LMFDB - Embedded newform 125.2.e.a.99.2

Newspace parameters

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.e (of order $10$, degree $4$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			99.2
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	125.99
Dual form			125.2.e.a.24.2

$q$-expansion

$f(q)$	$=$	$q+(1.53884 - 0.500000i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.500000 - 0.363271i) q^{4} +(1.30902 + 0.951057i) q^{6} +0.618034i q^{7} +(-1.31433 + 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +O(q^{10})$	\(q+(1.53884 - 0.500000i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.500000 - 0.363271i) q^{4} +(1.30902 + 0.951057i) q^{6} +0.618034i q^{7} +(-1.31433 + 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +(-1.61803 - 4.97980i) q^{11} +(0.587785 + 0.190983i) q^{12} +(-1.76336 - 0.572949i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.50000 + 4.61653i) q^{16} +(-3.07768 + 4.23607i) q^{17} -3.23607i q^{18} +(0.690983 + 0.502029i) q^{19} +(-0.500000 + 0.363271i) q^{21} +(-4.97980 - 6.85410i) q^{22} +(3.57971 - 1.16312i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(4.75528 - 1.54508i) q^{27} +(0.224514 + 0.309017i) q^{28} +(-2.92705 + 2.12663i) q^{29} +(2.42705 + 1.76336i) q^{31} +3.38197i q^{32} +(3.07768 - 4.23607i) q^{33} +(-2.61803 + 8.05748i) q^{34} +(-0.381966 - 1.17557i) q^{36} +(-0.224514 - 0.0729490i) q^{37} +(1.31433 + 0.427051i) q^{38} +(-0.572949 - 1.76336i) q^{39} +(-0.236068 + 0.726543i) q^{41} +(-0.587785 + 0.809017i) q^{42} +4.85410i q^{43} +(-2.61803 - 1.90211i) q^{44} +(4.92705 - 3.57971i) q^{46} +(-0.363271 - 0.500000i) q^{47} +(-4.61653 + 1.50000i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(-1.08981 + 0.354102i) q^{52} +(-2.04087 - 2.80902i) q^{53} +(6.54508 - 4.75528i) q^{54} +(-1.11803 - 0.812299i) q^{56} +0.854102i q^{57} +(-3.44095 + 4.73607i) q^{58} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(4.61653 + 1.50000i) q^{62} +(1.17557 + 0.381966i) q^{63} +(-1.30902 - 4.02874i) q^{64} +(2.61803 - 8.05748i) q^{66} +(2.80017 - 3.85410i) q^{67} +3.23607i q^{68} +(3.04508 + 2.21238i) q^{69} +(5.35410 - 3.88998i) q^{71} +(2.62866 + 3.61803i) q^{72} +(-8.55951 + 2.78115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(3.07768 - 1.00000i) q^{77} +(-1.76336 - 2.42705i) q^{78} +(-6.54508 + 4.75528i) q^{79} +(-0.809017 - 0.587785i) q^{81} +1.23607i q^{82} +(3.66547 - 5.04508i) q^{83} +(-0.118034 + 0.363271i) q^{84} +(2.42705 + 7.46969i) q^{86} +(-3.44095 - 1.11803i) q^{87} +(11.1352 + 3.61803i) q^{88} +(2.76393 + 8.50651i) q^{89} +(0.354102 - 1.08981i) q^{91} +(1.36733 - 1.88197i) q^{92} +3.00000i q^{93} +(-0.809017 - 0.587785i) q^{94} +(-2.73607 + 1.98787i) q^{96} +(2.26538 + 3.11803i) q^{97} +(10.1841 - 3.30902i) q^{98} -10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	$ 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49} - 24 q^{51} + 30 q^{54} + 26 q^{61} - 6 q^{64} + 12 q^{66} + 2 q^{69} + 16 q^{71} - 12 q^{74} + 40 q^{76} - 30 q^{79} - 2 q^{81} + 8 q^{84} + 6 q^{86} + 40 q^{89} - 24 q^{91} - 2 q^{94} - 4 q^{96} - 48 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 - 2 * q^14 - 12 * q^16 + 10 * q^19 - 4 * q^21 - 24 * q^26 - 10 * q^29 + 6 * q^31 - 12 * q^34 - 12 * q^36 - 18 * q^39 + 16 * q^41 - 12 * q^44 + 26 * q^46 + 44 * q^49 - 24 * q^51 + 30 * q^54 + 26 * q^61 - 6 * q^64 + 12 * q^66 + 2 * q^69 + 16 * q^71 - 12 * q^74 + 40 * q^76 - 30 * q^79 - 2 * q^81 + 8 * q^84 + 6 * q^86 + 40 * q^89 - 24 * q^91 - 2 * q^94 - 4 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.53884	−	0.500000i	1.08813	−	0.353553i	0.290604	−	0.956844i	$-0.406144\pi$
$2$	1.53884	−	0.500000i	1.08813	−	0.353553i	0.797522	+	0.603290i	$0.206144\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i	0.944254	−	0.329218i	$-0.106785\pi$
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i	−0.604896	+	0.796305i	$0.706785\pi$
$4$	0.500000	−	0.363271i	0.250000	−	0.181636i
$5$		0			0
$5$		0			0
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$			0.618034i			0.233595i	0.993156	+	0.116797i	$0.0372628\pi$
$7$			0.618034i			0.233595i	−0.993156	+	0.116797i	$0.962737\pi$
$8$	−1.31433	+	1.80902i	−0.464685	+	0.639584i
$9$	0.618034	−	1.90211i	0.206011	−	0.634038i
$10$		0			0
$11$	−1.61803	−	4.97980i	−0.487856	−	1.50147i	−0.827802	−	0.561020i	$-0.810409\pi$
$11$	−1.61803	−	4.97980i	−0.487856	−	1.50147i	0.339946	−	0.940445i	$-0.389591\pi$
$12$	0.587785	+	0.190983i	0.169679	+	0.0551320i
$13$	−1.76336	−	0.572949i	−0.489067	−	0.158907i	0.0540944	−	0.998536i	$-0.482773\pi$
$13$	−1.76336	−	0.572949i	−0.489067	−	0.158907i	−0.543161	+	0.839628i	$0.682773\pi$
$14$	0.309017	+	0.951057i	0.0825883	+	0.254181i
$15$		0			0
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	−3.07768	+	4.23607i	−0.746448	+	1.02740i	0.251774	+	0.967786i	$0.418986\pi$
$17$	−3.07768	+	4.23607i	−0.746448	+	1.02740i	−0.998222	+	0.0596113i	$0.981014\pi$
$18$		−	3.23607i		−	0.762749i
$19$	0.690983	+	0.502029i	0.158522	+	0.115173i	0.664219	−	0.747538i	$-0.268764\pi$
$19$	0.690983	+	0.502029i	0.158522	+	0.115173i	−0.505696	+	0.862712i	$0.668764\pi$
$20$		0			0
$21$	−0.500000	+	0.363271i	−0.109109	+	0.0792723i
$22$	−4.97980	−	6.85410i	−1.06170	−	1.46130i
$23$	3.57971	−	1.16312i	0.746422	−	0.242527i	0.0889808	−	0.996033i	$-0.471639\pi$
$23$	3.57971	−	1.16312i	0.746422	−	0.242527i	0.657441	+	0.753506i	$0.271639\pi$
$24$	−2.23607			−0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	4.75528	−	1.54508i	0.915155	−	0.297352i
$28$	0.224514	+	0.309017i	0.0424292	+	0.0583987i
$29$	−2.92705	+	2.12663i	−0.543540	+	0.394905i	−0.825398	−	0.564551i	$-0.809049\pi$
$29$	−2.92705	+	2.12663i	−0.543540	+	0.394905i	0.281858	+	0.959456i	$0.409049\pi$
$30$		0			0
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	0.784008	−	0.620750i	$-0.213172\pi$
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	−0.348097	+	0.937459i	$0.613172\pi$
$32$			3.38197i			0.597853i
$33$	3.07768	−	4.23607i	0.535756	−	0.737405i
$34$	−2.61803	+	8.05748i	−0.448989	+	1.38185i
$35$		0			0
$36$	−0.381966	−	1.17557i	−0.0636610	−	0.195928i
$37$	−0.224514	−	0.0729490i	−0.0369099	−	0.0119927i	0.290504	−	0.956874i	$-0.406177\pi$
$37$	−0.224514	−	0.0729490i	−0.0369099	−	0.0119927i	−0.327414	+	0.944881i	$0.606177\pi$
$38$	1.31433	+	0.427051i	0.213212	+	0.0692768i
$39$	−0.572949	−	1.76336i	−0.0917453	−	0.282363i
$40$		0			0
$41$	−0.236068	+	0.726543i	−0.0368676	+	0.113467i	−0.967797	−	0.251733i	$-0.918999\pi$
$41$	−0.236068	+	0.726543i	−0.0368676	+	0.113467i	0.930929	+	0.365200i	$0.118999\pi$
