LMFDB - Embedded newform 637.2.q.h.491.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(491,637)] 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("637.491"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.5
Root			$1.40744 + 0.138282i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.h.589.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.10554 - 0.638282i) q^{2} +(-0.583963 - 1.01145i) q^{3} +(-0.185192 + 0.320762i) q^{4} +1.81487i q^{5} +(-1.29118 - 0.745466i) q^{6} +3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(1.15840 + 2.00641i) q^{10} +(-2.40625 + 1.38925i) q^{11} +0.432581 q^{12} +(3.58305 + 0.402155i) q^{13} +(1.83566 - 1.05982i) q^{15} +(1.56102 + 2.70377i) q^{16} +(-1.37198 + 2.37634i) q^{17} -2.08840i q^{18} +(5.08351 + 2.93497i) q^{19} +(-0.582143 - 0.336100i) q^{20} +(-1.77346 + 3.07173i) q^{22} +(3.49955 + 6.06139i) q^{23} +(3.06060 - 1.76704i) q^{24} +1.70623 q^{25} +(4.21789 - 1.84240i) q^{26} -5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} -2.06697i q^{31} +(-1.78956 - 1.03320i) q^{32} +(2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(0.302965 + 0.524751i) q^{36} +(1.50950 - 0.871512i) q^{37} +7.49334 q^{38} +(-1.68561 - 3.85893i) q^{39} -5.49171 q^{40} +(-5.51406 + 3.18355i) q^{41} +(4.55195 - 7.88422i) q^{43} -1.02911i q^{44} +(2.57127 + 1.48452i) q^{45} +(7.73776 + 4.46740i) q^{46} -6.65932i q^{47} +(1.82316 - 3.15780i) q^{48} +(1.88631 - 1.08906i) q^{50} +3.20474 q^{51} +(-0.792549 + 1.07483i) q^{52} -10.4879 q^{53} +(-5.98587 + 3.45594i) q^{54} +(-2.52131 - 4.36703i) q^{55} -6.85564i q^{57} +(3.88720 + 2.24427i) q^{58} +(-2.66212 - 1.53698i) q^{59} +0.785080i q^{60} +(0.540892 - 0.936853i) q^{61} +(-1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(-0.729860 + 6.50279i) q^{65} +4.14254 q^{66} +(4.34568 - 2.50898i) q^{67} +(-0.508159 - 0.880158i) q^{68} +(4.08721 - 7.07925i) q^{69} +(2.35453 + 1.35939i) q^{71} +(4.28709 + 2.47515i) q^{72} +7.67213i q^{73} +(1.11254 - 1.92698i) q^{74} +(-0.996377 - 1.72578i) q^{75} +(-1.88285 + 1.08706i) q^{76} +(-4.32659 - 3.19030i) q^{78} -15.7399 q^{79} +(-4.90700 + 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(-4.06400 + 7.03905i) q^{82} -7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} -11.6217i q^{86} +(2.05328 - 3.55639i) q^{87} +(-4.20379 - 7.28117i) q^{88} +(13.9118 - 8.03198i) q^{89} +3.79017 q^{90} -2.59235 q^{92} +(-2.09064 + 1.20703i) q^{93} +(-4.25052 - 7.36212i) q^{94} +(-5.32659 + 9.22592i) q^{95} +2.41340i q^{96} +(12.3209 + 7.11347i) q^{97} +4.54548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29}+ \cdots - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	1.10554	−	0.638282i	0.781733	−	0.451334i	−0.0553113	−	0.998469i	$-0.517615\pi$
$2$	1.10554	−	0.638282i	0.781733	−	0.451334i	0.837044	+	0.547136i	$0.184282\pi$
$3$	−0.583963	−	1.01145i	−0.337151	−	0.583963i	0.646745	−	0.762707i	$-0.276130\pi$
$3$	−0.583963	−	1.01145i	−0.337151	−	0.583963i	−0.983896	+	0.178744i	$0.942797\pi$
$4$	−0.185192	+	0.320762i	−0.0925960	+	0.160381i
$5$			1.81487i			0.811636i	0.913954	+	0.405818i	$0.133013\pi$
$5$			1.81487i			0.811636i	−0.913954	+	0.405818i	$0.866987\pi$
$6$	−1.29118	−	0.745466i	−0.527124	−	0.304335i
$7$		0			0
$7$		0			0
$8$			3.02595i			1.06983i
$9$	0.817975	−	1.41677i	0.272658	−	0.472258i
$10$	1.15840	+	2.00641i	0.366319	+	0.634482i
$11$	−2.40625	+	1.38925i	−0.725510	+	0.418874i	−0.816777	−	0.576953i	$-0.804242\pi$
$11$	−2.40625	+	1.38925i	−0.725510	+	0.418874i	0.0912671	+	0.995826i	$0.470908\pi$
$12$	0.432581			0.124875
$13$	3.58305	+	0.402155i	0.993760	+	0.111538i
$13$	3.58305	+	0.402155i	0.993760	+	0.111538i
$14$		0			0
$15$	1.83566	−	1.05982i	0.473965	−	0.273644i
$16$	1.56102	+	2.70377i	0.390256	+	0.675943i
$17$	−1.37198	+	2.37634i	−0.332754	+	0.576347i	−0.983051	−	0.183334i	$-0.941311\pi$
$17$	−1.37198	+	2.37634i	−0.332754	+	0.576347i	0.650297	+	0.759680i	$0.274645\pi$
$18$		−	2.08840i		−	0.492240i
$19$	5.08351	+	2.93497i	1.16624	+	0.673327i	0.952791	−	0.303628i	$-0.0981979\pi$
$19$	5.08351	+	2.93497i	1.16624	+	0.673327i	0.213446	+	0.976955i	$0.431531\pi$
$20$	−0.582143	−	0.336100i	−0.130171	−	0.0751543i
$21$		0			0
$22$	−1.77346	+	3.07173i	−0.378103	+	0.654894i
$23$	3.49955	+	6.06139i	0.729706	+	1.26389i	0.957007	+	0.290063i	$0.0936763\pi$
$23$	3.49955	+	6.06139i	0.729706	+	1.26389i	−0.227302	+	0.973824i	$0.572990\pi$
$24$	3.06060	−	1.76704i	0.624743	−	0.360696i
$25$	1.70623			0.341247
$26$	4.21789	−	1.84240i	0.827195	−	0.361325i
$27$	−5.41444			−1.04201
$28$		0			0
$29$	1.75806	+	3.04505i	0.326463	+	0.565451i	0.981807	−	0.189879i	$-0.0608097\pi$
$29$	1.75806	+	3.04505i	0.326463	+	0.565451i	−0.655344	+	0.755330i	$0.727476\pi$
$30$	1.35293	−	2.34334i	0.247009	−	0.427833i
$31$		−	2.06697i		−	0.371238i	−0.982622	−	0.185619i	$-0.940571\pi$
$31$		−	2.06697i		−	0.371238i	0.982622	−	0.185619i	$-0.0594290\pi$
$32$	−1.78956	−	1.03320i	−0.316352	−	0.182646i
$33$	2.81031	+	1.62254i	0.489213	+	0.282447i
$34$			3.50284i			0.600732i
$35$		0			0
$36$	0.302965	+	0.524751i	0.0504942	+	0.0874585i
$37$	1.50950	−	0.871512i	0.248161	−	0.143276i	−0.370761	−	0.928728i	$-0.620903\pi$
$37$	1.50950	−	0.871512i	0.248161	−	0.143276i	0.618922	+	0.785453i	$0.287570\pi$
$38$	7.49334			1.21558
$39$	−1.68561	−	3.85893i	−0.269913	−	0.617924i
$40$	−5.49171			−0.868316
$41$	−5.51406	+	3.18355i	−0.861152	+	0.497186i	−0.864398	−	0.502808i	$-0.832300\pi$
$41$	−5.51406	+	3.18355i	−0.861152	+	0.497186i	0.00324599	+	0.999995i	$0.498967\pi$
$42$		0			0
$43$	4.55195	−	7.88422i	0.694167	−	1.20233i	−0.276294	−	0.961073i	$-0.589106\pi$
$43$	4.55195	−	7.88422i	0.694167	−	1.20233i	0.970461	−	0.241259i	$-0.0775603\pi$
$44$		−	1.02911i		−	0.155144i
$45$	2.57127	+	1.48452i	0.383302	+	0.221299i
$46$	7.73776	+	4.46740i	1.14087	+	0.658681i
$47$		−	6.65932i		−	0.971361i	−0.874136	−	0.485681i	$-0.838572\pi$
$47$		−	6.65932i		−	0.971361i	0.874136	−	0.485681i	$-0.161428\pi$
$48$	1.82316	−	3.15780i	0.263150	−	0.455790i
$49$		0			0
$50$	1.88631	−	1.08906i	0.266764	−	0.154016i
$51$	3.20474			0.448753
$52$	−0.792549	+	1.07483i	−0.109907	+	0.149052i
$53$	−10.4879			−1.44063			−0.720313	−	0.693649i	$-0.756002\pi$
$53$	−10.4879			−1.44063			−0.720313	+	0.693649i	$0.756002\pi$
$54$	−5.98587	+	3.45594i	−0.814573	+	0.470294i
$55$	−2.52131	−	4.36703i	−0.339973	−	0.588850i
$56$		0			0
$57$		−	6.85564i		−	0.908052i
$58$	3.88720	+	2.24427i	0.510414	+	0.294688i
$59$	−2.66212	−	1.53698i	−0.346579	−	0.200097i	0.316598	−	0.948560i	$-0.397459\pi$
$59$	−2.66212	−	1.53698i	−0.346579	−	0.200097i	−0.663177	+	0.748462i	$0.730793\pi$
$60$			0.785080i			0.101353i
$61$	0.540892	−	0.936853i	0.0692541	−	0.119952i	−0.829319	−	0.558775i	$-0.811271\pi$
$61$	0.540892	−	0.936853i	0.0692541	−	0.119952i	0.898573	+	0.438824i	$0.144605\pi$
$62$	−1.31931	−	2.28511i	−0.167552	−	0.290209i
$63$		0			0
$64$	−8.88199			−1.11025
$65$	−0.729860	+	6.50279i	−0.0905280	+	0.806572i
$66$	4.14254			0.509912
$67$	4.34568	−	2.50898i	0.530910	−	0.306521i	−0.210477	−	0.977599i	$-0.567502\pi$
$67$	4.34568	−	2.50898i	0.530910	−	0.306521i	0.741387	+	0.671078i	$0.234168\pi$
$68$	−0.508159	−	0.880158i	−0.0616234	−	0.106735i
$69$	4.08721	−	7.07925i	0.492042	−	0.852242i
$70$		0			0
$71$	2.35453	+	1.35939i	0.279431	+	0.161330i	0.633166	−	0.774016i	$-0.281755\pi$
$71$	2.35453	+	1.35939i	0.279431	+	0.161330i	−0.353735	+	0.935346i	$0.615088\pi$
$72$	4.28709	+	2.47515i	0.505238	+	0.291699i
$73$			7.67213i			0.897955i	0.893543	+	0.448978i	$0.148212\pi$
$73$			7.67213i			0.897955i	−0.893543	+	0.448978i	$0.851788\pi$
$74$	1.11254	−	1.92698i	0.129330	−	0.224006i
$75$	−0.996377	−	1.72578i	−0.115052	−	0.199275i
$76$	−1.88285	+	1.08706i	−0.215978	+	0.124695i
$77$		0			0
$78$	−4.32659	−	3.19030i	−0.489890	−	0.361230i
$79$	−15.7399			−1.77087			−0.885436	−	0.464761i	$-0.846140\pi$
$79$	−15.7399			−1.77087			−0.885436	+	0.464761i	$0.846140\pi$
$80$	−4.90700	+	2.83306i	−0.548620	+	0.316746i
$81$	0.707906	+	1.22613i	0.0786563	+	0.136237i
$82$	−4.06400	+	7.03905i	−0.448794	+	0.777333i
