LMFDB - Embedded newform 1110.2.u.e.191.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(191,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("1110.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.u (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.15
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.17773 + 1.27002i) q^{6} -5.10391 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99148 + 0.225919i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.17773 + 1.27002i) q^{6} -5.10391 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99148 + 0.225919i) q^{9} +1.00000 q^{10} +2.52188 q^{11} +(-0.0652635 + 1.73082i) q^{12} +(4.82201 + 4.82201i) q^{13} +(-3.60901 - 3.60901i) q^{14} +(1.27002 - 1.17773i) q^{15} -1.00000 q^{16} +(2.16139 - 2.16139i) q^{17} +(1.95555 + 2.27505i) q^{18} +(2.84634 + 2.84634i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-8.83396 - 0.333099i) q^{21} +(1.78324 + 1.78324i) q^{22} +(1.47717 - 1.47717i) q^{23} +(-1.27002 + 1.17773i) q^{24} -1.00000i q^{25} +6.81935i q^{26} +(5.16297 + 0.586260i) q^{27} -5.10391i q^{28} +(4.98506 + 4.98506i) q^{29} +(1.73082 + 0.0652635i) q^{30} +(-2.75008 + 2.75008i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.36492 + 0.164587i) q^{33} +3.05666 q^{34} +(-3.60901 + 3.60901i) q^{35} +(-0.225919 + 2.99148i) q^{36} +(-5.45849 + 2.68420i) q^{37} +4.02534i q^{38} +(8.03133 + 8.66073i) q^{39} +1.00000i q^{40} -4.87039 q^{41} +(-6.01102 - 6.48209i) q^{42} +(-6.39822 - 6.39822i) q^{43} +2.52188i q^{44} +(2.27505 - 1.95555i) q^{45} +2.08904 q^{46} -0.0691642i q^{47} +(-1.73082 - 0.0652635i) q^{48} +19.0499 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.88203 - 3.59991i) q^{51} +(-4.82201 + 4.82201i) q^{52} +4.54376i q^{53} +(3.23623 + 4.06532i) q^{54} +(1.78324 - 1.78324i) q^{55} +(3.60901 - 3.60901i) q^{56} +(4.74075 + 5.11228i) q^{57} +7.04993i q^{58} +(-9.35679 + 9.35679i) q^{59} +(1.17773 + 1.27002i) q^{60} +(4.43926 - 4.43926i) q^{61} -3.88920 q^{62} +(-15.2683 - 1.15307i) q^{63} -1.00000i q^{64} +6.81935 q^{65} +(2.97008 + 3.20284i) q^{66} -14.1658i q^{67} +(2.16139 + 2.16139i) q^{68} +(2.65313 - 2.46032i) q^{69} -5.10391 q^{70} -1.36435i q^{71} +(-2.27505 + 1.95555i) q^{72} -12.8981i q^{73} +(-5.75775 - 1.96172i) q^{74} +(0.0652635 - 1.73082i) q^{75} +(-2.84634 + 2.84634i) q^{76} -12.8714 q^{77} +(-0.445055 + 11.8031i) q^{78} +(-3.36382 - 3.36382i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(8.89792 + 1.35166i) q^{81} +(-3.44389 - 3.44389i) q^{82} -9.73857i q^{83} +(0.333099 - 8.83396i) q^{84} -3.05666i q^{85} -9.04844i q^{86} +(8.30290 + 8.95358i) q^{87} +(-1.78324 + 1.78324i) q^{88} +(-7.24712 - 7.24712i) q^{89} +(2.99148 + 0.225919i) q^{90} +(-24.6111 - 24.6111i) q^{91} +(1.47717 + 1.47717i) q^{92} +(-4.93938 + 4.58042i) q^{93} +(0.0489065 - 0.0489065i) q^{94} +4.02534 q^{95} +(-1.17773 - 1.27002i) q^{96} +(-4.90712 - 4.90712i) q^{97} +(13.4703 + 13.4703i) q^{98} +(7.54415 + 0.569740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) $ 40 * q - 24 * q^7 - 8 * q^9	$ 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) $ 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.73082	+	0.0652635i	0.999290	+	0.0376799i
$3$	1.73082	+	0.0652635i	0.999290	+	0.0376799i
$4$			1.00000i			0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	1.17773	+	1.27002i	0.480805	+	0.518485i
$7$	−5.10391			−1.92910			−0.964549	−	0.263904i	$-0.914990\pi$
$7$	−5.10391			−1.92910			−0.964549	+	0.263904i	$0.914990\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.99148	+	0.225919i	0.997160	+	0.0753063i
$10$	1.00000			0.316228
$11$	2.52188			0.760375			0.380187	−	0.924909i	$-0.375859\pi$
$11$	2.52188			0.760375			0.380187	+	0.924909i	$0.375859\pi$
$12$	−0.0652635	+	1.73082i	−0.0188400	+	0.499645i
$13$	4.82201	+	4.82201i	1.33738	+	1.33738i	0.898586	+	0.438798i	$0.144596\pi$
$13$	4.82201	+	4.82201i	1.33738	+	1.33738i	0.438798	+	0.898586i	$0.355404\pi$
$14$	−3.60901	−	3.60901i	−0.964549	−	0.964549i
$15$	1.27002	−	1.17773i	0.327919	−	0.304088i
$16$	−1.00000			−0.250000
$17$	2.16139	−	2.16139i	0.524213	−	0.524213i	−0.394628	−	0.918841i	$-0.629127\pi$
$17$	2.16139	−	2.16139i	0.524213	−	0.524213i	0.918841	+	0.394628i	$0.129127\pi$
$18$	1.95555	+	2.27505i	0.460927	+	0.536233i
$19$	2.84634	+	2.84634i	0.652996	+	0.652996i	0.953713	−	0.300717i	$-0.0972260\pi$
$19$	2.84634	+	2.84634i	0.652996	+	0.652996i	−0.300717	+	0.953713i	$0.597226\pi$
$20$	0.707107	+	0.707107i	0.158114	+	0.158114i
$21$	−8.83396	−	0.333099i	−1.92773	−	0.0726883i
$22$	1.78324	+	1.78324i	0.380187	+	0.380187i
$23$	1.47717	−	1.47717i	0.308012	−	0.308012i	−0.536126	−	0.844138i	$-0.680113\pi$
$23$	1.47717	−	1.47717i	0.308012	−	0.308012i	0.844138	+	0.536126i	$0.180113\pi$
$24$	−1.27002	+	1.17773i	−0.259242	+	0.240402i
$25$		−	1.00000i		−	0.200000i
$26$			6.81935i			1.33738i
$27$	5.16297	+	0.586260i	0.993615	+	0.112826i
$28$		−	5.10391i		−	0.964549i
$29$	4.98506	+	4.98506i	0.925702	+	0.925702i	0.997425	−	0.0717228i	$-0.0228497\pi$
$29$	4.98506	+	4.98506i	0.925702	+	0.925702i	−0.0717228	+	0.997425i	$0.522850\pi$
$30$	1.73082	+	0.0652635i	0.316003	+	0.0119154i
$31$	−2.75008	+	2.75008i	−0.493929	+	0.493929i	−0.909542	−	0.415613i	$-0.863567\pi$
$31$	−2.75008	+	2.75008i	−0.493929	+	0.493929i	0.415613	+	0.909542i	$0.363567\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.36492	+	0.164587i	0.759835	+	0.0286509i
$34$	3.05666			0.524213
$35$	−3.60901	+	3.60901i	−0.610034	+	0.610034i
$36$	−0.225919	+	2.99148i	−0.0376532	+	0.498580i
$37$	−5.45849	+	2.68420i	−0.897370	+	0.441279i
$37$	−5.45849	+	2.68420i	−0.897370	+	0.441279i
$38$			4.02534i			0.652996i
$39$	8.03133	+	8.66073i	1.28604	+	1.38683i
$40$			1.00000i			0.158114i
$41$	−4.87039			−0.760627			−0.380314	−	0.924858i	$-0.624184\pi$
$41$	−4.87039			−0.760627			−0.380314	+	0.924858i	$0.624184\pi$
$42$	−6.01102	−	6.48209i	−0.927520	−	1.00021i
$43$	−6.39822	−	6.39822i	−0.975719	−	0.975719i	0.0239935	−	0.999712i	$-0.492362\pi$
$43$	−6.39822	−	6.39822i	−0.975719	−	0.975719i	−0.999712	+	0.0239935i	$0.992362\pi$
$44$			2.52188i			0.380187i
$45$	2.27505	−	1.95555i	0.339144	−	0.291516i
$46$	2.08904			0.308012
$47$		−	0.0691642i		−	0.0100886i	−0.999987	−	0.00504432i	$-0.998394\pi$
$47$		−	0.0691642i		−	0.0100886i	0.999987	−	0.00504432i	$-0.00160566\pi$
$48$	−1.73082	−	0.0652635i	−0.249822	−	0.00941998i
$49$	19.0499			2.72142
$50$	0.707107	−	0.707107i	0.100000	−	0.100000i
$51$	3.88203	−	3.59991i	0.543593	−	0.504088i
$52$	−4.82201	+	4.82201i	−0.668692	+	0.668692i
$53$			4.54376i			0.624133i	0.950060	+	0.312067i	$0.101021\pi$
$53$			4.54376i			0.624133i	−0.950060	+	0.312067i	$0.898979\pi$
$54$	3.23623	+	4.06532i	0.440395	+	0.553220i
$55$	1.78324	−	1.78324i	0.240452	−	0.240452i
$56$	3.60901	−	3.60901i	0.482274	−	0.482274i
$57$	4.74075	+	5.11228i	0.627928	+	0.677137i
$58$			7.04993i			0.925702i
$59$	−9.35679	+	9.35679i	−1.21815	+	1.21815i	−0.249871	+	0.968279i	$0.580388\pi$
$59$	−9.35679	+	9.35679i	−1.21815	+	1.21815i	−0.968279	+	0.249871i	$0.919612\pi$
$60$	1.17773	+	1.27002i	0.152044	+	0.163959i
$61$	4.43926	−	4.43926i	0.568389	−	0.568389i	−0.363288	−	0.931677i	$-0.618346\pi$
$61$	4.43926	−	4.43926i	0.568389	−	0.568389i	0.931677	+	0.363288i	$0.118346\pi$
$62$	−3.88920			−0.493929
$63$	−15.2683	−	1.15307i	−1.92362	−	0.145273i
$64$		−	1.00000i		−	0.125000i
$65$	6.81935			0.845836
$66$	2.97008	+	3.20284i	0.365592	+	0.394243i
$67$		−	14.1658i		−	1.73063i	−0.501232	−	0.865313i	$-0.667120\pi$
$67$		−	14.1658i		−	1.73063i	0.501232	−	0.865313i	$-0.332880\pi$
$68$	2.16139	+	2.16139i	0.262106	+	0.262106i
$69$	2.65313	−	2.46032i	0.319399	−	0.296187i
$70$	−5.10391			−0.610034
$71$		−	1.36435i		−	0.161918i	−0.996717	−	0.0809590i	$-0.974202\pi$
$71$		−	1.36435i		−	0.161918i	0.996717	−	0.0809590i	$-0.0257983\pi$
$72$	−2.27505	+	1.95555i	−0.268117	+	0.230464i
$73$		−	12.8981i		−	1.50961i	−0.655948	−	0.754806i	$-0.727731\pi$
$73$		−	12.8981i		−	1.50961i	0.655948	−	0.754806i	$-0.272269\pi$
$74$	−5.75775	−	1.96172i	−0.669325	−	0.228045i
$75$	0.0652635	−	1.73082i	0.00753598	−	0.199858i
$76$	−2.84634	+	2.84634i	−0.326498	+	0.326498i
$77$	−12.8714			−1.46684
$78$	−0.445055	+	11.8031i	−0.0503925	+	1.33643i
$79$	−3.36382	−	3.36382i	−0.378459	−	0.378459i	0.492087	−	0.870546i	$-0.336234\pi$
$79$	−3.36382	−	3.36382i	−0.378459	−	0.378459i	−0.870546	+	0.492087i	$0.836234\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$	8.89792	+	1.35166i	0.988658	+	0.150185i
