LMFDB - Embedded newform 990.2.n.a.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(91,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,0,-1,-1,0,-5,-1,0,4,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	990.181
Dual form			990.2.n.a.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.92705 + 2.12663i) q^{7} +(-0.809017 - 0.587785i) q^{8} +1.00000 q^{10} +(-2.80902 - 1.76336i) q^{11} +(0.190983 + 0.587785i) q^{13} +(-2.92705 - 2.12663i) q^{14} +(0.309017 - 0.951057i) q^{16} +(2.00000 - 6.15537i) q^{17} +(0.500000 + 0.363271i) q^{19} +(0.309017 + 0.951057i) q^{20} +(0.809017 - 3.21644i) q^{22} -4.85410 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.500000 + 0.363271i) q^{26} +(1.11803 - 3.44095i) q^{28} +(3.00000 - 2.17963i) q^{29} +(-2.85410 - 8.78402i) q^{31} +1.00000 q^{32} +6.47214 q^{34} +(1.11803 + 3.44095i) q^{35} +(0.500000 - 0.363271i) q^{37} +(-0.190983 + 0.587785i) q^{38} +(-0.809017 + 0.587785i) q^{40} +(-7.54508 - 5.48183i) q^{41} +0.763932 q^{43} +(3.30902 - 0.224514i) q^{44} +(-1.50000 - 4.61653i) q^{46} +(-2.11803 - 1.53884i) q^{47} +(1.88197 - 5.79210i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-0.500000 - 0.363271i) q^{52} +(1.88197 + 5.79210i) q^{53} +(-2.54508 + 2.12663i) q^{55} +3.61803 q^{56} +(3.00000 + 2.17963i) q^{58} +(-11.8262 + 8.59226i) q^{59} +(3.47214 - 10.6861i) q^{61} +(7.47214 - 5.42882i) q^{62} +(0.309017 + 0.951057i) q^{64} +0.618034 q^{65} -8.18034 q^{67} +(2.00000 + 6.15537i) q^{68} +(-2.92705 + 2.12663i) q^{70} +(0.0901699 - 0.277515i) q^{71} +(-8.85410 + 6.43288i) q^{73} +(0.500000 + 0.363271i) q^{74} -0.618034 q^{76} +(11.9721 - 0.812299i) q^{77} +(-1.38197 - 4.25325i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(2.88197 - 8.86978i) q^{82} +(1.52786 - 4.70228i) q^{83} +(-5.23607 - 3.80423i) q^{85} +(0.236068 + 0.726543i) q^{86} +(1.23607 + 3.07768i) q^{88} +5.14590 q^{89} +(-1.80902 - 1.31433i) q^{91} +(3.92705 - 2.85317i) q^{92} +(0.809017 - 2.48990i) q^{94} +(0.500000 - 0.363271i) q^{95} +(4.61803 + 14.2128i) q^{97} +6.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8} + 4 q^{10} - 9 q^{11} + 3 q^{13} - 5 q^{14} - q^{16} + 8 q^{17} + 2 q^{19} - q^{20} + q^{22} - 6 q^{23} - q^{25} - 2 q^{26} + 12 q^{29} + 2 q^{31} + 4 q^{32}+ \cdots + 2 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - q^5 - 5 * q^7 - q^8 + 4 * q^10 - 9 * q^11 + 3 * q^13 - 5 * q^14 - q^16 + 8 * q^17 + 2 * q^19 - q^20 + q^22 - 6 * q^23 - q^25 - 2 * q^26 + 12 * q^29 + 2 * q^31 + 4 * q^32 + 8 * q^34 + 2 * q^37 - 3 * q^38 - q^40 - 19 * q^41 + 12 * q^43 + 11 * q^44 - 6 * q^46 - 4 * q^47 + 12 * q^49 - q^50 - 2 * q^52 + 12 * q^53 + q^55 + 10 * q^56 + 12 * q^58 - 16 * q^59 - 4 * q^61 + 12 * q^62 - q^64 - 2 * q^65 + 12 * q^67 + 8 * q^68 - 5 * q^70 - 22 * q^71 - 22 * q^73 + 2 * q^74 + 2 * q^76 + 30 * q^77 - 10 * q^79 - q^80 + 16 * q^82 + 24 * q^83 - 12 * q^85 - 8 * q^86 - 4 * q^88 + 34 * q^89 - 5 * q^91 + 9 * q^92 + q^94 + 2 * q^95 + 14 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−2.92705	+	2.12663i	−1.10632	+	0.803789i	−0.982080	−	0.188463i	$-0.939650\pi$
$7$	−2.92705	+	2.12663i	−1.10632	+	0.803789i	−0.124241	+	0.992252i	$0.539650\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$		0			0
$10$	1.00000			0.316228
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$12$		0			0
$13$	0.190983	+	0.587785i	0.0529692	+	0.163022i	0.974042	−	0.226369i	$-0.0726855\pi$
$13$	0.190983	+	0.587785i	0.0529692	+	0.163022i	−0.921073	+	0.389391i	$0.872685\pi$
$14$	−2.92705	−	2.12663i	−0.782287	−	0.568365i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.00000	−	6.15537i	0.485071	−	1.49290i	−0.346806	−	0.937937i	$-0.612734\pi$
$17$	2.00000	−	6.15537i	0.485071	−	1.49290i	0.831878	−	0.554959i	$-0.187266\pi$
$18$		0			0
$19$	0.500000	+	0.363271i	0.114708	+	0.0833401i	0.643660	−	0.765311i	$-0.277415\pi$
$19$	0.500000	+	0.363271i	0.114708	+	0.0833401i	−0.528952	+	0.848651i	$0.677415\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$		0			0
$22$	0.809017	−	3.21644i	0.172483	−	0.685747i
$23$	−4.85410			−1.01215			−0.506075	−	0.862489i	$-0.668904\pi$
$23$	−4.85410			−1.01215			−0.506075	+	0.862489i	$0.668904\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−0.500000	+	0.363271i	−0.0980581	+	0.0712434i
$27$		0			0
$28$	1.11803	−	3.44095i	0.211289	−	0.650279i
$29$	3.00000	−	2.17963i	0.557086	−	0.404747i	−0.273305	−	0.961927i	$-0.588117\pi$
$29$	3.00000	−	2.17963i	0.557086	−	0.404747i	0.830391	+	0.557181i	$0.188117\pi$
$30$		0			0
$31$	−2.85410	−	8.78402i	−0.512612	−	1.57766i	−0.787586	−	0.616205i	$-0.788669\pi$
$31$	−2.85410	−	8.78402i	−0.512612	−	1.57766i	0.274974	−	0.961452i	$-0.411331\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	6.47214			1.10996
$35$	1.11803	+	3.44095i	0.188982	+	0.581628i
$36$		0			0
$37$	0.500000	−	0.363271i	0.0821995	−	0.0597214i	−0.545927	−	0.837833i	$-0.683822\pi$
$37$	0.500000	−	0.363271i	0.0821995	−	0.0597214i	0.628126	+	0.778112i	$0.283822\pi$
$38$	−0.190983	+	0.587785i	−0.0309815	+	0.0953514i
$39$		0			0
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−7.54508	−	5.48183i	−1.17834	−	0.856117i	−0.186360	−	0.982481i	$-0.559669\pi$
$41$	−7.54508	−	5.48183i	−1.17834	−	0.856117i	−0.991984	+	0.126364i	$0.959669\pi$
$42$		0			0
$43$	0.763932			0.116499			0.0582493	−	0.998302i	$-0.481448\pi$
$43$	0.763932			0.116499			0.0582493	+	0.998302i	$0.481448\pi$
$44$	3.30902	−	0.224514i	0.498853	−	0.0338468i
$45$		0			0
$46$	−1.50000	−	4.61653i	−0.221163	−	0.680670i
$47$	−2.11803	−	1.53884i	−0.308947	−	0.224463i	0.422498	−	0.906364i	$-0.361154\pi$
$47$	−2.11803	−	1.53884i	−0.308947	−	0.224463i	−0.731445	+	0.681901i	$0.761154\pi$
$48$		0			0
$49$	1.88197	−	5.79210i	0.268852	−	0.827442i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$		0			0
$52$	−0.500000	−	0.363271i	−0.0693375	−	0.0503767i
$53$	1.88197	+	5.79210i	0.258508	+	0.795606i	0.993118	+	0.117116i	$0.0373650\pi$
$53$	1.88197	+	5.79210i	0.258508	+	0.795606i	−0.734610	+	0.678489i	$0.762635\pi$
$54$		0			0
$55$	−2.54508	+	2.12663i	−0.343179	+	0.286754i
$56$	3.61803			0.483480
$57$		0			0
$58$	3.00000	+	2.17963i	0.393919	+	0.286199i
$59$	−11.8262	+	8.59226i	−1.53965	+	1.11862i	−0.589087	+	0.808069i	$0.700513\pi$
$59$	−11.8262	+	8.59226i	−1.53965	+	1.11862i	−0.950558	+	0.310548i	$0.899487\pi$
$60$		0			0
$61$	3.47214	−	10.6861i	0.444561	−	1.36822i	−0.438403	−	0.898779i	$-0.644456\pi$
$61$	3.47214	−	10.6861i	0.444561	−	1.36822i	0.882964	−	0.469441i	$-0.155544\pi$
$62$	7.47214	−	5.42882i	0.948962	−	0.689461i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.618034			0.0766577
$66$		0			0
$67$	−8.18034			−0.999388			−0.499694	−	0.866202i	$-0.666554\pi$
$67$	−8.18034			−0.999388			−0.499694	+	0.866202i	$0.666554\pi$
$68$	2.00000	+	6.15537i	0.242536	+	0.746448i
$69$		0			0
$70$	−2.92705	+	2.12663i	−0.349850	+	0.254181i
$71$	0.0901699	−	0.277515i	0.0107012	−	0.0329349i	−0.945563	−	0.325438i	$-0.894488\pi$
$71$	0.0901699	−	0.277515i	0.0107012	−	0.0329349i	0.956265	+	0.292503i	$0.0944882\pi$
$72$		0			0
$73$	−8.85410	+	6.43288i	−1.03629	+	0.752912i	−0.969559	−	0.244859i	$-0.921258\pi$
$73$	−8.85410	+	6.43288i	−1.03629	+	0.752912i	−0.0667355	+	0.997771i	$0.521258\pi$
$74$	0.500000	+	0.363271i	0.0581238	+	0.0422294i
$75$		0			0
$76$	−0.618034			−0.0708934
$77$	11.9721	−	0.812299i	1.36435	−	0.0925701i
$78$		0			0
