LMFDB - Embedded newform 950.2.bb.b.307.2

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:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			307.2
Character	$\chi$	$=$	950.307
Dual form			950.2.bb.b.393.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 + 0.0871557i) q^{2} +(1.70330 + 0.794263i) q^{3} +(0.984808 - 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(0.852228 - 3.18056i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.342020 + 0.407604i) q^{9} +O(q^{10})$	\(q+(-0.996195 + 0.0871557i) q^{2} +(1.70330 + 0.794263i) q^{3} +(0.984808 - 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(0.852228 - 3.18056i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.342020 + 0.407604i) q^{9} +(0.892233 - 1.54539i) q^{11} +(1.81535 + 0.486421i) q^{12} +(0.0370424 + 0.0794377i) q^{13} +(-0.571781 + 3.24273i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-0.407961 - 4.66301i) q^{17} +(-0.376244 - 0.376244i) q^{18} +(2.36507 + 3.66148i) q^{19} +(3.97780 - 4.74056i) q^{21} +(-0.754148 + 1.61728i) q^{22} +(-3.86668 - 2.70748i) q^{23} +(-1.85083 - 0.326352i) q^{24} +(-0.0438249 - 0.0759070i) q^{26} +(-1.20044 - 4.48011i) q^{27} +(0.286983 - 3.28023i) q^{28} +(-1.51413 + 1.27051i) q^{29} +(6.29770 - 3.63598i) q^{31} +(-0.906308 + 0.422618i) q^{32} +(2.74719 - 1.92360i) q^{33} +(0.812817 + 4.60971i) q^{34} +(0.407604 + 0.342020i) q^{36} +(0.443988 - 0.443988i) q^{37} +(-2.67519 - 3.44142i) q^{38} +0.164728i q^{39} +(-1.43910 - 3.95390i) q^{41} +(-3.54950 + 5.06920i) q^{42} +(-3.26551 - 4.66363i) q^{43} +(0.610323 - 1.67685i) q^{44} +(4.08794 + 2.36017i) q^{46} +(-0.152522 - 0.0133439i) q^{47} +(1.87223 + 0.163799i) q^{48} +(-3.32748 - 1.92112i) q^{49} +(3.00878 - 8.26654i) q^{51} +(0.0502739 + 0.0717985i) q^{52} +(2.65105 - 3.78609i) q^{53} +(1.58634 + 4.35844i) q^{54} +3.29276i q^{56} +(1.12026 + 8.11509i) q^{57} +(1.39764 - 1.39764i) q^{58} +(10.0191 + 8.40702i) q^{59} +(2.37516 + 13.4702i) q^{61} +(-5.95684 + 4.17103i) q^{62} +(1.58789 - 0.740444i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-2.56908 + 2.15572i) q^{66} +(-0.536994 + 6.13787i) q^{67} +(-1.21149 - 4.52133i) q^{68} +(-4.43567 - 7.68281i) q^{69} +(-2.75320 - 0.485463i) q^{71} +(-0.435862 - 0.305194i) q^{72} +(-3.26278 + 6.99705i) q^{73} +(-0.403603 + 0.480995i) q^{74} +(2.96495 + 3.19516i) q^{76} +(-4.15483 - 4.15483i) q^{77} +(-0.0143570 - 0.164101i) q^{78} +(12.5159 - 4.55541i) q^{79} +(1.79086 - 10.1565i) q^{81} +(1.77823 + 3.81343i) q^{82} +(4.98805 + 1.33654i) q^{83} +(3.09418 - 5.35927i) q^{84} +(3.65954 + 4.36127i) q^{86} +(-3.58814 + 0.961438i) q^{87} +(-0.461854 + 1.72366i) q^{88} +(-6.11897 - 2.22712i) q^{89} +(0.284225 - 0.0501165i) q^{91} +(-4.27808 - 1.99490i) q^{92} +(13.6148 - 1.19114i) q^{93} +0.153105 q^{94} -1.87939 q^{96} +(8.32443 - 0.728294i) q^{97} +(3.48225 + 1.62380i) q^{98} +(0.935070 - 0.164878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{6}+O(q^{10}) $ 48 * q - 48 * q^6	$ 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) $ 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.996195	+	0.0871557i	−0.704416	+	0.0616284i
$2$	−0.996195	+	0.0871557i	−0.704416	+	0.0616284i
$3$	1.70330	+	0.794263i	0.983402	+	0.458568i	0.846715	−	0.532047i	$-0.178577\pi$
$3$	1.70330	+	0.794263i	0.983402	+	0.458568i	0.136687	+	0.990614i	$0.456355\pi$
$4$	0.984808	−	0.173648i	0.492404	−	0.0868241i
$5$		0			0
$5$		0			0
$6$	−1.76604	−	0.642788i	−0.720985	−	0.262417i
$7$	0.852228	−	3.18056i	0.322112	−	1.20214i	−0.595072	−	0.803673i	$-0.702876\pi$
$7$	0.852228	−	3.18056i	0.322112	−	1.20214i	0.917183	−	0.398465i	$-0.130457\pi$
$8$	−0.965926	+	0.258819i	−0.341506	+	0.0915064i
$9$	0.342020	+	0.407604i	0.114007	+	0.135868i
$10$		0			0
$11$	0.892233	−	1.54539i	0.269018	−	0.465954i	−0.699590	−	0.714544i	$-0.746634\pi$
$11$	0.892233	−	1.54539i	0.269018	−	0.465954i	0.968609	+	0.248591i	$0.0799674\pi$
$12$	1.81535	+	0.486421i	0.524045	+	0.140418i
$13$	0.0370424	+	0.0794377i	0.0102737	+	0.0220321i	0.911378	−	0.411571i	$-0.135020\pi$
$13$	0.0370424	+	0.0794377i	0.0102737	+	0.0220321i	−0.901104	+	0.433603i	$0.857242\pi$
$14$	−0.571781	+	3.24273i	−0.152815	+	0.866656i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−0.407961	−	4.66301i	−0.0989450	−	1.13095i	−0.869621	−	0.493720i	$-0.835637\pi$
$17$	−0.407961	−	4.66301i	−0.0989450	−	1.13095i	0.770676	−	0.637227i	$-0.219919\pi$
$18$	−0.376244	−	0.376244i	−0.0886815	−	0.0886815i
$19$	2.36507	+	3.66148i	0.542585	+	0.840001i
$19$	2.36507	+	3.66148i	0.542585	+	0.840001i
$20$		0			0
$21$	3.97780	−	4.74056i	0.868027	−	1.03447i
$22$	−0.754148	+	1.61728i	−0.160785	+	0.344804i
$23$	−3.86668	−	2.70748i	−0.806258	−	0.564548i	0.0961816	−	0.995364i	$-0.469337\pi$
$23$	−3.86668	−	2.70748i	−0.806258	−	0.564548i	−0.902440	+	0.430816i	$0.858226\pi$
$24$	−1.85083	−	0.326352i	−0.377800	−	0.0666163i
$25$		0			0
$26$	−0.0438249	−	0.0759070i	−0.00859477	−	0.0148866i
$27$	−1.20044	−	4.48011i	−0.231025	−	0.862198i
$28$	0.286983	−	3.28023i	0.0542346	−	0.619904i
$29$	−1.51413	+	1.27051i	−0.281167	+	0.235927i	−0.772454	−	0.635071i	$-0.780971\pi$
$29$	−1.51413	+	1.27051i	−0.281167	+	0.235927i	0.491287	+	0.870998i	$0.336527\pi$
$30$		0			0
$31$	6.29770	−	3.63598i	1.13110	−	0.653042i	0.186890	−	0.982381i	$-0.440159\pi$
$31$	6.29770	−	3.63598i	1.13110	−	0.653042i	0.944212	+	0.329339i	$0.106826\pi$
$32$	−0.906308	+	0.422618i	−0.160214	+	0.0747091i
$33$	2.74719	−	1.92360i	0.478224	−	0.334856i
$34$	0.812817	+	4.60971i	0.139397	+	0.790559i
$35$		0			0
$36$	0.407604	+	0.342020i	0.0679340	+	0.0570034i
$37$	0.443988	−	0.443988i	0.0729912	−	0.0729912i	−0.669669	−	0.742660i	$-0.733564\pi$
$37$	0.443988	−	0.443988i	0.0729912	−	0.0729912i	0.742660	+	0.669669i	$0.233564\pi$
$38$	−2.67519	−	3.44142i	−0.433973	−	0.558272i
$39$			0.164728i			0.0263776i
$40$		0			0
$41$	−1.43910	−	3.95390i	−0.224750	−	0.617495i	0.775148	−	0.631779i	$-0.217675\pi$
$41$	−1.43910	−	3.95390i	−0.224750	−	0.617495i	−0.999898	+	0.0142845i	$0.995453\pi$
$42$	−3.54950	+	5.06920i	−0.547699	+	0.782195i
$43$	−3.26551	−	4.66363i	−0.497985	−	0.711197i	0.488950	−	0.872312i	$-0.337380\pi$
$43$	−3.26551	−	4.66363i	−0.497985	−	0.711197i	−0.986936	+	0.161115i	$0.948491\pi$
$44$	0.610323	−	1.67685i	0.0920097	−	0.252795i
$45$		0			0
$46$	4.08794	+	2.36017i	0.602734	+	0.347988i
$47$	−0.152522	−	0.0133439i	−0.0222476	−	0.00194641i	0.0760265	−	0.997106i	$-0.475777\pi$
$47$	−0.152522	−	0.0133439i	−0.0222476	−	0.00194641i	−0.0982741	+	0.995159i	$0.531332\pi$
$48$	1.87223	+	0.163799i	0.270234	+	0.0236424i
$49$	−3.32748	−	1.92112i	−0.475354	−	0.274446i
$50$		0			0
$51$	3.00878	−	8.26654i	0.421313	−	1.15755i
$52$	0.0502739	+	0.0717985i	0.00697173	+	0.00995666i
$53$	2.65105	−	3.78609i	0.364150	−	0.520059i	−0.594710	−	0.803940i	$-0.702733\pi$
$53$	2.65105	−	3.78609i	0.364150	−	0.520059i	0.958860	+	0.283881i	$0.0916220\pi$
$54$	1.58634	+	4.35844i	0.215874	+	0.593109i
$55$		0			0
$56$			3.29276i			0.440013i
$57$	1.12026	+	8.11509i	0.148381	+	1.07487i
$58$	1.39764	−	1.39764i	0.183519	−	0.183519i
$59$	10.0191	+	8.40702i	1.30437	+	1.09450i	0.989372	+	0.145410i	$0.0464500\pi$
$59$	10.0191	+	8.40702i	1.30437	+	1.09450i	0.315003	+	0.949091i	$0.397994\pi$
$60$		0			0
$61$	2.37516	+	13.4702i	0.304108	+	1.72468i	0.627674	+	0.778476i	$0.284007\pi$
$61$	2.37516	+	13.4702i	0.304108	+	1.72468i	−0.323566	+	0.946206i	$0.604882\pi$
$62$	−5.95684	+	4.17103i	−0.756520	+	0.529721i
$63$	1.58789	−	0.740444i	0.200055	−	0.0932871i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$		0			0
$66$	−2.56908	+	2.15572i	−0.316232	+	0.265350i
$67$	−0.536994	+	6.13787i	−0.0656043	+	0.749861i	0.890145	+	0.455678i	$0.150603\pi$
$67$	−0.536994	+	6.13787i	−0.0656043	+	0.749861i	−0.955749	+	0.294183i	$0.904952\pi$
$68$	−1.21149	−	4.52133i	−0.146914	−	0.548292i
$69$	−4.43567	−	7.68281i	−0.533992	−	0.924902i
$70$		0			0
$71$	−2.75320	−	0.485463i	−0.326744	−	0.0576138i	0.00786993	−	0.999969i	$-0.497495\pi$
$71$	−2.75320	−	0.485463i	−0.326744	−	0.0576138i	−0.334614	+	0.942355i	$0.608606\pi$
$72$	−0.435862	−	0.305194i	−0.0513668	−	0.0359674i
$73$	−3.26278	+	6.99705i	−0.381879	+	0.818943i	0.617594	+	0.786497i	$0.288107\pi$
$73$	−3.26278	+	6.99705i	−0.381879	+	0.818943i	−0.999473	+	0.0324460i	$0.989670\pi$
$74$	−0.403603	+	0.480995i	−0.0469179	+	0.0559145i
$75$		0			0
$76$	2.96495	+	3.19516i	0.340103	+	0.366510i
$77$	−4.15483	−	4.15483i	−0.473486	−	0.473486i
