LMFDB - Embedded newform 637.2.bb.a.362.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, not 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			362.3
Character	$\chi$	$=$	637.362
Dual form			637.2.bb.a.227.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.270646 - 0.270646i) q^{2} +(-0.792292 - 0.457430i) q^{3} -1.85350i q^{4} +(-0.959617 - 3.58134i) q^{5} +(0.0906291 + 0.338232i) q^{6} +(-1.04293 + 1.04293i) q^{8} +(-1.08152 - 1.87324i) q^{9} +O(q^{10})$	\(q+(-0.270646 - 0.270646i) q^{2} +(-0.792292 - 0.457430i) q^{3} -1.85350i q^{4} +(-0.959617 - 3.58134i) 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} +(0.0226729 + 0.0846164i) q^{11} +(-0.847848 + 1.46852i) q^{12} +(-1.63590 - 3.21307i) q^{13} +(-0.877916 + 3.27643i) q^{15} -3.14247 q^{16} +5.89043 q^{17} +(-0.214277 + 0.799692i) q^{18} +(3.58643 + 0.960980i) q^{19} +(-6.63802 + 1.77865i) q^{20} +(0.0167648 - 0.0290374i) q^{22} +0.446373i q^{23} +(1.30338 - 0.349239i) q^{24} +(-7.57501 + 4.37343i) q^{25} +(-0.426856 + 1.31235i) q^{26} +4.72345i q^{27} +(0.706429 + 1.22357i) q^{29} +(1.12436 - 0.649147i) q^{30} +(1.94183 + 0.520311i) q^{31} +(2.93637 + 2.93637i) q^{32} +(0.0207425 - 0.0774122i) q^{33} +(-1.59422 - 1.59422i) q^{34} +(-3.47205 + 2.00459i) q^{36} +(1.87469 - 1.87469i) q^{37} +(-0.710566 - 1.23074i) q^{38} +(-0.173647 + 3.29400i) q^{39} +(4.73592 + 2.73428i) q^{40} +(-3.00264 - 0.804556i) q^{41} +(8.64788 + 4.99286i) q^{43} +(0.156837 - 0.0420243i) q^{44} +(-5.67087 + 5.67087i) q^{45} +(0.120809 - 0.120809i) q^{46} +(-8.84037 + 2.36877i) q^{47} +(2.48976 + 1.43746i) q^{48} +(3.23380 + 0.866493i) q^{50} +(-4.66694 - 2.69446i) q^{51} +(-5.95544 + 3.03214i) q^{52} +(-6.28118 - 10.8793i) q^{53} +(1.27838 - 1.27838i) q^{54} +(0.281283 - 0.162399i) q^{55} +(-2.40192 - 2.40192i) q^{57} +(0.139962 - 0.522347i) q^{58} +(-5.05813 - 5.05813i) q^{59} +(6.07286 + 1.62722i) q^{60} +(-0.110587 + 0.0638473i) q^{61} +(-0.384727 - 0.666367i) q^{62} +4.69551i q^{64} +(-9.93727 + 8.94203i) q^{65} +(-0.0265652 + 0.0153374i) q^{66} +(9.61759 - 2.57703i) q^{67} -10.9179i q^{68} +(0.204185 - 0.353658i) q^{69} +(-9.83277 + 2.63468i) q^{71} +(3.08161 + 0.825716i) q^{72} +(2.37094 - 8.84847i) q^{73} -1.01475 q^{74} +8.00216 q^{75} +(1.78118 - 6.64744i) q^{76} +(0.938505 - 0.844511i) q^{78} +(1.75744 - 3.04398i) q^{79} +(3.01557 + 11.2543i) 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} +(-0.989217 - 3.69181i) q^{86} -1.29257i q^{87} +(-0.111896 - 0.0646030i) q^{88} +(-1.19449 - 1.19449i) q^{89} +3.06959 q^{90} +0.827354 q^{92} +(-1.30049 - 1.30049i) q^{93} +(3.03371 + 1.75151i) q^{94} -13.7664i q^{95} +(-0.983278 - 3.66964i) q^{96} +(0.452103 + 1.68727i) q^{97} +(0.133986 - 0.133986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.270646	−	0.270646i	−0.191376	−	0.191376i	0.604915	−	0.796290i	$-0.293207\pi$
$2$	−0.270646	−	0.270646i	−0.191376	−	0.191376i	−0.796290	+	0.604915i	$0.793207\pi$
$3$	−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	$0.751741\pi$
$4$		−	1.85350i		−	0.926751i
$5$	−0.959617	−	3.58134i	−0.429154	−	1.60162i	−0.754681	−	0.656091i	$-0.772209\pi$
$5$	−0.959617	−	3.58134i	−0.429154	−	1.60162i	0.325528	−	0.945533i	$-0.394458\pi$
$6$	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
$11$	0.0226729	+	0.0846164i	0.00683614	+	0.0255128i	0.969260	−	0.246040i	$-0.0791295\pi$
$11$	0.0226729	+	0.0846164i	0.00683614	+	0.0255128i	−0.962424	+	0.271553i	$0.912463\pi$
$12$	−0.847848	+	1.46852i	−0.244753	+	0.423924i
$13$	−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
$16$	−3.14247			−0.785618
$17$	5.89043			1.42864			0.714319	−	0.699820i	$-0.246736\pi$
$17$	5.89043			1.42864			0.714319	+	0.699820i	$0.246736\pi$
$18$	−0.214277	+	0.799692i	−0.0505055	+	0.188489i
$19$	3.58643	+	0.960980i	0.822782	+	0.220464i	0.645563	−	0.763707i	$-0.276623\pi$
$19$	3.58643	+	0.960980i	0.822782	+	0.220464i	0.177220	+	0.984171i	$0.443290\pi$
$20$	−6.63802	+	1.77865i	−1.48431	+	0.397719i
$21$		0			0
$22$	0.0167648	−	0.0290374i	0.00357426	−	0.00619080i
$23$			0.446373i			0.0930753i	0.998917	+	0.0465377i	$0.0148187\pi$
$23$			0.446373i			0.0930753i	−0.998917	+	0.0465377i	$0.985181\pi$
$24$	1.30338	−	0.349239i	0.266051	−	0.0712882i
$25$	−7.57501	+	4.37343i	−1.51500	+	0.874686i
$26$	−0.426856	+	1.31235i	−0.0837133	+	0.257374i
$27$			4.72345i			0.909029i
$28$		0			0
$29$	0.706429	+	1.22357i	0.131181	+	0.227212i	0.924132	−	0.382073i	$-0.124790\pi$
$29$	0.706429	+	1.22357i	0.131181	+	0.227212i	−0.792951	+	0.609285i	$0.791457\pi$
$30$	1.12436	−	0.649147i	0.205278	−	0.118518i
$31$	1.94183	+	0.520311i	0.348762	+	0.0934505i	0.428947	−	0.903329i	$-0.358885\pi$
$31$	1.94183	+	0.520311i	0.348762	+	0.0934505i	−0.0801853	+	0.996780i	$0.525551\pi$
$32$	2.93637	+	2.93637i	0.519081	+	0.519081i
$33$	0.0207425	−	0.0774122i	0.00361081	−	0.0134757i
$34$	−1.59422	−	1.59422i	−0.273406	−	0.273406i
$35$		0			0
$36$	−3.47205	+	2.00459i	−0.578675	+	0.334098i
$37$	1.87469	−	1.87469i	0.308197	−	0.308197i	−0.536013	−	0.844210i	$-0.680070\pi$
$37$	1.87469	−	1.87469i	0.308197	−	0.308197i	0.844210	+	0.536013i	$0.180070\pi$
$38$	−0.710566	−	1.23074i	−0.115269	−	0.199652i
$39$	−0.173647	+	3.29400i	−0.0278058	+	0.527463i
$40$	4.73592	+	2.73428i	0.748815	+	0.432328i
$41$	−3.00264	−	0.804556i	−0.468934	−	0.125651i	0.0166112	−	0.999862i	$-0.494712\pi$
$41$	−3.00264	−	0.804556i	−0.468934	−	0.125651i	−0.485545	+	0.874211i	$0.661379\pi$
$42$		0			0
$43$	8.64788	+	4.99286i	1.31879	+	0.761404i	0.983534	−	0.180724i	$-0.0578439\pi$
$43$	8.64788	+	4.99286i	1.31879	+	0.761404i	0.335256	+	0.942127i	$0.391177\pi$
$44$	0.156837	−	0.0420243i	0.0236440	−	0.00633539i
$45$	−5.67087	+	5.67087i	−0.845363	+	0.845363i
$46$	0.120809	−	0.120809i	0.0178123	−	0.0178123i
$47$	−8.84037	+	2.36877i	−1.28950	+	0.345521i	−0.837471	−	0.546482i	$-0.815967\pi$
$47$	−8.84037	+	2.36877i	−1.28950	+	0.345521i	−0.452030	+	0.892003i	$0.649300\pi$
$48$	2.48976	+	1.43746i	0.359365	+	0.207480i
$49$		0			0
$50$	3.23380	+	0.866493i	0.457328	+	0.122541i
$51$	−4.66694	−	2.69446i	−0.653503	−	0.377300i
$52$	−5.95544	+	3.03214i	−0.825870	+	0.420482i
$53$	−6.28118	−	10.8793i	−0.862786	−	1.49439i	−0.869229	−	0.494410i	$-0.835384\pi$
$53$	−6.28118	−	10.8793i	−0.862786	−	1.49439i	0.00644326	−	0.999979i	$-0.497949\pi$
$54$	1.27838	−	1.27838i	0.173966	−	0.173966i
$55$	0.281283	−	0.162399i	0.0379282	−	0.0218978i
$56$		0			0
$57$	−2.40192	−	2.40192i	−0.318142	−	0.318142i
$58$	0.139962	−	0.522347i	0.0183780	−	0.0685875i
$59$	−5.05813	−	5.05813i	−0.658513	−	0.658513i	0.296515	−	0.955028i	$-0.404175\pi$
$59$	−5.05813	−	5.05813i	−0.658513	−	0.658513i	−0.955028	+	0.296515i	$0.904175\pi$
$60$	6.07286	+	1.62722i	0.784003	+	0.210073i
$61$	−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
$65$	−9.93727	+	8.94203i	−1.23257	+	1.10912i
$66$	−0.0265652	+	0.0153374i	−0.00326995	+	0.00188791i
$67$	9.61759	−	2.57703i	1.17498	−	0.314834i	0.382044	−	0.924144i	$-0.375220\pi$
$67$	9.61759	−	2.57703i	1.17498	−	0.314834i	0.792932	+	0.609310i	$0.208554\pi$
$68$		−	10.9179i		−	1.32399i
$69$	0.204185	−	0.353658i	0.0245810	−	0.0425755i
$70$		0			0
$71$	−9.83277	+	2.63468i	−1.16694	+	0.312679i	−0.789732	−	0.613451i	$-0.789781\pi$
$71$	−9.83277	+	2.63468i	−1.16694	+	0.312679i	−0.377203	+	0.926131i	$0.623114\pi$
$72$	3.08161	+	0.825716i	0.363172	+	0.0973116i
$73$	2.37094	−	8.84847i	0.277498	−	1.03563i	−0.676652	−	0.736303i	$-0.736570\pi$
$73$	2.37094	−	8.84847i	0.277498	−	1.03563i	0.954149	−	0.299332i	$-0.0967637\pi$
$74$	−1.01475			−0.117963
$75$	8.00216			0.924010
$76$	1.78118	−	6.64744i	0.204315	−	0.762514i
$77$		0			0
$78$	0.938505	−	0.844511i	0.106265	−	0.0956221i
$79$	1.75744	−	3.04398i	0.197728	−	0.342474i	−0.750064	−	0.661366i	$-0.769977\pi$