$79$	−1.38197	−	4.25325i	−0.155483	−	0.478528i	0.842726	−	0.538342i	$-0.180949\pi$
$79$	−1.38197	−	4.25325i	−0.155483	−	0.478528i	−0.998210	+	0.0598139i	$0.980949\pi$
$80$	−0.809017	−	0.587785i	−0.0904508	−	0.0657164i
$81$		0			0
$82$	2.88197	−	8.86978i	0.318260	−	0.979503i
$83$	1.52786	−	4.70228i	0.167705	−	0.516143i	−0.831521	−	0.555494i	$-0.812529\pi$
$83$	1.52786	−	4.70228i	0.167705	−	0.516143i	0.999225	+	0.0393515i	$0.0125292\pi$
$84$		0			0
$85$	−5.23607	−	3.80423i	−0.567931	−	0.412626i
$86$	0.236068	+	0.726543i	0.0254559	+	0.0783451i
$87$		0			0
$88$	1.23607	+	3.07768i	0.131765	+	0.328082i
$89$	5.14590			0.545464			0.272732	−	0.962090i	$-0.412073\pi$
$89$	5.14590			0.545464			0.272732	+	0.962090i	$0.412073\pi$
$90$		0			0
$91$	−1.80902	−	1.31433i	−0.189637	−	0.137779i
$92$	3.92705	−	2.85317i	0.409423	−	0.297463i
$93$		0			0
$94$	0.809017	−	2.48990i	0.0834437	−	0.256813i
$95$	0.500000	−	0.363271i	0.0512989	−	0.0372708i
$96$		0			0
$97$	4.61803	+	14.2128i	0.468890	+	1.44310i	0.854023	+	0.520235i	$0.174156\pi$
$97$	4.61803	+	14.2128i	0.468890	+	1.44310i	−0.385133	+	0.922861i	$0.625844\pi$
$98$	6.09017			0.615200
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.23607	−	3.80423i	−0.122993	−	0.378535i	0.870537	−	0.492103i	$-0.163772\pi$
$101$	−1.23607	−	3.80423i	−0.122993	−	0.378535i	−0.993530	+	0.113569i	$0.963772\pi$
$102$		0			0
$103$	7.97214	−	5.79210i	0.785518	−	0.570712i	−0.121112	−	0.992639i	$-0.538646\pi$
$103$	7.97214	−	5.79210i	0.785518	−	0.570712i	0.906630	+	0.421927i	$0.138646\pi$
$104$	0.190983	−	0.587785i	0.0187274	−	0.0576371i
$105$		0			0
$106$	−4.92705	+	3.57971i	−0.478557	+	0.347692i
$107$	14.4721	+	10.5146i	1.39907	+	1.01649i	0.994800	+	0.101849i	$0.0324759\pi$
$107$	14.4721	+	10.5146i	1.39907	+	1.01649i	0.404274	+	0.914638i	$0.367524\pi$
$108$		0			0
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	−2.80902	−	1.76336i	−0.267829	−	0.168129i
$111$		0			0
$112$	1.11803	+	3.44095i	0.105644	+	0.325140i
$113$	−10.0902	−	7.33094i	−0.949203	−	0.689637i	0.00141497	−	0.999999i	$-0.499550\pi$
$113$	−10.0902	−	7.33094i	−0.949203	−	0.689637i	−0.950618	+	0.310362i	$0.899550\pi$
$114$		0			0
$115$	−1.50000	+	4.61653i	−0.139876	+	0.430493i
$116$	−1.14590	+	3.52671i	−0.106394	+	0.327447i
$117$		0			0
$118$	−11.8262	−	8.59226i	−1.08869	−	0.790982i
$119$	7.23607	+	22.2703i	0.663329	+	2.04152i
$120$		0			0
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$	11.2361			1.01727
$123$		0			0
$124$	7.47214	+	5.42882i	0.671018	+	0.487523i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	3.89919	−	12.0005i	0.345997	−	1.06487i	−0.615051	−	0.788487i	$-0.710865\pi$
$127$	3.89919	−	12.0005i	0.345997	−	1.06487i	0.961048	−	0.276382i	$-0.0891354\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$		0			0
$130$	0.190983	+	0.587785i	0.0167503	+	0.0515522i
$131$	−20.9443			−1.82991			−0.914955	−	0.403556i	$-0.867774\pi$
$131$	−20.9443			−1.82991			−0.914955	+	0.403556i	$0.867774\pi$
$132$		0			0
$133$	−2.23607			−0.193892
$134$	−2.52786	−	7.77997i	−0.218374	−	0.672087i
$135$		0			0
$136$	−5.23607	+	3.80423i	−0.448989	+	0.326210i
$137$	−4.76393	+	14.6619i	−0.407010	+	1.25265i	0.512195	+	0.858869i	$0.328833\pi$
$137$	−4.76393	+	14.6619i	−0.407010	+	1.25265i	−0.919205	+	0.393779i	$0.871167\pi$
$138$		0			0
$139$	6.16312	−	4.47777i	0.522749	−	0.379799i	−0.294890	−	0.955531i	$-0.595283\pi$
$139$	6.16312	−	4.47777i	0.522749	−	0.379799i	0.817638	+	0.575732i	$0.195283\pi$
$140$	−2.92705	−	2.12663i	−0.247381	−	0.179733i
$141$		0			0
$142$	0.291796			0.0244870
$143$	0.500000	−	1.98787i	0.0418121	−	0.166234i
$144$		0			0
$145$	−1.14590	−	3.52671i	−0.0951617	−	0.292877i
$146$	−8.85410	−	6.43288i	−0.732771	−	0.532389i
$147$		0			0
$148$	−0.190983	+	0.587785i	−0.0156987	+	0.0483157i
$149$	2.76393	−	8.50651i	0.226430	−	0.696880i	−0.771713	−	0.635971i	$-0.780600\pi$
$149$	2.76393	−	8.50651i	0.226430	−	0.696880i	0.998143	−	0.0609095i	$-0.0194001\pi$
$150$		0			0
$151$	10.0902	+	7.33094i	0.821126	+	0.596583i	0.917035	−	0.398807i	$-0.130576\pi$
$151$	10.0902	+	7.33094i	0.821126	+	0.596583i	−0.0959085	+	0.995390i	$0.530576\pi$
$152$	−0.190983	−	0.587785i	−0.0154908	−	0.0476757i
$153$		0			0
$154$	4.47214	+	11.1352i	0.360375	+	0.897297i
$155$	−9.23607			−0.741859
$156$		0			0
$157$	4.54508	+	3.30220i	0.362737	+	0.263544i	0.754193	−	0.656653i	$-0.228028\pi$
$157$	4.54508	+	3.30220i	0.362737	+	0.263544i	−0.391456	+	0.920197i	$0.628028\pi$
$158$	3.61803	−	2.62866i	0.287835	−	0.209125i
$159$		0			0
$160$	0.309017	−	0.951057i	0.0244299	−	0.0751876i
$161$	14.2082	−	10.3229i	1.11976	−	0.813556i
$162$		0			0
$163$	5.52786	+	17.0130i	0.432976	+	1.33256i	0.895147	+	0.445771i	$0.147071\pi$
$163$	5.52786	+	17.0130i	0.432976	+	1.33256i	−0.462171	+	0.886791i	$0.652929\pi$
$164$	9.32624			0.728257
$165$		0			0
$166$	4.94427			0.383750
$167$	3.57295	+	10.9964i	0.276483	+	0.850927i	0.988823	+	0.149093i	$0.0476354\pi$
$167$	3.57295	+	10.9964i	0.276483	+	0.850927i	−0.712340	+	0.701834i	$0.752365\pi$
$168$		0			0
$169$	10.2082	−	7.41669i	0.785246	−	0.570515i
$170$	2.00000	−	6.15537i	0.153393	−	0.472095i
$171$		0			0
$172$	−0.618034	+	0.449028i	−0.0471246	+	0.0342381i
$173$	−19.8713	−	14.4374i	−1.51079	−	1.09765i	−0.965826	−	0.259192i	$-0.916544\pi$
$173$	−19.8713	−	14.4374i	−1.51079	−	1.09765i	−0.544963	−	0.838460i	$-0.683456\pi$
$174$		0			0
$175$	3.61803			0.273498
$176$	−2.54508	+	2.12663i	−0.191843	+	0.160301i
$177$		0			0
$178$	1.59017	+	4.89404i	0.119188	+	0.366824i
$179$	−9.01722	−	6.55139i	−0.673979	−	0.489674i	0.197376	−	0.980328i	$-0.436758\pi$
$179$	−9.01722	−	6.55139i	−0.673979	−	0.489674i	−0.871355	+	0.490654i	$0.836758\pi$
$180$		0			0
$181$	−7.52786	+	23.1684i	−0.559542	+	1.72209i	0.124095	+	0.992270i	$0.460397\pi$
$181$	−7.52786	+	23.1684i	−0.559542	+	1.72209i	−0.683637	+	0.729822i	$0.739603\pi$
$182$	0.690983	−	2.12663i	0.0512191	−	0.157636i
$183$		0			0
$184$	3.92705	+	2.85317i	0.289506	+	0.210338i
$185$	−0.190983	−	0.587785i	−0.0140413	−	0.0432148i
$186$		0			0
$187$	−16.4721	+	13.7638i	−1.20456	+	1.00651i
$188$	2.61803			0.190940
$189$		0			0
$190$	0.500000	+	0.363271i	0.0362738	+	0.0263545i
$191$	−11.0902	+	8.05748i	−0.802457	+	0.583019i	−0.911634	−	0.411004i	$-0.865178\pi$
$191$	−11.0902	+	8.05748i	−0.802457	+	0.583019i	0.109177	+	0.994022i	$0.465178\pi$
$192$		0			0
$193$	−1.14590	+	3.52671i	−0.0824835	+	0.253858i	−0.983790	−	0.179323i	$-0.942609\pi$
$193$	−1.14590	+	3.52671i	−0.0824835	+	0.253858i	0.901307	+	0.433182i	$0.142609\pi$
$194$	−12.0902	+	8.78402i	−0.868024	+	0.630656i
$195$		0			0
$196$	1.88197	+	5.79210i	0.134426	+	0.413721i
$197$	−3.61803			−0.257774			−0.128887	−	0.991659i	$-0.541140\pi$
$197$	−3.61803			−0.257774			−0.128887	+	0.991659i	$0.541140\pi$
$198$		0			0
$199$	−12.9443			−0.917595			−0.458798	−	0.888541i	$-0.651720\pi$
$199$	−12.9443			−0.917595			−0.458798	+	0.888541i	$0.651720\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$		0			0
$202$	3.23607	−	2.35114i	0.227689	−	0.165426i
$203$	−4.14590	+	12.7598i	−0.290985	+	0.895560i
$204$		0			0
$205$	−7.54508	+	5.48183i	−0.526972	+	0.382867i
$206$	7.97214	+	5.79210i	0.555445	+	0.403554i
$207$		0			0
$208$	0.618034			0.0428529
$209$	−0.763932	−	1.90211i	−0.0528423	−	0.131572i
$210$		0			0
$211$	−7.23607	−	22.2703i	−0.498151	−	1.53315i	−0.811987	−	0.583675i	$-0.801614\pi$
