LMFDB - Embedded newform 209.2.e.b.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(45,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.e (of order $3$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 14 x^{16} - 11 x^{15} + 130 x^{14} - 92 x^{13} + 629 x^{12} - 276 x^{11} + 2060 x^{10} + \cdots + 9 $ x^18 - x^17 + 14x^16 - 11x^15 + 130x^14 - 92x^13 + 629x^12 - 276x^11 + 2060x^10 - 681x^9 + 3955x^8 - 115x^7 + 4735x^6 + 105x^5 + 2904x^4 + 1230x^3 + 639x^2 + 81x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.1
Root			$-1.34782 - 2.33450i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34782 - 2.33450i) q^{2} +(0.0468836 + 0.0812047i) q^{3} +(-2.63325 + 4.56093i) q^{4} +(1.12231 + 1.94390i) q^{5} +(0.126382 - 0.218899i) q^{6} +0.215810 q^{7} +8.80535 q^{8} +(1.49560 - 2.59046i) q^{9} +O(q^{10})$	\(q+(-1.34782 - 2.33450i) q^{2} +(0.0468836 + 0.0812047i) q^{3} +(-2.63325 + 4.56093i) q^{4} +(1.12231 + 1.94390i) q^{5} +(0.126382 - 0.218899i) q^{6} +0.215810 q^{7} +8.80535 q^{8} +(1.49560 - 2.59046i) q^{9} +(3.02535 - 5.24006i) q^{10} -1.00000 q^{11} -0.493826 q^{12} +(2.79775 - 4.84584i) q^{13} +(-0.290874 - 0.503808i) q^{14} +(-0.105236 + 0.182274i) q^{15} +(-6.60155 - 11.4342i) q^{16} +(3.92883 + 6.80493i) q^{17} -8.06324 q^{18} +(4.31293 + 0.631370i) q^{19} -11.8213 q^{20} +(0.0101179 + 0.0175248i) q^{21} +(1.34782 + 2.33450i) q^{22} +(-1.86718 + 3.23406i) q^{23} +(0.412826 + 0.715036i) q^{24} +(-0.0191576 + 0.0331819i) q^{25} -15.0835 q^{26} +0.561778 q^{27} +(-0.568283 + 0.984295i) q^{28} +(2.21240 - 3.83198i) q^{29} +0.567357 q^{30} -2.53830 q^{31} +(-8.99009 + 15.5713i) q^{32} +(-0.0468836 - 0.0812047i) q^{33} +(10.5907 - 18.3437i) q^{34} +(0.242206 + 0.419512i) q^{35} +(7.87661 + 13.6427i) q^{36} +1.18058 q^{37} +(-4.33914 - 10.9195i) q^{38} +0.524673 q^{39} +(9.88233 + 17.1167i) q^{40} +(-2.15267 - 3.72853i) q^{41} +(0.0272744 - 0.0472406i) q^{42} +(0.239243 + 0.414382i) q^{43} +(2.63325 - 4.56093i) q^{44} +6.71412 q^{45} +10.0665 q^{46} +(0.115048 - 0.199269i) q^{47} +(0.619009 - 1.07215i) q^{48} -6.95343 q^{49} +0.103284 q^{50} +(-0.368395 + 0.638079i) q^{51} +(14.7344 + 25.5207i) q^{52} +(-4.78073 + 8.28047i) q^{53} +(-0.757178 - 1.31147i) q^{54} +(-1.12231 - 1.94390i) q^{55} +1.90028 q^{56} +(0.150935 + 0.379831i) q^{57} -11.9277 q^{58} +(4.86482 + 8.42612i) q^{59} +(-0.554225 - 0.959946i) q^{60} +(3.73333 - 6.46632i) q^{61} +(3.42117 + 5.92565i) q^{62} +(0.322766 - 0.559048i) q^{63} +22.0620 q^{64} +12.5598 q^{65} +(-0.126382 + 0.218899i) q^{66} +(-4.29770 + 7.44384i) q^{67} -41.3824 q^{68} -0.350161 q^{69} +(0.652901 - 1.13086i) q^{70} +(-3.03066 - 5.24926i) q^{71} +(13.1693 - 22.8099i) q^{72} +(-2.53780 - 4.39560i) q^{73} +(-1.59121 - 2.75605i) q^{74} -0.00359270 q^{75} +(-14.2367 + 18.0084i) q^{76} -0.215810 q^{77} +(-0.707167 - 1.22485i) q^{78} +(1.16317 + 2.01467i) q^{79} +(14.8180 - 25.6655i) q^{80} +(-4.46047 - 7.72577i) q^{81} +(-5.80283 + 10.0508i) q^{82} -11.9076 q^{83} -0.106572 q^{84} +(-8.81873 + 15.2745i) q^{85} +(0.644916 - 1.11703i) q^{86} +0.414900 q^{87} -8.80535 q^{88} +(0.252381 - 0.437137i) q^{89} +(-9.04945 - 15.6741i) q^{90} +(0.603782 - 1.04578i) q^{91} +(-9.83354 - 17.0322i) q^{92} +(-0.119004 - 0.206122i) q^{93} -0.620259 q^{94} +(3.61313 + 9.09249i) q^{95} -1.68595 q^{96} +(1.84449 + 3.19476i) q^{97} +(9.37199 + 16.2328i) q^{98} +(-1.49560 + 2.59046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) $ 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.34782	−	2.33450i	−0.953055	−	1.65074i	−0.738758	−	0.673971i	$-0.764587\pi$
$2$	−1.34782	−	2.33450i	−0.953055	−	1.65074i	−0.214297	−	0.976769i	$-0.568746\pi$
$3$	0.0468836	+	0.0812047i	0.0270682	+	0.0468836i	0.879242	−	0.476375i	$-0.158050\pi$
$3$	0.0468836	+	0.0812047i	0.0270682	+	0.0468836i	−0.852174	+	0.523259i	$0.824716\pi$
$4$	−2.63325	+	4.56093i	−1.31663	+	2.28047i
$5$	1.12231	+	1.94390i	0.501912	+	0.869337i	0.999998	+	0.00220931i	$0.000703246\pi$
$5$	1.12231	+	1.94390i	0.501912	+	0.869337i	−0.498085	+	0.867128i	$0.665963\pi$
$6$	0.126382	−	0.218899i	0.0515950	−	0.0893652i
$7$	0.215810			0.0815685			0.0407843	−	0.999168i	$-0.487014\pi$
$7$	0.215810			0.0815685			0.0407843	+	0.999168i	$0.487014\pi$
$8$	8.80535			3.11316
$9$	1.49560	−	2.59046i	0.498535	−	0.863487i
$10$	3.02535	−	5.24006i	0.956700	−	1.65705i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−0.493826			−0.142555
$13$	2.79775	−	4.84584i	0.775955	−	1.34399i	−0.158301	−	0.987391i	$-0.550601\pi$
$13$	2.79775	−	4.84584i	0.775955	−	1.34399i	0.934256	−	0.356603i	$-0.116065\pi$
$14$	−0.290874	−	0.503808i	−0.0777393	−	0.134648i
$15$	−0.105236	+	0.182274i	−0.0271718	+	0.0470629i
$16$	−6.60155	−	11.4342i	−1.65039	−	2.85856i
$17$	3.92883	+	6.80493i	0.952881	+	1.65044i	0.739144	+	0.673547i	$0.235230\pi$
$17$	3.92883	+	6.80493i	0.952881	+	1.65044i	0.213737	+	0.976891i	$0.431436\pi$
$18$	−8.06324			−1.90052
$19$	4.31293	+	0.631370i	0.989454	+	0.144846i
$19$	4.31293	+	0.631370i	0.989454	+	0.144846i
$20$	−11.8213			−2.64332
$21$	0.0101179	+	0.0175248i	0.00220792	+	0.00382422i
$22$	1.34782	+	2.33450i	0.287357	+	0.497717i
$23$	−1.86718	+	3.23406i	−0.389335	+	0.674348i	−0.992360	−	0.123374i	$-0.960628\pi$
$23$	−1.86718	+	3.23406i	−0.389335	+	0.674348i	0.603025	+	0.797722i	$0.293962\pi$
$24$	0.412826	+	0.715036i	0.0842678	+	0.145956i
$25$	−0.0191576	+	0.0331819i	−0.00383151	+	0.00663637i
$26$	−15.0835			−2.95811
$27$	0.561778			0.108114
$28$	−0.568283	+	0.984295i	−0.107395	+	0.186014i
$29$	2.21240	−	3.83198i	0.410832	−	0.711581i	−0.584149	−	0.811646i	$-0.698572\pi$
$29$	2.21240	−	3.83198i	0.410832	−	0.711581i	0.994981	+	0.100065i	$0.0319051\pi$
$30$	0.567357			0.103585
$31$	−2.53830			−0.455891			−0.227946	−	0.973674i	$-0.573201\pi$
$31$	−2.53830			−0.455891			−0.227946	+	0.973674i	$0.573201\pi$
$32$	−8.99009	+	15.5713i	−1.58924	+	2.75264i
$33$	−0.0468836	−	0.0812047i	−0.00816138	−	0.0141359i
$34$	10.5907	−	18.3437i	1.81630	−	3.14592i
$35$	0.242206	+	0.419512i	0.0409402	+	0.0709105i
$36$	7.87661	+	13.6427i	1.31277	+	2.27378i
$37$	1.18058			0.194086			0.0970428	−	0.995280i	$-0.469062\pi$
$37$	1.18058			0.194086			0.0970428	+	0.995280i	$0.469062\pi$
$38$	−4.33914	−	10.9195i	−0.703901	−	1.77138i
$39$	0.524673			0.0840150
$40$	9.88233	+	17.1167i	1.56253	+	2.70639i
$41$	−2.15267	−	3.72853i	−0.336190	−	0.582298i	0.647523	−	0.762046i	$-0.275805\pi$
$41$	−2.15267	−	3.72853i	−0.336190	−	0.582298i	−0.983713	+	0.179748i	$0.942472\pi$
$42$	0.0272744	−	0.0472406i	0.00420853	−	0.00728939i
$43$	0.239243	+	0.414382i	0.0364843	+	0.0631926i	0.883691	−	0.468071i	$-0.155051\pi$
$43$	0.239243	+	0.414382i	0.0364843	+	0.0631926i	−0.847207	+	0.531263i	$0.821717\pi$
$44$	2.63325	−	4.56093i	0.396978	−	0.687586i
