LMFDB - Embedded newform 507.2.f.g.239.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(239,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.5
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38407 - 1.38407i) q^{2} +(0.526444 - 1.65011i) q^{3} +1.83129i q^{4} +(1.04664 + 1.04664i) q^{5} +(-3.01250 + 1.55523i) q^{6} +(3.17096 + 3.17096i) q^{7} +(-0.233508 + 0.233508i) q^{8} +(-2.44571 - 1.73738i) q^{9} -2.89724i q^{10} +(0.108328 - 0.108328i) q^{11} +(3.02182 + 0.964071i) q^{12} -8.77764i q^{14} +(2.27806 - 1.17607i) q^{15} +4.30896 q^{16} +3.16727 q^{17} +(0.980382 + 5.78968i) q^{18} +(0.846216 - 0.846216i) q^{19} +(-1.91670 + 1.91670i) q^{20} +(6.90175 - 3.56309i) q^{21} -0.299868 q^{22} +6.70271 q^{23} +(0.262385 + 0.508243i) q^{24} -2.80909i q^{25} +(-4.15440 + 3.12106i) q^{27} +(-5.80694 + 5.80694i) q^{28} +1.98510i q^{29} +(-4.78076 - 1.52523i) q^{30} +(3.64859 - 3.64859i) q^{31} +(-5.49688 - 5.49688i) q^{32} +(-0.121725 - 0.235783i) q^{33} +(-4.38372 - 4.38372i) q^{34} +6.63770i q^{35} +(3.18164 - 4.47881i) q^{36} +(2.31488 + 2.31488i) q^{37} -2.34244 q^{38} -0.488797 q^{40} +(-5.91863 - 5.91863i) q^{41} +(-14.4841 - 4.62094i) q^{42} -2.78318i q^{43} +(0.198381 + 0.198381i) q^{44} +(-0.741369 - 4.37819i) q^{45} +(-9.27700 - 9.27700i) q^{46} +(-4.06533 + 4.06533i) q^{47} +(2.26843 - 7.11025i) q^{48} +13.1099i q^{49} +(-3.88798 + 3.88798i) q^{50} +(1.66739 - 5.22634i) q^{51} +0.628103i q^{53} +(10.0697 + 1.43021i) q^{54} +0.226762 q^{55} -1.48089 q^{56} +(-0.950863 - 1.84183i) q^{57} +(2.74752 - 2.74752i) q^{58} +(-6.20927 + 6.20927i) q^{59} +(2.15372 + 4.17179i) q^{60} +5.83263 q^{61} -10.0998 q^{62} +(-2.24610 - 13.2644i) q^{63} +6.59818i q^{64} +(-0.157864 + 0.494815i) q^{66} +(0.475547 - 0.475547i) q^{67} +5.80019i q^{68} +(3.52860 - 11.0602i) q^{69} +(9.18702 - 9.18702i) q^{70} +(8.09127 + 8.09127i) q^{71} +(0.976786 - 0.165402i) q^{72} +(-3.92370 - 3.92370i) q^{73} -6.40789i q^{74} +(-4.63531 - 1.47883i) q^{75} +(1.54967 + 1.54967i) q^{76} +0.687010 q^{77} -5.46386 q^{79} +(4.50993 + 4.50993i) q^{80} +(2.96302 + 8.49826i) q^{81} +16.3836i q^{82} +(-6.40765 - 6.40765i) q^{83} +(6.52505 + 12.6391i) q^{84} +(3.31499 + 3.31499i) q^{85} +(-3.85212 + 3.85212i) q^{86} +(3.27563 + 1.04505i) q^{87} +0.0505912i q^{88} +(3.75466 - 3.75466i) q^{89} +(-5.03360 + 7.08582i) q^{90} +12.2746i q^{92} +(-4.09979 - 7.94134i) q^{93} +11.2534 q^{94} +1.77137 q^{95} +(-11.9642 + 6.17664i) q^{96} +(3.16443 - 3.16443i) q^{97} +(18.1451 - 18.1451i) q^{98} +(-0.453148 + 0.0767327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) $ 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.38407	−	1.38407i	−0.978684	−	0.978684i	0.0210936	−	0.999778i	$-0.493285\pi$
$2$	−1.38407	−	1.38407i	−0.978684	−	0.978684i	−0.999778	+	0.0210936i	$0.993285\pi$
$3$	0.526444	−	1.65011i	0.303943	−	0.952690i
$3$	0.526444	−	1.65011i	0.303943	−	0.952690i
$4$			1.83129i			0.915644i
$5$	1.04664	+	1.04664i	0.468071	+	0.468071i	0.901289	−	0.433218i	$-0.142622\pi$
$5$	1.04664	+	1.04664i	0.468071	+	0.468071i	−0.433218	+	0.901289i	$0.642622\pi$
$6$	−3.01250	+	1.55523i	−1.22985	+	0.634919i
$7$	3.17096	+	3.17096i	1.19851	+	1.19851i	0.974613	+	0.223896i	$0.0718777\pi$
$7$	3.17096	+	3.17096i	1.19851	+	1.19851i	0.223896	+	0.974613i	$0.428122\pi$
$8$	−0.233508	+	0.233508i	−0.0825576	+	0.0825576i
$9$	−2.44571	−	1.73738i	−0.815238	−	0.579127i
$10$		−	2.89724i		−	0.916188i
$11$	0.108328	−	0.108328i	0.0326623	−	0.0326623i	−0.690587	−	0.723249i	$-0.742648\pi$
$11$	0.108328	−	0.108328i	0.0326623	−	0.0326623i	0.723249	+	0.690587i	$0.242648\pi$
$12$	3.02182	+	0.964071i	0.872325	+	0.278303i
$13$		0			0
$13$		0			0
$14$		−	8.77764i		−	2.34592i
$15$	2.27806	−	1.17607i	0.588194	−	0.303660i
$16$	4.30896			1.07724
$17$	3.16727			0.768177			0.384088	−	0.923296i	$-0.374516\pi$
$17$	3.16727			0.768177			0.384088	+	0.923296i	$0.374516\pi$
$18$	0.980382	+	5.78968i	0.231078	+	1.36464i
$19$	0.846216	−	0.846216i	0.194135	−	0.194135i	−0.603345	−	0.797480i	$-0.706166\pi$
$19$	0.846216	−	0.846216i	0.194135	−	0.194135i	0.797480	+	0.603345i	$0.206166\pi$
$20$	−1.91670	+	1.91670i	−0.428587	+	0.428587i
$21$	6.90175	−	3.56309i	1.50609	−	0.777530i
$22$	−0.299868			−0.0639321
$23$	6.70271			1.39761			0.698805	−	0.715312i	$-0.253715\pi$
$23$	6.70271			1.39761			0.698805	+	0.715312i	$0.253715\pi$
$24$	0.262385	+	0.508243i	0.0535590	+	0.103745i
$25$		−	2.80909i		−	0.561819i
$26$		0			0
$27$	−4.15440	+	3.12106i	−0.799514	+	0.600648i
$28$	−5.80694	+	5.80694i	−1.09741	+	1.09741i
$29$			1.98510i			0.368624i	0.982868	+	0.184312i	$0.0590058\pi$
$29$			1.98510i			0.368624i	−0.982868	+	0.184312i	$0.940994\pi$
$30$	−4.78076	−	1.52523i	−0.872843	−	0.278469i
$31$	3.64859	−	3.64859i	0.655306	−	0.655306i	−0.298960	−	0.954266i	$-0.596640\pi$
$31$	3.64859	−	3.64859i	0.655306	−	0.655306i	0.954266	+	0.298960i	$0.0966397\pi$
$32$	−5.49688	−	5.49688i	−0.971720	−	0.971720i
$33$	−0.121725	−	0.235783i	−0.0211896	−	0.0410445i
$34$	−4.38372	−	4.38372i	−0.751802	−	0.751802i
$35$			6.63770i			1.12198i
$36$	3.18164	−	4.47881i	0.530274	−	0.746468i
$37$	2.31488	+	2.31488i	0.380563	+	0.380563i	0.871305	−	0.490742i	$-0.163274\pi$
$37$	2.31488	+	2.31488i	0.380563	+	0.380563i	−0.490742	+	0.871305i	$0.663274\pi$
$38$	−2.34244			−0.379994
$39$		0			0
$40$	−0.488797			−0.0772856
$41$	−5.91863	−	5.91863i	−0.924334	−	0.924334i	0.0729976	−	0.997332i	$-0.476743\pi$
$41$	−5.91863	−	5.91863i	−0.924334	−	0.924334i	−0.997332	+	0.0729976i	$0.976743\pi$
$42$	−14.4841	−	4.62094i	−2.23494	−	0.713026i
$43$		−	2.78318i		−	0.424432i	−0.977223	−	0.212216i	$-0.931932\pi$
$43$		−	2.78318i		−	0.424432i	0.977223	−	0.212216i	$-0.0680680\pi$
$44$	0.198381	+	0.198381i	0.0299070	+	0.0299070i
$45$	−0.741369	−	4.37819i	−0.110517	−	0.652662i
$46$	−9.27700	−	9.27700i	−1.36782	−	1.36782i
$47$	−4.06533	+	4.06533i	−0.592990	+	0.592990i	−0.938438	−	0.345448i	$-0.887727\pi$
$47$	−4.06533	+	4.06533i	−0.592990	+	0.592990i	0.345448	+	0.938438i	$0.387727\pi$
$48$	2.26843	−	7.11025i	0.327419	−	1.02628i
$49$			13.1099i			1.87285i
$50$	−3.88798	+	3.88798i	−0.549843	+	0.549843i
$51$	1.66739	−	5.22634i	0.233482	−	0.731835i
$52$		0			0
$53$			0.628103i			0.0862766i	0.999069	+	0.0431383i	$0.0137356\pi$
$53$			0.628103i			0.0862766i	−0.999069	+	0.0431383i	$0.986264\pi$
$54$	10.0697	+	1.43021i	1.37032	+	0.194627i
$55$	0.226762			0.0305765
$56$	−1.48089			−0.197892
$57$	−0.950863	−	1.84183i	−0.125945	−	0.243957i
$58$	2.74752	−	2.74752i	0.360767	−	0.360767i
$59$	−6.20927	+	6.20927i	−0.808378	+	0.808378i	−0.984388	−	0.176011i	$-0.943681\pi$
$59$	−6.20927	+	6.20927i	−0.808378	+	0.808378i	0.176011	+	0.984388i	$0.443681\pi$
$60$	2.15372	+	4.17179i	0.278045	+	0.538576i
$61$	5.83263			0.746792			0.373396	−	0.927672i	$-0.378193\pi$
$61$	5.83263			0.746792			0.373396	+	0.927672i	$0.378193\pi$
$62$	−10.0998			−1.28267
$63$	−2.24610	−	13.2644i	−0.282981	−	1.67116i
$64$			6.59818i			0.824773i
$65$		0			0
$66$	−0.157864	+	0.494815i	−0.0194317	+	0.0609075i
$67$	0.475547	−	0.475547i	0.0580973	−	0.0580973i	−0.677461	−	0.735558i	$-0.736920\pi$
$67$	0.475547	−	0.475547i	0.0580973	−	0.0580973i	0.735558	+	0.677461i	$0.236920\pi$
$68$			5.80019i			0.703377i
$69$	3.52860	−	11.0602i	0.424794	−	1.33149i
$70$	9.18702	−	9.18702i	1.09806	−	1.09806i
$71$	8.09127	+	8.09127i	0.960257	+	0.960257i	0.999240	−	0.0389831i	$-0.0124119\pi$
$71$	8.09127	+	8.09127i	0.960257	+	0.960257i	−0.0389831	+	0.999240i	$0.512412\pi$
$72$	0.976786	−	0.165402i	0.115115	−	0.0194928i
$73$	−3.92370	−	3.92370i	−0.459235	−	0.459235i	0.439169	−	0.898404i	$-0.355273\pi$
$73$	−3.92370	−	3.92370i	−0.459235	−	0.459235i	−0.898404	+	0.439169i	$0.855273\pi$
$74$		−	6.40789i		−	0.744902i
$75$	−4.63531	−	1.47883i	−0.535239	−	0.170761i
$76$	1.54967	+	1.54967i	0.177759	+	0.177759i
$77$	0.687010			0.0782921
$78$		0			0
$79$	−5.46386			−0.614733			−0.307366	−	0.951591i	$-0.599448\pi$
$79$	−5.46386			−0.614733			−0.307366	+	0.951591i	$0.599448\pi$
$80$	4.50993	+	4.50993i	0.504225	+	0.504225i
$81$	2.96302	+	8.49826i	0.329225	+	0.944252i
$82$			16.3836i			1.80926i
