LMFDB - Embedded newform 475.2.l.c.176.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			176.1
Root			$0.653994 + 1.13275i$ of defining polynomial
Character	$\chi$	$=$	475.176
Dual form			475.2.l.c.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.289414 + 0.105338i) q^{2} +(0.285463 - 1.61894i) q^{3} +(-1.45942 + 1.22460i) q^{4} +(0.0879194 + 0.498616i) q^{6} +(0.0445979 + 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +(0.279590 + 0.101762i) q^{9} +O(q^{10})$	\(q+(-0.289414 + 0.105338i) q^{2} +(0.285463 - 1.61894i) q^{3} +(-1.45942 + 1.22460i) q^{4} +(0.0879194 + 0.498616i) q^{6} +(0.0445979 + 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +(0.279590 + 0.101762i) q^{9} +(1.68341 - 2.91575i) q^{11} +(1.56595 + 2.71230i) q^{12} +(-0.0369645 - 0.209636i) q^{13} +(-0.0210442 - 0.0176582i) q^{14} +(0.597325 - 3.38760i) q^{16} +(-2.36261 + 0.859918i) q^{17} -0.0916368 q^{18} +(0.949628 - 4.25420i) q^{19} +(0.137788 - 0.0501507i) q^{21} +(-0.180063 + 1.02119i) q^{22} +(4.57098 - 3.83550i) q^{23} +(-1.51463 - 1.27092i) q^{24} +(0.0327807 + 0.0567779i) q^{26} +(2.71044 - 4.69462i) q^{27} +(-0.159683 - 0.0581198i) q^{28} +(4.51826 + 1.64451i) q^{29} +(-4.03407 - 6.98722i) q^{31} +(0.601676 + 3.41227i) q^{32} +(-4.23989 - 3.55769i) q^{33} +(0.593190 - 0.497745i) q^{34} +(-0.532659 + 0.193872i) q^{36} -1.84372 q^{37} +(0.173294 + 1.33126i) q^{38} -0.349941 q^{39} +(-0.523087 + 2.96657i) q^{41} +(-0.0345950 + 0.0290286i) q^{42} +(1.87518 + 1.57346i) q^{43} +(1.11383 + 6.31683i) q^{44} +(-0.918881 + 1.59155i) q^{46} +(-7.15887 - 2.60562i) q^{47} +(-5.31381 - 1.93407i) q^{48} +(3.49602 - 6.05529i) q^{49} +(0.717721 + 4.07040i) q^{51} +(0.310668 + 0.260681i) q^{52} +(6.43452 - 5.39920i) q^{53} +(-0.289917 + 1.64420i) q^{54} +0.107279 q^{56} +(-6.61622 - 2.75181i) q^{57} -1.48088 q^{58} +(-9.80610 + 3.56913i) q^{59} +(-0.757296 + 0.635447i) q^{61} +(1.90354 + 1.59726i) q^{62} +(0.00460841 + 0.0261356i) q^{63} +(2.90628 + 5.03383i) q^{64} +(1.60184 + 0.583024i) q^{66} +(9.37780 + 3.41324i) q^{67} +(2.39499 - 4.14824i) q^{68} +(-4.90462 - 8.49505i) q^{69} +(4.73200 + 3.97062i) q^{71} +(0.274133 - 0.230025i) q^{72} +(-2.73409 + 15.5058i) q^{73} +(0.533599 - 0.194214i) q^{74} +(3.82379 + 7.37160i) q^{76} +0.300307 q^{77} +(0.101278 - 0.0368621i) q^{78} +(-0.178596 + 1.01287i) q^{79} +(-6.14281 - 5.15443i) q^{81} +(-0.161105 - 0.913670i) q^{82} +(8.96939 + 15.5354i) q^{83} +(-0.139676 + 0.241926i) q^{84} +(-0.708449 - 0.257854i) q^{86} +(3.95217 - 6.84536i) q^{87} +(-2.02470 - 3.50689i) q^{88} +(0.113975 + 0.646383i) q^{89} +(0.0145450 - 0.0122047i) q^{91} +(-1.97403 + 11.1953i) q^{92} +(-12.4635 + 4.53634i) q^{93} +2.34635 q^{94} +5.69603 q^{96} +(15.7991 - 5.75040i) q^{97} +(-0.373946 + 2.12075i) q^{98} +(0.767379 - 0.643907i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.289414	+	0.105338i	−0.204647	+	0.0744854i	−0.442310	−	0.896862i	$-0.645841\pi$
$2$	−0.289414	+	0.105338i	−0.204647	+	0.0744854i	0.237663	+	0.971348i	$0.423619\pi$
$3$	0.285463	−	1.61894i	0.164812	−	0.934697i	−0.784445	−	0.620198i	$-0.787052\pi$
$3$	0.285463	−	1.61894i	0.164812	−	0.934697i	0.949258	−	0.314499i	$-0.101837\pi$
$4$	−1.45942	+	1.22460i	−0.729712	+	0.612301i
$5$		0			0
$5$		0			0
$6$	0.0879194	+	0.498616i	0.0358929	+	0.203559i
$7$	0.0445979	+	0.0772459i	0.0168564	+	0.0291962i	0.874331	−	0.485331i	$-0.161301\pi$
$7$	0.0445979	+	0.0772459i	0.0168564	+	0.0291962i	−0.857474	+	0.514527i	$0.827968\pi$
$8$	0.601369	−	1.04160i	0.212616	−	0.368262i
$9$	0.279590	+	0.101762i	0.0931966	+	0.0339208i
$10$		0			0
$11$	1.68341	−	2.91575i	0.507567	−	0.879133i	−0.492394	−	0.870372i	$-0.663878\pi$
$11$	1.68341	−	2.91575i	0.507567	−	0.879133i	0.999962	−	0.00876033i	$-0.00278854\pi$
$12$	1.56595	+	2.71230i	0.452051	+	0.782975i
$13$	−0.0369645	−	0.209636i	−0.0102521	−	0.0581426i	0.979253	−	0.202644i	$-0.0649534\pi$
$13$	−0.0369645	−	0.209636i	−0.0102521	−	0.0581426i	−0.989505	+	0.144501i	$0.953842\pi$
$14$	−0.0210442	−	0.0176582i	−0.00562431	−	0.00471935i
$15$		0			0
$16$	0.597325	−	3.38760i	0.149331	−	0.846899i
$17$	−2.36261	+	0.859918i	−0.573016	+	0.208561i	−0.612243	−	0.790670i	$-0.709733\pi$
$17$	−2.36261	+	0.859918i	−0.573016	+	0.208561i	0.0392271	+	0.999230i	$0.487510\pi$
$18$	−0.0916368			−0.0215990
$19$	0.949628	−	4.25420i	0.217860	−	0.975980i
$19$	0.949628	−	4.25420i	0.217860	−	0.975980i
$20$		0			0
$21$	0.137788	−	0.0501507i	0.0300678	−	0.0109438i
$22$	−0.180063	+	1.02119i	−0.0383896	+	0.217718i
$23$	4.57098	−	3.83550i	0.953114	−	0.799758i	−0.0267049	−	0.999643i	$-0.508501\pi$
$23$	4.57098	−	3.83550i	0.953114	−	0.799758i	0.979819	+	0.199885i	$0.0640570\pi$
$24$	−1.51463	−	1.27092i	−0.309172	−	0.259426i
$25$		0			0
$26$	0.0327807	+	0.0567779i	0.00642883	+	0.0111351i
$27$	2.71044	−	4.69462i	0.521624	−	0.903479i
$28$	−0.159683	−	0.0581198i	−0.0301772	−	0.0109836i
$29$	4.51826	+	1.64451i	0.839019	+	0.305378i	0.725555	−	0.688164i	$-0.241583\pi$
$29$	4.51826	+	1.64451i	0.839019	+	0.305378i	0.113464	+	0.993542i	$0.463805\pi$
$30$		0			0
$31$	−4.03407	−	6.98722i	−0.724541	−	1.25494i	−0.959163	−	0.282855i	$-0.908718\pi$
$31$	−4.03407	−	6.98722i	−0.724541	−	1.25494i	0.234621	−	0.972087i	$-0.424615\pi$
$32$	0.601676	+	3.41227i	0.106362	+	0.603210i
$33$	−4.23989	−	3.55769i	−0.738070	−	0.619314i
$34$	0.593190	−	0.497745i	0.101731	−	0.0853626i
$35$		0			0
$36$	−0.532659	+	0.193872i	−0.0887765	+	0.0323120i
$37$	−1.84372			−0.303106			−0.151553	−	0.988449i	$-0.548427\pi$
$37$	−1.84372			−0.303106			−0.151553	+	0.988449i	$0.548427\pi$
$38$	0.173294	+	1.33126i	0.0281119	+	0.215959i
$39$	−0.349941			−0.0560354
$40$		0			0
$41$	−0.523087	+	2.96657i	−0.0816925	+	0.463301i	0.916329	+	0.400426i	$0.131138\pi$
$41$	−0.523087	+	2.96657i	−0.0816925	+	0.463301i	−0.998021	+	0.0628748i	$0.979973\pi$
$42$	−0.0345950	+	0.0290286i	−0.00533812	+	0.00447922i
$43$	1.87518	+	1.57346i	0.285962	+	0.239951i	0.774473	−	0.632607i	$-0.218015\pi$
$43$	1.87518	+	1.57346i	0.285962	+	0.239951i	−0.488511	+	0.872558i	$0.662460\pi$
$44$	1.11383	+	6.31683i	0.167916	+	0.952298i
$45$		0			0
$46$	−0.918881	+	1.59155i	−0.135482	+	0.234661i
$47$	−7.15887	−	2.60562i	−1.04423	−	0.380068i	−0.237747	−	0.971327i	$-0.576409\pi$
$47$	−7.15887	−	2.60562i	−1.04423	−	0.380068i	−0.806482	+	0.591259i	$0.798631\pi$
$48$	−5.31381	−	1.93407i	−0.766983	−	0.279159i
$49$	3.49602	−	6.05529i	0.499432	−	0.865041i
$50$		0			0
$51$	0.717721	+	4.07040i	0.100501	+	0.569970i
$52$	0.310668	+	0.260681i	0.0430818	+	0.0361500i
$53$	6.43452	−	5.39920i	0.883849	−	0.741637i	−0.0831178	−	0.996540i	$-0.526488\pi$
$53$	6.43452	−	5.39920i	0.883849	−	0.741637i	0.966967	+	0.254902i	$0.0820433\pi$
$54$	−0.289917	+	1.64420i	−0.0394527	+	0.223747i
$55$		0			0
$56$	0.107279			0.0143358
$57$	−6.61622	−	2.75181i	−0.876340	−	0.364486i
$58$	−1.48088			−0.194449
$59$	−9.80610	+	3.56913i	−1.27665	+	0.464661i	−0.889321	−	0.457283i	$-0.848823\pi$
$59$	−9.80610	+	3.56913i	−1.27665	+	0.464661i	−0.387324	+	0.921944i	$0.626600\pi$
$60$		0			0
$61$	−0.757296	+	0.635447i	−0.0969618	+	0.0813606i	−0.689980	−	0.723828i	$-0.742381\pi$
$61$	−0.757296	+	0.635447i	−0.0969618	+	0.0813606i	0.593018	+	0.805189i	$0.297936\pi$
$62$	1.90354	+	1.59726i	0.241750	+	0.202852i
$63$	0.00460841	+	0.0261356i	0.000580605	+	0.00329277i
$64$	2.90628	+	5.03383i	0.363285	+	0.629228i
$65$		0			0
$66$	1.60184	+	0.583024i	0.197173	+	0.0717653i
$67$	9.37780	+	3.41324i	1.14568	+	0.416994i	0.843962	−	0.536403i	$-0.180217\pi$
$67$	9.37780	+	3.41324i	1.14568	+	0.416994i	0.301719	+	0.953397i	$0.402440\pi$
$68$	2.39499	−	4.14824i	0.290435	−	0.503048i
$69$	−4.90462	−	8.49505i	−0.590447	−	1.02268i
$70$		0			0
$71$	4.73200	+	3.97062i	0.561585	+	0.471226i	0.878841	−	0.477114i	$-0.158317\pi$
$71$	4.73200	+	3.97062i	0.561585	+	0.471226i	−0.317256	+	0.948340i	$0.602762\pi$
$72$	0.274133	−	0.230025i	0.0323068	−	0.0271087i
$73$	−2.73409	+	15.5058i	−0.320001	+	1.81482i	0.222695	+	0.974888i	$0.428515\pi$
$73$	−2.73409	+	15.5058i	−0.320001	+	1.81482i	−0.542696	+	0.839929i	$0.682597\pi$
$74$	0.533599	−	0.194214i	0.0620296	−	0.0225769i
$75$		0			0
$76$	3.82379	+	7.37160i	0.438619	+	0.845580i
$77$	0.300307			0.0342231
$78$	0.101278	−	0.0368621i	0.0114675	−	0.00417381i
$79$	−0.178596	+	1.01287i	−0.0200936	+	0.113957i	−0.993205	−	0.116379i	$-0.962871\pi$