$79$	1.75744	−	3.04398i	0.197728	−	0.342474i	0.947791	+	0.318891i	$0.103311\pi$
$80$	3.01557	+	11.2543i	0.337151	+	1.25826i
$81$	−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	$-0.695886\pi$
$83$	2.17980	−	2.17980i	0.239264	−	0.239264i	0.816545	+	0.577281i	$0.195886\pi$
$84$		0			0
$85$	−5.65256	−	21.0956i	−0.613106	−	2.28814i
$86$	−0.989217	−	3.69181i	−0.106670	−	0.398098i
$87$		−	1.29257i		−	0.138578i
$88$	−0.111896	−	0.0646030i	−0.0119281	−	0.00688670i
$89$	−1.19449	−	1.19449i	−0.126616	−	0.126616i	0.640959	−	0.767575i	$-0.278537\pi$
$89$	−1.19449	−	1.19449i	−0.126616	−	0.126616i	−0.767575	+	0.640959i	$0.778537\pi$
$90$	3.06959			0.323564
$91$		0			0
$92$	0.827354			0.0862576
$93$	−1.30049	−	1.30049i	−0.134854	−	0.134854i
$94$	3.03371	+	1.75151i	0.312903	+	0.180655i
$95$		−	13.7664i		−	1.41240i
$96$	−0.983278	−	3.66964i	−0.100355	−	0.374531i
$97$	0.452103	+	1.68727i	0.0459041	+	0.171317i	0.985072	−	0.172141i	$-0.0550685\pi$
$97$	0.452103	+	1.68727i	0.0459041	+	0.171317i	−0.939168	+	0.343458i	$0.888402\pi$
$98$		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	−0.644898	−	0.764269i	$-0.723100\pi$
$101$	3.41120	−	5.90838i	0.339427	−	0.587905i	0.984325	+	0.176363i	$0.0564334\pi$
$102$	0.533844	+	1.99233i	0.0528584	+	0.197270i
$103$	−5.00029	+	8.66076i	−0.492693	+	0.853370i	−0.999965	−	0.00841640i	$-0.997321\pi$
$103$	−5.00029	+	8.66076i	−0.492693	+	0.853370i	0.507271	+	0.861787i	$0.330654\pi$
$104$	5.05716	+	1.64489i	0.495895	+	0.161295i
$105$		0			0
$106$	−1.24447	+	4.64442i	−0.120873	+	0.451106i
$107$	−0.0598871			−0.00578950			−0.00289475	−	0.999996i	$-0.500921\pi$
$107$	−0.0598871			−0.00578950			−0.00289475	+	0.999996i	$0.500921\pi$
$108$	8.75493			0.842443
$109$	−4.25671	+	15.8862i	−0.407719	+	1.52163i	0.391267	+	0.920277i	$0.372037\pi$
$109$	−4.25671	+	15.8862i	−0.407719	+	1.52163i	−0.798986	+	0.601350i	$0.794630\pi$
$110$	−0.120081	−	0.0321755i	−0.0114492	−	0.00306781i
$111$	−2.34284	+	0.627762i	−0.222372	+	0.0595845i
$112$		0			0
$113$	2.74673	−	4.75748i	0.258391	−	0.447546i	−0.707420	−	0.706793i	$-0.750141\pi$
$113$	2.74673	−	4.75748i	0.258391	−	0.447546i	0.965811	+	0.259247i	$0.0834744\pi$
$114$			1.30014i			0.121769i
$115$	1.59862	−	0.428348i	0.149072	−	0.0399436i
$116$	2.26789	−	1.30937i	0.210569	−	0.121572i
$117$	−4.24961	+	6.53941i	−0.392876	+	0.604569i
$118$			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
$122$	0.0472098	+	0.0126498i	0.00427418	+	0.00114526i
$123$	2.01094	+	2.01094i	0.181321	+	0.181321i
$124$	0.964397	−	3.59918i	0.0866054	−	0.323216i
$125$	9.82324	+	9.82324i	0.878617	+	0.878617i
$126$		0			0
$127$	14.7405	−	8.51045i	1.30801	−	0.755180i	0.326247	−	0.945285i	$-0.394216\pi$
$127$	14.7405	−	8.51045i	1.30801	−	0.755180i	0.981764	+	0.190104i	$0.0608826\pi$
$128$	7.14355	−	7.14355i	0.631407	−	0.631407i
$129$	−4.56777	−	7.91161i	−0.402170	−	0.696578i
$130$	5.10960	+	0.269359i	0.448142	+	0.0236243i
$131$	−2.35567	−	1.36005i	−0.205816	−	0.118828i	0.393549	−	0.919303i	$-0.371247\pi$
$131$	−2.35567	−	1.36005i	−0.205816	−	0.118828i	−0.599365	+	0.800475i	$0.704580\pi$
$132$	−0.143484	−	0.0384463i	−0.0124886	−	0.00334632i
$133$		0			0
$134$	−3.30042	−	1.90550i	−0.285113	−	0.164610i
$135$	16.9163	−	4.53271i	1.45592	−	0.390113i
$136$	−6.14333	+	6.14333i	−0.526786	+	0.526786i
$137$	−3.04603	+	3.04603i	−0.260240	+	0.260240i	−0.825152	−	0.564911i	$-0.808910\pi$
$137$	−3.04603	+	3.04603i	−0.260240	+	0.260240i	0.564911	+	0.825152i	$0.308910\pi$
$138$	−0.150978	+	0.0404544i	−0.0128521	+	0.00344371i
$139$	12.1251	+	7.00040i	1.02843	+	0.593766i	0.916535	−	0.399953i	$-0.130974\pi$
$139$	12.1251	+	7.00040i	1.02843	+	0.593766i	0.111898	+	0.993720i	$0.464307\pi$
$140$		0			0
$141$	8.08771	+	2.16709i	0.681108	+	0.182502i
$142$	3.37426	+	1.94813i	0.283162	+	0.163484i
$143$	0.234788	−	0.211273i	0.0196340	−	0.0176676i
$144$	3.39863	+	5.88660i	0.283219	+	0.490550i
$145$	3.70412	−	3.70412i	0.307611	−	0.307611i
$146$	−3.03649	+	1.75312i	−0.251301	+	0.145089i
$147$		0			0
$148$	−3.47473	−	3.47473i	−0.285621	−	0.285621i
$149$	−2.37346	+	8.85786i	−0.194441	+	0.725664i	0.797970	+	0.602698i	$0.205908\pi$
$149$	−2.37346	+	8.85786i	−0.194441	+	0.725664i	−0.992411	+	0.122967i	$0.960759\pi$
$150$	−2.16575	−	2.16575i	−0.176833	−	0.176833i
$151$	−7.33161	−	1.96450i	−0.596638	−	0.159869i	−0.0521530	−	0.998639i	$-0.516608\pi$
$151$	−7.33161	−	1.96450i	−0.596638	−	0.159869i	−0.544485	+	0.838770i	$0.683275\pi$
$152$	−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
$156$	6.10544	+	0.321856i	0.488826	+	0.0257691i
$157$	0.438021	−	0.252891i	0.0349578	−	0.0201829i	−0.482419	−	0.875940i	$-0.660242\pi$
$157$	0.438021	−	0.252891i	0.0349578	−	0.0201829i	0.517377	+	0.855758i	$0.326908\pi$
$158$	−1.29948	+	0.348196i	−0.103381	+	0.0277010i
$159$			11.4928i			0.911438i
$160$	7.69834	−	13.3339i	0.608607	−	1.05414i
$161$		0			0
$162$	0.801452	−	0.214748i	0.0629680	−	0.0168722i
$163$	−4.28976	−	1.14944i	−0.336000	−	0.0900308i	0.0868745	−	0.996219i	$-0.472312\pi$
$163$	−4.28976	−	1.14944i	−0.336000	−	0.0900308i	−0.422874	+	0.906188i	$0.638979\pi$
$164$	−1.49125	+	5.56541i	−0.116447	+	0.434585i
$165$	−0.297144			−0.0231327
$166$	−1.17991			−0.0915785
$167$	2.07730	−	7.75258i	0.160746	−	0.599913i	−0.837798	−	0.545980i	$-0.816158\pi$
$167$	2.07730	−	7.75258i	0.160746	−	0.599913i	0.998545	−	0.0539330i	$-0.0171757\pi$
$168$		0			0
$169$	−7.64768	+	10.5125i	−0.588283	+	0.808655i
$170$	−4.17960	+	7.23929i	−0.320561	+	0.555228i
$171$	−2.07863	−	7.75755i	−0.158957	−	0.593234i
$172$	9.25427	−	16.0289i	0.705631	−	1.22219i
$173$	−0.631547	−	1.09387i	−0.0480157	−	0.0831656i	0.841019	−	0.541006i	$-0.181956\pi$
$173$	−0.631547	−	1.09387i	−0.0480157	−	0.0831656i	−0.889034	+	0.457841i	$0.848623\pi$
$174$	−0.349828	+	0.349828i	−0.0265204	+	0.0265204i
$175$		0			0
$176$	−0.0712489	−	0.265905i	−0.00537059	−	0.0200433i
$177$	1.69378	+	6.32126i	0.127312	+	0.475135i
$178$			0.646569i			0.0484624i
$179$	1.46377	+	0.845110i	0.109408	+	0.0631665i	0.553705	−	0.832713i	$-0.313213\pi$
$179$	1.46377	+	0.845110i	0.109408	+	0.0631665i	−0.444298	+	0.895879i	$0.646547\pi$
$180$	10.5110	+	10.5110i	0.783441	+	0.783441i
$181$	8.30825			0.617547			0.308774	−	0.951136i	$-0.400081\pi$
$181$	8.30825			0.617547			0.308774	+	0.951136i	$0.400081\pi$
$182$		0			0
$183$	0.116823			0.00863578
$184$	−0.465538	−	0.465538i	−0.0343199	−	0.0343199i
$185$	−8.51287	−	4.91491i	−0.625879	−	0.361351i
$186$			0.703943i			0.0516156i
$187$	0.133553	+	0.498427i	0.00976637	+	0.0364486i
$188$	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
$193$	−3.47003	−	12.9503i	−0.249779	−	0.932186i	−0.970921	−	0.239400i	$-0.923049\pi$
$193$	−3.47003	−	12.9503i	−0.249779	−	0.932186i	0.721143	−	0.692787i	$-0.243617\pi$
$194$	0.334293	−	0.579013i	0.0240009	−	0.0415707i
$195$	11.9636	−	2.53909i	0.856730	−	0.181828i
$196$		0			0
$197$	4.28034	−	15.9744i	0.304961	−	1.13813i	−0.628017	−	0.778199i	$-0.716133\pi$
$197$	4.28034	−	15.9744i	0.304961	−	1.13813i	0.932979	−	0.359932i	$-0.117200\pi$
$198$	−0.0725253			−0.00515415
$199$	−12.9622			−0.918863			−0.459432	−	0.888213i	$-0.651947\pi$
$199$	−12.9622			−0.918863			−0.459432	+	0.888213i	$0.651947\pi$
$200$	3.33903	−	12.4614i	0.236105	−	0.881157i
$201$	−8.79875	−	2.35762i	−0.620616	−	0.166294i
$202$	−2.52231	+	0.675850i	−0.177469	+	0.0475526i
$203$		0			0
$204$	−4.99419	+	8.65018i	−0.349663	+	0.605634i
$205$			11.5256i			0.804980i
$206$	3.69731	−	0.990691i	0.257604	−	0.0690247i
$207$	0.836164	−	0.482760i	0.0581174	−	0.0335541i
$208$	5.14076	+	10.0970i	0.356448	+	0.700100i
$209$			0.325259i			0.0224986i
$210$		0			0
$211$	−3.19052	−	5.52614i	−0.219644	−	0.380435i	0.735055	−	0.678008i	$-0.237156\pi$