$42$	−0.587785	+	0.809017i	−0.0906972	+	0.124834i
$43$			4.85410i			0.740244i	0.928983	+	0.370122i	$0.120684\pi$
$43$			4.85410i			0.740244i	−0.928983	+	0.370122i	$0.879316\pi$
$44$	−2.61803	−	1.90211i	−0.394683	−	0.286754i
$45$		0			0
$46$	4.92705	−	3.57971i	0.726454	−	0.527800i
$47$	−0.363271	−	0.500000i	−0.0529886	−	0.0729325i	0.781700	−	0.623654i	$-0.214353\pi$
$47$	−0.363271	−	0.500000i	−0.0529886	−	0.0729325i	−0.834689	+	0.550722i	$0.814353\pi$
$48$	−4.61653	+	1.50000i	−0.666338	+	0.216506i
$49$	6.61803			0.945433
$50$		0			0
$51$	−5.23607			−0.733196
$52$	−1.08981	+	0.354102i	−0.151130	+	0.0491051i
$53$	−2.04087	−	2.80902i	−0.280335	−	0.385848i	0.645510	−	0.763752i	$-0.276645\pi$
$53$	−2.04087	−	2.80902i	−0.280335	−	0.385848i	−0.925845	+	0.377904i	$0.876645\pi$
$54$	6.54508	−	4.75528i	0.890673	−	0.647112i
$55$		0			0
$56$	−1.11803	−	0.812299i	−0.149404	−	0.108548i
$57$			0.854102i			0.113129i
$58$	−3.44095	+	4.73607i	−0.451820	+	0.621876i
$59$	3.35410	−	10.3229i	0.436667	−	1.34392i	−0.454702	−	0.890644i	$-0.650254\pi$
$59$	3.35410	−	10.3229i	0.436667	−	1.34392i	0.891369	−	0.453279i	$-0.149746\pi$
$60$		0			0
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	0.961827	+	0.273659i	$0.0882338\pi$
$61$	2.69098	+	8.28199i	0.344545	+	1.06040i	−0.617282	+	0.786742i	$0.711766\pi$
$62$	4.61653	+	1.50000i	0.586299	+	0.190500i
$63$	1.17557	+	0.381966i	0.148108	+	0.0481232i
$64$	−1.30902	−	4.02874i	−0.163627	−	0.503593i
$65$		0			0
$66$	2.61803	−	8.05748i	0.322258	−	0.991807i
$67$	2.80017	−	3.85410i	0.342095	−	0.470853i	−0.602957	−	0.797774i	$-0.706011\pi$
$67$	2.80017	−	3.85410i	0.342095	−	0.470853i	0.945052	+	0.326920i	$0.106011\pi$
$68$			3.23607i			0.392431i
$69$	3.04508	+	2.21238i	0.366585	+	0.266340i
$70$		0			0
$71$	5.35410	−	3.88998i	0.635415	−	0.461656i	−0.222857	−	0.974851i	$-0.571538\pi$
$71$	5.35410	−	3.88998i	0.635415	−	0.461656i	0.858272	+	0.513195i	$0.171538\pi$
$72$	2.62866	+	3.61803i	0.309790	+	0.426389i
$73$	−8.55951	+	2.78115i	−1.00181	+	0.325509i	−0.763590	−	0.645701i	$-0.776565\pi$
$73$	−8.55951	+	2.78115i	−1.00181	+	0.325509i	−0.238224	+	0.971210i	$0.576565\pi$
$74$	−0.381966			−0.0444026
$75$		0			0
$76$	0.527864			0.0605502
$77$	3.07768	−	1.00000i	0.350735	−	0.113961i
$78$	−1.76336	−	2.42705i	−0.199661	−	0.274809i
$79$	−6.54508	+	4.75528i	−0.736380	+	0.535011i	−0.891575	−	0.452873i	$-0.850399\pi$
$79$	−6.54508	+	4.75528i	−0.736380	+	0.535011i	0.155196	+	0.987884i	$0.450399\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$			1.23607i			0.136501i
$83$	3.66547	−	5.04508i	0.402337	−	0.553770i	−0.558991	−	0.829174i	$-0.688811\pi$
$83$	3.66547	−	5.04508i	0.402337	−	0.553770i	0.961329	+	0.275404i	$0.0888115\pi$
$84$	−0.118034	+	0.363271i	−0.0128786	+	0.0396361i
$85$		0			0
$86$	2.42705	+	7.46969i	0.261716	+	0.805478i
$87$	−3.44095	−	1.11803i	−0.368909	−	0.119866i
$88$	11.1352	+	3.61803i	1.18701	+	0.385684i
$89$	2.76393	+	8.50651i	0.292976	+	0.901688i	0.983894	+	0.178754i	$0.0572068\pi$
$89$	2.76393	+	8.50651i	0.292976	+	0.901688i	−0.690918	+	0.722934i	$0.742793\pi$
$90$		0			0
$91$	0.354102	−	1.08981i	0.0371200	−	0.114244i
$92$	1.36733	−	1.88197i	0.142554	−	0.196209i
$93$			3.00000i			0.311086i
$94$	−0.809017	−	0.587785i	−0.0834437	−	0.0606254i
$95$		0			0
$96$	−2.73607	+	1.98787i	−0.279249	+	0.202886i
$97$	2.26538	+	3.11803i	0.230015	+	0.316588i	0.908387	−	0.418130i	$-0.137314\pi$
$97$	2.26538	+	3.11803i	0.230015	+	0.316588i	−0.678372	+	0.734718i	$0.737314\pi$
$98$	10.1841	−	3.30902i	1.02875	−	0.334261i
$99$	−10.4721			−1.05249
$100$		0			0
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$	−8.05748	+	2.61803i	−0.797809	+	0.259224i
$103$	5.03280	+	6.92705i	0.495896	+	0.682543i	0.981462	−	0.191658i	$-0.0613863\pi$
$103$	5.03280	+	6.92705i	0.495896	+	0.682543i	−0.485566	+	0.874200i	$0.661386\pi$
$104$	3.35410	−	2.43690i	0.328897	−	0.238957i
$105$		0			0
$106$	−4.54508	−	3.30220i	−0.441458	−	0.320738i
$107$		−	16.4164i		−	1.58703i	−0.608548	−	0.793517i	$-0.708248\pi$
$107$		−	16.4164i		−	1.58703i	0.608548	−	0.793517i	$-0.291752\pi$
$108$	1.81636	−	2.50000i	0.174779	−	0.240563i
$109$	−3.09017	+	9.51057i	−0.295985	+	0.910947i	0.686904	+	0.726748i	$0.258969\pi$
$109$	−3.09017	+	9.51057i	−0.295985	+	0.910947i	−0.982889	+	0.184199i	$0.941031\pi$
$110$		0			0
$111$	−0.0729490	−	0.224514i	−0.00692401	−	0.0213099i
$112$	−2.85317	−	0.927051i	−0.269599	−	0.0875981i
$113$	−16.0292	−	5.20820i	−1.50790	−	0.489947i	−0.565590	−	0.824687i	$-0.691352\pi$
$113$	−16.0292	−	5.20820i	−1.50790	−	0.489947i	−0.942311	+	0.334740i	$0.891352\pi$
$114$	0.427051	+	1.31433i	0.0399970	+	0.123098i
$115$		0			0
$116$	−0.690983	+	2.12663i	−0.0641562	+	0.197452i
$117$	−2.17963	+	3.00000i	−0.201507	+	0.277350i
$118$		−	17.5623i		−	1.61674i
$119$	−2.61803	−	1.90211i	−0.239995	−	0.174366i
$120$		0			0
$121$	−13.2812	+	9.64932i	−1.20738	+	0.877211i
$122$	8.28199	+	11.3992i	0.749817	+	1.03203i
$123$	−0.726543	+	0.236068i	−0.0655101	+	0.0212855i
$124$	1.85410			0.166503
$125$		0			0
$126$	2.00000			0.178174
$127$	−18.9151	+	6.14590i	−1.67845	+	0.545360i	−0.984609	−	0.174772i	$-0.944081\pi$
$127$	−18.9151	+	6.14590i	−1.67845	+	0.545360i	−0.693837	+	0.720132i	$0.744081\pi$
$128$	−8.00448	−	11.0172i	−0.707503	−	0.973794i
$129$	−3.92705	+	2.85317i	−0.345758	+	0.251208i
$130$		0			0
$131$	−5.50000	−	3.99598i	−0.480537	−	0.349131i	0.320996	−	0.947080i	$-0.395982\pi$
$131$	−5.50000	−	3.99598i	−0.480537	−	0.349131i	−0.801534	+	0.597950i	$0.795982\pi$
$132$		−	3.23607i		−	0.281664i
$133$	−0.310271	+	0.427051i	−0.0269039	+	0.0370300i
$134$	2.38197	−	7.33094i	0.205771	−	0.633297i
$135$		0			0
$136$	−3.61803	−	11.1352i	−0.310244	−	0.954832i
$137$	−11.3597	−	3.69098i	−0.970523	−	0.315342i	−0.219496	−	0.975613i	$-0.570441\pi$
$137$	−11.3597	−	3.69098i	−0.970523	−	0.315342i	−0.751027	+	0.660271i	$0.770441\pi$
$138$	5.79210	+	1.88197i	0.493056	+	0.160204i
$139$	−1.54508	−	4.75528i	−0.131052	−	0.403338i	0.863903	−	0.503659i	$-0.168013\pi$
$139$	−1.54508	−	4.75528i	−0.131052	−	0.403338i	−0.994955	+	0.100321i	$0.968013\pi$
$140$		0			0
$141$	0.190983	−	0.587785i	0.0160837	−	0.0495004i
$142$	6.29412	−	8.66312i	0.528191	−	0.726993i
$143$			9.70820i			0.811841i
$144$	7.85410	+	5.70634i	0.654508	+	0.475528i
$145$		0			0
$146$	−11.7812	+	8.55951i	−0.975015	+	0.708390i
$147$	3.88998	+	5.35410i	0.320840	+	0.441599i
$148$	−0.138757	+	0.0450850i	−0.0114058	+	0.00370596i
$149$	3.94427			0.323127			0.161564	−	0.986862i	$-0.448346\pi$
