LMFDB - Embedded newform 531.2.m.a.121.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(4,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(174))

chi = DirichletCharacter(H, H._module([58, 6]))

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

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

chi := DirichletCharacter("531.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.m (of order $87$, degree $56$, 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:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$3248$
Relative dimension:	$58$ over $\Q(\zeta_{87})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{87}]$

Embedding invariants

Embedding label			121.48
Character	$\chi$	$=$	531.121
Dual form			531.2.m.a.79.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66787 + 1.17535i) q^{2} +(-0.290573 + 1.70750i) q^{3} +(0.727620 + 2.03718i) q^{4} +(-0.424311 + 0.234866i) q^{5} +(-2.49155 + 2.50636i) q^{6} +(-4.04904 + 2.05389i) q^{7} +(-0.0890992 + 0.320906i) q^{8} +(-2.83113 - 0.992308i) q^{9} +O(q^{10})$	\(q+(1.66787 + 1.17535i) q^{2} +(-0.290573 + 1.70750i) q^{3} +(0.727620 + 2.03718i) q^{4} +(-0.424311 + 0.234866i) q^{5} +(-2.49155 + 2.50636i) q^{6} +(-4.04904 + 2.05389i) q^{7} +(-0.0890992 + 0.320906i) q^{8} +(-2.83113 - 0.992308i) q^{9} +(-0.983743 - 0.106988i) q^{10} +(1.00803 - 0.380694i) q^{11} +(-3.68992 + 0.650463i) q^{12} +(0.685670 + 5.39629i) q^{13} +(-9.16730 - 1.33342i) q^{14} +(-0.277741 - 0.792758i) q^{15} +(2.82171 - 2.31039i) q^{16} +(-0.0752497 - 1.38790i) q^{17} +(-3.55565 - 4.98261i) q^{18} +(0.438184 - 0.415070i) q^{19} +(-0.787201 - 0.693506i) q^{20} +(-2.33048 - 7.51055i) q^{21} +(2.12870 + 0.549837i) q^{22} +(-0.540585 + 1.70556i) q^{23} +(-0.522059 - 0.245384i) q^{24} +(-2.52982 + 4.03774i) q^{25} +(-5.19892 + 9.80620i) q^{26} +(2.51702 - 4.54583i) q^{27} +(-7.13031 - 6.75419i) q^{28} +(0.855398 + 9.44964i) q^{29} +(0.468532 - 1.64866i) q^{30} +(8.75643 - 2.60237i) q^{31} +(8.08610 - 0.585000i) q^{32} +(0.357131 + 1.83183i) q^{33} +(1.50576 - 2.40327i) q^{34} +(1.23566 - 1.82247i) q^{35} +(-0.0384762 - 6.48956i) q^{36} +(-0.121813 - 0.438730i) q^{37} +(1.21868 - 0.177262i) q^{38} +(-9.41343 - 0.397232i) q^{39} +(-0.0375641 - 0.157090i) q^{40} +(4.99619 - 5.46888i) q^{41} +(4.94059 - 15.2657i) q^{42} +(-5.63590 + 4.61463i) q^{43} +(1.50900 + 1.77654i) q^{44} +(1.43434 - 0.243889i) q^{45} +(-2.90626 + 2.20928i) q^{46} +(2.06260 + 1.14170i) q^{47} +(3.12509 + 5.48941i) q^{48} +(8.04135 - 10.9843i) q^{49} +(-8.96515 + 3.76099i) q^{50} +(2.39171 + 0.274796i) q^{51} +(-10.4943 + 5.32328i) q^{52} +(11.8120 - 1.28464i) q^{53} +(9.54100 - 4.62347i) q^{54} +(-0.338305 + 0.398283i) q^{55} +(-0.298340 - 1.48236i) q^{56} +(0.581409 + 0.868808i) q^{57} +(-9.67994 + 16.7661i) q^{58} +(-5.09778 + 5.74567i) q^{59} +(1.41290 - 1.14263i) q^{60} +(-4.51973 - 3.18506i) q^{61} +(17.6633 + 5.95144i) q^{62} +(13.5015 - 1.79694i) q^{63} +(7.92436 + 4.76793i) q^{64} +(-1.55834 - 2.12866i) q^{65} +(-1.55739 + 3.47500i) q^{66} +(-5.28554 - 5.38184i) q^{67} +(2.77265 - 1.16316i) q^{68} +(-2.75518 - 1.41864i) q^{69} +(4.20296 - 1.58730i) q^{70} +(-7.28507 + 4.38328i) q^{71} +(0.570689 - 0.820115i) q^{72} +(-0.170573 - 0.428107i) q^{73} +(0.312493 - 0.874917i) q^{74} +(-6.15935 - 5.49293i) q^{75} +(1.16440 + 0.590648i) q^{76} +(-3.29964 + 3.61182i) q^{77} +(-15.2335 - 11.7266i) q^{78} +(-3.69022 - 3.25100i) q^{79} +(-0.654649 + 1.64304i) q^{80} +(7.03065 + 5.61871i) q^{81} +(14.7608 - 3.24910i) q^{82} +(-7.15775 - 0.517837i) q^{83} +(13.6047 - 10.2124i) q^{84} +(0.357899 + 0.571227i) q^{85} +(-14.8237 + 1.07244i) q^{86} +(-16.3839 - 1.28521i) q^{87} +(0.0323526 + 0.357402i) q^{88} +(8.09968 + 3.74731i) q^{89} +(2.67894 + 1.27907i) q^{90} +(-13.8597 - 20.4415i) q^{91} +(-3.86789 + 0.139731i) q^{92} +(1.89918 + 15.7078i) q^{93} +(2.09826 + 4.32848i) q^{94} +(-0.0884405 + 0.279033i) q^{95} +(-1.35071 + 13.9770i) q^{96} +(18.9296 - 2.75339i) q^{97} +(26.3223 - 8.86903i) q^{98} +(-3.23163 + 0.0775221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9}+O(q^{10}) $ 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18} - 120 q^{19} - 31 q^{20} - 60 q^{21} - 29 q^{22} - 29 q^{23} - 16 q^{24} + 29 q^{25} - 92 q^{26} - 55 q^{27} - 132 q^{28} - 27 q^{29} - 64 q^{30} - 21 q^{31} - 49 q^{32} - 32 q^{33} - 17 q^{34} - 136 q^{35} - 70 q^{36} - 120 q^{37} - 33 q^{38} - 80 q^{39} - 17 q^{40} - 17 q^{41} - 68 q^{42} - 21 q^{43} - 104 q^{44} - 58 q^{45} - 116 q^{46} - 17 q^{47} + 106 q^{48} + 19 q^{49} - 5 q^{50} - 250 q^{51} - 21 q^{52} - 108 q^{53} + 175 q^{54} - 116 q^{55} - q^{56} + 63 q^{57} - 58 q^{58} - 17 q^{59} - 816 q^{60} - 27 q^{61} - 128 q^{62} + 95 q^{63} - 256 q^{64} - 59 q^{65} + 67 q^{66} - 15 q^{67} - 43 q^{68} - 302 q^{69} - 41 q^{70} - 134 q^{71} + 210 q^{72} - 144 q^{73} - 51 q^{74} - 47 q^{75} - 9 q^{76} - 85 q^{77} + 36 q^{78} - 39 q^{79} - 128 q^{80} - 22 q^{81} - 164 q^{82} - 35 q^{83} - 190 q^{84} - 17 q^{85} + 31 q^{86} - 75 q^{87} - 29 q^{88} - 36 q^{89} - 86 q^{90} - 136 q^{91} - 31 q^{92} - 41 q^{94} - 13 q^{95} - 30 q^{96} - 3 q^{97} - 156 q^{98} - 86 q^{99}+O(q^{100}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{29}\right)$

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 $

$2$	1.66787	+	1.17535i	1.17936	+	0.831097i	0.988604	−	0.150540i	$-0.0481013\pi$
$2$	1.66787	+	1.17535i	1.17936	+	0.831097i	0.190756	+	0.981637i	$0.438906\pi$
$3$	−0.290573	+	1.70750i	−0.167762	+	0.985827i
$3$	−0.290573	+	1.70750i	−0.167762	+	0.985827i
$4$	0.727620	+	2.03718i	0.363810	+	1.01859i
$5$	−0.424311	+	0.234866i	−0.189758	+	0.105035i	−0.576306	−	0.817234i	$-0.695506\pi$
$5$	−0.424311	+	0.234866i	−0.189758	+	0.105035i	0.386548	+	0.922269i	$0.373667\pi$
$6$	−2.49155	+	2.50636i	−1.01717	+	1.02322i
$7$	−4.04904	+	2.05389i	−1.53039	+	0.776297i	−0.997553	−	0.0699184i	$-0.977726\pi$
$7$	−4.04904	+	2.05389i	−1.53039	+	0.776297i	−0.532841	+	0.846216i	$0.678876\pi$
$8$	−0.0890992	+	0.320906i	−0.0315013	+	0.113457i
$9$	−2.83113	−	0.992308i	−0.943712	−	0.330769i
$10$	−0.983743	−	0.106988i	−0.311087	−	0.0338327i
$11$	1.00803	−	0.380694i	0.303932	−	0.114783i	−0.196648	−	0.980474i	$-0.563005\pi$
$11$	1.00803	−	0.380694i	0.303932	−	0.114783i	0.500579	+	0.865691i	$0.333120\pi$
$12$	−3.68992	+	0.650463i	−1.06519	+	0.187772i
$13$	0.685670	+	5.39629i	0.190171	+	1.49666i	0.746324	+	0.665583i	$0.231817\pi$
$13$	0.685670	+	5.39629i	0.190171	+	1.49666i	−0.556153	+	0.831080i	$0.687723\pi$
$14$	−9.16730	−	1.33342i	−2.45006	−	0.356372i
$15$	−0.277741	−	0.792758i	−0.0717123	−	0.204689i
$16$	2.82171	−	2.31039i	0.705426	−	0.577597i
$17$	−0.0752497	−	1.38790i	−0.0182507	−	0.336615i	−0.993372	−	0.114943i	$-0.963331\pi$
$17$	−0.0752497	−	1.38790i	−0.0182507	−	0.336615i	0.975121	−	0.221672i	$-0.0711513\pi$
$18$	−3.55565	−	4.98261i	−0.838075	−	1.17441i
$19$	0.438184	−	0.415070i	0.100526	−	0.0952235i	−0.635786	−	0.771865i	$-0.719324\pi$
$19$	0.438184	−	0.415070i	0.100526	−	0.0952235i	0.736312	+	0.676642i	$0.236565\pi$
$20$	−0.787201	−	0.693506i	−0.176023	−	0.155073i
$21$	−2.33048	−	7.51055i	−0.508553	−	1.63894i
$22$	2.12870	+	0.549837i	0.453841	+	0.117226i
$23$	−0.540585	+	1.70556i	−0.112720	+	0.355635i	−0.992892	−	0.119020i	$-0.962025\pi$
$23$	−0.540585	+	1.70556i	−0.112720	+	0.355635i	0.880172	+	0.474655i	$0.157427\pi$
$24$	−0.522059	−	0.245384i	−0.106565	−	0.0500887i
$25$	−2.52982	+	4.03774i	−0.505964	+	0.807547i
$26$	−5.19892	+	9.80620i	−1.01959	+	1.92315i
$27$	2.51702	−	4.54583i	0.484401	−	0.874846i
$28$	−7.13031	−	6.75419i	−1.34750	−	1.27642i
$29$	0.855398	+	9.44964i	0.158843	+	1.75475i	0.550677	+	0.834719i	$0.314370\pi$
$29$	0.855398	+	9.44964i	0.158843	+	1.75475i	−0.391833	+	0.920036i	$0.628159\pi$
$30$	0.468532	−	1.64866i	0.0855419	−	0.301002i
$31$	8.75643	−	2.60237i	1.57270	−	0.467400i	0.623435	−	0.781875i	$-0.285736\pi$
$31$	8.75643	−	2.60237i	1.57270	−	0.467400i	0.949266	+	0.314475i	$0.101828\pi$
$32$	8.08610	−	0.585000i	1.42943	−	0.103414i
$33$	0.357131	+	1.83183i	0.0621684	+	0.318880i
$34$	1.50576	−	2.40327i	0.258235	−	0.412158i
$35$	1.23566	−	1.82247i	0.208865	−	0.308053i
$36$	−0.0384762	−	6.48956i	−0.00641269	−	1.08159i
$37$	−0.121813	−	0.438730i	−0.0200259	−	0.0721268i	0.952862	−	0.303404i	$-0.0981233\pi$
$37$	−0.121813	−	0.438730i	−0.0200259	−	0.0721268i	−0.972888	+	0.231277i	$0.925709\pi$
$38$	1.21868	−	0.177262i	0.197697	−	0.0287558i
$39$	−9.41343	−	0.397232i	−1.50735	−	0.0636080i
$40$	−0.0375641	−	0.157090i	−0.00593940	−	0.0248381i
$41$	4.99619	−	5.46888i	0.780273	−	0.854095i	−0.212115	−	0.977245i	$-0.568035\pi$
$41$	4.99619	−	5.46888i	0.780273	−	0.854095i	0.992388	+	0.123150i	$0.0392995\pi$
$42$	4.94059	−	15.2657i	0.762349	−	2.35555i
$43$	−5.63590	+	4.61463i	−0.859466	+	0.703724i	−0.956555	−	0.291552i	$-0.905828\pi$
$43$	−5.63590	+	4.61463i	−0.859466	+	0.703724i	0.0970891	+	0.995276i	$0.469047\pi$
$44$	1.50900	+	1.77654i	0.227491	+	0.267823i
$45$	1.43434	−	0.243889i	0.213819	−	0.0363569i
$46$	−2.90626	+	2.20928i	−0.428504	+	0.325740i
$47$	2.06260	+	1.14170i	0.300862	+	0.166534i	0.627502	−	0.778615i	$-0.284077\pi$
$47$	2.06260	+	1.14170i	0.300862	+	0.166534i	−0.326640	+	0.945149i	$0.605917\pi$
$48$	3.12509	+	5.48941i	0.451068	+	0.792328i
$49$	8.04135	−	10.9843i	1.14876	−	1.56919i
$50$	−8.96515	+	3.76099i	−1.26786	+	0.531884i
$51$	2.39171	+	0.274796i	0.334906	+	0.0384792i
$52$	−10.4943	+	5.32328i	−1.45530	+	0.738207i
$53$	11.8120	−	1.28464i	1.62251	−	0.176459i	0.748762	−	0.662839i	$-0.230648\pi$
$53$	11.8120	−	1.28464i	1.62251	−	0.176459i	0.873747	+	0.486380i	$0.161683\pi$
$54$	9.54100	−	4.62347i	1.29837	−	0.629175i
$55$	−0.338305	+	0.398283i	−0.0456170	+	0.0537045i
$56$	−0.298340	−	1.48236i	−0.0398673	−	0.198089i
$57$	0.581409	+	0.868808i	0.0770094	+	0.115076i
