LMFDB - Embedded newform 1110.2.u.e.191.1

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			191.1
Character	$\chi$	$=$	1110.191
Dual form			1110.2.u.e.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.27002 + 1.17773i) q^{6} -5.10391 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99148 - 0.225919i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.27002 + 1.17773i) 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} +(1.17773 - 1.27002i) q^{15} -1.00000 q^{16} +(-2.16139 + 2.16139i) q^{17} +(-2.27505 - 1.95555i) 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} +(-1.17773 + 1.27002i) 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} +(-8.66073 - 8.03133i) q^{39} +1.00000i q^{40} +4.87039 q^{41} +(-6.48209 - 6.01102i) q^{42} +(-6.39822 - 6.39822i) q^{43} -2.52188i q^{44} +(-1.95555 + 2.27505i) 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} +(3.59991 - 3.88203i) q^{51} +(-4.82201 + 4.82201i) q^{52} -4.54376i q^{53} +(4.06532 + 3.23623i) q^{54} +(1.78324 - 1.78324i) q^{55} +(-3.60901 + 3.60901i) q^{56} +(-5.11228 - 4.74075i) q^{57} +7.04993i q^{58} +(9.35679 - 9.35679i) q^{59} +(1.27002 + 1.17773i) 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} +(-3.20284 - 2.97008i) q^{66} -14.1658i q^{67} +(-2.16139 - 2.16139i) q^{68} +(2.46032 - 2.65313i) q^{69} -5.10391 q^{70} +1.36435i q^{71} +(1.95555 - 2.27505i) 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} +(8.95358 + 8.30290i) 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} +(4.58042 - 4.93938i) q^{93} +(0.0489065 - 0.0489065i) q^{94} -4.02534 q^{95} +(-1.27002 - 1.17773i) 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
$6$	1.27002	+	1.17773i	0.518485	+	0.480805i
$7$	−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	$-0.624141\pi$
$11$	−2.52188			−0.760375			−0.380187	+	0.924909i	$0.624141\pi$
$12$	−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
$15$	1.17773	−	1.27002i	0.304088	−	0.327919i
$16$	−1.00000			−0.250000
$17$	−2.16139	+	2.16139i	−0.524213	+	0.524213i	−0.918841	−	0.394628i	$-0.870873\pi$
$17$	−2.16139	+	2.16139i	−0.524213	+	0.524213i	0.394628	+	0.918841i	$0.370873\pi$
$18$	−2.27505	−	1.95555i	−0.536233	−	0.460927i
$19$	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	−0.844138	−	0.536126i	$-0.819887\pi$
$23$	−1.47717	+	1.47717i	−0.308012	+	0.308012i	0.536126	+	0.844138i	$0.319887\pi$
$24$	−1.17773	+	1.27002i	−0.240402	+	0.259242i
$25$		−	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	0.0717228	−	0.997425i	$-0.477150\pi$
$29$	−4.98506	−	4.98506i	−0.925702	−	0.925702i	−0.997425	+	0.0717228i	$0.977150\pi$
$30$	−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
$39$	−8.66073	−	8.03133i	−1.38683	−	1.28604i
$40$			1.00000i			0.158114i
$41$	4.87039			0.760627			0.380314	−	0.924858i	$-0.375816\pi$
$41$	4.87039			0.760627			0.380314	+	0.924858i	$0.375816\pi$
$42$	−6.48209	−	6.01102i	−1.00021	−	0.927520i
$43$	−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
$45$	−1.95555	+	2.27505i	−0.291516	+	0.339144i
$46$	2.08904			0.308012
$47$			0.0691642i			0.0100886i	0.999987	+	0.00504432i	$0.00160566\pi$
$47$			0.0691642i			0.0100886i	−0.999987	+	0.00504432i	$0.998394\pi$
$48$	1.73082	−	0.0652635i	0.249822	−	0.00941998i
$49$	19.0499			2.72142
$50$	−0.707107	+	0.707107i	−0.100000	+	0.100000i
$51$	3.59991	−	3.88203i	0.504088	−	0.543593i
$52$	−4.82201	+	4.82201i	−0.668692	+	0.668692i
$53$		−	4.54376i		−	0.624133i	−0.950060	−	0.312067i	$-0.898979\pi$
$53$		−	4.54376i		−	0.624133i	0.950060	−	0.312067i	$-0.101021\pi$
$54$	4.06532	+	3.23623i	0.553220	+	0.440395i
$55$	1.78324	−	1.78324i	0.240452	−	0.240452i
$56$	−3.60901	+	3.60901i	−0.482274	+	0.482274i
$57$	−5.11228	−	4.74075i	−0.677137	−	0.627928i
$58$			7.04993i			0.925702i
$59$	9.35679	−	9.35679i	1.21815	−	1.21815i	0.249871	−	0.968279i	$-0.419612\pi$
$59$	9.35679	−	9.35679i	1.21815	−	1.21815i	0.968279	−	0.249871i	$-0.0803882\pi$
$60$	1.27002	+	1.17773i	0.163959	+	0.152044i
$61$	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
$66$	−3.20284	−	2.97008i	−0.394243	−	0.365592i
$67$		−	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
$69$	2.46032	−	2.65313i	0.296187	−	0.319399i
$70$	−5.10391			−0.610034
$71$			1.36435i			0.161918i	0.996717	+	0.0809590i	$0.0257983\pi$
$71$			1.36435i			0.161918i	−0.996717	+	0.0809590i	$0.974202\pi$
$72$	1.95555	−	2.27505i	0.230464	−	0.268117i
