LMFDB - Embedded newform 625.2.d.q.376.3

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			376.3
Root			$3.18910i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.q.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88186 + 1.36725i) q^{2} +(0.711454 + 2.18963i) q^{3} +(1.05398 + 3.24381i) q^{4} +(-1.65491 + 5.09330i) q^{6} -3.59425 q^{7} +(-1.01405 + 3.12093i) q^{8} +(-1.86126 + 1.35229i) q^{9} +O(q^{10})$	\(q+(1.88186 + 1.36725i) q^{2} +(0.711454 + 2.18963i) q^{3} +(1.05398 + 3.24381i) q^{4} +(-1.65491 + 5.09330i) q^{6} -3.59425 q^{7} +(-1.01405 + 3.12093i) q^{8} +(-1.86126 + 1.35229i) q^{9} +(0.402719 + 0.292592i) q^{11} +(-6.35290 + 4.61565i) q^{12} +(2.14219 - 1.55639i) q^{13} +(-6.76385 - 4.91423i) q^{14} +(-0.656686 + 0.477110i) q^{16} +(-1.57821 + 4.85722i) q^{17} -5.35154 q^{18} +(-0.305085 + 0.938956i) q^{19} +(-2.55714 - 7.87007i) q^{21} +(0.357812 + 1.10123i) q^{22} +(5.18889 + 3.76995i) q^{23} -7.55514 q^{24} +6.15926 q^{26} +(1.30262 + 0.946409i) q^{27} +(-3.78826 - 11.6591i) q^{28} +(-1.72123 - 5.29739i) q^{29} +(1.87112 - 5.75872i) q^{31} +4.67497 q^{32} +(-0.354153 + 1.08997i) q^{33} +(-9.61099 + 6.98279i) q^{34} +(-6.34830 - 4.61231i) q^{36} +(-3.71834 + 2.70153i) q^{37} +(-1.85791 + 1.34985i) q^{38} +(4.93199 + 3.58330i) q^{39} +(2.32572 - 1.68973i) q^{41} +(5.94817 - 18.3066i) q^{42} +9.48858 q^{43} +(-0.524658 + 1.61473i) q^{44} +(4.61029 + 14.1890i) q^{46} +(-1.65891 - 5.10560i) q^{47} +(-1.51190 - 1.09846i) q^{48} +5.91861 q^{49} -11.7583 q^{51} +(7.30646 + 5.30846i) q^{52} +(0.0950536 + 0.292545i) q^{53} +(1.15737 + 3.56201i) q^{54} +(3.64476 - 11.2174i) q^{56} -2.27302 q^{57} +(4.00375 - 12.3223i) q^{58} +(1.02458 - 0.744401i) q^{59} +(5.03715 + 3.65970i) q^{61} +(11.3948 - 8.27879i) q^{62} +(6.68984 - 4.86045i) q^{63} +(10.1110 + 7.34607i) q^{64} +(-2.15673 + 1.56695i) q^{66} +(1.63354 - 5.02753i) q^{67} -17.4193 q^{68} +(-4.56314 + 14.0439i) q^{69} +(-0.0469591 - 0.144525i) q^{71} +(-2.33298 - 7.18017i) q^{72} +(-12.0334 - 8.74276i) q^{73} -10.6910 q^{74} -3.36735 q^{76} +(-1.44747 - 1.05165i) q^{77} +(4.38203 + 13.4865i) q^{78} +(-5.12616 - 15.7767i) q^{79} +(-3.27835 + 10.0897i) q^{81} +6.68696 q^{82} +(-4.51040 + 13.8816i) q^{83} +(22.8339 - 16.5898i) q^{84} +(17.8561 + 12.9733i) q^{86} +(10.3748 - 7.53770i) q^{87} +(-1.32154 + 0.960155i) q^{88} +(-9.20843 - 6.69032i) q^{89} +(-7.69955 + 5.59405i) q^{91} +(-6.76004 + 20.8052i) q^{92} +13.9407 q^{93} +(3.85879 - 11.8761i) q^{94} +(3.32603 + 10.2365i) q^{96} +(-0.262415 - 0.807629i) q^{97} +(11.1380 + 8.09220i) q^{98} -1.14523 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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.88186	+	1.36725i	1.33067	+	0.966790i	0.999732	+	0.0231389i	$0.00736600\pi$
$2$	1.88186	+	1.36725i	1.33067	+	0.966790i	0.330941	+	0.943652i	$0.392634\pi$
$3$	0.711454	+	2.18963i	0.410758	+	1.26418i	0.915990	+	0.401200i	$0.131407\pi$
$3$	0.711454	+	2.18963i	0.410758	+	1.26418i	−0.505232	+	0.862983i	$0.668593\pi$
$4$	1.05398	+	3.24381i	0.526990	+	1.62191i
$5$		0			0
$5$		0			0
$6$	−1.65491	+	5.09330i	−0.675616	+	2.07933i
$7$	−3.59425			−1.35850			−0.679249	−	0.733908i	$-0.737694\pi$
$7$	−3.59425			−1.35850			−0.679249	+	0.733908i	$0.737694\pi$
$8$	−1.01405	+	3.12093i	−0.358522	+	1.10342i
$9$	−1.86126	+	1.35229i	−0.620421	+	0.450762i
$10$		0			0
$11$	0.402719	+	0.292592i	0.121424	+	0.0882199i	0.646840	−	0.762626i	$-0.276090\pi$
$11$	0.402719	+	0.292592i	0.121424	+	0.0882199i	−0.525416	+	0.850846i	$0.676090\pi$
$12$	−6.35290	+	4.61565i	−1.83392	+	1.33242i
$13$	2.14219	−	1.55639i	0.594136	−	0.431665i	−0.249657	−	0.968334i	$-0.580318\pi$
$13$	2.14219	−	1.55639i	0.594136	−	0.431665i	0.843793	+	0.536669i	$0.180318\pi$
$14$	−6.76385	−	4.91423i	−1.80772	−	1.31338i
$15$		0			0
$16$	−0.656686	+	0.477110i	−0.164171	+	0.119278i
$17$	−1.57821	+	4.85722i	−0.382772	+	1.17805i	0.555312	+	0.831642i	$0.312599\pi$
$17$	−1.57821	+	4.85722i	−0.382772	+	1.17805i	−0.938084	+	0.346408i	$0.887401\pi$
$18$	−5.35154			−1.26137
$19$	−0.305085	+	0.938956i	−0.0699914	+	0.215411i	−0.979934	−	0.199323i	$-0.936126\pi$
$19$	−0.305085	+	0.938956i	−0.0699914	+	0.215411i	0.909942	+	0.414735i	$0.136126\pi$
$20$		0			0
$21$	−2.55714	−	7.87007i	−0.558014	−	1.71739i
$22$	0.357812	+	1.10123i	0.0762858	+	0.234784i
$23$	5.18889	+	3.76995i	1.08196	+	0.786089i	0.978023	−	0.208495i	$-0.0668566\pi$
$23$	5.18889	+	3.76995i	1.08196	+	0.786089i	0.103935	+	0.994584i	$0.466857\pi$
$24$	−7.55514			−1.54219
$25$		0			0
$26$	6.15926			1.20793
$27$	1.30262	+	0.946409i	0.250689	+	0.182136i
$28$	−3.78826	−	11.6591i	−0.715914	−	2.20336i
$29$	−1.72123	−	5.29739i	−0.319624	−	0.983701i	−0.973809	−	0.227367i	$-0.926988\pi$
$29$	−1.72123	−	5.29739i	−0.319624	−	0.983701i	0.654185	−	0.756334i	$-0.273012\pi$
$30$		0			0
$31$	1.87112	−	5.75872i	0.336063	−	1.03430i	−0.630133	−	0.776487i	$-0.717000\pi$
$31$	1.87112	−	5.75872i	0.336063	−	1.03430i	0.966196	−	0.257809i	$-0.0830004\pi$
$32$	4.67497			0.826426
$33$	−0.354153	+	1.08997i	−0.0616501	+	0.189740i
$34$	−9.61099	+	6.98279i	−1.64827	+	1.19754i
$35$		0			0
$36$	−6.34830	−	4.61231i	−1.05805	−	0.768719i
$37$	−3.71834	+	2.70153i	−0.611292	+	0.444129i	−0.849869	−	0.526994i	$-0.823319\pi$
$37$	−3.71834	+	2.70153i	−0.611292	+	0.444129i	0.238577	+	0.971124i	$0.423319\pi$
$38$	−1.85791	+	1.34985i	−0.301393	+	0.218975i
$39$	4.93199	+	3.58330i	0.789750	+	0.573787i
$40$		0			0
$41$	2.32572	−	1.68973i	0.363217	−	0.263892i	−0.391176	−	0.920316i	$-0.627932\pi$
$41$	2.32572	−	1.68973i	0.363217	−	0.263892i	0.754392	+	0.656424i	$0.227932\pi$
$42$	5.94817	−	18.3066i	0.917822	−	2.82477i
$43$	9.48858			1.44700			0.723498	−	0.690327i	$-0.242533\pi$
$43$	9.48858			1.44700			0.723498	+	0.690327i	$0.242533\pi$
$44$	−0.524658	+	1.61473i	−0.0790952	+	0.243430i
$45$		0			0
$46$	4.61029	+	14.1890i	0.679750	+	2.09205i
$47$	−1.65891	−	5.10560i	−0.241977	−	0.744728i	−0.996119	−	0.0880167i	$-0.971947\pi$
$47$	−1.65891	−	5.10560i	−0.241977	−	0.744728i	0.754142	−	0.656711i	$-0.228053\pi$
$48$	−1.51190	−	1.09846i	−0.218223	−	0.158549i
$49$	5.91861			0.845515
$50$		0			0
$51$	−11.7583			−1.64650
$52$	7.30646	+	5.30846i	1.01322	+	0.736150i
$53$	0.0950536	+	0.292545i	0.0130566	+	0.0401841i	0.957373	−	0.288856i	$-0.0932749\pi$
$53$	0.0950536	+	0.292545i	0.0130566	+	0.0401841i	−0.944316	+	0.329040i	$0.893275\pi$
$54$	1.15737	+	3.56201i	0.157498	+	0.484728i
$55$		0			0
$56$	3.64476	−	11.2174i	0.487051	−	1.49899i
$57$	−2.27302			−0.301069
$58$	4.00375	−	12.3223i	0.525718	−	1.61799i
$59$	1.02458	−	0.744401i	0.133389	−	0.0969128i	−0.519090	−	0.854720i	$-0.673729\pi$
$59$	1.02458	−	0.744401i	0.133389	−	0.0969128i	0.652479	+	0.757807i	$0.273729\pi$
$60$		0			0
$61$	5.03715	+	3.65970i	0.644940	+	0.468577i	0.861544	−	0.507683i	$-0.169498\pi$
$61$	5.03715	+	3.65970i	0.644940	+	0.468577i	−0.216603	+	0.976260i	$0.569498\pi$
$62$	11.3948	−	8.27879i	1.44714	−	1.05141i
$63$	6.68984	−	4.86045i	0.842841	−	0.612359i
$64$	10.1110	+	7.34607i	1.26387	+	0.918259i
$65$		0			0
$66$	−2.15673	+	1.56695i	−0.265475	+	0.192879i
$67$	1.63354	−	5.02753i	0.199569	−	0.614210i	−0.800324	−	0.599568i	$-0.795339\pi$
$67$	1.63354	−	5.02753i	0.199569	−	0.614210i	0.999893	−	0.0146423i	$-0.00466097\pi$
$68$	−17.4193			−2.11240
$69$	−4.56314	+	14.0439i	−0.549337	+	1.69069i
$70$		0			0
$71$	−0.0469591	−	0.144525i	−0.00557302	−	0.0171520i	0.948231	−	0.317580i	$-0.102870\pi$
$71$	−0.0469591	−	0.144525i	−0.00557302	−	0.0171520i	−0.953804	+	0.300428i	$0.902870\pi$
$72$	−2.33298	−	7.18017i	−0.274944	−	0.846191i
$73$	−12.0334	−	8.74276i	−1.40840	−	1.02326i	−0.993553	−	0.113372i	$-0.963835\pi$
$73$	−12.0334	−	8.74276i	−1.40840	−	1.02326i	−0.414848	−	0.909891i	$-0.636165\pi$
$74$	−10.6910			−1.24281
$75$		0			0
$76$	−3.36735			−0.386262
$77$	−1.44747	−	1.05165i	−0.164955	−	0.119846i
$78$	4.38203	+	13.4865i	0.496167	+	1.52705i
$79$	−5.12616	−	15.7767i	−0.576738	−	1.77502i	−0.630184	−	0.776446i	$-0.717021\pi$
