LMFDB - Embedded newform 950.2.bb.e.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.4
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.e.857.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(0.0833140 - 0.952283i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(0.732278 + 0.614454i) q^{6} +(0.790865 + 2.95155i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.05452 + 0.362268i) q^{9} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(0.0833140 - 0.952283i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(0.732278 + 0.614454i) q^{6} +(0.790865 + 2.95155i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.05452 + 0.362268i) q^{9} +(0.697545 + 1.20818i) q^{11} +(-0.923348 + 0.247410i) q^{12} +(-2.65096 + 0.231929i) q^{13} +(-2.87139 - 1.04510i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.485119 - 0.339684i) q^{17} +(-1.47518 + 1.47518i) q^{18} +(-2.07775 + 3.83183i) q^{19} +(2.87660 - 0.507222i) q^{21} +(-1.38978 - 0.121590i) q^{22} +(0.943203 + 0.439823i) q^{23} +(0.326944 - 0.898272i) q^{24} +(1.33054 - 2.30456i) q^{26} +(1.25838 - 4.69635i) q^{27} +(2.50306 - 1.75266i) q^{28} +(-0.928771 + 5.26732i) q^{29} +(-3.38574 - 1.95476i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(1.20865 - 0.563602i) q^{33} +(0.556506 - 0.202551i) q^{34} +(-0.362268 - 2.05452i) q^{36} +(-0.611533 - 0.611533i) q^{37} +(-1.94710 - 3.89985i) q^{38} +2.54378i q^{39} +(6.37921 + 7.60244i) q^{41} +(-1.23446 + 2.64730i) q^{42} +(2.07457 + 4.44893i) q^{43} +(0.896747 - 1.06870i) q^{44} +(-0.901281 + 0.520355i) q^{46} +(-2.17324 - 3.10371i) q^{47} +(0.548294 + 0.783044i) q^{48} +(-2.02399 + 1.16855i) q^{49} +(-0.363892 + 0.433670i) q^{51} +(1.12462 + 2.41176i) q^{52} +(-3.07886 + 6.60263i) q^{53} +(3.12525 + 3.72452i) q^{54} +3.05567i q^{56} +(3.47588 + 2.29786i) q^{57} +(-3.78202 - 3.78202i) q^{58} +(2.48207 + 14.0765i) q^{59} +(11.5621 - 4.20827i) q^{61} +(3.54322 - 1.65223i) q^{62} +(0.555599 + 6.35052i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.231576 + 1.31334i) q^{66} +(-4.48775 + 3.14235i) q^{67} +(-0.153278 + 0.572041i) q^{68} +(0.497418 - 0.861553i) q^{69} +(-2.65555 + 7.29606i) q^{71} +(1.89075 + 0.881673i) q^{72} +(13.2476 + 1.15902i) q^{73} +(0.851699 - 0.150178i) q^{74} +(4.31138 + 0.641887i) q^{76} +(-3.01435 + 3.01435i) q^{77} +(-2.08375 - 1.45905i) q^{78} +(2.36397 - 1.98361i) q^{79} +(1.51379 + 0.550975i) q^{81} +(-9.88652 + 0.864958i) q^{82} +(10.7941 - 2.89227i) q^{83} +(-1.46049 - 2.52964i) q^{84} +(-4.83428 - 0.852413i) q^{86} +(4.93860 + 1.32329i) q^{87} +(0.361076 + 1.34755i) q^{88} +(-13.2874 - 11.1494i) q^{89} +(-2.78110 - 7.64100i) q^{91} +(0.0907038 - 1.03675i) q^{92} +(-2.14356 + 3.06132i) q^{93} +3.78893 q^{94} -0.955921 q^{96} +(-1.56957 + 2.24158i) q^{97} +(0.203692 - 2.32821i) q^{98} +(0.995436 + 2.73494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$	0.0833140	−	0.952283i	0.0481013	−	0.549801i	−0.933464	−	0.358672i	$-0.883230\pi$
$3$	0.0833140	−	0.952283i	0.0481013	−	0.549801i	0.981565	−	0.191129i	$-0.0612148\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	0.732278	+	0.614454i	0.298951	+	0.250850i
$7$	0.790865	+	2.95155i	0.298919	+	1.11558i	0.938055	+	0.346487i	$0.112625\pi$
$7$	0.790865	+	2.95155i	0.298919	+	1.11558i	−0.639136	+	0.769094i	$0.720708\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	2.05452	+	0.362268i	0.684840	+	0.120756i
$10$		0			0
$11$	0.697545	+	1.20818i	0.210318	+	0.364281i	0.951814	−	0.306676i	$-0.0992168\pi$
$11$	0.697545	+	1.20818i	0.210318	+	0.364281i	−0.741496	+	0.670957i	$0.765883\pi$
$12$	−0.923348	+	0.247410i	−0.266548	+	0.0714212i
$13$	−2.65096	+	0.231929i	−0.735243	+	0.0643254i	−0.448626	−	0.893720i	$-0.648086\pi$
$13$	−2.65096	+	0.231929i	−0.735243	+	0.0643254i	−0.286617	+	0.958045i	$0.592531\pi$
$14$	−2.87139	−	1.04510i	−0.767411	−	0.279315i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.485119	−	0.339684i	−0.117659	−	0.0823854i	0.513266	−	0.858230i	$-0.328435\pi$
$17$	−0.485119	−	0.339684i	−0.117659	−	0.0823854i	−0.630925	+	0.775844i	$0.717324\pi$
$18$	−1.47518	+	1.47518i	−0.347703	+	0.347703i
$19$	−2.07775	+	3.83183i	−0.476670	+	0.879082i
$19$	−2.07775	+	3.83183i	−0.476670	+	0.879082i
$20$		0			0
$21$	2.87660	−	0.507222i	0.627725	−	0.110685i
$22$	−1.38978	−	0.121590i	−0.296302	−	0.0259231i
$23$	0.943203	+	0.439823i	0.196671	+	0.0917094i	0.518459	−	0.855103i	$-0.326506\pi$
$23$	0.943203	+	0.439823i	0.196671	+	0.0917094i	−0.321788	+	0.946812i	$0.604284\pi$
$24$	0.326944	−	0.898272i	0.0667372	−	0.183359i
$25$		0			0
$26$	1.33054	−	2.30456i	0.260941	−	0.451962i
$27$	1.25838	−	4.69635i	0.242176	−	0.903813i
$28$	2.50306	−	1.75266i	0.473033	−	0.331221i
$29$	−0.928771	+	5.26732i	−0.172469	+	0.978117i	0.768557	+	0.639781i	$0.220975\pi$
$29$	−0.928771	+	5.26732i	−0.172469	+	0.978117i	−0.941025	+	0.338336i	$0.890136\pi$
$30$		0			0
$31$	−3.38574	−	1.95476i	−0.608097	−	0.351085i	0.164124	−	0.986440i	$-0.447520\pi$
$31$	−3.38574	−	1.95476i	−0.608097	−	0.351085i	−0.772220	+	0.635355i	$0.780854\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$	1.20865	−	0.563602i	0.210399	−	0.0981105i
$34$	0.556506	−	0.202551i	0.0954399	−	0.0347373i
$35$		0			0
$36$	−0.362268	−	2.05452i	−0.0603779	−	0.342420i
$37$	−0.611533	−	0.611533i	−0.100535	−	0.100535i	0.655050	−	0.755585i	$-0.272648\pi$
$37$	−0.611533	−	0.611533i	−0.100535	−	0.100535i	−0.755585	+	0.655050i	$0.772648\pi$
$38$	−1.94710	−	3.89985i	−0.315862	−	0.632638i
$39$			2.54378i			0.407331i
$40$		0			0
$41$	6.37921	+	7.60244i	0.996265	+	1.18730i	0.982284	+	0.187400i	$0.0600060\pi$
$41$	6.37921	+	7.60244i	0.996265	+	1.18730i	0.0139811	+	0.999902i	$0.495550\pi$
$42$	−1.23446	+	2.64730i	−0.190481	+	0.408488i
$43$	2.07457	+	4.44893i	0.316369	+	0.678456i	0.998612	−	0.0526699i	$-0.0167731\pi$
$43$	2.07457	+	4.44893i	0.316369	+	0.678456i	−0.682243	+	0.731126i	$0.738995\pi$
$44$	0.896747	−	1.06870i	0.135190	−	0.161113i
$45$		0			0
$46$	−0.901281	+	0.520355i	−0.132887	+	0.0767221i
$47$	−2.17324	−	3.10371i	−0.316999	−	0.452722i	0.628755	−	0.777603i	$-0.283565\pi$
$47$	−2.17324	−	3.10371i	−0.316999	−	0.452722i	−0.945755	+	0.324881i	$0.894676\pi$
$48$	0.548294	+	0.783044i	0.0791394	+	0.113023i
$49$	−2.02399	+	1.16855i	−0.289142	+	0.166936i
$50$		0			0
$51$	−0.363892	+	0.433670i	−0.0509551	+	0.0607260i
$52$	1.12462	+	2.41176i	0.155957	+	0.334451i
$53$	−3.07886	+	6.60263i	−0.422914	+	0.906942i	0.573246	+	0.819384i	$0.305684\pi$
$53$	−3.07886	+	6.60263i	−0.422914	+	0.906942i	−0.996159	+	0.0875580i	$0.972094\pi$
$54$	3.12525	+	3.72452i	0.425292	+	0.506843i
$55$		0			0
$56$			3.05567i			0.408331i
$57$	3.47588	+	2.29786i	0.460392	+	0.304358i
$58$	−3.78202	−	3.78202i	−0.496603	−	0.496603i
$59$	2.48207	+	14.0765i	0.323138	+	1.83261i	0.522448	+	0.852671i	$0.325019\pi$
$59$	2.48207	+	14.0765i	0.323138	+	1.83261i	−0.199310	+	0.979937i	$0.563870\pi$
$60$		0			0
$61$	11.5621	−	4.20827i	1.48038	−	0.538813i	0.529481	−	0.848322i	$-0.322387\pi$
$61$	11.5621	−	4.20827i	1.48038	−	0.538813i	0.950897	+	0.309508i	$0.100164\pi$
$62$	3.54322	−	1.65223i	0.449990	−	0.209834i
$63$	0.555599	+	6.35052i	0.0699989	+	0.800091i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−0.231576	+	1.31334i	−0.0285051	+	0.161660i
$67$	−4.48775	+	3.14235i	−0.548266	+	0.383900i	−0.814637	−	0.579971i	$-0.803064\pi$
$67$	−4.48775	+	3.14235i	−0.548266	+	0.383900i	0.266372	+	0.963870i	$0.414175\pi$
$68$	−0.153278	+	0.572041i	−0.0185877	+	0.0693702i
$69$	0.497418	−	0.861553i	0.0598821	−	0.103719i
$70$		0			0
$71$	−2.65555	+	7.29606i	−0.315155	+	0.865883i	0.676439	+	0.736499i	$0.263522\pi$
$71$	−2.65555	+	7.29606i	−0.315155	+	0.865883i	−0.991595	+	0.129384i	$0.958700\pi$
$72$	1.89075	+	0.881673i	0.222827	+	0.103906i
$73$	13.2476	+	1.15902i	1.55052	+	0.135653i	0.829991	−	0.557776i	$-0.188345\pi$
$73$	13.2476	+	1.15902i	1.55052	+	0.135653i	0.720525	+	0.693429i	$0.243901\pi$
$74$	0.851699	−	0.150178i	0.0990080	−	0.0174578i
$75$		0			0
$76$	4.31138	+	0.641887i	0.494549	+	0.0736295i
$77$	−3.01435	+	3.01435i	−0.343517	+	0.343517i
$78$	−2.08375	−	1.45905i	−0.235938	−	0.165205i
$79$	2.36397	−	1.98361i	0.265968	−	0.223173i	−0.500044	−	0.866000i	$-0.666683\pi$
$79$	2.36397	−	1.98361i	0.265968	−	0.223173i	0.766012	+	0.642827i	$0.222238\pi$
$80$		0			0
$81$	1.51379	+	0.550975i	0.168199	+	0.0612195i