$73$		−	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	$0.179490\pi$
$83$			9.73857i			1.06895i	−0.845185	+	0.534474i	$0.820510\pi$
$84$	0.333099	+	8.83396i	0.0363441	+	0.963864i
$85$		−	3.05666i		−	0.331541i
$86$			9.04844i			0.975719i
$87$	8.95358	+	8.30290i	0.959925	+	0.890164i
$88$	−1.78324	+	1.78324i	−0.190094	+	0.190094i
$89$	7.24712	+	7.24712i	0.768193	+	0.768193i	0.977788	−	0.209595i	$-0.0672146\pi$
$89$	7.24712	+	7.24712i	0.768193	+	0.768193i	−0.209595	+	0.977788i	$0.567215\pi$
$90$	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
$93$	4.58042	−	4.93938i	0.474967	−	0.512190i
$94$	0.0489065	−	0.0489065i	0.00504432	−	0.00504432i
$95$	−4.02534			−0.412991
$96$	−1.27002	−	1.17773i	−0.129621	−	0.120201i
$97$	−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	$-0.820874\pi$
$101$	−17.0003			−1.69159			−0.845796	+	0.533507i	$0.820874\pi$
$102$	−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
$105$	−6.01102	+	6.48209i	−0.586615	+	0.632587i
$106$	−3.21292	+	3.21292i	−0.312067	+	0.312067i
$107$			17.6140i			1.70280i	0.524513	+	0.851402i	$0.324247\pi$
$107$			17.6140i			1.70280i	−0.524513	+	0.851402i	$0.675753\pi$
$108$	−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
$111$	9.27248	−	5.00211i	0.880105	−	0.474779i
$112$	5.10391			0.482274
$113$	−4.81041	−	4.81041i	−0.452526	−	0.452526i	0.443666	−	0.896192i	$-0.353678\pi$
$113$	−4.81041	−	4.81041i	−0.452526	−	0.452526i	−0.896192	+	0.443666i	$0.853678\pi$
$114$	0.262708	+	6.96714i	0.0246049	+	0.652533i
$115$		−	2.08904i		−	0.194804i
$116$	4.98506	−	4.98506i	0.462851	−	0.462851i
$117$	15.5143	+	13.3356i	1.43430	+	1.23287i
$118$	−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
$126$	11.6116	+	9.98095i	1.03445	+	0.889173i
$127$	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
$129$	11.4917	+	10.6566i	1.01179	+	0.938261i
$130$	4.82201	+	4.82201i	0.422918	+	0.422918i
$131$	1.16781	+	1.16781i	0.102032	+	0.102032i	0.756280	−	0.654248i	$-0.227015\pi$
$131$	1.16781	+	1.16781i	0.102032	+	0.102032i	−0.654248	+	0.756280i	$0.727015\pi$
$132$	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
$135$	3.23623	−	4.06532i	0.278530	−	0.349887i
$136$			3.05666i			0.262106i
$137$		−	9.28520i		−	0.793288i	−0.917973	−	0.396644i	$-0.870175\pi$
$137$		−	9.28520i		−	0.793288i	0.917973	−	0.396644i	$-0.129825\pi$
$138$	−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	$-0.940490\pi$
$149$		−	4.53764i		−	0.371738i	0.982575	−	0.185869i	$-0.0595100\pi$
$150$	1.17773	−	1.27002i	0.0961610	−	0.103697i
$151$		−	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
$153$	−5.97745	+	6.95404i	−0.483248	+	0.562201i
$154$	−9.10149	−	9.10149i	−0.733419	−	0.733419i
$155$		−	3.88920i		−	0.312388i
$156$	8.03133	−	8.66073i	0.643021	−	0.693413i
$157$	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
$162$	−7.24755	−	5.33601i	−0.569421	−	0.419236i
$163$	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
$165$	−2.97008	+	3.20284i	−0.231221	+	0.249341i
$166$	6.88621	−	6.88621i	0.534474	−	0.534474i
$167$	13.7065	−	13.7065i	1.06064	−	1.06064i	0.0626045	−	0.998038i	$-0.480059\pi$
$167$	13.7065	−	13.7065i	1.06064	−	1.06064i	0.998038	−	0.0626045i	$-0.0199407\pi$
$168$	6.01102	−	6.48209i	0.463760	−	0.500104i
$169$			33.5035i			2.57719i
$170$	−2.16139	+	2.16139i	−0.165771	+	0.165771i
$171$	9.15783	+	7.87174i	0.700317	+	0.601967i
$172$	6.39822	−	6.39822i	0.487859	−	0.487859i
$173$	12.3062			0.935621			0.467810	−	0.883829i	$-0.345043\pi$
$173$	12.3062			0.935621			0.467810	+	0.883829i	$0.345043\pi$
$174$	−0.460104	−	12.2022i	−0.0348804	−	0.925044i
$175$			5.10391i			0.385820i
$176$	2.52188			0.190094
$177$	−15.5843	+	16.8056i	−1.17139	+	1.26318i
$178$		−	10.2490i		−	0.768193i
$179$	−3.97415	−	3.97415i	−0.297042	−	0.297042i	0.542812	−	0.839854i	$-0.317360\pi$
$179$	−3.97415	−	3.97415i	−0.297042	−	0.297042i	−0.839854	+	0.542812i	$0.817360\pi$
$180$	−2.27505	−	1.95555i	−0.169572	−	0.145758i
$181$	−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
$183$	−7.39384	+	7.97328i	−0.546568	+	0.589402i
$184$			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	$-0.456345\pi$
$191$	15.5800	−	15.5800i	1.12733	−	1.12733i	0.990610	−	0.136716i	$-0.0436547\pi$
$192$	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	$0.230793\pi$
$197$			18.6163i			1.32636i	−0.748462	+	0.663178i	$0.769207\pi$