$211$	−3.19052	−	5.52614i	−0.219644	−	0.380435i	−0.954699	+	0.297572i	$0.903823\pi$
$212$	−20.1648	+	11.6422i	−1.38493	+	0.799587i
$213$	8.99561	+	2.41037i	0.616369	+	0.165156i
$214$	0.0162082	+	0.0162082i	0.00110797	+	0.00110797i
$215$	9.58246	−	35.7622i	0.653519	−	2.43896i
$216$	−4.92625	−	4.92625i	−0.335189	−	0.335189i
$217$		0			0
$218$	5.45161	−	3.14749i	0.369229	−	0.213175i
$219$	−5.92604	+	5.92604i	−0.400444	+	0.400444i
$220$	−0.301006	−	0.521358i	−0.0202938	−	0.0351500i
$221$	−9.63614	−	18.9264i	−0.648197	−	1.27313i
$222$	0.803981	+	0.464178i	0.0539596	+	0.0311536i
$223$	−12.3622	−	3.31244i	−0.827834	−	0.221817i	−0.180065	−	0.983655i	$-0.557631\pi$
$223$	−12.3622	−	3.31244i	−0.827834	−	0.221817i	−0.647769	+	0.761837i	$0.724298\pi$
$224$		0			0
$225$	16.3850	+	9.45986i	1.09233	+	0.630658i
$226$	−2.03098	+	0.544201i	−0.135099	+	0.0361997i
$227$	8.38467	−	8.38467i	0.556510	−	0.556510i	−0.371802	−	0.928312i	$-0.621260\pi$
$227$	8.38467	−	8.38467i	0.556510	−	0.556510i	0.928312	+	0.371802i	$0.121260\pi$
$228$	−4.45196	+	4.45196i	−0.294838	+	0.294838i
$229$	−15.2594	+	4.08875i	−1.00837	+	0.270192i	−0.724949	−	0.688803i	$-0.758137\pi$
$229$	−15.2594	+	4.08875i	−1.00837	+	0.270192i	−0.283423	+	0.958995i	$0.591470\pi$
$230$	−0.548589	−	0.316728i	−0.0361729	−	0.0208844i
$231$		0			0
$232$	−2.01286	−	0.539345i	−0.132151	−	0.0354098i
$233$	11.6063	+	6.70088i	0.760352	+	0.438989i	0.829422	−	0.558623i	$-0.188670\pi$
$233$	11.6063	+	6.70088i	0.760352	+	0.438989i	−0.0690703	+	0.997612i	$0.522003\pi$
$234$	2.92000	−	0.619727i	0.190887	−	0.0405128i
$235$	16.9667	+	29.3873i	1.10679	+	1.91701i
$236$	−9.37526	+	9.37526i	−0.610277	+	0.610277i
$237$	−2.78482	+	1.60781i	−0.180893	+	0.104439i
$238$		0			0
$239$	−14.4526	−	14.4526i	−0.934861	−	0.934861i	0.0631438	−	0.998004i	$-0.479887\pi$
$239$	−14.4526	−	14.4526i	−0.934861	−	0.934861i	−0.998004	+	0.0631438i	$0.979887\pi$
$240$	2.75883	−	10.2961i	0.178081	−	0.664609i
$241$	−0.721809	−	0.721809i	−0.0464958	−	0.0464958i	0.683477	−	0.729972i	$-0.260467\pi$
$241$	−0.721809	−	0.721809i	−0.0464958	−	0.0464958i	−0.729972	+	0.683477i	$0.760467\pi$
$242$	−4.06396	−	1.08894i	−0.261241	−	0.0699994i
$243$	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
$247$	−2.77933	−	13.0955i	−0.176844	−	0.833247i
$248$	−2.56785	+	1.48255i	−0.163058	+	0.0941418i
$249$	−2.72414	+	0.729932i	−0.172635	+	0.0462575i
$250$		−	5.31724i		−	0.336292i
$251$	5.59470	−	9.69030i	0.353134	−	0.611646i	−0.633663	−	0.773609i	$-0.718449\pi$
$251$	5.59470	−	9.69030i	0.353134	−	0.611646i	0.986797	+	0.161963i	$0.0517826\pi$
$252$		0			0
$253$	−0.0377705	+	0.0101206i	−0.00237461	+	0.000636275i
$254$	−6.29278	−	1.68615i	−0.394844	−	0.105798i
$255$	−5.17130	+	19.2996i	−0.323839	+	1.20859i
$256$	5.52428			0.345267
$257$	9.42673			0.588023			0.294012	−	0.955802i	$-0.405010\pi$
$257$	9.42673			0.588023			0.294012	+	0.955802i	$0.405010\pi$
$258$	−0.904996	+	3.37749i	−0.0563426	+	0.210273i
$259$		0			0
$260$	16.5741	+	18.4187i	1.02788	+	1.14228i
$261$	1.52803	−	2.64662i	0.0945826	−	0.163822i
$262$	0.269462	+	1.00564i	0.0166474	+	0.0621289i
$263$	−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
$268$	−4.77652	−	17.8262i	−0.291772	−	1.08891i
$269$			23.5848i			1.43799i	0.695015	+	0.718995i	$0.255398\pi$
$269$			23.5848i			1.43799i	−0.695015	+	0.718995i	$0.744602\pi$
$270$	−5.80508	−	3.35157i	−0.353286	−	0.203970i
$271$	6.42801	+	6.42801i	0.390474	+	0.390474i	0.874856	−	0.484382i	$-0.160956\pi$
$271$	6.42801	+	6.42801i	0.390474	+	0.390474i	−0.484382	+	0.874856i	$0.660956\pi$
$272$	−18.5105			−1.12236
$273$		0			0
$274$	1.64879			0.0996072
$275$	−0.541811	−	0.541811i	−0.0326725	−	0.0326725i
$276$	−0.655506	−	0.378457i	−0.0394568	−	0.0227804i
$277$			12.6627i			0.760828i	0.924816	+	0.380414i	$0.124219\pi$
$277$			12.6627i			0.760828i	−0.924816	+	0.380414i	$0.875781\pi$
$278$	−1.38697	−	5.17622i	−0.0831846	−	0.310449i
$279$	−1.12545	−	4.20023i	−0.0673788	−	0.251461i
$280$		0			0
$281$	−23.5896	+	23.5896i	−1.40724	+	1.40724i	−0.633468	+	0.773769i	$0.718369\pi$
$281$	−23.5896	+	23.5896i	−1.40724	+	1.40724i	−0.773769	+	0.633468i	$0.781631\pi$
$282$	−1.60239	−	2.77542i	−0.0954209	−	0.165274i
$283$	11.4194	−	19.7790i	0.678813	−	1.17574i	−0.296526	−	0.955025i	$-0.595828\pi$
$283$	11.4194	−	19.7790i	0.678813	−	1.17574i	0.975339	−	0.220713i	$-0.0708385\pi$
$284$	4.88339	+	18.2251i	0.289776	+	1.08146i
$285$	−6.29716	+	10.9070i	−0.373012	+	0.646075i
$286$	−0.120725	−	0.00636415i	−0.00713860	−	0.000376320i
$287$		0			0
$288$	2.32479	−	8.67624i	0.136990	−	0.511252i
$289$	17.6971			1.04101
$290$	−2.00501			−0.117738
$291$	0.413611	−	1.54362i	0.0242463	−	0.0904885i
$292$	−16.4007	−	4.39454i	−0.959776	−	0.257171i
$293$	−11.5762	+	3.10184i	−0.676290	+	0.181211i	−0.580587	−	0.814198i	$-0.697177\pi$
$293$	−11.5762	+	3.10184i	−0.676290	+	0.181211i	−0.0957036	+	0.995410i	$0.530510\pi$
$294$		0			0
$295$	−13.2610	+	22.9688i	−0.772087	+	1.33729i
$296$			3.91035i			0.227284i
$297$	−0.399682	+	0.107094i	−0.0231919	+	0.00621424i
$298$	3.03971	−	1.75498i	0.176086	−	0.101663i
$299$	1.43423	−	0.730221i	0.0829437	−	0.0422298i
$300$		−	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
$304$	−11.2702	−	3.01985i	−0.646393	−	0.173200i
$305$	0.334780	+	0.334780i	0.0191694	+	0.0191694i
$306$	−1.26218	+	4.71053i	−0.0721542	+	0.269283i
$307$	18.9842	+	18.9842i	1.08348	+	1.08348i	0.996182	+	0.0873012i	$0.0278243\pi$
$307$	18.9842	+	18.9842i	1.08348	+	1.08348i	0.0873012	+	0.996182i	$0.472176\pi$
$308$		0			0
$309$	7.92339	−	4.57457i	0.450746	−	0.260238i
$310$	−2.01730	+	2.01730i	−0.114575	+	0.114575i
$311$	14.8991	+	25.8060i	0.844851	+	1.46333i	0.885750	+	0.464162i	$0.153644\pi$
$311$	14.8991	+	25.8060i	0.844851	+	1.46333i	−0.0408993	+	0.999163i	$0.513022\pi$
$312$	−3.25433	−	3.61653i	−0.184240	−	0.204746i
$313$	−14.1617	−	8.17629i	−0.800469	−	0.462151i	0.0431661	−	0.999068i	$-0.486256\pi$
$313$	−14.1617	−	8.17629i	−0.800469	−	0.462151i	−0.843635	+	0.536917i	$0.819589\pi$
$314$	−0.186992	−	0.0501045i	−0.0105526	−	0.00282756i
$315$		0			0
$316$	−5.64202	−	3.25742i	−0.317388	−	0.183244i
$317$	−16.4961	+	4.42013i	−0.926516	+	0.248259i	−0.690368	−	0.723458i	$-0.742551\pi$
$317$	−16.4961	+	4.42013i	−0.926516	+	0.248259i	−0.236147	+	0.971717i	$0.575885\pi$
$318$	3.11048	−	3.11048i	0.174427	−	0.174427i
$319$	−0.0875174	+	0.0875174i	−0.00490004	+	0.00490004i
$320$	16.8162	−	4.50589i	0.940056	−	0.251887i
$321$	0.0474481	+	0.0273942i	0.00264829	+	0.00152899i
$322$		0			0
$323$	21.1256	+	5.66058i	1.17546	+	0.314963i
$324$	3.47969	+	2.00900i	0.193316	+	0.111611i
$325$	26.4441	+	17.1846i	1.46685	+	0.953228i
$326$	0.849915	+	1.47210i	0.0470724	+	0.0815318i
$327$	10.6394	−	10.6394i	0.588361	−	0.588361i
$328$	3.97066	−	2.29246i	0.219243	−	0.126580i
$329$		0			0
$330$	0.0804209	+	0.0804209i	0.00442702	+	0.00442702i
$331$	5.63617	−	21.0345i	0.309792	−	1.15616i	−0.618950	−	0.785430i	$-0.712442\pi$
$331$	5.63617	−	21.0345i	0.309792	−	1.15616i	0.928742	−	0.370728i	$-0.120892\pi$
$332$	−4.04026	−	4.04026i	−0.221738	−	0.221738i
$333$	−5.53924	−	1.48423i	−0.303548	−	0.0813355i
$334$	−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	$0.211679\pi$
$337$			22.6556i			1.23413i	−0.786912	+	0.617066i	$0.788321\pi$
$338$	4.91498	−	0.775358i	0.267340	−	0.0421739i
$339$	−4.35243	+	2.51288i	−0.236392	+	0.136481i
$340$	−39.1008	+	10.4770i	−2.12054	+	0.568196i
$341$			0.176107i			0.00953674i
$342$	−1.53698	+	2.66212i	−0.0831101	+	0.143951i
$343$		0			0
$344$	−14.2264	+	3.81195i	−0.767036	+	0.205527i
$345$	−1.46251	−	0.391878i	−0.0787389	−	0.0210980i
$346$	−0.125126	+	0.466978i	−0.00672683	+	0.0251049i
$347$	11.8708			0.637259			0.318630	−	0.947879i	$-0.396777\pi$