$83$	−6.40765	−	6.40765i	−0.703331	−	0.703331i	0.261793	−	0.965124i	$-0.415686\pi$
$83$	−6.40765	−	6.40765i	−0.703331	−	0.703331i	−0.965124	+	0.261793i	$0.915686\pi$
$84$	6.52505	+	12.6391i	0.711941	+	1.37904i
$85$	3.31499	+	3.31499i	0.359561	+	0.359561i
$86$	−3.85212	+	3.85212i	−0.415384	+	0.415384i
$87$	3.27563	+	1.04505i	0.351185	+	0.112041i
$88$			0.0505912i			0.00539304i
$89$	3.75466	−	3.75466i	0.397993	−	0.397993i	−0.479532	−	0.877525i	$-0.659193\pi$
$89$	3.75466	−	3.75466i	0.397993	−	0.397993i	0.877525	+	0.479532i	$0.159193\pi$
$90$	−5.03360	+	7.08582i	−0.530588	+	0.746911i
$91$		0			0
$92$			12.2746i			1.27971i
$93$	−4.09979	−	7.94134i	−0.425128	−	0.823479i
$94$	11.2534			1.16070
$95$	1.77137			0.181738
$96$	−11.9642	+	6.17664i	−1.22110	+	0.630401i
$97$	3.16443	−	3.16443i	0.321299	−	0.321299i	−0.527966	−	0.849265i	$-0.677045\pi$
$97$	3.16443	−	3.16443i	0.321299	−	0.321299i	0.849265	+	0.527966i	$0.177045\pi$
$98$	18.1451	−	18.1451i	1.83293	−	1.83293i
$99$	−0.453148	+	0.0767327i	−0.0455431	+	0.00771193i
$100$	5.14426			0.514426
$101$	1.68098			0.167263			0.0836317	−	0.996497i	$-0.473348\pi$
$101$	1.68098			0.167263			0.0836317	+	0.996497i	$0.473348\pi$
$102$	−9.54140	+	4.92583i	−0.944740	+	0.487730i
$103$			4.41524i			0.435046i	0.976055	+	0.217523i	$0.0697977\pi$
$103$			4.41524i			0.435046i	−0.976055	+	0.217523i	$0.930202\pi$
$104$		0			0
$105$	10.9529	+	3.49438i	1.06890	+	0.341016i
$106$	0.869337	−	0.869337i	0.0844375	−	0.0844375i
$107$		−	15.4776i		−	1.49628i	−0.663541	−	0.748140i	$-0.730947\pi$
$107$		−	15.4776i		−	1.49628i	0.663541	−	0.748140i	$-0.269053\pi$
$108$	−5.71556	−	7.60790i	−0.549980	−	0.732070i
$109$	−8.78130	+	8.78130i	−0.841096	+	0.841096i	−0.989002	−	0.147905i	$-0.952747\pi$
$109$	−8.78130	+	8.78130i	−0.841096	+	0.841096i	0.147905	+	0.989002i	$0.452747\pi$
$110$	−0.313854	−	0.313854i	−0.0299248	−	0.0299248i
$111$	5.03845	−	2.60114i	0.478228	−	0.246889i
$112$	13.6635	+	13.6635i	1.29108	+	1.29108i
$113$			4.79085i			0.450685i	0.974280	+	0.225343i	$0.0723502\pi$
$113$			4.79085i			0.450685i	−0.974280	+	0.225343i	$0.927650\pi$
$114$	−1.23316	+	3.86528i	−0.115496	+	0.362017i
$115$	7.01531	+	7.01531i	0.654181	+	0.654181i
$116$	−3.63530			−0.337529
$117$		0			0
$118$	17.1881			1.58229
$119$	10.0433	+	10.0433i	0.920667	+	0.920667i
$120$	−0.257325	+	0.806568i	−0.0234904	+	0.0736293i
$121$			10.9765i			0.997866i
$122$	−8.07276	−	8.07276i	−0.730873	−	0.730873i
$123$	−12.8822	+	6.65055i	−1.16155	+	0.599660i
$124$	6.68162	+	6.68162i	0.600027	+	0.600027i
$125$	8.17330	−	8.17330i	0.731042	−	0.731042i
$126$	−15.2501	+	21.4676i	−1.35859	+	1.91249i
$127$		−	15.9755i		−	1.41759i	−0.705413	−	0.708796i	$-0.749239\pi$
$127$		−	15.9755i		−	1.41759i	0.705413	−	0.708796i	$-0.250761\pi$
$128$	−1.86142	+	1.86142i	−0.164528	+	0.164528i
$129$	−4.59255	−	1.46519i	−0.404352	−	0.129003i
$130$		0			0
$131$			18.7681i			1.63978i	0.572524	+	0.819888i	$0.305965\pi$
$131$			18.7681i			1.63978i	−0.572524	+	0.819888i	$0.694035\pi$
$132$	0.431786	−	0.222913i	0.0375821	−	0.0194021i
$133$	5.36663			0.465346
$134$	−1.31638			−0.113718
$135$	−7.61477	−	1.08153i	−0.655375	−	0.0930835i
$136$	−0.739584	+	0.739584i	−0.0634188	+	0.0634188i
$137$	−4.18839	+	4.18839i	−0.357838	+	0.357838i	−0.863016	−	0.505177i	$-0.831427\pi$
$137$	−4.18839	+	4.18839i	−0.357838	+	0.357838i	0.505177	+	0.863016i	$0.331427\pi$
$138$	−20.1919	+	10.4242i	−1.71885	+	0.887369i
$139$	−14.9698			−1.26972			−0.634859	−	0.772628i	$-0.718942\pi$
$139$	−14.9698			−1.26972			−0.634859	+	0.772628i	$0.718942\pi$
$140$	−12.1555			−1.02733
$141$	4.56807	+	8.84841i	0.384701	+	0.745170i
$142$		−	22.3977i		−	1.87958i
$143$		0			0
$144$	−10.5385	−	7.48630i	−0.878206	−	0.623858i
$145$	−2.07769	+	2.07769i	−0.172542	+	0.172542i
$146$			10.8613i			0.898891i
$147$	21.6328	+	6.90165i	1.78424	+	0.569239i
$148$	−4.23920	+	4.23920i	−0.348460	+	0.348460i
$149$	12.4536	+	12.4536i	1.02024	+	1.02024i	0.999791	+	0.0204461i	$0.00650865\pi$
$149$	12.4536	+	12.4536i	1.02024	+	1.02024i	0.0204461	+	0.999791i	$0.493491\pi$
$150$	4.36878	+	8.46238i	0.356709	+	0.690951i
$151$	−7.85127	−	7.85127i	−0.638928	−	0.638928i	0.311363	−	0.950291i	$-0.399214\pi$
$151$	−7.85127	−	7.85127i	−0.638928	−	0.638928i	−0.950291	+	0.311363i	$0.899214\pi$
$152$			0.395197i			0.0320547i
$153$	−7.74624	−	5.50276i	−0.626247	−	0.444872i
$154$	−0.950869	−	0.950869i	−0.0766232	−	0.0766232i
$155$	7.63751			0.613459
$156$		0			0
$157$	10.4654			0.835227			0.417614	−	0.908625i	$-0.362867\pi$
$157$	10.4654			0.835227			0.417614	+	0.908625i	$0.362867\pi$
$158$	7.56236	+	7.56236i	0.601629	+	0.601629i
$159$	1.03644	+	0.330661i	0.0821948	+	0.0262231i
$160$		−	11.5065i		−	0.909668i
$161$	21.2540	+	21.2540i	1.67505	+	1.67505i
$162$	7.66115	−	15.8632i	0.601917	−	1.24633i
$163$	−1.37114	−	1.37114i	−0.107396	−	0.107396i	0.651367	−	0.758763i	$-0.274196\pi$
$163$	−1.37114	−	1.37114i	−0.107396	−	0.107396i	−0.758763	+	0.651367i	$0.774196\pi$
$164$	10.8387	−	10.8387i	0.846362	−	0.846362i
$165$	0.119377	−	0.374181i	0.00929351	−	0.0291300i
$166$			17.7372i			1.37668i
$167$	9.88695	−	9.88695i	0.765075	−	0.765075i	−0.212160	−	0.977235i	$-0.568050\pi$
$167$	9.88695	−	9.88695i	0.765075	−	0.765075i	0.977235	+	0.212160i	$0.0680497\pi$
$168$	−0.779605	+	2.44363i	−0.0601478	+	0.188530i
$169$		0			0
$170$		−	9.17635i		−	0.703794i
$171$	−3.53980	+	0.599403i	−0.270695	+	0.0458375i
$172$	5.09681			0.388628
$173$	−17.9530			−1.36494			−0.682471	−	0.730912i	$-0.739095\pi$
$173$	−17.9530			−1.36494			−0.682471	+	0.730912i	$0.739095\pi$
$174$	−3.08729	−	5.98012i	−0.234047	−	0.453351i
$175$	8.90752	−	8.90752i	0.673345	−	0.673345i
$176$	0.466783	−	0.466783i	0.0351851	−	0.0351851i
$177$	6.97713	+	13.5148i	0.524433	+	1.01583i
$178$	−10.3934			−0.779018
$179$	−1.76719			−0.132086			−0.0660431	−	0.997817i	$-0.521037\pi$
$179$	−1.76719			−0.132086			−0.0660431	+	0.997817i	$0.521037\pi$
$180$	8.01773	−	1.35766i	0.597606	−	0.101194i
$181$			16.9949i			1.26322i	0.775286	+	0.631611i	$0.217606\pi$
$181$			16.9949i			1.26322i	−0.775286	+	0.631611i	$0.782394\pi$
$182$		0			0
$183$	3.07055	−	9.62447i	0.226982	−	0.711461i
$184$	−1.56514	+	1.56514i	−0.115383	+	0.115383i
$185$			4.84568i			0.356261i
$186$	−5.31697	+	16.6657i	−0.389859	+	1.22199i
$187$	0.343106	−	0.343106i	0.0250904	−	0.0250904i
$188$	−7.44479	−	7.44479i	−0.542967	−	0.542967i
$189$	−23.0702	−	3.27667i	−1.67811	−	0.238343i
$190$	−2.45169	−	2.45169i	−0.177864	−	0.177864i
$191$		−	22.3761i		−	1.61908i	−0.587066	−	0.809539i	$-0.699717\pi$
$191$		−	22.3761i		−	1.61908i	0.587066	−	0.809539i	$-0.300283\pi$
$192$	10.8877	+	3.47358i	0.785753	+	0.250684i
$193$	−13.9367	−	13.9367i	−1.00318	−	1.00318i	−0.999995	−	0.00318807i	$-0.998985\pi$
$193$	−13.9367	−	13.9367i	−1.00318	−	1.00318i	−0.00318807	−	0.999995i	$-0.501015\pi$
$194$	−8.75956			−0.628900
$195$		0			0
$196$	−24.0081			−1.71486
$197$	−1.05277	−	1.05277i	−0.0750064	−	0.0750064i	0.668608	−	0.743615i	$-0.266890\pi$
$197$	−1.05277	−	1.05277i	−0.0750064	−	0.0750064i	−0.743615	+	0.668608i	$0.766890\pi$
$198$	0.733391	+	0.520985i	0.0521198	+	0.0370248i
$199$		−	19.6776i		−	1.39491i	−0.716629	−	0.697454i	$-0.754316\pi$
$199$		−	19.6776i		−	1.39491i	0.716629	−	0.697454i	$-0.245684\pi$
$200$	0.655946	+	0.655946i	0.0463824	+	0.0463824i
$201$	−0.534355	−	1.03505i	−0.0376905	−	0.0730070i
$202$	−2.32659	−	2.32659i	−0.163698	−	0.163698i
$203$	−6.29468	+	6.29468i	−0.441800	+	0.441800i
$204$	9.57095	+	3.05348i	0.670100	+	0.213786i
$205$		−	12.3893i		−	0.865309i
$206$	6.11099	−	6.11099i	0.425773	−	0.425773i
$207$	−16.3929	−	11.6451i	−1.13938	−	0.809393i
$208$		0			0
$209$		−	0.183339i		−	0.0126818i
$210$	−10.3231	−	19.9960i	−0.712363	−	1.37986i
$211$	−23.5891			−1.62394			−0.811969	−	0.583700i	$-0.801604\pi$
$211$	−23.5891			−1.62394			−0.811969	+	0.583700i	$0.801604\pi$
$212$	−1.15024			−0.0789986
$213$	17.6111	−	9.09186i	1.20669	−	0.622964i
$214$	−21.4221	+	21.4221i	−1.46438	+	1.46438i
$215$	2.91299	−	2.91299i	0.198664	−	0.198664i
$216$	0.241293	−	1.69888i	0.0164179	−	0.115594i
$217$	23.1390			1.57078
