LMFDB - Embedded newform 637.2.r.f.324.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 $ x^16 - 11x^14 + 85x^12 - 334x^10 + 952x^8 - 1050x^6 + 853x^4 - 93*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			324.6
Root			$-0.929293 + 0.536527i$ of defining polynomial
Character	$\chi$	$=$	637.324
Dual form			637.2.r.f.116.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929293 + 0.536527i) q^{2} +(-1.21570 - 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(0.541640 + 0.312716i) q^{5} -2.60903i q^{6} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +O(q^{10})$	\(q+(0.929293 + 0.536527i) q^{2} +(-1.21570 - 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(0.541640 + 0.312716i) q^{5} -2.60903i q^{6} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +(0.335561 + 0.581209i) q^{10} +(0.613597 - 0.354260i) q^{11} +(-1.03159 + 1.78676i) q^{12} +(-0.848553 - 3.50428i) q^{13} -1.52068i q^{15} +(0.791426 - 1.37079i) q^{16} +(1.67157 + 2.89524i) q^{17} +(-2.70585 + 1.56222i) q^{18} +(-4.50573 - 2.60138i) q^{19} -0.530712i q^{20} +0.760282 q^{22} +(-2.21570 + 3.83771i) q^{23} +(-6.43627 + 3.71598i) q^{24} +(-2.30442 - 3.99137i) q^{25} +(1.09159 - 3.71177i) q^{26} -0.214623 q^{27} -6.59711 q^{29} +(0.815886 - 1.41316i) q^{30} +(3.80238 - 2.19530i) q^{31} +(-3.82335 + 2.20741i) q^{32} +(-1.49190 - 0.861351i) q^{33} +3.58737i q^{34} +2.47076 q^{36} +(0.366683 + 0.211704i) q^{37} +(-2.79143 - 4.83489i) q^{38} +(-6.34722 + 6.04692i) q^{39} +(0.955864 - 1.65561i) q^{40} +5.01604i q^{41} +11.2059 q^{43} +(-0.520670 - 0.300609i) q^{44} +(-1.57711 + 0.910544i) q^{45} +(-4.11807 + 2.37757i) q^{46} +(-6.99116 - 4.03635i) q^{47} -3.84855 q^{48} -4.94553i q^{50} +(4.06426 - 7.03950i) q^{51} +(-2.21516 + 2.11036i) q^{52} +(0.348553 + 0.603712i) q^{53} +(-0.199447 - 0.115151i) q^{54} +0.443132 q^{55} +12.6500i q^{57} +(-6.13065 - 3.53953i) q^{58} +(8.54177 - 4.93159i) q^{59} +(-1.11750 + 0.645188i) q^{60} +(2.34855 - 4.06781i) q^{61} +4.71136 q^{62} -7.90305 q^{64} +(0.636233 - 2.16341i) q^{65} +(-0.924277 - 1.60089i) q^{66} +(9.02470 - 5.21041i) q^{67} +(1.41841 - 2.45676i) q^{68} +10.7745 q^{69} -14.0876i q^{71} +(7.70775 + 4.45007i) q^{72} +(-4.40273 + 2.54191i) q^{73} +(0.227170 + 0.393471i) q^{74} +(-5.60297 + 9.70463i) q^{75} +4.41482i q^{76} +(-9.14277 + 2.21390i) q^{78} +(1.95586 - 3.38766i) q^{79} +(0.857336 - 0.494983i) q^{80} +(4.62851 + 8.01682i) q^{81} +(-2.69124 + 4.66137i) q^{82} -10.2035i q^{83} +2.09090i q^{85} +(10.4136 + 6.01230i) q^{86} +(8.02012 + 13.8913i) q^{87} +(-1.08285 - 1.87555i) q^{88} +(11.5866 + 6.68955i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(-9.24512 - 5.33767i) q^{93} +(-4.33122 - 7.50190i) q^{94} +(-1.62699 - 2.81802i) q^{95} +(9.29610 + 5.36711i) q^{96} +0.202023i q^{97} +2.06302i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9	$ 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) $ 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 + 12 * q^13 + 2 * q^16 - 8 * q^17 - 36 * q^22 - 12 * q^23 + 6 * q^26 - 32 * q^27 - 16 * q^29 + 38 * q^30 - 56 * q^36 - 34 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^43 - 36 * q^48 + 16 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^55 + 12 * q^61 - 44 * q^62 + 88 * q^64 - 30 * q^65 - 2 * q^66 + 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 20 * q^78 + 20 * q^79 - 24 * q^81 + 16 * q^82 + 68 * q^87 + 4 * q^88 + 216 * q^90 + 12 * q^92 + 26 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.929293	+	0.536527i	0.657109	+	0.379382i	0.791175	−	0.611590i	$-0.209470\pi$
$2$	0.929293	+	0.536527i	0.657109	+	0.379382i	−0.134065	+	0.990972i	$0.542803\pi$
$3$	−1.21570	−	2.10566i	−0.701886	−	1.21570i	−0.967804	−	0.251707i	$-0.919008\pi$
$3$	−1.21570	−	2.10566i	−0.701886	−	1.21570i	0.265918	−	0.963996i	$-0.414325\pi$
$4$	−0.424277	−	0.734868i	−0.212138	−	0.367434i
$5$	0.541640	+	0.312716i	0.242229	+	0.139851i	0.616201	−	0.787589i	$-0.288671\pi$
$5$	0.541640	+	0.312716i	0.242229	+	0.139851i	−0.373972	+	0.927440i	$0.622004\pi$
$6$		−	2.60903i		−	1.06513i
$7$		0			0
$7$		0			0
$8$		−	3.05665i		−	1.08069i
$9$	−1.45586	+	2.52163i	−0.485288	+	0.840544i
$10$	0.335561	+	0.581209i	0.106114	+	0.183795i
$11$	0.613597	−	0.354260i	0.185006	−	0.106814i	−0.404636	−	0.914478i	$-0.632602\pi$
$11$	0.613597	−	0.354260i	0.185006	−	0.106814i	0.589643	+	0.807664i	$0.299269\pi$
$12$	−1.03159	+	1.78676i	−0.297794	+	0.515794i
$13$	−0.848553	−	3.50428i	−0.235346	−	0.971912i
$13$	−0.848553	−	3.50428i	−0.235346	−	0.971912i
$14$		0			0
$15$		−	1.52068i		−	0.392637i
$16$	0.791426	−	1.37079i	0.197856	−	0.342697i
$17$	1.67157	+	2.89524i	0.405414	+	0.702199i	0.994370	−	0.105967i	$-0.0337939\pi$
$17$	1.67157	+	2.89524i	0.405414	+	0.702199i	−0.588955	+	0.808166i	$0.700461\pi$
$18$	−2.70585	+	1.56222i	−0.637775	+	0.368219i
$19$	−4.50573	−	2.60138i	−1.03368	−	0.596798i	−0.115646	−	0.993290i	$-0.536894\pi$
$19$	−4.50573	−	2.60138i	−1.03368	−	0.596798i	−0.918038	+	0.396492i	$0.870227\pi$
$20$		−	0.530712i		−	0.118671i
$21$		0			0
$22$	0.760282			0.162093
$23$	−2.21570	+	3.83771i	−0.462006	+	0.800218i	−0.999061	−	0.0433296i	$-0.986203\pi$
$23$	−2.21570	+	3.83771i	−0.462006	+	0.800218i	0.537055	+	0.843547i	$0.319537\pi$
$24$	−6.43627	+	3.71598i	−1.31380	+	0.758522i
$25$	−2.30442	−	3.99137i	−0.460883	−	0.798274i
$26$	1.09159	−	3.71177i	0.214078	−	0.727938i
$27$	−0.214623			−0.0413042
$28$		0			0
$29$	−6.59711			−1.22505			−0.612526	−	0.790450i	$-0.709847\pi$
$29$	−6.59711			−1.22505			−0.612526	+	0.790450i	$0.709847\pi$
$30$	0.815886	−	1.41316i	0.148960	−	0.258006i
$31$	3.80238	−	2.19530i	0.682927	−	0.394288i	−0.118030	−	0.993010i	$-0.537658\pi$
$31$	3.80238	−	2.19530i	0.682927	−	0.394288i	0.800957	+	0.598722i	$0.204325\pi$
$32$	−3.82335	+	2.20741i	−0.675879	+	0.390219i
$33$	−1.49190	−	0.861351i	−0.259707	−	0.149942i
$34$			3.58737i			0.615228i
$35$		0			0
$36$	2.47076			0.411793
$37$	0.366683	+	0.211704i	0.0602823	+	0.0348040i	0.529838	−	0.848099i	$-0.322253\pi$
$37$	0.366683	+	0.211704i	0.0602823	+	0.0348040i	−0.469556	+	0.882903i	$0.655586\pi$
$38$	−2.79143	−	4.83489i	−0.452829	−	0.784323i
$39$	−6.34722	+	6.04692i	−1.01637	+	0.968282i
$40$	0.955864	−	1.65561i	0.151135	−	0.261774i
$41$			5.01604i			0.783374i	0.920099	+	0.391687i	$0.128108\pi$
$41$			5.01604i			0.783374i	−0.920099	+	0.391687i	$0.871892\pi$
$42$		0			0
$43$	11.2059			1.70889			0.854445	−	0.519542i	$-0.173897\pi$
$43$	11.2059			1.70889			0.854445	+	0.519542i	$0.173897\pi$
$44$	−0.520670	−	0.300609i	−0.0784939	−	0.0453185i
$45$	−1.57711	+	0.910544i	−0.235101	+	0.135736i
$46$	−4.11807	+	2.37757i	−0.607177	+	0.350554i
$47$	−6.99116	−	4.03635i	−1.01977	−	0.588762i	−0.105729	−	0.994395i	$-0.533718\pi$
$47$	−6.99116	−	4.03635i	−1.01977	−	0.588762i	−0.914036	+	0.405633i	$0.867051\pi$
$48$	−3.84855			−0.555491
$49$		0			0
$50$		−	4.94553i		−	0.699404i
$51$	4.06426	−	7.03950i	0.569110	−	0.985727i
$52$	−2.21516	+	2.11036i	−0.307188	+	0.292654i
$53$	0.348553	+	0.603712i	0.0478774	+	0.0829262i	0.888971	−	0.457964i	$-0.151421\pi$
$53$	0.348553	+	0.603712i	0.0478774	+	0.0829262i	−0.841094	+	0.540890i	$0.818088\pi$
$54$	−0.199447	−	0.115151i	−0.0271414	−	0.0156701i
$55$	0.443132			0.0597519
$56$		0			0
$57$			12.6500i			1.67554i
$58$	−6.13065	−	3.53953i	−0.804993	−	0.464763i
$59$	8.54177	−	4.93159i	1.11204	−	0.642039i	0.172686	−	0.984977i	$-0.444756\pi$
$59$	8.54177	−	4.93159i	1.11204	−	0.642039i	0.939358	+	0.342938i	$0.111422\pi$
$60$	−1.11750	+	0.645188i	−0.144268	+	0.0832934i
$61$	2.34855	−	4.06781i	0.300701	−	0.520830i	−0.675594	−	0.737274i	$-0.736113\pi$
$61$	2.34855	−	4.06781i	0.300701	−	0.520830i	0.976295	+	0.216444i	$0.0694459\pi$
$62$	4.71136			0.598344
$63$		0			0
$64$	−7.90305			−0.987881
$65$	0.636233	−	2.16341i	0.0789150	−	0.268338i
$66$	−0.924277	−	1.60089i	−0.113771	−	0.197056i
$67$	9.02470	−	5.21041i	1.10254	−	0.636553i	0.165655	−	0.986184i	$-0.447026\pi$
$67$	9.02470	−	5.21041i	1.10254	−	0.636553i	0.936888	+	0.349631i	$0.113693\pi$
$68$	1.41841	−	2.45676i	0.172008	−	0.297926i
$69$	10.7745			1.29710
$70$		0			0
$71$		−	14.0876i		−	1.67189i	−0.548812	−	0.835946i	$-0.684920\pi$