$347$	11.8708			0.637259			0.318630	+	0.947879i	$0.396777\pi$
$348$	−2.39578			−0.128427
$349$	5.38273	−	20.0886i	0.288131	−	1.07532i	−0.658390	−	0.752677i	$-0.728762\pi$
$349$	5.38273	−	20.0886i	0.288131	−	1.07532i	0.946521	−	0.322642i	$-0.104571\pi$
$350$		0			0
$351$	15.1768	−	7.72709i	0.810078	−	0.412441i
$352$	−0.181889	+	0.315041i	−0.00969470	+	0.0167917i
$353$	−7.23488	−	27.0009i	−0.385074	−	1.43712i	−0.838050	−	0.545593i	$-0.816305\pi$
$353$	−7.23488	−	27.0009i	−0.385074	−	1.43712i	0.452977	−	0.891522i	$-0.350362\pi$
$354$	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
$359$	4.06106	+	15.1561i	0.214334	+	0.799907i	0.986400	+	0.164364i	$0.0525571\pi$
$359$	4.06106	+	15.1561i	0.214334	+	0.799907i	−0.772065	+	0.635543i	$0.780776\pi$
$360$		−	11.8287i		−	0.623426i
$361$	−4.51552	−	2.60704i	−0.237659	−	0.137212i
$362$	−2.24859	−	2.24859i	−0.118183	−	0.118183i
$363$	−10.0564			−0.527826
$364$		0			0
$365$	−33.9646			−1.77779
$366$	−0.0316176	−	0.0316176i	−0.00165268	−	0.00165268i
$367$	−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	$0.706584\pi$
$368$		−	1.40272i		−	0.0731216i
$369$	1.74028	+	6.49481i	0.0905953	+	0.338106i
$370$	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
$375$	−3.28943	−	12.2763i	−0.169865	−	0.633947i
$376$	6.74945	−	11.6904i	0.348076	−	0.602886i
$377$	2.77578	−	4.27145i	0.142960	−	0.219991i
$378$		0			0
$379$	−0.368612	+	1.37568i	−0.0189343	+	0.0706638i	−0.974747	−	0.223314i	$-0.928312\pi$
$379$	−0.368612	+	1.37568i	−0.0189343	+	0.0706638i	0.955812	+	0.293978i	$0.0949792\pi$
$380$	−25.5160			−1.30894
$381$	−15.5718			−0.797765
$382$	−2.04348	+	7.62638i	−0.104554	+	0.390199i
$383$	−10.5704	−	2.83233i	−0.540122	−	0.144725i	−0.0215638	−	0.999767i	$-0.506865\pi$
$383$	−10.5704	−	2.83233i	−0.540122	−	0.144725i	−0.518559	+	0.855042i	$0.673531\pi$
$384$	−8.92746	+	2.39211i	−0.455578	+	0.122072i
$385$		0			0
$386$	−2.56581	+	4.44411i	−0.130596	+	0.226199i
$387$		−	21.5994i		−	1.09796i
$388$	3.12736	−	0.837974i	0.158768	−	0.0425417i
$389$	23.9984	−	13.8555i	1.21677	−	0.702502i	0.252544	−	0.967586i	$-0.418733\pi$
$389$	23.9984	−	13.8555i	1.21677	−	0.702502i	0.964225	+	0.265084i	$0.0853995\pi$
$390$	−3.92509	−	2.55070i	−0.198755	−	0.129160i
$391$			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
$395$	−12.5880	−	3.37294i	−0.633371	−	0.169711i
$396$	−0.248343	−	0.248343i	−0.0124797	−	0.0124797i
$397$	3.25335	−	12.1417i	0.163281	−	0.609373i	−0.834972	−	0.550292i	$-0.814516\pi$
$397$	3.25335	−	12.1417i	0.163281	−	0.609373i	0.998253	−	0.0590806i	$-0.0188169\pi$
$398$	3.50816	+	3.50816i	0.175848	+	0.175848i
$399$		0			0
$400$	23.8042	−	13.7434i	1.19021	−	0.687169i
$401$	−17.4913	+	17.4913i	−0.873475	+	0.873475i	−0.992849	−	0.119374i	$-0.961911\pi$
$401$	−17.4913	+	17.4913i	−0.873475	+	0.873475i	0.119374	+	0.992849i	$0.461911\pi$
$402$	1.74327	+	3.01943i	0.0869462	+	0.150595i
$403$	−1.50483	−	7.09040i	−0.0749610	−	0.353198i
$404$	−10.9512	−	6.32267i	−0.544842	−	0.314565i
$405$	7.76359	+	2.08025i	0.385776	+	0.103368i
$406$		0			0
$407$	0.201134	+	0.116125i	0.00996983	+	0.00575609i
$408$	7.67746	−	2.05717i	0.380091	−	0.101845i
$409$	−8.05291	+	8.05291i	−0.398191	+	0.398191i	−0.877594	−	0.479404i	$-0.840853\pi$
$409$	−8.05291	+	8.05291i	−0.398191	+	0.398191i	0.479404	+	0.877594i	$0.340853\pi$
$410$	3.11934	−	3.11934i	0.154053	−	0.154053i
$411$	3.80670	−	1.02000i	0.187771	−	0.0503130i
$412$	16.0527	+	9.26805i	0.790861	+	0.456604i
$413$		0			0
$414$	−0.356961	−	0.0956475i	−0.0175437	−	0.00470082i
$415$	−9.89837	−	5.71482i	−0.485892	−	0.280530i
$416$	4.63116	−	14.2384i	0.227061	−	0.698093i
$417$	−6.40439	−	11.0927i	−0.313624	−	0.543213i
$418$	0.0880299	−	0.0880299i	0.00430568	−	0.00430568i
$419$	−25.2233	+	14.5627i	−1.23224	+	0.711435i	−0.967497	−	0.252884i	$-0.918621\pi$
$419$	−25.2233	+	14.5627i	−1.23224	+	0.711435i	−0.264744	+	0.964319i	$0.585288\pi$
$420$		0			0
$421$	24.9431	+	24.9431i	1.21565	+	1.21565i	0.969140	+	0.246512i	$0.0792845\pi$
$421$	24.9431	+	24.9431i	1.21565	+	1.21565i	0.246512	+	0.969140i	$0.420715\pi$
$422$	−0.632127	+	2.35913i	−0.0307714	+	0.114841i
$423$	13.9983	+	13.9983i	0.680619	+	0.680619i
$424$	17.8973	+	4.79556i	0.869168	+	0.232893i
$425$	−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
$429$	−0.282664	+	0.0599912i	−0.0136471	+	0.00289640i
$430$	−12.2724	+	7.08545i	−0.591826	+	0.341691i
$431$	3.15664	−	0.845820i	0.152050	−	0.0407417i	−0.181991	−	0.983300i	$-0.558254\pi$
$431$	3.15664	−	0.845820i	0.152050	−	0.0407417i	0.334041	+	0.942558i	$0.391588\pi$
$432$		−	14.8433i		−	0.714149i
$433$	9.82888	−	17.0241i	0.472346	−	0.818127i	−0.527153	−	0.849770i	$-0.676741\pi$
$433$	9.82888	−	17.0241i	0.472346	−	0.818127i	0.999499	+	0.0316430i	$0.0100740\pi$
$434$		0			0
$435$	−4.62913	+	1.24037i	−0.221950	+	0.0594713i
$436$	29.4452	+	7.88981i	1.41017	+	0.377854i
$437$	−0.428956	+	1.60089i	−0.0205197	+	0.0765807i
$438$	3.20771			0.153271
$439$	37.8075			1.80445			0.902226	−	0.431263i	$-0.141932\pi$
$439$	37.8075			1.80445			0.902226	+	0.431263i	$0.141932\pi$
$440$	−0.123988	+	0.462731i	−0.00591091	+	0.0220598i
$441$		0			0
$442$	−2.51436	+	7.73033i	−0.119596	+	0.367694i
$443$	2.31623	−	4.01183i	0.110047	−	0.190608i	−0.805742	−	0.592267i	$-0.798233\pi$
$443$	2.31623	−	4.01183i	0.110047	−	0.190608i	0.915789	+	0.401659i	$0.131566\pi$
$444$	1.16356	+	4.34245i	0.0552200	+	0.206084i
$445$	−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	−0.998366	−	0.0571356i	$-0.981803\pi$
$449$	−3.43957	−	12.8367i	−0.162324	−	0.605800i	0.836043	−	0.548664i	$-0.184863\pi$
$450$	−1.87425	−	6.99480i	−0.0883530	−	0.329738i
$451$		−	0.272315i		−	0.0128228i
$452$	−8.81800	−	5.09107i	−0.414764	−	0.239464i
$453$	4.91016	+	4.91016i	0.230700	+	0.230700i
$454$	−4.53855			−0.213005
$455$		0			0
$456$	5.01008			0.234619
$457$	−0.254661	−	0.254661i	−0.0119125	−	0.0119125i	0.701125	−	0.713038i	$-0.252681\pi$
$457$	−0.254661	−	0.254661i	−0.0119125	−	0.0119125i	−0.713038	+	0.701125i	$0.752681\pi$
$458$	5.23651	+	3.02330i	0.244686	+	0.141270i
$459$			27.8232i			1.29867i
$460$	−0.793943	−	2.96304i	−0.0370178	−	0.138152i
$461$	6.55396	+	24.4597i	0.305249	+	1.13920i	0.932731	+	0.360573i	$0.117419\pi$
$461$	6.55396	+	24.4597i	0.305249	+	1.13920i	−0.627483	+	0.778631i	$0.715915\pi$
$462$		0			0
$463$	18.4801	−	18.4801i	0.858844	−	0.858844i	−0.132358	−	0.991202i	$-0.542255\pi$
$463$	18.4801	−	18.4801i	0.858844	−	0.858844i	0.991202	+	0.132358i	$0.0422548\pi$
$464$	−2.21993	−	3.84504i	−0.103058	−	0.178501i
$465$	−3.40952	+	5.90546i	−0.158113	+	0.273859i
$466$	−1.32762	−	4.95475i	−0.0615009	−	0.229525i
$467$	15.6223	−	27.0587i	0.722916	−	1.25213i	−0.236911	−	0.971531i	$-0.576135\pi$
$467$	15.6223	−	27.0587i	0.722916	−	1.25213i	0.959826	−	0.280595i	$-0.0905318\pi$
$468$	12.1208	+	7.87665i	0.560285	+	0.364098i
$469$		0			0
$470$	3.36156	−	12.5455i	0.155057	−	0.578682i
$471$	−0.462721			−0.0213210
$472$	10.5506			0.485631
$473$	−0.226405	+	0.844955i	−0.0104101	+	0.0388511i
$474$	1.18885	+	0.318551i	0.0546056	+	0.0146315i
$475$	−31.3700	+	8.40556i	−1.43935	+	0.385673i
$476$		0			0
$477$	−13.5864	+	23.5323i	−0.622077	+	1.07747i
$478$			7.82307i			0.357819i
$479$	−28.7805	+	7.71172i	−1.31502	+	0.352357i	−0.847108	−	0.531420i	$-0.821659\pi$
$479$	−28.7805	+	7.71172i	−1.31502	+	0.352357i	−0.467907	+	0.883778i	$0.654992\pi$
$480$	−12.1987	+	7.04290i	−0.556791	+	0.321463i
$481$	−9.09030	−	2.95671i	−0.414482	−	0.134814i
$482$			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
$486$	−5.97213	−	1.60023i	−0.270901	−	0.0725878i
$487$	−10.1388	−	10.1388i	−0.459433	−	0.459433i	0.439037	−	0.898469i	$-0.355320\pi$
