LMFDB - Embedded newform 600.2.w.j.293.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.3
Character	$\chi$	$=$	600.293
Dual form			600.2.w.j.557.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30986 + 0.533177i) q^{2} +(0.667305 - 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(-0.0218716 + 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(-1.13026 + 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})$	\(q+(-1.30986 + 0.533177i) q^{2} +(0.667305 - 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(-0.0218716 + 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(-1.13026 + 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} -3.68607 q^{11} +(-1.27731 - 3.22001i) q^{12} +(-3.88771 + 3.88771i) q^{13} +(0.452626 - 1.07407i) q^{14} +(0.0980619 - 3.99880i) q^{16} +(-0.880105 - 0.880105i) q^{17} +(3.90038 + 1.66945i) q^{18} -6.32919 q^{19} +(0.542584 + 1.32036i) q^{21} +(4.82821 - 1.96533i) q^{22} +(2.06626 - 2.06626i) q^{23} +(3.38993 + 3.53672i) q^{24} +(3.01950 - 7.16518i) q^{26} +(-4.81715 + 1.94809i) q^{27} +(-0.0202063 + 1.64820i) q^{28} +1.37122i q^{29} +3.32075 q^{31} +(2.00362 + 5.29013i) q^{32} +(-2.45973 + 5.89160i) q^{33} +(1.62206 + 0.683558i) q^{34} +(-5.99904 - 0.107144i) q^{36} +(-2.44147 - 2.44147i) q^{37} +(8.29032 - 3.37458i) q^{38} +(3.61961 + 8.80819i) q^{39} -0.648104i q^{41} +(-1.41469 - 1.44018i) q^{42} +(-0.819412 + 0.819412i) q^{43} +(-5.27640 + 5.14859i) q^{44} +(-1.60482 + 3.80818i) q^{46} +(-6.28508 - 6.28508i) q^{47} +(-6.32602 - 2.82515i) q^{48} +6.32075i q^{49} +(-1.99401 + 0.819412i) q^{51} +(-0.134798 + 10.9953i) q^{52} +(5.60782 + 5.60782i) q^{53} +(5.27109 - 5.12011i) q^{54} +(-0.852318 - 2.16968i) q^{56} +(-4.22349 + 10.1162i) q^{57} +(-0.731106 - 1.79611i) q^{58} -6.12026i q^{59} +5.13471i q^{61} +(-4.34971 + 1.77055i) q^{62} +(2.47245 + 0.0138443i) q^{63} +(-5.44503 - 5.86102i) q^{64} +(0.0806201 - 9.02862i) q^{66} +(-4.90636 - 4.90636i) q^{67} +(-2.48912 - 0.0305156i) q^{68} +(-1.92377 - 4.68141i) q^{69} -4.13251i q^{71} +(7.91501 - 3.05821i) q^{72} +(-4.69820 - 4.69820i) q^{73} +(4.49972 + 1.89624i) q^{74} +(-9.05987 + 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-9.43750 - 9.60756i) q^{78} -1.10079i q^{79} +(-0.100786 + 8.99944i) q^{81} +(0.345554 + 0.848922i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(2.62091 + 1.13215i) q^{84} +(0.636420 - 1.51020i) q^{86} +(2.19169 + 0.915024i) q^{87} +(4.16621 - 9.55717i) q^{88} -15.3562 q^{89} -4.53130i q^{91} +(0.0716428 - 5.84382i) q^{92} +(2.21595 - 5.30771i) q^{93} +(11.5836 + 4.88148i) q^{94} +(9.79248 + 0.327652i) q^{96} +(5.42154 - 5.42154i) q^{97} +(-3.37008 - 8.27927i) q^{98} +(7.77542 + 7.86299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.30986	+	0.533177i	−0.926208	+	0.377013i
$2$	−1.30986	+	0.533177i	−0.926208	+	0.377013i
$3$	0.667305	−	1.59834i	0.385268	−	0.922805i
$3$	0.667305	−	1.59834i	0.385268	−	0.922805i
$4$	1.43144	−	1.39677i	0.715722	−	0.698385i
$5$		0			0
$5$		0			0
$6$	−0.0218716	+	2.44939i	−0.00892904	+	0.999960i
$7$	−0.582772	+	0.582772i	−0.220267	+	0.220267i	−0.808611	−	0.588344i	$-0.799780\pi$
$7$	−0.582772	+	0.582772i	−0.220267	+	0.220267i	0.588344	+	0.808611i	$0.299780\pi$
$8$	−1.13026	+	2.59278i	−0.399606	+	0.916687i
$9$	−2.10941	−	2.13317i	−0.703136	−	0.711055i
$10$		0			0
$11$	−3.68607			−1.11139			−0.555695	−	0.831386i	$-0.687548\pi$
$11$	−3.68607			−1.11139			−0.555695	+	0.831386i	$0.687548\pi$
$12$	−1.27731	−	3.22001i	−0.368728	−	0.929537i
$13$	−3.88771	+	3.88771i	−1.07826	+	1.07826i	−0.0815911	+	0.996666i	$0.526000\pi$
$13$	−3.88771	+	3.88771i	−1.07826	+	1.07826i	−0.996666	+	0.0815911i	$0.974000\pi$
$14$	0.452626	−	1.07407i	0.120969	−	0.287057i
$15$		0			0
$16$	0.0980619	−	3.99880i	0.0245155	−	0.999699i
$17$	−0.880105	−	0.880105i	−0.213457	−	0.213457i	0.592277	−	0.805734i	$-0.298229\pi$
$17$	−0.880105	−	0.880105i	−0.213457	−	0.213457i	−0.805734	+	0.592277i	$0.798229\pi$
$18$	3.90038	+	1.66945i	0.919328	+	0.393493i
$19$	−6.32919			−1.45201			−0.726007	−	0.687687i	$-0.758626\pi$
$19$	−6.32919			−1.45201			−0.726007	+	0.687687i	$0.758626\pi$
$20$		0			0
$21$	0.542584	+	1.32036i	0.118402	+	0.288125i
$22$	4.82821	−	1.96533i	1.02938	−	0.419009i
$23$	2.06626	−	2.06626i	0.430844	−	0.430844i	−0.458071	−	0.888916i	$-0.651460\pi$
$23$	2.06626	−	2.06626i	0.430844	−	0.430844i	0.888916	+	0.458071i	$0.151460\pi$
$24$	3.38993	+	3.53672i	0.691967	+	0.721929i
$25$		0			0
$26$	3.01950	−	7.16518i	0.592173	−	1.40521i
$27$	−4.81715	+	1.94809i	−0.927061	+	0.374910i
$28$	−0.0202063	+	1.64820i	−0.00381863	+	0.311481i
$29$			1.37122i			0.254630i	0.991862	+	0.127315i	$0.0406359\pi$
$29$			1.37122i			0.254630i	−0.991862	+	0.127315i	$0.959364\pi$
$30$		0			0
$31$	3.32075			0.596425			0.298212	−	0.954500i	$-0.403610\pi$
$31$	3.32075			0.596425			0.298212	+	0.954500i	$0.403610\pi$
$32$	2.00362	+	5.29013i	0.354194	+	0.935172i
$33$	−2.45973	+	5.89160i	−0.428184	+	1.02560i
$34$	1.62206	+	0.683558i	0.278181	+	0.117229i
$35$		0			0
$36$	−5.99904	−	0.107144i	−0.999841	−	0.0178574i
$37$	−2.44147	−	2.44147i	−0.401376	−	0.401376i	0.477342	−	0.878718i	$-0.341600\pi$
$37$	−2.44147	−	2.44147i	−0.401376	−	0.401376i	−0.878718	+	0.477342i	$0.841600\pi$
$38$	8.29032	−	3.37458i	1.34487	−	0.547429i
$39$	3.61961	+	8.80819i	0.579602	+	1.41044i
$40$		0			0
$41$		−	0.648104i		−	0.101217i	−0.998719	−	0.0506084i	$-0.983884\pi$
$41$		−	0.648104i		−	0.101217i	0.998719	−	0.0506084i	$-0.0161160\pi$
$42$	−1.41469	−	1.44018i	−0.218292	−	0.222225i
$43$	−0.819412	+	0.819412i	−0.124959	+	0.124959i	−0.766821	−	0.641861i	$-0.778162\pi$
$43$	−0.819412	+	0.819412i	−0.124959	+	0.124959i	0.641861	+	0.766821i	$0.278162\pi$
$44$	−5.27640	+	5.14859i	−0.795447	+	0.776179i
$45$		0			0
$46$	−1.60482	+	3.80818i	−0.236617	+	0.561485i
$47$	−6.28508	−	6.28508i	−0.916772	−	0.916772i	0.0800208	−	0.996793i	$-0.474501\pi$
$47$	−6.28508	−	6.28508i	−0.916772	−	0.916772i	−0.996793	+	0.0800208i	$0.974501\pi$
$48$	−6.32602	−	2.82515i	−0.913082	−	0.407776i
$49$			6.32075i			0.902965i
$50$		0			0
$51$	−1.99401	+	0.819412i	−0.279217	+	0.114741i
$52$	−0.134798	+	10.9953i	−0.0186931	+	1.52477i
$53$	5.60782	+	5.60782i	0.770293	+	0.770293i	0.978158	−	0.207864i	$-0.0666512\pi$
$53$	5.60782	+	5.60782i	0.770293	+	0.770293i	−0.207864	+	0.978158i	$0.566651\pi$
$54$	5.27109	−	5.12011i	0.717305	−	0.696759i
$55$		0			0
$56$	−0.852318	−	2.16968i	−0.113896	−	0.289936i
$57$	−4.22349	+	10.1162i	−0.559415	+	1.33993i
$58$	−0.731106	−	1.79611i	−0.0959989	−	0.235840i
$59$		−	6.12026i		−	0.796790i	−0.917214	−	0.398395i	$-0.869567\pi$
$59$		−	6.12026i		−	0.796790i	0.917214	−	0.398395i	$-0.130433\pi$
$60$		0			0
$61$			5.13471i			0.657432i	0.944429	+	0.328716i	$0.106616\pi$
$61$			5.13471i			0.657432i	−0.944429	+	0.328716i	$0.893384\pi$
$62$	−4.34971	+	1.77055i	−0.552413	+	0.224860i
$63$	2.47245	+	0.0138443i	0.311500	+	0.00174421i
$64$	−5.44503	−	5.86102i	−0.680629	−	0.732628i
$65$		0			0
$66$	0.0806201	−	9.02862i	0.00992365	−	1.11135i
$67$	−4.90636	−	4.90636i	−0.599408	−	0.599408i	0.340747	−	0.940155i	$-0.389320\pi$
$67$	−4.90636	−	4.90636i	−0.599408	−	0.599408i	−0.940155	+	0.340747i	$0.889320\pi$
$68$	−2.48912	−	0.0305156i	−0.301851	−	0.00370056i
$69$	−1.92377	−	4.68141i	−0.231594	−	0.563576i
$70$		0			0
$71$		−	4.13251i		−	0.490439i	−0.969468	−	0.245220i	$-0.921140\pi$
$71$		−	4.13251i		−	0.490439i	0.969468	−	0.245220i	$-0.0788601\pi$
$72$	7.91501	−	3.05821i	0.932793	−	0.360414i
$73$	−4.69820	−	4.69820i	−0.549883	−	0.549883i	0.376524	−	0.926407i	$-0.377119\pi$
$73$	−4.69820	−	4.69820i	−0.549883	−	0.549883i	−0.926407	+	0.376524i	$0.877119\pi$
$74$	4.49972	+	1.89624i	0.523082	+	0.220433i
$75$		0			0
$76$	−9.05987	+	8.84042i	−1.03924	+	1.01407i
$77$	2.14814	−	2.14814i	0.244803	−	0.244803i
$78$	−9.43750	−	9.60756i	−1.06859	−	1.08784i
$79$		−	1.10079i		−	0.123848i	−0.998081	−	0.0619241i	$-0.980276\pi$
$79$		−	1.10079i		−	0.123848i	0.998081	−	0.0619241i	$-0.0197237\pi$
$80$		0			0
$81$	−0.100786	+	8.99944i	−0.0111985	+	0.999937i
