LMFDB - Embedded newform 637.2.h.l.471.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] 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("637.165"); 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([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-4,-1,8,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == 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 $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.6
Root			$0.217953 + 0.377506i$ of defining polynomial
Character	$\chi$	$=$	637.471
Dual form			637.2.h.l.165.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.85816 q^{2} +(1.14703 - 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 + 0.170921i) q^{5} +(2.13137 - 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(-0.183365 + 0.317598i) q^{10} +(2.09137 - 3.62236i) q^{11} +(1.66637 - 2.88623i) q^{12} +(2.72221 - 2.36423i) q^{13} +(0.226381 + 0.392104i) q^{15} -4.79501 q^{16} -0.841305 q^{17} +(-2.10227 - 3.64125i) q^{18} +(0.675876 + 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} -4.11519 q^{23} +(-1.16637 + 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} +(5.05830 - 4.39312i) q^{26} +1.69131 q^{27} +(4.11931 + 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +(-0.640350 - 1.10912i) q^{31} -6.87618 q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 - 2.84683i) q^{36} +3.04485 q^{37} +(1.25589 + 2.17526i) q^{38} +(-1.57459 - 8.12012i) q^{39} +(0.100344 - 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} +0.446581 q^{45} -7.64669 q^{46} +(-5.83204 + 10.1014i) q^{47} +(-5.50003 + 9.52634i) q^{48} +(4.60921 + 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(3.95472 - 3.43466i) q^{52} +(-2.32398 - 4.02525i) q^{53} +3.14272 q^{54} +(0.412757 + 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} -6.05811 q^{59} +(0.328878 + 0.569634i) q^{60} +(-5.68285 - 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(0.135465 + 0.698587i) q^{65} +(-8.91498 - 15.4412i) q^{66} +(-6.69851 + 11.6022i) q^{67} -1.22222 q^{68} +(-4.72026 + 8.17574i) q^{69} +(2.98520 - 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} +(1.94273 + 3.36491i) q^{73} +5.65782 q^{74} +11.3810 q^{75} +(0.981887 + 1.70068i) q^{76} +(-2.92585 - 15.0885i) q^{78} +(5.36669 - 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(5.01421 + 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(-4.94994 + 8.57354i) q^{86} +18.8999 q^{87} +(-2.12662 + 3.68341i) q^{88} +11.9841 q^{89} +0.829819 q^{90} -5.97840 q^{92} -2.93801 q^{93} +(-10.8369 + 18.7700i) q^{94} -0.266785 q^{95} +(-7.88721 + 13.6611i) q^{96} +(9.73637 - 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.85816			1.31392			0.656959	−	0.753926i	$-0.271842\pi$
$2$	1.85816			1.31392			0.656959	+	0.753926i	$0.271842\pi$
$3$	1.14703	−	1.98672i	0.662240	−	1.14703i	−0.317785	−	0.948163i	$-0.602939\pi$
$3$	1.14703	−	1.98672i	0.662240	−	1.14703i	0.980026	−	0.198871i	$-0.0637276\pi$
$4$	1.45276			0.726381
$5$	−0.0986811	+	0.170921i	−0.0441315	+	0.0764381i	−0.887247	−	0.461294i	$-0.847385\pi$
$5$	−0.0986811	+	0.170921i	−0.0441315	+	0.0764381i	0.843116	+	0.537732i	$0.180719\pi$
$6$	2.13137	−	3.69165i	0.870130	−	1.50711i
$7$		0			0
$7$		0			0
$8$	−1.01686			−0.359513
$9$	−1.13137	−	1.95960i	−0.377125	−	0.653199i
$10$	−0.183365	+	0.317598i	−0.0579852	+	0.100433i
$11$	2.09137	−	3.62236i	0.630571	−	1.09218i	−0.356864	−	0.934156i	$-0.616154\pi$
$11$	2.09137	−	3.62236i	0.630571	−	1.09218i	0.987435	−	0.158025i	$-0.0505127\pi$
$12$	1.66637	−	2.88623i	0.481039	−	0.833184i
$13$	2.72221	−	2.36423i	0.755005	−	0.655719i
$13$	2.72221	−	2.36423i	0.755005	−	0.655719i
$14$		0			0
$15$	0.226381	+	0.392104i	0.0584514	+	0.101241i
$16$	−4.79501			−1.19875
$17$	−0.841305			−0.204047			−0.102023	−	0.994782i	$-0.532532\pi$
$17$	−0.841305			−0.204047			−0.102023	+	0.994782i	$0.532532\pi$
$18$	−2.10227	−	3.64125i	−0.495511	−	0.858250i
$19$	0.675876	+	1.17065i	0.155057	+	0.268566i	0.933080	−	0.359670i	$-0.117111\pi$
$19$	0.675876	+	1.17065i	0.155057	+	0.268566i	−0.778023	+	0.628236i	$0.783777\pi$
$20$	−0.143360	+	0.248307i	−0.0320563	+	0.0555232i
$21$		0			0
$22$	3.88610	−	6.73092i	0.828519	−	1.43504i
$23$	−4.11519			−0.858077			−0.429038	−	0.903286i	$-0.641147\pi$
$23$	−4.11519			−0.858077			−0.429038	+	0.903286i	$0.641147\pi$
$24$	−1.16637	+	2.02021i	−0.238084	+	0.412373i
$25$	2.48052	+	4.29639i	0.496105	+	0.859279i
$26$	5.05830	−	4.39312i	0.992015	−	0.861561i
$27$	1.69131			0.325492
$28$		0			0
$29$	4.11931	+	7.13485i	0.764936	+	1.32491i	0.940280	+	0.340401i	$0.110563\pi$
$29$	4.11931	+	7.13485i	0.764936	+	1.32491i	−0.175344	+	0.984507i	$0.556104\pi$
$30$	0.420653	+	0.728592i	0.0768003	+	0.133022i
$31$	−0.640350	−	1.10912i	−0.115010	−	0.199203i	0.802774	−	0.596284i	$-0.203357\pi$
$31$	−0.640350	−	1.10912i	−0.115010	−	0.199203i	−0.917784	+	0.397080i	$0.870023\pi$
$32$	−6.87618			−1.21555
$33$	−4.79774	−	8.30993i	−0.835180	−	1.44657i
$34$	−1.56328			−0.268100
$35$		0			0
$36$	−1.64362	−	2.84683i	−0.273936	−	0.474471i
$37$	3.04485			0.500570			0.250285	−	0.968172i	$-0.419476\pi$
$37$	3.04485			0.500570			0.250285	+	0.968172i	$0.419476\pi$
$38$	1.25589	+	2.17526i	0.203732	+	0.352874i
$39$	−1.57459	−	8.12012i	−0.252137	−	1.30026i
$40$	0.100344	−	0.173802i	0.0158659	−	0.0274805i
$41$	2.69848	+	4.67390i	0.421431	+	0.729941i	0.996080	−	0.0884599i	$-0.0281945\pi$
$41$	2.69848	+	4.67390i	0.421431	+	0.729941i	−0.574648	+	0.818400i	$0.694861\pi$
$42$		0			0
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	−0.994465	−	0.105070i	$-0.966493\pi$
$43$	−2.66389	+	4.61399i	−0.406239	+	0.703627i	0.588226	+	0.808697i	$0.299827\pi$
$44$	3.03826	−	5.26242i	0.458035	−	0.793340i
$45$	0.446581			0.0665724
$46$	−7.64669			−1.12744
$47$	−5.83204	+	10.1014i	−0.850690	+	1.47344i	0.0298969	+	0.999553i	$0.490482\pi$
$47$	−5.83204	+	10.1014i	−0.850690	+	1.47344i	−0.880587	+	0.473885i	$0.842851\pi$
$48$	−5.50003	+	9.52634i	−0.793862	+	1.37501i
$49$		0			0
$50$	4.60921	+	7.98339i	0.651841	+	1.12902i
$51$	−0.965006	+	1.67144i	−0.135128	+	0.234048i
$52$	3.95472	−	3.43466i	0.548422	−	0.476302i
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	0.661103	−	0.750295i	$-0.270089\pi$
$53$	−2.32398	−	4.02525i	−0.319223	−	0.552911i	−0.980326	+	0.197384i	$0.936755\pi$
$54$	3.14272			0.427670
$55$	0.412757	+	0.714916i	0.0556562	+	0.0963993i
$56$		0			0
$57$	3.10101			0.410739
$58$	7.65434	+	13.2577i	1.00506	+	1.74082i
$59$	−6.05811			−0.788698			−0.394349	−	0.918961i	$-0.629030\pi$
$59$	−6.05811			−0.788698			−0.394349	+	0.918961i	$0.629030\pi$
$60$	0.328878	+	0.569634i	0.0424580	+	0.0735394i
$61$	−5.68285	−	9.84298i	−0.727614	−	1.26026i	−0.957889	−	0.287139i	$-0.907296\pi$
$61$	−5.68285	−	9.84298i	−0.727614	−	1.26026i	0.230275	−	0.973126i	$-0.426038\pi$
$62$	−1.18987	−	2.06092i	−0.151114	−	0.261737i
$63$		0			0
$64$	−3.18704			−0.398380
$65$	0.135465	+	0.698587i	0.0168023	+	0.0866490i
$66$	−8.91498	−	15.4412i	−1.09736	−	1.90068i
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	0.0885411	+	0.996073i	$0.471780\pi$
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	−0.906895	+	0.421357i	$0.861554\pi$
$68$	−1.22222			−0.148216
$69$	−4.72026	+	8.17574i	−0.568253	+	0.984243i
$70$		0			0
$71$	2.98520	−	5.17051i	0.354278	−	0.613627i	−0.632716	−	0.774384i	$-0.718060\pi$
$71$	2.98520	−	5.17051i	0.354278	−	0.613627i	0.986994	+	0.160757i	$0.0513934\pi$
$72$	1.15044	+	1.99263i	0.135581	+	0.234833i
$73$	1.94273	+	3.36491i	0.227380	+	0.393833i	0.957031	−	0.289986i	$-0.0936508\pi$
$73$	1.94273	+	3.36491i	0.227380	+	0.393833i	−0.729651	+	0.683820i	$0.760317\pi$
$74$	5.65782			0.657708
$75$	11.3810			1.31416
$76$	0.981887	+	1.70068i	0.112630	+	0.195081i
$77$		0			0
$78$	−2.92585	−	15.0885i	−0.331287	−	1.70844i
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	−0.388441	−	0.921474i	$-0.626986\pi$
$79$	5.36669	−	9.29537i	0.603799	−	1.04581i	0.992240	−	0.124337i	$-0.0396805\pi$
$80$	0.473177	−	0.819566i	0.0529028	−	0.0916303i
