LMFDB - Embedded newform 91.2.r.a.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(25,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, 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("91.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			51.6
Root			$-0.929293 + 0.536527i$ of defining polynomial
Character	$\chi$	$=$	91.51
Dual form			91.2.r.a.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.929293 + 0.536527i) q^{2} +(1.21570 + 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(-0.541640 - 0.312716i) q^{5} +2.60903i q^{6} +(-2.34996 - 1.21561i) q^{7} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +O(q^{10})$	\(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} +(-2.34996 - 1.21561i) q^{7} -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} +(-1.53159 - 2.39047i) q^{14} -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} +(-0.297185 - 6.42602i) q^{21} +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} +(0.103717 + 2.24266i) q^{28} -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} +(0.892689 + 1.39329i) q^{35} +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} +(3.17157 - 6.13111i) q^{42} +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} +(4.04458 + 5.71326i) q^{49} -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} +(-3.71570 + 7.18300i) q^{56} +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} +(6.48654 - 4.15596i) q^{63} -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} +(0.0820297 + 1.77373i) q^{70} -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} +(-1.87257 + 0.0866008i) q^{77} +(-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} +(-4.59619 + 2.94480i) q^{84} +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} +(2.26578 - 9.26640i) q^{91} +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} +(0.693276 + 7.47932i) q^{98} +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} - 26 q^{14} + 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^{42} + 16 q^{43} + 36 q^{48} + 40 q^{49} + 16 q^{51} - 42 q^{52} - 20 q^{53} + 24 q^{55} - 36 q^{56} - 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} - 76 q^{77} + 20 q^{78} + 20 q^{79} - 24 q^{81} - 16 q^{82} - 68 q^{87} + 4 q^{88} - 216 q^{90} + 56 q^{91} + 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 - 26 * q^14 + 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^42 + 16 * q^43 + 36 * q^48 + 40 * q^49 + 16 * q^51 - 42 * q^52 - 20 * q^53 + 24 * q^55 - 36 * q^56 - 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 - 76 * q^77 + 20 * q^78 + 20 * q^79 - 24 * q^81 - 16 * q^82 - 68 * q^87 + 4 * q^88 - 216 * q^90 + 56 * q^91 + 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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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	$0.0809918\pi$
$3$	1.21570	+	2.10566i	0.701886	+	1.21570i	−0.265918	+	0.963996i	$0.585675\pi$
$4$	−0.424277	−	0.734868i	−0.212138	−	0.367434i
$5$	−0.541640	−	0.312716i	−0.242229	−	0.139851i	0.373972	−	0.927440i	$-0.377996\pi$
$5$	−0.541640	−	0.312716i	−0.242229	−	0.139851i	−0.616201	+	0.787589i	$0.711329\pi$
$6$			2.60903i			1.06513i
$7$	−2.34996	−	1.21561i	−0.888200	−	0.459458i
$7$	−2.34996	−	1.21561i	−0.888200	−	0.459458i
$8$		−	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
$14$	−1.53159	−	2.39047i	−0.409334	−	0.638881i
$15$		−	1.52068i		−	0.392637i
$16$	0.791426	−	1.37079i	0.197856	−	0.342697i
$17$	−1.67157	−	2.89524i	−0.405414	−	0.702199i	0.588955	−	0.808166i	$-0.299539\pi$
$17$	−1.67157	−	2.89524i	−0.405414	−	0.702199i	−0.994370	+	0.105967i	$0.966206\pi$