$71$		−	14.0876i		−	1.67189i	0.548812	−	0.835946i	$-0.315080\pi$
$72$	7.70775	+	4.45007i	0.908368	+	0.524446i
$73$	−4.40273	+	2.54191i	−0.515300	+	0.297509i	−0.735010	−	0.678057i	$-0.762822\pi$
$73$	−4.40273	+	2.54191i	−0.515300	+	0.297509i	0.219710	+	0.975565i	$0.429489\pi$
$74$	0.227170	+	0.393471i	0.0264080	+	0.0457400i
$75$	−5.60297	+	9.70463i	−0.646975	+	1.12059i
$76$			4.41482i			0.506415i
$77$		0			0
$78$	−9.14277	+	2.21390i	−1.03521	+	0.250675i
$79$	1.95586	−	3.38766i	0.220052	−	0.381141i	−0.734772	−	0.678315i	$-0.762711\pi$
$79$	1.95586	−	3.38766i	0.220052	−	0.381141i	0.954823	+	0.297174i	$0.0960440\pi$
$80$	0.857336	−	0.494983i	0.0958530	−	0.0553408i
$81$	4.62851	+	8.01682i	0.514279	+	0.890757i
$82$	−2.69124	+	4.66137i	−0.297198	+	0.514762i
$83$		−	10.2035i		−	1.11998i	−0.828499	−	0.559990i	$-0.810805\pi$
$83$		−	10.2035i		−	1.11998i	0.828499	−	0.559990i	$-0.189195\pi$
$84$		0			0
$85$			2.09090i			0.226790i
$86$	10.4136	+	6.01230i	1.12293	+	0.648323i
$87$	8.02012	+	13.8913i	0.859847	+	1.48930i
$88$	−1.08285	−	1.87555i	−0.115432	−	0.199935i
$89$	11.5866	+	6.68955i	1.22818	+	0.709090i	0.966649	−	0.256104i	$-0.0824391\pi$
$89$	11.5866	+	6.68955i	1.22818	+	0.709090i	0.261532	+	0.965195i	$0.415772\pi$
$90$	−1.95413			−0.205983
$91$		0			0
$92$	3.76028			0.392036
$93$	−9.24512	−	5.33767i	−0.958674	−	0.553491i
$94$	−4.33122	−	7.50190i	−0.446731	−	0.773761i
$95$	−1.62699	−	2.81802i	−0.166925	−	0.289123i
$96$	9.29610	+	5.36711i	0.948780	+	0.547778i
$97$			0.202023i			0.0205123i	0.999947	+	0.0102562i	$0.00326470\pi$
$97$			0.202023i			0.0205123i	−0.999947	+	0.0102562i	$0.996735\pi$
$98$		0			0
$99$			2.06302i			0.207341i
$100$	−1.95542	+	3.38689i	−0.195542	+	0.338689i
$101$	8.66723	+	15.0121i	0.862421	+	1.49376i	0.869585	+	0.493783i	$0.164386\pi$
$101$	8.66723	+	15.0121i	0.862421	+	1.49376i	−0.00716374	+	0.999974i	$0.502280\pi$
$102$	7.55377	−	4.36117i	0.747934	−	0.431820i
$103$	5.40739	−	9.36587i	0.532806	−	0.922847i	−0.466460	−	0.884542i	$-0.654471\pi$
$103$	5.40739	−	9.36587i	0.532806	−	0.922847i	0.999266	−	0.0383047i	$-0.0121957\pi$
$104$	−10.7114	+	2.59373i	−1.05034	+	0.254336i
$105$		0			0
$106$			0.748033i			0.0726554i
$107$	3.05839	−	5.29729i	0.295666	−	0.512108i	−0.679474	−	0.733700i	$-0.737792\pi$
$107$	3.05839	−	5.29729i	0.295666	−	0.512108i	0.975140	+	0.221592i	$0.0711252\pi$
$108$	0.0910594	+	0.157720i	0.00876220	+	0.0151766i
$109$	9.87196	−	5.69958i	0.945563	−	0.545921i	0.0538629	−	0.998548i	$-0.482847\pi$
$109$	9.87196	−	5.69958i	0.945563	−	0.545921i	0.891700	+	0.452628i	$0.149513\pi$
$110$	0.411799	+	0.237752i	0.0392635	+	0.0226688i
$111$		−	1.02948i		−	0.0977137i
$112$		0			0
$113$	−0.923456			−0.0868714			−0.0434357	−	0.999056i	$-0.513830\pi$
$113$	−0.923456			−0.0868714			−0.0434357	+	0.999056i	$0.513830\pi$
$114$	−6.78709	+	11.7556i	−0.635669	+	1.10101i
$115$	−2.40023	+	1.38577i	−0.223822	+	0.129224i
$116$	2.79900	+	4.84801i	0.259880	+	0.450126i
$117$	10.0719	+	2.96201i	0.931145	+	0.273838i
$118$	10.5837			0.974312
$119$		0			0
$120$	−4.64819			−0.424319
$121$	−5.24900	+	9.09153i	−0.477182	+	0.826503i
$122$	4.36499	−	2.52013i	0.395187	−	0.228162i
$123$	10.5621	−	6.09801i	0.952349	−	0.549839i
$124$	−3.22652	−	1.86283i	−0.289750	−	0.167287i
$125$		−	6.00967i		−	0.537521i
$126$		0			0
$127$	8.50972			0.755116			0.377558	−	0.925986i	$-0.376764\pi$
$127$	8.50972			0.755116			0.377558	+	0.925986i	$0.376764\pi$
$128$	0.302447	+	0.174618i	0.0267328	+	0.0154342i
$129$	−13.6231	−	23.5959i	−1.19945	−	2.07750i
$130$	1.75198	−	1.66909i	0.153659	−	0.146389i
$131$	−3.50152	+	6.06482i	−0.305930	+	0.529885i	−0.977468	−	0.211084i	$-0.932301\pi$
$131$	−3.50152	+	6.06482i	−0.305930	+	0.529885i	0.671538	+	0.740970i	$0.265634\pi$
$132$			1.46180i			0.127234i
$133$		0			0
$134$	11.1821			0.965988
$135$	−0.116248	−	0.0671160i	−0.0100051	−	0.00577642i
$136$	8.84974	−	5.10940i	0.758859	−	0.438128i
$137$	5.38403	−	3.10847i	0.459989	−	0.265575i	−0.252051	−	0.967714i	$-0.581105\pi$
$137$	5.38403	−	3.10847i	0.459989	−	0.265575i	0.712040	+	0.702139i	$0.247772\pi$
$138$	10.0127	+	5.78084i	0.852338	+	0.492097i
$139$	−6.53140			−0.553986			−0.276993	−	0.960872i	$-0.589338\pi$
$139$	−6.53140			−0.553986			−0.276993	+	0.960872i	$0.589338\pi$
$140$		0			0
$141$			19.6280i			1.65297i
$142$	7.55839	−	13.0915i	0.634286	−	1.09862i
$143$	−1.76210	−	1.84961i	−0.147354	−	0.154672i
$144$	2.30442	+	3.99137i	0.192035	+	0.332614i
$145$	−3.57326	−	2.06302i	−0.296743	−	0.171325i
$146$	−5.45523			−0.451478
$147$		0			0
$148$		−	0.359285i		−	0.0295330i
$149$	3.20203	+	1.84869i	0.262320	+	0.151451i	0.625393	−	0.780310i	$-0.284939\pi$
$149$	3.20203	+	1.84869i	0.262320	+	0.151451i	−0.363072	+	0.931761i	$0.618272\pi$
$150$	−10.4136	+	6.01230i	−0.850267	+	0.490902i
$151$	4.22425	−	2.43887i	0.343764	−	0.198473i	−0.318171	−	0.948033i	$-0.603069\pi$
$151$	4.22425	−	2.43887i	0.343764	−	0.198473i	0.661935	+	0.749561i	$0.269735\pi$
$152$	−7.95152	+	13.7724i	−0.644954	+	1.11709i
$153$	−9.73430			−0.786971
$154$		0			0
$155$	2.74603			0.220566
$156$	7.13667	+	2.09881i	0.571391	+	0.168039i
$157$	−4.75984	−	8.24428i	−0.379876	−	0.657965i	0.611168	−	0.791501i	$-0.290700\pi$
$157$	−4.75984	−	8.24428i	−0.379876	−	0.657965i	−0.991044	+	0.133536i	$0.957367\pi$
$158$	3.63514	−	2.09875i	0.289196	−	0.166968i
$159$	0.847473	−	1.46787i	0.0672090	−	0.116409i
$160$	−2.76117			−0.218290
$161$		0			0
$162$			9.93329i			0.780433i
$163$	−20.5325	−	11.8544i	−1.60823	−	0.928511i	−0.989767	−	0.142696i	$-0.954423\pi$
$163$	−20.5325	−	11.8544i	−1.60823	−	0.928511i	−0.618461	−	0.785815i	$-0.712244\pi$
$164$	3.68613	−	2.12819i	0.287838	−	0.166184i
$165$	−0.538716	−	0.933084i	−0.0419390	−	0.0726405i
$166$	5.47446	−	9.48204i	0.424901	−	0.735949i
$167$			1.13193i			0.0875914i	0.999041	+	0.0437957i	$0.0139451\pi$
$167$			1.13193i			0.0875914i	−0.999041	+	0.0437957i	$0.986055\pi$
$168$		0			0
$169$	−11.5599	+	5.94713i	−0.889224	+	0.457472i
$170$	−1.12183	+	1.94306i	−0.0860402	+	0.149026i
$171$	13.1195	−	7.57452i	1.00327	−	0.579238i
$172$	−4.75442	−	8.23489i	−0.362521	−	0.627905i
$173$	−5.99458	+	10.3829i	−0.455760	+	0.789399i	−0.998732	−	0.0503522i	$-0.983966\pi$
$173$	−5.99458	+	10.3829i	−0.455760	+	0.789399i	0.542972	+	0.839751i	$0.317299\pi$
$174$			17.2121i			1.30484i
$175$		0			0
$176$		−	1.12148i		−	0.0845350i
$177$	−20.7685	−	11.9907i	−1.56106	−	0.901276i
$178$	7.17825	+	12.4331i	0.538033	+	0.931900i
$179$	4.73538	+	8.20192i	0.353939	+	0.613040i	0.986936	−	0.161114i	$-0.0515088\pi$
$179$	4.73538	+	8.20192i	0.353939	+	0.613040i	−0.632997	+	0.774154i	$0.718175\pi$
$180$	1.33826	+	0.772645i	0.0997480	+	0.0575896i
$181$	11.4314			0.849690			0.424845	−	0.905266i	$-0.360329\pi$
$181$	11.4314			0.849690			0.424845	+	0.905266i	$0.360329\pi$
$182$		0			0
$183$	−11.4206			−0.844233
$184$	11.7305	+	6.77264i	0.864788	+	0.499285i
$185$	0.132407	+	0.229335i	0.00973473	+	0.0168611i
$186$	−5.72761	−	9.92052i	−0.419969	−	0.727408i
$187$	2.05134	+	1.18434i	0.150009	+	0.0866075i
$188$			6.85011i			0.499595i
$189$		0			0
$190$		−	3.49169i		−	0.253314i
$191$	−7.84377	+	13.5858i	−0.567555	+	0.983034i	0.429252	+	0.903185i	$0.358777\pi$
$191$	−7.84377	+	13.5858i	−0.567555	+	0.983034i	−0.996807	+	0.0798496i	$0.974556\pi$
$192$	9.60776	+	16.6411i	0.693380	+	1.20097i
$193$	−19.9248	+	11.5036i	−1.43422	+	0.828045i	−0.997439	−	0.0715256i	$-0.977213\pi$
$193$	−19.9248	+	11.5036i	−1.43422	+	0.828045i	−0.436776	+	0.899570i	$0.643880\pi$
$194$	−0.108391	+	0.187739i	−0.00778202	+	0.0134788i
$195$	−5.32888	+	1.29038i	−0.381609	+	0.0924057i
$196$		0			0
$197$		−	10.2035i		−	0.726970i	−0.931600	−	0.363485i	$-0.881587\pi$
$197$		−	10.2035i		−	0.726970i	0.931600	−	0.363485i	$-0.118413\pi$
$198$	−1.10687	+	1.91715i	−0.0786616	+	0.136246i
$199$	−5.96173	−	10.3260i	−0.422616	−	0.731992i	0.573579	−	0.819150i	$-0.305555\pi$
$199$	−5.96173	−	10.3260i	−0.422616	−	0.731992i	−0.996194	+	0.0871586i	$0.972221\pi$
$200$	−12.2002	+	7.04381i	−0.862687	+	0.498072i
$201$	−21.9427	−	12.6686i	−1.54772	−	0.893576i
$202$			18.6008i			1.30875i
$203$		0			0
$204$	−6.89747			−0.482920
$205$	−1.56860	+	2.71689i	−0.109555	+	0.189756i
$206$	10.0501	−	5.80243i	0.700223	−	0.404274i