$149$	3.94427			0.323127			0.161564	+	0.986862i	$0.448346\pi$
$150$		0			0
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	−1.81636	+	0.590170i	−0.147326	+	0.0478691i
$153$	6.15537	+	8.47214i	0.497632	+	0.684932i
$154$	4.23607	−	3.07768i	0.341352	−	0.248007i
$155$		0			0
$156$	−0.927051	−	0.673542i	−0.0742235	−	0.0539265i
$157$			13.1803i			1.05191i	0.850514	+	0.525953i	$0.176291\pi$
$157$			13.1803i			1.05191i	−0.850514	+	0.525953i	$0.823709\pi$
$158$	−7.69421	+	10.5902i	−0.612118	+	0.842509i
$159$	1.07295	−	3.30220i	0.0850904	−	0.261881i
$160$		0			0
$161$	0.718847	+	2.21238i	0.0566531	+	0.174360i
$162$	−1.53884	−	0.500000i	−0.120903	−	0.0392837i
$163$	−10.4616	−	3.39919i	−0.819417	−	0.266245i	−0.130836	−	0.991404i	$-0.541766\pi$
$163$	−10.4616	−	3.39919i	−0.819417	−	0.266245i	−0.688581	+	0.725159i	$0.741766\pi$
$164$	0.145898	+	0.449028i	0.0113927	+	0.0350632i
$165$		0			0
$166$	3.11803	−	9.59632i	0.242006	−	0.744819i
$167$	8.55951	−	11.7812i	0.662355	−	0.911653i	−0.337202	−	0.941432i	$-0.609480\pi$
$167$	8.55951	−	11.7812i	0.662355	−	0.911653i	0.999556	+	0.0297794i	$0.00948048\pi$
$168$		−	1.38197i		−	0.106621i
$169$	−7.73607	−	5.62058i	−0.595082	−	0.432352i
$170$		0			0
$171$	1.38197	−	1.00406i	0.105682	−	0.0767822i
$172$	1.76336	+	2.42705i	0.134455	+	0.185061i
$173$	17.9641	−	5.83688i	1.36578	−	0.443770i	0.467813	−	0.883827i	$-0.345042\pi$
$173$	17.9641	−	5.83688i	1.36578	−	0.443770i	0.897970	+	0.440057i	$0.145042\pi$
$174$	−5.85410			−0.443798
$175$		0			0
$176$	25.4164			1.91583
$177$	10.3229	−	3.35410i	0.775914	−	0.252110i
$178$	8.50651	+	11.7082i	0.637590	+	0.877567i
$179$	−0.427051	+	0.310271i	−0.0319193	+	0.0231907i	−0.603631	−	0.797264i	$-0.706280\pi$
$179$	−0.427051	+	0.310271i	−0.0319193	+	0.0231907i	0.571711	+	0.820455i	$0.306280\pi$
$180$		0			0
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	0.578977	−	0.815344i	$-0.303452\pi$
$181$	−0.236068	−	0.171513i	−0.0175468	−	0.0127485i	−0.596524	+	0.802595i	$0.703452\pi$
$182$		−	1.85410i		−	0.137435i
$183$	−5.11855	+	7.04508i	−0.378374	+	0.520788i
$184$	−2.60081	+	8.00448i	−0.191734	+	0.590098i
$185$		0			0
$186$	1.50000	+	4.61653i	0.109985	+	0.338500i
$187$	26.0746	+	8.47214i	1.90676	+	0.619544i
$188$	−0.363271	−	0.118034i	−0.0264943	−	0.00860851i
$189$	0.954915	+	2.93893i	0.0694598	+	0.213775i
$190$		0			0
$191$	−0.562306	+	1.73060i	−0.0406870	+	0.125222i	−0.969337	−	0.245736i	$-0.920970\pi$
$191$	−0.562306	+	1.73060i	−0.0406870	+	0.125222i	0.928650	+	0.370958i	$0.120970\pi$
$192$	2.48990	−	3.42705i	0.179693	−	0.247326i
$193$		−	7.70820i		−	0.554849i	−0.960747	−	0.277424i	$-0.910519\pi$
$193$		−	7.70820i		−	0.554849i	0.960747	−	0.277424i	$-0.0894808\pi$
$194$	5.04508	+	3.66547i	0.362216	+	0.263165i
$195$		0			0
$196$	3.30902	−	2.40414i	0.236358	−	0.171724i
$197$	−2.17963	−	3.00000i	−0.155292	−	0.213741i	0.724281	−	0.689505i	$-0.242172\pi$
$197$	−2.17963	−	3.00000i	−0.155292	−	0.213741i	−0.879573	+	0.475764i	$0.842172\pi$
$198$	−16.1150	+	5.23607i	−1.14524	+	0.372111i
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$		0			0
$201$	4.76393			0.336022
$202$	2.26538	−	0.736068i	0.159392	−	0.0517896i
$203$	−1.31433	−	1.80902i	−0.0922477	−	0.126968i
$204$	−2.61803	+	1.90211i	−0.183299	+	0.133175i
$205$		0			0
$206$	11.2082	+	8.14324i	0.780913	+	0.567366i
$207$		−	7.52786i		−	0.523223i
$208$	5.29007	−	7.28115i	0.366800	−	0.504857i
$209$	1.38197	−	4.25325i	0.0955926	−	0.294204i
$210$		0			0
$211$	−2.83688	−	8.73102i	−0.195299	−	0.601068i	−0.999973	−	0.00735149i	$-0.997660\pi$
$211$	−2.83688	−	8.73102i	−0.195299	−	0.601068i	0.804674	−	0.593717i	$-0.202340\pi$
$212$	−2.04087	−	0.663119i	−0.140168	−	0.0455432i
$213$	6.29412	+	2.04508i	0.431266	+	0.140127i
$214$	−8.20820	−	25.2623i	−0.561101	−	1.72689i
$215$		0			0
$216$	−3.45492	+	10.6331i	−0.235077	+	0.723493i
$217$	−1.08981	+	1.50000i	−0.0739814	+	0.101827i
$218$			16.1803i			1.09587i
$219$	−7.28115	−	5.29007i	−0.492015	−	0.357470i
$220$		0			0
$221$	7.85410	−	5.70634i	0.528324	−	0.383850i
$222$	−0.224514	−	0.309017i	−0.0150684	−	0.0207399i
$223$	−0.171513	+	0.0557281i	−0.0114854	+	0.00373183i	−0.314754	−	0.949173i	$-0.601922\pi$
$223$	−0.171513	+	0.0557281i	−0.0114854	+	0.00373183i	0.303269	+	0.952905i	$0.401922\pi$
$224$	−2.09017			−0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	−14.0413	+	4.56231i	−0.931956	+	0.302811i	−0.735362	−	0.677674i	$-0.762988\pi$
$227$	−14.0413	+	4.56231i	−0.931956	+	0.302811i	−0.196594	+	0.980485i	$0.562988\pi$
$228$	0.310271	+	0.427051i	0.0205482	+	0.0282821i
$229$	17.5623	−	12.7598i	1.16055	−	0.843189i	0.170702	−	0.985323i	$-0.445396\pi$
$229$	17.5623	−	12.7598i	1.16055	−	0.843189i	0.989847	+	0.142134i	$0.0453963\pi$
$230$		0			0
$231$	2.61803	+	1.90211i	0.172254	+	0.125150i
$232$		−	8.09017i		−	0.531146i
$233$	1.73060	−	2.38197i	0.113375	−	0.156048i	−0.748558	−	0.663069i	$-0.769254\pi$
$233$	1.73060	−	2.38197i	0.113375	−	0.156048i	0.861933	+	0.507021i	$0.169254\pi$
$234$	−1.85410	+	5.70634i	−0.121206	+	0.373035i
$235$		0			0
$236$	−2.07295	−	6.37988i	−0.134937	−	0.415295i
$237$	−7.69421	−	2.50000i	−0.499793	−	0.162392i
$238$	−4.97980	−	1.61803i	−0.322792	−	0.104882i
$239$	6.34346	+	19.5232i	0.410324	+	1.26285i	0.916367	+	0.400340i	$0.131108\pi$
$239$	6.34346	+	19.5232i	0.410324	+	1.26285i	−0.506043	+	0.862508i	$0.668892\pi$
$240$		0			0
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	−0.922740	−	0.385423i	$-0.874055\pi$
$241$	0.781153	−	2.40414i	0.0503185	−	0.154864i	0.973058	+	0.230559i	$0.0740554\pi$
$242$	−15.6129	+	21.4894i	−1.00364	+	1.38139i
$243$		−	16.0000i		−	1.02640i
$244$	4.35410	+	3.16344i	0.278743	+	0.202519i
$245$		0			0
$246$	−1.00000	+	0.726543i	−0.0637577	+	0.0463227i
$247$	−0.930812	−	1.28115i	−0.0592262	−	0.0815178i
$248$	−6.37988	+	2.07295i	−0.405123	+	0.131632i
$249$	6.23607			0.395195
$250$		0			0
$251$	−29.1803			−1.84185			−0.920923	−	0.389744i	$-0.872564\pi$
$251$	−29.1803			−1.84185			−0.920923	+	0.389744i	$0.872564\pi$
$252$	0.726543	−	0.236068i	0.0457679	−	0.0148709i
$253$	−11.5842	−	15.9443i	−0.728292	−	1.00241i
$254$	−26.0344	+	18.9151i	−1.63355	+	1.18684i
$255$		0			0
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$			22.8541i			1.42560i	0.701367	+	0.712800i	$0.252573\pi$
$257$			22.8541i			1.42560i	−0.701367	+	0.712800i	$0.747427\pi$
$258$	−4.61653	+	6.35410i	−0.287412	+	0.395589i
$259$	0.0450850	−	0.138757i	0.00280144	−	0.00862196i
$260$		0			0
$261$	2.23607	+	6.88191i	0.138409	+	0.425980i
$262$	−10.4616	−	3.39919i	−0.646321	−	0.210002i
