LMFDB - Embedded newform 605.2.g.f.366.2

Newspace parameters

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.2
Root			$-0.437016 + 1.34500i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.f.81.2

$q$-expansion

$f(q)$	$=$	$q+(0.335106 - 0.243469i) q^{2} +(0.874032 + 2.68999i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.947822 + 0.688633i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.490035 + 1.50817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +O(q^{10})$	\(q+(0.335106 - 0.243469i) q^{2} +(0.874032 + 2.68999i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.947822 + 0.688633i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.490035 + 1.50817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +0.414214 q^{10} -5.17157 q^{12} +(5.52431 - 4.01365i) q^{13} +(0.255998 + 0.787881i) q^{14} +(-0.874032 + 2.68999i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(-0.947822 - 0.688633i) q^{17} +(-0.639995 + 1.96970i) q^{18} +(-1.47923 + 1.07472i) q^{20} -5.65685 q^{21} +2.82843 q^{23} +(-3.62867 + 2.63638i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.874032 - 2.68999i) q^{26} +(-4.57649 - 3.32502i) q^{27} +(-2.95846 - 2.14944i) q^{28} +(2.36610 - 7.28210i) q^{29} +(0.362036 + 1.11423i) q^{30} -4.41421 q^{32} -0.485281 q^{34} +(-1.61803 + 1.17557i) q^{35} +(-2.82508 - 8.69469i) q^{36} +(1.13003 - 3.47788i) q^{37} +(15.6251 + 11.3523i) q^{39} +(-0.490035 + 1.50817i) q^{40} +(1.85410 + 5.70634i) q^{41} +(-1.89564 + 1.37727i) q^{42} -6.00000 q^{43} -5.00000 q^{45} +(0.947822 - 0.688633i) q^{46} +(-0.874032 - 2.68999i) q^{47} +(2.62210 - 8.06998i) q^{48} +(2.42705 + 1.76336i) q^{49} +(0.335106 + 0.243469i) q^{50} +(1.02399 - 3.15152i) q^{51} +(3.85816 + 11.8742i) q^{52} +(-0.277611 + 0.201696i) q^{53} -2.34315 q^{54} -3.17157 q^{56} +(-0.980070 - 3.01635i) q^{58} +(-2.98413 + 9.18421i) q^{59} +(-4.18389 - 3.03977i) q^{60} +(-10.7710 - 7.82560i) q^{61} +(-3.09017 - 9.51057i) q^{63} +(3.37487 - 2.45199i) q^{64} +6.82843 q^{65} -4.48528 q^{67} +(1.73302 - 1.25912i) q^{68} +(2.47214 + 7.60845i) q^{69} +(-0.255998 + 0.787881i) q^{70} +(9.15298 + 6.65003i) q^{71} +(-6.41464 - 4.66051i) q^{72} +(-2.11010 + 6.49422i) q^{73} +(-0.468074 - 1.44058i) q^{74} +(-2.28825 + 1.66251i) q^{75} +8.00000 q^{78} +(-3.23607 + 2.35114i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.01063 + 1.46081i) q^{82} +(4.85410 + 3.52671i) q^{83} +(3.19621 - 9.83692i) q^{84} +(-0.362036 - 1.11423i) q^{85} +(-2.01063 + 1.46081i) q^{86} +21.6569 q^{87} +9.31371 q^{89} +(-1.67553 + 1.21734i) q^{90} +(4.22020 + 12.9884i) q^{91} +(-1.59810 + 4.91846i) q^{92} +(-0.947822 - 0.688633i) q^{94} +(-3.85816 - 11.8742i) q^{96} +(6.19453 - 4.50059i) q^{97} +1.24264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - 6 * q^8 - 10 * q^9	$ 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} - 10 q^{9} - 8 q^{10} - 64 q^{12} + 8 q^{13} + 4 q^{14} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 2 q^{20} + 8 q^{24} - 2 q^{25} + 4 q^{28} - 4 q^{29} - 8 q^{30} - 24 q^{32} + 64 q^{34} - 4 q^{35} - 10 q^{36} + 4 q^{37} + 16 q^{39} + 6 q^{40} - 12 q^{41} - 16 q^{42} - 48 q^{43} - 40 q^{45} + 8 q^{46} + 6 q^{49} - 2 q^{50} + 16 q^{51} - 8 q^{52} - 12 q^{53} - 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} - 4 q^{61} + 20 q^{63} + 14 q^{64} + 32 q^{65} + 32 q^{67} - 24 q^{68} - 16 q^{69} - 4 q^{70} - 30 q^{72} + 8 q^{73} + 20 q^{74} + 64 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} + 12 q^{83} - 32 q^{84} + 8 q^{85} + 12 q^{86} + 128 q^{87} - 16 q^{89} + 10 q^{90} - 16 q^{91} + 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} - 24 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - 6 * q^8 - 10 * q^9 - 8 * q^10 - 64 * q^12 + 8 * q^13 + 4 * q^14 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 2 * q^20 + 8 * q^24 - 2 * q^25 + 4 * q^28 - 4 * q^29 - 8 * q^30 - 24 * q^32 + 64 * q^34 - 4 * q^35 - 10 * q^36 + 4 * q^37 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 16 * q^42 - 48 * q^43 - 40 * q^45 + 8 * q^46 + 6 * q^49 - 2 * q^50 + 16 * q^51 - 8 * q^52 - 12 * q^53 - 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 - 4 * q^61 + 20 * q^63 + 14 * q^64 + 32 * q^65 + 32 * q^67 - 24 * q^68 - 16 * q^69 - 4 * q^70 - 30 * q^72 + 8 * q^73 + 20 * q^74 + 64 * q^78 - 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 + 12 * q^83 - 32 * q^84 + 8 * q^85 + 12 * q^86 + 128 * q^87 - 16 * q^89 + 10 * q^90 - 16 * q^91 + 16 * q^92 - 8 * q^94 + 8 * q^96 + 4 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.335106	−	0.243469i	0.236956	−	0.172158i	−0.462970	−	0.886374i	$-0.653216\pi$
$2$	0.335106	−	0.243469i	0.236956	−	0.172158i	0.699926	+	0.714215i	$0.253216\pi$
$3$	0.874032	+	2.68999i	0.504623	+	1.55307i	0.801404	+	0.598123i	$0.204087\pi$
$3$	0.874032	+	2.68999i	0.504623	+	1.55307i	−0.296781	+	0.954945i	$0.595913\pi$
$4$	−0.565015	+	1.73894i	−0.282508	+	0.869469i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	0.947822	+	0.688633i	0.386947	+	0.281133i
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	0.763710	+	0.645560i	$0.223376\pi$
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	−0.997305	+	0.0733714i	$0.976624\pi$
$8$	0.490035	+	1.50817i	0.173254	+	0.533220i
$9$	−4.04508	+	2.93893i	−1.34836	+	0.979642i
$10$	0.414214			0.130986
$11$		0			0
$11$		0			0
$12$	−5.17157			−1.49290
$13$	5.52431	−	4.01365i	1.53217	−	1.11319i	0.577151	−	0.816637i	$-0.304164\pi$
$13$	5.52431	−	4.01365i	1.53217	−	1.11319i	0.955018	−	0.296549i	$-0.0958356\pi$
$14$	0.255998	+	0.787881i	0.0684184	+	0.210570i
$15$	−0.874032	+	2.68999i	−0.225674	+	0.694553i
$16$	−2.42705	−	1.76336i	−0.606763	−	0.440839i
$17$	−0.947822	−	0.688633i	−0.229881	−	0.167018i	0.466882	−	0.884319i	$-0.345377\pi$
$17$	−0.947822	−	0.688633i	−0.229881	−	0.167018i	−0.696763	+	0.717301i	$0.745377\pi$
$18$	−0.639995	+	1.96970i	−0.150848	+	0.464263i
$19$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$19$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$20$	−1.47923	+	1.07472i	−0.330766	+	0.240315i
$21$	−5.65685			−1.23443
$22$		0			0
$23$	2.82843			0.589768			0.294884	−	0.955533i	$-0.404719\pi$
$23$	2.82843			0.589768			0.294884	+	0.955533i	$0.404719\pi$
$24$	−3.62867	+	2.63638i	−0.740699	+	0.538149i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.874032	−	2.68999i	0.171412	−	0.527551i
$27$	−4.57649	−	3.32502i	−0.880746	−	0.639900i
$28$	−2.95846	−	2.14944i	−0.559096	−	0.406207i
$29$	2.36610	−	7.28210i	0.439373	−	1.35225i	−0.449165	−	0.893449i	$-0.648278\pi$
$29$	2.36610	−	7.28210i	0.439373	−	1.35225i	0.888538	−	0.458803i	$-0.151722\pi$
$30$	0.362036	+	1.11423i	0.0660984	+	0.203430i
$31$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$31$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$32$	−4.41421			−0.780330
$33$		0			0