$198$	5.73739	+	4.93165i	0.407738	+	0.350477i
$199$	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
$204$	3.88203	+	3.59991i	0.271797	+	0.252044i
$205$	−3.44389	+	3.44389i	−0.240531	+	0.240531i
$206$	6.74438			0.469904
$207$	−4.08521	+	4.75265i	−0.283942	+	0.330332i
$208$	−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
$216$	−3.23623	+	4.06532i	−0.220197	+	0.276610i
$217$	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
$222$	−10.0937	−	3.01961i	−0.677442	−	0.202663i
$223$	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	−0.321180	−	0.947018i	$-0.604079\pi$
$227$	9.42921	−	9.42921i	0.625838	−	0.625838i	0.947018	+	0.321180i	$0.104079\pi$
$228$	4.74075	−	5.11228i	0.313964	−	0.338569i
$229$	−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	$-0.421549\pi$
$233$	7.44823			0.487950			0.243975	+	0.969782i	$0.421549\pi$
$234$	−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
$237$	6.04170	+	5.60263i	0.392450	+	0.363930i
$238$	−15.6009			−1.01126
$239$	−19.5319	+	19.5319i	−1.26341	+	1.26341i	−0.313982	+	0.949429i	$0.601663\pi$
$239$	−19.5319	+	19.5319i	−1.26341	+	1.26341i	−0.949429	+	0.313982i	$0.898337\pi$
$240$	−1.17773	+	1.27002i	−0.0760219	+	0.0819797i
$241$	−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
$246$	6.18551	+	5.73599i	0.394374	+	0.365713i
$247$			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	0.732436	−	0.680836i	$-0.238383\pi$
$251$	0.817495	+	0.817495i	0.0515998	+	0.0515998i	−0.680836	+	0.732436i	$0.738383\pi$
$252$	−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	−0.866156	−	0.499775i	$-0.833416\pi$
$257$	−5.87353	+	5.87353i	−0.366381	+	0.366381i	0.499775	+	0.866156i	$0.333416\pi$
$258$	−0.590533	−	15.6612i	−0.0367650	−	0.975026i
$259$	27.8596	−	13.6999i	1.73111	−	0.851271i
$260$		−	6.81935i		−	0.422918i
$261$	−16.0389	−	13.7865i	−0.992784	−	0.853362i
$262$		−	1.65153i		−	0.102032i
$263$	23.1214			1.42572			0.712862	−	0.701304i	$-0.247399\pi$
$263$	23.1214			1.42572			0.712862	+	0.701304i	$0.247399\pi$
$264$	2.97008	−	3.20284i	0.182796	−	0.197121i
$265$	3.21292	+	3.21292i	0.197368	+	0.197368i
$266$			20.5450i			1.25969i
$267$	−13.0164	−	12.0705i	−0.796593	−	0.738702i
$268$	14.1658			0.865313
$269$			7.67575i			0.467999i	0.972237	+	0.233999i	$0.0751813\pi$
$269$			7.67575i			0.467999i	−0.972237	+	0.233999i	$0.924819\pi$
$270$	−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
$273$	44.2036	+	40.9912i	2.67532	+	2.48090i
$274$	−6.56563	+	6.56563i	−0.396644	+	0.396644i
$275$			2.52188i			0.152075i
$276$	2.65313	+	2.46032i	0.159699	+	0.148094i
$277$	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
$279$	−7.60552	+	8.84811i	−0.455331	+	0.529723i
$280$		−	5.10391i		−	0.305017i
$281$	8.56400	−	8.56400i	0.510885	−	0.510885i	−0.403912	−	0.914798i	$-0.632350\pi$
$281$	8.56400	−	8.56400i	0.510885	−	0.510885i	0.914798	+	0.403912i	$0.132350\pi$
$282$	−0.0814565	+	0.0878401i	−0.00485066	+	0.00523080i
$283$	−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
$288$	2.27505	+	1.95555i	0.134058	+	0.115232i
$289$			7.65683i			0.450402i
$290$	−4.98506	−	4.98506i	−0.292733	−	0.292733i
$291$	8.81360	+	8.17309i	0.516662	+	0.479115i
$292$	12.8981			0.754806
$293$		−	22.3923i		−	1.30817i	−0.756421	−	0.654085i	$-0.773054\pi$
$293$		−	22.3923i		−	1.30817i	0.756421	−	0.654085i	$-0.226946\pi$
$294$	24.1939	+	22.4356i	1.41101	+	1.30847i
$295$			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
$309$	7.94304	−	8.56553i	0.451864	−	0.487276i
$310$	−2.75008	+	2.75008i	−0.156194	+	0.156194i
$311$	−14.7246	−	14.7246i	−0.834955	−	0.834955i	0.153234	−	0.988190i	$-0.451031\pi$
$311$	−14.7246	−	14.7246i	−0.834955	−	0.834955i	−0.988190	+	0.153234i	$0.951031\pi$
$312$	−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
$315$	9.98095	−	11.6116i	0.562363	−	0.654241i
$316$	3.36382	−	3.36382i	0.189229	−	0.189229i
$317$	14.8309			0.832987			0.416493	−	0.909139i	$-0.363259\pi$
$317$	14.8309			0.832987			0.416493	+	0.909139i	$0.363259\pi$
$318$	5.35131	−	5.77068i	0.300086	−	0.323604i
$319$	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
$327$	2.48235	+	2.30195i	0.137274	+	0.127298i
$328$	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
$333$	−15.7226	+	9.26290i	−0.861590	+	0.507604i
$334$	−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
$339$	8.63991	+	8.01202i	0.469255	+	0.435153i