$263$	10.3759	+	3.37132i	0.639803	+	0.207885i	0.610913	−	0.791698i	$-0.290803\pi$
$263$	10.3759	+	3.37132i	0.639803	+	0.207885i	0.0288905	+	0.999583i	$0.490803\pi$
$264$	3.61803	+	11.1352i	0.222675	+	0.685322i
$265$		0			0
$266$	−0.263932	+	0.812299i	−0.0161827	+	0.0498053i
$267$	−5.25731	+	7.23607i	−0.321742	+	0.442840i
$268$		−	2.94427i		−	0.179850i
$269$	−10.3262	−	7.50245i	−0.629602	−	0.457433i	0.226660	−	0.973974i	$-0.427219\pi$
$269$	−10.3262	−	7.50245i	−0.629602	−	0.457433i	−0.856262	+	0.516541i	$0.827219\pi$
$270$		0			0
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	−0.373593	−	0.927593i	$-0.621874\pi$
$271$	6.47214	−	4.70228i	0.393154	−	0.285643i	0.766747	+	0.641950i	$0.221874\pi$
$272$	−14.9394	−	20.5623i	−0.905834	−	1.24677i
$273$	1.08981	−	0.354102i	0.0659585	−	0.0214312i
$274$	−19.3262			−1.16754
$275$		0			0
$276$	2.32624			0.140023
$277$	23.4989	−	7.63525i	1.41191	−	0.458758i	0.498889	−	0.866666i	$-0.333742\pi$
$277$	23.4989	−	7.63525i	1.41191	−	0.458758i	0.913023	+	0.407908i	$0.133742\pi$
$278$	−4.75528	−	6.54508i	−0.285203	−	0.392548i
$279$	4.85410	−	3.52671i	0.290607	−	0.211139i
$280$		0			0
$281$	−8.16312	−	5.93085i	−0.486971	−	0.353805i	0.317047	−	0.948410i	$-0.397309\pi$
$281$	−8.16312	−	5.93085i	−0.486971	−	0.353805i	−0.804018	+	0.594605i	$0.797309\pi$
$282$		−	1.00000i		−	0.0595491i
$283$	17.5478	−	24.1525i	1.04311	−	1.43572i	0.148474	−	0.988916i	$-0.452564\pi$
$283$	17.5478	−	24.1525i	1.04311	−	1.43572i	0.894634	−	0.446799i	$-0.147436\pi$
$284$	1.26393	−	3.88998i	0.0750006	−	0.230828i
$285$		0			0
$286$	4.85410	+	14.9394i	0.287029	+	0.883385i
$287$	−0.449028	−	0.145898i	−0.0265053	−	0.00861209i
$288$	6.43288	+	2.09017i	0.379061	+	0.123164i
$289$	−3.21885	−	9.90659i	−0.189344	−	0.582741i
$290$		0			0
$291$	−1.19098	+	3.66547i	−0.0698167	+	0.214874i
$292$	−3.26944	+	4.50000i	−0.191330	+	0.263343i
$293$			19.5279i			1.14083i	0.821357	+	0.570415i	$0.193218\pi$
$293$			19.5279i			1.14083i	−0.821357	+	0.570415i	$0.806782\pi$
$294$	8.66312	+	6.29412i	0.505243	+	0.367081i
$295$		0			0
$296$	0.427051	−	0.310271i	0.0248218	−	0.0180341i
$297$	−15.3884	−	21.1803i	−0.892927	−	1.22901i
$298$	6.06961	−	1.97214i	0.351603	−	0.114243i
$299$	−6.97871			−0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$	22.4091	−	7.28115i	1.28950	−	0.418983i
$303$	0.865300	+	1.19098i	0.0497102	+	0.0684202i
$304$	−3.35410	+	2.43690i	−0.192371	+	0.139766i
$305$		0			0
$306$	13.7082	+	9.95959i	0.783646	+	0.569352i
$307$			9.23607i			0.527130i	0.964642	+	0.263565i	$0.0848984\pi$
$307$			9.23607i			0.527130i	−0.964642	+	0.263565i	$0.915102\pi$
$308$	1.17557	−	1.61803i	0.0669843	−	0.0921960i
$309$	−2.64590	+	8.14324i	−0.150520	+	0.463253i
$310$		0			0
$311$	2.62868	+	8.09024i	0.149059	+	0.458755i	0.997511	−	0.0705172i	$-0.0224650\pi$
$311$	2.62868	+	8.09024i	0.149059	+	0.458755i	−0.848452	+	0.529272i	$0.822465\pi$
$312$	3.94298	+	1.28115i	0.223227	+	0.0725310i
$313$	15.9434	+	5.18034i	0.901177	+	0.292810i	0.722723	−	0.691138i	$-0.242890\pi$
$313$	15.9434	+	5.18034i	0.901177	+	0.292810i	0.178454	+	0.983948i	$0.442890\pi$
$314$	6.59017	+	20.2825i	0.371905	+	1.14461i
$315$		0			0
$316$	−1.54508	+	4.75528i	−0.0869178	+	0.267506i
$317$	4.49801	−	6.19098i	0.252634	−	0.347720i	−0.663798	−	0.747912i	$-0.731056\pi$
$317$	4.49801	−	6.19098i	0.252634	−	0.347720i	0.916431	+	0.400192i	$0.131056\pi$
$318$		−	5.61803i		−	0.315044i
$319$	15.3262	+	11.1352i	0.858105	+	0.623449i
$320$		0			0
$321$	13.2812	−	9.64932i	0.741282	−	0.538573i
$322$	2.21238	+	3.04508i	0.123291	+	0.169696i
$323$	−4.25325	+	1.38197i	−0.236657	+	0.0768946i
$324$	−0.618034			−0.0343352
$325$		0			0
$326$	−17.7984			−0.985761
$327$	−9.51057	+	3.09017i	−0.525935	+	0.170887i
$328$	−1.00406	−	1.38197i	−0.0554398	−	0.0763063i
$329$	0.309017	−	0.224514i	0.0170367	−	0.0123779i
$330$		0			0
$331$	18.7082	+	13.5923i	1.02830	+	0.747101i	0.967967	−	0.251078i	$-0.0807850\pi$
$331$	18.7082	+	13.5923i	1.02830	+	0.747101i	0.0603290	+	0.998179i	$0.480785\pi$
$332$		−	3.85410i		−	0.211521i
$333$	−0.277515	+	0.381966i	−0.0152077	+	0.0209316i
$334$	7.28115	−	22.4091i	0.398407	−	1.22617i
$335$		0			0
$336$	−0.927051	−	2.85317i	−0.0505748	−	0.155653i
$337$	7.46969	+	2.42705i	0.406900	+	0.132210i	0.505314	−	0.862936i	$-0.331377\pi$
$337$	7.46969	+	2.42705i	0.406900	+	0.132210i	−0.0984135	+	0.995146i	$0.531377\pi$
$338$	−14.7149	−	4.78115i	−0.800384	−	0.260060i
$339$	−5.20820	−	16.0292i	−0.282871	−	0.870587i
$340$		0			0
$341$	4.85410	−	14.9394i	0.262864	−	0.809013i
$342$	1.62460	−	2.23607i	0.0878482	−	0.120913i
$343$			8.41641i			0.454443i
$344$	−8.78115	−	6.37988i	−0.473448	−	0.343980i
$345$		0			0
$346$	24.7254	−	17.9641i	1.32925	−	0.965755i
$347$	11.7027	+	16.1074i	0.628234	+	0.864690i	0.997920	−	0.0644668i	$-0.0205347\pi$
$347$	11.7027	+	16.1074i	0.628234	+	0.864690i	−0.369686	+	0.929157i	$0.620535\pi$
$348$	−2.12663	+	0.690983i	−0.113999	+	0.0370406i
$349$	−21.7082			−1.16201			−0.581007	−	0.813899i	$-0.697341\pi$
$349$	−21.7082			−1.16201			−0.581007	+	0.813899i	$0.697341\pi$
$350$		0			0
$351$	−9.27051			−0.494823
$352$	16.8415	−	5.47214i	0.897655	−	0.291666i
$353$	7.58821	+	10.4443i	0.403880	+	0.555893i	0.961712	−	0.274061i	$-0.0883670\pi$
$353$	7.58821	+	10.4443i	0.403880	+	0.555893i	−0.557833	+	0.829953i	$0.688367\pi$
$354$	14.2082	−	10.3229i	0.755158	−	0.548654i
$355$		0			0
$356$	4.47214	+	3.24920i	0.237023	+	0.172207i
$357$		−	3.23607i		−	0.171271i
$358$	−0.502029	+	0.690983i	−0.0265330	+	0.0365196i
$359$	−4.24671	+	13.0700i	−0.224133	+	0.689810i	0.774246	+	0.632885i	$0.218130\pi$
$359$	−4.24671	+	13.0700i	−0.224133	+	0.689810i	−0.998378	+	0.0569247i	$0.981870\pi$
$360$		0			0
$361$	−5.64590	−	17.3763i	−0.297153	−	0.914541i
$362$	−0.449028	−	0.145898i	−0.0236004	−	0.00766823i
$363$	−15.6129	−	5.07295i	−0.819466	−	0.266261i
$364$	−0.218847	−	0.673542i	−0.0114707	−	0.0353032i
$365$		0			0
$366$	−4.35410	+	13.4005i	−0.227593	+	0.700458i
$367$	−15.0251	+	20.6803i	−0.784306	+	1.07950i	0.210488	+	0.977597i	$0.432495\pi$
$367$	−15.0251	+	20.6803i	−0.784306	+	1.07950i	−0.994794	+	0.101908i	$0.967505\pi$
$368$			18.2705i			0.952416i
$369$	1.23607	+	0.898056i	0.0643471	+	0.0467509i
$370$		0			0
$371$	1.73607	−	1.26133i	0.0901322	−	0.0654848i
$372$	1.08981	+	1.50000i	0.0565042	+	0.0777714i
$373$	−26.8869	+	8.73607i	−1.39215	+	0.452336i	−0.906644	−	0.421897i	$-0.861364\pi$
$373$	−26.8869	+	8.73607i	−1.39215	+	0.452336i	−0.485505	+	0.874234i	$0.661364\pi$
$374$	44.3607			2.29384
$375$		0			0
$376$	1.38197			0.0712695