$82$	0.345554	+	0.848922i	0.0381601	+	0.0937478i
$83$	−6.27439	−	6.27439i	−0.688703	−	0.688703i	0.273242	−	0.961945i	$-0.411904\pi$
$83$	−6.27439	−	6.27439i	−0.688703	−	0.688703i	−0.961945	+	0.273242i	$0.911904\pi$
$84$	2.62091	+	1.13215i	0.285965	+	0.123528i
$85$		0			0
$86$	0.636420	−	1.51020i	0.0686269	−	0.162849i
$87$	2.19169	+	0.915024i	0.234974	+	0.0981009i
$88$	4.16621	−	9.55717i	0.444119	−	1.01880i
$89$	−15.3562			−1.62775			−0.813875	−	0.581040i	$-0.802646\pi$
$89$	−15.3562			−1.62775			−0.813875	+	0.581040i	$0.802646\pi$
$90$		0			0
$91$		−	4.53130i		−	0.475009i
$92$	0.0716428	−	5.84382i	0.00746928	−	0.609260i
$93$	2.21595	−	5.30771i	0.229784	−	0.550384i
$94$	11.5836	+	4.88148i	1.19476	+	0.503486i
$95$		0			0
$96$	9.79248	+	0.327652i	0.999441	+	0.0334409i
$97$	5.42154	−	5.42154i	0.550474	−	0.550474i	−0.376104	−	0.926578i	$-0.622736\pi$
$97$	5.42154	−	5.42154i	0.550474	−	0.550474i	0.926578	+	0.376104i	$0.122736\pi$
$98$	−3.37008	−	8.27927i	−0.340430	−	0.836333i
$99$	7.77542	+	7.86299i	0.781459	+	0.790260i
$100$		0			0
$101$	9.84442			0.979556			0.489778	−	0.871847i	$-0.337078\pi$
$101$	9.84442			0.979556			0.489778	+	0.871847i	$0.337078\pi$
$102$	2.17497	−	2.13647i	0.215354	−	0.211542i
$103$	8.28098	+	8.28098i	0.815949	+	0.815949i	0.985518	−	0.169569i	$-0.0542377\pi$
$103$	8.28098	+	8.28098i	0.815949	+	0.815949i	−0.169569	+	0.985518i	$0.554238\pi$
$104$	−5.68587	−	14.4741i	−0.557545	−	1.41930i
$105$		0			0
$106$	−10.3354	−	4.35547i	−1.00386	−	0.423041i
$107$	5.84678	−	5.84678i	0.565230	−	0.565230i	−0.365559	−	0.930788i	$-0.619122\pi$
$107$	5.84678	−	5.84678i	0.565230	−	0.565230i	0.930788	+	0.365559i	$0.119122\pi$
$108$	−4.17444	+	9.51704i	−0.401686	+	0.915777i
$109$	−11.7033			−1.12097			−0.560487	−	0.828163i	$-0.689386\pi$
$109$	−11.7033			−1.12097			−0.560487	+	0.828163i	$0.689386\pi$
$110$		0			0
$111$	−5.53152	+	2.27311i	−0.525029	+	0.215754i
$112$	2.27324	+	2.38754i	0.214801	+	0.225601i
$113$	−8.58333	+	8.58333i	−0.807452	+	0.807452i	−0.984248	−	0.176796i	$-0.943427\pi$
$113$	−8.58333	+	8.58333i	−0.807452	+	0.807452i	0.176796	+	0.984248i	$0.443427\pi$
$114$	0.138429	−	15.5027i	0.0129651	−	1.45196i
$115$		0			0
$116$	1.91529	+	1.96283i	0.177830	+	0.182244i
$117$	16.4939	+	0.0923560i	1.52486	+	0.00853832i
$118$	3.26318	+	8.01666i	0.300400	+	0.737993i
$119$	1.02580			0.0940350
$120$		0			0
$121$	2.58708			0.235189
$122$	−2.73771	−	6.72573i	−0.247861	−	0.608919i
$123$	−1.03589	−	0.432483i	−0.0934033	−	0.0389956i
$124$	4.75347	−	4.63833i	0.426874	−	0.416535i
$125$		0			0
$126$	−3.24594	+	1.30012i	−0.289171	+	0.115824i
$127$	0.0146460	−	0.0146460i	0.00129962	−	0.00129962i	−0.706457	−	0.707756i	$-0.749707\pi$
$127$	0.0146460	−	0.0146460i	0.00129962	−	0.00129962i	0.707756	+	0.706457i	$0.249707\pi$
$128$	10.2572	+	4.77393i	0.906615	+	0.421959i
$129$	0.762905	+	1.85650i	0.0671701	+	0.163456i
$130$		0			0
$131$	5.23989			0.457811			0.228906	−	0.973449i	$-0.426485\pi$
$131$	5.23989			0.457811			0.228906	+	0.973449i	$0.426485\pi$
$132$	4.70826	+	11.8692i	0.409801	+	1.03308i
$133$	3.68847	−	3.68847i	0.319831	−	0.319831i
$134$	9.04259	+	3.81066i	0.781161	+	0.329191i
$135$		0			0
$136$	3.27666	−	1.28717i	0.280972	−	0.110374i
$137$	14.0984	+	14.0984i	1.20450	+	1.20450i	0.972782	+	0.231722i	$0.0744360\pi$
$137$	14.0984	+	14.0984i	1.20450	+	1.20450i	0.231722	+	0.972782i	$0.425564\pi$
$138$	5.01588	+	5.10627i	0.426980	+	0.434674i
$139$	9.22166			0.782171			0.391085	−	0.920354i	$-0.372100\pi$
$139$	9.22166			0.782171			0.391085	+	0.920354i	$0.372100\pi$
$140$		0			0
$141$	−14.2398	+	5.85165i	−1.19921	+	0.492798i
$142$	2.20336	+	5.41300i	0.184902	+	0.454249i
$143$	14.3304	−	14.3304i	1.19836	−	1.19836i
$144$	−8.73695	+	8.22592i	−0.728079	+	0.685493i
$145$		0			0
$146$	8.65895	+	3.64899i	0.716619	+	0.301993i
$147$	10.1027	+	4.21787i	0.833260	+	0.347884i
$148$	−6.90501	−	0.0846526i	−0.567589	−	0.00695840i
$149$			14.0054i			1.14737i	0.819076	+	0.573685i	$0.194487\pi$
$149$			14.0054i			1.14737i	−0.819076	+	0.573685i	$0.805513\pi$
$150$		0			0
$151$	13.1301			1.06851			0.534255	−	0.845323i	$-0.320592\pi$
$151$	13.1301			1.06851			0.534255	+	0.845323i	$0.320592\pi$
$152$	7.15361	−	16.4102i	0.580234	−	1.33104i
$153$	−0.0209077	+	3.73391i	−0.00169028	+	0.301869i
$154$	−1.66841	+	3.95909i	−0.134444	+	0.319032i
$155$		0			0
$156$	17.4843	+	7.55265i	1.39986	+	0.604696i
$157$	−6.36936	−	6.36936i	−0.508330	−	0.508330i	0.405683	−	0.914014i	$-0.367034\pi$
$157$	−6.36936	−	6.36936i	−0.508330	−	0.508330i	−0.914014	+	0.405683i	$0.867034\pi$
$158$	0.586914	+	1.44187i	0.0466924	+	0.114709i
$159$	12.7054	−	5.22110i	1.00760	−	0.414060i
$160$		0			0
$161$			2.40831i			0.189802i
$162$	−4.66628	−	11.8417i	−0.366618	−	0.930372i
$163$	−3.46013	+	3.46013i	−0.271018	+	0.271018i	−0.829510	−	0.558492i	$-0.811380\pi$
$163$	−3.46013	+	3.46013i	−0.271018	+	0.271018i	0.558492	+	0.829510i	$0.311380\pi$
$164$	−0.905253	−	0.927724i	−0.0706884	−	0.0724431i
$165$		0			0
$166$	11.5639	+	4.87318i	0.897533	+	0.378232i
$167$	−0.954151	−	0.954151i	−0.0738345	−	0.0738345i	0.669225	−	0.743060i	$-0.266626\pi$
$167$	−0.954151	−	0.954151i	−0.0738345	−	0.0738345i	−0.743060	+	0.669225i	$0.766626\pi$
$168$	−4.03666	−	0.0855420i	−0.311435	−	0.00659971i
$169$		−	17.2286i		−	1.32528i
$170$		0			0
$171$	13.3508	+	13.5012i	1.02096	+	1.03246i
$172$	−0.0284113	+	2.31747i	−0.00216634	+	0.176706i
$173$	−1.80240	−	1.80240i	−0.137034	−	0.137034i	0.635262	−	0.772296i	$-0.280892\pi$
$173$	−1.80240	−	1.80240i	−0.137034	−	0.137034i	−0.772296	+	0.635262i	$0.780892\pi$
$174$	−3.35867	−	0.0299909i	−0.254620	−	0.00227360i
$175$		0			0
$176$	−0.361463	+	14.7398i	−0.0272463	+	1.11106i
$177$	−9.78228	−	4.08408i	−0.735281	−	0.306978i
$178$	20.1144	−	8.18756i	1.50763	−	0.613683i
$179$		−	24.0166i		−	1.79508i	−0.440930	−	0.897541i	$-0.645351\pi$
$179$		−	24.0166i		−	1.79508i	0.440930	−	0.897541i	$-0.354649\pi$
$180$		0			0
$181$		−	21.7210i		−	1.61451i	−0.590205	−	0.807253i	$-0.700953\pi$
$181$		−	21.7210i		−	1.61451i	0.590205	−	0.807253i	$-0.299047\pi$
$182$	2.41599	+	5.93535i	0.179085	+	0.439957i
$183$	8.20703	+	3.42641i	0.606681	+	0.253288i
$184$	3.02195	+	7.69276i	0.222781	+	0.567117i
$185$		0			0
$186$	−0.0726302	+	8.13383i	−0.00532550	+	0.596401i
$187$	3.24412	+	3.24412i	0.237234	+	0.237234i
$188$	−17.7755	−	0.217921i	−1.29641	−	0.0158935i
$189$	1.67201	−	3.94259i	0.121621	−	0.286781i
$190$		0			0
$191$		−	12.9839i		−	0.939479i	−0.882805	−	0.469739i	$-0.844348\pi$
$191$		−	12.9839i		−	0.939479i	0.882805	−	0.469739i	$-0.155652\pi$
$192$	−13.0014	+	4.79195i	−0.938297	+	0.345829i
$193$	−9.48630	−	9.48630i	−0.682839	−	0.682839i	0.277800	−	0.960639i	$-0.410395\pi$
$193$	−9.48630	−	9.48630i	−0.682839	−	0.682839i	−0.960639	+	0.277800i	$0.910395\pi$
$194$	−4.21079	+	9.99208i	−0.302317	+	0.717389i
$195$		0			0
$196$	8.82864	+	9.04780i	0.630617	+	0.646272i
$197$	−12.8606	+	12.8606i	−0.916280	+	0.916280i	−0.996757	−	0.0804765i	$-0.974356\pi$
$197$	−12.8606	+	12.8606i	−0.916280	+	0.916280i	0.0804765	+	0.996757i	$0.474356\pi$
$198$	−14.3770	−	6.15370i	−1.02173	−	0.437324i
$199$			0.0463625i			0.00328655i	0.999999	+	0.00164328i	$0.000523071\pi$
$199$			0.0463625i			0.00328655i	−0.999999	+	0.00164328i	$0.999477\pi$
$200$		0			0
$201$	−11.1161	+	4.56802i	−0.784069	+	0.322203i
$202$	−12.8948	+	5.24882i	−0.907273	+	0.369306i
$203$	−0.799111	−	0.799111i	−0.0560866	−	0.0560866i
$204$	−1.70978	+	3.95812i	−0.119708	+	0.277123i
$205$		0			0
$206$	−15.2621	−	6.43165i	−1.06336	−	0.448115i
$207$	−8.76625	−	0.0490858i	−0.609296	−	0.00341170i
$208$	15.1649	+	15.9274i	1.05150	+	1.10437i
$209$	23.3298			1.61376
$210$		0			0
$211$		−	0.591066i		−	0.0406907i	−0.999793	−	0.0203453i	$-0.993523\pi$
$211$		−	0.591066i		−	0.0406907i	0.999793	−	0.0203453i	$-0.00647657\pi$
$212$	15.8601	+	0.194439i	1.08928	+	0.0133541i
$213$	−6.60518	−	2.75765i	−0.452579	−	0.188951i
$214$	−4.54107	+	10.7758i	−0.310421	+	0.736619i
$215$		0			0
$216$	0.393647	−	14.6917i	0.0267843	−	0.999641i
$217$	−1.93524	+	1.93524i	−0.131373	+	0.131373i