$340$	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	0.815533	−	0.578711i	$-0.196444\pi$
$347$	4.41151	+	4.41151i	0.236822	+	0.236822i	−0.578711	+	0.815533i	$0.696444\pi$
$348$	−8.30290	+	8.95358i	−0.445082	+	0.479962i
$349$	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
$351$	−27.7228	−	22.0689i	−1.47974	−	1.17795i
$352$	−1.78324	−	1.78324i	−0.0950469	−	0.0950469i
$353$	−18.6335	−	18.6335i	−0.991762	−	0.991762i	0.00820423	−	0.999966i	$-0.497388\pi$
$353$	−18.6335	−	18.6335i	−0.991762	−	0.991762i	−0.999966	+	0.00820423i	$0.997388\pi$
$354$	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
$357$	−18.3736	+	19.8135i	−0.972436	+	1.04864i
$358$			5.62030i			0.297042i
$359$			9.49276i			0.501009i	0.968115	+	0.250504i	$0.0805964\pi$
$359$			9.49276i			0.501009i	−0.968115	+	0.250504i	$0.919404\pi$
$360$	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
$372$	4.93938	+	4.58042i	0.256095	+	0.237484i
$373$			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
$375$	−1.27002	−	1.17773i	−0.0655837	−	0.0608176i
$376$	0.0489065	+	0.0489065i	0.00252216	+	0.00252216i
$377$		−	48.0759i		−	2.47604i
$378$	−20.7491	−	16.5174i	−1.06722	−	0.849564i
$379$	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	−0.544570	−	0.838716i	$-0.683307\pi$
$383$	5.75655	−	5.75655i	0.294146	−	0.294146i	0.838716	+	0.544570i	$0.183307\pi$
$384$	1.17773	−	1.27002i	0.0601006	−	0.0648106i
$385$	−9.10149	+	9.10149i	−0.463855	+	0.463855i
$386$		−	14.4180i		−	0.733858i
$387$	−20.5856	−	17.6947i	−1.04643	−	0.899470i
$388$	4.90712	−	4.90712i	0.249121	−	0.249121i
$389$	−23.0070	+	23.0070i	−1.16650	+	1.16650i	−0.183478	+	0.983024i	$0.558736\pi$
$389$	−23.0070	+	23.0070i	−1.16650	+	1.16650i	−0.983024	+	0.183478i	$0.941264\pi$
$390$	−8.66073	−	8.03133i	−0.438553	−	0.406682i
$391$		−	6.38548i		−	0.322927i
$392$	13.4703	−	13.4703i	0.680355	−	0.680355i
$393$	−2.09748	−	1.94505i	−0.105804	−	0.0981150i
$394$	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
$399$	26.0926	+	24.1964i	1.30626	+	1.21133i
$400$			1.00000i			0.0500000i
$401$	−5.94884	−	5.94884i	−0.297071	−	0.297071i	0.542795	−	0.839866i	$-0.317366\pi$
$401$	−5.94884	−	5.94884i	−0.297071	−	0.297071i	−0.839866	+	0.542795i	$0.817366\pi$
$402$	16.6834	−	17.9909i	0.832094	−	0.897304i
$403$	−26.5218			−1.32115
$404$		−	17.0003i		−	0.845796i
$405$	−5.33601	+	7.24755i	−0.265148	+	0.360134i
$406$		−	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	$-0.869109\pi$
$419$		−	16.3639i		−	0.799429i	0.916640	−	0.399714i	$-0.130891\pi$
$420$	−6.48209	−	6.01102i	−0.316294	−	0.293308i
$421$	−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
$426$	−1.60683	+	1.73275i	−0.0778510	+	0.0839521i
$427$	−22.6576	+	22.6576i	−1.09648	+	1.09648i
$428$	−17.6140			−0.851402
$429$	21.8413	+	20.2540i	1.05451	+	0.977874i
$430$	−6.39822	−	6.39822i	−0.308549	−	0.308549i
$431$	−12.8119	−	12.8119i	−0.617127	−	0.617127i	0.327666	−	0.944793i	$-0.393738\pi$
$431$	−12.8119	−	12.8119i	−0.617127	−	0.617127i	−0.944793	+	0.327666i	$0.893738\pi$
$432$	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
$438$	15.1905	−	16.3809i	0.725829	−	0.782711i
$439$	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	$-0.282388\pi$
$443$	26.5884			1.26325			0.631626	+	0.775273i	$0.282388\pi$
$444$	5.00211	+	9.27248i	0.237389	+	0.440053i
$445$	−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	−0.347008	−	0.937862i	$-0.612802\pi$
$449$	12.5200	−	12.5200i	0.590854	−	0.590854i	0.937862	+	0.347008i	$0.112802\pi$
$450$	−1.95555	+	2.27505i	−0.0921854	+	0.107247i
$451$	−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
$459$	9.89204	−	12.4263i	0.461721	−	0.580010i
$460$	2.08904			0.0974019
$461$	−18.4973	+	18.4973i	−0.861506	+	0.861506i	−0.991513	−	0.130007i	$-0.958500\pi$
$461$	−18.4973	+	18.4973i	−0.861506	+	0.861506i	0.130007	+	0.991513i	$0.458500\pi$
$462$	16.3470	+	15.1590i	0.760533	+	0.705263i
$463$	−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	$0.588802\pi$
$467$	−26.7256	+	26.7256i	−1.23671	+	1.23671i	−0.961337	+	0.275374i	$0.911198\pi$
$468$	−13.3356	+	15.5143i	−0.616436	+	0.717150i
$469$			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	−0.797308	−	0.603572i	$-0.793743\pi$
$479$	−4.24011	+	4.24011i	−0.193736	+	0.193736i	0.603572	+	0.797308i	$0.293743\pi$
$480$	1.73082	−	0.0652635i	0.0790008	−	0.00297886i
$481$	−39.2641	−	13.3776i	−1.79029	−	0.609968i
$482$			23.6668i			1.07799i
