LMFDB - Embedded newform 637.2.bb.b.423.3

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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			423.3
Character	$\chi$	$=$	637.423
Dual form			637.2.bb.b.509.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0825572 + 0.0825572i) q^{2} +(-2.25055 + 1.29935i) q^{3} -1.98637i q^{4} +(-1.70537 - 0.456951i) q^{5} +(-0.293070 - 0.0785278i) q^{6} +(0.329103 - 0.329103i) q^{8} +(1.87664 - 3.25044i) q^{9} +O(q^{10})$	\(q+(0.0825572 + 0.0825572i) q^{2} +(-2.25055 + 1.29935i) q^{3} -1.98637i q^{4} +(-1.70537 - 0.456951i) q^{5} +(-0.293070 - 0.0785278i) q^{6} +(0.329103 - 0.329103i) q^{8} +(1.87664 - 3.25044i) q^{9} +(-0.103066 - 0.178515i) q^{10} +(1.89103 + 0.506699i) q^{11} +(2.58100 + 4.47042i) q^{12} +(1.85749 - 3.09026i) q^{13} +(4.43175 - 1.18748i) q^{15} -3.91840 q^{16} -4.27814 q^{17} +(0.423277 - 0.113417i) q^{18} +(1.10462 + 4.12248i) q^{19} +(-0.907674 + 3.38749i) q^{20} +(0.114286 + 0.197949i) q^{22} +6.39620i q^{23} +(-0.313041 + 1.16828i) q^{24} +(-1.63066 - 0.941462i) q^{25} +(0.408473 - 0.101774i) q^{26} +1.95756i q^{27} +(-3.57954 + 6.19995i) q^{29} +(0.463908 + 0.267837i) q^{30} +(1.10769 + 4.13397i) q^{31} +(-0.981699 - 0.981699i) q^{32} +(-4.91422 + 1.31676i) q^{33} +(-0.353191 - 0.353191i) q^{34} +(-6.45657 - 3.72770i) q^{36} +(-2.00041 + 2.00041i) q^{37} +(-0.249147 + 0.431534i) q^{38} +(-0.165023 + 9.36832i) q^{39} +(-0.711626 + 0.410857i) q^{40} +(2.94901 + 11.0059i) q^{41} +(-1.55234 + 0.896243i) q^{43} +(1.00649 - 3.75627i) q^{44} +(-4.68565 + 4.68565i) q^{45} +(-0.528052 + 0.528052i) q^{46} +(1.71543 - 6.40208i) q^{47} +(8.81854 - 5.09139i) q^{48} +(-0.0568982 - 0.212347i) q^{50} +(9.62816 - 5.55882i) q^{51} +(-6.13840 - 3.68966i) q^{52} +(-2.13896 + 3.70479i) q^{53} +(-0.161611 + 0.161611i) q^{54} +(-2.99335 - 1.72821i) q^{55} +(-7.84255 - 7.84255i) q^{57} +(-0.807367 + 0.216333i) q^{58} +(1.19310 + 1.19310i) q^{59} +(-2.35878 - 8.80308i) q^{60} +(2.66960 + 1.54129i) q^{61} +(-0.249841 + 0.432737i) q^{62} +7.67470i q^{64} +(-4.57980 + 4.42125i) q^{65} +(-0.514413 - 0.296996i) q^{66} +(0.00510122 - 0.0190380i) q^{67} +8.49797i q^{68} +(-8.31093 - 14.3949i) q^{69} +(1.23109 - 4.59449i) q^{71} +(-0.452121 - 1.68734i) q^{72} +(0.954158 - 0.255666i) q^{73} -0.330297 q^{74} +4.89317 q^{75} +(8.18877 - 2.19417i) q^{76} +(-0.787046 + 0.759799i) q^{78} +(2.96860 + 5.14176i) q^{79} +(6.68230 + 1.79052i) q^{80} +(3.08636 + 5.34573i) q^{81} +(-0.665151 + 1.15208i) q^{82} +(-9.87683 + 9.87683i) q^{83} +(7.29580 + 1.95490i) q^{85} +(-0.202148 - 0.0541654i) q^{86} -18.6044i q^{87} +(0.789099 - 0.455587i) q^{88} +(-5.68247 - 5.68247i) q^{89} -0.773669 q^{90} +12.7052 q^{92} +(-7.86441 - 7.86441i) q^{93} +(0.670159 - 0.386917i) q^{94} -7.53509i q^{95} +(3.48493 + 0.933785i) q^{96} +(-14.2676 - 3.82300i) q^{97} +(5.19577 - 5.19577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0825572	+	0.0825572i	0.0583768	+	0.0583768i	0.735692	−	0.677316i	$-0.236857\pi$
$2$	0.0825572	+	0.0825572i	0.0583768	+	0.0583768i	−0.677316	+	0.735692i	$0.736857\pi$
$3$	−2.25055	+	1.29935i	−1.29935	+	0.750182i	−0.980292	−	0.197552i	$-0.936701\pi$
$3$	−2.25055	+	1.29935i	−1.29935	+	0.750182i	−0.319062	+	0.947734i	$0.603368\pi$
$4$		−	1.98637i		−	0.993184i
$5$	−1.70537	−	0.456951i	−0.762663	−	0.204355i	−0.143535	−	0.989645i	$-0.545847\pi$
$5$	−1.70537	−	0.456951i	−0.762663	−	0.204355i	−0.619128	+	0.785290i	$0.712514\pi$
$6$	−0.293070	−	0.0785278i	−0.119645	−	0.0320589i
$7$		0			0
$7$		0			0
$8$	0.329103	−	0.329103i	0.116356	−	0.116356i
$9$	1.87664	−	3.25044i	0.625547	−	1.08348i
$10$	−0.103066	−	0.178515i	−0.0325922	−	0.0564514i
$11$	1.89103	+	0.506699i	0.570166	+	0.152775i	0.532373	−	0.846510i	$-0.321301\pi$
$11$	1.89103	+	0.506699i	0.570166	+	0.152775i	0.0377930	+	0.999286i	$0.487967\pi$
$12$	2.58100	+	4.47042i	0.745069	+	1.29050i
$13$	1.85749	−	3.09026i	0.515175	−	0.857085i
$13$	1.85749	−	3.09026i	0.515175	−	0.857085i
$14$		0			0
$15$	4.43175	−	1.18748i	1.14427	−	0.306607i
$16$	−3.91840			−0.979599
$17$	−4.27814			−1.03760			−0.518801	−	0.854895i	$-0.673621\pi$
$17$	−4.27814			−1.03760			−0.518801	+	0.854895i	$0.673621\pi$
$18$	0.423277	−	0.113417i	0.0997674	−	0.0267326i
$19$	1.10462	+	4.12248i	0.253416	+	0.945762i	0.968965	+	0.247199i	$0.0795101\pi$
$19$	1.10462	+	4.12248i	0.253416	+	0.945762i	−0.715549	+	0.698563i	$0.753823\pi$
$20$	−0.907674	+	3.38749i	−0.202962	+	0.757465i
$21$		0			0
$22$	0.114286	+	0.197949i	0.0243659	+	0.0422030i
$23$			6.39620i			1.33370i	0.745192	+	0.666850i	$0.232358\pi$
$23$			6.39620i			1.33370i	−0.745192	+	0.666850i	$0.767642\pi$
$24$	−0.313041	+	1.16828i	−0.0638992	+	0.238475i
$25$	−1.63066	−	0.941462i	−0.326132	−	0.188292i
$26$	0.408473	−	0.101774i	0.0801081	−	0.0199596i
$27$			1.95756i			0.376733i
$28$		0			0
$29$	−3.57954	+	6.19995i	−0.664704	+	1.15130i	0.314661	+	0.949204i	$0.398109\pi$
$29$	−3.57954	+	6.19995i	−0.664704	+	1.15130i	−0.979365	+	0.202097i	$0.935224\pi$
$30$	0.463908	+	0.267837i	0.0846976	+	0.0489002i
$31$	1.10769	+	4.13397i	0.198948	+	0.742483i	0.991210	+	0.132302i	$0.0422367\pi$
$31$	1.10769	+	4.13397i	0.198948	+	0.742483i	−0.792262	+	0.610181i	$0.791097\pi$
$32$	−0.981699	−	0.981699i	−0.173541	−	0.173541i
$33$	−4.91422	+	1.31676i	−0.855456	+	0.229219i
$34$	−0.353191	−	0.353191i	−0.0605718	−	0.0605718i
$35$		0			0
$36$	−6.45657	−	3.72770i	−1.07609	−	0.621284i
$37$	−2.00041	+	2.00041i	−0.328866	+	0.328866i	−0.852155	−	0.523289i	$-0.824705\pi$
$37$	−2.00041	+	2.00041i	−0.328866	+	0.328866i	0.523289	+	0.852155i	$0.324705\pi$
$38$	−0.249147	+	0.431534i	−0.0404169	+	0.0700041i
$39$	−0.165023	+	9.36832i	−0.0264248	+	1.50013i
$40$	−0.711626	+	0.410857i	−0.112518	+	0.0649623i
$41$	2.94901	+	11.0059i	0.460558	+	1.71883i	0.671212	+	0.741266i	$0.265774\pi$
$41$	2.94901	+	11.0059i	0.460558	+	1.71883i	−0.210654	+	0.977561i	$0.567559\pi$
$42$		0			0
$43$	−1.55234	+	0.896243i	−0.236730	+	0.136676i	−0.613673	−	0.789561i	$-0.710309\pi$
$43$	−1.55234	+	0.896243i	−0.236730	+	0.136676i	0.376943	+	0.926236i	$0.376975\pi$
$44$	1.00649	−	3.75627i	0.151734	−	0.566279i
$45$	−4.68565	+	4.68565i	−0.698496	+	0.698496i
$46$	−0.528052	+	0.528052i	−0.0778571	+	0.0778571i
$47$	1.71543	−	6.40208i	0.250222	−	0.933839i	−0.720465	−	0.693491i	$-0.756072\pi$
$47$	1.71543	−	6.40208i	0.250222	−	0.933839i	0.970687	−	0.240348i	$-0.0772617\pi$
$48$	8.81854	−	5.09139i	1.27285	−	0.734878i
$49$		0			0
$50$	−0.0568982	−	0.212347i	−0.00804663	−	0.0300304i
$51$	9.62816	−	5.55882i	1.34821	−	0.778390i
$52$	−6.13840	−	3.68966i	−0.851243	−	0.511664i
$53$	−2.13896	+	3.70479i	−0.293809	+	0.508893i	−0.974707	−	0.223486i	$-0.928256\pi$
$53$	−2.13896	+	3.70479i	−0.293809	+	0.508893i	0.680898	+	0.732378i	$0.261590\pi$
$54$	−0.161611	+	0.161611i	−0.0219925	+	0.0219925i
$55$	−2.99335	−	1.72821i	−0.403624	−	0.233032i
$56$		0			0
$57$	−7.84255	−	7.84255i	−1.03877	−	1.03877i
$58$	−0.807367	+	0.216333i	−0.106013	+	0.0284060i
$59$	1.19310	+	1.19310i	0.155328	+	0.155328i	0.780493	−	0.625165i	$-0.214968\pi$
$59$	1.19310	+	1.19310i	0.155328	+	0.155328i	−0.625165	+	0.780493i	$0.714968\pi$
$60$	−2.35878	−	8.80308i	−0.304517	−	1.13647i
$61$	2.66960	+	1.54129i	0.341807	+	0.197342i	0.661071	−	0.750323i	$-0.270102\pi$
$61$	2.66960	+	1.54129i	0.341807	+	0.197342i	−0.319264	+	0.947666i	$0.603436\pi$
$62$	−0.249841	+	0.432737i	−0.0317298	+	0.0549577i
$63$		0			0
$64$			7.67470i			0.959338i
$65$	−4.57980	+	4.42125i	−0.568054	+	0.548388i
$66$	−0.514413	−	0.296996i	−0.0633198	−	0.0365577i
$67$	0.00510122	−	0.0190380i	0.000623213	−	0.00232586i	−0.965614	−	0.259982i	$-0.916283\pi$
$67$	0.00510122	−	0.0190380i	0.000623213	−	0.00232586i	0.966237	+	0.257656i	$0.0829501\pi$
$68$			8.49797i			1.03053i
$69$	−8.31093	−	14.3949i	−1.00052	−	1.73295i
$70$		0			0
$71$	1.23109	−	4.59449i	0.146104	−	0.545266i	−0.853600	−	0.520929i	$-0.825586\pi$
$71$	1.23109	−	4.59449i	0.146104	−	0.545266i	0.999704	−	0.0243373i	$-0.00774758\pi$
$72$	−0.452121	−	1.68734i	−0.0532830	−	0.198855i
$73$	0.954158	−	0.255666i	0.111676	−	0.0299234i	−0.202548	−	0.979272i	$-0.564922\pi$
$73$	0.954158	−	0.255666i	0.111676	−	0.0299234i	0.314224	+	0.949349i	$0.398256\pi$
$74$	−0.330297			−0.0383962
$75$	4.89317			0.565014
$76$	8.18877	−	2.19417i	0.939316	−	0.251689i
$77$		0			0
$78$	−0.787046	+	0.759799i	−0.0891154	+	0.0860303i
$79$	2.96860	+	5.14176i	0.333993	+	0.578493i	0.983291	−	0.182041i	$-0.0582704\pi$
$79$	2.96860	+	5.14176i	0.333993	+	0.578493i	−0.649298	+	0.760534i	$0.724937\pi$
