LMFDB - Embedded newform 637.2.bd.b.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	637.97
Dual form			637.2.bd.b.440.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0707322 - 0.263976i) q^{2} +(-2.17048 - 1.25313i) q^{3} +(1.66737 - 0.962657i) q^{4} +(-1.04692 - 1.04692i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} +(1.64065 + 2.84169i) q^{9} +O(q^{10})$	\(q+(-0.0707322 - 0.263976i) q^{2} +(-2.17048 - 1.25313i) q^{3} +(1.66737 - 0.962657i) q^{4} +(-1.04692 - 1.04692i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} +(1.64065 + 2.84169i) q^{9} +(-0.202311 + 0.350412i) q^{10} +(-4.43396 + 1.18808i) q^{11} -4.82532 q^{12} +(-2.80779 + 2.26193i) q^{13} +(0.960393 + 3.58423i) q^{15} +(1.77873 - 3.08085i) q^{16} +(-1.17081 - 2.02791i) q^{17} +(0.634091 - 0.634091i) q^{18} +(0.438561 - 1.63673i) q^{19} +(-2.75342 - 0.737778i) q^{20} +(0.627247 + 1.08642i) q^{22} +(4.15065 + 2.39638i) q^{23} +(0.695851 + 2.59695i) q^{24} -2.80792i q^{25} +(0.795696 + 0.581199i) q^{26} -0.705008i q^{27} +(-2.87534 + 4.98024i) q^{29} +(0.878222 - 0.507042i) q^{30} +(4.17096 + 4.17096i) q^{31} +(-3.01146 - 0.806919i) q^{32} +(11.1126 + 2.97762i) q^{33} +(-0.452505 + 0.452505i) q^{34} +(5.47114 + 3.15877i) q^{36} +(-8.24256 + 2.20859i) q^{37} -0.463079 q^{38} +(8.92873 - 1.39095i) q^{39} +1.58827i q^{40} +(-0.829479 + 0.222258i) q^{41} +(1.70069 - 0.981895i) q^{43} +(-6.24934 + 6.24934i) q^{44} +(1.25739 - 4.69264i) q^{45} +(0.339003 - 1.26518i) q^{46} +(-5.67880 + 5.67880i) q^{47} +(-7.72139 + 4.45794i) q^{48} +(-0.741225 + 0.198611i) q^{50} +5.86871i q^{51} +(-2.50417 + 6.47441i) q^{52} -13.0827 q^{53} +(-0.186105 + 0.0498668i) q^{54} +(5.88581 + 3.39817i) q^{55} +(-3.00292 + 3.00292i) q^{57} +(1.51804 + 0.406759i) q^{58} +(-1.49637 - 0.400951i) q^{59} +(5.05172 + 5.05172i) q^{60} +(8.45262 - 4.88012i) q^{61} +(0.806013 - 1.39606i) q^{62} -6.26289i q^{64} +(5.30758 + 0.571475i) q^{65} -3.14408i q^{66} +(-0.141189 - 0.526925i) q^{67} +(-3.90436 - 2.25418i) q^{68} +(-6.00594 - 10.4026i) q^{69} +(1.77061 + 0.474435i) q^{71} +(0.911040 - 3.40005i) q^{72} +(-1.67079 + 1.67079i) q^{73} +(1.16603 + 2.01962i) q^{74} +(-3.51868 + 6.09453i) q^{75} +(-0.844368 - 3.15123i) q^{76} +(-0.998725 - 2.25859i) q^{78} +4.26678 q^{79} +(-5.08758 + 1.36321i) q^{80} +(4.03849 - 6.99486i) q^{81} +(0.117342 + 0.203242i) q^{82} +(3.88518 + 3.88518i) q^{83} +(-0.897309 + 3.34880i) q^{85} +(-0.379490 - 0.379490i) q^{86} +(12.4817 - 7.20634i) q^{87} +(4.26455 + 2.46214i) q^{88} +(-3.63117 - 13.5517i) q^{89} -1.32768 q^{90} +9.22757 q^{92} +(-3.82624 - 14.2797i) q^{93} +(1.90074 + 1.09739i) q^{94} +(-2.17267 + 1.25439i) q^{95} +(5.52514 + 5.52514i) q^{96} +(0.734114 - 2.73975i) q^{97} +(-10.6507 - 10.6507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0707322	−	0.263976i	−0.0500152	−	0.186659i	0.936399	−	0.350938i	$-0.114137\pi$
$2$	−0.0707322	−	0.263976i	−0.0500152	−	0.186659i	−0.986414	+	0.164278i	$0.947470\pi$
$3$	−2.17048	−	1.25313i	−1.25313	−	0.723493i	−0.281397	−	0.959591i	$-0.590798\pi$
$3$	−2.17048	−	1.25313i	−1.25313	−	0.723493i	−0.971729	+	0.236099i	$0.924131\pi$
$4$	1.66737	−	0.962657i	0.833685	−	0.481328i
$5$	−1.04692	−	1.04692i	−0.468196	−	0.468196i	0.433134	−	0.901330i	$-0.357408\pi$
$5$	−1.04692	−	1.04692i	−0.468196	−	0.468196i	−0.901330	+	0.433134i	$0.857408\pi$
$6$	−0.177273	+	0.661591i	−0.0723713	+	0.270093i
$7$		0			0
$7$		0			0
$8$	−0.758543	−	0.758543i	−0.268186	−	0.268186i
$9$	1.64065	+	2.84169i	0.546883	+	0.947230i
$10$	−0.202311	+	0.350412i	−0.0639763	+	0.110810i
$11$	−4.43396	+	1.18808i	−1.33689	+	0.358218i	−0.855279	−	0.518168i	$-0.826614\pi$
$11$	−4.43396	+	1.18808i	−1.33689	+	0.358218i	−0.481609	+	0.876386i	$0.659948\pi$
$12$	−4.82532			−1.39295
$13$	−2.80779	+	2.26193i	−0.778741	+	0.627346i
$13$	−2.80779	+	2.26193i	−0.778741	+	0.627346i
$14$		0			0
$15$	0.960393	+	3.58423i	0.247972	+	0.925445i
$16$	1.77873	−	3.08085i	0.444682	−	0.770213i
$17$	−1.17081	−	2.02791i	−0.283964	−	0.491840i	0.688393	−	0.725337i	$-0.258316\pi$
$17$	−1.17081	−	2.02791i	−0.283964	−	0.491840i	−0.972357	+	0.233497i	$0.924983\pi$
$18$	0.634091	−	0.634091i	0.149457	−	0.149457i
$19$	0.438561	−	1.63673i	0.100613	−	0.375492i	−0.897198	−	0.441629i	$-0.854401\pi$
$19$	0.438561	−	1.63673i	0.100613	−	0.375492i	0.997811	+	0.0661367i	$0.0210674\pi$
$20$	−2.75342	−	0.737778i	−0.615684	−	0.164972i
$21$		0			0
$22$	0.627247	+	1.08642i	0.133730	+	0.231626i
$23$	4.15065	+	2.39638i	0.865471	+	0.499680i	0.865841	−	0.500320i	$-0.166784\pi$
$23$	4.15065	+	2.39638i	0.865471	+	0.499680i	−0.000369324		1.00000i	$0.500118\pi$
$24$	0.695851	+	2.59695i	0.142040	+	0.530101i
$25$		−	2.80792i		−	0.561585i
$26$	0.795696	+	0.581199i	0.156049	+	0.113982i
$27$		−	0.705008i		−	0.135679i
$28$		0			0
$29$	−2.87534	+	4.98024i	−0.533938	+	0.924808i	0.465276	+	0.885166i	$0.345955\pi$
$29$	−2.87534	+	4.98024i	−0.533938	+	0.924808i	−0.999214	+	0.0396419i	$0.987378\pi$
$30$	0.878222	−	0.507042i	0.160341	−	0.0925727i
$31$	4.17096	+	4.17096i	0.749127	+	0.749127i	0.974315	−	0.225189i	$-0.0722998\pi$
$31$	4.17096	+	4.17096i	0.749127	+	0.749127i	−0.225189	+	0.974315i	$0.572300\pi$
$32$	−3.01146	−	0.806919i	−0.532356	−	0.142644i
$33$	11.1126	+	2.97762i	1.93446	+	0.518336i
$34$	−0.452505	+	0.452505i	−0.0776040	+	0.0776040i
$35$		0			0
$36$	5.47114	+	3.15877i	0.911857	+	0.526461i
$37$	−8.24256	+	2.20859i	−1.35507	+	0.363090i	−0.862003	−	0.506902i	$-0.830790\pi$
$37$	−8.24256	+	2.20859i	−1.35507	+	0.363090i	−0.493066	+	0.869992i	$0.664124\pi$
$38$	−0.463079			−0.0751214
$39$	8.92873	−	1.39095i	1.42974	−	0.222730i
$40$			1.58827i			0.251127i
$41$	−0.829479	+	0.222258i	−0.129543	+	0.0347109i	−0.323008	−	0.946396i	$-0.604694\pi$
$41$	−0.829479	+	0.222258i	−0.129543	+	0.0347109i	0.193465	+	0.981107i	$0.438027\pi$
$42$		0			0
$43$	1.70069	−	0.981895i	0.259353	−	0.149738i	−0.364686	−	0.931130i	$-0.618824\pi$
$43$	1.70069	−	0.981895i	0.259353	−	0.149738i	0.624039	+	0.781393i	$0.285490\pi$
$44$	−6.24934	+	6.24934i	−0.942123	+	0.942123i
$45$	1.25739	−	4.69264i	0.187441	−	0.699538i
$46$	0.339003	−	1.26518i	0.0499832	−	0.186540i
$47$	−5.67880	+	5.67880i	−0.828339	+	0.828339i	−0.987287	−	0.158948i	$-0.949190\pi$
$47$	−5.67880	+	5.67880i	−0.828339	+	0.828339i	0.158948	+	0.987287i	$0.449190\pi$
$48$	−7.72139	+	4.45794i	−1.11449	+	0.643449i
$49$		0			0
$50$	−0.741225	+	0.198611i	−0.104825	+	0.0280878i
$51$			5.86871i			0.821783i
$52$	−2.50417	+	6.47441i	−0.347266	+	0.897839i
$53$	−13.0827			−1.79704			−0.898521	−	0.438931i	$-0.855357\pi$
$53$	−13.0827			−1.79704			−0.898521	+	0.438931i	$0.855357\pi$
$54$	−0.186105	+	0.0498668i	−0.0253257	+	0.00678601i
$55$	5.88581	+	3.39817i	0.793642	+	0.458210i
$56$		0			0
$57$	−3.00292	+	3.00292i	−0.397747	+	0.397747i
$58$	1.51804	+	0.406759i	0.199329	+	0.0534100i
$59$	−1.49637	−	0.400951i	−0.194811	−	0.0521994i	0.160094	−	0.987102i	$-0.448820\pi$
$59$	−1.49637	−	0.400951i	−0.194811	−	0.0521994i	−0.354905	+	0.934902i	$0.615487\pi$
$60$	5.05172	+	5.05172i	0.652174	+	0.652174i
$61$	8.45262	−	4.88012i	1.08225	−	0.624836i	0.150746	−	0.988573i	$-0.451833\pi$
$61$	8.45262	−	4.88012i	1.08225	−	0.624836i	0.931502	+	0.363737i	$0.118499\pi$
$62$	0.806013	−	1.39606i	0.102364	−	0.177299i
$63$		0			0
$64$		−	6.26289i		−	0.782861i
$65$	5.30758	+	0.571475i	0.658324	+	0.0708827i
$66$		−	3.14408i		−	0.387009i
$67$	−0.141189	−	0.526925i	−0.0172490	−	0.0643742i	0.956765	−	0.290862i	$-0.0939422\pi$
$67$	−0.141189	−	0.526925i	−0.0172490	−	0.0643742i	−0.974014	+	0.226488i	$0.927276\pi$
$68$	−3.90436	−	2.25418i	−0.473473	−	0.273360i
$69$	−6.00594	−	10.4026i	−0.723030	−	1.25232i
$70$		0			0
$71$	1.77061	+	0.474435i	0.210133	+	0.0563050i	0.362350	−	0.932042i	$-0.381975\pi$
$71$	1.77061	+	0.474435i	0.210133	+	0.0563050i	−0.152217	+	0.988347i	$0.548641\pi$
$72$	0.911040	−	3.40005i	0.107367	−	0.400699i
$73$	−1.67079	+	1.67079i	−0.195551	+	0.195551i	−0.798090	−	0.602538i	$-0.794156\pi$
$73$	−1.67079	+	1.67079i	−0.195551	+	0.195551i	0.602538	+	0.798090i	$0.294156\pi$
$74$	1.16603	+	2.01962i	0.135548	+	0.234776i
$75$	−3.51868	+	6.09453i	−0.406302	+	0.703736i
$76$	−0.844368	−	3.15123i	−0.0968557	−	0.361470i
$77$		0			0
$78$	−0.998725	−	2.25859i	−0.113083	−	0.255735i
$79$	4.26678			0.480050			0.240025	−	0.970767i	$-0.422844\pi$
$79$	4.26678			0.480050			0.240025	+	0.970767i	$0.422844\pi$