$207$	−6.45152	−	11.1744i	−0.448412	−	0.776672i
$208$	−5.47519	−	1.61019i	−0.379636	−	0.111646i
$209$	−3.68627			−0.254984
$210$		0			0
$211$	−15.5893			−1.07321			−0.536606	−	0.843833i	$-0.680294\pi$
$211$	−15.5893			−1.07321			−0.536606	+	0.843833i	$0.680294\pi$
$212$	0.295766	−	0.512281i	0.0203133	−	0.0351836i
$213$	−29.6637	+	17.1263i	−2.03252	+	1.17348i
$214$	5.68428	−	3.28182i	0.388570	−	0.224341i
$215$	6.06959	+	3.50428i	0.413942	+	0.238990i
$216$			0.656028i			0.0446370i
$217$		0			0
$218$	12.2319			0.828451
$219$	10.7048	+	6.18042i	0.723364	+	0.417634i
$220$	−0.188010	−	0.325643i	−0.0126757	−	0.0219549i
$221$	8.72731	−	8.31440i	0.587062	−	0.559287i
$222$	0.552343	−	0.956687i	0.0370709	−	0.0642086i
$223$		−	6.76662i		−	0.453126i	−0.973996	−	0.226563i	$-0.927251\pi$
$223$		−	6.76662i		−	0.453126i	0.973996	−	0.226563i	$-0.0727490\pi$
$224$		0			0
$225$	13.4197			0.894645
$226$	−0.858161	−	0.495459i	−0.0570840	−	0.0329575i
$227$	14.5704	−	8.41225i	0.967074	−	0.558340i	0.0687311	−	0.997635i	$-0.478105\pi$
$227$	14.5704	−	8.41225i	0.967074	−	0.558340i	0.898343	+	0.439295i	$0.144772\pi$
$228$	9.29610	−	5.36711i	0.615650	−	0.355445i
$229$	9.54855	+	5.51286i	0.630986	+	0.364300i	0.781134	−	0.624364i	$-0.214642\pi$
$229$	9.54855	+	5.51286i	0.630986	+	0.364300i	−0.150148	+	0.988664i	$0.547975\pi$
$230$	−2.97402			−0.196101
$231$		0			0
$232$			20.1651i			1.32390i
$233$	8.67743	−	15.0298i	0.568477	−	0.984632i	−0.428239	−	0.903665i	$-0.640866\pi$
$233$	8.67743	−	15.0298i	0.568477	−	0.984632i	0.996717	−	0.0809664i	$-0.0258006\pi$
$234$	7.77052	+	8.15642i	0.507975	+	0.533202i
$235$	−2.52446	−	4.37249i	−0.164678	−	0.285230i
$236$	−7.24814	−	4.18472i	−0.471814	−	0.272402i
$237$	−9.51100			−0.617806
$238$		0			0
$239$		−	19.7223i		−	1.27573i	−0.770148	−	0.637865i	$-0.779818\pi$
$239$		−	19.7223i		−	1.27573i	0.770148	−	0.637865i	$-0.220182\pi$
$240$	−2.08453	−	1.20350i	−0.134556	−	0.0776858i
$241$	−2.41112	+	1.39206i	−0.155314	+	0.0896706i	−0.575643	−	0.817701i	$-0.695248\pi$
$241$	−2.41112	+	1.39206i	−0.155314	+	0.0896706i	0.420329	+	0.907372i	$0.361915\pi$
$242$	−9.75571	+	5.63246i	−0.627121	+	0.362069i
$243$	10.9318	−	18.9345i	0.701278	−	1.21465i
$244$	−3.98574			−0.255161
$245$		0			0
$246$	13.0870			0.834397
$247$	−5.29262	+	17.9967i	−0.336761	+	1.14510i
$248$	−6.71028	−	11.6226i	−0.426103	−	0.738033i
$249$	−21.4851	+	12.4044i	−1.36156	+	0.786098i
$250$	3.22435	−	5.58475i	0.203926	−	0.353210i
$251$	23.5608			1.48714			0.743572	−	0.668655i	$-0.233130\pi$
$251$	23.5608			1.48714			0.743572	+	0.668655i	$0.233130\pi$
$252$		0			0
$253$			3.13974i			0.197394i
$254$	7.90803	+	4.56570i	0.496194	+	0.286478i
$255$	4.40273	−	2.54191i	0.275709	−	0.159181i
$256$	8.09042	+	14.0130i	0.505651	+	0.875814i
$257$	1.71615	−	2.97245i	0.107050	−	0.185417i	−0.807524	−	0.589835i	$-0.799193\pi$
$257$	1.71615	−	2.97245i	0.107050	−	0.185417i	0.914574	+	0.404419i	$0.132526\pi$
$258$		−	29.2367i		−	1.82019i
$259$		0			0
$260$	−1.85976	+	0.450337i	−0.115338	+	0.0279287i
$261$	9.60450	−	16.6355i	0.594503	−	1.02971i
$262$	−6.50788	+	3.75733i	−0.402058	+	0.232128i
$263$	10.7245	+	18.5754i	0.661303	+	1.14541i	0.980273	+	0.197646i	$0.0633298\pi$
$263$	10.7245	+	18.5754i	0.661303	+	1.14541i	−0.318970	+	0.947765i	$0.603337\pi$
$264$	−2.63285	+	4.56023i	−0.162041	+	0.280663i
$265$			0.435992i			0.0267828i
$266$		0			0
$267$		−	32.5300i		−	1.99080i
$268$	−7.65794	−	4.42131i	−0.467783	−	0.270075i
$269$	7.32843	+	12.6932i	0.446822	+	0.773919i	0.998177	−	0.0603517i	$-0.0192222\pi$
$269$	7.32843	+	12.6932i	0.446822	+	0.773919i	−0.551355	+	0.834271i	$0.685889\pi$
$270$	−0.0720191	−	0.124741i	−0.00438294	−	0.00759148i
$271$	−1.76986	−	1.02183i	−0.107511	−	0.0620717i	0.445280	−	0.895391i	$-0.353104\pi$
$271$	−1.76986	−	1.02183i	−0.107511	−	0.0620717i	−0.552792	+	0.833320i	$0.686437\pi$
$272$	5.29168			0.320856
$273$		0			0
$274$	6.67112			0.403017
$275$	−2.82797	−	1.63273i	−0.170533	−	0.0984572i
$276$	−4.57138	−	7.91787i	−0.275165	−	0.476600i
$277$	−2.71678	−	4.70560i	−0.163236	−	0.282732i	0.772792	−	0.634660i	$-0.218860\pi$
$277$	−2.71678	−	4.70560i	−0.163236	−	0.282732i	−0.936027	+	0.351927i	$0.885526\pi$
$278$	−6.06959	−	3.50428i	−0.364030	−	0.210173i
$279$			12.7843i			0.765373i
$280$		0			0
$281$			20.2356i			1.20715i	0.797305	+	0.603577i	$0.206258\pi$
$281$			20.2356i			1.20715i	−0.797305	+	0.603577i	$0.793742\pi$
$282$	−10.5310	+	18.2401i	−0.627109	+	1.08618i
$283$	−0.867593	−	1.50272i	−0.0515731	−	0.0893272i	0.839086	−	0.543998i	$-0.183090\pi$
$283$	−0.867593	−	1.50272i	−0.0515731	−	0.0893272i	−0.890659	+	0.454671i	$0.849757\pi$
$284$	−10.3525	+	5.97704i	−0.614310	+	0.354672i
$285$	−3.95586	+	6.85176i	−0.234325	+	0.405863i
$286$	−0.645140	−	2.66424i	−0.0381479	−	0.157540i
$287$		0			0
$288$		−	12.8548i		−	0.757474i
$289$	2.91173	−	5.04326i	0.171278	−	0.296662i
$290$	−2.21373	−	3.83430i	−0.129995	−	0.225158i
$291$	0.425392	−	0.245600i	0.0249369	−	0.0143973i
$292$	3.73595	+	2.15695i	0.218630	+	0.126226i
$293$		−	27.2441i		−	1.59162i	−0.605547	−	0.795810i	$-0.707046\pi$
$293$		−	27.2441i		−	1.59162i	0.605547	−	0.795810i	$-0.292954\pi$
$294$		0			0
$295$	6.16875			0.359159
$296$	0.647107	−	1.12082i	0.0376123	−	0.0651465i
$297$	−0.131692	+	0.0760324i	−0.00764154	+	0.00441185i
$298$	1.98375	+	3.43595i	0.114915	+	0.199039i
$299$	15.3285	+	4.50794i	0.886472	+	0.260701i
$300$	9.50884			0.548993
$301$		0			0
$302$	5.23409			0.301188
$303$	21.0735	−	36.5004i	1.21064	−	2.09690i
$304$	−7.13190	+	4.11760i	−0.409042	+	0.236161i
$305$	2.54414	−	1.46886i	0.145677	−	0.0841067i
$306$	−9.04601	−	5.22272i	−0.517126	−	0.298563i
$307$		−	12.7138i		−	0.725612i	−0.931865	−	0.362806i	$-0.881819\pi$
$307$		−	12.7138i		−	0.725612i	0.931865	−	0.362806i	$-0.118181\pi$
$308$		0			0
$309$	−26.2951			−1.49588
$310$	2.55186	+	1.47332i	0.144936	+	0.0836788i
$311$	−4.80939	−	8.33011i	−0.272716	−	0.472357i	0.696841	−	0.717226i	$-0.254588\pi$
$311$	−4.80939	−	8.33011i	−0.272716	−	0.472357i	−0.969556	+	0.244869i	$0.921255\pi$
$312$	18.4833	+	19.4013i	1.04641	+	1.09838i
$313$	−4.51273	+	7.81628i	−0.255075	+	0.441802i	−0.964916	−	0.262559i	$-0.915433\pi$
$313$	−4.51273	+	7.81628i	−0.255075	+	0.441802i	0.709841	+	0.704362i	$0.248767\pi$
$314$		−	10.2151i		−	0.576473i
$315$		0			0
$316$	−3.31931			−0.186726
$317$	21.3269	+	12.3131i	1.19784	+	0.691572i	0.960073	−	0.279750i	$-0.0902517\pi$
$317$	21.3269	+	12.3131i	1.19784	+	0.691572i	0.237766	+	0.971323i	$0.423585\pi$
$318$	1.57510	−	0.909386i	0.0883273	−	0.0509958i
$319$	−4.04797	+	2.33709i	−0.226643	+	0.130852i
$320$	−4.28061	−	2.47141i	−0.239293	−	0.138156i
$321$	−14.8724			−0.830095
$322$		0			0
$323$		−	17.3935i		−	0.967802i
$324$	3.92754	−	6.80269i	0.218196	−	0.377927i
$325$	−12.0314	+	11.4622i	−0.667384	+	0.635809i
$326$	−12.7205	−	22.0325i	−0.704521	−	1.22027i
$327$	−24.0027	−	13.8580i	−1.32735	−	0.766348i
$328$	15.3323			0.846584
$329$		0			0
$330$		−	1.15614i		−	0.0636436i
$331$	11.4071	+	6.58591i	0.626993	+	0.361994i	0.779586	−	0.626295i	$-0.215429\pi$
$331$	11.4071	+	6.58591i	0.626993	+	0.361994i	−0.152594	+	0.988289i	$0.548763\pi$
$332$	−7.49823	+	4.32911i	−0.411519	+	0.237591i
$333$	−1.06768	+	0.616426i	−0.0585085	+	0.0337799i
$334$	−0.607311	+	1.05189i	−0.0332306	+	0.0575571i
$335$	6.51752			0.356090
$336$		0			0
$337$	17.0307			0.927720			0.463860	−	0.885909i	$-0.346464\pi$
$337$	17.0307			0.927720			0.463860	+	0.885909i	$0.346464\pi$
$338$	−13.9333	−	0.675587i	−0.757874	−	0.0367471i
$339$	1.12265	+	1.94448i	0.0609738	+	0.105610i
$340$	1.53654	−	0.887121i	0.0833305	−	0.0481109i
$341$	1.55542	−	2.69406i	0.0842306	−	0.145892i
$342$	16.2558			0.879010
$343$		0			0
$344$		−	34.2527i		−	1.84678i
$345$	5.83592	+	3.36937i	0.314195	+	0.181401i
$346$	−11.1414	+	6.43251i	−0.598968	+	0.345814i
$347$	−0.229959	−	0.398300i	−0.0123448	−	0.0213819i	0.859787	−	0.510653i	$-0.170596\pi$
$347$	−0.229959	−	0.398300i	−0.0123448	−	0.0213819i	−0.872132	+	0.489271i	$0.837263\pi$
$348$	6.80550	−	11.7875i	0.364813	−	0.631875i
$349$			6.87822i			0.368183i	0.982909	+	0.184091i	$0.0589342\pi$
$349$			6.87822i			0.368183i	−0.982909	+	0.184091i	$0.941066\pi$
$350$		0			0