$45$	6.71412			1.00088
$46$	10.0665			1.48423
$47$	0.115048	−	0.199269i	0.0167815	−	0.0290664i	−0.857513	−	0.514463i	$-0.827991\pi$
$47$	0.115048	−	0.199269i	0.0167815	−	0.0290664i	0.874294	+	0.485396i	$0.161325\pi$
$48$	0.619009	−	1.07215i	0.0893462	−	0.154752i
$49$	−6.95343			−0.993347
$50$	0.103284			0.0146066
$51$	−0.368395	+	0.638079i	−0.0515856	+	0.0893489i
$52$	14.7344	+	25.5207i	2.04329	+	3.53908i
$53$	−4.78073	+	8.28047i	−0.656684	+	1.13741i	0.324785	+	0.945788i	$0.394708\pi$
$53$	−4.78073	+	8.28047i	−0.656684	+	1.13741i	−0.981469	+	0.191622i	$0.938625\pi$
$54$	−0.757178	−	1.31147i	−0.103039	−	0.178469i
$55$	−1.12231	−	1.94390i	−0.151332	−	0.262115i
$56$	1.90028			0.253936
$57$	0.150935	+	0.379831i	0.0199919	+	0.0503099i
$58$	−11.9277			−1.56618
$59$	4.86482	+	8.42612i	0.633346	+	1.09699i	0.986863	+	0.161559i	$0.0516523\pi$
$59$	4.86482	+	8.42612i	0.633346	+	1.09699i	−0.353517	+	0.935428i	$0.615014\pi$
$60$	−0.554225	−	0.959946i	−0.0715502	−	0.123929i
$61$	3.73333	−	6.46632i	0.478004	−	0.827927i	−0.521678	−	0.853142i	$-0.674694\pi$
$61$	3.73333	−	6.46632i	0.478004	−	0.827927i	0.999682	+	0.0252154i	$0.00802716\pi$
$62$	3.42117	+	5.92565i	0.434489	+	0.752558i
$63$	0.322766	−	0.559048i	0.0406647	−	0.0704334i
$64$	22.0620			2.75775
$65$	12.5598			1.55785
$66$	−0.126382	+	0.218899i	−0.0155565	+	0.0269446i
$67$	−4.29770	+	7.44384i	−0.525048	+	0.909410i	0.474527	+	0.880241i	$0.342619\pi$
$67$	−4.29770	+	7.44384i	−0.525048	+	0.909410i	−0.999575	+	0.0291686i	$0.990714\pi$
$68$	−41.3824			−5.01836
$69$	−0.350161			−0.0421544
$70$	0.652901	−	1.13086i	0.0780366	−	0.135163i
$71$	−3.03066	−	5.24926i	−0.359674	−	0.622973i	0.628233	−	0.778026i	$-0.283779\pi$
$71$	−3.03066	−	5.24926i	−0.359674	−	0.622973i	−0.987906	+	0.155053i	$0.950445\pi$
$72$	13.1693	−	22.8099i	1.55202	−	2.68818i
$73$	−2.53780	−	4.39560i	−0.297027	−	0.514466i	0.678427	−	0.734667i	$-0.262662\pi$
$73$	−2.53780	−	4.39560i	−0.297027	−	0.514466i	−0.975454	+	0.220202i	$0.929328\pi$
$74$	−1.59121	−	2.75605i	−0.184974	−	0.320385i
$75$	−0.00359270			−0.000414849
$76$	−14.2367	+	18.0084i	−1.63306	+	2.06571i
$77$	−0.215810			−0.0245938
$78$	−0.707167	−	1.22485i	−0.0800709	−	0.138687i
$79$	1.16317	+	2.01467i	0.130867	+	0.226668i	0.924011	−	0.382366i	$-0.124891\pi$
$79$	1.16317	+	2.01467i	0.130867	+	0.226668i	−0.793144	+	0.609034i	$0.791557\pi$
$80$	14.8180	−	25.6655i	1.65670	−	2.86949i
$81$	−4.46047	−	7.72577i	−0.495608	−	0.858419i
$82$	−5.80283	+	10.0508i	−0.640815	+	1.10992i
$83$	−11.9076			−1.30703			−0.653515	−	0.756914i	$-0.726706\pi$
$83$	−11.9076			−1.30703			−0.653515	+	0.756914i	$0.726706\pi$
$84$	−0.106572			−0.0116280
$85$	−8.81873	+	15.2745i	−0.956525	+	1.65675i
$86$	0.644916	−	1.11703i	0.0695430	−	0.120452i
$87$	0.414900			0.0444820
$88$	−8.80535			−0.938654
$89$	0.252381	−	0.437137i	0.0267524	−	0.0463364i	−0.852339	−	0.522989i	$-0.824817\pi$
$89$	0.252381	−	0.437137i	0.0267524	−	0.0463364i	0.879092	+	0.476653i	$0.158150\pi$
$90$	−9.04945	−	15.6741i	−0.953896	−	1.65220i
$91$	0.603782	−	1.04578i	0.0632935	−	0.109628i
$92$	−9.83354	−	17.0322i	−1.02522	−	1.77573i
$93$	−0.119004	−	0.206122i	−0.0123402	−	0.0213738i
$94$	−0.620259			−0.0639748
$95$	3.61313	+	9.09249i	0.370699	+	0.932869i
$96$	−1.68595			−0.172072
$97$	1.84449	+	3.19476i	0.187280	+	0.324378i	0.944342	−	0.328964i	$-0.106700\pi$
$97$	1.84449	+	3.19476i	0.187280	+	0.324378i	−0.757062	+	0.653342i	$0.773366\pi$
$98$	9.37199	+	16.2328i	0.946714	+	1.63976i
$99$	−1.49560	+	2.59046i	−0.150314	+	0.260351i
$100$	−0.100893	−	0.174753i	−0.0100893	−	0.0174753i
$101$	−1.14428	+	1.98196i	−0.113860	+	0.197212i	−0.917324	−	0.398142i	$-0.869655\pi$
$101$	−1.14428	+	1.98196i	−0.113860	+	0.197212i	0.803463	+	0.595354i	$0.202988\pi$
$102$	1.98613			0.196656
$103$	8.94629			0.881504			0.440752	−	0.897629i	$-0.354712\pi$
$103$	8.94629			0.881504			0.440752	+	0.897629i	$0.354712\pi$
$104$	24.6352	−	42.6693i	2.41568	−	4.18407i
$105$	−0.0227109	+	0.0393365i	−0.00221636	+	0.00383885i
$106$	25.7743			2.50342
$107$	−19.2128			−1.85737			−0.928684	−	0.370871i	$-0.879059\pi$
$107$	−19.2128			−1.85737			−0.928684	+	0.370871i	$0.879059\pi$
$108$	−1.47931	+	2.56223i	−0.142346	+	0.246551i
$109$	−5.91744	−	10.2493i	−0.566788	−	0.981706i	−0.996881	−	0.0789214i	$-0.974852\pi$
$109$	−5.91744	−	10.2493i	−0.566788	−	0.981706i	0.430092	−	0.902785i	$-0.358481\pi$
$110$	−3.02535	+	5.24006i	−0.288456	+	0.499620i
$111$	0.0553497	+	0.0958684i	0.00525356	+	0.00909943i
$112$	−1.42468	−	2.46762i	−0.134620	−	0.233168i
$113$	6.37283			0.599506			0.299753	−	0.954017i	$-0.403096\pi$
$113$	6.37283			0.599506			0.299753	+	0.954017i	$0.403096\pi$
$114$	0.683281	−	0.864304i	0.0639951	−	0.0809495i
$115$	−8.38224			−0.781648
$116$	11.6516	+	20.1812i	1.08182	+	1.87377i
$117$	−8.36864	−	14.4949i	−0.773681	−	1.34006i
$118$	13.1138	−	22.7138i	1.20723	−	2.09098i
$119$	0.847881	+	1.46857i	0.0777251	+	0.134624i
$120$	−0.926638	+	1.60498i	−0.0845901	+	0.146514i
$121$	1.00000			0.0909091
$122$	−20.1275			−1.82226
$123$	0.201849	−	0.349613i	0.0182001	−	0.0315236i
$124$	6.68398	−	11.5770i	0.600239	−	1.03964i
$125$	11.1371			0.996132
$126$	−1.74013			−0.155023
$127$	6.11579	−	10.5929i	0.542688	−	0.939964i	−0.456060	−	0.889949i	$-0.650740\pi$
$127$	6.11579	−	10.5929i	0.542688	−	0.939964i	0.998748	−	0.0500148i	$-0.0159269\pi$
$128$	−11.7555	−	20.3612i	−1.03905	−	1.79969i
$129$	−0.0224332	+	0.0388554i	−0.00197513	+	0.00342103i
$130$	−16.9283	−	29.3207i	−1.48471	−	2.57160i
$131$	−9.04738	−	15.6705i	−0.790473	−	1.36914i	−0.925674	−	0.378322i	$-0.876501\pi$
$131$	−9.04738	−	15.6705i	−0.790473	−	1.36914i	0.135201	−	0.990818i	$-0.456832\pi$
$132$	0.493826			0.0429820
$133$	0.930774	+	0.136256i	0.0807083	+	0.0118149i
$134$	23.1702			2.00160
$135$	0.630489	+	1.09204i	0.0542639	+	0.0939878i
$136$	34.5947	+	59.9198i	2.96647	+	5.13808i
$137$	−6.82791	+	11.8263i	−0.583348	+	1.01039i	0.411732	+	0.911305i	$0.364924\pi$
$137$	−6.82791	+	11.8263i	−0.583348	+	1.01039i	−0.995079	+	0.0990826i	$0.968409\pi$
$138$	0.471955	+	0.817450i	0.0401755	+	0.0695860i
$139$	−4.47118	+	7.74432i	−0.379241	+	0.656865i	−0.990952	−	0.134217i	$-0.957148\pi$
$139$	−4.47118	+	7.74432i	−0.379241	+	0.656865i	0.611711	+	0.791081i	$0.290482\pi$
$140$	−2.55116			−0.215612
$141$	0.0215755			0.00181698
$142$	−8.16960	+	14.1502i	−0.685577	+	1.18745i
$143$	−2.79775	+	4.84584i	−0.233959	+	0.405229i
$144$	−39.4932			−3.29110
$145$	9.93197			0.824805
$146$	−6.84101	+	11.8490i	−0.566166	+	0.980628i
$147$	−0.326001	−	0.564651i	−0.0268881	−	0.0465716i
$148$	−3.10876	+	5.38453i	−0.255538	+	0.442606i
$149$	10.1240	+	17.5353i	0.829389	+	1.43654i	0.898518	+	0.438937i	$0.144645\pi$
