LMFDB - Embedded newform 5.33.c.a.3.7

Newspace parameters

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 33 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$32.4333275711$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	5.3
Dual form			5.33.c.a.2.7

$q$-expansion

$f(q)$	$=$	$q+(-7096.95 + 7096.95i) q^{2} +(-4.70380e7 - 4.70380e7i) q^{3} +4.19423e9i q^{4} +(-3.87281e10 + 1.47591e11i) q^{5} +6.67652e11 q^{6} +(-3.04405e13 + 3.04405e13i) q^{7} +(-6.02475e13 - 6.02475e13i) q^{8} +2.57212e15i q^{9} +O(q^{10})$	\(q+(-7096.95 + 7096.95i) q^{2} +(-4.70380e7 - 4.70380e7i) q^{3} +4.19423e9i q^{4} +(-3.87281e10 + 1.47591e11i) q^{5} +6.67652e11 q^{6} +(-3.04405e13 + 3.04405e13i) q^{7} +(-6.02475e13 - 6.02475e13i) q^{8} +2.57212e15i q^{9} +(-7.72597e14 - 1.32230e15i) q^{10} +3.11706e16 q^{11} +(1.97288e17 - 1.97288e17i) q^{12} +(8.11181e17 + 8.11181e17i) q^{13} -4.32069e17i q^{14} +(8.76409e18 - 5.12070e18i) q^{15} -1.71589e19 q^{16} +(-5.99103e19 + 5.99103e19i) q^{17} +(-1.82542e19 - 1.82542e19i) q^{18} -3.24007e19i q^{19} +(-6.19032e20 - 1.62435e20i) q^{20} +2.86372e21 q^{21} +(-2.21216e20 + 2.21216e20i) q^{22} +(7.07294e20 + 7.07294e20i) q^{23} +5.66784e21i q^{24} +(-2.02833e22 - 1.14319e22i) q^{25} -1.15138e22 q^{26} +(3.38249e22 - 3.38249e22i) q^{27} +(-1.27675e23 - 1.27675e23i) q^{28} +1.29019e23i q^{29} +(-2.58569e22 + 9.85397e22i) q^{30} +1.94976e23 q^{31} +(3.80537e23 - 3.80537e23i) q^{32} +(-1.46620e24 - 1.46620e24i) q^{33} -8.50362e23i q^{34} +(-3.31385e24 - 5.67165e24i) q^{35} -1.07881e25 q^{36} +(-1.30388e25 + 1.30388e25i) q^{37} +(2.29947e23 + 2.29947e23i) q^{38} -7.63126e25i q^{39} +(1.12253e25 - 6.55873e24i) q^{40} +1.97064e25 q^{41} +(-2.03237e25 + 2.03237e25i) q^{42} +(-1.49066e26 - 1.49066e26i) q^{43} +1.30737e26i q^{44} +(-3.79622e26 - 9.96133e25i) q^{45} -1.00393e25 q^{46} +(-1.46092e25 + 1.46092e25i) q^{47} +(8.07122e26 + 8.07122e26i) q^{48} -7.48818e26i q^{49} +(2.25081e26 - 6.28184e25i) q^{50} +5.63612e27 q^{51} +(-3.40228e27 + 3.40228e27i) q^{52} +(1.61176e26 + 1.61176e26i) q^{53} +4.80108e26i q^{54} +(-1.20718e27 + 4.60051e27i) q^{55} +3.66792e27 q^{56} +(-1.52406e27 + 1.52406e27i) q^{57} +(-9.15643e26 - 9.15643e26i) q^{58} -1.65995e28i q^{59} +(2.14774e28 + 3.67586e28i) q^{60} +3.79371e28 q^{61} +(-1.38374e27 + 1.38374e27i) q^{62} +(-7.82965e28 - 7.82965e28i) q^{63} -6.82958e28i q^{64} +(-1.51139e29 + 8.83077e28i) q^{65} +2.08111e28 q^{66} +(-5.62478e27 + 5.62478e27i) q^{67} +(-2.51278e29 - 2.51278e29i) q^{68} -6.65393e28i q^{69} +(6.37697e28 + 1.67332e28i) q^{70} +2.56347e29 q^{71} +(1.54964e29 - 1.54964e29i) q^{72} +(2.59851e28 + 2.59851e28i) q^{73} -1.85071e29i q^{74} +(4.16355e29 + 1.49182e30i) q^{75} +1.35896e29 q^{76} +(-9.48847e29 + 9.48847e29i) q^{77} +(5.41587e29 + 5.41587e29i) q^{78} -6.46531e29i q^{79} +(6.64534e29 - 2.53251e30i) q^{80} +1.58408e30 q^{81} +(-1.39855e29 + 1.39855e29i) q^{82} +(5.85299e30 + 5.85299e30i) q^{83} +1.20111e31i q^{84} +(-6.52203e30 - 1.11625e31i) q^{85} +2.11582e30 q^{86} +(6.06880e30 - 6.06880e30i) q^{87} +(-1.87795e30 - 1.87795e30i) q^{88} -1.03268e31i q^{89} +(3.40111e30 - 1.98721e30i) q^{90} -4.93855e31 q^{91} +(-2.96656e30 + 2.96656e30i) q^{92} +(-9.17129e30 - 9.17129e30i) q^{93} -2.07362e29i q^{94} +(4.78207e30 + 1.25482e30i) q^{95} -3.57994e31 q^{96} +(4.86752e31 - 4.86752e31i) q^{97} +(5.31433e30 + 5.31433e30i) q^{98} +8.01744e31i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30q - 2q^{2} - 2792232q^{3} + 229266409900q^{5} - 645476451240q^{6} + 21807690136848q^{7} + 340768936037220q^{8} + O(q^{10}) $	$ 30q - 2q^{2} - 2792232q^{3} + 229266409900q^{5} - 645476451240q^{6} + 21807690136848q^{7} + 340768936037220q^{8} - 17555754485145450q^{10} - 60908362837533640q^{11} + 444566273630869608q^{12} + 649759187023107138q^{13} + 6285624407445962400q^{15} - 46108906958970522120q^{16} - $$21\!\cdots\!02$$q^{17} + $$24\!\cdots\!58$$q^{18} - $$30\!\cdots\!00$$q^{20} + $$45\!\cdots\!60$$q^{21} - $$11\!\cdots\!44$$q^{22} + $$13\!\cdots\!08$$q^{23} + $$35\!\cdots\!50$$q^{25} - $$23\!\cdots\!40$$q^{26} + $$17\!\cdots\!60$$q^{27} + $$59\!\cdots\!12$$q^{28} + $$12\!\cdots\!00$$q^{30} - $$12\!\cdots\!40$$q^{31} + $$31\!\cdots\!68$$q^{32} - $$16\!\cdots\!04$$q^{33} - $$81\!\cdots\!00$$q^{35} + $$31\!\cdots\!80$$q^{36} - $$12\!\cdots\!02$$q^{37} + $$57\!\cdots\!80$$q^{38} + $$21\!\cdots\!00$$q^{40} - $$15\!\cdots\!40$$q^{41} + $$79\!\cdots\!36$$q^{42} - $$54\!\cdots\!52$$q^{43} + $$10\!\cdots\!50$$q^{45} - $$34\!\cdots\!40$$q^{46} + $$27\!\cdots\!48$$q^{47} - $$31\!\cdots\!92$$q^{48} + $$44\!\cdots\!50$$q^{50} - $$61\!\cdots\!40$$q^{51} + $$60\!\cdots\!28$$q^{52} - $$11\!\cdots\!82$$q^{53} - $$71\!\cdots\!00$$q^{55} - $$47\!\cdots\!00$$q^{56} + $$44\!\cdots\!20$$q^{57} - $$29\!\cdots\!80$$q^{58} + $$34\!\cdots\!00$$q^{60} + $$50\!\cdots\!60$$q^{61} - $$21\!\cdots\!24$$q^{62} + $$21\!\cdots\!08$$q^{63} - $$34\!\cdots\!50$$q^{65} + $$13\!\cdots\!20$$q^{66} - $$73\!\cdots\!52$$q^{67} + $$10\!\cdots\!12$$q^{68} - $$36\!\cdots\!00$$q^{70} + $$81\!\cdots\!60$$q^{71} - $$95\!\cdots\!20$$q^{72} - $$37\!\cdots\!42$$q^{73} + $$10\!\cdots\!00$$q^{75} - $$66\!\cdots\!00$$q^{76} + $$63\!\cdots\!56$$q^{77} - $$91\!\cdots\!84$$q^{78} + $$58\!\cdots\!00$$q^{80} - $$14\!\cdots\!70$$q^{81} + $$27\!\cdots\!36$$q^{82} + $$49\!\cdots\!28$$q^{83} - $$44\!\cdots\!50$$q^{85} + $$16\!\cdots\!60$$q^{86} + $$36\!\cdots\!80$$q^{87} - $$47\!\cdots\!60$$q^{88} + $$81\!\cdots\!50$$q^{90} - $$10\!\cdots\!40$$q^{91} - $$18\!\cdots\!52$$q^{92} + $$11\!\cdots\!16$$q^{93} - $$10\!\cdots\!00$$q^{95} + $$38\!\cdots\!60$$q^{96} - $$15\!\cdots\!02$$q^{97} + $$12\!\cdots\!02$$q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−7096.95	+	7096.95i	−0.108291	+	0.108291i	−0.759176	−	0.650885i	$-0.774398\pi$
$2$	−7096.95	+	7096.95i	−0.108291	+	0.108291i	0.650885	+	0.759176i	$0.274398\pi$
$3$	−4.70380e7	−	4.70380e7i	−1.09272	−	1.09272i	−0.995237	−	0.0974813i	$-0.968921\pi$
$3$	−4.70380e7	−	4.70380e7i	−1.09272	−	1.09272i	−0.0974813	−	0.995237i	$-0.531079\pi$
$4$			4.19423e9i			0.976546i
$5$	−3.87281e10	+	1.47591e11i	−0.253809	+	0.967254i
$5$	−3.87281e10	+	1.47591e11i	−0.253809	+	0.967254i
$6$	6.67652e11			0.236663
$7$	−3.04405e13	+	3.04405e13i	−0.915973	+	0.915973i	−0.996734	−	0.0807601i	$-0.974265\pi$
$7$	−3.04405e13	+	3.04405e13i	−0.915973	+	0.915973i	0.0807601	+	0.996734i	$0.474265\pi$
$8$	−6.02475e13	−	6.02475e13i	−0.214042	−	0.214042i
$9$			2.57212e15i			1.38807i
$10$	−7.72597e14	−	1.32230e15i	−0.0772597	−	0.132230i
$11$	3.11706e16			0.678362			0.339181	−	0.940721i	$-0.389850\pi$
$11$	3.11706e16			0.678362			0.339181	+	0.940721i	$0.389850\pi$
$12$	1.97288e17	−	1.97288e17i	1.06709	−	1.06709i
$13$	8.11181e17	+	8.11181e17i	1.21906	+	1.21906i	0.967963	+	0.251094i	$0.0807904\pi$
