LMFDB - Embedded newform 531.2.m.a.130.4

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			130.4
Character	$\chi$	$=$	531.130
Dual form			531.2.m.a.241.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96308 - 1.72943i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(0.610661 + 4.80597i) q^{4} +(-1.03490 - 0.150531i) q^{5} +(4.51359 + 0.401670i) q^{6} +(0.232023 + 2.56317i) q^{7} +(4.17642 - 6.15976i) q^{8} +(0.897734 - 2.86253i) q^{9} +O(q^{10})$	\(q+(-1.96308 - 1.72943i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(0.610661 + 4.80597i) q^{4} +(-1.03490 - 0.150531i) q^{5} +(4.51359 + 0.401670i) q^{6} +(0.232023 + 2.56317i) q^{7} +(4.17642 - 6.15976i) q^{8} +(0.897734 - 2.86253i) q^{9} +(1.77126 + 2.08529i) q^{10} +(-0.888776 + 0.904969i) q^{11} +(-5.77980 - 6.08314i) q^{12} +(4.26785 + 0.154180i) q^{13} +(3.97735 - 5.43298i) q^{14} +(1.59907 - 0.850887i) q^{15} +(-9.47019 + 2.44612i) q^{16} +(2.08363 - 0.963988i) q^{17} +(-6.71286 + 4.06681i) q^{18} +(0.889752 + 0.195849i) q^{19} +(0.0914704 - 5.06562i) q^{20} +(-2.95180 - 3.34036i) q^{21} +(3.30982 - 0.239453i) q^{22} +(-5.64858 - 2.13325i) q^{23} +(0.484920 + 12.8810i) q^{24} +(-3.74445 - 1.11284i) q^{25} +(-8.11149 - 7.68361i) q^{26} +(1.68155 + 4.91654i) q^{27} +(-12.1768 + 2.68033i) q^{28} +(1.95403 + 9.70899i) q^{29} +(-4.61065 - 1.09512i) q^{30} +(-0.975413 + 3.07746i) q^{31} +(9.54699 + 4.84274i) q^{32} +(0.312929 - 2.17457i) q^{33} +(-5.75748 - 1.71110i) q^{34} +(0.145715 - 2.68756i) q^{35} +(14.3054 + 2.56644i) q^{36} +(-2.06885 - 3.05133i) q^{37} +(-1.40795 - 1.92323i) q^{38} +(-6.11607 + 4.16037i) q^{39} +(-5.24941 + 5.74606i) q^{40} +(6.18850 + 5.06709i) q^{41} +(0.0177049 + 11.6623i) q^{42} +(-10.7074 + 2.76567i) q^{43} +(-4.89199 - 3.71880i) q^{44} +(-1.35996 + 2.82730i) q^{45} +(7.39930 + 13.9566i) q^{46} +(-3.97886 + 0.578741i) q^{47} +(10.7127 - 13.1241i) q^{48} +(0.370184 - 0.0675730i) q^{49} +(5.42609 + 8.66035i) q^{50} +(-1.92045 + 3.48198i) q^{51} +(1.86523 + 20.6053i) q^{52} +(2.04940 - 2.41274i) q^{53} +(5.20179 - 12.5597i) q^{54} +(1.05602 - 0.802766i) q^{55} +(16.7576 + 9.27569i) q^{56} +(-1.44290 + 0.638807i) q^{57} +(12.9551 - 22.4389i) q^{58} +(-4.72741 - 6.05406i) q^{59} +(5.06582 + 7.16548i) q^{60} +(0.212758 + 0.187435i) q^{61} +(7.23707 - 4.35440i) q^{62} +(7.54546 + 1.63688i) q^{63} +(-3.12569 - 7.84489i) q^{64} +(-4.39360 - 0.802003i) q^{65} +(-4.37507 + 3.72766i) q^{66} +(-0.858840 - 1.77170i) q^{67} +(5.90529 + 9.42517i) q^{68} +(10.0726 - 2.81313i) q^{69} +(-4.93399 + 5.02389i) q^{70} +(-3.93283 + 9.87066i) q^{71} +(-13.8832 - 17.4849i) q^{72} +(1.54335 + 0.167849i) q^{73} +(-1.21573 + 9.56793i) q^{74} +(6.36826 - 2.28545i) q^{75} +(-0.397908 + 4.39571i) q^{76} +(-2.52581 - 2.06811i) q^{77} +(19.2014 + 2.41017i) q^{78} +(-0.0649163 + 3.59506i) q^{79} +(10.1689 - 1.10594i) q^{80} +(-7.38815 - 5.13958i) q^{81} +(-3.38534 - 20.6497i) q^{82} +(-12.3172 + 6.24796i) q^{83} +(14.2511 - 16.2261i) q^{84} +(-2.30146 + 0.683983i) q^{85} +(25.8024 + 13.0884i) q^{86} +(-12.6820 - 11.5506i) q^{87} +(1.86249 + 9.25417i) q^{88} +(-11.2180 - 3.77977i) q^{89} +(7.55933 - 3.19825i) q^{90} +(0.595048 + 10.9750i) q^{91} +(6.80298 - 28.4496i) q^{92} +(-1.79347 - 5.29624i) q^{93} +(8.81170 + 5.74503i) q^{94} +(-0.891324 - 0.336619i) q^{95} +(-18.2928 + 3.02747i) q^{96} +(-4.92848 - 6.73222i) q^{97} +(-0.843563 - 0.507555i) q^{98} +(1.79262 + 3.35657i) 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 $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{26}{29}\right)$

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 $

$2$	−1.96308	−	1.72943i	−1.38811	−	1.22289i	−0.945270	−	0.326288i	$-0.894202\pi$
$2$	−1.96308	−	1.72943i	−1.38811	−	1.22289i	−0.442837	−	0.896602i	$-0.646028\pi$
$3$	−1.39602	+	1.02525i	−0.805992	+	0.591927i
$3$	−1.39602	+	1.02525i	−0.805992	+	0.591927i
$4$	0.610661	+	4.80597i	0.305331	+	2.40298i
$5$	−1.03490	−	0.150531i	−0.462822	−	0.0673193i	−0.0914625	−	0.995809i	$-0.529154\pi$
$5$	−1.03490	−	0.150531i	−0.462822	−	0.0673193i	−0.371359	+	0.928489i	$0.621108\pi$
$6$	4.51359	+	0.401670i	1.84266	+	0.163981i
$7$	0.232023	+	2.56317i	0.0876964	+	0.968789i	0.914040	+	0.405623i	$0.132945\pi$
$7$	0.232023	+	2.56317i	0.0876964	+	0.968789i	−0.826344	+	0.563166i	$0.809583\pi$
$8$	4.17642	−	6.15976i	1.47659	−	2.17780i
$9$	0.897734	−	2.86253i	0.299245	−	0.954176i
$10$	1.77126	+	2.08529i	0.560122	+	0.659427i
$11$	−0.888776	+	0.904969i	−0.267976	+	0.272859i	−0.834284	−	0.551335i	$-0.814118\pi$
$11$	−0.888776	+	0.904969i	−0.267976	+	0.272859i	0.566308	+	0.824194i	$0.308371\pi$
$12$	−5.77980	−	6.08314i	−1.66848	−	1.75605i
$13$	4.26785	+	0.154180i	1.18369	+	0.0427619i	0.620935	−	0.783862i	$-0.286753\pi$
$13$	4.26785	+	0.154180i	1.18369	+	0.0427619i	0.562754	+	0.826624i	$0.309742\pi$
$14$	3.97735	−	5.43298i	1.06299	−	1.45203i
$15$	1.59907	−	0.850887i	0.412879	−	0.219698i
$16$	−9.47019	+	2.44612i	−2.36755	+	0.611529i
$17$	2.08363	−	0.963988i	0.505354	−	0.233802i	−0.150611	−	0.988593i	$-0.548124\pi$
$17$	2.08363	−	0.963988i	0.505354	−	0.233802i	0.655965	+	0.754792i	$0.272262\pi$
$18$	−6.71286	+	4.06681i	−1.58224	+	0.958556i
$19$	0.889752	+	0.195849i	0.204123	+	0.0449309i	0.315855	−	0.948808i	$-0.397709\pi$
$19$	0.889752	+	0.195849i	0.204123	+	0.0449309i	−0.111732	+	0.993738i	$0.535640\pi$
$20$	0.0914704	−	5.06562i	0.0204534	−	1.13271i
$21$	−2.95180	−	3.34036i	−0.644135	−	0.728926i
$22$	3.30982	−	0.239453i	0.705656	−	0.0510516i
$23$	−5.64858	−	2.13325i	−1.17781	−	0.444814i	−0.314387	−	0.949295i	$-0.601799\pi$
$23$	−5.64858	−	2.13325i	−1.17781	−	0.444814i	−0.863423	+	0.504481i	$0.831684\pi$
$24$	0.484920	+	12.8810i	0.0989839	+	2.62932i
$25$	−3.74445	−	1.11284i	−0.748891	−	0.222567i
$26$	−8.11149	−	7.68361i	−1.59079	−	1.50688i
$27$	1.68155	+	4.91654i	0.323614	+	0.946189i
$28$	−12.1768	+	2.68033i	−2.30121	+	0.506534i
$29$	1.95403	+	9.70899i	0.362854	+	1.80291i	0.566715	+	0.823914i	$0.308214\pi$
$29$	1.95403	+	9.70899i	0.362854	+	1.80291i	−0.203861	+	0.979000i	$0.565349\pi$
$30$	−4.61065	−	1.09512i	−0.841786	−	0.199941i
$31$	−0.975413	+	3.07746i	−0.175189	+	0.552729i	−0.999918	−	0.0128000i	$-0.995926\pi$
$31$	−0.975413	+	3.07746i	−0.175189	+	0.552729i	0.824729	+	0.565529i	$0.191328\pi$
$32$	9.54699	+	4.84274i	1.68769	+	0.856084i
$33$	0.312929	−	2.17457i	0.0544740	−	0.378544i
$34$	−5.75748	−	1.71110i	−0.987399	−	0.293451i
$35$	0.145715	−	2.68756i	0.0246304	−	0.454280i
$36$	14.3054	+	2.56644i	2.38424	+	0.427741i
$37$	−2.06885	−	3.05133i	−0.340117	−	0.501635i	0.618712	−	0.785618i	$-0.287655\pi$
$37$	−2.06885	−	3.05133i	−0.340117	−	0.501635i	−0.958830	+	0.283982i	$0.908344\pi$
$38$	−1.40795	−	1.92323i	−0.228399	−	0.311989i
$39$	−6.11607	+	4.16037i	−0.979355	+	0.666192i
$40$	−5.24941	+	5.74606i	−0.830005	+	0.908532i
$41$	6.18850	+	5.06709i	0.966481	+	0.791347i	0.978004	−	0.208586i	$-0.0668863\pi$
$41$	6.18850	+	5.06709i	0.966481	+	0.791347i	−0.0115227	+	0.999934i	$0.503668\pi$
$42$	0.0177049	+	11.6623i	0.00273192	+	1.79953i
$43$	−10.7074	+	2.76567i	−1.63286	+	0.421761i	−0.950867	−	0.309601i	$-0.899805\pi$
$43$	−10.7074	+	2.76567i	−1.63286	+	0.421761i	−0.681990	+	0.731362i	$0.738885\pi$
$44$	−4.89199	−	3.71880i	−0.737496	−	0.560630i
$45$	−1.35996	+	2.82730i	−0.202731	+	0.421469i
$46$	7.39930	+	13.9566i	1.09097	+	2.05778i
$47$	−3.97886	+	0.578741i	−0.580376	+	0.0844180i	−0.427799	−	0.903874i	$-0.640711\pi$
$47$	−3.97886	+	0.578741i	−0.580376	+	0.0844180i	−0.152576	+	0.988292i	$0.548757\pi$
$48$	10.7127	−	13.1241i	1.54624	−	1.89430i
$49$	0.370184	−	0.0675730i	0.0528834	−	0.00965329i
$50$	5.42609	+	8.66035i	0.767365	+	1.22476i
$51$	−1.92045	+	3.48198i	−0.268917	+	0.487575i
$52$	1.86523	+	20.6053i	0.258660	+	2.85744i
$53$	2.04940	−	2.41274i	0.281507	−	0.331416i	−0.603177	−	0.797608i	$-0.706099\pi$
$53$	2.04940	−	2.41274i	0.281507	−	0.331416i	0.884684	+	0.466192i	$0.154374\pi$
$54$	5.20179	−	12.5597i	0.707875	−	1.70916i
$55$	1.05602	−	0.802766i	0.142394	−	0.108245i
$56$	16.7576	+	9.27569i	2.23932	+	1.23952i
$57$	−1.44290	+	0.638807i	−0.191117	+	0.0846121i
$58$	12.9551	−	22.4389i	1.70109	−	2.94637i
$59$	−4.72741	−	6.05406i	−0.615456	−	0.788171i
$59$	−4.72741	−	6.05406i	−0.615456	−	0.788171i
$60$	5.06582	+	7.16548i	0.653995	+	0.925060i
$61$	0.212758	+	0.187435i	0.0272409	+	0.0239986i	0.674552	−	0.738227i	$-0.264337\pi$
