LMFDB - Embedded newform 261.2.x.a.2.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.10
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13739 - 0.839433i) q^{2} +(-0.756704 - 1.55801i) q^{3} +(-0.000498633 - 0.00161653i) q^{4} +(-1.18474 + 3.01866i) q^{5} +(-0.447178 + 2.40727i) q^{6} +(4.21652 + 1.30062i) q^{7} +(-0.934565 + 2.67083i) q^{8} +(-1.85480 + 2.35791i) q^{9} +O(q^{10})$	\(q+(-1.13739 - 0.839433i) q^{2} +(-0.756704 - 1.55801i) q^{3} +(-0.000498633 - 0.00161653i) q^{4} +(-1.18474 + 3.01866i) q^{5} +(-0.447178 + 2.40727i) q^{6} +(4.21652 + 1.30062i) q^{7} +(-0.934565 + 2.67083i) q^{8} +(-1.85480 + 2.35791i) q^{9} +(3.88147 - 2.43889i) q^{10} +(2.98785 + 0.565332i) q^{11} +(-0.00214125 + 0.00200011i) q^{12} +(-3.08454 + 0.231155i) q^{13} +(-3.70405 - 5.01881i) q^{14} +(5.59960 - 0.438398i) q^{15} +(3.30216 - 2.25137i) q^{16} +(2.87374 + 2.87374i) q^{17} +(4.08894 - 1.12488i) q^{18} +(-1.42303 - 2.26473i) q^{19} +(0.00547050 + 0.000409957i) q^{20} +(-1.16427 - 7.55357i) q^{21} +(-2.92380 - 3.15110i) q^{22} +(0.373700 - 2.47934i) q^{23} +(4.86838 - 0.564967i) q^{24} +(-4.04344 - 3.75176i) q^{25} +(3.70237 + 2.32636i) q^{26} +(5.07718 + 1.10556i) q^{27} -0.00746466i q^{28} +(-5.14047 + 1.60487i) q^{29} +(-6.73694 - 4.20186i) q^{30} +(4.36433 + 10.0032i) q^{31} +(0.00956293 + 0.000357820i) q^{32} +(-1.38012 - 5.08289i) q^{33} +(-0.856255 - 5.68088i) q^{34} +(-8.92160 + 11.1873i) q^{35} +(0.00473649 + 0.00182261i) q^{36} +(4.07179 + 1.42478i) q^{37} +(-0.282554 + 3.77043i) q^{38} +(2.69423 + 4.63084i) q^{39} +(-6.95512 - 5.98536i) q^{40} +(5.29884 + 1.41982i) q^{41} +(-5.01649 + 9.56870i) q^{42} +(5.85815 + 2.55588i) q^{43} +(-0.000575966 - 0.00511184i) q^{44} +(-4.92026 - 8.39250i) q^{45} +(-2.50628 + 2.50628i) q^{46} +(1.78914 - 9.45581i) q^{47} +(-6.00642 - 3.44118i) q^{48} +(10.3037 + 7.02498i) q^{49} +(1.44962 + 7.66142i) q^{50} +(2.30275 - 6.65189i) q^{51} +(0.00191172 + 0.00487100i) q^{52} +(-2.29909 + 1.83346i) q^{53} +(-4.84669 - 5.51941i) q^{54} +(-5.24635 + 8.34953i) q^{55} +(-7.41436 + 10.0461i) q^{56} +(-2.45167 + 3.93083i) q^{57} +(7.19390 + 2.48971i) q^{58} +(-10.6823 + 6.16743i) q^{59} +(-0.00350083 - 0.00883332i) q^{60} +(-7.21218 + 3.81175i) q^{61} +(3.43303 - 15.0411i) q^{62} +(-10.8875 + 7.52976i) q^{63} +(-6.25993 - 4.99213i) q^{64} +(2.95659 - 9.58504i) q^{65} +(-2.69701 + 6.93976i) q^{66} +(2.09840 - 3.07778i) q^{67} +(0.00321254 - 0.00607843i) q^{68} +(-4.14562 + 1.29390i) q^{69} +(19.5384 - 5.23529i) q^{70} +(-7.09131 - 3.41500i) q^{71} +(-4.56414 - 7.15747i) q^{72} +(10.3562 - 1.16687i) q^{73} +(-3.43521 - 5.03853i) q^{74} +(-2.78560 + 9.13869i) q^{75} +(-0.00295144 + 0.00342964i) q^{76} +(11.8630 + 6.26980i) q^{77} +(0.822888 - 7.52870i) q^{78} +(-4.37071 - 5.07886i) q^{79} +(2.88394 + 12.6354i) q^{80} +(-2.11944 - 8.74688i) q^{81} +(-4.83501 - 6.06292i) q^{82} +(3.49952 - 3.77159i) q^{83} +(-0.0116300 + 0.00564854i) q^{84} +(-12.0795 + 5.27021i) q^{85} +(-4.51751 - 7.82456i) q^{86} +(6.39021 + 6.79450i) q^{87} +(-4.30225 + 7.45171i) q^{88} +(-0.192907 + 1.71210i) q^{89} +(-1.44868 + 13.6758i) q^{90} +(-13.3067 - 3.03716i) q^{91} +(-0.00419427 + 0.000632184i) q^{92} +(12.2825 - 14.3691i) q^{93} +(-9.97248 + 9.25310i) q^{94} +(8.52237 - 1.61252i) q^{95} +(-0.00667882 - 0.0151699i) q^{96} +(0.00557688 + 0.149045i) q^{97} +(-5.82240 - 16.6395i) q^{98} +(-6.87486 + 5.99649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.13739	−	0.839433i	−0.804257	−	0.593569i	0.112207	−	0.993685i	$-0.464208\pi$
$2$	−1.13739	−	0.839433i	−0.804257	−	0.593569i	−0.916465	+	0.400116i	$0.868970\pi$
$3$	−0.756704	−	1.55801i	−0.436883	−	0.899518i
$3$	−0.756704	−	1.55801i	−0.436883	−	0.899518i
$4$	−0.000498633	−	0.00161653i	−0.000249317	−	0.000808265i
$5$	−1.18474	+	3.01866i	−0.529830	+	1.34998i	0.376109	+	0.926576i	$0.377262\pi$
$5$	−1.18474	+	3.01866i	−0.529830	+	1.34998i	−0.905939	+	0.423409i	$0.860833\pi$
$6$	−0.447178	+	2.40727i	−0.182560	+	0.982765i
$7$	4.21652	+	1.30062i	1.59369	+	0.491590i	0.959530	−	0.281608i	$-0.0908677\pi$
$7$	4.21652	+	1.30062i	1.59369	+	0.491590i	0.634165	+	0.773198i	$0.281344\pi$
$8$	−0.934565	+	2.67083i	−0.330419	+	0.944282i
$9$	−1.85480	+	2.35791i	−0.618266	+	0.785969i
$10$	3.88147	−	2.43889i	1.22743	−	0.771245i
$11$	2.98785	+	0.565332i	0.900870	+	0.170454i	0.615661	−	0.788011i	$-0.288889\pi$
$11$	2.98785	+	0.565332i	0.900870	+	0.170454i	0.285210	+	0.958465i	$0.407937\pi$
$12$	−0.00214125	+	0.00200011i	−0.000618127	+	0.000577382i
$13$	−3.08454	+	0.231155i	−0.855498	+	0.0641107i	−0.495255	−	0.868748i	$-0.664925\pi$
$13$	−3.08454	+	0.231155i	−0.855498	+	0.0641107i	−0.360243	+	0.932858i	$0.617306\pi$
$14$	−3.70405	−	5.01881i	−0.989948	−	1.34133i
$15$	5.59960	−	0.438398i	1.44581	−	0.113194i
$16$	3.30216	−	2.25137i	0.825539	−	0.562843i
$17$	2.87374	+	2.87374i	0.696984	+	0.696984i	0.963759	−	0.266775i	$-0.0859580\pi$
$17$	2.87374	+	2.87374i	0.696984	+	0.696984i	−0.266775	+	0.963759i	$0.585958\pi$
$18$	4.08894	−	1.12488i	0.963772	−	0.265137i
$19$	−1.42303	−	2.26473i	−0.326465	−	0.519566i	0.642655	−	0.766156i	$-0.277833\pi$
$19$	−1.42303	−	2.26473i	−0.326465	−	0.519566i	−0.969120	+	0.246590i	$0.920690\pi$
$20$	0.00547050		0.000409957i	0.00122324		9.16692e-5i
$21$	−1.16427	−	7.55357i	−0.254064	−	1.64832i
$22$	−2.92380	−	3.15110i	−0.623356	−	0.671818i
$23$	0.373700	−	2.47934i	0.0779219	−	0.516978i	−0.915486	−	0.402349i	$-0.868194\pi$
$23$	0.373700	−	2.47934i	0.0779219	−	0.516978i	0.993408	−	0.114629i	$-0.0365680\pi$
$24$	4.86838	−	0.564967i	0.993753	−	0.115323i
$25$	−4.04344	−	3.75176i	−0.808687	−	0.750352i
$26$	3.70237	+	2.32636i	0.726095	+	0.456236i
$27$	5.07718	+	1.10556i	0.977103	+	0.212765i
$28$		−	0.00746466i		−	0.00141069i
$29$	−5.14047	+	1.60487i	−0.954561	+	0.298017i
$29$	−5.14047	+	1.60487i	−0.954561	+	0.298017i
$30$	−6.73694	−	4.20186i	−1.22999	−	0.767151i
$31$	4.36433	+	10.0032i	0.783857	+	1.79662i	0.573933	+	0.818902i	$0.305417\pi$
$31$	4.36433	+	10.0032i	0.783857	+	1.79662i	0.209924	+	0.977718i	$0.432678\pi$
$32$	0.00956293		0.000357820i	0.00169050		6.32542e-5i
$33$	−1.38012	−	5.08289i	−0.240249	−	0.884818i
$34$	−0.856255	−	5.68088i	−0.146846	−	0.974263i
$35$	−8.92160	+	11.1873i	−1.50803	+	1.89100i
$36$	0.00473649	+	0.00182261i	0.000789415	+	0.000303768i
$37$	4.07179	+	1.42478i	0.669398	+	0.234232i	0.643516	−	0.765433i	$-0.277475\pi$
$37$	4.07179	+	1.42478i	0.669398	+	0.234232i	0.0258816	+	0.999665i	$0.491761\pi$
$38$	−0.282554	+	3.77043i	−0.0458364	+	0.611644i
$39$	2.69423	+	4.63084i	0.431422	+	0.741528i
$40$	−6.95512	−	5.98536i	−1.09970	−	0.946369i
$41$	5.29884	+	1.41982i	0.827540	+	0.221739i	0.647640	−	0.761946i	$-0.275756\pi$
$41$	5.29884	+	1.41982i	0.827540	+	0.221739i	0.179900	+	0.983685i	$0.442423\pi$
$42$	−5.01649	+	9.56870i	−0.774061	+	1.47648i
$43$	5.85815	+	2.55588i	0.893359	+	0.389768i	0.795870	−	0.605468i	$-0.207014\pi$
$43$	5.85815	+	2.55588i	0.893359	+	0.389768i	0.0974893	+	0.995237i	$0.468919\pi$
$44$	−0.000575966	−	0.00511184i	−8.68301e−5	−	0.000770639i
$45$	−4.92026	−	8.39250i	−0.733470	−	1.25108i
$46$	−2.50628	+	2.50628i	−0.369531	+	0.369531i
$47$	1.78914	−	9.45581i	0.260972	−	1.37927i	−0.569399	−	0.822062i	$-0.692824\pi$
$47$	1.78914	−	9.45581i	0.260972	−	1.37927i	0.830371	−	0.557211i	$-0.188128\pi$
$48$	−6.00642	−	3.44118i	−0.866952	−	0.496691i
$49$	10.3037	+	7.02498i	1.47196	+	1.00357i
$50$	1.44962	+	7.66142i	0.205007	+	1.08349i
$51$	2.30275	−	6.65189i	0.322449	−	0.931451i
$52$	0.00191172	+	0.00487100i	0.000265109	+	0.000675485i
$53$	−2.29909	+	1.83346i	−0.315804	+	0.251845i	−0.768544	−	0.639797i	$-0.779018\pi$
$53$	−2.29909	+	1.83346i	−0.315804	+	0.251845i	0.452739	+	0.891643i	$0.350447\pi$
$54$	−4.84669	−	5.51941i	−0.659552	−	0.751096i
$55$	−5.24635	+	8.34953i	−0.707418	+	1.12585i
$56$	−7.41436	+	10.0461i	−0.990786	+	1.34247i
$57$	−2.45167	+	3.93083i	−0.324732	+	0.520651i
$58$	7.19390	+	2.48971i	0.944606	+	0.326916i
$59$	−10.6823	+	6.16743i	−1.39072	+	0.802931i	−0.993395	−	0.114747i	$-0.963394\pi$
$59$	−10.6823	+	6.16743i	−1.39072	+	0.802931i	−0.397323	+	0.917679i	$0.630061\pi$
$60$	−0.00350083	−	0.00883332i	−0.000451955	−	0.00114038i
$61$	−7.21218	+	3.81175i	−0.923426	+	0.488045i	−0.860201	−	0.509955i	$-0.829662\pi$
$61$	−7.21218	+	3.81175i	−0.923426	+	0.488045i	−0.0632243	+	0.997999i	$0.520138\pi$
$62$	3.43303	−	15.0411i	0.435995	−	1.91022i
$63$	−10.8875	+	7.52976i	−1.37170	+	0.948661i
$64$	−6.25993	−	4.99213i	−0.782492	−	0.624016i
$65$	2.95659	−	9.58504i	0.366720	−	1.18888i
$66$	−2.69701	+	6.93976i	−0.331979	+	0.854225i
$67$	2.09840	−	3.07778i	0.256360	−	0.376011i	−0.676385	−	0.736549i	$-0.736454\pi$
$67$	2.09840	−	3.07778i	0.256360	−	0.376011i	0.932745	+	0.360537i	$0.117407\pi$
$68$	0.00321254	−	0.00607843i	0.000389578	−	0.000737118i
$69$	−4.14562	+	1.29390i	−0.499074	+	0.155767i
$70$	19.5384	−	5.23529i	2.33528	−	0.625737i
$71$	−7.09131	−	3.41500i	−0.841584	−	0.405285i	−0.0371370	−	0.999310i	$-0.511824\pi$
$71$	−7.09131	−	3.41500i	−0.841584	−	0.405285i	−0.804447	+	0.594025i	$0.797538\pi$
$72$	−4.56414	−	7.15747i	−0.537889	−	0.843516i
$73$	10.3562	−	1.16687i	1.21210	−	0.136571i	0.517321	−	0.855791i	$-0.326929\pi$
$73$	10.3562	−	1.16687i	1.21210	−	0.136571i	0.694783	+	0.719220i	$0.255501\pi$
$74$	−3.43521	−	5.03853i	−0.399335	−	0.585717i
$75$	−2.78560	+	9.13869i	−0.321654	+	1.05525i
$76$	−0.00295144	+	0.00342964i	−0.000338554	+	0.000393406i
$77$	11.8630	+	6.26980i	1.35192	+	0.714510i
$78$	0.822888	−	7.52870i	0.0931738	−	0.852458i