$13$	8.11181e17	+	8.11181e17i	1.21906	+	1.21906i	0.251094	+	0.967963i	$0.419210\pi$
$14$		−	4.32069e17i		−	0.198383i
$15$	8.76409e18	−	5.12070e18i	1.33428	−	0.779596i
$16$	−1.71589e19			−0.930189
$17$	−5.99103e19	+	5.99103e19i	−1.23117	+	1.23117i	−0.267659	+	0.963514i	$0.586250\pi$
$17$	−5.99103e19	+	5.99103e19i	−1.23117	+	1.23117i	−0.963514	+	0.267659i	$0.913750\pi$
$18$	−1.82542e19	−	1.82542e19i	−0.150315	−	0.150315i
$19$		−	3.24007e19i		−	0.112330i	−0.998421	−	0.0561652i	$-0.982113\pi$
$19$		−	3.24007e19i		−	0.112330i	0.998421	−	0.0561652i	$-0.0178874\pi$
$20$	−6.19032e20	−	1.62435e20i	−0.944569	−	0.247856i
$21$	2.86372e21			2.00180
$22$	−2.21216e20	+	2.21216e20i	−0.0734605	+	0.0734605i
$23$	7.07294e20	+	7.07294e20i	0.115333	+	0.115333i	0.762418	−	0.647085i	$-0.224012\pi$
$23$	7.07294e20	+	7.07294e20i	0.115333	+	0.115333i	−0.647085	+	0.762418i	$0.724012\pi$
$24$			5.66784e21i			0.467775i
$25$	−2.02833e22	−	1.14319e22i	−0.871162	−	0.490995i
$26$	−1.15138e22			−0.264026
$27$	3.38249e22	−	3.38249e22i	0.424049	−	0.424049i
$28$	−1.27675e23	−	1.27675e23i	−0.894490	−	0.894490i
$29$			1.29019e23i			0.515568i	0.966203	+	0.257784i	$0.0829924\pi$
$29$			1.29019e23i			0.515568i	−0.966203	+	0.257784i	$0.917008\pi$
$30$	−2.58569e22	+	9.85397e22i	−0.0600671	+	0.228913i
$31$	1.94976e23			0.268037			0.134019	−	0.990979i	$-0.457212\pi$
$31$	1.94976e23			0.268037			0.134019	+	0.990979i	$0.457212\pi$
$32$	3.80537e23	−	3.80537e23i	0.314773	−	0.314773i
$33$	−1.46620e24	−	1.46620e24i	−0.741259	−	0.741259i
$34$		−	8.50362e23i		−	0.266650i
$35$	−3.31385e24	−	5.67165e24i	−0.653497	−	1.11846i
$36$	−1.07881e25			−1.35551
$37$	−1.30388e25	+	1.30388e25i	−1.05684	+	1.05684i	−0.0585575	+	0.998284i	$0.518650\pi$
$37$	−1.30388e25	+	1.30388e25i	−1.05684	+	1.05684i	−0.998284	+	0.0585575i	$0.981350\pi$
$38$	2.29947e23	+	2.29947e23i	0.0121644	+	0.0121644i
$39$		−	7.63126e25i		−	2.66417i
$40$	1.12253e25	−	6.55873e24i	0.261359	−	0.152707i
$41$	1.97064e25			0.309076			0.154538	−	0.987987i	$-0.450611\pi$
$41$	1.97064e25			0.309076			0.154538	+	0.987987i	$0.450611\pi$
$42$	−2.03237e25	+	2.03237e25i	−0.216777	+	0.216777i
$43$	−1.49066e26	−	1.49066e26i	−1.09114	−	1.09114i	−0.995407	−	0.0957369i	$-0.969479\pi$
$43$	−1.49066e26	−	1.49066e26i	−1.09114	−	1.09114i	−0.0957369	−	0.995407i	$-0.530521\pi$
$44$			1.30737e26i			0.662452i
$45$	−3.79622e26	−	9.96133e25i	−1.34262	−	0.352304i
$46$	−1.00393e25			−0.0249791
$47$	−1.46092e25	+	1.46092e25i	−0.0257669	+	0.0257669i	−0.719873	−	0.694106i	$-0.755800\pi$
$47$	−1.46092e25	+	1.46092e25i	−0.0257669	+	0.0257669i	0.694106	+	0.719873i	$0.255800\pi$
$48$	8.07122e26	+	8.07122e26i	1.01643	+	1.01643i
$49$		−	7.48818e26i		−	0.678015i
$50$	2.25081e26	−	6.28184e25i	0.147509	−	0.0411687i
$51$	5.63612e27			2.69065
$52$	−3.40228e27	+	3.40228e27i	−1.19047	+	1.19047i
$53$	1.61176e26	+	1.61176e26i	0.0415802	+	0.0415802i	0.727591	−	0.686011i	$-0.240640\pi$
$53$	1.61176e26	+	1.61176e26i	0.0415802	+	0.0415802i	−0.686011	+	0.727591i	$0.740640\pi$
$54$			4.80108e26i			0.0918414i
$55$	−1.20718e27	+	4.60051e27i	−0.172174	+	0.656149i
$56$	3.66792e27			0.392114
$57$	−1.52406e27	+	1.52406e27i	−0.122746	+	0.122746i
$58$	−9.15643e26	−	9.15643e26i	−0.0558314	−	0.0558314i
$59$		−	1.65995e28i		−	0.769950i	−0.922927	−	0.384975i	$-0.874210\pi$
$59$		−	1.65995e28i		−	0.769950i	0.922927	−	0.384975i	$-0.125790\pi$
$60$	2.14774e28	+	3.67586e28i	0.761311	+	1.30298i
$61$	3.79371e28			1.03225			0.516127	−	0.856512i	$-0.327373\pi$
$61$	3.79371e28			1.03225			0.516127	+	0.856512i	$0.327373\pi$
$62$	−1.38374e27	+	1.38374e27i	−0.0290260	+	0.0290260i
$63$	−7.82965e28	−	7.82965e28i	−1.27143	−	1.27143i
$64$		−	6.82958e28i		−	0.862014i
$65$	−1.51139e29	+	8.83077e28i	−1.48855	+	0.869731i
$66$	2.08111e28			0.160543
$67$	−5.62478e27	+	5.62478e27i	−0.0341121	+	0.0341121i	−0.723957	−	0.689845i	$-0.757679\pi$
$67$	−5.62478e27	+	5.62478e27i	−0.0341121	+	0.0341121i	0.689845	+	0.723957i	$0.257679\pi$
$68$	−2.51278e29	−	2.51278e29i	−1.20230	−	1.20230i
$69$		−	6.65393e28i		−	0.252054i
$70$	6.37697e28	+	1.67332e28i	0.191887	+	0.0503514i
$71$	2.56347e29			0.614744			0.307372	−	0.951589i	$-0.400550\pi$
$71$	2.56347e29			0.614744			0.307372	+	0.951589i	$0.400550\pi$
$72$	1.54964e29	−	1.54964e29i	0.297105	−	0.297105i
$73$	2.59851e28	+	2.59851e28i	0.0399538	+	0.0399538i	0.726801	−	0.686848i	$-0.241006\pi$
$73$	2.59851e28	+	2.59851e28i	0.0399538	+	0.0399538i	−0.686848	+	0.726801i	$0.741006\pi$
$74$		−	1.85071e29i		−	0.228893i
$75$	4.16355e29	+	1.49182e30i	0.415416	+	1.48845i
$76$	1.35896e29			0.109696
$77$	−9.48847e29	+	9.48847e29i	−0.621362	+	0.621362i
$78$	5.41587e29	+	5.41587e29i	0.288506	+	0.288506i
$79$		−	6.46531e29i		−	0.280903i	−0.990088	−	0.140451i	$-0.955145\pi$
$79$		−	6.46531e29i		−	0.280903i	0.990088	−	0.140451i	$-0.0448554\pi$
$80$	6.64534e29	−	2.53251e30i	0.236090	−	0.899729i
$81$	1.58408e30			0.461335
$82$	−1.39855e29	+	1.39855e29i	−0.0334701	+	0.0334701i
$83$	5.85299e30	+	5.85299e30i	1.15379	+	1.15379i	0.985786	+	0.168007i	$0.0537332\pi$
$83$	5.85299e30	+	5.85299e30i	1.15379	+	1.15379i	0.168007	+	0.985786i	$0.446267\pi$
$84$			1.20111e31i			1.95485i
$85$	−6.52203e30	−	1.11625e31i	−0.878375	−	1.50334i
$86$	2.11582e30			0.236322
$87$	6.06880e30	−	6.06880e30i	0.563371	−	0.563371i
$88$	−1.87795e30	−	1.87795e30i	−0.145198	−	0.145198i
$89$		−	1.03268e31i		−	0.666383i	−0.942859	−	0.333191i	$-0.891874\pi$
$89$		−	1.03268e31i		−	0.666383i	0.942859	−	0.333191i	$-0.108126\pi$
$90$	3.40111e30	−	1.98721e30i	0.183544	−	0.107242i
$91$	−4.93855e31			−2.23325
$92$	−2.96656e30	+	2.96656e30i	−0.112628	+	0.112628i
$93$	−9.17129e30	−	9.17129e30i	−0.292889	−	0.292889i
$94$		−	2.07362e29i		−	0.00558064i
$95$	4.78207e30	+	1.25482e30i	0.108652	+	0.0285104i
$96$	−3.57994e31			−0.687917
$97$	4.86752e31	−	4.86752e31i	0.792429	−	0.792429i	−0.189460	−	0.981888i	$-0.560674\pi$
$97$	4.86752e31	−	4.86752e31i	0.792429	−	0.792429i	0.981888	+	0.189460i	$0.0606736\pi$
$98$	5.31433e30	+	5.31433e30i	0.0734228	+	0.0734228i
$99$			8.01744e31i			0.941613i
$100$	4.79479e31	−	8.50730e31i	0.479479	−	0.850730i
$101$	1.32253e32			1.12788			0.563939	−	0.825817i	$-0.309285\pi$
$101$	1.32253e32			1.12788			0.563939	+	0.825817i	$0.309285\pi$
$102$	−3.99993e31	+	3.99993e31i	−0.291373	+	0.291373i
$103$	−5.17852e31	−	5.17852e31i	−0.322708	−	0.322708i	0.527097	−	0.849805i	$-0.323280\pi$
$103$	−5.17852e31	−	5.17852e31i	−0.322708	−	0.322708i	−0.849805	+	0.527097i	$0.823280\pi$
$104$		−	9.77432e31i		−	0.521859i
$105$	−1.10906e32	+	4.22660e32i	−0.508075	+	1.93625i
$106$	−2.28772e30			−0.00900552
$107$	−1.05685e32	+	1.05685e32i	−0.357992	+	0.357992i	−0.863072	−	0.505080i	$-0.831463\pi$
$107$	−1.05685e32	+	1.05685e32i	−0.357992	+	0.357992i	0.505080	+	0.863072i	$0.331463\pi$