$82$	−9.88652	+	0.864958i	−1.09178	+	0.0955187i
$83$	10.7941	−	2.89227i	1.18481	−	0.317468i	0.387975	−	0.921670i	$-0.373175\pi$
$83$	10.7941	−	2.89227i	1.18481	−	0.317468i	0.796831	+	0.604202i	$0.206508\pi$
$84$	−1.46049	−	2.52964i	−0.159352	−	0.276006i
$85$		0			0
$86$	−4.83428	−	0.852413i	−0.521293	−	0.0919181i
$87$	4.93860	+	1.32329i	0.529474	+	0.141872i
$88$	0.361076	+	1.34755i	0.0384908	+	0.143650i
$89$	−13.2874	−	11.1494i	−1.40846	−	1.18184i	−0.957194	−	0.289446i	$-0.906529\pi$
$89$	−13.2874	−	11.1494i	−1.40846	−	1.18184i	−0.451263	−	0.892391i	$-0.649027\pi$
$90$		0			0
$91$	−2.78110	−	7.64100i	−0.291538	−	0.800994i
$92$	0.0907038	−	1.03675i	0.00945653	−	0.108089i
$93$	−2.14356	+	3.06132i	−0.222277	+	0.317444i
$94$	3.78893			0.390798
$95$		0			0
$96$	−0.955921			−0.0975632
$97$	−1.56957	+	2.24158i	−0.159366	+	0.227598i	−0.890892	−	0.454215i	$-0.849920\pi$
$97$	−1.56957	+	2.24158i	−0.159366	+	0.227598i	0.731526	+	0.681814i	$0.238809\pi$
$98$	0.203692	−	2.32821i	0.0205760	−	0.235185i
$99$	0.995436	+	2.73494i	0.100045	+	0.274872i
$100$		0			0
$101$	−10.8772	−	9.12706i	−1.08232	−	0.908176i	−0.0862104	−	0.996277i	$-0.527476\pi$
$101$	−10.8772	−	9.12706i	−1.08232	−	0.908176i	−0.996112	+	0.0881010i	$0.971920\pi$
$102$	−0.146522	−	0.546826i	−0.0145078	−	0.0541439i
$103$	10.6275	+	2.84764i	1.04716	+	0.280586i	0.741079	−	0.671418i	$-0.234314\pi$
$103$	10.6275	+	2.84764i	1.04716	+	0.280586i	0.306084	+	0.952005i	$0.400981\pi$
$104$	−2.62065	−	0.462092i	−0.256976	−	0.0453119i
$105$		0			0
$106$	−3.64260	−	6.30917i	−0.353801	−	0.612801i
$107$	−12.4276	+	3.32996i	−1.20142	+	0.321919i	−0.803390	−	0.595453i	$-0.796972\pi$
$107$	−12.4276	+	3.32996i	−1.20142	+	0.321919i	−0.398029	+	0.917373i	$0.630306\pi$
$108$	−4.84352	+	0.423753i	−0.466068	+	0.0407756i
$109$	1.73276	+	0.630674i	0.165968	+	0.0604076i	0.423668	−	0.905817i	$-0.360742\pi$
$109$	1.73276	+	0.630674i	0.165968	+	0.0604076i	−0.257700	+	0.966225i	$0.582965\pi$
$110$		0			0
$111$	−0.633301	+	0.531403i	−0.0601103	+	0.0504385i
$112$	−2.50306	−	1.75266i	−0.236517	−	0.165611i
$113$	−4.34093	+	4.34093i	−0.408360	+	0.408360i	−0.881166	−	0.472806i	$-0.843241\pi$
$113$	−4.34093	+	4.34093i	−0.408360	+	0.408360i	0.472806	+	0.881166i	$0.343241\pi$
$114$	−3.87598	+	1.52928i	−0.363019	+	0.143230i
$115$		0			0
$116$	5.26732	−	0.928771i	0.489059	−	0.0862343i
$117$	−5.53047	−	0.483853i	−0.511292	−	0.0447322i
$118$	−12.9545	−	6.04077i	−1.19256	−	0.556098i
$119$	0.618930	−	1.70050i	0.0567372	−	0.155884i
$120$		0			0
$121$	4.52686	−	7.84075i	0.411533	−	0.712796i
$122$	−3.18455	+	11.8849i	−0.288315	+	1.07601i
$123$	7.77116	−	5.44142i	0.700701	−	0.490636i
$124$	−0.678880	+	3.85012i	−0.0609652	+	0.345751i
$125$		0			0
$126$	−5.52072	−	3.18739i	−0.491825	−	0.283955i
$127$	−0.189203	−	2.16260i	−0.0167890	−	0.191899i	−0.999958	−	0.00919910i	$-0.997072\pi$
$127$	−0.189203	−	2.16260i	−0.0167890	−	0.191899i	0.983169	−	0.182700i	$-0.0584838\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$	4.40948	−	1.60492i	0.388233	−	0.141305i
$130$		0			0
$131$	3.23618	+	18.3533i	0.282746	+	1.60353i	0.713227	+	0.700933i	$0.247233\pi$
$131$	3.23618	+	18.3533i	0.282746	+	1.60353i	−0.430481	+	0.902599i	$0.641656\pi$
$132$	−0.942995	−	0.942995i	−0.0820771	−	0.0820771i
$133$	−12.9531	−	3.10213i	−1.12317	−	0.268989i
$134$		−	5.47853i		−	0.473273i
$135$		0			0
$136$	−0.380672	−	0.453667i	−0.0326424	−	0.0389017i
$137$	4.54126	−	9.73877i	0.387986	−	0.832039i	−0.611191	−	0.791483i	$-0.709309\pi$
$137$	4.54126	−	9.73877i	0.387986	−	0.832039i	0.999177	−	0.0405562i	$-0.0129130\pi$
$138$	0.420436	+	0.901627i	0.0357899	+	0.0767516i
$139$	2.84298	−	3.38813i	0.241138	−	0.287377i	−0.631879	−	0.775067i	$-0.717716\pi$
$139$	2.84298	−	3.38813i	0.241138	−	0.287377i	0.873017	+	0.487690i	$0.162160\pi$
$140$		0			0
$141$	−3.13667	+	1.81096i	−0.264155	+	0.152510i
$142$	−4.45342	−	6.36014i	−0.373723	−	0.533731i
$143$	−2.12937	−	3.04106i	−0.178067	−	0.254306i
$144$	−1.80672	+	1.04311i	−0.150560	+	0.0869257i
$145$		0			0
$146$	−8.54793	+	10.1870i	−0.707432	+	0.843085i
$147$	0.944166	+	2.02477i	0.0778735	+	0.167000i
$148$	−0.365496	+	0.783809i	−0.0300436	+	0.0644287i
$149$	−4.99005	−	5.94691i	−0.408801	−	0.487190i	0.521881	−	0.853018i	$-0.325230\pi$
$149$	−4.99005	−	5.94691i	−0.408801	−	0.487190i	−0.930683	+	0.365828i	$0.880786\pi$
$150$		0			0
$151$		−	22.0595i		−	1.79517i	−0.440837	−	0.897587i	$-0.645318\pi$
$151$		−	22.0595i		−	1.79517i	0.440837	−	0.897587i	$-0.354682\pi$
$152$	−2.99871	+	3.16350i	−0.243227	+	0.256594i
$153$	−0.873631	−	0.873631i	−0.0706289	−	0.0706289i
$154$	−0.740251	−	4.19817i	−0.0596511	−	0.338298i
$155$		0			0
$156$	2.39037	−	0.870025i	0.191383	−	0.0696578i
$157$	18.7545	−	8.74538i	1.49677	−	0.697957i	0.510017	−	0.860164i	$-0.329639\pi$
$157$	18.7545	−	8.74538i	1.49677	−	0.697957i	0.986757	+	0.162207i	$0.0518612\pi$
$158$	0.268958	+	3.07420i	0.0213972	+	0.244571i
$159$	6.03106	+	3.48204i	0.478295	+	0.276143i
$160$		0			0
$161$	−0.552212	+	3.13175i	−0.0435204	+	0.246816i
$162$	−1.31961	+	0.923999i	−0.103678	+	0.0725962i
$163$	−5.90785	+	22.0484i	−0.462739	+	1.72696i	0.201541	+	0.979480i	$0.435405\pi$
$163$	−5.90785	+	22.0484i	−0.462739	+	1.72696i	−0.664280	+	0.747484i	$0.731262\pi$
$164$	4.96214	−	8.59468i	0.387478	−	0.671132i
$165$		0			0
$166$	−3.82203	+	10.5009i	−0.296647	+	0.815032i
$167$	11.8601	+	5.53046i	0.917763	+	0.427960i	0.823324	−	0.567571i	$-0.192117\pi$
$167$	11.8601	+	5.53046i	0.917763	+	0.427960i	0.0944381	+	0.995531i	$0.469895\pi$
$168$	2.90986	+	0.254580i	0.224501	+	0.0196413i
$169$	−5.82873	+	1.02776i	−0.448363	+	0.0790586i
$170$		0			0
$171$	−5.65694	+	7.11988i	−0.432597	+	0.544471i
$172$	3.47108	−	3.47108i	0.264668	−	0.264668i
$173$	−17.2884	−	12.1055i	−1.31441	−	0.920363i	−0.314829	−	0.949148i	$-0.601947\pi$
$173$	−17.2884	−	12.1055i	−1.31441	−	0.920363i	−0.999586	+	0.0287855i	$0.990836\pi$
$174$	−3.91665	+	3.28646i	−0.296920	+	0.249146i
$175$		0			0
$176$	−1.31096	−	0.477149i	−0.0988170	−	0.0359665i
$177$	13.6116	−	1.19086i	1.02311	−	0.0895108i
$178$	16.7544	−	4.48933i	1.25579	−	0.336489i
$179$	−1.00014	−	1.73230i	−0.0747543	−	0.129478i	0.826225	−	0.563340i	$-0.190484\pi$
$179$	−1.00014	−	1.73230i	−0.0747543	−	0.129478i	−0.900979	+	0.433862i	$0.857151\pi$
$180$		0			0
$181$	−2.17945	−	0.384296i	−0.161997	−	0.0285645i	0.0920611	−	0.995753i	$-0.470654\pi$
$181$	−2.17945	−	0.384296i	−0.161997	−	0.0285645i	−0.254059	+	0.967189i	$0.581766\pi$
$182$	7.85431	+	2.10456i	0.582200	+	0.156000i
$183$	−3.04418	−	11.3610i	−0.225032	−	0.839831i
$184$	0.797230	+	0.668955i	0.0587726	+	0.0493160i
$185$		0			0
$186$	−1.27819	−	3.51181i	−0.0937216	−	0.257498i
$187$	0.0720082	−	0.823058i	0.00526576	−	0.0601879i
$188$	−2.17324	+	3.10371i	−0.158500	+	0.226361i
$189$	14.8567			1.08067
$190$		0			0
$191$	−20.9414			−1.51527			−0.757635	−	0.652679i	$-0.773645\pi$
$191$	−20.9414			−1.51527			−0.757635	+	0.652679i	$0.773645\pi$
$192$	0.548294	−	0.783044i	0.0395697	−	0.0565114i
$193$	1.70593	−	19.4988i	0.122795	−	1.40356i	−0.645647	−	0.763636i	$-0.723412\pi$
$193$	1.70593	−	19.4988i	0.122795	−	1.40356i	0.768442	−	0.639920i	$-0.221032\pi$
$194$	−0.935927	−	2.57144i	−0.0671956	−	0.184619i
$195$		0			0
$196$	1.79033	+	1.50226i	0.127880	+	0.107304i
$197$	−6.01834	−	22.4607i	−0.428789	−	1.60026i	−0.755508	−	0.655140i	$-0.772610\pi$
$197$	−6.01834	−	22.4607i	−0.428789	−	1.60026i	0.326719	−	0.945121i	$-0.394057\pi$
$198$	−2.81129	−	0.753282i	−0.199790	−	0.0535335i
$199$	−4.25695	−	0.750615i	−0.301767	−	0.0532097i	0.0207145	−	0.999785i	$-0.493406\pi$
$199$	−4.25695	−	0.750615i	−0.301767	−	0.0532097i	−0.322482	+	0.946576i	$0.604517\pi$
$200$		0			0
$201$	2.61852	+	4.53541i	0.184696	+	0.319903i
$202$	13.7154	−	3.67502i	0.965009	−	0.258573i
$203$	−16.2813	+	1.42443i	−1.14272	+	0.0999753i
$204$	0.531975	+	0.193623i	0.0372457	+	0.0135563i
$205$		0			0
$206$	−8.42836	+	7.07223i	−0.587232	+	0.492746i
$207$	1.77850	+	1.24532i	0.123614	+	0.0865555i
$208$	1.88167	−	1.88167i	0.130470	−	0.130470i
$209$	−6.07889	+	0.162566i	−0.420485	+	0.0112449i
$210$		0			0
$211$	5.66680	−	0.999209i	0.390118	−	0.0687884i	0.0248513	−	0.999691i	$-0.492089\pi$
$211$	5.66680	−	0.999209i	0.390118	−	0.0687884i	0.365267	+	0.930903i	$0.380978\pi$
$212$	7.25748	+	0.634947i	0.498446	+	0.0436083i
