LMFDB - Embedded newform 250.2.d.d.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(51,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("250.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			51.2
Root			$1.66637 + 0.917186i$ of defining polynomial
Character	$\chi$	$=$	250.51
Dual form			250.2.d.d.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.720859 - 2.21858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.720859 - 2.21858i) q^{6} -3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.97539 - 1.43521i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.720859 - 2.21858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.720859 - 2.21858i) q^{6} -3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.97539 - 1.43521i) q^{9} +(3.05361 - 2.21858i) q^{11} +(-1.88723 - 1.37116i) q^{12} +(2.56969 + 1.86699i) q^{13} +(-3.05361 + 2.21858i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.430307 + 1.32435i) q^{17} -2.44172 q^{18} +(1.20945 + 3.72230i) q^{19} +(-2.72086 + 8.37394i) q^{21} +(1.16637 - 3.58973i) q^{22} +(0.720859 - 0.523735i) q^{23} -2.33275 q^{24} +3.17632 q^{26} +(1.05361 - 0.765491i) q^{27} +(-1.16637 + 3.58973i) q^{28} +(0.0152089 - 0.0468081i) q^{29} +(-1.72466 - 5.30795i) q^{31} -1.00000 q^{32} +(-2.72086 - 8.37394i) q^{33} +(1.12656 + 0.818492i) q^{34} +(-1.97539 + 1.43521i) q^{36} +(5.70152 + 4.14240i) q^{37} +(3.16637 + 2.30051i) q^{38} +(5.99445 - 4.35522i) q^{39} +(1.20477 + 0.875319i) q^{41} +(2.72086 + 8.37394i) q^{42} -2.69767 q^{43} +(-1.16637 - 3.58973i) q^{44} +(0.275344 - 0.847421i) q^{46} +(-1.16637 + 3.58973i) q^{47} +(-1.88723 + 1.37116i) q^{48} +7.24660 q^{49} +3.24836 q^{51} +(2.56969 - 1.86699i) q^{52} +(-3.58963 + 11.0477i) q^{53} +(0.402443 - 1.23859i) q^{54} +(1.16637 + 3.58973i) q^{56} +9.13004 q^{57} +(-0.0152089 - 0.0468081i) q^{58} +(0.558282 + 0.405615i) q^{59} +(-8.38168 + 6.08965i) q^{61} +(-4.51521 - 3.28049i) q^{62} +(7.45605 + 5.41714i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.12330 - 5.17538i) q^{66} +(-4.73519 - 14.5734i) q^{67} +1.39250 q^{68} +(-0.642308 - 1.97682i) q^{69} +(-2.06969 + 6.36986i) q^{71} +(-0.754532 + 2.32221i) q^{72} +(4.18158 - 3.03810i) q^{73} +7.04746 q^{74} +3.91385 q^{76} +(-11.5257 + 8.37394i) q^{77} +(2.28968 - 7.04690i) q^{78} +(-0.558282 + 1.71821i) q^{79} +(-3.20239 - 9.85596i) q^{81} +1.48918 q^{82} +(3.08023 + 9.47997i) q^{83} +(7.12330 + 5.17538i) q^{84} +(-2.18246 + 1.58565i) q^{86} +(-0.0928839 - 0.0674841i) q^{87} +(-3.05361 - 2.21858i) q^{88} +(-11.7390 + 8.52891i) q^{89} +(-9.69922 - 7.04690i) q^{91} +(-0.275344 - 0.847421i) q^{92} -13.0193 q^{93} +(1.16637 + 3.58973i) q^{94} +(-0.720859 + 2.21858i) q^{96} +(0.0278640 - 0.0857567i) q^{97} +(5.86263 - 4.25945i) q^{98} -9.21619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 + 2 * q^8 - q^9	$ 8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{11} - 2 q^{12} + 13 q^{13} - q^{14} - 2 q^{16} + 11 q^{17} - 14 q^{18} + 20 q^{19} - 19 q^{21} - q^{22} + 3 q^{23} + 2 q^{24} + 22 q^{26} - 15 q^{27} + q^{28} - 15 q^{29} - 9 q^{31} - 8 q^{32} - 19 q^{33} - q^{34} - q^{36} + 6 q^{37} + 15 q^{38} - 12 q^{39} - 9 q^{41} + 19 q^{42} - 12 q^{43} + q^{44} + 7 q^{46} + q^{47} - 2 q^{48} - 4 q^{49} + 26 q^{51} + 13 q^{52} - 7 q^{53} - 25 q^{54} - q^{56} + 15 q^{58} + 10 q^{59} + 6 q^{61} - 21 q^{62} + 8 q^{63} - 2 q^{64} - 26 q^{66} + 11 q^{67} - 24 q^{68} + 43 q^{69} - 9 q^{71} + 6 q^{72} + 8 q^{73} + 24 q^{74} - 10 q^{76} - 33 q^{77} - 23 q^{78} - 10 q^{79} - 17 q^{81} - 26 q^{82} - 27 q^{83} + 26 q^{84} - 23 q^{86} - q^{88} - 15 q^{89} + q^{91} - 7 q^{92} + 46 q^{93} - q^{94} - 3 q^{96} + 36 q^{97} + 19 q^{98} - 42 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 + 2 * q^8 - q^9 + q^11 - 2 * q^12 + 13 * q^13 - q^14 - 2 * q^16 + 11 * q^17 - 14 * q^18 + 20 * q^19 - 19 * q^21 - q^22 + 3 * q^23 + 2 * q^24 + 22 * q^26 - 15 * q^27 + q^28 - 15 * q^29 - 9 * q^31 - 8 * q^32 - 19 * q^33 - q^34 - q^36 + 6 * q^37 + 15 * q^38 - 12 * q^39 - 9 * q^41 + 19 * q^42 - 12 * q^43 + q^44 + 7 * q^46 + q^47 - 2 * q^48 - 4 * q^49 + 26 * q^51 + 13 * q^52 - 7 * q^53 - 25 * q^54 - q^56 + 15 * q^58 + 10 * q^59 + 6 * q^61 - 21 * q^62 + 8 * q^63 - 2 * q^64 - 26 * q^66 + 11 * q^67 - 24 * q^68 + 43 * q^69 - 9 * q^71 + 6 * q^72 + 8 * q^73 + 24 * q^74 - 10 * q^76 - 33 * q^77 - 23 * q^78 - 10 * q^79 - 17 * q^81 - 26 * q^82 - 27 * q^83 + 26 * q^84 - 23 * q^86 - q^88 - 15 * q^89 + q^91 - 7 * q^92 + 46 * q^93 - q^94 - 3 * q^96 + 36 * q^97 + 19 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.720859	−	2.21858i	0.416188	−	1.28090i	−0.494996	−	0.868895i	$-0.664830\pi$
$3$	0.720859	−	2.21858i	0.416188	−	1.28090i	0.911184	−	0.412000i	$-0.135170\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.720859	−	2.21858i	−0.294289	−	0.905730i
$7$	−3.77447			−1.42661			−0.713307	−	0.700851i	$-0.752804\pi$
$7$	−3.77447			−1.42661			−0.713307	+	0.700851i	$0.752804\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−1.97539	−	1.43521i	−0.658464	−	0.478402i
$10$		0			0
$11$	3.05361	−	2.21858i	0.920698	−	0.668926i	−0.0230000	−	0.999735i	$-0.507322\pi$
$11$	3.05361	−	2.21858i	0.920698	−	0.668926i	0.943698	+	0.330810i	$0.107322\pi$
$12$	−1.88723	−	1.37116i	−0.544797	−	0.395818i
$13$	2.56969	+	1.86699i	0.712705	+	0.517810i	0.884045	−	0.467402i	$-0.154810\pi$
$13$	2.56969	+	1.86699i	0.712705	+	0.517810i	−0.171340	+	0.985212i	$0.554810\pi$
$14$	−3.05361	+	2.21858i	−0.816111	+	0.592939i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.430307	+	1.32435i	0.104365	+	0.321201i	0.989581	−	0.143979i	$-0.0459896\pi$
$17$	0.430307	+	1.32435i	0.104365	+	0.321201i	−0.885216	+	0.465180i	$0.845990\pi$
$18$	−2.44172			−0.575519
$19$	1.20945	+	3.72230i	0.277466	+	0.853953i	0.988556	+	0.150852i	$0.0482018\pi$
$19$	1.20945	+	3.72230i	0.277466	+	0.853953i	−0.711090	+	0.703101i	$0.751798\pi$
$20$		0			0
$21$	−2.72086	+	8.37394i	−0.593740	+	1.82734i
$22$	1.16637	−	3.58973i	0.248672	−	0.765333i
$23$	0.720859	−	0.523735i	0.150310	−	0.109206i	−0.510089	−	0.860122i	$-0.670387\pi$
$23$	0.720859	−	0.523735i	0.150310	−	0.109206i	0.660398	+	0.750916i	$0.270387\pi$
$24$	−2.33275			−0.476170
$25$		0			0
$26$	3.17632			0.622927
$27$	1.05361	−	0.765491i	0.202767	−	0.147319i
$28$	−1.16637	+	3.58973i	−0.220424	+	0.678396i
$29$	0.0152089	−	0.0468081i	0.00282422	−	0.00869205i	−0.949634	−	0.313360i	$-0.898545\pi$
$29$	0.0152089	−	0.0468081i	0.00282422	−	0.00869205i	0.952459	+	0.304668i	$0.0985454\pi$
$30$		0			0
$31$	−1.72466	−	5.30795i	−0.309757	−	0.953335i	−0.977859	−	0.209265i	$-0.932893\pi$
$31$	−1.72466	−	5.30795i	−0.309757	−	0.953335i	0.668102	−	0.744070i	$-0.267107\pi$
$32$	−1.00000			−0.176777
$33$	−2.72086	−	8.37394i	−0.473641	−	1.45772i
$34$	1.12656	+	0.818492i	0.193203	+	0.140370i
$35$		0			0
$36$	−1.97539	+	1.43521i	−0.329232	+	0.239201i
$37$	5.70152	+	4.14240i	0.937324	+	0.681006i	0.947775	−	0.318940i	$-0.103327\pi$
$37$	5.70152	+	4.14240i	0.937324	+	0.681006i	−0.0104512	+	0.999945i	$0.503327\pi$
$38$	3.16637	+	2.30051i	0.513654	+	0.373191i
$39$	5.99445	−	4.35522i	0.959880	−	0.697394i
$40$		0			0
$41$	1.20477	+	0.875319i	0.188154	+	0.136702i	0.677875	−	0.735178i	$-0.262901\pi$
$41$	1.20477	+	0.875319i	0.188154	+	0.136702i	−0.489721	+	0.871879i	$0.662901\pi$
$42$	2.72086	+	8.37394i	0.419838	+	1.29213i
$43$	−2.69767			−0.411391			−0.205695	−	0.978616i	$-0.565946\pi$
$43$	−2.69767			−0.411391			−0.205695	+	0.978616i	$0.565946\pi$
$44$	−1.16637	−	3.58973i	−0.175838	−	0.541172i
$45$		0			0
$46$	0.275344	−	0.847421i	0.0405972	−	0.124945i
$47$	−1.16637	+	3.58973i	−0.170133	+	0.523616i	−0.999378	−	0.0352696i	$-0.988771\pi$
$47$	−1.16637	+	3.58973i	−0.170133	+	0.523616i	0.829245	+	0.558886i	$0.188771\pi$
$48$	−1.88723	+	1.37116i	−0.272399	+	0.197909i
$49$	7.24660			1.03523
$50$		0			0
$51$	3.24836			0.454861
$52$	2.56969	−	1.86699i	0.356352	−	0.258905i
$53$	−3.58963	+	11.0477i	−0.493073	+	1.51752i	0.326864	+	0.945071i	$0.394008\pi$
$53$	−3.58963	+	11.0477i	−0.493073	+	1.51752i	−0.819938	+	0.572453i	$0.805992\pi$
$54$	0.402443	−	1.23859i	0.0547655	−	0.168551i
$55$		0			0
$56$	1.16637	+	3.58973i	0.155863	+	0.479698i
$57$	9.13004			1.20930
$58$	−0.0152089	−	0.0468081i	−0.00199702	−	0.00614620i
$59$	0.558282	+	0.405615i	0.0726821	+	0.0528066i	0.623533	−	0.781797i	$-0.285697\pi$
$59$	0.558282	+	0.405615i	0.0726821	+	0.0528066i	−0.550851	+	0.834604i	$0.685697\pi$