$149$	10.1240	+	17.5353i	0.829389	+	1.43654i	−0.0691284	+	0.997608i	$0.522022\pi$
$150$	0.00484232	+	0.00838715i	0.000395374	+	0.000684808i
$151$	−19.2844			−1.56934			−0.784670	−	0.619914i	$-0.787167\pi$
$151$	−19.2844			−1.56934			−0.784670	+	0.619914i	$0.787167\pi$
$152$	37.9769	+	5.55943i	3.08033	+	0.450930i
$153$	23.5039			1.90018
$154$	0.290874	+	0.503808i	0.0234393	+	0.0405980i
$155$	−2.84875	−	4.93419i	−0.228817	−	0.396323i
$156$	−1.38160	+	2.39300i	−0.110616	+	0.191593i
$157$	3.90071	+	6.75623i	0.311311	+	0.539206i	0.978646	−	0.205551i	$-0.0658987\pi$
$157$	3.90071	+	6.75623i	0.311311	+	0.539206i	−0.667336	+	0.744757i	$0.732565\pi$
$158$	3.13550	−	5.43084i	0.249447	−	0.432055i
$159$	−0.896551			−0.0711011
$160$	−40.3587			−3.19063
$161$	−0.402957	+	0.697942i	−0.0317575	+	0.0550055i
$162$	−12.0239	+	20.8259i	−0.944684	+	1.63624i
$163$	−15.4013			−1.20633			−0.603163	−	0.797618i	$-0.706093\pi$
$163$	−15.4013			−1.20633			−0.603163	+	0.797618i	$0.706093\pi$
$164$	22.6741			1.77055
$165$	0.105236	−	0.182274i	0.00819259	−	0.0141900i
$166$	16.0494	+	27.7983i	1.24567	+	2.15757i
$167$	2.23653	−	3.87378i	0.173068	−	0.299762i	−0.766423	−	0.642336i	$-0.777965\pi$
$167$	2.23653	−	3.87378i	0.173068	−	0.299762i	0.939491	+	0.342574i	$0.111299\pi$
$168$	0.0890921	+	0.154312i	0.00687360	+	0.0119054i
$169$	−9.15478	−	15.8565i	−0.704214	−	1.21973i
$170$	47.5443			3.64648
$171$	8.08597	−	10.2282i	0.618350	−	0.782170i
$172$	−2.51995			−0.192145
$173$	−0.717913	−	1.24346i	−0.0545819	−	0.0945386i	0.837443	−	0.546524i	$-0.184049\pi$
$173$	−0.717913	−	1.24346i	−0.0545819	−	0.0945386i	−0.892025	+	0.451985i	$0.850716\pi$
$174$	−0.559212	−	0.968583i	−0.0423937	−	0.0734281i
$175$	−0.00413439	+	0.00716098i	−0.000312531	+	0.000541319i
$176$	6.60155	+	11.4342i	0.497611	+	0.861887i
$177$	−0.456160	+	0.790093i	−0.0342871	+	0.0593870i
$178$	−1.36066			−0.101986
$179$	−4.79509			−0.358402			−0.179201	−	0.983813i	$-0.557351\pi$
$179$	−4.79509			−0.358402			−0.179201	+	0.983813i	$0.557351\pi$
$180$	−17.6800	+	30.6226i	−1.31779	+	2.28248i
$181$	−3.65848	+	6.33668i	−0.271933	+	0.471002i	−0.969357	−	0.245657i	$-0.920996\pi$
$181$	−3.65848	+	6.33668i	−0.271933	+	0.471002i	0.697424	+	0.716659i	$0.254330\pi$
$182$	−3.25516			−0.241289
$183$	0.700127			0.0517549
$184$	−16.4412	+	28.4770i	−1.21206	+	2.09935i
$185$	1.32497	+	2.29492i	0.0974139	+	0.168726i
$186$	−0.320794	+	0.555631i	−0.0235217	+	0.0407408i
$187$	−3.92883	−	6.80493i	−0.287304	−	0.497626i
$188$	0.605903	+	1.04945i	0.0441900	+	0.0765393i
$189$	0.121237			0.00881872
$190$	16.3565	−	20.6899i	1.18663	−	1.50100i
$191$	3.04093			0.220034			0.110017	−	0.993930i	$-0.464909\pi$
$191$	3.04093			0.220034			0.110017	+	0.993930i	$0.464909\pi$
$192$	1.03435	+	1.79154i	0.0746475	+	0.129293i
$193$	−6.28497	−	10.8859i	−0.452402	−	0.783584i	0.546132	−	0.837699i	$-0.316100\pi$
$193$	−6.28497	−	10.8859i	−0.452402	−	0.783584i	−0.998535	+	0.0541151i	$0.982766\pi$
$194$	4.97210	−	8.61193i	0.356976	−	0.618301i
$195$	0.588846	+	1.01991i	0.0421681	+	0.0730374i
$196$	18.3101	−	31.7141i	1.30787	−	2.26529i
$197$	−4.33412			−0.308793			−0.154397	−	0.988009i	$-0.549343\pi$
$197$	−4.33412			−0.308793			−0.154397	+	0.988009i	$0.549343\pi$
$198$	8.06324			0.573029
$199$	11.0464	−	19.1329i	0.783057	−	1.35629i	−0.147097	−	0.989122i	$-0.546993\pi$
$199$	11.0464	−	19.1329i	0.783057	−	1.35629i	0.930153	−	0.367172i	$-0.119674\pi$
$200$	−0.168689	+	0.292178i	−0.0119281	+	0.0206601i
$201$	−0.805967			−0.0568485
$202$	6.16916			0.434061
$203$	0.477457	−	0.826980i	0.0335109	−	0.0580426i
$204$	−1.94016	−	3.36045i	−0.135838	−	0.235279i
$205$	4.83191	−	8.36912i	0.337476	−	0.584525i
$206$	−12.0580	−	20.8851i	−0.840122	−	1.45513i
$207$	5.58514	+	9.67374i	0.388194	+	0.672371i
$208$	−73.8779			−5.12251
$209$	−4.31293	−	0.631370i	−0.298332	−	0.0436727i
$210$	0.122441			0.00844925
$211$	1.21252	+	2.10015i	0.0834736	+	0.144580i	0.904740	−	0.425965i	$-0.140065\pi$
$211$	1.21252	+	2.10015i	0.0834736	+	0.144580i	−0.821266	+	0.570545i	$0.806732\pi$
$212$	−25.1778	−	43.6092i	−1.72922	−	2.99509i
$213$	0.284177	−	0.492208i	0.0194715	−	0.0337256i
$214$	25.8954	+	44.8522i	1.77017	+	3.06603i
$215$	−0.537010	+	0.930129i	−0.0366238	+	0.0634343i
$216$	4.94666			0.336577
$217$	−0.547790			−0.0371864
$218$	−15.9513	+	27.6285i	−1.08036	+	1.87124i
$219$	0.237962	−	0.412163i	0.0160800	−	0.0278514i
$220$	11.8213			0.796992
$221$	43.9675			2.95757
$222$	0.149203	−	0.258427i	0.0100139	−	0.0173445i
$223$	−2.32182	−	4.02151i	−0.155480	−	0.269300i	0.777753	−	0.628570i	$-0.216359\pi$
$223$	−2.32182	−	4.02151i	−0.155480	−	0.269300i	−0.933234	+	0.359269i	$0.883026\pi$
$224$	−1.94015	+	3.36044i	−0.129632	+	0.224529i
$225$	0.0573042	+	0.0992538i	0.00382028	+	0.00661692i
$226$	−8.58945	−	14.8774i	−0.571362	−	0.989627i
$227$	−9.52294			−0.632060			−0.316030	−	0.948749i	$-0.602350\pi$
$227$	−9.52294			−0.632060			−0.316030	+	0.948749i	$0.602350\pi$
$228$	−2.12984	−	0.311786i	−0.141052	−	0.0206486i
$229$	−7.67584			−0.507234			−0.253617	−	0.967305i	$-0.581620\pi$
$229$	−7.67584			−0.507234			−0.253617	+	0.967305i	$0.581620\pi$
$230$	11.2978	+	19.5683i	0.744953	+	1.29030i
$231$	−0.0101179	−	0.0175248i	−0.000665712	−	0.00115305i
$232$	19.4809	−	33.7420i	1.27899	−	2.21527i
$233$	9.54325	+	16.5294i	0.625199	+	1.08288i	0.988502	+	0.151206i	$0.0483156\pi$
$233$	9.54325	+	16.5294i	0.625199	+	1.08288i	−0.363303	+	0.931671i	$0.618351\pi$
$234$	−22.5589	+	39.0732i	−1.47472	+	2.55429i
$235$	0.516479			0.0336914
$236$	−51.2413			−3.33552
$237$	−0.109067	+	0.188910i	−0.00708468	+	0.0122710i
$238$	2.28559	−	3.95875i	0.148153	−	0.256608i
$239$	20.7710			1.34356			0.671782	−	0.740749i	$-0.265529\pi$
$239$	20.7710			1.34356			0.671782	+	0.740749i	$0.265529\pi$
$240$	2.77888			0.179376
$241$	7.44802	−	12.9003i	0.479769	−	0.830984i	−0.519962	−	0.854190i	$-0.674054\pi$
$241$	7.44802	−	12.9003i	0.479769	−	0.830984i	0.999731	+	0.0232053i	$0.00738713\pi$
$242$	−1.34782	−	2.33450i	−0.0866414	−	0.150067i
$243$	1.26091	−	2.18397i	0.0808876	−	0.140101i
$244$	19.6616	+	34.0549i	1.25871	+	2.18014i
$245$	−7.80390	−	13.5167i	−0.498573	−	0.863553i
$246$	−1.08823			−0.0693829
$247$	15.1260	−	19.1334i	0.962445	−	1.21743i
$248$	−22.3506			−1.41926
$249$	−0.558271	−	0.966954i	−0.0353790	−	0.0612782i
$250$	−15.0108	−	25.9995i	−0.949368	−	1.64435i
$251$	−10.8893	+	18.8608i	−0.687326	+	1.19048i	0.285373	+	0.958416i	$0.407882\pi$
$251$	−10.8893	+	18.8608i	−0.687326	+	1.19048i	−0.972700	+	0.232068i	$0.925451\pi$
$252$	1.69985	+	2.94423i	0.107081	+	0.185469i
$253$	1.86718	−	3.23406i	0.117389	−	0.203324i
$254$	−32.9720			−2.06885
$255$	−1.65381			−0.103566
$256$	−9.62670	+	16.6739i	−0.601669	+	1.04212i
$257$	6.17242	−	10.6909i	0.385025	−	0.666882i	−0.606748	−	0.794894i	$-0.707526\pi$