$34$	−0.485281			−0.0832251
$35$	−1.61803	+	1.17557i	−0.273498	+	0.198708i
$36$	−2.82508	−	8.69469i	−0.470846	−	1.44911i
$37$	1.13003	−	3.47788i	0.185776	−	0.571759i	−0.814185	−	0.580605i	$-0.802816\pi$
$37$	1.13003	−	3.47788i	0.185776	−	0.571759i	0.999961	+	0.00884630i	$0.00281590\pi$
$38$		0			0
$39$	15.6251	+	11.3523i	2.50202	+	1.81782i
$40$	−0.490035	+	1.50817i	−0.0774813	+	0.238463i
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	0.984994	+	0.172588i	$0.0552131\pi$
$41$	1.85410	+	5.70634i	0.289562	+	0.891180i	−0.695432	+	0.718592i	$0.744787\pi$
$42$	−1.89564	+	1.37727i	−0.292504	+	0.212517i
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$		0			0
$45$	−5.00000			−0.745356
$46$	0.947822	−	0.688633i	0.139749	−	0.101533i
$47$	−0.874032	−	2.68999i	−0.127491	−	0.392376i	0.866856	−	0.498559i	$-0.166137\pi$
$47$	−0.874032	−	2.68999i	−0.127491	−	0.392376i	−0.994347	+	0.106183i	$0.966137\pi$
$48$	2.62210	−	8.06998i	0.378467	−	1.16480i
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$	0.335106	+	0.243469i	0.0473911	+	0.0344317i
$51$	1.02399	−	3.15152i	0.143388	−	0.441302i
$52$	3.85816	+	11.8742i	0.535031	+	1.64666i
$53$	−0.277611	+	0.201696i	−0.0381328	+	0.0277051i	−0.606688	−	0.794940i	$-0.707502\pi$
$53$	−0.277611	+	0.201696i	−0.0381328	+	0.0277051i	0.568556	+	0.822645i	$0.307502\pi$
$54$	−2.34315			−0.318862
$55$		0			0
$56$	−3.17157			−0.423819
$57$		0			0
$58$	−0.980070	−	3.01635i	−0.128689	−	0.396066i
$59$	−2.98413	+	9.18421i	−0.388501	+	1.19568i	0.545408	+	0.838171i	$0.316375\pi$
$59$	−2.98413	+	9.18421i	−0.388501	+	1.19568i	−0.933909	+	0.357512i	$0.883625\pi$
$60$	−4.18389	−	3.03977i	−0.540138	−	0.392433i
$61$	−10.7710	−	7.82560i	−1.37909	−	1.00197i	−0.996965	−	0.0778539i	$-0.975193\pi$
$61$	−10.7710	−	7.82560i	−1.37909	−	1.00197i	−0.382123	−	0.924112i	$-0.624807\pi$
$62$		0			0
$63$	−3.09017	−	9.51057i	−0.389325	−	1.19822i
$64$	3.37487	−	2.45199i	0.421859	−	0.306499i
$65$	6.82843			0.846962
$66$		0			0
$67$	−4.48528			−0.547964			−0.273982	−	0.961735i	$-0.588341\pi$
$67$	−4.48528			−0.547964			−0.273982	+	0.961735i	$0.588341\pi$
$68$	1.73302	−	1.25912i	0.210160	−	0.152690i
$69$	2.47214	+	7.60845i	0.297610	+	0.915950i
$70$	−0.255998	+	0.787881i	−0.0305976	+	0.0941698i
$71$	9.15298	+	6.65003i	1.08626	+	0.789213i	0.978764	−	0.204992i	$-0.0657169\pi$
$71$	9.15298	+	6.65003i	1.08626	+	0.789213i	0.107496	+	0.994206i	$0.465717\pi$
$72$	−6.41464	−	4.66051i	−0.755973	−	0.549246i
$73$	−2.11010	+	6.49422i	−0.246969	+	0.760091i	0.748338	+	0.663318i	$0.230852\pi$
$73$	−2.11010	+	6.49422i	−0.246969	+	0.760091i	−0.995306	+	0.0967733i	$0.969148\pi$
$74$	−0.468074	−	1.44058i	−0.0544125	−	0.167464i
$75$	−2.28825	+	1.66251i	−0.264224	+	0.191970i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−3.23607	+	2.35114i	−0.364086	+	0.264524i	−0.754754	−	0.656007i	$-0.772244\pi$
$79$	−3.23607	+	2.35114i	−0.364086	+	0.264524i	0.390668	+	0.920532i	$0.372244\pi$
$80$	−0.927051	−	2.85317i	−0.103647	−	0.318994i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.01063	+	1.46081i	0.222037	+	0.161320i
$83$	4.85410	+	3.52671i	0.532807	+	0.387107i	0.821407	−	0.570343i	$-0.193190\pi$
$83$	4.85410	+	3.52671i	0.532807	+	0.387107i	−0.288600	+	0.957450i	$0.593190\pi$
$84$	3.19621	−	9.83692i	0.348735	−	1.07330i
$85$	−0.362036	−	1.11423i	−0.0392683	−	0.120855i
$86$	−2.01063	+	1.46081i	−0.216812	+	0.157523i
$87$	21.6569			2.32186
$88$		0			0
$89$	9.31371			0.987251			0.493626	−	0.869675i	$-0.335671\pi$
$89$	9.31371			0.987251			0.493626	+	0.869675i	$0.335671\pi$
$90$	−1.67553	+	1.21734i	−0.176616	+	0.128319i
$91$	4.22020	+	12.9884i	0.442397	+	1.36156i
$92$	−1.59810	+	4.91846i	−0.166614	+	0.512785i
$93$		0			0
$94$	−0.947822	−	0.688633i	−0.0977604	−	0.0710271i
$95$		0			0
$96$	−3.85816	−	11.8742i	−0.393772	−	1.21191i
$97$	6.19453	−	4.50059i	0.628959	−	0.456965i	−0.227081	−	0.973876i	$-0.572918\pi$
$97$	6.19453	−	4.50059i	0.628959	−	0.456965i	0.856039	+	0.516911i	$0.172918\pi$
$98$	1.24264			0.125526
$99$		0			0
$100$	−1.82843			−0.182843
$101$	10.7710	−	7.82560i	1.07176	−	0.778676i	0.0955291	−	0.995427i	$-0.469546\pi$
$101$	10.7710	−	7.82560i	1.07176	−	0.778676i	0.976227	+	0.216750i	$0.0695457\pi$
$102$	−0.424151	−	1.30540i	−0.0419973	−	0.129254i
$103$	0.362036	−	1.11423i	0.0356725	−	0.109789i	−0.931635	−	0.363396i	$-0.881617\pi$
$103$	0.362036	−	1.11423i	0.0356725	−	0.109789i	0.967307	+	0.253608i	$0.0816172\pi$
$104$	8.76038	+	6.36479i	0.859026	+	0.624119i
$105$	−4.57649	−	3.32502i	−0.446620	−	0.324488i
$106$	−0.0439223	+	0.135179i	−0.00426611	+	0.0131297i
$107$	−1.13003	−	3.47788i	−0.109244	−	0.336219i	0.881459	−	0.472261i	$-0.156562\pi$
$107$	−1.13003	−	3.47788i	−0.109244	−	0.336219i	−0.990703	+	0.136042i	$0.956562\pi$
$108$	8.36778	−	6.07955i	0.805190	−	0.585005i
$109$	3.65685			0.350263			0.175132	−	0.984545i	$-0.443965\pi$
$109$	3.65685			0.350263			0.175132	+	0.984545i	$0.443965\pi$
$110$		0			0
$111$	10.3431			0.981728
$112$	4.85410	−	3.52671i	0.458670	−	0.333243i
$113$	2.57817	+	7.93480i	0.242534	+	0.746443i	0.996032	+	0.0889933i	$0.0283650\pi$
$113$	2.57817	+	7.93480i	0.242534	+	0.746443i	−0.753498	+	0.657450i	$0.771635\pi$
$114$		0			0
$115$	2.28825	+	1.66251i	0.213380	+	0.155030i
$116$	11.3262	+	8.22899i	1.05161	+	0.764043i
$117$	−10.5505	+	32.4711i	−0.975394	+	3.00195i
$118$	1.23607	+	3.80423i	0.113789	+	0.350207i
$119$	1.89564	−	1.37727i	0.173773	−	0.126254i
$120$	−4.48528			−0.409448
$121$		0			0
$122$	−5.51472			−0.499279
$123$	−13.7295	+	9.97505i	−1.23794	+	0.899420i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−3.35106	−	2.43469i	−0.298536	−	0.216899i
$127$	−12.6667	−	9.20287i	−1.12398	−	0.816622i	−0.139176	−	0.990268i	$-0.544445\pi$
$127$	−12.6667	−	9.20287i	−1.12398	−	0.816622i	−0.984808	+	0.173645i	$0.944445\pi$
$128$	3.26209	−	10.0397i	0.288331	−	0.887391i
$129$	−5.24419	−	16.1400i	−0.461725	−	1.42104i
$130$	2.28825	−	1.66251i	0.200692	−	0.145812i
$131$	11.3137			0.988483			0.494242	−	0.869325i	$-0.335446\pi$
$131$	11.3137			0.988483			0.494242	+	0.869325i	$0.335446\pi$
$132$		0			0
$133$		0			0
$134$	−1.50304	+	1.09203i	−0.129843	+	0.0943366i
$135$	−1.74806	−	5.37999i	−0.150449	−	0.463036i
$136$	0.574112	−	1.76693i	0.0492297	−	0.151513i
$137$	−18.5836	−	13.5018i	−1.58770	−	1.15353i	−0.907129	−	0.420853i	$-0.861731\pi$
$137$	−18.5836	−	13.5018i	−1.58770	−	1.15353i	−0.680573	−	0.732680i	$-0.738269\pi$
$138$	2.68085	+	1.94775i	0.228209	+	0.165803i
$139$	−1.23607	+	3.80423i	−0.104842	+	0.322670i	−0.989693	−	0.143203i	$-0.954260\pi$
$139$	−1.23607	+	3.80423i	−0.104842	+	0.322670i	0.884851	+	0.465873i	$0.154260\pi$
$140$	−1.13003	−	3.47788i	−0.0955050	−	0.293934i
$141$	6.47214	−	4.70228i	0.545052	−	0.396004i
$142$	4.68629			0.393265
$143$		0			0
$144$	15.0000			1.25000
$145$	6.19453	−	4.50059i	0.514427	−	0.373753i
