LMFDB - Embedded newform 91.2.r.a.51.3

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			51.3
Root			$0.929293 - 0.536527i$ of defining polynomial
Character	$\chi$	$=$	91.51
Dual form			91.2.r.a.25.3

$q$-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} +(-2.66870 + 2.80123i) 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} +(8.41040 - 2.47340i) 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} +(-2.93520 + 0.863208i) 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} +(1.55545 - 1.63270i) 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} +(6.25390 - 7.20338i) 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	0.134065	−	0.990972i	$-0.457197\pi$
$2$	−0.929293	−	0.536527i	−0.657109	−	0.379382i	−0.791175	+	0.611590i	$0.790530\pi$
$3$	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	0.616201	−	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
$7$	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	−0.589643	−	0.807664i	$-0.700731\pi$
$11$	−0.613597	+	0.354260i	−0.185006	+	0.106814i	0.404636	+	0.914478i	$0.367398\pi$
$12$	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	−0.115646	−	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
$21$	0.297185	+	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
$26$	−2.66870	+	2.80123i	−0.523374	+	0.549366i
$27$	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	−0.118030	−	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
$35$	0.892689	+	1.39329i	0.150892	+	0.235509i
$36$	2.47076			0.411793
$37$	−0.366683	−	0.211704i	−0.0602823	−	0.0348040i	0.469556	−	0.882903i	$-0.344414\pi$
$37$	−0.366683	−	0.211704i	−0.0602823	−	0.0348040i	−0.529838	+	0.848099i	$0.677747\pi$
$38$	2.79143	+	4.83489i	0.452829	+	0.784323i
$39$	8.41040	−	2.47340i	1.34674	−	0.396060i
$40$	−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	$0.871892\pi$
$42$	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	−0.105729	−	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
$49$	4.04458	+	5.71326i	0.577797	+	0.816180i
$50$			4.94553i			0.699404i
$51$	4.06426	−	7.03950i	0.569110	−	0.985727i
$52$	−2.93520	+	0.863208i	−0.407040	+	0.119705i
$53$	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	0.172686	−	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	−0.976295	−	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
$65$	1.55545	−	1.63270i	0.192930	−	0.202512i
$66$	0.924277	+	1.60089i	0.113771	+	0.197056i
$67$	−9.02470	+	5.21041i	−1.10254	+	0.636553i	−0.936888	−	0.349631i	$-0.886307\pi$
$67$	−9.02470	+	5.21041i	−1.10254	+	0.636553i	−0.165655	+	0.986184i	$0.552974\pi$
$68$	−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	$0.315080\pi$
$71$			14.0876i			1.67189i	−0.548812	+	0.835946i	$0.684920\pi$
$72$	−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
$77$	−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	$-0.810805\pi$
$83$		−	10.2035i		−	1.11998i	0.828499	−	0.559990i	$-0.189195\pi$
$84$	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	0.966649	−	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
$91$	6.25390	−	7.20338i	0.655587	−	0.755120i
$92$	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	$0.996735\pi$
$98$	−0.693276	−	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	−0.891700	−	0.452628i	$-0.850487\pi$
$109$	−9.87196	+	5.69958i	−0.945563	+	0.545921i	−0.0538629	+	0.998548i	$0.517153\pi$
$110$	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
$117$	7.60112	+	7.24149i	0.702723	+	0.669476i
$118$	−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
