LMFDB - Embedded newform 63.2.f.a.22.3

Newspace parameters

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
Defining polynomial:	$x^{6} - x^{3} + 1$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.2.f.a.43.3

$q$-expansion

$f(q)$	$=$	$q+(0.439693 + 0.761570i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(-0.673648 + 1.16679i) q^{5} +(-1.50000 + 0.264490i) q^{6} +(-0.500000 - 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})$	\(q+(0.439693 + 0.761570i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(-0.673648 + 1.16679i) q^{5} +(-1.50000 + 0.264490i) q^{6} +(-0.500000 - 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} -1.18479 q^{10} +(-0.826352 - 1.43128i) q^{11} +(1.36571 + 1.62760i) q^{12} +(1.68479 - 2.91815i) q^{13} +(0.439693 - 0.761570i) q^{14} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 + 0.0362770i) q^{16} +0.467911 q^{17} +(0.458111 - 2.59808i) q^{18} -3.22668 q^{19} +(0.826352 + 1.43128i) q^{20} +(1.70574 - 0.300767i) q^{21} +(0.726682 - 1.25865i) q^{22} +(-4.47178 + 7.74535i) q^{23} +(-1.68092 + 4.61830i) q^{24} +(1.59240 + 2.75811i) q^{25} +2.96316 q^{26} +(4.50000 - 2.59808i) q^{27} -1.22668 q^{28} +(-3.13429 - 5.42874i) q^{29} +(0.701867 - 1.92836i) q^{30} +(-4.61721 + 7.99724i) q^{31} +(2.81908 - 4.88279i) q^{32} +(2.81908 - 0.497079i) q^{33} +(0.205737 + 0.356347i) q^{34} +1.34730 q^{35} +(-3.45811 + 1.25865i) q^{36} +9.23442 q^{37} +(-1.41875 - 2.45734i) q^{38} +(3.75150 + 4.47086i) q^{39} +(-1.91147 + 3.31077i) q^{40} +(-1.70574 + 2.95442i) q^{41} +(0.979055 + 1.16679i) q^{42} +(2.20574 + 3.82045i) q^{43} -2.02734 q^{44} +(3.79813 - 1.38241i) q^{45} -7.86484 q^{46} +(-4.67752 - 8.10170i) q^{47} +(-0.0714517 + 0.0125989i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.40033 + 2.42544i) q^{50} +(-0.277189 + 0.761570i) q^{51} +(-2.06670 - 3.57964i) q^{52} -0.573978 q^{53} +(3.95723 + 2.28471i) q^{54} +2.22668 q^{55} +(-1.41875 - 2.45734i) q^{56} +(1.91147 - 5.25173i) q^{57} +(2.75624 - 4.77396i) q^{58} +(5.19846 - 9.00400i) q^{59} +(-2.81908 + 0.497079i) q^{60} +(-3.81908 - 6.61484i) q^{61} -8.12061 q^{62} +(-0.520945 + 2.95442i) q^{63} +5.04189 q^{64} +(2.26991 + 3.93161i) q^{65} +(1.61809 + 1.92836i) q^{66} +(-0.298133 + 0.516382i) q^{67} +(0.286989 - 0.497079i) q^{68} +(-9.95723 - 11.8666i) q^{69} +(0.592396 + 1.02606i) q^{70} -0.554378 q^{71} +(-6.52094 - 5.47172i) q^{72} +2.04963 q^{73} +(4.06031 + 7.03266i) q^{74} +(-5.43242 + 0.957882i) q^{75} +(-1.97906 + 3.42782i) q^{76} +(-0.826352 + 1.43128i) q^{77} +(-1.75537 + 4.82283i) q^{78} +(1.20187 + 2.08169i) q^{79} -0.0564370 q^{80} +(1.56283 + 8.86327i) q^{81} -3.00000 q^{82} +(7.52481 + 13.0334i) q^{83} +(0.726682 - 1.99654i) q^{84} +(-0.315207 + 0.545955i) q^{85} +(-1.93969 + 3.35965i) q^{86} +(10.6925 - 1.88538i) q^{87} +(-2.34477 - 4.06126i) q^{88} +9.08647 q^{89} +(2.72281 + 2.28471i) q^{90} -3.36959 q^{91} +(5.48545 + 9.50108i) q^{92} +(-10.2811 - 12.2525i) q^{93} +(4.11334 - 7.12452i) q^{94} +(2.17365 - 3.76487i) q^{95} +(6.27719 + 7.48086i) q^{96} +(0.949493 + 1.64457i) q^{97} -0.879385 q^{98} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6q - 3q^{2} - 3q^{4} - 3q^{5} - 9q^{6} - 3q^{7} + 12q^{8} + O(q^{10}) $	$ 6q - 3q^{2} - 3q^{4} - 3q^{5} - 9q^{6} - 3q^{7} + 12q^{8} - 6q^{11} + 18q^{12} + 3q^{13} - 3q^{14} - 9q^{15} - 3q^{16} + 12q^{17} + 9q^{18} - 6q^{19} + 6q^{20} - 9q^{22} - 12q^{23} - 27q^{24} + 6q^{25} - 6q^{26} + 27q^{27} + 6q^{28} - 9q^{29} + 18q^{30} + 3q^{31} - 9q^{34} + 6q^{35} - 27q^{36} - 6q^{37} - 6q^{38} - 18q^{39} + 9q^{40} + 9q^{42} + 3q^{43} + 30q^{44} + 9q^{45} - 3q^{47} - 3q^{49} + 6q^{50} + 9q^{51} + 21q^{52} + 12q^{53} - 27q^{54} - 6q^{56} - 9q^{57} + 9q^{58} + 3q^{59} - 6q^{61} - 60q^{62} + 24q^{64} - 15q^{65} + 36q^{66} + 12q^{67} - 6q^{68} - 9q^{69} + 18q^{71} - 36q^{72} - 42q^{73} + 30q^{74} - 9q^{75} - 15q^{76} - 6q^{77} + 54q^{78} + 21q^{79} - 30q^{80} - 18q^{82} + 18q^{83} - 9q^{84} - 9q^{85} - 6q^{86} + 9q^{87} - 27q^{88} + 24q^{89} + 27q^{90} - 6q^{91} - 3q^{92} - 27q^{93} + 18q^{94} + 12q^{95} + 27q^{96} + 3q^{97} + 6q^{98} + 18q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.439693	+	0.761570i	0.310910	+	0.538511i	0.978560	−	0.205964i	$-0.0660330\pi$
$2$	0.439693	+	0.761570i	0.310910	+	0.538511i	−0.667650	+	0.744475i	$0.732700\pi$
$3$	−0.592396	+	1.62760i	−0.342020	+	0.939693i
$3$	−0.592396	+	1.62760i	−0.342020	+	0.939693i
$4$	0.613341	−	1.06234i	0.306670	−	0.531169i
$5$	−0.673648	+	1.16679i	−0.301265	+	0.521806i	−0.976423	−	0.215867i	$-0.930742\pi$
$5$	−0.673648	+	1.16679i	−0.301265	+	0.521806i	0.675158	+	0.737673i	$0.264075\pi$
$6$	−1.50000	+	0.264490i	−0.612372	+	0.107978i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	2.83750			1.00321
$9$	−2.29813	−	1.92836i	−0.766044	−	0.642788i
$10$	−1.18479			−0.374664
$11$	−0.826352	−	1.43128i	−0.249154	−	0.431548i	0.714137	−	0.700006i	$-0.246819\pi$
$11$	−0.826352	−	1.43128i	−0.249154	−	0.431548i	−0.963291	+	0.268458i	$0.913486\pi$
$12$	1.36571	+	1.62760i	0.394248	+	0.469846i
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	−0.532024	−	0.846729i	$-0.678568\pi$
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	0.999301	+	0.0373813i	$0.0119016\pi$
$14$	0.439693	−	0.761570i	0.117513	−	0.203538i
$15$	−1.50000	−	1.78763i	−0.387298	−	0.461564i
$16$	0.0209445	+	0.0362770i	0.00523613	+	0.00906925i
$17$	0.467911			0.113485			0.0567426	−	0.998389i	$-0.481929\pi$
$17$	0.467911			0.113485			0.0567426	+	0.998389i	$0.481929\pi$
$18$	0.458111	−	2.59808i	0.107978	−	0.612372i
$19$	−3.22668			−0.740252			−0.370126	−	0.928982i	$-0.620685\pi$
$19$	−3.22668			−0.740252			−0.370126	+	0.928982i	$0.620685\pi$
$20$	0.826352	+	1.43128i	0.184778	+	0.320045i
$21$	1.70574	−	0.300767i	0.372222	−	0.0656328i
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.153279	+	0.988183i	$0.548983\pi$
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.779152	+	0.626835i	$0.784350\pi$
$24$	−1.68092	+	4.61830i	−0.343117	+	0.942706i
$25$	1.59240	+	2.75811i	0.318479	+	0.551622i
$26$	2.96316			0.581124
$27$	4.50000	−	2.59808i	0.866025	−	0.500000i
$28$	−1.22668			−0.231821
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	−0.995239	−	0.0974595i	$-0.968928\pi$
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	0.413217	−	0.910632i	$-0.364405\pi$
$30$	0.701867	−	1.92836i	0.128143	−	0.352069i
$31$	−4.61721	+	7.99724i	−0.829276	+	1.43635i	0.0693317	+	0.997594i	$0.477913\pi$
$31$	−4.61721	+	7.99724i	−0.829276	+	1.43635i	−0.898607	+	0.438754i	$0.855420\pi$
$32$	2.81908	−	4.88279i	0.498347	−	0.863163i
$33$	2.81908	−	0.497079i	0.490738	−	0.0865304i
$34$	0.205737	+	0.356347i	0.0352836	+	0.0611130i
$35$	1.34730			0.227735
$36$	−3.45811	+	1.25865i	−0.576352	+	0.209775i
$37$	9.23442			1.51813			0.759065	−	0.651015i	$-0.225657\pi$
$37$	9.23442			1.51813			0.759065	+	0.651015i	$0.225657\pi$
$38$	−1.41875	−	2.45734i	−0.230151	−	0.398634i
$39$	3.75150	+	4.47086i	0.600720	+	0.715910i
$40$	−1.91147	+	3.31077i	−0.302231	+	0.523479i
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	−0.967927	−	0.251231i	$-0.919165\pi$
