LMFDB - Embedded newform 625.2.d.m.376.2

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			376.2
Root			$-3.18910i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.m.251.2

$q$-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	$-0.992634\pi$
$2$	−1.88186	−	1.36725i	−1.33067	−	0.966790i	−0.330941	−	0.943652i	$-0.607366\pi$
$3$	−0.711454	−	2.18963i	−0.410758	−	1.26418i	−0.915990	−	0.401200i	$-0.868593\pi$
$3$	−0.711454	−	2.18963i	−0.410758	−	1.26418i	0.505232	−	0.862983i	$-0.331407\pi$
$4$	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	$-0.262306\pi$
$7$	3.59425			1.35850			0.679249	+	0.733908i	$0.262306\pi$
$8$	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	−0.843793	−	0.536669i	$-0.819682\pi$
$13$	−2.14219	+	1.55639i	−0.594136	+	0.431665i	0.249657	+	0.968334i	$0.419682\pi$
$14$	−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	$-0.687401\pi$
$17$	1.57821	−	4.85722i	0.382772	−	1.17805i	0.938084	−	0.346408i	$-0.112599\pi$
$18$	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	−0.103935	−	0.994584i	$-0.533143\pi$
$23$	−5.18889	−	3.76995i	−1.08196	−	0.786089i	−0.978023	+	0.208495i	$0.933143\pi$
$24$	−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	−0.238577	−	0.971124i	$-0.576681\pi$
$37$	3.71834	−	2.70153i	0.611292	−	0.444129i	0.849869	+	0.526994i	$0.176681\pi$
$38$	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	$-0.757467\pi$
$43$	−9.48858			−1.44700			−0.723498	+	0.690327i	$0.757467\pi$
$44$	−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	$0.0280529\pi$
$47$	1.65891	+	5.10560i	0.241977	+	0.744728i	−0.754142	+	0.656711i	$0.771947\pi$
$48$	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	0.944316	−	0.329040i	$-0.106725\pi$
$53$	−0.0950536	−	0.292545i	−0.0130566	−	0.0401841i	−0.957373	+	0.288856i	$0.906725\pi$
$54$	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	$0.204661\pi$
$67$	−1.63354	+	5.02753i	−0.199569	+	0.614210i	−0.999893	+	0.0146423i	$0.995339\pi$
$68$	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	$0.0361652\pi$
$73$	12.0334	+	8.74276i	1.40840	+	1.02326i	0.414848	+	0.909891i	$0.363835\pi$
$74$	−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	$-0.604271\pi$
$83$	4.51040	−	13.8816i	0.495081	−	1.52370i	0.816831	−	0.576877i	$-0.195729\pi$
$84$	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	0.963494	−	0.267729i	$-0.0862730\pi$
$97$	0.262415	+	0.807629i	0.0266442	+	0.0820023i	−0.936850	+	0.349731i	$0.886273\pi$
$98$	−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	0.962909	−	0.269826i	$-0.0869660\pi$
$103$	0.256765	+	0.790241i	0.0252998	+	0.0778648i	−0.937609	+	0.347690i	$0.886966\pi$
$104$	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	$-0.501112\pi$
$107$	−0.0722844			−0.00698800			−0.00349400	+	0.999994i	$0.501112\pi$
$108$	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	−0.484336	−	0.874882i	$-0.660939\pi$
$113$	2.10538	−	1.52965i	0.198057	−	0.143897i	0.682394	+	0.730985i	$0.260939\pi$
$114$	−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	0.395974	−	0.918262i	$-0.370407\pi$
$127$	−4.00045	−	2.90650i	−0.354983	−	0.257910i	−0.750956	+	0.660352i	$0.770407\pi$
$128$	−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	−0.507365	−	0.861731i	$-0.669380\pi$
$137$	1.81898	−	1.32156i	0.155406	−	0.112909i	0.662771	+	0.748822i	$0.269380\pi$
$138$	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	$-0.596725\pi$
$157$	−7.49835			−0.598433			−0.299217	+	0.954185i	$0.596725\pi$
$158$	−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	−0.647929	−	0.761701i	$-0.724365\pi$
$163$	−1.57968	+	1.14770i	−0.123730	+	0.0898951i	0.524199	+	0.851596i	$0.324365\pi$
$164$	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	−0.955229	−	0.295866i	$-0.904392\pi$
$167$	−0.110189	+	0.339126i	−0.00852665	+	0.0262423i	0.946703	+	0.322109i	$0.104392\pi$
$168$	−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	0.850128	−	0.526576i	$-0.176524\pi$
$173$	8.04998	+	5.84865i	0.612029	+	0.444665i	−0.238100	+	0.971241i	$0.576524\pi$