$146$	0.874032	+	2.68999i	0.0723354	+	0.222625i
$147$	−2.62210	+	8.06998i	−0.216267	+	0.665601i
$148$	5.40932	+	3.93010i	0.444644	+	0.323053i
$149$	−9.43059	−	6.85173i	−0.772584	−	0.561315i	0.130160	−	0.991493i	$-0.458451\pi$
$149$	−9.43059	−	6.85173i	−0.772584	−	0.561315i	−0.902744	+	0.430178i	$0.858451\pi$
$150$	−0.362036	+	1.11423i	−0.0295601	+	0.0909767i
$151$	−3.70820	−	11.4127i	−0.301769	−	0.928751i	−0.980863	−	0.194699i	$-0.937627\pi$
$151$	−3.70820	−	11.4127i	−0.301769	−	0.928751i	0.679094	−	0.734052i	$-0.262373\pi$
$152$		0			0
$153$	5.85786			0.473580
$154$		0			0
$155$		0			0
$156$	−28.5694	+	20.7569i	−2.28738	+	1.66188i
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	−0.961438	−	0.275020i	$-0.911315\pi$
$157$	−4.32624	−	13.3148i	−0.345271	−	1.06264i	0.616167	−	0.787616i	$-0.288685\pi$
$158$	−0.511996	+	1.57576i	−0.0407322	+	0.125361i
$159$	−0.785202	−	0.570482i	−0.0622705	−	0.0452422i
$160$	−3.57117	−	2.59461i	−0.282326	−	0.205122i
$161$	−1.74806	+	5.37999i	−0.137767	+	0.424002i
$162$	−0.127999	−	0.393941i	−0.0100566	−	0.0309509i
$163$	0.392601	−	0.285241i	0.0307509	−	0.0223418i	−0.572304	−	0.820042i	$-0.693950\pi$
$163$	0.392601	−	0.285241i	0.0307509	−	0.0223418i	0.603055	+	0.797700i	$0.293950\pi$
$164$	−10.9706			−0.856657
$165$		0			0
$166$	2.48528			0.192895
$167$	−8.87537	+	6.44833i	−0.686797	+	0.498987i	−0.875606	−	0.483027i	$-0.839537\pi$
$167$	−8.87537	+	6.44833i	−0.686797	+	0.498987i	0.188809	+	0.982014i	$0.439537\pi$
$168$	−2.77206	−	8.53151i	−0.213869	−	0.658220i
$169$	10.3914	−	31.9816i	0.799342	−	2.46012i
$170$	−0.392601	−	0.285241i	−0.0301111	−	0.0218770i
$171$		0			0
$172$	3.39009	−	10.4336i	0.258492	−	0.795556i
$173$	1.89802	+	5.84152i	0.144304	+	0.444122i	0.996921	−	0.0784144i	$-0.0249857\pi$
$173$	1.89802	+	5.84152i	0.144304	+	0.444122i	−0.852617	+	0.522537i	$0.824986\pi$
$174$	7.25734	−	5.27276i	0.550177	−	0.399727i
$175$	−2.00000			−0.151186
$176$		0			0
$177$	−27.3137			−2.05302
$178$	3.12108	−	2.26760i	0.233935	−	0.169963i
$179$	−0.511996	−	1.57576i	−0.0382684	−	0.117778i	0.930097	−	0.367313i	$-0.119722\pi$
$179$	−0.511996	−	1.57576i	−0.0382684	−	0.117778i	−0.968366	+	0.249535i	$0.919722\pi$
$180$	2.82508	−	8.69469i	0.210569	−	0.648064i
$181$	1.06281	+	0.772178i	0.0789982	+	0.0573956i	0.626583	−	0.779354i	$-0.284453\pi$
$181$	1.06281	+	0.772178i	0.0789982	+	0.0573956i	−0.547585	+	0.836750i	$0.684453\pi$
$182$	4.57649	+	3.32502i	0.339232	+	0.246467i
$183$	11.6366	−	35.8138i	0.860203	−	2.64743i
$184$	1.38603	+	4.26576i	0.102179	+	0.314476i
$185$	2.95846	−	2.14944i	0.217510	−	0.158030i
$186$		0			0
$187$		0			0
$188$	5.17157			0.377176
$189$	9.15298	−	6.65003i	0.665782	−	0.483719i
$190$		0			0
$191$	−5.96826	+	18.3684i	−0.431848	+	1.32909i	0.464433	+	0.885608i	$0.346258\pi$
$191$	−5.96826	+	18.3684i	−0.431848	+	1.32909i	−0.896282	+	0.443485i	$0.853742\pi$
$192$	9.54558	+	6.93527i	0.688893	+	0.500510i
$193$	5.52431	+	4.01365i	0.397649	+	0.288909i	0.768583	−	0.639751i	$-0.220962\pi$
$193$	5.52431	+	4.01365i	0.397649	+	0.288909i	−0.370934	+	0.928659i	$0.620962\pi$
$194$	0.980070	−	3.01635i	0.0703649	−	0.216561i
$195$	5.96826	+	18.3684i	0.427396	+	1.31539i
$196$	−4.43769	+	3.22417i	−0.316978	+	0.230298i
$197$	−5.17157			−0.368459			−0.184230	−	0.982883i	$-0.558979\pi$
$197$	−5.17157			−0.368459			−0.184230	+	0.982883i	$0.558979\pi$
$198$		0			0
$199$	21.6569			1.53521			0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569			1.53521			0.767607	+	0.640921i	$0.221447\pi$
$200$	−1.28293	+	0.932102i	−0.0907167	+	0.0659096i
$201$	−3.92028	−	12.0654i	−0.276515	−	0.851026i
$202$	1.70414	−	5.24481i	0.119903	−	0.369023i
$203$	12.3891	+	9.00117i	0.869541	+	0.631758i
$204$	4.90173	+	3.56132i	0.343190	+	0.249342i
$205$	−1.85410	+	5.70634i	−0.129496	+	0.398548i
$206$	−0.149960	−	0.461530i	−0.0104482	−	0.0321563i
$207$	−11.4412	+	8.31254i	−0.795220	+	0.577761i
$208$	−20.4853			−1.42040
$209$		0			0
$210$	−2.34315			−0.161692
$211$	12.9443	−	9.40456i	0.891120	−	0.647437i	−0.0450495	−	0.998985i	$-0.514345\pi$
$211$	12.9443	−	9.40456i	0.891120	−	0.647437i	0.936170	+	0.351548i	$0.114345\pi$
$212$	−0.193883	−	0.596709i	−0.0133159	−	0.0409821i
$213$	−9.88854	+	30.4338i	−0.677552	+	2.08529i
$214$	−1.22543	−	0.890329i	−0.0837689	−	0.0608617i
$215$	−4.85410	−	3.52671i	−0.331047	−	0.240520i
$216$	2.77206	−	8.53151i	0.188615	−	0.580496i
$217$		0			0
$218$	1.22543	−	0.890329i	0.0829968	−	0.0603007i
$219$	−19.3137			−1.30510
$220$		0			0
$221$	−8.00000			−0.538138
$222$	3.46605	−	2.51823i	0.232626	−	0.169013i
$223$	−1.59810	−	4.91846i	−0.107017	−	0.329364i	0.883182	−	0.469031i	$-0.155397\pi$
$223$	−1.59810	−	4.91846i	−0.107017	−	0.329364i	−0.990199	+	0.139667i	$0.955397\pi$
$224$	2.72813	−	8.39633i	0.182281	−	0.561004i
$225$	−4.04508	−	2.93893i	−0.269672	−	0.195928i
$226$	2.79584	+	2.03129i	0.185976	+	0.135120i
$227$	0.830110	−	2.55482i	0.0550963	−	0.169569i	−0.919722	−	0.392571i	$-0.871586\pi$
$227$	0.830110	−	2.55482i	0.0550963	−	0.169569i	0.974818	+	0.223002i	$0.0715857\pi$
$228$		0			0
$229$	17.2432	−	12.5279i	1.13946	−	0.827866i	0.152416	−	0.988316i	$-0.451295\pi$
$229$	17.2432	−	12.5279i	1.13946	−	0.827866i	0.987044	+	0.160451i	$0.0512947\pi$
$230$	1.17157			0.0772512
$231$		0			0
$232$	12.1421			0.797170
$233$	−17.9134	+	13.0148i	−1.17354	+	0.852629i	−0.991429	−	0.130648i	$-0.958294\pi$
$233$	−17.9134	+	13.0148i	−1.17354	+	0.852629i	−0.182115	+	0.983277i	$0.558294\pi$
$234$	4.37016	+	13.4500i	0.285686	+	0.879252i
$235$	0.874032	−	2.68999i	0.0570156	−	0.175476i
$236$	−14.2847	−	10.3784i	−0.929854	−	0.675579i
$237$	−9.15298	−	6.65003i	−0.594550	−	0.431966i
$238$	0.299920	−	0.923060i	0.0194410	−	0.0598331i
$239$	−0.212076	−	0.652702i	−0.0137180	−	0.0422198i	0.943963	−	0.330051i	$-0.107066\pi$
$239$	−0.212076	−	0.652702i	−0.0137180	−	0.0422198i	−0.957681	+	0.287831i	$0.907066\pi$
$240$	6.86474	−	4.98752i	0.443117	−	0.321943i
$241$	6.00000			0.386494			0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000			0.386494			0.193247	+	0.981150i	$0.438098\pi$
$242$		0			0
$243$	−14.1421			−0.907218
$244$	19.6940	−	14.3085i	1.26078	−	0.916011i
$245$	0.927051	+	2.85317i	0.0592271	+	0.182282i
$246$	−2.17222	+	6.68539i	−0.138495	+	0.426245i
$247$		0			0
$248$		0			0
$249$	−5.24419	+	16.1400i	−0.332337	+	1.02283i
$250$	0.127999	+	0.393941i	0.00809537	+	0.0249150i
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	−0.850391	−	0.526151i	$-0.823635\pi$
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	0.237614	+	0.971360i	$0.423635\pi$
$252$	18.2843			1.15180
$253$		0			0
$254$	−6.48528			−0.406923
$255$	2.68085	−	1.94775i	0.167881	−	0.121973i
$256$	1.22697	+	3.77623i	0.0766857	+	0.236014i
$257$	4.11416	−	12.6621i	0.256634	−	0.789839i	−0.736869	−	0.676036i	$-0.763696\pi$
