LMFDB - Embedded newform 625.2.e.c.374.1

Newspace parameters

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.e (of order $10$, degree $4$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
Defining polynomial:	$x^{8} - x^{6} + x^{4} - x^{2} + 1$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			374.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	625.374
Dual form			625.2.e.c.249.1

$q$-expansion

$f(q)$	$=$	$q+(-0.951057 - 1.30902i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} -0.618034i q^{7} +(-2.12663 + 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 1.30902i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} -0.618034i q^{7} +(-2.12663 + 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(-0.363271 + 0.500000i) q^{12} +(1.08981 - 1.50000i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-4.97980 + 1.61803i) q^{17} +3.23607i q^{18} +(-0.263932 - 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(-8.05748 - 2.61803i) q^{22} +(-2.21238 - 3.04508i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-2.93893 - 4.04508i) q^{27} +(0.363271 + 0.118034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} -3.38197i q^{32} +(4.97980 - 1.61803i) q^{33} +(6.85410 + 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(0.138757 - 0.190983i) q^{37} +(-0.812299 + 1.11803i) q^{38} +(1.50000 - 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(-0.951057 + 0.309017i) q^{42} -4.85410i q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(-0.587785 - 0.190983i) q^{47} +(2.85317 + 3.92705i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(0.673542 + 0.927051i) q^{52} +(-3.30220 - 1.07295i) q^{53} +(-2.50000 + 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} -0.854102i q^{57} +(-5.56758 + 1.80902i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-2.85317 + 3.92705i) q^{62} +(-0.726543 + 1.00000i) q^{63} +(3.42705 - 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(4.53077 - 1.47214i) q^{67} -3.23607i q^{68} +(-1.16312 - 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(4.25325 + 1.38197i) q^{72} +(5.29007 + 7.28115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(-1.90211 - 2.61803i) q^{77} +(-2.85317 - 0.927051i) q^{78} +(2.50000 - 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} -1.23607i q^{82} +(5.93085 - 1.92705i) q^{83} +(0.309017 + 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(2.12663 - 2.92705i) q^{87} +(-6.88191 + 9.47214i) q^{88} +(-7.23607 + 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(2.21238 - 0.718847i) q^{92} -3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(3.66547 + 1.19098i) q^{97} +(-6.29412 - 8.66312i) q^{98} -10.4721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + O(q^{10}) $	$ 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.951057	−	1.30902i	−0.672499	−	0.925615i	0.327315	−	0.944915i	$-0.393856\pi$
$2$	−0.951057	−	1.30902i	−0.672499	−	0.925615i	−0.999814	+	0.0193004i	$0.993856\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i	0.570408	−	0.821362i	$-0.306785\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i	−0.0213149	+	0.999773i	$0.506785\pi$
$4$	−0.190983	+	0.587785i	−0.0954915	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.500000	−	1.53884i	−0.204124	−	0.628230i
$7$		−	0.618034i		−	0.233595i	−0.993156	−	0.116797i	$-0.962737\pi$
$7$		−	0.618034i		−	0.233595i	0.993156	−	0.116797i	$-0.0372628\pi$
$8$	−2.12663	+	0.690983i	−0.751876	+	0.244299i
$9$	−1.61803	−	1.17557i	−0.539345	−	0.391857i
$10$		0			0
$11$	4.23607	−	3.07768i	1.27722	−	0.927957i	0.277757	−	0.960651i	$-0.410409\pi$
$11$	4.23607	−	3.07768i	1.27722	−	0.927957i	0.999465	+	0.0326948i	$0.0104089\pi$
$12$	−0.363271	+	0.500000i	−0.104867	+	0.144338i
$13$	1.08981	−	1.50000i	0.302260	−	0.416025i	−0.630688	−	0.776037i	$-0.717227\pi$
$13$	1.08981	−	1.50000i	0.302260	−	0.416025i	0.932948	+	0.360011i	$0.117227\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$		0			0
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−4.97980	+	1.61803i	−1.20778	+	0.392431i	−0.842617	−	0.538513i	$-0.818986\pi$
$17$	−4.97980	+	1.61803i	−1.20778	+	0.392431i	−0.365161	+	0.930944i	$0.618986\pi$
$18$			3.23607i			0.762749i
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	0.916206	−	0.400707i	$-0.131236\pi$
$19$	−0.263932	−	0.812299i	−0.0605502	−	0.186354i	−0.976756	+	0.214353i	$0.931236\pi$
$20$		0			0
$21$	0.190983	−	0.587785i	0.0416759	−	0.128265i
$22$	−8.05748	−	2.61803i	−1.71786	−	0.558167i
$23$	−2.21238	−	3.04508i	−0.461314	−	0.634944i	0.513467	−	0.858110i	$-0.328361\pi$
$23$	−2.21238	−	3.04508i	−0.461314	−	0.634944i	−0.974781	+	0.223165i	$0.928361\pi$
$24$	−2.23607			−0.456435
$25$		0			0
$26$	−3.00000			−0.588348
$27$	−2.93893	−	4.04508i	−0.565597	−	0.778477i
$28$	0.363271	+	0.118034i	0.0686518	+	0.0223063i
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	−0.791982	−	0.610544i	$-0.790951\pi$
$29$	1.11803	−	3.44095i	0.207614	−	0.638969i	0.999596	−	0.0284251i	$-0.00904922\pi$
$30$		0			0
$31$	−0.927051	−	2.85317i	−0.166503	−	0.512444i	0.832641	−	0.553814i	$-0.186828\pi$
$31$	−0.927051	−	2.85317i	−0.166503	−	0.512444i	−0.999144	+	0.0413693i	$0.986828\pi$
$32$		−	3.38197i		−	0.597853i
$33$	4.97980	−	1.61803i	0.866871	−	0.281664i
$34$	6.85410	+	4.97980i	1.17547	+	0.854028i
$35$		0			0
$36$	1.00000	−	0.726543i	0.166667	−	0.121090i
$37$	0.138757	−	0.190983i	0.0228116	−	0.0313974i	−0.797459	−	0.603373i	$-0.793823\pi$
$37$	0.138757	−	0.190983i	0.0228116	−	0.0313974i	0.820270	+	0.571976i	$0.193823\pi$
$38$	−0.812299	+	1.11803i	−0.131772	+	0.181369i
$39$	1.50000	−	1.08981i	0.240192	−	0.174510i
$40$		0			0
$41$	0.618034	+	0.449028i	0.0965207	+	0.0701264i	0.634999	−	0.772513i	$-0.281001\pi$
$41$	0.618034	+	0.449028i	0.0965207	+	0.0701264i	−0.538478	+	0.842639i	$0.681001\pi$
$42$	−0.951057	+	0.309017i	−0.146751	+	0.0476824i
$43$		−	4.85410i		−	0.740244i	−0.928983	−	0.370122i	$-0.879316\pi$
$43$		−	4.85410i		−	0.740244i	0.928983	−	0.370122i	$-0.120684\pi$
$44$	1.00000	+	3.07768i	0.150756	+	0.463978i
$45$		0			0
$46$	−1.88197	+	5.79210i	−0.277481	+	0.853998i
$47$	−0.587785	−	0.190983i	−0.0857373	−	0.0278577i	0.265834	−	0.964019i	$-0.414353\pi$
$47$	−0.587785	−	0.190983i	−0.0857373	−	0.0278577i	−0.351572	+	0.936161i	$0.614353\pi$
$48$	2.85317	+	3.92705i	0.411820	+	0.566821i
$49$	6.61803			0.945433
$50$		0			0
$51$	−5.23607			−0.733196
