LMFDB - Embedded newform 625.2.d.m.251.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.4
Root			$-1.80544i$ of defining polynomial
Character	$\chi$	$=$	625.251
Dual form			625.2.d.m.376.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36191 - 0.989484i) q^{2} +(0.219507 - 0.675574i) q^{3} +(0.257680 - 0.793058i) q^{4} +(-0.369521 - 1.13727i) q^{6} +4.59110 q^{7} +(0.606623 + 1.86699i) q^{8} +(2.01883 + 1.46677i) q^{9} +O(q^{10})$	\(q+(1.36191 - 0.989484i) q^{2} +(0.219507 - 0.675574i) q^{3} +(0.257680 - 0.793058i) q^{4} +(-0.369521 - 1.13727i) q^{6} +4.59110 q^{7} +(0.606623 + 1.86699i) q^{8} +(2.01883 + 1.46677i) q^{9} +(-3.16713 + 2.30105i) q^{11} +(-0.479206 - 0.348164i) q^{12} +(-0.463518 - 0.336765i) q^{13} +(6.25266 - 4.54282i) q^{14} +(4.02276 + 2.92270i) q^{16} +(0.0718808 + 0.221226i) q^{17} +4.20081 q^{18} +(-1.71507 - 5.27846i) q^{19} +(1.00778 - 3.10163i) q^{21} +(-2.03648 + 6.26765i) q^{22} +(-3.99061 + 2.89935i) q^{23} +1.39445 q^{24} -0.964492 q^{26} +(3.15809 - 2.29449i) q^{27} +(1.18304 - 3.64101i) q^{28} +(1.27643 - 3.92845i) q^{29} +(-1.08011 - 3.32424i) q^{31} +4.44444 q^{32} +(0.859324 + 2.64473i) q^{33} +(0.316795 + 0.230165i) q^{34} +(1.68345 - 1.22310i) q^{36} +(-4.38203 - 3.18373i) q^{37} +(-7.55872 - 5.49173i) q^{38} +(-0.329255 + 0.239218i) q^{39} +(-8.43214 - 6.12630i) q^{41} +(-1.69651 - 5.22132i) q^{42} -1.38833 q^{43} +(1.00876 + 3.10465i) q^{44} +(-2.56598 + 7.89729i) q^{46} +(-0.284425 + 0.875370i) q^{47} +(2.85753 - 2.07611i) q^{48} +14.0782 q^{49} +0.165233 q^{51} +(-0.386514 + 0.280819i) q^{52} +(-0.380455 + 1.17092i) q^{53} +(2.03067 - 6.24976i) q^{54} +(2.78507 + 8.57157i) q^{56} -3.94246 q^{57} +(-2.14876 - 6.61320i) q^{58} +(-3.64689 - 2.64962i) q^{59} +(9.43214 - 6.85285i) q^{61} +(-4.76029 - 3.45856i) q^{62} +(9.26868 + 6.73409i) q^{63} +(-1.99259 + 1.44770i) q^{64} +(3.78724 + 2.75159i) q^{66} +(0.912982 + 2.80987i) q^{67} +0.193968 q^{68} +(1.08276 + 3.33238i) q^{69} +(0.990558 - 3.04862i) q^{71} +(-1.51378 + 4.65893i) q^{72} +(-8.32657 + 6.04961i) q^{73} -9.11816 q^{74} -4.62806 q^{76} +(-14.5406 + 10.5644i) q^{77} +(-0.211713 + 0.651586i) q^{78} +(-2.97123 + 9.14449i) q^{79} +(1.45651 + 4.48267i) q^{81} -17.5457 q^{82} +(3.23955 + 9.97030i) q^{83} +(-2.20009 - 1.59846i) q^{84} +(-1.89077 + 1.37373i) q^{86} +(-2.37377 - 1.72465i) q^{87} +(-6.21731 - 4.51714i) q^{88} +(-5.87207 + 4.26631i) q^{89} +(-2.12806 - 1.54612i) q^{91} +(1.27105 + 3.91189i) q^{92} -2.48286 q^{93} +(0.478804 + 1.47361i) q^{94} +(0.975587 - 3.00255i) q^{96} +(2.57093 - 7.91252i) q^{97} +(19.1733 - 13.9302i) q^{98} -9.76903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9	$ 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9} - 3 q^{11} + 15 q^{12} - 5 q^{13} - q^{14} + q^{16} - 25 q^{17} - 10 q^{18} + 10 q^{19} + 7 q^{21} - 35 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} + 35 q^{28} - 8 q^{31} + 60 q^{32} - 6 q^{34} + q^{36} - 5 q^{37} - 35 q^{38} + q^{39} - 8 q^{41} - 10 q^{42} - 31 q^{44} + 42 q^{46} - 5 q^{47} - 25 q^{48} - 8 q^{49} - 28 q^{51} + 15 q^{52} - 10 q^{53} + 50 q^{54} + 35 q^{56} - 20 q^{57} + 35 q^{58} - 15 q^{59} + 17 q^{61} + 5 q^{62} + 10 q^{63} + 37 q^{64} + 44 q^{66} - 10 q^{67} + 80 q^{68} - 9 q^{69} - 13 q^{71} + 20 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 45 q^{77} + 5 q^{78} - 55 q^{79} - 19 q^{81} - 90 q^{82} - 15 q^{83} + 59 q^{84} + 7 q^{86} - 60 q^{87} + 40 q^{88} - 28 q^{91} + 45 q^{92} - 80 q^{93} + 4 q^{94} - 43 q^{96} + 40 q^{97} + 45 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9 - 3 * q^11 + 15 * q^12 - 5 * q^13 - q^14 + q^16 - 25 * q^17 - 10 * q^18 + 10 * q^19 + 7 * q^21 - 35 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 + 35 * q^28 - 8 * q^31 + 60 * q^32 - 6 * q^34 + q^36 - 5 * q^37 - 35 * q^38 + q^39 - 8 * q^41 - 10 * q^42 - 31 * q^44 + 42 * q^46 - 5 * q^47 - 25 * q^48 - 8 * q^49 - 28 * q^51 + 15 * q^52 - 10 * q^53 + 50 * q^54 + 35 * q^56 - 20 * q^57 + 35 * q^58 - 15 * q^59 + 17 * q^61 + 5 * q^62 + 10 * q^63 + 37 * q^64 + 44 * q^66 - 10 * q^67 + 80 * q^68 - 9 * q^69 - 13 * q^71 + 20 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 45 * q^77 + 5 * q^78 - 55 * q^79 - 19 * q^81 - 90 * q^82 - 15 * q^83 + 59 * q^84 + 7 * q^86 - 60 * q^87 + 40 * q^88 - 28 * q^91 + 45 * q^92 - 80 * q^93 + 4 * q^94 - 43 * q^96 + 40 * q^97 + 45 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.36191	−	0.989484i	0.963014	−	0.699671i	0.00916528	−	0.999958i	$-0.497083\pi$
$2$	1.36191	−	0.989484i	0.963014	−	0.699671i	0.953849	+	0.300287i	$0.0970826\pi$
$3$	0.219507	−	0.675574i	0.126733	−	0.390043i	−0.867480	−	0.497472i	$-0.834262\pi$
$3$	0.219507	−	0.675574i	0.126733	−	0.390043i	0.994213	+	0.107429i	$0.0342618\pi$
$4$	0.257680	−	0.793058i	0.128840	−	0.396529i
$5$		0			0
$5$		0			0
$6$	−0.369521	−	1.13727i	−0.150856	−	0.464288i
$7$	4.59110			1.73527			0.867637	−	0.497198i	$-0.165638\pi$
$7$	4.59110			1.73527			0.867637	+	0.497198i	$0.165638\pi$
$8$	0.606623	+	1.86699i	0.214474	+	0.660082i
$9$	2.01883	+	1.46677i	0.672945	+	0.488923i
$10$		0			0
$11$	−3.16713	+	2.30105i	−0.954926	+	0.693794i	−0.951967	−	0.306201i	$-0.900942\pi$
$11$	−3.16713	+	2.30105i	−0.954926	+	0.693794i	−0.00295900	+	0.999996i	$0.500942\pi$
$12$	−0.479206	−	0.348164i	−0.138335	−	0.100506i
$13$	−0.463518	−	0.336765i	−0.128557	−	0.0934019i	0.521649	−	0.853160i	$-0.325317\pi$
$13$	−0.463518	−	0.336765i	−0.128557	−	0.0934019i	−0.650205	+	0.759758i	$0.725317\pi$
$14$	6.25266	−	4.54282i	1.67109	−	1.21412i
$15$		0			0
$16$	4.02276	+	2.92270i	1.00569	+	0.730676i
$17$	0.0718808	+	0.221226i	0.0174337	+	0.0536553i	0.959395	−	0.282066i	$-0.0910198\pi$
$17$	0.0718808	+	0.221226i	0.0174337	+	0.0536553i	−0.941961	+	0.335722i	$0.891020\pi$
$18$	4.20081			0.990140
$19$	−1.71507	−	5.27846i	−0.393465	−	1.21096i	−0.930151	−	0.367178i	$-0.880324\pi$
$19$	−1.71507	−	5.27846i	−0.393465	−	1.21096i	0.536685	−	0.843782i	$-0.319676\pi$
$20$		0			0
$21$	1.00778	−	3.10163i	0.219916	−	0.676831i
$22$	−2.03648	+	6.26765i	−0.434179	+	1.33627i
$23$	−3.99061	+	2.89935i	−0.832100	+	0.604556i	−0.920153	−	0.391560i	$-0.871936\pi$
$23$	−3.99061	+	2.89935i	−0.832100	+	0.604556i	0.0880529	+	0.996116i	$0.471936\pi$
$24$	1.39445			0.284641
$25$		0			0
$26$	−0.964492			−0.189152
$27$	3.15809	−	2.29449i	0.607775	−	0.441574i
$28$	1.18304	−	3.64101i	0.223573	−	0.688086i
$29$	1.27643	−	3.92845i	0.237028	−	0.729496i	−0.759818	−	0.650135i	$-0.774712\pi$
$29$	1.27643	−	3.92845i	0.237028	−	0.729496i	0.996846	−	0.0793604i	$-0.0252878\pi$
$30$		0			0
$31$	−1.08011	−	3.32424i	−0.193994	−	0.597051i	−0.999987	−	0.00512633i	$-0.998368\pi$
$31$	−1.08011	−	3.32424i	−0.193994	−	0.597051i	0.805993	−	0.591925i	$-0.201632\pi$
$32$	4.44444			0.785674
$33$	0.859324	+	2.64473i	0.149589	+	0.460388i
$34$	0.316795	+	0.230165i	0.0543299	+	0.0394730i
$35$		0			0
$36$	1.68345	−	1.22310i	0.280574	−	0.203849i
$37$	−4.38203	−	3.18373i	−0.720401	−	0.523402i	0.166112	−	0.986107i	$-0.446879\pi$
$37$	−4.38203	−	3.18373i	−0.720401	−	0.523402i	−0.886512	+	0.462705i	$0.846879\pi$
$38$	−7.55872	−	5.49173i	−1.22619	−	0.890876i
$39$	−0.329255	+	0.239218i	−0.0527230	+	0.0383055i
$40$		0			0
$41$	−8.43214	−	6.12630i	−1.31688	−	0.956768i	−0.999965	−	0.00831339i	$-0.997354\pi$
$41$	−8.43214	−	6.12630i	−1.31688	−	0.956768i	−0.316913	−	0.948455i	$-0.602646\pi$
$42$	−1.69651	−	5.22132i	−0.261777	−	0.805666i
$43$	−1.38833			−0.211718			−0.105859	−	0.994381i	$-0.533759\pi$
$43$	−1.38833			−0.211718			−0.105859	+	0.994381i	$0.533759\pi$
$44$	1.00876	+	3.10465i	0.152077	+	0.468044i
$45$		0			0
$46$	−2.56598	+	7.89729i	−0.378334	+	1.16439i
$47$	−0.284425	+	0.875370i	−0.0414876	+	0.127686i	−0.969655	−	0.244477i	$-0.921384\pi$
$47$	−0.284425	+	0.875370i	−0.0414876	+	0.127686i	0.928167	+	0.372163i	$0.121384\pi$
$48$	2.85753	−	2.07611i	0.412448	−	0.299661i
$49$	14.0782			2.01118
$50$		0			0
$51$	0.165233			0.0231373
$52$	−0.386514	+	0.280819i	−0.0535998	+	0.0389425i
$53$	−0.380455	+	1.17092i	−0.0522595	+	0.160838i	−0.973780	−	0.227491i	$-0.926948\pi$
$53$	−0.380455	+	1.17092i	−0.0522595	+	0.160838i	0.921521	+	0.388329i	$0.126948\pi$
$54$	2.03067	−	6.24976i	0.276339	−	0.850485i
$55$		0			0
$56$	2.78507	+	8.57157i	0.372171	+	1.14542i
$57$	−3.94246			−0.522191
$58$	−2.14876	−	6.61320i	−0.282146	−	0.868356i
$59$	−3.64689	−	2.64962i	−0.474785	−	0.344951i	0.324518	−	0.945879i	$-0.394798\pi$
$59$	−3.64689	−	2.64962i	−0.474785	−	0.344951i	−0.799303	+	0.600928i	$0.794798\pi$