$82$	−3.44389	−	3.44389i	−0.380314	−	0.380314i
$83$		−	9.73857i		−	1.06895i	−0.845185	−	0.534474i	$-0.820510\pi$
$83$		−	9.73857i		−	1.06895i	0.845185	−	0.534474i	$-0.179490\pi$
$84$	0.333099	−	8.83396i	0.0363441	−	0.963864i
$85$		−	3.05666i		−	0.331541i
$86$		−	9.04844i		−	0.975719i
$87$	8.30290	+	8.95358i	0.890164	+	0.959925i
$88$	−1.78324	+	1.78324i	−0.190094	+	0.190094i
$89$	−7.24712	−	7.24712i	−0.768193	−	0.768193i	0.209595	−	0.977788i	$-0.432785\pi$
$89$	−7.24712	−	7.24712i	−0.768193	−	0.768193i	−0.977788	+	0.209595i	$0.932785\pi$
$90$	2.99148	+	0.225919i	0.315330	+	0.0238140i
$91$	−24.6111	−	24.6111i	−2.57994	−	2.57994i
$92$	1.47717	+	1.47717i	0.154006	+	0.154006i
$93$	−4.93938	+	4.58042i	−0.512190	+	0.474967i
$94$	0.0489065	−	0.0489065i	0.00504432	−	0.00504432i
$95$	4.02534			0.412991
$96$	−1.17773	−	1.27002i	−0.120201	−	0.129621i
$97$	−4.90712	−	4.90712i	−0.498242	−	0.498242i	0.412648	−	0.910890i	$-0.364604\pi$
$97$	−4.90712	−	4.90712i	−0.498242	−	0.498242i	−0.910890	+	0.412648i	$0.864604\pi$
$98$	13.4703	+	13.4703i	1.36071	+	1.36071i
$99$	7.54415	+	0.569740i	0.758216	+	0.0572610i
$100$	1.00000			0.100000
$101$	17.0003			1.69159			0.845796	−	0.533507i	$-0.179126\pi$
$101$	17.0003			1.69159			0.845796	+	0.533507i	$0.179126\pi$
$102$	5.29053	+	0.199488i	0.523841	+	0.0197523i
$103$	−4.76900	+	4.76900i	−0.469904	+	0.469904i	−0.901883	−	0.431980i	$-0.857815\pi$
$103$	−4.76900	+	4.76900i	−0.469904	+	0.469904i	0.431980	+	0.901883i	$0.357815\pi$
$104$	−6.81935			−0.668692
$105$	−6.48209	+	6.01102i	−0.632587	+	0.586615i
$106$	−3.21292	+	3.21292i	−0.312067	+	0.312067i
$107$		−	17.6140i		−	1.70280i	−0.524513	−	0.851402i	$-0.675753\pi$
$107$		−	17.6140i		−	1.70280i	0.524513	−	0.851402i	$-0.324247\pi$
$108$	−0.586260	+	5.16297i	−0.0564129	+	0.496807i
$109$	−1.38209	−	1.38209i	−0.132380	−	0.132380i	0.637812	−	0.770192i	$-0.279840\pi$
$109$	−1.38209	−	1.38209i	−0.132380	−	0.132380i	−0.770192	+	0.637812i	$0.779840\pi$
$110$	2.52188			0.240452
$111$	−9.62284	+	4.28963i	−0.913360	+	0.407153i
$112$	5.10391			0.482274
$113$	4.81041	+	4.81041i	0.452526	+	0.452526i	0.896192	−	0.443666i	$-0.146322\pi$
$113$	4.81041	+	4.81041i	0.452526	+	0.452526i	−0.443666	+	0.896192i	$0.646322\pi$
$114$	−0.262708	+	6.96714i	−0.0246049	+	0.652533i
$115$		−	2.08904i		−	0.194804i
$116$	−4.98506	+	4.98506i	−0.462851	+	0.462851i
$117$	13.3356	+	15.5143i	1.23287	+	1.43430i
$118$	−13.2325			−1.21815
$119$	−11.0315	+	11.0315i	−1.01126	+	1.01126i
$120$	−0.0652635	+	1.73082i	−0.00595772	+	0.158002i
$121$	−4.64013			−0.421830
$122$	6.27806			0.568389
$123$	−8.42977	−	0.317859i	−0.760087	−	0.0286604i
$124$	−2.75008	−	2.75008i	−0.246965	−	0.246965i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−9.98095	−	11.6116i	−0.889173	−	1.03445i
$127$	13.6854			1.21438			0.607190	−	0.794557i	$-0.292297\pi$
$127$	13.6854			1.21438			0.607190	+	0.794557i	$0.292297\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−10.6566	−	11.4917i	−0.938261	−	1.01179i
$130$	4.82201	+	4.82201i	0.422918	+	0.422918i
$131$	−1.16781	−	1.16781i	−0.102032	−	0.102032i	0.654248	−	0.756280i	$-0.272985\pi$
$131$	−1.16781	−	1.16781i	−0.102032	−	0.102032i	−0.756280	+	0.654248i	$0.772985\pi$
$132$	−0.164587	+	4.36492i	−0.0143254	+	0.379917i
$133$	−14.5275	−	14.5275i	−1.25969	−	1.25969i
$134$	10.0167	−	10.0167i	0.865313	−	0.865313i
$135$	4.06532	−	3.23623i	0.349887	−	0.278530i
$136$			3.05666i			0.262106i
$137$			9.28520i			0.793288i	0.917973	+	0.396644i	$0.129825\pi$
$137$			9.28520i			0.793288i	−0.917973	+	0.396644i	$0.870175\pi$
$138$	3.61575	+	0.136338i	0.307793	+	0.0116059i
$139$			5.21169i			0.442050i	0.975268	+	0.221025i	$0.0709403\pi$
$139$			5.21169i			0.442050i	−0.975268	+	0.221025i	$0.929060\pi$
$140$	−3.60901	−	3.60901i	−0.305017	−	0.305017i
$141$	0.00451390	−	0.119711i	0.000380139	−	0.0100815i
$142$	0.964738	−	0.964738i	0.0809590	−	0.0809590i
$143$	12.1605	+	12.1605i	1.01691	+	1.01691i
$144$	−2.99148	−	0.225919i	−0.249290	−	0.0188266i
$145$	7.04993			0.585465
$146$	9.12036	−	9.12036i	0.754806	−	0.754806i
$147$	32.9720	+	1.24327i	2.71949	+	0.102543i
$148$	−2.68420	−	5.45849i	−0.220640	−	0.448685i
$149$			4.53764i			0.371738i	0.982575	+	0.185869i	$0.0595100\pi$
$149$			4.53764i			0.371738i	−0.982575	+	0.185869i	$0.940490\pi$
$150$	1.27002	−	1.17773i	0.103697	−	0.0961610i
$151$		−	4.08345i		−	0.332307i	−0.986100	−	0.166153i	$-0.946865\pi$
$151$		−	4.08345i		−	0.332307i	0.986100	−	0.166153i	$-0.0531347\pi$
$152$	−4.02534			−0.326498
$153$	6.95404	−	5.97745i	0.562201	−	0.483248i
$154$	−9.10149	−	9.10149i	−0.733419	−	0.733419i
$155$			3.88920i			0.312388i
$156$	−8.66073	+	8.03133i	−0.693413	+	0.643021i
$157$	0.162952			0.0130050			0.00650250	−	0.999979i	$-0.497930\pi$
$157$	0.162952			0.0130050			0.00650250	+	0.999979i	$0.497930\pi$
$158$		−	4.75715i		−	0.378459i
$159$	−0.296542	+	7.86443i	−0.0235173	+	0.623690i
$160$	−1.00000			−0.0790569
$161$	−7.53936	+	7.53936i	−0.594185	+	0.594185i
$162$	5.33601	+	7.24755i	0.419236	+	0.569421i
$163$	6.42172	−	6.42172i	0.502988	−	0.502988i	−0.409377	−	0.912365i	$-0.634254\pi$
$163$	6.42172	−	6.42172i	0.502988	−	0.502988i	0.912365	+	0.409377i	$0.134254\pi$
$164$		−	4.87039i		−	0.380314i
$165$	3.20284	−	2.97008i	0.249341	−	0.231221i
$166$	6.88621	−	6.88621i	0.534474	−	0.534474i
$167$	−13.7065	+	13.7065i	−1.06064	+	1.06064i	−0.0626045	+	0.998038i	$0.519941\pi$
$167$	−13.7065	+	13.7065i	−1.06064	+	1.06064i	−0.998038	+	0.0626045i	$0.980059\pi$
$168$	6.48209	−	6.01102i	0.500104	−	0.463760i
$169$			33.5035i			2.57719i
$170$	2.16139	−	2.16139i	0.165771	−	0.165771i
$171$	7.87174	+	9.15783i	0.601967	+	0.700317i
$172$	6.39822	−	6.39822i	0.487859	−	0.487859i
$173$	−12.3062			−0.935621			−0.467810	−	0.883829i	$-0.654957\pi$
$173$	−12.3062			−0.935621			−0.467810	+	0.883829i	$0.654957\pi$
$174$	−0.460104	+	12.2022i	−0.0348804	+	0.925044i
$175$			5.10391i			0.385820i
$176$	−2.52188			−0.190094
$177$	−16.8056	+	15.5843i	−1.26318	+	1.17139i
$178$		−	10.2490i		−	0.768193i
$179$	3.97415	+	3.97415i	0.297042	+	0.297042i	0.839854	−	0.542812i	$-0.182640\pi$
$179$	3.97415	+	3.97415i	0.297042	+	0.297042i	−0.542812	+	0.839854i	$0.682640\pi$
$180$	1.95555	+	2.27505i	0.145758	+	0.169572i
$181$	−13.8542			−1.02978			−0.514888	−	0.857258i	$-0.672166\pi$
$181$	−13.8542			−1.02978			−0.514888	+	0.857258i	$0.672166\pi$
$182$		−	34.8053i		−	2.57994i
$183$	7.97328	−	7.39384i	0.589402	−	0.546568i
$184$			2.08904i			0.154006i
$185$	−1.96172	+	5.75775i	−0.144228	+	0.423318i
$186$	−6.73151	−	0.253823i	−0.493578	−	0.0186112i
$187$	5.45075	−	5.45075i	0.398598	−	0.398598i
$188$	0.0691642			0.00504432
$189$	−26.3514	−	2.99222i	−1.91678	−	0.217652i
$190$	2.84634	+	2.84634i	0.206496	+	0.206496i
$191$	−15.5800	+	15.5800i	−1.12733	+	1.12733i	−0.136716	+	0.990610i	$0.543655\pi$
$191$	−15.5800	+	15.5800i	−1.12733	+	1.12733i	−0.990610	+	0.136716i	$0.956345\pi$
$192$	0.0652635	−	1.73082i	0.00470999	−	0.124911i
$193$	10.1951	+	10.1951i	0.733858	+	0.733858i	0.971382	−	0.237524i	$-0.0763358\pi$
$193$	10.1951	+	10.1951i	0.733858	+	0.733858i	−0.237524	+	0.971382i	$0.576336\pi$
$194$		−	6.93971i		−	0.498242i
$195$	11.8031	+	0.445055i	0.845235	+	0.0318710i
$196$			19.0499i			1.36071i
$197$		−	18.6163i		−	1.32636i	−0.748462	−	0.663178i	$-0.769207\pi$
$197$		−	18.6163i		−	1.32636i	0.748462	−	0.663178i	$-0.230793\pi$
$198$	4.93165	+	5.73739i	0.350477	+	0.407738i
$199$	11.0077	−	11.0077i	0.780313	−	0.780313i	−0.199571	−	0.979883i	$-0.563955\pi$
$199$	11.0077	−	11.0077i	0.780313	−	0.780313i	0.979883	+	0.199571i	$0.0639547\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$	0.924509	−	24.5184i	0.0652099	−	1.72940i
$202$	12.0210	+	12.0210i	0.845796	+	0.845796i
$203$	−25.4433	−	25.4433i	−1.78577	−	1.78577i
$204$	3.59991	+	3.88203i	0.252044	+	0.271797i
$205$	−3.44389	+	3.44389i	−0.240531	+	0.240531i
$206$	−6.74438			−0.469904
$207$	4.75265	−	4.08521i	0.330332	−	0.283942i
$208$	−4.82201	−	4.82201i	−0.334346	−	0.334346i
$209$	7.17814	+	7.17814i	0.496522	+	0.496522i
$210$	−8.83396	−	0.333099i	−0.609601	−	0.0229860i
$211$	5.42872			0.373728			0.186864	−	0.982386i	$-0.440168\pi$
$211$	5.42872			0.373728			0.186864	+	0.982386i	$0.440168\pi$
$212$	−4.54376			−0.312067
$213$	0.0890421	−	2.36144i	0.00610106	−	0.161803i
$214$	12.4549	−	12.4549i	0.851402	−	0.851402i
$215$	−9.04844			−0.617099
$216$	−4.06532	+	3.23623i	−0.276610	+	0.220197i