$80$	6.68230	+	1.79052i	0.747104	+	0.200186i
$81$	3.08636	+	5.34573i	0.342929	+	0.593970i
$82$	−0.665151	+	1.15208i	−0.0734536	+	0.127225i
$83$	−9.87683	+	9.87683i	−1.08412	+	1.08412i	−0.0880033	+	0.996120i	$0.528049\pi$
$83$	−9.87683	+	9.87683i	−1.08412	+	1.08412i	−0.996120	+	0.0880033i	$0.971951\pi$
$84$		0			0
$85$	7.29580	+	1.95490i	0.791340	+	0.212039i
$86$	−0.202148	−	0.0541654i	−0.0217982	−	0.00584081i
$87$		−	18.6044i		−	1.99460i
$88$	0.789099	−	0.455587i	0.0841183	−	0.0485657i
$89$	−5.68247	−	5.68247i	−0.602341	−	0.602341i	0.338592	−	0.940933i	$-0.390049\pi$
$89$	−5.68247	−	5.68247i	−0.602341	−	0.602341i	−0.940933	+	0.338592i	$0.890049\pi$
$90$	−0.773669			−0.0815519
$91$		0			0
$92$	12.7052			1.32461
$93$	−7.86441	−	7.86441i	−0.815501	−	0.815501i
$94$	0.670159	−	0.386917i	0.0691216	−	0.0399074i
$95$		−	7.53509i		−	0.773084i
$96$	3.48493	+	0.933785i	0.355680	+	0.0953041i
$97$	−14.2676	−	3.82300i	−1.44866	−	0.388167i	−0.553102	−	0.833113i	$-0.686556\pi$
$97$	−14.2676	−	3.82300i	−1.44866	−	0.388167i	−0.895557	+	0.444946i	$0.853223\pi$
$98$		0			0
$99$	5.19577	−	5.19577i	0.522194	−	0.522194i
$100$	−1.87009	+	3.23909i	−0.187009	+	0.323909i
$101$	8.00479	+	13.8647i	0.796506	+	1.37959i	0.921878	+	0.387480i	$0.126654\pi$
$101$	8.00479	+	13.8647i	0.796506	+	1.37959i	−0.125372	+	0.992110i	$0.540012\pi$
$102$	1.25379	+	0.335953i	0.124144	+	0.0332643i
$103$	−5.90755	−	10.2322i	−0.582088	−	1.00821i	−0.995232	−	0.0975405i	$-0.968902\pi$
$103$	−5.90755	−	10.2322i	−0.582088	−	1.00821i	0.413143	−	0.910666i	$-0.364431\pi$
$104$	−0.405710	−	1.62832i	−0.0397831	−	0.159670i
$105$		0			0
$106$	−0.482444	+	0.129271i	−0.0468591	+	0.0125559i
$107$	7.99112			0.772531			0.386265	−	0.922388i	$-0.373765\pi$
$107$	7.99112			0.772531			0.386265	+	0.922388i	$0.373765\pi$
$108$	3.88844			0.374165
$109$	11.9616	−	3.20509i	1.14571	−	0.306992i	0.364465	−	0.931217i	$-0.381252\pi$
$109$	11.9616	−	3.20509i	1.14571	−	0.306992i	0.781245	+	0.624225i	$0.214585\pi$
$110$	−0.104446	−	0.389799i	−0.00995857	−	0.0371659i
$111$	1.90278	−	7.10127i	0.180604	−	0.674022i
$112$		0			0
$113$	4.27217	+	7.39961i	0.401892	+	0.696097i	0.993954	−	0.109795i	$-0.0350195\pi$
$113$	4.27217	+	7.39961i	0.401892	+	0.696097i	−0.592063	+	0.805892i	$0.701686\pi$
$114$		−	1.29492i		−	0.121280i
$115$	2.92275	−	10.9079i	0.272548	−	1.01716i
$116$	12.3154	+	7.11029i	1.14345	+	0.660174i
$117$	−6.55887	−	11.8370i	−0.606368	−	1.09433i
$118$			0.196998i			0.0181351i
$119$		0			0
$120$	1.06770	−	1.84931i	0.0974671	−	0.168818i
$121$	−6.20705	−	3.58364i	−0.564277	−	0.325785i
$122$	0.0931497	+	0.347640i	0.00843338	+	0.0314738i
$123$	−20.9374	−	20.9374i	−1.88786	−	1.88786i
$124$	8.21159	−	2.20029i	0.737422	−	0.197592i
$125$	8.59274	+	8.59274i	0.768558	+	0.768558i
$126$		0			0
$127$	−5.29483	−	3.05697i	−0.469840	−	0.271262i	0.246333	−	0.969185i	$-0.420774\pi$
$127$	−5.29483	−	3.05697i	−0.469840	−	0.271262i	−0.716173	+	0.697923i	$0.754108\pi$
$128$	−2.59700	+	2.59700i	−0.229545	+	0.229545i
$129$	2.32907	−	4.03408i	0.205064	−	0.355181i
$130$	−0.743101	−	0.0130897i	−0.0651743	−	0.00114804i
$131$	−4.99207	+	2.88218i	−0.436159	+	0.251817i	−0.701967	−	0.712209i	$-0.747695\pi$
$131$	−4.99207	+	2.88218i	−0.436159	+	0.251817i	0.265808	+	0.964026i	$0.414361\pi$
$132$	2.61557	+	9.76146i	0.227657	+	0.849626i
$133$		0			0
$134$	0.00199287	−	0.00115058i	0.000172157	−	9.93951e-5i
$135$	0.894511	−	3.33836i	0.0769872	−	0.287320i
$136$	−1.40795	+	1.40795i	−0.120731	+	0.120731i
$137$	4.43760	−	4.43760i	0.379130	−	0.379130i	−0.491658	−	0.870788i	$-0.663609\pi$
$137$	4.43760	−	4.43760i	0.379130	−	0.379130i	0.870788	+	0.491658i	$0.163609\pi$
$138$	0.502280	−	1.87453i	0.0427569	−	0.159571i
$139$	18.1314	−	10.4682i	1.53789	−	0.887900i	0.538927	−	0.842353i	$-0.318830\pi$
$139$	18.1314	−	10.4682i	1.53789	−	0.887900i	0.998962	−	0.0455477i	$-0.0145033\pi$
$140$		0			0
$141$	4.45791	+	16.6371i	0.375424	+	1.40110i
$142$	0.480944	−	0.277673i	0.0403599	−	0.0233018i
$143$	5.07839	−	4.90258i	0.424677	−	0.409974i
$144$	−7.35343	+	12.7365i	−0.612786	+	1.06138i
$145$	8.93750	−	8.93750i	0.742219	−	0.742219i
$146$	0.0998797	+	0.0576656i	0.00826610	+	0.00477244i
$147$		0			0
$148$	3.97356	+	3.97356i	0.326624	+	0.326624i
$149$	−14.9308	+	4.00070i	−1.22318	+	0.327750i	−0.811921	−	0.583768i	$-0.801578\pi$
$149$	−14.9308	+	4.00070i	−1.22318	+	0.327750i	−0.411260	+	0.911518i	$0.634911\pi$
$150$	0.403966	+	0.403966i	0.0329837	+	0.0329837i
$151$	1.14419	+	4.27019i	0.0931131	+	0.347503i	0.996727	−	0.0808459i	$-0.0257622\pi$
$151$	1.14419	+	4.27019i	0.0931131	+	0.347503i	−0.903614	+	0.428349i	$0.859095\pi$
$152$	1.72026	+	0.993190i	0.139531	+	0.0805583i
$153$	−8.02854	+	13.9058i	−0.649069	+	1.12422i
$154$		0			0
$155$		−	7.55609i		−	0.606920i
$156$	18.6089	+	0.327796i	1.48991	+	0.0262447i
$157$	6.00211	+	3.46532i	0.479020	+	0.276563i	0.720008	−	0.693966i	$-0.244138\pi$
$157$	6.00211	+	3.46532i	0.479020	+	0.276563i	−0.240988	+	0.970528i	$0.577471\pi$
$158$	−0.179410	+	0.669569i	−0.0142731	+	0.0532680i
$159$		−	11.1171i		−	0.881642i
$160$	1.22557	+	2.12274i	0.0968896	+	0.167818i
$161$		0			0
$162$	−0.186527	+	0.696129i	−0.0146550	+	0.0546931i
$163$	3.34785	+	12.4944i	0.262224	+	0.978634i	0.963928	+	0.266165i	$0.0857566\pi$
$163$	3.34785	+	12.4944i	0.262224	+	0.978634i	−0.701703	+	0.712469i	$0.747577\pi$
$164$	21.8617	−	5.85782i	1.70711	−	0.457419i
$165$	8.98224			0.699267
$166$	−1.63081			−0.126575
$167$	0.900490	−	0.241286i	0.0696820	−	0.0186712i	−0.223810	−	0.974633i	$-0.571849\pi$
$167$	0.900490	−	0.241286i	0.0696820	−	0.0186712i	0.293492	+	0.955962i	$0.405183\pi$
$168$		0			0
$169$	−6.09946	−	11.4803i	−0.469189	−	0.883098i
$170$	0.440929	+	0.763712i	0.0338177	+	0.0585740i
$171$	15.4728	+	4.14593i	1.18324	+	0.317047i
$172$	1.78027	+	3.08352i	0.135744	+	0.235116i
$173$	0.263780	−	0.456880i	0.0200548	−	0.0347360i	−0.855824	−	0.517267i	$-0.826949\pi$
$173$	0.263780	−	0.456880i	0.0200548	−	0.0347360i	0.875879	+	0.482531i	$0.160283\pi$
$174$	1.53592	−	1.53592i	0.116438	−	0.116438i
$175$		0			0
$176$	−7.40979	−	1.98545i	−0.558534	−	0.149659i
$177$	−4.23538	−	1.13487i	−0.318351	−	0.0853018i
$178$		−	0.938258i		−	0.0703254i
$179$	−7.16206	+	4.13502i	−0.535317	+	0.309066i	−0.743179	−	0.669093i	$-0.766683\pi$
$179$	−7.16206	+	4.13502i	−0.535317	+	0.309066i	0.207862	+	0.978158i	$0.433350\pi$
$180$	9.30743	+	9.30743i	0.693735	+	0.693735i
$181$	−14.9785			−1.11334			−0.556672	−	0.830732i	$-0.687922\pi$
$181$	−14.9785			−1.11334			−0.556672	+	0.830732i	$0.687922\pi$
$182$		0			0
$183$	−8.01075			−0.592171
$184$	2.10501	+	2.10501i	0.155183	+	0.155183i
$185$	4.32553	−	2.49734i	0.318019	−	0.183608i
$186$		−	1.29853i		−	0.0952126i
$187$	−8.09007	−	2.16773i	−0.591605	−	0.158520i
$188$	−12.7169	−	3.40748i	−0.927475	−	0.248516i
$189$		0			0
$190$	0.622076	−	0.622076i	0.0451301	−	0.0451301i
$191$	7.26461	−	12.5827i	0.525649	−	0.910450i	−0.473905	−	0.880576i	$-0.657156\pi$
$191$	7.26461	−	12.5827i	0.525649	−	0.910450i	0.999554	−	0.0298741i	$-0.00951063\pi$
$192$	−9.97216	−	17.2723i	−0.719678	−	1.24652i
$193$	−18.9107	−	5.06711i	−1.36122	−	0.364738i	−0.496957	−	0.867775i	$-0.665549\pi$
$193$	−18.9107	−	5.06711i	−1.36122	−	0.364738i	−0.864265	+	0.503037i	$0.832216\pi$
$194$	−0.862280	−	1.49351i	−0.0619081	−	0.107228i
$195$	4.56229	−	15.9010i	0.326712	−	1.13869i
$196$		0			0
$197$	−21.0175	+	5.63163i	−1.49744	+	0.401237i	−0.912240	−	0.409655i	$-0.865649\pi$
$197$	−21.0175	+	5.63163i	−1.49744	+	0.401237i	−0.585196	+	0.810892i	$0.698982\pi$
$198$	0.857896			0.0609680
$199$	−19.2813			−1.36682			−0.683408	−	0.730037i	$-0.739503\pi$
$199$	−19.2813			−1.36682			−0.683408	+	0.730037i	$0.739503\pi$
$200$	−0.846494	+	0.226817i	−0.0598562	+	0.0160384i
$201$	0.0132566	+	0.0494742i	0.000935047	+	0.00348964i
$202$	−0.483778	+	1.80548i	−0.0340385	+	0.127033i
$203$		0			0
$204$	−11.0419	−	19.1251i	−0.773085	−	1.33902i
$205$		−	20.1166i		−	1.40500i
$206$	0.357029	−	1.33245i	0.0248754	−	0.0928363i
$207$	20.7905	+	12.0034i	1.44504	+	0.834292i
$208$	−7.27838	+	12.1089i	−0.504665	+	0.839600i
$209$			8.35542i			0.577957i
$210$		0			0
$211$	1.51130	−	2.61764i	0.104042	−	0.180206i	−0.809304	−	0.587389i	$-0.800156\pi$
$211$	1.51130	−	2.61764i	0.104042	−	0.180206i	0.913346	+	0.407184i	$0.133489\pi$
$212$	7.35909	+	4.24877i	0.505424	+	0.291807i
$213$	3.19925	+	11.9397i	0.219209	+	0.818098i
$214$	0.659724	+	0.659724i	0.0450978	+	0.0450978i
$215$	3.05685	−	0.819079i	0.208475	−	0.0558607i
$216$	0.644241	+	0.644241i	0.0438350	+	0.0438350i