$213$	6.72667	+	3.13670i	0.460904	+	0.214923i
$214$	4.40042	−	12.0901i	0.300807	−	0.826459i
$215$		0			0
$216$	2.43101	−	4.21063i	0.165409	−	0.286497i
$217$	3.09190	−	11.5391i	0.209892	−	0.783326i
$218$	−1.51049	+	1.05766i	−0.102303	+	0.0716335i
$219$	2.20742	−	12.5189i	0.149164	−	0.845950i
$220$		0			0
$221$	1.36481	+	0.787974i	0.0918071	+	0.0530049i
$222$	−0.0720531	−	0.823570i	−0.00483589	−	0.0552744i
$223$	14.1382	−	6.59276i	0.946766	−	0.441484i	0.112995	−	0.993596i	$-0.463956\pi$
$223$	14.1382	−	6.59276i	0.946766	−	0.441484i	0.833770	+	0.552111i	$0.186178\pi$
$224$	2.87139	−	1.04510i	0.191853	−	0.0698287i
$225$		0			0
$226$	−1.06603	−	6.04573i	−0.0709110	−	0.402156i
$227$	14.5578	+	14.5578i	0.966237	+	0.966237i	0.999448	−	0.0332111i	$-0.0105734\pi$
$227$	14.5578	+	14.5578i	0.966237	+	0.966237i	−0.0332111	+	0.999448i	$0.510573\pi$
$228$	0.970456	−	4.05217i	0.0642700	−	0.268362i
$229$			12.9143i			0.853402i	0.904393	+	0.426701i	$0.140324\pi$
$229$			12.9143i			0.853402i	−0.904393	+	0.426701i	$0.859676\pi$
$230$		0			0
$231$	2.61938	+	3.12165i	0.172342	+	0.205390i
$232$	−2.26041	+	4.84746i	−0.148403	+	0.318251i
$233$	4.22648	+	9.06373i	0.276886	+	0.593784i	0.994743	−	0.102407i	$-0.0326543\pi$
$233$	4.22648	+	9.06373i	0.276886	+	0.593784i	−0.717856	+	0.696191i	$0.754877\pi$
$234$	3.56849	−	4.25277i	0.233280	−	0.278012i
$235$		0			0
$236$	12.3787	−	7.14684i	0.805784	−	0.465220i
$237$	−1.69200	−	2.41643i	−0.109908	−	0.156964i
$238$	1.03796	+	1.48236i	0.0672810	+	0.0960873i
$239$	15.6059	−	9.01008i	1.00946	−	0.582814i	0.0984285	−	0.995144i	$-0.468618\pi$
$239$	15.6059	−	9.01008i	1.00946	−	0.582814i	0.911034	+	0.412330i	$0.135285\pi$
$240$		0			0
$241$	8.60095	−	10.2502i	0.554036	−	0.660274i	−0.414237	−	0.910169i	$-0.635952\pi$
$241$	8.60095	−	10.2502i	0.554036	−	0.660274i	0.968273	+	0.249895i	$0.0803960\pi$
$242$	3.82627	+	8.20546i	0.245962	+	0.527467i
$243$	6.81514	−	14.6151i	0.437191	−	0.937560i
$244$	−7.90896	−	9.42553i	−0.506319	−	0.603407i
$245$		0			0
$246$			9.48683i			0.604858i
$247$	4.61932	−	10.6399i	0.293921	−	0.677001i
$248$	−2.76444	−	2.76444i	−0.175542	−	0.175542i
$249$	−1.85496	−	10.5200i	−0.117553	−	0.666678i
$250$		0			0
$251$	9.11469	−	3.31748i	0.575314	−	0.209397i	−0.0379439	−	0.999280i	$-0.512081\pi$
$251$	9.11469	−	3.31748i	0.575314	−	0.209397i	0.613258	+	0.789883i	$0.289859\pi$
$252$	5.77751	−	2.69410i	0.363949	−	0.169712i
$253$	0.126540	+	1.44636i	0.00795550	+	0.0909318i
$254$	1.88002	+	1.08543i	0.117963	+	0.0681058i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.27138	−	1.59044i	0.141685	−	0.0992088i	−0.500585	−	0.865687i	$-0.666882\pi$
$257$	2.27138	−	1.59044i	0.141685	−	0.0992088i	0.642270	+	0.766479i	$0.277993\pi$
$258$	−1.21450	+	4.53258i	−0.0756116	+	0.282186i
$259$	1.32133	−	2.28861i	0.0821034	−	0.142207i
$260$		0			0
$261$	−3.81636	+	10.4854i	−0.236227	+	0.649028i
$262$	−16.8903	−	7.87608i	−1.04349	−	0.486586i
$263$	−11.6187	−	1.01650i	−0.716438	−	0.0626802i	−0.276893	−	0.960901i	$-0.589305\pi$
$263$	−11.6187	−	1.01650i	−0.716438	−	0.0626802i	−0.439545	+	0.898220i	$0.644860\pi$
$264$	1.31334	−	0.231576i	0.0808302	−	0.0142525i
$265$		0			0
$266$	9.97069	−	8.83122i	0.611342	−	0.541477i
$267$	−11.7244	+	11.7244i	−0.717523	+	0.717523i
$268$	4.48775	+	3.14235i	0.274133	+	0.191950i
$269$	3.03962	−	2.55054i	0.185329	−	0.155509i	−0.545403	−	0.838174i	$-0.683623\pi$
$269$	3.03962	−	2.55054i	0.185329	−	0.155509i	0.730732	+	0.682665i	$0.239179\pi$
$270$		0			0
$271$	5.11557	+	1.86191i	0.310749	+	0.113103i	0.492687	−	0.870207i	$-0.336015\pi$
$271$	5.11557	+	1.86191i	0.310749	+	0.113103i	−0.181938	+	0.983310i	$0.558237\pi$
$272$	0.589967	−	0.0516154i	0.0357720	−	0.00312965i
$273$	−7.50810	+	2.01179i	−0.454411	+	0.121759i
$274$	5.37277	+	9.30592i	0.324581	+	0.562191i
$275$		0			0
$276$	−0.979722	−	0.172751i	−0.0589723	−	0.0103984i
$277$	−12.6547	−	3.39081i	−0.760345	−	0.203734i	−0.142243	−	0.989832i	$-0.545431\pi$
$277$	−12.6547	−	3.39081i	−0.760345	−	0.203734i	−0.618102	+	0.786098i	$0.712098\pi$
$278$	1.14473	+	4.27218i	0.0686561	+	0.256228i
$279$	−6.24793	−	5.24263i	−0.374054	−	0.313868i
$280$		0			0
$281$	−1.84394	−	5.06618i	−0.110000	−	0.302223i	0.872463	−	0.488680i	$-0.162522\pi$
$281$	−1.84394	−	5.06618i	−0.110000	−	0.302223i	−0.982463	+	0.186457i	$0.940299\pi$
$282$	0.315670	−	3.60813i	0.0187979	−	0.214861i
$283$	−3.47143	+	4.95771i	−0.206355	+	0.294706i	−0.908967	−	0.416867i	$-0.863128\pi$
$283$	−3.47143	+	4.95771i	−0.206355	+	0.294706i	0.702612	+	0.711573i	$0.252017\pi$
$284$	7.76430			0.460726
$285$		0			0
$286$	3.71245			0.219522
$287$	−17.3939	+	24.8410i	−1.02673	+	1.46632i
$288$	0.181826	−	2.07828i	0.0107142	−	0.122464i
$289$	−5.69439	−	15.6452i	−0.334964	−	0.920306i
$290$		0			0
$291$	2.00385	+	1.68143i	0.117468	+	0.0985674i
$292$	−3.44183	−	12.8451i	−0.201418	−	0.751702i
$293$	−9.13876	−	2.44872i	−0.533892	−	0.143056i	−0.0182071	−	0.999834i	$-0.505796\pi$
$293$	−9.13876	−	2.44872i	−0.533892	−	0.143056i	−0.515685	+	0.856778i	$0.672462\pi$
$294$	−2.20015	−	0.387945i	−0.128315	−	0.0226254i
$295$		0			0
$296$	−0.432419	−	0.748972i	−0.0251338	−	0.0435331i
$297$	6.55183	−	1.75556i	0.380176	−	0.101868i
$298$	7.73360	−	0.676603i	0.447996	−	0.0391945i
$299$	−2.60240	−	0.947195i	−0.150501	−	0.0547777i
$300$		0			0
$301$	−11.4905	+	9.64170i	−0.662303	+	0.555738i
$302$	18.0701	+	12.6528i	1.03982	+	0.728086i
$303$	−9.59776	+	9.59776i	−0.551377	+	0.551377i
$304$	−0.871401	−	4.27091i	−0.0499783	−	0.244953i
$305$		0			0
$306$	1.21673	−	0.214542i	0.0695558	−	0.0122646i
$307$	3.58814	+	0.313921i	0.204786	+	0.0179164i	0.189087	−	0.981960i	$-0.439447\pi$
$307$	3.58814	+	0.313921i	0.204786	+	0.0179164i	0.0156988	+	0.999877i	$0.495003\pi$
$308$	3.86353	+	1.80159i	0.220145	+	0.102655i
$309$	3.59718	−	9.88318i	0.204637	−	0.562234i
$310$		0			0
$311$	4.98525	−	8.63471i	0.282688	−	0.489630i	−0.689358	−	0.724421i	$-0.742107\pi$
$311$	4.98525	−	8.63471i	0.282688	−	0.489630i	0.972046	+	0.234791i	$0.0754406\pi$
$312$	−0.658380	+	2.45711i	−0.0372734	+	0.139106i
$313$	24.4030	−	17.0872i	1.37934	−	0.965825i	0.380179	−	0.924913i	$-0.375862\pi$
$313$	24.4030	−	17.0872i	1.37934	−	0.965825i	0.999163	−	0.0409123i	$-0.0130264\pi$
$314$	−3.59336	+	20.3790i	−0.202785	+	1.15005i
$315$		0			0
$316$	−2.67251	−	1.54297i	−0.150340	−	0.0867990i
$317$	0.240318	+	2.74684i	0.0134976	+	0.154278i	0.999952	−	0.00975497i	$-0.00310515\pi$
$317$	0.240318	+	2.74684i	0.0134976	+	0.154278i	−0.986455	+	0.164033i	$0.947550\pi$
$318$	−6.31159	+	2.94314i	−0.353937	+	0.165043i
$319$	−7.01176	+	2.55207i	−0.392583	+	0.142889i
$320$		0			0
$321$	2.13567	+	12.1120i	0.119202	+	0.676026i
$322$	−2.24864	−	2.24864i	−0.125312	−	0.125312i
$323$	2.30957	−	1.15311i	0.128508	−	0.0641610i
$324$		−	1.61094i		−	0.0894969i
$325$		0			0
$326$	−14.6724	−	17.4859i	−0.812628	−	0.968453i
$327$	0.744943	−	1.59754i	0.0411955	−	0.0883439i
$328$	4.19418	+	8.99446i	0.231585	+	0.496636i
$329$	7.44200	−	8.86903i	0.410291	−	0.488966i
$330$		0			0
$331$	−3.12645	+	1.80506i	−0.171845	+	0.0992148i	−0.583456	−	0.812145i	$-0.698300\pi$
$331$	−3.12645	+	1.80506i	−0.171845	+	0.0992148i	0.411610	+	0.911360i	$0.364966\pi$
$332$	−6.40965	−	9.15392i	−0.351775	−	0.502387i
$333$	−1.03487	−	1.47795i	−0.0567104	−	0.0809909i
$334$	−11.3330	+	6.54309i	−0.620112	+	0.358022i
$335$		0			0
$336$	−1.87757	+	2.23760i	−0.102430	+	0.122071i
$337$	1.56044	+	3.34638i	0.0850026	+	0.182289i	0.944214	−	0.329331i	$-0.106823\pi$
$337$	1.56044	+	3.34638i	0.0850026	+	0.182289i	−0.859212	+	0.511620i	$0.829046\pi$
$338$	2.50133	−	5.36411i	0.136054	−	0.291769i
$339$	3.77213	+	4.49545i	0.204874	+	0.244159i
$340$		0			0
$341$		−	5.45413i		−	0.295357i
$342$	−2.58757	−	8.71769i	−0.139920	−	0.471399i
$343$	10.0750	+	10.0750i	0.544001	+	0.544001i
$344$	0.852413	+	4.83428i	0.0459590	+	0.260647i
$345$		0			0
$346$	19.8325	−	7.21843i	1.06620	−	0.388065i
$347$	−3.81557	+	1.77923i	−0.204830	+	0.0955140i	−0.522327	−	0.852746i	$-0.674936\pi$
$347$	−3.81557	+	1.77923i	−0.204830	+	0.0955140i	0.317496	+	0.948260i	$0.397158\pi$
$348$	−0.445612	−	5.09336i	−0.0238873	−	0.273033i
$349$	−17.1292	−	9.88954i	−0.916905	−	0.529375i	−0.0342584	−	0.999413i	$-0.510907\pi$
$349$	−17.1292	−	9.88954i	−0.916905	−	0.529375i	−0.882646	+	0.470038i	$0.844240\pi$