$217$	14.0362	−	14.0362i	0.952837	−	0.952837i
$218$		−	1.95457i		−	0.132380i
$219$	0.841778	−	22.3244i	0.0568821	−	1.50854i
$220$	1.78324	+	1.78324i	0.120226	+	0.120226i
$221$	20.8444			1.40215
$222$	−9.83760	−	3.77115i	−0.660257	−	0.253103i
$223$	0.585115			0.0391822			0.0195911	−	0.999808i	$-0.493764\pi$
$223$	0.585115			0.0391822			0.0195911	+	0.999808i	$0.493764\pi$
$224$	3.60901	+	3.60901i	0.241137	+	0.241137i
$225$	0.225919	−	2.99148i	0.0150613	−	0.199432i
$226$			6.80295i			0.452526i
$227$	−9.42921	+	9.42921i	−0.625838	+	0.625838i	−0.947018	−	0.321180i	$-0.895921\pi$
$227$	−9.42921	+	9.42921i	−0.625838	+	0.625838i	0.321180	+	0.947018i	$0.395921\pi$
$228$	−5.11228	+	4.74075i	−0.338569	+	0.313964i
$229$	−10.8504			−0.717016			−0.358508	−	0.933527i	$-0.616714\pi$
$229$	−10.8504			−0.717016			−0.358508	+	0.933527i	$0.616714\pi$
$230$	1.47717	−	1.47717i	0.0974019	−	0.0974019i
$231$	−22.2782	−	0.840036i	−1.46580	−	0.0552703i
$232$	−7.04993			−0.462851
$233$	−7.44823			−0.487950			−0.243975	−	0.969782i	$-0.578451\pi$
$233$	−7.44823			−0.487950			−0.243975	+	0.969782i	$0.578451\pi$
$234$	−1.54062	+	20.3999i	−0.100713	+	1.33359i
$235$	−0.0489065	−	0.0489065i	−0.00319031	−	0.00319031i
$236$	−9.35679	−	9.35679i	−0.609075	−	0.609075i
$237$	−5.60263	−	6.04170i	−0.363930	−	0.392450i
$238$	−15.6009			−1.01126
$239$	19.5319	−	19.5319i	1.26341	−	1.26341i	0.313982	−	0.949429i	$-0.398337\pi$
$239$	19.5319	−	19.5319i	1.26341	−	1.26341i	0.949429	−	0.313982i	$-0.101663\pi$
$240$	−1.27002	+	1.17773i	−0.0819797	+	0.0760219i
$241$	−16.7350	−	16.7350i	−1.07799	−	1.07799i	−0.996689	−	0.0813043i	$-0.974091\pi$
$241$	−16.7350	−	16.7350i	−1.07799	−	1.07799i	−0.0813043	−	0.996689i	$-0.525909\pi$
$242$	−3.28107	−	3.28107i	−0.210915	−	0.210915i
$243$	15.3125	+	2.92020i	0.982297	+	0.187331i
$244$	4.43926	+	4.43926i	0.284194	+	0.284194i
$245$	13.4703	−	13.4703i	0.860588	−	0.860588i
$246$	−5.73599	−	6.18551i	−0.365713	−	0.394374i
$247$			27.4502i			1.74661i
$248$		−	3.88920i		−	0.246965i
$249$	0.635574	−	16.8557i	0.0402779	−	1.06819i
$250$		−	1.00000i		−	0.0632456i
$251$	−0.817495	−	0.817495i	−0.0515998	−	0.0515998i	0.680836	−	0.732436i	$-0.261617\pi$
$251$	−0.817495	−	0.817495i	−0.0515998	−	0.0515998i	−0.732436	+	0.680836i	$0.761617\pi$
$252$	1.15307	−	15.2683i	0.0726366	−	0.961810i
$253$	3.72525	−	3.72525i	0.234204	−	0.234204i
$254$	9.67701	+	9.67701i	0.607190	+	0.607190i
$255$	0.199488	−	5.29053i	0.0124925	−	0.331306i
$256$	1.00000			0.0625000
$257$	5.87353	−	5.87353i	0.366381	−	0.366381i	−0.499775	−	0.866156i	$-0.666584\pi$
$257$	5.87353	−	5.87353i	0.366381	−	0.366381i	0.866156	+	0.499775i	$0.166584\pi$
$258$	0.590533	−	15.6612i	0.0367650	−	0.975026i
$259$	27.8596	−	13.6999i	1.73111	−	0.851271i
$260$			6.81935i			0.422918i
$261$	13.7865	+	16.0389i	0.853362	+	0.992784i
$262$		−	1.65153i		−	0.102032i
$263$	−23.1214			−1.42572			−0.712862	−	0.701304i	$-0.752601\pi$
$263$	−23.1214			−1.42572			−0.712862	+	0.701304i	$0.752601\pi$
$264$	−3.20284	+	2.97008i	−0.197121	+	0.182796i
$265$	3.21292	+	3.21292i	0.197368	+	0.197368i
$266$		−	20.5450i		−	1.25969i
$267$	−12.0705	−	13.0164i	−0.738702	−	0.796593i
$268$	14.1658			0.865313
$269$		−	7.67575i		−	0.467999i	−0.972237	−	0.233999i	$-0.924819\pi$
$269$		−	7.67575i		−	0.467999i	0.972237	−	0.233999i	$-0.0751813\pi$
$270$	5.16297	+	0.586260i	0.314209	+	0.0356786i
$271$	−7.78777			−0.473074			−0.236537	−	0.971623i	$-0.576012\pi$
$271$	−7.78777			−0.473074			−0.236537	+	0.971623i	$0.576012\pi$
$272$	−2.16139	+	2.16139i	−0.131053	+	0.131053i
$273$	−40.9912	−	44.2036i	−2.48090	−	2.67532i
$274$	−6.56563	+	6.56563i	−0.396644	+	0.396644i
$275$		−	2.52188i		−	0.152075i
$276$	2.46032	+	2.65313i	0.148094	+	0.159699i
$277$	0.279231	−	0.279231i	0.0167774	−	0.0167774i	−0.698668	−	0.715446i	$-0.746224\pi$
$277$	0.279231	−	0.279231i	0.0167774	−	0.0167774i	0.715446	+	0.698668i	$0.246224\pi$
$278$	−3.68522	+	3.68522i	−0.221025	+	0.221025i
$279$	−8.84811	+	7.60552i	−0.529723	+	0.455331i
$280$		−	5.10391i		−	0.305017i
$281$	−8.56400	+	8.56400i	−0.510885	+	0.510885i	−0.914798	−	0.403912i	$-0.867650\pi$
$281$	−8.56400	+	8.56400i	−0.510885	+	0.510885i	0.403912	+	0.914798i	$0.367650\pi$
$282$	0.0878401	−	0.0814565i	0.00523080	−	0.00485066i
$283$	−7.11377	+	7.11377i	−0.422870	+	0.422870i	−0.886191	−	0.463321i	$-0.846658\pi$
$283$	−7.11377	+	7.11377i	−0.422870	+	0.422870i	0.463321	+	0.886191i	$0.346658\pi$
$284$	1.36435			0.0809590
$285$	6.96714	+	0.262708i	0.412698	+	0.0155615i
$286$			17.1976i			1.01691i
$287$	24.8580			1.46732
$288$	−1.95555	−	2.27505i	−0.115232	−	0.134058i
$289$			7.65683i			0.450402i
$290$	4.98506	+	4.98506i	0.292733	+	0.292733i
$291$	−8.17309	−	8.81360i	−0.479115	−	0.516662i
$292$	12.8981			0.754806
$293$			22.3923i			1.30817i	0.756421	+	0.654085i	$0.226946\pi$
$293$			22.3923i			1.30817i	−0.756421	+	0.654085i	$0.773054\pi$
$294$	22.4356	+	24.1939i	1.30847	+	1.41101i
$295$			13.2325i			0.770426i
$296$	1.96172	−	5.75775i	0.114023	−	0.334662i
$297$	13.0204	+	1.47848i	0.755520	+	0.0857899i
$298$	−3.20860	+	3.20860i	−0.185869	+	0.185869i
$299$	14.2459			0.823860
$300$	1.73082	+	0.0652635i	0.0999290	+	0.00376799i
$301$	32.6559	+	32.6559i	1.88226	+	1.88226i
$302$	2.88744	−	2.88744i	0.166153	−	0.166153i
$303$	29.4244	+	1.10950i	1.69039	+	0.0637390i
$304$	−2.84634	−	2.84634i	−0.163249	−	0.163249i
$305$		−	6.27806i		−	0.359481i
$306$	9.14394	+	0.690558i	0.522724	+	0.0394766i
$307$		−	14.5985i		−	0.833180i	−0.909095	−	0.416590i	$-0.863225\pi$
$307$		−	14.5985i		−	0.833180i	0.909095	−	0.416590i	$-0.136775\pi$
$308$		−	12.8714i		−	0.733419i
$309$	−8.56553	+	7.94304i	−0.487276	+	0.451864i
$310$	−2.75008	+	2.75008i	−0.156194	+	0.156194i
$311$	14.7246	+	14.7246i	0.834955	+	0.834955i	0.988190	−	0.153234i	$-0.0489689\pi$
$311$	14.7246	+	14.7246i	0.834955	+	0.834955i	−0.153234	+	0.988190i	$0.548969\pi$
$312$	−11.8031	−	0.445055i	−0.668217	−	0.0251963i
$313$	0.123805	+	0.123805i	0.00699787	+	0.00699787i	0.710597	−	0.703599i	$-0.248425\pi$
$313$	0.123805	+	0.123805i	0.00699787	+	0.00699787i	−0.703599	+	0.710597i	$0.748425\pi$
$314$	0.115225	+	0.115225i	0.00650250	+	0.00650250i
$315$	−11.6116	+	9.98095i	−0.654241	+	0.562363i
$316$	3.36382	−	3.36382i	0.189229	−	0.189229i
$317$	−14.8309			−0.832987			−0.416493	−	0.909139i	$-0.636741\pi$
$317$	−14.8309			−0.832987			−0.416493	+	0.909139i	$0.636741\pi$
$318$	−5.77068	+	5.35131i	−0.323604	+	0.300086i
$319$	12.5717	+	12.5717i	0.703880	+	0.703880i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	1.14955	−	30.4866i	0.0641616	−	1.70160i
$322$	−10.6623			−0.594185
$323$	12.3041			0.684618
$324$	−1.35166	+	8.89792i	−0.0750925	+	0.494329i
$325$	4.82201	−	4.82201i	0.267477	−	0.267477i
$326$	9.08168			0.502988
$327$	−2.30195	−	2.48235i	−0.127298	−	0.137274i
$328$	3.44389	−	3.44389i	0.190157	−	0.190157i
$329$			0.353008i			0.0194620i
$330$	4.36492	+	0.164587i	0.240281	+	0.00906020i
$331$	−0.578555	−	0.578555i	−0.0318003	−	0.0318003i	0.691028	−	0.722828i	$-0.257158\pi$
$331$	−0.578555	−	0.578555i	−0.0318003	−	0.0318003i	−0.722828	+	0.691028i	$0.757158\pi$
$332$	9.73857			0.534474
$333$	−16.9354	+	6.79655i	−0.928053	+	0.372449i
$334$	−19.3840			−1.06064
$335$	−10.0167	−	10.0167i	−0.547272	−	0.547272i
$336$	8.83396	+	0.333099i	0.481932	+	0.0181721i
$337$		−	33.2306i		−	1.81019i	−0.425212	−	0.905094i	$-0.639800\pi$
$337$		−	33.2306i		−	1.81019i	0.425212	−	0.905094i	$-0.360200\pi$
$338$	−23.6905	+	23.6905i	−1.28860	+	1.28860i
$339$	8.01202	+	8.63991i	0.435153	+	0.469255i
$340$	3.05666			0.165771
$341$	−6.93537	+	6.93537i	−0.375571	+	0.375571i
$342$	−0.909401	+	12.0417i	−0.0491748	+	0.651142i
$343$	−61.5018			−3.32078
$344$	9.04844			0.487859
$345$	0.136338	−	3.61575i	0.00734019	−	0.194665i
$346$	−8.70178	−	8.70178i	−0.467810	−	0.467810i
$347$	−4.41151	−	4.41151i	−0.236822	−	0.236822i	0.578711	−	0.815533i	$-0.303556\pi$
$347$	−4.41151	−	4.41151i	−0.236822	−	0.236822i	−0.815533	+	0.578711i	$0.803556\pi$
$348$	−8.95358	+	8.30290i	−0.479962	+	0.445082i
$349$	14.9035			0.797766			0.398883	−	0.917002i	$-0.369398\pi$
$349$	14.9035			0.797766			0.398883	+	0.917002i	$0.369398\pi$
$350$	−3.60901	+	3.60901i	−0.192910	+	0.192910i
$351$	22.0689	+	27.7228i	1.17795	+	1.47974i
$352$	−1.78324	−	1.78324i	−0.0950469	−	0.0950469i
$353$	18.6335	+	18.6335i	0.991762	+	0.991762i	0.999966	−	0.00820423i	$-0.00261152\pi$