$18$	−2.70585	+	1.56222i	−0.637775	+	0.368219i
$19$	4.50573	+	2.60138i	1.03368	+	0.596798i	0.918038	−	0.396492i	$-0.129773\pi$
$19$	4.50573	+	2.60138i	1.03368	+	0.596798i	0.115646	+	0.993290i	$0.463106\pi$
$20$			0.530712i			0.118671i
$21$	−0.297185	−	6.42602i	−0.0648510	−	1.40227i
$22$	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
$28$	0.103717	+	2.24266i	0.0196006	+	0.423824i
$29$	−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	−0.800957	−	0.598722i	$-0.795675\pi$
$31$	−3.80238	+	2.19530i	−0.682927	+	0.394288i	0.118030	+	0.993010i	$0.462342\pi$
$32$	−3.82335	+	2.20741i	−0.675879	+	0.390219i
$33$	1.49190	+	0.861351i	0.259707	+	0.149942i
$34$		−	3.58737i		−	0.615228i
$35$	0.892689	+	1.39329i	0.150892	+	0.235509i
$36$	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	$-0.871892\pi$
$41$		−	5.01604i		−	0.783374i	0.920099	−	0.391687i	$-0.128108\pi$
$42$	3.17157	−	6.13111i	0.489383	−	0.946050i
$43$	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	0.914036	−	0.405633i	$-0.132949\pi$
$47$	6.99116	+	4.03635i	1.01977	+	0.588762i	0.105729	+	0.994395i	$0.466282\pi$
$48$	3.84855			0.555491
$49$	4.04458	+	5.71326i	0.577797	+	0.816180i
$50$		−	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
$56$	−3.71570	+	7.18300i	−0.496532	+	0.959869i
$57$			12.6500i			1.67554i
$58$	−6.13065	−	3.53953i	−0.804993	−	0.464763i
$59$	−8.54177	+	4.93159i	−1.11204	+	0.642039i	−0.939358	−	0.342938i	$-0.888578\pi$
$59$	−8.54177	+	4.93159i	−1.11204	+	0.642039i	−0.172686	+	0.984977i	$0.555244\pi$
$60$	−1.11750	+	0.645188i	−0.144268	+	0.0832934i
$61$	−2.34855	+	4.06781i	−0.300701	+	0.520830i	−0.976295	−	0.216444i	$-0.930554\pi$
$61$	−2.34855	+	4.06781i	−0.300701	+	0.520830i	0.675594	+	0.737274i	$0.263887\pi$
$62$	−4.71136			−0.598344
$63$	6.48654	−	4.15596i	0.817227	−	0.523601i
$64$	−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
$70$	0.0820297	+	1.77373i	0.00980443	+	0.212001i
$71$		−	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	−0.219710	−	0.975565i	$-0.570511\pi$
$73$	4.40273	−	2.54191i	0.515300	−	0.297509i	0.735010	+	0.678057i	$0.237178\pi$
$74$	0.227170	+	0.393471i	0.0264080	+	0.0457400i
$75$	5.60297	−	9.70463i	0.646975	−	1.12059i
$76$		−	4.41482i		−	0.506415i
$77$	−1.87257	+	0.0866008i	−0.213399	+	0.00986908i
$78$	−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	$0.189195\pi$
$83$			10.2035i			1.11998i	−0.828499	+	0.559990i	$0.810805\pi$
$84$	−4.59619	+	2.94480i	−0.501486	+	0.321304i
$85$			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	−0.261532	−	0.965195i	$-0.584228\pi$
$89$	−11.5866	−	6.68955i	−1.22818	−	0.709090i	−0.966649	+	0.256104i	$0.917561\pi$
$90$	1.95413			0.205983
$91$	2.26578	−	9.26640i	0.237518	−	0.971383i
$92$	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	$-0.996735\pi$
$97$		−	0.202023i		−	0.0205123i	0.999947	−	0.0102562i	$-0.00326470\pi$
$98$	0.693276	+	7.47932i	0.0700315	+	0.755526i
$99$			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	$-0.835614\pi$
$101$	−8.66723	−	15.0121i	−0.862421	−	1.49376i	0.00716374	−	0.999974i	$-0.497720\pi$
$102$	7.55377	−	4.36117i	0.747934	−	0.431820i
$103$	−5.40739	+	9.36587i	−0.532806	+	0.922847i	0.466460	+	0.884542i	$0.345529\pi$
$103$	−5.40739	+	9.36587i	−0.532806	+	0.922847i	−0.999266	+	0.0383047i	$0.987804\pi$
$104$	10.7114	−	2.59373i	1.05034	−	0.254336i
$105$	−1.84855	+	3.57353i	−0.180400	+	0.348740i
$106$			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
$112$	−3.52616	+	2.25923i	−0.333191	+	0.213477i
$113$	−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