$58$	−9.67994	+	16.7661i	−1.27104	+	2.20150i
$59$	−5.09778	+	5.74567i	−0.663674	+	0.748022i
$59$	−5.09778	+	5.74567i	−0.663674	+	0.748022i
$60$	1.41290	−	1.14263i	0.182405	−	0.147513i
$61$	−4.51973	−	3.18506i	−0.578692	−	0.407805i	0.249397	−	0.968401i	$-0.419767\pi$
$61$	−4.51973	−	3.18506i	−0.578692	−	0.407805i	−0.828089	+	0.560596i	$0.810572\pi$
$62$	17.6633	+	5.95144i	2.24324	+	0.755834i
$63$	13.5015	−	1.79694i	1.70103	−	0.226394i
$64$	7.92436	+	4.76793i	0.990545	+	0.595991i
$65$	−1.55834	−	2.12866i	−0.193288	−	0.264028i
$66$	−1.55739	+	3.47500i	−0.191702	+	0.427743i
$67$	−5.28554	−	5.38184i	−0.645732	−	0.657497i	0.310342	−	0.950625i	$-0.399557\pi$
$67$	−5.28554	−	5.38184i	−0.645732	−	0.657497i	−0.956073	+	0.293128i	$0.905304\pi$
$68$	2.77265	−	1.16316i	0.336233	−	0.141054i
$69$	−2.75518	−	1.41864i	−0.331684	−	0.170784i
$70$	4.20296	−	1.58730i	0.502350	−	0.189718i
$71$	−7.28507	+	4.38328i	−0.864578	+	0.520200i	−0.877423	−	0.479718i	$-0.840739\pi$
$71$	−7.28507	+	4.38328i	−0.864578	+	0.520200i	0.0128444	+	0.999918i	$0.495911\pi$
$72$	0.570689	−	0.820115i	0.0672564	−	0.0966515i
$73$	−0.170573	−	0.428107i	−0.0199641	−	0.0501061i	0.918657	−	0.395057i	$-0.129275\pi$
$73$	−0.170573	−	0.428107i	−0.0199641	−	0.0501061i	−0.938621	+	0.344950i	$0.887896\pi$
$74$	0.312493	−	0.874917i	0.0363266	−	0.101707i
$75$	−6.15935	−	5.49293i	−0.711221	−	0.634269i
$76$	1.16440	+	0.590648i	0.133566	+	0.0677519i
$77$	−3.29964	+	3.61182i	−0.376029	+	0.411605i
$78$	−15.2335	−	11.7266i	−1.72485	−	1.32777i
$79$	−3.69022	−	3.25100i	−0.415183	−	0.365766i	0.427648	−	0.903945i	$-0.359342\pi$
$79$	−3.69022	−	3.25100i	−0.415183	−	0.365766i	−0.842831	+	0.538179i	$0.819112\pi$
$80$	−0.654649	+	1.64304i	−0.0731920	+	0.183698i
$81$	7.03065	+	5.61871i	0.781183	+	0.624302i
$82$	14.7608	−	3.24910i	1.63006	−	0.358803i
$83$	−7.15775	−	0.517837i	−0.785665	−	0.0568400i	−0.326507	−	0.945195i	$-0.605872\pi$
$83$	−7.15775	−	0.517837i	−0.785665	−	0.0568400i	−0.459158	+	0.888355i	$0.651849\pi$
$84$	13.6047	−	10.2124i	1.48439	−	1.11427i
$85$	0.357899	+	0.571227i	0.0388196	+	0.0619582i
$86$	−14.8237	+	1.07244i	−1.59848	+	0.115644i
$87$	−16.3839	−	1.28521i	−1.75653	−	0.137789i
$88$	0.0323526	+	0.357402i	0.00344880	+	0.0380991i
$89$	8.09968	+	3.74731i	0.858564	+	0.397214i	0.799231	−	0.601024i	$-0.205241\pi$
$89$	8.09968	+	3.74731i	0.858564	+	0.397214i	0.0593331	+	0.998238i	$0.481103\pi$
$90$	2.67894	+	1.27907i	0.282385	+	0.134826i
$91$	−13.8597	−	20.4415i	−1.45289	−	2.14285i
$92$	−3.86789	+	0.139731i	−0.403255	+	0.0145680i
$93$	1.89918	+	15.7078i	0.196936	+	1.62882i
$94$	2.09826	+	4.32848i	0.216419	+	0.446448i
$95$	−0.0884405	+	0.279033i	−0.00907380	+	0.0286282i
$96$	−1.35071	+	13.9770i	−0.137856	+	1.42652i
$97$	18.9296	−	2.75339i	1.92201	−	0.279565i	0.926665	−	0.375889i	$-0.122663\pi$
$97$	18.9296	−	2.75339i	1.92201	−	0.279565i	0.995350	+	0.0963242i	$0.0307086\pi$
$98$	26.3223	−	8.86903i	2.65896	−	0.895907i
$99$	−3.23163	+	0.0775221i	−0.324791	+	0.00779127i
$100$	−10.0664	−	2.21577i	−1.00664	−	0.221577i
$101$	7.42790	−	4.84283i	0.739104	−	0.481879i	−0.120581	−	0.992703i	$-0.538476\pi$
$101$	7.42790	−	4.84283i	0.739104	−	0.481879i	0.859685	+	0.510824i	$0.170660\pi$
$102$	3.66607	+	3.26941i	0.362995	+	0.323720i
$103$	13.3053	−	2.42873i	1.31101	−	0.239310i	0.521606	−	0.853187i	$-0.325333\pi$
$103$	13.3053	−	2.42873i	1.31101	−	0.239310i	0.789402	+	0.613876i	$0.210391\pi$
$104$	−1.79280	−	0.260769i	−0.175798	−	0.0255705i
$105$	2.75282	+	2.63946i	0.268648	+	0.257585i
$106$	21.2108	+	11.7407i	2.06018	+	1.14035i
$107$	−1.86951	+	11.4035i	−0.180733	+	1.10242i	0.728165	+	0.685402i	$0.240374\pi$
$107$	−1.86951	+	11.4035i	−0.180733	+	1.10242i	−0.908898	+	0.417019i	$0.863075\pi$
$108$	11.0921	+	1.81999i	1.06734	+	0.175129i
$109$	−9.38043	−	7.13082i	−0.898483	−	0.683009i	0.0503692	−	0.998731i	$-0.483960\pi$
$109$	−9.38043	−	7.13082i	−0.898483	−	0.683009i	−0.948852	+	0.315722i	$0.897753\pi$
$110$	−1.03237	+	0.266657i	−0.0984325	+	0.0254248i
$111$	0.784529	−	0.0805128i	0.0744642	−	0.00764194i
$112$	−6.67991	+	15.1503i	−0.631193	+	1.43157i
$113$	2.38912	−	1.32243i	0.224750	−	0.124404i	−0.367897	−	0.929866i	$-0.619922\pi$
$113$	2.38912	−	1.32243i	0.224750	−	0.124404i	0.592647	+	0.805463i	$0.298083\pi$
$114$	−0.0514401	+	2.13241i	−0.00481781	+	0.199719i
$115$	−0.171202	−	0.850654i	−0.0159647	−	0.0793239i
$116$	−18.6283	+	8.61835i	−1.72959	+	0.800193i
$117$	3.41356	−	15.9580i	0.315584	−	1.47532i
$118$	−15.2556	+	3.59135i	−1.40439	+	0.330610i
$119$	3.15528	+	5.46510i	0.289244	+	0.500985i
$120$	0.279147	−	0.0184946i	0.0254825	−	0.00168832i
$121$	−7.38266	+	6.50395i	−0.671151	+	0.591268i
$122$	−3.79475	−	10.6245i	−0.343561	−	0.961899i
$123$	7.88637	+	10.1201i	0.711090	+	0.912500i
$124$	11.6729	+	15.9449i	1.04825	+	1.43190i
$125$	0.256385	−	4.72874i	0.0229318	−	0.422952i
$126$	24.6307	+	12.8719i	2.19428	+	1.14672i
$127$	8.04023	+	6.11202i	0.713455	+	0.542354i	0.897744	−	0.440518i	$-0.145205\pi$
$127$	8.04023	+	6.11202i	0.713455	+	0.542354i	−0.184289	+	0.982872i	$0.558998\pi$
$128$	1.07132	+	2.42980i	0.0946921	+	0.214766i
$129$	−6.24185	−	10.9642i	−0.549564	−	0.965343i
$130$	−0.0971819	−	5.38192i	−0.00852342	−	0.472026i
$131$	−1.19067	−	9.37068i	−0.104029	−	0.818720i	−0.955638	−	0.294543i	$-0.904833\pi$
$131$	−1.19067	−	9.37068i	−0.104029	−	0.818720i	0.851609	−	0.524177i	$-0.175627\pi$
$132$	−3.47192	+	2.06041i	−0.302191	+	0.179336i
$133$	−0.921717	+	2.58061i	−0.0799230	+	0.223768i
$134$	−2.49004	−	15.1886i	−0.215106	−	1.31209i
$135$	−0.000338381		2.52001i	−2.91232e−5		0.216888i
$136$	0.452090	+	0.0995125i	0.0387664	+	0.00853312i
$137$	12.3499	+	3.67032i	1.05512	+	0.313577i	0.765413	−	0.643539i	$-0.222534\pi$
$137$	12.3499	+	3.67032i	1.05512	+	0.313577i	0.289706	+	0.957116i	$0.406443\pi$
$138$	−2.92787	−	5.60440i	−0.249237	−	0.477078i
$139$	−11.6352	−	14.7455i	−0.986884	−	1.25070i	−0.968020	−	0.250873i	$-0.919282\pi$
$139$	−11.6352	−	14.7455i	−0.986884	−	1.25070i	−0.0188642	−	0.999822i	$-0.506005\pi$
$140$	4.61179	+	1.19121i	0.389768	+	0.100676i
$141$	−2.54879	+	3.19016i	−0.214647	+	0.268660i
$142$	−17.3024	−	1.25177i	−1.45199	−	0.105046i
$143$	2.74551	+	5.17858i	0.229591	+	0.433054i
$144$	−10.2812	+	3.74103i	−0.856771	+	0.311752i
$145$	−2.58235	−	3.80868i	−0.214453	−	0.316294i
$146$	0.218681	−	0.914508i	0.0180982	−	0.0756852i
$147$	16.4192	+	16.9224i	1.35423	+	1.39573i
$148$	0.805141	−	0.567384i	0.0661822	−	0.0466387i
$149$	13.9553	−	4.14745i	1.14326	−	0.339772i	0.342948	−	0.939355i	$-0.388575\pi$
$149$	13.9553	−	4.14745i	1.14326	−	0.339772i	0.800313	+	0.599582i	$0.204667\pi$
$150$	−3.81687	−	16.4009i	−0.311646	−	1.33913i
$151$	−3.89227	+	0.140612i	−0.316748	+	0.0114428i	−0.194020	−	0.980998i	$-0.562153\pi$
$151$	−3.89227	+	0.140612i	−0.316748	+	0.0114428i	−0.122728	+	0.992440i	$0.539164\pi$
$152$	0.0941566	+	0.177598i	0.00763711	+	0.0144051i
$153$	−1.16418	+	4.00400i	−0.0941184	+	0.323704i
$154$	−9.74851	+	2.14581i	−0.785557	+	0.172914i
$155$	−3.10424	+	3.16080i	−0.249338	+	0.253881i
$156$	−6.04016	−	19.4659i	−0.483600	−	1.55852i
$157$	1.34966	−	6.70608i	0.107715	−	0.535203i	−0.889255	−	0.457412i	$-0.848776\pi$
$157$	1.34966	−	6.70608i	0.107715	−	0.535203i	0.996970	−	0.0777911i	$-0.0247867\pi$
$158$	−2.33374	−	9.75954i	−0.185663	−	0.776428i
$159$	−1.23874	+	20.5424i	−0.0982382	+	1.62912i
$160$	−3.29362	+	2.14737i	−0.260384	+	0.169764i
$161$	−1.31419	−	8.01620i	−0.103573	−	0.631765i
$162$	5.12224	+	17.6347i	0.402441	+	1.38552i
$163$	−0.539152	−	1.35317i	−0.0422296	−	0.105988i	0.906349	−	0.422530i	$-0.138858\pi$
$163$	−0.539152	−	1.35317i	−0.0422296	−	0.105988i	−0.948579	+	0.316541i	$0.897478\pi$
$164$	14.7764	+	6.19888i	1.15384	+	0.484051i
$165$	−0.581768	−	0.693387i	−0.0452906	−	0.0539801i
$166$	−11.3295	−	9.27653i	−0.879342	−	0.719999i
$167$	−9.16811	+	12.5235i	−0.709450	+	0.969095i	0.290476	+	0.956882i	$0.406186\pi$
$167$	−9.16811	+	12.5235i	−0.709450	+	0.969095i	−0.999925	+	0.0122130i	$0.996112\pi$
$168$	2.61783	−	0.0786819i	0.201970	−	0.00607044i
$169$	−16.0629	+	4.14900i	−1.23561	+	0.319154i
$170$	−0.0744628	+	1.37339i	−0.00571104	+	0.105334i
$171$	−1.65243	+	0.740305i	−0.126365	+	0.0566125i
$172$	−13.5016	−	8.12366i	−1.02949	−	0.619423i
$173$	3.22963	+	0.589534i	0.245544	+	0.0448214i	0.300940	−	0.953643i	$-0.402700\pi$
$173$	3.22963	+	0.589534i	0.245544	+	0.0448214i	−0.0553959	+	0.998464i	$0.517642\pi$
$174$	−25.8155	−	21.4003i	−1.95707	−	1.62235i
$175$	1.95028	−	21.5449i	0.147428	−	1.62864i
$176$	1.96480	−	3.40314i	0.148103	−	0.256521i
$177$	−8.32947	−	10.3740i	−0.626081	−	0.779758i
$178$	9.10479	+	15.7700i	0.682433	+	1.18201i
$179$	−0.838558	+	0.387958i	−0.0626768	+	0.0289974i	−0.450977	−	0.892536i	$-0.648924\pi$
$179$	−0.838558	+	0.387958i	−0.0626768	+	0.0289974i	0.388300	+	0.921533i	$0.373062\pi$
$180$	1.54050	+	2.74455i	0.114822	+	0.204567i
$181$	−3.33596	+	3.92740i	−0.247960	+	0.291921i	−0.872035	−	0.489443i	$-0.837200\pi$
$181$	−3.33596	+	3.92740i	−0.247960	+	0.291921i	0.624075	+	0.781364i	$0.285476\pi$
$182$	0.909783	−	50.3837i	0.0674376	−	3.73469i
$183$	6.75181	−	6.79196i	0.499108	−	0.502076i
$184$	−0.499161	−	0.325441i	−0.0367986	−	0.0239919i
$185$	0.154729	+	0.157548i	0.0113759	+	0.0115832i
$186$	−15.2946	+	28.4307i	−1.12145	+	2.08464i
$187$	−0.604218	−	1.37039i	−0.0441848	−	0.100213i
$188$	−0.825057	+	5.03262i	−0.0601734	+	0.367042i
$189$	−0.854874	+	23.5759i	−0.0621829	+	1.71490i
$190$	−0.475468	+	0.361441i	−0.0344941	+	0.0262217i
$191$	11.3128	−	14.3369i	0.818566	−	1.03738i	−0.179990	−	0.983668i	$-0.557607\pi$
$191$	11.3128	−	14.3369i	0.818566	−	1.03738i	0.998556	−	0.0537146i	$-0.0171061\pi$
$192$	−10.4439	+	12.1454i	−0.753721	+	0.876522i
$193$	−14.0960	−	5.32354i	−1.01465	−	0.383196i	−0.210485	−	0.977597i	$-0.567504\pi$