$353$	18.6335	+	18.6335i	0.991762	+	0.991762i	−0.00820423	+	0.999966i	$0.502612\pi$
$354$	−22.9031	−	0.863600i	−1.21729	−	0.0458998i
$355$	−0.964738	−	0.964738i	−0.0512030	−	0.0512030i
$356$	7.24712	−	7.24712i	0.384097	−	0.384097i
$357$	−19.8135	+	18.3736i	−1.04864	+	0.972436i
$358$			5.62030i			0.297042i
$359$		−	9.49276i		−	0.501009i	−0.968115	−	0.250504i	$-0.919404\pi$
$359$		−	9.49276i		−	0.501009i	0.968115	−	0.250504i	$-0.0805964\pi$
$360$	−0.225919	+	2.99148i	−0.0119070	+	0.157665i
$361$		−	2.79664i		−	0.147192i
$362$	−9.79640	−	9.79640i	−0.514888	−	0.514888i
$363$	−8.03123	−	0.302831i	−0.421530	−	0.0158945i
$364$	24.6111	−	24.6111i	1.28997	−	1.28997i
$365$	−9.12036	−	9.12036i	−0.477381	−	0.477381i
$366$	10.8662	+	0.409728i	0.567985	+	0.0214168i
$367$	−5.07778			−0.265058			−0.132529	−	0.991179i	$-0.542310\pi$
$367$	−5.07778			−0.265058			−0.132529	+	0.991179i	$0.542310\pi$
$368$	−1.47717	+	1.47717i	−0.0770029	+	0.0770029i
$369$	−14.5697	−	1.10031i	−0.758467	−	0.0572800i
$370$	−5.45849	+	2.68420i	−0.283773	+	0.139545i
$371$		−	23.1909i		−	1.20401i
$372$	−4.58042	−	4.93938i	−0.237484	−	0.256095i
$373$			2.58217i			0.133700i	0.997763	+	0.0668499i	$0.0212949\pi$
$373$			2.58217i			0.133700i	−0.997763	+	0.0668499i	$0.978705\pi$
$374$	7.70853			0.398598
$375$	−1.17773	−	1.27002i	−0.0608176	−	0.0655837i
$376$	0.0489065	+	0.0489065i	0.00252216	+	0.00252216i
$377$			48.0759i			2.47604i
$378$	−16.5174	−	20.7491i	−0.849564	−	1.06722i
$379$	10.7934			0.554419			0.277209	−	0.960810i	$-0.410590\pi$
$379$	10.7934			0.554419			0.277209	+	0.960810i	$0.410590\pi$
$380$			4.02534i			0.206496i
$381$	23.6869	+	0.893155i	1.21352	+	0.0457577i
$382$	−22.0334			−1.12733
$383$	−5.75655	+	5.75655i	−0.294146	+	0.294146i	−0.838716	−	0.544570i	$-0.816693\pi$
$383$	−5.75655	+	5.75655i	−0.294146	+	0.294146i	0.544570	+	0.838716i	$0.316693\pi$
$384$	1.27002	−	1.17773i	0.0648106	−	0.0601006i
$385$	−9.10149	+	9.10149i	−0.463855	+	0.463855i
$386$			14.4180i			0.733858i
$387$	−17.6947	−	20.5856i	−0.899470	−	1.04643i
$388$	4.90712	−	4.90712i	0.249121	−	0.249121i
$389$	23.0070	−	23.0070i	1.16650	−	1.16650i	0.183478	−	0.983024i	$-0.441264\pi$
$389$	23.0070	−	23.0070i	1.16650	−	1.16650i	0.983024	−	0.183478i	$-0.0587357\pi$
$390$	8.03133	+	8.66073i	0.406682	+	0.438553i
$391$		−	6.38548i		−	0.322927i
$392$	−13.4703	+	13.4703i	−0.680355	+	0.680355i
$393$	−1.94505	−	2.09748i	−0.0981150	−	0.105804i
$394$	13.1637	−	13.1637i	0.663178	−	0.663178i
$395$	−4.75715			−0.239358
$396$	−0.569740	+	7.54415i	−0.0286305	+	0.379108i
$397$		−	8.20919i		−	0.412008i	−0.978551	−	0.206004i	$-0.933954\pi$
$397$		−	8.20919i		−	0.412008i	0.978551	−	0.206004i	$-0.0660459\pi$
$398$	15.5672			0.780313
$399$	−24.1964	−	26.0926i	−1.21133	−	1.30626i
$400$			1.00000i			0.0500000i
$401$	5.94884	+	5.94884i	0.297071	+	0.297071i	0.839866	−	0.542795i	$-0.182634\pi$
$401$	5.94884	+	5.94884i	0.297071	+	0.297071i	−0.542795	+	0.839866i	$0.682634\pi$
$402$	17.9909	−	16.6834i	0.897304	−	0.832094i
$403$	−26.5218			−1.32115
$404$			17.0003i			0.845796i
$405$	7.24755	−	5.33601i	0.360134	−	0.265148i
$406$		−	35.9823i		−	1.78577i
$407$	−13.7656	+	6.76922i	−0.682337	+	0.335538i
$408$	−0.199488	+	5.29053i	−0.00987615	+	0.261920i
$409$	17.8854	−	17.8854i	0.884374	−	0.884374i	−0.109601	−	0.993976i	$-0.534957\pi$
$409$	17.8854	−	17.8854i	0.884374	−	0.884374i	0.993976	+	0.109601i	$0.0349574\pi$
$410$	−4.87039			−0.240531
$411$	−0.605985	+	16.0710i	−0.0298910	+	0.792724i
$412$	−4.76900	−	4.76900i	−0.234952	−	0.234952i
$413$	47.7562	−	47.7562i	2.34993	−	2.34993i
$414$	6.24932	+	0.471953i	0.307137	+	0.0231952i
$415$	−6.88621	−	6.88621i	−0.338031	−	0.338031i
$416$		−	6.81935i		−	0.334346i
$417$	−0.340134	+	9.02051i	−0.0166564	+	0.441736i
$418$			10.1514i			0.496522i
$419$			16.3639i			0.799429i	0.916640	+	0.399714i	$0.130891\pi$
$419$			16.3639i			0.799429i	−0.916640	+	0.399714i	$0.869109\pi$
$420$	−6.01102	−	6.48209i	−0.293308	−	0.316294i
$421$	−1.58888	+	1.58888i	−0.0774373	+	0.0774373i	−0.744765	−	0.667327i	$-0.767438\pi$
$421$	−1.58888	+	1.58888i	−0.0774373	+	0.0774373i	0.667327	+	0.744765i	$0.267438\pi$
$422$	3.83868	+	3.83868i	0.186864	+	0.186864i
$423$	0.0156255	−	0.206903i	0.000759738	−	0.0100600i
$424$	−3.21292	−	3.21292i	−0.156033	−	0.156033i
$425$	−2.16139	−	2.16139i	−0.104843	−	0.104843i
$426$	1.73275	−	1.60683i	0.0839521	−	0.0778510i
$427$	−22.6576	+	22.6576i	−1.09648	+	1.09648i
$428$	17.6140			0.851402
$429$	20.2540	+	21.8413i	0.977874	+	1.05451i
$430$	−6.39822	−	6.39822i	−0.308549	−	0.308549i
$431$	12.8119	+	12.8119i	0.617127	+	0.617127i	0.944793	−	0.327666i	$-0.106262\pi$
$431$	12.8119	+	12.8119i	0.617127	+	0.617127i	−0.327666	+	0.944793i	$0.606262\pi$
$432$	−5.16297	−	0.586260i	−0.248404	−	0.0282064i
$433$	10.0976			0.485259			0.242629	−	0.970119i	$-0.421990\pi$
$433$	10.0976			0.485259			0.242629	+	0.970119i	$0.421990\pi$
$434$	19.8501			0.952837
$435$	12.2022	+	0.460104i	0.585049	+	0.0220603i
$436$	1.38209	−	1.38209i	0.0661900	−	0.0661900i
$437$	8.40908			0.402261
$438$	16.3809	−	15.1905i	0.782711	−	0.725829i
$439$	0.758341	−	0.758341i	0.0361937	−	0.0361937i	−0.688778	−	0.724972i	$-0.741853\pi$
$439$	0.758341	−	0.758341i	0.0361937	−	0.0361937i	0.724972	+	0.688778i	$0.241853\pi$
$440$			2.52188i			0.120226i
$441$	56.9875	+	4.30374i	2.71369	+	0.204940i
$442$	14.7392	+	14.7392i	0.701074	+	0.701074i
$443$	−26.5884			−1.26325			−0.631626	−	0.775273i	$-0.717612\pi$
$443$	−26.5884			−1.26325			−0.631626	+	0.775273i	$0.717612\pi$
$444$	−4.28963	−	9.62284i	−0.203577	−	0.456680i
$445$	−10.2490			−0.485848
$446$	0.413739	+	0.413739i	0.0195911	+	0.0195911i
$447$	−0.296143	+	7.85385i	−0.0140071	+	0.371474i
$448$			5.10391i			0.241137i
$449$	−12.5200	+	12.5200i	−0.590854	+	0.590854i	−0.937862	−	0.347008i	$-0.887198\pi$
$449$	−12.5200	+	12.5200i	−0.590854	+	0.590854i	0.347008	+	0.937862i	$0.387198\pi$
$450$	2.27505	−	1.95555i	0.107247	−	0.0921854i
$451$	−12.2825			−0.578362
$452$	−4.81041	+	4.81041i	−0.226263	+	0.226263i
$453$	0.266501	−	7.06772i	0.0125213	−	0.332071i
$454$	−13.3349			−0.625838
$455$	−34.8053			−1.63170
$456$	−6.96714	−	0.262708i	−0.326266	−	0.0123024i
$457$	7.21832	+	7.21832i	0.337659	+	0.337659i	0.855485	−	0.517827i	$-0.173259\pi$
$457$	7.21832	+	7.21832i	0.337659	+	0.337659i	−0.517827	+	0.855485i	$0.673259\pi$
$458$	−7.67241	−	7.67241i	−0.358508	−	0.358508i
$459$	12.4263	−	9.89204i	0.580010	−	0.461721i
$460$	2.08904			0.0974019
$461$	18.4973	−	18.4973i	0.861506	−	0.861506i	−0.130007	−	0.991513i	$-0.541500\pi$
$461$	18.4973	−	18.4973i	0.861506	−	0.861506i	0.991513	+	0.130007i	$0.0414999\pi$
$462$	−15.1590	−	16.3470i	−0.705263	−	0.760533i
$463$	−20.2551	−	20.2551i	−0.941333	−	0.941333i	0.0570389	−	0.998372i	$-0.481834\pi$
$463$	−20.2551	−	20.2551i	−0.941333	−	0.941333i	−0.998372	+	0.0570389i	$0.981834\pi$
$464$	−4.98506	−	4.98506i	−0.231425	−	0.231425i
$465$	−0.253823	+	6.73151i	−0.0117708	+	0.312166i
$466$	−5.26670	−	5.26670i	−0.243975	−	0.243975i
$467$	26.7256	−	26.7256i	1.23671	−	1.23671i	0.275374	−	0.961337i	$-0.411198\pi$
$467$	26.7256	−	26.7256i	1.23671	−	1.23671i	0.961337	−	0.275374i	$-0.0888018\pi$
$468$	−15.5143	+	13.3356i	−0.717150	+	0.616436i
$469$			72.3009i			3.33855i
$470$		−	0.0691642i		−	0.00319031i
$471$	0.282041	+	0.0106348i	0.0129958	+	0.000490027i
$472$		−	13.2325i		−	0.609075i
$473$	−16.1355	−	16.1355i	−0.741912	−	0.741912i
$474$	0.310469	−	8.23378i	0.0142603	−	0.378190i
$475$	2.84634	−	2.84634i	0.130599	−	0.130599i
$476$	−11.0315	−	11.0315i	−0.505629	−	0.505629i
$477$	−1.02652	+	13.5926i	−0.0470012	+	0.622361i
$478$	27.6222			1.26341
$479$	4.24011	−	4.24011i	0.193736	−	0.193736i	−0.603572	−	0.797308i	$-0.706257\pi$
$479$	4.24011	−	4.24011i	0.193736	−	0.193736i	0.797308	+	0.603572i	$0.206257\pi$
$480$	−1.73082	−	0.0652635i	−0.0790008	−	0.00297886i
$481$	−39.2641	−	13.3776i	−1.79029	−	0.609968i
$482$		−	23.6668i		−	1.07799i
$483$	−13.5413	+	12.5572i	−0.616152	+	0.571374i
$484$		−	4.64013i		−	0.210915i
$485$	−6.93971			−0.315116
$486$	8.76267	+	12.8925i	0.397483	+	0.584814i
$487$	−15.4326	−	15.4326i	−0.699319	−	0.699319i	0.264944	−	0.964264i	$-0.414646\pi$
$487$	−15.4326	−	15.4326i	−0.699319	−	0.699319i	−0.964264	+	0.264944i	$0.914646\pi$
$488$			6.27806i			0.284194i
$489$	11.5339	−	10.6957i	0.521583	−	0.483678i
$490$	19.0499			0.860588
$491$		−	4.62335i		−	0.208649i	−0.994543	−	0.104324i	$-0.966732\pi$
$491$		−	4.62335i		−	0.208649i	0.994543	−	0.104324i	$-0.0332680\pi$