$83$		−	7.97408i		−	0.875269i	−0.899153	−	0.437635i	$-0.855816\pi$
$83$		−	7.97408i		−	0.875269i	0.899153	−	0.437635i	$-0.144184\pi$
$84$		0			0
$85$	−4.31275	−	2.48997i	−0.467784	−	0.270075i
$86$		−	11.6217i		−	1.25320i
$87$	2.05328	−	3.55639i	0.220135	−	0.381285i
$88$	−4.20379	−	7.28117i	−0.448125	−	0.776176i
$89$	13.9118	−	8.03198i	1.47465	−	0.851388i	0.475055	−	0.879956i	$-0.342428\pi$
$89$	13.9118	−	8.03198i	1.47465	−	0.851388i	0.999592	+	0.0285683i	$0.00909482\pi$
$90$	3.79017			0.399519
$91$		0			0
$92$	−2.59235			−0.270271
$93$	−2.09064	+	1.20703i	−0.216789	+	0.125163i
$94$	−4.25052	−	7.36212i	−0.438408	−	0.759345i
$95$	−5.32659	+	9.22592i	−0.546497	+	0.946560i
$96$			2.41340i			0.246317i
$97$	12.3209	+	7.11347i	1.25100	+	0.722263i	0.971307	−	0.237827i	$-0.0764353\pi$
$97$	12.3209	+	7.11347i	1.25100	+	0.722263i	0.279689	+	0.960091i	$0.409769\pi$
$98$		0			0
$99$			4.54548i			0.456838i
$100$	−0.315981	+	0.547295i	−0.0315981	+	0.0547295i
$101$	0.0365612	+	0.0633259i	0.00363798	+	0.00630117i	0.867839	−	0.496846i	$-0.165509\pi$
$101$	0.0365612	+	0.0633259i	0.00363798	+	0.00630117i	−0.864201	+	0.503147i	$0.832175\pi$
$102$	3.54296	−	2.04553i	0.350805	−	0.202537i
$103$	−12.9196			−1.27301			−0.636503	−	0.771275i	$-0.719620\pi$
$103$	−12.9196			−1.27301			−0.636503	+	0.771275i	$0.719620\pi$
$104$	−1.21690	+	10.8421i	−0.119327	+	1.06316i
$105$		0			0
$106$	−11.5948	+	6.69425i	−1.12618	+	0.650203i
$107$	−2.00427	−	3.47150i	−0.193761	−	0.335603i	0.752733	−	0.658326i	$-0.228735\pi$
$107$	−2.00427	−	3.47150i	−0.193761	−	0.335603i	−0.946493	+	0.322723i	$0.895402\pi$
$108$	1.00271	−	1.73675i	0.0964860	−	0.167119i
$109$		−	1.98589i		−	0.190214i	−0.995467	−	0.0951071i	$-0.969681\pi$
$109$		−	1.98589i		−	0.190214i	0.995467	−	0.0951071i	$-0.0303194\pi$
$110$	−5.57479	−	3.21861i	−0.531536	−	0.306882i
$111$	−1.76299	−	1.01786i	−0.167335	−	0.0966110i
$112$		0			0
$113$	5.28711	−	9.15754i	0.497369	−	0.861469i	−0.502626	−	0.864504i	$-0.667633\pi$
$113$	5.28711	−	9.15754i	0.497369	−	0.861469i	0.999995	+	0.00303506i	$0.000966090\pi$
$114$	−4.37583	−	7.57916i	−0.409834	−	0.709854i
$115$	−11.0007	+	6.35123i	−1.02582	+	0.592256i
$116$	−1.30231			−0.120917
$117$	3.50061	−	4.74743i	0.323632	−	0.438900i
$118$	−3.92410			−0.361243
$119$		0			0
$120$	3.20695	+	5.55461i	0.292753	+	0.507064i
$121$	−1.63999	+	2.84054i	−0.149090	+	0.258231i
$122$		−	1.38097i		−	0.125027i
$123$	6.44001	+	3.71814i	0.580676	+	0.335254i
$124$	0.663004	+	0.382786i	0.0595395	+	0.0343752i
$125$			12.1710i			1.08860i
$126$		0			0
$127$	5.63478	+	9.75972i	0.500006	+	0.866035i	1.00000		6.53271e-6i	$2.07943e-6\pi$
$127$	5.63478	+	9.75972i	0.500006	+	0.866035i	−0.499994	+	0.866029i	$0.666665\pi$
$128$	−6.24025	+	3.60281i	−0.551566	+	0.318447i
$129$	−10.6327			−0.936156
$130$	3.34373	+	7.65493i	0.293264	+	0.671382i
$131$	−3.06481			−0.267774			−0.133887	−	0.990997i	$-0.542746\pi$
$131$	−3.06481			−0.267774			−0.133887	+	0.990997i	$0.542746\pi$
$132$	−1.04090	+	0.600962i	−0.0905984	+	0.0523070i
$133$		0			0
$134$	3.20288	−	5.54754i	0.276686	−	0.479235i
$135$		−	9.82653i		−	0.845733i
$136$	−7.19067	−	4.15154i	−0.616595	−	0.355991i
$137$	18.9512	+	10.9415i	1.61911	+	0.934796i	0.987150	+	0.159799i	$0.0510845\pi$
$137$	18.9512	+	10.9415i	1.61911	+	0.934796i	0.631965	+	0.774997i	$0.282249\pi$
$138$		−	10.4352i		−	0.888300i
$139$	5.53535	−	9.58750i	0.469502	−	0.813201i	−0.529890	−	0.848066i	$-0.677767\pi$
$139$	5.53535	−	9.58750i	0.469502	−	0.813201i	0.999392	+	0.0348652i	$0.0111002\pi$
$140$		0			0
$141$	−6.73559	+	3.88879i	−0.567239	+	0.327495i
$142$	3.47069			0.291254
$143$	−9.18040	+	4.01006i	−0.767703	+	0.335338i
$144$	5.10752			0.425626
$145$	−5.52637	+	3.19065i	−0.458940	+	0.264969i
$146$	4.89699	+	8.48183i	0.405277	+	0.701961i
$147$		0			0
$148$			0.645588i			0.0530670i
$149$	−1.99824	−	1.15369i	−0.163702	−	0.0945136i	0.415911	−	0.909406i	$-0.363463\pi$
$149$	−1.99824	−	1.15369i	−0.163702	−	0.0945136i	−0.579613	+	0.814892i	$0.696796\pi$
$150$	−2.20306	−	1.27194i	−0.179879	−	0.103853i
$151$		−	20.6158i		−	1.67769i	−0.544371	−	0.838845i	$-0.683232\pi$
$151$		−	20.6158i		−	1.67769i	0.544371	−	0.838845i	$-0.316768\pi$
$152$	−8.88105	+	15.3824i	−0.720348	+	1.24768i
$153$	2.24449	+	3.88757i	0.181456	+	0.314292i
$154$		0			0
$155$	3.75128			0.301310
$156$	1.54996	+	0.173964i	0.124096	+	0.0139283i
$157$	−2.89649			−0.231165			−0.115582	−	0.993298i	$-0.536873\pi$
$157$	−2.89649			−0.231165			−0.115582	+	0.993298i	$0.536873\pi$
$158$	−17.4010	+	10.0465i	−1.38435	+	0.799254i
$159$	6.12455	+	10.6080i	0.485709	+	0.841272i
$160$	1.87513	−	3.24782i	0.148242	−	0.256763i
$161$		0			0
$162$	1.56523	+	0.903688i	0.122976	+	0.0710004i
$163$	−20.2944	−	11.7170i	−1.58958	−	0.917743i	−0.993376	−	0.114907i	$-0.963343\pi$
$163$	−20.2944	−	11.7170i	−1.58958	−	0.917743i	−0.596201	−	0.802835i	$-0.703324\pi$
$164$		−	2.35827i		−	0.184150i
$165$	−2.94470	+	5.10037i	−0.229244	+	0.397063i
$166$	−5.08971	−	8.81564i	−0.395038	−	0.684226i
$167$	−6.58349	+	3.80098i	−0.509446	+	0.294129i	−0.732606	−	0.680653i	$-0.761696\pi$
$167$	−6.58349	+	3.80098i	−0.509446	+	0.294129i	0.223160	+	0.974782i	$0.428363\pi$
$168$		0			0
$169$	12.6765	+	2.88188i	0.975119	+	0.221683i
$170$	−6.35721			−0.487576
$171$	8.31637	−	4.80146i	0.635969	−	0.367177i
$172$	1.68597	+	2.92019i	0.128554	+	0.222662i
$173$	−2.69861	+	4.67412i	−0.205171	+	0.355367i	−0.950187	−	0.311679i	$-0.899108\pi$
$173$	−2.69861	+	4.67412i	−0.205171	+	0.355367i	0.745016	+	0.667047i	$0.232442\pi$
$174$		−	5.24229i		−	0.397417i
$175$		0			0
$176$	−7.51241	−	4.33729i	−0.566269	−	0.326936i
$177$			3.59015i			0.269852i
$178$	10.2533	−	17.7593i	0.768520	−	1.33112i
$179$	−6.14571	−	10.6447i	−0.459352	−	0.795621i	0.539575	−	0.841938i	$-0.318585\pi$
$179$	−6.14571	−	10.6447i	−0.459352	−	0.795621i	−0.998927	+	0.0463168i	$0.985252\pi$
$180$	−0.952357	+	0.549843i	−0.0709845	+	0.0409829i
$181$	21.8525			1.62428			0.812140	−	0.583463i	$-0.198303\pi$
$181$	21.8525			1.62428			0.812140	+	0.583463i	$0.198303\pi$
$182$		0			0
$183$	−1.26344			−0.0933964
$184$	−18.3415	+	10.5894i	−1.35215	+	0.780664i
$185$	1.58168	+	2.73956i	0.116288	+	0.201416i
$186$	−1.54085	+	2.66883i	−0.112981	+	0.195688i
$187$		−	7.62407i		−	0.557527i
$188$	2.13606	+	1.23325i	0.155788	+	0.0899442i
$189$		0			0
$190$			13.5995i			0.986609i
$191$	−1.37858	+	2.38777i	−0.0997507	+	0.172773i	−0.911581	−	0.411120i	$-0.865138\pi$
$191$	−1.37858	+	2.38777i	−0.0997507	+	0.172773i	0.811831	+	0.583893i	$0.198471\pi$
$192$	5.18675	+	8.98371i	0.374321	+	0.648344i
$193$	11.2491	−	6.49467i	0.809728	−	0.467497i	−0.0371334	−	0.999310i	$-0.511823\pi$
$193$	11.2491	−	6.49467i	0.809728	−	0.467497i	0.846861	+	0.531814i	$0.178489\pi$
$194$	18.1616			1.30393
$195$	7.00347	−	3.05917i	0.501529	−	0.219071i
$196$		0			0
$197$	16.4772	−	9.51312i	1.17395	−	0.677781i	0.219344	−	0.975648i	$-0.429608\pi$
$197$	16.4772	−	9.51312i	1.17395	−	0.677781i	0.954608	+	0.297866i	$0.0962749\pi$
$198$	2.90130	+	5.02519i	0.206186	+	0.357125i
$199$	10.0159	−	17.3480i	0.710006	−	1.22977i	−0.254848	−	0.966981i	$-0.582025\pi$
$199$	10.0159	−	17.3480i	0.710006	−	1.22977i	0.964854	−	0.262786i	$-0.0846412\pi$
$200$			5.16298i			0.365078i
$201$	−5.07543	−	2.93030i	−0.357993	−	0.206688i
$202$	0.0808396	+	0.0466728i	0.00568785	+	0.00328388i
$203$		0			0
$204$	−0.593492	+	1.02796i	−0.0415528	+	0.0719715i
$205$	−5.77773	−	10.0073i	−0.403534	−	0.698942i
$206$	−14.2831	+	8.24634i	−0.995150	+	0.574550i
$207$	11.4502			0.795842
$208$	4.50590	+	10.3155i	0.312428	+	0.715254i
$209$	−16.3096			−1.12816
$210$		0			0
$211$	−5.00015	−	8.66052i	−0.344225	−	0.596215i	0.640988	−	0.767551i	$-0.278525\pi$
$211$	−5.00015	−	8.66052i	−0.344225	−	0.596215i	−0.985213	+	0.171336i	$0.945192\pi$
$212$	1.94228	−	3.36413i	0.133396	−	0.231049i
$213$		−	3.17532i		−	0.217570i
$214$	−4.43160	−	2.55858i	−0.302938	−	0.174901i
$215$	14.3089	+	8.26122i	0.975856	+	0.563411i
$216$		−	16.3838i		−	1.11478i
$217$		0			0
$218$	−1.26756	−	2.19548i	−0.0858501	−	0.148697i