$60$		0			0
$61$	9.43214	−	6.85285i	1.20766	−	0.877417i	0.212645	−	0.977129i	$-0.431792\pi$
$61$	9.43214	−	6.85285i	1.20766	−	0.877417i	0.995016	+	0.0997121i	$0.0317922\pi$
$62$	−4.76029	−	3.45856i	−0.604558	−	0.439237i
$63$	9.26868	+	6.73409i	1.16774	+	0.848416i
$64$	−1.99259	+	1.44770i	−0.249074	+	0.180963i
$65$		0			0
$66$	3.78724	+	2.75159i	0.466177	+	0.338697i
$67$	0.912982	+	2.80987i	0.111539	+	0.343280i	0.991209	−	0.132303i	$-0.0422371\pi$
$67$	0.912982	+	2.80987i	0.111539	+	0.343280i	−0.879671	+	0.475583i	$0.842237\pi$
$68$	0.193968			0.0235220
$69$	1.08276	+	3.33238i	0.130348	+	0.401171i
$70$		0			0
$71$	0.990558	−	3.04862i	0.117558	−	0.361805i	−0.874914	−	0.484278i	$-0.839082\pi$
$71$	0.990558	−	3.04862i	0.117558	−	0.361805i	0.992472	+	0.122473i	$0.0390824\pi$
$72$	−1.51378	+	4.65893i	−0.178400	+	0.549060i
$73$	−8.32657	+	6.04961i	−0.974551	+	0.708053i	−0.956484	−	0.291784i	$-0.905751\pi$
$73$	−8.32657	+	6.04961i	−0.974551	+	0.708053i	−0.0180667	+	0.999837i	$0.505751\pi$
$74$	−9.11816			−1.05996
$75$		0			0
$76$	−4.62806			−0.530875
$77$	−14.5406	+	10.5644i	−1.65706	+	1.20392i
$78$	−0.211713	+	0.651586i	−0.0239718	+	0.0737775i
$79$	−2.97123	+	9.14449i	−0.334289	+	1.02884i	0.632782	+	0.774330i	$0.281913\pi$
$79$	−2.97123	+	9.14449i	−0.334289	+	1.02884i	−0.967071	+	0.254506i	$0.918087\pi$
$80$		0			0
$81$	1.45651	+	4.48267i	0.161834	+	0.498074i
$82$	−17.5457			−1.93759
$83$	3.23955	+	9.97030i	0.355587	+	1.09438i	0.955669	+	0.294445i	$0.0951346\pi$
$83$	3.23955	+	9.97030i	0.355587	+	1.09438i	−0.600082	+	0.799939i	$0.704865\pi$
$84$	−2.20009	−	1.59846i	−0.240049	−	0.174406i
$85$		0			0
$86$	−1.89077	+	1.37373i	−0.203887	+	0.148133i
$87$	−2.37377	−	1.72465i	−0.254495	−	0.184902i
$88$	−6.21731	−	4.51714i	−0.662768	−	0.481529i
$89$	−5.87207	+	4.26631i	−0.622438	+	0.452228i	−0.853772	−	0.520646i	$-0.825691\pi$
$89$	−5.87207	+	4.26631i	−0.622438	+	0.452228i	0.231334	+	0.972874i	$0.425691\pi$
$90$		0			0
$91$	−2.12806	−	1.54612i	−0.223081	−	0.162078i
$92$	1.27105	+	3.91189i	0.132516	+	0.407843i
$93$	−2.48286			−0.257461
$94$	0.478804	+	1.47361i	0.0493848	+	0.151991i
$95$		0			0
$96$	0.975587	−	3.00255i	0.0995704	−	0.306446i
$97$	2.57093	−	7.91252i	0.261039	−	0.803394i	−0.731541	−	0.681797i	$-0.761199\pi$
$97$	2.57093	−	7.91252i	0.261039	−	0.803394i	0.992580	−	0.121597i	$-0.0388015\pi$
$98$	19.1733	−	13.9302i	1.93679	−	1.40716i
$99$	−9.76903			−0.981824
$100$		0			0
$101$	−3.56513			−0.354744			−0.177372	−	0.984144i	$-0.556760\pi$
$101$	−3.56513			−0.354744			−0.177372	+	0.984144i	$0.556760\pi$
$102$	0.225032	−	0.163495i	0.0222815	−	0.0161885i
$103$	0.123398	−	0.379779i	0.0121587	−	0.0374207i	−0.944793	−	0.327668i	$-0.893737\pi$
$103$	0.123398	−	0.379779i	0.0121587	−	0.0374207i	0.956952	+	0.290247i	$0.0937374\pi$
$104$	0.347558	−	1.06967i	0.0340809	−	0.104890i
$105$		0			0
$106$	0.640462	+	1.97114i	0.0622071	+	0.191454i
$107$	1.64372			0.158904			0.0794522	−	0.996839i	$-0.474683\pi$
$107$	1.64372			0.158904			0.0794522	+	0.996839i	$0.474683\pi$
$108$	−1.00588	−	3.09579i	−0.0967913	−	0.297893i
$109$	−0.0606078	−	0.0440342i	−0.00580518	−	0.00421771i	0.584879	−	0.811121i	$-0.301142\pi$
$109$	−0.0606078	−	0.0440342i	−0.00580518	−	0.00421771i	−0.590684	+	0.806903i	$0.701142\pi$
$110$		0			0
$111$	−3.11273	+	2.26153i	−0.295447	+	0.214655i
$112$	18.4689	+	13.4184i	1.74515	+	1.26792i
$113$	11.4337	+	8.30708i	1.07559	+	0.781464i	0.976909	−	0.213655i	$-0.0685367\pi$
$113$	11.4337	+	8.30708i	1.07559	+	0.781464i	0.0986840	+	0.995119i	$0.468537\pi$
$114$	−5.36926	+	3.90100i	−0.502878	+	0.365362i
$115$		0			0
$116$	−2.78658	−	2.02457i	−0.258728	−	0.187977i
$117$	−0.441808	−	1.35975i	−0.0408452	−	0.125709i
$118$	−7.58848			−0.698576
$119$	0.330012	+	1.01567i	0.0302522	+	0.0931066i
$120$		0			0
$121$	1.33667	−	4.11386i	0.121516	−	0.373987i
$122$	6.06492	−	18.6659i	0.549092	−	1.68993i
$123$	−5.98969	+	4.35176i	−0.540072	+	0.392385i
$124$	−2.91464			−0.261742
$125$		0			0
$126$	19.2864			1.71817
$127$	9.55647	−	6.94318i	0.848000	−	0.616108i	−0.0765941	−	0.997062i	$-0.524405\pi$
$127$	9.55647	−	6.94318i	0.848000	−	0.616108i	0.924594	+	0.380955i	$0.124405\pi$
$128$	−4.02807	+	12.3971i	−0.356034	+	1.09576i
$129$	−0.304748	+	0.937917i	−0.0268315	+	0.0825790i
$130$		0			0
$131$	−5.17210	−	15.9181i	−0.451888	−	1.39077i	−0.874750	−	0.484575i	$-0.838974\pi$
$131$	−5.17210	−	15.9181i	−0.451888	−	1.39077i	0.422862	−	0.906194i	$-0.361026\pi$
$132$	2.31885			0.201830
$133$	−7.87408	−	24.2339i	−0.682770	−	2.10135i
$134$	4.02372	+	2.92340i	0.347596	+	0.252544i
$135$		0			0
$136$	−0.369424	+	0.268402i	−0.0316778	+	0.0230153i
$137$	8.43168	+	6.12598i	0.720367	+	0.523378i	0.886502	−	0.462726i	$-0.153128\pi$
$137$	8.43168	+	6.12598i	0.720367	+	0.523378i	−0.166134	+	0.986103i	$0.553128\pi$
$138$	4.77195	+	3.46702i	0.406215	+	0.295133i
$139$	−5.38800	+	3.91461i	−0.457004	+	0.332033i	−0.792355	−	0.610060i	$-0.791145\pi$
$139$	−5.38800	+	3.91461i	−0.457004	+	0.332033i	0.335351	+	0.942093i	$0.391145\pi$
$140$		0			0
$141$	0.528944	+	0.384300i	0.0445451	+	0.0323639i
$142$	−1.66752	−	5.13208i	−0.139935	−	0.430675i
$143$	2.24294			0.187564
$144$	3.83435	+	11.8009i	0.319529	+	0.983409i
$145$		0			0
$146$	−5.35403	+	16.4780i	−0.443103	+	1.36373i
$147$	3.09027	−	9.51089i	0.254882	−	0.784445i
$148$	−3.65404	+	2.65482i	−0.300360	+	0.218225i
$149$	−12.0316			−0.985667			−0.492834	−	0.870124i	$-0.664039\pi$
$149$	−12.0316			−0.985667			−0.492834	+	0.870124i	$0.664039\pi$
$150$		0			0
$151$	−1.54218			−0.125501			−0.0627505	−	0.998029i	$-0.519987\pi$
$151$	−1.54218			−0.125501			−0.0627505	+	0.998029i	$0.519987\pi$
$152$	8.81445	−	6.40407i	0.714946	−	0.519439i
$153$	−0.179373	+	0.552052i	−0.0145014	+	0.0446308i
$154$	−9.34970	+	28.7754i	−0.753420	+	2.31879i
$155$		0			0
$156$	0.104871	+	0.322760i	0.00839641	+	0.0258415i
$157$	9.82482			0.784106			0.392053	−	0.919943i	$-0.371765\pi$
$157$	9.82482			0.784106			0.392053	+	0.919943i	$0.371765\pi$
$158$	5.00179	+	15.3939i	0.397921	+	1.22468i
$159$	0.707530	+	0.514051i	0.0561108	+	0.0407669i
$160$		0			0
$161$	−18.3213	+	13.3112i	−1.44392	+	1.04907i
$162$	6.41915	+	4.66379i	0.504336	+	0.366422i
$163$	−4.51518	−	3.28047i	−0.353656	−	0.256946i	0.396745	−	0.917929i	$-0.370140\pi$
$163$	−4.51518	−	3.28047i	−0.353656	−	0.256946i	−0.750401	+	0.660982i	$0.770140\pi$
$164$	−7.03131	+	5.10854i	−0.549053	+	0.398910i
$165$		0			0
$166$	14.2774	+	10.3732i	1.10814	+	0.805113i
$167$	6.75534	+	20.7908i	0.522744	+	1.60884i	0.768735	+	0.639568i	$0.220887\pi$
$167$	6.75534	+	20.7908i	0.522744	+	1.60884i	−0.245991	+	0.969272i	$0.579113\pi$
$168$	6.40207			0.493930
$169$	−3.91578	−	12.0515i	−0.301214	−	0.927042i
$170$		0			0
$171$	4.27982	−	13.1719i	0.327286	−	1.00728i
$172$	−0.357744	+	1.10102i	−0.0272777	+	0.0839522i
$173$	18.9622	−	13.7768i	1.44167	−	1.04743i	0.453977	−	0.891013i	$-0.350005\pi$
$173$	18.9622	−	13.7768i	1.44167	−	1.04743i	0.987691	−	0.156420i	$-0.0499953\pi$
$174$	−4.93937			−0.374453
$175$		0			0
$176$	−19.4659			−1.46730
$177$	−2.59053	+	1.88213i	−0.194716	+	0.141470i
$178$	−3.77577	+	11.6206i	−0.283006	+	0.871004i
$179$	−1.95259	+	6.00947i	−0.145944	+	0.449169i	−0.997131	−	0.0756932i	$-0.975883\pi$
$179$	−1.95259	+	6.00947i	−0.145944	+	0.449169i	0.851187	+	0.524862i	$0.175883\pi$
$180$		0			0
$181$	−4.12158	−	12.6849i	−0.306355	−	0.942863i	−0.979168	−	0.203051i	$-0.934914\pi$
$181$	−4.12158	−	12.6849i	−0.306355	−	0.942863i	0.672813	−	0.739812i	$-0.265086\pi$
$182$	−4.42808			−0.328231
$183$	−2.55918	−	7.87636i	−0.189180	−	0.582237i
$184$	−7.83387	−	5.69164i	−0.577520	−	0.419593i
$185$		0			0
$186$	−3.38143	+	2.45675i	−0.247938	+	0.180138i
$187$	−0.736710	−	0.535251i	−0.0538736	−	0.0391414i
$188$	0.620928	+	0.451131i	0.0452859	+	0.0329021i
$189$	14.4991	−	10.5342i	1.05466	−	0.766253i
$190$		0			0
$191$	2.24974	+	1.63453i	0.162785	+	0.118270i	0.666196	−	0.745777i	$-0.267922\pi$
$191$	2.24974	+	1.63453i	0.162785	+	0.118270i	−0.503410	+	0.864047i	$0.667922\pi$
$192$	0.540642	+	1.66393i	0.0390175	+	0.120084i
$193$	−22.5667			−1.62438			−0.812192	−	0.583391i	$-0.801726\pi$
$193$	−22.5667			−1.62438			−0.812192	+	0.583391i	$0.801726\pi$
$194$	−4.32793	−	13.3200i	−0.310728	−	0.956321i
$195$		0			0
$196$	3.62768	−	11.1649i	0.259120	−	0.797490i
$197$	−0.393014	+	1.20957i	−0.0280011	+	0.0861786i	−0.964080	−	0.265610i	$-0.914427\pi$
