LMFDB - Embedded newform 50.2.d.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,2,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, 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("50.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, 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:	$0.399252010106$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.1
Root			$1.66637 + 0.917186i$ of defining polynomial
Character	$\chi$	$=$	50.11
Dual form			50.2.d.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.720859 + 2.21858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.02373 + 0.951057i) q^{5} +(-0.720859 - 2.21858i) q^{6} +3.77447 q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.97539 - 1.43521i) q^{9} +(1.07822 - 1.95894i) q^{10} +(3.05361 - 2.21858i) q^{11} +(1.88723 + 1.37116i) q^{12} +(-2.56969 - 1.86699i) q^{13} +(-3.05361 + 2.21858i) q^{14} +(-0.651166 - 5.17538i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.430307 - 1.32435i) q^{17} +2.44172 q^{18} +(1.20945 + 3.72230i) q^{19} +(0.279141 + 2.21858i) q^{20} +(-2.72086 + 8.37394i) q^{21} +(-1.16637 + 3.58973i) q^{22} +(-0.720859 + 0.523735i) q^{23} -2.33275 q^{24} +(3.19098 - 3.84937i) q^{25} +3.17632 q^{26} +(-1.05361 + 0.765491i) q^{27} +(1.16637 - 3.58973i) q^{28} +(0.0152089 - 0.0468081i) q^{29} +(3.56882 + 3.80423i) q^{30} +(-1.72466 - 5.30795i) q^{31} +1.00000 q^{32} +(2.72086 + 8.37394i) q^{33} +(1.12656 + 0.818492i) q^{34} +(-7.63851 + 3.58973i) q^{35} +(-1.97539 + 1.43521i) q^{36} +(-5.70152 - 4.14240i) q^{37} +(-3.16637 - 2.30051i) q^{38} +(5.99445 - 4.35522i) q^{39} +(-1.52988 - 1.63079i) q^{40} +(1.20477 + 0.875319i) q^{41} +(-2.72086 - 8.37394i) q^{42} +2.69767 q^{43} +(-1.16637 - 3.58973i) q^{44} +(5.36263 + 1.02576i) q^{45} +(0.275344 - 0.847421i) q^{46} +(1.16637 - 3.58973i) q^{47} +(1.88723 - 1.37116i) q^{48} +7.24660 q^{49} +(-0.318958 + 4.98982i) q^{50} +3.24836 q^{51} +(-2.56969 + 1.86699i) q^{52} +(3.58963 - 11.0477i) q^{53} +(0.402443 - 1.23859i) q^{54} +(-4.06969 + 7.39396i) q^{55} +(1.16637 + 3.58973i) q^{56} -9.13004 q^{57} +(0.0152089 + 0.0468081i) q^{58} +(0.558282 + 0.405615i) q^{59} +(-5.12330 - 0.979986i) q^{60} +(-8.38168 + 6.08965i) q^{61} +(4.51521 + 3.28049i) q^{62} +(-7.45605 - 5.41714i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(6.97599 + 1.33437i) q^{65} +(-7.12330 - 5.17538i) q^{66} +(4.73519 + 14.5734i) q^{67} -1.39250 q^{68} +(-0.642308 - 1.97682i) q^{69} +(4.06969 - 7.39396i) q^{70} +(-2.06969 + 6.36986i) q^{71} +(0.754532 - 2.32221i) q^{72} +(-4.18158 + 3.03810i) q^{73} +7.04746 q^{74} +(6.23987 + 9.85429i) q^{75} +3.91385 q^{76} +(11.5257 - 8.37394i) q^{77} +(-2.28968 + 7.04690i) q^{78} +(-0.558282 + 1.71821i) q^{79} +(2.19625 + 0.420099i) q^{80} +(-3.20239 - 9.85596i) q^{81} -1.48918 q^{82} +(-3.08023 - 9.47997i) q^{83} +(7.12330 + 5.17538i) q^{84} +(2.13035 + 2.27088i) q^{85} +(-2.18246 + 1.58565i) q^{86} +(0.0928839 + 0.0674841i) q^{87} +(3.05361 + 2.21858i) q^{88} +(-11.7390 + 8.52891i) q^{89} +(-4.94138 + 2.32221i) q^{90} +(-9.69922 - 7.04690i) q^{91} +(0.275344 + 0.847421i) q^{92} +13.0193 q^{93} +(1.16637 + 3.58973i) q^{94} +(-5.98771 - 6.38268i) q^{95} +(-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} + q^{11} + 2 q^{12} - 13 q^{13} - q^{14} - 10 q^{15} - 2 q^{16} - 11 q^{17} + 14 q^{18} + 20 q^{19} + 5 q^{20} - 19 q^{21} + q^{22}+ \cdots - 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 - 10 * q^15 - 2 * q^16 - 11 * q^17 + 14 * q^18 + 20 * q^19 + 5 * q^20 - 19 * q^21 + q^22 - 3 * q^23 + 2 * q^24 + 30 * q^25 + 22 * q^26 + 15 * q^27 - q^28 - 15 * q^29 - 10 * q^30 - 9 * q^31 + 8 * q^32 + 19 * q^33 - q^34 - 15 * q^35 - q^36 - 6 * q^37 - 15 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 - 19 * q^42 + 12 * q^43 + q^44 + 15 * q^45 + 7 * q^46 - q^47 + 2 * q^48 - 4 * q^49 - 5 * q^50 + 26 * q^51 - 13 * q^52 + 7 * q^53 - 25 * q^54 - 25 * q^55 - q^56 - 15 * q^58 + 10 * q^59 - 10 * q^60 + 6 * q^61 + 21 * q^62 - 8 * q^63 - 2 * q^64 - 10 * q^65 - 26 * q^66 - 11 * q^67 + 24 * q^68 + 43 * q^69 + 25 * q^70 - 9 * q^71 - 6 * q^72 - 8 * q^73 + 24 * q^74 + 30 * q^75 - 10 * q^76 + 33 * q^77 + 23 * q^78 - 10 * q^79 - 17 * q^81 + 26 * q^82 + 27 * q^83 + 26 * q^84 + 5 * q^85 - 23 * q^86 + q^88 - 15 * q^89 + 20 * q^90 + q^91 + 7 * q^92 - 46 * q^93 - q^94 - 30 * q^95 - 3 * q^96 - 36 * q^97 - 19 * q^98 - 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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	$0.335170\pi$
$3$	−0.720859	+	2.21858i	−0.416188	+	1.28090i	−0.911184	+	0.412000i	$0.864830\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.02373	+	0.951057i	−0.905040	+	0.425325i
$5$	−2.02373	+	0.951057i	−0.905040	+	0.425325i
$6$	−0.720859	−	2.21858i	−0.294289	−	0.905730i
$7$	3.77447			1.42661			0.713307	−	0.700851i	$-0.247196\pi$
$7$	3.77447			1.42661			0.713307	+	0.700851i	$0.247196\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.97539	−	1.43521i	−0.658464	−	0.478402i
$10$	1.07822	−	1.95894i	0.340962	−	0.619471i
$11$	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	0.171340	−	0.985212i	$-0.445190\pi$
$13$	−2.56969	−	1.86699i	−0.712705	−	0.517810i	−0.884045	+	0.467402i	$0.845190\pi$
$14$	−3.05361	+	2.21858i	−0.816111	+	0.592939i
$15$	−0.651166	−	5.17538i	−0.168130	−	1.33628i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.430307	−	1.32435i	−0.104365	−	0.321201i	0.885216	−	0.465180i	$-0.154010\pi$
$17$	−0.430307	−	1.32435i	−0.104365	−	0.321201i	−0.989581	+	0.143979i	$0.954010\pi$
$18$	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	$0.751798\pi$
$20$	0.279141	+	2.21858i	0.0624178	+	0.496089i
$21$	−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	−0.660398	−	0.750916i	$-0.729613\pi$
$23$	−0.720859	+	0.523735i	−0.150310	+	0.109206i	0.510089	+	0.860122i	$0.329613\pi$
$24$	−2.33275			−0.476170
$25$	3.19098	−	3.84937i	0.638197	−	0.769873i
$26$	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	$0.0985454\pi$
$30$	3.56882	+	3.80423i	0.651574	+	0.694553i
$31$	−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
$35$	−7.63851	+	3.58973i	−1.29114	+	0.606775i