$79$	−4.37071	−	5.07886i	−0.491743	−	0.571416i	0.456191	−	0.889882i	$-0.349213\pi$
$79$	−4.37071	−	5.07886i	−0.491743	−	0.571416i	−0.947934	+	0.318466i	$0.896832\pi$
$80$	2.88394	+	12.6354i	0.322434	+	1.41268i
$81$	−2.11944	−	8.74688i	−0.235494	−	0.971876i
$82$	−4.83501	−	6.06292i	−0.533938	−	0.669537i
$83$	3.49952	−	3.77159i	0.384123	−	0.413986i	−0.511159	−	0.859486i	$-0.670784\pi$
$83$	3.49952	−	3.77159i	0.384123	−	0.413986i	0.895282	+	0.445500i	$0.146974\pi$
$84$	−0.0116300	+	0.00564854i	−0.00126894	+	0.000616306i
$85$	−12.0795	+	5.27021i	−1.31020	+	0.571635i
$86$	−4.51751	−	7.82456i	−0.487136	−	0.843744i
$87$	6.39021	+	6.79450i	0.685103	+	0.728446i
$88$	−4.30225	+	7.45171i	−0.458621	+	0.794355i
$89$	−0.192907	+	1.71210i	−0.0204481	+	0.181482i	−0.999785	−	0.0207556i	$-0.993393\pi$
$89$	−0.192907	+	1.71210i	−0.0204481	+	0.181482i	0.979336	+	0.202238i	$0.0648214\pi$
$90$	−1.44868	+	13.6758i	−0.152704	+	1.44156i
$91$	−13.3067	−	3.03716i	−1.39492	−	0.318381i
$92$	−0.00419427		0.000632184i	−0.000437282		6.59097e-5i
$93$	12.2825	−	14.3691i	1.27364	−	1.49001i
$94$	−9.97248	+	9.25310i	−1.02858	+	0.954385i
$95$	8.52237	−	1.61252i	0.874377	−	0.165441i
$96$	−0.00667882	−	0.0151699i	−0.000681654	−	0.00154827i
$97$	0.00557688	+	0.149045i	0.000566246	+	0.0151332i	0.999555	−	0.0298235i	$-0.00949452\pi$
$97$	0.00557688	+	0.149045i	0.000566246	+	0.0151332i	−0.998989	+	0.0449567i	$0.985685\pi$
$98$	−5.82240	−	16.6395i	−0.588151	−	1.68084i
$99$	−6.87486	+	5.99649i	−0.690949	+	0.602670i
$100$	−0.00404864	+	0.00840709i	−0.000404864	+	0.000840709i
$101$	3.88276	−	8.89938i	0.386349	−	0.885521i	−0.609352	−	0.792900i	$-0.708570\pi$
$101$	3.88276	−	8.89938i	0.386349	−	0.885521i	0.995701	−	0.0926218i	$-0.0295248\pi$
$102$	−8.20294	+	5.63280i	−0.812213	+	0.557730i
$103$	0.910271	+	12.1467i	0.0896916	+	1.19685i	0.842531	+	0.538648i	$0.181065\pi$
$103$	0.910271	+	12.1467i	0.0896916	+	1.19685i	−0.752840	+	0.658204i	$0.771316\pi$
$104$	2.26533	−	8.45433i	0.222134	−	0.829015i
$105$	24.1810	+	5.43446i	2.35982	+	0.530349i
$106$	4.15403	−	0.155433i	0.403476	−	0.0150970i
$107$	1.04706	+	2.17424i	0.101223	+	0.210192i	0.945430	−	0.325826i	$-0.105642\pi$
$107$	1.04706	+	2.17424i	0.101223	+	0.210192i	−0.844207	+	0.536018i	$0.819928\pi$
$108$	−0.000744477	−	0.00875868i	−7.16373e−5	−	0.000842804i
$109$	−1.53792	+	0.351021i	−0.147306	+	0.0336217i	−0.295538	−	0.955331i	$-0.595499\pi$
$109$	−1.53792	+	0.351021i	−0.147306	+	0.0336217i	0.148232	+	0.988953i	$0.452642\pi$
$110$	12.9760	−	5.09272i	1.23722	−	0.485571i
$111$	−0.861313	−	7.42203i	−0.0817522	−	0.704467i
$112$	16.8518	−	5.19809i	1.59235	−	0.491174i
$113$	0.200980	−	5.37132i	0.0189067	−	0.505291i	−0.957383	−	0.288822i	$-0.906736\pi$
$113$	0.200980	−	5.37132i	0.0189067	−	0.505291i	0.976289	−	0.216469i	$-0.0694540\pi$
$114$	6.08818	−	2.41287i	0.570210	−	0.225986i
$115$	7.04154	+	4.06544i	0.656627	+	0.379104i
$116$	0.00515753	+	0.00750948i	0.000478864	+	0.000697237i
$117$	5.17617	−	7.70181i	0.478537	−	0.712033i
$118$	17.3271	+	1.95230i	1.59509	+	0.179724i
$119$	8.37952	+	15.8548i	0.768150	+	1.45341i
$120$	−4.06230	+	15.3653i	−0.370836	+	1.40265i
$121$	−1.63197	−	0.640501i	−0.148361	−	0.0582273i
$122$	11.4028	+	1.71869i	1.03236	+	0.155603i
$123$	−1.79756	−	9.33004i	−0.162080	−	0.841261i
$124$	0.0139942	−	0.0120430i	0.00125672	−	0.00108149i
$125$	1.50728	−	0.725868i	0.134815	−	0.0649236i
$126$	18.7041	+	0.575081i	1.66630	+	0.0512323i
$127$	−7.43551	+	2.60180i	−0.659795	+	0.230872i	−0.639347	−	0.768919i	$-0.720795\pi$
$127$	−7.43551	+	2.60180i	−0.659795	+	0.230872i	−0.0204485	+	0.999791i	$0.506509\pi$
$128$	2.92448	+	10.9143i	0.258490	+	0.964698i
$129$	−0.450786	−	11.0611i	−0.0396895	−	0.973876i
$130$	−11.4088	+	8.42008i	−1.00062	+	0.738490i
$131$	3.08535	−	2.27709i	0.269569	−	0.198951i	−0.450645	−	0.892703i	$-0.648806\pi$
$131$	3.08535	−	2.27709i	0.269569	−	0.198951i	0.720213	+	0.693753i	$0.244044\pi$
$132$	−0.00752847	+	0.00476551i	−0.000655269	+	0.000414784i
$133$	−3.05465	−	11.4001i	−0.264872	−	0.988516i
$134$	−4.97030	+	1.73918i	−0.429368	+	0.150242i
$135$	−9.35243	+	14.0165i	−0.804929	+	1.20635i
$136$	−10.3610	+	4.98958i	−0.888446	+	0.427853i
$137$	7.70095	−	6.62720i	0.657936	−	0.566200i	−0.258683	−	0.965962i	$-0.583288\pi$
$137$	7.70095	−	6.62720i	0.657936	−	0.566200i	0.916619	+	0.399763i	$0.130907\pi$
$138$	5.80133	+	2.00830i	0.493842	+	0.170958i
$139$	10.4709	+	1.57823i	0.888127	+	0.133864i	0.577232	−	0.816580i	$-0.304133\pi$
$139$	10.4709	+	1.57823i	0.888127	+	0.133864i	0.310896	+	0.950444i	$0.399371\pi$
$140$	0.0225333	+	0.00884366i	0.00190441	+	0.000747425i
$141$	−16.0861	+	4.36775i	−1.35470	+	0.367831i
$142$	5.19894	+	9.83687i	0.436285	+	0.825492i
$143$	−9.34683	−	1.05313i	−0.781621	−	0.0880676i
$144$	−0.816313	+	11.9620i	−0.0680261	+	0.996835i
$145$	1.24555	−	17.4187i	0.103437	−	1.44654i
$146$	−12.7586	−	7.36617i	−1.05591	−	0.609629i
$147$	3.14811	−	21.3692i	0.259652	−	1.76250i
$148$	0.000272870	−	0.00729261i	2.24298e−5	−	0.000599449i
$149$	6.38169	−	1.96849i	0.522808	−	0.161265i	−0.0221079	−	0.999756i	$-0.507038\pi$
$149$	6.38169	−	1.96849i	0.522808	−	0.161265i	0.544916	+	0.838491i	$0.316562\pi$
$150$	10.8396	−	8.05595i	0.885053	−	0.657765i
$151$	−6.34826	+	2.49151i	−0.516614	+	0.202756i	−0.609301	−	0.792939i	$-0.708550\pi$
$151$	−6.34826	+	2.49151i	−0.516614	+	0.202756i	0.0926867	+	0.995695i	$0.470455\pi$
$152$	7.37864	−	1.68413i	0.598487	−	0.136601i
$153$	−12.1062	+	1.44580i	−0.978730	+	0.116886i
$154$	−8.22985	−	17.0895i	−0.663180	−	1.37711i
$155$	−35.3667	+	1.32333i	−2.84072	+	0.106292i
$156$	0.00614246	−	0.00666439i	0.000491790	−	0.000533578i
$157$	−1.24605	+	4.65033i	−0.0994457	+	0.371137i	−0.997656	−	0.0684296i	$-0.978201\pi$
$157$	−1.24605	+	4.65033i	−0.0994457	+	0.371137i	0.898210	+	0.439566i	$0.144868\pi$
$158$	0.707848	+	9.44557i	0.0563133	+	0.751449i
$159$	4.59628	+	2.19462i	0.364509	+	0.174045i
$160$	−0.0124097	+	0.0284433i	−0.000981071	+	0.00224864i
$161$	4.80040	−	9.96814i	0.378325	−	0.785599i
$162$	−4.93179	+	11.7278i	−0.387478	+	0.921420i
$163$	−7.25206	−	20.7252i	−0.568025	−	1.62332i	−0.765802	−	0.643076i	$-0.777658\pi$
$163$	−7.25206	−	20.7252i	−0.568025	−	1.62332i	0.197777	−	0.980247i	$-0.436628\pi$
$164$	−0.000346998	−	0.00927370i	−2.70960e−5	−	0.000724155i
$165$	16.9786	+	1.85576i	1.32178	+	0.144471i
$166$	−7.14633	+	1.35216i	−0.554662	+	0.104948i
$167$	1.91823	−	1.77985i	0.148437	−	0.137729i	−0.602459	−	0.798150i	$-0.705812\pi$
$167$	1.91823	−	1.77985i	0.148437	−	0.137729i	0.750896	+	0.660420i	$0.229622\pi$
$168$	21.2624	+	3.94974i	1.64043	+	0.304729i
$169$	−3.39382	+	0.511537i	−0.261063	+	0.0393490i
$170$	18.1631	+	4.14560i	1.39304	+	0.317953i
$171$	7.97946	+	0.845263i	0.610205	+	0.0646389i
$172$	0.00121059	−	0.0107443i	9.23069e−5	−	0.000819246i
$173$	−4.18398	+	7.24687i	−0.318102	+	0.550969i	−0.980092	−	0.198544i	$-0.936379\pi$
$173$	−4.18398	+	7.24687i	−0.318102	+	0.550969i	0.661990	+	0.749513i	$0.269712\pi$
$174$	−1.56465	−	13.0922i	−0.118616	−	0.992514i
$175$	−12.1696	−	21.0784i	−0.919935	−	1.59337i
$176$	11.1391	−	4.85995i	0.839643	−	0.366332i
$177$	17.6923	+	11.9762i	1.32983	+	0.900189i
$178$	1.65660	−	1.78540i	0.124168	−	0.133821i
$179$	3.19062	+	4.00091i	0.238478	+	0.299042i	0.886640	−	0.462460i	$-0.153033\pi$
$179$	3.19062	+	4.00091i	0.238478	+	0.299042i	−0.648162	+	0.761503i	$0.724462\pi$
$180$	−0.0111133	+	0.0121385i	−0.000828338	+	0.000904753i
$181$	−0.321975	−	1.41066i	−0.0239322	−	0.104854i	0.961551	−	0.274626i	$-0.0885540\pi$
$181$	−0.321975	−	1.41066i	−0.0239322	−	0.104854i	−0.985483	+	0.169772i	$0.945697\pi$
$182$	12.5854	+	14.6245i	0.932893	+	1.08404i
$183$	11.3962	+	8.35230i	0.842434	+	0.617420i
$184$	6.27265	+	3.31519i	0.462426	+	0.244399i
$185$	−9.12491	+	10.6033i	−0.670877	+	0.779573i
$186$	−26.0319	+	6.03294i	−1.90876	+	0.442357i
$187$	6.96168	+	10.2109i	0.509089	+	0.746696i
$188$	−0.0161777	+	0.00182279i	−0.00117988	+	0.000132941i
$189$	19.9701	+	11.2651i	1.45261	+	0.819417i
$190$	−11.0469	−	5.31990i	−0.801425	−	0.385946i
$191$	−1.53073	+	0.410157i	−0.110759	+	0.0296779i	−0.313773	−	0.949498i	$-0.601593\pi$
$191$	−1.53073	+	0.410157i	−0.110759	+	0.0296779i	0.203014	+	0.979176i	$0.434926\pi$
$192$	−3.04088	+	13.5306i	−0.219457	+	0.976488i
$193$	9.91161	−	18.7537i	0.713454	−	1.34992i	−0.214315	−	0.976765i	$-0.568752\pi$
$193$	9.91161	−	18.7537i	0.713454	−	1.34992i	0.927769	−	0.373155i	$-0.121724\pi$
$194$	0.118770	−	0.174204i	0.00852722	−	0.0125071i
$195$	−17.1709	+	2.64663i	−1.22963	+	0.189529i
$196$	0.00621829	−	0.0201592i	0.000444164	−	0.00143994i
$197$	−4.25191	−	3.39079i	−0.302936	−	0.241584i	0.460209	−	0.887811i	$-0.347774\pi$
$197$	−4.25191	−	3.39079i	−0.302936	−	0.241584i	−0.763145	+	0.646227i	$0.776346\pi$
$198$	12.8531	−	1.04937i	0.913427	−	0.0745758i
$199$	−0.237729	+	1.04156i	−0.0168521	+	0.0738340i	−0.982655	−	0.185444i	$-0.940628\pi$
$199$	−0.237729	+	1.04156i	−0.0168521	+	0.0738340i	0.965803	+	0.259278i	$0.0834847\pi$
$200$	13.7992	−	7.29308i	0.975750	−	0.515699i
$201$	−6.38309	−	0.940357i	−0.450228	−	0.0663277i
$202$	−11.8867	+	6.86276i	−0.836342	+	0.482862i
$203$	−23.7622	+	0.0811443i	−1.66778	+	0.00569522i
$204$	−0.0119012		0.000405609i	−0.000833251		2.83983e-5i
$205$	−10.5637	+	14.3133i	−0.737799	+	0.999683i
$206$	9.16103	−	14.5797i	0.638279	−	1.01581i
$207$	5.15291	+	5.47983i	0.358152	+	0.380874i
$208$	−9.66523	+	7.70777i	−0.670163	+	0.534437i
$209$	−2.97146	−	7.57117i	−0.205540	−	0.523709i
$210$	−22.9414	−	26.4795i	−1.58311	−	1.82726i
$211$	−2.78439	−	14.7158i	−0.191685	−	1.01308i	−0.937777	−	0.347237i	$-0.887120\pi$