$193$	−14.0960	−	5.32354i	−1.01465	−	0.383196i	−0.804169	+	0.594401i	$0.797389\pi$
$194$	34.8083	+	17.6566i	2.49909	+	1.26767i
$195$	4.08751	−	2.04234i	0.292713	−	0.146255i
$196$	28.2282	+	8.38929i	2.01630	+	0.599235i
$197$	−5.23805	+	1.76490i	−0.373195	+	0.125744i	−0.499648	−	0.866228i	$-0.666537\pi$
$197$	−5.23805	+	1.76490i	−0.373195	+	0.125744i	0.126453	+	0.991973i	$0.459641\pi$
$198$	−5.48104	−	3.66899i	−0.389520	−	0.260744i
$199$	−0.0748004	−	0.269407i	−0.00530246	−	0.0190977i	0.960851	−	0.277064i	$-0.0893614\pi$
$199$	−0.0748004	−	0.269407i	−0.00530246	−	0.0190977i	−0.966154	+	0.257966i	$0.916948\pi$
$200$	−1.07033	−	1.17159i	−0.0756837	−	0.0828442i
$201$	10.7254	−	7.46126i	0.756508	−	0.526277i
$202$	18.0808	+	0.653185i	1.27216	+	0.0459579i
$203$	−22.8721	−	36.5051i	−1.60530	−	2.56216i
$204$	1.18044	+	5.07229i	0.0826474	+	0.355131i
$205$	−0.835484	+	3.49393i	−0.0583528	+	0.244027i
$206$	25.0460	+	11.5875i	1.74504	+	0.807342i
$207$	3.22291	−	4.29226i	0.224008	−	0.298332i
$208$	14.4023	+	13.6426i	0.998620	+	0.945943i
$209$	0.283687	−	0.585215i	0.0196230	−	0.0404802i
$210$	1.48905	+	7.63779i	0.102754	+	0.527058i
$211$	4.14029	+	0.149572i	0.285029	+	0.0102970i	0.178248	−	0.983986i	$-0.442957\pi$
$211$	4.14029	+	0.149572i	0.285029	+	0.0102970i	0.106781	+	0.994283i	$0.465946\pi$
$212$	11.2117	+	23.1286i	0.770024	+	1.58848i
$213$	−5.36762	−	13.7129i	−0.367783	−	0.939595i
$214$	−16.5212	+	16.8223i	−1.12937	+	1.14995i
$215$	1.30755	−	3.28171i	0.0891744	−	0.223811i
$216$	1.23452	+	1.21276i	0.0839986	+	0.0825177i
$217$	−30.1102	+	28.5219i	−2.04401	+	1.93619i
$218$	−7.26412	−	22.9185i	−0.491988	−	1.55224i
$219$	0.780558	−	0.166858i	0.0527452	−	0.0112752i
$220$	−1.05753	−	0.399390i	−0.0712989	−	0.0269269i
$221$	7.43791	−	1.35771i	0.500328	−	0.0913294i
$222$	1.40312	+	0.787811i	0.0941713	+	0.0528744i
$223$	−20.5951	−	8.63990i	−1.37915	−	0.578570i	−0.432736	−	0.901521i	$-0.642452\pi$
$223$	−20.5951	−	8.63990i	−1.37915	−	0.578570i	−0.946416	+	0.322950i	$0.895325\pi$
$224$	−31.5394	+	18.9766i	−2.10732	+	1.26793i
$225$	11.1689	−	8.92102i	0.744596	−	0.594734i
$226$	5.53905	+	0.602408i	0.368452	+	0.0400716i
$227$	−0.580445	+	4.56816i	−0.0385255	+	0.303200i	0.961109	+	0.276169i	$0.0890649\pi$
$227$	−0.580445	+	4.56816i	−0.0385255	+	0.303200i	−0.999635	+	0.0270306i	$0.991395\pi$
$228$	−1.34688	+	1.81660i	−0.0891991	+	0.120307i
$229$	10.7480	+	7.00744i	0.710246	+	0.463065i	0.849770	−	0.527154i	$-0.176741\pi$
$229$	10.7480	+	7.00744i	0.710246	+	0.463065i	−0.139523	+	0.990219i	$0.544557\pi$
$230$	0.714273	−	1.62000i	0.0470977	−	0.106820i
$231$	−5.20841	−	6.68364i	−0.342688	−	0.439751i
$232$	−3.10866	−	0.567453i	−0.204094	−	0.0372551i
$233$	4.58155	+	1.54371i	0.300148	+	0.101131i	0.465346	−	0.885129i	$-0.345930\pi$
$233$	4.58155	+	1.54371i	0.300148	+	0.101131i	−0.165198	+	0.986260i	$0.552826\pi$
$234$	24.4496	−	22.6038i	1.59832	−	1.47765i
$235$	−1.14333			−0.0745826
$236$	−15.4142	−	6.20444i	−1.00338	−	0.403875i
$237$	6.62338	−	5.35642i	0.430235	−	0.347937i
$238$	−1.16082	+	12.8236i	−0.0752445	+	0.831232i
$239$	−5.73167	+	5.04947i	−0.370751	+	0.326623i	−0.825925	−	0.563779i	$-0.809347\pi$
$239$	−5.73167	+	5.04947i	−0.370751	+	0.326623i	0.455175	+	0.890402i	$0.349577\pi$
$240$	−2.61528	−	1.59524i	−0.168816	−	0.102972i
$241$	0.295122	−	16.3438i	0.0190105	−	1.05280i	−0.840541	−	0.541748i	$-0.817763\pi$
$241$	0.295122	−	16.3438i	0.0190105	−	1.05280i	0.859551	−	0.511049i	$-0.170743\pi$
$242$	−19.9577	+	2.17053i	−1.28293	+	0.139527i
$243$	−11.6369	+	10.3722i	−0.746507	+	0.665378i
$244$	3.19991	−	11.5250i	0.204853	−	0.737814i
$245$	−0.832189	+	6.54941i	−0.0531666	+	0.418426i
$246$	1.25876	+	26.1482i	0.0802556	+	1.66715i
$247$	2.54029	+	2.07997i	0.161635	+	0.132345i
$248$	0.0549272	+	3.04186i	0.00348788	+	0.193158i
$249$	2.96405	−	12.0714i	0.187839	−	0.764994i
$250$	5.98554	−	7.58558i	0.378559	−	0.479754i
$251$	−14.5147	−	17.0880i	−0.916160	−	1.07859i	−0.996646	−	0.0818316i	$-0.973923\pi$
$251$	−14.5147	−	17.0880i	−0.916160	−	1.07859i	0.0804858	−	0.996756i	$-0.474353\pi$
$252$	13.4846	+	26.1975i	0.849452	+	1.65029i
$253$	0.104373	+	1.92505i	0.00656189	+	0.121027i
$254$	6.22628	+	19.6441i	0.390671	+	1.23258i
$255$	−1.07937	+	0.445130i	−0.0675926	+	0.0278751i
$256$	2.58035	−	12.8210i	0.161272	−	0.801313i
$257$	14.6085	+	18.5136i	0.911252	+	1.15485i	0.987478	+	0.157755i	$0.0504256\pi$
$257$	14.6085	+	18.5136i	0.911252	+	1.15485i	−0.0762260	+	0.997091i	$0.524287\pi$
$258$	2.47617	−	25.6232i	0.154160	−	1.59523i
$259$	1.39433	+	1.52625i	0.0866394	+	0.0948364i
$260$	3.20260	−	4.72348i	0.198617	−	0.292938i
$261$	6.95521	−	27.6020i	0.430517	−	1.70852i
$262$	9.02794	−	17.0285i	0.557748	−	1.05202i
$263$	0.645683	−	1.33198i	0.0398145	−	0.0821331i	−0.879002	−	0.476818i	$-0.841790\pi$
$263$	0.645683	−	1.33198i	0.0398145	−	0.0821331i	0.918816	+	0.394685i	$0.129146\pi$
$264$	−0.619665	−	0.0486090i	−0.0381377	−	0.00299168i
$265$	−4.71026	+	3.31933i	−0.289349	+	0.203905i
$266$	−4.57042	+	3.22078i	−0.280231	+	0.197479i
$267$	−8.75209	+	12.7414i	−0.535619	+	0.779758i
$268$	7.11794	−	14.6836i	0.434797	−	0.896941i
$269$	−8.97555	+	16.9297i	−0.547249	+	1.03222i	0.443469	+	0.896290i	$0.353748\pi$
$269$	−8.97555	+	16.9297i	−0.547249	+	1.03222i	−0.990718	+	0.135932i	$0.956597\pi$
$270$	−2.96245	+	4.20264i	−0.180289	+	0.255765i
$271$	12.4596	−	18.3765i	0.756867	−	1.11630i	−0.232746	−	0.972538i	$-0.574771\pi$
$271$	12.4596	−	18.3765i	0.756867	−	1.11630i	0.989613	−	0.143758i	$-0.0459186\pi$
$272$	−3.41892	−	3.74238i	−0.207302	−	0.226915i
$273$	38.9312	−	17.7257i	2.35622	−	1.07281i
$274$	16.2840	+	20.6370i	0.983753	+	1.24673i
$275$	−1.01299	+	5.03323i	−0.0610854	+	0.303515i
$276$	0.885311	−	6.64503i	0.0532895	−	0.399984i
$277$	−0.371682	−	1.17267i	−0.0223322	−	0.0704588i	0.941446	−	0.337163i	$-0.109467\pi$
$277$	−0.371682	−	1.17267i	−0.0223322	−	0.0704588i	−0.963778	+	0.266705i	$0.914065\pi$
$278$	−2.07488	−	38.2689i	−0.124443	−	2.29522i
$279$	−27.3730	−	1.32140i	−1.63878	−	0.0791103i
$280$	0.474744	+	0.558912i	0.0283714	+	0.0334014i
$281$	14.3644	−	18.2042i	0.856908	−	1.08597i	−0.138511	−	0.990361i	$-0.544232\pi$
$281$	14.3644	−	18.2042i	0.856908	−	1.08597i	0.995419	−	0.0956130i	$-0.0304811\pi$
$282$	−8.00059	+	2.32504i	−0.476428	+	0.138454i
$283$	0.152128	+	8.42483i	0.00904307	+	0.500804i	0.972495	+	0.232923i	$0.0748291\pi$
$283$	0.152128	+	8.42483i	0.00904307	+	0.500804i	−0.963452	+	0.267881i	$0.913677\pi$
$284$	−14.2303	−	11.6517i	−0.844413	−	0.691399i
$285$	−0.450751	−	0.232092i	−0.0267002	−	0.0137479i
$286$	−1.50749	+	11.8641i	−0.0891399	+	0.701540i
$287$	−8.99729	+	32.4053i	−0.531093	+	1.91283i
$288$	−23.4733	−	6.36769i	−1.38318	−	0.375219i
$289$	14.9797	−	1.62915i	0.881162	−	0.0958321i
$290$	0.169512	−	9.38754i	0.00995407	−	0.551255i
$291$	−0.799012	+	33.1225i	−0.0468389	+	1.94168i
$292$	0.748019	−	0.658988i	0.0437745	−	0.0385643i
$293$	0.0336555	−	0.371794i	0.00196617	−	0.0217205i	−0.994886	−	0.101008i	$-0.967793\pi$
$293$	0.0336555	−	0.371794i	0.00196617	−	0.0217205i	0.996852	+	0.0792875i	$0.0252645\pi$
$294$	7.49534	+	47.5226i	0.437137	+	2.77157i
$295$	0.813582	−	3.63524i	0.0473685	−	0.211652i
$296$	0.151645			0.00881417
$297$	0.806653	−	5.54054i	0.0468068	−	0.321495i
$298$	28.1502	+	9.48492i	1.63070	+	0.549447i
$299$	−9.57439	−	1.74770i	−0.553701	−	0.101072i
$300$	6.70845	−	16.5445i	0.387312	−	0.955197i
$301$	13.3420	−	30.2603i	0.769022	−	1.74418i
$302$	−6.65705	−	4.34025i	−0.383070	−	0.249753i
$303$	6.11080	+	14.0904i	0.351056	+	0.809470i
$304$	0.277453	−	2.18358i	0.0159130	−	0.125237i
$305$	2.66583	+	0.289927i	0.152645	+	0.0166011i
$306$	−6.64779	+	5.30982i	−0.380029	+	0.303542i
$307$	7.64733	−	4.60125i	0.436456	−	0.262607i	−0.280325	−	0.959905i	$-0.590442\pi$
$307$	7.64733	−	4.60125i	0.436456	−	0.262607i	0.716781	+	0.697298i	$0.245615\pi$
$308$	−9.75882	−	4.09394i	−0.556060	−	0.233274i
$309$	0.280920	+	23.4245i	0.0159810	+	1.33257i
$310$	−8.89250	+	1.62323i	−0.505060	+	0.0921932i
$311$	−3.50826	−	1.32494i	−0.198935	−	0.0751302i	0.251836	−	0.967770i	$-0.418966\pi$
$311$	−3.50826	−	1.32494i	−0.198935	−	0.0751302i	−0.450771	+	0.892640i	$0.648851\pi$
$312$	0.966202	−	2.98543i	0.0547004	−	0.169017i
$313$	−7.75722	−	24.4743i	−0.438464	−	1.38337i	−0.875192	−	0.483775i	$-0.839265\pi$
$313$	−7.75722	−	24.4743i	−0.438464	−	1.38337i	0.436729	−	0.899593i	$-0.356137\pi$
$314$	10.1330	−	9.59852i	0.571840	−	0.541676i
$315$	−5.30678	+	3.93349i	−0.299003	+	0.221627i
$316$	3.93781	−	9.88316i	0.221519	−	0.555971i
$317$	−12.2521	+	12.4754i	−0.688148	+	0.700686i	−0.965594	−	0.260055i	$-0.916259\pi$
$317$	−12.2521	+	12.4754i	−0.688148	+	0.700686i	0.277446	+	0.960741i	$0.410512\pi$
$318$	−26.2105	+	32.8060i	−1.46981	+	1.83967i
$319$	4.45968	+	9.19985i	0.249694	+	0.515093i
$320$	−4.48222	−	0.161924i	−0.250563	−	0.00905185i
$321$	−18.9283	−	6.50576i	−1.05648	−	0.363116i
$322$	7.22994	−	14.9146i	0.402909	−	0.831158i
$323$	−0.609048	−	0.576921i	−0.0338883	−	0.0321007i
$324$	−6.33071	+	18.4110i	−0.351706	+	1.02283i
$325$	−23.5234	−	10.8831i	−1.30485	−	0.603686i
$326$	0.691212	−	2.89060i	0.0382827	−	0.160095i
$327$	14.9016	−	13.9451i	0.824060	−	0.771166i
$328$	1.30984	+	2.09058i	0.0723238	+	0.115433i
$329$	−10.6965	−	0.386421i	−0.589716	−	0.0213041i
$330$	−0.155340	−	1.84026i	−0.00855119	−	0.101303i
$331$	−4.38074	−	4.79520i	−0.240787	−	0.263568i	0.606043	−	0.795432i	$-0.292756\pi$
$331$	−4.38074	−	4.79520i	−0.240787	−	0.263568i	−0.846830	+	0.531864i	$0.821492\pi$
$332$	−4.15319	−	14.9584i	−0.227936	−	0.820951i
$333$	−0.0904869	+	1.36298i	−0.00495865	+	0.0746909i
$334$	−30.0106	+	10.1118i	−1.64211	+	0.553291i
$335$	3.50672	+	1.04218i	0.191593	+	0.0569405i
$336$	−23.9282	−	15.8082i	−1.30539	−	0.862411i
$337$	−14.6131	−	7.41254i	−0.796025	−	0.403787i	0.00681772	−	0.999977i	$-0.497830\pi$
