LMFDB - Embedded newform 637.2.bd.b.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.3
Character	$\chi$	$=$	637.97
Dual form			637.2.bd.b.440.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0990633 - 0.369709i) q^{2} +(-0.792292 - 0.457430i) q^{3} +(1.60518 - 0.926751i) q^{4} +(2.62172 + 2.62172i) q^{5} +(-0.0906291 + 0.338232i) q^{6} +(-1.04293 - 1.04293i) q^{8} +(-1.08152 - 1.87324i) q^{9} +O(q^{10})$	\(q+(-0.0990633 - 0.369709i) q^{2} +(-0.792292 - 0.457430i) q^{3} +(1.60518 - 0.926751i) q^{4} +(2.62172 + 2.62172i) q^{5} +(-0.0906291 + 0.338232i) q^{6} +(-1.04293 - 1.04293i) q^{8} +(-1.08152 - 1.87324i) q^{9} +(0.709559 - 1.22899i) q^{10} +(-0.0846164 + 0.0226729i) q^{11} -1.69570 q^{12} +(1.63590 - 3.21307i) q^{13} +(-0.877916 - 3.27643i) q^{15} +(1.57124 - 2.72146i) q^{16} +(2.94521 + 5.10126i) q^{17} +(-0.585415 + 0.585415i) q^{18} +(0.960980 - 3.58643i) q^{19} +(6.63802 + 1.77865i) q^{20} +(0.0167648 + 0.0290374i) q^{22} +(0.386571 + 0.223187i) q^{23} +(0.349239 + 1.30338i) q^{24} +8.74686i q^{25} +(-1.34996 - 0.286509i) q^{26} +4.72345i q^{27} +(0.706429 - 1.22357i) q^{29} +(-1.12436 + 0.649147i) q^{30} +(1.42152 + 1.42152i) q^{31} +(-4.01115 - 1.07478i) q^{32} +(0.0774122 + 0.0207425i) q^{33} +(1.59422 - 1.59422i) q^{34} +(-3.47205 - 2.00459i) q^{36} +(-2.56087 + 0.686183i) q^{37} -1.42113 q^{38} +(-2.76587 + 1.79738i) q^{39} -5.46857i q^{40} +(3.00264 - 0.804556i) q^{41} +(8.64788 - 4.99286i) q^{43} +(-0.114812 + 0.114812i) q^{44} +(2.07568 - 7.74655i) q^{45} +(0.0442192 - 0.165028i) q^{46} +(-6.47160 + 6.47160i) q^{47} +(-2.48976 + 1.43746i) q^{48} +(3.23380 - 0.866493i) q^{50} -5.38892i q^{51} +(-0.351808 - 6.67363i) q^{52} +12.5624 q^{53} +(1.74630 - 0.467921i) q^{54} +(-0.281283 - 0.162399i) q^{55} +(-2.40192 + 2.40192i) q^{57} +(-0.522347 - 0.139962i) q^{58} +(-6.90954 - 1.85141i) q^{59} +(-4.44564 - 4.44564i) q^{60} +(-0.110587 + 0.0638473i) q^{61} +(0.384727 - 0.666367i) q^{62} -4.69551i q^{64} +(12.7127 - 4.13492i) q^{65} -0.0306748i q^{66} +(-2.57703 - 9.61759i) q^{67} +(9.45519 + 5.45896i) q^{68} +(-0.204185 - 0.353658i) q^{69} +(-9.83277 - 2.63468i) q^{71} +(-0.825716 + 3.08161i) q^{72} +(-6.47753 + 6.47753i) q^{73} +(0.507376 + 0.878801i) q^{74} +(4.00108 - 6.93007i) q^{75} +(-1.78118 - 6.64744i) q^{76} +(0.938505 + 0.844511i) q^{78} -3.51488 q^{79} +(11.2543 - 3.01557i) q^{80} +(-1.08390 + 1.87736i) q^{81} +(-0.594903 - 1.03040i) q^{82} +(-2.17980 - 2.17980i) q^{83} +(-5.65256 + 21.0956i) q^{85} +(-2.70259 - 2.70259i) q^{86} +(-1.11940 + 0.646284i) q^{87} +(0.111896 + 0.0646030i) q^{88} +(0.437215 + 1.63171i) q^{89} -3.06959 q^{90} +0.827354 q^{92} +(-0.476012 - 1.77650i) q^{93} +(3.03371 + 1.75151i) q^{94} +(11.9220 - 6.88319i) q^{95} +(2.68637 + 2.68637i) q^{96} +(-0.452103 + 1.68727i) q^{97} +(0.133986 + 0.133986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	−0.0990633	−	0.369709i	−0.0700483	−	0.261424i	0.922017	−	0.387150i	$-0.126541\pi$
$2$	−0.0990633	−	0.369709i	−0.0700483	−	0.261424i	−0.992065	+	0.125726i	$0.959874\pi$
$3$	−0.792292	−	0.457430i	−0.457430	−	0.264097i	0.253533	−	0.967327i	$-0.418407\pi$
$3$	−0.792292	−	0.457430i	−0.457430	−	0.264097i	−0.710963	+	0.703229i	$0.751741\pi$
$4$	1.60518	−	0.926751i	0.802590	−	0.463375i
$5$	2.62172	+	2.62172i	1.17247	+	1.17247i	0.981619	+	0.190851i	$0.0611248\pi$
$5$	2.62172	+	2.62172i	1.17247	+	1.17247i	0.190851	+	0.981619i	$0.438875\pi$
$6$	−0.0906291	+	0.338232i	−0.0369992	+	0.138083i
$7$		0			0
$7$		0			0
$8$	−1.04293	−	1.04293i	−0.368733	−	0.368733i
$9$	−1.08152	−	1.87324i	−0.360505	−	0.624413i
$10$	0.709559	−	1.22899i	0.224382	−	0.388641i
$11$	−0.0846164	+	0.0226729i	−0.0255128	+	0.00683614i	−0.271553	−	0.962424i	$-0.587537\pi$
$11$	−0.0846164	+	0.0226729i	−0.0255128	+	0.00683614i	0.246040	+	0.969260i	$0.420871\pi$
$12$	−1.69570			−0.489505
$13$	1.63590	−	3.21307i	0.453716	−	0.891146i
$13$	1.63590	−	3.21307i	0.453716	−	0.891146i
$14$		0			0
$15$	−0.877916	−	3.27643i	−0.226677	−	0.845970i
$16$	1.57124	−	2.72146i	0.392809	−	0.680365i
$17$	2.94521	+	5.10126i	0.714319	+	1.23724i	0.963221	+	0.268709i	$0.0865969\pi$
$17$	2.94521	+	5.10126i	0.714319	+	1.23724i	−0.248902	+	0.968529i	$0.580070\pi$
$18$	−0.585415	+	0.585415i	−0.137984	+	0.137984i
$19$	0.960980	−	3.58643i	0.220464	−	0.822782i	−0.763707	−	0.645563i	$-0.776623\pi$
$19$	0.960980	−	3.58643i	0.220464	−	0.822782i	0.984171	−	0.177220i	$-0.0567104\pi$
$20$	6.63802	+	1.77865i	1.48431	+	0.397719i
$21$		0			0
$22$	0.0167648	+	0.0290374i	0.00357426	+	0.00619080i
$23$	0.386571	+	0.223187i	0.0806056	+	0.0465377i	0.539761	−	0.841818i	$-0.318515\pi$
$23$	0.386571	+	0.223187i	0.0806056	+	0.0465377i	−0.459155	+	0.888356i	$0.651848\pi$
$24$	0.349239	+	1.30338i	0.0712882	+	0.266051i
$25$			8.74686i			1.74937i
$26$	−1.34996	−	0.286509i	−0.264749	−	0.0561890i
$27$			4.72345i			0.909029i
$28$		0			0
$29$	0.706429	−	1.22357i	0.131181	−	0.227212i	−0.792951	−	0.609285i	$-0.791457\pi$
$29$	0.706429	−	1.22357i	0.131181	−	0.227212i	0.924132	+	0.382073i	$0.124790\pi$
$30$	−1.12436	+	0.649147i	−0.205278	+	0.118518i
$31$	1.42152	+	1.42152i	0.255312	+	0.255312i	0.823144	−	0.567832i	$-0.192218\pi$
$31$	1.42152	+	1.42152i	0.255312	+	0.255312i	−0.567832	+	0.823144i	$0.692218\pi$
$32$	−4.01115	−	1.07478i	−0.709078	−	0.189997i
$33$	0.0774122	+	0.0207425i	0.0134757	+	0.00361081i
$34$	1.59422	−	1.59422i	0.273406	−	0.273406i
$35$		0			0
$36$	−3.47205	−	2.00459i	−0.578675	−	0.334098i
$37$	−2.56087	+	0.686183i	−0.421004	+	0.112808i	−0.463100	−	0.886306i	$-0.653263\pi$
$37$	−2.56087	+	0.686183i	−0.421004	+	0.112808i	0.0420961	+	0.999114i	$0.486596\pi$
$38$	−1.42113			−0.230538
$39$	−2.76587	+	1.79738i	−0.442893	+	0.287812i
$40$		−	5.46857i		−	0.864657i
$41$	3.00264	−	0.804556i	0.468934	−	0.125651i	−0.0166112	−	0.999862i	$-0.505288\pi$
$41$	3.00264	−	0.804556i	0.468934	−	0.125651i	0.485545	+	0.874211i	$0.338621\pi$
$42$		0			0
$43$	8.64788	−	4.99286i	1.31879	−	0.761404i	0.335256	−	0.942127i	$-0.391177\pi$
$43$	8.64788	−	4.99286i	1.31879	−	0.761404i	0.983534	+	0.180724i	$0.0578439\pi$
$44$	−0.114812	+	0.114812i	−0.0173086	+	0.0173086i
$45$	2.07568	−	7.74655i	0.309424	−	1.15479i
$46$	0.0442192	−	0.165028i	0.00651977	−	0.0243321i
$47$	−6.47160	+	6.47160i	−0.943980	+	0.943980i	−0.998512	−	0.0545322i	$-0.982633\pi$
$47$	−6.47160	+	6.47160i	−0.943980	+	0.943980i	0.0545322	+	0.998512i	$0.482633\pi$
$48$	−2.48976	+	1.43746i	−0.359365	+	0.207480i
$49$		0			0
$50$	3.23380	−	0.866493i	0.457328	−	0.122541i
$51$		−	5.38892i		−	0.754600i
$52$	−0.351808	−	6.67363i	−0.0487871	−	0.925466i
$53$	12.5624			1.72557			0.862786	−	0.505570i	$-0.168718\pi$
$53$	12.5624			1.72557			0.862786	+	0.505570i	$0.168718\pi$
$54$	1.74630	−	0.467921i	0.237642	−	0.0636759i
$55$	−0.281283	−	0.162399i	−0.0379282	−	0.0218978i
$56$		0			0
$57$	−2.40192	+	2.40192i	−0.318142	+	0.318142i
$58$	−0.522347	−	0.139962i	−0.0685875	−	0.0183780i
$59$	−6.90954	−	1.85141i	−0.899545	−	0.241032i	−0.220724	−	0.975336i	$-0.570842\pi$
$59$	−6.90954	−	1.85141i	−0.899545	−	0.241032i	−0.678821	+	0.734304i	$0.737509\pi$
$60$	−4.44564	−	4.44564i	−0.573930	−	0.573930i
$61$	−0.110587	+	0.0638473i	−0.0141592	+	0.00817481i	−0.507063	−	0.861909i	$-0.669269\pi$
$61$	−0.110587	+	0.0638473i	−0.0141592	+	0.00817481i	0.492904	+	0.870084i	$0.335935\pi$
$62$	0.384727	−	0.666367i	0.0488604	−	0.0846287i
$63$		0			0
$64$		−	4.69551i		−	0.586939i
$65$	12.7127	−	4.13492i	1.57681	−	0.512873i
$66$		−	0.0306748i		−	0.00377581i
$67$	−2.57703	−	9.61759i	−0.314834	−	1.17498i	−0.924144	−	0.382044i	$-0.875220\pi$
$67$	−2.57703	−	9.61759i	−0.314834	−	1.17498i	0.609310	−	0.792932i	$-0.291446\pi$
$68$	9.45519	+	5.45896i	1.14661	+	0.661996i
$69$	−0.204185	−	0.353658i	−0.0245810	−	0.0425755i
$70$		0			0
$71$	−9.83277	−	2.63468i	−1.16694	−	0.312679i	−0.377203	−	0.926131i	$-0.623114\pi$
$71$	−9.83277	−	2.63468i	−1.16694	−	0.312679i	−0.789732	+	0.613451i	$0.789781\pi$
$72$	−0.825716	+	3.08161i	−0.0973116	+	0.363172i
$73$	−6.47753	+	6.47753i	−0.758137	+	0.758137i	−0.975983	−	0.217846i	$-0.930097\pi$
$73$	−6.47753	+	6.47753i	−0.758137	+	0.758137i	0.217846	+	0.975983i	$0.430097\pi$
$74$	0.507376	+	0.878801i	0.0589813	+	0.102159i
$75$	4.00108	−	6.93007i	0.462005	−	0.800216i
$76$	−1.78118	−	6.64744i	−0.204315	−	0.762514i
$77$		0			0
$78$	0.938505	+	0.844511i	0.106265	+	0.0956221i
$79$	−3.51488			−0.395455			−0.197728	−	0.980257i	$-0.563356\pi$
