LMFDB - Embedded newform 260.2.p.d.103.17

Newspace parameters

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.p (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			103.17
Character	$\chi$	$=$	260.103
Dual form			260.2.p.d.207.17

$q$-expansion

$f(q)$	$=$	$q+(0.0324895 + 1.41384i) q^{2} +(2.32949 - 2.32949i) q^{3} +(-1.99789 + 0.0918700i) q^{4} +(-2.23599 - 0.0191440i) q^{5} +(3.36921 + 3.21784i) q^{6} +(1.97121 - 1.97121i) q^{7} +(-0.194800 - 2.82171i) q^{8} -7.85303i q^{9} +O(q^{10})$	\(q+(0.0324895 + 1.41384i) q^{2} +(2.32949 - 2.32949i) q^{3} +(-1.99789 + 0.0918700i) q^{4} +(-2.23599 - 0.0191440i) q^{5} +(3.36921 + 3.21784i) q^{6} +(1.97121 - 1.97121i) q^{7} +(-0.194800 - 2.82171i) q^{8} -7.85303i q^{9} +(-0.0455796 - 3.16195i) q^{10} +2.76564 q^{11} +(-4.44005 + 4.86807i) q^{12} +(0.543628 + 3.56433i) q^{13} +(2.85102 + 2.72293i) q^{14} +(-5.25330 + 5.16411i) q^{15} +(3.98312 - 0.367092i) q^{16} +(-1.79865 + 1.79865i) q^{17} +(11.1029 - 0.255141i) q^{18} -2.06756i q^{19} +(4.46901 - 0.167172i) q^{20} -9.18381i q^{21} +(0.0898542 + 3.91017i) q^{22} +(-1.07900 + 1.07900i) q^{23} +(-7.02693 - 6.11936i) q^{24} +(4.99927 + 0.0856113i) q^{25} +(-5.02174 + 0.884407i) q^{26} +(-11.3051 - 11.3051i) q^{27} +(-3.75716 + 4.11935i) q^{28} +7.19247i q^{29} +(-7.47190 - 7.25955i) q^{30} -2.08767 q^{31} +(0.648419 + 5.61957i) q^{32} +(6.44252 - 6.44252i) q^{33} +(-2.60144 - 2.48457i) q^{34} +(-4.44533 + 4.36986i) q^{35} +(0.721458 + 15.6895i) q^{36} +(2.10529 + 2.10529i) q^{37} +(2.92320 - 0.0671739i) q^{38} +(9.56945 + 7.03670i) q^{39} +(0.381551 + 6.31304i) q^{40} +2.07353i q^{41} +(12.9844 - 0.298378i) q^{42} +(-1.37442 + 1.37442i) q^{43} +(-5.52543 + 0.254079i) q^{44} +(-0.150338 + 17.5593i) q^{45} +(-1.56059 - 1.49048i) q^{46} +(-3.03509 + 3.03509i) q^{47} +(8.42350 - 10.1338i) q^{48} -0.771320i q^{49} +(0.0413830 + 7.07095i) q^{50} +8.37988i q^{51} +(-1.41356 - 7.07120i) q^{52} +(-4.80760 - 4.80760i) q^{53} +(15.6163 - 16.3509i) q^{54} +(-6.18392 - 0.0529453i) q^{55} +(-5.94617 - 5.17819i) q^{56} +(-4.81635 - 4.81635i) q^{57} +(-10.1690 + 0.233680i) q^{58} +9.65260i q^{59} +(10.0211 - 10.7999i) q^{60} +6.83718 q^{61} +(-0.0678274 - 2.95163i) q^{62} +(-15.4800 - 15.4800i) q^{63} +(-7.92411 + 1.09934i) q^{64} +(-1.14731 - 7.98021i) q^{65} +(9.31801 + 8.89938i) q^{66} +(10.5309 - 10.5309i) q^{67} +(3.42827 - 3.75875i) q^{68} +5.02705i q^{69} +(-6.32271 - 6.14301i) q^{70} -3.76638 q^{71} +(-22.1590 + 1.52977i) q^{72} +(-0.228478 + 0.228478i) q^{73} +(-2.90815 + 3.04495i) q^{74} +(11.8452 - 11.4463i) q^{75} +(0.189946 + 4.13075i) q^{76} +(5.45164 - 5.45164i) q^{77} +(-9.63786 + 13.7583i) q^{78} +3.36550 q^{79} +(-8.91323 + 0.744560i) q^{80} -29.1110 q^{81} +(-2.93164 + 0.0673679i) q^{82} +(2.38904 + 2.38904i) q^{83} +(0.843717 + 18.3482i) q^{84} +(4.05619 - 3.98733i) q^{85} +(-1.98786 - 1.89855i) q^{86} +(16.7548 + 16.7548i) q^{87} +(-0.538746 - 7.80383i) q^{88} -3.39594 q^{89} +(-24.8309 + 0.357938i) q^{90} +(8.09764 + 5.95444i) q^{91} +(2.05660 - 2.25486i) q^{92} +(-4.86321 + 4.86321i) q^{93} +(-4.38974 - 4.19252i) q^{94} +(-0.0395813 + 4.62303i) q^{95} +(14.6012 + 11.5802i) q^{96} +(-5.33246 - 5.33246i) q^{97} +(1.09052 - 0.0250598i) q^{98} -21.7186i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) $ 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.0324895	+	1.41384i	0.0229736	+	0.999736i
$2$	0.0324895	+	1.41384i	0.0229736	+	0.999736i
$3$	2.32949	−	2.32949i	1.34493	−	1.34493i	0.453856	−	0.891075i	$-0.350048\pi$
$3$	2.32949	−	2.32949i	1.34493	−	1.34493i	0.891075	−	0.453856i	$-0.149952\pi$
$4$	−1.99789	+	0.0918700i	−0.998944	+	0.0459350i
$5$	−2.23599	−	0.0191440i	−0.999963	−	0.00856145i
$5$	−2.23599	−	0.0191440i	−0.999963	−	0.00856145i
$6$	3.36921	+	3.21784i	1.37547	+	1.31368i
$7$	1.97121	−	1.97121i	0.745047	−	0.745047i	−0.228498	−	0.973544i	$-0.573381\pi$
$7$	1.97121	−	1.97121i	0.745047	−	0.745047i	0.973544	+	0.228498i	$0.0733814\pi$
$8$	−0.194800	−	2.82171i	−0.0688722	−	0.997625i
$9$		−	7.85303i		−	2.61768i
$10$	−0.0455796	−	3.16195i	−0.0144135	−	0.999896i
$11$	2.76564			0.833871			0.416935	−	0.908936i	$-0.363104\pi$
$11$	2.76564			0.833871			0.416935	+	0.908936i	$0.363104\pi$
$12$	−4.44005	+	4.86807i	−1.28173	+	1.40529i
$13$	0.543628	+	3.56433i	0.150775	+	0.988568i
$13$	0.543628	+	3.56433i	0.150775	+	0.988568i
$14$	2.85102	+	2.72293i	0.761966	+	0.727734i
$15$	−5.25330	+	5.16411i	−1.35640	+	1.33337i
$16$	3.98312	−	0.367092i	0.995780	−	0.0917730i
$17$	−1.79865	+	1.79865i	−0.436237	+	0.436237i	−0.890744	−	0.454506i	$-0.849816\pi$
$17$	−1.79865	+	1.79865i	−0.436237	+	0.436237i	0.454506	+	0.890744i	$0.349816\pi$
$18$	11.1029	−	0.255141i	2.61699	−	0.0601374i
$19$		−	2.06756i		−	0.474330i	−0.971469	−	0.237165i	$-0.923782\pi$
$19$		−	2.06756i		−	0.474330i	0.971469	−	0.237165i	$-0.0762182\pi$
$20$	4.46901	−	0.167172i	0.999301	−	0.0373809i
$21$		−	9.18381i		−	2.00407i
$22$	0.0898542	+	3.91017i	0.0191570	+	0.833651i
$23$	−1.07900	+	1.07900i	−0.224988	+	0.224988i	−0.810595	−	0.585607i	$-0.800856\pi$
$23$	−1.07900	+	1.07900i	−0.224988	+	0.224988i	0.585607	+	0.810595i	$0.300856\pi$
$24$	−7.02693	−	6.11936i	−1.43437	−	1.24911i
$25$	4.99927	+	0.0856113i	0.999853	+	0.0171223i
$26$	−5.02174	+	0.884407i	−0.984843	+	0.173446i
$27$	−11.3051	−	11.3051i	−2.17567	−	2.17567i
$28$	−3.75716	+	4.11935i	−0.710036	+	0.778484i
$29$			7.19247i			1.33561i	0.744337	+	0.667804i	$0.232766\pi$
$29$			7.19247i			1.33561i	−0.744337	+	0.667804i	$0.767234\pi$
$30$	−7.47190	−	7.25955i	−1.36418	−	1.32541i
$31$	−2.08767			−0.374957			−0.187478	−	0.982269i	$-0.560031\pi$
$31$	−2.08767			−0.374957			−0.187478	+	0.982269i	$0.560031\pi$
$32$	0.648419	+	5.61957i	0.114625	+	0.993409i
$33$	6.44252	−	6.44252i	1.12150	−	1.12150i
$34$	−2.60144	−	2.48457i	−0.446144	−	0.426100i
$35$	−4.44533	+	4.36986i	−0.751398	+	0.738641i
$36$	0.721458	+	15.6895i	0.120243	+	2.61491i
$37$	2.10529	+	2.10529i	0.346108	+	0.346108i	0.858658	−	0.512549i	$-0.171299\pi$
$37$	2.10529	+	2.10529i	0.346108	+	0.346108i	−0.512549	+	0.858658i	$0.671299\pi$
$38$	2.92320	−	0.0671739i	0.474205	−	0.0108971i
$39$	9.56945	+	7.03670i	1.53234	+	1.12677i
$40$	0.381551	+	6.31304i	0.0603285	+	0.998179i
$41$			2.07353i			0.323831i	0.986805	+	0.161915i	$0.0517671\pi$
$41$			2.07353i			0.323831i	−0.986805	+	0.161915i	$0.948233\pi$
$42$	12.9844	−	0.298378i	2.00354	−	0.0460407i
$43$	−1.37442	+	1.37442i	−0.209596	+	0.209596i	−0.804096	−	0.594500i	$-0.797350\pi$
$43$	−1.37442	+	1.37442i	−0.209596	+	0.209596i	0.594500	+	0.804096i	$0.297350\pi$
$44$	−5.52543	+	0.254079i	−0.832991	+	0.0383038i
$45$	−0.150338	+	17.5593i	−0.0224111	+	2.61758i
$46$	−1.56059	−	1.49048i	−0.230097	−	0.219760i
$47$	−3.03509	+	3.03509i	−0.442713	+	0.442713i	−0.892923	−	0.450210i	$-0.851349\pi$
$47$	−3.03509	+	3.03509i	−0.442713	+	0.442713i	0.450210	+	0.892923i	$0.351349\pi$
$48$	8.42350	−	10.1338i	1.21583	−	1.46268i
$49$		−	0.771320i		−	0.110189i
$50$	0.0413830	+	7.07095i	0.00585244	+	0.999983i