$61$	0.212758	+	0.187435i	0.0272409	+	0.0239986i	−0.647312	+	0.762225i	$0.724107\pi$
$62$	7.23707	−	4.35440i	0.919108	−	0.553009i
$63$	7.54546	+	1.63688i	0.950638	+	0.206227i
$64$	−3.12569	−	7.84489i	−0.390711	−	0.980611i
$65$	−4.39360	−	0.802003i	−0.544958	−	0.0994762i
$66$	−4.37507	+	3.72766i	−0.538534	+	0.458844i
$67$	−0.858840	−	1.77170i	−0.104924	−	0.216447i	0.840853	−	0.541263i	$-0.182054\pi$
$67$	−0.858840	−	1.77170i	−0.104924	−	0.216447i	−0.945777	+	0.324816i	$0.894697\pi$
$68$	5.90529	+	9.42517i	0.716121	+	1.14297i
$69$	10.0726	−	2.81313i	1.21260	−	0.338661i
$70$	−4.93399	+	5.02389i	−0.589725	+	0.600470i
$71$	−3.93283	+	9.87066i	−0.466741	+	1.17143i	0.487694	+	0.873014i	$0.337838\pi$
$71$	−3.93283	+	9.87066i	−0.466741	+	1.17143i	−0.954435	+	0.298417i	$0.903541\pi$
$72$	−13.8832	−	17.4849i	−1.63615	−	2.06062i
$73$	1.54335	+	0.167849i	0.180635	+	0.0196453i	0.197990	−	0.980204i	$-0.436559\pi$
$73$	1.54335	+	0.167849i	0.180635	+	0.0196453i	−0.0173542	+	0.999849i	$0.505524\pi$
$74$	−1.21573	+	9.56793i	−0.141326	+	1.11225i
$75$	6.36826	−	2.28545i	0.735343	−	0.263901i
$76$	−0.397908	+	4.39571i	−0.0456431	+	0.504223i
$77$	−2.52581	−	2.06811i	−0.287843	−	0.235683i
$78$	19.2014	+	2.41017i	2.17413	+	0.272899i
$79$	−0.0649163	+	3.59506i	−0.00730366	+	0.404476i	0.975518	+	0.219919i	$0.0705793\pi$
$79$	−0.0649163	+	3.59506i	−0.00730366	+	0.404476i	−0.982822	+	0.184557i	$0.940915\pi$
$80$	10.1689	−	1.10594i	1.13692	−	0.123647i
$81$	−7.38815	−	5.13958i	−0.820905	−	0.571064i
$82$	−3.38534	−	20.6497i	−0.373849	−	2.28038i
$83$	−12.3172	+	6.24796i	−1.35199	+	0.685803i	−0.971068	−	0.238803i	$-0.923245\pi$
$83$	−12.3172	+	6.24796i	−1.35199	+	0.685803i	−0.380925	+	0.924606i	$0.624394\pi$
$84$	14.2511	−	16.2261i	1.55492	−	1.77041i
$85$	−2.30146	+	0.683983i	−0.249628	+	0.0741884i
$86$	25.8024	+	13.0884i	2.78235	+	1.41135i
$87$	−12.6820	−	11.5506i	−1.35965	−	1.23835i
$88$	1.86249	+	9.25417i	0.198542	+	0.986498i
$89$	−11.2180	−	3.77977i	−1.18910	−	0.400655i	−0.345910	−	0.938268i	$-0.612430\pi$
$89$	−11.2180	−	3.77977i	−1.18910	−	0.400655i	−0.843192	+	0.537613i	$0.819326\pi$
$90$	7.55933	−	3.19825i	0.796823	−	0.337125i
$91$	0.595048	+	10.9750i	0.0623780	+	1.15049i
$92$	6.80298	−	28.4496i	0.709259	−	2.96607i
$93$	−1.79347	−	5.29624i	−0.185974	−	0.549194i
$94$	8.81170	+	5.74503i	0.908858	+	0.592555i
$95$	−0.891324	−	0.336619i	−0.0914479	−	0.0345364i
$96$	−18.2928	+	3.02747i	−1.86700	+	0.308990i
$97$	−4.92848	−	6.73222i	−0.500412	−	0.683553i	0.480724	−	0.876872i	$-0.340374\pi$
$97$	−4.92848	−	6.73222i	−0.500412	−	0.683553i	−0.981136	+	0.193319i	$0.938075\pi$
$98$	−0.843563	−	0.507555i	−0.0852128	−	0.0512708i
$99$	1.79262	+	3.35657i	0.180165	+	0.337348i
$100$	3.06166	−	18.6753i	0.306166	−	1.86753i
$101$	4.12276	+	2.90532i	0.410230	+	0.289090i	0.762724	−	0.646724i	$-0.223862\pi$
$101$	4.12276	+	2.90532i	0.410230	+	0.289090i	−0.352494	+	0.935814i	$0.614666\pi$
$102$	9.79184	−	3.51412i	0.969537	−	0.347949i
$103$	−13.9742	+	5.86234i	−1.37692	+	0.577634i	−0.945826	−	0.324674i	$-0.894745\pi$
$103$	−13.9742	+	5.86234i	−1.37692	+	0.577634i	−0.431093	+	0.902308i	$0.641872\pi$
$104$	18.7740	−	25.6450i	1.84095	−	2.51470i
$105$	2.55199	+	3.90128i	0.249049	+	0.380726i
$106$	−8.19581	+	1.19211i	−0.796047	+	0.115788i
$107$	2.25949	+	8.13794i	0.218433	+	0.786725i	0.988816	+	0.149143i	$0.0476514\pi$
$107$	2.25949	+	8.13794i	0.218433	+	0.786725i	−0.770383	+	0.637582i	$0.779935\pi$
$108$	−22.6019	+	11.0838i	−2.17487	+	1.06654i
$109$	−5.07797	+	9.57807i	−0.486382	+	0.917413i	0.511913	+	0.859037i	$0.328937\pi$
$109$	−5.07797	+	9.57807i	−0.486382	+	0.917413i	−0.998295	+	0.0583757i	$0.981408\pi$
$110$	−3.46138	−	0.250418i	−0.330030	−	0.0238764i
$111$	6.01652	+	2.13862i	0.571063	+	0.202989i
$112$	−8.46712	−	23.7062i	−0.800068	−	2.24002i
$113$	−20.9675	−	3.04981i	−1.97246	−	0.286902i	−0.998076	−	0.0620034i	$-0.980251\pi$
$113$	−20.9675	−	3.04981i	−1.97246	−	0.286902i	−0.974382	−	0.224898i	$-0.927795\pi$
$114$	3.93731	+	1.24137i	0.368763	+	0.116265i
$115$	5.52460	+	3.05799i	0.515172	+	0.285159i
$116$	−45.4678	+	15.3199i	−4.22158	+	1.42242i
$117$	4.27274	−	12.0784i	0.395015	−	1.11665i
$118$	−1.18979	+	20.0603i	−0.109529	+	1.84670i
$119$	2.95432	+	5.11703i	0.270822	+	0.469078i
$120$	1.43714	−	13.4036i	0.131192	−	1.22357i
$121$	0.169548	+	9.38958i	0.0154135	+	0.853598i
$122$	−0.0935059	−	0.735901i	−0.00846562	−	0.0666253i
$123$	−13.8343	−	0.729011i	−1.24740	−	0.0657327i
$124$	−15.3858	−	2.80852i	−1.38169	−	0.252212i
$125$	8.45330	+	3.91091i	0.756086	+	0.349803i
$126$	−11.9815	−	16.2626i	−1.06739	−	1.44879i
$127$	8.18061	−	15.4303i	0.725912	−	1.36921i	−0.195530	−	0.980698i	$-0.562643\pi$
$127$	8.18061	−	15.4303i	0.725912	−	1.36921i	0.921442	−	0.388517i	$-0.127012\pi$
$128$	−0.229756	+	0.643268i	−0.0203077	+	0.0568574i
$129$	12.1122	−	14.8386i	1.06642	−	1.30647i
$130$	7.23797	+	9.17281i	0.634812	+	0.804508i
$131$	−8.22859	−	0.297266i	−0.718935	−	0.0259722i	−0.325782	−	0.945445i	$-0.605627\pi$
$131$	−8.22859	−	0.297266i	−0.718935	−	0.0259722i	−0.393154	+	0.919473i	$0.628616\pi$
$132$	10.6420	+	0.176003i	0.926267	+	0.0153191i
$133$	−0.295553	+	2.32603i	−0.0256277	+	0.201692i
$134$	−1.37805	+	4.96328i	−0.119045	+	0.428762i
$135$	−1.00015	−	5.34126i	−0.0860789	−	0.459703i
$136$	2.76416	−	16.8607i	0.237025	−	1.44579i
$137$	−0.293956	−	0.927443i	−0.0251144	−	0.0792368i	0.939883	−	0.341498i	$-0.110934\pi$
$137$	−0.293956	−	0.927443i	−0.0251144	−	0.0792368i	−0.964997	+	0.262261i	$0.915532\pi$
$138$	−24.6385	−	11.8975i	−2.09737	−	1.01278i
$139$	7.37072	−	16.7171i	0.625177	−	1.41793i	−0.265867	−	0.964010i	$-0.585658\pi$
$139$	7.37072	−	16.7171i	0.625177	−	1.41793i	0.891044	−	0.453918i	$-0.149974\pi$
$140$	13.0053	−	0.940886i	1.09915	−	0.0795194i
$141$	4.96120	−	4.88725i	0.417809	−	0.411580i
$142$	24.7911	−	12.5753i	2.08042	−	1.05530i
$143$	−3.93269	+	3.72524i	−0.328868	+	0.311520i
$144$	−1.49963	+	29.3046i	−0.124969	+	2.44205i
$145$	−0.560726	−	10.3420i	−0.0465658	−	0.858855i
$146$	−2.73944	−	2.99861i	−0.226717	−	0.248167i
$147$	−0.447504	+	0.473863i	−0.0369095	+	0.0390836i
$148$	13.4012	−	11.8062i	1.10157	−	0.970460i
$149$	−0.142886	+	0.450811i	−0.0117057	+	0.0369319i	−0.958937	−	0.283618i	$-0.908465\pi$
$149$	−0.142886	+	0.450811i	−0.0117057	+	0.0369319i	0.947232	+	0.320550i	$0.103868\pi$
$150$	−16.4539	−	6.52692i	−1.34346	−	0.532921i
$151$	0.272492	−	1.13954i	0.0221751	−	0.0927346i	−0.960387	−	0.278670i	$-0.910106\pi$
$151$	0.272492	−	1.13954i	0.0221751	−	0.0927346i	0.982562	+	0.185936i	$0.0595316\pi$
$152$	4.92236	−	4.66271i	0.399256	−	0.378195i
$153$	−0.888902	−	6.82985i	−0.0718635	−	0.552161i
$154$	1.38171	+	8.42808i	0.111342	+	0.679154i
$155$	1.47271	−	3.03804i	0.118291	−	0.244021i
$156$	−23.7294	−	26.8530i	−1.89987	−	2.14996i
$157$	−0.421968	+	0.233569i	−0.0336767	+	0.0186408i	−0.501032	−	0.865429i	$-0.667046\pi$
$157$	−0.421968	+	0.233569i	−0.0336767	+	0.0186408i	0.467355	+	0.884070i	$0.345207\pi$
$158$	6.34483	−	6.94512i	0.504768	−	0.552524i
$159$	−0.387344	+	5.46938i	−0.0307184	+	0.433750i
$160$	−9.15121	−	6.44887i	−0.723467	−	0.509828i
$161$	4.15730	−	14.9733i	0.327641	−	1.18006i
$162$	5.61499	+	22.8667i	0.441155	+	1.79658i
$163$	17.7979	+	1.93564i	1.39404	+	0.151611i	0.774113	−	0.633047i	$-0.218196\pi$
$163$	17.7979	+	1.93564i	1.39404	+	0.151611i	0.619928	+	0.784658i	$0.287162\pi$
$164$	−20.5732	+	32.8360i	−1.60650	+	2.56406i
$165$	−0.651190	+	2.20336i	−0.0506951	+	0.171531i
$166$	34.9851	+	9.03654i	2.71537	+	0.701372i
$167$	−2.22538	+	0.406220i	−0.172205	+	0.0314342i	−0.264985	−	0.964252i	$-0.585367\pi$
$167$	−2.22538	+	0.406220i	−0.172205	+	0.0314342i	0.0927801	+	0.995687i	$0.470425\pi$
$168$	−32.9037	+	4.23162i	−2.53858	+	0.326477i
$169$	5.22467	+	0.377986i	0.401898	+	0.0290758i
$170$	5.70085	+	2.63749i	0.437235	+	0.202286i
$171$	1.35938	−	2.37112i	0.103955	−	0.181324i
$172$	−19.8303	−	49.7703i	−1.51205	−	3.79495i
$173$	−3.28151	−	1.37663i	−0.249488	−	0.104663i	0.258550	−	0.965998i	$-0.416755\pi$
$173$	−3.28151	−	1.37663i	−0.249488	−	0.104663i	−0.508038	+	0.861335i	$0.669629\pi$
$174$	4.91986	+	44.6073i	0.372974	+	3.38167i
$175$	1.98359	−	9.85589i	0.149946	−	0.745035i
$176$	6.20321	−	10.7443i	0.467585	−	0.809880i
$177$	12.8065	+	3.60482i	0.962592	+	0.270955i
$178$	15.4849	+	26.8207i	1.16064	+	2.01029i
$179$	17.5362	−	5.90864i	1.31072	−	0.441632i	0.424722	−	0.905324i	$-0.360372\pi$