$483$	−12.5572	+	13.5413i	−0.571374	+	0.616152i
$484$		−	4.64013i		−	0.210915i
$485$	6.93971			0.315116
$486$	12.8925	+	8.76267i	0.584814	+	0.397483i
$487$	−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
$489$	−10.6957	+	11.5339i	−0.483678	+	0.521583i
$490$	19.0499			0.860588
$491$			4.62335i			0.208649i	0.994543	+	0.104324i	$0.0332680\pi$
$491$			4.62335i			0.208649i	−0.994543	+	0.104324i	$0.966732\pi$
$492$	−0.317859	−	8.42977i	−0.0143302	−	0.380044i
$493$	21.5493			0.970530
$494$	19.4102	−	19.4102i	0.873307	−	0.873307i
$495$	4.93165	−	5.73739i	0.221661	−	0.257876i
$496$	2.75008	−	2.75008i	0.123482	−	0.123482i
$497$		−	6.96350i		−	0.312356i
$498$	−11.4694	+	12.3682i	−0.513955	+	0.554233i
$499$	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
$501$	−22.8290	+	24.6181i	−1.01992	+	1.09985i
$502$		−	1.15611i		−	0.0515998i
$503$	2.11670	−	2.11670i	0.0943789	−	0.0943789i	−0.658341	−	0.752720i	$-0.728741\pi$
$503$	2.11670	−	2.11670i	0.0943789	−	0.0943789i	0.752720	+	0.658341i	$0.228741\pi$
$504$	−9.98095	+	11.6116i	−0.444587	+	0.517223i
$505$	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	$-0.485082\pi$
$509$	2.11394			0.0936987			0.0468493	+	0.998902i	$0.485082\pi$
$510$	3.59991	−	3.88203i	0.159407	−	0.171899i
$511$			65.8309i			2.91219i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−16.3643	−	13.0269i	−0.722502	−	0.575152i
$514$	8.30643			0.366381
$515$		−	6.74438i		−	0.297193i
$516$	−10.6566	+	11.4917i	−0.469130	+	0.505895i
$517$		−	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	$-0.250590\pi$
$521$	32.2201			1.41159			0.705794	+	0.708417i	$0.250590\pi$
$522$	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
$531$	25.8768	−	30.1045i	1.12296	−	1.30643i
$532$	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
$537$	7.13791	+	6.61917i	0.308023	+	0.285638i
$538$	5.42757	−	5.42757i	0.233999	−	0.233999i
$539$	−48.0416			−2.06930
$540$	4.06532	+	3.23623i	0.174944	+	0.139265i
$541$	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
$549$	12.2770	−	14.2829i	0.523971	−	0.609578i
$550$	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
$555$	−3.01961	+	10.0937i	−0.128175	+	0.428452i
$556$	−5.21169			−0.221025
$557$	3.36050	+	3.36050i	0.142389	+	0.142389i	0.774708	−	0.632319i	$-0.217897\pi$
$557$	3.36050	+	3.36050i	0.142389	+	0.142389i	−0.632319	+	0.774708i	$0.717897\pi$
$558$	11.6345	−	0.878644i	0.492527	−	0.0371960i
$559$		−	61.7045i		−	2.60982i
$560$	−3.60901	+	3.60901i	−0.152509	+	0.152509i
$561$	−9.07854	+	9.79001i	−0.383296	+	0.413334i
$562$	−12.1113			−0.510885
$563$	−4.35089	+	4.35089i	−0.183368	+	0.183368i	−0.792822	−	0.609454i	$-0.791389\pi$
$563$	−4.35089	+	4.35089i	−0.183368	+	0.183368i	0.609454	+	0.792822i	$0.291389\pi$
$564$	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	$-0.974212\pi$
$569$	−25.7059	−	25.7059i	−1.07765	−	1.07765i	−0.0809257	−	0.996720i	$-0.525788\pi$
$570$	−5.11228	−	4.74075i	−0.214130	−	0.198568i
$571$	−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
$573$	−25.9493	+	27.9829i	−1.08405	+	1.16900i
$574$	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
$579$	−18.3112	−	16.9805i	−0.760989	−	0.705685i
$580$			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	0.783436	−	0.621473i	$-0.213465\pi$
$587$	3.92406	+	3.92406i	0.161963	+	0.161963i	−0.621473	+	0.783436i	$0.713465\pi$
$588$	−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	$-0.767042\pi$
$593$		−	32.5461i		−	1.33651i	0.743934	−	0.668253i	$-0.232958\pi$
$594$	−10.2522	−	8.16137i	−0.420655	−	0.334865i
$595$			15.6009i			0.639576i
$596$	4.53764			0.185869
$597$	−18.3339	+	19.7707i	−0.750357	+	0.809161i
$598$	10.0733	+	10.0733i	0.411930	+	0.411930i
$599$		−	15.7962i		−	0.645415i	−0.946499	−	0.322707i	$-0.895407\pi$
$599$		−	15.7962i		−	0.645415i	0.946499	−	0.322707i	$-0.104593\pi$
$600$	1.27002	+	1.17773i	0.0518485	+	0.0480805i
$601$	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
$606$	−21.5908	−	20.0217i	−0.877064	−	0.813325i
$607$	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
$609$	−45.6983	−	42.3773i	−1.85179	−	1.71721i
$610$	4.43926	−	4.43926i	0.179740	−	0.179740i
$611$	−0.333510	+	0.333510i	−0.0134924	+	0.0134924i
$612$	−6.95404	−	5.97745i	−0.281100	−	0.241624i
$613$		−	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
$615$	5.73599	−	6.18551i	0.231297	−	0.249424i
$616$	9.10149	−	9.10149i	0.366709	−	0.366709i