$130$	−2.32146	+	0.682713i	−0.203606	+	0.0598779i
$131$	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	−0.712040	−	0.702139i	$-0.752228\pi$
$137$	−5.38403	+	3.10847i	−0.459989	+	0.265575i	0.252051	+	0.967714i	$0.418895\pi$
$138$	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
$143$	0.720757	+	2.45082i	0.0602727	+	0.204948i
$144$	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	0.363072	−	0.931761i	$-0.381728\pi$
$149$	−3.20203	−	1.84869i	−0.262320	−	0.151451i	−0.625393	+	0.780310i	$0.715061\pi$
$150$	−10.4136	+	6.01230i	−0.850267	+	0.490902i
$151$	−4.22425	+	2.43887i	−0.343764	+	0.198473i	−0.661935	−	0.749561i	$-0.730265\pi$
$151$	−4.22425	+	2.43887i	−0.343764	+	0.198473i	0.318171	+	0.948033i	$0.396931\pi$
$152$	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
$156$	−5.38595	−	5.13113i	−0.431221	−	0.410819i
$157$	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	$0.0455770\pi$
$163$	20.5325	+	11.8544i	1.60823	+	0.928511i	0.618461	+	0.785815i	$0.287756\pi$
$164$	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	$0.986055\pi$
$168$	−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	$0.639671\pi$
$182$	−9.67652	+	3.33866i	−0.717271	+	0.247478i
$183$	−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	0.436776	−	0.899570i	$-0.356120\pi$
$193$	19.9248	−	11.5036i	1.43422	−	0.828045i	0.997439	+	0.0715256i	$0.0227868\pi$
$194$	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	$0.118413\pi$
$197$			10.2035i			0.726970i	−0.931600	+	0.363485i	$0.881587\pi$
$198$	−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
$208$	−4.13206	−	3.93656i	−0.286507	−	0.272952i
$209$	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
$221$	−11.5641	+	3.40087i	−0.777888	+	0.228767i
$222$	−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	$-0.0727490\pi$
$224$	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	0.0687311	−	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
$231$	−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	$-0.0258006\pi$
$234$	−3.17840	−	10.8077i	−0.207779	−	0.706520i
$235$	−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	$0.220182\pi$
$239$			19.7223i			1.27573i	−0.770148	+	0.637865i	$0.779818\pi$
$240$	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
$245$	0.404077	+	4.35934i	0.0258155	+	0.278508i
$246$	13.0870			0.834397
$247$	−12.9393	+	13.5819i	−0.823309	+	0.864196i
$248$	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	0.445280	−	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
$273$	22.7707	+	4.41140i	1.37815	+	0.266990i
$274$	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	$-0.793742\pi$
$281$		−	20.2356i		−	1.20715i	0.797305	−	0.603577i	$-0.206258\pi$
$282$	−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	$-0.707046\pi$
$293$		−	27.2441i		−	1.59162i	0.605547	−	0.795810i	$-0.292954\pi$
$294$	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
$299$	11.5683	+	11.0209i	0.669009	+	0.637357i
$300$	−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	$-0.881819\pi$
$307$		−	12.7138i		−	0.725612i	0.931865	−	0.362806i	$-0.118181\pi$
$308$	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	$0.745412\pi$
$312$	7.56031	+	25.7077i	0.428018	+	1.45541i
$313$	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	−0.237766	−	0.971323i	$-0.576415\pi$
$317$	−21.3269	−	12.3131i	−1.19784	−	0.691572i	−0.960073	+	0.279750i	$0.909748\pi$
$318$	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
$325$	−15.9423	+	4.68843i	−0.884319	+	0.260067i