$219$	7.76000	−	4.48024i	0.524372	−	0.302747i
$220$	1.86770			0.125921
$221$	−5.87153	+	7.96280i	−0.394962	+	0.535636i
$222$	−2.59873			−0.174415
$223$	−7.25954	+	4.19130i	−0.486135	+	0.280670i	−0.722970	−	0.690880i	$-0.757223\pi$
$223$	−7.25954	+	4.19130i	−0.486135	+	0.280670i	0.236835	+	0.971550i	$0.423890\pi$
$224$		0			0
$225$	1.39566	−	2.41735i	0.0930439	−	0.161157i
$226$		−	13.4987i		−	0.897918i
$227$	0.796500	+	0.459860i	0.0528656	+	0.0305220i	0.526200	−	0.850361i	$-0.323616\pi$
$227$	0.796500	+	0.459860i	0.0528656	+	0.0305220i	−0.473334	+	0.880883i	$0.656950\pi$
$228$	2.19903	+	1.26961i	0.145634	+	0.0840820i
$229$		−	24.6208i		−	1.62699i	−0.581574	−	0.813494i	$-0.697563\pi$
$229$		−	24.6208i		−	1.62699i	0.581574	−	0.813494i	$-0.302437\pi$
$230$	−8.10776	+	14.0430i	−0.534610	+	0.925971i
$231$		0			0
$232$	−9.21415	+	5.31979i	−0.604939	+	0.349261i
$233$	17.2769			1.13185			0.565925	−	0.824457i	$-0.308519\pi$
$233$	17.2769			1.13185			0.565925	+	0.824457i	$0.308519\pi$
$234$	0.839858	−	7.48283i	0.0549032	−	0.489168i
$235$	12.0858			0.788392
$236$	0.986008	−	0.569272i	0.0641837	−	0.0370565i
$237$	9.19149	+	15.9201i	0.597051	+	1.03412i
$238$		0			0
$239$			14.4828i			0.936816i	0.883512	+	0.468408i	$0.155172\pi$
$239$			14.4828i			0.936816i	−0.883512	+	0.468408i	$0.844828\pi$
$240$	5.73101	+	3.30880i	0.369935	+	0.213582i
$241$	7.30441	+	4.21720i	0.470518	+	0.271654i	0.716457	−	0.697632i	$-0.245763\pi$
$241$	7.30441	+	4.21720i	0.470518	+	0.271654i	−0.245938	+	0.969285i	$0.579096\pi$
$242$			4.18710i			0.269157i
$243$	−7.29488	+	12.6351i	−0.467967	+	0.810543i
$244$	0.200338	+	0.346995i	0.0128253	+	0.0222141i
$245$		0			0
$246$	9.49290			0.605245
$247$	17.0342	+	12.5605i	1.08386	+	0.799205i
$248$	6.25453			0.397163
$249$	−8.06541	+	4.65657i	−0.511124	+	0.295098i
$250$	7.76851	+	13.4555i	0.491324	+	0.850998i
$251$	7.33631	−	12.7069i	0.463064	−	0.802050i	−0.536048	−	0.844188i	$-0.680083\pi$
$251$	7.33631	−	12.7069i	0.463064	−	0.802050i	0.999112	+	0.0421373i	$0.0134167\pi$
$252$		0			0
$253$	−16.8415	−	9.72346i	−1.05882	−	0.611309i
$254$	12.4589	+	7.19315i	0.781742	+	0.451339i
$255$			5.81620i			0.364224i
$256$	4.28277	−	7.41797i	0.267673	−	0.463623i
$257$	−14.6643	−	25.3993i	−0.914733	−	1.58436i	−0.807292	−	0.590152i	$-0.799068\pi$
$257$	−14.6643	−	25.3993i	−0.914733	−	1.58436i	−0.107441	−	0.994211i	$-0.534266\pi$
$258$	−11.7548	+	6.78665i	−0.731824	+	0.422519i
$259$		0			0
$260$	−1.95068	−	1.43838i	−0.120976	−	0.0892043i
$261$	5.75219			0.356052
$262$	−3.38826	+	1.95622i	−0.209328	+	0.120855i
$263$	−9.95747	−	17.2468i	−0.614004	−	1.06349i	−0.990558	−	0.137091i	$-0.956225\pi$
$263$	−9.95747	−	17.2468i	−0.614004	−	1.06349i	0.376555	−	0.926394i	$-0.377109\pi$
$264$	−4.90971	+	8.50386i	−0.302172	+	0.523377i
$265$		−	19.0342i		−	1.16926i
$266$		0			0
$267$	−16.2479	−	9.38075i	−0.994357	−	0.574092i
$268$			1.85857i			0.113530i
$269$	−11.1625	+	19.3340i	−0.680589	+	1.17881i	0.294213	+	0.955740i	$0.404943\pi$
$269$	−11.1625	+	19.3340i	−0.680589	+	1.17881i	−0.974801	+	0.223074i	$0.928391\pi$
$270$	−6.27210	−	10.8636i	−0.381708	−	0.661137i
$271$	8.14054	−	4.69994i	0.494502	−	0.285501i	−0.231938	−	0.972731i	$-0.574507\pi$
$271$	8.14054	−	4.69994i	0.494502	−	0.285501i	0.726440	+	0.687230i	$0.241173\pi$
$272$	−8.56677			−0.519437
$273$		0			0
$274$	27.9351			1.68762
$275$	−4.10562	+	2.37038i	−0.247578	+	0.142939i
$276$	1.51384	+	2.62204i	0.0911223	+	0.157828i
$277$	−7.17133	+	12.4211i	−0.430883	+	0.746312i	−0.996950	−	0.0780478i	$-0.975131\pi$
$277$	−7.17133	+	12.4211i	−0.430883	+	0.746312i	0.566066	+	0.824360i	$0.308465\pi$
$278$		−	14.1324i		−	0.847608i
$279$	−2.92842	−	1.69073i	−0.175320	−	0.101221i
$280$		0			0
$281$			0.0988416i			0.00589640i	0.999996	+	0.00294820i	$0.000938442\pi$
$281$			0.0988416i			0.00589640i	−0.999996	+	0.00294820i	$0.999062\pi$
$282$	−4.96429	+	8.59841i	−0.295619	+	0.512028i
$283$	0.310336	+	0.537518i	0.0184476	+	0.0319521i	0.875102	−	0.483939i	$-0.160794\pi$
$283$	0.310336	+	0.537518i	0.0184476	+	0.0319521i	−0.856654	+	0.515891i	$0.827461\pi$
$284$	−0.872079	+	0.503495i	−0.0517484	+	0.0298769i
$285$	12.4421			0.737007
$286$	−7.58972	+	10.2930i	−0.448789	+	0.608635i
$287$		0			0
$288$	−2.92763	+	1.69027i	−0.172512	+	0.0995998i
$289$	4.73534	+	8.20186i	0.278550	+	0.482462i
$290$	−4.07307	+	7.05477i	−0.239179	+	0.414270i
$291$		−	16.6160i		−	0.974047i
$292$	−2.46093	−	1.42082i	−0.144015	−	0.0831471i
$293$	−21.5586	−	12.4469i	−1.25947	−	0.727153i	−0.286496	−	0.958082i	$-0.592490\pi$
$293$	−21.5586	−	12.4469i	−1.25947	−	0.727153i	−0.972971	+	0.230928i	$0.925824\pi$
$294$		0			0
$295$	2.78942	−	4.83142i	0.162406	−	0.281296i
$296$	2.63715	+	4.56767i	0.153281	+	0.265491i
$297$	13.0285	−	7.52200i	0.755989	−	0.436471i
$298$	−2.94551			−0.170629
$299$	10.1014	+	23.1256i	0.584182	+	1.33739i
$300$	0.738085			0.0426133
$301$		0			0
$302$	−13.1587	−	22.7915i	−0.757197	−	1.31150i
$303$	0.0427008	−	0.0739599i	0.00245310	−	0.00424889i
$304$			18.3262i			1.05108i
$305$	1.70027	+	0.981651i	0.0973571	+	0.0562091i
$306$	4.96274	+	2.86524i	0.283701	+	0.163795i
$307$		−	9.89767i		−	0.564890i	−0.959284	−	0.282445i	$-0.908855\pi$
$307$		−	9.89767i		−	0.564890i	0.959284	−	0.282445i	$-0.0911455\pi$
$308$		0			0
$309$	7.54456	+	13.0676i	0.429195	+	0.743387i
$310$	4.14718	−	2.39437i	0.235544	−	0.135991i
$311$	7.23790			0.410423			0.205212	−	0.978718i	$-0.434212\pi$
$311$	7.23790			0.410423			0.205212	+	0.978718i	$0.434212\pi$
$312$	11.6769	−	5.10056i	0.661076	−	0.288763i
$313$	−32.6606			−1.84609			−0.923043	−	0.384696i	$-0.874306\pi$
$313$	−32.6606			−1.84609			−0.923043	+	0.384696i	$0.874306\pi$
$314$	−3.20217	+	1.84877i	−0.180709	+	0.104332i
$315$		0			0
$316$	2.91490	−	5.04875i	0.163976	−	0.284014i
$317$			17.1744i			0.964608i	0.876004	+	0.482304i	$0.160200\pi$
$317$			17.1744i			0.964608i	−0.876004	+	0.482304i	$0.839800\pi$
$318$	13.5418	+	7.81838i	0.759388	+	0.438433i
$319$	−8.46064	−	4.88475i	−0.473705	−	0.273494i
$320$		−	16.1197i		−	0.901118i
$321$	−2.34084	+	4.05446i	−0.130653	+	0.226298i
$322$		0			0
$323$	−13.9489	+	8.05342i	−0.776140	+	0.448105i
$324$	−0.524395			−0.0291330
$325$	6.11353	+	0.686170i	0.339118	+	0.0380619i
$326$	−29.9149			−1.65683
$327$	−2.00864	+	1.15969i	−0.111078	+	0.0641309i
$328$	−9.63324	−	16.6853i	−0.531907	−	0.921289i
$329$		0			0
$330$			7.51819i			0.413863i
$331$	17.2633	+	9.96698i	0.948877	+	0.547835i	0.892732	−	0.450588i	$-0.148786\pi$
$331$	17.2633	+	9.96698i	0.948877	+	0.547835i	0.0561454	+	0.998423i	$0.482119\pi$
$332$	2.55778	+	1.47674i	0.140377	+	0.0810465i
$333$		−	2.85150i		−	0.156261i
$334$	−4.85219	+	8.40424i	−0.265500	+	0.459860i
$335$	4.55348	+	7.88687i	0.248783	+	0.430905i
$336$		0			0
$337$	1.27189			0.0692842			0.0346421	−	0.999400i	$-0.488971\pi$
$337$	1.27189			0.0692842			0.0346421	+	0.999400i	$0.488971\pi$
$338$	15.8538	−	4.90518i	0.862335	−	0.266807i
$339$	−12.3499			−0.670754
$340$	1.59738	−	0.922245i	0.0866298	−	0.0500158i
$341$	2.87152	+	4.97363i	0.155502	+	0.269337i
$342$	6.12937	−	10.6164i	0.331438	−	0.574068i
$343$		0			0
$344$	23.8572	+	13.7740i	1.28630	+	0.742643i
$345$	12.8479	+	7.41777i	0.691710	+	0.399359i
$346$			6.88989i			0.370403i
$347$	−12.9417	+	22.4156i	−0.694744	+	1.20333i	0.275522	+	0.961295i	$0.411149\pi$
$347$	−12.9417	+	22.4156i	−0.694744	+	1.20333i	−0.970267	+	0.242038i	$0.922184\pi$
$348$	0.760503	+	1.31723i	0.0407672	+	0.0706109i
$349$	14.9967	−	8.65837i	0.802757	−	0.463472i	−0.0416774	−	0.999131i	$-0.513270\pi$
$349$	14.9967	−	8.65837i	0.802757	−	0.463472i	0.844434	+	0.535659i	$0.179937\pi$
$350$		0			0
$351$	−19.4002	−	2.17744i	−1.03551	−	0.116223i
$352$	5.74148			0.306022
$353$	21.9533	−	12.6747i	1.16846	−	0.674608i	0.215140	−	0.976583i	$-0.430979\pi$
$353$	21.9533	−	12.6747i	1.16846	−	0.674608i	0.953316	+	0.301975i	$0.0976459\pi$
$354$	2.29153	+	3.96904i	0.121793	+	0.210952i
$355$	−2.46711	+	4.27317i	−0.130941	+	0.226796i
$356$			5.94983i			0.315341i
$357$		0			0
$358$	−13.5886	−	7.84539i	−0.718181	−	0.414642i