$179$	17.5362	−	5.90864i	1.31072	−	0.441632i	0.885997	+	0.463691i	$0.153475\pi$
$180$	−14.4184	−	4.80942i	−1.07468	−	0.358473i
$181$	−12.0840	+	9.18603i	−0.898198	+	0.682793i	−0.948783	−	0.315927i	$-0.897684\pi$
$181$	−12.0840	+	9.18603i	−0.898198	+	0.682793i	0.0505852	+	0.998720i	$0.483891\pi$
$182$	17.8124	−	22.5739i	1.32034	−	1.67329i
$183$	−0.489182	−	0.0435330i	−0.0361614	−	0.00321805i
$184$	−36.7311	+	25.8845i	−2.70786	+	1.90823i
$185$	1.68174	+	3.46925i	0.123644	+	0.255064i
$186$	−5.63874	+	13.4986i	−0.413452	+	0.989766i
$187$	−0.979497	+	2.74239i	−0.0716279	+	0.200543i
$188$	−5.21114	−	18.7688i	−0.380061	−	1.36886i
$189$	−12.2118	+	5.45085i	−0.888278	+	0.396491i
$190$	1.16758	+	2.20229i	0.0847053	+	0.159771i
$191$	3.97010	+	9.00435i	0.287266	+	0.651532i	0.998687	−	0.0512348i	$-0.0163157\pi$
$191$	3.97010	+	9.00435i	0.287266	+	0.651532i	−0.711421	+	0.702766i	$0.751948\pi$
$192$	12.4065	+	7.74700i	0.895360	+	0.559092i
$193$	11.1005	+	11.3027i	0.799029	+	0.813587i	0.985642	−	0.168846i	$-0.0540042\pi$
$193$	11.1005	+	11.3027i	0.799029	+	0.813587i	−0.186614	+	0.982433i	$0.559751\pi$
$194$	−1.96788	+	21.7393i	−0.141286	+	1.56079i
$195$	6.95579	−	3.38491i	0.498115	−	0.242399i
$196$	0.550811	+	1.73783i	0.0393436	+	0.124130i
$197$	−4.48668	−	2.69955i	−0.319663	−	0.192335i	0.346674	−	0.937986i	$-0.387311\pi$
$197$	−4.48668	−	2.69955i	−0.319663	−	0.192335i	−0.666337	+	0.745651i	$0.732139\pi$
$198$	2.28589	−	9.68942i	0.162451	−	0.688597i
$199$	−8.64117	−	12.7448i	−0.612556	−	0.903453i	0.387272	−	0.921965i	$-0.373417\pi$
$199$	−8.64117	−	12.7448i	−0.612556	−	0.903453i	−0.999829	+	0.0185125i	$0.994107\pi$
$200$	−22.4932	+	18.4173i	−1.59051	+	1.30230i
$201$	3.01538	+	1.59280i	0.212689	+	0.112347i
$202$	−3.06877	−	12.8334i	−0.215918	−	0.902954i
$203$	−24.4325	+	7.26122i	−1.71482	+	0.509638i
$204$	−17.9070	−	7.10333i	−1.25374	−	0.497332i
$205$	−5.64173	−	6.17550i	−0.394036	−	0.431316i
$206$	37.5710	+	12.6591i	2.61769	+	0.882004i
$207$	−11.1774	+	14.2541i	−0.776884	+	0.990730i
$208$	−40.7945	+	8.97954i	−2.82859	+	0.622619i
$209$	−0.968028	+	0.631132i	−0.0669599	+	0.0436563i
$210$	1.73721	−	12.0720i	0.119879	−	0.833048i
$211$	4.97595	+	20.8091i	0.342559	+	1.43256i	0.829199	+	0.558953i	$0.188797\pi$
$211$	4.97595	+	20.8091i	0.342559	+	1.43256i	−0.486641	+	0.873602i	$0.661778\pi$
$212$	12.8470	+	8.37599i	0.882339	+	0.575265i
$213$	−4.62957	−	17.8117i	−0.317213	−	1.22044i
$214$	9.63843	−	19.8831i	0.658870	−	1.35918i
$215$	11.4974	−	1.25041i	0.784114	−	0.0852776i
$216$	37.3076	+	10.1756i	2.53846	+	0.692363i
$217$	−8.11439	−	1.78611i	−0.550841	−	0.121249i
$218$	26.5331	−	10.0205i	1.79705	−	0.678676i
$219$	−2.32663	+	1.34800i	−0.157219	+	0.0910891i
$220$	4.50294	+	4.58498i	0.303588	+	0.309119i
$221$	9.04124	−	3.79291i	0.608179	−	0.255138i
$222$	−8.11232	−	14.6034i	−0.544463	−	0.980118i
$223$	11.6056	−	18.5232i	0.777171	−	1.24041i	−0.188866	−	0.982003i	$-0.560481\pi$
$223$	11.6056	−	18.5232i	0.777171	−	1.24041i	0.966037	−	0.258405i	$-0.0831970\pi$
$224$	−10.1977	+	25.5942i	−0.681361	+	1.71009i
$225$	−6.54705	+	9.71958i	−0.436470	+	0.647972i
$226$	35.8865	+	42.2488i	2.38713	+	2.81035i
$227$	20.6566	−	0.746239i	1.37103	−	0.0495296i	0.659243	−	0.751930i	$-0.270877\pi$
$227$	20.6566	−	0.746239i	1.37103	−	0.0495296i	0.711782	+	0.702400i	$0.247888\pi$
$228$	−3.95121	−	6.54445i	−0.261675	−	0.433417i
$229$	−0.530314	+	0.373713i	−0.0350441	+	0.0246956i	−0.593429	−	0.804887i	$-0.702226\pi$
$229$	−0.530314	+	0.373713i	−0.0350441	+	0.0246956i	0.558384	+	0.829582i	$0.311421\pi$
$230$	−5.55665	−	15.5575i	−0.366395	−	1.02583i
$231$	5.64641	+	0.297543i	0.371506	+	0.0195769i
$232$	67.9658	+	28.5125i	4.46218	+	1.87194i
$233$	5.60490	−	3.37235i	0.367189	−	0.220930i	−0.319986	−	0.947422i	$-0.603678\pi$
$233$	5.60490	−	3.37235i	0.367189	−	0.220930i	0.687175	+	0.726492i	$0.258851\pi$
$234$	−29.2765	+	16.3215i	−1.91387	+	1.06697i
$235$	4.20484			0.274294
$236$	26.2088	−	26.4167i	1.70604	−	1.71958i
$237$	−3.59520	−	5.08532i	−0.233533	−	0.330327i
$238$	3.04997	−	15.1544i	0.197700	−	0.982316i
$239$	0.302689	+	16.7629i	0.0195793	+	1.08430i	0.849877	+	0.526980i	$0.176676\pi$
$239$	0.302689	+	16.7629i	0.0195793	+	1.08430i	−0.830298	+	0.557320i	$0.811830\pi$
$240$	−13.0621	+	11.9696i	−0.843158	+	0.772633i
$241$	−3.66919	+	4.65003i	−0.236354	+	0.299535i	−0.888796	−	0.458304i	$-0.848457\pi$
$241$	−3.66919	+	4.65003i	−0.236354	+	0.299535i	0.652442	+	0.757839i	$0.273745\pi$
$242$	15.9058	−	18.7257i	1.02246	−	1.20373i
$243$	15.5833	−	0.399734i	0.999671	−	0.0256429i
$244$	−0.770884	+	1.13697i	−0.0493508	+	0.0727869i
$245$	−0.393276	+	0.0142075i	−0.0251255	+	0.000907681i
$246$	25.8970	+	25.3565i	1.65113	+	1.61667i
$247$	3.76713	+	0.973037i	0.239697	+	0.0619129i
$248$	14.8827	+	18.8611i	0.945052	+	1.19768i
$249$	10.7894	−	21.3505i	0.683750	−	1.35303i
$250$	−9.83086	−	22.2968i	−0.621758	−	1.41017i
$251$	0.890309	+	0.676795i	0.0561958	+	0.0427189i	0.632895	−	0.774238i	$-0.281866\pi$
$251$	0.890309	+	0.676795i	0.0561958	+	0.0427189i	−0.576699	+	0.816957i	$0.695660\pi$
$252$	−3.25905	+	37.2628i	−0.205301	+	2.34733i
$253$	6.95085	−	3.21580i	0.436996	−	0.202176i
$254$	−42.7447	+	16.1431i	−2.68204	+	1.01291i
$255$	2.51162	−	3.31442i	0.157284	−	0.207557i
$256$	−13.2131	+	7.31377i	−0.825821	+	0.457111i
$257$	−11.2715	+	25.5643i	−0.703099	+	1.59466i	0.0973437	+	0.995251i	$0.468965\pi$
$257$	−11.2715	+	25.5643i	−0.703099	+	1.59466i	−0.800443	+	0.599409i	$0.795402\pi$
$258$	−49.4395	+	8.18228i	−3.07797	+	0.509407i
$259$	7.34107	−	6.01081i	0.456152	−	0.373493i
$260$	1.17140	−	21.6052i	0.0726472	−	1.33990i
$261$	29.5465	+	3.12263i	1.82888	+	0.193286i
$262$	15.6393	+	14.8143i	0.966198	+	0.915231i
$263$	−20.6896	+	13.4891i	−1.27577	+	0.831775i	−0.991892	−	0.127085i	$-0.959438\pi$
$263$	−20.6896	+	13.4891i	−1.27577	+	0.831775i	−0.283881	+	0.958860i	$0.591622\pi$
$264$	−12.0879	−	11.0095i	−0.743958	−	0.677587i
$265$	−2.48412	+	2.18845i	−0.152598	+	0.134436i
$266$	4.60290	−	4.05505i	0.282222	−	0.248631i
$267$	19.5357	−	6.22456i	1.19556	−	0.380937i
$268$	7.99025	−	5.20946i	0.488082	−	0.318218i
$269$	15.5000	+	14.6824i	0.945051	+	0.895199i	0.994622	−	0.103571i	$-0.0330269\pi$
$269$	15.5000	+	14.6824i	0.945051	+	0.895199i	−0.0495714	+	0.998771i	$0.515786\pi$
$270$	−7.27396	+	12.2150i	−0.442679	+	0.743382i
$271$	−0.651120	+	12.0092i	−0.0395527	+	0.729507i	0.909752	+	0.415151i	$0.136271\pi$
$271$	−0.651120	+	12.0092i	−0.0395527	+	0.729507i	−0.949305	+	0.314356i	$0.898211\pi$
$272$	−17.3743	+	14.2259i	−1.05347	+	0.862575i
$273$	−12.0828	−	14.7113i	−0.731285	−	0.890366i
$274$	−1.02689	+	2.32902i	−0.0620364	+	0.140701i
$275$	4.33506	−	2.39955i	0.261414	−	0.144699i
$276$	19.6708	+	46.6908i	1.18404	+	2.81046i
$277$	27.9751	−	10.5651i	1.68086	−	0.634798i	0.685244	−	0.728313i	$-0.259695\pi$
$277$	27.9751	−	10.5651i	1.68086	−	0.634798i	0.995618	+	0.0935153i	$0.0298104\pi$
$278$	−43.3804	+	20.0699i	−2.60178	+	1.20371i
$279$	7.93367	+	5.55489i	0.474976	+	0.332563i
$280$	−15.9461	−	12.1219i	−0.952964	−	0.724425i
$281$	−12.0851	−	27.4095i	−0.720937	−	1.63512i	−0.771369	−	0.636388i	$-0.780428\pi$
$281$	−12.0851	−	27.4095i	−0.720937	−	1.63512i	0.0504319	−	0.998727i	$-0.483940\pi$
$282$	−18.1914	+	1.01401i	−1.08328	+	0.0603833i
$283$	2.07703	+	2.63225i	0.123466	+	0.156471i	0.842862	−	0.538129i	$-0.180869\pi$
$283$	2.07703	+	2.63225i	0.123466	+	0.156471i	−0.719396	+	0.694600i	$0.755581\pi$
$284$	−49.8397	−	12.8734i	−2.95744	−	0.763897i
$285$	1.58942	−	0.443901i	0.0941493	−	0.0262944i
$286$	14.1627	−	0.511642i	0.837460	−	0.0302540i
$287$	−11.5520	+	17.0379i	−0.681891	+	1.00571i
$288$	22.4331	−	22.9810i	1.32189	−	1.35417i
$289$	−7.59334	+	8.93957i	−0.446667	+	0.525857i
$290$	−16.7850	+	21.2719i	−0.985648	+	1.24913i
$291$	13.7824	+	4.34538i	0.807941	+	0.254731i
$292$	0.135785	+	7.51978i	0.00794624	+	0.440062i
$293$	2.56421	−	12.7408i	0.149803	−	0.744325i	−0.832053	−	0.554696i	$-0.812835\pi$
$293$	2.56421	−	12.7408i	0.149803	−	0.744325i	0.981856	−	0.189629i	$-0.0607286\pi$
$294$	1.69800	−	0.156305i	0.0990293	−	0.00911590i
$295$	3.98108	+	6.97697i	0.231787	+	0.406215i
$296$	−27.4358			−1.59468
$297$	−5.94384	−	2.84795i	−0.344897	−	0.165255i
$298$	1.06014	−	0.637867i	0.0614124	−	0.0369506i
$299$	−23.7784	−	9.97531i	−1.37514	−	0.576887i
$300$	14.8727	+	29.2100i	0.858673	+	1.68644i
$301$	−9.57325	−	26.8031i	−0.551793	−	1.54491i
$302$	−2.50568	+	1.76576i	−0.144186	+	0.101608i