$218$	24.3078			1.64633
$219$	−8.54015	+	4.40892i	−0.577090	+	0.297927i
$220$			0.415266i			0.0279972i
$221$		0			0
$222$	−10.5737	−	3.37340i	−0.709661	−	0.226408i
$223$	−8.91990	+	8.91990i	−0.597321	+	0.597321i	−0.939599	−	0.342278i	$-0.888802\pi$
$223$	−8.91990	+	8.91990i	−0.597321	+	0.597321i	0.342278	+	0.939599i	$0.388802\pi$
$224$		−	34.8607i		−	2.32923i
$225$	−4.88046	+	6.87024i	−0.325364	+	0.458016i
$226$	6.63086	−	6.63086i	0.441079	−	0.441079i
$227$	−15.7094	−	15.7094i	−1.04267	−	1.04267i	−0.999048	−	0.0436223i	$-0.986110\pi$
$227$	−15.7094	−	15.7094i	−1.04267	−	1.04267i	−0.0436223	−	0.999048i	$-0.513890\pi$
$228$	3.37293	−	1.74130i	0.223378	−	0.115321i
$229$	−7.05247	−	7.05247i	−0.466040	−	0.466040i	0.434589	−	0.900629i	$-0.356894\pi$
$229$	−7.05247	−	7.05247i	−0.466040	−	0.466040i	−0.900629	+	0.434589i	$0.856894\pi$
$230$		−	19.4193i		−	1.28047i
$231$	0.361672	−	1.13364i	0.0237963	−	0.0745881i
$232$	−0.463538	−	0.463538i	−0.0304327	−	0.0304327i
$233$	22.9574			1.50399			0.751996	−	0.659168i	$-0.229091\pi$
$233$	22.9574			1.50399			0.751996	+	0.659168i	$0.229091\pi$
$234$		0			0
$235$	−8.50987			−0.555123
$236$	−11.3710	−	11.3710i	−0.740186	−	0.740186i
$237$	−2.87642	+	9.01596i	−0.186844	+	0.585650i
$238$		−	27.8012i		−	1.80208i
$239$	−12.6819	−	12.6819i	−0.820323	−	0.820323i	0.165831	−	0.986154i	$-0.446969\pi$
$239$	−12.6819	−	12.6819i	−0.820323	−	0.820323i	−0.986154	+	0.165831i	$0.946969\pi$
$240$	9.81609	−	5.06764i	0.633626	−	0.327115i
$241$	−1.99604	−	1.99604i	−0.128576	−	0.128576i	0.639890	−	0.768466i	$-0.278980\pi$
$241$	−1.99604	−	1.99604i	−0.128576	−	0.128576i	−0.768466	+	0.639890i	$0.778980\pi$
$242$	15.1923	−	15.1923i	0.976596	−	0.976596i
$243$	15.5829	−	0.415449i	0.999645	−	0.0266510i
$244$			10.6812i			0.683796i
$245$	−13.7214	+	13.7214i	−0.876627	+	0.876627i
$246$	27.0347	+	8.62503i	1.72367	+	0.549912i
$247$		0			0
$248$			1.70395i			0.108201i
$249$	−13.9466	+	7.20004i	−0.883828	+	0.456284i
$250$	−22.6248			−1.43092
$251$	17.1932			1.08522			0.542612	−	0.839984i	$-0.317435\pi$
$251$	17.1932			1.08522			0.542612	+	0.839984i	$0.317435\pi$
$252$	24.2910	−	4.11325i	1.53019	−	0.259110i
$253$	0.726094	−	0.726094i	0.0456491	−	0.0456491i
$254$	−22.1111	+	22.1111i	−1.38738	+	1.38738i
$255$	7.21526	−	3.72494i	0.451837	−	0.233265i
$256$	18.3490			1.14681
$257$	9.50799			0.593092			0.296546	−	0.955019i	$-0.404165\pi$
$257$	9.50799			0.593092			0.296546	+	0.955019i	$0.404165\pi$
$258$	4.32848	+	8.38433i	0.269480	+	0.521986i
$259$			14.6807i			0.912217i
$260$		0			0
$261$	3.44888	−	4.85499i	0.213480	−	0.300517i
$262$	25.9763	−	25.9763i	1.60482	−	1.60482i
$263$			7.24943i			0.447019i	0.974702	+	0.223510i	$0.0717514\pi$
$263$			7.24943i			0.447019i	−0.974702	+	0.223510i	$0.928249\pi$
$264$	0.0834809	+	0.0266334i	0.00513789	+	0.00163917i
$265$	−0.657397	+	0.657397i	−0.0403836	+	0.0403836i
$266$	−7.42778	−	7.42778i	−0.455427	−	0.455427i
$267$	−4.21897	−	8.17221i	−0.258197	−	0.500131i
$268$	0.870863	+	0.870863i	0.0531964	+	0.0531964i
$269$			26.7779i			1.63268i	0.577573	+	0.816339i	$0.304000\pi$
$269$			26.7779i			1.63268i	−0.577573	+	0.816339i	$0.696000\pi$
$270$	9.04245	+	12.0363i	0.550306	+	0.732505i
$271$	−1.19552	−	1.19552i	−0.0726228	−	0.0726228i	0.669862	−	0.742485i	$-0.266353\pi$
$271$	−1.19552	−	1.19552i	−0.0726228	−	0.0726228i	−0.742485	+	0.669862i	$0.766353\pi$
$272$	13.6477			0.827511
$273$		0			0
$274$	11.5940			0.700421
$275$	−0.304305	−	0.304305i	−0.0183503	−	0.0183503i
$276$	20.2544	+	6.46189i	1.21917	+	0.388960i
$277$			24.9616i			1.49980i	0.661552	+	0.749899i	$0.269898\pi$
$277$			24.9616i			1.49980i	−0.661552	+	0.749899i	$0.730102\pi$
$278$	20.7192	+	20.7192i	1.24265	+	1.24265i
$279$	−15.2624	+	2.58442i	−0.913735	+	0.154725i
$280$	−1.54996	−	1.54996i	−0.0926276	−	0.0926276i
$281$	−2.53054	+	2.53054i	−0.150959	+	0.150959i	−0.778546	−	0.627587i	$-0.784043\pi$
$281$	−2.53054	+	2.53054i	−0.150959	+	0.150959i	0.627587	+	0.778546i	$0.284043\pi$
$282$	5.92428	−	18.5693i	0.352786	−	1.10579i
$283$			5.11893i			0.304289i	0.988358	+	0.152144i	$0.0486179\pi$
$283$			5.11893i			0.304289i	−0.988358	+	0.152144i	$0.951382\pi$
$284$	−14.8174	+	14.8174i	−0.879254	+	0.879254i
$285$	0.932525	−	2.92295i	0.0552380	−	0.173140i
$286$		0			0
$287$		−	37.5354i		−	2.21565i
$288$	3.89362	+	22.9939i	0.229434	+	1.35493i
$289$	−6.96837			−0.409904
$290$	5.75132			0.337729
$291$	−3.55575	−	6.88754i	−0.208442	−	0.403755i
$292$	7.18543	−	7.18543i	0.420496	−	0.420496i
$293$	−0.198293	+	0.198293i	−0.0115844	+	0.0115844i	−0.712875	−	0.701291i	$-0.752607\pi$
$293$	−0.198293	+	0.198293i	−0.0115844	+	0.0115844i	0.701291	+	0.712875i	$0.252607\pi$
$294$	−20.3889	−	39.4937i	−1.18911	−	2.30332i
$295$	−12.9977			−0.756757
$296$	−1.08108			−0.0628367
$297$	−0.111940	+	0.788139i	−0.00649542	+	0.0457325i
$298$		−	34.4732i		−	1.99698i
$299$		0			0
$300$	2.70817	−	8.48859i	0.156356	−	0.490089i
$301$	8.82536	−	8.82536i	0.508685	−	0.508685i
$302$			21.7334i			1.25062i
$303$	0.884941	−	2.77379i	0.0508385	−	0.159350i
$304$	3.64631	−	3.64631i	0.209130	−	0.209130i
$305$	6.10466	+	6.10466i	0.349552	+	0.349552i
$306$	3.10514	+	18.3375i	0.177509	+	1.04829i
$307$	12.9424	+	12.9424i	0.738660	+	0.738660i	0.972319	−	0.233659i	$-0.0750699\pi$
$307$	12.9424	+	12.9424i	0.738660	+	0.738660i	−0.233659	+	0.972319i	$0.575070\pi$
$308$			1.25811i			0.0716877i
$309$	7.28562	+	2.32438i	0.414464	+	0.132229i
$310$	−10.5708	−	10.5708i	−0.600383	−	0.600383i
$311$	−6.76425			−0.383565			−0.191783	−	0.981437i	$-0.561427\pi$
$311$	−6.76425			−0.383565			−0.191783	+	0.981437i	$0.561427\pi$
$312$		0			0
$313$	−25.3673			−1.43385			−0.716923	−	0.697153i	$-0.754450\pi$
$313$	−25.3673			−1.43385			−0.716923	+	0.697153i	$0.754450\pi$
$314$	−14.4848	−	14.4848i	−0.817424	−	0.817424i
$315$	11.5322	−	16.2339i	0.649766	−	0.914677i
$316$		−	10.0059i		−	0.562876i
$317$	−5.65535	−	5.65535i	−0.317636	−	0.317636i	0.530222	−	0.847859i	$-0.322108\pi$
$317$	−5.65535	−	5.65535i	−0.317636	−	0.317636i	−0.847859	+	0.530222i	$0.822108\pi$
$318$	−0.976843	−	1.89216i	−0.0547786	−	0.106107i
$319$	0.215043	+	0.215043i	0.0120401	+	0.0120401i
$320$	−6.90592	+	6.90592i	−0.386052	+	0.386052i
$321$	−25.5398	−	8.14811i	−1.42549	−	0.454783i
$322$		−	58.8339i		−	3.27869i
$323$	2.68020	−	2.68020i	0.149130	−	0.149130i
$324$	−15.5628	+	5.42615i	−0.864599	+	0.301453i
$325$		0			0
$326$			3.79550i			0.210214i
$327$	9.86723	+	19.1130i	0.545659	+	1.05695i
$328$	2.76410			0.152622
$329$	−25.7820			−1.42141
$330$	−0.683119	+	0.352666i	−0.0376044	+	0.0194136i
$331$	−16.6395	+	16.6395i	−0.914589	+	0.914589i	−0.996629	−	0.0820401i	$-0.973856\pi$
$331$	−16.6395	+	16.6395i	−0.914589	+	0.914589i	0.0820401	+	0.996629i	$0.473856\pi$
$332$	11.7343	−	11.7343i	0.644001	−	0.644001i
$333$	−1.63970	−	9.68334i	−0.0898552	−	0.530644i
$334$	−27.3684			−1.49753
$335$	0.995452			0.0543873
$336$	29.7394	−	15.3532i	1.62242	−	0.837586i
$337$			8.25174i			0.449501i	0.974416	+	0.224750i	$0.0721567\pi$
$337$			8.25174i			0.449501i	−0.974416	+	0.224750i	$0.927843\pi$
$338$		0			0
$339$	7.90542	+	2.52212i	0.429364	+	0.136983i
$340$	−6.07071	+	6.07071i	−0.329230	+	0.329230i
$341$		−	0.790492i		−	0.0428075i
$342$	5.72894	+	4.06971i	0.309786	+	0.220065i
$343$	−19.3744	+	19.3744i	−1.04612	+	1.04612i
$344$	0.649896	+	0.649896i	0.0350400	+	0.0350400i
$345$	15.2692	−	7.88285i	0.822066	−	0.424399i
$346$	24.8482	+	24.8482i	1.33585	+	1.33585i
$347$			3.83606i			0.205930i	0.994685	+	0.102965i	$0.0328330\pi$
$347$			3.83606i			0.205930i	−0.994685	+	0.102965i	$0.967167\pi$
$348$	−1.91378	+	5.99863i	−0.102589	+	0.321560i
$349$	8.17613	+	8.17613i	0.437658	+	0.437658i	0.891223	−	0.453565i	$-0.149848\pi$
$349$	8.17613	+	8.17613i	0.437658	+	0.437658i	−0.453565	+	0.891223i	$0.649848\pi$
$350$	−24.6572			−1.31798
$351$		0			0
$352$	−1.19094			−0.0634771
$353$	−7.24062	−	7.24062i	−0.385379	−	0.385379i	0.487656	−	0.873036i	$-0.337852\pi$
$353$	−7.24062	−	7.24062i	−0.385379	−	0.385379i	−0.873036	+	0.487656i	$0.837852\pi$
$354$	9.04857	−	28.3622i	0.480926	−	1.50743i
$355$			16.9373i			0.898937i