$60$		0			0
$61$	−8.38168	+	6.08965i	−1.07316	+	0.779700i	−0.976478	−	0.215615i	$-0.930824\pi$
$61$	−8.38168	+	6.08965i	−1.07316	+	0.779700i	−0.0966862	+	0.995315i	$0.530824\pi$
$62$	−4.51521	−	3.28049i	−0.573432	−	0.416623i
$63$	7.45605	+	5.41714i	0.939374	+	0.682495i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$		0			0
$66$	−7.12330	−	5.17538i	−0.876818	−	0.637045i
$67$	−4.73519	−	14.5734i	−0.578496	−	1.78043i	−0.623955	−	0.781461i	$-0.714475\pi$
$67$	−4.73519	−	14.5734i	−0.578496	−	1.78043i	0.0454589	−	0.998966i	$-0.485525\pi$
$68$	1.39250			0.168866
$69$	−0.642308	−	1.97682i	−0.0773248	−	0.237981i
$70$		0			0
$71$	−2.06969	+	6.36986i	−0.245627	+	0.755963i	0.749905	+	0.661545i	$0.230099\pi$
$71$	−2.06969	+	6.36986i	−0.245627	+	0.755963i	−0.995533	+	0.0944182i	$0.969901\pi$
$72$	−0.754532	+	2.32221i	−0.0889225	+	0.273675i
$73$	4.18158	−	3.03810i	0.489417	−	0.355582i	−0.315543	−	0.948911i	$-0.602187\pi$
$73$	4.18158	−	3.03810i	0.489417	−	0.355582i	0.804960	+	0.593329i	$0.202187\pi$
$74$	7.04746			0.819251
$75$		0			0
$76$	3.91385			0.448950
$77$	−11.5257	+	8.37394i	−1.31348	+	0.954299i
$78$	2.28968	−	7.04690i	0.259255	−	0.797904i
$79$	−0.558282	+	1.71821i	−0.0628116	+	0.193314i	−0.977538	−	0.210760i	$-0.932406\pi$
$79$	−0.558282	+	1.71821i	−0.0628116	+	0.193314i	0.914726	+	0.404074i	$0.132406\pi$
$80$		0			0
$81$	−3.20239	−	9.85596i	−0.355822	−	1.09511i
$82$	1.48918			0.164453
$83$	3.08023	+	9.47997i	0.338099	+	1.04056i	0.965175	+	0.261604i	$0.0842514\pi$
$83$	3.08023	+	9.47997i	0.338099	+	1.04056i	−0.627076	+	0.778958i	$0.715749\pi$
$84$	7.12330	+	5.17538i	0.777216	+	0.564680i
$85$		0			0
$86$	−2.18246	+	1.58565i	−0.235341	+	0.170985i
$87$	−0.0928839	−	0.0674841i	−0.00995820	−	0.00723505i
$88$	−3.05361	−	2.21858i	−0.325516	−	0.236501i
$89$	−11.7390	+	8.52891i	−1.24434	+	0.904063i	−0.997879	−	0.0650909i	$-0.979266\pi$
$89$	−11.7390	+	8.52891i	−1.24434	+	0.904063i	−0.246457	+	0.969154i	$0.579266\pi$
$90$		0			0
$91$	−9.69922	−	7.04690i	−1.01675	−	0.738716i
$92$	−0.275344	−	0.847421i	−0.0287066	−	0.0883497i
$93$	−13.0193			−1.35004
$94$	1.16637	+	3.58973i	0.120302	+	0.370253i
$95$		0			0
$96$	−0.720859	+	2.21858i	−0.0735724	+	0.226432i
$97$	0.0278640	−	0.0857567i	0.00282917	−	0.00870727i	−0.949632	−	0.313367i	$-0.898543\pi$
$97$	0.0278640	−	0.0857567i	0.00282917	−	0.00870727i	0.952461	+	0.304660i	$0.0985429\pi$
$98$	5.86263	−	4.25945i	0.592215	−	0.430269i
$99$	−9.21619			−0.926261
$100$		0			0
$101$	16.3785			1.62972			0.814859	−	0.579659i	$-0.196814\pi$
$101$	16.3785			1.62972			0.814859	+	0.579659i	$0.196814\pi$
$102$	2.62798	−	1.90934i	0.260208	−	0.189052i
$103$	0.375822	−	1.15666i	0.0370308	−	0.113969i	−0.930832	−	0.365446i	$-0.880916\pi$
$103$	0.375822	−	1.15666i	0.0370308	−	0.113969i	0.967863	+	0.251477i	$0.0809163\pi$
$104$	0.981536	−	3.02086i	0.0962475	−	0.296219i
$105$		0			0
$106$	3.58963	+	11.0477i	0.348656	+	1.07305i
$107$	10.8125			1.04528			0.522641	−	0.852553i	$-0.324947\pi$
$107$	10.8125			1.04528			0.522641	+	0.852553i	$0.324947\pi$
$108$	−0.402443	−	1.23859i	−0.0387250	−	0.119183i
$109$	−9.23519	−	6.70976i	−0.884571	−	0.642678i	0.0498859	−	0.998755i	$-0.484114\pi$
$109$	−9.23519	−	6.70976i	−0.884571	−	0.642678i	−0.934457	+	0.356077i	$0.884114\pi$
$110$		0			0
$111$	13.3002	−	9.66317i	1.26240	−	0.917187i
$112$	3.05361	+	2.21858i	0.288539	+	0.209636i
$113$	−8.43232	−	6.12644i	−0.793246	−	0.576327i	0.115679	−	0.993287i	$-0.463096\pi$
$113$	−8.43232	−	6.12644i	−0.793246	−	0.576327i	−0.908925	+	0.416960i	$0.863096\pi$
$114$	7.38636	−	5.36650i	0.691796	−	0.502619i
$115$		0			0
$116$	−0.0398173	−	0.0289290i	−0.00369695	−	0.00268599i
$117$	−2.39663	−	7.37608i	−0.221569	−	0.681919i
$118$	0.690074			0.0635265
$119$	−1.62418	−	4.99871i	−0.148888	−	0.458231i
$120$		0			0
$121$	1.00326	−	3.08770i	0.0912051	−	0.280700i
$122$	−3.20152	+	9.85326i	−0.289852	+	0.892072i
$123$	2.81044	−	2.04190i	0.253408	−	0.184112i
$124$	−5.58111			−0.501198
$125$		0			0
$126$	9.21619			0.821043
$127$	−2.87115	+	2.08601i	−0.254773	+	0.185104i	−0.707840	−	0.706373i	$-0.750330\pi$
$127$	−2.87115	+	2.08601i	−0.254773	+	0.185104i	0.453066	+	0.891477i	$0.350330\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−1.94464	+	5.98498i	−0.171216	+	0.526948i
$130$		0			0
$131$	1.25252	+	3.85486i	0.109433	+	0.336801i	0.990745	−	0.135734i	$-0.0433392\pi$
$131$	1.25252	+	3.85486i	0.109433	+	0.336801i	−0.881312	+	0.472535i	$0.843339\pi$
$132$	−8.80489			−0.766367
$133$	−4.56502	−	14.0497i	−0.395837	−	1.21826i
$134$	−12.3969	−	9.00687i	−1.07093	−	0.778075i
$135$		0			0
$136$	1.12656	−	0.818492i	0.0966015	−	0.0701851i
$137$	−2.88636	−	2.09706i	−0.246598	−	0.179164i	0.457620	−	0.889148i	$-0.348702\pi$
$137$	−2.88636	−	2.09706i	−0.246598	−	0.179164i	−0.704218	+	0.709984i	$0.748702\pi$
$138$	−1.68158	−	1.22174i	−0.143146	−	0.104002i
$139$	8.04650	−	5.84613i	0.682495	−	0.495862i	−0.191689	−	0.981456i	$-0.561397\pi$
$139$	8.04650	−	5.84613i	0.682495	−	0.495862i	0.874185	+	0.485594i	$0.161397\pi$
$140$		0			0
$141$	7.12330	+	5.17538i	0.599890	+	0.435846i
$142$	2.06969	+	6.36986i	0.173685	+	0.534547i
$143$	11.9889			1.00256
$144$	0.754532	+	2.32221i	0.0628777	+	0.193518i
$145$		0			0
$146$	1.59722	−	4.91575i	0.132187	−	0.406830i
$147$	5.22378	−	16.0771i	0.430850	−	1.32602i
$148$	5.70152	−	4.14240i	0.468662	−	0.340503i
$149$	−19.5103			−1.59834			−0.799171	−	0.601104i	$-0.794728\pi$
$149$	−19.5103			−1.59834			−0.799171	+	0.601104i	$0.794728\pi$
$150$		0			0
$151$	−18.4324			−1.50001			−0.750003	−	0.661435i	$-0.769948\pi$
$151$	−18.4324			−1.50001			−0.750003	+	0.661435i	$0.769948\pi$
$152$	3.16637	−	2.30051i	0.256827	−	0.186596i
$153$	1.05069	−	3.23368i	0.0849430	−	0.261428i
$154$	−4.40244	+	13.5493i	−0.354759	+	1.09184i
$155$		0			0
$156$	−2.28968	−	7.04690i	−0.183321	−	0.564203i
$157$	−10.1564			−0.810572			−0.405286	−	0.914190i	$-0.632828\pi$
$157$	−10.1564			−0.810572			−0.405286	+	0.914190i	$0.632828\pi$
$158$	0.558282	+	1.71821i	0.0444145	+	0.136694i
$159$	21.9226	+	15.9277i	1.73858	+	1.26315i
$160$		0			0
$161$	−2.72086	+	1.97682i	−0.214434	+	0.155795i
$162$	−8.38398	−	6.09132i	−0.658708	−	0.478579i
$163$	−15.0481	−	10.9331i	−1.17865	−	0.856343i	−0.186636	−	0.982429i	$-0.559758\pi$
$163$	−15.0481	−	10.9331i	−1.17865	−	0.856343i	−0.992019	+	0.126086i	$0.959758\pi$
$164$	1.20477	−	0.875319i	0.0940770	−	0.0683510i
$165$		0			0
$166$	8.06414	+	5.85894i	0.625899	+	0.454742i
$167$	−0.671048	−	2.06527i	−0.0519273	−	0.159816i	0.921730	−	0.387832i	$-0.126776\pi$
$167$	−0.671048	−	2.06527i	−0.0519273	−	0.159816i	−0.973657	+	0.228016i	$0.926776\pi$
$168$	8.80489			0.679312
$169$	−0.899554	−	2.76854i	−0.0691965	−	0.212965i
$170$		0			0
$171$	2.95313	−	9.08880i	0.225831	−	0.695038i
$172$	−0.833625	+	2.56564i	−0.0635633	+	0.195628i
$173$	−5.17306	+	3.75845i	−0.393300	+	0.285750i	−0.766807	−	0.641878i	$-0.778155\pi$
$173$	−5.17306	+	3.75845i	−0.393300	+	0.285750i	0.373506	+	0.927628i	$0.378155\pi$
$174$	−0.114811			−0.00870378
$175$		0			0
$176$	−3.77447			−0.284511
$177$	1.30233	−	0.946199i	0.0978892	−	0.0711207i
$178$	−4.48391	+	13.8001i	−0.336084	+	1.03436i
$179$	2.47630	−	7.62127i	0.185087	−	0.569640i	−0.814862	−	0.579654i	$-0.803188\pi$
$179$	2.47630	−	7.62127i	0.185087	−	0.569640i	0.999950	+	0.0100140i	$0.00318759\pi$
$180$		0			0
$181$	−3.35682	−	10.3312i	−0.249510	−	0.767913i	−0.994862	−	0.101242i	$-0.967718\pi$
$181$	−3.35682	−	10.3312i	−0.249510	−	0.767913i	0.745352	−	0.666671i	$-0.232282\pi$
$182$	−11.9889			−0.888676
$183$	7.46834	+	22.9852i	0.552075	+	1.69911i
$184$	−0.720859	−	0.523735i	−0.0531424	−	0.0386102i
$185$		0			0
$186$	−10.5328	+	7.65256i	−0.772306	+	0.561113i
$187$	4.25215	+	3.08937i	0.310948	+	0.225917i
$188$	3.05361	+	2.21858i	0.222707	+	0.161806i
$189$	−3.97681	+	2.88932i	−0.289270	+	0.210167i
$190$		0			0
$191$	6.62243	+	4.81147i	0.479182	+	0.348146i	0.801009	−	0.598652i	$-0.204297\pi$
$191$	6.62243	+	4.81147i	0.479182	+	0.348146i	−0.321827	+	0.946798i	$0.604297\pi$
$192$	0.720859	+	2.21858i	0.0520235	+	0.160112i
$193$	17.5576			1.26382			0.631912	−	0.775040i	$-0.282270\pi$
$193$	17.5576			1.26382			0.631912	+	0.775040i	$0.282270\pi$
$194$	−0.0278640	−	0.0857567i	−0.00200052	−	0.00615697i
$195$		0			0
$196$	2.23932	−	6.89193i	0.159952	−	0.492281i
$197$	−1.47012	+	4.52458i	−0.104742	+	0.322363i	−0.989670	−	0.143365i	$-0.954208\pi$