$359$		−	5.27044i		−	0.278163i	−0.990281	−	0.139082i	$-0.955585\pi$
$359$		−	5.27044i		−	0.278163i	0.990281	−	0.139082i	$-0.0444151\pi$
$360$	−4.49208	+	7.78052i	−0.236754	+	0.410069i
$361$	7.72804	+	13.3854i	0.406739	+	0.704493i
$362$	24.1587	−	13.9480i	1.26975	−	0.733092i
$363$	3.83077			0.201063
$364$		0			0
$365$	−13.9240			−0.728813
$366$	−1.39678	+	0.806433i	−0.0730110	+	0.0421529i
$367$	12.6588	+	21.9257i	0.660783	+	1.14451i	0.980410	+	0.196967i	$0.0631092\pi$
$367$	12.6588	+	21.9257i	0.660783	+	1.14451i	−0.319627	+	0.947544i	$0.603557\pi$
$368$	−10.9257	+	18.9240i	−0.569544	+	0.986479i
$369$			10.4162i			0.542248i
$370$	3.49722	+	2.01912i	0.181812	+	0.104969i
$371$		0			0
$372$		−	0.894130i		−	0.0463585i
$373$	3.39391	−	5.87842i	0.175730	−	0.304373i	−0.764684	−	0.644406i	$-0.777105\pi$
$373$	3.39391	−	5.87842i	0.175730	−	0.304373i	0.940414	+	0.340033i	$0.110438\pi$
$374$	−4.86631	−	8.42869i	−0.251631	−	0.435837i
$375$	12.3104	−	7.10739i	0.635704	−	0.367024i
$376$	20.1507			1.03920
$377$	5.07464	+	11.6176i	0.261357	+	0.598336i
$378$		0			0
$379$	10.6717	−	6.16130i	0.548168	−	0.316485i	−0.200215	−	0.979752i	$-0.564164\pi$
$379$	10.6717	−	6.16130i	0.548168	−	0.316485i	0.748383	+	0.663267i	$0.230831\pi$
$380$	−1.97288	−	3.41714i	−0.101207	−	0.175295i
$381$	6.58100	−	11.3986i	0.337155	−	0.583969i
$382$			3.51970i			0.180083i
$383$	6.28662	+	3.62958i	0.321232	+	0.185463i	0.651941	−	0.758269i	$-0.273955\pi$
$383$	6.28662	+	3.62958i	0.321232	+	0.185463i	−0.330710	+	0.943732i	$0.607288\pi$
$384$	7.28815	+	4.20782i	0.371922	+	0.214729i
$385$		0			0
$386$	8.29086	−	14.3602i	0.421994	−	0.730915i
$387$	−7.44677	−	12.8982i	−0.378541	−	0.655652i
$388$	−4.56346	+	2.63472i	−0.231675	+	0.133757i
$389$	7.14811			0.362424			0.181212	−	0.983444i	$-0.441998\pi$
$389$	7.14811			0.362424			0.181212	+	0.983444i	$0.441998\pi$
$390$	5.78999	−	7.85221i	0.293187	−	0.397612i
$391$	−19.2052			−0.971250
$392$		0			0
$393$	1.78974	+	3.09991i	0.0902802	+	0.156370i
$394$	12.1441	−	21.0342i	0.611811	−	1.05969i
$395$		−	28.5659i		−	1.43730i
$396$	−1.45802	−	0.841786i	−0.0732681	−	0.0423014i
$397$	19.4520	+	11.2306i	0.976266	+	0.563647i	0.901141	−	0.433527i	$-0.142731\pi$
$397$	19.4520	+	11.2306i	0.976266	+	0.563647i	0.0751252	+	0.997174i	$0.476064\pi$
$398$		−	25.5718i		−	1.28180i
$399$		0			0
$400$	2.66347	+	4.61327i	0.133174	+	0.230663i
$401$	−2.64547	+	1.52736i	−0.132108	+	0.0762729i	−0.564598	−	0.825366i	$-0.690969\pi$
$401$	−2.64547	+	1.52736i	−0.132108	+	0.0762729i	0.432489	+	0.901639i	$0.357635\pi$
$402$	−7.48144			−0.373140
$403$	0.831240	−	7.40605i	0.0414070	−	0.368921i
$404$	−0.0270834			−0.00134745
$405$	−2.22527	+	1.28476i	−0.110575	+	0.0638403i
$406$		0			0
$407$	−2.42149	+	4.19414i	−0.120029	+	0.207896i
$408$			9.69737i			0.480091i
$409$	−4.85482	−	2.80293i	−0.240055	−	0.138596i	0.375147	−	0.926965i	$-0.377592\pi$
$409$	−4.85482	−	2.80293i	−0.240055	−	0.138596i	−0.615202	+	0.788369i	$0.710926\pi$
$410$	−12.7750	−	7.37564i	−0.630912	−	0.364257i
$411$		−	25.5577i		−	1.26067i
$412$	2.39261	−	4.14412i	0.117875	−	0.204166i
$413$		0			0
$414$	12.6586	−	7.30844i	0.622136	−	0.359190i
$415$	14.4719			0.710400
$416$	−5.99657	−	4.42169i	−0.294006	−	0.216791i
$417$	−12.9297			−0.633172
$418$	−18.0308	+	10.4101i	−0.881916	+	0.509175i
$419$	3.06969	+	5.31687i	0.149964	+	0.259746i	0.931214	−	0.364473i	$-0.118751\pi$
$419$	3.06969	+	5.31687i	0.149964	+	0.259746i	−0.781250	+	0.624219i	$0.785417\pi$
$420$		0			0
$421$		−	1.92589i		−	0.0938622i	−0.998898	−	0.0469311i	$-0.985056\pi$
$421$		−	1.92589i		−	0.0938622i	0.998898	−	0.0469311i	$-0.0149441\pi$
$422$	−11.0557	−	6.38302i	−0.538184	−	0.310720i
$423$	−9.43475	−	5.44716i	−0.458733	−	0.264850i
$424$		−	31.7359i		−	1.54123i
$425$	−2.34092	+	4.05459i	−0.113551	+	0.196677i
$426$	−2.02675	−	3.51044i	−0.0981965	−	0.170081i
$427$		0			0
$428$	1.48470			0.0717658
$429$	9.41700	+	6.94381i	0.454657	+	0.335250i
$430$	21.0920			1.01714
$431$	9.30923	−	5.37469i	0.448410	−	0.258890i	−0.258749	−	0.965945i	$-0.583310\pi$
$431$	9.30923	−	5.37469i	0.448410	−	0.258890i	0.707158	+	0.707055i	$0.249977\pi$
$432$	−8.45207	−	14.6394i	−0.406651	−	0.704340i
$433$	−20.1328	+	34.8710i	−0.967520	+	1.67579i	−0.264835	+	0.964294i	$0.585318\pi$
$433$	−20.1328	+	34.8710i	−0.967520	+	1.67579i	−0.702685	+	0.711501i	$0.748016\pi$
$434$		0			0
$435$	6.45439	+	3.72644i	0.309464	+	0.178669i
$436$	0.637000	+	0.367772i	0.0305068	+	0.0176131i
$437$			41.0842i			1.96532i
$438$	5.71931	−	9.90614i	0.273279	−	0.473334i
$439$	10.9754	+	19.0099i	0.523826	+	0.907294i	0.999615	+	0.0277345i	$0.00882930\pi$
$439$	10.9754	+	19.0099i	0.523826	+	0.907294i	−0.475789	+	0.879560i	$0.657837\pi$
$440$	13.2144	−	7.62934i	0.629972	−	0.363715i
$441$		0			0
$442$	−1.40868	+	12.5509i	−0.0670042	+	0.596984i
$443$	−27.8963			−1.32539			−0.662697	−	0.748887i	$-0.730588\pi$
$443$	−27.8963			−1.32539			−0.662697	+	0.748887i	$0.730588\pi$
$444$	0.652982	−	0.376999i	0.0309892	−	0.0178916i
$445$	14.5770	+	25.2481i	0.691017	+	1.19688i
$446$	−5.35046	+	9.26727i	−0.253352	+	0.438818i
$447$			2.69484i			0.127461i
$448$		0			0
$449$	19.1056	+	11.0306i	0.901648	+	0.520567i	0.877734	−	0.479147i	$-0.159054\pi$
$449$	19.1056	+	11.0306i	0.901648	+	0.520567i	0.0239134	+	0.999714i	$0.492387\pi$
$450$		−	3.56329i		−	0.167975i
$451$	8.84546	−	15.3208i	0.416516	−	0.721427i
$452$	1.95826	+	3.39181i	0.0921088	+	0.159537i
$453$	−20.8519	+	12.0389i	−0.979708	+	0.565635i
$454$	1.17408			0.0551023
$455$		0			0
$456$	20.7448			0.971464
$457$	4.77724	−	2.75814i	0.223470	−	0.129020i	−0.384086	−	0.923297i	$-0.625483\pi$
$457$	4.77724	−	2.75814i	0.223470	−	0.129020i	0.607556	+	0.794277i	$0.292150\pi$
$458$	−15.7150	−	27.2192i	−0.734314	−	1.27187i
$459$	7.42851	−	12.8665i	0.346733	−	0.600559i
$460$		−	4.70479i		−	0.219362i
$461$	−25.0092	−	14.4391i	−1.16479	−	0.672494i	−0.212346	−	0.977195i	$-0.568110\pi$
$461$	−25.0092	−	14.4391i	−1.16479	−	0.672494i	−0.952448	+	0.304700i	$0.901444\pi$
$462$		0			0
$463$			14.2284i			0.661251i	0.943762	+	0.330625i	$0.107260\pi$
$463$			14.2284i			0.661251i	−0.943762	+	0.330625i	$0.892740\pi$
$464$	−5.48874	+	9.50678i	−0.254808	+	0.441341i
$465$	−2.19061	−	3.79424i	−0.101587	−	0.175954i
$466$	19.1003	−	11.0276i	0.884804	−	0.510842i
$467$	−4.54326			−0.210237			−0.105118	−	0.994460i	$-0.533522\pi$
$467$	−4.54326			−0.210237			−0.105118	+	0.994460i	$0.533522\pi$
$468$	0.874509	+	2.00205i	0.0404242	+	0.0925448i
$469$		0			0
$470$	13.3613	−	7.71416i	0.616312	−	0.355828i
$471$	1.69144	+	2.92966i	0.0779374	+	0.134992i
$472$	4.65081	−	8.05545i	0.214071	−	0.370782i
$473$			25.2951i			1.16307i
$474$	20.3231	+	11.7335i	0.933469	+	0.538939i
$475$	8.67366	+	5.00774i	0.397975	+	0.229771i
$476$		0			0
$477$	−8.57886	+	14.8590i	−0.392799	+	0.680348i
$478$	9.24413	+	16.0113i	0.422817	+	0.732340i
$479$	1.44239	−	0.832764i	0.0659044	−	0.0380499i	−0.466686	−	0.884423i	$-0.654552\pi$
$479$	1.44239	−	0.832764i	0.0659044	−	0.0380499i	0.532590	+	0.846373i	$0.321219\pi$
$480$	−4.38002			−0.199920
$481$	5.75911	−	2.51562i	0.262593	−	0.114702i
$482$	10.7671			0.490426
$483$		0			0
$484$	−0.607426	−	1.05209i	−0.0276103	−	0.0478224i
$485$	−12.9100	+	22.3608i	−0.586215	+	1.01535i
$486$			18.6248i			0.844837i
$487$	−1.28598	−	0.742463i	−0.0582735	−	0.0336442i	0.470580	−	0.882357i	$-0.344045\pi$
$487$	−1.28598	−	0.742463i	−0.0582735	−	0.0336442i	−0.528854	+	0.848713i	$0.677378\pi$
$488$	2.83487	+	1.63671i	0.128328	+	0.0740904i
$489$			27.3691i			1.23767i
$490$		0			0
$491$	7.99791	+	13.8528i	0.360941	+	0.625167i	0.988116	−	0.153711i	$-0.0491224\pi$
$491$	7.99791	+	13.8528i	0.360941	+	0.625167i	−0.627175	+	0.778878i	$0.715789\pi$
$492$	−2.38528	+	1.37714i	−0.107537	+	0.0620863i
$493$	−9.64808			−0.434528
$494$	26.8490	+	3.01348i	1.20800	+	0.135583i
$495$	−8.24947			−0.370786
$496$	5.58860	−	3.22658i	0.250936	−	0.144878i
$497$		0			0
$498$	−5.94440	+	10.2960i	−0.266375	+	0.461375i
$499$		−	17.7199i		−	0.793253i	−0.917980	−	0.396627i	$-0.870181\pi$
