LMFDB - Embedded newform 900.2.r.g.851.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(551,900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("900.551"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,2,0,0,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			851.16
Character	$\chi$	$=$	900.851
Dual form			900.2.r.g.551.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.645549 - 1.25828i) q^{2} +(-1.67915 - 0.424796i) q^{3} +(-1.16653 - 1.62456i) q^{4} +(-1.61849 + 1.83861i) q^{6} +(2.78632 - 1.60868i) q^{7} +(-2.79721 + 0.419091i) q^{8} +(2.63910 + 1.42659i) q^{9} +(-1.56397 - 2.70887i) q^{11} +(1.26868 + 3.22342i) q^{12} +(0.923481 - 1.59952i) q^{13} +(-0.225466 - 4.54445i) q^{14} +(-1.27840 + 3.79021i) q^{16} -5.85246i q^{17} +(3.49872 - 2.39978i) q^{18} +2.24186i q^{19} +(-5.36201 + 1.51760i) q^{21} +(-4.41814 + 0.219199i) q^{22} +(1.87409 - 3.24603i) q^{23} +(4.87496 + 0.484526i) q^{24} +(-1.41649 - 2.19456i) q^{26} +(-3.82543 - 3.51655i) q^{27} +(-5.86374 - 2.64996i) q^{28} +(-6.90237 + 3.98509i) q^{29} +(-1.03895 - 0.599838i) q^{31} +(3.94387 + 4.05535i) q^{32} +(1.47542 + 5.21298i) q^{33} +(-7.36403 - 3.77805i) q^{34} +(-0.761003 - 5.95154i) q^{36} -2.66428 q^{37} +(2.82088 + 1.44723i) q^{38} +(-2.23013 + 2.29354i) q^{39} +(-0.208259 - 0.120238i) q^{41} +(-1.55187 + 7.72659i) q^{42} +(-4.61084 + 2.66207i) q^{43} +(-2.57631 + 5.70075i) q^{44} +(-2.87459 - 4.45360i) q^{46} +(2.28989 + 3.96621i) q^{47} +(3.75669 - 5.82128i) q^{48} +(1.67571 - 2.90242i) q^{49} +(-2.48611 + 9.82717i) q^{51} +(-3.67578 + 0.365637i) q^{52} -13.0794i q^{53} +(-6.89430 + 2.54336i) q^{54} +(-7.11972 + 5.66754i) q^{56} +(0.952332 - 3.76441i) q^{57} +(0.558533 + 11.2577i) q^{58} +(-3.47411 + 6.01734i) q^{59} +(1.66785 + 2.88880i) q^{61} +(-1.42546 + 0.920065i) q^{62} +(9.64830 - 0.270519i) q^{63} +(7.64873 - 2.34457i) q^{64} +(7.51183 + 1.50874i) q^{66} +(7.48148 + 4.31943i) q^{67} +(-9.50769 + 6.82709i) q^{68} +(-4.52579 + 4.65446i) q^{69} -11.3298 q^{71} +(-7.97997 - 2.88446i) q^{72} -13.1688 q^{73} +(-1.71992 + 3.35240i) q^{74} +(3.64203 - 2.61520i) q^{76} +(-8.71543 - 5.03186i) q^{77} +(1.44625 + 4.28672i) q^{78} +(11.6449 - 6.72318i) q^{79} +(4.92966 + 7.52984i) q^{81} +(-0.285735 + 0.184428i) q^{82} +(-0.623311 - 1.07961i) q^{83} +(8.72040 + 6.94058i) q^{84} +(0.373105 + 7.52023i) q^{86} +(13.2830 - 3.75946i) q^{87} +(5.51001 + 6.92183i) q^{88} -14.3274i q^{89} -5.94235i q^{91} +(-7.45956 + 0.742017i) q^{92} +(1.48975 + 1.44856i) q^{93} +(6.46884 - 0.320942i) q^{94} +(-4.89966 - 8.48489i) q^{96} +(-3.32238 - 5.75453i) q^{97} +(-2.57030 - 3.98217i) q^{98} +(-0.263000 - 9.38013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.645549	−	1.25828i	0.456472	−	0.889738i
$2$	0.645549	−	1.25828i	0.456472	−	0.889738i
$3$	−1.67915	−	0.424796i	−0.969458	−	0.245256i
$3$	−1.67915	−	0.424796i	−0.969458	−	0.245256i
$4$	−1.16653	−	1.62456i	−0.583267	−	0.812281i
$5$		0			0
$5$		0			0
$6$	−1.61849	+	1.83861i	−0.660744	+	0.750611i
$7$	2.78632	−	1.60868i	1.05313	−	0.608024i	0.129606	−	0.991566i	$-0.458629\pi$
$7$	2.78632	−	1.60868i	1.05313	−	0.608024i	0.923524	+	0.383541i	$0.125296\pi$
$8$	−2.79721	+	0.419091i	−0.988962	+	0.148171i
$9$	2.63910	+	1.42659i	0.879699	+	0.475532i
$10$		0			0
$11$	−1.56397	−	2.70887i	−0.471554	−	0.816756i	0.527916	−	0.849297i	$-0.322974\pi$
$11$	−1.56397	−	2.70887i	−0.471554	−	0.816756i	−0.999470	+	0.0325405i	$0.989640\pi$
$12$	1.26868	+	3.22342i	0.366236	+	0.930522i
$13$	0.923481	−	1.59952i	0.256128	−	0.443626i	−0.709074	−	0.705134i	$-0.750887\pi$
$13$	0.923481	−	1.59952i	0.256128	−	0.443626i	0.965201	+	0.261509i	$0.0842200\pi$
$14$	−0.225466	−	4.54445i	−0.0602584	−	1.21456i
$15$		0			0
$16$	−1.27840	+	3.79021i	−0.319600	+	0.947553i
$17$		−	5.85246i		−	1.41943i	−0.704488	−	0.709715i	$-0.748823\pi$
$17$		−	5.85246i		−	1.41943i	0.704488	−	0.709715i	$-0.251177\pi$
$18$	3.49872	−	2.39978i	0.824656	−	0.565634i
$19$			2.24186i			0.514317i	0.966369	+	0.257158i	$0.0827862\pi$
$19$			2.24186i			0.514317i	−0.966369	+	0.257158i	$0.917214\pi$
$20$		0			0
$21$	−5.36201	+	1.51760i	−1.17009	+	0.331168i
$22$	−4.41814	+	0.219199i	−0.941950	+	0.0467335i
$23$	1.87409	−	3.24603i	0.390776	−	0.676843i	−0.601776	−	0.798665i	$-0.705540\pi$
$23$	1.87409	−	3.24603i	0.390776	−	0.676843i	0.992552	+	0.121821i	$0.0388735\pi$
$24$	4.87496	+	0.484526i	0.995097	+	0.0989034i
$25$		0			0
$26$	−1.41649	−	2.19456i	−0.277796	−	0.430389i
$27$	−3.82543	−	3.51655i	−0.736204	−	0.676760i
$28$	−5.86374	−	2.64996i	−1.10814	−	0.500796i
$29$	−6.90237	+	3.98509i	−1.28174	+	0.740012i	−0.977166	−	0.212478i	$-0.931847\pi$
$29$	−6.90237	+	3.98509i	−1.28174	+	0.740012i	−0.304572	+	0.952489i	$0.598513\pi$
$30$		0			0
$31$	−1.03895	−	0.599838i	−0.186601	−	0.107734i	0.403789	−	0.914852i	$-0.367693\pi$
$31$	−1.03895	−	0.599838i	−0.186601	−	0.107734i	−0.590390	+	0.807118i	$0.701026\pi$
$32$	3.94387	+	4.05535i	0.697185	+	0.716891i
$33$	1.47542	+	5.21298i	0.256838	+	0.907463i
$34$	−7.36403	−	3.77805i	−1.26292	−	0.647930i
$35$		0			0
$36$	−0.761003	−	5.95154i	−0.126834	−	0.991924i
$37$	−2.66428			−0.438004			−0.219002	−	0.975724i	$-0.570280\pi$
$37$	−2.66428			−0.438004			−0.219002	+	0.975724i	$0.570280\pi$
$38$	2.82088	+	1.44723i	0.457607	+	0.234771i
$39$	−2.23013	+	2.29354i	−0.357107	+	0.367260i
$40$		0			0
$41$	−0.208259	−	0.120238i	−0.0325246	−	0.0187781i	0.483650	−	0.875262i	$-0.339311\pi$
$41$	−0.208259	−	0.120238i	−0.0325246	−	0.0187781i	−0.516174	+	0.856484i	$0.672644\pi$
$42$	−1.55187	+	7.72659i	−0.239459	+	1.19224i
$43$	−4.61084	+	2.66207i	−0.703147	+	0.405962i	−0.808519	−	0.588471i	$-0.799730\pi$
$43$	−4.61084	+	2.66207i	−0.703147	+	0.405962i	0.105371	+	0.994433i	$0.466397\pi$
$44$	−2.57631	+	5.70075i	−0.388393	+	0.859421i
$45$		0			0
$46$	−2.87459	−	4.45360i	−0.423835	−	0.656648i
$47$	2.28989	+	3.96621i	0.334015	+	0.578532i	0.983295	−	0.182018i	$-0.0582629\pi$
$47$	2.28989	+	3.96621i	0.334015	+	0.578532i	−0.649280	+	0.760550i	$0.724930\pi$
$48$	3.75669	−	5.82128i	0.542232	−	0.840229i
$49$	1.67571	−	2.90242i	0.239388	−	0.414631i
$50$		0			0
$51$	−2.48611	+	9.82717i	−0.348124	+	1.37608i
$52$	−3.67578	+	0.365637i	−0.509739	+	0.0507048i
$53$		−	13.0794i		−	1.79659i	−0.439391	−	0.898296i	$-0.644806\pi$
$53$		−	13.0794i		−	1.79659i	0.439391	−	0.898296i	$-0.355194\pi$
$54$	−6.89430	+	2.54336i	−0.938195	+	0.346107i
$55$		0			0
$56$	−7.11972	+	5.66754i	−0.951413	+	0.757356i
$57$	0.952332	−	3.76441i	0.126139	−	0.498609i
$58$	0.558533	+	11.2577i	0.0733390	+	1.47821i
$59$	−3.47411	+	6.01734i	−0.452291	+	0.783391i	−0.998528	−	0.0542396i	$-0.982727\pi$
$59$	−3.47411	+	6.01734i	−0.452291	+	0.783391i	0.546237	+	0.837631i	$0.316060\pi$
$60$		0			0
$61$	1.66785	+	2.88880i	0.213546	+	0.369873i	0.952822	−	0.303530i	$-0.0981653\pi$
$61$	1.66785	+	2.88880i	0.213546	+	0.369873i	−0.739276	+	0.673403i	$0.764832\pi$
$62$	−1.42546	+	0.920065i	−0.181033	+	0.116848i
$63$	9.64830	−	0.270519i	1.21557	−	0.0340822i
$64$	7.64873	−	2.34457i	0.956091	−	0.293071i
$65$		0			0
$66$	7.51183	+	1.50874i	0.924643	+	0.185713i
$67$	7.48148	+	4.31943i	0.914008	+	0.527703i	0.881718	−	0.471776i	$-0.156387\pi$
$67$	7.48148	+	4.31943i	0.914008	+	0.527703i	0.0322893	+	0.999479i	$0.489720\pi$
$68$	−9.50769	+	6.82709i	−1.15298	+	0.827907i
$69$	−4.52579	+	4.65446i	−0.544841	+	0.560331i
$70$		0			0
$71$	−11.3298			−1.34460			−0.672300	−	0.740278i	$-0.734694\pi$
$71$	−11.3298			−1.34460			−0.672300	+	0.740278i	$0.734694\pi$
$72$	−7.97997	−	2.88446i	−0.940448	−	0.339937i
$73$	−13.1688			−1.54130			−0.770648	−	0.637261i	$-0.780067\pi$
$73$	−13.1688			−1.54130			−0.770648	+	0.637261i	$0.780067\pi$
$74$	−1.71992	+	3.35240i	−0.199937	+	0.389709i
$75$		0			0
$76$	3.64203	−	2.61520i	0.417770	−	0.299984i
$77$	−8.71543	−	5.03186i	−0.993215	−	0.573433i
$78$	1.44625	+	4.28672i	0.163756	+	0.485375i
$79$	11.6449	−	6.72318i	1.31015	−	0.756416i	0.328031	−	0.944667i	$-0.393615\pi$
$79$	11.6449	−	6.72318i	1.31015	−	0.756416i	0.982121	+	0.188251i	$0.0602817\pi$
$80$		0			0
$81$	4.92966	+	7.52984i	0.547740	+	0.836649i
$82$	−0.285735	+	0.184428i	−0.0315541	+	0.0203667i
$83$	−0.623311	−	1.07961i	−0.0684172	−	0.118502i	0.829788	−	0.558079i	$-0.188462\pi$
