LMFDB - Embedded newform 330.2.m.d.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [330,2,Mod(31,330)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(330, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("330.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.m (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.63506326670$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	330.181
Dual form			330.2.m.d.31.1

$q$-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^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-2.92705 + 2.12663i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +1.00000 q^{10} +(2.80902 + 1.76336i) q^{11} -1.00000 q^{12} +(0.190983 + 0.587785i) q^{13} +(2.92705 + 2.12663i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.00000 + 6.15537i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.500000 + 0.363271i) q^{19} +(-0.309017 - 0.951057i) q^{20} -3.61803 q^{21} +(0.809017 - 3.21644i) q^{22} +4.85410 q^{23} +(0.309017 + 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.500000 - 0.363271i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.11803 - 3.44095i) q^{28} +(-3.00000 + 2.17963i) q^{29} +(0.809017 + 0.587785i) q^{30} +(-2.85410 - 8.78402i) q^{31} -1.00000 q^{32} +(1.23607 + 3.07768i) q^{33} +6.47214 q^{34} +(-1.11803 - 3.44095i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.500000 - 0.363271i) q^{37} +(0.190983 - 0.587785i) q^{38} +(-0.190983 + 0.587785i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(7.54508 + 5.48183i) q^{41} +(1.11803 + 3.44095i) q^{42} +0.763932 q^{43} +(-3.30902 + 0.224514i) q^{44} -1.00000 q^{45} +(-1.50000 - 4.61653i) q^{46} +(2.11803 + 1.53884i) q^{47} +(0.809017 - 0.587785i) q^{48} +(1.88197 - 5.79210i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-5.23607 + 3.80423i) q^{51} +(-0.500000 - 0.363271i) q^{52} +(-1.88197 - 5.79210i) q^{53} +1.00000 q^{54} +(-2.54508 + 2.12663i) q^{55} -3.61803 q^{56} +(0.190983 + 0.587785i) q^{57} +(3.00000 + 2.17963i) q^{58} +(11.8262 - 8.59226i) q^{59} +(0.309017 - 0.951057i) q^{60} +(3.47214 - 10.6861i) q^{61} +(-7.47214 + 5.42882i) q^{62} +(-2.92705 - 2.12663i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.618034 q^{65} +(2.54508 - 2.12663i) q^{66} -8.18034 q^{67} +(-2.00000 - 6.15537i) q^{68} +(3.92705 + 2.85317i) q^{69} +(-2.92705 + 2.12663i) q^{70} +(-0.0901699 + 0.277515i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-8.85410 + 6.43288i) q^{73} +(-0.500000 - 0.363271i) q^{74} +(-0.309017 - 0.951057i) q^{75} -0.618034 q^{76} +(-11.9721 + 0.812299i) q^{77} +0.618034 q^{78} +(-1.38197 - 4.25325i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(2.88197 - 8.86978i) q^{82} +(-1.52786 + 4.70228i) q^{83} +(2.92705 - 2.12663i) q^{84} +(-5.23607 - 3.80423i) q^{85} +(-0.236068 - 0.726543i) q^{86} -3.70820 q^{87} +(1.23607 + 3.07768i) q^{88} -5.14590 q^{89} +(0.309017 + 0.951057i) q^{90} +(-1.80902 - 1.31433i) q^{91} +(-3.92705 + 2.85317i) q^{92} +(2.85410 - 8.78402i) q^{93} +(0.809017 - 2.48990i) q^{94} +(-0.500000 + 0.363271i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(4.61803 + 14.2128i) q^{97} -6.09017 q^{98} +(-0.809017 + 3.21644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{4} + q^{5} - q^{6} - 5 q^{7} + q^{8} - q^{9} + 4 q^{10} + 9 q^{11} - 4 q^{12} + 3 q^{13} + 5 q^{14} - q^{15} - q^{16} - 8 q^{17} + q^{18} + 2 q^{19} + q^{20} - 10 q^{21}+ \cdots - q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^4 + q^5 - q^6 - 5 * q^7 + q^8 - q^9 + 4 * q^10 + 9 * q^11 - 4 * q^12 + 3 * q^13 + 5 * q^14 - q^15 - q^16 - 8 * q^17 + q^18 + 2 * q^19 + q^20 - 10 * q^21 + q^22 + 6 * q^23 - q^24 - q^25 + 2 * q^26 + q^27 - 12 * q^29 + q^30 + 2 * q^31 - 4 * q^32 - 4 * q^33 + 8 * q^34 - q^36 + 2 * q^37 + 3 * q^38 - 3 * q^39 - q^40 + 19 * q^41 + 12 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 4 * q^47 + q^48 + 12 * q^49 + q^50 - 12 * q^51 - 2 * q^52 - 12 * q^53 + 4 * q^54 + q^55 - 10 * q^56 + 3 * q^57 + 12 * q^58 + 16 * q^59 - q^60 - 4 * q^61 - 12 * q^62 - 5 * q^63 - q^64 + 2 * q^65 - q^66 + 12 * q^67 - 8 * q^68 + 9 * q^69 - 5 * q^70 + 22 * q^71 + q^72 - 22 * q^73 - 2 * q^74 + q^75 + 2 * q^76 - 30 * q^77 - 2 * q^78 - 10 * q^79 + q^80 - q^81 + 16 * q^82 - 24 * q^83 + 5 * q^84 - 12 * q^85 + 8 * q^86 + 12 * q^87 - 4 * q^88 - 34 * q^89 - q^90 - 5 * q^91 - 9 * q^92 - 2 * q^93 + q^94 - 2 * q^95 - q^96 + 14 * q^97 - 2 * q^98 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−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
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−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
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	1.00000			0.316228
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$11$	2.80902	+	1.76336i	0.846950	+	0.531672i
$12$	−1.00000			−0.288675
$13$	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
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.00000	+	6.15537i	−0.485071	+	1.49290i	0.346806	+	0.937937i	$0.387266\pi$
$17$	−2.00000	+	6.15537i	−0.485071	+	1.49290i	−0.831878	+	0.554959i	$0.812734\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	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
$21$	−3.61803			−0.789520
$22$	0.809017	−	3.21644i	0.172483	−	0.685747i
$23$	4.85410			1.01215			0.506075	−	0.862489i	$-0.331096\pi$
$23$	4.85410			1.01215			0.506075	+	0.862489i	$0.331096\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	0.500000	−	0.363271i	0.0980581	−	0.0712434i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.11803	−	3.44095i	0.211289	−	0.650279i
$29$	−3.00000	+	2.17963i	−0.557086	+	0.404747i	−0.830391	−	0.557181i	$-0.811883\pi$
$29$	−3.00000	+	2.17963i	−0.557086	+	0.404747i	0.273305	+	0.961927i	$0.411883\pi$
$30$	0.809017	+	0.587785i	0.147706	+	0.107314i
$31$	−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
$33$	1.23607	+	3.07768i	0.215172	+	0.535756i
$34$	6.47214			1.10996
$35$	−1.11803	−	3.44095i	−0.188982	−	0.581628i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	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
$39$	−0.190983	+	0.587785i	−0.0305818	+	0.0941210i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	7.54508	+	5.48183i	1.17834	+	0.856117i	0.991984	−	0.126364i	$-0.0403308\pi$
$41$	7.54508	+	5.48183i	1.17834	+	0.856117i	0.186360	+	0.982481i	$0.440331\pi$
$42$	1.11803	+	3.44095i	0.172516	+	0.530951i
$43$	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
$45$	−1.00000			−0.149071
$46$	−1.50000	−	4.61653i	−0.221163	−	0.680670i
$47$	2.11803	+	1.53884i	0.308947	+	0.224463i	0.731445	−	0.681901i	$-0.238846\pi$
$47$	2.11803	+	1.53884i	0.308947	+	0.224463i	−0.422498	+	0.906364i	$0.638846\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	1.88197	−	5.79210i	0.268852	−	0.827442i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−5.23607	+	3.80423i	−0.733196	+	0.532698i
$52$	−0.500000	−	0.363271i	−0.0693375	−	0.0503767i
$53$	−1.88197	−	5.79210i	−0.258508	−	0.795606i	−0.993118	−	0.117116i	$-0.962635\pi$
$53$	−1.88197	−	5.79210i	−0.258508	−	0.795606i	0.734610	−	0.678489i	$-0.237365\pi$
$54$	1.00000			0.136083
$55$	−2.54508	+	2.12663i	−0.343179	+	0.286754i
$56$	−3.61803			−0.483480
$57$	0.190983	+	0.587785i	0.0252963	+	0.0778541i
$58$	3.00000	+	2.17963i	0.393919	+	0.286199i
$59$	11.8262	−	8.59226i	1.53965	−	1.11862i	0.589087	−	0.808069i	$-0.299487\pi$
$59$	11.8262	−	8.59226i	1.53965	−	1.11862i	0.950558	−	0.310548i	$-0.100513\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	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