$80$	−5.08758	+	1.36321i	−0.568809	+	0.152412i
$81$	4.03849	−	6.99486i	0.448721	−	0.777207i
$82$	0.117342	+	0.203242i	0.0129582	+	0.0224443i
$83$	3.88518	+	3.88518i	0.426454	+	0.426454i	0.887419	−	0.460965i	$-0.152496\pi$
$83$	3.88518	+	3.88518i	0.426454	+	0.426454i	−0.460965	+	0.887419i	$0.652496\pi$
$84$		0			0
$85$	−0.897309	+	3.34880i	−0.0973268	+	0.363228i
$86$	−0.379490	−	0.379490i	−0.0409215	−	0.0409215i
$87$	12.4817	−	7.20634i	1.33818	−	0.772600i
$88$	4.26455	+	2.46214i	0.454603	+	0.262465i
$89$	−3.63117	−	13.5517i	−0.384904	−	1.43648i	−0.838319	−	0.545180i	$-0.816461\pi$
$89$	−3.63117	−	13.5517i	−0.384904	−	1.43648i	0.453415	−	0.891299i	$-0.350205\pi$
$90$	−1.32768			−0.139950
$91$		0			0
$92$	9.22757			0.962041
$93$	−3.82624	−	14.2797i	−0.396762	−	1.48074i
$94$	1.90074	+	1.09739i	0.196047	+	0.113188i
$95$	−2.17267	+	1.25439i	−0.222911	+	0.128698i
$96$	5.52514	+	5.52514i	0.563908	+	0.563908i
$97$	0.734114	−	2.73975i	0.0745380	−	0.278180i	−0.918590	−	0.395212i	$-0.870671\pi$
$97$	0.734114	−	2.73975i	0.0745380	−	0.278180i	0.993128	+	0.117032i	$0.0373380\pi$
$98$		0			0
$99$	−10.6507	−	10.6507i	−1.07044	−	1.07044i
$100$	−2.70307	−	4.68185i	−0.270307	−	0.468185i
$101$	−5.32015	+	9.21476i	−0.529374	+	0.916903i	0.470039	+	0.882646i	$0.344240\pi$
$101$	−5.32015	+	9.21476i	−0.529374	+	0.916903i	−0.999413	+	0.0342575i	$0.989093\pi$
$102$	1.54920	−	0.415107i	0.153394	−	0.0411017i
$103$	−17.2155			−1.69629			−0.848145	−	0.529765i	$-0.822280\pi$
$103$	−17.2155			−1.69629			−0.848145	+	0.529765i	$0.822280\pi$
$104$	3.84560	+	0.414061i	0.377092	+	0.0406020i
$105$		0			0
$106$	0.925366	+	3.45351i	0.0898794	+	0.335435i
$107$	2.02845	−	3.51338i	0.196097	−	0.339651i	−0.751162	−	0.660118i	$-0.770506\pi$
$107$	2.02845	−	3.51338i	0.196097	−	0.339651i	0.947260	+	0.320467i	$0.103840\pi$
$108$	−0.678681	−	1.17551i	−0.0653061	−	0.113113i
$109$	−5.60132	+	5.60132i	−0.536509	+	0.536509i	−0.922502	−	0.385993i	$-0.873859\pi$
$109$	−5.60132	+	5.60132i	−0.536509	+	0.536509i	0.385993	+	0.922502i	$0.373859\pi$
$110$	0.480721	−	1.79407i	0.0458349	−	0.171058i
$111$	20.6579	+	5.53528i	1.96077	+	0.525385i
$112$		0			0
$113$	−9.23138	−	15.9892i	−0.868415	−	1.50414i	−0.863616	−	0.504150i	$-0.831806\pi$
$113$	−9.23138	−	15.9892i	−0.868415	−	1.50414i	−0.00479920	−	0.999988i	$-0.501528\pi$
$114$	1.00510	+	0.580297i	0.0941365	+	0.0543497i
$115$	−1.83658	−	6.85421i	−0.171262	−	0.639159i
$116$			11.0719i			1.02800i
$117$	−11.0343	−	4.26784i	−1.02012	−	0.394562i
$118$			0.423366i			0.0389740i
$119$		0			0
$120$	1.99030	−	3.44730i	0.181688	−	0.314694i
$121$	8.72217	−	5.03575i	0.792925	−	0.457795i
$122$	−1.88611	−	1.88611i	−0.170760	−	0.170760i
$123$	2.07888	+	0.557035i	0.187447	+	0.0502262i
$124$	10.9697	+	2.93933i	0.985112	+	0.263960i
$125$	−8.17426	+	8.17426i	−0.731128	+	0.731128i
$126$		0			0
$127$	−2.52084	−	1.45541i	−0.223689	−	0.129147i	0.383968	−	0.923346i	$-0.374557\pi$
$127$	−2.52084	−	1.45541i	−0.223689	−	0.129147i	−0.607657	+	0.794200i	$0.707890\pi$
$128$	−7.67618	+	2.05683i	−0.678485	+	0.181799i
$129$	−4.92175			−0.433336
$130$	−0.224561	−	1.44150i	−0.0196953	−	0.126428i
$131$		−	9.91023i		−	0.865861i	−0.901427	−	0.432931i	$-0.857480\pi$
$131$		−	9.91023i		−	0.865861i	0.901427	−	0.432931i	$-0.142520\pi$
$132$	21.3953	−	5.73284i	1.86222	−	0.498980i
$133$		0			0
$134$	−0.129109	+	0.0745412i	−0.0111533	+	0.00643938i
$135$	−0.738086	+	0.738086i	−0.0635243	+	0.0635243i
$136$	−0.650144	+	2.42637i	−0.0557493	+	0.208059i
$137$	−0.140972	+	0.526114i	−0.0120440	+	0.0449489i	−0.971686	−	0.236275i	$-0.924074\pi$
$137$	−0.140972	+	0.526114i	−0.0120440	+	0.0449489i	0.959642	+	0.281223i	$0.0907402\pi$
$138$	−2.32122	+	2.32122i	−0.197596	+	0.197596i
$139$	3.32499	−	1.91968i	0.282022	−	0.162825i	−0.352317	−	0.935881i	$-0.614606\pi$
$139$	3.32499	−	1.91968i	0.282022	−	0.162825i	0.634338	+	0.773056i	$0.281273\pi$
$140$		0			0
$141$	19.4420	−	5.20946i	1.63731	−	0.438716i
$142$		−	0.500958i		−	0.0420394i
$143$	9.76228	−	13.3652i	0.816363	−	1.11765i
$144$	11.6731			0.972757
$145$	8.22416	−	2.20366i	0.682979	−	0.183004i
$146$	0.559228	+	0.322870i	0.0462820	+	0.0267210i
$147$		0			0
$148$	−11.6173	+	11.6173i	−0.954936	+	0.954936i
$149$	−22.5930	−	6.05379i	−1.85089	−	0.495946i	−0.851307	−	0.524668i	$-0.824189\pi$
$149$	−22.5930	−	6.05379i	−1.85089	−	0.495946i	−0.999587	+	0.0287228i	$0.990856\pi$
$150$	1.85770	+	0.497768i	0.151680	+	0.0406426i
$151$	−4.66151	−	4.66151i	−0.379348	−	0.379348i	0.491519	−	0.870867i	$-0.336442\pi$
$151$	−4.66151	−	4.66151i	−0.379348	−	0.379348i	−0.870867	+	0.491519i	$0.836442\pi$
$152$	−1.57420	+	0.908865i	−0.127685	+	0.0737187i
$153$	3.84179	−	6.65417i	0.310590	−	0.537958i
$154$		0			0
$155$		−	8.73331i		−	0.701476i
$156$	13.5485	−	10.9145i	1.08475	−	0.873861i
$157$		−	10.9614i		−	0.874816i	−0.899263	−	0.437408i	$-0.855897\pi$
$157$		−	10.9614i		−	0.874816i	0.899263	−	0.437408i	$-0.144103\pi$
$158$	−0.301799	−	1.12633i	−0.0240098	−	0.0896058i
$159$	28.3956	+	16.3942i	2.25192	+	1.30015i
$160$	2.30798	+	3.99754i	0.182462	+	0.316033i
$161$		0			0
$162$	−2.13213	−	0.571302i	−0.167516	−	0.0448857i
$163$	1.00078	−	3.73496i	0.0783870	−	0.292544i	−0.915593	−	0.402106i	$-0.868278\pi$
$163$	1.00078	−	3.73496i	0.0783870	−	0.292544i	0.993980	+	0.109562i	$0.0349448\pi$
$164$	−1.16909	+	1.16909i	−0.0912906	+	0.0912906i
$165$	−8.51668	−	14.7513i	−0.663023	−	1.14839i
$166$	0.750788	−	1.30040i	0.0582724	−	0.100931i
$167$	−6.30900	−	23.5455i	−0.488205	−	1.82201i	−0.565172	−	0.824973i	$-0.691190\pi$
$167$	−6.30900	−	23.5455i	−0.488205	−	1.82201i	0.0769673	−	0.997034i	$-0.475476\pi$
$168$		0			0
$169$	2.76737	−	12.7020i	0.212875	−	0.977079i
$170$	0.947472			0.0726678
$171$	5.37061	−	1.43905i	0.410701	−	0.110047i
$172$	1.89046	−	3.27436i	0.144146	−	0.249668i
$173$	−2.39991	−	4.15677i	−0.182462	−	0.316033i	0.760257	−	0.649623i	$-0.225073\pi$
$173$	−2.39991	−	4.15677i	−0.182462	−	0.316033i	−0.942718	+	0.333590i	$0.891740\pi$
$174$	−2.78516	−	2.78516i	−0.211143	−	0.211143i
$175$		0			0
$176$	−4.22653	+	15.7736i	−0.318587	+	1.18898i
$177$	2.74540	+	2.74540i	0.206357	+	0.206357i
$178$	−3.32049	+	1.91709i	−0.248881	+	0.143692i
$179$	9.64786	+	5.57019i	0.721115	+	0.416336i	0.815163	−	0.579232i	$-0.196647\pi$
$179$	9.64786	+	5.57019i	0.721115	+	0.416336i	−0.0940481	+	0.995568i	$0.529981\pi$
$180$	−2.42087	−	9.03481i	−0.180441	−	0.673415i
$181$	4.32449			0.321437			0.160718	−	0.987000i	$-0.448619\pi$
$181$	4.32449			0.321437			0.160718	+	0.987000i	$0.448619\pi$
$182$		0			0
$183$	−24.4616			−1.80826
$184$	−1.33069	−	4.96621i	−0.0980999	−	0.366114i
$185$	10.9415	+	6.31708i	0.804435	+	0.464441i
$186$	−3.49887	+	2.02007i	−0.256549	+	0.148119i
$187$	7.60064	+	7.60064i	0.555814	+	0.555814i
$188$	−4.00193	+	14.9354i	−0.291871	+	1.08928i
$189$		0			0
$190$	0.484806	+	0.484806i	0.0351715	+	0.0351715i
$191$	3.15973	+	5.47282i	0.228630	+	0.395999i	0.957402	−	0.288757i	$-0.0932420\pi$
$191$	3.15973	+	5.47282i	0.228630	+	0.395999i	−0.728772	+	0.684756i	$0.759909\pi$
$192$	−7.84819	+	13.5935i	−0.566394	+	0.981024i
$193$	−11.5064	+	3.08313i	−0.828250	+	0.221929i	−0.647950	−	0.761683i	$-0.724373\pi$
$193$	−11.5064	+	3.08313i	−0.828250	+	0.221929i	−0.180300	+	0.983612i	$0.557707\pi$
$194$	−0.775155			−0.0556529
$195$	−10.8039	−	7.89144i	−0.773680	−	0.565118i
$196$		0			0
$197$	−0.533499	−	1.99105i	−0.0380103	−	0.141856i	0.944313	−	0.329048i	$-0.106728\pi$
$197$	−0.533499	−	1.99105i	−0.0380103	−	0.141856i	−0.982323	+	0.187192i	$0.940061\pi$
$198$	−2.05819	+	3.56488i	−0.146269	+	0.253345i
$199$	9.28142	+	16.0759i	0.657942	+	1.13959i	0.981147	+	0.193261i	$0.0619063\pi$
$199$	9.28142	+	16.0759i	0.657942	+	1.13959i	−0.323205	+	0.946329i	$0.604760\pi$
$200$	−2.12993	+	2.12993i	−0.150609	+	0.150609i
$201$	−0.353856	+	1.32061i	−0.0249591	+	0.0931485i
$202$	2.80878	+	0.752611i	0.197625	+	0.0529536i
$203$		0			0
$204$	5.64955	+	9.78531i	0.395548	+	0.685109i
$205$	1.10108	+	0.635711i	0.0769030	+	0.0443999i
$206$	1.21769	+	4.54447i	0.0848403	+	0.316628i
$207$			15.7265i			1.09307i
$208$	1.97436	+	12.6737i	0.136897	+	0.878766i
$209$			7.77825i			0.538033i
$210$		0			0
$211$	−1.40368	+	2.43124i	−0.0966332	+	0.167374i	−0.910289	−	0.413973i	$-0.864141\pi$
$211$	−1.40368	+	2.43124i	−0.0966332	+	0.167374i	0.813656	+	0.581347i	$0.197474\pi$
$212$	−21.8136	+	12.5941i	−1.49817	+	0.864967i