$108$	1.41870e32	+	1.41870e32i	0.414104	+	0.414104i
$109$			2.00633e32i			0.505333i	0.967553	+	0.252667i	$0.0813076\pi$
$109$			2.00633e32i			0.505333i	−0.967553	+	0.252667i	$0.918692\pi$
$110$	−2.40823e31	−	4.12169e31i	−0.0524101	−	0.0896999i
$111$	1.22664e33			2.30966
$112$	5.22327e32	−	5.22327e32i	0.852028	−	0.852028i
$113$	−5.67464e32	−	5.67464e32i	−0.802941	−	0.802941i	0.180613	−	0.983554i	$-0.442192\pi$
$113$	−5.67464e32	−	5.67464e32i	−0.802941	−	0.802941i	−0.983554	+	0.180613i	$0.942192\pi$
$114$		−	2.16324e31i		−	0.0265845i
$115$	−1.31783e32	+	7.69983e31i	−0.140829	+	0.0822840i
$116$	−5.41137e32			−0.503476
$117$	−2.08645e33	+	2.08645e33i	−1.69213	+	1.69213i
$118$	1.17806e32	+	1.17806e32i	0.0833786	+	0.0833786i
$119$		−	3.64740e33i		−	2.25544i
$120$	−8.36523e32	−	2.19505e32i	−0.452458	−	0.118725i
$121$	−1.13977e33			−0.539824
$122$	−2.69238e32	+	2.69238e32i	−0.111784	+	0.111784i
$123$	−9.26949e32	−	9.26949e32i	−0.337733	−	0.337733i
$124$			8.17777e32i			0.261751i
$125$	2.47278e33	−	2.55091e33i	0.696026	−	0.718017i
$126$	1.11133e33			0.275369
$127$	3.88082e33	−	3.88082e33i	0.847353	−	0.847353i	−0.142449	−	0.989802i	$-0.545498\pi$
$127$	3.88082e33	−	3.88082e33i	0.847353	−	0.847353i	0.989802	+	0.142449i	$0.0454977\pi$
$128$	2.11909e33	+	2.11909e33i	0.408121	+	0.408121i
$129$			1.40235e34i			2.38463i
$130$	4.45909e32	−	1.69934e33i	0.0670120	−	0.255380i
$131$	−1.29669e34			−1.72384			−0.861918	−	0.507047i	$-0.830737\pi$
$131$	−1.29669e34			−1.72384			−0.861918	+	0.507047i	$0.830737\pi$
$132$	6.14959e33	−	6.14959e33i	0.723874	−	0.723874i
$133$	9.86294e32	+	9.86294e32i	0.102892	+	0.102892i
$134$		−	7.98376e31i		−	0.00738807i
$135$	3.68229e33	+	6.30224e33i	0.302536	+	0.517791i
$136$	7.21889e33			0.527045
$137$	−7.81980e33	+	7.81980e33i	−0.507769	+	0.507769i	−0.913841	−	0.406072i	$-0.866898\pi$
$137$	−7.81980e33	+	7.81980e33i	−0.507769	+	0.507769i	0.406072	+	0.913841i	$0.366898\pi$
$138$	4.72226e32	+	4.72226e32i	0.0272951	+	0.0272951i
$139$			9.15332e33i			0.471348i	0.971832	+	0.235674i	$0.0757298\pi$
$139$			9.15332e33i			0.471348i	−0.971832	+	0.235674i	$0.924270\pi$
$140$	2.37882e34	−	1.38991e34i	1.09223	−	0.638170i
$141$	1.37438e33			0.0563119
$142$	−1.81928e33	+	1.81928e33i	−0.0665712	+	0.0665712i
$143$	2.52850e34	+	2.52850e34i	0.826962	+	0.826962i
$144$		−	4.41348e34i		−	1.29117i
$145$	−1.90421e34	−	4.99667e33i	−0.498686	−	0.130856i
$146$	−3.68830e32			−0.00865328
$147$	−3.52229e34	+	3.52229e34i	−0.740879	+	0.740879i
$148$	−5.46878e34	−	5.46878e34i	−1.03205	−	1.03205i
$149$			3.01233e34i			0.510413i	0.966887	+	0.255207i	$0.0821435\pi$
$149$			3.01233e34i			0.510413i	−0.966887	+	0.255207i	$0.917857\pi$
$150$	−1.35422e34	−	7.63251e33i	−0.206172	−	0.116200i
$151$	−6.55243e33			−0.0896957			−0.0448478	−	0.998994i	$-0.514280\pi$
$151$	−6.55243e33			−0.0896957			−0.0448478	+	0.998994i	$0.514280\pi$
$152$	−1.95206e33	+	1.95206e33i	−0.0240434	+	0.0240434i
$153$	−1.54096e35	−	1.54096e35i	−1.70895	−	1.70895i
$154$		−	1.34679e34i		−	0.134576i
$155$	−7.55107e33	+	2.87768e34i	−0.0680301	+	0.259260i
$156$	3.20073e35			2.60169
$157$	−6.66947e34	+	6.66947e34i	−0.489437	+	0.489437i	−0.908129	−	0.418691i	$-0.862489\pi$
$157$	−6.66947e34	+	6.66947e34i	−0.489437	+	0.489437i	0.418691	+	0.908129i	$0.362489\pi$
$158$	4.58840e33	+	4.58840e33i	0.0304192	+	0.0304192i
$159$		−	1.51628e34i		−	0.0908709i
$160$	4.14265e34	+	7.09015e34i	0.224573	+	0.384358i
$161$	−4.30607e34			−0.211284
$162$	−1.12421e34	+	1.12421e34i	−0.0499584	+	0.0499584i
$163$	1.22414e35	+	1.22414e35i	0.492981	+	0.492981i	0.909244	−	0.416263i	$-0.136661\pi$
$163$	1.22414e35	+	1.22414e35i	0.492981	+	0.492981i	−0.416263	+	0.909244i	$0.636661\pi$
$164$			8.26532e34i			0.301827i
$165$	2.73182e35	−	1.59615e35i	0.905124	−	0.528848i
$166$	−8.30767e34			−0.249891
$167$	−1.95331e35	+	1.95331e35i	−0.533712	+	0.533712i	−0.921675	−	0.387963i	$-0.873179\pi$
$167$	−1.95331e35	+	1.95331e35i	−0.533712	+	0.533712i	0.387963	+	0.921675i	$0.373179\pi$
$168$	−1.72532e35	−	1.72532e35i	−0.428470	−	0.428470i
$169$			8.73249e35i			1.97220i
$170$	1.25506e35	+	3.29329e34i	0.257918	+	0.0676780i
$171$	8.33386e34			0.155922
$172$	6.25216e35	−	6.25216e35i	1.06555	−	1.06555i
$173$	−4.25483e35	−	4.25483e35i	−0.660913	−	0.660913i	0.294682	−	0.955595i	$-0.404786\pi$
$173$	−4.25483e35	−	4.25483e35i	−0.660913	−	0.660913i	−0.955595	+	0.294682i	$0.904786\pi$
$174$			8.61400e34i			0.122016i
$175$	9.65426e35	−	2.69443e35i	1.24770	−	0.348223i
$176$	−5.34854e35			−0.631005
$177$	−7.80806e35	+	7.80806e35i	−0.841338	+	0.841338i
$178$	7.32885e34	+	7.32885e34i	0.0721632	+	0.0721632i
$179$			9.99817e35i			0.900061i	0.893013	+	0.450031i	$0.148587\pi$
$179$			9.99817e35i			0.900061i	−0.893013	+	0.450031i	$0.851413\pi$
$180$	4.17801e35	−	1.59222e36i	0.344041	−	1.31113i
$181$	−4.23579e35			−0.319211			−0.159605	−	0.987181i	$-0.551022\pi$
$181$	−4.23579e35			−0.319211			−0.159605	+	0.987181i	$0.551022\pi$
$182$	3.50486e35	−	3.50486e35i	0.241840	−	0.241840i
$183$	−1.78448e36	−	1.78448e36i	−1.12796	−	1.12796i
$184$		−	8.52253e34i		−	0.0493723i
$185$	−1.41944e36	−	2.42938e36i	−0.753999	−	1.29047i
$186$	1.30176e35			0.0634345
$187$	−1.86744e36	+	1.86744e36i	−0.835181	+	0.835181i
$188$	−6.12745e34	−	6.12745e34i	−0.0251625	−	0.0251625i
$189$			2.05929e36i			0.776836i
$190$	−4.28435e34	+	2.50327e34i	−0.0148535	+	0.00867862i
$191$	5.31256e36			1.69344			0.846721	−	0.532037i	$-0.178573\pi$
$191$	5.31256e36			1.69344			0.846721	+	0.532037i	$0.178573\pi$
$192$	−3.21250e36	+	3.21250e36i	−0.941939	+	0.941939i
$193$	−2.64739e36	−	2.64739e36i	−0.714334	−	0.714334i	0.253105	−	0.967439i	$-0.418548\pi$
$193$	−2.64739e36	−	2.64739e36i	−0.714334	−	0.714334i	−0.967439	+	0.253105i	$0.918548\pi$
$194$			6.90892e35i			0.171626i
$195$	1.12631e37	+	2.95544e36i	2.57693	+	0.676190i
$196$	3.14072e36			0.662113
$197$	−1.01234e36	+	1.01234e36i	−0.196728	+	0.196728i	−0.798596	−	0.601868i	$-0.794423\pi$
$197$	−1.01234e36	+	1.01234e36i	−0.196728	+	0.196728i	0.601868	+	0.798596i	$0.294423\pi$
$198$	−5.68994e35	−	5.68994e35i	−0.101968	−	0.101968i
$199$		−	8.46667e36i		−	1.39979i	−0.714245	−	0.699896i	$-0.753230\pi$
$199$		−	8.46667e36i		−	1.39979i	0.714245	−	0.699896i	$-0.246770\pi$
$200$	5.33278e35	+	1.91076e36i	0.0813718	+	0.291559i
$201$	5.29156e35			0.0745499
$202$	−9.38590e35	+	9.38590e35i	−0.122139	+	0.122139i
$203$	−3.92741e36	−	3.92741e36i	−0.472247	−	0.472247i
$204$			2.36392e37i			2.62754i
$205$	−7.63192e35	+	2.90849e36i	−0.0784462	+	0.298955i
$206$	7.35035e35			0.0698928
$207$	−1.81924e36	+	1.81924e36i	−0.160090	+	0.160090i
$208$	−1.39190e37	−	1.39190e37i	−1.13395	−	1.13395i
$209$		−	1.00995e36i		−	0.0762007i
$210$	−2.21250e36	−	3.78669e36i	−0.154659	−	0.264698i
$211$	2.82040e37			1.82722			0.913612	−	0.406587i	$-0.133281\pi$