$492$	0.317859	−	8.42977i	0.0143302	−	0.380044i
$493$	21.5493			0.970530
$494$	−19.4102	+	19.4102i	−0.873307	+	0.873307i
$495$	5.73739	−	4.93165i	0.257876	−	0.221661i
$496$	2.75008	−	2.75008i	0.123482	−	0.123482i
$497$			6.96350i			0.312356i
$498$	12.3682	−	11.4694i	0.554233	−	0.513955i
$499$	6.56428	−	6.56428i	0.293858	−	0.293858i	−0.544744	−	0.838602i	$-0.683373\pi$
$499$	6.56428	−	6.56428i	0.293858	−	0.293858i	0.838602	+	0.544744i	$0.183373\pi$
$500$	0.707107	−	0.707107i	0.0316228	−	0.0316228i
$501$	−24.6181	+	22.8290i	−1.09985	+	1.01992i
$502$		−	1.15611i		−	0.0515998i
$503$	−2.11670	+	2.11670i	−0.0943789	+	0.0943789i	−0.752720	−	0.658341i	$-0.771259\pi$
$503$	−2.11670	+	2.11670i	−0.0943789	+	0.0943789i	0.658341	+	0.752720i	$0.271259\pi$
$504$	11.6116	−	9.98095i	0.517223	−	0.444587i
$505$	12.0210	−	12.0210i	0.534928	−	0.534928i
$506$	5.26830			0.234204
$507$	−2.18656	+	57.9885i	−0.0971083	+	2.57536i
$508$			13.6854i			0.607190i
$509$	−2.11394			−0.0936987			−0.0468493	−	0.998902i	$-0.514918\pi$
$509$	−2.11394			−0.0936987			−0.0468493	+	0.998902i	$0.514918\pi$
$510$	3.88203	−	3.59991i	0.171899	−	0.159407i
$511$			65.8309i			2.91219i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	13.0269	+	16.3643i	0.575152	+	0.722502i
$514$	8.30643			0.366381
$515$			6.74438i			0.297193i
$516$	11.4917	−	10.6566i	0.505895	−	0.469130i
$517$		−	0.174424i		−	0.00767114i
$518$	29.3870	+	10.0124i	1.29119	+	0.439921i
$519$	−21.2998	−	0.803144i	−0.934956	−	0.0352541i
$520$	−4.82201	+	4.82201i	−0.211459	+	0.211459i
$521$	−32.2201			−1.41159			−0.705794	−	0.708417i	$-0.749410\pi$
$521$	−32.2201			−1.41159			−0.705794	+	0.708417i	$0.749410\pi$
$522$	−1.59271	+	21.0897i	−0.0697112	+	0.923073i
$523$	6.90482	+	6.90482i	0.301927	+	0.301927i	0.841767	−	0.539841i	$-0.181515\pi$
$523$	6.90482	+	6.90482i	0.301927	+	0.301927i	−0.539841	+	0.841767i	$0.681515\pi$
$524$	1.16781	−	1.16781i	0.0510160	−	0.0510160i
$525$	−0.333099	+	8.83396i	−0.0145377	+	0.385546i
$526$	−16.3493	−	16.3493i	−0.712862	−	0.712862i
$527$			11.8880i			0.517848i
$528$	−4.36492	−	0.164587i	−0.189959	−	0.00716272i
$529$			18.6359i			0.810258i
$530$			4.54376i			0.197368i
$531$	−30.1045	+	25.8768i	−1.30643	+	1.12296i
$532$	14.5275	−	14.5275i	0.629847	−	0.629847i
$533$	−23.4850	−	23.4850i	−1.01725	−	1.01725i
$534$	0.668884	−	17.7391i	0.0289455	−	0.767647i
$535$	−12.4549	−	12.4549i	−0.538474	−	0.538474i
$536$	10.0167	+	10.0167i	0.432657	+	0.432657i
$537$	6.61917	+	7.13791i	0.285638	+	0.308023i
$538$	5.42757	−	5.42757i	0.233999	−	0.233999i
$539$	48.0416			2.06930
$540$	3.23623	+	4.06532i	0.139265	+	0.174944i
$541$	12.0638	+	12.0638i	0.518663	+	0.518663i	0.917167	−	0.398504i	$-0.130470\pi$
$541$	12.0638	+	12.0638i	0.518663	+	0.518663i	−0.398504	+	0.917167i	$0.630470\pi$
$542$	−5.50679	−	5.50679i	−0.236537	−	0.236537i
$543$	−23.9791	−	0.904175i	−1.02904	−	0.0388018i
$544$	−3.05666			−0.131053
$545$	−1.95457			−0.0837244
$546$	2.27152	−	60.2418i	0.0972121	−	2.57811i
$547$	−20.2713	+	20.2713i	−0.866737	+	0.866737i	−0.992110	−	0.125373i	$-0.959987\pi$
$547$	−20.2713	+	20.2713i	−0.866737	+	0.866737i	0.125373	+	0.992110i	$0.459987\pi$
$548$	−9.28520			−0.396644
$549$	14.2829	−	12.2770i	0.609578	−	0.523971i
$550$	1.78324	−	1.78324i	0.0760375	−	0.0760375i
$551$			28.3784i			1.20896i
$552$	−0.136338	+	3.61575i	−0.00580293	+	0.153896i
$553$	17.1686	+	17.1686i	0.730084	+	0.730084i
$554$	0.394892			0.0167774
$555$	−3.77115	+	9.83760i	−0.160077	+	0.417583i
$556$	−5.21169			−0.221025
$557$	−3.36050	−	3.36050i	−0.142389	−	0.142389i	0.632319	−	0.774708i	$-0.282103\pi$
$557$	−3.36050	−	3.36050i	−0.142389	−	0.142389i	−0.774708	+	0.632319i	$0.782103\pi$
$558$	−11.6345	−	0.878644i	−0.492527	−	0.0371960i
$559$		−	61.7045i		−	2.60982i
$560$	3.60901	−	3.60901i	0.152509	−	0.152509i
$561$	9.79001	−	9.07854i	0.413334	−	0.383296i
$562$	−12.1113			−0.510885
$563$	4.35089	−	4.35089i	0.183368	−	0.183368i	−0.609454	−	0.792822i	$-0.708611\pi$
$563$	4.35089	−	4.35089i	0.183368	−	0.183368i	0.792822	+	0.609454i	$0.208611\pi$
$564$	0.119711	+	0.00451390i	0.00504073	+	0.000190069i
$565$	6.80295			0.286202
$566$	−10.0604			−0.422870
$567$	−45.4142	−	6.89878i	−1.90722	−	0.289722i
$568$	0.964738	+	0.964738i	0.0404795	+	0.0404795i
$569$	25.7059	+	25.7059i	1.07765	+	1.07765i	0.996720	+	0.0809257i	$0.0257876\pi$
$569$	25.7059	+	25.7059i	1.07765	+	1.07765i	0.0809257	+	0.996720i	$0.474212\pi$
$570$	4.74075	+	5.11228i	0.198568	+	0.214130i
$571$	−24.4214			−1.02200			−0.511001	−	0.859580i	$-0.670725\pi$
$571$	−24.4214			−1.02200			−0.511001	+	0.859580i	$0.670725\pi$
$572$	−12.1605	+	12.1605i	−0.508456	+	0.508456i
$573$	−27.9829	+	25.9493i	−1.16900	+	1.08405i
$574$	17.5773	+	17.5773i	0.733662	+	0.733662i
$575$	−1.47717	−	1.47717i	−0.0616023	−	0.0616023i
$576$	0.225919	−	2.99148i	0.00941329	−	0.124645i
$577$	4.61472	+	4.61472i	0.192113	+	0.192113i	0.796609	−	0.604495i	$-0.206625\pi$
$577$	4.61472	+	4.61472i	0.192113	+	0.192113i	−0.604495	+	0.796609i	$0.706625\pi$
$578$	−5.41419	+	5.41419i	−0.225201	+	0.225201i
$579$	16.9805	+	18.3112i	0.705685	+	0.760989i
$580$			7.04993i			0.292733i
$581$			49.7048i			2.06210i
$582$	0.452910	−	12.0114i	0.0187737	−	0.497888i
$583$			11.4588i			0.474575i
$584$	9.12036	+	9.12036i	0.377403	+	0.377403i
$585$	20.3999	+	1.54062i	0.843434	+	0.0636968i
$586$	−15.8337	+	15.8337i	−0.654085	+	0.654085i
$587$	−3.92406	−	3.92406i	−0.161963	−	0.161963i	0.621473	−	0.783436i	$-0.286535\pi$
$587$	−3.92406	−	3.92406i	−0.161963	−	0.161963i	−0.783436	+	0.621473i	$0.786535\pi$
$588$	−1.24327	+	32.9720i	−0.0512714	+	1.35974i
$589$	−15.6554			−0.645068
$590$	−9.35679	+	9.35679i	−0.385213	+	0.385213i
$591$	1.21497	−	32.2215i	0.0499770	−	1.32541i
$592$	5.45849	−	2.68420i	0.224342	−	0.110320i
$593$			32.5461i			1.33651i	0.743934	+	0.668253i	$0.232958\pi$
$593$			32.5461i			1.33651i	−0.743934	+	0.668253i	$0.767042\pi$
$594$	8.16137	+	10.2522i	0.334865	+	0.420655i
$595$			15.6009i			0.639576i
$596$	−4.53764			−0.185869
$597$	19.7707	−	18.3339i	0.809161	−	0.750357i
$598$	10.0733	+	10.0733i	0.411930	+	0.411930i
$599$			15.7962i			0.645415i	0.946499	+	0.322707i	$0.104593\pi$
$599$			15.7962i			0.645415i	−0.946499	+	0.322707i	$0.895407\pi$
$600$	1.17773	+	1.27002i	0.0480805	+	0.0518485i
$601$	21.8320			0.890546			0.445273	−	0.895395i	$-0.353107\pi$
$601$	21.8320			0.890546			0.445273	+	0.895395i	$0.353107\pi$
$602$			46.1825i			1.88226i
$603$	3.20032	−	42.3767i	0.130327	−	1.72571i
$604$	4.08345			0.166153
$605$	−3.28107	+	3.28107i	−0.133394	+	0.133394i
$606$	20.0217	+	21.5908i	0.813325	+	0.877064i
$607$	25.8401	−	25.8401i	1.04882	−	1.04882i	0.0500729	−	0.998746i	$-0.484055\pi$
$607$	25.8401	−	25.8401i	1.04882	−	1.04882i	0.998746	−	0.0500729i	$-0.0159454\pi$
$608$		−	4.02534i		−	0.163249i
$609$	−42.3773	−	45.6983i	−1.71721	−	1.85179i
$610$	4.43926	−	4.43926i	0.179740	−	0.179740i
$611$	0.333510	−	0.333510i	0.0134924	−	0.0134924i
$612$	5.97745	+	6.95404i	0.241624	+	0.281100i
$613$		−	21.7834i		−	0.879822i	−0.898041	−	0.439911i	$-0.855010\pi$
$613$		−	21.7834i		−	0.879822i	0.898041	−	0.439911i	$-0.144990\pi$
$614$	10.3227	−	10.3227i	0.416590	−	0.416590i
$615$	−6.18551	+	5.73599i	−0.249424	+	0.231297i
$616$	9.10149	−	9.10149i	0.366709	−	0.366709i
$617$	10.9168			0.439496			0.219748	−	0.975557i	$-0.429477\pi$
$617$	10.9168			0.439496			0.219748	+	0.975557i	$0.429477\pi$
$618$	−11.6733	−	0.440162i	−0.469570	−	0.0177059i
$619$			38.1104i			1.53179i	0.642968	+	0.765893i	$0.277703\pi$
$619$			38.1104i			1.53179i	−0.642968	+	0.765893i	$0.722297\pi$
$620$	−3.88920			−0.156194
$621$	8.49261	−	6.76060i	0.340797	−	0.271293i
$622$			20.8237i			0.834955i
$623$	36.9887	+	36.9887i	1.48192	+	1.48192i
$624$	−8.03133	−	8.66073i	−0.321510	−	0.346707i
$625$	−1.00000			−0.0400000
$626$			0.175087i			0.00699787i
$627$	11.9556	+	12.8925i	0.477461	+	0.514878i
$628$			0.162952i			0.00650250i
$629$	−5.99631	+	17.5995i	−0.239088	+	0.701737i
$630$	−15.2683	−	1.15307i	−0.608302	−	0.0459394i
$631$	−17.9394	+	17.9394i	−0.714158	+	0.714158i	−0.967402	−	0.253244i	$-0.918502\pi$
$631$	−17.9394	+	17.9394i	−0.714158	+	0.714158i	0.253244	+	0.967402i	$0.418502\pi$
$632$	4.75715			0.189229
$633$	9.39613	+	0.354297i	0.373463	+	0.0140820i
$634$	−10.4870	−	10.4870i	−0.416493	−	0.416493i
$635$	9.67701	−	9.67701i	0.384020	−	0.384020i
$636$	−7.86443	−	0.296542i	−0.311845	−	0.0117586i
$637$	91.8588	+	91.8588i	3.63958	+	3.63958i