$197$	−1.47012	+	4.52458i	−0.104742	+	0.322363i	0.884928	+	0.465728i	$0.154208\pi$
$198$	−7.45605	+	5.41714i	−0.529878	+	0.384979i
$199$	14.5320			1.03015			0.515073	−	0.857146i	$-0.327765\pi$
$199$	14.5320			1.03015			0.515073	+	0.857146i	$0.327765\pi$
$200$		0			0
$201$	−35.7457			−2.52130
$202$	13.2505	−	9.62702i	0.932299	−	0.677355i
$203$	−0.0574054	+	0.176676i	−0.00402907	+	0.0124002i
$204$	1.00380	−	3.08937i	0.0702799	−	0.216299i
$205$		0			0
$206$	−0.375822	−	1.15666i	−0.0261848	−	0.0805884i
$207$	−2.17565			−0.151218
$208$	−0.981536	−	3.02086i	−0.0680572	−	0.209459i
$209$	11.9514	+	8.68318i	0.826694	+	0.600628i
$210$		0			0
$211$	11.4362	−	8.30886i	0.787298	−	0.572006i	−0.119862	−	0.992791i	$-0.538245\pi$
$211$	11.4362	−	8.30886i	0.787298	−	0.572006i	0.907160	+	0.420785i	$0.138245\pi$
$212$	9.39777	+	6.82788i	0.645441	+	0.468941i
$213$	12.6401	+	9.18355i	0.866083	+	0.629246i
$214$	8.74748	−	6.35542i	0.597965	−	0.434447i
$215$		0			0
$216$	−1.05361	−	0.765491i	−0.0716890	−	0.0520851i
$217$	6.50966	+	20.0347i	0.441904	+	1.36004i
$218$	−11.4153			−0.773143
$219$	−3.72592	−	11.4672i	−0.251774	−	0.774882i
$220$		0			0
$221$	−1.36679	+	4.20655i	−0.0919402	+	0.282963i
$222$	5.08023	−	15.6353i	0.340963	−	1.04938i
$223$	3.73139	−	2.71102i	0.249873	−	0.181543i	−0.455798	−	0.890083i	$-0.650646\pi$
$223$	3.73139	−	2.71102i	0.249873	−	0.181543i	0.705670	+	0.708540i	$0.250646\pi$
$224$	3.77447			0.252192
$225$		0			0
$226$	−10.4229			−0.693322
$227$	−5.08578	+	3.69503i	−0.337555	+	0.245248i	−0.743630	−	0.668592i	$-0.766897\pi$
$227$	−5.08578	+	3.69503i	−0.337555	+	0.245248i	0.406075	+	0.913840i	$0.366897\pi$
$228$	2.82134	−	8.68318i	0.186848	−	0.575058i
$229$	5.48103	−	16.8689i	0.362196	−	1.11473i	−0.589522	−	0.807753i	$-0.700684\pi$
$229$	5.48103	−	16.8689i	0.362196	−	1.11473i	0.951718	−	0.306973i	$-0.0993163\pi$
$230$		0			0
$231$	10.2698	+	31.6072i	0.675703	+	2.07960i
$232$	−0.0492169			−0.00323125
$233$	−0.792338	−	2.43856i	−0.0519078	−	0.159756i	0.921742	−	0.387803i	$-0.126766\pi$
$233$	−0.792338	−	2.43856i	−0.0519078	−	0.159756i	−0.973650	+	0.228047i	$0.926766\pi$
$234$	−6.27447	−	4.55867i	−0.410175	−	0.298009i
$235$		0			0
$236$	0.558282	−	0.405615i	0.0363410	−	0.0264033i
$237$	3.40955	+	2.47718i	0.221474	+	0.160910i
$238$	−4.25215	−	3.08937i	−0.275626	−	0.200254i
$239$	−7.63851	+	5.54970i	−0.494094	+	0.358980i	−0.806757	−	0.590884i	$-0.798779\pi$
$239$	−7.63851	+	5.54970i	−0.494094	+	0.358980i	0.312662	+	0.949864i	$0.398779\pi$
$240$		0			0
$241$	23.8131	+	17.3012i	1.53394	+	1.11447i	0.953998	+	0.299812i	$0.0969240\pi$
$241$	23.8131	+	17.3012i	1.53394	+	1.11447i	0.579940	+	0.814659i	$0.303076\pi$
$242$	−1.00326	−	3.08770i	−0.0644917	−	0.198485i
$243$	−20.2677			−1.30017
$244$	3.20152	+	9.85326i	0.204956	+	0.630790i
$245$		0			0
$246$	1.07349	−	3.30386i	0.0684433	−	0.210647i
$247$	−3.84159	+	11.8232i	−0.244434	+	0.752292i
$248$	−4.51521	+	3.28049i	−0.286716	+	0.208311i
$249$	23.2524			1.47356
$250$		0			0
$251$	−6.00759			−0.379196			−0.189598	−	0.981862i	$-0.560718\pi$
$251$	−6.00759			−0.379196			−0.189598	+	0.981862i	$0.560718\pi$
$252$	7.45605	−	5.41714i	0.469687	−	0.341248i
$253$	1.03928	−	3.19856i	0.0653387	−	0.201092i
$254$	−1.09668	+	3.37524i	−0.0688119	+	0.211781i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	13.6286			0.850127			0.425063	−	0.905164i	$-0.360252\pi$
$257$	13.6286			0.850127			0.425063	+	0.905164i	$0.360252\pi$
$258$	1.94464	+	5.98498i	0.121068	+	0.372609i
$259$	−21.5202	−	15.6353i	−1.33720	−	0.971533i
$260$		0			0
$261$	−0.0972227	+	0.0706365i	−0.00601794	+	0.00437229i
$262$	3.27914	+	2.38244i	0.202586	+	0.147187i
$263$	−7.41298	−	5.38584i	−0.457104	−	0.332105i	0.335290	−	0.942115i	$-0.391166\pi$
$263$	−7.41298	−	5.38584i	−0.457104	−	0.332105i	−0.792394	+	0.610010i	$0.791166\pi$
$264$	−7.12330	+	5.17538i	−0.438409	+	0.318523i
$265$		0			0
$266$	−11.9514	−	8.68318i	−0.732786	−	0.532400i
$267$	10.4598	+	32.1921i	0.640132	+	1.97012i
$268$	−15.3234			−0.936026
$269$	8.68419	+	26.7272i	0.529484	+	1.62959i	0.755274	+	0.655409i	$0.227504\pi$
$269$	8.68419	+	26.7272i	0.529484	+	1.62959i	−0.225790	+	0.974176i	$0.572496\pi$
$270$		0			0
$271$	−2.81162	+	8.65329i	−0.170794	+	0.525650i	−0.999416	−	0.0341581i	$-0.989125\pi$
$271$	−2.81162	+	8.65329i	−0.170794	+	0.525650i	0.828623	+	0.559808i	$0.189125\pi$
$272$	0.430307	−	1.32435i	0.0260912	−	0.0803004i
$273$	−22.6259	+	16.4386i	−1.36938	+	0.994912i
$274$	−3.56773			−0.215535
$275$		0			0
$276$	−2.07855			−0.125114
$277$	15.2006	−	11.0439i	0.913318	−	0.663564i	−0.0285338	−	0.999593i	$-0.509084\pi$
$277$	15.2006	−	11.0439i	0.913318	−	0.663564i	0.941852	+	0.336028i	$0.109084\pi$
$278$	3.07349	−	9.45923i	0.184336	−	0.567327i
$279$	−4.21112	+	12.9605i	−0.252113	+	0.775925i
$280$		0			0
$281$	2.43554	+	7.49583i	0.145292	+	0.447164i	0.997048	−	0.0767748i	$-0.0244622\pi$
$281$	2.43554	+	7.49583i	0.145292	+	0.447164i	−0.851756	+	0.523938i	$0.824462\pi$
$282$	8.80489			0.524323
$283$	5.65496	+	17.4042i	0.336153	+	1.03457i	0.966151	+	0.257975i	$0.0830554\pi$
$283$	5.65496	+	17.4042i	0.336153	+	1.03457i	−0.629999	+	0.776596i	$0.716945\pi$
$284$	5.41853	+	3.93679i	0.321530	+	0.233606i
$285$		0			0
$286$	9.69922	−	7.04690i	0.573527	−	0.416692i
$287$	−4.54738	−	3.30386i	−0.268423	−	0.195021i
$288$	1.97539	+	1.43521i	0.116401	+	0.0845703i
$289$	12.1846	−	8.85260i	0.716739	−	0.520741i
$290$		0			0
$291$	−0.170172	−	0.123637i	−0.00997564	−	0.00724773i
$292$	−1.59722	−	4.91575i	−0.0934704	−	0.287672i
$293$	29.4990			1.72335			0.861675	−	0.507461i	$-0.169416\pi$
$293$	29.4990			1.72335			0.861675	+	0.507461i	$0.169416\pi$
$294$	−5.22378	−	16.0771i	−0.304657	−	0.937638i
$295$		0			0
$296$	2.17779	−	6.70254i	0.126581	−	0.389577i
$297$	1.51901	−	4.67502i	0.0881417	−	0.271272i
$298$	−15.7841	+	11.4678i	−0.914350	+	0.664314i
$299$	2.83020			0.163674
$300$		0			0
$301$	10.1823			0.586896
$302$	−14.9121	+	10.8343i	−0.858095	+	0.623443i
$303$	11.8066	−	36.3369i	0.678269	−	2.08750i
$304$	1.20945	−	3.72230i	0.0693666	−	0.213488i
$305$		0			0
$306$	−1.05069	−	3.23368i	−0.0600638	−	0.184857i
$307$	−13.9131			−0.794064			−0.397032	−	0.917805i	$-0.629960\pi$
$307$	−13.9131			−0.794064			−0.397032	+	0.917805i	$0.629960\pi$
$308$	4.40244	+	13.5493i	0.250852	+	0.772044i
$309$	−2.29523	−	1.66758i	−0.130571	−	0.0948653i
$310$		0			0
$311$	−21.0050	+	15.2610i	−1.19108	+	0.865373i	−0.993378	−	0.114889i	$-0.963349\pi$
$311$	−21.0050	+	15.2610i	−1.19108	+	0.865373i	−0.197705	+	0.980262i	$0.563349\pi$
$312$	−5.99445	−	4.35522i	−0.339369	−	0.246566i
$313$	7.66454	+	5.56861i	0.433225	+	0.314757i	0.782937	−	0.622101i	$-0.213721\pi$
$313$	7.66454	+	5.56861i	0.433225	+	0.314757i	−0.349712	+	0.936857i	$0.613721\pi$
$314$	−8.21673	+	5.96980i	−0.463697	+	0.336895i
$315$		0			0
$316$	1.46160	+	1.06192i	0.0822215	+	0.0597374i
$317$	−7.57321	−	23.3079i	−0.425354	−	1.30910i	−0.902655	−	0.430365i	$-0.858385\pi$
$317$	−7.57321	−	23.3079i	−0.425354	−	1.30910i	0.477301	−	0.878740i	$-0.341615\pi$
$318$	27.0979			1.51957
$319$	−0.0574054	−	0.176676i	−0.00321408	−	0.00989194i
$320$		0			0
$321$	7.79427	−	23.9883i	0.435034	−	1.33890i
$322$	−1.03928	+	3.19856i	−0.0579166	+	0.178249i
$323$	−4.40918	+	3.20346i	−0.245333	+	0.178245i
$324$	−10.3632			−0.575731
$325$		0			0
$326$	−18.6004			−1.03018
$327$	−21.5434	+	15.6522i	−1.19135	+	0.865568i
$328$	0.460183	−	1.41630i	0.0254093	−	0.0782019i
$329$	4.40244	−	13.5493i	0.242715	−	0.746998i
$330$		0			0
$331$	−3.06247	−	9.42530i	−0.168328	−	0.518061i	0.830938	−	0.556365i	$-0.187804\pi$
$331$	−3.06247	−	9.42530i	−0.168328	−	0.518061i	−0.999266	+	0.0383039i	$0.987804\pi$
$332$	9.96783			0.547056
$333$	−5.31754	−	16.3657i	−0.291399	−	0.896835i
$334$	−1.75683	−	1.27641i	−0.0961293	−	0.0698420i
$335$		0			0
$336$	7.12330	−	5.17538i	0.388608	−	0.282340i
$337$	−8.03812	−	5.84003i	−0.437864	−	0.318127i	0.346922	−	0.937894i	$-0.387227\pi$
$337$	−8.03812	−	5.84003i	−0.437864	−	0.318127i	−0.784786	+	0.619767i	$0.787227\pi$
$338$	−2.35506	−	1.71105i	−0.128099	−	0.0930690i
$339$	−19.6705	+	14.2914i	−1.06835	+	0.776205i
$340$		0			0
$341$	−17.0425	−	12.3821i	−0.922904	−	0.670529i
$342$	−2.95313	−	9.08880i	−0.159687	−	0.491466i
$343$	−0.930796			−0.0502583
$344$	0.833625	+	2.56564i	0.0449461	+	0.138330i
$345$		0			0
$346$	−1.97593	+	6.08130i	−0.106227	+	0.326933i