$79$	−5.12616	−	15.7767i	−0.576738	−	1.77502i	0.0534460	−	0.998571i	$-0.482979\pi$
$80$		0			0
$81$	−3.27835	+	10.0897i	−0.364261	+	1.12108i
$82$	6.68696			0.738451
$83$	−4.51040	+	13.8816i	−0.495081	+	1.52370i	0.321750	+	0.946825i	$0.395729\pi$
$83$	−4.51040	+	13.8816i	−0.495081	+	1.52370i	−0.816831	+	0.576877i	$0.804271\pi$
$84$	22.8339	−	16.5898i	2.49138	−	1.81009i
$85$		0			0
$86$	17.8561	+	12.9733i	1.92548	+	1.39894i
$87$	10.3748	−	7.53770i	1.11229	−	0.808127i
$88$	−1.32154	+	0.960155i	−0.140877	+	0.102353i
$89$	−9.20843	−	6.69032i	−0.976092	−	0.709172i	−0.0192601	−	0.999815i	$-0.506131\pi$
$89$	−9.20843	−	6.69032i	−0.976092	−	0.709172i	−0.956832	+	0.290642i	$0.906131\pi$
$90$		0			0
$91$	−7.69955	+	5.59405i	−0.807132	+	0.586416i
$92$	−6.76004	+	20.8052i	−0.704782	+	2.16910i
$93$	13.9407			1.44558
$94$	3.85879	−	11.8761i	0.398004	−	1.22493i
$95$		0			0
$96$	3.32603	+	10.2365i	0.339461	+	1.04475i
$97$	−0.262415	−	0.807629i	−0.0266442	−	0.0820023i	0.936850	−	0.349731i	$-0.113727\pi$
$97$	−0.262415	−	0.807629i	−0.0266442	−	0.0820023i	−0.963494	+	0.267729i	$0.913727\pi$
$98$	11.1380	+	8.09220i	1.12510	+	0.817436i
$99$	−1.14523			−0.115100
$100$		0			0
$101$	−13.2498			−1.31841			−0.659203	−	0.751965i	$-0.729106\pi$
$101$	−13.2498			−1.31841			−0.659203	+	0.751965i	$0.729106\pi$
$102$	−22.1275	−	16.0766i	−2.19095	−	1.59182i
$103$	−0.256765	−	0.790241i	−0.0252998	−	0.0778648i	0.937609	−	0.347690i	$-0.113034\pi$
$103$	−0.256765	−	0.790241i	−0.0252998	−	0.0778648i	−0.962909	+	0.269826i	$0.913034\pi$
$104$	2.68510	+	8.26389i	0.263296	+	0.810341i
$105$		0			0
$106$	−0.221104	+	0.680489i	−0.0214756	+	0.0660950i
$107$	0.0722844			0.00698800			0.00349400	−	0.999994i	$-0.498888\pi$
$107$	0.0722844			0.00698800			0.00349400	+	0.999994i	$0.498888\pi$
$108$	−1.69704	+	5.22295i	−0.163298	+	0.502579i
$109$	−4.52743	+	3.28937i	−0.433649	+	0.315065i	−0.783106	−	0.621888i	$-0.786366\pi$
$109$	−4.52743	+	3.28937i	−0.433649	+	0.315065i	0.349457	+	0.936952i	$0.386366\pi$
$110$		0			0
$111$	−8.56079	−	6.21978i	−0.812554	−	0.590355i
$112$	2.36029	−	1.71485i	0.223026	−	0.162038i
$113$	−2.10538	+	1.52965i	−0.198057	+	0.143897i	−0.682394	−	0.730985i	$-0.739061\pi$
$113$	−2.10538	+	1.52965i	−0.198057	+	0.143897i	0.484336	+	0.874882i	$0.339061\pi$
$114$	−4.27750	−	3.10778i	−0.400624	−	0.291071i
$115$		0			0
$116$	15.3696	−	11.1667i	1.42703	−	1.03680i
$117$	−1.88249	+	5.79371i	−0.174036	+	0.535628i
$118$	2.94589			0.271191
$119$	5.67247	−	17.4581i	0.519994	−	1.60038i
$120$		0			0
$121$	−3.32261	−	10.2260i	−0.302056	−	0.929632i
$122$	4.47546	+	13.7741i	0.405189	+	1.24704i
$123$	5.35454	+	3.89030i	0.482802	+	0.350777i
$124$	20.6523			1.85463
$125$		0			0
$126$	19.2348			1.71357
$127$	4.00045	+	2.90650i	0.354983	+	0.257910i	0.750956	−	0.660352i	$-0.229593\pi$
$127$	4.00045	+	2.90650i	0.354983	+	0.257910i	−0.395974	+	0.918262i	$0.629593\pi$
$128$	6.09424	+	18.7562i	0.538660	+	1.65783i
$129$	6.75069	+	20.7765i	0.594365	+	1.82927i
$130$		0			0
$131$	0.835403	−	2.57111i	0.0729895	−	0.224639i	−0.907906	−	0.419174i	$-0.862320\pi$
$131$	0.835403	−	2.57111i	0.0729895	−	0.224639i	0.980896	+	0.194535i	$0.0623198\pi$
$132$	−3.90893			−0.340229
$133$	1.09655	−	3.37484i	0.0950831	−	0.292636i
$134$	9.94797	−	7.22763i	0.859374	−	0.624372i
$135$		0			0
$136$	−13.5587	−	9.85096i	−1.16265	−	0.844713i
$137$	−1.81898	+	1.32156i	−0.155406	+	0.112909i	−0.662771	−	0.748822i	$-0.730620\pi$
$137$	−1.81898	+	1.32156i	−0.155406	+	0.112909i	0.507365	+	0.861731i	$0.330620\pi$
$138$	−27.7887	+	20.1896i	−2.36553	+	1.71866i
$139$	8.73999	+	6.34997i	0.741316	+	0.538598i	0.893123	−	0.449812i	$-0.148509\pi$
$139$	8.73999	+	6.34997i	0.741316	+	0.538598i	−0.151807	+	0.988410i	$0.548509\pi$
$140$		0			0
$141$	9.99913	−	7.26479i	0.842079	−	0.611806i
$142$	0.109232	−	0.336181i	0.00916652	−	0.0282116i
$143$	1.31809			0.110224
$144$	0.577075	−	1.77606i	0.0480896	−	0.148005i
$145$		0			0
$146$	−10.6916	−	32.9052i	−0.884840	−	2.72326i
$147$	4.21082	+	12.9596i	0.347302	+	1.06889i
$148$	−12.6823	−	9.21425i	−1.04248	−	0.757407i
$149$	12.1878			0.998460			0.499230	−	0.866469i	$-0.333616\pi$
$149$	12.1878			0.998460			0.499230	+	0.866469i	$0.333616\pi$
$150$		0			0
$151$	17.0860			1.39044			0.695220	−	0.718797i	$-0.255307\pi$
$151$	17.0860			1.39044			0.695220	+	0.718797i	$0.255307\pi$
$152$	−2.62105	−	1.90430i	−0.212595	−	0.154459i
$153$	−3.63090	−	11.1748i	−0.293541	−	0.903426i
$154$	−1.28607	−	3.95810i	−0.103634	−	0.318953i
$155$		0			0
$156$	−6.42534	+	19.7752i	−0.514439	+	1.58328i
$157$	7.49835			0.598433			0.299217	−	0.954185i	$-0.403275\pi$
$157$	7.49835			0.598433			0.299217	+	0.954185i	$0.403275\pi$
$158$	11.9240	−	36.6982i	0.948620	−	2.91955i
$159$	−0.572939	+	0.416265i	−0.0454370	+	0.0330119i
$160$		0			0
$161$	−18.6502	−	13.5501i	−1.46984	−	1.06790i
$162$	−19.9645	+	14.5051i	−1.56856	+	1.13963i
$163$	1.57968	−	1.14770i	0.123730	−	0.0898951i	−0.524199	−	0.851596i	$-0.675635\pi$
$163$	1.57968	−	1.14770i	0.123730	−	0.0898951i	0.647929	+	0.761701i	$0.275635\pi$
$164$	7.93245	+	5.76326i	0.619420	+	0.450035i
$165$		0			0
$166$	−27.4675	+	19.9563i	−2.13189	+	1.54891i
$167$	0.110189	−	0.339126i	0.00852665	−	0.0262423i	−0.946703	−	0.322109i	$-0.895608\pi$
$167$	0.110189	−	0.339126i	0.00852665	−	0.0262423i	0.955229	+	0.295866i	$0.0956083\pi$
$168$	27.1550			2.09506
$169$	−1.85060	+	5.69557i	−0.142354	+	0.438121i
$170$		0			0
$171$	−0.701894	−	2.16021i	−0.0536752	−	0.165195i
$172$	10.0008	+	30.7792i	0.762552	+	2.34689i
$173$	−8.04998	−	5.84865i	−0.612029	−	0.444665i	0.238100	−	0.971241i	$-0.423476\pi$
$173$	−8.04998	−	5.84865i	−0.612029	−	0.444665i	−0.850128	+	0.526576i	$0.823476\pi$
$174$	29.8297			2.26138
$175$		0			0
$176$	−0.404058			−0.0304570
$177$	2.35890	+	1.71384i	0.177306	+	0.128820i
$178$	−8.18162	−	25.1804i	−0.613238	−	1.88735i
$179$	4.75342	+	14.6295i	0.355287	+	1.09346i	0.955843	+	0.293879i	$0.0949462\pi$
$179$	4.75342	+	14.6295i	0.355287	+	1.09346i	−0.600555	+	0.799583i	$0.705054\pi$
$180$		0			0
$181$	2.75618	−	8.48264i	0.204865	−	0.630509i	−0.794854	−	0.606801i	$-0.792453\pi$
$181$	2.75618	−	8.48264i	0.204865	−	0.630509i	0.999719	−	0.0237086i	$-0.00754739\pi$
$182$	−22.1379			−1.64097
$183$	−4.42969	+	13.6332i	−0.327452	+	1.00779i
$184$	−17.0276	+	12.3713i	−1.25529	+	0.912021i
$185$		0			0
$186$	26.2343	+	19.0604i	1.92360	+	1.39757i
$187$	−2.05676	+	1.49432i	−0.150405	+	0.109276i
$188$	14.8132	−	10.7624i	1.08036	−	0.784928i
$189$	−4.68194	−	3.40163i	−0.340561	−	0.247432i
$190$		0			0
$191$	9.21363	−	6.69410i	0.666675	−	0.484368i	−0.202235	−	0.979337i	$-0.564821\pi$
$191$	9.21363	−	6.69410i	0.666675	−	0.484368i	0.868911	+	0.494969i	$0.164821\pi$
$192$	−8.89167	+	27.3657i	−0.641701	+	1.97495i
$193$	−17.3321			−1.24759			−0.623795	−	0.781588i	$-0.714410\pi$
$193$	−17.3321			−1.24759			−0.623795	+	0.781588i	$0.714410\pi$
$194$	0.610403	−	1.87863i	0.0438244	−	0.134878i
$195$		0			0
$196$	6.23809	+	19.1989i	0.445578	+	1.37135i
$197$	−8.02237	−	24.6903i	−0.571570	−	1.75911i	−0.647572	−	0.762005i	$-0.724215\pi$
$197$	−8.02237	−	24.6903i	−0.571570	−	1.75911i	0.0760014	−	0.997108i	$-0.475785\pi$
$198$	−2.15517	−	1.56582i	−0.153161	−	0.111278i
$199$	−8.38571			−0.594447			−0.297223	−	0.954808i	$-0.596061\pi$
$199$	−8.38571			−0.594447			−0.297223	+	0.954808i	$0.596061\pi$
$200$		0			0
$201$	12.1706			0.858450
$202$	−24.9342	−	18.1158i	−1.75437	−	1.27462i
$203$	6.18651	+	19.0401i	0.434208	+	1.33636i
$204$	−12.3931	−	38.1419i	−0.867687	−	2.67047i
$205$		0			0
$206$	0.597262	−	1.83818i	0.0416132	−	0.128072i
$207$	−14.7559			−1.02561
$208$	−0.664174	+	2.04412i	−0.0460522	+	0.141734i
$209$	−0.397595	+	0.288870i	−0.0275022	+	0.0199815i
$210$		0			0
$211$	−12.8743	−	9.35372i	−0.886303	−	0.643936i	0.0486088	−	0.998818i	$-0.484521\pi$
$211$	−12.8743	−	9.35372i	−0.886303	−	0.643936i	−0.934911	+	0.354881i	$0.884521\pi$
$212$	−0.848777	+	0.616673i	−0.0582943	+	0.0423533i
$213$	0.283048	−	0.205646i	0.0193941	−	0.0140906i