$51$			8.37988i			1.17342i
$52$	−1.41356	−	7.07120i	−0.196026	−	0.980599i
$53$	−4.80760	−	4.80760i	−0.660375	−	0.660375i	0.295093	−	0.955468i	$-0.404649\pi$
$53$	−4.80760	−	4.80760i	−0.660375	−	0.660375i	−0.955468	+	0.295093i	$0.904649\pi$
$54$	15.6163	−	16.3509i	2.12511	−	2.22507i
$55$	−6.18392	−	0.0529453i	−0.833840	−	0.00713914i
$56$	−5.94617	−	5.17819i	−0.794590	−	0.691964i
$57$	−4.81635	−	4.81635i	−0.637941	−	0.637941i
$58$	−10.1690	+	0.233680i	−1.33526	+	0.0306837i
$59$			9.65260i			1.25666i	0.777947	+	0.628330i	$0.216261\pi$
$59$			9.65260i			1.25666i	−0.777947	+	0.628330i	$0.783739\pi$
$60$	10.0211	−	10.7999i	1.29372	−	1.39427i
$61$	6.83718			0.875412			0.437706	−	0.899118i	$-0.355791\pi$
$61$	6.83718			0.875412			0.437706	+	0.899118i	$0.355791\pi$
$62$	−0.0678274	−	2.95163i	−0.00861409	−	0.374858i
$63$	−15.4800	−	15.4800i	−1.95029	−	1.95029i
$64$	−7.92411	+	1.09934i	−0.990513	+	0.137417i
$65$	−1.14731	−	7.98021i	−0.142306	−	0.989823i
$66$	9.31801	+	8.89938i	1.14697	+	1.09544i
$67$	10.5309	−	10.5309i	1.28656	−	1.28656i	0.349695	−	0.936864i	$-0.386285\pi$
$67$	10.5309	−	10.5309i	1.28656	−	1.28656i	0.936864	−	0.349695i	$-0.113715\pi$
$68$	3.42827	−	3.75875i	0.415738	−	0.455815i
$69$			5.02705i			0.605186i
$70$	−6.32271	−	6.14301i	−0.755708	−	0.734230i
$71$	−3.76638			−0.446987			−0.223493	−	0.974705i	$-0.571746\pi$
$71$	−3.76638			−0.446987			−0.223493	+	0.974705i	$0.571746\pi$
$72$	−22.1590	+	1.52977i	−2.61146	+	0.180285i
$73$	−0.228478	+	0.228478i	−0.0267413	+	0.0267413i	−0.720351	−	0.693610i	$-0.756019\pi$
$73$	−0.228478	+	0.228478i	−0.0267413	+	0.0267413i	0.693610	+	0.720351i	$0.256019\pi$
$74$	−2.90815	+	3.04495i	−0.338066	+	0.353968i
$75$	11.8452	−	11.4463i	1.36776	−	1.32171i
$76$	0.189946	+	4.13075i	0.0217884	+	0.473830i
$77$	5.45164	−	5.45164i	0.621273	−	0.621273i
$78$	−9.63786	+	13.7583i	−1.09127	+	1.55782i
$79$	3.36550			0.378648			0.189324	−	0.981915i	$-0.439370\pi$
$79$	3.36550			0.378648			0.189324	+	0.981915i	$0.439370\pi$
$80$	−8.91323	+	0.744560i	−0.996529	+	0.0832443i
$81$	−29.1110			−3.23456
$82$	−2.93164	+	0.0673679i	−0.323745	+	0.00743954i
$83$	2.38904	+	2.38904i	0.262232	+	0.262232i	0.825960	−	0.563729i	$-0.190634\pi$
$83$	2.38904	+	2.38904i	0.262232	+	0.262232i	−0.563729	+	0.825960i	$0.690634\pi$
$84$	0.843717	+	18.3482i	0.0920570	+	2.00196i
$85$	4.05619	−	3.98733i	0.439956	−	0.432486i
$86$	−1.98786	−	1.89855i	−0.214356	−	0.204726i
$87$	16.7548	+	16.7548i	1.79630	+	1.79630i
$88$	−0.538746	−	7.80383i	−0.0574305	−	0.831891i
$89$	−3.39594			−0.359969			−0.179985	−	0.983669i	$-0.557605\pi$
$89$	−3.39594			−0.359969			−0.179985	+	0.983669i	$0.557605\pi$
$90$	−24.8309	+	0.357938i	−2.61741	+	0.0377300i
$91$	8.09764	+	5.95444i	0.848864	+	0.624195i
$92$	2.05660	−	2.25486i	0.214415	−	0.235085i
$93$	−4.86321	+	4.86321i	−0.504291	+	0.504291i
$94$	−4.38974	−	4.19252i	−0.452767	−	0.432426i
$95$	−0.0395813	+	4.62303i	−0.00406095	+	0.474313i
$96$	14.6012	+	11.5802i	1.49023	+	1.18190i
$97$	−5.33246	−	5.33246i	−0.541430	−	0.541430i	0.382518	−	0.923948i	$-0.375057\pi$
$97$	−5.33246	−	5.33246i	−0.541430	−	0.541430i	−0.923948	+	0.382518i	$0.875057\pi$
$98$	1.09052	−	0.0250598i	0.110160	−	0.00253142i
$99$		−	21.7186i		−	2.18281i
$100$	−9.99585	+	0.288241i	−0.999585	+	0.0288241i
$101$	2.70868			0.269524			0.134762	−	0.990878i	$-0.456973\pi$
$101$	2.70868			0.269524			0.134762	+	0.990878i	$0.456973\pi$
$102$	−11.8478	+	0.272258i	−1.17311	+	0.0269576i
$103$	−2.34247	+	2.34247i	−0.230810	+	0.230810i	−0.813031	−	0.582221i	$-0.802184\pi$
$103$	−2.34247	+	2.34247i	−0.230810	+	0.230810i	0.582221	+	0.813031i	$0.302184\pi$
$104$	9.95162	−	2.22829i	0.975836	−	0.218502i
$105$	−0.175815	+	20.5349i	−0.0171578	+	2.00400i
$106$	6.64098	−	6.95338i	0.645029	−	0.675372i
$107$	−4.03232	−	4.03232i	−0.389819	−	0.389819i	0.484804	−	0.874623i	$-0.338891\pi$
$107$	−4.03232	−	4.03232i	−0.389819	−	0.389819i	−0.874623	+	0.484804i	$0.838891\pi$
$108$	23.6249	+	21.5477i	2.27331	+	2.07343i
$109$	13.2900			1.27295			0.636477	−	0.771296i	$-0.280391\pi$
$109$	13.2900			1.27295			0.636477	+	0.771296i	$0.280391\pi$
$110$	−0.126057	−	8.74480i	−0.0120190	−	0.833784i
$111$	9.80852			0.930984
$112$	7.12794	−	8.57517i	0.673527	−	0.810278i
$113$	−8.26021	−	8.26021i	−0.777055	−	0.777055i	0.202274	−	0.979329i	$-0.435167\pi$
$113$	−8.26021	−	8.26021i	−0.777055	−	0.777055i	−0.979329	+	0.202274i	$0.935167\pi$
$114$	6.65307	−	6.96603i	0.623117	−	0.652429i
$115$	2.43329	−	2.39198i	0.226906	−	0.223053i
$116$	−0.660772	−	14.3698i	−0.0613511	−	1.33420i
$117$	27.9908	−	4.26913i	2.58775	−	0.394681i
$118$	−13.6472	+	0.313608i	−1.25633	+	0.0288700i
$119$			7.09103i			0.650034i
$120$	15.5950	+	13.8173i	1.42362	+	1.26134i
$121$	−3.35125			−0.304659
$122$	0.222137	+	9.66669i	0.0201113	+	0.875181i
$123$	4.83026	+	4.83026i	0.435530	+	0.435530i
$124$	4.17094	−	0.191794i	0.374561	−	0.0172236i
$125$	−11.1767	−	0.287132i	−0.999670	−	0.0256818i
$126$	21.3833	−	22.3891i	1.90497	−	1.99458i
$127$	−11.0132	−	11.0132i	−0.977260	−	0.977260i	0.0224874	−	0.999747i	$-0.492841\pi$
$127$	−11.0132	−	11.0132i	−0.977260	−	0.977260i	−0.999747	+	0.0224874i	$0.992841\pi$
$128$	−1.81174	−	11.1677i	−0.160137	−	0.987095i
$129$			6.40337i			0.563785i
$130$	11.2455	−	1.88139i	0.986292	−	0.165008i
$131$			0.116373i			0.0101676i	0.999987	+	0.00508378i	$0.00161822\pi$
$131$			0.116373i			0.0101676i	−0.999987	+	0.00508378i	$0.998382\pi$
$132$	−12.2796	+	13.4633i	−1.06880	+	1.17183i
$133$	−4.07559	−	4.07559i	−0.353398	−	0.353398i
$134$	15.2312	+	14.5469i	1.31578	+	1.25666i
$135$	25.0616	+	25.4944i	2.15696	+	2.19421i
$136$	5.42565	+	4.72490i	0.465246	+	0.405157i
$137$	11.3786	+	11.3786i	0.972143	+	0.972143i	0.999622	−	0.0274794i	$-0.00874807\pi$
$137$	11.3786	+	11.3786i	0.972143	+	0.972143i	−0.0274794	+	0.999622i	$0.508748\pi$
$138$	−7.10745	+	0.163326i	−0.605026	+	0.0139033i
$139$	13.9762			1.18545			0.592725	−	0.805405i	$-0.298052\pi$
$139$	13.9762			1.18545			0.592725	+	0.805405i	$0.298052\pi$
$140$	8.47982	−	9.13888i	0.716675	−	0.772376i
$141$			14.1404i			1.19084i
$142$	−0.122368	−	5.32506i	−0.0102689	−	0.446869i
$143$	1.50348	+	9.85765i	0.125727	+	0.824338i
$144$	−2.88279	−	31.2796i	−0.240232	−	2.60663i
$145$	0.137692	−	16.0823i	0.0114347	−	1.33556i
$146$	−0.330454	−	0.315608i	−0.0273486	−	0.0261199i
$147$	−1.79678	−	1.79678i	−0.148196	−	0.148196i
$148$	−4.39956	−	4.01273i	−0.361641	−	0.329845i
$149$	10.9656			0.898337			0.449169	−	0.893447i	$-0.351720\pi$
$149$	10.9656			0.898337			0.449169	+	0.893447i	$0.351720\pi$
$150$	16.5681	+	16.3753i	1.35278	+	1.33704i
$151$	−17.6591			−1.43708			−0.718540	−	0.695486i	$-0.755189\pi$
$151$	−17.6591			−1.43708			−0.718540	+	0.695486i	$0.755189\pi$
$152$	−5.83405	+	0.402760i	−0.473204	+	0.0326682i
$153$	14.1249	+	14.1249i	1.14193	+	1.14193i
$154$	7.88488	+	7.53063i	0.635381	+	0.606836i
$155$	4.66800	+	0.0399663i	0.374943	+	0.00321017i
$156$	−19.7652	−	13.1794i	−1.58248	−	1.05520i