$211$	−2.78439	−	14.7158i	−0.191685	−	1.01308i	0.746092	−	0.665843i	$-0.231928\pi$
$212$	0.00411025	+	0.00280232i	0.000282293	+	0.000192464i
$213$	0.0454197	+	13.6325i	0.00311210	+	0.934082i
$214$	0.634214	−	3.35190i	0.0433540	−	0.229131i
$215$	−14.6557	+	14.6557i	−0.999510	+	0.999510i
$216$	−7.69772	+	12.5271i	−0.523764	+	0.852359i
$217$	5.39195	+	47.8549i	0.366029	+	3.24860i
$218$	2.04388	+	0.891735i	0.138429	+	0.0603959i
$219$	−9.65458	−	15.2521i	−0.652396	−	1.03064i
$220$	0.0161133	+	0.00431754i	0.00108636	+	0.000291088i
$221$	−9.52845	−	8.19990i	−0.640953	−	0.551585i
$222$	−5.25065	+	9.16476i	−0.352400	+	0.615099i
$223$	0.0173348	−	0.231317i	0.00116083	−	0.0154901i	−0.996593	−	0.0824729i	$-0.973718\pi$
$223$	0.0173348	−	0.231317i	0.00116083	−	0.0154901i	0.997754	+	0.0669828i	$0.0213373\pi$
$224$	0.0398569	+	0.0139465i	0.00266305	+	0.000931842i
$225$	16.3461	−	2.57528i	1.08974	−	0.171685i
$226$	−4.73746	+	5.94058i	−0.315131	+	0.395162i
$227$	−3.27220	−	21.7096i	−0.217183	−	1.44092i	−0.785885	−	0.618373i	$-0.787792\pi$
$227$	−3.27220	−	21.7096i	−0.217183	−	1.44092i	0.568702	−	0.822544i	$-0.307446\pi$
$228$	0.00757678	+	0.00200316i	0.000501785	+	0.000132663i
$229$	−21.1166	−	0.790126i	−1.39542	−	0.0522130i	−0.670942	−	0.741510i	$-0.734110\pi$
$229$	−21.1166	−	0.790126i	−1.39542	−	0.0522130i	−0.724479	+	0.689297i	$0.757920\pi$
$230$	−4.59633	−	10.5349i	−0.303073	−	0.694651i
$231$	0.791613	−	23.2271i	0.0520843	−	1.52823i
$232$	0.517764	−	15.2292i	0.0339929	−	0.999845i
$233$		−	9.39919i		−	0.615761i	−0.951425	−	0.307881i	$-0.900380\pi$
$233$		−	9.39919i		−	0.615761i	0.951425	−	0.307881i	$-0.0996198\pi$
$234$	−12.3525	+	4.41493i	−0.807507	+	0.288613i
$235$	26.4242	+	16.6034i	1.72373	+	1.08309i
$236$	0.0152964	+	0.0141930i	0.000995710	+	0.000923884i
$237$	−4.60559	+	10.6528i	−0.299165	+	0.691974i
$238$	3.77827	−	25.0672i	0.244909	−	1.62487i
$239$	−3.52920	−	3.80357i	−0.228285	−	0.246033i	0.608514	−	0.793543i	$-0.291766\pi$
$239$	−3.52920	−	3.80357i	−0.228285	−	0.246033i	−0.836799	+	0.547511i	$0.815576\pi$
$240$	17.5038	−	14.0544i	1.12986	−	0.907210i
$241$	−9.66200	−	0.724067i	−0.622384	−	0.0466413i	−0.240194	−	0.970725i	$-0.577211\pi$
$241$	−9.66200	−	0.724067i	−0.622384	−	0.0466413i	−0.382190	+	0.924084i	$0.624830\pi$
$242$	1.31853	+	2.09843i	0.0847583	+	0.134892i
$243$	−12.0240	+	9.92091i	−0.771337	+	0.636427i
$244$	0.00975804	+	0.00975804i	0.000624695	+	0.000624695i
$245$	−33.4132	+	22.7807i	−2.13469	+	1.45541i
$246$	−5.78742	+	12.1208i	−0.368992	+	0.772796i
$247$	4.91289	+	6.65673i	0.312600	+	0.423558i
$248$	−30.7955	+	2.30780i	−1.95552	+	0.146546i
$249$	−8.52428	−	2.59832i	−0.540204	−	0.164662i
$250$	−2.32369	−	0.439665i	−0.146963	−	0.0278069i
$251$	14.7755	−	9.28408i	0.932623	−	0.586006i	0.0222313	−	0.999753i	$-0.492923\pi$
$251$	14.7755	−	9.28408i	0.932623	−	0.586006i	0.910392	+	0.413747i	$0.135780\pi$
$252$	0.0176010	+	0.0138455i	0.00110876	+	0.000872182i
$253$	2.51821	−	7.19663i	0.158318	−	0.452448i
$254$	10.6411	+	3.28235i	0.667684	+	0.205953i
$255$	17.3516	+	14.8319i	1.08660	+	0.928812i
$256$	−0.0148330	+	0.0377939i	−0.000927063	+	0.00236212i
$257$	4.66308	+	15.1173i	0.290875	+	0.942993i	0.976587	+	0.215121i	$0.0690146\pi$
$257$	4.66308	+	15.1173i	0.290875	+	0.942993i	−0.685712	+	0.727873i	$0.740509\pi$
$258$	−8.77234	+	12.9592i	−0.546142	+	0.806805i
$259$	15.3157	+	11.3035i	0.951669	+	0.702364i
$260$	−0.0169688			−0.00105236
$261$	5.75040	−	15.0974i	0.355941	−	0.934508i
$262$	−5.42072			−0.334893
$263$	5.72511	+	4.22533i	0.353026	+	0.260545i	0.755867	−	0.654725i	$-0.227216\pi$
$263$	5.72511	+	4.22533i	0.353026	+	0.260545i	−0.402842	+	0.915270i	$0.631977\pi$
$264$	14.8654	+	1.06421i	0.914900	+	0.0654977i
$265$	−2.81078	−	9.11233i	−0.172665	−	0.559766i
$266$	−6.09531	+	15.5306i	−0.373727	+	0.952241i
$267$	2.81344	−	0.995000i	0.172180	−	0.0608930i
$268$	−0.00602166	−	0.00185744i	−0.000367831	−	0.000113461i
$269$	10.3469	−	29.5698i	0.630863	−	1.80290i	0.0356076	−	0.999366i	$-0.488663\pi$
$269$	10.3469	−	29.5698i	0.630863	−	1.80290i	0.595255	−	0.803537i	$-0.297051\pi$
$270$	22.4033	−	8.09147i	1.36342	−	0.492431i
$271$	−12.2427	+	7.69261i	−0.743692	+	0.467293i	−0.849829	−	0.527059i	$-0.823295\pi$
$271$	−12.2427	+	7.69261i	−0.743692	+	0.467293i	0.106137	+	0.994352i	$0.466152\pi$
$272$	15.9594	+	3.01968i	0.967681	+	0.183095i
$273$	5.33728	+	23.0302i	0.323027	+	1.39385i
$274$	−14.3221	+	1.07329i	−0.865229	+	0.0648399i
$275$	−9.96019	−	13.4956i	−0.600622	−	0.813814i
$276$	0.00415877	+	0.00605634i	0.000250328	+	0.000364549i
$277$	15.0878	−	10.2867i	0.906536	−	0.618066i	−0.0177182	−	0.999843i	$-0.505640\pi$
$277$	15.0878	−	10.2867i	0.906536	−	0.618066i	0.924254	+	0.381777i	$0.124688\pi$
$278$	−10.5847	−	10.5847i	−0.634826	−	0.634826i
$279$	−31.6815	−	8.26316i	−1.89672	−	0.494702i
$280$	−21.5417	−	34.2834i	−1.28736	−	2.04883i
$281$	17.2566	+	1.29320i	1.02944	+	0.0771460i	0.578726	−	0.815522i	$-0.303550\pi$
$281$	17.2566	+	1.29320i	1.02944	+	0.0771460i	0.450715	+	0.892668i	$0.351169\pi$
$282$	21.9627	+	8.53537i	1.30786	+	0.508274i
$283$	11.1245	+	11.9894i	0.661285	+	0.712696i	0.971253	−	0.238051i	$-0.0765087\pi$
$283$	11.1245	+	11.9894i	0.661285	+	0.712696i	−0.309968	+	0.950747i	$0.600318\pi$
$284$	−0.00198448	+	0.0131661i	−0.000117757	+	0.000781267i
$285$	−8.96123	−	12.0578i	−0.530818	−	0.714240i
$286$	9.74697	+	9.04387i	0.576350	+	0.534775i
$287$	20.4960	+	12.8785i	1.20984	+	0.760194i
$288$	−0.0185810	+	0.0218848i	−0.00109490	+	0.00128957i
$289$		−	0.483245i		−	0.0284262i
$290$	−16.0385	+	18.7663i	−0.941812	+	1.10199i
$291$	0.227994	−	0.121472i	0.0133652	−	0.00712081i
$292$	−0.00705023	−	0.0161593i	−0.000412584	−	0.000945652i
$293$	−20.4157	−	0.763901i	−1.19270	−	0.0446276i	−0.566346	−	0.824168i	$-0.691643\pi$
$293$	−20.4157	−	0.763901i	−1.19270	−	0.0446276i	−0.626352	+	0.779540i	$0.715453\pi$
$294$	−21.5186	+	21.6625i	−1.25499	+	1.26338i
$295$	−5.96166	−	39.5530i	−0.347101	−	2.30287i
$296$	−7.61070	+	9.54351i	−0.442363	+	0.554705i
$297$	14.5448	+	6.17354i	0.843977	+	0.358225i
$298$	−8.91089	−	3.11806i	−0.516194	−	0.180624i
$299$	−0.579584	+	7.73401i	−0.0335182	+	0.447269i
$300$	0.0161620		5.38472e-5i	0.000933111		3.10887e-6i
$301$	21.3767	+	18.3962i	1.23214	+	1.06034i
$302$	9.31191	+	2.49512i	0.535840	+	0.143578i
$303$	−16.8034	+	0.684810i	−0.965332	+	0.0393413i
$304$	−9.79782	−	4.27475i	−0.561944	−	0.245173i
$305$	−2.96184	−	26.2870i	−0.169594	−	1.50519i
$306$	14.9832	+	8.51792i	0.856530	+	0.486937i
$307$	19.6555	−	19.6555i	1.12180	−	1.12180i	0.130327	−	0.991471i	$-0.458397\pi$
$307$	19.6555	−	19.6555i	1.12180	−	1.12180i	0.991471	−	0.130327i	$-0.0416027\pi$
$308$	0.00422001	−	0.0223033i	0.000240457	−	0.00127085i
$309$	18.2359	−	10.6097i	1.03741	−	0.603564i
$310$	41.3366	+	28.1828i	2.34776	+	1.60068i
$311$	1.56440	+	8.26804i	0.0887089	+	0.468838i	0.998548	+	0.0538757i	$0.0171575\pi$
$311$	1.56440	+	8.26804i	0.0887089	+	0.468838i	−0.909839	+	0.414962i	$0.863795\pi$
$312$	−14.8861	+	2.86801i	−0.842761	+	0.162369i
$313$	−0.899892	−	2.29289i	−0.0508649	−	0.129602i	0.903183	−	0.429256i	$-0.141224\pi$
$313$	−0.899892	−	2.29289i	−0.0508649	−	0.129602i	−0.954048	+	0.299654i	$0.903129\pi$
$314$	5.32089	−	4.24327i	0.300275	−	0.239461i
$315$	−9.83091	−	41.7866i	−0.553909	−	2.35441i
$316$	−0.00603074	+	0.00959787i	−0.000339256	+	0.000539923i
$317$	12.2165	−	16.5528i	0.686148	−	0.929697i	−0.313655	−	0.949537i	$-0.601554\pi$
$317$	12.2165	−	16.5528i	0.686148	−	0.929697i	0.999803	+	0.0198396i	$0.00631556\pi$
$318$	−3.38554	−	6.35442i	−0.189852	−	0.356338i
$319$	−16.2662	+	1.88904i	−0.910734	+	0.105766i
$320$	22.4859	−	12.9822i	1.25700	−	0.725729i
$321$	2.59518	−	3.27659i	0.144849	−	0.182881i
$322$	−13.8275	+	7.30806i	−0.770578	+	0.407262i
$323$	2.41885	−	10.5977i	0.134588	−	0.589670i
$324$	−0.0130828	+	0.00778763i	−0.000726821	+	0.000432646i
$325$	13.3394	+	10.6378i	0.739936	+	0.590080i
$326$	−9.14899	+	29.6603i	−0.506716	+	1.64273i
$327$	1.71065	+	2.13048i	0.0945990	+	0.117816i
$328$	−8.74421	+	12.8254i	−0.482818	+	0.708165i
$329$	19.8424	−	37.5436i	1.09395	−	2.06985i
$330$	−17.7535	−	16.3631i	−0.977299	−	0.900760i
$331$	−10.4325	+	2.79537i	−0.573420	+	0.153647i	−0.533865	−	0.845570i	$-0.679261\pi$
$331$	−10.4325	+	2.79537i	−0.573420	+	0.153647i	−0.0395553	+	0.999217i	$0.512594\pi$
$332$	−0.00784186	−	0.00377644i	−0.000430378	−	0.000207259i
$333$	−10.9118	+	6.95821i	−0.597965	+	0.381308i
$334$	−3.67584	+	0.414168i	−0.201133	+	0.0226623i
$335$	6.80473	+	9.98071i	0.371782	+	0.545304i
$336$	−20.8505	−	22.3219i	−1.13749	−	1.21776i
$337$	−13.0156	+	15.1244i	−0.709007	+	0.823881i	−0.990763	−	0.135605i	$-0.956702\pi$
$337$	−13.0156	+	15.1244i	−0.709007	+	0.823881i	0.281756	+	0.959486i	$0.409083\pi$
$338$	4.28951	+	2.26707i	0.233318	+	0.123312i
$339$	−8.52066	+	3.75137i	−0.462778	+	0.203746i
$340$	0.0145427	+	0.0168989i	0.000788687	+	0.000916471i
$341$	7.38487	+	32.3552i	0.399913	+	1.75213i
$342$	−8.36623	−	7.65962i	−0.452394	−	0.414185i
$343$	15.0508	+	18.8731i	0.812667	+	1.01905i
$344$	−12.3012	+	13.2575i	−0.663234	+	0.714796i
$345$	1.00563	−	14.0471i	0.0541416	−	0.756272i
$346$	10.8421	−	4.73035i	0.582874	−	0.254305i
$347$	−1.22914	−	2.12892i	−0.0659834	−	0.114287i	0.831146	−	0.556054i	$-0.187685\pi$
$347$	−1.22914	−	2.12892i	−0.0659834	−	0.114287i	−0.897130	+	0.441767i	$0.854352\pi$
$348$	0.00779713	−	0.0137179i	0.000417970	−	0.000735358i
$349$	−8.78202	+	15.2109i	−0.470091	+	0.814221i	−0.999415	−	0.0341983i	$-0.989112\pi$