$257$	6.17242	−	10.6909i	0.385025	−	0.666882i	0.991773	+	0.128012i	$0.0408596\pi$
$258$	0.120944			0.00752963
$259$	0.254780			0.0158313
$260$	−33.0730	+	57.2842i	−2.05110	+	3.55261i
$261$	−6.61774	−	11.4623i	−0.409628	−	0.709496i
$262$	−24.3885	+	42.2422i	−1.50673	+	2.60973i
$263$	0.558866	+	0.967985i	0.0344612	+	0.0596885i	0.882742	−	0.469859i	$-0.155695\pi$
$263$	0.558866	+	0.967985i	0.0344612	+	0.0596885i	−0.848280	+	0.529547i	$0.822362\pi$
$264$	−0.412826	−	0.715036i	−0.0254077	−	0.0440074i
$265$	−21.4618			−1.31839
$266$	−0.936429	−	2.35654i	−0.0574162	−	0.144489i
$267$	0.0473301			0.00289656
$268$	−22.6339	−	39.2031i	−1.38259	−	2.39471i
$269$	−10.1111	−	17.5129i	−0.616484	−	1.06778i	−0.990122	−	0.140207i	$-0.955223\pi$
$269$	−10.1111	−	17.5129i	−0.616484	−	1.06778i	0.373638	−	0.927575i	$-0.378110\pi$
$270$	1.69958	−	2.94375i	0.103433	−	0.179151i
$271$	−8.45255	−	14.6402i	−0.513456	−	0.889332i	−0.999878	−	0.0156079i	$-0.995032\pi$
$271$	−8.45255	−	14.6402i	−0.513456	−	0.889332i	0.486422	−	0.873724i	$-0.338302\pi$
$272$	51.8727	−	89.8462i	3.14525	−	5.44773i
$273$	0.113230			0.00685298
$274$	36.8113			2.22385
$275$	0.0191576	−	0.0331819i	0.00115524	−	0.00200094i
$276$	0.922063	−	1.59706i	0.0555017	−	0.0961317i
$277$	15.7092			0.943872			0.471936	−	0.881633i	$-0.343555\pi$
$277$	15.7092			0.943872			0.471936	+	0.881633i	$0.343555\pi$
$278$	24.1055			1.44575
$279$	−3.79628	+	6.57536i	−0.227278	+	0.393656i
$280$	2.13271	+	3.69396i	0.127454	+	0.220756i
$281$	10.6152	−	18.3860i	0.633247	−	1.09682i	−0.353636	−	0.935383i	$-0.615055\pi$
$281$	10.6152	−	18.3860i	0.633247	−	1.09682i	0.986884	−	0.161434i	$-0.0516118\pi$
$282$	−0.0290800	−	0.0503680i	−0.00173169	−	0.00299937i
$283$	8.88606	+	15.3911i	0.528221	+	0.914906i	0.999459	+	0.0328996i	$0.0104742\pi$
$283$	8.88606	+	15.3911i	0.528221	+	0.914906i	−0.471237	+	0.882006i	$0.656193\pi$
$284$	31.9220			1.89422
$285$	−0.568957	+	0.719691i	−0.0337021	+	0.0426308i
$286$	15.0835			0.891904
$287$	−0.464567	−	0.804653i	−0.0274225	−	0.0474972i
$288$	26.8912	+	46.5770i	1.58458	+	2.74458i
$289$	−22.3714	+	38.7484i	−1.31596	+	2.27932i
$290$	−13.3865	−	23.1862i	−0.786085	−	1.36154i
$291$	−0.172953	+	0.299563i	−0.0101387	+	0.0175607i
$292$	26.7307			1.56430
$293$	−21.1727			−1.23692			−0.618461	−	0.785816i	$-0.712243\pi$
$293$	−21.1727			−1.23692			−0.618461	+	0.785816i	$0.712243\pi$
$294$	−0.878785	+	1.52210i	−0.0512518	+	0.0887706i
$295$	−10.9197	+	18.9134i	−0.635768	+	1.10118i
$296$	10.3954			0.604220
$297$	−0.561778			−0.0325977
$298$	27.2907	−	47.2689i	1.58091	−	2.73821i
$299$	10.4478	+	18.0962i	0.604213	+	1.04653i
$300$	0.00946049	−	0.0163860i	0.000546202	−	0.000946049i
$301$	0.0516311	+	0.0894277i	0.00297597	+	0.00515453i
$302$	25.9919	+	45.0193i	1.49567	+	2.59057i
$303$	−0.214592			−0.0123280
$304$	−21.2528	−	53.4830i	−1.21893	−	3.06746i
$305$	16.7598			0.959664
$306$	−31.6791	−	54.8698i	−1.81097	−	3.13670i
$307$	12.4528	+	21.5688i	0.710717	+	1.23100i	0.964588	+	0.263760i	$0.0849627\pi$
$307$	12.4528	+	21.5688i	0.710717	+	1.23100i	−0.253871	+	0.967238i	$0.581704\pi$
$308$	0.568283	−	0.984295i	0.0323809	−	0.0560854i
$309$	0.419434	+	0.726481i	0.0238608	+	0.0413281i
$310$	−7.67923	+	13.3008i	−0.436151	+	0.755436i
$311$	−10.1103			−0.573300			−0.286650	−	0.958035i	$-0.592542\pi$
$311$	−10.1103			−0.573300			−0.286650	+	0.958035i	$0.592542\pi$
$312$	4.61994			0.261552
$313$	−0.540548	+	0.936256i	−0.0305536	+	0.0529203i	−0.880898	−	0.473306i	$-0.843060\pi$
$313$	−0.540548	+	0.936256i	−0.0305536	+	0.0529203i	0.850344	+	0.526227i	$0.176394\pi$
$314$	10.5149	−	18.2124i	0.593392	−	1.02779i
$315$	1.44897			0.0816405
$316$	−12.2517			−0.689212
$317$	1.49176	−	2.58381i	0.0837858	−	0.145121i	−0.821087	−	0.570803i	$-0.806632\pi$
$317$	1.49176	−	2.58381i	0.0837858	−	0.145121i	0.904873	+	0.425681i	$0.139966\pi$
$318$	1.20839	+	2.09300i	0.0677633	+	0.117369i
$319$	−2.21240	+	3.83198i	−0.123870	+	0.214550i
$320$	24.7604	+	42.8863i	1.38415	+	2.39742i
$321$	−0.900763	−	1.56017i	−0.0502757	−	0.0870801i
$322$	2.17246			0.121066
$323$	12.6483	+	31.8297i	0.703773	+	1.77105i
$324$	46.9823			2.61013
$325$	0.107196	+	0.185669i	0.00594616	+	0.0102991i
$326$	20.7583	+	35.9544i	1.14970	+	1.99133i
$327$	0.554862	−	0.961049i	0.0306839	−	0.0531461i
$328$	−18.9550	−	32.8310i	−1.04661	−	1.81279i
$329$	0.0248286	−	0.0430043i	0.00136884	−	0.00237091i
$330$	−0.567357			−0.0312320
$331$	7.10403			0.390473			0.195236	−	0.980756i	$-0.437453\pi$
$331$	7.10403			0.390473			0.195236	+	0.980756i	$0.437453\pi$
$332$	31.3558	−	54.3098i	1.72087	−	2.98064i
$333$	1.76568	−	3.05824i	0.0967584	−	0.167590i
$334$	−12.0578			−0.659773
$335$	−19.2934			−1.05411
$336$	0.133588	−	0.231382i	0.00728784	−	0.0126229i
$337$	8.13599	+	14.0919i	0.443196	+	0.767637i	0.997925	−	0.0643939i	$-0.0205114\pi$
$337$	8.13599	+	14.0919i	0.443196	+	0.767637i	−0.554729	+	0.832031i	$0.687178\pi$
$338$	−24.6780	+	42.7436i	−1.34231	+	2.32495i
$339$	0.298781	+	0.517504i	0.0162276	+	0.0281070i
$340$	−46.4439	−	80.4432i	−2.51877	−	4.36265i
$341$	2.53830			0.137456
$342$	−34.7762	−	5.09088i	−1.88048	−	0.275283i
$343$	−3.01129			−0.162594
$344$	2.10662	+	3.64878i	0.113581	+	0.196729i
$345$	−0.392989	−	0.680677i	−0.0211578	−	0.0366464i
$346$	−1.93524	+	3.35193i	−0.104039	+	0.180201i
$347$	12.2227	+	21.1703i	0.656147	+	1.13648i	0.981605	+	0.190924i	$0.0611483\pi$
$347$	12.2227	+	21.1703i	0.656147	+	1.13648i	−0.325458	+	0.945557i	$0.605518\pi$
$348$	−1.09254	+	1.89233i	−0.0585662	+	0.101440i
$349$	−8.35905			−0.447450			−0.223725	−	0.974652i	$-0.571822\pi$
$349$	−8.35905			−0.447450			−0.223725	+	0.974652i	$0.571822\pi$
$350$	0.0222897			0.00119144
$351$	1.57171	−	2.72229i	0.0838919	−	0.145305i
$352$	8.99009	−	15.5713i	0.479174	−	0.829953i
$353$	−2.91960			−0.155394			−0.0776972	−	0.996977i	$-0.524757\pi$
$353$	−2.91960			−0.155394			−0.0776972	+	0.996977i	$0.524757\pi$
$354$	2.45929			0.130710
$355$	6.80269	−	11.7826i	0.361049	−	0.625355i
$356$	1.32917	+	2.30219i	0.0704458	+	0.122016i
$357$	−0.0795033	+	0.137704i	−0.00420776	+	0.00728806i
$358$	6.46293	+	11.1941i	0.341576	+	0.591628i
$359$	−11.8294	−	20.4891i	−0.624330	−	1.08137i	−0.988670	−	0.150106i	$-0.952039\pi$
$359$	−11.8294	−	20.4891i	−0.624330	−	1.08137i	0.364340	−	0.931266i	$-0.381295\pi$
$360$	59.1202			3.11591
$361$	18.2027	+	5.44611i	0.958039	+	0.286637i
$362$	19.7240			1.03667
$363$	0.0468836	+	0.0812047i	0.00246075	+	0.00426214i
$364$	3.17982	+	5.50761i	0.166668	+	0.288677i
$365$	5.69639	−	9.86644i	0.298163	−	0.516433i
$366$	−0.943648	−	1.63445i	−0.0493253	−	0.0854339i
$367$	0.0136491	−	0.0236409i	0.000712478	−	0.00123405i	−0.865669	−	0.500617i	$-0.833107\pi$