$214$	0.136029	+	0.0988307i	0.00929874	+	0.00675593i
$215$		0			0
$216$	−4.27461	+	3.10568i	−0.290850	+	0.211315i
$217$	−6.72527	+	20.6982i	−0.456541	+	1.40509i
$218$	−13.0174			−0.881647
$219$	10.5822	−	32.5687i	0.715080	−	2.20079i
$220$		0			0
$221$	4.17892	+	12.8614i	0.281105	+	0.865151i
$222$	−7.60619	−	23.4094i	−0.510494	−	1.57114i
$223$	−0.307188	−	0.223185i	−0.0205708	−	0.0149456i	0.577452	−	0.816424i	$-0.304047\pi$
$223$	−0.307188	−	0.223185i	−0.0205708	−	0.0149456i	−0.598023	+	0.801479i	$0.704047\pi$
$224$	−16.8030			−1.12270
$225$		0			0
$226$	−6.05343			−0.402668
$227$	16.4238	+	11.9326i	1.09009	+	0.791994i	0.979414	−	0.201863i	$-0.0646997\pi$
$227$	16.4238	+	11.9326i	1.09009	+	0.791994i	0.110672	+	0.993857i	$0.464700\pi$
$228$	−2.39572	−	7.37326i	−0.158660	−	0.488306i
$229$	−3.68059	−	11.3277i	−0.243220	−	0.748556i	−0.995924	−	0.0901961i	$-0.971251\pi$
$229$	−3.68059	−	11.3277i	−0.243220	−	0.748556i	0.752704	−	0.658360i	$-0.228749\pi$
$230$		0			0
$231$	1.27291	−	3.91762i	0.0837516	−	0.257761i
$232$	18.2782			1.20002
$233$	5.89018	−	18.1281i	0.385878	−	1.18761i	−0.549963	−	0.835189i	$-0.685358\pi$
$233$	5.89018	−	18.1281i	0.385878	−	1.18761i	0.935841	−	0.352422i	$-0.114642\pi$
$234$	−11.4640	+	8.32909i	−0.749426	+	0.544490i
$235$		0			0
$236$	3.49458	+	2.53896i	0.227478	+	0.165273i
$237$	30.8981	−	22.4488i	2.00705	−	1.45821i
$238$	34.5443	−	25.0979i	2.23917	−	1.62685i
$239$	−3.33714	−	2.42457i	−0.215861	−	0.156832i	0.474600	−	0.880201i	$-0.342593\pi$
$239$	−3.33714	−	2.42457i	−0.215861	−	0.156832i	−0.690462	+	0.723369i	$0.742593\pi$
$240$		0			0
$241$	−13.0946	+	9.51378i	−0.843497	+	0.612836i	−0.923345	−	0.383971i	$-0.874556\pi$
$241$	−13.0946	+	9.51378i	−0.843497	+	0.612836i	0.0798483	+	0.996807i	$0.474556\pi$
$242$	7.72874	−	23.7866i	0.496822	−	1.52906i
$243$	−19.5948			−1.25701
$244$	−6.56234	+	20.1968i	−0.420111	+	1.29297i
$245$		0			0
$246$	4.75746	+	14.6420i	0.303325	+	0.933538i
$247$	0.807832	+	2.48625i	0.0514011	+	0.158196i
$248$	16.0752	+	11.6793i	1.02077	+	0.741636i
$249$	−33.6045			−2.12960
$250$		0			0
$251$	11.8718			0.749344			0.374672	−	0.927157i	$-0.377755\pi$
$251$	11.8718			0.749344			0.374672	+	0.927157i	$0.377755\pi$
$252$	22.8174	+	16.5778i	1.43736	+	1.04430i
$253$	0.986605	+	3.03646i	0.0620273	+	0.190901i
$254$	3.55437	+	10.9392i	0.223021	+	0.686388i
$255$		0			0
$256$	−6.45172	+	19.8563i	−0.403232	+	1.24102i
$257$	18.9164			1.17997			0.589986	−	0.807414i	$-0.299133\pi$
$257$	18.9164			1.17997			0.589986	+	0.807414i	$0.299133\pi$
$258$	−15.7028	+	48.3282i	−0.977613	+	3.00878i
$259$	13.3646	−	9.70998i	0.830438	−	0.603349i
$260$		0			0
$261$	10.3673	+	7.53225i	0.641717	+	0.466235i
$262$	5.08745	−	3.69625i	0.314304	−	0.228355i
$263$	−5.45846	+	3.96580i	−0.336583	+	0.244542i	−0.743219	−	0.669048i	$-0.766702\pi$
$263$	−5.45846	+	3.96580i	−0.336583	+	0.244542i	0.406636	+	0.913590i	$0.366702\pi$
$264$	−3.04260	−	2.21058i	−0.187259	−	0.136052i
$265$		0			0
$266$	6.67780	−	4.85170i	0.409442	−	0.297477i
$267$	8.09795	−	24.9229i	0.495586	−	1.52526i
$268$	18.0301			1.10136
$269$	−7.82829	+	24.0930i	−0.477299	+	1.46898i	0.365533	+	0.930798i	$0.380887\pi$
$269$	−7.82829	+	24.0930i	−0.477299	+	1.46898i	−0.842832	+	0.538177i	$0.819113\pi$
$270$		0			0
$271$	2.90703	+	8.94692i	0.176589	+	0.543487i	0.999702	−	0.0243910i	$-0.00776468\pi$
$271$	2.90703	+	8.94692i	0.176589	+	0.543487i	−0.823113	+	0.567878i	$0.807765\pi$
$272$	−1.28104	−	3.94265i	−0.0776747	−	0.239058i
$273$	−17.7268	−	12.8793i	−1.07287	−	0.779488i
$274$	−5.22995			−0.315953
$275$		0			0
$276$	−50.3653			−3.03163
$277$	−4.82770	−	3.50753i	−0.290068	−	0.210747i	0.433229	−	0.901284i	$-0.357374\pi$
$277$	−4.82770	−	3.50753i	−0.290068	−	0.210747i	−0.723297	+	0.690537i	$0.757374\pi$
$278$	7.76541	+	23.8995i	0.465738	+	1.43339i
$279$	4.30479	+	13.2488i	0.257721	+	0.793184i
$280$		0			0
$281$	3.42152	−	10.5304i	0.204111	−	0.628188i	−0.795638	−	0.605772i	$-0.792864\pi$
$281$	3.42152	−	10.5304i	0.204111	−	0.628188i	0.999749	−	0.0224160i	$-0.00713583\pi$
$282$	28.7497			1.71202
$283$	0.934487	−	2.87606i	0.0555495	−	0.170964i	−0.919432	−	0.393248i	$-0.871351\pi$
$283$	0.934487	−	2.87606i	0.0555495	−	0.170964i	0.974982	+	0.222284i	$0.0713513\pi$
$284$	0.419319	−	0.304653i	0.0248820	−	0.0180778i
$285$		0			0
$286$	2.48045	+	1.80215i	0.146672	+	0.106563i
$287$	−8.35921	+	6.07332i	−0.493429	+	0.358497i
$288$	−8.70136	+	6.32191i	−0.512732	+	0.372522i
$289$	−7.34860	−	5.33907i	−0.432270	−	0.314063i
$290$		0			0
$291$	1.58171	−	1.14918i	0.0927217	−	0.0673662i
$292$	15.6770	−	48.2487i	0.917425	−	2.82354i
$293$	−6.26426			−0.365962			−0.182981	−	0.983116i	$-0.558575\pi$
$293$	−6.26426			−0.365962			−0.182981	+	0.983116i	$0.558575\pi$
$294$	−9.79478	+	30.1452i	−0.571243	+	1.75811i
$295$		0			0
$296$	−4.66071	−	14.3442i	−0.270898	−	0.833740i
$297$	0.247678	+	0.762273i	0.0143717	+	0.0442316i
$298$	22.9356	+	16.6637i	1.32862	+	0.965302i
$299$	16.9831			0.982158
$300$		0			0
$301$	−34.1043			−1.96574
$302$	32.1534	+	23.3608i	1.85022	+	1.34426i
$303$	−9.42664	−	29.0122i	−0.541546	−	1.66671i
$304$	−0.247640	−	0.762158i	−0.0142031	−	0.0437128i
$305$		0			0
$306$	8.44584	−	25.9936i	0.482817	−	1.48596i
$307$	−25.8734			−1.47667			−0.738337	−	0.674432i	$-0.764388\pi$
$307$	−25.8734			−1.47667			−0.738337	+	0.674432i	$0.764388\pi$
$308$	1.88575	−	5.80374i	0.107451	−	0.330699i
$309$	1.54766	−	1.12444i	0.0880433	−	0.0639672i
$310$		0			0
$311$	7.28339	+	5.29169i	0.413003	+	0.300064i	0.774817	−	0.632186i	$-0.217842\pi$
$311$	7.28339	+	5.29169i	0.413003	+	0.300064i	−0.361813	+	0.932251i	$0.617842\pi$
$312$	−16.1845	+	11.7588i	−0.916269	+	0.665708i
$313$	−26.8815	+	19.5306i	−1.51943	+	1.10393i	−0.557667	+	0.830065i	$0.688304\pi$
$313$	−26.8815	+	19.5306i	−1.51943	+	1.10393i	−0.961767	+	0.273869i	$0.911696\pi$
$314$	14.1108	+	10.2521i	0.796319	+	0.578560i
$315$		0			0
$316$	45.7738	−	33.2566i	2.57498	−	1.87083i
$317$	8.02495	−	24.6983i	0.450726	−	1.38719i	−0.425354	−	0.905027i	$-0.639850\pi$
$317$	8.02495	−	24.6983i	0.450726	−	1.38719i	0.876080	−	0.482166i	$-0.160150\pi$
$318$	−1.64733			−0.0923774
$319$	0.856806	−	2.63698i	0.0479719	−	0.147642i
$320$		0			0
$321$	0.0514270	+	0.158276i	0.00287038	+	0.00883411i
$322$	−16.5705	−	50.9988i	−0.923438	−	2.84205i
$323$	−4.07923	−	2.96374i	−0.226975	−	0.164907i
$324$	−36.1845			−2.01025
$325$		0			0
$326$	4.54192			0.251554
$327$	−10.4236	−	7.57317i	−0.576425	−	0.418797i
$328$	2.91515	+	8.97190i	0.160962	+	0.495390i
$329$	5.96253	+	18.3508i	0.328725	+	1.01171i
$330$		0			0
$331$	3.74787	−	11.5348i	0.206002	−	0.634008i	−0.793669	−	0.608350i	$-0.791832\pi$
$331$	3.74787	−	11.5348i	0.206002	−	0.634008i	0.999671	−	0.0256585i	$-0.00816824\pi$
$332$	−49.7832			−2.73221
$333$	3.26757	−	10.0565i	0.179061	−	0.551095i
$334$	0.671028	−	0.487530i	0.0367170	−	0.0266765i
$335$		0			0
$336$	5.43413	+	3.94812i	0.296456	+	0.215388i
$337$	−24.4743	+	17.7816i	−1.33320	+	0.968626i	−0.333535	+	0.942738i	$0.608241\pi$
$337$	−24.4743	+	17.7816i	−1.33320	+	0.968626i	−0.999665	+	0.0258885i	$0.991759\pi$
$338$	−11.2698	+	8.18801i	−0.612998	+	0.445369i
$339$	−4.84724	−	3.52173i	−0.263266	−	0.191274i
$340$		0			0
$341$	2.43849	−	1.77167i	0.132052	−	0.0959412i
$342$	1.63268	−	5.02486i	0.0882851	−	0.271713i
$343$	3.88680			0.209867
$344$	−9.62193	+	29.6132i	−0.518780	+	1.59664i
$345$		0			0
$346$	−7.15234	−	22.0126i	−0.384512	−	1.18341i
$347$	4.11868	+	12.6760i	0.221102	+	0.680483i	0.998664	+	0.0516759i	$0.0164563\pi$
$347$	4.11868	+	12.6760i	0.221102	+	0.680483i	−0.777562	+	0.628807i	$0.783544\pi$
$348$	35.3857	+	25.7092i	1.89687	+	1.37816i
$349$	−27.4444			−1.46906			−0.734532	−	0.678574i	$-0.762598\pi$
$349$	−27.4444			−1.46906			−0.734532	+	0.678574i	$0.762598\pi$
$350$		0			0
$351$	4.26344			0.227566
$352$	1.88270	+	1.36786i	0.100348	+	0.0729072i
$353$	−4.80719	−	14.7950i	−0.255861	−	0.787459i	−0.993659	−	0.112437i	$-0.964134\pi$