$79$	−3.51488			−0.395455			−0.197728	+	0.980257i	$0.563356\pi$
$80$	11.2543	−	3.01557i	1.25826	−	0.337151i
$81$	−1.08390	+	1.87736i	−0.120433	+	0.208596i
$82$	−0.594903	−	1.03040i	−0.0656961	−	0.113789i
$83$	−2.17980	−	2.17980i	−0.239264	−	0.239264i	0.577281	−	0.816545i	$-0.304114\pi$
$83$	−2.17980	−	2.17980i	−0.239264	−	0.239264i	−0.816545	+	0.577281i	$0.804114\pi$
$84$		0			0
$85$	−5.65256	+	21.0956i	−0.613106	+	2.28814i
$86$	−2.70259	−	2.70259i	−0.291428	−	0.291428i
$87$	−1.11940	+	0.646284i	−0.120012	+	0.0692890i
$88$	0.111896	+	0.0646030i	0.0119281	+	0.00688670i
$89$	0.437215	+	1.63171i	0.0463447	+	0.172961i	0.985219	−	0.171299i	$-0.0547965\pi$
$89$	0.437215	+	1.63171i	0.0463447	+	0.172961i	−0.938874	+	0.344260i	$0.888130\pi$
$90$	−3.06959			−0.323564
$91$		0			0
$92$	0.827354			0.0862576
$93$	−0.476012	−	1.77650i	−0.0493601	−	0.184214i
$94$	3.03371	+	1.75151i	0.312903	+	0.180655i
$95$	11.9220	−	6.88319i	1.22318	−	0.706200i
$96$	2.68637	+	2.68637i	0.274176	+	0.274176i
$97$	−0.452103	+	1.68727i	−0.0459041	+	0.171317i	−0.985072	−	0.172141i	$-0.944932\pi$
$97$	−0.452103	+	1.68727i	−0.0459041	+	0.171317i	0.939168	+	0.343458i	$0.111598\pi$
$98$		0			0
$99$	0.133986	+	0.133986i	0.0134661	+	0.0134661i
$100$	8.10616	+	14.0403i	0.810616	+	1.40403i
$101$	−3.41120	+	5.90838i	−0.339427	+	0.587905i	−0.984325	−	0.176363i	$-0.943567\pi$
$101$	−3.41120	+	5.90838i	−0.339427	+	0.587905i	0.644898	+	0.764269i	$0.276900\pi$
$102$	−1.99233	+	0.533844i	−0.197270	+	0.0528584i
$103$	−10.0006			−0.985387			−0.492693	−	0.870203i	$-0.663988\pi$
$103$	−10.0006			−0.985387			−0.492693	+	0.870203i	$0.663988\pi$
$104$	−5.05716	+	1.64489i	−0.495895	+	0.161295i
$105$		0			0
$106$	−1.24447	−	4.64442i	−0.120873	−	0.451106i
$107$	0.0299435	−	0.0518637i	0.00289475	−	0.00501386i	−0.864574	−	0.502505i	$-0.832412\pi$
$107$	0.0299435	−	0.0518637i	0.00289475	−	0.00501386i	0.867469	+	0.497491i	$0.165745\pi$
$108$	4.37746	+	7.58199i	0.421222	+	0.729577i
$109$	−11.6295	+	11.6295i	−1.11391	+	1.11391i	−0.121291	+	0.992617i	$0.538703\pi$
$109$	−11.6295	+	11.6295i	−1.11391	+	1.11391i	−0.992617	+	0.121291i	$0.961297\pi$
$110$	−0.0321755	+	0.120081i	−0.00306781	+	0.0114492i
$111$	2.34284	+	0.627762i	0.222372	+	0.0595845i
$112$		0			0
$113$	2.74673	+	4.75748i	0.258391	+	0.447546i	0.965811	−	0.259247i	$-0.0834744\pi$
$113$	2.74673	+	4.75748i	0.258391	+	0.447546i	−0.707420	+	0.706793i	$0.750141\pi$
$114$	1.12595	+	0.650069i	0.105455	+	0.0608845i
$115$	0.428348	+	1.59862i	0.0399436	+	0.149072i
$116$		−	2.61874i		−	0.243144i
$117$	−7.78810	+	0.410559i	−0.720010	+	0.0379562i
$118$			2.73793i			0.252047i
$119$		0			0
$120$	−2.50149	+	4.33271i	−0.228354	+	0.395520i
$121$	−9.51963	+	5.49616i	−0.865421	+	0.499651i
$122$	0.0345600	+	0.0345600i	0.00312892	+	0.00312892i
$123$	−2.74700	−	0.736057i	−0.247689	−	0.0663680i
$124$	3.59918	+	0.964397i	0.323216	+	0.0866054i
$125$	−9.82324	+	9.82324i	−0.878617	+	0.878617i
$126$		0			0
$127$	14.7405	+	8.51045i	1.30801	+	0.755180i	0.981764	−	0.190104i	$-0.0608826\pi$
$127$	14.7405	+	8.51045i	1.30801	+	0.755180i	0.326247	+	0.945285i	$0.394216\pi$
$128$	−9.75827	+	2.61472i	−0.862518	+	0.231111i
$129$	−9.13554			−0.804339
$130$	−2.78807	−	4.29037i	−0.244530	−	0.376290i
$131$			2.72010i			0.237656i	0.992915	+	0.118828i	$0.0379137\pi$
$131$			2.72010i			0.237656i	−0.992915	+	0.118828i	$0.962086\pi$
$132$	0.143484	−	0.0384463i	0.0124886	−	0.00334632i
$133$		0			0
$134$	−3.30042	+	1.90550i	−0.285113	+	0.164610i
$135$	−12.3836	+	12.3836i	−1.06581	+	1.06581i
$136$	2.24861	−	8.39194i	0.192817	−	0.719603i
$137$	−1.11493	+	4.16096i	−0.0952545	+	0.355495i	−0.997058	−	0.0766518i	$-0.975577\pi$
$137$	−1.11493	+	4.16096i	−0.0952545	+	0.355495i	0.901803	+	0.432147i	$0.142244\pi$
$138$	−0.110524	+	0.110524i	−0.00940839	+	0.00940839i
$139$	−12.1251	+	7.00040i	−1.02843	+	0.593766i	−0.916535	−	0.399953i	$-0.869026\pi$
$139$	−12.1251	+	7.00040i	−1.02843	+	0.593766i	−0.111898	+	0.993720i	$0.535693\pi$
$140$		0			0
$141$	8.08771	−	2.16709i	0.681108	−	0.182502i
$142$			3.89627i			0.326967i
$143$	−0.0655741	+	0.308969i	−0.00548358	+	0.0258373i
$144$	−6.79726			−0.566438
$145$	5.05993	−	1.35580i	0.420204	−	0.112593i
$146$	3.03649	+	1.75312i	0.251301	+	0.145089i
$147$		0			0
$148$	−3.47473	+	3.47473i	−0.285621	+	0.285621i
$149$	8.85786	+	2.37346i	0.725664	+	0.194441i	0.602698	−	0.797970i	$-0.294092\pi$
$149$	8.85786	+	2.37346i	0.725664	+	0.194441i	0.122967	+	0.992411i	$0.460759\pi$
$150$	−2.95847	−	0.792720i	−0.241558	−	0.0647253i
$151$	5.36711	+	5.36711i	0.436770	+	0.436770i	0.890923	−	0.454154i	$-0.150058\pi$
$151$	5.36711	+	5.36711i	0.436770	+	0.436770i	−0.454154	+	0.890923i	$0.650058\pi$
$152$	−4.74264	+	2.73817i	−0.384679	+	0.222095i
$153$	6.37059	−	11.0342i	0.515031	−	0.892061i
$154$		0			0
$155$			7.45364i			0.598691i
$156$	−2.77398	+	5.44839i	−0.222097	+	0.436221i
$157$			0.505783i			0.0403658i	0.999796	+	0.0201829i	$0.00642486\pi$
$157$			0.505783i			0.0403658i	−0.999796	+	0.0201829i	$0.993575\pi$
$158$	0.348196	+	1.29948i	0.0277010	+	0.103381i
$159$	−9.95306	−	5.74640i	−0.789329	−	0.455719i
$160$	−7.69834	−	13.3339i	−0.608607	−	1.05414i
$161$		0			0
$162$	0.801452	+	0.214748i	0.0629680	+	0.0168722i
$163$	1.14944	−	4.28976i	0.0900308	−	0.336000i	−0.906188	−	0.422874i	$-0.861021\pi$
$163$	1.14944	−	4.28976i	0.0900308	−	0.336000i	0.996219	+	0.0868745i	$0.0276879\pi$
$164$	4.07416	−	4.07416i	0.318138	−	0.318138i
$165$	0.148572	+	0.257335i	0.0115663	+	0.0200335i
$166$	−0.589953	+	1.02183i	−0.0457892	+	0.0793093i
$167$	−2.07730	−	7.75258i	−0.160746	−	0.599913i	−0.998545	−	0.0539330i	$-0.982824\pi$
$167$	−2.07730	−	7.75258i	−0.160746	−	0.599913i	0.837798	−	0.545980i	$-0.183842\pi$
$168$		0			0
$169$	−7.64768	−	10.5125i	−0.588283	−	0.808655i
$170$	8.35921			0.641122
$171$	−7.75755	+	2.07863i	−0.593234	+	0.158957i
$172$	9.25427	−	16.0289i	0.705631	−	1.22219i
$173$	0.631547	+	1.09387i	0.0480157	+	0.0831656i	0.889034	−	0.457841i	$-0.151377\pi$
$173$	0.631547	+	1.09387i	0.0480157	+	0.0831656i	−0.841019	+	0.541006i	$0.818044\pi$
$174$	0.349828	+	0.349828i	0.0265204	+	0.0265204i
$175$		0			0
$176$	−0.0712489	+	0.265905i	−0.00537059	+	0.0200433i
$177$	4.62749	+	4.62749i	0.347823	+	0.347823i
$178$	0.559946	−	0.323285i	0.0419697	−	0.0242312i
$179$	−1.46377	−	0.845110i	−0.109408	−	0.0631665i	0.444298	−	0.895879i	$-0.353453\pi$
$179$	−1.46377	−	0.845110i	−0.109408	−	0.0631665i	−0.553705	+	0.832713i	$0.686787\pi$
$180$	−3.84728	−	14.3582i	−0.286759	−	1.07020i
$181$	−8.30825			−0.617547			−0.308774	−	0.951136i	$-0.599919\pi$
$181$	−8.30825			−0.617547			−0.308774	+	0.951136i	$0.599919\pi$
$182$		0			0
$183$	0.116823			0.00863578
$184$	−0.170399	−	0.635937i	−0.0125620	−	0.0468819i
$185$	−8.51287	−	4.91491i	−0.625879	−	0.361351i
$186$	−0.609633	+	0.351972i	−0.0447005	+	0.0258078i
$187$	−0.364874	−	0.364874i	−0.0266822	−	0.0266822i
$188$	−4.39052	+	16.3856i	−0.320211	+	1.19505i
$189$		0			0
$190$	−3.72581	−	3.72581i	−0.270299	−	0.270299i
$191$	−10.3140	−	17.8644i	−0.746296	−	1.29262i	−0.949587	−	0.313505i	$-0.898497\pi$
$191$	−10.3140	−	17.8644i	−0.746296	−	1.29262i	0.203290	−	0.979119i	$-0.434836\pi$
$192$	−2.14787	+	3.72022i	−0.155009	+	0.268484i
$193$	12.9503	−	3.47003i	0.932186	−	0.249779i	0.239400	−	0.970921i	$-0.423049\pi$
$193$	12.9503	−	3.47003i	0.932186	−	0.249779i	0.692787	+	0.721143i	$0.256383\pi$
$194$	0.668587			0.0480017
$195$	−11.9636	−	2.53909i	−0.856730	−	0.181828i
$196$		0			0
$197$	4.28034	+	15.9744i	0.304961	+	1.13813i	0.932979	+	0.359932i	$0.117200\pi$
$197$	4.28034	+	15.9744i	0.304961	+	1.13813i	−0.628017	+	0.778199i	$0.716133\pi$
$198$	0.0362627	−	0.0628088i	0.00257708	−	0.00446363i
$199$	−6.48108	−	11.2256i	−0.459432	−	0.795759i	0.539499	−	0.841986i	$-0.318614\pi$
$199$	−6.48108	−	11.2256i	−0.459432	−	0.795759i	−0.998931	+	0.0462272i	$0.985280\pi$
$200$	9.12240	−	9.12240i	0.645051	−	0.645051i
$201$	−2.35762	+	8.79875i	−0.166294	+	0.620616i
$202$	2.52231	+	0.675850i	0.177469	+	0.0475526i
$203$		0			0
$204$	−4.99419	−	8.65018i	−0.349663	−	0.605634i
$205$	9.98142	+	5.76278i	0.697133	+	0.402490i
$206$	0.990691	+	3.69731i	0.0690247	+	0.257604i
$207$		−	0.965519i		−	0.0671082i
$208$	−6.17387	−	9.50053i	−0.428081	−	0.658743i
$209$			0.325259i			0.0224986i
$210$		0			0
$211$	−3.19052	+	5.52614i	−0.219644	+	0.380435i	−0.954699	−	0.297572i	$-0.903823\pi$
$211$	−3.19052	+	5.52614i	−0.219644	+	0.380435i	0.735055	+	0.678008i	$0.237156\pi$