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	0.701536	+	0.712634i	$0.252498\pi$
$42$	0.979055	+	1.16679i	0.151072	+	0.180040i
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	0.983747	−	0.179558i	$-0.0574668\pi$
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	−0.647376	+	0.762171i	$0.724133\pi$
$44$	−2.02734			−0.305633
$45$	3.79813	−	1.38241i	0.566192	−	0.206077i
$46$	−7.86484			−1.15961
$47$	−4.67752	−	8.10170i	−0.682286	−	1.18175i	−0.974281	−	0.225335i	$-0.927652\pi$
$47$	−4.67752	−	8.10170i	−0.682286	−	1.18175i	0.291995	−	0.956420i	$-0.405681\pi$
$48$	−0.0714517	+	0.0125989i	−0.0103132	+	0.00181849i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−1.40033	+	2.42544i	−0.198037	+	0.343009i
$51$	−0.277189	+	0.761570i	−0.0388142	+	0.106641i
$52$	−2.06670	−	3.57964i	−0.286600	−	0.496406i
$53$	−0.573978			−0.0788419			−0.0394210	−	0.999223i	$-0.512551\pi$
$53$	−0.573978			−0.0788419			−0.0394210	+	0.999223i	$0.512551\pi$
$54$	3.95723	+	2.28471i	0.538511	+	0.310910i
$55$	2.22668			0.300246
$56$	−1.41875	−	2.45734i	−0.189588	−	0.328376i
$57$	1.91147	−	5.25173i	0.253181	−	0.695609i
$58$	2.75624	−	4.77396i	0.361913	−	0.626851i
$59$	5.19846	−	9.00400i	0.676782	−	1.17222i	−0.299162	−	0.954202i	$-0.596707\pi$
$59$	5.19846	−	9.00400i	0.676782	−	1.17222i	0.975945	−	0.218019i	$-0.0699595\pi$
$60$	−2.81908	+	0.497079i	−0.363941	+	0.0641727i
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	0.510937	−	0.859618i	$-0.329299\pi$
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	−0.999920	+	0.0126752i	$0.995965\pi$
$62$	−8.12061			−1.03132
$63$	−0.520945	+	2.95442i	−0.0656328	+	0.372222i
$64$	5.04189			0.630236
$65$	2.26991	+	3.93161i	0.281548	+	0.487656i
$66$	1.61809	+	1.92836i	0.199173	+	0.237365i
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	−0.883662	−	0.468125i	$-0.844930\pi$
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	0.847239	+	0.531211i	$0.178263\pi$
$68$	0.286989	−	0.497079i	0.0348025	−	0.0602797i
$69$	−9.95723	−	11.8666i	−1.19871	−	1.42857i
$70$	0.592396	+	1.02606i	0.0708049	+	0.122638i
$71$	−0.554378			−0.0657925			−0.0328963	−	0.999459i	$-0.510473\pi$
$71$	−0.554378			−0.0657925			−0.0328963	+	0.999459i	$0.510473\pi$
$72$	−6.52094	−	5.47172i	−0.768501	−	0.644849i
$73$	2.04963			0.239891			0.119946	−	0.992780i	$-0.461728\pi$
$73$	2.04963			0.239891			0.119946	+	0.992780i	$0.461728\pi$
$74$	4.06031	+	7.03266i	0.472001	+	0.817530i
$75$	−5.43242	+	0.957882i	−0.627282	+	0.110607i
$76$	−1.97906	+	3.42782i	−0.227013	+	0.393198i
$77$	−0.826352	+	1.43128i	−0.0941715	+	0.163110i
$78$	−1.75537	+	4.82283i	−0.198756	+	0.546078i
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	0.925682	−	0.378303i	$-0.123492\pi$
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	−0.790461	+	0.612512i	$0.790159\pi$
$80$	−0.0564370			−0.00630985
$81$	1.56283	+	8.86327i	0.173648	+	0.984808i
$82$	−3.00000			−0.331295
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	0.901187	+	0.433431i	$0.142697\pi$
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	−0.0752309	+	0.997166i	$0.523969\pi$
$84$	0.726682	−	1.99654i	0.0792875	−	0.217841i
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$	−1.93969	+	3.35965i	−0.209162	+	0.362280i
$87$	10.6925	−	1.88538i	1.14636	−	0.202134i
$88$	−2.34477	−	4.06126i	−0.249953	−	0.432932i
$89$	9.08647			0.963164			0.481582	−	0.876401i	$-0.340062\pi$
$89$	9.08647			0.963164			0.481582	+	0.876401i	$0.340062\pi$
$90$	2.72281	+	2.28471i	0.287010	+	0.240830i
$91$	−3.36959			−0.353228
$92$	5.48545	+	9.50108i	0.571898	+	0.990556i
$93$	−10.2811	−	12.2525i	−1.06610	−	1.27052i
$94$	4.11334	−	7.12452i	0.424259	−	0.734838i
$95$	2.17365	−	3.76487i	0.223012	−	0.386267i
$96$	6.27719	+	7.48086i	0.640663	+	0.763512i
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	0.910195	−	0.414181i	$-0.135932\pi$
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	−0.813788	+	0.581161i	$0.802598\pi$
$98$	−0.879385			−0.0888313
$99$	−0.860967	+	4.88279i	−0.0865304	+	0.490738i
$100$	3.90673			0.390673
$101$	0.854570	+	1.48016i	0.0850329	+	0.147281i	0.905405	−	0.424548i	$-0.139567\pi$
$101$	0.854570	+	1.48016i	0.0850329	+	0.147281i	−0.820372	+	0.571830i	$0.806234\pi$
$102$	−0.701867	+	0.123758i	−0.0694952	+	0.0122539i
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	−0.762381	−	0.647128i	$-0.775970\pi$
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	0.941620	+	0.336677i	$0.109303\pi$
$104$	4.78059	−	8.28023i	0.468776	−	0.811943i
$105$	−0.798133	+	2.19285i	−0.0778898	+	0.214001i
$106$	−0.252374	−	0.437124i	−0.0245127	−	0.0424573i
$107$	7.12836			0.689124			0.344562	−	0.938764i	$-0.388027\pi$
$107$	7.12836			0.689124			0.344562	+	0.938764i	$0.388027\pi$
$108$		−	6.37402i		−	0.613341i
$109$	0.403733			0.0386706			0.0193353	−	0.999813i	$-0.493845\pi$
$109$	0.403733			0.0386706			0.0193353	+	0.999813i	$0.493845\pi$
$110$	0.979055	+	1.69577i	0.0933493	+	0.161686i
$111$	−5.47044	+	15.0299i	−0.519231	+	1.42658i
$112$	0.0209445	−	0.0362770i	0.00197907	−	0.00342785i
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	0.300320	+	0.953839i	$0.402907\pi$
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	−0.976208	+	0.216835i	$0.930427\pi$
$114$	4.84002	−	0.853427i	0.453310	−	0.0799307i
$115$	−6.02481	−	10.4353i	−0.561817	−	0.973095i
$116$	−7.68954			−0.713956
$117$	−9.49912	+	3.45740i	−0.878194	+	0.319637i
$118$	9.14290			0.841672
$119$	−0.233956	−	0.405223i	−0.0214467	−	0.0371467i
$120$	−4.25624	−	5.07239i	−0.388540	−	0.463044i
$121$	4.13429	−	7.16079i	0.375844	−	0.650981i
$122$	3.35844	−	5.81699i	0.304059	−	0.526646i
$123$	−3.79813	−	4.52644i	−0.342466	−	0.408135i
$124$	5.66385	+	9.81007i	0.508629	+	0.880971i
$125$	−11.0273			−0.986315
$126$	−2.47906	+	0.902302i	−0.220852	+	0.0803835i
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	−3.42127	−	5.92582i	−0.302401	−	0.523774i
$129$	−7.52481	+	1.32683i	−0.662523	+	0.116821i
$130$	−1.99613	+	3.45740i	−0.175072	+	0.303234i
$131$	3.58260	−	6.20524i	0.313013	−	0.542154i	−0.666000	−	0.745952i	$-0.731995\pi$
$131$	3.58260	−	6.20524i	0.313013	−	0.542154i	0.979013	+	0.203797i	$0.0653284\pi$
$132$	1.20099	−	3.29969i	0.104533	−	0.287201i
$133$	1.61334	+	2.79439i	0.139894	+	0.242304i
$134$	−0.524348			−0.0452968
$135$			7.00076i			0.602529i
$136$	1.32770			0.113849
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	0.805925	−	0.592017i	$-0.201668\pi$
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	−0.915665	+	0.401943i	$0.868335\pi$
$138$	4.65910	−	12.8008i	0.396609	−	1.08967i
$139$	3.06670	−	5.31169i	0.260114	−	0.450531i	−0.706158	−	0.708055i	$-0.749573\pi$
$139$	3.06670	−	5.31169i	0.260114	−	0.450531i	0.966272	+	0.257523i	$0.0829064\pi$
$140$	0.826352	−	1.43128i	0.0698395	−	0.120966i
$141$	15.9572	−	2.81369i	1.34384	−	0.236956i
$142$	−0.243756	−	0.422197i	−0.0204555	−	0.0354300i
$143$	−5.56893			−0.465697
$144$	0.0218219	−	0.123758i	0.00181849	−	0.0103132i
$145$	8.44562			0.701371
$146$	0.901207	+	1.56094i	0.0745844	+	0.129184i