$326$	−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	0.152594	−	0.988289i	$-0.451237\pi$
$331$	−11.4071	−	6.58591i	−0.626993	−	0.361994i	−0.779586	+	0.626295i	$0.784571\pi$
$332$	−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	$0.346464\pi$
$338$	7.55175	+	11.7288i	0.410761	+	0.637965i
$339$	−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	$0.0589342\pi$
$349$			6.87822i			0.368183i	−0.982909	+	0.184091i	$0.941066\pi$
$350$	−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	−0.464247	−	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
$357$	18.1081	−	11.6019i	0.958383	−	0.614040i
$358$		−	10.1626i		−	0.537112i
$359$	−23.5617	−	13.6034i	−1.24354	−	0.717959i	−0.273728	−	0.961807i	$-0.588257\pi$
$359$	−23.5617	−	13.6034i	−1.24354	−	0.717959i	−0.969813	+	0.243848i	$0.921590\pi$
$360$	−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
$364$	−7.94692	−	1.53957i	−0.416532	−	0.0806952i
$365$	−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	$-0.905366\pi$
$379$		−	11.4059i		−	0.585884i	0.956130	−	0.292942i	$-0.0946343\pi$
$380$	−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
$385$	−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	$-0.422638\pi$
$390$	−4.25977	−	4.05823i	−0.215702	−	0.205496i
$391$	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	0.270195	−	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
$399$	15.3775	−	29.7270i	0.769838	−	1.48821i
$400$	−7.29510			−0.364755
$401$	10.9287	+	6.30971i	0.545756	+	0.315092i	0.747408	−	0.664365i	$-0.231298\pi$
$401$	10.9287	+	6.30971i	0.545756	+	0.315092i	−0.201653	+	0.979457i	$0.564631\pi$
$402$	13.5941	+	23.5457i	0.678013	+	1.17435i
$403$	−4.46643	−	15.1874i	−0.222489	−	0.756539i
$404$	−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	−0.834035	−	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
$413$	26.0677	−	1.20555i	1.28271	−	0.0593214i
$414$			13.8457i			0.680478i
$415$	3.19080	−	5.52663i	0.156630	−	0.271291i
$416$	−4.49107	−	15.2712i	−0.220193	−	0.748731i
$417$	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	$0.0332155\pi$
$421$			4.27439i			0.208321i	−0.994561	+	0.104160i	$0.966784\pi$
$422$	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
$429$	−4.28437	+	4.49714i	−0.206851	+	0.217124i
$430$	−3.76028	−	6.51300i	−0.181337	−	0.314085i
$431$	12.6498	−	7.30335i	0.609318	−	0.351790i	−0.163381	−	0.986563i	$-0.552240\pi$
$431$	12.6498	−	7.30335i	0.609318	−	0.351790i	0.772698	+	0.634773i	$0.218906\pi$
$432$	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	$-0.720151\pi$
$449$		−	32.6410i		−	1.54042i	0.637789	−	0.770211i	$-0.279849\pi$
$450$	−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
$455$	5.63997	−	1.94595i	0.264406	−	0.0912274i
$456$	38.6667			1.81074
$457$	2.74559	+	1.58517i	0.128433	+	0.0741511i	0.562840	−	0.826566i	$-0.309709\pi$
$457$	2.74559	+	1.58517i	0.128433	+	0.0741511i	−0.434407	+	0.900717i	$0.643042\pi$
$458$	−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	$-0.00149752\pi$
$462$	0.225944	+	4.88559i	0.0105119	+	0.227298i
$463$			17.2121i			0.799912i	0.916534	+	0.399956i	$0.130975\pi$
$463$			17.2121i			0.799912i	−0.916534	+	0.399956i	$0.869025\pi$
$464$	−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	−0.860616	−	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
$481$	−1.05302	+	1.10532i	−0.0480136	+	0.0503981i
$482$	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	−0.0772740	−	0.997010i	$-0.524622\pi$
$487$	16.4964	−	9.52422i	0.747525	−	0.431584i	0.824799	+	0.565426i	$0.191288\pi$