$349$	−8.78202	+	15.2109i	−0.470091	+	0.814221i	0.529324	+	0.848420i	$0.322446\pi$
$350$	−3.85228	+	34.1899i	−0.205913	+	1.82753i
$351$	−15.9163	−	2.23654i	−0.849551	−	0.119378i
$352$	0.0283703	+	0.00647534i	0.00151214	+	0.000345137i
$353$	23.9183	−	3.60510i	1.27304	−	0.191880i	0.522463	−	0.852662i	$-0.325013\pi$
$353$	23.9183	−	3.60510i	1.27304	−	0.191880i	0.750578	+	0.660782i	$0.229775\pi$
$354$	−10.0698	−	28.4732i	−0.535203	−	1.51333i
$355$	18.7100	−	17.3604i	0.993025	−	0.921393i
$356$	0.00286385		0.000541870i	0.000151784		2.87190e-5i
$357$	18.3612	−	25.0528i	0.971777	−	1.32594i
$358$	−0.270487	−	7.22892i	−0.0142957	−	0.382060i
$359$	7.94636	+	22.7094i	0.419393	+	1.19856i	0.938930	+	0.344108i	$0.111819\pi$
$359$	7.94636	+	22.7094i	0.419393	+	1.19856i	−0.519537	+	0.854448i	$0.673896\pi$
$360$	27.0133	−	5.29787i	1.42372	−	0.279222i
$361$	5.13977	−	10.6728i	0.270514	−	0.561729i
$362$	−0.817946	+	1.87475i	−0.0429903	+	0.0985348i
$363$	0.237010	+	3.02730i	0.0124398	+	0.158892i
$364$	0.00172549	+	0.0230251i	9.04403e−5	+	0.00120684i
$365$	−8.74702	+	32.6443i	−0.457840	+	1.70868i
$366$	−5.95079	−	19.0662i	−0.311053	−	0.996607i
$367$	9.27613	−	0.347088i	0.484210	−	0.0181179i	0.205828	−	0.978588i	$-0.434011\pi$
$367$	9.27613	−	0.347088i	0.484210	−	0.0181179i	0.278382	+	0.960470i	$0.410202\pi$
$368$	−4.34790	−	9.02851i	−0.226650	−	0.470643i
$369$	−13.1761	+	9.86069i	−0.685920	+	0.513327i
$370$	19.2794	−	4.40040i	1.00229	−	0.228766i
$371$	−12.0788	+	4.74058i	−0.627100	+	0.246119i
$372$	−0.0293526	−	0.0126902i	−0.00152186	−	0.000657954i
$373$	26.5481	−	8.18901i	1.37461	−	0.424011i	0.482526	−	0.875881i	$-0.339719\pi$
$373$	26.5481	−	8.18901i	1.37461	−	0.424011i	0.892084	+	0.451871i	$0.149243\pi$
$374$	0.653220	−	17.4577i	0.0337772	−	0.902715i
$375$	−2.27147	−	1.79909i	−0.117298	−	0.0929047i
$376$	23.5828	+	13.6156i	1.21619	+	0.702169i
$377$	15.4850	−	6.13853i	0.797519	−	0.316150i
$378$	−13.2575	−	29.5764i	−0.681893	−	1.52125i
$379$	25.8734	+	2.91523i	1.32903	+	0.149745i	0.747761	−	0.663969i	$-0.231129\pi$
$379$	25.8734	+	2.91523i	1.32903	+	0.149745i	0.581266	+	0.813714i	$0.302558\pi$
$380$	−0.00685622	−	0.0129726i	−0.000351717	−	0.000665481i
$381$	9.68011	+	9.61583i	0.495927	+	0.492634i
$382$	2.08533	+	0.818433i	0.106695	+	0.0418747i
$383$	24.6054	+	3.70867i	1.25728	+	0.189504i	0.743685	−	0.668530i	$-0.233076\pi$
$383$	24.6054	+	3.70867i	1.25728	+	0.189504i	0.513592	+	0.858034i	$0.328314\pi$
$384$	14.7917	−	12.8153i	0.754834	−	0.653977i
$385$	−32.9810	+	28.3824i	−1.68087	+	1.44650i
$386$	−27.0159	+	13.0102i	−1.37507	+	0.662199i
$387$	−16.8922	+	9.07231i	−0.858679	+	0.461171i
$388$	0.000238155	0	8.33341e-5i	1.20905e−5	0	4.23065e-6i
$389$	−5.53420	−	20.6539i	−0.280595	−	1.04720i	−0.951998	−	0.306103i	$-0.900975\pi$
$389$	−5.53420	−	20.6539i	−0.280595	−	1.04720i	0.671403	−	0.741092i	$-0.265692\pi$
$390$	21.7517	+	11.4035i	1.10144	+	0.577441i
$391$	8.19889	−	6.05106i	0.414636	−	0.306015i
$392$	−28.3921	+	20.9543i	−1.43402	+	1.05835i
$393$	−5.88244	−	3.08393i	−0.296730	−	0.155564i
$394$	1.98975	+	7.42585i	0.100242	+	0.374109i
$395$	20.5095	−	7.17658i	1.03194	−	0.361093i
$396$	0.0131215	+	0.00812336i	0.000659382	+	0.000408214i
$397$	−17.9235	+	8.63151i	−0.899555	+	0.433203i	−0.825728	−	0.564068i	$-0.809236\pi$
$397$	−17.9235	+	8.63151i	−0.899555	+	0.433203i	−0.0738269	+	0.997271i	$0.523521\pi$
$398$	1.14471	−	0.985101i	0.0573790	−	0.0493786i
$399$	−15.4501	+	13.3857i	−0.773470	+	0.670123i
$400$	−21.7987	−	3.28562i	−1.08993	−	0.164281i
$401$	−18.1533	−	7.12464i	−0.906532	−	0.355788i	−0.134161	−	0.990959i	$-0.542834\pi$
$401$	−18.1533	−	7.12464i	−0.906532	−	0.355788i	−0.772371	+	0.635172i	$0.780929\pi$
$402$	6.47071	+	6.42773i	0.322729	+	0.320586i
$403$	−15.7743	−	29.8463i	−0.785771	−	1.48675i
$404$	−0.0163222	−	0.00183907i	−0.000812059	−	9.14971e-5i
$405$	28.9148	+	3.96488i	1.43679	+	0.197016i
$406$	27.0951	+	19.8545i	1.34471	+	0.985362i
$407$	11.3604	+	6.55894i	0.563115	+	0.325114i
$408$	15.6140	+	12.3669i	0.773009	+	0.612252i
$409$	0.648126	−	17.3215i	0.0320478	−	0.856494i	−0.886864	−	0.462031i	$-0.847121\pi$
$409$	0.648126	−	17.3215i	0.0320478	−	0.856494i	0.918912	−	0.394464i	$-0.129070\pi$
$410$	24.0301	−	7.41230i	1.18676	−	0.366067i
$411$	−16.1526	−	6.98333i	−0.796748	−	0.344462i
$412$	0.0191816	−	0.00752824i	0.000945012	−	0.000370890i
$413$	−53.0637	+	12.1114i	−2.61109	+	0.595965i
$414$	−1.26093	−	10.5582i	−0.0619713	−	0.518909i
$415$	7.23913	+	15.0322i	0.355355	+	0.737902i
$416$	−0.0295800	+	0.00110681i	−0.00145028	+	5.42656e-5i
$417$	−5.46445	−	17.5080i	−0.267595	−	0.857370i
$418$	−2.97577	+	11.1057i	−0.145550	+	0.543199i
$419$	1.88175	+	25.1102i	0.0919293	+	1.22671i	0.832228	+	0.554433i	$0.187065\pi$
$419$	1.88175	+	25.1102i	0.0919293	+	1.22671i	−0.740299	+	0.672278i	$0.765316\pi$
$420$	−0.00327249	−	0.0417991i	−0.000159681	−	0.00203959i
$421$	−5.20999	+	11.9414i	−0.253919	+	0.581989i	−0.996102	−	0.0882082i	$-0.971886\pi$
$421$	−5.20999	+	11.9414i	−0.253919	+	0.581989i	0.742183	+	0.670198i	$0.233791\pi$
$422$	−9.18603	+	19.0750i	−0.447169	+	0.928556i
$423$	18.9774	+	21.7573i	0.922714	+	1.05787i
$424$	−2.74822	−	7.85397i	−0.133466	−	0.381423i
$425$	−0.838200	−	22.4014i	−0.0406587	−	1.08663i
$426$	11.3919	−	15.5436i	0.551939	−	0.753090i
$427$	−35.3680	+	6.69198i	−1.71158	+	0.323848i
$428$	0.00299263	−	0.00277675i	0.000144654	−	0.000134219i
$429$	5.43198	+	15.3594i	0.262259	+	0.741558i
$430$	28.9717	−	4.36679i	1.39714	−	0.210585i
$431$	−4.85938	−	1.10912i	−0.234068	−	0.0534245i	0.103878	−	0.994590i	$-0.466875\pi$
$431$	−4.85938	−	1.10912i	−0.234068	−	0.0534245i	−0.337946	+	0.941166i	$0.609732\pi$
$432$	19.2547	−	7.77988i	0.926391	−	0.374310i
$433$	−0.260851	+	2.31512i	−0.0125357	+	0.111257i	−0.998422	−	0.0561602i	$-0.982114\pi$
$433$	−0.260851	+	2.31512i	−0.0125357	+	0.111257i	0.985886	+	0.167418i	$0.0535428\pi$
$434$	34.0382	−	58.9559i	1.63389	−	2.82997i
$435$	−28.0810	+	11.2402i	−1.34638	+	0.538926i
$436$	0.00133430	+	0.00231107i	6.39012e−5	+	0.000110680i
$437$	−6.14683	+	2.68184i	−0.294043	+	0.128290i
$438$	−1.82211	+	25.4520i	−0.0870639	+	1.21615i
$439$	18.4465	−	19.8806i	0.880405	−	0.948851i	−0.118623	−	0.992939i	$-0.537848\pi$
$439$	18.4465	−	19.8806i	0.880405	−	0.948851i	0.999028	+	0.0440888i	$0.0140384\pi$
$440$	−17.3971	−	21.8153i	−0.829376	−	1.04000i
$441$	−35.6756	+	11.2653i	−1.69884	+	0.536445i
$442$	3.95432	+	17.3250i	0.188088	+	0.824066i
$443$	15.7551	+	18.3077i	0.748546	+	0.869826i	0.995056	−	0.0993140i	$-0.0316648\pi$
$443$	15.7551	+	18.3077i	0.748546	+	0.869826i	−0.246510	+	0.969140i	$0.579284\pi$
$444$	−0.0115684	+	0.00509321i	−0.000549014	+	0.000241713i
$445$	−4.93970	−	2.61071i	−0.234164	−	0.123759i
$446$	−0.213892	+	0.248547i	−0.0101281	+	0.0117690i
$447$	−7.89597	−	8.45317i	−0.373467	−	0.399821i
$448$	−19.9022	−	29.1912i	−0.940293	−	1.37916i
$449$	−12.8221	+	1.44471i	−0.605113	+	0.0681799i	−0.409205	−	0.912442i	$-0.634194\pi$
$449$	−12.8221	+	1.44471i	−0.605113	+	0.0681799i	−0.195908	+	0.980622i	$0.562765\pi$
$450$	−20.7537	−	10.7923i	−0.978337	−	0.508755i
$451$	15.0295	+	7.23781i	0.707710	+	0.340815i
$452$	−0.00878311	+	0.00235343i	−0.000413123	+	0.000110696i
$453$	8.68555	+	8.00533i	0.408083	+	0.376123i
$454$	−14.5020	+	27.4391i	−0.680612	+	1.28778i
$455$	24.9331	−	36.5701i	1.16888	−	1.71443i
$456$	−8.20733	−	10.2216i	−0.384344	−	0.478671i
$457$	−2.17325	+	7.04549i	−0.101660	+	0.329574i	−0.992087	−	0.125552i	$-0.959930\pi$
$457$	−2.17325	+	7.04549i	−0.101660	+	0.329574i	0.890427	+	0.455126i	$0.150406\pi$
$458$	23.3545	+	18.6246i	1.09129	+	0.870272i
$459$	11.4134	+	17.7676i	0.532731	+	0.829320i
$460$	0.00306075	−	0.0134100i	0.000142708	−	0.000625245i
$461$	−9.65436	+	5.10248i	−0.449648	+	0.237646i	−0.676732	−	0.736229i	$-0.736605\pi$
$461$	−9.65436	+	5.10248i	−0.449648	+	0.237646i	0.227084	+	0.973875i	$0.427081\pi$
$462$	−20.3980	+	25.7538i	−0.949001	+	1.19818i
$463$	21.8343	−	12.6060i	1.01473	−	0.585852i	0.102154	−	0.994769i	$-0.467427\pi$
$463$	21.8343	−	12.6060i	1.01473	−	0.585852i	0.912572	+	0.408916i	$0.134093\pi$
$464$	−13.3615	+	16.8726i	−0.620291	+	0.783292i
$465$	28.8239	+	54.1003i	1.33667	+	2.50884i
$466$	−7.88999	+	10.6906i	−0.365497	+	0.495231i
$467$	−13.8575	+	22.0540i	−0.641247	+	1.02054i	0.355074	+	0.934838i	$0.384456\pi$
$467$	−13.8575	+	22.0540i	−0.641247	+	1.02054i	−0.996321	+	0.0857007i	$0.972687\pi$
$468$	−0.0150312	−	0.00452705i	−0.000694818	−	0.000209263i
$469$	12.8510	−	10.2483i	0.593403	−	0.473223i
$470$	−16.1172	−	41.0660i	−0.743431	−	1.89423i
$471$	8.18816	−	1.57756i	0.377290	−	0.0726900i
$472$	−6.48887	−	34.2945i	−0.298675	−	1.57853i
$473$	16.0583	+	10.9484i	0.738363	+	0.503407i
$474$	14.1807	−	8.25033i	0.651340	−	0.378950i
$475$	−2.74282	+	14.4962i	−0.125849	+	0.665130i
$476$	0.0214515	−	0.0214515i	0.000983228	−	0.000983228i
$477$	−0.0587839	−	8.82174i	−0.00269153	−	0.403920i
$478$	0.821237	+	7.28868i	0.0375625	+	0.333377i
$479$	33.0310	+	14.4113i	1.50923	+	0.658469i	0.981590	−	0.191001i	$-0.0611734\pi$
$479$	33.0310	+	14.4113i	1.50923	+	0.658469i	0.527637	+	0.849470i	$0.323078\pi$
$480$	0.0537054	−	0.00218872i	0.00245131	−	9.99009e-5i
$481$	−12.8889	−	3.45358i	−0.587685	−	0.157470i
$482$	10.3817	+	8.93416i	0.472872	+	0.406940i
$483$	−19.1630	+	0.0638457i	−0.871945	+	0.00290508i
$484$	−0.000221634		0.00295750i	−1.00743e−5		0.000134432i
$485$	−0.456523	−	0.159744i	−0.0207297	−	0.00725362i
$486$	22.0039	−	1.19066i	0.998117	−	0.0540093i
$487$	15.9165	−	19.9587i	0.721246	−	0.904413i	−0.277162	−	0.960823i	$-0.589394\pi$