$257$	4.11416	−	12.6621i	0.256634	−	0.789839i	0.993503	−	0.113804i	$-0.0363035\pi$
$258$	−5.68693	−	4.13180i	−0.354053	−	0.257235i
$259$	5.91691	+	4.29889i	0.367659	+	0.267120i
$260$	−3.85816	+	11.8742i	−0.239273	+	0.736407i
$261$	11.8305	+	36.4105i	0.732289	+	2.25375i
$262$	3.79129	−	2.75453i	0.234227	−	0.170176i
$263$	22.9706			1.41643			0.708213	−	0.705999i	$-0.249502\pi$
$263$	22.9706			1.41643			0.708213	+	0.705999i	$0.249502\pi$
$264$		0			0
$265$	−0.343146			−0.0210793
$266$		0			0
$267$	8.14048	+	25.0538i	0.498189	+	1.53327i
$268$	2.53425	−	7.79962i	0.154804	−	0.476438i
$269$	4.29888	+	3.12332i	0.262107	+	0.190432i	0.711076	−	0.703116i	$-0.248208\pi$
$269$	4.29888	+	3.12332i	0.262107	+	0.190432i	−0.448968	+	0.893548i	$0.648208\pi$
$270$	−1.89564	−	1.37727i	−0.115365	−	0.0838178i
$271$	−4.73220	+	14.5642i	−0.287460	+	0.884712i	0.698190	+	0.715913i	$0.253989\pi$
$271$	−4.73220	+	14.5642i	−0.287460	+	0.884712i	−0.985650	+	0.168800i	$0.946011\pi$
$272$	1.08611	+	3.34270i	0.0658550	+	0.202681i
$273$	−31.2502	+	22.7046i	−1.89135	+	1.37415i
$274$	−9.51472			−0.574805
$275$		0			0
$276$	−14.6274			−0.880467
$277$	−0.947822	+	0.688633i	−0.0569491	+	0.0413760i	−0.615896	−	0.787828i	$-0.711206\pi$
$277$	−0.947822	+	0.688633i	−0.0569491	+	0.0413760i	0.558947	+	0.829204i	$0.311206\pi$
$278$	0.511996	+	1.57576i	0.0307075	+	0.0945079i
$279$		0			0
$280$	−2.56586	−	1.86420i	−0.153339	−	0.111407i
$281$	4.29888	+	3.12332i	0.256450	+	0.186322i	0.708580	−	0.705630i	$-0.249336\pi$
$281$	4.29888	+	3.12332i	0.256450	+	0.186322i	−0.452131	+	0.891952i	$0.649336\pi$
$282$	1.02399	−	3.15152i	0.0609779	−	0.187671i
$283$	−3.90209	−	12.0094i	−0.231955	−	0.713884i	−0.997511	−	0.0705145i	$-0.977536\pi$
$283$	−3.90209	−	12.0094i	−0.231955	−	0.713884i	0.765556	−	0.643370i	$-0.222464\pi$
$284$	−16.7356	+	12.1591i	−0.993073	+	0.721510i
$285$		0			0
$286$		0			0
$287$	−12.0000			−0.708338
$288$	17.8559	−	12.9730i	1.05217	−	0.764444i
$289$	−4.82914	−	14.8626i	−0.284067	−	0.874268i
$290$	0.980070	−	3.01635i	0.0575517	−	0.177126i
$291$	17.5208	+	12.7296i	1.02709	+	0.746221i
$292$	−10.1008	−	7.33866i	−0.591105	−	0.429463i
$293$	−4.58224	+	14.1027i	−0.267697	+	0.823887i	0.723363	+	0.690468i	$0.242595\pi$
$293$	−4.58224	+	14.1027i	−0.267697	+	0.823887i	−0.991060	+	0.133419i	$0.957405\pi$
$294$	1.08611	+	3.34270i	0.0633431	+	0.194950i
$295$	−7.81256	+	5.67616i	−0.454865	+	0.330479i
$296$	5.79899			0.337059
$297$		0			0
$298$	−4.82843			−0.279703
$299$	15.6251	−	11.3523i	0.903624	−	0.656521i
$300$	−1.59810	−	4.91846i	−0.0922666	−	0.283967i
$301$	3.70820	−	11.4127i	0.213737	−	0.657816i
$302$	−4.02127	−	2.92162i	−0.231398	−	0.168121i
$303$	30.4650	+	22.1341i	1.75017	+	1.27157i
$304$		0			0
$305$	−4.11416	−	12.6621i	−0.235576	−	0.725029i
$306$	1.96300	−	1.42621i	0.112217	−	0.0815308i
$307$	−27.6569			−1.57846			−0.789230	−	0.614098i	$-0.789520\pi$
$307$	−27.6569			−1.57846			−0.789230	+	0.614098i	$0.789520\pi$
$308$		0			0
$309$	3.31371			0.188510
$310$		0			0
$311$	8.44040	+	25.9769i	0.478611	+	1.47301i	0.841025	+	0.540996i	$0.181953\pi$
$311$	8.44040	+	25.9769i	0.478611	+	1.47301i	−0.362414	+	0.932017i	$0.618047\pi$
$312$	−9.46439	+	29.1284i	−0.535816	+	1.64907i
$313$	−17.2432	−	12.5279i	−0.974641	−	0.708118i	−0.0181361	−	0.999836i	$-0.505773\pi$
$313$	−17.2432	−	12.5279i	−0.974641	−	0.708118i	−0.956504	+	0.291718i	$0.905773\pi$
$314$	−4.69148	−	3.40856i	−0.264756	−	0.192356i
$315$	3.09017	−	9.51057i	0.174111	−	0.535860i
$316$	−2.26006	−	6.95575i	−0.127138	−	0.391292i
$317$	−17.2432	+	12.5279i	−0.968472	+	0.703636i	−0.955103	−	0.296275i	$-0.904256\pi$
$317$	−17.2432	+	12.5279i	−0.968472	+	0.703636i	−0.0133691	+	0.999911i	$0.504256\pi$
$318$	−0.402020			−0.0225442
$319$		0			0
$320$	4.17157			0.233198
$321$	8.36778	−	6.07955i	0.467044	−	0.339327i
$322$	0.724072	+	2.22846i	0.0403509	+	0.124187i
$323$		0			0
$324$	1.47923	+	1.07472i	0.0821794	+	0.0597068i
$325$	5.52431	+	4.01365i	0.306434	+	0.222637i
$326$	0.0621155	−	0.191172i	0.00344026	−	0.0105880i
$327$	3.19621	+	9.83692i	0.176751	+	0.543983i
$328$	−7.69757	+	5.59261i	−0.425027	+	0.308800i
$329$	5.65685			0.311872
$330$		0			0
$331$	15.3137			0.841718			0.420859	−	0.907126i	$-0.361729\pi$
$331$	15.3137			0.841718			0.420859	+	0.907126i	$0.361729\pi$
$332$	−8.87537	+	6.44833i	−0.487099	+	0.353898i
$333$	5.65015	+	17.3894i	0.309626	+	0.952932i
$334$	−1.40422	+	4.32175i	−0.0768356	+	0.236476i
$335$	−3.62867	−	2.63638i	−0.198255	−	0.144041i
$336$	13.7295	+	9.97505i	0.749004	+	0.544183i
$337$	−1.08611	+	3.34270i	−0.0591641	+	0.182088i	−0.976271	−	0.216554i	$-0.930518\pi$
$337$	−1.08611	+	3.34270i	−0.0591641	+	0.182088i	0.917107	+	0.398642i	$0.130518\pi$
$338$	−4.30428	−	13.2472i	−0.234122	−	0.720553i
$339$	−19.0912	+	13.8705i	−1.03689	+	0.753345i
$340$	2.14214			0.116174
$341$		0			0
$342$		0			0
$343$	−16.1803	+	11.7557i	−0.873656	+	0.634748i
$344$	−2.94021	−	9.04904i	−0.158525	−	0.487891i
$345$	−2.47214	+	7.60845i	−0.133095	+	0.409625i
$346$	2.05827	+	1.49542i	0.110653	+	0.0803941i
$347$	18.5836	+	13.5018i	0.997619	+	0.724812i	0.961576	−	0.274538i	$-0.0885249\pi$
$347$	18.5836	+	13.5018i	0.997619	+	0.724812i	0.0360423	+	0.999350i	$0.488525\pi$
$348$	−12.2364	+	37.6599i	−0.655943	+	2.01878i
$349$	−2.15402	−	6.62940i	−0.115302	−	0.354864i	0.876708	−	0.481023i	$-0.159735\pi$
$349$	−2.15402	−	6.62940i	−0.115302	−	0.354864i	−0.992010	+	0.126160i	$0.959735\pi$
$350$	−0.670212	+	0.486937i	−0.0358243	+	0.0260279i
$351$	−38.6274			−2.06178
$352$		0			0
$353$	−1.31371			−0.0699216			−0.0349608	−	0.999389i	$-0.511131\pi$
$353$	−1.31371			−0.0699216			−0.0349608	+	0.999389i	$0.511131\pi$
$354$	−9.15298	+	6.65003i	−0.486476	+	0.353445i
$355$	3.49613	+	10.7600i	0.185555	+	0.571080i
$356$	−5.26239	+	16.1960i	−0.278906	+	0.858384i
$357$	5.36169	+	3.89550i	0.283771	+	0.206172i
$358$	−0.555221	−	0.403392i	−0.0293444	−	0.0213199i
$359$	7.20433	−	22.1727i	0.380230	−	1.17023i	−0.559652	−	0.828728i	$-0.689065\pi$
$359$	7.20433	−	22.1727i	0.380230	−	1.17023i	0.939882	−	0.341500i	$-0.110935\pi$
$360$	−2.45017	−	7.54086i	−0.129136	−	0.397438i
$361$	15.3713	−	11.1679i	0.809017	−	0.587785i
$362$	0.544156			0.0286002
$363$		0			0
$364$	−24.9706			−1.30881
$365$	−5.52431	+	4.01365i	−0.289156	+	0.210084i
$366$	−4.82004	−	14.8346i	−0.251948	−	0.775415i
$367$	2.62210	−	8.06998i	0.136872	−	0.421250i	−0.859004	−	0.511968i	$-0.828916\pi$
$367$	2.62210	−	8.06998i	0.136872	−	0.421250i	0.995877	+	0.0907188i	$0.0289165\pi$
$368$	−6.86474	−	4.98752i	−0.357849	−	0.259993i
$369$	−24.2705	−	17.6336i	−1.26347	−	0.917966i
$370$	0.468074	−	1.44058i	0.0243340	−	0.0748923i
$371$	−0.212076	−	0.652702i	−0.0110104	−	0.0338866i
$372$		0			0
$373$	−3.79899			−0.196704			−0.0983521	−	0.995152i	$-0.531357\pi$
$373$	−3.79899			−0.196704			−0.0983521	+	0.995152i	$0.531357\pi$