$78$	−0.0143570	−	0.164101i	−0.00162561	−	0.0185808i
$79$	12.5159	−	4.55541i	1.40815	−	0.512523i	0.477561	−	0.878599i	$-0.341521\pi$
$79$	12.5159	−	4.55541i	1.40815	−	0.512523i	0.930585	+	0.366075i	$0.119299\pi$
$80$		0			0
$81$	1.79086	−	10.1565i	0.198984	−	1.12850i
$82$	1.77823	+	3.81343i	0.196373	+	0.421122i
$83$	4.98805	+	1.33654i	0.547509	+	0.146705i	0.521962	−	0.852969i	$-0.325200\pi$
$83$	4.98805	+	1.33654i	0.547509	+	0.146705i	0.0255477	+	0.999674i	$0.491867\pi$
$84$	3.09418	−	5.35927i	0.337603	−	0.584745i
$85$		0			0
$86$	3.65954	+	4.36127i	0.394619	+	0.470288i
$87$	−3.58814	+	0.961438i	−0.384689	+	0.103077i
$88$	−0.461854	+	1.72366i	−0.0492338	+	0.183743i
$89$	−6.11897	−	2.22712i	−0.648610	−	0.236075i	−0.00329858	−	0.999995i	$-0.501050\pi$
$89$	−6.11897	−	2.22712i	−0.648610	−	0.236075i	−0.645311	+	0.763920i	$0.723272\pi$
$90$		0			0
$91$	0.284225	−	0.0501165i	0.0297949	−	0.00525364i
$92$	−4.27808	−	1.99490i	−0.446021	−	0.207983i
$93$	13.6148	−	1.19114i	1.41179	−	0.123516i
$94$	0.153105			0.0157915
$95$		0			0
$96$	−1.87939			−0.191814
$97$	8.32443	−	0.728294i	0.845218	−	0.0739470i	0.343685	−	0.939085i	$-0.388325\pi$
$97$	8.32443	−	0.728294i	0.845218	−	0.0739470i	0.501534	+	0.865138i	$0.332769\pi$
$98$	3.48225	+	1.62380i	0.351761	+	0.164029i
$99$	0.935070	−	0.164878i	0.0939781	−	0.0165709i
$100$		0			0
$101$	−11.0617	−	4.02612i	−1.10068	−	0.400614i	−0.273111	−	0.961982i	$-0.588053\pi$
$101$	−11.0617	−	4.02612i	−1.10068	−	0.400614i	−0.827566	+	0.561369i	$0.810275\pi$
$102$	−2.27685	+	8.49732i	−0.225442	+	0.841360i
$103$	−10.7624	+	2.88377i	−1.06045	+	0.284146i	−0.746563	−	0.665315i	$-0.768297\pi$
$103$	−10.7624	+	2.88377i	−1.06045	+	0.284146i	−0.313885	+	0.949461i	$0.601631\pi$
$104$	−0.0563402	−	0.0671437i	−0.00552461	−	0.00658398i
$105$		0			0
$106$	−2.31098	+	4.00274i	−0.224462	+	0.388780i
$107$	15.2528	+	4.08698i	1.47454	+	0.395103i	0.904487	−	0.426501i	$-0.140254\pi$
$107$	15.2528	+	4.08698i	1.47454	+	0.395103i	0.570058	+	0.821605i	$0.306921\pi$
$108$	−1.96017	−	4.20360i	−0.188617	−	0.404491i
$109$	−0.837775	+	4.75126i	−0.0802443	+	0.455088i	0.918038	+	0.396494i	$0.129773\pi$
$109$	−0.837775	+	4.75126i	−0.0802443	+	0.455088i	−0.998282	+	0.0585947i	$0.981338\pi$
$110$		0			0
$111$	1.10889	−	0.403603i	0.105251	−	0.0383083i
$112$	−0.286983	−	3.28023i	−0.0271173	−	0.309952i
$113$	1.53763	+	1.53763i	0.144648	+	0.144648i	0.775722	−	0.631074i	$-0.217386\pi$
$113$	1.53763	+	1.53763i	0.144648	+	0.144648i	−0.631074	+	0.775722i	$0.717386\pi$
$114$	−1.82327	−	7.98657i	−0.170765	−	0.748011i
$115$		0			0
$116$	−1.27051	+	1.51413i	−0.117964	+	0.140584i
$117$	−0.0197099	+	0.0422679i	−0.00182218	+	0.00390767i
$118$	−10.7137	−	7.50180i	−0.986275	−	0.690597i
$119$	−15.1787	−	2.67641i	−1.39143	−	0.245346i
$120$		0			0
$121$	3.90784	+	6.76858i	0.355258	+	0.615325i
$122$	−3.54013	−	13.2119i	−0.320508	−	1.19615i
$123$	0.689210	−	7.87770i	0.0621439	−	0.710309i
$124$	5.57065	−	4.67433i	0.500259	−	0.419767i
$125$		0			0
$126$	−1.51731	+	0.876019i	−0.135173	+	0.0780420i
$127$	12.8553	−	5.99452i	1.14072	−	0.531927i	0.241926	−	0.970295i	$-0.422221\pi$
$127$	12.8553	−	5.99452i	1.14072	−	0.531927i	0.898796	+	0.438367i	$0.144443\pi$
$128$	−0.819152	+	0.573576i	−0.0724035	+	0.0506975i
$129$	−1.85800	−	10.5372i	−0.163588	−	0.927752i
$130$		0			0
$131$	−1.39611	−	1.17148i	−0.121979	−	0.102353i	0.579758	−	0.814789i	$-0.303147\pi$
$131$	−1.39611	−	1.17148i	−0.121979	−	0.102353i	−0.701737	+	0.712436i	$0.747592\pi$
$132$	2.37142	−	2.37142i	0.206406	−	0.206406i
$133$	13.6611	−	4.40183i	1.18457	−	0.381687i
$134$		−	6.16132i		−	0.532257i
$135$		0			0
$136$	1.60094	+	4.39854i	0.137279	+	0.377171i
$137$	−0.130902	+	0.186947i	−0.0111837	+	0.0159719i	−0.824705	−	0.565563i	$-0.808659\pi$
$137$	−0.130902	+	0.186947i	−0.0111837	+	0.0159719i	0.813521	+	0.581535i	$0.197548\pi$
$138$	5.08839	+	7.26698i	0.433153	+	0.618606i
$139$	−7.75531	+	21.3075i	−0.657797	+	1.80728i	−0.0711095	+	0.997469i	$0.522654\pi$
$139$	−7.75531	+	21.3075i	−0.657797	+	1.80728i	−0.586687	+	0.809814i	$0.699568\pi$
$140$		0			0
$141$	−0.249192	−	0.143871i	−0.0209858	−	0.0121161i
$142$	2.78503	+	0.243659i	0.233715	+	0.0204474i
$143$	0.155813	+	0.0136319i	0.0130297	+	0.00113995i
$144$	0.460802	+	0.266044i	0.0384002	+	0.0221704i
$145$		0			0
$146$	2.64053	−	7.25480i	0.218532	−	0.600411i
$147$	−4.14182	−	5.91514i	−0.341612	−	0.487872i
$148$	0.360145	−	0.514341i	0.0296038	−	0.0422786i
$149$	−0.939750	−	2.58194i	−0.0769873	−	0.211521i	0.895228	−	0.445607i	$-0.147012\pi$
$149$	−0.939750	−	2.58194i	−0.0769873	−	0.211521i	−0.972216	+	0.234087i	$0.924790\pi$
$150$		0			0
$151$		−	16.7726i		−	1.36494i	−0.730916	−	0.682468i	$-0.760907\pi$
$151$		−	16.7726i		−	1.36494i	0.730916	−	0.682468i	$-0.239093\pi$
$152$	−3.23215	−	2.92459i	−0.262162	−	0.237216i
$153$	1.76113	−	1.76113i	0.142379	−	0.142379i
$154$	4.50113	+	3.77690i	0.362712	+	0.304351i
$155$		0			0
$156$	0.0286047	+	0.162225i	0.00229021	+	0.0129884i
$157$	19.4425	−	13.6138i	1.55168	−	1.08650i	0.591800	−	0.806085i	$-0.298417\pi$
$157$	19.4425	−	13.6138i	1.55168	−	1.08650i	0.959879	−	0.280413i	$-0.0904715\pi$
$158$	−12.0712	+	5.62890i	−0.960335	+	0.447812i
$159$	7.52269	−	4.34322i	0.596588	−	0.344440i
$160$		0			0
$161$	−11.9066	+	9.99081i	−0.938370	+	0.787386i
$162$	−0.898850	+	10.2739i	−0.0706203	+	0.807194i
$163$	2.44692	+	9.13205i	0.191658	+	0.715277i	0.993107	+	0.117214i	$0.0373962\pi$
$163$	2.44692	+	9.13205i	0.191658	+	0.715277i	−0.801449	+	0.598063i	$0.795937\pi$
$164$	−2.10382	−	3.64393i	−0.164281	−	0.284543i
$165$		0			0
$166$	−5.08555	−	0.896721i	−0.394716	−	0.0695990i
$167$	−19.6489	−	13.7583i	−1.52047	−	1.06465i	−0.973829	−	0.227284i	$-0.927015\pi$
$167$	−19.6489	−	13.7583i	−1.52047	−	1.06465i	−0.546646	−	0.837364i	$-0.684096\pi$
$168$	−2.61531	+	5.60856i	−0.201776	+	0.432709i
$169$	8.35130	−	9.95269i	0.642408	−	0.765592i
$170$		0			0
$171$	−0.683530	+	2.21631i	−0.0522709	+	0.169486i
$172$	−4.02573	−	4.02573i	−0.306959	−	0.306959i
$173$	1.12005	+	12.8023i	0.0851561	+	0.973339i	0.911806	+	0.410622i	$0.134688\pi$
$173$	1.12005	+	12.8023i	0.0851561	+	0.973339i	−0.826650	+	0.562717i	$0.809756\pi$
$174$	3.49069	−	1.27051i	0.264628	−	0.0963168i
$175$		0			0
$176$	0.309869	−	1.75736i	0.0233573	−	0.132466i
$177$	10.3882	+	22.2775i	0.780822	+	1.67448i
$178$	6.28979	+	1.68534i	0.471440	+	0.126322i
$179$	−4.62396	+	8.00894i	−0.345611	+	0.598616i	−0.985465	−	0.169881i	$-0.945662\pi$
$179$	−4.62396	+	8.00894i	−0.345611	+	0.598616i	0.639853	+	0.768497i	$0.278995\pi$
$180$		0			0
$181$	−5.60398	−	6.67856i	−0.416540	−	0.496413i	0.516449	−	0.856318i	$-0.327254\pi$
$181$	−5.60398	−	6.67856i	−0.416540	−	0.496413i	−0.932989	+	0.359905i	$0.882809\pi$
$182$	−0.278775	+	0.0746976i	−0.0206642	+	0.00553696i
$183$	−6.65326	+	24.8303i	−0.491823	+	1.83551i
$184$	4.43567	+	1.61445i	0.327002	+	0.119019i
$185$		0			0
$186$	−13.4592	+	2.37322i	−0.986876	+	0.174013i
$187$	−7.57018	−	3.53003i	−0.553587	−	0.258142i
$188$	−0.152522	+	0.0133439i	−0.0111238	+	0.000973207i
$189$	−15.2723			−1.11090
$190$		0			0
$191$	−11.8345			−0.856316			−0.428158	−	0.903704i	$-0.640837\pi$
$191$	−11.8345			−0.856316			−0.428158	+	0.903704i	$0.640837\pi$
$192$	1.87223	−	0.163799i	0.135117	−	0.0118212i
$193$	7.91284	+	3.68982i	0.569579	+	0.265599i	0.686001	−	0.727601i	$-0.259365\pi$
$193$	7.91284	+	3.68982i	0.569579	+	0.265599i	−0.116422	+	0.993200i	$0.537143\pi$
$194$	−8.22928	+	1.45104i	−0.590828	+	0.104179i
$195$		0			0
$196$	−3.61053	−	1.31412i	−0.257895	−	0.0938660i
$197$	−4.44858	+	16.6023i	−0.316948	+	1.18287i	0.605213	+	0.796063i	$0.293088\pi$
$197$	−4.44858	+	16.6023i	−0.316948	+	1.18287i	−0.922162	+	0.386804i	$0.873579\pi$
$198$	−0.917142	+	0.245747i	−0.0651784	+	0.0174645i
$199$	2.43291	+	2.89943i	0.172465	+	0.205535i	0.845352	−	0.534210i	$-0.179391\pi$
$199$	2.43291	+	2.89943i	0.172465	+	0.205535i	−0.672888	+	0.739745i	$0.734946\pi$
$200$		0			0
$201$	−5.78975	+	10.0281i	−0.408377	+	0.707330i
$202$	11.3705	+	3.04671i	0.800024	+	0.214366i
$203$	2.75054	+	5.89854i	0.193050	+	0.413996i
$204$	1.52760	−	8.66342i	0.106953	−	0.606561i
$205$		0			0
$206$	10.4701	−	3.81080i	0.729485	−	0.265511i
$207$	−0.218904	−	2.50209i	−0.0152149	−	0.173907i
$208$	0.0619778	+	0.0619778i	0.00429739	+	0.00429739i
$209$	7.76862	−	0.388073i	0.537367	−	0.0268436i
$210$		0			0
$211$	−4.58000	+	5.45824i	−0.315301	+	0.375761i	−0.900298	−	0.435275i	$-0.856651\pi$