$211$	2.82040e37			1.82722			0.913612	+	0.406587i	$0.133281\pi$
$212$	−6.76010e35	+	6.76010e35i	−0.0406050	+	0.0406050i
$213$	−1.20580e37	−	1.20580e37i	−0.671742	−	0.671742i
$214$		−	1.50009e36i		−	0.0775346i
$215$	2.77738e37	−	1.62277e37i	1.33236	−	0.778472i
$216$	−4.07573e36			−0.181529
$217$	−5.93518e36	+	5.93518e36i	−0.245515	+	0.245515i
$218$	−1.42388e36	−	1.42388e36i	−0.0547230	−	0.0547230i
$219$		−	2.44457e36i		−	0.0873166i
$220$	−1.92956e37	−	5.06319e36i	−0.640760	−	0.168136i
$221$	−9.71962e37			−3.00174
$222$	−8.70538e36	+	8.70538e36i	−0.250115	+	0.250115i
$223$	1.30695e37	+	1.30695e37i	0.349446	+	0.349446i	0.859903	−	0.510457i	$-0.170524\pi$
$223$	1.30695e37	+	1.30695e37i	0.349446	+	0.349446i	−0.510457	+	0.859903i	$0.670524\pi$
$224$			2.31675e37i			0.576647i
$225$	2.94041e37	−	5.21711e37i	0.681535	−	1.20923i
$226$	8.05454e36			0.173902
$227$	1.43770e37	−	1.43770e37i	0.289238	−	0.289238i	−0.547541	−	0.836779i	$-0.684436\pi$
$227$	1.43770e37	−	1.43770e37i	0.289238	−	0.289238i	0.836779	+	0.547541i	$0.184436\pi$
$228$	−6.39228e36	−	6.39228e36i	−0.119867	−	0.119867i
$229$			3.75566e37i			0.656626i	0.944569	+	0.328313i	$0.106480\pi$
$229$			3.75566e37i			0.656626i	−0.944569	+	0.328313i	$0.893520\pi$
$230$	3.88802e35	−	1.48171e36i	0.00633991	−	0.0241611i
$231$	8.92637e37			1.35795
$232$	7.77308e36	−	7.77308e36i	0.110353	−	0.110353i
$233$	9.07091e37	+	9.07091e37i	1.20214	+	1.20214i	0.973514	+	0.228629i	$0.0734242\pi$
$233$	9.07091e37	+	9.07091e37i	1.20214	+	1.20214i	0.228629	+	0.973514i	$0.426576\pi$
$234$		−	2.96149e37i		−	0.366485i
$235$	−1.59041e36	−	2.72198e36i	−0.0183833	−	0.0314630i
$236$	6.96221e37			0.751891
$237$	−3.04115e37	+	3.04115e37i	−0.306948	+	0.306948i
$238$	2.58854e37	+	2.58854e37i	0.244244	+	0.244244i
$239$			2.98424e37i			0.263310i	0.991296	+	0.131655i	$0.0420292\pi$
$239$			2.98424e37i			0.263310i	−0.991296	+	0.131655i	$0.957971\pi$
$240$	−1.50383e38	+	8.78659e37i	−1.24113	+	0.725171i
$241$	−3.70032e37			−0.285737			−0.142868	−	0.989742i	$-0.545633\pi$
$241$	−3.70032e37			−0.285737			−0.142868	+	0.989742i	$0.545633\pi$
$242$	8.08892e36	−	8.08892e36i	0.0584581	−	0.0584581i
$243$	−1.37190e38	−	1.37190e38i	−0.928159	−	0.928159i
$244$			1.59117e38i			1.00804i
$245$	1.10519e38	+	2.90003e37i	0.655813	+	0.172086i
$246$	1.31570e37			0.0731469
$247$	2.62829e37	−	2.62829e37i	0.136937	−	0.136937i
$248$	−1.17468e37	−	1.17468e37i	−0.0573712	−	0.0573712i
$249$		−	5.50625e38i		−	2.52154i
$250$	5.54476e35	+	3.56529e37i	0.00238146	+	0.153128i
$251$	−2.91728e38			−1.17544			−0.587718	−	0.809066i	$-0.699974\pi$
$251$	−2.91728e38			−1.17544			−0.587718	+	0.809066i	$0.699974\pi$
$252$	3.28394e38	−	3.28394e38i	1.24161	−	1.24161i
$253$	2.20468e37	+	2.20468e37i	0.0782377	+	0.0782377i
$254$			5.50841e37i			0.183521i
$255$	−2.18276e38	+	8.31842e38i	−0.682910	+	2.60254i
$256$	2.63250e38			0.773623
$257$	−2.49201e38	+	2.49201e38i	−0.688049	+	0.688049i	−0.961800	−	0.273751i	$-0.911735\pi$
$257$	−2.49201e38	+	2.49201e38i	−0.688049	+	0.688049i	0.273751	+	0.961800i	$0.411735\pi$
$258$	−9.95240e37	−	9.95240e37i	−0.258233	−	0.258233i
$259$		−	7.93814e38i		−	1.93608i
$260$	−3.70383e38	−	6.33911e38i	−0.849332	−	1.45363i
$261$	−3.31853e38			−0.715644
$262$	9.20256e37	−	9.20256e37i	0.186676	−	0.186676i
$263$	5.70919e38	+	5.70919e38i	1.08964	+	1.08964i	0.995565	+	0.0940739i	$0.0299890\pi$
$263$	5.70919e38	+	5.70919e38i	1.08964	+	1.08964i	0.0940739	+	0.995565i	$0.470011\pi$
$264$			1.76670e38i			0.317321i
$265$	−3.00302e37	+	1.75461e37i	−0.0507721	+	0.0296652i
$266$	−1.39994e37			−0.0222845
$267$	−4.85749e38	+	4.85749e38i	−0.728169	+	0.728169i
$268$	−2.35916e37	−	2.35916e37i	−0.0333121	−	0.0333121i
$269$			2.51868e38i			0.335071i	0.985866	+	0.167536i	$0.0535809\pi$
$269$			2.51868e38i			0.335071i	−0.985866	+	0.167536i	$0.946419\pi$
$270$	−7.08597e37	−	1.85937e37i	−0.0888340	−	0.0233101i
$271$	−2.08963e38			−0.246922			−0.123461	−	0.992349i	$-0.539399\pi$
$271$	−2.08963e38			−0.246922			−0.123461	+	0.992349i	$0.539399\pi$
$272$	1.02800e39	−	1.02800e39i	1.14522	−	1.14522i
$273$	2.32299e39	+	2.32299e39i	2.44031	+	2.44031i
$274$		−	1.10994e38i		−	0.109974i
$275$	−6.32243e38	−	3.56338e38i	−0.590964	−	0.333073i
$276$	2.79081e38			0.246142
$277$	8.79489e38	−	8.79489e38i	0.732072	−	0.732072i	−0.238958	−	0.971030i	$-0.576806\pi$
$277$	8.79489e38	−	8.79489e38i	0.732072	−	0.732072i	0.971030	+	0.238958i	$0.0768057\pi$
$278$	−6.49607e37	−	6.49607e37i	−0.0510427	−	0.0510427i
$279$			5.01502e38i			0.372054i
$280$	−1.42052e38	+	5.41354e38i	−0.0995218	+	0.379274i
$281$	−1.51613e39			−1.00331			−0.501654	−	0.865068i	$-0.667275\pi$
$281$	−1.51613e39			−1.00331			−0.501654	+	0.865068i	$0.667275\pi$
$282$	−9.75389e36	+	9.75389e36i	−0.00609807	+	0.00609807i
$283$	−7.58472e38	−	7.58472e38i	−0.448081	−	0.448081i	0.446635	−	0.894716i	$-0.352622\pi$
$283$	−7.58472e38	−	7.58472e38i	−0.448081	−	0.448081i	−0.894716	+	0.446635i	$0.852622\pi$
$284$			1.07518e39i			0.600326i
$285$	−1.65915e38	−	2.83963e38i	−0.0875723	−	0.149880i
$286$	−3.58892e38			−0.179105
$287$	−5.99872e38	+	5.99872e38i	−0.283106	+	0.283106i
$288$	9.78787e38	+	9.78787e38i	0.436926	+	0.436926i
$289$		−	4.81058e39i		−	2.03157i
$290$	1.70602e38	−	9.96798e37i	0.0681736	−	0.0398327i
$291$	−4.57917e39			−1.73180
$292$	−1.08988e38	+	1.08988e38i	−0.0390168	+	0.0390168i
$293$	−7.67115e38	−	7.67115e38i	−0.260003	−	0.260003i	0.565052	−	0.825055i	$-0.308856\pi$
$293$	−7.67115e38	−	7.67115e38i	−0.260003	−	0.260003i	−0.825055	+	0.565052i	$0.808856\pi$
$294$		−	4.99950e38i		−	0.160461i
$295$	2.44994e39	+	6.42867e38i	0.744737	+	0.195420i
$296$	1.57111e39			0.452417
$297$	1.05434e39	−	1.05434e39i	0.287659	−	0.287659i
$298$	−2.13783e38	−	2.13783e38i	−0.0552731	−	0.0552731i
$299$			1.14749e39i			0.281196i
$300$	−6.25703e39	+	1.74629e39i	−1.45354	+	0.405673i
$301$	9.07525e39			1.99892
$302$	4.65023e37	−	4.65023e37i	0.00971323	−	0.00971323i
$303$	−6.22089e39	−	6.22089e39i	−1.23245	−	1.23245i
$304$			5.55963e38i			0.104488i
$305$	−1.46923e39	+	5.59918e39i	−0.261995	+	0.998452i
$306$	2.18723e39			0.370128
$307$	2.83542e39	−	2.83542e39i	0.455411	−	0.455411i	−0.441735	−	0.897146i	$-0.645637\pi$
$307$	2.83542e39	−	2.83542e39i	0.455411	−	0.455411i	0.897146	+	0.441735i	$0.145637\pi$
$308$	−3.97969e39	−	3.97969e39i	−0.606789	−	0.606789i
$309$			4.87174e39i			0.705259i
$310$	−1.50638e38	−	2.57817e38i	−0.0207085	−	0.0354426i
$311$	2.65133e38			0.0346177			0.0173088	−	0.999850i	$-0.494490\pi$
$311$	2.65133e38			0.0346177			0.0173088	+	0.999850i	$0.494490\pi$
$312$	−4.59764e39	+	4.59764e39i	−0.570245	+	0.570245i
$313$	8.24421e39	+	8.24421e39i	0.971493	+	0.971493i	0.999605	−	0.0281114i	$-0.00894932\pi$
$313$	8.24421e39	+	8.24421e39i	0.971493	+	0.971493i	−0.0281114	+	0.999605i	$0.508949\pi$