$213$	−3.24855	−	3.24855i	−0.222587	−	0.222587i
$214$	−1.07092	−	0.286953i	−0.0732069	−	0.0196157i
$215$	−2.80845	−	0.752522i	−0.191535	−	0.0513216i
$216$	−0.534779	+	0.534779i	−0.0363871	+	0.0363871i
$217$		0			0
$218$	1.87481	+	1.08242i	0.126978	+	0.0733108i
$219$	5.72013	−	1.53270i	0.386531	−	0.103571i
$220$	13.0851			0.882197
$221$	7.87438	+	3.04565i	0.529688	+	0.204872i
$222$		−	5.84473i		−	0.392272i
$223$	−15.6678	+	4.19816i	−1.04919	+	0.281130i	−0.741917	−	0.670491i	$-0.766083\pi$
$223$	−15.6678	+	4.19816i	−1.04919	+	0.281130i	−0.307274	+	0.951621i	$0.599417\pi$
$224$		0			0
$225$	7.97924	−	4.60682i	0.531950	−	0.307121i
$226$	−3.56782	+	3.56782i	−0.237328	+	0.237328i
$227$	0.454277	−	1.69538i	0.0301514	−	0.112527i	−0.949210	−	0.314643i	$-0.898115\pi$
$227$	0.454277	−	1.69538i	0.0301514	−	0.112527i	0.979362	+	0.202116i	$0.0647819\pi$
$228$	−2.11620	+	7.89777i	−0.140149	+	0.523042i
$229$	−7.88016	+	7.88016i	−0.520736	+	0.520736i	−0.917794	−	0.397058i	$-0.870031\pi$
$229$	−7.88016	+	7.88016i	−0.520736	+	0.520736i	0.397058	+	0.917794i	$0.370031\pi$
$230$	−1.67944	+	0.969627i	−0.110739	+	0.0639353i
$231$		0			0
$232$	5.95880	−	1.59666i	0.391214	−	0.104826i
$233$			20.3654i			1.33418i	0.744976	+	0.667091i	$0.232461\pi$
$233$			20.3654i			1.33418i	−0.744976	+	0.667091i	$0.767539\pi$
$234$	−0.346127	+	3.21466i	−0.0226271	+	0.210149i
$235$	11.8905			0.775650
$236$	−2.88098	+	0.771957i	−0.187536	+	0.0502501i
$237$	−9.26095	−	5.34681i	−0.601563	−	0.347313i
$238$		0			0
$239$	14.6160	−	14.6160i	0.945430	−	0.945430i	−0.0531558	−	0.998586i	$-0.516928\pi$
$239$	14.6160	−	14.6160i	0.945430	−	0.945430i	0.998586	+	0.0531558i	$0.0169280\pi$
$240$	12.7508	+	3.41656i	0.823059	+	0.220538i
$241$	−13.7908	−	3.69524i	−0.888345	−	0.238031i	−0.214341	−	0.976759i	$-0.568760\pi$
$241$	−13.7908	−	3.69524i	−0.888345	−	0.238031i	−0.674004	+	0.738728i	$0.735427\pi$
$242$	−1.94626	−	1.94626i	−0.125110	−	0.125110i
$243$	−19.3626	+	11.1790i	−1.24211	+	0.717132i
$244$	9.39577	−	16.2740i	0.601503	−	1.04183i
$245$		0			0
$246$		−	0.588176i		−	0.0375007i
$247$	2.47078	+	5.58760i	0.157212	+	0.355530i
$248$		−	6.32771i		−	0.401810i
$249$	−3.56408	−	13.3013i	−0.225864	−	0.842937i
$250$	2.73599	+	1.57963i	0.173039	+	0.0999043i
$251$	−3.24540	−	5.62120i	−0.204848	−	0.354807i	0.745236	−	0.666801i	$-0.232337\pi$
$251$	−3.24540	−	5.62120i	−0.204848	−	0.354807i	−0.950084	+	0.311993i	$0.899003\pi$
$252$		0			0
$253$	−21.2509	−	5.69416i	−1.33603	−	0.357989i
$254$	−0.205889	+	0.768387i	−0.0129186	+	0.0482129i
$255$	6.14406	−	6.14406i	0.384756	−	0.384756i
$256$	−5.17698	−	8.96680i	−0.323561	−	0.560425i
$257$	11.0980	−	19.2224i	0.692277	−	1.19906i	−0.278813	−	0.960345i	$-0.589941\pi$
$257$	11.0980	−	19.2224i	0.692277	−	1.19906i	0.971090	−	0.238713i	$-0.0767257\pi$
$258$	0.348126	+	1.29923i	0.0216734	+	0.0808862i
$259$		0			0
$260$	9.39984	−	4.15652i	0.582953	−	0.257776i
$261$	−18.8697			−1.16801
$262$	−2.61607	+	0.700973i	−0.161621	+	0.0433062i
$263$	−5.05320	+	8.75240i	−0.311594	+	0.539696i	−0.978708	−	0.205260i	$-0.934196\pi$
$263$	−5.05320	+	8.75240i	−0.311594	+	0.539696i	0.667114	+	0.744956i	$0.267529\pi$
$264$	−6.17075	−	10.6880i	−0.379783	−	0.657804i
$265$	13.6965	+	13.6965i	0.841368	+	0.841368i
$266$		0			0
$267$	−9.10063	+	33.9640i	−0.556950	+	2.07857i
$268$	−0.742663	−	0.742663i	−0.0453654	−	0.0453654i
$269$	−8.97049	+	5.17912i	−0.546940	+	0.315776i	−0.747887	−	0.663826i	$-0.768932\pi$
$269$	−8.97049	+	5.17912i	−0.546940	+	0.315776i	0.200947	+	0.979602i	$0.435598\pi$
$270$	0.247044	+	0.142631i	0.0150346	+	0.00868022i
$271$	−0.846186	−	3.15801i	−0.0514022	−	0.191835i	0.935451	−	0.353458i	$-0.114994\pi$
$271$	−0.846186	−	3.15801i	−0.0514022	−	0.191835i	−0.986853	+	0.161622i	$0.948327\pi$
$272$	−8.33024			−0.505095
$273$		0			0
$274$	0.148853			0.00899252
$275$	3.33602	+	12.4502i	0.201170	+	0.750776i
$276$	−20.0282	−	11.5633i	−1.20556	−	0.696030i
$277$	14.4303	−	8.33132i	0.867030	−	0.500580i	0.000670170	−	1.00000i	$-0.499787\pi$
$277$	14.4303	−	8.33132i	0.867030	−	0.500580i	0.866360	+	0.499420i	$0.166453\pi$
$278$	−0.741934	−	0.741934i	−0.0444982	−	0.0444982i
$279$	−5.00949	+	18.6957i	−0.299910	+	1.11928i
$280$		0			0
$281$	8.02095	+	8.02095i	0.478490	+	0.478490i	0.904648	−	0.426159i	$-0.140134\pi$
$281$	8.02095	+	8.02095i	0.478490	+	0.478490i	−0.426159	+	0.904648i	$0.640134\pi$
$282$	−2.75035	−	4.76374i	−0.163781	−	0.283677i
$283$	7.22018	−	12.5057i	0.429195	−	0.743388i	−0.567607	−	0.823300i	$-0.692131\pi$
$283$	7.22018	−	12.5057i	0.429195	−	0.743388i	0.996802	+	0.0799119i	$0.0254639\pi$
$284$	3.40899	−	0.913435i	0.202286	−	0.0542024i
$285$	6.28763			0.372447
$286$	−4.21859	−	1.63166i	−0.249450	−	0.0964823i
$287$		0			0
$288$	−2.64774	−	9.88151i	−0.156020	−	0.582274i
$289$	5.75839	−	9.97383i	0.338729	−	0.586696i
$290$	−1.16343	−	2.01511i	−0.0683187	−	0.118331i
$291$	−5.02663	+	5.02663i	−0.294666	+	0.294666i
$292$	−1.17743	+	4.39423i	−0.0689039	+	0.257153i
$293$	15.9091	+	4.26283i	0.929420	+	0.249037i	0.691607	−	0.722274i	$-0.256903\pi$
$293$	15.9091	+	4.26283i	0.929420	+	0.249037i	0.237812	+	0.971311i	$0.423570\pi$
$294$		0			0
$295$	1.14681	+	1.98634i	0.0667701	+	0.115649i
$296$	7.92765	+	4.57703i	0.460785	+	0.266035i
$297$	0.837602	+	3.12597i	0.0486026	+	0.181387i
$298$			6.39222i			0.370292i
$299$	−17.0746	+	2.65994i	−0.987450	+	0.153828i
$300$			13.5491i			0.782259i
$301$		0			0
$302$	−0.900809	+	1.56025i	−0.0518357	+	0.0897821i
$303$	23.0945	−	13.3336i	1.32675	−	0.765997i
$304$	−4.26245	−	4.26245i	−0.244468	−	0.244468i
$305$	−13.9583	−	3.74012i	−0.799250	−	0.214158i
$306$	−2.02828	−	0.543477i	−0.115949	−	0.0310685i
$307$	−8.27574	+	8.27574i	−0.472322	+	0.472322i	−0.902665	−	0.430344i	$-0.858392\pi$
$307$	−8.27574	+	8.27574i	−0.472322	+	0.472322i	0.430344	+	0.902665i	$0.358392\pi$
$308$		0			0
$309$	37.3658	+	21.5731i	2.12566	+	1.22725i
$310$	−2.30539	+	0.617726i	−0.130937	+	0.0350845i
$311$	−12.9025			−0.731632			−0.365816	−	0.930687i	$-0.619210\pi$
$311$	−12.9025			−0.731632			−0.365816	+	0.930687i	$0.619210\pi$
$312$	−7.82792	−	5.71773i	−0.443169	−	0.323703i
$313$			5.96180i			0.336981i	0.985703	+	0.168490i	$0.0538892\pi$
$313$			5.96180i			0.336981i	−0.985703	+	0.168490i	$0.946111\pi$
$314$	−2.89355	+	0.775325i	−0.163293	+	0.0437541i
$315$		0			0
$316$	7.11430	−	4.10744i	0.400211	−	0.231062i
$317$	9.14807	−	9.14807i	0.513807	−	0.513807i	−0.401884	−	0.915691i	$-0.631644\pi$
$317$	9.14807	−	9.14807i	0.513807	−	0.513807i	0.915691	+	0.401884i	$0.131644\pi$
$318$	2.31920	−	8.65537i	0.130054	−	0.485369i
$319$	6.83225	−	25.4983i	0.382532	−	1.42763i
$320$	−6.55673	+	6.55673i	−0.366533	+	0.366533i
$321$	−8.80540	+	5.08380i	−0.491470	+	0.283750i
$322$		0			0
$323$	−3.83262	+	1.02695i	−0.213253	+	0.0571409i
$324$		−	15.5507i		−	0.863928i
$325$	6.35132	+	7.88406i	0.352308	+	0.437329i
$326$	−1.05673			−0.0585267
$327$	19.1767	−	5.13838i	1.06047	−	0.284153i
$328$	0.797788	+	0.460603i	0.0440505	+	0.0254325i
$329$		0			0
$330$	−3.29159	+	3.29159i	−0.181196	+	0.181196i
$331$	9.65252	+	2.58639i	0.530551	+	0.142161i	0.514142	−	0.857705i	$-0.328110\pi$
$331$	9.65252	+	2.58639i	0.530551	+	0.142161i	0.0164080	+	0.999865i	$0.494777\pi$
$332$	10.2181	+	2.73794i	0.560793	+	0.150264i
$333$	−19.7993	−	19.7993i	−1.08499	−	1.08499i
$334$	−5.76920	+	3.33085i	−0.315677	+	0.182256i
$335$	−0.403834	+	0.699462i	−0.0220638	+	0.0382157i
$336$		0			0
$337$			17.5327i			0.955069i	0.878613	+	0.477534i	$0.158469\pi$
$337$			17.5327i			0.955069i	−0.878613	+	0.477534i	$0.841531\pi$
$338$	−3.54878	+	0.167922i	−0.193028	+	0.00913374i
$339$			46.2723i			2.51317i
$340$	1.72760	+	6.44749i	0.0936923	+	0.349664i
$341$	−23.4493	−	13.5384i	−1.26985	−	0.733148i
$342$	−0.759751	−	1.31593i	−0.0410826	−	0.0711572i
$343$		0			0
$344$	−2.03486	−	0.545238i	−0.109712	−	0.0293973i
$345$	−4.60294	+	17.1784i	−0.247814	+	0.924853i
$346$	−0.927536	+	0.927536i	−0.0498647	+	0.0498647i
$347$	13.1271	+	22.7368i	0.704700	+	1.22058i	0.966800	+	0.255535i	$0.0822516\pi$
$347$	13.1271	+	22.7368i	0.704700	+	1.22058i	−0.262100	+	0.965041i	$0.584415\pi$
$348$	13.8745	−	24.0313i	0.743749	−	1.28821i
$349$	2.90133	+	10.8279i	0.155304	+	0.579604i	0.999079	+	0.0429064i	$0.0136617\pi$
$349$	2.90133	+	10.8279i	0.155304	+	0.579604i	−0.843775	+	0.536698i	$0.819672\pi$
$350$		0			0