$347$	6.06757	−	18.6741i	0.325724	−	1.00248i	−0.645388	−	0.763855i	$-0.723304\pi$
$347$	6.06757	−	18.6741i	0.325724	−	1.00248i	0.971113	−	0.238622i	$-0.0766956\pi$
$348$	−0.0928839	+	0.0674841i	−0.00497910	+	0.00361753i
$349$	1.48432			0.0794538			0.0397269	−	0.999211i	$-0.487351\pi$
$349$	1.48432			0.0794538			0.0397269	+	0.999211i	$0.487351\pi$
$350$		0			0
$351$	4.13662			0.220796
$352$	−3.05361	+	2.21858i	−0.162758	+	0.118251i
$353$	−3.17632	+	9.77569i	−0.169058	+	0.520308i	−0.999312	−	0.0370772i	$-0.988195\pi$
$353$	−3.17632	+	9.77569i	−0.169058	+	0.520308i	0.830254	+	0.557385i	$0.188195\pi$
$354$	0.497446	−	1.53098i	0.0264390	−	0.0813708i
$355$		0			0
$356$	4.48391	+	13.8001i	0.237647	+	0.731402i
$357$	−12.2608			−0.648911
$358$	−2.47630	−	7.62127i	−0.130877	−	0.402797i
$359$	8.39154	+	6.09681i	0.442889	+	0.321777i	0.786782	−	0.617231i	$-0.211746\pi$
$359$	8.39154	+	6.09681i	0.442889	+	0.321777i	−0.343893	+	0.939009i	$0.611746\pi$
$360$		0			0
$361$	2.97859	−	2.16408i	0.156768	−	0.113899i
$362$	−8.78826	−	6.38504i	−0.461901	−	0.335590i
$363$	−6.12710	−	4.45160i	−0.321589	−	0.233648i
$364$	−9.69922	+	7.04690i	−0.508377	+	0.369358i
$365$		0			0
$366$	19.5524	+	14.2056i	1.02202	+	0.742540i
$367$	−8.05741	−	24.7981i	−0.420593	−	1.29445i	−0.907151	−	0.420804i	$-0.861748\pi$
$367$	−8.05741	−	24.7981i	−0.420593	−	1.29445i	0.486558	−	0.873648i	$-0.338252\pi$
$368$	−0.891031			−0.0464482
$369$	−1.12364	−	3.45820i	−0.0584942	−	0.180027i
$370$		0			0
$371$	13.5489	−	41.6993i	0.703426	−	2.16492i
$372$	−4.02319	+	12.3821i	−0.208593	+	0.641982i
$373$	7.65001	−	5.55806i	0.396102	−	0.287785i	−0.371849	−	0.928293i	$-0.621276\pi$
$373$	7.65001	−	5.55806i	0.396102	−	0.287785i	0.767952	+	0.640508i	$0.221276\pi$
$374$	5.25595			0.271779
$375$		0			0
$376$	3.77447			0.194653
$377$	0.126472	−	0.0918876i	0.00651366	−	0.00473245i
$378$	−1.51901	+	4.67502i	−0.0781292	+	0.240457i
$379$	−10.9163	+	33.5968i	−0.560731	+	1.72575i	0.119576	+	0.992825i	$0.461846\pi$
$379$	−10.9163	+	33.5968i	−0.560731	+	1.72575i	−0.680307	+	0.732927i	$0.738154\pi$
$380$		0			0
$381$	2.55828	+	7.87358i	0.131065	+	0.403376i
$382$	8.18577			0.418820
$383$	−9.21407	−	28.3580i	−0.470817	−	1.44902i	−0.851517	−	0.524327i	$-0.824317\pi$
$383$	−9.21407	−	28.3580i	−0.470817	−	1.44902i	0.380700	−	0.924698i	$-0.375683\pi$
$384$	1.88723	+	1.37116i	0.0963075	+	0.0699715i
$385$		0			0
$386$	14.2044	−	10.3201i	0.722985	−	0.525280i
$387$	5.32895	+	3.87171i	0.270886	+	0.196810i
$388$	−0.0729490	−	0.0530006i	−0.00370343	−	0.00269070i
$389$	17.2942	−	12.5649i	0.876848	−	0.637068i	−0.0555675	−	0.998455i	$-0.517697\pi$
$389$	17.2942	−	12.5649i	0.876848	−	0.637068i	0.932416	+	0.361387i	$0.117697\pi$
$390$		0			0
$391$	1.00380	+	0.729301i	0.0507642	+	0.0368824i
$392$	−2.23932	−	6.89193i	−0.113103	−	0.348095i
$393$	9.45519			0.476951
$394$	1.47012	+	4.52458i	0.0740638	+	0.227945i
$395$		0			0
$396$	−2.84796	+	8.76511i	−0.143115	+	0.440464i
$397$	−6.49555	+	19.9913i	−0.326002	+	1.00333i	0.644984	+	0.764196i	$0.276864\pi$
$397$	−6.49555	+	19.9913i	−0.326002	+	1.00333i	−0.970986	+	0.239136i	$0.923136\pi$
$398$	11.7566	−	8.54169i	0.589307	−	0.428156i
$399$	−34.4610			−1.72521
$400$		0			0
$401$	16.7820			0.838053			0.419026	−	0.907974i	$-0.362371\pi$
$401$	16.7820			0.838053			0.419026	+	0.907974i	$0.362371\pi$
$402$	−28.9188	+	21.0108i	−1.44234	+	1.04792i
$403$	5.47805	−	16.8597i	0.272881	−	0.839842i
$404$	5.06122	−	15.5768i	0.251805	−	0.774977i
$405$		0			0
$406$	0.0574054	+	0.176676i	0.00284898	+	0.00876826i
$407$	26.6004			1.31853
$408$	−1.00380	−	3.08937i	−0.0496954	−	0.152947i
$409$	−29.4165	−	21.3723i	−1.45455	−	1.05679i	−0.984741	−	0.174025i	$-0.944323\pi$
$409$	−29.4165	−	21.3723i	−1.45455	−	1.05679i	−0.469809	−	0.882768i	$-0.655677\pi$
$410$		0			0
$411$	−6.73315	+	4.89192i	−0.332122	+	0.241301i
$412$	−0.983915	−	0.714856i	−0.0484740	−	0.0352184i
$413$	−2.10722	−	1.53098i	−0.103689	−	0.0753347i
$414$	−1.76013	+	1.27881i	−0.0865059	+	0.0628502i
$415$		0			0
$416$	−2.56969	−	1.86699i	−0.125990	−	0.0915368i
$417$	−7.16968	−	22.0660i	−0.351101	−	1.08058i
$418$	14.7727			0.722557
$419$	−10.6731	−	32.8484i	−0.521415	−	1.60475i	−0.771298	−	0.636474i	$-0.780392\pi$
$419$	−10.6731	−	32.8484i	−0.521415	−	1.60475i	0.249884	−	0.968276i	$-0.419608\pi$
$420$		0			0
$421$	3.00798	−	9.25762i	0.146600	−	0.451189i	−0.850613	−	0.525792i	$-0.823769\pi$
$421$	3.00798	−	9.25762i	0.146600	−	0.451189i	0.997213	+	0.0746033i	$0.0237691\pi$
$422$	4.36823	−	13.4440i	0.212642	−	0.654445i
$423$	7.45605	−	5.41714i	0.362526	−	0.263390i
$424$	11.6163			0.564136
$425$		0			0
$426$	15.6240			0.756984
$427$	31.6364	−	22.9852i	1.53099	−	1.11233i
$428$	3.34124	−	10.2833i	0.161505	−	0.497061i
$429$	8.64231	−	26.5983i	0.417255	−	1.28418i
$430$		0			0
$431$	−0.956560	−	2.94399i	−0.0460759	−	0.141807i	0.925372	−	0.379061i	$-0.123753\pi$
$431$	−0.956560	−	2.94399i	−0.0460759	−	0.141807i	−0.971448	+	0.237254i	$0.923753\pi$
$432$	−1.30233			−0.0626584
$433$	5.63542	+	17.3440i	0.270821	+	0.833501i	0.990295	+	0.138981i	$0.0443828\pi$
$433$	5.63542	+	17.3440i	0.270821	+	0.833501i	−0.719474	+	0.694519i	$0.755617\pi$
$434$	17.0425	+	12.3821i	0.818067	+	0.594360i
$435$		0			0
$436$	−9.23519	+	6.70976i	−0.442285	+	0.321339i
$437$	2.82134	+	2.04982i	0.134963	+	0.0980563i
$438$	−9.75458	−	7.08712i	−0.466092	−	0.338636i
$439$	21.4595	−	15.5912i	1.02421	−	0.744129i	0.0570645	−	0.998370i	$-0.481826\pi$
$439$	21.4595	−	15.5912i	1.02421	−	0.744129i	0.967141	+	0.254242i	$0.0818259\pi$
$440$		0			0
$441$	−14.3149	−	10.4004i	−0.681661	−	0.495256i
$442$	1.36679	+	4.20655i	0.0650115	+	0.200085i
$443$	−35.5267			−1.68793			−0.843963	−	0.536401i	$-0.819783\pi$
$443$	−35.5267			−1.68793			−0.843963	+	0.536401i	$0.819783\pi$
$444$	−5.08023	−	15.6353i	−0.241097	−	0.742020i
$445$		0			0
$446$	1.42527	−	4.38652i	0.0674883	−	0.207708i
$447$	−14.0641	+	43.2850i	−0.665211	+	2.04731i
$448$	3.05361	−	2.21858i	0.144269	−	0.104818i
$449$	16.1841			0.763776			0.381888	−	0.924209i	$-0.375274\pi$
$449$	16.1841			0.763776			0.381888	+	0.924209i	$0.375274\pi$
$450$		0			0
$451$	5.62087			0.264676
$452$	−8.43232	+	6.12644i	−0.396623	+	0.288163i
$453$	−13.2871	+	40.8936i	−0.624284	+	1.92135i
$454$	−1.94259	+	5.97869i	−0.0911705	+	0.280594i
$455$		0			0
$456$	−2.82134	−	8.68318i	−0.132121	−	0.406627i
$457$	−23.7205			−1.10960			−0.554799	−	0.831984i	$-0.687205\pi$
$457$	−23.7205			−1.10960			−0.554799	+	0.831984i	$0.687205\pi$
$458$	−5.48103	−	16.8689i	−0.256112	−	0.788230i
$459$	1.46715	+	1.06595i	0.0684807	+	0.0497542i
$460$		0			0
$461$	6.36936	−	4.62761i	0.296651	−	0.215529i	−0.429497	−	0.903068i	$-0.641309\pi$
$461$	6.36936	−	4.62761i	0.296651	−	0.215529i	0.726147	+	0.687539i	$0.241309\pi$
$462$	26.8867	+	19.5343i	1.25088	+	0.908818i
$463$	12.4775	+	9.06543i	0.579878	+	0.421306i	0.838680	−	0.544624i	$-0.183328\pi$
$463$	12.4775	+	9.06543i	0.579878	+	0.421306i	−0.258802	+	0.965930i	$0.583328\pi$
$464$	−0.0398173	+	0.0289290i	−0.00184847	+	0.00134299i
$465$		0			0
$466$	−2.07437	−	1.50712i	−0.0960932	−	0.0698158i
$467$	5.26481	+	16.2034i	0.243626	+	0.749805i	0.995859	+	0.0909075i	$0.0289768\pi$
$467$	5.26481	+	16.2034i	0.243626	+	0.749805i	−0.752233	+	0.658897i	$0.771023\pi$
$468$	−7.75567			−0.358506
$469$	17.8728	+	55.0069i	0.825290	+	2.53998i
$470$		0			0
$471$	−7.32136	+	22.5328i	−0.337350	+	1.03826i
$472$	0.213245	−	0.656300i	0.00981538	−	0.0302086i
$473$	−8.23762	+	5.98498i	−0.378766	+	0.275190i
$474$	4.21443			0.193575
$475$		0			0
$476$	−5.25595			−0.240906
$477$	22.9467	−	16.6718i	1.05066	−	0.763347i
$478$	−2.91765	+	8.97961i	−0.133450	+	0.410718i
$479$	−7.75544	+	23.8688i	−0.354355	+	1.09059i	0.602027	+	0.798476i	$0.294360\pi$
$479$	−7.75544	+	23.8688i	−0.354355	+	1.09059i	−0.956382	+	0.292118i	$0.905640\pi$
$480$		0			0
$481$	6.91734	+	21.2894i	0.315403	+	0.970712i
$482$	29.4346			1.34071
$483$	2.42437	+	7.46144i	0.110313	+	0.339507i
$484$	−2.62656	−	1.90831i	−0.119389	−	0.0867412i
$485$		0			0
$486$	−16.3969	+	11.9130i	−0.743778	+	0.540386i
$487$	−11.0735	−	8.04536i	−0.501788	−	0.364570i	0.307912	−	0.951415i	$-0.400370\pi$
$487$	−11.0735	−	8.04536i	−0.501788	−	0.364570i	−0.809699	+	0.586845i	$0.800370\pi$
$488$	8.38168	+	6.08965i	0.379421	+	0.275665i
$489$	−35.1033	+	25.5041i	−1.58743	+	1.15333i
$490$		0			0
$491$	2.08733	+	1.51654i	0.0942001	+	0.0684403i	0.633888	−	0.773425i	$-0.281458\pi$
