LMFDB - Embedded newform 1710.2.t.c.919.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.t (of order $6$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			919.10
Root			$1.78384 - 0.477979i$ of defining polynomial
Character	$\chi$	$=$	1710.919
Dual form			1710.2.t.c.1189.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.22489 + 0.223342i) q^{5} +1.07560i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.22489 + 0.223342i) q^{5} +1.07560i q^{7} -1.00000i q^{8} +(2.03848 - 0.919023i) q^{10} -0.410555 q^{11} +(3.30892 + 1.91041i) q^{13} +(0.537799 + 0.931495i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.08642 + 0.627244i) q^{17} +(3.85480 - 2.03482i) q^{19} +(1.30586 - 1.81514i) q^{20} +(-0.355551 + 0.205277i) q^{22} +(-3.23263 - 1.86636i) q^{23} +(4.90024 + 0.993820i) q^{25} +3.82081 q^{26} +(0.931495 + 0.537799i) q^{28} +(-1.18789 + 2.05749i) q^{29} +7.75919 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.627244 + 1.08642i) q^{34} +(-0.240226 + 2.39308i) q^{35} -2.08017i q^{37} +(2.32094 - 3.68961i) q^{38} +(0.223342 - 2.22489i) q^{40} +(2.80171 + 4.85270i) q^{41} +(-1.92233 + 1.10986i) q^{43} +(-0.205277 + 0.355551i) q^{44} -3.73273 q^{46} +(3.58819 + 2.07164i) q^{47} +5.84309 q^{49} +(4.74064 - 1.58945i) q^{50} +(3.30892 - 1.91041i) q^{52} +(-4.32940 - 2.49958i) q^{53} +(-0.913438 - 0.0916940i) q^{55} +1.07560 q^{56} +2.37579i q^{58} +(-1.25650 - 2.17633i) q^{59} +(-3.37731 + 5.84967i) q^{61} +(6.71965 - 3.87959i) q^{62} -1.00000 q^{64} +(6.93529 + 4.98945i) q^{65} +(-8.07251 - 4.66066i) q^{67} +1.25449i q^{68} +(0.988499 + 2.19258i) q^{70} +(-4.79760 - 8.30969i) q^{71} +(6.02521 - 3.47866i) q^{73} +(-1.04009 - 1.80148i) q^{74} +(0.165192 - 4.35577i) q^{76} -0.441592i q^{77} +(4.47277 + 7.74707i) q^{79} +(-0.919023 - 2.03848i) q^{80} +(4.85270 + 2.80171i) q^{82} -9.12070i q^{83} +(-2.55725 + 1.15290i) q^{85} +(-1.10986 + 1.92233i) q^{86} +0.410555i q^{88} +(2.72783 - 4.72474i) q^{89} +(-2.05483 + 3.55906i) q^{91} +(-3.23263 + 1.86636i) q^{92} +4.14328 q^{94} +(9.03096 - 3.66631i) q^{95} +(-10.5315 + 6.08034i) q^{97} +(5.06026 - 2.92155i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4}+O(q^{10}) $ 20 * q + 10 * q^4	$ 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.22489	+	0.223342i	0.994999	+	0.0998815i
$5$	2.22489	+	0.223342i	0.994999	+	0.0998815i
$6$		0			0
$7$			1.07560i			0.406538i	0.979123	+	0.203269i	$0.0651565\pi$
$7$			1.07560i			0.406538i	−0.979123	+	0.203269i	$0.934843\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.03848	−	0.919023i	0.644624	−	0.290621i
$11$	−0.410555			−0.123787			−0.0618935	−	0.998083i	$-0.519714\pi$
$11$	−0.410555			−0.123787			−0.0618935	+	0.998083i	$0.519714\pi$
$12$		0			0
$13$	3.30892	+	1.91041i	0.917729	+	0.529851i	0.882910	−	0.469543i	$-0.155581\pi$
$13$	3.30892	+	1.91041i	0.917729	+	0.529851i	0.0348191	+	0.999394i	$0.488914\pi$
$14$	0.537799	+	0.931495i	0.143733	+	0.248952i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.08642	+	0.627244i	−0.263495	+	0.152129i	−0.625928	−	0.779881i	$-0.715280\pi$
$17$	−1.08642	+	0.627244i	−0.263495	+	0.152129i	0.362433	+	0.932010i	$0.381946\pi$
$18$		0			0
$19$	3.85480	−	2.03482i	0.884352	−	0.466820i
$19$	3.85480	−	2.03482i	0.884352	−	0.466820i
$20$	1.30586	−	1.81514i	0.292000	−	0.405877i
$21$		0			0
$22$	−0.355551	+	0.205277i	−0.0758037	+	0.0437653i
$23$	−3.23263	−	1.86636i	−0.674051	−	0.389164i	0.123559	−	0.992337i	$-0.460569\pi$
$23$	−3.23263	−	1.86636i	−0.674051	−	0.389164i	−0.797610	+	0.603174i	$0.793903\pi$
$24$		0			0
$25$	4.90024	+	0.993820i	0.980047	+	0.198764i
$26$	3.82081			0.749323
$27$		0			0
$28$	0.931495	+	0.537799i	0.176036	+	0.101634i
$29$	−1.18789	+	2.05749i	−0.220586	+	0.382067i	−0.954986	−	0.296650i	$-0.904130\pi$
$29$	−1.18789	+	2.05749i	−0.220586	+	0.382067i	0.734400	+	0.678717i	$0.237464\pi$
$30$		0			0
$31$	7.75919			1.39359			0.696796	−	0.717270i	$-0.254608\pi$
$31$	7.75919			1.39359			0.696796	+	0.717270i	$0.254608\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−0.627244	+	1.08642i	−0.107571	+	0.186319i
$35$	−0.240226	+	2.39308i	−0.0406056	+	0.404505i
$36$		0			0
$37$		−	2.08017i		−	0.341978i	−0.985273	−	0.170989i	$-0.945304\pi$
$37$		−	2.08017i		−	0.341978i	0.985273	−	0.170989i	$-0.0546963\pi$
$38$	2.32094	−	3.68961i	0.376507	−	0.598534i
$39$		0			0
$40$	0.223342	−	2.22489i	0.0353134	−	0.351785i
$41$	2.80171	+	4.85270i	0.437554	+	0.757865i	0.997500	−	0.0706636i	$-0.0225117\pi$
$41$	2.80171	+	4.85270i	0.437554	+	0.757865i	−0.559947	+	0.828529i	$0.689178\pi$
$42$		0			0
$43$	−1.92233	+	1.10986i	−0.293153	+	0.169252i	−0.639363	−	0.768905i	$-0.720802\pi$
$43$	−1.92233	+	1.10986i	−0.293153	+	0.169252i	0.346210	+	0.938157i	$0.387469\pi$
$44$	−0.205277	+	0.355551i	−0.0309467	+	0.0536013i
$45$		0			0
$46$	−3.73273			−0.550360
$47$	3.58819	+	2.07164i	0.523391	+	0.302180i	0.738321	−	0.674450i	$-0.235619\pi$
$47$	3.58819	+	2.07164i	0.523391	+	0.302180i	−0.214930	+	0.976629i	$0.568952\pi$
$48$		0			0
$49$	5.84309			0.834727
$50$	4.74064	−	1.58945i	0.670428	−	0.224781i
$51$		0			0
$52$	3.30892	−	1.91041i	0.458864	−	0.264926i
$53$	−4.32940	−	2.49958i	−0.594689	−	0.343344i	0.172261	−	0.985051i	$-0.444893\pi$
$53$	−4.32940	−	2.49958i	−0.594689	−	0.343344i	−0.766949	+	0.641708i	$0.778226\pi$
$54$		0			0
$55$	−0.913438	−	0.0916940i	−0.123168	−	0.0123640i
$56$	1.07560			0.143733
$57$		0			0
$58$			2.37579i			0.311956i
$59$	−1.25650	−	2.17633i	−0.163583	−	0.283334i	0.772568	−	0.634932i	$-0.218972\pi$
$59$	−1.25650	−	2.17633i	−0.163583	−	0.283334i	−0.936151	+	0.351598i	$0.885638\pi$
$60$		0			0
$61$	−3.37731	+	5.84967i	−0.432420	+	0.748973i	−0.997081	−	0.0763496i	$-0.975674\pi$
$61$	−3.37731	+	5.84967i	−0.432420	+	0.748973i	0.564661	+	0.825323i	$0.309007\pi$
$62$	6.71965	−	3.87959i	0.853397	−	0.492709i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.93529	+	4.98945i	0.860217	+	0.618866i
$66$		0			0
$67$	−8.07251	−	4.66066i	−0.986214	−	0.569391i	−0.0820733	−	0.996626i	$-0.526154\pi$
$67$	−8.07251	−	4.66066i	−0.986214	−	0.569391i	−0.904140	+	0.427236i	$0.859488\pi$
$68$			1.25449i			0.152129i
$69$		0			0
$70$	0.988499	+	2.19258i	0.118148	+	0.262064i
$71$	−4.79760	−	8.30969i	−0.569371	−	0.986179i	−0.996628	−	0.0820491i	$-0.973854\pi$
$71$	−4.79760	−	8.30969i	−0.569371	−	0.986179i	0.427258	−	0.904130i	$-0.359480\pi$
$72$		0			0
$73$	6.02521	−	3.47866i	0.705198	−	0.407146i	−0.104083	−	0.994569i	$-0.533191\pi$
$73$	6.02521	−	3.47866i	0.705198	−	0.407146i	0.809280	+	0.587422i	$0.199857\pi$
$74$	−1.04009	−	1.80148i	−0.120907	−	0.209418i
$75$		0			0
$76$	0.165192	−	4.35577i	0.0189488	−	0.499641i
$77$		−	0.441592i		−	0.0503240i
$78$		0			0
$79$	4.47277	+	7.74707i	0.503226	+	0.871613i	0.999993	+	0.00372912i	$0.00118702\pi$
$79$	4.47277	+	7.74707i	0.503226	+	0.871613i	−0.496767	+	0.867884i	$0.665480\pi$
$80$	−0.919023	−	2.03848i	−0.102750	−	0.227909i
$81$		0			0
$82$	4.85270	+	2.80171i	0.535892	+	0.309397i
$83$		−	9.12070i		−	1.00113i	−0.865700	−	0.500563i	$-0.833126\pi$
$83$		−	9.12070i		−	1.00113i	0.865700	−	0.500563i	$-0.166874\pi$
$84$		0			0