$218$	15.3296	−	6.23994i	1.03825	−	0.422622i
$219$	−10.6445	+	4.37421i	−0.719287	+	0.295582i
$220$		0			0
$221$	6.84318			0.460322
$222$	6.03353	−	5.92673i	0.404944	−	0.397776i
$223$	−16.8577	−	16.8577i	−1.12888	−	1.12888i	−0.990360	−	0.138517i	$-0.955767\pi$
$223$	−16.8577	−	16.8577i	−1.12888	−	1.12888i	−0.138517	−	0.990360i	$-0.544233\pi$
$224$	−4.25060	−	1.91529i	−0.284005	−	0.127970i
$225$		0			0
$226$	6.66649	−	15.8194i	0.443448	−	1.05229i
$227$	−7.23390	+	7.23390i	−0.480131	+	0.480131i	−0.905173	−	0.425043i	$-0.860259\pi$
$227$	−7.23390	+	7.23390i	−0.480131	+	0.480131i	0.425043	+	0.905173i	$0.360259\pi$
$228$	8.08434	+	20.3800i	0.535399	+	1.34970i
$229$	23.0081			1.52042			0.760210	−	0.649677i	$-0.225096\pi$
$229$	23.0081			1.52042			0.760210	+	0.649677i	$0.225096\pi$
$230$		0			0
$231$	−2.00000	−	4.86692i	−0.131590	−	0.320220i
$232$	−3.55529	−	1.54984i	−0.233416	−	0.101752i
$233$	4.45082	−	4.45082i	0.291583	−	0.291583i	−0.546122	−	0.837705i	$-0.683897\pi$
$233$	4.45082	−	4.45082i	0.291583	−	0.291583i	0.837705	+	0.546122i	$0.183897\pi$
$234$	−21.6539	+	8.67320i	−1.41556	+	0.566985i
$235$		0			0
$236$	−8.54860	−	8.76081i	−0.556466	−	0.570280i
$237$	−1.75944	−	0.734560i	−0.114288	−	0.0477148i
$238$	−1.34365	+	0.546934i	−0.0870959	+	0.0354524i
$239$	4.03472			0.260984			0.130492	−	0.991449i	$-0.458344\pi$
$239$	4.03472			0.260984			0.130492	+	0.991449i	$0.458344\pi$
$240$		0			0
$241$	−11.4612			−0.738279			−0.369139	−	0.929374i	$-0.620347\pi$
$241$	−11.4612			−0.738279			−0.369139	+	0.929374i	$0.620347\pi$
$242$	−3.38871	+	1.37937i	−0.217834	+	0.0886696i
$243$	14.3169	+	6.16646i	0.918432	+	0.395578i
$244$	7.17201	+	7.35005i	0.459141	+	0.470538i
$245$		0			0
$246$	1.58746	+	0.0141751i	0.101213	+	0.000903769i
$247$	24.6060	−	24.6060i	1.56564	−	1.56564i
$248$	−3.75331	+	8.60999i	−0.238335	+	0.546735i
$249$	−14.2156	+	5.84170i	−0.900874	+	0.370203i
$250$		0			0
$251$	−17.4804			−1.10335			−0.551677	−	0.834058i	$-0.686012\pi$
$251$	−17.4804			−1.10335			−0.551677	+	0.834058i	$0.686012\pi$
$252$	3.55851	−	3.43363i	0.224165	−	0.216299i
$253$	−7.61636	+	7.61636i	−0.478836	+	0.478836i
$254$	−0.0113752	+	0.0269930i	−0.000713745	+	0.00169369i
$255$		0			0
$256$	−15.9808	−	0.784260i	−0.998798	−	0.0490162i
$257$	−6.77283	−	6.77283i	−0.422477	−	0.422477i	0.463578	−	0.886056i	$-0.346565\pi$
$257$	−6.77283	−	6.77283i	−0.422477	−	0.422477i	−0.886056	+	0.463578i	$0.846565\pi$
$258$	−1.98914	−	2.02498i	−0.123838	−	0.126070i
$259$	2.84565			0.176820
$260$		0			0
$261$	2.92505	−	2.89247i	0.181056	−	0.179040i
$262$	−6.86350	+	2.79379i	−0.424028	+	0.172601i
$263$	−15.3708	+	15.3708i	−0.947805	+	0.947805i	−0.998704	−	0.0508987i	$-0.983791\pi$
$263$	−15.3708	+	15.3708i	−0.947805	+	0.947805i	0.0508987	+	0.998704i	$0.483791\pi$
$264$	−12.4955	−	13.0366i	−0.769046	−	0.802345i
$265$		0			0
$266$	−2.86476	+	6.79798i	−0.175649	+	0.416811i
$267$	−10.2472	+	24.5444i	−0.627121	+	1.50209i
$268$	−13.8762	−	0.170117i	−0.847627	−	0.0103916i
$269$			9.58859i			0.584627i	0.956323	+	0.292313i	$0.0944250\pi$
$269$			9.58859i			0.584627i	−0.956323	+	0.292313i	$0.905575\pi$
$270$		0			0
$271$	−20.9078			−1.27006			−0.635030	−	0.772487i	$-0.719012\pi$
$271$	−20.9078			−1.27006			−0.635030	+	0.772487i	$0.719012\pi$
$272$	−3.60567	+	3.43306i	−0.218626	+	0.208160i
$273$	−7.24257	−	3.02376i	−0.438341	−	0.183006i
$274$	−25.9837	−	10.9499i	−1.56974	−	0.661507i
$275$		0			0
$276$	−9.29263	−	4.01412i	−0.559350	−	0.241621i
$277$	8.86336	+	8.86336i	0.532547	+	0.532547i	0.921330	−	0.388782i	$-0.127104\pi$
$277$	8.86336	+	8.86336i	0.532547	+	0.532547i	−0.388782	+	0.921330i	$0.627104\pi$
$278$	−12.0790	+	4.91678i	−0.724453	+	0.294889i
$279$	−7.00483	−	7.08372i	−0.419368	−	0.424091i
$280$		0			0
$281$		−	12.1925i		−	0.727341i	−0.931528	−	0.363670i	$-0.881523\pi$
$281$		−	12.1925i		−	0.727341i	0.931528	−	0.363670i	$-0.118477\pi$
$282$	15.5321	−	15.2571i	0.924922	−	0.908550i
$283$	11.6799	−	11.6799i	0.694298	−	0.694298i	−0.268877	−	0.963175i	$-0.586652\pi$
$283$	11.6799	−	11.6799i	0.694298	−	0.694298i	0.963175	+	0.268877i	$0.0866525\pi$
$284$	−5.77217	−	5.91546i	−0.342516	−	0.351018i
$285$		0			0
$286$	−11.1301	+	26.4113i	−0.658135	+	1.56173i
$287$	0.377697	+	0.377697i	0.0222947	+	0.0222947i
$288$	7.05827	−	15.4331i	0.415912	−	0.909405i
$289$		−	15.4508i		−	0.908872i
$290$		0			0
$291$	−5.04767	−	12.2833i	−0.295900	−	0.720060i
$292$	−13.2875	−	0.162900i	−0.777594	−	0.00953298i
$293$	5.16432	+	5.16432i	0.301703	+	0.301703i	0.841680	−	0.539977i	$-0.181567\pi$
$293$	5.16432	+	5.16432i	0.301703	+	0.301703i	−0.539977	+	0.841680i	$0.681567\pi$
$294$	−15.4820	−	0.138245i	−0.902929	−	0.00806261i
$295$		0			0
$296$	9.08971	−	3.57071i	0.528328	−	0.207544i
$297$	17.7563	−	7.18079i	1.03033	−	0.416672i
$298$	−7.46739	−	18.3451i	−0.432574	−	1.06270i
$299$			16.0660i			0.929122i
$300$		0			0
$301$		−	0.955061i		−	0.0550488i
$302$	−17.1985	+	7.00066i	−0.989663	+	0.402843i
$303$	6.56923	−	15.7348i	0.377392	−	0.903939i
$304$	−0.620652	+	25.3091i	−0.0355968	+	1.45158i
$305$		0			0
$306$	−1.96345	−	4.90203i	−0.112243	−	0.280230i
$307$	−9.19824	−	9.19824i	−0.524972	−	0.524972i	0.394097	−	0.919069i	$-0.371057\pi$
$307$	−9.19824	−	9.19824i	−0.524972	−	0.524972i	−0.919069	+	0.394097i	$0.871057\pi$
$308$	0.0744818	−	6.07539i	0.00424399	−	0.346177i
$309$	18.7618	−	7.70992i	1.06732	−	0.438602i
$310$		0			0
$311$			30.5690i			1.73341i	0.498821	+	0.866705i	$0.333767\pi$
$311$			30.5690i			1.73341i	−0.498821	+	0.866705i	$0.666233\pi$
$312$	−26.9288	−	0.570656i	−1.52454	−	0.0323071i
$313$	16.4612	+	16.4612i	0.930440	+	0.930440i	0.997733	−	0.0672931i	$-0.0214363\pi$
$313$	16.4612	+	16.4612i	0.930440	+	0.930440i	−0.0672931	+	0.997733i	$0.521436\pi$
$314$	11.7389	+	4.94694i	0.662467	+	0.279172i
$315$		0			0
$316$	−1.53755	−	1.57571i	−0.0864937	−	0.0886408i
$317$	0.000616701	0	0.000616701i	3.46374e−5	0	3.46374e-5i	−0.707089	−	0.707124i	$-0.749992\pi$
$317$	0.000616701	0	0.000616701i	3.46374e−5	0	3.46374e-5i	0.707124	+	0.707089i	$0.249992\pi$
$318$	−13.8584	+	13.6131i	−0.777141	+	0.763385i
$319$		−	5.05442i		−	0.282993i
$320$		0			0
$321$	−5.44358	−	13.2468i	−0.303831	−	0.739362i
$322$	−1.28406	−	3.15454i	−0.0715578	−	0.175796i
$323$	5.57034	+	5.57034i	0.309942	+	0.309942i
$324$	12.4259	+	13.0230i	0.690327	+	0.723498i
$325$		0			0
$326$	2.68740	−	6.37713i	0.148842	−	0.353196i
$327$	−7.80967	+	18.7059i	−0.431876	+	1.03444i
$328$	1.68039	+	0.732524i	0.0927841	+	0.0404469i
$329$	7.32553			0.403870
$330$		0			0
$331$		−	8.28613i		−	0.455447i	−0.973726	−	0.227724i	$-0.926872\pi$
$331$		−	8.28613i		−	0.455447i	0.973726	−	0.227724i	$-0.0731283\pi$
$332$	−17.7453	−	0.217550i	−0.973901	−	0.0119396i
$333$	−0.0579994	+	10.3581i	−0.00317835	+	0.567622i
$334$	1.75853	+	0.741069i	0.0962226	+	0.0405495i
$335$		0			0
$336$	5.33305	−	2.04021i	0.290942	−	0.111302i
$337$	−2.27666	+	2.27666i	−0.124018	+	0.124018i	−0.766392	−	0.642374i	$-0.777950\pi$
$337$	−2.27666	+	2.27666i	−0.124018	+	0.124018i	0.642374	+	0.766392i	$0.277950\pi$
$338$	9.18590	+	22.5670i	0.499647	+	1.22748i
$339$	7.99142	+	19.4468i	0.434035	+	1.05621i
$340$		0			0
$341$	−12.2405			−0.662861
$342$	−24.6862	−	10.5663i	−1.33488	−	0.571357i
$343$	−7.76296	−	7.76296i	−0.419161	−	0.419161i
$344$	−1.19841	−	3.05070i	−0.0646139	−	0.164483i
$345$		0			0
$346$	3.32189	+	1.39989i	0.178586	+	0.0752584i
$347$	18.6384	−	18.6384i	1.00056	−	1.00056i	0.000564305	−	1.00000i	$-0.499820\pi$
$347$	18.6384	−	18.6384i	1.00056	−	1.00056i	1.00000		0.000564305i	$-0.000179624\pi$
$348$	4.41536	−	1.75148i	0.236688	−	0.0938892i
$349$	−17.7267			−0.948889			−0.474445	−	0.880285i	$-0.657351\pi$
$349$	−17.7267			−0.948889			−0.474445	+	0.880285i	$0.657351\pi$
$350$		0			0
$351$	11.1541	−	26.3013i	0.595360	−	1.40386i
$352$	−7.38548	−	19.4998i	−0.393648	−	1.03934i
$353$	10.5779	−	10.5779i	0.563007	−	0.563007i	−0.367153	−	0.930160i	$-0.619668\pi$
$353$	10.5779	−	10.5779i	0.563007	−	0.563007i	0.930160	+	0.367153i	$0.119668\pi$
$354$	14.9909	+	0.133860i	0.796758	+	0.00711457i
