LMFDB - Embedded newform 1170.2.bs.g.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(361,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bs (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,0,0,0,0,4,6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-1.27597 + 0.609843i$ of defining polynomial
Character	$\chi$	$=$	1170.361
Dual form			1170.2.bs.g.901.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.24653 - 0.719687i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-3.49837 + 2.01978i) q^{11} +(3.13234 - 1.78561i) q^{13} +1.43937 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.15376 + 1.99837i) q^{17} +(-0.346241 - 0.199902i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(2.01978 - 3.49837i) q^{22} +(-0.780313 - 1.35154i) q^{23} -1.00000 q^{25} +(-1.81988 + 3.11256i) q^{26} +(-1.24653 + 0.719687i) q^{28} +(-3.93244 - 6.81119i) q^{29} +3.10713i q^{31} +(0.866025 + 0.500000i) q^{32} -2.30752i q^{34} +(-0.719687 + 1.24653i) q^{35} +(-5.40029 + 3.11786i) q^{37} +0.399804 q^{38} +1.00000 q^{40} +(0.659061 - 0.380509i) q^{41} +(-5.50367 + 9.53264i) q^{43} +4.03957i q^{44} +(1.35154 + 0.780313i) q^{46} +5.84016i q^{47} +(-2.46410 - 4.26795i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.0197847 - 3.60550i) q^{52} -10.6249 q^{53} +(2.01978 + 3.49837i) q^{55} +(0.719687 - 1.24653i) q^{56} +(6.81119 + 3.93244i) q^{58} +(3.00000 + 1.73205i) q^{59} +(2.84624 - 4.92983i) q^{61} +(-1.55356 - 2.69085i) q^{62} -1.00000 q^{64} +(-1.78561 - 3.13234i) q^{65} +(-9.00734 + 5.20039i) q^{67} +(1.15376 + 1.99837i) q^{68} -1.43937i q^{70} +(-5.19615 - 3.00000i) q^{71} +13.4608i q^{73} +(3.11786 - 5.40029i) q^{74} +(-0.346241 + 0.199902i) q^{76} +5.81445 q^{77} +0.931464 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.380509 + 0.659061i) q^{82} +10.3867i q^{83} +(1.99837 + 1.15376i) q^{85} -11.0073i q^{86} +(-2.01978 - 3.49837i) q^{88} +(0.840939 - 0.485517i) q^{89} +(-5.18966 - 0.0284776i) q^{91} -1.56063 q^{92} +(-2.92008 - 5.05772i) q^{94} +(-0.199902 + 0.346241i) q^{95} +(-10.6680 - 6.15919i) q^{97} +(4.26795 + 2.46410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} + 6 q^{22} - 12 q^{23} - 8 q^{25} - 30 q^{37} + 12 q^{38} + 8 q^{40} - 12 q^{41} + 4 q^{43} + 8 q^{49} - 10 q^{52} - 60 q^{53}+ \cdots + 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^10 + 6 * q^11 - 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 + 6 * q^22 - 12 * q^23 - 8 * q^25 - 30 * q^37 + 12 * q^38 + 8 * q^40 - 12 * q^41 + 4 * q^43 + 8 * q^49 - 10 * q^52 - 60 * q^53 + 6 * q^55 + 24 * q^59 + 26 * q^61 - 18 * q^62 - 8 * q^64 - 6 * q^65 + 24 * q^67 + 6 * q^68 - 6 * q^74 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 18 * q^85 - 6 * q^88 + 24 * q^89 - 66 * q^91 - 24 * q^92 - 6 * q^95 - 6 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−1.24653	−	0.719687i	−0.471146	−	0.272016i	0.245574	−	0.969378i	$-0.421024\pi$
$7$	−1.24653	−	0.719687i	−0.471146	−	0.272016i	−0.716719	+	0.697362i	$0.754357\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−3.49837	+	2.01978i	−1.05480	+	0.608988i	−0.923989	−	0.382420i	$-0.875091\pi$
$11$	−3.49837	+	2.01978i	−1.05480	+	0.608988i	−0.130809	+	0.991408i	$0.541758\pi$
$12$		0			0
$13$	3.13234	−	1.78561i	0.868756	−	0.495240i
$13$	3.13234	−	1.78561i	0.868756	−	0.495240i
$14$	1.43937			0.384689
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.15376	+	1.99837i	−0.279828	+	0.484676i	−0.971342	−	0.237687i	$-0.923611\pi$
$17$	−1.15376	+	1.99837i	−0.279828	+	0.484676i	0.691514	+	0.722363i	$0.256944\pi$
$18$		0			0
$19$	−0.346241	−	0.199902i	−0.0794331	−	0.0458607i	0.459757	−	0.888045i	$-0.347936\pi$
$19$	−0.346241	−	0.199902i	−0.0794331	−	0.0458607i	−0.539190	+	0.842184i	$0.681270\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		0			0
$22$	2.01978	−	3.49837i	0.430620	−	0.745855i
$23$	−0.780313	−	1.35154i	−0.162707	−	0.281816i	0.773132	−	0.634245i	$-0.218689\pi$
$23$	−0.780313	−	1.35154i	−0.162707	−	0.281816i	−0.935838	+	0.352429i	$0.885356\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.81988	+	3.11256i	−0.356908	+	0.610423i
$27$		0			0
$28$	−1.24653	+	0.719687i	−0.235573	+	0.136008i
$29$	−3.93244	−	6.81119i	−0.730236	−	1.26481i	−0.956782	−	0.290806i	$-0.906077\pi$
$29$	−3.93244	−	6.81119i	−0.730236	−	1.26481i	0.226546	−	0.974000i	$-0.427257\pi$
$30$		0			0
$31$			3.10713i			0.558057i	0.960283	+	0.279028i	$0.0900123\pi$
$31$			3.10713i			0.558057i	−0.960283	+	0.279028i	$0.909988\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	2.30752i		−	0.395736i
$35$	−0.719687	+	1.24653i	−0.121649	+	0.210703i
$36$		0			0
$37$	−5.40029	+	3.11786i	−0.887803	+	0.512573i	−0.873223	−	0.487321i	$-0.837974\pi$
$37$	−5.40029	+	3.11786i	−0.887803	+	0.512573i	−0.0145796	+	0.999894i	$0.504641\pi$
$38$	0.399804			0.0648568
$39$		0			0
$40$	1.00000			0.158114
$41$	0.659061	−	0.380509i	0.102928	−	0.0594255i	−0.447652	−	0.894208i	$-0.647740\pi$
$41$	0.659061	−	0.380509i	0.102928	−	0.0594255i	0.550580	+	0.834782i	$0.314406\pi$
$42$		0			0
$43$	−5.50367	+	9.53264i	−0.839302	+	1.45371i	0.0511772	+	0.998690i	$0.483703\pi$
$43$	−5.50367	+	9.53264i	−0.839302	+	1.45371i	−0.890479	+	0.455024i	$0.849631\pi$
$44$			4.03957i			0.608988i
$45$		0			0
$46$	1.35154	+	0.780313i	0.199274	+	0.115051i
$47$			5.84016i			0.851874i	0.904753	+	0.425937i	$0.140056\pi$
$47$			5.84016i			0.851874i	−0.904753	+	0.425937i	$0.859944\pi$
$48$		0			0
$49$	−2.46410	−	4.26795i	−0.352015	−	0.609707i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	0.0197847	−	3.60550i	0.00274365	−	0.499992i
$53$	−10.6249			−1.45945			−0.729723	−	0.683743i	$-0.760351\pi$
$53$	−10.6249			−1.45945			−0.729723	+	0.683743i	$0.760351\pi$
$54$		0			0
$55$	2.01978	+	3.49837i	0.272348	+	0.471720i
$56$	0.719687	−	1.24653i	0.0961722	−	0.166575i
$57$		0			0
$58$	6.81119	+	3.93244i	0.894353	+	0.516355i
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	0.682406	−	0.730974i	$-0.260934\pi$
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	−0.291839	+	0.956467i	$0.594267\pi$
$60$		0			0
$61$	2.84624	−	4.92983i	0.364424	−	0.631200i	−0.624260	−	0.781217i	$-0.714599\pi$
$61$	2.84624	−	4.92983i	0.364424	−	0.631200i	0.988684	+	0.150016i	$0.0479326\pi$
$62$	−1.55356	−	2.69085i	−0.197303	−	0.341738i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.78561	−	3.13234i	−0.221478	−	0.388519i
$66$		0			0
$67$	−9.00734	+	5.20039i	−1.10042	+	0.635329i	−0.936332	−	0.351116i	$-0.885802\pi$
$67$	−9.00734	+	5.20039i	−1.10042	+	0.635329i	−0.164090	+	0.986445i	$0.552469\pi$
$68$	1.15376	+	1.99837i	0.139914	+	0.242338i
$69$		0			0
$70$		−	1.43937i		−	0.172038i
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	0.158901	−	0.987294i	$-0.449205\pi$
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	−0.775571	+	0.631260i	$0.782538\pi$
$72$		0			0
$73$			13.4608i			1.57547i	0.616013	+	0.787736i	$0.288747\pi$
$73$			13.4608i			1.57547i	−0.616013	+	0.787736i	$0.711253\pi$
$74$	3.11786	−	5.40029i	0.362444	−	0.627771i
$75$		0			0
$76$	−0.346241	+	0.199902i	−0.0397165	+	0.0229303i
$77$	5.81445			0.662618
$78$		0			0
$79$	0.931464			0.104798			0.0523989	−	0.998626i	$-0.483313\pi$
$79$	0.931464			0.104798			0.0523989	+	0.998626i	$0.483313\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$		0			0