$217$		0			0
$218$	1.25212	+	0.722910i	0.0848040	+	0.0489616i
$219$	−1.81518	+	1.81518i	−0.122658	+	0.122658i
$220$	−3.43287	+	5.94590i	−0.231444	+	0.400873i
$221$	−7.94661	+	13.2206i	−0.534547	+	0.889313i
$222$	0.743349	−	0.429173i	0.0498903	−	0.0288042i
$223$	−1.13865	−	4.24949i	−0.0762495	−	0.284567i	0.917264	−	0.398279i	$-0.130392\pi$
$223$	−1.13865	−	4.24949i	−0.0762495	−	0.284567i	−0.993514	+	0.113712i	$0.963726\pi$
$224$		0			0
$225$	−6.12033	+	3.53357i	−0.408022	+	0.235571i
$226$	−0.258193	+	0.963589i	−0.0171747	+	0.0640970i
$227$	−2.89832	+	2.89832i	−0.192368	+	0.192368i	−0.796719	−	0.604351i	$-0.793433\pi$
$227$	−2.89832	+	2.89832i	−0.192368	+	0.192368i	0.604351	+	0.796719i	$0.293433\pi$
$228$	−15.5782	+	15.5782i	−1.03169	+	1.03169i
$229$	−3.51399	+	13.1144i	−0.232211	+	0.866623i	0.747176	+	0.664627i	$0.231409\pi$
$229$	−3.51399	+	13.1144i	−0.232211	+	0.866623i	−0.979386	+	0.201996i	$0.935257\pi$
$230$	1.14182	−	0.659228i	0.0752892	−	0.0434682i
$231$		0			0
$232$	0.862385	+	3.21846i	0.0566183	+	0.211303i
$233$	−14.1595	+	8.17501i	−0.927622	+	0.535563i	−0.886059	−	0.463573i	$-0.846567\pi$
$233$	−14.1595	+	8.17501i	−0.927622	+	0.535563i	−0.0415633	+	0.999136i	$0.513234\pi$
$234$	0.435746	−	1.51871i	0.0284856	−	0.0992811i
$235$	−5.85088	+	10.1340i	−0.381669	+	0.661071i
$236$	2.36993	−	2.36993i	0.154270	−	0.154270i
$237$	−13.3619	−	7.71452i	−0.867951	−	0.501112i
$238$		0			0
$239$	6.11495	+	6.11495i	0.395543	+	0.395543i	0.876658	−	0.481115i	$-0.159768\pi$
$239$	6.11495	+	6.11495i	0.395543	+	0.395543i	−0.481115	+	0.876658i	$0.659768\pi$
$240$	−17.3653	+	4.65303i	−1.12093	+	0.300352i
$241$	−9.49730	−	9.49730i	−0.611775	−	0.611775i	0.331633	−	0.943408i	$-0.392400\pi$
$241$	−9.49730	−	9.49730i	−0.611775	−	0.611775i	−0.943408	+	0.331633i	$0.892400\pi$
$242$	−0.216581	−	0.808292i	−0.0139224	−	0.0519590i
$243$	−18.9779	−	10.9569i	−1.21743	−	0.702885i
$244$	3.06158	−	5.30281i	0.195997	−	0.339478i
$245$		0			0
$246$		−	3.45707i		−	0.220414i
$247$	14.7914	+	4.24391i	0.941152	+	0.270034i
$248$	1.72505	+	0.995958i	0.109541	+	0.0632434i
$249$	9.39478	−	35.0618i	0.595370	−	2.22195i
$250$			1.41879i			0.0897319i
$251$	1.74301	+	3.01899i	0.110018	+	0.190557i	0.915777	−	0.401686i	$-0.131576\pi$
$251$	1.74301	+	3.01899i	0.110018	+	0.190557i	−0.805759	+	0.592243i	$0.798242\pi$
$252$		0			0
$253$	−3.24095	+	12.0954i	−0.203756	+	0.760430i
$254$	−0.184751	−	0.689501i	−0.0115923	−	0.0432631i
$255$	−18.9596	+	5.08022i	−1.18730	+	0.318136i
$256$	14.9206			0.932538
$257$	13.4479			0.838858			0.419429	−	0.907788i	$-0.362230\pi$
$257$	13.4479			0.838858			0.419429	+	0.907788i	$0.362230\pi$
$258$	0.525324	−	0.140760i	0.0327052	−	0.00876334i
$259$		0			0
$260$	8.78223	+	9.09717i	0.544651	+	0.564183i
$261$	13.4350	+	23.2702i	0.831608	+	1.44039i
$262$	−0.650076	−	0.174187i	−0.0401618	−	0.0107613i
$263$	−10.2679	−	17.7846i	−0.633147	−	1.09664i	−0.986904	−	0.161306i	$-0.948430\pi$
$263$	−10.2679	−	17.7846i	−0.633147	−	1.09664i	0.353757	−	0.935337i	$-0.384904\pi$
$264$	−1.18394	+	2.05064i	−0.0728663	+	0.126208i
$265$	5.34063	−	5.34063i	0.328072	−	0.328072i
$266$		0			0
$267$	20.1722	+	5.40513i	1.23452	+	0.330788i
$268$	−0.0378165	−	0.0101329i	−0.00231001	−	0.000618965i
$269$			10.7373i			0.654663i	0.944910	+	0.327332i	$0.106149\pi$
$269$			10.7373i			0.654663i	−0.944910	+	0.327332i	$0.893851\pi$
$270$	0.349454	−	0.201757i	0.0212671	−	0.0122786i
$271$	−1.05977	−	1.05977i	−0.0643762	−	0.0643762i	0.674186	−	0.738562i	$-0.264495\pi$
$271$	−1.05977	−	1.05977i	−0.0643762	−	0.0643762i	−0.738562	+	0.674186i	$0.764495\pi$
$272$	16.7635			1.01643
$273$		0			0
$274$	0.732712			0.0442647
$275$	−2.60658	−	2.60658i	−0.157183	−	0.157183i
$276$	−28.5937	+	16.5086i	−1.72114	+	0.993699i
$277$			4.71024i			0.283011i	0.989937	+	0.141506i	$0.0451943\pi$
$277$			4.71024i			0.283011i	−0.989937	+	0.141506i	$0.954806\pi$
$278$	2.36111	+	0.632656i	0.141610	+	0.0379442i
$279$	15.5160	+	4.15749i	0.928916	+	0.248902i
$280$		0			0
$281$	8.01227	−	8.01227i	0.477972	−	0.477972i	−0.426511	−	0.904483i	$-0.640257\pi$
$281$	8.01227	−	8.01227i	0.477972	−	0.477972i	0.904483	+	0.426511i	$0.140257\pi$
$282$	−1.00548	+	1.74155i	−0.0598757	+	0.103708i
$283$	3.93934	+	6.82313i	0.234169	+	0.405593i	0.959031	−	0.283301i	$-0.0914297\pi$
$283$	3.93934	+	6.82313i	0.234169	+	0.405593i	−0.724862	+	0.688894i	$0.758096\pi$
$284$	−9.12636	−	2.44540i	−0.541550	−	0.145108i
$285$	9.79075	+	16.9581i	0.579954	+	1.00451i
$286$	0.824001	+	0.0145147i	0.0487242	+	0.000858275i
$287$		0			0
$288$	−5.03325	+	1.34865i	−0.296587	+	0.0794703i
$289$	1.30249			0.0766172
$290$	1.47571			0.0866567
$291$	37.0774	−	9.93487i	2.17352	−	0.582392i
$292$	−0.507847	−	1.89531i	−0.0297195	−	0.110915i
$293$	−3.16216	+	11.8013i	−0.184735	+	0.689442i	0.809952	+	0.586497i	$0.199493\pi$
$293$	−3.16216	+	11.8013i	−0.184735	+	0.689442i	−0.994687	+	0.102945i	$0.967173\pi$
$294$		0			0
$295$	−1.48948	−	2.57986i	−0.0867210	−	0.150205i
$296$			1.31669i			0.0765308i
$297$	−0.991894	+	3.70180i	−0.0575556	+	0.214800i
$298$	−1.56293	−	0.902360i	−0.0905383	−	0.0522723i
$299$	19.7659	+	11.8809i	1.14309	+	0.687089i
$300$		−	9.71963i		−	0.561163i
$301$		0			0
$302$	−0.258073	+	0.446996i	−0.0148504	+	0.0257217i
$303$	−36.0303	−	20.8021i	−2.06989	−	1.19505i
$304$	−4.32832	−	16.1535i	−0.248246	−	0.926468i
$305$	−3.84835	−	3.84835i	−0.220356	−	0.220356i
$306$	−1.81084	+	0.485213i	−0.103519	+	0.0277378i
$307$	7.97207	+	7.97207i	0.454990	+	0.454990i	0.897007	−	0.442017i	$-0.145737\pi$
$307$	7.97207	+	7.97207i	0.454990	+	0.454990i	−0.442017	+	0.897007i	$0.645737\pi$
$308$		0			0
$309$	26.5904	+	15.3520i	1.51268	+	0.873345i
$310$	0.623810	−	0.623810i	0.0354300	−	0.0354300i
$311$	−6.52139	+	11.2954i	−0.369794	+	0.640502i	−0.989533	−	0.144306i	$-0.953905\pi$
$311$	−6.52139	+	11.2954i	−0.369794	+	0.640502i	0.619739	+	0.784808i	$0.287238\pi$
$312$	3.02884	+	3.13746i	0.171474	+	0.177623i
$313$	3.09510	−	1.78696i	0.174945	−	0.101005i	−0.409970	−	0.912099i	$-0.634461\pi$
$313$	3.09510	−	1.78696i	0.174945	−	0.101005i	0.584916	+	0.811094i	$0.301128\pi$
$314$	0.209430	+	0.781604i	0.0118188	+	0.0441085i
$315$		0			0
$316$	10.2134	−	5.89673i	0.574551	−	0.331717i
$317$	8.58569	−	32.0422i	0.482220	−	1.79967i	−0.110045	−	0.993927i	$-0.535099\pi$
$317$	8.58569	−	32.0422i	0.482220	−	1.79967i	0.592265	−	0.805743i	$-0.298234\pi$
$318$	0.917796	−	0.917796i	0.0514674	−	0.0514674i
$319$	−9.91051	+	9.91051i	−0.554882	+	0.554882i
$320$	3.50697	−	13.0882i	0.196045	−	0.731651i
$321$	−17.9844	+	10.3833i	−1.00379	+	0.579539i
$322$		0			0
$323$	−4.72570	−	17.6366i	−0.262945	−	0.981324i
$324$	10.6186	−	6.13064i	0.589921	−	0.340591i
$325$	−5.93830	+	3.29041i	−0.329397	+	0.182519i
$326$	−0.755110	+	1.30789i	−0.0418217	+	0.0724373i
$327$	−22.7555	+	22.7555i	−1.25838	+	1.25838i
$328$	4.59260	+	2.65154i	0.253584	+	0.146407i
$329$		0			0
$330$	0.741549	+	0.741549i	0.0408209	+	0.0408209i
$331$	0.915826	−	0.245395i	0.0503383	−	0.0134881i	−0.233562	−	0.972342i	$-0.575038\pi$
$331$	0.915826	−	0.245395i	0.0503383	−	0.0134881i	0.283900	+	0.958854i	$0.408372\pi$
$332$	19.6190	+	19.6190i	1.07673	+	1.07673i
$333$	2.74816	+	10.2563i	0.150598	+	0.562040i
$334$	0.0942618	+	0.0544221i	0.00515778	+	0.00297784i
$335$	−0.0173989	+	0.0301357i	−0.000950602	+	0.00164649i
$336$		0			0
$337$		−	14.1901i		−	0.772982i	−0.922293	−	0.386491i	$-0.873687\pi$
$337$		−	14.1901i		−	0.772982i	0.922293	−	0.386491i	$-0.126313\pi$
$338$	0.444225	−	1.45133i	0.0241626	−	0.0789421i
$339$	−19.2294	−	11.1021i	−1.04440	−	0.602984i
$340$	3.88316	−	14.4921i	0.210594	−	0.785947i
$341$			8.37871i			0.453732i
$342$	0.935117	+	1.61967i	0.0505654	+	0.0875818i
$343$		0			0
$344$	−0.215923	+	0.805837i	−0.0116418	+	0.0434478i
$345$	7.59538	+	28.3463i	0.408921	+	1.52612i
$346$	0.0594957	−	0.0159418i	0.00319851	−	0.000857038i
$347$	13.8421			0.743080			0.371540	−	0.928417i	$-0.378830\pi$
$347$	13.8421			0.743080			0.371540	+	0.928417i	$0.378830\pi$
$348$	−36.9551			−1.98100
$349$	−14.7875	+	3.96231i	−0.791559	+	0.212098i	−0.631875	−	0.775071i	$-0.717714\pi$
$349$	−14.7875	+	3.96231i	−0.791559	+	0.212098i	−0.159684	+	0.987168i	$0.551048\pi$
$350$		0			0
$351$	6.04939	+	3.63615i	0.322892	+	0.194084i
$352$	−1.35899	−	2.35384i	−0.0724345	−	0.125460i
$353$	−15.2137	−	4.07649i	−0.809742	−	0.216970i	−0.169885	−	0.985464i	$-0.554340\pi$
$353$	−15.2137	−	4.07649i	−0.809742	−	0.216970i	−0.639857	+	0.768494i	$0.721006\pi$
$354$	−0.255970	−	0.443353i	−0.0136046	−	0.0235639i