$491$	2.08733	+	1.51654i	0.0942001	+	0.0684403i	−0.539688	+	0.841865i	$0.681458\pi$
$492$	−1.07349	−	3.30386i	−0.0483967	−	0.148950i
$493$	0.0685347			0.00308665
$494$	3.84159	+	11.8232i	0.172841	+	0.531950i
$495$		0			0
$496$	−1.72466	+	5.30795i	−0.0774394	+	0.238334i
$497$	7.81199	−	24.0428i	0.350416	−	1.07847i
$498$	18.8116	−	13.6674i	0.842969	−	0.612453i
$499$	−39.0539			−1.74829			−0.874146	−	0.485664i	$-0.838578\pi$
$499$	−39.0539			−1.74829			−0.874146	+	0.485664i	$0.838578\pi$
$500$		0			0
$501$	−5.06570			−0.226319
$502$	−4.86025	+	3.53118i	−0.216923	+	0.157604i
$503$	−3.69387	+	11.3686i	−0.164702	+	0.506899i	−0.999014	−	0.0443923i	$-0.985865\pi$
$503$	−3.69387	+	11.3686i	−0.164702	+	0.506899i	0.834313	+	0.551292i	$0.185865\pi$
$504$	2.84796	−	8.76511i	0.126858	−	0.390429i
$505$		0			0
$506$	−1.03928	−	3.19856i	−0.0462014	−	0.142193i
$507$	−6.79067			−0.301584
$508$	1.09668	+	3.37524i	0.0486574	+	0.149752i
$509$	3.94254	+	2.86442i	0.174750	+	0.126963i	0.671722	−	0.740803i	$-0.265555\pi$
$509$	3.94254	+	2.86442i	0.174750	+	0.126963i	−0.496972	+	0.867767i	$0.665555\pi$
$510$		0			0
$511$	−15.7832	+	11.4672i	−0.698210	+	0.507279i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	4.12367	+	2.99602i	0.182064	+	0.132278i
$514$	11.0257	−	8.01067i	0.486325	−	0.353336i
$515$		0			0
$516$	5.09113	+	3.69892i	0.224125	+	0.162836i
$517$	4.40244	+	13.5493i	0.193619	+	0.595899i
$518$	−26.6004			−1.16876
$519$	4.60936	+	14.1861i	0.202328	+	0.622702i
$520$		0			0
$521$	−2.70131	+	8.31378i	−0.118347	+	0.364233i	−0.992630	−	0.121182i	$-0.961332\pi$
$521$	−2.70131	+	8.31378i	−0.118347	+	0.364233i	0.874284	+	0.485415i	$0.161332\pi$
$522$	−0.0371358	+	0.114292i	−0.00162539	+	0.00500243i
$523$	−17.0534	+	12.3900i	−0.745694	+	0.541778i	−0.894489	−	0.447090i	$-0.852460\pi$
$523$	−17.0534	+	12.3900i	−0.745694	+	0.541778i	0.148795	+	0.988868i	$0.452460\pi$
$524$	4.05324			0.177067
$525$		0			0
$526$	−9.16294			−0.399523
$527$	6.28743	−	4.56809i	0.273885	−	0.198989i
$528$	−2.72086	+	8.37394i	−0.118410	+	0.364429i
$529$	−6.86205	+	21.1192i	−0.298350	+	0.918227i
$530$		0			0
$531$	−0.520683	−	1.60250i	−0.0225957	−	0.0695425i
$532$	−14.7727			−0.640478
$533$	1.46169	+	4.49861i	0.0633126	+	0.194856i
$534$	27.3842	+	19.8958i	1.18503	+	0.860976i
$535$		0			0
$536$	−12.3969	+	9.00687i	−0.535464	+	0.389038i
$537$	−15.1233	−	10.9877i	−0.652619	−	0.474155i
$538$	22.7355	+	16.5183i	0.980197	+	0.712155i
$539$	22.1283	−	16.0771i	0.953133	−	0.692492i
$540$		0			0
$541$	−26.5406	−	19.2829i	−1.14107	−	0.829036i	−0.153802	−	0.988102i	$-0.549152\pi$
$541$	−26.5406	−	19.2829i	−1.14107	−	0.829036i	−0.987268	+	0.159066i	$0.949152\pi$
$542$	2.81162	+	8.65329i	0.120770	+	0.371690i
$543$	−25.3404			−1.08746
$544$	−0.430307	−	1.32435i	−0.0184492	−	0.0567809i
$545$		0			0
$546$	−8.64231	+	26.5983i	−0.369857	+	1.13830i
$547$	1.69044	−	5.20264i	0.0722781	−	0.222449i	−0.908391	−	0.418121i	$-0.862689\pi$
$547$	1.69044	−	5.20264i	0.0722781	−	0.222449i	0.980669	+	0.195672i	$0.0626888\pi$
$548$	−2.88636	+	2.09706i	−0.123299	+	0.0895820i
$549$	25.2970			1.07965
$550$		0			0
$551$	0.192628			0.00820623
$552$	−1.68158	+	1.22174i	−0.0715729	+	0.0520008i
$553$	2.10722	−	6.48535i	0.0896080	−	0.275785i
$554$	5.80613	−	17.8694i	0.246679	−	0.759199i
$555$		0			0
$556$	−3.07349	−	9.45923i	−0.130345	−	0.401161i
$557$	5.19840			0.220263			0.110132	−	0.993917i	$-0.464873\pi$
$557$	5.19840			0.220263			0.110132	+	0.993917i	$0.464873\pi$
$558$	4.21112	+	12.9605i	0.178271	+	0.548662i
$559$	−6.93218	−	5.03652i	−0.293200	−	0.213022i
$560$		0			0
$561$	9.91921	−	7.20673i	0.418789	−	0.304268i
$562$	6.37633	+	4.63268i	0.268969	+	0.195418i
$563$	−4.05741	−	2.94788i	−0.170999	−	0.124238i	0.498994	−	0.866605i	$-0.333703\pi$
$563$	−4.05741	−	2.94788i	−0.170999	−	0.124238i	−0.669993	+	0.742367i	$0.733703\pi$
$564$	7.12330	−	5.17538i	0.299945	−	0.217923i
$565$		0			0
$566$	14.8049	+	10.7564i	0.622296	+	0.452124i
$567$	12.0873	+	37.2010i	0.507620	+	1.56229i
$568$	6.69767			0.281028
$569$	−12.9303	−	39.7952i	−0.542064	−	1.66830i	−0.727869	−	0.685716i	$-0.759489\pi$
$569$	−12.9303	−	39.7952i	−0.542064	−	1.66830i	0.185805	−	0.982587i	$-0.440511\pi$
$570$		0			0
$571$	−13.7723	+	42.3869i	−0.576355	+	1.77384i	0.0551642	+	0.998477i	$0.482432\pi$
$571$	−13.7723	+	42.3869i	−0.576355	+	1.77384i	−0.631519	+	0.775360i	$0.717568\pi$
$572$	3.70477	−	11.4021i	0.154904	−	0.476747i
$573$	15.4485	−	11.2240i	0.645369	−	0.468888i
$574$	−5.62087			−0.234611
$575$		0			0
$576$	2.44172			0.101738
$577$	−20.3401	+	14.7779i	−0.846769	+	0.615213i	−0.924253	−	0.381780i	$-0.875311\pi$
$577$	−20.3401	+	14.7779i	−0.846769	+	0.615213i	0.0774845	+	0.996994i	$0.475311\pi$
$578$	4.65409	−	14.3238i	0.193584	−	0.595792i
$579$	12.6566	−	38.9529i	0.525989	−	1.61883i
$580$		0			0
$581$	−11.6262	−	35.7818i	−0.482337	−	1.48448i
$582$	−0.210344			−0.00871903
$583$	13.5489	+	41.6993i	0.561140	+	1.72701i
$584$	−4.18158	−	3.03810i	−0.173035	−	0.125717i
$585$		0			0
$586$	23.8652	−	17.3391i	0.985861	−	0.716270i
$587$	17.2770	+	12.5525i	0.713099	+	0.518097i	0.884172	−	0.467162i	$-0.154723\pi$
$587$	17.2770	+	12.5525i	0.713099	+	0.518097i	−0.171073	+	0.985258i	$0.554723\pi$
$588$	−13.6760	−	9.93622i	−0.563990	−	0.409763i
$589$	17.6719	−	12.8394i	0.728157	−	0.529037i
$590$		0			0
$591$	8.97836	+	6.52316i	0.369321	+	0.268327i
$592$	−2.17779	−	6.70254i	−0.0895065	−	0.275473i
$593$	33.4430			1.37334			0.686669	−	0.726970i	$-0.259072\pi$
$593$	33.4430			1.37334			0.686669	+	0.726970i	$0.259072\pi$
$594$	−1.51901	−	4.67502i	−0.0623256	−	0.191818i
$595$		0			0
$596$	−6.02900	+	18.5554i	−0.246957	+	0.760057i
$597$	10.4755	−	32.2403i	0.428734	−	1.31951i
$598$	2.28968	−	1.66355i	0.0936318	−	0.0680275i
$599$	26.3174			1.07530			0.537650	−	0.843168i	$-0.319312\pi$
$599$	26.3174			1.07530			0.537650	+	0.843168i	$0.319312\pi$
$600$		0			0
$601$	20.9964			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$601$	20.9964			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$602$	8.23762	−	5.98498i	0.335740	−	0.243930i
$603$	−11.5620	+	35.5842i	−0.470841	+	1.44910i
$604$	−5.69592	+	17.5302i	−0.231764	+	0.713295i
$605$		0			0
$606$	−11.8066	−	36.3369i	−0.479609	−	1.47608i
$607$	−9.32822			−0.378621			−0.189310	−	0.981917i	$-0.560625\pi$
$607$	−9.32822			−0.378621			−0.189310	+	0.981917i	$0.560625\pi$
$608$	−1.20945	−	3.72230i	−0.0490496	−	0.150959i
$609$	0.350587	+	0.254716i	0.0142065	+	0.0103216i
$610$		0			0
$611$	−9.69922	+	7.04690i	−0.392389	+	0.285087i
$612$	−2.75074	−	1.99853i	−0.111192	−	0.0807856i
$613$	−25.9724	−	18.8700i	−1.04902	−	0.762154i	−0.0769902	−	0.997032i	$-0.524531\pi$
$613$	−25.9724	−	18.8700i	−1.04902	−	0.762154i	−0.972025	+	0.234878i	$0.924531\pi$
$614$	−11.2560	+	8.17793i	−0.454253	+	0.330034i
$615$		0			0
$616$	11.5257	+	8.37394i	0.464385	+	0.337396i
$617$	9.86557	+	30.3631i	0.397173	+	1.22237i	0.927257	+	0.374427i	$0.122160\pi$
$617$	9.86557	+	30.3631i	0.397173	+	1.22237i	−0.530084	+	0.847945i	$0.677840\pi$
$618$	−2.83706			−0.114123
$619$	−1.40420	−	4.32167i	−0.0564394	−	0.173703i	0.918863	−	0.394577i	$-0.129109\pi$
$619$	−1.40420	−	4.32167i	−0.0564394	−	0.173703i	−0.975302	+	0.220875i	$0.929109\pi$
$620$		0			0
$621$	0.358589	−	1.10362i	0.0143897	−	0.0442868i
$622$	−8.02319	+	24.6928i	−0.321701	+	0.990093i
$623$	44.3086	−	32.1921i	1.77519	−	1.28975i
$624$	−7.40955			−0.296619
$625$		0			0
$626$	9.47389			0.378653
$627$	27.8796	−	20.2557i	1.11340	−	0.808934i
$628$	−3.13851	+	9.65934i	−0.125240	+	0.385450i
$629$	−3.03257	+	9.33329i	−0.120916	+	0.372143i
$630$		0			0
$631$	−8.31756	−	25.5988i	−0.331117	−	1.01907i	−0.968603	−	0.248611i	$-0.920026\pi$
$631$	−8.31756	−	25.5988i	−0.331117	−	1.01907i	0.637486	−	0.770462i	$-0.279974\pi$
$632$	1.80664			0.0718642
$633$	−10.1900	−	31.3615i	−0.405015	−	1.24651i
$634$	−19.8269	−	14.4051i	−0.787427	−	0.572100i
$635$		0			0
$636$	21.9226	−	15.9277i	0.869289	−	0.631575i
$637$	18.6215	+	13.5293i	0.737813	+	0.536052i
$638$	−0.150289	−	0.109192i	−0.00595001	−	0.00432293i
$639$	13.2305	−	9.61253i	0.523391	−	0.380266i
$640$		0			0
$641$	−28.9303	−	21.0191i	−1.14268	−	0.830205i	−0.155189	−	0.987885i	$-0.549599\pi$
$641$	−28.9303	−	21.0191i	−1.14268	−	0.830205i	−0.987490	+	0.157679i	$0.949599\pi$
$642$	−7.79427	−	23.9883i	−0.307615	−	0.946743i