$119$	0.408623	+	8.83566i	0.0374584	+	0.809963i
$120$	−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
$126$	8.25768	−	0.381893i	0.735652	−	0.0340218i
$127$	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	−0.671538	−	0.740970i	$-0.734366\pi$
$131$	3.50152	−	6.06482i	0.305930	−	0.529885i	0.977468	+	0.211084i	$0.0676995\pi$
$132$		−	1.46180i		−	0.127234i
$133$	−7.42599	−	11.5903i	−0.643915	−	1.00501i
$134$	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	$-0.410662\pi$
$139$	6.53140			0.553986			0.276993	+	0.960872i	$0.410662\pi$
$140$	0.645140	−	1.24715i	0.0545242	−	0.105403i
$141$			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
$147$	−7.11317	+	15.4621i	−0.586685	+	1.27529i
$148$		−	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
$154$	−1.78663	−	0.924207i	−0.143971	−	0.0744747i
$155$	2.74603			0.220566
$156$	7.13667	+	2.09881i	0.571391	+	0.168039i
$157$	4.75984	+	8.24428i	0.379876	+	0.657965i	0.991044	−	0.133536i	$-0.0426332\pi$
$157$	4.75984	+	8.24428i	0.379876	+	0.657965i	−0.611168	+	0.791501i	$0.709300\pi$
$158$	3.63514	−	2.09875i	0.289196	−	0.166968i
$159$	−0.847473	+	1.46787i	−0.0672090	+	0.116409i
$160$	2.76117			0.218290
$161$	9.87196	−	6.32501i	0.778020	−	0.498481i
$162$			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	$-0.986055\pi$
$167$		−	1.13193i		−	0.0875914i	0.999041	−	0.0437957i	$-0.0139451\pi$
$168$	−19.6421	+	0.908391i	−1.51542	+	0.0700839i
$169$	−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	−0.542972	−	0.839751i	$-0.682701\pi$
$173$	5.99458	−	10.3829i	0.455760	−	0.789399i	0.998732	+	0.0503522i	$0.0160344\pi$
$174$		−	17.2121i		−	1.30484i
$175$	0.563327	+	12.1808i	0.0425835	+	0.920783i
$176$		−	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	$-0.639671\pi$
$181$	−11.4314			−0.849690			−0.424845	+	0.905266i	$0.639671\pi$
$182$	7.07725	−	7.39555i	0.524601	−	0.548195i
$183$	−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
$189$	−0.504354	−	0.260898i	−0.0366864	−	0.0189775i
$190$		−	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
$196$	2.48248	−	5.39624i	0.177320	−	0.385446i
$197$		−	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	0.996194	−	0.0871586i	$-0.0277787\pi$
$199$	5.96173	+	10.3260i	0.422616	+	0.731992i	−0.573579	+	0.819150i	$0.694445\pi$
$200$	−12.2002	+	7.04381i	−0.862687	+	0.498072i
$201$	21.9427	+	12.6686i	1.54772	+	0.893576i
$202$		−	18.6008i		−	1.30875i
$203$	15.5029	+	8.01952i	1.08809	+	0.562860i
$204$	−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
$210$	−3.63514	+	2.32905i	−0.250849	+	0.160720i
$211$	−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
$217$	11.6041	−	0.536653i	0.787734	−	0.0364304i
$218$	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	$0.0727490\pi$
$223$			6.76662i			0.453126i	−0.973996	+	0.226563i	$0.927251\pi$
$224$	11.6680	−	0.539613i	0.779604	−	0.0360544i
$225$	13.4197			0.894645
$226$	−0.858161	−	0.495459i	−0.0570840	−	0.0329575i
$227$	−14.5704	+	8.41225i	−0.967074	+	0.558340i	−0.898343	−	0.439295i	$-0.855228\pi$
$227$	−14.5704	+	8.41225i	−0.967074	+	0.558340i	−0.0687311	+	0.997635i	$0.521895\pi$
$228$	9.29610	−	5.36711i	0.615650	−	0.355445i
$229$	−9.54855	−	5.51286i	−0.630986	−	0.364300i	0.150148	−	0.988664i	$-0.452025\pi$
$229$	−9.54855	−	5.51286i	−0.630986	−	0.364300i	−0.781134	+	0.624364i	$0.785358\pi$
$230$	2.97402			0.196101
$231$	−2.45884	−	3.83771i	−0.161780	−	0.252503i
$232$			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
$238$	−4.36084	+	8.43015i	−0.282671	+	0.546445i
$239$		−	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	−0.420329	−	0.907372i	$-0.638085\pi$