$355$		0			0
$356$	−21.9815	+	21.4490i	−1.16502	+	1.13680i
$357$	0.684521	−	1.63958i	0.0362287	−	0.0867759i
$358$	12.8051	+	31.4582i	0.676770	+	1.66262i
$359$	−24.7266			−1.30502			−0.652510	−	0.757780i	$-0.726284\pi$
$359$	−24.7266			−1.30502			−0.652510	+	0.757780i	$0.726284\pi$
$360$		0			0
$361$	21.0586			1.10835
$362$	11.5811	+	28.4513i	0.608691	+	1.49537i
$363$	1.72637	−	4.13505i	0.0906111	−	0.217034i
$364$	−6.32919	−	6.48630i	−0.331739	−	0.339974i
$365$		0			0
$366$	−12.5769	−	0.112304i	−0.657406	−	0.00587024i
$367$	−9.33767	+	9.33767i	−0.487423	+	0.487423i	−0.907492	−	0.420069i	$-0.862006\pi$
$367$	−9.33767	+	9.33767i	−0.487423	+	0.487423i	0.420069	+	0.907492i	$0.362006\pi$
$368$	−8.05992	−	8.46516i	−0.420152	−	0.441277i
$369$	−1.38251	+	1.36712i	−0.0719707	+	0.0711692i
$370$		0			0
$371$	−6.53616			−0.339341
$372$	−4.24164	−	10.6929i	−0.219919	−	0.554399i
$373$	11.9025	−	11.9025i	0.616291	−	0.616291i	−0.328287	−	0.944578i	$-0.606471\pi$
$373$	11.9025	−	11.9025i	0.616291	−	0.616291i	0.944578	+	0.328287i	$0.106471\pi$
$374$	−5.97903	−	2.51964i	−0.309168	−	0.130288i
$375$		0			0
$376$	23.3996	−	9.19207i	1.20674	−	0.474045i
$377$	−5.33092	−	5.33092i	−0.274557	−	0.274557i
$378$	−0.0879865	+	6.05570i	−0.00452554	+	0.311472i
$379$	−2.73341			−0.140406			−0.0702029	−	0.997533i	$-0.522365\pi$
$379$	−2.73341			−0.140406			−0.0702029	+	0.997533i	$0.522365\pi$
$380$		0			0
$381$	−0.0136360	−	0.0331827i	−0.000698593	−	0.00170000i
$382$	6.92270	+	17.0070i	0.354196	+	0.870153i
$383$	−17.6065	+	17.6065i	−0.899651	+	0.899651i	−0.995405	−	0.0957539i	$-0.969474\pi$
$383$	−17.6065	+	17.6065i	−0.899651	+	0.899651i	0.0957539	+	0.995405i	$0.469474\pi$
$384$	14.4750	−	13.2088i	0.738676	−	0.674060i
$385$		0			0
$386$	17.4836	+	7.36780i	0.889890	+	0.375011i
$387$	3.47642	+	0.0194659i	0.176716	+	0.000989506i
$388$	0.187980	−	15.3333i	0.00954322	−	0.778429i
$389$			25.1335i			1.27432i	0.770731	+	0.637160i	$0.219891\pi$
$389$			25.1335i			1.27432i	−0.770731	+	0.637160i	$0.780109\pi$
$390$		0			0
$391$	−3.63704			−0.183933
$392$	−16.3883	−	7.14408i	−0.827736	−	0.360831i
$393$	3.49660	−	8.37515i	0.176380	−	0.422470i
$394$	9.98855	−	23.7025i	0.503216	−	1.19412i
$395$		0			0
$396$	22.1129	+	0.394941i	1.11121	+	0.0198465i
$397$	−5.42664	−	5.42664i	−0.272355	−	0.272355i	0.557692	−	0.830048i	$-0.311687\pi$
$397$	−5.42664	−	5.42664i	−0.272355	−	0.272355i	−0.830048	+	0.557692i	$0.811687\pi$
$398$	−0.0247195	−	0.0607282i	−0.00123907	−	0.00304403i
$399$	−3.43411	−	8.35678i	−0.171921	−	0.418362i
$400$		0			0
$401$			5.15831i			0.257594i	0.991671	+	0.128797i	$0.0411115\pi$
$401$			5.15831i			0.257594i	−0.991671	+	0.128797i	$0.958888\pi$
$402$	12.1249	−	11.9103i	0.604736	−	0.594032i
$403$	−12.9101	+	12.9101i	−0.643099	+	0.643099i
$404$	14.0917	−	13.7504i	0.701090	−	0.684108i
$405$		0			0
$406$	1.47279	+	0.620652i	0.0730933	+	0.0308025i
$407$	8.99944	+	8.99944i	0.446085	+	0.446085i
$408$	0.129186	−	6.09617i	0.00639565	−	0.301806i
$409$			14.1638i			0.700356i	0.936683	+	0.350178i	$0.113879\pi$
$409$			14.1638i			0.700356i	−0.936683	+	0.350178i	$0.886121\pi$
$410$		0			0
$411$	31.9419	−	13.1261i	1.57558	−	0.647464i
$412$	23.4204	+	0.287124i	1.15384	+	0.0141456i
$413$	3.56672	+	3.56672i	0.175507	+	0.175507i
$414$	11.5087	−	4.60967i	0.565621	−	0.226553i
$415$		0			0
$416$	−28.3560	−	12.7770i	−1.39027	−	0.626444i
$417$	6.15365	−	14.7394i	0.301346	−	0.721791i
$418$	−30.5587	+	12.4389i	−1.49467	+	0.608407i
$419$			4.80514i			0.234746i	0.993088	+	0.117373i	$0.0374474\pi$
$419$			4.80514i			0.234746i	−0.993088	+	0.117373i	$0.962553\pi$
$420$		0			0
$421$			15.2187i			0.741716i	0.928690	+	0.370858i	$0.120936\pi$
$421$			15.2187i			0.741716i	−0.928690	+	0.370858i	$0.879064\pi$
$422$	0.315143	+	0.774212i	0.0153409	+	0.0376880i
$423$	−0.149308	+	26.6649i	−0.00725958	+	1.29649i
$424$	−20.8781	+	8.20157i	−1.01393	+	0.398304i
$425$		0			0
$426$	10.1221	+	0.0903846i	0.490420	+	0.00437915i
$427$	−2.99236	−	2.99236i	−0.144811	−	0.144811i
$428$	0.202724	−	16.5359i	0.00979903	−	0.799295i
$429$	−13.3421	−	32.4676i	−0.644164	−	1.56755i
$430$		0			0
$431$			27.8760i			1.34274i	0.741122	+	0.671370i	$0.234294\pi$
$431$			27.8760i			1.34274i	−0.741122	+	0.671370i	$0.765706\pi$
$432$	7.31764	+	19.4538i	0.352070	+	0.935974i
$433$	2.78003	+	2.78003i	0.133600	+	0.133600i	0.770744	−	0.637145i	$-0.219885\pi$
$433$	2.78003	+	2.78003i	0.133600	+	0.133600i	−0.637145	+	0.770744i	$0.719885\pi$
$434$	1.50306	−	3.56672i	0.0721492	−	0.171208i
$435$		0			0
$436$	−16.7526	+	16.3468i	−0.802305	+	0.782872i
$437$	−13.0777	+	13.0777i	−0.625592	+	0.625592i
$438$	11.6105	−	11.4050i	0.554771	−	0.544951i
$439$			10.8174i			0.516286i	0.966107	+	0.258143i	$0.0831105\pi$
$439$			10.8174i			0.516286i	−0.966107	+	0.258143i	$0.916889\pi$
$440$		0			0
$441$	13.4832	−	13.3331i	0.642058	−	0.634907i
$442$	−8.96358	+	3.64863i	−0.426354	+	0.173548i
$443$	−5.74963	−	5.74963i	−0.273173	−	0.273173i	0.557203	−	0.830376i	$-0.311874\pi$
$443$	−5.74963	−	5.74963i	−0.273173	−	0.273173i	−0.830376	+	0.557203i	$0.811874\pi$
$444$	−4.74305	+	10.9801i	−0.225095	+	0.521092i
$445$		0			0
$446$	31.0693	+	13.0930i	1.47118	+	0.619973i
$447$	22.3855	+	9.34590i	1.05880	+	0.442046i
$448$	6.58885	+	0.242427i	0.311294	+	0.0114536i
$449$	6.91183			0.326189			0.163095	−	0.986610i	$-0.447852\pi$
$449$	6.91183			0.326189			0.163095	+	0.986610i	$0.447852\pi$
$450$		0			0
$451$			2.38895i			0.112491i
$452$	−0.297608	+	24.2755i	−0.0139983	+	1.14182i
$453$	8.76176	−	20.9864i	0.411663	−	0.986026i
$454$	5.61841	−	13.3323i	0.263685	−	0.625716i
$455$		0			0
$456$	−21.4555	−	22.3845i	−1.00475	−	1.04825i
$457$	5.15748	−	5.15748i	0.241257	−	0.241257i	−0.576113	−	0.817370i	$-0.695431\pi$
$457$	5.15748	−	5.15748i	0.241257	−	0.241257i	0.817370	+	0.576113i	$0.195431\pi$
$458$	−30.1373	+	12.2674i	−1.40823	+	0.573219i
$459$	5.95412	+	2.52507i	0.277915	+	0.117860i
$460$		0			0
$461$	18.4555			0.859558			0.429779	−	0.902934i	$-0.358592\pi$
$461$	18.4555			0.859558			0.429779	+	0.902934i	$0.358592\pi$
$462$	5.21464	+	5.30861i	0.242607	+	0.246979i
$463$	19.6899	+	19.6899i	0.915068	+	0.915068i	0.996665	−	0.0815977i	$-0.0260023\pi$
$463$	19.6899	+	19.6899i	0.915068	+	0.915068i	−0.0815977	+	0.996665i	$0.526002\pi$
$464$	5.48325	+	0.134465i	0.254553	+	0.00624238i
$465$		0			0
$466$	−3.45685	+	8.20301i	−0.160136	+	0.379997i
$467$	−2.07946	+	2.07946i	−0.0962257	+	0.0962257i	−0.753581	−	0.657355i	$-0.771675\pi$
$467$	−2.07946	+	2.07946i	−0.0962257	+	0.0962257i	0.657355	+	0.753581i	$0.271675\pi$
$468$	23.7391	−	22.9060i	1.09734	−	1.05883i
$469$	5.71858			0.264060
$470$		0			0
$471$	−14.4307	+	5.93013i	−0.664933	+	0.273246i
$472$	15.8685	+	6.91747i	0.730407	+	0.318402i
$473$	3.02041	−	3.02041i	0.138879	−	0.138879i
$474$	2.69626	+	0.0240759i	0.123843	+	0.00110584i
$475$		0			0
$476$	1.46838	−	1.43281i	0.0673029	−	0.0656727i
$477$	0.133219	−	23.7916i	0.00609967	−	1.08934i
$478$	−5.28490	+	2.15122i	−0.241725	+	0.0983945i
$479$	19.7088			0.900517			0.450259	−	0.892898i	$-0.351332\pi$
$479$	19.7088			0.900517			0.450259	+	0.892898i	$0.351332\pi$
$480$		0			0
$481$	18.9835			0.865573
$482$	15.0125	−	6.11083i	0.683799	−	0.278341i
$483$	3.84931	+	1.60708i	0.175150	+	0.0731246i
$484$	3.70326	−	3.61356i	0.168330	−	0.164253i
$485$		0			0
$486$	−22.0409	−	0.443697i	−0.999797	−	0.0201265i
$487$	−4.21395	+	4.21395i	−0.190952	+	0.190952i	−0.796107	−	0.605155i	$-0.793111\pi$
$487$	−4.21395	+	4.21395i	−0.190952	+	0.190952i	0.605155	+	0.796107i	$0.293111\pi$
$488$	−13.3132	−	5.80354i	−0.602659	−	0.262714i
$489$	3.22151	+	7.83943i	0.145682	+	0.354511i
$490$		0			0
$491$	−27.7215			−1.25105			−0.625527	−	0.780203i	$-0.715116\pi$
$491$	−27.7215			−1.25105			−0.625527	+	0.780203i	$0.715116\pi$
$492$	−2.08690	+	0.827831i	−0.0940848	+	0.0373215i
$493$	1.20682	−	1.20682i	0.0543525	−	0.0543525i
$494$	−19.1110	+	45.3497i	−0.859843	+	2.04038i
$495$		0			0
$496$	0.325640	−	13.2790i	0.0146216	−	0.596246i
$497$	2.40831	+	2.40831i	0.108028	+	0.108028i