$351$	1.59468	+	1.97951i	0.0851175	+	0.105659i
$352$	14.3114			0.762799
$353$	−6.76519	+	1.81273i	−0.360075	+	0.0964817i	−0.434321	−	0.900758i	$-0.643012\pi$
$353$	−6.76519	+	1.81273i	−0.360075	+	0.0964817i	0.0742463	+	0.997240i	$0.476345\pi$
$354$	0.530531	−	0.918907i	0.0281974	−	0.0488394i
$355$	−1.35699	−	2.35038i	−0.0720218	−	0.124745i
$356$	−19.1002	−	19.1002i	−1.01231	−	1.01231i
$357$		0			0
$358$	0.787984	−	2.94080i	0.0416463	−	0.155426i
$359$	3.61441	+	3.61441i	0.190761	+	0.190761i	0.796025	−	0.605264i	$-0.206932\pi$
$359$	3.61441	+	3.61441i	0.190761	+	0.190761i	−0.605264	+	0.796025i	$0.706932\pi$
$360$	−4.51336	+	2.60579i	−0.237875	+	0.137337i
$361$	13.9679	+	8.06438i	0.735154	+	0.424441i
$362$	−0.305881	−	1.14156i	−0.0160767	−	0.0599992i
$363$	−25.2417			−1.32485
$364$		0			0
$365$	3.49837			0.183113
$366$	1.73023	+	6.45729i	0.0904404	+	0.337528i
$367$	−15.9153	−	9.18868i	−0.830770	−	0.479645i	0.0233461	−	0.999727i	$-0.492568\pi$
$367$	−15.9153	−	9.18868i	−0.830770	−	0.479645i	−0.854116	+	0.520082i	$0.825901\pi$
$368$	14.7658	−	8.52503i	0.769720	−	0.444398i
$369$	−1.99247	−	1.99247i	−0.103724	−	0.103724i
$370$	0.893642	−	3.33512i	0.0464582	−	0.173385i
$371$		0			0
$372$	−20.1262	−	20.1262i	−1.04350	−	1.04350i
$373$	−10.4260	−	18.0583i	−0.539837	−	0.935025i	−0.998912	−	0.0466277i	$-0.985153\pi$
$373$	−10.4260	−	18.0583i	−0.539837	−	0.935025i	0.459075	−	0.888397i	$-0.348181\pi$
$374$	1.46878	−	2.54400i	0.0759487	−	0.131547i
$375$	27.9854	−	7.49867i	1.44516	−	0.387230i
$376$	8.61524			0.444297
$377$	−3.19158	−	20.4873i	−0.164375	−	1.05515i
$378$		0			0
$379$	7.22021	+	26.9462i	0.370877	+	1.38413i	0.859276	+	0.511512i	$0.170914\pi$
$379$	7.22021	+	26.9462i	0.370877	+	1.38413i	−0.488399	+	0.872620i	$0.662419\pi$
$380$	−2.41509	+	4.18306i	−0.123892	+	0.214587i
$381$	3.64762	+	6.31787i	0.186873	+	0.323674i
$382$	1.22120	−	1.22120i	0.0624820	−	0.0624820i
$383$	−6.36142	+	23.7412i	−0.325054	+	1.21312i	0.589204	+	0.807984i	$0.299441\pi$
$383$	−6.36142	+	23.7412i	−0.325054	+	1.21312i	−0.914258	+	0.405132i	$0.867225\pi$
$384$	19.2384	+	5.15492i	0.981758	+	0.263061i
$385$		0			0
$386$	1.62775	+	2.81934i	0.0828502	+	0.143501i
$387$	5.58048	+	3.22189i	0.283672	+	0.163778i
$388$	−1.41340	−	5.27488i	−0.0717545	−	0.267792i
$389$		−	24.4888i		−	1.24163i	−0.783957	−	0.620815i	$-0.786802\pi$
$389$		−	24.4888i		−	1.24163i	0.783957	−	0.620815i	$-0.213198\pi$
$390$	−1.31897	+	3.41014i	−0.0667887	+	0.172679i
$391$		−	11.2229i		−	0.567565i
$392$		0			0
$393$	−12.4188	+	21.5099i	−0.626444	+	1.08503i
$394$	−0.487853	+	0.281662i	−0.0245777	+	0.0141899i
$395$	−4.46697	−	4.46697i	−0.224758	−	0.224758i
$396$	−28.0117	−	7.50570i	−1.40764	−	0.377176i
$397$	18.7029	+	5.01142i	0.938671	+	0.251516i	0.695548	−	0.718480i	$-0.255162\pi$
$397$	18.7029	+	5.01142i	0.938671	+	0.251516i	0.243122	+	0.969996i	$0.421828\pi$
$398$	3.58716	−	3.58716i	0.179808	−	0.179808i
$399$		0			0
$400$	−8.65079	−	4.99454i	−0.432539	−	0.249727i
$401$	12.7770	−	3.42360i	0.638055	−	0.170966i	0.0747328	−	0.997204i	$-0.476190\pi$
$401$	12.7770	−	3.42360i	0.638055	−	0.170966i	0.563322	+	0.826237i	$0.309523\pi$
$402$	0.373638			0.0186354
$403$	−21.1456	−	2.27678i	−1.05334	−	0.113414i
$404$			20.4859i			1.01921i
$405$	−11.5510	+	3.09509i	−0.573975	+	0.153796i
$406$		0			0
$407$	33.9232	−	19.5856i	1.68151	−	0.970821i
$408$	4.45167	−	4.45167i	0.220390	−	0.220390i
$409$	6.44521	−	24.0538i	0.318695	−	1.18939i	−0.601805	−	0.798643i	$-0.705551\pi$
$409$	6.44521	−	24.0538i	0.318695	−	1.18939i	0.920500	−	0.390743i	$-0.127782\pi$
$410$	0.0899304	−	0.335625i	0.00444135	−	0.0165753i
$411$	0.965263	−	0.965263i	0.0476129	−	0.0476129i
$412$	−28.7045	+	16.5726i	−1.41417	+	0.816472i
$413$		0			0
$414$	4.15142	−	1.11237i	0.204031	−	0.0546700i
$415$		−	8.13493i		−	0.399328i
$416$	10.2807	−	4.54605i	0.504055	−	0.222888i
$417$	−9.62241			−0.471212
$418$	2.05327	−	0.550173i	0.100429	−	0.0269098i
$419$	13.9899	+	8.07708i	0.683452	+	0.394591i	0.801154	−	0.598458i	$-0.204220\pi$
$419$	13.9899	+	8.07708i	0.683452	+	0.394591i	−0.117703	+	0.993049i	$0.537553\pi$
$420$		0			0
$421$	−12.8050	+	12.8050i	−0.624080	+	0.624080i	−0.946572	−	0.322492i	$-0.895479\pi$
$421$	−12.8050	+	12.8050i	−0.624080	+	0.624080i	0.322492	+	0.946572i	$0.395479\pi$
$422$	0.741075	+	0.198570i	0.0360750	+	0.00966626i
$423$	−25.4543	−	6.82047i	−1.23763	−	0.331622i
$424$	9.92376	+	9.92376i	0.481941	+	0.481941i
$425$	−5.69421	+	3.28755i	−0.276210	+	0.159470i
$426$	−0.627763	+	1.08732i	−0.0304152	+	0.0526807i
$427$		0			0
$428$		−	7.81080i		−	0.377549i
$429$	−37.9370	+	16.7754i	−1.83162	+	0.809924i
$430$			0.794591i			0.0383186i
$431$	5.78727	+	21.5984i	0.278763	+	1.04036i	0.953278	+	0.302096i	$0.0976863\pi$
$431$	5.78727	+	21.5984i	0.278763	+	1.04036i	−0.674515	+	0.738261i	$0.735647\pi$
$432$	−2.17202	−	1.25402i	−0.104502	−	0.0603340i
$433$	−9.21467	−	15.9603i	−0.442829	−	0.767002i	0.555069	−	0.831804i	$-0.312692\pi$
$433$	−9.21467	−	15.9603i	−0.442829	−	0.767002i	−0.997898	+	0.0648019i	$0.979358\pi$
$434$		0			0
$435$	−20.6118	−	5.52292i	−0.988261	−	0.264804i
$436$	−3.94732	+	14.7316i	−0.189043	+	0.705517i
$437$	5.74256	−	5.74256i	0.274704	−	0.274704i
$438$	−0.809195	−	1.40157i	−0.0386648	−	0.0669694i
$439$	7.79998	−	13.5100i	0.372273	−	0.644795i	−0.617642	−	0.786459i	$-0.711912\pi$
$439$	7.79998	−	13.5100i	0.372273	−	0.644795i	0.989915	+	0.141664i	$0.0452453\pi$
$440$	−1.88698	−	7.04230i	−0.0899582	−	0.335729i
$441$		0			0
$442$	0.247006	−	2.29407i	0.0117489	−	0.109118i
$443$	−29.5897			−1.40585			−0.702926	−	0.711263i	$-0.748123\pi$
$443$	−29.5897			−1.40585			−0.702926	+	0.711263i	$0.748123\pi$
$444$	39.7730	−	10.6571i	1.88754	−	0.505766i
$445$	−10.3860	+	17.9891i	−0.492344	+	0.852765i
$446$	2.21643	+	3.83897i	0.104951	+	0.181781i
$447$	41.4515	+	41.4515i	1.96059	+	1.96059i
$448$		0			0
$449$	−2.50811	+	9.36041i	−0.118365	+	0.441745i	−0.999517	−	0.0310893i	$-0.990102\pi$
$449$	−2.50811	+	9.36041i	−0.118365	+	0.441745i	0.881151	+	0.472834i	$0.156769\pi$
$450$	−1.78048	−	1.78048i	−0.0839326	−	0.0839326i
$451$	3.41381	−	1.97097i	0.160750	−	0.0928092i
$452$	−30.7843	−	17.7733i	−1.44797	−	0.835986i
$453$	4.27625	+	15.9592i	0.200916	+	0.749827i
$454$	−0.479673			−0.0225122
$455$		0			0
$456$	4.55569			0.213340
$457$	8.97136	+	33.4816i	0.419663	+	1.56620i	0.775309	+	0.631582i	$0.217594\pi$
$457$	8.97136	+	33.4816i	0.419663	+	1.56620i	−0.355646	+	0.934621i	$0.615739\pi$
$458$	2.63756	+	1.52279i	0.123245	+	0.0711555i
$459$	−1.42969	+	0.825433i	−0.0667323	+	0.0385279i
$460$	−9.66052	−	9.66052i	−0.450424	−	0.450424i
$461$	2.45042	−	9.14508i	0.114127	−	0.425929i	−0.885093	−	0.465414i	$-0.845905\pi$
$461$	2.45042	−	9.14508i	0.114127	−	0.425929i	0.999220	+	0.0394858i	$0.0125720\pi$
$462$		0			0
$463$	3.59580	+	3.59580i	0.167111	+	0.167111i	0.785708	−	0.618597i	$-0.212299\pi$
$463$	3.59580	+	3.59580i	0.167111	+	0.167111i	−0.618597	+	0.785708i	$0.712299\pi$
$464$	10.2289	+	17.7170i	0.474866	+	0.822491i
$465$	−10.9439	+	18.9555i	−0.507513	+	0.879038i
$466$	5.37598	−	1.44049i	0.249038	−	0.0667294i
$467$	24.1247			1.11636			0.558179	−	0.829721i	$-0.311500\pi$
$467$	24.1247			1.11636			0.558179	+	0.829721i	$0.311500\pi$
$468$	−22.5067	+	3.50617i	−1.04037	+	0.162073i
$469$		0			0
$470$	−0.841041	−	3.13881i	−0.0387943	−	0.144782i
$471$	−13.7360	+	23.7915i	−0.632923	+	1.09626i
$472$	0.830922	+	1.43920i	0.0382463	+	0.0662445i
$473$	−6.37423	+	6.37423i	−0.293087	+	0.293087i
$474$	−0.756384	+	2.82286i	−0.0347418	+	0.129658i
$475$	−4.59582	−	1.23145i	−0.210871	−	0.0565027i
$476$		0			0
$477$	−21.4641	−	37.1769i	−0.982772	−	1.70221i
$478$	−4.89210	−	2.82445i	−0.223759	−	0.129188i
$479$	6.34020	+	23.6619i	0.289691	+	1.08114i	0.945343	+	0.326078i	$0.105727\pi$
$479$	6.34020	+	23.6619i	0.289691	+	1.08114i	−0.655652	+	0.755063i	$0.727606\pi$
$480$		−	11.5687i		−	0.528039i
$481$	18.1477	−	24.8453i	0.827465	−	1.13285i
$482$			3.90182i			0.177723i
$483$		0			0
$484$	9.69539	−	16.7929i	0.440700	−	0.763314i
$485$	−3.63686	+	2.09974i	−0.165141	+	0.0953443i
$486$	4.32054	+	4.32054i	0.195984	+	0.195984i
$487$	36.9186	+	9.89230i	1.67294	+	0.448263i	0.965901	−	0.258911i	$-0.0833637\pi$
$487$	36.9186	+	9.89230i	1.67294	+	0.448263i	0.707039	+	0.707174i	$0.250030\pi$
$488$	−10.1135	−	2.70989i	−0.457815	−	0.122671i
$489$	−6.85254	+	6.85254i	−0.309883	+	0.309883i
$490$		0			0