$351$	0.182119	+	0.752098i	0.00972078	+	0.0401440i
$352$	−1.56400	+	2.70892i	−0.0833613	+	0.144386i
$353$	1.32784	−	0.766631i	0.0706740	−	0.0408036i	−0.464247	−	0.885706i	$-0.653675\pi$
$353$	1.32784	−	0.766631i	0.0706740	−	0.0408036i	0.534921	+	0.844902i	$0.320342\pi$
$354$	−12.8667	−	22.2857i	−0.683856	−	1.18447i
$355$	4.40542	−	7.63041i	0.233815	−	0.404980i
$356$		−	11.3529i		−	0.601701i
$357$		0			0
$358$			10.1626i			0.537112i
$359$	23.5617	+	13.6034i	1.24354	+	0.717959i	0.969813	−	0.243848i	$-0.0784099\pi$
$359$	23.5617	+	13.6034i	1.24354	+	0.717959i	0.273728	+	0.961807i	$0.411743\pi$
$360$	2.78322	+	4.82068i	0.146688	+	0.254072i
$361$	4.03438	+	6.98774i	0.212336	+	0.367776i
$362$	10.6231	+	6.13326i	0.558339	+	0.322357i
$363$	25.5249			1.33971
$364$		0			0
$365$	−3.17959			−0.166427
$366$	−10.6131	−	6.12745i	−0.554753	−	0.320287i
$367$	13.4907	+	23.3666i	0.704208	+	1.21972i	0.966977	+	0.254865i	$0.0820311\pi$
$367$	13.4907	+	23.3666i	0.704208	+	1.21972i	−0.262769	+	0.964859i	$0.584636\pi$
$368$	3.50713	+	6.07452i	0.182822	+	0.316656i
$369$	−12.6486	−	7.30267i	−0.658460	−	0.380162i
$370$			0.284159i			0.0147727i
$371$		0			0
$372$			9.05859i			0.469666i
$373$	−1.98619	+	3.44018i	−0.102841	+	0.178126i	−0.912854	−	0.408286i	$-0.866127\pi$
$373$	−1.98619	+	3.44018i	−0.102841	+	0.178126i	0.810013	+	0.586412i	$0.199460\pi$
$374$	1.27086	+	2.20120i	0.0657147	+	0.113821i
$375$	−12.6543	+	7.30597i	−0.653466	+	0.377279i
$376$	−12.3377	+	21.3695i	−0.636269	+	1.10205i
$377$	5.59800	+	23.1181i	0.288311	+	1.19064i
$378$		0			0
$379$			11.4059i			0.585884i	0.956130	+	0.292942i	$0.0946343\pi$
$379$			11.4059i			0.585884i	−0.956130	+	0.292942i	$0.905366\pi$
$380$	−1.38058	+	2.39124i	−0.0708225	+	0.122668i
$381$	−10.3453	−	17.9186i	−0.530005	−	0.917996i
$382$	−14.5783	+	8.41680i	−0.745892	+	0.430641i
$383$	20.6044	+	11.8960i	1.05284	+	0.607856i	0.923442	−	0.383737i	$-0.125363\pi$
$383$	20.6044	+	11.8960i	1.05284	+	0.607856i	0.129395	+	0.991593i	$0.458696\pi$
$384$		−	0.849134i		−	0.0433322i
$385$		0			0
$386$	−24.6879			−1.25658
$387$	−16.3143	+	28.2573i	−0.829304	+	1.43640i
$388$	0.148460	−	0.0857137i	0.00753694	−	0.00435145i
$389$	−14.2055	−	24.6046i	−0.720247	−	1.24751i	−0.960901	−	0.276894i	$-0.910695\pi$
$389$	−14.2055	−	24.6046i	−0.720247	−	1.24751i	0.240653	−	0.970611i	$-0.422638\pi$
$390$	−5.64441	−	1.65995i	−0.285816	−	0.0840549i
$391$	−14.8148			−0.749216
$392$		0			0
$393$	17.0272			0.858911
$394$	5.47446	−	9.48204i	0.275799	−	0.477698i
$395$	2.11875	−	1.22326i	0.106606	−	0.0615489i
$396$	1.51605	−	0.875291i	0.0761843	−	0.0439850i
$397$	−8.53825	−	4.92956i	−0.428522	−	0.247408i	0.270195	−	0.962806i	$-0.412912\pi$
$397$	−8.53825	−	4.92956i	−0.428522	−	0.247408i	−0.698717	+	0.715398i	$0.746245\pi$
$398$		−	12.7945i		−	0.641332i
$399$		0			0
$400$	−7.29510			−0.364755
$401$	−10.9287	−	6.30971i	−0.545756	−	0.315092i	0.201653	−	0.979457i	$-0.435369\pi$
$401$	−10.9287	−	6.30971i	−0.545756	−	0.315092i	−0.747408	+	0.664365i	$0.768702\pi$
$402$	−13.5941	−	23.5457i	−0.678013	−	1.17435i
$403$	−10.9195	−	11.4618i	−0.543938	−	0.570950i
$404$	7.35460	−	12.7385i	0.365905	−	0.633766i
$405$			5.78964i			0.287689i
$406$		0			0
$407$	0.299994			0.0148701
$408$	−21.5173	−	12.4230i	−1.06527	−	0.615031i
$409$	−15.6381	+	9.02867i	−0.773255	+	0.446439i	−0.834035	−	0.551712i	$-0.813975\pi$
$409$	−15.6381	+	9.02867i	−0.773255	+	0.446439i	0.0607793	+	0.998151i	$0.480641\pi$
$410$	−2.91537	+	1.68319i	−0.143980	+	0.0831268i
$411$	−13.0908	−	7.55795i	−0.645720	−	0.372806i
$412$	−9.17691			−0.452114
$413$		0			0
$414$		−	13.8457i		−	0.680478i
$415$	3.19080	−	5.52663i	0.156630	−	0.271291i
$416$	10.9797	+	11.5250i	0.538324	+	0.565058i
$417$	7.94024	+	13.7529i	0.388835	+	0.673483i
$418$	−3.42562	−	1.97778i	−0.167553	−	0.0967366i
$419$	−14.2805			−0.697647			−0.348823	−	0.937188i	$-0.613419\pi$
$419$	−14.2805			−0.697647			−0.348823	+	0.937188i	$0.613419\pi$
$420$		0			0
$421$		−	4.27439i		−	0.208321i	−0.994561	−	0.104160i	$-0.966784\pi$
$421$		−	4.27439i		−	0.208321i	0.994561	−	0.104160i	$-0.0332155\pi$
$422$	−14.4870	−	8.36410i	−0.705218	−	0.407158i
$423$	20.3564	−	11.7527i	0.989760	−	0.571438i
$424$	1.84534	−	1.06541i	0.0896175	−	0.0517407i
$425$	7.70398	−	13.3437i	0.373698	−	0.647263i
$426$	−36.7550			−1.78079
$427$		0			0
$428$	−5.19042			−0.250888
$429$	−1.75245	+	5.95894i	−0.0846092	+	0.287700i
$430$	3.76028	+	6.51300i	0.181337	+	0.314085i
$431$	−12.6498	+	7.30335i	−0.609318	+	0.351790i	−0.772698	−	0.634773i	$-0.781094\pi$
$431$	−12.6498	+	7.30335i	−0.609318	+	0.351790i	0.163381	+	0.986563i	$0.447760\pi$
$432$	−0.169858	+	0.294203i	−0.00817230	+	0.0141548i
$433$	−28.0099			−1.34607			−0.673035	−	0.739611i	$-0.735009\pi$
$433$	−28.0099			−1.34607			−0.673035	+	0.739611i	$0.735009\pi$
$434$		0			0
$435$			10.0321i			0.481001i
$436$	−8.37688	−	4.83640i	−0.401180	−	0.231621i
$437$	19.9667	−	11.5278i	0.955137	−	0.551448i
$438$	6.63193	+	11.4868i	0.316886	+	0.548863i
$439$	−8.53872	+	14.7895i	−0.407531	+	0.705864i	−0.994612	−	0.103664i	$-0.966943\pi$
$439$	−8.53872	+	14.7895i	−0.407531	+	0.705864i	0.587082	+	0.809528i	$0.300277\pi$
$440$		−	1.35450i		−	0.0645733i
$441$		0			0
$442$	12.5711	−	3.04407i	0.597947	−	0.144792i
$443$	−6.90783	+	11.9647i	−0.328201	+	0.568461i	−0.982155	−	0.188073i	$-0.939776\pi$
$443$	−6.90783	+	11.9647i	−0.328201	+	0.568461i	0.653954	+	0.756534i	$0.273109\pi$
$444$	−0.756531	+	0.436783i	−0.0359034	+	0.0207288i
$445$	4.18386	+	7.24665i	0.198334	+	0.343524i
$446$	3.63048	−	6.28817i	0.171908	−	0.297754i
$447$		−	8.98984i		−	0.425205i
$448$		0			0
$449$			32.6410i			1.54042i	0.637789	+	0.770211i	$0.279849\pi$
$449$			32.6410i			1.54042i	−0.637789	+	0.770211i	$0.720151\pi$
$450$	12.4708	+	7.20003i	0.587880	+	0.339412i
$451$	1.77698	+	3.07783i	0.0836749	+	0.144929i
$452$	0.391801	+	0.678619i	0.0184287	+	0.0319195i
$453$	−10.2709	−	5.92988i	−0.482567	−	0.278610i
$454$	18.0536			0.847298
$455$		0			0
$456$	38.6667			1.81074
$457$	−2.74559	−	1.58517i	−0.128433	−	0.0741511i	0.434407	−	0.900717i	$-0.356958\pi$
$457$	−2.74559	−	1.58517i	−0.128433	−	0.0741511i	−0.562840	+	0.826566i	$0.690291\pi$
$458$	5.91560	+	10.2461i	0.276418	+	0.478769i
$459$	−0.358756	−	0.621384i	−0.0167453	−	0.0290037i
$460$	2.03672	+	1.17590i	0.0949625	+	0.0548266i
$461$		−	0.202023i		−	0.00940915i	−0.999989	−	0.00470458i	$-0.998502\pi$
$461$		−	0.202023i		−	0.00940915i	0.999989	−	0.00470458i	$-0.00149752\pi$
$462$		0			0
$463$		−	17.2121i		−	0.799912i	−0.916534	−	0.399956i	$-0.869025\pi$
$463$		−	17.2121i		−	0.799912i	0.916534	−	0.399956i	$-0.130975\pi$
$464$	−5.22112	+	9.04325i	−0.242384	+	0.419822i
$465$	−3.33835	−	5.78219i	−0.154812	−	0.268143i
$466$	16.1277	−	9.31136i	0.747103	−	0.431340i
$467$	0.0955845	−	0.165557i	0.00442312	−	0.00766108i	−0.863805	−	0.503826i	$-0.831925\pi$
$467$	0.0955845	−	0.165557i	0.00442312	−	0.00766108i	0.868228	+	0.496165i	$0.165259\pi$
$468$	−2.09657	−	8.65821i	−0.0969139	−	0.400226i
$469$		0			0
$470$		−	5.41777i		−	0.249903i
$471$	−11.5731	+	20.0452i	−0.533260	+	0.923633i
$472$	−15.0742	−	26.1092i	−0.693845	−	1.20177i
$473$	6.87593	−	3.96982i	0.316156	−	0.182533i
$474$	−8.83850	−	5.10291i	−0.405966	−	0.234384i
$475$			23.9787i			1.10022i
$476$		0			0
$477$	−2.02978			−0.0929374
$478$	10.5816	−	18.3278i	0.483989	−	0.838294i
$479$	−18.6009	+	10.7392i	−0.849897	+	0.490688i	−0.860616	−	0.509254i	$-0.829921\pi$
$479$	−18.6009	+	10.7392i	−0.849897	+	0.490688i	0.0107189	+	0.999943i	$0.496588\pi$
$480$	3.35676	+	5.81408i	0.153214	+	0.265375i
$481$	0.430721	−	1.46460i	0.0196392	−	0.0667800i
$482$	−2.98752			−0.136078
$483$		0			0
$484$	8.90811			0.404914
$485$	−0.0631758	+	0.109424i	−0.00286867	+	0.00496868i
$486$	20.3178	−	11.7305i	0.921633	−	0.532105i
$487$	−16.4964	+	9.52422i	−0.747525	+	0.431584i	−0.824799	−	0.565426i	$-0.808712\pi$
$487$	−16.4964	+	9.52422i	−0.747525	+	0.431584i	0.0772740	+	0.997010i	$0.475378\pi$
$488$	−12.4339	−	7.17871i	−0.562856	−	0.324965i
$489$			57.6458i			2.60684i
$490$		0			0
$491$	−35.7559			−1.61364			−0.806821	−	0.590796i	$-0.798814\pi$
$491$	−35.7559			−1.61364			−0.806821	+	0.590796i	$0.798814\pi$