$82$	−0.380509	+	0.659061i	−0.0420202	+	0.0727811i
$83$			10.3867i			1.14008i	0.821616	+	0.570042i	$0.193073\pi$
$83$			10.3867i			1.14008i	−0.821616	+	0.570042i	$0.806927\pi$
$84$		0			0
$85$	1.99837	+	1.15376i	0.216754	+	0.125143i
$86$		−	11.0073i		−	1.18695i
$87$		0			0
$88$	−2.01978	−	3.49837i	−0.215310	−	0.372927i
$89$	0.840939	−	0.485517i	0.0891394	−	0.0514647i	−0.454768	−	0.890610i	$-0.650278\pi$
$89$	0.840939	−	0.485517i	0.0891394	−	0.0514647i	0.543907	+	0.839145i	$0.316944\pi$
$90$		0			0
$91$	−5.18966	−	0.0284776i	−0.544024	−	0.00298526i
$92$	−1.56063			−0.162707
$93$		0			0
$94$	−2.92008	−	5.05772i	−0.301183	−	0.521664i
$95$	−0.199902	+	0.346241i	−0.0205095	+	0.0355235i
$96$		0			0
$97$	−10.6680	−	6.15919i	−1.08317	−	0.625371i	−0.151424	−	0.988469i	$-0.548386\pi$
$97$	−10.6680	−	6.15919i	−1.08317	−	0.625371i	−0.931751	+	0.363098i	$0.881719\pi$
$98$	4.26795	+	2.46410i	0.431128	+	0.248912i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−2.41747	−	4.18718i	−0.240547	−	0.416640i	0.720323	−	0.693639i	$-0.243994\pi$
$101$	−2.41747	−	4.18718i	−0.240547	−	0.416640i	−0.960870	+	0.276999i	$0.910660\pi$
$102$		0			0
$103$	−5.73205			−0.564796			−0.282398	−	0.959297i	$-0.591130\pi$
$103$	−5.73205			−0.564796			−0.282398	+	0.959297i	$0.591130\pi$
$104$	1.78561	+	3.13234i	0.175094	+	0.307152i
$105$		0			0
$106$	9.20145	−	5.31246i	0.893724	−	0.515992i
$107$	−6.43774	−	11.1505i	−0.622360	−	1.07796i	−0.989045	−	0.147614i	$-0.952841\pi$
$107$	−6.43774	−	11.1505i	−0.622360	−	1.07796i	0.366685	−	0.930345i	$-0.380493\pi$
$108$		0			0
$109$			0.214254i			0.0205219i	0.999947	+	0.0102609i	$0.00326621\pi$
$109$			0.214254i			0.0205219i	−0.999947	+	0.0102609i	$0.996734\pi$
$110$	−3.49837	−	2.01978i	−0.333556	−	0.192579i
$111$		0			0
$112$			1.43937i			0.136008i
$113$	−0.0642973	+	0.111366i	−0.00604858	+	0.0104765i	−0.869034	−	0.494753i	$-0.835259\pi$
$113$	−0.0642973	+	0.111366i	−0.00604858	+	0.0104765i	0.862985	+	0.505229i	$0.168592\pi$
$114$		0			0
$115$	−1.35154	+	0.780313i	−0.126032	+	0.0727646i
$116$	−7.86488			−0.730236
$117$		0			0
$118$	−3.46410			−0.318896
$119$	2.87640	−	1.66069i	0.263679	−	0.152235i
$120$		0			0
$121$	2.65906	−	4.60563i	0.241733	−	0.418693i
$122$			5.69248i			0.515373i
$123$		0			0
$124$	2.69085	+	1.55356i	0.241646	+	0.139514i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−8.06218	−	13.9641i	−0.715403	−	1.23911i	−0.962804	−	0.270201i	$-0.912910\pi$
$127$	−8.06218	−	13.9641i	−0.715403	−	1.23911i	0.247401	−	0.968913i	$-0.420423\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	3.11256	+	1.81988i	0.272990	+	0.159614i
$131$	−2.78010			−0.242898			−0.121449	−	0.992598i	$-0.538754\pi$
$131$	−2.78010			−0.242898			−0.121449	+	0.992598i	$0.538754\pi$
$132$		0			0
$133$	0.287734	+	0.498370i	0.0249497	+	0.0432141i
$134$	5.20039	−	9.00734i	0.449245	−	0.778116i
$135$		0			0
$136$	−1.99837	−	1.15376i	−0.171359	−	0.0989340i
$137$	4.73487	+	2.73368i	0.404528	+	0.233554i	0.688436	−	0.725297i	$-0.258298\pi$
$137$	4.73487	+	2.73368i	0.404528	+	0.233554i	−0.283908	+	0.958851i	$0.591631\pi$
$138$		0			0
$139$	0.107258	−	0.185777i	0.00909753	−	0.0157574i	−0.861441	−	0.507858i	$-0.830437\pi$
$139$	0.107258	−	0.185777i	0.00909753	−	0.0157574i	0.870538	+	0.492101i	$0.163771\pi$
$140$	0.719687	+	1.24653i	0.0608246	+	0.105351i
$141$		0			0
$142$	6.00000			0.503509
$143$	−7.35154	+	12.5734i	−0.614767	+	1.05144i
$144$		0			0
$145$	−6.81119	+	3.93244i	−0.565639	+	0.326572i
$146$	−6.73042	−	11.6574i	−0.557014	−	0.964776i
$147$		0			0
$148$			6.23572i			0.512573i
$149$	−14.3149	−	8.26469i	−1.17272	−	0.677070i	−0.218400	−	0.975859i	$-0.570084\pi$
$149$	−14.3149	−	8.26469i	−1.17272	−	0.677070i	−0.954319	+	0.298790i	$0.903417\pi$
$150$		0			0
$151$		−	6.70830i		−	0.545914i	−0.962026	−	0.272957i	$-0.911998\pi$
$151$		−	6.70830i		−	0.545914i	0.962026	−	0.272957i	$-0.0880016\pi$
$152$	0.199902	−	0.346241i	0.0162142	−	0.0280838i
$153$		0			0
$154$	−5.03546	+	2.90723i	−0.405769	+	0.234271i
$155$	3.10713			0.249570
$156$		0			0
$157$	5.81684			0.464234			0.232117	−	0.972688i	$-0.425435\pi$
$157$	5.81684			0.464234			0.232117	+	0.972688i	$0.425435\pi$
$158$	−0.806671	+	0.465732i	−0.0641753	+	0.0370516i
$159$		0			0
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			2.24632i			0.177035i
$162$		0			0
$163$	3.61341	+	2.08620i	0.283024	+	0.163404i	0.634792	−	0.772683i	$-0.281086\pi$
$163$	3.61341	+	2.08620i	0.283024	+	0.163404i	−0.351768	+	0.936087i	$0.614419\pi$
$164$		−	0.761018i		−	0.0594255i
$165$		0			0
$166$	−5.19333	−	8.99511i	−0.403080	−	0.698156i
$167$	13.5174	−	7.80426i	1.04601	−	0.603912i	0.124477	−	0.992222i	$-0.460275\pi$
$167$	13.5174	−	7.80426i	1.04601	−	0.603912i	0.921528	+	0.388311i	$0.126941\pi$
$168$		0			0
$169$	6.62316	−	11.1863i	0.509474	−	0.860486i
$170$	−2.30752			−0.176979
$171$		0			0
$172$	5.50367	+	9.53264i	0.419651	+	0.726857i
$173$	−2.90723	+	5.03546i	−0.221032	+	0.382839i	−0.955122	−	0.296214i	$-0.904276\pi$
$173$	−2.90723	+	5.03546i	−0.221032	+	0.382839i	0.734089	+	0.679053i	$0.237609\pi$
$174$		0			0
$175$	1.24653	+	0.719687i	0.0942291	+	0.0544032i
$176$	3.49837	+	2.01978i	0.263700	+	0.152247i
$177$		0			0
$178$	−0.485517	+	0.840939i	−0.0363910	+	0.0630311i
$179$	8.43611	+	14.6118i	0.630545	+	1.09214i	0.987441	+	0.157991i	$0.0505018\pi$
$179$	8.43611	+	14.6118i	0.630545	+	1.09214i	−0.356896	+	0.934144i	$0.616165\pi$
$180$		0			0
$181$	12.6207			0.938088			0.469044	−	0.883175i	$-0.344599\pi$
$181$	12.6207			0.938088			0.469044	+	0.883175i	$0.344599\pi$
$182$	4.50861	−	2.57017i	0.334201	−	0.190513i
$183$		0			0
$184$	1.35154	−	0.780313i	0.0996370	−	0.0575254i
$185$	3.11786	+	5.40029i	0.229230	+	0.397037i
$186$		0			0
$187$		−	9.32138i		−	0.681647i
$188$	5.05772	+	2.92008i	0.368872	+	0.212969i
$189$		0			0
$190$		−	0.399804i		−	0.0290049i
$191$	0.670362	−	1.16110i	0.0485057	−	0.0840143i	−0.840753	−	0.541419i	$-0.817887\pi$
$191$	0.670362	−	1.16110i	0.0485057	−	0.0840143i	0.889259	+	0.457404i	$0.151221\pi$
$192$		0			0
$193$	−14.5004	+	8.37182i	−1.04376	+	0.602616i	−0.920897	−	0.389807i	$-0.872542\pi$
$193$	−14.5004	+	8.37182i	−1.04376	+	0.602616i	−0.122866	+	0.992423i	$0.539208\pi$
$194$	12.3184			0.884408
$195$		0			0
$196$	−4.92820			−0.352015
$197$	−0.863202	+	0.498370i	−0.0615006	+	0.0355074i	−0.530435	−	0.847726i	$-0.677971\pi$
$197$	−0.863202	+	0.498370i	−0.0615006	+	0.0355074i	0.468934	+	0.883233i	$0.344638\pi$
$198$		0			0
$199$	−1.30752	+	2.26469i	−0.0926875	+	0.160540i	−0.908641	−	0.417578i	$-0.862879\pi$
$199$	−1.30752	+	2.26469i	−0.0926875	+	0.160540i	0.815954	+	0.578117i	$0.196212\pi$
$200$		−	1.00000i		−	0.0707107i
$201$		0			0
$202$	4.18718	+	2.41747i	0.294609	+	0.170093i
$203$			11.3205i			0.794544i
$204$		0			0
$205$	−0.380509	−	0.659061i	−0.0265759	−	0.0460308i
$206$	4.96410	−	2.86603i	0.345865	−	0.199685i
$207$		0			0
$208$	−3.11256	−	1.81988i	−0.215817	−	0.126186i
$209$	1.61504			0.111714
$210$		0			0
$211$	4.56691	+	7.91011i	0.314399	+	0.544555i	0.979310	−	0.202368i	$-0.0648638\pi$
$211$	4.56691	+	7.91011i	0.314399	+	0.544555i	−0.664911	+	0.746923i	$0.731530\pi$
$212$	−5.31246	+	9.20145i	−0.364861	+	0.631958i
$213$		0			0
$214$	11.1505	+	6.43774i	0.762232	+	0.440075i