$377$	6.37988	−	2.07295i	0.328581	−	0.106762i
$378$	2.93893	+	4.04508i	0.151162	+	0.208057i
$379$	11.8090	−	8.57975i	0.606588	−	0.440712i	−0.241623	−	0.970370i	$-0.577680\pi$
$379$	11.8090	−	8.57975i	0.606588	−	0.440712i	0.848211	+	0.529658i	$0.177680\pi$
$380$		0			0
$381$	−16.0902	−	11.6902i	−0.824324	−	0.598907i
$382$			2.94427i			0.150642i
$383$	−19.6089	+	26.9894i	−1.00197	+	1.37909i	−0.0778591	+	0.996964i	$0.524808\pi$
$383$	−19.6089	+	26.9894i	−1.00197	+	1.37909i	−0.924110	+	0.382127i	$0.875192\pi$
$384$	4.20820	−	12.9515i	0.214749	−	0.660929i
$385$		0			0
$386$	−3.85410	−	11.8617i	−0.196169	−	0.603745i
$387$	9.23305	+	3.00000i	0.469342	+	0.152499i
$388$	2.26538	+	0.736068i	0.115007	+	0.0373682i
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	−0.997119	−	0.0758507i	$-0.975833\pi$
$389$	−4.63525	−	14.2658i	−0.235017	−	0.723307i	0.762102	−	0.647456i	$-0.224167\pi$
$390$		0			0
$391$	−6.09017	+	18.7436i	−0.307993	+	0.947905i
$392$	−8.69827	+	11.9721i	−0.439329	+	0.604684i
$393$		−	6.79837i		−	0.342933i
$394$	−4.85410	−	3.52671i	−0.244546	−	0.177673i
$395$		0			0
$396$	−5.23607	+	3.80423i	−0.263122	+	0.191170i
$397$	−17.0660	−	23.4894i	−0.856519	−	1.17890i	−0.982388	−	0.186850i	$-0.940172\pi$
$397$	−17.0660	−	23.4894i	−0.856519	−	1.17890i	0.125870	−	0.992047i	$-0.459828\pi$
$398$	27.0256	−	8.78115i	1.35467	−	0.440159i
$399$	−0.527864			−0.0264263
$400$		0			0
$401$	26.5967			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$401$	26.5967			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$402$	7.33094	−	2.38197i	0.365634	−	0.118802i
$403$	−3.26944	−	4.50000i	−0.162862	−	0.224161i
$404$	0.736068	−	0.534785i	0.0366208	−	0.0266065i
$405$		0			0
$406$	−2.92705	−	2.12663i	−0.145267	−	0.105543i
$407$			1.23607i			0.0612696i
$408$	6.88191	−	9.47214i	0.340705	−	0.468941i
$409$	−0.489357	+	1.50609i	−0.0241971	+	0.0744711i	−0.962426	−	0.271544i	$-0.912466\pi$
$409$	−0.489357	+	1.50609i	−0.0241971	+	0.0744711i	0.938229	+	0.346016i	$0.112466\pi$
$410$		0			0
$411$	−3.69098	−	11.3597i	−0.182063	−	0.560332i
$412$	5.03280	+	1.63525i	0.247948	+	0.0805632i
$413$	6.37988	+	2.07295i	0.313933	+	0.102003i
$414$	−3.76393	−	11.5842i	−0.184987	−	0.569332i
$415$		0			0
$416$	1.93769	−	5.96361i	0.0950033	−	0.292390i
$417$	2.93893	−	4.04508i	0.143920	−	0.198089i
$418$		−	7.23607i		−	0.353928i
$419$	−7.66312	−	5.56758i	−0.374368	−	0.271994i	0.384652	−	0.923062i	$-0.374321\pi$
$419$	−7.66312	−	5.56758i	−0.374368	−	0.271994i	−0.759020	+	0.651068i	$0.774321\pi$
$420$		0			0
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.998841	−	0.0481252i	$-0.984675\pi$
$421$	−25.8885	+	18.8091i	−1.26173	+	0.916701i	−0.262889	+	0.964826i	$0.584675\pi$
$422$	−8.73102	−	12.0172i	−0.425020	−	0.584989i
$423$	−1.17557	+	0.381966i	−0.0571582	+	0.0185718i
$424$	7.76393			0.377050
$425$		0			0
$426$	10.7082			0.518814
$427$	−5.11855	+	1.66312i	−0.247704	+	0.0804840i
$428$	−5.96361	−	8.20820i	−0.288262	−	0.396759i
$429$	−7.85410	+	5.70634i	−0.379200	+	0.275505i
$430$		0			0
$431$	24.1353	+	17.5353i	1.16255	+	0.844645i	0.990099	−	0.140372i	$-0.0448299\pi$
$431$	24.1353	+	17.5353i	1.16255	+	0.844645i	0.172456	+	0.985017i	$0.444830\pi$
$432$			24.2705i			1.16772i
$433$	−15.7844	+	21.7254i	−0.758552	+	1.04406i	0.238781	+	0.971073i	$0.423252\pi$
$433$	−15.7844	+	21.7254i	−0.758552	+	1.04406i	−0.997333	+	0.0729839i	$0.976748\pi$
$434$	−0.927051	+	2.85317i	−0.0444999	+	0.136957i
$435$		0			0
$436$	1.90983	+	5.87785i	0.0914643	+	0.281498i
$437$	3.05744	+	0.993422i	0.146257	+	0.0475218i
$438$	−13.8496	−	4.50000i	−0.661758	−	0.215018i
$439$	12.6631	+	38.9731i	0.604378	+	1.86008i	0.501013	+	0.865440i	$0.332961\pi$
$439$	12.6631	+	38.9731i	0.604378	+	1.86008i	0.103365	+	0.994644i	$0.467039\pi$
$440$		0			0
$441$	4.09017	−	12.5882i	0.194770	−	0.599440i
$442$	9.23305	−	12.7082i	0.439171	−	0.604468i
$443$		−	29.9443i		−	1.42270i	−0.702840	−	0.711348i	$-0.748085\pi$
$443$		−	29.9443i		−	1.42270i	0.702840	−	0.711348i	$-0.251915\pi$
$444$	−0.118034	−	0.0857567i	−0.00560165	−	0.00406983i
$445$		0			0
$446$	−0.236068	+	0.171513i	−0.0111781	+	0.00812140i
$447$	2.31838	+	3.19098i	0.109656	+	0.150928i
$448$	2.48990	−	0.809017i	0.117637	−	0.0382225i
$449$	−4.67376			−0.220568			−0.110284	−	0.993900i	$-0.535176\pi$
$449$	−4.67376			−0.220568			−0.110284	+	0.993900i	$0.535176\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−9.90659	+	3.21885i	−0.465967	+	0.151402i
$453$	8.55951	+	11.7812i	0.402161	+	0.553527i
$454$	−19.3262	+	14.0413i	−0.907025	+	0.658992i
$455$		0			0
$456$	−1.54508	−	1.12257i	−0.0723552	−	0.0525692i
$457$		−	21.4164i		−	1.00182i	−0.865500	−	0.500909i	$-0.832999\pi$
$457$		−	21.4164i		−	1.00182i	0.865500	−	0.500909i	$-0.167001\pi$
$458$	20.6457	−	28.4164i	0.964712	−	1.32781i
$459$	−8.09017	+	24.8990i	−0.377617	+	1.16218i
$460$		0			0
$461$	0.253289	+	0.779543i	0.0117968	+	0.0363069i	0.956782	−	0.290807i	$-0.0939238\pi$
$461$	0.253289	+	0.779543i	0.0117968	+	0.0363069i	−0.944985	+	0.327114i	$0.893924\pi$
$462$	4.97980	+	1.61803i	0.231681	+	0.0752778i
$463$	22.9439	+	7.45492i	1.06629	+	0.346459i	0.789042	−	0.614339i	$-0.210577\pi$
$463$	22.9439	+	7.45492i	1.06629	+	0.346459i	0.277250	+	0.960798i	$0.410577\pi$
$464$	−5.42705	−	16.7027i	−0.251945	−	0.775405i
$465$		0			0
$466$	1.47214	−	4.53077i	0.0681954	−	0.209884i
$467$	16.1352	−	22.2082i	0.746648	−	1.02767i	−0.251560	−	0.967842i	$-0.580944\pi$
$467$	16.1352	−	22.2082i	0.746648	−	1.02767i	0.998208	−	0.0598315i	$-0.0190563\pi$
$468$			2.29180i			0.105938i
$469$	2.38197	+	1.73060i	0.109989	+	0.0799117i
$470$		0			0
$471$	−10.6631	+	7.74721i	−0.491331	+	0.356973i
$472$	14.2658	+	19.6353i	0.656639	+	0.903786i
$473$	24.1724	−	7.85410i	1.11145	−	0.361132i
$474$	−13.0902			−0.601251
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	−6.60440	+	2.14590i	−0.302394	+	0.0982539i
$478$	19.5232	+	26.8713i	0.892969	+	1.22907i
$479$	−8.78115	+	6.37988i	−0.401221	+	0.291504i	−0.770038	−	0.637998i	$-0.779763\pi$
$479$	−8.78115	+	6.37988i	−0.401221	+	0.291504i	0.368817	+	0.929502i	$0.379763\pi$
$480$		0			0
$481$	0.354102	+	0.257270i	0.0161457	+	0.0117305i
$482$		−	4.09017i		−	0.186302i
$483$	−1.36733	+	1.88197i	−0.0622156	+	0.0856324i
$484$	−3.13525	+	9.64932i	−0.142512	+	0.438606i
$485$		0			0
$486$	−8.00000	−	24.6215i	−0.362887	−	1.11685i
$487$	−34.6341	−	11.2533i	−1.56942	−	0.509935i	−0.610116	−	0.792312i	$-0.708877\pi$
$487$	−34.6341	−	11.2533i	−1.56942	−	0.509935i	−0.959303	+	0.282377i	$0.908877\pi$
$488$	−18.5191	−	6.01722i	−0.838320	−	0.272387i