$350$		0			0
$351$	−2.24670	+	12.7417i	−0.119920	+	0.680100i
$352$	1.14279	−	0.800191i	0.0609110	−	0.0426503i
$353$	−3.84069	+	14.3336i	−0.204419	+	0.762902i	0.785207	+	0.619234i	$0.212557\pi$
$353$	−3.84069	+	14.3336i	−0.204419	+	0.762902i	−0.989626	+	0.143669i	$0.954110\pi$
$354$	−6.83181	+	11.8330i	−0.363107	+	0.628919i
$355$		0			0
$356$	−5.93248	+	16.2994i	−0.314421	+	0.863865i
$357$	−1.56779	−	0.731072i	−0.0829761	−	0.0386924i
$358$	1.99268	+	0.174337i	0.105316	+	0.00921398i
$359$	−8.43487	+	1.48729i	−0.445175	+	0.0784964i	−0.391742	−	0.920075i	$-0.628127\pi$
$359$	−8.43487	+	1.48729i	−0.445175	+	0.0784964i	−0.0534330	+	0.998571i	$0.517016\pi$
$360$		0			0
$361$	−10.3659	−	15.9232i	−0.545572	−	0.838064i
$362$	1.56488	−	1.56488i	0.0822482	−	0.0822482i
$363$	−7.08947	−	4.96410i	−0.372100	−	0.260548i
$364$	−6.22900	+	5.22675i	−0.326488	+	0.273956i
$365$		0			0
$366$	11.0525	+	4.02277i	0.577722	+	0.210274i
$367$	−20.8118	+	1.82080i	−1.08637	+	0.0950448i	−0.616244	−	0.787556i	$-0.711346\pi$
$367$	−20.8118	+	1.82080i	−1.08637	+	0.0950448i	−0.470124	+	0.882600i	$0.655791\pi$
$368$	−1.00525	+	0.269355i	−0.0524022	+	0.0140411i
$369$	10.3521	+	17.9304i	0.538909	+	0.933417i
$370$		0			0
$371$	−21.9230	−	3.86561i	−1.13818	−	0.200692i
$372$	3.60984	+	0.967255i	0.187162	+	0.0501498i
$373$	−4.46469	−	16.6625i	−0.231173	−	0.862749i	−0.979837	−	0.199799i	$-0.935971\pi$
$373$	−4.46469	−	16.6625i	−0.231173	−	0.862749i	0.748664	−	0.662950i	$-0.230696\pi$
$374$	0.632907	+	0.531072i	0.0327269	+	0.0274611i
$375$		0			0
$376$	−1.29589	−	3.56043i	−0.0668304	−	0.183615i
$377$	1.24049	−	14.1789i	0.0638884	−	0.730248i
$378$	−8.52146	+	12.1699i	−0.438297	+	0.625952i
$379$	11.6721			0.599555			0.299777	−	0.954009i	$-0.403088\pi$
$379$	11.6721			0.599555			0.299777	+	0.954009i	$0.403088\pi$
$380$		0			0
$381$	−2.07517			−0.106314
$382$	12.0115	−	17.1542i	0.614563	−	0.877686i
$383$	0.984281	−	11.2504i	0.0502944	−	0.574868i	−0.928680	−	0.370883i	$-0.879055\pi$
$383$	0.984281	−	11.2504i	0.0502944	−	0.574868i	0.978974	−	0.203985i	$-0.0653893\pi$
$384$	0.326944	+	0.898272i	0.0166843	+	0.0458397i
$385$		0			0
$386$	14.9940	+	12.5815i	0.763176	+	0.640380i
$387$	2.65055	+	9.89197i	0.134735	+	0.502837i
$388$	2.64322	+	0.708250i	0.134189	+	0.0359559i
$389$	15.6989	+	2.76814i	0.795967	+	0.140350i	0.556820	−	0.830633i	$-0.312021\pi$
$389$	15.6989	+	2.76814i	0.795967	+	0.140350i	0.239147	+	0.970983i	$0.423132\pi$
$390$		0			0
$391$	−0.308165	−	0.533757i	−0.0155846	−	0.0269933i
$392$	−2.25747	+	0.604887i	−0.114019	+	0.0305514i
$393$	17.7471	−	1.55267i	0.895224	−	0.0783219i
$394$	21.8507	+	7.95302i	1.10082	+	0.400667i
$395$		0			0
$396$	2.22954	−	1.87081i	0.112039	−	0.0940116i
$397$	8.24027	+	5.76990i	0.413567	+	0.289583i	0.761784	−	0.647831i	$-0.224324\pi$
$397$	8.24027	+	5.76990i	0.413567	+	0.289583i	−0.348217	+	0.937414i	$0.613213\pi$
$398$	3.05655	−	3.05655i	0.153211	−	0.153211i
$399$	−4.03328	+	12.0765i	−0.201917	+	0.604583i
$400$		0			0
$401$	−23.3135	+	4.11080i	−1.16422	+	0.205284i	−0.722176	−	0.691709i	$-0.756858\pi$
$401$	−23.3135	+	4.11080i	−1.16422	+	0.205284i	−0.442045	+	0.896993i	$0.645747\pi$
$402$	−5.21711	−	0.456438i	−0.260206	−	0.0227651i
$403$	9.42881	+	4.39672i	0.469682	+	0.219016i
$404$	−4.85640	+	13.3429i	−0.241615	+	0.663832i
$405$		0			0
$406$	8.17174	−	14.1539i	0.405557	−	0.702445i
$407$	0.312272	−	1.16542i	0.0154788	−	0.0577675i
$408$	−0.463735	+	0.324711i	−0.0229583	+	0.0160756i
$409$	−4.70502	+	26.6835i	−0.232648	+	1.31941i	0.614861	+	0.788635i	$0.289212\pi$
$409$	−4.70502	+	26.6835i	−0.232648	+	1.31941i	−0.847510	+	0.530780i	$0.821899\pi$
$410$		0			0
$411$	−8.89572	−	5.13594i	−0.438793	−	0.253337i
$412$	−0.958926	−	10.9606i	−0.0472429	−	0.539989i
$413$	−39.5846	+	18.4586i	−1.94783	+	0.908288i
$414$	−2.04021	+	0.742575i	−0.100271	+	0.0364956i
$415$		0			0
$416$	0.462092	+	2.62065i	0.0226559	+	0.128488i
$417$	−2.98960	−	2.98960i	−0.146401	−	0.146401i
$418$	3.35354	−	5.07278i	0.164027	−	0.248118i
$419$			16.7971i			0.820590i	0.911953	+	0.410295i	$0.134574\pi$
$419$			16.7971i			0.820590i	−0.911953	+	0.410295i	$0.865426\pi$
$420$		0			0
$421$	9.08726	+	10.8298i	0.442886	+	0.527811i	0.940594	−	0.339534i	$-0.110269\pi$
$421$	9.08726	+	10.8298i	0.442886	+	0.527811i	−0.497708	+	0.867345i	$0.665825\pi$
$422$	−2.43184	+	5.21509i	−0.118380	+	0.253867i
$423$	−3.34059	−	7.16393i	−0.162425	−	0.348322i
$424$	−4.68284	+	5.58079i	−0.227419	+	0.271027i
$425$		0			0
$426$	−6.42769	+	3.71103i	−0.311423	+	0.179800i
$427$	21.5650	+	30.7980i	1.04360	+	1.49042i
$428$	7.37962	+	10.5392i	0.356707	+	0.509431i
$429$	−3.07336	+	1.77440i	−0.148383	+	0.0856690i
$430$		0			0
$431$	14.3753	−	17.1318i	0.692435	−	0.825212i	−0.299213	−	0.954186i	$-0.596724\pi$
$431$	14.3753	−	17.1318i	0.692435	−	0.825212i	0.991648	+	0.128975i	$0.0411686\pi$
$432$	2.05478	+	4.40649i	0.0988605	+	0.212007i
$433$	15.2277	−	32.6559i	0.731796	−	1.56934i	−0.0876285	−	0.996153i	$-0.527929\pi$
$433$	15.2277	−	32.6559i	0.731796	−	1.56934i	0.819424	−	0.573188i	$-0.194293\pi$
$434$	7.67885	+	9.15130i	0.368597	+	0.439277i
$435$		0			0
$436$		−	1.84397i		−	0.0883100i
$437$	−3.64507	+	2.70035i	−0.174367	+	0.129175i
$438$	8.98877	+	8.98877i	0.429500	+	0.429500i
$439$	−5.19599	−	29.4679i	−0.247991	−	1.40643i	−0.813443	−	0.581645i	$-0.802409\pi$
$439$	−5.19599	−	29.4679i	−0.247991	−	1.40643i	0.565452	−	0.824781i	$-0.308702\pi$
$440$		0			0
$441$	−4.58166	+	1.66759i	−0.218174	+	0.0794090i
$442$	−1.42829	+	0.666024i	−0.0679370	+	0.0316796i
$443$	2.87161	+	32.8226i	0.136434	+	1.55945i	0.688243	+	0.725480i	$0.258382\pi$
$443$	2.87161	+	32.8226i	0.136434	+	1.55945i	−0.551809	+	0.833971i	$0.686062\pi$
$444$	0.715957	+	0.413358i	0.0339778	+	0.0196171i
$445$		0			0
$446$	−2.70888	+	15.3628i	−0.128269	+	0.727450i
$447$	−6.07889	+	4.25648i	−0.287521	+	0.201325i
$448$	−0.790865	+	2.95155i	−0.0373649	+	0.139448i
$449$	−1.77448	+	3.07349i	−0.0837428	+	0.145047i	−0.904855	−	0.425720i	$-0.860021\pi$
$449$	−1.77448	+	3.07349i	−0.0837428	+	0.145047i	0.821112	+	0.570767i	$0.193354\pi$
$450$		0			0
$451$	−4.73536	+	13.0103i	−0.222980	+	0.612631i
$452$	5.56382	+	2.59445i	0.261700	+	0.122033i
$453$	−21.0069	−	1.83786i	−0.986988	−	0.0863503i
$454$	−20.2751	+	3.57505i	−0.951558	+	0.167785i
$455$		0			0
$456$	2.76272	+	3.11918i	0.129376	+	0.146069i
$457$	−7.50169	+	7.50169i	−0.350914	+	0.350914i	−0.860450	−	0.509535i	$-0.829817\pi$
$457$	−7.50169	+	7.50169i	−0.350914	+	0.350914i	0.509535	+	0.860450i	$0.329817\pi$
$458$	−10.5788	−	7.40735i	−0.494315	−	0.346123i
$459$	−2.20574	+	1.85084i	−0.102955	+	0.0863896i
$460$		0			0
$461$	23.5998	+	8.58963i	1.09915	+	0.400059i	0.827004	−	0.562196i	$-0.190043\pi$
$461$	23.5998	+	8.58963i	1.09915	+	0.400059i	0.272149	+	0.962255i	$0.412266\pi$
$462$	−4.05952	+	0.355162i	−0.188866	+	0.0165236i
$463$	14.3333	−	3.84059i	0.666124	−	0.178487i	0.0901157	−	0.995931i	$-0.471276\pi$
$463$	14.3333	−	3.84059i	0.666124	−	0.178487i	0.576008	+	0.817444i	$0.304610\pi$
$464$	−2.67429	−	4.63201i	−0.124151	−	0.215036i
$465$		0			0
$466$	−9.84878	−	1.73661i	−0.456236	−	0.0804467i
$467$	−39.2993	−	10.5302i	−1.81855	−	0.487280i	−0.821946	−	0.569565i	$-0.807112\pi$
$467$	−39.2993	−	10.5302i	−1.81855	−	0.487280i	−0.996609	+	0.0822852i	$0.973778\pi$
$468$	1.43686	+	5.36243i	0.0664188	+	0.247878i
$469$	−12.8240	−	10.7606i	−0.592158	−	0.496879i
$470$		0			0
$471$	−6.76556	−	18.5882i	−0.311741	−	0.856500i
$472$	−1.24578	+	14.2393i	−0.0573415	+	0.655416i
$473$	−3.92802	+	5.60979i	−0.180611	+	0.257939i
$474$	2.94992			0.135494
$475$		0			0
$476$	−1.80963			−0.0829443
$477$	−8.71750	+	12.4499i	−0.399147	+	0.570041i
$478$	−1.57056	+	17.9516i	−0.0718358	+	0.821087i
$479$	0.208828	+	0.573749i	0.00954158	+	0.0262153i	0.944372	−	0.328879i	$-0.106671\pi$
$479$	0.208828	+	0.573749i	0.00954158	+	0.0262153i	−0.934830	+	0.355095i	$0.884449\pi$
$480$		0			0
$481$	1.76298	+	1.47931i	0.0803849	+	0.0674509i
$482$	3.46318	+	12.9248i	0.157744	+	0.588707i
$483$	2.93631	+	0.786781i	0.133607	+	0.0357998i
$484$	−8.91618	−	1.57216i	−0.405281	−	0.0714619i
$485$		0			0
$486$	8.06299	+	13.9655i	0.365745	+	0.633489i
$487$	−20.6321	+	5.52834i	−0.934928	+	0.250513i	−0.693955	−	0.720019i	$-0.744133\pi$
$487$	−20.6321	+	5.52834i	−0.934928	+	0.250513i	−0.240973	+	0.970532i	$0.577467\pi$