$157$	−13.6301	+	13.6301i	−1.08780	+	1.08780i	−0.0920491	+	0.995754i	$0.529342\pi$
$157$	−13.6301	+	13.6301i	−1.08780	+	1.08780i	−0.995754	+	0.0920491i	$0.970658\pi$
$158$	0.109344	+	4.75828i	0.00869890	+	0.378549i
$159$	−22.3985			−1.77632
$160$	−1.34228	−	12.5777i	−0.106116	−	0.994354i
$161$			4.25388i			0.335253i
$162$	−0.945804	−	41.1584i	−0.0743094	−	3.23371i
$163$	−4.50085	−	4.50085i	−0.352534	−	0.352534i	0.508518	−	0.861052i	$-0.330194\pi$
$163$	−4.50085	−	4.50085i	−0.352534	−	0.352534i	−0.861052	+	0.508518i	$0.830194\pi$
$164$	−0.190495	−	4.14268i	−0.0148752	−	0.323489i
$165$	−14.5287	+	14.2820i	−1.13106	+	1.11186i
$166$	−3.30011	+	3.45535i	−0.256138	+	0.268187i
$167$	7.06397	−	7.06397i	0.546626	−	0.546626i	−0.378837	−	0.925463i	$-0.623676\pi$
$167$	7.06397	−	7.06397i	0.546626	−	0.546626i	0.925463	+	0.378837i	$0.123676\pi$
$168$	−25.9141	+	1.78901i	−1.99931	+	0.138025i
$169$	−12.4089	+	3.87534i	−0.954534	+	0.298103i
$170$	5.76923	+	5.60527i	0.442480	+	0.429904i
$171$	−16.2366			−1.24164
$172$	2.61966	−	2.87220i	0.199747	−	0.219003i
$173$	2.54024	+	2.54024i	0.193131	+	0.193131i	0.797047	−	0.603917i	$-0.206394\pi$
$173$	2.54024	+	2.54024i	0.193131	+	0.193131i	−0.603917	+	0.797047i	$0.706394\pi$
$174$	−23.1442	+	24.2329i	−1.75456	+	1.83709i
$175$	10.0234	−	9.68584i	0.757694	−	0.732180i
$176$	11.0159	−	1.01524i	0.830352	−	0.0765268i
$177$	22.4856	+	22.4856i	1.69012	+	1.69012i
$178$	−0.110333	−	4.80132i	−0.00826978	−	0.359874i
$179$	0.176655			0.0132038			0.00660192	−	0.999978i	$-0.497899\pi$
$179$	0.176655			0.0132038			0.00660192	+	0.999978i	$0.497899\pi$
$180$	−1.31281	−	35.0953i	−0.0978511	−	2.61585i
$181$	13.6105			1.01166			0.505828	−	0.862634i	$-0.331187\pi$
$181$	13.6105			1.01166			0.505828	+	0.862634i	$0.331187\pi$
$182$	−8.15553	+	11.6422i	−0.604528	+	0.862980i
$183$	15.9271	−	15.9271i	1.17737	−	1.17737i
$184$	3.25482	+	2.83444i	0.239949	+	0.208958i
$185$	−4.66711	−	4.74771i	−0.343132	−	0.349059i
$186$	−7.03380	−	6.71779i	−0.515743	−	0.492573i
$187$	−4.97442	+	4.97442i	−0.363765	+	0.363765i
$188$	5.78494	−	6.34261i	0.421910	−	0.462582i
$189$	−44.5694			−3.24194
$190$	−6.53751	+	0.0942384i	−0.474281	+	0.00683677i
$191$			13.9159i			1.00692i	0.864020	+	0.503458i	$0.167939\pi$
$191$			13.9159i			1.00692i	−0.864020	+	0.503458i	$0.832061\pi$
$192$	−15.8982	+	21.0200i	−1.14736	+	1.51699i
$193$	17.4956	−	17.4956i	1.25936	−	1.25936i	0.307964	−	0.951398i	$-0.400352\pi$
$193$	17.4956	−	17.4956i	1.25936	−	1.25936i	0.951398	−	0.307964i	$-0.0996478\pi$
$194$	7.36600	−	7.71250i	0.528848	−	0.553725i
$195$	−21.2624	−	15.9172i	−1.52264	−	1.13985i
$196$	0.0708612	+	1.54101i	0.00506151	+	0.110072i
$197$	−1.46918	−	1.46918i	−0.104675	−	0.104675i	0.652830	−	0.757505i	$-0.273582\pi$
$197$	−1.46918	−	1.46918i	−0.104675	−	0.104675i	−0.757505	+	0.652830i	$0.773582\pi$
$198$	30.7067	−	0.705628i	2.18223	−	0.0501468i
$199$	−12.6116			−0.894010			−0.447005	−	0.894531i	$-0.647509\pi$
$199$	−12.6116			−0.894010			−0.447005	+	0.894531i	$0.647509\pi$
$200$	−0.732286	−	14.1232i	−0.0517805	−	0.998658i
$201$		−	49.0634i		−	3.46066i
$202$	0.0880037	+	3.82964i	0.00619192	+	0.269453i
$203$	14.1778	+	14.1778i	0.995090	+	0.995090i
$204$	−0.769859	−	16.7421i	−0.0539009	−	1.17218i
$205$	0.0396956	−	4.63638i	0.00277246	−	0.323819i
$206$	−3.38798	−	3.23577i	−0.236052	−	0.225447i
$207$	8.47345	+	8.47345i	0.588945	+	0.588945i
$208$	3.47377	+	13.9976i	0.240863	+	0.970559i
$209$		−	5.71811i		−	0.395530i
$210$	−29.0387	+	0.418594i	−2.00386	+	0.0288857i
$211$			1.88981i			0.130100i	0.997882	+	0.0650498i	$0.0207206\pi$
$211$			1.88981i			0.130100i	−0.997882	+	0.0650498i	$0.979279\pi$
$212$	10.0467	+	9.16338i	0.690012	+	0.629344i
$213$	−8.77373	+	8.77373i	−0.601166	+	0.601166i
$214$	5.57005	−	5.83206i	0.380760	−	0.398671i
$215$	3.09949	−	3.04686i	0.211383	−	0.207794i
$216$	−29.6975	+	34.1019i	−2.02066	+	2.32034i
$217$	−4.11523	+	4.11523i	−0.279360	+	0.279360i
$218$	0.431787	+	18.7900i	0.0292443	+	1.27262i
$219$			1.06447i			0.0719305i
$220$	12.3597	−	0.462338i	0.833288	−	0.0311708i
$221$	−7.38879	−	5.43320i	−0.497024	−	0.365476i
$222$	0.318674	+	13.8677i	0.0213880	+	0.930738i
$223$	−16.9564	−	16.9564i	−1.13548	−	1.13548i	−0.989250	−	0.146235i	$-0.953285\pi$
$223$	−16.9564	−	16.9564i	−1.13548	−	1.13548i	−0.146235	−	0.989250i	$-0.546715\pi$
$224$	12.3555	+	9.79917i	0.825537	+	0.654735i
$225$	0.672309	−	39.2594i	0.0448206	−	2.61729i
$226$	11.4102	−	11.9470i	0.758998	−	0.794702i
$227$	−11.9034	+	11.9034i	−0.790053	+	0.790053i	−0.981502	−	0.191449i	$-0.938681\pi$
$227$	−11.9034	+	11.9034i	−0.790053	+	0.790053i	0.191449	+	0.981502i	$0.438681\pi$
$228$	10.0650	+	9.18006i	0.666572	+	0.607964i
$229$	−11.3479			−0.749888			−0.374944	−	0.927048i	$-0.622338\pi$
$229$	−11.3479			−0.749888			−0.374944	+	0.927048i	$0.622338\pi$
$230$	3.46093	+	3.36257i	0.228207	+	0.221721i
$231$		−	25.3991i		−	1.67114i
$232$	20.2951	−	1.40109i	1.33244	−	0.0919862i
$233$	−13.9055	−	13.9055i	−0.910979	−	0.910979i	0.0853703	−	0.996349i	$-0.472793\pi$
$233$	−13.9055	−	13.9055i	−0.910979	−	0.910979i	−0.996349	+	0.0853703i	$0.972793\pi$
$234$	6.94528	+	39.4359i	0.454027	+	2.57800i
$235$	6.84452	−	6.72832i	0.446487	−	0.438907i
$236$	−0.886784	−	19.2848i	−0.0577247	−	1.25533i
$237$	7.83990	−	7.83990i	0.509256	−	0.509256i
$238$	−10.0256	+	0.230384i	−0.649862	+	0.0149336i
$239$		−	14.6554i		−	0.947981i	−0.880530	−	0.473991i	$-0.842813\pi$
$239$		−	14.6554i		−	0.947981i	0.880530	−	0.473991i	$-0.157187\pi$
$240$	−19.0288	+	22.4977i	−1.22830	+	1.45222i
$241$			21.9420i			1.41341i	0.707511	+	0.706703i	$0.249818\pi$
$241$			21.9420i			1.41341i	−0.707511	+	0.706703i	$0.750182\pi$
$242$	−0.108881	−	4.73814i	−0.00699911	−	0.304579i
$243$	−33.8986	+	33.8986i	−2.17460	+	2.17460i
$244$	−13.6599	+	0.628132i	−0.874488	+	0.0402120i
$245$	−0.0147661	+	1.72466i	−0.000943374	+	0.110185i
$246$	−6.67228	+	6.98615i	−0.425409	+	0.445421i
$247$	7.36946	−	1.12398i	0.468908	−	0.0715173i
$248$	0.406678	+	5.89081i	0.0258241	+	0.374066i
$249$	11.1305			0.705367
$250$	0.0428343	−	15.8113i	0.00270908	−	0.999996i
$251$			17.7075i			1.11769i	0.829273	+	0.558843i	$0.188755\pi$
$251$			17.7075i			1.11769i	−0.829273	+	0.558843i	$0.811245\pi$
$252$	32.3494	+	29.5051i	2.03782	+	1.85865i
$253$	−2.98413	+	2.98413i	−0.187611	+	0.187611i
$254$	15.2130	−	15.9287i	0.954551	−	0.999453i
$255$	0.160424	−	18.7373i	0.0100462	−	1.17337i
$256$	15.7305	−	2.92434i	0.983155	−	0.182771i
$257$	9.61099	−	9.61099i	0.599517	−	0.599517i	−0.340667	−	0.940184i	$-0.610653\pi$
$257$	9.61099	−	9.61099i	0.599517	−	0.599517i	0.940184	+	0.340667i	$0.110653\pi$
$258$	−9.05334	+	0.208042i	−0.563637	+	0.0129522i
$259$	8.29995			0.515734
$260$	3.02534	+	15.8382i	0.187624	+	0.982241i
$261$	56.4827			3.49619
$262$	−0.164533	+	0.00378090i	−0.0101649	+	0.000233585i
$263$	−0.442921	+	0.442921i	−0.0273117	+	0.0273117i	−0.720631	−	0.693319i	$-0.756148\pi$
$263$	−0.442921	+	0.442921i	−0.0273117	+	0.0273117i	0.693319	+	0.720631i	$0.256148\pi$