$241$	2.41112	−	1.39206i	0.155314	−	0.0896706i	0.575643	+	0.817701i	$0.304752\pi$
$242$	−9.75571	+	5.63246i	−0.627121	+	0.362069i
$243$	−10.9318	+	18.9345i	−0.701278	+	1.21465i
$244$	3.98574			0.255161
$245$	−0.404077	−	4.35934i	−0.0258155	−	0.278508i
$246$	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	$-0.766870\pi$
$251$	−23.5608			−1.48714			−0.743572	+	0.668655i	$0.766870\pi$
$252$	−5.80617	−	3.00348i	−0.365754	−	0.189201i
$253$			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	−0.914574	−	0.404419i	$-0.867474\pi$
$257$	−1.71615	+	2.97245i	−0.107050	+	0.185417i	0.807524	+	0.589835i	$0.200807\pi$
$258$			29.2367i			1.82019i
$259$	−0.604338	−	0.943239i	−0.0375517	−	0.0586100i
$260$	−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
$266$	−0.682378	−	14.7551i	−0.0418393	−	0.904691i
$267$		−	32.5300i		−	1.99080i
$268$	−7.65794	−	4.42131i	−0.467783	−	0.270075i
$269$	−7.32843	−	12.6932i	−0.446822	−	0.773919i	0.551355	−	0.834271i	$-0.314111\pi$
$269$	−7.32843	−	12.6932i	−0.446822	−	0.773919i	−0.998177	+	0.0603517i	$0.980778\pi$
$270$	−0.0720191	−	0.124741i	−0.00438294	−	0.00759148i
$271$	1.76986	+	1.02183i	0.107511	+	0.0620717i	0.552792	−	0.833320i	$-0.313563\pi$
$271$	1.76986	+	1.02183i	0.107511	+	0.0620717i	−0.445280	+	0.895391i	$0.646896\pi$
$272$	−5.29168			−0.320856
$273$	22.2664	−	6.49424i	1.34762	−	0.393049i
$274$	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
$280$	4.25881	−	2.72864i	0.254513	−	0.163067i
$281$			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	0.890659	−	0.454671i	$-0.150243\pi$
$283$	0.867593	+	1.50272i	0.0515731	+	0.0893272i	−0.839086	+	0.543998i	$0.816910\pi$
$284$	−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
$287$	−6.09755	+	11.7875i	−0.359927	+	0.695792i
$288$		−	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	$0.292954\pi$
$293$			27.2441i			1.59162i	−0.605547	+	0.795810i	$0.707046\pi$
$294$	−14.9061	+	10.5524i	−0.869340	+	0.615430i
$295$	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
$301$	−26.3335	−	13.6221i	−1.51784	−	0.785163i
$302$	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	$0.118181\pi$
$307$			12.7138i			0.725612i	−0.931865	+	0.362806i	$0.881819\pi$
$308$	0.858127	+	1.33935i	0.0488963	+	0.0763165i
$309$	−26.2951			−1.49588
$310$	2.55186	+	1.47332i	0.144936	+	0.0836788i
$311$	4.80939	+	8.33011i	0.272716	+	0.472357i	0.969556	−	0.244869i	$-0.0787448\pi$
$311$	4.80939	+	8.33011i	0.272716	+	0.472357i	−0.696841	+	0.717226i	$0.745412\pi$
$312$	18.4833	+	19.4013i	1.04641	+	1.09838i
$313$	4.51273	−	7.81628i	0.255075	−	0.441802i	−0.709841	−	0.704362i	$-0.751233\pi$
$313$	4.51273	−	7.81628i	0.255075	−	0.441802i	0.964916	+	0.262559i	$0.0845666\pi$
$314$			10.2151i			0.576473i
$315$	−4.81300	+	0.222587i	−0.271182	+	0.0125414i
$316$	−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
$322$	12.5675	−	0.581209i	0.700359	−	0.0323895i
$323$		−	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
$329$	−11.5223	−	17.9838i	−0.635244	−	0.991477i
$330$		−	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
$336$	−9.04393	−	4.67834i	−0.493387	−	0.255225i
$337$	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
$343$	−2.55948	−	18.3425i	−0.138199	−	0.990405i
$344$		−	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	$-0.941066\pi$
$349$		−	6.87822i		−	0.368183i	0.982909	−	0.184091i	$-0.0589342\pi$
$350$	−6.01184	+	11.6218i	−0.321347	+	0.621210i
$351$	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	−0.534921	−	0.844902i	$-0.679658\pi$
$353$	−1.32784	+	0.766631i	−0.0706740	+	0.0408036i	0.464247	+	0.885706i	$0.346325\pi$