$355$	−4.19892	+	7.27274i	−0.222856	+	0.385997i
$356$	−11.2875	+	11.2875i	−0.598235	+	0.598235i
$357$		0			0
$358$	−0.932655	−	0.249904i	−0.0492924	−	0.0132078i
$359$	6.40375	+	1.71588i	0.337977	+	0.0905607i	0.423816	−	0.905748i	$-0.360690\pi$
$359$	6.40375	+	1.71588i	0.337977	+	0.0905607i	−0.0858388	+	0.996309i	$0.527357\pi$
$360$			3.08413i			0.162548i
$361$	0.679814	−	0.392491i	0.0357797	−	0.0206574i
$362$	−1.23658	−	1.23658i	−0.0649934	−	0.0649934i
$363$	18.6257			0.977594
$364$		0			0
$365$	−1.74402			−0.0912859
$366$	−0.661345	−	0.661345i	−0.0345690	−	0.0345690i
$367$	28.4547	−	16.4284i	1.48533	−	0.857553i	0.485465	−	0.874256i	$-0.338650\pi$
$367$	28.4547	−	16.4284i	1.48533	−	0.857553i	0.999860	+	0.0167033i	$0.00531706\pi$
$368$		−	25.0628i		−	1.30649i
$369$	41.3081	+	11.0685i	2.15041	+	0.576202i
$370$	0.563277	+	0.150930i	0.0292834	+	0.00784646i
$371$		0			0
$372$	−15.6216	+	15.6216i	−0.809943	+	0.809943i
$373$	−3.93986	+	6.82405i	−0.203998	+	0.353336i	−0.949813	−	0.312818i	$-0.898727\pi$
$373$	−3.93986	+	6.82405i	−0.203998	+	0.353336i	0.745815	+	0.666153i	$0.232060\pi$
$374$	−0.488932	−	0.846855i	−0.0252821	−	0.0437899i
$375$	−30.5034	−	8.17336i	−1.57519	−	0.422070i
$376$	−1.54239	−	2.67150i	−0.0795428	−	0.137772i
$377$	12.5105	+	22.5781i	0.644324	+	1.16283i
$378$		0			0
$379$	10.8095	−	2.89639i	0.555245	−	0.148778i	0.0297243	−	0.999558i	$-0.490537\pi$
$379$	10.8095	−	2.89639i	0.555245	−	0.148778i	0.525521	+	0.850781i	$0.323870\pi$
$380$	−14.9675			−0.767815
$381$	15.8883			0.813984
$382$	1.63854	−	0.439044i	0.0838348	−	0.0224635i
$383$	0.623897	+	2.32841i	0.0318796	+	0.118976i	0.980032	−	0.198840i	$-0.0637173\pi$
$383$	0.623897	+	2.32841i	0.0318796	+	0.118976i	−0.948152	+	0.317816i	$0.897051\pi$
$384$	2.47025	−	9.21909i	0.126059	−	0.470460i
$385$		0			0
$386$	−1.14289	−	1.97954i	−0.0581715	−	0.100756i
$387$			6.72771i			0.341989i
$388$	−7.59389	+	28.3408i	−0.385522	+	1.43879i
$389$	14.5674	+	8.41049i	0.738596	+	0.426429i	0.821559	−	0.570124i	$-0.193105\pi$
$389$	14.5674	+	8.41049i	0.738596	+	0.426429i	−0.0829624	+	0.996553i	$0.526438\pi$
$390$	1.68939	−	0.936093i	0.0855457	−	0.0474009i
$391$		−	27.3638i		−	1.38385i
$392$		0			0
$393$	7.48993	−	12.9729i	0.377817	−	0.654398i
$394$	−2.20008	−	1.27022i	−0.110838	−	0.0639926i
$395$	−2.71301	−	10.1251i	−0.136506	−	0.509448i
$396$	−10.3207	−	10.3207i	−0.518635	−	0.518635i
$397$	−22.7234	+	6.08873i	−1.14046	+	0.305585i	−0.779135	−	0.626856i	$-0.784341\pi$
$397$	−22.7234	+	6.08873i	−1.14046	+	0.305585i	−0.361322	+	0.932441i	$0.617675\pi$
$398$	−1.59181	−	1.59181i	−0.0797903	−	0.0797903i
$399$		0			0
$400$	6.38957	+	3.68902i	0.319479	+	0.184451i
$401$	6.10116	−	6.10116i	0.304677	−	0.304677i	−0.538163	−	0.842841i	$-0.680882\pi$
$401$	6.10116	−	6.10116i	0.304677	−	0.304677i	0.842841	+	0.538163i	$0.180882\pi$
$402$	−0.00299003	+	0.00517888i	−0.000149129	+	0.000258299i
$403$	14.8326	+	4.25574i	0.738864	+	0.211994i
$404$	27.5404	−	15.9005i	1.37019	−	0.791078i
$405$	−2.82063	−	10.5267i	−0.140158	−	0.523078i
$406$		0			0
$407$	−4.79644	+	2.76922i	−0.237751	+	0.137265i
$408$	1.33923	−	4.99809i	0.0663019	−	0.247442i
$409$	−9.50054	+	9.50054i	−0.469771	+	0.469771i	−0.901841	−	0.432069i	$-0.857784\pi$
$409$	−9.50054	+	9.50054i	−0.469771	+	0.469771i	0.432069	+	0.901841i	$0.357784\pi$
$410$	1.66077	−	1.66077i	0.0820195	−	0.0820195i
$411$	−4.22102	+	15.7530i	−0.208207	+	0.777040i
$412$	−20.3249	+	11.7346i	−1.00133	+	0.578121i
$413$		0			0
$414$	0.725437	+	2.70737i	0.0356533	+	0.133060i
$415$	21.3568	−	12.3304i	1.04837	−	0.605275i
$416$	−4.85720	+	1.21021i	−0.238144	+	0.0593355i
$417$	−27.2038	+	47.1183i	−1.33217	+	2.30739i
$418$	−0.689800	+	0.689800i	−0.0337392	+	0.0337392i
$419$	15.0514	+	8.68991i	0.735308	+	0.424530i	0.820361	−	0.571846i	$-0.193773\pi$
$419$	15.0514	+	8.68991i	0.735308	+	0.424530i	−0.0850532	+	0.996376i	$0.527106\pi$
$420$		0			0
$421$	−21.2490	−	21.2490i	−1.03561	−	1.03561i	−0.999342	−	0.0362722i	$-0.988452\pi$
$421$	−21.2490	−	21.2490i	−1.03561	−	1.03561i	−0.0362722	−	0.999342i	$-0.511548\pi$
$422$	0.340874	−	0.0913368i	0.0165935	−	0.00444621i
$423$	−17.5903	−	17.5903i	−0.855271	−	0.855271i
$424$	0.515320	+	1.92320i	0.0250262	+	0.0933989i
$425$	6.97619	+	4.02771i	0.338395	+	0.195372i
$426$	−0.721591	+	1.24983i	−0.0349612	+	0.0605546i
$427$		0			0
$428$		−	15.8733i		−	0.767265i
$429$	−5.05898	+	17.6321i	−0.244250	+	0.851287i
$430$	0.319986	+	0.184744i	0.0154311	+	0.00890913i
$431$	−6.24554	+	23.3087i	−0.300837	+	1.12274i	0.635633	+	0.771991i	$0.280739\pi$
$431$	−6.24554	+	23.3087i	−0.300837	+	1.12274i	−0.936470	+	0.350748i	$0.885927\pi$
$432$		−	7.67051i		−	0.369048i
$433$	2.27124	+	3.93391i	0.109149	+	0.189051i	0.915426	−	0.402487i	$-0.131854\pi$
$433$	2.27124	+	3.93391i	0.109149	+	0.189051i	−0.806277	+	0.591538i	$0.798521\pi$
$434$		0			0
$435$	−8.50129	+	31.7273i	−0.407606	+	1.52121i
$436$	−6.36649	−	23.7601i	−0.304900	−	1.13790i
$437$	−26.3682	+	7.06534i	−1.26136	+	0.337981i
$438$	−0.299712			−0.0143208
$439$	17.0007			0.811400			0.405700	−	0.914006i	$-0.367028\pi$
$439$	17.0007			0.811400			0.405700	+	0.914006i	$0.367028\pi$
$440$	−1.55388	+	0.416362i	−0.0740785	+	0.0198493i
$441$		0			0
$442$	−1.74750	+	0.435405i	−0.0831203	+	0.0207101i
$443$	18.3082	+	31.7108i	0.869851	+	1.50663i	0.862149	+	0.506655i	$0.169118\pi$
$443$	18.3082	+	31.7108i	0.869851	+	1.50663i	0.00770183	+	0.999970i	$0.497548\pi$
$444$	−14.1057	−	3.77962i	−0.669429	−	0.179373i
$445$	7.09408	+	12.2873i	0.336292	+	0.582474i
$446$	0.256823	−	0.444830i	0.0121609	−	0.0210633i
$447$	28.4042	−	28.4042i	1.34347	−	1.34347i
$448$		0			0
$449$	−32.7480	−	8.77481i	−1.54547	−	0.414109i	−0.617445	−	0.786614i	$-0.711832\pi$
$449$	−32.7480	−	8.77481i	−1.54547	−	0.414109i	−0.928030	+	0.372505i	$0.878499\pi$
$450$	−0.796999	−	0.213555i	−0.0375709	−	0.0100671i
$451$			22.3066i			1.05038i
$452$	14.6984	−	8.48610i	0.691353	−	0.399153i
$453$	−8.12354	−	8.12354i	−0.381677	−	0.381677i
$454$	−0.478554			−0.0224596
$455$		0			0
$456$	−5.16202			−0.241734
$457$	1.60001	+	1.60001i	0.0748453	+	0.0748453i	0.743538	−	0.668693i	$-0.233146\pi$
$457$	1.60001	+	1.60001i	0.0748453	+	0.0748453i	−0.668693	+	0.743538i	$0.733146\pi$
$458$	−1.37279	+	0.792582i	−0.0641463	+	0.0370349i
$459$		−	8.37473i		−	0.390899i
$460$	−21.6670	−	5.80566i	−1.01023	−	0.270690i
$461$	24.5455	+	6.57694i	1.14320	+	0.306319i	0.780235	−	0.625486i	$-0.215099\pi$
$461$	24.5455	+	6.57694i	1.14320	+	0.306319i	0.362961	+	0.931804i	$0.381766\pi$
$462$		0			0
$463$	−22.6265	+	22.6265i	−1.05154	+	1.05154i	−0.0529442	+	0.998597i	$0.516861\pi$
$463$	−22.6265	+	22.6265i	−1.05154	+	1.05154i	−0.998597	+	0.0529442i	$0.983139\pi$
$464$	14.0261	−	24.2939i	0.651144	−	1.12781i
$465$	9.81804	+	17.0053i	0.455301	+	0.788604i
$466$	−1.84388	−	0.494066i	−0.0854160	−	0.0228871i
$467$	−5.64704	−	9.78095i	−0.261314	−	0.452609i	0.705278	−	0.708931i	$-0.250822\pi$
$467$	−5.64704	−	9.78095i	−0.261314	−	0.452609i	−0.966591	+	0.256323i	$0.917489\pi$
$468$	−23.5126	+	13.0283i	−1.08687	+	0.602235i
$469$		0			0
$470$	−1.31967	+	0.353604i	−0.0608718	+	0.0163105i
$471$	−18.0107			−0.829889
$472$	0.785306			0.0361466
$473$	−3.38964	+	0.908251i	−0.155856	+	0.0417614i
$474$	−0.466235	−	1.74001i	−0.0214149	−	0.0799215i
$475$	2.07991	−	7.76231i	0.0954326	−	0.356159i
$476$		0			0
$477$	8.02814	+	13.9051i	0.367583	+	0.636673i
$478$			1.00967i			0.0461810i
$479$	5.19059	−	19.3716i	0.237164	−	0.885109i	−0.739997	−	0.672610i	$-0.765173\pi$
$479$	5.19059	−	19.3716i	0.237164	−	0.885109i	0.977161	−	0.212499i	$-0.0681602\pi$
$480$	−5.51639	−	3.18489i	−0.251788	−	0.145370i
$481$	2.46606	+	9.89755i	0.112442	+	0.451289i
$482$		−	1.56814i		−	0.0714269i
$483$		0			0
$484$	−7.11843	+	12.3295i	−0.323565	+	0.560431i
$485$	22.5846	+	13.0392i	1.02551	+	0.592081i
$486$	−0.662191	−	2.47133i	−0.0300376	−	0.112102i
$487$	−22.2146	−	22.2146i	−1.00664	−	1.00664i	−0.999978	−	0.00665970i	$-0.997880\pi$
$487$	−22.2146	−	22.2146i	−1.00664	−	1.00664i	−0.00665970	−	0.999978i	$-0.502120\pi$
$488$	1.38582	−	0.371329i	0.0627331	−	0.0168093i
$489$	−23.7691	−	23.7691i	−1.07488	−	1.07488i
$490$		0			0
$491$	−16.8341	−	9.71919i	−0.759714	−	0.438621i	0.0694792	−	0.997583i	$-0.477866\pi$
$491$	−16.8341	−	9.71919i	−0.759714	−	0.438621i	−0.829193	+	0.558962i	$0.811200\pi$
$492$	−41.5894	+	41.5894i	−1.87499	+	1.87499i
$493$	15.3138	−	26.5243i	0.689698	−	1.19459i
$494$	0.870768	+	1.57150i	0.0391777	+	0.0707051i
$495$	−11.2349	+	6.48647i	−0.504971	+	0.291545i
$496$	−4.34038	−	16.1985i	−0.194889	−	0.727336i