$52$	0.673542	+	0.927051i	0.0934035	+	0.128559i
$53$	−3.30220	−	1.07295i	−0.453592	−	0.147381i	0.0733062	−	0.997309i	$-0.476645\pi$
$53$	−3.30220	−	1.07295i	−0.453592	−	0.147381i	−0.526898	+	0.849929i	$0.676645\pi$
$54$	−2.50000	+	7.69421i	−0.340207	+	1.04705i
$55$		0			0
$56$	0.427051	+	1.31433i	0.0570671	+	0.175634i
$57$		−	0.854102i		−	0.113129i
$58$	−5.56758	+	1.80902i	−0.731059	+	0.237536i
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.155646	−	0.987813i	$-0.549746\pi$
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.987563	+	0.157223i	$0.949746\pi$
$60$		0			0
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	−0.938987	−	0.343953i	$-0.888234\pi$
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	0.0369561	+	0.999317i	$0.488234\pi$
$62$	−2.85317	+	3.92705i	−0.362353	+	0.498736i
$63$	−0.726543	+	1.00000i	−0.0915358	+	0.125988i
$64$	3.42705	−	2.48990i	0.428381	−	0.311237i
$65$		0			0
$66$	−6.85410	−	4.97980i	−0.843682	−	0.612971i
$67$	4.53077	−	1.47214i	0.553521	−	0.179850i	−0.0188826	−	0.999822i	$-0.506011\pi$
$67$	4.53077	−	1.47214i	0.553521	−	0.179850i	0.572404	+	0.819972i	$0.306011\pi$
$68$		−	3.23607i		−	0.392431i
$69$	−1.16312	−	3.57971i	−0.140023	−	0.430947i
$70$		0			0
$71$	−2.04508	+	6.29412i	−0.242707	+	0.746975i	0.753298	+	0.657679i	$0.228462\pi$
$71$	−2.04508	+	6.29412i	−0.242707	+	0.746975i	−0.996005	+	0.0892960i	$0.971538\pi$
$72$	4.25325	+	1.38197i	0.501251	+	0.162866i
$73$	5.29007	+	7.28115i	0.619156	+	0.852194i	0.997291	−	0.0735557i	$-0.0234347\pi$
$73$	5.29007	+	7.28115i	0.619156	+	0.852194i	−0.378136	+	0.925750i	$0.623435\pi$
$74$	−0.381966			−0.0444026
$75$		0			0
$76$	0.527864			0.0605502
$77$	−1.90211	−	2.61803i	−0.216766	−	0.298353i
$78$	−2.85317	−	0.927051i	−0.323058	−	0.104968i
$79$	2.50000	−	7.69421i	0.281272	−	0.865666i	−0.706219	−	0.707993i	$-0.749601\pi$
$79$	2.50000	−	7.69421i	0.281272	−	0.865666i	0.987491	−	0.157673i	$-0.0503992\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	1.23607i		−	0.136501i
$83$	5.93085	−	1.92705i	0.650996	−	0.211521i	0.0351426	−	0.999382i	$-0.488811\pi$
$83$	5.93085	−	1.92705i	0.650996	−	0.211521i	0.615853	+	0.787861i	$0.288811\pi$
$84$	0.309017	+	0.224514i	0.0337165	+	0.0244965i
$85$		0			0
$86$	−6.35410	+	4.61653i	−0.685180	+	0.497813i
$87$	2.12663	−	2.92705i	0.227998	−	0.313813i
$88$	−6.88191	+	9.47214i	−0.733614	+	1.00973i
$89$	−7.23607	+	5.25731i	−0.767022	+	0.557274i	−0.901056	−	0.433703i	$-0.857207\pi$
$89$	−7.23607	+	5.25731i	−0.767022	+	0.557274i	0.134034	+	0.990977i	$0.457207\pi$
$90$		0			0
$91$	−0.927051	−	0.673542i	−0.0971813	−	0.0706064i
$92$	2.21238	−	0.718847i	0.230657	−	0.0749450i
$93$		−	3.00000i		−	0.311086i
$94$	0.309017	+	0.951057i	0.0318727	+	0.0980940i
$95$		0			0
$96$	1.04508	−	3.21644i	0.106664	−	0.328277i
$97$	3.66547	+	1.19098i	0.372172	+	0.120926i	0.489130	−	0.872211i	$-0.337314\pi$
$97$	3.66547	+	1.19098i	0.372172	+	0.120926i	−0.116958	+	0.993137i	$0.537314\pi$
$98$	−6.29412	−	8.66312i	−0.635803	−	0.875107i
$99$	−10.4721			−1.05249
$100$		0			0
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$	4.97980	+	6.85410i	0.493073	+	0.678657i
$103$	8.14324	+	2.64590i	0.802377	+	0.260708i	0.681366	−	0.731943i	$-0.261386\pi$
$103$	8.14324	+	2.64590i	0.802377	+	0.260708i	0.121011	+	0.992651i	$0.461386\pi$
$104$	−1.28115	+	3.94298i	−0.125627	+	0.386641i
$105$		0			0
$106$	1.73607	+	5.34307i	0.168622	+	0.518965i
$107$			16.4164i			1.58703i	0.608548	+	0.793517i	$0.291752\pi$
$107$			16.4164i			1.58703i	−0.608548	+	0.793517i	$0.708248\pi$
$108$	2.93893	−	0.954915i	0.282798	−	0.0918867i
$109$	8.09017	+	5.87785i	0.774898	+	0.562996i	0.903443	−	0.428707i	$-0.141031\pi$
$109$	8.09017	+	5.87785i	0.774898	+	0.562996i	−0.128546	+	0.991704i	$0.541031\pi$
$110$		0			0
$111$	0.190983	−	0.138757i	0.0181273	−	0.0131703i
$112$	1.76336	−	2.42705i	0.166621	−	0.229335i
$113$	9.90659	−	13.6353i	0.931934	−	1.28270i	−0.0271666	−	0.999631i	$-0.508648\pi$
$113$	9.90659	−	13.6353i	0.931934	−	1.28270i	0.959100	−	0.283066i	$-0.0913515\pi$
$114$	−1.11803	+	0.812299i	−0.104713	+	0.0760788i
$115$		0			0
$116$	1.80902	+	1.31433i	0.167963	+	0.122032i
$117$	−3.52671	+	1.14590i	−0.326045	+	0.105938i
$118$			17.5623i			1.61674i
$119$	1.00000	+	3.07768i	0.0916698	+	0.282131i
$120$		0			0
$121$	5.07295	−	15.6129i	0.461177	−	1.41936i
$122$	13.4005	+	4.35410i	1.21323	+	0.394202i
$123$	0.449028	+	0.618034i	0.0404875	+	0.0557262i
$124$	1.85410			0.166503
$125$		0			0
$126$	2.00000			0.178174
$127$	11.6902	+	16.0902i	1.03734	+	1.42777i	0.899294	+	0.437346i	$0.144081\pi$
$127$	11.6902	+	16.0902i	1.03734	+	1.42777i	0.138043	+	0.990426i	$0.455919\pi$
$128$	−12.9515	−	4.20820i	−1.14476	−	0.371956i
$129$	1.50000	−	4.61653i	0.132068	−	0.406462i
$130$		0			0
$131$	2.10081	+	6.46564i	0.183549	+	0.564905i	0.999920	−	0.0126218i	$-0.00401775\pi$
$131$	2.10081	+	6.46564i	0.183549	+	0.564905i	−0.816371	+	0.577527i	$0.804018\pi$
$132$			3.23607i			0.281664i
$133$	−0.502029	+	0.163119i	−0.0435314	+	0.0141442i
$134$	−6.23607	−	4.53077i	−0.538714	−	0.391399i
$135$		0			0
$136$	9.47214	−	6.88191i	0.812229	−	0.590119i
$137$	7.02067	−	9.66312i	0.599816	−	0.825576i	−0.395875	−	0.918304i	$-0.629559\pi$
$137$	7.02067	−	9.66312i	0.599816	−	0.825576i	0.995691	+	0.0927283i	$0.0295588\pi$
$138$	−3.57971	+	4.92705i	−0.304725	+	0.419418i
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	−0.402869	−	0.915258i	$-0.631987\pi$
$139$	4.04508	−	2.93893i	0.343100	−	0.249276i	0.745968	+	0.665981i	$0.231987\pi$
$140$		0			0
$141$	−0.500000	−	0.363271i	−0.0421076	−	0.0305930i
$142$	10.1841	−	3.30902i	0.854631	−	0.277687i
$143$		−	9.70820i		−	0.811841i
$144$	−3.00000	−	9.23305i	−0.250000	−	0.769421i
$145$		0			0
$146$	4.50000	−	13.8496i	0.372423	−	1.14620i
$147$	6.29412	+	2.04508i	0.519131	+	0.168676i
$148$	0.0857567	+	0.118034i	0.00704916	+	0.00970233i
$149$	3.94427			0.323127			0.161564	−	0.986862i	$-0.448346\pi$
$149$	3.94427			0.323127			0.161564	+	0.986862i	$0.448346\pi$
$150$		0			0
$151$	14.5623			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$151$	14.5623			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$152$	1.12257	+	1.54508i	0.0910524	+	0.125323i
$153$	9.95959	+	3.23607i	0.805185	+	0.261621i
$154$	−1.61803	+	4.97980i	−0.130385	+	0.401283i
$155$		0			0
$156$	0.354102	+	1.08981i	0.0283508	+	0.0872549i
$157$		−	13.1803i		−	1.05191i	−0.850514	−	0.525953i	$-0.823709\pi$