$264$	−19.4339	−	16.9239i	−1.19608	−	1.04160i
$265$	10.6577	+	10.8418i	0.654697	+	0.666004i
$266$	5.62981	−	5.89464i	0.345186	−	0.361424i
$267$	−7.91081	+	7.91081i	−0.484134	+	0.484134i
$268$	−20.0722	+	22.0071i	−1.22610	+	1.34430i
$269$		−	19.9649i		−	1.21728i	−0.793446	−	0.608641i	$-0.791715\pi$
$269$		−	19.9649i		−	1.21728i	0.793446	−	0.608641i	$-0.208285\pi$
$270$	−35.2308	+	36.2614i	−2.14408	+	2.20680i
$271$	−19.6206			−1.19186			−0.595932	−	0.803035i	$-0.703217\pi$
$271$	−19.6206			−1.19186			−0.595932	+	0.803035i	$0.703217\pi$
$272$	−6.50398	+	7.82452i	−0.394361	+	0.474431i
$273$	32.7342	−	4.99258i	1.98116	−	0.302165i
$274$	−15.7179	+	16.4573i	−0.949553	+	0.994220i
$275$	13.8262	+	0.236770i	0.833749	+	0.0142778i
$276$	−0.461835	−	10.0435i	−0.0277992	−	0.604547i
$277$	−2.71322	+	2.71322i	−0.163022	+	0.163022i	−0.783904	−	0.620882i	$-0.786775\pi$
$277$	−2.71322	+	2.71322i	−0.163022	+	0.163022i	0.620882	+	0.783904i	$0.286775\pi$
$278$	0.454081	+	19.7602i	0.0272340	+	1.18514i
$279$			16.3946i			0.981516i
$280$	13.1964	+	11.6922i	0.788637	+	0.698742i
$281$			10.7683i			0.642383i	0.947014	+	0.321191i	$0.104083\pi$
$281$			10.7683i			0.642383i	−0.947014	+	0.321191i	$0.895917\pi$
$282$	−19.9923	+	0.459415i	−1.19052	+	0.0273578i
$283$	9.22116	−	9.22116i	0.548141	−	0.548141i	−0.377762	−	0.925903i	$-0.623306\pi$
$283$	9.22116	−	9.22116i	0.548141	−	0.548141i	0.925903	+	0.377762i	$0.123306\pi$
$284$	7.52480	−	0.346017i	0.446515	−	0.0205323i
$285$	10.6771	+	10.8615i	0.632456	+	0.643380i
$286$	−13.8883	+	2.44595i	−0.821232	+	0.144632i
$287$	4.08735	+	4.08735i	0.241269	+	0.241269i
$288$	44.1307	−	5.09206i	2.60042	−	0.300052i
$289$			10.5297i			0.619394i
$290$	22.7422	−	0.327830i	1.33547	−	0.0192508i
$291$	−24.8438			−1.45637
$292$	0.435483	−	0.477464i	0.0254847	−	0.0279415i
$293$	−1.67405	+	1.67405i	−0.0977990	+	0.0977990i	−0.754313	−	0.656514i	$-0.772030\pi$
$293$	−1.67405	+	1.67405i	−0.0977990	+	0.0977990i	0.656514	+	0.754313i	$0.272030\pi$
$294$	2.48199	−	2.59874i	0.144752	−	0.151562i
$295$	0.184789	−	21.5831i	0.0107588	−	1.25661i
$296$	5.53042	−	6.35064i	0.321449	−	0.369124i
$297$	−31.2658	−	31.2658i	−1.81422	−	1.81422i
$298$	0.356267	+	15.5036i	0.0206380	+	0.898100i
$299$	−4.43250	−	3.25935i	−0.256338	−	0.188493i
$300$	−22.6138	+	23.9567i	−1.30561	+	1.38314i
$301$			5.41852i			0.312318i
$302$	−0.573736	−	24.9672i	−0.0330148	−	1.43670i
$303$	6.30984	−	6.30984i	0.362491	−	0.362491i
$304$	−0.758984	−	8.23533i	−0.0435307	−	0.472329i
$305$	−15.2878	−	0.130891i	−0.875380	−	0.00749479i
$306$	−19.5114	+	20.4292i	−1.11539	+	1.16786i
$307$	−19.6500	+	19.6500i	−1.12149	+	1.12149i	−0.129968	+	0.991518i	$0.541487\pi$
$307$	−19.6500	+	19.6500i	−1.12149	+	1.12149i	−0.991518	+	0.129968i	$0.958513\pi$
$308$	−10.3909	+	11.3926i	−0.592079	+	0.649155i
$309$			10.9135i			0.620847i
$310$	0.0951552	+	6.60111i	0.00540445	+	0.374918i
$311$		−	33.7067i		−	1.91133i	−0.294458	−	0.955664i	$-0.595139\pi$
$311$		−	33.7067i		−	1.91133i	0.294458	−	0.955664i	$-0.404861\pi$
$312$	17.9914	−	28.3730i	1.01856	−	1.60630i
$313$	−14.3198	−	14.3198i	−0.809405	−	0.809405i	0.175139	−	0.984544i	$-0.443963\pi$
$313$	−14.3198	−	14.3198i	−0.809405	−	0.809405i	−0.984544	+	0.175139i	$0.943963\pi$
$314$	−19.7137	−	18.8280i	−1.11251	−	1.06253i
$315$	34.3166	+	34.9093i	1.93352	+	1.96692i
$316$	−6.72390	+	0.309189i	−0.378249	+	0.0173932i
$317$	−19.1858	−	19.1858i	−1.07758	−	1.07758i	−0.996726	−	0.0808584i	$-0.974234\pi$
$317$	−19.1858	−	19.1858i	−1.07758	−	1.07758i	−0.0808584	−	0.996726i	$-0.525766\pi$
$318$	−0.727717	−	31.6679i	−0.0408083	−	1.77585i
$319$			19.8918i			1.11372i
$320$	17.7392	−	2.30641i	0.991653	−	0.128932i
$321$	−18.7865			−1.04856
$322$	−6.01430	+	0.138206i	−0.335164	+	0.00770194i
$323$	3.71882	+	3.71882i	0.206921	+	0.206921i
$324$	58.1606	−	2.67443i	3.23115	−	0.148579i
$325$	2.41260	+	17.8656i	0.133827	+	0.991005i
$326$	6.21725	−	6.50971i	0.344342	−	0.360540i
$327$	30.9590	−	30.9590i	1.71204	−	1.71204i
$328$	5.85090	−	0.403923i	0.323062	−	0.0223029i
$329$			11.9656i			0.659684i
$330$	−20.6646	−	20.0773i	−1.13755	−	1.10522i
$331$	13.7338			0.754877			0.377439	−	0.926035i	$-0.376805\pi$
$331$	13.7338			0.754877			0.377439	+	0.926035i	$0.376805\pi$
$332$	−4.99253	−	4.55356i	−0.274000	−	0.249909i
$333$	16.5330	−	16.5330i	0.906000	−	0.906000i
$334$	10.2168	+	9.75782i	0.559040	+	0.533924i
$335$	−23.7486	+	23.3454i	−1.29753	+	1.27550i
$336$	−3.37130	−	36.5802i	−0.183920	−	1.99561i
$337$	−7.13548	+	7.13548i	−0.388694	+	0.388694i	−0.874221	−	0.485527i	$-0.838628\pi$
$337$	−7.13548	+	7.13548i	−0.388694	+	0.388694i	0.485527	+	0.874221i	$0.338628\pi$
$338$	−5.88228	−	17.4183i	−0.319954	−	0.947433i
$339$	−38.4841			−2.09017
$340$	−7.73751	+	8.33888i	−0.419625	+	0.452239i
$341$	−5.77374			−0.312666
$342$	−0.527519	−	22.9560i	−0.0285250	−	1.24132i
$343$	12.2780	+	12.2780i	0.662951	+	0.662951i
$344$	4.14594	+	3.61047i	0.223534	+	0.194663i
$345$	0.0962377	−	11.2404i	0.00518127	−	0.605164i
$346$	−3.50896	+	3.67402i	−0.188643	+	0.197517i
$347$	−22.6909	−	22.6909i	−1.21811	−	1.21811i	−0.968293	−	0.249817i	$-0.919630\pi$
$347$	−22.6909	−	22.6909i	−1.21811	−	1.21811i	−0.249817	−	0.968293i	$-0.580370\pi$
$348$	−35.0134	−	31.9349i	−1.87692	−	1.71189i
$349$	17.6400			0.944247			0.472124	−	0.881532i	$-0.343488\pi$
$349$	17.6400			0.944247			0.472124	+	0.881532i	$0.343488\pi$
$350$	14.0199	+	13.8567i	0.749394	+	0.740673i
$351$	34.1493	−	46.4409i	1.82276	−	2.47883i
$352$	1.79329	+	15.5417i	0.0955828	+	0.828375i
$353$	−24.4668	+	24.4668i	−1.30224	+	1.30224i	−0.375359	+	0.926879i	$0.622481\pi$
$353$	−24.4668	+	24.4668i	−1.30224	+	1.30224i	−0.926879	+	0.375359i	$0.877519\pi$
$354$	−31.0605	+	32.5216i	−1.65085	+	1.72850i
$355$	8.42157	+	0.0721034i	0.446970	+	0.00382685i
$356$	6.78472	−	0.311985i	0.359589	−	0.0165352i
$357$	16.5185	+	16.5185i	0.874251	+	0.874251i
$358$	0.00573945	+	0.249762i	0.000303339	+	0.0132004i
$359$		−	26.5212i		−	1.39973i	−0.714273	−	0.699867i	$-0.753243\pi$
$359$		−	26.5212i		−	1.39973i	0.714273	−	0.699867i	$-0.246757\pi$
$360$	49.5765	−	2.99633i	2.61291	−	0.157921i
$361$	14.7252			0.775011
$362$	0.442197	+	19.2430i	0.0232414	+	1.01139i
$363$	−7.80671	+	7.80671i	−0.409746	+	0.409746i
$364$	−16.7252	−	11.1524i	−0.876640	−	0.584543i
$365$	0.515247	−	0.506499i	0.0269693	−	0.0265114i
$366$	23.0359	+	22.0010i	1.20411	+	1.15001i
$367$	5.52850	+	5.52850i	0.288586	+	0.288586i	0.836521	−	0.547935i	$-0.184586\pi$
$367$	5.52850	+	5.52850i	0.288586	+	0.288586i	−0.547935	+	0.836521i	$0.684586\pi$
$368$	−3.90170	+	4.69389i	−0.203390	+	0.244686i
$369$	16.2835			0.847684
$370$	6.56088	−	6.75279i	0.341084	−	0.351061i
$371$	−18.9536			−0.984020
$372$	9.26936	−	10.1629i	0.480594	−	0.526923i
$373$	−13.6242	−	13.6242i	−0.705432	−	0.705432i	0.260139	−	0.965571i	$-0.416232\pi$
$373$	−13.6242	−	13.6242i	−0.705432	−	0.705432i	−0.965571	+	0.260139i	$0.916232\pi$
$374$	−7.19465	−	6.87142i	−0.372026	−	0.355312i
$375$	−26.7048	+	25.3670i	−1.37903	+	1.30995i
