LMFDB - Embedded newform 250.2.e.c.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(49,250)]

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([7]))

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

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.e (of order $10$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.3
Root			$1.86824 + 0.357358i$ of defining polynomial
Character	$\chi$	$=$	250.49
Dual form			250.2.e.c.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-2.21858 + 0.720859i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.720859 + 2.21858i) q^{6} +3.77447i q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.97539 - 1.43521i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-2.21858 + 0.720859i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.720859 + 2.21858i) q^{6} +3.77447i q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.97539 - 1.43521i) q^{9} +(3.05361 + 2.21858i) q^{11} +(1.37116 + 1.88723i) q^{12} +(1.86699 + 2.56969i) q^{13} +(3.05361 + 2.21858i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.32435 - 0.430307i) q^{17} -2.44172i q^{18} +(-1.20945 + 3.72230i) q^{19} +(-2.72086 - 8.37394i) q^{21} +(3.58973 - 1.16637i) q^{22} +(-0.523735 + 0.720859i) q^{23} +2.33275 q^{24} +3.17632 q^{26} +(0.765491 - 1.05361i) q^{27} +(3.58973 - 1.16637i) q^{28} +(-0.0152089 - 0.0468081i) q^{29} +(-1.72466 + 5.30795i) q^{31} +1.00000i q^{32} +(-8.37394 - 2.72086i) q^{33} +(-1.12656 + 0.818492i) q^{34} +(-1.97539 - 1.43521i) q^{36} +(-4.14240 - 5.70152i) q^{37} +(2.30051 + 3.16637i) q^{38} +(-5.99445 - 4.35522i) q^{39} +(1.20477 - 0.875319i) q^{41} +(-8.37394 - 2.72086i) q^{42} -2.69767i q^{43} +(1.16637 - 3.58973i) q^{44} +(0.275344 + 0.847421i) q^{46} +(-3.58973 + 1.16637i) q^{47} +(1.37116 - 1.88723i) q^{48} -7.24660 q^{49} +3.24836 q^{51} +(1.86699 - 2.56969i) q^{52} +(11.0477 - 3.58963i) q^{53} +(-0.402443 - 1.23859i) q^{54} +(1.16637 - 3.58973i) q^{56} -9.13004i q^{57} +(-0.0468081 - 0.0152089i) q^{58} +(-0.558282 + 0.405615i) q^{59} +(-8.38168 - 6.08965i) q^{61} +(3.28049 + 4.51521i) q^{62} +(5.41714 + 7.45605i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.12330 + 5.17538i) q^{66} +(14.5734 + 4.73519i) q^{67} +1.39250i q^{68} +(0.642308 - 1.97682i) q^{69} +(-2.06969 - 6.36986i) q^{71} +(-2.32221 + 0.754532i) q^{72} +(-3.03810 + 4.18158i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-8.37394 + 11.5257i) q^{77} +(-7.04690 + 2.28968i) q^{78} +(0.558282 + 1.71821i) q^{79} +(-3.20239 + 9.85596i) q^{81} -1.48918i q^{82} +(9.47997 + 3.08023i) q^{83} +(-7.12330 + 5.17538i) q^{84} +(-2.18246 - 1.58565i) q^{86} +(0.0674841 + 0.0928839i) q^{87} +(-2.21858 - 3.05361i) q^{88} +(11.7390 + 8.52891i) q^{89} +(-9.69922 + 7.04690i) q^{91} +(0.847421 + 0.275344i) q^{92} -13.0193i q^{93} +(-1.16637 + 3.58973i) q^{94} +(-0.720859 - 2.21858i) q^{96} +(0.0857567 - 0.0278640i) q^{97} +(-4.25945 + 5.86263i) q^{98} +9.21619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9	$ 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46} + 8 q^{49} + 52 q^{51} + 50 q^{54} - 2 q^{56} - 20 q^{59} + 12 q^{61} + 4 q^{64} - 52 q^{66} - 86 q^{69} - 18 q^{71} - 48 q^{74} - 20 q^{76} + 20 q^{79} - 34 q^{81} - 52 q^{84} - 46 q^{86} + 30 q^{89} + 2 q^{91} + 2 q^{94} - 6 q^{96} + 84 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−2.21858	+	0.720859i	−1.28090	+	0.416188i	−0.868895	−	0.494996i	$-0.835170\pi$
$3$	−2.21858	+	0.720859i	−1.28090	+	0.416188i	−0.412000	+	0.911184i	$0.635170\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.720859	+	2.21858i	−0.294289	+	0.905730i
$7$			3.77447i			1.42661i	0.700851	+	0.713307i	$0.252804\pi$
$7$			3.77447i			1.42661i	−0.700851	+	0.713307i	$0.747196\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	1.97539	−	1.43521i	0.658464	−	0.478402i
$10$		0			0
$11$	3.05361	+	2.21858i	0.920698	+	0.668926i	0.943698	−	0.330810i	$-0.107322\pi$
$11$	3.05361	+	2.21858i	0.920698	+	0.668926i	−0.0230000	+	0.999735i	$0.507322\pi$
$12$	1.37116	+	1.88723i	0.395818	+	0.544797i
$13$	1.86699	+	2.56969i	0.517810	+	0.712705i	0.985212	−	0.171340i	$-0.0548098\pi$
$13$	1.86699	+	2.56969i	0.517810	+	0.712705i	−0.467402	+	0.884045i	$0.654810\pi$
$14$	3.05361	+	2.21858i	0.816111	+	0.592939i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.32435	−	0.430307i	−0.321201	−	0.104365i	0.143979	−	0.989581i	$-0.454010\pi$
$17$	−1.32435	−	0.430307i	−0.321201	−	0.104365i	−0.465180	+	0.885216i	$0.654010\pi$
$18$		−	2.44172i		−	0.575519i
$19$	−1.20945	+	3.72230i	−0.277466	+	0.853953i	0.711090	+	0.703101i	$0.248202\pi$
$19$	−1.20945	+	3.72230i	−0.277466	+	0.853953i	−0.988556	+	0.150852i	$0.951798\pi$
$20$		0			0
$21$	−2.72086	−	8.37394i	−0.593740	−	1.82734i
$22$	3.58973	−	1.16637i	0.765333	−	0.248672i
$23$	−0.523735	+	0.720859i	−0.109206	+	0.150310i	−0.860122	−	0.510089i	$-0.829613\pi$
$23$	−0.523735	+	0.720859i	−0.109206	+	0.150310i	0.750916	+	0.660398i	$0.229613\pi$
$24$	2.33275			0.476170
$25$		0			0
$26$	3.17632			0.622927
$27$	0.765491	−	1.05361i	0.147319	−	0.202767i
$28$	3.58973	−	1.16637i	0.678396	−	0.220424i
$29$	−0.0152089	−	0.0468081i	−0.00282422	−	0.00869205i	0.949634	−	0.313360i	$-0.101455\pi$
$29$	−0.0152089	−	0.0468081i	−0.00282422	−	0.00869205i	−0.952459	+	0.304668i	$0.901455\pi$
$30$		0			0
$31$	−1.72466	+	5.30795i	−0.309757	+	0.953335i	0.668102	+	0.744070i	$0.267107\pi$
$31$	−1.72466	+	5.30795i	−0.309757	+	0.953335i	−0.977859	+	0.209265i	$0.932893\pi$
$32$			1.00000i			0.176777i
$33$	−8.37394	−	2.72086i	−1.45772	−	0.473641i
$34$	−1.12656	+	0.818492i	−0.193203	+	0.140370i
$35$		0			0
$36$	−1.97539	−	1.43521i	−0.329232	−	0.239201i
$37$	−4.14240	−	5.70152i	−0.681006	−	0.937324i	0.318940	−	0.947775i	$-0.396673\pi$
$37$	−4.14240	−	5.70152i	−0.681006	−	0.937324i	−0.999945	+	0.0104512i	$0.996673\pi$
$38$	2.30051	+	3.16637i	0.373191	+	0.513654i
$39$	−5.99445	−	4.35522i	−0.959880	−	0.697394i
$40$		0			0
$41$	1.20477	−	0.875319i	0.188154	−	0.136702i	−0.489721	−	0.871879i	$-0.662901\pi$
$41$	1.20477	−	0.875319i	0.188154	−	0.136702i	0.677875	+	0.735178i	$0.262901\pi$
$42$	−8.37394	−	2.72086i	−1.29213	−	0.419838i
$43$		−	2.69767i		−	0.411391i	−0.978616	−	0.205695i	$-0.934054\pi$
$43$		−	2.69767i		−	0.411391i	0.978616	−	0.205695i	$-0.0659456\pi$
$44$	1.16637	−	3.58973i	0.175838	−	0.541172i
$45$		0			0
$46$	0.275344	+	0.847421i	0.0405972	+	0.124945i
$47$	−3.58973	+	1.16637i	−0.523616	+	0.170133i	−0.558886	−	0.829245i	$-0.688771\pi$
$47$	−3.58973	+	1.16637i	−0.523616	+	0.170133i	0.0352696	+	0.999378i	$0.488771\pi$
$48$	1.37116	−	1.88723i	0.197909	−	0.272399i
$49$	−7.24660			−1.03523
$50$		0			0
$51$	3.24836			0.454861
$52$	1.86699	−	2.56969i	0.258905	−	0.356352i
$53$	11.0477	−	3.58963i	1.51752	−	0.493073i	0.572453	−	0.819938i	$-0.305992\pi$
$53$	11.0477	−	3.58963i	1.51752	−	0.493073i	0.945071	+	0.326864i	$0.105992\pi$
$54$	−0.402443	−	1.23859i	−0.0547655	−	0.168551i
$55$		0			0
$56$	1.16637	−	3.58973i	0.155863	−	0.479698i
$57$		−	9.13004i		−	1.20930i
$58$	−0.0468081	−	0.0152089i	−0.00614620	−	0.00199702i
$59$	−0.558282	+	0.405615i	−0.0726821	+	0.0528066i	−0.623533	−	0.781797i	$-0.714303\pi$
$59$	−0.558282	+	0.405615i	−0.0726821	+	0.0528066i	0.550851	+	0.834604i	$0.314303\pi$
$60$		0			0
$61$	−8.38168	−	6.08965i	−1.07316	−	0.779700i	−0.0966862	−	0.995315i	$-0.530824\pi$
$61$	−8.38168	−	6.08965i	−1.07316	−	0.779700i	−0.976478	+	0.215615i	$0.930824\pi$
$62$	3.28049	+	4.51521i	0.416623	+	0.573432i
$63$	5.41714	+	7.45605i	0.682495	+	0.939374i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		0			0
$66$	−7.12330	+	5.17538i	−0.876818	+	0.637045i
$67$	14.5734	+	4.73519i	1.78043	+	0.578496i	0.998966	−	0.0454589i	$-0.0144750\pi$
$67$	14.5734	+	4.73519i	1.78043	+	0.578496i	0.781461	+	0.623955i	$0.214475\pi$
$68$			1.39250i			0.168866i
$69$	0.642308	−	1.97682i	0.0773248	−	0.237981i
$70$		0			0
$71$	−2.06969	−	6.36986i	−0.245627	−	0.755963i	−0.995533	−	0.0944182i	$-0.969901\pi$
$71$	−2.06969	−	6.36986i	−0.245627	−	0.755963i	0.749905	−	0.661545i	$-0.230099\pi$
$72$	−2.32221	+	0.754532i	−0.273675	+	0.0889225i
$73$	−3.03810	+	4.18158i	−0.355582	+	0.489417i	−0.948911	−	0.315543i	$-0.897813\pi$