$157$		−	13.1803i		−	1.05191i	0.850514	−	0.525953i	$-0.176291\pi$
$158$	−12.4495	+	4.04508i	−0.990428	+	0.321810i
$159$	−2.80902	−	2.04087i	−0.222770	−	0.161852i
$160$		0			0
$161$	−1.88197	+	1.36733i	−0.148320	+	0.107761i
$162$	0.951057	−	1.30902i	0.0747221	−	0.102846i
$163$	6.46564	−	8.89919i	0.506428	−	0.697038i	−0.476884	−	0.878966i	$-0.658234\pi$
$163$	6.46564	−	8.89919i	0.506428	−	0.697038i	0.983312	+	0.181928i	$0.0582338\pi$
$164$	−0.381966	+	0.277515i	−0.0298265	+	0.0216702i
$165$		0			0
$166$	−8.16312	−	5.93085i	−0.633581	−	0.460323i
$167$	13.8496	−	4.50000i	1.07171	−	0.348220i	0.280558	−	0.959837i	$-0.409480\pi$
$167$	13.8496	−	4.50000i	1.07171	−	0.348220i	0.791154	+	0.611617i	$0.209480\pi$
$168$			1.38197i			0.106621i
$169$	2.95492	+	9.09429i	0.227301	+	0.699561i
$170$		0			0
$171$	−0.527864	+	1.62460i	−0.0403668	+	0.124236i
$172$	2.85317	+	0.927051i	0.217552	+	0.0706870i
$173$	−11.1024	−	15.2812i	−0.844100	−	1.16180i	−0.985132	−	0.171799i	$-0.945042\pi$
$173$	−11.1024	−	15.2812i	−0.844100	−	1.16180i	0.141032	−	0.990005i	$-0.454958\pi$
$174$	−5.85410			−0.443798
$175$		0			0
$176$	25.4164			1.91583
$177$	−6.37988	−	8.78115i	−0.479541	−	0.660032i
$178$	13.7638	+	4.47214i	1.03164	+	0.335201i
$179$	0.163119	−	0.502029i	0.0121921	−	0.0375234i	−0.944775	−	0.327719i	$-0.893720\pi$
$179$	0.163119	−	0.502029i	0.0121921	−	0.0375234i	0.956967	+	0.290195i	$0.0937202\pi$
$180$		0			0
$181$	0.0901699	+	0.277515i	0.00670228	+	0.0206275i	0.954352	−	0.298685i	$-0.0965480\pi$
$181$	0.0901699	+	0.277515i	0.00670228	+	0.0206275i	−0.947649	+	0.319313i	$0.896548\pi$
$182$			1.85410i			0.137435i
$183$	−8.28199	+	2.69098i	−0.612223	+	0.198923i
$184$	6.80902	+	4.94704i	0.501967	+	0.364701i
$185$		0			0
$186$	−3.92705	+	2.85317i	−0.287945	+	0.209205i
$187$	−16.1150	+	22.1803i	−1.17844	+	1.62199i
$188$	0.224514	−	0.309017i	0.0163744	−	0.0225374i
$189$	−2.50000	+	1.81636i	−0.181848	+	0.132120i
$190$		0			0
$191$	1.47214	+	1.06957i	0.106520	+	0.0773913i	0.639770	−	0.768566i	$-0.279030\pi$
$191$	1.47214	+	1.06957i	0.106520	+	0.0773913i	−0.533250	+	0.845958i	$0.679030\pi$
$192$	4.02874	−	1.30902i	0.290749	−	0.0944702i
$193$			7.70820i			0.554849i	0.960747	+	0.277424i	$0.0894808\pi$
$193$			7.70820i			0.554849i	−0.960747	+	0.277424i	$0.910519\pi$
$194$	−1.92705	−	5.93085i	−0.138354	−	0.425810i
$195$		0			0
$196$	−1.26393	+	3.88998i	−0.0902809	+	0.277856i
$197$	−3.52671	−	1.14590i	−0.251268	−	0.0816419i	0.180675	−	0.983543i	$-0.442172\pi$
$197$	−3.52671	−	1.14590i	−0.251268	−	0.0816419i	−0.431943	+	0.901901i	$0.642172\pi$
$198$	9.95959	+	13.7082i	0.707797	+	0.974200i
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$		0			0
$201$	4.76393			0.336022
$202$	−1.40008	−	1.92705i	−0.0985096	−	0.135587i
$203$	−2.12663	−	0.690983i	−0.149260	−	0.0484975i
$204$	1.00000	−	3.07768i	0.0700140	−	0.215481i
$205$		0			0
$206$	−4.28115	−	13.1760i	−0.298282	−	0.918018i
$207$			7.52786i			0.523223i
$208$	8.55951	−	2.78115i	0.593495	−	0.192838i
$209$	−3.61803	−	2.62866i	−0.250265	−	0.181828i
$210$		0			0
$211$	7.42705	−	5.39607i	0.511299	−	0.371481i	−0.302017	−	0.953303i	$-0.597660\pi$
$211$	7.42705	−	5.39607i	0.511299	−	0.371481i	0.813316	+	0.581822i	$0.197660\pi$
$212$	1.26133	−	1.73607i	0.0866283	−	0.119234i
$213$	−3.88998	+	5.35410i	−0.266537	+	0.366857i
$214$	21.4894	−	15.6129i	1.46898	−	1.06728i
$215$		0			0
$216$	9.04508	+	6.57164i	0.615440	+	0.447143i
$217$	−1.76336	+	0.572949i	−0.119704	+	0.0388943i
$218$		−	16.1803i		−	1.09587i
$219$	2.78115	+	8.55951i	0.187933	+	0.578398i
$220$		0			0
$221$	−3.00000	+	9.23305i	−0.201802	+	0.621082i
$222$	−0.363271	−	0.118034i	−0.0243812	−	0.00792192i
$223$	0.106001	+	0.145898i	0.00709836	+	0.00977005i	0.812551	−	0.582890i	$-0.198078\pi$
$223$	0.106001	+	0.145898i	0.00709836	+	0.00977005i	−0.805453	+	0.592660i	$0.798078\pi$
$224$	−2.09017			−0.139655
$225$		0			0
$226$	−27.2705			−1.81401
$227$	8.67802	+	11.9443i	0.575981	+	0.792769i	0.993247	−	0.116015i	$-0.0370120\pi$
$227$	8.67802	+	11.9443i	0.575981	+	0.792769i	−0.417267	+	0.908784i	$0.637012\pi$
$228$	0.502029	+	0.163119i	0.0332477	+	0.0108028i
$229$	−6.70820	+	20.6457i	−0.443291	+	1.36431i	0.441057	+	0.897479i	$0.354604\pi$
$229$	−6.70820	+	20.6457i	−0.443291	+	1.36431i	−0.884348	+	0.466829i	$0.845396\pi$
$230$		0			0
$231$	−1.00000	−	3.07768i	−0.0657952	−	0.202497i
$232$			8.09017i			0.531146i
$233$	2.80017	−	0.909830i	0.183445	−	0.0596049i	−0.215854	−	0.976426i	$-0.569254\pi$
$233$	2.80017	−	0.909830i	0.183445	−	0.0596049i	0.399299	+	0.916821i	$0.369254\pi$
$234$	4.85410	+	3.52671i	0.317323	+	0.230548i
$235$		0			0
$236$	5.42705	−	3.94298i	0.353271	−	0.256666i
$237$	4.75528	−	6.54508i	0.308889	−	0.425149i
$238$	3.07768	−	4.23607i	0.199497	−	0.274584i
$239$	−16.6074	+	12.0660i	−1.07424	+	0.780483i	−0.976670	−	0.214745i	$-0.931108\pi$
$239$	−16.6074	+	12.0660i	−1.07424	+	0.780483i	−0.0975727	+	0.995228i	$0.531108\pi$
$240$		0			0
$241$	−2.04508	−	1.48584i	−0.131736	−	0.0957114i	0.519966	−	0.854187i	$-0.325945\pi$
$241$	−2.04508	−	1.48584i	−0.131736	−	0.0957114i	−0.651702	+	0.758475i	$0.725945\pi$
$242$	−25.2623	+	8.20820i	−1.62392	+	0.527643i
$243$			16.0000i			1.02640i
$244$	−1.66312	−	5.11855i	−0.106470	−	0.327682i
$245$		0			0
$246$	0.381966	−	1.17557i	0.0243533	−	0.0749516i
$247$	−1.50609	−	0.489357i	−0.0958299	−	0.0311370i
$248$	3.94298	+	5.42705i	0.250380	+	0.344618i
$249$	6.23607			0.395195
$250$		0			0
$251$	−29.1803			−1.84185			−0.920923	−	0.389744i	$-0.872564\pi$
$251$	−29.1803			−1.84185			−0.920923	+	0.389744i	$0.872564\pi$
$252$	−0.449028	−	0.618034i	−0.0282861	−	0.0389325i
$253$	−18.7436	−	6.09017i	−1.17840	−	0.382886i
$254$	9.94427	−	30.6053i	0.623959	−	1.92035i
$255$		0			0
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$		−	22.8541i		−	1.42560i	−0.701367	−	0.712800i	$-0.747427\pi$
$257$		−	22.8541i		−	1.42560i	0.701367	−	0.712800i	$-0.252573\pi$
$258$	−7.46969	+	2.42705i	−0.465043	+	0.151102i
$259$	−0.118034	−	0.0857567i	−0.00733428	−	0.00532866i
$260$		0			0
$261$	−5.85410	+	4.25325i	−0.362360	+	0.263270i
$262$	6.46564	−	8.89919i	0.399448	−	0.549794i
$263$	−6.41264	+	8.82624i	−0.395420	+	0.544249i	−0.959587	−	0.281412i	$-0.909197\pi$
$263$	−6.41264	+	8.82624i	−0.395420	+	0.544249i	0.564167	+	0.825661i	$0.309197\pi$
$264$	−9.47214	+	6.88191i	−0.582970	+	0.423552i
$265$		0			0
$266$	0.690983	+	0.502029i	0.0423669	+	0.0307813i