$374$		0			0
$375$	−2.82843			−0.146059
$376$	3.62867	−	2.63638i	0.187134	−	0.135961i
$377$	−16.1567	−	49.7253i	−0.832114	−	2.56098i
$378$	1.44814	−	4.45693i	0.0744845	−	0.229240i
$379$	−18.0760	−	13.1330i	−0.928501	−	0.674595i	0.0171244	−	0.999853i	$-0.494549\pi$
$379$	−18.0760	−	13.1330i	−0.928501	−	0.674595i	−0.945625	+	0.325258i	$0.894549\pi$
$380$		0			0
$381$	13.6846	−	42.1168i	0.701083	−	2.15771i
$382$	2.47214	+	7.60845i	0.126485	+	0.389282i
$383$	27.6216	−	20.0682i	1.41140	−	1.02544i	0.418278	−	0.908319i	$-0.362634\pi$
$383$	27.6216	−	20.0682i	1.41140	−	1.02544i	0.993118	−	0.117121i	$-0.0373664\pi$
$384$	29.8579			1.52368
$385$		0			0
$386$	2.82843			0.143963
$387$	24.2705	−	17.6336i	1.23374	−	0.896364i
$388$	4.32624	+	13.3148i	0.219631	+	0.675956i
$389$	−7.61029	+	23.4221i	−0.385857	+	1.18755i	0.550000	+	0.835165i	$0.314628\pi$
$389$	−7.61029	+	23.4221i	−0.385857	+	1.18755i	−0.935857	+	0.352381i	$0.885372\pi$
$390$	6.47214	+	4.70228i	0.327729	+	0.238109i
$391$	−2.68085	−	1.94775i	−0.135576	−	0.0985019i
$392$	−1.47010	+	4.52452i	−0.0742515	+	0.228523i
$393$	9.88854	+	30.4338i	0.498811	+	1.53518i
$394$	−1.73302	+	1.25912i	−0.0873085	+	0.0634333i
$395$	−4.00000			−0.201262
$396$		0			0
$397$	13.3137			0.668196			0.334098	−	0.942538i	$-0.391568\pi$
$397$	13.3137			0.668196			0.334098	+	0.942538i	$0.391568\pi$
$398$	7.25734	−	5.27276i	0.363777	−	0.264300i
$399$		0			0
$400$	0.927051	−	2.85317i	0.0463525	−	0.142658i
$401$	−14.0071	−	10.1767i	−0.699480	−	0.508202i	0.180283	−	0.983615i	$-0.442299\pi$
$401$	−14.0071	−	10.1767i	−0.699480	−	0.508202i	−0.879763	+	0.475413i	$0.842299\pi$
$402$	−4.25125	−	3.08871i	−0.212033	−	0.154051i
$403$		0			0
$404$	7.52245	+	23.1517i	0.374256	+	1.15184i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	6.34315			0.314805
$407$		0			0
$408$	5.25483			0.260153
$409$	−28.2918	+	20.5552i	−1.39894	+	1.01639i	−0.404122	+	0.914705i	$0.632423\pi$
$409$	−28.2918	+	20.5552i	−1.39894	+	1.01639i	−0.994817	+	0.101683i	$0.967577\pi$
$410$	0.767994	+	2.36364i	0.0379285	+	0.116732i
$411$	20.0770	−	61.7907i	0.990326	−	3.04791i
$412$	1.73302	+	1.25912i	0.0853800	+	0.0620322i
$413$	−15.6251	−	11.3523i	−0.768862	−	0.558611i
$414$	−1.81018	+	5.57116i	−0.0889655	+	0.273808i
$415$	1.85410	+	5.70634i	0.0910143	+	0.280113i
$416$	−24.3855	+	17.7171i	−1.19560	+	0.868652i
$417$	−11.3137			−0.554035
$418$		0			0
$419$	−14.3431			−0.700709			−0.350354	−	0.936617i	$-0.613939\pi$
$419$	−14.3431			−0.700709			−0.350354	+	0.936617i	$0.613939\pi$
$420$	8.36778	−	6.07955i	0.408306	−	0.296652i
$421$	−1.85410	−	5.70634i	−0.0903634	−	0.278110i	0.895654	−	0.444751i	$-0.146708\pi$
$421$	−1.85410	−	5.70634i	−0.0903634	−	0.278110i	−0.986018	+	0.166641i	$0.946708\pi$
$422$	2.04798	−	6.30305i	0.0996943	−	0.306828i
$423$	11.4412	+	8.31254i	0.556292	+	0.404169i
$424$	−0.440231	−	0.319847i	−0.0213795	−	0.0155331i
$425$	0.362036	−	1.11423i	0.0175613	−	0.0540482i
$426$	4.09597	+	12.6061i	0.198450	+	0.610767i
$427$	21.5420	−	15.6512i	1.04249	−	0.757415i
$428$	6.68629			0.323194
$429$		0			0
$430$	−2.48528			−0.119851
$431$	−9.15298	+	6.65003i	−0.440884	+	0.320321i	−0.785986	−	0.618244i	$-0.787844\pi$
$431$	−9.15298	+	6.65003i	−0.440884	+	0.320321i	0.345102	+	0.938565i	$0.387844\pi$
$432$	5.24419	+	16.1400i	0.252311	+	0.776534i
$433$	1.13003	−	3.47788i	0.0543058	−	0.167136i	−0.920225	−	0.391390i	$-0.871994\pi$
$433$	1.13003	−	3.47788i	0.0543058	−	0.167136i	0.974531	+	0.224254i	$0.0719944\pi$
$434$		0			0
$435$	17.5208	+	12.7296i	0.840056	+	0.610337i
$436$	−2.06618	+	6.35904i	−0.0989520	+	0.304543i
$437$		0			0
$438$	−6.47214	+	4.70228i	−0.309251	+	0.224684i
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		0			0
$441$	−15.0000			−0.714286
$442$	−2.68085	+	1.94775i	−0.127515	+	0.0926450i
$443$	−6.54238	−	20.1354i	−0.310838	−	0.956660i	−0.977434	−	0.211241i	$-0.932249\pi$
$443$	−6.54238	−	20.1354i	−0.310838	−	0.956660i	0.666596	−	0.745419i	$-0.267751\pi$
$444$	−5.84403	+	17.9861i	−0.277346	+	0.853582i
$445$	7.53495	+	5.47446i	0.357191	+	0.259514i
$446$	−1.73302	−	1.25912i	−0.0820611	−	0.0596209i
$447$	10.1885	−	31.3569i	0.481898	−	1.48313i
$448$	2.57817	+	7.93480i	0.121807	+	0.374884i
$449$	13.4519	−	9.77335i	0.634833	−	0.461233i	−0.223238	−	0.974764i	$-0.571663\pi$
$449$	13.4519	−	9.77335i	0.634833	−	0.461233i	0.858071	+	0.513531i	$0.171663\pi$
$450$	−2.07107			−0.0976311
$451$		0			0
$452$	−15.2548			−0.717527
$453$	27.4589	−	19.9501i	1.29013	−	0.937337i
$454$	−0.343843	−	1.05824i	−0.0161373	−	0.0496656i
$455$	−4.22020	+	12.9884i	−0.197846	+	0.608907i
$456$		0			0
$457$	13.3369	+	9.68981i	0.623873	+	0.453270i	0.854272	−	0.519826i	$-0.174003\pi$
$457$	13.3369	+	9.68981i	0.623873	+	0.453270i	−0.230399	+	0.973096i	$0.574003\pi$
$458$	2.72813	−	8.39633i	0.127477	−	0.392335i
$459$	2.04798	+	6.30305i	0.0955917	+	0.294201i
$460$	−4.18389	+	3.03977i	−0.195075	+	0.141730i
$461$	−32.6274			−1.51961			−0.759805	−	0.650151i	$-0.774706\pi$
$461$	−32.6274			−1.51961			−0.759805	+	0.650151i	$0.774706\pi$
$462$		0			0
$463$	22.1421			1.02903			0.514516	−	0.857481i	$-0.327972\pi$
$463$	22.1421			1.02903			0.514516	+	0.857481i	$0.327972\pi$
$464$	−18.5836	+	13.5018i	−0.862721	+	0.626803i
$465$		0			0
$466$	−2.83417	+	8.72268i	−0.131290	+	0.404071i
$467$	7.41996	+	5.39092i	0.343355	+	0.249462i	0.746076	−	0.665861i	$-0.231936\pi$
$467$	7.41996	+	5.39092i	0.343355	+	0.249462i	−0.402721	+	0.915323i	$0.631936\pi$
$468$	−50.5040	−	36.6933i	−2.33455	−	1.69615i
$469$	2.77206	−	8.53151i	0.128002	−	0.393949i
$470$	−0.362036	−	1.11423i	−0.0166995	−	0.0513957i
$471$	32.0354	−	23.2751i	1.47612	−	1.07246i
$472$	−15.3137			−0.704871
$473$		0			0
$474$	−4.68629			−0.215248
$475$		0			0
$476$	1.32391	+	4.07458i	0.0606814	+	0.186758i
$477$	0.530189	−	1.63176i	0.0242757	−	0.0747129i
$478$	−0.229980	−	0.167090i	−0.0105191	−	0.00764254i
$479$	29.1246	+	21.1603i	1.33074	+	0.966837i	0.999731	+	0.0232090i	$0.00738832\pi$
$479$	29.1246	+	21.1603i	1.33074	+	0.966837i	0.331007	+	0.943628i	$0.392612\pi$
$480$	3.85816	−	11.8742i	0.176100	−	0.541981i
$481$	−7.71633	−	23.7484i	−0.351834	−	1.08283i
$482$	2.01063	−	1.46081i	0.0915819	−	0.0665382i
$483$	−16.0000			−0.728025
$484$		0			0
$485$	7.65685			0.347680
$486$	−4.73911	+	3.44317i	−0.214970	+	0.156185i
$487$	−2.32218	−	7.14692i	−0.105228	−	0.323858i	0.884556	−	0.466434i	$-0.154461\pi$
$487$	−2.32218	−	7.14692i	−0.105228	−	0.323858i	−0.989784	+	0.142576i	$0.954461\pi$
$488$	6.52418	−	20.0794i	0.295336	−	0.908950i
$489$	1.11044	+	0.806784i	0.0502160	+	0.0364840i
$490$	1.00532	+	0.730406i	0.0454156	+	0.0329964i
$491$	−7.20433	+	22.1727i	−0.325127	+	1.00064i	0.646256	+	0.763120i	$0.276334\pi$
$491$	−7.20433	+	22.1727i	−0.325127	+	1.00064i	−0.971383	+	0.237517i	$0.923666\pi$
$492$	−9.58862	−	29.5107i	−0.432289	−	1.33045i