$314$		−	9.46659e38i		−	0.106003i
$315$	1.45882e40	−	8.52361e39i	1.55250	−	0.907099i
$316$	2.71170e39			0.274315
$317$	−1.40618e40	+	1.40618e40i	−1.35236	+	1.35236i	−0.469353	+	0.883011i	$0.655513\pi$
$317$	−1.40618e40	+	1.40618e40i	−1.35236	+	1.35236i	−0.883011	+	0.469353i	$0.844487\pi$
$318$	1.07610e38	+	1.07610e38i	0.00984050	+	0.00984050i
$319$			4.02160e39i			0.349742i
$320$	1.00799e40	+	2.64497e39i	0.833787	+	0.218787i
$321$	9.94243e39			0.782370
$322$	3.05600e38	−	3.05600e38i	0.0228802	−	0.0228802i
$323$	1.94114e39	+	1.94114e39i	0.138298	+	0.138298i
$324$			6.64400e39i			0.450515i
$325$	−7.18013e39	−	2.57268e40i	−0.463446	−	1.66055i
$326$	−1.73754e39			−0.106771
$327$	9.43735e39	−	9.43735e39i	0.552187	−	0.552187i
$328$	−1.18726e39	−	1.18726e39i	−0.0661553	−	0.0661553i
$329$		−	8.89424e38i		−	0.0472035i
$330$	−8.05975e38	+	3.07154e39i	−0.0407473	+	0.155286i
$331$	−9.25577e39			−0.445825			−0.222913	−	0.974838i	$-0.571556\pi$
$331$	−9.25577e39			−0.445825			−0.222913	+	0.974838i	$0.571556\pi$
$332$	−2.45488e40	+	2.45488e40i	−1.12673	+	1.12673i
$333$	−3.35373e40	−	3.35373e40i	−1.46697	−	1.46697i
$334$		−	2.77251e39i		−	0.115592i
$335$	−6.12331e38	−	1.04801e39i	−0.0243371	−	0.0416530i
$336$	−4.91384e40			−1.86205
$337$	2.98555e40	−	2.98555e40i	1.07881	−	1.07881i	0.0821975	−	0.996616i	$-0.473806\pi$
$337$	2.98555e40	−	2.98555e40i	1.07881	−	1.07881i	0.996616	−	0.0821975i	$-0.0261938\pi$
$338$	−6.19741e39	−	6.19741e39i	−0.213571	−	0.213571i
$339$			5.33847e40i			1.75478i
$340$	4.68180e40	−	2.73549e40i	1.46808	−	0.857774i
$341$	6.07753e39			0.181826
$342$	−5.91450e38	+	5.91450e38i	−0.0168850	+	0.0168850i
$343$	−1.08249e40	−	1.08249e40i	−0.294930	−	0.294930i
$344$			1.79616e40i			0.467101i
$345$	9.82062e39	+	2.57694e39i	0.243800	+	0.0639734i
$346$	6.03927e39			0.143142
$347$	1.11720e40	−	1.11720e40i	0.252847	−	0.252847i	−0.569290	−	0.822137i	$-0.692782\pi$
$347$	1.11720e40	−	1.11720e40i	0.252847	−	0.252847i	0.822137	+	0.569290i	$0.192782\pi$
$348$	2.54540e40	+	2.54540e40i	0.550158	+	0.550158i
$349$		−	2.84935e40i		−	0.588218i	−0.955772	−	0.294109i	$-0.904977\pi$
$349$		−	2.84935e40i		−	0.588218i	0.955772	−	0.294109i	$-0.0950229\pi$
$350$	−4.93936e39	+	8.76381e39i	−0.0974052	+	0.172824i
$351$	5.48762e40			1.03388
$352$	1.18616e40	−	1.18616e40i	0.213530	−	0.213530i
$353$	−4.16523e40	−	4.16523e40i	−0.716546	−	0.716546i	0.251350	−	0.967896i	$-0.419125\pi$
$353$	−4.16523e40	−	4.16523e40i	−0.716546	−	0.716546i	−0.967896	+	0.251350i	$0.919125\pi$
$354$		−	1.10827e40i		−	0.182219i
$355$	−9.92782e39	+	3.78345e40i	−0.156027	+	0.594614i
$356$	4.33128e40			0.650753
$357$	−1.71566e41	+	1.71566e41i	−2.46456	+	2.46456i
$358$	−7.09565e39	−	7.09565e39i	−0.0974684	−	0.0974684i
$359$			7.75800e40i			1.01915i	0.860426	+	0.509576i	$0.170198\pi$
$359$			7.75800e40i			1.01915i	−0.860426	+	0.509576i	$0.829802\pi$
$360$	1.68698e40	+	2.88727e40i	0.211968	+	0.362784i
$361$	8.21486e40			0.987382
$362$	3.00612e39	−	3.00612e39i	0.0345676	−	0.0345676i
$363$	5.36126e40	+	5.36126e40i	0.589876	+	0.589876i
$364$		−	2.07134e41i		−	2.18087i
$365$	−4.84153e39	+	2.82882e39i	−0.0487862	+	0.0285049i
$366$	2.53288e40			0.244296
$367$	1.41573e41	−	1.41573e41i	1.30715	−	1.30715i	0.383679	−	0.923466i	$-0.374657\pi$
$367$	1.41573e41	−	1.41573e41i	1.30715	−	1.30715i	0.923466	−	0.383679i	$-0.125343\pi$
$368$	−1.21364e40	−	1.21364e40i	−0.107282	−	0.107282i
$369$			5.06872e40i			0.429019i
$370$	2.73149e40	+	7.16747e39i	0.221397	+	0.0580949i
$371$	−9.81256e39			−0.0761727
$372$	3.84665e40	−	3.84665e40i	0.286020	−	0.286020i
$373$	1.36751e40	+	1.36751e40i	0.0974070	+	0.0974070i	0.754131	−	0.656724i	$-0.228058\pi$
$373$	1.36751e40	+	1.36751e40i	0.0974070	+	0.0974070i	−0.656724	+	0.754131i	$0.728058\pi$
$374$		−	2.65063e40i		−	0.180885i
$375$	−2.36304e41	+	3.67502e39i	−1.54515	+	0.0240303i
$376$	1.76034e39			0.0110304
$377$	−1.04658e41	+	1.04658e41i	−0.628507	+	0.628507i
$378$	−1.46147e40	−	1.46147e40i	−0.0841243	−	0.0841243i
$379$			1.18815e41i			0.655607i	0.944746	+	0.327803i	$0.106308\pi$
$379$			1.18815e41i			0.655607i	−0.944746	+	0.327803i	$0.893692\pi$
$380$	−5.26301e39	+	2.00571e40i	−0.0278417	+	0.106104i
$381$	−3.65092e41			−1.85184
$382$	−3.77030e40	+	3.77030e40i	−0.183384	+	0.183384i
$383$	−1.67057e41	−	1.67057e41i	−0.779263	−	0.779263i	0.200442	−	0.979705i	$-0.435762\pi$
$383$	−1.67057e41	−	1.67057e41i	−0.779263	−	0.779263i	−0.979705	+	0.200442i	$0.935762\pi$
$384$		−	1.99355e41i		−	0.891924i
$385$	−1.03295e41	−	1.76789e41i	−0.443308	−	0.758722i
$386$	3.75768e40			0.154712
$387$	3.83414e41	−	3.83414e41i	1.51458	−	1.51458i
$388$	2.04155e41	+	2.04155e41i	0.773843	+	0.773843i
$389$		−	1.48996e40i		−	0.0541976i	−0.999633	−	0.0270988i	$-0.991373\pi$
$389$		−	1.48996e40i		−	0.0541976i	0.999633	−	0.0270988i	$-0.00862687\pi$
$390$	−1.00908e41	+	5.89589e40i	−0.352284	+	0.205833i
$391$	−8.47484e40			−0.283990
$392$	−4.51144e40	+	4.51144e40i	−0.145124	+	0.145124i
$393$	6.09937e41	+	6.09937e41i	1.88367	+	1.88367i
$394$		−	1.43690e40i		−	0.0426077i
$395$	9.54224e40	+	2.50389e40i	0.271705	+	0.0712956i
$396$	−3.36270e41			−0.919529
$397$	3.39786e41	−	3.39786e41i	0.892396	−	0.892396i	−0.102352	−	0.994748i	$-0.532637\pi$
$397$	3.39786e41	−	3.39786e41i	0.892396	−	0.892396i	0.994748	+	0.102352i	$0.0326368\pi$
$398$	6.00876e40	+	6.00876e40i	0.151585	+	0.151585i
$399$		−	9.27865e40i		−	0.224863i
$400$	3.48041e41	+	1.96159e41i	0.810345	+	0.456718i
$401$	−4.80069e41			−1.07397			−0.536987	−	0.843590i	$-0.680438\pi$
$401$	−4.80069e41			−1.07397			−0.536987	+	0.843590i	$0.680438\pi$
$402$	−3.75540e39	+	3.75540e39i	−0.00807308	+	0.00807308i
$403$	1.58161e41	+	1.58161e41i	0.326753	+	0.326753i
$404$			5.54698e41i			1.10142i
$405$	−6.13484e40	+	2.33796e41i	−0.117091	+	0.446228i
$406$	5.57452e40			0.102280
$407$	−4.06427e41	+	4.06427e41i	−0.716922	+	0.716922i
$408$	−3.39562e41	−	3.39562e41i	−0.575912	−	0.575912i
$409$		−	8.18705e41i		−	1.33523i	−0.744509	−	0.667613i	$-0.767316\pi$
$409$		−	8.18705e41i		−	1.33523i	0.744509	−	0.667613i	$-0.232684\pi$
$410$	−1.52251e40	−	2.60578e40i	−0.0238791	−	0.0408692i
$411$	7.35655e41			1.10970
$412$	2.17199e41	−	2.17199e41i	0.315140	−	0.315140i
$413$	5.05296e41	+	5.05296e41i	0.705254	+	0.705254i
$414$		−	2.58222e40i		−	0.0346727i
$415$	−1.09052e42	+	6.37175e41i	−1.40885	+	0.823169i
$416$	6.17369e41			0.767452
$417$	4.30553e41	−	4.30553e41i	0.515051	−	0.515051i
$418$	7.16757e39	+	7.16757e39i	0.00825185	+	0.00825185i
$419$		−	3.60887e41i		−	0.399896i	−0.979807	−	0.199948i	$-0.935923\pi$
$419$		−	3.60887e41i		−	0.399896i	0.979807	−	0.199948i	$-0.0640773\pi$
$420$	−1.77273e42	−	4.65167e41i	−1.89084	−	0.496158i
$421$	3.67988e41			0.377850			0.188925	−	0.981991i	$-0.439500\pi$