$73$	−3.03810	+	4.18158i	−0.355582	+	0.489417i	0.593329	+	0.804960i	$0.297813\pi$
$74$	−7.04746			−0.819251
$75$		0			0
$76$	3.91385			0.448950
$77$	−8.37394	+	11.5257i	−0.954299	+	1.31348i
$78$	−7.04690	+	2.28968i	−0.797904	+	0.259255i
$79$	0.558282	+	1.71821i	0.0628116	+	0.193314i	0.977538	−	0.210760i	$-0.0675938\pi$
$79$	0.558282	+	1.71821i	0.0628116	+	0.193314i	−0.914726	+	0.404074i	$0.867594\pi$
$80$		0			0
$81$	−3.20239	+	9.85596i	−0.355822	+	1.09511i
$82$		−	1.48918i		−	0.164453i
$83$	9.47997	+	3.08023i	1.04056	+	0.338099i	0.778958	−	0.627076i	$-0.215749\pi$
$83$	9.47997	+	3.08023i	1.04056	+	0.338099i	0.261604	+	0.965175i	$0.415749\pi$
$84$	−7.12330	+	5.17538i	−0.777216	+	0.564680i
$85$		0			0
$86$	−2.18246	−	1.58565i	−0.235341	−	0.170985i
$87$	0.0674841	+	0.0928839i	0.00723505	+	0.00995820i
$88$	−2.21858	−	3.05361i	−0.236501	−	0.325516i
$89$	11.7390	+	8.52891i	1.24434	+	0.904063i	0.997879	−	0.0650909i	$-0.0207337\pi$
$89$	11.7390	+	8.52891i	1.24434	+	0.904063i	0.246457	+	0.969154i	$0.420734\pi$
$90$		0			0
$91$	−9.69922	+	7.04690i	−1.01675	+	0.738716i
$92$	0.847421	+	0.275344i	0.0883497	+	0.0287066i
$93$		−	13.0193i		−	1.35004i
$94$	−1.16637	+	3.58973i	−0.120302	+	0.370253i
$95$		0			0
$96$	−0.720859	−	2.21858i	−0.0735724	−	0.226432i
$97$	0.0857567	−	0.0278640i	0.00870727	−	0.00282917i	−0.304660	−	0.952461i	$-0.598543\pi$
$97$	0.0857567	−	0.0278640i	0.00870727	−	0.00282917i	0.313367	+	0.949632i	$0.398543\pi$
$98$	−4.25945	+	5.86263i	−0.430269	+	0.592215i
$99$	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	$0.196814\pi$
$102$	1.90934	−	2.62798i	0.189052	−	0.260208i
$103$	−1.15666	+	0.375822i	−0.113969	+	0.0370308i	−0.365446	−	0.930832i	$-0.619084\pi$
$103$	−1.15666	+	0.375822i	−0.113969	+	0.0370308i	0.251477	+	0.967863i	$0.419084\pi$
$104$	−0.981536	−	3.02086i	−0.0962475	−	0.296219i
$105$		0			0
$106$	3.58963	−	11.0477i	0.348656	−	1.07305i
$107$		−	10.8125i		−	1.04528i	−0.852553	−	0.522641i	$-0.824947\pi$
$107$		−	10.8125i		−	1.04528i	0.852553	−	0.522641i	$-0.175053\pi$
$108$	−1.23859	−	0.402443i	−0.119183	−	0.0387250i
$109$	9.23519	−	6.70976i	0.884571	−	0.642678i	−0.0498859	−	0.998755i	$-0.515886\pi$
$109$	9.23519	−	6.70976i	0.884571	−	0.642678i	0.934457	+	0.356077i	$0.115886\pi$
$110$		0			0
$111$	13.3002	+	9.66317i	1.26240	+	0.917187i
$112$	−2.21858	−	3.05361i	−0.209636	−	0.288539i
$113$	−6.12644	−	8.43232i	−0.576327	−	0.793246i	0.416960	−	0.908925i	$-0.363096\pi$
$113$	−6.12644	−	8.43232i	−0.576327	−	0.793246i	−0.993287	+	0.115679i	$0.963096\pi$
$114$	−7.38636	−	5.36650i	−0.691796	−	0.502619i
$115$		0			0
$116$	−0.0398173	+	0.0289290i	−0.00369695	+	0.00268599i
$117$	7.37608	+	2.39663i	0.681919	+	0.221569i
$118$			0.690074i			0.0635265i
$119$	1.62418	−	4.99871i	0.148888	−	0.458231i
$120$		0			0
$121$	1.00326	+	3.08770i	0.0912051	+	0.280700i
$122$	−9.85326	+	3.20152i	−0.892072	+	0.289852i
$123$	−2.04190	+	2.81044i	−0.184112	+	0.253408i
$124$	5.58111			0.501198
$125$		0			0
$126$	9.21619			0.821043
$127$	−2.08601	+	2.87115i	−0.185104	+	0.254773i	−0.891477	−	0.453066i	$-0.850330\pi$
$127$	−2.08601	+	2.87115i	−0.185104	+	0.254773i	0.706373	+	0.707840i	$0.250330\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	1.94464	+	5.98498i	0.171216	+	0.526948i
$130$		0			0
$131$	1.25252	−	3.85486i	0.109433	−	0.336801i	−0.881312	−	0.472535i	$-0.843339\pi$
$131$	1.25252	−	3.85486i	0.109433	−	0.336801i	0.990745	+	0.135734i	$0.0433392\pi$
$132$			8.80489i			0.766367i
$133$	−14.0497	−	4.56502i	−1.21826	−	0.395837i
$134$	12.3969	−	9.00687i	1.07093	−	0.778075i
$135$		0			0
$136$	1.12656	+	0.818492i	0.0966015	+	0.0701851i
$137$	2.09706	+	2.88636i	0.179164	+	0.246598i	0.889148	−	0.457620i	$-0.151298\pi$
$137$	2.09706	+	2.88636i	0.179164	+	0.246598i	−0.709984	+	0.704218i	$0.751298\pi$
$138$	−1.22174	−	1.68158i	−0.104002	−	0.143146i
$139$	−8.04650	−	5.84613i	−0.682495	−	0.495862i	0.191689	−	0.981456i	$-0.438603\pi$
$139$	−8.04650	−	5.84613i	−0.682495	−	0.495862i	−0.874185	+	0.485594i	$0.838603\pi$
$140$		0			0
$141$	7.12330	−	5.17538i	0.599890	−	0.435846i
$142$	−6.36986	−	2.06969i	−0.534547	−	0.173685i
$143$			11.9889i			1.00256i
$144$	−0.754532	+	2.32221i	−0.0628777	+	0.193518i
$145$		0			0
$146$	1.59722	+	4.91575i	0.132187	+	0.406830i
$147$	16.0771	−	5.22378i	1.32602	−	0.430850i
$148$	−4.14240	+	5.70152i	−0.340503	+	0.468662i
$149$	19.5103			1.59834			0.799171	−	0.601104i	$-0.205272\pi$
$149$	19.5103			1.59834			0.799171	+	0.601104i	$0.205272\pi$
$150$		0			0
$151$	−18.4324			−1.50001			−0.750003	−	0.661435i	$-0.769948\pi$
$151$	−18.4324			−1.50001			−0.750003	+	0.661435i	$0.769948\pi$
$152$	2.30051	−	3.16637i	0.186596	−	0.256827i
$153$	−3.23368	+	1.05069i	−0.261428	+	0.0849430i
$154$	4.40244	+	13.5493i	0.354759	+	1.09184i
$155$		0			0
$156$	−2.28968	+	7.04690i	−0.183321	+	0.564203i
$157$			10.1564i			0.810572i	0.914190	+	0.405286i	$0.132828\pi$
$157$			10.1564i			0.810572i	−0.914190	+	0.405286i	$0.867172\pi$
$158$	1.71821	+	0.558282i	0.136694	+	0.0444145i
$159$	−21.9226	+	15.9277i	−1.73858	+	1.26315i
$160$		0			0
$161$	−2.72086	−	1.97682i	−0.214434	−	0.155795i
$162$	6.09132	+	8.38398i	0.478579	+	0.658708i
$163$	−10.9331	−	15.0481i	−0.856343	−	1.17865i	−0.982429	−	0.186636i	$-0.940242\pi$
$163$	−10.9331	−	15.0481i	−0.856343	−	1.17865i	0.126086	−	0.992019i	$-0.459758\pi$
$164$	−1.20477	−	0.875319i	−0.0940770	−	0.0683510i
$165$		0			0
$166$	8.06414	−	5.85894i	0.625899	−	0.454742i
$167$	2.06527	+	0.671048i	0.159816	+	0.0519273i	0.387832	−	0.921730i	$-0.373224\pi$
$167$	2.06527	+	0.671048i	0.159816	+	0.0519273i	−0.228016	+	0.973657i	$0.573224\pi$
$168$			8.80489i			0.679312i
$169$	0.899554	−	2.76854i	0.0691965	−	0.212965i
$170$		0			0
$171$	2.95313	+	9.08880i	0.225831	+	0.695038i
$172$	−2.56564	+	0.833625i	−0.195628	+	0.0635633i
$173$	3.75845	−	5.17306i	0.285750	−	0.393300i	−0.641878	−	0.766807i	$-0.721845\pi$
$173$	3.75845	−	5.17306i	0.285750	−	0.393300i	0.927628	+	0.373506i	$0.121845\pi$
$174$	0.114811			0.00870378
$175$		0			0
$176$	−3.77447			−0.284511
$177$	0.946199	−	1.30233i	0.0711207	−	0.0978892i
$178$	13.8001	−	4.48391i	1.03436	−	0.336084i
$179$	−2.47630	−	7.62127i	−0.185087	−	0.569640i	0.814862	−	0.579654i	$-0.196812\pi$
$179$	−2.47630	−	7.62127i	−0.185087	−	0.569640i	−0.999950	+	0.0100140i	$0.996812\pi$
$180$		0			0
$181$	−3.35682	+	10.3312i	−0.249510	+	0.767913i	0.745352	+	0.666671i	$0.232282\pi$
$181$	−3.35682	+	10.3312i	−0.249510	+	0.767913i	−0.994862	+	0.101242i	$0.967718\pi$
$182$			11.9889i			0.888676i
$183$	22.9852	+	7.46834i	1.69911	+	0.552075i
$184$	0.720859	−	0.523735i	0.0531424	−	0.0386102i
$185$		0			0
$186$	−10.5328	−	7.65256i	−0.772306	−	0.561113i
$187$	−3.08937	−	4.25215i	−0.225917	−	0.310948i
$188$	2.21858	+	3.05361i	0.161806	+	0.222707i
$189$	3.97681	+	2.88932i	0.289270	+	0.210167i
$190$		0			0
$191$	6.62243	−	4.81147i	0.479182	−	0.348146i	−0.321827	−	0.946798i	$-0.604297\pi$
$191$	6.62243	−	4.81147i	0.479182	−	0.348146i	0.801009	+	0.598652i	$0.204297\pi$
$192$	−2.21858	−	0.720859i	−0.160112	−	0.0520235i
$193$			17.5576i			1.26382i	0.775040	+	0.631912i	$0.217730\pi$
$193$			17.5576i			1.26382i	−0.775040	+	0.631912i	$0.782270\pi$
$194$	0.0278640	−	0.0857567i	0.00200052	−	0.00615697i
$195$		0			0
$196$	2.23932	+	6.89193i	0.159952	+	0.492281i
$197$	−4.52458	+	1.47012i	−0.322363	+	0.104742i	−0.465728	−	0.884928i	$-0.654208\pi$
$197$	−4.52458	+	1.47012i	−0.322363	+	0.104742i	0.143365	+	0.989670i	$0.454208\pi$
$198$	5.41714	−	7.45605i	0.384979	−	0.529878i
$199$	−14.5320			−1.03015			−0.515073	−	0.857146i	$-0.672235\pi$
$199$	−14.5320			−1.03015			−0.515073	+	0.857146i	$0.672235\pi$
$200$		0			0
$201$	−35.7457			−2.52130
$202$	9.62702	−	13.2505i	0.677355	−	0.932299i
$203$	0.176676	−	0.0574054i	0.0124002	−	0.00402907i
$204$	−1.00380	−	3.08937i	−0.0702799	−	0.216299i
$205$		0			0
$206$	−0.375822	+	1.15666i	−0.0261848	+	0.0805884i
$207$			2.17565i			0.151218i
$208$	−3.02086	−	0.981536i	−0.209459	−	0.0680572i
$209$	−11.9514	+	8.68318i	−0.826694	+	0.600628i
$210$		0			0
$211$	11.4362	+	8.30886i	0.787298	+	0.572006i	0.907160	−	0.420785i	$-0.138245\pi$