$267$	−8.50651	+	2.76393i	−0.520590	+	0.169150i
$268$			2.94427i			0.179850i
$269$	3.94427	+	12.1392i	0.240487	+	0.740141i	0.996346	+	0.0854076i	$0.0272192\pi$
$269$	3.94427	+	12.1392i	0.240487	+	0.740141i	−0.755860	+	0.654734i	$0.772781\pi$
$270$		0			0
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	−0.997640	−	0.0686657i	$-0.978126\pi$
$271$	−2.47214	+	7.60845i	−0.150172	+	0.462181i	0.847468	+	0.530846i	$0.178126\pi$
$272$	−24.1724	−	7.85410i	−1.46567	−	0.476225i
$273$	−0.673542	−	0.927051i	−0.0407646	−	0.0561077i
$274$	−19.3262			−1.16754
$275$		0			0
$276$	2.32624			0.140023
$277$	−14.5231	−	19.9894i	−0.872610	−	1.20104i	−0.978413	−	0.206657i	$-0.933742\pi$
$277$	−14.5231	−	19.9894i	−0.872610	−	1.20104i	0.105804	−	0.994387i	$-0.466258\pi$
$278$	−7.69421	−	2.50000i	−0.461468	−	0.149940i
$279$	−1.85410	+	5.70634i	−0.111002	+	0.341630i
$280$		0			0
$281$	3.11803	+	9.59632i	0.186006	+	0.572469i	0.999964	−	0.00845524i	$-0.00269142\pi$
$281$	3.11803	+	9.59632i	0.186006	+	0.572469i	−0.813958	+	0.580924i	$0.802691\pi$
$282$			1.00000i			0.0595491i
$283$	28.3929	−	9.22542i	1.68778	−	0.548395i	0.701389	−	0.712779i	$-0.252564\pi$
$283$	28.3929	−	9.22542i	1.68778	−	0.548395i	0.986396	+	0.164384i	$0.0525638\pi$
$284$	−3.30902	−	2.40414i	−0.196354	−	0.142660i
$285$		0			0
$286$	−12.7082	+	9.23305i	−0.751452	+	0.545962i
$287$	0.277515	−	0.381966i	0.0163812	−	0.0225467i
$288$	−3.97574	+	5.47214i	−0.234273	+	0.322449i
$289$	8.42705	−	6.12261i	0.495709	−	0.360154i
$290$		0			0
$291$	3.11803	+	2.26538i	0.182782	+	0.132799i
$292$	−5.29007	+	1.71885i	−0.309578	+	0.100588i
$293$		−	19.5279i		−	1.14083i	−0.821357	−	0.570415i	$-0.806782\pi$
$293$		−	19.5279i		−	1.14083i	0.821357	−	0.570415i	$-0.193218\pi$
$294$	−3.30902	−	10.1841i	−0.192986	−	0.593949i
$295$		0			0
$296$	−0.163119	+	0.502029i	−0.00948110	+	0.0291798i
$297$	−24.8990	−	8.09017i	−1.44479	−	0.469439i
$298$	−3.75123	−	5.16312i	−0.217303	−	0.299091i
$299$	−6.97871			−0.403589
$300$		0			0
$301$	−3.00000			−0.172917
$302$	−13.8496	−	19.0623i	−0.796954	−	1.09691i
$303$	1.40008	+	0.454915i	0.0804328	+	0.0261342i
$304$	1.28115	−	3.94298i	0.0734792	−	0.226146i
$305$		0			0
$306$	−5.23607	−	16.1150i	−0.299326	−	0.921231i
$307$		−	9.23607i		−	0.527130i	−0.964642	−	0.263565i	$-0.915102\pi$
$307$		−	9.23607i		−	0.527130i	0.964642	−	0.263565i	$-0.0848984\pi$
$308$	1.90211	−	0.618034i	0.108383	−	0.0352158i
$309$	6.92705	+	5.03280i	0.394066	+	0.286306i
$310$		0			0
$311$	−6.88197	+	5.00004i	−0.390240	+	0.283526i	−0.765554	−	0.643372i	$-0.777535\pi$
$311$	−6.88197	+	5.00004i	−0.390240	+	0.283526i	0.375314	+	0.926898i	$0.377535\pi$
$312$	−2.43690	+	3.35410i	−0.137962	+	0.189889i
$313$	−9.85359	+	13.5623i	−0.556958	+	0.766587i	−0.990936	−	0.134337i	$-0.957110\pi$
$313$	−9.85359	+	13.5623i	−0.556958	+	0.766587i	0.433978	+	0.900924i	$0.357110\pi$
$314$	−17.2533	+	12.5352i	−0.973659	+	0.707405i
$315$		0			0
$316$	4.04508	+	2.93893i	0.227554	+	0.165328i
$317$	7.27794	−	2.36475i	0.408770	−	0.132817i	−0.0974121	−	0.995244i	$-0.531056\pi$
$317$	7.27794	−	2.36475i	0.408770	−	0.132817i	0.506182	+	0.862427i	$0.331056\pi$
$318$			5.61803i			0.315044i
$319$	−5.85410	−	18.0171i	−0.327767	−	1.00876i
$320$		0			0
$321$	−5.07295	+	15.6129i	−0.283144	+	0.871429i
$322$	3.57971	+	1.16312i	0.199490	+	0.0648181i
$323$	2.62866	+	3.61803i	0.146262	+	0.201313i
$324$	−0.618034			−0.0343352
$325$		0			0
$326$	−17.7984			−0.985761
$327$	5.87785	+	8.09017i	0.325046	+	0.447387i
$328$	−1.62460	−	0.527864i	−0.0897034	−	0.0291464i
$329$	−0.118034	+	0.363271i	−0.00650742	+	0.0200278i
$330$		0			0
$331$	−7.14590	−	21.9928i	−0.392774	−	1.20883i	−0.930682	−	0.365830i	$-0.880785\pi$
$331$	−7.14590	−	21.9928i	−0.392774	−	1.20883i	0.537907	−	0.843004i	$-0.319215\pi$
$332$			3.85410i			0.211521i
$333$	−0.449028	+	0.145898i	−0.0246066	+	0.00799516i
$334$	−19.0623	−	13.8496i	−1.04304	−	0.757815i
$335$		0			0
$336$	2.42705	−	1.76336i	0.132406	−	0.0961989i
$337$	−4.61653	+	6.35410i	−0.251478	+	0.346130i	−0.916028	−	0.401114i	$-0.868623\pi$
$337$	−4.61653	+	6.35410i	−0.251478	+	0.346130i	0.664550	+	0.747244i	$0.268623\pi$
$338$	9.09429	−	12.5172i	0.494664	−	0.680847i
$339$	13.6353	−	9.90659i	0.740565	−	0.538052i
$340$		0			0
$341$	−12.7082	−	9.23305i	−0.688188	−	0.499998i
$342$	2.62866	−	0.854102i	0.142141	−	0.0461845i
$343$		−	8.41641i		−	0.454443i
$344$	3.35410	+	10.3229i	0.180841	+	0.556572i
$345$		0			0
$346$	−9.44427	+	29.0665i	−0.507727	+	1.56262i
$347$	18.9354	+	6.15248i	1.01650	+	0.330282i	0.769441	−	0.638717i	$-0.220535\pi$
$347$	18.9354	+	6.15248i	1.01650	+	0.330282i	0.247063	+	0.969000i	$0.420535\pi$
$348$	1.31433	+	1.80902i	0.0704554	+	0.0969735i
$349$	−21.7082			−1.16201			−0.581007	−	0.813899i	$-0.697341\pi$
$349$	−21.7082			−1.16201			−0.581007	+	0.813899i	$0.697341\pi$
$350$		0			0
$351$	−9.27051			−0.494823
$352$	−10.4086	−	14.3262i	−0.554781	−	0.763591i
$353$	12.2780	+	3.98936i	0.653491	+	0.212332i	0.616953	−	0.787000i	$-0.288367\pi$
$353$	12.2780	+	3.98936i	0.653491	+	0.212332i	0.0365381	+	0.999332i	$0.488367\pi$
$354$	−5.42705	+	16.7027i	−0.288445	+	0.887741i
$355$		0			0
$356$	−1.70820	−	5.25731i	−0.0905346	−	0.278637i
$357$			3.23607i			0.171271i
$358$	−0.812299	+	0.263932i	−0.0429313	+	0.0139492i
$359$	11.1180	+	8.07772i	0.586787	+	0.426326i	0.841165	−	0.540779i	$-0.181870\pi$
$359$	11.1180	+	8.07772i	0.586787	+	0.426326i	−0.254377	+	0.967105i	$0.581870\pi$
$360$		0			0
$361$	14.7812	−	10.7391i	0.777955	−	0.565218i
$362$	0.277515	−	0.381966i	0.0145858	−	0.0200757i
$363$	9.64932	−	13.2812i	0.506458	−	0.697080i
$364$	0.572949	−	0.416272i	0.0300307	−	0.0218186i
$365$		0			0
$366$	11.3992	+	8.28199i	0.595845	+	0.432907i
$367$	−24.3112	+	7.89919i	−1.26903	+	0.412334i	−0.864705	−	0.502279i	$-0.832495\pi$
$367$	−24.3112	+	7.89919i	−1.26903	+	0.412334i	−0.404329	+	0.914614i	$0.632495\pi$
$368$		−	18.2705i		−	0.952416i
$369$	−0.472136	−	1.45309i	−0.0245784	−	0.0756446i
$370$		0			0
$371$	−0.663119	+	2.04087i	−0.0344274	+	0.105957i
$372$	1.76336	+	0.572949i	0.0914257	+	0.0297060i
$373$	16.6170	+	22.8713i	0.860395	+	1.18423i	0.981475	+	0.191589i	$0.0613642\pi$
$373$	16.6170	+	22.8713i	0.860395	+	1.18423i	−0.121080	+	0.992643i	$0.538636\pi$
$374$	44.3607			2.29384
$375$		0			0
$376$	1.38197			0.0712695
$377$	−3.94298	−	5.42705i	−0.203074	−	0.279507i
$378$	4.75528	+	1.54508i	0.244585	+	0.0794706i