$487$	−10.1388	−	10.1388i	−0.459433	−	0.459433i	−0.898469	+	0.439037i	$0.855320\pi$
$488$	0.0487462	−	0.181923i	0.00220664	−	0.00823528i
$489$	2.87295	+	2.87295i	0.129920	+	0.129920i
$490$		0			0
$491$	16.5417	−	9.55034i	0.746515	−	0.431001i	−0.0779183	−	0.996960i	$-0.524827\pi$
$491$	16.5417	−	9.55034i	0.746515	−	0.431001i	0.824433	+	0.565959i	$0.191494\pi$
$492$	3.72729	−	3.72729i	0.168039	−	0.168039i
$493$	4.16117	+	7.20736i	0.187410	+	0.324603i
$494$	−2.79203	+	4.29646i	−0.125619	+	0.193307i
$495$	−0.608423	−	0.351273i	−0.0273466	−	0.0157886i
$496$	−6.10213	−	1.63506i	−0.273994	−	0.0734164i
$497$		0			0
$498$	0.934831	+	0.539725i	0.0418908	+	0.0241856i
$499$	−22.3030	+	5.97607i	−0.998420	+	0.267526i	−0.720783	−	0.693160i	$-0.756218\pi$
$499$	−22.3030	+	5.97607i	−0.998420	+	0.267526i	−0.277636	+	0.960686i	$0.589551\pi$
$500$	18.2074	−	18.2074i	0.814259	−	0.814259i
$501$	−5.19209	+	5.19209i	−0.231966	+	0.231966i
$502$	−4.13682	+	1.10846i	−0.184635	+	0.0494729i
$503$	−10.9978	−	6.34957i	−0.490367	−	0.283113i	0.234360	−	0.972150i	$-0.424701\pi$
$503$	−10.9978	−	6.34957i	−0.490367	−	0.283113i	−0.724727	+	0.689036i	$0.758034\pi$
$504$		0			0
$505$	−24.4334	−	6.54690i	−1.08727	−	0.291333i
$506$	0.0129615	+	0.00748334i	0.000576210	+	0.000332675i
$507$	10.8679	−	4.83071i	0.482662	−	0.214539i
$508$	−15.7741	−	27.3216i	−0.699864	−	1.21220i
$509$	−7.68399	+	7.68399i	−0.340587	+	0.340587i	−0.856588	−	0.516001i	$-0.827420\pi$
$509$	−7.68399	+	7.68399i	−0.340587	+	0.340587i	0.516001	+	0.856588i	$0.327420\pi$
$510$	6.62294	−	3.82375i	0.293269	−	0.169319i
$511$		0			0
$512$	−15.7822	−	15.7822i	−0.697483	−	0.697483i
$513$	−4.53914	+	16.9403i	−0.200408	+	0.747933i
$514$	−2.55130	−	2.55130i	−0.112533	−	0.112533i
$515$	35.8155	+	9.59673i	1.57822	+	0.422883i
$516$	−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
$520$	1.03798	−	19.6899i	0.0455182	−	0.863458i
$521$	28.6041	−	16.5146i	1.25317	−	0.723518i	0.281432	−	0.959581i	$-0.409191\pi$
$521$	28.6041	−	16.5146i	1.25317	−	0.723518i	0.971738	+	0.236064i	$0.0758574\pi$
$522$	−1.12985	+	0.302743i	−0.0494523	+	0.0132507i
$523$			15.6359i			0.683712i	0.939752	+	0.341856i	$0.111055\pi$
$523$			15.6359i			0.683712i	−0.939752	+	0.341856i	$0.888945\pi$
$524$	−2.52085	+	4.36624i	−0.110124	+	0.190740i
$525$		0			0
$526$	5.08247	−	1.36184i	0.221606	−	0.0593792i
$527$	11.4382	+	3.06485i	0.498255	+	0.133507i
$528$	−0.0651828	+	0.243266i	−0.00283672	+	0.0105868i
$529$	22.8008			0.991337
$530$	17.8274			0.774375
$531$	−4.00465	+	14.9455i	−0.173787	+	0.648581i
$532$		0			0
$533$	2.32692	+	10.9639i	0.100790	+	0.474899i
$534$	0.295760	−	0.512272i	0.0127988	−	0.0221682i
$535$	0.0574687	+	0.214476i	0.00248459	+	0.00927261i
$536$	−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
$541$	3.18712	+	11.8945i	0.137025	+	0.511384i	0.999981	+	0.00610564i	$0.00194350\pi$
$541$	3.18712	+	11.8945i	0.137025	+	0.511384i	−0.862956	+	0.505278i	$0.831390\pi$
$542$		−	3.47943i		−	0.149454i
$543$	−6.58256	−	3.80044i	−0.282485	−	0.163093i
$544$	17.2965	+	17.2965i	0.741579	+	0.741579i
$545$	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	$0.472764\pi$
$548$	5.64583	+	5.64583i	0.241178	+	0.241178i
$549$	0.239202	+	0.138104i	0.0102089	+	0.00589412i
$550$			0.293278i			0.0125054i
$551$	1.35773	+	5.06711i	0.0578412	+	0.215866i
$552$	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
$557$	−3.31424	−	12.3689i	−0.140429	−	0.524088i	−0.999916	−	0.0129309i	$-0.995884\pi$
$557$	−3.31424	−	12.3689i	−0.140429	−	0.524088i	0.859488	−	0.511157i	$-0.170783\pi$
$558$	−0.832177	+	1.44137i	−0.0352288	+	0.0610181i
$559$	1.89536	−	35.9541i	0.0801653	−	1.52070i
$560$		0			0
$561$	0.122182	−	0.455991i	0.00515855	−	0.0192520i
$562$	12.7689			0.538621
$563$	10.0474			0.423447			0.211723	−	0.977330i	$-0.432092\pi$
$563$	10.0474			0.423447			0.211723	+	0.977330i	$0.432092\pi$
$564$	4.01671	−	14.9906i	0.169134	−	0.631217i
$565$	−19.6740	−	5.27162i	−0.827690	−	0.221779i
$566$	−8.44371	+	2.26249i	−0.354916	+	0.0950993i
$567$		0			0
$568$	7.50713	−	13.0027i	0.314992	−	0.545583i
$569$		−	5.89515i		−	0.247138i	−0.992336	−	0.123569i	$-0.960566\pi$
$569$		−	5.89515i		−	0.247138i	0.992336	−	0.123569i	$-0.0394340\pi$
$570$	4.65623	−	1.24763i	0.195028	−	0.0522577i
$571$	0.761139	−	0.439444i	0.0318527	−	0.0183901i	−0.483989	−	0.875074i	$-0.660813\pi$
$571$	0.761139	−	0.439444i	0.0318527	−	0.0183901i	0.515842	+	0.856684i	$0.327479\pi$
$572$	−0.391596	−	0.435180i	−0.0163734	−	0.0181958i
$573$			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
$577$	0.150636	+	0.0403629i	0.00627107	+	0.00168033i	0.261953	−	0.965081i	$-0.415633\pi$
$577$	0.150636	+	0.0403629i	0.00627107	+	0.00168033i	−0.255682	+	0.966761i	$0.582300\pi$
$578$	−4.78966	−	4.78966i	−0.199224	−	0.199224i
$579$	−3.17460	+	11.8478i	−0.131932	+	0.492376i
$580$	−6.86560	−	6.86560i	−0.285079	−	0.285079i
$581$		0			0
$582$	−0.529716	+	0.305832i	−0.0219574	+	0.0126771i
$583$	0.778156	−	0.778156i	0.0322279	−	0.0322279i
$584$	6.75564	+	11.7011i	0.279550	+	0.484195i
$585$	27.4979	+	8.94395i	1.13690	+	0.369787i
$586$	3.97256	+	2.29356i	0.164105	+	0.0947460i
$587$	38.7558	+	10.3846i	1.59962	+	0.428617i	0.944928	−	0.327278i	$-0.106131\pi$
$587$	38.7558	+	10.3846i	1.59962	+	0.428617i	0.654693	+	0.755895i	$0.272798\pi$
$588$		0			0
$589$	6.46420	+	3.73211i	0.266353	+	0.153779i
$590$	9.80544	−	2.62736i	0.403684	−	0.108167i
$591$	−10.6985	+	10.6985i	−0.440076	+	0.440076i
$592$	−5.89115	+	5.89115i	−0.242125	+	0.242125i
$593$	2.34322	−	0.627863i	0.0962244	−	0.0257833i	−0.210386	−	0.977618i	$-0.567472\pi$
$593$	2.34322	−	0.627863i	0.0962244	−	0.0257833i	0.306610	+	0.951835i	$0.400805\pi$
$594$	0.137157	+	0.0791875i	0.00562761	+	0.00324910i
$595$		0			0
$596$	16.4181	+	4.39921i	0.672510	+	0.180199i
$597$	10.2698	+	5.92928i	0.420316	+	0.242669i
$598$	−0.585800	−	0.190537i	−0.0239551	−	0.00779164i
$599$	5.34796	+	9.26293i	0.218512	+	0.378473i	0.954353	−	0.298681i	$-0.0965465\pi$
$599$	5.34796	+	9.26293i	0.218512	+	0.378473i	−0.735842	+	0.677154i	$0.763213\pi$
$600$	−8.34573	+	8.34573i	−0.340713	+	0.340713i
$601$	30.2246	−	17.4502i	1.23289	−	0.711807i	0.265255	−	0.964178i	$-0.414544\pi$
$601$	30.2246	−	17.4502i	1.23289	−	0.711807i	0.967630	+	0.252371i	$0.0812104\pi$
$602$		0			0
$603$	−15.2290	−	15.2290i	−0.620171	−	0.620171i
$604$	−3.64120	+	13.5892i	−0.148159	+	0.552935i
$605$	−28.8188	−	28.8188i	−1.17165	−	1.17165i
$606$	2.30756	+	0.618308i	0.0937381	+	0.0251171i
$607$	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
$611$	22.0730	+	24.5297i	0.892977	+	0.992365i
$612$	−20.4519	+	11.8079i	−0.826718	+	0.477306i
$613$	13.1947	−	3.53552i	0.532930	−	0.142798i	0.0176892	−	0.999844i	$-0.494369\pi$
$613$	13.1947	−	3.53552i	0.532930	−	0.142798i	0.515241	+	0.857045i	$0.327702\pi$
$614$		−	10.2760i		−	0.414704i
$615$	5.27214	−	9.13161i	0.212593	−	0.368222i
$616$		0			0
$617$	−14.8331	+	3.97453i	−0.597160	+	0.160008i	−0.544723	−	0.838616i	$-0.683365\pi$
$617$	−14.8331	+	3.97453i	−0.597160	+	0.160008i	−0.0524363	+	0.998624i	$0.516699\pi$
$618$	−3.38252	−	0.906344i	−0.136065	−	0.0364585i
$619$	−1.22023	+	4.55397i	−0.0490453	+	0.183039i	−0.986103	−	0.166135i	$-0.946871\pi$
$619$	−1.22023	+	4.55397i	−0.0490453	+	0.183039i	0.937058	+	0.349174i	$0.113538\pi$
$620$	−13.8153			−0.554837
$621$	−2.10842			−0.0846081
$622$	2.95191	−	11.0167i	0.118361	−	0.441728i
$623$		0			0
$624$	0.545682	−	10.3513i	0.0218448	−	0.414384i
$625$	3.88665	−	6.73187i	0.155466	−	0.269275i
$626$	1.61994	+	6.04570i	0.0647458	+	0.241635i
$627$	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	−0.995251	−	0.0973445i	$-0.968965\pi$
$631$	−4.57205	−	17.0631i	−0.182011	−	0.679273i	0.813240	−	0.581928i	$-0.197702\pi$