$303$	−8.73412	+	0.170977i	−0.501762	+	0.00982237i
$304$	−8.90519	+	0.321708i	−0.510747	+	0.0184512i
$305$	−0.191969	−	0.226004i	−0.0109921	−	0.0129409i
$306$	−10.0667	+	14.9448i	−0.575478	+	0.854339i
$307$	−8.04892	+	20.2013i	−0.459376	+	1.15295i	0.498787	+	0.866725i	$0.333779\pi$
$307$	−8.04892	+	20.2013i	−0.459376	+	1.15295i	−0.958163	+	0.286223i	$0.907600\pi$
$308$	8.39687	−	13.4019i	0.478456	−	0.763643i
$309$	13.4979	−	22.5110i	0.767868	−	1.28060i
$310$	−8.14512	+	3.41697i	−0.462612	+	0.194071i
$311$	15.4172	+	15.6981i	0.874230	+	0.890159i	0.994727	−	0.102555i	$-0.0327017\pi$
$311$	15.4172	+	15.6981i	0.874230	+	0.890159i	−0.120497	+	0.992714i	$0.538449\pi$
$312$	0.0835712	+	55.0489i	0.00473129	+	3.11653i
$313$	−2.92113	+	1.10320i	−0.165112	+	0.0623565i	−0.434483	−	0.900680i	$-0.643069\pi$
$313$	−2.92113	+	1.10320i	−0.165112	+	0.0623565i	0.269372	+	0.963036i	$0.413184\pi$
$314$	1.23230	+	0.271249i	0.0695425	+	0.0153075i
$315$	−7.56240	−	2.82983i	−0.426093	−	0.159443i
$316$	−17.3174	+	1.88338i	−0.974178	+	0.105948i
$317$	10.7074	−	22.0882i	0.601387	−	1.24060i	−0.351192	−	0.936304i	$-0.614223\pi$
$317$	10.7074	−	22.0882i	0.601387	−	1.24060i	0.952578	−	0.304293i	$-0.0984202\pi$
$318$	10.2193	−	10.0669i	0.573069	−	0.564526i
$319$	−10.5230	−	6.86078i	−0.589177	−	0.384130i
$320$	2.05388	+	8.58920i	0.114816	+	0.480151i
$321$	−11.4977	−	9.04418i	−0.641739	−	0.504797i
$322$	−34.0563	+	22.2039i	−1.89788	+	1.23738i
$323$	2.04271	−	0.449634i	0.113659	−	0.0250183i
$324$	20.1890	−	38.6457i	1.12161	−	2.14698i
$325$	−15.8092	−	5.32674i	−0.876936	−	0.295474i
$326$	−31.5912	−	34.5801i	−1.74968	−	1.91521i
$327$	−2.73095	−	18.5773i	−0.151022	−	1.02733i
$328$	57.0578	−	16.9573i	3.15049	−	0.936313i
$329$	−2.40660	−	10.0642i	−0.132680	−	0.554859i
$330$	5.08889	−	3.19918i	0.280134	−	0.176109i
$331$	16.1329	−	13.2095i	0.886745	−	0.726060i	−0.0758170	−	0.997122i	$-0.524156\pi$
$331$	16.1329	−	13.2095i	0.886745	−	0.726060i	0.962562	+	0.271062i	$0.0873749\pi$
$332$	−37.5492	−	55.3809i	−2.06078	−	3.03942i
$333$	−10.5918	+	3.18287i	−0.580427	+	0.174420i
$334$	5.07113	+	3.05120i	0.277480	+	0.166954i
$335$	0.622120	+	1.96281i	0.0339901	+	0.107240i
$336$	36.1250	+	24.4134i	1.97078	+	1.33186i
$337$	2.93254	−	32.3960i	0.159746	−	1.76472i	−0.381983	−	0.924169i	$-0.624759\pi$
$337$	2.93254	−	32.3960i	0.159746	−	1.76472i	0.541729	−	0.840553i	$-0.317770\pi$
$338$	−9.60274	−	9.77771i	−0.522320	−	0.531837i
$339$	32.3978	−	17.2393i	1.75961	−	0.936311i
$340$	−4.69261	−	10.6430i	−0.254493	−	0.577200i
$341$	−1.91809	−	3.61789i	−0.103870	−	0.195920i
$342$	−6.76926	+	2.30374i	−0.366040	+	0.124572i
$343$	5.07877	+	18.2921i	0.274228	+	0.987680i
$344$	−27.6825	+	77.5053i	−1.49254	+	4.17881i
$345$	−10.8476	+	1.39507i	−0.584017	+	0.0751082i
$346$	4.06108	+	8.37757i	0.218325	+	0.450381i
$347$	−7.89867	+	5.56620i	−0.424023	+	0.298809i	−0.768338	−	0.640045i	$-0.778916\pi$
$347$	−7.89867	+	5.56620i	−0.424023	+	0.298809i	0.344315	+	0.938854i	$0.388111\pi$
$348$	47.7672	−	68.0026i	2.56059	−	3.64532i
$349$	−9.66686	+	12.2510i	−0.517455	+	0.655779i	−0.972010	−	0.234939i	$-0.924511\pi$
$349$	−9.66686	+	12.2510i	−0.517455	+	0.655779i	0.454555	+	0.890719i	$0.349798\pi$
$350$	−20.9390	+	15.9174i	−1.11924	+	0.850822i
$351$	6.41856	+	21.2423i	0.342598	+	1.13383i
$352$	−12.8677	+	4.33562i	−0.685849	+	0.231089i
$353$	10.2416	+	17.7389i	0.545104	+	0.944149i	0.998600	+	0.0528902i	$0.0168433\pi$
$353$	10.2416	+	17.7389i	0.545104	+	0.944149i	−0.453496	+	0.891258i	$0.649823\pi$
$354$	−18.9058	−	29.2244i	−1.00483	−	1.55326i
$355$	5.55593	−	9.62315i	0.294878	−	0.510744i
$356$	11.3151	−	56.2213i	0.599698	−	2.97972i
$357$	−9.37051	−	4.11456i	−0.495940	−	0.217766i
$358$	−44.6436	−	18.7285i	−2.35949	−	0.989832i
$359$	−4.98073	−	12.5007i	−0.262873	−	0.659761i	0.736997	−	0.675896i	$-0.236243\pi$
$359$	−4.98073	−	12.5007i	−0.262873	−	0.659761i	−0.999870	+	0.0161350i	$0.994864\pi$
$360$	11.7357	+	20.1850i	0.618525	+	1.06384i
$361$	−16.4906	−	7.62938i	−0.867928	−	0.401546i
$362$	39.6085	+	2.86553i	2.08178	+	0.150609i
$363$	−9.86334	−	12.9342i	−0.517691	−	0.678869i
$364$	−52.3822	+	9.56180i	−2.74557	+	0.501175i
$365$	−1.57195	−	0.406029i	−0.0822795	−	0.0212525i
$366$	0.885016	+	0.931464i	0.0462605	+	0.0486884i
$367$	−14.2850	+	22.7996i	−0.745669	+	1.19013i	0.230491	+	0.973075i	$0.425967\pi$
$367$	−14.2850	+	22.7996i	−0.745669	+	1.19013i	−0.976159	+	0.217055i	$0.930355\pi$
$368$	58.7113	+	6.38523i	3.06054	+	0.332853i
$369$	20.0603	−	13.1659i	1.04430	−	0.685387i
$370$	2.69843	−	9.71886i	0.140285	−	0.505259i
$371$	6.65979	+	4.69316i	0.345759	+	0.243657i
$372$	24.3583	−	11.8535i	1.26292	−	0.614578i
$373$	−16.7072	+	18.2879i	−0.865067	+	0.946912i	−0.999028	−	0.0440750i	$-0.985966\pi$
$373$	−16.7072	+	18.2879i	−0.865067	+	0.946912i	0.133961	+	0.990987i	$0.457230\pi$
$374$	6.66560	−	3.68956i	0.344670	−	0.190782i
$375$	−15.8106	+	3.20702i	−0.816456	+	0.165610i
$376$	−13.0525	+	26.9259i	−0.673130	+	1.38859i
$377$	6.84256	+	41.7378i	0.352410	+	2.14961i
$378$	33.3996	+	10.4190i	1.71789	+	0.535894i
$379$	16.8600	−	15.9706i	0.866038	−	0.820355i	−0.118964	−	0.992899i	$-0.537957\pi$
$379$	16.8600	−	15.9706i	0.866038	−	0.820355i	0.985002	+	0.172544i	$0.0551985\pi$
$380$	1.07348	−	4.48923i	0.0550686	−	0.230293i
$381$	4.39957	+	29.9281i	0.225397	+	1.53326i
$382$	7.77876	−	24.5423i	0.397996	−	1.25569i
$383$	−6.01739	+	5.30118i	−0.307474	+	0.270878i	−0.800755	−	0.598993i	$-0.795568\pi$
$383$	−6.01739	+	5.30118i	−0.307474	+	0.270878i	0.493280	+	0.869870i	$0.335798\pi$
$384$	−0.338766	−	1.13357i	−0.0172876	−	0.0578473i
$385$	2.30265	+	2.52051i	0.117354	+	0.128457i
$386$	−2.24386	−	41.3856i	−0.114210	−	2.10647i
$387$	−1.69554	+	33.1330i	−0.0861890	+	1.68424i
$388$	29.3452	−	27.7972i	1.48978	−	1.41119i
$389$	24.1125	−	12.2311i	1.22255	−	0.620144i	0.281877	−	0.959451i	$-0.409043\pi$
$389$	24.1125	−	12.2311i	1.22255	−	0.620144i	0.940676	+	0.339307i	$0.110193\pi$
$390$	−19.5087	−	5.38469i	−0.987863	−	0.272664i
$391$	−13.8260	+	1.00026i	−0.699209	+	0.0505852i
$392$	1.12981	−	2.56246i	0.0570640	−	0.129424i
$393$	11.7920	−	8.02135i	0.594829	−	0.404624i
$394$	4.13904	+	13.0588i	0.208522	+	0.657894i
$395$	0.608348	−	3.71076i	0.0306093	−	0.186709i
$396$	−15.0369	+	10.6650i	−0.755631	+	0.535935i
$397$	−1.79740	+	6.47366i	−0.0902091	+	0.324904i	−0.994861	−	0.101247i	$-0.967717\pi$
$397$	−1.79740	+	6.47366i	−0.0902091	+	0.324904i	0.904652	+	0.426151i	$0.140131\pi$
$398$	−5.07786	+	39.9633i	−0.254530	+	2.00318i
$399$	−1.97216	−	3.55020i	−0.0987315	−	0.177732i
$400$	38.1828	+	1.37939i	1.90914	+	0.0689695i
$401$	−5.87513	−	7.44566i	−0.293390	−	0.371818i	0.616012	−	0.787737i	$-0.288747\pi$
$401$	−5.87513	−	7.44566i	−0.293390	−	0.371818i	−0.909402	+	0.415919i	$0.863460\pi$
$402$	−3.16481	−	8.34167i	−0.157847	−	0.416045i
$403$	−4.63740	+	12.9838i	−0.231006	+	0.646767i
$404$	−11.4452	+	21.5880i	−0.569422	+	1.07404i
$405$	6.87234	+	6.43110i	0.341489	+	0.319564i
$406$	60.5206	+	27.9998i	3.00359	+	1.38961i
$407$	4.60010	+	0.839699i	0.228019	+	0.0416223i
$408$	13.4275	+	26.3717i	0.664762	+	1.30560i
$409$	−1.22326	−	9.62717i	−0.0604863	−	0.476033i	−0.993290	−	0.115649i	$-0.963105\pi$
$409$	−1.22326	−	9.62717i	−0.0604863	−	0.476033i	0.932804	−	0.360384i	$-0.117354\pi$
$410$	0.395089	+	21.8800i	0.0195120	+	1.08057i
$411$	1.36123	+	0.993349i	0.0671444	+	0.0489983i
$412$	−36.7077	−	63.5796i	−1.80846	−	3.13234i
$413$	14.4207	−	13.5218i	0.709599	−	0.665367i
$414$	46.5937	−	8.65143i	2.28995	−	0.425195i
$415$	13.6876	−	4.61190i	0.671900	−	0.226389i
$416$	39.9985	+	22.1401i	1.96109	+	1.08551i
$417$	6.84952	+	30.8942i	0.335423	+	1.51290i
$418$	2.99181	+	0.435171i	0.146334	+	0.0212849i
$419$	3.34629	+	9.36890i	0.163477	+	0.457701i	0.995243	−	0.0974254i	$-0.0310607\pi$
$419$	3.34629	+	9.36890i	0.163477	+	0.457701i	−0.831766	+	0.555126i	$0.812670\pi$
$420$	−17.1910	+	14.6471i	−0.838835	+	0.714708i
$421$	6.02719	+	0.436045i	0.293747	+	0.0212516i	0.218245	−	0.975894i	$-0.429967\pi$
$421$	6.02719	+	0.436045i	0.293747	+	0.0212516i	0.0755026	+	0.997146i	$0.475944\pi$
$422$	26.2196	−	49.4554i	1.27635	−	2.40745i
$423$	−1.91529	+	11.9091i	−0.0931247	+	0.579043i
$424$	−6.30275	−	22.7004i	−0.306088	−	1.10243i
$425$	−8.87481	+	1.29088i	−0.430491	+	0.0626167i
$426$	−21.7159	+	42.9724i	−1.05214	+	2.08202i
$427$	−0.431064	+	0.588826i	−0.0208607	+	0.0284953i