$638$			17.7791i			0.703880i
$639$	0.308232	−	4.08142i	0.0121935	−	0.161458i
$640$		−	1.00000i		−	0.0395285i
$641$			17.7585i			0.701418i	0.936484	+	0.350709i	$0.114059\pi$
$641$			17.7585i			0.701418i	−0.936484	+	0.350709i	$0.885941\pi$
$642$	22.3701	−	20.7444i	0.882879	−	0.818717i
$643$	10.8079	−	10.8079i	0.426221	−	0.426221i	−0.461118	−	0.887339i	$-0.652551\pi$
$643$	10.8079	−	10.8079i	0.426221	−	0.426221i	0.887339	+	0.461118i	$0.152551\pi$
$644$	−7.53936	−	7.53936i	−0.297092	−	0.297092i
$645$	−15.6612	−	0.590533i	−0.616660	−	0.0232522i
$646$	8.70031	+	8.70031i	0.342309	+	0.342309i
$647$	22.9188	+	22.9188i	0.901032	+	0.901032i	0.995525	−	0.0944933i	$-0.0301231\pi$
$647$	22.9188	+	22.9188i	0.901032	+	0.901032i	−0.0944933	+	0.995525i	$0.530123\pi$
$648$	−7.24755	+	5.33601i	−0.284711	+	0.209618i
$649$	−23.5967	+	23.5967i	−0.926251	+	0.926251i
$650$	6.81935			0.267477
$651$	25.2101	−	23.3780i	0.988064	−	0.916258i
$652$	6.42172	+	6.42172i	0.251494	+	0.251494i
$653$	8.84098	+	8.84098i	0.345974	+	0.345974i	0.858608	−	0.512633i	$-0.171330\pi$
$653$	8.84098	+	8.84098i	0.345974	+	0.345974i	−0.512633	+	0.858608i	$0.671330\pi$
$654$	0.127562	−	3.38300i	0.00498807	−	0.132286i
$655$	−1.65153			−0.0645307
$656$	4.87039			0.190157
$657$	2.91393	−	38.5845i	0.113683	−	1.50533i
$658$	−0.249614	+	0.249614i	−0.00973098	+	0.00973098i
$659$	19.8111			0.771732			0.385866	−	0.922555i	$-0.373903\pi$
$659$	19.8111			0.771732			0.385866	+	0.922555i	$0.373903\pi$
$660$	2.97008	+	3.20284i	0.115610	+	0.124671i
$661$	−12.4769	+	12.4769i	−0.485294	+	0.485294i	−0.906818	−	0.421523i	$-0.861496\pi$
$661$	−12.4769	+	12.4769i	−0.485294	+	0.485294i	0.421523	+	0.906818i	$0.361496\pi$
$662$		−	0.818200i		−	0.0318003i
$663$	36.0780	+	1.36038i	1.40115	+	0.0528328i
$664$	6.88621	+	6.88621i	0.267237	+	0.267237i
$665$	−20.5450			−0.796700
$666$	−16.7810	−	7.16923i	−0.650251	−	0.277802i
$667$	14.7276			0.570254
$668$	−13.7065	−	13.7065i	−0.530321	−	0.530321i
$669$	1.01273	+	0.0381867i	0.0391544	+	0.00147638i
$670$		−	14.1658i		−	0.547272i
$671$	11.1953	−	11.1953i	0.432188	−	0.432188i
$672$	6.01102	+	6.48209i	0.231880	+	0.250052i
$673$	17.8938			0.689754			0.344877	−	0.938648i	$-0.387921\pi$
$673$	17.8938			0.689754			0.344877	+	0.938648i	$0.387921\pi$
$674$	23.4976	−	23.4976i	0.905094	−	0.905094i
$675$	0.586260	−	5.16297i	0.0225652	−	0.198723i
$676$	−33.5035			−1.28860
$677$	1.54229			0.0592751			0.0296375	−	0.999561i	$-0.490565\pi$
$677$	1.54229			0.0592751			0.0296375	+	0.999561i	$0.490565\pi$
$678$	−0.443985	+	11.7747i	−0.0170511	+	0.452204i
$679$	25.0455	+	25.0455i	0.961158	+	0.961158i
$680$	2.16139	+	2.16139i	0.0828853	+	0.0828853i
$681$	−16.9356	+	15.7049i	−0.648976	+	0.601812i
$682$	−9.80809			−0.375571
$683$	8.13767	−	8.13767i	0.311379	−	0.311379i	−0.534064	−	0.845444i	$-0.679336\pi$
$683$	8.13767	−	8.13767i	0.311379	−	0.311379i	0.845444	+	0.534064i	$0.179336\pi$
$684$	−9.15783	+	7.87174i	−0.350158	+	0.300984i
$685$	6.56563	+	6.56563i	0.250860	+	0.250860i
$686$	−43.4883	−	43.4883i	−1.66039	−	1.66039i
$687$	−18.7801	−	0.708137i	−0.716507	−	0.0270171i
$688$	6.39822	+	6.39822i	0.243930	+	0.243930i
$689$	−21.9100	+	21.9100i	−0.834705	+	0.834705i
$690$	2.65313	−	2.46032i	0.101003	−	0.0936626i
$691$		−	32.6581i		−	1.24237i	−0.783663	−	0.621187i	$-0.786651\pi$
$691$		−	32.6581i		−	1.24237i	0.783663	−	0.621187i	$-0.213349\pi$
$692$		−	12.3062i		−	0.467810i
$693$	−38.5047	−	2.90790i	−1.46267	−	0.110462i
$694$		−	6.23882i		−	0.236822i
$695$	3.68522	+	3.68522i	0.139789	+	0.139789i
$696$	−12.2022	−	0.460104i	−0.462522	−	0.0174402i
$697$	−10.5268	+	10.5268i	−0.398731	+	0.398731i
$698$	10.5384	+	10.5384i	0.398883	+	0.398883i
$699$	−12.8916	−	0.486098i	−0.487603	−	0.0183859i
$700$	−5.10391			−0.192910
$701$	14.4490	−	14.4490i	0.545732	−	0.545732i	−0.379472	−	0.925203i	$-0.623894\pi$
$701$	14.4490	−	14.4490i	0.545732	−	0.545732i	0.925203	+	0.379472i	$0.123894\pi$
$702$	−3.99791	+	35.2081i	−0.150891	+	1.32884i
$703$	−23.1769	−	7.89658i	−0.874133	−	0.297825i
$704$		−	2.52188i		−	0.0950469i
$705$	−0.0814565	−	0.0878401i	−0.00306783	−	0.00330825i
$706$			26.3518i			0.991762i
$707$	−86.7680			−3.26324
$708$	−15.5843	−	16.8056i	−0.585693	−	0.631592i
$709$	−15.5170	−	15.5170i	−0.582752	−	0.582752i	0.352906	−	0.935659i	$-0.385193\pi$
$709$	−15.5170	−	15.5170i	−0.582752	−	0.582752i	−0.935659	+	0.352906i	$0.885193\pi$
$710$		−	1.36435i		−	0.0512030i
$711$	−9.30284	−	10.8227i	−0.348884	−	0.405885i
$712$	10.2490			0.384097
$713$			8.12469i			0.304272i
$714$	−27.0024	−	1.01817i	−1.01054	−	0.0381041i
$715$	17.1976			0.643152
$716$	−3.97415	+	3.97415i	−0.148521	+	0.148521i
$717$	35.0809	−	32.5314i	1.31012	−	1.21491i
$718$	6.71239	−	6.71239i	0.250504	−	0.250504i
$719$		−	29.0910i		−	1.08491i	−0.840085	−	0.542455i	$-0.817495\pi$
$719$		−	29.0910i		−	1.08491i	0.840085	−	0.542455i	$-0.182505\pi$
$720$	−2.27505	+	1.95555i	−0.0847859	+	0.0728790i
$721$	24.3406	−	24.3406i	0.906490	−	0.906490i
$722$	1.97752	−	1.97752i	0.0735958	−	0.0735958i
$723$	−27.8730	−	30.0574i	−1.03661	−	1.11785i
$724$		−	13.8542i		−	0.514888i
$725$	4.98506	−	4.98506i	0.185140	−	0.185140i
$726$	−5.46481	−	5.89307i	−0.202818	−	0.218712i
$727$	−16.8955	+	16.8955i	−0.626620	+	0.626620i	−0.947216	−	0.320596i	$-0.896117\pi$
$727$	−16.8955	+	16.8955i	−0.626620	+	0.626620i	0.320596	+	0.947216i	$0.396117\pi$
$728$	34.8053			1.28997
$729$	26.3126	+	6.05369i	0.974541	+	0.224211i
$730$		−	12.8981i		−	0.477381i
$731$	−27.6580			−1.02297
$732$	7.39384	+	7.97328i	0.273284	+	0.294701i
$733$			1.93766i			0.0715691i	0.999360	+	0.0357845i	$0.0113930\pi$
$733$			1.93766i			0.0715691i	−0.999360	+	0.0357845i	$0.988607\pi$
$734$	−3.59053	−	3.59053i	−0.132529	−	0.132529i
$735$	24.1939	−	22.4356i	0.892404	−	0.827550i
$736$	−2.08904			−0.0770029
$737$		−	35.7244i		−	1.31592i
$738$	−9.52428	−	11.0804i	−0.350594	−	0.407874i
$739$		−	20.9810i		−	0.771800i	−0.922541	−	0.385900i	$-0.873891\pi$
$739$		−	20.9810i		−	0.771800i	0.922541	−	0.385900i	$-0.126109\pi$
$740$	−5.75775	−	1.96172i	−0.211659	−	0.0721142i
$741$	−1.79150	+	47.5113i	−0.0658122	+	1.74537i
$742$	16.3985	−	16.3985i	0.602007	−	0.602007i
$743$	20.4459			0.750088			0.375044	−	0.927007i	$-0.377628\pi$
$743$	20.4459			0.750088			0.375044	+	0.927007i	$0.377628\pi$
$744$	0.253823	−	6.73151i	0.00930560	−	0.246789i
$745$	3.20860	+	3.20860i	0.117554	+	0.117554i
$746$	−1.82587	+	1.82587i	−0.0668499	+	0.0668499i
$747$	2.20013	−	29.1328i	0.0804985	−	1.06591i
$748$	5.45075	+	5.45075i	0.199299	+	0.199299i
$749$			89.9001i			3.28488i
$750$	0.0652635	−	1.73082i	0.00238309	−	0.0632006i
$751$			6.66294i			0.243134i	0.992583	+	0.121567i	$0.0387920\pi$
$751$			6.66294i			0.243134i	−0.992583	+	0.121567i	$0.961208\pi$
$752$			0.0691642i			0.00252216i
$753$	−1.36159	−	1.46829i	−0.0496189	−	0.0535075i
$754$	−33.9948	+	33.9948i	−1.23802	+	1.23802i
$755$	−2.88744	−	2.88744i	−0.105085	−	0.105085i
$756$	2.99222	−	26.3514i	0.108826	−	0.958390i
$757$	−25.6892	−	25.6892i	−0.933692	−	0.933692i	0.0642427	−	0.997934i	$-0.479537\pi$
$757$	−25.6892	−	25.6892i	−0.933692	−	0.933692i	−0.997934	+	0.0642427i	$0.979537\pi$
$758$	7.63207	+	7.63207i	0.277209	+	0.277209i
$759$	6.69086	−	6.20462i	0.242863	−	0.225213i
$760$	−2.84634	+	2.84634i	−0.103248	+	0.103248i
$761$	32.0342			1.16124			0.580619	−	0.814175i	$-0.302810\pi$
$761$	32.0342			1.16124			0.580619	+	0.814175i	$0.302810\pi$
$762$	16.1176	+	17.3807i	0.583880	+	0.629637i
$763$	7.05405	+	7.05405i	0.255374	+	0.255374i
$764$	−15.5800	−	15.5800i	−0.563663	−	0.563663i
$765$	0.690558	−	9.14394i	0.0249672	−	0.330600i
$766$	−8.14100			−0.294146
$767$	−90.2370			−3.25827
$768$	1.73082	+	0.0652635i	0.0624556	+	0.00235500i
$769$	−4.95008	+	4.95008i	−0.178504	+	0.178504i	−0.790704	−	0.612199i	$-0.790285\pi$
$769$	−4.95008	+	4.95008i	−0.178504	+	0.178504i	0.612199	+	0.790704i	$0.290285\pi$
$770$	−12.8714			−0.463855
$771$	10.5494	−	9.78271i	0.379926	−	0.352316i
$772$	−10.1951	+	10.1951i	−0.366929	+	0.366929i
$773$		−	24.3133i		−	0.874489i	−0.899343	−	0.437245i	$-0.855954\pi$
$773$		−	24.3133i		−	0.874489i	0.899343	−	0.437245i	$-0.144046\pi$
$774$	2.04421	−	27.0682i	0.0734778	−	0.972948i
$775$	2.75008	+	2.75008i	0.0987858	+	0.0987858i
$776$	6.93971			0.249121
$777$	49.1142	−	21.8939i	1.76196	−	0.785438i
$778$	32.5368			1.16650
$779$	−13.8628	−	13.8628i	−0.496687	−	0.496687i
$780$	−0.445055	+	11.8031i	−0.0159355	+	0.422618i