$63$	−2.92705	−	2.12663i	−0.368774	−	0.267930i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.618034			−0.0766577
$66$	2.54508	−	2.12663i	0.313278	−	0.261770i
$67$	−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
$69$	3.92705	+	2.85317i	0.472761	+	0.343481i
$70$	−2.92705	+	2.12663i	−0.349850	+	0.254181i
$71$	−0.0901699	+	0.277515i	−0.0107012	+	0.0329349i	−0.956265	−	0.292503i	$-0.905512\pi$
$71$	−0.0901699	+	0.277515i	−0.0107012	+	0.0329349i	0.945563	+	0.325438i	$0.105512\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	−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
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$	−0.618034			−0.0708934
$77$	−11.9721	+	0.812299i	−1.36435	+	0.0925701i
$78$	0.618034			0.0699786
$79$	−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
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	2.88197	−	8.86978i	0.318260	−	0.979503i
$83$	−1.52786	+	4.70228i	−0.167705	+	0.516143i	−0.999225	−	0.0393515i	$-0.987471\pi$
$83$	−1.52786	+	4.70228i	−0.167705	+	0.516143i	0.831521	+	0.555494i	$0.187471\pi$
$84$	2.92705	−	2.12663i	0.319367	−	0.232034i
$85$	−5.23607	−	3.80423i	−0.567931	−	0.412626i
$86$	−0.236068	−	0.726543i	−0.0254559	−	0.0783451i
$87$	−3.70820			−0.397561
$88$	1.23607	+	3.07768i	0.131765	+	0.328082i
$89$	−5.14590			−0.545464			−0.272732	−	0.962090i	$-0.587927\pi$
$89$	−5.14590			−0.545464			−0.272732	+	0.962090i	$0.587927\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	−1.80902	−	1.31433i	−0.189637	−	0.137779i
$92$	−3.92705	+	2.85317i	−0.409423	+	0.297463i
$93$	2.85410	−	8.78402i	0.295957	−	0.910861i
$94$	0.809017	−	2.48990i	0.0834437	−	0.256813i
$95$	−0.500000	+	0.363271i	−0.0512989	+	0.0372708i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	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
$99$	−0.809017	+	3.21644i	−0.0813093	+	0.323264i
$100$	1.00000			0.100000
$101$	1.23607	+	3.80423i	0.122993	+	0.378535i	0.993530	−	0.113569i	$-0.0362282\pi$
$101$	1.23607	+	3.80423i	0.122993	+	0.378535i	−0.870537	+	0.492103i	$0.836228\pi$
$102$	5.23607	+	3.80423i	0.518448	+	0.376675i
$103$	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
$105$	1.11803	−	3.44095i	0.109109	−	0.335803i
$106$	−4.92705	+	3.57971i	−0.478557	+	0.347692i
$107$	−14.4721	−	10.5146i	−1.39907	−	1.01649i	−0.994800	−	0.101849i	$-0.967524\pi$
$107$	−14.4721	−	10.5146i	−1.39907	−	1.01649i	−0.404274	−	0.914638i	$-0.632476\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	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
$111$	0.618034			0.0586612
$112$	1.11803	+	3.44095i	0.105644	+	0.325140i
$113$	10.0902	+	7.33094i	0.949203	+	0.689637i	0.950618	−	0.310362i	$-0.100450\pi$
$113$	10.0902	+	7.33094i	0.949203	+	0.689637i	−0.00141497	+	0.999999i	$0.500450\pi$
$114$	0.500000	−	0.363271i	0.0468293	−	0.0340235i
$115$	−1.50000	+	4.61653i	−0.139876	+	0.430493i
$116$	1.14590	−	3.52671i	0.106394	−	0.327447i
$117$	−0.500000	+	0.363271i	−0.0462250	+	0.0335844i
$118$	−11.8262	−	8.59226i	−1.08869	−	0.790982i
$119$	−7.23607	−	22.2703i	−0.663329	−	2.04152i
$120$	−1.00000			−0.0912871
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$	−11.2361			−1.01727
$123$	2.88197	+	8.86978i	0.259858	+	0.799761i
$124$	7.47214	+	5.42882i	0.671018	+	0.487523i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	−1.11803	+	3.44095i	−0.0996024	+	0.306545i
$127$	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
$129$	0.618034	+	0.449028i	0.0544149	+	0.0395347i
$130$	0.190983	+	0.587785i	0.0167503	+	0.0515522i
$131$	20.9443			1.82991			0.914955	−	0.403556i	$-0.132226\pi$
$131$	20.9443			1.82991			0.914955	+	0.403556i	$0.132226\pi$
$132$	−2.80902	−	1.76336i	−0.244494	−	0.153480i
$133$	−2.23607			−0.193892
$134$	2.52786	+	7.77997i	0.218374	+	0.672087i
$135$	−0.809017	−	0.587785i	−0.0696291	−	0.0505885i
$136$	−5.23607	+	3.80423i	−0.448989	+	0.326210i
$137$	4.76393	−	14.6619i	0.407010	−	1.25265i	−0.512195	−	0.858869i	$-0.671167\pi$
$137$	4.76393	−	14.6619i	0.407010	−	1.25265i	0.919205	−	0.393779i	$-0.128833\pi$
$138$	1.50000	−	4.61653i	0.127688	−	0.392985i
$139$	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
$141$	0.809017	+	2.48990i	0.0681315	+	0.209687i
$142$	0.291796			0.0244870
$143$	−0.500000	+	1.98787i	−0.0418121	+	0.166234i
$144$	1.00000			0.0833333
$145$	−1.14590	−	3.52671i	−0.0951617	−	0.292877i
$146$	8.85410	+	6.43288i	0.732771	+	0.532389i
$147$	4.92705	−	3.57971i	0.406376	−	0.295250i
$148$	−0.190983	+	0.587785i	−0.0156987	+	0.0483157i
$149$	−2.76393	+	8.50651i	−0.226430	+	0.696880i	0.771713	+	0.635971i	$0.219400\pi$
$149$	−2.76393	+	8.50651i	−0.226430	+	0.696880i	−0.998143	+	0.0609095i	$0.980600\pi$
$150$	−0.809017	+	0.587785i	−0.0660560	+	0.0479925i
$151$	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
$153$	−6.47214			−0.523241
$154$	4.47214	+	11.1352i	0.360375	+	0.897297i
$155$	9.23607			0.741859
$156$	−0.190983	−	0.587785i	−0.0152909	−	0.0470605i
$157$	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
$159$	1.88197	−	5.79210i	0.149250	−	0.459343i
$160$	0.309017	−	0.951057i	0.0244299	−	0.0751876i
$161$	−14.2082	+	10.3229i	−1.11976	+	0.813556i
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	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
$165$	−3.30902	+	0.224514i	−0.257607	+	0.0174784i
$166$	4.94427			0.383750
$167$	−3.57295	−	10.9964i	−0.276483	−	0.850927i	−0.988823	−	0.149093i	$-0.952365\pi$
$167$	−3.57295	−	10.9964i	−0.276483	−	0.850927i	0.712340	−	0.701834i	$-0.247635\pi$
$168$	−2.92705	−	2.12663i	−0.225827	−	0.164073i
$169$	10.2082	−	7.41669i	0.785246	−	0.570515i
$170$	−2.00000	+	6.15537i	−0.153393	+	0.472095i
$171$	−0.190983	+	0.587785i	−0.0146048	+	0.0449491i
$172$	−0.618034	+	0.449028i	−0.0471246	+	0.0342381i
$173$	19.8713	+	14.4374i	1.51079	+	1.09765i	0.965826	+	0.259192i	$0.0834563\pi$
$173$	19.8713	+	14.4374i	1.51079	+	1.09765i	0.544963	+	0.838460i	$0.316544\pi$
$174$	1.14590	+	3.52671i	0.0868703	+	0.267359i
$175$	3.61803			0.273498
$176$	2.54508	−	2.12663i	0.191843	−	0.160301i
$177$	14.6180			1.09876
$178$	1.59017	+	4.89404i	0.119188	+	0.366824i
$179$	9.01722	+	6.55139i	0.673979	+	0.489674i	0.871355	−	0.490654i	$-0.163242\pi$
$179$	9.01722	+	6.55139i	0.673979	+	0.489674i	−0.197376	+	0.980328i	$0.563242\pi$
$180$	0.809017	−	0.587785i	0.0603006	−	0.0438109i
$181$	−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
$183$	9.09017	−	6.60440i	0.671965	−	0.488211i
$184$	3.92705	+	2.85317i	0.289506	+	0.210338i
$185$	0.190983	+	0.587785i	0.0140413	+	0.0432148i
$186$	−9.23607			−0.677221
$187$	−16.4721	+	13.7638i	−1.20456	+	1.00651i
$188$	−2.61803			−0.190940
$189$	−1.11803	−	3.44095i	−0.0813250	−	0.250293i
$190$	0.500000	+	0.363271i	0.0362738	+	0.0263545i
$191$	11.0902	−	8.05748i	0.802457	−	0.583019i	−0.109177	−	0.994022i	$-0.534822\pi$
$191$	11.0902	−	8.05748i	0.802457	−	0.583019i	0.911634	+	0.411004i	$0.134822\pi$
$192$	−0.309017	+	0.951057i	−0.0223014	+	0.0686366i
$193$	−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
$195$	−0.500000	−	0.363271i	−0.0358057	−	0.0260144i
$196$	1.88197	+	5.79210i	0.134426	+	0.413721i
$197$	3.61803			0.257774			0.128887	−	0.991659i	$-0.458860\pi$
$197$	3.61803			0.257774			0.128887	+	0.991659i	$0.458860\pi$
$198$	3.30902	−	0.224514i	0.235162	−	0.0159555i
$199$	−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
$201$	−6.61803	−	4.80828i	−0.466800	−	0.339150i
$202$	3.23607	−	2.35114i	0.227689	−	0.165426i
$203$	4.14590	−	12.7598i	0.290985	−	0.895560i
$204$	2.00000	−	6.15537i	0.140028	−	0.430962i