$428$	−37.7309	+	15.8286i	−1.82379	+	0.765102i
$429$	1.67081	−	9.23249i	0.0806676	−	0.445749i
$430$	−24.7328	−	17.4292i	−1.19272	−	0.840512i
$431$	1.98932	−	12.1343i	0.0958223	−	0.584490i	−0.894649	−	0.446770i	$-0.852574\pi$
$431$	1.98932	−	12.1343i	0.0958223	−	0.584490i	0.990471	−	0.137720i	$-0.0439775\pi$
$432$	−27.9510	−	42.4473i	−1.34479	−	2.04225i
$433$	−33.0584	−	19.8906i	−1.58869	−	0.955881i	−0.987653	−	0.156656i	$-0.949929\pi$
$433$	−33.0584	−	19.8906i	−1.58869	−	0.955881i	−0.601033	−	0.799224i	$-0.705244\pi$
$434$	12.8402	+	17.5395i	0.616352	+	0.841925i
$435$	11.3859	+	13.8627i	0.545911	+	0.664666i
$436$	−49.1328	−	18.5556i	−2.35303	−	0.888652i
$437$	−4.60804	−	3.00434i	−0.220432	−	0.143717i
$438$	6.89863	+	1.37752i	0.329629	+	0.0658205i
$439$	1.45295	−	6.07613i	0.0693455	−	0.289998i	−0.927038	−	0.374967i	$-0.877654\pi$
$439$	1.45295	−	6.07613i	0.0693455	−	0.289998i	0.996384	+	0.0849693i	$0.0270792\pi$
$440$	−0.534459	−	9.85752i	−0.0254793	−	0.469939i
$441$	0.138897	−	1.12032i	0.00661413	−	0.0533488i
$442$	−24.3082	−	8.19040i	−1.15622	−	0.389577i
$443$	−5.01870	−	24.9364i	−0.238445	−	1.18477i	−0.900346	−	0.435174i	$-0.856687\pi$
$443$	−5.01870	−	24.9364i	−0.238445	−	1.18477i	0.661901	−	0.749591i	$-0.269750\pi$
$444$	−6.60410	+	30.2212i	−0.313417	+	1.43423i
$445$	11.0405	+	5.60034i	0.523371	+	0.265481i
$446$	−54.8174	+	16.2915i	−2.59568	+	0.771425i
$447$	−0.262721	−	0.775834i	−0.0124263	−	0.0366957i
$448$	19.3826	−	9.83188i	0.915741	−	0.464513i
$449$	5.56318	+	33.9339i	0.262543	+	1.60144i	0.708051	+	0.706161i	$0.249575\pi$
$449$	5.56318	+	33.9339i	0.262543	+	1.60144i	−0.445508	+	0.895278i	$0.646977\pi$
$450$	29.6617	−	7.75766i	1.39827	−	0.365700i
$451$	−10.0858	+	1.09689i	−0.474920	+	0.0516506i
$452$	1.85323	−	102.632i	0.0871685	−	4.82738i
$453$	0.787909	+	1.87019i	0.0370192	+	0.0878693i
$454$	−41.8411	−	34.2592i	−1.96370	−	1.60786i
$455$	1.03626	−	11.4476i	0.0485806	−	0.536673i
$456$	−2.09127	+	11.5559i	−0.0979329	+	0.541153i
$457$	−1.54170	+	12.1333i	−0.0721175	+	0.567572i	0.914508	+	0.404568i	$0.132578\pi$
$457$	−1.54170	+	12.1333i	−0.0721175	+	0.567572i	−0.986625	+	0.163004i	$0.947882\pi$
$458$	1.68736	+	0.183511i	0.0788450	+	0.00857491i
$459$	8.24321	+	8.62325i	0.384760	+	0.402499i
$460$	−11.3229	+	28.4184i	−0.527935	+	1.32502i
$461$	20.1652	−	20.5326i	0.939189	−	0.956301i	−0.0599330	−	0.998202i	$-0.519089\pi$
$461$	20.1652	−	20.5326i	0.939189	−	0.956301i	0.999122	+	0.0419016i	$0.0133416\pi$
$462$	−10.5698	−	10.3492i	−0.491750	−	0.481486i
$463$	17.2467	+	27.5266i	0.801520	+	1.27927i	0.956610	+	0.291371i	$0.0941114\pi$
$463$	17.2467	+	27.5266i	0.801520	+	1.27927i	−0.155090	+	0.987900i	$0.549567\pi$
$464$	−42.2543	−	87.1661i	−1.96161	−	4.04659i
$465$	1.05882	+	5.75105i	0.0491014	+	0.266699i
$466$	−16.8351	−	3.07307i	−0.779871	−	0.142357i
$467$	11.2520	+	28.2403i	0.520678	+	1.30680i	0.920690	+	0.390294i	$0.127627\pi$
$467$	11.2520	+	28.2403i	0.520678	+	1.30680i	−0.400012	+	0.916510i	$0.630994\pi$
$468$	60.6577	+	13.1588i	2.80390	+	0.608266i
$469$	4.34189	−	2.61243i	0.200490	−	0.120631i
$470$	−8.25444	−	7.27197i	−0.380749	−	0.335431i
$471$	0.349609	−	0.758688i	0.0161091	−	0.0349585i
$472$	−57.0352	+	3.83538i	−2.62526	+	0.176537i
$473$	7.01359	−	12.1479i	0.322485	−	0.558561i
$474$	−1.73703	+	16.2005i	−0.0797846	+	0.744116i
$475$	−3.11369	−	1.72350i	−0.142866	−	0.0790794i
$476$	−22.7882	+	17.3231i	−1.04450	+	0.794005i
$477$	−5.06673	−	8.03248i	−0.231990	−	0.367782i
$478$	28.3960	−	33.4303i	1.29880	−	1.52907i
$479$	−0.792816	−	8.75830i	−0.0362247	−	0.400177i	−0.993734	−	0.111774i	$-0.964347\pi$
$479$	−0.792816	−	8.75830i	−0.0362247	−	0.400177i	0.957509	−	0.288403i	$-0.0931244\pi$
$480$	19.3870	−	0.379514i	0.884889	−	0.0173224i
$481$	−8.35910	−	13.3416i	−0.381142	−	0.608324i
$482$	15.2448	−	2.78278i	0.694383	−	0.126752i
$483$	9.54762	+	25.1652i	0.434432	+	1.14506i
$484$	−45.0224	+	6.54869i	−2.04647	+	0.297668i
$485$	4.08709	+	7.70907i	0.185585	+	0.350051i
$486$	−31.2826	−	26.1655i	−1.41901	−	1.18689i
$487$	−12.4378	−	9.45497i	−0.563610	−	0.428445i	0.284185	−	0.958770i	$-0.408277\pi$
$487$	−12.4378	−	9.45497i	−0.563610	−	0.428445i	−0.847795	+	0.530324i	$0.822070\pi$
$488$	2.04312	−	0.527732i	0.0924878	−	0.0238893i
$489$	−26.8307	+	15.5451i	−1.21333	+	0.702974i
$490$	0.796602	+	0.652251i	0.0359868	+	0.0294657i
$491$	5.42080	−	5.93366i	0.244637	−	0.267782i	−0.603732	−	0.797187i	$-0.706320\pi$
$491$	5.42080	−	5.93366i	0.244637	−	0.267782i	0.848369	+	0.529405i	$0.177585\pi$
$492$	−4.94446	−	66.9323i	−0.222913	−	3.01754i
$493$	13.4308	+	18.3463i	0.604894	+	0.826274i
$494$	−5.71238	−	8.42514i	−0.257012	−	0.379065i
$495$	−1.34992	−	3.74356i	−0.0606742	−	0.168261i
$496$	1.70951	−	31.5301i	0.0767594	−	1.41574i
$497$	−26.2127	−	7.79031i	−1.17580	−	0.349443i
$498$	−58.1046	+	23.2533i	−2.60373	+	1.04200i
$499$	4.17254	+	2.11654i	0.186789	+	0.0947492i	0.543288	−	0.839546i	$-0.317179\pi$
$499$	4.17254	+	2.11654i	0.186789	+	0.0947492i	−0.356499	+	0.934296i	$0.616030\pi$
$500$	−13.6336	+	43.0145i	−0.609713	+	1.92367i
$501$	2.69020	−	2.84866i	0.120189	−	0.127269i
$502$	−0.577279	−	2.86833i	−0.0257652	−	0.128020i
$503$	−7.18486	+	1.58151i	−0.320357	+	0.0705159i	−0.372238	−	0.928137i	$-0.621409\pi$
$503$	−7.18486	+	1.58151i	−0.320357	+	0.0705159i	0.0518808	+	0.998653i	$0.483478\pi$
$504$	41.5958	−	39.6419i	1.85282	−	1.76579i
$505$	−3.82931	−	3.62732i	−0.170402	−	0.161413i
$506$	−19.2066	−	5.70811i	−0.853836	−	0.253757i
$507$	−7.68126	+	4.82890i	−0.341137	+	0.214459i
$508$	79.1529	+	29.8931i	3.51184	+	1.32629i
$509$	−0.797804	+	0.0577182i	−0.0353621	+	0.00255832i	−0.0898274	−	0.995957i	$-0.528632\pi$
$509$	−0.797804	+	0.0577182i	−0.0353621	+	0.00255832i	0.0544654	+	0.998516i	$0.482655\pi$
$510$	−10.6626	+	2.16279i	−0.472146	+	0.0957701i
$511$	−0.0721348	+	3.99482i	−0.00319106	+	0.176720i
$512$	39.9213	+	8.78734i	1.76429	+	0.388349i
$513$	0.533260	+	4.70383i	0.0235440	+	0.207679i
$514$	66.3386	−	30.6915i	2.92607	−	1.35374i
$515$	15.3444	−	3.96340i	0.676154	−	0.174648i
$516$	78.7103	+	49.1493i	3.46503	+	2.16368i
$517$	3.01257	−	4.11511i	0.132493	−	0.180983i
$518$	−24.8064	−	0.896154i	−1.08993	−	0.0393747i
$519$	5.99243	−	1.44256i	0.263039	−	0.0633212i
$520$	−23.2896	+	23.7140i	−1.02132	+	1.03993i
$521$	10.6875	+	12.5823i	0.468226	+	0.551239i	0.944694	−	0.327953i	$-0.106359\pi$
$521$	10.6875	+	12.5823i	0.468226	+	0.551239i	−0.476468	+	0.879192i	$0.658083\pi$
$522$	−52.6017	−	57.2285i	−2.30231	−	2.50482i
$523$	−15.4697	+	22.8161i	−0.676441	+	0.997676i	0.322256	+	0.946653i	$0.395559\pi$
$523$	−15.4697	+	22.8161i	−0.676441	+	0.997676i	−0.998697	+	0.0510238i	$0.983752\pi$
$524$	−3.59623	−	39.7278i	−0.157102	−	1.73552i
$525$	7.33560	+	15.7927i	0.320152	+	0.689249i
$526$	63.9437	+	9.30087i	2.78808	+	0.405537i
$527$	0.934241	+	7.35257i	0.0406962	+	0.320283i
$528$	2.35575	+	21.3590i	0.102521	+	0.929533i
$529$	10.0976	+	8.89575i	0.439026	+	0.386772i
$530$	8.66130			0.376223
$531$	−21.5739	+	8.09740i	−0.936226	+	0.351397i
$532$	−11.3593			−0.492488
$533$	25.6303	+	22.5797i	1.11017	+	0.978037i
$534$	−49.1151	−	21.5663i	−2.12542	−	0.933263i
$535$	−1.11334	−	8.76209i	−0.0481338	−	0.378818i
$536$	−14.5001	−	2.10910i	−0.626308	−	0.0910991i
$537$	−18.4231	+	26.2275i	−0.795014	+	1.13180i
$538$	−5.03561	−	55.6288i	−0.217101	−	2.39833i
$539$	−0.267859	+	0.395062i	−0.0115375	+	0.0170165i
$540$	25.0592	−	8.06837i	1.07837	−	0.347207i
$541$	−6.27651	−	7.38927i	−0.269848	−	0.317690i	0.610502	−	0.792015i	$-0.290968\pi$
$541$	−6.27651	−	7.38927i	−0.269848	−	0.317690i	−0.880350	+	0.474325i	$0.842692\pi$
$542$	22.0473	−	22.4490i	0.947011	−	0.964265i
$543$	7.45155	−	25.2130i	0.319777	−	1.08199i
$544$	24.5607	+	0.887279i	1.05303	+	0.0380418i
$545$	6.69699	−	9.14797i	0.286868	−	0.391856i
$546$	−1.72254	+	49.7757i	−0.0737177	+	2.13021i
$547$	−37.8350	+	9.77265i	−1.61771	+	0.417848i	−0.946313	−	0.323252i	$-0.895224\pi$
$547$	−37.8350	+	9.77265i	−1.61771	+	0.417848i	−0.671395	+	0.741100i	$0.734304\pi$
$548$	4.27775	−	1.97910i	0.182736	−	0.0845429i
$549$	0.727539	−	0.440760i	0.0310506	−	0.0188112i
$550$	−12.6599	−	2.78666i	−0.539821	−	0.118824i
$551$	−0.162898	+	9.02129i	−0.00693970	+	0.384320i
$552$	24.7393	−	73.7938i	1.05298	−	3.14087i
$553$	−9.22983	+	0.667744i	−0.392492	+	0.0283954i
$554$	−73.1891	−	27.6407i	−3.10951	−	1.17434i
$555$	−5.90458	−	3.11893i	−0.250635	−	0.132391i