$215$	9.53264	+	5.50367i	0.650121	+	0.375347i
$216$		0			0
$217$	2.23616	−	3.87314i	0.151800	−	0.262926i
$218$	−0.107127	−	0.185550i	−0.00725557	−	0.0125670i
$219$		0			0
$220$	4.03957			0.272348
$221$	−0.0456536	+	8.31975i	−0.00307099	+	0.559647i
$222$		0			0
$223$	5.03326	−	2.90595i	0.337052	−	0.194597i	−0.321916	−	0.946768i	$-0.604327\pi$
$223$	5.03326	−	2.90595i	0.337052	−	0.194597i	0.658968	+	0.752171i	$0.270993\pi$
$224$	−0.719687	−	1.24653i	−0.0480861	−	0.0832876i
$225$		0			0
$226$		−	0.128595i		−	0.00855399i
$227$	9.99674	+	5.77162i	0.663507	+	0.383076i	0.793612	−	0.608424i	$-0.208198\pi$
$227$	9.99674	+	5.77162i	0.663507	+	0.383076i	−0.130105	+	0.991500i	$0.541531\pi$
$228$		0			0
$229$		−	12.8755i		−	0.850836i	−0.904997	−	0.425418i	$-0.860127\pi$
$229$		−	12.8755i		−	0.850836i	0.904997	−	0.425418i	$-0.139873\pi$
$230$	0.780313	−	1.35154i	0.0514523	−	0.0891180i
$231$		0			0
$232$	6.81119	−	3.93244i	0.447177	−	0.258177i
$233$	10.4149			0.682303			0.341152	−	0.940008i	$-0.389183\pi$
$233$	10.4149			0.682303			0.341152	+	0.940008i	$0.389183\pi$
$234$		0			0
$235$	5.84016			0.380970
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$		0			0
$238$	−1.66069	+	2.87640i	−0.107647	+	0.186449i
$239$		−	18.3801i		−	1.18891i	−0.804128	−	0.594456i	$-0.797367\pi$
$239$		−	18.3801i		−	1.18891i	0.804128	−	0.594456i	$-0.202633\pi$
$240$		0			0
$241$	0.536681	+	0.309853i	0.0345707	+	0.0199594i	0.517186	−	0.855873i	$-0.326980\pi$
$241$	0.536681	+	0.309853i	0.0345707	+	0.0199594i	−0.482615	+	0.875833i	$0.660313\pi$
$242$			5.31812i			0.341862i
$243$		0			0
$244$	−2.84624	−	4.92983i	−0.182212	−	0.315600i
$245$	−4.26795	+	2.46410i	−0.272669	+	0.157426i
$246$		0			0
$247$	−1.44149	−	0.00791002i	−0.0917200	−	0.000503302i
$248$	−3.10713			−0.197303
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	2.65376	−	4.59645i	0.167504	−	0.290125i	−0.770038	−	0.637998i	$-0.779763\pi$
$251$	2.65376	−	4.59645i	0.167504	−	0.290125i	0.937542	+	0.347873i	$0.113096\pi$
$252$		0			0
$253$	5.45965	+	3.15213i	0.343245	+	0.198173i
$254$	13.9641	+	8.06218i	0.876186	+	0.505866i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.3686	−	21.4230i	−0.771529	−	1.33633i	−0.936725	−	0.350067i	$-0.886159\pi$
$257$	−12.3686	−	21.4230i	−0.771529	−	1.33633i	0.165195	−	0.986261i	$-0.447175\pi$
$258$		0			0
$259$	8.97553			0.557713
$260$	−3.60550	−	0.0197847i	−0.223603	−	0.00122700i
$261$		0			0
$262$	2.40764	−	1.39005i	0.148744	−	0.0858775i
$263$	2.56466	+	4.44211i	0.158143	+	0.273912i	0.934199	−	0.356752i	$-0.116116\pi$
$263$	2.56466	+	4.44211i	0.158143	+	0.273912i	−0.776056	+	0.630664i	$0.782782\pi$
$264$		0			0
$265$			10.6249i			0.652684i
$266$	−0.498370	−	0.287734i	−0.0305570	−	0.0176421i
$267$		0			0
$268$			10.4008i			0.635329i
$269$	3.40687	−	5.90087i	0.207720	−	0.359782i	−0.743276	−	0.668985i	$-0.766729\pi$
$269$	3.40687	−	5.90087i	0.207720	−	0.359782i	0.950996	+	0.309203i	$0.100062\pi$
$270$		0			0
$271$	−19.0709	+	11.0106i	−1.15848	+	0.668846i	−0.950938	−	0.309381i	$-0.899878\pi$
$271$	−19.0709	+	11.0106i	−1.15848	+	0.668846i	−0.207538	+	0.978227i	$0.566545\pi$
$272$	2.30752			0.139914
$273$		0			0
$274$	−5.46736			−0.330295
$275$	3.49837	−	2.01978i	0.210960	−	0.121798i
$276$		0			0
$277$	12.7152	−	22.0233i	0.763980	−	1.32325i	−0.176805	−	0.984246i	$-0.556576\pi$
$277$	12.7152	−	22.0233i	0.763980	−	1.32325i	0.940784	−	0.339006i	$-0.110091\pi$
$278$			0.214517i			0.0128659i
$279$		0			0
$280$	−1.24653	−	0.719687i	−0.0744947	−	0.0430095i
$281$			25.0954i			1.49707i	0.663098	+	0.748533i	$0.269241\pi$
$281$			25.0954i			1.49707i	−0.663098	+	0.748533i	$0.730759\pi$
$282$		0			0
$283$	0.882986	+	1.52938i	0.0524881	+	0.0909120i	0.891076	−	0.453855i	$-0.149952\pi$
$283$	0.882986	+	1.52938i	0.0524881	+	0.0909120i	−0.838588	+	0.544767i	$0.816618\pi$
$284$	−5.19615	+	3.00000i	−0.308335	+	0.178017i
$285$		0			0
$286$	0.0799217	−	14.5647i	0.00472587	−	0.861226i
$287$	−1.09539			−0.0646588
$288$		0			0
$289$	5.83768	+	10.1112i	0.343393	+	0.594774i
$290$	3.93244	−	6.81119i	0.230921	−	0.399967i
$291$		0			0
$292$	11.6574	+	6.73042i	0.682200	+	0.393868i
$293$	15.9374	+	9.20145i	0.931072	+	0.537555i	0.887150	−	0.461480i	$-0.152682\pi$
$293$	15.9374	+	9.20145i	0.931072	+	0.537555i	0.0439215	+	0.999035i	$0.486015\pi$
$294$		0			0
$295$	1.73205	−	3.00000i	0.100844	−	0.174667i
$296$	−3.11786	−	5.40029i	−0.181222	−	0.313886i
$297$		0			0
$298$	16.5294			0.957521
$299$	−4.85754	−	2.84016i	−0.280919	−	0.164250i
$300$		0			0
$301$	13.7210	−	7.92184i	0.790867	−	0.456607i
$302$	3.35415	+	5.80956i	0.193010	+	0.334303i
$303$		0			0
$304$			0.399804i			0.0229303i
$305$	−4.92983	−	2.84624i	−0.282281	−	0.162975i
$306$		0			0
$307$			8.40730i			0.479830i	0.970794	+	0.239915i	$0.0771196\pi$
$307$			8.40730i			0.479830i	−0.970794	+	0.239915i	$0.922880\pi$
$308$	2.90723	−	5.03546i	0.165655	−	0.286922i
$309$		0			0
$310$	−2.69085	+	1.55356i	−0.152830	+	0.0882365i
$311$	33.6601			1.90869			0.954344	−	0.298708i	$-0.0965557\pi$
$311$	33.6601			1.90869			0.954344	+	0.298708i	$0.0965557\pi$
$312$		0			0
$313$	27.0008			1.52618			0.763088	−	0.646294i	$-0.223682\pi$
$313$	27.0008			1.52618			0.763088	+	0.646294i	$0.223682\pi$
$314$	−5.03753	+	2.90842i	−0.284284	+	0.164132i
$315$		0			0
$316$	0.465732	−	0.806671i	0.0261995	−	0.0453788i
$317$		−	10.2569i		−	0.576086i	−0.957617	−	0.288043i	$-0.906995\pi$
$317$		−	10.2569i		−	0.576086i	0.957617	−	0.288043i	$-0.0930047\pi$
$318$		0			0
$319$	27.5143	+	15.8854i	1.54050	+	0.889410i
$320$			1.00000i			0.0559017i
$321$		0			0
$322$	−1.12316	−	1.94537i	−0.0625914	−	0.108411i
$323$	0.798957	−	0.461278i	0.0444551	−	0.0256662i
$324$		0			0
$325$	−3.13234	+	1.78561i	−0.173751	+	0.0990481i
$326$	−4.17240			−0.231088
$327$		0			0
$328$	0.380509	+	0.659061i	0.0210101	+	0.0363905i
$329$	4.20308	−	7.27995i	0.231724	−	0.401357i
$330$		0			0
$331$	−3.92256	−	2.26469i	−0.215603	−	0.124479i	0.388310	−	0.921529i	$-0.373059\pi$
$331$	−3.92256	−	2.26469i	−0.215603	−	0.124479i	−0.603913	+	0.797050i	$0.706392\pi$
$332$	8.99511	+	5.19333i	0.493671	+	0.285021i
$333$		0			0
$334$	−7.80426	+	13.5174i	−0.427030	+	0.739638i
$335$	5.20039	+	9.00734i	0.284128	+	0.492124i
$336$		0			0
$337$	6.72755			0.366473			0.183236	−	0.983069i	$-0.441343\pi$
$337$	6.72755			0.366473			0.183236	+	0.983069i	$0.441343\pi$
$338$	−0.142667	+	12.9992i	−0.00776009	+	0.707064i
$339$		0			0
$340$	1.99837	−	1.15376i	0.108377	−	0.0625714i
$341$	−6.27573	−	10.8699i	−0.339850	−	0.588637i
$342$		0			0
$343$			17.1691i			0.927047i
$344$	−9.53264	−	5.50367i	−0.513965	−	0.296738i
$345$		0			0
$346$		−	5.81445i		−	0.312587i
$347$	1.57286	−	2.72427i	0.0844355	−	0.146247i	−0.820715	−	0.571338i	$-0.806425\pi$
$347$	1.57286	−	2.72427i	0.0844355	−	0.146247i	0.905151	+	0.425091i	$0.139758\pi$
$348$		0			0
$349$	−9.09752	+	5.25246i	−0.486979	+	0.281158i	−0.723320	−	0.690513i	$-0.757385\pi$
$349$	−9.09752	+	5.25246i	−0.486979	+	0.281158i	0.236341	+	0.971670i	$0.424052\pi$
$350$	−1.43937			−0.0769378
$351$		0			0
$352$	−4.03957			−0.215310
$353$	28.5767	−	16.4988i	1.52099	−	0.878141i	0.521292	−	0.853378i	$-0.325450\pi$
$353$	28.5767	−	16.4988i	1.52099	−	0.878141i	0.999693	−	0.0247633i	$-0.00788320\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		−	0.971033i		−	0.0514647i