$497$		0			0
$498$	3.67021	−	2.11900i	0.164466	−	0.0949545i
$499$	4.32098	−	16.1261i	0.193434	−	0.721904i	−0.799233	−	0.601021i	$-0.794761\pi$
$499$	4.32098	−	16.1261i	0.193434	−	0.721904i	0.992667	−	0.120883i	$-0.0385726\pi$
$500$	17.0683	−	17.0683i	0.763320	−	0.763320i
$501$	−1.71308	+	1.71308i	−0.0765348	+	0.0765348i
$502$	−0.105341	+	0.393138i	−0.00470160	+	0.0175466i
$503$	−25.9585	+	14.9871i	−1.15743	+	0.668243i	−0.950687	−	0.310153i	$-0.899620\pi$
$503$	−25.9585	+	14.9871i	−1.15743	+	0.668243i	−0.206743	+	0.978395i	$0.566287\pi$
$504$		0			0
$505$	−7.31560	−	27.3022i	−0.325540	−	1.21493i
$506$	−1.26612	+	0.730997i	−0.0562861	+	0.0324968i
$507$	28.6441	+	17.9115i	1.27213	+	0.795479i
$508$	−6.07227	+	10.5175i	−0.269413	+	0.466638i
$509$	9.91537	−	9.91537i	0.439491	−	0.439491i	−0.452350	−	0.891841i	$-0.649414\pi$
$509$	9.91537	−	9.91537i	0.439491	−	0.439491i	0.891841	+	0.452350i	$0.149414\pi$
$510$	−1.98466	−	1.14585i	−0.0878824	−	0.0507389i
$511$		0			0
$512$	6.42580	+	6.42580i	0.283983	+	0.283983i
$513$	−8.07001	+	2.16235i	−0.356300	+	0.0954702i
$514$	1.11022	+	1.11022i	0.0489698	+	0.0489698i
$515$	5.39893	+	20.1491i	0.237905	+	0.887874i
$516$	−8.01316	−	4.62640i	−0.352760	−	0.203666i
$517$	6.48785	−	11.2373i	0.285335	−	0.494215i
$518$		0			0
$519$			1.37097i			0.0601791i
$520$	−0.0521804	+	2.96228i	−0.00228826	+	0.129904i
$521$	0.757986	+	0.437623i	0.0332080	+	0.0191726i	0.516512	−	0.856280i	$-0.327230\pi$
$521$	0.757986	+	0.437623i	0.0332080	+	0.0191726i	−0.483304	+	0.875453i	$0.660563\pi$
$522$	−0.811961	+	3.03028i	−0.0355386	+	0.132632i
$523$		−	13.5328i		−	0.591748i	−0.955227	−	0.295874i	$-0.904389\pi$
$523$		−	13.5328i		−	0.591748i	0.955227	−	0.295874i	$-0.0956109\pi$
$524$	5.72506	+	9.91610i	0.250100	+	0.433187i
$525$		0			0
$526$	0.620553	−	2.31593i	0.0270574	−	0.100980i
$527$	−4.73887	−	17.6857i	−0.206428	−	0.770401i
$528$	19.2559	−	5.15960i	0.838004	−	0.224543i
$529$	−17.9114			−0.778755
$530$	0.881814			0.0383036
$531$	6.11711	−	1.63908i	0.265460	−	0.0711298i
$532$		0			0
$533$	39.4888	+	11.3301i	1.71045	+	0.490759i
$534$	1.21913	+	2.11159i	0.0527569	+	0.0913776i
$535$	−13.6278	−	3.65155i	−0.589180	−	0.157870i
$536$	−0.00458664	−	0.00794430i	−0.000198113	−	0.000343141i
$537$	10.7457	−	18.6121i	0.463711	−	0.803171i
$538$	−0.886440	+	0.886440i	−0.0382171	+	0.0382171i
$539$		0			0
$540$	−6.63121	−	1.77683i	−0.285362	−	0.0764625i
$541$	−11.8679	−	3.18000i	−0.510241	−	0.136719i	−0.00549222	−	0.999985i	$-0.501748\pi$
$541$	−11.8679	−	3.18000i	−0.510241	−	0.136719i	−0.504749	+	0.863266i	$0.668415\pi$
$542$		−	0.174983i		−	0.00751615i
$543$	33.7098	−	19.4624i	1.44663	−	0.835211i
$544$	4.19985	+	4.19985i	0.180067	+	0.180067i
$545$	−21.8634			−0.936526
$546$		0			0
$547$	16.2786			0.696022			0.348011	−	0.937490i	$-0.386857\pi$
$547$	16.2786			0.696022			0.348011	+	0.937490i	$0.386857\pi$
$548$	−8.81471	−	8.81471i	−0.376546	−	0.376546i
$549$	10.0198	−	5.78491i	0.427633	−	0.246894i
$550$		−	0.430384i		−	0.0183516i
$551$	−29.5132	−	7.90803i	−1.25730	−	0.336894i
$552$	−7.47258	−	2.00227i	−0.318054	−	0.0852224i
$553$		0			0
$554$	−0.388865	+	0.388865i	−0.0165213	+	0.0165213i
$555$	−6.48987	+	11.2408i	−0.275480	+	0.477145i
$556$	−20.7937	−	36.0157i	−0.881849	−	1.52741i
$557$	−7.98185	−	2.13873i	−0.338202	−	0.0906210i	0.0857210	−	0.996319i	$-0.472681\pi$
$557$	−7.98185	−	2.13873i	−0.338202	−	0.0906210i	−0.423923	+	0.905698i	$0.639347\pi$
$558$	0.937724	+	1.62418i	0.0396970	+	0.0687572i
$559$	−0.113826	+	6.46190i	−0.00481433	+	0.273309i
$560$		0			0
$561$	21.0237	−	5.63329i	0.887623	−	0.237838i
$562$	1.32294			0.0558049
$563$	28.1534			1.18652			0.593261	−	0.805010i	$-0.297840\pi$
$563$	28.1534			1.18652			0.593261	+	0.805010i	$0.297840\pi$
$564$	33.0475	−	8.85505i	1.39155	−	0.372865i
$565$	−3.90435	−	14.5712i	−0.164257	−	0.613016i
$566$	−0.238078	+	0.888519i	−0.0100072	+	0.0373472i
$567$		0			0
$568$	−1.10691	−	1.91722i	−0.0464448	−	0.0804447i
$569$			9.96097i			0.417586i	0.977960	+	0.208793i	$0.0669534\pi$
$569$			9.96097i			0.417586i	−0.977960	+	0.208793i	$0.933047\pi$
$570$	−0.591715	+	2.20831i	−0.0247842	+	0.0924959i
$571$	4.46188	+	2.57607i	0.186724	+	0.107805i	0.590448	−	0.807076i	$-0.298951\pi$
$571$	4.46188	+	2.57607i	0.186724	+	0.107805i	−0.403724	+	0.914881i	$0.632284\pi$
$572$	−9.73833	−	10.0876i	−0.407180	−	0.421782i
$573$			37.7572i			1.57733i
$574$		0			0
$575$	6.02177	−	10.4300i	0.251125	−	0.434962i
$576$	24.9461	+	14.4027i	1.03942	+	0.600111i
$577$	3.47849	+	12.9819i	0.144812	+	0.540444i	0.999764	+	0.0217373i	$0.00691975\pi$
$577$	3.47849	+	12.9819i	0.144812	+	0.540444i	−0.854952	+	0.518707i	$0.826414\pi$
$578$	0.107530	+	0.107530i	0.00447267	+	0.00447267i
$579$	49.1434	−	13.1679i	2.04233	−	0.547240i
$580$	−17.7532	−	17.7532i	−0.737161	−	0.737161i
$581$		0			0
$582$	3.88120	+	2.24081i	0.160881	+	0.0928847i
$583$	−5.92205	+	5.92205i	−0.245266	+	0.245266i
$584$	0.229876	−	0.398157i	0.00951234	−	0.0164759i
$585$	5.77635	+	23.1835i	0.238823	+	0.958518i
$586$	−1.23535	+	0.713227i	−0.0510317	+	0.0294631i
$587$	−9.73498	−	36.3314i	−0.401806	−	1.49956i	−0.809872	−	0.586607i	$-0.800463\pi$
$587$	−9.73498	−	36.3314i	−0.401806	−	1.49956i	0.408066	−	0.912952i	$-0.366203\pi$
$588$		0			0
$589$	−15.8186	+	9.13289i	−0.651795	+	0.376314i
$590$	0.0900184	−	0.335953i	0.00370600	−	0.0138310i
$591$	39.9834	−	39.9834i	1.64470	−	1.64470i
$592$	7.83841	−	7.83841i	0.322157	−	0.322157i
$593$	−9.45795	+	35.2975i	−0.388391	+	1.44950i	0.444360	+	0.895848i	$0.353431\pi$
$593$	−9.45795	+	35.2975i	−0.388391	+	1.44950i	−0.832751	+	0.553648i	$0.813235\pi$
$594$	−0.387498	+	0.223722i	−0.0158992	+	0.00917944i
$595$		0			0
$596$	7.94687	+	29.6581i	0.325517	+	1.21484i
$597$	43.3935	−	25.0532i	1.77598	−	1.02536i
$598$	0.650969	+	2.61267i	0.0266201	+	0.106840i
$599$	−2.66014	+	4.60749i	−0.108690	+	0.188257i	−0.915240	−	0.402909i	$-0.867999\pi$
$599$	−2.66014	+	4.60749i	−0.108690	+	0.188257i	0.806550	+	0.591166i	$0.201332\pi$
$600$	1.61036	−	1.61036i	0.0657426	−	0.0657426i
$601$	21.4564	+	12.3879i	0.875225	+	0.505312i	0.869081	−	0.494669i	$-0.164711\pi$
$601$	21.4564	+	12.3879i	0.875225	+	0.505312i	0.00614424	+	0.999981i	$0.498044\pi$
$602$		0			0
$603$	−0.0523087	−	0.0523087i	−0.00213017	−	0.00213017i
$604$	8.48216	−	2.27279i	0.345134	−	0.0924785i
$605$	8.94774	+	8.94774i	0.363777	+	0.363777i
$606$	−1.25720	−	4.69193i	−0.0510702	−	0.190596i
$607$	19.5367	+	11.2795i	0.792971	+	0.457822i	0.841007	−	0.541024i	$-0.181963\pi$
$607$	19.5367	+	11.2795i	0.792971	+	0.457822i	−0.0480365	+	0.998846i	$0.515296\pi$
$608$	2.96263	−	5.13143i	0.120151	−	0.208107i
$609$		0			0
$610$		−	0.635418i		−	0.0257273i
$611$	−16.5977	−	17.1929i	−0.671472	−	0.695552i
$612$	27.6221	+	15.9476i	1.11656	+	0.644645i
$613$	5.95385	−	22.2201i	0.240474	−	0.897459i	−0.735131	−	0.677925i	$-0.762879\pi$
$613$	5.95385	−	22.2201i	0.240474	−	0.897459i	0.975605	−	0.219535i	$-0.0704539\pi$
$614$			1.31630i			0.0531217i
$615$	26.1385	+	45.2733i	1.05401	+	1.82560i
$616$		0			0
$617$	7.79350	−	29.0858i	0.313755	−	1.17095i	−0.611389	−	0.791330i	$-0.709389\pi$
$617$	7.79350	−	29.0858i	0.313755	−	1.17095i	0.925143	−	0.379618i	$-0.123945\pi$
$618$	0.927815	+	3.46265i	0.0373222	+	0.139288i
$619$	10.3214	−	2.76561i	0.414852	−	0.111159i	−0.0453549	−	0.998971i	$-0.514442\pi$
$619$	10.3214	−	2.76561i	0.414852	−	0.111159i	0.460207	+	0.887812i	$0.347775\pi$
$620$	−15.0092			−0.602783
$621$	−12.5210			−0.502449
$622$	−1.47090	+	0.394127i	−0.0589778	+	0.0158031i
$623$		0			0
$624$	0.646624	−	36.7088i	0.0258857	−	1.46953i
$625$	−6.01999	−	10.4269i	−0.240800	−	0.417077i
$626$	0.403049	+	0.107997i	0.0161091	+	0.00431641i
$627$	−10.8566	−	18.8043i	−0.433573	−	0.750970i
$628$	6.88340	−	11.9224i	0.274678	−	0.475755i
$629$	8.55805	−	8.55805i	0.341232	−	0.341232i
$630$		0			0
$631$	13.6759	+	3.66444i	0.544428	+	0.145879i	0.520543	−	0.853836i	$-0.325730\pi$
$631$	13.6759	+	3.66444i	0.544428	+	0.145879i	0.0238855	+	0.999715i	$0.492396\pi$
$632$	2.66915	+	0.715196i	0.106173	+	0.0284490i
$633$			7.85483i			0.312202i
$634$	3.35413	−	1.93651i	0.133209	−	0.0769085i
$635$	7.63273	+	7.63273i	0.302896	+	0.302896i
$636$	−22.0826			−0.875633
$637$		0			0
$638$	−1.63637			−0.0647844
$639$	−12.6238	−	12.6238i	−0.499390	−	0.499390i
$640$	5.61554	−	3.24213i	0.221974	−	0.128157i
$641$		−	37.0275i		−	1.46250i	−0.682111	−	0.731248i	$-0.738938\pi$
$641$		−	37.0275i		−	1.46250i	0.682111	−	0.731248i	$-0.261062\pi$
$642$	−2.34196	−	0.627525i	−0.0924296	−	0.0247664i