$617$	−10.9168			−0.439496			−0.219748	−	0.975557i	$-0.570523\pi$
$617$	−10.9168			−0.439496			−0.219748	+	0.975557i	$0.570523\pi$
$618$	−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
$621$	6.76060	−	8.49261i	0.271293	−	0.340797i
$622$			20.8237i			0.834955i
$623$	−36.9887	−	36.9887i	−1.48192	−	1.48192i
$624$	8.66073	+	8.03133i	0.346707	+	0.321510i
$625$	−1.00000			−0.0400000
$626$		−	0.175087i		−	0.00699787i
$627$	12.8925	+	11.9556i	0.514878	+	0.477461i
$628$			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	$-0.885941\pi$
$641$		−	17.7585i		−	0.701418i	0.936484	−	0.350709i	$-0.114059\pi$
$642$	−20.7444	+	22.3701i	−0.818717	+	0.882879i
$643$	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	0.0944933	−	0.995525i	$-0.469877\pi$
$647$	−22.9188	−	22.9188i	−0.901032	−	0.901032i	−0.995525	+	0.0944933i	$0.969877\pi$
$648$	5.33601	−	7.24755i	0.209618	−	0.284711i
$649$	−23.5967	+	23.5967i	−0.926251	+	0.926251i
$650$	−6.81935			−0.267477
$651$	−23.3780	+	25.2101i	−0.916258	+	0.988064i
$652$	6.42172	+	6.42172i	0.251494	+	0.251494i
$653$	−8.84098	−	8.84098i	−0.345974	−	0.345974i	0.512633	−	0.858608i	$-0.328670\pi$
$653$	−8.84098	−	8.84098i	−0.345974	−	0.345974i	−0.858608	+	0.512633i	$0.828670\pi$
$654$	−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	$-0.626097\pi$
$659$	−19.8111			−0.771732			−0.385866	+	0.922555i	$0.626097\pi$
$660$	−3.20284	−	2.97008i	−0.124671	−	0.115610i
$661$	−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
$666$	17.6674	+	4.56766i	0.684597	+	0.176993i
$667$	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
$672$	6.48209	+	6.01102i	0.250052	+	0.231880i
$673$	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	$-0.509435\pi$
$677$	−1.54229			−0.0592751			−0.0296375	+	0.999561i	$0.509435\pi$
$678$	−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
$681$	−15.7049	+	16.9356i	−0.601812	+	0.648976i
$682$	−9.80809			−0.375571
$683$	−8.13767	+	8.13767i	−0.311379	+	0.311379i	−0.845444	−	0.534064i	$-0.820664\pi$
$683$	−8.13767	+	8.13767i	−0.311379	+	0.311379i	0.534064	+	0.845444i	$0.320664\pi$
$684$	−7.87174	+	9.15783i	−0.300984	+	0.350158i
$685$	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
$690$	2.46032	−	2.65313i	0.0936626	−	0.101003i
$691$		−	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	−0.925203	−	0.379472i	$-0.876106\pi$
$701$	−14.4490	+	14.4490i	−0.545732	+	0.545732i	0.379472	+	0.925203i	$0.376106\pi$
$702$	3.99791	+	35.2081i	0.150891	+	1.32884i
$703$	−23.1769	−	7.89658i	−0.874133	−	0.297825i
$704$			2.52188i			0.0950469i
$705$	0.0878401	+	0.0814565i	0.00330825	+	0.00306783i
$706$			26.3518i			0.991762i
$707$	86.7680			3.26324
$708$	−16.8056	−	15.5843i	−0.631592	−	0.585693i
$709$	−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
$711$	−10.8227	−	9.30284i	−0.405885	−	0.348884i
$712$	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
$717$	32.5314	−	35.0809i	1.21491	−	1.31012i
$718$	6.71239	−	6.71239i	0.250504	−	0.250504i
$719$			29.0910i			1.08491i	0.840085	+	0.542455i	$0.182505\pi$
$719$			29.0910i			1.08491i	−0.840085	+	0.542455i	$0.817495\pi$
$720$	1.95555	−	2.27505i	0.0728790	−	0.0847859i
$721$	24.3406	−	24.3406i	0.906490	−	0.906490i
$722$	−1.97752	+	1.97752i	−0.0735958	+	0.0735958i
$723$	30.0574	+	27.8730i	1.11785	+	1.03661i
$724$		−	13.8542i		−	0.514888i
$725$	−4.98506	+	4.98506i	−0.185140	+	0.185140i
$726$	−5.89307	−	5.46481i	−0.218712	−	0.202818i
$727$	−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
$732$	−7.97328	−	7.39384i	−0.294701	−	0.273284i
$733$			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
$735$	22.4356	−	24.1939i	0.827550	−	0.892404i
$736$	−2.08904			−0.0770029
$737$			35.7244i			1.31592i
$738$	−11.0804	−	9.52428i	−0.407874	−	0.350594i
$739$		−	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	$-0.622372\pi$
$743$	−20.4459			−0.750088			−0.375044	+	0.927007i	$0.622372\pi$
$744$	−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
$753$	−1.46829	−	1.36159i	−0.0535075	−	0.0496189i
$754$	−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
$759$	−6.20462	+	6.69086i	−0.225213	+	0.242863i
$760$	−2.84634	+	2.84634i	−0.103248	+	0.103248i
$761$	−32.0342			−1.16124			−0.580619	−	0.814175i	$-0.697190\pi$
$761$	−32.0342			−1.16124			−0.580619	+	0.814175i	$0.697190\pi$
$762$	17.3807	+	16.1176i	0.629637	+	0.583880i