$36$	−1.97539	+	1.43521i	−0.329232	+	0.239201i
$37$	−5.70152	−	4.14240i	−0.937324	−	0.681006i	0.0104512	−	0.999945i	$-0.496673\pi$
$37$	−5.70152	−	4.14240i	−0.937324	−	0.681006i	−0.947775	+	0.318940i	$0.896673\pi$
$38$	−3.16637	−	2.30051i	−0.513654	−	0.373191i
$39$	5.99445	−	4.35522i	0.959880	−	0.697394i
$40$	−1.52988	−	1.63079i	−0.241895	−	0.257851i
$41$	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	$-0.434054\pi$
$43$	2.69767			0.411391			0.205695	+	0.978616i	$0.434054\pi$
$44$	−1.16637	−	3.58973i	−0.175838	−	0.541172i
$45$	5.36263	+	1.02576i	0.799413	+	0.152912i
$46$	0.275344	−	0.847421i	0.0405972	−	0.124945i
$47$	1.16637	−	3.58973i	0.170133	−	0.523616i	−0.829245	−	0.558886i	$-0.811229\pi$
$47$	1.16637	−	3.58973i	0.170133	−	0.523616i	0.999378	+	0.0352696i	$0.0112290\pi$
$48$	1.88723	−	1.37116i	0.272399	−	0.197909i
$49$	7.24660			1.03523
$50$	−0.318958	+	4.98982i	−0.0451075	+	0.705667i
$51$	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	$-0.605992\pi$
$53$	3.58963	−	11.0477i	0.493073	−	1.51752i	0.819938	−	0.572453i	$-0.194008\pi$
$54$	0.402443	−	1.23859i	0.0547655	−	0.168551i
$55$	−4.06969	+	7.39396i	−0.548757	+	0.997001i
$56$	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	$0.685697\pi$
$60$	−5.12330	−	0.979986i	−0.661415	−	0.126516i
$61$	−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
$65$	6.97599	+	1.33437i	0.865265	+	0.165508i
$66$	−7.12330	−	5.17538i	−0.876818	−	0.637045i
$67$	4.73519	+	14.5734i	0.578496	+	1.78043i	0.623955	+	0.781461i	$0.285525\pi$
$67$	4.73519	+	14.5734i	0.578496	+	1.78043i	−0.0454589	+	0.998966i	$0.514475\pi$
$68$	−1.39250			−0.168866
$69$	−0.642308	−	1.97682i	−0.0773248	−	0.237981i
$70$	4.06969	−	7.39396i	0.486421	−	0.883747i
$71$	−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	−0.804960	−	0.593329i	$-0.797813\pi$
$73$	−4.18158	+	3.03810i	−0.489417	+	0.355582i	0.315543	+	0.948911i	$0.397813\pi$
$74$	7.04746			0.819251
$75$	6.23987	+	9.85429i	0.720518	+	1.13788i
$76$	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	$0.132406\pi$
$80$	2.19625	+	0.420099i	0.245548	+	0.0469685i
$81$	−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	$-0.915749\pi$
$83$	−3.08023	−	9.47997i	−0.338099	−	1.04056i	0.627076	−	0.778958i	$-0.284251\pi$
$84$	7.12330	+	5.17538i	0.777216	+	0.564680i
$85$	2.13035	+	2.27088i	0.231069	+	0.246311i
$86$	−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	$0.579266\pi$
$90$	−4.94138	+	2.32221i	−0.520868	+	0.244783i
$91$	−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
$95$	−5.98771	−	6.38268i	−0.614326	−	0.654849i
$96$	−0.720859	+	2.21858i	−0.0735724	+	0.226432i
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	−0.952461	−	0.304660i	$-0.901457\pi$
$97$	−0.0278640	+	0.0857567i	−0.00282917	+	0.00870727i	0.949632	+	0.313367i	$0.101457\pi$
$98$	−5.86263	+	4.25945i	−0.592215	+	0.430269i
$99$	−9.21619			−0.926261
$100$	−2.67490	−	4.22433i	−0.267490	−	0.422433i
$101$	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	−0.967863	−	0.251477i	$-0.919084\pi$
$103$	−0.375822	+	1.15666i	−0.0370308	+	0.113969i	0.930832	+	0.365446i	$0.119084\pi$
$104$	0.981536	−	3.02086i	0.0962475	−	0.296219i
$105$	−2.45780	−	19.5343i	−0.239857	−	1.90635i
$106$	3.58963	+	11.0477i	0.348656	+	1.07305i
$107$	−10.8125			−1.04528			−0.522641	−	0.852553i	$-0.675053\pi$
$107$	−10.8125			−1.04528			−0.522641	+	0.852553i	$0.675053\pi$
$108$	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	$0.884114\pi$
$110$	−1.05361	−	8.37394i	−0.100458	−	0.798424i
$111$	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	0.908925	−	0.416960i	$-0.136904\pi$
$113$	8.43232	+	6.12644i	0.793246	+	0.576327i	−0.115679	+	0.993287i	$0.536904\pi$
$114$	7.38636	−	5.36650i	0.691796	−	0.502619i
$115$	0.960724	−	1.74548i	0.0895880	−	0.162767i
$116$	−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
$120$	4.72086	−	2.21858i	0.430954	−	0.202527i
$121$	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
$125$	−2.79673	+	10.8249i	−0.250147	+	0.968208i
$126$	9.21619			0.821043
$127$	2.87115	−	2.08601i	0.254773	−	0.185104i	−0.453066	−	0.891477i	$-0.649670\pi$
$127$	2.87115	−	2.08601i	0.254773	−	0.185104i	0.707840	+	0.706373i	$0.249670\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.94464	+	5.98498i	−0.171216	+	0.526948i
$130$	−6.42801	+	3.02086i	−0.563774	+	0.264947i
$131$	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
$135$	1.40420	−	2.55119i	0.120854	−	0.219571i
$136$	1.12656	−	0.818492i	0.0966015	−	0.0701851i
$137$	2.88636	+	2.09706i	0.246598	+	0.179164i	0.704218	−	0.709984i	$-0.251298\pi$
$137$	2.88636	+	2.09706i	0.246598	+	0.179164i	−0.457620	+	0.889148i	$0.651298\pi$
$138$	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	$0.161397\pi$
$140$	1.05361	+	8.37394i	0.0890461	+	0.707727i
$141$	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
$145$	0.0137385	+	0.109192i	0.00114092	+	0.00906786i
$146$	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	$0.794728\pi$
$150$	−10.8404	−	4.30459i	−0.885112	−	0.351468i
$151$	−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
$155$	8.53840	+	9.10162i	0.685821	+	0.731059i
$156$	−2.28968	−	7.04690i	−0.183321	−	0.564203i
$157$	10.1564			0.810572			0.405286	−	0.914190i	$-0.367172\pi$
$157$	10.1564			0.810572			0.405286	+	0.914190i	$0.367172\pi$
$158$	−0.558282	−	1.71821i	−0.0444145	−	0.136694i
$159$	21.9226	+	15.9277i	1.73858	+	1.26315i
$160$	−2.02373	+	0.951057i	−0.159990	+	0.0751876i
$161$	−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	0.992019	−	0.126086i	$-0.0402416\pi$
$163$	15.0481	+	10.9331i	1.17865	+	0.856343i	0.186636	+	0.982429i	$0.440242\pi$
$164$	1.20477	−	0.875319i	0.0940770	−	0.0683510i
$165$	−13.4704	−	14.3589i	−1.04867	−	1.11784i
$166$	8.06414	+	5.85894i	0.625899	+	0.454742i
$167$	0.671048	+	2.06527i	0.0519273	+	0.159816i	0.973657	−	0.228016i	$-0.0732240\pi$
$167$	0.671048	+	2.06527i	0.0519273	+	0.159816i	−0.921730	+	0.387832i	$0.873224\pi$
$168$	−8.80489			−0.679312
$169$	−0.899554	−	2.76854i	−0.0691965	−	0.212965i
$170$	−3.05828	−	0.584988i	−0.234560	−	0.0448666i