$556$	84.8429	+	25.2150i	3.59814	+	1.06935i
$557$	4.08440	+	3.86895i	0.173062	+	0.163933i	0.769328	−	0.638854i	$-0.220591\pi$
$557$	4.08440	+	3.86895i	0.173062	+	0.163933i	−0.596266	+	0.802787i	$0.703350\pi$
$558$	−5.96763	−	24.6254i	−0.252630	−	1.04248i
$559$	−46.1238	+	10.1526i	−1.95083	+	0.429410i
$560$	5.19413	+	25.8081i	0.219492	+	1.09059i
$561$	−1.44423	−	4.83265i	−0.0609755	−	0.204035i
$562$	−23.6788	+	74.7074i	−0.998830	+	3.15134i
$563$	6.34549	+	3.21877i	0.267431	+	0.135655i	0.580983	−	0.813916i	$-0.302668\pi$
$563$	6.34549	+	3.21877i	0.267431	+	0.135655i	−0.313552	+	0.949571i	$0.601519\pi$
$564$	26.5176	+	20.8589i	1.11659	+	0.878319i
$565$	21.2402	+	6.31250i	0.893583	+	0.265569i
$566$	0.474920	−	8.75939i	0.0199624	−	0.368185i
$567$	11.4594	−	20.1296i	0.481250	−	0.845364i
$568$	44.3757	+	65.4493i	1.86196	+	2.74619i
$569$	4.36322	+	5.96008i	0.182916	+	0.249860i	0.888617	−	0.458650i	$-0.151667\pi$
$569$	4.36322	+	5.96008i	0.182916	+	0.249860i	−0.705701	+	0.708509i	$0.749368\pi$
$570$	−3.88786	−	1.87738i	−0.162845	−	0.0786348i
$571$	−6.43442	+	7.04318i	−0.269272	+	0.294748i	−0.858070	−	0.513532i	$-0.828337\pi$
$571$	−6.43442	+	7.04318i	−0.269272	+	0.294748i	0.588799	+	0.808280i	$0.299601\pi$
$572$	−20.3049	−	16.6255i	−0.848992	−	0.695148i
$573$	−14.7740	−	8.49990i	−0.617193	−	0.355088i
$574$	52.1433	−	13.4684i	2.17642	−	0.562161i
$575$	18.7769	+	14.2738i	0.783050	+	0.595259i
$576$	−25.2623	+	1.90475i	−1.05259	+	0.0793647i
$577$	−4.06447	−	7.66641i	−0.169206	−	0.319157i	0.784378	−	0.620283i	$-0.212982\pi$
$577$	−4.06447	−	7.66641i	−0.169206	−	0.319157i	−0.953584	+	0.301126i	$0.902637\pi$
$578$	30.3667	−	4.41695i	1.26309	−	0.183721i
$579$	−27.0845	−	4.39807i	−1.12559	−	0.182778i
$580$	49.3608	−	9.01028i	2.04960	−	0.374131i
$581$	−18.8725	−	30.1216i	−0.782963	−	1.24965i
$582$	−19.5410	−	32.3661i	−0.810001	−	1.34162i
$583$	0.361999	+	3.99903i	0.0149925	+	0.165623i
$584$	7.47959	−	8.80565i	0.309507	−	0.364380i
$585$	−6.24004	+	11.8568i	−0.257994	+	0.490219i
$586$	−27.0680	+	20.5766i	−1.11817	+	0.850011i
$587$	13.5618	+	7.50675i	0.559754	+	0.309837i	0.738713	−	0.674020i	$-0.235434\pi$
$587$	13.5618	+	7.50675i	0.559754	+	0.309837i	−0.178959	+	0.983857i	$0.557273\pi$
$588$	−2.55064	−	1.86132i	−0.105187	−	0.0767595i
$589$	−1.47059	+	2.54714i	−0.0605948	+	0.104953i
$590$	4.25100	−	20.5813i	0.175011	−	0.847320i
$591$	9.03119	−	0.831344i	0.371494	−	0.0341969i
$592$	27.0563	+	23.8360i	1.11201	+	0.979653i
$593$	30.4449	−	18.3181i	1.25022	−	0.752233i	0.272503	−	0.962155i	$-0.412149\pi$
$593$	30.4449	−	18.3181i	1.25022	−	0.752233i	0.977718	+	0.209922i	$0.0673211\pi$
$594$	6.74290	+	15.8702i	0.276665	+	0.651163i
$595$	−2.28716	−	5.74034i	−0.0937644	−	0.235331i
$596$	−2.25384	−	0.411414i	−0.0923208	−	0.0168522i
$597$	25.1298	+	8.93259i	1.02849	+	0.365587i
$598$	29.4273	+	60.7053i	1.20337	+	2.48243i
$599$	3.51632	+	5.61225i	0.143673	+	0.229310i	0.911454	−	0.411402i	$-0.134961\pi$
$599$	3.51632	+	5.61225i	0.143673	+	0.229310i	−0.767781	+	0.640713i	$0.778639\pi$
$600$	12.5187	−	48.7719i	0.511073	−	1.99111i
$601$	−3.66260	+	3.72933i	−0.149401	+	0.152123i	−0.784096	−	0.620640i	$-0.786873\pi$
$601$	−3.66260	+	3.72933i	−0.149401	+	0.152123i	0.634695	+	0.772763i	$0.281126\pi$
$602$	−27.5610	+	69.1729i	−1.12330	+	2.81928i
$603$	−5.84254	+	0.867943i	−0.237927	+	0.0353454i
$604$	5.64300	+	0.613713i	0.229610	+	0.0249716i
$605$	1.23795	−	9.74281i	0.0503299	−	0.396101i
$606$	17.4415	+	14.7694i	0.708511	+	0.599965i
$607$	1.83596	−	20.2819i	0.0745192	−	0.823219i	−0.869631	−	0.493703i	$-0.835643\pi$
$607$	1.83596	−	20.2819i	0.0745192	−	0.823219i	0.944150	−	0.329516i	$-0.106886\pi$
$608$	7.54601	+	6.17861i	0.306031	+	0.250576i
$609$	26.6636	−	35.1861i	1.08046	−	1.42581i
$610$	−0.0140062	+	0.775660i	−0.000567093	+	0.0314055i
$611$	−17.0704	+	1.85652i	−0.690594	+	0.0751067i
$612$	32.2812	−	8.44276i	1.30489	−	0.341278i
$613$	2.31581	+	14.1258i	0.0935347	+	0.570537i	0.991462	+	0.130393i	$0.0416240\pi$
$613$	2.31581	+	14.1258i	0.0935347	+	0.570537i	−0.897928	+	0.440143i	$0.854928\pi$
$614$	50.7373	−	25.7367i	2.04759	−	1.03865i
$615$	14.2074	+	2.83694i	0.572897	+	0.114396i
$616$	−23.2879	+	6.92107i	−0.938297	+	0.278858i
$617$	8.68623	+	4.40612i	0.349694	+	0.177384i	0.618449	−	0.785825i	$-0.287761\pi$
$617$	8.68623	+	4.40612i	0.349694	+	0.177384i	−0.268754	+	0.963209i	$0.586612\pi$
$618$	−65.4285	+	20.8472i	−2.63192	+	0.838596i
$619$	−5.33759	−	26.5209i	−0.214536	−	1.06597i	−0.930068	−	0.367386i	$-0.880253\pi$
$619$	−5.33759	−	26.5209i	−0.214536	−	1.06597i	0.715533	−	0.698579i	$-0.246184\pi$
$620$	15.5000	+	5.22257i	0.622497	+	0.209744i
$621$	0.989878	−	31.3586i	0.0397224	−	1.25838i
$622$	−3.11646	−	57.4796i	−0.124958	−	2.30472i
$623$	7.08539	−	29.6306i	0.283870	−	1.18712i
$624$	47.7436	−	54.3601i	1.91127	−	2.17614i
$625$	8.20173	+	5.34734i	0.328069	+	0.213894i
$626$	7.64231	+	2.88621i	0.305448	+	0.115356i
$627$	0.704317	−	1.87354i	0.0281277	−	0.0748220i
$628$	−1.38020	−	1.88533i	−0.0550761	−	0.0752329i
$629$	−7.25216	−	4.36348i	−0.289163	−	0.173983i
$630$	9.95162	+	18.6338i	0.396482	+	0.742389i
$631$	3.13721	−	19.1361i	0.124890	−	0.761797i	−0.847908	−	0.530143i	$-0.822138\pi$
$631$	3.13721	−	19.1361i	0.124890	−	0.761797i	0.972798	−	0.231654i	$-0.0744136\pi$
$632$	21.8736	+	15.4143i	0.870084	+	0.613150i
$633$	−28.2810	−	23.9483i	−1.12407	−	0.951858i
$634$	−59.2194	+	24.8432i	−2.35190	+	0.986651i
$635$	−10.7888	+	14.7374i	−0.428142	+	0.584835i
$636$	−26.5222	+	1.47838i	−1.05167	+	0.0586214i
$637$	1.59031	−	0.231317i	0.0630103	−	0.00916510i
$638$	8.79232	+	31.6671i	0.348091	+	1.25371i
$639$	24.7244	+	20.1191i	0.978083	+	0.795898i
$640$	0.334606	−	0.631134i	0.0132265	−	0.0249478i
$641$	−44.6025	−	3.22683i	−1.76169	−	0.127452i	−0.846997	−	0.531598i	$-0.821592\pi$
$641$	−44.6025	−	3.22683i	−1.76169	−	0.127452i	−0.914695	+	0.404146i	$0.867569\pi$
$642$	6.92963	+	37.6389i	0.273491	+	1.48549i
$643$	10.6626	+	29.8531i	0.420492	+	1.17729i	0.945338	+	0.326093i	$0.105732\pi$
$643$	10.6626	+	29.8531i	0.420492	+	1.17729i	−0.524846	+	0.851197i	$0.675877\pi$
$644$	74.4996	+	10.8363i	2.93570	+	0.427009i
$645$	−14.7686	+	13.5333i	−0.581511	+	0.532871i
$646$	−4.78761	−	2.65005i	−0.188366	−	0.104265i
$647$	−7.03164	+	2.36923i	−0.276442	+	0.0931442i	−0.454108	−	0.890947i	$-0.650042\pi$
$647$	−7.03164	+	2.36923i	−0.276442	+	0.0931442i	0.177666	+	0.984091i	$0.443145\pi$
$648$	−62.5146	+	24.0442i	−2.45580	+	0.944543i
$649$	9.68034	+	1.10255i	0.379987	+	0.0432787i
$650$	21.8225	+	37.7977i	0.855949	+	1.48255i
$651$	13.1591	−	5.82582i	0.515744	−	0.228332i
$652$	1.56588	+	86.7183i	0.0613246	+	3.39615i
$653$	2.32535	+	18.3007i	0.0909980	+	0.716163i	0.970642	+	0.240530i	$0.0773212\pi$
$653$	2.32535	+	18.3007i	0.0909980	+	0.716163i	−0.879644	+	0.475633i	$0.842219\pi$
$654$	−26.7671	+	41.1918i	−1.04668	+	1.61073i
$655$	8.47103	+	1.54629i	0.330990	+	0.0604187i
$656$	−71.0009	−	32.8485i	−2.77212	−	1.28252i
$657$	1.86599	−	4.26720i	0.0727993	−	0.166479i
$658$	−12.6810	+	23.9189i	−0.494357	+	0.932457i
$659$	−2.03483	+	5.69710i	−0.0792657	+	0.221928i	−0.974807	−	0.223052i	$-0.928398\pi$
$659$	−2.03483	+	5.69710i	−0.0792657	+	0.221928i	0.895541	+	0.444979i	$0.146789\pi$
$660$	−10.9869	−	1.78409i	−0.427665	−	0.0694456i
$661$	5.54043	+	7.02148i	0.215498	+	0.273104i	0.880819	−	0.473453i	$-0.156993\pi$
$661$	5.54043	+	7.02148i	0.215498	+	0.273104i	−0.665321	+	0.746557i	$0.731705\pi$
$662$	−54.5151	−	1.96941i	−2.11879	−	0.0765433i
$663$	−8.73307	+	14.5645i	−0.339164	+	0.565637i
$664$	−12.9560	+	101.965i	−0.502792	+	3.95702i
$665$	0.656007	−	2.36272i	0.0254389	−	0.0916225i
$666$	26.2971	+	12.0695i	1.01899	+	0.467685i
$667$	9.67426	−	59.0104i	0.374589	−	2.28489i
$668$	−3.31123	−	10.4471i	−0.128115	−	0.404209i
$669$	2.78924	+	37.7574i	0.107838	+	1.45979i
$670$	2.17327	−	4.92907i	0.0839607	−	0.190427i
$671$	−0.358718	+	0.0259519i	−0.0138481	+	0.00100186i
$672$	−12.0043	−	46.1852i	−0.463076	−	1.78163i
$673$	12.7507	−	6.46784i	0.491504	−	0.249317i	−0.189115	−	0.981955i	$-0.560562\pi$
$673$	12.7507	−	6.46784i	0.491504	−	0.249317i	0.680618	+	0.732638i	$0.261711\pi$
$674$	−61.7834	+	58.5243i	−2.37981	+	2.25427i
$675$	−0.825177	−	20.2811i	−0.0317611	−	0.780618i
$676$	1.37392	+	25.3404i	0.0528429	+	0.974631i
$677$	26.1572	+	28.6319i	1.00530	+	1.10042i	0.994940	+	0.100469i	$0.0320342\pi$