$487$	15.9165	−	19.9587i	0.721246	−	0.904413i	0.998408	+	0.0564097i	$0.0179653\pi$
$488$	−3.44030	−	22.8249i	−0.155735	−	1.03323i
$489$	−26.8024	+	26.9816i	−1.21205	+	1.22015i
$490$	57.1268	+	2.13754i	2.58073	+	0.0965640i
$491$	−0.878033	−	2.01247i	−0.0396251	−	0.0908217i	0.895624	−	0.444812i	$-0.146729\pi$
$491$	−0.878033	−	2.01247i	−0.0396251	−	0.0908217i	−0.935249	+	0.353990i	$0.884825\pi$
$492$	−0.0141860	+	0.00755807i	−0.000639553	+	0.000340744i
$493$	−19.3843	−	10.1604i	−0.873027	−	0.457601i
$494$		−	11.6954i		−	0.526199i
$495$	−9.95646	−	27.8571i	−0.447510	−	1.25208i
$496$	36.9325	+	23.2063i	1.65832	+	1.04199i
$497$	−25.4590	−	23.6225i	−1.14199	−	1.05962i
$498$	7.51433	+	10.1109i	0.336725	+	0.453079i
$499$	−0.309675	+	2.05456i	−0.0138629	+	0.0919747i	−0.994692	−	0.102894i	$-0.967190\pi$
$499$	−0.309675	+	2.05456i	−0.0138629	+	0.0919747i	0.980829	+	0.194868i	$0.0624280\pi$
$500$	−0.00192497	−	0.00207462i	−8.60871e−5	−	9.27799e-5i
$501$	−4.22456	−	1.64180i	−0.188739	−	0.0733500i
$502$	−24.5989	−	1.84344i	−1.09790	−	0.0822765i
$503$	−9.69963	−	15.4369i	−0.432485	−	0.688296i	0.557388	−	0.830252i	$-0.311804\pi$
$503$	−9.69963	−	15.4369i	−0.432485	−	0.688296i	−0.989873	+	0.141956i	$0.954661\pi$
$504$	−9.93562	−	36.1159i	−0.442568	−	1.60873i
$505$	22.2641	+	22.2641i	0.990741	+	0.990741i
$506$	−8.90528	+	6.07152i	−0.395888	+	0.269912i
$507$	3.36510	+	4.90053i	0.149449	+	0.217640i
$508$	0.00791348	+	0.0107224i	0.000351104	+	0.000475729i
$509$	6.07458	−	0.455227i	0.269251	−	0.0201776i	0.0605796	−	0.998163i	$-0.480705\pi$
$509$	6.07458	−	0.455227i	0.269251	−	0.0201776i	0.208672	+	0.977986i	$0.433086\pi$
$510$	−7.28517	−	31.4353i	−0.322593	−	1.39198i
$511$	45.1849	+	8.54944i	1.99886	+	0.378205i
$512$	19.1834	−	12.0538i	0.847796	−	0.532706i
$513$	−4.72116	−	13.0717i	−0.208444	−	0.577130i
$514$	7.38625	−	21.1087i	0.325793	−	0.931064i
$515$	−37.7452	−	11.6429i	−1.66325	−	0.513046i
$516$	−0.0176558	+	0.00624414i	−0.000777254	+	0.000274883i
$517$	10.6913	−	27.2411i	0.470205	−	1.19806i
$518$	−7.93140	−	25.7130i	−0.348486	−	1.12976i
$519$	14.4567	+	1.03496i	0.634580	+	0.0454296i
$520$	22.8369	+	16.8544i	1.00146	+	0.739115i
$521$	0.0255955			0.00112136			0.000560679	−	1.00000i	$-0.499822\pi$
$521$	0.0255955			0.00112136			0.000560679		1.00000i	$0.499822\pi$
$522$	−19.2138	+	12.3446i	−0.840963	+	0.540310i
$523$	−42.0983			−1.84083			−0.920415	−	0.390943i	$-0.872149\pi$
$523$	−42.0983			−1.84083			−0.920415	+	0.390943i	$0.872149\pi$
$524$	−0.00521945	−	0.00385213i	−0.000228013	−	0.000168281i
$525$	−23.6316	+	34.9105i	−1.03137	+	1.52362i
$526$	−2.96482	−	9.61170i	−0.129272	−	0.419090i
$527$	−16.2045	+	41.2884i	−0.705880	+	1.79855i
$528$	−16.0009	−	13.6773i	−0.696348	−	0.595230i
$529$	15.9707	+	4.92631i	0.694378	+	0.214187i
$530$	−4.45224	+	12.7238i	−0.193393	+	0.552685i
$531$	5.27130	−	36.6272i	0.228755	−	1.58949i
$532$	−0.0169055	+	0.0106224i	−0.000732946	+	0.000460540i
$533$	−16.6727	−	3.15465i	−0.722175	−	0.136643i
$534$	−4.03522	−	1.22999i	−0.174621	−	0.0532270i
$535$	−7.80378	+	0.584812i	−0.337387	+	0.0252836i
$536$	6.25916	+	8.48086i	0.270354	+	0.366317i
$537$	3.81911	−	7.99853i	0.164807	−	0.345162i
$538$	−36.5904	+	24.9469i	−1.57752	+	1.07554i
$539$	26.8146	+	26.8146i	1.15499	+	1.15499i
$540$	0.0273215	+	0.00812940i	0.00117573	+	0.000349834i
$541$	−10.3427	−	16.4603i	−0.444666	−	0.707682i	0.546912	−	0.837190i	$-0.315803\pi$
$541$	−10.3427	−	16.4603i	−0.444666	−	0.707682i	−0.991578	+	0.129508i	$0.958660\pi$
$542$	20.3822	+	1.52743i	0.875491	+	0.0656089i
$543$	−1.95419	+	1.56909i	−0.0838623	+	0.0673363i
$544$	0.0264531	+	0.0285096i	0.00113417	+	0.00122234i
$545$	0.762421	−	5.05833i	0.0326585	−	0.216675i
$546$	13.2617	−	30.6747i	0.567550	−	1.31275i
$547$	−33.3658	−	30.9589i	−1.42662	−	1.32371i	−0.870104	−	0.492867i	$-0.835949\pi$
$547$	−33.3658	−	30.9589i	−1.42662	−	1.32371i	−0.556512	−	0.830839i	$-0.687861\pi$
$548$	−0.0145530	−	0.00914426i	−0.000621674	−	0.000390624i
$549$	4.38940	−	24.0757i	0.187335	−	1.02753i
$550$			23.7107i			1.01103i
$551$	10.9496	+	9.35802i	0.466470	+	0.398665i
$552$	0.418570	−	12.2815i	0.0178155	−	0.522735i
$553$	−11.8235	−	27.0998i	−0.502787	−	1.15240i
$554$	−25.7957	−	0.965206i	−1.09595	−	0.0410077i
$555$	23.4250	+	6.19313i	0.994335	+	0.262884i
$556$	−0.00266987	−	0.0177134i	−0.000113228	−	0.000751217i
$557$	−11.4703	+	14.3833i	−0.486012	+	0.609440i	−0.963010	−	0.269464i	$-0.913153\pi$
$557$	−11.4703	+	14.3833i	−0.486012	+	0.609440i	0.476998	+	0.878904i	$0.341725\pi$
$558$	29.0979	+	35.9929i	1.23181	+	1.52370i
$559$	−18.6605	−	6.52959i	−0.789255	−	0.276172i
$560$	−4.27367	+	57.0282i	−0.180596	+	2.40988i
$561$	10.6408	−	18.5730i	0.449254	−	0.784154i
$562$	−18.5419	−	15.9566i	−0.782145	−	0.673090i
$563$	8.45864	+	2.26649i	0.356489	+	0.0955210i	0.432619	−	0.901577i	$-0.357590\pi$
$563$	8.45864	+	2.26649i	0.356489	+	0.0955210i	−0.0761296	+	0.997098i	$0.524256\pi$
$564$	0.0150817	+	0.0238258i	0.000635053	+	0.00100325i
$565$	15.9761	+	6.97028i	0.672118	+	0.293242i
$566$	−2.58865	−	22.9749i	−0.108809	−	0.965709i
$567$	2.43974	−	39.6380i	0.102459	−	1.66464i
$568$	15.7482	−	15.7482i	0.660779	−	0.660779i
$569$	1.48185	−	7.83174i	0.0621222	−	0.328324i	−0.937695	−	0.347460i	$-0.887044\pi$
$569$	1.48185	−	7.83174i	0.0621222	−	0.328324i	0.999817	+	0.0191367i	$0.00609176\pi$
$570$	0.0707550	+	21.2367i	0.00296360	+	0.889509i
$571$	−23.9150	−	16.3050i	−1.00081	−	0.682341i	−0.0521509	−	0.998639i	$-0.516608\pi$
$571$	−23.9150	−	16.3050i	−1.00081	−	0.682341i	−0.948660	+	0.316298i	$0.897560\pi$
$572$	0.00295822	+	0.0156346i	0.000123689	+	0.000653714i
$573$	1.79733	+	2.07452i	0.0750847	+	0.0866643i
$574$	−12.5014	−	31.8529i	−0.521797	−	1.32952i
$575$	−10.8129	+	8.62302i	−0.450930	+	0.359605i
$576$	23.3819	−	5.50094i	0.974245	−	0.229206i
$577$	18.8876	−	30.0595i	0.786302	−	1.25139i	−0.177328	−	0.984152i	$-0.556745\pi$
$577$	18.8876	−	30.0595i	0.786302	−	1.25139i	0.963630	−	0.267241i	$-0.0861119\pi$
$578$	−0.405652	+	0.549639i	−0.0168729	+	0.0228620i
$579$	−36.7186	−	1.25142i	−1.52597	−	0.0520073i
$580$	−0.0287788	+	0.00667206i	−0.00119498	+	0.000277042i
$581$	19.6612	−	11.3514i	0.815685	−	0.470936i
$582$	−0.361286	−	0.0532247i	−0.0149758	−	0.00220623i
$583$	−7.90585	+	4.17836i	−0.327427	+	0.173050i
$584$	−6.56206	+	28.7503i	−0.271540	+	1.18969i
$585$	17.1167	+	24.7497i	0.707690	+	1.02327i
$586$	22.5794	+	18.0065i	0.932746	+	0.743840i
$587$	−12.0384	+	39.0276i	−0.496878	+	1.61084i	0.265777	+	0.964034i	$0.414371\pi$
$587$	−12.0384	+	39.0276i	−0.496878	+	1.61084i	−0.762655	+	0.646805i	$0.776105\pi$
$588$	−0.0361137	+	0.00556638i	−0.00148930	+	0.000229553i
$589$	16.4439	−	24.1188i	0.677560	−	0.993799i
$590$	−26.4214	+	49.9917i	−1.08775	+	2.05812i
$591$	−2.06545	+	9.19035i	−0.0849612	+	0.378041i
$592$	16.6534	−	4.46226i	0.684450	−	0.183398i
$593$	−32.3213	−	15.5651i	−1.32728	−	0.639183i	−0.370182	−	0.928959i	$-0.620705\pi$
$593$	−32.3213	−	15.5651i	−1.32728	−	0.639183i	−0.957094	+	0.289777i	$0.906419\pi$
$594$	−11.3609	−	19.2312i	−0.466143	−	0.789064i
$595$	−57.7878	+	6.51113i	−2.36907	+	0.266930i
$596$	−0.00636424	−	0.00933463i	−0.000260690	−	0.000382361i
$597$	1.80265	−	0.417766i	0.0737774	−	0.0170980i
$598$	7.15140	−	8.31008i	0.292443	−	0.339824i
$599$	−2.87288	−	1.51836i	−0.117383	−	0.0620386i	0.407547	−	0.913184i	$-0.366384\pi$
$599$	−2.87288	−	1.51836i	−0.117383	−	0.0620386i	−0.524929	+	0.851146i	$0.675908\pi$
$600$	−21.8046	−	15.9806i	−0.890169	−	0.652405i
$601$	10.8718	+	12.6333i	0.443470	+	0.515322i	0.934569	−	0.355782i	$-0.115786\pi$
$601$	10.8718	+	12.6333i	0.443470	+	0.515322i	−0.491099	+	0.871104i	$0.663405\pi$
$602$	−8.87137	−	38.8680i	−0.361570	−	1.58414i
$603$	3.36502	+	10.6565i	0.137034	+	0.433966i
$604$	0.00719305	+	0.00901980i	0.000292681	+	0.000367011i
$605$	3.86690	−	4.16753i	0.157212	−	0.169434i
$606$	19.6869	+	13.3265i	0.799727	+	0.541351i
$607$	−37.2678	+	16.2598i	−1.51265	+	0.659963i	−0.982215	−	0.187761i	$-0.939877\pi$
$607$	−37.2678	+	16.2598i	−1.51265	+	0.659963i	−0.530437	+	0.847724i	$0.677972\pi$
$608$	−0.0127979	−	0.0221667i	−0.000519025	−	0.000898978i
$609$	18.1074	+	36.9604i	0.733748	+	1.49771i
$610$	−18.6974	+	32.3849i	−0.757037	+	1.31123i
$611$	−3.33292	+	29.5804i	−0.134835	+	1.19670i
$612$	0.00837374	+	0.0188491i	0.000338488	+	0.000761931i
$613$	−20.1472	−	4.59846i	−0.813737	−	0.185730i	−0.204651	−	0.978835i	$-0.565606\pi$
$613$	−20.1472	−	4.59846i	−0.813737	−	0.185730i	−0.609085	+	0.793105i	$0.708463\pi$
$614$	−38.8555	+	5.85652i	−1.56808	+	0.236350i
$615$	30.2938	+	5.62742i	1.22156	+	0.226920i
$616$	−27.8324	+	25.8247i	−1.12140	+	1.04051i
$617$	−15.7004	+	2.97068i	−0.632075	+	0.119595i	−0.492070	−	0.870556i	$-0.663760\pi$
$617$	−15.7004	+	2.97068i	−0.632075	+	0.119595i	−0.140005	+	0.990151i	$0.544712\pi$
$618$	−29.6475	−	3.24048i	−1.19260	−	0.130351i
$619$	0.551984	+	14.7521i	0.0221861	+	0.592937i	0.965404	+	0.260760i	$0.0839733\pi$
$619$	0.551984	+	14.7521i	0.0221861	+	0.592937i	−0.943217	+	0.332176i	$0.892217\pi$
$620$	0.0197742	+	0.0565114i	0.000794151	+	0.00226955i
$621$	4.63841	−	12.1749i	0.186133	−	0.488562i
$622$	5.16114	−	10.7172i	0.206943	−	0.429721i
$623$	−3.04020	+	6.96820i	−0.121803	+	0.279175i
$624$	19.3225	+	9.22605i	0.773519	+	0.369338i
$625$	−1.65560	−	22.0924i	−0.0662240	−	0.883697i
$626$	−0.901196	+	3.36331i	−0.0360191	+	0.134425i
$627$	−9.54745	+	10.3587i	−0.381288	+	0.413687i
$628$	0.00813872		0.000304529i	0.000324770		1.21520e-5i
$629$	7.60681	+	15.7957i	0.303303	+	0.629816i
$630$	−23.8954	+	55.7801i	−0.952017	+	2.22233i