$85$	−2.55725	+	1.15290i	−0.277372	+	0.125050i
$86$	−1.10986	+	1.92233i	−0.119679	+	0.207291i
$87$		0			0
$88$			0.410555i			0.0437653i
$89$	2.72783	−	4.72474i	0.289149	−	0.500821i	−0.684458	−	0.729053i	$-0.739961\pi$
$89$	2.72783	−	4.72474i	0.289149	−	0.500821i	0.973607	+	0.228231i	$0.0732943\pi$
$90$		0			0
$91$	−2.05483	+	3.55906i	−0.215404	+	0.373091i
$92$	−3.23263	+	1.86636i	−0.337025	+	0.194582i
$93$		0			0
$94$	4.14328			0.427347
$95$	9.03096	−	3.66631i	0.926556	−	0.376156i
$96$		0			0
$97$	−10.5315	+	6.08034i	−1.06931	+	0.617365i	−0.927992	−	0.372599i	$-0.878467\pi$
$97$	−10.5315	+	6.08034i	−1.06931	+	0.617365i	−0.141316	+	0.989965i	$0.545133\pi$
$98$	5.06026	−	2.92155i	0.511164	−	0.295121i
$99$		0			0
$100$	3.31079	−	3.74682i	0.331079	−	0.374682i
$101$	1.54404	−	2.67436i	0.153638	−	0.266109i	−0.778924	−	0.627118i	$-0.784234\pi$
$101$	1.54404	−	2.67436i	0.153638	−	0.266109i	0.932562	+	0.361009i	$0.117568\pi$
$102$		0			0
$103$		−	14.7954i		−	1.45784i	−0.684600	−	0.728919i	$-0.740023\pi$
$103$		−	14.7954i		−	1.45784i	0.684600	−	0.728919i	$-0.259977\pi$
$104$	1.91041	−	3.30892i	0.187331	−	0.324466i
$105$		0			0
$106$	−4.99916			−0.485561
$107$			5.37650i			0.519766i	0.965640	+	0.259883i	$0.0836840\pi$
$107$			5.37650i			0.519766i	−0.965640	+	0.259883i	$0.916316\pi$
$108$		0			0
$109$	8.16051	+	14.1344i	0.781636	+	1.35383i	0.930988	+	0.365049i	$0.118948\pi$
$109$	8.16051	+	14.1344i	0.781636	+	1.35383i	−0.149353	+	0.988784i	$0.547719\pi$
$110$	−0.836907	+	0.377309i	−0.0797960	+	0.0359750i
$111$		0			0
$112$	0.931495	−	0.537799i	0.0880180	−	0.0508172i
$113$			9.79888i			0.921801i	0.887452	+	0.460900i	$0.152473\pi$
$113$			9.79888i			0.921801i	−0.887452	+	0.460900i	$0.847527\pi$
$114$		0			0
$115$	−6.77541	−	4.87443i	−0.631810	−	0.454543i
$116$	1.18789	+	2.05749i	0.110293	+	0.191033i
$117$		0			0
$118$	−2.17633	−	1.25650i	−0.200347	−	0.115670i
$119$	−0.674662	−	1.16855i	−0.0618461	−	0.107121i
$120$		0			0
$121$	−10.8314			−0.984677
$122$			6.75461i			0.611534i
$123$		0			0
$124$	3.87959	−	6.71965i	0.348398	−	0.603443i
$125$	10.6805	+	3.30556i	0.955294	+	0.295659i
$126$		0			0
$127$	−15.8129	−	9.12955i	−1.40316	−	0.810117i	−0.408448	−	0.912782i	$-0.633930\pi$
$127$	−15.8129	−	9.12955i	−1.40316	−	0.810117i	−0.994716	+	0.102665i	$0.967263\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	8.50087	+	0.853346i	0.745575	+	0.0748434i
$131$	9.70176	+	16.8039i	0.847647	+	1.46817i	0.883302	+	0.468804i	$0.155315\pi$
$131$	9.70176	+	16.8039i	0.847647	+	1.46817i	−0.0356553	+	0.999364i	$0.511352\pi$
$132$		0			0
$133$	2.18865	+	4.14621i	0.189780	+	0.359522i
$134$	−9.32133			−0.805240
$135$		0			0
$136$	0.627244	+	1.08642i	0.0537857	+	0.0931596i
$137$	−7.65772	−	4.42119i	−0.654244	−	0.377728i	0.135837	−	0.990731i	$-0.456628\pi$
$137$	−7.65772	−	4.42119i	−0.654244	−	0.377728i	−0.790080	+	0.613004i	$0.789961\pi$
$138$		0			0
$139$	5.28333	−	9.15100i	0.448127	−	0.776178i	−0.550138	−	0.835074i	$-0.685425\pi$
$139$	5.28333	−	9.15100i	0.448127	−	0.776178i	0.998264	+	0.0588961i	$0.0187581\pi$
$140$	1.95236	+	1.40458i	0.165004	+	0.118709i
$141$		0			0
$142$	−8.30969	−	4.79760i	−0.697334	−	0.402606i
$143$	−1.35849	−	0.784326i	−0.113603	−	0.0655886i
$144$		0			0
$145$	−3.10245	+	4.31238i	−0.257645	+	0.358124i
$146$	3.47866	−	6.02521i	0.287896	−	0.498650i
$147$		0			0
$148$	−1.80148	−	1.04009i	−0.148081	−	0.0854945i
$149$	−1.18192	−	2.04715i	−0.0968267	−	0.167709i	0.813543	−	0.581505i	$-0.197536\pi$
$149$	−1.18192	−	2.04715i	−0.0968267	−	0.167709i	−0.910370	+	0.413796i	$0.864203\pi$
$150$		0			0
$151$	−4.02935			−0.327904			−0.163952	−	0.986468i	$-0.552424\pi$
$151$	−4.02935			−0.327904			−0.163952	+	0.986468i	$0.552424\pi$
$152$	−2.03482	−	3.85480i	−0.165046	−	0.312666i
$153$		0			0
$154$	−0.220796	−	0.382430i	−0.0177922	−	0.0308171i
$155$	17.2633	+	1.73295i	1.38662	+	0.139194i
$156$		0			0
$157$	−16.8513	+	9.72912i	−1.34488	+	0.776469i	−0.987520	−	0.157497i	$-0.949658\pi$
$157$	−16.8513	+	9.72912i	−1.34488	+	0.776469i	−0.357364	+	0.933965i	$0.616324\pi$
$158$	7.74707	+	4.47277i	0.616324	+	0.355835i
$159$		0			0
$160$	−1.81514	−	1.30586i	−0.143499	−	0.103238i
$161$	2.00745	−	3.47701i	0.158210	−	0.274027i
$162$		0			0
$163$		−	13.4340i		−	1.05223i	−0.850412	−	0.526117i	$-0.823647\pi$
$163$		−	13.4340i		−	1.05223i	0.850412	−	0.526117i	$-0.176353\pi$
$164$	5.60342			0.437554
$165$		0			0
$166$	−4.56035	−	7.89876i	−0.353952	−	0.613063i
$167$	−3.38132	−	1.95221i	−0.261655	−	0.151066i	0.363435	−	0.931620i	$-0.381604\pi$
$167$	−3.38132	−	1.95221i	−0.261655	−	0.151066i	−0.625089	+	0.780553i	$0.714937\pi$
$168$		0			0
$169$	0.799296	+	1.38442i	0.0614843	+	0.106494i
$170$	−1.63819	+	2.27707i	−0.125643	+	0.174643i
$171$		0			0
$172$			2.21972i			0.169252i
$173$	13.1394	−	7.58604i	0.998970	−	0.576756i	0.0910267	−	0.995848i	$-0.470985\pi$
$173$	13.1394	−	7.58604i	0.998970	−	0.576756i	0.907943	+	0.419093i	$0.137652\pi$
$174$		0			0
$175$	−1.06895	+	5.27068i	−0.0808050	+	0.398426i
$176$	0.205277	+	0.355551i	0.0154734	+	0.0268007i
$177$		0			0
$178$		−	5.45566i		−	0.408919i
$179$	8.91162			0.666085			0.333043	−	0.942912i	$-0.391925\pi$
$179$	8.91162			0.666085			0.333043	+	0.942912i	$0.391925\pi$
$180$		0			0
$181$	4.61274	−	7.98950i	0.342862	−	0.593855i	−0.642101	−	0.766620i	$-0.721937\pi$
$181$	4.61274	−	7.98950i	0.342862	−	0.593855i	0.984963	+	0.172765i	$0.0552702\pi$
$182$			4.10965i			0.304628i
$183$		0			0
$184$	−1.86636	+	3.23263i	−0.137590	+	0.238313i
$185$	0.464589	−	4.62814i	0.0341573	−	0.340268i
$186$		0			0
$187$	0.446034	−	0.257518i	0.0326172	−	0.0188316i
$188$	3.58819	−	2.07164i	0.261695	−	0.151090i
$189$		0			0
$190$	5.98788	−	7.69060i	0.434407	−	0.557935i
$191$	−19.7445			−1.42867			−0.714333	−	0.699806i	$-0.753270\pi$
$191$	−19.7445			−1.42867			−0.714333	+	0.699806i	$0.753270\pi$
$192$		0			0
$193$	−11.9562	+	6.90289i	−0.860623	+	0.496881i	−0.864221	−	0.503113i	$-0.832188\pi$
$193$	−11.9562	+	6.90289i	−0.860623	+	0.496881i	0.00359794	+	0.999994i	$0.498855\pi$
$194$	−6.08034	+	10.5315i	−0.436543	+	0.756115i
$195$		0			0
$196$	2.92155	−	5.06026i	0.208682	−	0.361447i
$197$		−	8.42005i		−	0.599904i	−0.953954	−	0.299952i	$-0.903029\pi$
$197$		−	8.42005i		−	0.599904i	0.953954	−	0.299952i	$-0.0969706\pi$
$198$		0			0
$199$	3.33252	−	5.77210i	0.236236	−	0.409173i	−0.723395	−	0.690434i	$-0.757419\pi$
$199$	3.33252	−	5.77210i	0.236236	−	0.409173i	0.959631	+	0.281261i	$0.0907528\pi$
$200$	0.993820	−	4.90024i	0.0702737	−	0.346499i
$201$		0			0
$202$		−	3.08809i		−	0.217277i
$203$	−2.21303	−	1.27769i	−0.155324	−	0.0896766i
$204$		0			0
$205$	5.14967	+	11.4225i	0.359669	+	0.797779i
$206$	−7.39772	−	12.8132i	−0.515424	−	0.892740i
$207$		0			0
$208$		−	3.82081i		−	0.264926i
$209$	−1.58261	+	0.835406i	−0.109471	+	0.0577863i
$210$		0			0
$211$	−6.10606	−	10.5760i	−0.420359	−	0.728083i	0.575616	−	0.817720i	$-0.304762\pi$
$211$	−6.10606	−	10.5760i	−0.420359	−	0.728083i	−0.995974	+	0.0896377i	$0.971429\pi$
$212$	−4.32940	+	2.49958i	−0.297344	+	0.171672i
$213$		0			0
$214$	2.68825	+	4.65618i	0.183765	+	0.318290i