$357$		0			0
$358$	−14.6118	−	8.43611i	−0.772256	−	0.445862i
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$		0			0
$361$	−9.42008	−	16.3161i	−0.495794	−	0.858740i
$362$	−10.9298	+	6.31034i	−0.574459	+	0.331664i
$363$		0			0
$364$	−2.61949	+	4.48014i	−0.137299	+	0.234823i
$365$	13.4608			0.704573
$366$		0			0
$367$	9.89924	+	17.1460i	0.516736	+	0.895013i	0.999811	+	0.0194340i	$0.00618643\pi$
$367$	9.89924	+	17.1460i	0.516736	+	0.895013i	−0.483075	+	0.875579i	$0.660480\pi$
$368$	−0.780313	+	1.35154i	−0.0406766	+	0.0704540i
$369$		0			0
$370$	−5.40029	−	3.11786i	−0.280748	−	0.162090i
$371$	13.2443	+	7.64662i	0.687611	+	0.396993i
$372$		0			0
$373$	−2.39557	+	4.14924i	−0.124038	+	0.214840i	−0.921356	−	0.388719i	$-0.872918\pi$
$373$	−2.39557	+	4.14924i	−0.124038	+	0.214840i	0.797319	+	0.603559i	$0.206251\pi$
$374$	4.66069	+	8.07255i	0.240999	+	0.417422i
$375$		0			0
$376$	−5.84016			−0.301183
$377$	−24.4799	−	14.3132i	−1.26078	−	0.737166i
$378$		0			0
$379$	−16.8833	+	9.74760i	−0.867239	+	0.500700i	−0.866430	−	0.499299i	$-0.833591\pi$
$379$	−16.8833	+	9.74760i	−0.867239	+	0.500700i	−0.000808945		1.00000i	$0.500257\pi$
$380$	0.199902	+	0.346241i	0.0102548	+	0.0177618i
$381$		0			0
$382$			1.34072i			0.0685974i
$383$	−11.1383	−	6.43068i	−0.569139	−	0.328592i	0.187667	−	0.982233i	$-0.439908\pi$
$383$	−11.1383	−	6.43068i	−0.569139	−	0.328592i	−0.756805	+	0.653640i	$0.773241\pi$
$384$		0			0
$385$		−	5.81445i		−	0.296332i
$386$	8.37182	−	14.5004i	0.426114	−	0.738051i
$387$		0			0
$388$	−10.6680	+	6.15919i	−0.541587	+	0.312686i
$389$	−6.94233			−0.351990			−0.175995	−	0.984391i	$-0.556314\pi$
$389$	−6.94233			−0.351990			−0.175995	+	0.984391i	$0.556314\pi$
$390$		0			0
$391$	3.60117			0.182119
$392$	4.26795	−	2.46410i	0.215564	−	0.124456i
$393$		0			0
$394$	0.498370	−	0.863202i	0.0251075	−	0.0434875i
$395$		−	0.931464i		−	0.0468670i
$396$		0			0
$397$	−3.75184	−	2.16612i	−0.188299	−	0.108715i	0.402887	−	0.915250i	$-0.368007\pi$
$397$	−3.75184	−	2.16612i	−0.188299	−	0.108715i	−0.591186	+	0.806535i	$0.701340\pi$
$398$		−	2.61504i		−	0.131080i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	20.5448	−	11.8616i	1.02596	−	0.592339i	0.110136	−	0.993917i	$-0.464871\pi$
$401$	20.5448	−	11.8616i	1.02596	−	0.592339i	0.915825	+	0.401578i	$0.131538\pi$
$402$		0			0
$403$	5.54813	+	9.73259i	0.276372	+	0.484815i
$404$	−4.83494			−0.240547
$405$		0			0
$406$	−5.66025	−	9.80385i	−0.280914	−	0.486557i
$407$	12.5948	−	21.8149i	0.624302	−	1.08132i
$408$		0			0
$409$	−33.2373	−	19.1896i	−1.64348	−	0.948864i	−0.979583	−	0.201039i	$-0.935568\pi$
$409$	−33.2373	−	19.1896i	−1.64348	−	0.948864i	−0.663897	−	0.747824i	$-0.731099\pi$
$410$	0.659061	+	0.380509i	0.0325487	+	0.0187920i
$411$		0			0
$412$	−2.86603	+	4.96410i	−0.141199	+	0.244564i
$413$	−2.49307	−	4.31812i	−0.122676	−	0.212481i
$414$		0			0
$415$	10.3867			0.509861
$416$	3.60550	+	0.0197847i	0.176774	+	0.000970026i
$417$		0			0
$418$	−1.39866	+	0.807519i	−0.0684109	+	0.0394970i
$419$	−19.2946	−	33.4192i	−0.942602	−	1.63263i	−0.760482	−	0.649359i	$-0.775037\pi$
$419$	−19.2946	−	33.4192i	−0.942602	−	1.63263i	−0.182120	−	0.983276i	$-0.558296\pi$
$420$		0			0
$421$		−	40.6199i		−	1.97969i	−0.142134	−	0.989847i	$-0.545397\pi$
$421$		−	40.6199i		−	1.97969i	0.142134	−	0.989847i	$-0.454603\pi$
$422$	−7.91011	−	4.56691i	−0.385058	−	0.222314i
$423$		0			0
$424$		−	10.6249i		−	0.515992i
$425$	1.15376	−	1.99837i	0.0559655	−	0.0969352i
$426$		0			0
$427$	−7.09587	+	4.09680i	−0.343393	+	0.198258i
$428$	−12.8755			−0.622360
$429$		0			0
$430$	−11.0073			−0.530821
$431$	−10.1945	+	5.88581i	−0.491053	+	0.283509i	−0.725011	−	0.688737i	$-0.758165\pi$
$431$	−10.1945	+	5.88581i	−0.491053	+	0.283509i	0.233958	+	0.972247i	$0.424832\pi$
$432$		0			0
$433$	−16.5004	+	28.5795i	−0.792959	+	1.37345i	0.131168	+	0.991360i	$0.458127\pi$
$433$	−16.5004	+	28.5795i	−0.792959	+	1.37345i	−0.924127	+	0.382085i	$0.875206\pi$
$434$			4.47232i			0.214678i
$435$		0			0
$436$	0.185550	+	0.107127i	0.00888622	+	0.00513046i
$437$			0.623945i			0.0298473i
$438$		0			0
$439$	0.348718	+	0.603998i	0.0166434	+	0.0288272i	0.874227	−	0.485517i	$-0.161369\pi$
$439$	0.348718	+	0.603998i	0.0166434	+	0.0288272i	−0.857584	+	0.514344i	$0.828035\pi$
$440$	−3.49837	+	2.01978i	−0.166778	+	0.0962895i
$441$		0			0
$442$	−4.12034	−	7.22794i	−0.195985	−	0.343798i
$443$	−28.6297			−1.36024			−0.680120	−	0.733101i	$-0.738072\pi$
$443$	−28.6297			−1.36024			−0.680120	+	0.733101i	$0.738072\pi$
$444$		0			0
$445$	−0.485517	−	0.840939i	−0.0230157	−	0.0398644i
$446$	−2.90595	+	5.03326i	−0.137601	+	0.238332i
$447$		0			0
$448$	1.24653	+	0.719687i	0.0588932	+	0.0340020i
$449$	5.87601	+	3.39251i	0.277306	+	0.160103i	0.632203	−	0.774803i	$-0.282151\pi$
$449$	5.87601	+	3.39251i	0.277306	+	0.160103i	−0.354897	+	0.934905i	$0.615484\pi$
$450$		0			0
$451$	−1.53709	+	2.66232i	−0.0723788	+	0.125364i
$452$	0.0642973	+	0.111366i	0.00302429	+	0.00523823i
$453$		0			0
$454$	−11.5432			−0.541751
$455$	−0.0284776	+	5.18966i	−0.00133505	+	0.243295i
$456$		0			0
$457$	15.5355	−	8.96940i	0.726718	−	0.419571i	−0.0905021	−	0.995896i	$-0.528847\pi$
$457$	15.5355	−	8.96940i	0.726718	−	0.419571i	0.817220	+	0.576325i	$0.195514\pi$
$458$	6.43774	+	11.1505i	0.300816	+	0.521029i
$459$		0			0
$460$			1.56063i			0.0727646i
$461$	23.2937	+	13.4486i	1.08489	+	0.626364i	0.932213	−	0.361911i	$-0.117876\pi$
$461$	23.2937	+	13.4486i	1.08489	+	0.626364i	0.152682	+	0.988275i	$0.451209\pi$
$462$		0			0
$463$			26.8402i			1.24737i	0.781677	+	0.623684i	$0.214365\pi$
$463$			26.8402i			1.24737i	−0.781677	+	0.623684i	$0.785635\pi$
$464$	−3.93244	+	6.81119i	−0.182559	+	0.316202i
$465$		0			0
$466$	−9.01957	+	5.20745i	−0.417824	+	0.241231i
$467$	−9.48726			−0.439018			−0.219509	−	0.975610i	$-0.570446\pi$
$467$	−9.48726			−0.439018			−0.219509	+	0.975610i	$0.570446\pi$
$468$		0			0
$469$	14.9706			0.691279
$470$	−5.05772	+	2.92008i	−0.233295	+	0.134693i
$471$		0			0
$472$	−1.73205	+	3.00000i	−0.0797241	+	0.138086i
$473$		−	44.4649i		−	2.04450i
$474$		0			0
$475$	0.346241	+	0.199902i	0.0158866	+	0.00917214i
$476$		−	3.32138i		−	0.152235i
$477$		0			0
$478$	9.19007	+	15.9177i	0.420344	+	0.728057i
$479$	−9.71206	+	5.60726i	−0.443755	+	0.256202i	−0.705189	−	0.709019i	$-0.749138\pi$
$479$	−9.71206	+	5.60726i	−0.443755	+	0.256202i	0.261434	+	0.965221i	$0.415805\pi$
$480$		0			0
$481$	−11.3483	+	19.4091i	−0.517437	+	0.884977i
$482$	−0.619706			−0.0282268
$483$		0			0
$484$	−2.65906	−	4.60563i	−0.120866	−	0.209347i
$485$	−6.15919	+	10.6680i	−0.279674	+	0.484410i
$486$		0			0
$487$	24.0137	+	13.8643i	1.08816	+	0.628252i	0.933087	−	0.359650i	$-0.117104\pi$
$487$	24.0137	+	13.8643i	1.08816	+	0.628252i	0.155077	+	0.987902i	$0.450437\pi$
$488$	4.92983	+	2.84624i	0.223163	+	0.128843i
$489$		0			0
$490$	2.46410	−	4.26795i	0.111317	−	0.192806i
$491$	−13.9377	−	24.1409i	−0.629002	−	1.08946i	−0.987752	−	0.156029i	$-0.950131\pi$
$491$	−13.9377	−	24.1409i	−0.629002	−	1.08946i	0.358751	−	0.933433i	$-0.383203\pi$
$492$		0			0
$493$	18.1484			0.817361
$494$	1.25232	−	0.713896i	0.0563448	−	0.0321197i
$495$		0			0
$496$	2.69085	−	1.55356i	0.120823	−	0.0697571i
$497$	4.31812	+	7.47921i	0.193694	+	0.335488i
$498$		0			0