$147$	−1.11334	−	1.32683i	−0.0918268	−	0.109435i
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	−0.874719	−	0.484630i	$-0.838954\pi$
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	0.857062	+	0.515214i	$0.172288\pi$
$150$	−3.11809	−	3.71599i	−0.254591	−	0.303410i
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	0.911902	−	0.410408i	$-0.134614\pi$
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	−0.811375	+	0.584526i	$0.801280\pi$
$152$	−9.15570			−0.742625
$153$	−1.07532	−	0.902302i	−0.0869346	−	0.0729468i
$154$	−1.45336			−0.117115
$155$	−6.22075	−	10.7747i	−0.499663	−	0.865441i
$156$	7.05051	−	1.24319i	0.564492	−	0.0995352i
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	−0.994248	−	0.107106i	$-0.965841\pi$
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	0.589881	+	0.807491i	$0.299175\pi$
$158$	−1.05690	+	1.83061i	−0.0840828	+	0.145636i
$159$	0.340022	−	0.934204i	0.0269655	−	0.0740872i
$160$	3.79813	+	6.57856i	0.300269	+	0.520081i
$161$	8.94356			0.704852
$162$	−6.06283	+	5.08732i	−0.476341	+	0.399698i
$163$	−2.59627			−0.203355			−0.101678	−	0.994817i	$-0.532421\pi$
$163$	−2.59627			−0.203355			−0.101678	+	0.994817i	$0.532421\pi$
$164$	2.09240	+	3.62414i	0.163389	+	0.282998i
$165$	−1.31908	+	3.62414i	−0.102690	+	0.282139i
$166$	−6.61721	+	11.4613i	−0.513595	+	0.889573i
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.0656422	−	0.997843i	$-0.479090\pi$
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.831337	−	0.555769i	$-0.187576\pi$
$168$	4.84002	−	0.853427i	0.373416	−	0.0658433i
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$	−0.554378			−0.0425188
$171$	7.41534	+	6.22221i	0.567066	+	0.475825i
$172$	5.41147			0.412621
$173$	2.37598	+	4.11532i	0.180643	+	0.312882i	0.942100	−	0.335333i	$-0.108849\pi$
$173$	2.37598	+	4.11532i	0.180643	+	0.312882i	−0.761457	+	0.648215i	$0.775516\pi$
$174$	6.13728	+	7.31412i	0.465266	+	0.554482i
$175$	1.59240	−	2.75811i	0.120374	−	0.208494i
$176$	0.0346151	−	0.0599551i	0.00260921	−	0.00451929i
$177$	11.5753	+	13.7949i	0.870054	+	1.03689i
$178$	3.99525	+	6.91998i	0.299457	+	0.518674i
$179$	−8.53209			−0.637718			−0.318859	−	0.947802i	$-0.603300\pi$
$179$	−8.53209			−0.637718			−0.318859	+	0.947802i	$0.603300\pi$
$180$	0.860967	−	4.88279i	0.0641727	−	0.363941i
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$	−1.48158	−	2.56617i	−0.109822	−	0.190218i
$183$	13.0287	−	2.29731i	0.963108	−	0.169822i
$184$	−12.6887	+	21.9774i	−0.935421	+	1.62020i
$185$	−6.22075	+	10.7747i	−0.457359	+	0.792169i
$186$	4.81062	−	13.2171i	0.352732	−	0.969123i
$187$	−0.386659	−	0.669713i	−0.0282753	−	0.0489743i
$188$	−11.4757			−0.836948
$189$	−4.50000	−	2.59808i	−0.327327	−	0.188982i
$190$	3.82295			0.277346
$191$	−6.45471	−	11.1799i	−0.467046	−	0.808948i	0.532245	−	0.846590i	$-0.321349\pi$
$191$	−6.45471	−	11.1799i	−0.467046	−	0.808948i	−0.999291	+	0.0376425i	$0.988015\pi$
$192$	−2.98680	+	8.20616i	−0.215553	+	0.592228i
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	−0.854313	−	0.519759i	$-0.826022\pi$
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	0.877281	+	0.479977i	$0.159355\pi$
$194$	−0.834970	+	1.44621i	−0.0599473	+	0.103832i
$195$	−7.74376	+	1.36543i	−0.554542	+	0.0977807i
$196$	0.613341	+	1.06234i	0.0438101	+	0.0758812i
$197$	11.4456			0.815467			0.407733	−	0.913101i	$-0.366319\pi$
$197$	11.4456			0.815467			0.407733	+	0.913101i	$0.366319\pi$
$198$	−4.09714	+	1.49124i	−0.291171	+	0.105978i
$199$	−3.63816			−0.257902			−0.128951	−	0.991651i	$-0.541161\pi$
$199$	−3.63816			−0.257902			−0.128951	+	0.991651i	$0.541161\pi$
$200$	4.51842	+	7.82613i	0.319500	+	0.553391i
$201$	−0.663848	−	0.791143i	−0.0468242	−	0.0558029i
$202$	−0.751497	+	1.30163i	−0.0528751	+	0.0915824i
$203$	−3.13429	+	5.42874i	−0.219984	+	0.381023i
$204$	0.639033	+	0.761570i	0.0447413	+	0.0533206i
$205$	−2.29813	−	3.98048i	−0.160509	−	0.278009i
$206$	3.19934			0.222909
$207$	25.2126	−	9.17664i	1.75240	−	0.637820i
$208$	0.141149			0.00978691
$209$	2.66637	+	4.61830i	0.184437	+	0.319454i
$210$	−2.02094	+	0.356347i	−0.139458	+	0.0245903i
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	−0.948668	−	0.316273i	$-0.897569\pi$
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	0.748234	+	0.663435i	$0.230902\pi$
$212$	−0.352044	+	0.609758i	−0.0241785	+	0.0418784i
$213$	0.328411	−	0.902302i	0.0225024	−	0.0618247i
$214$	3.13429	+	5.42874i	0.214255	+	0.371101i
$215$	−5.94356			−0.405348
$216$	12.7687	−	7.37203i	0.868802	−	0.501603i
$217$	9.23442			0.626873
$218$	0.177519	+	0.307471i	0.0120231	+	0.0208246i
$219$	−1.21419	+	3.33597i	−0.0820476	+	0.225424i
$220$	1.36571	−	2.36549i	0.0920765	−	0.159481i
$221$	0.788333	−	1.36543i	0.0530290	−	0.0918490i
$222$	−13.8516	+	2.44242i	−0.929661	+	0.163924i
$223$	−3.54189	−	6.13473i	−0.237182	−	0.410812i	0.722722	−	0.691139i	$-0.242891\pi$
$223$	−3.54189	−	6.13473i	−0.237182	−	0.410812i	−0.959905	+	0.280327i	$0.909557\pi$
$224$	−5.63816			−0.376715
$225$	1.65910	−	9.40923i	0.110607	−	0.627282i
$226$	−12.6364			−0.840561
$227$	5.97178	+	10.3434i	0.396361	+	0.686517i	0.993274	−	0.115789i	$-0.0369395\pi$
$227$	5.97178	+	10.3434i	0.396361	+	0.686517i	−0.596913	+	0.802306i	$0.703606\pi$
$228$	−4.40673	−	5.25173i	−0.291843	−	0.347804i
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636403\pi$
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	0.995484	−	0.0949315i	$-0.0302632\pi$
$230$	5.29813	−	9.17664i	0.349349	−	0.605089i
$231$	−1.84002	−	2.19285i	−0.121065	−	0.144279i
$232$	−8.89352	−	15.4040i	−0.583888	−	1.01132i
$233$	16.2540			1.06484			0.532418	−	0.846481i	$-0.321283\pi$
$233$	16.2540			1.06484			0.532418	+	0.846481i	$0.321283\pi$
$234$	−6.80974	−	5.71405i	−0.445167	−	0.373539i
$235$	12.6040			0.822195
$236$	−6.37686	−	11.0450i	−0.415098	−	0.718971i
$237$	−4.10014	+	0.722965i	−0.266333	+	0.0469616i
$238$	0.205737	−	0.356347i	0.0133360	−	0.0230985i
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	−0.511565	−	0.859244i	$-0.670934\pi$
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	0.999910	+	0.0134062i	$0.00426745\pi$
$240$	0.0334331	−	0.0918566i	0.00215809	−	0.00592932i
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	0.999991	+	0.00424420i	$0.00135097\pi$
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$242$	7.27126			0.467414
$243$	−15.3516	−	2.70691i	−0.984808	−	0.173648i
$244$	−9.36959			−0.599826
$245$	−0.673648	−	1.16679i	−0.0430378	−	0.0745437i
$246$	1.77719	−	4.88279i	0.113309	−	0.311315i
$247$	−5.43629	+	9.41593i	−0.345903	+	0.599121i
$248$	−13.1013	+	22.6922i	−0.831935	+	1.44095i
$249$	−25.6707	+	4.52644i	−1.62682	+	0.286851i
$250$	−4.84864	−	8.39809i	−0.306655	−	0.531142i
$251$	19.0651			1.20338			0.601690	−	0.798730i	$-0.294494\pi$
$251$	19.0651			1.20338			0.601690	+	0.798730i	$0.294494\pi$
$252$	2.81908	+	2.36549i	0.177585	+	0.149012i
$253$	14.7811			0.929277
$254$	−9.13310	−	15.8190i	−0.573062	−	0.992572i
$255$	−0.701867	−	0.836452i	−0.0439526	−	0.0523807i
$256$	8.05051	−	13.9439i	0.503157	−	0.871493i
$257$	−13.2909	+	23.0204i	−0.829061	+	1.43598i	0.0697146	+	0.997567i	$0.477791\pi$