$205$	−7.54508	+	5.48183i	−0.526972	+	0.382867i
$206$	−7.97214	−	5.79210i	−0.555445	−	0.403554i
$207$	1.50000	+	4.61653i	0.104257	+	0.320871i
$208$	0.618034			0.0428529
$209$	0.763932	+	1.90211i	0.0528423	+	0.131572i
$210$	−3.61803			−0.249668
$211$	−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
$213$	−0.236068	+	0.171513i	−0.0161751	+	0.0117519i
$214$	−5.52786	+	17.0130i	−0.377877	+	1.16299i
$215$	−0.236068	+	0.726543i	−0.0160997	+	0.0495498i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	27.0344	+	19.6417i	1.83522	+	1.33336i
$218$	−1.23607	−	3.80423i	−0.0837171	−	0.257655i
$219$	−10.9443			−0.739545
$220$	0.809017	−	3.21644i	0.0545439	−	0.216852i
$221$	−4.00000			−0.269069
$222$	−0.190983	−	0.587785i	−0.0128179	−	0.0394496i
$223$	−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
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	3.85410	−	11.8617i	0.256371	−	0.789029i
$227$	3.38197	−	2.45714i	0.224469	−	0.163086i	−0.469867	−	0.882737i	$-0.655698\pi$
$227$	3.38197	−	2.45714i	0.224469	−	0.163086i	0.694336	+	0.719651i	$0.255698\pi$
$228$	−0.500000	−	0.363271i	−0.0331133	−	0.0240582i
$229$	−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
$231$	−10.1631	−	6.37988i	−0.668684	−	0.419765i
$232$	−3.70820			−0.243456
$233$	−5.03444	−	15.4944i	−0.329817	−	1.01507i	−0.969219	−	0.246200i	$-0.920818\pi$
$233$	−5.03444	−	15.4944i	−0.329817	−	1.01507i	0.639402	−	0.768873i	$-0.279182\pi$
$234$	0.500000	+	0.363271i	0.0326860	+	0.0237478i
$235$	−2.11803	+	1.53884i	−0.138165	+	0.100383i
$236$	−4.51722	+	13.9026i	−0.294046	+	0.904981i
$237$	1.38197	−	4.25325i	0.0897683	−	0.276279i
$238$	−18.9443	+	13.7638i	−1.22797	+	0.892176i
$239$	−17.9443	−	13.0373i	−1.16072	−	0.843311i	−0.170850	−	0.985297i	$-0.554651\pi$
$239$	−17.9443	−	13.0373i	−1.16072	−	0.843311i	−0.989869	+	0.141986i	$0.954651\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−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
$243$	−1.00000			−0.0641500
$244$	3.47214	+	10.6861i	0.222281	+	0.684110i
$245$	4.92705	+	3.57971i	0.314778	+	0.228699i
$246$	7.54508	−	5.48183i	0.481057	−	0.349508i
$247$	−0.118034	+	0.363271i	−0.00751032	+	0.0231144i
$248$	2.85410	−	8.78402i	0.181236	−	0.557786i
$249$	−4.00000	+	2.90617i	−0.253490	+	0.184171i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	3.55573	+	10.9434i	0.224436	+	0.690742i	0.998348	+	0.0574495i	$0.0182968\pi$
$251$	3.55573	+	10.9434i	0.224436	+	0.690742i	−0.773913	+	0.633292i	$0.781703\pi$
$252$	3.61803			0.227915
$253$	13.6353	+	8.55951i	0.857241	+	0.538132i
$254$	−12.6180			−0.791726
$255$	−2.00000	−	6.15537i	−0.125245	−	0.385464i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	4.09017	−	2.97168i	0.255138	−	0.185368i	−0.452863	−	0.891580i	$-0.649597\pi$
$257$	4.09017	−	2.97168i	0.255138	−	0.185368i	0.708001	+	0.706212i	$0.249597\pi$
$258$	0.236068	−	0.726543i	0.0146970	−	0.0452326i
$259$	−0.690983	+	2.12663i	−0.0429356	+	0.132142i
$260$	0.500000	−	0.363271i	0.0310087	−	0.0225291i
$261$	−3.00000	−	2.17963i	−0.185695	−	0.134916i
$262$	−6.47214	−	19.9192i	−0.399850	−	1.23061i
$263$	−8.14590			−0.502298			−0.251149	−	0.967948i	$-0.580808\pi$
$263$	−8.14590			−0.502298			−0.251149	+	0.967948i	$0.580808\pi$
$264$	−0.809017	+	3.21644i	−0.0497916	+	0.197958i
$265$	6.09017			0.374116
$266$	0.690983	+	2.12663i	0.0423669	+	0.130392i
$267$	−4.16312	−	3.02468i	−0.254779	−	0.185108i
$268$	6.61803	−	4.80828i	0.404261	−	0.293713i
$269$	−7.65248	+	23.5519i	−0.466580	+	1.43598i	0.390405	+	0.920643i	$0.372335\pi$
$269$	−7.65248	+	23.5519i	−0.466580	+	1.43598i	−0.856985	+	0.515341i	$0.827665\pi$
$270$	−0.309017	+	0.951057i	−0.0188062	+	0.0578795i
$271$	−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
$273$	−0.690983	−	2.12663i	−0.0418202	−	0.128709i
$274$	−15.4164			−0.931339
$275$	−1.23607	−	3.07768i	−0.0745377	−	0.185591i
$276$	−4.85410			−0.292183
$277$	−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
$279$	7.47214	−	5.42882i	0.447345	−	0.325015i
$280$	1.11803	−	3.44095i	0.0668153	−	0.205636i
$281$	2.43769	−	7.50245i	0.145421	−	0.447559i	−0.851644	−	0.524120i	$-0.824394\pi$
$281$	2.43769	−	7.50245i	0.145421	−	0.447559i	0.997065	+	0.0765616i	$0.0243942\pi$
$282$	2.11803	−	1.53884i	0.126127	−	0.0916367i
$283$	−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
$285$	−0.618034			−0.0366092
$286$	2.04508	−	0.138757i	0.120928	−	0.00820489i
$287$	−33.7426			−1.99177
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−20.1353	−	14.6291i	−1.18443	−	0.860536i
$290$	−3.00000	+	2.17963i	−0.176166	+	0.127992i
$291$	−4.61803	+	14.2128i	−0.270714	+	0.833172i
$292$	3.38197	−	10.4086i	0.197915	−	0.609118i
$293$	−8.92705	+	6.48588i	−0.521524	+	0.378909i	−0.817178	−	0.576386i	$-0.804463\pi$
$293$	−8.92705	+	6.48588i	−0.521524	+	0.378909i	0.295654	+	0.955295i	$0.404463\pi$
$294$	−4.92705	−	3.57971i	−0.287351	−	0.208773i
$295$	4.51722	+	13.9026i	0.263003	+	0.809439i
$296$	0.618034			0.0359225
$297$	−2.54508	+	2.12663i	−0.147681	+	0.123399i
$298$	8.94427			0.518128
$299$	0.927051	+	2.85317i	0.0536127	+	0.165003i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	−2.23607	+	1.62460i	−0.128885	+	0.0936403i
$302$	3.85410	−	11.8617i	0.221779	−	0.682564i
$303$	−1.23607	+	3.80423i	−0.0710102	+	0.218547i
$304$	0.500000	−	0.363271i	0.0286770	−	0.0208350i
$305$	9.09017	+	6.60440i	0.520502	+	0.378167i
$306$	2.00000	+	6.15537i	0.114332	+	0.351879i
$307$	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
$309$	9.85410			0.560580
$310$	−2.85410	−	8.78402i	−0.162102	−	0.498899i
$311$	22.5623	+	16.3925i	1.27939	+	0.929532i	0.999534	−	0.0305099i	$-0.00971310\pi$
$311$	22.5623	+	16.3925i	1.27939	+	0.929532i	0.279857	+	0.960042i	$0.409713\pi$
$312$	−0.500000	+	0.363271i	−0.0283069	+	0.0205662i
$313$	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
$315$	2.92705	−	2.12663i	0.164921	−	0.119822i
$316$	3.61803	+	2.62866i	0.203530	+	0.147873i
$317$	3.37132	+	10.3759i	0.189352	+	0.582767i	0.999996	−	0.00277297i	$-0.000882666\pi$
$317$	3.37132	+	10.3759i	0.189352	+	0.582767i	−0.810644	+	0.585540i	$0.800883\pi$
$318$	−6.09017			−0.341520
$319$	−12.2705	+	0.832544i	−0.687017	+	0.0466135i
$320$	−1.00000			−0.0559017
$321$	−5.52786	−	17.0130i	−0.308535	−	0.949574i
$322$	14.2082	+	10.3229i	0.791792	+	0.575271i
$323$	−3.23607	+	2.35114i	−0.180060	+	0.130821i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	0.190983	−	0.587785i	0.0105938	−	0.0326045i
$326$	14.4721	−	10.5146i	0.801537	−	0.582351i
$327$	3.23607	+	2.35114i	0.178955	+	0.130018i
$328$	2.88197	+	8.86978i	0.159130	+	0.489752i
$329$	−9.47214			−0.522216
$330$	1.23607	+	3.07768i	0.0680433	+	0.169421i
$331$	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
$333$	0.500000	+	0.363271i	0.0273998	+	0.0199071i
$334$	−9.35410	+	6.79615i	−0.511834	+	0.371869i
$335$	2.52786	−	7.77997i	0.138112	−	0.425065i
$336$	−1.11803	+	3.44095i	−0.0609938	+	0.187719i
$337$	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
$339$	3.85410	+	11.8617i	0.209326	+	0.644239i
$340$	6.47214			0.351001
$341$	7.47214	−	29.7073i	0.404639	−	1.60874i
$342$	0.618034			0.0334195
$343$	−1.01722	−	3.13068i	−0.0549248	−	0.169041i
$344$	0.618034	+	0.449028i	0.0333222	+	0.0242100i
$345$	−3.92705	+	2.85317i	−0.211425	+	0.153609i
$346$	7.59017	−	23.3601i	0.408050	−	1.25585i
$347$	1.18034	−	3.63271i	0.0633640	−	0.195014i	−0.914363	−	0.404896i	$-0.867308\pi$
$347$	1.18034	−	3.63271i	0.0633640	−	0.195014i	0.977727	+	0.209881i	$0.0673078\pi$
$348$	3.00000	−	2.17963i	0.160817	−	0.116840i
$349$	−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