$353$	−4.80719	−	14.7950i	−0.255861	−	0.787459i	0.737798	−	0.675022i	$-0.235866\pi$
$354$	2.09587	+	6.45042i	0.111394	+	0.342836i
$355$		0			0
$356$	11.9967	−	36.9219i	0.635821	−	1.95686i
$357$	42.2624			2.23676
$358$	−11.0569	+	34.0298i	−0.584377	+	1.79853i
$359$	17.7846	−	12.9212i	0.938634	−	0.681957i	−0.00945775	−	0.999955i	$-0.503011\pi$
$359$	17.7846	−	12.9212i	0.938634	−	0.681957i	0.948091	+	0.317998i	$0.103011\pi$
$360$		0			0
$361$	14.5828	+	10.5950i	0.767514	+	0.557631i
$362$	16.7846	−	12.1947i	0.882179	−	0.640940i
$363$	20.0272	−	14.5506i	1.05115	−	0.763708i
$364$	−26.2612	−	19.0799i	−1.37646	−	1.00006i
$365$		0			0
$366$	−26.9760	+	19.5992i	−1.41006	+	1.02447i
$367$	−3.74230	+	11.5176i	−0.195347	+	0.601215i	0.804626	+	0.593782i	$0.202366\pi$
$367$	−3.74230	+	11.5176i	−0.195347	+	0.601215i	−0.999972	+	0.00743290i	$0.997634\pi$
$368$	−5.20615			−0.271389
$369$	−2.04377	+	6.29008i	−0.106395	+	0.327449i
$370$		0			0
$371$	−0.341646	−	1.05148i	−0.0177374	−	0.0545901i
$372$	14.6932	+	45.2210i	0.761806	+	2.34460i
$373$	5.73273	+	4.16507i	0.296829	+	0.215659i	0.726225	−	0.687458i	$-0.241273\pi$
$373$	5.73273	+	4.16507i	0.296829	+	0.215659i	−0.429395	+	0.903117i	$0.641273\pi$
$374$	−5.91364			−0.305787
$375$		0			0
$376$	17.6164			0.908499
$377$	−11.9320	−	8.66911i	−0.614529	−	0.446482i
$378$	−4.15986	−	12.8027i	−0.213960	−	0.658502i
$379$	−6.64478	−	20.4505i	−0.341319	−	1.05047i	−0.963525	−	0.267619i	$-0.913763\pi$
$379$	−6.64478	−	20.4505i	−0.341319	−	1.05047i	0.622205	−	0.782854i	$-0.286237\pi$
$380$		0			0
$381$	−3.51802	+	10.8273i	−0.180234	+	0.554702i
$382$	26.4912			1.35541
$383$	−7.68885	+	23.6638i	−0.392882	+	1.20917i	0.537717	+	0.843125i	$0.319287\pi$
$383$	−7.68885	+	23.6638i	−0.392882	+	1.20917i	−0.930599	+	0.366040i	$0.880713\pi$
$384$	−36.7333	+	26.6883i	−1.87454	+	1.36193i
$385$		0			0
$386$	−32.6164	−	23.6972i	−1.66013	−	1.20616i
$387$	−17.6608	+	12.8313i	−0.897747	+	0.652251i
$388$	2.34322	−	1.70245i	0.118959	−	0.0864287i
$389$	28.6507	+	20.8159i	1.45265	+	1.05541i	0.985204	+	0.171387i	$0.0548247\pi$
$389$	28.6507	+	20.8159i	1.45265	+	1.05541i	0.467443	+	0.884023i	$0.345175\pi$
$390$		0			0
$391$	−26.5006	+	19.2538i	−1.34019	+	0.973709i
$392$	−6.00178	+	18.4716i	−0.303136	+	0.932955i
$393$	6.22412			0.313965
$394$	18.6608	−	57.4322i	0.940120	−	2.89339i
$395$		0			0
$396$	−1.20705	−	3.71493i	−0.0606567	−	0.186682i
$397$	−1.69868	−	5.22800i	−0.0852543	−	0.262386i	0.899337	−	0.437256i	$-0.144050\pi$
$397$	−1.69868	−	5.22800i	−0.0852543	−	0.262386i	−0.984592	+	0.174870i	$0.944050\pi$
$398$	−15.7807	−	11.4653i	−0.791014	−	0.574706i
$399$	8.16980			0.409001
$400$		0			0
$401$	24.8463			1.24077			0.620383	−	0.784299i	$-0.286977\pi$
$401$	24.8463			1.24077			0.620383	+	0.784299i	$0.286977\pi$
$402$	22.9034	+	16.6403i	1.14232	+	0.829941i
$403$	−4.95452	−	15.2484i	−0.246802	−	0.759579i
$404$	−13.9650	−	42.9800i	−0.694786	−	2.13833i
$405$		0			0
$406$	−14.3905	+	44.2893i	−0.714187	+	2.19804i
$407$	−2.28789			−0.113407
$408$	11.9236	−	36.6970i	0.590306	−	1.81677i
$409$	−3.18071	+	2.31092i	−0.157276	+	0.114268i	−0.663640	−	0.748052i	$-0.730989\pi$
$409$	−3.18071	+	2.31092i	−0.157276	+	0.114268i	0.506364	+	0.862320i	$0.330989\pi$
$410$		0			0
$411$	−4.18785	−	3.04265i	−0.206571	−	0.150083i
$412$	2.29277	−	1.66580i	0.112957	−	0.0820679i
$413$	−3.68259	+	2.67556i	−0.181209	+	0.131656i
$414$	−27.7686	−	20.1750i	−1.36475	−	0.991549i
$415$		0			0
$416$	10.0147	−	7.27608i	0.491010	−	0.356739i
$417$	−7.68599	+	23.6551i	−0.376385	+	1.15839i
$418$	−1.14317			−0.0559144
$419$	−1.47279	+	4.53278i	−0.0719504	+	0.221441i	−0.980565	−	0.196195i	$-0.937141\pi$
$419$	−1.47279	+	4.53278i	−0.0719504	+	0.221441i	0.908614	+	0.417636i	$0.137141\pi$
$420$		0			0
$421$	4.96223	+	15.2722i	0.241844	+	0.744320i	0.996139	+	0.0877847i	$0.0279788\pi$
$421$	4.96223	+	15.2722i	0.241844	+	0.744320i	−0.754295	+	0.656535i	$0.772021\pi$
$422$	−11.4387	−	35.2047i	−0.556827	−	1.71374i
$423$	9.99190	+	7.25954i	0.485823	+	0.352971i
$424$	−1.00940			−0.0490209
$425$		0			0
$426$	0.813824			0.0394299
$427$	−18.1047	−	13.1539i	−0.876150	−	0.636560i
$428$	0.0761863	+	0.234477i	0.00368260	+	0.0113339i
$429$	0.937758	+	2.88612i	0.0452754	+	0.139343i
$430$		0			0
$431$	−12.7838	+	39.3445i	−0.615774	+	1.89516i	−0.226633	+	0.973980i	$0.572772\pi$
$431$	−12.7838	+	39.3445i	−0.615774	+	1.89516i	−0.389142	+	0.921178i	$0.627228\pi$
$432$	−1.30695			−0.0628808
$433$	−4.69254	+	14.4422i	−0.225509	+	0.694046i	0.772730	+	0.634734i	$0.218890\pi$
$433$	−4.69254	+	14.4422i	−0.225509	+	0.694046i	−0.998240	+	0.0593113i	$0.981110\pi$
$434$	−40.9556	+	29.7560i	−1.96593	+	1.42833i
$435$		0			0
$436$	−15.4419	−	11.2192i	−0.739534	−	0.537303i
$437$	−5.12287	+	3.72198i	−0.245060	+	0.178047i
$438$	64.4437	−	46.8211i	3.07924	−	2.23720i
$439$	−13.8499	−	10.0625i	−0.661018	−	0.480258i	0.205988	−	0.978554i	$-0.433959\pi$
$439$	−13.8499	−	10.0625i	−0.661018	−	0.480258i	−0.867007	+	0.498297i	$0.833959\pi$
$440$		0			0
$441$	−11.0161	+	8.00365i	−0.524575	+	0.381126i
$442$	−9.72059	+	29.9169i	−0.462361	+	1.42300i
$443$	−35.3909			−1.68147			−0.840736	−	0.541445i	$-0.817877\pi$
$443$	−35.3909			−1.68147			−0.840736	+	0.541445i	$0.817877\pi$
$444$	11.1529	−	34.3251i	0.529294	−	1.62900i
$445$		0			0
$446$	−0.272934	−	0.840005i	−0.0129238	−	0.0397754i
$447$	8.67103	+	26.6867i	0.410126	+	1.26224i
$448$	−36.3414	−	26.4036i	−1.71697	−	1.24745i
$449$	20.6830			0.976090			0.488045	−	0.872818i	$-0.337710\pi$
$449$	20.6830			0.976090			0.488045	+	0.872818i	$0.337710\pi$
$450$		0			0
$451$	1.43101			0.0673838
$452$	−7.18092	−	5.21724i	−0.337762	−	0.245398i
$453$	12.1559	+	37.4120i	0.571134	+	1.75777i
$454$	14.5924	+	44.9108i	0.684856	+	2.10777i
$455$		0			0
$456$	2.30496	−	7.09395i	0.107940	−	0.332205i
$457$	−41.7664			−1.95375			−0.976876	−	0.213807i	$-0.931414\pi$
$457$	−41.7664			−1.95375			−0.976876	+	0.213807i	$0.931414\pi$
$458$	8.56143	−	26.3494i	0.400050	−	1.23123i
$459$	−6.65273	+	4.83349i	−0.310523	+	0.225608i
$460$		0			0
$461$	8.63895	+	6.27657i	0.402356	+	0.292329i	0.770500	−	0.637440i	$-0.220007\pi$
$461$	8.63895	+	6.27657i	0.402356	+	0.292329i	−0.368144	+	0.929769i	$0.620007\pi$
$462$	7.75180	−	5.63202i	0.360647	−	0.262025i
$463$	−6.33487	+	4.60255i	−0.294406	+	0.213899i	−0.725177	−	0.688563i	$-0.758242\pi$
$463$	−6.33487	+	4.60255i	−0.294406	+	0.213899i	0.430770	+	0.902462i	$0.358242\pi$
$464$	3.65774	+	2.65751i	0.169807	+	0.123372i
$465$		0			0
$466$	35.8701	−	26.0611i	1.66165	−	1.20726i
$467$	−1.53921	+	4.73721i	−0.0712262	+	0.219212i	−0.980333	−	0.197352i	$-0.936766\pi$
$467$	−1.53921	+	4.73721i	−0.0712262	+	0.219212i	0.909106	+	0.416564i	$0.136766\pi$
$468$	−20.7778			−0.960455
$469$	−5.87136	+	18.0702i	−0.271114	+	0.834403i
$470$		0			0
$471$	5.33473	+	16.4186i	0.245811	+	0.756530i
$472$	1.28425	+	3.95251i	0.0591123	+	0.181929i
$473$	3.82123	+	2.77629i	0.175700	+	0.127654i
$474$	88.8388			4.08050
$475$		0			0
$476$	62.6094			2.86970
$477$	−0.572525	−	0.415964i	−0.0262141	−	0.0190457i
$478$	−2.96502	−	9.12539i	−0.135617	−	0.417385i
$479$	−5.06728	−	15.5955i	−0.231530	−	0.712576i	−0.997563	−	0.0697744i	$-0.977772\pi$
$479$	−5.06728	−	15.5955i	−0.231530	−	0.712576i	0.766033	−	0.642801i	$-0.222228\pi$
$480$		0			0
$481$	−3.76075	+	11.5744i	−0.171475	+	0.527746i
$482$	−37.6498			−1.71490
$483$	16.4010	−	50.4772i	0.746273	−	2.29679i
$484$	29.6691	−	21.5559i	1.34860	−	0.979813i
$485$		0			0
$486$	−36.8745	−	26.7909i	−1.67266	−	1.21526i
$487$	0.709110	−	0.515199i	0.0321328	−	0.0233459i	−0.571603	−	0.820530i	$-0.693678\pi$
$487$	0.709110	−	0.515199i	0.0321328	−	0.0233459i	0.603736	+	0.797185i	$0.293678\pi$
$488$	−16.5296	+	12.0095i	−0.748261	+	0.543643i
$489$	3.63691	+	2.64237i	0.164467	+	0.119492i
$490$		0			0
$491$	−9.87957	+	7.17793i	−0.445859	+	0.323935i	−0.787959	−	0.615728i	$-0.788862\pi$
$491$	−9.87957	+	7.17793i	−0.445859	+	0.323935i	0.342100	+	0.939664i	$0.388862\pi$