$257$	−13.2909	+	23.0204i	−0.829061	+	1.43598i	−0.898776	+	0.438409i	$0.855542\pi$
$258$	−4.31908	−	5.14728i	−0.268894	−	0.320455i
$259$	−4.61721	−	7.99724i	−0.286900	−	0.496925i
$260$	5.56893			0.345370
$261$	−3.26558	+	18.5200i	−0.202134	+	1.14636i
$262$	6.30096			0.389275
$263$	0.367059	+	0.635765i	0.0226338	+	0.0392029i	0.877120	−	0.480270i	$-0.159461\pi$
$263$	0.367059	+	0.635765i	0.0226338	+	0.0392029i	−0.854487	+	0.519473i	$0.826128\pi$
$264$	7.99912	−	1.41046i	0.492312	−	0.0868079i
$265$	0.386659	−	0.669713i	0.0237523	−	0.0411402i
$266$	−1.41875	+	2.45734i	−0.0869890	+	0.150669i
$267$	−5.38279	+	14.7891i	−0.329421	+	0.905078i
$268$	0.365715	+	0.633436i	0.0223396	+	0.0386933i
$269$	−20.8503			−1.27126			−0.635632	−	0.771992i	$-0.719261\pi$
$269$	−20.8503			−1.27126			−0.635632	+	0.771992i	$0.719261\pi$
$270$	−5.33157	+	3.07818i	−0.324469	+	0.187332i
$271$	6.95811			0.422675			0.211338	−	0.977413i	$-0.432218\pi$
$271$	6.95811			0.422675			0.211338	+	0.977413i	$0.432218\pi$
$272$	0.00980018	+	0.0169744i	0.000594223	+	0.00102922i
$273$	1.99613	−	5.48432i	0.120811	−	0.331926i
$274$	1.12954	−	1.95642i	0.0682379	−	0.118191i
$275$	2.63176	−	4.55834i	0.158701	−	0.274878i
$276$	−18.7135	+	3.29969i	−1.12642	+	0.198618i
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$	5.39363			0.323488
$279$	26.0326	−	9.47508i	1.55853	−	0.567258i
$280$	3.82295			0.228465
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	−0.979159	−	0.203095i	$-0.934900\pi$
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	0.313694	−	0.949524i	$-0.398433\pi$
$282$	9.15910	+	10.9154i	0.545416	+	0.650002i
$283$	9.29726	−	16.1033i	0.552665	−	0.957243i	−0.445417	−	0.895323i	$-0.646944\pi$
$283$	9.29726	−	16.1033i	0.552665	−	0.957243i	0.998081	−	0.0619196i	$-0.0197222\pi$
$284$	−0.340022	+	0.588936i	−0.0201766	+	0.0349469i
$285$	4.84002	+	5.76811i	0.286698	+	0.341674i
$286$	−2.44862	−	4.24113i	−0.144790	−	0.250783i
$287$	3.41147			0.201373
$288$	−15.8944	+	5.78509i	−0.936587	+	0.340890i
$289$	−16.7811			−0.987121
$290$	3.71348	+	6.43193i	0.218063	+	0.377696i
$291$	−3.23917	+	0.571153i	−0.189884	+	0.0334816i
$292$	1.25712	−	2.17740i	0.0735675	−	0.127423i
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	−0.991406	−	0.130822i	$-0.958238\pi$
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	0.608998	+	0.793171i	$0.291572\pi$
$294$	0.520945	−	1.43128i	0.0303821	−	0.0834741i
$295$	7.00387	+	12.1311i	0.407781	+	0.706298i
$296$	26.2026			1.52300
$297$	−7.43717	−	4.29385i	−0.431548	−	0.249154i
$298$	−0.379081			−0.0219595
$299$	15.0680	+	26.0986i	0.871408	+	1.50932i
$300$	−2.31433	+	6.35857i	−0.133618	+	0.367112i
$301$	2.20574	−	3.82045i	0.127137	−	0.220207i
$302$	−1.08630	+	1.88153i	−0.0625098	+	0.108270i
$303$	−2.91534	+	0.514054i	−0.167482	+	0.0295316i
$304$	−0.0675813	−	0.117054i	−0.00387606	−	0.00671353i
$305$	10.2909			0.589253
$306$	0.214355	−	1.21567i	0.0122539	−	0.0694952i
$307$	6.31046			0.360157			0.180078	−	0.983652i	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$	1.01367	+	1.75573i	0.0577592	+	0.100042i
$309$	4.05051	+	4.82721i	0.230425	+	0.274610i
$310$	5.47044	−	9.47508i	0.310700	−	0.538148i
$311$	4.76217	−	8.24833i	0.270038	−	0.467720i	−0.698833	−	0.715285i	$-0.746297\pi$
$311$	4.76217	−	8.24833i	0.270038	−	0.467720i	0.968871	+	0.247565i	$0.0796304\pi$
$312$	10.6449	+	12.6860i	0.602646	+	0.718206i
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	0.999998	−	0.00205946i	$-0.000655547\pi$
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	−0.501782	+	0.864994i	$0.667322\pi$
$314$	−8.91117			−0.502886
$315$	−3.09627	−	2.59808i	−0.174455	−	0.146385i
$316$	2.94862			0.165873
$317$	−4.03849	−	6.99486i	−0.226824	−	0.392871i	0.730041	−	0.683403i	$-0.239501\pi$
$317$	−4.03849	−	6.99486i	−0.226824	−	0.392871i	−0.956865	+	0.290533i	$0.906168\pi$
$318$	0.860967	−	0.151812i	0.0482806	−	0.00851318i
$319$	−5.18004	+	8.97210i	−0.290027	+	0.502341i
$320$	−3.39646	+	5.88284i	−0.189868	+	0.328861i
$321$	−4.22281	+	11.6021i	−0.235694	+	0.647565i
$322$	3.93242	+	6.81115i	0.219145	+	0.379570i
$323$	−1.50980			−0.0840075
$324$	10.3743	+	3.77595i	0.576352	+	0.209775i
$325$	10.7314			0.595273
$326$	−1.14156	−	1.97724i	−0.0632251	−	0.109509i
$327$	−0.239170	+	0.657115i	−0.0132261	+	0.0363385i
$328$	−4.84002	+	8.38316i	−0.267246	+	0.462883i
$329$	−4.67752	+	8.10170i	−0.257880	+	0.446661i
$330$	−3.34002	+	0.588936i	−0.183862	+	0.0324199i
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	−0.986839	−	0.161706i	$-0.948300\pi$
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	0.353378	−	0.935481i	$-0.385033\pi$
$332$	18.4611			1.01318
$333$	−21.2219	−	17.8073i	−1.16295	−	0.975835i
$334$	20.3868			1.11552
$335$	−0.401674	−	0.695720i	−0.0219458	−	0.0380112i
$336$	0.0466368	+	0.0555796i	0.00254425	+	0.00303211i
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$	−0.723689	+	1.25347i	−0.0393635	+	0.0681795i
$339$	−15.9982	−	19.0660i	−0.868905	−	1.03552i
$340$	0.386659	+	0.669713i	0.0209695	+	0.0363203i
$341$	15.2618			0.826471
$342$	−1.47818	+	8.38316i	−0.0799307	+	0.453310i
$343$	1.00000			0.0539949
$344$	6.25877	+	10.8405i	0.337450	+	0.584481i
$345$	20.5535	−	3.62414i	1.10656	−	0.195117i
$346$	−2.08940	+	3.61895i	−0.112327	+	0.194556i
$347$	−6.47313	+	11.2118i	−0.347496	+	0.601880i	−0.985804	−	0.167901i	$-0.946301\pi$
$347$	−6.47313	+	11.2118i	−0.347496	+	0.601880i	0.638308	+	0.769781i	$0.279635\pi$
$348$	4.55525	−	12.5155i	0.244187	−	0.670899i
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	0.845785	−	0.533524i	$-0.179132\pi$
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	−0.884938	+	0.465710i	$0.845799\pi$
$350$	2.80066			0.149702
$351$		−	17.5089i		−	0.934555i
$352$	−9.31820			−0.496662
$353$	−7.16637	−	12.4125i	−0.381428	−	0.660652i	0.609839	−	0.792525i	$-0.291234\pi$
$353$	−7.16637	−	12.4125i	−0.381428	−	0.660652i	−0.991267	+	0.131873i	$0.957901\pi$
$354$	−5.41622	+	14.8809i	−0.287869	+	0.790913i
$355$	0.373455	−	0.646844i	0.0198210	−	0.0343309i
$356$	5.57310	−	9.65289i	0.295374	−	0.511602i
$357$	0.798133	−	0.140732i	0.0422417	−	0.00744835i
$358$	−3.75150	−	6.49778i	−0.198273	−	0.343418i
$359$	−20.9368			−1.10500			−0.552500	−	0.833513i	$-0.686326\pi$
$359$	−20.9368			−1.10500			−0.552500	+	0.833513i	$0.686326\pi$
$360$	10.7772	−	3.92258i	0.568008	−	0.206738i
$361$	−8.58853			−0.452028
$362$	−7.57785	−	13.1252i	−0.398283	−	0.689846i
$363$	9.20574	+	10.9710i	0.483176	+	0.575827i
$364$	−2.06670	+	3.57964i	−0.108325	+	0.187624i
$365$	−1.38073	+	2.39149i	−0.0722707	+	0.125176i
$366$	7.47818	+	8.91215i	0.390891	+	0.465845i
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	0.979373	−	0.202063i	$-0.0647645\pi$
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	−0.664678	+	0.747130i	$0.731431\pi$
$368$	−0.374638			−0.0195293
$369$	9.61721	−	3.50038i	0.500652	−	0.182222i
$370$	−10.9409			−0.568789
$371$	0.286989	+	0.497079i	0.0148997	+	0.0258071i
$372$	−19.3221	+	3.40700i	−1.00180	+	0.176645i
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$	0.340022	−	0.588936i	0.0175821	−	0.0304532i