$421$	3.67988e41			0.377850			0.188925	+	0.981991i	$0.439500\pi$
$422$	−2.00163e41	+	2.00163e41i	−0.197872	+	0.197872i
$423$	−3.75767e40	−	3.75767e40i	−0.0357662	−	0.0357662i
$424$		−	1.94209e40i		−	0.0177998i
$425$	1.90007e42	−	5.30294e41i	1.67705	−	0.468052i
$426$	1.71150e41			0.145487
$427$	−1.15482e42	+	1.15482e42i	−0.945517	+	0.945517i
$428$	−4.43268e41	−	4.43268e41i	−0.349596	−	0.349596i
$429$		−	2.37871e42i		−	1.80727i
$430$	−8.19418e40	+	3.12277e41i	−0.0599805	+	0.228583i
$431$	−1.24481e42			−0.877944			−0.438972	−	0.898501i	$-0.644657\pi$
$431$	−1.24481e42			−0.877944			−0.438972	+	0.898501i	$0.644657\pi$
$432$	−5.80400e41	+	5.80400e41i	−0.394446	+	0.394446i
$433$	−1.38645e42	−	1.38645e42i	−0.908023	−	0.908023i	0.0880895	−	0.996113i	$-0.471924\pi$
$433$	−1.38645e42	−	1.38645e42i	−0.908023	−	0.908023i	−0.996113	+	0.0880895i	$0.971924\pi$
$434$		−	8.42433e40i		−	0.0531741i
$435$	6.60669e41	+	1.13074e42i	0.401935	+	0.687912i
$436$	−8.41500e41			−0.493481
$437$	2.29168e40	−	2.29168e40i	0.0129554	−	0.0129554i
$438$	1.73490e40	+	1.73490e40i	0.00945560	+	0.00945560i
$439$		−	3.05218e41i		−	0.160390i	−0.996779	−	0.0801952i	$-0.974446\pi$
$439$		−	3.05218e41i		−	0.160390i	0.996779	−	0.0801952i	$-0.0255544\pi$
$440$	3.49898e41	−	2.04439e41i	0.177296	−	0.103591i
$441$	1.92605e42			0.941131
$442$	6.89797e41	−	6.89797e41i	0.325061	−	0.325061i
$443$	−1.39251e42	−	1.39251e42i	−0.632906	−	0.632906i	0.315890	−	0.948796i	$-0.397697\pi$
$443$	−1.39251e42	−	1.39251e42i	−0.632906	−	0.632906i	−0.948796	+	0.315890i	$0.897697\pi$
$444$			5.14480e42i			2.25549i
$445$	1.52414e42	+	3.99936e41i	0.644562	+	0.169134i
$446$	−1.85507e41			−0.0756838
$447$	1.41694e42	−	1.41694e42i	0.557738	−	0.557738i
$448$	2.07896e42	+	2.07896e42i	0.789582	+	0.789582i
$449$			3.83257e42i			1.40459i	0.711887	+	0.702294i	$0.247841\pi$
$449$			3.83257e42i			1.40459i	−0.711887	+	0.702294i	$0.752159\pi$
$450$	1.61576e41	+	5.78936e41i	0.0571449	+	0.204753i
$451$	6.14260e41			0.209666
$452$	2.38008e42	−	2.38008e42i	0.784109	−	0.784109i
$453$	3.08213e41	+	3.08213e41i	0.0980121	+	0.0980121i
$454$			2.04066e41i			0.0626436i
$455$	1.91261e42	−	7.28886e42i	0.566817	−	2.16012i
$456$	1.83642e41			0.0525454
$457$	−3.65794e42	+	3.65794e42i	−1.01059	+	1.01059i	−0.0106511	+	0.999943i	$0.503390\pi$
$457$	−3.65794e42	+	3.65794e42i	−1.01059	+	1.01059i	−0.999943	+	0.0106511i	$0.996610\pi$
$458$	−2.66537e41	−	2.66537e41i	−0.0711066	−	0.0711066i
$459$			4.05292e42i			1.04416i
$460$	−3.22949e41	−	5.52727e41i	−0.0803541	−	0.137526i
$461$	−4.44456e42			−1.06811			−0.534053	−	0.845451i	$-0.679332\pi$
$461$	−4.44456e42			−1.06811			−0.534053	+	0.845451i	$0.679332\pi$
$462$	−6.33500e41	+	6.33500e41i	−0.147053	+	0.147053i
$463$	3.29200e42	+	3.29200e42i	0.738183	+	0.738183i	0.972226	−	0.234043i	$-0.0751956\pi$
$463$	3.29200e42	+	3.29200e42i	0.738183	+	0.738183i	−0.234043	+	0.972226i	$0.575196\pi$
$464$		−	2.21383e42i		−	0.479576i
$465$	1.70879e42	−	9.98416e41i	0.357636	−	0.208961i
$466$	−1.28752e42			−0.260362
$467$	−2.22020e42	+	2.22020e42i	−0.433832	+	0.433832i	−0.889930	−	0.456098i	$-0.849247\pi$
$467$	−2.22020e42	+	2.22020e42i	−0.433832	+	0.433832i	0.456098	+	0.889930i	$0.349247\pi$
$468$	−8.75107e42	−	8.75107e42i	−1.65245	−	1.65245i
$469$		−	3.42442e41i		−	0.0624916i
$470$	3.06048e40	+	8.03074e39i	0.00539790	+	0.00141641i
$471$	6.27437e42			1.06963
$472$	−1.00008e42	+	1.00008e42i	−0.164802	+	0.164802i
$473$	−4.64646e42	−	4.64646e42i	−0.740191	−	0.740191i
$474$		−	4.31658e41i		−	0.0664793i
$475$	−3.70401e41	+	6.57195e41i	−0.0551537	+	0.0978580i
$476$	1.52980e43			2.20254
$477$	−4.14564e41	+	4.14564e41i	−0.0577162	+	0.0577162i
$478$	−2.11790e41	−	2.11790e41i	−0.0285141	−	0.0285141i
$479$			8.47094e41i			0.110297i	0.998478	+	0.0551484i	$0.0175632\pi$
$479$			8.47094e41i			0.110297i	−0.998478	+	0.0551484i	$0.982437\pi$
$480$	1.38644e42	−	5.28368e42i	0.174599	−	0.665390i
$481$	−2.11536e43			−2.57670
$482$	2.62610e41	−	2.62610e41i	0.0309427	−	0.0309427i
$483$	2.02549e42	+	2.02549e42i	0.230874	+	0.230874i
$484$		−	4.78048e42i		−	0.527163i
$485$	5.29894e42	+	9.06914e42i	0.565355	+	0.967606i
$486$	1.94726e42			0.201022
$487$	−9.87049e42	+	9.87049e42i	−0.985996	+	0.985996i	−0.999903	−	0.0139070i	$-0.995573\pi$
$487$	−9.87049e42	+	9.87049e42i	−0.985996	+	0.985996i	0.0139070	+	0.999903i	$0.495573\pi$
$488$	−2.28561e42	−	2.28561e42i	−0.220946	−	0.220946i
$489$		−	1.15162e43i		−	1.07738i
$490$	−9.90163e41	+	5.78535e41i	−0.0896539	+	0.0523832i
$491$	1.85335e43			1.62425			0.812125	−	0.583483i	$-0.198311\pi$
$491$	1.85335e43			1.62425			0.812125	+	0.583483i	$0.198311\pi$
$492$	3.88784e42	−	3.88784e42i	0.329812	−	0.329812i
$493$	−7.72958e42	−	7.72958e42i	−0.634754	−	0.634754i
$494$			3.73056e41i			0.0296581i
$495$	−1.18330e43	−	3.10500e42i	−0.910780	−	0.238990i
$496$	−3.34559e42			−0.249325
$497$	−7.80332e42	+	7.80332e42i	−0.563089	+	0.563089i
$498$	3.90776e42	+	3.90776e42i	0.273060	+	0.273060i
$499$			2.37069e43i			1.60423i	0.597170	+	0.802115i	$0.296292\pi$
$499$			2.37069e43i			1.60423i	−0.597170	+	0.802115i	$0.703708\pi$
$500$	1.06991e43	+	1.03714e43i	0.701177	+	0.679701i
$501$	1.83759e43			1.16639
$502$	2.07038e42	−	2.07038e42i	0.127289	−	0.127289i
$503$	4.52928e42	+	4.52928e42i	0.269738	+	0.269738i	0.828994	−	0.559257i	$-0.188913\pi$
$503$	4.52928e42	+	4.52928e42i	0.269738	+	0.269738i	−0.559257	+	0.828994i	$0.688913\pi$
$504$			9.43433e42i			0.544280i
$505$	−5.12189e42	+	1.95193e43i	−0.286265	+	1.09094i
$506$	−3.12930e41			−0.0169449
$507$	4.10758e43	−	4.10758e43i	2.15506	−	2.15506i
$508$	1.62771e43	+	1.62771e43i	0.827479	+	0.827479i
$509$		−	2.95053e43i		−	1.45350i	−0.686900	−	0.726752i	$-0.741029\pi$
$509$		−	2.95053e43i		−	1.45350i	0.686900	−	0.726752i	$-0.258971\pi$
$510$	−4.35445e42	−	7.45264e42i	−0.207879	−	0.355785i
$511$	−1.58200e42			−0.0731933
$512$	−1.09697e43	+	1.09697e43i	−0.491898	+	0.491898i
$513$	−1.09595e42	−	1.09595e42i	−0.0476336	−	0.0476336i
$514$		−	3.53713e42i		−	0.149019i
$515$	9.64859e42	−	5.63750e42i	0.394047	−	0.230235i
$516$	−5.88177e43			−2.32870
$517$	−4.55378e41	+	4.55378e41i	−0.0174793	+	0.0174793i
$518$	5.63366e42	+	5.63366e42i	0.209660	+	0.209660i
$519$			4.00277e43i			1.44438i
$520$	1.44260e43	+	3.78541e42i	0.504770	+	0.132452i
$521$	−5.20733e43			−1.76690			−0.883449	−	0.468528i	$-0.844784\pi$
$521$	−5.20733e43			−1.76690			−0.883449	+	0.468528i	$0.844784\pi$
$522$	2.35514e42	−	2.35514e42i	0.0774978	−	0.0774978i
$523$	8.98796e42	+	8.98796e42i	0.286836	+	0.286836i	0.835828	−	0.548992i	$-0.184988\pi$
$523$	8.98796e42	+	8.98796e42i	0.286836	+	0.286836i	−0.548992	+	0.835828i	$0.684988\pi$
$524$		−	5.43863e43i		−	1.68341i
$525$	−5.80857e43	−	3.27376e43i	−1.74390	−	0.982875i
$526$	−8.10358e42			−0.235996
$527$	−1.16811e43	+	1.16811e43i	−0.330000	+	0.330000i