$171$	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	−0.373506	−	0.927628i	$-0.621845\pi$
$173$	5.17306	−	3.75845i	0.393300	−	0.285750i	0.766807	+	0.641878i	$0.221845\pi$
$174$	−0.114811			−0.00870378
$175$	12.0443	−	14.5293i	0.910461	−	1.09831i
$176$	−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	$0.00318759\pi$
$180$	2.63270	−	4.78318i	0.196230	−	0.356517i
$181$	−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
$185$	15.4780	+	2.96063i	1.13797	+	0.217670i
$186$	−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
$190$	8.59580	+	1.64421i	0.623605	+	0.119283i
$191$	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	$-0.717730\pi$
$193$	−17.5576			−1.26382			−0.631912	+	0.775040i	$0.717730\pi$
$194$	−0.0278640	−	0.0857567i	−0.00200052	−	0.00615697i
$195$	−7.98910	+	14.5149i	−0.572111	+	1.03943i
$196$	2.23932	−	6.89193i	0.159952	−	0.492281i
$197$	1.47012	−	4.52458i	0.104742	−	0.322363i	−0.884928	−	0.465728i	$-0.845792\pi$
$197$	1.47012	−	4.52458i	0.104742	−	0.322363i	0.989670	+	0.143365i	$0.0457924\pi$
$198$	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	$0.327765\pi$
$200$	4.64703	+	1.84529i	0.328595	+	0.130481i
$201$	−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
$205$	−3.27062	−	0.625604i	−0.228430	−	0.0436941i
$206$	−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
$210$	13.4704	+	14.3589i	0.929545	+	0.990860i
$211$	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
$215$	−5.45936	+	2.56564i	−0.372325	+	0.174975i
$216$	−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
$220$	5.77447	+	6.15537i	0.389315	+	0.414995i
$221$	−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	−0.705670	−	0.708540i	$-0.749354\pi$
$223$	−3.73139	+	2.71102i	−0.249873	+	0.181543i	0.455798	+	0.890083i	$0.349354\pi$
$224$	3.77447			0.252192
$225$	−11.8281	+	3.02429i	−0.788538	+	0.201619i
$226$	−10.4229			−0.693322
$227$	5.08578	−	3.69503i	0.337555	−	0.245248i	−0.406075	−	0.913840i	$-0.633103\pi$
$227$	5.08578	−	3.69503i	0.337555	−	0.245248i	0.743630	+	0.668592i	$0.233103\pi$
$228$	−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	$-0.0993163\pi$
$230$	0.248723	+	1.97682i	0.0164003	+	0.130348i
$231$	10.2698	+	31.6072i	0.675703	+	2.07960i
$232$	0.0492169			0.00323125
$233$	0.792338	+	2.43856i	0.0519078	+	0.159756i	0.973650	−	0.228047i	$-0.0732341\pi$
$233$	0.792338	+	2.43856i	0.0519078	+	0.159756i	−0.921742	+	0.387803i	$0.873234\pi$
$234$	−6.27447	−	4.55867i	−0.410175	−	0.298009i
$235$	1.05361	+	8.37394i	0.0687298	+	0.546256i
$236$	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	$0.398779\pi$
$240$	−2.51521	+	4.56972i	−0.162356	+	0.294974i
$241$	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
$245$	−14.6652	+	6.89193i	−0.936924	+	0.440309i
$246$	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
$250$	−4.10011	−	10.4014i	−0.259314	−	0.657842i
$251$	−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
$255$	−6.57380	+	3.08937i	−0.411667	+	0.193464i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−13.6286			−0.850127			−0.425063	−	0.905164i	$-0.639748\pi$
$257$	−13.6286			−0.850127			−0.425063	+	0.905164i	$0.639748\pi$
$258$	−1.94464	−	5.98498i	−0.121068	−	0.372609i
$259$	−21.5202	−	15.6353i	−1.33720	−	0.971533i
$260$	3.42476	−	6.22221i	0.212394	−	0.385885i
$261$	−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	0.792394	−	0.610010i	$-0.208834\pi$
$263$	7.41298	+	5.38584i	0.457104	+	0.332105i	−0.335290	+	0.942115i	$0.608834\pi$
$264$	−7.12330	+	5.17538i	−0.438409	+	0.318523i
$265$	3.24258	+	25.7716i	0.199190	+	1.58314i
$266$	−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	$0.572496\pi$
$270$	0.363534	+	2.88932i	0.0221240	+	0.175838i
$271$	−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
$275$	1.20390	−	18.8339i	0.0725977	−	1.13573i
$276$	−2.07855			−0.125114
$277$	−15.2006	+	11.0439i	−0.913318	+	0.663564i	−0.941852	−	0.336028i	$-0.890916\pi$
$277$	−15.2006	+	11.0439i	−0.913318	+	0.663564i	0.0285338	+	0.999593i	$0.490916\pi$
$278$	−3.07349	+	9.45923i	−0.184336	+	0.567327i
$279$	−4.21112	+	12.9605i	−0.252113	+	0.775925i
$280$	−5.77447	−	6.15537i	−0.345090	−	0.367854i
$281$	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	$-0.916945\pi$
$283$	−5.65496	−	17.4042i	−0.336153	−	1.03457i	0.629999	−	0.776596i	$-0.283055\pi$
$284$	5.41853	+	3.93679i	0.321530	+	0.233606i
$285$	18.4768	−	8.68318i	1.09447	−	0.514347i
$286$	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
$290$	−0.0752958	−	0.0802625i	−0.00442152	−	0.00471318i
$291$	−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	$-0.830584\pi$
$293$	−29.4990			−1.72335			−0.861675	+	0.507461i	$0.830584\pi$
$294$	−5.22378	−	16.0771i	−0.304657	−	0.937638i
$295$	−1.51558	−	0.289899i	−0.0882402	−	0.0168786i
$296$	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
$300$	11.3002	−	2.88932i	0.652418	−	0.166815i
$301$	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
$305$	11.1707	−	20.2953i	0.639631	−	1.16210i
$306$	−1.05069	−	3.23368i	−0.0600638	−	0.184857i
$307$	13.9131			0.794064			0.397032	−	0.917805i	$-0.370040\pi$
$307$	13.9131			0.794064			0.397032	+	0.917805i	$0.370040\pi$
$308$	−4.40244	−	13.5493i	−0.250852	−	0.772044i
$309$	−2.29523	−	1.66758i	−0.130571	−	0.0948653i
$310$	−12.2575	−	2.34462i	−0.696180	−	0.133165i
$311$	−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	0.349712	−	0.936857i	$-0.386279\pi$
$313$	−7.66454	−	5.56861i	−0.433225	−	0.314757i	−0.782937	+	0.622101i	$0.786279\pi$
$314$	−8.21673	+	5.96980i	−0.463697	+	0.336895i
$315$	20.2411	+	3.87171i	1.14045	+	0.218146i
$316$	1.46160	+	1.06192i	0.0822215	+	0.0597374i
$317$	7.57321	+	23.3079i	0.425354	+	1.30910i	0.902655	+	0.430365i	$0.141615\pi$
$317$	7.57321	+	23.3079i	0.425354	+	1.30910i	−0.477301	+	0.878740i	$0.658385\pi$
$318$	−27.0979			−1.51957
$319$	−0.0574054	−	0.176676i	−0.00321408	−	0.00989194i
$320$	1.07822	−	1.95894i	0.0602741	−	0.109508i
$321$	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
$325$	−15.3866	+	3.93416i	−0.853494	+	0.218228i
$326$	−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
$330$	19.3377	+	3.69892i	1.06451	+	0.203619i