$174$	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	$-0.285590\pi$
$193$	17.3321			1.24759			0.623795	+	0.781588i	$0.285590\pi$
$194$	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	$0.275785\pi$
$197$	8.02237	+	24.6903i	0.571570	+	1.75911i	−0.0760014	+	0.997108i	$0.524215\pi$
$198$	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	0.598023	−	0.801479i	$-0.295953\pi$
$223$	0.307188	+	0.223185i	0.0205708	+	0.0149456i	−0.577452	+	0.816424i	$0.695953\pi$
$224$	−16.8030			−1.12270
$225$		0			0
$226$	−6.05343			−0.402668
$227$	−16.4238	−	11.9326i	−1.09009	−	0.791994i	−0.110672	−	0.993857i	$-0.535300\pi$
$227$	−16.4238	−	11.9326i	−1.09009	−	0.791994i	−0.979414	+	0.201863i	$0.935300\pi$
$228$	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	$0.314642\pi$
$233$	−5.89018	+	18.1281i	−0.385878	+	1.18761i	−0.935841	+	0.352422i	$0.885358\pi$
$234$	−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	$-0.700867\pi$
$257$	−18.9164			−1.17997			−0.589986	+	0.807414i	$0.700867\pi$
$258$	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	−0.406636	−	0.913590i	$-0.633298\pi$
$263$	5.45846	−	3.96580i	0.336583	−	0.244542i	0.743219	+	0.669048i	$0.233298\pi$
$264$	−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	0.723297	−	0.690537i	$-0.242626\pi$
$277$	4.82770	+	3.50753i	0.290068	+	0.210747i	−0.433229	+	0.901284i	$0.642626\pi$
$278$	−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	−0.974982	−	0.222284i	$-0.928649\pi$
$283$	−0.934487	+	2.87606i	−0.0555495	+	0.170964i	0.919432	+	0.393248i	$0.128649\pi$
$284$	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	$-0.441425\pi$
$293$	6.26426			0.365962			0.182981	+	0.983116i	$0.441425\pi$
$294$	−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	$-0.235612\pi$
$307$	25.8734			1.47667			0.738337	+	0.674432i	$0.235612\pi$
$308$	−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	$-0.311696\pi$
$313$	26.8815	−	19.5306i	1.51943	−	1.10393i	0.961767	−	0.273869i	$-0.0883035\pi$
$314$	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	$0.360150\pi$
$317$	−8.02495	+	24.6983i	−0.450726	+	1.38719i	−0.876080	+	0.482166i	$0.839850\pi$
$318$	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	$-0.391759\pi$
$337$	24.4743	−	17.7816i	1.33320	−	0.968626i	0.999665	−	0.0258885i	$-0.00824149\pi$
$338$	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	$-0.983544\pi$
$347$	−4.11868	−	12.6760i	−0.221102	−	0.680483i	0.777562	−	0.628807i	$-0.216456\pi$
$348$	−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	$0.0358657\pi$
$353$	4.80719	+	14.7950i	0.255861	+	0.787459i	−0.737798	+	0.675022i	$0.764134\pi$
$354$	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	$-0.797634\pi$
$367$	3.74230	−	11.5176i	0.195347	−	0.601215i	0.999972	−	0.00743290i	$-0.00236599\pi$
$368$	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	0.429395	−	0.903117i	$-0.358727\pi$
$373$	−5.73273	−	4.16507i	−0.296829	−	0.215659i	−0.726225	+	0.687458i	$0.758727\pi$
$374$	−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	$-0.680713\pi$
$383$	7.68885	−	23.6638i	0.392882	−	1.20917i	0.930599	−	0.366040i	$-0.119287\pi$
$384$	−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	0.984592	−	0.174870i	$-0.0559505\pi$
$397$	1.69868	+	5.22800i	0.0852543	+	0.262386i	−0.899337	+	0.437256i	$0.855950\pi$
$398$	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	$-0.781110\pi$
$433$	4.69254	−	14.4422i	0.225509	−	0.694046i	0.998240	−	0.0593113i	$-0.0188905\pi$
$434$	−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	$-0.182123\pi$
$443$	35.3909			1.68147			0.840736	+	0.541445i	$0.182123\pi$
$444$	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	$-0.0685863\pi$
$457$	41.7664			1.95375			0.976876	+	0.213807i	$0.0685863\pi$
$458$	−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	−0.430770	−	0.902462i	$-0.641758\pi$
$463$	6.33487	−	4.60255i	0.294406	−	0.213899i	0.725177	+	0.688563i	$0.241758\pi$
$464$	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	−0.909106	−	0.416564i	$-0.863234\pi$