$354$	−12.8667	−	22.2857i	−0.683856	−	1.18447i
$355$	−4.40542	+	7.63041i	−0.233815	+	0.404980i
$356$			11.3529i			0.601701i
$357$	−18.1081	+	11.6019i	−0.958383	+	0.614040i
$358$			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
$364$	−7.77090	+	2.26647i	−0.407306	+	0.118795i
$365$	−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	$-0.917969\pi$
$367$	−13.4907	−	23.3666i	−0.704208	−	1.21972i	0.262769	−	0.964859i	$-0.415364\pi$
$368$	3.50713	+	6.07452i	0.182822	+	0.316656i
$369$	12.6486	+	7.30267i	0.658460	+	0.380162i
$370$		−	0.284159i		−	0.0147727i
$371$	−0.0852056	−	1.84240i	−0.00442365	−	0.0956526i
$372$			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
$378$	−0.328714	−	0.513050i	−0.0169072	−	0.0263885i
$379$			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	−0.129395	−	0.991593i	$-0.541304\pi$
$383$	−20.6044	−	11.8960i	−1.05284	−	0.607856i	−0.923442	+	0.383737i	$0.874637\pi$
$384$			0.849134i			0.0433322i
$385$	1.04134	+	0.538676i	0.0530716	+	0.0274535i
$386$	−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
$392$	17.4635	−	12.3629i	0.882038	−	0.624420i
$393$	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	0.698717	−	0.715398i	$-0.253755\pi$
$397$	8.53825	+	4.92956i	0.428522	+	0.247408i	−0.270195	+	0.962806i	$0.587088\pi$
$398$			12.7945i			0.641332i
$399$	15.3775	−	29.7270i	0.769838	−	1.48821i
$400$	−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
$406$	10.1041	+	15.7702i	0.501456	+	0.782663i
$407$	0.299994			0.0148701
$408$	−21.5173	−	12.4230i	−1.06527	−	0.615031i
$409$	15.6381	−	9.02867i	0.773255	−	0.446439i	−0.0607793	−	0.998151i	$-0.519359\pi$
$409$	15.6381	−	9.02867i	0.773255	−	0.446439i	0.834035	+	0.551712i	$0.186025\pi$
$410$	−2.91537	+	1.68319i	−0.143980	+	0.0831268i
$411$	13.0908	+	7.55795i	0.645720	+	0.372806i
$412$	9.17691			0.452114
$413$	26.0677	−	1.20555i	1.28271	−	0.0593214i
$414$		−	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	$-0.386581\pi$
$419$	14.2805			0.697647			0.348823	+	0.937188i	$0.386581\pi$
$420$	3.41037	−	0.157720i	0.166409	−	0.00769593i
$421$		−	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
$427$	10.4639	−	6.70425i	0.506382	−	0.324441i
$428$	−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	$-0.264991\pi$
$433$	28.0099			1.34607			0.673035	+	0.739611i	$0.264991\pi$
$434$	11.0715	+	5.72718i	0.531449	+	0.274914i
$435$			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	−0.587082	−	0.809528i	$-0.699723\pi$
$439$	8.53872	−	14.7895i	0.407531	−	0.705864i	0.994612	+	0.103664i	$0.0330566\pi$
$440$			1.35450i			0.0645733i
$441$	−20.2951	+	1.88120i	−0.966433	+	0.0895810i
$442$	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
$448$	18.5718	+	9.60703i	0.877436	+	0.453890i
$449$			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
$455$	−4.12499	+	4.31051i	−0.193382	+	0.202080i
$456$	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	$0.00149752\pi$
$461$			0.202023i			0.00940915i	−0.999989	+	0.00470458i	$0.998502\pi$
$462$	−0.225944	−	4.88559i	−0.0105119	−	0.227298i
$463$		−	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	−0.868228	−	0.496165i	$-0.834741\pi$
$467$	−0.0955845	+	0.165557i	−0.00442312	+	0.00766108i	0.863805	+	0.503826i	$0.168075\pi$
$468$	2.09657	+	8.65821i	0.0969139	+	0.400226i
$469$	−27.5415	+	1.27371i	−1.27175	+	0.0588146i
$470$		−	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
$476$	6.31968	−	4.04905i	0.289662	−	0.185588i
$477$	−2.02978			−0.0929374
$478$	10.5816	−	18.3278i	0.483989	−	0.838294i