$488$	−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
$494$	19.3115	−	5.67927i	0.868864	−	0.255522i
$495$	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	0.116247	−	0.993220i	$-0.462914\pi$
$499$	−15.3192	−	8.84457i	−0.685784	−	0.395937i	−0.802031	+	0.597283i	$0.796247\pi$
$500$	−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
$507$	−1.53079	−	31.5712i	−0.0679849	−	1.40212i
$508$	−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
$511$	−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
$520$	4.99060	+	4.75448i	0.218852	+	0.208498i
$521$	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	0.708577	−	0.705633i	$-0.249337\pi$
$541$	10.5079	+	6.06674i	0.451770	+	0.260829i	−0.256807	+	0.966463i	$0.582671\pi$
$542$	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
$546$	−18.7939	−	16.3166i	−0.804303	−	0.698287i
$547$	−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	−0.991943	−	0.126686i	$-0.959566\pi$
$557$	−32.5267	+	18.7793i	−1.37820	+	0.795705i	−0.386258	+	0.922391i	$0.626233\pi$
$558$	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	$0.711653\pi$
$572$	1.49523	−	1.56949i	0.0625188	−	0.0656236i
$573$	−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	0.233092	−	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
$581$	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
$585$	1.85254	+	6.29927i	0.0765930	+	0.260443i
$586$	−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	$0.901686\pi$
$588$	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	0.327212	−	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
$595$	2.54172	−	4.91353i	0.104201	−	0.201435i
$596$			3.13743i			0.128514i
$597$	−14.4954	+	25.1067i	−0.593256	+	1.02755i
$598$	−4.83726	−	16.4484i	−0.197810	−	0.672624i
$599$	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
$611$	−20.0768	+	21.0739i	−0.812222	+	0.852559i
$612$	−4.13003	−	7.15343i	−0.166947	−	0.289160i
$613$	−33.3285	+	19.2422i	−1.34613	+	0.777186i	−0.987698	−	0.156371i	$-0.950020\pi$
$613$	−33.3285	+	19.2422i	−1.34613	+	0.777186i	−0.358428	+	0.933557i	$0.616687\pi$
$614$	−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	$-0.980156\pi$
$617$		−	3.09503i		−	0.124601i	0.998057	−	0.0623007i	$-0.0198438\pi$
$618$	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
$623$	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	$0.0337561\pi$
$631$			5.31780i			0.211698i	−0.994382	+	0.105849i	$0.966244\pi$
$632$	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
$637$	23.4529	−	9.32532i	0.929238	−	0.369483i
$638$	−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	$-0.122054\pi$
$644$	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	−0.326962	−	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
$663$	−21.2196	−	20.2157i	−0.824101	−	0.785111i
$664$	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
$676$	0.534242	+	11.0182i	0.0205478	+	0.423779i
$677$	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	−0.591580	−	0.806246i	$-0.701496\pi$
$683$	−4.94304	+	2.85387i	−0.189140	+	0.109200i	0.402440	+	0.915446i	$0.368162\pi$
$684$	−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
$689$	2.41134	−	0.709145i	0.0918647	−	0.0270163i
$690$	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
$693$	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	$0.360731\pi$
$702$	−0.572763	+	0.601207i	−0.0216175	+	0.0226911i
$703$	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	−0.0465891	−	0.998914i	$-0.514835\pi$