$499$		−	36.8040i		−	1.64757i	−0.566901	−	0.823786i	$-0.691858\pi$
$499$		−	36.8040i		−	1.64757i	0.566901	−	0.823786i	$-0.308142\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$		0			0
$502$			5.30752i			0.236886i
$503$	−19.2848	+	33.4022i	−0.859865	+	1.48933i	0.0121928	+	0.999926i	$0.496119\pi$
$503$	−19.2848	+	33.4022i	−0.859865	+	1.48933i	−0.872057	+	0.489404i	$0.837215\pi$
$504$		0			0
$505$	−4.18718	+	2.41747i	−0.186327	+	0.107576i
$506$	−6.30426			−0.280258
$507$		0			0
$508$	−16.1244			−0.715403
$509$	−24.9870	+	14.4262i	−1.10753	+	0.639431i	−0.938188	−	0.346126i	$-0.887497\pi$
$509$	−24.9870	+	14.4262i	−1.10753	+	0.639431i	−0.169340	+	0.985558i	$0.554163\pi$
$510$		0			0
$511$	9.68759	−	16.7794i	0.428554	−	0.742277i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	21.4230	+	12.3686i	0.944927	+	0.545554i
$515$			5.73205i			0.252584i
$516$		0			0
$517$	−11.7959	−	20.4310i	−0.518781	−	0.898556i
$518$	−7.77304	+	4.48777i	−0.341528	+	0.197181i
$519$		0			0
$520$	3.13234	−	1.78561i	0.137362	−	0.0783044i
$521$	10.6422			0.466241			0.233121	−	0.972448i	$-0.425106\pi$
$521$	10.6422			0.466241			0.233121	+	0.972448i	$0.425106\pi$
$522$		0			0
$523$	−19.0759	−	33.0404i	−0.834130	−	1.44476i	−0.894737	−	0.446594i	$-0.852637\pi$
$523$	−19.0759	−	33.0404i	−0.834130	−	1.44476i	0.0606070	−	0.998162i	$-0.480696\pi$
$524$	−1.39005	+	2.40764i	−0.0607246	+	0.105178i
$525$		0			0
$526$	−4.44211	−	2.56466i	−0.193685	−	0.111824i
$527$	−6.20919	−	3.58488i	−0.270477	−	0.156160i
$528$		0			0
$529$	10.2822	−	17.8093i	0.447053	−	0.774319i
$530$	−5.31246	−	9.20145i	−0.230759	−	0.399686i
$531$		0			0
$532$	0.575468			0.0249497
$533$	1.38496	−	2.36871i	0.0599894	−	0.102600i
$534$		0			0
$535$	−11.1505	+	6.43774i	−0.482078	+	0.278328i
$536$	−5.20039	−	9.00734i	−0.224623	−	0.389058i
$537$		0			0
$538$			6.81373i			0.293761i
$539$	17.2407	+	9.95391i	0.742609	+	0.428745i
$540$		0			0
$541$		−	1.46593i		−	0.0630252i	−0.999503	−	0.0315126i	$-0.989968\pi$
$541$		−	1.46593i		−	0.0630252i	0.999503	−	0.0315126i	$-0.0100324\pi$
$542$	11.0106	−	19.0709i	0.472946	−	0.819166i
$543$		0			0
$544$	−1.99837	+	1.15376i	−0.0856794	+	0.0494670i
$545$	0.214254			0.00917765
$546$		0			0
$547$	−16.2374			−0.694262			−0.347131	−	0.937817i	$-0.612844\pi$
$547$	−16.2374			−0.694262			−0.347131	+	0.937817i	$0.612844\pi$
$548$	4.73487	−	2.73368i	0.202264	−	0.116777i
$549$		0			0
$550$	−2.01978	+	3.49837i	−0.0861239	+	0.149171i
$551$			3.14441i			0.133957i
$552$		0			0
$553$	−1.16110	−	0.670362i	−0.0493751	−	0.0285067i
$554$			25.4303i			1.08043i
$555$		0			0
$556$	−0.107258	−	0.185777i	−0.00454877	−	0.00787869i
$557$	−28.8599	+	16.6623i	−1.22283	+	0.706004i	−0.965521	−	0.260324i	$-0.916171\pi$
$557$	−28.8599	+	16.6623i	−1.22283	+	0.706004i	−0.257314	+	0.966328i	$0.582837\pi$
$558$		0			0
$559$	−0.217777	+	39.6869i	−0.00921099	+	1.67858i
$560$	1.43937			0.0608246
$561$		0			0
$562$	−12.5477	−	21.7332i	−0.529293	−	0.916762i
$563$	−3.75678	+	6.50693i	−0.158329	+	0.274234i	−0.934266	−	0.356576i	$-0.883944\pi$
$563$	−3.75678	+	6.50693i	−0.158329	+	0.274234i	0.775937	+	0.630810i	$0.217277\pi$
$564$		0			0
$565$	0.111366	+	0.0642973i	0.00468521	+	0.00270501i
$566$	−1.52938	−	0.882986i	−0.0642845	−	0.0371147i
$567$		0			0
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	−6.45619	−	11.1825i	−0.270658	−	0.468793i	0.698373	−	0.715734i	$-0.253908\pi$
$569$	−6.45619	−	11.1825i	−0.270658	−	0.468793i	−0.969030	+	0.246941i	$0.920574\pi$
$570$		0			0
$571$	3.47470			0.145412			0.0727059	−	0.997353i	$-0.476837\pi$
$571$	3.47470			0.145412			0.0727059	+	0.997353i	$0.476837\pi$
$572$	7.21311	+	12.6533i	0.301595	+	0.529062i
$573$		0			0
$574$	0.948635	−	0.547694i	0.0395952	−	0.0228603i
$575$	0.780313	+	1.35154i	0.0325413	+	0.0563632i
$576$		0			0
$577$		−	8.80287i		−	0.366468i	−0.983069	−	0.183234i	$-0.941343\pi$
$577$		−	8.80287i		−	0.366468i	0.983069	−	0.183234i	$-0.0586566\pi$
$578$	−10.1112	−	5.83768i	−0.420569	−	0.242815i
$579$		0			0
$580$			7.86488i			0.326572i
$581$	7.47514	−	12.9473i	0.310121	−	0.537146i
$582$		0			0
$583$	37.1699	−	21.4601i	1.53942	−	0.888785i
$584$	−13.4608			−0.557014
$585$		0			0
$586$	−18.4029			−0.760217
$587$	−30.9967	+	17.8960i	−1.27937	+	0.738646i	−0.976733	−	0.214459i	$-0.931201\pi$
$587$	−30.9967	+	17.8960i	−1.27937	+	0.738646i	−0.302639	+	0.953105i	$0.597868\pi$
$588$		0			0
$589$	0.621121	−	1.07581i	0.0255929	−	0.0443281i
$590$			3.46410i			0.142615i
$591$		0			0
$592$	5.40029	+	3.11786i	0.221951	+	0.128143i
$593$		−	3.93555i		−	0.161613i	−0.996730	−	0.0808067i	$-0.974250\pi$
$593$		−	3.93555i		−	0.161613i	0.996730	−	0.0808067i	$-0.0257497\pi$
$594$		0			0
$595$	−1.66069	−	2.87640i	−0.0680817	−	0.117921i
$596$	−14.3149	+	8.26469i	−0.586360	+	0.338535i
$597$		0			0
$598$	5.62683	+	0.0308766i	0.230098	+	0.00126264i
$599$	9.50704			0.388447			0.194223	−	0.980957i	$-0.437781\pi$
$599$	9.50704			0.388447			0.194223	+	0.980957i	$0.437781\pi$
$600$		0			0
$601$	−17.4935	−	30.2996i	−0.713574	−	1.23595i	−0.963507	−	0.267683i	$-0.913742\pi$
$601$	−17.4935	−	30.2996i	−0.713574	−	1.23595i	0.249933	−	0.968263i	$-0.419591\pi$
$602$	−7.92184	+	13.7210i	−0.322870	+	0.559227i
$603$		0			0
$604$	−5.80956	−	3.35415i	−0.236388	−	0.136478i
$605$	−4.60563	−	2.65906i	−0.187245	−	0.108106i
$606$		0			0
$607$	8.08054	−	13.9959i	0.327979	−	0.568076i	−0.654132	−	0.756381i	$-0.726966\pi$
$607$	8.08054	−	13.9959i	0.327979	−	0.568076i	0.982111	+	0.188304i	$0.0602991\pi$
$608$	−0.199902	−	0.346241i	−0.00810710	−	0.0140419i
$609$		0			0
$610$	5.69248			0.230482
$611$	10.4283	+	18.2934i	0.421883	+	0.740071i
$612$		0			0
$613$	−7.68335	+	4.43598i	−0.310327	+	0.179168i	−0.647073	−	0.762428i	$-0.724007\pi$
$613$	−7.68335	+	4.43598i	−0.310327	+	0.179168i	0.336746	+	0.941596i	$0.390674\pi$
$614$	−4.20365	−	7.28094i	−0.169646	−	0.293835i
$615$		0			0
$616$			5.81445i			0.234271i
$617$	9.39557	+	5.42453i	0.378251	+	0.218383i	0.677057	−	0.735930i	$-0.263255\pi$
$617$	9.39557	+	5.42453i	0.378251	+	0.218383i	−0.298806	+	0.954314i	$0.596588\pi$
$618$		0			0
$619$		−	5.82727i		−	0.234218i	−0.993119	−	0.117109i	$-0.962637\pi$
$619$		−	5.82727i		−	0.234218i	0.993119	−	0.117109i	$-0.0373627\pi$
$620$	1.55356	−	2.69085i	0.0623926	−	0.108067i
$621$		0			0
$622$	−29.1505	+	16.8300i	−1.16883	+	0.674823i
$623$	−1.39768			−0.0559969
$624$		0			0
$625$	1.00000			0.0400000
$626$	−23.3834	+	13.5004i	−0.934589	+	0.539585i
$627$		0			0
$628$	2.90842	−	5.03753i	0.116059	−	0.201019i
$629$		−	14.3890i		−	0.573729i
$630$		0			0
$631$	−8.17169	−	4.71793i	−0.325310	−	0.187818i	0.328447	−	0.944522i	$-0.393475\pi$
$631$	−8.17169	−	4.71793i	−0.325310	−	0.187818i	−0.653757	+	0.756705i	$0.726808\pi$
$632$			0.931464i			0.0370516i
$633$		0			0
$634$	5.12846	+	8.88276i	0.203677	+	0.352779i
$635$	−13.9641	+	8.06218i	−0.554148	+	0.319938i
$636$		0			0
$637$	−15.3393	−	8.96875i	−0.607766	−	0.355355i
$638$	−31.7707			−1.25782
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−20.2877	+	35.1392i	−0.801314	+	1.38792i	0.117437	+	0.993080i	$0.462532\pi$
$641$	−20.2877	+	35.1392i	−0.801314	+	1.38792i	−0.918751	+	0.394837i	$0.870801\pi$
$642$		0			0
$643$	−5.08527	−	2.93598i	−0.200543	−	0.115784i	0.396365	−	0.918093i	$-0.370271\pi$