$467$	1.53921	−	4.73721i	0.0712262	−	0.219212i	0.980333	+	0.197352i	$0.0632342\pi$
$468$	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	−0.603736	−	0.797185i	$-0.706322\pi$
$487$	−0.709110	+	0.515199i	−0.0321328	+	0.0233459i	0.571603	+	0.820530i	$0.306322\pi$
$488$	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	0.998939	−	0.0460467i	$-0.0146623\pi$
$503$	3.67174	+	11.3005i	0.163715	+	0.503863i	−0.835224	+	0.549909i	$0.814662\pi$
$504$	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	−0.0313501	−	0.999508i	$-0.509981\pi$
$523$	−22.6777	−	16.4763i	−0.991627	−	0.720459i	−0.960277	+	0.279049i	$0.909981\pi$
$524$	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	$-0.959085\pi$
$547$	−6.19203	−	19.0571i	−0.264752	−	0.814822i	0.726999	−	0.686639i	$-0.240915\pi$
$548$	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	$-0.710458\pi$
$557$	−28.9839			−1.22809			−0.614043	+	0.789272i	$0.710458\pi$
$558$	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	−0.796349	−	0.604837i	$-0.793238\pi$
$563$	−11.0856	+	8.05414i	−0.467201	+	0.339441i	0.329148	+	0.944278i	$0.393238\pi$
$564$	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	0.989187	−	0.146657i	$-0.0468514\pi$
$577$	27.7533	+	20.1639i	1.15538	+	0.839436i	0.166197	+	0.986093i	$0.446851\pi$
$578$	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	−0.960679	−	0.277660i	$-0.910441\pi$
$587$	−24.0700	+	17.4879i	−0.993475	+	0.721802i	−0.0327956	+	0.999462i	$0.510441\pi$
$588$	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	$-0.598355\pi$
$593$	−14.8105			−0.608195			−0.304098	+	0.952641i	$0.598355\pi$
$594$	−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	$-0.462455\pi$
$607$	5.79849			0.235353			0.117677	+	0.993052i	$0.462455\pi$
$608$	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	−0.651931	−	0.758278i	$-0.726041\pi$
$613$	−3.27371	+	2.37849i	−0.132224	+	0.0960664i	0.519707	+	0.854344i	$0.326041\pi$
$614$	−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	$-0.630869\pi$
$617$	11.4877	−	35.3555i	0.462477	−	1.42336i	0.862128	−	0.506690i	$-0.169131\pi$
$618$	−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	$-0.182680\pi$
$643$	42.5897			1.67957			0.839787	+	0.542916i	$0.182680\pi$
$644$	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	$0.0810611\pi$
$647$	8.46763	+	26.0607i	0.332897	+	1.02455i	−0.634852	+	0.772634i	$0.718939\pi$
$648$	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	$0.0378066\pi$
$653$	6.62577	+	20.3920i	0.259286	+	0.798001i	−0.733668	+	0.679508i	$0.762193\pi$
$654$	−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	−0.0122940	−	0.999924i	$-0.503913\pi$
$673$	−25.0882	−	18.2276i	−0.967078	−	0.702623i	−0.954784	+	0.297301i	$0.903913\pi$
$674$	−70.3690			−2.71051
$675$		0			0
$676$	−20.4259			−0.785611
$677$	7.76560	+	5.64204i	0.298456	+	0.216841i	0.726928	−	0.686714i	$-0.240948\pi$
$677$	7.76560	+	5.64204i	0.298456	+	0.216841i	−0.428471	+	0.903555i	$0.640948\pi$
$678$	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	−0.956059	−	0.293174i	$-0.905288\pi$
$683$	−0.268335	+	0.825850i	−0.0102675	+	0.0316003i	0.945791	+	0.324774i	$0.105288\pi$
$684$	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	−0.186050	−	0.982540i	$-0.559569\pi$
$727$	−31.7622	−	23.0766i	−1.17799	−	0.855863i	−0.991944	+	0.126677i	$0.959569\pi$
$728$	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	−0.945717	−	0.324993i	$-0.894638\pi$
$733$	0.281840	−	0.867416i	0.0104100	−	0.0320387i	0.956127	+	0.292954i	$0.0946382\pi$
$734$	−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	$-0.431968\pi$
$743$	11.5631			0.424211			0.212105	+	0.977247i	$0.431968\pi$
$744$	−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	$-0.399370\pi$
$757$	17.1080			0.621800			0.310900	+	0.950443i	$0.399370\pi$
$758$	−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	0.189039	−	0.981970i	$-0.439463\pi$
$773$	−19.0854	−	13.8663i	−0.686454	−	0.498738i	−0.875492	+	0.483232i	$0.839463\pi$