$677$	26.1572	+	28.6319i	1.00530	+	1.10042i	0.0103627	+	0.999946i	$0.496701\pi$
$678$	−93.4137	−	22.1876i	−3.58753	−	0.852110i
$679$	16.1123	−	14.1946i	0.618334	−	0.544738i
$680$	−5.39868	+	17.0330i	−0.207030	+	0.653187i
$681$	−28.0719	+	22.2199i	−1.07572	+	0.851468i
$682$	−2.49153	+	10.4194i	−0.0954057	+	0.398980i
$683$	−4.59752	+	4.35500i	−0.175919	+	0.166639i	−0.770593	−	0.637328i	$-0.780040\pi$
$683$	−4.59752	+	4.35500i	−0.175919	+	0.166639i	0.594674	+	0.803967i	$0.297281\pi$
$684$	12.2256	+	5.08520i	0.467459	+	0.194438i
$685$	0.164607	+	1.00406i	0.00628933	+	0.0383632i
$686$	21.6648	−	44.6922i	0.827166	−	1.70636i
$687$	0.357179	−	1.06541i	0.0136272	−	0.0406480i
$688$	94.6355	−	52.3829i	3.60794	−	1.99708i
$689$	9.11854	−	9.98125i	0.347389	−	0.380255i
$690$	23.7075	+	16.0216i	0.902528	+	0.609931i
$691$	−22.5752	−	15.9088i	−0.858800	−	0.605198i	0.0607578	−	0.998153i	$-0.480648\pi$
$691$	−22.5752	−	15.9088i	−0.858800	−	0.605198i	−0.919558	+	0.392955i	$0.871453\pi$
$692$	4.61215	−	16.6115i	0.175328	−	0.631473i
$693$	−8.18754	+	5.37359i	−0.311019	+	0.204126i
$694$	25.1321	+	2.73328i	0.954000	+	0.103754i
$695$	−10.1444	+	16.1910i	−0.384799	+	0.614161i
$696$	−124.114	+	29.8779i	−4.70453	+	1.13252i
$697$	17.7791	+	4.59229i	0.673433	+	0.173945i
$698$	40.1640	−	7.33150i	1.52023	−	0.277501i
$699$	−4.36704	+	10.4543i	−0.165177	+	0.395417i
$700$	48.5784	+	3.51447i	1.83609	+	0.132834i
$701$	5.00528	+	2.31569i	0.189047	+	0.0874624i	0.512129	−	0.858909i	$-0.328857\pi$
$701$	5.00528	+	2.31569i	0.189047	+	0.0874624i	−0.323082	+	0.946371i	$0.604719\pi$
$702$	24.1369	−	52.8009i	0.910990	−	1.99284i
$703$	−1.24316	−	3.12011i	−0.0468868	−	0.117677i
$704$	9.87742	+	4.14370i	0.372269	+	0.156171i
$705$	−5.87004	+	4.31100i	−0.221078	+	0.162362i
$706$	10.5732	−	52.5350i	0.397927	−	1.97718i
$707$	−6.49026	+	11.2415i	−0.244091	+	0.422778i
$708$	−9.50422	+	63.7487i	−0.357190	+	2.39582i
$709$	8.19428	+	14.1929i	0.307743	+	0.533026i	0.977868	−	0.209222i	$-0.0670931\pi$
$709$	8.19428	+	14.1929i	0.307743	+	0.533026i	−0.670126	+	0.742248i	$0.733760\pi$
$710$	−27.5493	+	9.28243i	−1.03391	+	0.348363i
$711$	10.2327	+	3.41323i	0.383756	+	0.128006i
$712$	−70.1334	+	53.3140i	−2.62836	+	1.99803i
$713$	12.0747	−	15.3025i	0.452201	−	0.573082i
$714$	11.2792	+	24.2828i	0.422114	+	0.908762i
$715$	4.63071	−	3.26327i	0.173179	−	0.122039i
$716$	39.1054	+	80.6703i	1.46144	+	3.01479i
$717$	−17.6087	−	23.0909i	−0.657607	−	0.862347i
$718$	−11.8415	+	33.1537i	−0.441920	+	1.23728i
$719$	−6.47725	−	23.3290i	−0.241561	−	0.870023i	−0.980544	−	0.196299i	$-0.937108\pi$
$719$	−6.47725	−	23.3290i	−0.241561	−	0.870023i	0.738983	−	0.673724i	$-0.235306\pi$
$720$	5.96321	−	30.1017i	0.222236	−	1.12182i
$721$	−18.2685	−	34.4581i	−0.680356	−	1.28329i
$722$	19.1780	+	43.4964i	0.713730	+	1.61877i
$723$	0.354827	−	10.2534i	0.0131962	−	0.381327i
$724$	−51.5270	−	52.4658i	−1.91499	−	1.94988i
$725$	3.48774	−	38.5294i	0.129532	−	1.43094i
$726$	−3.00624	+	42.4488i	−0.111572	+	1.57542i
$727$	−5.02277	−	15.8470i	−0.186284	−	0.587733i	−0.999979	−	0.00644133i	$-0.997950\pi$
$727$	−5.02277	−	15.8470i	−0.186284	−	0.587733i	0.813695	−	0.581292i	$-0.197453\pi$
$728$	70.0886	+	42.1709i	2.59766	+	1.56296i
$729$	−21.3448	+	16.5348i	−0.790548	+	0.612400i
$730$	2.38366	+	3.51564i	0.0882233	+	0.130120i
$731$	−19.6441	+	16.0844i	−0.726562	+	0.594903i
$732$	−0.0895066	−	2.37758i	−0.00330826	−	0.0878777i
$733$	−9.66432	−	40.4155i	−0.356960	−	1.49278i	−0.802030	−	0.597284i	$-0.796247\pi$
$733$	−9.66432	−	40.4155i	−0.356960	−	1.49278i	0.445070	−	0.895496i	$-0.353179\pi$
$734$	67.4728	−	20.0526i	2.49047	−	0.740156i
$735$	0.534454	−	0.423039i	0.0197136	−	0.0156040i
$736$	−43.5961	−	47.7208i	−1.60697	−	1.75901i
$737$	2.36665	+	0.797416i	0.0871765	+	0.0293732i
$738$	−62.1494	−	8.84728i	−2.28775	−	0.325673i
$739$	45.2529	−	9.96092i	1.66466	−	0.366418i	0.719871	−	0.694108i	$-0.244201\pi$
$739$	45.2529	−	9.96092i	1.66466	−	0.366418i	0.944785	+	0.327690i	$0.106270\pi$
$740$	−15.6461	+	10.2009i	−0.575163	+	0.374993i
$741$	−6.25659	+	2.50387i	−0.229842	+	0.0919818i
$742$	−4.95721	−	20.7307i	−0.181985	−	0.761048i
$743$	32.3114	+	21.0663i	1.18539	+	0.772848i	0.978647	−	0.205547i	$-0.0658973\pi$
$743$	32.3114	+	21.0663i	1.18539	+	0.772848i	0.206744	+	0.978395i	$0.433713\pi$
$744$	−40.1138	−	11.0720i	−1.47064	−	0.405918i
$745$	0.215734	−	0.445036i	0.00790388	−	0.0163049i
$746$	64.4252	−	7.00667i	2.35878	−	0.256532i
$747$	6.82737	+	40.8675i	0.249800	+	1.49526i
$748$	−13.7780	−	3.03276i	−0.503772	−	0.110889i
$749$	−20.3347	+	7.67965i	−0.743014	+	0.280608i
$750$	36.5838	+	21.0477i	1.33585	+	0.768553i
$751$	−20.6459	−	21.0221i	−0.753381	−	0.767108i	0.224902	−	0.974381i	$-0.427794\pi$
$751$	−20.6459	−	21.0221i	−0.753381	−	0.767108i	−0.978283	+	0.207274i	$0.933541\pi$
$752$	36.2648	−	15.2135i	1.32244	−	0.554780i
$753$	−1.93677	−	0.0320313i	−0.0705798	−	0.00116729i
$754$	58.7500	−	93.7683i	2.13955	−	3.41484i
$755$	−0.453538	+	1.13829i	−0.0165059	+	0.0414268i
$756$	−33.6539	−	55.3609i	−1.22398	−	2.01346i
$757$	19.6828	+	23.1724i	0.715384	+	0.842216i	0.992955	−	0.118490i	$-0.0378052\pi$
$757$	19.6828	+	23.1724i	0.715384	+	0.842216i	−0.277571	+	0.960705i	$0.589529\pi$
$758$	−60.7175	+	2.19348i	−2.20536	+	0.0796707i
$759$	−6.40651	+	11.6157i	−0.232542	+	0.421622i
$760$	−5.79604	+	4.08448i	−0.210244	+	0.148160i
$761$	17.1285	+	47.9562i	0.620907	+	1.73841i	0.672871	+	0.739760i	$0.265061\pi$
$761$	17.1285	+	47.9562i	0.620907	+	1.73841i	−0.0519641	+	0.998649i	$0.516548\pi$
$762$	43.1218	−	66.3600i	1.56214	−	2.40397i
$763$	−25.7285	−	10.7934i	−0.931433	−	0.390747i
$764$	−40.8502	+	24.5787i	−1.47791	+	0.889228i
$765$	−0.108174	+	7.20203i	−0.00391106	+	0.260390i
$766$	20.9806			0.758061
$767$	−19.2424	−	26.5667i	−0.694804	−	0.959268i
$768$	10.9474	−	23.7569i	0.395029	−	0.857253i
$769$	−5.12797	+	25.4794i	−0.184919	+	0.918810i	0.773576	+	0.633703i	$0.218466\pi$
$769$	−5.12797	+	25.4794i	−0.184919	+	0.918810i	−0.958496	+	0.285107i	$0.907971\pi$
$770$	−0.161254	−	8.93022i	−0.00581119	−	0.321823i
$771$	−10.4745	−	47.2444i	−0.377230	−	1.70147i
$772$	−47.5418	+	60.2506i	−1.71107	+	2.16846i
$773$	−20.1979	+	23.7788i	−0.726468	+	0.855264i	−0.994124	−	0.108251i	$-0.965475\pi$
$773$	−20.1979	+	23.7788i	−0.726468	+	0.855264i	0.267656	+	0.963515i	$0.413751\pi$
$774$	60.6295	−	62.1103i	2.17928	−	2.23251i
$775$	7.07710	−	10.4379i	0.254217	−	0.374942i
$776$	−62.0522	+	2.24170i	−2.22755	+	0.0804722i
$777$	−4.08570	+	15.9176i	−0.146574	+	0.571041i
$778$	−68.4877	−	17.6901i	−2.45540	−	0.634222i
$779$	4.51384	+	5.72047i	0.161725	+	0.204957i
$780$	20.5154	+	31.3623i	0.734569	+	1.12295i
$781$	−5.43724	−	12.3319i	−0.194560	−	0.441270i
$782$	28.8713	+	21.9474i	1.03244	+	0.784838i
$783$	−44.4489	+	25.9332i	−1.58847	+	0.926777i
$784$	−3.34042	+	1.54544i	−0.119301	+	0.0551944i
$785$	0.471854	−	0.178202i	0.0168412	−	0.00636028i
$786$	−37.0211	−	4.64691i	−1.32050	−	0.165750i
$787$	34.2551	−	18.9609i	1.22106	−	0.675885i	0.263651	−	0.964618i	$-0.415073\pi$
$787$	34.2551	−	18.9609i	1.22106	−	0.675885i	0.957410	+	0.288733i	$0.0932341\pi$
$788$	10.2341	−	23.2113i	0.364574	−	0.826870i
$789$	15.0533	−	40.0430i	0.535912	−	1.42557i
$790$	−7.61173	+	6.23242i	−0.270813	+	0.221740i
$791$	2.95225	−	54.4510i	0.104970	−	1.93606i
$792$	28.1624	+	2.97635i	1.00071	+	0.105760i
$793$	0.879122	+	0.832749i	0.0312185	+	0.0295718i
$794$	14.7242	−	9.59984i	0.522542	−	0.340686i
$795$	1.22417	−	5.60196i	0.0434169	−	0.198681i
$796$	55.9741	−	49.3119i	1.98395	−	1.74781i
$797$	15.3715	−	13.5419i	0.544485	−	0.479679i	−0.343755	−	0.939060i	$-0.611699\pi$
$797$	15.3715	−	13.5419i	0.544485	−	0.479679i	0.888239	+	0.459381i	$0.151929\pi$
$798$	−2.26830	+	10.3800i	−0.0802970	+	0.367449i
$799$	−7.73255	+	5.04145i	−0.273558	+	0.178354i
$800$	−30.3591	−	28.7577i	−1.07336	−	1.01674i
$801$	−20.8905	+	28.7185i	−0.738128	+	1.01472i
$802$	−1.34337	+	24.7770i	−0.0474361	+	0.874908i
$803$	−1.52359	+	1.24750i	−0.0537663	+	0.0440235i
$804$	−5.81354	+	15.4645i	−0.205028	+	0.545390i
$805$	−6.55633	+	14.8700i	−0.231080	+	0.524100i
$806$	31.5581	−	17.4681i	1.11159	−	0.615288i
$807$	−36.6913	−	4.60553i	−1.29160	−	0.162122i
$808$	35.1144	−	13.2614i	1.23532	−	0.466534i
$809$	12.4537	−	5.76171i	0.437850	−	0.202571i	−0.188565	−	0.982061i	$-0.560384\pi$
$809$	12.4537	−	5.76171i	0.437850	−	0.202571i	0.626415	+	0.779490i	$0.284522\pi$
$810$	−2.36883	−	24.5100i	−0.0832321	−	0.861193i