$488$	12.2573	−	1.07238i	0.554863	−	0.0485442i
$489$	20.5041	+	7.46289i	0.927228	+	0.337483i
$490$		0			0
$491$	18.2549	−	15.3177i	0.823832	−	0.691277i	−0.130034	−	0.991510i	$-0.541509\pi$
$491$	18.2549	−	15.3177i	0.823832	−	0.691277i	0.953866	+	0.300232i	$0.0970641\pi$
$492$	−7.77116	−	5.44142i	−0.350351	−	0.245318i
$493$	2.23979	−	2.23979i	0.100875	−	0.100875i
$494$	6.06617	+	9.88673i	0.272930	+	0.444825i
$495$		0			0
$496$	3.85012	−	0.678880i	0.172875	−	0.0304826i
$497$	−23.6348	−	2.06778i	−1.06017	−	0.0927526i
$498$	9.68145	+	4.51453i	0.433836	+	0.202301i
$499$	−12.9563	+	35.5971i	−0.580002	+	1.59354i	0.208172	+	0.978092i	$0.433249\pi$
$499$	−12.9563	+	35.5971i	−0.580002	+	1.59354i	−0.788175	+	0.615451i	$0.788974\pi$
$500$		0			0
$501$	6.25467	−	10.8334i	0.279438	−	0.484001i
$502$	−2.51045	+	9.36914i	−0.112047	+	0.418165i
$503$	−15.8181	+	11.0760i	−0.705295	+	0.493853i	−0.870351	−	0.492431i	$-0.836108\pi$
$503$	−15.8181	+	11.0760i	−0.705295	+	0.493853i	0.165056	+	0.986284i	$0.447219\pi$
$504$	−1.10697	+	6.27793i	−0.0493083	+	0.279641i
$505$		0			0
$506$	−1.25737	−	0.725942i	−0.0558968	−	0.0322721i
$507$	0.493106	+	5.63622i	0.0218996	+	0.250313i
$508$	−1.96746	+	0.917443i	−0.0872921	+	0.0407050i
$509$	−4.95331	+	1.80286i	−0.219552	+	0.0799103i	−0.449454	−	0.893303i	$-0.648381\pi$
$509$	−4.95331	+	1.80286i	−0.219552	+	0.0799103i	0.229902	+	0.973214i	$0.426159\pi$
$510$		0			0
$511$	7.05619	+	40.0176i	0.312147	+	1.77028i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	15.3810	+	14.5798i	0.679088	+	0.643713i
$514$			2.77284i			0.122305i
$515$		0			0
$516$	−3.01626	−	3.59464i	−0.132784	−	0.158245i
$517$	2.23392	−	4.79065i	0.0982475	−	0.210692i
$518$	1.11684	+	2.39506i	0.0490709	+	0.105233i
$519$	−12.9682	+	15.4549i	−0.569241	+	0.678396i
$520$		0			0
$521$	23.7652	−	13.7208i	1.04117	−	0.601120i	0.121006	−	0.992652i	$-0.461388\pi$
$521$	23.7652	−	13.7208i	1.04117	−	0.601120i	0.920165	+	0.391532i	$0.128055\pi$
$522$	−6.40013	−	9.14034i	−0.280126	−	0.400062i
$523$	−10.8953	−	15.5601i	−0.476419	−	0.680397i	0.506958	−	0.861971i	$-0.330770\pi$
$523$	−10.8953	−	15.5601i	−0.476419	−	0.680397i	−0.983377	+	0.181574i	$0.941881\pi$
$524$	16.1396	−	9.31820i	0.705061	−	0.407067i
$525$		0			0
$526$	7.49687	−	8.93442i	0.326879	−	0.389559i
$527$	0.978486	+	2.09837i	0.0426235	+	0.0914065i
$528$	−0.563602	+	1.20865i	−0.0245276	+	0.0525997i
$529$	−14.0879	−	16.7893i	−0.612519	−	0.729971i
$530$		0			0
$531$			29.8197i			1.29406i
$532$	1.51516	+	13.2329i	0.0656904	+	0.573718i
$533$	−18.6742	−	18.6742i	−0.808870	−	0.808870i
$534$	−2.87923	−	16.3289i	−0.124597	−	0.706623i
$535$		0			0
$536$	−5.14813	+	1.87377i	−0.222365	+	0.0809344i
$537$	−1.73297	+	0.808096i	−0.0747831	+	0.0348719i
$538$	0.345828	+	3.95284i	0.0149097	+	0.170419i
$539$	−2.82365	−	1.63024i	−0.121623	−	0.0702193i
$540$		0			0
$541$	6.47639	−	36.7294i	0.278442	−	1.57912i	−0.449370	−	0.893346i	$-0.648352\pi$
$541$	6.47639	−	36.7294i	0.278442	−	1.57912i	0.727812	−	0.685776i	$-0.240537\pi$
$542$	−4.45936	+	3.12248i	−0.191546	+	0.134122i
$543$	−0.547538	+	2.04344i	−0.0234971	+	0.0876923i
$544$	−0.296110	+	0.512878i	−0.0126956	+	0.0219895i
$545$		0			0
$546$	2.65851	−	7.30419i	0.113774	−	0.312590i
$547$	−33.4317	−	15.5895i	−1.42944	−	0.666558i	−0.454851	−	0.890568i	$-0.650307\pi$
$547$	−33.4317	−	15.5895i	−1.42944	−	0.666558i	−0.974587	+	0.224010i	$0.928085\pi$
$548$	−10.7047	−	0.936536i	−0.457280	−	0.0400068i
$549$	25.2791	−	4.45739i	1.07889	−	0.190237i
$550$		0			0
$551$	−18.2537	−	14.5031i	−0.777635	−	0.617853i
$552$	0.703455	−	0.703455i	0.0299410	−	0.0299410i
$553$	7.72430	+	5.40861i	0.328471	+	0.229998i
$554$	10.0360	−	8.42121i	0.426389	−	0.357783i
$555$		0			0
$556$	−4.15615	−	1.51272i	−0.176260	−	0.0641534i
$557$	27.5029	−	2.40620i	1.16534	−	0.101954i	0.511976	−	0.859000i	$-0.328914\pi$
$557$	27.5029	−	2.40620i	1.16534	−	0.101954i	0.653361	+	0.757046i	$0.273358\pi$
$558$	7.87818	−	2.11095i	0.333510	−	0.0893637i
$559$	−6.53143	−	11.3128i	−0.276250	−	0.478479i
$560$		0			0
$561$	−0.777785	−	0.137144i	−0.0328381	−	0.00579024i
$562$	5.20761	+	1.39538i	0.219670	+	0.0588604i
$563$	5.55520	+	20.7323i	0.234124	+	0.873762i	0.978542	+	0.206048i	$0.0660603\pi$
$563$	5.55520	+	20.7323i	0.234124	+	0.873762i	−0.744418	+	0.667714i	$0.767273\pi$
$564$	2.77455	+	2.32812i	0.116829	+	0.0980316i
$565$		0			0
$566$	−2.06999	−	5.68726i	−0.0870083	−	0.239053i
$567$	−0.429025	+	4.90378i	−0.0180173	+	0.205939i
$568$	−4.45342	+	6.36014i	−0.186861	+	0.266866i
$569$	2.51409			0.105396			0.0526980	−	0.998610i	$-0.483218\pi$
$569$	2.51409			0.105396			0.0526980	+	0.998610i	$0.483218\pi$
$570$		0			0
$571$	−19.9326			−0.834151			−0.417076	−	0.908872i	$-0.636945\pi$
$571$	−19.9326			−0.834151			−0.417076	+	0.908872i	$0.636945\pi$
$572$	−2.12937	+	3.04106i	−0.0890336	+	0.127153i
$573$	−1.74471	+	19.9422i	−0.0728865	+	0.833096i
$574$	−10.3719	−	28.4965i	−0.432913	−	1.18942i
$575$		0			0
$576$	1.59813	+	1.34099i	0.0665889	+	0.0558747i
$577$	−3.17960	−	11.8664i	−0.132368	−	0.494005i	0.867627	−	0.497216i	$-0.165645\pi$
$577$	−3.17960	−	11.8664i	−0.132368	−	0.494005i	−0.999995	+	0.00321116i	$0.998978\pi$
$578$	16.0820	+	4.30915i	0.668922	+	0.179237i
$579$	−18.4263	−	3.24905i	−0.765770	−	0.135026i
$580$		0			0
$581$	17.0734	+	29.5719i	0.708322	+	1.22685i
$582$	−2.52671	+	0.677031i	−0.104736	+	0.0280638i
$583$	−10.1248	+	0.885809i	−0.419328	+	0.0366864i
$584$	12.4962	+	4.54826i	0.517098	+	0.188208i
$585$		0			0
$586$	7.24765	−	6.08150i	0.299398	−	0.251225i
$587$	22.7088	+	15.9009i	0.937294	+	0.656300i	0.939080	−	0.343698i	$-0.111680\pi$
$587$	22.7088	+	15.9009i	0.937294	+	0.656300i	−0.00178641	+	0.999998i	$0.500569\pi$
$588$	1.57974	−	1.57974i	0.0651473	−	0.0651473i
$589$	14.5250	−	8.91207i	0.598494	−	0.367216i
$590$		0			0
$591$	−21.8904	+	3.85987i	−0.900450	+	0.158774i
$592$	0.861547	+	0.0753756i	0.0354094	+	0.00309792i
$593$	20.5246	+	9.57079i	0.842845	+	0.393025i	0.795574	−	0.605857i	$-0.207170\pi$
$593$	20.5246	+	9.57079i	0.842845	+	0.393025i	0.0472715	+	0.998882i	$0.484947\pi$
$594$	−2.31991	+	6.37389i	−0.0951870	+	0.261524i
$595$		0			0
$596$	−3.88157	+	6.72308i	−0.158995	+	0.275388i
$597$	−1.06946	+	3.99128i	−0.0437701	+	0.163352i
$598$	2.26857	−	1.58847i	0.0927687	−	0.0649574i
$599$	−3.43137	+	19.4603i	−0.140202	+	0.795126i	0.830893	+	0.556432i	$0.187830\pi$
$599$	−3.43137	+	19.4603i	−0.140202	+	0.795126i	−0.971095	+	0.238693i	$0.923281\pi$
$600$		0			0
$601$	38.8793	+	22.4470i	1.58592	+	0.915632i	0.993969	+	0.109659i	$0.0349758\pi$
$601$	38.8793	+	22.4470i	1.58592	+	0.915632i	0.591952	+	0.805973i	$0.298358\pi$
$602$	−1.30732	−	14.9427i	−0.0532824	−	0.609021i
$603$	−10.3585	+	4.83027i	−0.421833	+	0.196704i
$604$	−20.7291	+	7.54478i	−0.843456	+	0.306993i
$605$		0			0
$606$	−2.35698	−	13.3671i	−0.0957456	−	0.543000i
$607$	−12.1021	−	12.1021i	−0.491211	−	0.491211i	0.417477	−	0.908688i	$-0.362914\pi$
$607$	−12.1021	−	12.1021i	−0.491211	−	0.491211i	−0.908688	+	0.417477i	$0.862914\pi$
$608$	3.99834	+	1.73588i	0.162154	+	0.0703993i
$609$			15.6231i			0.633079i
$610$		0			0
$611$	6.48100	+	7.72375i	0.262193	+	0.312470i
$612$	−0.522145	+	1.11974i	−0.0211065	+	0.0452630i
$613$	6.68166	+	14.3289i	0.269870	+	0.578737i	0.993806	−	0.111130i	$-0.0354468\pi$
$613$	6.68166	+	14.3289i	0.269870	+	0.578737i	−0.723936	+	0.689867i	$0.757669\pi$
$614$	−2.31522	+	2.75917i	−0.0934347	+	0.111351i
$615$		0			0
$616$	−3.69181	+	2.13147i	−0.148747	+	0.0858792i
$617$	4.69416	+	6.70395i	0.188980	+	0.269891i	0.902450	−	0.430794i	$-0.141767\pi$
$617$	4.69416	+	6.70395i	0.188980	+	0.269891i	−0.713470	+	0.700685i	$0.752878\pi$
$618$	6.03257	+	8.61540i	0.242665	+	0.346562i
$619$	22.2890	−	12.8686i	0.895872	−	0.517232i	0.0200135	−	0.999800i	$-0.493629\pi$
$619$	22.2890	−	12.8686i	0.895872	−	0.517232i	0.875859	+	0.482568i	$0.160296\pi$
$620$		0			0
$621$	3.25247	−	3.87615i	0.130517	−	0.155544i
$622$	4.21372	+	9.03635i	0.168955	+	0.362325i
$623$	22.3995	−	48.0360i	0.897419	−	1.92452i
$624$	−1.63511	−	1.94865i	−0.0654569	−	0.0780085i
$625$		0			0
$626$			29.7906i			1.19067i
$627$	−0.351647	+	5.80236i	−0.0140434	+	0.231724i
$628$	−14.6324	−	14.6324i	−0.583896	−	0.583896i
$629$	0.0889382	+	0.504394i	0.00354620	+	0.0201115i
$630$		0			0