$79$	−0.178596	+	1.01287i	−0.0200936	+	0.113957i	0.973111	+	0.230336i	$0.0739824\pi$
$80$		0			0
$81$	−6.14281	−	5.15443i	−0.682535	−	0.572715i
$82$	−0.161105	−	0.913670i	−0.0177910	−	0.100898i
$83$	8.96939	+	15.5354i	0.984518	+	1.70524i	0.644059	+	0.764976i	$0.277249\pi$
$83$	8.96939	+	15.5354i	0.984518	+	1.70524i	0.340459	+	0.940259i	$0.389418\pi$
$84$	−0.139676	+	0.241926i	−0.0152399	+	0.0263963i
$85$		0			0
$86$	−0.708449	−	0.257854i	−0.0763940	−	0.0278052i
$87$	3.95217	−	6.84536i	0.423717	−	0.733899i
$88$	−2.02470	−	3.50689i	−0.215834	−	0.373836i
$89$	0.113975	+	0.646383i	0.0120813	+	0.0685164i	0.990252	−	0.139285i	$-0.0444804\pi$
$89$	0.113975	+	0.646383i	0.0120813	+	0.0685164i	−0.978171	+	0.207801i	$0.933369\pi$
$90$		0			0
$91$	0.0145450	−	0.0122047i	0.00152473	−	0.00127940i
$92$	−1.97403	+	11.1953i	−0.205806	+	1.16719i
$93$	−12.4635	+	4.53634i	−1.29240	+	0.470397i
$94$	2.34635			0.242008
$95$		0			0
$96$	5.69603			0.581349
$97$	15.7991	−	5.75040i	1.60416	−	0.583865i	0.623883	−	0.781518i	$-0.285554\pi$
$97$	15.7991	−	5.75040i	1.60416	−	0.583865i	0.980272	+	0.197653i	$0.0633319\pi$
$98$	−0.373946	+	2.12075i	−0.0377742	+	0.214228i
$99$	0.767379	−	0.643907i	0.0771245	−	0.0647151i
$100$		0			0
$101$	0.638978	+	3.62382i	0.0635806	+	0.360584i	0.999954	+	0.00957849i	$0.00304897\pi$
$101$	0.638978	+	3.62382i	0.0635806	+	0.360584i	−0.936373	+	0.351005i	$0.885840\pi$
$102$	−0.636488	−	1.10243i	−0.0630217	−	0.109157i
$103$	−1.76710	+	3.06071i	−0.174118	+	0.301580i	−0.939856	−	0.341572i	$-0.889041\pi$
$103$	−1.76710	+	3.06071i	−0.174118	+	0.301580i	0.765738	+	0.643153i	$0.222374\pi$
$104$	−0.240587	−	0.0875664i	−0.0235915	−	0.00858659i
$105$		0			0
$106$	−1.29350	+	2.24041i	−0.125636	+	0.217608i
$107$	−0.943300	−	1.63384i	−0.0911923	−	0.157950i	0.816821	−	0.576891i	$-0.195734\pi$
$107$	−0.943300	−	1.63384i	−0.0911923	−	0.157950i	−0.908013	+	0.418942i	$0.862401\pi$
$108$	1.79336	+	10.1706i	0.172566	+	0.978671i
$109$	−10.0810	−	8.45901i	−0.965589	−	0.810226i	0.0162639	−	0.999868i	$-0.494823\pi$
$109$	−10.0810	−	8.45901i	−0.965589	−	0.810226i	−0.981853	+	0.189642i	$0.939267\pi$
$110$		0			0
$111$	−0.526315	+	2.98488i	−0.0499556	+	0.283312i
$112$	0.288318	−	0.104939i	0.0272434	−	0.00991580i
$113$	−12.3456			−1.16138			−0.580689	−	0.814125i	$-0.697217\pi$
$113$	−12.3456			−1.16138			−0.580689	+	0.814125i	$0.697217\pi$
$114$	2.20470	+	0.0994730i	0.206489	+	0.00931650i
$115$		0			0
$116$	−8.60793	+	3.13303i	−0.799226	+	0.290895i
$117$	0.0109982	−	0.0623737i	0.00101678	−	0.00576645i
$118$	2.46206	−	2.06591i	0.226651	−	0.190183i
$119$	−0.171793	−	0.144151i	−0.0157482	−	0.0132143i
$120$		0			0
$121$	−0.167744	−	0.290542i	−0.0152495	−	0.0264129i
$122$	0.152235	−	0.263680i	0.0137827	−	0.0238724i
$123$	4.65339	+	1.69370i	0.419582	+	0.152716i
$124$	14.4440	+	5.25718i	1.29711	+	0.472109i
$125$		0			0
$126$	−0.00408681	−	0.00707857i	−0.000364082	−	0.000630609i
$127$	−3.68344	−	20.8898i	−0.326852	−	1.85367i	−0.496325	−	0.868137i	$-0.665318\pi$
$127$	−3.68344	−	20.8898i	−0.326852	−	1.85367i	0.169473	−	0.985535i	$-0.445793\pi$
$128$	−6.67993	−	5.60512i	−0.590428	−	0.495428i
$129$	3.08264	−	2.58664i	0.271411	−	0.227741i
$130$		0			0
$131$	−6.53156	+	2.37729i	−0.570665	+	0.207705i	−0.611204	−	0.791473i	$-0.709315\pi$
$131$	−6.53156	+	2.37729i	−0.570665	+	0.207705i	0.0405392	+	0.999178i	$0.487092\pi$
$132$	10.5445			0.917785
$133$	0.370971	−	0.116374i	0.0321673	−	0.0100909i
$134$	−3.07361			−0.265520
$135$		0			0
$136$	−0.525106	+	2.97802i	−0.0450275	+	0.255363i
$137$	−16.0922	+	13.5029i	−1.37485	+	1.15363i	−0.403772	+	0.914860i	$0.632301\pi$
$137$	−16.0922	+	13.5029i	−1.37485	+	1.15363i	−0.971075	+	0.238774i	$0.923254\pi$
$138$	2.31432	+	1.94194i	0.197008	+	0.165309i
$139$	2.72999	+	15.4826i	0.231555	+	1.31321i	0.849749	+	0.527188i	$0.176754\pi$
$139$	2.72999	+	15.4826i	0.231555	+	1.31321i	−0.618194	+	0.786026i	$0.712135\pi$
$140$		0			0
$141$	−6.26194	+	10.8460i	−0.527351	+	0.913398i
$142$	−1.78777	−	0.650694i	−0.150026	−	0.0546050i
$143$	−0.673473	−	0.245124i	−0.0563187	−	0.0204983i
$144$	0.511736	−	0.886353i	0.0426447	−	0.0738627i
$145$		0			0
$146$	−0.842068	−	4.77561i	−0.0696901	−	0.395232i
$147$	−8.80518	−	7.38842i	−0.726239	−	0.609387i
$148$	2.69077	−	2.25782i	0.221180	−	0.185592i
$149$	−3.38951	+	19.2229i	−0.277679	+	1.57480i	0.452641	+	0.891693i	$0.350482\pi$
$149$	−3.38951	+	19.2229i	−0.277679	+	1.57480i	−0.730320	+	0.683105i	$0.760629\pi$
$150$		0			0
$151$	11.2284			0.913758			0.456879	−	0.889529i	$-0.348967\pi$
$151$	11.2284			0.913758			0.456879	+	0.889529i	$0.348967\pi$
$152$	−3.86010	−	3.54748i	−0.313096	−	0.287739i
$153$	−0.748068			−0.0604777
$154$	−0.0869131	+	0.0316338i	−0.00700365	+	0.00254912i
$155$		0			0
$156$	0.510712	−	0.428538i	0.0408897	−	0.0343105i
$157$	−3.53362	−	2.96506i	−0.282014	−	0.236637i	0.490797	−	0.871274i	$-0.336705\pi$
$157$	−3.53362	−	2.96506i	−0.282014	−	0.236637i	−0.772811	+	0.634636i	$0.781150\pi$
$158$	−0.0550055	−	0.311951i	−0.00437600	−	0.0248175i
$159$	−6.90418	−	11.9584i	−0.547537	−	0.948362i
$160$		0			0
$161$	0.500133	+	0.182034i	0.0394160	+	0.0143463i
$162$	2.32078	+	0.844694i	0.182337	+	0.0663654i
$163$	−0.287367	+	0.497735i	−0.0225084	+	0.0389856i	−0.877060	−	0.480381i	$-0.840499\pi$
$163$	−0.287367	+	0.497735i	−0.0225084	+	0.0389856i	0.854552	+	0.519366i	$0.173832\pi$
$164$	−2.86947	−	4.97007i	−0.224068	−	0.388097i
$165$		0			0
$166$	−4.23234	−	3.55136i	−0.328494	−	0.275639i
$167$	−3.15765	+	2.64958i	−0.244346	+	0.205031i	−0.756733	−	0.653724i	$-0.773206\pi$
$167$	−3.15765	+	2.64958i	−0.244346	+	0.205031i	0.512387	+	0.858755i	$0.328761\pi$
$168$	0.0306243	−	0.173679i	0.00236272	−	0.0133996i
$169$	12.1734	−	4.43076i	0.936417	−	0.340828i
$170$		0			0
$171$	0.698424	−	1.09279i	0.0534098	−	0.0835681i
$172$	−4.66355			−0.355592
$173$	−6.04652	+	2.20075i	−0.459709	+	0.167320i	−0.561485	−	0.827487i	$-0.689770\pi$
$173$	−6.04652	+	2.20075i	−0.459709	+	0.167320i	0.101776	+	0.994807i	$0.467547\pi$
$174$	−0.422737	+	2.39746i	−0.0320476	+	0.181751i
$175$		0			0
$176$	−8.87186	−	7.44437i	−0.668741	−	0.561141i
$177$	2.97893	+	16.8944i	0.223910	+	1.26986i
$178$	−0.101075	−	0.175066i	−0.00757587	−	0.0131218i
$179$	−1.91516	+	3.31715i	−0.143146	+	0.247936i	−0.928680	−	0.370883i	$-0.879055\pi$
$179$	−1.91516	+	3.31715i	−0.143146	+	0.247936i	0.785534	+	0.618819i	$0.212388\pi$
$180$		0			0
$181$	−15.6814	−	5.70755i	−1.16559	−	0.424239i	−0.314496	−	0.949259i	$-0.601836\pi$
$181$	−15.6814	−	5.70755i	−1.16559	−	0.424239i	−0.851090	+	0.525020i	$0.824058\pi$
$182$	−0.00292391	+	0.00506435i	−0.000216734	+	0.000375395i
$183$	0.812572	+	1.40742i	0.0600670	+	0.104039i
$184$	−1.24622	−	7.06769i	−0.0918729	−	0.521037i
$185$		0			0
$186$	3.12926	−	2.62576i	0.229449	−	0.192530i
$187$	−1.46993	+	8.33637i	−0.107492	+	0.609616i
$188$	13.6387	−	4.96407i	0.994703	−	0.362042i
$189$	0.483520			0.0351709
$190$		0			0
$191$	7.92694			0.573573			0.286787	−	0.957994i	$-0.407413\pi$
$191$	7.92694			0.573573			0.286787	+	0.957994i	$0.407413\pi$
$192$	8.97912	−	3.26813i	0.648012	−	0.235857i
$193$	3.69296	−	20.9438i	0.265825	−	1.50757i	−0.500851	−	0.865533i	$-0.666980\pi$
$193$	3.69296	−	20.9438i	0.265825	−	1.50757i	0.766676	−	0.642034i	$-0.221909\pi$
$194$	−3.96675	+	3.32850i	−0.284796	+	0.238972i
$195$		0			0
$196$	2.31314	+	13.1185i	0.165224	+	0.937034i
$197$	1.44371	+	2.50058i	0.102860	+	0.178159i	0.912862	−	0.408268i	$-0.133867\pi$
$197$	1.44371	+	2.50058i	0.102860	+	0.178159i	−0.810002	+	0.586427i	$0.800534\pi$
$198$	−0.154262	+	0.267190i	−0.0109629	+	0.0189884i
$199$	−10.9144	−	3.97251i	−0.773701	−	0.281604i	−0.0751574	−	0.997172i	$-0.523946\pi$
$199$	−10.9144	−	3.97251i	−0.773701	−	0.281604i	−0.698544	+	0.715568i	$0.746168\pi$
$200$		0			0
$201$	8.20286	−	14.2078i	0.578585	−	1.00214i
$202$	−0.566656	−	0.981477i	−0.0398698	−	0.0690565i
$203$	0.0744732	+	0.422359i	0.00522700	+	0.0296438i
$204$	−6.03208	−	5.06152i	−0.422330	−	0.354377i
$205$		0			0
$206$	0.189015	−	1.07196i	0.0131693	−	0.0746867i
$207$	1.66831	−	0.607215i	0.115955	−	0.0422043i
$208$	−0.732242			−0.0507719
$209$	−10.8056	−	9.93045i	−0.747437	−	0.686903i
$210$		0			0
$211$	22.2708	−	8.10590i	1.53318	−	0.558033i	0.568784	−	0.822487i	$-0.307414\pi$
$211$	22.2708	−	8.10590i	1.53318	−	0.558033i	0.964398	+	0.264454i	$0.0851916\pi$