$215$	−4.52485	+	2.03997i	−0.308592	+	0.139125i
$216$		0			0
$217$			8.34576i			0.566547i
$218$	14.1344	+	8.16051i	0.957304	+	0.552700i
$219$		0			0
$220$	−0.536128	+	0.745213i	−0.0361458	+	0.0502423i
$221$	−4.79316			−0.322423
$222$		0			0
$223$	0.493682	−	0.285027i	0.0330594	−	0.0190868i	−0.483379	−	0.875411i	$-0.660591\pi$
$223$	0.493682	−	0.285027i	0.0330594	−	0.0190868i	0.516439	+	0.856324i	$0.327257\pi$
$224$	0.537799	−	0.931495i	0.0359332	−	0.0622381i
$225$		0			0
$226$	4.89944	+	8.48608i	0.325906	+	0.564485i
$227$			2.46316i			0.163486i	0.996653	+	0.0817428i	$0.0260486\pi$
$227$			2.46316i			0.163486i	−0.996653	+	0.0817428i	$0.973951\pi$
$228$		0			0
$229$	11.0250			0.728553			0.364276	−	0.931291i	$-0.381316\pi$
$229$	11.0250			0.728553			0.364276	+	0.931291i	$0.381316\pi$
$230$	−8.30489	−	0.833673i	−0.547608	−	0.0549708i
$231$		0			0
$232$	2.05749	+	1.18789i	0.135081	+	0.0779890i
$233$	−14.9579	+	8.63595i	−0.979925	+	0.565760i	−0.902247	−	0.431219i	$-0.858084\pi$
$233$	−14.9579	+	8.63595i	−0.979925	+	0.565760i	−0.0776772	+	0.996979i	$0.524750\pi$
$234$		0			0
$235$	7.52062	+	5.41055i	0.490591	+	0.352946i
$236$	−2.51301			−0.163583
$237$		0			0
$238$	−1.16855	−	0.674662i	−0.0757457	−	0.0437318i
$239$	6.90743			0.446805			0.223402	−	0.974726i	$-0.428284\pi$
$239$	6.90743			0.446805			0.223402	+	0.974726i	$0.428284\pi$
$240$		0			0
$241$	−11.0140	+	19.0767i	−0.709471	+	1.22884i	0.255582	+	0.966787i	$0.417733\pi$
$241$	−11.0140	+	19.0767i	−0.709471	+	1.22884i	−0.965053	+	0.262053i	$0.915600\pi$
$242$	−9.38031	+	5.41572i	−0.602989	+	0.348136i
$243$		0			0
$244$	3.37731	+	5.84967i	0.216210	+	0.374487i
$245$	13.0002	+	1.30501i	0.830553	+	0.0833738i
$246$		0			0
$247$	16.6426	+	0.631167i	1.05894	+	0.0401602i
$248$		−	7.75919i		−	0.492709i
$249$		0			0
$250$	10.9024	−	2.47755i	0.689527	−	0.156694i
$251$	−10.5663	+	18.3014i	−0.666940	+	1.15517i	0.311815	+	0.950143i	$0.399063\pi$
$251$	−10.5663	+	18.3014i	−0.666940	+	1.15517i	−0.978755	+	0.205032i	$0.934270\pi$
$252$		0			0
$253$	1.32717	+	0.766244i	0.0834387	+	0.0481734i
$254$	−18.2591			−1.14568
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−22.8775	−	13.2083i	−1.42706	−	0.823913i	−0.430172	−	0.902747i	$-0.641547\pi$
$257$	−22.8775	−	13.2083i	−1.42706	−	0.823913i	−0.996888	+	0.0788341i	$0.974880\pi$
$258$		0			0
$259$	2.23743			0.139027
$260$	7.78864	−	3.51141i	0.483031	−	0.217769i
$261$		0			0
$262$	16.8039	+	9.70176i	1.03815	+	0.599377i
$263$	−20.7173	+	11.9611i	−1.27748	+	0.737555i	−0.976385	−	0.216039i	$-0.930686\pi$
$263$	−20.7173	+	11.9611i	−1.27748	+	0.737555i	−0.301097	+	0.953593i	$0.597353\pi$
$264$		0			0
$265$	−9.07416	−	6.52821i	−0.557421	−	0.401025i
$266$	3.96853	+	2.49640i	0.243326	+	0.153064i
$267$		0			0
$268$	−8.07251	+	4.66066i	−0.493107	+	0.284695i
$269$	3.89266	+	6.74229i	0.237340	+	0.411085i	0.959950	−	0.280171i	$-0.0903911\pi$
$269$	3.89266	+	6.74229i	0.237340	+	0.411085i	−0.722610	+	0.691256i	$0.757058\pi$
$270$		0			0
$271$	−0.421189	−	0.729521i	−0.0255854	−	0.0443152i	0.852949	−	0.521994i	$-0.174812\pi$
$271$	−0.421189	−	0.729521i	−0.0255854	−	0.0443152i	−0.878535	+	0.477679i	$0.841478\pi$
$272$	1.08642	+	0.627244i	0.0658738	+	0.0380322i
$273$		0			0
$274$	−8.84238			−0.534188
$275$	−2.01182	−	0.408018i	−0.121317	−	0.0246044i
$276$		0			0
$277$			5.55485i			0.333758i	0.985977	+	0.166879i	$0.0533690\pi$
$277$			5.55485i			0.333758i	−0.985977	+	0.166879i	$0.946631\pi$
$278$		−	10.5667i		−	0.633747i
$279$		0			0
$280$	2.39308	+	0.240226i	0.143014	+	0.0143562i
$281$	8.05993	−	13.9602i	0.480815	−	0.832796i	−0.518943	−	0.854809i	$-0.673674\pi$
$281$	8.05993	−	13.9602i	0.480815	−	0.832796i	0.999758	+	0.0220130i	$0.00700751\pi$
$282$		0			0
$283$	4.78552	−	2.76292i	0.284469	−	0.164239i	−0.350976	−	0.936385i	$-0.614150\pi$
$283$	4.78552	−	2.76292i	0.284469	−	0.164239i	0.635445	+	0.772146i	$0.280817\pi$
$284$	−9.59521			−0.569371
$285$		0			0
$286$	−1.56865			−0.0927563
$287$	−5.21956	+	3.01351i	−0.308101	+	0.177882i
$288$		0			0
$289$	−7.71313	+	13.3595i	−0.453714	+	0.785855i
$290$	−0.530612	+	5.28585i	−0.0311586	+	0.310396i
$291$		0			0
$292$		−	6.95732i		−	0.407146i
$293$		−	0.546541i		−	0.0319293i	−0.999873	−	0.0159646i	$-0.994918\pi$
$293$		−	0.546541i		−	0.0319293i	0.999873	−	0.0159646i	$-0.00508192\pi$
$294$		0			0
$295$	−2.30951	−	5.12271i	−0.134465	−	0.298256i
$296$	−2.08017			−0.120907
$297$		0			0
$298$	−2.04715	−	1.18192i	−0.118588	−	0.0684668i
$299$	−7.13102	−	12.3513i	−0.412397	−	0.714293i
$300$		0			0
$301$	−1.19376	−	2.06766i	−0.0688073	−	0.119178i
$302$	−3.48952	+	2.01468i	−0.200799	+	0.115932i
$303$		0			0
$304$	−3.68961	−	2.32094i	−0.211614	−	0.133115i
$305$	−8.82060	+	12.2606i	−0.505066	+	0.702037i
$306$		0			0
$307$	−21.2877	+	12.2904i	−1.21495	+	0.701452i	−0.963834	−	0.266505i	$-0.914131\pi$
$307$	−21.2877	+	12.2904i	−1.21495	+	0.701452i	−0.251117	+	0.967957i	$0.580798\pi$
$308$	−0.382430	−	0.220796i	−0.0217909	−	0.0125810i
$309$		0			0
$310$	15.8169	−	7.13088i	0.898342	−	0.405007i
$311$	−21.5698			−1.22311			−0.611556	−	0.791201i	$-0.709456\pi$
$311$	−21.5698			−1.22311			−0.611556	+	0.791201i	$0.709456\pi$
$312$		0			0
$313$	25.3785	+	14.6523i	1.43447	+	0.828194i	0.997458	−	0.0712588i	$-0.0227016\pi$
$313$	25.3785	+	14.6523i	1.43447	+	0.828194i	0.437017	+	0.899453i	$0.356035\pi$
$314$	−9.72912	+	16.8513i	−0.549046	+	0.950976i
$315$		0			0
$316$	8.94554			0.503226
$317$	7.10418	+	4.10160i	0.399011	+	0.230369i	0.686057	−	0.727548i	$-0.259340\pi$
$317$	7.10418	+	4.10160i	0.399011	+	0.230369i	−0.287046	+	0.957917i	$0.592673\pi$
$318$		0			0
$319$	0.487695	−	0.844713i	0.0273057	−	0.0472948i
$320$	−2.22489	−	0.223342i	−0.124375	−	0.0124852i
$321$		0			0
$322$		−	4.01491i		−	0.223742i
$323$	−2.91160	+	4.62857i	−0.162006	+	0.257540i
$324$		0			0
$325$	14.3159	+	12.6499i	0.794103	+	0.701691i
$326$	−6.71701	−	11.6342i	−0.372021	−	0.644359i
$327$		0			0
$328$	4.85270	−	2.80171i	0.267946	−	0.154699i
$329$	−2.22825	+	3.85944i	−0.122847	+	0.212778i
$330$		0			0
$331$	−27.0826			−1.48860			−0.744298	−	0.667847i	$-0.767216\pi$
$331$	−27.0826			−1.48860			−0.744298	+	0.667847i	$0.767216\pi$
$332$	−7.89876	−	4.56035i	−0.433501	−	0.250282i
$333$		0			0
$334$	−3.90441			−0.213640
$335$	−16.9195	−	12.1724i	−0.924410	−	0.665048i
$336$		0			0
$337$	−23.9964	+	13.8543i	−1.30717	+	0.754693i	−0.981622	−	0.190834i	$-0.938881\pi$
$337$	−23.9964	+	13.8543i	−1.30717	+	0.754693i	−0.325544	+	0.945527i	$0.605547\pi$
$338$	1.38442	+	0.799296i	0.0753026	+	0.0434760i
$339$		0			0
$340$	−0.280179	+	2.79109i	−0.0151949	+	0.151368i
$341$	−3.18557			−0.172508
$342$		0			0
$343$			13.8140i			0.745885i
$344$	1.10986	+	1.92233i	0.0598396	+	0.103645i
$345$		0			0
$346$	7.58604	−	13.1394i	0.407828	−	0.706379i
$347$	−2.04836	+	1.18262i	−0.109962	+	0.0634865i	−0.553972	−	0.832535i	$-0.686889\pi$
$347$	−2.04836	+	1.18262i	−0.109962	+	0.0634865i	0.444010	+	0.896022i	$0.353555\pi$
$348$		0			0
$349$	−16.7894			−0.898718			−0.449359	−	0.893351i	$-0.648348\pi$
$349$	−16.7894			−0.898718			−0.449359	+	0.893351i	$0.648348\pi$