$498$	15.5057	−	15.2312i	0.694825	−	0.682527i
$499$	−5.14705			−0.230414			−0.115207	−	0.993342i	$-0.536753\pi$
$499$	−5.14705			−0.230414			−0.115207	+	0.993342i	$0.536753\pi$
$500$		0			0
$501$	−2.16177	+	0.888353i	−0.0965809	+	0.0396887i
$502$	22.8968	−	9.32016i	1.02193	−	0.415979i
$503$	−12.2281	+	12.2281i	−0.545224	+	0.545224i	−0.925056	−	0.379832i	$-0.875982\pi$
$503$	−12.2281	+	12.2281i	−0.545224	+	0.545224i	0.379832	+	0.925056i	$0.375982\pi$
$504$	−2.83040	+	6.39488i	−0.126076	+	0.284851i
$505$		0			0
$506$	5.91546	−	14.0372i	0.262974	−	0.624030i
$507$	−27.5372	−	11.4967i	−1.22297	−	0.510587i
$508$	0.000507817	−	0.0414220i	2.25307e−5	−	0.00183780i
$509$		−	35.8361i		−	1.58841i	−0.607651	−	0.794204i	$-0.707888\pi$
$509$		−	35.8361i		−	1.58841i	0.607651	−	0.794204i	$-0.292112\pi$
$510$		0			0
$511$	5.47596			0.242242
$512$	21.3506	−	7.49332i	0.943574	−	0.331161i
$513$	30.4886	−	12.3298i	1.34611	−	0.544375i
$514$	12.4825	+	5.26031i	0.550581	+	0.232022i
$515$		0			0
$516$	3.68516	+	1.59187i	0.162230	+	0.0700783i
$517$	23.1672	+	23.1672i	1.01889	+	1.01889i
$518$	−3.72738	+	1.51723i	−0.163772	+	0.0666634i
$519$	−4.08361	+	1.67811i	−0.179251	+	0.0736608i
$520$		0			0
$521$			18.1715i			0.796107i	0.917362	+	0.398054i	$0.130314\pi$
$521$			18.1715i			0.796107i	−0.917362	+	0.398054i	$0.869686\pi$
$522$	−2.28919	+	5.34829i	−0.100195	+	0.234088i
$523$	−21.7444	+	21.7444i	−0.950815	+	0.950815i	−0.998846	−	0.0480305i	$-0.984706\pi$
$523$	−21.7444	+	21.7444i	−0.950815	+	0.950815i	0.0480305	+	0.998846i	$0.484706\pi$
$524$	7.50061	−	7.31893i	0.327666	−	0.319729i
$525$		0			0
$526$	11.9382	−	28.3289i	0.520529	−	1.23520i
$527$	−2.92261	−	2.92261i	−0.127311	−	0.127311i
$528$	23.3181	+	10.4137i	1.01479	+	0.453198i
$529$			14.4612i			0.628746i
$530$		0			0
$531$	−13.0555	+	12.9101i	−0.566561	+	0.560252i
$532$	0.127889	−	10.4318i	0.00554471	−	0.452275i
$533$	2.51964	+	2.51964i	0.109138	+	0.109138i
$534$	0.335864	−	37.6133i	0.0145342	−	1.62768i
$535$		0			0
$536$	18.2666	−	7.17567i	0.788996	−	0.309942i
$537$	−38.3867	−	16.0264i	−1.65651	−	0.691589i
$538$	−5.11242	−	12.5597i	−0.220412	−	0.541486i
$539$		−	23.2987i		−	1.00355i
$540$		0			0
$541$			26.6843i			1.14725i	0.819119	+	0.573623i	$0.194463\pi$
$541$			26.6843i			1.14725i	−0.819119	+	0.573623i	$0.805537\pi$
$542$	27.3862	−	11.1476i	1.17634	−	0.478830i
$543$	−34.7176	−	14.4945i	−1.48987	−	0.622019i
$544$	2.89247	−	6.41927i	0.124014	−	0.275224i
$545$		0			0
$546$	11.0989	+	0.0991067i	0.474990	+	0.00424138i
$547$	22.2551	+	22.2551i	0.951559	+	0.951559i	0.998880	−	0.0473207i	$-0.0150683\pi$
$547$	22.2551	+	22.2551i	0.951559	+	0.951559i	−0.0473207	+	0.998880i	$0.515068\pi$
$548$	39.8732	+	0.488829i	1.70330	+	0.0208817i
$549$	10.9532	−	10.8312i	0.467470	−	0.462264i
$550$		0			0
$551$		−	8.67873i		−	0.369726i
$552$	14.3122	+	0.303295i	0.609169	+	0.0129091i
$553$	0.641507	+	0.641507i	0.0272797	+	0.0272797i
$554$	−16.3355	−	6.88398i	−0.694027	−	0.292472i
$555$		0			0
$556$	13.2003	−	12.8805i	0.559817	−	0.546257i
$557$	7.30615	−	7.30615i	0.309572	−	0.309572i	−0.535172	−	0.844743i	$-0.679753\pi$
$557$	7.30615	−	7.30615i	0.309572	−	0.309572i	0.844743	+	0.535172i	$0.179753\pi$
$558$	12.9522	+	5.54383i	0.548310	+	0.234689i
$559$		−	6.37128i		−	0.269476i
$560$		0			0
$561$	7.35005	−	3.02041i	0.310319	−	0.127522i
$562$	6.50074	+	15.9704i	0.274217	+	0.673669i
$563$	−21.3458	−	21.3458i	−0.899616	−	0.899616i	0.0957856	−	0.995402i	$-0.469464\pi$
$563$	−21.3458	−	21.3458i	−0.899616	−	0.899616i	−0.995402	+	0.0957856i	$0.969464\pi$
$564$	−12.2100	+	28.2660i	−0.514134	+	1.19021i
$565$		0			0
$566$	−9.07152	+	21.5264i	−0.381304	+	0.904823i
$567$	−5.18588	−	5.30335i	−0.217787	−	0.222720i
$568$	10.7147	+	4.67081i	0.449579	+	0.195983i
$569$	35.6410			1.49415			0.747075	−	0.664740i	$-0.231458\pi$
$569$	35.6410			1.49415			0.747075	+	0.664740i	$0.231458\pi$
$570$		0			0
$571$			9.49296i			0.397268i	0.980074	+	0.198634i	$0.0636505\pi$
$571$			9.49296i			0.397268i	−0.980074	+	0.198634i	$0.936350\pi$
$572$	0.496873	−	40.5293i	0.0207753	−	1.69462i
$573$	−20.7527	−	8.66419i	−0.866955	−	0.361952i
$574$	−0.696108	−	0.293349i	−0.0290550	−	0.0122441i
$575$		0			0
$576$	−1.01673	+	23.9785i	−0.0423636	+	0.999102i
$577$	−10.6312	+	10.6312i	−0.442582	+	0.442582i	−0.892879	−	0.450297i	$-0.851318\pi$
$577$	−10.6312	+	10.6312i	−0.442582	+	0.442582i	0.450297	+	0.892879i	$0.351318\pi$
$578$	8.23803	+	20.2384i	0.342657	+	0.841805i
$579$	−21.4926	+	8.83212i	−0.893203	+	0.367050i
$580$		0			0
$581$	7.31307			0.303397
$582$	13.1609	+	13.3981i	0.545537	+	0.555367i
$583$	−20.6708	−	20.6708i	−0.856097	−	0.856097i
$584$	17.4916	−	6.87124i	0.723808	−	0.284334i
$585$		0			0
$586$	−9.51801	−	4.01102i	−0.393186	−	0.165694i
$587$	17.1910	−	17.1910i	0.709550	−	0.709550i	−0.256891	−	0.966441i	$-0.582698\pi$
$587$	17.1910	−	17.1910i	0.709550	−	0.709550i	0.966441	+	0.256891i	$0.0826980\pi$
$588$	20.3529	−	8.07357i	0.839339	−	0.332949i
$589$	−21.0177			−0.866018
$590$		0			0
$591$	11.9737	+	29.1376i	0.492534	+	1.19856i
$592$	−10.0024	+	9.52355i	−0.411095	+	0.391415i
$593$	9.69544	−	9.69544i	0.398144	−	0.398144i	−0.479434	−	0.877578i	$-0.659158\pi$
$593$	9.69544	−	9.69544i	0.398144	−	0.398144i	0.877578	+	0.479434i	$0.159158\pi$
$594$	−19.4296	+	18.8731i	−0.797206	+	0.774372i
$595$		0			0
$596$	19.5624	+	20.0480i	0.801307	+	0.821198i
$597$	0.0741033	+	0.0309379i	0.00303285	+	0.00126621i
$598$	−8.56604	−	21.0442i	−0.350291	−	0.860560i
$599$	−26.8502			−1.09707			−0.548535	−	0.836128i	$-0.684814\pi$
$599$	−26.8502			−1.09707			−0.548535	+	0.836128i	$0.684814\pi$
$600$		0			0
$601$	−42.9566			−1.75224			−0.876119	−	0.482095i	$-0.839876\pi$
$601$	−42.9566			−1.75224			−0.876119	+	0.482095i	$0.839876\pi$
$602$	0.509217	+	1.25099i	0.0207541	+	0.0509866i
$603$	−0.116555	+	20.8156i	−0.00474649	+	0.847677i
$604$	18.7950	−	18.3397i	0.764756	−	0.746232i
$605$		0			0
$606$	−0.215313	+	24.1128i	−0.00874650	+	0.979517i
$607$	−32.0417	+	32.0417i	−1.30053	+	1.30053i	−0.372498	+	0.928033i	$0.621499\pi$
$607$	−32.0417	+	32.0417i	−1.30053	+	1.30053i	−0.928033	+	0.372498i	$0.878501\pi$
$608$	−12.6813	−	33.4822i	−0.514294	−	1.35788i
$609$	−1.81051	+	0.744004i	−0.0733654	+	0.0301486i
$610$		0			0
$611$	48.8691			1.97703
$612$	5.18549	+	5.37408i	0.209611	+	0.217234i
$613$	−20.1419	+	20.1419i	−0.813522	+	0.813522i	−0.985160	−	0.171638i	$-0.945094\pi$
$613$	−20.1419	+	20.1419i	−0.813522	+	0.813522i	0.171638	+	0.985160i	$0.445094\pi$
$614$	16.9527	+	7.14408i	0.684154	+	0.288311i
$615$		0			0
$616$	3.14170	+	7.99760i	0.126583	+	0.322232i
$617$	−7.33463	−	7.33463i	−0.295281	−	0.295281i	0.543881	−	0.839162i	$-0.316954\pi$
$617$	−7.33463	−	7.33463i	−0.295281	−	0.295281i	−0.839162	+	0.543881i	$0.816954\pi$
$618$	−20.4645	+	20.1022i	−0.823202	+	0.808631i
$619$	−11.9287			−0.479456			−0.239728	−	0.970840i	$-0.577058\pi$
$619$	−11.9287			−0.479456			−0.239728	+	0.970840i	$0.577058\pi$
$620$		0			0
$621$	−5.92821	+	13.9787i	−0.237891	+	0.560947i
$622$	−16.2987	−	40.0410i	−0.653519	−	1.60550i
$623$	8.94914	−	8.94914i	0.358540	−	0.358540i
$624$	35.5771	−	13.6104i	1.42422	−	0.544850i
$625$		0			0
$626$	−30.3385	−	12.7850i	−1.21257	−	0.510993i
$627$	15.5681	−	37.2890i	0.621729	−	1.48918i
$628$	−18.0139	−	0.220843i	−0.718834	−	0.00881260i
$629$			4.29751i			0.171353i
$630$		0			0
$631$	7.13985			0.284233			0.142116	−	0.989850i	$-0.454609\pi$
$631$	7.13985			0.284233			0.142116	+	0.989850i	$0.454609\pi$
$632$	2.85410	+	1.24417i	0.113530	+	0.0494905i
$633$	−0.944728	−	0.394421i	−0.0375496	−	0.0156768i
$634$	−0.000478978		0.00113660i	−1.90227e−5		4.51402e-5i
$635$		0			0
$636$	10.8943	−	25.2202i	0.431988	−	1.00005i
$637$	−24.5733	−	24.5733i	−0.973628	−	0.973628i
$638$	2.69490	+	6.62057i	0.106692	+	0.262111i
$639$	−8.81533	+	8.71716i	−0.348729	+	0.344846i
$640$		0			0
$641$		−	30.0187i		−	1.18567i	−0.805325	−	0.592834i	$-0.798009\pi$
$641$		−	30.0187i		−	1.18567i	0.805325	−	0.592834i	$-0.201991\pi$
$642$	14.1932	+	14.4489i	0.560160	+	0.570254i