$197$	−0.393014	+	1.20957i	−0.0280011	+	0.0861786i	0.936079	+	0.351789i	$0.114427\pi$
$198$	−13.3045	+	9.66629i	−0.945511	+	0.686954i
$199$	−8.62648			−0.611515			−0.305757	−	0.952109i	$-0.598910\pi$
$199$	−8.62648			−0.611515			−0.305757	+	0.952109i	$0.598910\pi$
$200$		0			0
$201$	2.09868			0.148030
$202$	−4.85538	+	3.52764i	−0.341623	+	0.248204i
$203$	5.86023	−	18.0359i	0.411308	−	1.26588i
$204$	0.0425773	−	0.131039i	0.00298101	−	0.00917459i
$205$		0			0
$206$	−0.207729	−	0.639324i	−0.0144732	−	0.0445438i
$207$	−12.3091			−0.855538
$208$	−0.880354	−	2.70945i	−0.0610415	−	0.187867i
$209$	17.5779	+	12.7711i	1.21589	+	0.883394i
$210$		0			0
$211$	17.0149	−	12.3621i	1.17136	−	0.851039i	0.180185	−	0.983633i	$-0.442330\pi$
$211$	17.0149	−	12.3621i	1.17136	−	0.851039i	0.991171	+	0.132593i	$0.0423305\pi$
$212$	0.830571	+	0.603445i	0.0570439	+	0.0414448i
$213$	−1.84214	−	1.33839i	−0.126221	−	0.0917050i
$214$	2.23859	−	1.62643i	0.153027	−	0.111181i
$215$		0			0
$216$	6.19957	+	4.50425i	0.421827	+	0.306475i
$217$	−4.95890	−	15.2619i	−0.336632	−	1.03605i
$218$	−0.126113			−0.00854148
$219$	2.25921	+	6.95314i	0.152663	+	0.469850i
$220$		0			0
$221$	0.0411833	−	0.126749i	0.00277029	−	0.00852608i
$222$	−2.00150	+	6.15999i	−0.134332	+	0.413432i
$223$	−5.12542	+	3.72384i	−0.343224	+	0.249367i	−0.746021	−	0.665923i	$-0.768038\pi$
$223$	−5.12542	+	3.72384i	−0.343224	+	0.249367i	0.402797	+	0.915289i	$0.368038\pi$
$224$	20.4049			1.36336
$225$		0			0
$226$	23.7914			1.58258
$227$	−9.11148	+	6.61988i	−0.604750	+	0.439377i	−0.847562	−	0.530697i	$-0.821930\pi$
$227$	−9.11148	+	6.61988i	−0.604750	+	0.439377i	0.242812	+	0.970073i	$0.421930\pi$
$228$	−1.01589	+	3.12660i	−0.0672792	+	0.207064i
$229$	4.64788	−	14.3047i	0.307140	−	0.945281i	−0.671729	−	0.740797i	$-0.734448\pi$
$229$	4.64788	−	14.3047i	0.307140	−	0.945281i	0.978870	−	0.204484i	$-0.0655518\pi$
$230$		0			0
$231$	3.94525	+	12.1422i	0.259578	+	0.798900i
$232$	8.10872			0.532363
$233$	2.41883	+	7.44438i	0.158463	+	0.487698i	0.998495	−	0.0548381i	$-0.0174643\pi$
$233$	2.41883	+	7.44438i	0.158463	+	0.487698i	−0.840033	+	0.542536i	$0.817464\pi$
$234$	−1.94715	−	1.41469i	−0.127289	−	0.0924810i
$235$		0			0
$236$	−3.04103	+	2.20944i	−0.197954	+	0.143822i
$237$	5.52557	+	4.01456i	0.358925	+	0.260774i
$238$	1.45444	+	1.05671i	0.0942772	+	0.0684964i
$239$	−7.06988	+	5.13657i	−0.457313	+	0.332257i	−0.792476	−	0.609903i	$-0.791208\pi$
$239$	−7.06988	+	5.13657i	−0.457313	+	0.332257i	0.335163	+	0.942160i	$0.391208\pi$
$240$		0			0
$241$	0.486132	+	0.353195i	0.0313145	+	0.0227513i	0.603332	−	0.797490i	$-0.293839\pi$
$241$	0.486132	+	0.353195i	0.0313145	+	0.0227513i	−0.572018	+	0.820241i	$0.693839\pi$
$242$	−2.25017	−	6.92531i	−0.144646	−	0.445176i
$243$	15.0589			0.966031
$244$	−3.00423	−	9.24607i	−0.192326	−	0.591919i
$245$		0			0
$246$	−3.85140	+	11.8534i	−0.245556	+	0.755745i
$247$	−0.982634	+	3.02423i	−0.0625235	+	0.192427i
$248$	5.55112	−	4.03312i	0.352496	−	0.256104i
$249$	7.44678			0.471921
$250$		0			0
$251$	−14.1908			−0.895712			−0.447856	−	0.894106i	$-0.647812\pi$
$251$	−14.1908			−0.895712			−0.447856	+	0.894106i	$0.647812\pi$
$252$	7.72888	−	5.61536i	0.486873	−	0.353734i
$253$	5.96722	−	18.3652i	0.375156	−	1.15461i
$254$	6.14486	−	18.9119i	0.385563	−	1.18664i
$255$		0			0
$256$	5.25868	+	16.1846i	0.328668	+	1.01153i
$257$	17.6859			1.10322			0.551609	−	0.834103i	$-0.314014\pi$
$257$	17.6859			1.10322			0.551609	+	0.834103i	$0.314014\pi$
$258$	0.513015	+	1.57890i	0.0319389	+	0.0982980i
$259$	−20.1183	−	14.6168i	−1.25009	−	0.908245i
$260$		0			0
$261$	8.33904	−	6.05867i	0.516174	−	0.375022i
$262$	−22.7946	−	16.5612i	−1.40825	−	1.02316i
$263$	−19.6873	−	14.3036i	−1.21397	−	0.882000i	−0.218384	−	0.975863i	$-0.570078\pi$
$263$	−19.6873	−	14.3036i	−1.21397	−	0.882000i	−0.995585	+	0.0938630i	$0.970078\pi$
$264$	−4.41641	+	3.20871i	−0.271811	+	0.197482i
$265$		0			0
$266$	−34.7029	−	25.2131i	−2.12777	−	1.54591i
$267$	1.59324	+	4.90350i	0.0975050	+	0.300090i
$268$	2.46365			0.150491
$269$	9.26490	+	28.5144i	0.564891	+	1.73856i	0.668275	+	0.743915i	$0.267033\pi$
$269$	9.26490	+	28.5144i	0.564891	+	1.73856i	−0.103384	+	0.994642i	$0.532967\pi$
$270$		0			0
$271$	−8.55920	+	26.3425i	−0.519934	+	1.60019i	0.254187	+	0.967155i	$0.418192\pi$
$271$	−8.55920	+	26.3425i	−0.519934	+	1.60019i	−0.774121	+	0.633038i	$0.781808\pi$
$272$	−0.357420	+	1.10003i	−0.0216718	+	0.0666989i
$273$	−1.51165	+	1.09827i	−0.0914889	+	0.0664706i
$274$	17.5447			1.05992
$275$		0			0
$276$	2.92177			0.175870
$277$	1.85594	−	1.34842i	0.111513	−	0.0810189i	−0.530631	−	0.847603i	$-0.678045\pi$
$277$	1.85594	−	1.34842i	0.111513	−	0.0810189i	0.642144	+	0.766584i	$0.278045\pi$
$278$	−3.46451	+	10.6627i	−0.207788	+	0.639505i
$279$	2.69533	−	8.29536i	0.161365	−	0.496630i
$280$		0			0
$281$	−0.500078	−	1.53908i	−0.0298321	−	0.0918139i	0.935032	−	0.354564i	$-0.115371\pi$
$281$	−0.500078	−	1.53908i	−0.0298321	−	0.0918139i	−0.964864	+	0.262750i	$0.915371\pi$
$282$	1.10063			0.0655416
$283$	4.01481	+	12.3563i	0.238656	+	0.734506i	0.996615	+	0.0822051i	$0.0261963\pi$
$283$	4.01481	+	12.3563i	0.238656	+	0.734506i	−0.757960	+	0.652301i	$0.773804\pi$
$284$	−2.16249	−	1.57114i	−0.128320	−	0.0932300i
$285$		0			0
$286$	3.05467	−	2.21935i	0.180627	−	0.131233i
$287$	−38.7128	−	28.1265i	−2.28514	−	1.66025i
$288$	8.97259	+	6.51897i	0.528715	+	0.384134i
$289$	13.7095	−	9.96055i	0.806442	−	0.585914i
$290$		0			0
$291$	−4.78115	−	3.47371i	−0.280276	−	0.203632i
$292$	2.65210	+	8.16231i	0.155202	+	0.477663i
$293$	11.7009			0.683572			0.341786	−	0.939778i	$-0.388968\pi$
$293$	11.7009			0.683572			0.341786	+	0.939778i	$0.388968\pi$
$294$	−5.20220	−	16.0107i	−0.303398	−	0.933765i
$295$		0			0
$296$	3.28576	−	10.1125i	0.190981	−	0.587780i
$297$	−4.72235	+	14.5339i	−0.274018	+	0.843342i
$298$	−16.3859	+	11.9051i	−0.949211	+	0.689642i
$299$	2.82612			0.163439
$300$		0			0
$301$	−6.37395			−0.367388
$302$	−2.10031	+	1.52596i	−0.120859	+	0.0878094i
$303$	−0.782572	+	2.40851i	−0.0449576	+	0.138365i
$304$	8.52804	−	26.2466i	0.489116	−	1.50535i
$305$		0			0
$306$	0.301958	+	0.929330i	0.0172618	+	0.0531263i
$307$	−26.5673			−1.51628			−0.758138	−	0.652094i	$-0.773891\pi$
$307$	−26.5673			−1.51628			−0.758138	+	0.652094i	$0.773891\pi$
$308$	4.63134	+	14.2538i	0.263895	+	0.812185i
$309$	−0.229482	−	0.166728i	−0.0130548	−	0.00948485i
$310$		0			0
$311$	10.9145	−	7.92981i	0.618902	−	0.449658i	−0.233636	−	0.972324i	$-0.575062\pi$
$311$	10.9145	−	7.92981i	0.618902	−	0.449658i	0.852538	+	0.522666i	$0.175062\pi$
$312$	−0.646353	−	0.469603i	−0.0365925	−	0.0265860i
$313$	13.7487	+	9.98904i	0.777124	+	0.564614i	0.904115	−	0.427290i	$-0.140532\pi$
$313$	13.7487	+	9.98904i	0.777124	+	0.564614i	−0.126990	+	0.991904i	$0.540532\pi$
$314$	13.3805	−	9.72150i	0.755105	−	0.548616i
$315$		0			0
$316$	6.48649	+	4.71271i	0.364893	+	0.265111i
$317$	−5.19021	−	15.9738i	−0.291511	−	0.897180i	−0.984371	−	0.176107i	$-0.943649\pi$
$317$	−5.19021	−	15.9738i	−0.291511	−	0.897180i	0.692860	−	0.721072i	$-0.256351\pi$
$318$	1.47224			0.0825588
$319$	4.99696	+	15.3791i	0.279776	+	0.861063i
$320$		0			0
$321$	0.360808	−	1.11045i	0.0201384	−	0.0619795i
$322$	−11.7807	+	36.2573i	−0.656513	+	2.02054i
$323$	1.04445	−	0.758839i	0.0581149	−	0.0422230i
$324$	3.93033			0.218351
$325$		0			0
$326$	−9.39524			−0.520354
$327$	−0.0430522	+	0.0312793i	−0.00238079	+	0.00172975i
$328$	6.32265	−	19.4591i	0.349110	−	1.07445i
$329$	−1.30582	+	4.01891i	−0.0719924	+	0.221570i
$330$		0			0
$331$	3.96604	+	12.2062i	0.217994	+	0.670915i	0.998928	+	0.0463015i	$0.0147435\pi$
$331$	3.96604	+	12.2062i	0.217994	+	0.670915i	−0.780934	+	0.624614i	$0.785257\pi$
$332$	8.74180			0.479768
$333$	−4.17679	−	12.8548i	−0.228887	−	0.704441i
$334$	29.7723	+	21.6308i	1.62907	+	1.18359i
$335$		0			0
$336$	13.1192	−	9.53166i	0.715711	−	0.519995i
$337$	17.1815	+	12.4831i	0.935935	+	0.679997i	0.947439	−	0.319937i	$-0.103662\pi$
$337$	17.1815	+	12.4831i	0.935935	+	0.679997i	−0.0115037	+	0.999934i	$0.503662\pi$
$338$	−17.2577	−	12.5385i	−0.938697	−	0.682003i
$339$	8.12183	−	5.90085i	0.441117	−	0.320490i
$340$		0			0
$341$	11.0701	+	8.04291i	0.599480	+	0.435548i
$342$	−7.20470	−	22.1738i	−0.389586	−	1.19902i
$343$	32.4969			1.75467
$344$	−0.842191	−	2.59200i	−0.0454079	−	0.139751i
$345$		0			0
$346$	12.1928	−	37.5255i	0.655488	−	2.01739i
$347$	−8.84658	+	27.2270i	−0.474909	+	1.46162i	0.371171	+	0.928565i	$0.378956\pi$