$350$	1.70960	+	5.09902i	0.0913821	+	0.272554i
$351$		0			0
$352$	0.355551	+	0.205277i	0.0189509	+	0.0109413i
$353$			23.0018i			1.22426i	0.790756	+	0.612132i	$0.209688\pi$
$353$			23.0018i			1.22426i	−0.790756	+	0.612132i	$0.790312\pi$
$354$		0			0
$355$	−8.81822	−	19.5596i	−0.468023	−	1.03812i
$356$	−2.72783	−	4.72474i	−0.144575	−	0.250411i
$357$		0			0
$358$	7.71769	−	4.45581i	0.407892	−	0.235497i
$359$	−1.84432	−	3.19445i	−0.0973393	−	0.168597i	0.813243	−	0.581924i	$-0.197700\pi$
$359$	−1.84432	−	3.19445i	−0.0973393	−	0.168597i	−0.910583	+	0.413327i	$0.864367\pi$
$360$		0			0
$361$	10.7190	−	15.6877i	0.564157	−	0.825667i
$362$		−	9.22548i		−	0.484881i
$363$		0			0
$364$	2.05483	+	3.55906i	0.107702	+	0.186546i
$365$	14.1823	−	6.39394i	0.742338	−	0.334674i
$366$		0			0
$367$	9.72280	+	5.61346i	0.507526	+	0.293020i	0.731816	−	0.681502i	$-0.238673\pi$
$367$	9.72280	+	5.61346i	0.507526	+	0.293020i	−0.224290	+	0.974522i	$0.572006\pi$
$368$			3.73273i			0.194582i
$369$		0			0
$370$	−1.91173	−	4.24038i	−0.0993859	−	0.220447i
$371$	2.68854	−	4.65669i	0.139582	−	0.241763i
$372$		0			0
$373$		−	2.73993i		−	0.141868i	−0.997481	−	0.0709340i	$-0.977402\pi$
$373$		−	2.73993i		−	0.141868i	0.997481	−	0.0709340i	$-0.0225980\pi$
$374$	0.257518	−	0.446034i	0.0133159	−	0.0230639i
$375$		0			0
$376$	2.07164	−	3.58819i	0.106837	−	0.185047i
$377$	−7.86129	+	4.53872i	−0.404877	+	0.233756i
$378$		0			0
$379$	−36.3082			−1.86503			−0.932515	−	0.361132i	$-0.882390\pi$
$379$	−36.3082			−1.86503			−0.932515	+	0.361132i	$0.882390\pi$
$380$	1.34036	−	9.65419i	0.0687589	−	0.495250i
$381$		0			0
$382$	−17.0993	+	9.87227i	−0.874875	+	0.505109i
$383$	9.30230	−	5.37069i	0.475326	−	0.274429i	−0.243141	−	0.969991i	$-0.578178\pi$
$383$	9.30230	−	5.37069i	0.475326	−	0.274429i	0.718466	+	0.695562i	$0.244844\pi$
$384$		0			0
$385$	0.0986258	−	0.982491i	0.00502644	−	0.0500724i
$386$	−6.90289	+	11.9562i	−0.351348	+	0.608552i
$387$		0			0
$388$			12.1607i			0.617365i
$389$	−3.04431	+	5.27291i	−0.154353	+	0.267347i	−0.932823	−	0.360334i	$-0.882663\pi$
$389$	−3.04431	+	5.27291i	−0.154353	+	0.267347i	0.778470	+	0.627681i	$0.215996\pi$
$390$		0			0
$391$	4.68266			0.236812
$392$		−	5.84309i		−	0.295121i
$393$		0			0
$394$	−4.21002	−	7.29198i	−0.212098	−	0.367364i
$395$	8.22116	+	18.2353i	0.413652	+	0.917517i
$396$		0			0
$397$	−19.8802	+	11.4778i	−0.997759	+	0.576056i	−0.907584	−	0.419870i	$-0.862076\pi$
$397$	−19.8802	+	11.4778i	−0.997759	+	0.576056i	−0.0901743	+	0.995926i	$0.528742\pi$
$398$		−	6.66504i		−	0.334088i
$399$		0			0
$400$	−1.58945	−	4.74064i	−0.0794723	−	0.237032i
$401$	−9.06197	−	15.6958i	−0.452533	−	0.783810i	0.546010	−	0.837779i	$-0.316146\pi$
$401$	−9.06197	−	15.6958i	−0.452533	−	0.783810i	−0.998543	+	0.0539687i	$0.982813\pi$
$402$		0			0
$403$	25.6745	+	14.8232i	1.27894	+	0.738396i
$404$	−1.54404	−	2.67436i	−0.0768190	−	0.133054i
$405$		0			0
$406$	−2.55539			−0.126822
$407$			0.854024i			0.0423324i
$408$		0			0
$409$	19.7968	−	34.2890i	0.978888	−	1.69548i	0.312431	−	0.949941i	$-0.398857\pi$
$409$	19.7968	−	34.2890i	0.978888	−	1.69548i	0.666457	−	0.745543i	$-0.267810\pi$
$410$	10.1710	+	7.31730i	0.502309	+	0.361376i
$411$		0			0
$412$	−12.8132	−	7.39772i	−0.631263	−	0.364460i
$413$	2.34085	−	1.35149i	0.115186	−	0.0665025i
$414$		0			0
$415$	2.03703	−	20.2925i	0.0999940	−	0.996121i
$416$	−1.91041	−	3.30892i	−0.0936653	−	0.162233i
$417$		0			0
$418$	−0.952875	+	1.51479i	−0.0466066	+	0.0740906i
$419$	−27.5268			−1.34477			−0.672385	−	0.740201i	$-0.734730\pi$
$419$	−27.5268			−1.34477			−0.672385	+	0.740201i	$0.734730\pi$
$420$		0			0
$421$	0.443296	+	0.767812i	0.0216049	+	0.0374209i	0.876626	−	0.481173i	$-0.159789\pi$
$421$	0.443296	+	0.767812i	0.0216049	+	0.0374209i	−0.855021	+	0.518594i	$0.826456\pi$
$422$	−10.5760	−	6.10606i	−0.514832	−	0.297239i
$423$		0			0
$424$	−2.49958	+	4.32940i	−0.121390	+	0.210254i
$425$	−5.94707	+	1.99394i	−0.288475	+	0.0967203i
$426$		0			0
$427$	−6.29189	−	3.63262i	−0.304486	−	0.175795i
$428$	4.65618	+	2.68825i	0.225065	+	0.129941i
$429$		0			0
$430$	−2.89865	+	4.02909i	−0.139785	+	0.194300i
$431$	4.26551	−	7.38807i	0.205462	−	0.355871i	−0.744818	−	0.667268i	$-0.767464\pi$
$431$	4.26551	−	7.38807i	0.205462	−	0.355871i	0.950280	+	0.311397i	$0.100797\pi$
$432$		0			0
$433$	12.5809	+	7.26356i	0.604597	+	0.349064i	0.770848	−	0.637019i	$-0.219833\pi$
$433$	12.5809	+	7.26356i	0.604597	+	0.349064i	−0.166251	+	0.986084i	$0.553166\pi$
$434$	4.17288	+	7.22764i	0.200305	+	0.346938i
$435$		0			0
$436$	16.3210			0.781636
$437$	−16.2589	−	0.616616i	−0.777768	−	0.0294968i
$438$		0			0
$439$	6.98935	+	12.1059i	0.333583	+	0.577784i	0.983212	−	0.182469i	$-0.0584088\pi$
$439$	6.98935	+	12.1059i	0.333583	+	0.577784i	−0.649628	+	0.760252i	$0.725075\pi$
$440$	−0.0916940	+	0.913438i	−0.00437134	+	0.0435464i
$441$		0			0
$442$	−4.15100	+	2.39658i	−0.197443	+	0.113994i
$443$	19.1733	+	11.0697i	0.910951	+	0.525938i	0.880737	−	0.473606i	$-0.157048\pi$
$443$	19.1733	+	11.0697i	0.910951	+	0.525938i	0.0302139	+	0.999543i	$0.490381\pi$
$444$		0			0
$445$	7.12434	−	9.90277i	0.337726	−	0.469436i
$446$	0.285027	−	0.493682i	0.0134964	−	0.0233765i
$447$		0			0
$448$		−	1.07560i		−	0.0508172i
$449$	33.0859			1.56142			0.780711	−	0.624892i	$-0.214857\pi$
$449$	33.0859			1.56142			0.780711	+	0.624892i	$0.214857\pi$
$450$		0			0
$451$	−1.15026	−	1.99230i	−0.0541634	−	0.0938138i
$452$	8.48608	+	4.89944i	0.399151	+	0.230450i
$453$		0			0
$454$	1.23158	+	2.13316i	0.0578009	+	0.100114i
$455$	−5.36664	+	7.45958i	−0.251592	+	0.349711i
$456$		0			0
$457$			29.1810i			1.36503i	0.730871	+	0.682515i	$0.239114\pi$
$457$			29.1810i			1.36503i	−0.730871	+	0.682515i	$0.760886\pi$
$458$	9.54793	−	5.51250i	0.446145	−	0.257582i
$459$		0			0
$460$	−7.60908	+	3.43046i	−0.354775	+	0.159946i
$461$	−10.1373	−	17.5583i	−0.472141	−	0.817773i	0.527350	−	0.849648i	$-0.323186\pi$
$461$	−10.1373	−	17.5583i	−0.472141	−	0.817773i	−0.999492	+	0.0318749i	$0.989852\pi$
$462$		0			0
$463$		−	15.3688i		−	0.714251i	−0.934057	−	0.357125i	$-0.883757\pi$
$463$		−	15.3688i		−	0.714251i	0.934057	−	0.357125i	$-0.116243\pi$
$464$	2.37579			0.110293
$465$		0			0
$466$	−8.63595	+	14.9579i	−0.400053	+	0.692911i
$467$			38.1609i			1.76587i	0.469491	+	0.882937i	$0.344437\pi$
$467$			38.1609i			1.76587i	−0.469491	+	0.882937i	$0.655563\pi$
$468$		0			0
$469$	5.01300	−	8.68277i	0.231479	−	0.400933i
$470$	9.21833	+	0.925367i	0.425210	+	0.0426840i
$471$		0			0
$472$	−2.17633	+	1.25650i	−0.100174	+	0.0578352i
$473$	0.789223	−	0.455658i	0.0362885	−	0.0209512i
$474$		0			0
$475$	20.9117	−	6.14014i	0.959494	−	0.281729i
$476$	−1.34932			−0.0618461
$477$		0			0
$478$	5.98201	−	3.45372i	0.273611	−	0.157969i
$479$	15.1215	−	26.1912i	0.690918	−	1.19670i	−0.280620	−	0.959819i	$-0.590540\pi$
$479$	15.1215	−	26.1912i	0.690918	−	1.19670i	0.971538	−	0.236886i	$-0.0761266\pi$
$480$		0			0
$481$	3.97397	−	6.88312i	0.181197	−	0.313843i
$482$			22.0279i			1.00334i
$483$		0			0
$484$	−5.41572	+	9.38031i	−0.246169	+	0.426378i
$485$	−24.7893	+	11.1760i	−1.12562	+	0.507474i
$486$		0			0