$351$	−0.618034			−0.0329882
$352$	−2.80902	−	1.76336i	−0.149721	−	0.0939872i
$353$	−24.6525			−1.31212			−0.656059	−	0.754709i	$-0.727778\pi$
$353$	−24.6525			−1.31212			−0.656059	+	0.754709i	$0.727778\pi$
$354$	−4.51722	−	13.9026i	−0.240088	−	0.738914i
$355$	−0.236068	−	0.171513i	−0.0125292	−	0.00910299i
$356$	4.16312	−	3.02468i	0.220645	−	0.160308i
$357$	7.23607	−	22.2703i	0.382973	−	1.17867i
$358$	3.44427	−	10.6004i	0.182035	−	0.560247i
$359$	−20.4164	+	14.8334i	−1.07754	+	0.782876i	−0.977252	−	0.212082i	$-0.931975\pi$
$359$	−20.4164	+	14.8334i	−1.07754	+	0.782876i	−0.100285	+	0.994959i	$0.531975\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	−5.75329	−	17.7068i	−0.302805	−	0.931937i
$362$	24.3607			1.28037
$363$	−1.95492	+	10.8249i	−0.102606	+	0.568160i
$364$	2.23607			0.117202
$365$	−3.38197	−	10.4086i	−0.177020	−	0.544812i
$366$	−9.09017	−	6.60440i	−0.475151	−	0.345217i
$367$	−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
$369$	−2.88197	+	8.86978i	−0.150029	+	0.461742i
$370$	0.500000	−	0.363271i	0.0259938	−	0.0188856i
$371$	17.8262	+	12.9515i	0.925492	+	0.672409i
$372$	2.85410	+	8.78402i	0.147978	+	0.455430i
$373$	−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
$375$	1.00000			0.0516398
$376$	0.809017	+	2.48990i	0.0417219	+	0.128407i
$377$	−1.85410	−	1.34708i	−0.0954911	−	0.0693784i
$378$	−2.92705	+	2.12663i	−0.150551	+	0.109382i
$379$	−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
$381$	10.2082	−	7.41669i	0.522982	−	0.379969i
$382$	−11.0902	−	8.05748i	−0.567422	−	0.412257i
$383$	−8.79180	−	27.0584i	−0.449240	−	1.38262i	−0.877766	−	0.479089i	$-0.840967\pi$
$383$	−8.79180	−	27.0584i	−0.449240	−	1.38262i	0.428527	−	0.903529i	$-0.359033\pi$
$384$	1.00000			0.0510310
$385$	2.92705	−	11.6372i	0.149176	−	0.593086i
$386$	3.70820			0.188743
$387$	0.236068	+	0.726543i	0.0120000	+	0.0369322i
$388$	−12.0902	−	8.78402i	−0.613785	−	0.445941i
$389$	−2.85410	+	2.07363i	−0.144709	+	0.105137i	−0.657784	−	0.753206i	$-0.728506\pi$
$389$	−2.85410	+	2.07363i	−0.144709	+	0.105137i	0.513075	+	0.858344i	$0.328506\pi$
$390$	−0.190983	+	0.587785i	−0.00967080	+	0.0297637i
$391$	−9.70820	+	29.8788i	−0.490965	+	1.51103i
$392$	4.92705	−	3.57971i	0.248854	−	0.180803i
$393$	16.9443	+	12.3107i	0.854725	+	0.620994i
$394$	−1.11803	−	3.44095i	−0.0563257	−	0.173353i
$395$	4.47214			0.225018
$396$	−1.23607	−	3.07768i	−0.0621148	−	0.154659i
$397$	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
$399$	−1.80902	−	1.31433i	−0.0905641	−	0.0657987i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−0.517221	+	1.59184i	−0.0258288	+	0.0794928i	−0.963140	−	0.269001i	$-0.913307\pi$
$401$	−0.517221	+	1.59184i	−0.0258288	+	0.0794928i	0.937311	+	0.348493i	$0.113307\pi$
$402$	−2.52786	+	7.77997i	−0.126078	+	0.388029i
$403$	4.61803	−	3.35520i	0.230041	−	0.167134i
$404$	−3.23607	−	2.35114i	−0.161000	−	0.116974i
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−13.4164			−0.665845
$407$	2.04508	−	0.138757i	0.101371	−	0.00687794i
$408$	−6.47214			−0.320418
$409$	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
$411$	12.4721	−	9.06154i	0.615205	−	0.446973i
$412$	−3.04508	+	9.37181i	−0.150021	+	0.461716i
$413$	−16.3435	+	50.3000i	−0.804209	+	2.47510i
$414$	3.92705	−	2.85317i	0.193004	−	0.140226i
$415$	−4.00000	−	2.90617i	−0.196352	−	0.142658i
$416$	−0.190983	−	0.587785i	−0.00936371	−	0.0288185i
$417$	7.61803			0.373057
$418$	1.57295	−	1.31433i	0.0769355	−	0.0642859i
$419$	−11.2016			−0.547235			−0.273618	−	0.961839i	$-0.588220\pi$
$419$	−11.2016			−0.547235			−0.273618	+	0.961839i	$0.588220\pi$
$420$	1.11803	+	3.44095i	0.0545545	+	0.167901i
$421$	−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
$423$	−0.809017	+	2.48990i	−0.0393358	+	0.121063i
$424$	1.88197	−	5.79210i	0.0913963	−	0.281289i
$425$	5.23607	−	3.80423i	0.253987	−	0.184532i
$426$	0.236068	+	0.171513i	0.0114375	+	0.00830985i
$427$	12.5623	+	38.6628i	0.607933	+	1.87102i
$428$	17.8885			0.864675
$429$	−1.57295	+	1.31433i	−0.0759427	+	0.0634563i
$430$	0.763932			0.0368401
$431$	0.673762	+	2.07363i	0.0324540	+	0.0998831i	0.965971	−	0.258649i	$-0.0832773\pi$
$431$	0.673762	+	2.07363i	0.0324540	+	0.0998831i	−0.933517	+	0.358532i	$0.883277\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	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
$435$	1.14590	−	3.52671i	0.0549416	−	0.169093i
$436$	−3.23607	+	2.35114i	−0.154980	+	0.112599i
$437$	2.42705	+	1.76336i	0.116102	+	0.0843527i
$438$	3.38197	+	10.4086i	0.161597	+	0.497343i
$439$	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
$441$	6.09017			0.290008
$442$	1.23607	+	3.80423i	0.0587938	+	0.180949i
$443$	−23.3262	−	16.9475i	−1.10826	−	0.805200i	−0.125874	−	0.992046i	$-0.540173\pi$
$443$	−23.3262	−	16.9475i	−1.10826	−	0.805200i	−0.982389	+	0.186846i	$0.940173\pi$
$444$	−0.500000	+	0.363271i	−0.0237289	+	0.0172401i
$445$	1.59017	−	4.89404i	0.0753813	−	0.232000i
$446$	−2.35410	+	7.24518i	−0.111470	+	0.343069i
$447$	−7.23607	+	5.25731i	−0.342254	+	0.248662i
$448$	−2.92705	−	2.12663i	−0.138290	−	0.100474i
$449$	−5.75329	−	17.7068i	−0.271514	−	0.835636i	−0.990121	−	0.140218i	$-0.955220\pi$
$449$	−5.75329	−	17.7068i	−0.271514	−	0.835636i	0.718606	−	0.695417i	$-0.244780\pi$
$450$	−1.00000			−0.0471405
$451$	11.5279	+	28.7032i	0.542826	+	1.35158i
$452$	−12.4721			−0.586640
$453$	3.85410	+	11.8617i	0.181082	+	0.557312i
$454$	−3.38197	−	2.45714i	−0.158724	−	0.115319i
$455$	1.80902	−	1.31433i	0.0848080	−	0.0616166i
$456$	−0.190983	+	0.587785i	−0.00894360	+	0.0275256i
$457$	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
$459$	−5.23607	−	3.80423i	−0.244399	−	0.177566i
$460$	−1.50000	−	4.61653i	−0.0699379	−	0.215247i
$461$	−24.7639			−1.15337			−0.576686	−	0.816966i	$-0.695654\pi$
$461$	−24.7639			−1.15337			−0.576686	+	0.816966i	$0.695654\pi$
$462$	−2.92705	+	11.6372i	−0.136179	+	0.541411i
$463$	−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
$465$	7.47214	+	5.42882i	0.346512	+	0.251756i
$466$	−13.1803	+	9.57608i	−0.610567	+	0.443603i
$467$	2.18034	−	6.71040i	0.100894	−	0.310520i	−0.887851	−	0.460131i	$-0.847802\pi$
$467$	2.18034	−	6.71040i	0.100894	−	0.310520i	0.988745	+	0.149611i	$0.0478023\pi$
$468$	0.190983	−	0.587785i	0.00882819	−	0.0271704i
$469$	23.9443	−	17.3965i	1.10564	−	0.803297i
$470$	2.11803	+	1.53884i	0.0976976	+	0.0709815i
$471$	1.73607	+	5.34307i	0.0799938	+	0.246196i
$472$	14.6180			0.672850
$473$	2.14590	+	1.34708i	0.0986685	+	0.0619390i
$474$	−4.47214			−0.205412
$475$	−0.190983	−	0.587785i	−0.00876290	−	0.0269694i
$476$	18.9443	+	13.7638i	0.868309	+	0.630864i
$477$	4.92705	−	3.57971i	0.225594	−	0.163904i
$478$	−6.85410	+	21.0948i	−0.313499	+	0.964852i
$479$	−12.0557	+	37.1037i	−0.550840	+	1.69531i	0.155843	+	0.987782i	$0.450191\pi$
$479$	−12.0557	+	37.1037i	−0.550840	+	1.69531i	−0.706683	+	0.707530i	$0.749809\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	0.309017	+	0.224514i	0.0140900	+	0.0102370i
$482$	7.91641	+	24.3642i	0.360582	+	1.10976i
$483$	−17.5623			−0.799113
$484$	−9.69098	−	5.20431i	−0.440499	−	0.236560i
$485$	−14.9443			−0.678584
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−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
$489$	−5.52786	+	17.0130i	−0.249979	+	0.769355i
$490$	1.88197	−	5.79210i	0.0850186	−	0.261660i
$491$	1.88197	−	1.36733i	0.0849319	−	0.0617067i	−0.544509	−	0.838755i	$-0.683284\pi$
$491$	1.88197	−	1.36733i	0.0849319	−	0.0617067i	0.629441	+	0.777048i	$0.283284\pi$
$492$	−7.54508	−	5.48183i	−0.340159	−	0.247140i