$643$	32.7048	−	32.7048i	1.28975	−	1.28975i	0.354812	−	0.934938i	$-0.384545\pi$
$643$	32.7048	−	32.7048i	1.28975	−	1.28975i	0.934938	−	0.354812i	$-0.115455\pi$
$644$	3.36386	+	3.44736i	0.132555	+	0.135845i
$645$		0			0
$646$	−10.2663	−	4.32637i	−0.403923	−	0.170219i
$647$	2.53026	+	2.53026i	0.0994747	+	0.0994747i	0.755093	−	0.655618i	$-0.227592\pi$
$647$	2.53026	+	2.53026i	0.0994747	+	0.0994747i	−0.655618	+	0.755093i	$0.727592\pi$
$648$	−23.2197	−	10.4330i	−0.912154	−	0.409847i
$649$			22.5597i			0.885545i
$650$		0			0
$651$	1.80179	+	4.38458i	0.0706176	+	0.171845i
$652$	−0.119972	+	9.78598i	−0.00469847	+	0.383248i
$653$	−23.8061	−	23.8061i	−0.931604	−	0.931604i	0.0662023	−	0.997806i	$-0.478912\pi$
$653$	−23.8061	−	23.8061i	−0.931604	−	0.931604i	−0.997806	+	0.0662023i	$0.978912\pi$
$654$	0.255970	−	28.6660i	0.0100092	−	1.12093i
$655$		0			0
$656$	−2.59164	−	0.0635543i	−0.101186	−	0.00248138i
$657$	−0.111610	+	19.9325i	−0.00435432	+	0.777640i
$658$	−9.59539	+	3.90581i	−0.374067	+	0.152264i
$659$		−	15.7130i		−	0.612093i	−0.952017	−	0.306047i	$-0.900994\pi$
$659$		−	15.7130i		−	0.612093i	0.952017	−	0.306047i	$-0.0990063\pi$
$660$		0			0
$661$		−	25.2637i		−	0.982643i	−0.870978	−	0.491322i	$-0.836514\pi$
$661$		−	25.2637i		−	0.982643i	0.870978	−	0.491322i	$-0.163486\pi$
$662$	4.41798	+	10.8536i	0.171710	+	0.421839i
$663$	4.56649	−	10.9378i	0.177348	−	0.424788i
$664$	23.3598	−	9.17644i	0.906536	−	0.356115i
$665$		0			0
$666$	−5.44675	−	13.5986i	−0.211057	−	0.526935i
$667$	2.83330	+	2.83330i	0.109706	+	0.109706i
$668$	−2.69854	−	0.0330830i	−0.104410	−	0.00128002i
$669$	−38.1937	+	15.6952i	−1.47665	+	0.606812i
$670$		0			0
$671$		−	18.9269i		−	0.730664i
$672$	−5.89773	+	5.51584i	−0.227510	+	0.212778i
$673$	15.4486	+	15.4486i	0.595498	+	0.595498i	0.939111	−	0.343613i	$-0.111651\pi$
$673$	15.4486	+	15.4486i	0.595498	+	0.595498i	−0.343613	+	0.939111i	$0.611651\pi$
$674$	1.76824	−	4.19597i	0.0681099	−	0.161623i
$675$		0			0
$676$	−24.0644	−	24.6618i	−0.925554	−	0.948529i
$677$	−3.86002	+	3.86002i	−0.148353	+	0.148353i	−0.777382	−	0.629029i	$-0.783453\pi$
$677$	−3.86002	+	3.86002i	−0.148353	+	0.148353i	0.629029	+	0.777382i	$0.283453\pi$
$678$	−20.8362	−	21.2117i	−0.800210	−	0.814630i
$679$			6.31904i			0.242503i
$680$		0			0
$681$	6.73505	+	16.3895i	0.258088	+	0.628046i
$682$	16.0333	−	6.52637i	0.613947	−	0.249908i
$683$	20.9584	+	20.9584i	0.801949	+	0.801949i	0.983400	−	0.181451i	$-0.0580793\pi$
$683$	20.9584	+	20.9584i	0.801949	+	0.801949i	−0.181451	+	0.983400i	$0.558079\pi$
$684$	37.9691	+	0.678136i	1.45178	+	0.0259292i
$685$		0			0
$686$	14.3074	+	6.02932i	0.546259	+	0.230201i
$687$	15.3534	−	36.7749i	0.585770	−	1.40305i
$688$	3.19631	+	3.35702i	0.121858	+	0.127985i
$689$	−43.6032			−1.66115
$690$		0			0
$691$			26.8902i			1.02295i	0.859298	+	0.511475i	$0.170901\pi$
$691$			26.8902i			1.02295i	−0.859298	+	0.511475i	$0.829099\pi$
$692$	−5.09759	−	0.0624943i	−0.193781	−	0.00237568i
$693$	−9.11363	−	0.0510309i	−0.346198	−	0.00193850i
$694$	−14.4761	+	34.3513i	−0.549504	+	1.30396i
$695$		0			0
$696$	−4.84963	+	4.64836i	−0.183825	+	0.176196i
$697$	−0.570399	+	0.570399i	−0.0216054	+	0.0216054i
$698$	23.2194	−	9.45148i	0.878869	−	0.357744i
$699$	−4.14389	−	10.0840i	−0.156736	−	0.381412i
$700$		0			0
$701$	−35.7956			−1.35198			−0.675990	−	0.736911i	$-0.736284\pi$
$701$	−35.7956			−1.35198			−0.675990	+	0.736911i	$0.736284\pi$
$702$	−0.586964	+	40.3980i	−0.0221535	+	1.52472i
$703$	15.4525	+	15.4525i	0.582804	+	0.582804i
$704$	20.0708	+	21.6041i	0.756445	+	0.814236i
$705$		0			0
$706$	−8.21566	+	19.4955i	−0.309200	+	0.733723i
$707$	−5.73705	+	5.73705i	−0.215764	+	0.215764i
$708$	−19.7073	+	7.81748i	−0.740646	+	0.293799i
$709$	31.6856			1.18998			0.594988	−	0.803735i	$-0.297157\pi$
$709$	31.6856			1.18998			0.594988	+	0.803735i	$0.297157\pi$
$710$		0			0
$711$	−2.34816	+	2.32201i	−0.0880628	+	0.0870821i
$712$	17.3564	−	39.8152i	0.650459	−	1.49214i
$713$	6.86153	−	6.86153i	0.256966	−	0.256966i
$714$	−0.0224359	+	2.51259i	−0.000839642	+	0.0940312i
$715$		0			0
$716$	−33.5456	−	34.3784i	−1.25366	−	1.28478i
$717$	2.69238	−	6.44887i	0.100549	−	0.240837i
$718$	32.3883	−	13.1837i	1.20872	−	0.492010i
$719$	−47.9558			−1.78845			−0.894225	−	0.447618i	$-0.852272\pi$
$719$	−47.9558			−1.78845			−0.894225	+	0.447618i	$0.852272\pi$
$720$		0			0
$721$	−9.65184			−0.359453
$722$	−27.5837	+	11.2280i	−1.02656	+	0.417861i
$723$	−7.64809	+	18.3189i	−0.284435	+	0.681287i
$724$	−30.3392	−	31.0923i	−1.12755	−	1.15554i
$725$		0			0
$726$	−0.0565836	+	6.33678i	−0.00210002	+	0.235180i
$727$	−20.8052	+	20.8052i	−0.771622	+	0.771622i	−0.978390	−	0.206768i	$-0.933705\pi$
$727$	−20.8052	+	20.8052i	−0.771622	+	0.771622i	0.206768	+	0.978390i	$0.433705\pi$
$728$	11.7487	+	5.12153i	0.435435	+	0.189817i
$729$	19.4099	−	18.7685i	0.718884	−	0.695130i
$730$		0			0
$731$	1.44234			0.0533468
$732$	16.5338	−	6.55862i	0.611108	−	0.242414i
$733$	11.3990	−	11.3990i	0.421033	−	0.421033i	−0.464526	−	0.885559i	$-0.653775\pi$
$733$	11.3990	−	11.3990i	0.421033	−	0.421033i	0.885559	+	0.464526i	$0.153775\pi$
$734$	7.25237	−	17.2096i	0.267690	−	0.635219i
$735$		0			0
$736$	15.0708	+	6.79077i	0.555516	+	0.250311i
$737$	18.0852	+	18.0852i	0.666176	+	0.666176i
$738$	1.08198	−	2.52785i	0.0398281	−	0.0930514i
$739$	−9.60683			−0.353393			−0.176697	−	0.984265i	$-0.556541\pi$
$739$	−9.60683			−0.353393			−0.176697	+	0.984265i	$0.556541\pi$
$740$		0			0
$741$	−22.9092	−	55.7487i	−0.841591	−	2.04798i
$742$	8.56143	−	3.48493i	0.314300	−	0.127936i
$743$	−2.71436	+	2.71436i	−0.0995802	+	0.0995802i	−0.755142	−	0.655562i	$-0.772432\pi$
$743$	−2.71436	+	2.71436i	−0.0995802	+	0.0995802i	0.655562	+	0.755142i	$0.272432\pi$
$744$	11.2571	+	11.7446i	0.412706	+	0.430577i
$745$		0			0
$746$	−9.24445	+	21.9368i	−0.338463	+	0.803163i
$747$	−0.149054	+	26.6196i	−0.00545359	+	0.973958i
$748$	9.17508	+	0.112483i	0.335474	+	0.00411277i
$749$			6.81468i			0.249003i
$750$		0			0
$751$	−18.9690			−0.692189			−0.346094	−	0.938200i	$-0.612492\pi$
$751$	−18.9690			−0.692189			−0.346094	+	0.938200i	$0.612492\pi$
$752$	−25.7491	+	24.5164i	−0.938972	+	0.894022i
$753$	−11.6648	+	27.9397i	−0.425087	+	1.01818i
$754$	9.82507	+	4.14041i	0.357808	+	0.150785i
$755$		0			0
$756$	−3.11352	−	7.97901i	−0.113237	−	0.290194i
$757$	0.279592	+	0.279592i	0.0101620	+	0.0101620i	0.712170	−	0.702008i	$-0.247713\pi$
$757$	0.279592	+	0.279592i	0.0101620	+	0.0101620i	−0.702008	+	0.712170i	$0.747713\pi$
$758$	3.58037	−	1.45739i	0.130045	−	0.0529349i
$759$	7.09113	+	17.2560i	0.257392	+	0.626353i
$760$		0			0
$761$		−	20.3237i		−	0.736733i	−0.929681	−	0.368366i	$-0.879917\pi$
$761$		−	20.3237i		−	0.736733i	0.929681	−	0.368366i	$-0.120083\pi$
$762$	0.0355534	+	0.0361941i	0.00128797	+	0.00131117i
$763$	6.82036	−	6.82036i	0.246914	−	0.246914i
$764$	−18.1355	−	18.5857i	−0.656118	−	0.672406i
$765$		0			0
$766$	13.6746	−	32.4494i	0.494083	−	1.17244i
$767$	23.7938	+	23.7938i	0.859144	+	0.859144i
$768$	−11.9176	+	25.0194i	−0.430038	+	0.902811i
$769$			25.1716i			0.907711i	0.891075	+	0.453855i	$0.149952\pi$
$769$			25.1716i			0.907711i	−0.891075	+	0.453855i	$0.850048\pi$
$770$		0			0
$771$	−15.3448	+	6.30577i	−0.552631	+	0.227097i
$772$	−26.8293	−	0.328916i	−0.965607	−	0.0118379i
$773$	−24.0474	−	24.0474i	−0.864925	−	0.864925i	0.126980	−	0.991905i	$-0.459472\pi$
$773$	−24.0474	−	24.0474i	−0.864925	−	0.864925i	−0.991905	+	0.126980i	$0.959472\pi$
$774$	−4.56398	+	1.82805i	−0.164049	+	0.0657079i
$775$		0			0
$776$	7.92913	+	20.1846i	0.284639	+	0.724585i
$777$	1.89891	−	4.54832i	0.0681231	−	0.163170i
$778$	−13.4006	−	32.9213i	−0.480436	−	1.18029i
$779$			4.10197i			0.146968i
$780$		0			0
$781$			15.2327i			0.545070i
$782$	4.76400	−	1.93919i	0.170360	−	0.0693453i
$783$	−2.67127	−	6.60539i	−0.0954634	−	0.236058i
$784$	25.2754	+	0.619825i	0.902693	+	0.0221366i
$785$		0			0
$786$	−0.114605	+	12.8345i	−0.00408782	+	0.457793i
$787$	6.79695	+	6.79695i	0.242285	+	0.242285i	0.817795	−	0.575510i	$-0.195196\pi$