$367$	0.0136491	−	0.0236409i	0.000712478	−	0.00123405i	0.866381	+	0.499383i	$0.166440\pi$
$368$	49.3053			2.57021
$369$	−12.8781			−0.670409
$370$	3.57166	−	6.18629i	0.185682	−	0.321610i
$371$	−1.03173	+	1.78701i	−0.0535647	+	0.0927768i
$372$	1.25348			0.0649897
$373$	−7.11982			−0.368650			−0.184325	−	0.982865i	$-0.559010\pi$
$373$	−7.11982			−0.368650			−0.184325	+	0.982865i	$0.559010\pi$
$374$	−10.5907	+	18.3437i	−0.547634	+	0.948530i
$375$	0.522147	+	0.904385i	0.0269635	+	0.0467022i
$376$	1.01304	−	1.75464i	0.0522436	−	0.0904886i
$377$	−12.3794	−	21.4418i	−0.637574	−	1.10431i
$378$	−0.163407	−	0.283028i	−0.00840473	−	0.0145574i
$379$	−30.4001			−1.56155			−0.780773	−	0.624814i	$-0.785175\pi$
$379$	−30.4001			−1.56155			−0.780773	+	0.624814i	$0.785175\pi$
$380$	−50.9845	−	7.46361i	−2.61545	−	0.382875i
$381$	1.14692			0.0587585
$382$	−4.09864	−	7.09904i	−0.209704	−	0.363219i
$383$	−12.8099	−	22.1873i	−0.654553	−	1.13372i	−0.982006	−	0.188852i	$-0.939524\pi$
$383$	−12.8099	−	22.1873i	−0.654553	−	1.13372i	0.327453	−	0.944868i	$-0.393810\pi$
$384$	1.10228	−	1.90921i	0.0562506	−	0.0974288i
$385$	−0.242206	−	0.419512i	−0.0123439	−	0.0213803i
$386$	−16.9421	+	29.3445i	−0.862328	+	1.49360i
$387$	1.43125			0.0727547
$388$	−19.4281			−0.986311
$389$	−9.62278	+	16.6671i	−0.487894	+	0.845058i	−0.999903	−	0.0139223i	$-0.995568\pi$
$389$	−9.62278	+	16.6671i	−0.487894	+	0.845058i	0.512009	+	0.858980i	$0.328902\pi$
$390$	1.58732	−	2.74932i	0.0803771	−	0.139217i
$391$	−29.3434			−1.48396
$392$	−61.2274			−3.09245
$393$	0.848347	−	1.46938i	0.0427934	−	0.0741204i
$394$	5.84163	+	10.1180i	0.294297	+	0.509737i
$395$	−2.61088	+	4.52217i	−0.131367	+	0.227535i
$396$	−7.87661	−	13.6427i	−0.395815	−	0.685571i
$397$	8.92868	+	15.4649i	0.448118	+	0.776163i	0.998264	−	0.0589059i	$-0.0187612\pi$
$397$	8.92868	+	15.4649i	0.448118	+	0.776163i	−0.550146	+	0.835069i	$0.685428\pi$
$398$	−59.5542			−2.98518
$399$	0.0325734	+	0.0819714i	0.00163071	+	0.00410370i
$400$	0.505878			0.0252939
$401$	2.94296	+	5.09736i	0.146965	+	0.254550i	0.930104	−	0.367296i	$-0.119716\pi$
$401$	2.94296	+	5.09736i	0.146965	+	0.254550i	−0.783140	+	0.621846i	$0.786383\pi$
$402$	1.08630	+	1.88153i	0.0541797	+	0.0938421i
$403$	−7.10151	+	12.3002i	−0.353751	+	0.612715i
$404$	−6.02638	−	10.4380i	−0.299823	−	0.519309i
$405$	10.0121	−	17.3414i	0.497503	−	0.861701i
$406$	−2.57411			−0.127751
$407$	−1.18058			−0.0585190
$408$	−3.24385	+	5.61851i	−0.160594	+	0.278158i
$409$	−0.355064	+	0.614989i	−0.0175568	+	0.0304092i	−0.874670	−	0.484718i	$-0.838922\pi$
$409$	−0.355064	+	0.614989i	−0.0175568	+	0.0304092i	0.857114	+	0.515128i	$0.172255\pi$
$410$	−26.0503			−1.28653
$411$	−1.28047			−0.0631608
$412$	−23.5579	+	40.8034i	−1.16061	+	2.01024i
$413$	1.04988	+	1.81844i	0.0516611	+	0.0894796i
$414$	15.0556	−	26.0770i	0.739940	−	1.28161i
$415$	−13.3640	−	23.1472i	−0.656014	−	1.13625i
$416$	50.3040	+	87.1291i	2.46636	+	4.27186i
$417$	−0.838500			−0.0410615
$418$	4.33914	+	10.9195i	0.212234	+	0.534090i
$419$	12.1340			0.592787			0.296393	−	0.955066i	$-0.404216\pi$
$419$	12.1340			0.592787			0.296393	+	0.955066i	$0.404216\pi$
$420$	−0.119607	−	0.207166i	−0.00583624	−	0.0101087i
$421$	8.13407	+	14.0886i	0.396430	+	0.686638i	0.993283	−	0.115714i	$-0.0369155\pi$
$421$	8.13407	+	14.0886i	0.396430	+	0.686638i	−0.596852	+	0.802351i	$0.703582\pi$
$422$	3.26853	−	5.66127i	0.159110	−	0.275586i
$423$	−0.344133	−	0.596056i	−0.0167323	−	0.0289813i
$424$	−42.0960	+	72.9125i	−2.04436	+	3.54094i
$425$	−0.301067			−0.0146039
$426$	−1.53208			−0.0742295
$427$	0.805690	−	1.39550i	0.0389901	−	0.0675328i
$428$	50.5921	−	87.6281i	2.44546	−	4.23567i
$429$	−0.524673			−0.0253315
$430$	2.89518			0.139618
$431$	18.4001	−	31.8698i	0.886299	−	1.53512i	0.0420821	−	0.999114i	$-0.486601\pi$
$431$	18.4001	−	31.8698i	0.886299	−	1.53512i	0.844217	−	0.536001i	$-0.180066\pi$
$432$	−3.70861	−	6.42350i	−0.178431	−	0.309051i
$433$	−11.2433	+	19.4740i	−0.540319	+	0.935860i	0.458566	+	0.888660i	$0.348363\pi$
$433$	−11.2433	+	19.4740i	−0.540319	+	0.935860i	−0.998885	+	0.0471998i	$0.984970\pi$
$434$	0.738323	+	1.27881i	0.0354407	+	0.0613850i
$435$	0.465646	+	0.806523i	0.0223260	+	0.0386698i
$436$	62.3286			2.98500
$437$	−10.0949	+	12.7694i	−0.482906	+	0.610843i
$438$	−1.28292			−0.0613005
$439$	16.3712	+	28.3557i	0.781353	+	1.35334i	0.931154	+	0.364627i	$0.118803\pi$
$439$	16.3712	+	28.3557i	0.781353	+	1.35334i	−0.149801	+	0.988716i	$0.547863\pi$
$440$	−9.88233	−	17.1167i	−0.471122	−	0.816007i
$441$	−10.3996	+	18.0126i	−0.495218	+	0.857742i
$442$	−59.2604	−	102.642i	−2.81873	−	4.88218i
$443$	9.65847	−	16.7290i	0.458888	−	0.794817i	−0.540015	−	0.841656i	$-0.681581\pi$
$443$	9.65847	−	16.7290i	0.458888	−	0.794817i	0.998902	+	0.0468385i	$0.0149146\pi$
$444$	−0.582999			−0.0276679
$445$	1.13300			0.0537093
$446$	−6.25880	+	10.8406i	−0.296363	+	0.513316i
$447$	−0.949297	+	1.64423i	−0.0449002	+	0.0777695i
$448$	4.76121			0.224946
$449$	−21.4206			−1.01090			−0.505451	−	0.862855i	$-0.668674\pi$
$449$	−21.4206			−1.01090			−0.505451	+	0.862855i	$0.668674\pi$
$450$	0.154472	−	0.267553i	0.00728188	−	0.0126126i
$451$	2.15267	+	3.72853i	0.101365	+	0.175569i
$452$	−16.7813	+	29.0660i	−0.789325	+	1.36715i
$453$	−0.904120	−	1.56598i	−0.0424793	−	0.0735762i
$454$	12.8352	+	22.2313i	0.602388	+	1.04337i
$455$	2.71052			0.127071
$456$	1.32904	+	3.34455i	0.0622380	+	0.156623i
$457$	25.7204			1.20315			0.601574	−	0.798817i	$-0.294541\pi$
$457$	25.7204			1.20315			0.601574	+	0.798817i	$0.294541\pi$
$458$	10.3457	+	17.9192i	0.483422	+	0.837311i
$459$	2.20713	+	3.82286i	0.103020	+	0.178436i
$460$	22.0726	−	38.2308i	1.02914	−	1.78252i
$461$	−18.6190	−	32.2490i	−0.867173	−	1.50199i	−0.864873	−	0.501990i	$-0.832601\pi$
$461$	−18.6190	−	32.2490i	−0.867173	−	1.50199i	−0.00229990	−	0.999997i	$-0.500732\pi$
$462$	−0.0272744	+	0.0472406i	−0.00126892	+	0.00219783i
$463$	25.5742			1.18853			0.594267	−	0.804268i	$-0.297442\pi$
$463$	25.5742			1.18853			0.594267	+	0.804268i	$0.297442\pi$
$464$	−58.4210			−2.71213
$465$	0.267119	−	0.462664i	0.0123874	−	0.0214555i
$466$	25.7252	−	44.5574i	1.19170	−	2.06408i
$467$	34.4549			1.59438			0.797191	−	0.603727i	$-0.206318\pi$
$467$	34.4549			1.59438			0.797191	+	0.603727i	$0.206318\pi$
$468$	88.1471			4.07460
$469$	−0.927487	+	1.60646i	−0.0428274	+	0.0741792i
$470$	−0.696123	−	1.20572i	−0.0321097	−	0.0556157i
$471$	−0.365758	+	0.633512i	−0.0168533	+	0.0291907i
$472$	42.8365	+	74.1950i	1.97171	+	3.41510i
$473$	−0.239243	−	0.414382i	−0.0110004	−	0.0190533i
$474$	0.588014			0.0270084
$475$	−0.103575	+	0.131016i	−0.00475236	+	0.00601141i
$476$	−8.93074			−0.409340
$477$	14.3002	+	24.7686i	0.654759	+	1.13408i
$478$	−27.9956	−	48.4899i	−1.28049	−	2.21788i