$337$	−14.6131	−	7.41254i	−0.796025	−	0.403787i	−0.802843	+	0.596190i	$0.796680\pi$
$338$	−31.6674	−	11.9596i	−1.72248	−	0.650515i
$339$	1.56384	+	4.46369i	0.0849363	+	0.242435i
$340$	−0.903279	+	1.14474i	−0.0489872	+	0.0620823i
$341$	7.83601	−	5.95678i	0.424344	−	0.322578i
$342$	−3.62616	−	0.707456i	−0.196080	−	0.0382548i
$343$	−4.85751	+	29.6295i	−0.262281	+	1.59984i
$344$	−0.978708	−	2.21975i	−0.0527684	−	0.119681i
$345$	1.50224	−	0.0451516i	0.0808780	−	0.00243088i
$346$	4.69369	+	4.77920i	0.252334	+	0.256932i
$347$	18.0969	+	11.7988i	0.971491	+	0.633390i	0.930702	−	0.365778i	$-0.119197\pi$
$347$	18.0969	+	11.7988i	0.971491	+	0.633390i	0.0407885	+	0.999168i	$0.487013\pi$
$348$	−9.30299	−	34.3121i	−0.498693	−	1.83932i
$349$	−0.0995123	+	5.51098i	−0.00532677	+	0.294996i	0.986234	+	0.165355i	$0.0528769\pi$
$349$	−0.0995123	+	5.51098i	−0.00532677	+	0.294996i	−0.991561	+	0.129641i	$0.958617\pi$
$350$	28.5756	−	33.6418i	1.52743	−	1.79823i
$351$	26.2565	+	10.4656i	1.40147	+	0.558614i
$352$	7.92830	−	3.66802i	0.422580	−	0.195506i
$353$	10.0180	+	17.3518i	0.533207	+	0.923542i	0.999248	+	0.0387784i	$0.0123466\pi$
$353$	10.0180	+	17.3518i	0.533207	+	0.923542i	−0.466041	+	0.884763i	$0.654320\pi$
$354$	−1.69938	−	27.0925i	−0.0903211	−	1.43995i
$355$	2.06165	−	3.57088i	0.109421	−	0.189523i
$356$	−1.74047	+	19.2271i	−0.0922449	+	1.01904i
$357$	−10.2485	+	3.79964i	−0.542409	+	0.201098i
$358$	−1.85459	−	0.338535i	−0.0980181	−	0.0178921i
$359$	−27.1610	−	16.3422i	−1.43350	−	0.862509i	−0.434234	−	0.900800i	$-0.642981\pi$
$359$	−27.1610	−	16.3422i	−1.43350	−	0.862509i	−0.999267	+	0.0382911i	$0.987809\pi$
$360$	−0.0495329	+	0.482019i	−0.00261061	+	0.0254046i
$361$	−1.00892	+	18.6084i	−0.0531009	+	0.979388i
$362$	−10.1800	+	2.62946i	−0.535049	+	0.138201i
$363$	−8.96032	−	14.4958i	−0.470295	−	0.760831i
$364$	31.5585	−	43.1084i	1.65412	−	2.25949i
$365$	0.172924	+	0.141588i	0.00905123	+	0.00741108i
$366$	19.2440	−	3.39236i	1.00590	−	0.177321i
$367$	14.4834	+	6.07595i	0.756027	+	0.317162i	0.730866	−	0.682521i	$-0.239117\pi$
$367$	14.4834	+	6.07595i	0.756027	+	0.317162i	0.0251611	+	0.999683i	$0.491990\pi$
$368$	2.41515	+	6.06156i	0.125898	+	0.315981i
$369$	−19.5717	+	10.5254i	−1.01886	+	0.547929i
$370$	0.0728935	+	0.444631i	0.00378955	+	0.0231152i
$371$	−45.1890	+	29.4622i	−2.34609	+	1.52960i
$372$	−30.6178	+	15.2983i	−1.58746	+	0.793179i
$373$	7.21795	+	30.1850i	0.373731	+	1.56292i	0.765860	+	0.643007i	$0.222314\pi$
$373$	7.21795	+	30.1850i	0.373731	+	1.56292i	−0.392129	+	0.919910i	$0.628261\pi$
$374$	0.602933	−	2.99580i	0.0311769	−	0.154909i
$375$	7.99985	+	1.81182i	0.413110	+	0.0935621i
$376$	−0.550154	+	0.560178i	−0.0283720	+	0.0288890i
$377$	−50.4065	+	11.0953i	−2.59607	+	0.571438i
$378$	−29.1358	+	38.3168i	−1.49858	+	1.97080i
$379$	−2.73245	−	5.15395i	−0.140357	−	0.264741i	0.803361	−	0.595492i	$-0.203043\pi$
$379$	−2.73245	−	5.15395i	−0.140357	−	0.264741i	−0.943718	+	0.330751i	$0.892698\pi$
$380$	−0.632792	+	0.0228602i	−0.0324615	+	0.00117270i
$381$	−12.7726	+	11.9527i	−0.654359	+	0.612357i
$382$	35.7191	−	10.6156i	1.82755	−	0.543140i
$383$	21.7174	−	15.3043i	1.10971	−	0.782012i	0.131846	−	0.991270i	$-0.457910\pi$
$383$	21.7174	−	15.3043i	1.10971	−	0.782012i	0.977860	+	0.209258i	$0.0671049\pi$
$384$	−4.46018	+	1.12325i	−0.227608	+	0.0573205i
$385$	0.551780	−	2.30751i	0.0281213	−	0.117601i
$386$	−17.2533	−	25.4467i	−0.878169	−	1.29520i
$387$	20.5351	−	7.47209i	1.04386	−	0.379828i
$388$	19.3827	+	36.5597i	0.984010	+	1.85604i
$389$	−1.18544	−	0.0857625i	−0.0601044	−	0.00434833i	0.0420728	−	0.999115i	$-0.486604\pi$
$389$	−1.18544	−	0.0857625i	−0.0601044	−	0.00434833i	−0.102177	+	0.994766i	$0.532581\pi$
$390$	9.21789	+	1.39790i	0.466766	+	0.0707855i
$391$	2.40783	+	0.621934i	0.121769	+	0.0314526i
$392$	2.80846	+	3.55921i	0.141849	+	0.179767i
$393$	16.3464	+	0.689794i	0.824569	+	0.0347955i
$394$	−10.8107	−	3.21291i	−0.544637	−	0.161864i
$395$	2.32935	+	0.512729i	0.117202	+	0.0257982i
$396$	−2.50932	−	6.52701i	−0.126098	−	0.327994i
$397$	2.54648	+	15.5328i	0.127804	+	0.779571i	0.970486	+	0.241159i	$0.0775274\pi$
$397$	2.54648	+	15.5328i	0.127804	+	0.779571i	−0.842682	+	0.538412i	$0.819024\pi$
$398$	0.191890	−	0.537251i	0.00961856	−	0.0269300i
$399$	−4.13858	−	2.32369i	−0.207188	−	0.116330i
$400$	2.19034	+	17.2382i	0.109517	+	0.861909i
$401$	0.356953	+	19.7680i	0.0178254	+	0.987167i	0.878424	+	0.477882i	$0.158596\pi$
$401$	0.356953	+	19.7680i	0.0178254	+	0.987167i	−0.860598	+	0.509284i	$0.829910\pi$
$402$	26.6580	+	0.161633i	1.32958	+	0.00806154i
$403$	20.0472	+	45.4679i	0.998622	+	2.26492i
$404$	15.2704	+	11.6083i	0.759731	+	0.577533i
$405$	−4.30282	−	0.732823i	−0.213809	−	0.0364143i
$406$	4.75866	−	87.7683i	0.236168	−	4.35587i
$407$	−0.289813	−	0.395879i	−0.0143655	−	0.0196230i
$408$	−0.301283	+	0.743029i	−0.0149157	+	0.0367854i
$409$	−11.0754	−	31.0087i	−0.547641	−	1.53328i	−0.820744	−	0.571297i	$-0.806441\pi$
$409$	−11.0754	−	31.0087i	−0.547641	−	1.53328i	0.273102	−	0.961985i	$-0.411950\pi$
$410$	−5.50007	+	4.84543i	−0.271629	+	0.239299i
$411$	−9.85562	+	20.0209i	−0.486142	+	0.987559i
$412$	14.6290	+	25.3381i	0.720717	+	1.24832i
$413$	8.84014	−	33.7347i	0.434995	−	1.65998i
$414$	10.4203	−	3.37087i	0.512129	−	0.165669i
$415$	3.15873	−	1.46138i	0.155056	−	0.0717366i
$416$	8.70123	+	43.2338i	0.426613	+	2.11971i
$417$	28.5588	−	15.5825i	1.39853	−	0.763078i
$418$	1.16098	−	0.642630i	0.0567856	−	0.0314321i
$419$	−4.81563	+	10.9221i	−0.235259	+	0.533578i	−0.992880	−	0.119117i	$-0.961994\pi$
$419$	−4.81563	+	10.9221i	−0.235259	+	0.533578i	0.757621	+	0.652694i	$0.226361\pi$
$420$	−3.37406	+	7.52852i	−0.164637	+	0.367354i
$421$	2.63682	−	0.681083i	0.128511	−	0.0331939i	−0.185282	−	0.982685i	$-0.559320\pi$
$421$	2.63682	−	0.681083i	0.128511	−	0.0331939i	0.313793	+	0.949491i	$0.398400\pi$
$422$	6.72966	+	5.11575i	0.327595	+	0.249031i
$423$	−4.70659	−	5.27904i	−0.228842	−	0.256676i
$424$	−0.640195	+	3.90502i	−0.0310906	+	0.189644i
$425$	5.79434	+	3.20730i	0.281067	+	0.155577i
$426$	7.16500	−	29.1802i	0.347145	−	1.41378i
$427$	24.8423	+	3.61342i	1.20220	+	0.174865i
$428$	−24.5914	+	4.48889i	−1.18867	+	0.216979i
$429$	−9.64021	+	3.18321i	−0.465434	+	0.153687i
$430$	6.03798	−	3.93663i	0.291177	−	0.189841i
$431$	21.0171	+	4.62622i	1.01236	+	0.222837i	0.690023	−	0.723787i	$-0.257600\pi$
$431$	21.0171	+	4.62622i	1.01236	+	0.222837i	0.322337	+	0.946625i	$0.395531\pi$
$432$	−3.40036	−	18.6423i	−0.163600	−	0.896928i
$433$	4.77127	−	1.60763i	0.229292	−	0.0772576i	−0.202310	−	0.979322i	$-0.564845\pi$
$433$	4.77127	−	1.60763i	0.229292	−	0.0772576i	0.431602	+	0.902064i	$0.357948\pi$
$434$	−83.7429	+	12.1807i	−4.01979	+	0.584694i
$435$	7.25370	−	3.30267i	0.347788	−	0.158351i
$436$	7.70140	−	24.2982i	0.368830	−	1.16367i
$437$	0.471053	+	0.971731i	0.0225335	+	0.0464842i
$438$	1.49798	+	0.639130i	0.0715764	+	0.0305388i
$439$	−6.03428	+	0.217994i	−0.288000	+	0.0104043i	−0.179726	−	0.983717i	$-0.557521\pi$
$439$	−6.03428	+	0.217994i	−0.288000	+	0.0104043i	−0.108274	+	0.994121i	$0.534533\pi$
$440$	−0.0976689	−	0.144051i	−0.00465618	−	0.00686735i
$441$	−33.6660	+	23.1186i	−1.60314	+	1.10089i
$442$	14.0012	+	6.47766i	0.665971	+	0.308111i
$443$	3.78040	+	41.7624i	0.179612	+	1.98419i	0.177089	+	0.984195i	$0.443332\pi$
$443$	3.78040	+	41.7624i	0.179612	+	1.98419i	0.00252330	+	0.999997i	$0.499197\pi$
$444$	0.734858	+	1.53965i	0.0348748	+	0.0730684i
$445$	−4.31689	+	0.312311i	−0.204640	+	0.0148050i
$446$	−24.1950	−	38.6167i	−1.14567	−	1.82855i
$447$	3.02676	+	25.0338i	0.143161	+	1.18406i
$448$	−41.8789	−	3.02978i	−1.97859	−	0.143144i
$449$	−39.9887	+	8.80218i	−1.88718	+	0.415400i	−0.999025	−	0.0441379i	$-0.985946\pi$
$449$	−39.9887	+	8.80218i	−1.88718	+	0.415400i	−0.888158	+	0.459538i	$0.848015\pi$
$450$	29.1136	−	1.75167i	1.37243	−	0.0825745i
$451$	2.95432	−	7.41479i	0.139114	−	0.349149i
$452$	4.43241	+	3.90485i	0.208483	+	0.183669i
$453$	0.890891	−	6.68692i	0.0418577	−	0.314179i
$454$	−6.33729	+	6.93686i	−0.297424	+	0.325563i
$455$	10.6818	+	5.41839i	0.500772	+	0.254018i
$456$	−0.330609	+	0.109168i	−0.0154822	+	0.00511224i
$457$	8.79114	−	24.6134i	0.411232	−	1.15137i	−0.539671	−	0.841876i	$-0.681451\pi$
$457$	8.79114	−	24.6134i	0.411232	−	1.15137i	0.950903	−	0.309489i	$-0.100158\pi$
$458$	9.69001	+	24.3201i	0.452785	+	1.13640i
$459$	−6.49856	−	3.15129i	−0.303327	−	0.147090i
$460$	1.60837	−	0.967723i	0.0749906	−	0.0451203i
$461$	33.2826	−	12.5696i	1.55013	−	0.585424i	0.577213	−	0.816594i	$-0.304140\pi$
$461$	33.2826	−	12.5696i	1.55013	−	0.585424i	0.972913	+	0.231170i	$0.0742554\pi$
$462$	−0.831325	−	17.2691i	−0.0386767	−	0.803432i
$463$	7.59588	−	3.18656i	0.353011	−	0.148092i	−0.203192	−	0.979139i	$-0.565131\pi$
$463$	7.59588	−	3.18656i	0.353011	−	0.148092i	0.556202	+	0.831047i	$0.312258\pi$
$464$	24.2460	+	24.6878i	1.12559	+	1.14610i
$465$	−4.49507	−	6.21894i	−0.208454	−	0.288396i
$466$	5.82703	+	7.95962i	0.269932	+	0.368722i
$467$	5.60304	+	3.37124i	0.259278	+	0.156002i	0.639258	−	0.768992i	$-0.279242\pi$
$467$	5.60304	+	3.37124i	0.259278	+	0.156002i	−0.379980	+	0.924995i	$0.624069\pi$
$468$	34.9932	−	4.65733i	1.61756	−	0.215285i
$469$	32.4551	+	10.9354i	1.49864	+	0.504949i
$470$	−1.90692	−	1.34381i	−0.0879598	−	0.0619854i
$471$	11.0585	+	4.25316i	0.509547	+	0.195975i
$472$	−1.38961	−	2.14784i	−0.0639621	−	0.0988624i
$473$	−3.92437	+	6.79722i	−0.180443	+	0.312536i
$474$	17.3426	−	1.14902i	0.796571	−	0.0527761i
$475$	0.567416	+	2.81932i	0.0260348	+	0.129359i
$476$	−8.83757	+	10.4044i	−0.405069	+	0.476885i
$477$	−34.7163	−	8.08421i	−1.58955	−	0.370150i
$478$	−15.4945	+	1.68513i	−0.708704	+	0.0770762i
$479$	−15.1999	+	7.71020i	−0.694501	+	0.352288i	−0.763930	−	0.645299i	$-0.776733\pi$
$479$	−15.1999	+	7.71020i	−0.694501	+	0.352288i	0.0694292	+	0.997587i	$0.477882\pi$