$356$	6.87586	+	6.87586i	0.364420	+	0.364420i
$357$	21.8598	−	11.2853i	1.15694	−	0.597281i
$358$	2.44592	+	2.44592i	0.129271	+	0.129271i
$359$	−7.50270	+	7.50270i	−0.395977	+	0.395977i	−0.876812	−	0.480834i	$-0.840334\pi$
$359$	−7.50270	+	7.50270i	−0.395977	+	0.395977i	0.480834	+	0.876812i	$0.340334\pi$
$360$	1.19546	+	0.849227i	0.0630062	+	0.0447582i
$361$			17.5678i			0.924623i
$362$	23.5221	−	23.5221i	1.23629	−	1.23629i
$363$	18.1125	+	5.77853i	0.950658	+	0.303294i
$364$		0			0
$365$		−	8.21340i		−	0.429909i
$366$	−17.5708	+	9.07107i	−0.918439	+	0.474152i
$367$	−14.0058			−0.731096			−0.365548	−	0.930792i	$-0.619118\pi$
$367$	−14.0058			−0.731096			−0.365548	+	0.930792i	$0.619118\pi$
$368$	28.8817			1.50556
$369$	4.19236	+	24.7582i	0.218246	+	1.28886i
$370$	6.70675	−	6.70675i	0.348667	−	0.348667i
$371$	−1.99169	+	1.99169i	−0.103403	+	0.103403i
$372$	14.5429	−	7.50789i	0.754014	−	0.389266i
$373$	−19.9776			−1.03440			−0.517200	−	0.855865i	$-0.673026\pi$
$373$	−19.9776			−1.03440			−0.517200	+	0.855865i	$0.673026\pi$
$374$	−0.949764			−0.0491111
$375$	−9.18404	−	17.7896i	−0.474262	−	0.918652i
$376$		−	1.89858i		−	0.0979116i
$377$		0			0
$378$	27.3955	+	36.4658i	1.40907	+	1.87560i
$379$	6.29483	−	6.29483i	0.323344	−	0.323344i	−0.526705	−	0.850048i	$-0.676573\pi$
$379$	6.29483	−	6.29483i	0.323344	−	0.323344i	0.850048	+	0.526705i	$0.176573\pi$
$380$			3.24388i			0.166408i
$381$	−26.3612	−	8.41019i	−1.35053	−	0.430867i
$382$	−30.9701	+	30.9701i	−1.58457	+	1.58457i
$383$	−16.5930	−	16.5930i	−0.847862	−	0.847862i	0.142004	−	0.989866i	$-0.454645\pi$
$383$	−16.5930	−	16.5930i	−0.847862	−	0.847862i	−0.989866	+	0.142004i	$0.954645\pi$
$384$	2.09161	+	4.05147i	0.106737	+	0.206751i
$385$	0.719052	+	0.719052i	0.0366463	+	0.0366463i
$386$			38.5786i			1.96360i
$387$	−4.83545	+	6.80687i	−0.245800	+	0.346013i
$388$	5.79498	+	5.79498i	0.294195	+	0.294195i
$389$	−33.0750			−1.67697			−0.838484	−	0.544926i	$-0.816558\pi$
$389$	−33.0750			−1.67697			−0.838484	+	0.544926i	$0.816558\pi$
$390$		0			0
$391$	21.2293			1.07361
$392$	−3.06128	−	3.06128i	−0.154618	−	0.154618i
$393$	30.9694	+	9.88036i	1.56220	+	0.498398i
$394$			2.91420i			0.146815i
$395$	−5.71869	−	5.71869i	−0.287739	−	0.287739i
$396$	−0.140520	−	0.829845i	−0.00706138	−	0.0417013i
$397$	23.6911	+	23.6911i	1.18902	+	1.18902i	0.977338	+	0.211684i	$0.0678949\pi$
$397$	23.6911	+	23.6911i	1.18902	+	1.18902i	0.211684	+	0.977338i	$0.432105\pi$
$398$	−27.2351	+	27.2351i	−1.36517	+	1.36517i
$399$	2.82523	−	8.85552i	0.141438	−	0.443331i
$400$		−	12.1043i		−	0.605213i
$401$	−12.1119	+	12.1119i	−0.604838	+	0.604838i	−0.941592	−	0.336755i	$-0.890671\pi$
$401$	−12.1119	+	12.1119i	−0.604838	+	0.604838i	0.336755	+	0.941592i	$0.390671\pi$
$402$	−0.693000	+	2.17217i	−0.0345637	+	0.108338i
$403$		0			0
$404$			3.07835i			0.153154i
$405$	−5.79340	+	11.9958i	−0.287876	+	0.596078i
$406$	17.4245			0.864765
$407$	0.501534			0.0248601
$408$	0.831044	+	1.60974i	0.0411428	+	0.0796942i
$409$	−8.69291	+	8.69291i	−0.429837	+	0.429837i	−0.888573	−	0.458736i	$-0.848302\pi$
$409$	−8.69291	+	8.69291i	−0.429837	+	0.429837i	0.458736	+	0.888573i	$0.348302\pi$
$410$	−17.1477	+	17.1477i	−0.846864	+	0.846864i
$411$	4.70634	+	9.11625i	0.232147	+	0.449672i
$412$	−8.08557			−0.398348
$413$	−39.3786			−1.93770
$414$	6.57121	+	38.8066i	0.322957	+	1.90724i
$415$		−	13.4130i		−	0.658418i
$416$		0			0
$417$	−7.88074	+	24.7017i	−0.385922	+	1.20965i
$418$	−0.253753	+	0.253753i	−0.0124115	+	0.0124115i
$419$		−	18.0119i		−	0.879940i	−0.898012	−	0.439970i	$-0.854989\pi$
$419$		−	18.0119i		−	0.879940i	0.898012	−	0.439970i	$-0.145011\pi$
$420$	−6.39921	+	20.0579i	−0.312250	+	0.978728i
$421$	15.2469	−	15.2469i	0.743088	−	0.743088i	−0.230083	−	0.973171i	$-0.573900\pi$
$421$	15.2469	−	15.2469i	0.743088	−	0.743088i	0.973171	+	0.230083i	$0.0738996\pi$
$422$	32.6489	+	32.6489i	1.58932	+	1.58932i
$423$	17.0057	−	2.87961i	0.826843	−	0.140011i
$424$	−0.146667	−	0.146667i	−0.00712278	−	0.00712278i
$425$		−	8.89717i		−	0.431576i
$426$	−36.9587	−	11.7912i	−1.79065	−	0.571283i
$427$	18.4950	+	18.4950i	0.895037	+	0.895037i
$428$	28.3440			1.37006
$429$		0			0
$430$	−8.06355			−0.388859
$431$	21.3784	+	21.3784i	1.02976	+	1.02976i	0.999543	+	0.0302162i	$0.00961957\pi$
$431$	21.3784	+	21.3784i	1.02976	+	1.02976i	0.0302162	+	0.999543i	$0.490380\pi$
$432$	−17.9011	+	13.4485i	−0.861268	+	0.647042i
$433$		−	19.2897i		−	0.927005i	−0.886096	−	0.463503i	$-0.846592\pi$
$433$		−	19.2897i		−	0.927005i	0.886096	−	0.463503i	$-0.153408\pi$
$434$	−32.0260	−	32.0260i	−1.53730	−	1.53730i
$435$	2.33462	+	4.52219i	0.111937	+	0.216823i
$436$	−16.0811	−	16.0811i	−0.770145	−	0.770145i
$437$	5.67194	−	5.67194i	0.271326	−	0.271326i
$438$	17.9224	+	5.71789i	0.856365	+	0.273211i
$439$			17.3861i			0.829793i	0.909869	+	0.414896i	$0.136182\pi$
$439$			17.3861i			0.829793i	−0.909869	+	0.414896i	$0.863818\pi$
$440$	−0.0529507	+	0.0529507i	−0.00252432	+	0.00252432i
$441$	22.7769	−	32.0632i	1.08462	−	1.52682i
$442$		0			0
$443$			1.43321i			0.0680940i	0.999420	+	0.0340470i	$0.0108396\pi$
$443$			1.43321i			0.0680940i	−0.999420	+	0.0340470i	$0.989160\pi$
$444$	4.76344	+	9.22685i	0.226063	+	0.437887i
$445$	7.85954			0.372578
$446$	24.6915			1.16918
$447$	27.1059	−	13.9936i	1.28206	−	0.661876i
$448$	−20.9226	+	20.9226i	−0.988498	+	0.988498i
$449$	27.3135	−	27.3135i	1.28900	−	1.28900i	0.353610	−	0.935393i	$-0.384954\pi$
$449$	27.3135	−	27.3135i	1.28900	−	1.28900i	0.935393	−	0.353610i	$-0.115046\pi$
$450$	16.2638	−	2.75398i	0.766681	−	0.129824i
$451$	−1.28231			−0.0603817
$452$	−8.77343			−0.412667
$453$	−17.0887	+	8.82219i	−0.802898	+	0.414503i
$454$			43.4858i			2.04089i
$455$		0			0
$456$	0.652117	+	0.208049i	0.0305382	+	0.00974279i
$457$	3.28879	−	3.28879i	0.153843	−	0.153843i	−0.625989	−	0.779832i	$-0.715304\pi$
$457$	3.28879	−	3.28879i	0.153843	−	0.153843i	0.779832	+	0.625989i	$0.215304\pi$
$458$			19.5222i			0.912212i
$459$	−13.1581	+	9.88524i	−0.614168	+	0.461404i
$460$	−12.8471	+	12.8471i	−0.598997	+	0.598997i
$461$	5.76221	+	5.76221i	0.268373	+	0.268373i	0.828444	−	0.560072i	$-0.189226\pi$
$461$	5.76221	+	5.76221i	0.268373	+	0.268373i	−0.560072	+	0.828444i	$0.689226\pi$
$462$	−2.06962	+	1.06846i	−0.0962872	+	0.0497091i
$463$	−4.68191	−	4.68191i	−0.217587	−	0.217587i	0.589894	−	0.807481i	$-0.299170\pi$
$463$	−4.68191	−	4.68191i	−0.217587	−	0.217587i	−0.807481	+	0.589894i	$0.799170\pi$
$464$			8.55373i			0.397097i
$465$	4.02072	−	12.6027i	0.186456	−	0.584437i
$466$	−31.7747	−	31.7747i	−1.47193	−	1.47193i
$467$	−15.0964			−0.698578			−0.349289	−	0.937015i	$-0.613577\pi$
$467$	−15.0964			−0.698578			−0.349289	+	0.937015i	$0.613577\pi$
$468$		0			0
$469$	3.01588			0.139260
$470$	11.7782	+	11.7782i	0.543290	+	0.543290i
$471$	5.50943	−	17.2690i	0.253861	−	0.795713i
$472$		−	2.89983i		−	0.133475i
$473$	−0.301498	−	0.301498i	−0.0138629	−	0.0138629i
$474$	16.4599	−	8.49755i	0.756027	−	0.390305i
$475$	−2.37710	−	2.37710i	−0.109069	−	0.109069i
$476$	−18.3922	+	18.3922i	−0.843004	+	0.843004i
$477$	1.09125	−	1.53616i	0.0499650	−	0.0703359i
$478$			35.1052i			1.60567i
$479$	−13.0148	+	13.0148i	−0.594660	+	0.594660i	−0.938886	−	0.344227i	$-0.888141\pi$
$479$	−13.0148	+	13.0148i	−0.594660	+	0.594660i	0.344227	+	0.938886i	$0.388141\pi$
$480$	−18.9870	−	6.05753i	−0.866632	−	0.276487i
$481$		0			0
$482$			5.52530i			0.251671i
$483$	46.2604	−	23.8823i	2.10492	−	1.08668i
$484$	−20.1012			−0.913691
$485$	6.62402			0.300781
$486$	−22.1428	−	20.9928i	−1.00442	−	0.952253i
$487$	20.1793	−	20.1793i	0.914411	−	0.914411i	−0.0822048	−	0.996615i	$-0.526196\pi$
$487$	20.1793	−	20.1793i	0.914411	−	0.914411i	0.996615	+	0.0822048i	$0.0261962\pi$
$488$	−1.36197	+	1.36197i	−0.0616533	+	0.0616533i
$489$	−2.98436	+	1.54070i	−0.134957	+	0.0696729i
$490$	37.9826			1.71588
$491$	37.9959			1.71473			0.857366	−	0.514708i	$-0.172100\pi$
$491$	37.9959			1.71473			0.857366	+	0.514708i	$0.172100\pi$
$492$	−12.1791	−	23.5910i	−0.549075	−	1.06357i
$493$			6.28737i			0.283169i
$494$		0			0
$495$	−0.554594	−	0.393971i	−0.0249271	−	0.0177077i