$493$	−7.25734	+	5.27276i	−0.326854	+	0.237473i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.3060	+	13.3001i	−0.821135	+	0.596589i
$498$	2.17222	+	6.68539i	0.0973393	+	0.299580i
$499$	−0.511996	+	1.57576i	−0.0229201	+	0.0705408i	−0.961862	−	0.273534i	$-0.911807\pi$
$499$	−0.511996	+	1.57576i	−0.0229201	+	0.0705408i	0.938942	+	0.344075i	$0.111807\pi$
$500$	−1.47923	−	1.07472i	−0.0661531	−	0.0480631i
$501$	−25.1033	−	18.2386i	−1.12153	−	0.814843i
$502$	−1.53599	+	4.72729i	−0.0685545	+	0.210989i
$503$	−8.84636	−	27.2263i	−0.394440	−	1.21396i	−0.929397	−	0.369081i	$-0.879672\pi$
$503$	−8.84636	−	27.2263i	−0.394440	−	1.21396i	0.534957	−	0.844879i	$-0.320328\pi$
$504$	12.8293	−	9.32102i	0.571462	−	0.415191i
$505$	13.3137			0.592452
$506$		0			0
$507$	95.1127			4.22410
$508$	23.1601	−	16.8268i	1.02756	−	0.746567i
$509$	2.87809	+	8.85786i	0.127569	+	0.392618i	0.994360	−	0.106053i	$-0.0338215\pi$
$509$	2.87809	+	8.85786i	0.127569	+	0.392618i	−0.866791	+	0.498671i	$0.833821\pi$
$510$	0.424151	−	1.30540i	0.0187817	−	0.0578043i
$511$	−11.0486	−	8.02730i	−0.488762	−	0.355107i
$512$	18.4111	+	13.3764i	0.813663	+	0.591161i
$513$		0			0
$514$	−1.70414	−	5.24481i	−0.0751665	−	0.231339i
$515$	0.947822	−	0.688633i	0.0417660	−	0.0303448i
$516$	31.0294			1.36599
$517$		0			0
$518$	3.02944			0.133106
$519$	−14.0547	+	10.2113i	−0.616934	+	0.448228i
$520$	3.34617	+	10.2984i	0.146739	+	0.451617i
$521$	0.830110	−	2.55482i	0.0363678	−	0.111928i	−0.931225	−	0.364446i	$-0.881258\pi$
$521$	0.830110	−	2.55482i	0.0363678	−	0.111928i	0.967592	+	0.252517i	$0.0812585\pi$
$522$	12.8293	+	9.32102i	0.561522	+	0.407970i
$523$	−30.4174	−	22.0995i	−1.33006	−	0.966345i	−0.999747	−	0.0224738i	$-0.992846\pi$
$523$	−30.4174	−	22.0995i	−1.33006	−	0.966345i	−0.330313	−	0.943872i	$-0.607154\pi$
$524$	−6.39242	+	19.6738i	−0.279254	+	0.859455i
$525$	−1.74806	−	5.37999i	−0.0762918	−	0.234802i
$526$	7.69757	−	5.59261i	0.335630	−	0.243849i
$527$		0			0
$528$		0			0
$529$	−15.0000			−0.652174
$530$	−0.114990	+	0.0835452i	−0.00499485	+	0.00362897i
$531$	−14.9207	−	45.9211i	−0.647502	−	1.99280i
$532$		0			0
$533$	33.1459	+	24.0819i	1.43571	+	1.04310i
$534$	8.82774	+	6.41373i	0.382014	+	0.277549i
$535$	1.13003	−	3.47788i	0.0488555	−	0.150362i
$536$	−2.19794	−	6.76458i	−0.0949368	−	0.292185i
$537$	3.79129	−	2.75453i	0.163606	−	0.118867i
$538$	2.20101			0.0948923
$539$		0			0
$540$	10.3431			0.445098
$541$	−4.85410	+	3.52671i	−0.208694	+	0.151625i	−0.687223	−	0.726447i	$-0.741170\pi$
$541$	−4.85410	+	3.52671i	−0.208694	+	0.151625i	0.478529	+	0.878072i	$0.341170\pi$
$542$	1.96014	+	6.03269i	0.0841952	+	0.259126i
$543$	−1.14822	+	3.53387i	−0.0492750	+	0.151653i
$544$	4.18389	+	3.03977i	0.179383	+	0.130329i
$545$	2.95846	+	2.14944i	0.126726	+	0.0920721i
$546$	−4.94427	+	15.2169i	−0.211595	+	0.651223i
$547$	−10.5066	−	32.3359i	−0.449229	−	1.38258i	−0.877779	−	0.479066i	$-0.840975\pi$
$547$	−10.5066	−	32.3359i	−0.449229	−	1.38258i	0.428550	−	0.903518i	$-0.359025\pi$
$548$	33.9787	−	24.6870i	1.45150	−	1.05458i
$549$	66.5685			2.84108
$550$		0			0
$551$		0			0
$552$	−10.2634	+	7.45682i	−0.436840	+	0.317383i
$553$	−2.47214	−	7.60845i	−0.105126	−	0.323544i
$554$	−0.149960	+	0.461530i	−0.00637120	+	0.0196085i
$555$	8.36778	+	6.07955i	0.355193	+	0.258062i
$556$	−5.91691	−	4.29889i	−0.250933	−	0.182314i
$557$	11.7866	−	36.2753i	0.499413	−	1.53703i	−0.310552	−	0.950556i	$-0.600514\pi$
$557$	11.7866	−	36.2753i	0.499413	−	1.53703i	0.809965	−	0.586478i	$-0.199486\pi$
$558$		0			0
$559$	−33.1459	+	24.0819i	−1.40192	+	1.01856i
$560$	6.00000			0.253546
$561$		0			0
$562$	2.20101			0.0928440
$563$	−9.43059	+	6.85173i	−0.397452	+	0.288766i	−0.768502	−	0.639847i	$-0.778998\pi$
$563$	−9.43059	+	6.85173i	−0.397452	+	0.288766i	0.371050	+	0.928613i	$0.378998\pi$
$564$	4.52012	+	13.9115i	0.190331	+	0.585780i
$565$	−2.57817	+	7.93480i	−0.108465	+	0.333820i
$566$	−4.23152	−	3.07438i	−0.177864	−	0.129226i
$567$	1.61803	+	1.17557i	0.0679510	+	0.0493693i
$568$	−5.54411	+	17.0630i	−0.232626	+	0.715949i
$569$	6.28638	+	19.3475i	0.263539	+	0.811089i	0.992026	+	0.126030i	$0.0402235\pi$
$569$	6.28638	+	19.3475i	0.263539	+	0.811089i	−0.728488	+	0.685059i	$0.759776\pi$
$570$		0			0
$571$	45.9411			1.92258			0.961288	−	0.275545i	$-0.0888584\pi$
$571$	45.9411			1.92258			0.961288	+	0.275545i	$0.0888584\pi$
$572$		0			0
$573$	−54.6274			−2.28209
$574$	−4.02127	+	2.92162i	−0.167845	+	0.121946i
$575$	0.874032	+	2.68999i	0.0364497	+	0.112181i
$576$	−6.44543	+	19.8370i	−0.268560	+	0.826542i
$577$	−5.63930	−	4.09719i	−0.234767	−	0.170568i	0.464182	−	0.885740i	$-0.346349\pi$
$577$	−5.63930	−	4.09719i	−0.234767	−	0.170568i	−0.698949	+	0.715172i	$0.746349\pi$
$578$	−5.23684	−	3.80479i	−0.217824	−	0.158258i
$579$	−5.96826	+	18.3684i	−0.248033	+	0.763366i
$580$	4.32624	+	13.3148i	0.179637	+	0.552867i
$581$	−9.70820	+	7.05342i	−0.402764	+	0.292625i
$582$	8.97056			0.371842
$583$		0			0
$584$	−10.8284			−0.448084
$585$	−27.6216	+	20.0682i	−1.14201	+	0.829720i
$586$	1.89802	+	5.84152i	0.0784067	+	0.241311i
$587$	8.07836	−	24.8626i	0.333430	−	1.02619i	−0.634061	−	0.773283i	$-0.718613\pi$
$587$	8.07836	−	24.8626i	0.333430	−	1.02619i	0.967490	−	0.252908i	$-0.0813870\pi$
$588$	−12.5517	−	9.11932i	−0.517622	−	0.376075i
$589$		0			0
$590$	−1.23607	+	3.80423i	−0.0508881	+	0.156618i
$591$	−4.52012	−	13.9115i	−0.185933	−	0.572243i
$592$	−8.87537	+	6.44833i	−0.364776	+	0.265025i
$593$	20.4853			0.841230			0.420615	−	0.907239i	$-0.361814\pi$
$593$	20.4853			0.841230			0.420615	+	0.907239i	$0.361814\pi$
$594$		0			0
$595$	2.34315			0.0960596
$596$	17.2432	−	12.5279i	0.706307	−	0.513162i
$597$	18.9288	+	58.2568i	0.774704	+	2.38429i
$598$	2.47214	−	7.60845i	0.101093	−	0.311133i
$599$	−4.57649	−	3.32502i	−0.186990	−	0.135856i	0.490352	−	0.871525i	$-0.336868\pi$
$599$	−4.57649	−	3.32502i	−0.186990	−	0.135856i	−0.677342	+	0.735668i	$0.736868\pi$
$600$	−3.62867	−	2.63638i	−0.148140	−	0.107630i
$601$	−13.5786	+	41.7905i	−0.553881	+	1.70467i	0.145000	+	0.989432i	$0.453682\pi$
$601$	−13.5786	+	41.7905i	−0.553881	+	1.70467i	−0.698881	+	0.715238i	$0.746318\pi$
$602$	−1.53599	−	4.72729i	−0.0626022	−	0.192670i
$603$	18.1433	−	13.1819i	0.738854	−	0.536809i
$604$	21.9411			0.892772
$605$		0			0
$606$	15.5980			0.633625
$607$	14.7923	−	10.7472i	0.600400	−	0.436216i	−0.245621	−	0.969366i	$-0.578992\pi$
$607$	14.7923	−	10.7472i	0.600400	−	0.436216i	0.846021	+	0.533150i	$0.178992\pi$
$608$		0			0
$609$	−13.3847	+	41.1938i	−0.542374	+	1.66926i
$610$	−4.46150	−	3.24147i	−0.180641	−	0.131243i
$611$	−15.6251	−	11.3523i	−0.632125	−	0.459265i
$612$	−3.30978	+	10.1865i	−0.133790	+	0.411763i
$613$	7.86629	+	24.2099i	0.317716	+	0.977831i	0.974622	+	0.223858i	$0.0718650\pi$
$613$	7.86629	+	24.2099i	0.317716	+	0.977831i	−0.656905	+	0.753973i	$0.728135\pi$