$709$	−24.8955	−	14.3734i	−0.934969	−	0.539804i	−0.888380	+	0.459110i	$0.848168\pi$
$710$	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	$0.798409\pi$
$728$	22.0183	+	19.1160i	0.816051	+	0.708486i
$729$	−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
$735$	−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	−0.339077	−	0.940759i	$-0.610115\pi$
$739$	8.32135	−	4.80433i	0.306106	−	0.176730i	0.645183	+	0.764028i	$0.276781\pi$
$740$	−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	$-0.799036\pi$
$743$		−	32.1771i		−	1.18046i	0.807234	−	0.590231i	$-0.200964\pi$
$744$	−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
$754$	17.6057	−	18.4800i	0.641161	−	0.673002i
$755$	−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	−0.300746	−	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
$763$	−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
$767$	−10.0335	−	34.1174i	−0.362290	−	1.23191i
$768$	−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	$0.749248\pi$
$770$	0.678695	+	1.05929i	0.0244585	+	0.0381743i
$771$	−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
$777$	1.25144	−	2.41923i	0.0448953	−	0.0867893i
$778$			30.4866i			1.09300i
$779$	13.0486	−	22.6009i	0.467516	−	0.809761i
$780$	−1.31266	−	4.46350i	−0.0470008	−	0.159819i
$781$	−4.99068	−	8.64412i	−0.178581	−	0.309311i
$782$	−13.7673	−	7.94854i	−0.492316	−	0.284239i
$783$	−1.41589			−0.0505998
$784$	11.0327	−	1.02264i	0.394024	−	0.0365230i
$785$			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
$791$	−2.17008	−	1.12256i	−0.0771592	−	0.0399137i
$792$	6.30594			0.224072
$793$	12.2619	+	11.6817i	0.435432	+	0.414831i
$794$	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	$-0.377158\pi$
$797$	21.2530			0.752821			0.376410	+	0.926453i	$0.377158\pi$
$798$	−30.2396	+	19.3746i	−1.07047	+	0.685854i
$799$			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
$805$	−7.32498	+	0.338759i	−0.258172	+	0.0119397i
$806$	−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	$-0.0619303\pi$
$812$	0.684230	+	14.7951i	0.0240118	+	0.519206i
$813$		−	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
$819$	9.05945	+	26.2572i	0.316563	+	0.917500i
$820$	2.66207			0.0929636
$821$	33.4879	+	19.3342i	1.16873	+	0.674769i	0.953382	−	0.301767i	$-0.0975764\pi$
$821$	33.4879	+	19.3342i	1.16873	+	0.674769i	0.215353	+	0.976536i	$0.430910\pi$
$822$	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
$826$	−24.8713	−	12.8657i	−0.865384	−	0.447655i
$827$		−	27.3451i		−	0.950881i	−0.879748	−	0.475440i	$-0.842289\pi$
$827$		−	27.3451i		−	0.950881i	0.879748	−	0.475440i	$-0.157711\pi$
$828$	−5.47446	+	9.48204i	−0.190251	+	0.329524i
$829$	−12.5043	−	21.6581i	−0.434292	−	0.752217i	0.562945	−	0.826494i	$-0.309668\pi$
$829$	−12.5043	−	21.6581i	−0.434292	−	0.752217i	−0.997238	+	0.0742776i	$0.976335\pi$
$830$	−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
$833$	9.78048	−	21.2601i	0.338873	−	0.736620i
$834$		−	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	$-0.0483729\pi$
$840$	−10.9230	−	5.65039i	−0.376880	−	0.194957i
$841$	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
$845$	−4.40155	−	6.83617i	−0.151418	−	0.235171i
$846$	−25.2227			−0.867174
$847$	−23.3867	+	14.9840i	−0.803576	+	0.514855i
$848$	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	$-0.110213\pi$
$854$	13.3210	−	0.616058i	0.455836	−	0.0210811i
$855$	9.47469			0.324028
$856$	16.1920	+	9.34845i	0.553431	+	0.319523i
$857$	−1.33518	−	2.31261i	−0.0456090	−	0.0789972i	0.842320	−	0.538978i	$-0.181190\pi$