$496$	15.7216	−	15.7216i	0.705921	−	0.705921i
$497$			51.3141i			2.30175i
$498$	29.2684	+	9.33767i	1.31155	+	0.418431i
$499$	−11.2432	+	11.2432i	−0.503315	+	0.503315i	−0.912466	−	0.409152i	$-0.865825\pi$
$499$	−11.2432	+	11.2432i	−0.503315	+	0.503315i	0.409152	+	0.912466i	$0.365825\pi$
$500$	14.9677	+	14.9677i	0.669375	+	0.669375i
$501$	−11.1096	−	21.5195i	−0.496341	−	0.961419i
$502$	−23.7965	−	23.7965i	−1.06209	−	1.06209i
$503$		−	4.11260i		−	0.183372i	−0.995788	−	0.0916859i	$-0.970774\pi$
$503$		−	4.11260i		−	0.183372i	0.995788	−	0.0916859i	$-0.0292256\pi$
$504$	3.62183	+	2.57287i	0.161329	+	0.114605i
$505$	1.75938	+	1.75938i	0.0782912	+	0.0782912i
$506$	−2.00993			−0.0893521
$507$		0			0
$508$	29.2557			1.29801
$509$	−17.2162	−	17.2162i	−0.763093	−	0.763093i	0.213787	−	0.976880i	$-0.431420\pi$
$509$	−17.2162	−	17.2162i	−0.763093	−	0.763093i	−0.976880	+	0.213787i	$0.931420\pi$
$510$	−15.1420	−	4.83084i	−0.670498	−	0.213913i
$511$		−	24.8838i		−	1.10079i
$512$	−21.6735	−	21.6735i	−0.957841	−	0.957841i
$513$	−0.874427	+	6.15661i	−0.0386069	+	0.271821i
$514$	−13.1597	−	13.1597i	−0.580450	−	0.580450i
$515$	−4.62116	+	4.62116i	−0.203633	+	0.203633i
$516$	2.68319	−	8.41029i	0.118121	−	0.370242i
$517$			0.880782i			0.0387368i
$518$	20.3191	−	20.3191i	0.892772	−	0.892772i
$519$	−9.45126	+	29.6244i	−0.414864	+	1.30037i
$520$		0			0
$521$			14.5577i			0.637784i	0.947791	+	0.318892i	$0.103311\pi$
$521$			14.5577i			0.637784i	−0.947791	+	0.318892i	$0.896689\pi$
$522$	−11.4931	+	1.94616i	−0.503040	+	0.0851811i
$523$	−3.71977			−0.162654			−0.0813270	−	0.996687i	$-0.525916\pi$
$523$	−3.71977			−0.162654			−0.0813270	+	0.996687i	$0.525916\pi$
$524$	−34.3698			−1.50145
$525$	−10.0091	−	19.3877i	−0.436831	−	0.846147i
$526$	10.0337	−	10.0337i	0.437491	−	0.437491i
$527$	11.5561	−	11.5561i	0.503391	−	0.503391i
$528$	−0.524507	−	1.01598i	−0.0228262	−	0.0442148i
$529$	21.9263			0.953316
$530$	1.81976			0.0790455
$531$	25.9739	−	4.39823i	1.12717	−	0.190867i
$532$			9.82785i			0.426091i
$533$		0			0
$534$	−5.47155	+	17.1502i	−0.236777	+	0.742163i
$535$	16.1995	−	16.1995i	0.700365	−	0.700365i
$536$			0.222088i			0.00959274i
$537$	−0.930329	+	2.91606i	−0.0401467	+	0.125837i
$538$	37.0624	−	37.0624i	1.59788	−	1.59788i
$539$	1.42018	+	1.42018i	0.0611715	+	0.0611715i
$540$	1.98060	−	13.9448i	0.0852313	−	0.600091i
$541$	−2.30265	−	2.30265i	−0.0989985	−	0.0989985i	0.655873	−	0.754871i	$-0.272301\pi$
$541$	−2.30265	−	2.30265i	−0.0989985	−	0.0989985i	−0.754871	+	0.655873i	$0.772301\pi$
$542$			3.30937i			0.142150i
$543$	28.0434	+	8.94687i	1.20346	+	0.383947i
$544$	−17.4101	−	17.4101i	−0.746453	−	0.746453i
$545$	−18.3817			−0.787386
$546$		0			0
$547$	−25.9324			−1.10879			−0.554395	−	0.832253i	$-0.687050\pi$
$547$	−25.9324			−1.10879			−0.554395	+	0.832253i	$0.687050\pi$
$548$	−7.67015	−	7.67015i	−0.327653	−	0.327653i
$549$	−14.2649	−	10.1335i	−0.608813	−	0.432487i
$550$			0.842357i			0.0359182i
$551$	1.67983	+	1.67983i	0.0715630	+	0.0715630i
$552$	1.75869	+	3.40660i	0.0748547	+	0.144995i
$553$	−17.3257	−	17.3257i	−0.736763	−	0.736763i
$554$	34.5486	−	34.5486i	1.46783	−	1.46783i
$555$	7.99589	+	2.55098i	0.339407	+	0.108283i
$556$		−	27.4140i		−	1.16261i
$557$	−6.37725	+	6.37725i	−0.270213	+	0.270213i	−0.829186	−	0.558973i	$-0.811195\pi$
$557$	−6.37725	+	6.37725i	−0.270213	+	0.270213i	0.558973	+	0.829186i	$0.311195\pi$
$558$	24.7012	+	17.5472i	1.04568	+	0.742831i
$559$		0			0
$560$			28.6016i			1.20864i
$561$	−0.385536	−	0.746788i	−0.0162773	−	0.0315294i
$562$	7.00488			0.295483
$563$	−8.75049			−0.368789			−0.184395	−	0.982852i	$-0.559032\pi$
$563$	−8.75049			−0.368789			−0.184395	+	0.982852i	$0.559032\pi$
$564$	−16.2040	+	8.36545i	−0.682311	+	0.352249i
$565$	−5.01429	+	5.01429i	−0.210953	+	0.210953i
$566$	7.08494	−	7.08494i	0.297802	−	0.297802i
$567$	−17.5520	+	36.3433i	−0.737115	+	1.52627i
$568$	−3.77875			−0.158553
$569$	−31.5099			−1.32096			−0.660481	−	0.750843i	$-0.729648\pi$
$569$	−31.5099			−1.32096			−0.660481	+	0.750843i	$0.729648\pi$
$570$	−5.33623	+	2.75488i	−0.223510	+	0.115389i
$571$		−	34.4177i		−	1.44034i	−0.693799	−	0.720169i	$-0.744064\pi$
$571$		−	34.4177i		−	1.44034i	0.693799	−	0.720169i	$-0.255936\pi$
$572$		0			0
$573$	−36.9230	−	11.7798i	−1.54248	−	0.492107i
$574$	−51.9516	+	51.9516i	−2.16842	+	2.16842i
$575$		−	18.8285i		−	0.785204i
$576$	11.4635	−	16.1373i	0.477648	−	0.672386i
$577$	27.5186	−	27.5186i	1.14562	−	1.14562i	0.158211	−	0.987405i	$-0.449427\pi$
$577$	27.5186	−	27.5186i	1.14562	−	1.14562i	0.987405	−	0.158211i	$-0.0505726\pi$
$578$	9.64470	+	9.64470i	0.401167	+	0.401167i
$579$	−30.3339	+	15.6601i	−1.26063	+	0.650813i
$580$	−3.80484	−	3.80484i	−0.157988	−	0.157988i
$581$		−	40.6368i		−	1.68590i
$582$	−4.61142	+	14.4542i	−0.191150	+	0.599147i
$583$	0.0680414	+	0.0680414i	0.00281799	+	0.00281799i
$584$	1.83243			0.0758266
$585$		0			0
$586$	0.548902			0.0226749
$587$	−2.80955	−	2.80955i	−0.115963	−	0.115963i	0.646744	−	0.762707i	$-0.276130\pi$
$587$	−2.80955	−	2.80955i	−0.115963	−	0.115963i	−0.762707	+	0.646744i	$0.776130\pi$
$588$	−12.6389	+	39.6159i	−0.521220	+	1.63373i
$589$		−	6.17499i		−	0.254436i
$590$	17.9897	+	17.9897i	0.740625	+	0.740625i
$591$	−2.29140	+	1.18295i	−0.0942555	+	0.0486602i
$592$	9.97470	+	9.97470i	0.409958	+	0.409958i
$593$	−11.5666	+	11.5666i	−0.474985	+	0.474985i	−0.903523	−	0.428539i	$-0.859029\pi$
$593$	−11.5666	+	11.5666i	−0.474985	+	0.474985i	0.428539	+	0.903523i	$0.359029\pi$
$594$	1.24577	−	0.935905i	0.0511146	−	0.0384007i
$595$			21.0234i			0.861876i
$596$	−22.8061	+	22.8061i	−0.934174	+	0.934174i
$597$	−32.4702	−	10.3592i	−1.32892	−	0.423972i
$598$		0			0
$599$			2.33031i			0.0952139i	0.998866	+	0.0476069i	$0.0151595\pi$
$599$			2.33031i			0.0952139i	−0.998866	+	0.0476069i	$0.984841\pi$
$600$	1.42770	−	0.737063i	0.0582856	−	0.0300905i
$601$	−3.90549			−0.159308			−0.0796542	−	0.996823i	$-0.525382\pi$
$601$	−3.90549			−0.159308			−0.0796542	+	0.996823i	$0.525382\pi$
$602$	−24.4298			−0.995684
$603$	−1.98926	+	0.336846i	−0.0810088	+	0.0137174i
$604$	14.3779	−	14.3779i	0.585030	−	0.585030i
$605$	−11.4885	+	11.4885i	−0.467073	+	0.467073i
$606$	−5.06394	+	2.61430i	−0.205708	+	0.106199i
$607$	27.1575			1.10229			0.551144	−	0.834410i	$-0.314192\pi$
$607$	27.1575			1.10229			0.551144	+	0.834410i	$0.314192\pi$
$608$	−9.30309			−0.377290
$609$	7.07310	+	13.7007i	0.286617	+	0.555180i
$610$		−	16.8985i		−	0.684201i
$611$		0			0
$612$	10.0771	−	14.1856i	0.407344	−	0.573419i
$613$	−4.38429	+	4.38429i	−0.177080	+	0.177080i	−0.790082	−	0.613002i	$-0.789962\pi$
$613$	−4.38429	+	4.38429i	−0.177080	+	0.177080i	0.613002	+	0.790082i	$0.289962\pi$
$614$		−	35.8262i		−	1.44583i
$615$	−20.4437	−	6.52229i	−0.824371	−	0.263004i
$616$	−0.160422	+	0.160422i	−0.00646360	+	0.00646360i
$617$	−29.0963	−	29.0963i	−1.17137	−	1.17137i	−0.981882	−	0.189492i	$-0.939316\pi$
$617$	−29.0963	−	29.0963i	−1.17137	−	1.17137i	−0.189492	−	0.981882i	$-0.560684\pi$
$618$	−6.86670	−	13.3009i	−0.276219	−	0.535040i
$619$	7.15152	+	7.15152i	0.287444	+	0.287444i	0.836069	−	0.548625i	$-0.184848\pi$
$619$	7.15152	+	7.15152i	0.287444	+	0.287444i	−0.548625	+	0.836069i	$0.684848\pi$
$620$			13.9865i			0.561711i
$621$	−27.8457	+	20.9195i	−1.11741	+	0.839472i
$622$	9.36218	+	9.36218i	0.375389	+	0.375389i
$623$	23.8117			0.953996
$624$		0			0
$625$	3.06353			0.122541
$626$	35.1101	+	35.1101i	1.40328	+	1.40328i
$627$	−0.302529	−	0.0965176i	−0.0120818	−	0.00385454i
$628$			19.1651i			0.764771i
$629$	7.33185	+	7.33185i	0.292340	+	0.292340i
$630$	−38.4302	+	6.50748i	−1.53109	+	0.259264i
$631$	8.97854	+	8.97854i	0.357430	+	0.357430i	0.862865	−	0.505435i	$-0.168668\pi$
$631$	8.97854	+	8.97854i	0.357430	+	0.357430i	−0.505435	+	0.862865i	$0.668668\pi$
$632$	1.27586	−	1.27586i	0.0507508	−	0.0507508i
$633$	−12.4183	+	38.9245i	−0.493584	+	1.54711i
$634$			15.6548i			0.621731i
$635$	16.7205	−	16.7205i	0.663534	−	0.663534i
$636$	−0.605536	+	1.89802i	−0.0240111	+	0.0752612i
$637$		0			0
$638$		−	0.595269i		−	0.0235669i
$639$	−5.73132	−	33.8465i	−0.226727	−	1.33895i
$640$	−3.89647			−0.154021