$212$	20.1648	−	11.6422i	1.38493	−	0.799587i
$213$	6.58525	+	6.58525i	0.451214	+	0.451214i
$214$	−0.0221408	−	0.00593261i	−0.00151351	−	0.000405545i
$215$	35.7622	+	9.58246i	2.43896	+	0.653519i
$216$	4.92625	−	4.92625i	0.335189	−	0.335189i
$217$		0			0
$218$	5.45161	+	3.14749i	0.369229	+	0.213175i
$219$	8.09512	−	2.16908i	0.547017	−	0.146573i
$220$	−0.602013			−0.0405877
$221$	21.2088	−	1.11805i	1.42666	−	0.0752080i
$222$		−	0.928357i		−	0.0623072i
$223$	12.3622	−	3.31244i	0.827834	−	0.221817i	0.180065	−	0.983655i	$-0.442369\pi$
$223$	12.3622	−	3.31244i	0.827834	−	0.221817i	0.647769	+	0.761837i	$0.275702\pi$
$224$		0			0
$225$	16.3850	−	9.45986i	1.09233	−	0.630658i
$226$	1.48678	−	1.48678i	0.0988994	−	0.0988994i
$227$	−3.06900	+	11.4537i	−0.203697	+	0.760207i	0.786146	+	0.618041i	$0.212073\pi$
$227$	−3.06900	+	11.4537i	−0.203697	+	0.760207i	−0.989843	+	0.142166i	$0.954593\pi$
$228$	−1.62953	+	6.08148i	−0.107918	+	0.402756i
$229$	−11.1707	+	11.1707i	−0.738180	+	0.738180i	−0.972226	−	0.234046i	$-0.924803\pi$
$229$	−11.1707	+	11.1707i	−0.738180	+	0.738180i	0.234046	+	0.972226i	$0.424803\pi$
$230$	0.548589	−	0.316728i	0.0361729	−	0.0208844i
$231$		0			0
$232$	−2.01286	+	0.539345i	−0.132151	+	0.0354098i
$233$			13.4018i			0.877979i	0.898492	+	0.438989i	$0.144663\pi$
$233$			13.4018i			0.877979i	−0.898492	+	0.438989i	$0.855337\pi$
$234$	0.923302	+	2.83866i	0.0603582	+	0.185569i
$235$	−33.9335			−2.21358
$236$	−12.8068	+	3.43158i	−0.833654	+	0.223377i
$237$	2.78482	+	1.60781i	0.180893	+	0.104439i
$238$		0			0
$239$	−14.4526	+	14.4526i	−0.934861	+	0.934861i	−0.998004	−	0.0631438i	$-0.979887\pi$
$239$	−14.4526	+	14.4526i	−0.934861	+	0.934861i	0.0631438	+	0.998004i	$0.479887\pi$
$240$	−10.2961	−	2.75883i	−0.664609	−	0.178081i
$241$	−0.986010	−	0.264201i	−0.0635145	−	0.0170187i	0.226922	−	0.973913i	$-0.427134\pi$
$241$	−0.986010	−	0.264201i	−0.0635145	−	0.0170187i	−0.290436	+	0.956894i	$0.593800\pi$
$242$	2.97503	+	2.97503i	0.191242	+	0.191242i
$243$	13.9894	−	8.07679i	0.897421	−	0.518126i
$244$	−0.118341	+	0.204973i	−0.00757601	+	0.0131220i
$245$		0			0
$246$			1.08851i			0.0694007i
$247$	−9.95138	−	8.95472i	−0.633191	−	0.569775i
$248$		−	2.96509i		−	0.188284i
$249$	0.729932	+	2.72414i	0.0462575	+	0.172635i
$250$	4.60486	+	2.65862i	0.291237	+	0.168146i
$251$	−5.59470	−	9.69030i	−0.353134	−	0.611646i	0.633663	−	0.773609i	$-0.281551\pi$
$251$	−5.59470	−	9.69030i	−0.353134	−	0.611646i	−0.986797	+	0.161963i	$0.948217\pi$
$252$		0			0
$253$	−0.0377705	−	0.0101206i	−0.00237461	−	0.000636275i
$254$	1.68615	−	6.29278i	0.105798	−	0.394844i
$255$	14.1283	−	14.1283i	0.884746	−	0.884746i
$256$	−2.76214	−	4.78417i	−0.172634	−	0.299010i
$257$	4.71336	−	8.16379i	0.294012	−	0.509243i	−0.680743	−	0.732522i	$-0.738343\pi$
$257$	4.71336	−	8.16379i	0.294012	−	0.509243i	0.974754	+	0.223279i	$0.0716762\pi$
$258$	0.904996	+	3.37749i	0.0563426	+	0.210273i
$259$		0			0
$260$	16.5741	−	18.4187i	1.02788	−	1.14228i
$261$	−3.05606			−0.189165
$262$	1.00564	−	0.269462i	0.0621289	−	0.0166474i
$263$	−6.87360	+	11.9054i	−0.423844	+	0.734120i	−0.996312	−	0.0858074i	$-0.972653\pi$
$263$	−6.87360	+	11.9054i	−0.423844	+	0.734120i	0.572467	+	0.819928i	$0.305986\pi$
$264$	−0.0591027	−	0.102369i	−0.00363752	−	0.00630037i
$265$	32.9350	+	32.9350i	2.02318	+	2.02318i
$266$		0			0
$267$	0.399991	−	1.49279i	0.0244790	−	0.0913570i
$268$	−13.0497	−	13.0497i	−0.797137	−	0.797137i
$269$	20.4250	−	11.7924i	1.24534	−	0.718995i	0.275161	−	0.961398i	$-0.411269\pi$
$269$	20.4250	−	11.7924i	1.24534	−	0.718995i	0.970176	+	0.242403i	$0.0779355\pi$
$270$	5.80508	+	3.35157i	0.353286	+	0.203970i
$271$	−2.35282	−	8.78083i	−0.142923	−	0.533397i	−0.999839	−	0.0179406i	$-0.994289\pi$
$271$	−2.35282	−	8.78083i	−0.142923	−	0.533397i	0.856916	−	0.515457i	$-0.172378\pi$
$272$	18.5105			1.12236
$273$		0			0
$274$	1.64879			0.0996072
$275$	−0.198317	−	0.740128i	−0.0119589	−	0.0446314i
$276$	−0.655506	−	0.378457i	−0.0394568	−	0.0227804i
$277$	−10.9662	+	6.33135i	−0.658897	+	0.380414i	−0.791856	−	0.610707i	$-0.790885\pi$
$277$	−10.9662	+	6.33135i	−0.658897	+	0.380414i	0.132960	+	0.991121i	$0.457552\pi$
$278$	3.78926	+	3.78926i	0.227265	+	0.227265i
$279$	1.12545	−	4.20023i	0.0673788	−	0.251461i
$280$		0			0
$281$	−23.5896	−	23.5896i	−1.40724	−	1.40724i	−0.773769	−	0.633468i	$-0.781631\pi$
$281$	−23.5896	−	23.5896i	−1.40724	−	1.40724i	−0.633468	−	0.773769i	$-0.718369\pi$
$282$	−1.60239	−	2.77542i	−0.0954209	−	0.165274i
$283$	−11.4194	+	19.7790i	−0.678813	+	1.17574i	0.296526	+	0.955025i	$0.404172\pi$
$283$	−11.4194	+	19.7790i	−0.678813	+	1.17574i	−0.975339	+	0.220713i	$0.929162\pi$
$284$	−18.2251	+	4.88339i	−1.08146	+	0.289776i
$285$	−12.5943			−0.746023
$286$	0.120725	−	0.00636415i	0.00713860	−	0.000376320i
$287$		0			0
$288$	2.32479	+	8.67624i	0.136990	+	0.511252i
$289$	−8.84857	+	15.3262i	−0.520504	+	0.901540i
$290$	−1.00251	−	1.73639i	−0.0588692	−	0.101964i
$291$	1.13001	−	1.13001i	0.0662422	−	0.0662422i
$292$	−4.39454	+	16.4007i	−0.257171	+	0.959776i
$293$	11.5762	+	3.10184i	0.676290	+	0.181211i	0.580587	−	0.814198i	$-0.302823\pi$
$293$	11.5762	+	3.10184i	0.676290	+	0.181211i	0.0957036	+	0.995410i	$0.469490\pi$
$294$		0			0
$295$	−13.2610	−	22.9688i	−0.772087	−	1.33729i
$296$	3.38646	+	1.95517i	0.196834	+	0.113642i
$297$	−0.107094	−	0.399682i	−0.00621424	−	0.0231919i
$298$		−	3.50996i		−	0.203326i
$299$	1.34951	−	0.876969i	0.0780439	−	0.0507164i
$300$		−	14.8320i		−	0.856327i
$301$		0			0
$302$	1.45259	−	2.51596i	0.0835870	−	0.144777i
$303$	5.40534	−	3.12078i	0.310529	−	0.179284i
$304$	−8.25039	−	8.25039i	−0.473192	−	0.473192i
$305$	−0.457318	−	0.122538i	−0.0261859	−	0.00701650i
$306$	−4.71053	−	1.26218i	−0.269283	−	0.0721542i
$307$	−18.9842	+	18.9842i	−1.08348	+	1.08348i	−0.0873012	+	0.996182i	$0.527824\pi$
$307$	−18.9842	+	18.9842i	−1.08348	+	1.08348i	−0.996182	+	0.0873012i	$0.972176\pi$
$308$		0			0
$309$	7.92339	+	4.57457i	0.450746	+	0.260238i
$310$	2.75568	−	0.738382i	0.156512	−	0.0419373i
$311$	29.7982			1.68970			0.844851	−	0.535001i	$-0.179689\pi$
$311$	29.7982			1.68970			0.844851	+	0.535001i	$0.179689\pi$
$312$	4.75917	+	1.01006i	0.269435	+	0.0571836i
$313$			16.3526i			0.924302i	0.886801	+	0.462151i	$0.152922\pi$
$313$			16.3526i			0.924302i	−0.886801	+	0.462151i	$0.847078\pi$
$314$	0.186992	−	0.0501045i	0.0105526	−	0.00282756i
$315$		0			0
$316$	−5.64202	+	3.25742i	−0.317388	+	0.183244i
$317$	12.0760	−	12.0760i	0.678257	−	0.678257i	−0.281349	−	0.959606i	$-0.590782\pi$
$317$	12.0760	−	12.0760i	0.678257	−	0.678257i	0.959606	+	0.281349i	$0.0907819\pi$
$318$	−1.13851	+	4.24899i	−0.0638447	+	0.238272i
$319$	−0.0320336	+	0.119551i	−0.00179354	+	0.00669357i
$320$	12.3103	−	12.3103i	0.688169	−	0.688169i
$321$	−0.0474481	+	0.0273942i	−0.00264829	+	0.00152899i
$322$		0			0
$323$	21.1256	−	5.66058i	1.17546	−	0.314963i
$324$			4.01800i			0.223222i
$325$	28.1043	+	14.3090i	1.55895	+	0.793719i
$326$	−1.69983			−0.0941448
$327$	14.5337	−	3.89429i	0.803716	−	0.215355i
$328$	−3.97066	−	2.29246i	−0.219243	−	0.126580i
$329$		0			0
$330$	0.0804209	−	0.0804209i	0.00442702	−	0.00442702i
$331$	−21.0345	−	5.63617i	−1.15616	−	0.309792i	−0.370728	−	0.928742i	$-0.620892\pi$
$331$	−21.0345	−	5.63617i	−1.15616	−	0.309792i	−0.785430	+	0.618950i	$0.787558\pi$
$332$	−5.51909	−	1.47884i	−0.302900	−	0.0811617i
$333$	4.05500	+	4.05500i	0.222213	+	0.222213i
$334$	−2.66042	+	1.53599i	−0.145571	+	0.0840457i
$335$	18.4584	−	31.9709i	1.00849	−	1.74676i
$336$		0			0
$337$		−	22.6556i		−	1.23413i	−0.786912	−	0.617066i	$-0.788321\pi$
$337$		−	22.6556i		−	1.23413i	0.786912	−	0.617066i	$-0.211679\pi$
$338$	−3.12897	+	3.86882i	−0.170194	+	0.210436i
$339$		−	5.02575i		−	0.272962i
$340$	10.4770	+	39.1008i	0.568196	+	2.12054i
$341$	−0.152513	−	0.0880536i	−0.00825906	−	0.00476837i
$342$	1.53698	+	2.66212i	0.0831101	+	0.143951i
$343$		0			0
$344$	−14.2264	−	3.81195i	−0.767036	−	0.205527i
$345$	0.391878	−	1.46251i	0.0210980	−	0.0787389i
$346$	0.341851	−	0.341851i	0.0183780	−	0.0183780i
$347$	−5.93541	−	10.2804i	−0.318630	−	0.551883i	0.661573	−	0.749881i	$-0.269889\pi$
$347$	−5.93541	−	10.2804i	−0.318630	−	0.551883i	−0.980202	+	0.197998i	$0.936556\pi$
$348$	−1.19789	+	2.07481i	−0.0642136	+	0.111221i
$349$	−5.38273	−	20.0886i	−0.288131	−	1.07532i	−0.946521	−	0.322642i	$-0.895429\pi$
$349$	−5.38273	−	20.0886i	−0.288131	−	1.07532i	0.658390	−	0.752677i	$-0.271238\pi$
$350$		0			0