$212$	−2.77882	+	15.7595i	−0.190850	+	1.08236i
$213$	7.77902	−	6.52737i	0.533010	−	0.447248i
$214$	0.445111	+	0.373492i	0.0304272	+	0.0255314i
$215$		0			0
$216$	−3.25995	−	5.64639i	−0.221811	−	0.384188i
$217$	0.359823	−	0.623232i	0.0244264	−	0.0423077i
$218$	3.80866	+	1.38624i	0.257955	+	0.0938879i
$219$	24.3225	+	8.85268i	1.64356	+	0.598209i
$220$		0			0
$221$	0.267602	+	0.463501i	0.0180009	+	0.0311784i
$222$	−0.162099	−	0.919308i	−0.0108794	−	0.0616999i
$223$	6.75335	+	5.66673i	0.452237	+	0.379472i	0.840265	−	0.542175i	$-0.182399\pi$
$223$	6.75335	+	5.66673i	0.452237	+	0.379472i	−0.388028	+	0.921648i	$0.626844\pi$
$224$	−0.236751	+	0.198657i	−0.0158186	+	0.0132734i
$225$		0			0
$226$	3.57300	−	1.30047i	0.237672	−	0.0865057i
$227$	1.04512			0.0693671			0.0346835	−	0.999398i	$-0.488958\pi$
$227$	1.04512			0.0693671			0.0346835	+	0.999398i	$0.488958\pi$
$228$	13.0258	−	4.08618i	0.862651	−	0.270614i
$229$	−13.4837			−0.891031			−0.445515	−	0.895274i	$-0.646980\pi$
$229$	−13.4837			−0.891031			−0.445515	+	0.895274i	$0.646980\pi$
$230$		0			0
$231$	0.0857266	−	0.486179i	0.00564039	−	0.0319883i
$232$	4.43007	−	3.71727i	0.290848	−	0.244051i
$233$	−8.59336	−	7.21068i	−0.562970	−	0.472388i	0.316335	−	0.948648i	$-0.397548\pi$
$233$	−8.59336	−	7.21068i	−0.562970	−	0.472388i	−0.879305	+	0.476260i	$0.841992\pi$
$234$	0.00338731	+	0.0192104i	0.000221435	+	0.00125582i
$235$		0			0
$236$	9.94050	−	17.2174i	0.647071	−	1.12076i
$237$	1.58879	+	0.578273i	0.103203	+	0.0375629i
$238$	0.0649038	+	0.0236231i	0.00420709	+	0.00153126i
$239$	10.1645	−	17.6054i	0.657487	−	1.13880i	−0.323777	−	0.946133i	$-0.604953\pi$
$239$	10.1645	−	17.6054i	0.657487	−	1.13880i	0.981264	−	0.192667i	$-0.0617137\pi$
$240$		0			0
$241$	−0.667594	−	3.78611i	−0.0430035	−	0.243885i	0.955727	−	0.294254i	$-0.0950713\pi$
$241$	−0.667594	−	3.78611i	−0.0430035	−	0.243885i	−0.998731	+	0.0503694i	$0.983960\pi$
$242$	0.0791528	+	0.0664171i	0.00508814	+	0.00426945i
$243$	2.35961	−	1.97995i	0.151369	−	0.127014i
$244$	0.327046	−	1.85477i	0.0209370	−	0.118740i
$245$		0			0
$246$	−1.52517			−0.0972413
$247$	−0.926936	−	0.0418221i	−0.0589795	−	0.00266107i
$248$	−9.70387			−0.616197
$249$	27.7114	−	10.0861i	1.75614	−	0.639183i
$250$		0			0
$251$	−6.08068	+	5.10229i	−0.383809	+	0.322054i	−0.814196	−	0.580591i	$-0.802822\pi$
$251$	−6.08068	+	5.10229i	−0.383809	+	0.322054i	0.430387	+	0.902645i	$0.358377\pi$
$252$	−0.0387313	−	0.0324994i	−0.00243984	−	0.00204727i
$253$	−3.48855	−	19.7846i	−0.219323	−	1.24385i
$254$	3.26654	+	5.65781i	0.204961	+	0.355002i
$255$		0			0
$256$	−8.40034	−	3.05747i	−0.525021	−	0.191092i
$257$	22.7666	+	8.28638i	1.42014	+	0.516890i	0.934090	−	0.357038i	$-0.116213\pi$
$257$	22.7666	+	8.28638i	1.42014	+	0.516890i	0.486054	+	0.873929i	$0.338436\pi$
$258$	−0.619688	+	1.07333i	−0.0385801	+	0.0668227i
$259$	−0.0822262	−	0.142420i	−0.00510928	−	0.00884954i
$260$		0			0
$261$	1.09591	+	0.919578i	0.0678351	+	0.0569204i
$262$	1.63991	−	1.37605i	0.101314	−	0.0850124i
$263$	2.14928	−	12.1892i	0.132530	−	0.751617i	−0.844017	−	0.536316i	$-0.819816\pi$
$263$	2.14928	−	12.1892i	0.132530	−	0.751617i	0.976548	−	0.215301i	$-0.0690733\pi$
$264$	−6.25543	+	2.27679i	−0.384995	+	0.140127i
$265$		0			0
$266$	−0.0951057	+	0.0727576i	−0.00583131	+	0.00446105i
$267$	1.07899			0.0660333
$268$	−17.8660	+	6.50271i	−1.09134	+	0.397216i
$269$	−4.23334	+	24.0085i	−0.258111	+	1.46382i	0.529846	+	0.848094i	$0.322250\pi$
$269$	−4.23334	+	24.0085i	−0.258111	+	1.46382i	−0.787958	+	0.615729i	$0.788862\pi$
$270$		0			0
$271$	13.3432	+	11.1963i	0.810540	+	0.680124i	0.950737	−	0.310000i	$-0.100329\pi$
$271$	13.3432	+	11.1963i	0.810540	+	0.680124i	−0.140196	+	0.990124i	$0.544773\pi$
$272$	1.50181	+	8.51721i	0.0910608	+	0.516432i
$273$	−0.0156066	−	0.0270315i	−0.000944557	−	0.00163602i
$274$	3.23493	−	5.60306i	0.195429	−	0.338494i
$275$		0			0
$276$	17.5610	+	6.39167i	1.05705	+	0.384733i
$277$	10.3920	−	17.9994i	0.624393	−	1.08148i	−0.364265	−	0.931295i	$-0.618680\pi$
$277$	10.3920	−	17.9994i	0.624393	−	1.08148i	0.988658	−	0.150185i	$-0.0479870\pi$
$278$	−2.42100	−	4.19330i	−0.145202	−	0.251498i
$279$	−0.416850	−	2.36407i	−0.0249562	−	0.141533i
$280$		0			0
$281$	−4.60383	+	3.86307i	−0.274641	+	0.230452i	−0.769696	−	0.638410i	$-0.779592\pi$
$281$	−4.60383	+	3.86307i	−0.274641	+	0.230452i	0.495055	+	0.868862i	$0.335148\pi$
$282$	0.669797	−	3.79861i	0.0398859	−	0.226204i
$283$	10.8759	−	3.95849i	0.646502	−	0.235308i	0.00210419	−	0.999998i	$-0.499330\pi$
$283$	10.8759	−	3.95849i	0.646502	−	0.235308i	0.644398	+	0.764690i	$0.277108\pi$
$284$	−11.7684			−0.698327
$285$		0			0
$286$	0.220734			0.0130523
$287$	−0.252484	+	0.0918968i	−0.0149037	+	0.00542450i
$288$	−0.179019	+	1.01526i	−0.0105488	+	0.0598251i
$289$	−8.18031	+	6.86409i	−0.481195	+	0.403770i
$290$		0			0
$291$	−4.79951	−	27.2194i	−0.281352	−	1.59563i
$292$	−14.9982	−	25.9777i	−0.877706	−	1.52023i
$293$	8.73466	−	15.1289i	0.510284	−	0.883838i	−0.489645	−	0.871922i	$-0.662874\pi$
$293$	8.73466	−	15.1289i	0.510284	−	0.883838i	0.999929	−	0.0119163i	$-0.00379316\pi$
$294$	3.32663	+	1.21079i	0.194013	+	0.0706149i
$295$		0			0
$296$	−1.10876	+	1.92042i	−0.0644452	+	0.111622i
$297$	−9.12556	−	15.8059i	−0.529519	−	0.917153i
$298$	−1.04393	−	5.92042i	−0.0604732	−	0.342961i
$299$	−0.973024	−	0.816464i	−0.0562714	−	0.0472173i
$300$		0			0
$301$	−0.0379144	+	0.215023i	−0.00218535	+	0.0123937i
$302$	−3.24967	+	1.18278i	−0.186998	+	0.0680616i
$303$	6.04917			0.347516
$304$	−13.8443	−	5.75810i	−0.794024	−	0.330250i
$305$		0			0
$306$	0.216502	−	0.0788002i	0.0123766	−	0.00450470i
$307$	−5.14924	+	29.2028i	−0.293883	+	1.66669i	0.377827	+	0.925876i	$0.376672\pi$
$307$	−5.14924	+	29.2028i	−0.293883	+	1.66669i	−0.671709	+	0.740815i	$0.734440\pi$
$308$	−0.438275	+	0.367756i	−0.0249730	+	0.0209549i
$309$	4.45067	+	3.73455i	0.253190	+	0.212451i
$310$		0			0
$311$	5.81119	+	10.0653i	0.329522	+	0.570749i	0.982417	−	0.186699i	$-0.0597790\pi$
$311$	5.81119	+	10.0653i	0.329522	+	0.570749i	−0.652895	+	0.757449i	$0.726446\pi$
$312$	−0.210444	+	0.364499i	−0.0119140	+	0.0206357i
$313$	−0.446226	−	0.162413i	−0.0252222	−	0.00918012i	0.329378	−	0.944198i	$-0.393161\pi$
$313$	−0.446226	−	0.162413i	−0.0252222	−	0.00918012i	−0.354600	+	0.935018i	$0.615383\pi$
$314$	1.33501	+	0.485905i	0.0753392	+	0.0274212i
$315$		0			0
$316$	−0.979713	−	1.69691i	−0.0551132	−	0.0954588i
$317$	3.51260	+	19.9209i	0.197287	+	1.11887i	0.909124	+	0.416526i	$0.136753\pi$
$317$	3.51260	+	19.9209i	0.197287	+	1.11887i	−0.711836	+	0.702345i	$0.752136\pi$
$318$	3.25784	+	2.73366i	0.182691	+	0.153296i
$319$	12.4011	−	10.4057i	0.694327	−	0.582609i
$320$		0			0
$321$	−2.91438	+	1.06075i	−0.162665	+	0.0592051i
$322$	−0.163921			−0.00913495
$323$	1.41467	+	10.8676i	0.0787141	+	0.604689i
$324$	15.2771			0.848728
$325$		0			0
$326$	0.0307377	−	0.174322i	0.00170241	−	0.00965483i
$327$	−16.5724	+	13.9059i	−0.916457	+	0.768999i
$328$	2.77542	+	2.32886i	0.153247	+	0.128590i
$329$	−0.117998	−	0.669199i	−0.00650543	−	0.0368941i
$330$		0			0
$331$	3.00653	−	5.20746i	0.165254	−	0.286228i	−0.771492	−	0.636240i	$-0.780489\pi$
$331$	3.00653	−	5.20746i	0.165254	−	0.286228i	0.936745	+	0.350012i	$0.113822\pi$
$332$	−32.1149	−	11.6889i	−1.76253	−	0.641509i
$333$	−0.515486	−	0.187621i	−0.0282484	−	0.0102816i
$334$	0.634767	−	1.09945i	0.0347329	−	0.0601591i
$335$		0			0
$336$	−0.0875862	−	0.496726i	−0.00477822	−	0.0270986i
$337$	6.79277	+	5.69981i	0.370026	+	0.310488i	0.808772	−	0.588123i	$-0.200133\pi$
$337$	6.79277	+	5.69981i	0.370026	+	0.310488i	−0.438746	+	0.898611i	$0.644577\pi$
$338$	−3.05643	+	2.56465i	−0.166248	+	0.139499i
$339$	−3.52422	+	19.9869i	−0.191409	+	1.08554i
$340$		0			0
$341$	−27.1640			−1.47101
$342$	−0.0870209	+	0.389841i	−0.00470555	+	0.0210802i
$343$	1.24803			0.0673874
$344$	2.76660	−	1.00696i	0.149165	−	0.0542916i
$345$		0			0
$346$	1.51813	−	1.27386i	0.0816150	−	0.0684831i
$347$	−15.2988	−	12.8372i	−0.821284	−	0.689139i	0.131989	−	0.991251i	$-0.457864\pi$
$347$	−15.2988	−	12.8372i	−0.821284	−	0.689139i	−0.953272	+	0.302112i	$0.902308\pi$
$348$	2.61495	+	14.8301i	0.140176	+	0.794977i
$349$	0.405107	+	0.701666i	0.0216849	+	0.0375593i	0.876664	−	0.481103i	$-0.159764\pi$
$349$	0.405107	+	0.701666i	0.0216849	+	0.0375593i	−0.854979	+	0.518662i	$0.826430\pi$