$643$	−28.2255			−1.11311			−0.556553	−	0.830812i	$-0.687876\pi$
$643$	−28.2255			−1.11311			−0.556553	+	0.830812i	$0.687876\pi$
$644$	1.03928	+	3.19856i	0.0409532	+	0.126041i
$645$		0			0
$646$	−1.68416	+	5.18330i	−0.0662623	+	0.203934i
$647$	−0.394848	+	1.21522i	−0.0155231	+	0.0477751i	−0.958518	−	0.285032i	$-0.907996\pi$
$647$	−0.394848	+	1.21522i	−0.0155231	+	0.0477751i	0.942995	+	0.332807i	$0.107996\pi$
$648$	−8.38398	+	6.09132i	−0.329354	+	0.239290i
$649$	2.60466			0.102242
$650$		0			0
$651$	49.1410			1.92599
$652$	−15.0481	+	10.9331i	−0.589327	+	0.428171i
$653$	8.47040	−	26.0692i	0.331472	−	1.02017i	−0.636961	−	0.770896i	$-0.719809\pi$
$653$	8.47040	−	26.0692i	0.331472	−	1.02017i	0.968434	−	0.249272i	$-0.0801912\pi$
$654$	−8.22884	+	25.3258i	−0.321773	+	0.990316i
$655$		0			0
$656$	−0.460183	−	1.41630i	−0.0179671	−	0.0552971i
$657$	−12.6206			−0.492375
$658$	−4.40244	−	13.5493i	−0.171625	−	0.528208i
$659$	33.3535	+	24.2327i	1.29927	+	0.943972i	0.999948	−	0.0101814i	$-0.00324090\pi$
$659$	33.3535	+	24.2327i	1.29927	+	0.943972i	0.299318	+	0.954153i	$0.403241\pi$
$660$		0			0
$661$	21.4653	−	15.5955i	0.834904	−	0.606593i	−0.0860388	−	0.996292i	$-0.527421\pi$
$661$	21.4653	−	15.5955i	0.834904	−	0.606593i	0.920942	+	0.389699i	$0.127421\pi$
$662$	−8.01764	−	5.82516i	−0.311614	−	0.226401i
$663$	8.34728	+	6.06465i	0.324181	+	0.235532i
$664$	8.06414	−	5.85894i	0.312949	−	0.227371i
$665$		0			0
$666$	−13.9215	−	10.1146i	−0.539447	−	0.391931i
$667$	−0.0135516	−	0.0417075i	−0.000524719	−	0.00161492i
$668$	−2.17156			−0.0840201
$669$	−3.32479	−	10.2326i	−0.128544	−	0.395617i
$670$		0			0
$671$	−12.0840	+	37.1908i	−0.466499	+	1.43574i
$672$	2.72086	−	8.37394i	0.104959	−	0.323032i
$673$	−6.42142	+	4.66543i	−0.247527	+	0.179839i	−0.704630	−	0.709575i	$-0.748887\pi$
$673$	−6.42142	+	4.66543i	−0.247527	+	0.179839i	0.457103	+	0.889414i	$0.348887\pi$
$674$	−9.93566			−0.382707
$675$		0			0
$676$	−2.91102			−0.111962
$677$	23.8667	−	17.3402i	0.917271	−	0.666436i	−0.0255722	−	0.999673i	$-0.508141\pi$
$677$	23.8667	−	17.3402i	0.917271	−	0.666436i	0.942843	+	0.333237i	$0.108141\pi$
$678$	−7.51346	+	23.1240i	−0.288553	+	0.888073i
$679$	−0.105172	+	0.323686i	−0.00403613	+	0.0124219i
$680$		0			0
$681$	4.53159	+	13.9468i	0.173651	+	0.534442i
$682$	−21.0657			−0.806647
$683$	−11.6650	−	35.9012i	−0.446349	−	1.37372i	−0.880997	−	0.473121i	$-0.843127\pi$
$683$	−11.6650	−	35.9012i	−0.446349	−	1.37372i	0.434648	−	0.900600i	$-0.356873\pi$
$684$	−7.73139	−	5.61719i	−0.295617	−	0.214779i
$685$		0			0
$686$	−0.753030	+	0.547108i	−0.0287508	+	0.0208887i
$687$	−33.4738	−	24.3201i	−1.27711	−	0.927872i
$688$	2.18246	+	1.58565i	0.0832055	+	0.0604523i
$689$	−29.8503	+	21.6875i	−1.13721	+	0.826228i
$690$		0			0
$691$	−14.2843	−	10.3782i	−0.543401	−	0.394804i	0.281945	−	0.959430i	$-0.409020\pi$
$691$	−14.2843	−	10.3782i	−0.543401	−	0.394804i	−0.825347	+	0.564626i	$0.809020\pi$
$692$	1.97593	+	6.08130i	0.0751137	+	0.231176i
$693$	34.7862			1.32142
$694$	−6.06757	−	18.6741i	−0.230322	−	0.708858i
$695$		0			0
$696$	−0.0354785	+	0.109192i	−0.00134481	+	0.00413889i
$697$	−0.640805	+	1.97219i	−0.0242722	+	0.0747022i
$698$	1.20084	−	0.872461i	0.0454524	−	0.0330231i
$699$	−5.98131			−0.226234
$700$		0			0
$701$	−16.8372			−0.635931			−0.317965	−	0.948102i	$-0.603000\pi$
$701$	−16.8372			−0.635931			−0.317965	+	0.948102i	$0.603000\pi$
$702$	3.34659	−	2.43144i	0.126309	−	0.0917688i
$703$	−8.52354	+	26.2328i	−0.321471	+	0.989387i
$704$	−1.16637	+	3.58973i	−0.0439594	+	0.135293i
$705$		0			0
$706$	3.17632	+	9.77569i	0.119542	+	0.367913i
$707$	−61.8200			−2.32498
$708$	−0.497446	−	1.53098i	−0.0186952	−	0.0575378i
$709$	23.1615	+	16.8278i	0.869849	+	0.631982i	0.930546	−	0.366174i	$-0.119333\pi$
$709$	23.1615	+	16.8278i	0.869849	+	0.631982i	−0.0606978	+	0.998156i	$0.519333\pi$
$710$		0			0
$711$	3.56882	−	2.59290i	0.133841	−	0.0972412i
$712$	11.7390	+	8.52891i	0.439939	+	0.319635i
$713$	−4.02319	−	2.92302i	−0.150670	−	0.109468i
$714$	−9.91921	+	7.20673i	−0.371217	+	0.269705i
$715$		0			0
$716$	−6.48304	−	4.71020i	−0.242283	−	0.176029i
$717$	6.80615	+	20.9472i	0.254180	+	0.782286i
$718$	10.3725			0.387099
$719$	−2.54857	−	7.84368i	−0.0950455	−	0.292520i	0.892220	−	0.451601i	$-0.149147\pi$
$719$	−2.54857	−	7.84368i	−0.0950455	−	0.292520i	−0.987266	+	0.159081i	$0.949147\pi$
$720$		0			0
$721$	−1.41853	+	4.36578i	−0.0528287	+	0.162590i
$722$	1.13772	−	3.50155i	0.0423416	−	0.130314i
$723$	55.5500	−	40.3595i	2.06593	−	1.50098i
$724$	−10.8629			−0.403716
$725$		0			0
$726$	−7.57351			−0.281079
$727$	−1.71013	+	1.24248i	−0.0634251	+	0.0460810i	−0.619046	−	0.785355i	$-0.712481\pi$
$727$	−1.71013	+	1.24248i	−0.0634251	+	0.0460810i	0.555621	+	0.831436i	$0.312481\pi$
$728$	−3.70477	+	11.4021i	−0.137308	+	0.422591i
$729$	−5.00295	+	15.3975i	−0.185295	+	0.570278i
$730$		0			0
$731$	−1.16082	−	3.57265i	−0.0429346	−	0.132139i
$732$	24.1681			0.893277
$733$	−13.9537	−	42.9451i	−0.515393	−	1.58622i	−0.782567	−	0.622567i	$-0.786090\pi$
$733$	−13.9537	−	42.9451i	−0.515393	−	1.58622i	0.267174	−	0.963648i	$-0.413910\pi$
$734$	−21.0946	−	15.3261i	−0.778614	−	0.565697i
$735$		0			0
$736$	−0.720859	+	0.523735i	−0.0265712	+	0.0193051i
$737$	−46.7917	−	33.9961i	−1.72359	−	1.25226i
$738$	−2.94172	−	2.13728i	−0.108286	−	0.0786745i
$739$	−24.2478	+	17.6171i	−0.891969	+	0.648054i	−0.936391	−	0.350959i	$-0.885856\pi$
$739$	−24.2478	+	17.6171i	−0.891969	+	0.648054i	0.0444213	+	0.999013i	$0.485856\pi$
$740$		0			0
$741$	23.4614	+	17.0457i	0.861876	+	0.626190i
$742$	−13.5489	−	41.6993i	−0.497397	−	1.53083i
$743$	−17.6562			−0.647741			−0.323871	−	0.946101i	$-0.604984\pi$
$743$	−17.6562			−0.647741			−0.323871	+	0.946101i	$0.604984\pi$
$744$	4.02319	+	12.3821i	0.147497	+	0.453950i
$745$		0			0
$746$	2.92204	−	8.99312i	0.106984	−	0.329262i
$747$	7.52105	−	23.1474i	0.275181	−	0.846920i
$748$	4.25215	−	3.08937i	0.155474	−	0.112959i
$749$	−40.8113			−1.49121
$750$		0			0
$751$	30.1342			1.09961			0.549806	−	0.835293i	$-0.314702\pi$
$751$	30.1342			1.09961			0.549806	+	0.835293i	$0.314702\pi$
$752$	3.05361	−	2.21858i	0.111354	−	0.0809031i
$753$	−4.33063	+	13.3283i	−0.157817	+	0.485710i
$754$	0.0483082	−	0.148677i	0.00175928	−	0.00541451i
$755$		0			0
$756$	1.51901	+	4.67502i	0.0552457	+	0.170029i
$757$	4.90706			0.178350			0.0891750	−	0.996016i	$-0.471577\pi$
$757$	4.90706			0.178350			0.0891750	+	0.996016i	$0.471577\pi$
$758$	10.9163	+	33.5968i	0.396497	+	1.22029i
$759$	−6.34708	−	4.61142i	−0.230384	−	0.167384i
$760$		0			0
$761$	−10.7466	+	7.80786i	−0.389564	+	0.283035i	−0.765277	−	0.643701i	$-0.777398\pi$
$761$	−10.7466	+	7.80786i	−0.389564	+	0.283035i	0.375713	+	0.926736i	$0.377398\pi$
$762$	6.69767	+	4.86614i	0.242631	+	0.176282i
$763$	34.8579	+	25.3258i	1.26194	+	0.916854i
$764$	6.62243	−	4.81147i	0.239591	−	0.174073i
$765$		0			0
$766$	−24.1227	−	17.5262i	−0.871590	−	0.633247i
$767$	0.677332	+	2.08461i	0.0244571	+	0.0752711i
$768$	2.33275			0.0841758
$769$	−8.83716	−	27.1980i	−0.318676	−	0.980784i	−0.974215	−	0.225623i	$-0.927558\pi$
$769$	−8.83716	−	27.1980i	−0.318676	−	0.980784i	0.655539	−	0.755162i	$-0.272442\pi$
$770$		0			0
$771$	9.82428	−	30.2360i	0.353813	−	1.08892i
$772$	5.42560	−	16.6983i	0.195272	−	0.600984i
$773$	−36.4564	+	26.4871i	−1.31124	+	0.952675i	−0.311247	+	0.950329i	$0.600747\pi$
$773$	−36.4564	+	26.4871i	−1.31124	+	0.952675i	−0.999997	+	0.00234562i	$0.999253\pi$
$774$	6.58695			0.236763
$775$		0			0
$776$	−0.0901699			−0.00323691
$777$	−50.2012	+	36.4733i	−1.80096	+	1.30847i
$778$	6.60578	−	20.3305i	0.236829	−	0.728884i
$779$	−1.80109	+	5.54318i	−0.0645307	+	0.198605i
$780$		0			0
$781$	7.81199	+	24.0428i	0.279535	+	0.860320i
$782$	1.24076			0.0443695
$783$	−0.0198070	−	0.0609596i	−0.000707844	−	0.00217852i
$784$	−5.86263	−	4.25945i	−0.209379	−	0.152123i
$785$		0			0
$786$	7.64941	−	5.55762i	0.272846	−	0.198234i
$787$	20.8458	+	15.1454i	0.743074	+	0.539875i	0.893672	−	0.448720i	$-0.148120\pi$
$787$	20.8458	+	15.1454i	0.743074	+	0.539875i	−0.150598	+	0.988595i	$0.548120\pi$
$788$	3.84883	+	2.79634i	0.137109	+	0.0996156i
$789$	−17.2926	+	12.5638i	−0.615633	+	0.447284i
$790$		0			0
$791$	31.8275	+	23.1240i	1.13166	+	0.822196i
$792$	2.84796	+	8.76511i	0.101198	+	0.311455i
$793$	−32.9077			−1.16859
$794$	6.49555	+	19.9913i	0.230519	+	0.709463i
$795$		0			0
$796$	4.49063	−	13.8207i	0.159166	−	0.489863i