$480$	−2.70960	−	6.24784i	−0.123676	−	0.285173i
$481$	2.28399	−	0.958163i	0.104141	−	0.0436885i
$482$	19.7019	−	26.9124i	0.897397	−	1.22583i
$483$	14.0696	+	0.0853067i	0.640187	+	0.00388159i
$484$	−18.6215	−	10.3074i	−0.846432	−	0.468519i
$485$	−7.38538	+	5.61422i	−0.335353	+	0.254928i
$486$	−31.5998	+	3.62207i	−1.43339	+	0.164301i
$487$	6.60061	+	7.77084i	0.299102	+	0.352130i	0.891098	−	0.453811i	$-0.149936\pi$
$487$	6.60061	+	7.77084i	0.299102	+	0.352130i	−0.591996	+	0.805941i	$0.701660\pi$
$488$	1.42481	−	1.16662i	0.0644981	−	0.0528105i
$489$	2.46720	−	0.527410i	0.111571	−	0.0238503i
$490$	−9.08582	+	9.94543i	−0.410455	+	0.449289i
$491$	1.74511	+	7.29794i	0.0787559	+	0.329352i	0.997916	−	0.0645337i	$-0.0205560\pi$
$491$	1.74511	+	7.29794i	0.0787559	+	0.329352i	−0.919160	+	0.393885i	$0.871131\pi$
$492$	−14.8782	+	23.4296i	−0.670763	+	1.05629i
$493$	13.0508	−	1.89829i	0.587777	−	0.0854946i
$494$	1.79218	+	6.45483i	0.0806338	+	0.290417i
$495$	1.35301	−	0.791891i	0.0608131	−	0.0355929i
$496$	18.6956	−	27.5739i	0.839456	−	1.23810i
$497$	20.4948	−	32.7108i	0.919316	−	1.46728i
$498$	19.1318	−	16.6497i	0.857315	−	0.746091i
$499$	−16.2755	+	1.17748i	−0.728593	+	0.0527110i	−0.431469	−	0.902128i	$-0.642005\pi$
$499$	−16.2755	+	1.17748i	−0.728593	+	0.0527110i	−0.297124	+	0.954839i	$0.596028\pi$
$500$	9.81987	−	2.91842i	0.439158	−	0.130516i
$501$	−18.7199	−	19.2936i	−0.836342	−	0.861973i
$502$	−4.12421	−	45.5604i	−0.184072	−	2.03346i
$503$	−9.52464	−	9.02222i	−0.424683	−	0.402281i	0.445285	−	0.895389i	$-0.353102\pi$
$503$	−9.52464	−	9.02222i	−0.424683	−	0.402281i	−0.869968	+	0.493108i	$0.835861\pi$
$504$	−0.626320	+	4.49281i	−0.0278985	+	0.200126i
$505$	−2.01433	+	3.79942i	−0.0896363	+	0.169072i
$506$	−2.08853	+	3.33341i	−0.0928464	+	0.148188i
$507$	−2.41698	−	28.6331i	−0.107342	−	1.27164i
$508$	−6.60108	+	20.8266i	−0.292876	+	0.924033i
$509$	10.6164	+	2.74219i	0.470565	+	0.121545i	0.477875	−	0.878428i	$-0.341407\pi$
$509$	10.6164	+	2.74219i	0.470565	+	0.121545i	−0.00730983	+	0.999973i	$0.502327\pi$
$510$	−2.32342	−	0.526214i	−0.102883	−	0.0233011i
$511$	1.56994	+	1.38308i	0.0694501	+	0.0611840i
$512$	23.2286	−	22.0033i	1.02657	−	0.972417i
$513$	−0.783921	−	3.03665i	−0.0346110	−	0.134071i
$514$	2.60510	+	48.0483i	0.114906	+	2.11932i
$515$	−5.07515	+	4.15549i	−0.223638	+	0.183113i
$516$	17.7944	−	20.6936i	0.783354	−	0.910983i
$517$	2.51380	+	0.365642i	0.110557	+	0.0160809i
$518$	0.531683	+	4.18440i	0.0233608	+	0.183852i
$519$	−1.94507	+	5.34330i	−0.0853792	+	0.234545i
$520$	0.821948	−	0.310419i	0.0360448	−	0.0136128i
$521$	4.92929	+	0.536093i	0.215956	+	0.0234866i	0.215457	−	0.976513i	$-0.430876\pi$
$521$	4.92929	+	0.536093i	0.215956	+	0.0234866i	0.000498693		1.00000i	$0.499841\pi$
$522$	44.0424	−	37.8617i	1.92768	−	1.65716i
$523$	−3.89022	+	14.0113i	−0.170108	+	0.612672i	0.828503	+	0.559984i	$0.189193\pi$
$523$	−3.89022	+	14.0113i	−0.170108	+	0.612672i	−0.998611	+	0.0526881i	$0.983221\pi$
$524$	18.2234	−	9.24390i	0.796095	−	0.403822i
$525$	36.2213	+	9.59048i	1.58083	+	0.418563i
$526$	2.64245	−	1.46266i	0.115216	−	0.0637748i
$527$	−4.27075	−	11.9572i	−0.186037	−	0.520864i
$528$	5.23995	+	4.34377i	0.228040	+	0.189038i
$529$	16.1840	+	11.4049i	0.703652	+	0.495865i
$530$	−11.7575			−0.510711
$531$	20.1340	−	11.2082i	0.873739	−	0.486394i
$532$	−5.92784			−0.257005
$533$	32.9374	+	23.2110i	1.42668	+	1.00538i
$534$	−29.5729	+	10.9641i	−1.27974	+	0.474465i
$535$	−1.88504	−	5.27773i	−0.0814975	−	0.228176i
$536$	2.19800	−	1.21664i	0.0949393	−	0.0525511i
$537$	−0.418778	−	1.54457i	−0.0180716	−	0.0666531i
$538$	−34.8683	+	17.6871i	−1.50328	+	0.762544i
$539$	3.92423	−	14.1338i	0.169029	−	0.608786i
$540$	−5.13396	+	1.83292i	−0.220931	+	0.0788762i
$541$	23.2485	+	2.52843i	0.999532	+	0.108706i	0.593230	−	0.805033i	$-0.297853\pi$
$541$	23.2485	+	2.52843i	0.999532	+	0.108706i	0.406302	+	0.913739i	$0.366818\pi$
$542$	42.3798	−	16.0053i	1.82037	−	0.687484i
$543$	−5.73670	−	6.83736i	−0.246185	−	0.293419i
$544$	−1.42040	−	11.1787i	−0.0608990	−	0.479281i
$545$	5.65500	+	0.822543i	0.242234	+	0.0352339i
$546$	85.7660	+	16.1936i	3.67045	+	0.693022i
$547$	−25.0143	+	20.4815i	−1.06954	+	0.875727i	−0.992615	−	0.121310i	$-0.961290\pi$
$547$	−25.0143	+	20.4815i	−1.06954	+	0.875727i	−0.0769207	+	0.997037i	$0.524509\pi$
$548$	1.50887	+	27.8295i	0.0644558	+	1.18882i
$549$	9.63540	+	13.5023i	0.411229	+	0.576264i
$550$	−7.60533	+	7.20415i	−0.324292	+	0.307186i
$551$	4.29708	+	3.78563i	0.183062	+	0.161273i
$552$	0.700735	−	0.757754i	0.0298253	−	0.0322521i
$553$	21.6191	+	5.58413i	0.919336	+	0.237461i
$554$	0.758378	−	2.39271i	0.0322204	−	0.101657i
$555$	−0.313974	+	0.218421i	−0.0133275	+	0.00927147i
$556$	21.5732	−	34.4321i	0.914909	−	1.46025i
$557$	0.0130962	−	0.0247021i	0.000554906	−	0.00104666i	−0.883234	−	0.468932i	$-0.844639\pi$
$557$	0.0130962	−	0.0247021i	0.000554906	−	0.00104666i	0.883789	+	0.467885i	$0.154984\pi$
$558$	−44.1014	−	34.3767i	−1.86696	−	1.45528i
$559$	−28.7662	−	27.2488i	−1.21668	−	1.15250i
$560$	−0.723932	−	7.99733i	−0.0305917	−	0.337949i
$561$	2.51552	−	0.633505i	0.106205	−	0.0267466i
$562$	45.3542	−	13.4791i	1.91315	−	0.568581i
$563$	8.98454	−	0.649999i	0.378653	−	0.0273942i	0.118481	−	0.992956i	$-0.462198\pi$
$563$	8.98454	−	0.649999i	0.378653	−	0.0273942i	0.260172	+	0.965562i	$0.416221\pi$
$564$	−8.35348	−	2.87113i	−0.351745	−	0.120896i
$565$	−0.703136	+	1.12224i	−0.0295811	+	0.0472132i
$566$	−9.64838	+	14.2303i	−0.405552	+	0.598144i
$567$	−40.0076	−	8.31023i	−1.68016	−	0.348997i
$568$	−0.757528	−	2.72837i	−0.0317852	−	0.114480i
$569$	−6.10785	+	0.888411i	−0.256054	+	0.0372441i	−0.270757	−	0.962648i	$-0.587274\pi$
$569$	−6.10785	+	0.888411i	−0.256054	+	0.0372441i	0.0147024	+	0.999892i	$0.495320\pi$
$570$	−0.479004	−	0.916888i	−0.0200633	−	0.0384042i
$571$	−5.07523	−	21.2243i	−0.212392	−	0.888208i	−0.971461	−	0.237198i	$-0.923771\pi$
$571$	−5.07523	−	21.2243i	−0.212392	−	0.888208i	0.759069	−	0.651010i	$-0.225654\pi$
$572$	−8.55203	+	9.36114i	−0.357578	+	0.391409i
$573$	21.1931	+	23.4826i	0.885356	+	0.980999i
$574$	−53.0938	+	43.4728i	−2.21609	+	1.81452i
$575$	−5.51904	−	6.49751i	−0.230160	−	0.270965i
$576$	−17.7037	−	21.3621i	−0.737654	−	0.890086i
$577$	5.52238	−	4.19801i	0.229900	−	0.174765i	−0.483882	−	0.875133i	$-0.660774\pi$
$577$	5.52238	−	4.19801i	0.229900	−	0.174765i	0.713782	+	0.700368i	$0.246981\pi$
$578$	26.8990	+	14.8892i	1.11885	+	0.619310i
$579$	13.1859	−	22.5221i	0.547986	−	0.935988i
$580$	5.88001	−	8.03199i	0.244154	−	0.333510i
$581$	30.0456	−	12.6045i	1.24650	−	0.522922i
$582$	−40.2631	+	54.3048i	−1.66896	+	2.25101i
$583$	11.4178	−	5.79172i	0.472877	−	0.239869i
$584$	0.152580	−	0.0165941i	0.00631381	−	0.000686668i
$585$	2.29958	+	7.57289i	0.0950760	+	0.313101i
$586$	0.493121	−	0.580547i	0.0203706	−	0.0239822i
$587$	−4.13981	−	20.5695i	−0.170868	−	0.848993i	−0.969105	−	0.246649i	$-0.920670\pi$
$587$	−4.13981	−	20.5695i	−0.170868	−	0.848993i	0.798237	−	0.602344i	$-0.205766\pi$
$588$	−22.5271	+	45.7620i	−0.929000	+	1.88719i
$589$	2.75676	−	4.77485i	0.113590	−	0.196744i
$590$	5.62962	−	5.10686i	0.231768	−	0.210246i
$591$	−1.49154	−	9.45682i	−0.0613540	−	0.389001i
$592$	−1.35736	−	0.956533i	−0.0557871	−	0.0393132i
$593$	−27.4576	−	9.25155i	−1.12755	−	0.379915i	−0.307124	−	0.951670i	$-0.599367\pi$
$593$	−27.4576	−	9.25155i	−1.12755	−	0.379915i	−0.820425	+	0.571754i	$0.806263\pi$
$594$	7.85745	−	8.29278i	0.322395	−	0.340257i
$595$	−2.62238	−	1.57784i	−0.107507	−	0.0646849i
$596$	18.6032	+	25.4117i	0.762019	+	1.04090i
$597$	0.481748	−	0.0494397i	0.0197166	−	0.00202343i
$598$	−13.9147	−	14.1682i	−0.569013	−	0.579380i
$599$	43.8291	−	18.3868i	1.79081	−	0.751266i	0.802925	−	0.596080i	$-0.203276\pi$
$599$	43.8291	−	18.3868i	1.79081	−	0.751266i	0.987885	−	0.155186i	$-0.0495975\pi$
$600$	2.31151	−	1.48716i	0.0943670	−	0.0607130i
$601$	−31.0248	+	11.7169i	−1.26553	+	0.477943i	−0.892991	−	0.450074i	$-0.851398\pi$
$601$	−31.0248	+	11.7169i	−1.26553	+	0.477943i	−0.372538	+	0.928017i	$0.621512\pi$
$602$	57.8192	−	34.7886i	2.35653	−	1.41788i
$603$	9.62363	+	20.4816i	0.391905	+	0.834076i
$604$	−3.11854	−	7.82695i	−0.126892	−	0.318474i
$605$	1.60499	−	4.49363i	0.0652520	−	0.182692i
$606$	−6.36909	+	30.6832i	−0.258727	+	1.24642i
$607$	40.1335	+	20.3579i	1.62897	+	0.826300i	0.998755	+	0.0498780i	$0.0158832\pi$
$607$	40.1335	+	20.3579i	1.62897	+	0.826300i	0.630214	+	0.776422i	$0.282967\pi$
$608$	3.30038	−	3.61263i	0.133848	−	0.146512i
$609$	68.9786	−	28.4467i	2.79515	−	1.15272i
$610$	4.10549	+	3.61684i	0.166226	+	0.146442i
$611$	−4.74667	+	11.9132i	−0.192030	+	0.481958i
$612$	−9.00396	+	0.541738i	−0.363963	+	0.0218985i
$613$	18.4171	−	4.05391i	0.743860	−	0.163736i	0.173159	−	0.984894i	$-0.444603\pi$
$613$	18.4171	−	4.05391i	0.743860	−	0.163736i	0.570701	+	0.821158i	$0.306672\pi$
$614$	18.1628	+	1.31401i	0.732991	+	0.0530292i
$615$	−5.72314	−	2.44183i	−0.230779	−	0.0984643i
$616$	−0.865060	−	1.38068i	−0.0348543	−	0.0556294i
$617$	23.6428	−	1.71047i	0.951822	−	0.0688608i	0.412497	−	0.910959i	$-0.364657\pi$
$617$	23.6428	−	1.71047i	0.951822	−	0.0688608i	0.539324	+	0.842098i	$0.318680\pi$
$618$	−27.0635	+	39.3992i	−1.08865	+	1.58487i
$619$	2.14742	+	23.7227i	0.0863122	+	0.953497i	0.917561	+	0.397596i	$0.130155\pi$
$619$	2.14742	+	23.7227i	0.0863122	+	0.953497i	−0.831248	+	0.555901i	$0.812373\pi$
$620$	−8.69783	−	4.02405i	−0.349313	−	0.161610i
$621$	6.39255	+	6.75035i	0.256524	+	0.270882i
$622$	−4.29405	−	6.33324i	−0.172176	−	0.253940i
$623$	−40.4925	+	1.46283i	−1.62230	+	0.0586070i
$624$	−27.4797	+	20.6278i	−1.10007	+	0.825773i
$625$	−9.39034	−	19.3713i	−0.375614	−	0.774851i
$626$	15.8278	−	49.9373i	0.632607	−	1.99590i
$627$	0.916825	+	0.654443i	0.0366145	+	0.0261359i
$628$	14.6435	−	2.12996i	0.584341	−	0.0849947i