$492$	−6.97584	+	21.4694i	−0.314495	+	0.967916i
$493$	28.4471			1.28119
$494$	−1.87910	+	5.78328i	−0.0845447	+	0.260202i
$495$		0			0
$496$	1.51880	+	4.67440i	0.0681963	+	0.209887i
$497$	0.168783	+	0.519459i	0.00757093	+	0.0233009i
$498$	−63.2388	−	45.9457i	−2.83380	−	2.05887i
$499$	−3.34603			−0.149789			−0.0748945	−	0.997191i	$-0.523862\pi$
$499$	−3.34603			−0.149789			−0.0748945	+	0.997191i	$0.523862\pi$
$500$		0			0
$501$	0.820954			0.0366775
$502$	22.3411	+	16.2317i	0.997131	+	0.724458i
$503$	−3.67174	−	11.3005i	−0.163715	−	0.503863i	0.835224	−	0.549909i	$-0.185338\pi$
$503$	−3.67174	−	11.3005i	−0.163715	−	0.503863i	−0.998939	+	0.0460467i	$0.985338\pi$
$504$	8.38530	+	25.8073i	0.373511	+	1.14955i
$505$		0			0
$506$	−2.29494	+	7.06311i	−0.102023	+	0.313994i
$507$	−13.7878			−0.612339
$508$	−5.21175	+	16.0401i	−0.231234	+	0.711665i
$509$	−29.3821	+	21.3474i	−1.30234	+	0.946205i	−0.999976	−	0.00698772i	$-0.997776\pi$
$509$	−29.3821	+	21.3474i	−1.30234	+	0.946205i	−0.302364	+	0.953193i	$0.597776\pi$
$510$		0			0
$511$	43.2509	+	31.4236i	1.91331	+	1.39010i
$512$	−7.37987	+	5.36179i	−0.326147	+	0.236960i
$513$	−1.28605	+	0.934368i	−0.0567804	+	0.0412533i
$514$	35.5979	+	25.8634i	1.57016	+	1.14078i
$515$		0			0
$516$	−60.2800	+	43.7960i	−2.65368	+	1.92801i
$517$	0.825784	−	2.54150i	0.0363180	−	0.111775i
$518$	38.4263			1.68835
$519$	7.07920	−	21.7875i	0.310742	−	0.956366i
$520$		0			0
$521$	0.0631087	+	0.194229i	0.00276484	+	0.00850931i	0.952429	−	0.304759i	$-0.0985760\pi$
$521$	0.0631087	+	0.194229i	0.00276484	+	0.00850931i	−0.949665	+	0.313269i	$0.898576\pi$
$522$	9.21122	+	28.3492i	0.403164	+	1.24081i
$523$	22.6777	+	16.4763i	0.991627	+	0.720459i	0.960277	−	0.279049i	$-0.0900193\pi$
$523$	22.6777	+	16.4763i	0.991627	+	0.720459i	0.0313501	+	0.999508i	$0.490019\pi$
$524$	9.22069			0.402808
$525$		0			0
$526$	−15.6943			−0.684303
$527$	25.0184	+	18.1769i	1.08982	+	0.791798i
$528$	−0.287469	−	0.884738i	−0.0125105	−	0.0385033i
$529$	5.60468	+	17.2494i	0.243682	+	0.749975i
$530$		0			0
$531$	−0.900370	+	2.77105i	−0.0390727	+	0.120253i
$532$	12.1031			0.524736
$533$	2.35224	−	7.23946i	0.101887	−	0.313576i
$534$	49.3150	−	35.8294i	2.13407	−	1.55049i
$535$		0			0
$536$	14.0341	+	10.1964i	0.606180	+	0.440416i
$537$	−28.6514	+	20.8165i	−1.23640	+	0.898297i
$538$	−47.6728	+	34.6363i	−2.05532	+	1.49328i
$539$	2.38353	+	1.73174i	0.102666	+	0.0745912i
$540$		0			0
$541$	7.54179	−	5.47943i	0.324247	−	0.235579i	−0.413739	−	0.910396i	$-0.635777\pi$
$541$	7.54179	−	5.47943i	0.324247	−	0.235579i	0.737985	+	0.674817i	$0.235777\pi$
$542$	−6.76205	+	20.8114i	−0.290455	+	0.893928i
$543$	20.5347			0.881230
$544$	−7.37808	+	22.7074i	−0.316333	+	0.973571i
$545$		0			0
$546$	−15.7501	−	48.4738i	−0.674042	−	2.07449i
$547$	6.19203	+	19.0571i	0.264752	+	0.814822i	0.991750	+	0.128184i	$0.0409147\pi$
$547$	6.19203	+	19.0571i	0.264752	+	0.814822i	−0.726999	+	0.686639i	$0.759085\pi$
$548$	−6.20407	−	4.50752i	−0.265025	−	0.192552i
$549$	−14.3244			−0.611351
$550$		0			0
$551$	5.49914			0.234271
$552$	−39.2028	−	28.4825i	−1.66858	−	1.21230i
$553$	18.4247	+	56.7053i	0.783497	+	2.41136i
$554$	−4.28937	−	13.2013i	−0.182238	−	0.560870i
$555$		0			0
$556$	−11.3864	+	35.0436i	−0.482890	+	1.48618i
$557$	28.9839			1.22809			0.614043	−	0.789272i	$-0.289542\pi$
$557$	28.9839			1.22809			0.614043	+	0.789272i	$0.289542\pi$
$558$	−10.0134	+	30.8180i	−0.423900	+	1.30463i
$559$	20.3263	−	14.7679i	0.859712	−	0.624617i
$560$		0			0
$561$	−4.73531	−	3.44040i	−0.199925	−	0.145254i
$562$	20.8364	−	15.1385i	0.878931	−	0.638581i
$563$	11.0856	−	8.05414i	0.467201	−	0.339441i	−0.329148	−	0.944278i	$-0.606762\pi$
$563$	11.0856	−	8.05414i	0.467201	−	0.339441i	0.796349	+	0.604837i	$0.206762\pi$
$564$	34.1045	+	24.7784i	1.43606	+	1.04336i
$565$		0			0
$566$	5.69085	−	4.13465i	0.239204	−	0.173792i
$567$	11.7832	−	36.2649i	0.494848	−	1.52298i
$568$	0.498673			0.0209239
$569$	10.6967	−	32.9210i	0.448428	−	1.38012i	−0.430251	−	0.902709i	$-0.641575\pi$
$569$	10.6967	−	32.9210i	0.448428	−	1.38012i	0.878680	−	0.477412i	$-0.158425\pi$
$570$		0			0
$571$	−13.1084	−	40.3435i	−0.548569	−	1.68832i	−0.712348	−	0.701826i	$-0.752368\pi$
$571$	−13.1084	−	40.3435i	−0.548569	−	1.68832i	0.163779	−	0.986497i	$-0.447632\pi$
$572$	1.38924	+	4.27563i	0.0580869	+	0.178773i
$573$	21.2127	+	15.4119i	0.886172	+	0.643842i
$574$	−24.0346			−1.00318
$575$		0			0
$576$	−28.7532			−1.19805
$577$	−27.7533	−	20.1639i	−1.15538	−	0.839436i	−0.166197	−	0.986093i	$-0.553149\pi$
$577$	−27.7533	−	20.1639i	−1.15538	−	0.839436i	−0.989187	+	0.146657i	$0.953149\pi$
$578$	−6.52917	−	20.0947i	−0.271578	−	0.835830i
$579$	−12.3310	−	37.9508i	−0.512458	−	1.57718i
$580$		0			0
$581$	16.2115	−	49.8938i	0.672566	−	2.06995i
$582$	4.54777			0.188511
$583$	−0.0473165	+	0.145625i	−0.00195965	+	0.00603118i
$584$	39.4881	−	28.6898i	1.63403	−	1.18719i
$585$		0			0
$586$	−11.7884	−	8.56480i	−0.486976	−	0.353808i
$587$	24.0700	−	17.4879i	0.993475	−	0.721802i	0.0327956	−	0.999462i	$-0.489559\pi$
$587$	24.0700	−	17.4879i	0.993475	−	0.721802i	0.960679	+	0.277660i	$0.0895590\pi$
$588$	−37.6003	+	27.3182i	−1.55061	+	1.12658i
$589$	4.83633	+	3.51380i	0.199278	+	0.144784i
$590$		0			0
$591$	48.3551	−	35.1321i	1.98906	−	1.44514i
$592$	1.15285	−	3.54812i	0.0473820	−	0.145827i
$593$	14.8105			0.608195			0.304098	−	0.952641i	$-0.401645\pi$
$593$	14.8105			0.608195			0.304098	+	0.952641i	$0.401645\pi$
$594$	−0.576123	+	1.77312i	−0.0236386	+	0.0727522i
$595$		0			0
$596$	12.8456	+	39.5348i	0.526178	+	1.61941i
$597$	−5.96604	−	18.3616i	−0.244174	−	0.751490i
$598$	31.9597	+	23.2201i	1.30693	+	0.949541i
$599$	27.2394			1.11297			0.556486	−	0.830857i	$-0.312149\pi$
$599$	27.2394			1.11297			0.556486	+	0.830857i	$0.312149\pi$
$600$		0			0
$601$	33.1682			1.35296			0.676480	−	0.736461i	$-0.263505\pi$
$601$	33.1682			1.35296			0.676480	+	0.736461i	$0.263505\pi$
$602$	−64.1794	−	46.6291i	−2.61576	−	1.90046i
$603$	3.75821	+	11.5666i	0.153046	+	0.471027i
$604$	18.0083	+	55.4238i	0.732747	+	2.25516i
$605$		0			0
$606$	21.9273	−	67.4853i	0.890736	−	2.74140i
$607$	−5.79849			−0.235353			−0.117677	−	0.993052i	$-0.537545\pi$
$607$	−5.79849			−0.235353			−0.117677	+	0.993052i	$0.537545\pi$
$608$	−1.42627	+	4.38959i	−0.0578427	+	0.178022i
$609$	−37.2894	+	27.0924i	−1.51104	+	1.09784i
$610$		0			0
$611$	−11.5000	−	8.35524i	−0.465240	−	0.338017i
$612$	32.4220	−	23.5559i	1.31058	−	0.952192i
$613$	3.27371	−	2.37849i	0.132224	−	0.0960664i	−0.519707	−	0.854344i	$-0.673959\pi$
$613$	3.27371	−	2.37849i	0.132224	−	0.0960664i	0.651931	+	0.758278i	$0.273959\pi$
$614$	−48.6900	−	35.3754i	−1.96497	−	1.42763i
$615$		0			0
$616$	4.74994	−	3.45103i	0.191380	−	0.139046i
$617$	−11.4877	+	35.3555i	−0.462477	+	1.42336i	0.399651	+	0.916667i	$0.369131\pi$
$617$	−11.4877	+	35.3555i	−0.462477	+	1.42336i	−0.862128	+	0.506690i	$0.830869\pi$
$618$	4.44986			0.179000
$619$	−11.6536	+	35.8660i	−0.468397	+	1.44158i	0.386262	+	0.922389i	$0.373766\pi$
$619$	−11.6536	+	35.8660i	−0.468397	+	1.44158i	−0.854659	+	0.519189i	$0.826234\pi$
$620$		0			0
$621$	3.19124	+	9.82163i	0.128060	+	0.394128i
$622$	6.47123	+	19.9164i	0.259473	+	0.798575i
$623$	33.0974	+	24.0466i	1.32602	+	0.963409i
$624$	−4.94839			−0.198094
$625$		0			0
$626$	−77.2903			−3.08914
$627$	−0.915388	−	0.665069i	−0.0365571	−	0.0265603i
$628$	7.90310	+	24.3232i	0.315368	+	0.970603i
$629$	−7.25364	−	22.3244i	−0.289221	−	0.890132i
$630$		0			0
$631$	5.72376	−	17.6159i	0.227859	−	0.701279i	−0.770129	−	0.637888i	$-0.779808\pi$
$631$	5.72376	−	17.6159i	0.227859	−	0.701279i	0.997989	−	0.0633911i	$-0.0201916\pi$
$632$	54.4362			2.16536
$633$	11.3217	−	34.8447i	0.449998	−	1.38495i
$634$	48.8705	−	35.5065i	1.94089	−	1.41014i
$635$		0			0
$636$	−1.95415	−	1.41977i	−0.0774871	−	0.0562977i
$637$	12.6788	−	9.21166i	0.502351	−	0.364979i
$638$	5.21779	−	3.79094i	0.206574	−	0.150085i
$639$	0.282843	+	0.205497i	0.0111891	+	0.00812935i
$640$		0			0