$347$	−8.84658	+	27.2270i	−0.474909	+	1.46162i	−0.846080	+	0.533056i	$0.821044\pi$
$348$	−1.97942	+	1.43813i	−0.106108	+	0.0770920i
$349$	19.9124			1.06588			0.532942	−	0.846152i	$-0.321086\pi$
$349$	19.9124			1.06588			0.532942	+	0.846152i	$0.321086\pi$
$350$		0			0
$351$	−2.23654			−0.119377
$352$	−14.0761	+	10.2269i	−0.750260	+	0.545096i
$353$	−7.63011	+	23.4831i	−0.406110	+	1.24988i	0.513855	+	0.857877i	$0.328217\pi$
$353$	−7.63011	+	23.4831i	−0.406110	+	1.24988i	−0.919965	+	0.392000i	$0.871783\pi$
$354$	−1.66573	+	5.12658i	−0.0885324	+	0.272475i
$355$		0			0
$356$	1.87031	+	5.75624i	0.0991265	+	0.305080i
$357$	0.758602			0.0401495
$358$	3.28702	+	10.1164i	0.173724	+	0.534668i
$359$	−17.3947	−	12.6380i	−0.918058	−	0.667008i	0.0249816	−	0.999688i	$-0.492047\pi$
$359$	−17.3947	−	12.6380i	−0.918058	−	0.667008i	−0.943040	+	0.332679i	$0.892047\pi$
$360$		0			0
$361$	−9.54930	+	6.93797i	−0.502595	+	0.365156i
$362$	−18.1647	−	13.1975i	−0.954718	−	0.693643i
$363$	−2.48581	−	1.80604i	−0.130471	−	0.0947927i
$364$	−1.77452	+	1.28927i	−0.0930103	+	0.0675760i
$365$		0			0
$366$	−11.2789	−	8.19460i	−0.589557	−	0.428338i
$367$	0.353463	+	1.08785i	0.0184506	+	0.0567852i	0.959858	−	0.280487i	$-0.0904958\pi$
$367$	0.353463	+	1.08785i	0.0184506	+	0.0567852i	−0.941407	+	0.337272i	$0.890496\pi$
$368$	−24.5272			−1.27857
$369$	−8.03721	−	24.7360i	−0.418400	−	1.28770i
$370$		0			0
$371$	−1.74671	+	5.37581i	−0.0906845	+	0.279098i
$372$	−0.639784	+	1.96905i	−0.0331713	+	0.102091i
$373$	9.33566	−	6.78275i	0.483382	−	0.351198i	−0.319251	−	0.947670i	$-0.603431\pi$
$373$	9.33566	−	6.78275i	0.483382	−	0.351198i	0.802634	+	0.596472i	$0.203431\pi$
$374$	−1.53295			−0.0792671
$375$		0			0
$376$	−1.80685			−0.0931812
$377$	−1.91462	+	1.39105i	−0.0986077	+	0.0716427i
$378$	9.32302	−	28.6933i	0.479524	−	1.47582i
$379$	6.52188	−	20.0723i	0.335007	−	1.03104i	−0.631712	−	0.775203i	$-0.717648\pi$
$379$	6.52188	−	20.0723i	0.335007	−	1.03104i	0.966719	−	0.255841i	$-0.0823525\pi$
$380$		0			0
$381$	−2.59292	−	7.98018i	−0.132839	−	0.408837i
$382$	4.68127			0.239515
$383$	0.265176	+	0.816129i	0.0135499	+	0.0417022i	0.957603	−	0.288092i	$-0.0930208\pi$
$383$	0.265176	+	0.816129i	0.0135499	+	0.0417022i	−0.944053	+	0.329794i	$0.893021\pi$
$384$	7.49097	+	5.44251i	0.382272	+	0.277737i
$385$		0			0
$386$	−30.7337	+	22.3293i	−1.56430	+	1.13653i
$387$	−2.80280	−	2.03635i	−0.142474	−	0.103514i
$388$	−5.61260	−	4.07780i	−0.284937	−	0.207019i
$389$	27.4537	−	19.9463i	1.39196	−	1.01132i	0.396310	−	0.918117i	$-0.370290\pi$
$389$	27.4537	−	19.9463i	1.39196	−	1.01132i	0.995647	−	0.0931998i	$-0.0297095\pi$
$390$		0			0
$391$	−0.928260	−	0.674421i	−0.0469442	−	0.0341069i
$392$	8.54019	+	26.2840i	0.431345	+	1.32754i
$393$	−11.8891			−0.599728
$394$	0.661604	+	2.03621i	0.0333311	+	0.102583i
$395$		0			0
$396$	−2.51728	+	7.74740i	−0.126498	+	0.389322i
$397$	8.29049	−	25.5155i	0.416088	−	1.28059i	−0.495186	−	0.868787i	$-0.664900\pi$
$397$	8.29049	−	25.5155i	0.416088	−	1.28059i	0.911274	−	0.411800i	$-0.135100\pi$
$398$	−11.7485	+	8.53576i	−0.588897	+	0.427859i
$399$	−18.1002			−0.906145
$400$		0			0
$401$	3.79757			0.189642			0.0948208	−	0.995494i	$-0.469772\pi$
$401$	3.79757			0.189642			0.0948208	+	0.995494i	$0.469772\pi$
$402$	2.85821	−	2.07661i	0.142555	−	0.103572i
$403$	−0.618838	+	1.90459i	−0.0308265	+	0.0948743i
$404$	−0.918663	+	2.82736i	−0.0457052	+	0.140666i
$405$		0			0
$406$	−9.86518	−	30.3619i	−0.489601	−	1.50684i
$407$	21.2044			1.05106
$408$	0.100234	+	0.308489i	0.00496234	+	0.0152725i
$409$	11.4681	+	8.33207i	0.567062	+	0.411994i	0.834037	−	0.551709i	$-0.186024\pi$
$409$	11.4681	+	8.33207i	0.567062	+	0.411994i	−0.266975	+	0.963703i	$0.586024\pi$
$410$		0			0
$411$	5.98936	−	4.35153i	0.295434	−	0.214645i
$412$	−0.269389	−	0.195723i	−0.0132719	−	0.00964257i
$413$	−16.7432	−	12.1647i	−0.823881	−	0.598585i
$414$	−16.7638	+	12.1796i	−0.823896	+	0.598595i
$415$		0			0
$416$	−2.06008	−	1.49673i	−0.101004	−	0.0733834i
$417$	1.46190	+	4.49928i	0.0715897	+	0.220331i
$418$	36.5762			1.78900
$419$	−6.05576	−	18.6377i	−0.295843	−	0.910512i	−0.982937	−	0.183943i	$-0.941114\pi$
$419$	−6.05576	−	18.6377i	−0.295843	−	0.910512i	0.687094	−	0.726569i	$-0.258886\pi$
$420$		0			0
$421$	−7.96770	+	24.5221i	−0.388322	+	1.19513i	0.545720	+	0.837968i	$0.316256\pi$
$421$	−7.96770	+	24.5221i	−0.388322	+	1.19513i	−0.934042	+	0.357164i	$0.883744\pi$
$422$	10.9407	−	33.6720i	0.532584	−	1.63913i
$423$	−1.85817	+	1.35004i	−0.0903474	+	0.0656412i
$424$	−2.41689			−0.117375
$425$		0			0
$426$	−3.83313			−0.185716
$427$	43.3039	−	31.4621i	2.09562	−	1.52256i
$428$	0.423554	−	1.30356i	0.0204732	−	0.0630102i
$429$	0.492341	−	1.51527i	0.0237704	−	0.0731579i
$430$		0			0
$431$	2.91259	+	8.96402i	0.140294	+	0.431782i	0.996376	−	0.0850590i	$-0.0271079\pi$
$431$	2.91259	+	8.96402i	0.140294	+	0.431782i	−0.856081	+	0.516841i	$0.827108\pi$
$432$	19.4103			0.933881
$433$	0.541277	+	1.66588i	0.0260121	+	0.0800571i	0.963220	−	0.268715i	$-0.0865989\pi$
$433$	0.541277	+	1.66588i	0.0260121	+	0.0800571i	−0.937208	+	0.348772i	$0.886599\pi$
$434$	−21.8550	−	15.8786i	−1.04907	−	0.762197i
$435$		0			0
$436$	−0.0505391	+	0.0367188i	−0.00242038	+	0.00175851i
$437$	22.1483	+	16.0917i	1.05950	+	0.769769i
$438$	9.95686	+	7.23408i	0.475757	+	0.345658i
$439$	−22.7197	+	16.5068i	−1.08435	+	0.787827i	−0.978436	−	0.206549i	$-0.933777\pi$
$439$	−22.7197	+	16.5068i	−1.08435	+	0.787827i	−0.105914	+	0.994375i	$0.533777\pi$
$440$		0			0
$441$	28.4216	+	20.6495i	1.35341	+	0.983311i
$442$	−0.0693285	−	0.213371i	−0.00329762	−	0.0101490i
$443$	−29.9110			−1.42111			−0.710557	−	0.703640i	$-0.751557\pi$
$443$	−29.9110			−1.42111			−0.710557	+	0.703640i	$0.751557\pi$
$444$	0.991436	+	3.05133i	0.0470515	+	0.144810i
$445$		0			0
$446$	−3.29568	+	10.1430i	−0.156055	+	0.480287i
$447$	−2.64102	+	8.12823i	−0.124916	+	0.384452i
$448$	−9.14821	+	6.64656i	−0.432212	+	0.314021i
$449$	6.29974			0.297303			0.148652	−	0.988890i	$-0.452507\pi$
$449$	6.29974			0.297303			0.148652	+	0.988890i	$0.452507\pi$
$450$		0			0
$451$	40.8026			1.92132
$452$	9.53424	−	6.92703i	0.448453	−	0.325820i
$453$	−0.338520	+	1.04186i	−0.0159051	+	0.0489508i
$454$	−5.85873	+	18.0313i	−0.274964	+	0.846252i
$455$		0			0
$456$	−2.39159	−	7.36055i	−0.111996	−	0.344689i
$457$	19.1809			0.897243			0.448622	−	0.893722i	$-0.351915\pi$
$457$	19.1809			0.897243			0.448622	+	0.893722i	$0.351915\pi$
$458$	−7.82429	−	24.0807i	−0.365605	−	1.12522i
$459$	0.734607	+	0.533724i	0.0342885	+	0.0249121i
$460$		0			0
$461$	−5.72064	+	4.15629i	−0.266437	+	0.193578i	−0.712980	−	0.701184i	$-0.752655\pi$
$461$	−5.72064	+	4.15629i	−0.266437	+	0.193578i	0.446543	+	0.894762i	$0.352655\pi$
$462$	17.3876	+	12.6328i	0.808944	+	0.587732i
$463$	7.78146	+	5.65356i	0.361635	+	0.262743i	0.753734	−	0.657180i	$-0.228251\pi$
$463$	7.78146	+	5.65356i	0.361635	+	0.262743i	−0.392099	+	0.919923i	$0.628251\pi$
$464$	16.6165	−	12.0726i	0.771401	−	0.560456i
$465$		0			0
$466$	10.6603	+	7.74517i	0.493830	+	0.358788i
$467$	−5.93992	−	18.2812i	−0.274867	−	0.845953i	−0.989255	−	0.146203i	$-0.953295\pi$
$467$	−5.93992	−	18.2812i	−0.274867	−	0.845953i	0.714388	−	0.699750i	$-0.246705\pi$
$468$	−1.19220			−0.0551096
$469$	4.19160	+	12.9004i	0.193550	+	0.595686i
$470$		0			0
$471$	2.15662	−	6.63739i	0.0993717	−	0.305835i
$472$	2.73454	−	8.41605i	0.125867	−	0.387380i
$473$	4.39701	−	3.19462i	0.202175	−	0.146889i
$474$	11.4977			0.528105
$475$		0			0
$476$	0.890525			0.0408172
$477$	−2.48554	+	1.80585i	−0.113805	+	0.0826843i
$478$	−4.54598	+	13.9911i	−0.207928	+	0.639937i
$479$	−11.7425	+	36.1398i	−0.536529	+	1.65127i	0.203792	+	0.979014i	$0.434673\pi$
$479$	−11.7425	+	36.1398i	−0.536529	+	1.65127i	−0.740321	+	0.672253i	$0.765327\pi$
$480$		0			0
$481$	0.958977	+	2.95143i	0.0437256	+	0.134574i
$482$	1.01155			0.0460747
$483$	4.97104	+	15.2993i	0.226190	+	0.696142i
$484$	−2.91809	−	2.12012i	−0.132641	−	0.0963691i
$485$		0			0
$486$	20.5089	−	14.9006i	0.930302	−	0.675904i
$487$	13.5502	+	9.84481i	0.614019	+	0.446111i	0.850827	−	0.525445i	$-0.176101\pi$
$487$	13.5502	+	9.84481i	0.614019	+	0.446111i	−0.236808	+	0.971556i	$0.576101\pi$
$488$	18.5160	+	13.4527i	0.838180	+	0.608973i
$489$	−3.20732	+	2.33025i	−0.145040	+	0.105378i
$490$		0			0
$491$	7.24115	+	5.26100i	0.326789	+	0.237426i	0.739067	−	0.673632i	$-0.235267\pi$
$491$	7.24115	+	5.26100i	0.326789	+	0.237426i	−0.412278	+	0.911058i	$0.635267\pi$
$492$	1.90778	+	5.87153i	0.0860092	+	0.264709i