$211$	−7.23607	−	22.2703i	−0.498151	−	1.53315i	0.313836	−	0.949477i	$-0.398386\pi$
$212$	−4.92705	−	3.57971i	−0.338391	−	0.245856i
$213$		0			0
$214$	−5.52786	+	17.0130i	−0.377877	+	1.16299i
$215$	0.236068	−	0.726543i	0.0160997	−	0.0495498i
$216$		0			0
$217$	27.0344	+	19.6417i	1.83522	+	1.33336i
$218$	1.23607	+	3.80423i	0.0837171	+	0.257655i
$219$		0			0
$220$	0.809017	−	3.21644i	0.0545439	−	0.216852i
$221$	4.00000			0.269069
$222$		0			0
$223$	−6.16312	−	4.47777i	−0.412713	−	0.299854i	0.361986	−	0.932183i	$-0.382099\pi$
$223$	−6.16312	−	4.47777i	−0.412713	−	0.299854i	−0.774699	+	0.632330i	$0.782099\pi$
$224$	−2.92705	+	2.12663i	−0.195572	+	0.142091i
$225$		0			0
$226$	3.85410	−	11.8617i	0.256371	−	0.789029i
$227$	−3.38197	+	2.45714i	−0.224469	+	0.163086i	−0.694336	−	0.719651i	$-0.744302\pi$
$227$	−3.38197	+	2.45714i	−0.224469	+	0.163086i	0.469867	+	0.882737i	$0.344302\pi$
$228$		0			0
$229$	−3.56231	−	10.9637i	−0.235404	−	0.724498i	−0.997068	−	0.0765260i	$-0.975617\pi$
$229$	−3.56231	−	10.9637i	−0.235404	−	0.724498i	0.761664	−	0.647972i	$-0.224383\pi$
$230$	−4.85410			−0.320070
$231$		0			0
$232$	−3.70820			−0.243456
$233$	5.03444	+	15.4944i	0.329817	+	1.01507i	0.969219	+	0.246200i	$0.0791821\pi$
$233$	5.03444	+	15.4944i	0.329817	+	1.01507i	−0.639402	+	0.768873i	$0.720818\pi$
$234$		0			0
$235$	−2.11803	+	1.53884i	−0.138165	+	0.100383i
$236$	4.51722	−	13.9026i	0.294046	−	0.904981i
$237$		0			0
$238$	−18.9443	+	13.7638i	−1.22797	+	0.892176i
$239$	17.9443	+	13.0373i	1.16072	+	0.843311i	0.989869	−	0.141986i	$-0.0453487\pi$
$239$	17.9443	+	13.0373i	1.16072	+	0.843311i	0.170850	+	0.985297i	$0.445349\pi$
$240$		0			0
$241$	−25.6180			−1.65020			−0.825101	−	0.564985i	$-0.808882\pi$
$241$	−25.6180			−1.65020			−0.825101	+	0.564985i	$0.808882\pi$
$242$	−7.94427	+	7.60845i	−0.510677	+	0.489090i
$243$		0			0
$244$	3.47214	+	10.6861i	0.222281	+	0.684110i
$245$	−4.92705	−	3.57971i	−0.314778	−	0.228699i
$246$		0			0
$247$	−0.118034	+	0.363271i	−0.00751032	+	0.0231144i
$248$	−2.85410	+	8.78402i	−0.181236	+	0.557786i
$249$		0			0
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−3.55573	−	10.9434i	−0.224436	−	0.690742i	−0.998348	−	0.0574495i	$-0.981703\pi$
$251$	−3.55573	−	10.9434i	−0.224436	−	0.690742i	0.773913	−	0.633292i	$-0.218297\pi$
$252$		0			0
$253$	13.6353	+	8.55951i	0.857241	+	0.538132i
$254$	12.6180			0.791726
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−4.09017	+	2.97168i	−0.255138	+	0.185368i	−0.708001	−	0.706212i	$-0.750403\pi$
$257$	−4.09017	+	2.97168i	−0.255138	+	0.185368i	0.452863	+	0.891580i	$0.350403\pi$
$258$		0			0
$259$	−0.690983	+	2.12663i	−0.0429356	+	0.132142i
$260$	−0.500000	+	0.363271i	−0.0310087	+	0.0225291i
$261$		0			0
$262$	−6.47214	−	19.9192i	−0.399850	−	1.23061i
$263$	8.14590			0.502298			0.251149	−	0.967948i	$-0.419192\pi$
$263$	8.14590			0.502298			0.251149	+	0.967948i	$0.419192\pi$
$264$		0			0
$265$	6.09017			0.374116
$266$	−0.690983	−	2.12663i	−0.0423669	−	0.130392i
$267$		0			0
$268$	6.61803	−	4.80828i	0.404261	−	0.293713i
$269$	7.65248	−	23.5519i	0.466580	−	1.43598i	−0.390405	−	0.920643i	$-0.627665\pi$
$269$	7.65248	−	23.5519i	0.466580	−	1.43598i	0.856985	−	0.515341i	$-0.172335\pi$
$270$		0			0
$271$	−0.527864	+	0.383516i	−0.0320655	+	0.0232969i	−0.603703	−	0.797210i	$-0.706309\pi$
$271$	−0.527864	+	0.383516i	−0.0320655	+	0.0232969i	0.571637	+	0.820507i	$0.306309\pi$
$272$	−5.23607	−	3.80423i	−0.317483	−	0.230665i
$273$		0			0
$274$	−15.4164			−0.931339
$275$	1.23607	+	3.07768i	0.0745377	+	0.185591i
$276$		0			0
$277$	−2.55573	−	7.86572i	−0.153559	−	0.472605i	0.844453	−	0.535629i	$-0.179926\pi$
$277$	−2.55573	−	7.86572i	−0.153559	−	0.472605i	−0.998012	+	0.0630239i	$0.979926\pi$
$278$	6.16312	+	4.47777i	0.369639	+	0.268559i
$279$		0			0
$280$	1.11803	−	3.44095i	0.0668153	−	0.205636i
$281$	−2.43769	+	7.50245i	−0.145421	+	0.447559i	−0.997065	−	0.0765616i	$-0.975606\pi$
$281$	−2.43769	+	7.50245i	−0.145421	+	0.447559i	0.851644	+	0.524120i	$0.175606\pi$
$282$		0			0
$283$	−3.00000	−	2.17963i	−0.178331	−	0.129565i	0.495039	−	0.868871i	$-0.335154\pi$
$283$	−3.00000	−	2.17963i	−0.178331	−	0.129565i	−0.673370	+	0.739306i	$0.735154\pi$
$284$	0.0901699	+	0.277515i	0.00535060	+	0.0164675i
$285$		0			0
$286$	2.04508	−	0.138757i	0.120928	−	0.00820489i
$287$	33.7426			1.99177
$288$		0			0
$289$	−20.1353	−	14.6291i	−1.18443	−	0.860536i
$290$	3.00000	−	2.17963i	0.176166	−	0.127992i
$291$		0			0
$292$	3.38197	−	10.4086i	0.197915	−	0.609118i
$293$	8.92705	−	6.48588i	0.521524	−	0.378909i	−0.295654	−	0.955295i	$-0.595537\pi$
$293$	8.92705	−	6.48588i	0.521524	−	0.378909i	0.817178	+	0.576386i	$0.195537\pi$
$294$		0			0
$295$	4.51722	+	13.9026i	0.263003	+	0.809439i
$296$	−0.618034			−0.0359225
$297$		0			0
$298$	8.94427			0.518128
$299$	−0.927051	−	2.85317i	−0.0536127	−	0.165003i
$300$		0			0
$301$	−2.23607	+	1.62460i	−0.128885	+	0.0936403i
$302$	−3.85410	+	11.8617i	−0.221779	+	0.682564i
$303$		0			0
$304$	0.500000	−	0.363271i	0.0286770	−	0.0208350i
$305$	−9.09017	−	6.60440i	−0.520502	−	0.378167i
$306$		0			0
$307$	26.8328			1.53143			0.765715	−	0.643180i	$-0.222385\pi$
$307$	26.8328			1.53143			0.765715	+	0.643180i	$0.222385\pi$
$308$	−9.20820	+	7.69421i	−0.524686	+	0.438418i
$309$		0			0
$310$	−2.85410	−	8.78402i	−0.162102	−	0.498899i
$311$	−22.5623	−	16.3925i	−1.27939	−	0.929532i	−0.279857	−	0.960042i	$-0.590287\pi$
$311$	−22.5623	−	16.3925i	−1.27939	−	0.929532i	−0.999534	+	0.0305099i	$0.990287\pi$
$312$		0			0
$313$	1.76393	−	5.42882i	0.0997033	−	0.306855i	−0.888748	−	0.458397i	$-0.848424\pi$
$313$	1.76393	−	5.42882i	0.0997033	−	0.306855i	0.988451	+	0.151542i	$0.0484238\pi$
$314$	−1.73607	+	5.34307i	−0.0979720	+	0.301527i
$315$		0			0
$316$	3.61803	+	2.62866i	0.203530	+	0.147873i
$317$	−3.37132	−	10.3759i	−0.189352	−	0.582767i	0.810644	−	0.585540i	$-0.199117\pi$
$317$	−3.37132	−	10.3759i	−0.189352	−	0.582767i	−0.999996	+	0.00277297i	$0.999117\pi$
$318$		0			0
$319$	−12.2705	+	0.832544i	−0.687017	+	0.0466135i
$320$	1.00000			0.0559017
$321$		0			0
$322$	14.2082	+	10.3229i	0.791792	+	0.575271i
$323$	3.23607	−	2.35114i	0.180060	−	0.130821i
$324$		0			0
$325$	0.190983	−	0.587785i	0.0105938	−	0.0326045i
$326$	−14.4721	+	10.5146i	−0.801537	+	0.582351i
$327$		0			0
$328$	2.88197	+	8.86978i	0.159130	+	0.489752i
$329$	9.47214			0.522216
$330$		0			0
$331$	7.67376			0.421788			0.210894	−	0.977509i	$-0.432362\pi$
$331$	7.67376			0.421788			0.210894	+	0.977509i	$0.432362\pi$
$332$	1.52786	+	4.70228i	0.0838524	+	0.258071i
$333$		0			0
$334$	−9.35410	+	6.79615i	−0.511834	+	0.371869i
$335$	−2.52786	+	7.77997i	−0.138112	+	0.425065i
$336$		0			0
$337$	16.1803	−	11.7557i	0.881399	−	0.640374i	−0.0522220	−	0.998635i	$-0.516630\pi$
$337$	16.1803	−	11.7557i	0.881399	−	0.640374i	0.933621	+	0.358261i	$0.116630\pi$
$338$	10.2082	+	7.41669i	0.555253	+	0.403415i
$339$		0			0
$340$	6.47214			0.351001
$341$	−7.47214	+	29.7073i	−0.404639	+	1.60874i
$342$		0			0
$343$	−1.01722	−	3.13068i	−0.0549248	−	0.169041i
$344$	−0.618034	−	0.449028i	−0.0333222	−	0.0242100i
$345$		0			0
$346$	7.59017	−	23.3601i	0.408050	−	1.25585i
$347$	−1.18034	+	3.63271i	−0.0633640	+	0.195014i	−0.977727	−	0.209881i	$-0.932692\pi$
$347$	−1.18034	+	3.63271i	−0.0633640	+	0.195014i	0.914363	+	0.404896i	$0.132692\pi$
$348$		0			0
$349$	−8.09017	−	5.87785i	−0.433057	−	0.314634i	0.349813	−	0.936819i	$-0.386245\pi$