$492$	−8.96247	−	5.17448i	−0.404059	−	0.233284i
$493$	−11.0275	−	19.1002i	−0.496654	−	0.860230i
$494$	−14.5741	+	13.8846i	−0.655721	+	0.624697i
$495$	−0.645140	+	1.11741i	−0.0289969	+	0.0502240i
$496$		−	6.94968i		−	0.312050i
$497$		0			0
$498$	−26.6213			−1.19293
$499$	15.3192	+	8.84457i	0.685784	+	0.395937i	0.802031	−	0.597283i	$-0.203753\pi$
$499$	15.3192	+	8.84457i	0.685784	+	0.395937i	−0.116247	+	0.993220i	$0.537086\pi$
$500$	−4.41632	+	2.54976i	−0.197504	+	0.114029i
$501$	2.38346	−	1.37609i	0.106485	−	0.0614792i
$502$	21.8949	+	12.6410i	0.977217	+	0.564196i
$503$	−11.3305			−0.505203			−0.252601	−	0.967570i	$-0.581286\pi$
$503$	−11.3305			−0.505203			−0.252601	+	0.967570i	$0.581286\pi$
$504$		0			0
$505$			10.8415i			0.482441i
$506$	−1.68456	+	2.91774i	−0.0748878	+	0.129709i
$507$	26.5760	+	17.1113i	1.18028	+	0.759939i
$508$	−3.61048	−	6.25353i	−0.160189	−	0.277455i
$509$	16.7588	+	9.67569i	0.742821	+	0.428868i	0.823094	−	0.567905i	$-0.192246\pi$
$509$	16.7588	+	9.67569i	0.742821	+	0.428868i	−0.0802734	+	0.996773i	$0.525579\pi$
$510$	5.45523			0.241562
$511$		0			0
$512$			16.6645i			0.736472i
$513$	0.967032	+	0.558316i	0.0426955	+	0.0246502i
$514$	3.18961	−	1.84152i	0.140687	−	0.0812259i
$515$	5.85772	−	3.38195i	0.258122	−	0.149027i
$516$	−11.5599	+	20.0224i	−0.508897	+	0.881435i
$517$	−5.71967			−0.251551
$518$		0			0
$519$	29.1505			1.27957
$520$	−6.61280	−	1.94474i	−0.289991	−	0.0852827i
$521$	−3.85550	−	6.67791i	−0.168912	−	0.292565i	0.769125	−	0.639098i	$-0.220692\pi$
$521$	−3.85550	−	6.67791i	−0.168912	−	0.292565i	−0.938038	+	0.346533i	$0.887359\pi$
$522$	17.8508	−	10.3062i	0.781307	−	0.451088i
$523$	−17.5251	+	30.3543i	−0.766317	+	1.32730i	0.173230	+	0.984881i	$0.444580\pi$
$523$	−17.5251	+	30.3543i	−0.766317	+	1.32730i	−0.939547	+	0.342419i	$0.888754\pi$
$524$	5.94246			0.259597
$525$		0			0
$526$			23.0160i			1.00355i
$527$	12.7119	+	7.33919i	0.553737	+	0.319700i
$528$	−2.36146	+	1.36339i	−0.102769	+	0.0593339i
$529$	1.68133	+	2.91214i	0.0731011	+	0.126615i
$530$	−0.233922	+	0.405165i	−0.0101609	+	0.0175992i
$531$			28.7189i			1.24630i
$532$		0			0
$533$	17.5776	−	4.25637i	0.761370	−	0.184364i
$534$	17.4532	−	30.2299i	0.755275	−	1.30818i
$535$	3.31309	−	1.91282i	0.143238	−	0.0826982i
$536$	−15.9264	−	27.5854i	−0.687917	−	1.19151i
$537$	11.5136	−	19.9422i	0.496849	−	0.860568i
$538$			15.7276i			0.678066i
$539$		0			0
$540$			0.113903i			0.00490160i
$541$	−10.5079	−	6.06674i	−0.451770	−	0.260829i	0.256807	−	0.966463i	$-0.417329\pi$
$541$	−10.5079	−	6.06674i	−0.451770	−	0.260829i	−0.708577	+	0.705633i	$0.750663\pi$
$542$	−1.09648	−	1.89916i	−0.0470978	−	0.0815758i
$543$	−13.8972	−	24.0706i	−0.596385	−	1.03297i
$544$	−12.7820	−	7.37967i	−0.548022	−	0.316401i
$545$	7.12940			0.305390
$546$		0			0
$547$	−5.12546			−0.219149			−0.109575	−	0.993979i	$-0.534949\pi$
$547$	−5.12546			−0.219149			−0.109575	+	0.993979i	$0.534949\pi$
$548$	−4.56864	−	2.63770i	−0.195162	−	0.112677i
$549$	6.83835	+	11.8444i	0.291854	+	0.505505i
$550$	−1.75201	−	3.03457i	−0.0747058	−	0.129394i
$551$	29.7248	+	17.1616i	1.26632	+	0.731109i
$552$		−	32.9340i		−	1.40177i
$553$		0			0
$554$		−	5.83051i		−	0.247715i
$555$	0.321934	−	0.557606i	0.0136653	−	0.0236691i
$556$	2.77112	+	4.79972i	0.117522	+	0.203554i
$557$	32.5267	−	18.7793i	1.37820	−	0.795705i	0.386258	−	0.922391i	$-0.373767\pi$
$557$	32.5267	−	18.7793i	1.37820	−	0.795705i	0.991943	+	0.126686i	$0.0404341\pi$
$558$	−6.85911	+	11.8803i	−0.290369	+	0.502934i
$559$	−9.50884	−	39.2687i	−0.402181	−	1.66089i
$560$		0			0
$561$		−	5.75922i		−	0.243154i
$562$	−10.8569	+	18.8048i	−0.457973	+	0.793232i
$563$	−14.3504	−	24.8557i	−0.604799	−	1.04754i	−0.992083	−	0.125583i	$-0.959920\pi$
$563$	−14.3504	−	24.8557i	−0.604799	−	1.04754i	0.387284	−	0.921960i	$-0.373413\pi$
$564$	14.4240	−	8.32769i	0.607359	−	0.350659i
$565$	−0.500180	−	0.288779i	−0.0210428	−	0.0121490i
$566$		−	1.86195i		−	0.0782636i
$567$		0			0
$568$	−43.0610			−1.80680
$569$	8.97417	−	15.5437i	0.376217	−	0.651627i	−0.614291	−	0.789079i	$-0.710558\pi$
$569$	8.97417	−	15.5437i	0.376217	−	0.651627i	0.990508	+	0.137452i	$0.0438914\pi$
$570$	−7.35231	+	4.24486i	−0.307955	+	0.177798i
$571$	8.91370	+	15.4390i	0.373027	+	0.646101i	0.990030	−	0.140860i	$-0.0449867\pi$
$571$	8.91370	+	15.4390i	0.373027	+	0.646101i	−0.617003	+	0.786961i	$0.711653\pi$
$572$	−0.611601	+	2.07965i	−0.0255723	+	0.0869547i
$573$	38.1428			1.59344
$574$		0			0
$575$	20.4236			0.851724
$576$	11.5058	−	19.9286i	0.479407	−	0.830357i
$577$	28.6282	−	16.5285i	1.19181	−	0.688091i	0.233092	−	0.972455i	$-0.425116\pi$
$577$	28.6282	−	16.5285i	1.19181	−	0.688091i	0.958717	+	0.284363i	$0.0917822\pi$
$578$	5.41170	−	3.12445i	0.225097	−	0.129960i
$579$	48.4451	+	27.9698i	2.01331	+	1.16239i
$580$			3.50117i			0.145378i
$581$		0			0
$582$	0.527085			0.0218484
$583$	0.427742	+	0.246957i	0.0177153	+	0.0102279i
$584$	7.76975	+	13.4576i	0.321515	+	0.556880i
$585$	4.52906	+	4.75398i	0.187254	+	0.196553i
$586$	14.6172	−	25.3178i	0.603832	−	1.04587i
$587$			14.7295i			0.607953i	0.952680	+	0.303976i	$0.0983144\pi$
$587$			14.7295i			0.607953i	−0.952680	+	0.303976i	$0.901686\pi$
$588$		0			0
$589$	−22.8433			−0.941241
$590$	5.73258	+	3.30970i	0.236006	+	0.136258i
$591$	−21.4851	+	12.4044i	−0.883779	+	0.510250i
$592$	0.580404	−	0.335097i	0.0238545	−	0.0137724i
$593$	−7.97598	−	4.60494i	−0.327534	−	0.189102i	0.327212	−	0.944951i	$-0.393891\pi$
$593$	−7.97598	−	4.60494i	−0.327534	−	0.189102i	−0.654746	+	0.755849i	$0.727224\pi$
$594$	−0.163174			−0.00669510
$595$		0			0
$596$		−	3.13743i		−	0.128514i
$597$	−14.4954	+	25.1067i	−0.593256	+	1.02755i
$598$	11.8261	+	12.4134i	0.483604	+	0.507621i
$599$	5.28727	+	9.15782i	0.216032	+	0.374178i	0.953591	−	0.301104i	$-0.0973551\pi$
$599$	5.28727	+	9.15782i	0.216032	+	0.374178i	−0.737559	+	0.675282i	$0.764022\pi$
$600$	29.6637	+	17.1263i	1.21102	+	0.699180i
$601$	−4.08916			−0.166800			−0.0834001	−	0.996516i	$-0.526578\pi$
$601$	−4.08916			−0.166800			−0.0834001	+	0.996516i	$0.526578\pi$
$602$		0			0
$603$			30.3426i			1.23565i
$604$	−3.58450	−	2.06951i	−0.145851	−	0.0842072i
$605$	−5.68613	+	3.28289i	−0.231174	+	0.133469i
$606$	39.1670	−	22.6131i	1.59105	−	0.918593i
$607$	1.80353	−	3.12380i	0.0732030	−	0.126791i	−0.827100	−	0.562054i	$-0.810011\pi$
$607$	1.80353	−	3.12380i	0.0732030	−	0.126791i	0.900303	+	0.435263i	$0.143345\pi$
$608$	22.9693			0.931527
$609$		0			0
$610$	3.15233			0.127634
$611$	−8.21211	+	27.9240i	−0.332226	+	1.12968i
$612$	4.13003	+	7.15343i	0.166947	+	0.289160i
$613$	33.3285	−	19.2422i	1.34613	−	0.777186i	0.358428	−	0.933557i	$-0.383313\pi$
$613$	33.3285	−	19.2422i	1.34613	−	0.777186i	0.987698	+	0.156371i	$0.0499796\pi$
$614$	6.82128	−	11.8148i	0.275284	−	0.476806i
$615$	7.62778			0.307582
$616$		0			0
$617$			3.09503i			0.124601i	0.998057	+	0.0623007i	$0.0198438\pi$
$617$			3.09503i			0.124601i	−0.998057	+	0.0623007i	$0.980156\pi$
$618$	−24.4359	−	14.1080i	−0.982954	−	0.567509i
$619$	−10.6255	+	6.13462i	−0.427074	+	0.246571i	−0.698099	−	0.716001i	$-0.745971\pi$
$619$	−10.6255	+	6.13462i	−0.427074	+	0.246571i	0.271025	+	0.962572i	$0.412637\pi$
$620$	−1.16507	−	2.01797i	−0.0467905	−	0.0810435i
$621$	0.475540	−	0.823660i	0.0190828	−	0.0330523i
$622$		−	10.3215i		−	0.413854i
$623$		0			0
$624$	3.26570	+	13.4864i	0.130733	+	0.539888i
$625$	−9.64277	+	16.7018i	−0.385711	+	0.668071i
$626$	−8.38730	+	4.84241i	−0.335224	+	0.193542i
$627$	4.48140	+	7.76202i	0.178970	+	0.309985i
$628$	−4.03897	+	6.99571i	−0.161173	+	0.279159i
$629$			1.41551i			0.0564402i
$630$		0			0
$631$		−	5.31780i		−	0.211698i	−0.994382	−	0.105849i	$-0.966244\pi$
$631$		−	5.31780i		−	0.211698i	0.994382	−	0.105849i	$-0.0337561\pi$
$632$	−10.3549	−	5.97840i	−0.411896	−	0.237808i
$633$	18.9520	+	32.8258i	0.753273	+	1.30471i
$634$	13.2126	+	22.8849i	0.524740	+	0.908877i
$635$	4.60921	+	2.66113i	0.182911	+	0.105604i
$636$	−1.43825			−0.0570304
$637$		0			0
$638$	−5.01566			−0.198572
$639$	35.5238	+	20.5097i	1.40530	+	0.811349i
$640$	0.109212	+	0.189160i	0.00431697	+	0.00747721i
$641$	6.09521	+	10.5572i	0.240746	+	0.416985i	0.960927	−	0.276801i	$-0.0892744\pi$