$479$	18.6009	−	10.7392i	0.849897	−	0.490688i	−0.0107189	−	0.999943i	$-0.503412\pi$
$479$	18.6009	−	10.7392i	0.849897	−	0.490688i	0.860616	+	0.509254i	$0.170079\pi$
$480$	3.35676	+	5.81408i	0.153214	+	0.265375i
$481$	−0.430721	+	1.46460i	−0.0196392	+	0.0667800i
$482$	2.98752			0.136078
$483$	25.3197	+	13.0976i	1.15209	+	0.595964i
$484$	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
$490$	1.96340	−	4.26790i	0.0886973	−	0.192804i
$491$	−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
$497$	−17.1251	+	33.1053i	−0.768164	+	1.48497i
$498$	−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	$-0.418714\pi$
$503$	11.3305			0.505203			0.252601	+	0.967570i	$0.418714\pi$
$504$	−12.7033	−	19.8271i	−0.565851	−	0.883169i
$505$			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	0.0802734	−	0.996773i	$-0.474421\pi$
$509$	−16.7588	−	9.67569i	−0.742821	−	0.428868i	−0.823094	+	0.567905i	$0.807754\pi$
$510$	−5.45523			−0.241562
$511$	−13.4362	+	0.621384i	−0.594382	+	0.0274884i
$512$			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
$518$	−0.0555330	−	1.20079i	−0.00243998	−	0.0527597i
$519$	29.1505			1.27957
$520$	−6.61280	−	1.94474i	−0.289991	−	0.0852827i
$521$	3.85550	+	6.67791i	0.168912	+	0.292565i	0.938038	−	0.346533i	$-0.112641\pi$
$521$	3.85550	+	6.67791i	0.168912	+	0.292565i	−0.769125	+	0.639098i	$0.779308\pi$
$522$	17.8508	−	10.3062i	0.781307	−	0.451088i
$523$	17.5251	−	30.3543i	0.766317	−	1.32730i	−0.173230	−	0.984881i	$-0.555420\pi$
$523$	17.5251	−	30.3543i	0.766317	−	1.32730i	0.939547	−	0.342419i	$-0.111246\pi$
$524$	−5.94246			−0.259597
$525$	−24.9638	+	15.9944i	−1.08951	+	0.698054i
$526$			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
$532$	−5.36671	+	10.3746i	−0.232676	+	0.449797i
$533$	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
$539$	4.50573	+	2.07281i	0.194075	+	0.0892821i
$540$			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
$546$	24.1763	+	5.91148i	1.03465	+	0.252988i
$547$	−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
$553$	−8.71427	+	5.58327i	−0.370568	+	0.237425i
$554$		−	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
$560$	2.61641	−	0.121001i	0.110563	−	0.00511323i
$561$		−	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	$0.0400800\pi$
$563$	14.3504	+	24.8557i	0.604799	+	1.04754i	−0.387284	+	0.921960i	$0.626587\pi$
$564$	14.4240	−	8.32769i	0.607359	−	0.350659i
$565$	0.500180	+	0.288779i	0.0210428	+	0.0121490i
$566$			1.86195i			0.0782636i
$567$	−1.13146	−	24.4656i	−0.0475170	−	1.02746i
$568$	−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
$574$	−11.9907	+	7.68250i	−0.500483	+	0.320662i
$575$	20.4236			0.851724
$576$	11.5058	−	19.9286i	0.479407	−	0.830357i
$577$	−28.6282	+	16.5285i	−1.19181	+	0.688091i	−0.958717	−	0.284363i	$-0.908218\pi$
$577$	−28.6282	+	16.5285i	−1.19181	+	0.688091i	−0.233092	+	0.972455i	$0.574884\pi$
$578$	5.41170	−	3.12445i	0.225097	−	0.129960i
$579$	−48.4451	−	27.9698i	−2.01331	−	1.16239i
$580$		−	3.50117i		−	0.145378i
$581$	12.4035	−	23.9778i	0.514584	−	0.994766i
$582$	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	$-0.901686\pi$
$587$		−	14.7295i		−	0.607953i	0.952680	−	0.303976i	$-0.0983144\pi$
$588$	14.3806	−	1.33297i	0.593045	−	0.0549708i
$589$	−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	0.654746	−	0.755849i	$-0.272776\pi$
$593$	7.97598	+	4.60494i	0.327534	+	0.189102i	−0.327212	+	0.944951i	$0.606109\pi$
$594$	0.163174			0.00669510
$595$	2.54172	−	4.91353i	0.104201	−	0.201435i
$596$		−	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	$-0.473422\pi$
$601$	4.08916			0.166800			0.0834001	+	0.996516i	$0.473422\pi$