$211$	11.4362	+	8.30886i	0.787298	+	0.572006i	−0.119862	+	0.992791i	$0.538245\pi$
$212$	−6.82788	−	9.39777i	−0.468941	−	0.645441i
$213$	9.18355	+	12.6401i	0.629246	+	0.866083i
$214$	−8.74748	−	6.35542i	−0.597965	−	0.434447i
$215$		0			0
$216$	−1.05361	+	0.765491i	−0.0716890	+	0.0520851i
$217$	−20.0347	−	6.50966i	−1.36004	−	0.441904i
$218$		−	11.4153i		−	0.773143i
$219$	3.72592	−	11.4672i	0.251774	−	0.774882i
$220$		0			0
$221$	−1.36679	−	4.20655i	−0.0919402	−	0.282963i
$222$	15.6353	−	5.08023i	1.04938	−	0.340963i
$223$	−2.71102	+	3.73139i	−0.181543	+	0.249873i	−0.890083	−	0.455798i	$-0.849354\pi$
$223$	−2.71102	+	3.73139i	−0.181543	+	0.249873i	0.708540	+	0.705670i	$0.249354\pi$
$224$	−3.77447			−0.252192
$225$		0			0
$226$	−10.4229			−0.693322
$227$	−3.69503	+	5.08578i	−0.245248	+	0.337555i	−0.913840	−	0.406075i	$-0.866897\pi$
$227$	−3.69503	+	5.08578i	−0.245248	+	0.337555i	0.668592	+	0.743630i	$0.266897\pi$
$228$	−8.68318	+	2.82134i	−0.575058	+	0.186848i
$229$	−5.48103	−	16.8689i	−0.362196	−	1.11473i	−0.951718	−	0.306973i	$-0.900684\pi$
$229$	−5.48103	−	16.8689i	−0.362196	−	1.11473i	0.589522	−	0.807753i	$-0.299316\pi$
$230$		0			0
$231$	10.2698	−	31.6072i	0.675703	−	2.07960i
$232$			0.0492169i			0.00323125i
$233$	−2.43856	−	0.792338i	−0.159756	−	0.0519078i	0.228047	−	0.973650i	$-0.426766\pi$
$233$	−2.43856	−	0.792338i	−0.159756	−	0.0519078i	−0.387803	+	0.921742i	$0.626766\pi$
$234$	6.27447	−	4.55867i	0.410175	−	0.298009i
$235$		0			0
$236$	0.558282	+	0.405615i	0.0363410	+	0.0264033i
$237$	−2.47718	−	3.40955i	−0.160910	−	0.221474i
$238$	−3.08937	−	4.25215i	−0.200254	−	0.275626i
$239$	7.63851	+	5.54970i	0.494094	+	0.358980i	0.806757	−	0.590884i	$-0.201221\pi$
$239$	7.63851	+	5.54970i	0.494094	+	0.358980i	−0.312662	+	0.949864i	$0.601221\pi$
$240$		0			0
$241$	23.8131	−	17.3012i	1.53394	−	1.11447i	0.579940	−	0.814659i	$-0.303076\pi$
$241$	23.8131	−	17.3012i	1.53394	−	1.11447i	0.953998	−	0.299812i	$-0.0969240\pi$
$242$	3.08770	+	1.00326i	0.198485	+	0.0644917i
$243$		−	20.2677i		−	1.30017i
$244$	−3.20152	+	9.85326i	−0.204956	+	0.630790i
$245$		0			0
$246$	1.07349	+	3.30386i	0.0684433	+	0.210647i
$247$	−11.8232	+	3.84159i	−0.752292	+	0.244434i
$248$	3.28049	−	4.51521i	0.208311	−	0.286716i
$249$	−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	$0.560718\pi$
$252$	5.41714	−	7.45605i	0.341248	−	0.469687i
$253$	−3.19856	+	1.03928i	−0.201092	+	0.0653387i
$254$	1.09668	+	3.37524i	0.0688119	+	0.211781i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$		−	13.6286i		−	0.850127i	−0.905164	−	0.425063i	$-0.860252\pi$
$257$		−	13.6286i		−	0.850127i	0.905164	−	0.425063i	$-0.139748\pi$
$258$	5.98498	+	1.94464i	0.372609	+	0.121068i
$259$	21.5202	−	15.6353i	1.33720	−	0.971533i
$260$		0			0
$261$	−0.0972227	−	0.0706365i	−0.00601794	−	0.00437229i
$262$	−2.38244	−	3.27914i	−0.147187	−	0.202586i
$263$	−5.38584	−	7.41298i	−0.332105	−	0.457104i	0.610010	−	0.792394i	$-0.291166\pi$
$263$	−5.38584	−	7.41298i	−0.332105	−	0.457104i	−0.942115	+	0.335290i	$0.891166\pi$
$264$	7.12330	+	5.17538i	0.438409	+	0.318523i
$265$		0			0
$266$	−11.9514	+	8.68318i	−0.732786	+	0.532400i
$267$	−32.1921	−	10.4598i	−1.97012	−	0.640132i
$268$		−	15.3234i		−	0.936026i
$269$	−8.68419	+	26.7272i	−0.529484	+	1.62959i	0.225790	+	0.974176i	$0.427504\pi$
$269$	−8.68419	+	26.7272i	−0.529484	+	1.62959i	−0.755274	+	0.655409i	$0.772496\pi$
$270$		0			0
$271$	−2.81162	−	8.65329i	−0.170794	−	0.525650i	0.828623	−	0.559808i	$-0.189125\pi$
$271$	−2.81162	−	8.65329i	−0.170794	−	0.525650i	−0.999416	+	0.0341581i	$0.989125\pi$
$272$	1.32435	−	0.430307i	0.0803004	−	0.0260912i
$273$	16.4386	−	22.6259i	0.994912	−	1.36938i
$274$	3.56773			0.215535
$275$		0			0
$276$	−2.07855			−0.125114
$277$	11.0439	−	15.2006i	0.663564	−	0.913318i	−0.336028	−	0.941852i	$-0.609084\pi$
$277$	11.0439	−	15.2006i	0.663564	−	0.913318i	0.999593	+	0.0285338i	$0.00908382\pi$
$278$	−9.45923	+	3.07349i	−0.567327	+	0.184336i
$279$	4.21112	+	12.9605i	0.252113	+	0.775925i
$280$		0			0
$281$	2.43554	−	7.49583i	0.145292	−	0.447164i	−0.851756	−	0.523938i	$-0.824462\pi$
$281$	2.43554	−	7.49583i	0.145292	−	0.447164i	0.997048	+	0.0767748i	$0.0244622\pi$
$282$		−	8.80489i		−	0.524323i
$283$	17.4042	+	5.65496i	1.03457	+	0.336153i	0.776596	−	0.629999i	$-0.216945\pi$
$283$	17.4042	+	5.65496i	1.03457	+	0.336153i	0.257975	+	0.966151i	$0.416945\pi$
$284$	−5.41853	+	3.93679i	−0.321530	+	0.233606i
$285$		0			0
$286$	9.69922	+	7.04690i	0.573527	+	0.416692i
$287$	3.30386	+	4.54738i	0.195021	+	0.268423i
$288$	1.43521	+	1.97539i	0.0845703	+	0.116401i
$289$	−12.1846	−	8.85260i	−0.716739	−	0.520741i
$290$		0			0
$291$	−0.170172	+	0.123637i	−0.00997564	+	0.00724773i
$292$	4.91575	+	1.59722i	0.287672	+	0.0934704i
$293$			29.4990i			1.72335i	0.507461	+	0.861675i	$0.330584\pi$
$293$			29.4990i			1.72335i	−0.507461	+	0.861675i	$0.669416\pi$
$294$	5.22378	−	16.0771i	0.304657	−	0.937638i
$295$		0			0
$296$	2.17779	+	6.70254i	0.126581	+	0.389577i
$297$	4.67502	−	1.51901i	0.271272	−	0.0881417i
$298$	11.4678	−	15.7841i	0.664314	−	0.914350i
$299$	−2.83020			−0.163674
$300$		0			0
$301$	10.1823			0.586896
$302$	−10.8343	+	14.9121i	−0.623443	+	0.858095i
$303$	−36.3369	+	11.8066i	−2.08750	+	0.678269i
$304$	−1.20945	−	3.72230i	−0.0693666	−	0.213488i
$305$		0			0
$306$	−1.05069	+	3.23368i	−0.0600638	+	0.184857i
$307$			13.9131i			0.794064i	0.917805	+	0.397032i	$0.129960\pi$
$307$			13.9131i			0.794064i	−0.917805	+	0.397032i	$0.870040\pi$
$308$	13.5493	+	4.40244i	0.772044	+	0.250852i
$309$	2.29523	−	1.66758i	0.130571	−	0.0948653i
$310$		0			0
$311$	−21.0050	−	15.2610i	−1.19108	−	0.865373i	−0.197705	−	0.980262i	$-0.563349\pi$
$311$	−21.0050	−	15.2610i	−1.19108	−	0.865373i	−0.993378	+	0.114889i	$0.963349\pi$
$312$	4.35522	+	5.99445i	0.246566	+	0.339369i
$313$	5.56861	+	7.66454i	0.314757	+	0.433225i	0.936857	−	0.349712i	$-0.113721\pi$
$313$	5.56861	+	7.66454i	0.314757	+	0.433225i	−0.622101	+	0.782937i	$0.713721\pi$
$314$	8.21673	+	5.96980i	0.463697	+	0.336895i
$315$		0			0
$316$	1.46160	−	1.06192i	0.0822215	−	0.0597374i
$317$	23.3079	+	7.57321i	1.30910	+	0.425354i	0.878740	−	0.477301i	$-0.158385\pi$
$317$	23.3079	+	7.57321i	1.30910	+	0.425354i	0.430365	+	0.902655i	$0.358385\pi$
$318$			27.0979i			1.51957i
$319$	0.0574054	−	0.176676i	0.00321408	−	0.00989194i
$320$		0			0
$321$	7.79427	+	23.9883i	0.435034	+	1.33890i
$322$	−3.19856	+	1.03928i	−0.178249	+	0.0579166i
$323$	3.20346	−	4.40918i	0.178245	−	0.245333i
$324$	10.3632			0.575731
$325$		0			0
$326$	−18.6004			−1.03018
$327$	−15.6522	+	21.5434i	−0.865568	+	1.19135i
$328$	−1.41630	+	0.460183i	−0.0782019	+	0.0254093i
$329$	−4.40244	−	13.5493i	−0.242715	−	0.746998i
$330$		0			0
$331$	−3.06247	+	9.42530i	−0.168328	+	0.518061i	−0.999266	−	0.0383039i	$-0.987804\pi$
$331$	−3.06247	+	9.42530i	−0.168328	+	0.518061i	0.830938	+	0.556365i	$0.187804\pi$
$332$		−	9.96783i		−	0.547056i
$333$	−16.3657	−	5.31754i	−0.896835	−	0.291399i
$334$	1.75683	−	1.27641i	0.0961293	−	0.0698420i
$335$		0			0
$336$	7.12330	+	5.17538i	0.388608	+	0.282340i
$337$	5.84003	+	8.03812i	0.318127	+	0.437864i	0.937894	−	0.346922i	$-0.112773\pi$
$337$	5.84003	+	8.03812i	0.318127	+	0.437864i	−0.619767	+	0.784786i	$0.712773\pi$
$338$	−1.71105	−	2.35506i	−0.0930690	−	0.128099i
$339$	19.6705	+	14.2914i	1.06835	+	0.776205i
$340$		0			0
$341$	−17.0425	+	12.3821i	−0.922904	+	0.670529i
$342$	9.08880	+	2.95313i	0.491466	+	0.159687i
$343$		−	0.930796i		−	0.0502583i
$344$	−0.833625	+	2.56564i	−0.0449461	+	0.138330i
$345$		0			0
$346$	−1.97593	−	6.08130i	−0.106227	−	0.326933i
$347$	18.6741	−	6.06757i	1.00248	−	0.325724i	0.238622	−	0.971113i	$-0.423304\pi$
$347$	18.6741	−	6.06757i	1.00248	−	0.325724i	0.763855	+	0.645388i	$0.223304\pi$
$348$	0.0674841	−	0.0928839i	0.00361753	−	0.00497910i
$349$	−1.48432			−0.0794538			−0.0397269	−	0.999211i	$-0.512649\pi$
$349$	−1.48432			−0.0794538			−0.0397269	+	0.999211i	$0.512649\pi$
$350$		0			0
$351$	4.13662			0.220796
$352$	−2.21858	+	3.05361i	−0.118251	+	0.162758i
$353$	9.77569	−	3.17632i	0.520308	−	0.169058i	−0.0370772	−	0.999312i	$-0.511805\pi$