$632$	1.34177	+	5.00757i	0.0533729	+	0.199190i
$633$			5.83776i			0.232030i
$634$	5.66090	+	3.26832i	0.224823	+	0.129802i
$635$	−44.6241	−	44.6241i	−1.77085	−	1.77085i
$636$	21.3019			0.844676
$637$		0			0
$638$	0.0473725			0.00187549
$639$	15.5697	+	15.5697i	0.615927	+	0.615927i
$640$	−32.4386	−	18.7284i	−1.28225	−	0.740306i
$641$		−	37.2148i		−	1.46990i	−0.678124	−	0.734948i	$-0.737207\pi$
$641$		−	37.2148i		−	1.46990i	0.678124	−	0.734948i	$-0.262793\pi$
$642$	−0.00542751	−	0.0202557i	−0.000214207	−	0.000799431i
$643$	−2.17224	−	8.10691i	−0.0856648	−	0.319705i	0.909774	−	0.415103i	$-0.136254\pi$
$643$	−2.17224	−	8.10691i	−0.0856648	−	0.319705i	−0.995439	+	0.0953976i	$0.969588\pi$
$644$		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	$0.336290\pi$
$647$	−12.9222	+	22.3819i	−0.508024	+	0.879923i	−0.999957	+	0.00928983i	$0.997043\pi$
$648$	−0.827533	−	3.08840i	−0.0325086	−	0.121324i
$649$	0.313319	−	0.542684i	0.0122988	−	0.0213022i
$650$	−2.50605	−	11.8079i	−0.0982955	−	0.463144i
$651$		0			0
$652$	−2.13048	+	7.95107i	−0.0834362	+	0.311388i
$653$	32.0109			1.25268			0.626341	−	0.779549i	$-0.284552\pi$
$653$	32.0109			1.25268			0.626341	+	0.779549i	$0.284552\pi$
$654$	−5.75902			−0.225196
$655$	−2.61025	+	9.74159i	−0.101991	+	0.380636i
$656$	9.43572	+	2.52829i	0.368403	+	0.0987133i
$657$	−19.1395	+	5.12842i	−0.746703	+	0.200079i
$658$		0			0
$659$	1.93932	−	3.35900i	0.0755452	−	0.130848i	−0.825778	−	0.563995i	$-0.809264\pi$
$659$	1.93932	−	3.35900i	0.0755452	−	0.130848i	0.901323	+	0.433147i	$0.142597\pi$
$660$			0.550758i			0.0214382i
$661$	8.97619	−	2.40516i	0.349133	−	0.0935500i	−0.0799905	−	0.996796i	$-0.525489\pi$
$661$	8.97619	−	2.40516i	0.349133	−	0.0935500i	0.429124	+	0.903246i	$0.358822\pi$
$662$	−7.21829	+	4.16748i	−0.280547	+	0.161974i
$663$	−1.02286	+	19.4031i	−0.0397245	+	0.753553i
$664$			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
$668$	−14.3694	−	3.85027i	−0.555969	−	0.148972i
$669$	8.27927	+	8.27927i	0.320095	+	0.320095i
$670$	−3.65710	+	13.6485i	−0.141286	+	0.527287i
$671$	−0.00790985	−	0.00790985i	−0.000305356	−	0.000305356i
$672$		0			0
$673$	24.3896	−	14.0814i	0.940151	−	0.542797i	0.0501436	−	0.998742i	$-0.484032\pi$
$673$	24.3896	−	14.0814i	0.940151	−	0.542797i	0.890008	+	0.455945i	$0.150699\pi$
$674$	6.13166	−	6.13166i	0.236183	−	0.236183i
$675$	−20.6577	−	35.7802i	−0.795115	−	1.37718i
$676$	19.4850	+	14.1750i	0.749422	+	0.545192i
$677$	24.5782	+	14.1902i	0.944617	+	0.545375i	0.891405	−	0.453209i	$-0.149721\pi$
$677$	24.5782	+	14.1902i	0.944617	+	0.545375i	0.0532122	+	0.998583i	$0.483054\pi$
$678$	1.85807	+	0.497868i	0.0713586	+	0.0191205i
$679$		0			0
$680$	27.8966	+	16.1061i	1.06979	+	0.617641i
$681$	−10.4785	+	2.80771i	−0.401537	+	0.107592i
$682$	0.0476627	−	0.0476627i	0.00182510	−	0.00182510i
$683$	17.2778	−	17.2778i	0.661118	−	0.661118i	−0.294526	−	0.955644i	$-0.595162\pi$
$683$	17.2778	−	17.2778i	0.661118	−	0.661118i	0.955644	+	0.294526i	$0.0951616\pi$
$684$	−14.3786	+	3.85274i	−0.549780	+	0.147313i
$685$	13.8319	+	7.98586i	0.528490	+	0.305124i
$686$		0			0
$687$	13.9603	+	3.74064i	0.532617	+	0.142714i
$688$	−27.1757	−	15.6899i	−1.03606	−	0.598172i
$689$	−24.6807	+	37.9793i	−0.940259	+	1.44690i
$690$	0.289762	+	0.501883i	0.0110311	+	0.0191063i
$691$	22.9402	−	22.9402i	0.872688	−	0.872688i	−0.120077	−	0.992765i	$-0.538314\pi$
$691$	22.9402	−	22.9402i	0.872688	−	0.872688i	0.992765	+	0.120077i	$0.0383140\pi$
$692$	−2.02749	+	1.17057i	−0.0770738	+	0.0444986i
$693$		0			0
$694$	−3.21279	−	3.21279i	−0.121956	−	0.121956i
$695$	13.4354	−	50.1416i	0.509634	−	1.90198i
$696$	1.34806	+	1.34806i	0.0510983	+	0.0510983i
$697$	−17.6869	−	4.73918i	−0.669937	−	0.179509i
$698$	−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	$-0.616492\pi$
$701$		−	49.4461i		−	1.86755i	0.357856	−	0.933777i	$-0.383508\pi$
$702$	−6.19884	−	2.01623i	−0.233960	−	0.0760978i
$703$	8.52496	−	4.92189i	0.321525	−	0.185632i
$704$	−0.397317	+	0.106461i	−0.0149745	+	0.00401240i
$705$		−	31.0444i		−	1.16920i
$706$	−5.34960	+	9.26578i	−0.201335	+	0.348722i
$707$		0			0
$708$	11.7165	−	3.13942i	0.440332	−	0.117987i
$709$	17.2101	+	4.61145i	0.646341	+	0.173186i	0.567074	−	0.823667i	$-0.308075\pi$
$709$	17.2101	+	4.61145i	0.646341	+	0.173186i	0.0792669	+	0.996853i	$0.474742\pi$
$710$	3.73892	−	13.9539i	0.140319	−	0.523679i
$711$	−7.60280			−0.285127
$712$	2.49156			0.0933750
$713$	−0.232253	+	0.866779i	−0.00869794	+	0.0324611i
$714$		0			0
$715$	−0.981949	−	0.638115i	−0.0367228	−	0.0238641i
$716$	1.56641	−	2.71311i	0.0585396	−	0.101394i
$717$	4.83963	+	18.0617i	0.180739	+	0.674528i
$718$	3.00282	−	5.20104i	0.112064	−	0.194101i
$719$	13.9168	+	24.1047i	0.519011	+	0.898953i	0.999756	+	0.0220927i	$0.00703289\pi$
$719$	13.9168	+	24.1047i	0.519011	+	0.898953i	−0.480745	+	0.876860i	$0.659634\pi$
$720$	17.8205	−	17.8205i	0.664132	−	0.664132i
$721$		0			0
$722$	0.516523	+	1.92769i	0.0192230	+	0.0717412i
$723$	0.241707	+	0.902062i	0.00898917	+	0.0335480i
$724$		−	15.3994i		−	0.572312i
$725$	−10.7024	−	6.17904i	−0.397478	−	0.229484i
$726$	2.72174	+	2.72174i	0.101013	+	0.101013i
$727$	−47.3797			−1.75722			−0.878608	−	0.477544i	$-0.841527\pi$
$727$	−47.3797			−1.75722			−0.878608	+	0.477544i	$0.841527\pi$
$728$		0			0
$729$	−8.27491			−0.306478
$730$	9.19237	+	9.19237i	0.340225	+	0.340225i
$731$	50.9397	+	29.4101i	1.88407	+	1.08777i
$732$		−	0.216531i		−	0.00800322i
$733$	−7.74821	−	28.9167i	−0.286187	−	1.06806i	−0.947968	−	0.318366i	$-0.896866\pi$
$733$	−7.74821	−	28.9167i	−0.286187	−	1.06806i	0.661781	−	0.749697i	$-0.269801\pi$
$734$	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
$739$	3.28151	+	12.2468i	0.120712	+	0.450505i	0.999651	−	0.0264308i	$-0.00841417\pi$
$739$	3.28151	+	12.2468i	0.120712	+	0.450505i	−0.878938	+	0.476936i	$0.841748\pi$
$740$	−9.10979	+	15.7786i	−0.334883	+	0.580034i
$741$	−3.78824	+	11.6468i	−0.139165	+	0.427857i
$742$		0			0
$743$	−5.17566	+	19.3158i	−0.189877	+	0.708629i	0.803657	+	0.595093i	$0.202885\pi$
$743$	−5.17566	+	19.3158i	−0.189877	+	0.708629i	−0.993534	+	0.113537i	$0.963782\pi$
$744$	2.71265			0.0994505
$745$	34.0006			1.24569
$746$	−0.186613	+	0.696448i	−0.00683238	+	0.0254988i
$747$	−6.44076	−	1.72580i	−0.235655	−	0.0631436i
$748$	0.923835	−	0.247541i	0.0337788	−	0.00905099i
$749$		0			0
$750$	−2.43227	+	4.21281i	−0.0888138	+	0.153830i
$751$			31.9306i			1.16516i	0.812772	+	0.582582i	$0.197958\pi$
$751$			31.9306i			1.16516i	−0.812772	+	0.582582i	$0.802042\pi$
$752$	27.7806	−	7.44379i	1.01305	−	0.271447i
$753$	−8.86527	+	5.11837i	−0.323068	+	0.186524i
$754$	−1.90730	+	0.404797i	−0.0694599	+	0.0147418i
$755$			28.1422i			1.02420i
$756$		0			0
$757$	0.983838	+	1.70406i	0.0357582	+	0.0619350i	0.883351	−	0.468713i	$-0.155282\pi$
$757$	0.983838	+	1.70406i	0.0357582	+	0.0619350i	−0.847592	+	0.530648i	$0.821949\pi$
$758$	0.472085	−	0.272558i	0.0171469	−	0.00989976i
$759$	0.0345548	+	0.00925892i	0.00125426	+	0.000336077i
$760$	14.3574	+	14.3574i	0.520799	+	0.520799i
$761$	−1.79980	+	6.71695i	−0.0652427	+	0.243489i	−0.990844	−	0.135010i	$-0.956893\pi$
$761$	−1.79980	+	6.71695i	−0.0652427	+	0.243489i	0.925601	+	0.378500i	$0.123560\pi$
$762$	4.21443	+	4.21443i	0.152673	+	0.152673i
$763$		0			0
$764$	−33.1117	+	19.1171i	−1.19794	+	0.691631i
$765$	−33.4038	+	33.4038i	−1.20772	+	1.20772i
$766$	2.09428	+	3.62739i	0.0756693	+	0.131063i
$767$	−7.97756	+	24.5267i	−0.288053	+	0.885609i
$768$	−4.37684	−	2.52697i	−0.157936	−	0.0911843i
$769$	−2.45316	−	0.657322i	−0.0884631	−	0.0237036i	0.214316	−	0.976764i	$-0.431248\pi$
$769$	−2.45316	−	0.657322i	−0.0884631	−	0.0237036i	−0.302779	+	0.953061i	$0.597914\pi$
$770$		0			0
$771$	−7.46873	−	4.31207i	−0.268980	−	0.155295i