$349$	−8.09017	−	5.87785i	−0.433057	−	0.314634i	−0.782870	+	0.622185i	$0.786245\pi$
$350$	1.11803	+	3.44095i	0.0597614	+	0.183927i
$351$		0			0
$352$	−2.80902	−	1.76336i	−0.149721	−	0.0939872i
$353$	24.6525			1.31212			0.656059	−	0.754709i	$-0.272222\pi$
$353$	24.6525			1.31212			0.656059	+	0.754709i	$0.272222\pi$
$354$		0			0
$355$	−0.236068	−	0.171513i	−0.0125292	−	0.00910299i
$356$	−4.16312	+	3.02468i	−0.220645	+	0.160308i
$357$		0			0
$358$	3.44427	−	10.6004i	0.182035	−	0.560247i
$359$	20.4164	−	14.8334i	1.07754	−	0.782876i	0.100285	−	0.994959i	$-0.468025\pi$
$359$	20.4164	−	14.8334i	1.07754	−	0.782876i	0.977252	+	0.212082i	$0.0680245\pi$
$360$		0			0
$361$	−5.75329	−	17.7068i	−0.302805	−	0.931937i
$362$	−24.3607			−1.28037
$363$		0			0
$364$	2.23607			0.117202
$365$	3.38197	+	10.4086i	0.177020	+	0.544812i
$366$		0			0
$367$	−6.76393	+	4.91428i	−0.353074	+	0.256524i	−0.750158	−	0.661259i	$-0.770022\pi$
$367$	−6.76393	+	4.91428i	−0.353074	+	0.256524i	0.397083	+	0.917783i	$0.370022\pi$
$368$	−1.50000	+	4.61653i	−0.0781929	+	0.240653i
$369$		0			0
$370$	0.500000	−	0.363271i	0.0259938	−	0.0188856i
$371$	−17.8262	−	12.9515i	−0.925492	−	0.672409i
$372$		0			0
$373$	−13.8541			−0.717338			−0.358669	−	0.933465i	$-0.616769\pi$
$373$	−13.8541			−0.717338			−0.358669	+	0.933465i	$0.616769\pi$
$374$	−18.1803	−	11.4127i	−0.940083	−	0.590136i
$375$		0			0
$376$	0.809017	+	2.48990i	0.0417219	+	0.128407i
$377$	1.85410	+	1.34708i	0.0954911	+	0.0693784i
$378$		0			0
$379$	−10.1180	+	31.1401i	−0.519728	+	1.59956i	0.254782	+	0.966999i	$0.417996\pi$
$379$	−10.1180	+	31.1401i	−0.519728	+	1.59956i	−0.774510	+	0.632561i	$0.782004\pi$
$380$	−0.190983	+	0.587785i	−0.00979722	+	0.0301527i
$381$		0			0
$382$	−11.0902	−	8.05748i	−0.567422	−	0.412257i
$383$	8.79180	+	27.0584i	0.449240	+	1.38262i	0.877766	+	0.479089i	$0.159033\pi$
$383$	8.79180	+	27.0584i	0.449240	+	1.38262i	−0.428527	+	0.903529i	$0.640967\pi$
$384$		0			0
$385$	2.92705	−	11.6372i	0.149176	−	0.593086i
$386$	−3.70820			−0.188743
$387$		0			0
$388$	−12.0902	−	8.78402i	−0.613785	−	0.445941i
$389$	2.85410	−	2.07363i	0.144709	−	0.105137i	−0.513075	−	0.858344i	$-0.671494\pi$
$389$	2.85410	−	2.07363i	0.144709	−	0.105137i	0.657784	+	0.753206i	$0.271494\pi$
$390$		0			0
$391$	−9.70820	+	29.8788i	−0.490965	+	1.51103i
$392$	−4.92705	+	3.57971i	−0.248854	+	0.180803i
$393$		0			0
$394$	−1.11803	−	3.44095i	−0.0563257	−	0.173353i
$395$	−4.47214			−0.225018
$396$		0			0
$397$	12.6738			0.636078			0.318039	−	0.948078i	$-0.396976\pi$
$397$	12.6738			0.636078			0.318039	+	0.948078i	$0.396976\pi$
$398$	−4.00000	−	12.3107i	−0.200502	−	0.617081i
$399$		0			0
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	0.517221	−	1.59184i	0.0258288	−	0.0794928i	−0.937311	−	0.348493i	$-0.886693\pi$
$401$	0.517221	−	1.59184i	0.0258288	−	0.0794928i	0.963140	+	0.269001i	$0.0866934\pi$
$402$		0			0
$403$	4.61803	−	3.35520i	0.230041	−	0.167134i
$404$	3.23607	+	2.35114i	0.161000	+	0.116974i
$405$		0			0
$406$	−13.4164			−0.665845
$407$	−2.04508	+	0.138757i	−0.101371	+	0.00687794i
$408$		0			0
$409$	4.39261	+	13.5191i	0.217201	+	0.668475i	0.998990	+	0.0449321i	$0.0143071\pi$
$409$	4.39261	+	13.5191i	0.217201	+	0.668475i	−0.781790	+	0.623542i	$0.785693\pi$
$410$	−7.54508	−	5.48183i	−0.372625	−	0.270728i
$411$		0			0
$412$	−3.04508	+	9.37181i	−0.150021	+	0.461716i
$413$	16.3435	−	50.3000i	0.804209	−	2.47510i
$414$		0			0
$415$	−4.00000	−	2.90617i	−0.196352	−	0.142658i
$416$	0.190983	+	0.587785i	0.00936371	+	0.0288185i
$417$		0			0
$418$	1.57295	−	1.31433i	0.0769355	−	0.0642859i
$419$	11.2016			0.547235			0.273618	−	0.961839i	$-0.411780\pi$
$419$	11.2016			0.547235			0.273618	+	0.961839i	$0.411780\pi$
$420$		0			0
$421$	−21.7984	−	15.8374i	−1.06239	−	0.771870i	−0.0878591	−	0.996133i	$-0.528003\pi$
$421$	−21.7984	−	15.8374i	−1.06239	−	0.771870i	−0.974529	+	0.224263i	$0.928003\pi$
$422$	18.9443	−	13.7638i	0.922193	−	0.670012i
$423$		0			0
$424$	1.88197	−	5.79210i	0.0913963	−	0.281289i
$425$	−5.23607	+	3.80423i	−0.253987	+	0.184532i
$426$		0			0
$427$	12.5623	+	38.6628i	0.607933	+	1.87102i
$428$	−17.8885			−0.864675
$429$		0			0
$430$	0.763932			0.0368401
$431$	−0.673762	−	2.07363i	−0.0324540	−	0.0998831i	0.933517	−	0.358532i	$-0.116723\pi$
$431$	−0.673762	−	2.07363i	−0.0324540	−	0.0998831i	−0.965971	+	0.258649i	$0.916723\pi$
$432$		0			0
$433$	26.7984	−	19.4702i	1.28785	−	0.935676i	0.288088	−	0.957604i	$-0.406980\pi$
$433$	26.7984	−	19.4702i	1.28785	−	0.935676i	0.999760	+	0.0219278i	$0.00698040\pi$
$434$	−10.3262	+	31.7809i	−0.495675	+	1.52553i
$435$		0			0
$436$	−3.23607	+	2.35114i	−0.154980	+	0.112599i
$437$	−2.42705	−	1.76336i	−0.116102	−	0.0843527i
$438$		0			0
$439$	20.1803			0.963155			0.481578	−	0.876403i	$-0.340064\pi$
$439$	20.1803			0.963155			0.481578	+	0.876403i	$0.340064\pi$
$440$	3.30902	−	0.224514i	0.157751	−	0.0107033i
$441$		0			0
$442$	1.23607	+	3.80423i	0.0587938	+	0.180949i
$443$	23.3262	+	16.9475i	1.10826	+	0.805200i	0.982389	−	0.186846i	$-0.0598266\pi$
$443$	23.3262	+	16.9475i	1.10826	+	0.805200i	0.125874	+	0.992046i	$0.459827\pi$
$444$		0			0
$445$	1.59017	−	4.89404i	0.0753813	−	0.232000i
$446$	2.35410	−	7.24518i	0.111470	−	0.343069i
$447$		0			0
$448$	−2.92705	−	2.12663i	−0.138290	−	0.100474i
$449$	5.75329	+	17.7068i	0.271514	+	0.835636i	0.990121	+	0.140218i	$0.0447805\pi$
$449$	5.75329	+	17.7068i	0.271514	+	0.835636i	−0.718606	+	0.695417i	$0.755220\pi$
$450$		0			0
$451$	11.5279	+	28.7032i	0.542826	+	1.35158i
$452$	12.4721			0.586640
$453$		0			0
$454$	−3.38197	−	2.45714i	−0.158724	−	0.115319i
$455$	−1.80902	+	1.31433i	−0.0848080	+	0.0616166i
$456$		0			0
$457$	3.05573	−	9.40456i	0.142941	−	0.439927i	−0.853800	−	0.520602i	$-0.825708\pi$
$457$	3.05573	−	9.40456i	0.142941	−	0.439927i	0.996740	+	0.0806750i	$0.0257076\pi$
$458$	9.32624	−	6.77591i	0.435786	−	0.316617i
$459$		0			0
$460$	−1.50000	−	4.61653i	−0.0699379	−	0.215247i
$461$	24.7639			1.15337			0.576686	−	0.816966i	$-0.304346\pi$
$461$	24.7639			1.15337			0.576686	+	0.816966i	$0.304346\pi$
$462$		0			0
$463$	−3.38197			−0.157173			−0.0785866	−	0.996907i	$-0.525041\pi$
$463$	−3.38197			−0.157173			−0.0785866	+	0.996907i	$0.525041\pi$
$464$	−1.14590	−	3.52671i	−0.0531970	−	0.163723i
$465$		0			0
$466$	−13.1803	+	9.57608i	−0.610567	+	0.443603i
$467$	−2.18034	+	6.71040i	−0.100894	+	0.310520i	−0.988745	−	0.149611i	$-0.952198\pi$
$467$	−2.18034	+	6.71040i	−0.100894	+	0.310520i	0.887851	+	0.460131i	$0.152198\pi$
$468$		0			0
$469$	23.9443	−	17.3965i	1.10564	−	0.803297i
$470$	−2.11803	−	1.53884i	−0.0976976	−	0.0709815i
$471$		0			0
$472$	14.6180			0.672850
$473$	−2.14590	−	1.34708i	−0.0986685	−	0.0619390i
$474$		0			0
$475$	−0.190983	−	0.587785i	−0.00876290	−	0.0269694i
$476$	−18.9443	−	13.7638i	−0.868309	−	0.630864i
$477$		0			0
$478$	−6.85410	+	21.0948i	−0.313499	+	0.964852i
$479$	12.0557	−	37.1037i	0.550840	−	1.69531i	−0.155843	−	0.987782i	$-0.549809\pi$
$479$	12.0557	−	37.1037i	0.550840	−	1.69531i	0.706683	−	0.707530i	$-0.250191\pi$
$480$		0			0
$481$	0.309017	+	0.224514i	0.0140900	+	0.0102370i
$482$	−7.91641	−	24.3642i	−0.360582	−	1.10976i
$483$		0			0
$484$	−9.69098	−	5.20431i	−0.440499	−	0.236560i
$485$	14.9443			0.678584
$486$		0			0
$487$	−32.6525	−	23.7234i	−1.47962	−	1.07501i	−0.977677	−	0.210112i	$-0.932617\pi$