$491$	10.2155	+	5.89793i	0.461020	+	0.266170i	0.712473	−	0.701700i	$-0.247575\pi$
$491$	10.2155	+	5.89793i	0.461020	+	0.266170i	−0.251453	+	0.967869i	$0.580908\pi$
$492$	4.00250	−	1.07247i	0.180447	−	0.0483505i
$493$	13.4660			0.606476
$494$	1.30023	−	1.04745i	0.0585001	−	0.0471271i
$495$			22.3009i			1.00235i
$496$	20.2691	−	5.43109i	0.910110	−	0.243863i
$497$		0			0
$498$	−3.25914	+	1.88166i	−0.146045	+	0.0843193i
$499$	10.8271	−	10.8271i	0.484686	−	0.484686i	−0.421938	−	0.906625i	$-0.638650\pi$
$499$	10.8271	−	10.8271i	0.484686	−	0.484686i	0.906625	+	0.421938i	$0.138650\pi$
$500$	−5.76051	+	21.4985i	−0.257618	+	0.961443i
$501$	−15.8119	+	59.0110i	−0.706426	+	2.63642i
$502$	−1.25431	+	1.25431i	−0.0559826	+	0.0559826i
$503$	21.5683	−	12.4524i	0.961682	−	0.555227i	0.0649915	−	0.997886i	$-0.479298\pi$
$503$	21.5683	−	12.4524i	0.961682	−	0.555227i	0.896690	+	0.442659i	$0.145965\pi$
$504$		0			0
$505$	15.2169	−	4.07735i	0.677142	−	0.181440i
$506$			6.01249i			0.267288i
$507$	−21.9238	+	24.1016i	−0.973669	+	1.07039i
$508$	−5.60424			−0.248648
$509$	−32.3493	+	8.66796i	−1.43386	+	0.384201i	−0.890378	−	0.455222i	$-0.849560\pi$
$509$	−32.3493	+	8.66796i	−1.43386	+	0.384201i	−0.543478	+	0.839423i	$0.682893\pi$
$510$	−2.05647	−	1.18730i	−0.0910619	−	0.0525746i
$511$		0			0
$512$	−13.2395	+	13.2395i	−0.585111	+	0.585111i
$513$	−1.15391	−	0.309189i	−0.0509464	−	0.0136510i
$514$	−5.85924	−	1.56998i	−0.258440	−	0.0692488i
$515$	18.0232	+	18.0232i	0.794196	+	0.794196i
$516$	−8.20638	+	4.73796i	−0.361266	+	0.208577i
$517$	18.4327	−	31.9264i	0.810670	−	1.40412i
$518$		0			0
$519$			12.0296i			0.528039i
$520$	−3.59254	−	4.45952i	−0.157543	−	0.195563i
$521$		−	22.9606i		−	1.00592i	−0.864309	−	0.502962i	$-0.832244\pi$
$521$		−	22.9606i		−	1.00592i	0.864309	−	0.502962i	$-0.167756\pi$
$522$	1.33470	+	4.98116i	0.0584181	+	0.218019i
$523$	−2.92715	−	1.68999i	−0.127995	−	0.0738980i	0.434635	−	0.900607i	$-0.356877\pi$
$523$	−2.92715	−	1.68999i	−0.127995	−	0.0738980i	−0.562630	+	0.826709i	$0.690211\pi$
$524$	−9.54015	−	16.5240i	−0.416764	−	0.721856i
$525$		0			0
$526$	2.66785	+	0.714848i	0.116324	+	0.0311688i
$527$	3.57491	−	13.3417i	0.155725	−	0.581175i
$528$	28.9399	−	28.9399i	1.25945	−	1.25945i
$529$	−0.0147097	−	0.0254780i	−0.000639552	−	0.00110774i
$530$	2.64676	−	4.58433i	0.114968	−	0.199130i
$531$	−1.31564	−	4.91004i	−0.0570939	−	0.213078i
$532$		0			0
$533$	1.82627	−	2.50027i	0.0791046	−	0.108299i
$534$	9.60940			0.415840
$535$	−5.80184	+	1.55460i	−0.250835	+	0.0672111i
$536$	−0.292598	+	0.506794i	−0.0126383	+	0.0218902i
$537$	−13.9603	−	24.1800i	−0.602432	−	1.04344i
$538$	2.00167	+	2.00167i	0.0862979	+	0.0862979i
$539$		0			0
$540$	−0.520139	+	1.94119i	−0.0223832	+	0.0835353i
$541$	−22.7480	−	22.7480i	−0.978012	−	0.978012i	0.0217516	−	0.999763i	$-0.493076\pi$
$541$	−22.7480	−	22.7480i	−0.978012	−	0.978012i	−0.999763	+	0.0217516i	$0.993076\pi$
$542$	−0.773787	+	0.446746i	−0.0332370	+	0.0191894i
$543$	−9.38621	−	5.41913i	−0.402801	−	0.232557i
$544$	1.88950	+	7.05172i	0.0810118	+	0.302340i
$545$	11.7282			0.502383
$546$		0			0
$547$	−13.1782			−0.563460			−0.281730	−	0.959494i	$-0.590908\pi$
$547$	−13.1782			−0.563460			−0.281730	+	0.959494i	$0.590908\pi$
$548$	0.271415	+	1.01293i	0.0115943	+	0.0432704i
$549$	27.7356	+	16.0132i	1.18373	+	0.683425i
$550$	3.05059	−	1.76126i	0.130078	−	0.0751004i
$551$	6.89031	+	6.89031i	0.293537	+	0.293537i
$552$	−3.33505	+	12.4466i	−0.141949	+	0.529761i
$553$		0			0
$554$	−3.21995	−	3.21995i	−0.136803	−	0.136803i
$555$	−15.8322	−	27.4222i	−0.672039	−	1.16401i
$556$	3.69599	−	6.40164i	0.156745	−	0.271490i
$557$	3.94410	−	1.05682i	0.167117	−	0.0447788i	−0.174290	−	0.984694i	$-0.555763\pi$
$557$	3.94410	−	1.05682i	0.167117	−	0.0447788i	0.341407	+	0.939916i	$0.389097\pi$
$558$	5.28954			0.223924
$559$	−2.55421	+	6.60379i	−0.108032	+	0.279311i
$560$		0			0
$561$	−6.97247	−	26.0216i	−0.294378	−	1.09863i
$562$	1.55000	−	2.68468i	0.0653828	−	0.113246i
$563$	−10.2301	−	17.7191i	−0.431149	−	0.746772i	0.565824	−	0.824526i	$-0.308558\pi$
$563$	−10.2301	−	17.7191i	−0.431149	−	0.746772i	−0.996973	+	0.0777545i	$0.975225\pi$
$564$	27.4021	−	27.4021i	1.15383	−	1.15383i
$565$	−7.07491	+	26.4039i	−0.297644	+	1.11082i
$566$	−3.81191	−	1.02140i	−0.160227	−	0.0429326i
$567$		0			0
$568$	−0.983208	−	1.70297i	−0.0412545	−	0.0714549i
$569$	−8.00992	−	4.62453i	−0.335793	−	0.193870i	0.322617	−	0.946530i	$-0.395437\pi$
$569$	−8.00992	−	4.62453i	−0.335793	−	0.193870i	−0.658410	+	0.752659i	$0.728771\pi$
$570$	−0.444738	−	1.65978i	−0.0186280	−	0.0695207i
$571$		−	40.7214i		−	1.70414i	−0.523430	−	0.852069i	$-0.675348\pi$
$571$		−	40.7214i		−	1.70414i	0.523430	−	0.852069i	$-0.324652\pi$
$572$	3.41129	−	31.6824i	0.142633	−	1.32471i
$573$		−	15.8382i		−	0.661650i
$574$		0			0
$575$	6.72885	−	11.6547i	0.280613	−	0.486035i
$576$	17.7972	−	10.2752i	0.741549	−	0.428134i
$577$	−7.72857	−	7.72857i	−0.321745	−	0.321745i	0.527691	−	0.849436i	$-0.323058\pi$
$577$	−7.72857	−	7.72857i	−0.321745	−	0.321745i	−0.849436	+	0.527691i	$0.823058\pi$
$578$	−3.04016	−	0.814608i	−0.126454	−	0.0338832i
$579$	28.8380	+	7.72711i	1.19847	+	0.321128i
$580$	11.5914	−	11.5914i	0.481305	−	0.481305i
$581$		0			0
$582$	1.68246	+	0.971367i	0.0697401	+	0.0402644i
$583$	58.0080	−	15.5432i	2.40244	−	0.643733i
$584$	2.53474			0.104888
$585$	7.08393	+	16.0201i	0.292884	+	0.662349i
$586$		−	4.50114i		−	0.185941i
$587$	15.6037	−	4.18099i	0.644033	−	0.172568i	0.0780032	−	0.996953i	$-0.475146\pi$
$587$	15.6037	−	4.18099i	0.644033	−	0.172568i	0.566029	+	0.824385i	$0.308479\pi$
$588$		0			0
$589$	8.65597	−	4.99753i	0.356663	−	0.205920i
$590$	0.443230	−	0.443230i	0.0182475	−	0.0182475i
$591$	−1.33708	+	4.99007i	−0.0550003	+	0.205264i
$592$	−7.85696	+	29.3226i	−0.322919	+	1.20515i
$593$	32.7121	−	32.7121i	1.34333	−	1.34333i	0.450600	−	0.892726i	$-0.351210\pi$
$593$	32.7121	−	32.7121i	1.34333	−	1.34333i	0.892726	−	0.450600i	$-0.148790\pi$
$594$	0.765937	−	0.442214i	0.0314268	−	0.0181443i
$595$		0			0
$596$	−43.4987	+	11.6554i	−1.78178	+	0.477425i
$597$		−	46.5231i		−	1.90407i
$598$	1.90989	+	4.31915i	0.0781010	+	0.176623i
$599$	−11.7977			−0.482042			−0.241021	−	0.970520i	$-0.577482\pi$
$599$	−11.7977			−0.482042			−0.241021	+	0.970520i	$0.577482\pi$
$600$	7.29204	−	1.95390i	0.297696	−	0.0797675i
$601$	11.5727	+	6.68152i	0.472062	+	0.272545i	0.717102	−	0.696968i	$-0.245468\pi$
$601$	11.5727	+	6.68152i	0.472062	+	0.272545i	−0.245041	+	0.969513i	$0.578801\pi$
$602$		0			0
$603$	1.26572	−	1.26572i	0.0515439	−	0.0515439i
$604$	−12.2599	−	3.28503i	−0.498848	−	0.133666i
$605$	−14.4034	−	3.85938i	−0.585582	−	0.156906i
$606$	−5.15329	−	5.15329i	−0.209338	−	0.209338i
$607$	−29.5465	+	17.0587i	−1.19926	+	0.692392i	−0.960390	−	0.278660i	$-0.910110\pi$
$607$	−29.5465	+	17.0587i	−1.19926	+	0.692392i	−0.238868	+	0.971052i	$0.576776\pi$
$608$	−2.64142	+	4.57508i	−0.107124	+	0.185544i
$609$		0			0
$610$			3.94921i			0.159899i
$611$	3.09985	−	28.7899i	0.125407	−	1.16472i
$612$		−	14.7933i		−	0.597984i
$613$	−1.05301	−	3.92990i	−0.0425308	−	0.158727i	0.941395	−	0.337307i	$-0.109516\pi$
$613$	−1.05301	−	3.92990i	−0.0425308	−	0.158727i	−0.983925	+	0.178580i	$0.942850\pi$
$614$	2.76996	+	1.59924i	0.111787	+	0.0645400i
$615$	−1.59325	−	2.75959i	−0.0642461	−	0.111277i
$616$		0			0
$617$	−17.7169	−	4.74724i	−0.713257	−	0.191117i	−0.116096	−	0.993238i	$-0.537038\pi$
$617$	−17.7169	−	4.74724i	−0.713257	−	0.191117i	−0.597161	+	0.802121i	$0.703705\pi$
$618$	3.05183	−	11.3896i	0.122763	−	0.458156i
$619$	−25.6416	+	25.6416i	−1.03062	+	1.03062i	−0.0311060	+	0.999516i	$0.509903\pi$
$619$	−25.6416	+	25.6416i	−1.03062	+	1.03062i	−0.999516	+	0.0311060i	$0.990097\pi$
$620$	−8.40718	−	14.5617i	−0.337641	−	0.584811i
$621$	1.68947	−	2.92624i	0.0677960	−	0.117426i
$622$	0.912620	+	3.40595i	0.0365927	+	0.136566i
$623$		0			0
$624$	11.5965	−	29.9822i	0.464231	−	1.20025i
$625$	3.07595			0.123038
$626$	1.57377	−	0.421691i	0.0629006	−	0.0168542i
$627$	9.74713	−	16.8825i	0.389263	−	0.674223i
$628$	−10.5521	−	18.2767i	−0.421074	−	0.729321i
$629$	14.1293	+	14.1293i	0.563373	+	0.563373i
$630$		0			0
$631$	6.52992	−	24.3700i	0.259952	−	0.970153i	−0.705316	−	0.708893i	$-0.749195\pi$
$631$	6.52992	−	24.3700i	0.259952	−	0.970153i	0.965268	−	0.261261i	$-0.0841383\pi$
$632$	−3.23654	−	3.23654i	−0.128742	−	0.128742i