$81$	5.33411	−	9.23895i	0.592679	−	1.02655i
$82$	5.01421	+	8.68486i	0.553726	+	0.959082i
$83$	−3.07390			−0.337404			−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390			−0.337404			−0.168702	+	0.985667i	$0.553958\pi$
$84$		0			0
$85$	0.0830210	−	0.143797i	0.00900489	−	0.0155969i
$86$	−4.94994	+	8.57354i	−0.533765	+	0.924509i
$87$	18.8999			2.02629
$88$	−2.12662	+	3.68341i	−0.226698	+	0.392653i
$89$	11.9841			1.27032			0.635159	−	0.772382i	$-0.280935\pi$
$89$	11.9841			1.27032			0.635159	+	0.772382i	$0.280935\pi$
$90$	0.829819			0.0874706
$91$		0			0
$92$	−5.97840			−0.623291
$93$	−2.93801			−0.304658
$94$	−10.8369	+	18.7700i	−1.11774	+	1.93598i
$95$	−0.266785			−0.0273715
$96$	−7.88721	+	13.6611i	−0.804986	+	1.39428i
$97$	9.73637	−	16.8639i	0.988578	−	1.71227i	0.363771	−	0.931488i	$-0.381489\pi$
$97$	9.73637	−	16.8639i	0.988578	−	1.71227i	0.624807	−	0.780779i	$-0.285178\pi$
$98$		0			0
$99$	−9.46448			−0.951216
$100$	3.60361	+	6.24164i	0.360361	+	0.624164i
$101$	−8.46697	+	14.6652i	−0.842495	+	1.45924i	0.0452843	+	0.998974i	$0.485581\pi$
$101$	−8.46697	+	14.6652i	−0.842495	+	1.45924i	−0.887779	+	0.460270i	$0.847753\pi$
$102$	−1.79314	+	3.10580i	−0.177547	+	0.307520i
$103$	−3.61712	+	6.26504i	−0.356406	+	0.617313i	−0.987357	−	0.158509i	$-0.949331\pi$
$103$	−3.61712	+	6.26504i	−0.356406	+	0.617313i	0.630952	+	0.775822i	$0.282665\pi$
$104$	−2.76809	+	2.40408i	−0.271434	+	0.235739i
$105$		0			0
$106$	−4.31833	−	7.47957i	−0.419434	−	0.726480i
$107$	−9.85249			−0.952477			−0.476238	−	0.879316i	$-0.658000\pi$
$107$	−9.85249			−0.952477			−0.476238	+	0.879316i	$0.658000\pi$
$108$	2.45707			0.236431
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	0.980179	+	0.198115i	$0.0634821\pi$
$109$	6.90796	+	11.9649i	0.661662	+	1.14603i	−0.318516	+	0.947917i	$0.603185\pi$
$110$	0.766969	+	1.32843i	0.0731277	+	0.126661i
$111$	3.49255	−	6.04927i	0.331498	−	0.574171i
$112$		0			0
$113$	2.13432	−	3.69675i	0.200780	−	0.347761i	−0.748000	−	0.663699i	$-0.768986\pi$
$113$	2.13432	−	3.69675i	0.200780	−	0.347761i	0.948780	+	0.315938i	$0.102319\pi$
$114$	5.76218			0.539677
$115$	0.406092	−	0.703371i	0.0378682	−	0.0655897i
$116$	5.98437	+	10.3652i	0.555635	+	0.962388i
$117$	−7.71277	−	2.65961i	−0.713046	−	0.245881i
$118$	−11.2569			−1.03629
$119$		0			0
$120$	−0.230197	−	0.398713i	−0.0210140	−	0.0363973i
$121$	−3.24765	−	5.62509i	−0.295240	−	0.511372i
$122$	−10.5596	−	18.2898i	−0.956026	−	1.65589i
$123$	12.3810			1.11636
$124$	−0.930276	−	1.61129i	−0.0835412	−	0.144698i
$125$	−1.96593			−0.175839
$126$		0			0
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	0.910515	−	0.413477i	$-0.135686\pi$
$127$	1.09512	+	1.89680i	0.0971761	+	0.168314i	−0.813339	+	0.581791i	$0.802352\pi$
$128$	7.83033			0.692110
$129$	6.11114	+	10.5848i	0.538056	+	0.931941i
$130$	0.251715	+	1.29809i	0.0220769	+	0.113850i
$131$	1.13806	−	1.97117i	0.0994326	−	0.172222i	−0.812017	−	0.583633i	$-0.801631\pi$
$131$	1.13806	−	1.97117i	0.0994326	−	0.172222i	0.911450	+	0.411411i	$0.134964\pi$
$132$	−6.96998	−	12.0724i	−0.606659	−	1.05076i
$133$		0			0
$134$	−12.4469	+	21.5587i	−1.07525	+	1.86239i
$135$	−0.166900	+	0.289079i	−0.0143645	+	0.0248800i
$136$	0.855486			0.0733573
$137$	13.4480			1.14894			0.574469	−	0.818526i	$-0.305209\pi$
$137$	13.4480			1.14894			0.574469	+	0.818526i	$0.305209\pi$
$138$	−8.77101	+	15.1918i	−0.746638	+	1.29321i
$139$	2.02270	−	3.50342i	0.171563	−	0.297156i	−0.767403	−	0.641165i	$-0.778452\pi$
$139$	2.02270	−	3.50342i	0.171563	−	0.297156i	0.938966	+	0.344009i	$0.111785\pi$
$140$		0			0
$141$	13.3791	+	23.1733i	1.12672	+	1.95154i
$142$	5.54698	−	9.60765i	0.465492	−	0.806256i
$143$	−2.87093	−	14.8053i	−0.240079	−	1.23808i
$144$	5.42494	+	9.39628i	0.452079	+	0.783023i
$145$	−1.62599			−0.135031
$146$	3.60991	+	6.25255i	0.298758	+	0.517465i
$147$		0			0
$148$	4.42344			0.363605
$149$	−7.67596	−	13.2952i	−0.628840	−	1.08918i	−0.987785	−	0.155823i	$-0.950197\pi$
$149$	−7.67596	−	13.2952i	−0.628840	−	1.08918i	0.358945	−	0.933359i	$-0.383136\pi$
$150$	21.1477			1.72670
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	0.714203	−	0.699939i	$-0.246789\pi$
$151$	−3.06054	−	5.30101i	−0.249063	−	0.431390i	−0.963266	+	0.268548i	$0.913456\pi$
$152$	−0.687268	−	1.19038i	−0.0557448	−	0.0965528i
$153$	0.951831	+	1.64862i	0.0769510	+	0.133283i
$154$		0			0
$155$	0.252762			0.0203023
$156$	−2.28751	−	11.7966i	−0.183147	−	0.944484i
$157$	2.26834	+	3.92888i	0.181033	+	0.313559i	0.942233	−	0.334959i	$-0.108722\pi$
$157$	2.26834	+	3.92888i	0.181033	+	0.313559i	−0.761199	+	0.648518i	$0.775389\pi$
$158$	9.97217	−	17.2723i	0.793343	−	1.37411i
$159$	−10.6627			−0.845611
$160$	0.678549	−	1.17528i	0.0536440	−	0.0929142i
$161$		0			0
$162$	9.91163	−	17.1674i	0.778731	−	1.34880i
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	0.828128	−	0.560538i	$-0.189406\pi$
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	−0.899505	+	0.436911i	$0.856072\pi$
$164$	3.92025	+	6.79007i	0.306120	+	0.530215i
$165$	1.89379			0.147431
$166$	−5.71180			−0.443322
$167$	−5.35397	−	9.27336i	−0.414303	−	0.717594i	0.581052	−	0.813866i	$-0.302641\pi$
$167$	−5.35397	−	9.27336i	−0.414303	−	0.717594i	−0.995355	+	0.0962726i	$0.969308\pi$
$168$		0			0
$169$	1.82086	−	12.8718i	0.140066	−	0.990142i
$170$	0.154266	−	0.267197i	0.0118317	−	0.0204931i
$171$	1.52934	−	2.64889i	0.116951	−	0.202566i
$172$	−3.87000	+	6.70303i	−0.295085	+	0.511102i
$173$	−6.74634	−	11.6850i	−0.512915	−	0.888395i	−0.999888	−	0.0149778i	$-0.995232\pi$
$173$	−6.74634	−	11.6850i	−0.512915	−	0.888395i	0.486973	−	0.873417i	$-0.338101\pi$
$174$	35.1191			2.66237
$175$		0			0
$176$	−10.0281	+	17.3692i	−0.755898	+	1.30925i
$177$	−6.94886	+	12.0358i	−0.522308	+	0.904664i
$178$	22.2685			1.66909
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	−0.992615	−	0.121309i	$-0.961291\pi$
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	0.601364	+	0.798975i	$0.294624\pi$
$180$	0.648776			0.0483569
$181$	−12.5209			−0.930674			−0.465337	−	0.885133i	$-0.654067\pi$
$181$	−12.5209			−0.930674			−0.465337	+	0.885133i	$0.654067\pi$
$182$		0			0
$183$	−26.0737			−1.92742
$184$	4.18455			0.308489
$185$	−0.300469	+	0.520428i	−0.0220909	+	0.0382626i
$186$	−5.45930			−0.400295
$187$	−1.75948	+	3.04751i	−0.128666	+	0.222856i
$188$	−8.47256	+	14.6749i	−0.617925	+	1.07028i
$189$		0			0
$190$	−0.495729			−0.0359640
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	0.525135	−	0.851019i	$-0.324015\pi$
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	−0.999572	+	0.0292704i	$0.990682\pi$
$192$	−3.65565	+	6.33176i	−0.263823	+	0.456956i
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	−0.884160	−	0.467184i	$-0.845269\pi$
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	0.846673	+	0.532113i	$0.178602\pi$
$194$	18.0917	−	31.3358i	1.29891	−	2.24978i
$195$	1.54328	+	0.532172i	0.110517	+	0.0381096i
$196$		0			0
$197$	−0.739167	−	1.28027i	−0.0526635	−	0.0912158i	0.838492	−	0.544914i	$-0.183438\pi$
$197$	−0.739167	−	1.28027i	−0.0526635	−	0.0912158i	−0.891155	+	0.453698i	$0.850104\pi$
$198$	−17.5865			−1.24982
$199$	−14.0999			−0.999512			−0.499756	−	0.866166i	$-0.666577\pi$
$199$	−14.0999			−0.999512			−0.499756	+	0.866166i	$0.666577\pi$
$200$	−2.52233	−	4.36881i	−0.178356	−	0.308922i
$201$	15.3668	+	26.6162i	1.08389	+	1.87736i
$202$	−15.7330	+	27.2503i	−1.10697	+	1.91733i
$203$		0			0
$204$	−1.40192	+	2.42820i	−0.0981543	+	0.170008i
$205$	−1.06516			−0.0743937
$206$	−6.72120	+	11.6415i	−0.468288	+	0.811099i
$207$	4.65582	+	8.06412i	0.323602	+	0.560495i
$208$	−13.0530	+	11.3365i	−0.905064	+	0.786044i
$209$	5.65402			0.391097
$210$		0			0
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.812501	−	0.582959i	$-0.801895\pi$
$211$	−13.2346	−	22.9230i	−0.911108	−	1.57809i	−0.0986067	−	0.995126i	$-0.531439\pi$
$212$	−3.37619	−	5.84774i	−0.231878	−	0.401624i
$213$	−6.84825	−	11.8615i	−0.469234	−	0.812737i
$214$	−18.3075			−1.25148