$857$	−1.33518	−	2.31261i	−0.0456090	−	0.0789972i	−0.887929	+	0.459981i	$0.847856\pi$
$858$	6.39427	−	1.88048i	0.218297	−	0.0641984i
$859$	19.4798	−	33.7401i	0.664644	−	1.15120i	−0.314738	−	0.949179i	$-0.601917\pi$
$859$	19.4798	−	33.7401i	0.664644	−	1.15120i	0.979382	−	0.202018i	$-0.0647500\pi$
$860$		−	5.94713i		−	0.202795i
$861$	−32.2332	+	1.49069i	−1.09850	+	0.0508026i
$862$	−15.6738			−0.533851
$863$	21.4754	+	12.3988i	0.731030	+	0.422060i	0.818799	−	0.574081i	$-0.194640\pi$
$863$	21.4754	+	12.3988i	0.731030	+	0.422060i	−0.0877689	+	0.996141i	$0.527974\pi$
$864$	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
$868$	−5.31770	−	8.29976i	−0.180494	−	0.281712i
$869$			2.77154i			0.0940181i
$870$	−5.38249	+	9.32274i	−0.182483	+	0.316070i
$871$	10.6008	+	36.0464i	0.359194	+	1.22138i
$872$	−17.4216	−	30.1752i	−0.589971	−	1.02186i
$873$	−0.509428	−	0.294118i	−0.0172415	−	0.00995439i
$874$	−24.7399			−0.836839
$875$	7.30542	−	14.1225i	0.246968	−	0.477426i
$876$			10.4888i			0.354385i
$877$	−1.71335	−	0.989201i	−0.0578556	−	0.0334029i	0.470793	−	0.882244i	$-0.343968\pi$
$877$	−1.71335	−	0.989201i	−0.0578556	−	0.0334029i	−0.528649	+	0.848841i	$0.677301\pi$
$878$	−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	$-0.593270\pi$
$881$	−17.1466			−0.577683			−0.288841	+	0.957377i	$0.593270\pi$
$882$	19.8694	+	9.14069i	0.669038	+	0.307783i
$883$	10.2168			0.343822			0.171911	−	0.985112i	$-0.445006\pi$
$883$	10.2168			0.343822			0.171911	+	0.985112i	$0.445006\pi$
$884$	7.40558	+	7.05521i	0.249077	+	0.237292i
$885$	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	$0.493780\pi$
$887$	−25.4965	+	44.1613i	−0.856090	+	1.48279i	−0.875630	+	0.482983i	$0.839553\pi$
$888$	3.14676			0.105598
$889$	19.9975	+	10.3445i	0.670694	+	0.346944i
$890$		−	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
$896$	−0.498470	−	0.778003i	−0.0166527	−	0.0259913i
$897$	−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
$903$	3.33024	+	72.0097i	0.110823	+	2.39633i
$904$		−	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
$910$	−6.28524	−	1.21765i	−0.208354	−	0.0403646i
$911$	−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
$917$	15.6009	−	9.99556i	0.515187	−	0.330082i
$918$			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
$924$	−1.77698	+	3.43517i	−0.0584585	+	0.113009i
$925$			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
$931$	−3.36139	−	36.2639i	−0.110165	−	1.18850i
$932$	−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
$936$	−22.1347	+	23.2340i	−0.723496	+	0.759426i
$937$	7.16949			0.234217			0.117109	−	0.993119i	$-0.462637\pi$
$937$	7.16949			0.234217			0.117109	+	0.993119i	$0.462637\pi$
$938$	26.2775	+	13.5931i	0.857990	+	0.443831i
$939$	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
$945$	0.191591	+	0.299032i	0.00623247	+	0.00972752i
$946$	8.51968			0.276999
$947$	38.2832	+	22.1028i	1.24404	+	0.718244i	0.969913	−	0.243451i	$-0.0782794\pi$
$947$	38.2832	+	22.1028i	1.24404	+	0.718244i	0.274122	+	0.961695i	$0.411613\pi$
$948$	−4.03529	−	6.98933i	−0.131060	−	0.227003i
$949$	5.17163	+	17.5853i	0.167878	+	0.570844i
$950$	12.8652	−	22.2832i	0.417403	−	0.722963i
$951$		−	59.8762i		−	1.94162i
$952$	27.0075	−	1.24902i	0.875320	−	0.0404810i
$953$	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
$959$	−16.4309	+	0.759882i	−0.530582	+	0.0245379i
$960$		−	12.0180i		−	0.387879i
$961$	−5.86129	+	10.1520i	−0.189074	+	0.327485i
$962$	1.57160	−	0.462187i	0.0506703	−	0.0149015i
$963$	8.90521	+	15.4243i	0.286966	+	0.497040i
$964$	2.04597	+	1.18124i	0.0658961	+	0.0380451i