$493$	−7.41641	−	22.8254i	−0.334018	−	1.02800i
$494$	0.381966			0.0171855
$495$	−2.80902	−	1.76336i	−0.126256	−	0.0792569i
$496$	−9.23607			−0.414712
$497$	−0.326238	−	1.00406i	−0.0146338	−	0.0450381i
$498$	4.00000	+	2.90617i	0.179244	+	0.130229i
$499$	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
$501$	3.57295	−	10.9964i	0.159628	−	0.491283i
$502$	9.30902	−	6.76340i	0.415482	−	0.301865i
$503$	3.88197	+	2.82041i	0.173088	+	0.125756i	0.670957	−	0.741497i	$-0.265884\pi$
$503$	3.88197	+	2.82041i	0.173088	+	0.125756i	−0.497868	+	0.867253i	$0.665884\pi$
$504$	−1.11803	−	3.44095i	−0.0498012	−	0.153272i
$505$	−4.00000			−0.177998
$506$	3.92705	−	15.6129i	0.174579	−	0.694079i
$507$	12.6180			0.560387
$508$	3.89919	+	12.0005i	0.172998	+	0.532434i
$509$	20.5623	+	14.9394i	0.911408	+	0.662177i	0.941371	−	0.337374i	$-0.109539\pi$
$509$	20.5623	+	14.9394i	0.911408	+	0.662177i	−0.0299624	+	0.999551i	$0.509539\pi$
$510$	−5.23607	+	3.80423i	−0.231857	+	0.168454i
$511$	12.2361	−	37.6587i	0.541292	−	1.66592i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.500000	+	0.363271i	−0.0220755	+	0.0160388i
$514$	−4.09017	−	2.97168i	−0.180410	−	0.131075i
$515$	3.04508	+	9.37181i	0.134182	+	0.412971i
$516$	−0.763932			−0.0336302
$517$	3.23607	+	8.05748i	0.142322	+	0.354368i
$518$	2.23607			0.0982472
$519$	7.59017	+	23.3601i	0.333171	+	1.02540i
$520$	−0.500000	−	0.363271i	−0.0219265	−	0.0159305i
$521$	−30.1976	+	21.9398i	−1.32298	+	0.961201i	−0.323089	+	0.946369i	$0.604721\pi$
$521$	−30.1976	+	21.9398i	−1.32298	+	0.961201i	−0.999890	+	0.0148321i	$0.995279\pi$
$522$	−1.14590	+	3.52671i	−0.0501546	+	0.154360i
$523$	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
$525$	2.92705	+	2.12663i	0.127747	+	0.0928136i
$526$	2.51722	+	7.74721i	0.109756	+	0.337794i
$527$	59.7771			2.60393
$528$	3.30902	−	0.224514i	0.144006	−	0.00977072i
$529$	0.562306			0.0244481
$530$	−1.88197	−	5.79210i	−0.0817474	−	0.251593i
$531$	11.8262	+	8.59226i	0.513215	+	0.372873i
$532$	1.80902	−	1.31433i	0.0784308	−	0.0569833i
$533$	−1.78115	+	5.48183i	−0.0771503	+	0.237444i
$534$	−1.59017	+	4.89404i	−0.0688134	+	0.211786i
$535$	14.4721	−	10.5146i	0.625685	−	0.454587i
$536$	−6.61803	−	4.80828i	−0.285856	−	0.207686i
$537$	3.44427	+	10.6004i	0.148631	+	0.457440i
$538$	24.7639			1.06765
$539$	15.5000	−	12.9515i	0.667632	−	0.557861i
$540$	1.00000			0.0430331
$541$	−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
$543$	−19.7082	+	14.3188i	−0.845760	+	0.614481i
$544$	2.00000	−	6.15537i	0.0857493	−	0.263909i
$545$	−1.23607	+	3.80423i	−0.0529473	+	0.162955i
$546$	−1.80902	+	1.31433i	−0.0774188	+	0.0562480i
$547$	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
$549$	11.2361			0.479544
$550$	−2.54508	+	2.12663i	−0.108523	+	0.0906797i
$551$	−2.29180			−0.0976338
$552$	1.50000	+	4.61653i	0.0638442	+	0.196492i
$553$	13.0902	+	9.51057i	0.556651	+	0.404430i
$554$	−6.69098	+	4.86128i	−0.284273	+	0.206536i
$555$	−0.190983	+	0.587785i	−0.00810678	+	0.0249501i
$556$	−2.35410	+	7.24518i	−0.0998362	+	0.307264i
$557$	−11.0623	+	8.03724i	−0.468725	+	0.340549i	−0.796944	−	0.604053i	$-0.793552\pi$
$557$	−11.0623	+	8.03724i	−0.468725	+	0.340549i	0.328219	+	0.944602i	$0.393552\pi$
$558$	−7.47214	−	5.42882i	−0.316321	−	0.229820i
$559$	0.145898	+	0.449028i	0.00617083	+	0.0189919i
$560$	−3.61803			−0.152890
$561$	−21.4164	+	1.45309i	−0.904201	+	0.0613493i
$562$	−7.88854			−0.332758
$563$	14.0000	+	43.0876i	0.590030	+	1.81592i	0.578057	+	0.815996i	$0.303811\pi$
$563$	14.0000	+	43.0876i	0.590030	+	1.81592i	0.0119724	+	0.999928i	$0.496189\pi$
$564$	−2.11803	−	1.53884i	−0.0891853	−	0.0647969i
$565$	−10.0902	+	7.33094i	−0.424497	+	0.308415i
$566$	−1.14590	+	3.52671i	−0.0481657	+	0.148239i
$567$	1.11803	−	3.44095i	0.0469530	−	0.144507i
$568$	−0.236068	+	0.171513i	−0.00990519	+	0.00719654i
$569$	−12.0172	−	8.73102i	−0.503788	−	0.366023i	0.306674	−	0.951815i	$-0.400784\pi$
$569$	−12.0172	−	8.73102i	−0.503788	−	0.366023i	−0.810462	+	0.585791i	$0.800784\pi$
$570$	0.190983	+	0.587785i	0.00799940	+	0.0246196i
$571$	−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
$573$	13.7082			0.572668
$574$	10.4271	+	32.0912i	0.435217	+	1.33946i
$575$	−3.92705	−	2.85317i	−0.163769	−	0.118985i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−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
$579$	−3.00000	+	2.17963i	−0.124676	+	0.0905822i
$580$	3.00000	+	2.17963i	0.124568	+	0.0905041i
$581$	−5.52786	−	17.0130i	−0.229334	−	0.705819i
$582$	14.9443			0.619460
$583$	4.92705	−	19.5887i	0.204058	−	0.811280i
$584$	−10.9443			−0.452877
$585$	−0.190983	−	0.587785i	−0.00789618	−	0.0243019i
$586$	8.92705	+	6.48588i	0.368773	+	0.267929i
$587$	−28.1803	+	20.4742i	−1.16313	+	0.845061i	−0.990170	−	0.139868i	$-0.955332\pi$
$587$	−28.1803	+	20.4742i	−1.16313	+	0.845061i	−0.172957	+	0.984929i	$0.555332\pi$
$588$	−1.88197	+	5.79210i	−0.0776110	+	0.238862i
$589$	1.76393	−	5.42882i	0.0726816	−	0.223691i
$590$	11.8262	−	8.59226i	0.486879	−	0.353738i
$591$	2.92705	+	2.12663i	0.120403	+	0.0874777i
$592$	−0.190983	−	0.587785i	−0.00784935	−	0.0241578i
$593$	−2.58359			−0.106095			−0.0530477	−	0.998592i	$-0.516894\pi$
$593$	−2.58359			−0.106095			−0.0530477	+	0.998592i	$0.516894\pi$
$594$	2.80902	+	1.76336i	0.115255	+	0.0723514i
$595$	23.4164			0.959979
$596$	−2.76393	−	8.50651i	−0.113215	−	0.348440i
$597$	−10.4721	−	7.60845i	−0.428596	−	0.311393i
$598$	2.42705	−	1.76336i	0.0992495	−	0.0721090i
$599$	−1.32624	+	4.08174i	−0.0541886	+	0.166775i	−0.974488	−	0.224439i	$-0.927945\pi$
$599$	−1.32624	+	4.08174i	−0.0541886	+	0.166775i	0.920299	+	0.391215i	$0.127945\pi$
$600$	0.309017	−	0.951057i	0.0126156	−	0.0388267i
$601$	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
$603$	−2.52786	−	7.77997i	−0.102943	−	0.316825i
$604$	−12.4721			−0.507484
$605$	−10.8992	+	1.48584i	−0.443115	+	0.0604080i
$606$	4.00000			0.162489
$607$	−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
$609$	10.8541	−	7.88597i	0.439830	−	0.319555i
$610$	3.47214	−	10.6861i	0.140583	−	0.432669i
$611$	−0.500000	+	1.53884i	−0.0202278	+	0.0622549i
$612$	5.23607	−	3.80423i	0.211656	−	0.153777i
$613$	−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
$615$	−9.32624			−0.376070
$616$	−10.1631	−	6.37988i	−0.409484	−	0.257053i
$617$	23.0557			0.928189			0.464094	−	0.885786i	$-0.346380\pi$
$617$	23.0557			0.928189			0.464094	+	0.885786i	$0.346380\pi$
$618$	−3.04508	−	9.37181i	−0.122491	−	0.376989i
$619$	−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
$621$	−1.50000	+	4.61653i	−0.0601929	+	0.185255i
$622$	8.61803	−	26.5236i	0.345552	−	1.06350i
$623$	15.0623	−	10.9434i	0.603459	−	0.438438i
$624$	0.500000	+	0.363271i	0.0200160	+	0.0145425i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−5.70820			−0.228146
$627$	−0.500000	+	1.98787i	−0.0199681	+	0.0793879i
$628$	−5.61803			−0.224184
$629$	1.23607	+	3.80423i	0.0492853	+	0.151684i
$630$	−2.92705	−	2.12663i	−0.116617	−	0.0847268i
$631$	−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
$633$	7.23607	−	22.2703i	0.287608	−	0.885166i
$634$	8.82624	−	6.41264i	0.350535	−	0.254678i
$635$	10.2082	+	7.41669i	0.405100	+	0.294323i
$636$	1.88197	+	5.79210i	0.0746248	+	0.229672i
$637$	3.76393			0.149132
$638$	4.58359	+	11.4127i	0.181466	+	0.451832i
$639$	−0.291796			−0.0115433
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−30.2984	−	22.0131i	−1.19671	−	0.869463i	−0.202756	−	0.979229i	$-0.564990\pi$
$641$	−30.2984	−	22.0131i	−1.19671	−	0.869463i	−0.993957	+	0.109766i	$0.964990\pi$
$642$	−14.4721	+	10.5146i	−0.571170	+	0.414979i