$376$	9.15538	+	7.97291i	0.472153	+	0.411172i
$377$	−25.6364	+	3.91003i	−1.32034	+	0.201377i
$378$	−1.44804	−	63.0140i	−0.0744790	−	3.24109i
$379$			26.5880i			1.36574i	0.730542	+	0.682868i	$0.239268\pi$
$379$			26.5880i			1.36574i	−0.730542	+	0.682868i	$0.760732\pi$
$380$	−0.345639	−	9.23994i	−0.0177309	−	0.473999i
$381$	−51.3101			−2.62869
$382$	−19.6748	+	0.452119i	−1.00665	+	0.0231324i
$383$	8.03967	+	8.03967i	0.410808	+	0.410808i	0.882020	−	0.471212i	$-0.156183\pi$
$383$	8.03967	+	8.03967i	0.410808	+	0.410808i	−0.471212	+	0.882020i	$0.656183\pi$
$384$	−30.2355	−	21.7946i	−1.54295	−	1.11220i
$385$	−12.2942	+	12.0854i	−0.626569	+	0.615931i
$386$	25.3044	+	24.1676i	1.28796	+	1.23010i
$387$	10.7933	+	10.7933i	0.548656	+	0.548656i
$388$	11.1436	+	10.1638i	0.565729	+	0.515988i
$389$		−	15.3855i		−	0.780076i	−0.920799	−	0.390038i	$-0.872462\pi$
$389$		−	15.3855i		−	0.780076i	0.920799	−	0.390038i	$-0.127538\pi$
$390$	21.8135	−	30.5788i	1.10457	−	1.54842i
$391$		−	3.88150i		−	0.196296i
$392$	−2.17644	+	0.150253i	−0.109927	+	0.00758893i
$393$	0.271090	+	0.271090i	0.0136747	+	0.0136747i
$394$	2.02945	−	2.12492i	0.102242	−	0.107052i
$395$	−7.52521	−	0.0644291i	−0.378635	−	0.00324178i
$396$	1.99529	+	43.3914i	0.100267	+	2.18050i
$397$	0.850203	+	0.850203i	0.0426705	+	0.0426705i	0.728120	−	0.685450i	$-0.240394\pi$
$397$	0.850203	+	0.850203i	0.0426705	+	0.0426705i	−0.685450	+	0.728120i	$0.740394\pi$
$398$	−0.409744	−	17.8307i	−0.0205386	−	0.893774i
$399$	−18.9881			−0.950592
$400$	19.9441	−	1.49419i	0.997205	−	0.0747095i
$401$		−	2.07340i		−	0.103541i	−0.998659	−	0.0517704i	$-0.983514\pi$
$401$		−	2.07340i		−	0.103541i	0.998659	−	0.0517704i	$-0.0164864\pi$
$402$	69.3678	−	1.59405i	3.45975	−	0.0795038i
$403$	−1.13492	−	7.44116i	−0.0565342	−	0.370670i
$404$	−5.41164	+	0.248846i	−0.269239	+	0.0123806i
$405$	65.0919	+	0.557301i	3.23444	+	0.0276925i
$406$	−19.5846	+	20.5058i	−0.971967	+	1.01769i
$407$	5.82248	+	5.82248i	0.288610	+	0.288610i
$408$	23.6456	−	1.63240i	1.17063	−	0.0808158i
$409$	5.67158			0.280442			0.140221	−	0.990120i	$-0.455219\pi$
$409$	5.67158			0.280442			0.140221	+	0.990120i	$0.455219\pi$
$410$	6.55639	−	0.0945105i	0.323797	−	0.00466754i
$411$	53.0128			2.61493
$412$	4.46479	−	4.89519i	0.219964	−	0.241169i
$413$	19.0273	+	19.0273i	0.936271	+	0.936271i
$414$	−11.7048	+	12.2554i	−0.575260	+	0.602320i
$415$	−5.29613	−	5.38760i	−0.259977	−	0.264467i
$416$	−19.6775	+	5.36614i	−0.964770	+	0.263097i
$417$	32.5575	−	32.5575i	1.59435	−	1.59435i
$418$	8.08450	−	0.185779i	0.395426	−	0.00908673i
$419$	19.1062			0.933399			0.466699	−	0.884416i	$-0.345443\pi$
$419$	19.1062			0.933399			0.466699	+	0.884416i	$0.345443\pi$
$420$	−1.53528	−	41.0426i	−0.0749140	−	2.00267i
$421$			20.3290i			0.990773i	0.868673	+	0.495387i	$0.164974\pi$
$421$			20.3290i			0.990773i	−0.868673	+	0.495387i	$0.835026\pi$
$422$	−2.67188	+	0.0613989i	−0.130065	+	0.00298885i
$423$	23.8347	+	23.8347i	1.15888	+	1.15888i
$424$	−12.6291	+	14.5022i	−0.613325	+	0.704288i
$425$	−9.14593	+	8.83796i	−0.443643	+	0.428704i
$426$	−12.6897	−	12.1196i	−0.614818	−	0.587197i
$427$	13.4775	−	13.4775i	0.652222	−	0.652222i
$428$	8.42657	+	7.68567i	0.407314	+	0.371501i
$429$	26.4656	+	19.4609i	1.27777	+	0.939583i
$430$	4.40848	+	4.28319i	0.212596	+	0.206554i
$431$	−34.3570			−1.65492			−0.827460	−	0.561524i	$-0.810215\pi$
$431$	−34.3570			−1.65492			−0.827460	+	0.561524i	$0.810215\pi$
$432$	−49.1795	−	40.8795i	−2.36615	−	1.96682i
$433$	20.9912	+	20.9912i	1.00877	+	1.00877i	0.999961	+	0.00881105i	$0.00280468\pi$
$433$	20.9912	+	20.9912i	1.00877	+	1.00877i	0.00881105	+	0.999961i	$0.497195\pi$
$434$	−5.95199	−	5.68458i	−0.285704	−	0.272869i
$435$	−37.1427	−	37.7842i	−1.78086	−	1.81161i
$436$	−26.5520	+	1.22095i	−1.27161	+	0.0584731i
$437$	2.23090	+	2.23090i	0.106718	+	0.106718i
$438$	−1.50500	+	0.0345842i	−0.0719115	+	0.00165250i
$439$	16.6708			0.795656			0.397828	−	0.917460i	$-0.369764\pi$
$439$	16.6708			0.795656			0.397828	+	0.917460i	$0.369764\pi$
$440$	1.05523	+	17.4596i	0.0503062	+	0.832352i
$441$	−6.05720			−0.288438
$442$	7.44161	−	10.6231i	0.353962	−	0.505289i
$443$	21.7096	−	21.7096i	1.03146	−	1.03146i	0.0319665	−	0.999489i	$-0.489823\pi$
$443$	21.7096	−	21.7096i	1.03146	−	1.03146i	0.999489	−	0.0319665i	$-0.0101770\pi$
$444$	−19.5963	+	0.901108i	−0.930001	+	0.0427647i
$445$	7.59328	+	0.0650119i	0.359956	+	0.00308186i
$446$	23.4227	−	24.5246i	1.10910	−	1.16127i
$447$	25.5443	−	25.5443i	1.20820	−	1.20820i
$448$	−13.4530	+	17.7871i	−0.635596	+	0.840361i
$449$	31.2426			1.47443			0.737215	−	0.675658i	$-0.236140\pi$
$449$	31.2426			1.47443			0.737215	+	0.675658i	$0.236140\pi$
$450$	55.5284	−	0.324982i	2.61763	−	0.0153198i
$451$			5.73462i			0.270033i
$452$	17.2618	+	15.7441i	0.811929	+	0.740541i
$453$	−41.1367	+	41.1367i	−1.93277	+	1.93277i
$454$	−17.2162	−	16.4427i	−0.807995	−	0.771694i
$455$	−17.9922	−	13.4691i	−0.843489	−	0.631439i
$456$	−12.6521	+	14.5286i	−0.592490	+	0.680363i
$457$	−22.4089	−	22.4089i	−1.04824	−	1.04824i	−0.998776	−	0.0494661i	$-0.984248\pi$
$457$	−22.4089	−	22.4089i	−1.04824	−	1.04824i	−0.0494661	−	0.998776i	$-0.515752\pi$
$458$	−0.368686	−	16.0441i	−0.0172276	−	0.749690i
$459$	40.6678			1.89821
$460$	−4.64170	+	5.00245i	−0.216420	+	0.233241i
$461$			14.9213i			0.694953i	0.937689	+	0.347477i	$0.112961\pi$
$461$			14.9213i			0.694953i	−0.937689	+	0.347477i	$0.887039\pi$
$462$	35.9103	−	0.825204i	1.67070	−	0.0383920i
$463$	−12.5507	−	12.5507i	−0.583282	−	0.583282i	0.352522	−	0.935804i	$-0.385324\pi$
$463$	−12.5507	−	12.5507i	−0.583282	−	0.583282i	−0.935804	+	0.352522i	$0.885324\pi$
$464$	2.64030	+	28.6485i	0.122573	+	1.32997i
$465$	10.9672	−	10.7810i	0.508590	−	0.499955i
$466$	19.2084	−	20.1119i	0.889810	−	0.931667i
$467$	−14.2920	−	14.2920i	−0.661354	−	0.661354i	0.294346	−	0.955699i	$-0.404898\pi$
$467$	−14.2920	−	14.2920i	−0.661354	−	0.661354i	−0.955699	+	0.294346i	$0.904898\pi$
$468$	−55.5304	+	11.1008i	−2.56689	+	0.513133i
$469$		−	41.5173i		−	1.91709i
$470$	9.73514	+	9.45846i	0.449048	+	0.436286i
$471$			63.5025i			2.92604i
$472$	27.2368	−	1.88032i	1.25368	−	0.0865490i
$473$	−3.80113	+	3.80113i	−0.174776	+	0.174776i
$474$	11.3391	+	10.8296i	0.520821	+	0.497422i
$475$	0.177006	−	10.3363i	0.00812161	−	0.474261i
$476$	−0.651453	−	14.1671i	−0.0298593	−	0.649348i
$477$	−37.7543	+	37.7543i	−1.72865	+	1.72865i
$478$	20.7204	−	0.476148i	0.947731	−	0.0217785i
$479$		−	0.392894i		−	0.0179518i	−0.999960	−	0.00897588i	$-0.997143\pi$
$479$		−	0.392894i		−	0.0179518i	0.999960	−	0.00897588i	$-0.00285715\pi$
$480$	−32.4264	−	26.1728i	−1.48006	−	1.19462i
$481$	−6.35947	+	8.64847i	−0.289967	+	0.394336i
$482$	−31.0224	+	0.712883i	−1.41303	+	0.0324709i
$483$	9.90936	+	9.90936i	0.450891	+	0.450891i
$484$	6.69543	−	0.307880i	0.304338	−	0.0139945i
$485$	11.8212	+	12.0254i	0.536775	+	0.546045i
$486$	−49.0285	−	46.8258i	−2.22398	−	2.12406i
$487$	8.76391	−	8.76391i	0.397131	−	0.397131i	−0.480089	−	0.877220i	$-0.659396\pi$