$781$		−	3.44071i		−	0.123118i
$782$	4.51521	−	4.51521i	0.161464	−	0.161464i
$783$	22.8152	+	28.6603i	0.815348	+	1.02423i
$784$	−19.0499			−0.680355
$785$	0.115225	−	0.115225i	0.00411254	−	0.00411254i
$786$	0.107785	−	2.85851i	0.00384456	−	0.101960i
$787$	−17.1843			−0.612556			−0.306278	−	0.951942i	$-0.599084\pi$
$787$	−17.1843			−0.612556			−0.306278	+	0.951942i	$0.599084\pi$
$788$	18.6163			0.663178
$789$	−40.0189	−	1.50898i	−1.42471	−	0.0537212i
$790$	−3.36382	−	3.36382i	−0.119679	−	0.119679i
$791$	−24.5519	−	24.5519i	−0.872966	−	0.872966i
$792$	−5.73739	+	4.93165i	−0.203869	+	0.175239i
$793$	42.8122			1.52031
$794$	5.80478	−	5.80478i	0.206004	−	0.206004i
$795$	5.35131	+	5.77068i	0.189791	+	0.204665i
$796$	11.0077	+	11.0077i	0.390156	+	0.390156i
$797$	−7.12438	−	7.12438i	−0.252358	−	0.252358i	0.569578	−	0.821937i	$-0.307106\pi$
$797$	−7.12438	−	7.12438i	−0.252358	−	0.252358i	−0.821937	+	0.569578i	$0.807106\pi$
$798$	1.34084	−	35.5597i	0.0474652	−	1.25880i
$799$	−0.149490	−	0.149490i	−0.00528859	−	0.00528859i
$800$	−0.707107	+	0.707107i	−0.0250000	+	0.0250000i
$801$	−20.0424	−	23.3169i	−0.708162	−	0.823861i
$802$			8.41293i			0.297071i
$803$		−	32.5275i		−	1.14787i
$804$	24.5184	+	0.924509i	0.864699	+	0.0326049i
$805$			10.6623i			0.375795i
$806$	−18.7537	−	18.7537i	−0.660573	−	0.660573i
$807$	0.500946	−	13.2853i	0.0176342	−	0.467666i
$808$	−12.0210	+	12.0210i	−0.422898	+	0.422898i
$809$	−5.02798	−	5.02798i	−0.176774	−	0.176774i	0.613174	−	0.789948i	$-0.289893\pi$
$809$	−5.02798	−	5.02798i	−0.176774	−	0.176774i	−0.789948	+	0.613174i	$0.789893\pi$
$810$	8.89792	+	1.35166i	0.312641	+	0.0474927i
$811$	17.0198			0.597645			0.298822	−	0.954309i	$-0.403406\pi$
$811$	17.0198			0.597645			0.298822	+	0.954309i	$0.403406\pi$
$812$	25.4433	−	25.4433i	0.892885	−	0.892885i
$813$	−13.4792	−	0.508258i	−0.472738	−	0.0178254i
$814$	−14.5203	−	4.94721i	−0.508938	−	0.173400i
$815$		−	9.08168i		−	0.318117i
$816$	−3.88203	+	3.59991i	−0.135898	+	0.126022i
$817$		−	36.4231i		−	1.27428i
$818$	25.2937			0.884374
$819$	−68.0635	−	79.1837i	−2.37833	−	2.76690i
$820$	−3.44389	−	3.44389i	−0.120266	−	0.120266i
$821$		−	8.34944i		−	0.291397i	−0.989329	−	0.145699i	$-0.953457\pi$
$821$		−	8.34944i		−	0.291397i	0.989329	−	0.145699i	$-0.0465430\pi$
$822$	−11.7924	+	10.9354i	−0.411308	+	0.381417i
$823$	−13.7886			−0.480641			−0.240321	−	0.970694i	$-0.577253\pi$
$823$	−13.7886			−0.480641			−0.240321	+	0.970694i	$0.577253\pi$
$824$		−	6.74438i		−	0.234952i
$825$	0.164587	−	4.36492i	0.00573017	−	0.151967i
$826$	67.5375			2.34993
$827$	−27.8494	+	27.8494i	−0.968420	+	0.968420i	−0.999516	−	0.0310964i	$-0.990100\pi$
$827$	−27.8494	+	27.8494i	−0.968420	+	0.968420i	0.0310964	+	0.999516i	$0.490100\pi$
$828$	4.08521	+	4.75265i	0.141971	+	0.165166i
$829$	−17.6252	+	17.6252i	−0.612150	+	0.612150i	−0.943506	−	0.331356i	$-0.892494\pi$
$829$	−17.6252	+	17.6252i	−0.612150	+	0.612150i	0.331356	+	0.943506i	$0.392494\pi$
$830$		−	9.73857i		−	0.338031i
$831$	0.501522	−	0.465075i	0.0173976	−	0.0161333i
$832$	4.82201	−	4.82201i	0.167173	−	0.167173i
$833$	41.1742	−	41.1742i	1.42660	−	1.42660i
$834$	−6.61897	+	6.13795i	−0.229196	+	0.212540i
$835$			19.3840i			0.670809i
$836$	−7.17814	+	7.17814i	−0.248261	+	0.248261i
$837$	−15.8109	+	12.5863i	−0.546503	+	0.435047i
$838$	−11.5710	+	11.5710i	−0.399714	+	0.399714i
$839$	24.9207			0.860359			0.430180	−	0.902743i	$-0.358450\pi$
$839$	24.9207			0.860359			0.430180	+	0.902743i	$0.358450\pi$
$840$	0.333099	−	8.83396i	0.0114930	−	0.304801i
$841$			20.7016i			0.713848i
$842$	−2.24702			−0.0774373
$843$	−15.3817	+	14.2638i	−0.529773	+	0.491273i
$844$			5.42872i			0.186864i
$845$	23.6905	+	23.6905i	0.814979	+	0.814979i
$846$	0.157352	−	0.135254i	0.00540986	−	0.00465012i
$847$	23.6828			0.813751
$848$		−	4.54376i		−	0.156033i
$849$	−12.7769	+	11.8484i	−0.438503	+	0.406636i
$850$		−	3.05666i		−	0.104843i
$851$	−4.09810	+	12.0281i	−0.140481	+	0.412320i
$852$	2.36144	+	0.0890421i	0.0809016	+	0.00305053i
$853$	17.6868	−	17.6868i	0.605585	−	0.605585i	−0.336204	−	0.941789i	$-0.609143\pi$
$853$	17.6868	−	17.6868i	0.605585	−	0.605585i	0.941789	+	0.336204i	$0.109143\pi$
$854$	−32.0427			−1.09648
$855$	12.0417	+	0.909401i	0.411818	+	0.0311008i
$856$	12.4549	+	12.4549i	0.425701	+	0.425701i
$857$	23.1778	−	23.1778i	0.791739	−	0.791739i	−0.190038	−	0.981777i	$-0.560861\pi$
$857$	23.1778	−	23.1778i	0.791739	−	0.791739i	0.981777	+	0.190038i	$0.0608611\pi$
$858$	−1.12237	+	29.7659i	−0.0383172	+	1.01619i
$859$	−26.4659	−	26.4659i	−0.903003	−	0.903003i	0.0926917	−	0.995695i	$-0.470453\pi$
$859$	−26.4659	−	26.4659i	−0.903003	−	0.903003i	−0.995695	+	0.0926917i	$0.970453\pi$
$860$		−	9.04844i		−	0.308549i
$861$	43.0248	+	1.62232i	1.46628	+	0.0552887i
$862$			18.1187i			0.617127i
$863$		−	14.7592i		−	0.502408i	−0.967934	−	0.251204i	$-0.919174\pi$
$863$		−	14.7592i		−	0.502408i	0.967934	−	0.251204i	$-0.0808265\pi$
$864$	−3.23623	−	4.06532i	−0.110099	−	0.138305i
$865$	−8.70178	+	8.70178i	−0.295869	+	0.295869i
$866$	7.14007	+	7.14007i	0.242629	+	0.242629i
$867$	−0.499712	+	13.2526i	−0.0169711	+	0.450082i
$868$	14.0362	+	14.0362i	0.476419	+	0.476419i
$869$	−8.48313	−	8.48313i	−0.287771	−	0.287771i
$870$	8.30290	+	8.95358i	0.281495	+	0.303555i
$871$	68.3075	−	68.3075i	2.31451	−	2.31451i
$872$	1.95457			0.0661900
$873$	−13.5709	−	15.7882i	−0.459307	−	0.534348i
$874$	5.94612	+	5.94612i	0.201131	+	0.201131i
$875$	3.60901	+	3.60901i	0.122007	+	0.122007i
$876$	22.3244	+	0.841778i	0.754270	+	0.0284410i
$877$	−33.6017			−1.13465			−0.567324	−	0.823495i	$-0.692021\pi$
$877$	−33.6017			−1.13465			−0.567324	+	0.823495i	$0.692021\pi$
$878$	1.07246			0.0361937
$879$	−1.46140	+	38.7570i	−0.0492918	+	1.30724i
$880$	−1.78324	+	1.78324i	−0.0601129	+	0.0601129i
$881$	52.1433			1.75675			0.878377	−	0.477969i	$-0.158627\pi$
$881$	52.1433			1.75675			0.878377	+	0.477969i	$0.158627\pi$
$882$	37.2530	+	43.3395i	1.25438	+	1.45932i
$883$	−29.7194	+	29.7194i	−1.00014	+	1.00014i	−0.000137791		1.00000i	$0.500044\pi$
$883$	−29.7194	+	29.7194i	−1.00014	+	1.00014i	−1.00000		0.000137791i	$0.999956\pi$
$884$			20.8444i			0.701074i
$885$	−0.863600	+	22.9031i	−0.0290296	+	0.769879i
$886$	−18.8008	−	18.8008i	−0.631626	−	0.631626i
$887$	−44.9094			−1.50791			−0.753955	−	0.656926i	$-0.771856\pi$
$887$	−44.9094			−1.50791			−0.753955	+	0.656926i	$0.771856\pi$
$888$	3.77115	−	9.83760i	0.126552	−	0.330128i
$889$	−69.8489			−2.34266
$890$	−7.24712	−	7.24712i	−0.242924	−	0.242924i
$891$	22.4395	+	3.40873i	0.751751	+	0.114197i
$892$			0.585115i			0.0195911i
$893$	0.196865	−	0.196865i	0.00658784	−	0.00658784i
$894$	−5.76291	+	5.34410i	−0.192741	+	0.178734i
$895$	5.62030			0.187866
$896$	−3.60901	+	3.60901i	−0.120569	+	0.120569i
$897$	24.6570	+	0.929736i	0.823275	+	0.0310430i
$898$	−17.7059			−0.590854
$899$	−27.4186			−0.914462
$900$	2.99148	+	0.225919i	0.0997160	+	0.00753063i
$901$	9.82081	+	9.82081i	0.327179	+	0.327179i
$902$	−8.68506	−	8.68506i	−0.289181	−	0.289181i
$903$	54.3903	+	58.6528i	1.81000	+	1.95184i
$904$	−6.80295			−0.226263
$905$	−9.79640	+	9.79640i	−0.325643	+	0.325643i
$906$	5.18608	−	4.80919i	0.172296	−	0.159775i
$907$	8.59972	+	8.59972i	0.285549	+	0.285549i	0.835317	−	0.549768i	$-0.185284\pi$
$907$	8.59972	+	8.59972i	0.285549	+	0.285549i	−0.549768	+	0.835317i	$0.685284\pi$
$908$	−9.42921	−	9.42921i	−0.312919	−	0.312919i
$909$	50.8560	+	3.84069i	1.68679	+	0.127388i
$910$	−24.6111	−	24.6111i	−0.815850	−	0.815850i
$911$	−23.2956	+	23.2956i	−0.771818	+	0.771818i	−0.978424	−	0.206606i	$-0.933758\pi$
$911$	−23.2956	+	23.2956i	−0.771818	+	0.771818i	0.206606	+	0.978424i	$0.433758\pi$
$912$	−4.74075	−	5.11228i	−0.156982	−	0.169284i
$913$		−	24.5595i		−	0.812801i
$914$			10.2082i			0.337659i
$915$	0.409728	−	10.8662i	0.0135452	−	0.359225i
$916$		−	10.8504i		−	0.358508i
$917$	5.96040	+	5.96040i	0.196830	+	0.196830i
$918$	15.7815	+	1.79200i	0.520866	+	0.0591447i
$919$	12.2237	−	12.2237i	0.403223	−	0.403223i	−0.476144	−	0.879367i	$-0.657966\pi$
$919$	12.2237	−	12.2237i	0.403223	−	0.403223i	0.879367	+	0.476144i	$0.157966\pi$
$920$	1.47717	+	1.47717i	0.0487009	+	0.0487009i
$921$	0.952749	−	25.2674i	0.0313941	−	0.832588i
$922$	26.1592			0.861506
$923$	6.57888	−	6.57888i	0.216547	−	0.216547i
$924$	0.840036	−	22.2782i	0.0276352	−	0.732898i
$925$	2.68420	+	5.45849i	0.0882559	+	0.179474i
$926$		−	28.6450i		−	0.941333i
$927$	−15.3438	+	13.1890i	−0.503956	+	0.433183i