$629$	−0.599747	+	0.202078i	−0.0239135	+	0.00805739i
$630$	−13.4742	+	0.323228i	−0.536826	+	0.0128777i
$631$	5.36974	+	1.18197i	0.213766	+	0.0470534i	0.320562	−	0.947228i	$-0.396128\pi$
$631$	5.36974	+	1.18197i	0.213766	+	0.0470534i	−0.106796	+	0.994281i	$0.534059\pi$
$632$	1.37206	−	0.894554i	0.0545777	−	0.0355835i
$633$	−1.45845	+	7.02610i	−0.0579682	+	0.279262i
$634$	−35.0978	+	6.40673i	−1.39391	+	0.254444i
$635$	−4.84706	−	0.705024i	−0.192350	−	0.0279780i
$636$	−42.7499	+	12.4235i	−1.69515	+	0.492624i
$637$	64.7884	+	35.8619i	2.56701	+	1.42090i
$638$	−3.37487	+	20.5858i	−0.133612	+	0.815000i
$639$	24.9746	−	5.18063i	0.987979	−	0.204942i
$640$	−1.02525	−	0.779373i	−0.0405265	−	0.0308074i
$641$	−21.1052	+	5.45141i	−0.833607	+	0.215318i	−0.642533	−	0.766258i	$-0.722117\pi$
$641$	−21.1052	+	5.45141i	−0.833607	+	0.215318i	−0.191074	+	0.981576i	$0.561197\pi$
$642$	−23.9234	−	33.0982i	−0.944183	−	1.30628i
$643$	−8.64994	+	19.6184i	−0.341120	+	0.773676i	0.658654	+	0.752446i	$0.271126\pi$
$643$	−8.64994	+	19.6184i	−0.341120	+	0.773676i	−0.999775	+	0.0212299i	$0.993242\pi$
$644$	15.3742	−	8.50999i	0.605830	−	0.335341i
$645$	5.22360	+	3.18623i	0.205679	+	0.125458i
$646$	−0.337728	−	1.67807i	−0.0132877	−	0.0660228i
$647$	16.3281	−	7.55416i	0.641922	−	0.296985i	−0.0717945	−	0.997419i	$-0.522873\pi$
$647$	16.3281	−	7.55416i	0.641922	−	0.296985i	0.713716	+	0.700435i	$0.247011\pi$
$648$	−2.42951	+	1.75556i	−0.0954400	+	0.0689648i
$649$	−2.95136	+	7.73248i	−0.115851	+	0.303526i
$650$	−26.4425	−	45.7998i	−1.03716	−	1.79642i
$651$	−39.9520	−	59.7009i	−1.56584	−	2.33986i
$652$	2.36436	−	2.08294i	0.0925954	−	0.0815744i
$653$	−6.49923	−	18.1965i	−0.254334	−	0.712083i	−0.999003	−	0.0446486i	$-0.985783\pi$
$653$	−6.49923	−	18.1965i	−0.254334	−	0.712083i	0.744668	−	0.667435i	$-0.232608\pi$
$654$	41.2442	−	5.74400i	1.61278	−	0.224608i
$655$	2.70606	+	3.69643i	0.105735	+	0.144432i
$656$	1.46253	−	26.9747i	0.0571020	−	1.05318i
$657$	0.0581024	+	1.38129i	0.00226679	+	0.0538892i
$658$	−17.3861	−	13.2166i	−0.677782	−	0.515237i
$659$	6.41044	+	14.5392i	0.249715	+	0.566365i	0.994943	−	0.100446i	$-0.0320268\pi$
$659$	6.41044	+	14.5392i	0.249715	+	0.566365i	−0.745227	+	0.666811i	$0.767659\pi$
$660$	0.989250	−	1.68969i	0.0385065	−	0.0657711i
$661$	0.447423	+	24.7782i	0.0174027	+	0.963762i	0.884752	+	0.466062i	$0.154328\pi$
$661$	0.447423	+	24.7782i	0.0174027	+	0.963762i	−0.867349	+	0.497700i	$0.834178\pi$
$662$	−1.67046	−	13.1467i	−0.0649241	−	0.510959i
$663$	0.157040	+	13.0948i	0.00609892	+	0.508559i
$664$	0.803926	−	2.25083i	0.0311984	−	0.0873490i
$665$	−0.215003	−	1.31146i	−0.00833747	−	0.0508563i
$666$	−1.75290	+	2.16692i	−0.0679234	+	0.0839664i
$667$	−16.5794	−	3.64940i	−0.641957	−	0.141305i
$668$	−32.1835	−	9.56480i	−1.24522	−	0.370073i
$669$	20.7370	−	32.6557i	0.801740	−	1.26254i
$670$	4.62382	+	5.85984i	0.178634	+	0.226385i
$671$	−5.76854	−	1.48999i	−0.222692	−	0.0575206i
$672$	−23.2382	−	59.3678i	−0.896432	−	2.29016i
$673$	−13.8884	−	1.00478i	−0.535360	−	0.0387313i	−0.198169	−	0.980168i	$-0.563500\pi$
$673$	−13.8884	−	1.00478i	−0.535360	−	0.0387313i	−0.337190	+	0.941436i	$0.609477\pi$
$674$	−15.6604	−	29.5386i	−0.603215	−	1.13778i
$675$	11.9873	+	21.6632i	0.461390	+	0.833817i
$676$	−20.1400	−	29.7043i	−0.774615	−	1.14247i
$677$	6.33582	−	26.4959i	0.243505	−	1.01832i	−0.706902	−	0.707312i	$-0.749908\pi$
$677$	6.33582	−	26.4959i	0.243505	−	1.01832i	0.950407	−	0.311009i	$-0.100667\pi$
$678$	−2.63811	+	9.28291i	−0.101316	+	0.356508i
$679$	−70.9918	+	50.0280i	−2.72441	+	1.91990i
$680$	−0.215199	+	0.0639561i	−0.00825249	+	0.00245260i
$681$	−7.63149	−	2.31850i	−0.292439	−	0.0888449i
$682$	20.0707	−	0.725074i	0.768547	−	0.0277645i
$683$	4.86613	+	9.17850i	0.186197	+	0.351206i	0.958984	−	0.283460i	$-0.0914825\pi$
$683$	4.86613	+	9.17850i	0.186197	+	0.351206i	−0.772786	+	0.634666i	$0.781138\pi$
$684$	−2.71048	−	2.82765i	−0.103638	−	0.108118i
$685$	−6.10221	+	1.34320i	−0.233153	+	0.0513209i
$686$	−42.9267	+	43.7088i	−1.63895	+	1.66881i
$687$	−15.0883	+	16.3160i	−0.575654	+	0.622495i
$688$	−5.24125	+	26.0422i	−0.199821	+	0.992851i
$689$	15.0315	+	62.8604i	0.572653	+	2.39479i
$690$	2.55861	+	1.69035i	0.0974046	+	0.0643506i
$691$	42.1952	−	27.5103i	1.60518	−	1.04654i	0.646161	−	0.763201i	$-0.276374\pi$
$691$	42.1952	−	27.5103i	1.60518	−	1.04654i	0.959019	−	0.283340i	$-0.0914425\pi$
$692$	1.14895	+	7.00830i	0.0436766	+	0.266416i
$693$	12.9258	−	6.95129i	0.491009	−	0.264058i
$694$	16.3155	+	40.9489i	0.619329	+	1.55440i
$695$	8.40014	+	3.52396i	0.318636	+	0.133671i
$696$	1.87222	−	5.14317i	0.0709663	−	0.194951i
$697$	−7.96621	−	6.52267i	−0.301742	−	0.247064i
$698$	−6.64330	+	9.07462i	−0.251452	+	0.343479i
$699$	−3.96716	+	7.37446i	−0.150052	+	0.278928i
$700$	45.3100	−	11.7034i	1.71256	−	0.442348i
$701$	1.17224	−	21.6207i	0.0442750	−	0.816604i	−0.889103	−	0.457708i	$-0.848670\pi$
$701$	1.17224	−	21.6207i	0.0442750	−	0.816604i	0.933378	−	0.358896i	$-0.116847\pi$
$702$	31.4916	+	48.3158i	1.18857	+	1.82356i
$703$	−0.235480	−	0.141684i	−0.00888130	−	0.00534370i
$704$	9.80309	+	1.78945i	0.369468	+	0.0674424i
$705$	0.332221	−	1.95224i	0.0125122	−	0.0735256i
$706$	−3.68560	+	40.7152i	−0.138710	+	1.53234i
$707$	−20.1293	+	34.8649i	−0.757039	+	1.31123i
$708$	15.0731	−	24.5170i	0.566480	−	0.921405i
$709$	13.5522	+	23.4730i	0.508962	+	0.881548i	0.999946	+	0.0103792i	$0.00330388\pi$
$709$	13.5522	+	23.4730i	0.508962	+	0.881548i	−0.490984	+	0.871168i	$0.663363\pi$
$710$	7.63559	−	3.53260i	0.286559	−	0.132576i
$711$	7.22153	+	12.8659i	0.270828	+	0.482508i
$712$	−1.92421	+	2.26535i	−0.0721128	+	0.0848977i
$713$	−0.295079	+	16.3415i	−0.0110508	+	0.611993i
$714$	−21.5591	−	5.70829i	−0.806828	−	0.213627i
$715$	−2.38122	−	1.55250i	−0.0890525	−	0.0580602i
$716$	−1.40049	−	1.42601i	−0.0523389	−	0.0532925i
$717$	−6.95651	−	11.2541i	−0.259796	−	0.420291i
$718$	−26.0931	−	59.1802i	−0.973785	−	2.20859i
$719$	6.56699	−	40.0569i	0.244907	−	1.49387i	−0.522461	−	0.852663i	$-0.674986\pi$
$719$	6.56699	−	40.0569i	0.244907	−	1.49387i	0.767369	−	0.641206i	$-0.221566\pi$
$720$	3.48381	−	4.00207i	0.129834	−	0.149148i
$721$	−48.8853	+	37.1616i	−1.82058	+	1.38397i
$722$	−23.5541	+	29.8505i	−0.876592	+	1.11092i
$723$	27.8214	+	5.25299i	1.03469	+	0.195361i
$724$	−10.4281	−	3.93831i	−0.387559	−	0.146366i
$725$	−40.3192	−	20.4520i	−1.49742	−	0.759569i
$726$	2.09298	−	34.7085i	0.0776776	−	1.28815i
$727$	−29.8691	−	8.87697i	−1.10778	−	0.329229i	−0.321386	−	0.946948i	$-0.604149\pi$
$727$	−29.8691	−	8.87697i	−1.10778	−	0.329229i	−0.786398	+	0.617720i	$0.788057\pi$
$728$	7.79470	−	2.62634i	0.288891	−	0.0973386i
$729$	−14.3292	−	22.8839i	−0.530712	−	0.847552i
$730$	0.121998	+	0.439396i	0.00451534	+	0.0162628i
$731$	6.82873	+	7.47480i	0.252570	+	0.276465i
$732$	18.7492	+	8.81271i	0.692991	+	0.325727i
$733$	17.3263	+	0.625928i	0.639960	+	0.0231192i	0.354182	−	0.935177i	$-0.384759\pi$
$733$	17.3263	+	0.625928i	0.639960	+	0.0231192i	0.285778	+	0.958296i	$0.407748\pi$
$734$	17.0150	+	27.1569i	0.628035	+	1.00238i
$735$	−10.9413	−	3.32404i	−0.403577	−	0.122609i
$736$	−3.37347	+	14.1076i	−0.124348	+	0.520013i
$737$	−7.37680	−	3.41287i	−0.271728	−	0.125715i
$738$	−45.0140	−	5.44863i	−1.65699	−	0.200567i
$739$	−24.0299	−	22.7624i	−0.883955	−	0.837327i	0.103597	−	0.994619i	$-0.466965\pi$
$739$	−24.0299	−	22.7624i	−0.883955	−	0.837327i	−0.987552	+	0.157292i	$0.949723\pi$
$740$	−0.208371	+	0.429847i	−0.00765987	+	0.0158015i
$741$	−4.28969	+	3.73317i	−0.157586	+	0.137141i
$742$	−109.998	−	3.97377i	−4.03814	−	0.145882i
$743$	0.399942	+	0.825038i	0.0146725	+	0.0302677i	0.907056	−	0.421011i	$-0.138324\pi$
$743$	0.399942	+	0.825038i	0.0146725	+	0.0302677i	−0.892383	+	0.451278i	$0.850968\pi$
$744$	−5.20995	−	0.790094i	−0.191006	−	0.0289662i
$745$	−4.94728	+	5.03742i	−0.181254	+	0.184557i
$746$	−23.4393	+	58.8281i	−0.858172	+	2.15385i
$747$	19.7507	+	8.56876i	0.722640	+	0.313514i
$748$	2.35210	−	2.22803i	0.0860012	−	0.0814647i
$749$	−15.8519	−	50.0132i	−0.579214	−	1.82744i
$750$	11.2132	+	12.4245i	0.409447	+	0.453678i
$751$	−25.7991	−	9.74336i	−0.941424	−	0.355540i	−0.165388	−	0.986229i	$-0.552888\pi$
$751$	−25.7991	−	9.74336i	−0.941424	−	0.355540i	−0.776036	+	0.630688i	$0.782773\pi$
$752$	8.45782	−	1.54388i	0.308425	−	0.0562997i
$753$	33.3955	−	19.8186i	1.21700	−	0.722230i
$754$	−97.1123	−	40.7397i	−3.53662	−	1.48365i
$755$	1.61851	−	0.973823i	0.0589035	−	0.0354410i
$756$	−48.6506	+	15.4128i	−1.76940	+	0.560558i
$757$	−32.5995	−	3.54541i	−1.18485	−	0.128860i	−0.505601	−	0.862768i	$-0.668729\pi$
$757$	−32.5995	−	3.54541i	−1.18485	−	0.128860i	−0.679250	+	0.733907i	$0.737695\pi$
$758$	1.50032	−	11.8077i	0.0544942	−	0.428875i
$759$	−3.31736	−	0.381150i	−0.120413	−	0.0138349i
$760$	−0.0816634	−	0.0532427i	−0.00296224	−	0.00193131i
$761$	−7.61709	+	17.2759i	−0.276119	+	0.626250i	−0.997823	−	0.0659521i	$-0.978992\pi$
$761$	−7.61709	+	17.2759i	−0.276119	+	0.626250i	0.721704	+	0.692202i	$0.243359\pi$
$762$	−35.3516	+	4.92334i	−1.28065	+	0.178354i
$763$	52.6277	+	9.60661i	1.90525	+	0.347783i
$764$	37.4384	+	12.6145i	1.35447	+	0.456375i
$765$	−0.446427	−	1.97237i	−0.0161406	−	0.0713110i
$766$	54.2096			1.95867
$767$	−34.5007	−	23.5695i	−1.24575	−	0.851044i
$768$	21.1421	+	8.13139i	0.762901	+	0.293416i
$769$	−1.65442	+	18.2765i	−0.0596598	+	0.659067i	0.910000	+	0.414608i	$0.136081\pi$
$769$	−1.65442	+	18.2765i	−0.0596598	+	0.659067i	−0.969660	+	0.244458i	$0.921390\pi$
$770$	3.63242	−	3.20008i	0.130903	−	0.115323i
$771$	−35.8568	+	19.5645i	−1.29135	+	0.704598i
$772$	0.588475	−	32.5897i	0.0211797	−	1.17293i
$773$	2.52173	−	0.274254i	0.0907002	−	0.00986424i	−0.0626564	−	0.998035i	$-0.519957\pi$
$773$	2.52173	−	0.274254i	0.0907002	−	0.00986424i	0.153357	+	0.988171i	$0.450992\pi$
$774$	43.0321	+	11.6735i	1.54676	+	0.419594i