$641$	15.9470	−	11.5862i	0.629868	−	0.457626i	−0.226486	−	0.974014i	$-0.572724\pi$
$641$	15.9470	−	11.5862i	0.629868	−	0.457626i	0.856355	+	0.516388i	$0.172724\pi$
$642$	−0.119625	+	0.368166i	−0.00472120	+	0.0145304i
$643$	−42.5897			−1.67957			−0.839787	−	0.542916i	$-0.817320\pi$
$643$	−42.5897			−1.67957			−0.839787	+	0.542916i	$0.817320\pi$
$644$	24.2972	−	74.7792i	0.957445	−	2.94671i
$645$		0			0
$646$	−3.62436	−	11.1546i	−0.142599	−	0.438874i
$647$	−8.46763	−	26.0607i	−0.332897	−	1.02455i	−0.967749	−	0.251917i	$-0.918939\pi$
$647$	−8.46763	−	26.0607i	−0.332897	−	1.02455i	0.634852	−	0.772634i	$-0.281061\pi$
$648$	−28.1649	−	20.4630i	−1.10642	−	0.803864i
$649$	0.630424			0.0247463
$650$		0			0
$651$	−50.1062			−1.96382
$652$	5.38789	+	3.91453i	0.211006	+	0.153305i
$653$	−6.62577	−	20.3920i	−0.259286	−	0.798001i	−0.992955	−	0.118494i	$-0.962193\pi$
$653$	−6.62577	−	20.3920i	−0.259286	−	0.798001i	0.733668	−	0.679508i	$-0.237807\pi$
$654$	−9.26126	−	28.5032i	−0.362144	−	1.11456i
$655$		0			0
$656$	−0.721078	+	2.21925i	−0.0281534	+	0.0866471i
$657$	34.2200			1.33505
$658$	−13.8694	+	42.6858i	−0.540687	+	1.66406i
$659$	29.7186	−	21.5918i	1.15767	−	0.841097i	0.168189	−	0.985755i	$-0.446208\pi$
$659$	29.7186	−	21.5918i	1.15767	−	0.841097i	0.989482	+	0.144658i	$0.0462080\pi$
$660$		0			0
$661$	12.7433	+	9.25853i	0.495656	+	0.360115i	0.807355	−	0.590066i	$-0.200898\pi$
$661$	12.7433	+	9.25853i	0.495656	+	0.360115i	−0.311699	+	0.950181i	$0.600898\pi$
$662$	22.8239	−	16.5825i	0.887074	−	0.644497i
$663$	−25.1886	+	18.3006i	−0.978244	+	0.710736i
$664$	−38.7497	−	28.1533i	−1.50378	−	1.09256i
$665$		0			0
$666$	19.8989	−	14.4574i	0.771065	−	0.560212i
$667$	11.0396	−	33.9765i	0.427457	−	1.31558i
$668$	1.21620			0.0470561
$669$	0.270143	−	0.831415i	0.0104443	−	0.0321444i
$670$		0			0
$671$	0.957753	+	2.94766i	0.0369736	+	0.113793i
$672$	−11.9546	−	36.7924i	−0.461157	−	1.41930i
$673$	25.0882	+	18.2276i	0.967078	+	0.702623i	0.954784	−	0.297301i	$-0.0960866\pi$
$673$	25.0882	+	18.2276i	0.967078	+	0.702623i	0.0122940	+	0.999924i	$0.496087\pi$
$674$	−70.3690			−2.71051
$675$		0			0
$676$	−20.4259			−0.785611
$677$	−7.76560	−	5.64204i	−0.298456	−	0.216841i	0.428471	−	0.903555i	$-0.359052\pi$
$677$	−7.76560	−	5.64204i	−0.298456	−	0.216841i	−0.726928	+	0.686714i	$0.759052\pi$
$678$	−4.30674	−	13.2548i	−0.165399	−	0.509046i
$679$	0.943183	+	2.90282i	0.0361960	+	0.111400i
$680$		0			0
$681$	−14.4432	+	44.4515i	−0.553464	+	1.70339i
$682$	7.01120			0.268473
$683$	0.268335	−	0.825850i	0.0102675	−	0.0316003i	−0.945791	−	0.324774i	$-0.894712\pi$
$683$	0.268335	−	0.825850i	0.0102675	−	0.0316003i	0.956059	+	0.293174i	$0.0947116\pi$
$684$	6.26753	−	4.55363i	0.239645	−	0.174112i
$685$		0			0
$686$	7.31440	+	5.31422i	0.279265	+	0.202898i
$687$	22.1849	−	16.1183i	0.846407	−	0.614951i
$688$	−6.23102	+	4.52710i	−0.237555	+	0.172594i
$689$	0.658937	+	0.478746i	0.0251035	+	0.0182388i
$690$		0			0
$691$	10.6284	−	7.72200i	0.404324	−	0.293759i	−0.366976	−	0.930231i	$-0.619607\pi$
$691$	10.6284	−	7.72200i	0.404324	−	0.293759i	0.771300	+	0.636472i	$0.219607\pi$
$692$	10.4874	−	32.2770i	0.398672	−	1.22699i
$693$	4.11625			0.156364
$694$	−9.58046	+	29.4856i	−0.363669	+	1.11926i
$695$		0			0
$696$	13.0041	+	40.0226i	0.492920	+	1.51705i
$697$	4.53695	+	13.9633i	0.171849	+	0.528898i
$698$	−51.6464	−	37.5233i	−1.95484	−	1.42028i
$699$	43.8844			1.65986
$700$		0			0
$701$	7.13602			0.269524			0.134762	−	0.990878i	$-0.456973\pi$
$701$	7.13602			0.269524			0.134762	+	0.990878i	$0.456973\pi$
$702$	8.02318	+	5.82918i	0.302815	+	0.220008i
$703$	−1.40221	−	4.31556i	−0.0528854	−	0.162764i
$704$	1.92248	+	5.91680i	0.0724564	+	0.222998i
$705$		0			0
$706$	11.1820	−	34.4147i	0.420841	−	1.29521i
$707$	47.6231			1.79105
$708$	−3.07316	+	9.45821i	−0.115496	+	0.355461i
$709$	6.47629	−	4.70530i	0.243222	−	0.176711i	−0.459496	−	0.888180i	$-0.651970\pi$
$709$	6.47629	−	4.70530i	0.243222	−	0.176711i	0.702718	+	0.711469i	$0.251970\pi$
$710$		0			0
$711$	30.8758	+	22.4325i	1.15793	+	0.841286i
$712$	30.2179	−	21.9546i	1.13246	−	0.822782i
$713$	31.4191	−	22.8273i	1.17666	−	0.854890i
$714$	79.5317	+	57.7832i	2.97640	+	2.16248i
$715$		0			0
$716$	−42.4455	+	30.8384i	−1.58626	+	1.15249i
$717$	2.93470	−	9.03207i	0.109598	−	0.337309i
$718$	51.1345			1.90832
$719$	−12.7490	+	39.2374i	−0.475458	+	1.46331i	0.369881	+	0.929079i	$0.379398\pi$
$719$	−12.7490	+	39.2374i	−0.475458	+	1.46331i	−0.845339	+	0.534230i	$0.820602\pi$
$720$		0			0
$721$	0.922877	+	2.84032i	0.0343697	+	0.105779i
$722$	12.9567	+	39.8765i	0.482197	+	1.48405i
$723$	−30.1479	−	21.9037i	−1.12121	−	0.814608i
$724$	30.4210			1.13059
$725$		0			0
$726$	57.5825			2.13709
$727$	31.7622	+	23.0766i	1.17799	+	0.855863i	0.991944	−	0.126677i	$-0.0404313\pi$
$727$	31.7622	+	23.0766i	1.17799	+	0.855863i	0.186050	+	0.982540i	$0.440431\pi$
$728$	−9.65091	−	29.7025i	−0.357687	−	1.10085i
$729$	−4.10574	−	12.6362i	−0.152064	−	0.468006i
$730$		0			0
$731$	−14.9750	+	46.0882i	−0.553869	+	1.70463i
$732$	−48.8924			−1.80711
$733$	−0.281840	+	0.867416i	−0.0104100	+	0.0320387i	−0.956127	−	0.292954i	$-0.905362\pi$
$733$	−0.281840	+	0.867416i	−0.0104100	+	0.0320387i	0.945717	+	0.324993i	$0.105362\pi$
$734$	−22.7899	+	16.5579i	−0.841192	+	0.611162i
$735$		0			0
$736$	24.2579	+	17.6244i	0.894159	+	0.649645i
$737$	2.12887	−	1.54672i	0.0784181	−	0.0569741i
$738$	−12.4462	+	9.04269i	−0.458151	+	0.332866i
$739$	9.46071	+	6.87361i	0.348018	+	0.252850i	0.748037	−	0.663657i	$-0.230997\pi$
$739$	9.46071	+	6.87361i	0.348018	+	0.252850i	−0.400019	+	0.916507i	$0.630997\pi$
$740$		0			0
$741$	−4.86924	+	3.53771i	−0.178876	+	0.129961i
$742$	0.794704	−	2.44585i	0.0291745	−	0.0897898i
$743$	−11.5631			−0.424211			−0.212105	−	0.977247i	$-0.568032\pi$
$743$	−11.5631			−0.424211			−0.212105	+	0.977247i	$0.568032\pi$
$744$	−14.1366	+	43.5079i	−0.518272	+	1.59508i
$745$		0			0
$746$	5.09348	+	15.6761i	0.186486	+	0.573943i
$747$	−10.3768	−	31.9366i	−0.379669	−	1.16850i
$748$	−7.01509	−	5.09676i	−0.256497	−	0.186356i
$749$	−0.259808			−0.00949318
$750$		0			0
$751$	−27.2430			−0.994112			−0.497056	−	0.867718i	$-0.665586\pi$
$751$	−27.2430			−0.994112			−0.497056	+	0.867718i	$0.665586\pi$
$752$	3.52531	+	2.56129i	0.128555	+	0.0934006i
$753$	8.44627	+	25.9949i	0.307799	+	0.947308i
$754$	−10.6015	−	32.6280i	−0.386083	−	1.18824i
$755$		0			0
$756$	6.09958	−	18.7726i	0.221840	−	0.682752i
$757$	−17.1080			−0.621800			−0.310900	−	0.950443i	$-0.600630\pi$
$757$	−17.1080			−0.621800			−0.310900	+	0.950443i	$0.600630\pi$
$758$	15.4564	−	47.5700i	0.561403	−	1.72782i
$759$	−5.94680	+	4.32060i	−0.215855	+	0.156828i
$760$		0			0
$761$	−30.5139	−	22.1697i	−1.10613	−	0.803650i	−0.124079	−	0.992272i	$-0.539598\pi$
$761$	−30.5139	−	22.1697i	−1.10613	−	0.803650i	−0.982050	+	0.188623i	$0.939598\pi$
$762$	−21.4241	+	15.5655i	−0.776112	+	0.563879i
$763$	16.2727	−	11.8228i	0.589112	−	0.428015i
$764$	31.4254	+	22.8319i	1.13693	+	0.826028i
$765$		0			0
$766$	−46.8236	+	34.0194i	−1.69181	+	1.22917i
$767$	1.03626	−	3.18929i	0.0374173	−	0.115159i
$768$	−48.0682			−1.73451
$769$	−1.83354	+	5.64306i	−0.0661192	+	0.203494i	−0.978658	−	0.205496i	$-0.934119\pi$
$769$	−1.83354	+	5.64306i	−0.0661192	+	0.203494i	0.912539	+	0.408991i	$0.134119\pi$
$770$		0			0
$771$	13.4581	+	41.4199i	0.484683	+	1.49170i
$772$	−18.2676	−	56.2220i	−0.657467	−	2.02347i
$773$	19.0854	+	13.8663i	0.686454	+	0.498738i	0.875492	−	0.483232i	$-0.160537\pi$
$773$	19.0854	+	13.8663i	0.686454	+	0.498738i	−0.189039	+	0.981970i	$0.560537\pi$
$774$	−50.7786			−1.82520
$775$		0			0
$776$	2.78666			0.100035
$777$	30.7696	+	22.3554i	1.10385	+	0.801996i
$778$	25.4559	+	78.3452i	0.912638	+	2.80881i
$779$	0.877044	+	2.69926i	0.0314234	+	0.0967111i
$780$		0			0
$781$	0.0233757	−	0.0719429i	0.000836447	−	0.00257432i
$782$	−76.1952			−2.72473
$783$	2.77139	−	8.52948i	0.0990416	−	0.304819i
$784$	−3.88666	+	2.82383i	−0.138809	+	0.100851i
$785$		0			0
$786$	11.7129	+	8.50992i	0.417785	+	0.303539i