$602$	−17.1629	−	26.7875i	−0.699507	−	1.09178i
$603$			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	−0.900303	−	0.435263i	$-0.856655\pi$
$607$	−1.80353	+	3.12380i	−0.0732030	+	0.126791i	0.827100	+	0.562054i	$0.189989\pi$
$608$	−22.9693			−0.931527
$609$	1.96056	+	42.3932i	0.0794459	+	1.71786i
$610$	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
$616$	0.264709	+	5.72379i	0.0106654	+	0.230618i
$617$			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	−0.271025	−	0.962572i	$-0.587363\pi$
$619$	10.6255	−	6.13462i	0.427074	−	0.246571i	0.698099	+	0.716001i	$0.254029\pi$
$620$	−1.16507	−	2.01797i	−0.0467905	−	0.0810435i
$621$	−0.475540	+	0.823660i	−0.0190828	+	0.0330523i
$622$			10.3215i			0.413854i
$623$	19.0962	+	29.8050i	0.765073	+	1.19411i
$624$	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
$630$	−4.59211	−	2.37546i	−0.182954	−	0.0946406i
$631$		−	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
$637$	−16.5888	+	19.0213i	−0.657273	+	0.753653i
$638$	−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	$0.122054\pi$
$643$			18.9733i			0.748235i	−0.927381	+	0.374117i	$0.877946\pi$
$644$	−8.83649	−	4.57104i	−0.348207	−	0.180124i
$645$		−	17.0406i		−	0.670974i
$646$	9.33211	−	16.1637i	0.367167	−	0.635952i
$647$	9.85587	+	17.0709i	0.387474	+	0.671125i	0.992109	−	0.125378i	$-0.0400143\pi$
$647$	9.85587	+	17.0709i	0.387474	+	0.671125i	−0.604635	+	0.796503i	$0.706681\pi$
$648$	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
$651$	15.2371	+	23.7818i	0.597188	+	0.932080i
$652$			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
$658$	−1.05879	−	22.8942i	−0.0412759	−	0.892509i
$659$	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	−0.654945	−	0.755676i	$-0.727308\pi$
$661$	−8.43242	+	4.86846i	−0.327983	+	0.189361i	0.326962	+	0.945037i	$0.393975\pi$
$662$	7.06704	+	12.2405i	0.274668	+	0.475740i
$663$	28.1171	+	8.26889i	1.09198	+	0.321137i
$664$	31.1886			1.21035
$665$	0.397725	+	8.60002i	0.0154231	+	0.333494i
$666$	−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
$672$	15.3211	+	23.9129i	0.591025	+	0.922461i
$673$	−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	$-0.449113\pi$
$677$	24.3169	−	42.1182i	0.934576	−	1.61873i	0.775389	−	0.631484i	$-0.217554\pi$
$678$		−	2.40932i		−	0.0925296i
$679$	−0.245582	+	0.474745i	−0.00942455	+	0.0182191i
$680$	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
$686$	7.46278	−	18.4188i	0.284930	−	0.703234i
$687$		−	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	−0.384521	−	0.923116i	$-0.625633\pi$
$691$	−36.1766	−	20.8866i	−1.37622	−	0.794563i	−0.991703	+	0.128553i	$0.958967\pi$
$692$	−10.1734			−0.386736
$693$	2.50783	−	4.84801i	0.0952646	−	0.184161i
$694$		−	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
$700$	8.71229	−	5.58200i	0.329294	−	0.210980i
$701$	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
$707$	2.11875	+	45.8137i	0.0796837	+	1.72300i
$708$			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
$714$	−23.0525	+	1.06611i	−0.862718	+	0.0398982i
$715$	−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	−0.902596	−	0.430488i	$-0.858341\pi$
$719$	−2.10450	+	3.64509i	−0.0784844	+	0.135939i	0.824112	+	0.566427i	$0.191675\pi$
$720$		−	2.88251i		−	0.107425i
$721$	24.0924	−	15.4361i	0.897247	−	0.574870i
$722$			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	$-0.798409\pi$
$727$	−43.4680			−1.61214			−0.806070	+	0.591820i	$0.798409\pi$
$728$	−28.3242	−	6.92569i	−1.04976	−	0.256683i
$729$	−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	0.347448	−	0.937699i	$-0.387048\pi$