$787$	6.79695	+	6.79695i	0.242285	+	0.242285i	−0.575510	+	0.817795i	$0.695196\pi$
$788$	−0.445912	+	36.3725i	−0.0158850	+	1.29572i
$789$	14.3108	+	34.8249i	0.509479	+	1.23980i
$790$		0			0
$791$		−	10.0043i		−	0.355710i
$792$	−29.1752	+	11.2728i	−1.03670	+	0.400560i
$793$	−19.9623	−	19.9623i	−0.708881	−	0.708881i
$794$	10.0015	+	4.21476i	0.354939	+	0.149576i
$795$		0			0
$796$	0.0647578	+	0.0663654i	0.00229528	+	0.00235226i
$797$	−6.72322	+	6.72322i	−0.238149	+	0.238149i	−0.816083	−	0.577935i	$-0.803859\pi$
$797$	−6.72322	+	6.72322i	−0.238149	+	0.238149i	0.577935	+	0.816083i	$0.303859\pi$
$798$	8.95384	+	9.11519i	0.316963	+	0.322674i
$799$			11.0630i			0.391382i
$800$		0			0
$801$	32.3924	+	32.7572i	1.14453	+	1.15742i
$802$	−2.75030	−	6.75665i	−0.0971164	−	0.238585i
$803$	17.3179	+	17.3179i	0.611135	+	0.611135i
$804$	−9.53159	+	22.0655i	−0.336153	+	0.778190i
$805$		0			0
$806$	10.0270	−	23.7938i	0.353187	−	0.838101i
$807$	15.3259	+	6.39851i	0.539496	+	0.225238i
$808$	−11.1267	+	25.5244i	−0.391437	+	0.897946i
$809$	35.3381			1.24242			0.621212	−	0.783643i	$-0.286641\pi$
$809$	35.3381			1.24242			0.621212	+	0.783643i	$0.286641\pi$
$810$		0			0
$811$			37.1596i			1.30485i	0.757854	+	0.652425i	$0.226248\pi$
$811$			37.1596i			1.30485i	−0.757854	+	0.652425i	$0.773752\pi$
$812$	−2.26006	−	0.0277074i	−0.0793125	−	0.000972338i
$813$	−13.9519	+	33.4179i	−0.489314	+	1.17202i
$814$	−16.5863	−	6.98967i	−0.581348	−	0.244988i
$815$		0			0
$816$	3.08113	+	8.05399i	0.107861	+	0.281946i
$817$	5.18621	−	5.18621i	0.181443	−	0.181443i
$818$	−7.55184	−	18.5526i	−0.264044	−	0.648676i
$819$	−9.66601	+	9.55836i	−0.337758	+	0.333996i
$820$		0			0
$821$	28.5674			0.997010			0.498505	−	0.866887i	$-0.333882\pi$
$821$	28.5674			0.997010			0.498505	+	0.866887i	$0.333882\pi$
$822$	−34.8408	+	34.2241i	−1.21521	+	1.19370i
$823$	28.5682	+	28.5682i	0.995823	+	0.995823i	0.999991	−	0.00416817i	$-0.00132677\pi$
$823$	28.5682	+	28.5682i	0.995823	+	0.995823i	−0.00416817	+	0.999991i	$0.501327\pi$
$824$	−30.8304	+	12.1111i	−1.07403	+	0.421911i
$825$		0			0
$826$	−6.57357	−	2.77019i	−0.228724	−	0.0963872i
$827$	5.31276	−	5.31276i	0.184743	−	0.184743i	−0.608676	−	0.793419i	$-0.708299\pi$
$827$	5.31276	−	5.31276i	0.184743	−	0.184743i	0.793419	+	0.608676i	$0.208299\pi$
$828$	−12.6170	+	12.1742i	−0.438469	+	0.423082i
$829$	−4.51176			−0.156700			−0.0783500	−	0.996926i	$-0.524965\pi$
$829$	−4.51176			−0.156700			−0.0783500	+	0.996926i	$0.524965\pi$
$830$		0			0
$831$	20.0813	−	8.25214i	0.696611	−	0.286263i
$832$	43.9547	+	1.61725i	1.52385	+	0.0560679i
$833$	5.56292	−	5.56292i	0.192744	−	0.192744i
$834$	−0.201692	+	22.5875i	−0.00698403	+	0.782140i
$835$		0			0
$836$	33.3953	−	32.5864i	1.15500	−	1.12702i
$837$	−15.9966	+	6.46913i	−0.552922	+	0.223606i
$838$	−2.56199	−	6.29404i	−0.0885025	−	0.217424i
$839$	42.7255			1.47505			0.737523	−	0.675322i	$-0.235995\pi$
$839$	42.7255			1.47505			0.737523	+	0.675322i	$0.235995\pi$
$840$		0			0
$841$	27.1197			0.935164
$842$	−8.11428	−	19.9343i	−0.279637	−	0.686983i
$843$	−19.4877	−	8.13608i	−0.671193	−	0.280221i
$844$	−0.825584	−	0.846078i	−0.0284178	−	0.0291232i
$845$		0			0
$846$	−14.0215	−	35.0068i	−0.482071	−	1.20356i
$847$	−1.50768	+	1.50768i	−0.0518045	+	0.0518045i
$848$	22.9745	−	21.8746i	0.788946	−	0.751178i
$849$	−10.8744	−	26.4625i	−0.373210	−	0.908192i
$850$		0			0
$851$	−10.0894			−0.345861
$852$	−13.3067	+	5.27851i	−0.455881	+	0.180839i
$853$	28.1027	−	28.1027i	0.962217	−	0.962217i	−0.0370946	−	0.999312i	$-0.511810\pi$
$853$	28.1027	−	28.1027i	0.962217	−	0.962217i	0.999312	+	0.0370946i	$0.0118103\pi$
$854$	5.51503	+	2.32410i	0.188720	+	0.0795292i
$855$		0			0
$856$	8.55106	+	21.7678i	0.292269	+	0.744008i
$857$	−35.8406	−	35.8406i	−1.22429	−	1.22429i	−0.966092	−	0.258198i	$-0.916871\pi$
$857$	−35.8406	−	35.8406i	−1.22429	−	1.22429i	−0.258198	−	0.966092i	$-0.583129\pi$
$858$	34.7872	+	35.4141i	1.18762	+	1.20902i
$859$	−1.55128			−0.0529289			−0.0264645	−	0.999650i	$-0.508425\pi$
$859$	−1.55128			−0.0529289			−0.0264645	+	0.999650i	$0.508425\pi$
$860$		0			0
$861$	0.855728	−	0.351651i	0.0291631	−	0.0119842i
$862$	−14.8629	−	36.5136i	−0.506231	−	1.24366i
$863$	−22.7893	+	22.7893i	−0.775758	+	0.775758i	−0.979107	−	0.203348i	$-0.934818\pi$
$863$	−22.7893	+	22.7893i	−0.775758	+	0.775758i	0.203348	+	0.979107i	$0.434818\pi$
$864$	−19.9574	−	21.5801i	−0.678965	−	0.734171i
$865$		0			0
$866$	−5.12369	−	2.15919i	−0.174110	−	0.0733723i
$867$	−24.6957	−	10.3104i	−0.838712	−	0.350160i
$868$	−0.0671001	+	5.47328i	−0.00227753	+	0.185775i
$869$			4.05757i			0.137644i
$870$		0			0
$871$	38.1490			1.29263
$872$	13.2278	−	30.3441i	0.447948	−	1.02758i
$873$	−23.0013	−	0.128793i	−0.778476	−	0.00435900i
$874$	10.1572	−	24.1027i	0.343572	−	0.815285i
$875$		0			0
$876$	−9.12720	+	21.1293i	−0.308379	+	0.713894i
$877$	−22.8089	−	22.8089i	−0.770202	−	0.770202i	0.207940	−	0.978142i	$-0.433324\pi$
$877$	−22.8089	−	22.8089i	−0.770202	−	0.770202i	−0.978142	+	0.207940i	$0.933324\pi$
$878$	−5.76759	−	14.1692i	−0.194647	−	0.478188i
$879$	11.7005	−	4.80819i	0.394649	−	0.162176i
$880$		0			0
$881$		−	1.47551i		−	0.0497114i	−0.999691	−	0.0248557i	$-0.992087\pi$
$881$		−	1.47551i		−	0.0497114i	0.999691	−	0.0248557i	$-0.00791262\pi$
$882$	−10.5522	+	24.6533i	−0.355310	+	0.830121i
$883$	3.02812	−	3.02812i	0.101904	−	0.101904i	−0.654316	−	0.756221i	$-0.727044\pi$
$883$	3.02812	−	3.02812i	0.101904	−	0.101904i	0.756221	+	0.654316i	$0.227044\pi$
$884$	9.79563	−	9.55836i	0.329463	−	0.321482i
$885$		0			0
$886$	10.5968	+	4.46561i	0.356005	+	0.150025i
$887$	−19.9170	−	19.9170i	−0.668749	−	0.668749i	0.288678	−	0.957426i	$-0.406784\pi$
$887$	−19.9170	−	19.9170i	−0.668749	−	0.668749i	−0.957426	+	0.288678i	$0.906784\pi$
$888$	0.358371	−	16.9112i	0.0120261	−	0.567504i
$889$			0.0170705i			0.000572528i
$890$		0			0
$891$	0.371504	−	33.1725i	0.0124459	−	1.11132i
$892$	−47.6773	−	0.584504i	−1.59635	−	0.0195706i
$893$	39.7794	+	39.7794i	1.33117	+	1.33117i
$894$	−34.3048	−	0.306321i	−1.14733	−	0.0102449i
$895$		0			0
$896$	−8.75970	+	3.19548i	−0.292641	+	0.106754i
$897$	25.6790	+	10.7209i	0.857398	+	0.357961i
$898$	−9.05349	+	3.68523i	−0.302119	+	0.122978i
$899$			4.55350i			0.151868i
$900$		0			0
$901$		−	9.87094i		−	0.328849i
$902$	−1.27374	−	3.12918i	−0.0424108	−	0.104190i
$903$	−1.52652	−	0.637317i	−0.0507993	−	0.0212086i
$904$	−12.5533	−	31.9561i	−0.417518	−	1.06284i
$905$		0			0
$906$	−0.287176	+	32.1607i	−0.00954077	+	1.06847i
$907$	−6.11318	−	6.11318i	−0.202985	−	0.202985i	0.598293	−	0.801278i	$-0.295846\pi$
$907$	−6.11318	−	6.11318i	−0.202985	−	0.202985i	−0.801278	+	0.598293i	$0.795846\pi$
$908$	−0.250819	+	20.4590i	−0.00832372	+	0.678956i
$909$	−20.7659	−	20.9998i	−0.688762	−	0.696518i
$910$		0			0
$911$			28.1492i			0.932625i	0.884620	+	0.466313i	$0.154418\pi$
$911$			28.1492i			0.932625i	−0.884620	+	0.466313i	$0.845582\pi$
$912$	40.0385	+	17.8809i	1.32581	+	0.592096i
$913$	23.1278	+	23.1278i	0.765419	+	0.765419i
$914$	−4.00570	+	9.50541i	−0.132497	+	0.314411i
$915$		0			0
$916$	32.9349	−	32.1371i	1.08820	−	1.06184i
$917$	−3.05366	+	3.05366i	−0.100841	+	0.100841i
$918$	−9.14535	−	0.132878i	−0.301842	−	0.00438561i
$919$		−	49.4285i		−	1.63049i	−0.579113	−	0.815247i	$-0.696601\pi$
$919$		−	49.4285i		−	1.63049i	0.579113	−	0.815247i	$-0.303399\pi$
$920$		0			0
$921$	−20.8400	+	8.56393i	−0.686701	+	0.282191i
$922$	−24.1740	+	9.84005i	−0.796129	+	0.324065i
$923$	16.0660	+	16.0660i	0.528819	+	0.528819i
$924$	−9.66086	−	4.17318i	−0.317819	−	0.137288i
$925$		0			0
$926$	−36.2892	−	15.2927i	−1.19254	−	0.502550i
$927$	0.196722	−	35.1327i	0.00646120	−	1.15391i
$928$	−7.25396	+	2.74741i	−0.238123	+	0.0901883i
$929$	−38.9204			−1.27694			−0.638468	−	0.769649i	$-0.720431\pi$
$929$	−38.9204			−1.27694			−0.638468	+	0.769649i	$0.720431\pi$
$930$		0			0
$931$		−	40.0052i		−	1.31112i
$932$	0.154322	−	12.5879i	0.00505499	−	0.412329i
$933$	48.8598	+	20.3988i	1.59960	+	0.667828i
$934$	1.61507	−	3.83251i	0.0528466	−	0.125403i
$935$		0			0
$936$	−18.8818	+	42.6607i	−0.617172	+	1.39441i