$83$	−0.623311	−	1.07961i	−0.0684172	−	0.118502i	−0.898205	+	0.439577i	$0.855128\pi$
$84$	8.72040	+	6.94058i	0.951474	+	0.757280i
$85$		0			0
$86$	0.373105	+	7.52023i	0.0402330	+	0.810927i
$87$	13.2830	−	3.75946i	1.42408	−	0.403056i
$88$	5.51001	+	6.92183i	0.587369	+	0.737870i
$89$		−	14.3274i		−	1.51871i	−0.650679	−	0.759353i	$-0.725516\pi$
$89$		−	14.3274i		−	1.51871i	0.650679	−	0.759353i	$-0.274484\pi$
$90$		0			0
$91$		−	5.94235i		−	0.622927i
$92$	−7.45956	+	0.742017i	−0.777713	+	0.0773607i
$93$	1.48975	+	1.44856i	0.154479	+	0.150209i
$94$	6.46884	−	0.320942i	0.667210	−	0.0331027i
$95$		0			0
$96$	−4.89966	−	8.48489i	−0.500070	−	0.865985i
$97$	−3.32238	−	5.75453i	−0.337337	−	0.584284i	0.646594	−	0.762834i	$-0.276193\pi$
$97$	−3.32238	−	5.75453i	−0.337337	−	0.584284i	−0.983931	+	0.178550i	$0.942859\pi$
$98$	−2.57030	−	3.98217i	−0.259640	−	0.402260i
$99$	−0.263000	−	9.38013i	−0.0264325	−	0.942738i
$100$		0			0
$101$	4.33548	−	2.50309i	0.431397	−	0.249067i	−0.268545	−	0.963267i	$-0.586543\pi$
$101$	4.33548	−	2.50309i	0.431397	−	0.249067i	0.699941	+	0.714200i	$0.253209\pi$
$102$	10.7604	+	9.47213i	1.06544	+	0.937881i
$103$	12.8787	+	7.43554i	1.26898	+	0.732646i	0.974795	−	0.223103i	$-0.0716186\pi$
$103$	12.8787	+	7.43554i	1.26898	+	0.732646i	0.294185	+	0.955749i	$0.404952\pi$
$104$	−1.91282	+	4.86120i	−0.187568	+	0.476680i
$105$		0			0
$106$	−16.4575	−	8.44338i	−1.59850	−	0.820094i
$107$	−2.95929			−0.286085			−0.143042	−	0.989717i	$-0.545689\pi$
$107$	−2.95929			−0.286085			−0.143042	+	0.989717i	$0.545689\pi$
$108$	−1.25035	+	10.3168i	−0.120315	+	0.992736i
$109$	3.71238			0.355582			0.177791	−	0.984068i	$-0.443105\pi$
$109$	3.71238			0.355582			0.177791	+	0.984068i	$0.443105\pi$
$110$		0			0
$111$	4.47372	+	1.13177i	0.424627	+	0.107423i
$112$	2.53521	+	12.6173i	0.239555	+	1.19222i
$113$	−0.652093	−	0.376486i	−0.0613437	−	0.0354168i	0.469014	−	0.883190i	$-0.344609\pi$
$113$	−0.652093	−	0.376486i	−0.0613437	−	0.0354168i	−0.530358	+	0.847774i	$0.677943\pi$
$114$	−4.12191	−	3.62841i	−0.386052	−	0.339832i
$115$		0			0
$116$	14.5259	+	6.56459i	1.34869	+	0.609507i
$117$	4.71902	−	2.90384i	0.436273	−	0.268460i
$118$	5.32879	+	8.25589i	0.490555	+	0.760017i
$119$	−9.41475	−	16.3068i	−0.863049	−	1.49484i
$120$		0			0
$121$	0.608004	−	1.05309i	0.0552731	−	0.0957358i
$122$	4.71159	−	0.233759i	0.426567	−	0.0211635i
$123$	0.298622	+	0.290366i	0.0269258	+	0.0261814i
$124$	0.237496	+	2.38757i	0.0213278	+	0.214410i
$125$		0			0
$126$	5.88806	−	12.3149i	0.524550	−	1.09710i
$127$		−	6.08119i		−	0.539619i	−0.962914	−	0.269809i	$-0.913039\pi$
$127$		−	6.08119i		−	0.539619i	0.962914	−	0.269809i	$-0.0869606\pi$
$128$	1.98750	−	11.1378i	0.175672	−	0.984449i
$129$	8.87314	−	2.51135i	0.781237	−	0.221112i
$130$		0			0
$131$	4.89535	−	8.47899i	0.427709	−	0.740813i	−0.568961	−	0.822365i	$-0.692654\pi$
$131$	4.89535	−	8.47899i	0.427709	−	0.740813i	0.996669	+	0.0815519i	$0.0259876\pi$
$132$	6.74767	−	8.47802i	0.587309	−	0.737917i
$133$	3.60643	+	6.24652i	0.312717	+	0.541642i
$134$	10.2647	−	6.62538i	0.886736	−	0.572346i
$135$		0			0
$136$	2.45272	+	16.3705i	0.210319	+	1.40376i
$137$	4.91309	−	2.83657i	0.419753	−	0.242345i	−0.275218	−	0.961382i	$-0.588750\pi$
$137$	4.91309	−	2.83657i	0.419753	−	0.242345i	0.694972	+	0.719037i	$0.255417\pi$
$138$	2.93499	+	8.69939i	0.249843	+	0.740541i
$139$	−7.99193	−	4.61414i	−0.677866	−	0.391366i	0.121184	−	0.992630i	$-0.461331\pi$
$139$	−7.99193	−	4.61414i	−0.677866	−	0.391366i	−0.799051	+	0.601264i	$0.794664\pi$
$140$		0			0
$141$	−2.16025	−	7.63261i	−0.181925	−	0.642782i
$142$	−7.31394	+	14.2561i	−0.613773	+	1.19634i
$143$	−5.77718			−0.483112
$144$	−8.78091	+	8.17897i	−0.731743	+	0.681581i
$145$		0			0
$146$	−8.50113	+	16.5701i	−0.703558	+	1.37135i
$147$	−4.04671	+	4.16176i	−0.333767	+	0.343257i
$148$	3.10797	+	4.32828i	0.255473	+	0.355782i
$149$	9.77937	+	5.64612i	0.801157	+	0.462548i	0.843876	−	0.536539i	$-0.180269\pi$
$149$	9.77937	+	5.64612i	0.801157	+	0.462548i	−0.0427186	+	0.999087i	$0.513602\pi$
$150$		0			0
$151$	18.6166	−	10.7483i	1.51500	−	0.874686i	0.515156	−	0.857096i	$-0.327734\pi$
$151$	18.6166	−	10.7483i	1.51500	−	0.874686i	0.999845	−	0.0175900i	$-0.00559935\pi$
$152$	−0.939542	−	6.27093i	−0.0762069	−	0.508640i
$153$	8.34909	−	15.4452i	0.674984	−	1.24867i
$154$	−11.9577	+	7.71814i	−0.963580	+	0.621945i
$155$		0			0
$156$	6.32752	+	0.947499i	0.506607	+	0.0758606i
$157$	−0.597759	+	1.03535i	−0.0477064	+	0.0826299i	−0.888893	−	0.458116i	$-0.848525\pi$
$157$	−0.597759	+	1.03535i	−0.0477064	+	0.0826299i	0.841186	+	0.540746i	$0.181858\pi$
$158$	−0.942293	−	18.9927i	−0.0749648	−	1.51097i
$159$	−5.55607	+	21.9623i	−0.440625	+	1.74172i
$160$		0			0
$161$		−	12.0593i		−	0.950405i
$162$	12.6570	−	1.34200i	0.994426	−	0.105438i
$163$		−	12.8215i		−	1.00426i	−0.864793	−	0.502128i	$-0.832550\pi$
$163$		−	12.8215i		−	1.00426i	0.864793	−	0.502128i	$-0.167450\pi$
$164$	0.0476065	+	0.478592i	0.00371744	+	0.0373717i
$165$		0			0
$166$	−1.76082	+	0.0873607i	−0.136666	+	0.00678050i
$167$	5.56047	−	9.63102i	0.430282	−	0.745271i	−0.566615	−	0.823983i	$-0.691747\pi$
$167$	5.56047	−	9.63102i	0.430282	−	0.745271i	0.996897	+	0.0787119i	$0.0250807\pi$
$168$	14.3626	−	6.49222i	1.10810	−	0.500885i
$169$	4.79437	+	8.30409i	0.368797	+	0.638776i
$170$		0			0
$171$	−3.19822	+	5.91647i	−0.244574	+	0.452444i
$172$	9.70341	+	4.38520i	0.739878	+	0.334369i
$173$	0.663076	−	0.382827i	0.0504128	−	0.0291058i	−0.474582	−	0.880211i	$-0.657401\pi$
$173$	0.663076	−	0.382827i	0.0504128	−	0.0291058i	0.524995	+	0.851106i	$0.324067\pi$
$174$	3.84436	−	19.1406i	0.291440	−	1.45105i
$175$		0			0
$176$	12.2666	−	2.46475i	0.924628	−	0.185787i
$177$	8.38971	−	8.62824i	0.630609	−	0.648538i
$178$	−18.0279	−	9.24906i	−1.35125	−	0.693247i
$179$	11.3200			0.846095			0.423048	−	0.906107i	$-0.360960\pi$
$179$	11.3200			0.846095			0.423048	+	0.906107i	$0.360960\pi$
$180$		0			0
$181$	3.20266			0.238052			0.119026	−	0.992891i	$-0.462023\pi$
$181$	3.20266			0.238052			0.119026	+	0.992891i	$0.462023\pi$
$182$	−7.47713	−	3.83607i	−0.554242	−	0.284349i
$183$	−1.57342	−	5.55922i	−0.116310	−	0.410950i
$184$	−3.88185	+	9.86522i	−0.286174	+	0.727274i
$185$		0			0
$186$	2.78440	−	0.939399i	0.204162	−	0.0688800i
$187$	−15.8536	+	9.15307i	−1.15933	+	0.669339i
$188$	3.77212	−	8.34679i	0.275110	−	0.608753i
$189$	−16.3159	−	3.64432i	−1.18680	−	0.265085i
$190$		0			0
$191$	−0.889821	−	1.54121i	−0.0643852	−	0.111518i	0.832036	−	0.554722i	$-0.187175\pi$
$191$	−0.889821	−	1.54121i	−0.0643852	−	0.111518i	−0.896421	+	0.443203i	$0.853842\pi$
$192$	−13.8393	+	0.687734i	−0.998768	+	0.0496329i
$193$	−7.07295	+	12.2507i	−0.509122	+	0.881825i	0.490822	+	0.871260i	$0.336697\pi$
$193$	−7.07295	+	12.2507i	−0.509122	+	0.881825i	−0.999944	+	0.0105656i	$0.996637\pi$
$194$	−9.38557	+	0.465651i	−0.673845	+	0.0334318i
$195$		0			0
$196$	−6.66993	+	0.663471i	−0.476424	+	0.0473908i
$197$			8.50994i			0.606308i	0.952942	+	0.303154i	$0.0980396\pi$
$197$			8.50994i			0.606308i	−0.952942	+	0.303154i	$0.901960\pi$
$198$	−11.9726	−	5.72440i	−0.850855	−	0.406816i
$199$			3.02029i			0.214103i	0.994253	+	0.107052i	$0.0341410\pi$
$199$			3.02029i			0.214103i	−0.994253	+	0.107052i	$0.965859\pi$
$200$		0			0
$201$	−10.7276	−	10.4311i	−0.756670	−	0.735752i
$202$	−0.350823	−	7.07112i	−0.0246838	−	0.497522i
$203$	−12.8215	+	22.2074i	−0.899891	+	1.55866i
$204$	18.8650	−	7.42489i	1.32081	−	0.519846i
$205$		0			0
$206$	17.6698	−	11.4050i	1.23112	−	0.794627i
$207$	9.57668	−	5.89300i	0.665625	−	0.409592i
$208$	4.88192	+	5.54501i	0.338501	+	0.384477i
$209$	6.07290	−	3.50619i	0.420071	−	0.242528i
$210$		0			0
$211$	20.9510	+	12.0961i	1.44233	+	0.832729i	0.998005	−	0.0631364i	$-0.0201103\pi$
$211$	20.9510	+	12.0961i	1.44233	+	0.832729i	0.444325	+	0.895866i	$0.353444\pi$
$212$	−21.2483	+	15.2575i	−1.45934	+	1.04789i
$213$	19.0245	+	4.81286i	1.30353	+	0.329772i
$214$	−1.91036	+	3.72361i	−0.130590	+	0.254541i
$215$		0			0
$216$	12.1743	+	8.23330i	0.828354	+	0.560205i
$217$	−3.85979			−0.262020
$218$	2.39652	−	4.67121i	0.162313	−	0.316374i
$219$	22.1125	+	5.59407i	1.49422	+	0.378012i
$220$		0			0
$221$	−9.36111	−	5.40464i	−0.629696	−	0.363555i