$487$	−32.6525	−	23.7234i	−1.47962	−	1.07501i	−0.501948	−	0.864898i	$-0.667383\pi$
$488$	−9.09017	+	6.60440i	−0.411493	+	0.298967i
$489$		0			0
$490$	1.88197	−	5.79210i	0.0850186	−	0.261660i
$491$	−1.88197	+	1.36733i	−0.0849319	+	0.0617067i	−0.629441	−	0.777048i	$-0.716716\pi$
$491$	−1.88197	+	1.36733i	−0.0849319	+	0.0617067i	0.544509	+	0.838755i	$0.316716\pi$
$492$		0			0
$493$	−7.41641	−	22.8254i	−0.334018	−	1.02800i
$494$	−0.381966			−0.0171855
$495$		0			0
$496$	−9.23607			−0.414712
$497$	0.326238	+	1.00406i	0.0146338	+	0.0450381i
$498$		0			0
$499$	27.2533	−	19.8007i	1.22002	−	0.886400i	0.223923	−	0.974607i	$-0.428114\pi$
$499$	27.2533	−	19.8007i	1.22002	−	0.886400i	0.996102	+	0.0882071i	$0.0281137\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$		0			0
$502$	9.30902	−	6.76340i	0.415482	−	0.301865i
$503$	−3.88197	−	2.82041i	−0.173088	−	0.125756i	0.497868	−	0.867253i	$-0.334116\pi$
$503$	−3.88197	−	2.82041i	−0.173088	−	0.125756i	−0.670957	+	0.741497i	$0.734116\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$	−3.92705	+	15.6129i	−0.174579	+	0.694079i
$507$		0			0
$508$	3.89919	+	12.0005i	0.172998	+	0.532434i
$509$	−20.5623	−	14.9394i	−0.911408	−	0.662177i	0.0299624	−	0.999551i	$-0.490461\pi$
$509$	−20.5623	−	14.9394i	−0.911408	−	0.662177i	−0.941371	+	0.337374i	$0.890461\pi$
$510$		0			0
$511$	12.2361	−	37.6587i	0.541292	−	1.66592i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$		0			0
$514$	−4.09017	−	2.97168i	−0.180410	−	0.131075i
$515$	−3.04508	−	9.37181i	−0.134182	−	0.412971i
$516$		0			0
$517$	3.23607	+	8.05748i	0.142322	+	0.354368i
$518$	−2.23607			−0.0982472
$519$		0			0
$520$	−0.500000	−	0.363271i	−0.0219265	−	0.0159305i
$521$	30.1976	−	21.9398i	1.32298	−	0.961201i	0.323089	−	0.946369i	$-0.395279\pi$
$521$	30.1976	−	21.9398i	1.32298	−	0.961201i	0.999890	−	0.0148321i	$-0.00472138\pi$
$522$		0			0
$523$	0.708204	−	2.17963i	0.0309676	−	0.0953085i	−0.934378	−	0.356283i	$-0.884044\pi$
$523$	0.708204	−	2.17963i	0.0309676	−	0.0953085i	0.965346	+	0.260975i	$0.0840439\pi$
$524$	16.9443	−	12.3107i	0.740214	−	0.537797i
$525$		0			0
$526$	2.51722	+	7.74721i	0.109756	+	0.337794i
$527$	−59.7771			−2.60393
$528$		0			0
$529$	0.562306			0.0244481
$530$	1.88197	+	5.79210i	0.0817474	+	0.251593i
$531$		0			0
$532$	1.80902	−	1.31433i	0.0784308	−	0.0569833i
$533$	1.78115	−	5.48183i	0.0771503	−	0.237444i
$534$		0			0
$535$	14.4721	−	10.5146i	0.625685	−	0.454587i
$536$	6.61803	+	4.80828i	0.285856	+	0.207686i
$537$		0			0
$538$	24.7639			1.06765
$539$	−15.5000	+	12.9515i	−0.667632	+	0.557861i
$540$		0			0
$541$	−4.65248	−	14.3188i	−0.200026	−	0.615615i	−0.999881	−	0.0154228i	$-0.995091\pi$
$541$	−4.65248	−	14.3188i	−0.200026	−	0.615615i	0.799856	−	0.600193i	$-0.204909\pi$
$542$	−0.527864	−	0.383516i	−0.0226737	−	0.0164734i
$543$		0			0
$544$	2.00000	−	6.15537i	0.0857493	−	0.263909i
$545$	1.23607	−	3.80423i	0.0529473	−	0.162955i
$546$		0			0
$547$	15.5623	+	11.3067i	0.665396	+	0.483439i	0.868481	−	0.495723i	$-0.165097\pi$
$547$	15.5623	+	11.3067i	0.665396	+	0.483439i	−0.203085	+	0.979161i	$0.565097\pi$
$548$	−4.76393	−	14.6619i	−0.203505	−	0.626324i
$549$		0			0
$550$	−2.54508	+	2.12663i	−0.108523	+	0.0906797i
$551$	2.29180			0.0976338
$552$		0			0
$553$	13.0902	+	9.51057i	0.556651	+	0.404430i
$554$	6.69098	−	4.86128i	0.284273	−	0.206536i
$555$		0			0
$556$	−2.35410	+	7.24518i	−0.0998362	+	0.307264i
$557$	11.0623	−	8.03724i	0.468725	−	0.340549i	−0.328219	−	0.944602i	$-0.606448\pi$
$557$	11.0623	−	8.03724i	0.468725	−	0.340549i	0.796944	+	0.604053i	$0.206448\pi$
$558$		0			0
$559$	0.145898	+	0.449028i	0.00617083	+	0.0189919i
$560$	3.61803			0.152890
$561$		0			0
$562$	−7.88854			−0.332758
$563$	−14.0000	−	43.0876i	−0.590030	−	1.81592i	−0.578057	−	0.815996i	$-0.696189\pi$
$563$	−14.0000	−	43.0876i	−0.590030	−	1.81592i	−0.0119724	−	0.999928i	$-0.503811\pi$
$564$		0			0
$565$	−10.0902	+	7.33094i	−0.424497	+	0.308415i
$566$	1.14590	−	3.52671i	0.0481657	−	0.148239i
$567$		0			0
$568$	−0.236068	+	0.171513i	−0.00990519	+	0.00719654i
$569$	12.0172	+	8.73102i	0.503788	+	0.366023i	0.810462	−	0.585791i	$-0.199216\pi$
$569$	12.0172	+	8.73102i	0.503788	+	0.366023i	−0.306674	+	0.951815i	$0.599216\pi$
$570$		0			0
$571$	−21.5066			−0.900022			−0.450011	−	0.893023i	$-0.648580\pi$
$571$	−21.5066			−0.900022			−0.450011	+	0.893023i	$0.648580\pi$
$572$	0.763932	+	1.90211i	0.0319416	+	0.0795313i
$573$		0			0
$574$	10.4271	+	32.0912i	0.435217	+	1.33946i
$575$	3.92705	+	2.85317i	0.163769	+	0.118985i
$576$		0			0
$577$	−2.20163	+	6.77591i	−0.0916549	+	0.282085i	−0.986367	−	0.164558i	$-0.947380\pi$
$577$	−2.20163	+	6.77591i	−0.0916549	+	0.282085i	0.894713	+	0.446642i	$0.147380\pi$
$578$	7.69098	−	23.6704i	0.319903	−	0.984559i
$579$		0			0
$580$	3.00000	+	2.17963i	0.124568	+	0.0905041i
$581$	5.52786	+	17.0130i	0.229334	+	0.705819i
$582$		0			0
$583$	4.92705	−	19.5887i	0.204058	−	0.811280i
$584$	10.9443			0.452877
$585$		0			0
$586$	8.92705	+	6.48588i	0.368773	+	0.267929i
$587$	28.1803	−	20.4742i	1.16313	−	0.845061i	0.172957	−	0.984929i	$-0.444668\pi$
$587$	28.1803	−	20.4742i	1.16313	−	0.845061i	0.990170	+	0.139868i	$0.0446678\pi$
$588$		0			0
$589$	1.76393	−	5.42882i	0.0726816	−	0.223691i
$590$	−11.8262	+	8.59226i	−0.486879	+	0.353738i
$591$		0			0
$592$	−0.190983	−	0.587785i	−0.00784935	−	0.0241578i
$593$	2.58359			0.106095			0.0530477	−	0.998592i	$-0.483106\pi$
$593$	2.58359			0.106095			0.0530477	+	0.998592i	$0.483106\pi$
$594$		0			0
$595$	23.4164			0.959979
$596$	2.76393	+	8.50651i	0.113215	+	0.348440i
$597$		0			0
$598$	2.42705	−	1.76336i	0.0992495	−	0.0721090i
$599$	1.32624	−	4.08174i	0.0541886	−	0.166775i	−0.920299	−	0.391215i	$-0.872055\pi$
$599$	1.32624	−	4.08174i	0.0541886	−	0.166775i	0.974488	+	0.224439i	$0.0720550\pi$
$600$		0			0
$601$	28.3885	−	20.6255i	1.15799	−	0.841331i	0.168470	−	0.985707i	$-0.446117\pi$
$601$	28.3885	−	20.6255i	1.15799	−	0.841331i	0.989523	+	0.144376i	$0.0461174\pi$
$602$	−2.23607	−	1.62460i	−0.0911353	−	0.0662137i
$603$		0			0
$604$	−12.4721			−0.507484
$605$	10.8992	−	1.48584i	0.443115	−	0.0604080i
$606$		0			0
$607$	−5.05573	−	15.5599i	−0.205206	−	0.631558i	−0.999705	−	0.0242929i	$-0.992267\pi$
$607$	−5.05573	−	15.5599i	−0.205206	−	0.631558i	0.794499	−	0.607265i	$-0.207733\pi$
$608$	0.500000	+	0.363271i	0.0202777	+	0.0147326i
$609$		0			0
$610$	3.47214	−	10.6861i	0.140583	−	0.432669i
$611$	0.500000	−	1.53884i	0.0202278	−	0.0622549i
$612$		0			0
$613$	−36.7426	−	26.6951i	−1.48402	−	1.07820i	−0.976233	−	0.216723i	$-0.930463\pi$
$613$	−36.7426	−	26.6951i	−1.48402	−	1.07820i	−0.507788	−	0.861482i	$-0.669537\pi$
$614$	8.29180	+	25.5195i	0.334630	+	1.02988i
$615$		0			0
$616$	−10.1631	−	6.37988i	−0.409484	−	0.257053i
$617$	−23.0557			−0.928189			−0.464094	−	0.885786i	$-0.653620\pi$
$617$	−23.0557			−0.928189			−0.464094	+	0.885786i	$0.653620\pi$
$618$		0			0
$619$	−19.2082	−	13.9556i	−0.772043	−	0.560922i	0.130537	−	0.991443i	$-0.458330\pi$
$619$	−19.2082	−	13.9556i	−0.772043	−	0.560922i	−0.902580	+	0.430521i	$0.858330\pi$
$620$	7.47214	−	5.42882i	0.300088	−	0.218027i
$621$		0			0
$622$	8.61803	−	26.5236i	0.345552	−	1.06350i
$623$	−15.0623	+	10.9434i	−0.603459	+	0.438438i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	5.70820			0.228146
$627$		0			0
$628$	−5.61803			−0.224184
$629$	−1.23607	−	3.80423i	−0.0492853	−	0.151684i
$630$		0			0