$489$	−3.39919	−	10.4616i	−0.153717	−	0.473091i
$490$		0			0
$491$	−13.3647	+	41.1325i	−0.603143	+	1.85628i	−0.0940550	+	0.995567i	$0.529983\pi$
$491$	−13.3647	+	41.1325i	−0.603143	+	1.85628i	−0.509088	+	0.860715i	$0.670017\pi$
$492$	−0.277515	+	0.381966i	−0.0125113	+	0.0172204i
$493$		−	18.9443i		−	0.853207i
$494$	−2.07295	−	1.50609i	−0.0932664	−	0.0677620i
$495$		0			0
$496$	−11.7812	+	8.55951i	−0.528989	+	0.384333i
$497$	2.40414	+	3.30902i	0.107840	+	0.148430i
$498$	9.59632	−	3.11803i	0.430021	−	0.139722i
$499$	−7.56231			−0.338535			−0.169268	−	0.985570i	$-0.554140\pi$
$499$	−7.56231			−0.338535			−0.169268	+	0.985570i	$0.554140\pi$
$500$		0			0
$501$	14.5623			0.650596
$502$	−44.9039	+	14.5902i	−2.00416	+	0.651191i
$503$	−21.9928	−	30.2705i	−0.980611	−	1.34970i	−0.936500	−	0.350669i	$-0.885954\pi$
$503$	−21.9928	−	30.2705i	−0.980611	−	1.34970i	−0.0441115	−	0.999027i	$-0.514046\pi$
$504$	−2.23607	+	1.62460i	−0.0996024	+	0.0723654i
$505$		0			0
$506$	−25.7984	−	18.7436i	−1.14688	−	0.833255i
$507$		−	9.56231i		−	0.424677i
$508$	−7.22494	+	9.94427i	−0.320555	+	0.441206i
$509$	6.28115	−	19.3314i	0.278407	−	0.856849i	−0.709891	−	0.704312i	$-0.751256\pi$
$509$	6.28115	−	19.3314i	0.278407	−	0.856849i	0.988298	−	0.152537i	$-0.0487444\pi$
$510$		0			0
$511$	−1.71885	−	5.29007i	−0.0760373	−	0.234019i
$512$	5.03280	+	1.63525i	0.222420	+	0.0722687i
$513$	4.06150	+	1.31966i	0.179319	+	0.0582644i
$514$	11.4271	+	35.1688i	0.504026	+	1.55123i
$515$		0			0
$516$	−0.927051	+	2.85317i	−0.0408111	+	0.125604i
$517$	−1.90211	+	2.61803i	−0.0836548	+	0.115141i
$518$		−	0.236068i		−	0.0103722i
$519$	15.2812	+	11.1024i	0.670768	+	0.487342i
$520$		0			0
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.970412	−	0.241453i	$-0.922376\pi$
$521$	−23.7533	+	17.2578i	−1.04065	+	0.756077i	−0.0702381	+	0.997530i	$0.522376\pi$
$522$	6.88191	+	9.47214i	0.301213	+	0.414584i
$523$	−12.5025	+	4.06231i	−0.546696	+	0.177632i	−0.569326	−	0.822112i	$-0.692796\pi$
$523$	−12.5025	+	4.06231i	−0.546696	+	0.177632i	0.0226305	+	0.999744i	$0.492796\pi$
$524$	−4.20163			−0.183549
$525$		0			0
$526$	17.6525			0.769685
$527$	−14.9394	+	4.85410i	−0.650770	+	0.211448i
$528$	14.9394	+	20.5623i	0.650153	+	0.894860i
$529$	−7.14590	+	5.19180i	−0.310691	+	0.225730i
$530$		0			0
$531$	−17.5623	−	12.7598i	−0.762139	−	0.553727i
$532$			0.326238i			0.0141442i
$533$	0.832544	−	1.14590i	0.0360615	−	0.0496344i
$534$	−4.47214	+	13.7638i	−0.193528	+	0.595619i
$535$		0			0
$536$	3.29180	+	10.1311i	0.142184	+	0.437597i
$537$	−0.502029	−	0.163119i	−0.0216641	−	0.00703910i
$538$	−19.6417	−	6.38197i	−0.846813	−	0.275146i
$539$	−10.7082	−	32.9565i	−0.461235	−	1.41954i
$540$		0			0
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	−0.592462	−	0.805599i	$-0.701844\pi$
$541$	8.38197	−	25.7970i	0.360369	−	1.10910i	0.952831	−	0.303503i	$-0.0981561\pi$
$542$	7.60845	−	10.4721i	0.326811	−	0.449817i
$543$		−	0.291796i		−	0.0125222i
$544$	−14.3262	−	10.4086i	−0.614232	−	0.446266i
$545$		0			0
$546$	1.50000	−	1.08981i	0.0641941	−	0.0466397i
$547$	12.5150	+	17.2254i	0.535103	+	0.736506i	0.987897	−	0.155109i	$-0.0495729\pi$
$547$	12.5150	+	17.2254i	0.535103	+	0.736506i	−0.452794	+	0.891615i	$0.649573\pi$
$548$	−7.02067	+	2.28115i	−0.299908	+	0.0974460i
$549$	17.4164			0.743314
$550$		0			0
$551$	−3.09017			−0.131646
$552$	−8.00448	+	2.60081i	−0.340693	+	0.110698i
$553$	−2.93893	−	4.04508i	−0.124976	−	0.172015i
$554$	32.3435	−	23.4989i	1.37414	−	0.998373i
$555$		0			0
$556$	−2.50000	−	1.81636i	−0.106024	−	0.0770307i
$557$			4.76393i			0.201854i	0.994894	+	0.100927i	$0.0321809\pi$
$557$			4.76393i			0.201854i	−0.994894	+	0.100927i	$0.967819\pi$
$558$	5.70634	−	7.85410i	0.241569	−	0.332491i
$559$	2.78115	−	8.55951i	0.117630	−	0.362029i
$560$		0			0
$561$	8.47214	+	26.0746i	0.357694	+	1.10087i
$562$	−15.5272	−	5.04508i	−0.654974	−	0.212814i
$563$	−7.02067	−	2.28115i	−0.295886	−	0.0961391i	0.157312	−	0.987549i	$-0.449717\pi$
$563$	−7.02067	−	2.28115i	−0.295886	−	0.0961391i	−0.453198	+	0.891410i	$0.649717\pi$
$564$	−0.118034	−	0.363271i	−0.00497013	−	0.0152965i
$565$		0			0
$566$	14.9271	−	45.9407i	0.627431	−	1.93103i
$567$	0.363271	−	0.500000i	0.0152560	−	0.0209980i
$568$			14.7984i			0.620926i
$569$	16.6074	+	12.0660i	0.696218	+	0.505832i	0.878698	−	0.477377i	$-0.158413\pi$
$569$	16.6074	+	12.0660i	0.696218	+	0.505832i	−0.182480	+	0.983210i	$0.558413\pi$
$570$		0			0
$571$	6.57295	−	4.77553i	0.275069	−	0.199850i	−0.441695	−	0.897165i	$-0.645623\pi$
$571$	6.57295	−	4.77553i	0.275069	−	0.199850i	0.716764	+	0.697316i	$0.245623\pi$
$572$	3.52671	+	4.85410i	0.147459	+	0.202960i
$573$	−1.73060	+	0.562306i	−0.0722968	+	0.0234907i
$574$	−0.763932			−0.0318859
$575$		0			0
$576$	−8.47214			−0.353006
$577$	32.1239	−	10.4377i	1.33734	−	0.434527i	0.448923	−	0.893571i	$-0.351808\pi$
$577$	32.1239	−	10.4377i	1.33734	−	0.434527i	0.888414	+	0.459044i	$0.151808\pi$
$578$	−9.90659	−	13.6353i	−0.412060	−	0.567152i
$579$	6.23607	−	4.53077i	0.259162	−	0.188292i
$580$		0			0
$581$	3.11803	+	2.26538i	0.129358	+	0.0939840i
$582$			6.23607i			0.258493i
$583$	−10.6861	+	14.7082i	−0.442575	+	0.609152i
$584$	6.21885	−	19.1396i	0.257338	−	0.792004i
$585$		0			0
$586$	9.76393	+	30.0503i	0.403344	+	1.24137i
$587$	5.03280	+	1.63525i	0.207726	+	0.0674942i	0.411032	−	0.911621i	$-0.365169\pi$
$587$	5.03280	+	1.63525i	0.207726	+	0.0674942i	−0.203306	+	0.979115i	$0.565169\pi$
$588$	3.88998	+	1.26393i	0.160420	+	0.0521237i
$589$	0.791796	+	2.43690i	0.0326254	+	0.100411i
$590$		0			0
$591$	1.14590	−	3.52671i	0.0471359	−	0.145070i
$592$	0.673542	−	0.927051i	0.0276824	−	0.0381016i
$593$			10.9098i			0.448013i	0.974588	+	0.224007i	$0.0719137\pi$
$593$			10.9098i			0.448013i	−0.974588	+	0.224007i	$0.928086\pi$
$594$	−34.2705	−	24.8990i	−1.40614	−	1.02162i
$595$		0			0
$596$	1.97214	−	1.43284i	0.0807818	−	0.0586914i
$597$	10.3229	+	14.2082i	0.422487	+	0.581503i
$598$	−10.7391	+	3.48936i	−0.439156	+	0.142690i
$599$	9.47214			0.387021			0.193510	−	0.981098i	$-0.438013\pi$
$599$	9.47214			0.387021			0.193510	+	0.981098i	$0.438013\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	−4.61653	+	1.50000i	−0.188156	+	0.0611354i
$603$	−5.60034	−	7.70820i	−0.228063	−	0.313902i
$604$	7.28115	−	5.29007i	0.296266	−	0.215250i
$605$		0			0
$606$	1.92705	+	1.40008i	0.0782811	+	0.0568745i
$607$		−	35.5623i		−	1.44343i	−0.692191	−	0.721715i	$-0.743354\pi$
$607$		−	35.5623i		−	1.44343i	0.692191	−	0.721715i	$-0.256646\pi$
$608$	−1.69784	+	2.33688i	−0.0688566	+	0.0947730i