$222$	4.31209	−	4.89858i	0.289409	−	0.328771i
$223$	−2.32763	+	1.34386i	−0.155869	+	0.0899912i	−0.575906	−	0.817516i	$-0.695351\pi$
$223$	−2.32763	+	1.34386i	−0.155869	+	0.0899912i	0.420037	+	0.907507i	$0.362017\pi$
$224$	17.5127	+	4.95506i	1.17011	+	0.331074i
$225$		0			0
$226$	−0.894682	+	0.577475i	−0.0595134	+	0.0384130i
$227$	−5.37905	−	9.31679i	−0.357020	−	0.618377i	0.630441	−	0.776237i	$-0.282874\pi$
$227$	−5.37905	−	9.31679i	−0.357020	−	0.618377i	−0.987462	+	0.157860i	$0.949541\pi$
$228$	−7.22645	+	2.84419i	−0.478583	+	0.188361i
$229$	−1.29262	+	2.23888i	−0.0854185	+	0.147949i	−0.905569	−	0.424198i	$-0.860556\pi$
$229$	−1.29262	+	2.23888i	−0.0854185	+	0.147949i	0.820151	+	0.572147i	$0.193889\pi$
$230$		0			0
$231$	12.4970	+	12.1515i	0.822243	+	0.799512i
$232$	17.6372	−	14.0398i	1.15794	−	0.921760i
$233$		−	0.981108i		−	0.0642746i	−0.999483	−	0.0321373i	$-0.989769\pi$
$233$		−	0.981108i		−	0.0642746i	0.999483	−	0.0321373i	$-0.0102314\pi$
$234$	−0.607491	−	7.81241i	−0.0397129	−	0.510713i
$235$		0			0
$236$	13.8282	−	1.37552i	0.900140	−	0.0895387i
$237$	−22.4095	+	6.34252i	−1.45565	+	0.411991i
$238$	−26.5962	+	1.31953i	−1.72398	+	0.0855326i
$239$	−3.85799	+	6.68223i	−0.249552	+	0.432238i	−0.963402	−	0.268062i	$-0.913617\pi$
$239$	−3.85799	+	6.68223i	−0.249552	+	0.432238i	0.713849	+	0.700299i	$0.246950\pi$
$240$		0			0
$241$	12.0087	+	20.7997i	0.773549	+	1.33983i	0.935606	+	0.353045i	$0.114854\pi$
$241$	12.0087	+	20.7997i	0.773549	+	1.33983i	−0.162058	+	0.986781i	$0.551813\pi$
$242$	−0.932590	−	1.44486i	−0.0599491	−	0.0928793i
$243$	−5.07899	−	14.7378i	−0.325817	−	0.945433i
$244$	2.74743	−	6.07940i	0.175886	−	0.389194i
$245$		0			0
$246$	0.558137	−	0.188304i	0.0355855	−	0.0120058i
$247$	3.58588	+	2.07031i	0.228164	+	0.131731i
$248$	3.15754	+	1.24246i	0.200504	+	0.0788961i
$249$	0.588020	+	2.07760i	0.0372643	+	0.131663i
$250$		0			0
$251$	−18.6357			−1.17628			−0.588138	−	0.808761i	$-0.700139\pi$
$251$	−18.6357			−1.17628			−0.588138	+	0.808761i	$0.700139\pi$
$252$	−11.6945	−	15.3587i	−0.736687	−	0.967506i
$253$	−11.7241			−0.737088
$254$	−7.65184	−	3.92571i	−0.480119	−	0.246321i
$255$		0			0
$256$	−12.7314	−	9.69081i	−0.795712	−	0.605675i
$257$	6.57278	+	3.79480i	0.409999	+	0.236713i	0.690789	−	0.723056i	$-0.257263\pi$
$257$	6.57278	+	3.79480i	0.409999	+	0.236713i	−0.280790	+	0.959769i	$0.590597\pi$
$258$	2.56807	−	12.7861i	0.159881	−	0.796027i
$259$	−7.42352	+	4.28597i	−0.461275	+	0.266317i
$260$		0			0
$261$	−23.9011	+	0.670139i	−1.47944	+	0.0414806i
$262$	−7.50875	−	11.6333i	−0.463892	−	0.718709i
$263$	−6.69385	−	11.5941i	−0.412760	−	0.714922i	0.582430	−	0.812881i	$-0.302102\pi$
$263$	−6.69385	−	11.5941i	−0.412760	−	0.714922i	−0.995190	+	0.0979587i	$0.968769\pi$
$264$	−6.31177	−	13.9634i	−0.388462	−	0.859390i
$265$		0			0
$266$	10.1880	−	0.505463i	0.624666	−	0.0309919i
$267$	−6.08625	+	24.0579i	−0.372472	+	1.47232i
$268$	−1.71021	−	17.1929i	−0.104468	−	1.05022i
$269$			3.84328i			0.234329i	0.993113	+	0.117164i	$0.0373805\pi$
$269$			3.84328i			0.234329i	−0.993113	+	0.117164i	$0.962620\pi$
$270$		0			0
$271$		−	8.94629i		−	0.543448i	−0.962375	−	0.271724i	$-0.912406\pi$
$271$		−	8.94629i		−	0.543448i	0.962375	−	0.271724i	$-0.0875939\pi$
$272$	22.1821	+	7.48179i	1.34499	+	0.453650i
$273$	−2.52429	+	9.97810i	−0.152777	+	0.603902i
$274$	−0.397562	−	8.01318i	−0.0240176	−	0.484094i
$275$		0			0
$276$	12.8409	+	1.92284i	0.772934	+	0.115741i
$277$	5.53218	+	9.58202i	0.332396	+	0.575728i	0.982981	−	0.183706i	$-0.0588095\pi$
$277$	5.53218	+	9.58202i	0.332396	+	0.575728i	−0.650585	+	0.759434i	$0.725476\pi$
$278$	−10.9651	+	7.07742i	−0.657640	+	0.424476i
$279$	−1.88616	−	3.06519i	−0.112922	−	0.183508i
$280$		0			0
$281$	25.4234	−	14.6782i	1.51663	−	0.875628i	0.516822	−	0.856093i	$-0.327115\pi$
$281$	25.4234	−	14.6782i	1.51663	−	0.875628i	0.999809	−	0.0195348i	$-0.00621853\pi$
$282$	−10.9985	−	2.20903i	−0.654951	−	0.131546i
$283$	4.32753	+	2.49850i	0.257245	+	0.148520i	0.623077	−	0.782160i	$-0.285882\pi$
$283$	4.32753	+	2.49850i	0.257245	+	0.148520i	−0.365832	+	0.930681i	$0.619216\pi$
$284$	13.2166	+	18.4060i	0.784261	+	1.09219i
$285$		0			0
$286$	−3.72945	+	7.26931i	−0.220527	+	0.429843i
$287$	−0.773702			−0.0456702
$288$	4.62292	+	16.3288i	0.272408	+	0.962182i
$289$	−17.2513			−1.01478
$290$		0			0
$291$	3.13428	+	11.0741i	0.183734	+	0.649173i
$292$	15.3619	+	21.3936i	0.898986	+	1.25196i
$293$	−8.15253	−	4.70687i	−0.476276	−	0.274978i	0.242587	−	0.970130i	$-0.422004\pi$
$293$	−8.15253	−	4.70687i	−0.476276	−	0.274978i	−0.718863	+	0.695151i	$0.755337\pi$
$294$	2.62431	+	7.77852i	0.153053	+	0.453652i
$295$		0			0
$296$	7.45253	−	1.11657i	0.433169	−	0.0648996i
$297$	−3.54303	+	15.8624i	−0.205587	+	0.920428i
$298$	13.4175	−	8.66033i	0.777252	−	0.501679i
$299$	−3.46138	−	5.99529i	−0.200177	−	0.346716i
$300$		0			0
$301$	−8.56485	+	14.8348i	−0.493670	+	0.855062i
$302$	−1.50644	−	30.3635i	−0.0866860	−	1.74722i
$303$	−8.34324	+	2.36137i	−0.479306	+	0.135657i
$304$	−8.49710	−	2.86599i	−0.487342	−	0.164376i
$305$		0			0
$306$	−14.0446	−	20.4761i	−0.802879	−	1.17054i
$307$		−	18.3474i		−	1.04714i	−0.851982	−	0.523571i	$-0.824600\pi$
$307$		−	18.3474i		−	1.04714i	0.851982	−	0.523571i	$-0.175400\pi$
$308$	1.99228	+	20.0286i	0.113521	+	1.14123i
$309$	−18.4668	−	17.9562i	−1.05054	−	1.02149i
$310$		0			0
$311$	−15.6249	+	27.0632i	−0.886009	+	1.53461i	−0.0414569	+	0.999140i	$0.513200\pi$
$311$	−15.6249	+	27.0632i	−0.886009	+	1.53461i	−0.844552	+	0.535473i	$0.820133\pi$
$312$	5.27694	−	7.35012i	0.298748	−	0.416119i
$313$	2.56596	+	4.44437i	0.145037	+	0.251211i	0.929387	−	0.369108i	$-0.120337\pi$
$313$	2.56596	+	4.44437i	0.145037	+	0.251211i	−0.784350	+	0.620318i	$0.787003\pi$
$314$	0.916876	+	1.42052i	0.0517423	+	0.0801644i
$315$		0			0
$316$	−24.5064	−	11.0750i	−1.37859	−	0.623018i
$317$	12.8315	−	7.40826i	0.720688	−	0.416089i	−0.0943181	−	0.995542i	$-0.530067\pi$
$317$	12.8315	−	7.40826i	0.720688	−	0.416089i	0.815006	+	0.579453i	$0.196734\pi$
$318$	24.0479	+	21.1688i	1.34854	+	1.18709i
$319$	21.5902	+	12.4651i	1.20882	+	0.697911i
$320$		0			0
$321$	4.96909	+	1.25709i	0.277347	+	0.0701641i
$322$	−15.1740	−	7.78486i	−0.845611	−	0.433833i
$323$	13.1204			0.730037
$324$	6.48208	−	16.7923i	0.360115	−	0.932908i
$325$		0			0
$326$	−16.1330	−	8.27690i	−0.893525	−	0.458415i
$327$	−6.23365	−	1.57701i	−0.344722	−	0.0872086i
$328$	0.632935	+	0.249052i	0.0349480	+	0.0137516i
$329$	12.7607	+	7.36742i	0.703523	+	0.406179i
$330$		0			0
$331$	22.0656	−	12.7396i	1.21283	−	0.700230i	0.249458	−	0.968386i	$-0.419747\pi$
$331$	22.0656	−	12.7396i	1.21283	−	0.700230i	0.963376	+	0.268156i	$0.0864141\pi$
$332$	−1.02677	+	2.27200i	−0.0563515	+	0.124692i
$333$	−7.03128	−	3.80084i	−0.385312	−	0.208285i
$334$	−8.52896	−	13.2139i	−0.466684	−	0.723033i
$335$		0			0
$336$	1.10276	−	22.2633i	0.0601607	−	1.21456i
$337$	2.38437	−	4.12986i	0.129885	−	0.224968i	−0.793747	−	0.608248i	$-0.791872\pi$
$337$	2.38437	−	4.12986i	0.129885	−	0.224968i	0.923632	+	0.383281i	$0.125206\pi$
$338$	13.5439	−	0.671959i	0.736689	−	0.0365497i
$339$	0.935032	+	0.909183i	0.0507840	+	0.0493800i
$340$		0			0
$341$			3.75251i			0.203210i
$342$	5.37997	+	7.84362i	0.290915	+	0.424135i
$343$			11.7388i			0.633835i
$344$	11.7818	−	9.37873i	0.635234	−	0.505667i
$345$		0			0
$346$	−0.0536555	−	1.08147i	−0.00288454	−	0.0581401i
$347$	−10.1960	+	17.6599i	−0.547348	+	0.948035i	0.451107	+	0.892470i	$0.351029\pi$
$347$	−10.1960	+	17.6599i	−0.547348	+	0.948035i	−0.998455	+	0.0555651i	$0.982304\pi$
$348$	−21.6025	−	17.1935i	−1.15802	−	0.921667i
$349$	−0.618705	−	1.07163i	−0.0331185	−	0.0573630i	0.848991	−	0.528407i	$-0.177211\pi$
$349$	−0.618705	−	1.07163i	−0.0331185	−	0.0573630i	−0.882110	+	0.471044i	$0.843877\pi$
$350$		0			0
$351$	−9.15748	+	2.87137i	−0.488790	+	0.153262i
$352$	4.81733	−	17.0259i	0.256765	−	0.907483i
$353$	−1.63238	+	0.942454i	−0.0868827	+	0.0501617i	−0.542812	−	0.839854i	$-0.682640\pi$
$353$	−1.63238	+	0.942454i	−0.0868827	+	0.0501617i	0.455929	+	0.890016i	$0.349307\pi$
$354$	−5.44076	−	16.1265i	−0.289173	−	0.857116i
$355$		0			0
$356$	−23.2758	+	16.7134i	−1.23362	+	0.885811i
$357$	8.88171	+	31.3810i	0.470070	+	1.66086i