$631$	11.9879	−	4.36325i	0.477232	−	0.173698i	−0.0921934	−	0.995741i	$-0.529388\pi$
$631$	11.9879	−	4.36325i	0.477232	−	0.173698i	0.569426	+	0.822043i	$0.307166\pi$
$632$	2.79682	−	1.30418i	0.111251	−	0.0518774i
$633$	−0.479407	−	5.47964i	−0.0190547	−	0.217796i
$634$	−2.38792	−	1.37867i	−0.0948366	−	0.0547539i
$635$		0			0
$636$	1.20930	−	6.85827i	0.0479518	−	0.271948i
$637$	5.09449	−	3.56720i	0.201851	−	0.141338i
$638$	1.93124	−	7.20750i	0.0764587	−	0.285348i
$639$	−8.09900	+	14.0279i	−0.320392	+	0.554935i
$640$		0			0
$641$	4.16617	−	11.4465i	0.164554	−	0.452108i	−0.829821	−	0.558030i	$-0.811557\pi$
$641$	4.16617	−	11.4465i	0.164554	−	0.452108i	0.994374	+	0.105923i	$0.0337795\pi$
$642$	−11.1465	−	5.19772i	−0.439919	−	0.205138i
$643$	−26.3636	−	2.30651i	−1.03968	−	0.0909600i	−0.445490	−	0.895287i	$-0.646971\pi$
$643$	−26.3636	−	2.30651i	−1.03968	−	0.0909600i	−0.594187	+	0.804327i	$0.702526\pi$
$644$	3.13175	−	0.552212i	0.123408	−	0.0217602i
$645$		0			0
$646$	−0.380139	+	2.55329i	−0.0149564	+	0.100458i
$647$	−4.66488	+	4.66488i	−0.183395	+	0.183395i	−0.792833	−	0.609438i	$-0.791395\pi$
$647$	−4.66488	+	4.66488i	−0.183395	+	0.183395i	0.609438	+	0.792833i	$0.291395\pi$
$648$	1.31961	+	0.923999i	0.0518391	+	0.0362981i
$649$	−15.2757	+	12.8178i	−0.599623	+	0.503143i
$650$		0			0
$651$	−10.7309	−	3.90573i	−0.420578	−	0.153078i
$652$	22.7393	−	1.98943i	0.890541	−	0.0779122i
$653$	8.98921	−	2.40865i	0.351775	−	0.0942578i	−0.0786044	−	0.996906i	$-0.525046\pi$
$653$	8.98921	−	2.40865i	0.351775	−	0.0942578i	0.430379	+	0.902648i	$0.358380\pi$
$654$	0.881343	+	1.52653i	0.0344632	+	0.0596921i
$655$		0			0
$656$	−9.77351	−	1.72333i	−0.381592	−	0.0672849i
$657$	26.7976	+	7.18041i	1.04548	+	0.280134i
$658$	2.99653	+	11.1832i	0.116817	+	0.435966i
$659$	3.93974	+	3.30584i	0.153471	+	0.128777i	0.716290	−	0.697803i	$-0.245839\pi$
$659$	3.93974	+	3.30584i	0.153471	+	0.128777i	−0.562819	+	0.826580i	$0.690283\pi$
$660$		0			0
$661$	−9.61287	−	26.4112i	−0.373897	−	1.02727i	−0.973841	−	0.227232i	$-0.927032\pi$
$661$	−9.61287	−	26.4112i	−0.373897	−	1.02727i	0.599943	−	0.800043i	$-0.295190\pi$
$662$	0.314642	−	3.59637i	0.0122289	−	0.139777i
$663$	0.864082	−	1.23404i	0.0335582	−	0.0479260i
$664$	11.1749			0.433669
$665$		0			0
$666$	1.80424			0.0699128
$667$	−3.19271	+	4.55966i	−0.123622	+	0.176551i
$668$	1.14054	−	13.0364i	0.0441286	−	0.504393i
$669$	−5.10026	−	14.0129i	−0.197188	−	0.541769i
$670$		0			0
$671$	13.1495	+	11.0337i	0.507629	+	0.425952i
$672$	−0.756004	−	2.82145i	−0.0291635	−	0.108840i
$673$	−16.4857	−	4.41732i	−0.635476	−	0.170275i	−0.0733224	−	0.997308i	$-0.523360\pi$
$673$	−16.4857	−	4.41732i	−0.635476	−	0.170275i	−0.562153	+	0.827033i	$0.690027\pi$
$674$	−3.63622	−	0.641164i	−0.140062	−	0.0246967i
$675$		0			0
$676$	2.95932	+	5.12570i	0.113820	+	0.197142i
$677$	20.2409	−	5.42355i	0.777923	−	0.208444i	0.152054	−	0.988372i	$-0.451411\pi$
$677$	20.2409	−	5.42355i	0.777923	−	0.208444i	0.625869	+	0.779928i	$0.284745\pi$
$678$	−5.84606	+	0.511464i	−0.224517	+	0.0196427i
$679$	−7.85746	−	2.85988i	−0.301542	−	0.109752i
$680$		0			0
$681$	15.0760	−	12.6503i	0.577715	−	0.484761i
$682$	4.46776	+	3.12836i	0.171079	+	0.119791i
$683$	26.3082	−	26.3082i	1.00665	−	1.00665i	0.00667617	−	0.999978i	$-0.497875\pi$
$683$	26.3082	−	26.3082i	1.00665	−	1.00665i	0.999978	−	0.00667617i	$-0.00212511\pi$
$684$	8.62528	+	2.88064i	0.329796	+	0.110144i
$685$		0			0
$686$	−14.0318	+	2.47418i	−0.535736	+	0.0944648i
$687$	12.2981	+	1.07594i	0.469201	+	0.0410498i
$688$	−4.44893	−	2.07457i	−0.169614	−	0.0790923i
$689$	6.63058	−	18.2174i	0.252605	−	0.694026i
$690$		0			0
$691$	5.37744	−	9.31400i	0.204567	−	0.354321i	−0.745427	−	0.666587i	$-0.767755\pi$
$691$	5.37744	−	9.31400i	0.204567	−	0.354321i	0.949995	+	0.312266i	$0.101088\pi$
$692$	−5.46245	+	20.3861i	−0.207651	+	0.774964i
$693$	−7.28505	+	5.10104i	−0.276736	+	0.193773i
$694$	0.731061	−	4.14606i	0.0277507	−	0.157382i
$695$		0			0
$696$	4.42783	+	2.55641i	0.167836	+	0.0969004i
$697$	−0.512246	−	5.85500i	−0.0194027	−	0.221774i
$698$	17.9259	−	8.35900i	0.678507	−	0.316393i
$699$	8.98336	−	3.26967i	0.339782	−	0.123670i
$700$		0			0
$701$	0.799194	+	4.53246i	0.0301851	+	0.171188i	0.996174	−	0.0873968i	$-0.0278548\pi$
$701$	0.799194	+	4.53246i	0.0301851	+	0.171188i	−0.965988	+	0.258585i	$0.916744\pi$
$702$	−9.14871	−	9.14871i	−0.345296	−	0.345296i
$703$	3.61391	−	1.07268i	0.136301	−	0.0404567i
$704$			1.39509i			0.0525795i
$705$		0			0
$706$	−9.53850	−	11.3675i	−0.358986	−	0.427823i
$707$	18.3365	−	39.3229i	0.689617	−	1.47889i
$708$	−5.77450	−	12.3834i	−0.217019	−	0.465398i
$709$	−16.2517	+	19.3680i	−0.610346	+	0.727382i	−0.979378	−	0.202034i	$-0.935245\pi$
$709$	−16.2517	+	19.3680i	−0.610346	+	0.727382i	0.369032	+	0.929417i	$0.379689\pi$
$710$		0			0
$711$	5.57543	−	3.21898i	0.209095	−	0.120721i
$712$	−9.94893	−	14.2085i	−0.372852	−	0.532487i
$713$	−2.33369	−	3.33286i	−0.0873975	−	0.124817i
$714$	1.49810	−	0.864931i	0.0560652	−	0.0323692i
$715$		0			0
$716$	−1.28576	+	1.53231i	−0.0480512	+	0.0572651i
$717$	−7.27996	−	15.6119i	−0.271875	−	0.583038i
$718$	3.61972	−	7.76251i	0.135087	−	0.289694i
$719$	17.3436	+	20.6694i	0.646809	+	0.770837i	0.985429	−	0.170086i	$-0.0544046\pi$
$719$	17.3436	+	20.6694i	0.646809	+	0.770837i	−0.338620	+	0.940923i	$0.609960\pi$
$720$		0			0
$721$			33.6198i			1.25207i
$722$	18.9892	+	0.641958i	0.706703	+	0.0238912i
$723$	−9.04453	−	9.04453i	−0.336370	−	0.336370i
$724$	0.384296	+	2.17945i	0.0142823	+	0.0809987i
$725$		0			0
$726$	8.13270	−	2.96006i	0.301833	−	0.109858i
$727$	17.8713	−	8.33350i	0.662808	−	0.309072i	−0.0619466	−	0.998079i	$-0.519731\pi$
$727$	17.8713	−	8.33350i	0.662808	−	0.309072i	0.724755	+	0.689007i	$0.241953\pi$
$728$	−0.708697	−	8.10044i	−0.0262660	−	0.300222i
$729$	−9.16457	−	5.29117i	−0.339429	−	0.195969i
$730$		0			0
$731$	0.504817	−	2.86296i	0.0186713	−	0.105890i
$732$	−9.63469	+	6.74629i	−0.356109	+	0.249350i
$733$	10.1270	−	37.7944i	0.374049	−	1.39597i	−0.480681	−	0.876895i	$-0.659611\pi$
$733$	10.1270	−	37.7944i	0.374049	−	1.39597i	0.854730	−	0.519073i	$-0.173723\pi$
$734$	10.4457	−	18.0924i	0.385556	−	0.667803i
$735$		0			0
$736$	0.355944	−	0.977947i	0.0131203	−	0.0360476i
$737$	−6.92695	−	3.23009i	−0.255157	−	0.118982i
$738$	−20.6254	−	1.80449i	−0.759232	−	0.0664242i
$739$	45.8950	−	8.09253i	1.68828	−	0.297689i	0.754701	−	0.656069i	$-0.227782\pi$
$739$	45.8950	−	8.09253i	1.68828	−	0.297689i	0.933575	+	0.358381i	$0.116671\pi$
$740$		0			0
$741$	−9.74735	−	5.28536i	−0.358078	−	0.194162i
$742$	15.7410	−	15.7410i	0.577871	−	0.577871i
$743$	24.5372	+	17.1811i	0.900183	+	0.630315i	0.929326	−	0.369260i	$-0.120389\pi$
$743$	24.5372	+	17.1811i	0.900183	+	0.630315i	−0.0291432	+	0.999575i	$0.509278\pi$
$744$	−2.86285	+	2.40222i	−0.104957	+	0.0880695i
$745$		0			0
$746$	16.2099	+	5.89993i	0.593487	+	0.216012i
$747$	23.2245	−	2.03188i	0.849740	−	0.0743426i
$748$	−0.798050	+	0.213837i	−0.0291796	+	0.00781864i
$749$	−19.6571	−	34.0470i	−0.718254	−	1.24405i
$750$		0			0
$751$	−25.1743	−	4.43891i	−0.918623	−	0.161978i	−0.305707	−	0.952126i	$-0.598893\pi$
$751$	−25.1743	−	4.43891i	−0.918623	−	0.161978i	−0.612916	+	0.790148i	$0.710004\pi$
$752$	3.65982	+	0.980646i	0.133460	+	0.0357605i
$753$	−2.39980	−	8.95616i	−0.0874534	−	0.326381i
$754$	10.9031	+	9.14880i	0.397068	+	0.333180i
$755$		0			0
$756$	−5.08130	−	13.9607i	−0.184805	−	0.507747i
$757$	−3.09819	+	35.4125i	−0.112606	+	1.28709i	0.704128	+	0.710073i	$0.251338\pi$
$757$	−3.09819	+	35.4125i	−0.112606	+	1.28709i	−0.816733	+	0.577015i	$0.804217\pi$
$758$	−6.69484	+	9.56122i	−0.243167	+	0.347279i
$759$	1.38789			0.0503771
$760$		0			0
$761$	−15.6523			−0.567394			−0.283697	−	0.958914i	$-0.591561\pi$
$761$	−15.6523			−0.567394			−0.283697	+	0.958914i	$0.591561\pi$
$762$	1.19027	−	1.69988i	0.0431188	−	0.0615800i
$763$	−0.491083	+	5.61311i	−0.0177784	+	0.203208i
$764$	7.16239	+	19.6785i	0.259126	+	0.711944i
$765$		0			0
$766$	8.65121	+	7.25923i	0.312581	+	0.262287i
$767$	−9.84461	−	36.7406i	−0.355468	−	1.32663i
$768$	−0.923348	−	0.247410i	−0.0333185	−	0.00892766i
$769$	52.1671	+	9.19846i	1.88119	+	0.331705i	0.992042	−	0.125910i	$-0.0401851\pi$
$769$	52.1671	+	9.19846i	1.88119	+	0.331705i	0.889150	+	0.457615i	$0.151296\pi$
$770$		0			0
$771$	−1.32531	−	2.29550i	−0.0477298	−	0.0826705i