$331$	−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
$335$	−23.4429	−	24.9893i	−1.28082	−	1.36531i
$336$	7.12330	−	5.17538i	0.388608	−	0.282340i
$337$	8.03812	+	5.84003i	0.437864	+	0.318127i	0.784786	−	0.619767i	$-0.212773\pi$
$337$	8.03812	+	5.84003i	0.437864	+	0.318127i	−0.346922	+	0.937894i	$0.612773\pi$
$338$	2.35506	+	1.71105i	0.128099	+	0.0930690i
$339$	−19.6705	+	14.2914i	−1.06835	+	0.776205i
$340$	2.81805	−	1.32435i	0.152830	−	0.0718228i
$341$	−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
$345$	3.17993	+	3.38968i	0.171201	+	0.182494i
$346$	−1.97593	+	6.08130i	−0.106227	+	0.326933i
$347$	−6.06757	+	18.6741i	−0.325724	+	1.00248i	0.645388	+	0.763855i	$0.276696\pi$
$347$	−6.06757	+	18.6741i	−0.325724	+	1.00248i	−0.971113	+	0.238622i	$0.923304\pi$
$348$	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	$0.487351\pi$
$350$	−1.20390	+	18.8339i	−0.0643510	+	1.00671i
$351$	4.13662			0.220796
$352$	3.05361	−	2.21858i	0.162758	−	0.118251i
$353$	3.17632	−	9.77569i	0.169058	−	0.520308i	−0.830254	−	0.557385i	$-0.811805\pi$
$353$	3.17632	−	9.77569i	0.169058	−	0.520308i	0.999312	+	0.0370772i	$0.0118048\pi$
$354$	0.497446	−	1.53098i	0.0264390	−	0.0813708i
$355$	−1.86959	−	14.8593i	−0.0992277	−	0.788649i
$356$	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	$0.611746\pi$
$360$	0.681583	+	5.41714i	0.0359226	+	0.285508i
$361$	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
$365$	5.57300	−	10.1252i	0.291704	−	0.529978i
$366$	19.5524	+	14.2056i	1.02202	+	0.742540i
$367$	8.05741	+	24.7981i	0.420593	+	1.29445i	0.907151	+	0.420804i	$0.138252\pi$
$367$	8.05741	+	24.7981i	0.420593	+	1.29445i	−0.486558	+	0.873648i	$0.661748\pi$
$368$	0.891031			0.0464482
$369$	−1.12364	−	3.45820i	−0.0584942	−	0.180027i
$370$	−14.2622	+	6.70254i	−0.741455	+	0.348448i
$371$	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	−0.767952	−	0.640508i	$-0.778724\pi$
$373$	−7.65001	+	5.55806i	−0.396102	+	0.287785i	0.371849	+	0.928293i	$0.378724\pi$
$374$	5.25595			0.271779
$375$	−21.9998	−	14.0080i	−1.13606	−	0.723369i
$376$	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	$0.738154\pi$
$380$	−7.92059	+	3.72230i	−0.406318	+	0.190950i
$381$	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	$0.175683\pi$
$383$	9.21407	+	28.3580i	0.470817	+	1.44902i	−0.380700	+	0.924698i	$0.624317\pi$
$384$	1.88723	+	1.37116i	0.0963075	+	0.0699715i
$385$	−15.3609	+	27.9083i	−0.782865	+	1.42234i
$386$	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	$0.117697\pi$
$390$	−2.06831	−	16.4386i	−0.104733	−	0.832403i
$391$	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
$395$	−0.504306	−	4.00816i	−0.0253744	−	0.201673i
$396$	−2.84796	+	8.76511i	−0.143115	+	0.440464i
$397$	6.49555	−	19.9913i	0.326002	−	1.00333i	−0.644984	−	0.764196i	$-0.723136\pi$
$397$	6.49555	−	19.9913i	0.326002	−	1.00333i	0.970986	−	0.239136i	$-0.0768642\pi$
$398$	−11.7566	+	8.54169i	−0.589307	+	0.428156i
$399$	−34.4610			−1.72521
$400$	−4.84416	+	1.23859i	−0.242208	+	0.0619295i
$401$	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
$405$	15.8544	+	16.9002i	0.787810	+	0.839776i
$406$	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	$-0.655677\pi$
$410$	3.01371	−	1.41630i	0.148836	−	0.0699459i
$411$	−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
$415$	15.2495	+	16.2554i	0.748571	+	0.797948i
$416$	−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	$-0.419608\pi$
$420$	−19.3377	−	3.69892i	−0.943585	−	0.180489i
$421$	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
$425$	−6.47100	−	2.56956i	−0.313890	−	0.124642i
$426$	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
$430$	2.90867	−	5.28457i	0.140269	−	0.254845i
$431$	−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	$-0.955617\pi$
$433$	−5.63542	−	17.3440i	−0.270821	−	0.833501i	0.719474	−	0.694519i	$-0.244383\pi$
$434$	17.0425	+	12.3821i	0.818067	+	0.594360i
$435$	−0.252153	−	0.0482319i	−0.0120898	−	0.00231254i
$436$	−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	$0.0818259\pi$
$440$	−8.28968	−	1.58565i	−0.395195	−	0.0755929i
$441$	−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	$-0.180217\pi$
$443$	35.5267			1.68793			0.843963	+	0.536401i	$0.180217\pi$
$444$	−5.08023	−	15.6353i	−0.241097	−	0.742020i
$445$	15.6452	−	28.4247i	0.741653	−	1.34746i
$446$	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	$0.375274\pi$
$450$	7.79148	−	9.39907i	0.367294	−	0.443076i
$451$	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
$455$	26.3306	+	5.03652i	1.23440	+	0.236116i
$456$	−2.82134	−	8.68318i	−0.132121	−	0.406627i
$457$	23.7205			1.10960			0.554799	−	0.831984i	$-0.312795\pi$
$457$	23.7205			1.10960			0.554799	+	0.831984i	$0.312795\pi$
$458$	5.48103	+	16.8689i	0.256112	+	0.788230i
$459$	1.46715	+	1.06595i	0.0684807	+	0.0497542i
$460$	−1.36317	−	1.45309i	−0.0635580	−	0.0677504i
$461$	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	0.258802	−	0.965930i	$-0.416672\pi$
$463$	−12.4775	−	9.06543i	−0.579878	−	0.421306i	−0.838680	+	0.544624i	$0.816672\pi$
$464$	−0.0398173	+	0.0289290i	−0.00184847	+	0.00134299i
$465$	−26.3476	+	12.3821i	−1.22184	+	0.574206i
$466$	−2.07437	−	1.50712i	−0.0960932	−	0.0698158i
$467$	−5.26481	−	16.2034i	−0.243626	−	0.749805i	−0.995859	−	0.0909075i	$-0.971023\pi$
$467$	−5.26481	−	16.2034i	−0.243626	−	0.749805i	0.752233	−	0.658897i	$-0.228977\pi$
$468$	7.75567			0.358506
$469$	17.8728	+	55.0069i	0.825290	+	2.53998i
$470$	−5.77447	−	6.15537i	−0.266356	−	0.283926i
$471$	−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
$475$	18.1878	+	7.22218i	0.834514	+	0.331376i
$476$	−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	$0.905640\pi$
$480$	−0.651166	−	5.17538i	−0.0297215	−	0.236223i
$481$	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
$485$	−0.0251701	−	0.200049i	−0.00114292	−	0.00908375i
$486$	−16.3969	+	11.9130i	−0.743778	+	0.540386i
$487$	11.0735	+	8.04536i	0.501788	+	0.364570i	0.809699	−	0.586845i	$-0.199630\pi$
$487$	11.0735	+	8.04536i	0.501788	+	0.364570i	−0.307912	+	0.951415i	$0.599630\pi$
$488$	−8.38168	−	6.08965i	−0.379421	−	0.275665i