$211$	−4.58000	+	5.45824i	−0.315301	+	0.375761i	0.584997	+	0.811035i	$0.301096\pi$
$212$	1.95333	−	4.18892i	0.134155	−	0.287696i
$213$	−4.30394	−	3.01365i	−0.294901	−	0.206492i
$214$	−15.5510	−	2.74206i	−1.06304	−	0.187443i
$215$		0			0
$216$	2.31908	+	4.01676i	0.157793	+	0.273306i
$217$	−6.19737	−	23.1289i	−0.420705	−	1.57009i
$218$	0.420488	−	4.80620i	0.0284790	−	0.325517i
$219$	−11.1150	+	9.32659i	−0.751082	+	0.630232i
$220$		0			0
$221$	0.355307	−	0.205137i	0.0239005	−	0.0137990i
$222$	−1.06949	+	0.498713i	−0.0717797	+	0.0334714i
$223$	−17.4965	+	12.2512i	−1.17165	+	0.820399i	−0.986732	−	0.162355i	$-0.948091\pi$
$223$	−17.4965	+	12.2512i	−1.17165	+	0.820399i	−0.184918	+	0.982754i	$0.559202\pi$
$224$	0.571781	+	3.24273i	0.0382037	+	0.216664i
$225$		0			0
$226$	−1.66579	−	1.39777i	−0.110807	−	0.0929780i
$227$	−15.2554	+	15.2554i	−1.01254	+	1.01254i	−0.0126188	+	0.999920i	$0.504017\pi$
$227$	−15.2554	+	15.2554i	−1.01254	+	1.01254i	−0.999920	+	0.0126188i	$0.995983\pi$
$228$	2.51241	+	7.79728i	0.166388	+	0.516387i
$229$		−	11.0502i		−	0.730219i	−0.930965	−	0.365109i	$-0.881032\pi$
$229$		−	11.0502i		−	0.730219i	0.930965	−	0.365109i	$-0.118968\pi$
$230$		0			0
$231$	−3.77690	−	10.3769i	−0.248502	−	0.682753i
$232$	1.13371	−	1.61910i	0.0744315	−	0.106299i
$233$	−0.447144	−	0.638588i	−0.0292934	−	0.0418353i	0.804238	−	0.594307i	$-0.202574\pi$
$233$	−0.447144	−	0.638588i	−0.0292934	−	0.0418353i	−0.833532	+	0.552472i	$0.813685\pi$
$234$	0.0159510	−	0.0438249i	0.00104275	−	0.00286492i
$235$		0			0
$236$	11.3267	+	6.53950i	0.737308	+	0.425685i
$237$	24.9365	+	2.18166i	1.61980	+	0.141714i
$238$	15.3542	+	1.34332i	0.995262	+	0.0870742i
$239$	−20.7057	−	11.9544i	−1.33934	−	0.773268i	−0.352630	−	0.935763i	$-0.614713\pi$
$239$	−20.7057	−	11.9544i	−1.33934	−	0.773268i	−0.986709	+	0.162495i	$0.948046\pi$
$240$		0			0
$241$	−8.63802	+	23.7328i	−0.556424	+	1.52876i	0.268363	+	0.963318i	$0.413517\pi$
$241$	−8.63802	+	23.7328i	−0.556424	+	1.52876i	−0.824787	+	0.565443i	$0.808705\pi$
$242$	−4.48289	−	6.40223i	−0.288171	−	0.411551i
$243$	3.13626	−	4.47905i	0.201191	−	0.287331i
$244$	4.67815	+	12.8531i	0.299488	+	0.822836i
$245$		0			0
$246$			7.90779i			0.504183i
$247$	−0.203252	+	0.323506i	−0.0129326	+	0.0205842i
$248$	−5.14205	+	5.14205i	−0.326521	+	0.326521i
$249$	7.43458	+	6.23836i	0.471148	+	0.395340i
$250$		0			0
$251$	2.24897	+	12.7545i	0.141954	+	0.805059i	0.969763	+	0.244049i	$0.0784759\pi$
$251$	2.24897	+	12.7545i	0.141954	+	0.805059i	−0.827809	+	0.561010i	$0.810413\pi$
$252$	1.43519	−	1.00493i	0.0904082	−	0.0633045i
$253$	−7.63410	+	3.55984i	−0.479952	+	0.223805i
$254$	−12.2839	+	7.09212i	−0.770761	+	0.444999i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−2.06554	+	23.6092i	−0.128845	+	1.47270i	0.606539	+	0.795053i	$0.292557\pi$
$257$	−2.06554	+	23.6092i	−0.128845	+	1.47270i	−0.735384	+	0.677650i	$0.762998\pi$
$258$	2.76931	+	10.3352i	0.172410	+	0.643442i
$259$	−1.03375	−	1.79051i	−0.0642342	−	0.111257i
$260$		0			0
$261$	−1.03573	−	0.182627i	−0.0641099	−	0.0113043i
$262$	1.49290	+	1.04534i	0.0922318	+	0.0645814i
$263$	−10.8143	+	23.1913i	−0.666838	+	1.43004i	0.223484	+	0.974708i	$0.428257\pi$
$263$	−10.8143	+	23.1913i	−0.666838	+	1.43004i	−0.890322	+	0.455331i	$0.849521\pi$
$264$	−2.15572	+	2.56908i	−0.132675	+	0.158116i
$265$		0			0
$266$	−13.2255	+	5.57573i	−0.810907	+	0.341870i
$267$	−8.65353	−	8.65353i	−0.529587	−	0.529587i
$268$	0.536994	+	6.13787i	0.0328022	+	0.374930i
$269$	25.0224	−	9.10741i	1.52564	−	0.555289i	0.563094	−	0.826393i	$-0.309611\pi$
$269$	25.0224	−	9.10741i	1.52564	−	0.555289i	0.962550	+	0.271104i	$0.0873888\pi$
$270$		0			0
$271$	1.14223	−	6.47790i	0.0693854	−	0.393504i	−0.930261	−	0.366900i	$-0.880419\pi$
$271$	1.14223	−	6.47790i	0.0693854	−	0.393504i	0.999646	−	0.0266049i	$-0.00846960\pi$
$272$	−1.97820	−	4.24227i	−0.119946	−	0.257225i
$273$	0.523926	+	0.140386i	0.0317095	+	0.00849652i
$274$	0.114110	−	0.197644i	0.00689364	−	0.0119401i
$275$		0			0
$276$	−5.70239	−	6.79584i	−0.343244	−	0.409062i
$277$	12.5075	−	3.35138i	0.751504	−	0.201365i	0.137319	−	0.990527i	$-0.456152\pi$
$277$	12.5075	−	3.35138i	0.751504	−	0.201365i	0.614185	+	0.789162i	$0.289485\pi$
$278$	5.86872	−	21.9024i	0.351983	−	1.31362i
$279$	3.63598	+	1.32339i	0.217681	+	0.0792292i
$280$		0			0
$281$	−1.45685	+	0.256882i	−0.0869085	+	0.0153243i	−0.216933	−	0.976186i	$-0.569605\pi$
$281$	−1.45685	+	0.256882i	−0.0869085	+	0.0153243i	0.130025	+	0.991511i	$0.458494\pi$
$282$	0.260783	+	0.121605i	0.0155294	+	0.00724149i
$283$	−28.8571	+	2.52467i	−1.71538	+	0.150076i	−0.902021	−	0.431691i	$-0.857917\pi$
$283$	−28.8571	+	2.52467i	−1.71538	+	0.150076i	−0.813355	+	0.581767i	$0.802361\pi$
$284$	−2.79567			−0.165892
$285$		0			0
$286$	−0.156408			−0.00924861
$287$	−13.8020	+	1.20752i	−0.814709	+	0.0712778i
$288$	−0.482236	−	0.224870i	−0.0284160	−	0.0132506i
$289$	−4.83552	+	0.852633i	−0.284442	+	0.0501549i
$290$		0			0
$291$	14.7575	+	5.37128i	0.865099	+	0.314870i
$292$	−1.99818	+	7.45733i	−0.116935	+	0.436407i
$293$	−17.3024	+	4.63618i	−1.01082	+	0.270848i	−0.725972	−	0.687724i	$-0.758610\pi$
$293$	−17.3024	+	4.63618i	−1.01082	+	0.270848i	−0.284848	+	0.958573i	$0.591943\pi$
$294$	4.64160	+	5.53165i	0.270704	+	0.322612i
$295$		0			0
$296$	−0.313947	+	0.543773i	−0.0182478	+	0.0316061i
$297$	−7.99461	−	2.14215i	−0.463895	−	0.124300i
$298$	1.16120	+	2.49021i	0.0672668	+	0.144254i
$299$	0.0718447	−	0.407452i	0.00415489	−	0.0235635i
$300$		0			0
$301$	−17.6159	+	6.41166i	−1.01536	+	0.369562i
$302$	1.46183	+	16.7088i	0.0841188	+	0.961482i
$303$	−15.6436	−	15.6436i	−0.898699	−	0.898699i
$304$	3.47474	+	2.63176i	0.199290	+	0.150942i
$305$		0			0
$306$	−1.60094	+	1.90792i	−0.0915194	+	0.109069i
$307$	3.84122	−	8.23752i	0.219230	−	0.470140i	−0.765677	−	0.643225i	$-0.777596\pi$
$307$	3.84122	−	8.23752i	0.219230	−	0.470140i	0.984907	+	0.173085i	$0.0553736\pi$
$308$	−4.81318	−	3.37023i	−0.274257	−	0.192037i
$309$	−20.6220	−	3.63622i	−1.17315	−	0.206857i
$310$		0			0
$311$	12.0787	+	20.9209i	0.684920	+	1.18632i	0.973462	+	0.228848i	$0.0734960\pi$
$311$	12.0787	+	20.9209i	0.684920	+	1.18632i	−0.288543	+	0.957467i	$0.593171\pi$
$312$	−0.0426347	−	0.159115i	−0.00241371	−	0.00900810i
$313$	2.56256	−	29.2902i	0.144844	−	1.65558i	−0.481807	−	0.876277i	$-0.660019\pi$
$313$	2.56256	−	29.2902i	0.144844	−	1.65558i	0.626651	−	0.779300i	$-0.284425\pi$
$314$	−18.1820	+	15.2565i	−1.02607	+	0.860974i
$315$		0			0
$316$	11.5347	−	6.65956i	0.648877	−	0.374630i
$317$	2.92095	−	1.36206i	0.164057	−	0.0765010i	−0.338855	−	0.940839i	$-0.610040\pi$
$317$	2.92095	−	1.36206i	0.164057	−	0.0765010i	0.502912	+	0.864338i	$0.332262\pi$
$318$	−7.11552	+	4.98234i	−0.399019	+	0.279396i
$319$	0.612475	+	3.47352i	0.0342920	+	0.194480i
$320$		0			0
$321$	22.7340	+	19.0761i	1.26889	+	1.06472i
$322$	10.9905	−	10.9905i	0.612478	−	0.612478i
$323$	16.1087	−	12.5221i	0.896310	−	0.696748i
$324$		−	10.3131i		−	0.572953i
$325$		0			0
$326$	−3.23352	−	8.88403i	−0.179088	−	0.492041i
$327$	−5.20073	+	7.42742i	−0.287601	+	0.410737i
$328$	2.41341	+	3.44670i	0.133258	+	0.190312i
$329$	−0.172425	+	0.473733i	−0.00950608	+	0.0261177i
$330$		0			0
$331$	13.8617	+	8.00303i	0.761906	+	0.439886i	0.829979	−	0.557794i	$-0.188352\pi$
$331$	13.8617	+	8.00303i	0.761906	+	0.439886i	−0.0680740	+	0.997680i	$0.521685\pi$
$332$	5.14436	+	0.450073i	0.282333	+	0.0247010i
$333$	0.332824	+	0.0291184i	0.0182387	+	0.00159568i
$334$	20.7732	+	11.9934i	1.13666	+	0.656250i
$335$		0			0
$336$	2.11654	−	5.81515i	0.115467	−	0.317243i
$337$	−6.74583	−	9.63404i	−0.367469	−	0.524800i	0.592253	−	0.805752i	$-0.298239\pi$
$337$	−6.74583	−	9.63404i	−0.367469	−	0.524800i	−0.959722	+	0.280952i	$0.909350\pi$
$338$	−7.45209	+	10.6427i	−0.405340	+	0.578886i
$339$	1.39777	+	3.84033i	0.0759163	+	0.208578i
$340$		0			0
$341$		−	12.9766i		−	0.702721i
$342$	0.487765	−	2.26745i	0.0263753	−	0.122610i
$343$	7.35231	−	7.35231i	0.396987	−	0.396987i
$344$	4.36127	+	3.65954i	0.235144	+	0.197309i
$345$		0			0
$346$	−2.23158	−	12.6559i	−0.119971	−	0.680387i
$347$	−26.1928	+	18.3404i	−1.40610	+	0.984562i	−0.408688	+	0.912674i	$0.634014\pi$
$347$	−26.1928	+	18.3404i	−1.40610	+	0.984562i	−0.997413	+	0.0718885i	$0.977097\pi$
$348$	−3.36667	+	1.56991i	−0.180473	+	0.0841558i
$349$	7.53234	−	4.34880i	0.403197	−	0.232786i	−0.284666	−	0.958627i	$-0.591883\pi$
$349$	7.53234	−	4.34880i	0.403197	−	0.232786i	0.687862	+	0.725841i	$0.258549\pi$
$350$		0			0