$643$	33.2886	+	8.91965i	1.31277	+	0.351757i	0.846266	−	0.532761i	$-0.178845\pi$
$643$	33.2886	+	8.91965i	1.31277	+	0.351757i	0.466507	+	0.884517i	$0.345512\pi$
$644$		0			0
$645$	−5.81530	+	5.81530i	−0.228977	+	0.228977i
$646$	1.06588	−	1.84617i	0.0419366	−	0.0726364i
$647$	−3.03363	−	5.25440i	−0.119264	−	0.206572i	0.800212	−	0.599717i	$-0.204720\pi$
$647$	−3.03363	−	5.25440i	−0.119264	−	0.206572i	−0.919476	+	0.393145i	$0.871387\pi$
$648$	2.77503	+	0.743567i	0.109013	+	0.0292101i
$649$	1.65164	+	2.86072i	0.0648325	+	0.112293i
$650$	−0.761896	−	0.218602i	−0.0298840	−	0.00857428i
$651$		0			0
$652$	24.8184	−	6.65007i	0.971964	−	0.260437i
$653$	30.2018			1.18189			0.590943	−	0.806713i	$-0.298756\pi$
$653$	30.2018			1.18189			0.590943	+	0.806713i	$0.298756\pi$
$654$	−3.75726			−0.146921
$655$	9.83033	−	2.63403i	0.384103	−	0.102920i
$656$	−11.5554	−	43.1253i	−0.451162	−	1.68376i
$657$	0.959586	−	3.58123i	0.0374370	−	0.139717i
$658$		0			0
$659$	4.37179	+	7.57216i	0.170301	+	0.294969i	0.938525	−	0.345211i	$-0.112193\pi$
$659$	4.37179	+	7.57216i	0.170301	+	0.294969i	−0.768224	+	0.640181i	$0.778859\pi$
$660$		−	17.8420i		−	0.694501i
$661$	4.64874	−	17.3494i	0.180815	−	0.674812i	−0.814673	−	0.579921i	$-0.803083\pi$
$661$	4.64874	−	17.3494i	0.180815	−	0.674812i	0.995488	−	0.0948903i	$-0.0302500\pi$
$662$	0.0958671	+	0.0553489i	0.00372598	+	0.00215120i
$663$	0.705990	−	40.0790i	0.0274184	−	1.55654i
$664$			6.50100i			0.252288i
$665$		0			0
$666$	−0.619849	+	1.07361i	−0.0240187	+	0.0416015i
$667$	−39.6561	−	22.8955i	−1.53549	−	0.886516i
$668$	−0.479282	−	1.78870i	−0.0185440	−	0.0692071i
$669$	8.08418	+	8.08418i	0.312552	+	0.312552i
$670$	−0.00392433	+	0.00105152i	−0.000151610	+	4.06238e-5i
$671$	4.26731	+	4.26731i	0.164738	+	0.164738i
$672$		0			0
$673$	22.0524	+	12.7319i	0.850057	+	0.490780i	0.860670	−	0.509163i	$-0.170045\pi$
$673$	22.0524	+	12.7319i	0.850057	+	0.490780i	−0.0106133	+	0.999944i	$0.503378\pi$
$674$	1.17149	−	1.17149i	0.0451242	−	0.0451242i
$675$	1.84297	−	3.19212i	0.0709359	−	0.122865i
$676$	−22.8040	+	12.1158i	−0.877079	+	0.465991i
$677$	−18.9268	+	10.9274i	−0.727415	+	0.419973i	−0.817476	−	0.575963i	$-0.804627\pi$
$677$	−18.9268	+	10.9274i	−0.727415	+	0.419973i	0.0900609	+	0.995936i	$0.471294\pi$
$678$	−0.670968	−	2.50409i	−0.0257684	−	0.0961689i
$679$		0			0
$680$	3.04444	−	1.75771i	0.116749	−	0.0674050i
$681$	2.75686	−	10.2887i	0.105643	−	0.394265i
$682$	−0.691723	+	0.691723i	−0.0264874	+	0.0264874i
$683$	−22.6628	+	22.6628i	−0.867167	+	0.867167i	−0.992158	−	0.124991i	$-0.960110\pi$
$683$	−22.6628	+	22.6628i	−0.867167	+	0.867167i	0.124991	+	0.992158i	$0.460110\pi$
$684$	8.23535	−	30.7348i	0.314887	−	1.17517i
$685$	−9.59550	+	5.53997i	−0.366625	+	0.211671i
$686$		0			0
$687$	−9.13183	−	34.0804i	−0.348401	−	1.30025i
$688$	6.08268	−	3.51184i	0.231900	−	0.133888i
$689$	7.47569	+	13.4916i	0.284801	+	0.513988i
$690$	−1.71314	+	2.96725i	−0.0652182	+	0.112961i
$691$	19.8856	−	19.8856i	0.756483	−	0.756483i	−0.219198	−	0.975680i	$-0.570344\pi$
$691$	19.8856	−	19.8856i	0.756483	−	0.756483i	0.975680	+	0.219198i	$0.0703439\pi$
$692$	−0.907533	−	0.523964i	−0.0344992	−	0.0199181i
$693$		0			0
$694$	1.14276	+	1.14276i	0.0433786	+	0.0433786i
$695$	−35.7042	+	9.56691i	−1.35434	+	0.362894i
$696$	−6.12276	−	6.12276i	−0.232083	−	0.232083i
$697$	−12.6163	−	47.0846i	−0.477876	−	1.78346i
$698$	−1.54794	−	0.893701i	−0.0585902	−	0.0338271i
$699$	21.2445	−	36.7965i	0.803540	−	1.39177i
$700$		0			0
$701$			41.8411i			1.58032i	0.612904	+	0.790158i	$0.290001\pi$
$701$			41.8411i			1.58032i	−0.612904	+	0.790158i	$0.709999\pi$
$702$	0.199230	+	0.799611i	0.00751944	+	0.0301794i
$703$	−10.4563	−	6.03698i	−0.394369	−	0.227689i
$704$	−3.88876	+	14.5131i	−0.146563	+	0.546981i
$705$		−	30.4095i		−	1.14529i
$706$	−0.919455	−	1.59254i	−0.0346041	−	0.0599361i
$707$		0			0
$708$	−2.25426	+	8.41303i	−0.0847204	+	0.316181i
$709$	9.67328	+	36.1012i	0.363288	+	1.35581i	0.869727	+	0.493532i	$0.164295\pi$
$709$	9.67328	+	36.1012i	0.363288	+	1.35581i	−0.506440	+	0.862275i	$0.669039\pi$
$710$	−0.947068	+	0.253766i	−0.0355428	+	0.00952368i
$711$	22.2840			0.835714
$712$	−3.74024			−0.140171
$713$	−26.4417	+	7.08503i	−0.990249	+	0.265336i
$714$		0			0
$715$	−10.9008	+	6.04011i	−0.407665	+	0.225887i
$716$	8.21367	+	14.2265i	0.306959	+	0.531669i
$717$	−21.7075	−	5.81649i	−0.810680	−	0.217221i
$718$	0.387018	+	0.670334i	0.0144434	+	0.0250166i
$719$	−14.7469	+	25.5425i	−0.549968	+	0.952573i	0.448308	+	0.893879i	$0.352027\pi$
$719$	−14.7469	+	25.5425i	−0.549968	+	0.952573i	−0.998276	+	0.0586936i	$0.981307\pi$
$720$	18.3602	−	18.3602i	0.684246	−	0.684246i
$721$		0			0
$722$	0.0885265	+	0.0237206i	0.00329461	+	0.000882789i
$723$	33.7145	+	9.03377i	1.25386	+	0.335969i
$724$			29.7528i			1.10576i
$725$	11.6740	−	6.74000i	0.433562	−	0.250317i
$726$	1.53768	+	1.53768i	0.0570688	+	0.0570688i
$727$	3.04387			0.112891			0.0564455	−	0.998406i	$-0.482023\pi$
$727$	3.04387			0.112891			0.0564455	+	0.998406i	$0.482023\pi$
$728$		0			0
$729$	38.4293			1.42331
$730$	−0.143981	−	0.143981i	−0.00532898	−	0.00532898i
$731$	6.64113	−	3.83426i	0.245631	−	0.141815i
$732$			15.9123i			0.588135i
$733$	1.26813	+	0.339796i	0.0468396	+	0.0125506i	0.282163	−	0.959367i	$-0.408948\pi$
$733$	1.26813	+	0.339796i	0.0468396	+	0.0125506i	−0.235323	+	0.971917i	$0.575615\pi$
$734$	3.70542	+	0.992865i	0.136770	+	0.0366473i
$735$		0			0
$736$	6.27914	−	6.27914i	0.231452	−	0.231452i
$737$	0.0192931	−	0.0334166i	0.000710669	−	0.00123091i
$738$	2.49650	+	4.32406i	0.0918974	+	0.159171i
$739$	28.9849	+	7.76649i	1.06623	+	0.285695i	0.748942	−	0.662635i	$-0.230562\pi$
$739$	28.9849	+	7.76649i	1.06623	+	0.285695i	0.317285	+	0.948330i	$0.397229\pi$
$740$	−4.96065	−	8.59209i	−0.182357	−	0.315852i
$741$	−38.8030	+	9.66809i	−1.42546	+	0.355166i
$742$		0			0
$743$	−39.4397	+	10.5678i	−1.44690	+	0.387697i	−0.894946	−	0.446175i	$-0.852786\pi$
$743$	−39.4397	+	10.5678i	−1.44690	+	0.387697i	−0.551958	+	0.833872i	$0.686119\pi$
$744$	−5.17641			−0.189776
$745$	27.2906			0.999852
$746$	−0.888638	+	0.238110i	−0.0325354	+	0.00871782i
$747$	13.5688	+	50.6393i	0.496455	+	1.85280i
$748$	−4.30591	+	16.0699i	−0.157440	+	0.587573i
$749$		0			0
$750$	−1.84350	−	3.19304i	−0.0673153	−	0.116593i
$751$			35.8754i			1.30911i	0.756013	+	0.654556i	$0.227145\pi$
$751$			35.8754i			1.30911i	−0.756013	+	0.654556i	$0.772855\pi$
$752$	−6.72175	+	25.0859i	−0.245117	+	0.914789i
$753$	−7.84547	−	4.52958i	−0.285905	−	0.165067i
$754$	−0.831150	+	2.89682i	−0.0302687	+	0.105496i
$755$		−	7.80507i		−	0.284056i
$756$		0			0
$757$	−0.439138	+	0.760610i	−0.0159607	+	0.0276448i	−0.873895	−	0.486114i	$-0.838414\pi$
$757$	−0.439138	+	0.760610i	−0.0159607	+	0.0276448i	0.857935	+	0.513759i	$0.171747\pi$
$758$	1.13152	+	0.653282i	0.0410986	+	0.0237283i
$759$	−8.42227	−	31.4323i	−0.305709	−	1.14092i
$760$	−2.47982	−	2.47982i	−0.0899527	−	0.0899527i
$761$	−35.3341	+	9.46773i	−1.28086	+	0.343205i	−0.834181	−	0.551490i	$-0.814059\pi$
$761$	−35.3341	+	9.46773i	−1.28086	+	0.343205i	−0.446677	+	0.894695i	$0.647393\pi$
$762$	1.31170	+	1.31170i	0.0475178	+	0.0475178i
$763$		0			0
$764$	−24.9938	−	14.4302i	−0.904245	−	0.522066i
$765$	20.0459	−	20.0459i	0.724760	−	0.724760i
$766$	−0.140720	+	0.243735i	−0.00508443	+	0.00880649i
$767$	5.90316	−	1.47082i	0.213151	−	0.0531082i
$768$	−33.5795	+	19.3871i	−1.21170	+	0.699573i
$769$	−7.85943	−	29.3318i	−0.283418	−	1.05773i	−0.949987	−	0.312288i	$-0.898904\pi$
$769$	−7.85943	−	29.3318i	−0.283418	−	1.05773i	0.666569	−	0.745443i	$-0.267762\pi$
$770$		0			0
$771$	−30.2652	+	17.4736i	−1.08997	+	0.629297i
$772$	−10.0651	+	37.5636i	−0.362252	+	1.35194i
$773$	−14.0260	+	14.0260i	−0.504481	+	0.504481i	−0.912827	−	0.408346i	$-0.866106\pi$
$773$	−14.0260	+	14.0260i	−0.504481	+	0.504481i	0.408346	+	0.912827i	$0.366106\pi$
$774$	−0.555421	+	0.555421i	−0.0199642	+	0.0199642i
$775$	2.08570	−	7.78395i	0.0749206	−	0.279608i
$776$	−5.95369	+	3.43737i	−0.213725	+	0.123394i
$777$		0			0
$778$	0.508297	+	1.89699i	0.0182233	+	0.0680104i
$779$	−42.1139	+	24.3145i	−1.50889	+	0.871157i
$780$	−31.5853	−	9.06239i	−1.13093	−	0.324486i
$781$	4.65605	−	8.06451i	0.166606	−	0.288571i
$782$	2.25908	−	2.25908i	0.0807846	−	0.0807846i
$783$	−12.1368	−	7.00718i	−0.433733	−	0.250416i
$784$		0			0
$785$	−8.65231	−	8.65231i	−0.308814	−	0.308814i
$786$	1.68936	−	0.452662i	0.0602574	−	0.0161459i
$787$	−6.21503	−	6.21503i	−0.221542	−	0.221542i	0.587606	−	0.809148i	$-0.300071\pi$