$358$	7.30760	−	14.2437i	0.386219	−	0.752803i
$359$	9.20394			0.485766			0.242883	−	0.970056i	$-0.421907\pi$
$359$	9.20394			0.485766			0.242883	+	0.970056i	$0.421907\pi$
$360$		0			0
$361$	13.9741			0.735478
$362$	2.06747	−	4.02984i	0.108664	−	0.211804i
$363$	−1.46828	+	1.51003i	−0.0770648	+	0.0792558i
$364$	−9.65371	+	6.93195i	−0.505992	+	0.363333i
$365$		0			0
$366$	−8.01077	−	1.60895i	−0.418730	−	0.0841012i
$367$	−22.5635	+	13.0271i	−1.17781	+	0.680007i	−0.955506	−	0.294971i	$-0.904690\pi$
$367$	−22.5635	+	13.0271i	−1.17781	+	0.680007i	−0.222301	+	0.974978i	$0.571357\pi$
$368$	9.90728	+	11.2529i	0.516453	+	0.586600i
$369$	−0.378084	−	0.614422i	−0.0196823	−	0.0319855i
$370$		0			0
$371$	−21.0406	−	36.4433i	−1.09237	−	1.89204i
$372$	0.615439	−	4.10998i	0.0319090	−	0.213092i
$373$	18.0286	−	31.2265i	0.933486	−	1.61685i	0.156175	−	0.987729i	$-0.450083\pi$
$373$	18.0286	−	31.2265i	0.933486	−	1.61685i	0.777311	−	0.629117i	$-0.216583\pi$
$374$	1.28286	+	25.8570i	0.0663349	+	1.33703i
$375$		0			0
$376$	−8.06751	−	10.1346i	−0.416050	−	0.522654i
$377$			14.7206i			0.758149i
$378$	−15.1183	+	18.1773i	−0.777599	+	0.934941i
$379$		−	32.4422i		−	1.66644i	−0.552939	−	0.833222i	$-0.686494\pi$
$379$		−	32.4422i		−	1.66644i	0.552939	−	0.833222i	$-0.313506\pi$
$380$		0			0
$381$	−2.58327	+	10.2112i	−0.132345	+	0.523138i
$382$	−2.51370	+	0.124714i	−0.128612	+	0.00638090i
$383$	10.7400	−	18.6022i	0.548788	−	0.950528i	−0.449570	−	0.893245i	$-0.648423\pi$
$383$	10.7400	−	18.6022i	0.548788	−	0.950528i	0.998358	−	0.0572834i	$-0.0182438\pi$
$384$	−8.06860	+	17.8577i	−0.411749	+	0.911297i
$385$		0			0
$386$	10.8489	+	16.8082i	0.552193	+	0.855514i
$387$	−15.9662	+	0.447659i	−0.811606	+	0.0227558i
$388$	−5.47292	+	12.1103i	−0.277846	+	0.614806i
$389$	0.812139	−	0.468889i	0.0411771	−	0.0237736i	−0.479270	−	0.877667i	$-0.659099\pi$
$389$	0.812139	−	0.468889i	0.0411771	−	0.0237736i	0.520447	+	0.853894i	$0.325765\pi$
$390$		0			0
$391$	−18.9973	−	10.9681i	−0.960733	−	0.554679i
$392$	−3.47094	+	8.82094i	−0.175309	+	0.445525i
$393$	−11.8219	+	12.1580i	−0.596335	+	0.613289i
$394$	10.7079	+	5.49358i	0.539455	+	0.276763i
$395$		0			0
$396$	−14.9318	+	11.3695i	−0.750351	+	0.571338i
$397$	−1.87601			−0.0941544			−0.0470772	−	0.998891i	$-0.514991\pi$
$397$	−1.87601			−0.0941544			−0.0470772	+	0.998891i	$0.514991\pi$
$398$	3.80037	+	1.94975i	0.190496	+	0.0977320i
$399$	−3.40224	−	12.0209i	−0.170325	−	0.601795i
$400$		0			0
$401$	12.8578	+	7.42347i	0.642090	+	0.370711i	0.785419	−	0.618964i	$-0.212448\pi$
$401$	12.8578	+	7.42347i	0.642090	+	0.370711i	−0.143329	+	0.989675i	$0.545781\pi$
$402$	−20.0504	+	6.76460i	−1.00002	+	0.337388i
$403$	−1.91890	+	1.10788i	−0.0955873	+	0.0551873i
$404$	−9.12391	−	4.12332i	−0.453932	−	0.205143i
$405$		0			0
$406$	19.6663	+	30.4690i	0.976021	+	1.51215i
$407$	4.16684	+	7.21719i	0.206543	+	0.357743i
$408$	2.83567	−	28.5305i	0.140387	−	1.41247i
$409$	−11.0678	+	19.1701i	−0.547270	+	0.947899i	0.451191	+	0.892428i	$0.350999\pi$
$409$	−11.0678	+	19.1701i	−0.547270	+	0.947899i	−0.998460	+	0.0554713i	$0.982334\pi$
$410$		0			0
$411$	−9.45478	+	2.67597i	−0.466370	+	0.131996i
$412$	−2.94398	−	29.5961i	−0.145040	−	1.45810i
$413$			22.3550i			1.10002i
$414$	−1.23283	−	15.8544i	−0.0605903	−	0.779199i
$415$		0			0
$416$	10.1287	−	2.56325i	0.496600	−	0.125674i
$417$	11.4596	+	11.1428i	0.561178	+	0.545664i
$418$	−0.491413	−	9.90483i	−0.0240358	−	0.484461i
$419$	−13.9401	+	24.1450i	−0.681019	+	1.17956i	0.293652	+	0.955912i	$0.405129\pi$
$419$	−13.9401	+	24.1450i	−0.681019	+	1.17956i	−0.974670	+	0.223646i	$0.928204\pi$
$420$		0			0
$421$	−2.65309	−	4.59530i	−0.129304	−	0.223961i	0.794103	−	0.607783i	$-0.207941\pi$
$421$	−2.65309	−	4.59530i	−0.129304	−	0.223961i	−0.923407	+	0.383822i	$0.874608\pi$
$422$	28.7452	−	18.5537i	1.39929	−	0.903178i
$423$	0.385073	+	13.7340i	0.0187229	+	0.667768i
$424$	5.48145	+	36.5857i	0.266203	+	1.77676i
$425$		0			0
$426$	18.3371	−	20.8311i	0.888437	−	1.00927i
$427$	9.29431	+	5.36607i	0.449783	+	0.259682i
$428$	3.45211	+	4.80754i	0.166864	+	0.232381i
$429$	9.70076	+	2.45413i	0.468357	+	0.118486i
$430$		0			0
$431$	25.2887			1.21811			0.609056	−	0.793127i	$-0.291549\pi$
$431$	25.2887			1.21811			0.609056	+	0.793127i	$0.291549\pi$
$432$	18.2189	−	10.0036i	0.876556	−	0.481300i
$433$	24.8471			1.19408			0.597038	−	0.802213i	$-0.296344\pi$
$433$	24.8471			1.19408			0.597038	+	0.802213i	$0.296344\pi$
$434$	−2.49169	+	4.85670i	−0.119605	+	0.233129i
$435$		0			0
$436$	−4.33062	−	6.03099i	−0.207399	−	0.288832i
$437$	7.27712	+	4.20145i	0.348112	+	0.200983i
$438$	21.3136	−	24.2124i	1.01840	−	1.15691i
$439$	−6.34768	+	3.66484i	−0.302958	+	0.174913i	−0.643771	−	0.765218i	$-0.722631\pi$
$439$	−6.34768	+	3.66484i	−0.302958	+	0.174913i	0.340813	+	0.940131i	$0.389298\pi$
$440$		0			0
$441$	8.56294	−	5.26920i	0.407759	−	0.250914i
$442$	−12.8436	+	8.28993i	−0.610908	+	0.394312i
$443$	17.5978	+	30.4803i	0.836097	+	1.44816i	0.893135	+	0.449790i	$0.148501\pi$
$443$	17.5978	+	30.4803i	0.836097	+	1.44816i	−0.0570380	+	0.998372i	$0.518166\pi$
$444$	−3.38011	−	8.58809i	−0.160413	−	0.407573i
$445$		0			0
$446$	0.188349	+	3.79633i	0.00891860	+	0.179761i
$447$	−14.0226	−	13.6349i	−0.663245	−	0.644910i
$448$	17.5401	−	18.8371i	0.828693	−	0.889968i
$449$		−	23.0398i		−	1.08732i	−0.839307	−	0.543658i	$-0.817039\pi$
$449$		−	23.0398i		−	1.08732i	0.839307	−	0.543658i	$-0.182961\pi$
$450$		0			0
$451$			0.752197i			0.0354196i
$452$	0.149063	+	1.49855i	0.00701135	+	0.0704858i
$453$	−35.8260	+	10.1398i	−1.68325	+	0.476408i
$454$	−15.1956	+	0.753906i	−0.713163	+	0.0353825i
$455$		0			0
$456$	−1.08624	+	10.9290i	−0.0508677	+	0.511795i
$457$	17.3359	+	30.0267i	0.810940	+	1.40459i	0.912207	+	0.409729i	$0.134377\pi$
$457$	17.3359	+	30.0267i	0.810940	+	1.40459i	−0.101267	+	0.994859i	$0.532290\pi$
$458$	1.98269	+	3.07178i	0.0926449	+	0.143535i
$459$	−20.5805	+	22.3882i	−0.960614	+	1.04499i
$460$		0			0
$461$	−23.2641	+	13.4315i	−1.08352	+	0.625568i	−0.931843	−	0.362863i	$-0.881799\pi$
$461$	−23.2641	+	13.4315i	−1.08352	+	0.625568i	−0.151673	+	0.988431i	$0.548466\pi$
$462$	23.3574	−	7.88032i	1.08669	−	0.366626i
$463$	−7.51295	−	4.33760i	−0.349156	−	0.201586i	0.315157	−	0.949039i	$-0.397943\pi$
$463$	−7.51295	−	4.33760i	−0.349156	−	0.201586i	−0.664314	+	0.747454i	$0.731276\pi$
$464$	−6.28032	−	31.2560i	−0.291557	−	1.45102i
$465$		0			0
$466$	−1.23451	−	0.633353i	−0.0571875	−	0.0293395i
$467$	14.3724			0.665077			0.332538	−	0.943090i	$-0.392095\pi$
$467$	14.3724			0.665077			0.332538	+	0.943090i	$0.392095\pi$
$468$	−10.2224	−	4.27890i	−0.472529	−	0.197792i
$469$	27.7944			1.28342
$470$		0			0
$471$	1.44354	−	1.48458i	0.0665149	−	0.0684059i
$472$	7.19600	−	18.2877i	0.331223	−	0.841760i
$473$	14.4224	+	8.32680i	0.663144	+	0.382866i
$474$	−6.48576	+	32.2918i	−0.297901	+	1.48321i
$475$		0			0
$476$	−15.5088	+	34.3173i	−0.710846	+	1.57293i
$477$	18.6590	−	34.5177i	0.854336	−	1.58046i
$478$	5.91759	+	9.16813i	0.270664	+	0.419341i
$479$	−12.6519	−	21.9137i	−0.578079	−	1.00126i	−0.995700	−	0.0926401i	$-0.970469\pi$
$479$	−12.6519	−	21.9137i	−0.578079	−	1.00126i	0.417621	−	0.908621i	$-0.362864\pi$
$480$		0			0
$481$	−2.46041	+	4.26155i	−0.112185	+	0.194310i
$482$	33.9240	−	1.68309i	1.54520	−	0.0766627i
$483$	−5.12274	+	20.2494i	−0.233093	+	0.921378i
$484$	−2.42007	+	0.240729i	−0.110003	+	0.0109422i
$485$		0			0
$486$	−21.8231	−	3.12321i	−0.989914	−	0.141672i
$487$			1.60501i			0.0727298i	0.999339	+	0.0363649i	$0.0115779\pi$
$487$			1.60501i			0.0727298i	−0.999339	+	0.0363649i	$0.988422\pi$
$488$	−5.87598	−	7.38158i	−0.265993	−	0.334149i
$489$	−5.44652	+	21.5292i	−0.246300	+	0.973585i
$490$		0			0
$491$	−0.831852	+	1.44081i	−0.0375410	+	0.0650229i	−0.884185	−	0.467136i	$-0.845286\pi$
$491$	−0.831852	+	1.44081i	−0.0375410	+	0.0650229i	0.846644	+	0.532159i	$0.178619\pi$
$492$	0.123366	−	0.823851i	0.00556175	−	0.0371421i
$493$	23.3226	+	40.3959i	1.05040	+	1.81934i
$494$	4.91989	−	3.17556i	0.221356	−	0.142875i
$495$		0			0
$496$	3.60171	−	3.17101i	0.161721	−	0.142382i
$497$	−31.5684	+	18.2261i	−1.41604	+	0.817550i
$498$	2.99380	+	0.601300i	0.134155	+	0.0269449i
$499$	3.64109	+	2.10218i	0.162997	+	0.0941066i	0.579280	−	0.815129i	$-0.303334\pi$