$493$	0.960829			0.0432736
$494$	1.65418	+	5.09103i	0.0744249	+	0.229056i
$495$		0			0
$496$	5.37075	−	16.5295i	0.241154	−	0.742194i
$497$	4.54775	−	13.9965i	0.203995	−	0.627831i
$498$	10.1418	−	7.36847i	0.454466	−	0.330189i
$499$	−36.3310			−1.62640			−0.813200	−	0.581985i	$-0.802276\pi$
$499$	−36.3310			−1.62640			−0.813200	+	0.581985i	$0.802276\pi$
$500$		0			0
$501$	15.5286			0.693765
$502$	−19.3265	+	14.0415i	−0.862583	+	0.626704i
$503$	3.79921	−	11.6928i	0.169398	−	0.521354i	−0.829935	−	0.557860i	$-0.811623\pi$
$503$	3.79921	−	11.6928i	0.169398	−	0.521354i	0.999333	+	0.0365056i	$0.0116227\pi$
$504$	−6.94991	+	21.3896i	−0.309574	+	0.952770i
$505$		0			0
$506$	−10.0453	−	30.9162i	−0.446567	−	1.37439i
$507$	−9.00125			−0.399759
$508$	−3.04383	−	9.36795i	−0.135048	−	0.415636i
$509$	25.1841	+	18.2973i	1.11626	+	0.811013i	0.983639	−	0.180153i	$-0.0576594\pi$
$509$	25.1841	+	18.2973i	1.11626	+	0.811013i	0.132625	+	0.991166i	$0.457659\pi$
$510$		0			0
$511$	−38.2281	+	27.7744i	−1.69111	+	1.22867i
$512$	2.08496	+	1.51482i	0.0921433	+	0.0669460i
$513$	−17.5277	−	12.7346i	−0.773868	−	0.562248i
$514$	24.0866	−	17.4999i	1.06241	−	0.771889i
$515$		0			0
$516$	0.665295	+	0.483365i	0.0292880	+	0.0212790i
$517$	−1.11346	−	3.42689i	−0.0489701	−	0.150714i
$518$	−41.8624			−1.83933
$519$	−5.14493	−	15.8345i	−0.225837	−	0.695056i
$520$		0			0
$521$	5.01130	−	15.4232i	0.219549	−	0.675702i	−0.779250	−	0.626713i	$-0.784400\pi$
$521$	5.01130	−	15.4232i	0.219549	−	0.675702i	0.998799	−	0.0489896i	$-0.0156001\pi$
$522$	5.36205	−	16.5027i	0.234691	−	0.722303i
$523$	24.7504	−	17.9822i	1.08226	−	0.786307i	0.104183	−	0.994558i	$-0.466777\pi$
$523$	24.7504	−	17.9822i	1.08226	−	0.786307i	0.978075	+	0.208251i	$0.0667771\pi$
$524$	−13.9567			−0.609701
$525$		0			0
$526$	−40.9655			−1.78618
$527$	0.657770	−	0.477898i	0.0286529	−	0.0208176i
$528$	−4.27291	+	13.1507i	−0.185954	+	0.572309i
$529$	0.411359	−	1.26603i	0.0178852	−	0.0550449i
$530$		0			0
$531$	−3.47608	−	10.6983i	−0.150849	−	0.464266i
$532$	−21.2479			−0.921214
$533$	1.84532	+	5.67930i	0.0799295	+	0.245998i
$534$	7.02179	+	5.10163i	0.303863	+	0.220769i
$535$		0			0
$536$	−4.69218	+	3.40907i	−0.202671	+	0.147249i
$537$	3.63123	+	2.63824i	0.156699	+	0.113849i
$538$	40.8325	+	29.6666i	1.76041	+	1.27902i
$539$	−44.5876	+	32.3948i	−1.92052	+	1.39534i
$540$		0			0
$541$	−14.8062	−	10.7573i	−0.636567	−	0.462493i	0.222102	−	0.975023i	$-0.428708\pi$
$541$	−14.8062	−	10.7573i	−0.636567	−	0.462493i	−0.858669	+	0.512530i	$0.828708\pi$
$542$	14.4086	+	44.3452i	0.618904	+	1.90479i
$543$	−9.47432			−0.406582
$544$	0.319470	+	0.983228i	0.0136972	+	0.0421555i
$545$		0			0
$546$	−0.971996	+	2.99150i	−0.0415976	+	0.128024i
$547$	−2.02592	+	6.23515i	−0.0866223	+	0.266596i	−0.984980	−	0.172669i	$-0.944761\pi$
$547$	−2.02592	+	6.23515i	−0.0866223	+	0.266596i	0.898358	+	0.439265i	$0.144761\pi$
$548$	7.03093	−	5.10827i	0.300346	−	0.218214i
$549$	29.0935			1.24168
$550$		0			0
$551$	−22.9254			−0.976653
$552$	−5.56471	+	4.04300i	−0.236850	+	0.172081i
$553$	−13.6412	+	41.9833i	−0.580083	+	1.78531i
$554$	1.19338	−	3.67285i	0.0507020	−	0.156045i
$555$		0			0
$556$	1.71613	+	5.28171i	0.0727802	+	0.223994i
$557$	−35.5383			−1.50581			−0.752904	−	0.658131i	$-0.771347\pi$
$557$	−35.5383			−1.50581			−0.752904	+	0.658131i	$0.771347\pi$
$558$	−4.53734	−	13.9645i	−0.192081	−	0.591164i
$559$	0.643514	+	0.467540i	0.0272177	+	0.0197748i
$560$		0			0
$561$	−0.523315	+	0.380210i	−0.0220944	+	0.0160525i
$562$	−2.20396	−	1.60127i	−0.0929682	−	0.0675454i
$563$	−30.9432	−	22.4816i	−1.30410	−	0.947486i	−0.304115	−	0.952635i	$-0.598361\pi$
$563$	−30.9432	−	22.4816i	−1.30410	−	0.947486i	−0.999987	+	0.00514973i	$0.998361\pi$
$564$	0.441070	−	0.320456i	0.0185724	−	0.0134936i
$565$		0			0
$566$	17.6942	+	12.8556i	0.743741	+	0.540360i
$567$	6.68697	+	20.5804i	0.280826	+	0.864295i
$568$	6.29266			0.264034
$569$	2.33585	+	7.18901i	0.0979240	+	0.301379i	0.988005	−	0.154424i	$-0.0493522\pi$
$569$	2.33585	+	7.18901i	0.0979240	+	0.301379i	−0.890081	+	0.455803i	$0.849352\pi$
$570$		0			0
$571$	7.11549	−	21.8992i	0.297774	−	0.916454i	−0.684501	−	0.729011i	$-0.739980\pi$
$571$	7.11549	−	21.8992i	0.297774	−	0.916454i	0.982276	−	0.187443i	$-0.0600199\pi$
$572$	0.577960	−	1.77878i	0.0241657	−	0.0743745i
$573$	1.59808	−	1.16107i	0.0667607	−	0.0485045i
$574$	−80.5540			−3.36226
$575$		0			0
$576$	−6.14617			−0.256090
$577$	−18.0546	+	13.1175i	−0.751624	+	0.546087i	−0.896330	−	0.443388i	$-0.853777\pi$
$577$	−18.0546	+	13.1175i	−0.751624	+	0.546087i	0.144706	+	0.989475i	$0.453777\pi$
$578$	8.81529	−	27.1307i	0.366668	−	1.12849i
$579$	−4.95354	+	15.2454i	−0.205862	+	0.633579i
$580$		0			0
$581$	14.8731	+	45.7747i	0.617040	+	1.89905i
$582$	−9.94866			−0.412385
$583$	−1.48940	−	4.58390i	−0.0616846	−	0.189846i
$584$	−16.3457	−	11.8758i	−0.676389	−	0.491425i
$585$		0			0
$586$	15.9355	−	11.5778i	0.658290	−	0.478276i
$587$	17.0530	+	12.3897i	0.703851	+	0.511378i	0.881184	−	0.472773i	$-0.156747\pi$
$587$	17.0530	+	12.3897i	0.703851	+	0.511378i	−0.177333	+	0.984151i	$0.556747\pi$
$588$	−6.74638	−	4.90153i	−0.278216	−	0.202136i
$589$	−15.6944	+	11.4026i	−0.646676	+	0.469838i
$590$		0			0
$591$	0.730887	+	0.531020i	0.0300647	+	0.0218433i
$592$	−8.32273	−	25.6147i	−0.342062	−	1.05276i
$593$	34.3547			1.41078			0.705390	−	0.708819i	$-0.250772\pi$
$593$	34.3547			1.41078			0.705390	+	0.708819i	$0.250772\pi$
$594$	7.94965	+	24.4665i	0.326178	+	1.00387i
$595$		0			0
$596$	−3.10030	+	9.54175i	−0.126993	+	0.390846i
$597$	−1.89357	+	5.82782i	−0.0774988	+	0.238517i
$598$	3.84891	−	2.79640i	0.157394	−	0.114353i
$599$	0.498231			0.0203572			0.0101786	−	0.999948i	$-0.496760\pi$
$599$	0.498231			0.0203572			0.0101786	+	0.999948i	$0.496760\pi$
$600$		0			0
$601$	27.8635			1.13657			0.568287	−	0.822830i	$-0.307606\pi$
$601$	27.8635			1.13657			0.568287	+	0.822830i	$0.307606\pi$
$602$	−8.68073	+	6.30692i	−0.353800	+	0.257051i
$603$	−2.27827	+	7.01180i	−0.0927784	+	0.285543i
$604$	−0.397390	+	1.22304i	−0.0161696	+	0.0497648i
$605$		0			0
$606$	1.31739	+	4.05451i	0.0535153	+	0.164703i
$607$	−14.1000			−0.572303			−0.286152	−	0.958184i	$-0.592376\pi$
$607$	−14.1000			−0.572303			−0.286152	+	0.958184i	$0.592376\pi$
$608$	−7.62255	−	23.4598i	−0.309135	−	0.951420i
$609$	−10.8982	−	7.91804i	−0.441619	−	0.320855i
$610$		0			0
$611$	0.426630	−	0.309965i	0.0172596	−	0.0125398i
$612$	0.391588	+	0.284506i	0.0158290	+	0.0115005i
$613$	25.7475	+	18.7067i	1.03993	+	0.755556i	0.970272	−	0.242015i	$-0.0778084\pi$
$613$	25.7475	+	18.7067i	1.03993	+	0.755556i	0.0696606	+	0.997571i	$0.477808\pi$
$614$	−36.1822	+	26.2879i	−1.46020	+	1.06089i
$615$		0			0
$616$	−28.5443	−	20.7387i	−1.15008	−	0.835585i
$617$	−10.4961	−	32.3038i	−0.422559	−	1.30050i	−0.905312	−	0.424746i	$-0.860363\pi$
$617$	−10.4961	−	32.3038i	−0.422559	−	1.30050i	0.482753	−	0.875756i	$-0.339637\pi$
$618$	−0.477508			−0.0192082
$619$	0.348700	+	1.07319i	0.0140155	+	0.0431351i	0.957820	−	0.287370i	$-0.0927809\pi$
$619$	0.348700	+	1.07319i	0.0140155	+	0.0431351i	−0.943804	+	0.330505i	$0.892781\pi$
$620$		0			0
$621$	−5.95019	+	18.3128i	−0.238773	+	0.734868i
$622$	7.01805	−	21.5993i	0.281398	−	0.866055i
$623$	−26.9593	+	19.5871i	−1.08010	+	0.784739i
$624$	−2.02368			−0.0810119
$625$		0			0
$626$	28.6085			1.14343
$627$	12.4863	−	9.07181i	0.498654	−	0.362293i
$628$	2.53166	−	7.79165i	0.101024	−	0.310921i
$629$	0.389341	−	1.19827i	0.0155240	−	0.0477781i
$630$		0			0
$631$	10.1296	+	31.1758i	0.403254	+	1.24109i	0.922345	+	0.386368i	$0.126271\pi$
$631$	10.1296	+	31.1758i	0.403254	+	1.24109i	−0.519091	+	0.854719i	$0.673729\pi$
$632$	−18.8751			−0.750813
$633$	−4.61659	−	14.2084i	−0.183493	−	0.564733i
$634$	−22.8744	−	16.6193i	−0.908460	−	0.660035i
$635$		0			0
$636$	0.589988	−	0.428652i	0.0233946	−	0.0169971i
$637$	−6.52551	−	4.74106i	−0.258550	−	0.187848i
$638$	22.0227	+	16.0005i	0.871889	+	0.633464i
$639$	6.47140	−	4.70175i	0.256005	−	0.185998i
$640$		0			0
$641$	−24.6043	−	17.8761i	−0.971812	−	0.706063i	−0.0159485	−	0.999873i	$-0.505077\pi$
$641$	−24.6043	−	17.8761i	−0.971812	−	0.706063i	−0.955864	+	0.293810i	$0.905077\pi$
$642$	−0.607388	−	1.86935i	−0.0239717	−	0.0737773i
$643$	1.06932			0.0421700			0.0210850	−	0.999778i	$-0.493288\pi$
$643$	1.06932			0.0421700			0.0210850	+	0.999778i	$0.493288\pi$
$644$	5.83552	+	17.9599i	0.229952	+	0.707719i
$645$		0			0
$646$	0.671589	−	2.06694i	0.0264233	−	0.0813226i