$489$	−35.1033	+	25.5041i	−1.58743	+	1.15333i
$490$	7.81341	−	14.1957i	0.352974	−	0.641295i
$491$	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
$495$	18.6511	−	8.76511i	0.838304	−	0.393963i
$496$	−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	$0.838578\pi$
$500$	9.43085	+	6.00492i	0.421760	+	0.268548i
$501$	−5.06570			−0.226319
$502$	4.86025	−	3.53118i	0.216923	−	0.157604i
$503$	3.69387	−	11.3686i	0.164702	−	0.506899i	−0.834313	−	0.551292i	$-0.814135\pi$
$503$	3.69387	−	11.3686i	0.164702	−	0.506899i	0.999014	+	0.0443923i	$0.0141352\pi$
$504$	2.84796	−	8.76511i	0.126858	−	0.390429i
$505$	−33.1456	+	15.5768i	−1.47496	+	0.693160i
$506$	−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	$0.665555\pi$
$510$	3.50243	−	6.36334i	0.155090	−	0.281773i
$511$	−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
$515$	−0.339487	−	2.69820i	−0.0149596	−	0.118897i
$516$	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
$520$	0.886640	+	7.04690i	0.0388817	+	0.309027i
$521$	−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	−0.148795	−	0.988868i	$-0.547540\pi$
$523$	17.0534	−	12.3900i	0.745694	−	0.541778i	0.894489	+	0.447090i	$0.147540\pi$
$524$	4.05324			0.177067
$525$	23.5522	+	37.1947i	1.02790	+	1.62331i
$526$	−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
$530$	−17.7715	−	18.9437i	−0.771943	−	0.822863i
$531$	−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
$535$	21.8816	−	10.2833i	0.946022	−	0.444585i
$536$	−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
$540$	−1.99241	−	2.12383i	−0.0857395	−	0.0913951i
$541$	−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
$545$	25.0709	+	4.79557i	1.07392	+	0.205419i
$546$	−8.64231	+	26.5983i	−0.369857	+	1.13830i
$547$	−1.69044	+	5.20264i	−0.0722781	+	0.222449i	−0.980669	−	0.195672i	$-0.937311\pi$
$547$	−1.69044	+	5.20264i	−0.0722781	+	0.222449i	0.908391	+	0.418121i	$0.137311\pi$
$548$	2.88636	−	2.09706i	0.123299	−	0.0895820i
$549$	25.2970			1.07965
$550$	10.0963	+	15.9446i	0.430508	+	0.679879i
$551$	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
$555$	−17.7258	+	32.2049i	−0.752420	+	1.36702i
$556$	−3.07349	−	9.45923i	−0.130345	−	0.401161i
$557$	−5.19840			−0.220263			−0.110132	−	0.993917i	$-0.535127\pi$
$557$	−5.19840			−0.220263			−0.110132	+	0.993917i	$0.535127\pi$
$558$	−4.21112	−	12.9605i	−0.178271	−	0.548662i
$559$	−6.93218	−	5.03652i	−0.293200	−	0.213022i
$560$	8.28968	+	1.58565i	0.350303	+	0.0670059i
$561$	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	0.669993	−	0.742367i	$-0.266297\pi$
$563$	4.05741	+	2.94788i	0.170999	+	0.124238i	−0.498994	+	0.866605i	$0.666297\pi$
$564$	7.12330	−	5.17538i	0.299945	−	0.217923i
$565$	−22.8913	−	4.37866i	−0.963046	−	0.184212i
$566$	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	$-0.440511\pi$
$570$	−9.84416	+	17.8852i	−0.412327	+	0.749129i
$571$	−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
$575$	−0.284202	+	4.44608i	−0.0118520	+	0.185414i
$576$	2.44172			0.101738
$577$	20.3401	−	14.7779i	0.846769	−	0.615213i	−0.0774845	−	0.996994i	$-0.524689\pi$
$577$	20.3401	−	14.7779i	0.846769	−	0.615213i	0.924253	+	0.381780i	$0.124689\pi$
$578$	−4.65409	+	14.3238i	−0.193584	+	0.595792i
$579$	12.6566	−	38.9529i	0.525989	−	1.61883i
$580$	0.108093	+	0.0206760i	0.00448831	+	0.000858524i
$581$	−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
$585$	−11.8652	−	12.6479i	−0.490566	−	0.522925i
$586$	23.8652	−	17.3391i	0.985861	−	0.716270i
$587$	−17.2770	−	12.5525i	−0.713099	−	0.518097i	0.171073	−	0.985258i	$-0.445277\pi$
$587$	−17.2770	−	12.5525i	−0.713099	−	0.518097i	−0.884172	+	0.467162i	$0.845277\pi$
$588$	13.6760	+	9.93622i	0.563990	+	0.409763i
$589$	17.6719	−	12.8394i	0.728157	−	0.529037i
$590$	1.39653	−	0.656300i	0.0574940	−	0.0270194i
$591$	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	$-0.740928\pi$
$593$	−33.4430			−1.37334			−0.686669	+	0.726970i	$0.740928\pi$
$594$	−1.51901	−	4.67502i	−0.0623256	−	0.191818i
$595$	8.04095	+	8.57136i	0.329647	+	0.351391i
$596$	−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	$0.319312\pi$
$600$	−7.44376	+	8.97961i	−0.303890	+	0.366591i
$601$	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
$605$	0.906260	+	7.20284i	0.0368447	+	0.292837i
$606$	−11.8066	−	36.3369i	−0.479609	−	1.47608i
$607$	9.32822			0.378621			0.189310	−	0.981917i	$-0.439375\pi$
$607$	9.32822			0.378621			0.189310	+	0.981917i	$0.439375\pi$
$608$	1.20945	+	3.72230i	0.0490496	+	0.150959i
$609$	0.350587	+	0.254716i	0.0142065	+	0.0103216i
$610$	2.89199	+	22.9852i	0.117093	+	0.930643i
$611$	−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	0.972025	−	0.234878i	$-0.0754690\pi$
$613$	25.9724	+	18.8700i	1.04902	+	0.762154i	0.0769902	+	0.997032i	$0.475469\pi$
$614$	−11.2560	+	8.17793i	−0.454253	+	0.330034i
$615$	3.74560	−	6.80514i	0.151037	−	0.274410i
$616$	11.5257	+	8.37394i	0.464385	+	0.337396i
$617$	−9.86557	−	30.3631i	−0.397173	−	1.22237i	−0.927257	−	0.374427i	$-0.877840\pi$
$617$	−9.86557	−	30.3631i	−0.397173	−	1.22237i	0.530084	−	0.847945i	$-0.322160\pi$
$618$	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	$0.929109\pi$
$620$	11.2947	−	5.30795i	0.453605	−	0.213172i
$621$	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
$625$	−4.63525	−	24.5665i	−0.185410	−	0.982661i
$626$	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
$630$	−18.6511	+	8.76511i	−0.743077	+	0.349210i
$631$	−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
$635$	−3.82652	+	6.95215i	−0.151851	+	0.275888i
$636$	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
$640$	0.279141	+	2.21858i	0.0110340	+	0.0876969i
$641$	−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	$-0.312124\pi$
$643$	28.2255			1.11311			0.556553	+	0.830812i	$0.312124\pi$
$644$	1.03928	+	3.19856i	0.0409532	+	0.126041i
$645$	−1.75663	−	13.9615i	−0.0691672	−	0.549732i
$646$	−1.68416	+	5.18330i	−0.0662623	+	0.203934i
$647$	0.394848	−	1.21522i	0.0155231	−	0.0477751i	−0.942995	−	0.332807i	$-0.892004\pi$
$647$	0.394848	−	1.21522i	0.0155231	−	0.0477751i	0.958518	+	0.285032i	$0.0920042\pi$