$215$	−0.525751	−	0.910628i	−0.0358559	−	0.0621043i
$216$	−1.71981			−0.117019
$217$		0			0
$218$	12.8361	+	22.2328i	0.869370	+	1.50579i
$219$	8.91352			0.602320
$220$	0.599638	+	1.03860i	0.0404276	+	0.0700227i
$221$	−2.29021	+	1.98904i	−0.154056	+	0.133797i
$222$	6.48971	−	11.2405i	0.435561	−	0.754414i
$223$	−0.364024	−	0.630508i	−0.0243769	−	0.0422219i	0.853580	−	0.520962i	$-0.174427\pi$
$223$	−0.364024	−	0.630508i	−0.0243769	−	0.0422219i	−0.877956	+	0.478740i	$0.841093\pi$
$224$		0			0
$225$	5.61280	−	9.72165i	0.374187	−	0.648110i
$226$	3.96591	−	6.86916i	0.263808	−	0.456929i
$227$	2.85195			0.189291			0.0946454	−	0.995511i	$-0.469828\pi$
$227$	2.85195			0.189291			0.0946454	+	0.995511i	$0.469828\pi$
$228$	4.50503			0.298353
$229$	1.58676	−	2.74835i	0.104856	−	0.181616i	−0.808823	−	0.588052i	$-0.799895\pi$
$229$	1.58676	−	2.74835i	0.104856	−	0.181616i	0.913679	+	0.406436i	$0.133228\pi$
$230$	0.754584	−	1.30698i	0.0497558	−	0.0861795i
$231$		0			0
$232$	−4.18874	−	7.25511i	−0.275004	−	0.476321i
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	−0.997625	−	0.0688769i	$-0.978058\pi$
$233$	−6.70354	+	11.6109i	−0.439163	+	0.760653i	0.558462	+	0.829530i	$0.311392\pi$
$234$	−14.3316	−	4.94198i	−0.936884	−	0.323068i
$235$	−1.15102	−	1.99363i	−0.0750845	−	0.130050i
$236$	−8.80099			−0.572896
$237$	−12.3115	−	21.3242i	−0.799721	−	1.38516i
$238$		0			0
$239$	−15.5538			−1.00609			−0.503046	−	0.864259i	$-0.667788\pi$
$239$	−15.5538			−1.00609			−0.503046	+	0.864259i	$0.667788\pi$
$240$	−1.08550	−	1.88014i	−0.0700687	−	0.121363i
$241$	7.57574			0.487996			0.243998	−	0.969776i	$-0.421541\pi$
$241$	7.57574			0.487996			0.243998	+	0.969776i	$0.421541\pi$
$242$	−6.03465	−	10.4523i	−0.387922	−	0.671900i
$243$	−9.69985	−	16.8006i	−0.622245	−	1.07776i
$244$	−8.25583	−	14.2995i	−0.528525	−	0.915433i
$245$		0			0
$246$	23.0059			1.46680
$247$	4.60756	+	1.58883i	0.293172	+	0.101095i
$248$	0.651143	+	1.12781i	0.0413476	+	0.0716162i
$249$	−3.52587	+	6.10698i	−0.223443	+	0.387014i
$250$	−3.65302			−0.231038
$251$	0.637382	−	1.10398i	0.0402312	−	0.0696825i	−0.845209	−	0.534436i	$-0.820524\pi$
$251$	0.637382	−	1.10398i	0.0402312	−	0.0696825i	0.885440	+	0.464754i	$0.153857\pi$
$252$		0			0
$253$	−8.60638	+	14.9067i	−0.541079	+	0.937176i
$254$	2.03491	+	3.52456i	0.127682	+	0.221151i
$255$	−0.190456	−	0.329879i	−0.0119268	−	0.0206578i
$256$	20.9241			1.30776
$257$	8.48019			0.528980			0.264490	−	0.964388i	$-0.414796\pi$
$257$	8.48019			0.528980			0.264490	+	0.964388i	$0.414796\pi$
$258$	11.3555	+	19.6683i	0.706962	+	1.22449i
$259$		0			0
$260$	0.196798	+	1.01488i	0.0122049	+	0.0629402i
$261$	9.32095	−	16.1444i	0.576952	−	0.999311i
$262$	2.11470	−	3.66276i	0.130646	−	0.226286i
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	−0.993009	−	0.118038i	$-0.962339\pi$
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	0.598729	+	0.800952i	$0.295673\pi$
$264$	4.87861	+	8.45000i	0.300258	+	0.520062i
$265$	0.917333			0.0563513
$266$		0			0
$267$	13.7462	−	23.8092i	0.841255	−	1.45710i
$268$	−9.73135	+	16.8552i	−0.594437	+	1.02959i
$269$	4.71172			0.287278			0.143639	−	0.989630i	$-0.454120\pi$
$269$	4.71172			0.287278			0.143639	+	0.989630i	$0.454120\pi$
$270$	−0.310127	+	0.537156i	−0.0188737	+	0.0326903i
$271$	18.0112			1.09410			0.547052	−	0.837098i	$-0.315750\pi$
$271$	18.0112			1.09410			0.547052	+	0.837098i	$0.315750\pi$
$272$	4.03407			0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	20.7508			1.25132
$276$	−6.85742	+	11.8774i	−0.412768	+	0.714936i
$277$	−26.1209			−1.56945			−0.784725	−	0.619844i	$-0.787196\pi$
$277$	−26.1209			−1.56945			−0.784725	+	0.619844i	$0.787196\pi$
$278$	3.75850	−	6.50991i	0.225420	−	0.390439i
$279$	−1.44895	+	2.50965i	−0.0867463	+	0.150249i
$280$		0			0
$281$	−3.66197			−0.218455			−0.109227	−	0.994017i	$-0.534838\pi$
$281$	−3.66197			−0.218455			−0.109227	+	0.994017i	$0.534838\pi$
$282$	24.8605	+	43.0596i	1.48042	+	2.56416i
$283$	3.82263	−	6.62099i	0.227232	−	0.393577i	−0.729755	−	0.683709i	$-0.760366\pi$
$283$	3.82263	−	6.62099i	0.227232	−	0.393577i	0.956987	+	0.290132i	$0.0936991\pi$
$284$	4.33678	−	7.51153i	0.257341	−	0.445727i
$285$	−0.306011	+	0.530027i	−0.0181265	+	0.0313961i
$286$	−5.33465	−	27.5106i	−0.315445	−	1.62674i
$287$		0			0
$288$	7.77953	+	13.4745i	0.458413	+	0.793995i
$289$	−16.2922			−0.958365
$290$	−3.02135			−0.177420
$291$	−22.3359	−	38.6869i	−1.30935	−	2.26787i
$292$	2.82233	+	4.88842i	0.165164	+	0.286073i
$293$	−8.57670	+	14.8553i	−0.501056	+	0.867855i	0.498943	+	0.866635i	$0.333722\pi$
$293$	−8.57670	+	14.8553i	−0.501056	+	0.867855i	−0.999999	+	0.00122001i	$0.999612\pi$
$294$		0			0
$295$	0.597821	−	1.03546i	0.0348065	−	0.0602866i
$296$	−3.09617			−0.179961
$297$	3.53715	−	6.12652i	0.205246	−	0.355497i
$298$	−14.2632	−	24.7045i	−0.826244	−	1.43110i
$299$	−11.2024	+	9.72925i	−0.647852	+	0.562657i
$300$	16.5339			0.954583
$301$		0			0
$302$	−5.68698	−	9.85014i	−0.327249	−	0.566812i
$303$	19.4238	+	33.6430i	1.11587	+	1.93274i
$304$	−3.24083	−	5.61328i	−0.185874	−	0.321944i
$305$	2.24316			0.128443
$306$	1.76866	+	3.06340i	0.101107	+	0.175123i
$307$	28.0696			1.60201			0.801007	−	0.598655i	$-0.204298\pi$
$307$	28.0696			1.60201			0.801007	+	0.598655i	$0.204298\pi$
$308$		0			0
$309$	8.29793	+	14.3724i	0.472052	+	0.817619i
$310$	0.469672			0.0266756
$311$	−11.7670	−	20.3811i	−0.667248	−	1.15571i	−0.978671	−	0.205436i	$-0.934139\pi$
$311$	−11.7670	−	20.3811i	−0.667248	−	1.15571i	0.311423	−	0.950271i	$-0.399194\pi$
$312$	1.60113	+	8.25699i	0.0906464	+	0.467460i
$313$	−1.67430	+	2.89997i	−0.0946370	+	0.163916i	−0.909457	−	0.415798i	$-0.863502\pi$
$313$	−1.67430	+	2.89997i	−0.0946370	+	0.163916i	0.814820	+	0.579714i	$0.196836\pi$
$314$	4.21494	+	7.30050i	0.237863	+	0.411991i
$315$		0			0
$316$	7.79652	−	13.5040i	0.438588	−	0.759658i
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	−0.745544	−	0.666456i	$-0.767810\pi$
$317$	3.63917	−	6.30323i	0.204396	−	0.354025i	0.949940	+	0.312432i	$0.101144\pi$
$318$	−19.8131			−1.11106
$319$	34.4600			1.92939
$320$	0.314501	−	0.544732i	0.0175811	−	0.0304514i
$321$	−11.3011	+	19.5742i	−0.630768	+	1.09252i
$322$		0			0
$323$	−0.568618	−	0.984875i	−0.0316388	−	0.0547999i
$324$	7.74919	−	13.4220i	0.430511	−	0.745666i
$325$	16.9102	+	5.83116i	0.938007	+	0.323455i
$326$	−1.69329	−	2.93286i	−0.0937826	−	0.162436i
$327$	31.6946			1.75272
$328$	−2.74396	−	4.75268i	−0.151510	−	0.262423i
$329$		0			0
$330$	3.51896			0.193712
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	0.992927	−	0.118728i	$-0.0378818\pi$
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	−0.599285	+	0.800536i	$0.704548\pi$
$332$	−4.46564			−0.245084
$333$	−3.44486	−	5.96668i	−0.188777	−	0.326972i
$334$	−9.94855	−	17.2314i	−0.544360	−	0.942860i
$335$	−1.32203	−	2.28983i	−0.0722304	−	0.125107i
$336$		0			0
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	3.38344	−	23.9180i	0.184035	−	1.30097i
$339$	−4.89627	−	8.48060i	−0.265929	−	0.460603i
$340$	0.120610	−	0.208902i	0.00654098	−	0.0113293i
$341$	−5.35683			−0.290089
$342$	2.84175	−	4.92206i	0.153664	−	0.266155i
$343$		0			0
$344$	2.70879	−	4.69176i	0.146048	−	0.252963i
$345$	−0.931602	−	1.61358i	−0.0501558	−	0.0868723i
$346$	−12.5358	−	21.7126i	−0.673928	−	1.16728i
$347$	−7.70278			−0.413507			−0.206753	−	0.978393i	$-0.566290\pi$
$347$	−7.70278			−0.413507			−0.206753	+	0.978393i	$0.566290\pi$
$348$	27.4571			1.47186
$349$	11.1850	+	19.3730i	0.598721	+	1.03702i	0.993010	+	0.118029i	$0.0376575\pi$
$349$	11.1850	+	19.3730i	0.598721	+	1.03702i	−0.394289	+	0.918986i	$0.629009\pi$
$350$		0			0
$351$	4.60409	−	3.99863i	0.245748	−	0.213431i
$352$	−14.3806	+	24.9080i	−0.766490	+	1.32760i
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	0.401450	+	0.915881i	$0.368506\pi$
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	−0.993901	+	0.110275i	$0.964827\pi$
$354$	−12.9121	+	22.3644i	−0.686270	+	1.18865i
$355$	0.589165	+	1.02046i	0.0312697	+	0.0541606i