$479$	−13.5575	+	23.4824i	−0.619460	+	1.07294i	0.370124	+	0.928982i	$0.379315\pi$
$479$	−13.5575	+	23.4824i	−0.619460	+	1.07294i	−0.989584	+	0.143954i	$0.954018\pi$
$480$	−1.89216	−	3.27732i	−0.0863648	−	0.149588i
$481$	3.30296	−	5.72089i	0.150602	−	0.260850i
$482$	−40.1544			−1.82898
$483$	−0.0755683			−0.00343848
$484$	−2.63325	+	4.56093i	−0.119693	+	0.207315i
$485$	−4.14018	+	7.17101i	−0.187996	+	0.325619i
$486$	−6.79795			−0.308361
$487$	25.2102			1.14238			0.571192	−	0.820817i	$-0.306481\pi$
$487$	25.2102			1.14238			0.571192	+	0.820817i	$0.306481\pi$
$488$	32.8733	−	56.9382i	1.48810	−	2.57747i
$489$	−0.722070	−	1.25066i	−0.0326531	−	0.0565569i
$490$	−21.0365	+	36.4364i	−0.950334	+	1.64603i
$491$	3.14604	+	5.44910i	0.141979	+	0.245914i	0.928242	−	0.371978i	$-0.121320\pi$
$491$	3.14604	+	5.44910i	0.141979	+	0.245914i	−0.786263	+	0.617892i	$0.787987\pi$
$492$	1.06304	+	1.84124i	0.0479256	+	0.0830096i
$493$	34.7685			1.56589
$494$	−65.0540	−	9.52325i	−2.92692	−	0.428471i
$495$	−6.71412			−0.301777
$496$	16.7567	+	29.0234i	0.752398	+	1.30319i
$497$	−0.654047	−	1.13284i	−0.0293380	−	0.0508150i
$498$	−1.50490	+	2.60657i	−0.0674363	+	0.116803i
$499$	−4.19930	−	7.27339i	−0.187986	−	0.325602i	0.756592	−	0.653887i	$-0.226863\pi$
$499$	−4.19930	−	7.27339i	−0.187986	−	0.325602i	−0.944579	+	0.328285i	$0.893529\pi$
$500$	−29.3268	+	50.7955i	−1.31153	+	2.27164i
$501$	0.419426			0.0187386
$502$	58.7074			2.62024
$503$	−5.75923	+	9.97528i	−0.256791	+	0.444776i	−0.965381	−	0.260845i	$-0.915999\pi$
$503$	−5.75923	+	9.97528i	−0.256791	+	0.444776i	0.708589	+	0.705621i	$0.249332\pi$
$504$	2.84207	−	4.92261i	0.126596	−	0.219271i
$505$	−5.13696			−0.228592
$506$	−10.0665			−0.447512
$507$	0.858417	−	1.48682i	0.0381236	−	0.0660321i
$508$	32.2088	+	55.7874i	1.42904	+	2.47516i
$509$	−6.34543	+	10.9906i	−0.281256	+	0.487150i	−0.971694	−	0.236241i	$-0.924084\pi$
$509$	−6.34543	+	10.9906i	−0.281256	+	0.487150i	0.690438	+	0.723391i	$0.257418\pi$
$510$	2.22905	+	3.86082i	0.0987039	+	0.170960i
$511$	−0.547683	−	0.948614i	−0.0242281	−	0.0419642i
$512$	4.87828			0.215592
$513$	2.42291	+	0.354690i	0.106974	+	0.0156599i
$514$	−33.2773			−1.46780
$515$	10.0405	+	17.3907i	0.442438	+	0.766325i
$516$	−0.118144	−	0.204632i	−0.00520102	−	0.00900843i
$517$	−0.115048	+	0.199269i	−0.00505982	+	0.00876386i
$518$	−0.343399	−	0.594784i	−0.0150881	−	0.0261333i
$519$	0.0673166	−	0.116596i	0.00295487	−	0.00511799i
$520$	110.593			4.84983
$521$	−14.2894			−0.626031			−0.313015	−	0.949748i	$-0.601339\pi$
$521$	−14.2894			−0.626031			−0.313015	+	0.949748i	$0.601339\pi$
$522$	−17.8391	+	30.8982i	−0.780795	+	1.35238i
$523$	−3.34378	+	5.79159i	−0.146213	+	0.253249i	−0.929825	−	0.368002i	$-0.880042\pi$
$523$	−3.34378	+	5.79159i	−0.146213	+	0.253249i	0.783612	+	0.621251i	$0.213375\pi$
$524$	95.2962			4.16304
$525$	−0.000775340	0		−3.38386e−5	0
$526$	1.50651	−	2.60934i	0.0656868	−	0.113773i
$527$	−9.97253	−	17.2729i	−0.434410	−	0.752421i
$528$	−0.619009	+	1.07215i	−0.0269389	+	0.0466595i
$529$	4.52724	+	7.84142i	0.196837	+	0.340931i
$530$	28.9268	+	50.1026i	1.25650	+	2.17632i
$531$	29.1034			1.26298
$532$	−3.07242	+	3.88640i	−0.133206	+	0.168497i
$533$	−24.0905			−1.04347
$534$	−0.0637926	−	0.110492i	−0.00276058	−	0.00478146i
$535$	−21.5627	−	37.3477i	−0.932236	−	1.61468i
$536$	−37.8428	+	65.5456i	−1.63456	+	2.83114i
$537$	−0.224811	−	0.389384i	−0.00970130	−	0.0168032i
$538$	−27.2559	+	47.2087i	−1.17509	+	2.03531i
$539$	6.95343			0.299505
$540$	−6.64096			−0.285781
$541$	−21.6812	+	37.5529i	−0.932146	+	1.61452i	−0.152501	+	0.988303i	$0.548733\pi$
$541$	−21.6812	+	37.5529i	−0.932146	+	1.61452i	−0.779645	+	0.626221i	$0.784601\pi$
$542$	−22.7851	+	39.4649i	−0.978703	+	1.69516i
$543$	−0.686091			−0.0294430
$544$	−141.282			−6.05742
$545$	13.2824	−	23.0058i	0.568956	−	0.985460i
$546$	−0.152614	−	0.264335i	−0.00653126	−	0.0113125i
$547$	−9.61252	+	16.6494i	−0.411002	+	0.711876i	−0.995000	−	0.0998795i	$-0.968154\pi$
$547$	−9.61252	+	16.6494i	−0.411002	+	0.711876i	0.583998	+	0.811755i	$0.301488\pi$
$548$	−35.9593	−	62.2832i	−1.53610	−	2.66061i
$549$	−11.1672	−	19.3421i	−0.476603	−	0.825501i
$550$	−0.103284			−0.00440404
$551$	11.9613	−	15.1302i	0.509569	−	0.644570i
$552$	−3.08329			−0.131234
$553$	0.251024	+	0.434786i	0.0106746	+	0.0184890i
$554$	−21.1732	−	36.6730i	−0.899562	−	1.55809i
$555$	−0.124239	+	0.215188i	−0.00527365	+	0.00913422i
$556$	−23.5475	−	40.7855i	−0.998638	−	1.72969i
$557$	10.3851	−	17.9875i	0.440030	−	0.762154i	−0.557661	−	0.830069i	$-0.688301\pi$
$557$	10.3851	−	17.9875i	0.440030	−	0.762154i	0.997691	+	0.0679144i	$0.0216345\pi$
$558$	20.4669			0.866432
$559$	2.67737			0.113241
$560$	3.19787	−	5.53887i	0.135135	−	0.234060i
$561$	0.368395	−	0.638079i	0.0155537	−	0.0269397i
$562$	−57.2294			−2.41408
$563$	20.3001			0.855546			0.427773	−	0.903886i	$-0.359298\pi$
$563$	20.3001			0.855546			0.427773	+	0.903886i	$0.359298\pi$
$564$	−0.0568138	+	0.0984044i	−0.00239229	+	0.00414357i
$565$	7.15229	+	12.3881i	0.300899	+	0.521172i
$566$	23.9537	−	41.4890i	1.00685	−	1.74391i
$567$	−0.962615	−	1.66730i	−0.0404260	−	0.0700199i
$568$	−26.6861	−	46.2216i	−1.11972	−	1.93942i
$569$	35.3675			1.48268			0.741342	−	0.671127i	$-0.234190\pi$
$569$	35.3675			1.48268			0.741342	+	0.671127i	$0.234190\pi$
$570$	2.44697	+	0.358212i	0.102492	+	0.0150038i
$571$	10.3172			0.431763			0.215882	−	0.976420i	$-0.430737\pi$
$571$	10.3172			0.431763			0.215882	+	0.976420i	$0.430737\pi$
$572$	−14.7344	−	25.5207i	−0.616075	−	1.06707i
$573$	0.142570	+	0.246938i	0.00595593	+	0.0103160i
$574$	−1.25231	+	2.16906i	−0.0522703	+	0.0905348i
$575$	−0.0715414	−	0.123913i	−0.00298348	−	0.00516754i
$576$	32.9960	−	57.1508i	1.37484	−	2.38128i
$577$	−15.6117			−0.649923			−0.324961	−	0.945727i	$-0.605351\pi$
$577$	−15.6117			−0.649923			−0.324961	+	0.945727i	$0.605351\pi$
$578$	120.611			5.01675
$579$	0.589324	−	1.02074i	0.0244915	−	0.0424205i
$580$	−26.1534	+	45.2990i	−1.08596	+	1.88094i
$581$	−2.56978			−0.106613
$582$	0.932440			0.0386509
$583$	4.78073	−	8.28047i	0.197998	−	0.342942i
$584$	−22.3462	−	38.7048i	−0.924693	−	1.60162i
$585$	18.7844	−	32.5356i	0.776640	−	1.34518i
$586$	28.5370	+	49.4276i	1.17885	+	2.04183i
$587$	−2.61795	−	4.53442i	−0.108054	−	0.187156i	0.806928	−	0.590650i	$-0.201129\pi$
$587$	−2.61795	−	4.53442i	−0.108054	−	0.187156i	−0.914982	+	0.403495i	$0.867795\pi$
$588$	3.43378			0.141607
$589$	−10.9475	−	1.60260i	−0.451084	−	0.0660341i
$590$	58.8712			2.42369
$591$	−0.203199	−	0.351951i	−0.00835849	−	0.0144773i
$592$	−7.79364	−	13.4990i	−0.320317	−	0.554805i
$593$	3.30918	−	5.73167i	0.135892	−	0.235371i	−0.790046	−	0.613048i	$-0.789943\pi$
$593$	3.30918	−	5.73167i	0.135892	−	0.235371i	0.925938	+	0.377676i	$0.123277\pi$