$772$	−24.0035	+	6.43171i	−0.863904	+	0.231482i
$773$	6.08636	−	6.08636i	0.218911	−	0.218911i	−0.589128	−	0.808039i	$-0.700529\pi$
$773$	6.08636	−	6.08636i	0.218911	−	0.218911i	0.808039	+	0.589128i	$0.200529\pi$
$774$	−5.84579	+	5.84579i	−0.210123	+	0.210123i
$775$	−16.9849	+	4.55109i	−0.610115	+	0.163480i
$776$	−2.23123	−	1.28820i	−0.0800964	−	0.0462437i
$777$		0			0
$778$	−10.2450	−	2.74514i	−0.367302	−	0.0984181i
$779$	−9.99560	−	5.77096i	−0.358129	−	0.206766i
$780$	−4.70621	−	22.1745i	−0.168509	−	0.793975i
$781$	−0.445875	−	0.772278i	−0.0159547	−	0.0276343i
$782$	0.711618	−	0.711618i	0.0254474	−	0.0254474i
$783$	−5.77948	+	3.33679i	−0.206542	+	0.119247i
$784$		0			0
$785$	−1.32602	−	1.32602i	−0.0473277	−	0.0473277i
$786$	0.246520	−	0.920025i	0.00879307	−	0.0328162i
$787$	−4.29200	−	4.29200i	−0.152993	−	0.152993i	0.626460	−	0.779453i	$-0.284503\pi$
$787$	−4.29200	−	4.29200i	−0.152993	−	0.152993i	−0.779453	+	0.626460i	$0.784503\pi$
$788$	−29.6086	−	7.93361i	−1.05476	−	0.282623i
$789$	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
$793$	0.386055	+	0.250876i	0.0137092	+	0.00890885i
$794$	−4.16660	+	2.40559i	−0.147867	+	0.0853710i
$795$	41.1596	−	11.0287i	1.45978	−	0.391147i
$796$			24.0254i			0.851557i
$797$	−0.799767	+	1.38524i	−0.0283292	+	0.0490676i	−0.879842	−	0.475266i	$-0.842352\pi$
$797$	−0.799767	+	1.38524i	−0.0283292	+	0.0490676i	0.851513	+	0.524333i	$0.175685\pi$
$798$		0			0
$799$	−52.0736	+	13.9531i	−1.84223	+	0.493624i
$800$	−35.0850	−	9.40099i	−1.24044	−	0.332375i
$801$	−0.945709	+	3.52943i	−0.0334150	+	0.124706i
$802$	9.46791			0.334324
$803$	0.802482			0.0283190
$804$	−4.36985	+	16.3085i	−0.154113	+	0.575157i
$805$		0			0
$806$	−1.51171	+	2.32626i	−0.0532478	+	0.0819392i
$807$	10.7884	−	18.6861i	0.379770	−	0.657781i
$808$	2.60439	+	9.71971i	0.0916221	+	0.341938i
$809$	−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	−0.344850	+	0.938658i	$0.612070\pi$
$811$	−36.5518	+	36.5518i	−1.28351	+	1.28351i	−0.938658	+	0.344850i	$0.887930\pi$
$812$		0			0
$813$	−2.15250	−	8.03323i	−0.0754914	−	0.281738i
$814$	−0.0230074	−	0.0858647i	−0.000806408	−	0.00300956i
$815$			16.4661i			0.576782i
$816$	14.6657	+	8.46726i	0.513403	+	0.296414i
$817$	26.2169	+	26.2169i	0.917215	+	0.917215i
$818$	4.35897			0.152408
$819$		0			0
$820$	21.3626			0.746016
$821$	−14.6049	−	14.6049i	−0.509714	−	0.509714i	0.404725	−	0.914439i	$-0.367367\pi$
$821$	−14.6049	−	14.6049i	−0.509714	−	0.509714i	−0.914439	+	0.404725i	$0.867367\pi$
$822$	−1.30633	−	0.754208i	−0.0455634	−	0.0263060i
$823$		−	51.9954i		−	1.81245i	−0.422799	−	0.906224i	$-0.638952\pi$
$823$		−	51.9954i		−	1.81245i	0.422799	−	0.906224i	$-0.361048\pi$
$824$	−3.81763	−	14.2476i	−0.132993	−	0.496338i
$825$	0.181432	+	0.677114i	0.00631666	+	0.0235741i
$826$		0			0
$827$	30.9176	−	30.9176i	1.07511	−	1.07511i	0.0781709	−	0.996940i	$-0.475092\pi$
$827$	30.9176	−	30.9176i	1.07511	−	1.07511i	0.996940	−	0.0781709i	$-0.0249080\pi$
$828$	−0.894796	−	1.54983i	−0.0310963	−	0.0538604i
$829$	−22.5718	+	39.0955i	−0.783951	+	1.35784i	0.145673	+	0.989333i	$0.453465\pi$
$829$	−22.5718	+	39.0955i	−0.783951	+	1.35784i	−0.929624	+	0.368510i	$0.879868\pi$
$830$	1.13226	+	4.22565i	0.0393013	+	0.146674i
$831$	5.79231	−	10.0326i	0.200933	−	0.348026i
$832$	15.0870	−	7.68138i	0.523048	−	0.266304i
$833$		0			0
$834$	−1.26888	+	4.73552i	−0.0439377	+	0.163978i
$835$	−29.7580			−1.02982
$836$	0.602867			0.0208506
$837$	−2.45766	+	9.17212i	−0.0849492	+	0.317035i
$838$	10.7679	+	2.88526i	0.371972	+	0.0996696i
$839$	29.8547	−	7.99955i	1.03070	−	0.276175i	0.296445	−	0.955050i	$-0.404199\pi$
$839$	29.8547	−	7.99955i	1.03070	−	0.276175i	0.734254	+	0.678875i	$0.237532\pi$
$840$		0			0
$841$	13.5019	−	23.3860i	0.465583	−	0.806414i
$842$		−	13.5015i		−	0.465292i
$843$	29.4804	−	7.89926i	1.01536	−	0.272065i
$844$	−10.2427	+	5.91363i	−0.352569	+	0.203556i
$845$	44.9877	+	17.3009i	1.54763	+	0.595170i
$846$		−	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
$850$	19.0484	+	5.10401i	0.653356	+	0.175066i
$851$	0.836810	+	0.836810i	0.0286855	+	0.0286855i
$852$	4.46762	−	16.6734i	0.153058	−	0.571221i
$853$	−22.8132	−	22.8132i	−0.781108	−	0.781108i	0.198910	−	0.980018i	$-0.436260\pi$
$853$	−22.8132	−	22.8132i	−0.781108	−	0.781108i	−0.980018	+	0.198910i	$0.936260\pi$
$854$		0			0
$855$	−25.7877	+	14.8885i	−0.881922	+	0.509178i
$856$	0.0624583	−	0.0624583i	0.00213478	−	0.00213478i
$857$	−12.8148	−	22.1959i	−0.437745	−	0.758196i	0.559771	−	0.828648i	$-0.310889\pi$
$857$	−12.8148	−	22.1959i	−0.437745	−	0.758196i	−0.997515	+	0.0704518i	$0.977556\pi$
$858$	0.0927381	+	0.0602654i	0.00316603	+	0.00205743i
$859$	−5.71477	−	3.29942i	−0.194985	−	0.112575i	0.399329	−	0.916808i	$-0.369243\pi$
$859$	−5.71477	−	3.29942i	−0.194985	−	0.112575i	−0.594314	+	0.804233i	$0.702576\pi$
$860$	−66.2854	−	17.7611i	−2.26031	−	0.605649i
$861$		0			0
$862$	−1.08325	−	0.625415i	−0.0368956	−	0.0213017i
$863$	42.9816	−	11.5169i	1.46311	−	0.392039i	0.562548	−	0.826765i	$-0.309821\pi$
$863$	42.9816	−	11.5169i	1.46311	−	0.392039i	0.900563	+	0.434725i	$0.143154\pi$
$864$	−13.8698	+	13.8698i	−0.471860	+	0.471860i
$865$	−3.31148	+	3.31148i	−0.112594	+	0.112594i
$866$	−7.26766	+	1.94736i	−0.246965	+	0.0661741i
$867$	−14.0213	−	8.09521i	−0.476189	−	0.274928i
$868$		0			0
$869$	0.297417	+	0.0796926i	0.0100892	+	0.00270339i
$870$	1.58856	+	0.917153i	0.0538571	+	0.0310944i
$871$	−24.0136	−	26.6863i	−0.813669	−	0.904230i
$872$	−12.1288	−	21.0078i	−0.410735	−	0.711413i
$873$	2.67171	−	2.67171i	0.0904236	−	0.0904236i
$874$	0.549368	−	0.317178i	0.0185827	−	0.0107287i
$875$		0			0
$876$	10.9839	+	10.9839i	0.371112	+	0.371112i
$877$	−13.6400	+	50.9050i	−0.460589	+	1.71894i	0.210527	+	0.977588i	$0.432482\pi$
$877$	−13.6400	+	50.9050i	−0.460589	+	1.71894i	−0.671115	+	0.741353i	$0.734185\pi$
$878$	−10.2324	−	10.2324i	−0.345328	−	0.345328i
$879$	10.5906	+	2.83775i	0.357213	+	0.0957150i
$880$	−0.883923	+	0.510333i	−0.0297970	+	0.0172033i
$881$	−14.4790	−	25.0784i	−0.487811	−	0.844914i	0.512090	−	0.858932i	$-0.328871\pi$
$881$	−14.4790	−	25.0784i	−0.487811	−	0.844914i	−0.999902	+	0.0140175i	$0.995538\pi$
$882$		0			0
$883$			56.4022i			1.89808i	0.315149	+	0.949042i	$0.397946\pi$
$883$			56.4022i			1.89808i	−0.315149	+	0.949042i	$0.602054\pi$
$884$	−35.0801	+	17.8606i	−1.17987	+	0.600717i
$885$	21.0132	−	12.1320i	0.706352	−	0.407812i
$886$	−1.71266	+	0.458907i	−0.0575381	+	0.0154173i
$887$			44.1021i			1.48080i	0.672165	+	0.740402i	$0.265365\pi$
$887$			44.1021i			1.48080i	−0.672165	+	0.740402i	$0.734635\pi$
$888$	1.78871	−	3.09814i	0.0600253	−	0.103967i
$889$		0			0
$890$	2.31558	−	0.620459i	0.0776186	−	0.0207978i
$891$	−0.183431	−	0.0491501i	−0.00614516	−	0.00164659i
$892$	−6.13962	+	22.9134i	−0.205570	+	0.767196i
$893$	−33.9817			−1.13715
$894$	−3.21112			−0.107396
$895$	1.62196	−	6.05325i	0.0542163	−	0.202338i
$896$		0			0
$897$	−1.47036	−	0.0775116i	−0.0490937	−	0.00258804i
$898$	−2.54328	+	4.40510i	−0.0848705	+	0.147000i
$899$	0.735125	+	2.74353i	0.0245178	+	0.0915017i
$900$	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
$905$	−7.97274	−	29.7547i	−0.265023	−	0.989079i
$906$		−	2.65783i		−	0.0883005i
$907$	8.56547	+	4.94528i	0.284412	+	0.164205i	0.635419	−	0.772168i	$-0.280827\pi$
$907$	8.56547	+	4.94528i	0.284412	+	0.164205i	−0.351007	+	0.936373i	$0.614161\pi$
$908$	−15.5410	−	15.5410i	−0.515746	−	0.515746i
$909$	−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	$0.438016\pi$
$912$	7.54795	+	7.54795i	0.249938	+	0.249938i
$913$	0.233869	+	0.135024i	0.00773993	+	0.00446865i
$914$			0.137846i			0.00455953i
$915$	−0.112105	−	0.418382i	−0.00370608	−	0.0138313i
$916$	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