$643$	−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
$645$	−0.618034	+	0.449028i	−0.0243351	+	0.0176805i
$646$	3.23607	+	2.35114i	0.127321	+	0.0925044i
$647$	−9.52786	−	29.3238i	−0.374579	−	1.15284i	−0.943762	−	0.330625i	$-0.892741\pi$
$647$	−9.52786	−	29.3238i	−0.374579	−	1.15284i	0.569183	−	0.822211i	$-0.307259\pi$
$648$	−1.00000			−0.0392837
$649$	48.3713	−	3.28195i	1.89874	−	0.128828i
$650$	−0.618034			−0.0242413
$651$	10.3262	+	31.7809i	0.404717	+	1.24559i
$652$	−14.4721	−	10.5146i	−0.566773	−	0.411784i
$653$	12.8262	−	9.31881i	0.501929	−	0.364673i	−0.307824	−	0.951443i	$-0.599601\pi$
$653$	12.8262	−	9.31881i	0.501929	−	0.364673i	0.809754	+	0.586770i	$0.199601\pi$
$654$	1.23607	−	3.80423i	0.0483341	−	0.148757i
$655$	−6.47214	+	19.9192i	−0.252887	+	0.778307i
$656$	7.54508	−	5.48183i	0.294586	−	0.214029i
$657$	−8.85410	−	6.43288i	−0.345431	−	0.250971i
$658$	2.92705	+	9.00854i	0.114108	+	0.351189i
$659$	28.2705			1.10126			0.550631	−	0.834749i	$-0.314387\pi$
$659$	28.2705			1.10126			0.550631	+	0.834749i	$0.314387\pi$
$660$	2.54508	−	2.12663i	0.0990673	−	0.0827788i
$661$	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
$663$	−3.23607	−	2.35114i	−0.125678	−	0.0913108i
$664$	−4.00000	+	2.90617i	−0.155230	+	0.112781i
$665$	0.690983	−	2.12663i	0.0267952	−	0.0824671i
$666$	0.190983	−	0.587785i	0.00740044	−	0.0227762i
$667$	−14.5623	+	10.5801i	−0.563855	+	0.409664i
$668$	9.35410	+	6.79615i	0.361921	+	0.262951i
$669$	−2.35410	−	7.24518i	−0.0910148	−	0.280115i
$670$	−8.18034			−0.316034
$671$	28.5967	−	23.8949i	1.10397	−	0.922453i
$672$	3.61803			0.139569
$673$	−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
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	−3.89919	+	12.0005i	−0.149969	+	0.461556i
$677$	4.43769	−	13.6578i	0.170554	−	0.524913i	−0.828848	−	0.559474i	$-0.811003\pi$
$677$	4.43769	−	13.6578i	0.170554	−	0.524913i	0.999403	+	0.0345610i	$0.0110033\pi$
$678$	10.0902	−	7.33094i	0.387511	−	0.281543i
$679$	−43.7426	−	31.7809i	−1.67869	−	1.21964i
$680$	−2.00000	−	6.15537i	−0.0766965	−	0.236048i
$681$	4.18034			0.160191
$682$	−30.5623	+	2.07363i	−1.17029	+	0.0794033i
$683$	31.1246			1.19095			0.595475	−	0.803374i	$-0.296964\pi$
$683$	31.1246			1.19095			0.595475	+	0.803374i	$0.296964\pi$
$684$	−0.190983	−	0.587785i	−0.00730242	−	0.0224745i
$685$	12.4721	+	9.06154i	0.476536	+	0.346224i
$686$	−2.66312	+	1.93487i	−0.101678	+	0.0738736i
$687$	3.56231	−	10.9637i	0.135910	−	0.418289i
$688$	0.236068	−	0.726543i	0.00900001	−	0.0276992i
$689$	3.04508	−	2.21238i	0.116008	−	0.0842851i
$690$	3.92705	+	2.85317i	0.149500	+	0.108618i
$691$	−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
$693$	−4.47214	−	11.1352i	−0.169882	−	0.422990i
$694$	−3.81966			−0.144992
$695$	2.35410	+	7.24518i	0.0892962	+	0.274825i
$696$	−3.00000	−	2.17963i	−0.113715	−	0.0826186i
$697$	−48.8328	+	35.4791i	−1.84967	+	1.34387i
$698$	−3.09017	+	9.51057i	−0.116965	+	0.359980i
$699$	5.03444	−	15.4944i	0.190420	−	0.586053i
$700$	−2.92705	+	2.12663i	−0.110632	+	0.0803789i
$701$	16.2361	+	11.7962i	0.613228	+	0.445536i	0.850549	−	0.525895i	$-0.176270\pi$
$701$	16.2361	+	11.7962i	0.613228	+	0.445536i	−0.237322	+	0.971431i	$0.576270\pi$
$702$	0.190983	+	0.587785i	0.00720819	+	0.0221845i
$703$	0.381966			0.0144061
$704$	−0.809017	+	3.21644i	−0.0304910	+	0.121224i
$705$	−2.61803			−0.0986009
$706$	7.61803	+	23.4459i	0.286708	+	0.882398i
$707$	−11.7082	−	8.50651i	−0.440332	−	0.319920i
$708$	−11.8262	+	8.59226i	−0.444457	+	0.322917i
$709$	−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
$711$	3.61803	−	2.62866i	0.135687	−	0.0985823i
$712$	−4.16312	−	3.02468i	−0.156019	−	0.113355i
$713$	−13.8541	−	42.6385i	−0.518840	−	1.59683i
$714$	−23.4164			−0.876337
$715$	−1.73607	−	1.08981i	−0.0649253	−	0.0407567i
$716$	−11.1459			−0.416542
$717$	−6.85410	−	21.0948i	−0.255971	−	0.787798i
$718$	20.4164	+	14.8334i	0.761934	+	0.553577i
$719$	19.3262	−	14.0413i	0.720747	−	0.523653i	−0.165876	−	0.986147i	$-0.553045\pi$
$719$	19.3262	−	14.0413i	0.720747	−	0.523653i	0.886623	+	0.462493i	$0.153045\pi$
$720$	−0.309017	+	0.951057i	−0.0115164	+	0.0354438i
$721$	−11.0172	+	33.9075i	−0.410303	+	1.26278i
$722$	−15.0623	+	10.9434i	−0.560561	+	0.407271i
$723$	−20.7254	−	15.0579i	−0.770787	−	0.560009i
$724$	−7.52786	−	23.1684i	−0.279771	−	0.861046i
$725$	3.70820			0.137719
$726$	10.8992	−	1.48584i	0.404507	−	0.0551447i
$727$	−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
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−8.85410	+	6.43288i	−0.327705	+	0.238092i
$731$	−1.52786	+	4.70228i	−0.0565101	+	0.173920i
$732$	−3.47214	+	10.6861i	−0.128334	+	0.394971i
$733$	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
$735$	1.88197	+	5.79210i	0.0694174	+	0.213645i
$736$	−4.85410			−0.178925
$737$	−22.9787	−	14.4248i	−0.846432	−	0.531346i
$738$	9.32624			0.343304
$739$	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
$741$	−0.309017	+	0.224514i	−0.0113520	+	0.00824773i
$742$	6.80902	−	20.9560i	0.249967	−	0.769319i
$743$	−2.20820	+	6.79615i	−0.0810111	+	0.249327i	−0.983356	−	0.181687i	$-0.941844\pi$
$743$	−2.20820	+	6.79615i	−0.0810111	+	0.249327i	0.902345	+	0.431014i	$0.141844\pi$
$744$	7.47214	−	5.42882i	0.273942	−	0.199030i
$745$	−7.23607	−	5.25731i	−0.265109	−	0.192613i
$746$	4.28115	+	13.1760i	0.156744	+	0.482409i
$747$	−4.94427			−0.180901
$748$	5.23607	−	20.8172i	0.191450	−	0.761154i
$749$	64.7214			2.36487
$750$	−0.309017	−	0.951057i	−0.0112837	−	0.0347277i
$751$	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
$753$	−3.55573	+	10.9434i	−0.129578	+	0.398800i
$754$	−0.708204	+	2.17963i	−0.0257913	+	0.0793774i
$755$	−10.0902	+	7.33094i	−0.367219	+	0.266800i
$756$	2.92705	+	2.12663i	0.106456	+	0.0773447i
$757$	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
$759$	6.00000	+	14.9394i	0.217786	+	0.542265i
$760$	−0.618034			−0.0224184
$761$	−2.43769	−	7.50245i	−0.0883663	−	0.271964i	0.897102	−	0.441824i	$-0.145668\pi$
$761$	−2.43769	−	7.50245i	−0.0883663	−	0.271964i	−0.985468	+	0.169860i	$0.945668\pi$
$762$	−10.2082	−	7.41669i	−0.369804	−	0.268678i
$763$	−11.7082	+	8.50651i	−0.423865	+	0.307956i
$764$	−4.23607	+	13.0373i	−0.153256	+	0.471672i
$765$	2.00000	−	6.15537i	0.0723102	−	0.222548i
$766$	−23.0172	+	16.7230i	−0.831646	+	0.604226i
$767$	7.30902	+	5.31031i	0.263913	+	0.191744i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	−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
$771$	5.05573			0.182078
$772$	−1.14590	−	3.52671i	−0.0412418	−	0.126929i
$773$	−3.07295	−	2.23263i	−0.110526	−	0.0803021i	0.531149	−	0.847278i	$-0.321760\pi$
$773$	−3.07295	−	2.23263i	−0.110526	−	0.0803021i	−0.641675	+	0.766976i	$0.721760\pi$
$774$	0.618034	−	0.449028i	0.0222148	−	0.0161400i
$775$	−2.85410	+	8.78402i	−0.102522	+	0.315531i
$776$	−4.61803	+	14.2128i	−0.165778	+	0.510211i
$777$	−1.80902	+	1.31433i	−0.0648981	+	0.0471512i
$778$	2.85410	+	2.07363i	0.102325	+	0.0743431i
$779$	1.78115	+	5.48183i	0.0638164	+	0.196407i
$780$	0.618034			0.0221292
$781$	−0.742646	+	0.620541i	−0.0265740	+	0.0222047i
$782$	31.4164			1.12345
$783$	−1.14590	−	3.52671i	−0.0409511	−	0.126034i
$784$	−4.92705	−	3.57971i	−0.175966	−	0.127847i
$785$	−4.54508	+	3.30220i	−0.162221	+	0.117860i
$786$	6.47214	−	19.9192i	0.230853	−	0.710494i
$787$	−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
$789$	−6.59017	−	4.78804i	−0.234616	−	0.170459i
$790$	−1.38197	−	4.25325i	−0.0491681	−	0.151324i
$791$	−45.1246			−1.60445
$792$	−2.54508	+	2.12663i	−0.0904357	+	0.0755664i