$614$	−9.26797	+	6.73358i	−0.374025	+	0.271745i
$615$	−16.9706			−0.684319
$616$		0			0
$617$	11.6569			0.469287			0.234644	−	0.972081i	$-0.424608\pi$
$617$	11.6569			0.469287			0.234644	+	0.972081i	$0.424608\pi$
$618$	1.11044	−	0.806784i	0.0446686	−	0.0324536i
$619$	−7.92840	−	24.4011i	−0.318669	−	0.980764i	−0.974218	−	0.225610i	$-0.927562\pi$
$619$	−7.92840	−	24.4011i	−0.318669	−	0.980764i	0.655548	−	0.755153i	$-0.272438\pi$
$620$		0			0
$621$	−12.9443	−	9.40456i	−0.519436	−	0.377392i
$622$	9.15298	+	6.65003i	0.367001	+	0.266642i
$623$	−5.75619	+	17.7157i	−0.230617	+	0.709766i
$624$	−17.9048	−	55.1053i	−0.716765	−	2.20598i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−8.82843			−0.352855
$627$		0			0
$628$	25.5980			1.02147
$629$	−3.46605	+	2.51823i	−0.138200	+	0.100408i
$630$	−1.27999	−	3.93941i	−0.0509960	−	0.156950i
$631$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$631$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$632$	−5.13171	−	3.72841i	−0.204129	−	0.148308i
$633$	36.6119	+	26.6001i	1.45519	+	1.05726i
$634$	−2.72813	+	8.39633i	−0.108348	+	0.333461i
$635$	−4.83823	−	14.8906i	−0.191999	−	0.590914i
$636$	1.43568	−	1.04309i	0.0569286	−	0.0413610i
$637$	20.4853			0.811656
$638$		0			0
$639$	−56.5685			−2.23782
$640$	8.54027	−	6.20487i	0.337584	−	0.245269i
$641$	9.27051	+	28.5317i	0.366163	+	1.12693i	0.949250	+	0.314524i	$0.101845\pi$
$641$	9.27051	+	28.5317i	0.366163	+	1.12693i	−0.583086	+	0.812410i	$0.698155\pi$
$642$	1.32391	−	4.07458i	0.0522507	−	0.160811i
$643$	−40.0106	−	29.0694i	−1.57786	−	1.14639i	−0.919091	−	0.394044i	$-0.871076\pi$
$643$	−40.0106	−	29.0694i	−1.57786	−	1.14639i	−0.658773	−	0.752341i	$-0.728924\pi$
$644$	−8.36778	−	6.07955i	−0.329737	−	0.239568i
$645$	5.24419	−	16.1400i	0.206490	−	0.635510i
$646$		0			0
$647$	28.4068	−	20.6387i	1.11679	−	0.811392i	0.133067	−	0.991107i	$-0.457518\pi$
$647$	28.4068	−	20.6387i	1.11679	−	0.811392i	0.983719	+	0.179715i	$0.0575176\pi$
$648$	1.58579			0.0622956
$649$		0			0
$650$	2.82843			0.110940
$651$		0			0
$652$	0.274191	+	0.843874i	0.0107382	+	0.0330487i
$653$	0.106038	−	0.326351i	0.00414958	−	0.0127711i	−0.948960	−	0.315396i	$-0.897863\pi$
$653$	0.106038	−	0.326351i	0.00414958	−	0.0127711i	0.953110	+	0.302624i	$0.0978628\pi$
$654$	3.46605	+	2.51823i	0.135533	+	0.0984706i
$655$	9.15298	+	6.65003i	0.357637	+	0.259838i
$656$	5.56231	−	17.1190i	0.217172	−	0.668385i
$657$	−10.5505	−	32.4711i	−0.411614	−	1.26682i
$658$	1.89564	−	1.37727i	0.0738999	−	0.0536914i
$659$	−21.9411			−0.854705			−0.427352	−	0.904085i	$-0.640554\pi$
$659$	−21.9411			−0.854705			−0.427352	+	0.904085i	$0.640554\pi$
$660$		0			0
$661$	−0.627417			−0.0244037			−0.0122018	−	0.999926i	$-0.503884\pi$
$661$	−0.627417			−0.0244037			−0.0122018	+	0.999926i	$0.503884\pi$
$662$	5.13171	−	3.72841i	0.199450	−	0.144909i
$663$	−6.99226	−	21.5200i	−0.271557	−	0.835766i
$664$	−2.94021	+	9.04904i	−0.114102	+	0.351171i
$665$		0			0
$666$	6.12717	+	4.45165i	0.237423	+	0.172498i
$667$	6.69234	−	20.5969i	0.259128	−	0.797515i
$668$	−6.19853	−	19.0771i	−0.239828	−	0.738116i
$669$	11.8338	−	8.59778i	0.457522	−	0.332409i
$670$	−1.85786			−0.0717756
$671$		0			0
$672$	24.9706			0.963260
$673$	−3.62867	+	2.63638i	−0.139875	+	0.101625i	−0.655522	−	0.755176i	$-0.727551\pi$
$673$	−3.62867	+	2.63638i	−0.139875	+	0.101625i	0.515647	+	0.856801i	$0.327551\pi$
$674$	0.449881	+	1.38459i	0.0173288	+	0.0533324i
$675$	1.74806	−	5.37999i	0.0672830	−	0.207076i
$676$	49.7426	+	36.1401i	1.91318	+	1.39001i
$677$	−13.8921	−	10.0932i	−0.533917	−	0.387913i	0.287904	−	0.957659i	$-0.407042\pi$
$677$	−13.8921	−	10.0932i	−0.533917	−	0.387913i	−0.821821	+	0.569746i	$0.807042\pi$
$678$	−3.02052	+	9.29620i	−0.116002	+	0.357018i
$679$	4.73220	+	14.5642i	0.181605	+	0.558923i
$680$	1.50304	−	1.09203i	0.0576391	−	0.0418773i
$681$	7.59798			0.291155
$682$		0			0
$683$	31.7990			1.21675			0.608377	−	0.793648i	$-0.291821\pi$
$683$	31.7990			1.21675			0.608377	+	0.793648i	$0.291821\pi$
$684$		0			0
$685$	−7.09829	−	21.8463i	−0.271212	−	0.834704i
$686$	−2.55998	+	7.87881i	−0.0977405	+	0.300814i
$687$	48.7710	+	35.4342i	1.86073	+	1.35190i
$688$	14.5623	+	10.5801i	0.555183	+	0.403364i
$689$	−0.724072	+	2.22846i	−0.0275849	+	0.0848977i
$690$	1.02399	+	3.15152i	0.0389827	+	0.119976i
$691$	13.4995	−	9.80796i	0.513545	−	0.373112i	−0.300622	−	0.953743i	$-0.597194\pi$
$691$	13.4995	−	9.80796i	0.513545	−	0.373112i	0.814167	+	0.580631i	$0.197194\pi$
$692$	−11.2304			−0.426918
$693$		0			0
$694$	9.51472			0.361174
$695$	−3.23607	+	2.35114i	−0.122751	+	0.0891839i
$696$	10.6126	+	32.6623i	0.402270	+	1.23806i
$697$	2.17222	−	6.68539i	0.0822785	−	0.253227i
$698$	−2.33588	−	1.69711i	−0.0884142	−	0.0642367i
$699$	−50.6666	−	36.8115i	−1.91639	−	1.39234i
$700$	1.13003	−	3.47788i	0.0427111	−	0.131451i
$701$	10.0824	+	31.0305i	0.380808	+	1.17201i	0.939476	+	0.342615i	$0.111313\pi$
$701$	10.0824	+	31.0305i	0.380808	+	1.17201i	−0.558668	+	0.829391i	$0.688687\pi$
$702$	−12.9443	+	9.40456i	−0.488550	+	0.354952i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	−0.440231	+	0.319847i	−0.0165683	+	0.0120376i
$707$	8.22832	+	25.3242i	0.309458	+	0.952414i
$708$	15.4327	−	47.4968i	0.579995	−	1.78504i
$709$	16.6879	+	12.1245i	0.626728	+	0.455345i	0.855265	−	0.518190i	$-0.173394\pi$
$709$	16.6879	+	12.1245i	0.626728	+	0.455345i	−0.228537	+	0.973535i	$0.573394\pi$
$710$	3.79129	+	2.75453i	0.142285	+	0.103376i
$711$	6.18034	−	19.0211i	0.231781	−	0.713348i
$712$	4.56404	+	14.0467i	0.171045	+	0.526422i
$713$		0			0
$714$	2.74517			0.102735
$715$		0			0
$716$	3.02944			0.113215
$717$	1.57040	−	1.14096i	0.0586478	−	0.0426101i
$718$	−2.98413	−	9.18421i	−0.111367	−	0.342752i
$719$	9.16447	−	28.2053i	0.341777	−	1.05188i	−0.621509	−	0.783407i	$-0.713480\pi$
$719$	9.16447	−	28.2053i	0.341777	−	1.05188i	0.963287	−	0.268475i	$-0.0865197\pi$
$720$	12.1353	+	8.81678i	0.452254	+	0.328582i
$721$	1.89564	+	1.37727i	0.0705975	+	0.0512921i
$722$	2.43198	−	7.48487i	0.0905090	−	0.278558i
$723$	5.24419	+	16.1400i	0.195034	+	0.600252i
$724$	−1.94328	+	1.41187i	−0.0722213	+	0.0524718i
$725$	7.65685			0.284368
$726$		0			0
$727$	−36.4853			−1.35316			−0.676582	−	0.736367i	$-0.736540\pi$
$727$	−36.4853			−1.35316			−0.676582	+	0.736367i	$0.736540\pi$
$728$	−17.5208	+	12.7296i	−0.649363	+	0.471790i
$729$	−13.2877	−	40.8954i	−0.492138	−	1.51465i
$730$	−0.874032	+	2.68999i	−0.0323494	+	0.0995611i
$731$	5.68693	+	4.13180i	0.210339	+	0.152820i
$732$	55.7031	+	40.4707i	2.05885	+	1.49584i
$733$	10.3384	−	31.8184i	0.381858	−	1.17524i	−0.556875	−	0.830596i	$-0.688000\pi$
$733$	10.3384	−	31.8184i	0.381858	−	1.17524i	0.938734	−	0.344643i	$-0.112000\pi$
$734$	−1.08611	−	3.34270i	−0.0400890	−	0.123381i
$735$	−6.86474	+	4.98752i	−0.253210	+	0.183968i
$736$	−12.4853			−0.460214
$737$		0			0