$356$	17.4101			0.922735
$357$		0			0
$358$	−9.72670	+	16.8471i	−0.514072	+	0.890399i
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	−0.827332	−	0.561713i	$-0.810142\pi$
$359$	1.37921	−	2.38887i	0.0727920	−	0.126079i	0.900124	+	0.435634i	$0.143476\pi$
$360$	−0.454108			−0.0239336
$361$	8.58638	−	14.8721i	0.451915	−	0.782740i
$362$	−23.2659			−1.22283
$363$	−14.9006			−0.782081
$364$		0			0
$365$	−0.766844			−0.0401385
$366$	−48.4491			−2.53248
$367$	−7.07485	+	12.2540i	−0.369304	+	0.639654i	−0.989457	−	0.144827i	$-0.953737\pi$
$367$	−7.07485	+	12.2540i	−0.369304	+	0.639654i	0.620153	+	0.784481i	$0.287071\pi$
$368$	19.7324			1.02862
$369$	6.10597	−	10.5759i	0.317864	−	0.550557i
$370$	−0.558320	+	0.967039i	−0.0290257	+	0.0502740i
$371$		0			0
$372$	−4.26823			−0.221298
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	0.923890	−	0.382657i	$-0.124991\pi$
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	−0.793336	+	0.608784i	$0.791658\pi$
$374$	−3.26940	+	5.66276i	−0.169056	+	0.292814i
$375$	−2.25499	+	3.90576i	−0.116447	+	0.201693i
$376$	5.93034	−	10.2716i	0.305834	−	0.529720i
$377$	28.0820	+	9.68358i	1.44630	+	0.498730i
$378$		0			0
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	0.933289	−	0.359127i	$-0.116925\pi$
$379$	3.02982	+	5.24780i	0.155631	+	0.269561i	−0.777657	+	0.628688i	$0.783592\pi$
$380$	−0.387575			−0.0198822
$381$	5.02456			0.257416
$382$	−12.1837	−	21.1028i	−0.623371	−	1.07971i
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	0.802168	−	0.597098i	$-0.203680\pi$
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	−0.918186	+	0.396149i	$0.870346\pi$
$384$	8.98165	−	15.5567i	0.458343	−	0.793873i
$385$		0			0
$386$	−0.967705	+	1.67611i	−0.0492549	+	0.0853120i
$387$	12.0554			0.612811
$388$	14.1446	−	24.4992i	0.718085	−	1.24376i
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	0.803216	−	0.595688i	$-0.203121\pi$
$389$	−2.25383	−	3.90374i	−0.114273	−	0.197927i	−0.917489	+	0.397761i	$0.869787\pi$
$390$	2.86766	+	0.988862i	0.145210	+	0.0500730i
$391$	3.46213			0.175088
$392$		0			0
$393$	−2.61078	−	4.52201i	−0.131697	−	0.228105i
$394$	−1.37349	−	2.37896i	−0.0691955	−	0.119850i
$395$	1.05918	+	1.83456i	0.0532932	+	0.0923065i
$396$	−13.7496			−0.690945
$397$	2.00174	+	3.46712i	0.100465	+	0.174010i	0.911876	−	0.410465i	$-0.134634\pi$
$397$	2.00174	+	3.46712i	0.100465	+	0.174010i	−0.811412	+	0.584475i	$0.801300\pi$
$398$	−26.1998			−1.31328
$399$		0			0
$400$	−11.8941	−	20.6012i	−0.594706	−	1.03006i
$401$	12.6135			0.629887			0.314944	−	0.949110i	$-0.398014\pi$
$401$	12.6135			0.629887			0.314944	+	0.949110i	$0.398014\pi$
$402$	28.5541	+	49.4571i	1.42415	+	2.46670i
$403$	−4.36537	−	1.50532i	−0.217455	−	0.0749853i
$404$	−12.3005	+	21.3051i	−0.611972	+	1.05997i
$405$	1.05275	+	1.82342i	0.0523116	+	0.0906064i
$406$		0			0
$407$	6.36790	−	11.0295i	0.315645	−	0.546713i
$408$	0.981272	−	1.69961i	0.0485802	−	0.0841434i
$409$	−20.6952			−1.02331			−0.511657	−	0.859190i	$-0.670968\pi$
$409$	−20.6952			−1.02331			−0.511657	+	0.859190i	$0.670968\pi$
$410$	−1.97923			−0.0977472
$411$	15.4253	−	26.7174i	0.760873	−	1.31787i
$412$	−5.25482	+	9.10162i	−0.258886	+	0.448404i
$413$		0			0
$414$	8.65126	+	14.9844i	0.425186	+	0.736444i
$415$	0.303336	−	0.525393i	0.0148902	−	0.0257905i
$416$	−18.7184	+	16.2569i	−0.917746	+	0.797058i
$417$	−4.64021	−	8.03708i	−0.227232	−	0.393577i
$418$	10.5061			0.513869
$419$	−10.9088	−	18.8945i	−0.532928	−	0.923058i	−0.999261	−	0.0384484i	$-0.987758\pi$
$419$	−10.9088	−	18.8945i	−0.532928	−	0.923058i	0.466333	−	0.884609i	$-0.345575\pi$
$420$		0			0
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	−24.5920	−	42.5947i	−1.19712	−	2.07348i
$423$	26.3928			1.28326
$424$	2.36315	+	4.09310i	0.114765	+	0.198779i
$425$	−2.08688	−	3.61458i	−0.101228	−	0.175333i
$426$	−12.7251	−	22.0406i	−0.616535	−	1.06787i
$427$		0			0
$428$	−14.3133			−0.691861
$429$	−32.7070	−	11.2784i	−1.57911	−	0.544528i
$430$	−0.976930	−	1.69209i	−0.0471118	−	0.0816000i
$431$	−10.2138	+	17.6908i	−0.491980	+	0.852134i	−0.999957	−	0.00923613i	$-0.997060\pi$
$431$	−10.2138	+	17.6908i	−0.491980	+	0.852134i	0.507977	+	0.861370i	$0.330393\pi$
$432$	−8.10983			−0.390184
$433$	13.1743	−	22.8186i	0.633117	−	1.09659i	−0.353794	−	0.935323i	$-0.615109\pi$
$433$	13.1743	−	22.8186i	0.633117	−	1.09659i	0.986911	−	0.161267i	$-0.0515581\pi$
$434$		0			0
$435$	−1.86507	+	3.23039i	−0.0894231	+	0.154885i
$436$	10.0356	+	17.3822i	0.480619	+	0.832457i
$437$	−2.78136	−	4.81745i	−0.133050	−	0.230450i
$438$	16.5628			0.791399
$439$	−25.1310			−1.19944			−0.599720	−	0.800210i	$-0.704721\pi$
$439$	−25.1310			−1.19944			−0.599720	+	0.800210i	$0.704721\pi$
$440$	−0.419714	−	0.726967i	−0.0200091	−	0.0346568i
$441$		0			0
$442$	−4.25558	+	3.69595i	−0.202417	+	0.175799i
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	−0.997685	−	0.0679994i	$-0.978338\pi$
$443$	−9.25995	+	16.0387i	−0.439953	+	0.762022i	0.557732	+	0.830021i	$0.311672\pi$
$444$	5.07384	−	8.78815i	0.240794	−	0.417067i
$445$	−1.18261	+	2.04834i	−0.0560611	+	0.0971006i
$446$	−0.676415	−	1.17159i	−0.0320292	−	0.0554762i
$447$	−35.2184			−1.66577
$448$		0			0
$449$	−5.82155	+	10.0832i	−0.274736	+	0.475856i	−0.970068	−	0.242832i	$-0.921924\pi$
$449$	−5.82155	+	10.0832i	−0.274736	+	0.475856i	0.695333	+	0.718688i	$0.255257\pi$
$450$	10.4295	−	18.0644i	0.491651	−	0.851564i
$451$	22.5740			1.06297
$452$	3.10066	−	5.37050i	0.145843	−	0.252607i
$453$	−14.0422			−0.659759
$454$	5.29939			0.248713
$455$		0			0
$456$	−3.15328			−0.147666
$457$	20.5184			0.959812			0.479906	−	0.877320i	$-0.340671\pi$
$457$	20.5184			0.959812			0.479906	+	0.877320i	$0.340671\pi$
$458$	2.94845	−	5.10687i	0.137772	−	0.238629i
$459$	−1.42291			−0.0664156
$460$	0.589955	−	1.02183i	0.0275068	−	0.0476431i
$461$	1.02038	−	1.76734i	0.0475236	−	0.0823134i	−0.841285	−	0.540592i	$-0.818200\pi$
$461$	1.02038	−	1.76734i	0.0475236	−	0.0823134i	0.888809	+	0.458278i	$0.151534\pi$
$462$		0			0
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	−19.7521	−	34.2116i	−0.916968	−	1.58824i
$465$	0.289926	−	0.502167i	0.0134450	−	0.0232874i
$466$	−12.4563	+	21.5749i	−0.577025	+	0.999436i
$467$	−6.46371	+	11.1955i	−0.299105	+	0.518065i	−0.975931	−	0.218078i	$-0.930021\pi$
$467$	−6.46371	+	11.1955i	−0.299105	+	0.518065i	0.676827	+	0.736142i	$0.263355\pi$
$468$	−11.2048	−	3.86378i	−0.517943	−	0.178603i
$469$		0			0
$470$	−2.13879	−	3.70449i	−0.0986549	−	0.170875i
$471$	10.4075			0.479550
$472$	6.16022			0.283547
$473$	11.1423	+	19.2991i	0.512326	+	0.887374i
$474$	−22.8768	−	39.6238i	−1.05077	−	1.81998i
$475$	−3.35305	+	5.80766i	−0.153849	+	0.266474i
$476$		0			0
$477$	−5.25858	+	9.10814i	−0.240774	+	0.417033i
$478$	−28.9015			−1.32192
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	−0.0576873	−	0.998335i	$-0.518373\pi$
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	0.893427	−	0.449209i	$-0.148294\pi$
$480$	−1.55664	−	2.69618i	−0.0710505	−	0.123063i
$481$	8.28872	−	7.19872i	0.377933	−	0.328233i
$482$	14.0769			0.641187
$483$		0			0
$484$	−4.71806	−	8.17191i	−0.214457	−	0.371451i
$485$	1.92159	+	3.32829i	0.0872550	+	0.151130i
$486$	−18.0239	−	31.2183i	−0.817580	−	1.41609i
$487$	36.7496			1.66528			0.832642	−	0.553812i	$-0.186827\pi$
$487$	36.7496			1.66528			0.832642	+	0.553812i	$0.186827\pi$
$488$	5.77864	+	10.0089i	0.261587	+	0.453081i
$489$	−4.18103			−0.189073
$490$		0			0
$491$	4.09899	+	7.09965i	0.184985	+	0.320403i	0.943571	−	0.331169i	$-0.107443\pi$
$491$	4.09899	+	7.09965i	0.184985	+	0.320403i	−0.758587	+	0.651572i	$0.774110\pi$
$492$	17.9866			0.810900
$493$	−3.46560	−	6.00259i	−0.156083	−	0.270343i
$494$	8.56159	+	2.95231i	0.385204	+	0.132831i
$495$	0.933965	−	1.61768i	0.0419786	−	0.0727091i
$496$	3.07048	+	5.31823i	0.137869	+	0.238795i
$497$		0			0
$498$	−6.55163	+	11.3478i	−0.293585	+	0.508505i
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.267211	−	0.963638i	$-0.413898\pi$