$793$	6.94427			0.246598
$794$	−3.91641	−	12.0535i	−0.138988	−	0.427761i
$795$	4.92705	+	3.57971i	0.174744	+	0.126959i
$796$	10.4721	−	7.60845i	0.371175	−	0.269674i
$797$	4.24671	−	13.0700i	0.150426	−	0.462964i	−0.847243	−	0.531206i	$-0.821739\pi$
$797$	4.24671	−	13.0700i	0.150426	−	0.462964i	0.997669	+	0.0682419i	$0.0217390\pi$
$798$	−0.690983	+	2.12663i	−0.0244605	+	0.0752818i
$799$	−13.7082	+	9.95959i	−0.484961	+	0.352345i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	−1.59017	−	4.89404i	−0.0561859	−	0.172922i
$802$	1.67376			0.0591026
$803$	−36.2148	+	2.45714i	−1.27799	+	0.0867107i
$804$	8.18034			0.288498
$805$	−5.42705	−	16.7027i	−0.191278	−	0.588694i
$806$	−4.61803	−	3.35520i	−0.162663	−	0.118182i
$807$	−20.0344	+	14.5559i	−0.705246	+	0.512391i
$808$	−1.23607	+	3.80423i	−0.0434847	+	0.133832i
$809$	−1.07953	+	3.32244i	−0.0379541	+	0.116811i	−0.968239	−	0.250028i	$-0.919560\pi$
$809$	−1.07953	+	3.32244i	−0.0379541	+	0.116811i	0.930284	+	0.366839i	$0.119560\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	−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
$813$	−0.652476			−0.0228833
$814$	−0.763932	−	1.90211i	−0.0267758	−	0.0666690i
$815$	−17.8885			−0.626608
$816$	2.00000	+	6.15537i	0.0700140	+	0.215481i
$817$	0.381966	+	0.277515i	0.0133633	+	0.00970901i
$818$	11.5000	−	8.35524i	0.402088	−	0.292134i
$819$	0.690983	−	2.12663i	0.0241449	−	0.0743104i
$820$	2.88197	−	8.86978i	0.100643	−	0.309746i
$821$	−10.3262	+	7.50245i	−0.360388	+	0.261837i	−0.753214	−	0.657776i	$-0.771498\pi$
$821$	−10.3262	+	7.50245i	−0.360388	+	0.261837i	0.392826	+	0.919613i	$0.371498\pi$
$822$	−12.4721	−	9.06154i	−0.435016	−	0.316057i
$823$	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
$825$	0.809017	−	3.21644i	0.0281664	−	0.111982i
$826$	52.8885			1.84023
$827$	−3.00000	−	9.23305i	−0.104320	−	0.321065i	0.885250	−	0.465115i	$-0.153987\pi$
$827$	−3.00000	−	9.23305i	−0.104320	−	0.321065i	−0.989570	+	0.144051i	$0.953987\pi$
$828$	−3.92705	−	2.85317i	−0.136474	−	0.0991545i
$829$	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
$831$	2.55573	−	7.86572i	0.0886572	−	0.272859i
$832$	−0.500000	+	0.363271i	−0.0173344	+	0.0125942i
$833$	31.8885	+	23.1684i	1.10487	+	0.802737i
$834$	−2.35410	−	7.24518i	−0.0815159	−	0.250880i
$835$	11.5623			0.400130
$836$	−1.73607	−	1.08981i	−0.0600432	−	0.0376920i
$837$	9.23607			0.319245
$838$	3.46149	+	10.6534i	0.119575	+	0.368015i
$839$	−26.7984	−	19.4702i	−0.925183	−	0.672185i	0.0196260	−	0.999807i	$-0.493752\pi$
$839$	−26.7984	−	19.4702i	−0.925183	−	0.672185i	−0.944809	+	0.327623i	$0.893752\pi$
$840$	2.92705	−	2.12663i	0.100993	−	0.0733756i
$841$	−4.71227	+	14.5029i	−0.162492	+	0.500099i
$842$	−8.32624	+	25.6255i	−0.286941	+	0.883114i
$843$	6.38197	−	4.63677i	0.219807	−	0.159699i
$844$	18.9443	+	13.7638i	0.652089	+	0.473770i
$845$	3.89919	+	12.0005i	0.134136	+	0.412828i
$846$	2.61803			0.0900099
$847$	−35.0623	−	18.8294i	−1.20476	−	0.646985i
$848$	−6.09017			−0.209137
$849$	−1.14590	−	3.52671i	−0.0393271	−	0.121036i
$850$	−5.23607	−	3.80423i	−0.179596	−	0.130484i
$851$	2.42705	−	1.76336i	0.0831982	−	0.0604471i
$852$	0.0901699	−	0.277515i	0.00308917	−	0.00950749i
$853$	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
$855$	−0.500000	−	0.363271i	−0.0170996	−	0.0124236i
$856$	−5.52786	−	17.0130i	−0.188939	−	0.581493i
$857$	55.2361			1.88683			0.943414	−	0.331617i	$-0.107594\pi$
$857$	55.2361			1.88683			0.943414	+	0.331617i	$0.107594\pi$
$858$	1.73607	+	1.08981i	0.0592684	+	0.0372056i
$859$	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
$861$	−27.2984	−	19.8334i	−0.930326	−	0.675921i
$862$	1.76393	−	1.28157i	0.0600798	−	0.0436505i
$863$	−0.0450850	+	0.138757i	−0.00153471	+	0.00472335i	−0.951821	−	0.306654i	$-0.900790\pi$
$863$	−0.0450850	+	0.138757i	−0.00153471	+	0.00472335i	0.950286	+	0.311378i	$0.100790\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−19.8713	+	14.4374i	−0.675645	+	0.490885i
$866$	−26.7984	−	19.4702i	−0.910646	−	0.661623i
$867$	−7.69098	−	23.6704i	−0.261199	−	0.803889i
$868$	−33.4164			−1.13423
$869$	3.61803	−	14.3844i	0.122733	−	0.487956i
$870$	−3.70820			−0.125720
$871$	−1.56231	−	4.80828i	−0.0529367	−	0.162922i
$872$	3.23607	+	2.35114i	0.109587	+	0.0796197i
$873$	−12.0902	+	8.78402i	−0.409190	+	0.297294i
$874$	0.927051	−	2.85317i	0.0313580	−	0.0965099i
$875$	−1.11803	+	3.44095i	−0.0377964	+	0.116326i
$876$	8.85410	−	6.43288i	0.299152	−	0.217347i
$877$	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
$879$	−11.0344			−0.372182
$880$	1.23607	+	3.07768i	0.0416678	+	0.103749i
$881$	7.79837			0.262734			0.131367	−	0.991334i	$-0.458063\pi$
$881$	7.79837			0.262734			0.131367	+	0.991334i	$0.458063\pi$
$882$	−1.88197	−	5.79210i	−0.0633691	−	0.195030i
$883$	−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
$885$	−4.51722	+	13.9026i	−0.151845	+	0.467330i
$886$	−8.90983	+	27.4216i	−0.299332	+	0.921248i
$887$	−1.01722	+	0.739054i	−0.0341549	+	0.0248150i	−0.604732	−	0.796429i	$-0.706720\pi$
$887$	−1.01722	+	0.739054i	−0.0341549	+	0.0248150i	0.570577	+	0.821244i	$0.306720\pi$
$888$	0.500000	+	0.363271i	0.0167789	+	0.0121906i
$889$	14.1074	+	43.4181i	0.473147	+	1.45620i
$890$	−5.14590			−0.172491
$891$	−3.30902	+	0.224514i	−0.110856	+	0.00752150i
$892$	7.61803			0.255071
$893$	0.500000	+	1.53884i	0.0167319	+	0.0514954i
$894$	7.23607	+	5.25731i	0.242010	+	0.175831i
$895$	−9.01722	+	6.55139i	−0.301412	+	0.218989i
$896$	−1.11803	+	3.44095i	−0.0373509	+	0.114954i
$897$	−0.927051	+	2.85317i	−0.0309533	+	0.0952646i
$898$	−15.0623	+	10.9434i	−0.502636	+	0.365186i
$899$	27.7082	+	20.1312i	0.924120	+	0.671413i
$900$	0.309017	+	0.951057i	0.0103006	+	0.0317019i
$901$	39.4164			1.31315
$902$	23.7361	−	19.8334i	0.790325	−	0.660381i
$903$	−2.76393			−0.0919779
$904$	3.85410	+	11.8617i	0.128186	+	0.394514i
$905$	−19.7082	−	14.3188i	−0.655123	−	0.475975i
$906$	10.0902	−	7.33094i	0.335223	−	0.243554i
$907$	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
$909$	−3.23607	+	2.35114i	−0.107334	+	0.0779824i
$910$	−1.80902	−	1.31433i	−0.0599683	−	0.0435695i
$911$	−3.29180	−	10.1311i	−0.109062	−	0.335659i	0.881600	−	0.471997i	$-0.156467\pi$
$911$	−3.29180	−	10.1311i	−0.109062	−	0.335659i	−0.990662	+	0.136338i	$0.956467\pi$
$912$	0.618034			0.0204652
$913$	−12.5836	+	10.5146i	−0.416456	+	0.347983i
$914$	−9.88854			−0.327084
$915$	3.47214	+	10.6861i	0.114785	+	0.353273i
$916$	9.32624	+	6.77591i	0.308148	+	0.223882i
$917$	−61.3050	+	44.5407i	−2.02447	+	1.47086i
$918$	−2.00000	+	6.15537i	−0.0660098	+	0.203157i
$919$	−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
$921$	21.7082	+	15.7719i	0.715310	+	0.519703i
$922$	7.65248	+	23.5519i	0.252021	+	0.775640i
$923$	−0.180340			−0.00593596
$924$	11.9721	−	0.812299i	0.393854	−	0.0267227i
$925$	−0.618034			−0.0203208
$926$	1.04508	+	3.21644i	0.0343436	+	0.105699i
$927$	7.97214	+	5.79210i	0.261839	+	0.190237i
$928$	3.00000	−	2.17963i	0.0984798	−	0.0715498i
$929$	−2.17376	+	6.69015i	−0.0713188	+	0.219497i	−0.980362	−	0.197204i	$-0.936814\pi$
$929$	−2.17376	+	6.69015i	−0.0713188	+	0.219497i	0.909044	+	0.416701i	$0.136814\pi$
$930$	2.85410	−	8.78402i	0.0935897	−	0.288039i
$931$	3.04508	−	2.21238i	0.0997986	−	0.0725079i
$932$	13.1803	+	9.57608i	0.431736	+	0.313675i
$933$	8.61803	+	26.5236i	0.282142	+	0.868343i
$934$	−7.05573			−0.230870
$935$	−8.00000	−	19.9192i	−0.261628	−	0.651427i
$936$	−0.618034			−0.0202011
$937$	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
$939$	4.61803	−	3.35520i	0.150704	−	0.109493i
$940$	0.809017	−	2.48990i	0.0263872	−	0.0812115i