$350$		0			0
$351$	−1.08435	−	0.394671i	−0.0578783	−	0.0210660i
$352$	10.9622	+	3.98992i	0.584288	+	0.212663i
$353$	−10.4751	+	18.1435i	−0.557536	+	0.965681i	0.440165	+	0.897917i	$0.354920\pi$
$353$	−10.4751	+	18.1435i	−0.557536	+	0.965681i	−0.997701	+	0.0677639i	$0.978414\pi$
$354$	−2.64177	−	4.57568i	−0.140408	−	0.243195i
$355$		0			0
$356$	−0.957899	−	0.803773i	−0.0507686	−	0.0425999i
$357$	−0.282413	+	0.236973i	−0.0149469	+	0.0125419i
$358$	0.204851	−	1.16177i	0.0108267	−	0.0614015i
$359$	−24.1518	+	8.79055i	−1.27469	+	0.463948i	−0.888671	−	0.458545i	$-0.848371\pi$
$359$	−24.1518	+	8.79055i	−1.27469	+	0.463948i	−0.386015	+	0.922493i	$0.626149\pi$
$360$		0			0
$361$	−17.1964	−	8.07982i	−0.905074	−	0.425253i
$362$	5.13963			0.270133
$363$	−0.518256	+	0.188630i	−0.0272014	+	0.00990049i
$364$	−0.00628141	+	0.0356236i	−0.000329235	+	0.00186719i
$365$		0			0
$366$	−0.383425	−	0.321731i	−0.0200419	−	0.0168172i
$367$	4.21721	+	23.9170i	0.220137	+	1.24846i	0.871767	+	0.489921i	$0.162974\pi$
$367$	4.21721	+	23.9170i	0.220137	+	1.24846i	−0.651630	+	0.758537i	$0.725915\pi$
$368$	−10.2628	−	17.7757i	−0.534985	−	0.926621i
$369$	−0.448136	+	0.776194i	−0.0233290	+	0.0404070i
$370$		0			0
$371$	0.704033	+	0.256247i	0.0365515	+	0.0133037i
$372$	12.6343	−	21.8833i	0.655059	−	1.13460i
$373$	5.44043	+	9.42310i	0.281695	+	0.487910i	0.971802	−	0.235797i	$-0.0757701\pi$
$373$	5.44043	+	9.42310i	0.281695	+	0.487910i	−0.690107	+	0.723707i	$0.742437\pi$
$374$	−0.452720	−	2.56750i	−0.0234096	−	0.132763i
$375$		0			0
$376$	−7.01914	+	5.88976i	−0.361985	+	0.303741i
$377$	0.177734	−	1.00798i	0.00915375	−	0.0519135i
$378$	−0.139938	+	0.0509331i	−0.00719761	+	0.00261972i
$379$	19.3318			0.993008			0.496504	−	0.868034i	$-0.334617\pi$
$379$	19.3318			0.993008			0.496504	+	0.868034i	$0.334617\pi$
$380$		0			0
$381$	−34.8709			−1.78649
$382$	−2.29417	+	0.835009i	−0.117380	+	0.0427228i
$383$	0.181124	−	1.02720i	0.00925498	−	0.0524876i	−0.979831	−	0.199830i	$-0.935961\pi$
$383$	0.181124	−	1.02720i	0.00925498	−	0.0524876i	0.989086	+	0.147343i	$0.0470720\pi$
$384$	−10.9813	+	9.21437i	−0.560385	+	0.470219i
$385$		0			0
$386$	1.13739	+	6.45045i	0.0578915	+	0.328319i
$387$	0.364162	+	0.630747i	0.0185114	+	0.0320627i
$388$	−16.0156	+	27.7399i	−0.813070	+	1.40828i
$389$	−24.9988	−	9.09880i	−1.26749	−	0.461328i	−0.381213	−	0.924487i	$-0.624493\pi$
$389$	−24.9988	−	9.09880i	−1.26749	−	0.461328i	−0.886275	+	0.463160i	$0.846716\pi$
$390$		0			0
$391$	−7.50120	+	12.9925i	−0.379352	+	0.657056i
$392$	−4.20480	−	7.28293i	−0.212374	−	0.367843i
$393$	1.98418	+	11.2529i	0.100089	+	0.567632i
$394$	−0.681238	−	0.571627i	−0.0343203	−	0.0287981i
$395$		0			0
$396$	−0.331401	+	1.87947i	−0.0166535	+	0.0944468i
$397$	−3.47457	+	1.26464i	−0.174384	+	0.0634705i	−0.427737	−	0.903903i	$-0.640689\pi$
$397$	−3.47457	+	1.26464i	−0.174384	+	0.0634705i	0.253353	+	0.967374i	$0.418467\pi$
$398$	3.57724			0.179311
$399$	−0.0825037	−	0.633801i	−0.00413035	−	0.0317298i
$400$		0			0
$401$	19.0147	−	6.92080i	0.949551	−	0.345608i	0.179620	−	0.983736i	$-0.442513\pi$
$401$	19.0147	−	6.92080i	0.949551	−	0.345608i	0.769930	+	0.638128i	$0.220291\pi$
$402$	−0.877404	+	4.97601i	−0.0437609	+	0.248181i
$403$	−1.31566	+	1.10397i	−0.0655375	+	0.0549925i
$404$	−5.37028	−	4.50620i	−0.267181	−	0.224192i
$405$		0			0
$406$	−0.0660441	−	0.114392i	−0.00327772	−	0.00567717i
$407$	−3.10374	+	5.37583i	−0.153847	+	0.266470i
$408$	4.67135	+	1.70023i	0.231266	+	0.0841741i
$409$	−11.7244	−	4.26733i	−0.579733	−	0.211006i	0.0354746	−	0.999371i	$-0.488706\pi$
$409$	−11.7244	−	4.26733i	−0.579733	−	0.211006i	−0.615208	+	0.788365i	$0.710928\pi$
$410$		0			0
$411$	17.2668	+	29.9069i	0.851707	+	1.47520i
$412$	−1.16920	−	6.63087i	−0.0576024	−	0.326679i
$413$	−0.713032	−	0.598305i	−0.0350860	−	0.0294407i
$414$	−0.418870	+	0.351473i	−0.0205863	+	0.0172740i
$415$		0			0
$416$	0.693095	−	0.252266i	0.0339818	−	0.0123683i
$417$	25.8447			1.26562
$418$	4.17334	+	1.73577i	0.204125	+	0.0848994i
$419$	28.9962			1.41656			0.708279	−	0.705933i	$-0.249472\pi$
$419$	28.9962			1.41656			0.708279	+	0.705933i	$0.249472\pi$
$420$		0			0
$421$	2.53458	−	14.3743i	0.123528	−	0.700561i	−0.858644	−	0.512573i	$-0.828692\pi$
$421$	2.53458	−	14.3743i	0.123528	−	0.700561i	0.982171	−	0.187988i	$-0.0601965\pi$
$422$	−5.59162	+	4.69193i	−0.272196	+	0.228399i
$423$	−1.73639	−	1.45701i	−0.0844264	−	0.0708422i
$424$	−1.75430	−	9.94912i	−0.0851963	−	0.483172i
$425$		0			0
$426$	−1.56378	+	2.70854i	−0.0757653	+	0.131229i
$427$	−0.0828595	−	0.0301584i	−0.00400985	−	0.00145947i
$428$	3.37749	+	1.22930i	0.163257	+	0.0594207i
$429$	−0.589094	+	1.02034i	−0.0284417	+	0.0492625i
$430$		0			0
$431$	2.34566	+	13.3029i	0.112986	+	0.640778i	0.987727	+	0.156187i	$0.0499204\pi$
$431$	2.34566	+	13.3029i	0.112986	+	0.640778i	−0.874741	+	0.484591i	$0.838969\pi$
$432$	−14.2845	−	11.9861i	−0.687261	−	0.576681i
$433$	−29.1254	+	24.4391i	−1.39968	+	1.17447i	−0.438438	+	0.898761i	$0.644468\pi$
$433$	−29.1254	+	24.4391i	−1.39968	+	1.17447i	−0.961241	+	0.275709i	$0.911087\pi$
$434$	−0.0384878	+	0.218275i	−0.00184747	+	0.0104775i
$435$		0			0
$436$	25.0714			1.20070
$437$	−11.9763	−	23.0881i	−0.572903	−	1.10446i
$438$	−7.97181			−0.380908
$439$	22.3525	−	8.13563i	1.06682	−	0.388292i	0.251836	−	0.967770i	$-0.418966\pi$
$439$	22.3525	−	8.13563i	1.06682	−	0.388292i	0.814988	+	0.579478i	$0.196743\pi$
$440$		0			0
$441$	1.59365	−	1.33723i	0.0758882	−	0.0636778i
$442$	−0.126272	−	0.105955i	−0.00600616	−	0.00503977i
$443$	3.35126	+	19.0059i	0.159223	+	0.902999i	0.954823	+	0.297176i	$0.0960449\pi$
$443$	3.35126	+	19.0059i	0.159223	+	0.902999i	−0.795600	+	0.605823i	$0.792844\pi$
$444$	−2.88717	−	5.00073i	−0.137019	−	0.237324i
$445$		0			0
$446$	−2.55144	−	0.928648i	−0.120814	−	0.0439727i
$447$	30.1531	+	10.9748i	1.42619	+	0.519092i
$448$	−0.259228	+	0.448997i	−0.0122474	+	0.0212131i
$449$	13.2068	+	22.8749i	0.623268	+	1.07953i	0.988873	+	0.148761i	$0.0475287\pi$
$449$	13.2068	+	22.8749i	0.623268	+	1.07953i	−0.365605	+	0.930770i	$0.619138\pi$
$450$		0			0
$451$	7.76923	+	6.51916i	0.365839	+	0.306975i
$452$	18.0175	−	15.1185i	0.847472	−	0.711113i
$453$	3.20531	−	18.1782i	0.150599	−	0.854087i
$454$	−0.302473	+	0.110091i	−0.0141958	+	0.00516683i
$455$		0			0
$456$	−6.84509	+	5.23661i	−0.320551	+	0.245227i
$457$	38.4641			1.79927			0.899637	−	0.436638i	$-0.143831\pi$
$457$	38.4641			1.79927			0.899637	+	0.436638i	$0.143831\pi$
$458$	3.90239	−	1.42035i	0.182347	−	0.0663687i
$459$	−2.36671	+	13.4223i	−0.110469	+	0.626498i
$460$		0			0
$461$	26.0330	+	21.8442i	1.21248	+	1.01739i	0.999184	+	0.0403991i	$0.0128629\pi$
$461$	26.0330	+	21.8442i	1.21248	+	1.01739i	0.213292	+	0.976989i	$0.431582\pi$
$462$	0.0264028	+	0.149738i	0.00122837	+	0.00696642i
$463$	−2.69723	−	4.67174i	−0.125351	−	0.217114i	0.796519	−	0.604613i	$-0.206672\pi$
$463$	−2.69723	−	4.67174i	−0.125351	−	0.217114i	−0.921870	+	0.387499i	$0.873339\pi$
$464$	8.26981	−	14.3237i	0.383916	−	0.664963i
$465$		0			0
$466$	3.24660	+	1.18167i	0.150396	+	0.0547396i
$467$	11.2144	−	19.4240i	0.518942	−	0.898834i	−0.480815	−	0.876822i	$-0.659659\pi$
$467$	11.2144	−	19.4240i	0.518942	−	0.898834i	0.999758	−	0.0220125i	$-0.00700736\pi$
$468$	0.0603320	+	0.104498i	0.00278885	+	0.00483043i
$469$	0.154572	+	0.876620i	0.00713746	+	0.0404786i
$470$		0			0
$471$	−5.80898	+	4.87431i	−0.267664	+	0.224597i
$472$	−2.17947	+	12.3604i	−0.100318	+	0.568934i
$473$	7.74452	−	2.81878i	0.356093	−	0.129607i
$474$	−0.520734			−0.0239181
$475$		0			0
$476$	0.427246			0.0195828
$477$	2.34846	−	0.854770i	0.107529	−	0.0391372i
$478$	−1.08723	+	6.16597i	−0.0497286	+	0.282025i
$479$	−22.0166	+	18.4741i	−1.00596	+	0.844104i	−0.987800	−	0.155731i	$-0.950227\pi$
$479$	−22.0166	+	18.4741i	−1.00596	+	0.844104i	−0.0181649	+	0.999835i	$0.505782\pi$
$480$		0			0
$481$	0.0681522	+	0.386510i	0.00310747	+	0.0176233i
$482$	0.592033	+	1.02543i	0.0269664	+	0.0467071i
$483$	0.437472	−	0.757723i	0.0199057	−	0.0344776i
$484$	0.600609	+	0.218604i	0.0273004	+	0.00993653i
$485$		0			0
$486$	−0.474341	+	0.821582i	−0.0215165	+	0.0372677i
$487$	−17.2221	−	29.8295i	−0.780406	−	1.35170i	−0.931705	−	0.363215i	$-0.881679\pi$
$487$	−17.2221	−	29.8295i	−0.780406	−	1.35170i	0.151299	−	0.988488i	$-0.451654\pi$