$787$	−6.21503	−	6.21503i	−0.221542	−	0.221542i	−0.809148	+	0.587606i	$0.800071\pi$
$788$	11.1865	+	41.7485i	0.398502	+	1.48723i
$789$	46.2169	+	26.6833i	1.64536	+	0.949951i
$790$	0.611921	−	1.05988i	0.0217712	−	0.0377087i
$791$		0			0
$792$		−	3.41989i		−	0.121521i
$793$	9.72176	−	5.38683i	0.345230	−	0.191292i
$794$	−2.37865	−	1.37332i	−0.0844152	−	0.0487372i
$795$	−5.07997	+	18.9587i	−0.180168	+	0.672396i
$796$			38.2998i			1.35750i
$797$	−12.3887	−	21.4579i	−0.438832	−	0.760079i	0.558768	−	0.829324i	$-0.311274\pi$
$797$	−12.3887	−	21.4579i	−0.438832	−	0.760079i	−0.997600	+	0.0692450i	$0.977941\pi$
$798$		0			0
$799$	−7.33886	+	27.3890i	−0.259630	+	0.968953i
$800$	0.676585	+	2.52505i	0.0239209	+	0.0892739i
$801$	−29.1345	+	7.80656i	−1.02942	+	0.275831i
$802$	1.00739			0.0355722
$803$	1.93388			0.0682452
$804$	0.0982740	−	0.0263324i	0.00346586	−	0.000928674i
$805$		0			0
$806$	0.873195	+	1.57588i	0.0307570	+	0.0555080i
$807$	−13.9515	−	24.1647i	−0.491117	−	0.850639i
$808$	7.19733	+	1.92852i	0.253201	+	0.0678450i
$809$	−3.75373	−	6.50166i	−0.131974	−	0.228586i	0.792463	−	0.609920i	$-0.208798\pi$
$809$	−3.75373	−	6.50166i	−0.131974	−	0.228586i	−0.924438	+	0.381334i	$0.875465\pi$
$810$	0.636195	−	1.10192i	0.0223536	−	0.0387176i
$811$	−32.4572	+	32.4572i	−1.13973	+	1.13973i	−0.151229	+	0.988499i	$0.548323\pi$
$811$	−32.4572	+	32.4572i	−1.13973	+	1.13973i	−0.988499	+	0.151229i	$0.951677\pi$
$812$		0			0
$813$	3.76207	+	1.00804i	0.131941	+	0.0353536i
$814$	−0.624600	−	0.167361i	−0.0218922	−	0.00586600i
$815$		−	22.8373i		−	0.799955i
$816$	−37.7270	+	21.7817i	−1.32071	+	0.762511i
$817$	−5.40948	−	5.40948i	−0.189254	−	0.189254i
$818$	−1.56868			−0.0548475
$819$		0			0
$820$	−39.9589			−1.39543
$821$	−22.2812	−	22.2812i	−0.777620	−	0.777620i	0.201806	−	0.979426i	$-0.435319\pi$
$821$	−22.2812	−	22.2812i	−0.777620	−	0.777620i	−0.979426	+	0.201806i	$0.935319\pi$
$822$	−1.64900	+	0.952052i	−0.0575156	+	0.0332066i
$823$			31.6549i			1.10342i	0.834036	+	0.551710i	$0.186024\pi$
$823$			31.6549i			1.10342i	−0.834036	+	0.551710i	$0.813976\pi$
$824$	−5.31164	−	1.42325i	−0.185040	−	0.0495813i
$825$	9.25310	+	2.47936i	0.322152	+	0.0863203i
$826$		0			0
$827$	25.1824	−	25.1824i	0.875678	−	0.875678i	−0.117406	−	0.993084i	$-0.537458\pi$
$827$	25.1824	−	25.1824i	0.875678	−	0.875678i	0.993084	+	0.117406i	$0.0374580\pi$
$828$	23.8431	−	41.2975i	0.828606	−	1.43519i
$829$	−1.05432	−	1.82614i	−0.0366182	−	0.0634246i	0.847135	−	0.531377i	$-0.178325\pi$
$829$	−1.05432	−	1.82614i	−0.0366182	−	0.0634246i	−0.883754	+	0.467952i	$0.844992\pi$
$830$	2.78112	+	0.745200i	0.0965342	+	0.0258663i
$831$	−6.12027	−	10.6006i	−0.212310	−	0.367732i
$832$	23.7169	+	14.2557i	0.822234	+	0.494227i
$833$		0			0
$834$	−6.13582	+	1.64409i	−0.212466	+	0.0569302i
$835$	−1.64592			−0.0569594
$836$	16.5969			0.574017
$837$	−8.09251	+	2.16838i	−0.279718	+	0.0749502i
$838$	0.525184	+	1.96001i	0.0181422	+	0.0677076i
$839$	6.14897	−	22.9483i	0.212286	−	0.792262i	−0.774818	−	0.632184i	$-0.782159\pi$
$839$	6.14897	−	22.9483i	0.212286	−	0.792262i	0.987104	−	0.160078i	$-0.0511746\pi$
$840$		0			0
$841$	−11.1262	−	19.2712i	−0.383663	−	0.664525i
$842$		−	3.50852i		−	0.120912i
$843$	−7.62121	+	28.4428i	−0.262489	+	0.979621i
$844$	−5.19960	−	3.00199i	−0.178978	−	0.103333i
$845$	5.15589	+	22.3652i	0.177368	+	0.769387i
$846$		−	2.90442i		−	0.0998559i
$847$		0			0
$848$	8.38131	−	14.5169i	0.287815	−	0.498511i
$849$	−17.7313	−	10.2372i	−0.608537	−	0.351339i
$850$	0.243419	+	0.908451i	0.00834919	+	0.0311596i
$851$	−12.7950	−	12.7950i	−0.438608	−	0.438608i
$852$	23.7167	−	6.35488i	0.812522	−	0.217715i
$853$	4.73993	+	4.73993i	0.162292	+	0.162292i	0.783581	−	0.621289i	$-0.213391\pi$
$853$	4.73993	+	4.73993i	0.162292	+	0.162292i	−0.621289	+	0.783581i	$0.713391\pi$
$854$		0			0
$855$	−24.4924	−	14.1407i	−0.837621	−	0.483601i
$856$	2.62990	−	2.62990i	0.0898883	−	0.0898883i
$857$	−5.66099	+	9.80512i	−0.193376	+	0.334936i	−0.946367	−	0.323094i	$-0.895277\pi$
$857$	−5.66099	+	9.80512i	−0.193376	+	0.334936i	0.752991	+	0.658031i	$0.228610\pi$
$858$	−1.87331	+	1.03800i	−0.0639539	+	0.0354368i
$859$	41.9548	−	24.2226i	1.43148	−	0.826465i	0.434246	−	0.900794i	$-0.357015\pi$
$859$	41.9548	−	24.2226i	1.43148	−	0.826465i	0.997234	+	0.0743295i	$0.0236816\pi$
$860$	−1.62699	−	6.07202i	−0.0554800	−	0.207054i
$861$		0			0
$862$	−2.43991	+	1.40868i	−0.0831038	+	0.0479800i
$863$	−4.85283	+	18.1110i	−0.165192	+	0.616506i	0.832823	+	0.553539i	$0.186723\pi$
$863$	−4.85283	+	18.1110i	−0.165192	+	0.616506i	−0.998016	+	0.0629669i	$0.979944\pi$
$864$	1.92174	−	1.92174i	0.0653788	−	0.0653788i
$865$	−0.658613	+	0.658613i	−0.0223935	+	0.0223935i
$866$	−0.137265	+	0.512280i	−0.00466445	+	0.0174080i
$867$	−2.93132	+	1.69240i	−0.0995529	+	0.0574769i
$868$		0			0
$869$	3.00837	+	11.2274i	0.102052	+	0.380863i
$870$	−3.32116	+	1.91747i	−0.112598	+	0.0650083i
$871$	−0.0493570	−	0.0511270i	−0.00167240	−	0.00173237i
$872$	2.88179	−	4.99140i	0.0975896	−	0.169030i
$873$	−39.2017	+	39.2017i	−1.32678	+	1.32678i
$874$	−2.76018	−	1.59359i	−0.0933645	−	0.0539040i
$875$		0			0
$876$	3.60561	+	3.60561i	0.121822	+	0.121822i
$877$	−6.84575	+	1.83431i	−0.231164	+	0.0619403i	−0.372542	−	0.928015i	$-0.621514\pi$
$877$	−6.84575	+	1.83431i	−0.231164	+	0.0619403i	0.141377	+	0.989956i	$0.454847\pi$
$878$	1.40353	+	1.40353i	0.0473669	+	0.0473669i
$879$	−8.21753	−	30.6683i	−0.277171	−	1.03441i
$880$	11.7291	+	6.77183i	0.395389	+	0.228278i
$881$	12.1808	−	21.0977i	0.410380	−	0.710800i	−0.584551	−	0.811357i	$-0.698729\pi$
$881$	12.1808	−	21.0977i	0.410380	−	0.710800i	0.994931	+	0.100557i	$0.0320626\pi$
$882$		0			0
$883$			4.51673i			0.152000i	0.997108	+	0.0760000i	$0.0242149\pi$
$883$			4.51673i			0.152000i	−0.997108	+	0.0760000i	$0.975785\pi$
$884$	26.2610	+	15.7849i	0.883252	+	0.530903i
$885$	6.70430	+	3.87073i	0.225362	+	0.130113i
$886$	−1.10648	+	4.12943i	−0.0371729	+	0.138731i
$887$			44.2291i			1.48507i	0.669809	+	0.742533i	$0.266376\pi$
$887$			44.2291i			1.48507i	−0.669809	+	0.742533i	$0.733624\pi$
$888$	−1.71084	−	2.96326i	−0.0574121	−	0.0994406i
$889$		0			0
$890$	−0.428738	+	1.60007i	−0.0143713	+	0.0536346i
$891$	3.12771	+	11.6728i	0.104782	+	0.391052i
$892$	−8.44106	+	2.26177i	−0.282628	+	0.0757298i
$893$	28.2873			0.946600
$894$	4.68994			0.156855
$895$	14.1034	−	3.77900i	0.471426	−	0.126318i
$896$		0			0
$897$	−59.9216	−	1.05552i	−2.00073	−	0.0352427i
$898$	−1.97916	−	3.42801i	−0.0660455	−	0.114394i
$899$	−29.5954	−	7.93007i	−0.987063	−	0.264483i
$900$	7.01898	+	12.1572i	0.233966	+	0.405241i
$901$	9.15079	−	15.8496i	0.304857	−	0.528028i
$902$	−1.84157	+	1.84157i	−0.0613176	+	0.0613176i
$903$		0			0
$904$	3.84122	+	1.02925i	0.127757	+	0.0342324i
$905$	25.5438	+	6.84445i	0.849106	+	0.227517i
$906$		−	1.34131i		−	0.0445622i
$907$	−29.3466	+	16.9433i	−0.974439	+	0.562593i	−0.900587	−	0.434676i	$-0.856863\pi$
$907$	−29.3466	+	16.9433i	−0.974439	+	0.562593i	−0.0738526	+	0.997269i	$0.523529\pi$
$908$	5.75712	+	5.75712i	0.191057	+	0.191057i
$909$	60.0885			1.99301
$910$		0			0
$911$	4.66390			0.154522			0.0772610	−	0.997011i	$-0.475383\pi$
$911$	4.66390			0.154522			0.0772610	+	0.997011i	$0.475383\pi$
$912$	30.7302	+	30.7302i	1.01758	+	1.01758i
$913$	−23.6819	+	13.6728i	−0.783757	+	0.452502i
$914$			0.264185i			0.00873846i
$915$	13.6613	+	3.66052i	0.451627	+	0.121013i
$916$	26.0500	+	6.98007i	0.860716	+	0.230628i
$917$		0			0
$918$	0.691394	−	0.691394i	0.0228194	−	0.0228194i
$919$	−12.0900	+	20.9405i	−0.398812	+	0.690763i	−0.993580	−	0.113135i	$-0.963911\pi$
$919$	−12.0900	+	20.9405i	−0.398812	+	0.690763i	0.594767	+	0.803898i	$0.297244\pi$
$920$	−2.62793	−	4.55170i	−0.0866402	−	0.150065i
$921$	−28.3000	−	7.58297i	−0.932518	−	0.249867i
$922$	1.48343	+	2.56938i	0.0488542	+	0.0846180i
$923$	−11.9115	−	12.3386i	−0.392070	−	0.406131i
$924$		0			0
$925$	5.14530	−	1.37868i	0.169177	−	0.0453307i
$926$	−3.73596			−0.122771
$927$	−44.3454			−1.45649
$928$	9.60051	−	2.57245i	0.315152	−	0.0844448i
$929$	−4.01941	−	15.0006i	−0.131872	−	0.492155i	0.868119	−	0.496357i	$-0.165329\pi$
$929$	−4.01941	−	15.0006i	−0.131872	−	0.492155i	−0.999991	+	0.00420200i	$0.998662\pi$
$930$	−0.593364	+	2.21446i	−0.0194572	+	0.0726151i
$931$		0			0
$932$	16.2386	+	28.1261i	0.531913	+	0.921300i
$933$		−	33.8944i		−	1.10965i
$934$	0.341285	−	1.27369i	0.0111672	−	0.0416765i
$935$	12.8060	+	7.39354i	0.418801	+	0.241795i
$936$	−6.05414	−	1.73704i	−0.197886	−	0.0567770i
$937$			25.4720i			0.832134i	0.909334	+	0.416067i	$0.136592\pi$