$353$	9.77569	−	3.17632i	0.520308	−	0.169058i	0.557385	+	0.830254i	$0.311805\pi$
$354$	−0.497446	−	1.53098i	−0.0264390	−	0.0813708i
$355$		0			0
$356$	4.48391	−	13.8001i	0.237647	−	0.731402i
$357$			12.2608i			0.648911i
$358$	−7.62127	−	2.47630i	−0.402797	−	0.130877i
$359$	−8.39154	+	6.09681i	−0.442889	+	0.321777i	−0.786782	−	0.617231i	$-0.788254\pi$
$359$	−8.39154	+	6.09681i	−0.442889	+	0.321777i	0.343893	+	0.939009i	$0.388254\pi$
$360$		0			0
$361$	2.97859	+	2.16408i	0.156768	+	0.113899i
$362$	6.38504	+	8.78826i	0.335590	+	0.461901i
$363$	−4.45160	−	6.12710i	−0.233648	−	0.321589i
$364$	9.69922	+	7.04690i	0.508377	+	0.369358i
$365$		0			0
$366$	19.5524	−	14.2056i	1.02202	−	0.742540i
$367$	24.7981	+	8.05741i	1.29445	+	0.420593i	0.873648	−	0.486558i	$-0.161748\pi$
$367$	24.7981	+	8.05741i	1.29445	+	0.420593i	0.420804	+	0.907151i	$0.361748\pi$
$368$		−	0.891031i		−	0.0464482i
$369$	1.12364	−	3.45820i	0.0584942	−	0.180027i
$370$		0			0
$371$	13.5489	+	41.6993i	0.703426	+	2.16492i
$372$	−12.3821	+	4.02319i	−0.641982	+	0.208593i
$373$	−5.55806	+	7.65001i	−0.287785	+	0.396102i	−0.928293	−	0.371849i	$-0.878724\pi$
$373$	−5.55806	+	7.65001i	−0.287785	+	0.396102i	0.640508	+	0.767952i	$0.278724\pi$
$374$	−5.25595			−0.271779
$375$		0			0
$376$	3.77447			0.194653
$377$	0.0918876	−	0.126472i	0.00473245	−	0.00651366i
$378$	4.67502	−	1.51901i	0.240457	−	0.0781292i
$379$	10.9163	+	33.5968i	0.560731	+	1.72575i	0.680307	+	0.732927i	$0.261846\pi$
$379$	10.9163	+	33.5968i	0.560731	+	1.72575i	−0.119576	+	0.992825i	$0.538154\pi$
$380$		0			0
$381$	2.55828	−	7.87358i	0.131065	−	0.403376i
$382$		−	8.18577i		−	0.418820i
$383$	−28.3580	−	9.21407i	−1.44902	−	0.470817i	−0.524327	−	0.851517i	$-0.675683\pi$
$383$	−28.3580	−	9.21407i	−1.44902	−	0.470817i	−0.924698	+	0.380700i	$0.875683\pi$
$384$	−1.88723	+	1.37116i	−0.0963075	+	0.0699715i
$385$		0			0
$386$	14.2044	+	10.3201i	0.722985	+	0.525280i
$387$	−3.87171	−	5.32895i	−0.196810	−	0.270886i
$388$	−0.0530006	−	0.0729490i	−0.00269070	−	0.00370343i
$389$	−17.2942	−	12.5649i	−0.876848	−	0.637068i	0.0555675	−	0.998455i	$-0.482303\pi$
$389$	−17.2942	−	12.5649i	−0.876848	−	0.637068i	−0.932416	+	0.361387i	$0.882303\pi$
$390$		0			0
$391$	1.00380	−	0.729301i	0.0507642	−	0.0368824i
$392$	6.89193	+	2.23932i	0.348095	+	0.113103i
$393$			9.45519i			0.476951i
$394$	−1.47012	+	4.52458i	−0.0740638	+	0.227945i
$395$		0			0
$396$	−2.84796	−	8.76511i	−0.143115	−	0.440464i
$397$	−19.9913	+	6.49555i	−1.00333	+	0.326002i	−0.764196	−	0.644984i	$-0.776864\pi$
$397$	−19.9913	+	6.49555i	−1.00333	+	0.326002i	−0.239136	+	0.970986i	$0.576864\pi$
$398$	−8.54169	+	11.7566i	−0.428156	+	0.589307i
$399$	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	$0.362371\pi$
$402$	−21.0108	+	28.9188i	−1.04792	+	1.44234i
$403$	−16.8597	+	5.47805i	−0.839842	+	0.272881i
$404$	−5.06122	−	15.5768i	−0.251805	−	0.774977i
$405$		0			0
$406$	0.0574054	−	0.176676i	0.00284898	−	0.00876826i
$407$		−	26.6004i		−	1.31853i
$408$	−3.08937	−	1.00380i	−0.152947	−	0.0496954i
$409$	29.4165	−	21.3723i	1.45455	−	1.05679i	0.469809	−	0.882768i	$-0.344323\pi$
$409$	29.4165	−	21.3723i	1.45455	−	1.05679i	0.984741	−	0.174025i	$-0.0556772\pi$
$410$		0			0
$411$	−6.73315	−	4.89192i	−0.332122	−	0.241301i
$412$	0.714856	+	0.983915i	0.0352184	+	0.0484740i
$413$	−1.53098	−	2.10722i	−0.0753347	−	0.103689i
$414$	1.76013	+	1.27881i	0.0865059	+	0.0628502i
$415$		0			0
$416$	−2.56969	+	1.86699i	−0.125990	+	0.0915368i
$417$	22.0660	+	7.16968i	1.08058	+	0.351101i
$418$			14.7727i			0.722557i
$419$	10.6731	−	32.8484i	0.521415	−	1.60475i	−0.249884	−	0.968276i	$-0.580392\pi$
$419$	10.6731	−	32.8484i	0.521415	−	1.60475i	0.771298	−	0.636474i	$-0.219608\pi$
$420$		0			0
$421$	3.00798	+	9.25762i	0.146600	+	0.451189i	0.997213	−	0.0746033i	$-0.0237691\pi$
$421$	3.00798	+	9.25762i	0.146600	+	0.451189i	−0.850613	+	0.525792i	$0.823769\pi$
$422$	13.4440	−	4.36823i	0.654445	−	0.212642i
$423$	−5.41714	+	7.45605i	−0.263390	+	0.362526i
$424$	−11.6163			−0.564136
$425$		0			0
$426$	15.6240			0.756984
$427$	22.9852	−	31.6364i	1.11233	−	1.53099i
$428$	−10.2833	+	3.34124i	−0.497061	+	0.161505i
$429$	−8.64231	−	26.5983i	−0.417255	−	1.28418i
$430$		0			0
$431$	−0.956560	+	2.94399i	−0.0460759	+	0.141807i	−0.971448	−	0.237254i	$-0.923753\pi$
$431$	−0.956560	+	2.94399i	−0.0460759	+	0.141807i	0.925372	+	0.379061i	$0.123753\pi$
$432$			1.30233i			0.0626584i
$433$	17.3440	+	5.63542i	0.833501	+	0.270821i	0.694519	−	0.719474i	$-0.255617\pi$
$433$	17.3440	+	5.63542i	0.833501	+	0.270821i	0.138981	+	0.990295i	$0.455617\pi$
$434$	−17.0425	+	12.3821i	−0.818067	+	0.594360i
$435$		0			0
$436$	−9.23519	−	6.70976i	−0.442285	−	0.321339i
$437$	−2.04982	−	2.82134i	−0.0980563	−	0.134963i
$438$	−7.08712	−	9.75458i	−0.338636	−	0.466092i
$439$	−21.4595	−	15.5912i	−1.02421	−	0.744129i	−0.0570645	−	0.998370i	$-0.518174\pi$
$439$	−21.4595	−	15.5912i	−1.02421	−	0.744129i	−0.967141	+	0.254242i	$0.918174\pi$
$440$		0			0
$441$	−14.3149	+	10.4004i	−0.681661	+	0.495256i
$442$	−4.20655	−	1.36679i	−0.200085	−	0.0650115i
$443$		−	35.5267i		−	1.68793i	−0.536401	−	0.843963i	$-0.680217\pi$
$443$		−	35.5267i		−	1.68793i	0.536401	−	0.843963i	$-0.319783\pi$
$444$	5.08023	−	15.6353i	0.241097	−	0.742020i
$445$		0			0
$446$	1.42527	+	4.38652i	0.0674883	+	0.207708i
$447$	−43.2850	+	14.0641i	−2.04731	+	0.665211i
$448$	−2.21858	+	3.05361i	−0.104818	+	0.144269i
$449$	−16.1841			−0.763776			−0.381888	−	0.924209i	$-0.624726\pi$
$449$	−16.1841			−0.763776			−0.381888	+	0.924209i	$0.624726\pi$
$450$		0			0
$451$	5.62087			0.264676
$452$	−6.12644	+	8.43232i	−0.288163	+	0.396623i
$453$	40.8936	−	13.2871i	1.92135	−	0.624284i
$454$	1.94259	+	5.97869i	0.0911705	+	0.280594i
$455$		0			0
$456$	−2.82134	+	8.68318i	−0.132121	+	0.406627i
$457$			23.7205i			1.10960i	0.831984	+	0.554799i	$0.187205\pi$
$457$			23.7205i			1.10960i	−0.831984	+	0.554799i	$0.812795\pi$
$458$	−16.8689	−	5.48103i	−0.788230	−	0.256112i
$459$	−1.46715	+	1.06595i	−0.0684807	+	0.0497542i
$460$		0			0
$461$	6.36936	+	4.62761i	0.296651	+	0.215529i	0.726147	−	0.687539i	$-0.241309\pi$
$461$	6.36936	+	4.62761i	0.296651	+	0.215529i	−0.429497	+	0.903068i	$0.641309\pi$
$462$	−19.5343	−	26.8867i	−0.908818	−	1.25088i
$463$	9.06543	+	12.4775i	0.421306	+	0.579878i	0.965930	−	0.258802i	$-0.0833277\pi$
$463$	9.06543	+	12.4775i	0.421306	+	0.579878i	−0.544624	+	0.838680i	$0.683328\pi$
$464$	0.0398173	+	0.0289290i	0.00184847	+	0.00134299i
$465$		0			0
$466$	−2.07437	+	1.50712i	−0.0960932	+	0.0698158i
$467$	−16.2034	−	5.26481i	−0.749805	−	0.243626i	−0.0909075	−	0.995859i	$-0.528977\pi$
$467$	−16.2034	−	5.26481i	−0.749805	−	0.243626i	−0.658897	+	0.752233i	$0.728977\pi$
$468$		−	7.75567i		−	0.358506i
$469$	−17.8728	+	55.0069i	−0.825290	+	2.53998i
$470$		0			0
$471$	−7.32136	−	22.5328i	−0.337350	−	1.03826i
$472$	0.656300	−	0.213245i	0.0302086	−	0.00981538i
$473$	5.98498	−	8.23762i	0.275190	−	0.378766i
$474$	−4.21443			−0.193575
$475$		0			0
$476$	−5.25595			−0.240906
$477$	16.6718	−	22.9467i	0.763347	−	1.05066i
$478$	8.97961	−	2.91765i	0.410718	−	0.133450i
$479$	7.75544	+	23.8688i	0.354355	+	1.09059i	0.956382	+	0.292118i	$0.0943598\pi$
$479$	7.75544	+	23.8688i	0.354355	+	1.09059i	−0.602027	+	0.798476i	$0.705640\pi$
$480$		0			0
$481$	6.91734	−	21.2894i	0.315403	−	0.970712i
$482$		−	29.4346i		−	1.34071i
$483$	7.46144	+	2.42437i	0.339507	+	0.110313i
$484$	2.62656	−	1.90831i	0.119389	−	0.0867412i
$485$		0			0
$486$	−16.3969	−	11.9130i	−0.743778	−	0.540386i
$487$	8.04536	+	11.0735i	0.364570	+	0.501788i	0.951415	−	0.307912i	$-0.0996301\pi$
$487$	8.04536	+	11.0735i	0.364570	+	0.501788i	−0.586845	+	0.809699i	$0.699630\pi$
$488$	6.08965	+	8.38168i	0.275665	+	0.379421i
$489$	35.1033	+	25.5041i	1.58743	+	1.15333i
$490$		0			0
$491$	2.08733	−	1.51654i	0.0942001	−	0.0684403i	−0.539688	−	0.841865i	$-0.681458\pi$
$491$	2.08733	−	1.51654i	0.0942001	−	0.0684403i	0.633888	+	0.773425i	$0.281458\pi$
$492$	3.30386	+	1.07349i	0.148950	+	0.0483967i
$493$			0.0685347i			0.00308665i
$494$	−3.84159	+	11.8232i	−0.172841	+	0.531950i
$495$		0			0
$496$	−1.72466	−	5.30795i	−0.0774394	−	0.238334i
$497$	24.0428	−	7.81199i	1.07847	−	0.350416i