$499$		−	17.7199i		−	0.793253i	0.917980	−	0.396627i	$-0.129819\pi$
$500$	−3.90398	−	2.25397i	−0.174591	−	0.100800i
$501$	7.68902	+	4.43926i	0.343520	+	0.198331i
$502$		−	18.7305i		−	0.835985i
$503$	−0.598451	+	1.03655i	−0.0266836	+	0.0462174i	−0.879059	−	0.476713i	$-0.841828\pi$
$503$	−0.598451	+	1.03655i	−0.0266836	+	0.0462174i	0.852375	+	0.522931i	$0.175161\pi$
$504$		0			0
$505$	−0.114929	+	0.0663540i	−0.00511425	+	0.00295272i
$506$	−24.8253			−1.10362
$507$	−4.48774	−	14.5046i	−0.199307	−	0.644174i
$508$	−4.17406			−0.185194
$509$	−5.44396	+	3.14307i	−0.241299	+	0.139314i	−0.615774	−	0.787923i	$-0.711156\pi$
$509$	−5.44396	+	3.14307i	−0.241299	+	0.139314i	0.374474	+	0.927237i	$0.377823\pi$
$510$	3.71237	+	6.43002i	0.164387	+	0.284726i
$511$		0			0
$512$		−	25.3457i		−	1.12013i
$513$	−27.5244	−	15.8912i	−1.21523	−	0.701614i
$514$	−32.4238	−	18.7199i	−1.43015	−	0.825699i
$515$		−	23.4474i		−	1.03322i
$516$	1.96909	−	3.41056i	0.0866843	−	0.150142i
$517$	9.25143	+	16.0240i	0.406878	+	0.704733i
$518$		0			0
$519$	6.30354			0.276695
$520$	−19.6771	−	2.20852i	−0.862898	−	0.0968499i
$521$	10.8473			0.475230			0.237615	−	0.971359i	$-0.423634\pi$
$521$	10.8473			0.475230			0.237615	+	0.971359i	$0.423634\pi$
$522$	6.35926	−	3.67152i	0.278337	−	0.160698i
$523$	0.673629	+	1.16676i	0.0294557	+	0.0510188i	0.880377	−	0.474274i	$-0.157289\pi$
$523$	0.673629	+	1.16676i	0.0294557	+	0.0510188i	−0.850922	+	0.525292i	$0.823956\pi$
$524$	0.567579	−	0.983076i	0.0247948	−	0.0429459i
$525$		0			0
$526$	−22.0167	−	12.7113i	−0.959974	−	0.554241i
$527$	4.91181	+	2.83583i	0.213962	+	0.123531i
$528$			10.1313i			0.440907i
$529$	−12.9936	+	22.5057i	−0.564941	+	0.978507i
$530$	−12.1492	−	21.0431i	−0.527728	−	0.914052i
$531$	−4.35510	+	2.51442i	−0.188995	+	0.109117i
$532$		0			0
$533$	−21.0375	+	9.18931i	−0.911233	+	0.398033i
$534$	−23.9502			−1.03643
$535$	6.30034	−	3.63750i	0.272388	−	0.157263i
$536$	7.59205	+	13.1498i	0.327926	+	0.567985i
$537$	−7.17773	+	12.4322i	−0.309742	+	0.536489i
$538$			28.4993i			1.22869i
$539$		0			0
$540$	3.15198	+	1.81980i	0.135640	+	0.0783115i
$541$		−	20.1571i		−	0.866621i	−0.901245	−	0.433310i	$-0.857345\pi$
$541$		−	20.1571i		−	0.866621i	0.901245	−	0.433310i	$-0.142655\pi$
$542$	5.99978	−	10.3919i	0.257712	−	0.446371i
$543$	−12.7610	−	22.1027i	−0.547628	−	0.948519i
$544$	4.91047	−	2.83506i	0.210535	−	0.121552i
$545$	3.60415			0.154385
$546$		0			0
$547$	−3.42286			−0.146351			−0.0731755	−	0.997319i	$-0.523313\pi$
$547$	−3.42286			−0.146351			−0.0731755	+	0.997319i	$0.523313\pi$
$548$	−7.01924	+	4.05256i	−0.299847	+	0.173117i
$549$	−0.884873	−	1.53264i	−0.0377654	−	0.0654117i
$550$	−3.02594	+	5.24109i	−0.129027	+	0.223481i
$551$			20.6394i			0.879266i
$552$	21.4214	+	12.3677i	0.911757	+	0.526403i
$553$		0			0
$554$			18.3093i			0.777889i
$555$	1.84729	−	3.19960i	0.0784130	−	0.135815i
$556$	2.05020	+	3.55106i	0.0869480	+	0.150598i
$557$	−20.4948	+	11.8327i	−0.868394	+	0.501367i	−0.866814	−	0.498631i	$-0.833836\pi$
$557$	−20.4948	+	11.8327i	−0.868394	+	0.501367i	−0.00157977	+	0.999999i	$0.500503\pi$
$558$	−4.31664			−0.182738
$559$	19.4806	−	26.4190i	0.823940	−	1.11740i
$560$		0			0
$561$	−7.71139	+	4.45217i	−0.325575	+	0.187971i
$562$	0.0630888	+	0.109273i	0.00266124	+	0.00460941i
$563$	−14.4037	+	24.9480i	−0.607045	+	1.05143i	0.384680	+	0.923050i	$0.374312\pi$
$563$	−14.4037	+	24.9480i	−0.607045	+	1.05143i	−0.991725	+	0.128382i	$0.959022\pi$
$564$		−	2.88069i		−	0.121299i
$565$	16.6198	+	9.59543i	0.699199	+	0.403683i
$566$	0.686177	+	0.396164i	0.0288422	+	0.0166520i
$567$		0			0
$568$	−4.11343	+	7.12467i	−0.172596	+	0.298945i
$569$	−13.8361	−	23.9648i	−0.580040	−	1.00466i	−0.995474	−	0.0950353i	$-0.969704\pi$
$569$	−13.8361	−	23.9648i	−0.580040	−	1.00466i	0.415434	−	0.909623i	$-0.363630\pi$
$570$	13.7552	−	7.94158i	0.576143	−	0.332636i
$571$	−12.9655			−0.542588			−0.271294	−	0.962497i	$-0.587452\pi$
$571$	−12.9655			−0.542588			−0.271294	+	0.962497i	$0.587452\pi$
$572$	0.413861	−	3.68736i	0.0173044	−	0.154176i
$573$	3.22016			0.134524
$574$		0			0
$575$	5.97105	+	10.3422i	0.249010	+	0.431298i
$576$	−7.26525	+	12.5838i	−0.302719	+	0.524324i
$577$			9.46047i			0.393844i	0.980419	+	0.196922i	$0.0630947\pi$
$577$			9.46047i			0.393844i	−0.980419	+	0.196922i	$0.936905\pi$
$578$	10.4702	+	6.04497i	0.435503	+	0.251438i
$579$	−13.1381	−	7.58529i	−0.546001	−	0.315234i
$580$		−	2.36354i		−	0.0981405i
$581$		0			0
$582$	−10.6057	−	18.3696i	−0.439620	−	0.761444i
$583$	25.2365	−	14.5703i	1.04519	−	0.603440i
$584$	−23.2155			−0.960663
$585$	8.61598	+	6.35317i	0.356227	+	0.262671i
$586$	−31.7784			−1.31275
$587$	18.6673	−	10.7776i	0.770481	−	0.444837i	−0.0625654	−	0.998041i	$-0.519928\pi$
$587$	18.6673	−	10.7776i	0.770481	−	0.444837i	0.833046	+	0.553204i	$0.186595\pi$
$588$		0			0
$589$	6.06647	−	10.5074i	0.249965	−	0.432951i
$590$		−	7.12175i		−	0.293198i
$591$	−19.2441	−	11.1106i	−0.791598	−	0.457029i
$592$	4.71274	+	2.72090i	0.193692	+	0.111828i
$593$			3.97234i			0.163124i	0.996668	+	0.0815622i	$0.0259909\pi$
$593$			3.97234i			0.163124i	−0.996668	+	0.0815622i	$0.974009\pi$
$594$	9.60231	−	16.6317i	0.393988	−	0.682407i
$595$		0			0
$596$	0.740117	−	0.427307i	0.0303164	−	0.0175032i
$597$	−23.3956			−0.957517
$598$	25.9282	+	19.1187i	1.06028	+	0.781821i
$599$	−19.5049			−0.796950			−0.398475	−	0.917179i	$-0.630460\pi$
$599$	−19.5049			−0.796950			−0.398475	+	0.917179i	$0.630460\pi$
$600$	5.22211	−	3.01498i	0.213192	−	0.123086i
$601$	−13.4368	−	23.2733i	−0.548100	−	0.949336i	−0.998405	−	0.0564616i	$-0.982018\pi$
$601$	−13.4368	−	23.2733i	−0.548100	−	0.949336i	0.450305	−	0.892875i	$-0.351315\pi$
$602$		0			0
$603$		−	8.20914i		−	0.334302i
$604$	6.61276	+	3.81788i	0.269070	+	0.155347i
$605$	−5.15523	−	2.97637i	−0.209590	−	0.121007i
$606$		−	0.109021i		−	0.00442866i
$607$	12.5102	−	21.6682i	0.507772	−	0.879487i	−0.492187	−	0.870489i	$-0.663803\pi$
$607$	12.5102	−	21.6682i	0.507772	−	0.879487i	0.999960	−	0.00899773i	$-0.00286411\pi$
$608$	−6.06482	−	10.5046i	−0.245961	−	0.426016i
$609$		0			0
$610$	2.50628			0.101476
$611$	2.67808	−	23.8607i	0.108343	−	0.965300i
$612$	−1.66265			−0.0672086
$613$	−18.4970	+	10.6793i	−0.747088	+	0.431332i	−0.824641	−	0.565657i	$-0.808623\pi$
$613$	−18.4970	+	10.6793i	−0.747088	+	0.431332i	0.0775527	+	0.996988i	$0.475289\pi$
$614$	−6.31751	−	10.9422i	−0.254954	−	0.441593i
$615$	−6.74796	+	11.6878i	−0.272104	+	0.471298i
$616$		0			0
$617$	−28.5425	−	16.4790i	−1.14908	−	0.663420i	−0.200415	−	0.979711i	$-0.564229\pi$
$617$	−28.5425	−	16.4790i	−1.14908	−	0.663420i	−0.948662	+	0.316291i	$0.897562\pi$
$618$	16.6816	+	9.63111i	0.671031	+	0.387420i
$619$		−	48.9117i		−	1.96593i	−0.183795	−	0.982965i	$-0.558838\pi$
$619$		−	48.9117i		−	1.96593i	0.183795	−	0.982965i	$-0.441162\pi$
$620$	−0.694707	+	1.20327i	−0.0279001	+	0.0483244i
$621$	−18.9481	−	32.8191i	−0.760361	−	1.31698i
$622$	8.00176	−	4.61982i	0.320841	−	0.185238i
$623$		0			0
$624$	7.80240	−	10.5814i	0.312346	−	0.423595i
$625$	−13.5576			−0.542304
$626$	−36.1075	+	20.8467i	−1.44315	+	0.833201i
$627$	9.52417	+	16.4964i	0.380359	+	0.658801i
$628$	0.536406	−	0.929083i	0.0214049	−	0.0370744i
$629$			4.78278i			0.190702i
$630$		0			0
$631$	4.65076	+	2.68512i	0.185144	+	0.106893i	0.589707	−	0.807617i	$-0.299243\pi$
$631$	4.65076	+	2.68512i	0.185144	+	0.106893i	−0.404563	+	0.914510i	$0.632576\pi$
$632$		−	47.6280i		−	1.89454i
$633$	−5.83981	+	10.1148i	−0.232111	+	0.402029i
$634$	10.9621	+	18.9869i	0.435360	+	0.754066i
$635$	−17.7127	+	10.2264i	−0.702905	+	0.405823i
$636$	−4.53687			−0.179899
$637$		0			0
$638$	−12.4714			−0.493747
$639$	3.85189	−	2.22389i	0.152378	−	0.0879757i
$640$	−6.53865	−	11.3253i	−0.258463	−	0.447671i
$641$	19.8510	−	34.3829i	0.784066	−	1.35804i	−0.145489	−	0.989360i	$-0.546475\pi$
$641$	19.8510	−	34.3829i	0.784066	−	1.35804i	0.929555	−	0.368683i	$-0.120191\pi$
$642$			5.97647i			0.235872i
$643$	−27.8388	−	16.0727i	−1.09785	−	0.633847i	−0.162198	−	0.986758i	$-0.551858\pi$