$633$	6.09330	−	3.51797i	0.242187	−	0.139827i
$634$	−3.06194	−	1.76781i	−0.121605	−	0.0702087i
$635$	1.11542	+	4.16281i	0.0442642	+	0.165196i
$636$	63.1280			2.50319
$637$		0			0
$638$	−7.21420			−0.285613
$639$	1.55676	+	5.80992i	0.0615846	+	0.229837i
$640$	10.1897	+	5.88301i	0.402782	+	0.232546i
$641$	9.82660	−	5.67339i	0.388127	−	0.224085i	−0.293221	−	0.956045i	$-0.594727\pi$
$641$	9.82660	−	5.67339i	0.388127	−	0.224085i	0.681348	+	0.731959i	$0.261394\pi$
$642$	1.96483	+	1.96483i	0.0775456	+	0.0775456i
$643$	−2.92632	+	10.9212i	−0.115403	+	0.430690i	−0.999317	−	0.0369602i	$-0.988233\pi$
$643$	−2.92632	+	10.9212i	−0.115403	+	0.430690i	0.883914	+	0.467650i	$0.154899\pi$
$644$		0			0
$645$	5.15267	+	5.15267i	0.202886	+	0.202886i
$646$	0.542179	+	0.939082i	0.0213318	+	0.0369477i
$647$	9.64081	−	16.6984i	0.379020	−	0.656481i	−0.611900	−	0.790935i	$-0.709595\pi$
$647$	9.64081	−	16.6984i	0.379020	−	0.656481i	0.990920	+	0.134454i	$0.0429280\pi$
$648$	−8.36927	+	2.24254i	−0.328776	+	0.0880953i
$649$	7.11120			0.279139
$650$	1.63196	−	2.23425i	0.0640108	−	0.0876346i
$651$		0			0
$652$	−1.92681	−	7.19096i	−0.0754598	−	0.281620i
$653$	−1.99409	+	3.45386i	−0.0780346	+	0.135160i	−0.902402	−	0.430895i	$-0.858198\pi$
$653$	−1.99409	+	3.45386i	−0.0780346	+	0.135160i	0.824367	+	0.566055i	$0.191531\pi$
$654$	−2.71282	−	4.69874i	−0.106080	−	0.183735i
$655$	−10.3752	+	10.3752i	−0.405393	+	0.405393i
$656$	−0.790674	+	2.95084i	−0.0308706	+	0.115211i
$657$	−7.48906	−	2.00669i	−0.292176	−	0.0782883i
$658$		0			0
$659$	−13.3526	−	23.1273i	−0.520143	−	0.900913i	−0.999726	−	0.0234170i	$-0.992545\pi$
$659$	−13.3526	−	23.1273i	−0.520143	−	0.900913i	0.479583	−	0.877496i	$-0.340788\pi$
$660$	−28.4009	−	16.3973i	−1.10550	−	0.638263i
$661$	−3.67516	−	13.7159i	−0.142947	−	0.533486i	−0.999838	−	0.0179886i	$-0.994274\pi$
$661$	−3.67516	−	13.7159i	−0.142947	−	0.533486i	0.856891	−	0.515498i	$-0.172393\pi$
$662$		−	2.73098i		−	0.106142i
$663$	−13.2746	−	16.4781i	−0.515542	−	0.639956i
$664$		−	5.89415i		−	0.228738i
$665$		0			0
$666$	−3.82609	+	6.62699i	−0.148258	+	0.256790i
$667$	−23.8691	+	13.7808i	−0.924216	+	0.533596i
$668$	−33.1857	−	33.1857i	−1.28399	−	1.28399i
$669$	39.2674	+	10.5217i	1.51816	+	0.406791i
$670$	0.213205	+	0.0571282i	0.00823684	+	0.00220705i
$671$	−31.6806	+	31.6806i	−1.22302	+	1.22302i
$672$		0			0
$673$	34.5521	+	19.9487i	1.33189	+	0.768965i	0.985589	−	0.169159i	$-0.0541052\pi$
$673$	34.5521	+	19.9487i	1.33189	+	0.768965i	0.346298	+	0.938124i	$0.387439\pi$
$674$	4.62822	−	1.24013i	0.178273	−	0.0477680i
$675$	−1.97961			−0.0761951
$676$	−7.61346	−	23.8430i	−0.292825	−	0.917039i
$677$			6.56822i			0.252437i	0.992002	+	0.126219i	$0.0402841\pi$
$677$			6.56822i			0.252437i	−0.992002	+	0.126219i	$0.959716\pi$
$678$	12.2148	−	3.27294i	0.469106	−	0.125697i
$679$		0			0
$680$	3.22086	−	1.85956i	0.123514	−	0.0713110i
$681$	−3.11053	+	3.11053i	−0.119196	+	0.119196i
$682$	−1.91521	+	7.14765i	−0.0733371	+	0.273698i
$683$	3.02219	−	11.2790i	0.115641	−	0.431578i	−0.883693	−	0.468067i	$-0.844951\pi$
$683$	3.02219	−	11.2790i	0.115641	−	0.431578i	0.999334	+	0.0364888i	$0.0116173\pi$
$684$	7.56949	−	7.56949i	0.289427	−	0.289427i
$685$	0.698384	−	0.403212i	0.0266839	−	0.0154060i
$686$		0			0
$687$	26.9785	−	7.22888i	1.02930	−	0.275799i
$688$		−	6.98610i		−	0.266343i
$689$	36.7334	−	29.5920i	1.39943	−	1.12737i
$690$	4.86026			0.185027
$691$	−19.0196	+	5.09630i	−0.723541	+	0.193872i	−0.601751	−	0.798684i	$-0.705530\pi$
$691$	−19.0196	+	5.09630i	−0.723541	+	0.193872i	−0.121790	+	0.992556i	$0.538863\pi$
$692$	−8.00308	−	4.62058i	−0.304231	−	0.175648i
$693$		0			0
$694$	5.07347	−	5.07347i	0.192586	−	0.192586i
$695$	−5.49074	−	1.47124i	−0.208276	−	0.0558073i
$696$	−14.9343	−	4.00162i	−0.566081	−	0.151681i
$697$	1.42188	+	1.42188i	0.0538577	+	0.0538577i
$698$	2.65309	−	1.53176i	0.100421	−	0.0579780i
$699$	25.5204	−	44.2027i	0.965271	−	1.67190i
$700$		0			0
$701$		−	1.58634i		−	0.0599153i	−0.999551	−	0.0299577i	$-0.990463\pi$
$701$		−	1.58634i		−	0.0599153i	0.999551	−	0.0299577i	$-0.00953725\pi$
$702$	0.409750	−	0.560972i	0.0154650	−	0.0211725i
$703$			14.4595i			0.545350i
$704$	7.44078	+	27.7694i	0.280435	+	1.04660i
$705$	−25.8081	−	14.9003i	−0.971988	−	0.561177i
$706$	0.957033	+	1.65763i	0.0360184	+	0.0623857i
$707$		0			0
$708$	7.22047	+	1.93472i	0.271362	+	0.0727111i
$709$	−4.46614	+	16.6679i	−0.167730	+	0.625975i	0.829947	+	0.557843i	$0.188371\pi$
$709$	−4.46614	+	16.6679i	−0.167730	+	0.625975i	−0.997676	+	0.0681325i	$0.978296\pi$
$710$	−0.524462	+	0.524462i	−0.0196827	+	0.0196827i
$711$	7.00029	+	12.1249i	0.262531	+	0.454718i
$712$	−7.52517	+	13.0340i	−0.282017	+	0.488469i
$713$	7.31700	+	27.3074i	0.274024	+	1.02267i
$714$		0			0
$715$	−24.2125	+	3.77191i	−0.905498	+	0.141061i
$716$	21.4487			0.801577
$717$	−50.0394	+	13.4080i	−1.86876	+	0.500732i
$718$	0.698463	−	1.20977i	0.0260664	−	0.0451483i
$719$	11.5856	+	20.0668i	0.432069	+	0.748365i	0.997051	−	0.0767379i	$-0.0244505\pi$
$719$	11.5856	+	20.0668i	0.432069	+	0.748365i	−0.564983	+	0.825103i	$0.691117\pi$
$720$	−12.2208	−	12.2208i	−0.455441	−	0.455441i
$721$		0			0
$722$	1.14082	−	4.25761i	0.0424570	−	0.158452i
$723$	25.3021	+	25.3021i	0.940994	+	0.940994i
$724$	7.21053	−	4.16300i	0.267977	−	0.154717i
$725$	13.9841	+	8.07374i	0.519358	+	0.299851i
$726$	1.78540	+	6.66321i	0.0662625	+	0.247295i
$727$	−18.3365			−0.680062			−0.340031	−	0.940414i	$-0.610438\pi$
$727$	−18.3365			−0.680062			−0.340031	+	0.940414i	$0.610438\pi$
$728$		0			0
$729$	31.8037			1.17792
$730$	−0.247447	−	0.923485i	−0.00915843	−	0.0341797i
$731$	−3.98239	−	2.29923i	−0.147294	−	0.0850401i
$732$	−40.7866	+	23.5482i	−1.50752	+	0.870365i
$733$	−14.3713	−	14.3713i	−0.530816	−	0.530816i	0.389999	−	0.920815i	$-0.372475\pi$
$733$	−14.3713	−	14.3713i	−0.530816	−	0.530816i	−0.920815	+	0.389999i	$0.872475\pi$
$734$	−1.29987	+	4.85119i	−0.0479791	+	0.179061i
$735$		0			0
$736$	−10.5659	−	10.5659i	−0.389463	−	0.389463i
$737$	1.25205	+	2.16862i	0.0461200	+	0.0798822i
$738$	−0.385033	+	0.666897i	−0.0141733	+	0.0245488i
$739$	32.0846	−	8.59704i	1.18025	−	0.316247i	0.385225	−	0.922823i	$-0.374124\pi$
$739$	32.0846	−	8.59704i	1.18025	−	0.316247i	0.795026	+	0.606576i	$0.207457\pi$
$740$	24.3247			0.894195
$741$	1.63919	−	15.2240i	0.0602170	−	0.559266i
$742$		0			0
$743$	1.88756	+	7.04445i	0.0692477	+	0.258436i	0.991868	−	0.127275i	$-0.0406230\pi$
$743$	1.88756	+	7.04445i	0.0692477	+	0.258436i	−0.922620	+	0.385711i	$0.873956\pi$
$744$	−7.92941	+	13.7341i	−0.290706	+	0.503518i
$745$	17.3153	+	29.9909i	0.634382	+	1.09878i
$746$	−4.02952	+	4.02952i	−0.147531	+	0.147531i
$747$	−4.66625	+	17.4147i	−0.170729	+	0.637170i
$748$	19.9899	+	5.35628i	0.730903	+	0.195845i
$749$		0			0
$750$	−3.95894	−	6.85709i	−0.144560	−	0.250385i
$751$	−6.19866	−	3.57880i	−0.226192	−	0.130592i	0.382622	−	0.923905i	$-0.375021\pi$
$751$	−6.19866	−	3.57880i	−0.226192	−	0.130592i	−0.608814	+	0.793313i	$0.708355\pi$
$752$	7.39449	+	27.5966i	0.269649	+	1.00634i
$753$			16.2676i			0.592824i
$754$	−5.18241	+	2.29161i	−0.188732	+	0.0834556i
$755$			9.76045i			0.355219i
$756$		0			0
$757$	7.08185	−	12.2661i	0.257394	−	0.445820i	−0.708149	−	0.706063i	$-0.750469\pi$
$757$	7.08185	−	12.2661i	0.257394	−	0.445820i	0.965543	+	0.260243i	$0.0838027\pi$
$758$	6.60245	−	3.81192i	0.239812	−	0.138455i
$759$	38.9891	+	38.9891i	1.41522	+	1.41522i
$760$	2.59957	+	0.696552i	0.0942963	+	0.0252666i
$761$	−13.9443	−	3.73637i	−0.505481	−	0.135443i	−0.00293843	−	0.999996i	$-0.500935\pi$
$761$	−13.9443	−	3.73637i	−0.505481	−	0.135443i	−0.502543	+	0.864552i	$0.667602\pi$
$762$	1.40976	−	1.40976i	0.0510703	−	0.0510703i
$763$		0			0
$764$	10.5369	+	6.08348i	0.381212	+	0.220093i
$765$	−10.9884	+	2.94434i	−0.397287	+	0.106453i
$766$	6.71706			0.242697
$767$	5.10842	−	2.25889i	0.184454	−	0.0815639i
$768$			25.9496i			0.936377i
$769$	−48.9223	+	13.1087i	−1.76418	+	0.472711i	−0.987559	−	0.157252i	$-0.949737\pi$
$769$	−48.9223	+	13.1087i	−1.76418	+	0.472711i	−0.776625	+	0.629963i	$0.783070\pi$
$770$		0			0
$771$	−48.1761	+	27.8145i	−1.73502	+	1.00171i
$772$	−16.2175	+	16.2175i	−0.583679	+	0.583679i
$773$	−3.03164	+	11.3142i	−0.109040	+	0.406944i	−0.998772	−	0.0495394i	$-0.984225\pi$
$773$	−3.03164	+	11.3142i	−0.109040	+	0.406944i	0.889732	+	0.456484i	$0.150891\pi$
$774$	0.455783	−	1.70100i	0.0163828	−	0.0611414i