$351$	15.1768	+	7.72709i	0.810078	+	0.412441i
$352$	0.363778			0.0193894
$353$	−27.0009	+	7.23488i	−1.43712	+	0.385074i	−0.891522	−	0.452977i	$-0.850362\pi$
$353$	−27.0009	+	7.23488i	−1.43712	+	0.385074i	−0.545593	+	0.838050i	$0.683695\pi$
$354$	1.25241	−	2.16924i	0.0665649	−	0.115294i
$355$	−18.8714	−	32.6862i	−1.00159	−	1.73480i
$356$	2.21400	+	2.21400i	0.117342	+	0.117342i
$357$		0			0
$358$	−0.167439	+	0.624890i	−0.00884941	+	0.0330265i
$359$	11.0950	+	11.0950i	0.585573	+	0.585573i	0.936429	−	0.350857i	$-0.114110\pi$
$359$	11.0950	+	11.0950i	0.585573	+	0.585573i	−0.350857	+	0.936429i	$0.614110\pi$
$360$	−10.2439	+	5.91434i	−0.539903	+	0.311713i
$361$	4.51552	+	2.60704i	0.237659	+	0.137212i
$362$	0.823042	+	3.07164i	0.0432581	+	0.161442i
$363$	10.0564			0.527826
$364$		0			0
$365$	−33.9646			−1.77779
$366$	−0.0115728	−	0.0431904i	−0.000604922	−	0.00225760i
$367$	−4.15012	−	2.39607i	−0.216635	−	0.125074i	0.387756	−	0.921762i	$-0.373250\pi$
$367$	−4.15012	−	2.39607i	−0.216635	−	0.125074i	−0.604391	+	0.796688i	$0.706584\pi$
$368$	1.21479	−	0.701358i	0.0633252	−	0.0365608i
$369$	−4.75453	−	4.75453i	−0.247511	−	0.247511i
$370$	−0.973774	+	3.63417i	−0.0506241	+	0.188932i
$371$		0			0
$372$	−2.41046	−	2.41046i	−0.124976	−	0.124976i
$373$	−0.941886	−	1.63140i	−0.0487690	−	0.0844704i	0.840610	−	0.541640i	$-0.182196\pi$
$373$	−0.941886	−	1.63140i	−0.0487690	−	0.0844704i	−0.889379	+	0.457170i	$0.848863\pi$
$374$	−0.0987516	+	0.171043i	−0.00510632	+	0.00884441i
$375$	12.2763	−	3.28943i	0.633947	−	0.169865i
$376$	13.4989			0.696153
$377$	−2.77578	−	4.27145i	−0.142960	−	0.219991i
$378$		0			0
$379$	−0.368612	−	1.37568i	−0.0189343	−	0.0706638i	0.955812	−	0.293978i	$-0.0949792\pi$
$379$	−0.368612	−	1.37568i	−0.0189343	−	0.0706638i	−0.974747	+	0.223314i	$0.928312\pi$
$380$	12.7580	−	22.0975i	0.654472	−	1.13358i
$381$	−7.78588	−	13.4855i	−0.398882	−	0.690885i
$382$	−5.58289	+	5.58289i	−0.285646	+	0.285646i
$383$	−2.83233	+	10.5704i	−0.144725	+	0.540122i	0.855042	+	0.518559i	$0.173531\pi$
$383$	−2.83233	+	10.5704i	−0.144725	+	0.540122i	−0.999767	+	0.0215638i	$0.993135\pi$
$384$	8.92746	+	2.39211i	0.455578	+	0.122072i
$385$		0			0
$386$	−2.56581	−	4.44411i	−0.130596	−	0.226199i
$387$	−18.7056	−	10.7997i	−0.950861	−	0.548980i
$388$	0.837974	+	3.12736i	0.0425417	+	0.158768i
$389$		−	27.7110i		−	1.40500i	−0.711682	−	0.702502i	$-0.752066\pi$
$389$		−	27.7110i		−	1.40500i	0.711682	−	0.702502i	$-0.247934\pi$
$390$	0.246426	+	4.67458i	0.0124783	+	0.236706i
$391$			2.62933i			0.132971i
$392$		0			0
$393$	1.24425	−	2.15511i	0.0627643	−	0.108711i
$394$	5.48187	−	3.16496i	0.276173	−	0.159448i
$395$	−9.21505	−	9.21505i	−0.463660	−	0.463660i
$396$	0.339242	+	0.0908997i	0.0170476	+	0.00456788i
$397$	12.1417	+	3.25335i	0.609373	+	0.163281i	0.550292	−	0.834972i	$-0.314516\pi$
$397$	12.1417	+	3.25335i	0.609373	+	0.163281i	0.0590806	+	0.998253i	$0.481183\pi$
$398$	−3.50816	+	3.50816i	−0.175848	+	0.175848i
$399$		0			0
$400$	23.8042	+	13.7434i	1.19021	+	0.687169i
$401$	23.8936	−	6.40227i	1.19319	−	0.319714i	0.393044	−	0.919520i	$-0.371422\pi$
$401$	23.8936	−	6.40227i	1.19319	−	0.319714i	0.800146	+	0.599806i	$0.204755\pi$
$402$	3.48653			0.173892
$403$	6.89288	−	2.24198i	0.343359	−	0.111681i
$404$			12.6453i			0.629129i
$405$	−7.76359	+	2.08025i	−0.385776	+	0.103368i
$406$		0			0
$407$	0.201134	−	0.116125i	0.00996983	−	0.00575609i
$408$	−5.62029	+	5.62029i	−0.278246	+	0.278246i
$409$	2.94757	−	11.0005i	0.145748	−	0.543939i	−0.853973	−	0.520317i	$-0.825814\pi$
$409$	2.94757	−	11.0005i	0.145748	−	0.543939i	0.999721	−	0.0236214i	$-0.00751964\pi$
$410$	1.14176	−	4.26110i	0.0563875	−	0.210441i
$411$	2.78670	−	2.78670i	0.137458	−	0.137458i
$412$	−16.0527	+	9.26805i	−0.790861	+	0.456604i
$413$		0			0
$414$	−0.356961	+	0.0956475i	−0.0175437	+	0.00470082i
$415$		−	11.4296i		−	0.561059i
$416$	−10.0152	+	11.1299i	−0.491035	+	0.545687i
$417$	12.8088			0.627249
$418$	0.120251	−	0.0322212i	0.00588167	−	0.00157599i
$419$	25.2233	+	14.5627i	1.23224	+	0.711435i	0.967497	−	0.252884i	$-0.0813791\pi$
$419$	25.2233	+	14.5627i	1.23224	+	0.711435i	0.264744	+	0.964319i	$0.414712\pi$
$420$		0			0
$421$	24.9431	−	24.9431i	1.21565	−	1.21565i	0.246512	−	0.969140i	$-0.420715\pi$
$421$	24.9431	−	24.9431i	1.21565	−	1.21565i	0.969140	−	0.246512i	$-0.0792845\pi$
$422$	2.35913	+	0.632127i	0.114841	+	0.0307714i
$423$	19.1220	+	5.12372i	0.929743	+	0.249124i
$424$	−13.1017	−	13.1017i	−0.636275	−	0.636275i
$425$	−44.6200	+	25.7614i	−2.16439	+	1.24961i
$426$	1.78227	−	3.08698i	0.0863513	−	0.149565i
$427$		0			0
$428$		−	0.111001i		−	0.00536543i
$429$	0.193286	−	0.214798i	0.00933192	−	0.0103706i
$430$		−	14.1709i		−	0.683381i
$431$	−0.845820	−	3.15664i	−0.0407417	−	0.152050i	0.942558	−	0.334041i	$-0.108412\pi$
$431$	−0.845820	−	3.15664i	−0.0407417	−	0.152050i	−0.983300	+	0.181991i	$0.941746\pi$
$432$	12.8547	+	7.42166i	0.618471	+	0.357075i
$433$	−9.82888	−	17.0241i	−0.472346	−	0.818127i	0.527153	−	0.849770i	$-0.323259\pi$
$433$	−9.82888	−	17.0241i	−0.472346	−	0.818127i	−0.999499	+	0.0316430i	$0.989926\pi$
$434$		0			0
$435$	−4.62913	−	1.24037i	−0.221950	−	0.0594713i
$436$	−7.88981	+	29.4452i	−0.377854	+	1.41017i
$437$	1.17193	−	1.17193i	0.0560610	−	0.0560610i
$438$	−1.60386	−	2.77796i	−0.0766353	−	0.132736i
$439$	18.9037	−	32.7422i	0.902226	−	1.56270i	0.0776279	−	0.996982i	$-0.475265\pi$
$439$	18.9037	−	32.7422i	0.902226	−	1.56270i	0.824598	−	0.565719i	$-0.191401\pi$
$440$	0.123988	+	0.462731i	0.00591091	+	0.0220598i
$441$		0			0
$442$	−2.51436	−	7.73033i	−0.119596	−	0.367694i
$443$	−4.63246			−0.220095			−0.110047	−	0.993926i	$-0.535100\pi$
$443$	−4.63246			−0.220095			−0.110047	+	0.993926i	$0.535100\pi$
$444$	4.34245	−	1.16356i	0.206084	−	0.0552200i
$445$	−3.13163	+	5.42414i	−0.148454	+	0.257129i
$446$	−2.44928	−	4.24228i	−0.115977	−	0.200878i
$447$	−5.93233	−	5.93233i	−0.280589	−	0.280589i
$448$		0			0
$449$	−3.43957	+	12.8367i	−0.162324	+	0.605800i	0.836043	+	0.548664i	$0.184863\pi$
$449$	−3.43957	+	12.8367i	−0.162324	+	0.605800i	−0.998366	+	0.0571356i	$0.981803\pi$
$450$	−5.12055	−	5.12055i	−0.241385	−	0.241385i
$451$	−0.235831	+	0.136157i	−0.0111049	+	0.00641140i
$452$	8.81800	+	5.09107i	0.414764	+	0.239464i
$453$	−1.79724	−	6.70741i	−0.0844419	−	0.315141i
$454$	4.53855			0.213005
$455$		0			0
$456$	5.01008			0.234619
$457$	−0.0932123	−	0.347873i	−0.00436029	−	0.0162728i	0.963711	−	0.266946i	$-0.0860146\pi$
$457$	−0.0932123	−	0.347873i	−0.00436029	−	0.0162728i	−0.968072	+	0.250673i	$0.919348\pi$
$458$	5.23651	+	3.02330i	0.244686	+	0.141270i
$459$	−24.0956	+	13.9116i	−1.12468	+	0.649337i
$460$	2.16909	+	2.16909i	0.101134	+	0.101134i
$461$	−6.55396	+	24.4597i	−0.305249	+	1.13920i	0.627483	+	0.778631i	$0.284085\pi$
$461$	−6.55396	+	24.4597i	−0.305249	+	1.13920i	−0.932731	+	0.360573i	$0.882581\pi$
$462$		0			0
$463$	18.4801	+	18.4801i	0.858844	+	0.858844i	0.991202	−	0.132358i	$-0.0422548\pi$
$463$	18.4801	+	18.4801i	0.858844	+	0.858844i	−0.132358	+	0.991202i	$0.542255\pi$
$464$	−2.21993	−	3.84504i	−0.103058	−	0.178501i
$465$	3.40952	−	5.90546i	0.158113	−	0.273859i
$466$	4.95475	−	1.32762i	0.229525	−	0.0615009i
$467$	31.2447			1.44583			0.722916	−	0.690936i	$-0.242802\pi$
$467$	31.2447			1.44583			0.722916	+	0.690936i	$0.242802\pi$
$468$	−12.1208	+	7.87665i	−0.560285	+	0.364098i
$469$		0			0
$470$	3.36156	+	12.5455i	0.155057	+	0.578682i
$471$	0.231360	−	0.400728i	0.0106605	−	0.0184646i
$472$	5.27530	+	9.13709i	0.242815	+	0.420569i
$473$	−0.618550	+	0.618550i	−0.0284410	+	0.0284410i
$474$	0.318551	−	1.18885i	0.0146315	−	0.0546056i
$475$	31.3700	+	8.40556i	1.43935	+	0.385673i
$476$		0			0
$477$	−13.5864	−	23.5323i	−0.622077	−	1.07747i
$478$	6.77498	+	3.91154i	0.309880	+	0.178909i
$479$	−7.71172	−	28.7805i	−0.352357	−	1.31502i	−0.883778	−	0.467907i	$-0.845008\pi$
$479$	−7.71172	−	28.7805i	−0.352357	−	1.31502i	0.531420	−	0.847108i	$-0.321659\pi$
$480$			14.0858i			0.642926i
$481$	−1.98456	+	9.35079i	−0.0904884	+	0.426359i
$482$			0.390709i			0.0177963i
$483$		0			0
$484$	−10.1871	+	17.6447i	−0.463052	+	0.802030i
$485$	−5.60885	+	3.23827i	−0.254685	+	0.147042i
$486$	−4.37190	−	4.37190i	−0.198313	−	0.198313i
$487$	13.8499	+	3.71106i	0.627597	+	0.168164i	0.558579	−	0.829451i	$-0.311347\pi$
$487$	13.8499	+	3.71106i	0.627597	+	0.168164i	0.0690178	+	0.997615i	$0.478013\pi$
$488$	0.181923	+	0.0487462i	0.00823528	+	0.00220664i
$489$	−2.87295	+	2.87295i	−0.129920	+	0.129920i