$498$	−13.6674	+	18.8116i	−0.612453	+	0.842969i
$499$	39.0539			1.74829			0.874146	−	0.485664i	$-0.161422\pi$
$499$	39.0539			1.74829			0.874146	+	0.485664i	$0.161422\pi$
$500$		0			0
$501$	−5.06570			−0.226319
$502$	−3.53118	+	4.86025i	−0.157604	+	0.216923i
$503$	11.3686	−	3.69387i	0.506899	−	0.164702i	−0.0443923	−	0.999014i	$-0.514135\pi$
$503$	11.3686	−	3.69387i	0.506899	−	0.164702i	0.551292	+	0.834313i	$0.314135\pi$
$504$	−2.84796	−	8.76511i	−0.126858	−	0.390429i
$505$		0			0
$506$	−1.03928	+	3.19856i	−0.0462014	+	0.142193i
$507$			6.79067i			0.301584i
$508$	3.37524	+	1.09668i	0.149752	+	0.0486574i
$509$	−3.94254	+	2.86442i	−0.174750	+	0.126963i	−0.671722	−	0.740803i	$-0.734445\pi$
$509$	−3.94254	+	2.86442i	−0.174750	+	0.126963i	0.496972	+	0.867767i	$0.334445\pi$
$510$		0			0
$511$	−15.7832	−	11.4672i	−0.698210	−	0.507279i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	2.99602	+	4.12367i	0.132278	+	0.182064i
$514$	−11.0257	−	8.01067i	−0.486325	−	0.353336i
$515$		0			0
$516$	5.09113	−	3.69892i	0.224125	−	0.162836i
$517$	−13.5493	−	4.40244i	−0.595899	−	0.193619i
$518$		−	26.6004i		−	1.16876i
$519$	−4.60936	+	14.1861i	−0.202328	+	0.622702i
$520$		0			0
$521$	−2.70131	−	8.31378i	−0.118347	−	0.364233i	0.874284	−	0.485415i	$-0.161332\pi$
$521$	−2.70131	−	8.31378i	−0.118347	−	0.364233i	−0.992630	+	0.121182i	$0.961332\pi$
$522$	−0.114292	+	0.0371358i	−0.00500243	+	0.00162539i
$523$	12.3900	−	17.0534i	0.541778	−	0.745694i	−0.447090	−	0.894489i	$-0.647540\pi$
$523$	12.3900	−	17.0534i	0.541778	−	0.745694i	0.988868	+	0.148795i	$0.0475396\pi$
$524$	−4.05324			−0.177067
$525$		0			0
$526$	−9.16294			−0.399523
$527$	4.56809	−	6.28743i	0.198989	−	0.273885i
$528$	8.37394	−	2.72086i	0.364429	−	0.118410i
$529$	6.86205	+	21.1192i	0.298350	+	0.918227i
$530$		0			0
$531$	−0.520683	+	1.60250i	−0.0225957	+	0.0695425i
$532$			14.7727i			0.640478i
$533$	4.49861	+	1.46169i	0.194856	+	0.0633126i
$534$	−27.3842	+	19.8958i	−1.18503	+	0.860976i
$535$		0			0
$536$	−12.3969	−	9.00687i	−0.535464	−	0.389038i
$537$	10.9877	+	15.1233i	0.474155	+	0.652619i
$538$	16.5183	+	22.7355i	0.712155	+	0.980197i
$539$	−22.1283	−	16.0771i	−0.953133	−	0.692492i
$540$		0			0
$541$	−26.5406	+	19.2829i	−1.14107	+	0.829036i	−0.987268	−	0.159066i	$-0.949152\pi$
$541$	−26.5406	+	19.2829i	−1.14107	+	0.829036i	−0.153802	+	0.988102i	$0.549152\pi$
$542$	−8.65329	−	2.81162i	−0.371690	−	0.120770i
$543$		−	25.3404i		−	1.08746i
$544$	0.430307	−	1.32435i	0.0184492	−	0.0567809i
$545$		0			0
$546$	−8.64231	−	26.5983i	−0.369857	−	1.13830i
$547$	5.20264	−	1.69044i	0.222449	−	0.0722781i	−0.195672	−	0.980669i	$-0.562689\pi$
$547$	5.20264	−	1.69044i	0.222449	−	0.0722781i	0.418121	+	0.908391i	$0.362689\pi$
$548$	2.09706	−	2.88636i	0.0895820	−	0.123299i
$549$	−25.2970			−1.07965
$550$		0			0
$551$	0.192628			0.00820623
$552$	−1.22174	+	1.68158i	−0.0520008	+	0.0715729i
$553$	−6.48535	+	2.10722i	−0.275785	+	0.0896080i
$554$	−5.80613	−	17.8694i	−0.246679	−	0.759199i
$555$		0			0
$556$	−3.07349	+	9.45923i	−0.130345	+	0.401161i
$557$		−	5.19840i		−	0.220263i	−0.993917	−	0.110132i	$-0.964873\pi$
$557$		−	5.19840i		−	0.220263i	0.993917	−	0.110132i	$-0.0351273\pi$
$558$	12.9605	+	4.21112i	0.548662	+	0.178271i
$559$	6.93218	−	5.03652i	0.293200	−	0.213022i
$560$		0			0
$561$	9.91921	+	7.20673i	0.418789	+	0.304268i
$562$	−4.63268	−	6.37633i	−0.195418	−	0.268969i
$563$	−2.94788	−	4.05741i	−0.124238	−	0.170999i	0.742367	−	0.669993i	$-0.233703\pi$
$563$	−2.94788	−	4.05741i	−0.124238	−	0.170999i	−0.866605	+	0.498994i	$0.833703\pi$
$564$	−7.12330	−	5.17538i	−0.299945	−	0.217923i
$565$		0			0
$566$	14.8049	−	10.7564i	0.622296	−	0.452124i
$567$	−37.2010	−	12.0873i	−1.56229	−	0.507620i
$568$			6.69767i			0.281028i
$569$	12.9303	−	39.7952i	0.542064	−	1.66830i	−0.185805	−	0.982587i	$-0.559489\pi$
$569$	12.9303	−	39.7952i	0.542064	−	1.66830i	0.727869	−	0.685716i	$-0.240511\pi$
$570$		0			0
$571$	−13.7723	−	42.3869i	−0.576355	−	1.77384i	−0.631519	−	0.775360i	$-0.717568\pi$
$571$	−13.7723	−	42.3869i	−0.576355	−	1.77384i	0.0551642	−	0.998477i	$-0.482432\pi$
$572$	11.4021	−	3.70477i	0.476747	−	0.154904i
$573$	−11.2240	+	15.4485i	−0.468888	+	0.645369i
$574$	5.62087			0.234611
$575$		0			0
$576$	2.44172			0.101738
$577$	−14.7779	+	20.3401i	−0.615213	+	0.846769i	−0.996994	−	0.0774845i	$-0.975311\pi$
$577$	−14.7779	+	20.3401i	−0.615213	+	0.846769i	0.381780	+	0.924253i	$0.375311\pi$
$578$	−14.3238	+	4.65409i	−0.595792	+	0.193584i
$579$	−12.6566	−	38.9529i	−0.525989	−	1.61883i
$580$		0			0
$581$	−11.6262	+	35.7818i	−0.482337	+	1.48448i
$582$			0.210344i			0.00871903i
$583$	41.6993	+	13.5489i	1.72701	+	0.561140i
$584$	4.18158	−	3.03810i	0.173035	−	0.125717i
$585$		0			0
$586$	23.8652	+	17.3391i	0.985861	+	0.716270i
$587$	−12.5525	−	17.2770i	−0.518097	−	0.713099i	0.467162	−	0.884172i	$-0.345277\pi$
$587$	−12.5525	−	17.2770i	−0.518097	−	0.713099i	−0.985258	+	0.171073i	$0.945277\pi$
$588$	−9.93622	−	13.6760i	−0.409763	−	0.563990i
$589$	−17.6719	−	12.8394i	−0.728157	−	0.529037i
$590$		0			0
$591$	8.97836	−	6.52316i	0.369321	−	0.268327i
$592$	6.70254	+	2.17779i	0.275473	+	0.0895065i
$593$			33.4430i			1.37334i	0.726970	+	0.686669i	$0.240928\pi$
$593$			33.4430i			1.37334i	−0.726970	+	0.686669i	$0.759072\pi$
$594$	1.51901	−	4.67502i	0.0623256	−	0.191818i
$595$		0			0
$596$	−6.02900	−	18.5554i	−0.246957	−	0.760057i
$597$	32.2403	−	10.4755i	1.31951	−	0.428734i
$598$	−1.66355	+	2.28968i	−0.0680275	+	0.0936318i
$599$	−26.3174			−1.07530			−0.537650	−	0.843168i	$-0.680688\pi$
$599$	−26.3174			−1.07530			−0.537650	+	0.843168i	$0.680688\pi$
$600$		0			0
$601$	20.9964			0.856462			0.428231	−	0.903669i	$-0.359137\pi$
$601$	20.9964			0.856462			0.428231	+	0.903669i	$0.359137\pi$
$602$	5.98498	−	8.23762i	0.243930	−	0.335740i
$603$	35.5842	−	11.5620i	1.44910	−	0.470841i
$604$	5.69592	+	17.5302i	0.231764	+	0.713295i
$605$		0			0
$606$	−11.8066	+	36.3369i	−0.479609	+	1.47608i
$607$			9.32822i			0.378621i	0.981917	+	0.189310i	$0.0606253\pi$
$607$			9.32822i			0.378621i	−0.981917	+	0.189310i	$0.939375\pi$
$608$	−3.72230	−	1.20945i	−0.150959	−	0.0490496i
$609$	−0.350587	+	0.254716i	−0.0142065	+	0.0103216i
$610$		0			0
$611$	−9.69922	−	7.04690i	−0.392389	−	0.285087i
$612$	1.99853	+	2.75074i	0.0807856	+	0.111192i
$613$	−18.8700	−	25.9724i	−0.762154	−	1.04902i	−0.997032	−	0.0769902i	$-0.975469\pi$
$613$	−18.8700	−	25.9724i	−0.762154	−	1.04902i	0.234878	−	0.972025i	$-0.424531\pi$
$614$	11.2560	+	8.17793i	0.454253	+	0.330034i
$615$		0			0
$616$	11.5257	−	8.37394i	0.464385	−	0.337396i
$617$	−30.3631	−	9.86557i	−1.22237	−	0.397173i	−0.374427	−	0.927257i	$-0.622160\pi$
$617$	−30.3631	−	9.86557i	−1.22237	−	0.397173i	−0.847945	+	0.530084i	$0.822160\pi$
$618$		−	2.83706i		−	0.114123i
$619$	1.40420	−	4.32167i	0.0564394	−	0.173703i	−0.918863	−	0.394577i	$-0.870891\pi$
$619$	1.40420	−	4.32167i	0.0564394	−	0.173703i	0.975302	+	0.220875i	$0.0708911\pi$
$620$		0			0
$621$	0.358589	+	1.10362i	0.0143897	+	0.0442868i
$622$	−24.6928	+	8.02319i	−0.990093	+	0.321701i
$623$	−32.1921	+	44.3086i	−1.28975	+	1.77519i
$624$	7.40955			0.296619
$625$		0			0
$626$	9.47389			0.378653
$627$	20.2557	−	27.8796i	0.808934	−	1.11340i
$628$	9.65934	−	3.13851i	0.385450	−	0.125240i
$629$	3.03257	+	9.33329i	0.120916	+	0.372143i
$630$		0			0
$631$	−8.31756	+	25.5988i	−0.331117	+	1.01907i	0.637486	+	0.770462i	$0.279974\pi$
$631$	−8.31756	+	25.5988i	−0.331117	+	1.01907i	−0.968603	+	0.248611i	$0.920026\pi$
$632$		−	1.80664i		−	0.0718642i
$633$	−31.3615	−	10.1900i	−1.24651	−	0.405015i
$634$	19.8269	−	14.4051i	0.787427	−	0.572100i
$635$		0			0
$636$	21.9226	+	15.9277i	0.869289	+	0.631575i
$637$	−13.5293	−	18.6215i	−0.536052	−	0.737813i
$638$	−0.109192	−	0.150289i	−0.00432293	−	0.00595001i
$639$	−13.2305	−	9.61253i	−0.523391	−	0.380266i
$640$		0			0
$641$	−28.9303	+	21.0191i	−1.14268	+	0.830205i	−0.987490	−	0.157679i	$-0.949599\pi$
$641$	−28.9303	+	21.0191i	−1.14268	+	0.830205i	−0.155189	+	0.987885i	$0.549599\pi$
$642$	23.9883	+	7.79427i	0.946743	+	0.307615i
$643$		−	28.2255i		−	1.11311i	−0.830812	−	0.556553i	$-0.812124\pi$