$487$	8.76391	−	8.76391i	0.397131	−	0.397131i	0.877220	+	0.480089i	$0.159396\pi$
$488$	−1.33188	−	19.2926i	−0.0602915	−	0.873333i
$489$	−20.9694			−0.948267
$490$	−2.43888	+	0.0351564i	−0.110177	+	0.00158821i
$491$		−	2.47325i		−	0.111616i	−0.998442	−	0.0558081i	$-0.982226\pi$
$491$		−	2.47325i		−	0.111616i	0.998442	−	0.0558081i	$-0.0177735\pi$
$492$	−10.0941	−	9.20657i	−0.455076	−	0.415064i
$493$	−12.9367	−	12.9367i	−0.582642	−	0.582642i
$494$	1.82856	+	10.3827i	0.0822709	+	0.467141i
$495$	−0.415781	+	48.5626i	−0.0186880	+	2.18273i
$496$	−8.31544	+	0.766367i	−0.373374	+	0.0344109i
$497$	−7.42431	+	7.42431i	−0.333026	+	0.333026i
$498$	0.361625	+	15.7368i	0.0162048	+	0.705181i
$499$			17.6033i			0.788032i	0.919104	+	0.394016i	$0.128915\pi$
$499$			17.6033i			0.788032i	−0.919104	+	0.394016i	$0.871085\pi$
$500$	22.3561	−	0.453142i	0.999795	−	0.0202651i
$501$		−	32.9109i		−	1.47035i
$502$	−25.0356	+	0.575308i	−1.11739	+	0.0256772i
$503$	−5.95062	+	5.95062i	−0.265325	+	0.265325i	−0.827213	−	0.561888i	$-0.810075\pi$
$503$	−5.95062	+	5.95062i	−0.265325	+	0.265325i	0.561888	+	0.827213i	$0.310075\pi$
$504$	−40.6645	+	46.6955i	−1.81134	+	2.07998i
$505$	−6.05657	−	0.0518549i	−0.269514	−	0.00230751i
$506$	−4.31604	−	4.12213i	−0.191871	−	0.183251i
$507$	−19.8789	+	37.9340i	−0.882853	+	1.68471i
$508$	23.0148	+	20.9913i	1.02112	+	0.931338i
$509$	−18.7434			−0.830785			−0.415392	−	0.909642i	$-0.636356\pi$
$509$	−18.7434			−0.830785			−0.415392	+	0.909642i	$0.636356\pi$
$510$	26.4968	−	0.381951i	1.17330	−	0.0169131i
$511$			0.900755i			0.0398471i
$512$	4.64563	+	22.1454i	0.205310	+	0.978697i
$513$	−23.3739	+	23.3739i	−1.03198	+	1.03198i
$514$	13.9007	+	13.2762i	0.613132	+	0.585586i
$515$	5.28257	−	5.19288i	0.232778	−	0.228826i
$516$	−0.588277	−	12.7932i	−0.0258975	−	0.563190i
$517$	−8.39396	+	8.39396i	−0.369166	+	0.369166i
$518$	0.269661	+	11.7348i	0.0118482	+	0.515597i
$519$	11.8349			0.519495
$520$	−22.2943	+	4.79192i	−0.977671	+	0.210140i
$521$	−12.6489			−0.554157			−0.277078	−	0.960847i	$-0.589366\pi$
$521$	−12.6489			−0.554157			−0.277078	+	0.960847i	$0.589366\pi$
$522$	1.83510	+	79.8575i	0.0803199	+	3.49527i
$523$	−14.7541	+	14.7541i	−0.645150	+	0.645150i	−0.951817	−	0.306667i	$-0.900786\pi$
$523$	−14.7541	+	14.7541i	−0.645150	+	0.645150i	0.306667	+	0.951817i	$0.400786\pi$
$524$	−0.0106912	−	0.232500i	−0.000467047	−	0.0101568i
$525$	0.786238	−	45.9123i	0.0343143	−	2.00378i
$526$	−0.640610	−	0.611829i	−0.0279319	−	0.0266770i
$527$	3.75499	−	3.75499i	0.163570	−	0.163570i
$528$	23.2963	−	28.0263i	1.01384	−	1.21969i
$529$			20.6715i			0.898761i
$530$	−14.9823	+	15.4205i	−0.650788	+	0.669825i
$531$	75.8022			3.28953
$532$	8.51699	+	7.76814i	0.369258	+	0.336792i
$533$	−7.39074	+	1.12723i	−0.320129	+	0.0488257i
$534$	−11.4416	−	10.9276i	−0.495128	−	0.472884i
$535$	8.93901	+	9.09340i	0.386467	+	0.393142i
$536$	−31.7667	−	27.6638i	−1.37211	−	1.19490i
$537$	0.411517	−	0.411517i	0.0177583	−	0.0177583i
$538$	28.2272	−	0.648650i	1.21696	−	0.0279653i
$539$		−	2.13319i		−	0.0918830i
$540$	−52.4125	−	48.6327i	−2.25547	−	2.09282i
$541$		−	30.7974i		−	1.32408i	−0.749467	−	0.662042i	$-0.769690\pi$
$541$		−	30.7974i		−	1.32408i	0.749467	−	0.662042i	$-0.230310\pi$
$542$	−0.637463	−	27.7403i	−0.0273814	−	1.19155i
$543$	31.7054	−	31.7054i	1.36061	−	1.36061i
$544$	−11.2739	−	8.94137i	−0.483366	−	0.383358i
$545$	−29.7163	−	0.254424i	−1.27291	−	0.0108983i
$546$	8.12223	+	46.1187i	0.347599	+	1.97370i
$547$	17.8667	+	17.8667i	0.763927	+	0.763927i	0.977030	−	0.213103i	$-0.0683570\pi$
$547$	17.8667	+	17.8667i	0.763927	+	0.763927i	−0.213103	+	0.977030i	$0.568357\pi$
$548$	−23.7786	−	21.6879i	−1.01577	−	0.926461i
$549$		−	53.6926i		−	2.29155i
$550$	0.114450	+	19.5557i	0.00488018	+	0.833857i
$551$	14.8708			0.633519
$552$	14.1849	−	0.979269i	0.603749	−	0.0416805i
$553$	6.63410	−	6.63410i	0.282111	−	0.282111i
$554$	−3.92421	−	3.74791i	−0.166724	−	0.159234i
$555$	−21.9317	−	0.187774i	−0.930949	−	0.00797057i
$556$	−27.9230	+	1.28400i	−1.18420	+	0.0544536i
$557$	10.5065	+	10.5065i	0.445173	+	0.445173i	0.893746	−	0.448573i	$-0.148068\pi$
$557$	10.5065	+	10.5065i	0.445173	+	0.445173i	−0.448573	+	0.893746i	$0.648068\pi$
$558$	−23.1793	+	0.532651i	−0.981257	+	0.0225489i
$559$	−5.64605	−	4.15170i	−0.238802	−	0.175598i
$560$	−16.1021	+	19.0375i	−0.680440	+	0.804481i
$561$			23.1757i			0.978479i
$562$	−15.2246	+	0.349857i	−0.642213	+	0.0147578i
$563$	−13.5627	+	13.5627i	−0.571601	+	0.571601i	−0.932576	−	0.360974i	$-0.882444\pi$
$563$	−13.5627	+	13.5627i	−0.571601	+	0.571601i	0.360974	+	0.932576i	$0.382444\pi$
$564$	−1.29908	−	28.2510i	−0.0547011	−	1.18958i
$565$	18.3116	+	18.6278i	0.770374	+	0.783679i
$566$	13.3368	+	12.7377i	0.560589	+	0.535404i
$567$	−57.3839	+	57.3839i	−2.40990	+	2.40990i
$568$	0.733690	+	10.6276i	0.0307849	+	0.445925i
$569$		−	18.7390i		−	0.785582i	−0.919628	−	0.392791i	$-0.871510\pi$
$569$		−	18.7390i		−	0.785582i	0.919628	−	0.392791i	$-0.128490\pi$
$570$	−15.0095	+	15.4486i	−0.628680	+	0.647070i
$571$		−	8.09676i		−	0.338839i	−0.985544	−	0.169419i	$-0.945811\pi$
$571$		−	8.09676i		−	0.338839i	0.985544	−	0.169419i	$-0.0541892\pi$
$572$	−3.90940	−	19.5564i	−0.163460	−	0.817693i
$573$	32.4168	+	32.4168i	1.35423	+	1.35423i
$574$	−5.64607	+	5.91166i	−0.235662	+	0.246748i
$575$	−5.48660	+	5.30185i	−0.228807	+	0.221102i
$576$	8.63314	+	62.2283i	0.359714	+	2.59284i
$577$	−19.0166	−	19.0166i	−0.791673	−	0.791673i	0.190093	−	0.981766i	$-0.439121\pi$
$577$	−19.0166	−	19.0166i	−0.791673	−	0.791673i	−0.981766	+	0.190093i	$0.939121\pi$
$578$	−14.8873	+	0.342105i	−0.619231	+	0.0142297i
$579$		−	81.5117i		−	3.38751i
$580$	1.20238	+	32.1432i	0.0499262	+	1.33467i
$581$	9.41860			0.390750
$582$	−0.807164	−	35.1252i	−0.0334580	−	1.45599i
$583$	−13.2961	−	13.2961i	−0.550667	−	0.550667i
$584$	0.689206	+	0.600191i	0.0285196	+	0.0248361i
$585$	−62.6688	+	9.00986i	−2.59104	+	0.372512i
$586$	−2.42123	−	2.31245i	−0.100020	−	0.0955264i
$587$	−6.97520	+	6.97520i	−0.287897	+	0.287897i	−0.836248	−	0.548351i	$-0.815256\pi$
$587$	−6.97520	+	6.97520i	−0.287897	+	0.287897i	0.548351	+	0.836248i	$0.315256\pi$
$588$	3.75484	+	3.42470i	0.154847	+	0.141232i
$589$			4.31638i			0.177853i
$590$	30.5210	−	0.439961i	1.25653	−	0.0181129i
$591$	−6.84487			−0.281560
$592$	9.15848	+	7.61280i	0.376411	+	0.312884i
$593$	26.5561	−	26.5561i	1.09053	−	1.09053i	0.0950558	−	0.995472i	$-0.469697\pi$
$593$	26.5561	−	26.5561i	1.09053	−	1.09053i	0.995472	−	0.0950558i	$-0.0303029\pi$
$594$	43.1890	−	45.2206i	1.77207	−	1.85542i
$595$	0.135751	−	15.8555i	0.00556523	−	0.650010i
$596$	−21.9081	+	1.00741i	−0.897389	+	0.0412651i
$597$	−29.3785	+	29.3785i	−1.20238	+	1.20238i
$598$	4.46419	−	6.37274i	0.182554	−	0.260601i
$599$	35.1399			1.43578			0.717889	−	0.696157i	$-0.245108\pi$
$599$	35.1399			1.43578			0.717889	+	0.696157i	$0.245108\pi$
$600$	−34.6056	−	31.1939i	−1.41277	−	1.27349i
$601$	23.8391			0.972417			0.486209	−	0.873843i	$-0.338380\pi$