$965$	14.3894			0.463211
$966$	16.5022	+	25.7563i	0.530948	+	0.828694i
$967$			43.9429i			1.41311i	0.707659	+	0.706554i	$0.249751\pi$
$967$			43.9429i			1.41311i	−0.707659	+	0.706554i	$0.750249\pi$
$968$	−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	−0.642764	−	0.766064i	$-0.722212\pi$
$971$	10.6585	−	18.4611i	0.342049	−	0.592446i	0.984813	+	0.173618i	$0.0555458\pi$
$972$	18.5525			0.595072
$973$	15.3485	+	7.93965i	0.492050	+	0.254533i
$974$	−20.4400			−0.654941
$975$	−29.2533	−	27.8693i	−0.936855	−	0.892531i
$976$	3.71741	+	6.43874i	0.118991	+	0.206099i
$977$	14.2432	−	8.22330i	0.455679	−	0.263087i	−0.254547	−	0.967061i	$-0.581926\pi$
$977$	14.2432	−	8.22330i	0.455679	−	0.263087i	0.710226	+	0.703974i	$0.248593\pi$
$978$	30.9286	−	53.5699i	0.988987	−	1.71298i
$979$	−9.47937			−0.302962
$980$	3.03210	−	2.14651i	0.0968568	−	0.0685677i
$981$		−	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
$987$	23.8600	−	46.1249i	0.759472	−	1.46817i
$988$	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
$994$	33.6761	−	21.5764i	1.06814	−	0.684362i
$995$			7.45731i			0.236413i
$996$	−18.2312	−	10.5258i	−0.577679	−	0.333523i
$997$	2.34855	+	4.06781i	0.0743794	+	0.128829i	0.900816	−	0.434201i	$-0.142969\pi$
$997$	2.34855	+	4.06781i	0.0743794	+	0.128829i	−0.826437	+	0.563029i	$0.809636\pi$
$998$	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	91.2.r.a.51.3	yes	16
3.2	odd	2		819.2.dl.e.415.6		16
7.2	even	3		637.2.c.f.246.6		8
7.3	odd	6		637.2.r.f.116.6		16
7.4	even	3	inner	91.2.r.a.25.6	yes	16
7.5	odd	6		637.2.c.e.246.6		8
7.6	odd	2		637.2.r.f.324.3		16
13.5	odd	4		1183.2.e.i.170.3		16
13.8	odd	4		1183.2.e.i.170.6		16
13.12	even	2	inner	91.2.r.a.51.6	yes	16
21.11	odd	6		819.2.dl.e.298.3		16
39.38	odd	2		819.2.dl.e.415.3		16
91.5	even	12		8281.2.a.cj.1.6		8
91.12	odd	6		637.2.c.e.246.3		8
91.18	odd	12		1183.2.e.i.508.3		16
91.25	even	6	inner	91.2.r.a.25.3	✓	16
91.38	odd	6		637.2.r.f.116.3		16
91.44	odd	12		8281.2.a.ck.1.6		8
91.47	even	12		8281.2.a.cj.1.3		8
91.51	even	6		637.2.c.f.246.3		8
91.60	odd	12		1183.2.e.i.508.6		16
91.86	odd	12		8281.2.a.ck.1.3		8
91.90	odd	2		637.2.r.f.324.6		16
273.116	odd	6		819.2.dl.e.298.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.3	✓	16	91.25	even	6	inner
91.2.r.a.25.6	yes	16	7.4	even	3	inner
91.2.r.a.51.3	yes	16	1.1	even	1	trivial
91.2.r.a.51.6	yes	16	13.12	even	2	inner
637.2.c.e.246.3		8	91.12	odd	6
637.2.c.e.246.6		8	7.5	odd	6
637.2.c.f.246.3		8	91.51	even	6
637.2.c.f.246.6		8	7.2	even	3
637.2.r.f.116.3		16	91.38	odd	6
637.2.r.f.116.6		16	7.3	odd	6
637.2.r.f.324.3		16	7.6	odd	2
637.2.r.f.324.6		16	91.90	odd	2
819.2.dl.e.298.3		16	21.11	odd	6
819.2.dl.e.298.6		16	273.116	odd	6
819.2.dl.e.415.3		16	39.38	odd	2
819.2.dl.e.415.6		16	3.2	odd	2
1183.2.e.i.170.3		16	13.5	odd	4
1183.2.e.i.170.6		16	13.8	odd	4
1183.2.e.i.508.3		16	91.18	odd	12
1183.2.e.i.508.6		16	91.60	odd	12
8281.2.a.cj.1.3		8	91.47	even	12
8281.2.a.cj.1.6		8	91.5	even	12
8281.2.a.ck.1.3		8	91.86	odd	12
8281.2.a.ck.1.6		8	91.44	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(-2.66870 + 2.80123i) 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} +(8.41040 - 2.47340i) 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} +(-2.93520 + 0.863208i) 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} +(1.55545 - 1.63270i) 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} +(6.25390 - 7.20338i) 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

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