$375$	6.53256	−	17.9480i	0.337340	−	0.926833i
$376$	−13.2724	−	22.9885i	−0.684474	−	1.18554i
$377$	−21.1225			−1.08786
$378$		−	4.56942i		−	0.235026i
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	−2.66637	−	4.61830i	−0.136782	−	0.236914i
$381$	12.3050	−	33.8077i	0.630404	−	1.73202i
$382$	5.67617	−	9.83142i	0.290418	−	0.503019i
$383$	−3.86618	+	6.69642i	−0.197553	+	0.342171i	−0.947734	−	0.319061i	$-0.896633\pi$
$383$	−3.86618	+	6.69642i	−0.197553	+	0.342171i	0.750182	+	0.661232i	$0.229966\pi$
$384$	11.6716	−	2.05802i	0.595613	−	0.105023i
$385$	−1.11334	−	1.92836i	−0.0567411	−	0.0982785i
$386$	0.561185			0.0285636
$387$	2.29813	−	13.0334i	0.116821	−	0.662523i
$388$	2.32945			0.118260
$389$	−2.69981	−	4.67620i	−0.136886	−	0.237093i	0.789431	−	0.613840i	$-0.210376\pi$
$389$	−2.69981	−	4.67620i	−0.136886	−	0.237093i	−0.926316	+	0.376747i	$0.877043\pi$
$390$	−4.44475	−	5.29704i	−0.225068	−	0.268226i
$391$	−2.09240	+	3.62414i	−0.105817	+	0.183280i
$392$	−1.41875	+	2.45734i	−0.0716576	+	0.124115i
$393$	7.97730	+	9.50698i	0.402402	+	0.479564i
$394$	5.03256	+	8.71664i	0.253536	+	0.439138i
$395$	−3.23854			−0.162949
$396$	4.65910	+	3.90945i	0.234129	+	0.196457i
$397$	−29.2344			−1.46723			−0.733617	−	0.679563i	$-0.762169\pi$
$397$	−29.2344			−1.46723			−0.733617	+	0.679563i	$0.762169\pi$
$398$	−1.59967	−	2.77071i	−0.0801842	−	0.138883i
$399$	−5.50387	+	0.970481i	−0.275538	+	0.0485848i
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	−0.289629	−	0.957139i	$-0.593532\pi$
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	0.973721	−	0.227743i	$-0.0731346\pi$
$402$	0.310622	−	0.853427i	0.0154924	−	0.0425650i
$403$	15.5581	+	26.9474i	0.775003	+	1.34235i
$404$	2.09657			0.104308
$405$	−11.3944	−	4.14722i	−0.566192	−	0.206077i
$406$	−5.51249			−0.273580
$407$	−7.63088	−	13.2171i	−0.378249	−	0.655146i
$408$	−0.786522	+	2.16095i	−0.0389386	+	0.106983i
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	−0.732628	−	0.680629i	$-0.761706\pi$
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	0.955756	+	0.294160i	$0.0950398\pi$
$410$	2.02094	−	3.50038i	0.0998073	−	0.172871i
$411$	4.38191	−	0.772649i	0.216144	−	0.0381120i
$412$	−2.23143	−	3.86495i	−0.109935	−	0.190412i
$413$	−10.3969			−0.511599
$414$	18.0744	+	15.1663i	0.888310	+	0.745381i
$415$	−20.2763			−0.995325
$416$	−9.49912	−	16.4530i	−0.465733	−	0.806673i
$417$	6.82857	+	8.13798i	0.334397	+	0.398518i
$418$	−2.34477	+	4.06126i	−0.114686	+	0.198643i
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	−0.868158	−	0.496287i	$-0.834696\pi$
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	0.863877	+	0.503704i	$0.168030\pi$
$420$	1.84002	+	2.19285i	0.0897839	+	0.107000i
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$	−5.12061			−0.249268
$423$	−4.87346	+	27.6387i	−0.236956	+	1.34384i
$424$	−1.62866			−0.0790947
$425$	0.745100	+	1.29055i	0.0361427	+	0.0626009i
$426$	0.831566	−	0.146628i	0.0402895	−	0.00710413i
$427$	−3.81908	+	6.61484i	−0.184818	+	0.320114i
$428$	4.37211	−	7.57272i	0.211334	−	0.366041i
$429$	3.29901	−	9.06396i	0.159278	−	0.437612i
$430$	−2.61334	−	4.52644i	−0.126026	−	0.218284i
$431$	−29.3191			−1.41225			−0.706126	−	0.708086i	$-0.749559\pi$
$431$	−29.3191			−1.41225			−0.706126	+	0.708086i	$0.749559\pi$
$432$	0.188501	+	0.108831i	0.00906925	+	0.00523613i
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$	4.06031	+	7.03266i	0.194901	+	0.337578i
$435$	−5.00316	+	13.7461i	−0.239883	+	0.659073i
$436$	0.247626	−	0.428901i	0.0118591	−	0.0205406i
$437$	14.4290	−	24.9918i	0.690233	−	1.19552i
$438$	−3.07444	+	0.542108i	−0.146903	+	0.0259029i
$439$	10.9650	+	18.9919i	0.523330	+	0.906434i	0.999631	+	0.0271516i	$0.00864370\pi$
$439$	10.9650	+	18.9919i	0.523330	+	0.906434i	−0.476302	+	0.879282i	$0.658023\pi$
$440$	6.31820			0.301208
$441$	2.81908	−	1.02606i	0.134242	−	0.0488600i
$442$	1.38650			0.0659489
$443$	9.35504	+	16.2034i	0.444471	+	0.769847i	0.998015	−	0.0629732i	$-0.0200583\pi$
$443$	9.35504	+	16.2034i	0.444471	+	0.769847i	−0.553544	+	0.832820i	$0.686725\pi$
$444$	12.6116	+	15.0299i	0.598519	+	0.713288i
$445$	−6.12108	+	10.6020i	−0.290167	+	0.502584i
$446$	3.11468	−	5.39479i	0.147485	−	0.255451i
$447$	−0.479933	−	0.571962i	−0.0227000	−	0.0270529i
$448$	−2.52094	−	4.36640i	−0.119103	−	0.206293i
$449$	6.68004			0.315251			0.157625	−	0.987499i	$-0.449616\pi$
$449$	6.68004			0.315251			0.157625	+	0.987499i	$0.449616\pi$
$450$	7.89528	−	2.87365i	0.372187	−	0.135465i
$451$	5.63816			0.265490
$452$	8.81345	+	15.2653i	0.414550	+	0.718022i
$453$	−4.21419	+	0.743076i	−0.198000	+	0.0349128i
$454$	−5.25150	+	9.09586i	−0.246465	+	0.426890i
$455$	2.26991	−	3.93161i	0.106415	−	0.184317i
$456$	5.42380	−	14.9018i	0.253993	−	0.697839i
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	0.998655	−	0.0518563i	$-0.0165138\pi$
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	−0.544236	+	0.838932i	$0.683180\pi$
$458$	15.4355			0.721254
$459$	2.10560	−	1.21567i	0.0982810	−	0.0567426i
$460$	−14.7811			−0.689170
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	0.877052	−	0.480395i	$-0.159507\pi$
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	−0.854560	+	0.519352i	$0.826173\pi$
$462$	0.860967	−	2.36549i	0.0400558	−	0.110052i
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	−0.860802	−	0.508941i	$-0.830037\pi$
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	0.871156	+	0.491006i	$0.163371\pi$
$464$	0.131292	−	0.227405i	0.00609509	−	0.0105570i
$465$	21.2219	−	3.74200i	0.984144	−	0.173531i
$466$	7.14677	+	12.3786i	0.331068	+	0.573426i
$467$	−34.2148			−1.58327			−0.791637	−	0.610992i	$-0.790771\pi$
$467$	−34.2148			−1.58327			−0.791637	+	0.610992i	$0.790771\pi$
$468$	−2.15328	+	12.2118i	−0.0995352	+	0.564492i
$469$	0.596267			0.0275330
$470$	5.54189	+	9.59883i	0.255628	+	0.442761i
$471$	−11.2819	−	13.4453i	−0.519844	−	0.619526i
$472$	14.7506	−	25.5488i	0.678952	−	1.17598i
$473$	3.64543	−	6.31407i	0.167617	−	0.290321i
$474$	−2.35339	−	2.80466i	−0.108095	−	0.128822i
$475$	−5.13816	−	8.89955i	−0.235755	−	0.408339i
$476$	−0.573978			−0.0263082
$477$	1.31908	+	1.10684i	0.0603964	+	0.0506786i
$478$	13.2781			0.607325
$479$	10.8965	+	18.8732i	0.497872	+	0.862339i	0.999997	−	0.00245553i	$-0.000781622\pi$
$479$	10.8965	+	18.8732i	0.497872	+	0.862339i	−0.502125	+	0.864795i	$0.667448\pi$
$480$	−12.9572	+	2.28471i	−0.591414	+	0.104282i
$481$	15.5581	−	26.9474i	0.709388	−	1.22870i
$482$	−6.87598	+	11.9095i	−0.313192	+	0.542465i
$483$	−5.29813	+	14.5565i	−0.241073	+	0.662344i
$484$	−5.07145	−	8.78401i	−0.230521	−	0.399273i
$485$	−2.55850			−0.116175
$486$	−4.68850	−	12.8816i	−0.212675	−	0.584319i
$487$	19.3928			0.878772			0.439386	−	0.898298i	$-0.355196\pi$
$487$	19.3928			0.878772			0.439386	+	0.898298i	$0.355196\pi$
$488$	−10.8366	−	18.7696i	−0.490551	−	0.849659i
$489$	1.53802	−	4.22567i	0.0695516	−	0.191091i
$490$	0.592396	−	1.02606i	0.0267617	−	0.0463527i
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	0.403987	+	0.914765i	$0.367624\pi$