$351$	0.311423	−	0.261315i	0.0166225	−	0.0139479i
$352$	−0.155527	+	1.77768i	−0.00828959	+	0.0947505i
$353$	−9.03078	−	33.7033i	−0.480660	−	1.79385i	−0.598857	−	0.800856i	$-0.704378\pi$
$353$	−9.03078	−	33.7033i	−0.480660	−	1.79385i	0.118197	−	0.992990i	$-0.462289\pi$
$354$	−12.2902	−	21.2873i	−0.653219	−	1.13141i
$355$		0			0
$356$	−6.41275	−	1.13074i	−0.339875	−	0.0599291i
$357$	−23.7281	−	16.6146i	−1.25582	−	0.879336i
$358$	3.90834	−	8.38147i	0.206562	−	0.442974i
$359$	19.2695	−	22.9644i	1.01700	−	1.21202i	0.0399103	−	0.999203i	$-0.487293\pi$
$359$	19.2695	−	22.9644i	1.01700	−	1.21202i	0.977093	−	0.212814i	$-0.0682628\pi$
$360$		0			0
$361$	−7.81286	+	17.3193i	−0.411203	+	0.911544i
$362$	6.16473	+	6.16473i	0.324011	+	0.324011i
$363$	1.28020	+	14.6328i	0.0671932	+	0.768022i
$364$	0.271204	−	0.0987102i	0.0142150	−	0.00517382i
$365$		0			0
$366$	4.46384	−	25.3157i	0.233329	−	1.32327i
$367$	3.91276	+	8.39093i	0.204244	+	0.438003i	0.981572	−	0.191093i	$-0.0612031\pi$
$367$	3.91276	+	8.39093i	0.204244	+	0.438003i	−0.777328	+	0.629096i	$0.783425\pi$
$368$	−4.55950	−	1.22171i	−0.237680	−	0.0636863i
$369$	1.11942	−	1.93890i	0.0582748	−	0.100935i
$370$		0			0
$371$	−9.78258	−	11.6584i	−0.507886	−	0.605275i
$372$	13.2011	−	3.53723i	0.684447	−	0.183397i
$373$	−0.489152	+	1.82554i	−0.0253273	+	0.0945230i	−0.977433	−	0.211248i	$-0.932247\pi$
$373$	−0.489152	+	1.82554i	−0.0253273	+	0.0945230i	0.952105	+	0.305771i	$0.0989140\pi$
$374$	7.84904	+	2.85682i	0.405864	+	0.147722i
$375$		0			0
$376$	0.150779	−	0.0265863i	0.00777581	−	0.00137109i
$377$	−0.157013	−	0.0732165i	−0.00808659	−	0.00377084i
$378$	15.2142	−	1.33107i	0.782534	−	0.0684628i
$379$	23.8751			1.22638			0.613192	−	0.789934i	$-0.289885\pi$
$379$	23.8751			1.22638			0.613192	+	0.789934i	$0.289885\pi$
$380$		0			0
$381$	26.6576			1.36571
$382$	11.7895	−	1.03145i	0.603203	−	0.0527734i
$383$	25.5111	+	11.8960i	1.30356	+	0.607859i	0.945434	−	0.325814i	$-0.105638\pi$
$383$	25.5111	+	11.8960i	1.30356	+	0.607859i	0.358125	+	0.933674i	$0.383416\pi$
$384$	−1.85083	+	0.326352i	−0.0944499	+	0.0166541i
$385$		0			0
$386$	−8.20432	−	2.98613i	−0.417589	−	0.151990i
$387$	0.784043	−	2.92609i	0.0398551	−	0.148741i
$388$	8.07150	−	2.16275i	0.409768	−	0.109797i
$389$	−0.142159	−	0.169419i	−0.00720777	−	0.00858988i	0.762429	−	0.647072i	$-0.224007\pi$
$389$	−0.142159	−	0.169419i	−0.00720777	−	0.00858988i	−0.769636	+	0.638483i	$0.779562\pi$
$390$		0			0
$391$	−11.0476	+	19.1349i	−0.558699	+	0.967694i
$392$	3.71132	+	0.994445i	0.187450	+	0.0502271i
$393$	−1.44754	−	3.10426i	−0.0730188	−	0.156589i
$394$	2.98467	−	16.9269i	0.150365	−	0.852764i
$395$		0			0
$396$	0.892233	−	0.324746i	0.0448364	−	0.0163191i
$397$	0.486094	+	5.55608i	0.0243963	+	0.278851i	0.998588	+	0.0531278i	$0.0169191\pi$
$397$	0.486094	+	5.55608i	0.0243963	+	0.278851i	−0.974191	+	0.225724i	$0.927525\pi$
$398$	−2.67636	−	2.67636i	−0.134154	−	0.134154i
$399$	26.7652	+	3.35287i	1.33994	+	0.167853i
$400$		0			0
$401$	21.0921	−	25.1365i	1.05329	−	1.25526i	0.0874333	−	0.996170i	$-0.472134\pi$
$401$	21.0921	−	25.1365i	1.05329	−	1.25526i	0.965854	−	0.259088i	$-0.0834220\pi$
$402$	4.89371	−	10.4946i	0.244076	−	0.523422i
$403$	0.522116	+	0.365590i	0.0260085	+	0.0182113i
$404$	−11.5927	−	2.04411i	−0.576760	−	0.101698i
$405$		0			0
$406$	−3.25416	−	5.63637i	−0.161501	−	0.279728i
$407$	−0.289996	−	1.08228i	−0.0143745	−	0.0536465i
$408$	−0.766715	+	8.76360i	−0.0379581	+	0.433863i
$409$	2.16162	−	1.81381i	0.106885	−	0.0896872i	−0.587779	−	0.809022i	$-0.699998\pi$
$409$	2.16162	−	1.81381i	0.106885	−	0.0896872i	0.694664	+	0.719334i	$0.255553\pi$
$410$		0			0
$411$	−0.371450	+	0.214457i	−0.0183223	+	0.0105784i
$412$	−10.0981	+	4.70882i	−0.497498	+	0.231987i
$413$	35.2775	−	24.7016i	1.73589	−	1.21549i
$414$	0.436142	+	2.47349i	0.0214352	+	0.121565i
$415$		0			0
$416$	−0.0671437	−	0.0563402i	−0.00329199	−	0.00276231i
$417$	−30.1334	+	30.1334i	−1.47564	+	1.47564i
$418$	−7.70524	+	1.06368i	−0.376875	+	0.0520261i
$419$			34.6418i			1.69236i	0.532897	+	0.846180i	$0.321103\pi$
$419$			34.6418i			1.69236i	−0.532897	+	0.846180i	$0.678897\pi$
$420$		0			0
$421$	−6.22989	−	17.1165i	−0.303626	−	0.834206i	−0.993863	−	0.110622i	$-0.964716\pi$
$421$	−6.22989	−	17.1165i	−0.303626	−	0.834206i	0.690236	−	0.723584i	$-0.257507\pi$
$422$	4.08686	−	5.83664i	0.198945	−	0.284123i
$423$	−0.0467265	−	0.0667324i	−0.00227192	−	0.00324464i
$424$	−1.58080	+	4.34322i	−0.0767706	+	0.210926i
$425$		0			0
$426$	4.55022	+	2.62707i	0.220459	+	0.127282i
$427$	44.8669	+	3.92535i	2.17126	+	0.189961i
$428$	15.7308	+	1.37627i	0.760376	+	0.0665243i
$429$	0.254569	+	0.146976i	0.0122907	+	0.00709605i
$430$		0			0
$431$	−3.63707	+	9.99276i	−0.175191	+	0.481334i	−0.995947	−	0.0899455i	$-0.971331\pi$
$431$	−3.63707	+	9.99276i	−0.175191	+	0.481334i	0.820755	+	0.571280i	$0.193553\pi$
$432$	−2.66034	−	3.79935i	−0.127996	−	0.182797i
$433$	−1.36577	+	1.95053i	−0.0656349	+	0.0937364i	−0.850628	−	0.525769i	$-0.823778\pi$
$433$	−1.36577	+	1.95053i	−0.0656349	+	0.0937364i	0.784993	+	0.619505i	$0.212667\pi$
$434$	8.18960	+	22.5007i	0.393114	+	1.08007i
$435$		0			0
$436$			4.82456i			0.231054i
$437$	0.768398	−	20.5612i	0.0367575	−	0.983573i
$438$	10.2598	−	10.2598i	0.490234	−	0.490234i
$439$	14.1862	+	11.9037i	0.677071	+	0.568130i	0.915149	−	0.403116i	$-0.132073\pi$
$439$	14.1862	+	11.9037i	0.677071	+	0.568130i	−0.238078	+	0.971246i	$0.576517\pi$
$440$		0			0
$441$	−0.355009	−	2.01335i	−0.0169052	−	0.0958740i
$442$	−0.336076	+	0.235323i	−0.0159855	+	0.0111932i
$443$	23.0029	−	10.7264i	1.09290	−	0.509628i	0.209292	−	0.977853i	$-0.432884\pi$
$443$	23.0029	−	10.7264i	1.09290	−	0.509628i	0.883609	+	0.468225i	$0.155106\pi$
$444$	1.02196	−	0.590028i	0.0485000	−	0.0280015i
$445$		0			0
$446$	16.3621	−	13.7295i	0.774770	−	0.650109i
$447$	0.450062	−	5.14423i	0.0212872	−	0.243314i
$448$	−0.852228	−	3.18056i	−0.0402640	−	0.150267i
$449$	−18.5442	−	32.1194i	−0.875153	−	1.51581i	−0.856600	−	0.515982i	$-0.827427\pi$
$449$	−18.5442	−	32.1194i	−0.875153	−	1.51581i	−0.0185532	−	0.999828i	$-0.505906\pi$
$450$		0			0
$451$	−7.39434	−	1.30382i	−0.348186	−	0.0613946i
$452$	1.78128	+	1.24726i	0.0837843	+	0.0586664i
$453$	13.3219	−	28.5688i	0.625915	−	1.34228i
$454$	13.8678	−	16.5270i	0.650848	−	0.775650i
$455$		0			0
$456$	−3.18242	−	7.54863i	−0.149031	−	0.353497i
$457$	13.9770	+	13.9770i	0.653815	+	0.653815i	0.953909	−	0.300095i	$-0.0970183\pi$
$457$	13.9770	+	13.9770i	0.653815	+	0.653815i	−0.300095	+	0.953909i	$0.597018\pi$
$458$	0.963090	+	11.0082i	0.0450022	+	0.514378i
$459$	−20.4011	+	7.42539i	−0.952242	+	0.346588i
$460$		0			0
$461$	4.60073	−	26.0920i	0.214277	−	1.21523i	−0.667879	−	0.744270i	$-0.732797\pi$
$461$	4.60073	−	26.0920i	0.214277	−	1.21523i	0.882156	−	0.470957i	$-0.156091\pi$
$462$	4.66694	+	10.0083i	0.217126	+	0.465627i
$463$	0.348598	+	0.0934066i	0.0162007	+	0.00434097i	0.266910	−	0.963721i	$-0.413997\pi$
$463$	0.348598	+	0.0934066i	0.0162007	+	0.00434097i	−0.250710	+	0.968062i	$0.580664\pi$
$464$	−0.988279	+	1.71175i	−0.0458797	+	0.0794659i
$465$		0			0
$466$	0.501099	+	0.597187i	0.0232130	+	0.0276641i
$467$	9.20282	−	2.46589i	0.425856	−	0.114108i	−0.0395244	−	0.999219i	$-0.512584\pi$
$467$	9.20282	−	2.46589i	0.425856	−	0.114108i	0.465380	+	0.885111i	$0.345918\pi$
$468$	−0.0120707	+	0.0450484i	−0.000557967	+	0.00208236i
$469$	19.0642	+	6.93881i	0.880304	+	0.320404i
$470$		0			0
$471$	43.9293	−	7.74593i	2.02416	−	0.356914i
$472$	−11.8536	−	5.52742i	−0.545606	−	0.254420i
$473$	−10.1207	+	0.885450i	−0.465352	+	0.0407130i
$474$	−25.0318			−1.14975
$475$		0			0
$476$	−15.4128			−0.706445
$477$	2.44994	−	0.214342i	0.112175	−	0.00981403i
$478$	21.6688	+	10.1043i	0.991108	+	0.462161i
$479$	−5.24484	+	0.924808i	−0.239643	+	0.0422555i	−0.292180	−	0.956363i	$-0.594381\pi$
$479$	−5.24484	+	0.924808i	−0.239643	+	0.0422555i	0.0525366	+	0.998619i	$0.483269\pi$
$480$		0			0
$481$	0.0517158	+	0.0188230i	0.00235804	+	0.000858256i
$482$	6.53670	−	24.3953i	0.297739	−	1.11118i
$483$	−28.2158	+	7.56041i	−1.28386	+	0.344010i
$484$	5.02382	+	5.98716i	0.228356	+	0.272144i
$485$		0			0
$486$	−2.73396	+	4.73535i	−0.124015	+	0.214800i
$487$	−25.5644	−	6.84995i	−1.15843	−	0.310401i	−0.372093	−	0.928196i	$-0.621360\pi$
$487$	−25.5644	−	6.84995i	−1.15843	−	0.310401i	−0.786340	+	0.617795i	$0.788026\pi$
$488$	−5.78057	−	12.3965i	−0.261674	−	0.561162i
$489$	−3.08539	+	17.4981i	−0.139526	+	0.791293i
$490$		0			0