$774$	−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	−0.293020	−	0.956106i	$-0.594660\pi$
$787$	14.7489	−	10.7157i	0.525743	−	0.381974i	0.818763	+	0.574132i	$0.194660\pi$
$788$	−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	0.874129	−	0.485694i	$-0.161433\pi$
$797$	−3.34652	−	10.2995i	−0.118540	−	0.364828i	−0.992669	+	0.120866i	$0.961433\pi$
$798$	−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	$0.0372348\pi$
$823$	40.4807	+	29.4110i	1.41107	+	1.02520i	0.417903	+	0.908492i	$0.362765\pi$
$824$	2.72666			0.0949879
$825$		0			0
$826$	−10.5883			−0.368413
$827$	25.5886	+	18.5912i	0.889804	+	0.646481i	0.935827	−	0.352460i	$-0.114655\pi$
$827$	25.5886	+	18.5912i	0.889804	+	0.646481i	−0.0460228	+	0.998940i	$0.514655\pi$
$828$	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	0.889610	−	0.456720i	$-0.150976\pi$
$853$	−2.87836	−	8.85867i	−0.0985530	−	0.303315i	−0.988163	+	0.153405i	$0.950976\pi$
$854$	−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	$-0.697434\pi$
$857$	−34.0314			−1.16249			−0.581245	+	0.813729i	$0.697434\pi$
$858$	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	−0.792305	−	0.610126i	$-0.791119\pi$
$863$	−13.4216	+	9.75136i	−0.456877	+	0.331940i	0.335428	+	0.942066i	$0.391119\pi$
$864$	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	0.938530	−	0.345198i	$-0.112188\pi$
$877$	26.6601	+	19.3697i	0.900249	+	0.654069i	−0.0382809	+	0.999267i	$0.512188\pi$
$878$	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	−0.864497	−	0.502638i	$-0.832363\pi$
$883$	3.87306	−	11.9201i	0.130339	−	0.401142i	0.994836	+	0.101496i	$0.0323629\pi$
$884$	−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	−0.890097	−	0.455772i	$-0.849363\pi$
$887$	−21.7915	+	15.8325i	−0.731687	+	0.531602i	0.158410	+	0.987373i	$0.449363\pi$
$888$	−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	$-0.657795\pi$
$907$	−28.6510			−0.951342			−0.475671	+	0.879623i	$0.657795\pi$
$908$	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	−0.347378	−	0.937725i	$-0.612928\pi$
$937$	13.3800	−	9.72114i	0.437106	−	0.317576i	0.784484	+	0.620149i	$0.212928\pi$
$938$	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	$-0.893983\pi$
$947$	−11.4679	−	35.2946i	−0.372657	−	1.14692i	0.572388	−	0.819983i	$-0.306017\pi$
$948$	−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	$0.00990167\pi$
$953$	6.45728	+	19.8735i	0.209172	+	0.643765i	−0.790344	+	0.612663i	$0.790098\pi$
$954$	−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	−0.901446	−	0.432892i	$-0.857493\pi$
$967$	2.55884	−	7.87529i	0.0822866	−	0.253252i	0.983732	+	0.179640i	$0.0574932\pi$
$968$	−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	0.209602	−	0.977787i	$-0.432783\pi$
$977$	−20.4908	−	14.8874i	−0.655558	−	0.476290i	−0.865160	+	0.501496i	$0.832783\pi$
$978$	−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	−0.973142	−	0.230204i	$-0.926061\pi$
$983$	−1.58467	+	4.87712i	−0.0505432	+	0.155556i	0.922599	+	0.385760i	$0.126061\pi$
$984$	−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	$0.148883\pi$
$997$	13.7504	+	42.3194i	0.435480	+	1.34027i	−0.457114	+	0.889408i	$0.651117\pi$
$998$	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.m.376.2		16
5.2	odd	4		625.2.e.j.249.7		32
5.3	odd	4		625.2.e.j.249.2		32
5.4	even	2		625.2.d.q.376.3		16
25.2	odd	20		625.2.e.j.374.2		32
25.3	odd	20		625.2.e.k.499.7		32
25.4	even	10		625.2.d.p.126.2		16
25.6	even	5		625.2.a.g.1.6	yes	8
25.8	odd	20		625.2.b.d.624.3		16
25.9	even	10		625.2.d.p.501.2		16
25.11	even	5	inner	625.2.d.m.251.2		16
25.12	odd	20		625.2.e.k.124.7		32
25.13	odd	20		625.2.e.k.124.2		32
25.14	even	10		625.2.d.q.251.3		16
25.16	even	5		625.2.d.n.501.3		16
25.17	odd	20		625.2.b.d.624.14		16
25.19	even	10		625.2.a.e.1.3	✓	8
25.21	even	5		625.2.d.n.126.3		16
25.22	odd	20		625.2.e.k.499.2		32
25.23	odd	20		625.2.e.j.374.7		32
75.44	odd	10		5625.2.a.be.1.6		8
75.56	odd	10		5625.2.a.s.1.3		8
100.19	odd	10		10000.2.a.bn.1.1		8
100.31	odd	10		10000.2.a.be.1.8		8

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