$631$	−1.38197	+	1.00406i	−0.0550152	+	0.0399709i	−0.614953	−	0.788564i	$-0.710825\pi$
$631$	−1.38197	+	1.00406i	−0.0550152	+	0.0399709i	0.559938	+	0.828535i	$0.310825\pi$
$632$	−1.38197	+	4.25325i	−0.0549717	+	0.169185i
$633$		0			0
$634$	8.82624	−	6.41264i	0.350535	−	0.254678i
$635$	−10.2082	−	7.41669i	−0.405100	−	0.294323i
$636$		0			0
$637$	3.76393			0.149132
$638$	−4.58359	−	11.4127i	−0.181466	−	0.451832i
$639$		0			0
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	30.2984	+	22.0131i	1.19671	+	0.869463i	0.993957	−	0.109766i	$-0.0350101\pi$
$641$	30.2984	+	22.0131i	1.19671	+	0.869463i	0.202756	+	0.979229i	$0.435010\pi$
$642$		0			0
$643$	−1.05573	+	3.24920i	−0.0416339	+	0.128136i	−0.969713	−	0.244247i	$-0.921459\pi$
$643$	−1.05573	+	3.24920i	−0.0416339	+	0.128136i	0.928079	+	0.372383i	$0.121459\pi$
$644$	−5.42705	+	16.7027i	−0.213856	+	0.658180i
$645$		0			0
$646$	3.23607	+	2.35114i	0.127321	+	0.0925044i
$647$	9.52786	+	29.3238i	0.374579	+	1.15284i	0.943762	+	0.330625i	$0.107259\pi$
$647$	9.52786	+	29.3238i	0.374579	+	1.15284i	−0.569183	+	0.822211i	$0.692741\pi$
$648$		0			0
$649$	48.3713	−	3.28195i	1.89874	−	0.128828i
$650$	0.618034			0.0242413
$651$		0			0
$652$	−14.4721	−	10.5146i	−0.566773	−	0.411784i
$653$	−12.8262	+	9.31881i	−0.501929	+	0.364673i	−0.809754	−	0.586770i	$-0.800399\pi$
$653$	−12.8262	+	9.31881i	−0.501929	+	0.364673i	0.307824	+	0.951443i	$0.400399\pi$
$654$		0			0
$655$	−6.47214	+	19.9192i	−0.252887	+	0.778307i
$656$	−7.54508	+	5.48183i	−0.294586	+	0.214029i
$657$		0			0
$658$	2.92705	+	9.00854i	0.114108	+	0.351189i
$659$	−28.2705			−1.10126			−0.550631	−	0.834749i	$-0.685613\pi$
$659$	−28.2705			−1.10126			−0.550631	+	0.834749i	$0.685613\pi$
$660$		0			0
$661$	41.4853			1.61359			0.806795	−	0.590831i	$-0.201200\pi$
$661$	41.4853			1.61359			0.806795	+	0.590831i	$0.201200\pi$
$662$	2.37132	+	7.29818i	0.0921641	+	0.283652i
$663$		0			0
$664$	−4.00000	+	2.90617i	−0.155230	+	0.112781i
$665$	−0.690983	+	2.12663i	−0.0267952	+	0.0824671i
$666$		0			0
$667$	−14.5623	+	10.5801i	−0.563855	+	0.409664i
$668$	−9.35410	−	6.79615i	−0.361921	−	0.262951i
$669$		0			0
$670$	−8.18034			−0.316034
$671$	−28.5967	+	23.8949i	−1.10397	+	0.922453i
$672$		0			0
$673$	−14.0902	−	43.3651i	−0.543136	−	1.67160i	−0.725381	−	0.688348i	$-0.758336\pi$
$673$	−14.0902	−	43.3651i	−0.543136	−	1.67160i	0.182245	−	0.983253i	$-0.441664\pi$
$674$	16.1803	+	11.7557i	0.623243	+	0.452813i
$675$		0			0
$676$	−3.89919	+	12.0005i	−0.149969	+	0.461556i
$677$	−4.43769	+	13.6578i	−0.170554	+	0.524913i	−0.999403	−	0.0345610i	$-0.988997\pi$
$677$	−4.43769	+	13.6578i	−0.170554	+	0.524913i	0.828848	+	0.559474i	$0.188997\pi$
$678$		0			0
$679$	−43.7426	−	31.7809i	−1.67869	−	1.21964i
$680$	2.00000	+	6.15537i	0.0766965	+	0.236048i
$681$		0			0
$682$	−30.5623	+	2.07363i	−1.17029	+	0.0794033i
$683$	−31.1246			−1.19095			−0.595475	−	0.803374i	$-0.703036\pi$
$683$	−31.1246			−1.19095			−0.595475	+	0.803374i	$0.703036\pi$
$684$		0			0
$685$	12.4721	+	9.06154i	0.476536	+	0.346224i
$686$	2.66312	−	1.93487i	0.101678	−	0.0738736i
$687$		0			0
$688$	0.236068	−	0.726543i	0.00900001	−	0.0276992i
$689$	−3.04508	+	2.21238i	−0.116008	+	0.0842851i
$690$		0			0
$691$	−0.465558	−	1.43284i	−0.0177107	−	0.0545078i	0.941811	−	0.336144i	$-0.109123\pi$
$691$	−0.465558	−	1.43284i	−0.0177107	−	0.0545078i	−0.959521	+	0.281636i	$0.909123\pi$
$692$	24.5623			0.933719
$693$		0			0
$694$	−3.81966			−0.144992
$695$	−2.35410	−	7.24518i	−0.0892962	−	0.274825i
$696$		0			0
$697$	−48.8328	+	35.4791i	−1.84967	+	1.34387i
$698$	3.09017	−	9.51057i	0.116965	−	0.359980i
$699$		0			0
$700$	−2.92705	+	2.12663i	−0.110632	+	0.0803789i
$701$	−16.2361	−	11.7962i	−0.613228	−	0.445536i	0.237322	−	0.971431i	$-0.423730\pi$
$701$	−16.2361	−	11.7962i	−0.613228	−	0.445536i	−0.850549	+	0.525895i	$0.823730\pi$
$702$		0			0
$703$	0.381966			0.0144061
$704$	0.809017	−	3.21644i	0.0304910	−	0.121224i
$705$		0			0
$706$	7.61803	+	23.4459i	0.286708	+	0.882398i
$707$	11.7082	+	8.50651i	0.440332	+	0.319920i
$708$		0			0
$709$	−7.61803	+	23.4459i	−0.286101	+	0.880529i	0.699965	+	0.714177i	$0.253199\pi$
$709$	−7.61803	+	23.4459i	−0.286101	+	0.880529i	−0.986066	+	0.166352i	$0.946801\pi$
$710$	0.0901699	−	0.277515i	0.00338402	−	0.0104149i
$711$		0			0
$712$	−4.16312	−	3.02468i	−0.156019	−	0.113355i
$713$	13.8541	+	42.6385i	0.518840	+	1.59683i
$714$		0			0
$715$	−1.73607	−	1.08981i	−0.0649253	−	0.0407567i
$716$	11.1459			0.416542
$717$		0			0
$718$	20.4164	+	14.8334i	0.761934	+	0.553577i
$719$	−19.3262	+	14.0413i	−0.720747	+	0.523653i	−0.886623	−	0.462493i	$-0.846955\pi$
$719$	−19.3262	+	14.0413i	−0.720747	+	0.523653i	0.165876	+	0.986147i	$0.446955\pi$
$720$		0			0
$721$	−11.0172	+	33.9075i	−0.410303	+	1.26278i
$722$	15.0623	−	10.9434i	0.560561	−	0.407271i
$723$		0			0
$724$	−7.52786	−	23.1684i	−0.279771	−	0.861046i
$725$	−3.70820			−0.137719
$726$		0			0
$727$	−46.6312			−1.72946			−0.864728	−	0.502241i	$-0.832509\pi$
$727$	−46.6312			−1.72946			−0.864728	+	0.502241i	$0.832509\pi$
$728$	0.690983	+	2.12663i	0.0256095	+	0.0788180i
$729$		0			0
$730$	−8.85410	+	6.43288i	−0.327705	+	0.238092i
$731$	1.52786	−	4.70228i	0.0565101	−	0.173920i
$732$		0			0
$733$	23.0344	−	16.7355i	0.850797	−	0.618140i	−0.0745690	−	0.997216i	$-0.523758\pi$
$733$	23.0344	−	16.7355i	0.850797	−	0.618140i	0.925366	+	0.379076i	$0.123758\pi$
$734$	−6.76393	−	4.91428i	−0.249661	−	0.181390i
$735$		0			0
$736$	−4.85410			−0.178925
$737$	22.9787	+	14.4248i	0.846432	+	0.531346i
$738$		0			0
$739$	8.53444	+	26.2663i	0.313945	+	0.966222i	0.976187	+	0.216932i	$0.0696050\pi$
$739$	8.53444	+	26.2663i	0.313945	+	0.966222i	−0.662242	+	0.749290i	$0.730395\pi$
$740$	0.500000	+	0.363271i	0.0183804	+	0.0133541i
$741$		0			0
$742$	6.80902	−	20.9560i	0.249967	−	0.769319i
$743$	2.20820	−	6.79615i	0.0810111	−	0.249327i	−0.902345	−	0.431014i	$-0.858156\pi$
$743$	2.20820	−	6.79615i	0.0810111	−	0.249327i	0.983356	+	0.181687i	$0.0581559\pi$
$744$		0			0
$745$	−7.23607	−	5.25731i	−0.265109	−	0.192613i
$746$	−4.28115	−	13.1760i	−0.156744	−	0.482409i
$747$		0			0
$748$	5.23607	−	20.8172i	0.191450	−	0.761154i
$749$	−64.7214			−2.36487
$750$		0			0
$751$	24.4721	+	17.7800i	0.893001	+	0.648803i	0.936659	−	0.350243i	$-0.113901\pi$
$751$	24.4721	+	17.7800i	0.893001	+	0.648803i	−0.0436578	+	0.999047i	$0.513901\pi$
$752$	−2.11803	+	1.53884i	−0.0772368	+	0.0561158i
$753$		0			0
$754$	−0.708204	+	2.17963i	−0.0257913	+	0.0793774i
$755$	10.0902	−	7.33094i	0.367219	−	0.266800i
$756$		0			0
$757$	0.572949	+	1.76336i	0.0208242	+	0.0640903i	0.960929	−	0.276796i	$-0.0892728\pi$
$757$	0.572949	+	1.76336i	0.0208242	+	0.0640903i	−0.940104	+	0.340887i	$0.889273\pi$
$758$	−32.7426			−1.18927
$759$		0			0
$760$	−0.618034			−0.0224184
$761$	2.43769	+	7.50245i	0.0883663	+	0.271964i	0.985468	−	0.169860i	$-0.0543316\pi$
$761$	2.43769	+	7.50245i	0.0883663	+	0.271964i	−0.897102	+	0.441824i	$0.854332\pi$
$762$		0			0
$763$	−11.7082	+	8.50651i	−0.423865	+	0.307956i
$764$	4.23607	−	13.0373i	0.153256	−	0.471672i
$765$		0			0
$766$	−23.0172	+	16.7230i	−0.831646	+	0.604226i
$767$	−7.30902	−	5.31031i	−0.263913	−	0.191744i
$768$		0			0
$769$	−34.7984			−1.25486			−0.627431	−	0.778672i	$-0.715893\pi$
$769$	−34.7984			−1.25486			−0.627431	+	0.778672i	$0.715893\pi$
$770$	11.9721	−	0.812299i	0.431446	−	0.0292732i
$771$		0			0
$772$	−1.14590	−	3.52671i	−0.0412418	−	0.126929i