$797$	−15.5882	+	47.9757i	−0.552164	+	1.69939i	0.151154	+	0.988510i	$0.451701\pi$
$797$	−15.5882	+	47.9757i	−0.552164	+	1.69939i	−0.703318	+	0.710875i	$0.748299\pi$
$798$	−27.8796	+	20.2557i	−0.986926	+	0.717044i
$799$	−5.25595			−0.185942
$800$		0			0
$801$	35.4299			1.25186
$802$	13.5769	−	9.86421i	0.479418	−	0.348317i
$803$	6.02866	−	18.5543i	0.212747	−	0.654768i
$804$	−11.0460	+	33.9961i	−0.389563	+	1.19895i
$805$		0			0
$806$	−5.47805	−	16.8597i	−0.192956	−	0.593858i
$807$	65.5564			2.30769
$808$	−5.06122	−	15.5768i	−0.178053	−	0.547991i
$809$	2.92626	+	2.12605i	0.102882	+	0.0747480i	0.638037	−	0.770006i	$-0.279747\pi$
$809$	2.92626	+	2.12605i	0.102882	+	0.0747480i	−0.535155	+	0.844754i	$0.679747\pi$
$810$		0			0
$811$	−40.8026	+	29.6448i	−1.43277	+	1.04097i	−0.443280	+	0.896383i	$0.646185\pi$
$811$	−40.8026	+	29.6448i	−1.43277	+	1.04097i	−0.989492	+	0.144586i	$0.953815\pi$
$812$	0.150289	+	0.109192i	0.00527412	+	0.00383187i
$813$	17.1712	+	12.4756i	0.602220	+	0.437538i
$814$	21.5202	−	15.6353i	0.754282	−	0.548018i
$815$		0			0
$816$	−2.62798	−	1.90934i	−0.0919975	−	0.0668401i
$817$	−3.26269	−	10.0415i	−0.114147	−	0.351308i
$818$	−36.3607			−1.27132
$819$	9.04601	+	27.8408i	0.316093	+	0.972835i
$820$		0			0
$821$	−3.48714	+	10.7323i	−0.121702	+	0.374560i	−0.993286	−	0.115686i	$-0.963093\pi$
$821$	−3.48714	+	10.7323i	−0.121702	+	0.374560i	0.871584	+	0.490246i	$0.163093\pi$
$822$	−2.57183	+	7.91529i	−0.0897030	+	0.276077i
$823$	0.871148	−	0.632926i	0.0303663	−	0.0220624i	−0.572499	−	0.819906i	$-0.694026\pi$
$823$	0.871148	−	0.632926i	0.0303663	−	0.0220624i	0.602865	+	0.797843i	$0.294026\pi$
$824$	−1.21619			−0.0423678
$825$		0			0
$826$	−2.60466			−0.0906278
$827$	−23.7689	+	17.2691i	−0.826526	+	0.600506i	−0.918574	−	0.395248i	$-0.870659\pi$
$827$	−23.7689	+	17.2691i	−0.826526	+	0.600506i	0.0920482	+	0.995755i	$0.470659\pi$
$828$	−0.672312	+	2.06916i	−0.0233644	+	0.0719084i
$829$	6.51402	−	20.0481i	0.226241	−	0.696299i	−0.771922	−	0.635717i	$-0.780704\pi$
$829$	6.51402	−	20.0481i	0.226241	−	0.696299i	0.998163	−	0.0605816i	$-0.0192955\pi$
$830$		0			0
$831$	−13.5442	−	41.6849i	−0.469845	−	1.44603i
$832$	−3.17632			−0.110119
$833$	3.11826	+	9.59702i	0.108041	+	0.332517i
$834$	−18.7705	−	13.6375i	−0.649968	−	0.472230i
$835$		0			0
$836$	11.9514	−	8.68318i	0.413347	−	0.300314i
$837$	−5.88030	−	4.27229i	−0.203253	−	0.147672i
$838$	−27.9425	−	20.3014i	−0.965258	−	0.701301i
$839$	2.76181	−	2.00657i	0.0953483	−	0.0692746i	−0.539090	−	0.842248i	$-0.681232\pi$
$839$	2.76181	−	2.00657i	0.0953483	−	0.0692746i	0.634438	+	0.772974i	$0.281232\pi$
$840$		0			0
$841$	23.4595	+	17.0443i	0.808949	+	0.587736i
$842$	−3.00798	−	9.25762i	−0.103662	−	0.319038i
$843$	18.3857			0.633239
$844$	−4.36823	−	13.4440i	−0.150361	−	0.462762i
$845$		0			0
$846$	2.84796	−	8.76511i	0.0979148	−	0.301351i
$847$	−3.78676	+	11.6544i	−0.130114	+	0.400451i
$848$	9.39777	−	6.82788i	0.322721	−	0.234470i
$849$	42.6889			1.46508
$850$		0			0
$851$	6.27951			0.215259
$852$	12.6401	−	9.18355i	0.433042	−	0.314623i
$853$	12.5449	−	38.6094i	0.429531	−	1.32196i	−0.469058	−	0.883167i	$-0.655406\pi$
$853$	12.5449	−	38.6094i	0.429531	−	1.32196i	0.898589	−	0.438792i	$-0.144594\pi$
$854$	12.0840	−	37.1908i	0.413507	−	1.27264i
$855$		0			0
$856$	−3.34124	−	10.2833i	−0.114201	−	0.351475i
$857$	43.0463			1.47043			0.735216	−	0.677833i	$-0.237081\pi$
$857$	43.0463			1.47043			0.735216	+	0.677833i	$0.237081\pi$
$858$	−8.64231	−	26.5983i	−0.295044	−	0.908051i
$859$	−6.17691	−	4.48779i	−0.210753	−	0.153121i	0.477401	−	0.878685i	$-0.341579\pi$
$859$	−6.17691	−	4.48779i	−0.210753	−	0.153121i	−0.688155	+	0.725564i	$0.741579\pi$
$860$		0			0
$861$	−10.6079	+	7.70709i	−0.361516	+	0.262657i
$862$	−2.50431	−	1.81949i	−0.0852970	−	0.0619719i
$863$	5.23799	+	3.80562i	0.178303	+	0.129545i	0.673357	−	0.739317i	$-0.264852\pi$
$863$	5.23799	+	3.80562i	0.178303	+	0.129545i	−0.495054	+	0.868862i	$0.664852\pi$
$864$	−1.05361	+	0.765491i	−0.0358445	+	0.0260425i
$865$		0			0
$866$	14.7537	+	10.7192i	0.501351	+	0.364253i
$867$	−10.8568	−	33.4138i	−0.368717	−	1.13479i
$868$	21.0657			0.715016
$869$	2.10722	+	6.48535i	0.0714824	+	0.220000i
$870$		0			0
$871$	15.0405	−	46.2898i	0.509627	−	1.56847i
$872$	−3.52753	+	10.8566i	−0.119457	+	0.367652i
$873$	−0.178121	+	0.129412i	−0.00602848	+	0.00437995i
$874$	3.48736			0.117962
$875$		0			0
$876$	−12.0573			−0.407379
$877$	−6.36784	+	4.62651i	−0.215027	+	0.156226i	−0.690085	−	0.723728i	$-0.742427\pi$
$877$	−6.36784	+	4.62651i	−0.215027	+	0.156226i	0.475058	+	0.879954i	$0.342427\pi$
$878$	8.19679	−	25.2271i	0.276628	−	0.851374i
$879$	21.2646	−	65.4457i	0.717238	−	2.20743i
$880$		0			0
$881$	5.95327	+	18.3223i	0.200571	+	0.617293i	0.999866	+	0.0163551i	$0.00520623\pi$
$881$	5.95327	+	18.3223i	0.200571	+	0.617293i	−0.799295	+	0.600938i	$0.794794\pi$
$882$	−17.6942			−0.595793
$883$	−1.93876	−	5.96688i	−0.0652444	−	0.200802i	0.913120	−	0.407691i	$-0.133666\pi$
$883$	−1.93876	−	5.96688i	−0.0652444	−	0.200802i	−0.978364	+	0.206889i	$0.933666\pi$
$884$	3.57830	+	2.59979i	0.120351	+	0.0874403i
$885$		0			0
$886$	−28.7417	+	20.8821i	−0.965597	+	0.701548i
$887$	18.8281	+	13.6794i	0.632185	+	0.459309i	0.857156	−	0.515056i	$-0.172229\pi$
$887$	18.8281	+	13.6794i	0.632185	+	0.459309i	−0.224972	+	0.974365i	$0.572229\pi$
$888$	−13.3002	−	9.66317i	−0.446326	−	0.324275i
$889$	10.8371	−	7.87358i	0.363463	−	0.264071i
$890$		0			0
$891$	−31.6451	−	22.9915i	−1.06015	−	0.770243i
$892$	−1.42527	−	4.38652i	−0.0477214	−	0.146871i
$893$	−14.7727			−0.494350
$894$	14.0641	+	43.2850i	0.470375	+	1.44767i
$895$		0			0
$896$	1.16637	−	3.58973i	0.0389658	−	0.119925i
$897$	2.04017	−	6.27900i	0.0681194	−	0.209650i
$898$	13.0932	−	9.51279i	0.436927	−	0.317446i
$899$	−0.274685			−0.00916126
$900$		0			0
$901$	−16.1757			−0.538890
$902$	4.54738	−	3.30386i	0.151411	−	0.110007i
$903$	7.33998	−	22.5901i	0.244259	−	0.751752i
$904$	−3.22086	+	9.91279i	−0.107124	+	0.329694i
$905$		0			0
$906$	13.2871	+	40.8936i	0.441436	+	1.35860i
$907$	17.6544			0.586206			0.293103	−	0.956081i	$-0.405312\pi$
$907$	17.6544			0.586206			0.293103	+	0.956081i	$0.405312\pi$
$908$	1.94259	+	5.97869i	0.0644673	+	0.198410i
$909$	−32.3539	−	23.5065i	−1.07311	−	0.779660i
$910$		0			0
$911$	28.2767	−	20.5442i	0.936847	−	0.680659i	−0.0108124	−	0.999942i	$-0.503442\pi$
$911$	28.2767	−	20.5442i	0.936847	−	0.680659i	0.947660	+	0.319282i	$0.103442\pi$
$912$	−7.38636	−	5.36650i	−0.244587	−	0.177703i
$913$	30.4378	+	22.1144i	1.00735	+	0.731879i
$914$	−19.1903	+	13.9426i	−0.634758	+	0.461179i
$915$		0			0
$916$	−14.3495	−	10.4255i	−0.474121	−	0.344469i
$917$	−4.72760	−	14.5500i	−0.156119	−	0.480485i
$918$	1.81350			0.0598544
$919$	11.2243	+	34.5449i	0.370256	+	1.13953i	0.946624	+	0.322340i	$0.104469\pi$
$919$	11.2243	+	34.5449i	0.370256	+	1.13953i	−0.576368	+	0.817190i	$0.695531\pi$
$920$		0			0
$921$	−10.0294	+	30.8673i	−0.330480	+	1.01711i
$922$	2.43288	−	7.48764i	0.0801226	−	0.246592i
$923$	−17.2110	+	12.5045i	−0.566505	+	0.411590i
$924$	33.2338			1.09331
$925$		0			0
$926$	15.4230			0.506832
$927$	−2.40244	+	1.74548i	−0.0789066	+	0.0573290i
$928$	−0.0152089	+	0.0468081i	−0.000499256	+	0.00153655i
$929$	5.88811	−	18.1217i	0.193183	−	0.594555i	−0.806810	−	0.590810i	$-0.798808\pi$
$929$	5.88811	−	18.1217i	0.193183	−	0.594555i	0.999993	−	0.00374449i	$-0.00119191\pi$
$930$		0			0
$931$	8.76439	+	26.9740i	0.287241	+	0.884037i
$932$	−2.56406			−0.0839885
$933$	18.7161	+	57.6022i	0.612737	+	1.88581i
$934$	13.7834	+	10.0143i	0.451008	+	0.327677i
$935$		0			0
$936$	−6.27447	+	4.55867i	−0.205087	+	0.149005i
$937$	48.1590	+	34.9896i	1.57329	+	1.14306i	0.923920	+	0.382586i	$0.124966\pi$
$937$	48.1590	+	34.9896i	1.57329	+	1.14306i	0.649367	+	0.760475i	$0.275034\pi$
$938$	46.7917	+	33.9961i	1.52780	+	1.11001i
$939$	17.8794	−	12.9902i	0.583474	−	0.423918i
$940$		0			0
$941$	−12.2598	−	8.90727i	−0.399658	−	0.290369i	0.369744	−	0.929134i	$-0.379446\pi$
$941$	−12.2598	−	8.90727i	−0.399658	−	0.290369i	−0.769402	+	0.638765i	$0.779446\pi$
$942$	7.32136	+	22.5328i	0.238543	+	0.734159i
$943$	1.32691			0.0432101
$944$	−0.213245	−	0.656300i	−0.00694052	−	0.0213607i
$945$		0			0
$946$	−3.14649	+	9.68391i	−0.102301	+	0.314851i
$947$	−0.778999	+	2.39751i	−0.0253141	+	0.0779087i	−0.962915	−	0.269803i	$-0.913041\pi$
$947$	−0.778999	+	2.39751i	−0.0253141	+	0.0779087i	0.937601	+	0.347712i	$0.113041\pi$