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	−0.994203	+	0.107519i	$0.965709\pi$
$492$	−7.13816	+	1.25865i	−0.321813	+	0.0567443i
$493$	−1.46657	−	2.54017i	−0.0660509	−	0.114403i
$494$	−9.56118			−0.430178
$495$	−5.11721	−	4.29385i	−0.230002	−	0.192994i
$496$	−0.386821			−0.0173688
$497$	0.277189	+	0.480105i	0.0124336	+	0.0215357i
$498$	−14.7344	−	17.5598i	−0.660265	−	0.786873i
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	−0.660403	−	0.750911i	$-0.729615\pi$
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	0.980510	+	0.196470i	$0.0629479\pi$
$500$	−6.76352	+	11.7148i	−0.302474	+	0.523900i
$501$	25.8106	+	30.7599i	1.15313	+	1.37425i
$502$	8.38279	+	14.5194i	0.374142	+	0.648033i
$503$	18.7033			0.833937			0.416969	−	0.908921i	$-0.363092\pi$
$503$	18.7033			0.833937			0.416969	+	0.908921i	$0.363092\pi$
$504$	−1.47818	+	8.38316i	−0.0658433	+	0.373416i
$505$	−2.30272			−0.102470
$506$	6.49912	+	11.2568i	0.288921	+	0.500426i
$507$	−2.80747	+	0.495032i	−0.124684	+	0.0219851i
$508$	−12.7400	+	22.0664i	−0.565248	+	0.979039i
$509$	12.8045	−	22.1781i	0.567551	−	0.983027i	−0.429257	−	0.903183i	$-0.641224\pi$
$509$	12.8045	−	22.1781i	0.567551	−	0.983027i	0.996807	−	0.0798442i	$-0.0254423\pi$
$510$	0.328411	−	0.902302i	0.0145423	−	0.0399546i
$511$	−1.02481	−	1.77503i	−0.0453351	−	0.0785228i
$512$	0.473897			0.0209435
$513$	−14.5201	+	8.38316i	−0.641077	+	0.370126i
$514$	−23.3756			−1.03105
$515$	2.45084	+	4.24497i	0.107997	+	0.187056i
$516$	−3.20574	+	8.80769i	−0.141125	+	0.387737i
$517$	−7.73055	+	13.3897i	−0.339989	+	0.588879i
$518$	4.06031	−	7.03266i	0.178400	−	0.308997i
$519$	−8.10560	+	1.42924i	−0.355796	+	0.0627365i
$520$	6.44087	+	11.1559i	0.282451	+	0.489220i
$521$	−21.2121			−0.929320			−0.464660	−	0.885489i	$-0.653824\pi$
$521$	−21.2121			−0.929320			−0.464660	+	0.885489i	$0.653824\pi$
$522$	−15.5401	+	5.65615i	−0.680173	+	0.247563i
$523$	20.8057			0.909770			0.454885	−	0.890550i	$-0.349680\pi$
$523$	20.8057			0.909770			0.454885	+	0.890550i	$0.349680\pi$
$524$	−4.39470	−	7.61185i	−0.191984	−	0.332525i
$525$	3.54576	+	4.22567i	0.154750	+	0.184423i
$526$	−0.322786	+	0.559082i	−0.0140741	+	0.0243771i
$527$	−2.16044	+	3.74200i	−0.0941104	+	0.163004i
$528$	0.0770768	+	0.0918566i	0.00335434	+	0.00399754i
$529$	−28.4937	−	49.3525i	−1.23885	−	2.14576i
$530$	0.680045			0.0295393
$531$	−29.3097	+	10.6679i	−1.27193	+	0.462946i
$532$	3.95811			0.171606
$533$	5.74763	+	9.95518i	0.248957	+	0.431207i
$534$	−13.6297	+	2.40328i	−0.589815	+	0.104000i
$535$	−4.80200	+	8.31731i	−0.207609	+	0.359589i
$536$	−0.845952	+	1.46523i	−0.0365396	+	0.0632884i
$537$	5.05438	−	13.8868i	0.218112	−	0.599259i
$538$	−9.16772	−	15.8790i	−0.395248	−	0.684590i
$539$	1.65270			0.0711870
$540$	7.43717	+	4.29385i	0.320045	+	0.184778i
$541$	26.7297			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$541$	26.7297			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$542$	3.05943	+	5.29909i	0.131414	+	0.227615i
$543$	10.2096	−	28.0507i	0.438136	−	1.20377i
$544$	1.31908	−	2.28471i	0.0565550	−	0.0979561i
$545$	−0.271974	+	0.471073i	−0.0116501	+	0.0201786i
$546$	5.05438	−	0.891223i	0.216307	−	0.0381408i
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	−0.928446	−	0.371467i	$-0.878855\pi$
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	0.142523	−	0.989792i	$-0.454479\pi$
$548$	−3.15125			−0.134615
$549$	−3.97906	+	22.5663i	−0.169822	+	0.963108i
$550$	4.62866			0.197367
$551$	10.1133	+	17.5168i	0.430843	+	0.746242i
$552$	−28.2536	−	33.6713i	−1.20255	−	1.43315i
$553$	1.20187	−	2.08169i	0.0511086	−	0.0885226i
$554$	7.85844	−	13.6112i	0.333873	−	0.578285i
$555$	−13.8516	−	16.5077i	−0.587969	−	0.700714i
$556$	−3.76187	−	6.51575i	−0.159539	−	0.276329i
$557$	32.3387			1.37024			0.685118	−	0.728432i	$-0.259751\pi$
$557$	32.3387			1.37024			0.685118	+	0.728432i	$0.259751\pi$
$558$	18.6623	+	15.6595i	0.790036	+	0.662919i
$559$	14.8648			0.628716
$560$	0.0282185	+	0.0488759i	0.00119245	+	0.00206538i
$561$	1.31908	−	0.232589i	0.0556915	−	0.00981992i
$562$	9.80974	−	16.9910i	0.413799	−	0.716721i
$563$	8.87093	−	15.3649i	0.373865	−	0.647553i	−0.616291	−	0.787518i	$-0.711366\pi$
$563$	8.87093	−	15.3649i	0.373865	−	0.647553i	0.990156	+	0.139965i	$0.0446990\pi$
$564$	6.79813	−	18.6777i	0.286253	−	0.786474i
$565$	−9.68004	−	16.7663i	−0.407243	−	0.705365i
$566$	16.3517			0.687315
$567$	6.89440	−	5.78509i	0.289538	−	0.242951i
$568$	−1.57304			−0.0660035
$569$	13.3007	+	23.0374i	0.557593	+	0.965779i	0.997697	+	0.0678320i	$0.0216082\pi$
$569$	13.3007	+	23.0374i	0.557593	+	0.965779i	−0.440104	+	0.897947i	$0.645058\pi$
$570$	−2.26470	+	6.22221i	−0.0948579	+	0.260620i
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	−0.741986	−	0.670416i	$-0.766116\pi$
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	0.951590	+	0.307371i	$0.0994491\pi$
$572$	−3.41565	+	5.91608i	−0.142815	+	0.247364i
$573$	22.0201	−	3.88273i	0.919902	−	0.162203i
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$	−28.4834			−1.18784
$576$	−11.5869	−	9.72259i	−0.482789	−	0.405108i
$577$	−32.9145			−1.37025			−0.685124	−	0.728427i	$-0.740252\pi$
$577$	−32.9145			−1.37025			−0.685124	+	0.728427i	$0.740252\pi$
$578$	−7.37851	−	12.7800i	−0.306905	−	0.531576i
$579$	0.710485	+	0.846723i	0.0295267	+	0.0351886i
$580$	5.18004	−	8.97210i	0.215090	−	0.372546i
$581$	7.52481	−	13.0334i	0.312182	−	0.540715i
$582$	−1.85921	−	2.21572i	−0.0770668	−	0.0918447i
$583$	0.474308	+	0.821525i	0.0196438	+	0.0340241i
$584$	5.81582			0.240660
$585$	2.36500	−	13.4126i	0.0977807	−	0.554542i
$586$	−11.5125			−0.475577
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	0.978592	−	0.205808i	$-0.0659821\pi$
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	−0.667531	+	0.744582i	$0.732649\pi$
$588$	−2.09240	+	0.368946i	−0.0862890	+	0.0152151i
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$	−6.15910	+	10.6679i	−0.253566	+	0.439189i
$591$	−6.78034	+	18.6288i	−0.278906	+	0.766288i
$592$	0.193411	+	0.334997i	0.00794913	+	0.0137683i
$593$	41.0009			1.68371			0.841853	−	0.539706i	$-0.181465\pi$
$593$	41.0009			1.68371			0.841853	+	0.539706i	$0.181465\pi$
$594$		−	7.55190i		−	0.309858i
$595$	0.630415			0.0258445
$596$	0.264396	+	0.457947i	0.0108301	+	0.0187582i
$597$	2.15523	−	5.92145i	0.0882077	−	0.242349i
$598$	−13.2506	+	22.9507i	−0.541858	+	0.938526i
$599$	−3.03684	+	5.25996i	−0.124082	+	0.214916i	−0.921374	−	0.388678i	$-0.872932\pi$
$599$	−3.03684	+	5.25996i	−0.124082	+	0.214916i	0.797292	+	0.603594i	$0.206265\pi$
$600$	−15.4145	+	2.71799i	−0.629293	+	0.110961i
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	0.973402	−	0.229102i	$-0.0735791\pi$
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	−0.685110	+	0.728440i	$0.740246\pi$
$602$	3.87939			0.158112
$603$	1.68092	−	0.611806i	0.0684524	−	0.0249147i
$604$	3.03064			0.123315
$605$	5.57011	+	9.64771i	0.226457	+	0.392235i
$606$	−1.67334	−	1.99421i	−0.0679749	−	0.0810094i
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.161377	+	0.986893i	$0.551594\pi$