$609$	0.690983	−	2.12663i	0.0280000	−	0.0861753i
$610$		0			0
$611$	0.354102	+	1.08981i	0.0143254	+	0.0440891i
$612$	6.15537	+	2.00000i	0.248816	+	0.0808452i
$613$	14.2456	+	4.62868i	0.575374	+	0.186951i	0.582227	−	0.813026i	$-0.302181\pi$
$613$	14.2456	+	4.62868i	0.575374	+	0.186951i	−0.00685287	+	0.999977i	$0.502181\pi$
$614$	4.61803	+	14.2128i	0.186369	+	0.573584i
$615$		0			0
$616$	−2.23607	+	6.88191i	−0.0900937	+	0.277280i
$617$	8.36775	−	11.5172i	0.336873	−	0.463666i	−0.606652	−	0.794968i	$-0.707488\pi$
$617$	8.36775	−	11.5172i	0.336873	−	0.463666i	0.943525	+	0.331302i	$0.107488\pi$
$618$			13.8541i			0.557294i
$619$	24.6976	+	17.9438i	0.992679	+	0.721223i	0.960506	−	0.278259i	$-0.0897573\pi$
$619$	24.6976	+	17.9438i	0.992679	+	0.721223i	0.0321727	+	0.999482i	$0.489757\pi$
$620$		0			0
$621$	15.2254	−	11.0619i	0.610975	−	0.443900i
$622$	8.09024	+	11.1353i	0.324389	+	0.446483i
$623$	−5.25731	+	1.70820i	−0.210630	+	0.0684377i
$624$	9.00000			0.360288
$625$		0			0
$626$	27.1246			1.08412
$627$	4.25325	−	1.38197i	0.169859	−	0.0551904i
$628$	4.78804	+	6.59017i	0.191064	+	0.262976i
$629$	1.00000	−	0.726543i	0.0398726	−	0.0289691i
$630$		0			0
$631$	8.28115	+	6.01661i	0.329667	+	0.239517i	0.740290	−	0.672288i	$-0.234688\pi$
$631$	8.28115	+	6.01661i	0.329667	+	0.239517i	−0.410622	+	0.911806i	$0.634688\pi$
$632$		−	18.0902i		−	0.719588i
$633$	5.39607	−	7.42705i	0.214474	−	0.295199i
$634$	3.82624	−	11.7759i	0.151959	−	0.467683i
$635$		0			0
$636$	−0.663119	−	2.04087i	−0.0262944	−	0.0809258i
$637$	−11.6699	−	3.79180i	−0.462380	−	0.150236i
$638$	29.1522	+	9.47214i	1.15415	+	0.375005i
$639$	−4.09017	−	12.5882i	−0.161805	−	0.497983i
$640$		0			0
$641$	−0.336881	+	1.03681i	−0.0133060	+	0.0409517i	−0.957489	−	0.288470i	$-0.906854\pi$
$641$	−0.336881	+	1.03681i	−0.0133060	+	0.0409517i	0.944183	+	0.329421i	$0.106854\pi$
$642$	15.6129	−	21.4894i	0.616193	−	0.848117i
$643$			30.8328i			1.21593i	0.793965	+	0.607964i	$0.208013\pi$
$643$			30.8328i			1.21593i	−0.793965	+	0.607964i	$0.791987\pi$
$644$	1.16312	+	0.845055i	0.0458333	+	0.0332998i
$645$		0			0
$646$	−5.85410	+	4.25325i	−0.230327	+	0.167342i
$647$	21.4783	+	29.5623i	0.844398	+	1.16221i	0.985069	+	0.172158i	$0.0550739\pi$
$647$	21.4783	+	29.5623i	0.844398	+	1.16221i	−0.140671	+	0.990056i	$0.544926\pi$
$648$	2.12663	−	0.690983i	0.0835418	−	0.0271444i
$649$	−56.8328			−2.23088
$650$		0			0
$651$	−1.85410			−0.0726680
$652$	−6.46564	+	2.10081i	−0.253214	+	0.0822742i
$653$	11.2209	+	15.4443i	0.439109	+	0.604381i	0.970014	−	0.243050i	$-0.0781480\pi$
$653$	11.2209	+	15.4443i	0.439109	+	0.604381i	−0.530905	+	0.847431i	$0.678148\pi$
$654$	−13.0902	+	9.51057i	−0.511866	+	0.371893i
$655$		0			0
$656$	−3.00000	−	2.17963i	−0.117130	−	0.0851002i
$657$			18.0000i			0.702247i
$658$	0.363271	−	0.500000i	0.0141618	−	0.0194920i
$659$	−4.79837	+	14.7679i	−0.186918	+	0.575275i	−0.999976	−	0.00690786i	$-0.997801\pi$
$659$	−4.79837	+	14.7679i	−0.186918	+	0.575275i	0.813058	+	0.582183i	$0.197801\pi$
$660$		0			0
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	0.996902	+	0.0786563i	$0.0250630\pi$
$661$	6.08359	+	18.7234i	0.236624	+	0.728255i	−0.760277	+	0.649598i	$0.774937\pi$
$662$	35.5851	+	11.5623i	1.38305	+	0.449382i
$663$	9.23305	+	3.00000i	0.358582	+	0.116510i
$664$	4.30902	+	13.2618i	0.167222	+	0.514657i
$665$		0			0
$666$	−0.236068	+	0.726543i	−0.00914745	+	0.0281530i
$667$	−8.00448	+	11.0172i	−0.309935	+	0.426588i
$668$		−	9.00000i		−	0.348220i
$669$	−0.145898	−	0.106001i	−0.00564074	−	0.00409824i
$670$		0			0
$671$	36.8885	−	26.8011i	1.42407	−	1.03464i
$672$	−1.22857	−	1.69098i	−0.0473932	−	0.0652311i
$673$	11.5842	−	3.76393i	0.446538	−	0.145089i	−0.0771122	−	0.997022i	$-0.524570\pi$
$673$	11.5842	−	3.76393i	0.446538	−	0.145089i	0.523650	+	0.851934i	$0.324570\pi$
$674$	12.7082			0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	−10.0984	+	3.28115i	−0.388111	+	0.126105i	−0.496571	−	0.867996i	$-0.665408\pi$
$677$	−10.0984	+	3.28115i	−0.388111	+	0.126105i	0.108460	+	0.994101i	$0.465408\pi$
$678$	−16.0292	−	22.0623i	−0.615598	−	0.847298i
$679$	−1.92705	+	1.40008i	−0.0739534	+	0.0537303i
$680$		0			0
$681$	−11.9443	−	8.67802i	−0.457705	−	0.332543i
$682$		−	25.4164i		−	0.973245i
$683$	7.91872	−	10.8992i	0.303002	−	0.417046i	−0.630181	−	0.776448i	$-0.717019\pi$
$683$	7.91872	−	10.8992i	0.303002	−	0.417046i	0.933183	+	0.359402i	$0.117019\pi$
$684$	0.326238	−	1.00406i	0.0124740	−	0.0383911i
$685$		0			0
$686$	4.20820	+	12.9515i	0.160670	+	0.494491i
$687$	20.6457	+	6.70820i	0.787684	+	0.255934i
$688$	−22.4091	−	7.28115i	−0.854338	−	0.277591i
$689$	1.98936	+	6.12261i	0.0757885	+	0.233253i
$690$		0			0
$691$	11.2082	−	34.4953i	0.426380	−	1.31226i	−0.475286	−	0.879831i	$-0.657656\pi$
$691$	11.2082	−	34.4953i	0.426380	−	1.31226i	0.901667	−	0.432432i	$-0.142344\pi$
$692$	6.86167	−	9.44427i	0.260841	−	0.359017i
$693$		−	6.47214i		−	0.245856i
$694$	26.0623	+	18.9354i	0.989312	+	0.718777i
$695$		0			0
$696$	6.54508	−	4.75528i	0.248091	−	0.180249i
$697$	−2.35114	−	3.23607i	−0.0890558	−	0.122575i
$698$	−33.4055	+	10.8541i	−1.26442	+	0.410834i
$699$	2.94427			0.111363
$700$		0			0
$701$	−41.0132			−1.54905			−0.774523	−	0.632546i	$-0.782010\pi$
$701$	−41.0132			−1.54905			−0.774523	+	0.632546i	$0.782010\pi$
$702$	−14.2658	+	4.63525i	−0.538430	+	0.174946i
$703$	−0.118513	−	0.163119i	−0.00446980	−	0.00615215i
$704$	−17.9443	+	13.0373i	−0.676300	+	0.491361i
$705$		0			0
$706$	16.8992	+	12.2780i	0.636009	+	0.462088i
$707$			0.909830i			0.0342177i
$708$	3.94298	−	5.42705i	0.148186	−	0.203961i
$709$	10.3647	−	31.8994i	0.389256	−	1.19801i	−0.544089	−	0.839027i	$-0.683125\pi$
$709$	10.3647	−	31.8994i	0.389256	−	1.19801i	0.933345	−	0.358980i	$-0.116875\pi$
$710$		0			0
$711$	5.00000	+	15.3884i	0.187515	+	0.577111i
$712$	−19.0211	−	6.18034i	−0.712847	−	0.231618i
$713$	10.7391	+	3.48936i	0.402184	+	0.130677i
$714$	−1.61803	−	4.97980i	−0.0605534	−	0.186364i
$715$		0			0
$716$	−0.100813	+	0.310271i	−0.00376756	+	0.0115954i
$717$	−12.0660	+	16.6074i	−0.450612	+	0.620214i
$718$			22.2361i			0.829843i
$719$	−18.8435	−	13.6906i	−0.702742	−	0.510572i	0.178082	−	0.984016i	$-0.443011\pi$
$719$	−18.8435	−	13.6906i	−0.702742	−	0.510572i	−0.880824	+	0.473443i	$0.843011\pi$
$720$		0			0
$721$	−4.28115	+	3.11044i	−0.159438	+	0.115839i
$722$	−17.3763	−	23.9164i	−0.646678	−	0.890077i
$723$	2.40414	−	0.781153i	0.0894110	−	0.0290514i
$724$	−0.180340			−0.00670228
$725$		0			0
$726$	−26.5623			−0.985820
$727$	−23.3601	+	7.59017i	−0.866380	+	0.281504i	−0.708291	−	0.705921i	$-0.750533\pi$