$928$		−	7.04993i		−	0.231425i
$929$	19.8991			0.652870			0.326435	−	0.945220i	$-0.394153\pi$
$929$	19.8991			0.652870			0.326435	+	0.945220i	$0.394153\pi$
$930$	−4.93938	+	4.58042i	−0.161969	+	0.150198i
$931$	54.2227	+	54.2227i	1.77708	+	1.77708i
$932$		−	7.44823i		−	0.243975i
$933$	24.5247	+	26.4466i	0.802902	+	0.865824i
$934$	37.7956			1.23671
$935$		−	7.70853i		−	0.252096i
$936$	−20.3999	−	1.54062i	−0.666793	−	0.0503567i
$937$	−7.83086			−0.255823			−0.127911	−	0.991786i	$-0.540827\pi$
$937$	−7.83086			−0.255823			−0.127911	+	0.991786i	$0.540827\pi$
$938$	−51.1245	+	51.1245i	−1.66927	+	1.66927i
$939$	0.206204	+	0.222364i	0.00672922	+	0.00725658i
$940$	0.0489065	−	0.0489065i	0.00159515	−	0.00159515i
$941$		−	17.6003i		−	0.573754i	−0.957967	−	0.286877i	$-0.907383\pi$
$941$		−	17.6003i		−	0.573754i	0.957967	−	0.286877i	$-0.0926171\pi$
$942$	0.191913	+	0.206953i	0.00625287	+	0.00674289i
$943$	−7.19441	+	7.19441i	−0.234282	+	0.234282i
$944$	9.35679	−	9.35679i	0.304538	−	0.304538i
$945$	−20.7491	+	16.5174i	−0.674967	+	0.537311i
$946$		−	22.8191i		−	0.741912i
$947$	−9.57257	+	9.57257i	−0.311067	+	0.311067i	−0.845323	−	0.534256i	$-0.820592\pi$
$947$	−9.57257	+	9.57257i	−0.311067	+	0.311067i	0.534256	+	0.845323i	$0.320592\pi$
$948$	6.04170	−	5.60263i	0.196225	−	0.181965i
$949$	62.1949	−	62.1949i	2.01893	−	2.01893i
$950$	4.02534			0.130599
$951$	−25.6696	−	0.967918i	−0.832395	−	0.0313869i
$952$		−	15.6009i		−	0.505629i
$953$	−17.5365			−0.568062			−0.284031	−	0.958815i	$-0.591672\pi$
$953$	−17.5365			−0.568062			−0.284031	+	0.958815i	$0.591672\pi$
$954$	−10.3373	+	8.88554i	−0.334681	+	0.287680i
$955$			22.0334i			0.712984i
$956$	19.5319	+	19.5319i	0.631706	+	0.631706i
$957$	20.9389	+	22.5798i	0.676858	+	0.729903i
$958$	5.99642			0.193736
$959$		−	47.3908i		−	1.53033i
$960$	−1.17773	−	1.27002i	−0.0380110	−	0.0409898i
$961$			15.8741i			0.512068i
$962$	−18.3045	−	37.2233i	−0.590160	−	1.20013i
$963$	3.97933	−	52.6918i	0.128232	−	1.69797i
$964$	16.7350	−	16.7350i	0.538997	−	0.538997i
$965$	14.4180			0.464133
$966$	−18.4545	−	0.695857i	−0.593763	−	0.0223888i
$967$	10.5050	+	10.5050i	0.337819	+	0.337819i	0.855546	−	0.517727i	$-0.173222\pi$
$967$	10.5050	+	10.5050i	0.337819	+	0.337819i	−0.517727	+	0.855546i	$0.673222\pi$
$968$	3.28107	−	3.28107i	0.105457	−	0.105457i
$969$	21.2962	+	0.803009i	0.684132	+	0.0257964i
$970$	−4.90712	−	4.90712i	−0.157558	−	0.157558i
$971$			11.2038i			0.359547i	0.983708	+	0.179774i	$0.0575365\pi$
$971$			11.2038i			0.359547i	−0.983708	+	0.179774i	$0.942463\pi$
$972$	−2.92020	+	15.3125i	−0.0936654	+	0.491148i
$973$		−	26.6000i		−	0.852758i
$974$		−	21.8250i		−	0.699319i
$975$	8.66073	−	8.03133i	0.277365	−	0.257208i
$976$	−4.43926	+	4.43926i	−0.142097	+	0.142097i
$977$	24.3250	+	24.3250i	0.778227	+	0.778227i	0.979529	−	0.201302i	$-0.0645173\pi$
$977$	24.3250	+	24.3250i	0.778227	+	0.778227i	−0.201302	+	0.979529i	$0.564517\pi$
$978$	15.7188	+	0.592702i	0.502630	+	0.0189525i
$979$	−18.2764	−	18.2764i	−0.584115	−	0.584115i
$980$	13.4703	+	13.4703i	0.430294	+	0.430294i
$981$	−3.82225	−	4.44673i	−0.122035	−	0.141973i
$982$	3.26920	−	3.26920i	0.104324	−	0.104324i
$983$	18.1520			0.578959			0.289479	−	0.957184i	$-0.406518\pi$
$983$	18.1520			0.578959			0.289479	+	0.957184i	$0.406518\pi$
$984$	6.18551	−	5.73599i	0.197187	−	0.182857i
$985$	−13.1637	−	13.1637i	−0.419431	−	0.419431i
$986$	15.2376	+	15.2376i	0.485265	+	0.485265i
$987$	−0.0230385	+	0.610994i	−0.000733325	+	0.0194481i
$988$	−27.4502			−0.873307
$989$	−18.9025			−0.601066
$990$	7.54415	+	0.569740i	0.239769	+	0.0181075i
$991$	16.8673	−	16.8673i	0.535807	−	0.535807i	−0.386488	−	0.922295i	$-0.626312\pi$
$991$	16.8673	−	16.8673i	0.535807	−	0.535807i	0.922295	+	0.386488i	$0.126312\pi$
$992$	3.88920			0.123482
$993$	−0.963616	−	1.03913i	−0.0305794	−	0.0329759i
$994$	−4.92394	+	4.92394i	−0.156178	+	0.156178i
$995$		−	15.5672i		−	0.493513i
$996$	16.8557	+	0.635574i	0.534094	+	0.0201389i
$997$	7.90680	+	7.90680i	0.250411	+	0.250411i	0.821139	−	0.570728i	$-0.193339\pi$
$997$	7.90680	+	7.90680i	0.250411	+	0.250411i	−0.570728	+	0.821139i	$0.693339\pi$
$998$	9.28330			0.293858
$999$	−29.7557	+	10.6584i	−0.941428	+	0.337215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.u.e.191.15	yes	40
3.2	odd	2	inner	1110.2.u.e.191.1	✓	40
37.31	odd	4	inner	1110.2.u.e.401.1	yes	40
111.68	even	4	inner	1110.2.u.e.401.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.u.e.191.1	✓	40	3.2	odd	2	inner
1110.2.u.e.191.15	yes	40	1.1	even	1	trivial
1110.2.u.e.401.1	yes	40	37.31	odd	4	inner
1110.2.u.e.401.15	yes	40	111.68	even	4	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.17773 + 1.27002i) q^{6} -5.10391 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99148 + 0.225919i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(1.17773 + 1.27002i) q^{6} -5.10391 q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.99148 + 0.225919i) q^{9} +1.00000 q^{10} +2.52188 q^{11} +(-0.0652635 + 1.73082i) q^{12} +(4.82201 + 4.82201i) q^{13} +(-3.60901 - 3.60901i) q^{14} +(1.27002 - 1.17773i) q^{15} -1.00000 q^{16} +(2.16139 - 2.16139i) q^{17} +(1.95555 + 2.27505i) q^{18} +(2.84634 + 2.84634i) q^{19} +(0.707107 + 0.707107i) q^{20} +(-8.83396 - 0.333099i) q^{21} +(1.78324 + 1.78324i) q^{22} +(1.47717 - 1.47717i) q^{23} +(-1.27002 + 1.17773i) q^{24} -1.00000i q^{25} +6.81935i q^{26} +(5.16297 + 0.586260i) q^{27} -5.10391i q^{28} +(4.98506 + 4.98506i) q^{29} +(1.73082 + 0.0652635i) q^{30} +(-2.75008 + 2.75008i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.36492 + 0.164587i) q^{33} +3.05666 q^{34} +(-3.60901 + 3.60901i) q^{35} +(-0.225919 + 2.99148i) q^{36} +(-5.45849 + 2.68420i) q^{37} +4.02534i q^{38} +(8.03133 + 8.66073i) q^{39} +1.00000i q^{40} -4.87039 q^{41} +(-6.01102 - 6.48209i) q^{42} +(-6.39822 - 6.39822i) q^{43} +2.52188i q^{44} +(2.27505 - 1.95555i) q^{45} +2.08904 q^{46} -0.0691642i q^{47} +(-1.73082 - 0.0652635i) q^{48} +19.0499 q^{49} +(0.707107 - 0.707107i) q^{50} +(3.88203 - 3.59991i) q^{51} +(-4.82201 + 4.82201i) q^{52} +4.54376i q^{53} +(3.23623 + 4.06532i) q^{54} +(1.78324 - 1.78324i) q^{55} +(3.60901 - 3.60901i) q^{56} +(4.74075 + 5.11228i) q^{57} +7.04993i q^{58} +(-9.35679 + 9.35679i) q^{59} +(1.17773 + 1.27002i) q^{60} +(4.43926 - 4.43926i) q^{61} -3.88920 q^{62} +(-15.2683 - 1.15307i) q^{63} -1.00000i q^{64} +6.81935 q^{65} +(2.97008 + 3.20284i) q^{66} -14.1658i q^{67} +(2.16139 + 2.16139i) q^{68} +(2.65313 - 2.46032i) q^{69} -5.10391 q^{70} -1.36435i q^{71} +(-2.27505 + 1.95555i) q^{72} -12.8981i q^{73} +(-5.75775 - 1.96172i) q^{74} +(0.0652635 - 1.73082i) q^{75} +(-2.84634 + 2.84634i) q^{76} -12.8714 q^{77} +(-0.445055 + 11.8031i) q^{78} +(-3.36382 - 3.36382i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(8.89792 + 1.35166i) q^{81} +(-3.44389 - 3.44389i) q^{82} -9.73857i q^{83} +(0.333099 - 8.83396i) q^{84} -3.05666i q^{85} -9.04844i q^{86} +(8.30290 + 8.95358i) q^{87} +(-1.78324 + 1.78324i) q^{88} +(-7.24712 - 7.24712i) q^{89} +(2.99148 + 0.225919i) q^{90} +(-24.6111 - 24.6111i) q^{91} +(1.47717 + 1.47717i) q^{92} +(-4.93938 + 4.58042i) q^{93} +(0.0489065 - 0.0489065i) q^{94} +4.02534 q^{95} +(-1.17773 - 1.27002i) q^{96} +(-4.90712 - 4.90712i) q^{97} +(13.4703 + 13.4703i) q^{98} +(7.54415 + 0.569740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{7} - 8 q^{9}+O(q^{10}) \) 40 * q - 24 * q^7 - 8 * q^9	\( 40 q - 24 q^{7} - 8 q^{9} + 40 q^{10} - 8 q^{12} - 16 q^{13} - 40 q^{16} + 8 q^{18} + 16 q^{19} - 24 q^{31} + 24 q^{33} - 8 q^{34} + 16 q^{39} - 20 q^{42} - 32 q^{43} - 8 q^{45} + 72 q^{46} + 96 q^{49} + 20 q^{51} + 16 q^{52} + 24 q^{54} - 16 q^{57} + 40 q^{61} - 24 q^{63} - 44 q^{66} - 24 q^{70} + 8 q^{72} + 8 q^{75} - 16 q^{76} + 48 q^{79} + 24 q^{81} - 56 q^{82} - 8 q^{84} + 12 q^{87} - 8 q^{90} - 64 q^{91} + 12 q^{93} + 24 q^{94} + 8 q^{97}+O(q^{100}) \) 40 * q - 24 * q^7 - 8 * q^9 + 40 * q^10 - 8 * q^12 - 16 * q^13 - 40 * q^16 + 8 * q^18 + 16 * q^19 - 24 * q^31 + 24 * q^33 - 8 * q^34 + 16 * q^39 - 20 * q^42 - 32 * q^43 - 8 * q^45 + 72 * q^46 + 96 * q^49 + 20 * q^51 + 16 * q^52 + 24 * q^54 - 16 * q^57 + 40 * q^61 - 24 * q^63 - 44 * q^66 - 24 * q^70 + 8 * q^72 + 8 * q^75 - 16 * q^76 + 48 * q^79 + 24 * q^81 - 56 * q^82 - 8 * q^84 + 12 * q^87 - 8 * q^90 - 64 * q^91 + 12 * q^93 + 24 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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