$499$	21.6266	−	37.4584i	0.968141	−	1.67687i	0.700929	−	0.713231i	$-0.252769\pi$
$500$	−2.85604			−0.127726
$501$	−24.5648			−1.09747
$502$	1.18436	−	2.05137i	0.0528605	−	0.0915571i
$503$	0.00909609	−	0.0157549i	0.000405575	−	0.000702476i	−0.865823	−	0.500351i	$-0.833204\pi$
$503$	0.00909609	−	0.0157549i	0.000405575	−	0.000702476i	0.866228	+	0.499649i	$0.166538\pi$
$504$		0			0
$505$	−1.67106	−	2.89436i	−0.0743612	−	0.128797i
$506$	−15.9920	+	27.6990i	−0.710933	+	1.23137i
$507$	−23.4842	−	18.3820i	−1.04297	−	0.816372i
$508$	1.59095	+	2.75560i	0.0705869	+	0.122260i
$509$	−43.1006			−1.91040			−0.955200	−	0.295960i	$-0.904361\pi$
$509$	−43.1006			−1.91040			−0.955200	+	0.295960i	$0.904361\pi$
$510$	−0.353897	−	0.612968i	−0.0156708	−	0.0271427i
$511$		0			0
$512$	23.2197			1.02617
$513$	1.14311	+	1.97993i	0.0504697	+	0.0874161i
$514$	15.7576			0.695036
$515$	−0.713884	−	1.23648i	−0.0314575	−	0.0544859i
$516$	8.87804	+	15.3772i	0.390834	+	0.676944i
$517$	24.3939	+	42.2514i	1.07284	+	1.85822i
$518$		0			0
$519$	−30.9531			−1.35869
$520$	−0.137748	−	0.710362i	−0.00604065	−	0.0311514i
$521$	10.4770	+	18.1467i	0.459006	+	0.795022i	0.998909	−	0.0467056i	$-0.0148723\pi$
$521$	10.4770	+	18.1467i	0.459006	+	0.795022i	−0.539903	+	0.841727i	$0.681539\pi$
$522$	17.3198	−	29.9988i	0.758068	−	1.31301i
$523$	34.7403			1.51909			0.759543	−	0.650457i	$-0.225423\pi$
$523$	34.7403			1.51909			0.759543	+	0.650457i	$0.225423\pi$
$524$	1.65333	−	2.86365i	0.0722260	−	0.125099i
$525$		0			0
$526$	−11.8814	+	20.5791i	−0.518052	+	0.897292i
$527$	0.538730	+	0.933107i	0.0234674	+	0.0406468i
$528$	23.0052	+	39.8462i	1.00117	+	1.73408i
$529$	−6.06520			−0.263704
$530$	1.70455			0.0740410
$531$	6.85398	+	11.8714i	0.297438	+	0.515177i
$532$		0			0
$533$	18.3960	+	6.34352i	0.796819	+	0.274769i
$534$	25.5427	−	44.2413i	1.10534	−	1.91451i
$535$	0.972255	−	1.68400i	0.0420343	−	0.0728055i
$536$	6.81142	−	11.7977i	0.294209	−	0.509584i
$537$	12.0085	+	20.7993i	0.518205	+	0.897557i
$538$	8.75513			0.377460
$539$		0			0
$540$	−0.242466	+	0.419964i	−0.0104341	+	0.0180724i
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	−0.828393	−	0.560148i	$-0.810744\pi$
$541$	1.64923	−	2.85655i	0.0709059	−	0.122813i	0.899299	+	0.437335i	$0.144078\pi$
$542$	33.4678			1.43756
$543$	−14.3619	+	24.8756i	−0.616330	+	1.06752i
$544$	5.78497			0.248029
$545$	−2.72674			−0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	19.5367			0.834567
$549$	−12.8589	+	22.2722i	−0.548803	+	0.950554i
$550$	38.5583			1.64413
$551$	−5.56828	+	9.64455i	−0.237217	+	0.410871i
$552$	4.79983	−	8.31354i	0.204294	−	0.353848i
$553$		0			0
$554$	−48.5368			−2.06213
$555$	0.689297	+	1.19390i	0.0292590	+	0.0506781i
$556$	2.93850	−	5.08963i	0.124620	−	0.215848i
$557$	7.14329	−	12.3725i	0.302671	−	0.524241i	−0.674069	−	0.738668i	$-0.735455\pi$
$557$	7.14329	−	12.3725i	0.302671	−	0.524241i	0.976740	+	0.214427i	$0.0687884\pi$
$558$	−2.69238	+	4.66334i	−0.113978	+	0.197415i
$559$	3.65686	+	18.8583i	0.154669	+	0.797621i
$560$		0			0
$561$	4.03637	+	6.99119i	0.170416	+	0.295168i
$562$	−6.80453			−0.287032
$563$	−6.78784			−0.286073			−0.143037	−	0.989717i	$-0.545687\pi$
$563$	−6.78784			−0.286073			−0.143037	+	0.989717i	$0.545687\pi$
$564$	19.4366	+	33.6652i	0.818430	+	1.41756i
$565$	0.421234	+	0.729599i	0.0177215	+	0.0306945i
$566$	7.10307	−	12.3029i	0.298564	−	0.517128i
$567$		0			0
$568$	−3.03552	+	5.25767i	−0.127367	+	0.220607i
$569$	−17.3212			−0.726143			−0.363072	−	0.931761i	$-0.618272\pi$
$569$	−17.3212			−0.726143			−0.363072	+	0.931761i	$0.618272\pi$
$570$	−0.568618	+	0.984875i	−0.0238168	+	0.0412519i
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	0.969440	−	0.245328i	$-0.0788957\pi$
$571$	6.50581	+	11.2684i	0.272260	+	0.471568i	−0.697180	+	0.716896i	$0.745562\pi$
$572$	−4.17078	−	21.5086i	−0.174389	−	0.899318i
$573$	−30.0837			−1.25676
$574$		0			0
$575$	−10.2078	−	17.6805i	−0.425696	−	0.737327i
$576$	3.60574	+	6.24532i	0.150239	+	0.260222i
$577$	−0.365767	−	0.633528i	−0.0152271	−	0.0263741i	0.858311	−	0.513129i	$-0.171514\pi$
$577$	−0.365767	−	0.633528i	−0.0152271	−	0.0263741i	−0.873539	+	0.486755i	$0.838180\pi$
$578$	−30.2735			−1.25921
$579$	1.19472	+	2.06931i	0.0496508	+	0.0859978i
$580$	−2.36218			−0.0980842
$581$		0			0
$582$	−41.5037	−	71.8865i	−1.72038	−	2.97979i
$583$	−19.4412			−0.805173
$584$	−1.97548	−	3.42163i	−0.0817459	−	0.141588i
$585$	1.21569	−	1.05582i	0.0502625	−	0.0436527i
$586$	−15.9369	+	27.6035i	−0.658347	+	1.14029i
$587$	−4.26142	−	7.38099i	−0.175888	−	0.304646i	0.764581	−	0.644528i	$-0.222946\pi$
$587$	−4.26142	−	7.38099i	−0.175888	−	0.304646i	−0.940468	+	0.339882i	$0.889613\pi$
$588$		0			0
$589$	0.865594	−	1.49925i	0.0356662	−	0.0617756i
$590$	1.11085	−	1.92404i	0.0457329	−	0.0792117i
$591$	−3.39140			−0.139503
$592$	−14.6001			−0.600059
$593$	−15.6547	+	27.1147i	−0.642860	+	1.11347i	0.341932	+	0.939725i	$0.388919\pi$
$593$	−15.6547	+	27.1147i	−0.642860	+	1.11347i	−0.984791	+	0.173741i	$0.944415\pi$
$594$	6.57259	−	11.3841i	0.269677	−	0.467093i
$595$		0			0
$596$	−11.1514	−	19.3147i	−0.456777	−	0.791161i
$597$	−16.1730	+	28.0125i	−0.661917	+	1.14647i
$598$	−20.8159	+	18.0785i	−0.851225	+	0.739285i
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	0.873587	−	0.486668i	$-0.161788\pi$
$599$	0.375116	+	0.649720i	0.0153268	+	0.0265468i	−0.858260	+	0.513215i	$0.828454\pi$
$600$	−11.5728			−0.472458
$601$	−4.77652	−	8.27318i	−0.194838	−	0.337470i	0.752009	−	0.659153i	$-0.229085\pi$
$601$	−4.77652	−	8.27318i	−0.194838	−	0.337470i	−0.946848	+	0.321683i	$0.895752\pi$
$602$		0			0
$603$	30.3141			1.23449
$604$	−4.44624	−	7.70111i	−0.180915	−	0.313354i
$605$	1.28193			0.0521177
$606$	36.0925	+	62.5141i	1.46616	+	2.53946i
$607$	11.1197	+	19.2599i	0.451336	+	0.781737i	0.998469	−	0.0553087i	$-0.0176143\pi$
$607$	11.1197	+	19.2599i	0.451336	+	0.781737i	−0.547133	+	0.837045i	$0.684281\pi$
$608$	−4.64745	−	8.04961i	−0.188479	−	0.326455i
$609$		0			0
$610$	4.16815			0.168764
$611$	8.00594	+	41.2863i	0.323886	+	1.67027i
$612$	1.38278	+	2.39505i	0.0558957	+	0.0968143i
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	−0.770228	−	0.637769i	$-0.779857\pi$
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	0.937438	+	0.348152i	$0.113191\pi$
$614$	52.1578			2.10492
$615$	−1.22177	+	2.11617i	−0.0492665	+	0.0853321i
$616$		0			0
$617$	−10.1656	+	17.6073i	−0.409252	+	0.708845i	−0.994806	−	0.101789i	$-0.967543\pi$
$617$	−10.1656	+	17.6073i	−0.409252	+	0.708845i	0.585554	+	0.810633i	$0.300877\pi$
$618$	15.4189	+	26.7063i	0.620238	+	1.07428i
$619$	2.67049	+	4.62542i	0.107336	+	0.185911i	0.914690	−	0.404156i	$-0.132435\pi$
$619$	2.67049	+	4.62542i	0.107336	+	0.185911i	−0.807354	+	0.590067i	$0.799101\pi$
$620$	0.367203			0.0147472
$621$	−6.96005			−0.279297
$622$	−21.8651	−	37.8714i	−0.876709	−	1.51850i
$623$		0			0
$624$	7.55018	+	38.9360i	0.302249	+	1.55869i
$625$	−12.2086	+	21.1459i	−0.488345	+	0.845838i
$626$	−3.11112	+	5.38862i	−0.124345	+	0.215372i
$627$	6.48536	−	11.2330i	0.259000	−	0.448601i
$628$	3.29536	+	5.70773i	0.131499	+	0.227763i
$629$	−2.56165			−0.102140
$630$		0			0
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	−0.923179	−	0.384369i	$-0.874419\pi$
$631$	−3.23331	+	5.60026i	−0.128716	+	0.222943i	0.794463	+	0.607312i	$0.207752\pi$
$632$	−5.45714	+	9.45205i	−0.217074	+	0.375982i
$633$	−60.7222			−2.41349
$634$	6.76217	−	11.7124i	0.268560	−	0.465160i
$635$	−0.432271			−0.0171541
$636$	−15.4904			−0.614236
$637$		0			0
$638$	64.0322			2.53506
$639$	−13.5095			−0.534428
$640$	−0.772706	+	1.33837i	−0.0305439	+	0.0529035i
$641$	23.3289			0.921434			0.460717	−	0.887547i	$-0.347592\pi$
$641$	23.3289			0.921434			0.460717	+	0.887547i	$0.347592\pi$
$642$	−20.9993	+	36.3719i	−0.828778	+	1.43549i
$643$	−1.79439	+	3.10797i	−0.0707637	+	0.122566i	−0.899236	−	0.437463i	$-0.855877\pi$
$643$	−1.79439	+	3.10797i	−0.0707637	+	0.122566i	0.828472	+	0.560030i	$0.189210\pi$
$644$		0			0