$601$	23.8391			0.972417			0.486209	+	0.873843i	$0.338380\pi$
$602$	−7.66092	+	0.176045i	−0.312236	+	0.00717506i
$603$	−82.6998	−	82.6998i	−3.36780	−	3.36780i
$604$	35.2810	−	1.62234i	1.43556	−	0.0660122i
$605$	7.49336	+	0.0641563i	0.304648	+	0.00260833i
$606$	9.12611	+	8.71610i	0.370723	+	0.354067i
$607$	21.1327	+	21.1327i	0.857750	+	0.857750i	0.991073	−	0.133323i	$-0.0425646\pi$
$607$	21.1327	+	21.1327i	0.857750	+	0.857750i	−0.133323	+	0.991073i	$0.542565\pi$
$608$	11.6188	−	1.34064i	0.471204	−	0.0543703i
$609$	66.0543			2.67665
$610$	−0.311636	−	21.6188i	−0.0126178	−	0.875321i
$611$	−12.4680	−	9.16811i	−0.504403	−	0.370902i
$612$	−29.5176	−	26.9223i	−1.19318	−	1.08827i
$613$	13.5802	−	13.5802i	0.548499	−	0.548499i	−0.377507	−	0.926007i	$-0.623219\pi$
$613$	13.5802	−	13.5802i	0.548499	−	0.548499i	0.926007	+	0.377507i	$0.123219\pi$
$614$	−28.4204	−	27.1436i	−1.14695	−	1.09543i
$615$	−10.7079	−	10.8929i	−0.431785	−	0.439243i
$616$	−16.4449	−	14.3210i	−0.662586	−	0.577009i
$617$	27.8314	+	27.8314i	1.12045	+	1.12045i	0.991673	+	0.128779i	$0.0411056\pi$
$617$	27.8314	+	27.8314i	1.12045	+	1.12045i	0.128779	+	0.991673i	$0.458894\pi$
$618$	−15.4300	+	0.354574i	−0.620684	+	0.0142631i
$619$			18.4469i			0.741443i	0.928744	+	0.370721i	$0.120890\pi$
$619$			18.4469i			0.741443i	−0.928744	+	0.370721i	$0.879110\pi$
$620$	−9.32982	+	0.349001i	−0.374695	+	0.0140162i
$621$	24.3964			0.978996
$622$	47.6558	−	1.09511i	1.91082	−	0.0439100i
$623$	−6.69411	+	6.69411i	−0.268194	+	0.268194i
$624$	40.6994	+	24.5151i	1.62928	+	0.981391i
$625$	24.9853	+	0.855988i	0.999414	+	0.0342395i
$626$	19.7807	−	20.7112i	0.790596	−	0.827786i
$627$	−13.3203	−	13.3203i	−0.531961	−	0.531961i
$628$	25.9793	−	28.4837i	1.03669	−	1.13662i
$629$	−7.57339			−0.301971
$630$	−48.2413	+	49.6524i	−1.92198	+	1.97820i
$631$	−2.29587			−0.0913973			−0.0456986	−	0.998955i	$-0.514551\pi$
$631$	−2.29587			−0.0913973			−0.0456986	+	0.998955i	$0.514551\pi$
$632$	−0.655599	−	9.49647i	−0.0260783	−	0.377749i
$633$	4.40228	+	4.40228i	0.174975	+	0.174975i
$634$	26.5024	−	27.7490i	1.05254	−	1.10206i
$635$	24.4144	+	24.8361i	0.968857	+	0.985591i
$636$	44.7497	−	2.05775i	1.77444	−	0.0815951i
$637$	2.74924	−	0.419311i	0.108929	−	0.0166137i
$638$	−28.1238	+	0.646273i	−1.11343	+	0.0255862i
$639$			29.5775i			1.17007i
$640$	3.83723	+	25.0055i	0.151680	+	0.988430i
$641$	38.1507			1.50686			0.753431	−	0.657527i	$-0.228397\pi$
$641$	38.1507			1.50686			0.753431	+	0.657527i	$0.228397\pi$
$642$	−0.610363	−	26.5611i	−0.0240891	−	1.04828i
$643$	23.1735	+	23.1735i	0.913875	+	0.913875i	0.996575	−	0.0826995i	$-0.0263542\pi$
$643$	23.1735	+	23.1735i	0.913875	+	0.913875i	−0.0826995	+	0.996575i	$0.526354\pi$
$644$	−0.390804	−	8.49878i	−0.0153998	−	0.334899i
$645$	0.122586	−	14.3178i	0.00482682	−	0.563765i
$646$	−5.13699	+	5.37864i	−0.202112	+	0.211620i
$647$	2.29915	+	2.29915i	0.0903891	+	0.0903891i	0.750856	−	0.660466i	$-0.229641\pi$
$647$	2.29915	+	2.29915i	0.0903891	+	0.0903891i	−0.660466	+	0.750856i	$0.729641\pi$
$648$	5.67083	+	82.1430i	0.222771	+	3.22688i
$649$			26.6956i			1.04789i
$650$	−25.1807	+	3.99147i	−0.987669	+	0.156558i
$651$			19.1728i			0.751441i
$652$	9.40569	+	8.57870i	0.368355	+	0.335968i
$653$	4.75371	+	4.75371i	0.186027	+	0.186027i	0.793976	−	0.607949i	$-0.208008\pi$
$653$	4.75371	+	4.75371i	0.186027	+	0.186027i	−0.607949	+	0.793976i	$0.708008\pi$
$654$	44.7769	+	42.7652i	1.75092	+	1.67225i
$655$	0.00222784	−	0.260208i	8.70490e−5	−	0.0101672i
$656$	0.761175	+	8.25911i	0.0297189	+	0.322464i
$657$	1.79425	+	1.79425i	0.0700002	+	0.0700002i
$658$	−16.9174	+	0.388756i	−0.659510	+	0.0151553i
$659$	35.0519			1.36543			0.682715	−	0.730685i	$-0.260799\pi$
$659$	35.0519			1.36543			0.682715	+	0.730685i	$0.260799\pi$
$660$	27.7147	−	29.8687i	1.07879	−	1.16264i
$661$			6.89099i			0.268028i	0.990979	+	0.134014i	$0.0427868\pi$
$661$			6.89099i			0.268028i	−0.990979	+	0.134014i	$0.957213\pi$
$662$	0.446204	+	19.4174i	0.0173422	+	0.754678i
$663$	−29.8687	+	4.55554i	−1.16000	+	0.176922i
$664$	6.27581	−	7.20658i	0.243549	−	0.279669i
$665$	9.03493	+	9.19098i	0.350360	+	0.356411i
$666$	23.9121	+	22.8378i	0.926575	+	0.884947i
$667$	−7.76069	−	7.76069i	−0.300495	−	0.300495i
$668$	−13.4641	+	14.7620i	−0.520940	+	0.571159i
$669$	−78.9995			−3.05430
$670$	−33.7783	−	32.8183i	−1.30497	−	1.26788i
$671$	18.9092			0.729980
$672$	51.6091	−	5.95496i	1.99086	−	0.229718i
$673$	−10.4035	−	10.4035i	−0.401024	−	0.401024i	0.477570	−	0.878594i	$-0.341518\pi$
$673$	−10.4035	−	10.4035i	−0.401024	−	0.401024i	−0.878594	+	0.477570i	$0.841518\pi$
$674$	−10.3203	−	9.85659i	−0.397521	−	0.379662i
$675$	−55.5493	−	57.4850i	−2.13809	−	2.21260i
$676$	24.4356	−	8.88251i	0.939833	−	0.341635i
$677$	−29.5371	+	29.5371i	−1.13520	+	1.13520i	−0.145903	+	0.989299i	$0.546609\pi$
$677$	−29.5371	+	29.5371i	−1.13520	+	1.13520i	−0.989299	+	0.145903i	$0.953391\pi$
$678$	−1.25033	−	54.4104i	−0.0480187	−	2.08962i
$679$	−21.0228			−0.806781
$680$	−12.0412	−	10.6687i	−0.461760	−	0.409125i
$681$			55.4574i			2.12513i
$682$	−0.187586	−	8.16315i	−0.00718304	−	0.312583i
$683$	6.74455	+	6.74455i	0.258073	+	0.258073i	0.824270	−	0.566197i	$-0.191586\pi$
$683$	6.74455	+	6.74455i	0.258073	+	0.258073i	−0.566197	+	0.824270i	$0.691586\pi$
$684$	32.4389	−	1.49166i	1.24033	−	0.0570349i
$685$	−25.2247	−	25.6603i	−0.963784	−	0.980430i
$686$	−16.9603	+	17.7581i	−0.647546	+	0.678006i
$687$	−26.4347	+	26.4347i	−1.00855	+	1.00855i
$688$	−4.96992	+	5.97900i	−0.189477	+	0.227947i
$689$	14.5223	−	19.7494i	0.553257	−	0.752394i
$690$	15.8953	−	0.229131i	0.605123	−	0.00872286i
$691$	10.6205			0.404021			0.202010	−	0.979383i	$-0.435252\pi$
$691$	10.6205			0.404021			0.202010	+	0.979383i	$0.435252\pi$
$692$	−5.30849	−	4.84174i	−0.201798	−	0.184055i
$693$	−42.8119	−	42.8119i	−1.62629	−	1.62629i
$694$	31.3441	−	32.8185i	1.18980	−	1.24577i
$695$	−31.2507	−	0.267561i	−1.18541	−	0.0101492i
$696$	44.0133	−	50.5410i	1.66832	−	1.91575i
$697$	−3.72956	−	3.72956i	−0.141267	−	0.141267i
$698$	0.573115	+	24.9401i	0.0216927	+	0.943998i
$699$	−64.7854			−2.45041
$700$	−19.1357	+	20.2721i	−0.723262	+	0.766212i
$701$	6.12695			0.231412			0.115706	−	0.993284i	$-0.463087\pi$
$701$	6.12695			0.231412			0.115706	+	0.993284i	$0.463087\pi$
$702$	66.7695	+	46.7729i	2.52005	+	1.76533i
$703$	4.35282	−	4.35282i	0.164170	−	0.164170i
$704$	−21.9152	+	3.04037i	−0.825960	+	0.114588i
$705$	0.270704	−	31.6178i	0.0101953	−	1.19079i
$706$	−35.3871	−	33.7973i	−1.33181	−	1.27198i
$707$	5.33937	−	5.33937i	0.200808	−	0.200808i
$708$	−46.9895	−	42.8580i	−1.76597	−	1.61070i
$709$	23.2312			0.872467			0.436233	−	0.899834i	$-0.356312\pi$
$709$	23.2312			0.872467			0.436233	+	0.899834i	$0.356312\pi$
$710$	0.171670	+	11.9091i	0.00644265	+	0.446940i
$711$		−	26.4294i		−	0.991180i
$712$	0.661530	+	9.58237i	0.0247919	+	0.359115i
$713$	2.25260	−	2.25260i	0.0843607	−	0.0843607i
$714$	−22.8178	+	23.8912i	−0.853935	+	0.894105i
$715$	−3.17304	−	22.0703i	−0.118665	−	0.825384i