$491$	−6.91431	+	2.51660i	−0.312038	+	0.113573i	−0.493292	−	0.869864i	$-0.664207\pi$
$491$	−6.91431	+	2.51660i	−0.312038	+	0.113573i	0.181254	+	0.983436i	$0.441984\pi$
$492$	−0.689210	−	7.87770i	−0.0310720	−	0.355154i
$493$	6.54209	+	6.54209i	0.294641	+	0.294641i
$494$	0.174283	−	0.339990i	0.00784135	−	0.0152969i
$495$		0			0
$496$	4.67433	−	5.57065i	0.209884	−	0.250129i
$497$	−3.89039	+	8.34298i	−0.174508	+	0.374234i
$498$	−7.95000	−	5.56665i	−0.356248	−	0.249448i
$499$	−32.5920	−	5.74685i	−1.45902	−	0.257265i	−0.612859	−	0.790192i	$-0.709981\pi$
$499$	−32.5920	−	5.74685i	−1.45902	−	0.257265i	−0.846161	+	0.532928i	$0.821092\pi$
$500$		0			0
$501$	−22.5402	−	39.0409i	−1.00702	−	1.74422i
$502$	−3.35204	−	12.5100i	−0.149609	−	0.558348i
$503$	−0.233914	+	2.67365i	−0.0104297	+	0.119212i	−0.999625	−	0.0273936i	$-0.991279\pi$
$503$	−0.233914	+	2.67365i	−0.0104297	+	0.119212i	0.989195	+	0.146606i	$0.0468348\pi$
$504$	−1.34214	+	1.12619i	−0.0597836	+	0.0501644i
$505$		0			0
$506$	7.29479	−	4.21165i	0.324293	−	0.187231i
$507$	22.1298	−	10.3193i	0.982820	−	0.458297i
$508$	11.6190	−	8.13574i	0.515512	−	0.360965i
$509$	−6.40712	−	36.3366i	−0.283991	−	1.61059i	−0.708869	−	0.705340i	$-0.750794\pi$
$509$	−6.40712	−	36.3366i	−0.283991	−	1.61059i	0.424878	−	0.905250i	$-0.360317\pi$
$510$		0			0
$511$	19.4739	+	16.3405i	0.861475	+	0.722863i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	13.5647	−	14.9912i	0.598897	−	0.661877i
$514$		−	23.6994i		−	1.04534i
$515$		0			0
$516$	−3.65954	−	10.0545i	−0.161102	−	0.442625i
$517$	−0.156707	+	0.223801i	−0.00689196	+	0.00984273i
$518$	1.18587	+	1.69360i	0.0521042	+	0.0744125i
$519$	−8.26058	+	22.6957i	−0.362599	+	0.996233i
$520$		0			0
$521$	6.83008	+	3.94335i	0.299231	+	0.172761i	0.642097	−	0.766623i	$-0.278064\pi$
$521$	6.83008	+	3.94335i	0.299231	+	0.172761i	−0.342866	+	0.939384i	$0.611398\pi$
$522$	1.04770	+	0.0916621i	0.0458567	+	0.00401194i
$523$	−4.68956	−	0.410283i	−0.205060	−	0.0179404i	−0.0158371	−	0.999875i	$-0.505041\pi$
$523$	−4.68956	−	0.410283i	−0.205060	−	0.0179404i	−0.189223	+	0.981934i	$0.560597\pi$
$524$	−1.57833	−	0.911249i	−0.0689496	−	0.0398081i
$525$		0			0
$526$	8.75189	−	24.0456i	0.381600	−	1.04844i
$527$	−19.5238	−	27.8829i	−0.850472	−	1.21460i
$528$	1.92360	−	2.74719i	0.0837141	−	0.119556i
$529$	−0.245691	−	0.675029i	−0.0106822	−	0.0293491i
$530$		0			0
$531$			6.95919i			0.302003i
$532$	12.6892	−	6.70719i	0.550147	−	0.290794i
$533$	0.260781	−	0.260781i	0.0112957	−	0.0112957i
$534$	9.37481	+	7.86640i	0.405688	+	0.340412i
$535$		0			0
$536$	−1.06990	−	6.06772i	−0.0462127	−	0.262085i
$537$	−14.2372	+	9.96900i	−0.614381	+	0.430194i
$538$	−24.1334	+	11.2536i	−1.04047	+	0.485177i
$539$	−5.93777	+	3.42817i	−0.255758	+	0.147662i
$540$		0			0
$541$	−6.17988	+	5.18553i	−0.265694	+	0.222944i	−0.765895	−	0.642966i	$-0.777704\pi$
$541$	−6.17988	+	5.18553i	−0.265694	+	0.222944i	0.500201	+	0.865909i	$0.333259\pi$
$542$	−0.573296	+	6.55280i	−0.0246252	+	0.281467i
$543$	−4.24073	−	15.8266i	−0.181987	−	0.679186i
$544$	2.34041	+	4.05371i	0.100344	+	0.173802i
$545$		0			0
$546$	−0.534168	−	0.0941882i	−0.0228603	−	0.00403088i
$547$	15.3460	+	10.7454i	0.656147	+	0.459439i	0.853639	−	0.520865i	$-0.174391\pi$
$547$	15.3460	+	10.7454i	0.656147	+	0.459439i	−0.197492	+	0.980305i	$0.563280\pi$
$548$	−0.0964499	+	0.206838i	−0.00412014	+	0.00883566i
$549$	−4.67815	+	5.57520i	−0.199659	+	0.237944i
$550$		0			0
$551$	−8.23296	−	2.53912i	−0.350736	−	0.108170i
$552$	6.27299	+	6.27299i	0.266996	+	0.266996i
$553$	−3.82236	−	43.6897i	−0.162543	−	1.85788i
$554$	−12.1678	+	4.42873i	−0.516961	+	0.188159i
$555$		0			0
$556$	−3.93747	+	22.3305i	−0.166986	+	0.947025i
$557$	12.6870	+	27.2073i	0.537564	+	1.15281i	0.968175	+	0.250273i	$0.0805204\pi$
$557$	12.6870	+	27.2073i	0.537564	+	1.15281i	−0.430611	+	0.902538i	$0.641702\pi$
$558$	−3.73749	−	1.00146i	−0.158220	−	0.0423950i
$559$	0.249506	−	0.432157i	0.0105530	−	0.0182783i
$560$		0			0
$561$	−10.0905	−	12.0254i	−0.426023	−	0.507714i
$562$	1.42892	−	0.382878i	0.0602753	−	0.0161507i
$563$	−0.0259379	+	0.0968017i	−0.00109315	+	0.00407971i	−0.966470	−	0.256779i	$-0.917339\pi$
$563$	−0.0259379	+	0.0968017i	−0.00109315	+	0.00407971i	0.965377	+	0.260858i	$0.0840055\pi$
$564$	−0.270389	−	0.0984137i	−0.0113855	−	0.00414397i
$565$		0			0
$566$	28.5273	−	5.03012i	1.19909	−	0.211432i
$567$	−30.7770	−	14.3516i	−1.29251	−	0.602709i
$568$	2.78503	−	0.243659i	0.116857	−	0.0102237i
$569$	26.3750			1.10570			0.552850	−	0.833281i	$-0.313540\pi$
$569$	26.3750			1.10570			0.552850	+	0.833281i	$0.313540\pi$
$570$		0			0
$571$	−24.1697			−1.01147			−0.505735	−	0.862689i	$-0.668779\pi$
$571$	−24.1697			−1.01147			−0.505735	+	0.862689i	$0.668779\pi$
$572$	0.155813	−	0.0136319i	0.00651487	−	0.000569977i
$573$	−20.1578	−	9.39971i	−0.842102	−	0.392679i
$574$	13.6443	−	2.40585i	0.569501	−	0.100418i
$575$		0			0
$576$	0.500000	+	0.181985i	0.0208333	+	0.00758271i
$577$	−7.22561	+	26.9664i	−0.300806	+	1.12262i	0.635689	+	0.771945i	$0.280716\pi$
$577$	−7.22561	+	26.9664i	−0.300806	+	1.12262i	−0.936496	+	0.350679i	$0.885951\pi$
$578$	4.74281	−	1.27083i	0.197275	−	0.0528596i
$579$	10.5473	+	12.5697i	0.438329	+	0.522381i
$580$		0			0
$581$	8.50191	−	14.7257i	0.352719	−	0.610927i
$582$	−15.1695	−	4.06464i	−0.628794	−	0.168485i
$583$	−3.48564	−	7.47499i	−0.144361	−	0.309582i
$584$	1.34063	−	7.60310i	0.0554758	−	0.314619i
$585$		0			0
$586$	16.8325	−	6.12654i	0.695346	−	0.253085i
$587$	1.07636	+	12.3028i	0.0444261	+	0.507792i	0.985510	+	0.169619i	$0.0542536\pi$
$587$	1.07636	+	12.3028i	0.0444261	+	0.507792i	−0.941084	+	0.338174i	$0.890191\pi$
$588$	−5.10605	−	5.10605i	−0.210570	−	0.210570i
$589$	28.2076	+	14.4596i	1.16227	+	0.595796i
$590$		0			0
$591$	−20.7639	+	24.7454i	−0.854112	+	1.01789i
$592$	0.265360	−	0.569066i	0.0109062	−	0.0233885i
$593$	22.1067	+	15.4793i	0.907815	+	0.635659i	0.931374	−	0.364063i	$-0.118611\pi$
$593$	22.1067	+	15.4793i	0.907815	+	0.635659i	−0.0235590	+	0.999722i	$0.507500\pi$
$594$	8.15089	+	1.43722i	0.334435	+	0.0589699i
$595$		0			0
$596$	−1.37382	−	2.37953i	−0.0562739	−	0.0974693i
$597$	1.84107	+	6.87098i	0.0753501	+	0.281210i
$598$	−0.0360596	+	0.412163i	−0.00147459	+	0.0168546i
$599$	−30.0738	+	25.2349i	−1.22878	+	1.03107i	−0.230465	+	0.973081i	$0.574025\pi$
$599$	−30.0738	+	25.2349i	−1.22878	+	1.03107i	−0.998317	+	0.0579896i	$0.981531\pi$
$600$		0			0
$601$	36.4203	−	21.0273i	1.48561	−	0.857720i	0.485748	−	0.874099i	$-0.338547\pi$
$601$	36.4203	−	21.0273i	1.48561	−	0.857720i	0.999866	+	0.0163790i	$0.00521382\pi$
$602$	16.9901	−	7.92259i	0.692463	−	0.322901i
$603$	−2.68548	+	1.88040i	−0.109361	+	0.0765756i
$604$	−2.91253	−	16.5178i	−0.118509	−	0.672099i
$605$		0			0
$606$	16.9475	+	14.2206i	0.688443	+	0.577672i
$607$	−13.5346	+	13.5346i	−0.549354	+	0.549354i	−0.926254	−	0.376900i	$-0.876990\pi$
$607$	−13.5346	+	13.5346i	−0.549354	+	0.549354i	0.376900	+	0.926254i	$0.376990\pi$
$608$	−3.69089	−	2.31890i	−0.149685	−	0.0940440i
$609$			12.2316i			0.495651i
$610$		0			0
$611$	−0.00458977	−	0.0126103i	−0.000185682	−	0.000510158i
$612$	1.42856	−	2.04019i	0.0577460	−	0.0824699i
$613$	−12.5952	−	17.9877i	−0.508713	−	0.726518i	0.479846	−	0.877353i	$-0.340693\pi$
$613$	−12.5952	−	17.9877i	−0.508713	−	0.726518i	−0.988559	+	0.150835i	$0.951804\pi$
$614$	−3.10866	+	8.54096i	−0.125455	+	0.344685i
$615$		0			0
$616$	5.08860	+	2.93791i	0.205026	+	0.118372i
$617$	24.2165	+	2.11867i	0.974921	+	0.0852945i	0.563469	−	0.826137i	$-0.309466\pi$
$617$	24.2165	+	2.11867i	0.974921	+	0.0852945i	0.411452	+	0.911432i	$0.365022\pi$
$618$	20.8605	+	1.82505i	0.839131	+	0.0734145i
$619$	30.7908	+	17.7771i	1.23759	+	0.714521i	0.968600	−	0.248623i	$-0.0799780\pi$
$619$	30.7908	+	17.7771i	1.23759	+	0.714521i	0.268986	+	0.963144i	$0.413311\pi$
$620$		0			0
$621$	−7.48808	+	20.5733i	−0.300486	+	0.825580i
$622$	−13.8561	−	19.7886i	−0.555579	−	0.793449i
$623$	−12.2983	+	17.5637i	−0.492719	+	0.703676i
$624$	0.0563402	+	0.154793i	0.00225541	+	0.00619670i
$625$		0			0
$626$			29.4020i			1.17514i
$627$	13.5405	+	5.50932i	0.540757	+	0.220021i
$628$	16.7831	−	16.7831i	0.669719	−	0.669719i
$629$	−2.25145	−	1.88919i	−0.0897713	−	0.0753271i
$630$		0			0
$631$	1.31098	+	7.43493i	0.0521892	+	0.295980i	0.999719	−	0.0236864i	$-0.00754031\pi$
$631$	1.31098	+	7.43493i	0.0521892	+	0.295980i	−0.947530	+	0.319666i	$0.896429\pi$
$632$	−10.9104	+	7.63953i	−0.433992	+	0.303884i
$633$	−12.1364	+	5.65930i	−0.482379	+	0.224937i