$643$	−5.08527	−	2.93598i	−0.200543	−	0.115784i	−0.596909	+	0.802309i	$0.703605\pi$
$644$	1.94537	+	1.12316i	0.0766585	+	0.0442588i
$645$		0			0
$646$	−0.461278	+	0.798957i	−0.0181487	+	0.0314345i
$647$	−19.3652	−	33.5416i	−0.761326	−	1.31866i	−0.942167	−	0.335143i	$-0.891215\pi$
$647$	−19.3652	−	33.5416i	−0.761326	−	1.31866i	0.180841	−	0.983512i	$-0.442118\pi$
$648$		0			0
$649$	−13.9935			−0.549292
$650$	1.81988	−	3.11256i	0.0713817	−	0.122085i
$651$		0			0
$652$	3.61341	−	2.08620i	0.141512	−	0.0817020i
$653$	−6.45492	−	11.1802i	−0.252601	−	0.437517i	0.711641	−	0.702544i	$-0.247953\pi$
$653$	−6.45492	−	11.1802i	−0.252601	−	0.437517i	−0.964241	+	0.265027i	$0.914619\pi$
$654$		0			0
$655$			2.78010i			0.108627i
$656$	−0.659061	−	0.380509i	−0.0257320	−	0.0148564i
$657$		0			0
$658$			8.40617i			0.327707i
$659$	−3.20654	+	5.55389i	−0.124909	+	0.216349i	−0.921697	−	0.387910i	$-0.873197\pi$
$659$	−3.20654	+	5.55389i	−0.124909	+	0.216349i	0.796788	+	0.604259i	$0.206531\pi$
$660$		0			0
$661$	−6.05300	+	3.49470i	−0.235434	+	0.135928i	−0.613076	−	0.790024i	$-0.710068\pi$
$661$	−6.05300	+	3.49470i	−0.235434	+	0.135928i	0.377642	+	0.925952i	$0.376735\pi$
$662$	4.52938			0.176039
$663$		0			0
$664$	−10.3867			−0.403080
$665$	0.498370	−	0.287734i	0.0193260	−	0.0111578i
$666$		0			0
$667$	−6.13707	+	10.6297i	−0.237628	+	0.411584i
$668$		−	15.6085i		−	0.603912i
$669$		0			0
$670$	−9.00734	−	5.20039i	−0.347984	−	0.200909i
$671$			22.9952i			0.887719i
$672$		0			0
$673$	−23.3083	−	40.3712i	−0.898470	−	1.55620i	−0.829450	−	0.558581i	$-0.811346\pi$
$673$	−23.3083	−	40.3712i	−0.898470	−	1.55620i	−0.0690207	−	0.997615i	$-0.521987\pi$
$674$	−5.82623	+	3.36377i	−0.224418	+	0.129568i
$675$		0			0
$676$	−6.37605	−	11.3290i	−0.245233	−	0.435730i
$677$	−6.85102			−0.263306			−0.131653	−	0.991296i	$-0.542028\pi$
$677$	−6.85102			−0.263306			−0.131653	+	0.991296i	$0.542028\pi$
$678$		0			0
$679$	8.86538	+	15.3553i	0.340222	+	0.589282i
$680$	−1.15376	+	1.99837i	−0.0442446	+	0.0766340i
$681$		0			0
$682$	10.8699	+	6.27573i	0.416229	+	0.240310i
$683$	21.2374	+	12.2614i	0.812627	+	0.469171i	0.847867	−	0.530208i	$-0.177886\pi$
$683$	21.2374	+	12.2614i	0.812627	+	0.469171i	−0.0352402	+	0.999379i	$0.511220\pi$
$684$		0			0
$685$	2.73368	−	4.73487i	0.104449	−	0.180910i
$686$	−8.58457	−	14.8689i	−0.327760	−	0.567698i
$687$		0			0
$688$	11.0073			0.419651
$689$	−33.2809	+	18.9720i	−1.26790	+	0.722776i
$690$		0			0
$691$	8.72060	−	5.03484i	0.331747	−	0.191534i	−0.324869	−	0.945759i	$-0.605320\pi$
$691$	8.72060	−	5.03484i	0.331747	−	0.191534i	0.656617	+	0.754225i	$0.271987\pi$
$692$	2.90723	+	5.03546i	0.110516	+	0.191420i
$693$		0			0
$694$			3.14572i			0.119410i
$695$	−0.185777	−	0.107258i	−0.00704692	−	0.00406854i
$696$		0			0
$697$			1.75606i			0.0665156i
$698$	5.25246	−	9.09752i	0.198808	−	0.344346i
$699$		0			0
$700$	1.24653	−	0.719687i	0.0471146	−	0.0272016i
$701$	10.4149			0.393366			0.196683	−	0.980467i	$-0.436983\pi$
$701$	10.4149			0.393366			0.196683	+	0.980467i	$0.436983\pi$
$702$		0			0
$703$	2.49307			0.0940279
$704$	3.49837	−	2.01978i	0.131850	−	0.0761235i
$705$		0			0
$706$	−16.4988	+	28.5767i	−0.620940	+	1.07550i
$707$			6.95928i			0.261731i
$708$		0			0
$709$	−0.325446	−	0.187896i	−0.0122224	−	0.00705660i	0.493876	−	0.869532i	$-0.335580\pi$
$709$	−0.325446	−	0.187896i	−0.0122224	−	0.00705660i	−0.506099	+	0.862476i	$0.668913\pi$
$710$		−	6.00000i		−	0.225176i
$711$		0			0
$712$	0.485517	+	0.840939i	0.0181955	+	0.0315155i
$713$	4.19941	−	2.42453i	0.157269	−	0.0907994i
$714$		0			0
$715$	12.5734	+	7.35154i	0.470219	+	0.274932i
$716$	16.8722			0.630545
$717$		0			0
$718$	−12.1244	−	21.0000i	−0.452477	−	0.783713i
$719$	9.66547	−	16.7411i	0.360461	−	0.624337i	−0.627576	−	0.778556i	$-0.715953\pi$
$719$	9.66547	−	16.7411i	0.360461	−	0.624337i	0.988037	+	0.154218i	$0.0492860\pi$
$720$		0			0
$721$	7.14520	+	4.12528i	0.266101	+	0.153634i
$722$	16.3161	+	9.42008i	0.607221	+	0.350579i
$723$		0			0
$724$	6.31034	−	10.9298i	0.234522	−	0.406204i
$725$	3.93244	+	6.81119i	0.146047	+	0.252961i
$726$		0			0
$727$	31.3390			1.16230			0.581150	−	0.813797i	$-0.302603\pi$
$727$	31.3390			1.16230			0.581150	+	0.813797i	$0.302603\pi$
$728$	0.0284776	−	5.18966i	0.00105545	−	0.192342i
$729$		0			0
$730$	−11.6574	+	6.73042i	−0.431461	+	0.249104i
$731$	−12.6998	−	21.9967i	−0.469720	−	0.813579i
$732$		0			0
$733$		−	19.6207i		−	0.724707i	−0.932041	−	0.362353i	$-0.881973\pi$
$733$		−	19.6207i		−	0.724707i	0.932041	−	0.362353i	$-0.118027\pi$
$734$	−17.1460	−	9.89924i	−0.632870	−	0.365387i
$735$		0			0
$736$		−	1.56063i		−	0.0575254i
$737$	21.0073	−	36.3858i	0.773815	−	1.34029i
$738$		0			0
$739$	−10.3601	+	5.98141i	−0.381103	+	0.220030i	−0.678298	−	0.734787i	$-0.737282\pi$
$739$	−10.3601	+	5.98141i	−0.381103	+	0.220030i	0.297195	+	0.954817i	$0.403949\pi$
$740$	6.23572			0.229230
$741$		0			0
$742$	−15.2932			−0.561432
$743$	17.2540	−	9.96162i	0.632989	−	0.365457i	−0.148920	−	0.988849i	$-0.547580\pi$
$743$	17.2540	−	9.96162i	0.632989	−	0.365457i	0.781909	+	0.623393i	$0.214246\pi$
$744$		0			0
$745$	−8.26469	+	14.3149i	−0.302795	+	0.524456i
$746$		−	4.79113i		−	0.175416i
$747$		0			0
$748$	−8.07255	−	4.66069i	−0.295162	−	0.170412i
$749$			18.5326i			0.677168i
$750$		0			0
$751$	21.4608	+	37.1713i	0.783117	+	1.35640i	0.930117	+	0.367262i	$0.119705\pi$
$751$	21.4608	+	37.1713i	0.783117	+	1.35640i	−0.147000	+	0.989136i	$0.546962\pi$
$752$	5.05772	−	2.92008i	0.184436	−	0.106484i
$753$		0			0
$754$	28.3568	+	0.155605i	1.03269	+	0.00566678i
$755$	−6.70830			−0.244140
$756$		0			0
$757$	17.8750	+	30.9604i	0.649678	+	1.12528i	0.983200	+	0.182533i	$0.0584295\pi$
$757$	17.8750	+	30.9604i	0.649678	+	1.12528i	−0.333522	+	0.942742i	$0.608237\pi$
$758$	9.74760	−	16.8833i	0.354049	−	0.613230i
$759$		0			0
$760$	−0.346241	−	0.199902i	−0.0125595	−	0.00725121i
$761$	−26.1232	−	15.0822i	−0.946965	−	0.546731i	−0.0548284	−	0.998496i	$-0.517461\pi$
$761$	−26.1232	−	15.0822i	−0.946965	−	0.546731i	−0.892137	+	0.451765i	$0.850795\pi$
$762$		0			0
$763$	0.154196	−	0.267076i	0.00558227	−	0.00966878i
$764$	−0.670362	−	1.16110i	−0.0242529	−	0.0420072i
$765$		0			0
$766$	12.8614			0.464700
$767$	12.4898	+	0.0685363i	0.450981	+	0.00247470i
$768$		0			0
$769$	−21.0236	+	12.1380i	−0.758132	+	0.437708i	−0.828625	−	0.559805i	$-0.810876\pi$
$769$	−21.0236	+	12.1380i	−0.758132	+	0.437708i	0.0704928	+	0.997512i	$0.477543\pi$
$770$	2.90723	+	5.03546i	0.104769	+	0.181465i
$771$		0			0
$772$			16.7436i			0.602616i
$773$	38.5671	+	22.2667i	1.38716	+	0.800879i	0.992995	−	0.118160i	$-0.0376995\pi$
$773$	38.5671	+	22.2667i	1.38716	+	0.800879i	0.394168	+	0.919038i	$0.371033\pi$
$774$		0			0
$775$		−	3.10713i		−	0.111611i
$776$	6.15919	−	10.6680i	0.221102	−	0.382960i
$777$		0			0
$778$	6.01223	−	3.47116i	0.215549	−	0.124447i
$779$	−0.304258			−0.0109012
$780$		0			0
$781$	24.2374			0.867283
$782$	−3.11871	+	1.80059i	−0.111525	+	0.0643889i
$783$		0			0
$784$	−2.46410	+	4.26795i	−0.0880036	+	0.152427i
$785$		−	5.81684i		−	0.207612i
$786$		0			0
$787$	−15.0864	−	8.71015i	−0.537773	−	0.310483i	0.206403	−	0.978467i	$-0.433824\pi$
$787$	−15.0864	−	8.71015i	−0.537773	−	0.310483i	−0.744176	+	0.667984i	$0.767158\pi$
$788$			0.996740i			0.0355074i
$789$		0			0