$643$		−	28.2255i		−	1.11311i	0.830812	−	0.556553i	$-0.187876\pi$
$644$	−1.03928	+	3.19856i	−0.0409532	+	0.126041i
$645$		0			0
$646$	−1.68416	−	5.18330i	−0.0662623	−	0.203934i
$647$	−1.21522	+	0.394848i	−0.0477751	+	0.0155231i	−0.332807	−	0.942995i	$-0.607996\pi$
$647$	−1.21522	+	0.394848i	−0.0477751	+	0.0155231i	0.285032	+	0.958518i	$0.407996\pi$
$648$	6.09132	−	8.38398i	0.239290	−	0.329354i
$649$	−2.60466			−0.102242
$650$		0			0
$651$	49.1410			1.92599
$652$	−10.9331	+	15.0481i	−0.428171	+	0.589327i
$653$	−26.0692	+	8.47040i	−1.02017	+	0.331472i	−0.770896	−	0.636961i	$-0.780191\pi$
$653$	−26.0692	+	8.47040i	−1.02017	+	0.331472i	−0.249272	+	0.968434i	$0.580191\pi$
$654$	8.22884	+	25.3258i	0.321773	+	0.990316i
$655$		0			0
$656$	−0.460183	+	1.41630i	−0.0179671	+	0.0552971i
$657$			12.6206i			0.492375i
$658$	−13.5493	−	4.40244i	−0.528208	−	0.171625i
$659$	−33.3535	+	24.2327i	−1.29927	+	0.943972i	−0.999948	−	0.0101814i	$-0.996759\pi$
$659$	−33.3535	+	24.2327i	−1.29927	+	0.943972i	−0.299318	+	0.954153i	$0.596759\pi$
$660$		0			0
$661$	21.4653	+	15.5955i	0.834904	+	0.606593i	0.920942	−	0.389699i	$-0.127421\pi$
$661$	21.4653	+	15.5955i	0.834904	+	0.606593i	−0.0860388	+	0.996292i	$0.527421\pi$
$662$	5.82516	+	8.01764i	0.226401	+	0.311614i
$663$	6.06465	+	8.34728i	0.235532	+	0.324181i
$664$	−8.06414	−	5.85894i	−0.312949	−	0.227371i
$665$		0			0
$666$	−13.9215	+	10.1146i	−0.539447	+	0.391931i
$667$	0.0417075	+	0.0135516i	0.00161492	+	0.000524719i
$668$		−	2.17156i		−	0.0840201i
$669$	3.32479	−	10.2326i	0.128544	−	0.395617i
$670$		0			0
$671$	−12.0840	−	37.1908i	−0.466499	−	1.43574i
$672$	8.37394	−	2.72086i	0.323032	−	0.104959i
$673$	4.66543	−	6.42142i	0.179839	−	0.247527i	−0.709575	−	0.704630i	$-0.751113\pi$
$673$	4.66543	−	6.42142i	0.179839	−	0.247527i	0.889414	+	0.457103i	$0.151113\pi$
$674$	9.93566			0.382707
$675$		0			0
$676$	−2.91102			−0.111962
$677$	17.3402	−	23.8667i	0.666436	−	0.917271i	−0.333237	−	0.942843i	$-0.608141\pi$
$677$	17.3402	−	23.8667i	0.666436	−	0.917271i	0.999673	+	0.0255722i	$0.00814076\pi$
$678$	23.1240	−	7.51346i	0.888073	−	0.288553i
$679$	0.105172	+	0.323686i	0.00403613	+	0.0124219i
$680$		0			0
$681$	4.53159	−	13.9468i	0.173651	−	0.534442i
$682$			21.0657i			0.806647i
$683$	−35.9012	−	11.6650i	−1.37372	−	0.446349i	−0.473121	−	0.880997i	$-0.656873\pi$
$683$	−35.9012	−	11.6650i	−1.37372	−	0.446349i	−0.900600	+	0.434648i	$0.856873\pi$
$684$	7.73139	−	5.61719i	0.295617	−	0.214779i
$685$		0			0
$686$	−0.753030	−	0.547108i	−0.0287508	−	0.0208887i
$687$	24.3201	+	33.4738i	0.927872	+	1.27711i
$688$	1.58565	+	2.18246i	0.0604523	+	0.0832055i
$689$	29.8503	+	21.6875i	1.13721	+	0.826228i
$690$		0			0
$691$	−14.2843	+	10.3782i	−0.543401	+	0.394804i	−0.825347	−	0.564626i	$-0.809020\pi$
$691$	−14.2843	+	10.3782i	−0.543401	+	0.394804i	0.281945	+	0.959430i	$0.409020\pi$
$692$	−6.08130	−	1.97593i	−0.231176	−	0.0751137i
$693$			34.7862i			1.32142i
$694$	6.06757	−	18.6741i	0.230322	−	0.708858i
$695$		0			0
$696$	−0.0354785	−	0.109192i	−0.00134481	−	0.00413889i
$697$	−1.97219	+	0.640805i	−0.0747022	+	0.0242722i
$698$	−0.872461	+	1.20084i	−0.0330231	+	0.0454524i
$699$	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	$0.603000\pi$
$702$	2.43144	−	3.34659i	0.0917688	−	0.126309i
$703$	26.2328	−	8.52354i	0.989387	−	0.321471i
$704$	1.16637	+	3.58973i	0.0439594	+	0.135293i
$705$		0			0
$706$	3.17632	−	9.77569i	0.119542	−	0.367913i
$707$			61.8200i			2.32498i
$708$	−1.53098	−	0.497446i	−0.0575378	−	0.0186952i
$709$	−23.1615	+	16.8278i	−0.869849	+	0.631982i	−0.930546	−	0.366174i	$-0.880667\pi$
$709$	−23.1615	+	16.8278i	−0.869849	+	0.631982i	0.0606978	+	0.998156i	$0.480667\pi$
$710$		0			0
$711$	3.56882	+	2.59290i	0.133841	+	0.0972412i
$712$	−8.52891	−	11.7390i	−0.319635	−	0.439939i
$713$	−2.92302	−	4.02319i	−0.109468	−	0.150670i
$714$	9.91921	+	7.20673i	0.371217	+	0.269705i
$715$		0			0
$716$	−6.48304	+	4.71020i	−0.242283	+	0.176029i
$717$	−20.9472	−	6.80615i	−0.782286	−	0.254180i
$718$			10.3725i			0.387099i
$719$	2.54857	−	7.84368i	0.0950455	−	0.292520i	−0.892220	−	0.451601i	$-0.850853\pi$
$719$	2.54857	−	7.84368i	0.0950455	−	0.292520i	0.987266	+	0.159081i	$0.0508531\pi$
$720$		0			0
$721$	−1.41853	−	4.36578i	−0.0528287	−	0.162590i
$722$	3.50155	−	1.13772i	0.130314	−	0.0423416i
$723$	−40.3595	+	55.5500i	−1.50098	+	2.06593i
$724$	10.8629			0.403716
$725$		0			0
$726$	−7.57351			−0.281079
$727$	−1.24248	+	1.71013i	−0.0460810	+	0.0634251i	−0.831436	−	0.555621i	$-0.812481\pi$
$727$	−1.24248	+	1.71013i	−0.0460810	+	0.0634251i	0.785355	+	0.619046i	$0.212481\pi$
$728$	11.4021	−	3.70477i	0.422591	−	0.137308i
$729$	5.00295	+	15.3975i	0.185295	+	0.570278i
$730$		0			0
$731$	−1.16082	+	3.57265i	−0.0429346	+	0.132139i
$732$		−	24.1681i		−	0.893277i
$733$	−42.9451	−	13.9537i	−1.58622	−	0.515393i	−0.622567	−	0.782567i	$-0.713910\pi$
$733$	−42.9451	−	13.9537i	−1.58622	−	0.515393i	−0.963648	+	0.267174i	$0.913910\pi$
$734$	21.0946	−	15.3261i	0.778614	−	0.565697i
$735$		0			0
$736$	−0.720859	−	0.523735i	−0.0265712	−	0.0193051i
$737$	33.9961	+	46.7917i	1.25226	+	1.72359i
$738$	−2.13728	−	2.94172i	−0.0786745	−	0.108286i
$739$	24.2478	+	17.6171i	0.891969	+	0.648054i	0.936391	−	0.350959i	$-0.114144\pi$
$739$	24.2478	+	17.6171i	0.891969	+	0.648054i	−0.0444213	+	0.999013i	$0.514144\pi$
$740$		0			0
$741$	23.4614	−	17.0457i	0.861876	−	0.626190i
$742$	41.6993	+	13.5489i	1.53083	+	0.497397i
$743$		−	17.6562i		−	0.647741i	−0.946101	−	0.323871i	$-0.895016\pi$
$743$		−	17.6562i		−	0.647741i	0.946101	−	0.323871i	$-0.104984\pi$
$744$	−4.02319	+	12.3821i	−0.147497	+	0.453950i
$745$		0			0
$746$	2.92204	+	8.99312i	0.106984	+	0.329262i
$747$	23.1474	−	7.52105i	0.846920	−	0.275181i
$748$	−3.08937	+	4.25215i	−0.112959	+	0.155474i
$749$	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	$0.314702\pi$
$752$	2.21858	−	3.05361i	0.0809031	−	0.111354i
$753$	13.3283	−	4.33063i	0.485710	−	0.157817i
$754$	−0.0483082	−	0.148677i	−0.00175928	−	0.00541451i
$755$		0			0
$756$	1.51901	−	4.67502i	0.0552457	−	0.170029i
$757$		−	4.90706i		−	0.178350i	−0.996016	−	0.0891750i	$-0.971577\pi$
$757$		−	4.90706i		−	0.178350i	0.996016	−	0.0891750i	$-0.0284231\pi$
$758$	33.5968	+	10.9163i	1.22029	+	0.396497i
$759$	6.34708	−	4.61142i	0.230384	−	0.167384i
$760$		0			0
$761$	−10.7466	−	7.80786i	−0.389564	−	0.283035i	0.375713	−	0.926736i	$-0.377398\pi$
$761$	−10.7466	−	7.80786i	−0.389564	−	0.283035i	−0.765277	+	0.643701i	$0.777398\pi$
$762$	−4.86614	−	6.69767i	−0.176282	−	0.242631i
$763$	25.3258	+	34.8579i	0.916854	+	1.26194i
$764$	−6.62243	−	4.81147i	−0.239591	−	0.174073i
$765$		0			0
$766$	−24.1227	+	17.5262i	−0.871590	+	0.633247i
$767$	−2.08461	−	0.677332i	−0.0752711	−	0.0244571i
$768$			2.33275i			0.0841758i
$769$	8.83716	−	27.1980i	0.318676	−	0.980784i	−0.655539	−	0.755162i	$-0.727558\pi$
$769$	8.83716	−	27.1980i	0.318676	−	0.980784i	0.974215	−	0.225623i	$-0.0724417\pi$
$770$		0			0
$771$	9.82428	+	30.2360i	0.353813	+	1.08892i
$772$	16.6983	−	5.42560i	0.600984	−	0.195272i
$773$	26.4871	−	36.4564i	0.952675	−	1.31124i	0.00234562	−	0.999997i	$-0.499253\pi$
$773$	26.4871	−	36.4564i	0.952675	−	1.31124i	0.950329	−	0.311247i	$-0.100747\pi$
$774$	−6.58695			−0.236763
$775$		0			0
$776$	−0.0901699			−0.00323691
$777$	−36.4733	+	50.2012i	−1.30847	+	1.80096i
$778$	−20.3305	+	6.60578i	−0.728884	+	0.236829i
$779$	1.80109	+	5.54318i	0.0645307	+	0.198605i
$780$		0			0
$781$	7.81199	−	24.0428i	0.279535	−	0.860320i
$782$		−	1.24076i		−	0.0443695i
$783$	−0.0609596	−	0.0198070i	−0.00217852	−	0.000707844i
$784$	5.86263	−	4.25945i	0.209379	−	0.152123i
$785$		0			0
$786$	7.64941	+	5.55762i	0.272846	+	0.198234i
$787$	−15.1454	−	20.8458i	−0.539875	−	0.743074i	0.448720	−	0.893672i	$-0.351880\pi$
$787$	−15.1454	−	20.8458i	−0.539875	−	0.743074i	−0.988595	+	0.150598i	$0.951880\pi$
$788$	2.79634	+	3.84883i	0.0996156	+	0.137109i
$789$	17.2926	+	12.5638i	0.615633	+	0.447284i
$790$		0			0
$791$	31.8275	−	23.1240i	1.13166	−	0.822196i
$792$	−8.76511	−	2.84796i	−0.311455	−	0.101198i
$793$		−	32.9077i		−	1.16859i
$794$	−6.49555	+	19.9913i	−0.230519	+	0.709463i
$795$		0			0
$796$	4.49063	+	13.8207i	0.159166	+	0.489863i