$763$	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
$771$	9.78271	−	10.5494i	0.352316	−	0.379926i
$772$	−10.1951	+	10.1951i	−0.366929	+	0.366929i
$773$			24.3133i			0.874489i	0.899343	+	0.437245i	$0.144046\pi$
$773$			24.3133i			0.874489i	−0.899343	+	0.437245i	$0.855954\pi$
$774$	2.04421	+	27.0682i	0.0734778	+	0.972948i
$775$	2.75008	+	2.75008i	0.0987858	+	0.0987858i
$776$	−6.93971			−0.249121
$777$	−47.3259	+	25.5303i	−1.69781	+	0.915895i
$778$	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
$783$	28.6603	+	22.8152i	1.02423	+	0.815348i
$784$	−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
$792$	−4.93165	+	5.73739i	−0.175239	+	0.203869i
$793$	42.8122			1.52031
$794$	−5.80478	+	5.80478i	−0.206004	+	0.206004i
$795$	−5.77068	−	5.35131i	−0.204665	−	0.189791i
$796$	11.0077	+	11.0077i	0.390156	+	0.390156i
$797$	7.12438	+	7.12438i	0.252358	+	0.252358i	0.821937	−	0.569578i	$-0.192894\pi$
$797$	7.12438	+	7.12438i	0.252358	+	0.252358i	−0.569578	+	0.821937i	$0.692894\pi$
$798$	−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
$801$	23.3169	+	20.0424i	0.823861	+	0.708162i
$802$			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	0.789948	−	0.613174i	$-0.210107\pi$
$809$	5.02798	+	5.02798i	0.176774	+	0.176774i	−0.613174	+	0.789948i	$0.710107\pi$
$810$	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
$816$	−3.59991	+	3.88203i	−0.126022	+	0.135898i
$817$		−	36.4231i		−	1.27428i
$818$	−25.2937			−0.884374
$819$	−79.1837	−	68.0635i	−2.76690	−	2.37833i
$820$	−3.44389	−	3.44389i	−0.120266	−	0.120266i
$821$			8.34944i			0.291397i	0.989329	+	0.145699i	$0.0465430\pi$
$821$			8.34944i			0.291397i	−0.989329	+	0.145699i	$0.953457\pi$
$822$	10.9354	−	11.7924i	0.381417	−	0.411308i
$823$	−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	−0.0310964	−	0.999516i	$-0.509900\pi$
$827$	27.8494	−	27.8494i	0.968420	−	0.968420i	0.999516	+	0.0310964i	$0.00989989\pi$
$828$	−4.75265	−	4.08521i	−0.165166	−	0.141971i
$829$	−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
$831$	−0.465075	+	0.501522i	−0.0161333	+	0.0173976i
$832$	4.82201	−	4.82201i	0.167173	−	0.167173i
$833$	−41.1742	+	41.1742i	−1.42660	+	1.42660i
$834$	−6.13795	+	6.61897i	−0.212540	+	0.229196i
$835$			19.3840i			0.670809i
$836$	7.17814	−	7.17814i	0.248261	−	0.248261i
$837$	12.5863	−	15.8109i	0.435047	−	0.546503i
$838$	−11.5710	+	11.5710i	−0.399714	+	0.399714i
$839$	−24.9207			−0.860359			−0.430180	−	0.902743i	$-0.641550\pi$
$839$	−24.9207			−0.860359			−0.430180	+	0.902743i	$0.641550\pi$
$840$	0.333099	+	8.83396i	0.0114930	+	0.304801i
$841$			20.7016i			0.713848i
$842$	2.24702			0.0774373
$843$	−14.2638	+	15.3817i	−0.491273	+	0.529773i
$844$			5.42872i			0.186864i
$845$	−23.6905	−	23.6905i	−0.814979	−	0.814979i
$846$	0.135254	−	0.157352i	0.00465012	−	0.00540986i
$847$	23.6828			0.813751
$848$			4.54376i			0.156033i
$849$	11.8484	−	12.7769i	0.406636	−	0.438503i
$850$		−	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	−0.981777	−	0.190038i	$-0.939139\pi$
$857$	−23.1778	+	23.1778i	−0.791739	+	0.791739i	0.190038	+	0.981777i	$0.439139\pi$
$858$	−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	$0.0808265\pi$
$863$			14.7592i			0.502408i	−0.967934	+	0.251204i	$0.919174\pi$
$864$	−4.06532	−	3.23623i	−0.138305	−	0.110099i
$865$	−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
$870$	8.95358	+	8.30290i	0.303555	+	0.281495i
$871$	68.3075	−	68.3075i	2.31451	−	2.31451i
$872$	−1.95457			−0.0661900
$873$	−15.7882	−	13.5709i	−0.534348	−	0.459307i
$874$	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	$-0.841373\pi$
$881$	−52.1433			−1.75675			−0.878377	+	0.477969i	$0.841373\pi$
$882$	−43.3395	−	37.2530i	−1.45932	−	1.25438i
$883$	−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	$-0.228144\pi$
$887$	44.9094			1.50791			0.753955	+	0.656926i	$0.228144\pi$
$888$	3.01961	−	10.0937i	0.101332	−	0.338721i
$889$	−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
$894$	5.34410	−	5.76291i	0.178734	−	0.192741i
$895$	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
$903$	−58.6528	−	54.3903i	−1.95184	−	1.81000i
$904$	−6.80295			−0.226263
$905$	9.79640	−	9.79640i	0.325643	−	0.325643i
$906$	4.80919	−	5.18608i	0.159775	−	0.172296i
$907$	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	−0.206606	−	0.978424i	$-0.566242\pi$
$911$	23.2956	−	23.2956i	0.771818	−	0.771818i	0.978424	+	0.206606i	$0.0662419\pi$