$787$	−14.7489	+	10.7157i	−0.525743	+	0.381974i	−0.818763	−	0.574132i	$-0.805340\pi$
$787$	−14.7489	+	10.7157i	−0.525743	+	0.381974i	0.293020	+	0.956106i	$0.405340\pi$
$788$	71.6354	−	52.0462i	2.55191	−	1.85407i
$789$	−12.5671	−	9.13052i	−0.447400	−	0.325055i
$790$		0			0
$791$	7.56725	−	5.49793i	0.269060	−	0.195484i
$792$	1.16133	−	3.57420i	0.0412660	−	0.127004i
$793$	16.4864			0.585451
$794$	3.95130	−	12.1609i	0.140227	−	0.431573i
$795$		0			0
$796$	−8.83836	−	27.2017i	−0.313267	−	0.964138i
$797$	3.34652	+	10.2995i	0.118540	+	0.364828i	0.992669	−	0.120866i	$-0.0385671\pi$
$797$	3.34652	+	10.2995i	0.118540	+	0.364828i	−0.874129	+	0.485694i	$0.838567\pi$
$798$	15.3744	+	11.1701i	0.544247	+	0.395419i
$799$	27.4171			0.969948
$800$		0			0
$801$	26.1865			0.925256
$802$	46.7572	+	33.9711i	1.65105	+	1.19956i
$803$	−2.28800	−	7.04175i	−0.0807418	−	0.248498i
$804$	12.8276	+	39.4792i	0.452394	+	1.39233i
$805$		0			0
$806$	11.5247	−	35.4694i	0.405941	−	1.24936i
$807$	−58.3242			−2.05311
$808$	13.4360	−	41.3518i	0.472677	−	1.45475i
$809$	−36.2583	+	26.3432i	−1.27477	+	0.926178i	−0.999382	−	0.0351545i	$-0.988808\pi$
$809$	−36.2583	+	26.3432i	−1.27477	+	0.926178i	−0.275392	+	0.961332i	$0.588808\pi$
$810$		0			0
$811$	2.47799	+	1.80036i	0.0870139	+	0.0632193i	0.630442	−	0.776237i	$-0.282874\pi$
$811$	2.47799	+	1.80036i	0.0870139	+	0.0632193i	−0.543428	+	0.839456i	$0.682874\pi$
$812$	−55.2422	+	40.1358i	−1.93862	+	1.40849i
$813$	−17.5222	+	12.7306i	−0.614531	+	0.446483i
$814$	−4.30549	−	3.12812i	−0.150907	−	0.109641i
$815$		0			0
$816$	7.72154	−	5.61003i	0.270308	−	0.196390i
$817$	−2.89483	+	8.90937i	−0.101277	+	0.311699i
$818$	−9.14524			−0.319756
$819$	6.76613	−	20.8240i	0.236428	−	0.727650i
$820$		0			0
$821$	6.27954	+	19.3264i	0.219157	+	0.674497i	0.998832	+	0.0483124i	$0.0153843\pi$
$821$	6.27954	+	19.3264i	0.219157	+	0.674497i	−0.779675	+	0.626184i	$0.784616\pi$
$822$	−3.72087	−	11.4517i	−0.129780	−	0.399423i
$823$	−40.4807	−	29.4110i	−1.41107	−	1.02520i	−0.993166	−	0.116710i	$-0.962765\pi$
$823$	−40.4807	−	29.4110i	−1.41107	−	1.02520i	−0.417903	−	0.908492i	$-0.637235\pi$
$824$	2.72666			0.0949879
$825$		0			0
$826$	−10.5883			−0.368413
$827$	−25.5886	−	18.5912i	−0.889804	−	0.646481i	0.0460228	−	0.998940i	$-0.485345\pi$
$827$	−25.5886	−	18.5912i	−0.889804	−	0.646481i	−0.935827	+	0.352460i	$0.885345\pi$
$828$	−15.5525	−	47.8656i	−0.540485	−	1.66344i
$829$	10.2399	+	31.5150i	0.355645	+	1.09456i	0.955635	+	0.294555i	$0.0951713\pi$
$829$	10.2399	+	31.5150i	0.355645	+	1.09456i	−0.599990	+	0.800008i	$0.704829\pi$
$830$		0			0
$831$	4.24550	−	13.0663i	0.147275	−	0.453265i
$832$	33.0930			1.14729
$833$	−9.34079	+	28.7480i	−0.323639	+	0.996059i
$834$	−46.8063	+	34.0067i	−1.62077	+	1.17756i
$835$		0			0
$836$	−1.35610	−	0.985262i	−0.0469016	−	0.0340760i
$837$	7.88746	−	5.73058i	0.272631	−	0.198078i
$838$	−8.96901	+	6.51636i	−0.309829	+	0.225104i
$839$	−8.40194	−	6.10437i	−0.290067	−	0.210746i	0.433229	−	0.901284i	$-0.357374\pi$
$839$	−8.40194	−	6.10437i	−0.290067	−	0.210746i	−0.723296	+	0.690538i	$0.757374\pi$
$840$		0			0
$841$	−1.63826	+	1.19026i	−0.0564916	+	0.0410436i
$842$	−11.5427	+	35.5246i	−0.397786	+	1.22426i
$843$	25.4918			0.877986
$844$	16.7725	−	51.6204i	0.577333	−	1.77685i
$845$		0			0
$846$	8.87772	+	27.3228i	0.305222	+	0.939378i
$847$	11.9423	+	36.7546i	0.410342	+	1.26290i
$848$	−0.201997	−	0.146759i	−0.00693659	−	0.00503973i
$849$	6.96235			0.238947
$850$		0			0
$851$	−29.4787			−1.01052
$852$	0.965405	+	0.701407i	0.0330742	+	0.0240298i
$853$	2.87836	+	8.85867i	0.0985530	+	0.303315i	0.988163	−	0.153405i	$-0.0490240\pi$
$853$	2.87836	+	8.85867i	0.0985530	+	0.303315i	−0.889610	+	0.456720i	$0.849024\pi$
$854$	−16.0859	−	49.5074i	−0.550449	−	1.69411i
$855$		0			0
$856$	−0.0733002	+	0.225595i	−0.00250535	+	0.00771067i
$857$	34.0314			1.16249			0.581245	−	0.813729i	$-0.302566\pi$
$857$	34.0314			1.16249			0.581245	+	0.813729i	$0.302566\pi$
$858$	−2.18132	+	6.71342i	−0.0744691	+	0.229192i
$859$	−27.0408	+	19.6463i	−0.922621	+	0.670323i	−0.944175	−	0.329444i	$-0.893139\pi$
$859$	−27.0408	+	19.6463i	−0.922621	+	0.670323i	0.0215540	+	0.999768i	$0.493139\pi$
$860$		0			0
$861$	−19.2455	−	13.9827i	−0.655886	−	0.476529i
$862$	−77.8510	+	56.5621i	−2.65162	+	1.92651i
$863$	13.4216	−	9.75136i	0.456877	−	0.331940i	−0.335428	−	0.942066i	$-0.608881\pi$
$863$	13.4216	−	9.75136i	0.456877	−	0.331940i	0.792305	+	0.610126i	$0.208881\pi$
$864$	6.08971	+	4.42444i	0.207176	+	0.150522i
$865$		0			0
$866$	−28.5767	+	20.7622i	−0.971076	+	0.705528i
$867$	6.46240	−	19.8892i	0.219475	−	0.675473i
$868$	−74.2296			−2.51952
$869$	2.55174	−	7.85344i	0.0865618	−	0.266410i
$870$		0			0
$871$	−4.32544	−	13.3123i	−0.146562	−	0.451072i
$872$	−5.67486	−	17.4654i	−0.192175	−	0.591454i
$873$	1.58057	+	1.14835i	0.0534942	+	0.0388658i
$874$	−14.7294			−0.498229
$875$		0			0
$876$	116.800			3.94632
$877$	−26.6601	−	19.3697i	−0.900249	−	0.654069i	0.0382809	−	0.999267i	$-0.487812\pi$
$877$	−26.6601	−	19.3697i	−0.900249	−	0.654069i	−0.938530	+	0.345198i	$0.887812\pi$
$878$	−12.3055	−	37.8724i	−0.415290	−	1.27813i
$879$	−4.45673	−	13.7164i	−0.150322	−	0.462643i
$880$		0			0
$881$	−15.4742	+	47.6246i	−0.521339	+	1.60452i	0.250106	+	0.968219i	$0.419535\pi$
$881$	−15.4742	+	47.6246i	−0.521339	+	1.60452i	−0.771444	+	0.636297i	$0.780465\pi$
$882$	−31.6737			−1.06651
$883$	−3.87306	+	11.9201i	−0.130339	+	0.401142i	−0.994836	−	0.101496i	$-0.967637\pi$
$883$	−3.87306	+	11.9201i	−0.130339	+	0.401142i	0.864497	+	0.502638i	$0.167637\pi$
$884$	−37.3155	+	27.1113i	−1.25506	+	0.911851i
$885$		0			0
$886$	−66.6006	−	48.3881i	−2.23749	−	1.62563i
$887$	21.7915	−	15.8325i	0.731687	−	0.531602i	−0.158410	−	0.987373i	$-0.550637\pi$
$887$	21.7915	−	15.8325i	0.731687	−	0.531602i	0.890097	+	0.455772i	$0.150637\pi$
$888$	28.0926	−	20.4105i	0.942726	−	0.684931i
$889$	−14.3786	−	10.4467i	−0.482243	−	0.350370i
$890$		0			0
$891$	−4.27243	+	3.10410i	−0.143132	+	0.103991i
$892$	0.400202	−	1.23169i	0.0133997	−	0.0412402i
$893$	5.30004			0.177359
$894$	−20.1697	+	62.0760i	−0.674576	+	2.07613i
$895$		0			0
$896$	−21.9042	−	67.4142i	−0.731768	−	2.25215i
$897$	12.0827	+	37.1867i	0.403429	+	1.24163i
$898$	38.9224	+	28.2788i	1.29886	+	0.943675i
$899$	−33.7268			−1.12485
$900$		0			0
$901$	−1.57097			−0.0523366
$902$	2.69296	+	1.95655i	0.0896659	+	0.0651461i
$903$	−24.2636	−	74.6758i	−0.807444	−	2.48506i
$904$	−2.63896	−	8.12189i	−0.0877706	−	0.270130i
$905$		0			0
$906$	−28.2759	+	87.0242i	−0.939403	+	2.89119i
$907$	28.6510			0.951342			0.475671	−	0.879623i	$-0.342205\pi$
$907$	28.6510			0.951342			0.475671	+	0.879623i	$0.342205\pi$
$908$	−21.3968	+	65.8524i	−0.710076	+	2.18539i
$909$	24.6614	−	17.9176i	0.817967	−	0.594288i
$910$		0			0
$911$	7.20082	+	5.23171i	0.238574	+	0.173334i	0.700648	−	0.713507i	$-0.252894\pi$
$911$	7.20082	+	5.23171i	0.238574	+	0.173334i	−0.462074	+	0.886841i	$0.652894\pi$
$912$	1.49266	−	1.08448i	0.0494269	−	0.0359108i
$913$	−5.87807	+	4.27067i	−0.194536	+	0.141338i
$914$	−78.5984	−	57.1051i	−2.59980	−	1.88887i
$915$		0			0
$916$	32.8657	−	23.8783i	1.08591	−	0.788962i
$917$	−3.00264	+	9.24119i	−0.0991560	+	0.305171i
$918$	−19.1280			−0.631320
$919$	5.31204	−	16.3488i	0.175228	−	0.539296i	−0.824416	−	0.565985i	$-0.808496\pi$
$919$	5.31204	−	16.3488i	0.175228	−	0.539296i	0.999644	+	0.0266884i	$0.00849619\pi$
$920$		0			0
$921$	−18.4077	−	56.6532i	−0.606556	−	1.86679i
$922$	7.67564	+	23.6232i	0.252784	+	0.777988i
$923$	−0.325533	−	0.236514i	−0.0107151	−	0.00778494i
$924$	14.0497			0.462200
$925$		0			0
$926$	−18.2141			−0.598554
$927$	1.54654	+	1.12363i	0.0507951	+	0.0369048i
$928$	−8.04669	−	24.7652i	−0.264146	−	0.812957i
$929$	10.7473	+	33.0767i	0.352607	+	1.08521i	0.957384	+	0.288818i	$0.0932621\pi$
$929$	10.7473	+	33.0767i	0.352607	+	1.08521i	−0.604777	+	0.796395i	$0.706738\pi$
$930$		0			0
$931$	−1.80568	+	5.55731i	−0.0591788	+	0.182134i
$932$	65.0123			2.12955