$645$	−2.41222			−0.0949810
$646$	−1.05658	−	1.83006i	−0.0415707	−	0.0720026i
$647$	−19.8262	+	34.3400i	−0.779448	+	1.35004i	0.152812	+	0.988255i	$0.451167\pi$
$647$	−19.8262	+	34.3400i	−0.779448	+	1.35004i	−0.932260	+	0.361788i	$0.882166\pi$
$648$	−5.42402	+	9.39467i	−0.213076	+	0.369058i
$649$	−12.6697	+	21.9446i	−0.497331	+	0.861402i
$650$	31.4218	+	10.8352i	1.23246	+	0.424993i
$651$		0			0
$652$	−1.32386	−	2.29299i	−0.0518464	−	0.0898005i
$653$	18.1355			0.709699			0.354849	−	0.934923i	$-0.384532\pi$
$653$	18.1355			0.709699			0.354849	+	0.934923i	$0.384532\pi$
$654$	58.8938			2.30293
$655$	0.224610	+	0.389035i	0.00877623	+	0.0152009i
$656$	−12.9392	−	22.4114i	−0.505192	−	0.875017i
$657$	4.39592	−	7.61395i	0.171501	−	0.297048i
$658$		0			0
$659$	−6.74052	+	11.6749i	−0.262573	+	0.454791i	−0.966925	−	0.255061i	$-0.917905\pi$
$659$	−6.74052	+	11.6749i	−0.262573	+	0.454791i	0.704352	+	0.709851i	$0.251238\pi$
$660$	2.75122			0.107091
$661$	5.15611	−	8.93064i	0.200549	−	0.347362i	−0.748156	−	0.663523i	$-0.769061\pi$
$661$	5.15611	−	8.93064i	0.200549	−	0.347362i	0.948706	+	0.316161i	$0.102394\pi$
$662$	13.3076	+	23.0494i	0.517213	+	0.895839i
$663$	1.32471	+	6.83150i	0.0514476	+	0.265314i
$664$	3.12571			0.121301
$665$		0			0
$666$	−6.40111	−	11.0870i	−0.248038	−	0.429614i
$667$	−16.9517	−	29.3613i	−0.656374	−	1.13687i
$668$	−7.77805	−	13.4720i	−0.300942	−	0.521247i
$669$	−1.67019			−0.0645733
$670$	−2.45655	−	4.25487i	−0.0949049	−	0.164380i
$671$	−47.5397			−1.83525
$672$		0			0
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	0.941163	−	0.337953i	$-0.109734\pi$
$673$	4.61528	+	7.99390i	0.177906	+	0.308142i	−0.763257	+	0.646095i	$0.776401\pi$
$674$	31.9237			1.22965
$675$	4.19533	+	7.26652i	0.161478	+	0.279689i
$676$	2.64527	−	18.6997i	0.101741	−	0.719221i
$677$	−10.5467	+	18.2674i	−0.405343	+	0.702075i	−0.994361	−	0.106045i	$-0.966181\pi$
$677$	−10.5467	+	18.2674i	−0.405343	+	0.702075i	0.589018	+	0.808120i	$0.299515\pi$
$678$	−9.09807	−	15.7583i	−0.349409	−	0.605194i
$679$		0			0
$680$	−0.0844203	+	0.146220i	−0.00323737	+	0.00560729i
$681$	3.27129	−	5.66604i	0.125356	−	0.217123i
$682$	−9.95385			−0.381153
$683$	−38.2212			−1.46249			−0.731246	−	0.682113i	$-0.761061\pi$
$683$	−38.2212			−1.46249			−0.731246	+	0.682113i	$0.761061\pi$
$684$	2.22176	−	3.84821i	0.0849512	−	0.147140i
$685$	−1.32706	+	2.29854i	−0.0507044	+	0.0878226i
$686$		0			0
$687$	−3.64013	−	6.30490i	−0.138880	−	0.240547i
$688$	12.7734	−	22.1241i	0.486980	−	0.843474i
$689$	−15.8430	−	5.46317i	−0.603570	−	0.208130i
$690$	−1.73107	−	2.99830i	−0.0659006	−	0.114143i
$691$	26.2322			0.997920			0.498960	−	0.866625i	$-0.333715\pi$
$691$	26.2322			0.997920			0.498960	+	0.866625i	$0.333715\pi$
$692$	−9.80084	−	16.9755i	−0.372572	−	0.645313i
$693$		0			0
$694$	−14.3130			−0.543314
$695$	0.399204	+	0.691442i	0.0151427	+	0.0262279i
$696$	−19.2185			−0.728476
$697$	−2.27024	−	3.93218i	−0.0859916	−	0.148942i
$698$	20.7836	+	35.9982i	0.786670	+	1.36255i
$699$	15.3784	+	26.6361i	0.581664	+	1.00747i
$700$		0			0
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$	8.55515	−	7.43011i	0.322893	−	0.280431i
$703$	2.05794	+	3.56446i	0.0776167	+	0.134436i
$704$	−6.66528	+	11.5446i	−0.251207	+	0.435104i
$705$	−5.28105			−0.198896
$706$	−20.6835	+	35.8248i	−0.778433	+	1.34828i
$707$		0			0
$708$	−10.0950	+	17.4851i	−0.379395	+	0.657131i
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.838745	+	0.544524i	$0.183290\pi$
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.0521988	+	0.998637i	$0.483377\pi$
$710$	1.09476	+	1.89619i	0.0410858	+	0.0711626i
$711$	−24.2869			−0.910830
$712$	−12.1861			−0.456695
$713$	2.63516	+	4.56423i	0.0986876	+	0.170932i
$714$		0			0
$715$	2.81384	+	0.970301i	0.105232	+	0.0362872i
$716$	−7.60461	+	13.1716i	−0.284197	+	0.492244i
$717$	−17.8408	+	30.9011i	−0.666275	+	1.15402i
$718$	2.56280	−	4.43890i	0.0956428	−	0.165658i
$719$	−24.6190	−	42.6413i	−0.918133	−	1.59025i	−0.802249	−	0.596990i	$-0.796363\pi$
$719$	−24.6190	−	42.6413i	−0.918133	−	1.59025i	−0.115884	−	0.993263i	$-0.536970\pi$
$720$	−2.14136			−0.0798037
$721$		0			0
$722$	15.9549	−	27.6347i	0.593779	−	1.02846i
$723$	8.68963	−	15.0509i	0.323171	−	0.559748i
$724$	−18.1900			−0.676024
$725$	−20.4361	+	35.3963i	−0.758977	+	1.31459i
$726$	−27.6878			−1.02759
$727$	32.0495			1.18865			0.594325	−	0.804225i	$-0.297419\pi$
$727$	32.0495			1.18865			0.594325	+	0.804225i	$0.297419\pi$
$728$		0			0
$729$	−12.4996			−0.462947
$730$	−1.42492			−0.0527387
$731$	2.24114	−	3.88178i	0.0828917	−	0.143573i
$732$	−37.8789			−1.40004
$733$	14.1005	−	24.4228i	0.520813	−	0.902075i	−0.478894	−	0.877873i	$-0.658962\pi$
$733$	14.1005	−	24.4228i	0.520813	−	0.902075i	0.999707	−	0.0242025i	$-0.00770464\pi$
$734$	−13.1462	+	22.7699i	−0.485236	+	0.840453i
$735$		0			0
$736$	28.2968			1.04303
$737$	28.0181	+	48.5288i	1.03206	+	1.78758i
$738$	11.3459	−	19.6516i	0.417648	−	0.723387i
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	−0.148180	−	0.988960i	$-0.547342\pi$
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	0.930555	−	0.366153i	$-0.119325\pi$
$740$	−0.436510	+	0.756058i	−0.0160464	+	0.0277932i
$741$	8.44160	−	7.33149i	0.310110	−	0.269329i
$742$		0			0
$743$	−7.95711	−	13.7821i	−0.291918	−	0.505617i	0.682345	−	0.731030i	$-0.260960\pi$
$743$	−7.95711	−	13.7821i	−0.291918	−	0.505617i	−0.974263	+	0.225413i	$0.927627\pi$
$744$	2.98753			0.109528
$745$	3.02989			0.111007
$746$	4.68521	+	8.11502i	0.171538	+	0.297112i
$747$	3.47773	+	6.02360i	0.127243	+	0.220392i
$748$	−2.55611	+	4.42731i	−0.0934605	+	0.161878i
$749$		0			0
$750$	−4.19014	+	7.25754i	−0.153002	+	0.265008i
$751$	18.1996			0.664114			0.332057	−	0.943259i	$-0.392257\pi$
$751$	18.1996			0.664114			0.332057	+	0.943259i	$0.392257\pi$
$752$	27.9646	−	48.4362i	1.01977	−	1.76629i
$753$	−1.46220	−	2.53260i	−0.0532855	−	0.0922931i
$754$	52.1809	+	17.9937i	1.90032	+	0.655290i
$755$	1.20807			0.0439662
$756$		0			0
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	0.908632	+	0.417598i	$0.137128\pi$
$757$	22.4502	+	38.8849i	0.815967	+	1.41330i	−0.0926649	+	0.995697i	$0.529539\pi$
$758$	5.62989	+	9.75126i	0.204487	+	0.354182i
$759$	19.7436	+	34.1970i	0.716648	+	1.24127i
$760$	0.271282			0.00984042
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	0.519631	−	0.854391i	$-0.326069\pi$
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	−0.999740	+	0.0228184i	$0.992736\pi$
$762$	9.33644			0.338223
$763$		0			0
$764$	−9.52554	−	16.4987i	−0.344622	−	0.596903i
$765$	−0.375711			−0.0135839
$766$	−4.21900	−	7.30752i	−0.152439	−	0.264031i
$767$	−16.4914	+	14.3227i	−0.595471	+	0.517164i
$768$	24.0006	−	41.5703i	0.866049	−	1.50004i
$769$	6.98127	+	12.0919i	0.251751	+	0.436045i	0.964008	−	0.265873i	$-0.0856603\pi$
$769$	6.98127	+	12.0919i	0.251751	+	0.436045i	−0.712257	+	0.701919i	$0.752327\pi$
$770$		0			0
$771$	9.72707	−	16.8478i	0.350312	−	0.606758i
$772$	−0.756579	+	1.31043i	−0.0272299	+	0.0471635i
$773$	−12.8113			−0.460790			−0.230395	−	0.973097i	$-0.574002\pi$
$773$	−12.8113			−0.460790			−0.230395	+	0.973097i	$0.574002\pi$
$774$	22.4009			0.805184
$775$	3.17681	−	5.50239i	0.114114	−	0.197652i
$776$	−9.90048	+	17.1481i	−0.355406	+	0.615582i
$777$		0			0
$778$	−4.18797	−	7.25378i	−0.150146	−	0.260061i
$779$	−3.64767	+	6.31795i	−0.130691	+	0.226364i
$780$	2.24202	+	0.773120i	0.0802772	+	0.0276821i
$781$	−12.4863	−	21.6269i	−0.446795	−	0.773871i
$782$	6.43320			0.230051
$783$	6.96701	+	12.0672i	0.248981	+	0.431247i
$784$		0			0
$785$	−0.895370			−0.0319571
$786$	−4.85125	−	8.40262i	−0.173039	−	0.299712i
$787$	27.3199			0.973848			0.486924	−	0.873444i	$-0.338119\pi$
$787$	27.3199			0.973848			0.486924	+	0.873444i	$0.338119\pi$
$788$	−1.07383	−	1.85993i	−0.0382537	−	0.0662574i
$789$	14.6686	+	25.4068i	0.522217	+	0.904506i
$790$	1.96813	+	3.40890i	0.0700229	+	0.121283i
$791$		0			0
$792$	9.62401			0.341974
$793$	−38.7410	−	13.3591i	−1.37573	−	0.474396i