$490$		0			0
$491$	16.5417	+	9.55034i	0.746515	+	0.431001i	0.824433	−	0.565959i	$-0.191494\pi$
$491$	16.5417	+	9.55034i	0.746515	+	0.431001i	−0.0779183	+	0.996960i	$0.524827\pi$
$492$	−5.09157	+	1.36428i	−0.229546	+	0.0615066i
$493$	8.32234			0.374820
$494$	−2.32483	+	4.56620i	−0.104599	+	0.205443i
$495$			0.702547i			0.0315771i
$496$	6.10213	−	1.63506i	0.273994	−	0.0734164i
$497$		0			0
$498$	0.934831	−	0.539725i	0.0418908	−	0.0241856i
$499$	16.3269	−	16.3269i	0.730894	−	0.730894i	−0.239903	−	0.970797i	$-0.577116\pi$
$499$	16.3269	−	16.3269i	0.730894	−	0.730894i	0.970797	+	0.239903i	$0.0771156\pi$
$500$	−6.66437	+	24.8718i	−0.298039	+	1.11230i
$501$	−1.90044	+	7.09253i	−0.0849053	+	0.316871i
$502$	−3.02836	+	3.02836i	−0.135162	+	0.135162i
$503$	10.9978	−	6.34957i	0.490367	−	0.283113i	−0.234360	−	0.972150i	$-0.575299\pi$
$503$	10.9978	−	6.34957i	0.490367	−	0.283113i	0.724727	+	0.689036i	$0.241966\pi$
$504$		0			0
$505$	−24.4334	+	6.54690i	−1.08727	+	0.291333i
$506$			0.0149667i			0.000665350i
$507$	1.25045	+	11.8273i	0.0555346	+	0.525267i
$508$	31.5483			1.39973
$509$	−10.4965	+	2.81254i	−0.465250	+	0.124663i	−0.483826	−	0.875164i	$-0.660753\pi$
$509$	−10.4965	+	2.81254i	−0.465250	+	0.124663i	0.0185761	+	0.999827i	$0.494087\pi$
$510$	−6.62294	−	3.82375i	−0.293269	−	0.169319i
$511$		0			0
$512$	−15.7822	+	15.7822i	−0.697483	+	0.697483i
$513$	16.9403	+	4.53914i	0.747933	+	0.200408i
$514$	−3.48515	−	0.933842i	−0.153723	−	0.0411900i
$515$	−26.2188	−	26.2188i	−1.15534	−	1.15534i
$516$	−14.6642	+	8.46637i	−0.645554	+	0.372711i
$517$	0.400874	−	0.694333i	0.0176304	−	0.0305367i
$518$		0			0
$519$		−	1.15556i		−	0.0507233i
$520$	−17.5709	−	8.94602i	−0.770536	−	0.392309i
$521$			33.0292i			1.44704i	0.690306	+	0.723518i	$0.257476\pi$
$521$			33.0292i			1.44704i	−0.690306	+	0.723518i	$0.742524\pi$
$522$	0.302743	+	1.12985i	0.0132507	+	0.0494523i
$523$	−13.5411	−	7.81797i	−0.592112	−	0.341856i	0.173820	−	0.984777i	$-0.444389\pi$
$523$	−13.5411	−	7.81797i	−0.592112	−	0.341856i	−0.765932	+	0.642922i	$0.777722\pi$
$524$	2.52085	+	4.36624i	0.110124	+	0.190740i
$525$		0			0
$526$	5.08247	+	1.36184i	0.221606	+	0.0593792i
$527$	−3.06485	+	11.4382i	−0.133507	+	0.498255i
$528$	0.178083	−	0.178083i	0.00775006	−	0.00775006i
$529$	−11.4004	−	19.7460i	−0.495668	−	0.858523i
$530$	8.91372	−	15.4390i	0.387187	−	0.670628i
$531$	4.00465	+	14.9455i	0.173787	+	0.648581i
$532$		0			0
$533$	2.32692	−	10.9639i	0.100790	−	0.474899i
$534$	−0.591521			−0.0255976
$535$	0.214476	−	0.0574687i	0.00927261	−	0.00248459i
$536$	−7.34285	+	12.7182i	−0.317163	+	0.549342i
$537$	0.773158	+	1.33915i	0.0333642	+	0.0577885i
$538$	−6.38313	−	6.38313i	−0.275196	−	0.275196i
$539$		0			0
$540$	−8.40138	+	31.3544i	−0.361538	+	1.34928i
$541$	8.70737	+	8.70737i	0.374359	+	0.374359i	0.869062	−	0.494703i	$-0.164723\pi$
$541$	8.70737	+	8.70737i	0.374359	+	0.374359i	−0.494703	+	0.869062i	$0.664723\pi$
$542$	−3.01327	+	1.73971i	−0.129431	+	0.0747271i
$543$	6.58256	+	3.80044i	0.282485	+	0.163093i
$544$	−6.33094	−	23.6274i	−0.271437	−	1.01302i
$545$	−60.9789			−2.61205
$546$		0			0
$547$	3.99754			0.170922			0.0854611	−	0.996342i	$-0.472764\pi$
$547$	3.99754			0.170922			0.0854611	+	0.996342i	$0.472764\pi$
$548$	2.06652	+	7.71234i	0.0882772	+	0.329455i
$549$	0.239202	+	0.138104i	0.0102089	+	0.00589412i
$550$	−0.253986	+	0.146639i	−0.0108300	+	0.00625271i
$551$	−3.70938	−	3.70938i	−0.158025	−	0.158025i
$552$	−0.155891	+	0.581794i	−0.00663517	+	0.0247628i
$553$		0			0
$554$	3.42711	+	3.42711i	0.145604	+	0.145604i
$555$	4.49646	+	7.78809i	0.190864	+	0.330586i
$556$	−12.9753	+	22.4738i	−0.550273	+	0.953101i
$557$	12.3689	−	3.31424i	0.524088	−	0.140429i	0.0129309	−	0.999916i	$-0.495884\pi$
$557$	12.3689	−	3.31424i	0.524088	−	0.140429i	0.511157	+	0.859488i	$0.329217\pi$
$558$	−1.66435			−0.0704577
$559$	−1.89536	−	35.9541i	−0.0801653	−	1.52070i
$560$		0			0
$561$	0.122182	+	0.455991i	0.00515855	+	0.0192520i
$562$	−6.38443	+	11.0581i	−0.269311	+	0.466460i
$563$	5.02369	+	8.70129i	0.211723	+	0.366716i	0.952254	−	0.305307i	$-0.0987591\pi$
$563$	5.02369	+	8.70129i	0.211723	+	0.366716i	−0.740531	+	0.672023i	$0.765426\pi$
$564$	10.9739	−	10.9739i	0.462083	−	0.462083i
$565$	−5.27162	+	19.6740i	−0.221779	+	0.827690i
$566$	8.44371	+	2.26249i	0.354916	+	0.0950993i
$567$		0			0
$568$	7.50713	+	13.0027i	0.314992	+	0.545583i
$569$	−5.10535	−	2.94758i	−0.214027	−	0.123569i	0.389154	−	0.921173i	$-0.372767\pi$
$569$	−5.10535	−	2.94758i	−0.214027	−	0.123569i	−0.603182	+	0.797604i	$0.706101\pi$
$570$	1.24763	+	4.65623i	0.0522577	+	0.195028i
$571$		−	0.878887i		−	0.0367803i	−0.999831	−	0.0183901i	$-0.994146\pi$
$571$		−	0.878887i		−	0.0367803i	0.999831	−	0.0183901i	$-0.00585409\pi$
$572$	0.181079	+	0.556722i	0.00757130	+	0.0232777i
$573$			18.8718i			0.788380i
$574$		0			0
$575$	−1.95218	+	3.38128i	−0.0814117	+	0.141009i
$576$	−8.79582	+	5.07827i	−0.366492	+	0.211594i
$577$	0.110273	+	0.110273i	0.00459074	+	0.00459074i	0.709398	−	0.704808i	$-0.248967\pi$
$577$	0.110273	+	0.110273i	0.00459074	+	0.00459074i	−0.704808	+	0.709398i	$0.748967\pi$
$578$	6.54280	+	1.75314i	0.272144	+	0.0729209i
$579$	−11.8478	−	3.17460i	−0.492376	−	0.131932i
$580$	6.86560	−	6.86560i	0.285079	−	0.285079i
$581$		0			0
$582$	−0.529716	−	0.305832i	−0.0219574	−	0.0126771i
$583$	−1.06298	+	0.284825i	−0.0440242	+	0.0117962i
$584$	13.5113			0.559101
$585$	−21.4946	−	19.3419i	−0.888693	−	0.799688i
$586$		−	4.58711i		−	0.189492i
$587$	−38.7558	+	10.3846i	−1.59962	+	0.428617i	−0.944928	−	0.327278i	$-0.893869\pi$
$587$	−38.7558	+	10.3846i	−1.59962	+	0.428617i	−0.654693	+	0.755895i	$0.727202\pi$
$588$		0			0
$589$	6.46420	−	3.73211i	0.266353	−	0.153779i
$590$	−7.17808	+	7.17808i	−0.295517	+	0.295517i
$591$	3.91591	−	14.6144i	0.161079	−	0.601155i
$592$	−2.15631	+	8.04746i	−0.0886238	+	0.330749i
$593$	1.71535	−	1.71535i	0.0704412	−	0.0704412i	−0.671008	−	0.741450i	$-0.734139\pi$
$593$	1.71535	−	1.71535i	0.0704412	−	0.0704412i	0.741450	+	0.671008i	$0.234139\pi$
$594$	−0.137157	+	0.0791875i	−0.00562761	+	0.00324910i
$595$		0			0
$596$	16.4181	−	4.39921i	0.672510	−	0.180199i
$597$			11.8586i			0.485339i
$598$	−0.457910	−	0.412049i	−0.0187253	−	0.0168499i
$599$	−10.6959			−0.437023			−0.218512	−	0.975834i	$-0.570120\pi$
$599$	−10.6959			−0.437023			−0.218512	+	0.975834i	$0.570120\pi$
$600$	−11.4005	+	3.05475i	−0.465422	+	0.124710i
$601$	−30.2246	−	17.4502i	−1.23289	−	0.711807i	−0.265255	−	0.964178i	$-0.585456\pi$
$601$	−30.2246	−	17.4502i	−1.23289	−	0.711807i	−0.967630	+	0.252371i	$0.918790\pi$
$602$		0			0
$603$	−15.2290	+	15.2290i	−0.620171	+	0.620171i
$604$	13.5892	+	3.64120i	0.552935	+	0.148159i
$605$	−39.3673	−	10.5484i	−1.60051	−	0.428854i
$606$	−1.68925	−	1.68925i	−0.0686211	−	0.0686211i
$607$	12.7887	−	7.38356i	0.519078	−	0.299690i	−0.217480	−	0.976065i	$-0.569784\pi$
$607$	12.7887	−	7.38356i	0.519078	−	0.299690i	0.736557	+	0.676375i	$0.236450\pi$
$608$	−7.70927	+	13.3528i	−0.312652	+	0.541529i
$609$		0			0
$610$			0.181214i			0.00733712i
$611$	10.2068	+	31.3806i	0.412925	+	1.26952i
$612$		−	23.6158i		−	0.954612i
$613$	−3.53552	−	13.1947i	−0.142798	−	0.532930i	−0.999844	−	0.0176892i	$-0.994369\pi$
$613$	−3.53552	−	13.1947i	−0.142798	−	0.532930i	0.857045	−	0.515241i	$-0.172298\pi$
$614$	8.89925	+	5.13798i	0.359145	+	0.207352i
$615$	−5.27214	−	9.13161i	−0.212593	−	0.368222i
$616$		0			0
$617$	−14.8331	−	3.97453i	−0.597160	−	0.160008i	−0.0524363	−	0.998624i	$-0.516699\pi$
$617$	−14.8331	−	3.97453i	−0.597160	−	0.160008i	−0.544723	+	0.838616i	$0.683365\pi$
$618$	0.906344	−	3.38252i	0.0364585	−	0.136065i
$619$	3.33374	−	3.33374i	0.133994	−	0.133994i	−0.636929	−	0.770923i	$-0.719795\pi$
$619$	3.33374	−	3.33374i	0.133994	−	0.133994i	0.770923	+	0.636929i	$0.219795\pi$
$620$	6.90766	+	11.9644i	0.277418	+	0.480503i
$621$	−1.05421	+	1.82595i	−0.0423041	+	0.0732728i
$622$	−2.95191	−	11.0167i	−0.118361	−	0.441728i
$623$		0			0
$624$	0.545682	+	10.3513i	0.0218448	+	0.414384i
$625$	−7.77330			−0.310932
$626$	6.04570	−	1.61994i	0.241635	−	0.0647458i
$627$	0.148783	−	0.257700i	0.00594183	−	0.0102915i
$628$	0.468734	+	0.811872i	0.0187045	+	0.0323972i
$629$	−11.0427	−	11.0427i	−0.440302	−	0.440302i
$630$		0			0
$631$	−4.57205	+	17.0631i	−0.182011	+	0.679273i	0.813240	+	0.581928i	$0.197702\pi$
$631$	−4.57205	+	17.0631i	−0.182011	+	0.679273i	−0.995251	+	0.0973445i	$0.968965\pi$
$632$	3.66579	+	3.66579i	0.145817	+	0.145817i