$647$	9.44602	−	29.0719i	0.371362	−	1.14293i	−0.574539	−	0.818477i	$-0.694819\pi$
$647$	9.44602	−	29.0719i	0.371362	−	1.14293i	0.945901	−	0.324456i	$-0.105181\pi$
$648$	−7.48556	+	5.43858i	−0.294061	+	0.213648i
$649$	17.6471			0.692709
$650$		0			0
$651$	−11.3991			−0.446765
$652$	−3.76508	+	2.73549i	−0.147452	+	0.107130i
$653$	−10.3058	+	31.7179i	−0.403296	+	1.24122i	0.519014	+	0.854766i	$0.326299\pi$
$653$	−10.3058	+	31.7179i	−0.403296	+	1.24122i	−0.922310	+	0.386451i	$0.873701\pi$
$654$	−0.0276828	+	0.0851989i	−0.00108248	+	0.00333154i
$655$		0			0
$656$	−16.0151	−	49.2893i	−0.625283	−	1.92442i
$657$	−25.6833			−1.00200
$658$	2.19824	+	6.76548i	0.0856962	+	0.263746i
$659$	8.18325	+	5.94548i	0.318774	+	0.231603i	0.735652	−	0.677360i	$-0.236876\pi$
$659$	8.18325	+	5.94548i	0.318774	+	0.231603i	−0.416878	+	0.908962i	$0.636876\pi$
$660$		0			0
$661$	24.9487	−	18.1263i	0.970392	−	0.705031i	0.0148510	−	0.999890i	$-0.495273\pi$
$661$	24.9487	−	18.1263i	0.970392	−	0.705031i	0.955541	+	0.294859i	$0.0952726\pi$
$662$	17.4793	+	12.6994i	0.679350	+	0.493577i
$663$	−0.0765885	−	0.0556448i	−0.00297445	−	0.00216106i
$664$	−16.6493	+	12.0964i	−0.646119	+	0.469433i
$665$		0			0
$666$	−18.4081	−	13.3742i	−0.713298	−	0.518241i
$667$	6.29621	+	19.3778i	0.243790	+	0.750310i
$668$	18.2290			0.705302
$669$	1.39066	+	4.28001i	0.0537660	+	0.165475i
$670$		0			0
$671$	−14.1040	+	43.4077i	−0.544480	+	1.67574i
$672$	4.47902	−	13.7850i	0.172782	−	0.531768i
$673$	24.9379	−	18.1185i	0.961286	−	0.698415i	0.00783693	−	0.999969i	$-0.497505\pi$
$673$	24.9379	−	18.1185i	0.961286	−	0.698415i	0.953449	+	0.301554i	$0.0975054\pi$
$674$	35.7514			1.37709
$675$		0			0
$676$	−10.5666			−0.406407
$677$	−33.3736	+	24.2474i	−1.28265	+	0.931902i	−0.999630	−	0.0272110i	$-0.991337\pi$
$677$	−33.3736	+	24.2474i	−1.28265	+	0.931902i	−0.283023	+	0.959113i	$0.591337\pi$
$678$	5.22238	−	16.0728i	0.200564	−	0.617273i
$679$	11.8034	−	36.3272i	0.452974	−	1.39411i
$680$		0			0
$681$	2.47218	+	7.60859i	0.0947342	+	0.291562i
$682$	23.0348			0.882048
$683$	6.90698	+	21.2575i	0.264288	+	0.813395i	0.991857	+	0.127360i	$0.0406504\pi$
$683$	6.90698	+	21.2575i	0.264288	+	0.813395i	−0.727568	+	0.686035i	$0.759350\pi$
$684$	−9.34329	−	6.78830i	−0.357250	−	0.259557i
$685$		0			0
$686$	44.2578	−	32.1552i	1.68977	−	1.22769i
$687$	−8.64364	−	6.27997i	−0.329775	−	0.239596i
$688$	−5.58490	−	4.05767i	−0.212922	−	0.154697i
$689$	0.570673	−	0.414618i	0.0217409	−	0.0157957i
$690$		0			0
$691$	−7.43406	−	5.40116i	−0.282805	−	0.205470i	0.437335	−	0.899299i	$-0.355922\pi$
$691$	−7.43406	−	5.40116i	−0.282805	−	0.205470i	−0.720140	+	0.693829i	$0.755922\pi$
$692$	−6.03965	−	18.5881i	−0.229593	−	0.706614i
$693$	−44.8506			−1.70373
$694$	14.8924	+	45.8342i	0.565309	+	1.73984i
$695$		0			0
$696$	1.77992	−	5.47804i	0.0674678	−	0.207644i
$697$	0.749192	−	2.30577i	0.0283777	−	0.0873374i
$698$	27.1188	−	19.7030i	1.02646	−	0.745768i
$699$	5.56018			0.210305
$700$		0			0
$701$	−35.9929			−1.35943			−0.679717	−	0.733475i	$-0.737897\pi$
$701$	−35.9929			−1.35943			−0.679717	+	0.733475i	$0.737897\pi$
$702$	−3.04595	+	2.21302i	−0.114962	+	0.0835249i
$703$	−9.28967	+	28.5907i	−0.350366	+	1.07832i
$704$	2.97956	−	9.17014i	0.112296	−	0.345613i
$705$		0			0
$706$	12.8446	+	39.5316i	0.483413	+	1.48779i
$707$	−16.3679			−0.615578
$708$	0.825111	+	2.53943i	0.0310096	+	0.0954376i
$709$	−16.3795	−	11.9004i	−0.615144	−	0.446928i	0.236078	−	0.971734i	$-0.424138\pi$
$709$	−16.3795	−	11.9004i	−0.615144	−	0.446928i	−0.851222	+	0.524806i	$0.824138\pi$
$710$		0			0
$711$	−19.4113	+	14.1031i	−0.727980	+	0.528908i
$712$	−11.5273	−	8.37508i	−0.432004	−	0.313870i
$713$	13.9484	+	10.1341i	0.522373	+	0.379526i
$714$	1.03315	−	0.750625i	0.0386645	−	0.0280914i
$715$		0			0
$716$	4.26271	+	3.09704i	0.159305	+	0.115742i
$717$	1.91824	+	5.90374i	0.0716381	+	0.220479i
$718$	−36.1951			−1.35079
$719$	−11.4418	−	35.2143i	−0.426708	−	1.31327i	−0.901349	−	0.433093i	$-0.857422\pi$
$719$	−11.4418	−	35.2143i	−0.426708	−	1.31327i	0.474641	−	0.880180i	$-0.342578\pi$
$720$		0			0
$721$	0.566531	−	1.74360i	0.0210987	−	0.0649352i
$722$	−6.14025	+	18.8977i	−0.228516	+	0.703301i
$723$	0.345319	−	0.250889i	0.0128425	−	0.00933066i
$724$	−11.1219			−0.413343
$725$		0			0
$726$	−5.17249			−0.191969
$727$	9.77211	−	7.09986i	0.362428	−	0.263319i	−0.391636	−	0.920120i	$-0.628091\pi$
$727$	9.77211	−	7.09986i	0.362428	−	0.263319i	0.754064	+	0.656801i	$0.228091\pi$
$728$	1.59568	−	4.91099i	0.0591397	−	0.182013i
$729$	−1.06397	+	3.27458i	−0.0394065	+	0.121281i
$730$		0			0
$731$	−0.0997940	−	0.307134i	−0.00369102	−	0.0113598i
$732$	−6.90586			−0.255248
$733$	13.7858	+	42.4282i	0.509188	+	1.56712i	0.793614	+	0.608422i	$0.208197\pi$
$733$	13.7858	+	42.4282i	0.509188	+	1.56712i	−0.284425	+	0.958698i	$0.591803\pi$
$734$	1.55779	+	1.13180i	0.0574992	+	0.0417756i
$735$		0			0
$736$	−17.7360	+	12.8860i	−0.653759	+	0.474984i
$737$	−9.35720	−	6.79840i	−0.344677	−	0.250422i
$738$	−35.4218	−	25.7354i	−1.30389	−	0.947335i
$739$	11.8491	−	8.60890i	0.435877	−	0.316683i	−0.348117	−	0.937451i	$-0.613179\pi$
$739$	11.8491	−	8.60890i	0.435877	−	0.316683i	0.783995	+	0.620768i	$0.213179\pi$
$740$		0			0
$741$	1.82740	+	1.32768i	0.0671312	+	0.0487737i
$742$	2.94043	+	9.04970i	0.107946	+	0.332225i
$743$	24.4397			0.896604			0.448302	−	0.893882i	$-0.352029\pi$
$743$	24.4397			0.896604			0.448302	+	0.893882i	$0.352029\pi$
$744$	−1.50616	−	4.63549i	−0.0552186	−	0.169945i
$745$		0			0
$746$	6.00288	−	18.4750i	0.219781	−	0.676417i
$747$	−8.08402	+	24.8801i	−0.295779	+	0.910314i
$748$	−0.614321	+	0.446330i	−0.0224618	+	0.0163194i
$749$	7.54648			0.275743
$750$		0			0
$751$	31.2863			1.14165			0.570826	−	0.821071i	$-0.306623\pi$
$751$	31.2863			1.14165			0.570826	+	0.821071i	$0.306623\pi$
$752$	−3.70262	+	2.69011i	−0.135021	+	0.0980982i
$753$	−3.11497	+	9.58690i	−0.113516	+	0.349366i
$754$	−1.23111	+	3.78896i	−0.0448343	+	0.137986i
$755$		0			0
$756$	−4.61812	−	14.2131i	−0.167959	−	0.516926i
$757$	−11.3251			−0.411617			−0.205808	−	0.978592i	$-0.565982\pi$
$757$	−11.3251			−0.411617			−0.205808	+	0.978592i	$0.565982\pi$
$758$	−10.9790	−	33.7899i	−0.398775	−	1.22730i
$759$	−11.0972	−	8.06260i	−0.402803	−	0.292654i
$760$		0			0
$761$	33.4397	−	24.2954i	1.21219	−	0.880707i	0.216761	−	0.976225i	$-0.430451\pi$
$761$	33.4397	−	24.2954i	1.21219	−	0.880707i	0.995428	+	0.0955176i	$0.0304506\pi$
$762$	−11.4276	−	8.30262i	−0.413977	−	0.300772i
$763$	−0.278257	−	0.202165i	−0.0100736	−	0.00731888i
$764$	1.87599	−	1.36299i	0.0678709	−	0.0493111i
$765$		0			0
$766$	1.16869	+	0.849104i	0.0422266	+	0.0306794i
$767$	0.798097	+	2.45629i	0.0288176	+	0.0886915i
$768$	12.0882			0.436195
$769$	6.99895	+	21.5406i	0.252389	+	0.776773i	0.994333	+	0.106311i	$0.0339039\pi$
$769$	6.99895	+	21.5406i	0.252389	+	0.776773i	−0.741944	+	0.670462i	$0.766096\pi$
$770$		0			0
$771$	3.88219	−	11.9481i	0.139814	−	0.430302i
$772$	−5.81498	+	17.8967i	−0.209286	+	0.644115i
$773$	−13.6353	+	9.90659i	−0.490426	+	0.356315i	−0.805348	−	0.592802i	$-0.798022\pi$
$773$	−13.6353	+	9.90659i	−0.490426	+	0.356315i	0.314922	+	0.949118i	$0.398022\pi$
$774$	−5.83210			−0.209630
$775$		0			0
$776$	16.3322			0.586292
$777$	−14.2909	+	10.3829i	−0.512682	+	0.372485i
$778$	17.6529	−	54.3300i	0.632886	−	1.94782i
$779$	−17.8757	+	55.0157i	−0.640463	+	1.97114i
$780$		0			0
$781$	3.87782	+	11.9347i	0.138759	+	0.427058i
$782$	−1.93153			−0.0690715
$783$	−4.98270	−	15.3352i	−0.178067	−	0.548035i
$784$	56.6333	+	41.1465i	2.02262	+	1.46952i
$785$		0			0
$786$	−16.1919	+	11.7641i	−0.577547	+	0.419612i
$787$	−16.2683	−	11.8196i	−0.579902	−	0.421323i	0.258787	−	0.965934i	$-0.416677\pi$
$787$	−16.2683	−	11.8196i	−0.579902	−	0.421323i	−0.838689	+	0.544611i	$0.816677\pi$
$788$	0.857990	+	0.623366i	0.0305646	+	0.0222065i
$789$	−13.9847	+	10.1605i	−0.497867	+	0.361722i
$790$		0			0
$791$	52.4934	+	38.1387i	1.86645	+	1.35605i
$792$	−5.92612	−	18.2387i	−0.210576	−	0.648085i
$793$	−6.67976			−0.237205
$794$	−13.9563	−	42.9531i	−0.495291	−	1.52435i
$795$		0			0
$796$	−2.22287	+	6.84130i	−0.0787876	+	0.242483i
$797$	−16.7403	+	51.5213i	−0.592971	+	1.82498i	−0.0283955	+	0.999597i	$0.509040\pi$
$797$	−16.7403	+	51.5213i	−0.592971	+	1.82498i	−0.564576	+	0.825381i	$0.690960\pi$
$798$	−24.6508	+	17.9099i	−0.872631	+	0.634003i
$799$	−0.214100			−0.00757430
$800$		0			0
$801$	−18.1124			−0.639971
$802$	5.17194	−	3.75763i	0.182627	−	0.132687i