$797$	−47.9757	+	15.5882i	−1.69939	+	0.552164i	−0.988510	−	0.151154i	$-0.951701\pi$
$797$	−47.9757	+	15.5882i	−1.69939	+	0.552164i	−0.710875	+	0.703318i	$0.751701\pi$
$798$	20.2557	−	27.8796i	0.717044	−	0.986926i
$799$	5.25595			0.185942
$800$		0			0
$801$	35.4299			1.25186
$802$	9.86421	−	13.5769i	0.348317	−	0.479418i
$803$	−18.5543	+	6.02866i	−0.654768	+	0.212747i
$804$	11.0460	+	33.9961i	0.389563	+	1.19895i
$805$		0			0
$806$	−5.47805	+	16.8597i	−0.192956	+	0.593858i
$807$		−	65.5564i		−	2.30769i
$808$	−15.5768	−	5.06122i	−0.547991	−	0.178053i
$809$	−2.92626	+	2.12605i	−0.102882	+	0.0747480i	−0.638037	−	0.770006i	$-0.720253\pi$
$809$	−2.92626	+	2.12605i	−0.102882	+	0.0747480i	0.535155	+	0.844754i	$0.320253\pi$
$810$		0			0
$811$	−40.8026	−	29.6448i	−1.43277	−	1.04097i	−0.989492	−	0.144586i	$-0.953815\pi$
$811$	−40.8026	−	29.6448i	−1.43277	−	1.04097i	−0.443280	−	0.896383i	$-0.646185\pi$
$812$	−0.109192	−	0.150289i	−0.00383187	−	0.00527412i
$813$	12.4756	+	17.1712i	0.437538	+	0.602220i
$814$	−21.5202	−	15.6353i	−0.754282	−	0.548018i
$815$		0			0
$816$	−2.62798	+	1.90934i	−0.0919975	+	0.0668401i
$817$	10.0415	+	3.26269i	0.351308	+	0.114147i
$818$		−	36.3607i		−	1.27132i
$819$	−9.04601	+	27.8408i	−0.316093	+	0.972835i
$820$		0			0
$821$	−3.48714	−	10.7323i	−0.121702	−	0.374560i	0.871584	−	0.490246i	$-0.163093\pi$
$821$	−3.48714	−	10.7323i	−0.121702	−	0.374560i	−0.993286	+	0.115686i	$0.963093\pi$
$822$	−7.91529	+	2.57183i	−0.276077	+	0.0897030i
$823$	−0.632926	+	0.871148i	−0.0220624	+	0.0303663i	−0.819906	−	0.572499i	$-0.805974\pi$
$823$	−0.632926	+	0.871148i	−0.0220624	+	0.0303663i	0.797843	+	0.602865i	$0.205974\pi$
$824$	1.21619			0.0423678
$825$		0			0
$826$	−2.60466			−0.0906278
$827$	−17.2691	+	23.7689i	−0.600506	+	0.826526i	−0.995755	−	0.0920482i	$-0.970659\pi$
$827$	−17.2691	+	23.7689i	−0.600506	+	0.826526i	0.395248	+	0.918574i	$0.370659\pi$
$828$	2.06916	−	0.672312i	0.0719084	−	0.0233644i
$829$	−6.51402	−	20.0481i	−0.226241	−	0.696299i	−0.998163	−	0.0605816i	$-0.980704\pi$
$829$	−6.51402	−	20.0481i	−0.226241	−	0.696299i	0.771922	−	0.635717i	$-0.219296\pi$
$830$		0			0
$831$	−13.5442	+	41.6849i	−0.469845	+	1.44603i
$832$			3.17632i			0.110119i
$833$	9.59702	+	3.11826i	0.332517	+	0.108041i
$834$	18.7705	−	13.6375i	0.649968	−	0.472230i
$835$		0			0
$836$	11.9514	+	8.68318i	0.413347	+	0.300314i
$837$	4.27229	+	5.88030i	0.147672	+	0.203253i
$838$	−20.3014	−	27.9425i	−0.701301	−	0.965258i
$839$	−2.76181	−	2.00657i	−0.0953483	−	0.0692746i	0.539090	−	0.842248i	$-0.318768\pi$
$839$	−2.76181	−	2.00657i	−0.0953483	−	0.0692746i	−0.634438	+	0.772974i	$0.718768\pi$
$840$		0			0
$841$	23.4595	−	17.0443i	0.808949	−	0.587736i
$842$	9.25762	+	3.00798i	0.319038	+	0.103662i
$843$			18.3857i			0.633239i
$844$	4.36823	−	13.4440i	0.150361	−	0.462762i
$845$		0			0
$846$	2.84796	+	8.76511i	0.0979148	+	0.301351i
$847$	−11.6544	+	3.78676i	−0.400451	+	0.130114i
$848$	−6.82788	+	9.39777i	−0.234470	+	0.322721i
$849$	−42.6889			−1.46508
$850$		0			0
$851$	6.27951			0.215259
$852$	9.18355	−	12.6401i	0.314623	−	0.433042i
$853$	−38.6094	+	12.5449i	−1.32196	+	0.429531i	−0.883167	−	0.469058i	$-0.844594\pi$
$853$	−38.6094	+	12.5449i	−1.32196	+	0.429531i	−0.438792	+	0.898589i	$0.644594\pi$
$854$	−12.0840	−	37.1908i	−0.413507	−	1.27264i
$855$		0			0
$856$	−3.34124	+	10.2833i	−0.114201	+	0.351475i
$857$		−	43.0463i		−	1.47043i	−0.677833	−	0.735216i	$-0.737081\pi$
$857$		−	43.0463i		−	1.47043i	0.677833	−	0.735216i	$-0.262919\pi$
$858$	−26.5983	−	8.64231i	−0.908051	−	0.295044i
$859$	6.17691	−	4.48779i	0.210753	−	0.153121i	−0.477401	−	0.878685i	$-0.658421\pi$
$859$	6.17691	−	4.48779i	0.210753	−	0.153121i	0.688155	+	0.725564i	$0.258421\pi$
$860$		0			0
$861$	−10.6079	−	7.70709i	−0.361516	−	0.262657i
$862$	1.81949	+	2.50431i	0.0619719	+	0.0852970i
$863$	3.80562	+	5.23799i	0.129545	+	0.178303i	0.868862	−	0.495054i	$-0.164852\pi$
$863$	3.80562	+	5.23799i	0.129545	+	0.178303i	−0.739317	+	0.673357i	$0.764852\pi$
$864$	1.05361	+	0.765491i	0.0358445	+	0.0260425i
$865$		0			0
$866$	14.7537	−	10.7192i	0.501351	−	0.364253i
$867$	33.4138	+	10.8568i	1.13479	+	0.368717i
$868$			21.0657i			0.715016i
$869$	−2.10722	+	6.48535i	−0.0714824	+	0.220000i
$870$		0			0
$871$	15.0405	+	46.2898i	0.509627	+	1.56847i
$872$	−10.8566	+	3.52753i	−0.367652	+	0.119457i
$873$	0.129412	−	0.178121i	0.00437995	−	0.00602848i
$874$	−3.48736			−0.117962
$875$		0			0
$876$	−12.0573			−0.407379
$877$	−4.62651	+	6.36784i	−0.156226	+	0.215027i	−0.879954	−	0.475058i	$-0.842427\pi$
$877$	−4.62651	+	6.36784i	−0.156226	+	0.215027i	0.723728	+	0.690085i	$0.242427\pi$
$878$	−25.2271	+	8.19679i	−0.851374	+	0.276628i
$879$	−21.2646	−	65.4457i	−0.717238	−	2.20743i
$880$		0			0
$881$	5.95327	−	18.3223i	0.200571	−	0.617293i	−0.799295	−	0.600938i	$-0.794794\pi$
$881$	5.95327	−	18.3223i	0.200571	−	0.617293i	0.999866	−	0.0163551i	$-0.00520623\pi$
$882$			17.6942i			0.595793i
$883$	−5.96688	−	1.93876i	−0.200802	−	0.0652444i	0.206889	−	0.978364i	$-0.433666\pi$
$883$	−5.96688	−	1.93876i	−0.200802	−	0.0652444i	−0.407691	+	0.913120i	$0.633666\pi$
$884$	−3.57830	+	2.59979i	−0.120351	+	0.0874403i
$885$		0			0
$886$	−28.7417	−	20.8821i	−0.965597	−	0.701548i
$887$	−13.6794	−	18.8281i	−0.459309	−	0.632185i	0.515056	−	0.857156i	$-0.327771\pi$
$887$	−13.6794	−	18.8281i	−0.459309	−	0.632185i	−0.974365	+	0.224972i	$0.927771\pi$
$888$	−9.66317	−	13.3002i	−0.324275	−	0.446326i
$889$	−10.8371	−	7.87358i	−0.363463	−	0.264071i
$890$		0			0
$891$	−31.6451	+	22.9915i	−1.06015	+	0.770243i
$892$	4.38652	+	1.42527i	0.146871	+	0.0477214i
$893$		−	14.7727i		−	0.494350i
$894$	−14.0641	+	43.2850i	−0.470375	+	1.44767i
$895$		0			0
$896$	1.16637	+	3.58973i	0.0389658	+	0.119925i
$897$	6.27900	−	2.04017i	0.209650	−	0.0681194i
$898$	−9.51279	+	13.0932i	−0.317446	+	0.436927i
$899$	0.274685			0.00916126
$900$		0			0
$901$	−16.1757			−0.538890
$902$	3.30386	−	4.54738i	0.110007	−	0.151411i
$903$	−22.5901	+	7.33998i	−0.751752	+	0.244259i
$904$	3.22086	+	9.91279i	0.107124	+	0.329694i
$905$		0			0
$906$	13.2871	−	40.8936i	0.441436	−	1.35860i
$907$		−	17.6544i		−	0.586206i	−0.956081	−	0.293103i	$-0.905312\pi$
$907$		−	17.6544i		−	0.586206i	0.956081	−	0.293103i	$-0.0946879\pi$
$908$	5.97869	+	1.94259i	0.198410	+	0.0644673i
$909$	32.3539	−	23.5065i	1.07311	−	0.779660i
$910$		0			0
$911$	28.2767	+	20.5442i	0.936847	+	0.680659i	0.947660	−	0.319282i	$-0.103442\pi$
$911$	28.2767	+	20.5442i	0.936847	+	0.680659i	−0.0108124	+	0.999942i	$0.503442\pi$
$912$	5.36650	+	7.38636i	0.177703	+	0.244587i
$913$	22.1144	+	30.4378i	0.731879	+	1.00735i
$914$	19.1903	+	13.9426i	0.634758	+	0.461179i
$915$		0			0
$916$	−14.3495	+	10.4255i	−0.474121	+	0.344469i
$917$	14.5500	+	4.72760i	0.480485	+	0.156119i
$918$			1.81350i			0.0598544i
$919$	−11.2243	+	34.5449i	−0.370256	+	1.13953i	0.576368	+	0.817190i	$0.304469\pi$
$919$	−11.2243	+	34.5449i	−0.370256	+	1.13953i	−0.946624	+	0.322340i	$0.895531\pi$
$920$		0			0
$921$	−10.0294	−	30.8673i	−0.330480	−	1.01711i
$922$	7.48764	−	2.43288i	0.246592	−	0.0801226i
$923$	12.5045	−	17.2110i	0.411590	−	0.566505i
$924$	−33.2338			−1.09331
$925$		0			0
$926$	15.4230			0.506832
$927$	−1.74548	+	2.40244i	−0.0573290	+	0.0789066i
$928$	0.0468081	−	0.0152089i	0.00153655	−	0.000499256i
$929$	−5.88811	−	18.1217i	−0.193183	−	0.594555i	−0.999993	−	0.00374449i	$-0.998808\pi$
$929$	−5.88811	−	18.1217i	−0.193183	−	0.594555i	0.806810	−	0.590810i	$-0.201192\pi$
$930$		0			0
$931$	8.76439	−	26.9740i	0.287241	−	0.884037i
$932$			2.56406i			0.0839885i
$933$	57.6022	+	18.7161i	1.88581	+	0.612737i
$934$	−13.7834	+	10.0143i	−0.451008	+	0.327677i
$935$		0			0
$936$	−6.27447	−	4.55867i	−0.205087	−	0.149005i
$937$	−34.9896	−	48.1590i	−1.14306	−	1.57329i	−0.760475	−	0.649367i	$-0.775034\pi$
$937$	−34.9896	−	48.1590i	−1.14306	−	1.57329i	−0.382586	−	0.923920i	$-0.624966\pi$
$938$	33.9961	+	46.7917i	1.11001	+	1.52780i
$939$	−17.8794	−	12.9902i	−0.583474	−	0.423918i
$940$		0			0
$941$	−12.2598	+	8.90727i	−0.399658	+	0.290369i	−0.769402	−	0.638765i	$-0.779446\pi$
$941$	−12.2598	+	8.90727i	−0.399658	+	0.290369i	0.369744	+	0.929134i	$0.379446\pi$