$633$	5.05565	−	2.91888i	0.200944	−	0.116015i
$634$	−5.66090	−	3.26832i	−0.224823	−	0.129802i
$635$	16.3336	+	60.9576i	0.648177	+	2.41903i
$636$	−21.3019			−0.844676
$637$		0			0
$638$	0.0473725			0.00187549
$639$	5.69890	+	21.2686i	0.225445	+	0.841372i
$640$	−32.4386	−	18.7284i	−1.28225	−	0.740306i
$641$	32.2289	−	18.6074i	1.27297	−	0.734948i	0.297421	−	0.954746i	$-0.403873\pi$
$641$	32.2289	−	18.6074i	1.27297	−	0.734948i	0.975545	+	0.219799i	$0.0705401\pi$
$642$	0.0148282	+	0.0148282i	0.000585224	+	0.000585224i
$643$	2.17224	−	8.10691i	0.0856648	−	0.319705i	−0.909774	−	0.415103i	$-0.863746\pi$
$643$	2.17224	−	8.10691i	0.0856648	−	0.319705i	0.995439	+	0.0953976i	$0.0304122\pi$
$644$		0			0
$645$	−23.9508	−	23.9508i	−0.943064	−	0.943064i
$646$	−4.18554	−	7.24956i	−0.164678	−	0.285230i
$647$	12.9222	−	22.3819i	0.508024	−	0.879923i	−0.491933	−	0.870633i	$-0.663710\pi$
$647$	12.9222	−	22.3819i	0.508024	−	0.879923i	0.999957	−	0.00928983i	$-0.00295709\pi$
$648$	3.08840	−	0.827533i	0.121324	−	0.0325086i
$649$	0.626637			0.0245977
$650$	2.50605	−	11.8079i	0.0982955	−	0.463144i
$651$		0			0
$652$	−2.13048	−	7.95107i	−0.0834362	−	0.311388i
$653$	−16.0054	+	27.7222i	−0.626341	+	1.08486i	0.361938	+	0.932202i	$0.382115\pi$
$653$	−16.0054	+	27.7222i	−0.626341	+	1.08486i	−0.988280	+	0.152653i	$0.951218\pi$
$654$	−2.87951	−	4.98746i	−0.112598	−	0.195025i
$655$	−7.13134	+	7.13134i	−0.278645	+	0.278645i
$656$	2.52829	−	9.43572i	0.0987133	−	0.368403i
$657$	19.1395	+	5.12842i	0.746703	+	0.200079i
$658$		0			0
$659$	1.93932	+	3.35900i	0.0755452	+	0.130848i	0.901323	−	0.433147i	$-0.142597\pi$
$659$	1.93932	+	3.35900i	0.0755452	+	0.130848i	−0.825778	+	0.563995i	$0.809264\pi$
$660$	0.476970	+	0.275379i	0.0185660	+	0.0107191i
$661$	2.40516	+	8.97619i	0.0935500	+	0.349133i	0.996796	−	0.0799905i	$-0.0254890\pi$
$661$	2.40516	+	8.97619i	0.0935500	+	0.349133i	−0.903246	+	0.429124i	$0.858822\pi$
$662$			8.33497i			0.323948i
$663$	−17.3150	−	8.81572i	−0.672459	−	0.342374i
$664$			4.54677i			0.176449i
$665$		0			0
$666$	1.09747	−	1.90087i	0.0425261	−	0.0736574i
$667$	0.546170	−	0.315331i	0.0211478	−	0.0122097i
$668$	−10.5191	−	10.5191i	−0.406998	−	0.406998i
$669$	−11.3097	−	3.03042i	−0.437258	−	0.117163i
$670$	−13.6485	−	3.65710i	−0.527287	−	0.141286i
$671$	0.00790985	−	0.00790985i	0.000305356	−	0.000305356i
$672$		0			0
$673$	24.3896	+	14.0814i	0.940151	+	0.542797i	0.890008	−	0.455945i	$-0.150699\pi$
$673$	24.3896	+	14.0814i	0.940151	+	0.542797i	0.0501436	+	0.998742i	$0.484032\pi$
$674$	−8.37600	+	2.24434i	−0.322631	+	0.0864488i
$675$	−41.3154			−1.59023
$676$	−22.0184	−	9.78699i	−0.846861	−	0.376423i
$677$		−	28.3805i		−	1.09075i	−0.838192	−	0.545375i	$-0.816387\pi$
$677$		−	28.3805i		−	1.09075i	0.838192	−	0.545375i	$-0.183613\pi$
$678$	−1.85807	+	0.497868i	−0.0713586	+	0.0191205i
$679$		0			0
$680$	27.8966	−	16.1061i	1.06979	−	0.617641i
$681$	7.67080	−	7.67080i	0.293946	−	0.293946i
$682$	−0.0174458	+	0.0651085i	−0.000668033	+	0.00249313i
$683$	6.32413	−	23.6020i	0.241986	−	0.903104i	−0.732888	−	0.680349i	$-0.761828\pi$
$683$	6.32413	−	23.6020i	0.241986	−	0.903104i	0.974874	−	0.222755i	$-0.0715051\pi$
$684$	−10.5259	+	10.5259i	−0.402467	+	0.402467i
$685$	−13.8319	+	7.98586i	−0.528490	+	0.305124i
$686$		0			0
$687$	13.9603	−	3.74064i	0.532617	−	0.142714i
$688$		−	31.3798i		−	1.19634i
$689$	20.5507	−	40.3638i	0.782920	−	1.53774i
$690$	−0.579524			−0.0220621
$691$	31.3370	−	8.39671i	1.19211	−	0.319426i	0.392393	−	0.919798i	$-0.371647\pi$
$691$	31.3370	−	8.39671i	1.19211	−	0.319426i	0.799721	+	0.600372i	$0.204981\pi$
$692$	2.02749	+	1.17057i	0.0770738	+	0.0444986i
$693$		0			0
$694$	−3.21279	+	3.21279i	−0.121956	+	0.121956i
$695$	−50.1416	−	13.4354i	−1.90198	−	0.509634i
$696$	1.84149	+	0.493426i	0.0698015	+	0.0187033i
$697$	12.9477	+	12.9477i	0.490428	+	0.490428i
$698$	−6.89372	+	3.98009i	−0.260931	+	0.150649i
$699$	6.13037	−	10.6181i	0.231872	−	0.401614i
$700$		0			0
$701$			49.4461i			1.86755i	0.357856	+	0.933777i	$0.383508\pi$
$701$			49.4461i			1.86755i	−0.357856	+	0.933777i	$0.616492\pi$
$702$	1.35331	−	6.37647i	0.0510774	−	0.240664i
$703$			9.84377i			0.371265i
$704$	0.106461	+	0.397317i	0.00401240	+	0.0149745i
$705$	26.8852	+	15.5222i	1.01256	+	0.584600i
$706$	5.34960	+	9.26578i	0.201335	+	0.348722i
$707$		0			0
$708$	11.7165	+	3.13942i	0.440332	+	0.117987i
$709$	−4.61145	+	17.2101i	−0.173186	+	0.646341i	0.823667	+	0.567074i	$0.191925\pi$
$709$	−4.61145	+	17.2101i	−0.173186	+	0.646341i	−0.996853	+	0.0792669i	$0.974742\pi$
$710$	−10.2149	+	10.2149i	−0.383359	+	0.383359i
$711$	3.80140	+	6.58422i	0.142564	+	0.246927i
$712$	1.24578	−	2.15775i	0.0466875	−	0.0808651i
$713$	0.232253	+	0.866779i	0.00869794	+	0.0324611i
$714$		0			0
$715$	−0.981949	+	0.638115i	−0.0367228	+	0.0238641i
$716$	−3.13283			−0.117079
$717$	18.0617	−	4.83963i	0.674528	−	0.180739i
$718$	3.00282	−	5.20104i	0.112064	−	0.194101i
$719$	−13.9168	−	24.1047i	−0.519011	−	0.898953i	−0.999756	−	0.0220927i	$-0.992967\pi$
$719$	−13.9168	−	24.1047i	−0.519011	−	0.898953i	0.480745	−	0.876860i	$-0.340366\pi$
$720$	−17.8205	−	17.8205i	−0.664132	−	0.664132i
$721$		0			0
$722$	0.516523	−	1.92769i	0.0192230	−	0.0717412i
$723$	0.660355	+	0.660355i	0.0245589	+	0.0245589i
$724$	−13.3362	+	7.69968i	−0.495637	+	0.286156i
$725$	10.7024	+	6.17904i	0.397478	+	0.229484i
$726$	−0.996224	−	3.71796i	−0.0369734	−	0.137986i
$727$	47.3797			1.75722			0.878608	−	0.477544i	$-0.158473\pi$
$727$	47.3797			1.75722			0.878608	+	0.477544i	$0.158473\pi$
$728$		0			0
$729$	−8.27491			−0.306478
$730$	3.36464	+	12.5570i	0.124531	+	0.464756i
$731$	50.9397	+	29.4101i	1.88407	+	1.08777i
$732$	0.187521	−	0.108266i	0.00693099	−	0.00400161i
$733$	21.1685	+	21.1685i	0.781877	+	0.781877i	0.980147	−	0.198271i	$-0.0635325\pi$
$733$	21.1685	+	21.1685i	0.781877	+	0.781877i	−0.198271	+	0.980147i	$0.563532\pi$
$734$	−0.474726	+	1.77170i	−0.0175225	+	0.0653947i
$735$		0			0
$736$	−1.31072	−	1.31072i	−0.0483136	−	0.0483136i
$737$	0.436117	+	0.755377i	0.0160646	+	0.0278247i
$738$	−1.28679	+	2.22879i	−0.0473675	+	0.0820430i
$739$	−12.2468	+	3.28151i	−0.450505	+	0.120712i	−0.476936	−	0.878938i	$-0.658252\pi$
$739$	−12.2468	+	3.28151i	−0.450505	+	0.120712i	0.0264308	+	0.999651i	$0.491586\pi$
$740$	−18.2196			−0.669765
$741$	3.78824	+	11.6468i	0.139165	+	0.427857i
$742$		0			0
$743$	−5.17566	−	19.3158i	−0.189877	−	0.708629i	−0.993534	−	0.113537i	$-0.963782\pi$
$743$	−5.17566	−	19.3158i	−0.189877	−	0.708629i	0.803657	−	0.595093i	$-0.202885\pi$
$744$	−1.35632	+	2.34922i	−0.0497252	+	0.0861266i
$745$	17.0003	+	29.4454i	0.622843	+	1.07880i
$746$	−0.509835	+	0.509835i	−0.0186664	+	0.0186664i
$747$	−1.72580	+	6.44076i	−0.0631436	+	0.235655i
$748$	−0.923835	−	0.247541i	−0.0337788	−	0.00905099i
$749$		0			0
$750$	−2.43227	−	4.21281i	−0.0888138	−	0.153830i
$751$	27.6527	+	15.9653i	1.00906	+	0.582582i	0.910917	−	0.412590i	$-0.135376\pi$
$751$	27.6527	+	15.9653i	1.00906	+	0.582582i	0.0981449	+	0.995172i	$0.468709\pi$
$752$	7.44379	+	27.7806i	0.271447	+	1.01305i
$753$			10.2367i			0.373047i
$754$	−1.30422	+	1.44937i	−0.0474967	+	0.0527831i
$755$			28.1422i			1.02420i
$756$		0			0
$757$	0.983838	−	1.70406i	0.0357582	−	0.0619350i	−0.847592	−	0.530648i	$-0.821949\pi$
$757$	0.983838	−	1.70406i	0.0357582	−	0.0619350i	0.883351	+	0.468713i	$0.155282\pi$
$758$	−0.472085	+	0.272558i	−0.0171469	+	0.00989976i
$759$	0.0252958	+	0.0252958i	0.000918181	+	0.000918181i
$760$	−19.6126	−	5.25518i	−0.711424	−	0.190626i
$761$	−6.71695	−	1.79980i	−0.243489	−	0.0652427i	0.135010	−	0.990844i	$-0.456893\pi$
$761$	−6.71695	−	1.79980i	−0.243489	−	0.0652427i	−0.378500	+	0.925601i	$0.623560\pi$
$762$	−4.21443	+	4.21443i	−0.152673	+	0.152673i
$763$		0			0
$764$	−33.1117	−	19.1171i	−1.19794	−	0.691631i
$765$	45.6305	−	12.2266i	1.64977	−	0.442055i
$766$	4.18855			0.151339
$767$	−17.2520	+	19.1721i	−0.622934	+	0.692266i
$768$			5.05394i			0.182369i
$769$	2.45316	−	0.657322i	0.0884631	−	0.0237036i	−0.214316	−	0.976764i	$-0.568752\pi$
$769$	2.45316	−	0.657322i	0.0884631	−	0.0237036i	0.302779	+	0.953061i	$0.402086\pi$
$770$		0			0
$771$	−7.46873	+	4.31207i	−0.268980	+	0.155295i
$772$	17.5718	−	17.5718i	0.632422	−	0.632422i
$773$	−2.22776	+	8.31412i	−0.0801270	+	0.299038i	−0.994347	−	0.106180i	$-0.966138\pi$
$773$	−2.22776	+	8.31412i	−0.0801270	+	0.299038i	0.914220	+	0.405218i	$0.132805\pi$
$774$	−2.13971	+	7.98550i	−0.0769102	+	0.287033i