$641$	30.3342			1.19813			0.599065	−	0.800700i	$-0.295539\pi$
$641$	30.3342			1.19813			0.599065	+	0.800700i	$0.295539\pi$
$642$	24.0712	+	46.6263i	0.950016	+	1.84019i
$643$	33.4616	−	33.4616i	1.31960	−	1.31960i	0.405502	−	0.914094i	$-0.367097\pi$
$643$	33.4616	−	33.4616i	1.31960	−	1.31960i	0.914094	−	0.405502i	$-0.132903\pi$
$644$	−38.9222	+	38.9222i	−1.53375	+	1.53375i
$645$	−3.27322	−	6.34027i	−0.128883	−	0.249648i
$646$	−7.41916			−0.291903
$647$	−19.2475			−0.756696			−0.378348	−	0.925663i	$-0.623508\pi$
$647$	−19.2475			−0.756696			−0.378348	+	0.925663i	$0.623508\pi$
$648$	−2.67630	−	1.29252i	−0.105135	−	0.0507751i
$649$			1.34528i			0.0528069i
$650$		0			0
$651$	12.1814	−	38.1819i	0.477427	−	1.49647i
$652$	2.51095	−	2.51095i	0.0983366	−	0.0983366i
$653$		−	9.85148i		−	0.385518i	−0.981246	−	0.192759i	$-0.938256\pi$
$653$		−	9.85148i		−	0.385518i	0.981246	−	0.192759i	$-0.0617436\pi$
$654$	12.7967	−	40.1106i	0.500391	−	1.56845i
$655$	−19.6434	+	19.6434i	−0.767532	+	0.767532i
$656$	−25.5031	−	25.5031i	−0.995730	−	0.995730i
$657$	2.77929	+	16.4132i	0.108430	+	0.640341i
$658$	35.6840	+	35.6840i	1.39111	+	1.39111i
$659$		−	4.63004i		−	0.180361i	−0.995925	−	0.0901805i	$-0.971256\pi$
$659$		−	4.63004i		−	0.180361i	0.995925	−	0.0901805i	$-0.0287444\pi$
$660$	0.685234	+	0.218614i	0.0266727	+	0.00850955i
$661$	21.7120	+	21.7120i	0.844498	+	0.844498i	0.989440	−	0.144942i	$-0.0462995\pi$
$661$	21.7120	+	21.7120i	0.844498	+	0.844498i	−0.144942	+	0.989440i	$0.546300\pi$
$662$	46.0604			1.79019
$663$		0			0
$664$	2.99247			0.116131
$665$	5.61693	+	5.61693i	0.217815	+	0.217815i
$666$	−11.1329	+	15.6719i	−0.431393	+	0.607272i
$667$			13.3056i			0.515193i
$668$	18.1059	+	18.1059i	0.700537	+	0.700537i
$669$	10.0230	+	19.4146i	0.387510	+	0.750613i
$670$	−1.37777	−	1.37777i	−0.0532280	−	0.0532280i
$671$	0.631840	−	0.631840i	0.0243919	−	0.0243919i
$672$	−57.5240	−	18.3522i	−2.21903	−	0.707952i
$673$		−	36.0212i		−	1.38851i	−0.719727	−	0.694257i	$-0.755733\pi$
$673$		−	36.0212i		−	1.38851i	0.719727	−	0.694257i	$-0.244267\pi$
$674$	11.4210	−	11.4210i	0.439919	−	0.439919i
$675$	8.76734	+	11.6701i	0.337455	+	0.449182i
$676$		0			0
$677$			5.60187i			0.215297i	0.994189	+	0.107649i	$0.0343322\pi$
$677$			5.60187i			0.215297i	−0.994189	+	0.107649i	$0.965668\pi$
$678$	−7.45086	−	14.4324i	−0.286149	−	0.554274i
$679$	20.0685			0.770159
$680$	−1.54816			−0.0593690
$681$	−34.1924	+	17.6521i	−1.31025	+	0.676430i
$682$	−1.09409	+	1.09409i	−0.0418950	+	0.0418950i
$683$	−1.82603	+	1.82603i	−0.0698711	+	0.0698711i	−0.741179	−	0.671308i	$-0.765733\pi$
$683$	−1.82603	+	1.82603i	−0.0698711	+	0.0698711i	0.671308	+	0.741179i	$0.265733\pi$
$684$	−1.09768	−	6.48240i	−0.0419709	−	0.247861i
$685$	−8.76747			−0.334988
$686$	53.6309			2.04764
$687$	−15.3501	+	7.92460i	−0.585642	+	0.302343i
$688$		−	11.9926i		−	0.457215i
$689$		0			0
$690$	−32.0440	−	10.2232i	−1.21989	−	0.389191i
$691$	−17.7451	+	17.7451i	−0.675054	+	0.675054i	−0.958877	−	0.283823i	$-0.908397\pi$
$691$	−17.7451	+	17.7451i	−0.675054	+	0.675054i	0.283823	+	0.958877i	$0.408397\pi$
$692$		−	32.8772i		−	1.24980i
$693$	−1.68023	−	1.19360i	−0.0638266	−	0.0453410i
$694$	5.30936	−	5.30936i	0.201541	−	0.201541i
$695$	−15.6679	−	15.6679i	−0.594319	−	0.594319i
$696$	−1.00891	+	0.520860i	−0.0382428	+	0.0197432i
$697$	−18.7459	−	18.7459i	−0.710052	−	0.710052i
$698$		−	22.6327i		−	0.856659i
$699$	12.0858	−	37.8823i	0.457127	−	1.43284i
$700$	16.3122	+	16.3122i	0.616544	+	0.616544i
$701$	−0.474084			−0.0179059			−0.00895296	−	0.999960i	$-0.502850\pi$
$701$	−0.474084			−0.0179059			−0.00895296	+	0.999960i	$0.502850\pi$
$702$		0			0
$703$	3.91777			0.147761
$704$	0.714771	+	0.714771i	0.0269390	+	0.0269390i
$705$	−4.47997	+	14.0422i	−0.168725	+	0.528860i
$706$			20.0430i			0.754329i
$707$	5.33031	+	5.33031i	0.200467	+	0.200467i
$708$	−24.7495	+	12.7771i	−0.930143	+	0.480194i
$709$	35.1122	+	35.1122i	1.31867	+	1.31867i	0.914832	+	0.403834i	$0.132323\pi$
$709$	35.1122	+	35.1122i	1.31867	+	1.31867i	0.403834	+	0.914832i	$0.367677\pi$
$710$	23.4423	−	23.4423i	0.879775	−	0.879775i
$711$	13.3630	+	9.49280i	0.501153	+	0.356008i
$712$			1.75349i			0.0657147i
$713$	24.4554	−	24.4554i	0.915862	−	0.915862i
$714$	−45.8750	−	14.6358i	−1.71683	−	0.547730i
$715$		0			0
$716$		−	3.23624i		−	0.120944i
$717$	−27.6028	+	14.2502i	−1.03085	+	0.532183i
$718$	20.7685			0.775074
$719$	1.69544			0.0632292			0.0316146	−	0.999500i	$-0.489935\pi$
$719$	1.69544			0.0632292			0.0316146	+	0.999500i	$0.489935\pi$
$720$	−3.19453	−	18.8654i	−0.119053	−	0.703073i
$721$	−14.0005	+	14.0005i	−0.521407	+	0.521407i
$722$	24.3151	−	24.3151i	0.904914	−	0.904914i
$723$	−4.34448	+	2.24287i	−0.161573	+	0.0834134i
$724$	−31.1226			−1.15666
$725$	5.57634			0.207100
$726$	−17.0710	−	33.0668i	−0.633564	−	1.22722i
$727$		−	20.3423i		−	0.754455i	−0.926121	−	0.377227i	$-0.876878\pi$
$727$		−	20.3423i		−	0.754455i	0.926121	−	0.377227i	$-0.123122\pi$
$728$		0			0
$729$	7.51800	−	25.9322i	0.278445	−	0.960452i
$730$	−11.3679	+	11.3679i	−0.420745	+	0.420745i
$731$		−	8.81511i		−	0.326038i
$732$	17.6252	+	5.62307i	0.651446	+	0.207835i
$733$	−3.64797	+	3.64797i	−0.134741	+	0.134741i	−0.771261	−	0.636520i	$-0.780373\pi$
$733$	−3.64797	+	3.64797i	−0.134741	+	0.134741i	0.636520	+	0.771261i	$0.280373\pi$
$734$	19.3850	+	19.3850i	0.715512	+	0.715512i
$735$	15.4182	+	29.8653i	0.568709	+	1.10160i
$736$	−36.8439	−	36.8439i	−1.35809	−	1.35809i
$737$		−	0.103031i		−	0.00379518i
$738$	28.4645	−	40.0695i	1.04779	−	1.47498i
$739$	−26.5480	−	26.5480i	−0.976584	−	0.976584i	0.0231482	−	0.999732i	$-0.492631\pi$
$739$	−26.5480	−	26.5480i	−0.976584	−	0.976584i	−0.999732	+	0.0231482i	$0.992631\pi$
$740$	−8.87383			−0.326209
$741$		0			0
$742$	5.51326			0.202398
$743$	−6.45650	−	6.45650i	−0.236866	−	0.236866i	0.578685	−	0.815551i	$-0.303566\pi$
$743$	−6.45650	−	6.45650i	−0.236866	−	0.236866i	−0.815551	+	0.578685i	$0.803566\pi$
$744$	2.81170	+	0.897034i	0.103082	+	0.0328869i
$745$			26.0688i			0.955087i
$746$	27.6503	+	27.6503i	1.01235	+	1.01235i
$747$	4.53875	+	26.8038i	0.166064	+	0.980699i
$748$	0.628326	+	0.628326i	0.0229739	+	0.0229739i
$749$	49.0789	−	49.0789i	1.79330	−	1.79330i
$750$	−11.9107	+	37.3334i	−0.434917	+	1.36322i
$751$		−	23.1057i		−	0.843137i	−0.906796	−	0.421569i	$-0.861480\pi$
$751$		−	23.1057i		−	0.843137i	0.906796	−	0.421569i	$-0.138520\pi$
$752$	−17.5173	+	17.5173i	−0.638792	+	0.638792i
$753$	9.05125	−	28.3706i	0.329846	−	1.03388i
$754$		0			0
$755$		−	16.4349i		−	0.598127i
$756$	6.00053	−	42.2481i	0.218237	−	1.53655i
$757$	37.9154			1.37806			0.689029	−	0.724734i	$-0.258037\pi$
$757$	37.9154			1.37806			0.689029	+	0.724734i	$0.258037\pi$
$758$	−17.4249			−0.632902
$759$	−0.815886	−	1.58038i	−0.0296148	−	0.0573642i
$760$	−0.413628	+	0.413628i	−0.0150039	+	0.0150039i
$761$	33.0810	−	33.0810i	1.19919	−	1.19919i	0.224774	−	0.974411i	$-0.427835\pi$
$761$	33.0810	−	33.0810i	1.19919	−	1.19919i	0.974411	−	0.224774i	$-0.0721645\pi$
$762$	24.8455	+	48.1260i	0.900056	+	1.74342i
$763$	−55.6903			−2.01612
$764$	40.9771			1.48250
$765$	−2.34812	−	13.8669i	−0.0848965	−	0.501360i
$766$			45.9317i			1.65958i
$767$		0			0
$768$	9.65974	−	30.2779i	0.348566	−	1.09256i
$769$	21.6783	−	21.6783i	0.781738	−	0.781738i	−0.198386	−	0.980124i	$-0.563570\pi$
$769$	21.6783	−	21.6783i	0.781738	−	0.781738i	0.980124	+	0.198386i	$0.0635699\pi$
$770$		−	1.99043i		−	0.0717302i
$771$	5.00543	−	15.6892i	0.180266	−	0.565033i
$772$	25.5221	−	25.5221i	0.918559	−	0.918559i
$773$	−1.91473	−	1.91473i	−0.0688681	−	0.0688681i	0.671834	−	0.740702i	$-0.265507\pi$
$773$	−1.91473	−	1.91473i	−0.0688681	−	0.0688681i	−0.740702	+	0.671834i	$0.765507\pi$
$774$	16.1138	−	2.72858i	0.579197	−	0.0980769i
$775$	−10.2492	−	10.2492i	−0.368163	−	0.368163i
$776$			1.47784i			0.0530513i
$777$	24.2248	+	7.72859i	0.869060	+	0.277262i
$778$	45.7780	+	45.7780i	1.64122	+	1.64122i
$779$	−10.0169			−0.358892
$780$		0			0
$781$	1.75303			0.0627283
$782$	−29.3828	−	29.3828i	−1.05073	−	1.05073i
$783$	−6.19562	−	8.24690i	−0.221413	−	0.294720i
$784$			56.4902i			2.01751i