$379$	−4.51064	+	13.8823i	−0.231696	+	0.713087i	0.765846	+	0.643024i	$0.222320\pi$
$379$	−4.51064	+	13.8823i	−0.231696	+	0.713087i	−0.997543	+	0.0700639i	$0.977680\pi$
$380$		0			0
$381$	6.14590	+	18.9151i	0.314864	+	0.969051i
$382$		−	2.94427i		−	0.150642i
$383$	−31.7279	+	10.3090i	−1.62122	+	0.526766i	−0.972229	−	0.234031i	$-0.924808\pi$
$383$	−31.7279	+	10.3090i	−1.62122	+	0.526766i	−0.648990	+	0.760797i	$0.724808\pi$
$384$	−11.0172	−	8.00448i	−0.562220	−	0.408477i
$385$		0			0
$386$	10.0902	−	7.33094i	0.513576	−	0.373135i
$387$	−5.70634	+	7.85410i	−0.290070	+	0.399246i
$388$	−1.40008	+	1.92705i	−0.0710785	+	0.0978312i
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	−0.235988	−	0.971756i	$-0.575833\pi$
$389$	12.1353	−	8.81678i	0.615282	−	0.447028i	0.851270	+	0.524727i	$0.175833\pi$
$390$		0			0
$391$	15.9443	+	11.5842i	0.806336	+	0.585838i
$392$	−14.0741	+	4.57295i	−0.710849	+	0.230969i
$393$			6.79837i			0.342933i
$394$	1.85410	+	5.70634i	0.0934083	+	0.287481i
$395$		0			0
$396$	2.00000	−	6.15537i	0.100504	−	0.309319i
$397$	−27.6134	−	8.97214i	−1.38588	−	0.450299i	−0.481280	−	0.876567i	$-0.659828\pi$
$397$	−27.6134	−	8.97214i	−1.38588	−	0.450299i	−0.904597	+	0.426268i	$0.859828\pi$
$398$	−16.7027	−	22.9894i	−0.837233	−	1.15235i
$399$	−0.527864			−0.0264263
$400$		0			0
$401$	26.5967			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$401$	26.5967			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$402$	−4.53077	−	6.23607i	−0.225974	−	0.311027i
$403$	−5.29007	−	1.71885i	−0.263517	−	0.0856219i
$404$	−0.281153	+	0.865300i	−0.0139879	+	0.0430503i
$405$		0			0
$406$	1.11803	+	3.44095i	0.0554871	+	0.170772i
$407$		−	1.23607i		−	0.0612696i
$408$	11.1352	−	3.61803i	0.551273	−	0.179119i
$409$	1.28115	+	0.930812i	0.0633489	+	0.0460257i	0.619009	−	0.785384i	$-0.287534\pi$
$409$	1.28115	+	0.930812i	0.0633489	+	0.0460257i	−0.555660	+	0.831410i	$0.687534\pi$
$410$		0			0
$411$	9.66312	−	7.02067i	0.476647	−	0.346304i
$412$	−3.11044	+	4.28115i	−0.153240	+	0.210917i
$413$	−3.94298	+	5.42705i	−0.194022	+	0.267048i
$414$	9.85410	−	7.15942i	0.484303	−	0.351867i
$415$		0			0
$416$	−5.07295	−	3.68571i	−0.248722	−	0.180707i
$417$	4.75528	−	1.54508i	0.232867	−	0.0756631i
$418$			7.23607i			0.353928i
$419$	2.92705	+	9.00854i	0.142996	+	0.440096i	0.996748	−	0.0805840i	$-0.0256785\pi$
$419$	2.92705	+	9.00854i	0.142996	+	0.440096i	−0.853752	+	0.520680i	$0.825679\pi$
$420$		0			0
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	−0.354429	−	0.935083i	$-0.615325\pi$
$421$	9.88854	−	30.4338i	0.481938	−	1.48325i	0.836367	−	0.548170i	$-0.184675\pi$
$422$	−14.1271	−	4.59017i	−0.687696	−	0.223446i
$423$	0.726543	+	1.00000i	0.0353257	+	0.0486217i
$424$	7.76393			0.377050
$425$		0			0
$426$	10.7082			0.518814
$427$	3.16344	+	4.35410i	0.153090	+	0.210710i
$428$	−9.64932	−	3.13525i	−0.466418	−	0.151548i
$429$	3.00000	−	9.23305i	0.144841	−	0.445776i
$430$		0			0
$431$	−9.21885	−	28.3727i	−0.444056	−	1.36666i	−0.883515	−	0.468402i	$-0.844830\pi$
$431$	−9.21885	−	28.3727i	−0.444056	−	1.36666i	0.439459	−	0.898263i	$-0.355170\pi$
$432$		−	24.2705i		−	1.16772i
$433$	−25.5398	+	8.29837i	−1.22736	+	0.398794i	−0.849758	−	0.527173i	$-0.823252\pi$
$433$	−25.5398	+	8.29837i	−1.22736	+	0.398794i	−0.377605	+	0.925967i	$0.623252\pi$
$434$	2.42705	+	1.76336i	0.116502	+	0.0846438i
$435$		0			0
$436$	−5.00000	+	3.63271i	−0.239457	+	0.173975i
$437$	−1.88960	+	2.60081i	−0.0903919	+	0.124414i
$438$	8.55951	−	11.7812i	0.408989	−	0.562925i
$439$	−33.1525	+	24.0867i	−1.58228	+	1.14959i	−0.668261	+	0.743927i	$0.732961\pi$
$439$	−33.1525	+	24.0867i	−1.58228	+	1.14959i	−0.914021	+	0.405667i	$0.867039\pi$
$440$		0			0
$441$	−10.7082	−	7.77997i	−0.509914	−	0.370475i
$442$	14.9394	−	4.85410i	0.710594	−	0.230886i
$443$			29.9443i			1.42270i	0.702840	+	0.711348i	$0.251915\pi$
$443$			29.9443i			1.42270i	−0.702840	+	0.711348i	$0.748085\pi$
$444$	0.0450850	+	0.138757i	0.00213964	+	0.00658513i
$445$		0			0
$446$	0.0901699	−	0.277515i	0.00426967	−	0.0131407i
$447$	3.75123	+	1.21885i	0.177427	+	0.0576495i
$448$	−1.53884	−	2.11803i	−0.0727034	−	0.100068i
$449$	−4.67376			−0.220568			−0.110284	−	0.993900i	$-0.535176\pi$
$449$	−4.67376			−0.220568			−0.110284	+	0.993900i	$0.535176\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	6.12261	+	8.42705i	0.287983	+	0.396375i
$453$	13.8496	+	4.50000i	0.650710	+	0.211428i
$454$	7.38197	−	22.7194i	0.346453	−	1.06627i
$455$		0			0
$456$	0.590170	+	1.81636i	0.0276372	+	0.0850587i
$457$			21.4164i			1.00182i	0.865500	+	0.500909i	$0.167001\pi$
$457$			21.4164i			1.00182i	−0.865500	+	0.500909i	$0.832999\pi$
$458$	33.4055	−	10.8541i	1.56094	−	0.507179i
$459$	21.1803	+	15.3884i	0.988614	+	0.718270i
$460$		0			0
$461$	−0.663119	+	0.481784i	−0.0308845	+	0.0224389i	−0.603120	−	0.797650i	$-0.706076\pi$
$461$	−0.663119	+	0.481784i	−0.0308845	+	0.0224389i	0.572236	+	0.820089i	$0.306076\pi$
$462$	−3.07768	+	4.23607i	−0.143187	+	0.197080i
$463$	−14.1801	+	19.5172i	−0.659005	+	0.907042i	−0.999448	−	0.0332229i	$-0.989423\pi$
$463$	−14.1801	+	19.5172i	−0.659005	+	0.907042i	0.340443	+	0.940265i	$0.389423\pi$
$464$	14.2082	−	10.3229i	0.659599	−	0.479227i
$465$		0			0
$466$	−3.85410	−	2.80017i	−0.178538	−	0.129715i
$467$	26.1073	−	8.48278i	1.20810	−	0.392536i	0.365367	−	0.930864i	$-0.380944\pi$
$467$	26.1073	−	8.48278i	1.20810	−	0.392536i	0.842736	+	0.538328i	$0.180944\pi$
$468$		−	2.29180i		−	0.105938i
$469$	−0.909830	−	2.80017i	−0.0420120	−	0.129300i
$470$		0			0
$471$	4.07295	−	12.5352i	0.187672	−	0.577594i
$472$	23.0826	+	7.50000i	1.06246	+	0.345215i
$473$	−14.9394	−	20.5623i	−0.686914	−	0.945456i
$474$	−13.0902			−0.601251
$475$		0			0
$476$	−2.00000			−0.0916698
$477$	4.08174	+	5.61803i	0.186890	+	0.257232i
$478$	31.5891	+	10.2639i	1.44485	+	0.469461i
$479$	3.35410	−	10.3229i	0.153253	−	0.471664i	−0.844727	−	0.535198i	$-0.820237\pi$
$479$	3.35410	−	10.3229i	0.153253	−	0.471664i	0.997980	+	0.0635340i	$0.0202371\pi$
$480$		0			0
$481$	−0.135255	−	0.416272i	−0.00616709	−	0.0189804i
$482$			4.09017i			0.186302i
$483$	−2.21238	+	0.718847i	−0.100667	+	0.0327087i
$484$	8.20820	+	5.96361i	0.373100	+	0.271073i
$485$		0			0
$486$	20.9443	−	15.2169i	0.950051	−	0.690253i
$487$	21.4050	−	29.4615i	0.969954	−	1.33503i	0.0278844	−	0.999611i	$-0.491123\pi$
$487$	21.4050	−	29.4615i	0.969954	−	1.33503i	0.942070	−	0.335417i	$-0.108877\pi$
$488$	11.4454	−	15.7533i	0.518110	−	0.713118i