$528$	2.51585e43	+	2.51585e43i	0.689511	+	0.689511i
$529$		−	3.66084e43i		−	0.973396i
$530$	8.85990e40	−	3.37647e41i	0.00228568	−	0.00871063i
$531$	4.26958e43			1.06874
$532$	−4.13675e42	+	4.13675e42i	−0.100478	+	0.100478i
$533$	1.59854e43	+	1.59854e43i	0.376781	+	0.376781i
$534$		−	6.89468e42i		−	0.157708i
$535$	−1.15052e43	−	1.96912e43i	−0.255408	−	0.437131i
$536$	6.77757e41			0.0146029
$537$	4.70293e43	−	4.70293e43i	0.983514	−	0.983514i
$538$	−1.78750e42	−	1.78750e42i	−0.0362851	−	0.0362851i
$539$		−	2.33411e43i		−	0.459940i
$540$	−2.64331e43	+	1.54444e43i	−0.505647	+	0.295441i
$541$	4.33440e43			0.804957			0.402478	−	0.915429i	$-0.368149\pi$
$541$	4.33440e43			0.804957			0.402478	+	0.915429i	$0.368149\pi$
$542$	1.48300e42	−	1.48300e42i	0.0267395	−	0.0267395i
$543$	1.99243e43	+	1.99243e43i	0.348807	+	0.348807i
$544$			4.55962e43i			0.775080i
$545$	−2.96116e43	−	7.77013e42i	−0.488786	−	0.128258i
$546$	−3.29723e43			−0.528527
$547$	−2.48838e43	+	2.48838e43i	−0.387364	+	0.387364i	−0.873746	−	0.486382i	$-0.838316\pi$
$547$	−2.48838e43	+	2.48838e43i	−0.387364	+	0.387364i	0.486382	+	0.873746i	$0.338316\pi$
$548$	−3.27981e43	−	3.27981e43i	−0.495860	−	0.495860i
$549$			9.75786e43i			1.43284i
$550$	7.01591e42	−	1.95809e42i	0.100065	−	0.0279273i
$551$	4.18032e42			0.0579140
$552$	−4.00882e42	+	4.00882e42i	−0.0539500	+	0.0539500i
$553$	1.96807e43	+	1.96807e43i	0.257300	+	0.257300i
$554$			1.24834e43i			0.158554i
$555$	−4.75053e43	+	1.81041e44i	−0.586212	+	2.23403i
$556$	−3.83912e43			−0.460293
$557$	7.53822e43	−	7.53822e43i	0.878184	−	0.878184i	−0.115163	−	0.993347i	$-0.536739\pi$
$557$	7.53822e43	−	7.53822e43i	0.878184	−	0.878184i	0.993347	+	0.115163i	$0.0367389\pi$
$558$	−3.55914e42	−	3.55914e42i	−0.0402901	−	0.0402901i
$559$		−	2.41838e44i		−	2.66033i
$560$	5.68622e43	+	9.73196e43i	0.607876	+	1.04038i
$561$	1.75681e44			1.82524
$562$	1.07599e43	−	1.07599e43i	0.108649	−	0.108649i
$563$	7.41872e43	+	7.41872e43i	0.728106	+	0.728106i	0.970242	−	0.242137i	$-0.0778482\pi$
$563$	7.41872e43	+	7.41872e43i	0.728106	+	0.728106i	−0.242137	+	0.970242i	$0.577848\pi$
$564$			5.76446e42i			0.0549911i
$565$	1.05730e44	−	6.17760e43i	0.980441	−	0.572855i
$566$	1.07657e43			0.0970462
$567$	−4.82201e43	+	4.82201e43i	−0.422571	+	0.422571i
$568$	−1.54442e43	−	1.54442e43i	−0.131581	−	0.131581i
$569$		−	5.94303e42i		−	0.0492280i	−0.999697	−	0.0246140i	$-0.992164\pi$
$569$		−	5.94303e42i		−	0.0492280i	0.999697	−	0.0246140i	$-0.00783567\pi$
$570$	3.19276e42	+	8.37784e41i	0.0257139	+	0.00674736i
$571$	−9.88482e43			−0.774090			−0.387045	−	0.922061i	$-0.626504\pi$
$571$	−9.88482e43			−0.774090			−0.387045	+	0.922061i	$0.626504\pi$
$572$	−1.06051e44	+	1.06051e44i	−0.807567	+	0.807567i
$573$	−2.49892e44	−	2.49892e44i	−1.85046	−	1.85046i
$574$		−	8.51453e42i		−	0.0613155i
$575$	−6.26058e42	−	2.24320e43i	−0.0438459	−	0.157102i
$576$	1.75665e44			1.19653
$577$	−4.75070e43	+	4.75070e43i	−0.314735	+	0.314735i	−0.846741	−	0.532006i	$-0.821438\pi$
$577$	−4.75070e43	+	4.75070e43i	−0.314735	+	0.314735i	0.532006	+	0.846741i	$0.321438\pi$
$578$	3.41405e43	+	3.41405e43i	0.220001	+	0.220001i
$579$			2.49056e44i			1.56113i
$580$	2.09572e43	−	7.98671e43i	0.127787	−	0.486990i
$581$	−3.56335e44			−2.11369
$582$	3.24981e43	−	3.24981e43i	0.187539	−	0.187539i
$583$	5.02395e42	+	5.02395e42i	0.0282065	+	0.0282065i
$584$		−	3.13107e42i		−	0.0171036i
$585$	−2.27138e44	−	3.88747e44i	−1.20725	−	2.06620i
$586$	1.08884e43			0.0563119
$587$	7.73947e43	−	7.73947e43i	0.389495	−	0.389495i	−0.485013	−	0.874507i	$-0.661185\pi$
$587$	7.73947e43	−	7.73947e43i	0.389495	−	0.389495i	0.874507	+	0.485013i	$0.161185\pi$
$588$	−1.47733e44	−	1.47733e44i	−0.723503	−	0.723503i
$589$		−	6.31738e42i		−	0.0301087i
$590$	−2.19495e43	+	1.28247e43i	−0.101810	+	0.0594861i
$591$	9.52365e43			0.429936
$592$	2.23732e44	−	2.23732e44i	0.983062	−	0.983062i
$593$	1.91536e44	+	1.91536e44i	0.819171	+	0.819171i	0.985988	−	0.166817i	$-0.0533490\pi$
$593$	1.91536e44	+	1.91536e44i	0.819171	+	0.819171i	−0.166817	+	0.985988i	$0.553349\pi$
$594$			1.49652e43i			0.0623017i
$595$	5.38324e44	+	1.41257e44i	2.18159	+	0.572451i
$596$	−1.26344e44			−0.498442
$597$	−3.98255e44	+	3.98255e44i	−1.52958	+	1.52958i
$598$	−8.14366e42	−	8.14366e42i	−0.0304509	−	0.0304509i
$599$			2.28716e44i			0.832659i	0.909214	+	0.416329i	$0.136684\pi$
$599$			2.28716e44i			0.832659i	−0.909214	+	0.416329i	$0.863316\pi$
$600$	6.47940e43	−	1.14963e44i	0.229675	−	0.407508i
$601$	2.35286e44			0.812089			0.406045	−	0.913853i	$-0.366908\pi$
$601$	2.35286e44			0.812089			0.406045	+	0.913853i	$0.366908\pi$
$602$	−6.44067e43	+	6.44067e43i	−0.216465	+	0.216465i
$603$	−1.44676e43	−	1.44676e43i	−0.0473499	−	0.0473499i
$604$		−	2.74824e43i		−	0.0875920i
$605$	4.41413e43	−	1.68221e44i	0.137012	−	0.522148i
$606$	8.82987e43			0.266927
$607$	−3.64849e44	+	3.64849e44i	−1.07422	+	1.07422i	−0.0772063	+	0.997015i	$0.524600\pi$
$607$	−3.64849e44	+	3.64849e44i	−1.07422	+	1.07422i	−0.997015	+	0.0772063i	$0.975400\pi$
$608$	−1.23297e43	−	1.23297e43i	−0.0353586	−	0.0353586i
$609$			3.69474e44i			1.03207i
$610$	−2.93101e43	−	5.01642e43i	−0.0797516	−	0.136495i
$611$	−2.37015e43			−0.0628226
$612$	6.46317e44	−	6.46317e44i	1.66887	−	1.66887i
$613$	−1.17915e44	−	1.17915e44i	−0.296621	−	0.296621i	0.543068	−	0.839689i	$-0.317263\pi$
$613$	−1.17915e44	−	1.17915e44i	−0.296621	−	0.296621i	−0.839689	+	0.543068i	$0.817263\pi$
$614$			4.02457e43i			0.0986337i
$615$	1.72709e44	−	1.00911e44i	0.412394	−	0.240954i
$616$	1.14331e44			0.265995
$617$	−4.22198e44	+	4.22198e44i	−0.957091	+	0.957091i	−0.999117	−	0.0420252i	$-0.986619\pi$
$617$	−4.22198e44	+	4.22198e44i	−0.957091	+	0.957091i	0.0420252	+	0.999117i	$0.486619\pi$
$618$	−3.45745e43	−	3.45745e43i	−0.0763731	−	0.0763731i
$619$		−	3.95394e44i		−	0.851098i	−0.904935	−	0.425549i	$-0.860081\pi$
$619$		−	3.95394e44i		−	0.851098i	0.904935	−	0.425549i	$-0.139919\pi$
$620$	−1.20697e44	−	3.16710e43i	−0.253179	−	0.0664346i
$621$	4.78483e43			0.0978139
$622$	−1.88164e42	+	1.88164e42i	−0.00374878	+	0.00374878i
$623$	3.14351e44	+	3.14351e44i	0.610389	+	0.610389i
$624$			1.30944e45i			2.47818i
$625$	2.80726e44	+	4.63753e44i	0.517848	+	0.855473i
$626$	−1.17018e44			−0.210408
$627$	−4.75060e43	+	4.75060e43i	−0.0832660	+	0.0832660i
$628$	−2.79733e44	−	2.79733e44i	−0.477958	−	0.477958i
$629$		−	1.56232e45i		−	2.60231i
$630$	−4.30399e43	+	1.64023e44i	−0.0698911	+	0.266352i
$631$	7.17521e44			1.13596			0.567982	−	0.823041i	$-0.307724\pi$
$631$	7.17521e44			1.13596			0.567982	+	0.823041i	$0.307724\pi$
$632$	−3.89519e43	+	3.89519e43i	−0.0601250	+	0.0601250i
$633$	−1.32666e45	−	1.32666e45i	−1.99664	−	1.99664i
$634$		−	1.99592e44i		−	0.292897i
$635$	4.22479e44	+	7.23073e44i	0.604540	+	1.03467i