$937$			25.4720i			0.832134i	−0.909334	+	0.416067i	$0.863408\pi$
$938$		0			0
$939$	−4.64378	+	8.04326i	−0.151544	+	0.262482i
$940$	20.1299	+	11.6220i	0.656565	+	0.379068i
$941$	4.63851	+	17.3112i	0.151211	+	0.564328i	0.999400	+	0.0346338i	$0.0110265\pi$
$941$	4.63851	+	17.3112i	0.151211	+	0.564328i	−0.848189	+	0.529694i	$0.822307\pi$
$942$	−1.48691	−	1.48691i	−0.0484463	−	0.0484463i
$943$	−70.3957	+	18.8625i	−2.29240	+	0.614246i
$944$	−4.67503	−	4.67503i	−0.152159	−	0.152159i
$945$		0			0
$946$	−0.354822	−	0.204856i	−0.0115362	−	0.00666046i
$947$	8.78872	−	8.78872i	0.285595	−	0.285595i	−0.549740	−	0.835336i	$-0.685273\pi$
$947$	8.78872	−	8.78872i	0.285595	−	0.285595i	0.835336	+	0.549740i	$0.185273\pi$
$948$	−15.3239	+	26.5417i	−0.497696	+	0.862035i
$949$	0.982264	−	3.42350i	0.0318856	−	0.111131i
$950$	0.812546	−	0.469124i	0.0263625	−	0.0152204i
$951$	22.3117	+	83.2684i	0.723506	+	2.70016i
$952$		0			0
$953$	25.0716	−	14.4751i	0.812147	−	0.468893i	−0.0355538	−	0.999368i	$-0.511320\pi$
$953$	25.0716	−	14.4751i	0.812147	−	0.468893i	0.847701	+	0.530474i	$0.177986\pi$
$954$	−0.485189	+	1.81075i	−0.0157086	+	0.0586252i
$955$	−18.1385	+	18.1385i	−0.586947	+	0.586947i
$956$	12.1465	−	12.1465i	0.392847	−	0.392847i
$957$	9.42681	−	35.1813i	0.304725	−	1.13725i
$958$	2.02778	−	1.17074i	0.0655147	−	0.0378249i
$959$		0			0
$960$	9.11358	+	34.0123i	0.294140	+	1.09774i
$961$	10.9841	−	6.34165i	0.354325	−	0.204569i
$962$	−0.613523	+	1.02070i	−0.0197808	+	0.0329088i
$963$	14.9965	−	25.9746i	0.483254	−	0.837021i
$964$	−18.8651	+	18.8651i	−0.607605	+	0.607605i
$965$	29.9342	+	17.2825i	0.963617	+	0.556344i
$966$		0			0
$967$	20.8937	+	20.8937i	0.671895	+	0.671895i	0.958153	−	0.286258i	$-0.0924113\pi$
$967$	20.8937	+	20.8937i	0.671895	+	0.671895i	−0.286258	+	0.958153i	$0.592411\pi$
$968$	−3.22215	+	0.863372i	−0.103564	+	0.0277498i
$969$	33.5515	+	33.5515i	1.07783	+	1.07783i
$970$	0.788040	+	2.94101i	0.0253024	+	0.0944300i
$971$	−35.5507	−	20.5252i	−1.14088	−	0.658685i	−0.194229	−	0.980956i	$-0.562220\pi$
$971$	−35.5507	−	20.5252i	−1.14088	−	0.658685i	−0.946647	+	0.322271i	$0.895554\pi$
$972$	−21.7644	+	37.6971i	−0.698094	+	1.20913i
$973$		0			0
$974$		−	3.66794i		−	0.117528i
$975$	9.08901	−	15.1212i	0.291081	−	0.484265i
$976$	−10.4606	−	6.03940i	−0.334834	−	0.193317i
$977$	5.90951	−	22.0546i	0.189062	−	0.705589i	−0.804662	−	0.593733i	$-0.797654\pi$
$977$	5.90951	−	22.0546i	0.189062	−	0.705589i	0.993724	−	0.111856i	$-0.0356796\pi$
$978$		−	3.92462i		−	0.125496i
$979$	−7.86639	−	13.6250i	−0.251411	−	0.435457i
$980$		0			0
$981$	12.0296	−	44.8951i	0.384076	−	1.43339i
$982$	−0.587390	−	2.19217i	−0.0187444	−	0.0699549i
$983$	−28.7452	+	7.70226i	−0.916831	+	0.245664i	−0.686230	−	0.727384i	$-0.740736\pi$
$983$	−28.7452	+	7.70226i	−0.916831	+	0.245664i	−0.230601	+	0.973048i	$0.574069\pi$
$984$	−13.7811			−0.439327
$985$	38.4159			1.22403
$986$	3.45403	−	0.925505i	0.109999	−	0.0294741i
$987$		0			0
$988$	8.42998	−	29.3811i	0.268193	−	0.934737i
$989$	−5.73255	−	9.92907i	−0.182285	−	0.315726i
$990$	−1.46303	−	0.392017i	−0.0464981	−	0.0124591i
$991$	1.24883	+	2.16303i	0.0396703	+	0.0687110i	0.885179	−	0.465251i	$-0.154036\pi$
$991$	1.24883	+	2.16303i	0.0396703	+	0.0687110i	−0.845509	+	0.533962i	$0.820703\pi$
$992$	2.97089	−	5.14574i	0.0943259	−	0.163377i
$993$	−1.74225	+	1.74225i	−0.0552888	+	0.0552888i
$994$		0			0
$995$	32.8817	+	8.81062i	1.04242	+	0.279315i
$996$	−69.6456	−	18.6615i	−2.20681	−	0.591312i
$997$			5.96661i			0.188965i	0.995527	+	0.0944823i	$0.0301196\pi$
$997$			5.96661i			0.188965i	−0.995527	+	0.0944823i	$0.969880\pi$
$998$	1.68806	−	0.974599i	0.0534345	−	0.0308504i
$999$	−3.91593	−	3.91593i	−0.123895	−	0.123895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.b.423.3		32
7.2	even	3		637.2.x.b.215.3		32
7.3	odd	6		91.2.bc.a.20.5	✓	32
7.4	even	3		91.2.bc.a.20.6	yes	32
7.5	odd	6		637.2.x.b.215.4		32
7.6	odd	2	inner	637.2.bb.b.423.4		32
13.2	odd	12		637.2.x.b.80.3		32
21.11	odd	6		819.2.fm.g.748.3		32
21.17	even	6		819.2.fm.g.748.4		32
91.2	odd	12	inner	637.2.bb.b.509.4		32
91.41	even	12		637.2.x.b.80.4		32
91.54	even	12	inner	637.2.bb.b.509.3		32
91.67	odd	12		91.2.bc.a.41.5	yes	32
91.80	even	12		91.2.bc.a.41.6	yes	32
273.80	odd	12		819.2.fm.g.496.3		32
273.158	even	12		819.2.fm.g.496.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.5	✓	32	7.3	odd	6
91.2.bc.a.20.6	yes	32	7.4	even	3
91.2.bc.a.41.5	yes	32	91.67	odd	12
91.2.bc.a.41.6	yes	32	91.80	even	12
637.2.x.b.80.3		32	13.2	odd	12
637.2.x.b.80.4		32	91.41	even	12
637.2.x.b.215.3		32	7.2	even	3
637.2.x.b.215.4		32	7.5	odd	6
637.2.bb.b.423.3		32	1.1	even	1	trivial
637.2.bb.b.423.4		32	7.6	odd	2	inner
637.2.bb.b.509.3		32	91.54	even	12	inner
637.2.bb.b.509.4		32	91.2	odd	12	inner
819.2.fm.g.496.3		32	273.80	odd	12
819.2.fm.g.496.4		32	273.158	even	12
819.2.fm.g.748.3		32	21.11	odd	6
819.2.fm.g.748.4		32	21.17	even	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)

\(f(q)\)	\(=\)	\(q+(0.0825572 + 0.0825572i) q^{2} +(-2.25055 + 1.29935i) q^{3} -1.98637i q^{4} +(-1.70537 - 0.456951i) q^{5} +(-0.293070 - 0.0785278i) q^{6} +(0.329103 - 0.329103i) q^{8} +(1.87664 - 3.25044i) q^{9} +O(q^{10})\)	\(q+(0.0825572 + 0.0825572i) q^{2} +(-2.25055 + 1.29935i) q^{3} -1.98637i q^{4} +(-1.70537 - 0.456951i) q^{5} +(-0.293070 - 0.0785278i) q^{6} +(0.329103 - 0.329103i) q^{8} +(1.87664 - 3.25044i) q^{9} +(-0.103066 - 0.178515i) q^{10} +(1.89103 + 0.506699i) q^{11} +(2.58100 + 4.47042i) q^{12} +(1.85749 - 3.09026i) q^{13} +(4.43175 - 1.18748i) q^{15} -3.91840 q^{16} -4.27814 q^{17} +(0.423277 - 0.113417i) q^{18} +(1.10462 + 4.12248i) q^{19} +(-0.907674 + 3.38749i) q^{20} +(0.114286 + 0.197949i) q^{22} +6.39620i q^{23} +(-0.313041 + 1.16828i) q^{24} +(-1.63066 - 0.941462i) q^{25} +(0.408473 - 0.101774i) q^{26} +1.95756i q^{27} +(-3.57954 + 6.19995i) q^{29} +(0.463908 + 0.267837i) q^{30} +(1.10769 + 4.13397i) q^{31} +(-0.981699 - 0.981699i) q^{32} +(-4.91422 + 1.31676i) q^{33} +(-0.353191 - 0.353191i) q^{34} +(-6.45657 - 3.72770i) q^{36} +(-2.00041 + 2.00041i) q^{37} +(-0.249147 + 0.431534i) q^{38} +(-0.165023 + 9.36832i) q^{39} +(-0.711626 + 0.410857i) q^{40} +(2.94901 + 11.0059i) q^{41} +(-1.55234 + 0.896243i) q^{43} +(1.00649 - 3.75627i) q^{44} +(-4.68565 + 4.68565i) q^{45} +(-0.528052 + 0.528052i) q^{46} +(1.71543 - 6.40208i) q^{47} +(8.81854 - 5.09139i) q^{48} +(-0.0568982 - 0.212347i) q^{50} +(9.62816 - 5.55882i) q^{51} +(-6.13840 - 3.68966i) q^{52} +(-2.13896 + 3.70479i) q^{53} +(-0.161611 + 0.161611i) q^{54} +(-2.99335 - 1.72821i) q^{55} +(-7.84255 - 7.84255i) q^{57} +(-0.807367 + 0.216333i) q^{58} +(1.19310 + 1.19310i) q^{59} +(-2.35878 - 8.80308i) q^{60} +(2.66960 + 1.54129i) q^{61} +(-0.249841 + 0.432737i) q^{62} +7.67470i q^{64} +(-4.57980 + 4.42125i) q^{65} +(-0.514413 - 0.296996i) q^{66} +(0.00510122 - 0.0190380i) q^{67} +8.49797i q^{68} +(-8.31093 - 14.3949i) q^{69} +(1.23109 - 4.59449i) q^{71} +(-0.452121 - 1.68734i) q^{72} +(0.954158 - 0.255666i) q^{73} -0.330297 q^{74} +4.89317 q^{75} +(8.18877 - 2.19417i) q^{76} +(-0.787046 + 0.759799i) q^{78} +(2.96860 + 5.14176i) q^{79} +(6.68230 + 1.79052i) q^{80} +(3.08636 + 5.34573i) q^{81} +(-0.665151 + 1.15208i) q^{82} +(-9.87683 + 9.87683i) q^{83} +(7.29580 + 1.95490i) q^{85} +(-0.202148 - 0.0541654i) q^{86} -18.6044i q^{87} +(0.789099 - 0.455587i) q^{88} +(-5.68247 - 5.68247i) q^{89} -0.773669 q^{90} +12.7052 q^{92} +(-7.86441 - 7.86441i) q^{93} +(0.670159 - 0.386917i) q^{94} -7.53509i q^{95} +(3.48493 + 0.933785i) q^{96} +(-14.2676 - 3.82300i) q^{97} +(5.19577 - 5.19577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} + 8 q^{9} - 16 q^{11} - 8 q^{15} - 24 q^{16} + 68 q^{18} + 4 q^{22} + 4 q^{29} - 12 q^{30} - 68 q^{32} - 8 q^{37} - 48 q^{43} + 60 q^{44} + 24 q^{46} - 44 q^{50} - 12 q^{51} - 36 q^{53} - 92 q^{57} - 28 q^{58} - 104 q^{60} - 32 q^{65} - 8 q^{67} + 84 q^{71} + 124 q^{72} + 48 q^{74} + 148 q^{78} + 40 q^{79} + 28 q^{81} + 36 q^{85} - 60 q^{86} + 228 q^{88} + 24 q^{92} - 84 q^{93} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 + 8 * q^9 - 16 * q^11 - 8 * q^15 - 24 * q^16 + 68 * q^18 + 4 * q^22 + 4 * q^29 - 12 * q^30 - 68 * q^32 - 8 * q^37 - 48 * q^43 + 60 * q^44 + 24 * q^46 - 44 * q^50 - 12 * q^51 - 36 * q^53 - 92 * q^57 - 28 * q^58 - 104 * q^60 - 32 * q^65 - 8 * q^67 + 84 * q^71 + 124 * q^72 + 48 * q^74 + 148 * q^78 + 40 * q^79 + 28 * q^81 + 36 * q^85 - 60 * q^86 + 228 * q^88 + 24 * q^92 - 84 * q^93 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more