$594$	0.757178	+	1.31147i	0.0310674	+	0.0538103i
$595$	−1.90317	+	3.29639i	−0.0780223	+	0.135139i
$596$	−106.636			−4.36799
$597$	2.07157			0.0847839
$598$	28.1636	−	48.7808i	1.15170	−	1.99480i
$599$	19.8772	−	34.4283i	0.812159	−	1.40670i	−0.0991913	−	0.995068i	$-0.531626\pi$
$599$	19.8772	−	34.4283i	0.812159	−	1.40670i	0.911350	−	0.411632i	$-0.135041\pi$
$600$	−0.0316350			−0.00129149
$601$	−13.5825			−0.554043			−0.277021	−	0.960864i	$-0.589347\pi$
$601$	−13.5825			−0.554043			−0.277021	+	0.960864i	$0.589347\pi$
$602$	0.139179	−	0.241065i	0.00567252	−	0.00982510i
$603$	12.8553	+	22.2661i	0.523509	+	0.906744i
$604$	50.7806	−	87.9546i	2.06623	−	3.57882i
$605$	1.12231	+	1.94390i	0.0456284	+	0.0790307i
$606$	0.289232	+	0.500965i	0.0117493	+	0.0203503i
$607$	−22.2351			−0.902494			−0.451247	−	0.892399i	$-0.649021\pi$
$607$	−22.2351			−0.902494			−0.451247	+	0.892399i	$0.649021\pi$
$608$	−48.6049	+	61.4819i	−1.97119	+	2.49342i
$609$	0.0895396			0.00362833
$610$	−22.5893	−	39.1257i	−0.914612	−	1.58415i
$611$	−0.643752	−	1.11501i	−0.0260434	−	0.0451085i
$612$	−61.8917	+	107.200i	−2.50182	+	4.33329i
$613$	−7.08099	−	12.2646i	−0.285999	−	0.495364i	0.686852	−	0.726797i	$-0.258992\pi$
$613$	−7.08099	−	12.2646i	−0.285999	−	0.495364i	−0.972851	+	0.231433i	$0.925659\pi$
$614$	33.5683	−	58.1419i	1.35470	−	2.34642i
$615$	0.906150			0.0365395
$616$	−1.90028			−0.0765646
$617$	−20.4531	+	35.4259i	−0.823412	+	1.42619i	0.0797143	+	0.996818i	$0.474599\pi$
$617$	−20.4531	+	35.4259i	−0.823412	+	1.42619i	−0.903127	+	0.429374i	$0.858734\pi$
$618$	1.13065	−	1.95834i	0.0454812	−	0.0787758i
$619$	12.3500			0.496390			0.248195	−	0.968710i	$-0.420163\pi$
$619$	12.3500			0.496390			0.248195	+	0.968710i	$0.420163\pi$
$620$	30.0060			1.20507
$621$	−1.04894	+	1.81682i	−0.0420927	+	0.0729066i
$622$	13.6268	+	23.6024i	0.546386	+	0.946369i
$623$	0.0544664	−	0.0943385i	0.00218215	−	0.00377959i
$624$	−3.46366	−	5.99923i	−0.138657	−	0.240162i
$625$	12.5951	+	21.8153i	0.503802	+	0.872611i
$626$	2.91425			0.116477
$627$	−0.150935	−	0.379831i	−0.00602778	−	0.0151690i
$628$	−41.0862			−1.63952
$629$	4.63828	+	8.03374i	0.184941	+	0.320326i
$630$	−1.95296	−	3.38263i	−0.0778079	−	0.134767i
$631$	17.0376	−	29.5101i	0.678258	−	1.17478i	−0.297247	−	0.954800i	$-0.596069\pi$
$631$	17.0376	−	29.5101i	0.678258	−	1.17478i	0.975505	−	0.219976i	$-0.0705980\pi$
$632$	10.2421	+	17.7399i	0.407410	+	0.705656i
$633$	−0.113695	+	0.196925i	−0.00451896	+	0.00782708i
$634$	−8.04254			−0.319410
$635$	27.4552			1.08953
$636$	2.36085	−	4.08911i	0.0936137	−	0.162144i
$637$	−19.4539	+	33.6952i	−0.770793	+	1.33505i
$638$	11.9277			0.472221
$639$	−18.1307			−0.717239
$640$	26.3867	−	45.7030i	1.04302	−	1.80657i
$641$	−11.6178	−	20.1227i	−0.458877	−	0.794799i	0.540025	−	0.841649i	$-0.318415\pi$
$641$	−11.6178	−	20.1227i	−0.458877	−	0.794799i	−0.998902	+	0.0468503i	$0.985082\pi$
$642$	−2.42814	+	4.20566i	−0.0958310	+	0.165984i
$643$	0.310158	+	0.537209i	0.0122314	+	0.0211855i	0.872076	−	0.489370i	$-0.162773\pi$
$643$	0.310158	+	0.537209i	0.0122314	+	0.0211855i	−0.859845	+	0.510555i	$0.829440\pi$
$644$	−2.12218	−	3.67572i	−0.0836255	−	0.144844i
$645$	−0.100708			−0.00396537
$646$	57.2588	−	72.4284i	2.25282	−	2.84966i
$647$	21.6992			0.853083			0.426541	−	0.904468i	$-0.359732\pi$
$647$	21.6992			0.853083			0.426541	+	0.904468i	$0.359732\pi$
$648$	−39.2761	−	68.0281i	−1.54291	−	2.67240i
$649$	−4.86482	−	8.42612i	−0.190961	−	0.330754i
$650$	0.288962	−	0.500498i	0.0113340	−	0.0196311i
$651$	−0.0256823	−	0.0444831i	−0.00100657	−	0.00174343i
$652$	40.5557	−	70.2445i	1.58828	−	2.75099i
$653$	−5.63795			−0.220630			−0.110315	−	0.993897i	$-0.535186\pi$
$653$	−5.63795			−0.220630			−0.110315	+	0.993897i	$0.535186\pi$
$654$	−2.99142			−0.116974
$655$	20.3079	−	35.1744i	0.793496	−	1.37438i
$656$	−28.4219	+	49.2281i	−1.10969	+	1.92204i
$657$	−15.1822			−0.592313
$658$	−0.133858			−0.00521833
$659$	−2.07926	+	3.60138i	−0.0809964	+	0.140290i	−0.903678	−	0.428212i	$-0.859144\pi$
$659$	−2.07926	+	3.60138i	−0.0809964	+	0.140290i	0.822682	+	0.568502i	$0.192477\pi$
$660$	0.554225	+	0.959946i	0.0215732	+	0.0373658i
$661$	17.9539	−	31.0970i	0.698324	−	1.20953i	−0.270723	−	0.962657i	$-0.587263\pi$
$661$	17.9539	−	31.0970i	0.698324	−	1.20953i	0.969047	−	0.246876i	$-0.0794040\pi$
$662$	−9.57497	−	16.5843i	−0.372142	−	0.644569i
$663$	2.06135	+	3.57037i	0.0800563	+	0.138662i
$664$	−104.851			−4.06900
$665$	0.779749	+	1.96225i	0.0302374	+	0.0760928i
$666$	−9.51927			−0.368864
$667$	8.26190	+	14.3100i	0.319902	+	0.554087i
$668$	11.7787	+	20.4013i	0.455732	+	0.789351i
$669$	0.217710	−	0.377085i	0.00841717	−	0.0145790i
$670$	26.0041	+	45.0404i	1.00463	+	1.74006i
$671$	−3.73333	+	6.46632i	−0.144124	+	0.249629i
$672$	−0.363845			−0.0140356
$673$	−27.5619			−1.06243			−0.531216	−	0.847237i	$-0.678265\pi$
$673$	−27.5619			−1.06243			−0.531216	+	0.847237i	$0.678265\pi$
$674$	21.9317	−	37.9869i	0.844779	−	1.46320i
$675$	−0.0107623	+	0.0186408i	−0.000414241	+	0.000717487i
$676$	96.4274			3.70875
$677$	−0.779510			−0.0299590			−0.0149795	−	0.999888i	$-0.504768\pi$
$677$	−0.779510			−0.0299590			−0.0149795	+	0.999888i	$0.504768\pi$
$678$	0.805408	−	1.39501i	0.0309315	−	0.0535750i
$679$	0.398060	+	0.689460i	0.0152761	+	0.0264591i
$680$	−77.6520	+	134.497i	−2.97782	+	5.15773i
$681$	−0.446470	−	0.773308i	−0.0171088	−	0.0296332i
$682$	−3.42117	−	5.92565i	−0.131003	−	0.226905i
$683$	−25.8086			−0.987538			−0.493769	−	0.869593i	$-0.664381\pi$
$683$	−25.8086			−0.987538			−0.493769	+	0.869593i	$0.664381\pi$
$684$	25.3577	+	63.8130i	0.969576	+	2.43995i
$685$	−30.6521			−1.17116
$686$	4.05868	+	7.02985i	0.154961	+	0.268401i
$687$	−0.359871	−	0.623315i	−0.0137299	−	0.0237809i
$688$	3.15875	−	5.47112i	0.120426	−	0.208585i
$689$	26.7505	+	46.3333i	1.01911	+	1.76516i
$690$	−1.05936	+	1.83486i	−0.0403291	+	0.0698521i
$691$	8.73241			0.332196			0.166098	−	0.986109i	$-0.446883\pi$
$691$	8.73241			0.332196			0.166098	+	0.986109i	$0.446883\pi$
$692$	7.56179			0.287456
$693$	−0.322766	+	0.559048i	−0.0122609	+	0.0212365i
$694$	32.9480	−	57.0676i	1.25069	−	2.16626i
$695$	−20.0722			−0.761382
$696$	3.65334			0.138480
$697$	16.9149	−	29.2975i	0.640698	−	1.10972i
$698$	11.2665	+	19.5142i	0.426444	+	0.738623i
$699$	−0.894843	+	1.54991i	−0.0338461	+	0.0586231i
$700$	−0.0217738	−	0.0377133i	−0.000822973	−	0.00142543i
$701$	7.75047	+	13.4242i	0.292731	+	0.507025i	0.974455	−	0.224585i	$-0.0721026\pi$
$701$	7.75047	+	13.4242i	0.292731	+	0.507025i	−0.681723	+	0.731610i	$0.738769\pi$
$702$	−8.47357			−0.319814
$703$	5.09175	+	0.745380i	0.192039	+	0.0281125i
$704$	−22.0620			−0.831494
$705$	0.0242144	+	0.0419406i	0.000911967	+	0.00157957i
$706$	3.93510	+	6.81579i	0.148099	+	0.256516i