$912$	5.11228	+	4.74075i	0.169284	+	0.156982i
$913$		−	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
$927$	−13.1890	+	15.3438i	−0.433183	+	0.503956i
$928$		−	7.04993i		−	0.231425i
$929$	−19.8991			−0.652870			−0.326435	−	0.945220i	$-0.605847\pi$
$929$	−19.8991			−0.652870			−0.326435	+	0.945220i	$0.605847\pi$
$930$	4.58042	−	4.93938i	0.150198	−	0.161969i
$931$	54.2227	+	54.2227i	1.77708	+	1.77708i
$932$			7.44823i			0.243975i
$933$	26.4466	+	24.5247i	0.865824	+	0.802902i
$934$	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
$939$	−0.222364	−	0.206204i	−0.00725658	−	0.00672922i
$940$	0.0489065	−	0.0489065i	0.00159515	−	0.00159515i
$941$			17.6003i			0.573754i	0.957967	+	0.286877i	$0.0926171\pi$
$941$			17.6003i			0.573754i	−0.957967	+	0.286877i	$0.907383\pi$
$942$	0.206953	+	0.191913i	0.00674289	+	0.00625287i
$943$	−7.19441	+	7.19441i	−0.234282	+	0.234282i
$944$	−9.35679	+	9.35679i	−0.304538	+	0.304538i
$945$	−16.5174	+	20.7491i	−0.537311	+	0.674967i
$946$		−	22.8191i		−	0.741912i
$947$	9.57257	−	9.57257i	0.311067	−	0.311067i	−0.534256	−	0.845323i	$-0.679408\pi$
$947$	9.57257	−	9.57257i	0.311067	−	0.311067i	0.845323	+	0.534256i	$0.179408\pi$
$948$	−5.60263	+	6.04170i	−0.181965	+	0.196225i
$949$	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	$-0.408328\pi$
$953$	17.5365			0.568062			0.284031	+	0.958815i	$0.408328\pi$
$954$	−8.88554	+	10.3373i	−0.287680	+	0.334681i
$955$			22.0334i			0.712984i
$956$	−19.5319	−	19.5319i	−0.631706	−	0.631706i
$957$	−22.5798	−	20.9389i	−0.729903	−	0.676858i
$958$	5.99642			0.193736
$959$			47.3908i			1.53033i
$960$	−1.27002	−	1.17773i	−0.0409898	−	0.0380110i
$961$			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	$-0.942463\pi$
$971$		−	11.2038i		−	0.359547i	0.983708	−	0.179774i	$-0.0575365\pi$
$972$	−2.92020	−	15.3125i	−0.0936654	−	0.491148i
$973$		−	26.6000i		−	0.852758i
$974$			21.8250i			0.699319i
$975$	−8.03133	+	8.66073i	−0.257208	+	0.277365i
$976$	−4.43926	+	4.43926i	−0.142097	+	0.142097i
$977$	−24.3250	−	24.3250i	−0.778227	−	0.778227i	0.201302	−	0.979529i	$-0.435483\pi$
$977$	−24.3250	−	24.3250i	−0.778227	−	0.778227i	−0.979529	+	0.201302i	$0.935483\pi$
$978$	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
$981$	−4.44673	−	3.82225i	−0.141973	−	0.122035i
$982$	3.26920	−	3.26920i	0.104324	−	0.104324i
$983$	−18.1520			−0.578959			−0.289479	−	0.957184i	$-0.593482\pi$
$983$	−18.1520			−0.578959			−0.289479	+	0.957184i	$0.593482\pi$
$984$	−5.73599	+	6.18551i	−0.182857	+	0.197187i
$985$	−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
$993$	1.03913	+	0.963616i	0.0329759	+	0.0305794i
$994$	−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
$999$	26.6084	−	17.0585i	0.841852	−	0.539708i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.27002 + 1.17773i) q^{6} -5.10391 q^{7} +(0.707107 - 0.707107i) q^{8} +(2.99148 - 0.225919i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.73082 + 0.0652635i) q^{3} +1.00000i q^{4} +(-0.707107 + 0.707107i) q^{5} +(1.27002 + 1.17773i) 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} +(1.17773 - 1.27002i) q^{15} -1.00000 q^{16} +(-2.16139 + 2.16139i) q^{17} +(-2.27505 - 1.95555i) 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} +(-1.17773 + 1.27002i) 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} +(-8.66073 - 8.03133i) q^{39} +1.00000i q^{40} +4.87039 q^{41} +(-6.48209 - 6.01102i) q^{42} +(-6.39822 - 6.39822i) q^{43} -2.52188i q^{44} +(-1.95555 + 2.27505i) 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} +(3.59991 - 3.88203i) q^{51} +(-4.82201 + 4.82201i) q^{52} -4.54376i q^{53} +(4.06532 + 3.23623i) q^{54} +(1.78324 - 1.78324i) q^{55} +(-3.60901 + 3.60901i) q^{56} +(-5.11228 - 4.74075i) q^{57} +7.04993i q^{58} +(9.35679 - 9.35679i) q^{59} +(1.27002 + 1.17773i) 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} +(-3.20284 - 2.97008i) q^{66} -14.1658i q^{67} +(-2.16139 - 2.16139i) q^{68} +(2.46032 - 2.65313i) q^{69} -5.10391 q^{70} +1.36435i q^{71} +(1.95555 - 2.27505i) 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} +(8.95358 + 8.30290i) 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} +(4.58042 - 4.93938i) q^{93} +(0.0489065 - 0.0489065i) q^{94} -4.02534 q^{95} +(-1.27002 - 1.17773i) 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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