$738$	−12.4264			−0.457422
$739$	30.6950	−	22.3012i	1.12913	−	0.820364i	0.143566	−	0.989641i	$-0.454143\pi$
$739$	30.6950	−	22.3012i	1.12913	−	0.820364i	0.985569	+	0.169277i	$0.0541431\pi$
$740$	2.06618	+	6.35904i	0.0759542	+	0.233763i
$741$		0			0
$742$	−0.229980	−	0.167090i	−0.00844284	−	0.00613408i
$743$	−23.9453	−	17.3973i	−0.878467	−	0.638243i	0.0543787	−	0.998520i	$-0.482682\pi$
$743$	−23.9453	−	17.3973i	−0.878467	−	0.638243i	−0.932845	+	0.360277i	$0.882682\pi$
$744$		0			0
$745$	−3.60217	−	11.0863i	−0.131973	−	0.406172i
$746$	−1.27306	+	0.924935i	−0.0466102	+	0.0338643i
$747$	−30.0000			−1.09764
$748$		0			0
$749$	7.31371			0.267237
$750$	−0.947822	+	0.688633i	−0.0346096	+	0.0251453i
$751$	−4.94427	−	15.2169i	−0.180419	−	0.555273i	0.819420	−	0.573193i	$-0.194295\pi$
$751$	−4.94427	−	15.2169i	−0.180419	−	0.555273i	−0.999839	+	0.0179203i	$0.994295\pi$
$752$	−2.62210	+	8.06998i	−0.0956180	+	0.294282i
$753$	−27.4589	−	19.9501i	−1.00066	−	0.727022i
$754$	−17.5208	−	12.7296i	−0.638069	−	0.463584i
$755$	3.70820	−	11.4127i	0.134955	−	0.415350i
$756$	6.39242	+	19.6738i	0.232490	+	0.715530i
$757$	7.53495	−	5.47446i	0.273862	−	0.198973i	−0.442374	−	0.896831i	$-0.645863\pi$
$757$	7.53495	−	5.47446i	0.273862	−	0.198973i	0.716236	+	0.697858i	$0.245863\pi$
$758$	−9.25483			−0.336151
$759$		0			0
$760$		0			0
$761$	24.2705	−	17.6336i	0.879805	−	0.639216i	−0.0533947	−	0.998573i	$-0.517004\pi$
$761$	24.2705	−	17.6336i	0.879805	−	0.639216i	0.933200	+	0.359358i	$0.117004\pi$
$762$	−5.66834	−	17.4454i	−0.205342	−	0.631979i
$763$	−2.26006	+	6.95575i	−0.0818197	+	0.251815i
$764$	−28.5694	−	20.7569i	−1.03360	−	0.750957i
$765$	4.73911	+	3.44317i	0.171343	+	0.124488i
$766$	4.37016	−	13.4500i	0.157900	−	0.485967i
$767$	20.3769	+	62.7137i	0.735768	+	2.26446i
$768$	−9.08562	+	6.60109i	−0.327849	+	0.238196i
$769$	14.9706			0.539852			0.269926	−	0.962881i	$-0.413001\pi$
$769$	14.9706			0.539852			0.269926	+	0.962881i	$0.413001\pi$
$770$		0			0
$771$	37.6569			1.35618
$772$	−10.1008	+	7.33866i	−0.363536	+	0.264124i
$773$	−9.35835	−	28.8021i	−0.336597	−	1.03594i	−0.965930	−	0.258803i	$-0.916672\pi$
$773$	−9.35835	−	28.8021i	−0.336597	−	1.03594i	0.629334	−	0.777135i	$-0.283328\pi$
$774$	3.83997	−	11.8182i	0.138025	−	0.424797i
$775$		0			0
$776$	9.82319	+	7.13697i	0.352632	+	0.256202i
$777$	−6.39242	+	19.6738i	−0.229327	+	0.705795i
$778$

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.335106 - 0.243469i) q^{2} +(0.874032 + 2.68999i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.947822 + 0.688633i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.490035 + 1.50817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +O(q^{10})\)	\(q+(0.335106 - 0.243469i) q^{2} +(0.874032 + 2.68999i) q^{3} +(-0.565015 + 1.73894i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.947822 + 0.688633i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(0.490035 + 1.50817i) q^{8} +(-4.04508 + 2.93893i) q^{9} +0.414214 q^{10} -5.17157 q^{12} +(5.52431 - 4.01365i) q^{13} +(0.255998 + 0.787881i) q^{14} +(-0.874032 + 2.68999i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(-0.947822 - 0.688633i) q^{17} +(-0.639995 + 1.96970i) q^{18} +(-1.47923 + 1.07472i) q^{20} -5.65685 q^{21} +2.82843 q^{23} +(-3.62867 + 2.63638i) q^{24} +(0.309017 + 0.951057i) q^{25} +(0.874032 - 2.68999i) q^{26} +(-4.57649 - 3.32502i) q^{27} +(-2.95846 - 2.14944i) q^{28} +(2.36610 - 7.28210i) q^{29} +(0.362036 + 1.11423i) q^{30} -4.41421 q^{32} -0.485281 q^{34} +(-1.61803 + 1.17557i) q^{35} +(-2.82508 - 8.69469i) q^{36} +(1.13003 - 3.47788i) q^{37} +(15.6251 + 11.3523i) q^{39} +(-0.490035 + 1.50817i) q^{40} +(1.85410 + 5.70634i) q^{41} +(-1.89564 + 1.37727i) q^{42} -6.00000 q^{43} -5.00000 q^{45} +(0.947822 - 0.688633i) q^{46} +(-0.874032 - 2.68999i) q^{47} +(2.62210 - 8.06998i) q^{48} +(2.42705 + 1.76336i) q^{49} +(0.335106 + 0.243469i) q^{50} +(1.02399 - 3.15152i) q^{51} +(3.85816 + 11.8742i) q^{52} +(-0.277611 + 0.201696i) q^{53} -2.34315 q^{54} -3.17157 q^{56} +(-0.980070 - 3.01635i) q^{58} +(-2.98413 + 9.18421i) q^{59} +(-4.18389 - 3.03977i) q^{60} +(-10.7710 - 7.82560i) q^{61} +(-3.09017 - 9.51057i) q^{63} +(3.37487 - 2.45199i) q^{64} +6.82843 q^{65} -4.48528 q^{67} +(1.73302 - 1.25912i) q^{68} +(2.47214 + 7.60845i) q^{69} +(-0.255998 + 0.787881i) q^{70} +(9.15298 + 6.65003i) q^{71} +(-6.41464 - 4.66051i) q^{72} +(-2.11010 + 6.49422i) q^{73} +(-0.468074 - 1.44058i) q^{74} +(-2.28825 + 1.66251i) q^{75} +8.00000 q^{78} +(-3.23607 + 2.35114i) q^{79} +(-0.927051 - 2.85317i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.01063 + 1.46081i) q^{82} +(4.85410 + 3.52671i) q^{83} +(3.19621 - 9.83692i) q^{84} +(-0.362036 - 1.11423i) q^{85} +(-2.01063 + 1.46081i) q^{86} +21.6569 q^{87} +9.31371 q^{89} +(-1.67553 + 1.21734i) q^{90} +(4.22020 + 12.9884i) q^{91} +(-1.59810 + 4.91846i) q^{92} +(-0.947822 - 0.688633i) q^{94} +(-3.85816 - 11.8742i) q^{96} +(6.19453 - 4.50059i) q^{97} +1.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - 6 * q^8 - 10 * q^9	\( 8 q - 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - 6 q^{8} - 10 q^{9} - 8 q^{10} - 64 q^{12} + 8 q^{13} + 4 q^{14} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 2 q^{20} + 8 q^{24} - 2 q^{25} + 4 q^{28} - 4 q^{29} - 8 q^{30} - 24 q^{32} + 64 q^{34} - 4 q^{35} - 10 q^{36} + 4 q^{37} + 16 q^{39} + 6 q^{40} - 12 q^{41} - 16 q^{42} - 48 q^{43} - 40 q^{45} + 8 q^{46} + 6 q^{49} - 2 q^{50} + 16 q^{51} - 8 q^{52} - 12 q^{53} - 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} - 4 q^{61} + 20 q^{63} + 14 q^{64} + 32 q^{65} + 32 q^{67} - 24 q^{68} - 16 q^{69} - 4 q^{70} - 30 q^{72} + 8 q^{73} + 20 q^{74} + 64 q^{78} - 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} + 12 q^{83} - 32 q^{84} + 8 q^{85} + 12 q^{86} + 128 q^{87} - 16 q^{89} + 10 q^{90} - 16 q^{91} + 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} - 24 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - 6 * q^8 - 10 * q^9 - 8 * q^10 - 64 * q^12 + 8 * q^13 + 4 * q^14 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 2 * q^20 + 8 * q^24 - 2 * q^25 + 4 * q^28 - 4 * q^29 - 8 * q^30 - 24 * q^32 + 64 * q^34 - 4 * q^35 - 10 * q^36 + 4 * q^37 + 16 * q^39 + 6 * q^40 - 12 * q^41 - 16 * q^42 - 48 * q^43 - 40 * q^45 + 8 * q^46 + 6 * q^49 - 2 * q^50 + 16 * q^51 - 8 * q^52 - 12 * q^53 - 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 - 4 * q^61 + 20 * q^63 + 14 * q^64 + 32 * q^65 + 32 * q^67 - 24 * q^68 - 16 * q^69 - 4 * q^70 - 30 * q^72 + 8 * q^73 + 20 * q^74 + 64 * q^78 - 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 + 12 * q^83 - 32 * q^84 + 8 * q^85 + 12 * q^86 + 128 * q^87 - 16 * q^89 + 10 * q^90 - 16 * q^91 + 16 * q^92 - 8 * q^94 + 8 * q^96 + 4 * q^97 - 24 * q^98

Introduction

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