$716$	−0.352938	+	0.0162293i	−0.0131899	+	0.000606518i
$717$	−34.1397	−	34.1397i	−1.27497	−	1.27497i
$718$	37.4967	−	0.861660i	1.39936	−	0.0321569i
$719$	−49.2456			−1.83655			−0.918276	−	0.395940i	$-0.870419\pi$
$719$	−49.2456			−1.83655			−0.918276	+	0.395940i	$0.870419\pi$
$720$	5.84705	+	69.9959i	0.217907	+	2.60859i
$721$			9.23498i			0.343929i
$722$	0.478415	+	20.8191i	0.0178048	+	0.774806i
$723$	51.1135	+	51.1135i	1.90093	+	1.90093i
$724$	−27.1922	+	1.25039i	−1.01059	+	0.0464704i
$725$	−0.615757	+	35.9571i	−0.0228686	+	1.33541i
$726$	−11.2911	−	10.7838i	−0.419051	−	0.400224i
$727$	25.1121	+	25.1121i	0.931356	+	0.931356i	0.997791	−	0.0664346i	$-0.0211624\pi$
$727$	25.1121	+	25.1121i	0.931356	+	0.931356i	−0.0664346	+	0.997791i	$0.521162\pi$
$728$	15.2243	−	24.0091i	0.564249	−	0.889838i
$729$			70.5996i			2.61480i
$730$	0.732850	+	0.712022i	0.0271240	+	0.0263531i
$731$		−	4.94419i		−	0.182867i
$732$	−30.3574	+	33.2839i	−1.12204	+	1.23021i
$733$	7.99950	−	7.99950i	0.295468	−	0.295468i	−0.543768	−	0.839236i	$-0.683003\pi$
$733$	7.99950	−	7.99950i	0.295468	−	0.295468i	0.839236	+	0.543768i	$0.183003\pi$
$734$	−7.63680	+	7.99604i	−0.281880	+	0.295139i
$735$	3.98318	+	4.05198i	0.146922	+	0.149459i
$736$	−6.76318	−	5.36389i	−0.249294	−	0.197715i
$737$	29.1247	−	29.1247i	1.07282	−	1.07282i
$738$	0.529043	+	23.0222i	0.0194743	+	0.847461i
$739$			22.0584i			0.811432i	0.913999	+	0.405716i	$0.132978\pi$
$739$			22.0584i			0.811432i	−0.913999	+	0.405716i	$0.867022\pi$
$740$	9.76053	+	9.05664i	0.358804	+	0.332929i
$741$	14.5488	−	19.7854i	0.534463	−	0.726834i
$742$	−0.615792	−	26.7973i	−0.0226064	−	0.983760i
$743$	7.61946	+	7.61946i	0.279531	+	0.279531i	0.832922	−	0.553391i	$-0.186666\pi$
$743$	7.61946	+	7.61946i	0.279531	+	0.279531i	−0.553391	+	0.832922i	$0.686666\pi$
$744$	14.6699	+	12.7752i	0.537825	+	0.468362i
$745$	−24.5189	−	0.209925i	−0.898305	−	0.00769107i
$746$	18.8197	−	19.7050i	0.689040	−	0.721453i
$747$	18.7612	−	18.7612i	0.686438	−	0.686438i
$748$	9.48134	−	10.3953i	0.346672	−	0.380091i
$749$	−15.8971			−0.580866
$750$	−36.7325	−	36.9321i	−1.34128	−	1.34857i
$751$			44.8924i			1.63815i	0.573687	+	0.819074i	$0.305512\pi$
$751$			44.8924i			1.63815i	−0.573687	+	0.819074i	$0.694488\pi$
$752$	−10.9750	+	13.2033i	−0.400216	+	0.481474i
$753$	41.2494	+	41.2494i	1.50321	+	1.50321i
$754$	−6.36107	−	36.1187i	−0.231656	−	1.31536i
$755$	39.4856	+	0.338066i	1.43703	+	0.0123035i
$756$	89.0446	−	4.09459i	3.23852	−	0.148919i
$757$	23.9690	−	23.9690i	0.871169	−	0.871169i	−0.121431	−	0.992600i	$-0.538748\pi$
$757$	23.9690	−	23.9690i	0.871169	−	0.871169i	0.992600	+	0.121431i	$0.0387483\pi$
$758$	−37.5912	+	0.863833i	−1.36538	+	0.0313758i
$759$			13.9030i			0.504647i
$760$	13.0526	−	0.788879i	0.473466	−	0.0286156i
$761$		−	38.3827i		−	1.39137i	−0.718347	−	0.695685i	$-0.755101\pi$
$761$		−	38.3827i		−	1.39137i	0.718347	−	0.695685i	$-0.244899\pi$
$762$	−1.66704	−	72.5442i	−0.0603904	−	2.62800i
$763$	26.1974	−	26.1974i	0.948410	−	0.948410i
$764$	−1.27845	−	27.8023i	−0.0462527	−	1.00585i
$765$	−31.3126	−	31.8534i	−1.13211	−	1.15166i
$766$	−11.1056	+	11.6280i	−0.401262	+	0.420137i
$767$	−34.4051	+	5.24742i	−1.24229	+	0.189473i
$768$	29.8318	−	43.4562i	1.07646	−	1.56809i
$769$	−22.2289			−0.801594			−0.400797	−	0.916167i	$-0.631267\pi$
$769$	−22.2289			−0.801594			−0.400797	+	0.916167i	$0.631267\pi$
$770$	−17.4863	−	16.9893i	−0.630163	−	0.612253i
$771$		−	44.7774i		−	1.61262i
$772$	−33.3470	+	36.5616i	−1.20018	+	1.31588i
$773$	29.7075	−	29.7075i	1.06850	−	1.06850i	0.0710290	−	0.997474i	$-0.477372\pi$
$773$	29.7075	−	29.7075i	1.06850	−	1.06850i	0.997474	−	0.0710290i	$-0.0226283\pi$
$774$	−14.9094	+	15.6107i	−0.535906	+	0.561116i
$775$	−10.4368	−	0.178728i	−0.374902	−

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0324895 + 1.41384i) q^{2} +(2.32949 - 2.32949i) q^{3} +(-1.99789 + 0.0918700i) q^{4} +(-2.23599 - 0.0191440i) q^{5} +(3.36921 + 3.21784i) q^{6} +(1.97121 - 1.97121i) q^{7} +(-0.194800 - 2.82171i) q^{8} -7.85303i q^{9} +O(q^{10})\)	\(q+(0.0324895 + 1.41384i) q^{2} +(2.32949 - 2.32949i) q^{3} +(-1.99789 + 0.0918700i) q^{4} +(-2.23599 - 0.0191440i) q^{5} +(3.36921 + 3.21784i) q^{6} +(1.97121 - 1.97121i) q^{7} +(-0.194800 - 2.82171i) q^{8} -7.85303i q^{9} +(-0.0455796 - 3.16195i) q^{10} +2.76564 q^{11} +(-4.44005 + 4.86807i) q^{12} +(0.543628 + 3.56433i) q^{13} +(2.85102 + 2.72293i) q^{14} +(-5.25330 + 5.16411i) q^{15} +(3.98312 - 0.367092i) q^{16} +(-1.79865 + 1.79865i) q^{17} +(11.1029 - 0.255141i) q^{18} -2.06756i q^{19} +(4.46901 - 0.167172i) q^{20} -9.18381i q^{21} +(0.0898542 + 3.91017i) q^{22} +(-1.07900 + 1.07900i) q^{23} +(-7.02693 - 6.11936i) q^{24} +(4.99927 + 0.0856113i) q^{25} +(-5.02174 + 0.884407i) q^{26} +(-11.3051 - 11.3051i) q^{27} +(-3.75716 + 4.11935i) q^{28} +7.19247i q^{29} +(-7.47190 - 7.25955i) q^{30} -2.08767 q^{31} +(0.648419 + 5.61957i) q^{32} +(6.44252 - 6.44252i) q^{33} +(-2.60144 - 2.48457i) q^{34} +(-4.44533 + 4.36986i) q^{35} +(0.721458 + 15.6895i) q^{36} +(2.10529 + 2.10529i) q^{37} +(2.92320 - 0.0671739i) q^{38} +(9.56945 + 7.03670i) q^{39} +(0.381551 + 6.31304i) q^{40} +2.07353i q^{41} +(12.9844 - 0.298378i) q^{42} +(-1.37442 + 1.37442i) q^{43} +(-5.52543 + 0.254079i) q^{44} +(-0.150338 + 17.5593i) q^{45} +(-1.56059 - 1.49048i) q^{46} +(-3.03509 + 3.03509i) q^{47} +(8.42350 - 10.1338i) q^{48} -0.771320i q^{49} +(0.0413830 + 7.07095i) q^{50} +8.37988i q^{51} +(-1.41356 - 7.07120i) q^{52} +(-4.80760 - 4.80760i) q^{53} +(15.6163 - 16.3509i) q^{54} +(-6.18392 - 0.0529453i) q^{55} +(-5.94617 - 5.17819i) q^{56} +(-4.81635 - 4.81635i) q^{57} +(-10.1690 + 0.233680i) q^{58} +9.65260i q^{59} +(10.0211 - 10.7999i) q^{60} +6.83718 q^{61} +(-0.0678274 - 2.95163i) q^{62} +(-15.4800 - 15.4800i) q^{63} +(-7.92411 + 1.09934i) q^{64} +(-1.14731 - 7.98021i) q^{65} +(9.31801 + 8.89938i) q^{66} +(10.5309 - 10.5309i) q^{67} +(3.42827 - 3.75875i) q^{68} +5.02705i q^{69} +(-6.32271 - 6.14301i) q^{70} -3.76638 q^{71} +(-22.1590 + 1.52977i) q^{72} +(-0.228478 + 0.228478i) q^{73} +(-2.90815 + 3.04495i) q^{74} +(11.8452 - 11.4463i) q^{75} +(0.189946 + 4.13075i) q^{76} +(5.45164 - 5.45164i) q^{77} +(-9.63786 + 13.7583i) q^{78} +3.36550 q^{79} +(-8.91323 + 0.744560i) q^{80} -29.1110 q^{81} +(-2.93164 + 0.0673679i) q^{82} +(2.38904 + 2.38904i) q^{83} +(0.843717 + 18.3482i) q^{84} +(4.05619 - 3.98733i) q^{85} +(-1.98786 - 1.89855i) q^{86} +(16.7548 + 16.7548i) q^{87} +(-0.538746 - 7.80383i) q^{88} -3.39594 q^{89} +(-24.8309 + 0.357938i) q^{90} +(8.09764 + 5.95444i) q^{91} +(2.05660 - 2.25486i) q^{92} +(-4.86321 + 4.86321i) q^{93} +(-4.38974 - 4.19252i) q^{94} +(-0.0395813 + 4.62303i) q^{95} +(14.6012 + 11.5802i) q^{96} +(-5.33246 - 5.33246i) q^{97} +(1.09052 - 0.0250598i) q^{98} -21.7186i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) \) 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Introduction

L-functions

Modular forms

Varieties

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