$775$	−12.4338	+	12.4338i	−0.446635	+	0.446635i
$776$	2.23123	−	1.28820i	0.0800964	−	0.0462437i
$777$		0			0
$778$	−10.2450	+	2.74514i	−0.367302	+	0.0984181i
$779$		−	11.5419i		−	0.413532i
$780$	−21.5568	+	7.01156i	−0.771857	+	0.251054i
$781$	0.891750			0.0319093
$782$	0.972088	−	0.260470i	0.0347618	−	0.00931439i
$783$	5.77948	+	3.33679i	0.206542	+	0.119247i
$784$		0			0
$785$	−1.32602	+	1.32602i	−0.0473277	+	0.0473277i
$786$	−0.920025	−	0.246520i	−0.0328162	−	0.00879307i
$787$	−5.86298	−	1.57098i	−0.208993	−	0.0559994i	0.152804	−	0.988257i	$-0.451170\pi$
$787$	−5.86298	−	1.57098i	−0.208993	−	0.0559994i	−0.361796	+	0.932257i	$0.617836\pi$
$788$	21.6750	+	21.6750i	0.772141	+	0.772141i
$789$	10.8918	−	6.28839i	0.387759	−	0.223873i
$790$	−2.49402	+	4.31976i	−0.0887331	+	0.153690i
$791$		0			0
$792$		−	0.279477i		−	0.00993077i
$793$	0.0242374	+	0.459771i	0.000860695	+	0.0163269i
$794$		−	4.81117i		−	0.170742i
$795$	−11.0287	−	41.1596i	−0.391147	−	1.45978i
$796$	−20.8066	−	12.0127i	−0.737470	−	0.425779i
$797$	0.799767	+	1.38524i	0.0283292	+	0.0490676i	0.879842	−	0.475266i	$-0.157648\pi$
$797$	0.799767	+	1.38524i	0.0283292	+	0.0490676i	−0.851513	+	0.524333i	$0.824315\pi$
$798$		0			0
$799$	−52.0736	−	13.9531i	−1.84223	−	0.493624i
$800$	9.40099	−	35.0850i	0.332375	−	1.24044i
$801$	2.58373	−	2.58373i	0.0912914	−	0.0912914i
$802$	−4.73396	−	8.19945i	−0.167162	−	0.289533i
$803$	0.401241	−	0.694970i	0.0141595	−	0.0245249i
$804$	4.36985	+	16.3085i	0.154113	+	0.575157i
$805$		0			0
$806$	−1.51171	−	2.32626i	−0.0532478	−	0.0819392i
$807$	−21.5768			−0.759540
$808$	9.71971	−	2.60439i	0.341938	−	0.0916221i
$809$	−21.3018	+	36.8958i	−0.748932	+	1.29719i	0.199403	+	0.979918i	$0.436100\pi$
$809$	−21.3018	+	36.8958i	−0.748932	+	1.29719i	−0.948335	+	0.317270i	$0.897234\pi$
$810$	1.53817	+	2.66420i	0.0540459	+	0.0936103i
$811$	36.5518	+	36.5518i	1.28351	+	1.28351i	0.938658	+	0.344850i	$0.112070\pi$
$811$	36.5518	+	36.5518i	1.28351	+	1.28351i	0.344850	+	0.938658i	$0.387930\pi$
$812$		0			0
$813$	−2.15250	+	8.03323i	−0.0754914	+	0.281738i
$814$	−0.0628573	−	0.0628573i	−0.00220315	−	0.00220315i
$815$	14.2601	−	8.23305i	0.499508	−	0.288391i
$816$	−14.6657	−	8.46726i	−0.513403	−	0.296414i
$817$	−9.59607	−	35.8130i	−0.335724	−	1.25294i
$818$	−4.35897			−0.152408
$819$		0			0
$820$	21.3626			0.746016
$821$	−5.34576	−	19.9506i	−0.186568	−	0.696282i	−0.994289	−	0.106717i	$-0.965966\pi$
$821$	−5.34576	−	19.9506i	−0.186568	−	0.696282i	0.807721	−	0.589565i	$-0.200701\pi$
$822$	−1.30633	−	0.754208i	−0.0455634	−	0.0263060i
$823$	45.0294	−	25.9977i	1.56963	−	0.906224i	0.573413	−	0.819266i	$-0.305619\pi$
$823$	45.0294	−	25.9977i	1.56963	−	0.906224i	0.996212	−	0.0869576i	$-0.0277145\pi$
$824$	10.4300	+	10.4300i	0.363345	+	0.363345i
$825$	−0.181432	+	0.677114i	−0.00631666	+	0.0235741i
$826$		0			0
$827$	30.9176	+	30.9176i	1.07511	+	1.07511i	0.996940	+	0.0781709i	$0.0249080\pi$
$827$	30.9176	+	30.9176i	1.07511	+	1.07511i	0.0781709	+	0.996940i	$0.475092\pi$
$828$	−0.894796	−	1.54983i	−0.0310963	−	0.0538604i
$829$	22.5718	−	39.0955i	0.783951	−	1.35784i	−0.145673	−	0.989333i	$-0.546535\pi$
$829$	22.5718	−	39.0955i	0.783951	−	1.35784i	0.929624	−	0.368510i	$-0.120132\pi$
$830$	−4.22565	+	1.13226i	−0.146674	+	0.0393013i
$831$	11.5846			0.401866
$832$	−15.0870	−	7.68138i	−0.523048	−	0.266304i
$833$		0			0
$834$	−1.26888	−	4.73552i	−0.0439377	−	0.163978i
$835$	14.8790	−	25.7712i	0.514910	−	0.891850i
$836$	0.301434	+	0.522098i	0.0104253	+	0.0180572i
$837$	−6.71446	+	6.71446i	−0.232086	+	0.232086i
$838$	2.88526	−	10.7679i	0.0996696	−	0.371972i
$839$	−29.8547	−	7.99955i	−1.03070	−	0.276175i	−0.296445	−	0.955050i	$-0.595801\pi$
$839$	−29.8547	−	7.99955i	−1.03070	−	0.276175i	−0.734254	+	0.678875i	$0.762468\pi$
$840$		0			0
$841$	13.5019	+	23.3860i	0.465583	+	0.806414i
$842$	−11.6926	−	6.75074i	−0.402955	−	0.232646i
$843$	7.89926	+	29.4804i	0.272065	+	1.01536i
$844$			11.8273i			0.407111i
$845$	7.51082	−	47.6110i	0.258380	−	1.63787i
$846$		−	7.57715i		−	0.260508i
$847$		0			0
$848$	19.7384	−	34.1879i	0.677820	−	1.17402i
$849$	18.0950	−	10.4472i	0.621019	−	0.358545i
$850$	13.9444	+	13.9444i	0.478290	+	0.478290i
$851$	−1.14310	−	0.306294i	−0.0391851	−	0.0104996i
$852$	16.6734	+	4.46762i	0.571221	+	0.153058i
$853$	22.8132	−	22.8132i	0.781108	−	0.781108i	−0.198910	−	0.980018i	$-0.563740\pi$
$853$	22.8132	−	22.8132i	0.781108	−	0.781108i	0.980018	+	0.198910i	$0.0637401\pi$
$854$		0			0
$855$	−25.7877	−	14.8885i	−0.881922	−	0.509178i
$856$	−0.0853196	+	0.0228613i	−0.00291616	+	0.000781384i
$857$	−25.6296			−0.875489			−0.437745	−	0.899099i	$-0.644223\pi$
$857$	−25.6296			−0.875489			−0.437745	+	0.899099i	$0.644223\pi$
$858$	−0.0985605	−	0.0501809i	−0.00336480	−	0.00171315i
$859$			6.59884i			0.225150i	0.993643	+	0.112575i	$0.0359098\pi$
$859$			6.59884i			0.225150i	−0.993643	+	0.112575i	$0.964090\pi$
$860$	66.2854	−	17.7611i	2.26031	−	0.605649i
$861$		0			0
$862$	−1.08325	+	0.625415i	−0.0368956	+	0.0213017i
$863$	−31.4647	+	31.4647i	−1.07107	+	1.07107i	−0.0737987	+	0.997273i	$0.523512\pi$
$863$	−31.4647	+	31.4647i	−1.07107	+	1.07107i	−0.997273	+	0.0737987i	$0.976488\pi$
$864$	5.07669	−	18.9465i	0.172713	−	0.644572i
$865$	−1.21209	+	4.52357i	−0.0412122	+	0.153806i
$866$	−5.32029	+	5.32029i	−0.180791	+	0.180791i
$867$	14.0213	−	8.09521i	0.476189	−	0.274928i
$868$		0			0
$869$	0.297417	−	0.0796926i	0.0100892	−	0.00270339i
$870$			1.83431i			0.0621888i
$871$	−35.1178	−	7.45322i	−1.18992	−	0.252543i
$872$	24.2577			0.821469
$873$	3.64962	−	0.977913i	0.123521	−	0.0330973i
$874$	−0.549368	−	0.317178i	−0.0185827	−	0.0107287i
$875$		0			0
$876$	10.9839	−	10.9839i	0.371112	−	0.371112i
$877$	50.9050	+	13.6400i	1.71894	+	0.460589i	0.977588	−	0.210527i	$-0.0675179\pi$
$877$	50.9050	+	13.6400i	1.71894	+	0.460589i	0.741353	+	0.671115i	$0.234185\pi$
$878$	−13.9778	−	3.74533i	−0.471727	−	0.126399i
$879$	−7.75288	−	7.75288i	−0.261498	−	0.261498i
$880$	−0.883923	+	0.510333i	−0.0297970	+	0.0172033i
$881$	14.4790	−	25.0784i	0.487811	−	0.844914i	−0.512090	−	0.858932i	$-0.671129\pi$
$881$	14.4790	−	25.0784i	0.487811	−	0.844914i	0.999902	+	0.0140175i	$0.00446206\pi$
$882$		0			0
$883$		−	56.4022i		−	1.89808i	−0.315149	−	0.949042i	$-0.602054\pi$
$883$		−	56.4022i		−	1.89808i	0.315149	−	0.949042i	$-0.397946\pi$
$884$	33.0078	−	21.4499i	1.11017	−	0.721439i
$885$			24.2640i			0.815625i
$886$	0.458907	+	1.71266i	0.0154173	+	0.0575381i
$887$	−38.1935	−	22.0510i	−1.28241	−	0.740402i	−0.305124	−	0.952313i	$-0.598698\pi$
$887$	−38.1935	−	22.0510i	−1.28241	−	0.740402i	−0.977289	+	0.211911i	$0.932031\pi$
$888$	−1.78871	−	3.09814i	−0.0600253	−	0.103967i
$889$		0			0
$890$	2.31558	+	0.620459i	0.0776186	+	0.0207978i
$891$	0.0491501	−	0.183431i	0.00164659	−	0.00614516i
$892$	16.7737	−	16.7737i	0.561626	−	0.561626i
$893$	16.9908	+	29.4290i	0.568577	+	0.984803i
$894$	−1.60556	+	2.78091i	−0.0536980	+	0.0930076i
$895$	−1.62196	−	6.05325i	−0.0542163	−	0.202338i
$896$		0			0
$897$	−1.47036	+	0.0775116i	−0.0490937	+	0.00258804i
$898$	5.08657			0.169741
$899$	2.74353	−	0.735125i	0.0915017	−	0.0245178i
$900$	17.5339	−	30.3696i	0.584462	−	1.01232i
$901$	36.9988	+	64.0838i	1.23261	+	2.13494i
$902$	0.0737008	+	0.0737008i	0.00245397	+	0.00245397i
$903$		0			0
$904$	2.09708	−	7.82640i	0.0697478	−	0.260302i
$905$	−21.7819	−	21.7819i	−0.724056	−	0.724056i
$906$	−2.30175	+	1.32891i	−0.0764705	+	0.0441502i
$907$	−8.56547	−	4.94528i	−0.284412	−	0.164205i	0.351007	−	0.936373i	$-0.385839\pi$
$907$	−8.56547	−	4.94528i	−0.284412	−	0.164205i	−0.635419	+	0.772168i	$0.719173\pi$
$908$	5.68840	+	21.2294i	0.188776	+	0.704522i
$909$	14.7571			0.489461
$910$		0			0
$911$	11.6807			0.387000			0.193500	−	0.981100i	$-0.438016\pi$
$911$	11.6807			0.387000			0.193500	+	0.981100i	$0.438016\pi$
$912$	2.76274	+	10.3107i	0.0914836	+	0.341421i
$913$	0.233869	+	0.135024i	0.00773993	+	0.00446865i
$914$	−0.119378	+	0.0689229i	−0.00394867	+	0.00227977i
$915$	0.306277	+	0.306277i	0.0101252	+	0.0101252i
$916$	−7.57851	+	28.2834i	−0.250401	+	0.934510i
$917$		0			0
$918$	7.53022	+	7.53022i	0.248534	+	0.248534i
$919$	4.44586	+	7.70045i	0.146655	+	0.254014i	0.929989	−	0.367587i	$-0.119816\pi$
$919$	4.44586	+	7.70045i	0.146655	+	0.254014i	−0.783334	+	0.621601i	$0.786483\pi$
$920$	1.22051	−	2.11399i	0.0402391	−	0.0696962i
$921$	23.7249	−	6.35708i	0.781763	−	0.209473i
$922$	9.69224			0.319197
$923$	−24.5508	+	27.2833i	−0.808101	+	0.898042i