$634$	−2.79112	+	1.61146i	−0.110850	+	0.0639991i
$635$		0			0
$636$	6.65421	−	5.58354i	0.263856	−	0.221402i
$637$	0.0293516	−	0.335490i	0.00116295	−	0.0132926i
$638$	−0.912881	−	3.40692i	−0.0361413	−	0.134881i
$639$	−0.743772	−	1.28825i	−0.0294232	−	0.0509624i
$640$		0			0
$641$	15.7180	+	2.77151i	0.620825	+	0.109468i	0.475209	−	0.879873i	$-0.342372\pi$
$641$	15.7180	+	2.77151i	0.620825	+	0.109468i	0.145616	+	0.989341i	$0.453484\pi$
$642$	−24.3101	−	17.0221i	−0.959442	−	0.671809i
$643$	−1.51557	+	3.25014i	−0.0597681	+	0.128173i	−0.933923	−	0.357474i	$-0.883638\pi$
$643$	−1.51557	+	3.25014i	−0.0597681	+	0.128173i	0.874155	+	0.485647i	$0.161416\pi$
$644$	−9.99081	+	11.9066i	−0.393693	+	0.469185i
$645$		0			0
$646$	−14.9560	+	13.8784i	−0.588436	+	0.546039i
$647$	−8.30544	−	8.30544i	−0.326520	−	0.326520i	0.524741	−	0.851262i	$-0.324162\pi$
$647$	−8.30544	−	8.30544i	−0.326520	−	0.326520i	−0.851262	+	0.524741i	$0.824162\pi$
$648$	0.898850	+	10.2739i	0.0353102	+	0.403597i
$649$	21.9315	−	7.98242i	0.860887	−	0.313337i
$650$		0			0
$651$	7.81443	−	44.3178i	0.306272	−	1.73695i
$652$	3.99551	+	8.56841i	0.156476	+	0.335565i
$653$	26.2051	+	7.02165i	1.02549	+	0.274778i	0.732087	−	0.681212i	$-0.238547\pi$
$653$	26.2051	+	7.02165i	1.02549	+	0.274778i	0.293400	+	0.955990i	$0.405213\pi$
$654$	4.53360	−	7.85243i	0.177278	−	0.307054i
$655$		0			0
$656$	−2.70463	−	3.22325i	−0.105598	−	0.125847i
$657$	−3.96796	+	1.06321i	−0.154805	+	0.0414798i
$658$	0.130480	−	0.486958i	0.00508664	−	0.0189836i
$659$	30.6896	+	11.1701i	1.19550	+	0.435125i	0.861650	−	0.507503i	$-0.169431\pi$
$659$	30.6896	+	11.1701i	1.19550	+	0.435125i	0.333846	+	0.942628i	$0.391654\pi$
$660$		0			0
$661$	10.7233	−	1.89080i	0.417086	−	0.0735435i	0.0388330	−	0.999246i	$-0.487636\pi$
$661$	10.7233	−	1.89080i	0.417086	−	0.0735435i	0.378253	+	0.925702i	$0.376525\pi$
$662$	−14.5064	−	6.76445i	−0.563808	−	0.262908i
$663$	0.768128	−	0.0672025i	0.0298316	−	0.00260993i
$664$	−5.16401			−0.200402
$665$		0			0
$666$	−0.334096			−0.0129459
$667$	9.29453	−	0.813166i	0.359886	−	0.0314859i
$668$	−21.7395	−	10.1373i	−0.841125	−	0.392223i
$669$	−39.5324	+	6.97063i	−1.52841	+	0.269500i
$670$		0			0
$671$	22.9359	+	8.34800i	0.885432	+	0.322271i
$672$	−1.60166	+	5.97749i	−0.0617856	+	0.230587i
$673$	−23.6779	+	6.34446i	−0.912714	+	0.244561i	−0.684468	−	0.729043i	$-0.739966\pi$
$673$	−23.6779	+	6.34446i	−0.912714	+	0.244561i	−0.228246	+	0.973604i	$0.573299\pi$
$674$	7.55982	+	9.00944i	0.291193	+	0.347031i
$675$		0			0
$676$	6.49616	−	11.2517i	0.249852	−	0.432757i
$677$	−10.9062	−	2.92231i	−0.419160	−	0.112314i	0.0430735	−	0.999072i	$-0.486285\pi$
$677$	−10.9062	−	2.92231i	−0.419160	−	0.112314i	−0.462233	+	0.886758i	$0.652952\pi$
$678$	−1.72715	−	3.70390i	−0.0663310	−	0.142247i
$679$	4.77793	−	27.0970i	0.183360	−	1.03989i
$680$		0			0
$681$	−38.1014	+	13.8678i	−1.46005	+	0.531415i
$682$	1.13098	+	12.9272i	0.0433076	+	0.495008i
$683$	7.89889	+	7.89889i	0.302242	+	0.302242i	0.841891	−	0.539648i	$-0.181443\pi$
$683$	7.89889	+	7.89889i	0.302242	+	0.302242i	−0.539648	+	0.841891i	$0.681443\pi$
$684$	−0.288287	+	2.30134i	−0.0110229	+	0.0879937i
$685$		0			0
$686$	−6.68353	+	7.96512i	−0.255178	+	0.304110i
$687$	8.77677	−	18.8218i	0.334855	−	0.718098i
$688$	−4.66363	−	3.26551i	−0.177799	−	0.124496i
$689$	0.398960	+	0.0703473i	0.0151992	+	0.00268002i
$690$		0			0
$691$	−4.76158	−	8.24730i	−0.181139	−	0.313742i	0.761130	−	0.648600i	$-0.224645\pi$
$691$	−4.76158	−	8.24730i	−0.181139	−	0.313742i	−0.942269	+	0.334858i	$0.891312\pi$
$692$	3.32613	+	12.4133i	0.126440	+	0.471882i
$693$	0.272488	−	3.11456i	0.0103510	−	0.118312i
$694$	24.4946	−	20.5534i	0.929803	−	0.780197i
$695$		0			0
$696$	3.21704	−	1.85736i	0.121941	−	0.0704029i
$697$	−17.8500	+	8.32358i	−0.676116	+	0.315278i
$698$	−7.12465	+	4.98874i	−0.269672	+	0.188826i
$699$	−0.254415	−	1.44286i	−0.00962285	−	0.0545739i
$700$		0			0
$701$	5.00206	+	4.19723i	0.188925	+	0.158527i	0.732344	−	0.680934i	$-0.238426\pi$
$701$	5.00206	+	4.19723i	0.188925	+	0.158527i	−0.543419	+	0.839461i	$0.682871\pi$
$702$	−0.287463	+	0.287463i	−0.0108496	+	0.0108496i
$703$	2.67572	+	0.575590i	0.100917	+	0.0217088i
$704$		−	1.78447i		−	0.0672546i
$705$		0			0
$706$	11.9338	+	32.7880i	0.449136	+	1.23399i
$707$	−22.2324	+	31.7511i	−0.836134	+	1.19412i
$708$	14.0988	+	20.1351i	0.529865	+	0.756725i
$709$	−10.2305	+	28.1080i	−0.384214	+	1.05562i	0.585350	+	0.810781i	$0.300957\pi$
$709$	−10.2305	+	28.1080i	−0.384214	+	1.05562i	−0.969564	+	0.244839i	$0.921265\pi$
$710$		0			0
$711$	6.13748	+	3.54348i	0.230174	+	0.132891i
$712$	6.48689	+	0.567530i	0.243107	+	0.0212691i
$713$	−34.1955	−	2.99172i	−1.28063	−	0.112041i
$714$	25.0858	+	14.4833i	0.938813	+	0.542024i
$715$		0			0
$716$	−3.16298	+	8.69021i	−0.118206	+	0.324768i
$717$	−25.7731	−	36.8078i	−0.962513	−	1.37461i
$718$	−17.1946	+	24.5565i	−0.641699	+	0.916441i
$719$	−17.1193	−	47.0348i	−0.638442	−	1.75410i	−0.656567	−	0.754268i	$-0.727992\pi$
$719$	−17.1193	−	47.0348i	−0.638442	−	1.75410i	0.0181251	−	0.999836i	$-0.494230\pi$
$720$		0			0
$721$			36.6880i			1.36633i
$722$	6.27366	−	17.9344i	0.233481	−	0.667448i
$723$	−33.5632	+	33.5632i	−1.24823	+	1.24823i
$724$	−6.67856	−	5.60398i	−0.248207	−	0.208270i
$725$		0			0
$726$	−2.55066	−	14.4655i	−0.0946639	−	0.536866i
$727$	5.92932	−	4.15175i	0.219906	−	0.153980i	−0.458433	−	0.888729i	$-0.651589\pi$
$727$	5.92932	−	4.15175i	0.219906	−	0.153980i	0.678339	+	0.734749i	$0.262700\pi$
$728$	−0.261569	+	0.121972i	−0.00969439	+	0.00452057i
$729$	−17.8948	+	10.3316i	−0.662770	+	0.382651i
$730$		0			0
$731$	−20.4144	+	17.1297i	−0.755052	+	0.633564i
$732$	−2.24045	+	25.6084i	−0.0828092	+	0.946514i
$733$	2.66857	+	9.95924i	0.0985659	+	0.367853i	0.997536	−	0.0701571i	$-0.0223501\pi$
$733$	2.66857	+	9.95924i	0.0985659	+	0.367853i	−0.898970	+	0.438010i	$0.855683\pi$
$734$	−4.62919	−	8.01798i	−0.170866	−	0.295949i
$735$		0			0
$736$	4.64863	+	0.819679i	0.171351	+	0.0302138i
$737$	9.00631	+	6.30628i	0.331752	+	0.232295i
$738$	−0.946176	+	2.02908i	−0.0348292	+	0.0746915i
$739$	−7.58687	+	9.04168i	−0.279087	+	0.332603i	−0.887319	−	0.461156i	$-0.847435\pi$
$739$	−7.58687	+	9.04168i	−0.279087	+	0.332603i	0.608232	+	0.793760i	$0.291879\pi$
$740$		0			0
$741$	−0.603147	+	0.389593i	−0.0221572	+	0.0143121i
$742$	10.7615	+	10.7615i	0.395065	+	0.395065i
$743$	−0.583326	−	6.66745i	−0.0214002	−	0.244605i	−0.999359	−	0.0358061i	$-0.988600\pi$
$743$	−0.583326	−	6.66745i	−0.0214002	−	0.244605i	0.977959	−	0.208799i	$-0.0669554\pi$
$744$	−12.8426	+	4.67433i	−0.470833	+	0.171369i
$745$		0			0
$746$	0.328185	−	1.86123i	0.0120157	−	0.0681444i
$747$	1.16123	+	2.49027i	0.0424873	+	0.0911143i
$748$	−8.06816	−	2.16186i	−0.295001	−	0.0790453i
$749$	25.9977	−	45.0294i	0.949937	−	1.64534i
$750$		0			0
$751$	−3.23061	−	3.85009i	−0.117887	−	0.140492i	0.703874	−	0.710325i	$-0.251452\pi$
$751$	−3.23061	−	3.85009i	−0.117887	−	0.140492i	−0.821760	+	0.569834i	$0.807008\pi$
$752$	−0.147888	+	0.0396264i	−0.00539291	+	0.00144503i
$753$	−6.29978	+	23.5111i	−0.229577	+	0.856792i
$754$	0.162797	+	0.0592532i	0.00592872	+	0.00215788i
$755$		0			0
$756$	−15.0403	+	2.65201i	−0.547010	+	0.0964527i
$757$	24.7939	+	11.5616i	0.901149	+	0.420213i	0.817265	−	0.576263i	$-0.195489\pi$
$757$	24.7939	+	11.5616i	0.901149	+	0.420213i	0.0838847	+	0.996475i	$0.473267\pi$
$758$	−23.7843	+	2.08086i	−0.863884	+	0.0755801i
$759$	−15.8306			−0.574615
$760$		0			0
$761$	5.14173			0.186388			0.0931938	−	0.995648i	$-0.470292\pi$
$761$	5.14173			0.186388			0.0931938	+	0.995648i	$0.470292\pi$
$762$	−26.5562	+	2.32337i	−0.962030	+	0.0841667i
$763$	14.3977	+	6.71375i	0.521231	+	0.243054i
$764$	−11.6547	+	2.05504i	−0.421653	+	0.0743488i
$765$		0			0
$766$	−26.4509	−	9.62733i	−0.955709	−	0.347850i
$767$	−0.296703	+	1.10731i	−0.0107133	+	0.0399826i
$768$	1.81535	−	0.486421i	0.0655057	−	0.0175522i
$769$	8.74618	+	10.4233i	0.315395	+	0.375873i	0.900331	−	0.435206i	$-0.143325\pi$
$769$	8.74618	+	10.4233i	0.315395	+	0.375873i	−0.584935	+	0.811080i	$0.698880\pi$
$770$		0			0
$771$	−22.2702	+	38.5731i	−0.802041	+	1.38918i
$772$	8.43335	+	2.25971i	0.303523	+	0.0813288i
$773$	14.4578	+	31.0049i	0.520012	+	1.11517i	0.974494	+	0.224413i	$0.0720464\pi$
$773$	14.4578	+	31.0049i	0.520012	+	1.11517i	−0.454483	+	0.890756i	$0.650176\pi$
$774$	−0.526034	+	2.98329i	−0.0189079	+	0.107232i
$775$		0			0
$776$	−7.85229	+	2.85800i	−0.281881	+	0.102596i