$785$	10.9535	+	10.9535i	0.390946	+	0.390946i
$786$	−29.1887	−	56.5388i	−1.04113	−	2.01667i
$787$	−37.8082	−	37.8082i	−1.34772	−	1.34772i	−0.888137	−	0.459578i	$-0.848001\pi$
$787$	−37.8082	−	37.8082i	−1.34772	−	1.34772i	−0.459578	−	0.888137i	$-0.651999\pi$
$788$	1.92792	−	1.92792i	0.0686792	−	0.0686792i
$789$	11.9623	+	3.81642i	0.425871	+	0.135868i
$790$			15.8301i			0.563210i
$791$	−15.1916	+	15.1916i	−0.540151	+	0.540151i
$792$	0.0878960	−	0.123731i	0.00312325	−	0.00439661i
$793$		0			0
$794$		−	65.5802i		−	2.32735i
$795$	0.738693	+	1.43086i	0.0261987	+	0.0507473i
$796$	36.0354			1.27724
$797$	−36.4286			−1.29037			−0.645183	−	0.764028i	$-0.723219\pi$
$797$	−36.4286			−1.29037			−0.645183	+	0.764028i	$0.723219\pi$
$798$	−16.1670	+	8.34633i	−0.572304	+	0.295457i
$799$	−12.8760	+	12.8760i	−0.455521	+	0.455521i
$800$	−15.4412	+	15.4412i	−0.545930	+	0.545930i
$801$	−15.7061	+	2.65955i	−0.554947	+	0.0939706i
$802$	33.5273			1.18389
$803$	−0.850098			−0.0299993
$804$	1.89548	−	0.978558i	0.0668484	−	0.0345111i
$805$			44.4905i			1.56808i
$806$		0			0
$807$	44.1864	+	14.0971i	1.55544	+	0.496241i
$808$	−0.392522	+	0.392522i	−0.0138089	+	0.0138089i
$809$			27.9069i			0.981154i	0.871398	+	0.490577i	$0.163214\pi$
$809$			27.9069i			0.981154i	−0.871398	+	0.490577i	$0.836786\pi$
$810$	24.6215	−	8.58459i	0.865111	−	0.301632i
$811$	−9.41030	+	9.41030i	−0.330440	+	0.330440i	−0.852754	−	0.522313i	$-0.825069\pi$
$811$	−9.41030	+	9.41030i	−0.330440	+	0.330440i	0.522313	+	0.852754i	$0.325069\pi$
$812$	−11.5274	−	11.5274i	−0.404531	−	0.404531i
$813$	−2.60212	+	1.34337i	−0.0912602	+	0.0471139i
$814$	−0.694157	−	0.694157i	−0.0243302	−	0.0243302i
$815$		−	2.87018i		−	0.100538i
$816$	7.18473	−	22.5201i	0.251516	−	0.788361i
$817$	−2.35518	−	2.35518i	−0.0823971	−	0.0823971i
$818$	24.0632			0.841349
$819$		0			0
$820$	22.6884			0.792315
$821$	9.06140	+	9.06140i	0.316245	+	0.316245i	0.847323	−	0.531078i	$-0.178213\pi$
$821$	9.06140	+	9.06140i	0.316245	+	0.316245i	−0.531078	+	0.847323i	$0.678213\pi$
$822$	6.10361	−	19.1314i	0.212888	−	0.667285i
$823$			20.7304i			0.722615i	0.932447	+	0.361308i	$0.117670\pi$
$823$			20.7304i			0.722615i	−0.932447	+	0.361308i	$0.882330\pi$
$824$	−1.03099	−	1.03099i	−0.0359164	−	0.0359164i
$825$	−0.662335	+	0.341936i	−0.0230596	+	0.0119047i
$826$	54.5027	+	54.5027i	1.89639	+	1.89639i
$827$	30.0036	−	30.0036i	1.04333	−	1.04333i	0.0443105	−	0.999018i	$-0.485891\pi$
$827$	30.0036	−	30.0036i	1.04333	−	1.04333i	0.999018	−	0.0443105i	$-0.0141091\pi$
$828$	21.3256	−	30.0201i	0.741116	−	1.04327i
$829$			1.86550i			0.0647914i	0.999475	+	0.0323957i	$0.0103137\pi$
$829$			1.86550i			0.0647914i	−0.999475	+	0.0323957i	$0.989686\pi$
$830$	−18.5645	+	18.5645i	−0.644383	+	0.644383i
$831$	41.1894	+	13.1409i	1.42884	+	0.455853i
$832$		0			0
$833$			41.5228i			1.43868i
$834$	45.0964	−	23.2814i	1.56156	−	0.806168i
$835$	20.6961			0.716219
$836$	0.335746			0.0116120
$837$	−3.77022	+	26.5451i	−0.130318	+	0.917534i
$838$	−24.9297	+	24.9297i	−0.861183	+	0.861183i
$839$	−18.7951	+	18.7951i	−0.648880	+	0.648880i	−0.952722	−	0.303843i	$-0.901730\pi$
$839$	−18.7951	+	18.7951i	−0.648880	+	0.648880i	0.303843	+	0.952722i	$0.401730\pi$
$840$	−3.37356	+	1.74163i	−0.116399	+	0.0600919i
$841$	25.0594			0.864116
$842$	−42.2055			−1.45450
$843$	2.84348	+	5.50785i	0.0979346	+	0.189701i
$844$		−	43.1984i		−	1.48695i
$845$		0			0
$846$	−27.5226	−	19.5514i	−0.946245	−	0.672191i
$847$	−34.8061	+	34.8061i	−1.19595	+	1.19595i
$848$			2.70647i			0.0929405i
$849$	8.44678	+	2.69483i	0.289893	+	0.0924863i
$850$	−12.3143	+	12.3143i	−0.422377	+	0.422377i
$851$	15.5159	+	15.5159i	0.531879	+	0.531879i
$852$	16.6498	+	32.2509i	0.570414	+	1.10490i
$853$	15.8825	+	15.8825i	0.543806	+	0.543806i	0.924642	−	0.380837i	$-0.124364\pi$
$853$	15.8825	+	15.8825i	0.543806	+	0.543806i	−0.380837	+	0.924642i	$0.624364\pi$
$854$		−	51.1967i		−	1.75192i
$855$	−4.33225	−	3.07753i	−0.148160	−	0.105249i
$856$	3.61415	+	3.61415i	0.123529	+	0.123529i
$857$	48.2304			1.64752			0.823759	−	0.566941i	$-0.191873\pi$
$857$	48.2304			1.64752			0.823759	+	0.566941i	$0.191873\pi$
$858$		0			0
$859$	−20.5416			−0.700870			−0.350435	−	0.936587i	$-0.613966\pi$
$859$	−20.5416			−0.700870			−0.350435	+	0.936587i	$0.613966\pi$
$860$	5.33452	+	5.33452i	0.181906	+	0.181906i
$861$	−61.9375	−	19.7603i	−2.11083	−	0.673430i
$862$		−	59.1782i		−	2.01562i
$863$	3.75723	+	3.75723i	0.127898	+	0.127898i	0.768158	−	0.640260i	$-0.221174\pi$
$863$	3.75723	+	3.75723i	0.127898	+	0.127898i	−0.640260	+	0.768158i	$0.721174\pi$
$864$	39.9923	+	5.68013i	1.36056	+	0.193242i
$865$	−18.7903	−	18.7903i	−0.638890	−	0.638890i
$866$	−26.6983	+	26.6983i	−0.907245	+	0.907245i
$867$	−3.66846	+	11.4986i	−0.124587	+	0.390512i
$868$			42.3742i			1.43828i
$869$	−0.591892	+	0.591892i	−0.0200786	+	0.0200786i
$870$	3.02775	−	9.49030i	0.102650	−	0.321751i
$871$		0			0
$872$		−	4.10101i		−	0.138878i
$873$	−13.2371	+	2.24147i	−0.448008	+	0.0758622i
$874$	−15.7007			−0.531084
$875$	51.8344			1.75232
$876$	−8.07401	−	15.6395i	−0.272796	−	0.528409i
$877$	−33.7528	+	33.7528i	−1.13975	+	1.13975i	−0.151257	+	0.988494i	$0.548332\pi$
$877$	−33.7528	+	33.7528i	−1.13975	+	1.13975i	−0.988494	+	0.151257i	$0.951668\pi$
$878$	24.0635	−	24.0635i	0.812105	−	0.812105i
$879$	0.222815	+	0.431595i	0.00751535	+	0.0145573i
$880$	0.977107			0.0329383
$881$	22.4226			0.755437			0.377718	−	0.925920i	$-0.376709\pi$
$881$	22.4226			0.755437			0.377718	+	0.925920i	$0.376709\pi$
$882$	−75.9024	+	12.8527i	−2.55577	+	0.432774i
$883$			21.7280i			0.731205i	0.930771	+	0.365602i	$0.119137\pi$
$883$			21.7280i			0.731205i	−0.930771	+	0.365602i	$0.880863\pi$
$884$		0			0
$885$	−6.84257	+	21.4476i	−0.230011	+	0.720955i
$886$	1.98366	−	1.98366i	0.0666425	−	0.0666425i
$887$		−	24.1403i		−	0.810553i	−0.914194	−	0.405276i	$-0.867175\pi$
$887$		−	24.1403i		−	0.810553i	0.914194	−	0.405276i	$-0.132825\pi$
$888$	−0.569131	+	1.78391i	−0.0190988	+	0.0598640i
$889$	50.6575	−	50.6575i	1.69900	−	1.69900i
$890$	−10.8781	−	10.8781i	−0.364636	−	0.364636i
$891$	1.24158	+	0.599624i	0.0415946	+	0.0200882i
$892$	−16.3349	−	16.3349i	−0.546933	−	0.546933i
$893$			6.88030i			0.230240i
$894$	−56.8845	−	18.1482i	−1.90250	−	0.606967i
$895$	−1.84961	−	1.84961i	−0.0618258	−	0.0618258i
$896$	−11.8050			−0.394376
$897$		0			0
$898$	−75.6075			−2.52305
$899$	7.24282	+	7.24282i	0.241562	+	0.241562i
$900$	−12.5814	−	8.93753i	−0.419379	−	0.297918i
$901$			1.98937i			0.0662757i
$902$	1.77481	+	1.77481i	0.0590946	+	0.0590946i
$903$	−9.91673	−	19.2088i	−0.330008	−	0.639230i
$904$	−1.11870	−	1.11870i	−0.0372075	−	0.0372075i
$905$	−17.7875	+	17.7875i	−0.591277	+	0.591277i
$906$	35.8624	+	11.4414i	1.19145	+	0.380116i
$907$			23.1138i			0.767481i	0.923441	+	0.383741i	$0.125364\pi$
$907$			23.1138i			0.767481i	−0.923441	+	0.383741i	$0.874636\pi$
$908$	28.7685	−	28.7685i	0.954715	−	0.954715i
$909$	−4.11119	−	2.92050i	−0.136359	−	0.0968667i
$910$		0			0
$911$			8.77371i			0.290686i	0.989381	+	0.145343i	$0.0464286\pi$
$911$			8.77371i			0.290686i	−0.989381	+	0.145343i	$0.953571\pi$
$912$	−4.09723	−	7.93639i	−0.135673	−	0.262800i
$913$	−1.38826			−0.0459447
$914$	−9.10382			−0.301128
$915$	13.2871	−	6.85958i	0.439258	−	0.226771i
$916$	12.9151	−	12.9151i	0.426727	−	0.426727i
$917$	−59.5128	+	59.5128i	−1.96529	+	1.96529i
$918$	31.8936	+	4.52987i	1.05264	+	0.149508i
$919$	−0.279814			−0.00923020			−0.00461510	−	0.999989i	$-0.501469\pi$
$919$	−0.279814			−0.00923020			−0.00461510	+	0.999989i	$0.501469\pi$
$920$	−3.27626			−0.108015
$921$	28.1697	−	14.5429i	0.928224	−	0.479204i
$922$		−	15.9506i		−	0.525304i
$923$		0			0
$924$	2.07602	+	0.662327i	0.0682962	+	0.0217889i
$925$	6.50270	−	6.50270i	0.213807	−	0.213807i
$926$			12.9602i			0.425898i
$927$	7.67094	−	10.7984i	0.251947	−	0.354666i
$928$	10.9119	−	10.9119i	0.358200	−	0.358200i
$929$	13.0263	+	13.0263i	0.427378	+	0.427378i	0.887734	−	0.460357i	$-0.152278\pi$
$929$	13.0263	+	13.0263i	0.427378	+	0.427378i	−0.460357	+	0.887734i	$0.652278\pi$
$930$	−23.0080	+	11.8781i	−0.754461	+	0.389497i