$707$	−0.246948	+	0.427726i	−0.00928742	+	0.0160863i
$708$	−2.40237	−	4.16103i	−0.0902867	−	0.156381i
$709$	6.69797	−	11.6012i	0.251548	−	0.435693i	−0.712404	−	0.701769i	$-0.752394\pi$
$709$	6.69797	−	11.6012i	0.251548	−	0.435693i	0.963952	+	0.266076i	$0.0857271\pi$
$710$	−36.6753			−1.37640
$711$	6.95858			0.260967
$712$	2.22231	−	3.84915i	0.0832844	−	0.144253i
$713$	4.73947	−	8.20900i	0.177494	−	0.307429i
$714$	0.428626			0.0160409
$715$	−12.5598			−0.469708
$716$	12.6267	−	21.8701i	0.471881	−	0.817323i
$717$	0.973819	+	1.68670i	0.0363679	+	0.0629911i
$718$	−31.8878	+	55.2313i	−1.19004	+	2.06121i
$719$	2.83980	+	4.91868i	0.105907	+	0.183436i	0.914108	−	0.405470i	$-0.132892\pi$
$719$	2.83980	+	4.91868i	0.105907	+	0.183436i	−0.808202	+	0.588906i	$0.799559\pi$
$720$	−44.3236	−	76.7708i	−1.65184	−	2.86108i
$721$	1.93070			0.0719030
$722$	−11.8202	−	49.8347i	−0.439901	−	1.85465i
$723$	1.39676			0.0519460
$724$	−19.2674	−	33.3722i	−0.716069	−	1.24027i
$725$	0.0847682	+	0.146823i	0.00314821	+	0.00545286i
$726$	0.126382	−	0.218899i	0.00469046	−	0.00812411i
$727$	7.29357	+	12.6328i	0.270504	+	0.468526i	0.968991	−	0.247096i	$-0.0794764\pi$
$727$	7.29357	+	12.6328i	0.270504	+	0.468526i	−0.698487	+	0.715623i	$0.746143\pi$
$728$	5.31651	−	9.20847i	0.197043	−	0.341289i
$729$	−26.5264			−0.982458
$730$	−30.7109			−1.13666
$731$	−1.87989	+	3.25607i	−0.0695303	+	0.120430i
$732$	−1.84361	+	3.19323i	−0.0681419	+	0.118025i
$733$	−19.0829			−0.704845			−0.352422	−	0.935841i	$-0.614642\pi$
$733$	−19.0829			−0.704845			−0.352422	+	0.935841i	$0.614642\pi$
$734$	−0.0735863			−0.00271612
$735$	0.731749	−	1.26743i	0.0269910	−	0.0467497i
$736$	−33.5723	−	58.1490i	−1.23749	−	2.14340i
$737$	4.29770	−	7.44384i	0.158308	−	0.274197i
$738$	17.3575	+	30.0640i	0.638937	+	1.10667i
$739$	−13.1812	−	22.8304i	−0.484877	−	0.839832i	0.514972	−	0.857207i	$-0.327802\pi$
$739$	−13.1812	−	22.8304i	−0.484877	−	0.839832i	−0.999849	+	0.0173754i	$0.994469\pi$
$740$	−13.9560			−0.513031
$741$	2.26288	+	0.331263i	0.0831290	+	0.0121692i
$742$	5.56235			0.204200
$743$	−13.5609	−	23.4882i	−0.497501	−	0.861697i	0.502495	−	0.864580i	$-0.332416\pi$
$743$	−13.5609	−	23.4882i	−0.497501	−	0.861697i	−0.999996	+	0.00288297i	$0.999082\pi$
$744$	−1.04788	−	1.81497i	−0.0384170	−	0.0665402i
$745$	−22.7245	+	39.3600i	−0.832561	+	1.44204i
$746$	9.59625	+	16.6212i	0.351344	+	0.608545i
$747$	−17.8091	+	30.8462i	−0.651600	+	1.12860i
$748$	41.3824			1.51309
$749$	−4.14631			−0.151503
$750$	1.40752	−	2.43790i	0.0513955	−	0.0890196i
$751$	21.7527	−	37.6767i	0.793766	−	1.37484i	−0.129854	−	0.991533i	$-0.541451\pi$
$751$	21.7527	−	37.6767i	0.793766	−	1.37484i	0.923620	−	0.383310i	$-0.125216\pi$
$752$	−3.03799			−0.110784
$753$	−2.04212			−0.0744189
$754$	−33.3706	+	57.7996i	−1.21529	+	2.10494i
$755$	−21.6430	−	37.4868i	−0.787670	−	1.36428i
$756$	−0.319249	+	0.552955i	−0.0116110	+	0.0201108i
$757$	4.62905	+	8.01775i	0.168246	+	0.291410i	0.937803	−	0.347168i	$-0.112856\pi$
$757$	4.62905	+	8.01775i	0.168246	+	0.291410i	−0.769558	+	0.638578i	$0.779523\pi$
$758$	40.9739	+	70.9689i	1.48824	+	2.57771i
$759$	0.350161			0.0127100
$760$	31.8149	+	80.0626i	1.15405	+	2.90417i
$761$	1.36776			0.0495811			0.0247906	−	0.999693i	$-0.492108\pi$
$761$	1.36776			0.0495811			0.0247906	+	0.999693i	$0.492108\pi$
$762$	−1.54584	−	2.67748i	−0.0560001	−	0.0969949i
$763$	−1.27704	−	2.21190i	−0.0462321	−	0.0800763i
$764$	−8.00754	+	13.8695i	−0.289703	+	0.501780i
$765$	26.3786	+	45.6891i	0.953722	+	1.65189i
$766$	−34.5308	+	59.8092i	−1.24765	+	2.16099i
$767$	54.4422			1.96579
$768$	−1.80534			−0.0651445
$769$	−4.78603	+	8.28965i	−0.172589	+	0.298933i	−0.939324	−	0.343031i	$-0.888547\pi$
$769$	−4.78603	+	8.28965i	−0.172589	+	0.298933i	0.766735	+	0.641963i	$0.221880\pi$
$770$	−0.652901	+	1.13086i	−0.0235289	+

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34782 - 2.33450i) q^{2} +(0.0468836 + 0.0812047i) q^{3} +(-2.63325 + 4.56093i) q^{4} +(1.12231 + 1.94390i) q^{5} +(0.126382 - 0.218899i) q^{6} +0.215810 q^{7} +8.80535 q^{8} +(1.49560 - 2.59046i) q^{9} +O(q^{10})\)	\(q+(-1.34782 - 2.33450i) q^{2} +(0.0468836 + 0.0812047i) q^{3} +(-2.63325 + 4.56093i) q^{4} +(1.12231 + 1.94390i) q^{5} +(0.126382 - 0.218899i) q^{6} +0.215810 q^{7} +8.80535 q^{8} +(1.49560 - 2.59046i) q^{9} +(3.02535 - 5.24006i) q^{10} -1.00000 q^{11} -0.493826 q^{12} +(2.79775 - 4.84584i) q^{13} +(-0.290874 - 0.503808i) q^{14} +(-0.105236 + 0.182274i) q^{15} +(-6.60155 - 11.4342i) q^{16} +(3.92883 + 6.80493i) q^{17} -8.06324 q^{18} +(4.31293 + 0.631370i) q^{19} -11.8213 q^{20} +(0.0101179 + 0.0175248i) q^{21} +(1.34782 + 2.33450i) q^{22} +(-1.86718 + 3.23406i) q^{23} +(0.412826 + 0.715036i) q^{24} +(-0.0191576 + 0.0331819i) q^{25} -15.0835 q^{26} +0.561778 q^{27} +(-0.568283 + 0.984295i) q^{28} +(2.21240 - 3.83198i) q^{29} +0.567357 q^{30} -2.53830 q^{31} +(-8.99009 + 15.5713i) q^{32} +(-0.0468836 - 0.0812047i) q^{33} +(10.5907 - 18.3437i) q^{34} +(0.242206 + 0.419512i) q^{35} +(7.87661 + 13.6427i) q^{36} +1.18058 q^{37} +(-4.33914 - 10.9195i) q^{38} +0.524673 q^{39} +(9.88233 + 17.1167i) q^{40} +(-2.15267 - 3.72853i) q^{41} +(0.0272744 - 0.0472406i) q^{42} +(0.239243 + 0.414382i) q^{43} +(2.63325 - 4.56093i) q^{44} +6.71412 q^{45} +10.0665 q^{46} +(0.115048 - 0.199269i) q^{47} +(0.619009 - 1.07215i) q^{48} -6.95343 q^{49} +0.103284 q^{50} +(-0.368395 + 0.638079i) q^{51} +(14.7344 + 25.5207i) q^{52} +(-4.78073 + 8.28047i) q^{53} +(-0.757178 - 1.31147i) q^{54} +(-1.12231 - 1.94390i) q^{55} +1.90028 q^{56} +(0.150935 + 0.379831i) q^{57} -11.9277 q^{58} +(4.86482 + 8.42612i) q^{59} +(-0.554225 - 0.959946i) q^{60} +(3.73333 - 6.46632i) q^{61} +(3.42117 + 5.92565i) q^{62} +(0.322766 - 0.559048i) q^{63} +22.0620 q^{64} +12.5598 q^{65} +(-0.126382 + 0.218899i) q^{66} +(-4.29770 + 7.44384i) q^{67} -41.3824 q^{68} -0.350161 q^{69} +(0.652901 - 1.13086i) q^{70} +(-3.03066 - 5.24926i) q^{71} +(13.1693 - 22.8099i) q^{72} +(-2.53780 - 4.39560i) q^{73} +(-1.59121 - 2.75605i) q^{74} -0.00359270 q^{75} +(-14.2367 + 18.0084i) q^{76} -0.215810 q^{77} +(-0.707167 - 1.22485i) q^{78} +(1.16317 + 2.01467i) q^{79} +(14.8180 - 25.6655i) q^{80} +(-4.46047 - 7.72577i) q^{81} +(-5.80283 + 10.0508i) q^{82} -11.9076 q^{83} -0.106572 q^{84} +(-8.81873 + 15.2745i) q^{85} +(0.644916 - 1.11703i) q^{86} +0.414900 q^{87} -8.80535 q^{88} +(0.252381 - 0.437137i) q^{89} +(-9.04945 - 15.6741i) q^{90} +(0.603782 - 1.04578i) q^{91} +(-9.83354 - 17.0322i) q^{92} +(-0.119004 - 0.206122i) q^{93} -0.620259 q^{94} +(3.61313 + 9.09249i) q^{95} -1.68595 q^{96} +(1.84449 + 3.19476i) q^{97} +(9.37199 + 16.2328i) q^{98} +(-1.49560 + 2.59046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more