$775$	11.7117	−	11.7117i	0.420698	−	0.420698i
$776$	−2.63508	+	1.52136i	−0.0945938	+	0.0546137i
$777$		0			0
$778$	−6.46445	+	1.73215i	−0.231762	+	0.0621004i
$779$			1.45511i			0.0521347i
$780$	−25.6108	−	2.75755i	−0.917013	−	0.0987361i
$781$	−8.41449			−0.301094
$782$	−2.96257	+	0.793818i	−0.105941	+	0.0283869i
$783$	3.51111	+	2.02714i	0.125477	+	0.0724441i
$784$		0			0
$785$	−11.4757	+	11.4757i	−0.409586	+	0.409586i
$786$	6.55652	+	1.75681i	0.233863	+	0.0626635i
$787$	33.9681	+	9.10172i	1.21083	+	0.324441i	0.807088	−	0.590431i	$-0.201042\pi$
$787$	33.9681	+	9.10172i	1.21083	+	0.324441i	0.403743	+	0.914872i	$0.367709\pi$
$788$	−2.80624	−	2.80624i	−0.0999680	−	0.0999680i
$789$	21.9357	−	12.6646i	0.780932	−	0.450871i
$790$	−0.863215	+	1.49513i	−0.0307118	+	0.0531944i
$791$		0			0
$792$			16.1580i			0.574151i
$793$	−12.6947	+	32.8216i	−0.450802	+	1.16553i
$794$		−	5.29158i		−	0.187791i
$795$	−12.5645	−	46.8913i	−0.445617	−	1.66306i
$796$	30.9511	+	17.8696i	1.09703	+	0.633373i
$797$	4.21417	+	7.29915i	0.149273	+	0.258549i	0.930959	−	0.365123i	$-0.118973\pi$
$797$	4.21417	+	7.29915i	0.149273	+	0.258549i	−0.781686	+	0.623673i	$0.785640\pi$
$798$		0			0
$799$	18.1649	+	4.86727i	0.642629	+	0.172192i
$800$	−2.26577	+	8.45596i	−0.0801069	+	0.298963i
$801$	32.5523	−	32.5523i	1.15018	−	1.15018i
$802$	−1.80750	−	3.13068i	−0.0638249	−	0.110548i
$803$	5.42319	−	9.39325i	0.191380	−	0.331480i
$804$	0.681283	+	2.54258i	0.0240270	+	0.0896700i
$805$		0			0
$806$	0.894660	+	5.74297i	0.0315130	+	0.202288i
$807$	25.9603			0.913847
$808$	11.0254	−	2.95424i	0.387871	−	0.103930i
$809$	−19.4561	+	33.6989i	−0.684040	+	1.18479i	0.289698	+	0.957118i	$0.406445\pi$
$809$	−19.4561	+	33.6989i	−0.684040	+	1.18479i	−0.973738	+	0.227673i	$0.926888\pi$
$810$	1.63406	+	2.83027i	0.0574149	+	0.0994456i
$811$	−33.4503	−	33.4503i	−1.17460	−	1.17460i	−0.981101	−	0.193499i	$-0.938016\pi$
$811$	−33.4503	−	33.4503i	−1.17460	−	1.17460i	−0.193499	−	0.981101i	$-0.561984\pi$
$812$		0			0
$813$	−2.12076	+	7.91477i	−0.0743782	+	0.277583i
$814$	−7.56959	−	7.56959i	−0.265314	−	0.265314i
$815$	−4.95793	+	2.86246i	−0.173669	+	0.100268i
$816$	18.0806	+	10.4388i	0.632948	+	0.365433i
$817$	−0.861242	−	3.21420i	−0.0301311	−	0.112451i
$818$	−6.80553			−0.237950
$819$		0			0
$820$	2.44788			0.0854838
$821$	−12.3056	−	45.9251i	−0.429468	−	1.60280i	−0.753968	−	0.656912i	$-0.771862\pi$
$821$	−12.3056	−	45.9251i	−0.429468	−	1.60280i	0.324499	−	0.945886i	$-0.394804\pi$
$822$	−0.323082	−	0.186531i	−0.0112688	−	0.00650603i
$823$	−31.5629	+	18.2229i	−1.10022	+	0.635210i	−0.936278	−	0.351261i	$-0.885753\pi$
$823$	−31.5629	+	18.2229i	−1.10022	+	0.635210i	−0.163938	+	0.986471i	$0.552420\pi$
$824$	13.0587	+	13.0587i	0.454920	+	0.454920i
$825$	8.36092	−	31.2034i	0.291090	−	1.08636i
$826$		0			0
$827$	4.04107	+	4.04107i	0.140522	+	0.140522i	0.773868	−	0.633347i	$-0.218319\pi$
$827$	4.04107	+	4.04107i	0.140522	+	0.140522i	−0.633347	+	0.773868i	$0.718319\pi$
$828$	15.1392	+	26.2219i	0.526124	+	0.911274i
$829$	−17.7840	+	30.8028i	−0.617664	+	1.06983i	0.372247	+	0.928134i	$0.378588\pi$
$829$	−17.7840	+	30.8028i	−0.617664	+	1.06983i	−0.989911	+	0.141692i	$0.954746\pi$
$830$	−2.14743	+	0.575402i	−0.0745383	+	0.0199725i
$831$	−41.7608			−1.44866
$832$	14.1662	+	17.5849i	0.491124	+	0.609646i
$833$		0			0
$834$	0.680614	+	2.54009i	0.0235677	+	0.0879560i
$835$	−18.0452	+	31.2552i	−0.624481	+	1.08163i
$836$	7.48778	+	12.9692i	0.258970	+	0.448550i
$837$	2.94056	−	2.94056i	0.101641	−	0.101641i
$838$	1.14262	−	4.26431i	0.0394711	−	0.147308i
$839$	−14.5158	−	3.88950i	−0.501142	−	0.134280i	−0.000611847	−	1.00000i	$-0.500195\pi$
$839$	−14.5158	−	3.88950i	−0.501142	−	0.134280i	−0.500530	+	0.865719i	$0.666861\pi$
$840$		0			0
$841$	−2.03520	−	3.52507i	−0.0701793	−	0.121554i
$842$	4.28596	+	2.47450i	0.147704	+	0.0852769i
$843$	−7.35803	−	27.4605i	−0.253424	−	0.945791i
$844$			5.40504i			0.186049i
$845$	−16.1952	+	10.4008i	−0.557132	+	0.357798i
$846$			7.20176i			0.247602i
$847$		0			0
$848$	−23.2705	+	40.3057i	−0.799113	+	1.38410i
$849$	−31.3425	+	18.0956i	−1.07567	+	0.621039i
$850$	1.27060	+	1.27060i	0.0435812	+	0.0435812i
$851$	−39.5047	−	10.5852i	−1.35420	−	0.362857i
$852$	−8.54378	−	2.28930i	−0.292705	−	0.0784301i
$853$	11.5963	−	11.5963i	0.397050	−	0.397050i	−0.480141	−	0.877191i	$-0.659415\pi$
$853$	11.5963	−	11.5963i	0.397050	−	0.397050i	0.877191	+	0.480141i	$0.159415\pi$
$854$		0			0
$855$	−7.12916	−	4.11603i	−0.243812	−	0.140765i
$856$	−4.20371	+	1.12638i	−0.143680	+	0.0384989i
$857$	46.8323			1.59976			0.799880	−	0.600160i	$-0.204896\pi$
$857$	46.8323			1.59976			0.799880	+	0.600160i	$0.204896\pi$
$858$	7.11168	+	8.82791i	0.242789	+	0.301380i
$859$		−	19.7674i		−	0.674455i	−0.941423	−	0.337228i	$-0.890511\pi$
$859$		−	19.7674i		−	0.674455i	0.941423	−	0.337228i	$-0.109489\pi$
$860$	−5.40715	+	1.44884i	−0.184382	+	0.0494050i
$861$		0			0
$862$	5.29211	−	3.05540i	0.180250	−	0.104067i
$863$	5.08332	−	5.08332i	0.173038	−	0.173038i	−0.615275	−	0.788313i	$-0.710955\pi$
$863$	5.08332	−	5.08332i	0.173038	−	0.173038i	0.788313	+	0.615275i	$0.210955\pi$
$864$	−0.568884	+	2.12311i	−0.0193538	+	0.0722295i
$865$	−1.83929	+	6.86431i	−0.0625376	+	0.233393i
$866$	−3.56136	+	3.56136i	−0.121020	+	0.121020i
$867$	−24.9969	+	14.4320i	−0.848940	+	0.490136i
$868$		0			0
$869$	−18.9187	+	5.06925i	−0.641773	+	0.171963i
$870$			5.83168i			0.197712i
$871$	1.58830	+	1.16014i	0.0538174	+	0.0393097i
$872$	8.49768			0.287768
$873$	8.98995	−	2.40885i	0.304264	−	0.0815272i
$874$	−1.92208	−	1.10971i	−0.0650154	−	0.0375366i
$875$		0			0
$876$	8.06211	−	8.06211i	0.272393	−	0.272393i
$877$	30.6945	+	8.22456i	1.03648	+	0.277724i	0.736653	−	0.676270i	$-0.236405\pi$
$877$	30.6945	+	8.22456i	1.03648	+	0.277724i	0.299825	+	0.953994i	$0.403072\pi$
$878$	−4.11802	−	1.10342i	−0.138976	−	0.0372386i
$879$	−29.1885	−	29.1885i	−0.984503	−	0.984503i
$880$	20.9385	−	12.0889i	0.705838	−	0.407516i
$881$	−8.45038	+	14.6365i	−0.284701	+	0.493116i	−0.972537	−	0.232750i	$-0.925228\pi$
$881$	−8.45038	+	14.6365i	−0.284701	+	0.493116i	0.687836	+	0.725866i	$0.258561\pi$
$882$		0			0
$883$		−	21.1502i		−	0.711760i	−0.934532	−	0.355880i	$-0.884181\pi$
$883$		−	21.1502i		−	0.711760i	0.934532	−	0.355880i	$-0.115819\pi$
$884$	16.0614	−	2.50210i	0.540204	−	0.0841548i
$885$		−	5.74841i		−	0.193231i
$886$	2.09295	+	7.81099i	0.0703140	+	0.262415i
$887$	−8.83730	−	5.10222i	−0.296727	−	0.171316i	0.344244	−	0.938880i	$-0.388135\pi$
$887$	−8.83730	−	5.10222i	−0.296727	−	0.171316i	−0.640972	+	0.767564i	$0.721468\pi$
$888$	−11.4712	−	19.8687i	−0.384948	−	0.666750i
$889$		0			0
$890$	5.48332	+	1.46925i	0.183801	+	0.0492494i
$891$	−9.59605	+	35.8129i	−0.321480	+	1.19978i
$892$	−22.0826	+	22.0826i	−0.739379	+	0.739379i
$893$	6.80419	+	11.7852i	0.227693	+	0.394377i
$894$	8.01026	−	13.8742i	0.267903	−	0.464022i
$895$	−4.26898	−	15.9321i	−0.142696	−	0.532550i
$896$		0			0
$897$	40.3933	+	15.6233i	1.34869	+	0.521647i
$898$	2.64833			0.0883759
$899$	−32.7653	+	8.77944i	−1.09278	+	0.292811i
$900$	8.86957	−	15.3625i	0.295652	−	0.512085i
$901$	15.3174	+	26.5304i	0.510295	+	0.883857i
$902$	−0.761755	−	0.761755i	−0.0253637	−	0.0253637i
$903$		0			0
$904$	−5.12611	+	19.1309i	−0.170492	+	0.636285i
$905$	−4.52739	−	4.52739i	−0.150496	−	0.150496i
$906$	3.91037	−	2.25765i	0.129913	−	0.0750056i
$907$	−13.5900	−	7.84622i	−0.451250	−	0.260529i	0.257108	−	0.966383i	$-0.417230\pi$
$907$	−13.5900	−	7.84622i	−0.451250	−	0.260529i	−0.708358	+	0.705853i	$0.750564\pi$
$908$	−0.874625	−	3.26415i	−0.0290255	−	0.108324i
$909$	−34.9140			−1.15802
$910$		0			0
$911$	−23.8232			−0.789296			−0.394648	−	0.918832i	$-0.629134\pi$
$911$	−23.8232			−0.789296			−0.394648	+	0.918832i	$0.629134\pi$
$912$	3.91017	+	14.5929i	0.129479	+	0.483220i
$913$	−21.8426	−	12.6108i	−0.722885	−	0.417358i
$914$	8.20378	−	4.73645i	0.271357	−	0.156668i
$915$	25.6094	+	25.6094i	0.846619	+	0.846619i
$916$	−5.55326	+	20.7250i	−0.183485	+	0.684774i
$917$		0			0
$918$	0.319020	+	0.319020i	0.0105292	+	0.0105292i
$919$	4.01647	+	6.95674i	0.132491	+	0.229482i	0.924636	−	0.380851i	$-0.124369\pi$
$919$	4.01647	+	6.95674i	0.132491	+	0.229482i	−0.792145	+	0.610333i	$0.791036\pi$
$920$	−3.80609	+	6.59234i	−0.125483	+	0.217343i
$921$	28.3329	−	7.59177i	0.933600	−	0.250157i
$922$	−2.58741			−0.0852117