$631$	18.7289	−	4.27475i	0.745586	−	0.170175i	0.167183	−	0.985926i	$-0.446533\pi$
$631$	18.7289	−	4.27475i	0.745586	−	0.170175i	0.578404	+	0.815751i	$0.303676\pi$
$632$	17.6495	−	6.92692i	0.702059	−	0.275538i
$633$	−20.8205	+	15.4736i	−0.827540	+	0.615022i
$634$	−27.7899	+	8.57206i	−1.10368	+	0.340440i
$635$	0.955180	−	25.5277i	0.0379052	−	1.01304i
$636$	0.00125581	−	0.00852434i	4.97960e−5	−	0.000338012i
$637$	−33.4062	−	19.2871i	−1.32360	−	0.764182i
$638$	20.0868	+	11.5058i	0.795243	+	0.455520i
$639$	21.2052	−	10.3865i	0.838865	−	0.410884i
$640$	−36.4113	−	4.10257i	−1.43928	−	0.162168i
$641$	−10.2957	−	19.4805i	−0.406657	−	0.769433i	0.592695	−	0.805427i	$-0.298064\pi$
$641$	−10.2957	−	19.4805i	−0.406657	−	0.769433i	−0.999352	+	0.0359941i	$0.988540\pi$
$642$	−5.70221	+	1.54828i	−0.225048	+	0.0611059i
$643$	35.2007	+	13.8152i	1.38818	+	0.544820i	0.937537	−	0.347885i	$-0.113100\pi$
$643$	35.2007	+	13.8152i	1.38818	+	0.544820i	0.450641	+	0.892705i	$0.351195\pi$
$644$	−0.0185074	−	0.00278955i	−0.000729295	−	0.000109924i
$645$	33.9237	+	11.7437i	1.33575	+	0.462408i
$646$	−11.6472	+	10.0232i	−0.458253	+	0.394359i
$647$	38.9427	−	18.7538i	1.53100	−	0.737289i	0.536683	−	0.843784i	$-0.319677\pi$
$647$	38.9427	−	18.7538i	1.53100	−	0.737289i	0.994313	+	0.106495i	$0.0339628\pi$
$648$	25.3422	+	2.51386i	0.995536	+	0.0987536i
$649$	−35.4038	+	12.3883i	−1.38972	+	0.486284i
$650$	−6.24238	−	23.2969i	−0.244846	−	0.913779i
$651$	70.4783	−	44.6127i	2.76226	−	1.74851i
$652$	−0.0298868	+	0.0220574i	−0.00117046	+	0.000863836i
$653$	13.6213	−	10.0530i	0.533042	−	0.393403i	−0.293775	−	0.955875i	$-0.594912\pi$
$653$	13.6213	−	10.0530i	0.533042	−	0.393403i	0.826816	+	0.562472i	$0.190150\pi$
$654$	−0.157277	−	3.85917i	−0.00615002	−	0.150905i
$655$	3.21844	+	12.0114i	0.125755	+	0.469323i
$656$	20.6942	−	7.24120i	0.807971	−	0.282721i
$657$	−16.4573	+	26.5833i	−0.642062	+	1.03711i
$658$	−54.0840	+	26.0455i	−2.10841	+	1.01536i
$659$	−24.1184	+	20.7556i	−0.939521	+	0.808524i	−0.981670	−	0.190588i	$-0.938961\pi$
$659$	−24.1184	+	20.7556i	−0.939521	+	0.808524i	0.0421488	+	0.999111i	$0.486580\pi$
$660$	−0.00546620	−	0.0283717i	−0.000212771	−	0.00110437i
$661$	27.7194	+	4.17803i	1.07816	+	0.162507i	0.664026	−	0.747709i	$-0.268846\pi$
$661$	27.7194	+	4.17803i	1.07816	+	0.162507i	0.414134	+	0.910216i	$0.364084\pi$
$662$	14.2123	+	5.57792i	0.552377	+	0.216792i
$663$	−5.56532	+	21.0503i	−0.216139	+	0.817527i
$664$	6.80275	+	12.8714i	0.263998	+	0.499509i
$665$	38.0320	+	4.28518i	1.47482	+	0.166172i
$666$	18.2520	+	1.24555i	0.707250	+	0.0482642i
$667$	2.05802	+	13.3447i	0.0796868	+	0.516709i
$668$	−0.00383368	−	0.00221337i	−0.000148329	−	8.56380e-5i
$669$	−0.373512	+	0.148031i	−0.0144408	+	0.00572320i
$670$	0.638493	−	17.0641i	0.0246671	−	0.659243i
$671$	−23.7038	+	7.31166i	−0.915076	+	0.282264i
$672$	−0.00843101	−	0.0726509i	−0.000325233	−	0.00280257i
$673$	−31.7488	+	12.4605i	−1.22383	+	0.480316i	−0.887227	−	0.461332i	$-0.847372\pi$
$673$	−31.7488	+	12.4605i	−1.22383	+	0.480316i	−0.336598	+	0.941648i	$0.609276\pi$
$674$	27.4998	−	6.27666i	1.05925	−	0.241768i
$675$	−16.3814	−	23.5186i	−0.630522	−	0.905232i
$676$	0.00251919	+	0.00523115i	9.68918e−5	+	0.000201198i
$677$	38.4136	−	1.43734i	1.47636	−	0.0552413i	0.712975	−	0.701190i	$-0.247347\pi$
$677$	38.4136	−	1.43734i	1.47636	−	0.0552413i	0.763381	+	0.645949i	$0.223538\pi$
$678$	12.8403	+	2.88575i	0.493130	+	0.110827i
$679$	−0.170337	+	0.635705i	−0.00653692	+	0.0243961i
$680$	−2.78682	−	37.1876i	−0.106870	−	1.42608i
$681$	−31.3477	+	21.5259i	−1.20125	+	0.824872i
$682$	18.7606	−	42.9997i	0.718379	−	1.64654i
$683$	−2.68952	+	5.58486i	−0.102912	+	0.213699i	−0.946067	−	0.323972i	$-0.894981\pi$
$683$	−2.68952	+	5.58486i	−0.102912	+	0.213699i	0.843155	+	0.537671i	$0.180696\pi$
$684$	−0.00261243	−	0.0133205i	−9.98888e−5	−	0.000509323i
$685$	10.8817	+	31.0980i	0.415767	+	1.18819i
$686$	−1.27594	−	34.1003i	−0.0487157	−	1.30195i
$687$	14.7480	+	33.4977i	0.562670	+	1.27802i
$688$	25.0988	−	4.74894i	0.956881	−	0.181052i
$689$	6.66783	−	6.18684i	0.254024	−	0.235700i
$690$	−12.9354	+	15.1329i	−0.492443	+	0.576101i
$691$	39.2432	−	5.91496i	1.49288	−	0.225016i	0.648688	−	0.761054i	$-0.275318\pi$
$691$	39.2432	−	5.91496i	1.49288	−	0.225016i	0.844194	+	0.536038i	$0.180080\pi$
$692$	0.0138010	+	0.00315000i	0.000524637	+	0.000119745i
$693$	−36.7872	+	16.3427i	−1.39743	+	0.620809i
$694$	−0.389082	+	3.45320i	−0.0147694	+	0.131082i
$695$	−17.1693	+	29.7382i	−0.651271	+	1.12803i
$696$	−24.1190	+	10.7173i	−0.914230	+	0.406238i
$697$	11.1473	+	19.3077i	0.422234	+	0.731331i
$698$	22.7571	−	9.92884i	0.861371	−	0.375812i
$699$	−14.6440	+	7.11240i	−0.553889	+	0.269016i
$700$	−0.0280056	+	0.0301829i	−0.00105851	+	0.00114081i
$701$	−7.57883	−	9.50355i	−0.286249	−	0.358944i	0.617829	−	0.786312i	$-0.288012\pi$
$701$	−7.57883	−	9.50355i	−0.286249	−	0.358944i	−0.904078	+	0.427368i	$0.859441\pi$
$702$	16.2257	+	15.9045i	0.612399	+	0.600277i
$703$	−2.56751	−	11.2490i	−0.0968356	−	0.424265i
$704$	−15.8815	−	18.4547i	−0.598558	−	0.695537i
$705$	5.87304	−	53.7331i	0.221191	−	2.02371i
$706$	−30.2307	−	15.9774i	−1.13775	−	0.601316i
$707$	27.9465	−	32.4744i	1.05104	−	1.22133i
$708$	0.0105380	−	0.0345718i	0.000396042	−	0.00129929i
$709$	−11.1961	−	16.4217i	−0.420479	−	0.616730i	0.556299	−	0.830982i	$-0.312221\pi$
$709$	−11.1961	−	16.4217i	−0.420479	−	0.616730i	−0.976778	+	0.214252i	$0.931269\pi$
$710$	−35.8535	+	4.03972i	−1.34556	+	0.151608i
$711$	20.0823	−	0.885465i	0.753144	−	0.0332075i
$712$	−4.39245	−	2.11529i	−0.164614	−	0.0792739i
$713$	26.4322	−	7.08248i	0.989893	−	0.265241i
$714$	−41.9140	+	13.0819i	−1.56859	+	0.489576i
$715$	14.2526	−	26.9672i	0.533016	−	1.00852i
$716$	0.00487665	−	0.00715273i	0.000182249	−	0.000267310i
$717$	−3.25545	+	8.37671i	−0.121577	+	0.312834i
$718$	10.0249	−	32.4999i	0.374126	−	1.21289i
$719$	−29.1784	−	23.2690i	−1.08817	−	0.867788i	−0.0963406	−	0.995348i	$-0.530714\pi$
$719$	−29.1784	−	23.2690i	−1.08817	−	0.867788i	−0.991831	+	0.127561i	$0.959285\pi$
$720$	−35.1421	−	16.6360i	−1.30967	−	0.619987i
$721$	−11.9601	+	52.4008i	−0.445419	+	1.95151i
$722$	−14.8051	+	7.82471i	−0.550988	+	0.291206i
$723$	6.18317	+	15.6014i	0.229955	+	0.580223i
$724$	−0.00211983	+	0.00122389i	−7.87829e−5	+	4.54853e-5i
$725$	26.8062	+	12.7966i	0.995559	+	0.475255i
$726$	2.27164	−	3.64217i	0.0843085	−	0.135174i
$727$	−23.8653	+	32.3363i	−0.885115	+	1.19929i	0.0939168	+	0.995580i	$0.470061\pi$
$727$	−23.8653	+	32.3363i	−0.885115	+	1.19929i	−0.979032	+	0.203708i	$0.934701\pi$
$728$	20.5477	−	32.7015i	0.761549	−	1.21200i
$729$	24.5555	+	11.2263i	0.909462	+	0.415788i
$730$	37.3515	−	29.7868i	1.38244	−	1.10246i
$731$	9.48984	+	24.1797i	0.350994	+	0.894319i
$732$	0.00781920	−	0.0225871i	0.000289006	−	0.000834843i
$733$	4.64467	+	24.5477i	0.171555	+	0.906690i	0.957509	+	0.288404i	$0.0931248\pi$
$733$	4.64467	+	24.5477i	0.171555	+	0.906690i	−0.785954	+	0.618285i	$0.787828\pi$
$734$	−10.8419	−	7.39192i	−0.400184	−	0.272841i
$735$	60.7766	+	34.8199i	2.24178	+	1.28435i
$736$	0.00446083	−	0.0235760i	0.000164428	−	0.000869024i
$737$	8.00966	−	8.00966i	0.295040	−	0.295040i
$738$	23.2638	−	0.155019i	0.856351	−	0.00570631i
$739$	−1.15450	−	10.2464i	−0.0424688	−	0.376921i	−0.996912	−	0.0785281i	$-0.974978\pi$
$739$	−1.15450	−	10.2464i	−0.0424688	−	0.376921i	0.954443	−	0.298393i	$-0.0964506\pi$
$740$	0.0216906	+	0.00946351i	0.000797362	+	0.000347886i
$741$	6.65366	−	12.6915i	0.244428	−	0.466235i
$742$	17.7177	+	4.74745i	0.650438	+	0.174284i
$743$	3.58789	+	3.08763i	0.131627	+	0.113274i	0.715637	−	0.698472i	$-0.246136\pi$
$743$	3.58789	+	3.08763i	0.131627	+	0.113274i	−0.584010	+	0.811746i	$0.698517\pi$
$744$	26.8987	+	46.2334i	0.986153	+	1.69500i
$745$	−1.61842	+	21.5963i	−0.0592942	+	0.791226i
$746$	−37.0697	−	12.9713i	−1.35722	−	0.474912i
$747$	2.40214	+	15.2471i	0.0878897	+	0.557862i
$748$	0.0130349	−	0.0163453i	0.000476604	−	0.000597642i
$749$	1.58708	+	10.5296i	0.0579905	+	0.384742i
$750$	1.07334	+	3.95302i	0.0391928	+	0.144344i
$751$	22.9912	+	0.860269i	0.838959	+	0.0313916i	0.453417	−	0.891298i	$-0.350205\pi$
$751$	22.9912	+	0.860269i	0.838959	+	0.0313916i	0.385542	+	0.922690i	$0.374014\pi$
$752$	−15.3806	−	35.2526i	−0.560871	−	1.28553i
$753$	−25.6454	−	15.9951i	−0.934571	−	0.582896i
$754$	−22.7654	−	6.01673i	−0.829068	−	0.219116i
$755$		−	22.1150i		−	0.804847i
$756$	0.00825265	−	0.0378994i	0.000300146	−	0.00137839i
$757$	−12.1214	−	7.61635i	−0.440558	−	0.276821i	0.293434	−	0.955979i	$-0.405202\pi$
$757$	−12.1214	−	7.61635i	−0.440558	−	0.276821i	−0.733992	+	0.679158i	$0.762345\pi$
$758$	−26.9810	−	25.0347i	−0.979995	−	0.909303i
$759$	−13.1180	+	1.52232i	−0.476152	+	0.0552566i
$760$	−3.65794	+	24.2688i	−0.132687	+	0.880323i
$761$	−2.44720	−	2.63746i	−0.0887111	−	0.0956078i	0.687136	−	0.726529i	$-0.258868\pi$
$761$	−2.44720	−	2.63746i	−0.0887111	−	0.0956078i	−0.775847	+	0.630921i	$0.782677\pi$
$762$	−2.93824	−	19.0628i	−0.106441	−	0.690571i
$763$	−6.94123	−	0.520173i	−0.251289	−	0.0188315i
$764$	0.00142630	+	0.00226994i	5.16018e−5	+	8.21237e-5i
$765$	9.97830	−	38.2574i	0.360766	−	1.38320i
$766$	−24.8728	−	24.8728i	−0.898691	−	0.898691i
$767$	31.5244	−	21.4930i	1.13828	−	0.776066i
$768$	0.0701075	−	0.00548878i	0.00252979	−	0.000198059i
$769$	−6.18445	−	8.37963i	−0.223017	−	0.302177i	0.678776	−	0.734345i	$-0.262511\pi$
$769$	−6.18445	−	8.37963i	−0.223017	−	0.302177i	−0.901793	+	0.432168i	$0.857749\pi$
$770$	61.3374	−	4.59660i	2.21045	−	0.165650i
$771$	20.0244	−	18.7045i	0.721162	−	0.673625i