$648$	8.38398	−	6.09132i	0.329354	−	0.239290i
$649$	2.60466			0.102242
$650$	10.1356	−	12.2268i	0.397550	−	0.479575i
$651$	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	$0.280191\pi$
$653$	−8.47040	+	26.0692i	−0.331472	+	1.02017i	−0.968434	+	0.249272i	$0.919809\pi$
$654$	−8.22884	+	25.3258i	−0.321773	+	0.990316i
$655$	−6.20096	−	6.60999i	−0.242291	−	0.258274i
$656$	−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	$0.403241\pi$
$660$	−17.8187	+	8.37394i	−0.693593	+	0.325955i
$661$	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
$665$	−22.6004	−	24.0912i	−0.876407	−	0.934217i
$666$	−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
$670$	33.6540	+	6.43735i	1.30017	+	0.248696i
$671$	−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	−0.457103	−	0.889414i	$-0.651113\pi$
$673$	6.42142	−	4.66543i	0.247527	−	0.179839i	0.704630	+	0.709575i	$0.251113\pi$
$674$	−9.93566			−0.382707
$675$	−0.415389	+	6.49839i	−0.0159883	+	0.250123i
$676$	−2.91102			−0.111962
$677$	−23.8667	+	17.3402i	−0.917271	+	0.666436i	−0.942843	−	0.333237i	$-0.891859\pi$
$677$	−23.8667	+	17.3402i	−0.917271	+	0.666436i	0.0255722	+	0.999673i	$0.491859\pi$
$678$	7.51346	−	23.1240i	0.288553	−	0.888073i
$679$	−0.105172	+	0.323686i	−0.00403613	+	0.0124219i
$680$	−1.50142	+	2.72783i	−0.0575768	+	0.104607i
$681$	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	$0.156873\pi$
$683$	11.6650	+	35.9012i	0.446349	+	1.37372i	−0.434648	+	0.900600i	$0.643127\pi$
$684$	−7.73139	−	5.61719i	−0.295617	−	0.214779i
$685$	−7.83564	−	1.49880i	−0.299384	−	0.0572663i
$686$	−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
$690$	−4.56502	−	0.873197i	−0.173787	−	0.0332421i
$691$	−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
$695$	−10.7240	+	19.4837i	−0.406783	+	0.739058i
$696$	−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
$700$	−10.0963	−	15.9446i	−0.381605	−	0.602648i
$701$	−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
$705$	−19.3377	−	3.69892i	−0.728301	−	0.139310i
$706$	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	$0.519333\pi$
$710$	10.2466	+	10.9225i	0.384548	+	0.409914i
$711$	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
$715$	24.2623	−	11.4021i	0.907359	−	0.426415i
$716$	−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	$0.949147\pi$
$720$	−3.73553	−	3.98193i	−0.139215	−	0.148398i
$721$	−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
$725$	−0.131650	−	0.207908i	−0.00488937	−	0.00772152i
$726$	−7.57351			−0.281079
$727$	1.71013	−	1.24248i	0.0634251	−	0.0460810i	−0.555621	−	0.831436i	$-0.687519\pi$
$727$	1.71013	−	1.24248i	0.0634251	−	0.0460810i	0.619046	+	0.785355i	$0.287519\pi$
$728$	3.70477	−	11.4021i	0.137308	−	0.422591i
$729$	−5.00295	+	15.3975i	−0.185295	+	0.570278i
$730$	1.44280	+	11.4672i	0.0534005	+	0.424420i
$731$	−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	$0.213910\pi$
$733$	13.9537	+	42.9451i	0.515393	+	1.58622i	−0.267174	+	0.963648i	$0.586090\pi$
$734$	−21.0946	−	15.3261i	−0.778614	−	0.565697i
$735$	−4.71874	−	37.5039i	−0.174053	−	1.38335i
$736$	−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	$0.485856\pi$
$740$	7.59869	−	13.8056i	0.279334	−	0.507503i
$741$	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	$-0.395016\pi$
$743$	17.6562			0.647741			0.323871	+	0.946101i	$0.395016\pi$
$744$	4.02319	+	12.3821i	0.147497	+	0.453950i
$745$	39.4835	−	18.5554i	1.44656	−	0.679816i
$746$	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
$750$	26.0319	−	1.59847i	0.950550	−	0.0583677i
$751$	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
$755$	37.3022	−	17.5302i	1.35757	−	0.637990i
$756$	1.51901	+	4.67502i	0.0552457	+	0.170029i
$757$	−4.90706			−0.178350			−0.0891750	−	0.996016i	$-0.528423\pi$
$757$	−4.90706			−0.178350			−0.0891750	+	0.996016i	$0.528423\pi$
$758$	−10.9163	−	33.5968i	−0.396497	−	1.22029i
$759$	−6.34708	−	4.61142i	−0.230384	−	0.167384i
$760$	4.21998	−	7.66701i	0.153075	−	0.278112i
$761$	−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
$765$	−0.949106	−	7.54337i	−0.0343150	−	0.272731i
$766$	−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	$-0.272442\pi$
$770$	−3.97681	−	31.6072i	−0.143314	−	1.13904i
$771$	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	$-0.399253\pi$
$773$	36.4564	−	26.4871i	1.31124	−	0.952675i	0.999997	−	0.00234562i	$-0.000746636\pi$
$774$	6.58695			0.236763
$775$	−25.9356	−	10.2987i	−0.931634	−	0.369941i
$776$	−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
$780$	11.3357	+	12.0834i	0.405883	+	0.432656i
$781$	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
$785$	−20.5539	+	9.65934i	−0.733600	+	0.344757i
$786$	7.64941	−	5.55762i	0.272846	−	0.198234i
$787$	−20.8458	−	15.1454i	−0.743074	−	0.539875i	0.150598	−	0.988595i	$-0.451880\pi$
$787$	−20.8458	−	15.1454i	−0.743074	−	0.539875i	−0.893672	+	0.448720i	$0.851880\pi$
$788$	−3.84883	−	2.79634i	−0.137109	−	0.0996156i
$789$	−17.2926	+	12.5638i	−0.615633	+	0.447284i
$790$	2.76393	+	2.94625i	0.0983363	+	0.104823i
$791$	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
$795$	−59.5137	−	11.3838i	−2.11073	−	0.403741i
$796$	4.49063	−	13.8207i	0.159166	−	0.489863i
$797$	15.5882	−	47.9757i	0.552164	−	1.69939i	−0.151154	−	0.988510i	$-0.548299\pi$
$797$	15.5882	−	47.9757i	0.552164	−	1.69939i	0.703318	−	0.710875i	$-0.251701\pi$
$798$	27.8796	−	20.2557i	0.986926	−	0.717044i
$799$	−5.25595			−0.185942
$800$	3.19098	−	3.84937i	0.112818	−	0.136096i
$801$	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
$805$	3.62622	−	6.58824i	0.127808	−	0.232205i
$806$	−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	$0.679747\pi$
$810$	−22.7601	−	4.35356i	−0.799709	−	0.152968i
$811$	−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
$815$	−40.8512	−	7.81402i	−1.43095	−	0.273713i
$816$	−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
$820$	−1.60566	+	2.91722i	−0.0560721	+	0.101874i
$821$	−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	−0.602865	−	0.797843i	$-0.705974\pi$
$823$	−0.871148	+	0.632926i	−0.0303663	+	0.0220624i	0.572499	+	0.819906i	$0.305974\pi$