$794$	3.71956	+	6.44247i	0.132002	+	0.228635i
$795$	1.05221	−	1.82248i	0.0373181	−	0.0646369i
$796$	−20.4837			−0.726027
$797$	−14.7002	+	25.4614i	−0.520707	+	0.901891i	0.479003	+	0.877813i	$0.340998\pi$
$797$	−14.7002	+	25.4614i	−0.520707	+	0.901891i	−0.999710	+	0.0240775i	$0.992335\pi$
$798$		0			0
$799$	4.90652	−	8.49835i	0.173580	−	0.300650i
$800$	−17.0565	−	29.5428i	−0.603040	−	1.04450i
$801$	−13.5586	−	23.4841i	−0.479068	−	0.829770i
$802$	23.4379			0.827621
$803$	16.2519			0.573517
$804$	22.3244	+	38.6669i	0.787320	+	1.36368i
$805$		0			0
$806$	−8.11157	−	2.79713i	−0.285718	−	0.0985246i
$807$	5.40450	−	9.36087i	0.190247	−	0.329518i
$808$	8.60968	−	14.9124i	0.302888	−	0.524617i
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	−0.808329	−	0.588731i	$-0.799628\pi$
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	0.914020	+	0.405668i	$0.132961\pi$
$810$	1.95618	+	3.38821i	0.0687332	+	0.119049i
$811$	−8.44807			−0.296652			−0.148326	−	0.988939i	$-0.547388\pi$
$811$	−8.44807			−0.296652			−0.148326	+	0.988939i	$0.547388\pi$
$812$		0			0
$813$	20.6595	−	35.7833i	0.724560	−	1.25497i
$814$	11.8326	−	20.4946i	0.414732	−	0.718337i
$815$	0.359701			0.0125998
$816$	4.62721	−	8.01456i	0.161985	−	0.280566i
$817$	−7.20184			−0.251960
$818$	−38.4551			−1.34455
$819$		0			0
$820$	−1.54742			−0.0540382
$821$	−34.2635			−1.19581			−0.597903	−	0.801569i	$-0.703999\pi$
$821$	−34.2635			−1.19581			−0.597903	+	0.801569i	$0.703999\pi$
$822$	28.6627	−	49.6452i	0.999725	−	1.73157i
$823$	−6.23732			−0.217419			−0.108710	−	0.994074i	$-0.534672\pi$
$823$	−6.23732			−0.217419			−0.108710	+	0.994074i	$0.534672\pi$
$824$	3.67809	−	6.37064i	0.128132	−	0.221932i
$825$	23.8018	−	41.2260i	0.828673	−	1.43530i
$826$		0			0
$827$	19.5232			0.678889			0.339445	−	0.940626i	$-0.389761\pi$
$827$	19.5232			0.678889			0.339445	+	0.940626i	$0.389761\pi$
$828$	6.76380	+	11.7152i	0.235058	+	0.407133i
$829$	16.3383	−	28.2988i	0.567453	−	0.982857i	−0.429364	−	0.903131i	$-0.641262\pi$
$829$	16.3383	−	28.2988i	0.567453	−	0.982857i	0.996817	−	0.0797254i	$-0.0254043\pi$
$830$	0.563647	−	0.976265i	0.0195645	−	0.0338866i
$831$	−29.9615	+	51.8949i	−1.03935	+	1.80021i
$832$	−8.67580	+	7.53489i	−0.300779	+	0.261225i
$833$		0			0
$834$	−8.62225	−	14.9342i	−0.298564	−	0.517128i
$835$	2.11334			0.0731353
$836$	8.21395			0.284085
$837$	−1.08303	−	1.87586i	−0.0374349	−	0.0648392i
$838$	−20.2702	−	35.1091i	−0.700223	−	1.21282i
$839$	12.3713	−	21.4278i	0.427106	−	0.739769i	−0.569508	−	0.821985i	$-0.692866\pi$
$839$	12.3713	−	21.4278i	0.427106	−	0.739769i	0.996615	+	0.0822161i	$0.0261998\pi$
$840$		0			0
$841$	−19.4374	+	33.6665i	−0.670255	+	1.16092i
$842$	17.5174			0.603689
$843$	−4.20040	+	7.27531i	−0.144669	+	0.250575i
$844$	−19.2267	−	33.3017i	−0.661812	−	1.14629i
$845$	2.02038	+	1.58143i	0.0695032	+	0.0544029i
$846$	49.0422			1.68610
$847$		0			0
$848$	11.1435	+	19.3011i	0.382670	+	0.662803i
$849$	−8.76938	−	15.1890i	−0.300964	−	0.521285i
$850$	−3.87776	−	6.71647i	−0.133006	−	0.230373i
$851$	−12.5301			−0.429528
$852$	−9.94888	−	17.2320i	−0.340843	−	0.590357i
$853$	−18.2245			−0.623994			−0.311997	−	0.950083i	$-0.600998\pi$
$853$	−18.2245			−0.623994			−0.311997	+	0.950083i	$0.600998\pi$
$854$		0			0
$855$	0.301833	+	0.522791i	0.0103225	+	0.0178791i
$856$	10.0186			0.342427
$857$	1.27340	+	2.20559i	0.0434984	+	0.0753414i	0.886955	−	0.461856i	$-0.152816\pi$
$857$	1.27340	+	2.20559i	0.0434984	+	0.0753414i	−0.843457	+	0.537197i	$0.819483\pi$
$858$	−60.7749	−	20.9571i	−2.07482	−	0.715465i
$859$	27.0045	−	46.7732i	0.921382	−	1.59588i	0.124104	−	0.992269i	$-0.460394\pi$
$859$	27.0045	−	46.7732i	0.921382	−	1.59588i	0.797278	−	0.603612i	$-0.206272\pi$
$860$	−0.763792	−	1.32293i	−0.0260451	−	0.0451114i
$861$		0			0
$862$	−18.9788	+	32.8723i	−0.646421	+	1.11963i
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	−0.876410	−	0.481565i	$-0.840069\pi$
$863$	−0.621545	+	1.07655i	−0.0211576	+	0.0366461i	0.855253	+	0.518211i	$0.173402\pi$
$864$	−11.6297			−0.395652
$865$	2.66295			0.0905429
$866$	24.4800	−	42.4006i	0.831864	−	1.44083i
$867$	−18.6877	+	32.3681i	−0.634668	+	1.09928i
$868$		0			0
$869$	−22.4474	−	38.8801i	−0.761477	−	1.31892i
$870$	−3.46560	+	6.00259i	−0.117495	+	0.203507i
$871$	9.19540	+	47.4203i	0.311574	+	1.60678i
$872$	−7.02440	−	12.1666i	−0.237876	−	0.412013i
$873$	−44.0619			−1.49127
$874$	−5.16821	−	8.95161i	−0.174817	−	0.302793i
$875$		0			0
$876$	12.9492			0.437514
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	0.859170	−	0.511690i	$-0.170981\pi$
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	−0.872722	+	0.488218i	$0.837647\pi$
$878$	−46.6975			−1.57597
$879$	19.6755	+	34.0790i	0.663639	+	1.14946i
$880$	−1.97917	−	3.42803i	−0.0667179	−	0.115559i
$881$	−18.5318	−	32.0980i	−0.624352	−	1.08141i	−0.988666	−	0.150133i	$-0.952030\pi$
$881$	−18.5318	−	32.0980i	−0.624352	−	1.08141i	0.364314	−	0.931276i	$-0.381304\pi$
$882$		0			0
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$	−3.32713	+	2.88960i	−0.111904	+	0.0971877i
$885$	−1.37144	−	2.37541i	−0.0461005	−	0.0798484i
$886$	−17.2065	+	29.8025i	−0.578063	+	1.00123i
$887$	49.2573			1.65390			0.826950	−	0.562276i	$-0.190074\pi$
$887$	49.2573			1.65390			0.826950	+	0.562276i	$0.190074\pi$
$888$	−3.55141	+	6.15123i	−0.119178	+	0.206422i
$889$		0			0
$890$	−2.19748	+	3.80614i	−0.0736597	+	0.127582i
$891$	−22.3112	−	38.6441i	−0.747452	−	1.29463i
$892$	−0.528840	−	0.915978i	−0.0177069	−	0.0306692i
$893$	−15.7669			−0.527620
$894$	−65.4414			−2.18869
$895$	−1.03311	−	1.78940i	−0.0345330	−	0.0598130i
$896$		0			0
$897$	6.47975	+	33.4159i	0.216353	+	1.11572i
$898$	−10.8174	+	18.7362i	−0.360980	+	0.625236i
$899$	5.27559	−	9.13760i	0.175951	−	0.304756i
$900$	8.15406	−	14.1233i	0.271802	−	0.470775i
$901$	1.95518	+	3.38647i	0.0651365	+	0.112820i
$902$	41.9462			1.39666
$903$		0			0
$904$	−2.17029	+	3.75906i	−0.0721829	+	0.125024i
$905$	1.23558	−	2.14009i	0.0410721	−	0.0711390i
$906$	−26.0926			−0.866870
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	−0.821488	−	0.570226i	$-0.806855\pi$
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	0.904574	+	0.426316i	$0.140189\pi$
$908$	4.14321			0.137497
$909$	38.3172			1.27090
$910$		0			0
$911$	49.0582			1.62537			0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582			1.62537			0.812685	+	0.582703i	$0.198005\pi$
$912$	−14.8694			−0.492374
$913$	−6.42866	+	11.1348i	−0.212757	+	0.368507i
$914$	38.1266			1.26111
$915$	2.57298	−	4.45653i	0.0850601	−	0.147328i
$916$	2.30518	−	3.99270i	0.0761654	−	0.131922i
$917$		0			0
$918$	−2.64399			−0.0872646
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	0.511611	−	0.859217i	$-0.329049\pi$
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	−0.999909	+	0.0134590i	$0.995716\pi$
$920$	−0.412937	+	0.715227i	−0.0136141	+	0.0235803i
$921$	32.1967	−	55.7664i	1.06092	−	1.83756i
$922$	1.89602	−	3.28401i	0.0624422	−	0.108153i
$923$	−4.09794	−	21.1329i	−0.134885	−	0.695598i
$924$		0			0
$925$	7.55282	+	13.0819i	0.248335	+	0.430129i
$926$	5.63311			0.185116
$927$	16.3693			0.537637
$928$	−28.3251	−	49.0605i	−0.929817	−	1.61049i
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	0.970411	−	0.241460i	$-0.0776261\pi$
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	−0.694316	+	0.719671i	$0.744293\pi$
$930$	0.538730	−	0.933107i	0.0176656	−	0.0305978i
$931$		0			0
$932$	−9.73865	+	16.8678i	−0.319000	+	0.552524i
$933$	−53.9888			−1.76751
$934$	−12.0106	+	20.8030i	−0.392999	+	0.680695i
$935$	−0.347255	−	0.601463i	−0.0113565	−	0.0196699i
$936$	7.84277	+	2.70444i	0.256349	+	0.0883973i
$937$	−44.0131			−1.43784			−0.718922	−	0.695091i	$-0.755364\pi$
$937$	−44.0131			−1.43784			−0.718922	+	0.695091i	$0.755364\pi$
$938$		0			0
$939$	3.84096	+	6.65273i	0.125345	+	0.217104i
$940$	−1.67216	−	2.89627i	−0.0545400	−	0.0944660i
$941$	26.5338	+	45.9578i	0.864976	+	1.49818i	0.867071	+	0.498184i	$0.166000\pi$
$941$	26.5338	+	45.9578i	0.864976	+	1.49818i	−0.00209573	+	0.999998i	$0.500667\pi$