$488$	0.206468	+	1.17094i	0.00934637	+	0.0530059i
$489$	0.723772	+	0.607317i	0.0327301	+	0.0274638i
$490$		0			0
$491$	−3.36638	+	19.0917i	−0.151923	+	0.861596i	0.809623	+	0.586950i	$0.199672\pi$
$491$	−3.36638	+	19.0917i	−0.151923	+	0.861596i	−0.961546	+	0.274645i	$0.911440\pi$
$492$	−8.86538	+	3.22674i	−0.399682	+	0.145472i
$493$	−12.0890			−0.544462
$494$	0.272674	−	0.0855378i	0.0122682	−	0.00384853i
$495$		0			0
$496$	−26.0796	+	9.49218i	−1.17101	+	0.426212i
$497$	−0.0956766	+	0.542609i	−0.00429168	+	0.0243393i
$498$	−6.95763	+	5.83814i	−0.311779	+	0.261613i
$499$	8.63214	+	7.24323i	0.386428	+	0.324251i	0.815220	−	0.579152i	$-0.196616\pi$
$499$	8.63214	+	7.24323i	0.386428	+	0.324251i	−0.428792	+	0.903403i	$0.641061\pi$
$500$		0			0
$501$	3.38813	+	5.86842i	0.151371	+	0.262181i
$502$	1.22237	−	2.11720i	0.0545570	−	0.0944955i
$503$	9.95307	+	3.62262i	0.443785	+	0.161525i	0.554241	−	0.832356i	$-0.313009\pi$
$503$	9.95307	+	3.62262i	0.443785	+	0.161525i	−0.110455	+	0.993881i	$0.535231\pi$
$504$	0.0299942	+	0.0109170i	0.00133605	+	0.000486282i
$505$		0			0
$506$	3.09371	+	5.35846i	0.137532	+	0.238213i
$507$	−3.69809	−	20.9729i	−0.164238	−	0.931439i
$508$	30.9574	+	25.9764i	1.37351	+	1.15251i
$509$	−1.66949	+	1.40087i	−0.0739990	+	0.0620925i	−0.679037	−	0.734104i	$-0.737602\pi$
$509$	−1.66949	+	1.40087i	−0.0739990	+	0.0620925i	0.605038	+	0.796197i	$0.293158\pi$
$510$		0			0
$511$	−1.31969	+	0.480330i	−0.0583799	+	0.0212485i
$512$	20.1933			0.892426
$513$	−17.3979	−	15.9889i	−0.768137	−	0.705926i
$514$	−7.46186			−0.329129
$515$		0			0
$516$	−1.33127	+	7.55002i	−0.0586060	+	0.332371i
$517$	−19.6487	+	16.4872i	−0.864147	+	0.725106i
$518$	0.0387997	+	0.0325568i	0.00170476	+	0.00143046i
$519$	1.83684	+	10.4172i	0.0806282	+	0.457265i
$520$		0			0
$521$	5.72367	−	9.91369i	0.250759	−	0.434327i	−0.712976	−	0.701188i	$-0.752653\pi$
$521$	5.72367	−	9.91369i	0.250759	−	0.434327i	0.963735	+	0.266862i	$0.0859866\pi$
$522$	−0.414039	−	0.150698i	−0.0181220	−	0.00659586i
$523$	−9.16414	−	3.33548i	−0.400720	−	0.145850i	0.133795	−	0.991009i	$-0.457284\pi$
$523$	−9.16414	−	3.33548i	−0.400720	−	0.145850i	−0.534515	+	0.845159i	$0.679506\pi$
$524$	6.62108	−	11.4680i	0.289243	−	0.500984i
$525$		0			0
$526$	0.661953	+	3.75412i	0.0288625	+	0.163688i
$527$	15.5394	+	13.0391i	0.676906	+	0.567991i
$528$	−14.5846	+	12.2379i	−0.634713	+	0.532588i
$529$	2.18882	−	12.4134i	0.0951661	−	0.539714i
$530$		0			0
$531$	−3.10489			−0.134741
$532$	−0.398893	+	0.624130i	−0.0172942	+	0.0270595i
$533$	0.641237			0.0277750
$534$	−0.312276	+	0.113659i	−0.0135135	+	0.00491851i
$535$		0			0
$536$	9.19476	−	7.71532i	0.397153	−	0.333251i
$537$	4.82357	+	4.04746i	0.208153	+	0.174661i
$538$	−1.30382	−	7.39433i	−0.0562117	−	0.318792i
$539$	−11.7705	−	20.3871i	−0.506991	−	0.878133i
$540$		0			0
$541$	−21.4401	−	7.80354i	−0.921780	−	0.335501i	−0.162834	−	0.986654i	$-0.552063\pi$
$541$	−21.4401	−	7.80354i	−0.921780	−	0.335501i	−0.758947	+	0.651153i	$0.774286\pi$
$542$	−5.04110	−	1.83481i	−0.216534	−	0.0788118i
$543$	−13.7166	+	23.7579i	−0.588638	+	1.01955i
$544$	−4.35580	−	7.54446i	−0.186753	−	0.323466i
$545$		0			0
$546$	0.00736423	+	0.00617933i	0.000315160	+	0.000264451i
$547$	−23.6840	+	19.8732i	−1.01265	+	0.849716i	−0.988687	−	0.149996i	$-0.952074\pi$
$547$	−23.6840	+	19.8732i	−1.01265	+	0.849716i	−0.0239661	+	0.999713i	$0.507629\pi$
$548$	6.94958	−	39.4130i	0.296871	−	1.68364i
$549$	−0.276397	+	0.100600i	−0.0117963	+	0.00429351i
$550$		0			0
$551$	11.2867	−	17.6599i	0.480831	−	0.752337i
$552$	−11.7979			−0.502154
$553$	−0.0862049	+	0.0313760i	−0.00366581	+	0.00133424i
$554$	−1.11156	+	6.30396i	−0.0472256	+	0.267830i
$555$		0			0
$556$	−22.9442	−	19.2525i	−0.973051	−	0.816486i
$557$	1.70677	+	9.67955i	0.0723180	+	0.410136i	0.999379	+	0.0352261i	$0.0112151\pi$
$557$	1.70677	+	9.67955i	0.0723180	+	0.410136i	−0.927061	+	0.374910i	$0.877674\pi$
$558$	0.369670	+	0.640287i	0.0156494	+	0.0271055i
$559$	0.260539	−	0.451267i	0.0110196	−	0.0190866i
$560$		0			0
$561$	13.0765	+	4.75946i	0.552090	+	0.200944i
$562$	0.925485	−	1.60299i	0.0390392	−	0.0676179i
$563$	16.7096	+	28.9420i	0.704228	+	1.21976i	0.966970	+	0.254892i	$0.0820398\pi$
$563$	16.7096	+	28.9420i	0.704228	+	1.21976i	−0.262742	+	0.964866i	$0.584627\pi$
$564$	−4.14321	−	23.4973i	−0.174461	−	0.989415i
$565$		0			0
$566$	−2.73065	+	2.29129i	−0.114778	+	0.0963099i
$567$	0.124202	−	0.704384i	0.00521599	−	0.0295814i
$568$	6.98148	−	2.54105i	0.292936	−	0.106620i
$569$	37.6326			1.57764			0.788820	−	0.614624i	$-0.210692\pi$
$569$	37.6326			1.57764			0.788820	+	0.614624i	$0.210692\pi$
$570$		0			0
$571$	−2.75232			−0.115181			−0.0575904	−	0.998340i	$-0.518342\pi$
$571$	−2.75232			−0.115181			−0.0575904	+	0.998340i	$0.518342\pi$
$572$	1.28306	−	0.466997i	0.0536476	−	0.0195261i
$573$	2.26285	−	12.8333i	0.0945319	−	0.536117i
$574$	0.0633924	−	0.0531925i	0.00264595	−	0.00222021i
$575$		0			0
$576$	0.300313	+	1.70316i	0.0125130	+	0.0709649i
$577$	0.0185500	+	0.0321295i	0.000772245	+	0.00133757i	0.866411	−	0.499331i	$-0.166421\pi$
$577$	0.0185500	+	0.0321295i	0.000772245	+	0.00133757i	−0.865639	+	0.500669i	$0.833088\pi$
$578$	1.64445	−	2.84827i	0.0684000	−	0.118472i
$579$	−32.8526	−	11.9574i	−1.36531	−	0.496932i
$580$		0			0
$581$	−0.800032	+	1.38570i	−0.0331909	+	0.0574884i
$582$	4.25629	+	7.37210i	0.176429	+	0.305584i
$583$	−4.91080	−	27.8505i	−0.203385	−	1.15345i
$584$	14.5067	+	12.1725i	0.600291	+	0.503704i
$585$		0			0
$586$	−0.934287	+	5.29861i	−0.0385951	+	0.218883i
$587$	−3.38927	+	1.23359i	−0.139890	+	0.0509158i	−0.411016	−	0.911628i	$-0.634826\pi$
$587$	−3.38927	+	1.23359i	−0.139890	+	0.0509158i	0.271126	+	0.962544i	$0.412604\pi$
$588$	21.8984			0.903074
$589$	−33.5559	+	10.5265i	−1.38265	+	0.433736i
$590$		0			0
$591$	4.46043	−	1.62346i	0.183478	−	0.0667804i
$592$	−1.10130	+	6.24578i	−0.0452632	+	0.256700i
$593$	−13.6689	+	11.4696i	−0.561314	+	0.470998i	−0.878751	−	0.477281i	$-0.841622\pi$
$593$	−13.6689	+	11.4696i	−0.561314	+	0.470998i	0.317437	+	0.948279i	$0.397178\pi$
$594$	4.30604	+	3.61319i	0.176679	+	0.148251i
$595$		0			0
$596$	−18.5936	−	32.2051i	−0.761625	−	1.31917i
$597$	−9.54694	+	16.5358i	−0.390730	+	0.676764i
$598$	0.367612	+	0.133800i	0.0150328	+	0.00547148i
$599$	20.6214	+	7.50558i	0.842568	+	0.306670i	0.727006	−	0.686631i	$-0.240911\pi$
$599$	20.6214	+	7.50558i	0.842568	+	0.306670i	0.115561	+	0.993300i	$0.463133\pi$
$600$		0			0
$601$	−5.14039	−	8.90342i	−0.209681	−	0.363178i	0.741933	−	0.670474i	$-0.233909\pi$
$601$	−5.14039	−	8.90342i	−0.209681	−	0.363178i	−0.951614	+	0.307296i	$0.900576\pi$
$602$	−0.0116772	−	0.0662246i	−0.000475926	−	0.00269911i
$603$	2.27460	+	1.90861i	0.0926288	+	0.0777248i
$604$	−16.3871	+	13.7504i	−0.666780	+	0.559495i
$605$		0			0
$606$	−1.75072	+	0.637208i	−0.0711180	+	0.0258848i
$607$	−32.2616			−1.30946			−0.654729	−	0.755864i	$-0.727217\pi$
$607$	−32.2616			−1.30946			−0.654729	+	0.755864i	$0.727217\pi$
$608$	15.0879	+	0.680743i	0.611893	+	0.0276078i
$609$	0.705034			0.0285694
$610$		0			0
$611$	−0.281607	+	1.59707i	−0.0113926	+	0.0646107i
$612$	1.09175	−	0.916086i	0.0441313	−	0.0370306i
$613$	12.5598	+	10.5389i	0.507286	+	0.425664i	0.860173	−	0.510002i	$-0.170355\pi$
$613$	12.5598	+	10.5389i	0.507286	+	0.425664i	−0.352887	+	0.935666i	$0.614800\pi$
$614$	−1.58591	−	8.99412i	−0.0640019	−	0.362973i
$615$		0			0
$616$	0.180595	−	0.312800i	0.00727639	−	0.0126031i
$617$	−12.0063	−	4.36994i	−0.483356	−	0.175927i	0.0888371	−	0.996046i	$-0.471685\pi$
$617$	−12.0063	−	4.36994i	−0.483356	−	0.175927i	−0.572193	+	0.820119i	$0.693907\pi$
$618$	−1.68148	−	0.612008i	−0.0676390	−	0.0246186i
$619$	−2.14103	+	3.70838i	−0.0860555	+	0.149052i	−0.905840	−	0.423619i	$-0.860760\pi$
$619$	−2.14103	+	3.70838i	−0.0860555	+	0.149052i	0.819785	+	0.572671i	$0.194093\pi$
$620$		0			0
$621$	−5.61687	−	31.8549i	−0.225397	−	1.27829i
$622$	−2.74210	−	2.30089i	−0.109948	−	0.0922575i
$623$	−0.0448474	+	0.0376314i	−0.00179677	+	0.00150767i
$624$	−0.209028	+	1.18546i	−0.00836783	+	0.0474563i
$625$		0			0
$626$	0.146252			0.00584542
$627$	−19.1614	+	14.6588i	−0.765234	+	0.585418i
$628$	8.78807			0.350682
$629$	4.35599	−	1.58545i	0.173685	−	0.0632160i
$630$		0			0
$631$	−17.4565	+	14.6477i	−0.694933	+	0.583118i	−0.920327	−	0.391150i	$-0.872077\pi$