$499$	3.64109	+	2.10218i	0.162997	+	0.0941066i	−0.416282	+	0.909235i	$0.636667\pi$
$500$		0			0
$501$	−13.4281	+	13.8099i	−0.599923	+	0.616979i
$502$	−12.0303	+	23.4489i	−0.536937	+	1.04658i
$503$	−4.66613			−0.208052			−0.104026	−	0.994575i	$-0.533173\pi$
$503$	−4.66613			−0.208052			−0.104026	+	0.994575i	$0.533173\pi$
$504$	−26.8749	+	4.80021i	−1.19710	+	0.213818i
$505$		0			0
$506$	−7.56848	+	14.7522i	−0.336460	+	0.655815i
$507$	−4.52292	−	15.9804i	−0.200870	−	0.709716i
$508$	−9.87927	+	7.09391i	−0.438322	+	0.314742i
$509$	−10.7945	−	6.23218i	−0.478456	−	0.276237i	0.241317	−	0.970446i	$-0.422421\pi$
$509$	−10.7945	−	6.23218i	−0.478456	−	0.276237i	−0.719773	+	0.694210i	$0.755754\pi$
$510$		0			0
$511$	−36.6926	+	21.1845i	−1.62318	+	0.937145i
$512$	−20.4125	+	9.76375i	−0.902112	+	0.431501i
$513$	7.88359	−	8.57606i	0.348069	−	0.378642i
$514$	9.01797	−	5.82067i	0.397766	−	0.256739i
$515$		0			0
$516$	−14.4307	−	11.4854i	−0.635275	−	0.505616i
$517$	7.16265	−	12.4061i	0.315013	−	0.545618i
$518$	0.600704	+	12.1077i	0.0263934	+	0.531980i
$519$	−1.27603	+	0.361152i	−0.0560115	+	0.0158528i
$520$		0			0
$521$		−	18.2767i		−	0.800716i	−0.916359	−	0.400358i	$-0.868886\pi$
$521$		−	18.2767i		−	0.800716i	0.916359	−	0.400358i	$-0.131114\pi$
$522$	−14.5861	+	30.5069i	−0.638417	+	1.33525i
$523$		−	29.7140i		−	1.29930i	−0.760233	−	0.649650i	$-0.774915\pi$
$523$		−	29.7140i		−	1.29930i	0.760233	−	0.649650i	$-0.225085\pi$
$524$	−19.4852	+	1.93823i	−0.851216	+	0.0846721i
$525$		0			0
$526$	−18.9098	+	0.938183i	−0.824507	+	0.0409067i
$527$	−3.51053	+	6.08042i	−0.152921	+	0.264867i
$528$	−21.6444	−	1.07211i	−0.941954	−	0.0466577i
$529$	4.47554	+	7.75186i	0.194589	+	0.337037i
$530$		0			0
$531$	−17.7528	+	10.9242i	−0.770407	+	0.474070i
$532$	5.94084	−	13.1456i	0.257568	−	0.569936i
$533$	−0.384647	+	0.222076i	−0.0166609	+	0.00961917i
$534$	26.3426	+	23.1888i	1.13996	+	1.00348i
$535$		0			0
$536$	−22.7375	−	8.94692i	−0.982109	−	0.386448i
$537$	−19.0080	−	4.80869i	−0.820254	−	0.207510i
$538$	4.83592	+	2.48103i	0.208491	+	0.106965i
$539$	−10.4831			−0.451537
$540$		0			0
$541$	−20.8938			−0.898295			−0.449147	−	0.893458i	$-0.648272\pi$
$541$	−20.8938			−0.898295			−0.449147	+	0.893458i	$0.648272\pi$
$542$	−11.2569	−	5.77527i	−0.483527	−	0.248069i
$543$	−5.37775	−	1.36048i	−0.230781	−	0.0583837i
$544$	23.7338	−	23.0814i	1.01758	−	0.989606i
$545$		0			0
$546$	10.9257	+	9.61761i	0.467576	+	0.411596i
$547$	27.6842	−	15.9835i	1.18369	−	0.683405i	0.226826	−	0.973935i	$-0.427165\pi$
$547$	27.6842	−	15.9835i	1.18369	−	0.683405i	0.956866	+	0.290530i	$0.0938317\pi$
$548$	−10.3395	−	4.67266i	−0.441680	−	0.199606i
$549$	0.280468	+	10.0032i	0.0119701	+	0.426924i
$550$		0			0
$551$	−8.93399	−	15.4741i	−0.380601	−	0.659220i
$552$	10.7089	−	14.9162i	0.455802	−	0.634876i
$553$	21.6309	−	37.4658i	0.919839	−	1.59321i
$554$	15.6281	−	0.775368i	0.663976	−	0.0329422i
$555$		0			0
$556$	1.82689	+	18.3659i	0.0774776	+	0.778889i
$557$		−	0.347675i		−	0.0147315i	−0.999973	−	0.00736573i	$-0.997655\pi$
$557$		−	0.347675i		−	0.0147315i	0.999973	−	0.00736573i	$-0.00234460\pi$
$558$	−5.07448	+	0.394590i	−0.214820	+	0.0167043i
$559$			9.83349i			0.415912i
$560$		0			0
$561$	30.5087	−	8.63484i	1.28808	−	0.364563i
$562$	−2.05724	−	41.4652i	−0.0867792	−	1.74910i
$563$	9.80425	−	16.9815i	0.413200	−	0.715683i	−0.582038	−	0.813162i	$-0.697744\pi$
$563$	9.80425	−	16.9815i	0.413200	−	0.715683i	0.995238	+	0.0974785i	$0.0310777\pi$
$564$	−9.87964	+	12.4131i	−0.416008	+	0.522688i
$565$		0			0
$566$	5.93744	−	3.83234i	0.249569	−	0.161085i
$567$	25.8487	+	13.0503i	1.08554	+	0.548060i
$568$	31.6918	−	4.74822i	1.32976	−	0.199231i
$569$	−6.42572	+	3.70989i	−0.269380	+	0.155527i	−0.628606	−	0.777724i	$-0.716374\pi$
$569$	−6.42572	+	3.70989i	−0.269380	+	0.155527i	0.359226	+	0.933251i	$0.383041\pi$
$570$		0			0
$571$	−0.776486	−	0.448304i	−0.0324949	−	0.0187610i	0.483665	−	0.875253i	$-0.339305\pi$
$571$	−0.776486	−	0.448304i	−0.0324949	−	0.0187610i	−0.516159	+	0.856493i	$0.672639\pi$
$572$	6.73927	+	9.38538i	0.281783	+	0.392423i
$573$	0.839441	+	2.96592i	0.0350681	+	0.123903i
$574$	−0.499462	+	0.973533i	−0.0208471	+	0.0406345i
$575$		0			0
$576$	23.5305	+	4.72409i	0.980436	+	0.196837i
$577$	−2.59834			−0.108170			−0.0540852	−	0.998536i	$-0.517224\pi$
$577$	−2.59834			−0.108170			−0.0540852	+	0.998536i	$0.517224\pi$
$578$	−11.1366	+	21.7070i	−0.463221	+	0.902892i
$579$	17.0806	−	17.5662i	0.709846	−	0.730028i
$580$		0			0
$581$	−3.47348	−	2.00542i	−0.144104	−	0.0831987i
$582$	15.9576	+	3.20506i	0.661464	+	0.132854i
$583$	−35.4304	+	20.4557i	−1.46738	+	0.847190i
$584$	36.8359	−	5.51894i	1.52428	−	0.228375i
$585$		0			0
$586$	−11.1854	+	7.21965i	−0.462065	+	0.298241i
$587$	−1.88410	−	3.26336i	−0.0777651	−	0.134693i	0.824520	−	0.565832i	$-0.191445\pi$
$587$	−1.88410	−	3.26336i	−0.0777651	−	0.134693i	−0.902285	+	0.431139i	$0.858112\pi$
$588$	11.4817	+	1.71930i	0.473496	+	0.0709026i
$589$	1.34475	−	2.32918i	0.0554095	−	0.0959720i
$590$		0			0
$591$	3.61499	−	14.2895i	0.148701	−	0.587790i
$592$	3.40601	−	10.0982i	0.139986	−	0.415032i
$593$			19.4602i			0.799135i	0.916704	+	0.399568i	$0.130840\pi$
$593$			19.4602i			0.799135i	−0.916704	+	0.399568i	$0.869160\pi$
$594$	17.6721	+	14.6981i	0.725095	+	0.603068i
$595$		0			0
$596$	−2.23549	−	22.4736i	−0.0915692	−	0.920553i
$597$	1.28301	−	5.07153i	0.0525101	−	0.207564i
$598$	−9.77824	+	0.485133i	−0.399862	+	0.0198386i
$599$	6.58019	−	11.3972i	0.268859	−	0.465678i	−0.699708	−	0.714429i	$-0.746687\pi$
$599$	6.58019	−	11.3972i	0.268859	−	0.465678i	0.968568	+	0.248751i	$0.0800200\pi$
$600$		0			0
$601$	−18.3619	−	31.8037i	−0.748998	−	1.29730i	−0.948304	−	0.317365i	$-0.897202\pi$
$601$	−18.3619	−	31.8037i	−0.748998	−	1.29730i	0.199306	−	0.979937i	$-0.436131\pi$
$602$	13.1372	+	20.3535i	0.535434	+	0.829548i
$603$	13.5823	+	22.0724i	0.553112	+	0.898859i
$604$	−39.1783	−	17.7056i	−1.59414	−	0.720431i
$605$		0			0
$606$	−2.41470	+	12.0225i	−0.0980905	+	0.488381i
$607$	−13.0616	−	7.54110i	−0.530152	−	0.306084i	0.210926	−	0.977502i	$-0.432352\pi$
$607$	−13.0616	−	7.54110i	−0.530152	−	0.306084i	−0.741079	+	0.671418i	$0.765685\pi$
$608$	−9.09151	+	8.84160i	−0.368709	+	0.358574i
$609$	30.9628	−	31.8431i	1.25468	−	1.29035i
$610$		0			0
$611$	8.45869			0.342202
$612$	−34.8312	+	4.45374i	−1.40797	+	0.180032i
$613$	−46.5249			−1.87912			−0.939562	−	0.342379i	$-0.888767\pi$
$613$	−46.5249			−1.87912			−0.939562	+	0.342379i	$0.888767\pi$
$614$	−23.0862	−	11.8441i	−0.931682	−	0.477991i
$615$		0			0
$616$	26.4877	+	10.4226i	1.06722	+	0.419938i
$617$	6.02034	+	3.47584i	0.242370	+	0.139932i	0.616265	−	0.787539i	$-0.288645\pi$
$617$	6.02034	+	3.47584i	0.242370	+	0.139932i	−0.373896	+	0.927471i	$0.621978\pi$
$618$	−34.5151	+	11.6447i	−1.38840	+	0.468419i
$619$	0.274332	−	0.158386i	0.0110263	−	0.00636606i	−0.494477	−	0.869191i	$-0.664640\pi$
$619$	0.274332	−	0.158386i	0.0110263	−	0.00636606i	0.505503	+	0.862825i	$0.331307\pi$
$620$		0			0
$621$	−18.5840	+	5.82710i	−0.745751	+	0.233834i
$622$	23.9664	+	37.1312i	0.960965	+	1.48882i
$623$	−23.0483	−	39.9208i	−0.923410	−	1.59939i
$624$	−5.84199	−	11.3847i	−0.233867	−	0.455754i
$625$		0			0
$626$	7.24871	−	0.359634i	0.289717	−	0.0143739i
$627$	−11.6867	+	3.30768i	−0.466723	+	0.132096i
$628$	2.37930	−	0.236673i	0.0949442	−	0.00944429i
$629$			15.5926i			0.621717i
$630$		0			0
$631$		−	15.4663i		−	0.615705i	−0.951434	−	0.307852i	$-0.900390\pi$
$631$		−	15.4663i		−	0.615705i	0.951434	−	0.307852i	$-0.0996103\pi$
$632$	−29.7555	+	23.6864i	−1.18361	+	0.942194i
$633$	−30.0416	−	29.2111i	−1.19405	−	1.16104i
$634$	−1.03831	−	20.9280i	−0.0412366	−	0.831156i
$635$		0			0
$636$	42.1604	−	16.5935i	1.67177	−	0.657976i
$637$	−3.09498	−	5.36066i	−0.122627	−	0.212397i
$638$	29.6221	−	19.1196i	1.17275	−	0.756954i
$639$	−29.9004	−	16.1630i	−1.18284	−	0.639400i
$640$		0			0
$641$	−5.66108	+	3.26843i	−0.223599	+	0.129095i	−0.607616	−	0.794231i	$-0.707874\pi$
$641$	−5.66108	+	3.26843i	−0.223599	+	0.129095i	0.384017	+	0.923326i	$0.374541\pi$
$642$	4.78956	−	5.44098i	0.189029	−	0.214739i
$643$	−12.6430	−	7.29945i	−0.498592	−	0.287862i	0.229540	−	0.973299i	$-0.426278\pi$