$636$	6.35963e43			0.0887397
$637$	6.07427e44	−	6.07427e44i	0.826539	−	0.826539i
$638$	−2.85411e43	−	2.85411e43i	−0.0378739	−	0.0378739i
$639$			6.59354e44i			0.853306i
$640$	−3.94827e44	+	2.30691e44i	−0.498342	+	0.291172i
$641$	−5.22495e44			−0.643212			−0.321606	−	0.946874i	$-0.604223\pi$
$641$	−5.22495e44			−0.643212			−0.321606	+	0.946874i	$0.604223\pi$
$642$	−7.05610e43	+	7.05610e43i	−0.0847235	+	0.0847235i
$643$	−9.54303e43	−	9.54303e43i	−0.111766	−	0.111766i	0.649012	−	0.760778i	$-0.275182\pi$
$643$	−9.54303e43	−	9.54303e43i	−0.111766	−	0.111766i	−0.760778	+	0.649012i	$0.775182\pi$
$644$		−	1.80607e44i		−	0.206329i
$645$	−2.06974e45	−	5.43103e44i	−2.30654	−	0.605239i
$646$	−2.75524e43			−0.0299529
$647$	3.59396e43	−	3.59396e43i	0.0381157	−	0.0381157i	−0.687792	−	0.725908i	$-0.741420\pi$
$647$	3.59396e43	−	3.59396e43i	0.0381157	−	0.0381157i	0.725908	+	0.687792i	$0.241420\pi$
$648$	−9.54367e43	−	9.54367e43i	−0.0987451	−	0.0987451i
$649$		−	5.17415e44i		−	0.522305i
$650$	2.33539e44	+	1.31625e44i	0.230009	+	0.129635i
$651$	5.58357e44			0.536557
$652$	−5.13434e44	+	5.13434e44i	−0.481419	+	0.481419i
$653$	8.40400e44	+	8.40400e44i	0.768910	+	0.768910i	0.977915	−	0.209005i	$-0.0670225\pi$
$653$	8.40400e44	+	8.40400e44i	0.768910	+	0.768910i	−0.209005	+	0.977915i	$0.567022\pi$
$654$			1.33953e44i			0.119594i
$655$	5.02184e44	−	1.91380e45i	0.437525	−	1.66739i
$656$	−3.38141e44			−0.287499
$657$	−6.68367e43	+	6.68367e43i	−0.0554587	+	0.0554587i
$658$	6.31220e42	+	6.31220e42i	0.00511172	+	0.00511172i
$659$		−	4.82839e44i		−	0.381624i	−0.981627	−	0.190812i	$-0.938888\pi$
$659$		−	4.82839e44i		−	0.381624i	0.981627	−	0.190812i	$-0.0611121\pi$
$660$	6.69464e44	+	1.14579e45i	0.516445	+	0.883896i
$661$	−1.23727e45			−0.931628			−0.465814	−	0.884883i	$-0.654238\pi$
$661$	−1.23727e45			−0.931628			−0.465814	+	0.884883i	$0.654238\pi$
$662$	6.56878e43	−	6.56878e43i	0.0482788	−	0.0482788i
$663$	4.57191e45	+	4.57191e45i	3.28006	+	3.28006i
$664$		−	7.05255e44i		−	0.493920i
$665$	−1.83766e44	+	1.07371e44i	−0.125637	+	0.0734076i
$666$	4.76026e44			0.317719
$667$	−9.12545e43	+	9.12545e43i	−0.0594622	+	0.0594622i
$668$	−8.19262e44	−	8.19262e44i	−0.521194	−	0.521194i
$669$		−	1.22952e45i		−	0.763693i
$670$	1.17833e43	+	3.09196e42i	0.00714614	+	0.00187515i
$671$	1.18252e45			0.700242
$672$	1.08975e45	−	1.08975e45i	0.630113	−	0.630113i
$673$	1.19050e45	+	1.19050e45i	0.672183	+	0.672183i	0.958219	−	0.286036i	$-0.0923377\pi$
$673$	1.19050e45	+	1.19050e45i	0.672183	+	0.672183i	−0.286036	+	0.958219i	$0.592338\pi$
$674$			4.23767e44i			0.233651i
$675$	−1.07276e45	+	2.99400e44i	−0.577622	+	0.161210i
$676$	−3.66261e45			−1.92594
$677$	9.03188e44	−	9.03188e44i	0.463831	−	0.463831i	−0.436078	−	0.899909i	$-0.643633\pi$
$677$	9.03188e44	−	9.03188e44i	0.463831	−	0.463831i	0.899909	+	0.436078i	$0.143633\pi$
$678$	−3.78869e44	−	3.78869e44i	−0.190026	−	0.190026i
$679$			2.96339e45i			1.45169i
$680$	−2.79574e44	+	1.06545e45i	−0.133769	+	0.509787i
$681$	−1.35253e45			−0.632111
$682$	−4.31319e43	+	4.31319e43i	−0.0196901	+	0.0196901i
$683$	−1.77118e45	−	1.77118e45i	−0.789827	−	0.789827i	0.191639	−	0.981466i	$-0.438620\pi$
$683$	−1.77118e45	−	1.77118e45i	−0.789827	−	0.789827i	−0.981466	+	0.191639i	$0.938620\pi$
$684$			3.49541e44i			0.152265i
$685$	−8.51288e44	−	1.45698e45i	−0.362266	−	0.620019i
$686$	1.53648e44			0.0638765
$687$	1.76658e45	−	1.76658e45i	0.717507	−	0.717507i
$688$	2.55781e45	+	2.55781e45i	1.01497	+	1.01497i
$689$			2.61486e44i			0.101377i
$690$	−8.79850e43	+	5.14081e43i	−0.0333291	+	0.0194736i
$691$	−6.30258e44			−0.233276			−0.116638	−	0.993175i	$-0.537212\pi$
$691$	−6.30258e44			−0.233276			−0.116638	+	0.993175i	$0.537212\pi$
$692$	1.78457e45	−	1.78457e45i	0.645412	−	0.645412i
$693$	−2.44055e45	−	2.44055e45i	−0.862493	−	0.862493i
$694$			1.58574e44i			0.0547622i
$695$	−1.35095e45	−	3.54491e44i	−0.455914	−	0.119632i
$696$	−7.31259e44			−0.241170
$697$	−1.18062e45	+	1.18062e45i	−0.380526	+	0.380526i
$698$	2.02217e44	+	2.02217e44i	0.0636987	+	0.0636987i
$699$		−	8.53354e45i		−	2.62721i
$700$	1.13011e45	+	4.04922e45i	0.340056	+	1.21844i
$701$	3.24603e45			0.954695			0.477348	−	0.878714i	$-0.341598\pi$
$701$	3.24603e45			0.954695			0.477348	+	0.878714i	$0.341598\pi$
$702$	−3.89454e44	+	3.89454e44i	−0.111960	+	0.111960i
$703$	4.22467e44	+	4.22467e44i	0.118715	+	0.118715i
$704$		−	2.12882e45i		−	0.584758i
$705$	−5.32270e43	+	2.02846e44i	−0.0142924	+	0.0544679i
$706$	5.91210e44			0.155191
$707$	−4.02583e45	+	4.02583e45i	−1.03311	+	1.03311i
$708$	−3.27488e45	−	3.27488e45i	−0.821606	−	0.821606i
$709$			1.57466e45i			0.386231i	0.981176	+	0.193116i	$0.0618593\pi$
$709$			1.57466e45i			0.386231i	−0.981176	+	0.193116i	$0.938141\pi$
$710$	−1.98053e44	−	3.38967e44i	−0.0474949	−	0.0812876i
$711$	1.66296e45			0.389912
$712$	−6.22161e44	+	6.22161e44i	−0.142634	+	0.142634i
$713$	1.37906e44	+	1.37906e44i	0.0309136	+	0.0309136i
$714$		−	2.43519e45i		−	0.533780i
$715$	−4.71108e45	+	2.75260e45i	−1.00977	+	0.589993i
$716$	−4.19347e45			−0.878951
$717$	1.40373e45	−	1.40373e45i	0.287724	−	0.287724i
$718$	−5.50582e44	−	5.50582e44i	−0.110365	−	0.110365i
$719$			3.33402e45i			0.653592i	0.945095	+	0.326796i	$0.105969\pi$
$719$			3.33402e45i			0.653592i	−0.945095	+	0.326796i	$0.894031\pi$
$720$	6.51392e45	+	1.70926e45i	1.24889	+	0.327709i
$721$	3.15273e45			0.591185
$722$	−5.83005e44	+	5.83005e44i	−0.106924	+	0.106924i
$723$	1.74055e45	+	1.74055e45i	0.312230	+	0.312230i
$724$		−	1.77659e45i		−	0.311724i
$725$	1.47493e45	−	2.61694e45i	0.253142	−	0.449144i
$726$	−7.60972e44			−0.127756
$727$	−5.07017e45	+	5.07017e45i	−0.832668	+	0.832668i	−0.987881	−	0.155213i	$-0.950394\pi$
$727$	−5.07017e45	+	5.07017e45i	−0.832668	+	0.832668i	0.155213	+	0.987881i	$0.450394\pi$
$728$	2.97535e45	+	2.97535e45i	0.478009	+	0.478009i
$729$			9.97095e45i			1.56710i
$730$	1.42841e43	−	5.44361e43i	0.00219628	−	0.00836992i
$731$	1.78611e46			2.68677
$732$	7.48454e45	−	7.48454e45i	1.10151	−	1.10151i
$733$	−7.72941e44	−	7.72941e44i	−0.111297	−	0.111297i	0.649265	−	0.760562i	$-0.275077\pi$
$733$	−7.72941e44	−	7.72941e44i	−0.111297	−	0.111297i	−0.760562	+	0.649265i	$0.775077\pi$
$734$			2.00948e45i			0.283104i
$735$	−3.83448e45	−	6.56271e45i	−0.528577	−	0.904660i
$736$	5.38303e44			0.0726076
$737$	−1.75328e44	+	1.75328e44i	−0.0231404	+	0.0231404i
$738$	−3.59725e44	−	3.59725e44i	−0.0464588	−	0.0464588i
$739$			1.08394e46i			1.36992i	0.728581	+	0.684959i	$0.240180\pi$
$739$			1.08394e46i			1.36992i	−0.728581	+	0.684959i	$0.759820\pi$
$740$	1.01894e46	−	5.95348e45i	1.26020	−	0.736315i
$741$	−2.47258e45			−0.299268
$742$	6.96393e43	−	6.96393e43i	0.00824882	−	0.00824882i

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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