$790$	0.465732	+	0.806671i	0.0165700	+	0.0287001i
$791$	0.160298	−	0.0925479i	0.00569953	−	0.00329062i
$792$		0			0
$793$	0.112624	−	20.5242i	0.00399940	−	0.728837i
$794$	4.33225			0.153746
$795$		0			0
$796$	1.30752	+	2.26469i	0.0463438	+	0.0802698i
$797$	−16.4801	+	28.5444i	−0.583756	+	1.01110i	0.411273	+	0.911512i	$0.365084\pi$
$797$	−16.4801	+	28.5444i	−0.583756	+	1.01110i	−0.995029	+	0.0995834i	$0.968249\pi$
$798$		0			0
$799$	−11.6708	−	6.73813i	−0.412883	−	0.238378i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$		0			0
$802$	−11.8616	+	20.5448i	−0.418847	+	0.725464i
$803$	−27.1880	−	47.0910i	−0.959444	−	1.66181i
$804$		0			0
$805$	2.24632			0.0791725
$806$	−9.67112	−	5.65461i	−0.340651	−	0.199175i
$807$		0			0
$808$	4.18718	−	2.41747i	0.147304	−	0.0850463i
$809$	12.6664	+	21.9389i	0.445327	+	0.771329i	0.998075	−	0.0620195i	$-0.0197541\pi$
$809$	12.6664	+	21.9389i	0.445327	+	0.771329i	−0.552748	+	0.833348i	$0.686421\pi$
$810$		0			0
$811$			42.4806i			1.49170i	0.666117	+	0.745848i	$0.267955\pi$
$811$			42.4806i			1.49170i	−0.666117	+	0.745848i	$0.732045\pi$
$812$	9.80385	+	5.66025i	0.344048	+	0.198636i
$813$		0			0
$814$			25.1896i			0.882896i
$815$	2.08620	−	3.61341i	0.0730765	−	0.126572i
$816$		0			0
$817$	3.81119	−	2.20039i	0.133337	−	0.0769820i
$818$	38.3792			1.34190
$819$		0			0
$820$	−0.761018			−0.0265759
$821$	−15.3744	+	8.87640i	−0.536569	+	0.309789i	−0.743687	−	0.668527i	$-0.766925\pi$
$821$	−15.3744	+	8.87640i	−0.536569	+	0.309789i	0.207118	+	0.978316i	$0.433592\pi$
$822$		0			0
$823$	16.2840	−	28.2048i	0.567626	−	0.983157i	−0.429174	−	0.903222i	$-0.641195\pi$
$823$	16.2840	−	28.2048i	0.567626	−	0.983157i	0.996800	−	0.0799351i	$-0.0254713\pi$
$824$		−	5.73205i		−	0.199685i
$825$		0			0
$826$	4.31812	+	2.49307i	0.150247	+	0.0867449i
$827$		−	26.6419i		−	0.926429i	−0.886246	−	0.463215i	$-0.846696\pi$
$827$		−	26.6419i		−	0.926429i	0.886246	−	0.463215i	$-0.153304\pi$
$828$		0			0
$829$	−8.58281	−	14.8659i	−0.298093	−	0.516313i	0.677606	−	0.735425i	$-0.263017\pi$
$829$	−8.58281	−	14.8659i	−0.298093	−	0.516313i	−0.975700	+	0.219112i	$0.929684\pi$
$830$	−8.99511	+	5.19333i	−0.312225	+	0.180263i
$831$		0			0
$832$	−3.13234	+	1.78561i	−0.108595	+	0.0619050i
$833$	11.3719			0.394014
$834$		0			0
$835$	−7.80426	−	13.5174i	−0.270077	−	0.467788i
$836$	0.807519	−	1.39866i	0.0279286	−	0.0483738i
$837$		0			0
$838$	33.4192	+	19.2946i	1.15445	+	0.666520i
$839$	38.9951	+	22.5138i	1.34626	+	0.777264i	0.987718	−	0.156249i	$-0.0499403\pi$
$839$	38.9951	+	22.5138i	1.34626	+	0.777264i	0.358543	+	0.933513i	$0.383274\pi$
$840$		0			0
$841$	−16.4282	+	28.4545i	−0.566490	+	0.981189i
$842$	20.3100	+	35.1779i	0.699928	+	1.21231i
$843$		0			0
$844$	9.13381			0.314399
$845$	−11.1863	−	6.62316i	−0.384821	−	0.227844i
$846$		0			0
$847$	−6.62922	+	3.82738i	−0.227783	+	0.131510i
$848$	5.31246	+	9.20145i	0.182431	+	0.315979i
$849$		0			0
$850$			2.30752i			0.0791472i
$851$	8.42784	+	4.86582i	0.288903	+	0.166798i
$852$		0			0
$853$			31.0013i			1.06146i	0.847540	+	0.530731i	$0.178083\pi$
$853$			31.0013i			1.06146i	−0.847540	+	0.530731i	$0.821917\pi$
$854$	4.09680	−	7.09587i	0.140190	−	0.242816i
$855$		0			0
$856$	11.1505	−	6.43774i	0.381116	−	0.220038i
$857$	27.3813			0.935326			0.467663	−	0.883907i	$-0.345096\pi$
$857$	27.3813			0.935326			0.467663	+	0.883907i	$0.345096\pi$
$858$		0			0
$859$	8.36050			0.285256			0.142628	−	0.989776i	$-0.454445\pi$
$859$	8.36050			0.285256			0.142628	+	0.989776i	$0.454445\pi$
$860$	9.53264	−	5.50367i	0.325060	−	0.187674i
$861$		0			0
$862$	5.88581	−	10.1945i	0.200471	−	0.347227i
$863$		−	40.2398i		−	1.36978i	−0.728647	−	0.684889i	$-0.759850\pi$
$863$		−	40.2398i		−	1.36978i	0.728647	−	0.684889i	$-0.240150\pi$
$864$		0			0
$865$	5.03546	+	2.90723i	0.171211	+	0.0988486i
$866$		−	33.0008i		−	1.12141i
$867$		0			0
$868$	−2.23616	−	3.87314i	−0.0759002	−	0.131463i
$869$	−3.25860	+	1.88136i	−0.110541	+	0.0638206i
$870$		0			0
$871$	−18.9282	+	32.3731i	−0.641358	+	1.09692i
$872$	−0.214254			−0.00725557
$873$		0			0
$874$	−0.311973	−	0.540352i	−0.0105526	−	0.0182777i
$875$	0.719687	−	1.24653i	0.0243299	−	0.0421405i
$876$		0			0
$877$	−45.0918	−	26.0338i	−1.52264	−	0.879098i	−0.999642	−	0.0267652i	$-0.991479\pi$
$877$	−45.0918	−	26.0338i	−1.52264	−	0.879098i	−0.523000	−	0.852333i	$-0.675187\pi$
$878$	−0.603998	−	0.348718i	−0.0203839	−	0.0117687i
$879$		0			0
$880$	2.01978	−	3.49837i	0.0680869	−	0.117930i
$881$	17.2542	+	29.8852i	0.581310	+	1.00686i	0.995324	+	0.0965881i	$0.0307929\pi$
$881$	17.2542	+	29.8852i	0.581310	+	1.00686i	−0.414015	+	0.910270i	$0.635874\pi$
$882$		0			0
$883$	−28.2064			−0.949222			−0.474611	−	0.880196i	$-0.657411\pi$
$883$	−28.2064			−0.949222			−0.474611	+	0.880196i	$0.657411\pi$
$884$	7.18229	+	4.19941i	0.241567	+	0.141242i
$885$		0			0
$886$	24.7941	−	14.3149i	0.832973	−	0.480917i
$887$	1.06098	+	1.83768i	0.0356244	+	0.0617032i	0.883288	−	0.468831i	$-0.155325\pi$
$887$	1.06098	+	1.83768i	0.0356244	+	0.0617032i	−0.847664	+	0.530534i	$0.821991\pi$
$888$		0			0
$889$			23.2090i			0.778404i
$890$	0.840939	+	0.485517i	0.0281884	+	0.0162746i
$891$		0			0
$892$		−	5.81191i		−	0.194597i
$893$	1.16746	−	2.02210i	0.0390676	−	0.0676670i
$894$		0			0
$895$	14.6118	−	8.43611i	0.488418	−	0.281988i
$896$	−1.43937			−0.0480861
$897$		0			0
$898$	−6.78503			−0.226419
$899$	21.1632	−	12.2186i	0.705833	−	0.407513i
$900$		0			0
$901$	12.2586	−	21.2325i	0.408393	−	0.707358i
$902$		−	3.07418i		−	0.102359i
$903$		0			0
$904$	−0.111366	−	0.0642973i	−0.00370398	−	0.00213850i
$905$		−	12.6207i		−	0.419526i
$906$		0			0
$907$	14.7272	+	25.5082i	0.489007	+	0.846986i	0.999920	−	0.0126471i	$-0.00402580\pi$
$907$	14.7272	+	25.5082i	0.489007	+	0.846986i	−0.510913	+	0.859633i	$0.670692\pi$
$908$	9.99674	−	5.77162i	0.331753	−	0.191538i
$909$		0			0
$910$	−2.57017	−	4.50861i	−0.0852002	−	0.149459i
$911$	−19.9986			−0.662582			−0.331291	−	0.943529i	$-0.607484\pi$
$911$	−19.9986			−0.662582			−0.331291	+	0.943529i	$0.607484\pi$
$912$		0			0
$913$	−20.9788	−	36.3364i	−0.694297	−	1.20256i
$914$	−8.96940	+	15.5355i	−0.296681	+	0.513867i
$915$		0			0
$916$	−11.1505	−	6.43774i	−0.368423	−	0.212709i
$917$	3.46549	+	2.00080i	0.114440	+	0.0660722i
$918$		0			0
$919$	14.8564	−	25.7321i	0.490068	−	0.848822i	−0.509867	−	0.860253i	$-0.670305\pi$
$919$	14.8564	−	25.7321i	0.490068	−	0.848822i	0.999935	+	0.0114312i	$0.00363874\pi$
$920$	−0.780313	−	1.35154i	−0.0257262	−	0.0445590i
$921$		0			0
$922$	−26.8972			−0.885813
$923$	−21.6330	−	0.118708i	−0.712058	−	0.00390733i
$924$		0			0
$925$	5.40029	−	3.11786i	0.177561	−	0.102515i
$926$	−13.4201	−	23.2443i	−0.441011	−	0.763854i
$927$		0			0
$928$		−	7.86488i		−	0.258177i
$929$	7.99348	+	4.61504i	0.262258	+	0.151414i	0.625364	−	0.780333i	$-0.284951\pi$
$929$	7.99348	+	4.61504i	0.262258	+	0.151414i	−0.363106	+	0.931748i	$0.618284\pi$
$930$		0			0
$931$			1.97032i			0.0645745i
$932$	5.20745	−	9.01957i	0.170576	−	0.295446i
$933$		0			0
$934$	8.21621	−	4.74363i	0.268843	−	0.155216i
$935$	−9.32138			−0.304842
$936$		0			0
$937$	−4.58731			−0.149861			−0.0749305	−	0.997189i	$-0.523873\pi$
$937$	−4.58731			−0.149861			−0.0749305	+	0.997189i	$0.523873\pi$
$938$	−12.9649	+	7.48531i	−0.423320	+	0.244404i
$939$		0			0