$824$	−1.21619			−0.0423678
$825$	40.9166	+	16.2475i	1.42453	+	0.565666i
$826$	−2.60466			−0.0906278
$827$	23.7689	−	17.2691i	0.826526	−	0.600506i	−0.0920482	−	0.995755i	$-0.529341\pi$
$827$	23.7689	−	17.2691i	0.826526	−	0.600506i	0.918574	+	0.395248i	$0.129341\pi$
$828$	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	$-0.0192955\pi$
$830$	−21.8919	−	4.18748i	−0.759877	−	0.145349i
$831$	−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
$835$	−3.32221	−	3.54136i	−0.114970	−	0.122554i
$836$	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	$0.281232\pi$
$840$	17.8187	−	8.37394i	0.614805	−	0.288928i
$841$	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
$845$	4.45350	+	4.74726i	0.153205	+	0.163311i
$846$	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
$850$	6.74550	−	1.72474i	0.231369	−	0.0591581i
$851$	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	$0.344594\pi$
$853$	−12.5449	+	38.6094i	−0.429531	+	1.32196i	−0.898589	+	0.438792i	$0.855406\pi$
$854$	12.0840	−	37.1908i	0.413507	−	1.27264i
$855$	2.66762	+	21.2019i	0.0912306	+	0.725089i
$856$	−3.34124	−	10.2833i	−0.114201	−	0.351475i
$857$	−43.0463			−1.47043			−0.735216	−	0.677833i	$-0.762919\pi$
$857$	−43.0463			−1.47043			−0.735216	+	0.677833i	$0.762919\pi$
$858$	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	$0.741579\pi$
$860$	0.753030	+	5.98498i	0.0256781	+	0.204086i
$861$	−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	0.495054	−	0.868862i	$-0.335148\pi$
$863$	−5.23799	−	3.80562i	−0.178303	−	0.129545i	−0.673357	+	0.739317i	$0.735148\pi$
$864$	−1.05361	+	0.765491i	−0.0358445	+	0.0260425i
$865$	−6.89439	+	12.5260i	−0.234416	+	0.425896i
$866$	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
$870$	0.232346	−	0.109192i	0.00787728	−	0.00370194i
$871$	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
$875$	−10.5562	+	40.8582i	−0.356863	+	1.38126i
$876$	−12.0573			−0.407379
$877$	6.36784	−	4.62651i	0.215027	−	0.156226i	−0.475058	−	0.879954i	$-0.657573\pi$
$877$	6.36784	−	4.62651i	0.215027	−	0.156226i	0.690085	+	0.723728i	$0.257573\pi$
$878$	−8.19679	+	25.2271i	−0.276628	+	0.851374i
$879$	21.2646	−	65.4457i	0.717238	−	2.20743i
$880$	7.63851	−	3.58973i	0.257494	−	0.121010i
$881$	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	0.978364	−	0.206889i	$-0.0663341\pi$
$883$	1.93876	+	5.96688i	0.0652444	+	0.200802i	−0.913120	+	0.407691i	$0.866334\pi$
$884$	3.57830	+	2.59979i	0.120351	+	0.0874403i
$885$	1.73568	−	3.15344i	0.0583443	−	0.106002i
$886$	−28.7417	+	20.8821i	−0.965597	+	0.701548i
$887$	−18.8281	−	13.6794i	−0.632185	−	0.459309i	0.224972	−	0.974365i	$-0.427771\pi$
$887$	−18.8281	−	13.6794i	−0.632185	−	0.459309i	−0.857156	+	0.515056i	$0.827771\pi$
$888$	13.3002	+	9.66317i	0.446326	+	0.324275i
$889$	10.8371	−	7.87358i	0.363463	−	0.264071i
$890$	4.05040	+	32.1921i	0.135770	+	1.07908i
$891$	−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
$895$	2.23689	+	17.7785i	0.0747709	+	0.594270i
$896$	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
$900$	−0.778806	+	12.1837i	−0.0259602	+	0.406124i
$901$	−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
$905$	16.6189	+	17.7151i	0.552430	+	0.588870i
$906$	13.2871	+	40.8936i	0.441436	+	1.35860i
$907$	−17.6544			−0.586206			−0.293103	−	0.956081i	$-0.594688\pi$
$907$	−17.6544			−0.586206			−0.293103	+	0.956081i	$0.594688\pi$
$908$	−1.94259	−	5.97869i	−0.0644673	−	0.198410i
$909$	−32.3539	−	23.5065i	−1.07311	−	0.779660i
$910$	−24.2623	+	11.4021i	−0.804288	+	0.377977i
$911$	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
$915$	36.9741	+	39.4130i	1.22233	+	1.30295i
$916$	−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	$0.695531\pi$
$920$	1.95693	+	0.374321i	0.0645180	+	0.0123410i
$921$	−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
$925$	−34.1390	+	8.72892i	−1.12249	+	0.287005i
$926$	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	$-0.00119191\pi$
$930$	14.0376	−	25.5041i	0.460313	−	0.836311i
$931$	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
$935$	11.5434	+	2.20802i	0.377509	+	0.0722100i
$936$	−6.27447	+	4.55867i	−0.205087	+	0.149005i
$937$	−48.1590	−	34.9896i	−1.57329	−	1.14306i	−0.923920	−	0.382586i	$-0.875034\pi$
$937$	−48.1590	−	34.9896i	−1.57329	−	1.14306i	−0.649367	−	0.760475i	$-0.724966\pi$
$938$	−46.7917	−	33.9961i	−1.52780	−	1.11001i
$939$	17.8794	−	12.9902i	0.583474	−	0.423918i
$940$	8.28968	+	1.58565i	0.270379	+	0.0517182i
$941$	−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
$945$	5.30009	−	9.62938i	0.172412	−	0.313244i
$946$	−3.14649	+	9.68391i	−0.102301	+	0.314851i
$947$	0.778999	−	2.39751i	0.0253141	−	0.0779087i	−0.937601	−	0.347712i	$-0.886959\pi$
$947$	0.778999	−	2.39751i	0.0253141	−	0.0779087i	0.962915	+	0.269803i	$0.0869587\pi$
$948$	−3.40955	+	2.47718i	−0.110737	+	0.0804551i
$949$	16.4175			0.532934
$950$	−18.9593	+	4.84766i	−0.615122	+	0.157279i
$951$	−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	$-0.730363\pi$
$953$	9.69336	−	29.8331i	0.313999	−	0.966389i	0.976165	−	0.217032i	$-0.0696375\pi$
$954$	8.76486	−	26.9755i	0.283773	−	0.873363i
$955$	−17.9780	−	3.43883i	−0.581754	−	0.111278i
$956$	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
$960$	3.56882	+	3.80423i	0.115183	+	0.122781i
$961$	−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
$965$	35.5319	−	16.6983i	1.14381	−	0.537537i
$966$	6.34708	+	4.61142i	0.204214	+	0.148370i
$967$	15.1746	+	46.7027i	0.487983	+	1.50186i	0.827613	+	0.561299i	$0.189698\pi$
$967$	15.1746	+	46.7027i	0.487983	+	1.50186i	−0.339630	+	0.940559i	$0.610302\pi$
$968$	3.24660			0.104350
$969$	3.92872	+	12.0913i	0.126209	+	0.388430i
$970$	0.137949	+	0.147048i	0.00442927	+	0.00472144i
$971$	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
$975$	2.36334	−	36.9723i	0.0756873	−	1.18406i
$976$	10.3603			0.331626
$977$	−12.6095	+	9.16131i	−0.403412	+	0.293096i	−0.770929	−	0.636921i	$-0.780208\pi$
$977$	−12.6095	+	9.16131i	−0.403412	+	0.293096i	0.367517	+	0.930017i	$0.380208\pi$
$978$	13.4083	−	41.2665i	0.428750	−	1.31956i
$979$	−16.9244	+	52.0879i	−0.540906	+	1.66474i