$643$	−12.6430	−	7.29945i	−0.498592	−	0.287862i	−0.728132	+	0.685437i	$0.759611\pi$
$644$	−19.5911	+	14.0676i	−0.771996	+	0.554340i
$645$		0			0
$646$	8.46985	−	16.5091i	0.333242	−	0.649542i
$647$	−44.3589			−1.74393			−0.871965	−	0.489569i	$-0.837154\pi$
$647$	−44.3589			−1.74393			−0.871965	+	0.489569i	$0.837154\pi$
$648$	−16.9450	−	18.9965i	−0.665661	−	0.746255i
$649$	21.7336			0.853119
$650$		0			0
$651$	6.48118	+	1.63963i	0.254017	+	0.0642620i
$652$	−20.8293	+	14.9567i	−0.815738	+	0.585750i
$653$	24.9534	+	14.4068i	0.976501	+	0.563783i	0.901212	−	0.433378i	$-0.142679\pi$
$653$	24.9534	+	14.4068i	0.976501	+	0.563783i	0.0752894	+	0.997162i	$0.476012\pi$
$654$	−6.00844	+	6.82564i	−0.234949	+	0.266904i
$655$		0			0
$656$	0.721967	−	0.635633i	0.0281881	−	0.0248173i
$657$	−34.7538	−	18.7866i	−1.35588	−	0.732935i
$658$	17.5080	−	11.3006i	0.682531	−	0.440541i
$659$	3.09024	+	5.35245i	0.120379	+	0.208502i	0.919917	−	0.392113i	$-0.128256\pi$
$659$	3.09024	+	5.35245i	0.120379	+	0.208502i	−0.799538	+	0.600615i	$0.794922\pi$
$660$		0			0
$661$	8.95623	−	15.5127i	0.348357	−	0.603372i	−0.637601	−	0.770367i	$-0.720073\pi$
$661$	8.95623	−	15.5127i	0.348357	−	0.603372i	0.985958	+	0.166995i	$0.0534063\pi$
$662$	−1.78553	−	35.9887i	−0.0693964	−	1.39874i
$663$	13.4228	+	13.0518i	0.521300	+	0.506889i
$664$	2.19598	+	2.75866i	0.0852206	+	0.107057i
$665$		0			0
$666$	−9.32155	+	6.39369i	−0.361203	+	0.247750i
$667$			29.8737i			1.15671i
$668$	−22.1327	+	2.20158i	−0.856338	+	0.0851816i
$669$	4.47930	−	1.26777i	0.173180	−	0.0490148i
$670$		0			0
$671$	5.21692	−	9.03598i	0.201397	−	0.348830i
$672$	−27.3015	−	15.7596i	−1.05318	−	0.607940i
$673$	−10.6989	−	18.5311i	−0.412413	−	0.714320i	0.582740	−	0.812659i	$-0.301981\pi$
$673$	−10.6989	−	18.5311i	−0.412413	−	0.714320i	−0.995153	+	0.0983386i	$0.968647\pi$
$674$	−3.65728	−	5.66623i	−0.140873	−	0.218255i
$675$		0			0
$676$	7.89771	−	17.4757i	0.303758	−	0.672144i
$677$	−22.6311	+	13.0660i	−0.869782	+	0.502169i	−0.867276	−	0.497828i	$-0.834131\pi$
$677$	−22.6311	+	13.0660i	−0.869782	+	0.502169i	−0.00250627	+	0.999997i	$0.500798\pi$
$678$	1.74762	−	0.589609i	0.0671168	−	0.0226438i
$679$	−18.5144	−	10.6893i	−0.710518	−	0.410218i
$680$		0			0
$681$	5.07450	+	17.9293i	0.194455	+	0.687052i
$682$	4.72171	+	2.42243i	0.180804	+	0.0927596i
$683$	9.44413			0.361370			0.180685	−	0.983541i	$-0.442169\pi$
$683$	9.44413			0.361370			0.180685	+	0.983541i	$0.442169\pi$
$684$	13.3425	−	1.70606i	0.510163	−	0.0652328i
$685$		0			0
$686$	14.7707	+	7.57796i	0.563947	+	0.289328i
$687$	3.12157	−	3.21032i	0.119095	−	0.122481i
$688$	−4.19531	−	20.8793i	−0.159945	−	0.796015i
$689$	−20.9207	−	12.0786i	−0.797014	−	0.460156i
$690$		0			0
$691$	−0.942002	+	0.543865i	−0.0358354	+	0.0206896i	−0.517811	−	0.855495i	$-0.673253\pi$
$691$	−0.942002	+	0.543865i	−0.0358354	+	0.0206896i	0.481975	+	0.876185i	$0.339920\pi$
$692$	−1.39543	−	0.630627i	−0.0530462	−	0.0239729i
$693$	−15.8224	−	25.7129i	−0.601045	−	0.976754i
$694$	15.6391	+	24.2297i	0.593654	+	0.919748i
$695$		0			0
$696$	−35.5797	+	16.0828i	−1.34864	+	0.609615i
$697$	−0.703691	+	1.21883i	−0.0266542	+	0.0461664i
$698$	−1.74781	+	0.0867152i	−0.0661557	+	0.00328222i
$699$	−0.416771	+	1.64743i	−0.0157637	+	0.0623115i
$700$		0			0
$701$			16.2662i			0.614367i	0.951650	+	0.307183i	$0.0993865\pi$
$701$			16.2662i			0.614367i	−0.951650	+	0.307183i	$0.900614\pi$
$702$	−2.29862	+	13.3763i	−0.0867556	+	0.504855i
$703$		−	5.97292i		−	0.225273i
$704$	−18.3135	−	17.0526i	−0.690216	−	0.642694i
$705$		0			0
$706$	0.132090	+	2.66239i	0.00497129	+	0.100200i
$707$	8.05336	−	13.9488i	0.302878	−	0.524600i
$708$	−23.8040	−	3.56447i	−0.894608	−	0.133961i
$709$	−19.4225	−	33.6408i	−0.729429	−	1.26341i	−0.957125	−	0.289675i	$-0.906453\pi$
$709$	−19.4225	−	33.6408i	−0.729429	−	1.26341i	0.227696	−	0.973732i	$-0.426881\pi$
$710$		0			0
$711$	40.3232	−	1.13058i	1.51224	−	0.0424001i
$712$	6.00450	+	40.0768i	0.225028	+	1.50194i
$713$	−3.89418	+	2.24831i	−0.145838	+	0.0841998i
$714$	45.2196	+	9.08228i	1.69230	+	0.339896i
$715$		0			0
$716$	−13.2051	−	18.3900i	−0.493499	−	0.687267i
$717$	9.31673	−	9.58161i	0.347940	−	0.357832i
$718$	5.94159	−	11.5811i	0.221738	−	0.432204i
$719$	10.3797			0.387099			0.193549	−	0.981091i	$-0.438000\pi$
$719$	10.3797			0.387099			0.193549	+	0.981091i	$0.438000\pi$
$720$		0			0
$721$	47.8457			1.78187
$722$	9.02095	−	17.5833i	0.335725	−	0.654383i
$723$	−11.3288	−	40.0271i	−0.421323	−	1.48862i
$724$	−3.73601	−	5.20291i	−0.138848	−	0.193365i
$725$		0			0
$726$	0.952187	+	2.82230i	0.0353390	+	0.104745i
$727$	9.07598	−	5.24002i	0.336610	−	0.194342i	−0.322162	−	0.946684i	$-0.604410\pi$
$727$	9.07598	−	5.24002i	0.336610	−	0.194342i	0.658772	+	0.752343i	$0.271076\pi$
$728$	2.49038	+	16.6220i	0.0922998	+	0.616051i
$729$	2.26781	+	26.9046i	0.0839929	+	0.996466i
$730$		0			0
$731$	15.5797	+	26.9848i	0.576235	+	0.998069i
$732$	−7.19585	+	9.04113i	−0.265966	+	0.334170i
$733$	13.6872	−	23.7069i	0.505548	−	0.875635i	−0.494431	−	0.869217i	$-0.664624\pi$
$733$	13.6872	−	23.7069i	0.505548	−	0.875635i	0.999979	−	0.00641848i	$-0.00204308\pi$
$734$	1.82582	+	36.8008i	0.0673922	+	1.35834i
$735$		0			0
$736$	20.5550	−	5.20181i	0.757666	−	0.191741i
$737$		−	27.0218i		−	0.995362i
$738$	−1.01719	+	0.0790961i	−0.0374432	+	0.00291157i
$739$			1.76648i			0.0649812i	0.999472	+	0.0324906i	$0.0103439\pi$
$739$			1.76648i			0.0649812i	−0.999472	+	0.0324906i	$0.989656\pi$
$740$		0			0
$741$	−5.14178	−	4.99963i	−0.188888	−	0.183666i
$742$	−59.4386	+	2.94896i	−2.18206	+	0.108260i
$743$	2.56338	−	4.43990i	0.0940412	−	0.162884i	−0.815167	−	0.579226i	$-0.803355\pi$
$743$	2.56338	−	4.43990i	0.0940412	−	0.162884i	0.909208	+	0.416342i	$0.136688\pi$
$744$	−4.77420	−	3.42759i	−0.175031	−	0.125661i
$745$		0			0
$746$	−27.6533	−	42.8433i	−1.01246	−	1.56860i
$747$	−0.104817	−	3.73840i	−0.00383506	−	0.136781i
$748$	33.3635	+	15.0778i	1.21989	+	0.551297i
$749$	−8.24551	+	4.76055i	−0.301284	+	0.173947i
$750$		0			0
$751$	12.8068	+	7.39403i	0.467328	+	0.269812i	0.715120	−	0.699001i	$-0.246372\pi$
$751$	12.8068	+	7.39403i	0.467328	+	0.269812i	−0.247793	+	0.968813i	$0.579705\pi$
$752$	−17.9602	+	3.60878i	−0.654940	+	0.131599i
$753$	31.2922	+	7.91639i	1.14035	+	0.288489i
$754$	18.5226	+	9.50287i	0.674554	+	0.346074i
$755$		0			0
$756$	13.1126	+	30.7573i	0.476900	+	1.11863i
$757$	11.6783			0.424454			0.212227	−	0.977220i	$-0.431928\pi$
$757$	11.6783			0.424454			0.212227	+	0.977220i	$0.431928\pi$
$758$	−40.8213	−	20.9430i	−1.48270	−	0.760685i
$759$	19.6865	+	4.98036i	0.714576	+	0.180775i
$760$		0			0
$761$	32.0963	+	18.5308i	1.16349	+	0.671741i	0.952138	−	0.305670i	$-0.0988803\pi$
$761$	32.0963	+	18.5308i	1.16349	+	0.671741i	0.211351	+	0.977410i	$0.432214\pi$
$762$	11.1810	+	9.84233i	0.405044	+	0.356550i
$763$	10.3439	−	5.97204i	0.374473	−	0.216202i
$764$	−1.46579	+	3.24345i	−0.0530305	+	0.117344i
$765$		0			0
$766$	−16.4736	−	25.5225i	−0.595215	−	0.922167i
$767$	6.41656	+	11.1138i	0.231688	+	0.401296i
$768$	17.2613	+	21.6806i	0.622864	+	0.782330i
$769$	24.6940	−	42.7713i	0.890490	−	1.54237i	0.0512015	−	0.998688i	$-0.483695\pi$
$769$	24.6940	−	42.7713i	0.890490	−	1.54237i	0.839289	−	0.543686i	$-0.182972\pi$
$770$		0			0
$771$	−9.42468	−	9.16413i	−0.339422	−	0.330038i
$772$	28.1529	−	2.80042i	1.01324	−	0.100789i
$773$			36.5028i			1.31291i	0.754363	+	0.656457i	$0.227946\pi$
$773$			36.5028i			1.31291i	−0.754363	+	0.656457i	$0.772054\pi$
$774$	−9.74366	+	20.3789i	−0.350228	+	0.732504i
$775$		0			0
$776$	11.7051	+	14.7042i	0.420187	+	0.527851i
$777$	14.2859	−	4.04331i	0.512503	−	0.145053i
$778$	−0.0657175	−	1.32459i	−0.00235609	−	0.0474888i
$779$	0.269557	−	0.466887i	0.00965789	−	0.0167280i
$780$		0			0
$781$	17.7195	+	30.6910i	0.634052	+	1.09821i
$782$	−26.0646	+	16.8234i	−0.932067	+	0.601605i
$783$	40.4183	+	9.02784i	1.44443	+	0.322629i
$784$	8.85855	+	10.0618i	0.316377	+	0.359348i
$785$		0			0
$786$	7.66654	+	22.7238i	0.273456	+	0.810531i
$787$	−16.0875	−	9.28811i	−0.573457	−	0.331086i	0.185072	−	0.982725i	$-0.440748\pi$
$787$	−16.0875	−	9.28811i	−0.573457	−	0.331086i	−0.758529	+	0.651639i	$0.774082\pi$
$788$	13.8249	−	9.92713i	0.492492	−	0.353639i