$948$	3.40955	−	2.47718i	0.110737	−	0.0804551i
$949$	16.4175			0.532934
$950$		0			0
$951$	−57.1697			−1.85385
$952$	−4.25215	+	3.08937i	−0.137813	+	0.100127i
$953$	−9.69336	+	29.8331i	−0.313999	+	0.966389i	0.662166	+	0.749357i	$0.269637\pi$
$953$	−9.69336	+	29.8331i	−0.313999	+	0.966389i	−0.976165	+	0.217032i	$0.930363\pi$
$954$	8.76486	−	26.9755i	0.283773	−	0.873363i
$955$		0			0
$956$	2.91765	+	8.97961i	0.0943636	+	0.290421i
$957$	−0.433350			−0.0140082
$958$	7.75544	+	23.8688i	0.250567	+	0.771166i
$959$	10.8945	+	7.91529i	0.351800	+	0.255598i
$960$		0			0
$961$	−0.120328	+	0.0874237i	−0.00388156	+	0.00282012i
$962$	18.1098	+	13.1576i	0.583884	+	0.424217i
$963$	−21.3589	−	15.5181i	−0.688280	−	0.500065i
$964$	23.8131	−	17.3012i	0.766969	−	0.557236i
$965$		0			0
$966$	6.34708	+	4.61142i	0.204214	+	0.148370i
$967$	−15.1746	−	46.7027i	−0.487983	−	1.50186i	−0.827613	−	0.561299i	$-0.810302\pi$
$967$	−15.1746	−	46.7027i	−0.487983	−	1.50186i	0.339630	−	0.940559i	$-0.389698\pi$
$968$	−3.24660			−0.104350
$969$	3.92872	+	12.0913i	0.126209	+	0.388430i
$970$		0			0
$971$	7.72049	−	23.7612i	0.247762	−	0.762534i	−0.747407	−	0.664366i	$-0.768702\pi$
$971$	7.72049	−	23.7612i	0.247762	−	0.762534i	0.995170	−	0.0981683i	$-0.0312983\pi$
$972$	−6.26306	+	19.2757i	−0.200888	+	0.618268i
$973$	−30.3713	+	22.0660i	−0.973658	+	0.707404i
$974$	−13.6876			−0.438579
$975$		0			0
$976$	10.3603			0.331626
$977$	12.6095	−	9.16131i	0.403412	−	0.293096i	−0.367517	−	0.930017i	$-0.619792\pi$
$977$	12.6095	−	9.16131i	0.403412	−	0.293096i	0.770929	+	0.636921i	$0.219792\pi$
$978$	−13.4083	+	41.2665i	−0.428750	+	1.31956i
$979$	−16.9244	+	52.0879i	−0.540906	+	1.66474i
$980$		0			0
$981$	8.61323	+	26.5088i	0.274999	+	0.846361i
$982$	2.58009			0.0823339
$983$	4.18993	+	12.8953i	0.133638	+	0.411296i	0.995376	−	0.0960585i	$-0.0306236\pi$
$983$	4.18993	+	12.8953i	0.133638	+	0.411296i	−0.861738	+	0.507354i	$0.830624\pi$
$984$	−2.81044	−	2.04190i	−0.0895934	−	0.0650934i
$985$		0			0
$986$	0.0554457	−	0.0402837i	0.00176575	−	0.00128289i
$987$	−26.8867	−	19.5343i	−0.855812	−	0.621784i
$988$	10.0574	+	7.30713i	0.319969	+	0.232471i
$989$	−1.94464	+	1.41286i	−0.0618359	+	0.0449264i
$990$		0			0
$991$	−25.1120	−	18.2449i	−0.797709	−	0.579570i	0.112532	−	0.993648i	$-0.464104\pi$
$991$	−25.1120	−	18.2449i	−0.797709	−	0.579570i	−0.910241	+	0.414079i	$0.864104\pi$
$992$	1.72466	+	5.30795i	0.0547579	+	0.168527i
$993$	−23.1184			−0.733639
$994$	−7.81199	−	24.0428i	−0.247781	−	0.762592i
$995$		0			0
$996$	7.18540	−	22.1144i	0.227678	−	0.700721i
$997$	−0.478723	+	1.47336i	−0.0151613	+	0.0466617i	−0.958351	−	0.285593i	$-0.907809\pi$
$997$	−0.478723	+	1.47336i	−0.0151613	+	0.0466617i	0.943190	+	0.332255i	$0.107809\pi$
$998$	−31.5952	+	22.9553i	−1.00013	+	0.726637i
$999$	9.17813			0.290383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.d.d.51.2		8
5.2	odd	4		250.2.e.c.199.3		16
5.3	odd	4		250.2.e.c.199.2		16
5.4	even	2		50.2.d.b.11.1	✓	8
15.14	odd	2		450.2.h.e.361.2		8
20.19	odd	2		400.2.u.d.161.2		8
25.3	odd	20		1250.2.b.e.1249.8		8
25.4	even	10		1250.2.a.l.1.1		4
25.9	even	10		50.2.d.b.41.1	yes	8
25.12	odd	20		250.2.e.c.49.2		16
25.13	odd	20		250.2.e.c.49.3		16
25.16	even	5	inner	250.2.d.d.201.2		8
25.21	even	5		1250.2.a.f.1.4		4
25.22	odd	20		1250.2.b.e.1249.1		8
75.59	odd	10		450.2.h.e.91.2		8
100.59	odd	10		400.2.u.d.241.2		8
100.71	odd	10		10000.2.a.x.1.1		4
100.79	odd	10		10000.2.a.t.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.1	✓	8	5.4	even	2
50.2.d.b.41.1	yes	8	25.9	even	10
250.2.d.d.51.2		8	1.1	even	1	trivial
250.2.d.d.201.2		8	25.16	even	5	inner
250.2.e.c.49.2		16	25.12	odd	20
250.2.e.c.49.3		16	25.13	odd	20
250.2.e.c.199.2		16	5.3	odd	4
250.2.e.c.199.3		16	5.2	odd	4
400.2.u.d.161.2		8	20.19	odd	2
400.2.u.d.241.2		8	100.59	odd	10
450.2.h.e.91.2		8	75.59	odd	10
450.2.h.e.361.2		8	15.14	odd	2
1250.2.a.f.1.4		4	25.21	even	5
1250.2.a.l.1.1		4	25.4	even	10
1250.2.b.e.1249.1		8	25.22	odd	20
1250.2.b.e.1249.8		8	25.3	odd	20
10000.2.a.t.1.4		4	100.79	odd	10
10000.2.a.x.1.1		4	100.71	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.720859 - 2.21858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.720859 - 2.21858i) q^{6} -3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.97539 - 1.43521i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.720859 - 2.21858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.720859 - 2.21858i) q^{6} -3.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.97539 - 1.43521i) q^{9} +(3.05361 - 2.21858i) q^{11} +(-1.88723 - 1.37116i) q^{12} +(2.56969 + 1.86699i) q^{13} +(-3.05361 + 2.21858i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.430307 + 1.32435i) q^{17} -2.44172 q^{18} +(1.20945 + 3.72230i) q^{19} +(-2.72086 + 8.37394i) q^{21} +(1.16637 - 3.58973i) q^{22} +(0.720859 - 0.523735i) q^{23} -2.33275 q^{24} +3.17632 q^{26} +(1.05361 - 0.765491i) q^{27} +(-1.16637 + 3.58973i) q^{28} +(0.0152089 - 0.0468081i) q^{29} +(-1.72466 - 5.30795i) q^{31} -1.00000 q^{32} +(-2.72086 - 8.37394i) q^{33} +(1.12656 + 0.818492i) q^{34} +(-1.97539 + 1.43521i) q^{36} +(5.70152 + 4.14240i) q^{37} +(3.16637 + 2.30051i) q^{38} +(5.99445 - 4.35522i) q^{39} +(1.20477 + 0.875319i) q^{41} +(2.72086 + 8.37394i) q^{42} -2.69767 q^{43} +(-1.16637 - 3.58973i) q^{44} +(0.275344 - 0.847421i) q^{46} +(-1.16637 + 3.58973i) q^{47} +(-1.88723 + 1.37116i) q^{48} +7.24660 q^{49} +3.24836 q^{51} +(2.56969 - 1.86699i) q^{52} +(-3.58963 + 11.0477i) q^{53} +(0.402443 - 1.23859i) q^{54} +(1.16637 + 3.58973i) q^{56} +9.13004 q^{57} +(-0.0152089 - 0.0468081i) q^{58} +(0.558282 + 0.405615i) q^{59} +(-8.38168 + 6.08965i) q^{61} +(-4.51521 - 3.28049i) q^{62} +(7.45605 + 5.41714i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-7.12330 - 5.17538i) q^{66} +(-4.73519 - 14.5734i) q^{67} +1.39250 q^{68} +(-0.642308 - 1.97682i) q^{69} +(-2.06969 + 6.36986i) q^{71} +(-0.754532 + 2.32221i) q^{72} +(4.18158 - 3.03810i) q^{73} +7.04746 q^{74} +3.91385 q^{76} +(-11.5257 + 8.37394i) q^{77} +(2.28968 - 7.04690i) q^{78} +(-0.558282 + 1.71821i) q^{79} +(-3.20239 - 9.85596i) q^{81} +1.48918 q^{82} +(3.08023 + 9.47997i) q^{83} +(7.12330 + 5.17538i) q^{84} +(-2.18246 + 1.58565i) q^{86} +(-0.0928839 - 0.0674841i) q^{87} +(-3.05361 - 2.21858i) q^{88} +(-11.7390 + 8.52891i) q^{89} +(-9.69922 - 7.04690i) q^{91} +(-0.275344 - 0.847421i) q^{92} -13.0193 q^{93} +(1.16637 + 3.58973i) q^{94} +(-0.720859 + 2.21858i) q^{96} +(0.0278640 - 0.0857567i) q^{97} +(5.86263 - 4.25945i) q^{98} -9.21619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 + 2 * q^8 - q^9	\( 8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{11} - 2 q^{12} + 13 q^{13} - q^{14} - 2 q^{16} + 11 q^{17} - 14 q^{18} + 20 q^{19} - 19 q^{21} - q^{22} + 3 q^{23} + 2 q^{24} + 22 q^{26} - 15 q^{27} + q^{28} - 15 q^{29} - 9 q^{31} - 8 q^{32} - 19 q^{33} - q^{34} - q^{36} + 6 q^{37} + 15 q^{38} - 12 q^{39} - 9 q^{41} + 19 q^{42} - 12 q^{43} + q^{44} + 7 q^{46} + q^{47} - 2 q^{48} - 4 q^{49} + 26 q^{51} + 13 q^{52} - 7 q^{53} - 25 q^{54} - q^{56} + 15 q^{58} + 10 q^{59} + 6 q^{61} - 21 q^{62} + 8 q^{63} - 2 q^{64} - 26 q^{66} + 11 q^{67} - 24 q^{68} + 43 q^{69} - 9 q^{71} + 6 q^{72} + 8 q^{73} + 24 q^{74} - 10 q^{76} - 33 q^{77} - 23 q^{78} - 10 q^{79} - 17 q^{81} - 26 q^{82} - 27 q^{83} + 26 q^{84} - 23 q^{86} - q^{88} - 15 q^{89} + q^{91} - 7 q^{92} + 46 q^{93} - q^{94} - 3 q^{96} + 36 q^{97} + 19 q^{98} - 42 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - 3 * q^6 - 4 * q^7 + 2 * q^8 - q^9 + q^11 - 2 * q^12 + 13 * q^13 - q^14 - 2 * q^16 + 11 * q^17 - 14 * q^18 + 20 * q^19 - 19 * q^21 - q^22 + 3 * q^23 + 2 * q^24 + 22 * q^26 - 15 * q^27 + q^28 - 15 * q^29 - 9 * q^31 - 8 * q^32 - 19 * q^33 - q^34 - q^36 + 6 * q^37 + 15 * q^38 - 12 * q^39 - 9 * q^41 + 19 * q^42 - 12 * q^43 + q^44 + 7 * q^46 + q^47 - 2 * q^48 - 4 * q^49 + 26 * q^51 + 13 * q^52 - 7 * q^53 - 25 * q^54 - q^56 + 15 * q^58 + 10 * q^59 + 6 * q^61 - 21 * q^62 + 8 * q^63 - 2 * q^64 - 26 * q^66 + 11 * q^67 - 24 * q^68 + 43 * q^69 - 9 * q^71 + 6 * q^72 + 8 * q^73 + 24 * q^74 - 10 * q^76 - 33 * q^77 - 23 * q^78 - 10 * q^79 - 17 * q^81 - 26 * q^82 - 27 * q^83 + 26 * q^84 - 23 * q^86 - q^88 - 15 * q^89 + q^91 - 7 * q^92 + 46 * q^93 - q^94 - 3 * q^96 + 36 * q^97 + 19 * q^98 - 42 * q^99

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