$803$	12.4508	−	38.3198i	0.439381	−	1.35228i
$804$	0.540788	−	1.66438i	0.0190721	−	0.0586980i
$805$		0			0
$806$	1.04176	+	3.20620i	0.0366944	+	0.112934i
$807$	21.2973			0.749701
$808$	−2.16269	−	6.65608i	−0.0760832	−	0.234160i
$809$	−12.4076	−	9.01462i	−0.436227	−	0.316937i	0.347907	−	0.937529i	$-0.386892\pi$
$809$	−12.4076	−	9.01462i	−0.436227	−	0.316937i	−0.784134	+	0.620592i	$0.786892\pi$
$810$		0			0
$811$	−9.35757	+	6.79868i	−0.328589	+	0.238734i	−0.739832	−	0.672792i	$-0.765095\pi$
$811$	−9.35757	+	6.79868i	−0.328589	+	0.238734i	0.411243	+	0.911526i	$0.365095\pi$
$812$	−12.7935	−	9.29501i	−0.448963	−	0.326191i
$813$	15.9175	+	11.5647i	0.558251	+	0.405593i
$814$	28.8784	−	20.9814i	1.01219	−	0.735397i
$815$		0			0
$816$	0.664693	+	0.482927i	0.0232689	+	0.0169058i
$817$	2.38108	+	7.32822i	0.0833036	+	0.256382i
$818$	23.8630			0.834349
$819$	−2.02839	−	6.24274i	−0.0708776	−	0.218139i
$820$		0			0
$821$	10.3111	−	31.7344i	0.359861	−	1.10754i	−0.593276	−	0.804999i	$-0.702166\pi$
$821$	10.3111	−	31.7344i	0.359861	−	1.10754i	0.953137	−	0.302539i	$-0.0978343\pi$
$822$	3.85119	−	11.8528i	0.134326	−	0.413412i
$823$	−24.2560	+	17.6230i	−0.845511	+	0.614300i	−0.923905	−	0.382623i	$-0.875021\pi$
$823$	−24.2560	+	17.6230i	−0.845511	+	0.614300i	0.0783937	+	0.996922i	$0.475021\pi$
$824$	0.783901			0.0273085
$825$		0			0
$826$	−34.8395			−1.21222
$827$	20.0013	−	14.5318i	0.695514	−	0.505320i	−0.182954	−	0.983121i	$-0.558566\pi$
$827$	20.0013	−	14.5318i	0.695514	−	0.505320i	0.878468	+	0.477801i	$0.158566\pi$
$828$	−3.17180	+	9.76179i	−0.110228	+	0.339246i
$829$	−0.0653280	+	0.201059i	−0.00226893	+	0.00698306i	−0.952185	−	0.305523i	$-0.901169\pi$
$829$	−0.0653280	+	0.201059i	−0.00226893	+	0.00698306i	0.949916	+	0.312506i	$0.101169\pi$
$830$		0			0
$831$	−0.503566	−	1.54982i	−0.0174685	−	0.0537625i
$832$	1.41114			0.0489225
$833$	1.01195	+	3.11448i	0.0350622	+	0.107910i
$834$	6.44294	+	4.68107i	0.223101	+	0.162092i
$835$		0			0
$836$	14.6577	−	10.6494i	0.506946	−	0.368318i
$837$	−11.0385	−	8.01995i	−0.381547	−	0.277210i
$838$	−26.6891	−	19.3908i	−0.921960	−	0.669843i
$839$	4.46346	−	3.24290i	0.154096	−	0.111957i	−0.508066	−	0.861318i	$-0.669639\pi$
$839$	4.46346	−	3.24290i	0.154096	−	0.111957i	0.662162	+	0.749361i	$0.269639\pi$
$840$		0			0
$841$	9.65802	+	7.01696i	0.333035	+	0.241964i
$842$	13.4129	+	41.2807i	0.462239	+	1.42263i
$843$	−1.14953			−0.0395920
$844$	−5.41942	−	16.6793i	−0.186544	−	0.574124i
$845$		0			0
$846$	−1.19482	+	3.67726i	−0.0410786	+	0.126427i
$847$	6.13681	−	18.8872i	0.210863	−	0.648970i
$848$	−4.95273	+	3.59837i	−0.170077	+	0.123568i
$849$	9.22888			0.316734
$850$		0			0
$851$	26.7177			0.915871
$852$	−1.53610	+	1.11604i	−0.0526260	+	0.0382350i
$853$	0.475718	−	1.46411i	0.0162883	−	0.0501302i	−0.942582	−	0.333975i	$-0.891610\pi$
$853$	0.475718	−	1.46411i	0.0162883	−	0.0501302i	0.958870	+	0.283845i	$0.0916100\pi$
$854$	27.8447	−	85.6971i	0.952825	−	2.93249i
$855$		0			0
$856$	0.997118	+	3.06881i	0.0340808	+	0.104890i
$857$	45.3407			1.54881			0.774404	−	0.632691i	$-0.218050\pi$
$857$	45.3407			1.54881			0.774404	+	0.632691i	$0.218050\pi$
$858$	−0.828811	−	2.55082i	−0.0282952	−	0.0870835i
$859$	17.6337	+	12.8116i	0.601654	+	0.437127i	0.846465	−	0.532444i	$-0.178726\pi$
$859$	17.6337	+	12.8116i	0.601654	+	0.437127i	−0.244812	+	0.969571i	$0.578726\pi$
$860$		0			0
$861$	−27.4993	+	19.9794i	−0.937173	+	0.680896i
$862$	12.8364	+	9.32621i	0.437211	+	0.317652i
$863$	−10.3458	−	7.51669i	−0.352176	−	0.255871i	0.397605	−	0.917557i	$-0.369841\pi$
$863$	−10.3458	−	7.51669i	−0.352176	−	0.255871i	−0.749782	+	0.661685i	$0.769841\pi$
$864$	14.0360	−	10.1977i	0.477513	−	0.346933i
$865$		0			0
$866$	2.38553	+	1.73319i	0.0810637	+	0.0588962i
$867$	−3.71975	−	11.4482i	−0.126329	−	0.388801i
$868$	−13.3814			−0.454194
$869$	−11.6317	−	35.7988i	−0.394579	−	1.21439i
$870$		0			0
$871$	0.523084	−	1.60989i	0.0177240	−	0.0545489i
$872$	0.0454454	−	0.139867i	0.00153898	−	0.00473648i
$873$	16.7961	−	12.2031i	0.568463	−	0.413012i
$874$	46.0863			1.55889
$875$		0			0
$876$	6.09640			0.205978
$877$	7.72887	−	5.61535i	0.260985	−	0.189617i	−0.449596	−	0.893232i	$-0.648432\pi$
$877$	7.72887	−	5.61535i	0.260985	−	0.189617i	0.710581	+	0.703615i	$0.248432\pi$
$878$	−14.6089	+	44.9615i	−0.493025	+	1.51738i
$879$	2.56843	−	7.90481i	0.0866309	−	0.266622i
$880$		0			0
$881$	−12.0929	−	37.2180i	−0.407419	−	1.25391i	−0.918859	−	0.394587i	$-0.870888\pi$
$881$	−12.0929	−	37.2180i	−0.407419	−	1.25391i	0.511440	−	0.859319i	$-0.329112\pi$
$882$	59.1400			1.99135
$883$	10.8234	+	33.3111i	0.364238	+	1.12101i	0.950457	+	0.310856i	$0.100616\pi$
$883$	10.8234	+	33.3111i	0.364238	+	1.12101i	−0.586220	+	0.810152i	$0.699384\pi$
$884$	−0.0899074	−	0.0653215i	−0.00302391	−	0.00219700i
$885$		0			0
$886$	−40.7360	+	29.5964i	−1.36855	+	0.994312i
$887$	29.3219	+	21.3036i	0.984531	+	0.715304i	0.958717	−	0.284363i	$-0.0917820\pi$
$887$	29.3219	+	21.3036i	0.984531	+	0.715304i	0.0258147	+	0.999667i	$0.491782\pi$
$888$	−6.11052	−	4.43955i	−0.205056	−	0.148982i
$889$	43.8747	−	31.8769i	1.47151	−	1.06912i
$890$		0			0
$891$	−14.9278	−	10.8457i	−0.500100	−	0.363344i
$892$	1.63250	+	5.02432i	0.0546601	+	0.168227i
$893$	5.10841			0.170946
$894$	4.44593	+	13.6832i	0.148694	+	0.457633i
$895$		0			0
$896$	−18.4933	+	56.9164i	−0.617817	+	1.90144i
$897$	0.620353	−	1.90925i	0.0207130	−	0.0637480i
$898$	8.57967	−	6.23349i	0.286307	−	0.208014i
$899$	−14.4378			−0.481528
$900$		0			0
$901$	−0.286386			−0.00954089
$902$	55.5694	−	40.3735i	1.85026	−	1.34429i
$903$	−1.39913	+	4.30607i	−0.0465601	+	0.143297i
$904$	−8.57332	+	26.3860i	−0.285144	+	0.877584i
$905$		0			0
$906$	0.569869	+	1.75388i	0.0189326	+	0.0582686i
$907$	40.8532			1.35651			0.678255	−	0.734827i	$-0.262737\pi$
$907$	40.8532			1.35651			0.678255	+	0.734827i	$0.262737\pi$
$908$	2.90210	+	8.93174i	0.0963095	+	0.296410i
$909$	−7.19741	−	5.22922i	−0.238723	−	0.173442i
$910$		0			0
$911$	−10.3124	+	7.49237i	−0.341664	+	0.248233i	−0.745364	−	0.666658i	$-0.767724\pi$
$911$	−10.3124	+	7.49237i	−0.341664	+	0.248233i	0.403700	+	0.914892i	$0.367724\pi$
$912$	−15.8595	−	11.5226i	−0.525162	−	0.381553i
$913$	−33.2023	−	24.1229i	−1.09884	−	0.798351i
$914$	26.1226	−	18.9792i	0.864058	−	0.627775i
$915$		0			0
$916$	−10.1468	−	7.37207i	−0.335259	−	0.243580i
$917$	−23.7456	−	73.0815i	−0.784150	−	2.41337i
$918$	1.52858			0.0504506
$919$	2.98883	+	9.19868i	0.0985924	+	0.303436i	0.988173	−	0.153341i	$-0.0490034\pi$
$919$	2.98883	+	9.19868i	0.0985924	+	0.303436i	−0.889581	+	0.456778i	$0.849003\pi$
$920$		0			0
$921$	−5.83172	+	17.9482i	−0.192162	+	0.591413i
$922$	−3.67840	+	11.3210i	−0.121142	+	0.372836i
$923$	−1.48581	+	1.07951i	−0.0489061	+	0.0355323i
$924$	10.6461			0.350231
$925$		0			0
$926$	16.1917			0.532094
$927$	0.806167	−	0.585715i	0.0264780	−	0.0192374i
$928$	5.67303	−	17.4598i	0.186226	−	0.573146i
$929$	3.37431	−	10.3850i	0.110707	−	0.340722i	−0.880320	−	0.474380i	$-0.842672\pi$
$929$	3.37431	−	10.3850i	0.110707	−	0.340722i	0.991028	+	0.133658i	$0.0426723\pi$
$930$		0			0
$931$	−24.1452	−	74.3113i	−0.791328	−	2.43546i
$932$	6.52711			0.213803
$933$	−2.96137	−	9.11417i	−0.0969510	−	0.298384i
$934$	−26.1786	−	19.0199i	−0.856589	−	0.622349i
$935$		0			0
$936$	2.27063	−	1.64971i	0.0742178	−	0.0539224i
$937$	12.9011	+	9.37319i	0.421460	+	0.306209i	0.778225	−	0.627985i	$-0.216120\pi$
$937$	12.9011	+	9.37319i	0.421460	+	0.306209i	−0.356765	+	0.934194i	$0.616120\pi$
$938$	18.4733	+	13.4216i	0.603175	+	0.438232i
$939$	9.76628	−	7.09562i	0.318710	−	0.231557i
$940$		0			0
$941$	−4.79505	−	3.48381i	−0.156314	−	0.113569i	0.506879	−	0.862017i	$-0.330799\pi$
$941$	−4.79505	−	3.48381i	−0.156314	−	0.113569i	−0.663193	+	0.748448i	$0.730799\pi$
$942$	−3.63047	−	11.1734i	−0.118287	−	0.364051i
$943$	51.4117			1.67419
$944$	−6.92649	−	21.3176i	−0.225438	−	0.693827i
$945$		0			0
$946$	2.82730	−	8.70154i	0.0919235	−	0.282912i
$947$	0.306045	−	0.941910i	0.00994513	−	0.0306080i	−0.945961	−	0.324281i	$-0.894878\pi$
$947$	0.306045	−	0.941910i	0.00994513	−	0.0306080i	0.955906	+	0.293673i	$0.0948777\pi$
$948$	4.60761	−	3.34763i	0.149648	−	0.108726i
$949$	5.89681			0.191418
$950$		0			0
$951$	−11.9308			−0.386882
$952$	−1.69606	+	1.23226i	−0.0549697	+	0.0399379i
$953$	16.5631	−	50.9759i	0.536531	−	1.65127i	−0.203787	−	0.979015i	$-0.565325\pi$
$953$	16.5631	−	50.9759i	0.536531	−	1.65127i	0.740318	−	0.672257i	$-0.234675\pi$