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.773986	+	0.633203i	$0.781740\pi$
$608$	−9.09627	+	15.7552i	−0.368902	+	0.638958i
$609$	−6.97906	−	8.31731i	−0.282806	−	0.337035i
$610$	4.52481	+	7.83721i	0.183204	+	0.317319i
$611$	−31.5226			−1.27527
$612$	−1.61809	+	0.588936i	−0.0654074	+	0.0238063i
$613$	−26.4938			−1.07008			−0.535038	−	0.844828i	$-0.679703\pi$
$613$	−26.4938			−1.07008			−0.535038	+	0.844828i	$0.679703\pi$
$614$	2.77466	+	4.80586i	0.111976	+	0.193949i
$615$	7.84002	−	1.38241i	0.316140	−	0.0557440i
$616$	−2.34477	+	4.06126i	−0.0944735	+	0.163633i
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	−0.842492	−	0.538708i	$-0.818913\pi$
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	0.887781	+	0.460266i	$0.152246\pi$
$618$	−1.89528	+	5.20723i	−0.0762392	+	0.209466i
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	0.797090	−	0.603861i	$-0.206372\pi$
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	−0.921504	+	0.388369i	$0.873038\pi$
$620$	−15.2618			−0.612927
$621$			46.4721i			1.86486i
$622$	8.37557			0.335830
$623$	−4.54323	−	7.86911i	−0.182021	−	0.315269i
$624$	−0.0836160	+	0.229733i	−0.00334732	+	0.00919668i
$625$	−0.533433	+	0.923933i	−0.0213373	+	0.0369573i
$626$	−7.75119	+	13.4255i	−0.309800	+	0.536589i
$627$	−9.09627	+	1.60392i	−0.363270	+	0.0640543i
$628$	6.21523	+	10.7651i	0.248015	+	0.429574i
$629$	4.32089			0.172285
$630$	0.617211	−	3.50038i	0.0245903	−	0.139458i
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	3.41029	+	5.90680i	0.135654	+	0.234960i
$633$	−6.48293	−	7.72605i	−0.257673	−	0.307083i
$634$	3.55138	−	6.15118i	0.141043	−	0.244295i
$635$	13.9927	−	24.2361i	0.555284	−	0.961781i
$636$	−0.783890	−	0.934204i	−0.0310833	−	0.0370436i
$637$	1.68479	+	2.91815i	0.0667539	+	0.115621i
$638$	−9.11051			−0.360689
$639$	1.27403	+	1.06904i	0.0504000	+	0.0422906i
$640$	9.21894			0.364411
$641$	−2.44444	−	4.23389i	−0.0965496	−	0.167229i	0.813705	−	0.581278i	$-0.197447\pi$
$641$	−2.44444	−	4.23389i	−0.0965496	−	0.167229i	−0.910254	+	0.414050i	$0.864114\pi$
$642$	−10.6925	+	1.88538i	−0.422001	+	0.0744101i
$643$	20.1839	−	34.9596i	0.795976	−	1.37867i	−0.126242	−	0.992000i	$-0.540291\pi$
$643$	20.1839	−	34.9596i	0.795976	−	1.37867i	0.922218	−	0.386671i	$-0.126375\pi$
$644$	5.48545	−	9.50108i	0.216157	−	0.374395i
$645$	3.52094	−	9.67372i	0.138637	−	0.380902i
$646$	−0.663848	−	1.14982i	−0.0261188	−	0.0452390i
$647$	−2.28075			−0.0896657			−0.0448329	−	0.998995i	$-0.514276\pi$
$647$	−2.28075			−0.0896657			−0.0448329	+	0.998995i	$0.514276\pi$
$648$	4.43453	+	25.1495i	0.174205	+	0.987965i
$649$	−17.1830			−0.674493
$650$	4.71853	+	8.17273i	0.185076	+	0.320561i
$651$	−5.47044	+	15.0299i	−0.214403	+	0.589068i
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	−0.998930	−	0.0462542i	$-0.985272\pi$
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	0.539522	+	0.841971i	$0.318605\pi$
$654$	−0.605600	+	0.106784i	−0.0236808	+	0.00417557i
$655$	4.82682	+	8.36030i	0.188599	+	0.326664i
$656$	−0.142903			−0.00557944
$657$	−4.71032	−	3.95243i	−0.183767	−	0.154199i
$658$	−8.22668			−0.320709
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.776101	+	0.630609i	$0.217195\pi$
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.158073	+	0.987427i	$0.449472\pi$
$660$	3.04101	+	3.62414i	0.118371	+	0.141069i
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	0.426571	+	0.904454i	$0.359721\pi$
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	−0.996566	+	0.0828055i	$0.973612\pi$
$662$	10.1348	−	17.5539i	0.393898	−	0.682252i
$663$	1.75537	+	2.09196i	0.0681728	+	0.0812452i
$664$	21.3516	+	36.9821i	0.828604	+	1.43518i
$665$	−4.34730			−0.168581
$666$	4.23039	−	23.9917i	0.163924	−	0.929661i
$667$	56.0634			2.17078
$668$	−14.2191	−	24.6282i	−0.550154	−	0.952894i
$669$	12.0831	−	2.13057i	0.467158	−	0.0823726i
$670$	0.353226	−	0.611806i	0.0136463	−	0.0236361i
$671$	−6.31180	+	10.9324i	−0.243664	+	0.422039i
$672$	3.34002	−	9.17664i	0.128844	−	0.353996i
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$	−25.5226			−0.983094
$675$	14.3316	+	8.27433i	0.551622	+	0.318479i
$676$	2.01899			0.0776535
$677$	−17.9454	−	31.0823i	−0.689697	−	1.19459i	−0.971936	−	0.235246i	$-0.924411\pi$
$677$	−17.9454	−	31.0823i	−0.689697	−	1.19459i	0.282239	−	0.959344i	$-0.408923\pi$
$678$	7.48576	−	20.5669i	0.287489	−	0.789869i
$679$	0.949493	−	1.64457i	0.0364382	−	0.0631128i
$680$	−0.894400	+	1.54915i	−0.0342987	+	0.0594070i
$681$	−20.3726	+	3.59224i	−0.780679	+	0.137655i
$682$	6.71048	+	11.6229i	0.256958	+	0.445064i
$683$	35.0642			1.34169			0.670847	−	0.741596i	$-0.265931\pi$
$683$	35.0642			1.34169			0.670847	+	0.741596i	$0.265931\pi$
$684$	11.1582	−	4.06126i	0.426645	−	0.155286i
$685$	3.46110			0.132242
$686$	0.439693	+	0.761570i	0.0167875	+	0.0290769i
$687$	19.5421	+	23.2893i	0.745576	+	0.888543i
$688$	−0.0923963	+	0.160035i	−0.00352257	+	0.00610128i
$689$	−0.967034	+	1.67495i	−0.0368411	+	0.0638106i
$690$	11.7973	+	14.0594i	0.449114	+	0.535233i
$691$	−1.03343	−	1.78996i	−0.0393136	−	0.0680932i	0.845699	−	0.533660i	$-0.179184\pi$
$691$	−1.03343	−	1.78996i	−0.0393136	−	0.0680932i	−0.885013	+	0.465567i	$0.845850\pi$
$692$	5.82915			0.221591
$693$	4.65910	−	1.69577i	0.176985	−	0.0644171i
$694$	−11.3847			−0.432159
$695$	4.13176	+	7.15642i	0.156727	+	0.271458i
$696$	30.3400	−	5.34976i	1.15004	−	0.202782i
$697$	−0.798133	+	1.38241i	−0.0302315	+	0.0523624i
$698$	0.643208	−	1.11407i	0.0243458	−	0.0421681i
$699$	−9.62882	+	26.4550i	−0.364196	+	1.00062i
$700$	−1.95336	−	3.38332i	−0.0738302	−	0.127878i
$701$	−7.36009			−0.277987			−0.138993	−	0.990293i	$-0.544387\pi$
$701$	−7.36009			−0.277987			−0.138993	+	0.990293i	$0.544387\pi$
$702$	13.3342	−	7.69852i	0.503268	−	0.290562i
$703$	−29.7965			−1.12380
$704$	−4.16637	−	7.21637i	−0.157026	−	0.271977i
$705$	−7.46657	+	20.5142i	−0.281207	+	0.772610i
$706$	6.30200	−	10.9154i	0.237179	−	0.410806i
$707$	0.854570	−	1.48016i	0.0321394	−	0.0556671i
$708$	21.7545	−	3.83590i	0.817584	−	0.144162i
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	0.767742	−	0.640760i	$-0.221380\pi$
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	−0.938785	+	0.344504i	$0.888047\pi$
$710$	0.656822			0.0246501
$711$	1.25221	−	7.10165i	0.0469616	−	0.266333i
$712$	25.7828			0.966252
$713$	−41.2943	−	71.5239i	−1.54648	−	2.67859i
$714$	0.458111	+	0.545955i	0.0171444	+	0.0204319i
$715$	3.75150	−	6.49778i	0.140298	−	0.243003i
$716$	−5.23308	+	9.06396i	−0.195569	+	0.338736i
$717$	16.8106	+	20.0341i	0.627804	+	0.748188i
$718$	−9.20574	−	15.9448i	−0.343555	−	0.595055i
$719$	−25.9537			−0.967908			−0.483954	−	0.875093i	$-0.660800\pi$
$719$	−25.9537			−0.967908			−0.483954	+	0.875093i	$0.660800\pi$
$720$	0.129700	+	0.108831i	0.00483362	+	0.00405589i
$721$	−3.63816			−0.135492
$722$	−3.77631	−	6.54076i	−0.140540	−	0.243422i
$723$	−26.6746	+	4.70345i	−0.992038	+	0.174923i
$724$	−10.5706	+	18.3088i	−0.392852	+	0.680440i
$725$	9.98205	−	17.2894i	0.370724	−	0.642113i
$726$	−4.30747	+	11.8347i	−0.159865	+	0.439226i
$727$	5.08007	+	8.79894i	0.188409	+	0.326335i	0.944720	−	0.327878i	$-0.106333\pi$