$777$	−0.338655	−	3.87085i	−0.0121492	−	0.138866i
$778$	0.156384	+	0.156384i	0.00560665	+	0.00560665i
$779$	11.0735	−	14.6205i	0.396751	−	0.523834i
$780$		0			0
$781$	−3.20672	+	3.82163i	−0.114746	+	0.136749i
$782$	9.33779	−	20.0250i	0.333919	−	0.716091i
$783$	7.50964	+	5.25831i	0.268373	+	0.187917i
$784$	−3.78387	−	0.667198i	−0.135138	−	0.0238285i
$785$		0			0
$786$	1.71259	+	2.96629i	0.0610860	+	0.105804i
$787$	−10.9121	−	40.7244i	−0.388973	−	1.45167i	−0.831807	−	0.555065i	$-0.812693\pi$
$787$	−10.9121	−	40.7244i	−0.388973	−	1.45167i	0.442834	−	0.896604i	$-0.353973\pi$
$788$	−1.49803	+	17.1226i	−0.0533652	+	0.609967i
$789$	−36.8400	+	30.9124i	−1.31154	+	1.10051i
$790$		0			0
$791$	6.20094	−	3.58011i	0.220480	−	0.127294i
$792$	−0.860535	+	0.401274i	−0.0305778	+	0.0142586i
$793$	−0.982060	+	0.687646i	−0.0348740	+	0.0244190i
$794$	−0.968488	−	5.49257i	−0.0343703	−	0.194924i
$795$		0			0
$796$	2.89943	+	2.43291i	0.102768	+	0.0862323i
$797$	21.0090	−	21.0090i	0.744176	−	0.744176i	−0.229203	−	0.973379i	$-0.573612\pi$
$797$	21.0090	−	21.0090i	0.744176	−	0.744176i	0.973379	+	0.229203i	$0.0736120\pi$
$798$	−26.9556	−	1.00737i	−0.954218	−	0.0356604i
$799$			0.716656i			0.0253535i
$800$		0			0
$801$	−1.18503	−	3.25584i	−0.0418709	−	0.115039i
$802$	−18.8210	+	26.8792i	−0.664593	+	0.949137i
$803$	7.90204	+	11.2853i	0.278857	+	0.398249i
$804$	−3.96042	+	10.8812i	−0.139673	+	0.383749i
$805$		0			0
$806$	−0.551993	−	0.318693i	−0.0194431	−	0.0112255i
$807$	49.8544	+	4.36169i	1.75496	+	0.153539i
$808$	11.7268	+	1.02596i	0.412547	+	0.0360932i
$809$	13.9609	+	8.06031i	0.490838	+	0.283385i	0.724922	−	0.688831i	$-0.241876\pi$
$809$	13.9609	+	8.06031i	0.490838	+	0.283385i	−0.234084	+	0.972216i	$0.575209\pi$
$810$		0			0
$811$	−2.63474	+	7.23890i	−0.0925184	+	0.254192i	−0.977317	−	0.211781i	$-0.932074\pi$
$811$	−2.63474	+	7.23890i	−0.0925184	+	0.254192i	0.884799	+	0.465973i	$0.154296\pi$
$812$	3.73302	+	5.33130i	0.131003	+	0.187092i
$813$	7.09071	−	10.1266i	0.248682	−	0.355155i
$814$	0.383219	+	1.05288i	0.0134318	+	0.0369036i
$815$		0			0
$816$		−	8.79707i		−	0.307959i
$817$	9.35262	−	22.9864i	0.327207	−	0.804193i
$818$	−1.99531	+	1.99531i	−0.0697642	+	0.0697642i
$819$	0.117638	+	0.0987102i	0.00411061	+	0.00344922i
$820$		0			0
$821$	−3.07209	−	17.4227i	−0.107217	−	0.608055i	−0.990312	−	0.138862i	$-0.955656\pi$
$821$	−3.07209	−	17.4227i	−0.107217	−	0.608055i	0.883095	−	0.469194i	$-0.155455\pi$
$822$	0.351345	−	0.246015i	0.0122546	−	0.00858074i
$823$	19.0942	−	8.90378i	0.665583	−	0.310366i	−0.0603045	−	0.998180i	$-0.519207\pi$
$823$	19.0942	−	8.90378i	0.665583	−	0.310366i	0.725887	+	0.687814i	$0.241429\pi$
$824$	9.64928	−	5.57101i	0.336148	−	0.194075i
$825$		0			0
$826$	−32.9904	+	27.6822i	−1.14788	+	0.963189i
$827$	−2.09350	+	23.9288i	−0.0727982	+	0.832087i	0.868759	+	0.495234i	$0.164918\pi$
$827$	−2.09350	+	23.9288i	−0.0727982	+	0.832087i	−0.941558	+	0.336852i	$0.890638\pi$
$828$	−0.650061	−	2.42606i	−0.0225912	−	0.0843114i
$829$	12.2908	+	21.2883i	0.426876	+	0.739372i	0.996594	−	0.0824691i	$-0.0262806\pi$
$829$	12.2908	+	21.2883i	0.426876	+	0.739372i	−0.569717	+	0.821841i	$0.692947\pi$
$830$		0			0
$831$	23.9659	+	4.22584i	0.831369	+	0.146593i
$832$	0.0717985	+	0.0502739i	0.00248917	+	0.00174293i
$833$	−7.60073	+	16.2998i	−0.263350	+	0.564755i
$834$	27.3924	−	32.6450i	0.948523	−	1.13041i
$835$		0			0
$836$	7.58321	−	1.73118i	0.262271	−	0.0598743i
$837$	−23.8496	−	23.8496i	−0.824364	−	0.824364i
$838$	−3.01923	−	34.5099i	−0.104297	−	1.19213i
$839$	2.96152	−	1.07791i	0.102243	−	0.0372135i	−0.290392	−	0.956908i	$-0.593786\pi$
$839$	2.96152	−	1.07791i	0.102243	−	0.0372135i	0.392635	+	0.919694i	$0.371564\pi$
$840$		0			0
$841$	−4.35739	+	24.7120i	−0.150255	+	0.852138i
$842$	7.69798	+	16.5084i	0.265290	+	0.568916i
$843$	−2.68549	−	0.719575i	−0.0924932	−	0.0247835i
$844$	−3.56261	+	6.17062i	−0.122630	+	0.212402i
$845$		0			0
$846$	0.0523648	+	0.0624060i	0.00180034	+	0.00214556i
$847$	24.8582	−	6.66074i	0.854139	−	0.228866i
$848$	1.19625	−	4.46447i	0.0410795	−	0.153311i
$849$	−51.1576	−	18.6198i	−1.75572	−	0.639031i
$850$		0			0
$851$	−2.91885	+	0.514672i	−0.100057	+	0.0176427i
$852$	−4.76187	−	2.22050i	−0.163139	−	0.0760729i
$853$	−17.9061	+	1.56658i	−0.613092	+	0.0536386i	−0.389473	−	0.921038i	$-0.627343\pi$
$853$	−17.9061	+	1.56658i	−0.613092	+	0.0536386i	−0.223619	+	0.974677i	$0.571787\pi$
$854$	−45.0383			−1.54118
$855$		0			0
$856$	−15.7909			−0.539721
$857$	22.9500	−	2.00787i	0.783959	−	0.0685875i	0.311854	−	0.950130i	$-0.399050\pi$
$857$	22.9500	−	2.00787i	0.783959	−	0.0685875i	0.472105	+	0.881543i	$0.343494\pi$
$858$	−0.266410	−	0.124229i	−0.00909510	−	0.00424111i
$859$	−46.8105	+	8.25396i	−1.59715	+	0.281622i	−0.900195	−	0.435488i	$-0.856576\pi$
$859$	−46.8105	+	8.25396i	−1.59715	+	0.281622i	−0.696960	+	0.717110i	$0.745465\pi$
$860$		0			0
$861$	−24.4681	−	8.90567i	−0.833872	−	0.303504i
$862$	2.75230	−	10.2717i	0.0937438	−	0.349856i
$863$	54.9302	−	14.7185i	1.86985	−	0.501024i	0.869877	−	0.493269i	$-0.164198\pi$
$863$	54.9302	−	14.7185i	1.86985	−	0.501024i	0.999970	−	0.00775464i	$-0.00246840\pi$
$864$	2.98135	+	3.55303i	0.101428	+	0.120877i
$865$		0			0
$866$	1.19058	−	2.06214i	0.0404575	−	0.0700744i
$867$	−8.91356	−	2.38838i	−0.302720	−	0.0811137i
$868$	−10.1195	−	21.7014i	−0.343479	−	0.736592i
$869$	4.12719	−	23.4064i	0.140005	−	0.794009i
$870$		0			0
$871$	−0.507470	+	0.184704i	−0.0171950	+	0.00625846i
$872$	−0.420488	−	4.80620i	−0.0142395	−	0.162758i
$873$	3.14398	+	3.14398i	0.106408	+	0.106408i
$874$	1.02655	+	20.5499i	0.0347235	+	0.695110i
$875$		0			0
$876$	−9.32659	+	11.1150i	−0.315116	+	0.375541i
$877$	18.9653	−	40.6713i	0.640413	−	1.37337i	−0.271280	−	0.962500i	$-0.587447\pi$
$877$	18.9653	−	40.6713i	0.640413	−	1.37337i	0.911694	−	0.410870i	$-0.134775\pi$
$878$	−15.1697	−	10.6219i	−0.511953	−	0.358473i
$879$	−33.1536	−	5.84588i	−1.11824	−	0.197177i
$880$		0			0
$881$	0.668039	+	1.15708i	0.0225068	+	0.0389829i	0.877059	−	0.480382i	$-0.159502\pi$
$881$	0.668039	+	1.15708i	0.0225068	+	0.0389829i	−0.854553	+	0.519365i	$0.826169\pi$
$882$	0.529133	+	1.97475i	0.0178168	+	0.0664934i
$883$	−4.92501	+	56.2931i	−0.165740	+	1.89441i	0.225679	+	0.974202i	$0.427540\pi$
$883$	−4.92501	+	56.2931i	−0.165740	+	1.89441i	−0.391419	+	0.920213i	$0.628016\pi$
$884$	0.314288	−	0.263719i	0.0105706	−	0.00886982i
$885$		0			0
$886$	−21.9805	+	12.6905i	−0.738450	+	0.426344i
$887$	−9.26022	+	4.31811i	−0.310928	+	0.144988i	−0.571818	−	0.820380i	$-0.693762\pi$
$887$	−9.26022	+	4.31811i	−0.310928	+	0.144988i	0.260890	+	0.965368i	$0.415984\pi$
$888$	−0.966645	+	0.676852i	−0.0324385	+	0.0227137i
$889$	−8.11028	−	45.9957i	−0.272010	−	1.54265i
$890$		0			0
$891$	−14.0979	−	11.8295i	−0.472297	−	0.396304i
$892$	−15.1033	+	15.1033i	−0.505695	+	0.505695i
$893$	−0.311867	−	0.590015i	−0.0104362	−	0.0197441i
$894$			5.16388i			0.172706i
$895$		0			0
$896$	1.12619	+	3.09418i	0.0376233	+	0.103369i
$897$	0.445997	−	0.636950i	0.0148914	−	0.0212671i
$898$	21.2730	+	30.3810i	0.709889	+	1.01383i
$899$	−4.91601	+	13.5066i	−0.163958	+	0.450471i
$900$		0			0
$901$	−18.7361	−	10.8173i	−0.624190	−	0.360376i
$902$	7.47984	+	0.654401i	0.249051	+	0.0217892i
$903$	−35.0977	−	3.07065i	−1.16798	−	0.102185i
$904$	−1.88321	−	1.08727i	−0.0626345	−	0.0361620i
$905$		0			0
$906$	−10.7812	+	29.6212i	−0.358182	+	0.984097i
$907$	−2.59132	−	3.70078i	−0.0860433	−	0.122883i	0.773823	−	0.633402i	$-0.218342\pi$
$907$	−2.59132	−	3.70078i	−0.0860433	−	0.122883i	−0.859866	+	0.510519i	$0.829453\pi$
$908$	−12.3746	+	17.6728i	−0.410665	+	0.586491i
$909$	−2.14225	−	5.88579i	−0.0710540	−	0.195219i
$910$		0			0
$911$		−	45.7057i		−	1.51430i	−0.653243	−	0.757148i	$-0.726592\pi$
$911$		−	45.7057i		−	1.51430i	0.653243	−	0.757148i	$-0.273408\pi$
$912$	3.82822	+	7.24254i	0.126765	+	0.239825i
$913$	6.51599	−	6.51599i	0.215648	−	0.215648i
$914$	−15.1420	−	12.7056i	−0.500851	−	0.420264i
$915$		0			0
$916$	−1.91885	−	10.8823i	−0.0634006	−	0.359563i
$917$	−4.91576	+	3.44206i	−0.162333	+	0.113667i
$918$	19.6763	−	9.17521i	0.649415	−	0.302827i
$919$	17.3858	−	10.0377i	0.573506	−	0.331114i	−0.185042	−	0.982731i	$-0.559242\pi$
$919$	17.3858	−	10.0377i	0.573506	−	0.331114i	0.758548	+	0.651617i	$0.225909\pi$
$920$		0			0
$921$	13.0855	−	10.9801i	0.431182	−	0.361805i
$922$	−2.30915	+	26.3937i	−0.0760479	+	0.869231i
$923$	−0.0634210	−	0.236690i	−0.00208753	−	0.00779076i