$980$	2.02282	+	16.0771i	0.0646167	+	0.513565i
$981$	8.61323	+	26.5088i	0.274999	+	0.846361i
$982$	−2.58009			−0.0823339
$983$	−4.18993	−	12.8953i	−0.133638	−	0.411296i	0.861738	−	0.507354i	$-0.169376\pi$
$983$	−4.18993	−	12.8953i	−0.133638	−	0.411296i	−0.995376	+	0.0960585i	$0.969376\pi$
$984$	−2.81044	−	2.04190i	−0.0895934	−	0.0650934i
$985$	1.32799	+	10.5547i	0.0423133	+	0.336301i
$986$	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
$990$	−9.93704	+	18.0540i	−0.315820	+	0.573793i
$991$	−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
$995$	−29.4089	+	13.8207i	−0.932324	+	0.438147i
$996$	7.18540	−	22.1144i	0.227678	−	0.700721i
$997$	0.478723	−	1.47336i	0.0151613	−	0.0466617i	−0.943190	−	0.332255i	$-0.892191\pi$
$997$	0.478723	−	1.47336i	0.0151613	−	0.0466617i	0.958351	+	0.285593i	$0.0921906\pi$
$998$	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	50.2.d.b.11.1	✓	8
3.2	odd	2		450.2.h.e.361.2		8
4.3	odd	2		400.2.u.d.161.2		8
5.2	odd	4		250.2.e.c.199.2		16
5.3	odd	4		250.2.e.c.199.3		16
5.4	even	2		250.2.d.d.51.2		8
25.3	odd	20		1250.2.b.e.1249.1		8
25.4	even	10		1250.2.a.f.1.4		4
25.9	even	10		250.2.d.d.201.2		8
25.12	odd	20		250.2.e.c.49.3		16
25.13	odd	20		250.2.e.c.49.2		16
25.16	even	5	inner	50.2.d.b.41.1	yes	8
25.21	even	5		1250.2.a.l.1.1		4
25.22	odd	20		1250.2.b.e.1249.8		8
75.41	odd	10		450.2.h.e.91.2		8
100.71	odd	10		10000.2.a.t.1.4		4
100.79	odd	10		10000.2.a.x.1.1		4
100.91	odd	10		400.2.u.d.241.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.1	✓	8	1.1	even	1	trivial
50.2.d.b.41.1	yes	8	25.16	even	5	inner
250.2.d.d.51.2		8	5.4	even	2
250.2.d.d.201.2		8	25.9	even	10
250.2.e.c.49.2		16	25.13	odd	20
250.2.e.c.49.3		16	25.12	odd	20
250.2.e.c.199.2		16	5.2	odd	4
250.2.e.c.199.3		16	5.3	odd	4
400.2.u.d.161.2		8	4.3	odd	2
400.2.u.d.241.2		8	100.91	odd	10
450.2.h.e.91.2		8	75.41	odd	10
450.2.h.e.361.2		8	3.2	odd	2
1250.2.a.f.1.4		4	25.4	even	10
1250.2.a.l.1.1		4	25.21	even	5
1250.2.b.e.1249.1		8	25.3	odd	20
1250.2.b.e.1249.8		8	25.22	odd	20
10000.2.a.t.1.4		4	100.71	odd	10
10000.2.a.x.1.1		4	100.79	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.720859 + 2.21858i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.02373 + 0.951057i) q^{5} +(-0.720859 - 2.21858i) q^{6} +3.77447 q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.97539 - 1.43521i) q^{9} +(1.07822 - 1.95894i) q^{10} +(3.05361 - 2.21858i) q^{11} +(1.88723 + 1.37116i) q^{12} +(-2.56969 - 1.86699i) q^{13} +(-3.05361 + 2.21858i) q^{14} +(-0.651166 - 5.17538i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.430307 - 1.32435i) q^{17} +2.44172 q^{18} +(1.20945 + 3.72230i) q^{19} +(0.279141 + 2.21858i) q^{20} +(-2.72086 + 8.37394i) q^{21} +(-1.16637 + 3.58973i) q^{22} +(-0.720859 + 0.523735i) q^{23} -2.33275 q^{24} +(3.19098 - 3.84937i) q^{25} +3.17632 q^{26} +(-1.05361 + 0.765491i) q^{27} +(1.16637 - 3.58973i) q^{28} +(0.0152089 - 0.0468081i) q^{29} +(3.56882 + 3.80423i) q^{30} +(-1.72466 - 5.30795i) q^{31} +1.00000 q^{32} +(2.72086 + 8.37394i) q^{33} +(1.12656 + 0.818492i) q^{34} +(-7.63851 + 3.58973i) q^{35} +(-1.97539 + 1.43521i) q^{36} +(-5.70152 - 4.14240i) q^{37} +(-3.16637 - 2.30051i) q^{38} +(5.99445 - 4.35522i) q^{39} +(-1.52988 - 1.63079i) q^{40} +(1.20477 + 0.875319i) q^{41} +(-2.72086 - 8.37394i) q^{42} +2.69767 q^{43} +(-1.16637 - 3.58973i) q^{44} +(5.36263 + 1.02576i) q^{45} +(0.275344 - 0.847421i) q^{46} +(1.16637 - 3.58973i) q^{47} +(1.88723 - 1.37116i) q^{48} +7.24660 q^{49} +(-0.318958 + 4.98982i) q^{50} +3.24836 q^{51} +(-2.56969 + 1.86699i) q^{52} +(3.58963 - 11.0477i) q^{53} +(0.402443 - 1.23859i) q^{54} +(-4.06969 + 7.39396i) q^{55} +(1.16637 + 3.58973i) q^{56} -9.13004 q^{57} +(0.0152089 + 0.0468081i) q^{58} +(0.558282 + 0.405615i) q^{59} +(-5.12330 - 0.979986i) q^{60} +(-8.38168 + 6.08965i) q^{61} +(4.51521 + 3.28049i) q^{62} +(-7.45605 - 5.41714i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(6.97599 + 1.33437i) q^{65} +(-7.12330 - 5.17538i) q^{66} +(4.73519 + 14.5734i) q^{67} -1.39250 q^{68} +(-0.642308 - 1.97682i) q^{69} +(4.06969 - 7.39396i) q^{70} +(-2.06969 + 6.36986i) q^{71} +(0.754532 - 2.32221i) q^{72} +(-4.18158 + 3.03810i) q^{73} +7.04746 q^{74} +(6.23987 + 9.85429i) q^{75} +3.91385 q^{76} +(11.5257 - 8.37394i) q^{77} +(-2.28968 + 7.04690i) q^{78} +(-0.558282 + 1.71821i) q^{79} +(2.19625 + 0.420099i) q^{80} +(-3.20239 - 9.85596i) q^{81} -1.48918 q^{82} +(-3.08023 - 9.47997i) q^{83} +(7.12330 + 5.17538i) q^{84} +(2.13035 + 2.27088i) q^{85} +(-2.18246 + 1.58565i) q^{86} +(0.0928839 + 0.0674841i) q^{87} +(3.05361 + 2.21858i) q^{88} +(-11.7390 + 8.52891i) q^{89} +(-4.94138 + 2.32221i) q^{90} +(-9.69922 - 7.04690i) q^{91} +(0.275344 + 0.847421i) q^{92} +13.0193 q^{93} +(1.16637 + 3.58973i) q^{94} +(-5.98771 - 6.38268i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 3 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + q^{11} + 2 q^{12} - 13 q^{13} - q^{14} - 10 q^{15} - 2 q^{16} - 11 q^{17} + 14 q^{18} + 20 q^{19} + 5 q^{20} - 19 q^{21} + q^{22}+ \cdots - 42 q^{99}+O(q^{100}) \) 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 - 10 * q^15 - 2 * q^16 - 11 * q^17 + 14 * q^18 + 20 * q^19 + 5 * q^20 - 19 * q^21 + q^22 - 3 * q^23 + 2 * q^24 + 30 * q^25 + 22 * q^26 + 15 * q^27 - q^28 - 15 * q^29 - 10 * q^30 - 9 * q^31 + 8 * q^32 + 19 * q^33 - q^34 - 15 * q^35 - q^36 - 6 * q^37 - 15 * q^38 - 12 * q^39 - 5 * q^40 - 9 * q^41 - 19 * q^42 + 12 * q^43 + q^44 + 15 * q^45 + 7 * q^46 - q^47 + 2 * q^48 - 4 * q^49 - 5 * q^50 + 26 * q^51 - 13 * q^52 + 7 * q^53 - 25 * q^54 - 25 * q^55 - q^56 - 15 * q^58 + 10 * q^59 - 10 * q^60 + 6 * q^61 + 21 * q^62 - 8 * q^63 - 2 * q^64 - 10 * q^65 - 26 * q^66 - 11 * q^67 + 24 * q^68 + 43 * q^69 + 25 * q^70 - 9 * q^71 - 6 * q^72 - 8 * q^73 + 24 * q^74 + 30 * q^75 - 10 * q^76 + 33 * q^77 + 23 * q^78 - 10 * q^79 - 17 * q^81 + 26 * q^82 + 27 * q^83 + 26 * q^84 + 5 * q^85 - 23 * q^86 + q^88 - 15 * q^89 + 20 * q^90 + q^91 + 7 * q^92 - 46 * q^93 - q^94 - 30 * q^95 - 3 * q^96 - 36 * q^97 - 19 * q^98 - 42 * q^99

Introduction

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