$487$		−	37.7499i		−	1.71061i	−0.518125	−	0.855305i	$-0.673370\pi$
$487$		−	37.7499i		−	1.71061i	0.518125	−	0.855305i	$-0.326630\pi$
$488$	5.84967	+	3.37731i	0.264802	+	0.152884i
$489$		0			0
$490$	11.9110	−	5.36994i	0.538085	−	0.242589i
$491$	10.6495	+	18.4456i	0.480607	+	0.832436i	0.999752	−	0.0222498i	$-0.00708291\pi$
$491$	10.6495	+	18.4456i	0.480607	+	0.832436i	−0.519145	+	0.854686i	$0.673750\pi$
$492$		0			0
$493$		−	2.98039i		−	0.134230i
$494$	14.7285	−	7.77467i	0.662665	−	0.349799i
$495$		0			0
$496$	−3.87959	−	6.71965i	−0.174199	−	0.301721i
$497$	8.93788	−	5.16029i	0.400919	−	0.231471i
$498$		0			0
$499$	−10.2460	−	17.7466i	−0.458674	−	0.794447i	0.540217	−	0.841526i	$-0.318342\pi$
$499$	−10.2460	−	17.7466i	−0.458674	−	0.794447i	−0.998891	+	0.0470789i	$0.985009\pi$
$500$	8.20296	−	7.59681i	0.366847	−	0.339740i
$501$		0			0
$502$			21.1326i			0.943196i
$503$	3.26234	+	1.88351i	0.145461	+	0.0839817i	0.570964	−	0.820975i	$-0.306570\pi$
$503$	3.26234	+	1.88351i	0.145461	+	0.0839817i	−0.425503	+	0.904957i	$0.639903\pi$
$504$		0			0
$505$	4.03262	−	5.60530i	0.179449	−	0.249432i
$506$	1.53249			0.0681274
$507$		0			0
$508$	−15.8129	+	9.12955i	−0.701582	+	0.405058i
$509$	4.50733	−	7.80693i	0.199784	−	0.346036i	−0.748674	−	0.662938i	$-0.769309\pi$
$509$	4.50733	−	7.80693i	0.199784	−	0.346036i	0.948458	+	0.316902i	$0.102643\pi$
$510$		0			0
$511$	3.74164	+	6.48070i	0.165520	+	0.286689i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−26.4167			−1.16519
$515$	3.30444	−	32.9182i	0.145611	−	1.45055i
$516$		0			0
$517$	−1.47315	−	0.850522i	−0.0647889	−	0.0374059i
$518$	1.93767	−	1.11871i	0.0851362	−	0.0491534i
$519$		0			0
$520$	4.98945	−	6.93529i	0.218802	−	0.304133i
$521$	−7.99789			−0.350394			−0.175197	−	0.984533i	$-0.556056\pi$
$521$	−7.99789			−0.350394			−0.175197	+	0.984533i	$0.556056\pi$
$522$		0			0
$523$	10.1372	+	5.85269i	0.443267	+	0.255920i	0.704982	−	0.709225i	$-0.250955\pi$
$523$	10.1372	+	5.85269i	0.443267	+	0.255920i	−0.261716	+	0.965145i	$0.584288\pi$
$524$	19.4035			0.847647
$525$		0			0
$526$	−11.9611	+	20.7173i	−0.521530	+	0.903316i
$527$	−8.42972	+	4.86690i	−0.367204	+	0.212006i
$528$		0			0
$529$	−4.53338	−	7.85205i	−0.197104	−	0.341393i
$530$	−11.1226	−	1.11652i	−0.483133	−	0.0484986i
$531$		0			0
$532$	4.68505	+	0.177680i	0.203123	+	0.00770341i
$533$			21.4096i			0.927353i
$534$		0			0
$535$	−1.20080	+	11.9621i	−0.0519150	+	0.517167i
$536$	−4.66066	+	8.07251i	−0.201310	+	0.348679i
$537$		0			0
$538$	6.74229	+	3.89266i	0.290681	+	0.167825i
$539$	−2.39891			−0.103328
$540$		0			0
$541$	−12.3595	+	21.4072i	−0.531375	+	0.920369i	0.467954	+	0.883753i	$0.344991\pi$
$541$	−12.3595	+	21.4072i	−0.531375	+	0.920369i	−0.999329	+	0.0366163i	$0.988342\pi$
$542$	−0.729521	−	0.421189i	−0.0313356	−	0.0180916i
$543$		0			0
$544$	1.25449			0.0537857
$545$	14.9994	+	33.2701i	0.642504	+	1.42513i
$546$		0			0
$547$	−27.0571	−	15.6214i	−1.15688	−	0.667924i	−0.206324	−	0.978484i	$-0.566150\pi$
$547$	−27.0571	−	15.6214i	−1.15688	−	0.667924i	−0.950554	+	0.310560i	$0.899484\pi$
$548$	−7.65772	+	4.42119i	−0.327122	+	0.188864i
$549$		0			0
$550$	−1.94629	+	0.652554i	−0.0829902	+	0.0278250i
$551$	−0.392461	+	10.3484i	−0.0167194	+	0.440856i
$552$		0			0
$553$	−8.33272	+	4.81090i	−0.354343	+	0.204580i
$554$	2.77742	+	4.81064i	0.118001	+	0.204384i
$555$		0			0
$556$	−5.28333	−	9.15100i	−0.224063	−	0.388089i
$557$	−1.27137	−	0.734027i	−0.0538698	−	0.0311017i	0.472823	−	0.881157i	$-0.343235\pi$
$557$	−1.27137	−	0.734027i	−0.0538698	−	0.0311017i	−0.526693	+	0.850056i	$0.676568\pi$
$558$		0			0
$559$	−8.48113			−0.358713
$560$	2.19258	−	0.988499i	0.0926535	−	0.0417717i
$561$		0			0
$562$		−	16.1199i		−	0.679975i
$563$		−	9.14417i		−	0.385381i	−0.981260	−	0.192690i	$-0.938279\pi$
$563$		−	9.14417i		−	0.385381i	0.981260	−	0.192690i	$-0.0617213\pi$
$564$		0			0
$565$	−2.18850	+	21.8014i	−0.0920708	+	0.917191i
$566$	2.76292	−	4.78552i	0.116134	−	0.201150i
$567$		0			0
$568$	−8.30969	+	4.79760i	−0.348667	+	0.201303i
$569$	26.6371			1.11668			0.558342	−	0.829611i	$-0.311438\pi$
$569$	26.6371			1.11668			0.558342	+	0.829611i	$0.311438\pi$
$570$		0			0
$571$	37.9441			1.58791			0.793957	−	0.607974i	$-0.208018\pi$
$571$	37.9441			1.58791			0.793957	+	0.607974i	$0.208018\pi$
$572$	−1.35849	+	0.784326i	−0.0568014	+	0.0327943i
$573$		0			0
$574$	−3.01351	+	5.21956i	−0.125782	+	0.217860i
$575$	−13.9858	−	12.3583i	−0.583250	−	0.515376i
$576$		0			0
$577$		−	11.2059i		−	0.466508i	−0.972416	−	0.233254i	$-0.925063\pi$
$577$		−	11.2059i		−	0.466508i	0.972416	−	0.233254i	$-0.0749373\pi$
$578$			15.4263i			0.641648i
$579$		0			0
$580$	2.18340	+	4.84299i	0.0906609	+	0.201094i
$581$	9.81020			0.406996
$582$		0			0
$583$	1.77745	+	1.02621i	0.0736147	+	0.0425014i
$584$	−3.47866	−	6.02521i	−0.143948	−	0.249325i
$585$		0			0
$586$	−0.273271	−	0.473319i	−0.0112887	−	0.0195526i
$587$	17.3126	−	9.99543i	0.714567	−	0.412555i	−0.0981828	−	0.995168i	$-0.531303\pi$
$587$	17.3126	−	9.99543i	0.714567	−	0.412555i	0.812750	+	0.582613i	$0.197970\pi$
$588$		0			0
$589$	29.9101	−	15.7886i	1.23243	−	0.650557i
$590$	−4.56145	−	3.28164i	−0.187792	−	0.135103i
$591$		0			0
$592$	−1.80148	+	1.04009i	−0.0740404	+	0.0427472i
$593$	−18.6911	−	10.7913i	−0.767552	−	0.443146i	0.0644489	−	0.997921i	$-0.479471\pi$
$593$	−18.6911	−	10.7913i	−0.767552	−	0.443146i	−0.832001	+	0.554775i	$0.812804\pi$
$594$		0			0
$595$	−1.24006	−	2.75057i	−0.0508375	−	0.112762i
$596$	−2.36384			−0.0968267
$597$		0			0
$598$	−12.3513	−	7.13102i	−0.505082	−	0.291609i
$599$	22.0781	−	38.2403i	0.902085	−	1.56246i	0.0773019	−	0.997008i	$-0.475369\pi$
$599$	22.0781	−	38.2403i	0.902085	−	1.56246i	0.824783	−	0.565449i	$-0.191297\pi$
$600$		0			0
$601$	22.7911			0.929667			0.464834	−	0.885398i	$-0.346114\pi$
$601$	22.7911			0.929667			0.464834	+	0.885398i	$0.346114\pi$
$602$	−2.06766	−	1.19376i	−0.0842714	−	0.0486541i
$603$		0			0
$604$	−2.01468	+	3.48952i	−0.0819760	+	0.141987i
$605$	−24.0987	−	2.41911i	−0.979753	−	0.0983510i
$606$		0			0
$607$		−	15.8927i		−	0.645064i	−0.946559	−	0.322532i	$-0.895466\pi$
$607$		−	15.8927i		−	0.645064i	0.946559	−	0.322532i	$-0.104534\pi$
$608$	−4.35577	−	0.165192i	−0.176650	−	0.00669942i
$609$		0			0
$610$	−1.50859	+	15.0282i	−0.0610809	+	0.608476i
$611$	7.91534	+	13.7098i	0.320221	+	0.554638i
$612$		0			0
$613$	33.0003	−	19.0527i	1.33287	−	0.769532i	0.347130	−	0.937817i	$-0.387156\pi$
$613$	33.0003	−	19.0527i	1.33287	−	0.769532i	0.985738	+	0.168285i	$0.0538230\pi$
$614$	−12.2904	+	21.2877i	−0.496001	+	0.859100i
$615$		0			0
$616$	−0.441592			−0.0177922
$617$	30.0827	+	17.3683i	1.21109	+	0.699221i	0.962996	−	0.269516i	$-0.0868638\pi$
$617$	30.0827	+	17.3683i	1.21109	+	0.699221i	0.248090	+	0.968737i	$0.420197\pi$
$618$		0			0
$619$	−19.6805			−0.791027			−0.395513	−	0.918460i	$-0.629433\pi$
$619$	−19.6805			−0.791027			−0.395513	+	0.918460i	$0.629433\pi$
$620$	10.1324	−	14.0840i	0.406928	−	0.565627i
$621$		0			0
$622$	−18.6800	+	10.7849i	−0.749000	+	0.432435i
$623$	5.08192	+	2.93405i	0.203603	+	0.117550i
$624$		0			0
$625$	23.0246	+	9.73991i	0.920986	+	0.389596i