$641$	6.09521	+	10.5572i	0.240746	+	0.416985i	−0.720181	+	0.693787i	$0.755941\pi$
$642$	−13.8208	−	7.97944i	−0.545463	−	0.314923i
$643$		−	18.9733i		−	0.748235i	−0.927381	−	0.374117i	$-0.877946\pi$
$643$		−	18.9733i		−	0.748235i	0.927381	−	0.374117i	$-0.122054\pi$
$644$		0			0
$645$		−	17.0406i		−	0.670974i
$646$	9.33211	−	16.1637i	0.367167	−	0.635952i
$647$	−9.85587	−	17.0709i	−0.387474	−	0.671125i	0.604635	−	0.796503i	$-0.293319\pi$
$647$	−9.85587	−	17.0709i	−0.387474	−	0.671125i	−0.992109	+	0.125378i	$0.959986\pi$
$648$	24.5046	−	14.1478i	0.962633	−	0.555776i
$649$	3.49414	−	6.05202i	0.137157	−	0.237563i
$650$	−17.3305	+	4.19655i	−0.679759	+	0.164602i
$651$		0			0
$652$			20.1182i			0.787891i
$653$	10.1986	−	17.6645i	0.399103	−	0.691267i	−0.594512	−	0.804087i	$-0.702655\pi$
$653$	10.1986	−	17.6645i	0.399103	−	0.691267i	0.993616	+	0.112819i	$0.0359882\pi$
$654$	−14.8704	−	25.7563i	−0.581478	−	1.00715i
$655$	−3.79313	+	2.18996i	−0.148210	+	0.0855690i
$656$	6.87593	+	3.96982i	0.268460	+	0.154996i
$657$		−	14.8027i		−	0.577510i
$658$		0			0
$659$	32.6628			1.27236			0.636181	−	0.771540i	$-0.280513\pi$
$659$	32.6628			1.27236			0.636181	+	0.771540i	$0.280513\pi$
$660$	−0.457129	+	0.791771i	−0.0177937	+	0.0308196i
$661$	8.43242	−	4.86846i	0.327983	−	0.189361i	−0.326962	−	0.945037i	$-0.606025\pi$
$661$	8.43242	−	4.86846i	0.327983	−	0.189361i	0.654945	+	0.755676i	$0.272692\pi$
$662$	7.06704	+	12.2405i	0.274668	+	0.475740i
$663$	−28.1171	−	8.26889i	−1.09198	−	0.321137i
$664$	−31.1886			−1.21035
$665$		0			0
$666$	−1.32292			−0.0512620
$667$	14.6172	−	25.3178i	0.565981	−	0.980308i
$668$	0.831819	−	0.480251i	0.0321841	−	0.0185815i
$669$	−14.2482	+	8.22620i	−0.550867	+	0.318043i
$670$	6.05668	+	3.49683i	0.233990	+	0.135094i
$671$		−	3.32800i		−	0.128476i
$672$		0			0
$673$	−39.4512			−1.52073			−0.760367	−	0.649494i	$-0.774981\pi$
$673$	−39.4512			−1.52073			−0.760367	+	0.649494i	$0.774981\pi$
$674$	15.8265	+	9.13742i	0.609613	+	0.351960i
$675$	0.494581	+	0.856639i	0.0190364	+	0.0329720i
$676$	9.27496	+	5.97179i	0.356729	+	0.229684i
$677$	−24.3169	+	42.1182i	−0.934576	+	1.61873i	−0.159187	+	0.987248i	$0.550887\pi$
$677$	−24.3169	+	42.1182i	−0.934576	+	1.61873i	−0.775389	+	0.631484i	$0.782446\pi$
$678$			2.40932i			0.0925296i
$679$		0			0
$680$	6.39117			0.245090
$681$	−35.4266	−	20.4536i	−1.35755	−	0.783783i
$682$	2.89088	−	1.66905i	0.110697	−	0.0639112i
$683$	4.94304	−	2.85387i	0.189140	−	0.109200i	−0.402440	−	0.915446i	$-0.631838\pi$
$683$	4.94304	−	2.85387i	0.189140	−	0.109200i	0.591580	+	0.806246i	$0.298504\pi$
$684$	−11.1326	−	6.42738i	−0.425664	−	0.245757i
$685$	3.88828			0.148563
$686$		0			0
$687$		−	26.8080i		−	1.02279i
$688$	8.86867	−	15.3610i	0.338115	−	0.585632i
$689$	1.81981	−	1.73371i	0.0693291	−	0.0660490i
$690$	3.61552	+	6.26226i	0.137640	+	0.238400i
$691$	36.1766	+	20.8866i	1.37622	+	0.794563i	0.991703	−	0.128553i	$-0.0410333\pi$
$691$	36.1766	+	20.8866i	1.37622	+	0.794563i	0.384521	+	0.923116i	$0.374367\pi$
$692$	10.1734			0.386736
$693$		0			0
$694$		−	0.493517i		−	0.0187336i
$695$	−3.53767	−	2.04247i	−0.134191	−	0.0774754i
$696$	42.4608	−	24.5147i	1.60947	−	0.929228i
$697$	−14.5226	+	8.38464i	−0.550084	+	0.317591i
$698$	−3.69035	+	6.39188i	−0.139682	+	0.241936i
$699$	−42.1967			−1.59603
$700$		0			0
$701$	22.4361			0.847399			0.423700	−	0.905803i	$-0.360731\pi$
$701$	22.4361			0.847399			0.423700	+	0.905803i	$0.360731\pi$
$702$	−0.234279	+	0.796631i	−0.00884231	+	0.0300669i
$703$	−1.10145	−	1.90776i	−0.0415419	−	0.0719527i
$704$	−4.84929	+	2.79974i	−0.182764	+	0.105519i
$705$	−6.13798	+	10.6313i	−0.231170	+	0.400398i
$706$	1.64527			0.0619207
$707$		0			0
$708$			20.3495i			0.764780i
$709$	24.8955	+	14.3734i	0.934969	+	0.539804i	0.888380	−	0.459110i	$-0.151832\pi$
$709$	24.8955	+	14.3734i	0.934969	+	0.539804i	0.0465891	+	0.998914i	$0.485165\pi$
$710$	8.18785	−	4.72726i	0.307285	−	0.177411i
$711$	5.69495	+	9.86394i	0.213577	+	0.369927i
$712$	20.4476	−	35.4163i	0.766307	−	1.32728i
$713$			19.4566i			0.728654i
$714$		0			0
$715$	−0.376021	−	1.55286i	−0.0140624	−	0.0580735i
$716$	4.01822	−	6.95976i	0.150168	−	0.260098i
$717$	−41.5284	+	23.9765i	−1.55091	+	0.895417i
$718$	14.5972	+	25.2830i	0.544762	+	0.943555i
$719$	2.10450	−	3.64509i	0.0784844	−	0.135939i	−0.824112	−	0.566427i	$-0.808325\pi$
$719$	2.10450	−	3.64509i	0.0784844	−	0.135939i	0.902596	+	0.430488i	$0.141659\pi$
$720$			2.88251i			0.107425i
$721$		0			0
$722$			8.65821i			0.322225i
$723$	5.86242	+	3.38467i	0.218026	+	0.125877i
$724$	−4.85008	−	8.40058i	−0.180252	−	0.312205i
$725$	15.2025	+	26.3315i	0.564606	+	0.977927i
$726$	23.7201	+	13.6948i	0.880335	+	0.508262i
$727$	43.4680			1.61214			0.806070	−	0.591820i	$-0.201591\pi$
$727$	43.4680			1.61214			0.806070	+	0.591820i	$0.201591\pi$
$728$		0			0
$729$	−25.3884			−0.940312
$730$	−2.95477	−	1.70594i	−0.109361	−	0.0631396i
$731$	18.7315	+	32.4439i	0.692809	+	1.19998i
$732$	4.84548	+	8.39261i	0.179094	+	0.310200i
$733$	7.87581	+	4.54710i	0.290900	+	0.167951i	0.638348	−	0.769748i	$-0.279618\pi$
$733$	7.87581	+	4.54710i	0.290900	+	0.167951i	−0.347448	+	0.937699i	$0.612952\pi$
$734$			28.9525i			1.06866i
$735$		0			0
$736$		−	19.5639i		−	0.721133i
$737$	3.69169	−	6.39419i	0.135985	−	0.235533i
$738$	−7.83617	−	13.5726i	−0.288453	−	0.499616i
$739$	−8.32135	+	4.80433i	−0.306106	+	0.176730i	−0.645183	−	0.764028i	$-0.723219\pi$
$739$	−8.32135	+	4.80433i	−0.306106	+	0.176730i	0.339077	+	0.940759i	$0.389885\pi$
$740$	0.112354	−	0.194603i	0.00413022	−	0.00715375i
$741$	44.3292	−	10.7342i	1.62847	−	0.394331i
$742$		0			0
$743$			32.1771i			1.18046i	0.807234	+	0.590231i	$0.200964\pi$
$743$			32.1771i			1.18046i	−0.807234	+	0.590231i	$0.799036\pi$
$744$	−16.3154	+	28.2591i	−0.598152	+	1.03603i
$745$	1.15623	+	2.00265i	0.0423610	+	0.0733714i
$746$	−3.69150	+	2.13129i	−0.135155	+	0.0780320i
$747$	25.7295	+	14.8549i	0.941392	+	0.543513i
$748$		−	2.00995i		−	0.0734911i
$749$		0			0
$750$	−15.6794			−0.572531
$751$	3.89892	−	6.75313i	0.142274	−	0.246425i	−0.786079	−	0.618126i	$-0.787892\pi$
$751$	3.89892	−	6.75313i	0.142274	−	0.246425i	0.928352	+	0.371701i	$0.121225\pi$
$752$	−11.0660	+	6.38894i	−0.403534	+	0.232981i
$753$	−28.6429	−	49.6110i	−1.04381	−	1.80793i
$754$	−7.20132	+	24.4870i	−0.262256	+	0.891762i
$755$	3.05070			0.111026
$756$		0			0
$757$	17.9970			0.654110			0.327055	−	0.945005i	$-0.393944\pi$
$757$	17.9970			0.654110			0.327055	+	0.945005i	$0.393944\pi$
$758$	−6.11960	+	10.5995i	−0.222274	+	0.384990i
$759$	6.61123	−	3.81699i	0.239972	−	0.138548i
$760$	−8.61373	+	4.97314i	−0.312453	+	0.180395i
$761$	−35.2290	−	20.3395i	−1.27705	−	0.737306i	−0.300746	−	0.953704i	$-0.597236\pi$
$761$	−35.2290	−	20.3395i	−1.27705	−	0.737306i	−0.976305	+	0.216398i	$0.930569\pi$
$762$		−	22.2021i		−	0.804299i
$763$		0			0
$764$	13.3117			0.481601
$765$	−5.27248	−	3.04407i	−0.190627	−	0.110059i
$766$	12.7650	+	22.1097i	0.461220	+	0.798856i
$767$	−24.5298	−	25.7480i	−0.885720	−	0.929707i
$768$	19.6711	−	34.0713i	0.709819	−	1.22944i
$769$			39.3098i			1.41755i	0.705435	+	0.708774i	$0.250752\pi$
$769$			39.3098i			1.41755i	−0.705435	+	0.708774i	$0.749248\pi$
$770$		0			0
$771$	−8.34529			−0.300548
$772$	16.9072	+	9.76138i	0.608504	+	0.351320i
$773$	11.6685	−	6.73679i	0.419685	−	0.242306i	−0.275257	−	0.961371i	$-0.588763\pi$
$773$	11.6685	−	6.73679i	0.419685	−	0.242306i	0.694943	+	0.719065i	$0.255430\pi$
$774$	−30.3216	+	17.5062i	−1.08989	+	0.629247i
$775$	−17.5245	−	10.1178i	−0.629500	−	0.363442i
$776$	0.617515			0.0221675
$777$		0			0
$778$		−	30.4866i		−	1.09300i
$779$	13.0486	−	22.6009i	0.467516	−	0.809761i
$780$	3.20917	+	3.36855i	0.114907	+	0.120613i
$781$	−4.99068	−	8.64412i	−0.178581	−	0.309311i
$782$	−13.7673	−	7.94854i	−0.492316	−	0.284239i
$783$	1.41589			0.0505998
$784$		0			0
$785$		−	5.95391i		−	0.212504i
$786$	15.8233	+	9.13558i	0.564398	+	0.325855i
$787$	−34.4930	+	19.9145i	−1.22954	+	0.709877i	−0.966934	−	0.255026i	$-0.917916\pi$
$787$	−34.4930	+	19.9145i	−1.22954	+	0.709877i	−0.262608	+	0.964903i	$0.584583\pi$
$788$	−7.49823	+	4.32911i	−0.267114	+	0.154218i
$789$	26.0757	−	45.1644i	0.928319	−	1.60790i
$790$	2.62525			0.0934022
$791$		0			0