$772$	−0.0352582	−	0.00667120i	−0.00126897	−	0.000240102i
$773$	23.8845	−	15.0076i	0.859067	−	0.539787i	−0.0289593	−	0.999581i	$-0.509219\pi$
$773$	23.8845	−	15.0076i	0.859067	−	0.539787i	0.888026	+	0.459793i	$0.152076\pi$
$774$	26.8287	+	3.86112i	0.964336	+	0.138785i
$775$	19.8826	−	56.8211i	0.714202	−	2.04107i
$776$	−0.403287	−	0.124397i	−0.0144771	−	0.00446561i
$777$	6.02152	−	32.4154i	0.216021	−	1.16289i
$778$	−11.0430	+	28.1372i	−0.395912	+	1.00877i
$779$	−4.32488	−	14.0209i	−0.154955	−	0.502351i
$780$	0.0128403	+	0.0264375i	0.000459757	+	0.000946615i
$781$	−19.2572	−	14.2124i	−0.689075	−	0.508561i
$782$	−14.4048			−0.515115
$783$	−27.8733	+	2.46510i	−0.996112	+	0.0880954i
$784$	49.8404			1.78002
$785$	−12.5615	−	9.27081i	−0.448339	−	0.330890i
$786$	4.10188	+	8.44555i	0.146309	+	0.301243i
$787$	−7.25656	−	23.5252i	−0.258668	−	0.838582i	−0.988004	−	0.154427i	$-0.950647\pi$
$787$	−7.25656	−	23.5252i	−0.258668	−	0.838582i	0.729336	−	0.684156i	$-0.239829\pi$
$788$	−0.00336116	+	0.00856410i	−0.000119736	+	0.000305084i
$789$	2.25089	−	12.1171i	0.0801339	−	0.431381i
$790$	−29.3516	−	9.05376i	−1.04428	−	0.322118i
$791$	7.83350	−	22.3869i	0.278527	−	0.795985i
$792$	−9.59063	−	23.9657i	−0.340788	−	0.851584i
$793$	21.3652	−	13.4246i	0.758700	−	0.476723i
$794$	27.6316	+	5.22819i	0.980610	+	0.185541i
$795$	−12.0702	+	11.2746i	−0.428085	+	0.399868i
$796$	0.00180225		0.000135060i	6.38789e−5		4.78707e-6i
$797$	−26.4675	−	35.8622i	−0.937528	−	1.27031i	−0.962686	−	0.270622i	$-0.912771\pi$
$797$	−26.4675	−	35.8622i	−0.937528	−	1.27031i	0.0251577	−	0.999683i	$-0.491991\pi$
$798$	28.8092	−	2.25550i	1.01983	−	0.0798437i
$799$	32.3151	−	22.0320i	1.14322	−	0.779437i
$800$	−0.0373247	−	0.0373247i	−0.00131963	−	0.00131963i
$801$	−3.67917	−	3.63046i	−0.129997	−	0.128276i
$802$	14.6667	+	23.3420i	0.517901	+	0.824234i
$803$	31.6025	+	2.36828i	1.11523	+	0.0835748i
$804$	0.00166271	+	0.0107873i	5.86391e−5	+	0.000380440i
$805$	24.4032	+	26.3004i	0.860100	+	0.926967i
$806$	−7.11251	+	47.1884i	−0.250527	+	1.66214i
$807$	−53.8996	+	6.25496i	−1.89736	+	0.220185i
$808$	20.1401	+	18.6873i	0.708525	+	0.657415i
$809$	12.3538	+	7.76244i	0.434338	+	0.272913i	0.731404	−	0.681944i	$-0.238865\pi$
$809$	12.3538	+	7.76244i	0.434338	+	0.272913i	−0.297066	+	0.954857i	$0.596008\pi$
$810$	−29.5592	−	28.7817i	−1.03861	−	1.01129i
$811$			32.1471i			1.12884i	0.825489	+	0.564419i	$0.190900\pi$
$811$			32.1471i			1.12884i	−0.825489	+	0.564419i	$0.809100\pi$
$812$	0.0119798	+	0.0383719i	0.000420409	+	0.00134659i
$813$	21.2493	+	13.2533i	0.745245	+	0.464812i
$814$	−7.41545	−	16.9964i	−0.259911	−	0.595723i
$815$	71.1541	+	2.66240i	2.49242	+	0.0932597i
$816$	−7.37184	−	27.1499i	−0.258066	−	0.950438i
$817$	−2.54790	−	16.9042i	−0.0891399	−	0.591404i
$818$	−15.2774	+	19.1573i	−0.534163	+	0.669819i
$819$	31.8426	−	25.7426i	1.11267	−	0.899519i
$820$	0.0284052	+	0.00993942i	0.000991954	+	0.000347100i
$821$	−1.28898	+	17.2002i	−0.0449857	+	0.600293i	0.928469	+	0.371411i	$0.121126\pi$
$821$	−1.28898	+	17.2002i	−0.0449857	+	0.600293i	−0.973454	+	0.228882i	$0.926493\pi$
$822$	12.5098	+	21.5018i	0.436328	+	0.749962i
$823$	33.1698	+	28.5449i	1.15623	+	0.995013i	0.999973	+	0.00729640i	$0.00232254\pi$
$823$	33.1698	+	28.5449i	1.15623	+	0.995013i	0.156253	+	0.987717i	$0.450058\pi$
$824$	−33.2926	−	8.92072i	−1.15980	−	0.310768i
$825$	−13.4894	+	25.7302i	−0.469639	+	0.895812i
$826$	70.5209	+	30.7680i	2.45374	+	1.07055i
$827$	4.55089	+	40.3902i	0.158250	+	1.40451i	0.782193	+	0.623036i	$0.214101\pi$
$827$	4.55089	+	40.3902i	0.158250	+	1.40451i	−0.623943	+	0.781470i	$0.714470\pi$
$828$	0.00628889	−	0.0110623i	0.000218554	−	0.000384440i
$829$	−21.4749	+	21.4749i	−0.745853	+	0.745853i	−0.973697	−	0.227845i	$-0.926832\pi$
$829$	−21.4749	+	21.4749i	−0.745853	+	0.745853i	0.227845	+	0.973697i	$0.426832\pi$
$830$	4.38481	−	23.1743i	0.152199	−	0.804390i
$831$	−27.4437	−	15.7230i	−0.952012	−	0.545423i
$832$	20.4630	+	13.9514i	0.709427	+	0.483679i
$833$	9.42233	+	49.7982i	0.326465	+	1.72541i
$834$	−8.48157	+	24.5005i	−0.293693	+	0.848382i
$835$	3.10018	+	7.89912i	0.107286	+	0.273360i
$836$	−0.0107573	+	0.00857870i	−0.000372051	+	0.000296700i
$837$	11.0994	+	55.6128i	0.383651	+	1.92226i
$838$	18.9380	−	30.1397i	0.654203	−	1.04116i
$839$	6.43804	−	8.72323i	0.222266	−	0.301159i	−0.679249	−	0.733908i	$-0.737694\pi$
$839$	6.43804	−	8.72323i	0.222266	−	0.301159i	0.901515	+	0.432749i	$0.142456\pi$
$840$	−37.1133	+	59.5046i	−1.28053	+	2.05310i
$841$	23.8488	−	16.4995i	0.822372	−	0.568950i
$842$	15.9498	−	9.20864i	0.549667	−	0.317351i
$843$	−11.0433	−	27.8645i	−0.380351	−	0.959705i
$844$	−0.0224002	+	0.0118389i	−0.000771047	+	0.000407510i
$845$	2.47663	−	10.8508i	0.0851987	−	0.373280i
$846$	−3.32101	−	40.6768i	−0.114179	−	1.39850i
$847$	−6.04818	−	4.82326i	−0.207818	−	0.165729i
$848$	−3.46415	+	11.2305i	−0.118959	+	0.385657i
$849$	10.2616	−	26.4046i	0.352179	−	0.906203i
$850$	−17.8511	+	26.1827i	−0.612287	+	0.898061i
$851$	5.05414	−	9.56290i	0.173254	−	0.327812i
$852$	0.0220147	−	0.00687103i	0.000754210	−	0.000235398i
$853$	0.663455	−	0.177772i	0.0227163	−	0.00608681i	−0.247443	−	0.968902i	$-0.579590\pi$
$853$	0.663455	−	0.177772i	0.0227163	−	0.00608681i	0.270159	+	0.962816i	$0.412924\pi$
$854$	45.8447	+	22.0777i	1.56877	+	0.755482i
$855$	−12.0051	+	23.0858i	−0.410566	+	0.789519i
$856$	−6.78558	+	0.764551i	−0.231926	+	0.0261318i
$857$	17.1238	+	25.1160i	0.584939	+	0.857947i	0.998622	−	0.0524734i	$-0.0167105\pi$
$857$	17.1238	+	25.1160i	0.584939	+	0.857947i	−0.413684	+	0.910421i	$0.635758\pi$
$858$	6.71488	−	22.0294i	0.229242	−	0.752072i
$859$	−2.50074	+	2.90592i	−0.0853243	+	0.0991486i	−0.799011	−	0.601316i	$-0.794643\pi$
$859$	−2.50074	+	2.90592i	−0.0853243	+	0.0991486i	0.713687	+	0.700465i	$0.247024\pi$
$860$	0.0309992	+	0.0163835i	0.00105706	+	0.000558674i
$861$	4.55544	−	41.6782i	0.155249	−	1.42039i
$862$	4.59598	+	5.34063i	0.156540	+	0.181902i
$863$	−5.21768	−	22.8602i	−0.177612	−	0.778169i	−0.982729	−	0.185052i	$-0.940755\pi$
$863$	−5.21768	−	22.8602i	−0.177612	−	0.778169i	0.805117	−	0.593116i	$-0.202103\pi$
$864$	0.0481571	+	0.0123891i	0.00163834	+	0.000421487i
$865$	−16.9189	−	21.2156i	−0.575260	−	0.721353i
$866$	2.24008	−	2.41423i	0.0761209	−	0.0820388i
$867$	−0.752902	+	0.365673i	−0.0255699	+	0.0124189i
$868$	0.0746702	−	0.0325783i	0.00253447	−	0.00110578i
$869$	−10.1878	−	17.6458i	−0.345597	−	0.598592i
$870$	41.3745	+	10.7876i	1.40273	+	0.365734i
$871$	−5.76116	+	9.97861i	−0.195209	+	0.338112i
$872$	0.499771	−	4.43559i	0.0169244	−	0.150208i
$873$	−0.361778	−	0.263299i	−0.0122443	−	0.00891132i
$874$	9.24258	+	2.10956i	0.312635	+	0.0713569i
$875$	7.29956	−	1.10023i	0.246770	−	0.0371946i
$876$	−0.0198414	+	0.0232121i	−0.000670380	+	0.000784266i
$877$	−36.6983	+	34.0511i	−1.23921	+	1.14982i	−0.256136	+	0.966641i	$0.582449\pi$
$877$	−36.6983	+	34.0511i	−1.23921	+	1.14982i	−0.983079	+	0.183183i	$0.941360\pi$
$878$	−37.6694	+	7.12743i	−1.27128	+	0.240539i
$879$	14.2585	+	32.3859i	0.480926	+	1.09235i
$880$	1.47361	+	39.3829i	0.0496752	+	1.32760i
$881$	−2.71734	−	7.76571i	−0.0915495	−	0.261633i	0.888999	−	0.457908i	$-0.151401\pi$
$881$	−2.71734	−	7.76571i	−0.0915495	−	0.261633i	−0.980549	+	0.196275i	$0.937115\pi$
$882$	50.0337	+	17.1342i	1.68472	+	0.576938i
$883$	0.610455	−	1.26762i	0.0205434	−	0.0426589i	−0.890445	−	0.455092i	$-0.849607\pi$
$883$	0.610455	−	1.26762i	0.0205434	−	0.0426589i	0.910988	+	0.412433i	$0.135321\pi$
$884$	−0.00850417	+	0.0194918i	−0.000286026	+	0.000655579i
$885$	−57.1128	+	39.2182i	−1.91983	+	1.31831i
$886$	−2.55157	−	34.0484i	−0.0857218	−	1.14388i
$887$	3.45853	−	12.9074i	0.116126	−	0.433388i	−0.883243	−	0.468916i	$-0.844645\pi$
$887$	3.45853	−	12.9074i	0.116126	−	0.433388i	0.999369	+	0.0355281i	$0.0113113\pi$
$888$	20.6279	+	4.63594i	0.692228	+	0.155572i
$889$	−34.7360	+	1.29973i	−1.16501	+	0.0435915i
$890$	3.42686	+	7.11594i	0.114869	+	0.238527i
$891$	−1.38768	−	27.3326i	−0.0464891	−	0.915675i
$892$	−0.000382575	0	8.73202e-5i	−1.28095e−5	0	2.92370e-6i
$893$	−23.9609	+	9.40396i	−0.801821	+	0.314692i
$894$	1.88494	+	16.2427i	0.0630418	+	0.543238i
$895$	−15.8574	+	4.89137i	−0.530056	+	0.163501i
$896$	−1.86429	+	49.8241i	−0.0622814	+	1.66451i
$897$	12.4883	−	4.94936i	0.416971	−	0.165254i
$898$	15.7965	+	9.12012i	0.527136	+	0.304342i
$899$	−38.4885	−	44.4167i	−1.28366	−	1.48138i
$900$	−0.0123137	−	0.0251398i	−0.000410457	−	0.000837993i
$901$	−11.8759	−	1.33809i	−0.395643	−	0.0445782i
$902$	−11.0187	−	20.8485i	−0.366884	−	0.694178i
$903$	12.4856	−	47.2257i	0.415494	−	1.57157i
$904$	14.1581	+	5.55663i	0.470890	+	0.184811i
$905$	4.63976	+	0.699332i	0.154231	+	0.0232466i
$906$	−3.15893	−	16.3961i	−0.104949	−	0.544725i
$907$	−21.6898	+	18.6656i	−0.720199	+	0.619782i	−0.934074	−	0.357079i	$-0.883773\pi$
$907$	−21.6898	+	18.6656i	−0.720199	+	0.619782i	0.213875	+	0.976861i	$0.431392\pi$
$908$	−0.0334626	+	0.0161147i	−0.00111049	+	0.000534786i
$909$	13.7822	+	25.6617i	0.457125	+	0.851146i
$910$	−59.0568	+	20.6649i	−1.95771	+	0.685034i
$911$	−7.25749	−	27.0853i	−0.240451	−	0.897377i	−0.975615	−	0.219488i	$-0.929561\pi$
$911$	−7.25749	−	27.0853i	−0.240451	−	0.897377i	0.735164	−	0.677889i	$-0.237105\pi$
$912$	0.753945	+	18.4998i	0.0249656	+	0.612591i
$913$	12.5882	−	9.29055i	0.416610	−	0.307472i
$914$	8.38605	−	6.18919i	0.277386	−	0.204720i
$915$	−38.7143	+	24.5061i	−1.27985	+	0.810146i
$916$	0.00925216	+	0.0345295i	0.000305700	+	0.00114089i
$917$	15.9711	−	5.58853i	0.527412	−	0.184549i
$918$	1.93320	−	29.7895i	0.0638053	−	0.983199i