$942$	19.3387			0.630090
$943$	−11.1048	−	19.2340i	−0.361620	−	0.626345i
$944$	29.0487			0.945453
$945$		0			0
$946$	20.7043	+	35.8609i	0.673154	+	1.16594i
$947$	−27.8817			−0.906034			−0.453017	−	0.891502i	$-0.649652\pi$
$947$	−27.8817			−0.906034			−0.453017	+	0.891502i	$0.649652\pi$
$948$	−17.8857	−	30.9790i	−0.580902	−	1.00615i
$949$	13.2439	+	4.56694i	0.429917	+	0.148249i
$950$	−6.23051	+	10.7916i	−0.202145	+	0.350125i
$951$	−8.34851	−	14.4600i	−0.270719	−	0.468899i
$952$		0			0
$953$	18.1784	−	31.4859i	0.588856	−	1.01993i	−0.405527	−	0.914083i	$-0.632912\pi$
$953$	18.1784	−	31.4859i	0.588856	−	1.01993i	0.994383	−	0.105845i	$-0.0337548\pi$
$954$	−9.77130	+	16.9244i	−0.316357	+	0.547947i
$955$	2.58815			0.0837505
$956$	−22.5960			−0.730807
$957$	39.5267	−	68.4623i	1.27772	−	2.21307i
$958$	33.9877	−	58.8685i	1.09809	−	1.90195i
$959$		0			0
$960$	−0.721486	−	1.24965i	−0.0232859	−	0.0403323i
$961$	14.6799	−	25.4263i	0.473545	−	0.820205i
$962$	15.4018	−	13.3764i	0.496573	−	0.431272i
$963$	11.1469	+	19.3069i	0.359202	+	0.622157i
$964$	11.0057			0.354471
$965$	−0.102784	−	0.178026i	−0.00330872	−	0.00573087i
$966$		0			0
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	3.30239	+	5.71990i	0.106143	+	0.183845i
$969$	−2.60890			−0.0838099
$970$	3.57063	+	6.18450i	0.114646	+	0.198572i
$971$	−18.4460	−	31.9494i	−0.591961	−	1.02531i	−0.993968	−	0.109669i	$-0.965021\pi$
$971$	−18.4460	−	31.9494i	−0.591961	−	1.02531i	0.402008	−	0.915636i	$-0.368313\pi$
$972$	−14.0916	−	24.4073i	−0.451987	−	0.782865i
$973$		0			0
$974$	68.2867			2.18805
$975$	30.9814	−	26.9072i	0.992200	−	0.861721i
$976$	27.2493	+	47.1972i	0.872229	+	1.51074i
$977$	0.221957	−	0.384441i	0.00710104	−	0.0122994i	−0.862453	−	0.506137i	$-0.831073\pi$
$977$	0.221957	−	0.384441i	0.00710104	−	0.0122994i	0.869554	+	0.493838i	$0.164406\pi$
$978$	−7.76904			−0.248426
$979$	25.0633	−	43.4109i	0.801026	−	1.38742i
$980$		0			0
$981$	15.6310	−	27.0736i	0.499058	−	0.864394i
$982$	7.61658	+	13.1923i	0.243055	+	0.420983i
$983$	22.7802	+	39.4564i	0.726575	+	1.25846i	0.958323	+	0.285688i	$0.0922222\pi$
$983$	22.7802	+	39.4564i	0.726575	+	1.25846i	−0.231748	+	0.972776i	$0.574444\pi$
$984$	−12.5897			−0.401344
$985$	0.291767			0.00929648
$986$	−6.43964	−	11.1538i	−0.205080	−	0.355209i
$987$		0			0
$988$	6.69369	+	2.30820i	0.212955	+	0.0734336i
$989$	10.9624	−	18.9875i	0.348585	−	0.603766i
$990$	1.73546	−	3.00590i	0.0551565	−	0.0955338i
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	0.0277842	+	0.999614i	$0.491155\pi$
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	−0.879583	+	0.475745i	$0.842178\pi$
$992$	4.40316	+	7.62650i	0.139801	+	0.242142i
$993$	32.8588			1.04274
$994$		0			0
$995$	1.39139	−	2.40996i	0.0441100	−	0.0764008i
$996$	−5.12225	+	8.87199i	−0.162305	+	0.281120i
$997$	−29.0852			−0.921139			−0.460569	−	0.887624i	$-0.652355\pi$
$997$	−29.0852			−0.921139			−0.460569	+	0.887624i	$0.652355\pi$
$998$	40.1857	−	69.6038i	1.27206	−	2.20327i
$999$	5.14977			0.162932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.l.471.6		12
7.2	even	3		637.2.f.j.393.1		12
7.3	odd	6		91.2.g.b.81.1	yes	12
7.4	even	3		637.2.g.l.263.1		12
7.5	odd	6		637.2.f.k.393.1		12
7.6	odd	2		91.2.h.b.16.6	yes	12
13.9	even	3		637.2.g.l.373.1		12
21.17	even	6		819.2.n.d.172.6		12
21.20	even	2		819.2.s.d.289.1		12
91.3	odd	6		1183.2.e.h.508.1		12
91.9	even	3		637.2.f.j.295.1		12
91.10	odd	6		1183.2.e.g.508.6		12
91.16	even	3		8281.2.a.ca.1.6		6
91.23	even	6		8281.2.a.cf.1.1		6
91.48	odd	6		91.2.g.b.9.1	✓	12
91.55	odd	6		1183.2.e.h.170.1		12
91.61	odd	6		637.2.f.k.295.1		12
91.62	odd	6		1183.2.e.g.170.6		12
91.68	odd	6		8281.2.a.bz.1.6		6
91.74	even	3	inner	637.2.h.l.165.6		12
91.75	odd	6		8281.2.a.ce.1.1		6
91.87	odd	6		91.2.h.b.74.6	yes	12
273.230	even	6		819.2.n.d.100.6		12
273.269	even	6		819.2.s.d.802.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	91.48	odd	6
91.2.g.b.81.1	yes	12	7.3	odd	6
91.2.h.b.16.6	yes	12	7.6	odd	2
91.2.h.b.74.6	yes	12	91.87	odd	6
637.2.f.j.295.1		12	91.9	even	3
637.2.f.j.393.1		12	7.2	even	3
637.2.f.k.295.1		12	91.61	odd	6
637.2.f.k.393.1		12	7.5	odd	6
637.2.g.l.263.1		12	7.4	even	3
637.2.g.l.373.1		12	13.9	even	3
637.2.h.l.165.6		12	91.74	even	3	inner
637.2.h.l.471.6		12	1.1	even	1	trivial
819.2.n.d.100.6		12	273.230	even	6
819.2.n.d.172.6		12	21.17	even	6
819.2.s.d.289.1		12	21.20	even	2
819.2.s.d.802.1		12	273.269	even	6
1183.2.e.g.170.6		12	91.62	odd	6
1183.2.e.g.508.6		12	91.10	odd	6
1183.2.e.h.170.1		12	91.55	odd	6
1183.2.e.h.508.1		12	91.3	odd	6
8281.2.a.bz.1.6		6	91.68	odd	6
8281.2.a.ca.1.6		6	91.16	even	3
8281.2.a.ce.1.1		6	91.75	odd	6
8281.2.a.cf.1.1		6	91.23	even	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.85816 q^{2} +(1.14703 - 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 + 0.170921i) q^{5} +(2.13137 - 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(-0.183365 + 0.317598i) q^{10} +(2.09137 - 3.62236i) q^{11} +(1.66637 - 2.88623i) q^{12} +(2.72221 - 2.36423i) q^{13} +(0.226381 + 0.392104i) q^{15} -4.79501 q^{16} -0.841305 q^{17} +(-2.10227 - 3.64125i) q^{18} +(0.675876 + 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} -4.11519 q^{23} +(-1.16637 + 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} +(5.05830 - 4.39312i) q^{26} +1.69131 q^{27} +(4.11931 + 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +(-0.640350 - 1.10912i) q^{31} -6.87618 q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 - 2.84683i) q^{36} +3.04485 q^{37} +(1.25589 + 2.17526i) q^{38} +(-1.57459 - 8.12012i) q^{39} +(0.100344 - 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} +0.446581 q^{45} -7.64669 q^{46} +(-5.83204 + 10.1014i) q^{47} +(-5.50003 + 9.52634i) q^{48} +(4.60921 + 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(3.95472 - 3.43466i) q^{52} +(-2.32398 - 4.02525i) q^{53} +3.14272 q^{54} +(0.412757 + 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} -6.05811 q^{59} +(0.328878 + 0.569634i) q^{60} +(-5.68285 - 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(0.135465 + 0.698587i) q^{65} +(-8.91498 - 15.4412i) q^{66} +(-6.69851 + 11.6022i) q^{67} -1.22222 q^{68} +(-4.72026 + 8.17574i) q^{69} +(2.98520 - 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} +(1.94273 + 3.36491i) q^{73} +5.65782 q^{74} +11.3810 q^{75} +(0.981887 + 1.70068i) q^{76} +(-2.92585 - 15.0885i) q^{78} +(5.36669 - 9.29537i) q^{79} +(0.473177 - 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(5.01421 + 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +(-4.94994 + 8.57354i) q^{86} +18.8999 q^{87} +(-2.12662 + 3.68341i) q^{88} +11.9841 q^{89} +0.829819 q^{90} -5.97840 q^{92} -2.93801 q^{93} +(-10.8369 + 18.7700i) q^{94} -0.266785 q^{95} +(-7.88721 + 13.6611i) q^{96} +(9.73637 - 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - q^{3} + 8 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} - 16 q^{16} + 10 q^{17} + 3 q^{18} + q^{19} + q^{20} - 5 q^{22} + 2 q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - q^3 + 8 * q^4 - q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 - 16 * q^16 + 10 * q^17 + 3 * q^18 + q^19 + q^20 - 5 * q^22 + 2 * q^23 + 11 * q^24 + 7 * q^25 + 16 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 + 26 * q^37 + 17 * q^38 - 20 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 - 14 * q^45 - 32 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 - 41 * q^52 - 2 * q^53 - 36 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 + 26 * q^59 + 20 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 5 * q^65 - 18 * q^66 - 11 * q^67 + 58 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 + 30 * q^73 + 6 * q^74 - 6 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 - 7 * q^86 + 32 * q^87 + 8 * q^89 + 16 * q^90 + 54 * q^92 + 14 * q^93 - 45 * q^94 + 12 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

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