$773$	3.07295	+	2.23263i	0.110526	+	0.0803021i	0.641675	−	0.766976i	$-0.278240\pi$
$773$	3.07295	+	2.23263i	0.110526	+	0.0803021i	−0.531149	+	0.847278i	$0.678240\pi$
$774$		0			0
$775$	−2.85410	+	8.78402i	−0.102522	+	0.315531i
$776$	4.61803	−	14.2128i	0.165778	−	0.510211i
$777$		0			0
$778$	2.85410	+	2.07363i	0.102325	+	0.0743431i
$779$	−1.78115	−	5.48183i	−0.0638164	−	0.196407i
$780$		0			0
$781$	−0.742646	+	0.620541i	−0.0265740	+	0.0222047i
$782$	−31.4164			−1.12345
$783$		0			0
$784$	−4.92705	−	3.57971i	−0.175966	−	0.127847i
$785$	4.54508	−	3.30220i	0.162221	−	0.117860i
$786$		0			0
$787$	−5.61803	+	17.2905i	−0.200261	+	0.616341i	0.799613	+	0.600515i	$0.205038\pi$
$787$	−5.61803	+	17.2905i	−0.200261	+	0.616341i	−0.999875	+	0.0158258i	$0.994962\pi$
$788$	2.92705	−	2.12663i	0.104272	−	0.0757580i
$789$		0			0
$790$	−1.38197	−	4.25325i	−0.0491681	−	0.151324i
$791$	45.1246			1.60445
$792$		0			0
$793$	6.94427			0.246598
$794$	3.91641	+	12.0535i	0.138988	+	0.427761i
$795$		0			0
$796$	10.4721	−	7.60845i	0.371175	−	0.269674i
$797$	−4.24671	+	13.0700i	−0.150426	+	0.462964i	−0.997669	−	0.0682419i	$-0.978261\pi$
$797$	−4.24671	+	13.0700i	−0.150426	+	0.462964i	0.847243	+	0.531206i	$0.178261\pi$
$798$		0			0
$799$	−13.7082	+	9.95959i	−0.484961	+	0.352345i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$		0			0
$802$	1.67376			0.0591026
$803$	36.2148	−	2.45714i	1.27799	−	0.0867107i
$804$		0			0
$805$	−5.42705	−	16.7027i	−0.191278	−	0.588694i
$806$	4.61803	+	3.35520i	0.162663	+	0.118182i
$807$		0			0
$808$	−1.23607	+	3.80423i	−0.0434847	+	0.133832i
$809$	1.07953	−	3.32244i	0.0379541	−	0.116811i	−0.930284	−	0.366839i	$-0.880440\pi$
$809$	1.07953	−	3.32244i	0.0379541	−	0.116811i	0.968239	+	0.250028i	$0.0804399\pi$
$810$		0			0
$811$	−21.2533	−	15.4414i	−0.746304	−	0.542222i	0.148375	−	0.988931i	$-0.452596\pi$
$811$	−21.2533	−	15.4414i	−0.746304	−	0.542222i	−0.894679	+	0.446710i	$0.852596\pi$
$812$	−4.14590	−	12.7598i	−0.145492	−	0.447780i
$813$		0			0
$814$	−0.763932	−	1.90211i	−0.0267758	−	0.0666690i
$815$	17.8885			0.626608
$816$		0			0
$817$	0.381966	+	0.277515i	0.0133633	+	0.00970901i
$818$	−11.5000	+	8.35524i	−0.402088	+	0.292134i
$819$		0			0
$820$	2.88197	−	8.86978i	0.100643	−	0.309746i
$821$	10.3262	−	7.50245i	0.360388	−	0.261837i	−0.392826	−	0.919613i	$-0.628502\pi$
$821$	10.3262	−	7.50245i	0.360388	−	0.261837i	0.753214	+	0.657776i	$0.228502\pi$
$822$		0			0
$823$	10.1697	+	31.2991i	0.354493	+	1.09102i	0.956303	+	0.292379i	$0.0944467\pi$
$823$	10.1697	+	31.2991i	0.354493	+	1.09102i	−0.601809	+	0.798640i	$0.705553\pi$
$824$	−9.85410			−0.343284
$825$		0			0
$826$	52.8885			1.84023
$827$	3.00000	+	9.23305i	0.104320	+	0.321065i	0.989570	−	0.144051i	$-0.0460128\pi$
$827$	3.00000	+	9.23305i	0.104320	+	0.321065i	−0.885250	+	0.465115i	$0.846013\pi$
$828$		0			0
$829$	18.8541	−	13.6983i	0.654830	−	0.475762i	−0.210083	−	0.977684i	$-0.567373\pi$
$829$	18.8541	−	13.6983i	0.654830	−	0.475762i	0.864913	+	0.501922i	$0.167373\pi$
$830$	1.52786	−	4.70228i	0.0530329	−	0.163219i
$831$		0			0
$832$	−0.500000	+	0.363271i	−0.0173344	+	0.0125942i
$833$	−31.8885	−	23.1684i	−1.10487	−	0.802737i
$834$		0			0
$835$	11.5623			0.400130
$836$	1.73607	+	1.08981i	0.0600432	+	0.0376920i
$837$		0			0
$838$	3.46149	+	10.6534i	0.119575	+	0.368015i
$839$	26.7984	+	19.4702i	0.925183	+	0.672185i	0.944809	−	0.327623i	$-0.106248\pi$
$839$	26.7984	+	19.4702i	0.925183	+	0.672185i	−0.0196260	+	0.999807i	$0.506248\pi$
$840$		0			0
$841$	−4.71227	+	14.5029i	−0.162492	+	0.500099i
$842$	8.32624	−	25.6255i	0.286941	−	0.883114i
$843$		0			0
$844$	18.9443	+	13.7638i	0.652089	+	0.473770i
$845$	−3.89919	−	12.0005i	−0.134136	−	0.412828i
$846$		0			0
$847$	−35.0623	−	18.8294i	−1.20476	−	0.646985i
$848$	6.09017			0.209137
$849$		0			0
$850$	−5.23607	−	3.80423i	−0.179596	−	0.130484i
$851$	−2.42705	+	1.76336i	−0.0831982	+	0.0604471i
$852$		0			0
$853$	15.0836	−	46.4225i	0.516452	−	1.58948i	−0.264171	−	0.964476i	$-0.585098\pi$
$853$	15.0836	−	46.4225i	0.516452	−	1.58948i	0.780624	−	0.625001i	$-0.214902\pi$
$854$	−32.8885	+	23.8949i	−1.12542	+	0.817668i
$855$		0			0
$856$	−5.52786	−	17.0130i	−0.188939	−	0.581493i
$857$	−55.2361			−1.88683			−0.943414	−	0.331617i	$-0.892406\pi$
$857$	−55.2361			−1.88683			−0.943414	+	0.331617i	$0.892406\pi$
$858$		0			0
$859$	51.0344			1.74127			0.870636	−	0.491927i	$-0.163707\pi$
$859$	51.0344			1.74127			0.870636	+	0.491927i	$0.163707\pi$
$860$	0.236068	+	0.726543i	0.00804985	+	0.0247749i
$861$		0			0
$862$	1.76393	−	1.28157i	0.0600798	−	0.0436505i
$863$	0.0450850	−	0.138757i	0.00153471	−	0.00472335i	−0.950286	−	0.311378i	$-0.899210\pi$
$863$	0.0450850	−	0.138757i	0.00153471	−	0.00472335i	0.951821	+	0.306654i	$0.0992096\pi$
$864$		0			0
$865$	−19.8713	+	14.4374i	−0.675645	+	0.490885i
$866$	26.7984	+	19.4702i	0.910646	+	0.661623i
$867$		0			0
$868$	−33.4164			−1.13423
$869$	−3.61803	+	14.3844i	−0.122733	+	0.487956i
$870$		0			0
$871$	−1.56231	−	4.80828i	−0.0529367	−	0.162922i
$872$	−3.23607	−	2.35114i	−0.109587	−	0.0796197i
$873$		0			0
$874$	0.927051	−	2.85317i	0.0313580	−	0.0965099i
$875$	1.11803	−	3.44095i	0.0377964	−	0.116326i
$876$		0			0
$877$	18.9164	+	13.7436i	0.638762	+	0.464088i	0.859425	−	0.511263i	$-0.170822\pi$
$877$	18.9164	+	13.7436i	0.638762	+	0.464088i	−0.220663	+	0.975350i	$0.570822\pi$
$878$	6.23607	+	19.1926i	0.210457	+	0.647720i
$879$		0			0
$880$	1.23607	+	3.07768i	0.0416678	+	0.103749i
$881$	−7.79837			−0.262734			−0.131367	−	0.991334i	$-0.541937\pi$
$881$	−7.79837			−0.262734			−0.131367	+	0.991334i	$0.541937\pi$
$882$		0			0
$883$	−20.4721	−	14.8739i	−0.688942	−	0.500546i	0.187370	−	0.982289i	$-0.440004\pi$
$883$	−20.4721	−	14.8739i	−0.688942	−	0.500546i	−0.876312	+	0.481744i	$0.840004\pi$
$884$	−3.23607	+	2.35114i	−0.108841	+	0.0790774i
$885$		0			0
$886$	−8.90983	+	27.4216i	−0.299332	+	0.921248i
$887$	1.01722	−	0.739054i	0.0341549	−	0.0248150i	−0.570577	−	0.821244i	$-0.693280\pi$
$887$	1.01722	−	0.739054i	0.0341549	−	0.0248150i	0.604732	+	0.796429i	$0.293280\pi$
$888$		0			0
$889$	14.1074	+	43.4181i	0.473147	+	1.45620i
$890$	5.14590			0.172491
$891$		0			0
$892$	7.61803			0.255071
$893$	−0.500000	−	1.53884i	−0.0167319	−	0.0514954i
$894$		0			0
$895$	−9.01722	+	6.55139i	−0.301412	+	0.218989i
$896$	1.11803	−	3.44095i	0.0373509	−	0.114954i
$897$		0			0
$898$	−15.0623	+	10.9434i	−0.502636	+	0.365186i
$899$	−27.7082	−	20.1312i	−0.924120	−	0.671413i
$900$		0			0
$901$	39.4164			1.31315
$902$	−23.7361	+	19.8334i	−0.790325	+	0.660381i
$903$		0			0
$904$	3.85410	+	11.8617i	0.128186	+	0.394514i
$905$	19.7082	+	14.3188i	0.655123	+	0.475975i
$906$		0			0
$907$	9.23607	−	28.4257i	0.306679	−	0.943860i	−0.672367	−	0.740218i	$-0.734722\pi$
$907$	9.23607	−	28.4257i	0.306679	−	0.943860i	0.979045	−	0.203642i	$-0.0652777\pi$
$908$	1.29180	−	3.97574i	0.0428698	−	0.131940i
$909$		0			0
$910$	−1.80902	−	1.31433i	−0.0599683	−	0.0435695i
$911$	3.29180	+	10.1311i	0.109062	+	0.335659i	0.990662	−	0.136338i	$-0.0435334\pi$
$911$	3.29180	+	10.1311i	0.109062	+	0.335659i	−0.881600	+	0.471997i	$0.843533\pi$
$912$		0			0
$913$	−12.5836	+	10.5146i	−0.416456	+	0.347983i
$914$	9.88854			0.327084
$915$		0			0
$916$	9.32624	+	6.77591i	0.308148	+	0.223882i
$917$	61.3050	−	44.5407i	2.02447	−	1.47086i
$918$		0			0
$919$	−5.58359	+	17.1845i	−0.184186	+	0.566865i	−0.999933	−	0.0115426i	$-0.996326\pi$