$921$	−6.35708	−	23.7249i	−0.209473	−	0.781763i
$922$	4.84612	−	8.39373i	0.159598	−	0.276433i
$923$	24.5508	+	27.2833i	0.808101	+	0.898042i
$924$		0			0
$925$	−6.00195	+	22.3996i	−0.197343	+	0.736493i
$926$	−10.0031			−0.328724
$927$	21.6316			0.710474
$928$	−1.51852	+	5.66719i	−0.0498478	+	0.186035i
$929$	4.93637	+	1.32270i	0.161957	+	0.0433963i	0.338886	−	0.940827i	$-0.389950\pi$
$929$	4.93637	+	1.32270i	0.161957	+	0.0433963i	−0.176929	+	0.984224i	$0.556616\pi$
$930$	2.52106	−	0.675516i	0.0826688	−	0.0221510i
$931$		0			0
$932$	12.4201	−	21.5122i	0.406834	−	0.704657i
$933$		−	27.2612i		−	0.892492i
$934$	−11.5514	+	3.09520i	−0.377975	+	0.101278i
$935$	1.65688	−	0.956598i	0.0541856	−	0.0312841i
$936$	−2.38812	−	11.2522i	−0.0780582	−	0.367791i
$937$		−	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
$941$	−22.9818	−	6.15795i	−0.749185	−	0.200743i	−0.136028	−	0.990705i	$-0.543434\pi$
$941$	−22.9818	−	6.15795i	−0.749185	−	0.200743i	−0.613156	+	0.789962i	$0.710100\pi$
$942$	0.125233	+	0.125233i	0.00408032	+	0.00408032i
$943$	0.359132	−	1.34030i	0.0116950	−	0.0436462i
$944$	15.8950	+	15.8950i	0.517339	+	0.517339i
$945$		0			0
$946$	0.289959	−	0.167408i	0.00942739	−	0.00544291i
$947$	38.2822	−	38.2822i	1.24400	−	1.24400i	0.285678	−	0.958326i	$-0.407781\pi$
$947$	38.2822	−	38.2822i	1.24400	−	1.24400i	0.958326	−	0.285678i	$-0.0922187\pi$
$948$	2.98009	+	5.16166i	0.0967887	+	0.167643i
$949$	−32.3094	+	6.85719i	−1.04881	+	0.222594i
$950$	10.7651	+	6.21522i	0.349265	+	0.201648i
$951$	15.0917	+	4.04380i	0.489381	+	0.131129i
$952$		0			0
$953$	33.5390	+	19.3637i	1.08643	+	0.627253i	0.932625	−	0.360848i	$-0.117513\pi$
$953$	33.5390	+	19.3637i	1.08643	+	0.627253i	0.153809	+	0.988101i	$0.450846\pi$
$954$	10.0460	−	2.69182i	0.325252	−	0.0871509i
$955$	−54.0810	+	54.0810i	−1.75002	+	1.75002i
$956$	−26.7879	+	26.7879i	−0.866383	+	0.866383i
$957$	0.109373	−	0.0293063i	0.00353551	−	0.000947338i
$958$	9.87648	+	5.70219i	0.319094	+	0.184229i
$959$		0			0
$960$	−15.3845	−	4.12227i	−0.496533	−	0.133046i
$961$	−23.3468	−	13.4793i	−0.753123	−	0.434816i
$962$	1.66003	+	3.26047i	0.0535216	+	0.105122i
$963$	0.0647688	+	0.112183i	0.00208715	+	0.00361504i
$964$	−1.33787	+	1.33787i	−0.0430900	+	0.0430900i
$965$	−43.0497	+	24.8547i	−1.38582	+	0.800103i
$966$		0			0
$967$	1.90329	+	1.90329i	0.0612056	+	0.0612056i	0.737047	−	0.675841i	$-0.236220\pi$
$967$	1.90329	+	1.90329i	0.0612056	+	0.0612056i	−0.675841	+	0.737047i	$0.736220\pi$
$968$	−4.19622	+	15.6605i	−0.134871	+	0.503347i
$969$	−14.1483	−	14.1483i	−0.454509	−	0.454509i
$970$	−2.39444	−	0.641587i	−0.0768807	−	0.0206001i
$971$	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
$975$	−13.0907	−	25.7115i	−0.419238	−	0.823428i
$976$	0.347516	−	0.200638i	0.0111237	−	0.00642227i
$977$	11.3007	−	3.02801i	0.361540	−	0.0968745i	−0.0734760	−	0.997297i	$-0.523409\pi$
$977$	11.3007	−	3.02801i	0.361540	−	0.0968745i	0.435016	+	0.900423i	$0.356743\pi$
$978$		−	1.55511i		−	0.0497268i
$979$	0.0739911	−	0.128156i	0.00236477	−	0.00409589i
$980$		0			0
$981$	34.3624	−	9.20739i	1.09711	−	0.293969i
$982$	−7.06169	−	1.89217i	−0.225348	−	0.0603817i
$983$	3.25273	−	12.1393i	0.103746	−	0.387185i	−0.894454	−	0.447160i	$-0.852435\pi$
$983$	3.25273	−	12.1393i	0.103746	−	0.387185i	0.998200	+	0.0599750i	$0.0191021\pi$
$984$	−4.19456			−0.133718
$985$	−61.3174			−1.95373
$986$	0.824439	−	3.07685i	0.0262555	−	0.0979868i
$987$		0			0
$988$	−24.2726	+	5.15149i	−0.772213	+	0.163891i
$989$	−2.22868	+	3.86019i	−0.0708679	+	0.122747i
$990$	0.0695966	+	0.259738i	0.00221192	+	0.00825501i
$991$	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
$996$	1.35293	+	5.04920i	0.0428692	+	0.159990i
$997$		−	35.3997i		−	1.12112i	−0.828114	−	0.560560i	$-0.810586\pi$
$997$		−	35.3997i		−	1.12112i	0.828114	−	0.560560i	$-0.189414\pi$
$998$	7.65362	+	4.41882i	0.242271	+	0.139875i
$999$	8.85499	+	8.85499i	0.280160	+	0.280160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.362.3		28
7.2	even	3		637.2.bd.a.440.3		28
7.3	odd	6		637.2.x.a.570.5		28
7.4	even	3		91.2.w.a.24.5	yes	28
7.5	odd	6		637.2.bd.b.440.3		28
7.6	odd	2		91.2.ba.a.89.3	yes	28
13.6	odd	12		637.2.x.a.19.5		28
21.11	odd	6		819.2.gh.b.388.3		28
21.20	even	2		819.2.et.b.271.5		28
91.6	even	12		91.2.w.a.19.5	✓	28
91.19	even	12		637.2.bd.a.97.3		28
91.32	odd	12		91.2.ba.a.45.3	yes	28
91.45	even	12	inner	637.2.bb.a.227.3		28
91.58	odd	12		637.2.bd.b.97.3		28
273.32	even	12		819.2.et.b.136.5		28
273.188	odd	12		819.2.gh.b.19.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.5	✓	28	91.6	even	12
91.2.w.a.24.5	yes	28	7.4	even	3
91.2.ba.a.45.3	yes	28	91.32	odd	12
91.2.ba.a.89.3	yes	28	7.6	odd	2
637.2.x.a.19.5		28	13.6	odd	12
637.2.x.a.570.5		28	7.3	odd	6
637.2.bb.a.227.3		28	91.45	even	12	inner
637.2.bb.a.362.3		28	1.1	even	1	trivial
637.2.bd.a.97.3		28	91.19	even	12
637.2.bd.a.440.3		28	7.2	even	3
637.2.bd.b.97.3		28	91.58	odd	12
637.2.bd.b.440.3		28	7.5	odd	6
819.2.et.b.136.5		28	273.32	even	12
819.2.et.b.271.5		28	21.20	even	2
819.2.gh.b.19.3		28	273.188	odd	12
819.2.gh.b.388.3		28	21.11	odd	6

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.270646 - 0.270646i) q^{2} +(-0.792292 - 0.457430i) q^{3} -1.85350i q^{4} +(-0.959617 - 3.58134i) q^{5} +(0.0906291 + 0.338232i) q^{6} +(-1.04293 + 1.04293i) q^{8} +(-1.08152 - 1.87324i) q^{9} +O(q^{10})\)	\(q+(-0.270646 - 0.270646i) q^{2} +(-0.792292 - 0.457430i) q^{3} -1.85350i q^{4} +(-0.959617 - 3.58134i) 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} +(0.0226729 + 0.0846164i) q^{11} +(-0.847848 + 1.46852i) q^{12} +(-1.63590 - 3.21307i) q^{13} +(-0.877916 + 3.27643i) q^{15} -3.14247 q^{16} +5.89043 q^{17} +(-0.214277 + 0.799692i) q^{18} +(3.58643 + 0.960980i) q^{19} +(-6.63802 + 1.77865i) q^{20} +(0.0167648 - 0.0290374i) q^{22} +0.446373i q^{23} +(1.30338 - 0.349239i) q^{24} +(-7.57501 + 4.37343i) q^{25} +(-0.426856 + 1.31235i) q^{26} +4.72345i q^{27} +(0.706429 + 1.22357i) q^{29} +(1.12436 - 0.649147i) q^{30} +(1.94183 + 0.520311i) q^{31} +(2.93637 + 2.93637i) q^{32} +(0.0207425 - 0.0774122i) q^{33} +(-1.59422 - 1.59422i) q^{34} +(-3.47205 + 2.00459i) q^{36} +(1.87469 - 1.87469i) q^{37} +(-0.710566 - 1.23074i) q^{38} +(-0.173647 + 3.29400i) q^{39} +(4.73592 + 2.73428i) q^{40} +(-3.00264 - 0.804556i) q^{41} +(8.64788 + 4.99286i) q^{43} +(0.156837 - 0.0420243i) q^{44} +(-5.67087 + 5.67087i) q^{45} +(0.120809 - 0.120809i) q^{46} +(-8.84037 + 2.36877i) q^{47} +(2.48976 + 1.43746i) q^{48} +(3.23380 + 0.866493i) q^{50} +(-4.66694 - 2.69446i) q^{51} +(-5.95544 + 3.03214i) q^{52} +(-6.28118 - 10.8793i) q^{53} +(1.27838 - 1.27838i) q^{54} +(0.281283 - 0.162399i) q^{55} +(-2.40192 - 2.40192i) q^{57} +(0.139962 - 0.522347i) q^{58} +(-5.05813 - 5.05813i) q^{59} +(6.07286 + 1.62722i) q^{60} +(-0.110587 + 0.0638473i) q^{61} +(-0.384727 - 0.666367i) q^{62} +4.69551i q^{64} +(-9.93727 + 8.94203i) q^{65} +(-0.0265652 + 0.0153374i) q^{66} +(9.61759 - 2.57703i) q^{67} -10.9179i q^{68} +(0.204185 - 0.353658i) q^{69} +(-9.83277 + 2.63468i) q^{71} +(3.08161 + 0.825716i) q^{72} +(2.37094 - 8.84847i) q^{73} -1.01475 q^{74} +8.00216 q^{75} +(1.78118 - 6.64744i) q^{76} +(0.938505 - 0.844511i) q^{78} +(1.75744 - 3.04398i) q^{79} +(3.01557 + 11.2543i) 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} +(-0.989217 - 3.69181i) q^{86} -1.29257i q^{87} +(-0.111896 - 0.0646030i) q^{88} +(-1.19449 - 1.19449i) q^{89} +3.06959 q^{90} +0.827354 q^{92} +(-1.30049 - 1.30049i) q^{93} +(3.03371 + 1.75151i) q^{94} -13.7664i q^{95} +(-0.983278 - 3.66964i) q^{96} +(0.452103 + 1.68727i) q^{97} +(0.133986 - 0.133986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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