$924$	−5.52146	−	9.56344i	−0.181643	−	0.314614i
$925$		0			0
$926$	−0.355412	−	0.0626688i	−0.0116796	−	0.00205942i
$927$	−4.85638	−	3.40047i	−0.159504	−	0.111686i
$928$	0.835329	−	1.79137i	0.0274210	−	0.0588046i
$929$	5.15730	−	6.14623i	0.169206	−	0.201651i	−0.674777	−	0.738021i	$-0.735760\pi$
$929$	5.15730	−	6.14623i	0.169206	−	0.201651i	0.843983	+	0.536370i	$0.180205\pi$
$930$		0			0
$931$	−0.835584	−	16.7271i	−0.0273852	−	0.548208i
$932$	−0.551241	−	0.551241i	−0.0180565	−	0.0180565i
$933$	3.95696	+	45.2282i	0.129545	+	1.48071i
$934$	−8.95288	+	3.25858i	−0.292947	+	0.106624i
$935$		0			0
$936$	0.00809852	−	0.0459290i	0.000264708	−	0.00150124i
$937$	5.33119	+	11.4328i	0.174162	+	0.373493i	0.973941	−	0.226803i	$-0.0728274\pi$
$937$	5.33119	+	11.4328i	0.174162	+	0.373493i	−0.799778	+	0.600296i	$0.795050\pi$
$938$	−19.5964	−	5.25085i	−0.639846	−	0.171446i
$939$	27.6289	−	47.8546i	0.901634	−	1.56168i
$940$		0			0
$941$	−13.7030	−	16.3306i	−0.446705	−	0.532363i	0.494959	−	0.868916i	$-0.335183\pi$
$941$	−13.7030	−	16.3306i	−0.446705	−	0.532363i	−0.941664	+	0.336554i	$0.890739\pi$
$942$	−43.0871	+	11.5451i	−1.40385	+	0.376161i
$943$	−5.14055	+	19.1848i	−0.167399	+	0.624743i
$944$	12.2902	+	4.47328i	0.400013	+	0.145593i
$945$		0			0
$946$	10.0051	−	1.76416i	0.325292	−	0.0573578i
$947$	27.9352	+	13.0264i	0.907771	+	0.423300i	0.819686	−	0.572813i	$-0.194148\pi$
$947$	27.9352	+	13.0264i	0.907771	+	0.423300i	0.0880844	+	0.996113i	$0.471925\pi$
$948$	24.9365	−	2.18166i	0.809900	−	0.0708571i
$949$	−0.676691			−0.0219663
$950$		0			0
$951$	6.05709			0.196415
$952$	15.3542	−	1.34332i	0.497631	−	0.0435371i
$953$	−6.14934	−	2.86748i	−0.199197	−	0.0928869i	0.320460	−	0.947262i	$-0.396162\pi$
$953$	−6.14934	−	2.86748i	−0.199197	−	0.0928869i	−0.519657	+	0.854375i	$0.673940\pi$
$954$	−2.42193	+	0.427052i	−0.0784130	+	0.0138263i
$955$		0			0
$956$	−22.4670	−	8.17731i	−0.726634	−	0.264473i
$957$	−1.71565	+	6.40291i	−0.0554592	+	0.206977i
$958$	5.14428	−	1.37841i	0.166204	−	0.0445343i
$959$	0.483037	+	0.575661i	0.0155981	+	0.0185891i
$960$		0			0
$961$	10.9407	−	18.9499i	0.352926	−	0.611287i
$962$	−0.0531596	−	0.0142441i	−0.00171393	−	0.000459247i
$963$	3.55090	+	7.61493i	0.114426	+	0.245388i
$964$	−4.38564	+	24.8722i	−0.141252	+	0.801079i
$965$		0			0
$966$	27.4495	−	9.99081i	0.883174	−	0.321449i
$967$	−4.26534	−	48.7531i	−0.137164	−	1.56779i	−0.683326	−	0.730114i	$-0.739467\pi$
$967$	−4.26534	−	48.7531i	−0.137164	−	1.56779i	0.546162	−	0.837680i	$-0.316088\pi$
$968$	−5.52652	−	5.52652i	−0.177629	−	0.177629i
$969$	37.3838	−	8.53440i	1.20094	−	0.274165i
$970$		0			0
$971$	−20.4328	+	24.3508i	−0.655718	+	0.781455i	−0.986764	−	0.162160i	$-0.948154\pi$
$971$	−20.4328	+	24.3508i	−0.655718	+	0.781455i	0.331046	+	0.943615i	$0.392598\pi$
$972$	2.31084	−	4.95561i	0.0741202	−	0.158951i
$973$	61.1606	+	42.8251i	1.96072	+	1.37291i
$974$	26.0641	+	4.59580i	0.835148	+	0.147259i
$975$		0			0
$976$	6.83900	+	11.8455i	0.218911	+	0.379165i
$977$	2.17901	+	8.13219i	0.0697128	+	0.260172i	0.991983	−	0.126375i	$-0.0403343\pi$
$977$	2.17901	+	8.13219i	0.0697128	+	0.260172i	−0.922270	+	0.386547i	$0.873668\pi$
$978$	1.54859	−	17.7005i	0.0495184	−	0.565998i
$979$	−8.90133	+	7.46910i	−0.284488	+	0.238714i
$980$		0			0
$981$	−2.22317	+	1.28355i	−0.0709803	+	0.0409805i
$982$	6.66866	−	3.10965i	0.212805	−	0.0992328i
$983$	−5.83010	+	4.08228i	−0.185951	+	0.130205i	−0.662846	−	0.748756i	$-0.730651\pi$
$983$	−5.83010	+	4.08228i	−0.185951	+	0.130205i	0.476894	+	0.878961i	$0.341763\pi$
$984$	1.37317	+	7.78766i	0.0437752	+	0.248261i
$985$		0			0
$986$	−7.08738	−	5.94702i	−0.225708	−	0.189392i
$987$	−0.669959	+	0.669959i	−0.0213250	+	0.0213250i
$988$	−0.143987	+	0.353885i	−0.00458085	+	0.0112586i
$989$			26.8740i			0.854545i
$990$		0			0
$991$	2.23427	+	6.13860i	0.0709739	+	0.194999i	0.970108	−	0.242675i	$-0.0780247\pi$
$991$	2.23427	+	6.13860i	0.0709739	+	0.194999i	−0.899134	+	0.437674i	$0.855803\pi$
$992$	−4.17103	+	5.95684i	−0.132430	+	0.189130i
$993$	17.2541	+	24.6414i	0.547541	+	0.781970i
$994$	3.14845	−	8.65030i	0.0998628	−	0.274371i
$995$		0			0
$996$	8.40492	+	4.85258i	0.266320	+	0.153760i
$997$	−22.7218	−	1.98790i	−0.719608	−	0.0629575i	−0.278531	−	0.960427i	$-0.589848\pi$
$997$	−22.7218	−	1.98790i	−0.719608	−	0.0629575i	−0.441076	+	0.897470i	$0.645403\pi$
$998$	32.9689	+	2.88440i	1.04361	+	0.0913042i
$999$	−2.52210	−	1.45614i	−0.0797958	−	0.0460701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.b.307.2	yes	48
5.2	odd	4	inner	950.2.bb.b.193.2	✓	48
5.3	odd	4	inner	950.2.bb.b.193.3	yes	48
5.4	even	2	inner	950.2.bb.b.307.3	yes	48
19.13	odd	18	inner	950.2.bb.b.507.3	yes	48
95.13	even	36	inner	950.2.bb.b.393.2	yes	48
95.32	even	36	inner	950.2.bb.b.393.3	yes	48
95.89	odd	18	inner	950.2.bb.b.507.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.b.193.2	✓	48	5.2	odd	4	inner
950.2.bb.b.193.3	yes	48	5.3	odd	4	inner
950.2.bb.b.307.2	yes	48	1.1	even	1	trivial
950.2.bb.b.307.3	yes	48	5.4	even	2	inner
950.2.bb.b.393.2	yes	48	95.13	even	36	inner
950.2.bb.b.393.3	yes	48	95.32	even	36	inner
950.2.bb.b.507.2	yes	48	95.89	odd	18	inner
950.2.bb.b.507.3	yes	48	19.13	odd	18	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)

\(f(q)\)	\(=\)	\(q+(-0.996195 + 0.0871557i) q^{2} +(1.70330 + 0.794263i) q^{3} +(0.984808 - 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(0.852228 - 3.18056i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.342020 + 0.407604i) q^{9} +O(q^{10})\)	\(q+(-0.996195 + 0.0871557i) q^{2} +(1.70330 + 0.794263i) q^{3} +(0.984808 - 0.173648i) q^{4} +(-1.76604 - 0.642788i) q^{6} +(0.852228 - 3.18056i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(0.342020 + 0.407604i) q^{9} +(0.892233 - 1.54539i) q^{11} +(1.81535 + 0.486421i) q^{12} +(0.0370424 + 0.0794377i) q^{13} +(-0.571781 + 3.24273i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-0.407961 - 4.66301i) q^{17} +(-0.376244 - 0.376244i) q^{18} +(2.36507 + 3.66148i) q^{19} +(3.97780 - 4.74056i) q^{21} +(-0.754148 + 1.61728i) q^{22} +(-3.86668 - 2.70748i) q^{23} +(-1.85083 - 0.326352i) q^{24} +(-0.0438249 - 0.0759070i) q^{26} +(-1.20044 - 4.48011i) q^{27} +(0.286983 - 3.28023i) q^{28} +(-1.51413 + 1.27051i) q^{29} +(6.29770 - 3.63598i) q^{31} +(-0.906308 + 0.422618i) q^{32} +(2.74719 - 1.92360i) q^{33} +(0.812817 + 4.60971i) q^{34} +(0.407604 + 0.342020i) q^{36} +(0.443988 - 0.443988i) q^{37} +(-2.67519 - 3.44142i) q^{38} +0.164728i q^{39} +(-1.43910 - 3.95390i) q^{41} +(-3.54950 + 5.06920i) q^{42} +(-3.26551 - 4.66363i) q^{43} +(0.610323 - 1.67685i) q^{44} +(4.08794 + 2.36017i) q^{46} +(-0.152522 - 0.0133439i) q^{47} +(1.87223 + 0.163799i) q^{48} +(-3.32748 - 1.92112i) q^{49} +(3.00878 - 8.26654i) q^{51} +(0.0502739 + 0.0717985i) q^{52} +(2.65105 - 3.78609i) q^{53} +(1.58634 + 4.35844i) q^{54} +3.29276i q^{56} +(1.12026 + 8.11509i) q^{57} +(1.39764 - 1.39764i) q^{58} +(10.0191 + 8.40702i) q^{59} +(2.37516 + 13.4702i) q^{61} +(-5.95684 + 4.17103i) q^{62} +(1.58789 - 0.740444i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-2.56908 + 2.15572i) q^{66} +(-0.536994 + 6.13787i) q^{67} +(-1.21149 - 4.52133i) q^{68} +(-4.43567 - 7.68281i) q^{69} +(-2.75320 - 0.485463i) q^{71} +(-0.435862 - 0.305194i) q^{72} +(-3.26278 + 6.99705i) q^{73} +(-0.403603 + 0.480995i) q^{74} +(2.96495 + 3.19516i) q^{76} +(-4.15483 - 4.15483i) q^{77} +(-0.0143570 - 0.164101i) q^{78} +(12.5159 - 4.55541i) q^{79} +(1.79086 - 10.1565i) q^{81} +(1.77823 + 3.81343i) q^{82} +(4.98805 + 1.33654i) q^{83} +(3.09418 - 5.35927i) q^{84} +(3.65954 + 4.36127i) q^{86} +(-3.58814 + 0.961438i) q^{87} +(-0.461854 + 1.72366i) q^{88} +(-6.11897 - 2.22712i) q^{89} +(0.284225 - 0.0501165i) q^{91} +(-4.27808 - 1.99490i) q^{92} +(13.6148 - 1.19114i) q^{93} +0.153105 q^{94} -1.87939 q^{96} +(8.32443 - 0.728294i) q^{97} +(3.48225 + 1.62380i) q^{98} +(0.935070 - 0.164878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{6}+O(q^{10}) \) 48 * q - 48 * q^6	\( 48 q - 48 q^{6} - 12 q^{11} + 36 q^{21} - 72 q^{31} + 48 q^{36} + 96 q^{41} + 72 q^{46} - 48 q^{51} - 108 q^{61} + 24 q^{66} - 60 q^{71} - 48 q^{76} - 168 q^{81} - 48 q^{86} + 252 q^{91}+O(q^{100}) \) 48 * q - 48 * q^6 - 12 * q^11 + 36 * q^21 - 72 * q^31 + 48 * q^36 + 96 * q^41 + 72 * q^46 - 48 * q^51 - 108 * q^61 + 24 * q^66 - 60 * q^71 - 48 * q^76 - 168 * q^81 - 48 * q^86 + 252 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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