$631$	−17.4565	+	14.6477i	−0.694933	+	0.583118i	0.225394	+	0.974268i	$0.427633\pi$
$632$	0.947603	+	0.795133i	0.0376936	+	0.0316287i
$633$	−6.76550	−	38.3690i	−0.268904	−	1.52503i
$634$	−3.11503	−	5.39540i	−0.123714	−	0.214279i
$635$		0			0
$636$	24.7204	+	8.99749i	0.980228	+	0.356774i
$637$	−1.39863	−	0.509061i	−0.0554159	−	0.0201698i
$638$	−2.49293	+	4.31788i	−0.0986959	+	0.170946i
$639$	0.918959	+	1.59168i	0.0363535	+	0.0629661i
$640$		0			0
$641$	−24.0251	−	20.1595i	−0.948935	−	0.796251i	0.0301829	−	0.999544i	$-0.490391\pi$
$641$	−24.0251	−	20.1595i	−0.948935	−	0.796251i	−0.979118	+	0.203293i	$0.934835\pi$
$642$	0.731726	−	0.613991i	0.0288789	−	0.0242323i
$643$	1.93601	−	10.9796i	0.0763487	−	0.432995i	−0.922542	−	0.385898i	$-0.873892\pi$
$643$	1.93601	−	10.9796i	0.0763487	−	0.432995i	0.998890	−	0.0470972i	$-0.0149971\pi$
$644$	−0.952825	+	0.346800i	−0.0375466	+	0.0136658i
$645$		0			0
$646$	−1.55420	−	2.99622i	−0.0611491	−	0.117885i
$647$	17.5536			0.690102			0.345051	−	0.938584i	$-0.387862\pi$
$647$	17.5536			0.690102			0.345051	+	0.938584i	$0.387862\pi$
$648$	−9.06297	+	3.29865i	−0.356027	+	0.129583i
$649$	−6.10100	+	34.6005i	−0.239485	+	1.35819i
$650$		0			0
$651$	−0.906260	−	0.760443i	−0.0355191	−	0.0298041i
$652$	−0.190136	−	1.07832i	−0.00744632	−	0.0422302i
$653$	−1.04766	−	1.81461i	−0.0409983	−	0.0710111i	0.844798	−	0.535085i	$-0.179720\pi$
$653$	−1.04766	−	1.81461i	−0.0409983	−	0.0710111i	−0.885796	+	0.464074i	$0.846387\pi$
$654$	3.33147	−	5.77028i	0.130271	−	0.225636i
$655$		0			0
$656$	9.73711	+	3.54402i	0.380170	+	0.138371i
$657$	−2.34233	+	4.05704i	−0.0913831	+	0.158280i
$658$	0.104642	+	0.181246i	0.00407939	+	0.00706571i
$659$	−2.25744	−	12.8026i	−0.0879373	−	0.498717i	−0.996684	−	0.0813691i	$-0.974071\pi$
$659$	−2.25744	−	12.8026i	−0.0879373	−	0.498717i	0.908747	−	0.417348i	$-0.137040\pi$
$660$		0			0
$661$	29.1833	−	24.4877i	1.13510	−	0.952462i	0.135833	−	0.990732i	$-0.456629\pi$
$661$	29.1833	−	24.4877i	1.13510	−	0.952462i	0.999267	+	0.0382694i	$0.0121845\pi$
$662$	−0.321588	+	1.82382i	−0.0124989	+	0.0708846i
$663$	0.826772	−	0.300920i	0.0321092	−	0.0116868i
$664$	21.5756			0.837298
$665$		0			0
$666$	0.168953			0.00654678
$667$	26.9604	−	9.81278i	1.04391	−	0.379952i
$668$	1.36367	−	7.73373i	0.0527618	−	0.299227i
$669$	11.1019	−	9.31564i	0.429226	−	0.360163i
$670$		0			0
$671$	0.577966	+	3.27781i	0.0223121	+	0.126538i
$672$	0.254031	+	0.439995i	0.00979947	+	0.0169732i
$673$	16.9749	−	29.4013i	0.654333	−	1.13334i	−0.327728	−	0.944772i	$-0.606283\pi$
$673$	16.9749	−	29.4013i	0.654333	−	1.13334i	0.982061	−	0.188566i	$-0.0603838\pi$
$674$	−2.56633	−	0.934069i	−0.0988514	−	0.0359790i
$675$		0			0
$676$	−12.3403	+	21.3740i	−0.474626	+	0.822076i
$677$	−8.27810	−	14.3381i	−0.318153	−	0.551058i	0.661949	−	0.749549i	$-0.269729\pi$
$677$	−8.27810	−	14.3381i	−0.318153	−	0.551058i	−0.980103	+	0.198491i	$0.936396\pi$
$678$	−1.08542	−	6.15572i	−0.0416853	−	0.236409i
$679$	1.14880	+	0.963959i	0.0440870	+	0.0369934i
$680$		0			0
$681$	0.298344	−	1.69199i	0.0114326	−	0.0648372i
$682$	7.86166	−	2.86141i	0.301038	−	0.109569i
$683$	−5.33328			−0.204072			−0.102036	−	0.994781i	$-0.532536\pi$
$683$	−5.33328			−0.204072			−0.102036	+	0.994781i	$0.532536\pi$
$684$	0.318942	+	2.45014i	0.0121950	+	0.0936835i
$685$		0			0
$686$	−0.361199	+	0.131466i	−0.0137906	+	0.00501938i
$687$	−3.84911	+	21.8294i	−0.146853	+	0.832844i
$688$	6.45035	−	5.41248i	0.245917	−	0.206349i
$689$	−1.36972	−	1.14933i	−0.0521820	−	0.0437859i
$690$		0			0
$691$	7.06510	+	12.2371i	0.268769	+	0.465522i	0.968544	−	0.248842i	$-0.0800498\pi$
$691$	7.06510	+	12.2371i	0.268769	+	0.465522i	−0.699775	+	0.714363i	$0.746717\pi$
$692$	6.12940	−	10.6164i	0.233005	−	0.403576i
$693$	0.0839627	+	0.0305599i	0.00318948	+	0.00116088i
$694$	5.77995	+	2.10373i	0.219404	+	0.0798565i
$695$		0			0
$696$	−4.75342	−	8.23317i	−0.180178	−	0.312078i
$697$	−1.31516	−	7.45866i	−0.0498153	−	0.282517i
$698$	−0.191156	−	0.160399i	−0.00723536	−	0.00607119i
$699$	−14.1268	+	11.8538i	−0.534324	+	0.448351i
$700$		0			0
$701$	35.8607	−	13.0522i	1.35444	−	0.492976i	0.440110	−	0.897944i	$-0.354939\pi$
$701$	35.8607	−	13.0522i	1.35444	−	0.492976i	0.914331	+	0.404967i	$0.132717\pi$
$702$	0.355400			0.0134137
$703$	−1.75085	+	7.84355i	−0.0660345	+	0.295825i
$704$	19.5699			0.737567
$705$		0			0
$706$	1.12046	−	6.35442i	0.0421689	−	0.239152i
$707$	−0.251428	+	0.210973i	−0.00945594	+	0.00793447i
$708$	−25.0364	−	21.0080i	−0.940926	−	0.789531i
$709$	5.75948	+	32.6636i	0.216302	+	1.22671i	0.878633	+	0.477497i	$0.158456\pi$
$709$	5.75948	+	32.6636i	0.216302	+	1.22671i	−0.662331	+	0.749211i	$0.730433\pi$
$710$		0			0
$711$	−0.153005	+	0.265013i	−0.00573815	+	0.00993878i
$712$	0.741814	+	0.269998i	0.0278007	+	0.0101186i
$713$	−45.2392	−	16.4657i	−1.69422	−	0.616646i
$714$	0.0567721	−	0.0983321i	0.00212464	−	0.00367999i
$715$		0			0
$716$	−1.26716	−	7.18644i	−0.0473561	−	0.268570i
$717$	−25.6006	−	21.4814i	−0.956072	−	0.802239i
$718$	6.06391	−	5.08822i	0.226303	−	0.189891i
$719$	7.35244	−	41.6978i	0.274200	−	1.55506i	−0.467292	−	0.884103i	$-0.654770\pi$
$719$	7.35244	−	41.6978i	0.274200	−	1.55506i	0.741492	−	0.670962i	$-0.234119\pi$
$720$		0			0
$721$	−0.315236			−0.0117400
$722$	5.82800	+	0.526975i	0.216896	+	0.0196120i
$723$	−6.32007			−0.235046
$724$	29.8752	−	10.8737i	1.11030	−	0.404118i
$725$		0			0
$726$	0.130121	−	0.109184i	0.00482923	−	0.00405221i
$727$	3.21863	+	2.70075i	0.119372	+	0.100165i	0.700520	−	0.713633i	$-0.252952\pi$
$727$	3.21863	+	2.70075i	0.119372	+	0.100165i	−0.581147	+	0.813798i	$0.697396\pi$
$728$	−0.00396552	−	0.0224896i	−0.000146972	−	0.000833520i
$729$	−14.5602	−	25.2189i	−0.539265	−	0.934034i
$730$		0			0
$731$	−5.78336	−	2.10497i	−0.213905	−	0.0778551i
$732$	−2.90941	−	1.05894i	−0.107535	−	0.0391395i
$733$	8.46787	−	14.6668i	0.312768	−	0.541730i	−0.666193	−	0.745780i	$-0.732077\pi$
$733$	8.46787	−	14.6668i	0.312768	−	0.541730i	0.978960	+	0.204050i	$0.0654105\pi$
$734$	−3.73990	−	6.47769i	−0.138042	−	0.239096i
$735$		0			0
$736$	15.8380	+	13.2897i	0.583798	+	0.489864i
$737$	25.7388	−	21.5975i	0.948103	−	0.795553i
$738$	0.0479340	−	0.271847i	0.00176448	−	0.0100068i
$739$	−19.5893	+	7.12993i	−0.720605	+	0.262279i	−0.676183	−	0.736734i	$-0.736367\pi$
$739$	−19.5893	+	7.12993i	−0.720605	+	0.262279i	−0.0444223	+	0.999013i	$0.514145\pi$
$740$		0			0
$741$	−0.332314	+	1.48872i	−0.0122079	+	0.0546894i
$742$	−0.230750			−0.00847109
$743$	42.6150	−	15.5106i	1.56339	−	0.569028i	0.591881	−	0.806025i	$-0.298385\pi$
$743$	42.6150	−	15.5106i	1.56339	−	0.569028i	0.971510	+	0.236997i	$0.0761633\pi$
$744$	−2.77010	+	15.7100i	−0.101557	+	0.575957i
$745$		0			0
$746$	−2.56715	−	2.15410i	−0.0939901	−	0.0788671i
$747$	0.926827	+	5.25630i	0.0339108	+	0.192318i
$748$	−8.06349	−	13.9664i	−0.294831	−	0.510661i
$749$	0.0841385	−	0.145732i	0.00307435	−	0.00532494i
$750$		0			0
$751$	8.15355	+	2.96765i	0.297527	+	0.108291i	0.486471	−	0.873697i	$-0.338284\pi$
$751$	8.15355	+	2.96765i	0.297527	+	0.108291i	−0.188943	+	0.981988i	$0.560506\pi$
$752$	−13.1030	+	22.6950i	−0.477816	+	0.827601i
$753$	6.52451	+	11.3008i	0.237767	+	0.411824i
$754$	0.0547399	+	0.310445i	0.00199351	+	0.0113058i
$755$		0			0
$756$	−0.705661	+	0.592119i	−0.0256646	+	0.0215352i
$757$	−1.74973	+	9.92320i	−0.0635950	+	0.360665i	0.936359	+	0.351045i	$0.114173\pi$
$757$	−1.74973	+	9.92320i	−0.0635950	+	0.360665i	−0.999954	+	0.00962040i	$0.996938\pi$
$758$	−5.59490	+	2.03638i	−0.203216	+	0.0739645i
$759$	−33.0259			−1.19877
$760$		0			0
$761$	4.52014			0.163855			0.0819275	−	0.996638i	$-0.473892\pi$
$761$	4.52014			0.163855			0.0819275	+	0.996638i	$0.473892\pi$
$762$	10.0921	−	3.67324i	0.365600	−	0.133067i
$763$	0.203829	−	1.15597i	0.00737912	−	0.0418491i
$764$	−11.5688	+	9.70735i	−0.418543	+	0.351200i
$765$		0			0
$766$	0.0557839	+	0.316366i	0.00201556	+	0.0114308i
$767$	1.11070	+	1.92378i	0.0401049	+	0.0694637i
$768$	−7.34787	+	12.7269i	−0.265143	+	0.459242i
$769$	37.1897	+	13.5360i	1.34110	+	0.488119i	0.910158	−	0.414262i	$-0.135960\pi$
$769$	37.1897	+	13.5360i	1.34110	+	0.488119i	0.430939	+	0.902381i	$0.358182\pi$
$770$		0			0
$771$	19.9142	−	34.4924i	0.717193	−	1.24221i
$772$	20.2582	+	35.0883i	0.729110	+	1.26286i
$773$	4.08049	+	23.1416i	0.146765	+	0.832347i	0.965933	+	0.258793i	$0.0833246\pi$