$792$	6.30594			0.224072
$793$	−16.2476	−	4.77823i	−0.576970	−	0.169680i
$794$	−5.28969	−	9.16201i	−0.187724	−	0.325148i
$795$	0.918051	−	0.530037i	0.0325599	−	0.0187985i
$796$	−5.05884	+	8.76217i	−0.179306	+	0.310567i
$797$	−21.2530			−0.752821			−0.376410	−	0.926453i	$-0.622842\pi$
$797$	−21.2530			−0.752821			−0.376410	+	0.926453i	$0.622842\pi$
$798$		0			0
$799$		−	26.9881i		−	0.954770i
$800$	17.6212	+	10.1736i	0.623003	+	0.359691i
$801$	−33.7371	+	19.4781i	−1.19204	+	0.688226i
$802$	−6.77067	−	11.7271i	−0.239081	−	0.414100i
$803$	−1.80100	+	3.11942i	−0.0635559	+	0.110082i
$804$			21.5000i			0.758246i
$805$		0			0
$806$	−3.99784	−	16.5099i	−0.140818	−	0.581537i
$807$	17.8184	−	30.8624i	0.627237	−	1.08641i
$808$	45.8867	−	26.4927i	1.61429	−	0.932010i
$809$	−10.7088	−	18.5481i	−0.376500	−	0.652117i	0.614050	−	0.789267i	$-0.289539\pi$
$809$	−10.7088	−	18.5481i	−0.376500	−	0.652117i	−0.990550	+	0.137150i	$0.956206\pi$
$810$	−3.10630	+	5.38027i	−0.109144	+	0.189043i
$811$		−	11.0116i		−	0.386669i	−0.981133	−	0.193335i	$-0.938070\pi$
$811$		−	11.0116i		−	0.386669i	0.981133	−	0.193335i	$-0.0619303\pi$
$812$		0			0
$813$			4.96896i			0.174269i
$814$	0.278782	+	0.160955i	0.00977131	+	0.00564147i
$815$	−7.41414	−	12.8417i	−0.259706	−	0.449824i
$816$	−6.43311	−	11.1425i	−0.225204	−	0.390065i
$817$	−50.4909	−	29.1509i	−1.76645	−	1.01986i
$818$	−19.3765			−0.677484
$819$		0			0
$820$	2.66207			0.0929636
$821$	−33.4879	−	19.3342i	−1.16873	−	0.674769i	−0.215353	−	0.976536i	$-0.569090\pi$
$821$	−33.4879	−	19.3342i	−1.16873	−	0.674769i	−0.953382	+	0.301767i	$0.902424\pi$
$822$	−8.11010	−	14.0471i	−0.282872	−	0.489949i
$823$	−10.2283	−	17.7160i	−0.356537	−	0.617540i	0.630843	−	0.775911i	$-0.282709\pi$
$823$	−10.2283	−	17.7160i	−0.356537	−	0.617540i	−0.987380	+	0.158371i	$0.949376\pi$
$824$	−28.6282	−	16.5285i	−0.997312	−	0.575798i
$825$			7.93965i			0.276423i
$826$		0			0
$827$			27.3451i			0.950881i	0.879748	+	0.475440i	$0.157711\pi$
$827$			27.3451i			0.950881i	−0.879748	+	0.475440i	$0.842289\pi$
$828$	−5.47446	+	9.48204i	−0.190251	+	0.329524i
$829$	12.5043	+	21.6581i	0.434292	+	0.752217i	0.997238	−	0.0742776i	$-0.0236651\pi$
$829$	12.5043	+	21.6581i	0.434292	+	0.752217i	−0.562945	+	0.826494i	$0.690332\pi$
$830$	5.93037	−	3.42390i	0.205846	−	0.118845i
$831$	−6.60560	+	11.4412i	−0.229146	+	0.396892i
$832$	6.70616	+	27.6945i	0.232494	+	0.960133i
$833$		0			0
$834$			17.0406i			0.590069i
$835$	−0.353972	+	0.613098i	−0.0122497	+	0.0212171i
$836$	1.56400	+	2.70892i	0.0540920	+	0.0936900i
$837$	−0.816077	+	0.471162i	−0.0282077	+	0.0162857i
$838$	−13.2707	−	7.66187i	−0.458430	−	0.264675i
$839$		−	8.76981i		−	0.302768i	−0.988475	−	0.151384i	$-0.951627\pi$
$839$		−	8.76981i		−	0.302768i	0.988475	−	0.151384i	$-0.0483729\pi$
$840$		0			0
$841$	14.5218			0.500753
$842$	2.29333	−	3.97216i	0.0790332	−	0.136890i
$843$	42.6092	−	24.6004i	1.46754	−	0.847284i
$844$	6.61418	+	11.4561i	0.227669	+	0.394335i
$845$	−8.12107	−	0.393767i	−0.279373	−	0.0135460i
$846$	25.2227			0.867174
$847$		0			0
$848$	1.10342			0.0378914
$849$	−2.10947	+	3.65371i	−0.0723968	+	0.125395i
$850$	14.3185	−	8.26679i	0.491120	−	0.283549i
$851$	−1.62492	+	0.938148i	−0.0557015	+	0.0321593i
$852$	25.1712	+	14.5326i	0.862352	+	0.497879i
$853$		−	19.8232i		−	0.678734i	−0.940654	−	0.339367i	$-0.889787\pi$
$853$		−	19.8232i		−	0.678734i	0.940654	−	0.339367i	$-0.110213\pi$
$854$		0			0
$855$	9.47469			0.324028
$856$	−16.1920	−	9.34845i	−0.553431	−	0.319523i
$857$	1.33518	+	2.31261i	0.0456090	+	0.0789972i	0.887929	−	0.459981i	$-0.152144\pi$
$857$	1.33518	+	2.31261i	0.0456090	+	0.0789972i	−0.842320	+	0.538978i	$0.818810\pi$
$858$	−4.82568	+	4.59736i	−0.164746	+	0.156951i
$859$	−19.4798	+	33.7401i	−0.664644	+	1.15120i	0.314738	+	0.949179i	$0.398083\pi$
$859$	−19.4798	+	33.7401i	−0.664644	+	1.15120i	−0.979382	+	0.202018i	$0.935250\pi$
$860$		−	5.94713i		−	0.202795i
$861$		0			0
$862$	−15.6738			−0.533851
$863$	−21.4754	−	12.3988i	−0.731030	−	0.422060i	0.0877689	−	0.996141i	$-0.472026\pi$
$863$	−21.4754	−	12.3988i	−0.731030	−	0.422060i	−0.818799	+	0.574081i	$0.805360\pi$
$864$	0.820578	−	0.473761i	0.0279166	−	0.0161177i
$865$	−6.49381	+	3.74920i	−0.220796	+	0.127477i
$866$	−26.0294	−	15.0281i	−0.884514	−	0.510675i
$867$	−14.1592			−0.480871
$868$		0			0
$869$		−	2.77154i		−	0.0940181i
$870$	−5.38249	+	9.32274i	−0.182483	+	0.316070i
$871$	−25.9167	−	27.2037i	−0.878153	−	0.921763i
$872$	−17.4216	−	30.1752i	−0.589971	−	1.02186i
$873$	−0.509428	−	0.294118i	−0.0172415	−	0.00995439i
$874$	24.7399			0.836839
$875$		0			0
$876$		−	10.4888i		−	0.354385i
$877$	1.71335	+	0.989201i	0.0578556	+	0.0334029i	0.528649	−	0.848841i	$-0.322699\pi$
$877$	1.71335	+	0.989201i	0.0578556	+	0.0334029i	−0.470793	+	0.882244i	$0.656032\pi$
$878$	−15.8699	+	9.16251i	−0.535584	+	0.309220i
$879$	−57.3668	+	33.1208i	−1.93494	+	1.11714i
$880$	0.350706	−	0.607440i	0.0118223	−	0.0204768i
$881$	17.1466			0.577683			0.288841	−	0.957377i	$-0.406730\pi$
$881$	17.1466			0.577683			0.288841	+	0.957377i	$0.406730\pi$
$882$		0			0
$883$	10.2168			0.343822			0.171911	−	0.985112i	$-0.445006\pi$
$883$	10.2168			0.343822			0.171911	+	0.985112i	$0.445006\pi$
$884$	−9.81278	−	2.88582i	−0.330039	−	0.0970606i
$885$	−7.49936	−	12.9893i	−0.252088	−	0.436630i
$886$	−12.8388	+	7.41248i	−0.431328	+	0.249027i
$887$	25.4965	−	44.1613i	0.856090	−	1.48279i	−0.0195395	−	0.999809i	$-0.506220\pi$
$887$	25.4965	−	44.1613i	0.856090	−	1.48279i	0.875630	−	0.482983i	$-0.160447\pi$
$888$	−3.14676			−0.105598
$889$		0			0
$890$			8.97901i			0.300977i
$891$	5.68008	+	3.27940i	0.190290	+	0.109864i
$892$	−4.97258	+	2.87092i	−0.166494	+	0.0961255i
$893$	21.0002	+	36.3733i	0.702743	+	1.21719i
$894$	4.82329	−	8.35419i	0.161315	−	0.279406i
$895$			5.92331i			0.197995i
$896$		0			0
$897$	−9.14277	−	37.7570i	−0.305268	−	1.26067i
$898$	−17.5128	+	30.3330i	−0.584409	+	1.01223i
$899$	−25.0847	+	14.4827i	−0.836621	+	0.483024i
$900$	−5.69365	−	9.86170i	−0.189788	−	0.328723i
$901$	−1.16526	+	2.01829i	−0.0388204	+	0.0672389i
$902$			3.81360i			0.126979i
$903$		0			0
$904$			2.82268i			0.0938811i
$905$	6.19170	+	3.57478i	0.205819	+	0.118830i
$906$	−6.36309	−	11.0212i	−0.211400	−	0.366155i
$907$	−2.89269	−	5.01028i	−0.0960501	−	0.166364i	0.813996	−	0.580870i	$-0.197288\pi$
$907$	−2.89269	−	5.01028i	−0.0960501	−	0.166364i	−0.910046	+	0.414506i	$0.863954\pi$
$908$	−12.3638	−	7.13824i	−0.410307	−	0.236891i
$909$	−50.4732			−1.67409
$910$		0			0
$911$	−1.70706			−0.0565573			−0.0282787	−	0.999600i	$-0.509003\pi$
$911$	−1.70706			−0.0565573			−0.0282787	+	0.999600i	$0.509003\pi$
$912$	17.3405	+	10.0116i	0.574202	+	0.331516i
$913$	−3.61470	−	6.26084i	−0.119629	−	0.207204i
$914$	−1.70097	−	2.94617i	−0.0562632	−	0.0974507i
$915$	−6.18583	−	3.57139i	−0.204497	−	0.118067i
$916$		−	9.35590i		−	0.309128i
$917$		0			0
$918$		−	0.769931i		−	0.0254115i
$919$	−18.6025	+	32.2205i	−0.613640	+	1.06286i	0.376982	+	0.926221i	$0.376962\pi$
$919$	−18.6025	+	32.2205i	−0.613640	+	1.06286i	−0.990622	+	0.136634i	$0.956371\pi$
$920$	4.23582	+	7.33666i	0.139651	+	0.241882i
$921$	−26.7708	+	15.4561i	−0.882128	+	0.509297i
$922$	0.108391	−	0.187739i	0.00356967	−	0.00618284i
$923$	−49.3669	+	11.9541i	−1.62493	+	0.393474i
$924$		0			0
$925$		−	1.95142i		−	0.0641623i
$926$	9.23474	−	15.9950i	0.303472	−	0.525630i
$927$	15.7449	+	27.2709i	0.517129	+	0.895693i
$928$	25.2230	−	14.5625i	0.827987	−	0.478038i
$929$	17.2379	+	9.95229i	0.565556	+	0.326524i	0.755373	−	0.655296i	$-0.227456\pi$
$929$	17.2379	+	9.95229i	0.565556	+	0.326524i	−0.189816	+	0.981820i	$0.560789\pi$
$930$		−	7.16447i		−	0.234932i
$931$		0			0
$932$	−14.7265			−0.482383
$933$	−11.6936	+	20.2539i	−0.382831	+	0.663082i
$934$	0.177652	−	0.102567i	0.00581295	−	0.00335611i
$935$	0.740724	+	1.28297i	0.0242243	+	0.0419577i
$936$	9.05385	−	30.7862i	0.295934	−	1.00628i
$937$	−7.16949			−0.234217			−0.117109	−	0.993119i	$-0.537363\pi$
$937$	−7.16949			−0.234217			−0.117109	+	0.993119i	$0.537363\pi$
$938$		0			0
$939$	21.9446			0.716134
$940$	−2.14214	+	3.71029i	−0.0698688	+	0.121016i
$941$	−2.65066	+	1.53036i	−0.0864091	+	0.0498883i	−0.542582	−	0.840003i	$-0.682553\pi$
