 + 8.37394i) q^{42} +2.69767 q^{43} +(-1.16637 + 3.58973i) q^{44} +(5.36263 - 1.02576i) q^{45} +(0.275344 + 0.847421i) q^{46} +(1.16637 + 3.58973i) q^{47} +(1.88723 + 1.37116i) q^{48} +7.24660 q^{49} +(-0.318958 - 4.98982i) q^{50} +3.24836 q^{51} +(-2.56969 - 1.86699i) q^{52} +(3.58963 + 11.0477i) q^{53} +(0.402443 + 1.23859i) q^{54} +(-4.06969 - 7.39396i) q^{55} +(1.16637 - 3.58973i) q^{56} -9.13004 q^{57} +(0.0152089 - 0.0468081i) q^{58} +(0.558282 - 0.405615i) q^{59} +(-5.12330 + 0.979986i) q^{60} +(-8.38168 - 6.08965i) q^{61} +(4.51521 - 3.28049i) q^{62} +(-7.45605 + 5.41714i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(6.97599 - 1.33437i) q^{65} +(-7.12330 + 5.17538i) q^{66} +(4.73519 - 14.5734i) q^{67} -1.39250 q^{68} +(-0.642308 + 1.97682i) q^{69} +(4.06969 + 7.39396i) q^{70} +(-2.06969 - 6.36986i) q^{71} +(0.754532 + 2.32221i) q^{72} +(-4.18158 - 3.03810i) q^{73} +7.04746 q^{74} +(6.23987 - 9.85429i) q^{75} +3.91385 q^{76} +(11.5257 + 8.37394i) q^{77} +(-2.28968 - 7.04690i) q^{78} +(-0.558282 - 1.71821i) q^{79} +(2.19625 - 0.420099i) q^{80} +(-3.20239 + 9.85596i) q^{81} -1.48918 q^{82} +(-3.08023 + 9.47997i) q^{83} +(7.12330 - 5.17538i) q^{84} +(2.13035 - 2.27088i) q^{85} +(-2.18246 - 1.58565i) q^{86} +(0.0928839 - 0.0674841i) q^{87} +(3.05361 - 2.21858i) q^{88} +(-11.7390 - 8.52891i) q^{89} +(-4.94138 - 2.32221i) q^{90} +(-9.69922 + 7.04690i) q^{91} +(0.275344 - 0.847421i) q^{92} +13.0193 q^{93} +(1.16637 - 3.58973i) q^{94} +(-5.98771 + 6.38268i) q^{95} +(-0.720859 - 2.21858i) q^{96} +(-0.0278640 - 0.0857567i) q^{97} +(-5.86263 - 4.25945i) q^{98} -9.21619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q - 2q^{2} - 3q^{3} - 2q^{4} - 3q^{6} + 4q^{7} - 2q^{8} - q^{9} + O(q^{10}) \)	\( 8q - 2q^{2} - 3q^{3} - 2q^{4} - 3q^{6} + 4q^{7} - 2q^{8} - q^{9} + q^{11} + 2q^{12} - 13q^{13} - q^{14} - 10q^{15} - 2q^{16} - 11q^{17} + 14q^{18} + 20q^{19} + 5q^{20} - 19q^{21} + q^{22} - 3q^{23} + 2q^{24} + 30q^{25} + 22q^{26} + 15q^{27} - q^{28} - 15q^{29} - 10q^{30} - 9q^{31} + 8q^{32} + 19q^{33} - q^{34} - 15q^{35} - q^{36} - 6q^{37} - 15q^{38} - 12q^{39} - 5q^{40} - 9q^{41} - 19q^{42} + 12q^{43} + q^{44} + 15q^{45} + 7q^{46} - q^{47} + 2q^{48} - 4q^{49} - 5q^{50} + 26q^{51} - 13q^{52} + 7q^{53} - 25q^{54} - 25q^{55} - q^{56} - 15q^{58} + 10q^{59} - 10q^{60} + 6q^{61} + 21q^{62} - 8q^{63} - 2q^{64} - 10q^{65} - 26q^{66} - 11q^{67} + 24q^{68} + 43q^{69} + 25q^{70} - 9q^{71} - 6q^{72} - 8q^{73} + 24q^{74} + 30q^{75} - 10q^{76} + 33q^{77} + 23q^{78} - 10q^{79} - 17q^{81} + 26q^{82} + 27q^{83} + 26q^{84} + 5q^{85} - 23q^{86} + q^{88} - 15q^{89} + 20q^{90} + q^{91} + 7q^{92} - 46q^{93} - q^{94} - 30q^{95} - 3q^{96} - 36q^{97} - 19q^{98} - 42q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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