$775$	−11.6445	+	41.9397i	−0.418283	+	1.50652i
$776$	−0.803035	+	6.31997i	−0.0288273	+	0.226874i
$777$	−3.01123	+	1.93734i	−0.108027	+	0.0695015i
$778$	−1.87636	−	1.53635i	−0.0672708	−	0.0550808i
$779$	−0.0807177	−	4.47014i	−0.00289201	−	0.160159i
$780$	7.13478	+	6.84097i	0.255466	+	0.244946i
$781$	−5.67486	+	7.19184i	−0.203062	+	0.257344i
$782$	3.28495	+	3.86734i	0.117470	+	0.138296i
$783$	45.1096	+	19.8964i	1.61208	+	0.711041i
$784$	−2.68778	−	49.5732i	−0.0959922	−	1.77047i
$785$	1.00235	+	3.16245i	0.0357754	+	0.112873i
$786$	26.4530	+	20.3633i	0.943546	+	0.726334i
$787$	6.02248	−	29.9239i	0.214678	−	1.06667i	−0.715232	−	0.698887i	$-0.753679\pi$
$787$	6.02248	−	29.9239i	0.214678	−	1.06667i	0.929910	−	0.367786i	$-0.119884\pi$
$788$	−7.40674	−	9.38668i	−0.263854	−	0.334387i
$789$	2.08674	+	1.48954i	0.0742897	+	0.0530291i
$790$	3.28241	+	3.59296i	0.116783	+	0.127832i
$791$	−6.95752	+	10.2616i	−0.247381	+	0.364859i
$792$	0.263058	−	1.04396i	0.00934735	−	0.0370953i
$793$	14.0885	−	26.5737i	0.500296	−	0.943659i
$794$	−14.0093	+	28.8997i	−0.497172	+	1.02561i
$795$	−4.29909	−	9.00729i	−0.152473	−	0.319456i
$796$	0.494405	−	0.348408i	0.0175237	−	0.0123490i
$797$	34.4272	−	24.2609i	1.21948	−	0.859366i	0.226080	−	0.974109i	$-0.427409\pi$
$797$	34.4272	−	24.2609i	1.21948	−	0.859366i	0.993395	+	0.114743i	$0.0366044\pi$
$798$	−4.17146	−	8.73988i	−0.147668	−	0.309389i
$799$	1.42935	−	2.94860i	0.0505668	−	0.104314i
$800$	−18.0943	+	34.1295i	−0.639730	+	1.20666i
$801$	−19.2128	−	18.6465i	−0.678851	−	0.658842i
$802$	−22.6389	+	33.3899i	−0.799409	+	1.17904i
$803$	−0.334920	−	0.366607i	−0.0118191	−	0.0129373i
$804$	23.0039	+	16.4205i	0.811286	+	0.579108i
$805$	2.44035	+	3.09270i	0.0860112	+	0.109003i
$806$	−20.0046	+	99.3968i	−0.704631	+	3.50110i
$807$	−26.2994	−	20.2451i	−0.925784	−	0.712661i
$808$	0.892273	+	2.81515i	0.0313900	+	0.0990367i
$809$	−1.23007	−	22.6872i	−0.0432468	−	0.797640i	−0.937053	−	0.349187i	$-0.886458\pi$
$809$	−1.23007	−	22.6872i	−0.0432468	−	0.797640i	0.893806	−	0.448453i	$-0.148025\pi$
$810$	−6.31521	−	6.27957i	−0.221894	−	0.220642i
$811$	−36.7970	−	43.3208i	−1.29212	−	1.52120i	−0.694849	−	0.719156i	$-0.744529\pi$
$811$	−36.7970	−	43.3208i	−1.29212	−	1.52120i	−0.597268	−	0.802042i	$-0.703747\pi$
$812$	57.7254	−	73.1564i	2.02576	−	2.56729i
$813$	27.7576	+	26.6145i	0.973501	+	0.933413i
$814$	−0.0180734	−	1.00090i	−0.000633473	−	0.0350817i
$815$	0.546581	+	0.447536i	0.0191459	+	0.0156765i
$816$	7.38358	−	4.75038i	0.258477	−	0.166297i
$817$	−0.554166	+	4.36134i	−0.0193878	+	0.152584i
$818$	17.9738	−	64.7358i	0.628440	−	2.26343i
$819$	18.9544	+	71.6258i	0.662320	+	2.50281i
$820$	−7.72570	+	0.840221i	−0.269793	+	0.0293418i
$821$	0.0880247	−	4.87480i	0.00307208	−	0.170132i	−0.994676	−	0.103055i	$-0.967138\pi$
$821$	0.0880247	−	4.87480i	0.00307208	−	0.170132i	0.997748	−	0.0670772i	$-0.0213674\pi$
$822$	−39.9694	+	21.8084i	−1.39409	+	0.760657i
$823$	3.18622	−	2.80698i	0.111065	−	0.0978453i	−0.603696	−	0.797215i	$-0.706306\pi$
$823$	3.18622	−	2.80698i	0.111065	−	0.0978453i	0.714760	+	0.699369i	$0.246536\pi$
$824$	−0.406093	+	4.48614i	−0.0141469	+	0.156282i
$825$	−8.29992	−	3.19220i	−0.288966	−	0.111138i
$826$	54.3942	−	45.8748i	1.89262	−	1.59619i
$827$	−16.5048			−0.573927			−0.286964	−	0.957941i	$-0.592646\pi$
$827$	−16.5048			−0.573927			−0.286964	+	0.957941i	$0.592646\pi$
$828$	11.0892	+	3.44254i	0.385375	+	0.119636i
$829$	−2.75214	−	0.927304i	−0.0955857	−	0.0322066i	0.271102	−	0.962551i	$-0.412612\pi$
$829$	−2.75214	−	0.927304i	−0.0955857	−	0.0322066i	−0.366688	+	0.930344i	$0.619508\pi$
$830$	6.98598	+	1.27522i	0.242487	+	0.0442634i
$831$	2.11034	−	0.293902i	0.0732067	−	0.0101953i
$832$	−20.2957	+	46.0314i	−0.703625	+	1.59585i
$833$	−15.8503	−	10.3340i	−0.549179	−	0.358052i
$834$	65.9472	+	7.57704i	2.28356	+	0.262371i
$835$	0.948796	−	7.46712i	0.0328344	−	0.258410i
$836$	1.39861	+	0.152108i	0.0483718	+	0.00526075i
$837$	10.2101	−	46.3555i	0.352914	−	1.60228i
$838$	−20.8691	+	12.5565i	−0.720910	+	0.433757i
$839$	17.6837	+	7.41851i	0.610508	+	0.256115i	0.670294	−	0.742096i	$-0.266168\pi$
$839$	17.6837	+	7.41851i	0.610508	+	0.256115i	−0.0597856	+	0.998211i	$0.519042\pi$
$840$	−1.09229	+	0.648223i	−0.0376877	+	0.0223658i
$841$	−60.0355	+	10.9588i	−2.07019	+	0.377890i
$842$	5.19838	+	1.96323i	0.179148	+	0.0676575i
$843$	26.9099	+	29.8169i	0.926826	+	1.02695i
$844$	2.70785	+	8.54336i	0.0932081	+	0.294075i
$845$	5.84122	−	5.53310i	0.200944	−	0.190344i
$846$	−1.64526	−	14.3366i	−0.0565653	−	0.492903i
$847$	16.5343	−	41.4979i	0.568125	−	1.42589i
$848$	30.3621	−	30.9153i	1.04264	−	1.06164i
$849$	−14.4296	−	2.18827i	−0.495224	−	0.0751011i
$850$	5.89449	+	12.1597i	0.202179	+	0.417075i
$851$	0.814133	+	0.0294114i	0.0279081	+	0.00100821i
$852$	24.0302	−	20.9126i	0.823260	−	0.716455i
$853$	−9.00712	+	18.5807i	−0.308398	+	0.636192i	−0.995947	−	0.0899463i	$-0.971330\pi$
$853$	−9.00712	+	18.5807i	−0.308398	+	0.636192i	0.687549	+	0.726138i	$0.258687\pi$
$854$	37.1867	+	35.2251i	1.27250	+	1.20538i
$855$	0.527273	−	0.702219i	0.0180324	−	0.0240154i
$856$	−3.49289	−	1.61598i	−0.119385	−	0.0552332i
$857$	−7.12097	+	29.7794i	−0.243248	+	1.01724i	0.707361	+	0.706852i	$0.249886\pi$
$857$	−7.12097	+	29.7794i	−0.243248	+	1.01724i	−0.950609	+	0.310392i	$0.899540\pi$
$858$	−19.8200	−	6.02143i	−0.676643	−	0.205568i
$859$	15.2391	+	24.3225i	0.519951	+	0.829872i	0.998847	−	0.0480000i	$-0.0152847\pi$
$859$	15.2391	+	24.3225i	0.519951	+	0.829872i	−0.478896	+	0.877872i	$0.658963\pi$
$860$	7.63685	+	0.275889i	0.260415	+	0.00940773i
$861$	−52.7178	−	24.7790i	−1.79662	−	0.844466i
$862$	29.6164	+	32.4184i	1.00874	+	1.10418i
$863$	−5.20276	−	18.7386i	−0.177104	−	0.637870i	−0.997787	−	0.0664873i	$-0.978821\pi$
$863$	−5.20276	−	18.7386i	−0.177104	−	0.637870i	0.820683	−	0.571383i	$-0.193593\pi$
$864$	17.6936	−	38.2305i	0.601947	−	1.30063i
$865$	−1.50883	+	0.508383i	−0.0513017	+	0.0172855i
$866$	9.84736	+	2.92659i	0.334627	+	0.0994497i
$867$	−1.57093	+	26.0514i	−0.0533517	+	0.884750i
$868$	−80.0130	−	40.5868i	−2.71582	−	1.37761i
$869$	−4.95748	−	1.87225i	−0.168171	−	0.0635119i
$870$	15.9800	+	3.01720i	0.541773	+	0.102293i
$871$	25.4179	−	32.2125i	0.861252	−	1.09148i
$872$	3.12411	−	2.37489i	0.105796	−	0.0804239i
$873$	−56.3246	−	10.9888i	−1.90630	−	0.371915i
$874$	−0.356470	+	2.17437i	−0.0120578	+	0.0735491i
$875$	8.67420	+	19.6735i	0.293242	+	0.665085i
$876$	0.907870	+	1.46873i	0.0306741	+	0.0496238i
$877$	−22.2442	−	22.6495i	−0.751134	−	0.764820i	0.226753	−	0.973952i	$-0.427189\pi$
$877$	−22.2442	−	22.6495i	−0.751134	−	0.764820i	−0.977887	+	0.209132i	$0.932936\pi$
$878$	−10.3206	−	6.72879i	−0.348303	−	0.227086i
$879$	0.625061	+	0.165500i	0.0210828	+	0.00558218i
$880$	−0.0344070	+	1.90545i	−0.00115986	+	0.0642328i
$881$	−4.11774	+	4.84778i	−0.138730	+	0.163326i	−0.827140	−	0.561997i	$-0.810033\pi$
$881$	−4.11774	+	4.84778i	−0.138730	+	0.163326i	0.688409	+	0.725322i	$0.258309\pi$
$882$	−83.3229	−	1.01045i	−2.80563	−	0.0340235i
$883$	−31.4392	+	14.5453i	−1.05801	+	0.489489i	−0.870191	−	0.492714i	$-0.836005\pi$
$883$	−31.4392	+	14.5453i	−1.05801	+	0.489489i	−0.187822	+	0.982203i	$0.560143\pi$
$884$	8.17787	+	14.1645i	0.275052	+	0.476403i
$885$	5.97078	+	2.44549i	0.200706	+	0.0822044i
$886$	−42.7802	+	74.0974i	−1.43723	+	2.48935i
$887$	−0.517165	+	5.71316i	−0.0173647	+	0.191829i	0.982616	+	0.185649i	$0.0594386\pi$
$887$	−0.517165	+	5.71316i	−0.0173647	+	0.191829i	−0.999981	+	0.00618048i	$0.998033\pi$
$888$	−0.0440638	+	0.258934i	−0.00147869	+	0.00868925i
$889$	−45.1086	−	8.23409i	−1.51289	−	0.276163i
$890$	−7.56708	−	4.55296i	−0.253649	−	0.152616i
$891$	9.22609	+	2.98729i	0.309086	+	0.100078i
$892$	2.61564	−	48.2426i	0.0875781	−	1.61528i
$893$	1.37768	−	0.355851i	0.0461024	−	0.0119081i
$894$	−24.3752	+	45.3106i	−0.815230	+	1.51541i
$895$	0.264691	−	0.361563i	0.00884765	−	0.0120857i
$896$	−9.32835	−	7.63798i	−0.311638	−	0.255167i
$897$	5.76626	−	15.8405i	0.192530	−	0.528898i
$898$	−77.0415	−	32.3198i	−2.57091	−	1.07853i
$899$	32.0817	+	80.5191i	1.06999	+	2.68546i
$900$	26.3005	+	16.2621i	0.876683	+	0.542069i
$901$	−2.67180	−	16.2973i	−0.0890105	−	0.542940i
$902$	13.6424	−	8.89453i	0.454242	−	0.296155i
$903$	47.7928	+	31.5744i	1.59044	+	1.05073i
$904$	0.211508	+	0.884511i	0.00703465	+	0.0294184i
$905$	0.493074	−	2.44994i	0.0163903	−	0.0814387i
$906$	9.34535	−	10.1058i	0.310478	−	0.335742i
$907$	−30.9978	+	31.5626i	−1.02926	+	1.04802i	−0.0304408	+	0.999537i	$0.509691\pi$
$907$	−30.9978	+	31.5626i	−1.02926	+	1.04802i	−0.998824	+	0.0484816i	$0.984562\pi$
$908$	−9.72853	+	2.14141i	−0.322852	+	0.0710652i
$909$	−25.8350	+	6.33993i	−0.856892	+	0.210282i
$910$	11.4474	+	21.5920i	0.379477	+	0.715769i
$911$	−54.9895	+	1.98655i	−1.82188	+	0.0658173i	−0.925788	−	0.378043i	$-0.876597\pi$
$911$	−54.9895	+	1.98655i	−1.82188	+	0.0658173i	−0.896096	+	0.443860i	$0.853609\pi$
$912$	3.64785	+	1.10824i	0.120792	+	0.0366975i
$913$	−7.41234	+	2.20292i	−0.245313	+	0.0729059i
$914$	43.5918	−	30.7192i	1.44189	−	1.01610i
$915$	−1.26967	+	4.46767i	−0.0419739	+	0.147697i
$916$	−6.45500	+	26.9943i	−0.213279	+	0.891918i
$917$	24.0674	+	35.4968i	0.794776	+	1.17221i
$918$	−7.13487	−	12.8940i	−0.235486	−	0.425566i
$919$	−7.74119	−	14.6014i	−0.255358	−	0.481657i	0.722377	−	0.691499i	$-0.243050\pi$
$919$	−7.74119	−	14.6014i	−0.255358	−	0.481657i	−0.977735	+	0.209843i	$0.932705\pi$
$920$	0.288234	+	0.0208527i	0.00950280	+	0.000687493i
$921$	5.63454	+	14.3948i	0.185664	+	0.474326i
$922$	70.2846	+	18.1543i	2.31470	+	0.597879i
$923$	−28.6486	−	36.3069i	−0.942981	−	1.19506i
$924$	9.82606	−	15.4736i	0.323254	−	0.509045i
$925$	2.07964	+	0.618061i	0.0683782	+	0.0203217i
$926$	16.4142	+	3.61305i	0.539406	+	0.118732i
$927$	−40.0791	−	6.32686i	−1.31637	−	0.207801i