$489$	8.89919	−	6.46564i	0.402435	−	0.292386i
$490$		0			0
$491$	34.9894	+	25.4213i	1.57905	+	1.14725i	0.917776	+	0.397099i	$0.129983\pi$
$491$	34.9894	+	25.4213i	1.57905	+	1.14725i	0.661272	+	0.750147i	$0.270017\pi$
$492$	−0.449028	+	0.145898i	−0.0202437	+	0.00657759i
$493$			18.9443i			0.853207i
$494$	0.791796	+	2.43690i	0.0356246	+	0.109641i
$495$		0			0
$496$	4.50000	−	13.8496i	0.202056	−	0.621864i
$497$	3.88998	+	1.26393i	0.174490	+	0.0566951i
$498$	−5.93085	−	8.16312i	−0.265768	−	0.365798i
$499$	−7.56231			−0.338535			−0.169268	−	0.985570i	$-0.554140\pi$
$499$	−7.56231			−0.338535			−0.169268	+	0.985570i	$0.554140\pi$
$500$		0			0
$501$	14.5623			0.650596
$502$	27.7522	+	38.1976i	1.23864	+	1.70484i
$503$	−35.5851	−	11.5623i	−1.58666	−	0.515538i	−0.622900	−	0.782301i	$-0.714046\pi$
$503$	−35.5851	−	11.5623i	−1.58666	−	0.515538i	−0.963762	+	0.266764i	$0.914046\pi$
$504$	0.854102	−	2.62866i	0.0380447	−	0.117090i
$505$		0			0
$506$	9.85410	+	30.3278i	0.438068	+	1.34824i
$507$			9.56231i			0.424677i
$508$	−11.6902	+	3.79837i	−0.518668	+	0.168526i
$509$	−16.4443	−	11.9475i	−0.728880	−	0.529562i	0.160329	−	0.987064i	$-0.448744\pi$
$509$	−16.4443	−	11.9475i	−0.728880	−	0.529562i	−0.889209	+	0.457502i	$0.848744\pi$
$510$		0			0
$511$	4.50000	−	3.26944i	0.199068	−	0.144632i
$512$	−3.11044	+	4.28115i	−0.137463	+	0.189202i
$513$	−2.51014	+	3.45492i	−0.110826	+	0.152538i
$514$	−29.9164	+	21.7355i	−1.31956	+	0.958714i
$515$		0			0
$516$	2.42705	+	1.76336i	0.106845	+	0.0776274i
$517$	−3.07768	+	1.00000i	−0.135356	+	0.0439799i
$518$			0.236068i			0.0103722i
$519$	−5.83688	−	17.9641i	−0.256211	−	0.788535i
$520$		0			0
$521$	9.07295	−	27.9237i	0.397493	−	1.22336i	−0.529510	−	0.848304i	$-0.677624\pi$
$521$	9.07295	−	27.9237i	0.397493	−	1.22336i	0.927003	−	0.375054i	$-0.122376\pi$
$522$	11.1352	+	3.61803i	0.487373	+	0.158357i
$523$	7.72696	+	10.6353i	0.337877	+	0.465047i	0.943820	−	0.330461i	$-0.107204\pi$
$523$	7.72696	+	10.6353i	0.337877	+	0.465047i	−0.605943	+	0.795508i	$0.707204\pi$
$524$	−4.20163			−0.183549
$525$		0			0
$526$	17.6525			0.769685
$527$	9.23305	+	12.7082i	0.402198	+	0.553578i
$528$	24.1724	+	7.85410i	1.05197	+	0.341806i
$529$	2.72949	−	8.40051i	0.118673	−	0.365239i
$530$		0			0
$531$	6.70820	+	20.6457i	0.291111	+	0.895948i
$532$		−	0.326238i		−	0.0141442i
$533$	1.34708	−	0.437694i	0.0583487	−	0.0189586i
$534$	11.7082	+	8.50651i	0.506664	+	0.368113i
$535$		0			0
$536$	−8.61803	+	6.26137i	−0.372242	+	0.270450i
$537$	0.310271	−	0.427051i	0.0133892	−	0.0184286i
$538$	12.1392	−	16.7082i	0.523359	−	0.720342i
$539$	28.0344	−	20.3682i	1.20753	−	0.877321i
$540$		0			0
$541$	−21.9443	−	15.9434i	−0.943458	−	0.685462i	0.00579261	−	0.999983i	$-0.498156\pi$
$541$	−21.9443	−	15.9434i	−0.943458	−	0.685462i	−0.949251	+	0.314521i	$0.898156\pi$
$542$	12.3107	−	4.00000i	0.528791	−	0.171815i
$543$			0.291796i			0.0125222i
$544$	5.47214	+	16.8415i	0.234616	+	0.722073i
$545$		0			0
$546$	−0.572949	+	1.76336i	−0.0245200	+	0.0754647i
$547$	20.2497	+	6.57953i	0.865815	+	0.281320i	0.708055	−	0.706157i	$-0.249573\pi$
$547$	20.2497	+	6.57953i	0.865815	+	0.281320i	0.157760	+	0.987478i	$0.449573\pi$
$548$	4.33901	+	5.97214i	0.185353	+	0.255117i
$549$	17.4164			0.743314
$550$		0			0
$551$	−3.09017			−0.131646
$552$	4.94704	+	6.80902i	0.210560	+	0.289811i
$553$	−4.75528	−	1.54508i	−0.202215	−	0.0657037i
$554$	−12.3541	+	38.0220i	−0.524875	+	1.61540i
$555$		0			0
$556$	0.954915	+	2.93893i	0.0404974	+	0.124638i
$557$		−	4.76393i		−	0.201854i	−0.994894	−	0.100927i	$-0.967819\pi$
$557$		−	4.76393i		−	0.201854i	0.994894	−	0.100927i	$-0.0321809\pi$
$558$	9.23305	−	3.00000i	0.390866	−	0.127000i
$559$	−7.28115	−	5.29007i	−0.307960	−	0.223746i
$560$		0			0
$561$	−22.1803	+	16.1150i	−0.936455	+	0.680374i
$562$	9.59632	−	13.2082i	0.404796	−	0.557154i
$563$	4.33901	−	5.97214i	0.182868	−	0.251696i	−0.707735	−	0.706478i	$-0.750283\pi$
$563$	4.33901	−	5.97214i	0.182868	−	0.251696i	0.890603	+	0.454782i	$0.150283\pi$
$564$	0.309017	−	0.224514i	0.0130120	−	0.00945374i
$565$		0			0
$566$	−39.0795	−	28.3929i	−1.64264	−	1.19344i
$567$	0.587785	−	0.190983i	0.0246847	−	0.00802053i
$568$		−	14.7984i		−	0.620926i
$569$	−6.34346	−	19.5232i	−0.265932	−	0.818453i	−0.991477	−	0.130279i	$-0.958413\pi$
$569$	−6.34346	−	19.5232i	−0.265932	−	0.818453i	0.725546	−	0.688174i	$-0.241587\pi$
$570$		0			0
$571$	−2.51064	+	7.72696i	−0.105067	+	0.323363i	−0.989746	−	0.142837i	$-0.954377\pi$
$571$	−2.51064	+	7.72696i	−0.105067	+	0.323363i	0.884679	+	0.466201i	$0.154377\pi$
$572$	5.70634	+	1.85410i	0.238594	+	0.0775239i
$573$	1.06957	+	1.47214i	0.0446819	+	0.0614994i
$574$	−0.763932			−0.0318859
$575$		0			0
$576$	−8.47214			−0.353006
$577$	−19.8537	−	27.3262i	−0.826519	−	1.13761i	−0.988561	−	0.150822i	$-0.951808\pi$
$577$	−19.8537	−	27.3262i	−0.826519	−	1.13761i	0.162042	−	0.986784i	$-0.448192\pi$
$578$	−16.0292	−	5.20820i	−0.666727	−	0.216633i
$579$	−2.38197	+	7.33094i	−0.0989911	+	0.304663i
$580$		0			0
$581$	−1.19098	−	3.66547i	−0.0494103	−	0.152069i
$582$		−	6.23607i		−	0.258493i
$583$	−17.2905	+	5.61803i	−0.716101	+	0.232675i
$584$	−16.2812	−	11.8290i	−0.673719	−	0.489485i
$585$		0			0
$586$	−25.5623	+	18.5721i	−1.05597	+	0.767206i
$587$	−3.11044	+	4.28115i	−0.128382	+	0.176702i	−0.868369	−	0.495919i	$-0.834831\pi$
$587$	−3.11044	+	4.28115i	−0.128382	+	0.176702i	0.739987	+	0.672621i	$0.234831\pi$
$588$	−2.40414	+	3.30902i	−0.0991451	+	0.136462i
$589$	−2.07295	+	1.50609i	−0.0854144	+	0.0620572i
$590$		0			0
$591$	−3.00000	−	2.17963i	−0.123404	−	0.0896579i
$592$	1.08981	−	0.354102i	0.0447911	−	0.0145535i
$593$		−	10.9098i		−	0.448013i	−0.974588	−	0.224007i	$-0.928086\pi$
$593$		−	10.9098i		−	0.448013i	0.974588	−	0.224007i	$-0.0719137\pi$
$594$	13.0902	+	40.2874i	0.537096	+	1.65301i
$595$		0			0
$596$	−0.753289	+	2.31838i	−0.0308559	+	0.0949647i
$597$	16.7027	+	5.42705i	0.683598	+	0.222114i
$598$	6.63715	+	9.13525i	0.271413	+	0.373568i
$599$	9.47214			0.387021			0.193510	−	0.981098i	$-0.438013\pi$
$599$	9.47214			0.387021			0.193510	+	0.981098i	$0.438013\pi$
$600$		0			0
$601$	2.72949			0.111338			0.0556691	−	0.998449i	$-0.482271\pi$
$601$	2.72949			0.111338			0.0556691	+	0.998449i	$0.482271\pi$
$602$	2.85317	+	3.92705i	0.116287	+	0.160055i
$603$	−9.06154	−	2.94427i	−0.369014	−	0.119900i
$604$	−2.78115	+	8.55951i	−0.113164	+	0.348281i
$605$		0			0
$606$	−0.736068	−	2.26538i	−0.0299007	−	0.0920249i