$924$		0			0
$925$	−6.00195	−	22.3996i	−0.197343	−	0.736493i
$926$	5.00157	−	8.66297i	0.164362	−	0.284683i
$927$	10.8158	+	18.7335i	0.355237	+	0.615288i
$928$	−4.14867	+	4.14867i	−0.136187	+	0.136187i
$929$	1.32270	−	4.93637i	0.0433963	−	0.161957i	−0.940827	−	0.338886i	$-0.889950\pi$
$929$	1.32270	−	4.93637i	0.0433963	−	0.161957i	0.984224	+	0.176929i	$0.0566164\pi$
$930$	−2.52106	−	0.675516i	−0.0826688	−	0.0221510i
$931$		0			0
$932$	12.4201	+	21.5122i	0.406834	+	0.704657i
$933$	−23.6089	−	13.6306i	−0.772921	−	0.446246i
$934$	−3.09520	−	11.5514i	−0.101278	−	0.377975i
$935$		−	1.91320i		−	0.0625682i
$936$	8.55067	+	7.69429i	0.279487	+	0.251496i
$937$		−	19.6472i		−	0.641846i	−0.947105	−	0.320923i	$-0.896007\pi$
$937$		−	19.6472i		−	0.641846i	0.947105	−	0.320923i	$-0.103993\pi$
$938$		0			0
$939$	7.48016	−	12.9560i	0.244106	−	0.422804i
$940$	−54.4693	+	31.4479i	−1.77659	+	1.02572i
$941$	−16.8238	−	16.8238i	−0.548441	−	0.548441i	0.377549	−	0.925990i	$-0.376767\pi$
$941$	−16.8238	−	16.8238i	−0.548441	−	0.548441i	−0.925990	+	0.377549i	$0.876767\pi$
$942$	−0.171072	−	0.0458386i	−0.00557383	−	0.00149350i
$943$	1.34030	+	0.359132i	0.0436462	+	0.0116950i
$944$	−15.8950	+	15.8950i	−0.517339	+	0.517339i
$945$		0			0
$946$	0.289959	+	0.167408i	0.00942739	+	0.00544291i
$947$	−52.2944	+	14.0122i	−1.69934	+	0.455337i	−0.972773	−	0.231759i	$-0.925552\pi$
$947$	−52.2944	+	14.0122i	−1.69934	+	0.455337i	−0.726567	+	0.687095i	$0.758885\pi$
$948$	5.96017			0.193577
$949$	10.2162	+	31.4093i	0.331632	+	1.01959i
$950$		−	12.4304i		−	0.403297i
$951$	−15.0917	+	4.04380i	−0.489381	+	0.131129i
$952$		0			0
$953$	33.5390	−	19.3637i	1.08643	−	0.627253i	0.153809	−	0.988101i	$-0.450846\pi$
$953$	33.5390	−	19.3637i	1.08643	−	0.627253i	0.932625	+	0.360848i	$0.117513\pi$
$954$	−7.35419	+	7.35419i	−0.238101	+	0.238101i
$955$	19.7950	−	73.8760i	0.640552	−	2.39057i
$956$	−9.80506	+	36.5930i	−0.317118	+	1.18350i
$957$	0.0800663	−	0.0800663i	0.00258817	−	0.00258817i
$958$	−9.87648	+	5.70219i	−0.319094	+	0.184229i
$959$		0			0
$960$	−15.3845	+	4.12227i	−0.496533	+	0.133046i
$961$		−	26.9586i		−	0.869632i
$962$	3.65367	−	0.192608i	0.117799	−	0.00620992i
$963$	−0.129538			−0.00417429
$964$	−1.82757	+	0.489696i	−0.0588621	+	0.0157721i
$965$	43.0497	+	24.8547i	1.38582	+	0.800103i
$966$		0			0
$967$	1.90329	−	1.90329i	0.0612056	−	0.0612056i	−0.675841	−	0.737047i	$-0.736220\pi$
$967$	1.90329	−	1.90329i	0.0612056	−	0.0612056i	0.737047	+	0.675841i	$0.236220\pi$
$968$	15.6605	+	4.19622i	0.503347	+	0.134871i
$969$	−19.3270	−	5.17864i	−0.620871	−	0.166362i
$970$	1.75285	+	1.75285i	0.0562806	+	0.0562806i
$971$	0.711680	−	0.410888i	0.0228389	−	0.0131860i	−0.488537	−	0.872543i	$-0.662469\pi$
$971$	0.711680	−	0.410888i	0.0228389	−	0.0131860i	0.511376	+	0.859357i	$0.329136\pi$
$972$	14.9703	−	25.9294i	0.480174	−	0.831686i
$973$		0			0
$974$		−	5.48805i		−	0.175848i
$975$	−15.7215	−	24.1927i	−0.503490	−	0.774785i
$976$			0.401277i			0.0128445i
$977$	−3.02801	−	11.3007i	−0.0968745	−	0.361540i	0.900423	−	0.435016i	$-0.143257\pi$
$977$	−3.02801	−	11.3007i	−0.0968745	−	0.361540i	−0.997297	+	0.0734760i	$0.976591\pi$
$978$	1.34676	+	0.777553i	0.0430647	+	0.0248634i
$979$	−0.0739911	−	0.128156i	−0.00236477	−	0.00409589i
$980$		0			0
$981$	34.3624	+	9.20739i	1.09711	+	0.293969i
$982$	1.89217	−	7.06169i	0.0603817	−	0.225348i
$983$	−8.88662	+	8.88662i	−0.283439	+	0.283439i	−0.834479	−	0.551040i	$-0.814231\pi$
$983$	−8.88662	+	8.88662i	−0.283439	+	0.283439i	0.551040	+	0.834479i	$0.314231\pi$
$984$	2.09728	+	3.63260i	0.0668589	+	0.115803i
$985$	−30.6587	+	53.1024i	−0.976867	+	1.69198i
$986$	−0.824439	−	3.07685i	−0.0262555	−	0.0979868i
$987$		0			0
$988$	−24.2726	−	5.15149i	−0.772213	−	0.163891i
$989$	4.45736			0.141736
$990$	0.259738	−	0.0695966i	0.00825501	−	0.00221192i
$991$	5.39652	−	9.34706i	0.171426	−	0.296919i	−0.767492	−	0.641058i	$-0.778496\pi$
$991$	5.39652	−	9.34706i	0.171426	−	0.296919i	0.938919	+	0.344139i	$0.111829\pi$
$992$	−4.17409	−	7.22973i	−0.132527	−	0.229544i
$993$	14.0873	+	14.0873i	0.447047	+	0.447047i
$994$		0			0
$995$	12.4387	−	46.4219i	0.394334	−	1.47167i
$996$	3.69627	+	3.69627i	0.117121	+	0.117121i
$997$	−30.6571	+	17.6999i	−0.970919	+	0.560560i	−0.899516	−	0.436887i	$-0.856081\pi$
$997$	−30.6571	+	17.6999i	−0.970919	+	0.560560i	−0.0714028	+	0.997448i	$0.522748\pi$
$998$	−7.65362	−	4.41882i	−0.242271	−	0.139875i
$999$	−3.24115	−	12.0961i	−0.102546	−	0.382705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.97.3		28
7.2	even	3		91.2.ba.a.45.3	yes	28
7.3	odd	6		91.2.w.a.19.5	✓	28
7.4	even	3		637.2.x.a.19.5		28
7.5	odd	6		637.2.bb.a.227.3		28
7.6	odd	2		637.2.bd.a.97.3		28
13.11	odd	12		637.2.bd.a.440.3		28
21.2	odd	6		819.2.et.b.136.5		28
21.17	even	6		819.2.gh.b.19.3		28
91.11	odd	12		637.2.bb.a.362.3		28
91.24	even	12		91.2.ba.a.89.3	yes	28
91.37	odd	12		91.2.w.a.24.5	yes	28
91.76	even	12	inner	637.2.bd.b.440.3		28
91.89	even	12		637.2.x.a.570.5		28
273.128	even	12		819.2.gh.b.388.3		28
273.206	odd	12		819.2.et.b.271.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.5	✓	28	7.3	odd	6
91.2.w.a.24.5	yes	28	91.37	odd	12
91.2.ba.a.45.3	yes	28	7.2	even	3
91.2.ba.a.89.3	yes	28	91.24	even	12
637.2.x.a.19.5		28	7.4	even	3
637.2.x.a.570.5		28	91.89	even	12
637.2.bb.a.227.3		28	7.5	odd	6
637.2.bb.a.362.3		28	91.11	odd	12
637.2.bd.a.97.3		28	7.6	odd	2
637.2.bd.a.440.3		28	13.11	odd	12
637.2.bd.b.97.3		28	1.1	even	1	trivial
637.2.bd.b.440.3		28	91.76	even	12	inner
819.2.et.b.136.5		28	21.2	odd	6
819.2.et.b.271.5		28	273.206	odd	12
819.2.gh.b.19.3		28	21.17	even	6
819.2.gh.b.388.3		28	273.128	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0990633 - 0.369709i) q^{2} +(-0.792292 - 0.457430i) q^{3} +(1.60518 - 0.926751i) q^{4} +(2.62172 + 2.62172i) q^{5} +(-0.0906291 + 0.338232i) q^{6} +(-1.04293 - 1.04293i) q^{8} +(-1.08152 - 1.87324i) q^{9} +O(q^{10})\)	\(q+(-0.0990633 - 0.369709i) q^{2} +(-0.792292 - 0.457430i) q^{3} +(1.60518 - 0.926751i) q^{4} +(2.62172 + 2.62172i) q^{5} +(-0.0906291 + 0.338232i) q^{6} +(-1.04293 - 1.04293i) q^{8} +(-1.08152 - 1.87324i) q^{9} +(0.709559 - 1.22899i) q^{10} +(-0.0846164 + 0.0226729i) q^{11} -1.69570 q^{12} +(1.63590 - 3.21307i) q^{13} +(-0.877916 - 3.27643i) q^{15} +(1.57124 - 2.72146i) q^{16} +(2.94521 + 5.10126i) q^{17} +(-0.585415 + 0.585415i) q^{18} +(0.960980 - 3.58643i) q^{19} +(6.63802 + 1.77865i) q^{20} +(0.0167648 + 0.0290374i) q^{22} +(0.386571 + 0.223187i) q^{23} +(0.349239 + 1.30338i) q^{24} +8.74686i q^{25} +(-1.34996 - 0.286509i) q^{26} +4.72345i q^{27} +(0.706429 - 1.22357i) q^{29} +(-1.12436 + 0.649147i) q^{30} +(1.42152 + 1.42152i) q^{31} +(-4.01115 - 1.07478i) q^{32} +(0.0774122 + 0.0207425i) q^{33} +(1.59422 - 1.59422i) q^{34} +(-3.47205 - 2.00459i) q^{36} +(-2.56087 + 0.686183i) q^{37} -1.42113 q^{38} +(-2.76587 + 1.79738i) q^{39} -5.46857i q^{40} +(3.00264 - 0.804556i) q^{41} +(8.64788 - 4.99286i) q^{43} +(-0.114812 + 0.114812i) q^{44} +(2.07568 - 7.74655i) q^{45} +(0.0442192 - 0.165028i) q^{46} +(-6.47160 + 6.47160i) q^{47} +(-2.48976 + 1.43746i) q^{48} +(3.23380 - 0.866493i) q^{50} -5.38892i q^{51} +(-0.351808 - 6.67363i) q^{52} +12.5624 q^{53} +(1.74630 - 0.467921i) q^{54} +(-0.281283 - 0.162399i) q^{55} +(-2.40192 + 2.40192i) q^{57} +(-0.522347 - 0.139962i) q^{58} +(-6.90954 - 1.85141i) q^{59} +(-4.44564 - 4.44564i) q^{60} +(-0.110587 + 0.0638473i) q^{61} +(0.384727 - 0.666367i) q^{62} -4.69551i q^{64} +(12.7127 - 4.13492i) q^{65} -0.0306748i q^{66} +(-2.57703 - 9.61759i) q^{67} +(9.45519 + 5.45896i) q^{68} +(-0.204185 - 0.353658i) q^{69} +(-9.83277 - 2.63468i) q^{71} +(-0.825716 + 3.08161i) q^{72} +(-6.47753 + 6.47753i) q^{73} +(0.507376 + 0.878801i) q^{74} +(4.00108 - 6.93007i) q^{75} +(-1.78118 - 6.64744i) q^{76} +(0.938505 + 0.844511i) q^{78} -3.51488 q^{79} +(11.2543 - 3.01557i) q^{80} +(-1.08390 + 1.87736i) q^{81} +(-0.594903 - 1.03040i) q^{82} +(-2.17980 - 2.17980i) q^{83} +(-5.65256 + 21.0956i) q^{85} +(-2.70259 - 2.70259i) q^{86} +(-1.11940 + 0.646284i) q^{87} +(0.111896 + 0.0646030i) q^{88} +(0.437215 + 1.63171i) q^{89} -3.06959 q^{90} +0.827354 q^{92} +(-0.476012 - 1.77650i) q^{93} +(3.03371 + 1.75151i) q^{94} +(11.9220 - 6.88319i) q^{95} +(2.68637 + 2.68637i) q^{96} +(-0.452103 + 1.68727i) q^{97} +(0.133986 + 0.133986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Introduction

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