$626$	29.3045			1.17124
$627$		0			0
$628$			19.4582i			0.776469i
$629$	1.30477	+	2.25994i	0.0520248	+	0.0901095i
$630$		0			0
$631$	−10.0442	+	17.3970i	−0.399851	+	0.692563i	−0.993707	−	0.112008i	$-0.964272\pi$
$631$	−10.0442	+	17.3970i	−0.399851	+	0.692563i	0.593856	+	0.804571i	$0.297605\pi$
$632$	7.74707	−	4.47277i	0.308162	−	0.177917i
$633$		0			0
$634$	8.20320			0.325791
$635$	−33.1428	−	23.8439i	−1.31523	−	0.946216i
$636$		0			0
$637$	19.3343	+	11.1627i	0.766053	+	0.442281i
$638$		−	0.975391i		−	0.0386161i
$639$		0			0
$640$	−2.03848	+	0.919023i	−0.0805780	+	0.0363276i
$641$	−10.1096	−	17.5104i	−0.399306	−	0.691618i	0.594335	−	0.804218i	$-0.297415\pi$
$641$	−10.1096	−	17.5104i	−0.399306	−	0.691618i	−0.993640	+	0.112600i	$0.964082\pi$
$642$		0			0
$643$	11.6160	−	6.70652i	0.458092	−	0.264479i	−0.253150	−	0.967427i	$-0.581467\pi$
$643$	11.6160	−	6.70652i	0.458092	−	0.264479i	0.711241	+	0.702948i	$0.248133\pi$
$644$	−2.00745	−	3.47701i	−0.0791048	−	0.137014i
$645$		0			0
$646$	−0.207231	+	5.46426i	−0.00815341	+	0.214988i
$647$			36.1642i			1.42176i	0.703313	+	0.710880i	$0.251703\pi$
$647$			36.1642i			1.42176i	−0.703313	+	0.710880i	$0.748297\pi$
$648$		0			0
$649$	0.515863	+	0.893501i	0.0202494	+	0.0350730i
$650$	18.7229	+	3.79720i	0.734372	+	0.148938i
$651$		0			0
$652$	−11.6342	−	6.71701i	−0.455631	−	0.263058i
$653$		−	28.2889i		−	1.10703i	−0.832839	−	0.553515i	$-0.813286\pi$
$653$		−	28.2889i		−	1.10703i	0.832839	−	0.553515i	$-0.186714\pi$
$654$		0			0
$655$	17.8323	+	39.5537i	0.696766	+	1.54549i
$656$	2.80171	−	4.85270i	0.109388	−	0.189466i
$657$		0			0
$658$			4.45650i			0.173732i
$659$	3.15825	−	5.47025i	0.123028	−	0.213091i	−0.797932	−	0.602747i	$-0.794073\pi$
$659$	3.15825	−	5.47025i	0.123028	−	0.213091i	0.920960	+	0.389656i	$0.127406\pi$
$660$		0			0
$661$	12.4189	−	21.5102i	0.483039	−	0.836649i	−0.516771	−	0.856124i	$-0.672866\pi$
$661$	12.4189	−	21.5102i	0.483039	−	0.836649i	0.999810	+	0.0194748i	$0.00619942\pi$
$662$	−23.4543	+	13.5413i	−0.911575	+	0.526298i
$663$		0			0
$664$	−9.12070			−0.353952
$665$	3.94348	+	9.71367i	0.152921	+	0.376680i
$666$		0			0
$667$	7.68005	−	4.43408i	0.297373	−	0.171688i
$668$	−3.38132	+	1.95221i	−0.130827	+	0.0755331i
$669$		0			0
$670$	−20.7389	−	2.08184i	−0.801213	−	0.0804286i
$671$	1.38657	−	2.40161i	0.0535279	−	0.0927131i
$672$		0			0
$673$		−	28.1903i		−	1.08665i	−0.839521	−	0.543327i	$-0.817164\pi$
$673$		−	28.1903i		−	1.08665i	0.839521	−	0.543327i	$-0.182836\pi$
$674$	−13.8543	+	23.9964i	−0.533648	+	0.924306i
$675$		0			0
$676$	1.59859			0.0614843
$677$		−	16.9194i		−	0.650266i	−0.945668	−	0.325133i	$-0.894591\pi$
$677$		−	16.9194i		−	0.650266i	0.945668	−	0.325133i	$-0.105409\pi$
$678$		0			0
$679$	−6.54000	−	11.3276i	−0.250982	−	0.434714i
$680$	1.15290	+	2.55725i	0.0442118	+	0.0980659i
$681$		0			0
$682$	−2.75879	+	1.59279i	−0.105639	+	0.0609909i
$683$		−	46.8587i		−	1.79300i	−0.443044	−	0.896500i	$-0.646101\pi$
$683$		−	46.8587i		−	1.79300i	0.443044	−	0.896500i	$-0.353899\pi$
$684$		0			0
$685$	−16.0501	−	11.5469i	−0.613244	−	0.441186i
$686$	6.90700	+	11.9633i	0.263710	+	0.456760i
$687$		0			0
$688$	1.92233	+	1.10986i	0.0732883	+	0.0423130i
$689$	−9.55042	−	16.5418i	−0.363842	−	0.630193i
$690$		0			0
$691$	−19.4802			−0.741061			−0.370531	−	0.928820i	$-0.620824\pi$
$691$	−19.4802			−0.741061			−0.370531	+	0.928820i	$0.620824\pi$
$692$		−	15.1721i		−	0.576756i
$693$		0			0
$694$	−1.18262	+	2.04836i	−0.0448917	+	0.0777547i
$695$	13.7986	−	19.1800i	0.523411	−	0.727537i
$696$		0			0
$697$	−6.08766	−	3.51471i	−0.230586	−	0.133129i
$698$	−14.5401	+	8.39471i	−0.550350	+	0.317745i
$699$		0			0
$700$	4.03007	+	3.56108i	0.152322	+	0.134596i
$701$	24.8870	+	43.1055i	0.939968	+	1.62807i	0.765527	+	0.643404i	$0.222478\pi$
$701$	24.8870	+	43.1055i	0.939968	+	1.62807i	0.174441	+	0.984668i	$0.444188\pi$
$702$		0			0
$703$	−4.23278	−	8.01865i	−0.159642	−	0.302429i
$704$	0.410555			0.0154734
$705$		0			0
$706$	11.5009	+	19.9202i	0.432843	+	0.749706i
$707$	2.87653	+	1.66077i	0.108183	+	0.0624596i
$708$		0			0
$709$	−12.3260	+	21.3493i	−0.462913	+	0.801790i	−0.999105	−	0.0423070i	$-0.986529\pi$
$709$	−12.3260	+	21.3493i	−0.462913	+	0.801790i	0.536191	+	0.844097i	$0.319863\pi$
$710$	−17.4166	−	12.5300i	−0.653634	−	0.470243i
$711$		0			0
$712$	−4.72474	−	2.72783i	−0.177067	−	0.102230i
$713$	−25.0826	−	14.4815i	−0.939352	−	0.542335i
$714$		0			0
$715$	−2.84732	−	2.04844i	−0.106484	−	0.0766075i
$716$	4.45581	−	7.71769i	0.166521	−	0.288423i
$717$		0			0
$718$	−3.19445	−	1.84432i	−0.119216	−	0.0688293i
$719$	16.3306	+	28.2854i	0.609027	+	1.05487i	0.991401	+	0.130858i	$0.0417733\pi$
$719$	16.3306	+	28.2854i	0.609027	+	1.05487i	−0.382374	+	0.924008i	$0.624893\pi$
$720$		0			0
$721$	15.9139			0.592666
$722$	1.43908	−	18.9454i	0.0535569	−	0.705076i
$723$		0			0
$724$	−4.61274	−	7.98950i	−0.171431	−	0.296927i
$725$	−7.86573	+	8.90164i	−0.292126	+	0.330599i
$726$		0			0
$727$	9.05449	−	5.22761i	0.335813	−	0.193881i	−0.322606	−	0.946533i	$-0.604559\pi$
$727$	9.05449	−	5.22761i	0.335813	−	0.193881i	0.658419	+	0.752652i	$0.271226\pi$
$728$	3.55906	+	2.05483i	0.131908	+	0.0761569i
$729$		0			0
$730$	9.08530	−	12.6285i	0.336262	−	0.467401i
$731$	1.39231	−	2.41154i	0.0514963	−	0.0891942i
$732$		0			0
$733$		−	20.8146i		−	0.768804i	−0.923166	−	0.384402i	$-0.874408\pi$
$733$		−	20.8146i		−	0.768804i	0.923166	−	0.384402i	$-0.125592\pi$
$734$	11.2269			0.414393
$735$		0			0
$736$	1.86636	+	3.23263i	0.0687950	+	0.119157i
$737$	3.31421	+	1.91346i	0.122080	+	0.0704831i
$738$		0			0
$739$	1.61058	+	2.78961i	0.0592461	+	0.102617i	0.894127	−	0.447813i	$-0.147797\pi$
$739$	1.61058	+	2.78961i	0.0592461	+	0.102617i	−0.834881	+	0.550430i	$0.814464\pi$
$740$	−3.77580	−	2.71642i	−0.138801	−	0.0998575i
$741$		0			0
$742$		−	5.37708i		−	0.197399i
$743$	36.4504	−	21.0447i	1.33724	−	0.772054i	0.350840	−	0.936435i	$-0.385896\pi$
$743$	36.4504	−	21.0447i	1.33724	−	0.772054i	0.986397	+	0.164381i	$0.0525628\pi$
$744$		0			0
$745$	−2.17243	−	4.81864i	−0.0795915	−	0.176541i
$746$	−1.36996	−	2.37285i	−0.0501579	−	0.0868761i
$747$		0			0
$748$		−	0.515036i		−	0.0188316i
$749$	−5.78295			−0.211304
$750$		0			0
$751$	−15.3356	+	26.5620i	−0.559602	+	0.969259i	0.437927	+	0.899010i	$0.355713\pi$
$751$	−15.3356	+	26.5620i	−0.559602	+	0.969259i	−0.997529	+	0.0702491i	$0.977621\pi$
$752$		−	4.14328i		−	0.151090i
$753$		0			0
$754$	−4.53872	+	7.86129i	−0.165290	+	0.286291i
$755$	−8.96485	−	0.899923i	−0.326264	−	0.0327515i
$756$		0			0
$757$	−24.7684	+	14.3000i	−0.900221	+	0.519743i	−0.877272	−	0.479994i	$-0.840639\pi$
$757$	−24.7684	+	14.3000i	−0.900221	+	0.519743i	−0.0229494	+	0.999737i	$0.507306\pi$
$758$	−31.4439	+	18.1541i	−1.14209	+	0.659387i
$759$		0			0
$760$	−3.66631	−	9.03096i	−0.132991	−	0.327587i
$761$	−35.0855			−1.27185			−0.635924	−	0.771752i	$-0.719381\pi$
$761$	−35.0855			−1.27185			−0.635924	+	0.771752i	$0.719381\pi$
$762$		0			0
$763$	−15.2029	+	8.77743i	−0.550384	+	0.317764i
$764$	−9.87227	+	17.0993i	−0.357166	+	0.618630i
$765$		0			0
$766$	5.37069	−	9.30230i	0.194051	−	0.336106i