$789$	6.31486	+	22.3117i	0.224815	+	0.794319i
$790$		0			0
$791$	−2.42258			−0.0861371
$792$	4.66679	+	26.1279i	0.165827	+	0.928415i
$793$	6.16090			0.218780
$794$	−1.21106	+	2.36055i	−0.0429789	+	0.0837728i
$795$		0			0
$796$	4.90665	−	3.52327i	0.173912	−	0.124879i
$797$	21.3916	+	12.3505i	0.757730	+	0.437476i	0.828480	−	0.560019i	$-0.189206\pi$
$797$	21.3916	+	12.3505i	0.757730	+	0.437476i	−0.0707502	+	0.997494i	$0.522539\pi$
$798$	−17.3219	−	3.47908i	−0.613189	−	0.123158i
$799$	23.2121	−	13.4015i	0.821186	−	0.474112i
$800$		0			0
$801$	20.4395	−	37.8115i	0.722192	−	1.33600i
$802$	17.6412	−	11.3865i	0.622931	−	0.402072i
$803$	20.5956	+	35.6727i	0.726804	+	1.25886i
$804$	−4.43177	+	29.5959i	−0.156297	+	1.04377i
$805$		0			0
$806$	0.155276	+	3.12970i	0.00546935	+	0.110239i
$807$	1.63261	−	6.45345i	0.0574707	−	0.227172i
$808$	−11.0782	+	8.81863i	−0.389730	+	0.310238i
$809$			39.1203i			1.37540i	0.725997	+	0.687698i	$0.241379\pi$
$809$			39.1203i			1.37540i	−0.725997	+	0.687698i	$0.758621\pi$
$810$		0			0
$811$			29.6949i			1.04273i	0.853334	+	0.521365i	$0.174577\pi$
$811$			29.6949i			1.04273i	−0.853334	+	0.521365i	$0.825423\pi$
$812$	51.0340	−	5.07645i	1.79094	−	0.178149i
$813$	−3.80035	+	15.0222i	−0.133284	+	0.526851i
$814$	11.7711	−	0.584008i	0.412578	−	0.0204695i
$815$		0			0
$816$	−34.0688	−	21.9859i	−1.19265	−	0.769661i
$817$	−5.96798	−	10.3368i	−0.208793	−	0.361641i
$818$	16.9765	+	26.3017i	0.593568	+	0.919616i
$819$	8.47732	−	15.6824i	0.296222	−	0.547988i
$820$		0			0
$821$	−23.3953	+	13.5073i	−0.816503	+	0.471408i	−0.849209	−	0.528057i	$-0.822921\pi$
$821$	−23.3953	+	13.5073i	−0.816503	+	0.471408i	0.0327064	+	0.999465i	$0.489587\pi$
$822$	−2.73640	+	13.6242i	−0.0954430	+	0.475199i
$823$	25.5552	+	14.7543i	0.890800	+	0.514304i	0.874204	−	0.485559i	$-0.161384\pi$
$823$	25.5552	+	14.7543i	0.890800	+	0.514304i	0.0165959	+	0.999862i	$0.494717\pi$
$824$	−39.1406	−	15.4014i	−1.36353	−	0.536532i
$825$		0			0
$826$	28.1288	+	14.4312i	0.978726	+	0.502127i
$827$	47.9246			1.66650			0.833251	−	0.552896i	$-0.186477\pi$
$827$	47.9246			1.66650			0.833251	+	0.552896i	$0.186477\pi$
$828$	−20.7451	−	8.68352i	−0.720941	−	0.301773i
$829$	−46.1027			−1.60121			−0.800607	−	0.599190i	$-0.795489\pi$
$829$	−46.1027			−1.60121			−0.800607	+	0.599190i	$0.795489\pi$
$830$		0			0
$831$	−5.21896	−	18.4397i	−0.181044	−	0.639666i
$832$	3.31328	−	14.3994i	0.114867	−	0.499210i
$833$	−16.9863	−	9.80705i	−0.588541	−	0.339794i
$834$	21.4185	−	7.22614i	0.741660	−	0.250221i
$835$		0			0
$836$	−12.7803	−	5.77571i	−0.442015	−	0.199757i
$837$	1.86507	+	5.94815i	0.0644663	+	0.205598i
$838$	21.3821	+	33.1273i	0.738632	+	1.14436i
$839$	23.3203	+	40.3919i	0.805105	+	1.39448i	0.916220	+	0.400675i	$0.131224\pi$
$839$	23.3203	+	40.3919i	0.805105	+	1.39448i	−0.111116	+	0.993807i	$0.535442\pi$
$840$		0			0
$841$	17.2618	−	29.8983i	0.595235	−	1.03098i
$842$	−7.49487	+	0.371847i	−0.258290	+	0.0128147i
$843$	−48.9249	+	13.8471i	−1.68506	+	0.476921i
$844$	−4.78925	−	48.1468i	−0.164853	−	1.65728i
$845$		0			0
$846$	17.5298	+	8.38142i	0.602685	+	0.288159i
$847$		−	3.91234i		−	0.134430i
$848$	49.5736	+	16.7207i	1.70236	+	0.574190i
$849$	−6.20522	−	6.03368i	−0.212963	−	0.207075i
$850$		0			0
$851$	−4.99311	+	8.64831i	−0.171161	+	0.296460i
$852$	−14.3739	−	36.5208i	−0.492441	−	1.25118i
$853$	4.29583	+	7.44060i	0.147086	+	0.254761i	0.930149	−	0.367181i	$-0.119677\pi$
$853$	4.29583	+	7.44060i	0.147086	+	0.254761i	−0.783063	+	0.621942i	$0.786344\pi$
$854$	12.7520	−	8.23078i	0.436363	−	0.281651i
$855$		0			0
$856$	8.27773	−	1.24021i	0.282927	−	0.0423895i
$857$	26.1333	−	15.0880i	0.892695	−	0.515398i	0.0178719	−	0.999840i	$-0.494311\pi$
$857$	26.1333	−	15.0880i	0.892695	−	0.515398i	0.874823	+	0.484443i	$0.160978\pi$
$858$	9.35029	−	10.6220i	0.319214	−	0.362629i
$859$	32.8056	+	18.9403i	1.11931	+	0.646236i	0.941225	−	0.337779i	$-0.109676\pi$
$859$	32.8056	+	18.9403i	1.11931	+	0.646236i	0.178088	+	0.984015i	$0.443009\pi$
$860$		0			0
$861$	1.29916	+	0.328666i	0.0442753	+	0.0112009i
$862$	16.3251	−	31.8202i	0.556034	−	1.08380i
$863$	−30.4048			−1.03499			−0.517495	−	0.855686i	$-0.673136\pi$
$863$	−30.4048			−1.03499			−0.517495	+	0.855686i	$0.673136\pi$
$864$	−0.826184	−	29.3823i	−0.0281074	−	0.999605i
$865$		0			0
$866$	16.0400	−	31.2646i	0.545062	−	1.06241i
$867$	28.9676	+	7.32830i	0.983791	+	0.248882i
$868$	4.50258	+	6.27047i	0.152828	+	0.212834i
$869$	−36.4245	−	21.0297i	−1.23562	−	0.713383i
$870$		0			0
$871$	13.8180	−	7.97783i	0.468205	−	0.270318i
$872$	−10.3843	+	1.55583i	−0.351657	+	0.0526869i
$873$	−0.558698	−	19.9265i	−0.0189091	−	0.674408i
$874$	9.98434	−	6.44441i	0.337725	−	0.217986i
$875$		0			0
$876$	−16.7070	−	42.4487i	−0.564478	−	1.43421i
$877$	4.27655	−	7.40720i	0.144409	−	0.250123i	−0.784743	−	0.619821i	$-0.787205\pi$
$877$	4.27655	−	7.40720i	0.144409	−	0.250123i	0.929152	+	0.369697i	$0.120539\pi$
$878$	0.513648	+	10.3530i	0.0173348	+	0.349396i
$879$	11.6899	+	11.3667i	0.394290	+	0.383390i
$880$		0			0
$881$		−	18.8765i		−	0.635964i	−0.948097	−	0.317982i	$-0.896995\pi$
$881$		−	18.8765i		−	0.635964i	0.948097	−	0.317982i	$-0.103005\pi$
$882$	−1.10233	−	14.1761i	−0.0371174	−	0.477334i
$883$		−	52.8298i		−	1.77787i	−0.458038	−	0.888933i	$-0.651448\pi$
$883$		−	52.8298i		−	1.77787i	0.458038	−	0.888933i	$-0.348552\pi$
$884$	2.13988	+	21.5124i	0.0719719	+	0.723540i
$885$		0			0
$886$	49.7129	−	2.46644i	1.67014	−	0.0828615i
$887$	7.71917	−	13.3700i	0.259184	−	0.448921i	−0.706839	−	0.707374i	$-0.749880\pi$
$887$	7.71917	−	13.3700i	0.259184	−	0.448921i	0.966024	+	0.258454i	$0.0832129\pi$
$888$	−12.9882	−	1.29091i	−0.435857	−	0.0433201i
$889$	−9.78270	−	16.9441i	−0.328101	−	0.568288i
$890$		0			0
$891$	12.6876	−	25.1302i	0.425049	−	0.841895i
$892$	4.89843	+	2.21372i	0.164012	+	0.0741208i
$893$	−8.89168	+	5.13361i	−0.297549	+	0.171790i
$894$	−26.2088	+	8.84231i	−0.876554	+	0.295731i
$895$		0			0
$896$	−12.3793	−	34.2306i	−0.413563	−	1.14356i
$897$	3.26540	+	11.5374i	0.109029	+	0.385222i
$898$	−28.9905	−	14.8733i	−0.967427	−	0.496330i
$899$	9.56163			0.318898
$900$		0			0
$901$	−76.5466			−2.55014
$902$	0.946473	+	0.485580i	0.0315141	+	0.0161680i
$903$	20.6834	−	21.2715i	0.688302	−	0.707871i
$904$	1.98182	+	0.779822i	0.0659143	+	0.0259365i
$905$		0			0
$906$	−10.3688	+	51.6249i	−0.344479	+	1.71512i
$907$	31.0477	−	17.9254i	1.03092	−	0.595203i	0.113674	−	0.993518i	$-0.463738\pi$
$907$	31.0477	−	17.9254i	1.03092	−	0.595203i	0.917249	+	0.398315i	$0.130405\pi$
$908$	−8.86085	+	19.6069i	−0.294058	+	0.650679i
$909$	15.0127	−	0.420925i	0.497938	−	0.0139612i
$910$		0			0
$911$	26.3466	+	45.6336i	0.872900	+	1.51191i	0.858983	+	0.512005i	$0.171097\pi$
$911$	26.3466	+	45.6336i	0.872900	+	1.51191i	0.0139176	+	0.999903i	$0.495570\pi$
$912$	13.0505	+	8.42196i	0.432144	+	0.278879i
$913$	−1.94968	+	3.37694i	−0.0645249	+	0.111760i
$914$	48.9731	−	2.42973i	1.61989	−	0.0803683i
$915$		0			0
$916$	5.14508	−	0.511791i	0.169998	−	0.0169100i
$917$		−	31.5002i		−	1.04023i
$918$	14.8849	+	40.3486i	0.491275	+	1.33170i
$919$			43.1318i			1.42279i	0.702795	+	0.711393i	$0.251935\pi$
$919$			43.1318i			1.42279i	−0.702795	+	0.711393i	$0.748065\pi$
$920$		0			0
$921$	−7.79391	+	30.8081i	−0.256818	+	1.01516i
$922$	1.88251	+	37.9434i	0.0619970	+	1.24960i
$923$	−10.4629	+	18.1222i	−0.344389	+	0.596500i
$924$	5.16273	−	34.4773i	0.169841	−	1.13422i
$925$		0			0
$926$	−10.3079	+	6.65325i	−0.338738	+	0.218639i
$927$	23.3807	+	37.9958i	0.767924	+	1.24795i
$928$	−43.3830	−	12.2749i	−1.42412	−	0.402942i
$929$	0.278475	−	0.160777i	0.00913645	−	0.00527493i	−0.495425	−	0.868651i	$-0.664988\pi$
$929$	0.278475	−	0.160777i	0.00913645	−	0.00527493i	0.504561	+	0.863376i	$0.331654\pi$
$930$		0			0
$931$	6.50681	+	3.75671i	0.213252	+	0.123121i
$932$	−1.59387	+	1.14450i	−0.0522090	+	0.0374892i
$933$	37.7330	−	38.8058i	1.23532	−	1.27044i
$934$	9.27810	−	18.0845i	0.303589	−	0.591744i
$935$		0			0
$936$	−11.9831	+	10.1003i	−0.391679	+	0.330140i
$937$	−28.1917			−0.920983			−0.460492	−	0.887664i	$-0.652327\pi$
$937$	−28.1917			−0.920983			−0.460492	+	0.887664i	$0.652327\pi$
$938$	17.9426	−	34.9731i	0.585847	−	1.14191i
$939$	−2.42068	−	8.55278i	−0.0789959	−	0.279109i