$928$	12.4449	+	75.9103i	0.408523	+	2.49188i
$929$	8.11200	−	22.7119i	0.266146	−	0.745153i	−0.731826	−	0.681492i	$-0.761331\pi$
$929$	8.11200	−	22.7119i	0.266146	−	0.745153i	0.997972	−	0.0636615i	$-0.0202778\pi$
$930$	−0.187751	−	15.6556i	−0.00615661	−	0.513369i
$931$	−1.03568	−	8.15088i	−0.0339429	−	0.267134i
$932$	0.188817	+	10.4567i	0.00618492	+	0.342520i
$933$	3.28174	−	5.60537i	0.107439	−	0.183512i
$934$	5.38275	+	12.2083i	0.176129	+	0.399468i
$935$	0.578234	+	0.439562i	0.0189103	+	0.0143752i
$936$	4.81688	+	2.51728i	0.157445	+	0.0822798i
$937$	−1.04575	+	19.2877i	−0.0341631	+	0.630102i	0.930448	+	0.366424i	$0.119418\pi$
$937$	−1.04575	+	19.2877i	−0.0341631	+	0.630102i	−0.964611	+	0.263677i	$0.915065\pi$
$938$	41.2779	+	56.3848i	1.34777	+	1.84103i
$939$	44.0440	−	6.13391i	1.43732	−	0.200173i
$940$	−0.831909	−	2.32917i	−0.0271339	−	0.0759692i
$941$	−29.8469	+	26.2944i	−0.972981	+	0.857174i	−0.989768	−	0.142685i	$-0.954426\pi$
$941$	−29.8469	+	26.2944i	−0.972981	+	0.857174i	0.0167868	+	0.999859i	$0.494656\pi$
$942$	13.4451	+	20.0913i	0.438066	+	0.654609i
$943$	6.62666	+	11.4777i	0.215794	+	0.373766i
$944$	−1.10969	+	27.9904i	−0.0361173	+	0.911011i
$945$	−5.17445	−	10.2043i	−0.168325	−	0.331946i
$946$	−14.5344	+	6.72435i	−0.472555	+	0.218627i
$947$	5.82370	+	28.9363i	0.189245	+	0.940303i	0.954872	+	0.297018i	$0.0959921\pi$
$947$	5.82370	+	28.9363i	0.189245	+	0.940303i	−0.765627	+	0.643285i	$0.777571\pi$
$948$	15.7313	+	9.59560i	0.510929	+	0.311651i
$949$	2.19323	−	1.21400i	0.0711953	−	0.0394082i
$950$	−2.36731	+	5.36917i	−0.0768058	+	0.174199i
$951$	−17.7416	−	24.5455i	−0.575310	−	0.795944i
$952$	−2.03492	+	0.525612i	−0.0659521	+	0.0170352i
$953$	−13.7868	−	10.4805i	−0.446599	−	0.339496i	0.357580	−	0.933882i	$-0.383602\pi$
$953$	−13.7868	−	10.4805i	−0.446599	−	0.339496i	−0.804180	+	0.594386i	$0.797395\pi$
$954$	−48.4004	−	54.2871i	−1.56702	−	1.75761i
$955$	−1.43290	+	8.74030i	−0.0463675	+	0.282829i
$956$	−14.4572	−	8.00236i	−0.467578	−	0.258815i
$957$	−17.0046	+	4.94170i	−0.549682	+	0.159742i
$958$	−34.4136	−	5.00559i	−1.11185	−	0.161723i
$959$	−57.5435	+	10.5039i	−1.85818	+	0.339190i
$960$	1.57890	−	7.60635i	0.0509586	−	0.245494i
$961$	43.9344	−	28.6443i	1.41724	−	0.924009i
$962$	4.93557	+	1.08640i	0.159129	+	0.0350270i
$963$	16.6087	−	30.4298i	0.535207	−	0.980587i
$964$	33.5101	−	11.2909i	1.07929	−	0.363654i
$965$	7.23141	−	1.05184i	0.232787	−	0.0338598i
$966$	23.3659	+	16.6789i	0.751785	+	0.536635i
$967$	1.24555	−	3.92977i	0.0400543	−	0.126373i	−0.931140	−	0.364662i	$-0.881184\pi$
$967$	1.24555	−	3.92977i	0.0400543	−	0.126373i	0.971194	+	0.238290i	$0.0765867\pi$
$968$	−1.42937	−	2.94864i	−0.0459417	−	0.0947728i
$969$	1.16207	−	0.872313i	0.0373309	−	0.0280227i
$970$	−18.9165	+	0.683376i	−0.607372	+	0.0219419i
$971$	18.1297	+	26.7392i	0.581808	+	0.858103i	0.998706	−	0.0508502i	$-0.0161931\pi$
$971$	18.1297	+	26.7392i	0.581808	+	0.858103i	−0.416898	+	0.908953i	$0.636883\pi$
$972$	−29.5973	−	16.1595i	−0.949335	−	0.518315i
$973$	77.3969	+	35.8076i	2.48123	+	1.14794i
$974$	1.87550	+	20.7187i	0.0600947	+	0.663871i
$975$	25.4182	−	37.0040i	0.814034	−	1.18508i
$976$	−20.1121	+	1.45504i	−0.643772	+	0.0465745i
$977$	−21.1069	−	33.6879i	−0.675271	−	1.07777i	−0.991628	−	0.129130i	$-0.958782\pi$
$977$	−21.1069	−	33.6879i	−0.675271	−	1.07777i	0.316357	−	0.948640i	$-0.397540\pi$
$978$	4.73486	+	2.02018i	0.151404	+	0.0645981i
$979$	9.59127	+	0.693893i	0.306538	+	0.0221769i
$980$	−13.9479	+	3.07016i	−0.445548	+	0.0980726i
$981$	19.4813	+	29.4966i	0.621990	+	0.941754i
$982$	−5.66701	+	14.2231i	−0.180841	+	0.453878i
$983$	4.20020	+	3.70028i	0.133966	+	0.118021i	0.725385	−	0.688344i	$-0.241662\pi$
$983$	4.20020	+	3.70028i	0.133966	+	0.118021i	−0.591419	+	0.806364i	$0.701432\pi$
$984$	−3.95027	+	1.62909i	−0.125930	+	0.0519335i
$985$	1.80804	−	1.97910i	0.0576091	−	0.0630595i
$986$	23.9981	+	12.1731i	0.764256	+	0.387671i
$987$	3.76792	−	18.1520i	0.119934	−	0.577784i
$988$	−2.38891	+	6.68845i	−0.0760014	+	0.212788i
$989$	−4.82386	−	12.1070i	−0.153390	−	0.384980i
$990$	3.18738	+	0.269485i	0.101302	+	0.00856479i
$991$	49.2363	−	29.6245i	1.56404	−	0.941054i	0.571308	−	0.820735i	$-0.306436\pi$
$991$	49.2363	−	29.6245i	1.56404	−	0.941054i	0.992735	−	0.120318i	$-0.0383916\pi$
$992$	69.2830	−	26.1656i	2.19974	−	0.830757i
$993$	9.46075	−	6.08677i	0.300228	−	0.193158i
$994$	72.6291	−	30.4688i	2.30366	−	0.966411i
$995$	0.0950130	+	0.0967442i	0.00301211	+	0.00306700i
$996$	26.7484	−	2.74507i	0.847555	−	0.0869809i
$997$	−21.0143	−	28.7051i	−0.665529	−	0.909100i	0.333910	−	0.942605i	$-0.391632\pi$
$997$	−21.0143	−	28.7051i	−0.665529	−	0.909100i	−0.999439	+	0.0335050i	$0.989333\pi$
$998$	−28.5294	−	17.1656i	−0.903082	−	0.543366i
$999$	−2.30100	−	0.550552i	−0.0728005	−	0.0174187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.m.a.121.48	yes	3248
9.7	even	3	inner	531.2.m.a.475.48	yes	3248
59.20	even	29	inner	531.2.m.a.256.48	yes	3248
531.79	even	87	inner	531.2.m.a.79.48	✓	3248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.2.m.a.79.48	✓	3248	531.79	even	87	inner
531.2.m.a.121.48	yes	3248	1.1	even	1	trivial
531.2.m.a.256.48	yes	3248	59.20	even	29	inner
531.2.m.a.475.48	yes	3248	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.m (of order \(87\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66787 + 1.17535i) q^{2} +(-0.290573 + 1.70750i) q^{3} +(0.727620 + 2.03718i) q^{4} +(-0.424311 + 0.234866i) q^{5} +(-2.49155 + 2.50636i) q^{6} +(-4.04904 + 2.05389i) q^{7} +(-0.0890992 + 0.320906i) q^{8} +(-2.83113 - 0.992308i) q^{9} +O(q^{10})\)	\(q+(1.66787 + 1.17535i) q^{2} +(-0.290573 + 1.70750i) q^{3} +(0.727620 + 2.03718i) q^{4} +(-0.424311 + 0.234866i) q^{5} +(-2.49155 + 2.50636i) q^{6} +(-4.04904 + 2.05389i) q^{7} +(-0.0890992 + 0.320906i) q^{8} +(-2.83113 - 0.992308i) q^{9} +(-0.983743 - 0.106988i) q^{10} +(1.00803 - 0.380694i) q^{11} +(-3.68992 + 0.650463i) q^{12} +(0.685670 + 5.39629i) q^{13} +(-9.16730 - 1.33342i) q^{14} +(-0.277741 - 0.792758i) q^{15} +(2.82171 - 2.31039i) q^{16} +(-0.0752497 - 1.38790i) q^{17} +(-3.55565 - 4.98261i) q^{18} +(0.438184 - 0.415070i) q^{19} +(-0.787201 - 0.693506i) q^{20} +(-2.33048 - 7.51055i) q^{21} +(2.12870 + 0.549837i) q^{22} +(-0.540585 + 1.70556i) q^{23} +(-0.522059 - 0.245384i) q^{24} +(-2.52982 + 4.03774i) q^{25} +(-5.19892 + 9.80620i) q^{26} +(2.51702 - 4.54583i) q^{27} +(-7.13031 - 6.75419i) q^{28} +(0.855398 + 9.44964i) q^{29} +(0.468532 - 1.64866i) q^{30} +(8.75643 - 2.60237i) q^{31} +(8.08610 - 0.585000i) q^{32} +(0.357131 + 1.83183i) q^{33} +(1.50576 - 2.40327i) q^{34} +(1.23566 - 1.82247i) q^{35} +(-0.0384762 - 6.48956i) q^{36} +(-0.121813 - 0.438730i) q^{37} +(1.21868 - 0.177262i) q^{38} +(-9.41343 - 0.397232i) q^{39} +(-0.0375641 - 0.157090i) q^{40} +(4.99619 - 5.46888i) q^{41} +(4.94059 - 15.2657i) q^{42} +(-5.63590 + 4.61463i) q^{43} +(1.50900 + 1.77654i) q^{44} +(1.43434 - 0.243889i) q^{45} +(-2.90626 + 2.20928i) q^{46} +(2.06260 + 1.14170i) q^{47} +(3.12509 + 5.48941i) q^{48} +(8.04135 - 10.9843i) q^{49} +(-8.96515 + 3.76099i) q^{50} +(2.39171 + 0.274796i) q^{51} +(-10.4943 + 5.32328i) q^{52} +(11.8120 - 1.28464i) q^{53} +(9.54100 - 4.62347i) q^{54} +(-0.338305 + 0.398283i) q^{55} +(-0.298340 - 1.48236i) q^{56} +(0.581409 + 0.868808i) q^{57} +(-9.67994 + 16.7661i) q^{58} +(-5.09778 + 5.74567i) q^{59} +(1.41290 - 1.14263i) q^{60} +(-4.51973 - 3.18506i) q^{61} +(17.6633 + 5.95144i) q^{62} +(13.5015 - 1.79694i) q^{63} +(7.92436 + 4.76793i) q^{64} +(-1.55834 - 2.12866i) q^{65} +(-1.55739 + 3.47500i) q^{66} +(-5.28554 - 5.38184i) q^{67} +(2.77265 - 1.16316i) q^{68} +(-2.75518 - 1.41864i) q^{69} +(4.20296 - 1.58730i) q^{70} +(-7.28507 + 4.38328i) q^{71} +(0.570689 - 0.820115i) q^{72} +(-0.170573 - 0.428107i) q^{73} +(0.312493 - 0.874917i) q^{74} +(-6.15935 - 5.49293i) q^{75} +(1.16440 + 0.590648i) q^{76} +(-3.29964 + 3.61182i) q^{77} +(-15.2335 - 11.7266i) q^{78} +(-3.69022 - 3.25100i) q^{79} +(-0.654649 + 1.64304i) q^{80} +(7.03065 + 5.61871i) q^{81} +(14.7608 - 3.24910i) q^{82} +(-7.15775 - 0.517837i) q^{83} +(13.6047 - 10.2124i) q^{84} +(0.357899 + 0.571227i) q^{85} +(-14.8237 + 1.07244i) q^{86} +(-16.3839 - 1.28521i) q^{87} +(0.0323526 + 0.357402i) q^{88} +(8.09968 + 3.74731i) q^{89} +(2.67894 + 1.27907i) q^{90} +(-13.8597 - 20.4415i) q^{91} +(-3.86789 + 0.139731i) q^{92} +(1.89918 + 15.7078i) q^{93} +(2.09826 + 4.32848i) q^{94} +(-0.0884405 + 0.279033i) q^{95} +(-1.35071 + 13.9770i) q^{96} +(18.9296 - 2.75339i) q^{97} +(26.3223 - 8.86903i) q^{98} +(-3.23163 + 0.0775221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9}+O(q^{10}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18} - 120 q^{19} - 31 q^{20} - 60 q^{21} - 29 q^{22} - 29 q^{23} - 16 q^{24} + 29 q^{25} - 92 q^{26} - 55 q^{27} - 132 q^{28} - 27 q^{29} - 64 q^{30} - 21 q^{31} - 49 q^{32} - 32 q^{33} - 17 q^{34} - 136 q^{35} - 70 q^{36} - 120 q^{37} - 33 q^{38} - 80 q^{39} - 17 q^{40} - 17 q^{41} - 68 q^{42} - 21 q^{43} - 104 q^{44} - 58 q^{45} - 116 q^{46} - 17 q^{47} + 106 q^{48} + 19 q^{49} - 5 q^{50} - 250 q^{51} - 21 q^{52} - 108 q^{53} + 175 q^{54} - 116 q^{55} - q^{56} + 63 q^{57} - 58 q^{58} - 17 q^{59} - 816 q^{60} - 27 q^{61} - 128 q^{62} + 95 q^{63} - 256 q^{64} - 59 q^{65} + 67 q^{66} - 15 q^{67} - 43 q^{68} - 302 q^{69} - 41 q^{70} - 134 q^{71} + 210 q^{72} - 144 q^{73} - 51 q^{74} - 47 q^{75} - 9 q^{76} - 85 q^{77} + 36 q^{78} - 39 q^{79} - 128 q^{80} - 22 q^{81} - 164 q^{82} - 35 q^{83} - 190 q^{84} - 17 q^{85} + 31 q^{86} - 75 q^{87} - 29 q^{88} - 36 q^{89} - 86 q^{90} - 136 q^{91} - 31 q^{92} - 41 q^{94} - 13 q^{95} - 30 q^{96} - 3 q^{97} - 156 q^{98} - 86 q^{99}+O(q^{100}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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