$767$		−	9.60172i		−	0.346698i
$768$		0			0
$769$	9.23956	−	16.0034i	0.333187	−	0.577097i	−0.649948	−	0.759979i	$-0.725209\pi$
$769$	9.23956	−	16.0034i	0.333187	−	0.577097i	0.983135	+	0.182882i	$0.0585426\pi$
$770$	−0.405833	−	0.900175i	−0.0146252	−	0.0324401i
$771$		0			0
$772$			13.8058i			0.496881i
$773$	39.7340	+	22.9404i	1.42913	+	0.825110i	0.997052	−	0.0767251i	$-0.0244464\pi$
$773$	39.7340	+	22.9404i	1.42913	+	0.825110i	0.432080	+	0.901835i	$0.357780\pi$
$774$		0			0
$775$	38.0219	+	7.71124i	1.36579	+	0.276996i
$776$	6.08034	+	10.5315i	0.218272	+	0.378058i
$777$		0			0
$778$			6.08863i			0.218288i
$779$	20.6744	+	13.0052i	0.740738	+	0.465961i
$780$		0			0
$781$	1.96968	+	3.41158i	0.0704807	+	0.122076i
$782$	4.05530	−	2.34133i	0.145017	−	0.0837257i
$783$		0			0
$784$	−2.92155	−	5.06026i	−0.104341	−	0.180724i
$785$	−39.6652	+	17.8826i	−1.41571	+	0.638257i
$786$		0			0
$787$		−	30.3497i		−	1.08185i	−0.841071	−	0.540925i	$-0.818074\pi$
$787$		−	30.3497i		−	1.08185i	0.841071	−	0.540925i	$-0.181926\pi$
$788$	−7.29198	−	4.21002i	−0.259766	−	0.149976i
$789$		0			0
$790$	16.2374	+	11.6816i	0.577700	+	0.415614i
$791$	−10.5396			−0.374747
$792$		0			0
$793$	−22.3505	+	12.9041i	−0.793689	+	0.458236i
$794$	−11.4778	+	19.8802i	−0.407333	+	0.705522i
$795$		0			0
$796$	−3.33252	−	5.77210i	−0.118118	−	0.204587i
$797$		−	24.0936i		−	0.853441i	−0.904384	−	0.426720i	$-0.859669\pi$
$797$		−	24.0936i		−	0.853441i	0.904384	−	0.426720i	$-0.140331\pi$
$798$		0			0
$799$	−5.19769			−0.183881
$800$	−3.74682	−	3.31079i	−0.132470	−	0.117054i
$801$		0			0
$802$	−15.6958	−	9.06197i	−0.554238	−	0.319989i
$803$	−2.47368	+	1.42818i	−0.0872943	+	0.0503994i
$804$		0			0
$805$	5.24292	−	7.28761i	0.184789	−	0.256854i
$806$	29.6464			1.04425
$807$		0			0
$808$	−2.67436	−	1.54404i	−0.0940837	−	0.0543192i
$809$	41.5203			1.45978			0.729888	−	0.683567i	$-0.239572\pi$
$809$	41.5203			1.45978			0.729888	+	0.683567i	$0.239572\pi$
$810$		0			0
$811$	9.91162	−	17.1674i	0.348044	−	0.602830i	−0.637858	−	0.770154i	$-0.720179\pi$
$811$	9.91162	−	17.1674i	0.348044	−	0.602830i	0.985902	+	0.167324i	$0.0535126\pi$
$812$	−2.21303	+	1.27769i	−0.0776622	+	0.0448383i
$813$		0			0
$814$	0.427012	+	0.739607i	0.0149668	+	0.0259232i
$815$	3.00038	−	29.8892i	0.105099	−	1.04697i
$816$		0			0
$817$	−5.15184	+	8.18990i	−0.180240	+	0.286528i
$818$		−	39.5936i		−	1.38436i
$819$		0			0
$820$	12.4670	+	1.25148i	0.435366	+	0.0437035i
$821$	−27.0794	+	46.9029i	−0.945078	+	1.63692i	−0.189484	+	0.981884i	$0.560681\pi$
$821$	−27.0794	+	46.9029i	−0.945078	+	1.63692i	−0.755595	+	0.655039i	$0.772652\pi$
$822$		0			0
$823$	8.46807	+	4.88904i	0.295178	+	0.170421i	0.640275	−	0.768146i	$-0.278820\pi$
$823$	8.46807	+	4.88904i	0.295178	+	0.170421i	−0.345096	+	0.938567i	$0.612154\pi$
$824$	−14.7954			−0.515424
$825$		0			0
$826$	1.35149	−	2.34085i	0.0470244	−	0.0814486i
$827$	−37.0141	−	21.3701i	−1.28711	−	0.743110i	−0.308968	−	0.951072i	$-0.599984\pi$
$827$	−37.0141	−	21.3701i	−1.28711	−	0.743110i	−0.978137	+	0.207962i	$0.933317\pi$
$828$		0			0
$829$	−39.3417			−1.36639			−0.683197	−	0.730234i	$-0.739411\pi$
$829$	−39.3417			−1.36639			−0.683197	+	0.730234i	$0.739411\pi$
$830$	−8.38214	−	18.5924i	−0.290948	−	0.645350i
$831$		0			0
$832$	−3.30892	−	1.91041i	−0.114716	−	0.0662314i
$833$	−6.34804	+	3.66504i	−0.219947	+	0.126986i
$834$		0			0
$835$	−7.08705	−	5.09863i	−0.245257	−	0.176445i
$836$	−0.0678204	+	1.78828i	−0.00234562	+	0.0618490i
$837$		0			0
$838$	−23.8389	+	13.7634i	−0.823500	+	0.475448i
$839$	8.04689	+	13.9376i	0.277809	+	0.481180i	0.970840	−	0.239728i	$-0.0770583\pi$
$839$	8.04689	+	13.9376i	0.277809	+	0.481180i	−0.693031	+	0.720908i	$0.743725\pi$
$840$		0			0
$841$	11.6778	+	20.2266i	0.402683	+	0.697468i
$842$	0.767812	+	0.443296i	0.0264605	+	0.0152770i
$843$		0			0
$844$	−12.2121			−0.420359
$845$	1.46914	+	3.25870i	0.0505401	+	0.112103i
$846$		0			0
$847$		−	11.6503i		−	0.400308i
$848$			4.99916i			0.171672i
$849$		0			0
$850$	−4.15335	+	4.70034i	−0.142459	+	0.161220i
$851$	−3.88235	+	6.72443i	−0.133085	+	0.230511i
$852$		0			0
$853$	−6.70983	+	3.87392i	−0.229740	+	0.132641i	−0.610452	−	0.792053i	$-0.709012\pi$
$853$	−6.70983	+	3.87392i	−0.229740	+	0.132641i	0.380712	+	0.924694i	$0.375679\pi$
$854$	−7.26524			−0.248612
$855$		0			0
$856$	5.37650			0.183765
$857$	22.3760	−	12.9188i	0.764349	−	0.441297i	−0.0665062	−	0.997786i	$-0.521185\pi$
$857$	22.3760	−	12.9188i	0.764349	−	0.441297i	0.830855	+	0.556489i	$0.187852\pi$
$858$		0			0
$859$	5.48101	−	9.49338i	0.187010	−	0.323910i	−0.757242	−	0.653134i	$-0.773454\pi$
$859$	5.48101	−	9.49338i	0.187010	−	0.323910i	0.944252	+	0.329224i	$0.106787\pi$
$860$	−0.495756	+	4.93862i	−0.0169051	+	0.168406i
$861$		0			0
$862$		−	8.53101i		−	0.290567i
$863$			9.48221i			0.322778i	0.986891	+	0.161389i	$0.0515974\pi$
$863$			9.48221i			0.322778i	−0.986891	+	0.161389i	$0.948403\pi$
$864$		0			0
$865$	30.9279	−	13.9435i	1.05158	−	0.474093i
$866$	14.5271			0.493652
$867$		0			0
$868$	7.22764	+	4.17288i	0.245322	+	0.141637i
$869$	−1.83632	−	3.18060i	−0.0622928	−	0.107894i
$870$		0			0
$871$	−17.8075	−	30.8435i	−0.603385	−	1.04509i
$872$	14.1344	−	8.16051i	0.478652	−	0.276350i
$873$		0			0
$874$	−14.3889	+	7.59544i	−0.486712	+	0.256919i
$875$	−3.55545	+	11.4879i	−0.120196	+	0.388363i
$876$		0			0
$877$	−27.0267	+	15.6039i	−0.912626	+	0.526905i	−0.881275	−	0.472603i	$-0.843314\pi$
$877$	−27.0267	+	15.6039i	−0.912626	+	0.526905i	−0.0313511	+	0.999508i	$0.509981\pi$
$878$	12.1059	+	6.98935i	0.408555	+	0.235879i
$879$		0			0
$880$	0.377309	+	0.836907i	0.0127191	+	0.0282121i
$881$	59.2914			1.99758			0.998789	−	0.0492058i	$-0.0156690\pi$
$881$	59.2914			1.99758			0.998789	+	0.0492058i	$0.0156690\pi$
$882$		0			0
$883$	−10.3188	−	5.95754i	−0.347254	−	0.200487i	0.316221	−	0.948685i	$-0.397586\pi$
$883$	−10.3188	−	5.95754i	−0.347254	−	0.200487i	−0.663475	+	0.748198i	$0.730919\pi$
$884$	−2.39658	+	4.15100i	−0.0806057	+	0.139613i
$885$		0			0
$886$	22.1394			0.743788
$887$	−31.9783	−	18.4627i	−1.07372	−	0.619915i	−0.144528	−	0.989501i	$-0.546166\pi$
$887$	−31.9783	−	18.4627i	−1.07372	−	0.619915i	−0.929197	+	0.369585i	$0.879500\pi$
$888$		0			0
$889$	9.81972	−	17.0083i	0.329343	−	0.570439i
$890$	1.21848	−	12.1382i	0.0408434	−	0.406874i
$891$		0			0
$892$		−	0.570054i		−	0.0190868i
$893$	18.0472	+	0.684437i	0.603925	+	0.0229038i
$894$		0			0
$895$	19.8273	+	1.99034i	0.662755	+	0.0665296i
$896$	−0.537799	−	0.931495i	−0.0179666	−	0.0311190i
$897$		0			0
$898$	28.6533	−	16.5430i	0.956172	−	0.552046i
$899$	−9.21709	+	15.9645i	−0.307407	+	0.532445i
$900$		0			0
$901$	6.27138			0.208930
$902$	−1.99230	−	1.15026i	−0.0663364	−	0.0382993i
$903$		0			0
$904$	9.79888			0.325906
$905$	12.0472	−	16.7455i	0.400463	−	0.556640i
$906$		0			0
$907$	32.6223	−	18.8345i	1.08321	−	0.625389i	0.151446	−	0.988466i	$-0.451607\pi$
$907$	32.6223	−	18.8345i	1.08321	−	0.625389i	0.931759	+	0.363077i	$0.118274\pi$
$908$	2.13316	+	1.23158i	0.0707914	+	0.0408714i
$909$		0			0
$910$	−0.917857	+	9.14351i	−0.0304267	+	0.303104i