$933$	−6.40505	+	19.7127i	−0.209692	+	0.645366i
$934$	−9.37351	+	6.81026i	−0.306711	+	0.222838i
$935$		0			0
$936$	−16.1728	−	11.7502i	−0.528625	−	0.384069i
$937$	−13.3800	+	9.72114i	−0.437106	+	0.317576i	−0.784484	−	0.620149i	$-0.787072\pi$
$937$	−13.3800	+	9.72114i	−0.437106	+	0.317576i	0.347378	+	0.937725i	$0.387072\pi$
$938$	−35.7555	+	25.9779i	−1.16746	+	0.848207i
$939$	−61.8897	−	44.9655i	−2.01970	−	1.46739i
$940$		0			0
$941$	−33.3301	+	24.2157i	−1.08653	+	0.789410i	−0.978810	−	0.204772i	$-0.934355\pi$
$941$	−33.3301	+	24.2157i	−1.08653	+	0.789410i	−0.107719	+	0.994181i	$0.534355\pi$
$942$	−12.4091	+	38.1913i	−0.404311	+	1.24434i
$943$	18.4381			0.600428
$944$	−0.317666	+	0.977675i	−0.0103391	+	0.0318206i
$945$		0			0
$946$	3.39513	+	10.4491i	0.110385	+	0.339731i
$947$	11.4679	+	35.2946i	0.372657	+	1.14692i	0.945046	+	0.326939i	$0.106017\pi$
$947$	11.4679	+	35.2946i	0.372657	+	1.14692i	−0.572388	+	0.819983i	$0.693983\pi$
$948$	105.386	+	76.5672i	3.42277	+	2.48679i
$949$	−39.3849			−1.27849
$950$		0			0
$951$	59.7895			1.93881
$952$	48.7333	+	35.4068i	1.57945	+	1.14754i
$953$	−6.45728	−	19.8735i	−0.209172	−	0.643765i	−0.999516	−	0.0311020i	$-0.990098\pi$
$953$	−6.45728	−	19.8735i	−0.209172	−	0.643765i	0.790344	−	0.612663i	$-0.209902\pi$
$954$	−0.508683	−	1.56557i	−0.0164692	−	0.0506871i
$955$		0			0
$956$	4.34759	−	13.3805i	0.140611	−	0.432756i
$957$	6.38358			0.206352
$958$	11.7870	−	36.2767i	0.380821	−	1.17205i
$959$	6.53784	−	4.75002i	0.211118	−	0.153386i
$960$		0			0
$961$	−4.58220	−	3.32917i	−0.147813	−	0.107392i
$962$	−22.9022	+	16.6394i	−0.738398	+	0.536477i
$963$	−0.134540	+	0.0977493i	−0.00433550	+	0.00314993i
$964$	−44.6624	−	32.4491i	−1.43848	−	1.04512i
$965$		0			0
$966$	99.8793	−	72.5666i	3.21356	−	2.33479i
$967$	−2.55884	+	7.87529i	−0.0822866	+	0.253252i	−0.983732	−	0.179640i	$-0.942507\pi$
$967$	−2.55884	+	7.87529i	−0.0822866	+	0.253252i	0.901446	+	0.432892i	$0.142507\pi$
$968$	35.2838			1.13407
$969$	3.58730	−	11.0406i	0.115241	−	0.354674i
$970$		0			0
$971$	−8.16042	−	25.1152i	−0.261880	−	0.805985i	−0.992396	−	0.123089i	$-0.960720\pi$
$971$	−8.16042	−	25.1152i	−0.261880	−	0.805985i	0.730515	−	0.682896i	$-0.239280\pi$
$972$	−20.6525	−	63.5618i	−0.662429	−	2.03875i
$973$	−31.4137	−	22.8234i	−1.00708	−	0.731684i
$974$	2.03885			0.0653289
$975$		0			0
$976$	−5.05390			−0.161771
$977$	20.4908	+	14.8874i	0.655558	+	0.476290i	0.865160	−	0.501496i	$-0.167217\pi$
$977$	20.4908	+	14.8874i	0.655558	+	0.476290i	−0.209602	+	0.977787i	$0.567217\pi$
$978$	3.23137	+	9.94513i	0.103328	+	0.318010i
$979$	−1.75087	−	5.38863i	−0.0559581	−	0.172221i
$980$		0			0
$981$	3.97857	−	12.2448i	0.127026	−	0.390946i
$982$	−28.4059			−0.906470
$983$	1.58467	−	4.87712i	0.0505432	−	0.155556i	−0.922599	−	0.385760i	$-0.873939\pi$
$983$	1.58467	−	4.87712i	0.0505432	−	0.155556i	0.973142	+	0.230204i	$0.0739393\pi$
$984$	−17.5712	+	12.7662i	−0.560148	+	0.406971i
$985$		0			0
$986$	53.5333	+	38.8942i	1.70485	+	1.23864i
$987$	−35.9393	+	26.1115i	−1.14396	+	0.831137i
$988$	−7.21350	+	5.24092i	−0.229492	+	0.166736i
$989$	49.2352	+	35.7715i	1.56559	+	1.13747i
$990$		0			0
$991$	21.4710	−	15.5996i	0.682049	−	0.495538i	−0.191988	−	0.981397i	$-0.561493\pi$
$991$	21.4710	−	15.5996i	0.682049	−	0.495538i	0.874037	+	0.485860i	$0.161493\pi$
$992$	8.74744	−	26.9218i	0.277731	−	0.854769i
$993$	27.9233			0.886120
$994$	−0.392606	+	1.20832i	−0.0124527	+	0.0383254i
$995$		0			0
$996$	−35.4184	−	109.007i	−1.12228	−	3.45401i
$997$	−13.7504	−	42.3194i	−0.435480	−	1.34027i	−0.892594	−	0.450862i	$-0.851117\pi$
$997$	−13.7504	−	42.3194i	−0.435480	−	1.34027i	0.457114	−	0.889408i	$-0.348883\pi$
$998$	−6.29675	−	4.57486i	−0.199320	−	0.144815i
$999$	−7.40034			−0.234136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.q.376.3		16
5.2	odd	4		625.2.e.j.249.2		32
5.3	odd	4		625.2.e.j.249.7		32
5.4	even	2		625.2.d.m.376.2		16
25.2	odd	20		625.2.e.j.374.7		32
25.3	odd	20		625.2.e.k.499.2		32
25.4	even	10		625.2.d.n.126.3		16
25.6	even	5		625.2.a.e.1.3	✓	8
25.8	odd	20		625.2.b.d.624.14		16
25.9	even	10		625.2.d.n.501.3		16
25.11	even	5	inner	625.2.d.q.251.3		16
25.12	odd	20		625.2.e.k.124.2		32
25.13	odd	20		625.2.e.k.124.7		32
25.14	even	10		625.2.d.m.251.2		16
25.16	even	5		625.2.d.p.501.2		16
25.17	odd	20		625.2.b.d.624.3		16
25.19	even	10		625.2.a.g.1.6	yes	8
25.21	even	5		625.2.d.p.126.2		16
25.22	odd	20		625.2.e.k.499.7		32
25.23	odd	20		625.2.e.j.374.2		32
75.44	odd	10		5625.2.a.s.1.3		8
75.56	odd	10		5625.2.a.be.1.6		8
100.19	odd	10		10000.2.a.be.1.8		8
100.31	odd	10		10000.2.a.bn.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.3	✓	8	25.6	even	5
625.2.a.g.1.6	yes	8	25.19	even	10
625.2.b.d.624.3		16	25.17	odd	20
625.2.b.d.624.14		16	25.8	odd	20
625.2.d.m.251.2		16	25.14	even	10
625.2.d.m.376.2		16	5.4	even	2
625.2.d.n.126.3		16	25.4	even	10
625.2.d.n.501.3		16	25.9	even	10
625.2.d.p.126.2		16	25.21	even	5
625.2.d.p.501.2		16	25.16	even	5
625.2.d.q.251.3		16	25.11	even	5	inner
625.2.d.q.376.3		16	1.1	even	1	trivial
625.2.e.j.249.2		32	5.2	odd	4
625.2.e.j.249.7		32	5.3	odd	4
625.2.e.j.374.2		32	25.23	odd	20
625.2.e.j.374.7		32	25.2	odd	20
625.2.e.k.124.2		32	25.12	odd	20
625.2.e.k.124.7		32	25.13	odd	20
625.2.e.k.499.2		32	25.3	odd	20
625.2.e.k.499.7		32	25.22	odd	20
5625.2.a.s.1.3		8	75.44	odd	10
5625.2.a.be.1.6		8	75.56	odd	10
10000.2.a.be.1.8		8	100.19	odd	10
10000.2.a.bn.1.1		8	100.31	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)

\(f(q)\)	\(=\)	\(q+(1.88186 + 1.36725i) q^{2} +(0.711454 + 2.18963i) q^{3} +(1.05398 + 3.24381i) q^{4} +(-1.65491 + 5.09330i) q^{6} -3.59425 q^{7} +(-1.01405 + 3.12093i) q^{8} +(-1.86126 + 1.35229i) q^{9} +O(q^{10})\)	\(q+(1.88186 + 1.36725i) q^{2} +(0.711454 + 2.18963i) q^{3} +(1.05398 + 3.24381i) q^{4} +(-1.65491 + 5.09330i) q^{6} -3.59425 q^{7} +(-1.01405 + 3.12093i) q^{8} +(-1.86126 + 1.35229i) q^{9} +(0.402719 + 0.292592i) q^{11} +(-6.35290 + 4.61565i) q^{12} +(2.14219 - 1.55639i) q^{13} +(-6.76385 - 4.91423i) q^{14} +(-0.656686 + 0.477110i) q^{16} +(-1.57821 + 4.85722i) q^{17} -5.35154 q^{18} +(-0.305085 + 0.938956i) q^{19} +(-2.55714 - 7.87007i) q^{21} +(0.357812 + 1.10123i) q^{22} +(5.18889 + 3.76995i) q^{23} -7.55514 q^{24} +6.15926 q^{26} +(1.30262 + 0.946409i) q^{27} +(-3.78826 - 11.6591i) q^{28} +(-1.72123 - 5.29739i) q^{29} +(1.87112 - 5.75872i) q^{31} +4.67497 q^{32} +(-0.354153 + 1.08997i) q^{33} +(-9.61099 + 6.98279i) q^{34} +(-6.34830 - 4.61231i) q^{36} +(-3.71834 + 2.70153i) q^{37} +(-1.85791 + 1.34985i) q^{38} +(4.93199 + 3.58330i) q^{39} +(2.32572 - 1.68973i) q^{41} +(5.94817 - 18.3066i) q^{42} +9.48858 q^{43} +(-0.524658 + 1.61473i) q^{44} +(4.61029 + 14.1890i) q^{46} +(-1.65891 - 5.10560i) q^{47} +(-1.51190 - 1.09846i) q^{48} +5.91861 q^{49} -11.7583 q^{51} +(7.30646 + 5.30846i) q^{52} +(0.0950536 + 0.292545i) q^{53} +(1.15737 + 3.56201i) q^{54} +(3.64476 - 11.2174i) q^{56} -2.27302 q^{57} +(4.00375 - 12.3223i) q^{58} +(1.02458 - 0.744401i) q^{59} +(5.03715 + 3.65970i) q^{61} +(11.3948 - 8.27879i) q^{62} +(6.68984 - 4.86045i) q^{63} +(10.1110 + 7.34607i) q^{64} +(-2.15673 + 1.56695i) q^{66} +(1.63354 - 5.02753i) q^{67} -17.4193 q^{68} +(-4.56314 + 14.0439i) q^{69} +(-0.0469591 - 0.144525i) q^{71} +(-2.33298 - 7.18017i) q^{72} +(-12.0334 - 8.74276i) q^{73} -10.6910 q^{74} -3.36735 q^{76} +(-1.44747 - 1.05165i) q^{77} +(4.38203 + 13.4865i) q^{78} +(-5.12616 - 15.7767i) q^{79} +(-3.27835 + 10.0897i) q^{81} +6.68696 q^{82} +(-4.51040 + 13.8816i) q^{83} +(22.8339 - 16.5898i) q^{84} +(17.8561 + 12.9733i) q^{86} +(10.3748 - 7.53770i) q^{87} +(-1.32154 + 0.960155i) q^{88} +(-9.20843 - 6.69032i) q^{89} +(-7.69955 + 5.59405i) q^{91} +(-6.76004 + 20.8052i) q^{92} +13.9407 q^{93} +(3.85879 - 11.8761i) q^{94} +(3.32603 + 10.2365i) q^{96} +(-0.262415 - 0.807629i) q^{97} +(11.1380 + 8.09220i) q^{98} -1.14523 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

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