$923$	−6.04465	+	2.67289i	−0.198962	+	0.0879791i
$924$		0			0
$925$	6.20155	+	23.1445i	0.203906	+	0.760986i
$926$	0.694867	−	1.20355i	0.0228348	−	0.0395509i
$927$	−28.2445	−	48.9210i	−0.927672	−	1.60678i
$928$	12.6776	−	12.6776i	0.416164	−	0.416164i
$929$	3.32217	−	12.3985i	0.108997	−	0.406781i	−0.889771	−	0.456407i	$-0.849136\pi$
$929$	3.32217	−	12.3985i	0.108997	−	0.406781i	0.998768	+	0.0496256i	$0.0158028\pi$
$930$	5.77788	+	1.54818i	0.189464	+	0.0507668i
$931$		0			0
$932$	19.6049	+	33.9567i	0.642180	+	1.11229i
$933$	28.0045	+	16.1684i	0.916827	+	0.529331i
$934$	−1.70639	−	6.36835i	−0.0558349	−	0.208379i
$935$		−	15.9145i		−	0.520460i
$936$	5.13265	+	11.6073i	0.167766	+	0.379397i
$937$			19.3918i			0.633501i	0.948509	+	0.316751i	$0.102592\pi$
$937$			19.3918i			0.633501i	−0.948509	+	0.316751i	$0.897408\pi$
$938$		0			0
$939$	7.47089	−	12.9400i	0.243803	−	0.422279i
$940$	19.8259	−	11.4465i	0.646648	−	0.373342i
$941$	1.88199	+	1.88199i	0.0613512	+	0.0613512i	0.737117	−	0.675765i	$-0.236187\pi$
$941$	1.88199	+	1.88199i	0.0613512	+	0.0613512i	−0.675765	+	0.737117i	$0.736187\pi$
$942$	7.25197	+	1.94316i	0.236282	+	0.0633116i
$943$	−3.97550	−	1.06523i	−0.129460	−	0.0346887i
$944$	−3.89691	+	3.89691i	−0.126834	+	0.126834i
$945$		0			0
$946$	2.13351	+	1.23178i	0.0693663	+	0.0400487i
$947$	−19.4341	+	5.20734i	−0.631523	+	0.169216i	−0.560360	−	0.828249i	$-0.689337\pi$
$947$	−19.4341	+	5.20734i	−0.631523	+	0.169216i	−0.0711620	+	0.997465i	$0.522671\pi$
$948$	−20.5886			−0.668686
$949$	0.912025	−	8.47044i	0.0296056	−	0.274962i
$950$			1.30029i			0.0421870i
$951$	−31.3194	+	8.39200i	−1.01560	+	0.272129i
$952$		0			0
$953$	24.0417	−	13.8805i	0.778788	−	0.449634i	−0.0572123	−	0.998362i	$-0.518221\pi$
$953$	24.0417	−	13.8805i	0.778788	−	0.449634i	0.836001	+	0.548728i	$0.184888\pi$
$954$	−8.29560	+	8.29560i	−0.268580	+	0.268580i
$955$	2.42161	−	9.03758i	0.0783616	−	0.292449i
$956$	10.3001	−	38.4405i	0.333129	−	1.24325i
$957$	−46.7818	+	46.7818i	−1.51224	+	1.51224i
$958$	5.79773	−	3.34732i	0.187316	−	0.108147i
$959$		0			0
$960$	22.4477	−	6.01483i	0.724495	−	0.194128i
$961$			3.79382i			0.122381i
$962$	−7.84220	−	3.03320i	−0.252843	−	0.0977944i
$963$	13.3119			0.428970
$964$	−26.5517	+	7.11450i	−0.855171	+	0.229143i
$965$	15.2741	+	8.81849i	0.491690	+	0.283877i
$966$		0			0
$967$	−4.10934	+	4.10934i	−0.132147	+	0.132147i	−0.770087	−	0.637939i	$-0.779787\pi$
$967$	−4.10934	+	4.10934i	−0.132147	+	0.132147i	0.637939	+	0.770087i	$0.279787\pi$
$968$	−10.4360	−	2.79631i	−0.335425	−	0.0898768i
$969$	9.60551	+	2.57379i	0.308573	+	0.0826820i
$970$	0.811524	+	0.811524i	0.0260565	+	0.0260565i
$971$	18.8523	−	10.8844i	0.604999	−	0.349296i	−0.166007	−	0.986125i	$-0.553087\pi$
$971$	18.8523	−	10.8844i	0.604999	−	0.349296i	0.771006	+	0.636828i	$0.219754\pi$
$972$	−21.5230	+	37.2790i	−0.690352	+	1.19572i
$973$		0			0
$974$		−	10.4453i		−	0.334690i
$975$	−3.90567	−	25.0712i	−0.125082	−	0.802920i
$976$		−	34.7217i		−	1.11141i
$977$	−2.39408	−	8.93483i	−0.0765934	−	0.285850i	0.916996	−	0.398895i	$-0.130606\pi$
$977$	−2.39408	−	8.93483i	−0.0765934	−	0.285850i	−0.993590	+	0.113045i	$0.963940\pi$
$978$	2.29360	+	1.32421i	0.0733413	+	0.0423436i
$979$	32.2009	+	55.7736i	1.02915	+	1.78253i
$980$		0			0
$981$	−25.1070	−	6.72740i	−0.801605	−	0.214789i
$982$	0.834347	−	3.11383i	0.0266251	−	0.0993662i
$983$	−38.8850	+	38.8850i	−1.24024	+	1.24024i	−0.280335	+	0.959902i	$0.590446\pi$
$983$	−38.8850	+	38.8850i	−1.24024	+	1.24024i	−0.959902	+	0.280335i	$0.909554\pi$
$984$	−1.15439	−	1.99946i	−0.0368005	−	0.0637404i
$985$	−1.52593	+	2.64299i	−0.0486203	+	0.0842128i
$986$	−0.952477	−	3.55469i	−0.0303331	−	0.113205i
$987$		0			0
$988$	9.49865	+	6.93808i	0.302192	+	0.220730i
$989$	9.41198			0.299284
$990$	5.88689	−	1.57739i	0.187098	−	0.0501327i
$991$	2.34950	−	4.06946i	0.0746345	−	0.129271i	−0.826293	−	0.563241i	$-0.809554\pi$
$991$	2.34950	−	4.06946i	0.0746345	−	0.129271i	0.900927	+	0.433970i	$0.142888\pi$
$992$	−9.19506	−	15.9263i	−0.291944	−	0.505661i
$993$	−17.7095	−	17.7095i	−0.561995	−	0.561995i
$994$		0			0
$995$	7.11326	−	26.5470i	0.225505	−	0.841598i
$996$	−18.7472	−	18.7472i	−0.594029	−	0.594029i
$997$	14.6274	−	8.44515i	0.463255	−	0.267461i	−0.250157	−	0.968205i	$-0.580482\pi$
$997$	14.6274	−	8.44515i	0.463255	−	0.267461i	0.713412	+	0.700745i	$0.247149\pi$
$998$	−3.62391	−	2.09227i	−0.114713	−	0.0662295i
$999$	1.55707	+	5.81107i	0.0492636	+	0.183854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.97.4		28
7.2	even	3		91.2.ba.a.45.4	yes	28
7.3	odd	6		91.2.w.a.19.4	✓	28
7.4	even	3		637.2.x.a.19.4		28
7.5	odd	6		637.2.bb.a.227.4		28
7.6	odd	2		637.2.bd.a.97.4		28
13.11	odd	12		637.2.bd.a.440.4		28
21.2	odd	6		819.2.et.b.136.4		28
21.17	even	6		819.2.gh.b.19.4		28
91.11	odd	12		637.2.bb.a.362.4		28
91.24	even	12		91.2.ba.a.89.4	yes	28
91.37	odd	12		91.2.w.a.24.4	yes	28
91.76	even	12	inner	637.2.bd.b.440.4		28
91.89	even	12		637.2.x.a.570.4		28
273.128	even	12		819.2.gh.b.388.4		28
273.206	odd	12		819.2.et.b.271.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.4	✓	28	7.3	odd	6
91.2.w.a.24.4	yes	28	91.37	odd	12
91.2.ba.a.45.4	yes	28	7.2	even	3
91.2.ba.a.89.4	yes	28	91.24	even	12
637.2.x.a.19.4		28	7.4	even	3
637.2.x.a.570.4		28	91.89	even	12
637.2.bb.a.227.4		28	7.5	odd	6
637.2.bb.a.362.4		28	91.11	odd	12
637.2.bd.a.97.4		28	7.6	odd	2
637.2.bd.a.440.4		28	13.11	odd	12
637.2.bd.b.97.4		28	1.1	even	1	trivial
637.2.bd.b.440.4		28	91.76	even	12	inner
819.2.et.b.136.4		28	21.2	odd	6
819.2.et.b.271.4		28	273.206	odd	12
819.2.gh.b.19.4		28	21.17	even	6
819.2.gh.b.388.4		28	273.128	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0707322 - 0.263976i) q^{2} +(-2.17048 - 1.25313i) q^{3} +(1.66737 - 0.962657i) q^{4} +(-1.04692 - 1.04692i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} +(1.64065 + 2.84169i) q^{9} +O(q^{10})\)	\(q+(-0.0707322 - 0.263976i) q^{2} +(-2.17048 - 1.25313i) q^{3} +(1.66737 - 0.962657i) q^{4} +(-1.04692 - 1.04692i) q^{5} +(-0.177273 + 0.661591i) q^{6} +(-0.758543 - 0.758543i) q^{8} +(1.64065 + 2.84169i) q^{9} +(-0.202311 + 0.350412i) q^{10} +(-4.43396 + 1.18808i) q^{11} -4.82532 q^{12} +(-2.80779 + 2.26193i) q^{13} +(0.960393 + 3.58423i) q^{15} +(1.77873 - 3.08085i) q^{16} +(-1.17081 - 2.02791i) q^{17} +(0.634091 - 0.634091i) q^{18} +(0.438561 - 1.63673i) q^{19} +(-2.75342 - 0.737778i) q^{20} +(0.627247 + 1.08642i) q^{22} +(4.15065 + 2.39638i) q^{23} +(0.695851 + 2.59695i) q^{24} -2.80792i q^{25} +(0.795696 + 0.581199i) q^{26} -0.705008i q^{27} +(-2.87534 + 4.98024i) q^{29} +(0.878222 - 0.507042i) q^{30} +(4.17096 + 4.17096i) q^{31} +(-3.01146 - 0.806919i) q^{32} +(11.1126 + 2.97762i) q^{33} +(-0.452505 + 0.452505i) q^{34} +(5.47114 + 3.15877i) q^{36} +(-8.24256 + 2.20859i) q^{37} -0.463079 q^{38} +(8.92873 - 1.39095i) q^{39} +1.58827i q^{40} +(-0.829479 + 0.222258i) q^{41} +(1.70069 - 0.981895i) q^{43} +(-6.24934 + 6.24934i) q^{44} +(1.25739 - 4.69264i) q^{45} +(0.339003 - 1.26518i) q^{46} +(-5.67880 + 5.67880i) q^{47} +(-7.72139 + 4.45794i) q^{48} +(-0.741225 + 0.198611i) q^{50} +5.86871i q^{51} +(-2.50417 + 6.47441i) q^{52} -13.0827 q^{53} +(-0.186105 + 0.0498668i) q^{54} +(5.88581 + 3.39817i) q^{55} +(-3.00292 + 3.00292i) q^{57} +(1.51804 + 0.406759i) q^{58} +(-1.49637 - 0.400951i) q^{59} +(5.05172 + 5.05172i) q^{60} +(8.45262 - 4.88012i) q^{61} +(0.806013 - 1.39606i) q^{62} -6.26289i q^{64} +(5.30758 + 0.571475i) q^{65} -3.14408i q^{66} +(-0.141189 - 0.526925i) q^{67} +(-3.90436 - 2.25418i) q^{68} +(-6.00594 - 10.4026i) q^{69} +(1.77061 + 0.474435i) q^{71} +(0.911040 - 3.40005i) q^{72} +(-1.67079 + 1.67079i) q^{73} +(1.16603 + 2.01962i) q^{74} +(-3.51868 + 6.09453i) q^{75} +(-0.844368 - 3.15123i) q^{76} +(-0.998725 - 2.25859i) q^{78} +4.26678 q^{79} +(-5.08758 + 1.36321i) q^{80} +(4.03849 - 6.99486i) q^{81} +(0.117342 + 0.203242i) q^{82} +(3.88518 + 3.88518i) q^{83} +(-0.897309 + 3.34880i) q^{85} +(-0.379490 - 0.379490i) q^{86} +(12.4817 - 7.20634i) q^{87} +(4.26455 + 2.46214i) q^{88} +(-3.63117 - 13.5517i) q^{89} -1.32768 q^{90} +9.22757 q^{92} +(-3.82624 - 14.2797i) q^{93} +(1.90074 + 1.09739i) q^{94} +(-2.17267 + 1.25439i) q^{95} +(5.52514 + 5.52514i) q^{96} +(0.734114 - 2.73975i) q^{97} +(-10.6507 - 10.6507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

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