$911$	39.7301			1.31632			0.658159	−	0.752879i	$-0.271335\pi$
$911$	39.7301			1.31632			0.658159	+	0.752879i	$0.271335\pi$
$912$		0			0
$913$			3.74455i			0.123926i
$914$	14.5905	+	25.2715i	0.482611	+	0.835907i
$915$		0			0
$916$	5.51250	−	9.54793i	0.182138	−	0.315472i
$917$	−18.0743	+	10.4352i	−0.596865	+	0.344600i
$918$		0			0
$919$	−9.04072			−0.298226			−0.149113	−	0.988820i	$-0.547642\pi$
$919$	−9.04072			−0.298226			−0.149113	+	0.988820i	$0.547642\pi$
$920$	−4.87443	+	6.77541i	−0.160705	+	0.223379i
$921$		0			0
$922$	−17.5583	−	10.1373i	−0.578253	−	0.333854i
$923$		−	36.6615i		−	1.20673i
$924$		0			0
$925$	2.06732	−	10.1933i	0.0679729	−	0.335155i
$926$	−7.68442	−	13.3098i	−0.252526	−	0.437387i
$927$		0			0
$928$	2.05749	−	1.18789i	0.0675405	−	0.0389945i
$929$	−16.8764	−	29.2308i	−0.553696	−	0.959030i	−0.998004	−	0.0631559i	$-0.979883\pi$
$929$	−16.8764	−	29.2308i	−0.553696	−	0.959030i	0.444307	−	0.895874i	$-0.353450\pi$
$930$		0			0
$931$	22.5240	−	11.8897i	0.738193	−	0.389668i
$932$			17.2719i			0.565760i
$933$		0			0
$934$	19.0804	+	33.0483i	0.624331	+	1.08137i
$935$	1.04989	−	0.473330i	0.0343351	−	0.0154795i
$936$		0			0
$937$	46.3764	+	26.7754i	1.51505	+	0.874715i	0.999844	+	0.0176489i	$0.00561812\pi$
$937$	46.3764	+	26.7754i	1.51505	+	0.874715i	0.515207	+	0.857066i	$0.327715\pi$
$938$		−	10.0260i		−	0.327360i
$939$		0			0
$940$	8.44599	−	3.80777i	0.275478	−	0.124196i
$941$	20.1287	−	34.8639i	0.656177	−	1.13653i	−0.325421	−	0.945569i	$-0.605506\pi$
$941$	20.1287	−	34.8639i	0.656177	−	1.13653i	0.981597	−	0.190962i	$-0.0611607\pi$
$942$		0			0
$943$		−	20.9160i		−	0.681120i
$944$	−1.25650	+	2.17633i	−0.0408957	+	0.0708334i
$945$		0			0
$946$	0.455658	−	0.789223i	0.0148147	−	0.0256599i
$947$	44.0513	−	25.4330i	1.43147	−	0.826462i	0.434240	−	0.900797i	$-0.357017\pi$
$947$	44.0513	−	25.4330i	1.43147	−	0.826462i	0.997233	+	0.0743353i	$0.0236835\pi$
$948$		0			0
$949$	26.5826			0.862907
$950$	15.0400	−	15.7734i	0.487962	−	0.511755i
$951$		0			0
$952$	−1.16855	+	0.674662i	−0.0378729	+	0.0218659i
$953$	7.79497	−	4.50043i	0.252504	−	0.145783i	−0.368406	−	0.929665i	$-0.620096\pi$
$953$	7.79497	−	4.50043i	0.252504	−	0.145783i	0.620910	+	0.783882i	$0.286763\pi$
$954$		0			0
$955$	−43.9294	−	4.40978i	−1.42152	−	0.142697i
$956$	3.45372	−	5.98201i	0.111701	−	0.193472i
$957$		0			0
$958$		−	30.2429i		−	0.977105i
$959$	4.75542	−	8.23663i	0.153560	−	0.265975i
$960$		0			0
$961$	29.2050			0.942097
$962$		−	7.94794i		−	0.256252i
$963$		0			0
$964$	11.0140	+	19.0767i	0.354736	+	0.614420i
$965$	−28.1428	+	12.6878i	−0.905948	+	0.408436i
$966$		0			0
$967$	27.4733	−	15.8617i	0.883480	−	0.510078i	0.0116759	−	0.999932i	$-0.496283\pi$
$967$	27.4733	−	15.8617i	0.883480	−	0.510078i	0.871804	+	0.489854i	$0.162950\pi$
$968$			10.8314i			0.348136i
$969$		0			0
$970$	−15.8802	+	22.0733i	−0.509882	+	0.708731i
$971$	8.90105	+	15.4171i	0.285648	+	0.494758i	0.972766	−	0.231788i	$-0.0744577\pi$
$971$	8.90105	+	15.4171i	0.285648	+	0.494758i	−0.687118	+	0.726546i	$0.741124\pi$
$972$		0			0
$973$	9.84279	+	5.68274i	0.315545	+	0.182180i
$974$	−18.8749	−	32.6923i	−0.604792	−	1.04753i
$975$		0			0
$976$	6.75461			0.216210
$977$			31.9251i			1.02137i	0.859767	+	0.510687i	$0.170609\pi$
$977$			31.9251i			1.02137i	−0.859767	+	0.510687i	$0.829391\pi$
$978$		0			0
$979$	−1.11992	+	1.93976i	−0.0357929	+	0.0619951i
$980$	7.63027	−	10.6060i	0.243740	−	0.338797i
$981$		0			0
$982$	18.4456	+	10.6495i	0.588621	+	0.339841i
$983$	−30.9561	+	17.8725i	−0.987346	+	0.570045i	−0.904480	−	0.426516i	$-0.859741\pi$
$983$	−30.9561	+	17.8725i	−0.987346	+	0.570045i	−0.0828663	+	0.996561i	$0.526407\pi$
$984$		0			0
$985$	1.88055	−	18.7336i	0.0599192	−	0.596904i
$986$	−1.49020	−	2.58110i	−0.0474576	−	0.0821989i
$987$		0			0
$988$	8.86789	−	14.0973i	0.282125	−	0.448495i
$989$	8.28560			0.263467
$990$		0			0
$991$	17.1480	+	29.7012i	0.544724	+	0.943490i	0.998624	+	0.0524376i	$0.0166991\pi$
$991$	17.1480	+	29.7012i	0.544724	+	0.943490i	−0.453900	+	0.891053i	$0.649968\pi$
$992$	−6.71965	−	3.87959i	−0.213349	−	0.123177i
$993$		0			0
$994$	5.16029	−	8.93788i	0.163674	−	0.283492i
$995$	8.70363	−	12.0980i	0.275924	−	0.383531i
$996$		0			0
$997$	−2.35098	−	1.35734i	−0.0744561	−	0.0429873i	0.462310	−	0.886719i	$-0.347021\pi$
$997$	−2.35098	−	1.35734i	−0.0744561	−	0.0429873i	−0.536766	+	0.843731i	$0.680354\pi$
$998$	−17.7466	−	10.2460i	−0.561759	−	0.324332i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.c.919.10		20
3.2	odd	2		570.2.q.c.349.1	yes	20
5.4	even	2	inner	1710.2.t.c.919.2		20
15.14	odd	2		570.2.q.c.349.9	yes	20
19.11	even	3	inner	1710.2.t.c.1189.2		20
57.11	odd	6		570.2.q.c.49.9	yes	20
95.49	even	6	inner	1710.2.t.c.1189.10		20
285.239	odd	6		570.2.q.c.49.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.1	✓	20	285.239	odd	6
570.2.q.c.49.9	yes	20	57.11	odd	6
570.2.q.c.349.1	yes	20	3.2	odd	2
570.2.q.c.349.9	yes	20	15.14	odd	2
1710.2.t.c.919.2		20	5.4	even	2	inner
1710.2.t.c.919.10		20	1.1	even	1	trivial
1710.2.t.c.1189.2		20	19.11	even	3	inner
1710.2.t.c.1189.10		20	95.49	even	6	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.22489 + 0.223342i) q^{5} +1.07560i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.22489 + 0.223342i) q^{5} +1.07560i q^{7} -1.00000i q^{8} +(2.03848 - 0.919023i) q^{10} -0.410555 q^{11} +(3.30892 + 1.91041i) q^{13} +(0.537799 + 0.931495i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.08642 + 0.627244i) q^{17} +(3.85480 - 2.03482i) q^{19} +(1.30586 - 1.81514i) q^{20} +(-0.355551 + 0.205277i) q^{22} +(-3.23263 - 1.86636i) q^{23} +(4.90024 + 0.993820i) q^{25} +3.82081 q^{26} +(0.931495 + 0.537799i) q^{28} +(-1.18789 + 2.05749i) q^{29} +7.75919 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.627244 + 1.08642i) q^{34} +(-0.240226 + 2.39308i) q^{35} -2.08017i q^{37} +(2.32094 - 3.68961i) q^{38} +(0.223342 - 2.22489i) q^{40} +(2.80171 + 4.85270i) q^{41} +(-1.92233 + 1.10986i) q^{43} +(-0.205277 + 0.355551i) q^{44} -3.73273 q^{46} +(3.58819 + 2.07164i) q^{47} +5.84309 q^{49} +(4.74064 - 1.58945i) q^{50} +(3.30892 - 1.91041i) q^{52} +(-4.32940 - 2.49958i) q^{53} +(-0.913438 - 0.0916940i) q^{55} +1.07560 q^{56} +2.37579i q^{58} +(-1.25650 - 2.17633i) q^{59} +(-3.37731 + 5.84967i) q^{61} +(6.71965 - 3.87959i) q^{62} -1.00000 q^{64} +(6.93529 + 4.98945i) q^{65} +(-8.07251 - 4.66066i) q^{67} +1.25449i q^{68} +(0.988499 + 2.19258i) q^{70} +(-4.79760 - 8.30969i) q^{71} +(6.02521 - 3.47866i) q^{73} +(-1.04009 - 1.80148i) q^{74} +(0.165192 - 4.35577i) q^{76} -0.441592i q^{77} +(4.47277 + 7.74707i) q^{79} +(-0.919023 - 2.03848i) q^{80} +(4.85270 + 2.80171i) q^{82} -9.12070i q^{83} +(-2.55725 + 1.15290i) q^{85} +(-1.10986 + 1.92233i) q^{86} +0.410555i q^{88} +(2.72783 - 4.72474i) q^{89} +(-2.05483 + 3.55906i) q^{91} +(-3.23263 + 1.86636i) q^{92} +4.14328 q^{94} +(9.03096 - 3.66631i) q^{95} +(-10.5315 + 6.08034i) q^{97} +(5.06026 - 2.92155i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 20 * q + 10 * q^4	\( 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

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