$643$	−27.8388	−	16.0727i	−1.09785	−	0.633847i	−0.935657	+	0.352911i	$0.885192\pi$
$644$		0			0
$645$		−	19.2970i		−	0.759818i
$646$	−10.2807	+	17.8067i	−0.404489	+	0.700596i
$647$	9.92502	+	17.1906i	0.390193	+	0.675833i	0.992475	−	0.122450i	$-0.0390751\pi$
$647$	9.92502	+	17.1906i	0.390193	+	0.675833i	−0.602282	+	0.798283i	$0.705742\pi$
$648$	−3.71020	+	2.14209i	−0.145751	+	0.0841491i
$649$	8.54096			0.335262
$650$	7.19670	−	3.14357i	0.282278	−	0.123301i
$651$		0			0
$652$	7.51671	−	4.33977i	0.294377	−	0.169959i
$653$	9.50024	+	16.4549i	0.371773	+	0.643930i	0.989838	−	0.142197i	$-0.0454165\pi$
$653$	9.50024	+	16.4549i	0.371773	+	0.643930i	−0.618065	+	0.786127i	$0.712083\pi$
$654$	−1.48042	+	2.56416i	−0.0578889	+	0.100266i
$655$		−	5.56225i		−	0.217335i
$656$	−17.2152	−	9.93918i	−0.672139	−	0.388060i
$657$	10.8697	+	6.27562i	0.424067	+	0.244835i
$658$		0			0
$659$	3.60729	−	6.24801i	0.140520	−	0.243388i	−0.787173	−	0.616733i	$-0.788456\pi$
$659$	3.60729	−	6.24801i	0.140520	−	0.243388i	0.927693	+	0.373345i	$0.121789\pi$
$660$	−1.09067	−	1.88909i	−0.0424542	−	0.0735329i
$661$	−14.5068	+	8.37548i	−0.564248	+	0.325769i	−0.754849	−	0.655899i	$-0.772290\pi$
$661$	−14.5068	+	8.37548i	−0.564248	+	0.325769i	0.190601	+	0.981668i	$0.438956\pi$
$662$	25.4470			0.989025
$663$	11.4828	+	1.28880i	0.445953	+	0.0500529i
$664$	24.1291			0.936393
$665$		0			0
$666$	−1.82006	−	3.15244i	−0.0705259	−	0.122155i
$667$	−12.3048	+	21.3126i	−0.476444	+	0.825226i
$668$		−	2.81564i		−	0.108941i
$669$	8.47860	+	4.89512i	0.327802	+	0.189256i
$670$	10.0681	+	5.81281i	0.388964	+	0.224569i
$671$			3.00573i			0.116035i
$672$		0			0
$673$	−18.6684	−	32.3346i	−0.719614	−	1.24641i	−0.961153	−	0.276016i	$-0.910986\pi$
$673$	−18.6684	−	32.3346i	−0.719614	−	1.24641i	0.241539	−	0.970391i	$-0.422348\pi$
$674$	1.40612	−	0.811824i	0.0541618	−	0.0312703i
$675$	−9.23831			−0.355583
$676$	−3.27199	+	3.53245i	−0.125846	+	0.135864i
$677$	−28.1341			−1.08128			−0.540641	−	0.841253i	$-0.681818\pi$
$677$	−28.1341			−1.08128			−0.540641	+	0.841253i	$0.681818\pi$
$678$	−13.6533	+	7.88271i	−0.524350	+	0.302734i
$679$		0			0
$680$	7.53452	−	13.0502i	0.288935	−	0.500451i
$681$		−	1.07416i		−	0.0411620i
$682$	6.34915	+	3.66568i	0.243122	+	0.140366i
$683$	−1.79295	−	1.03516i	−0.0686053	−	0.0396093i	0.465305	−	0.885150i	$-0.345945\pi$
$683$	−1.79295	−	1.03516i	−0.0686053	−	0.0396093i	−0.533910	+	0.845541i	$0.679278\pi$
$684$			3.55677i			0.135996i
$685$	−19.8574	+	34.3941i	−0.758714	+	1.31413i
$686$		0			0
$687$	−24.9028	+	14.3776i	−0.950100	+	0.548540i
$688$	28.4228			1.08361
$689$	−37.5788	−	4.21776i	−1.43164	−	0.160684i
$690$	18.9385			0.720977
$691$	−31.0542	+	17.9291i	−1.18136	+	0.682057i	−0.956328	−	0.292295i	$-0.905581\pi$
$691$	−31.0542	+	17.9291i	−1.18136	+	0.682057i	−0.225029	+	0.974352i	$0.572248\pi$
$692$	−0.999521	−	1.73122i	−0.0379961	−	0.0658112i
$693$		0			0
$694$			33.0417i			1.25425i
$695$	17.4001	+	10.0460i	0.660023	+	0.381065i
$696$	10.7614	+	6.21312i	0.407911	+	0.235508i
$697$		−	17.4710i		−	0.661763i
$698$	11.0530	−	19.1443i	0.418361	−	0.724622i
$699$	−10.0891	−	17.4748i	−0.381604	−	0.660958i
$700$		0			0
$701$	−44.8940			−1.69562			−0.847812	−	0.530297i	$-0.822081\pi$
$701$	−44.8940			−1.69562			−0.847812	+	0.530297i	$0.822081\pi$
$702$	−22.8375	+	9.97558i	−0.861946	+	0.376504i
$703$	10.2314			0.385885
$704$	21.3722	−	12.3393i	0.805497	−	0.465054i
$705$	−7.05767	−	12.2242i	−0.265807	−	0.460391i
$706$	16.1801	−	28.0248i	0.608947	−	1.05473i
$707$		0			0
$708$	−1.15158	−	0.664867i	−0.0432792	−	0.0249872i
$709$	−14.0864	−	8.13279i	−0.529026	−	0.305433i	0.211594	−	0.977358i	$-0.432135\pi$
$709$	−14.0864	−	8.13279i	−0.529026	−	0.305433i	−0.740620	+	0.671924i	$0.765468\pi$
$710$			6.29886i			0.236392i
$711$	−12.8748	+	22.2998i	−0.482843	+	0.836309i
$712$	24.3043	+	42.0963i	0.910843	+	1.57763i
$713$	12.5287	−	7.23344i	0.469203	−	0.270894i
$714$		0			0
$715$	−7.27775	−	16.6613i	−0.272173	−	0.623096i
$716$	4.55255			0.170137
$717$	14.6487	−	8.45743i	0.547066	−	0.315849i
$718$	−3.36403	−	5.82667i	−0.125544	−	0.217449i
$719$	5.00744	−	8.67314i	0.186746	−	0.323454i	−0.757417	−	0.652931i	$-0.773539\pi$
$719$	5.00744	−	8.67314i	0.186746	−	0.323454i	0.944164	+	0.329477i	$0.106873\pi$
$720$			9.26949i			0.345454i
$721$		0			0
$722$	17.0873	+	9.86534i	0.635922	+	0.367150i
$723$		−	9.85076i		−	0.366354i
$724$	−4.04690	+	7.00944i	−0.150402	+	0.260504i
$725$	2.99966	+	5.19556i	0.111405	+	0.192958i
$726$	4.23506	−	2.44511i	0.157178	−	0.0907466i
$727$	−34.5299			−1.28064			−0.640322	−	0.768106i	$-0.721199\pi$
$727$	−34.5299			−1.28064			−0.640322	+	0.768106i	$0.721199\pi$
$728$		0			0
$729$	21.2872			0.788415
$730$	−15.3934	+	8.88741i	−0.569737	+	0.328938i
$731$	12.4904	+	21.6340i	0.461973	+	0.800161i
$732$	0.233980	−	0.405265i	0.00864814	−	0.0149790i
$733$		−	33.1360i		−	1.22391i	−0.790894	−	0.611953i	$-0.790384\pi$
$733$		−	33.1360i		−	1.22391i	0.790894	−	0.611953i	$-0.209616\pi$
$734$	27.9895	+	16.1598i	1.03311	+	0.596468i
$735$		0			0
$736$		−	14.4629i		−	0.533111i
$737$	−6.97119	+	12.0745i	−0.256787	+	0.444768i
$738$	6.64850	+	11.5155i	0.244735	+	0.423893i
$739$	−3.47767	+	2.00784i	−0.127928	+	0.0738594i	−0.562598	−	0.826730i	$-0.690198\pi$
$739$	−3.47767	+	2.00784i	−0.127928	+	0.0738594i	0.434670	+	0.900590i	$0.356865\pi$
$740$	−1.17166			−0.0430711
$741$	2.75703	−	24.5641i	0.101282	−	0.902386i
$742$		0			0
$743$	10.8361	−	6.25622i	0.397538	−	0.229519i	−0.287883	−	0.957666i	$-0.592952\pi$
$743$	10.8361	−	6.25622i	0.397538	−	0.229519i	0.685421	+	0.728147i	$0.259618\pi$
$744$	−3.65241	−	6.32616i	−0.133904	−	0.231928i
$745$	2.09379	−	3.62656i	0.0767107	−	0.132867i
$746$		−	8.66508i		−	0.317251i
$747$	−11.2975	−	6.52260i	−0.413353	−	0.238650i
$748$	2.44551	+	1.41192i	0.0894168	+	0.0516248i
$749$		0			0
$750$	9.07304	−	15.7150i	0.331300	−	0.573829i
$751$	18.7579	+	32.4896i	0.684486	+	1.18556i	0.973598	+	0.228269i	$0.0733065\pi$
$751$	18.7579	+	32.4896i	0.684486	+	1.18556i	−0.289112	+	0.957295i	$0.593360\pi$
$752$	18.0053	−	10.3954i	0.656585	−	0.379080i
$753$	−17.1365			−0.624490
$754$	13.0255	+	9.60461i	0.474360	+	0.349779i
$755$	37.4150			1.36167
$756$		0			0
$757$	17.5223	+	30.3496i	0.636860	+	1.10307i	0.986118	+	0.166047i	$0.0531004\pi$
$757$	17.5223	+	30.3496i	0.636860	+	1.10307i	−0.349258	+	0.937027i	$0.613566\pi$
$758$	7.86530	−	13.6231i	0.285680	−	0.494813i
$759$			22.7126i			0.824414i
$760$	−27.9172	−	16.1180i	−1.01266	−	0.584661i
$761$	3.72586	+	2.15113i	0.135062	+	0.0779782i	0.566009	−	0.824399i	$-0.308487\pi$
$761$	3.72586	+	2.15113i	0.135062	+	0.0779782i	−0.430946	+	0.902378i	$0.641820\pi$
$762$		−	16.8021i		−	0.608677i
$763$		0			0
$764$	−0.510605	−	0.884394i	−0.0184730	−	0.0319962i
$765$	−7.05545	+	4.07347i	−0.255090	+	0.147277i
$766$	9.26679			0.334823
$767$	−8.92043	−	6.57766i	−0.322098	−	0.237506i
$768$	−10.0039			−0.360985
$769$	−10.6146	+	6.12834i	−0.382772	+	0.220994i	−0.679024	−	0.734116i	$-0.737597\pi$
$769$	−10.6146	+	6.12834i	−0.382772	+	0.220994i	0.296251	+	0.955110i	$0.404263\pi$
$770$		0			0
$771$	−17.1268	+	29.6645i	−0.616806	+	1.06834i
$772$			4.81105i			0.173153i
$773$	3.29372	+	1.90163i	0.118467	+	0.0683970i	0.558063	−	0.829799i	$-0.311545\pi$
$773$	3.29372	+	1.90163i	0.118467	+	0.0683970i	−0.439596	+	0.898196i	$0.644878\pi$
$774$	−16.4654	−	9.50628i	−0.591835	−	0.341696i
$775$		−	3.52673i		−	0.126684i
$776$	−21.5250	+	37.2824i	−0.772702	+	1.33836i
$777$		0			0
$778$	7.90250	−	4.56251i	0.283318	−	0.163574i
$779$	−37.3744			−1.33908
$780$	−0.315723	+	2.81298i	−0.0113047	+	0.100721i
$781$	−7.55409			−0.270307
$782$	−21.2321	+	12.2583i	−0.759258	+	0.438358i
$783$	−9.51891	−	16.4872i	−0.340178	−	0.589206i
$784$		0			0
$785$		−	5.25675i		−	0.187622i
$786$	3.95724	+	2.28471i	0.141150	+	0.0814930i
$787$	−15.0114	−	8.66684i	−0.535099	−	0.308940i	0.207991	−	0.978131i	$-0.433307\pi$
$787$	−15.0114	−	8.66684i	−0.535099	−	0.308940i	−0.743090	+	0.669191i	$0.766641\pi$
$788$			7.04701i			0.251039i
$789$	−11.6296	+	20.1430i	−0.414024	+	0.717110i