$941$	−2.65066	+	1.53036i	−0.0864091	+	0.0498883i	0.456173	+	0.889891i	$0.349220\pi$
$942$	−21.5096	+	12.4186i	−0.700820	+	0.404619i
$943$	−19.2501	−	11.1140i	−0.626869	−	0.361923i
$944$		−	15.6120i		−	0.508126i
$945$		0			0
$946$	8.51968			0.276999
$947$	−38.2832	−	22.1028i	−1.24404	−	0.718244i	−0.274122	−	0.961695i	$-0.588387\pi$
$947$	−38.2832	−	22.1028i	−1.24404	−	0.718244i	−0.969913	+	0.243451i	$0.921721\pi$
$948$	4.03529	+	6.98933i	0.131060	+	0.227003i
$949$	12.6435	+	13.2714i	0.410426	+	0.430809i
$950$	−12.8652	+	22.2832i	−0.417403	+	0.722963i
$951$		−	59.8762i		−	1.94162i
$952$		0			0
$953$	13.7002			0.443791			0.221896	−	0.975070i	$-0.428776\pi$
$953$	13.7002			0.443791			0.221896	+	0.975070i	$0.428776\pi$
$954$	−1.88626	−	1.08903i	−0.0610700	−	0.0352588i
$955$	−8.49700	+	4.90574i	−0.274956	+	0.158746i
$956$	−14.4933	+	8.36771i	−0.468747	+	0.270631i
$957$	9.84225	+	5.68242i	0.318155	+	0.183687i
$958$	−23.0476			−0.744634
$959$		0			0
$960$			12.0180i			0.387879i
$961$	−5.86129	+	10.1520i	−0.189074	+	0.327485i
$962$	1.18606	−	1.12995i	0.0382403	−	0.0364310i
$963$	8.90521	+	15.4243i	0.286966	+	0.497040i
$964$	2.04597	+	1.18124i	0.0658961	+	0.0380451i
$965$	−14.3894			−0.463211
$966$		0			0
$967$		−	43.9429i		−	1.41311i	−0.707659	−	0.706554i	$-0.750249\pi$
$967$		−	43.9429i		−	1.41311i	0.707659	−	0.706554i	$-0.249751\pi$
$968$	27.7897	+	16.0444i	0.893194	+	0.515686i
$969$	−36.6248	+	21.1454i	−1.17656	+	0.679287i
$970$	−0.117418	+	0.0677912i	−0.00377006	+	0.00217664i
$971$	−10.6585	+	18.4611i	−0.342049	+	0.592446i	−0.984813	−	0.173618i	$-0.944454\pi$
$971$	−10.6585	+	18.4611i	−0.342049	+	0.592446i	0.642764	+	0.766064i	$0.277788\pi$
$972$	−18.5525			−0.595072
$973$		0			0
$974$	−20.4400			−0.654941
$975$	38.7621	+	11.3995i	1.24138	+	0.365075i
$976$	−3.71741	−	6.43874i	−0.118991	−	0.206099i
$977$	−14.2432	+	8.22330i	−0.455679	+	0.263087i	−0.710226	−	0.703974i	$-0.751407\pi$
$977$	−14.2432	+	8.22330i	−0.455679	+	0.263087i	0.254547	+	0.967061i	$0.418074\pi$
$978$	−30.9286	+	53.5699i	−0.988987	+	1.71298i
$979$	9.47937			0.302962
$980$		0			0
$981$			33.1913i			1.05972i
$982$	−33.2277	−	19.1840i	−1.06034	−	0.612187i
$983$	10.1415	−	5.85521i	0.323464	−	0.186752i	−0.329471	−	0.944166i	$-0.606871\pi$
$983$	10.1415	−	5.85521i	0.323464	−	0.186752i	0.652936	+	0.757413i	$0.273537\pi$
$984$	−18.6395	−	32.2846i	−0.594206	−	1.02919i
$985$	3.19080	−	5.52663i	0.101667	−	0.176093i
$986$		−	23.6662i		−	0.753687i
$987$		0			0
$988$	15.4708	−	3.74621i	0.492190	−	0.119183i
$989$	−24.8290	+	43.0051i	−0.789517	+	1.36748i
$990$	−1.19905	+	0.692270i	−0.0381082	+	0.0220018i
$991$	15.6873	+	27.1713i	0.498325	+	0.863124i	0.999998	−	0.00193305i	$-0.000615311\pi$
$991$	15.6873	+	27.1713i	0.498325	+	0.863124i	−0.501673	+	0.865057i	$0.667282\pi$
$992$	−9.69187	+	16.7868i	−0.307717	+	0.532982i
$993$		−	32.0260i		−	1.01632i
$994$		0			0
$995$		−	7.45731i		−	0.236413i
$996$	18.2312	+	10.5258i	0.577679	+	0.333523i
$997$	−2.34855	−	4.06781i	−0.0743794	−	0.128829i	0.826437	−	0.563029i	$-0.190364\pi$
$997$	−2.34855	−	4.06781i	−0.0743794	−	0.128829i	−0.900816	+	0.434201i	$0.857031\pi$
$998$	9.49071	+	16.4384i	0.300423	+	0.520348i
$999$	−0.0786985	−	0.0454366i	−0.00248991	−	0.00143755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.f.324.6		16
7.2	even	3		637.2.c.e.246.3		8
7.3	odd	6		91.2.r.a.25.3	✓	16
7.4	even	3	inner	637.2.r.f.116.3		16
7.5	odd	6		637.2.c.f.246.3		8
7.6	odd	2		91.2.r.a.51.6	yes	16
13.12	even	2	inner	637.2.r.f.324.3		16
21.17	even	6		819.2.dl.e.298.6		16
21.20	even	2		819.2.dl.e.415.3		16
91.5	even	12		8281.2.a.ck.1.3		8
91.12	odd	6		637.2.c.f.246.6		8
91.25	even	6	inner	637.2.r.f.116.6		16
91.31	even	12		1183.2.e.i.508.6		16
91.34	even	4		1183.2.e.i.170.3		16
91.38	odd	6		91.2.r.a.25.6	yes	16
91.44	odd	12		8281.2.a.cj.1.3		8
91.47	even	12		8281.2.a.ck.1.6		8
91.51	even	6		637.2.c.e.246.6		8
91.73	even	12		1183.2.e.i.508.3		16
91.83	even	4		1183.2.e.i.170.6		16
91.86	odd	12		8281.2.a.cj.1.6		8
91.90	odd	2		91.2.r.a.51.3	yes	16
273.38	even	6		819.2.dl.e.298.3		16
273.272	even	2		819.2.dl.e.415.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.3	✓	16	7.3	odd	6
91.2.r.a.25.6	yes	16	91.38	odd	6
91.2.r.a.51.3	yes	16	91.90	odd	2
91.2.r.a.51.6	yes	16	7.6	odd	2
637.2.c.e.246.3		8	7.2	even	3
637.2.c.e.246.6		8	91.51	even	6
637.2.c.f.246.3		8	7.5	odd	6
637.2.c.f.246.6		8	91.12	odd	6
637.2.r.f.116.3		16	7.4	even	3	inner
637.2.r.f.116.6		16	91.25	even	6	inner
637.2.r.f.324.3		16	13.12	even	2	inner
637.2.r.f.324.6		16	1.1	even	1	trivial
819.2.dl.e.298.3		16	273.38	even	6
819.2.dl.e.298.6		16	21.17	even	6
819.2.dl.e.415.3		16	21.20	even	2
819.2.dl.e.415.6		16	273.272	even	2
1183.2.e.i.170.3		16	91.34	even	4
1183.2.e.i.170.6		16	91.83	even	4
1183.2.e.i.508.3		16	91.73	even	12
1183.2.e.i.508.6		16	91.31	even	12
8281.2.a.cj.1.3		8	91.44	odd	12
8281.2.a.cj.1.6		8	91.86	odd	12
8281.2.a.ck.1.3		8	91.5	even	12
8281.2.a.ck.1.6		8	91.47	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.929293 + 0.536527i) q^{2} +(-1.21570 - 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(0.541640 + 0.312716i) q^{5} -2.60903i q^{6} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +O(q^{10})\)	\(q+(0.929293 + 0.536527i) q^{2} +(-1.21570 - 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(0.541640 + 0.312716i) q^{5} -2.60903i q^{6} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +(0.335561 + 0.581209i) q^{10} +(0.613597 - 0.354260i) q^{11} +(-1.03159 + 1.78676i) q^{12} +(-0.848553 - 3.50428i) q^{13} -1.52068i q^{15} +(0.791426 - 1.37079i) q^{16} +(1.67157 + 2.89524i) q^{17} +(-2.70585 + 1.56222i) q^{18} +(-4.50573 - 2.60138i) q^{19} -0.530712i q^{20} +0.760282 q^{22} +(-2.21570 + 3.83771i) q^{23} +(-6.43627 + 3.71598i) q^{24} +(-2.30442 - 3.99137i) q^{25} +(1.09159 - 3.71177i) q^{26} -0.214623 q^{27} -6.59711 q^{29} +(0.815886 - 1.41316i) q^{30} +(3.80238 - 2.19530i) q^{31} +(-3.82335 + 2.20741i) q^{32} +(-1.49190 - 0.861351i) q^{33} +3.58737i q^{34} +2.47076 q^{36} +(0.366683 + 0.211704i) q^{37} +(-2.79143 - 4.83489i) q^{38} +(-6.34722 + 6.04692i) q^{39} +(0.955864 - 1.65561i) q^{40} +5.01604i q^{41} +11.2059 q^{43} +(-0.520670 - 0.300609i) q^{44} +(-1.57711 + 0.910544i) q^{45} +(-4.11807 + 2.37757i) q^{46} +(-6.99116 - 4.03635i) q^{47} -3.84855 q^{48} -4.94553i q^{50} +(4.06426 - 7.03950i) q^{51} +(-2.21516 + 2.11036i) q^{52} +(0.348553 + 0.603712i) q^{53} +(-0.199447 - 0.115151i) q^{54} +0.443132 q^{55} +12.6500i q^{57} +(-6.13065 - 3.53953i) q^{58} +(8.54177 - 4.93159i) q^{59} +(-1.11750 + 0.645188i) q^{60} +(2.34855 - 4.06781i) q^{61} +4.71136 q^{62} -7.90305 q^{64} +(0.636233 - 2.16341i) q^{65} +(-0.924277 - 1.60089i) q^{66} +(9.02470 - 5.21041i) q^{67} +(1.41841 - 2.45676i) q^{68} +10.7745 q^{69} -14.0876i q^{71} +(7.70775 + 4.45007i) q^{72} +(-4.40273 + 2.54191i) q^{73} +(0.227170 + 0.393471i) q^{74} +(-5.60297 + 9.70463i) q^{75} +4.41482i q^{76} +(-9.14277 + 2.21390i) q^{78} +(1.95586 - 3.38766i) q^{79} +(0.857336 - 0.494983i) q^{80} +(4.62851 + 8.01682i) q^{81} +(-2.69124 + 4.66137i) q^{82} -10.2035i q^{83} +2.09090i q^{85} +(10.4136 + 6.01230i) q^{86} +(8.02012 + 13.8913i) q^{87} +(-1.08285 - 1.87555i) q^{88} +(11.5866 + 6.68955i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(-9.24512 - 5.33767i) q^{93} +(-4.33122 - 7.50190i) q^{94} +(-1.62699 - 2.81802i) q^{95} +(9.29610 + 5.36711i) q^{96} +0.202023i q^{97} +2.06302i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9	\( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) \) 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 + 12 * q^13 + 2 * q^16 - 8 * q^17 - 36 * q^22 - 12 * q^23 + 6 * q^26 - 32 * q^27 - 16 * q^29 + 38 * q^30 - 56 * q^36 - 34 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^43 - 36 * q^48 + 16 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^55 + 12 * q^61 - 44 * q^62 + 88 * q^64 - 30 * q^65 - 2 * q^66 + 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 20 * q^78 + 20 * q^79 - 24 * q^81 + 16 * q^82 + 68 * q^87 + 4 * q^88 + 216 * q^90 + 12 * q^92 + 26 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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