$954$	−1.59822	+	4.91881i	−0.0517442	+	0.159252i
$955$		0			0
$956$	2.25183	+	6.93042i	0.0728294	+	0.224146i
$957$	11.4866			0.371308
$958$	19.7675	+	60.8380i	0.638658	+	1.96559i
$959$	38.7107	+	28.1250i	1.25003	+	0.908203i
$960$		0			0
$961$	15.1956	−	11.0402i	0.490180	−	0.356137i
$962$	4.22643	+	3.07068i	0.136266	+	0.0990027i
$963$	3.31840	+	2.41096i	0.106934	+	0.0776920i
$964$	0.405371	−	0.294519i	0.0130561	−	0.00948582i
$965$		0			0
$966$	21.9085	+	15.9175i	0.704895	+	0.512136i
$967$	9.18861	+	28.2796i	0.295486	+	0.909412i	0.983058	+	0.183296i	$0.0586765\pi$
$967$	9.18861	+	28.2796i	0.295486	+	0.909412i	−0.687572	+	0.726116i	$0.741323\pi$
$968$	8.49141			0.272924
$969$	−0.283387	−	0.872176i	−0.00910370	−	0.0280183i
$970$		0			0
$971$	18.7316	−	57.6498i	0.601125	−	1.85007i	0.0796154	−	0.996826i	$-0.474631\pi$
$971$	18.7316	−	57.6498i	0.601125	−	1.85007i	0.521509	−	0.853246i	$-0.325369\pi$
$972$	3.88039	−	11.9426i	0.124463	−	0.383059i
$973$	−24.7369	+	17.9724i	−0.793027	+	0.576168i
$974$	28.1954			0.903440
$975$		0			0
$976$	57.9720			1.85564
$977$	36.0117	−	26.1641i	1.15212	−	0.837062i	0.163356	−	0.986567i	$-0.447768\pi$
$977$	36.0117	−	26.1641i	1.15212	−	0.837062i	0.988761	+	0.149505i	$0.0477679\pi$
$978$	−2.06232	+	6.34718i	−0.0659458	+	0.202960i
$979$	8.78060	−	27.0239i	0.280629	−	0.863688i
$980$		0			0
$981$	−0.0577692	−	0.177795i	−0.00184443	−	0.00567657i
$982$	15.0675			0.480822
$983$	−11.8168	−	36.3685i	−0.376898	−	1.15997i	−0.942189	−	0.335082i	$-0.891236\pi$
$983$	−11.8168	−	36.3685i	−0.376898	−	1.15997i	0.565291	−	0.824892i	$-0.308764\pi$
$984$	−11.7582	−	8.54283i	−0.374838	−	0.272336i
$985$		0			0
$986$	1.30856	−	0.950724i	0.0416730	−	0.0302772i
$987$	2.42844	+	1.76436i	0.0772979	+	0.0561602i
$988$	2.14519	+	1.55857i	0.0682475	+	0.0495847i
$989$	5.54027	−	4.02524i	0.176170	−	0.127995i
$990$		0			0
$991$	−18.3713	−	13.3475i	−0.583584	−	0.423998i	0.256431	−	0.966563i	$-0.417453\pi$
$991$	−18.3713	−	13.3475i	−0.583584	−	0.423998i	−0.840014	+	0.542564i	$0.817453\pi$
$992$	−4.80049	−	14.7744i	−0.152416	−	0.469087i
$993$	9.11678			0.289312
$994$	−7.65574	−	23.5619i	−0.242825	−	0.747339i
$995$		0			0
$996$	1.91889	−	5.90573i	0.0608023	−	0.187130i
$997$	−6.37453	+	19.6188i	−0.201883	+	0.621333i	0.797944	+	0.602732i	$0.205921\pi$
$997$	−6.37453	+	19.6188i	−0.201883	+	0.621333i	−0.999827	+	0.0186012i	$0.994079\pi$
$998$	−49.4795	+	35.9490i	−1.56625	+	1.13794i
$999$	−21.1439			−0.668962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.m.251.4		16
5.2	odd	4		625.2.e.j.374.6		32
5.3	odd	4		625.2.e.j.374.3		32
5.4	even	2		625.2.d.q.251.1		16
25.2	odd	20		625.2.e.k.499.6		32
25.3	odd	20		625.2.b.d.624.12		16
25.4	even	10		625.2.a.e.1.7	✓	8
25.6	even	5		625.2.d.n.501.1		16
25.8	odd	20		625.2.e.k.124.6		32
25.9	even	10		625.2.d.q.376.1		16
25.11	even	5		625.2.d.n.126.1		16
25.12	odd	20		625.2.e.j.249.3		32
25.13	odd	20		625.2.e.j.249.6		32
25.14	even	10		625.2.d.p.126.4		16
25.16	even	5	inner	625.2.d.m.376.4		16
25.17	odd	20		625.2.e.k.124.3		32
25.19	even	10		625.2.d.p.501.4		16
25.21	even	5		625.2.a.g.1.2	yes	8
25.22	odd	20		625.2.b.d.624.5		16
25.23	odd	20		625.2.e.k.499.3		32
75.29	odd	10		5625.2.a.be.1.2		8
75.71	odd	10		5625.2.a.s.1.7		8
100.71	odd	10		10000.2.a.be.1.5		8
100.79	odd	10		10000.2.a.bn.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.7	✓	8	25.4	even	10
625.2.a.g.1.2	yes	8	25.21	even	5
625.2.b.d.624.5		16	25.22	odd	20
625.2.b.d.624.12		16	25.3	odd	20
625.2.d.m.251.4		16	1.1	even	1	trivial
625.2.d.m.376.4		16	25.16	even	5	inner
625.2.d.n.126.1		16	25.11	even	5
625.2.d.n.501.1		16	25.6	even	5
625.2.d.p.126.4		16	25.14	even	10
625.2.d.p.501.4		16	25.19	even	10
625.2.d.q.251.1		16	5.4	even	2
625.2.d.q.376.1		16	25.9	even	10
625.2.e.j.249.3		32	25.12	odd	20
625.2.e.j.249.6		32	25.13	odd	20
625.2.e.j.374.3		32	5.3	odd	4
625.2.e.j.374.6		32	5.2	odd	4
625.2.e.k.124.3		32	25.17	odd	20
625.2.e.k.124.6		32	25.8	odd	20
625.2.e.k.499.3		32	25.23	odd	20
625.2.e.k.499.6		32	25.2	odd	20
5625.2.a.s.1.7		8	75.71	odd	10
5625.2.a.be.1.2		8	75.29	odd	10
10000.2.a.be.1.5		8	100.71	odd	10
10000.2.a.bn.1.4		8	100.79	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36191 - 0.989484i) q^{2} +(0.219507 - 0.675574i) q^{3} +(0.257680 - 0.793058i) q^{4} +(-0.369521 - 1.13727i) q^{6} +4.59110 q^{7} +(0.606623 + 1.86699i) q^{8} +(2.01883 + 1.46677i) q^{9} +O(q^{10})\)	\(q+(1.36191 - 0.989484i) q^{2} +(0.219507 - 0.675574i) q^{3} +(0.257680 - 0.793058i) q^{4} +(-0.369521 - 1.13727i) q^{6} +4.59110 q^{7} +(0.606623 + 1.86699i) q^{8} +(2.01883 + 1.46677i) q^{9} +(-3.16713 + 2.30105i) q^{11} +(-0.479206 - 0.348164i) q^{12} +(-0.463518 - 0.336765i) q^{13} +(6.25266 - 4.54282i) q^{14} +(4.02276 + 2.92270i) q^{16} +(0.0718808 + 0.221226i) q^{17} +4.20081 q^{18} +(-1.71507 - 5.27846i) q^{19} +(1.00778 - 3.10163i) q^{21} +(-2.03648 + 6.26765i) q^{22} +(-3.99061 + 2.89935i) q^{23} +1.39445 q^{24} -0.964492 q^{26} +(3.15809 - 2.29449i) q^{27} +(1.18304 - 3.64101i) q^{28} +(1.27643 - 3.92845i) q^{29} +(-1.08011 - 3.32424i) q^{31} +4.44444 q^{32} +(0.859324 + 2.64473i) q^{33} +(0.316795 + 0.230165i) q^{34} +(1.68345 - 1.22310i) q^{36} +(-4.38203 - 3.18373i) q^{37} +(-7.55872 - 5.49173i) q^{38} +(-0.329255 + 0.239218i) q^{39} +(-8.43214 - 6.12630i) q^{41} +(-1.69651 - 5.22132i) q^{42} -1.38833 q^{43} +(1.00876 + 3.10465i) q^{44} +(-2.56598 + 7.89729i) q^{46} +(-0.284425 + 0.875370i) q^{47} +(2.85753 - 2.07611i) q^{48} +14.0782 q^{49} +0.165233 q^{51} +(-0.386514 + 0.280819i) q^{52} +(-0.380455 + 1.17092i) q^{53} +(2.03067 - 6.24976i) q^{54} +(2.78507 + 8.57157i) q^{56} -3.94246 q^{57} +(-2.14876 - 6.61320i) q^{58} +(-3.64689 - 2.64962i) q^{59} +(9.43214 - 6.85285i) q^{61} +(-4.76029 - 3.45856i) q^{62} +(9.26868 + 6.73409i) q^{63} +(-1.99259 + 1.44770i) q^{64} +(3.78724 + 2.75159i) q^{66} +(0.912982 + 2.80987i) q^{67} +0.193968 q^{68} +(1.08276 + 3.33238i) q^{69} +(0.990558 - 3.04862i) q^{71} +(-1.51378 + 4.65893i) q^{72} +(-8.32657 + 6.04961i) q^{73} -9.11816 q^{74} -4.62806 q^{76} +(-14.5406 + 10.5644i) q^{77} +(-0.211713 + 0.651586i) q^{78} +(-2.97123 + 9.14449i) q^{79} +(1.45651 + 4.48267i) q^{81} -17.5457 q^{82} +(3.23955 + 9.97030i) q^{83} +(-2.20009 - 1.59846i) q^{84} +(-1.89077 + 1.37373i) q^{86} +(-2.37377 - 1.72465i) q^{87} +(-6.21731 - 4.51714i) q^{88} +(-5.87207 + 4.26631i) q^{89} +(-2.12806 - 1.54612i) q^{91} +(1.27105 + 3.91189i) q^{92} -2.48286 q^{93} +(0.478804 + 1.47361i) q^{94} +(0.975587 - 3.00255i) q^{96} +(2.57093 - 7.91252i) q^{97} +(19.1733 - 13.9302i) q^{98} -9.76903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9	\( 16 q - 5 q^{2} - 3 q^{4} + 7 q^{6} + 20 q^{7} - 5 q^{8} - 12 q^{9} - 3 q^{11} + 15 q^{12} - 5 q^{13} - q^{14} + q^{16} - 25 q^{17} - 10 q^{18} + 10 q^{19} + 7 q^{21} - 35 q^{22} - 15 q^{23} + 10 q^{24} + 22 q^{26} + 35 q^{28} - 8 q^{31} + 60 q^{32} - 6 q^{34} + q^{36} - 5 q^{37} - 35 q^{38} + q^{39} - 8 q^{41} - 10 q^{42} - 31 q^{44} + 42 q^{46} - 5 q^{47} - 25 q^{48} - 8 q^{49} - 28 q^{51} + 15 q^{52} - 10 q^{53} + 50 q^{54} + 35 q^{56} - 20 q^{57} + 35 q^{58} - 15 q^{59} + 17 q^{61} + 5 q^{62} + 10 q^{63} + 37 q^{64} + 44 q^{66} - 10 q^{67} + 80 q^{68} - 9 q^{69} - 13 q^{71} + 20 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 45 q^{77} + 5 q^{78} - 55 q^{79} - 19 q^{81} - 90 q^{82} - 15 q^{83} + 59 q^{84} + 7 q^{86} - 60 q^{87} + 40 q^{88} - 28 q^{91} + 45 q^{92} - 80 q^{93} + 4 q^{94} - 43 q^{96} + 40 q^{97} + 45 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - 3 * q^4 + 7 * q^6 + 20 * q^7 - 5 * q^8 - 12 * q^9 - 3 * q^11 + 15 * q^12 - 5 * q^13 - q^14 + q^16 - 25 * q^17 - 10 * q^18 + 10 * q^19 + 7 * q^21 - 35 * q^22 - 15 * q^23 + 10 * q^24 + 22 * q^26 + 35 * q^28 - 8 * q^31 + 60 * q^32 - 6 * q^34 + q^36 - 5 * q^37 - 35 * q^38 + q^39 - 8 * q^41 - 10 * q^42 - 31 * q^44 + 42 * q^46 - 5 * q^47 - 25 * q^48 - 8 * q^49 - 28 * q^51 + 15 * q^52 - 10 * q^53 + 50 * q^54 + 35 * q^56 - 20 * q^57 + 35 * q^58 - 15 * q^59 + 17 * q^61 + 5 * q^62 + 10 * q^63 + 37 * q^64 + 44 * q^66 - 10 * q^67 + 80 * q^68 - 9 * q^69 - 13 * q^71 + 20 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 45 * q^77 + 5 * q^78 - 55 * q^79 - 19 * q^81 - 90 * q^82 - 15 * q^83 + 59 * q^84 + 7 * q^86 - 60 * q^87 + 40 * q^88 - 28 * q^91 + 45 * q^92 - 80 * q^93 + 4 * q^94 - 43 * q^96 + 40 * q^97 + 45 * q^98 - 44 * q^99

Introduction

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