$773$	4.08049	+	23.1416i	0.146765	+	0.832347i	−0.819168	+	0.573554i	$0.805564\pi$
$774$	−0.171835	−	0.144187i	−0.00617649	−	0.00518269i
$775$		0			0
$776$	3.51146	−	19.9145i	0.126054	−	0.714888i
$777$	−0.254042	+	0.0924638i	−0.00911372	+	0.00331712i
$778$	8.19345			0.293749
$779$	12.1237	+	5.04246i	0.434375	+	0.180665i
$780$		0			0
$781$	19.5432	−	7.11316i	0.699312	−	0.254529i
$782$	0.802352	−	4.55036i	0.0286920	−	0.162721i
$783$	19.9668	−	16.7541i	0.713555	−	0.598744i
$784$	−18.4246	−	15.4601i	−0.658022	−	0.552146i
$785$		0			0
$786$	−1.75961	−	3.04773i	−0.0627631	−	0.108709i
$787$	3.76242	−	6.51669i	0.134116	−	0.232295i	−0.791144	−	0.611630i	$-0.790514\pi$
$787$	3.76242	−	6.51669i	0.134116	−	0.232295i	0.925259	+	0.379335i	$0.123847\pi$
$788$	−5.16921	−	1.88144i	−0.184145	−	0.0670235i
$789$	−19.1200	−	6.95913i	−0.680692	−	0.247751i
$790$		0			0
$791$	−0.550589	−	0.953649i	−0.0195767	−	0.0339078i
$792$	−0.209217	−	1.18653i	−0.00743421	−	0.0421615i
$793$	0.161206	+	0.135268i	0.00572458	+	0.00480349i
$794$	0.872376	−	0.732010i	0.0309595	−	0.0259781i
$795$		0			0
$796$	20.7935	−	7.56821i	0.737006	−	0.268248i
$797$	18.7858			0.665426			0.332713	−	0.943028i	$-0.392036\pi$
$797$	18.7858			0.665426			0.332713	+	0.943028i	$0.392036\pi$
$798$	0.0906412	+	0.174740i	0.00320866	+	0.00618574i
$799$	19.1542			0.677627
$800$		0			0
$801$	−0.0339113	+	0.192320i	−0.00119820	+	0.00679531i
$802$	−4.77411	+	4.00596i	−0.168580	+	0.141455i
$803$	40.6085	+	34.0746i	1.43304	+	1.20247i
$804$	5.42742	+	30.7804i	0.191410	+	1.08554i
$805$		0			0
$806$	0.264480	−	0.458092i	0.00931590	−	0.0161356i
$807$	37.6599	+	13.7071i	1.32569	+	0.482512i
$808$	4.15884	+	1.51369i	0.146308	+	0.0532516i
$809$	9.74651	−	16.8815i	0.342669	−	0.593520i	−0.642258	−	0.766488i	$-0.722002\pi$
$809$	9.74651	−	16.8815i	0.342669	−	0.593520i	0.984927	+	0.172968i	$0.0553357\pi$
$810$		0			0
$811$	2.64049	+	14.9750i	0.0927201	+	0.525842i	0.995422	+	0.0955756i	$0.0304692\pi$
$811$	2.64049	+	14.9750i	0.0927201	+	0.525842i	−0.902702	+	0.430266i	$0.858420\pi$
$812$	−0.625910	−	0.525201i	−0.0219651	−	0.0184309i
$813$	21.9351	−	18.4057i	0.769297	−	0.645517i
$814$	0.331986	−	1.88279i	0.0116361	−	0.0659916i
$815$		0			0
$816$	14.2176			0.497715
$817$	8.47454	−	6.48318i	0.296487	−	0.226818i
$818$	3.84272			0.134357
$819$	0.00530861	−	0.00193218i	0.000185498	−	6.75157e-5i
$820$		0			0
$821$	−20.5043	+	17.2051i	−0.715604	+	0.600463i	−0.926165	−	0.377118i	$-0.876915\pi$
$821$	−20.5043	+	17.2051i	−0.715604	+	0.600463i	0.210562	+	0.977581i	$0.432471\pi$
$822$	−8.14759	−	6.83664i	−0.284180	−	0.238455i
$823$	−4.80109	−	27.2284i	−0.167356	−	0.949121i	−0.946602	−	0.322404i	$-0.895509\pi$
$823$	−4.80109	−	27.2284i	−0.167356	−	0.949121i	0.779247	−	0.626717i	$-0.215602\pi$
$824$	2.12536	+	3.68123i	0.0740404	+	0.128242i
$825$		0			0
$826$	0.269386	+	0.0980486i	0.00937314	+	0.00341155i
$827$	12.0489	+	4.38543i	0.418980	+	0.152496i	0.542903	−	0.839796i	$-0.317325\pi$
$827$	12.0489	+	4.38543i	0.418980	+	0.152496i	−0.123923	+	0.992292i	$0.539547\pi$
$828$	−1.69117	+	2.92920i	−0.0587724	+	0.101797i
$829$	−22.7266	−	39.3636i	−0.789326	−	1.36715i	−0.926380	−	0.376590i	$-0.877097\pi$
$829$	−22.7266	−	39.3636i	−0.789326	−	1.36715i	0.137054	−	0.990564i	$-0.456237\pi$
$830$		0			0
$831$	−26.1735	−	21.9622i	−0.907949	−	0.761860i
$832$	0.947842	−	0.795334i	0.0328605	−	0.0275732i
$833$	−3.05267	+	17.3126i	−0.105769	+	0.599844i
$834$	−7.47983	+	2.72243i	−0.259005	+	0.0942702i
$835$		0			0
$836$	27.9308	+	1.26020i	0.966006	+	0.0435849i
$837$	−43.7364			−1.51175
$838$	−8.39192	+	3.05441i	−0.289894	+	0.105513i
$839$	4.04829	−	22.9590i	0.139762	−	0.792632i	−0.831662	−	0.555282i	$-0.812610\pi$
$839$	4.04829	−	22.9590i	0.139762	−	0.792632i	0.971424	−	0.237350i	$-0.0762787\pi$
$840$		0			0
$841$	−4.50505	−	3.78019i	−0.155347	−	0.130351i
$842$	0.780620	+	4.42712i	0.0269019	+	0.152569i
$843$	4.93987	+	8.55610i	0.170138	+	0.294688i
$844$	−22.5760	+	39.1028i	−0.777098	+	1.34597i
$845$		0			0
$846$	0.656016	+	0.238770i	0.0225543	+	0.00820909i
$847$	0.0149621	−	0.0259151i	0.000514104	−	0.000890455i
$848$	−14.4468	−	25.0226i	−0.496106	−	0.859281i
$849$	−3.30391	−	18.7374i	−0.113390	−	0.643066i
$850$		0			0
$851$	−8.42760	+	7.07160i	−0.288894	+	0.242411i
$852$	−3.35945	+	19.0524i	−0.115093	+	0.652725i
$853$	−43.0221	+	15.6588i	−1.47305	+	0.536146i	−0.948927	−	0.315497i	$-0.897829\pi$
$853$	−43.0221	+	15.6588i	−1.47305	+	0.536146i	−0.524122	+	0.851643i	$0.675607\pi$
$854$	0.0271576			0.000929312
$855$		0			0
$856$	−2.26909			−0.0775558
$857$	6.06004	−	2.20568i	0.207007	−	0.0753444i	−0.236436	−	0.971647i	$-0.575979\pi$
$857$	6.06004	−	2.20568i	0.207007	−	0.0753444i	0.443443	+	0.896303i	$0.353757\pi$
$858$	0.0630114	−	0.357355i	0.00215117	−	0.0121999i
$859$	−11.1359	+	9.34415i	−0.379953	+	0.318818i	−0.812684	−	0.582705i	$-0.801994\pi$
$859$	−11.1359	+	9.34415i	−0.379953	+	0.318818i	0.432731	+	0.901523i	$0.357550\pi$
$860$		0			0
$861$	0.0767007	+	0.434991i	0.00261395	+	0.0148245i
$862$	−2.08017	−	3.60296i	−0.0708509	−	0.122717i
$863$	−2.28568	+	3.95891i	−0.0778054	+	0.134763i	−0.902303	−	0.431103i	$-0.858125\pi$
$863$	−2.28568	+	3.95891i	−0.0778054	+	0.134763i	0.824497	+	0.565866i	$0.191458\pi$
$864$	17.6501	+	6.42412i	0.600469	+	0.218553i
$865$		0			0
$866$	5.85494	−	10.1411i	0.198959	−	0.344607i
$867$	8.77740	+	15.2029i	0.298096	+	0.516318i
$868$	0.238077	+	1.35020i	0.00808085	+	0.0458288i
$869$	2.65262	+	2.22581i	0.0899841	+	0.0755056i
$870$		0			0
$871$	0.368892	−	2.09209i	0.0124994	−	0.0708879i
$872$	−14.8733	+	5.41346i	−0.503675	+	0.183323i
$873$	5.00244			0.169307
$874$	5.89817	+	5.42048i	0.199508	+	0.183351i
$875$		0			0
$876$	−46.3379	+	16.8656i	−1.56561	+	0.569836i
$877$	−5.72291	+	32.4562i	−0.193249	+	1.09597i	0.721641	+	0.692267i	$0.243388\pi$
$877$	−5.72291	+	32.4562i	−0.193249	+	1.09597i	−0.914890	+	0.403702i	$0.867723\pi$
$878$	−5.61213	+	4.70913i	−0.189400	+	0.158926i
$879$	−21.9994	−	18.4597i	−0.742020	−	0.622629i
$880$		0			0
$881$	8.12066	+	14.0654i	0.273592	+	0.473875i	0.969779	−	0.243985i	$-0.0784549\pi$
$881$	8.12066	+	14.0654i	0.273592	+	0.473875i	−0.696187	+	0.717860i	$0.745122\pi$
$882$	−0.320364	+	0.554887i	−0.0107872	+	0.0186840i
$883$	−26.7945	−	9.75238i	−0.901705	−	0.328194i	−0.150769	−	0.988569i	$-0.548175\pi$
$883$	−26.7945	−	9.75238i	−0.901705	−	0.328194i	−0.750936	+	0.660375i	$0.770397\pi$
$884$	−0.958150	−	0.348738i	−0.0322261	−	0.0117293i
$885$		0			0
$886$	−2.97195	−	5.14757i	−0.0998447	−	0.172936i
$887$	−6.70894	−	38.0483i	−0.225264	−	1.27754i	−0.862180	−	0.506602i	$-0.830901\pi$
$887$	−6.70894	−	38.0483i	−0.225264	−	1.27754i	0.636916	−	0.770933i	$-0.280210\pi$
$888$	2.79255	+	2.34322i	0.0937117	+	0.0786335i
$889$	1.44938	−	1.21617i	0.0486106	−	0.0407891i
$890$		0			0
$891$	−25.3699	+	9.23390i	−0.849925	+	0.309347i
$892$	−16.7955			−0.562355
$893$	−17.8831	+	27.9809i	−0.598435	+	0.936345i
$894$	−9.88282			−0.330531
$895$		0			0
$896$	0.135062	−	0.765974i	0.00451210	−	0.0255894i
$897$	−1.59957	+	1.34220i	−0.0534081	+	0.0448147i
$898$	−6.23184	−	5.22913i	−0.207959	−	0.174498i
$899$	−6.73642	−	38.2042i	−0.224672	−	1.27418i
$900$		0			0
$901$	−10.5594	+	18.2893i	−0.351783	+	0.609306i
$902$	−2.93524	−	1.06834i	−0.0977329	−	0.0355719i
$903$	0.337287	+	0.122762i	0.0112242	+	0.00408528i
$904$	−7.42428	+	12.8592i	−0.246928	+	0.427691i
$905$		0			0
$906$	0.987198	+	5.59868i	0.0327975	+	0.186004i
$907$	−21.9521	−	18.4200i	−0.728908	−	0.611627i	0.200926	−	0.979606i	$-0.435605\pi$
$907$	−21.9521	−	18.4200i	−0.728908	−	0.611627i	−0.929834	+	0.367980i	$0.880049\pi$
$908$	−1.52527	+	1.27986i	−0.0506180	+	0.0424735i
$909$	−0.190117	+	1.07821i	−0.00630579	+	0.0357619i
$910$		0			0
$911$	−47.5952			−1.57690			−0.788450	−	0.615099i	$-0.789116\pi$
$911$	−47.5952			−1.57690			−0.788450	+	0.615099i	$0.789116\pi$
$912$	−13.2741	+	20.7694i	−0.439548	+	0.687743i
$913$	60.3966			1.99884
$914$	−11.1321	+	4.05174i	−0.368216	+	0.134020i
$915$		0			0
$916$	19.6785	−	16.5122i	0.650196	−	0.545579i
$917$	−0.474930	−	0.398514i	−0.0156836	−	0.0131601i
$918$	−0.728919	−	4.13391i	−0.0240579	−	0.136439i
$919$	13.6098	+	23.5728i	0.448945	+	0.777596i	0.998318	−	0.0579814i	$-0.0184664\pi$
$919$	13.6098	+	23.5728i	0.448945	+	0.777596i	−0.549372	+	0.835578i	$0.685133\pi$