$772$	−18.9064	+	5.06594i	−0.680455	+	0.182327i
$773$	−3.68207	+	0.322140i	−0.132435	+	0.0115866i	−0.153180	−	0.988198i	$-0.548952\pi$
$773$	−3.68207	+	0.322140i	−0.132435	+	0.0115866i	0.0207455	+	0.999785i	$0.493396\pi$
$774$	−9.62332	−	3.50260i	−0.345903	−	0.125898i
$775$		0			0
$776$	−2.09626	+	1.75897i	−0.0752512	+	0.0631433i
$777$	−2.06932	−	1.44895i	−0.0742364	−	0.0519809i
$778$	−11.2721	+	11.2721i	−0.404123	+	0.404123i
$779$	−42.3857	+	8.64804i	−1.51863	+	0.309848i
$780$		0			0
$781$	−10.6673	+	1.88094i	−0.381707	+	0.0673053i
$782$	0.613984	+	0.0537167i	0.0219560	+	0.00192090i
$783$	23.5684	+	10.9901i	0.842267	+	0.392756i
$784$	0.799337	−	2.19616i	0.0285477	−	0.0784343i
$785$		0			0
$786$	−8.90746	+	15.4282i	−0.317718	+	0.550305i
$787$	11.2709	−	42.0635i	0.401764	−	1.49940i	−0.408184	−	0.912900i	$-0.633838\pi$
$787$	11.2709	−	42.0635i	0.401764	−	1.49940i	0.809947	−	0.586503i	$-0.199496\pi$
$788$	−19.0478	+	13.3374i	−0.678550	+	0.475125i
$789$	−1.93600	+	10.9796i	−0.0689233	+	0.390883i
$790$		0			0
$791$	−16.2455	−	9.37937i	−0.577625	−	0.333492i
$792$	0.253663	+	2.89938i	0.00901353	+	0.103025i
$793$	−29.6746	+	13.8375i	−1.05378	+	0.491385i
$794$	−9.45285	+	3.44056i	−0.335469	+	0.122101i
$795$		0			0
$796$	0.750615	+	4.25695i	0.0266048	+	0.150884i
$797$	17.0191	+	17.0191i	0.602847	+	0.602847i	0.941067	−	0.338220i	$-0.109825\pi$
$797$	17.0191	+	17.0191i	0.602847	+	0.602847i	−0.338220	+	0.941067i	$0.609825\pi$
$798$	−7.57912	−	10.2307i	−0.268298	−	0.362162i
$799$			2.24388i			0.0793828i
$800$		0			0
$801$	−23.2601	−	27.7203i	−0.821855	−	0.979449i
$802$	10.0047	−	21.4552i	0.353279	−	0.757608i
$803$	7.84051	+	16.8140i	0.276686	+	0.593354i
$804$	3.36630	−	4.01180i	0.118720	−	0.141485i
$805$		0			0
$806$	−9.00973	+	5.20177i	−0.317354	+	0.183224i
$807$	−2.17559	−	3.10707i	−0.0765845	−	0.109374i
$808$	−8.14431	−	11.6313i	−0.286516	−	0.409187i
$809$	−10.8111	+	6.24177i	−0.380097	+	0.219449i	−0.677860	−	0.735191i	$-0.737093\pi$
$809$	−10.8111	+	6.24177i	−0.380097	+	0.219449i	0.297764	+	0.954640i	$0.403759\pi$
$810$		0			0
$811$	−16.8039	+	20.0261i	−0.590065	+	0.703212i	−0.975619	−	0.219473i	$-0.929566\pi$
$811$	−16.8039	+	20.0261i	−0.590065	+	0.703212i	0.385553	+	0.922686i	$0.374011\pi$
$812$	6.90706	+	14.8122i	0.242390	+	0.519807i
$813$	2.19927	−	4.71634i	0.0771317	−	0.165409i
$814$	0.775541	+	0.924253i	0.0271827	+	0.0323951i
$815$		0			0
$816$		−	0.566116i		−	0.0198180i
$817$	−21.3580	−	1.29438i	−0.747222	−	0.0452847i
$818$	−19.1592	−	19.1592i	−0.669884	−	0.669884i
$819$	−2.94574	−	16.7061i	−0.102932	−	0.583758i
$820$		0			0
$821$	−3.31854	+	1.20785i	−0.115818	+	0.0421542i	−0.399279	−	0.916830i	$-0.630739\pi$
$821$	−3.31854	+	1.20785i	−0.115818	+	0.0421542i	0.283461	+	0.958984i	$0.408517\pi$
$822$	9.30949	−	4.34109i	0.324706	−	0.151413i
$823$	−0.0511605	−	0.584768i	−0.00178334	−	0.0203837i	0.995251	−	0.0973430i	$-0.0310344\pi$
$823$	−0.0511605	−	0.584768i	−0.00178334	−	0.0203837i	−0.997034	+	0.0769593i	$0.975479\pi$
$824$	9.52839	+	5.50122i	0.331937	+	0.191644i
$825$		0			0
$826$	7.58439	−	43.0132i	0.263895	−	1.49662i
$827$	12.8913	−	9.02661i	0.448276	−	0.313886i	−0.327549	−	0.944834i	$-0.606223\pi$
$827$	12.8913	−	9.02661i	0.448276	−	0.313886i	0.775825	+	0.630948i	$0.217334\pi$
$828$	0.561934	−	2.09716i	0.0195285	−	0.0728815i
$829$	10.6558	−	18.4564i	0.370091	−	0.641017i	−0.619488	−	0.785006i	$-0.712660\pi$
$829$	10.6558	−	18.4564i	0.370091	−	0.641017i	0.989579	+	0.143989i	$0.0459931\pi$
$830$		0			0
$831$	−4.28332	+	11.7683i	−0.148587	+	0.408239i
$832$	−2.41176	−	1.12462i	−0.0836127	−	0.0389892i
$833$	1.37882	+	0.120631i	0.0477731	+	0.00417961i
$834$	4.16369	−	0.734172i	0.144177	−	0.0254223i
$835$		0			0
$836$	2.23186	+	5.65668i	0.0771906	+	0.195640i
$837$	−13.4408	+	13.4408i	−0.464581	+	0.464581i
$838$	−13.7594	−	9.63440i	−0.475309	−	0.332815i
$839$	27.2587	−	22.8728i	0.941076	−	0.789657i	−0.0366962	−	0.999326i	$-0.511683\pi$
$839$	27.2587	−	22.8728i	0.941076	−	0.789657i	0.977772	+	0.209670i	$0.0672389\pi$
$840$		0			0
$841$	0.369002	+	0.134306i	0.0127242	+	0.00463124i
$842$	−14.0835	+	1.23214i	−0.485348	+	0.0424625i
$843$	−4.97807	+	1.33387i	−0.171454	+	0.0459409i
$844$	−2.87711	−	4.98330i	−0.0990341	−	0.171532i
$845$		0			0
$846$	7.78443	+	1.37261i	0.267634	+	0.0471911i
$847$	26.7225	+	7.16027i	0.918196	+	0.246030i
$848$	−1.88555	−	7.03696i	−0.0647500	−	0.241650i
$849$	4.43193	+	3.71883i	0.152103	+	0.127630i
$850$		0			0
$851$	−0.307833	−	0.845766i	−0.0105524	−	0.0289925i
$852$	0.646875	−	7.39381i	0.0221616	−	0.253308i
$853$	−26.5509	+	37.9186i	−0.909084	+	1.29831i	0.0450679	+	0.998984i	$0.485650\pi$
$853$	−26.5509	+	37.9186i	−0.909084	+	1.29831i	−0.954152	+	0.299323i	$0.903239\pi$
$854$	−37.5974			−1.28656
$855$		0			0
$856$	−12.8660			−0.439750
$857$	16.8459	−	24.0585i	0.575446	−	0.821822i	−0.420911	−	0.907102i	$-0.638290\pi$
$857$	16.8459	−	24.0585i	0.575446	−	0.821822i	0.996357	+	0.0852801i	$0.0271785\pi$
$858$	0.309299	−	3.53530i	0.0105593	−	0.120693i
$859$	−19.9187	−	54.7261i	−0.679616	−	1.86723i	−0.446506	−	0.894780i	$-0.647332\pi$
$859$	−19.9187	−	54.7261i	−0.679616	−	1.86723i	−0.233110	−	0.972450i	$-0.574890\pi$
$860$		0			0
$861$	22.2066	+	18.6335i	0.756797	+	0.635028i
$862$	5.78824	+	21.6020i	0.197148	+	0.735767i
$863$	21.5190	+	5.76600i	0.732515	+	0.196277i	0.605749	−	0.795656i	$-0.292874\pi$
$863$	21.5190	+	5.76600i	0.732515	+	0.196277i	0.126766	+	0.991933i	$0.459540\pi$
$864$	−4.78815	−	0.844281i	−0.162896	−	0.0287230i
$865$		0			0
$866$	18.0159	+	31.2044i	0.612205	+	1.06037i
$867$	−15.3731	+	4.11920i	−0.522097	+	0.139896i
$868$	−11.9007	+	1.04118i	−0.403937	+	0.0353399i
$869$	4.04554	+	1.47246i	0.137236	+	0.0499497i
$870$		0			0
$871$	11.1680	−	9.37108i	0.378414	−	0.317527i
$872$	1.51049	+	1.05766i	0.0511516	+	0.0358167i
$873$	−4.03677	+	4.03677i	−0.136624	+	0.136624i
$874$	−0.121271	−	4.53473i	−0.00410206	−	0.153389i
$875$		0			0
$876$	−12.5189	+	2.20742i	−0.422975	+	0.0745819i
$877$	39.2766	+	3.43625i	1.32628	+	0.116034i	0.728177	−	0.685389i	$-0.240368\pi$
$877$	39.2766	+	3.43625i	1.32628	+	0.116034i	0.598098	+	0.801423i	$0.295923\pi$
$878$	27.1190	+	12.6458i	0.915222	+	0.426775i
$879$	−3.09326	+	8.49867i	−0.104333	+	0.286653i
$880$		0			0
$881$	15.2247	−	26.3699i	0.512933	−	0.888425i	−0.486955	−	0.873427i	$-0.661892\pi$
$881$	15.2247	−	26.3699i	0.512933	−	0.888425i	0.999888	−	0.0149982i	$-0.00477425\pi$
$882$	1.26193	−	4.70957i	0.0424912	−	0.158579i
$883$	9.47100	−	6.63167i	0.318725	−	0.223173i	−0.403255	−	0.915088i	$-0.632121\pi$
$883$	9.47100	−	6.63167i	0.318725	−	0.223173i	0.721980	+	0.691914i	$0.243232\pi$
$884$	0.273661	−	1.55201i	0.00920420	−	0.0521996i
$885$		0			0
$886$	−28.5338	−	16.4740i	−0.958613	−	0.553455i
$887$	0.930884	+	10.6401i	0.0312560	+	0.357258i	0.995677	+	0.0928859i	$0.0296092\pi$
$887$	0.930884	+	10.6401i	0.0312560	+	0.357258i	−0.964421	+	0.264372i	$0.914835\pi$
$888$	−0.749259	+	0.349385i	−0.0251435	+	0.0117246i
$889$	6.23337	−	2.26876i	0.209061	−	0.0760918i
$890$		0			0
$891$	0.390259	+	2.21327i	0.0130742	+	0.0741473i
$892$	−11.0307	−	11.0307i	−0.369336	−	0.369336i
$893$	16.4083	−	1.87874i	0.549084	−	0.0628698i
$894$		−	7.42095i		−	0.248194i
$895$		0			0
$896$	−1.96415	−	2.34078i	−0.0656175	−	0.0781999i
$897$	−1.11881	+	2.39930i	−0.0373561	+	0.0801104i
$898$	−1.49985	−	3.21645i	−0.0500507	−	0.107334i
$899$	13.4409	−	16.0183i	0.448280	−	0.534239i
$900$		0			0
$901$	3.73642	−	2.15722i	0.124478	−	0.0718675i
$902$	−7.94132	−	11.3414i	−0.264417	−	0.377627i
$903$	8.22431	+	11.7455i	0.273688	+	0.390867i
$904$	−5.31653	+	3.06950i	−0.176825	+	0.102090i
$905$		0			0
$906$	13.5545	−	16.1537i	0.450319	−	0.536669i
$907$	15.0938	+	32.3687i	0.501180	+	1.07479i	0.980387	+	0.197083i	$0.0631468\pi$
$907$	15.0938	+	32.3687i	0.501180	+	1.07479i	−0.479206	+	0.877702i	$0.659075\pi$
$908$	8.70082	−	18.6590i	0.288747	−	0.619219i
$909$	−19.0410	−	22.6922i	−0.631550	−	0.752652i
$910$		0			0
$911$			24.5970i			0.814935i	0.913220	+	0.407468i	$0.133588\pi$
$911$			24.5970i			0.814935i	−0.913220	+	0.407468i	$0.866412\pi$
$912$	−4.13971	+	0.473994i	−0.137080	+	0.0156955i
$913$	11.0238	+	11.0238i	0.364833	+	0.364833i
$914$	−1.84223	−	10.4478i	−0.0609356	−	0.345583i
$915$		0			0
$916$	12.1355	−	4.41696i	0.400968	−	0.145940i