$919$	−5.58359	+	17.1845i	−0.184186	+	0.566865i	0.815748	+	0.578408i	$0.196326\pi$
$920$	3.92705	−	2.85317i	0.129471	−	0.0940662i
$921$		0			0
$922$	7.65248	+	23.5519i	0.252021	+	0.775640i
$923$	0.180340			0.00593596
$924$		0			0
$925$	−0.618034			−0.0203208
$926$	−1.04508	−	3.21644i	−0.0343436	−	0.105699i
$927$		0			0
$928$	3.00000	−	2.17963i	0.0984798	−	0.0715498i
$929$	2.17376	−	6.69015i	0.0713188	−	0.219497i	−0.909044	−	0.416701i	$-0.863186\pi$
$929$	2.17376	−	6.69015i	0.0713188	−	0.219497i	0.980362	+	0.197204i	$0.0631862\pi$
$930$		0			0
$931$	3.04508	−	2.21238i	0.0997986	−	0.0725079i
$932$	−13.1803	−	9.57608i	−0.431736	−	0.313675i
$933$		0			0
$934$	−7.05573			−0.230870
$935$	8.00000	+	19.9192i	0.261628	+	0.651427i
$936$		0			0
$937$	14.9443	+	45.9937i	0.488208	+	1.50255i	0.827280	+	0.561790i	$0.189887\pi$
$937$	14.9443	+	45.9937i	0.488208	+	1.50255i	−0.339072	+	0.940760i	$0.610113\pi$
$938$	23.9443	+	17.3965i	0.781808	+	0.568017i
$939$		0			0
$940$	0.809017	−	2.48990i	0.0263872	−	0.0812115i
$941$	−3.41641	+	10.5146i	−0.111372	+	0.342767i	−0.991173	−	0.132575i	$-0.957676\pi$
$941$	−3.41641	+	10.5146i	−0.111372	+	0.342767i	0.879801	+	0.475342i	$0.157676\pi$
$942$		0			0
$943$	36.6246	+	26.6093i	1.19266	+	0.866519i
$944$	4.51722	+	13.9026i	0.147023	+	0.452490i
$945$		0			0
$946$	0.618034	−	2.45714i	0.0200940	−	0.0798886i
$947$	3.30495			0.107396			0.0536982	−	0.998557i	$-0.482899\pi$
$947$	3.30495			0.107396			0.0536982	+	0.998557i	$0.482899\pi$
$948$		0			0
$949$	−5.47214	−	3.97574i	−0.177633	−	0.129058i
$950$	0.500000	−	0.363271i	0.0162221	−	0.0117861i
$951$		0			0
$952$	7.23607	−	22.2703i	0.234522	−	0.721785i
$953$	−36.2148	+	26.3116i	−1.17311	+	0.852316i	−0.991378	−	0.131032i	$-0.958171\pi$
$953$	−36.2148	+	26.3116i	−1.17311	+	0.852316i	−0.181734	+	0.983348i	$0.558171\pi$
$954$		0			0
$955$	4.23607	+	13.0373i	0.137076	+	0.421876i
$956$	−22.1803			−0.717363
$957$		0			0
$958$	39.0132			1.26046
$959$	−17.2361	−	53.0472i	−0.556582	−	1.71298i
$960$		0			0
$961$	−43.9336	+	31.9196i	−1.41721	+	1.02967i
$962$	−0.118034	+	0.363271i	−0.00380557	+	0.0117123i
$963$		0			0
$964$	20.7254	−	15.0579i	0.667521	−	0.484982i
$965$	3.00000	+	2.17963i	0.0965734	+	0.0701647i
$966$		0			0
$967$	−4.25735			−0.136907			−0.0684536	−	0.997654i	$-0.521807\pi$
$967$	−4.25735			−0.136907			−0.0684536	+	0.997654i	$0.521807\pi$
$968$	1.95492	−	10.8249i	0.0628333	−	0.347925i
$969$		0			0
$970$	4.61803	+	14.2128i	0.148276	+	0.456347i
$971$	4.69098	+	3.40820i	0.150541	+	0.109374i	0.660506	−	0.750821i	$-0.270342\pi$
$971$	4.69098	+	3.40820i	0.150541	+	0.109374i	−0.509965	+	0.860195i	$0.670342\pi$
$972$		0			0
$973$	−8.51722	+	26.2133i	−0.273050	+	0.840360i
$974$	12.4721	−	38.3853i	0.399633	−	1.22994i
$975$		0			0
$976$	−9.09017	−	6.60440i	−0.290969	−	0.211402i
$977$	7.67376	+	23.6174i	0.245505	+	0.755588i	0.995553	+	0.0942040i	$0.0300306\pi$
$977$	7.67376	+	23.6174i	0.245505	+	0.755588i	−0.750048	+	0.661384i	$0.769969\pi$
$978$		0			0
$979$	−14.4549	−	9.07405i	−0.461981	−	0.290008i
$980$	6.09017			0.194543
$981$		0			0
$982$	−1.88197	−	1.36733i	−0.0600559	−	0.0436332i
$983$	−26.7254	+	19.4172i	−0.852409	+	0.619311i	−0.925809	−	0.377991i	$-0.876615\pi$
$983$	−26.7254	+	19.4172i	−0.852409	+	0.619311i	0.0734004	+	0.997303i	$0.476615\pi$
$984$		0			0
$985$	−1.11803	+	3.44095i	−0.0356235	+	0.109638i
$986$	19.4164	−	14.1068i	0.618344	−	0.449254i
$987$		0			0
$988$	−0.118034	−	0.363271i	−0.00375516	−	0.0115572i
$989$	−3.70820			−0.117914
$990$		0			0
$991$	8.94427			0.284124			0.142062	−	0.989858i	$-0.454627\pi$
$991$	8.94427			0.284124			0.142062	+	0.989858i	$0.454627\pi$
$992$	−2.85410	−	8.78402i	−0.0906178	−	0.278893i
$993$		0			0
$994$	−0.854102	+	0.620541i	−0.0270905	+	0.0196824i
$995$	−4.00000	+	12.3107i	−0.126809	+	0.390277i
$996$		0			0
$997$	11.1459	−	8.09797i	0.352994	−	0.256465i	−0.397130	−	0.917762i	$-0.629994\pi$
$997$	11.1459	−	8.09797i	0.352994	−	0.256465i	0.750124	+	0.661297i	$0.229994\pi$
$998$	27.2533	+	19.8007i	0.862688	+	0.626779i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.a.181.1		4
3.2	odd	2		330.2.m.d.181.1	yes	4
11.9	even	5	inner	990.2.n.a.361.1		4
33.8	even	10		3630.2.a.bi.1.1		2
33.14	odd	10		3630.2.a.bc.1.2		2
33.20	odd	10		330.2.m.d.31.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.d.31.1	✓	4	33.20	odd	10
330.2.m.d.181.1	yes	4	3.2	odd	2
990.2.n.a.181.1		4	1.1	even	1	trivial
990.2.n.a.361.1		4	11.9	even	5	inner
3630.2.a.bc.1.2		2	33.14	odd	10
3630.2.a.bi.1.1		2	33.8	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-2.92705 + 2.12663i) q^{7} +(-0.809017 - 0.587785i) q^{8} +1.00000 q^{10} +(-2.80902 - 1.76336i) q^{11} +(0.190983 + 0.587785i) q^{13} +(-2.92705 - 2.12663i) q^{14} +(0.309017 - 0.951057i) q^{16} +(2.00000 - 6.15537i) q^{17} +(0.500000 + 0.363271i) q^{19} +(0.309017 + 0.951057i) q^{20} +(0.809017 - 3.21644i) q^{22} -4.85410 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.500000 + 0.363271i) q^{26} +(1.11803 - 3.44095i) q^{28} +(3.00000 - 2.17963i) q^{29} +(-2.85410 - 8.78402i) q^{31} +1.00000 q^{32} +6.47214 q^{34} +(1.11803 + 3.44095i) q^{35} +(0.500000 - 0.363271i) q^{37} +(-0.190983 + 0.587785i) q^{38} +(-0.809017 + 0.587785i) q^{40} +(-7.54508 - 5.48183i) q^{41} +0.763932 q^{43} +(3.30902 - 0.224514i) q^{44} +(-1.50000 - 4.61653i) q^{46} +(-2.11803 - 1.53884i) q^{47} +(1.88197 - 5.79210i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-0.500000 - 0.363271i) q^{52} +(1.88197 + 5.79210i) q^{53} +(-2.54508 + 2.12663i) q^{55} +3.61803 q^{56} +(3.00000 + 2.17963i) q^{58} +(-11.8262 + 8.59226i) q^{59} +(3.47214 - 10.6861i) q^{61} +(7.47214 - 5.42882i) q^{62} +(0.309017 + 0.951057i) q^{64} +0.618034 q^{65} -8.18034 q^{67} +(2.00000 + 6.15537i) q^{68} +(-2.92705 + 2.12663i) q^{70} +(0.0901699 - 0.277515i) q^{71} +(-8.85410 + 6.43288i) q^{73} +(0.500000 + 0.363271i) q^{74} -0.618034 q^{76} +(11.9721 - 0.812299i) q^{77} +(-1.38197 - 4.25325i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(2.88197 - 8.86978i) q^{82} +(1.52786 - 4.70228i) q^{83} +(-5.23607 - 3.80423i) q^{85} +(0.236068 + 0.726543i) q^{86} +(1.23607 + 3.07768i) q^{88} +5.14590 q^{89} +(-1.80902 - 1.31433i) q^{91} +(3.92705 - 2.85317i) q^{92} +(0.809017 - 2.48990i) q^{94} +(0.500000 - 0.363271i) q^{95} +(4.61803 + 14.2128i) q^{97} +6.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - q^{5} - 5 q^{7} - q^{8} + 4 q^{10} - 9 q^{11} + 3 q^{13} - 5 q^{14} - q^{16} + 8 q^{17} + 2 q^{19} - q^{20} + q^{22} - 6 q^{23} - q^{25} - 2 q^{26} + 12 q^{29} + 2 q^{31} + 4 q^{32}+ \cdots + 2 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - q^5 - 5 * q^7 - q^8 + 4 * q^10 - 9 * q^11 + 3 * q^13 - 5 * q^14 - q^16 + 8 * q^17 + 2 * q^19 - q^20 + q^22 - 6 * q^23 - q^25 - 2 * q^26 + 12 * q^29 + 2 * q^31 + 4 * q^32 + 8 * q^34 + 2 * q^37 - 3 * q^38 - q^40 - 19 * q^41 + 12 * q^43 + 11 * q^44 - 6 * q^46 - 4 * q^47 + 12 * q^49 - q^50 - 2 * q^52 + 12 * q^53 + q^55 + 10 * q^56 + 12 * q^58 - 16 * q^59 - 4 * q^61 + 12 * q^62 - q^64 - 2 * q^65 + 12 * q^67 + 8 * q^68 - 5 * q^70 - 22 * q^71 - 22 * q^73 + 2 * q^74 + 2 * q^76 + 30 * q^77 - 10 * q^79 - q^80 + 16 * q^82 + 24 * q^83 - 12 * q^85 - 8 * q^86 - 4 * q^88 + 34 * q^89 - 5 * q^91 + 9 * q^92 + q^94 + 2 * q^95 + 14 * q^97 + 2 * q^98

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