$919$	−38.2544	+	18.4224i	−1.26190	+	0.607698i	−0.940676	−	0.339307i	$-0.889808\pi$
$919$	−38.2544	+	18.4224i	−1.26190	+	0.607698i	−0.321221	+	0.947004i	$0.604093\pi$
$920$	−17.4389	+	15.0074i	−0.574943	+	0.494778i
$921$	−45.4969	−	15.7501i	−1.49917	−	0.518983i
$922$	15.2640	+	2.30068i	0.502692	+	0.0757687i
$923$	22.6629	+	8.89451i	0.745957	+	0.292766i
$924$	−0.0379421	+	0.0103022i	−0.00124820	+	0.000338916i
$925$	−11.1186	−	21.0374i	−0.365577	−	0.691705i
$926$	−35.4161	−	3.99043i	−1.16384	−	0.131134i
$927$	−30.3292	−	20.3834i	−0.996141	−	0.669478i
$928$	−0.0497322	+	0.0135079i	−0.00163254	+	0.000443418i
$929$	12.6917	+	7.32758i	0.416402	+	0.240410i	0.693537	−	0.720421i	$-0.256051\pi$
$929$	12.6917	+	7.32758i	0.416402	+	0.240410i	−0.277135	+	0.960831i	$0.589385\pi$
$930$	12.6296	−	85.7290i	0.414141	−	2.81116i
$931$	1.24719	−	33.3320i	0.0408752	−	1.09241i
$932$	−0.0151941	+	0.00468675i	−0.000497698	+	0.000153520i
$933$	11.6979	−	8.69381i	0.382973	−	0.284622i
$934$	34.2743	−	13.4517i	1.12149	−	0.440152i
$935$	−39.0710	+	8.91770i	−1.27776	+	0.291640i
$936$	15.7328	+	21.0225i	0.514242	+	0.687143i
$937$	−9.27767	−	19.2653i	−0.303088	−	0.629369i	0.692682	−	0.721243i	$-0.256429\pi$
$937$	−9.27767	−	19.2653i	−0.303088	−	0.629369i	−0.995771	+	0.0918733i	$0.970715\pi$
$938$	−23.2194	+	0.868808i	−0.758139	+	0.0283676i
$939$	−2.89139	+	3.13708i	−0.0943571	+	0.102375i
$940$	0.0136640	−	0.0509946i	0.000445669	−	0.00166326i
$941$	1.49867	+	19.9984i	0.0488553	+	0.651928i	0.966852	+	0.255339i	$0.0821872\pi$
$941$	1.49867	+	19.9984i	0.0488553	+	0.651928i	−0.917996	+	0.396589i	$0.870194\pi$
$942$	−10.6374	−	5.07911i	−0.346585	−	0.165486i
$943$	5.50039	−	12.6070i	0.179117	−	0.410542i
$944$	−21.3895	+	44.4157i	−0.696168	+	1.44561i
$945$	−57.6648	+	46.9367i	−1.87584	+	1.52685i
$946$	−9.07418	−	25.9325i	−0.295027	−	0.843138i
$947$	0.183957	+	4.91635i	0.00597780	+	0.159760i	0.999092	+	0.0426085i	$0.0135668\pi$
$947$	0.183957	+	4.91635i	0.00597780	+	0.159760i	−0.993114	+	0.117152i	$0.962624\pi$
$948$	0.0195171	+	0.00213322i	0.000633885	+	6.92838e-5i
$949$	−31.6745	+	5.99314i	−1.02820	+	0.194545i
$950$	15.2882	−	14.1854i	0.496016	−	0.460235i
$951$	−35.0337	−	6.50791i	−1.13605	−	0.211033i
$952$	−50.1768	+	7.56294i	−1.62624	+	0.245116i
$953$	−3.29447	−	0.751941i	−0.106718	−	0.0243578i	0.168828	−	0.985645i	$-0.446002\pi$
$953$	−3.29447	−	0.751941i	−0.106718	−	0.0243578i	−0.275547	+	0.961288i	$0.588859\pi$
$954$	−7.33840	+	10.0831i	−0.237590	+	0.326453i
$955$	0.575383	−	5.10666i	0.0186189	−	0.165248i
$956$	−0.00438881	+	0.00760165i	−0.000141944	+	0.000245855i
$957$	15.2519	+	23.9135i	0.493022	+	0.773014i
$958$	−25.4719	−	44.1186i	−0.822960	−	1.42541i
$959$	41.0907	−	17.9277i	1.32689	−	0.578915i
$960$	−37.2416	−	25.2096i	−1.20197	−	0.813636i
$961$	−59.9304	+	64.5896i	−1.93324	+	2.08354i
$962$	11.7607	+	14.7475i	0.379181	+	0.475478i
$963$	−7.06874	−	1.56391i	−0.227787	−	0.0503964i
$964$	0.00364732	+	0.0159800i	0.000117472	+	0.000514680i
$965$	44.8683	+	52.1379i	1.44436	+	1.67838i
$966$	21.8494	+	16.0134i	0.702992	+	0.515223i
$967$	−34.7888	−	18.3864i	−1.11873	−	0.591267i	−0.197508	−	0.980301i	$-0.563285\pi$
$967$	−34.7888	−	18.3864i	−1.11873	−	0.591267i	−0.921223	+	0.389034i	$0.872809\pi$
$968$	3.23585	−	3.76013i	0.104004	−	0.120855i
$969$	−18.3416	+	4.25070i	−0.589218	+	0.136552i
$970$	0.385151	+	0.564913i	0.0123665	+	0.0181383i
$971$	45.1933	−	5.09206i	1.45032	−	0.163412i	0.648609	−	0.761122i	$-0.275351\pi$
$971$	45.1933	−	5.09206i	1.45032	−	0.163412i	0.801712	+	0.597710i	$0.203923\pi$
$972$	0.0220330	+	0.0144902i	0.000706709	+	0.000464773i
$973$	42.0979	+	20.2733i	1.34960	+	0.649932i
$974$	−34.8573	+	9.33998i	−1.11690	+	0.299272i
$975$	6.47986	−	28.8326i	0.207522	−	0.923382i
$976$	−15.2341	+	28.8243i	−0.487632	+	0.922644i
$977$	−11.3322	+	16.6213i	−0.362550	+	0.531762i	−0.963565	−	0.267475i	$-0.913811\pi$
$977$	−11.3322	+	16.6213i	−0.362550	+	0.531762i	0.601015	+	0.799238i	$0.294763\pi$
$978$	53.1341	−	8.18983i	1.69904	−	0.261882i
$979$	−1.54428	+	5.00644i	−0.0493555	+	0.160006i
$980$	0.0534867	+	0.0426542i	0.00170857	+	0.00136254i
$981$	2.02486	−	4.27735i	0.0646489	−	0.136565i
$982$	−0.690670	+	3.02602i	−0.0220402	+	0.0965642i
$983$	14.2904	−	7.55267i	0.455791	−	0.240893i	−0.223583	−	0.974685i	$-0.571775\pi$
$983$	14.2904	−	7.55267i	0.455791	−	0.240893i	0.679374	+	0.733792i	$0.262251\pi$
$984$	26.5989	+	3.91855i	0.847942	+	0.124919i
$985$	15.2730	−	8.81788i	0.486639	−	0.280961i
$986$	13.5186	+	27.8282i	0.430520	+	0.886230i
$987$	−73.5082	−	2.50526i	−2.33979	−	0.0797434i
$988$	0.00831108	−	0.0112611i	0.000264411	−	0.000358264i
$989$	8.52609	−	13.5692i	0.271114	−	0.431475i
$990$	−12.0598	+	40.0422i	−0.383285	+	1.27263i
$991$	−11.8174	+	9.42407i	−0.375392	+	0.299365i	−0.792952	−	0.609284i	$-0.791457\pi$
$991$	−11.8174	+	9.42407i	−0.375392	+	0.299365i	0.417560	+	0.908649i	$0.362885\pi$
$992$	0.0381565	+	0.0972211i	0.00121147	+	0.00308677i
$993$	12.2495	+	14.1386i	0.388726	+	0.448676i
$994$	9.12735	+	48.2392i	0.289502	+	1.53006i
$995$	−2.86246	−	1.95159i	−0.0907460	−	0.0618696i
$996$	5.02270e−5		0.0150754i	1.59150e−6		0.000477681i
$997$	8.35845	−	44.1755i	0.264715	−	1.39905i	−0.557643	−	0.830081i	$-0.688294\pi$
$997$	8.35845	−	44.1755i	0.264715	−	1.39905i	0.822358	−	0.568971i	$-0.192658\pi$
$998$	2.07689	−	2.07689i	0.0657427	−	0.0657427i
$999$	19.0980	+	11.7355i	0.604234	+	0.371294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.10	✓	672
3.2	odd	2		783.2.be.a.89.19		672
9.4	even	3		783.2.be.a.611.19		672
9.5	odd	6	inner	261.2.x.a.176.10	yes	672
29.15	odd	28	inner	261.2.x.a.218.10	yes	672
87.44	even	28		783.2.be.a.305.19		672
261.131	even	84	inner	261.2.x.a.131.10	yes	672
261.247	odd	84		783.2.be.a.44.19		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.10	✓	672	1.1	even	1	trivial
261.2.x.a.131.10	yes	672	261.131	even	84	inner
261.2.x.a.176.10	yes	672	9.5	odd	6	inner
261.2.x.a.218.10	yes	672	29.15	odd	28	inner
783.2.be.a.44.19		672	261.247	odd	84
783.2.be.a.89.19		672	3.2	odd	2
783.2.be.a.305.19		672	87.44	even	28
783.2.be.a.611.19		672	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13739 - 0.839433i) q^{2} +(-0.756704 - 1.55801i) q^{3} +(-0.000498633 - 0.00161653i) q^{4} +(-1.18474 + 3.01866i) q^{5} +(-0.447178 + 2.40727i) q^{6} +(4.21652 + 1.30062i) q^{7} +(-0.934565 + 2.67083i) q^{8} +(-1.85480 + 2.35791i) q^{9} +O(q^{10})\)	\(q+(-1.13739 - 0.839433i) q^{2} +(-0.756704 - 1.55801i) q^{3} +(-0.000498633 - 0.00161653i) q^{4} +(-1.18474 + 3.01866i) q^{5} +(-0.447178 + 2.40727i) q^{6} +(4.21652 + 1.30062i) q^{7} +(-0.934565 + 2.67083i) q^{8} +(-1.85480 + 2.35791i) q^{9} +(3.88147 - 2.43889i) q^{10} +(2.98785 + 0.565332i) q^{11} +(-0.00214125 + 0.00200011i) q^{12} +(-3.08454 + 0.231155i) q^{13} +(-3.70405 - 5.01881i) q^{14} +(5.59960 - 0.438398i) q^{15} +(3.30216 - 2.25137i) q^{16} +(2.87374 + 2.87374i) q^{17} +(4.08894 - 1.12488i) q^{18} +(-1.42303 - 2.26473i) q^{19} +(0.00547050 + 0.000409957i) q^{20} +(-1.16427 - 7.55357i) q^{21} +(-2.92380 - 3.15110i) q^{22} +(0.373700 - 2.47934i) q^{23} +(4.86838 - 0.564967i) q^{24} +(-4.04344 - 3.75176i) q^{25} +(3.70237 + 2.32636i) q^{26} +(5.07718 + 1.10556i) q^{27} -0.00746466i q^{28} +(-5.14047 + 1.60487i) q^{29} +(-6.73694 - 4.20186i) q^{30} +(4.36433 + 10.0032i) q^{31} +(0.00956293 + 0.000357820i) q^{32} +(-1.38012 - 5.08289i) q^{33} +(-0.856255 - 5.68088i) q^{34} +(-8.92160 + 11.1873i) q^{35} +(0.00473649 + 0.00182261i) q^{36} +(4.07179 + 1.42478i) q^{37} +(-0.282554 + 3.77043i) q^{38} +(2.69423 + 4.63084i) q^{39} +(-6.95512 - 5.98536i) q^{40} +(5.29884 + 1.41982i) q^{41} +(-5.01649 + 9.56870i) q^{42} +(5.85815 + 2.55588i) q^{43} +(-0.000575966 - 0.00511184i) q^{44} +(-4.92026 - 8.39250i) q^{45} +(-2.50628 + 2.50628i) q^{46} +(1.78914 - 9.45581i) q^{47} +(-6.00642 - 3.44118i) q^{48} +(10.3037 + 7.02498i) q^{49} +(1.44962 + 7.66142i) q^{50} +(2.30275 - 6.65189i) q^{51} +(0.00191172 + 0.00487100i) q^{52} +(-2.29909 + 1.83346i) q^{53} +(-4.84669 - 5.51941i) q^{54} +(-5.24635 + 8.34953i) q^{55} +(-7.41436 + 10.0461i) q^{56} +(-2.45167 + 3.93083i) q^{57} +(7.19390 + 2.48971i) q^{58} +(-10.6823 + 6.16743i) q^{59} +(-0.00350083 - 0.00883332i) q^{60} +(-7.21218 + 3.81175i) q^{61} +(3.43303 - 15.0411i) q^{62} +(-10.8875 + 7.52976i) q^{63} +(-6.25993 - 4.99213i) q^{64} +(2.95659 - 9.58504i) q^{65} +(-2.69701 + 6.93976i) q^{66} +(2.09840 - 3.07778i) q^{67} +(0.00321254 - 0.00607843i) q^{68} +(-4.14562 + 1.29390i) q^{69} +(19.5384 - 5.23529i) q^{70} +(-7.09131 - 3.41500i) q^{71} +(-4.56414 - 7.15747i) q^{72} +(10.3562 - 1.16687i) q^{73} +(-3.43521 - 5.03853i) q^{74} +(-2.78560 + 9.13869i) q^{75} +(-0.00295144 + 0.00342964i) q^{76} +(11.8630 + 6.26980i) q^{77} +(0.822888 - 7.52870i) q^{78} +(-4.37071 - 5.07886i) q^{79} +(2.88394 + 12.6354i) q^{80} +(-2.11944 - 8.74688i) q^{81} +(-4.83501 - 6.06292i) q^{82} +(3.49952 - 3.77159i) q^{83} +(-0.0116300 + 0.00564854i) q^{84} +(-12.0795 + 5.27021i) q^{85} +(-4.51751 - 7.82456i) q^{86} +(6.39021 + 6.79450i) q^{87} +(-4.30225 + 7.45171i) q^{88} +(-0.192907 + 1.71210i) q^{89} +(-1.44868 + 13.6758i) q^{90} +(-13.3067 - 3.03716i) q^{91} +(-0.00419427 + 0.000632184i) q^{92} +(12.2825 - 14.3691i) q^{93} +(-9.97248 + 9.25310i) q^{94} +(8.52237 - 1.61252i) q^{95} +(-0.00667882 - 0.0151699i) q^{96} +(0.00557688 + 0.149045i) q^{97} +(-5.82240 - 16.6395i) q^{98} +(-6.87486 + 5.99649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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