$790$	−18.2331	−	31.5806i	−0.648704	−	1.12359i
$791$		0			0
$792$	−13.7544			−0.488740
$793$	2.31480	−	3.13927i	0.0822011	−	0.111479i
$794$	28.6731			1.01757
$795$	−19.2522	+	11.1153i	−0.682807	+	0.394219i
$796$	3.70972	+	6.42542i	0.131488	+	0.227743i
$797$	−25.1707	+	43.5969i	−0.891592	+	1.54428i	−0.0536245	+	0.998561i	$0.517077\pi$
$797$	−25.1707	+	43.5969i	−0.891592	+	1.54428i	−0.837967	+	0.545721i	$0.816256\pi$
$798$		0			0
$799$	15.8248	+	9.13645i	0.559841	+	0.323224i
$800$	−3.05340	−	1.76288i	−0.107954	−	0.0623273i
$801$		−	26.2798i		−	0.928552i
$802$	−1.94978	+	3.37711i	−0.0688490	+	0.119250i
$803$	−10.6585	−	18.4610i	−0.376130	−	0.651476i
$804$	1.87986	−	1.08534i	0.0662975	−	0.0382769i
$805$		0			0
$806$	−3.80818	−	8.71822i	−0.134137	−	0.307086i
$807$	26.0739			0.917845
$808$	−0.191621	+	0.110632i	−0.00674120	+	0.00389203i
$809$	−8.03694	−	13.9204i	−0.282564	−	0.489415i	0.689452	−	0.724332i	$-0.257852\pi$
$809$	−8.03694	−	13.9204i	−0.282564	−	0.489415i	−0.972015	+	0.234917i	$0.924518\pi$
$810$	−1.64008	+	2.84070i	−0.0576265	+	0.0998120i
$811$			36.9875i			1.29881i	0.760443	+	0.649404i	$0.224982\pi$
$811$			36.9875i			1.29881i	−0.760443	+	0.649404i	$0.775018\pi$
$812$		0			0
$813$	−9.50754	−	5.48918i	−0.333444	−	0.192514i
$814$			6.18237i			0.216692i
$815$	21.2648	−	36.8317i	0.744873	−	1.29016i
$816$	5.00267	+	8.66488i	0.175129	+	0.303332i
$817$	46.2798	−	26.7197i	1.61913	−	0.934803i
$818$	−7.15624			−0.250212
$819$		0			0
$820$	4.27996			0.149463
$821$	26.1021	−	15.0700i	0.910968	−	0.525948i	0.0302256	−	0.999543i	$-0.490377\pi$
$821$	26.1021	−	15.0700i	0.910968	−	0.525948i	0.880743	+	0.473595i	$0.157044\pi$
$822$	−16.3130	−	28.2550i	−0.568982	−	0.985507i
$823$	20.8251	−	36.0702i	0.725918	−	1.25733i	−0.232677	−	0.972554i	$-0.574749\pi$
$823$	20.8251	−	36.0702i	0.725918	−	1.25733i	0.958595	−	0.284773i	$-0.0919181\pi$
$824$		−	39.0940i		−	1.36190i
$825$	4.79506	+	2.76843i	0.166942	+	0.0963842i
$826$		0			0
$827$			37.6524i			1.30930i	0.755932	+	0.654651i	$0.227184\pi$
$827$			37.6524i			1.30930i	−0.755932	+	0.654651i	$0.772816\pi$
$828$	−2.12048	+	3.67278i	−0.0736918	+	0.127638i
$829$	3.73737	+	6.47332i	0.129804	+	0.224828i	0.923601	−	0.383356i	$-0.125232\pi$
$829$	3.73737	+	6.47332i	0.129804	+	0.224828i	−0.793796	+	0.608184i	$0.791898\pi$
$830$	15.9993	−	9.23718i	0.555343	−	0.320627i
$831$	16.7512			0.581091
$832$	−31.8246	−	3.57193i	−1.10332	−	0.123834i
$833$		0			0
$834$	−14.2943	+	8.25282i	−0.494971	+	0.285772i
$835$	−6.89829	−	11.9482i	−0.238725	−	0.413484i
$836$	3.02040	−	5.23149i	0.104463	−	0.180935i
$837$			11.1915i			0.386834i
$838$	6.78732	+	3.91866i	0.234464	+	0.135368i
$839$	9.51957	+	5.49613i	0.328652	+	0.189747i	0.655242	−	0.755419i	$-0.272566\pi$
$839$	9.51957	+	5.49613i	0.328652	+	0.189747i	−0.326590	+	0.945166i	$0.605900\pi$
$840$		0			0
$841$	8.31846	−	14.4080i	0.286843	−	0.496827i
$842$	−1.22926	−	2.12914i	−0.0423632	−	0.0733752i
$843$	0.0999736	−	0.0577198i	0.00344328	−	0.00198798i
$844$	3.70396			0.127495
$845$	−5.23025	+	23.0063i	−0.179926	+	0.791442i
$846$	−13.9073			−0.478143
$847$		0			0
$848$	−16.3719	−	28.3569i	−0.562213	−	0.973781i
$849$	0.362450	−	0.627781i	0.0124392	−	0.0215454i
$850$			5.97667i			0.204998i
$851$	10.5651	+	6.09979i	0.362169	+	0.209098i
$852$	1.01852	+	0.588045i	0.0348940	+	0.0201461i
$853$		−	35.2031i		−	1.20533i	−0.797994	−	0.602666i	$-0.794105\pi$
$853$		−	35.2031i		−	1.20533i	0.797994	−	0.602666i	$-0.205895\pi$
$854$		0			0
$855$	8.71404	+	15.0932i	0.298014	+	0.516175i
$856$	10.5046	−	6.06483i	0.359040	−	0.207292i
$857$	30.3681			1.03736			0.518678	−	0.854970i	$-0.326424\pi$
$857$	30.3681			1.03736			0.518678	+	0.854970i	$0.326424\pi$
$858$	14.8429	+	1.66594i	0.506730	+	0.0568743i
$859$	35.8306			1.22252			0.611262	−	0.791429i	$-0.290662\pi$
$859$	35.8306			1.22252			0.611262	+	0.791429i	$0.290662\pi$
$860$	−5.29977	+	3.05983i	−0.180721	+	0.104339i
$861$		0			0
$862$	6.86113	−	11.8838i	0.233691	−	0.404765i
$863$			32.3403i			1.10088i	0.834876	+	0.550438i	$0.185539\pi$
$863$			32.3403i			1.10088i	−0.834876	+	0.550438i	$0.814461\pi$
$864$	9.68945	+	5.59421i	0.329642	+	0.190319i
$865$	−8.48294	−	4.89763i	−0.288429	−	0.166524i
$866$			51.4016i			1.74670i
$867$	5.53053	−	9.57916i	0.187827	−	0.325325i
$868$		0			0
$869$	37.8740	−	21.8665i	1.28479	−	0.741772i
$870$	9.51409			0.322558
$871$	16.5798	−	7.24218i	0.561786	−	0.245392i
$872$	6.00921			0.203498
$873$	20.1564	−	11.6373i	0.682190	−	0.393862i
$874$	26.2233	+	45.4201i	0.887016	+	1.53636i
$875$		0			0
$876$			3.31882i			0.112133i
$877$	3.82446	+	2.20805i	0.129143	+	0.0745607i	0.563180	−	0.826334i	$-0.309578\pi$
$877$	3.82446	+	2.20805i	0.129143	+	0.0745607i	−0.434037	+	0.900895i	$0.642911\pi$
$878$	24.2674	+	14.0108i	0.818984	+	0.472841i
$879$			29.0740i			0.980642i
$880$	7.87164	−	13.6341i	0.265353	−	0.459605i
$881$	−9.97753	−	17.2816i	−0.336152	−	0.582232i	0.647554	−	0.762020i	$-0.275792\pi$
$881$	−9.97753	−	17.2816i	−0.336152	−	0.582232i	−0.983705	+	0.179788i	$0.942459\pi$
$882$		0			0
$883$	−12.9725			−0.436559			−0.218280	−	0.975886i	$-0.570045\pi$
$883$	−12.9725			−0.436559			−0.218280	+	0.975886i	$0.570045\pi$
$884$	−1.46680	−	3.35801i	−0.0493339	−	0.112942i
$885$	−6.51567			−0.219022
$886$	−30.8404	+	17.8057i	−1.03610	+	0.598195i
$887$	27.0862	+	46.9147i	0.909467	+	1.57524i	0.814806	+	0.579733i	$0.196843\pi$
$887$	27.0862	+	46.9147i	0.909467	+	1.57524i	0.0946605	+	0.995510i	$0.469823\pi$
$888$	3.07999	−	5.33470i	0.103358	−	0.179021i
$889$		0			0
$890$	32.2309	+	18.6085i	1.08038	+	0.623758i
$891$	−3.40679	−	1.96691i	−0.114132	−	0.0658941i
$892$		−	3.10478i		−	0.103956i
$893$	19.5449	−	33.8527i	0.654044	−	1.13284i
$894$	1.72007	+	2.97924i	0.0575276	+	0.0996408i
$895$	19.3187	−	11.1537i	0.645755	−	0.372827i
$896$		0			0
$897$	17.4916	−	23.7216i	0.584029	−	0.792043i
$898$	28.1626			0.939797
$899$	6.29401	−	3.63385i	0.209917	−	0.121196i
$900$	0.516930	+	0.895348i	0.0172310	+	0.0298449i
$901$	14.3892	−	24.9228i	0.479374	−	0.830300i
$902$		−	22.5836i		−	0.751951i
$903$		0			0
$904$	27.7102	+	15.9985i	0.921629	+	0.532103i
$905$			39.6594i			1.31832i
$906$	−15.3684	+	26.6188i	−0.510580	+	0.884350i
$907$	−1.29570	−	2.24421i	−0.0430229	−	0.0745178i	0.843712	−	0.536796i	$-0.180365\pi$
$907$	−1.29570	−	2.24421i	−0.0430229	−	0.0745178i	−0.886735	+	0.462278i	$0.847032\pi$
$908$	−0.295011	+	0.170325i	−0.00979029	+	0.00565242i
$909$	0.119625			0.00396770
$910$		0			0
$911$	3.59896			0.119239			0.0596195	−	0.998221i	$-0.481011\pi$
$911$	3.59896			0.119239			0.0596195	+	0.998221i	$0.481011\pi$
$912$	18.5361	−	10.7018i	0.613791	−	0.354373i
$913$	11.0780	+	19.1876i	0.366627	+	0.635017i
$914$	3.52094	−	6.09845i	0.116462	−	0.201719i
$915$		−	2.29299i		−	0.0758039i
$916$	7.89741	+	4.55957i	0.260938	+	0.150653i
$917$		0			0
$918$		−	18.9659i		−	0.625969i
$919$	13.9624	−	24.1836i	0.460578	−	0.797745i	−0.538412	−	0.842682i	$-0.680975\pi$
$919$	13.9624	−	24.1836i	0.460578	−	0.797745i	0.998990	+	0.0449372i	$0.0143088\pi$
$920$	−19.2185	−	33.2874i	−0.633615	−	1.09745i
$921$	−10.0110	+	5.77987i	−0.329875	+	0.190453i
$922$	−36.8648			−1.21408
$923$	7.88971	+	5.81764i	0.259693	+	0.191490i
$924$		0			0
$925$	2.57557	−	1.48700i	0.0846841	−	0.0488924i
$926$	9.08174	+	15.7300i	0.298445	+	0.516921i
$927$	−10.5679	+	18.3042i	−0.347096	+	0.601187i
$928$		−	7.26571i		−	0.238509i
$929$	23.0067	+	13.2830i	0.754827	+	0.435800i	0.827435	−	0.561561i	$-0.189799\pi$
$929$	23.0067	+	13.2830i	0.754827	+	0.435800i	−0.0726084	+	0.997361i	$0.523132\pi$
$930$	−4.84359	−	2.79645i	−0.158828	−	0.0916992i
$931$		0			0
$932$	−3.19955	+	5.54179i	−0.104805	+	0.181527i
$933$	−4.22666	−	7.32079i	−0.138375	−	0.239672i
$934$	−5.02274	+	2.89988i	−0.164349	+	0.0948869i
$935$	13.8367			0.452509
$936$	14.3655	+	10.5927i	0.469550	+	0.346232i
$937$	−3.02509			−0.0988255			−0.0494128	−	0.998778i	$-0.515735\pi$
$937$	−3.02509			−0.0988255			−0.0494128	+	0.998778i	$0.515735\pi$
$938$		0			0
$939$	19.0726	+	33.0347i	0.622410	+	1.07805i