$607$			35.5623i			1.44343i	0.692191	+	0.721715i	$0.256646\pi$
$607$			35.5623i			1.44343i	−0.692191	+	0.721715i	$0.743354\pi$
$608$	−2.74717	+	0.892609i	−0.111412	+	0.0362001i
$609$	−1.80902	−	1.31433i	−0.0733051	−	0.0532592i
$610$		0			0
$611$	−0.927051	+	0.673542i	−0.0375045	+	0.0272486i
$612$	−3.80423	+	5.23607i	−0.153777	+	0.211656i
$613$	−8.80427	+	12.1180i	−0.355601	+	0.489443i	−0.948917	−	0.315527i	$-0.897819\pi$
$613$	−8.80427	+	12.1180i	−0.355601	+	0.489443i	0.593316	+	0.804970i	$0.297819\pi$
$614$	−12.0902	+	8.78402i	−0.487920	+	0.354494i
$615$		0			0
$616$	5.85410	+	4.25325i	0.235868	+	0.171368i
$617$	13.5393	−	4.39919i	0.545072	−	0.177105i	−0.0235215	−	0.999723i	$-0.507488\pi$
$617$	13.5393	−	4.39919i	0.545072	−	0.177105i	0.568593	+	0.822619i	$0.307488\pi$
$618$		−	13.8541i		−	0.557294i
$619$	−9.43363	−	29.0337i	−0.379170	−	1.16696i	−0.940622	−	0.339455i	$-0.889757\pi$
$619$	−9.43363	−	29.0337i	−0.379170	−	1.16696i	0.561453	−	0.827509i	$-0.310243\pi$
$620$		0			0
$621$	−5.81559	+	17.8986i	−0.233372	+	0.718244i
$622$	13.0903	+	4.25329i	0.524872	+	0.170541i
$623$	3.24920	+	4.47214i	0.130176	+	0.179172i
$624$	9.00000			0.360288
$625$		0			0
$626$	27.1246			1.08412
$627$	−2.62866	−	3.61803i	−0.104978	−	0.144490i
$628$	7.74721	+	2.51722i	0.309147	+	0.100448i
$629$	−0.381966	+	1.17557i	−0.0152300	+	0.0468731i
$630$		0			0
$631$	−3.16312	−	9.73508i	−0.125922	−	0.387547i	0.868146	−	0.496309i	$-0.165312\pi$
$631$	−3.16312	−	9.73508i	−0.125922	−	0.387547i	−0.994068	+	0.108761i	$0.965312\pi$
$632$			18.0902i			0.719588i
$633$	8.73102	−	2.83688i	0.347027	−	0.112756i
$634$	−10.0172	−	7.27794i	−0.397835	−	0.289044i
$635$		0			0
$636$	1.73607	−	1.26133i	0.0688396	−	0.0500149i
$637$	7.21242	−	9.92705i	0.285767	−	0.393324i
$638$	−18.0171	+	24.7984i	−0.713303	+	0.981777i
$639$	10.7082	−	7.77997i	0.423610	−	0.307771i
$640$		0			0
$641$	0.881966	+	0.640786i	0.0348356	+	0.0253095i	0.605067	−	0.796175i	$-0.293146\pi$
$641$	0.881966	+	0.640786i	0.0348356	+	0.0253095i	−0.570231	+	0.821484i	$0.693146\pi$
$642$	25.2623	−	8.20820i	0.997022	−	0.323952i
$643$		−	30.8328i		−	1.21593i	−0.793965	−	0.607964i	$-0.791987\pi$
$643$		−	30.8328i		−	1.21593i	0.793965	−	0.607964i	$-0.208013\pi$
$644$	−0.444272	−	1.36733i	−0.0175068	−	0.0538803i
$645$		0			0
$646$	2.23607	−	6.88191i	0.0879769	−	0.270765i
$647$	34.7526	+	11.2918i	1.36626	+	0.443926i	0.898130	−	0.439731i	$-0.144926\pi$
$647$	34.7526	+	11.2918i	1.36626	+	0.443926i	0.468135	+	0.883657i	$0.344926\pi$
$648$	−1.31433	−	1.80902i	−0.0516317	−	0.0710649i
$649$	−56.8328			−2.23088
$650$		0			0
$651$	−1.85410			−0.0726680
$652$	3.99598	+	5.50000i	0.156495	+	0.215397i
$653$	18.1558	+	5.89919i	0.710493	+	0.230853i	0.641896	−	0.766791i	$-0.278148\pi$
$653$	18.1558	+	5.89919i	0.710493	+	0.230853i	0.0685963	+	0.997645i	$0.478148\pi$
$654$	5.00000	−	15.3884i	0.195515	−	0.601735i
$655$		0			0
$656$	1.14590	+	3.52671i	0.0447398	+	0.137695i
$657$		−	18.0000i		−	0.702247i
$658$	0.587785	−	0.190983i	0.0229143	−	0.00744529i
$659$	12.5623	+	9.12705i	0.489358	+	0.355539i	0.804937	−	0.593360i	$-0.202199\pi$
$659$	12.5623	+	9.12705i	0.489358	+	0.355539i	−0.315579	+	0.948899i	$0.602199\pi$
$660$		0			0
$661$	−15.9271	+	11.5717i	−0.619490	+	0.450086i	−0.852744	−	0.522330i	$-0.825063\pi$
$661$	−15.9271	+	11.5717i	−0.619490	+	0.450086i	0.233253	+	0.972416i	$0.425063\pi$
$662$	−21.9928	+	30.2705i	−0.854775	+	1.17650i
$663$	−5.70634	+	7.85410i	−0.221616	+	0.305028i
$664$	−11.2812	+	8.19624i	−0.437794	+	0.318076i
$665$		0			0
$666$	0.618034	+	0.449028i	0.0239483	+	0.0173995i
$667$	−12.9515	+	4.20820i	−0.501485	+	0.162942i
$668$			9.00000i			0.348220i
$669$	0.0557281	+	0.171513i	0.00215457	+	0.00663109i
$670$		0			0
$671$	−14.0902	+	43.3651i	−0.543945	+	1.67409i
$672$	−1.98787	−	0.645898i	−0.0766837	−	0.0249161i
$673$	−7.15942	−	9.85410i	−0.275976	−	0.379848i	0.648420	−	0.761283i	$-0.275430\pi$
$673$	−7.15942	−	9.85410i	−0.275976	−	0.379848i	−0.924396	+	0.381435i	$0.875430\pi$
$674$	12.7082			0.489502
$675$		0			0
$676$	−5.90983			−0.227301
$677$	6.24112	+	8.59017i	0.239866	+	0.330147i	0.911930	−	0.410346i	$-0.134592\pi$
$677$	6.24112	+	8.59017i	0.239866	+	0.330147i	−0.672064	+	0.740493i	$0.734592\pi$
$678$	−25.9358	−	8.42705i	−0.996058	−	0.323639i
$679$	0.736068	−	2.26538i	0.0282477	−	0.0869375i
$680$		0			0
$681$	4.56231	+	14.0413i	0.174828	+	0.538065i
$682$			25.4164i			0.973245i
$683$	12.8128	−	4.16312i	0.490267	−	0.159297i	−0.0534426	−	0.998571i	$-0.517019\pi$
$683$	12.8128	−	4.16312i	0.490267	−	0.159297i	0.543709	+	0.839274i	$0.317019\pi$
$684$	−0.854102	−	0.620541i	−0.0326574	−	0.0237270i
$685$		0			0
$686$	−11.0172	+	8.00448i	−0.420639	+	0.305612i
$687$	−12.7598	+	17.5623i	−0.486815	+	0.670044i
$688$	13.8496	−	19.0623i	0.528010	−	0.726744i
$689$	−5.20820	+	3.78398i	−0.198417	+	0.144158i
$690$		0			0
$691$	−29.3435	−	21.3193i	−1.11628	−	0.811023i	−0.132637	−	0.991165i	$-0.542344\pi$
$691$	−29.3435	−	21.3193i	−1.11628	−	0.811023i	−0.983641	+	0.180141i	$0.942344\pi$
$692$	11.1024	−	3.60739i	0.422050	−	0.137132i
$693$			6.47214i			0.245856i
$694$	−9.95492	−	30.6381i	−0.377883	−	1.16301i
$695$		0			0
$696$	−2.50000	+	7.69421i	−0.0947623	+	0.291648i
$697$	−3.80423	−	1.23607i	−0.144095	−	0.0468194i
$698$	20.6457	+	28.4164i	0.781452	+	1.07558i
$699$	2.94427			0.111363
$700$		0			0
$701$	−41.0132			−1.54905			−0.774523	−	0.632546i	$-0.782010\pi$
$701$	−41.0132			−1.54905			−0.774523	+	0.632546i	$0.782010\pi$
$702$	8.81678	+	12.1353i	0.332768	+	0.458016i
$703$	−0.191758	−	0.0623059i	−0.00723228	−	0.00234991i
$704$	6.85410	−	21.0948i	0.258324	−	0.795039i
$705$		0			0
$706$	−6.45492	−	19.8662i	−0.242934	−	0.747674i
$707$		−	0.909830i		−	0.0342177i
$708$	6.37988	−	2.07295i	0.239771	−	0.0779062i
$709$	−27.1353	−	19.7149i	−1.01909	−	0.740409i	−0.0529906	−	0.998595i	$-0.516875\pi$
$709$	−27.1353	−	19.7149i	−1.01909	−	0.740409i	−0.966095	+	0.258186i	$0.916875\pi$
$710$		0			0
$711$	−13.0902	+	9.51057i	−0.490920	+	0.356674i
$712$	11.7557	−	16.1803i	0.440564	−	0.606384i
$713$	−6.63715	+	9.13525i	−0.248563	+	0.342118i
$714$	4.23607	−	3.07768i	0.158531	−	0.115179i
$715$		0			0
$716$	0.263932	+	0.191758i	0.00986360	+	0.00716633i
$717$	−19.5232	+	6.34346i	−0.729106	+	0.236901i
$718$		−	22.2361i		−	0.829843i
$719$	7.19756	+	22.1518i	0.268424	+	0.826123i	0.990885	+	0.134712i	$0.0430108\pi$