$727$	−23.3601	+	7.59017i	−0.866380	+	0.281504i	−0.158089	+	0.987425i	$0.550533\pi$
$728$	1.50609	+	2.07295i	0.0558192	+	0.0768286i
$729$	10.5172	−	7.64121i	0.389527	−	0.283008i
$730$		0			0
$731$	−20.5623	−	14.9394i	−0.760524	−	0.552553i
$732$			5.38197i			0.198923i
$733$	11.7432	−	16.1631i	0.433745	−	0.596998i	−0.535063	−	0.844812i	$-0.679712\pi$
$733$	11.7432	−	16.1631i	0.433745	−	0.596998i	0.968808	+	0.247814i	$0.0797121\pi$
$734$	−12.7812	+	39.3363i	−0.471761	+	1.45193i
$735$		0			0
$736$	3.93363	+	12.1065i	0.144995	+	0.446250i
$737$	−23.7234	−	7.70820i	−0.873863	−	0.283935i
$738$	2.35114	+	0.763932i	0.0865467	+	0.0281207i
$739$	−4.93769	−	15.1967i	−0.181636	−	0.559018i	0.818238	−	0.574879i	$-0.194951\pi$
$739$	−4.93769	−	15.1967i	−0.181636	−	0.559018i	−0.999874	+	0.0158612i	$0.994951\pi$
$740$		0			0
$741$	0.489357	−	1.50609i	0.0179770	−	0.0553274i
$742$	2.04087	−	2.80902i	0.0749227	−	0.103122i
$743$		−	28.3607i		−	1.04045i	−0.854029	−	0.520226i	$-0.825848\pi$
$743$		−	28.3607i		−	1.04045i	0.854029	−	0.520226i	$-0.174152\pi$
$744$	−5.42705	−	3.94298i	−0.198965	−	0.144557i
$745$		0			0
$746$	−37.0066	+	26.8869i	−1.35491	+	0.984398i
$747$	−7.33094	−	10.0902i	−0.268225	−	0.369180i
$748$	16.1150	−	5.23607i	0.589221	−	0.191450i
$749$	10.1459			0.370723
$750$		0			0
$751$	−5.11146			−0.186520			−0.0932598	−	0.995642i	$-0.529729\pi$
$751$	−5.11146			−0.186520			−0.0932598	+	0.995642i	$0.529729\pi$
$752$	2.85317	−	0.927051i	0.104044	−	0.0338061i
$753$	−17.1518	−	23.6074i	−0.625045	−	0.860301i
$754$	8.78115	−	6.37988i	0.319791	−	0.232342i
$755$		0			0
$756$	1.54508	+	1.12257i	0.0561942	+	0.0408275i
$757$			30.4164i			1.10550i	0.833346	+	0.552752i	$0.186422\pi$
$757$			30.4164i			1.10550i	−0.833346	+	0.552752i	$0.813578\pi$
$758$	13.8823	−	19.1074i	0.504229	−	0.694012i
$759$	6.09017	−	18.7436i	0.221059	−	0.680350i
$760$		0			0
$761$	−5.70163	−	17.5478i	−0.206684	−	0.636107i	−0.999640	−	0.0268287i	$-0.991459\pi$
$761$	−5.70163	−	17.5478i	−0.206684	−	0.636107i	0.792956	−	0.609279i	$-0.208541\pi$
$762$	−30.6053	−	9.94427i	−1.10871	−	0.360243i
$763$	−5.87785	−	1.90983i	−0.212793	−	0.0691405i
$764$	0.347524	+	1.06957i	0.0125730	+	0.0386957i
$765$		0			0
$766$	−16.6803	+	51.3368i	−0.602685	+	1.85487i
$767$	−11.8290	+	16.2812i	−0.427119	+	0.587878i
$768$		−	13.5623i		−	0.489388i
$769$	10.8541	+	7.88597i	0.391409	+	0.284375i	0.766033	−	0.642802i	$-0.222228\pi$
$769$	10.8541	+	7.88597i	0.391409	+	0.284375i	−0.374624	+	0.927177i	$0.622228\pi$
$770$		0			0
$771$	−18.4894	+	13.4333i	−0.665878	+	0.483789i
$772$	−2.80017	−	3.85410i	−0.100780	−	0.138712i
$773$	−34.3893	+	11.1738i	−1.23690	+	0.401892i	−0.853208	−	0.521570i	$-0.825346\pi$
$773$	−34.3893	+	11.1738i	−1.23690	+	0.401892i	−0.383689	+	0.923462i	$0.625346\pi$
$774$	15.7082			0.564620
$775$		0			0
$776$	−8.61803			−0.309369
$777$	0.138757	−	0.0450850i	0.00497789	−	0.00161741i
$778$	−14.2658	−	19.6353i	−0.511455	−	0.703958i
$779$	−0.527864	+	0.383516i	−0.0189127	+	0.0137409i
$780$		0			0

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.53884 - 0.500000i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.500000 - 0.363271i) q^{4} +(1.30902 + 0.951057i) q^{6} +0.618034i q^{7} +(-1.31433 + 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +O(q^{10})\)	\(q+(1.53884 - 0.500000i) q^{2} +(0.587785 + 0.809017i) q^{3} +(0.500000 - 0.363271i) q^{4} +(1.30902 + 0.951057i) q^{6} +0.618034i q^{7} +(-1.31433 + 1.80902i) q^{8} +(0.618034 - 1.90211i) q^{9} +(-1.61803 - 4.97980i) q^{11} +(0.587785 + 0.190983i) q^{12} +(-1.76336 - 0.572949i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.50000 + 4.61653i) q^{16} +(-3.07768 + 4.23607i) q^{17} -3.23607i q^{18} +(0.690983 + 0.502029i) q^{19} +(-0.500000 + 0.363271i) q^{21} +(-4.97980 - 6.85410i) q^{22} +(3.57971 - 1.16312i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(4.75528 - 1.54508i) q^{27} +(0.224514 + 0.309017i) q^{28} +(-2.92705 + 2.12663i) q^{29} +(2.42705 + 1.76336i) q^{31} +3.38197i q^{32} +(3.07768 - 4.23607i) q^{33} +(-2.61803 + 8.05748i) q^{34} +(-0.381966 - 1.17557i) q^{36} +(-0.224514 - 0.0729490i) q^{37} +(1.31433 + 0.427051i) q^{38} +(-0.572949 - 1.76336i) q^{39} +(-0.236068 + 0.726543i) q^{41} +(-0.587785 + 0.809017i) q^{42} +4.85410i q^{43} +(-2.61803 - 1.90211i) q^{44} +(4.92705 - 3.57971i) q^{46} +(-0.363271 - 0.500000i) q^{47} +(-4.61653 + 1.50000i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(-1.08981 + 0.354102i) q^{52} +(-2.04087 - 2.80902i) q^{53} +(6.54508 - 4.75528i) q^{54} +(-1.11803 - 0.812299i) q^{56} +0.854102i q^{57} +(-3.44095 + 4.73607i) q^{58} +(3.35410 - 10.3229i) q^{59} +(2.69098 + 8.28199i) q^{61} +(4.61653 + 1.50000i) q^{62} +(1.17557 + 0.381966i) q^{63} +(-1.30902 - 4.02874i) q^{64} +(2.61803 - 8.05748i) q^{66} +(2.80017 - 3.85410i) q^{67} +3.23607i q^{68} +(3.04508 + 2.21238i) q^{69} +(5.35410 - 3.88998i) q^{71} +(2.62866 + 3.61803i) q^{72} +(-8.55951 + 2.78115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(3.07768 - 1.00000i) q^{77} +(-1.76336 - 2.42705i) q^{78} +(-6.54508 + 4.75528i) q^{79} +(-0.809017 - 0.587785i) q^{81} +1.23607i q^{82} +(3.66547 - 5.04508i) q^{83} +(-0.118034 + 0.363271i) q^{84} +(2.42705 + 7.46969i) q^{86} +(-3.44095 - 1.11803i) q^{87} +(11.1352 + 3.61803i) q^{88} +(2.76393 + 8.50651i) q^{89} +(0.354102 - 1.08981i) q^{91} +(1.36733 - 1.88197i) q^{92} +3.00000i q^{93} +(-0.809017 - 0.587785i) q^{94} +(-2.73607 + 1.98787i) q^{96} +(2.26538 + 3.11803i) q^{97} +(10.1841 - 3.30902i) q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	\( 8 q + 4 q^{4} + 6 q^{6} - 4 q^{9} - 4 q^{11} - 2 q^{14} - 12 q^{16} + 10 q^{19} - 4 q^{21} - 24 q^{26} - 10 q^{29} + 6 q^{31} - 12 q^{34} - 12 q^{36} - 18 q^{39} + 16 q^{41} - 12 q^{44} + 26 q^{46} + 44 q^{49} - 24 q^{51} + 30 q^{54} + 26 q^{61} - 6 q^{64} + 12 q^{66} + 2 q^{69} + 16 q^{71} - 12 q^{74} + 40 q^{76} - 30 q^{79} - 2 q^{81} + 8 q^{84} + 6 q^{86} + 40 q^{89} - 24 q^{91} - 2 q^{94} - 4 q^{96} - 48 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 - 4 * q^11 - 2 * q^14 - 12 * q^16 + 10 * q^19 - 4 * q^21 - 24 * q^26 - 10 * q^29 + 6 * q^31 - 12 * q^34 - 12 * q^36 - 18 * q^39 + 16 * q^41 - 12 * q^44 + 26 * q^46 + 44 * q^49 - 24 * q^51 + 30 * q^54 + 26 * q^61 - 6 * q^64 + 12 * q^66 + 2 * q^69 + 16 * q^71 - 12 * q^74 + 40 * q^76 - 30 * q^79 - 2 * q^81 + 8 * q^84 + 6 * q^86 + 40 * q^89 - 24 * q^91 - 2 * q^94 - 4 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

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