$940$		0			0
$941$	−23.0237	−	13.2927i	−0.750551	−	0.433331i	0.0753418	−	0.997158i	$-0.475995\pi$
$941$	−23.0237	−	13.2927i	−0.750551	−	0.433331i	−0.825893	+	0.563827i	$0.809329\pi$
$942$	−0.936143	−	2.77475i	−0.0305012	−	0.0904062i
$943$	−0.780595	+	0.450676i	−0.0254197	+	0.0146760i
$944$	−18.3657	−	20.8602i	−0.597752	−	0.678941i
$945$		0			0
$946$	19.7878	−	12.7721i	0.643358	−	0.415257i
$947$	−7.97563	−	13.8142i	−0.259173	−	0.448901i	0.706848	−	0.707366i	$-0.250117\pi$
$947$	−7.97563	−	13.8142i	−0.259173	−	0.448901i	−0.966021	+	0.258465i	$0.916783\pi$
$948$	36.4452	+	29.0068i	1.18369	+	0.942098i
$949$	−12.1612	+	21.0638i	−0.394768	+	0.683758i
$950$		0			0
$951$	−24.6930	+	6.98882i	−0.800725	+	0.226628i
$952$	33.1690	+	41.6679i	1.07501	+	1.35046i
$953$		−	47.3090i		−	1.53249i	−0.642550	−	0.766244i	$-0.722123\pi$
$953$		−	47.3090i		−	1.53249i	0.642550	−	0.766244i	$-0.277877\pi$
$954$	−31.3877	−	45.7611i	−1.01621	−	1.48157i
$955$		0			0
$956$	15.3562	−	1.52751i	0.496654	−	0.0494031i
$957$	−30.9580	−	30.1022i	−1.00073	−	0.973066i
$958$	−35.7409	+	1.77323i	−1.15474	+	0.0572906i
$959$	9.12628	−	15.8072i	0.294703	−	0.510441i
$960$		0			0
$961$	−14.7804	−	25.6004i	−0.476787	−	0.825819i
$962$	3.77391	+	5.84692i	0.121676	+	0.188512i
$963$	−7.80984	−	4.22170i	−0.251669	−	0.136042i
$964$	19.7818	−	43.7724i	0.637129	−	1.40981i
$965$		0			0
$966$	22.1724	+	19.5178i	0.713384	+	0.627975i
$967$	−7.40354	−	4.27444i	−0.238082	−	0.137457i	0.376213	−	0.926533i	$-0.377226\pi$
$967$	−7.40354	−	4.27444i	−0.238082	−	0.137457i	−0.614295	+	0.789077i	$0.710559\pi$
$968$	−1.25937	+	3.20053i	−0.0404777	+	0.102869i
$969$	−22.0311	−	5.57349i	−0.707741	−	0.179046i
$970$		0			0
$971$	57.5120			1.84565			0.922823	−	0.385224i	$-0.125876\pi$
$971$	57.5120			1.84565			0.922823	+	0.385224i	$0.125876\pi$
$972$	−18.0177	+	25.4433i	−0.577918	+	0.816095i
$973$	−29.6907			−0.951841
$974$	2.01955	+	1.03611i	0.0647105	+	0.0331991i
$975$		0			0
$976$	−13.0813	+	2.62846i	−0.418723	+	0.0841349i
$977$	−30.4604	−	17.5863i	−0.974514	−	0.562636i	−0.0739049	−	0.997265i	$-0.523546\pi$
$977$	−30.4604	−	17.5863i	−0.974514	−	0.562636i	−0.900610	+	0.434629i	$0.856879\pi$
$978$	23.5738	+	20.7514i	0.753806	+	0.663557i
$979$	−38.8112	+	22.4077i	−1.24041	+	0.716152i
$980$		0			0
$981$	9.79733	+	5.29606i	0.312805	+	0.169090i
$982$	1.27594	+	1.97682i	0.0407169	+	0.0630827i
$983$	25.6002	+	44.3409i	0.816520	+	1.41425i	0.908231	+	0.418469i	$0.137433\pi$
$983$	25.6002	+	44.3409i	0.816520	+	1.41425i	−0.0917112	+	0.995786i	$0.529234\pi$
$984$	−0.956996	−	0.687065i	−0.0305079	−	0.0219028i
$985$		0			0
$986$	65.8851	−	3.26880i	2.09821	−	0.104100i
$987$	−18.2976	−	17.7917i	−0.582418	−	0.566317i
$988$	−0.819706	−	8.24057i	−0.0260783	−	0.262168i
$989$			19.9559i			0.634561i
$990$		0			0
$991$			37.0240i			1.17611i	0.808822	+	0.588053i	$0.200105\pi$
$991$			37.0240i			1.17611i	−0.808822	+	0.588053i	$0.799895\pi$
$992$	−1.66494	−	6.57899i	−0.0528617	−	0.208883i
$993$	−42.4632	+	12.0183i	−1.34753	+	0.381389i
$994$	2.55449	+	51.4877i	0.0810235	+	1.63309i
$995$		0			0
$996$	2.68925	−	3.37887i	0.0852120	−	0.107063i
$997$	−21.6016	−	37.4150i	−0.684128	−	1.18494i	−0.973710	−	0.227791i	$-0.926850\pi$
$997$	−21.6016	−	37.4150i	−0.684128	−	1.18494i	0.289582	−	0.957153i	$-0.406484\pi$
$998$	4.99563	−	3.22444i	0.158134	−	0.102068i
$999$	10.1920	+	9.36905i	0.322461	+	0.296424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.r.g.851.16		48
4.3	odd	2	inner	900.2.r.g.851.23		48
5.2	odd	4		180.2.n.d.59.21	yes	48
5.3	odd	4		180.2.n.d.59.4	✓	48
5.4	even	2	inner	900.2.r.g.851.9		48
9.2	odd	6	inner	900.2.r.g.551.23		48
15.2	even	4		540.2.n.d.179.4		48
15.8	even	4		540.2.n.d.179.21		48
20.3	even	4		180.2.n.d.59.14	yes	48
20.7	even	4		180.2.n.d.59.11	yes	48
20.19	odd	2	inner	900.2.r.g.851.2		48
36.11	even	6	inner	900.2.r.g.551.16		48
45.2	even	12		180.2.n.d.119.14	yes	48
45.7	odd	12		540.2.n.d.359.11		48
45.29	odd	6	inner	900.2.r.g.551.2		48
45.38	even	12		180.2.n.d.119.11	yes	48
45.43	odd	12		540.2.n.d.359.14		48
60.23	odd	4		540.2.n.d.179.11		48
60.47	odd	4		540.2.n.d.179.14		48
180.7	even	12		540.2.n.d.359.21		48
180.43	even	12		540.2.n.d.359.4		48
180.47	odd	12		180.2.n.d.119.4	yes	48
180.83	odd	12		180.2.n.d.119.21	yes	48
180.119	even	6	inner	900.2.r.g.551.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.4	✓	48	5.3	odd	4
180.2.n.d.59.11	yes	48	20.7	even	4
180.2.n.d.59.14	yes	48	20.3	even	4
180.2.n.d.59.21	yes	48	5.2	odd	4
180.2.n.d.119.4	yes	48	180.47	odd	12
180.2.n.d.119.11	yes	48	45.38	even	12
180.2.n.d.119.14	yes	48	45.2	even	12
180.2.n.d.119.21	yes	48	180.83	odd	12
540.2.n.d.179.4		48	15.2	even	4
540.2.n.d.179.11		48	60.23	odd	4
540.2.n.d.179.14		48	60.47	odd	4
540.2.n.d.179.21		48	15.8	even	4
540.2.n.d.359.4		48	180.43	even	12
540.2.n.d.359.11		48	45.7	odd	12
540.2.n.d.359.14		48	45.43	odd	12
540.2.n.d.359.21		48	180.7	even	12
900.2.r.g.551.2		48	45.29	odd	6	inner
900.2.r.g.551.9		48	180.119	even	6	inner
900.2.r.g.551.16		48	36.11	even	6	inner
900.2.r.g.551.23		48	9.2	odd	6	inner
900.2.r.g.851.2		48	20.19	odd	2	inner
900.2.r.g.851.9		48	5.4	even	2	inner
900.2.r.g.851.16		48	1.1	even	1	trivial
900.2.r.g.851.23		48	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.645549 - 1.25828i) q^{2} +(-1.67915 - 0.424796i) q^{3} +(-1.16653 - 1.62456i) q^{4} +(-1.61849 + 1.83861i) q^{6} +(2.78632 - 1.60868i) q^{7} +(-2.79721 + 0.419091i) q^{8} +(2.63910 + 1.42659i) q^{9} +(-1.56397 - 2.70887i) q^{11} +(1.26868 + 3.22342i) q^{12} +(0.923481 - 1.59952i) q^{13} +(-0.225466 - 4.54445i) q^{14} +(-1.27840 + 3.79021i) q^{16} -5.85246i q^{17} +(3.49872 - 2.39978i) q^{18} +2.24186i q^{19} +(-5.36201 + 1.51760i) q^{21} +(-4.41814 + 0.219199i) q^{22} +(1.87409 - 3.24603i) q^{23} +(4.87496 + 0.484526i) q^{24} +(-1.41649 - 2.19456i) q^{26} +(-3.82543 - 3.51655i) q^{27} +(-5.86374 - 2.64996i) q^{28} +(-6.90237 + 3.98509i) q^{29} +(-1.03895 - 0.599838i) q^{31} +(3.94387 + 4.05535i) q^{32} +(1.47542 + 5.21298i) q^{33} +(-7.36403 - 3.77805i) q^{34} +(-0.761003 - 5.95154i) q^{36} -2.66428 q^{37} +(2.82088 + 1.44723i) q^{38} +(-2.23013 + 2.29354i) q^{39} +(-0.208259 - 0.120238i) q^{41} +(-1.55187 + 7.72659i) q^{42} +(-4.61084 + 2.66207i) q^{43} +(-2.57631 + 5.70075i) q^{44} +(-2.87459 - 4.45360i) q^{46} +(2.28989 + 3.96621i) q^{47} +(3.75669 - 5.82128i) q^{48} +(1.67571 - 2.90242i) q^{49} +(-2.48611 + 9.82717i) q^{51} +(-3.67578 + 0.365637i) q^{52} -13.0794i q^{53} +(-6.89430 + 2.54336i) q^{54} +(-7.11972 + 5.66754i) q^{56} +(0.952332 - 3.76441i) q^{57} +(0.558533 + 11.2577i) q^{58} +(-3.47411 + 6.01734i) q^{59} +(1.66785 + 2.88880i) q^{61} +(-1.42546 + 0.920065i) q^{62} +(9.64830 - 0.270519i) q^{63} +(7.64873 - 2.34457i) q^{64} +(7.51183 + 1.50874i) q^{66} +(7.48148 + 4.31943i) q^{67} +(-9.50769 + 6.82709i) q^{68} +(-4.52579 + 4.65446i) q^{69} -11.3298 q^{71} +(-7.97997 - 2.88446i) q^{72} -13.1688 q^{73} +(-1.71992 + 3.35240i) q^{74} +(3.64203 - 2.61520i) q^{76} +(-8.71543 - 5.03186i) q^{77} +(1.44625 + 4.28672i) q^{78} +(11.6449 - 6.72318i) q^{79} +(4.92966 + 7.52984i) q^{81} +(-0.285735 + 0.184428i) q^{82} +(-0.623311 - 1.07961i) q^{83} +(8.72040 + 6.94058i) q^{84} +(0.373105 + 7.52023i) q^{86} +(13.2830 - 3.75946i) q^{87} +(5.51001 + 6.92183i) q^{88} -14.3274i q^{89} -5.94235i q^{91} +(-7.45956 + 0.742017i) q^{92} +(1.48975 + 1.44856i) q^{93} +(6.46884 - 0.320942i) q^{94} +(-4.89966 - 8.48489i) q^{96} +(-3.32238 - 5.75453i) q^{97} +(-2.57030 - 3.98217i) q^{98} +(-0.263000 - 9.38013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{4} + 12 q^{9} + 42 q^{14} + 30 q^{16} - 12 q^{21} + 6 q^{24} + 4 q^{34} + 96 q^{36} + 96 q^{41} + 4 q^{46} - 32 q^{49} + 30 q^{54} + 6 q^{56} + 8 q^{61} + 20 q^{64} + 36 q^{66} + 96 q^{69} - 72 q^{74}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q + 2 * q^4 + 12 * q^9 + 42 * q^14 + 30 * q^16 - 12 * q^21 + 6 * q^24 + 4 * q^34 + 96 * q^36 + 96 * q^41 + 4 * q^46 - 32 * q^49 + 30 * q^54 + 6 * q^56 + 8 * q^61 + 20 * q^64 + 36 * q^66 + 96 * q^69 - 72 * q^74 + 36 * q^81 + 6 * q^84 + 108 * q^86 + 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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