$727$	5.08007	+	8.79894i	0.188409	+	0.326335i	−0.756311	+	0.654213i	$0.773000\pi$
$728$	−9.56118			−0.354361
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	−2.42839			−0.0898786
$731$	1.03209	+	1.78763i	0.0381732	+	0.0661179i
$732$	5.55051	−	15.2499i	0.205153	−	0.563652i
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	0.196441	+	0.980516i	$0.437062\pi$
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	−0.947372	+	0.320135i	$0.896272\pi$
$734$	−5.30154	+	9.18253i	−0.195683	+	0.338933i
$735$	2.29813	−	0.405223i	0.0847679	−	0.0149469i
$736$	25.2126	+	43.6695i	0.929349	+	1.60968i
$737$	0.985452			0.0362996
$738$	6.89440	+	5.78509i	0.253786	+	0.212952i
$739$	−25.3618			−0.932951			−0.466475	−	0.884534i	$-0.654476\pi$
$739$	−25.3618			−0.932951			−0.466475	+	0.884534i	$0.654476\pi$
$740$	7.63088	+	13.2171i	0.280517	+	0.485869i
$741$	−12.1049	−	14.4260i	−0.444684	−	0.529954i
$742$	−0.252374	+	0.437124i	−0.00926494	+	0.0160473i
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	−0.583377	−	0.812202i	$-0.698269\pi$
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	0.995076	+	0.0991184i	$0.0316023\pi$
$744$	−29.1725	−	34.7664i	−1.06951	−	1.27460i
$745$	−0.290393	−	0.502975i	−0.0106392	−	0.0184276i
$746$	0.686852			0.0251474
$747$	7.84002	−	44.4630i	0.286851	−	1.62682i
$748$	−0.948615			−0.0346848
$749$	−3.56418	−	6.17334i	−0.130232	−	0.225569i
$750$	16.5410	−	2.91663i	0.603992	−	0.106500i
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	−0.997827	−	0.0658924i	$-0.979011\pi$
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	0.555978	+	0.831197i	$0.312344\pi$
$752$	0.195937	−	0.339373i	0.00714508	−	0.0123756i
$753$	−11.2941	+	31.0303i	−0.411580	+	1.13081i
$754$	−9.28740	−	16.0862i	−0.338227	−	0.585827i
$755$	−3.32863			−0.121141
$756$	−5.52007	+	3.18701i	−0.200763	+	0.115911i
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	−3.04442	−	5.27308i	−0.110578	−	0.191527i
$759$	−8.75624	+	24.0576i	−0.317832	+	0.873235i
$760$	6.16772	−	10.6828i	0.223727	−	0.387506i
$761$	9.13610	−	15.8242i	0.331183	−	0.573626i	−0.651561	−	0.758596i	$-0.725886\pi$
$761$	9.13610	−	15.8242i	0.331183	−	0.573626i	0.982744	+	0.184970i	$0.0592188\pi$
$762$	31.1573	−	5.49388i	1.12871	−	0.199022i
$763$	−0.201867	−	0.349643i	−0.00730806	−	0.0126579i
$764$	−15.8357			−0.572917
$765$	1.77719	−	0.646844i	0.0642544	−	0.0233867i
$766$	−6.79973			−0.245684
$767$	−17.5167	−	30.3398i	−0.632490	−	1.09550i
$768$	17.9259	+	21.3633i	0.646846	+	0.770881i
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	−0.983310	−	0.181936i	$-0.941764\pi$
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	0.649217	+	0.760604i	$0.275097\pi$
$770$	0.979055	−	1.69577i	0.0352827	−	0.0611114i
$771$	−29.5945	−	35.2694i	−1.06582	−	1.27020i
$772$	−0.391407	−	0.677937i	−0.0140870	−	0.0243995i
$773$	−2.96080			−0.106493			−0.0532463	−	0.998581i	$-0.516957\pi$
$773$	−2.96080			−0.106493			−0.0532463	+	0.998581i	$0.516957\pi$
$774$	10.9363	−	3.98048i	0.393097	−	0.143076i

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.439693 + 0.761570i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(-0.673648 + 1.16679i) q^{5} +(-1.50000 + 0.264490i) q^{6} +(-0.500000 - 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\)	\(q+(0.439693 + 0.761570i) q^{2} +(-0.592396 + 1.62760i) q^{3} +(0.613341 - 1.06234i) q^{4} +(-0.673648 + 1.16679i) q^{5} +(-1.50000 + 0.264490i) q^{6} +(-0.500000 - 0.866025i) q^{7} +2.83750 q^{8} +(-2.29813 - 1.92836i) q^{9} -1.18479 q^{10} +(-0.826352 - 1.43128i) q^{11} +(1.36571 + 1.62760i) q^{12} +(1.68479 - 2.91815i) q^{13} +(0.439693 - 0.761570i) q^{14} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 + 0.0362770i) q^{16} +0.467911 q^{17} +(0.458111 - 2.59808i) q^{18} -3.22668 q^{19} +(0.826352 + 1.43128i) q^{20} +(1.70574 - 0.300767i) q^{21} +(0.726682 - 1.25865i) q^{22} +(-4.47178 + 7.74535i) q^{23} +(-1.68092 + 4.61830i) q^{24} +(1.59240 + 2.75811i) q^{25} +2.96316 q^{26} +(4.50000 - 2.59808i) q^{27} -1.22668 q^{28} +(-3.13429 - 5.42874i) q^{29} +(0.701867 - 1.92836i) q^{30} +(-4.61721 + 7.99724i) q^{31} +(2.81908 - 4.88279i) q^{32} +(2.81908 - 0.497079i) q^{33} +(0.205737 + 0.356347i) q^{34} +1.34730 q^{35} +(-3.45811 + 1.25865i) q^{36} +9.23442 q^{37} +(-1.41875 - 2.45734i) q^{38} +(3.75150 + 4.47086i) q^{39} +(-1.91147 + 3.31077i) q^{40} +(-1.70574 + 2.95442i) q^{41} +(0.979055 + 1.16679i) q^{42} +(2.20574 + 3.82045i) q^{43} -2.02734 q^{44} +(3.79813 - 1.38241i) q^{45} -7.86484 q^{46} +(-4.67752 - 8.10170i) q^{47} +(-0.0714517 + 0.0125989i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.40033 + 2.42544i) q^{50} +(-0.277189 + 0.761570i) q^{51} +(-2.06670 - 3.57964i) q^{52} -0.573978 q^{53} +(3.95723 + 2.28471i) q^{54} +2.22668 q^{55} +(-1.41875 - 2.45734i) q^{56} +(1.91147 - 5.25173i) q^{57} +(2.75624 - 4.77396i) q^{58} +(5.19846 - 9.00400i) q^{59} +(-2.81908 + 0.497079i) q^{60} +(-3.81908 - 6.61484i) q^{61} -8.12061 q^{62} +(-0.520945 + 2.95442i) q^{63} +5.04189 q^{64} +(2.26991 + 3.93161i) q^{65} +(1.61809 + 1.92836i) q^{66} +(-0.298133 + 0.516382i) q^{67} +(0.286989 - 0.497079i) q^{68} +(-9.95723 - 11.8666i) q^{69} +(0.592396 + 1.02606i) q^{70} -0.554378 q^{71} +(-6.52094 - 5.47172i) q^{72} +2.04963 q^{73} +(4.06031 + 7.03266i) q^{74} +(-5.43242 + 0.957882i) q^{75} +(-1.97906 + 3.42782i) q^{76} +(-0.826352 + 1.43128i) q^{77} +(-1.75537 + 4.82283i) q^{78} +(1.20187 + 2.08169i) q^{79} -0.0564370 q^{80} +(1.56283 + 8.86327i) q^{81} -3.00000 q^{82} +(7.52481 + 13.0334i) q^{83} +(0.726682 - 1.99654i) q^{84} +(-0.315207 + 0.545955i) q^{85} +(-1.93969 + 3.35965i) q^{86} +(10.6925 - 1.88538i) q^{87} +(-2.34477 - 4.06126i) q^{88} +9.08647 q^{89} +(2.72281 + 2.28471i) q^{90} -3.36959 q^{91} +(5.48545 + 9.50108i) q^{92} +(-10.2811 - 12.2525i) q^{93} +(4.11334 - 7.12452i) q^{94} +(2.17365 - 3.76487i) q^{95} +(6.27719 + 7.48086i) q^{96} +(0.949493 + 1.64457i) q^{97} -0.879385 q^{98} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6q - 3q^{2} - 3q^{4} - 3q^{5} - 9q^{6} - 3q^{7} + 12q^{8} + O(q^{10}) \)	\( 6q - 3q^{2} - 3q^{4} - 3q^{5} - 9q^{6} - 3q^{7} + 12q^{8} - 6q^{11} + 18q^{12} + 3q^{13} - 3q^{14} - 9q^{15} - 3q^{16} + 12q^{17} + 9q^{18} - 6q^{19} + 6q^{20} - 9q^{22} - 12q^{23} - 27q^{24} + 6q^{25} - 6q^{26} + 27q^{27} + 6q^{28} - 9q^{29} + 18q^{30} + 3q^{31} - 9q^{34} + 6q^{35} - 27q^{36} - 6q^{37} - 6q^{38} - 18q^{39} + 9q^{40} + 9q^{42} + 3q^{43} + 30q^{44} + 9q^{45} - 3q^{47} - 3q^{49} + 6q^{50} + 9q^{51} + 21q^{52} + 12q^{53} - 27q^{54} - 6q^{56} - 9q^{57} + 9q^{58} + 3q^{59} - 6q^{61} - 60q^{62} + 24q^{64} - 15q^{65} + 36q^{66} + 12q^{67} - 6q^{68} - 9q^{69} + 18q^{71} - 36q^{72} - 42q^{73} + 30q^{74} - 9q^{75} - 15q^{76} - 6q^{77} + 54q^{78} + 21q^{79} - 30q^{80} - 18q^{82} + 18q^{83} - 9q^{84} - 9q^{85} - 6q^{86} + 9q^{87} - 27q^{88} + 24q^{89} + 27q^{90} - 6q^{91} - 3q^{92} - 27q^{93} + 18q^{94} + 12q^{95} + 27q^{96} + 3q^{97} + 6q^{98} + 18q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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