$937$	4.49303	−	4.49303i	0.146781	−	0.146781i	−0.629897	−	0.776678i	$-0.716903\pi$
$937$	4.49303	−	4.49303i	0.146781	−	0.146781i	0.776678	+	0.629897i	$0.216903\pi$
$938$	−7.49052	+	3.04902i	−0.244574	+	0.0995540i
$939$	37.2952	−	15.3260i	1.21708	−	0.500145i
$940$		0			0
$941$	−23.2736			−0.758696			−0.379348	−	0.925254i	$-0.623852\pi$
$941$	−23.2736			−0.758696			−0.379348	+	0.925254i	$0.623852\pi$
$942$	15.7404	−	15.4618i	0.512849	−	0.503771i
$943$	−1.33915	−	1.33915i	−0.0436087	−	0.0436087i
$944$	−24.4737	−	0.600164i	−0.796550	−	0.0195337i
$945$		0			0
$946$	−2.34589	+	5.56671i	−0.0762713	+	0.180989i
$947$	−28.1797	+	28.1797i	−0.915717	+	0.915717i	−0.996714	−	0.0809978i	$-0.974189\pi$
$947$	−28.1797	+	28.1797i	−0.915717	+	0.915717i	0.0809978	+	0.996714i	$0.474189\pi$
$948$	−3.54454	+	1.40605i	−0.115121	+	0.0456663i
$949$	36.5305			1.18583
$950$		0			0
$951$	−0.000574173	−	0.00139723i	−1.86188e−5	−	4.53082e-5i
$952$	−1.15942	+	2.65968i	−0.0375770	+	0.0862006i
$953$	−28.5653	+	28.5653i	−0.925321	+	0.925321i	−0.997399	−	0.0720776i	$-0.977037\pi$
$953$	−28.5653	+	28.5653i	−0.925321	+	0.925321i	0.0720776	+	0.997399i	$0.477037\pi$
$954$	12.5106	+	31.2346i	0.405047	+	1.01126i
$955$		0			0
$956$	5.77547	−	5.63557i	0.186792	−	0.182267i
$957$	−8.07871	−	3.37284i	−0.261148	−	0.109028i
$958$	−25.8157	+	10.5083i	−0.834066	+	0.339507i
$959$	−16.4323			−0.530625
$960$		0			0
$961$	−19.9726			−0.644277
$962$	−24.8656	+	10.1216i	−0.801700	+	0.326332i
$963$	−24.8054	−	0.138895i	−0.799343	−	0.00447584i
$964$	−16.4060	+	16.0086i	−0.528402	+	0.515603i
$965$		0			0
$966$	−5.89890	−	0.0526736i	−0.189794	−	0.00169475i
$967$	37.0606	−	37.0606i	1.19179	−	1.19179i	0.215225	−	0.976565i	$-0.430952\pi$
$967$	37.0606	−	37.0606i	1.19179	−	1.19179i	0.976565	−	0.215225i	$-0.0690484\pi$
$968$	−2.92407	+	6.70774i	−0.0939832	+	0.215595i
$969$	12.6204	−	5.18621i	0.405427	−	0.166605i
$970$		0			0
$971$	11.8114			0.379044			0.189522	−	0.981876i	$-0.439306\pi$
$971$	11.8114			0.379044			0.189522	+	0.981876i	$0.439306\pi$
$972$	29.1070	−	11.1706i	0.933608	−	0.358296i
$973$	−5.37412	+	5.37412i	−0.172287	+	0.172287i
$974$	3.27288	−	7.76644i	0.104870	−	0.248853i
$975$		0			0
$976$	20.5327	+	0.503519i	0.657234	+	0.0161173i
$977$	5.34002	+	5.34002i	0.170842	+	0.170842i	0.787349	−	0.616507i	$-0.211453\pi$
$977$	5.34002	+	5.34002i	0.170842	+	0.170842i	−0.616507	+	0.787349i	$0.711453\pi$
$978$	−8.39953	−	8.55088i	−0.268587	−	0.273427i
$979$	56.6038			1.80907
$980$		0			0
$981$	24.6871	+	24.9651i	0.788197	+	0.797074i
$982$	36.3111	−	14.7805i	1.15874	−	0.471664i
$983$	42.6490	−	42.6490i	1.36029	−	1.36029i	0.486753	−	0.873540i	$-0.338181\pi$
$983$	42.6490	−	42.6490i	1.36029	−	1.36029i	0.873540	−	0.486753i	$-0.161819\pi$
$984$	2.29216	−	2.19703i	0.0730714	−	0.0700387i
$985$		0			0
$986$	−0.937311	+	2.22421i	−0.0298501	+	0.0708333i
$987$	4.88836	−	11.7087i	0.155598	−	0.372693i
$988$	0.853159	−	69.5912i	0.0271426	−	2.21399i
$989$			3.38623i			0.107676i
$990$		0			0
$991$	−31.5197			−1.00126			−0.500629	−	0.865662i	$-0.666898\pi$
$991$	−31.5197			−1.00126			−0.500629	+	0.865662i	$0.666898\pi$
$992$	6.65353	+	17.5672i	0.211250	+	0.557760i
$993$	−13.2441	−	5.52938i	−0.420289	−	0.175469i
$994$	−4.43860	−	1.87048i	−0.140784	−	0.0593282i
$995$		0			0
$996$	−12.1892	+	28.2179i	−0.386231	+	0.894120i
$997$	38.3474	+	38.3474i	1.21447	+	1.21447i	0.969540	+	0.244935i	$0.0787666\pi$
$997$	38.3474	+	38.3474i	1.21447	+	1.21447i	0.244935	+	0.969540i	$0.421233\pi$
$998$	6.74190	−	2.74429i	0.213411	−	0.0868690i
$999$	16.5172	+	7.00473i	0.522580	+	0.221620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.j.293.3		32
3.2	odd	2	inner	600.2.w.j.293.14		32
5.2	odd	4	inner	600.2.w.j.557.6		32
5.3	odd	4		120.2.w.c.77.11	yes	32
5.4	even	2		120.2.w.c.53.14	yes	32
8.5	even	2	inner	600.2.w.j.293.11		32
15.2	even	4	inner	600.2.w.j.557.11		32
15.8	even	4		120.2.w.c.77.6	yes	32
15.14	odd	2		120.2.w.c.53.3	✓	32
20.3	even	4		480.2.bi.c.17.3		32
20.19	odd	2		480.2.bi.c.113.11		32
24.5	odd	2	inner	600.2.w.j.293.6		32
40.3	even	4		480.2.bi.c.17.14		32
40.13	odd	4		120.2.w.c.77.3	yes	32
40.19	odd	2		480.2.bi.c.113.6		32
40.29	even	2		120.2.w.c.53.6	yes	32
40.37	odd	4	inner	600.2.w.j.557.14		32
60.23	odd	4		480.2.bi.c.17.6		32
60.59	even	2		480.2.bi.c.113.14		32
120.29	odd	2		120.2.w.c.53.11	yes	32
120.53	even	4		120.2.w.c.77.14	yes	32
120.59	even	2		480.2.bi.c.113.3		32
120.77	even	4	inner	600.2.w.j.557.3		32
120.83	odd	4		480.2.bi.c.17.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.3	✓	32	15.14	odd	2
120.2.w.c.53.6	yes	32	40.29	even	2
120.2.w.c.53.11	yes	32	120.29	odd	2
120.2.w.c.53.14	yes	32	5.4	even	2
120.2.w.c.77.3	yes	32	40.13	odd	4
120.2.w.c.77.6	yes	32	15.8	even	4
120.2.w.c.77.11	yes	32	5.3	odd	4
120.2.w.c.77.14	yes	32	120.53	even	4
480.2.bi.c.17.3		32	20.3	even	4
480.2.bi.c.17.6		32	60.23	odd	4
480.2.bi.c.17.11		32	120.83	odd	4
480.2.bi.c.17.14		32	40.3	even	4
480.2.bi.c.113.3		32	120.59	even	2
480.2.bi.c.113.6		32	40.19	odd	2
480.2.bi.c.113.11		32	20.19	odd	2
480.2.bi.c.113.14		32	60.59	even	2
600.2.w.j.293.3		32	1.1	even	1	trivial
600.2.w.j.293.6		32	24.5	odd	2	inner
600.2.w.j.293.11		32	8.5	even	2	inner
600.2.w.j.293.14		32	3.2	odd	2	inner
600.2.w.j.557.3		32	120.77	even	4	inner
600.2.w.j.557.6		32	5.2	odd	4	inner
600.2.w.j.557.11		32	15.2	even	4	inner
600.2.w.j.557.14		32	40.37	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30986 + 0.533177i) q^{2} +(0.667305 - 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(-0.0218716 + 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(-1.13026 + 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})\)	\(q+(-1.30986 + 0.533177i) q^{2} +(0.667305 - 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(-0.0218716 + 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(-1.13026 + 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} -3.68607 q^{11} +(-1.27731 - 3.22001i) q^{12} +(-3.88771 + 3.88771i) q^{13} +(0.452626 - 1.07407i) q^{14} +(0.0980619 - 3.99880i) q^{16} +(-0.880105 - 0.880105i) q^{17} +(3.90038 + 1.66945i) q^{18} -6.32919 q^{19} +(0.542584 + 1.32036i) q^{21} +(4.82821 - 1.96533i) q^{22} +(2.06626 - 2.06626i) q^{23} +(3.38993 + 3.53672i) q^{24} +(3.01950 - 7.16518i) q^{26} +(-4.81715 + 1.94809i) q^{27} +(-0.0202063 + 1.64820i) q^{28} +1.37122i q^{29} +3.32075 q^{31} +(2.00362 + 5.29013i) q^{32} +(-2.45973 + 5.89160i) q^{33} +(1.62206 + 0.683558i) q^{34} +(-5.99904 - 0.107144i) q^{36} +(-2.44147 - 2.44147i) q^{37} +(8.29032 - 3.37458i) q^{38} +(3.61961 + 8.80819i) q^{39} -0.648104i q^{41} +(-1.41469 - 1.44018i) q^{42} +(-0.819412 + 0.819412i) q^{43} +(-5.27640 + 5.14859i) q^{44} +(-1.60482 + 3.80818i) q^{46} +(-6.28508 - 6.28508i) q^{47} +(-6.32602 - 2.82515i) q^{48} +6.32075i q^{49} +(-1.99401 + 0.819412i) q^{51} +(-0.134798 + 10.9953i) q^{52} +(5.60782 + 5.60782i) q^{53} +(5.27109 - 5.12011i) q^{54} +(-0.852318 - 2.16968i) q^{56} +(-4.22349 + 10.1162i) q^{57} +(-0.731106 - 1.79611i) q^{58} -6.12026i q^{59} +5.13471i q^{61} +(-4.34971 + 1.77055i) q^{62} +(2.47245 + 0.0138443i) q^{63} +(-5.44503 - 5.86102i) q^{64} +(0.0806201 - 9.02862i) q^{66} +(-4.90636 - 4.90636i) q^{67} +(-2.48912 - 0.0305156i) q^{68} +(-1.92377 - 4.68141i) q^{69} -4.13251i q^{71} +(7.91501 - 3.05821i) q^{72} +(-4.69820 - 4.69820i) q^{73} +(4.49972 + 1.89624i) q^{74} +(-9.05987 + 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-9.43750 - 9.60756i) q^{78} -1.10079i q^{79} +(-0.100786 + 8.99944i) q^{81} +(0.345554 + 0.848922i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(2.62091 + 1.13215i) q^{84} +(0.636420 - 1.51020i) q^{86} +(2.19169 + 0.915024i) q^{87} +(4.16621 - 9.55717i) q^{88} -15.3562 q^{89} -4.53130i q^{91} +(0.0716428 - 5.84382i) q^{92} +(2.21595 - 5.30771i) q^{93} +(11.5836 + 4.88148i) q^{94} +(9.79248 + 0.327652i) q^{96} +(5.42154 - 5.42154i) q^{97} +(-3.37008 - 8.27927i) q^{98} +(7.77542 + 7.86299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

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