$940$	−2.23820	+	3.87667i	−0.0730020	+	0.126443i
$941$			6.48465i			0.211394i	0.994398	+	0.105697i	$0.0337073\pi$
$941$			6.48465i			0.211394i	−0.994398	+	0.105697i	$0.966293\pi$
$942$	3.73990	+	2.15923i	0.121852	+	0.0703515i
$943$	−38.5934	−	22.2819i	−1.25678	−	0.725599i
$944$		−	9.59704i		−	0.312357i
$945$		0			0
$946$	16.1454	+	27.9647i	0.524934	+	0.909212i
$947$	18.3193	−	10.5767i	0.595298	−	0.343695i	−0.171892	−	0.985116i	$-0.554988\pi$
$947$	18.3193	−	10.5767i	0.595298	−	0.343695i	0.767190	+	0.641420i	$0.221655\pi$
$948$	−6.80876			−0.221138
$949$	−3.08538	+	27.4897i	−0.100156	+	0.892352i
$950$	12.7854			0.414813
$951$	17.3711	−	10.0292i	0.563295	−	0.325219i
$952$		0			0
$953$	−18.1393	+	31.4182i	−0.587590	+	1.01774i	0.406957	+	0.913447i	$0.366590\pi$
$953$	−18.1393	+	31.4182i	−0.587590	+	1.01774i	−0.994547	+	0.104289i	$0.966743\pi$
$954$			21.9029i			0.709133i
$955$	−4.33351	−	2.50195i	−0.140229	−	0.0809613i
$956$	−4.64554	−	2.68211i	−0.150248	−	0.0867455i
$957$			11.4101i			0.368835i
$958$	1.06308	−	1.84130i	0.0343464	−	0.0594898i
$959$		0			0
$960$	−16.3043	+	9.41329i	−0.526219	+	0.303813i
$961$	26.7277			0.862182
$962$	4.76123	−	6.45705i	0.153508	−	0.208184i
$963$	−6.55779			−0.211322
$964$	−2.70544	+	1.56199i	−0.0871363	+	0.0503082i
$965$	11.7870	+	20.4157i	0.379437	+	0.657204i
$966$		0			0
$967$		−	16.2828i		−	0.523621i	−0.965119	−	0.261810i	$-0.915681\pi$
$967$		−	16.2828i		−	0.523621i	0.965119	−	0.261810i	$-0.0843195\pi$
$968$	−8.59534	−	4.96252i	−0.276265	−	0.159501i
$969$	16.2913	+	9.40580i	0.523353	+	0.302158i
$970$			32.9610i			1.05831i
$971$	−12.2605	+	21.2358i	−0.393458	+	0.681489i	−0.992903	−	0.118927i	$-0.962055\pi$
$971$	−12.2605	+	21.2358i	−0.393458	+	0.681489i	0.599445	+	0.800416i	$0.295388\pi$
$972$	−2.70191	−	4.67984i	−0.0866638	−	0.150106i
$973$		0			0
$974$	−1.89560			−0.0607390
$975$	−2.87604	−	6.58424i	−0.0921071	−	0.210865i
$976$	3.37738			0.108107
$977$	9.45681	−	5.45989i	0.302550	−	0.174677i	−0.341038	−	0.940050i	$-0.610778\pi$
$977$	9.45681	−	5.45989i	0.302550	−	0.174677i	0.643588	+	0.765372i	$0.277445\pi$
$978$	17.4692	+	30.2575i	0.558603	+	0.967528i
$979$	−22.3168	+	38.6538i	−0.713248	+	1.23538i
$980$		0			0
$981$	−2.81357	−	1.62441i	−0.0898302	−	0.0518635i
$982$	17.6840	+	10.2098i	0.564318	+	0.325809i
$983$		−	19.6715i		−	0.627423i	−0.949518	−	0.313711i	$-0.898428\pi$
$983$		−	19.6715i		−	0.627423i	0.949518	−	0.313711i	$-0.101572\pi$
$984$	−11.2509	+	19.4871i	−0.358666	+	0.621227i
$985$	17.2651	+	29.9040i	0.550112	+	0.952822i
$986$	−10.6663	+	6.15820i	−0.339685	+	0.196117i
$987$		0			0
$988$	−7.18352	+	3.13781i	−0.228538	+	0.0998271i
$989$	63.7191			2.02615
$990$	−9.12009	+	5.26549i	−0.289855	+	0.167348i
$991$	0.869000	+	1.50515i	0.0276047	+	0.0478127i	0.879498	−	0.475903i	$-0.157879\pi$
$991$	0.869000	+	1.50515i	0.0276047	+	0.0478127i	−0.851893	+	0.523716i	$0.824545\pi$
$992$	−2.13559	+	3.69895i	−0.0678050	+	0.117442i
$993$		−	23.2814i		−	0.738812i
$994$		0			0
$995$	31.4844	+	18.1775i	0.998123	+	0.576267i
$996$		−	3.44944i		−	0.109300i
$997$	−23.4768	+	40.6631i	−0.743519	+	1.28781i	0.207365	+	0.978264i	$0.433511\pi$
$997$	−23.4768	+	40.6631i	−0.743519	+	1.28781i	−0.950884	+	0.309549i	$0.899822\pi$
$998$	−11.3103	−	19.5900i	−0.358022	−	0.620112i
$999$	−8.17312	+	4.71875i	−0.258586	+	0.149295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.h.491.5		12
7.2	even	3		637.2.u.i.361.2		12
7.3	odd	6		637.2.k.h.569.5		12
7.4	even	3		637.2.k.g.569.5		12
7.5	odd	6		637.2.u.h.361.2		12
7.6	odd	2		91.2.q.a.36.5	✓	12
13.2	odd	12		8281.2.a.ch.1.4		6
13.4	even	6	inner	637.2.q.h.589.5		12
13.11	odd	12		8281.2.a.by.1.3		6
21.20	even	2		819.2.ct.a.127.2		12
28.27	even	2		1456.2.cc.c.673.2		12
91.4	even	6		637.2.u.i.30.2		12
91.17	odd	6		637.2.u.h.30.2		12
91.30	even	6		637.2.k.g.459.2		12
91.41	even	12		1183.2.a.p.1.4		6
91.55	odd	6		1183.2.c.i.337.9		12
91.62	odd	6		1183.2.c.i.337.4		12
91.69	odd	6		91.2.q.a.43.5	yes	12
91.76	even	12		1183.2.a.m.1.3		6
91.82	odd	6		637.2.k.h.459.2		12
273.251	even	6		819.2.ct.a.316.2		12
364.251	even	6		1456.2.cc.c.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.5	✓	12	7.6	odd	2
91.2.q.a.43.5	yes	12	91.69	odd	6
637.2.k.g.459.2		12	91.30	even	6
637.2.k.g.569.5		12	7.4	even	3
637.2.k.h.459.2		12	91.82	odd	6
637.2.k.h.569.5		12	7.3	odd	6
637.2.q.h.491.5		12	1.1	even	1	trivial
637.2.q.h.589.5		12	13.4	even	6	inner
637.2.u.h.30.2		12	91.17	odd	6
637.2.u.h.361.2		12	7.5	odd	6
637.2.u.i.30.2		12	91.4	even	6
637.2.u.i.361.2		12	7.2	even	3
819.2.ct.a.127.2		12	21.20	even	2
819.2.ct.a.316.2		12	273.251	even	6
1183.2.a.m.1.3		6	91.76	even	12
1183.2.a.p.1.4		6	91.41	even	12
1183.2.c.i.337.4		12	91.62	odd	6
1183.2.c.i.337.9		12	91.55	odd	6
1456.2.cc.c.225.2		12	364.251	even	6
1456.2.cc.c.673.2		12	28.27	even	2
8281.2.a.by.1.3		6	13.11	odd	12
8281.2.a.ch.1.4		6	13.2	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10554 - 0.638282i) q^{2} +(-0.583963 - 1.01145i) q^{3} +(-0.185192 + 0.320762i) q^{4} +1.81487i q^{5} +(-1.29118 - 0.745466i) q^{6} +3.02595i q^{8} +(0.817975 - 1.41677i) q^{9} +(1.15840 + 2.00641i) q^{10} +(-2.40625 + 1.38925i) q^{11} +0.432581 q^{12} +(3.58305 + 0.402155i) q^{13} +(1.83566 - 1.05982i) q^{15} +(1.56102 + 2.70377i) q^{16} +(-1.37198 + 2.37634i) q^{17} -2.08840i q^{18} +(5.08351 + 2.93497i) q^{19} +(-0.582143 - 0.336100i) q^{20} +(-1.77346 + 3.07173i) q^{22} +(3.49955 + 6.06139i) q^{23} +(3.06060 - 1.76704i) q^{24} +1.70623 q^{25} +(4.21789 - 1.84240i) q^{26} -5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} +(1.35293 - 2.34334i) q^{30} -2.06697i q^{31} +(-1.78956 - 1.03320i) q^{32} +(2.81031 + 1.62254i) q^{33} +3.50284i q^{34} +(0.302965 + 0.524751i) q^{36} +(1.50950 - 0.871512i) q^{37} +7.49334 q^{38} +(-1.68561 - 3.85893i) q^{39} -5.49171 q^{40} +(-5.51406 + 3.18355i) q^{41} +(4.55195 - 7.88422i) q^{43} -1.02911i q^{44} +(2.57127 + 1.48452i) q^{45} +(7.73776 + 4.46740i) q^{46} -6.65932i q^{47} +(1.82316 - 3.15780i) q^{48} +(1.88631 - 1.08906i) q^{50} +3.20474 q^{51} +(-0.792549 + 1.07483i) q^{52} -10.4879 q^{53} +(-5.98587 + 3.45594i) q^{54} +(-2.52131 - 4.36703i) q^{55} -6.85564i q^{57} +(3.88720 + 2.24427i) q^{58} +(-2.66212 - 1.53698i) q^{59} +0.785080i q^{60} +(0.540892 - 0.936853i) q^{61} +(-1.31931 - 2.28511i) q^{62} -8.88199 q^{64} +(-0.729860 + 6.50279i) q^{65} +4.14254 q^{66} +(4.34568 - 2.50898i) q^{67} +(-0.508159 - 0.880158i) q^{68} +(4.08721 - 7.07925i) q^{69} +(2.35453 + 1.35939i) q^{71} +(4.28709 + 2.47515i) q^{72} +7.67213i q^{73} +(1.11254 - 1.92698i) q^{74} +(-0.996377 - 1.72578i) q^{75} +(-1.88285 + 1.08706i) q^{76} +(-4.32659 - 3.19030i) q^{78} -15.7399 q^{79} +(-4.90700 + 2.83306i) q^{80} +(0.707906 + 1.22613i) q^{81} +(-4.06400 + 7.03905i) q^{82} -7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} -11.6217i q^{86} +(2.05328 - 3.55639i) q^{87} +(-4.20379 - 7.28117i) q^{88} +(13.9118 - 8.03198i) q^{89} +3.79017 q^{90} -2.59235 q^{92} +(-2.09064 + 1.20703i) q^{93} +(-4.25052 - 7.36212i) q^{94} +(-5.32659 + 9.22592i) q^{95} +2.41340i q^{96} +(12.3209 + 7.11347i) q^{97} +4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29}+ \cdots - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 18 * q^6 - 4 * q^9 - 12 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 + 12 * q^20 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 20 * q^25 + 42 * q^26 - 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 + 30 * q^33 - 10 * q^36 - 42 * q^37 - 4 * q^38 - 4 * q^39 - 92 * q^40 - 30 * q^41 + 2 * q^43 + 12 * q^46 + 2 * q^48 - 18 * q^50 + 52 * q^51 - 2 * q^52 - 44 * q^53 - 12 * q^54 + 6 * q^55 - 12 * q^58 - 18 * q^59 - 14 * q^61 + 4 * q^62 - 52 * q^64 + 60 * q^65 + 52 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 - 56 * q^79 + 72 * q^80 + 2 * q^81 - 14 * q^82 - 48 * q^85 + 2 * q^87 - 14 * q^88 + 12 * q^89 - 24 * q^90 + 24 * q^92 - 18 * q^93 - 4 * q^94 - 22 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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