$920$		0			0
$921$	45.8077	+	16.6727i	1.50942	+	0.549383i
$922$	−9.83534	−	3.57977i	−0.323910	−	0.117894i
$923$	0.657469	−	1.13877i	0.0216408	−	0.0374830i
$924$	0.470265	+	0.814523i	0.0154706	+	0.0267958i
$925$		0			0
$926$	1.27273	+	1.06795i	0.0418245	+	0.0350949i
$927$	−0.805528	+	0.675919i	−0.0264570	+	0.0222001i
$928$	−2.89300	+	16.4070i	−0.0949672	+	0.538586i
$929$	30.2956	−	11.0267i	0.993967	−	0.361774i	0.206712	−	0.978402i	$-0.433724\pi$
$929$	30.2956	−	11.0267i	0.993967	−	0.361774i	0.787255	+	0.616627i	$0.211501\pi$
$930$		0			0
$931$	−22.4405	−	20.6230i	−0.735457	−	0.675893i
$932$	21.3716			0.700049
$933$	17.9540	−	6.53472i	0.587787	−	0.213937i
$934$	−1.19953	+	6.80288i	−0.0392499	+	0.222597i
$935$		0			0
$936$	−0.0583546	−	0.0489653i	−0.00190738	−	0.00160048i
$937$	−3.15561	−	17.8964i	−0.103089	−	0.584649i	−0.991966	−	0.126503i	$-0.959625\pi$
$937$	−3.15561	−	17.8964i	−0.103089	−	0.584649i	0.888877	−	0.458146i	$-0.151486\pi$
$938$	−0.137077	−	0.237424i	−0.00447572	−	0.00775217i
$939$	−0.390318	+	0.676051i	−0.0127376	+	0.0220621i
$940$		0			0
$941$	−22.1364	−	8.05700i	−0.721627	−	0.262651i	−0.0450107	−	0.998987i	$-0.514332\pi$
$941$	−22.1364	−	8.05700i	−0.721627	−	0.262651i	−0.676616	+	0.736336i	$0.736554\pi$
$942$	1.16775	−	2.02260i	0.0380474	−	0.0659000i
$943$	8.98729	+	15.5664i	0.292666	+	0.506913i
$944$	6.23334	+	35.3510i	0.202878	+	1.15058i
$945$		0			0
$946$	−1.94445	+	1.63159i	−0.0632195	+	0.0530475i
$947$	1.46413	−	8.30348i	0.0475777	−	0.269827i	−0.951734	−	0.306924i	$-0.900700\pi$
$947$	1.46413	−	8.30348i	0.0475777	−	0.269827i	0.999312	+	0.0370976i	$0.0118113\pi$
$948$	−3.02688	+	1.10169i	−0.0983084	+	0.0357813i
$949$	3.35164			0.108799
$950$		0			0
$951$	33.2536			1.07832
$952$	−0.253459	+	0.0922515i	−0.00821465	+	0.00298989i
$953$	−8.69527	+	49.3134i	−0.281668	+	1.59742i	0.435284	+	0.900293i	$0.356648\pi$
$953$	−8.69527	+	49.3134i	−0.281668	+	1.59742i	−0.716952	+	0.697123i	$0.754463\pi$
$954$	−0.589639	+	0.494766i	−0.0190903	+	0.0160186i
$955$		0			0
$956$	6.72533	+	38.1413i	0.217513	+	1.23358i
$957$	−13.3062	−	23.0471i	−0.430130	−	0.745007i
$958$	4.42589	−	7.66587i	0.142994	−	0.247673i
$959$	−1.76072	−	0.640851i	−0.0568568	−	0.0206942i
$960$		0			0
$961$	−17.0475	+	29.5272i	−0.549920	+	0.952489i
$962$	−0.0604385	−	0.104683i	−0.00194862	−	0.00337510i
$963$	−0.0974734	−	0.552799i	−0.00314104	−	0.0178137i
$964$	5.61078	+	4.70801i	0.180711	+	0.151635i
$965$		0			0
$966$	−0.0467934	+	0.265378i	−0.00150555	+	0.00853841i
$967$	−5.64610	+	2.05501i	−0.181566	+	0.0660847i	−0.431203	−	0.902255i	$-0.641911\pi$
$967$	−5.64610	+	2.05501i	−0.181566	+	0.0660847i	0.249637	+	0.968339i	$0.419689\pi$
$968$	−0.403505			−0.0129692
$969$	17.9979	+	0.812039i	0.578175	+	0.0260864i
$970$		0			0
$971$	−33.8031	+	12.3033i	−1.08479	+	0.394832i	−0.821689	−	0.569936i	$-0.806968\pi$
$971$	−33.8031	+	12.3033i	−1.08479	+	0.394832i	−0.263103	+	0.964768i	$0.584746\pi$
$972$	−1.01902	+	5.77917i	−0.0326852	+	0.185367i
$973$	−1.07421	+	0.901371i	−0.0344377	+	0.0288966i
$974$	8.12650	+	6.81894i	0.260390	+	0.218493i
$975$		0			0
$976$	1.70029	+	2.94498i	0.0544248	+	0.0942666i
$977$	16.8174	−	29.1285i	0.538035	−	0.931905i	−0.460974	−	0.887413i	$-0.652500\pi$
$977$	16.8174	−	29.1285i	0.538035	−	0.931905i	0.999010	−	0.0444913i	$-0.0141667\pi$
$978$	−0.273444	−	0.0995253i	−0.00874376	−	0.00318247i
$979$	2.07656	+	0.755805i	0.0663671	+	0.0241556i
$980$		0			0
$981$	−1.95775	−	3.39092i	−0.0625062	−	0.108264i
$982$	−1.03681	−	5.88002i	−0.0330858	−	0.187639i
$983$	−34.5023	−	28.9508i	−1.10045	−	0.923388i	−0.102996	−	0.994682i	$-0.532843\pi$
$983$	−34.5023	−	28.9508i	−1.10045	−	0.923388i	−0.997455	+	0.0712938i	$0.977287\pi$
$984$	4.56257	−	3.82845i	0.145449	−	0.122046i
$985$		0			0
$986$	3.49873	−	1.27343i	0.111422	−	0.0405544i
$987$	−1.11708			−0.0355570
$988$	1.40401	−	1.07409i	0.0446674	−	0.0341714i
$989$	14.6064			0.464457
$990$		0			0
$991$	−1.06445	+	6.03681i	−0.0338134	+	0.191765i	−0.997036	−	0.0769404i	$-0.975485\pi$
$991$	−1.06445	+	6.03681i	−0.0338134	+	0.191765i	0.963222	+	0.268706i	$0.0865960\pi$
$992$	21.4151	−	17.9694i	0.679930	−	0.570529i
$993$	−7.57233	−	6.35394i	−0.240301	−	0.201636i
$994$	−0.0294673	−	0.167117i	−0.000934645	−	0.00530064i
$995$		0			0
$996$	−28.0912	+	48.6554i	−0.890104	+	1.54171i
$997$	−42.2085	−	15.3626i	−1.33676	−	0.486539i	−0.427967	−	0.903795i	$-0.640770\pi$
$997$	−42.2085	−	15.3626i	−1.33676	−	0.486539i	−0.908789	+	0.417255i	$0.862992\pi$
$998$	−3.26125	−	1.18700i	−0.103233	−	0.0375738i
$999$	−4.99729	+	8.65556i	−0.158107	+	0.273850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.176.1		18
5.2	odd	4		475.2.u.b.24.3		36
5.3	odd	4		475.2.u.b.24.4		36
5.4	even	2		95.2.k.a.81.3	yes	18
15.14	odd	2		855.2.bs.c.271.1		18
19.2	odd	18		9025.2.a.cf.1.3		9
19.4	even	9	inner	475.2.l.c.251.1		18
19.17	even	9		9025.2.a.cc.1.7		9
95.4	even	18		95.2.k.a.61.3	✓	18
95.23	odd	36		475.2.u.b.99.3		36
95.42	odd	36		475.2.u.b.99.4		36
95.59	odd	18		1805.2.a.s.1.7		9
95.74	even	18		1805.2.a.v.1.3		9
285.194	odd	18		855.2.bs.c.631.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.3	✓	18	95.4	even	18
95.2.k.a.81.3	yes	18	5.4	even	2
475.2.l.c.176.1		18	1.1	even	1	trivial
475.2.l.c.251.1		18	19.4	even	9	inner
475.2.u.b.24.3		36	5.2	odd	4
475.2.u.b.24.4		36	5.3	odd	4
475.2.u.b.99.3		36	95.23	odd	36
475.2.u.b.99.4		36	95.42	odd	36
855.2.bs.c.271.1		18	15.14	odd	2
855.2.bs.c.631.1		18	285.194	odd	18
1805.2.a.s.1.7		9	95.59	odd	18
1805.2.a.v.1.3		9	95.74	even	18
9025.2.a.cc.1.7		9	19.17	even	9
9025.2.a.cf.1.3		9	19.2	odd	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.289414 + 0.105338i) q^{2} +(0.285463 - 1.61894i) q^{3} +(-1.45942 + 1.22460i) q^{4} +(0.0879194 + 0.498616i) q^{6} +(0.0445979 + 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +(0.279590 + 0.101762i) q^{9} +O(q^{10})\)	\(q+(-0.289414 + 0.105338i) q^{2} +(0.285463 - 1.61894i) q^{3} +(-1.45942 + 1.22460i) q^{4} +(0.0879194 + 0.498616i) q^{6} +(0.0445979 + 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +(0.279590 + 0.101762i) q^{9} +(1.68341 - 2.91575i) q^{11} +(1.56595 + 2.71230i) q^{12} +(-0.0369645 - 0.209636i) q^{13} +(-0.0210442 - 0.0176582i) q^{14} +(0.597325 - 3.38760i) q^{16} +(-2.36261 + 0.859918i) q^{17} -0.0916368 q^{18} +(0.949628 - 4.25420i) q^{19} +(0.137788 - 0.0501507i) q^{21} +(-0.180063 + 1.02119i) q^{22} +(4.57098 - 3.83550i) q^{23} +(-1.51463 - 1.27092i) q^{24} +(0.0327807 + 0.0567779i) q^{26} +(2.71044 - 4.69462i) q^{27} +(-0.159683 - 0.0581198i) q^{28} +(4.51826 + 1.64451i) q^{29} +(-4.03407 - 6.98722i) q^{31} +(0.601676 + 3.41227i) q^{32} +(-4.23989 - 3.55769i) q^{33} +(0.593190 - 0.497745i) q^{34} +(-0.532659 + 0.193872i) q^{36} -1.84372 q^{37} +(0.173294 + 1.33126i) q^{38} -0.349941 q^{39} +(-0.523087 + 2.96657i) q^{41} +(-0.0345950 + 0.0290286i) q^{42} +(1.87518 + 1.57346i) q^{43} +(1.11383 + 6.31683i) q^{44} +(-0.918881 + 1.59155i) q^{46} +(-7.15887 - 2.60562i) q^{47} +(-5.31381 - 1.93407i) q^{48} +(3.49602 - 6.05529i) q^{49} +(0.717721 + 4.07040i) q^{51} +(0.310668 + 0.260681i) q^{52} +(6.43452 - 5.39920i) q^{53} +(-0.289917 + 1.64420i) q^{54} +0.107279 q^{56} +(-6.61622 - 2.75181i) q^{57} -1.48088 q^{58} +(-9.80610 + 3.56913i) q^{59} +(-0.757296 + 0.635447i) q^{61} +(1.90354 + 1.59726i) q^{62} +(0.00460841 + 0.0261356i) q^{63} +(2.90628 + 5.03383i) q^{64} +(1.60184 + 0.583024i) q^{66} +(9.37780 + 3.41324i) q^{67} +(2.39499 - 4.14824i) q^{68} +(-4.90462 - 8.49505i) q^{69} +(4.73200 + 3.97062i) q^{71} +(0.274133 - 0.230025i) q^{72} +(-2.73409 + 15.5058i) q^{73} +(0.533599 - 0.194214i) q^{74} +(3.82379 + 7.37160i) q^{76} +0.300307 q^{77} +(0.101278 - 0.0368621i) q^{78} +(-0.178596 + 1.01287i) q^{79} +(-6.14281 - 5.15443i) q^{81} +(-0.161105 - 0.913670i) q^{82} +(8.96939 + 15.5354i) q^{83} +(-0.139676 + 0.241926i) q^{84} +(-0.708449 - 0.257854i) q^{86} +(3.95217 - 6.84536i) q^{87} +(-2.02470 - 3.50689i) q^{88} +(0.113975 + 0.646383i) q^{89} +(0.0145450 - 0.0122047i) q^{91} +(-1.97403 + 11.1953i) q^{92} +(-12.4635 + 4.53634i) q^{93} +2.34635 q^{94} +5.69603 q^{96} +(15.7991 - 5.75040i) q^{97} +(-0.373946 + 2.12075i) q^{98} +(0.767379 - 0.643907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Introduction

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