$941$	3.41641	−	10.5146i	0.111372	−	0.342767i	−0.879801	−	0.475342i	$-0.842324\pi$
$941$	3.41641	−	10.5146i	0.111372	−	0.342767i	0.991173	+	0.132575i	$0.0423245\pi$
$942$	4.54508	−	3.30220i	0.148087	−	0.107591i
$943$	36.6246	+	26.6093i	1.19266	+	0.866519i
$944$	−4.51722	−	13.9026i	−0.147023	−	0.452490i
$945$	3.61803			0.117695
$946$	0.618034	−	2.45714i	0.0200940	−	0.0798886i
$947$	−3.30495			−0.107396			−0.0536982	−	0.998557i	$-0.517101\pi$
$947$	−3.30495			−0.107396			−0.0536982	+	0.998557i	$0.517101\pi$
$948$	1.38197	+	4.25325i	0.0448842	+	0.138139i
$949$	−5.47214	−	3.97574i	−0.177633	−	0.129058i
$950$	−0.500000	+	0.363271i	−0.0162221	+	0.0117861i
$951$	−3.37132	+	10.3759i	−0.109323	+	0.336460i
$952$	7.23607	−	22.2703i	0.234522	−	0.721785i
$953$	36.2148	−	26.3116i	1.17311	−	0.852316i	0.181734	−	0.983348i	$-0.441829\pi$
$953$	36.2148	−	26.3116i	1.17311	−	0.852316i	0.991378	+	0.131032i	$0.0418291\pi$
$954$	−4.92705	−	3.57971i	−0.159519	−	0.115897i
$955$	4.23607	+	13.0373i	0.137076	+	0.421876i
$956$	22.1803			0.717363
$957$	−10.4164	−	6.53888i	−0.336715	−	0.211372i
$958$	39.0132			1.26046
$959$	17.2361	+	53.0472i	0.556582	+	1.71298i
$960$	−0.809017	−	0.587785i	−0.0261109	−	0.0189707i
$961$	−43.9336	+	31.9196i	−1.41721	+	1.02967i
$962$	0.118034	−	0.363271i	0.00380557	−	0.0117123i
$963$	5.52786	−	17.0130i	0.178133	−	0.548237i
$964$	20.7254	−	15.0579i	0.667521	−	0.484982i
$965$	−3.00000	−	2.17963i	−0.0965734	−	0.0701647i
$966$	5.42705	+	16.7027i	0.174613	+	0.537402i
$967$	−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
$969$	−4.00000			−0.128499
$970$	4.61803	+	14.2128i	0.148276	+	0.456347i
$971$	−4.69098	−	3.40820i	−0.150541	−	0.109374i	0.509965	−	0.860195i	$-0.329658\pi$
$971$	−4.69098	−	3.40820i	−0.150541	−	0.109374i	−0.660506	+	0.750821i	$0.729658\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−8.51722	+	26.2133i	−0.273050	+	0.840360i
$974$	−12.4721	+	38.3853i	−0.399633	+	1.22994i
$975$	0.500000	−	0.363271i	0.0160128	−	0.0116340i
$976$	−9.09017	−	6.60440i	−0.290969	−	0.211402i
$977$	−7.67376	−	23.6174i	−0.245505	−	0.755588i	−0.995553	−	0.0942040i	$-0.969969\pi$
$977$	−7.67376	−	23.6174i	−0.245505	−	0.755588i	0.750048	−	0.661384i	$-0.230031\pi$
$978$	17.8885			0.572013
$979$	−14.4549	−	9.07405i	−0.461981	−	0.290008i
$980$	−6.09017			−0.194543
$981$	1.23607	+	3.80423i	0.0394646	+	0.121460i
$982$	−1.88197	−	1.36733i	−0.0600559	−	0.0436332i
$983$	26.7254	−	19.4172i	0.852409	−	0.619311i	−0.0734004	−	0.997303i	$-0.523385\pi$
$983$	26.7254	−	19.4172i	0.852409	−	0.619311i	0.925809	+	0.377991i	$0.123385\pi$
$984$	−2.88197	+	8.86978i	−0.0918737	+	0.282758i
$985$	−1.11803	+	3.44095i	−0.0356235	+	0.109638i
$986$	−19.4164	+	14.1068i	−0.618344	+	0.449254i
$987$	−7.66312	−	5.56758i	−0.243920	−	0.177218i
$988$	−0.118034	−	0.363271i	−0.00375516	−	0.0115572i
$989$	3.70820			0.117914
$990$	−0.809017	+	3.21644i	−0.0257122	+	0.102225i
$991$	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
$993$	6.20820	+	4.51052i	0.197011	+	0.143137i
$994$	−0.854102	+	0.620541i	−0.0270905	+	0.0196824i
$995$	4.00000	−	12.3107i	0.126809	−	0.390277i
$996$	1.52786	−	4.70228i	0.0484122	−	0.148998i
$997$	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
$999$	0.190983	+	0.587785i	0.00604243	+	0.0185967i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.d.31.1	✓	4	11.9	even	5	inner
330.2.m.d.181.1	yes	4	1.1	even	1	trivial
990.2.n.a.181.1		4	3.2	odd	2
990.2.n.a.361.1		4	33.20	odd	10
3630.2.a.bc.1.2		2	11.3	even	5
3630.2.a.bi.1.1		2	11.8	odd	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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-2.92705 + 2.12663i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +1.00000 q^{10} +(2.80902 + 1.76336i) q^{11} -1.00000 q^{12} +(0.190983 + 0.587785i) q^{13} +(2.92705 + 2.12663i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.00000 + 6.15537i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.500000 + 0.363271i) q^{19} +(-0.309017 - 0.951057i) q^{20} -3.61803 q^{21} +(0.809017 - 3.21644i) q^{22} +4.85410 q^{23} +(0.309017 + 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.500000 - 0.363271i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.11803 - 3.44095i) q^{28} +(-3.00000 + 2.17963i) q^{29} +(0.809017 + 0.587785i) q^{30} +(-2.85410 - 8.78402i) q^{31} -1.00000 q^{32} +(1.23607 + 3.07768i) q^{33} +6.47214 q^{34} +(-1.11803 - 3.44095i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.500000 - 0.363271i) q^{37} +(0.190983 - 0.587785i) q^{38} +(-0.190983 + 0.587785i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(7.54508 + 5.48183i) q^{41} +(1.11803 + 3.44095i) q^{42} +0.763932 q^{43} +(-3.30902 + 0.224514i) q^{44} -1.00000 q^{45} +(-1.50000 - 4.61653i) q^{46} +(2.11803 + 1.53884i) q^{47} +(0.809017 - 0.587785i) q^{48} +(1.88197 - 5.79210i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-5.23607 + 3.80423i) q^{51} +(-0.500000 - 0.363271i) q^{52} +(-1.88197 - 5.79210i) q^{53} +1.00000 q^{54} +(-2.54508 + 2.12663i) q^{55} -3.61803 q^{56} +(0.190983 + 0.587785i) q^{57} +(3.00000 + 2.17963i) q^{58} +(11.8262 - 8.59226i) q^{59} +(0.309017 - 0.951057i) q^{60} +(3.47214 - 10.6861i) q^{61} +(-7.47214 + 5.42882i) q^{62} +(-2.92705 - 2.12663i) q^{63} +(0.309017 + 0.951057i) q^{64} -0.618034 q^{65} +(2.54508 - 2.12663i) q^{66} -8.18034 q^{67} +(-2.00000 - 6.15537i) q^{68} +(3.92705 + 2.85317i) q^{69} +(-2.92705 + 2.12663i) q^{70} +(-0.0901699 + 0.277515i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-8.85410 + 6.43288i) q^{73} +(-0.500000 - 0.363271i) q^{74} +(-0.309017 - 0.951057i) q^{75} -0.618034 q^{76} +(-11.9721 + 0.812299i) q^{77} +0.618034 q^{78} +(-1.38197 - 4.25325i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(2.88197 - 8.86978i) q^{82} +(-1.52786 + 4.70228i) q^{83} +(2.92705 - 2.12663i) q^{84} +(-5.23607 - 3.80423i) q^{85} +(-0.236068 - 0.726543i) q^{86} -3.70820 q^{87} +(1.23607 + 3.07768i) q^{88} -5.14590 q^{89} +(0.309017 + 0.951057i) q^{90} +(-1.80902 - 1.31433i) q^{91} +(-3.92705 + 2.85317i) q^{92} +(2.85410 - 8.78402i) q^{93} +(0.809017 - 2.48990i) q^{94} +(-0.500000 + 0.363271i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(4.61803 + 14.2128i) q^{97} -6.09017 q^{98} +(-0.809017 + 3.21644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{4} + q^{5} - q^{6} - 5 q^{7} + q^{8} - q^{9} + 4 q^{10} + 9 q^{11} - 4 q^{12} + 3 q^{13} + 5 q^{14} - q^{15} - q^{16} - 8 q^{17} + q^{18} + 2 q^{19} + q^{20} - 10 q^{21}+ \cdots - q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^4 + q^5 - q^6 - 5 * q^7 + q^8 - q^9 + 4 * q^10 + 9 * q^11 - 4 * q^12 + 3 * q^13 + 5 * q^14 - q^15 - q^16 - 8 * q^17 + q^18 + 2 * q^19 + q^20 - 10 * q^21 + q^22 + 6 * q^23 - q^24 - q^25 + 2 * q^26 + q^27 - 12 * q^29 + q^30 + 2 * q^31 - 4 * q^32 - 4 * q^33 + 8 * q^34 - q^36 + 2 * q^37 + 3 * q^38 - 3 * q^39 - q^40 + 19 * q^41 + 12 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 4 * q^47 + q^48 + 12 * q^49 + q^50 - 12 * q^51 - 2 * q^52 - 12 * q^53 + 4 * q^54 + q^55 - 10 * q^56 + 3 * q^57 + 12 * q^58 + 16 * q^59 - q^60 - 4 * q^61 - 12 * q^62 - 5 * q^63 - q^64 + 2 * q^65 - q^66 + 12 * q^67 - 8 * q^68 + 9 * q^69 - 5 * q^70 + 22 * q^71 + q^72 - 22 * q^73 - 2 * q^74 + q^75 + 2 * q^76 - 30 * q^77 - 2 * q^78 - 10 * q^79 + q^80 - q^81 + 16 * q^82 - 24 * q^83 + 5 * q^84 - 12 * q^85 + 8 * q^86 + 12 * q^87 - 4 * q^88 - 34 * q^89 - q^90 - 5 * q^91 - 9 * q^92 - 2 * q^93 + q^94 - 2 * q^95 - q^96 + 14 * q^97 - 2 * q^98 - q^99

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