$719$	7.19756	+	22.1518i	0.268424	+	0.826123i	−0.722461	+	0.691412i	$0.756989\pi$
$720$		0			0
$721$	1.63525	−	5.03280i	0.0609001	−	0.187431i
$722$	−28.1154	−	9.13525i	−1.04635	−	0.339979i
$723$	−1.48584	−	2.04508i	−0.0552590	−	0.0760575i
$724$	−0.180340			−0.00670228
$725$		0			0
$726$	−26.5623			−0.985820
$727$	14.4374	+	19.8713i	0.535452	+	0.736987i	0.987949	−	0.154779i	$-0.0494667\pi$
$727$	14.4374	+	19.8713i	0.535452	+	0.736987i	−0.452497	+	0.891766i	$0.649467\pi$
$728$	2.43690	+	0.791796i	0.0903174	+	0.0293459i
$729$	−4.01722	+	12.3637i	−0.148786	+	0.457916i
$730$		0			0
$731$	7.85410	+	24.1724i	0.290494	+	0.894050i
$732$		−	5.38197i		−	0.198923i
$733$	19.0009	−	6.17376i	0.701814	−	0.228033i	0.0636931	−	0.997970i	$-0.479712\pi$
$733$	19.0009	−	6.17376i	0.701814	−	0.228033i	0.638121	+	0.769936i	$0.279712\pi$
$734$	33.4615	+	24.3112i	1.23509	+	0.897343i
$735$		0			0
$736$	−10.2984	+	7.48221i	−0.379603	+	0.275798i
$737$	14.6619	−	20.1803i	0.540077	−	0.743352i
$738$	−1.45309	+	2.00000i	−0.0534888	+	0.0736210i
$739$	12.9271	−	9.39205i	0.475529	−	0.345492i	−0.324063	−	0.946036i	$-0.605049\pi$
$739$	12.9271	−	9.39205i	0.475529	−	0.345492i	0.799592	+	0.600543i	$0.205049\pi$
$740$		0			0
$741$	−1.28115	−	0.930812i	−0.0470643	−	0.0341942i
$742$	3.30220	−	1.07295i	0.121227	−	0.0393892i
$743$			28.3607i			1.04045i	0.854029	+	0.520226i	$0.174152\pi$
$743$			28.3607i			1.04045i	−0.854029	+	0.520226i	$0.825848\pi$
$744$	2.07295	+	6.37988i	0.0759980	+	0.233898i
$745$		0			0
$746$	14.1353	−	43.5038i	0.517528	−	1.59279i
$747$	−11.8617	−	3.85410i	−0.433997	−	0.141014i
$748$	−9.95959	−	13.7082i	−0.364159	−	0.501222i
$749$	10.1459			0.370723
$750$		0			0
$751$	−5.11146			−0.186520			−0.0932598	−	0.995642i	$-0.529729\pi$
$751$	−5.11146			−0.186520			−0.0932598	+	0.995642i	$0.529729\pi$
$752$	−1.76336	−	2.42705i	−0.0643030	−	0.0885054i
$753$	−27.7522	−	9.01722i	−1.01134	−	0.328606i
$754$	−3.35410	+	10.3229i	−0.122149	+	0.375937i
$755$		0			0
$756$	−0.590170	−	1.81636i	−0.0214643	−	0.0660602i
$757$		−	30.4164i		−	1.10550i	−0.833346	−	0.552752i	$-0.813578\pi$
$757$		−	30.4164i		−	1.10550i	0.833346	−	0.552752i	$-0.186422\pi$
$758$	22.4621	−	7.29837i	0.815860	−	0.265089i
$759$	−15.9443	−	11.5842i	−0.578740	−	0.420480i
$760$		0			0
$761$	14.9271	−	10.8451i	0.541105	−	0.393136i	−0.283390	−	0.959005i	$-0.591459\pi$
$761$	14.9271	−	10.8451i	0.541105	−	0.393136i	0.824495	+	0.565869i	$0.191459\pi$
$762$	18.9151	−	26.0344i	0.685223	−	0.943128i
$763$	3.63271	−	5.00000i	0.131513	−	0.181012i
$764$	−0.909830	+	0.661030i	−0.0329165	+	0.0239152i
$765$		0			0
$766$	43.6697	+	31.7279i	1.57785	+	1.14638i
$767$	−19.1396	+	6.21885i	−0.691092	+	0.224550i
$768$			13.5623i			0.489388i
$769$	−4.14590	−	12.7598i	−0.149505	−	0.460129i	0.848058	−	0.529904i	$-0.177772\pi$
$769$	−4.14590	−	12.7598i	−0.149505	−	0.460129i	−0.997563	+	0.0697749i	$0.977772\pi$
$770$		0			0
$771$	7.06231	−	21.7355i	0.254343	−	0.782786i
$772$	−4.53077	−	1.47214i	−0.163066	−	0.0529833i
$773$	21.2538	+	29.2533i	0.764445	+	1.05217i	0.996831	+	0.0795442i	$0.0253465\pi$
$773$	21.2538	+	29.2533i	0.764445	+	1.05217i	−0.232387	+	0.972623i	$0.574654\pi$
$774$	15.7082			0.564620
$775$		0			0
$776$	−8.61803			−0.309369
$777$	−0.0857567	−	0.118034i	−0.00307650	−	0.00423445i
$778$	−23.0826	−	7.50000i	−0.827552	−	0.268888i
$779$	0.201626	−	0.620541i	0.00722401	−	0.0222332i
$780$		0			0
$781$	10.7082	+	32.9565i	0.383170	+	1.17927i

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 1.30902i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} -0.618034i q^{7} +(-2.12663 + 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 1.30902i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.190983 + 0.587785i) q^{4} +(-0.500000 - 1.53884i) q^{6} -0.618034i q^{7} +(-2.12663 + 0.690983i) q^{8} +(-1.61803 - 1.17557i) q^{9} +(4.23607 - 3.07768i) q^{11} +(-0.363271 + 0.500000i) q^{12} +(1.08981 - 1.50000i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(3.92705 + 2.85317i) q^{16} +(-4.97980 + 1.61803i) q^{17} +3.23607i q^{18} +(-0.263932 - 0.812299i) q^{19} +(0.190983 - 0.587785i) q^{21} +(-8.05748 - 2.61803i) q^{22} +(-2.21238 - 3.04508i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-2.93893 - 4.04508i) q^{27} +(0.363271 + 0.118034i) q^{28} +(1.11803 - 3.44095i) q^{29} +(-0.927051 - 2.85317i) q^{31} -3.38197i q^{32} +(4.97980 - 1.61803i) q^{33} +(6.85410 + 4.97980i) q^{34} +(1.00000 - 0.726543i) q^{36} +(0.138757 - 0.190983i) q^{37} +(-0.812299 + 1.11803i) q^{38} +(1.50000 - 1.08981i) q^{39} +(0.618034 + 0.449028i) q^{41} +(-0.951057 + 0.309017i) q^{42} -4.85410i q^{43} +(1.00000 + 3.07768i) q^{44} +(-1.88197 + 5.79210i) q^{46} +(-0.587785 - 0.190983i) q^{47} +(2.85317 + 3.92705i) q^{48} +6.61803 q^{49} -5.23607 q^{51} +(0.673542 + 0.927051i) q^{52} +(-3.30220 - 1.07295i) q^{53} +(-2.50000 + 7.69421i) q^{54} +(0.427051 + 1.31433i) q^{56} -0.854102i q^{57} +(-5.56758 + 1.80902i) q^{58} +(-8.78115 - 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-2.85317 + 3.92705i) q^{62} +(-0.726543 + 1.00000i) q^{63} +(3.42705 - 2.48990i) q^{64} +(-6.85410 - 4.97980i) q^{66} +(4.53077 - 1.47214i) q^{67} -3.23607i q^{68} +(-1.16312 - 3.57971i) q^{69} +(-2.04508 + 6.29412i) q^{71} +(4.25325 + 1.38197i) q^{72} +(5.29007 + 7.28115i) q^{73} -0.381966 q^{74} +0.527864 q^{76} +(-1.90211 - 2.61803i) q^{77} +(-2.85317 - 0.927051i) q^{78} +(2.50000 - 7.69421i) q^{79} +(0.309017 + 0.951057i) q^{81} -1.23607i q^{82} +(5.93085 - 1.92705i) q^{83} +(0.309017 + 0.224514i) q^{84} +(-6.35410 + 4.61653i) q^{86} +(2.12663 - 2.92705i) q^{87} +(-6.88191 + 9.47214i) q^{88} +(-7.23607 + 5.25731i) q^{89} +(-0.927051 - 0.673542i) q^{91} +(2.21238 - 0.718847i) q^{92} -3.00000i q^{93} +(0.309017 + 0.951057i) q^{94} +(1.04508 - 3.21644i) q^{96} +(3.66547 + 1.19098i) q^{97} +(-6.29412 - 8.66312i) q^{98} -10.4721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + O(q^{10}) \)	\( 8 q - 6 q^{4} - 4 q^{6} - 4 q^{9} + 16 q^{11} - 2 q^{14} + 18 q^{16} - 20 q^{19} + 6 q^{21} - 24 q^{26} + 6 q^{31} + 28 q^{34} + 8 q^{36} + 12 q^{39} - 4 q^{41} + 8 q^{44} - 24 q^{46} + 44 q^{49} - 24 q^{51} - 20 q^{54} - 10 q^{56} - 30 q^{59} - 34 q^{61} + 14 q^{64} - 28 q^{66} + 22 q^{69} + 6 q^{71} - 12 q^{74} + 40 q^{76} + 20 q^{79} - 2 q^{81} - 2 q^{84} - 24 q^{86} - 40 q^{89} + 6 q^{91} - 2 q^{94} - 14 q^{96} - 48 q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more