$942$	−22.5328	−	7.32136i	−0.734159	−	0.238543i
$943$			1.32691i			0.0432101i
$944$	0.213245	−	0.656300i	0.00694052	−	0.0213607i
$945$		0			0
$946$	−3.14649	−	9.68391i	−0.102301	−	0.314851i
$947$	−2.39751	+	0.778999i	−0.0779087	+	0.0253141i	−0.347712	−	0.937601i	$-0.613041\pi$
$947$	−2.39751	+	0.778999i	−0.0779087	+	0.0253141i	0.269803	+	0.962915i	$0.413041\pi$
$948$	−2.47718	+	3.40955i	−0.0804551	+	0.110737i
$949$	−16.4175			−0.532934
$950$		0			0
$951$	−57.1697			−1.85385
$952$	−3.08937	+	4.25215i	−0.100127	+	0.137813i
$953$	29.8331	−	9.69336i	0.966389	−	0.313999i	0.217032	−	0.976165i	$-0.430363\pi$
$953$	29.8331	−	9.69336i	0.966389	−	0.313999i	0.749357	+	0.662166i	$0.230363\pi$
$954$	−8.76486	−	26.9755i	−0.283773	−	0.873363i
$955$		0			0
$956$	2.91765	−	8.97961i	0.0943636	−	0.290421i
$957$			0.433350i			0.0140082i
$958$	23.8688	+	7.75544i	0.771166	+	0.250567i
$959$	−10.8945	+	7.91529i	−0.351800	+	0.255598i
$960$		0			0
$961$	−0.120328	−	0.0874237i	−0.00388156	−	0.00282012i
$962$	−13.1576	−	18.1098i	−0.424217	−	0.583884i
$963$	−15.5181	−	21.3589i	−0.500065	−	0.688280i
$964$	−23.8131	−	17.3012i	−0.766969	−	0.557236i
$965$		0			0
$966$	6.34708	−	4.61142i	0.204214	−	0.148370i
$967$	46.7027	+	15.1746i	1.50186	+	0.487983i	0.940559	−	0.339630i	$-0.110302\pi$
$967$	46.7027	+	15.1746i	1.50186	+	0.487983i	0.561299	+	0.827613i	$0.310302\pi$
$968$		−	3.24660i		−	0.104350i
$969$	−3.92872	+	12.0913i	−0.126209	+	0.388430i
$970$		0			0
$971$	7.72049	+	23.7612i	0.247762	+	0.762534i	0.995170	+	0.0981683i	$0.0312983\pi$
$971$	7.72049	+	23.7612i	0.247762	+	0.762534i	−0.747407	+	0.664366i	$0.768702\pi$
$972$	−19.2757	+	6.26306i	−0.618268	+	0.200888i
$973$	22.0660	−	30.3713i	0.707404	−	0.973658i
$974$	13.6876			0.438579
$975$		0			0
$976$	10.3603			0.331626
$977$	9.16131	−	12.6095i	0.293096	−	0.403412i	−0.636921	−	0.770929i	$-0.719792\pi$
$977$	9.16131	−	12.6095i	0.293096	−	0.403412i	0.930017	+	0.367517i	$0.119792\pi$
$978$	41.2665	−	13.4083i	1.31956	−	0.428750i
$979$	16.9244	+	52.0879i	0.540906	+	1.66474i
$980$		0			0
$981$	8.61323	−	26.5088i	0.274999	−	0.846361i
$982$		−	2.58009i		−	0.0823339i
$983$	12.8953	+	4.18993i	0.411296	+	0.133638i	0.507354	−	0.861738i	$-0.330624\pi$
$983$	12.8953	+	4.18993i	0.411296	+	0.133638i	−0.0960585	+	0.995376i	$0.530624\pi$
$984$	2.81044	−	2.04190i	0.0895934	−	0.0650934i
$985$		0			0
$986$	0.0554457	+	0.0402837i	0.00176575	+	0.00128289i
$987$	19.5343	+	26.8867i	0.621784	+	0.855812i
$988$	7.30713	+	10.0574i	0.232471	+	0.319969i
$989$	1.94464	+	1.41286i	0.0618359	+	0.0449264i
$990$		0			0
$991$	−25.1120	+	18.2449i	−0.797709	+	0.579570i	−0.910241	−	0.414079i	$-0.864104\pi$
$991$	−25.1120	+	18.2449i	−0.797709	+	0.579570i	0.112532	+	0.993648i	$0.464104\pi$
$992$	−5.30795	−	1.72466i	−0.168527	−	0.0547579i
$993$		−	23.1184i		−	0.733639i
$994$	7.81199	−	24.0428i	0.247781	−	0.762592i
$995$		0			0
$996$	7.18540	+	22.1144i	0.227678	+	0.700721i
$997$	−1.47336	+	0.478723i	−0.0466617	+	0.0151613i	−0.332255	−	0.943190i	$-0.607809\pi$
$997$	−1.47336	+	0.478723i	−0.0466617	+	0.0151613i	0.285593	+	0.958351i	$0.407809\pi$
$998$	22.9553	−	31.5952i	0.726637	−	1.00013i
$999$	−9.17813			−0.290383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.e.c.49.3		16
5.2	odd	4		250.2.d.d.201.2		8
5.3	odd	4		50.2.d.b.41.1	yes	8
5.4	even	2	inner	250.2.e.c.49.2		16
15.8	even	4		450.2.h.e.91.2		8
20.3	even	4		400.2.u.d.241.2		8
25.2	odd	20		250.2.d.d.51.2		8
25.6	even	5		1250.2.b.e.1249.8		8
25.8	odd	20		1250.2.a.l.1.1		4
25.11	even	5	inner	250.2.e.c.199.2		16
25.14	even	10	inner	250.2.e.c.199.3		16
25.17	odd	20		1250.2.a.f.1.4		4
25.19	even	10		1250.2.b.e.1249.1		8
25.23	odd	20		50.2.d.b.11.1	✓	8
75.23	even	20		450.2.h.e.361.2		8
100.23	even	20		400.2.u.d.161.2		8
100.67	even	20		10000.2.a.x.1.1		4
100.83	even	20		10000.2.a.t.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.b.11.1	✓	8	25.23	odd	20
50.2.d.b.41.1	yes	8	5.3	odd	4
250.2.d.d.51.2		8	25.2	odd	20
250.2.d.d.201.2		8	5.2	odd	4
250.2.e.c.49.2		16	5.4	even	2	inner
250.2.e.c.49.3		16	1.1	even	1	trivial
250.2.e.c.199.2		16	25.11	even	5	inner
250.2.e.c.199.3		16	25.14	even	10	inner
400.2.u.d.161.2		8	100.23	even	20
400.2.u.d.241.2		8	20.3	even	4
450.2.h.e.91.2		8	15.8	even	4
450.2.h.e.361.2		8	75.23	even	20
1250.2.a.f.1.4		4	25.17	odd	20
1250.2.a.l.1.1		4	25.8	odd	20
1250.2.b.e.1249.1		8	25.19	even	10
1250.2.b.e.1249.8		8	25.6	even	5
10000.2.a.t.1.4		4	100.83	even	20
10000.2.a.x.1.1		4	100.67	even	20

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.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-2.21858 + 0.720859i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.720859 + 2.21858i) q^{6} +3.77447i q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.97539 - 1.43521i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-2.21858 + 0.720859i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.720859 + 2.21858i) q^{6} +3.77447i q^{7} +(-0.951057 - 0.309017i) q^{8} +(1.97539 - 1.43521i) q^{9} +(3.05361 + 2.21858i) q^{11} +(1.37116 + 1.88723i) q^{12} +(1.86699 + 2.56969i) q^{13} +(3.05361 + 2.21858i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.32435 - 0.430307i) q^{17} -2.44172i q^{18} +(-1.20945 + 3.72230i) q^{19} +(-2.72086 - 8.37394i) q^{21} +(3.58973 - 1.16637i) q^{22} +(-0.523735 + 0.720859i) q^{23} +2.33275 q^{24} +3.17632 q^{26} +(0.765491 - 1.05361i) q^{27} +(3.58973 - 1.16637i) q^{28} +(-0.0152089 - 0.0468081i) q^{29} +(-1.72466 + 5.30795i) q^{31} +1.00000i q^{32} +(-8.37394 - 2.72086i) q^{33} +(-1.12656 + 0.818492i) q^{34} +(-1.97539 - 1.43521i) q^{36} +(-4.14240 - 5.70152i) q^{37} +(2.30051 + 3.16637i) q^{38} +(-5.99445 - 4.35522i) q^{39} +(1.20477 - 0.875319i) q^{41} +(-8.37394 - 2.72086i) q^{42} -2.69767i q^{43} +(1.16637 - 3.58973i) q^{44} +(0.275344 + 0.847421i) q^{46} +(-3.58973 + 1.16637i) q^{47} +(1.37116 - 1.88723i) q^{48} -7.24660 q^{49} +3.24836 q^{51} +(1.86699 - 2.56969i) q^{52} +(11.0477 - 3.58963i) q^{53} +(-0.402443 - 1.23859i) q^{54} +(1.16637 - 3.58973i) q^{56} -9.13004i q^{57} +(-0.0468081 - 0.0152089i) q^{58} +(-0.558282 + 0.405615i) q^{59} +(-8.38168 - 6.08965i) q^{61} +(3.28049 + 4.51521i) q^{62} +(5.41714 + 7.45605i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-7.12330 + 5.17538i) q^{66} +(14.5734 + 4.73519i) q^{67} +1.39250i q^{68} +(0.642308 - 1.97682i) q^{69} +(-2.06969 - 6.36986i) q^{71} +(-2.32221 + 0.754532i) q^{72} +(-3.03810 + 4.18158i) q^{73} -7.04746 q^{74} +3.91385 q^{76} +(-8.37394 + 11.5257i) q^{77} +(-7.04690 + 2.28968i) q^{78} +(0.558282 + 1.71821i) q^{79} +(-3.20239 + 9.85596i) q^{81} -1.48918i q^{82} +(9.47997 + 3.08023i) q^{83} +(-7.12330 + 5.17538i) q^{84} +(-2.18246 - 1.58565i) q^{86} +(0.0674841 + 0.0928839i) q^{87} +(-2.21858 - 3.05361i) q^{88} +(11.7390 + 8.52891i) q^{89} +(-9.69922 + 7.04690i) q^{91} +(0.847421 + 0.275344i) q^{92} -13.0193i q^{93} +(-1.16637 + 3.58973i) q^{94} +(-0.720859 - 2.21858i) q^{96} +(0.0857567 - 0.0278640i) q^{97} +(-4.25945 + 5.86263i) q^{98} +9.21619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9	\( 16 q + 4 q^{4} - 6 q^{6} + 2 q^{9} + 2 q^{11} + 2 q^{14} - 4 q^{16} - 40 q^{19} - 38 q^{21} - 4 q^{24} + 44 q^{26} + 30 q^{29} - 18 q^{31} + 2 q^{34} - 2 q^{36} + 24 q^{39} - 18 q^{41} - 2 q^{44} + 14 q^{46} + 8 q^{49} + 52 q^{51} + 50 q^{54} - 2 q^{56} - 20 q^{59} + 12 q^{61} + 4 q^{64} - 52 q^{66} - 86 q^{69} - 18 q^{71} - 48 q^{74} - 20 q^{76} + 20 q^{79} - 34 q^{81} - 52 q^{84} - 46 q^{86} + 30 q^{89} + 2 q^{91} + 2 q^{94} - 6 q^{96} + 84 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 6 * q^6 + 2 * q^9 + 2 * q^11 + 2 * q^14 - 4 * q^16 - 40 * q^19 - 38 * q^21 - 4 * q^24 + 44 * q^26 + 30 * q^29 - 18 * q^31 + 2 * q^34 - 2 * q^36 + 24 * q^39 - 18 * q^41 - 2 * q^44 + 14 * q^46 + 8 * q^49 + 52 * q^51 + 50 * q^54 - 2 * q^56 - 20 * q^59 + 12 * q^61 + 4 * q^64 - 52 * q^66 - 86 * q^69 - 18 * q^71 - 48 * q^74 - 20 * q^76 + 20 * q^79 - 34 * q^81 - 52 * q^84 - 46 * q^86 + 30 * q^89 + 2 * q^91 + 2 * q^94 - 6 * q^96 + 84 * q^99

Introduction

L-functions

Modular forms

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