$940$	2.92008	−	5.05772i	0.0952425	−	0.164965i
$941$		−	9.00734i		−	0.293631i	−0.989164	−	0.146815i	$-0.953098\pi$
$941$		−	9.00734i		−	0.293631i	0.989164	−	0.146815i	$-0.0469024\pi$
$942$		0			0
$943$	−1.02855	−	0.593832i	−0.0334941	−	0.0193378i
$944$		−	3.46410i		−	0.112747i
$945$		0			0
$946$	22.2325	+	38.5078i	0.722840	+	1.25200i
$947$	−47.3100	+	27.3144i	−1.53737	+	0.887600i	−0.538376	+	0.842705i	$0.680962\pi$
$947$	−47.3100	+	27.3144i	−1.53737	+	0.887600i	−0.998992	+	0.0448946i	$0.985705\pi$
$948$		0			0
$949$	24.0359	+	42.1640i	0.780237	+	1.36870i
$950$	−0.399804			−0.0129714
$951$		0			0
$952$	1.66069	+	2.87640i	0.0538233	+	0.0932247i
$953$	9.46862	−	16.4001i	0.306719	−	0.531252i	−0.670924	−	0.741526i	$-0.734102\pi$
$953$	9.46862	−	16.4001i	0.306719	−	0.531252i	0.977643	+	0.210274i	$0.0674356\pi$
$954$		0			0
$955$	−1.16110	−	0.670362i	−0.0375724	−	0.0216924i
$956$	−15.9177	−	9.19007i	−0.514814	−	0.297228i
$957$		0			0
$958$	5.60726	−	9.71206i	0.181162	−	0.313782i
$959$	−3.93479	−	6.81525i	−0.127061	−	0.220076i
$960$		0			0
$961$	21.3458			0.688573
$962$	0.123372	−	22.4829i	0.00397767	−	0.724877i
$963$		0			0
$964$	0.536681	−	0.309853i	0.0172853	−	0.00997970i
$965$	8.37182	+	14.5004i	0.269498	+	0.466785i
$966$		0			0
$967$		−	19.1583i		−	0.616089i	−0.951372	−	0.308044i	$-0.900325\pi$
$967$		−	19.1583i		−	0.616089i	0.951372	−	0.308044i	$-0.0996745\pi$
$968$	4.60563	+	2.65906i	0.148030	+	0.0854654i
$969$		0			0
$970$		−	12.3184i		−	0.395519i
$971$	11.1876	−	19.3775i	0.359027	−	0.621853i	−0.628772	−	0.777590i	$-0.716442\pi$
$971$	11.1876	−	19.3775i	0.359027	−	0.621853i	0.987799	+	0.155737i	$0.0497753\pi$
$972$		0			0
$973$	−0.267402	+	0.154385i	−0.00857253	+	0.00494935i
$974$	−27.7286			−0.888483
$975$		0			0
$976$	−5.69248			−0.182212
$977$	−3.91962	+	2.26299i	−0.125400	+	0.0723996i	−0.561388	−	0.827553i	$-0.689732\pi$
$977$	−3.91962	+	2.26299i	−0.125400	+	0.0723996i	0.435988	+	0.899952i	$0.356399\pi$
$978$		0			0
$979$	−1.96128	+	3.39703i	−0.0626827	+	0.108570i
$980$			4.92820i			0.157426i
$981$		0			0
$982$	24.1409	+	13.9377i	0.770366	+	0.444771i
$983$			12.1598i			0.387839i	0.981017	+	0.193919i	$0.0621200\pi$
$983$			12.1598i			0.387839i	−0.981017	+	0.193919i	$0.937880\pi$
$984$		0			0
$985$	0.498370	+	0.863202i	0.0158794	+	0.0275039i
$986$	−15.7169	+	9.07418i	−0.500530	+	0.288981i
$987$		0			0
$988$	−0.727597	+	1.24441i	−0.0231479	+	0.0395901i
$989$	17.1783			0.546240
$990$		0			0
$991$	28.1367	+	48.7341i	0.893790	+	1.54809i	0.835295	+	0.549802i	$0.185297\pi$
$991$	28.1367	+	48.7341i	0.893790	+	1.54809i	0.0584955	+	0.998288i	$0.481370\pi$
$992$	−1.55356	+	2.69085i	−0.0493257	+	0.0854346i
$993$		0			0
$994$	−7.47921	−	4.31812i	−0.237226	−	0.136962i
$995$	2.26469	+	1.30752i	0.0717955	+	0.0414511i
$996$		0			0
$997$	2.33056	−	4.03665i	0.0738097	−	0.127842i	−0.826758	−	0.562557i	$-0.809818\pi$
$997$	2.33056	−	4.03665i	0.0738097	−	0.127842i	0.900568	+	0.434715i	$0.143151\pi$
$998$	18.4020	+	31.8732i	0.582504	+	1.00893i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bs.g.361.1		8
3.2	odd	2		130.2.l.b.101.3	✓	8
12.11	even	2		1040.2.da.d.881.4		8
13.4	even	6	inner	1170.2.bs.g.901.1		8
15.2	even	4		650.2.n.e.49.1		8
15.8	even	4		650.2.n.d.49.4		8
15.14	odd	2		650.2.m.c.101.2		8
39.2	even	12		1690.2.a.u.1.4		4
39.5	even	4		1690.2.e.s.991.1		8
39.8	even	4		1690.2.e.t.991.1		8
39.11	even	12		1690.2.a.t.1.4		4
39.17	odd	6		130.2.l.b.121.3	yes	8
39.20	even	12		1690.2.e.t.191.1		8
39.23	odd	6		1690.2.d.k.1351.4		8
39.29	odd	6		1690.2.d.k.1351.8		8
39.32	even	12		1690.2.e.s.191.1		8
39.35	odd	6		1690.2.l.j.1161.1		8
39.38	odd	2		1690.2.l.j.361.1		8
156.95	even	6		1040.2.da.d.641.4		8
195.17	even	12		650.2.n.d.199.4		8
195.89	even	12		8450.2.a.cm.1.1		4
195.119	even	12		8450.2.a.ci.1.1		4
195.134	odd	6		650.2.m.c.251.2		8
195.173	even	12		650.2.n.e.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.3	✓	8	3.2	odd	2
130.2.l.b.121.3	yes	8	39.17	odd	6
650.2.m.c.101.2		8	15.14	odd	2
650.2.m.c.251.2		8	195.134	odd	6
650.2.n.d.49.4		8	15.8	even	4
650.2.n.d.199.4		8	195.17	even	12
650.2.n.e.49.1		8	15.2	even	4
650.2.n.e.199.1		8	195.173	even	12
1040.2.da.d.641.4		8	156.95	even	6
1040.2.da.d.881.4		8	12.11	even	2
1170.2.bs.g.361.1		8	1.1	even	1	trivial
1170.2.bs.g.901.1		8	13.4	even	6	inner
1690.2.a.t.1.4		4	39.11	even	12
1690.2.a.u.1.4		4	39.2	even	12
1690.2.d.k.1351.4		8	39.23	odd	6
1690.2.d.k.1351.8		8	39.29	odd	6
1690.2.e.s.191.1		8	39.32	even	12
1690.2.e.s.991.1		8	39.5	even	4
1690.2.e.t.191.1		8	39.20	even	12
1690.2.e.t.991.1		8	39.8	even	4
1690.2.l.j.361.1		8	39.38	odd	2
1690.2.l.j.1161.1		8	39.35	odd	6
8450.2.a.ci.1.1		4	195.119	even	12
8450.2.a.cm.1.1		4	195.89	even	12

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-1.24653 - 0.719687i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-3.49837 + 2.01978i) q^{11} +(3.13234 - 1.78561i) q^{13} +1.43937 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.15376 + 1.99837i) q^{17} +(-0.346241 - 0.199902i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(2.01978 - 3.49837i) q^{22} +(-0.780313 - 1.35154i) q^{23} -1.00000 q^{25} +(-1.81988 + 3.11256i) q^{26} +(-1.24653 + 0.719687i) q^{28} +(-3.93244 - 6.81119i) q^{29} +3.10713i q^{31} +(0.866025 + 0.500000i) q^{32} -2.30752i q^{34} +(-0.719687 + 1.24653i) q^{35} +(-5.40029 + 3.11786i) q^{37} +0.399804 q^{38} +1.00000 q^{40} +(0.659061 - 0.380509i) q^{41} +(-5.50367 + 9.53264i) q^{43} +4.03957i q^{44} +(1.35154 + 0.780313i) q^{46} +5.84016i q^{47} +(-2.46410 - 4.26795i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.0197847 - 3.60550i) q^{52} -10.6249 q^{53} +(2.01978 + 3.49837i) q^{55} +(0.719687 - 1.24653i) q^{56} +(6.81119 + 3.93244i) q^{58} +(3.00000 + 1.73205i) q^{59} +(2.84624 - 4.92983i) q^{61} +(-1.55356 - 2.69085i) q^{62} -1.00000 q^{64} +(-1.78561 - 3.13234i) q^{65} +(-9.00734 + 5.20039i) q^{67} +(1.15376 + 1.99837i) q^{68} -1.43937i q^{70} +(-5.19615 - 3.00000i) q^{71} +13.4608i q^{73} +(3.11786 - 5.40029i) q^{74} +(-0.346241 + 0.199902i) q^{76} +5.81445 q^{77} +0.931464 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.380509 + 0.659061i) q^{82} +10.3867i q^{83} +(1.99837 + 1.15376i) q^{85} -11.0073i q^{86} +(-2.01978 - 3.49837i) q^{88} +(0.840939 - 0.485517i) q^{89} +(-5.18966 - 0.0284776i) q^{91} -1.56063 q^{92} +(-2.92008 - 5.05772i) q^{94} +(-0.199902 + 0.346241i) q^{95} +(-10.6680 - 6.15919i) q^{97} +(4.26795 + 2.46410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{10} + 6 q^{11} - 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} + 6 q^{22} - 12 q^{23} - 8 q^{25} - 30 q^{37} + 12 q^{38} + 8 q^{40} - 12 q^{41} + 4 q^{43} + 8 q^{49} - 10 q^{52} - 60 q^{53}+ \cdots + 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^10 + 6 * q^11 - 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 + 6 * q^22 - 12 * q^23 - 8 * q^25 - 30 * q^37 + 12 * q^38 + 8 * q^40 - 12 * q^41 + 4 * q^43 + 8 * q^49 - 10 * q^52 - 60 * q^53 + 6 * q^55 + 24 * q^59 + 26 * q^61 - 18 * q^62 - 8 * q^64 - 6 * q^65 + 24 * q^67 + 6 * q^68 - 6 * q^74 - 6 * q^76 + 60 * q^77 + 20 * q^79 - 18 * q^85 - 6 * q^88 + 24 * q^89 - 66 * q^91 - 24 * q^92 - 6 * q^95 - 6 * q^97 + 48 * q^98

Introduction

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