$931$	11.0938	+	11.0938i	0.363586	+	0.363586i
$932$			42.0417i			1.37712i
$933$	−3.56100	+	11.1617i	−0.116582	+	0.365419i
$934$	20.8945	+	20.8945i	0.683687	+	0.683687i
$935$	0.718216			0.0234882
$936$		0			0
$937$	58.7234			1.91841			0.959205	−	0.282712i	$-0.0912341\pi$
$937$	58.7234			1.91841			0.959205	+	0.282712i	$0.0912341\pi$
$938$	−4.17418	−	4.17418i	−0.136292	−	0.136292i
$939$	−13.3545	+	41.8588i	−0.435807	+	1.36601i
$940$		−	15.5840i		−	0.508295i
$941$	−21.2364	−	21.2364i	−0.692286	−	0.692286i	0.270448	−	0.962734i	$-0.412828\pi$
$941$	−21.2364	−	21.2364i	−0.692286	−	0.692286i	−0.962734	+	0.270448i	$0.912828\pi$
$942$	−31.5269	+	16.2760i	−1.02720	+	0.530302i
$943$	−39.6708	−	39.6708i	−1.29186	−	1.29186i
$944$	−26.7555	+	26.7555i	−0.870817	+	0.870817i
$945$	−20.7166	−	27.5756i	−0.673912	−	0.897035i
$946$			0.834588i			0.0271348i
$947$	25.2698	−	25.2698i	0.821159	−	0.821159i	−0.165115	−	0.986274i	$-0.552800\pi$
$947$	25.2698	−	25.2698i	0.821159	−	0.821159i	0.986274	+	0.165115i	$0.0527995\pi$
$948$	−16.5108	−	5.26755i	−0.536247	−	0.171082i
$949$		0			0
$950$			6.58014i			0.213488i
$951$	−12.3092	+	6.35472i	−0.399152	+	0.206066i
$952$	−4.69038			−0.152016
$953$	20.1011			0.651140			0.325570	−	0.945518i	$-0.394444\pi$
$953$	20.1011			0.651140			0.325570	+	0.945518i	$0.394444\pi$
$954$	−3.63652	+	0.615780i	−0.117737	+	0.0199366i
$955$	23.4197	−	23.4197i	0.757844	−	0.757844i
$956$	23.2242	−	23.2242i	0.751124	−	0.751124i
$957$	0.468053	−	0.241636i	0.0151300	−	0.00781099i
$958$	36.0266			1.16397
$959$	−26.5624			−0.857745
$960$	7.75993	+	15.0311i	0.250451	+	0.485126i
$961$			4.37562i			0.141149i
$962$		0			0
$963$	−26.8905	+	37.8538i	−0.866535	+	1.21982i
$964$	3.65532	−	3.65532i	0.117730	−	0.117730i
$965$		−	29.1733i		−	0.939122i
$966$	−97.0824	−	30.9728i	−3.12357	−	0.996533i
$967$	−4.09441	+	4.09441i	−0.131667	+	0.131667i	−0.769869	−	0.638202i	$-0.779679\pi$
$967$	−4.09441	+	4.09441i	−0.131667	+	0.131667i	0.638202	+	0.769869i	$0.279679\pi$
$968$	−2.56311	−	2.56311i	−0.0823814	−	0.0823814i
$969$	−3.01164	−	5.83359i	−0.0967479	−	0.187402i
$970$	−9.16810	−	9.16810i	−0.294370	−	0.294370i
$971$		−	36.5458i		−	1.17281i	−0.810018	−	0.586405i	$-0.800543\pi$
$971$		−	36.5458i		−	1.17281i	0.810018	−	0.586405i	$-0.199457\pi$
$972$	0.760806	+	28.5368i	0.0244029	+	0.915319i
$973$	−47.4685	−	47.4685i	−1.52177	−	1.52177i
$974$	−55.8590			−1.78984
$975$		0			0
$976$	25.1326			0.804474
$977$	1.85263	+	1.85263i	0.0592709	+	0.0592709i	0.736121	−	0.676850i	$-0.236655\pi$
$977$	1.85263	+	1.85263i	0.0592709	+	0.0592709i	−0.676850	+	0.736121i	$0.736655\pi$
$978$	6.26299	+	1.99812i	0.200268	+	0.0638929i
$979$		−	0.813473i		−	0.0259987i
$980$	−25.1278	−	25.1278i	−0.802678	−	0.802678i
$981$	36.7330	−	6.22009i	1.17279	−	0.198592i
$982$	−52.5889	−	52.5889i	−1.67818	−	1.67818i
$983$	6.87065	−	6.87065i	0.219140	−	0.219140i	−0.588996	−	0.808136i	$-0.700477\pi$
$983$	6.87065	−	6.87065i	0.219140	−	0.219140i	0.808136	+	0.588996i	$0.200477\pi$
$984$	1.45514	−	4.56106i	0.0463882	−	0.145401i
$985$		−	2.20373i		−	0.0702167i
$986$	8.70214	−	8.70214i	0.277133	−	0.277133i
$987$	−13.5728	+	42.5431i	−0.432026	+	1.35416i
$988$		0			0
$989$		−	18.6549i		−	0.593190i
$990$	0.222313	+	1.31288i	0.00706557	+	0.0417260i
$991$	−29.0606			−0.923141			−0.461570	−	0.887104i	$-0.652714\pi$
$991$	−29.0606			−0.923141			−0.461570	+	0.887104i	$0.652714\pi$
$992$	−40.1117			−1.27355
$993$	18.6972	+	36.2167i	0.593337	+	1.14930i
$994$	71.0222	−	71.0222i	2.25269	−	2.25269i
$995$	20.5954	−	20.5954i	0.652916	−	0.652916i
$996$	−13.1854	−	25.5402i	−0.417794	−	0.809273i
$997$	23.4421			0.742418			0.371209	−	0.928549i	$-0.378943\pi$
$997$	23.4421			0.742418			0.371209	+	0.928549i	$0.378943\pi$
$998$	31.1227			0.985172
$999$	−16.8418	−	2.39205i	−0.532850	−	0.0756811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.g.239.5	✓	48
3.2	odd	2	inner	507.2.f.g.239.20	yes	48
13.2	odd	12		507.2.k.k.488.6		96
13.3	even	3		507.2.k.k.188.20		96
13.4	even	6		507.2.k.k.80.19		96
13.5	odd	4	inner	507.2.f.g.437.5	yes	48
13.6	odd	12		507.2.k.k.89.19		96
13.7	odd	12		507.2.k.k.89.5		96
13.8	odd	4	inner	507.2.f.g.437.19	yes	48
13.9	even	3		507.2.k.k.80.5		96
13.10	even	6		507.2.k.k.188.6		96
13.11	odd	12		507.2.k.k.488.20		96
13.12	even	2	inner	507.2.f.g.239.19	yes	48
39.2	even	12		507.2.k.k.488.19		96
39.5	even	4	inner	507.2.f.g.437.20	yes	48
39.8	even	4	inner	507.2.f.g.437.6	yes	48
39.11	even	12		507.2.k.k.488.5		96
39.17	odd	6		507.2.k.k.80.6		96
39.20	even	12		507.2.k.k.89.20		96
39.23	odd	6		507.2.k.k.188.19		96
39.29	odd	6		507.2.k.k.188.5		96
39.32	even	12		507.2.k.k.89.6		96
39.35	odd	6		507.2.k.k.80.20		96
39.38	odd	2	inner	507.2.f.g.239.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.5	✓	48	1.1	even	1	trivial
507.2.f.g.239.6	yes	48	39.38	odd	2	inner
507.2.f.g.239.19	yes	48	13.12	even	2	inner
507.2.f.g.239.20	yes	48	3.2	odd	2	inner
507.2.f.g.437.5	yes	48	13.5	odd	4	inner
507.2.f.g.437.6	yes	48	39.8	even	4	inner
507.2.f.g.437.19	yes	48	13.8	odd	4	inner
507.2.f.g.437.20	yes	48	39.5	even	4	inner
507.2.k.k.80.5		96	13.9	even	3
507.2.k.k.80.6		96	39.17	odd	6
507.2.k.k.80.19		96	13.4	even	6
507.2.k.k.80.20		96	39.35	odd	6
507.2.k.k.89.5		96	13.7	odd	12
507.2.k.k.89.6		96	39.32	even	12
507.2.k.k.89.19		96	13.6	odd	12
507.2.k.k.89.20		96	39.20	even	12
507.2.k.k.188.5		96	39.29	odd	6
507.2.k.k.188.6		96	13.10	even	6
507.2.k.k.188.19		96	39.23	odd	6
507.2.k.k.188.20		96	13.3	even	3
507.2.k.k.488.5		96	39.11	even	12
507.2.k.k.488.6		96	13.2	odd	12
507.2.k.k.488.19		96	39.2	even	12
507.2.k.k.488.20		96	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38407 - 1.38407i) q^{2} +(0.526444 - 1.65011i) q^{3} +1.83129i q^{4} +(1.04664 + 1.04664i) q^{5} +(-3.01250 + 1.55523i) q^{6} +(3.17096 + 3.17096i) q^{7} +(-0.233508 + 0.233508i) q^{8} +(-2.44571 - 1.73738i) q^{9} -2.89724i q^{10} +(0.108328 - 0.108328i) q^{11} +(3.02182 + 0.964071i) q^{12} -8.77764i q^{14} +(2.27806 - 1.17607i) q^{15} +4.30896 q^{16} +3.16727 q^{17} +(0.980382 + 5.78968i) q^{18} +(0.846216 - 0.846216i) q^{19} +(-1.91670 + 1.91670i) q^{20} +(6.90175 - 3.56309i) q^{21} -0.299868 q^{22} +6.70271 q^{23} +(0.262385 + 0.508243i) q^{24} -2.80909i q^{25} +(-4.15440 + 3.12106i) q^{27} +(-5.80694 + 5.80694i) q^{28} +1.98510i q^{29} +(-4.78076 - 1.52523i) q^{30} +(3.64859 - 3.64859i) q^{31} +(-5.49688 - 5.49688i) q^{32} +(-0.121725 - 0.235783i) q^{33} +(-4.38372 - 4.38372i) q^{34} +6.63770i q^{35} +(3.18164 - 4.47881i) q^{36} +(2.31488 + 2.31488i) q^{37} -2.34244 q^{38} -0.488797 q^{40} +(-5.91863 - 5.91863i) q^{41} +(-14.4841 - 4.62094i) q^{42} -2.78318i q^{43} +(0.198381 + 0.198381i) q^{44} +(-0.741369 - 4.37819i) q^{45} +(-9.27700 - 9.27700i) q^{46} +(-4.06533 + 4.06533i) q^{47} +(2.26843 - 7.11025i) q^{48} +13.1099i q^{49} +(-3.88798 + 3.88798i) q^{50} +(1.66739 - 5.22634i) q^{51} +0.628103i q^{53} +(10.0697 + 1.43021i) q^{54} +0.226762 q^{55} -1.48089 q^{56} +(-0.950863 - 1.84183i) q^{57} +(2.74752 - 2.74752i) q^{58} +(-6.20927 + 6.20927i) q^{59} +(2.15372 + 4.17179i) q^{60} +5.83263 q^{61} -10.0998 q^{62} +(-2.24610 - 13.2644i) q^{63} +6.59818i q^{64} +(-0.157864 + 0.494815i) q^{66} +(0.475547 - 0.475547i) q^{67} +5.80019i q^{68} +(3.52860 - 11.0602i) q^{69} +(9.18702 - 9.18702i) q^{70} +(8.09127 + 8.09127i) q^{71} +(0.976786 - 0.165402i) q^{72} +(-3.92370 - 3.92370i) q^{73} -6.40789i q^{74} +(-4.63531 - 1.47883i) q^{75} +(1.54967 + 1.54967i) q^{76} +0.687010 q^{77} -5.46386 q^{79} +(4.50993 + 4.50993i) q^{80} +(2.96302 + 8.49826i) q^{81} +16.3836i q^{82} +(-6.40765 - 6.40765i) q^{83} +(6.52505 + 12.6391i) q^{84} +(3.31499 + 3.31499i) q^{85} +(-3.85212 + 3.85212i) q^{86} +(3.27563 + 1.04505i) q^{87} +0.0505912i q^{88} +(3.75466 - 3.75466i) q^{89} +(-5.03360 + 7.08582i) q^{90} +12.2746i q^{92} +(-4.09979 - 7.94134i) q^{93} +11.2534 q^{94} +1.77137 q^{95} +(-11.9642 + 6.17664i) q^{96} +(3.16443 - 3.16443i) q^{97} +(18.1451 - 18.1451i) q^{98} +(-0.453148 + 0.0767327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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