$733$	−7.87581	−	4.54710i	−0.290900	−	0.167951i	−0.638348	+	0.769748i	$0.720382\pi$
$734$		−	28.9525i		−	1.06866i
$735$	8.68803	−	6.15050i	0.320463	−	0.226865i
$736$		−	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
$742$	0.909317	−	1.75784i	0.0333821	−	0.0645325i
$743$			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
$749$	−13.6265	+	8.73058i	−0.497903	+	0.319008i
$750$	−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
$756$	0.0222599	+	0.481327i	0.000809586	+	0.0175057i
$757$	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	0.976305	−	0.216398i	$-0.0694309\pi$
$761$	35.2290	+	20.3395i	1.27705	+	0.737306i	0.300746	+	0.953704i	$0.402764\pi$
$762$			22.2021i			0.804299i
$763$	−30.1271	+	1.39329i	−1.09068	+	0.0504406i
$764$	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	$-0.749248\pi$
$769$		−	39.3098i		−	1.41755i	0.705435	−

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929293 + 0.536527i) q^{2} +(1.21570 + 2.10566i) q^{3} +(-0.424277 - 0.734868i) q^{4} +(-0.541640 - 0.312716i) q^{5} +2.60903i q^{6} +(-2.34996 - 1.21561i) q^{7} -3.05665i q^{8} +(-1.45586 + 2.52163i) q^{9} +O(q^{10})\)	\(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} +(-2.34996 - 1.21561i) q^{7} -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} +(-1.53159 - 2.39047i) q^{14} -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} +(-0.297185 - 6.42602i) q^{21} +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} +(0.103717 + 2.24266i) q^{28} -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} +(0.892689 + 1.39329i) q^{35} +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} +(3.17157 - 6.13111i) q^{42} +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} +(4.04458 + 5.71326i) q^{49} -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} +(-3.71570 + 7.18300i) q^{56} +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} +(6.48654 - 4.15596i) q^{63} -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} +(0.0820297 + 1.77373i) q^{70} -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} +(-1.87257 + 0.0866008i) q^{77} +(-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} +(-4.59619 + 2.94480i) q^{84} +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} +(2.26578 - 9.26640i) q^{91} +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} +(0.693276 + 7.47932i) q^{98} +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	\( 16 q - 4 q^{3} + 6 q^{4} - 12 q^{9} - 6 q^{10} + 18 q^{12} - 12 q^{13} - 26 q^{14} + 2 q^{16} + 8 q^{17} - 36 q^{22} - 12 q^{23} - 6 q^{26} + 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} + 34 q^{38} + 18 q^{39} - 4 q^{40} + 16 q^{42} + 16 q^{43} + 36 q^{48} + 40 q^{49} + 16 q^{51} - 42 q^{52} - 20 q^{53} + 24 q^{55} - 36 q^{56} - 12 q^{61} + 44 q^{62} + 88 q^{64} - 30 q^{65} + 2 q^{66} - 2 q^{68} - 56 q^{69} + 42 q^{74} + 8 q^{75} - 76 q^{77} + 20 q^{78} + 20 q^{79} - 24 q^{81} - 16 q^{82} - 68 q^{87} + 4 q^{88} - 216 q^{90} + 56 q^{91} + 12 q^{92} - 26 q^{94} - 16 q^{95}+O(q^{100}) \) 16 * q - 4 * q^3 + 6 * q^4 - 12 * q^9 - 6 * q^10 + 18 * q^12 - 12 * q^13 - 26 * q^14 + 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^42 + 16 * q^43 + 36 * q^48 + 40 * q^49 + 16 * q^51 - 42 * q^52 - 20 * q^53 + 24 * q^55 - 36 * q^56 - 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 - 76 * q^77 + 20 * q^78 + 20 * q^79 - 24 * q^81 - 16 * q^82 - 68 * q^87 + 4 * q^88 - 216 * q^90 + 56 * q^91 + 12 * q^92 - 26 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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