$917$	−51.6112	+	24.0667i	−1.70435	+	0.794752i
$918$	−0.250955	−	2.86843i	−0.00828276	−	0.0946724i
$919$	−0.318967	−	0.184156i	−0.0105218	−	0.00607474i	0.494730	−	0.869047i	$-0.335267\pi$
$919$	−0.318967	−	0.184156i	−0.0105218	−	0.00607474i	−0.505252	+	0.862972i	$0.668600\pi$
$920$		0			0
$921$	0.597884	−	3.39077i	0.0197009	−	0.111730i
$922$	−20.5725	+	14.4050i	−0.677520	+	0.474404i
$923$	5.34757	−	19.9574i	0.176018	−	0.656906i
$924$	2.03751	−	3.52908i	0.0670292	−	0.116098i
$925$		0			0
$926$	−5.07520	+	13.9440i	−0.166782	+	0.458228i
$927$	20.8029	+	9.70055i	0.683257	+	0.318608i
$928$	5.32823	+	0.466160i	0.174908	+	0.0153024i
$929$	−7.74518	+	1.36568i	−0.254111	+	0.0448066i	−0.299252	−	0.954174i	$-0.596737\pi$
$929$	−7.74518	+	1.36568i	−0.254111	+	0.0448066i	0.0451414	+	0.998981i	$0.485626\pi$
$930$		0			0
$931$	−0.272337	−	10.1836i	−0.00892547	−	0.333753i
$932$	7.07157	−	7.07157i	0.231637	−	0.231637i
$933$	−7.80735	−	5.46677i	−0.255601	−	0.178974i
$934$	31.1670	−	26.1522i	1.01982	−	0.855727i
$935$		0			0
$936$	−5.21679	−	1.89876i	−0.170516	−	0.0620628i
$937$	−28.0456	+	2.45367i	−0.916209	+	0.0801579i	−0.535498	−	0.844536i	$-0.679876\pi$
$937$	−28.0456	+	2.45367i	−0.916209	+	0.0801579i	−0.380711	+	0.924694i	$0.624321\pi$
$938$	16.1701	−	4.33278i	0.527974	−	0.141470i
$939$	−14.2387	−	24.6622i	−0.464663	−	0.804821i
$940$		0			0
$941$	−6.98965	−	1.23246i	−0.227856	−	0.0401772i	0.0585543	−	0.998284i	$-0.481351\pi$
$941$	−6.98965	−	1.23246i	−0.227856	−	0.0401772i	−0.286410	+	0.958107i	$0.592462\pi$
$942$	19.1072	+	5.11975i	0.622545	+	0.166810i
$943$	2.67316	+	9.97637i	0.0870501	+	0.324875i
$944$	−10.9496	−	9.18780i	−0.356379	−	0.299037i
$945$		0			0
$946$	−2.34225	−	6.43529i	−0.0761533	−	0.209229i
$947$	1.61054	−	18.4085i	0.0523354	−	0.598196i	−0.924066	−	0.382233i	$-0.875155\pi$
$947$	1.61054	−	18.4085i	0.0523354	−	0.598196i	0.976401	−	0.215963i	$-0.0692892\pi$
$948$	−1.69200	+	2.41643i	−0.0549538	+	0.0784821i
$949$	−35.3877			−1.14873
$950$		0			0
$951$	2.63580			0.0854715
$952$	1.03796	−	1.48236i	0.0336405	−	0.0480436i
$953$	−2.87499	+	32.8612i	−0.0931299	+	1.06448i	0.795530	+	0.605914i	$0.207192\pi$
$953$	−2.87499	+	32.8612i	−0.0931299	+	1.06448i	−0.888660	+	0.458566i	$0.848363\pi$
$954$	−5.19819	−	14.2819i	−0.168298	−	0.462394i
$955$		0			0
$956$	−13.8042	−	11.5831i	−0.446461	−	0.374625i
$957$	1.84612	+	6.88980i	0.0596765	+	0.222716i
$958$	−0.589766	−	0.158027i	−0.0190545	−	0.00510563i
$959$	32.3360	+	5.70171i	1.04418	+	0.184118i
$960$		0			0
$961$	−7.85785	−	13.6102i	−0.253479	−	0.439039i
$962$	−2.22299	+	0.595647i	−0.0716719	+	0.0192044i
$963$	−26.7391	+	2.33936i	−0.861654	+	0.0753850i
$964$	−12.5737	−	4.57647i	−0.404973	−	0.147398i
$965$		0			0
$966$	−2.32869	+	1.95400i	−0.0749243	+	0.0628690i
$967$	−1.57716	−	1.10434i	−0.0507182	−	0.0355132i	0.547942	−	0.836516i	$-0.315411\pi$
$967$	−1.57716	−	1.10434i	−0.0507182	−	0.0355132i	−0.598661	+	0.801003i	$0.704300\pi$
$968$	6.40195	−	6.40195i	0.205766	−	0.205766i
$969$	−0.905672	−	2.29543i	−0.0290944	−	0.0737400i
$970$		0			0
$971$	−26.8676	+	4.73749i	−0.862223	+	0.152033i	−0.587237	−	0.809415i	$-0.699784\pi$
$971$	−26.8676	+	4.73749i	−0.862223	+	0.152033i	−0.274986	+	0.961448i	$0.588673\pi$
$972$	−16.0646	−	1.40547i	−0.515273	−	0.0450806i
$973$	12.2486	+	5.71163i	0.392673	+	0.183106i
$974$	7.30551	−	20.0717i	0.234084	−	0.643139i
$975$		0			0
$976$	−6.15208	+	10.6557i	−0.196923	+	0.341081i
$977$	3.38329	−	12.6266i	0.108241	−	0.403961i	−0.890452	−	0.455078i	$-0.849611\pi$
$977$	3.38329	−	12.6266i	0.108241	−	0.403961i	0.998693	+	0.0511167i	$0.0162781\pi$
$978$	−17.8739	+	12.5154i	−0.571545	+	0.400200i
$979$	4.20201	−	23.8308i	0.134297	−	0.761636i
$980$		0			0
$981$	3.33152	+	1.92346i	0.106367	+	0.0614112i
$982$	2.07693	+	23.7394i	0.0662775	+	0.757555i
$983$	−24.3319	+	11.3461i	−0.776066	+	0.361886i	−0.769957	−	0.638096i	$-0.779722\pi$
$983$	−24.3319	+	11.3461i	−0.776066	+	0.361886i	−0.00610908	+	0.999981i	$0.501945\pi$
$984$	8.91470	−	3.24469i	0.284190	−	0.103437i
$985$		0			0
$986$	0.550038	+	3.11942i	0.0175168	+	0.0993425i
$987$	−7.82581	−	7.82581i	−0.249098	−	0.249098i
$988$	−11.5781	−	0.701683i	−0.368350	−	0.0223235i
$989$			5.10869i			0.162447i
$990$		0			0
$991$	−8.12760	−	9.68610i	−0.258182	−	0.307689i	0.621346	−	0.783536i	$-0.286586\pi$
$991$	−8.12760	−	9.68610i	−0.258182	−	0.307689i	−0.879528	+	0.475847i	$0.842142\pi$
$992$	−1.65223	+	3.54322i	−0.0524584	+	0.112497i
$993$	1.45845	+	3.12765i	0.0462824	+	0.0992530i
$994$	15.2502	−	18.1745i	0.483707	−	0.576460i
$995$		0			0
$996$	−9.25114	+	5.34115i	−0.293134	+	0.169241i
$997$	21.5234	+	30.7386i	0.681653	+	0.973501i	0.999677	+	0.0254184i	$0.00809181\pi$
$997$	21.5234	+	30.7386i	0.681653	+	0.973501i	−0.318024	+	0.948083i	$0.603019\pi$
$998$	−21.7280	−	31.0308i	−0.687788	−	0.982263i
$999$	−3.64151	+	2.10243i	−0.115212	+	0.0665179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.143.4		120
5.2	odd	4	inner	950.2.bb.e.257.2		120
5.3	odd	4		190.2.r.a.67.9	✓	120
5.4	even	2		190.2.r.a.143.7	yes	120
19.2	odd	18	inner	950.2.bb.e.743.2		120
95.2	even	36	inner	950.2.bb.e.857.4		120
95.59	odd	18		190.2.r.a.173.9	yes	120
95.78	even	36		190.2.r.a.97.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.67.9	✓	120	5.3	odd	4
190.2.r.a.97.7	yes	120	95.78	even	36
190.2.r.a.143.7	yes	120	5.4	even	2
190.2.r.a.173.9	yes	120	95.59	odd	18
950.2.bb.e.143.4		120	1.1	even	1	trivial
950.2.bb.e.257.2		120	5.2	odd	4	inner
950.2.bb.e.743.2		120	19.2	odd	18	inner
950.2.bb.e.857.4		120	95.2	even	36	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.0833140 - 0.952283i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(0.732278 + 0.614454i) q^{6} +(0.790865 + 2.95155i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.05452 + 0.362268i) q^{9} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.0833140 - 0.952283i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(0.732278 + 0.614454i) q^{6} +(0.790865 + 2.95155i) q^{7} +(0.965926 + 0.258819i) q^{8} +(2.05452 + 0.362268i) q^{9} +(0.697545 + 1.20818i) q^{11} +(-0.923348 + 0.247410i) q^{12} +(-2.65096 + 0.231929i) q^{13} +(-2.87139 - 1.04510i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.485119 - 0.339684i) q^{17} +(-1.47518 + 1.47518i) q^{18} +(-2.07775 + 3.83183i) q^{19} +(2.87660 - 0.507222i) q^{21} +(-1.38978 - 0.121590i) q^{22} +(0.943203 + 0.439823i) q^{23} +(0.326944 - 0.898272i) q^{24} +(1.33054 - 2.30456i) q^{26} +(1.25838 - 4.69635i) q^{27} +(2.50306 - 1.75266i) q^{28} +(-0.928771 + 5.26732i) q^{29} +(-3.38574 - 1.95476i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(1.20865 - 0.563602i) q^{33} +(0.556506 - 0.202551i) q^{34} +(-0.362268 - 2.05452i) q^{36} +(-0.611533 - 0.611533i) q^{37} +(-1.94710 - 3.89985i) q^{38} +2.54378i q^{39} +(6.37921 + 7.60244i) q^{41} +(-1.23446 + 2.64730i) q^{42} +(2.07457 + 4.44893i) q^{43} +(0.896747 - 1.06870i) q^{44} +(-0.901281 + 0.520355i) q^{46} +(-2.17324 - 3.10371i) q^{47} +(0.548294 + 0.783044i) q^{48} +(-2.02399 + 1.16855i) q^{49} +(-0.363892 + 0.433670i) q^{51} +(1.12462 + 2.41176i) q^{52} +(-3.07886 + 6.60263i) q^{53} +(3.12525 + 3.72452i) q^{54} +3.05567i q^{56} +(3.47588 + 2.29786i) q^{57} +(-3.78202 - 3.78202i) q^{58} +(2.48207 + 14.0765i) q^{59} +(11.5621 - 4.20827i) q^{61} +(3.54322 - 1.65223i) q^{62} +(0.555599 + 6.35052i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.231576 + 1.31334i) q^{66} +(-4.48775 + 3.14235i) q^{67} +(-0.153278 + 0.572041i) q^{68} +(0.497418 - 0.861553i) q^{69} +(-2.65555 + 7.29606i) q^{71} +(1.89075 + 0.881673i) q^{72} +(13.2476 + 1.15902i) q^{73} +(0.851699 - 0.150178i) q^{74} +(4.31138 + 0.641887i) q^{76} +(-3.01435 + 3.01435i) q^{77} +(-2.08375 - 1.45905i) q^{78} +(2.36397 - 1.98361i) q^{79} +(1.51379 + 0.550975i) q^{81} +(-9.88652 + 0.864958i) q^{82} +(10.7941 - 2.89227i) q^{83} +(-1.46049 - 2.52964i) q^{84} +(-4.83428 - 0.852413i) q^{86} +(4.93860 + 1.32329i) q^{87} +(0.361076 + 1.34755i) q^{88} +(-13.2874 - 11.1494i) q^{89} +(-2.78110 - 7.64100i) q^{91} +(0.0907038 - 1.03675i) q^{92} +(-2.14356 + 3.06132i) q^{93} +3.78893 q^{94} -0.955921 q^{96} +(-1.56957 + 2.24158i) q^{97} +(0.203692 - 2.32821i) q^{98} +(0.995436 + 2.73494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

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