$811$	−19.5129	−	14.8333i	−0.685191	−	0.520869i	0.203674	−	0.979039i	$-0.434712\pi$
$811$	−19.5129	−	14.8333i	−0.685191	−	0.520869i	−0.888864	+	0.458170i	$0.848505\pi$
$812$	−49.8171	−	112.987i	−1.74824	−	3.96508i
$813$	−11.4034	−	17.4326i	−0.399936	−	0.611389i
$814$	−7.57817	−	9.60395i	−0.265615	−	0.336618i
$815$	−18.1277	−	4.68233i	−0.634987	−	0.164015i
$816$	9.66973	−	37.6726i	0.338508	−	1.31881i
$817$	−10.0685	+	0.363736i	−0.352254	+	0.0127255i
$818$	−14.2481	+	21.0144i	−0.498175	+	0.734753i
$819$	31.9505	+	8.14931i	1.11644	+	0.284760i
$820$	26.2341	−	30.8851i	0.916133	−	1.07855i
$821$	6.48324	−	8.21631i	0.226266	−	0.286751i	−0.658700	−	0.752405i	$-0.728894\pi$
$821$	6.48324	−	8.21631i	0.226266	−	0.286751i	0.884967	+	0.465654i	$0.154181\pi$
$822$	−0.954272	−	4.30417i	−0.0332841	−	0.150125i
$823$	−0.707480	−	39.1802i	−0.0246612	−	1.36574i	−0.742650	−	0.669680i	$-0.766431\pi$
$823$	−0.707480	−	39.1802i	−0.0246612	−	1.36574i	0.717988	−	0.696055i	$-0.245063\pi$
$824$	−22.2515	+	110.561i	−0.775168	+	3.85158i
$825$	−3.59169	+	7.79433i	−0.125047	+	0.271364i
$826$	−51.6941	+	1.60482i	−1.79867	+	0.0558387i
$827$	31.0986			1.08140			0.540701	−	0.841215i	$-0.318159\pi$
$827$	31.0986			1.08140			0.540701	+	0.841215i	$0.318159\pi$
$828$	−75.3304	−	45.0139i	−2.61791	−	1.56434i
$829$	−26.7982	+	16.1239i	−0.930738	+	0.560007i	−0.898259	−	0.439466i	$-0.855168\pi$
$829$	−26.7982	+	16.1239i	−0.930738	+	0.560007i	−0.0324791	+	0.999472i	$0.510340\pi$
$830$	−34.8459	−	14.6183i	−1.20952	−	0.507407i
$831$	−28.2219	+	43.4306i	−0.979006	+	1.50659i
$832$	−12.1305	−	33.9627i	−0.420548	−	1.17745i
$833$	0.706185	−	0.497650i	0.0244679	−	0.0172426i
$834$	39.9832	−	72.4936i	1.38450	−	2.51025i
$835$	2.36420	−	0.0854090i	0.0818165	−	0.00295570i
$836$	−3.62434	−	4.26690i	−0.125350	−	0.147574i
$837$	−16.7707	+	0.379242i	−0.579680	+	0.0131085i
$838$	9.63382	−	24.1791i	0.332795	−	0.835252i
$839$	17.2182	−	27.4812i	0.594438	−	0.948757i	−0.404969	−	0.914330i	$-0.632718\pi$
$839$	17.2182	−	27.4812i	0.594438	−	0.948757i	0.999407	−	0.0344266i	$-0.0109605\pi$
$840$	34.6891	+	0.573706i	1.19689	+	0.0197947i
$841$	−63.7041	+	26.7246i	−2.19669	+	0.921539i
$842$	−11.0778	−	11.2796i	−0.381765	−	0.388720i
$843$	44.9726	+	25.8740i	1.54894	+	0.891147i
$844$	−96.9690	+	36.6215i	−3.33781	+	1.26057i
$845$	−5.35012	−	1.17765i	−0.184050	−	0.0405124i
$846$	24.3559	−	20.0662i	0.837373	−	0.689892i
$847$	−24.0278	+	2.61318i	−0.825605	+	0.0897899i
$848$	−13.5064	+	27.8622i	−0.463811	+	0.956792i
$849$	−5.59828	−	1.54520i	−0.192132	−	0.0530313i
$850$	19.6544	+	12.8142i	0.674141	+	0.439525i
$851$	5.17681	+	21.6490i	0.177459	+	0.742120i
$852$	82.7755	−	33.1265i	2.83584	−	1.13489i
$853$	−6.66026	+	4.34234i	−0.228043	+	0.148679i	−0.655091	−	0.755550i	$-0.727370\pi$
$853$	−6.66026	+	4.34234i	−0.228043	+	0.148679i	0.427048	+	0.904229i	$0.359554\pi$
$854$	1.86455	−	0.410418i	0.0638035	−	0.0140442i
$855$	−1.76375	+	2.24925i	−0.0603191	+	0.0769226i
$856$	59.5643	+	20.0696i	2.03587	+	0.685963i
$857$	3.42263	+	3.74645i	0.116915	+	0.127976i	0.793972	−	0.607954i	$-0.208009\pi$
$857$	3.42263	+	3.74645i	0.116915	+	0.127976i	−0.677057	+	0.735930i	$0.736745\pi$
$858$	−19.2469	+	15.2346i	−0.657077	+	0.520100i
$859$	15.0666	−	4.47773i	0.514066	−	0.152778i	−0.0174153	−	0.999848i	$-0.505544\pi$
$859$	15.0666	−	4.47773i	0.514066	−	0.152778i	0.531481	+	0.847070i	$0.321636\pi$
$860$	13.0304	+	54.4924i	0.444335	+	1.85818i
$861$	−1.34129	−	35.6288i	−0.0457110	−	1.21423i
$862$	−24.8907	+	20.3803i	−0.847779	+	0.694155i
$863$	−1.31487	−	1.93928i	−0.0447585	−	0.0660139i	0.804651	−	0.593748i	$-0.202352\pi$
$863$	−1.31487	−	1.93928i	−0.0447585	−	0.0660139i	−0.849410	+	0.527734i	$0.823042\pi$
$864$	−7.75582	+	55.0815i	−0.263858	+	1.87391i
$865$	3.18881	+	1.91864i	0.108423	+	0.0652359i
$866$	30.4970	+	96.2190i	1.03633	+	3.26965i
$867$	1.43517	−	20.2649i	0.0487408	−	0.688231i
$868$	3.62885	−	40.0882i	0.123171	−	1.36068i
$869$	−3.19572	−	3.25395i	−0.108407	−	0.110383i
$870$	1.62318	−	46.9047i	0.0550310	−	1.59022i
$871$	−3.39224	−	7.69375i	−0.114942	−	0.260693i
$872$	37.7909	+	71.2811i	1.27976	+	2.41388i
$873$	−23.6956	+	8.06419i	−0.801976	+	0.272931i
$874$	3.85016	+	13.8670i	0.130234	+	0.469059i
$875$	−8.06299	+	22.5747i	−0.272579	+	0.763164i
$876$	−7.89920	−	10.3585i	−0.266889	−	0.349983i
$877$	−5.19256	−	10.7117i	−0.175340	−	0.361708i	0.793815	−	0.608159i	$-0.208092\pi$
$877$	−5.19256	−	10.7117i	−0.175340	−	0.361708i	−0.969155	+	0.246451i	$0.920735\pi$
$878$	−13.3605	+	9.41516i	−0.450895	+	0.317746i
$879$	9.48279	+	20.4153i	0.319847	+	0.688592i
$880$	−8.03705	+	10.1855i	−0.270929	+	0.343353i
$881$	−46.7751	+	35.5575i	−1.57589	+	1.19796i	−0.701590	+	0.712581i	$0.747526\pi$
$881$	−46.7751	+	35.5575i	−1.57589	+	1.19796i	−0.874303	+	0.485381i	$0.838681\pi$
$882$	−2.21019	+	1.95907i	−0.0744209	+	0.0659655i
$883$	−24.7798	+	8.34928i	−0.833906	+	0.280976i	−0.703687	−	0.710510i	$-0.748464\pi$
$883$	−24.7798	+	8.34928i	−0.833906	+	0.280976i	−0.130218	+	0.991485i	$0.541568\pi$
$884$	23.7497	+	41.1357i	0.798789	+	1.38354i
$885$	−12.7108	−	5.65839i	−0.427268	−	0.190205i
$886$	−33.2737	+	57.6317i	−1.11785	+	1.93617i
$887$	3.34862	−	16.6383i	0.112436	−	0.558660i	−0.883487	−	0.468455i	$-0.844811\pi$
$887$	3.34862	−	16.6383i	0.112436	−	0.558660i	0.995923	−	0.0902054i	$-0.0287524\pi$
$888$	38.3009	−	28.1285i	1.28529	−	0.943931i
$889$	41.4486	+	17.3882i	1.39014	+	0.583180i
$890$	−11.9880	−	30.0877i	−0.401840	−	1.00854i
$891$	11.2176	−	2.11811i	0.375803	−	0.0709595i
$892$	96.1092	+	44.4648i	3.21797	+	1.48879i
$893$	−3.65354	−	0.264320i	−0.122261	−	0.00884514i
$894$	−0.826007	+	1.97738i	−0.0276258	+	0.0661336i
$895$	−19.0377	+	3.47512i	−0.636360	+	0.116161i
$896$	−1.70212	−	0.439651i	−0.0568637	−	0.0146877i
$897$	43.4222	−	10.4530i	1.44983	−	0.349016i
$898$	47.7653	−	76.2360i	1.59395	−	2.54403i
$899$	−31.7850	−	3.45683i	−1.06009	−	0.115292i
$900$	−50.7100	−	25.5295i	−1.69033	−	0.850984i
$901$	1.94433	−	7.00286i	0.0647751	−	0.233299i
$902$	21.6961	+	15.2893i	0.722402	+	0.509078i
$903$	40.8443	+	27.6027i	1.35921	+	0.918560i
$904$	−106.355	+	116.418i	−3.53732	+	3.87199i
$905$	13.8885	−	7.68762i	0.461671	−	0.255545i
$906$	1.68764	−	5.03397i	0.0560680	−	0.167242i
$907$	−11.5343	+	23.7939i	−0.382989	+	0.790065i	0.617007	+	0.786958i	$0.288345\pi$
$907$	−11.5343	+	23.7939i	−0.382989	+	0.790065i	−0.999995	+	0.00310655i	$0.999011\pi$
$908$	16.2006	+	98.8191i	0.537635	+	3.27943i
$909$	12.0177	−	9.19332i	0.398602	−	0.304923i
$910$	−21.8321	+	20.6805i	−0.723728	+	0.685552i
$911$	4.15535	−	17.3774i	0.137673	−	0.575739i	−0.860165	−	0.510016i	$-0.829639\pi$
$911$	4.15535	−	17.3774i	0.137673	−	0.575739i	0.997838	−	0.0657227i	$-0.0209353\pi$
$912$	12.1020	−	9.57913i	0.400736	−	0.317197i
$913$	5.29305	−	16.6998i	0.175175	−	0.552682i
$914$	24.0102	−	21.1524i	0.794185	−	0.699659i
$915$	0.499702	+	0.118689i	0.0165196	+	0.00392374i
$916$	−2.11989	−	2.32046i	−0.0700432	−	0.0766700i
$917$	−1.14728	−	21.1603i	−0.0378864	−	0.698774i
$918$	−1.26879	−	31.1842i	−0.0418764	−	1.02923i
$919$	37.6539	−	35.6677i	1.24209	−	1.17657i	0.264881	−	0.964281i	$-0.414667\pi$
$919$	37.6539	−	35.6677i	1.24209	−	1.17657i	0.977207	−	0.212287i	$-0.0680911\pi$
$920$	41.9095	−	21.2587i	1.38172	−	0.700880i
$921$	−9.47487	−	36.4535i	−0.312208	−	1.20118i
$922$	−75.0957	+	5.43290i	−2.47315	+	0.178923i
$923$	−18.3066	+	41.5201i	−0.602569	+	1.36665i
$924$	2.01806	+	27.3181i	0.0663893	+	0.898701i
$925$	4.35109	+	13.7278i	0.143063	+	0.451369i
$926$	13.7488	−	83.8639i	0.451813	−	2.75594i
$927$	4.23601	+	45.2644i	0.139129	+	1.48668i
$928$	−28.3630	+	102.154i	−0.931063	+	3.35338i
$929$	6.21718	−	48.9299i	0.203979	−	1.60534i	−0.480964	−	0.876740i	$-0.659713\pi$
$929$	6.21718	−	48.9299i	0.203979	−	1.60534i	0.684943	−	0.728596i	$-0.259827\pi$
$930$	7.86749	−	13.1209i	0.257985	−	0.430252i
$931$	0.342606	+	0.0123770i	0.0112285	+	0.000405639i
$932$	19.6301	+	24.8776i	0.643006	+	0.814892i
$933$	−37.6172	−	6.10840i	−1.23153	−	0.199980i
$934$	26.7511	−	74.8974i	0.875321	−	2.45072i
$935$	1.42650	−	2.69066i	0.0466514	−	0.0879939i
$936$	−56.5555	−	76.7636i	−1.84857	−	2.50910i
$937$	−42.1316	−	19.4921i	−1.37638	−	0.636780i	−0.414447	−	0.910073i	$-0.636025\pi$
$937$	−42.1316	−	19.4921i	−1.37638	−	0.636780i	−0.961931	+	0.273293i	$0.911887\pi$
$938$	−13.0415	−	2.38058i	−0.425820	−	0.0777288i
$939$	2.94689	−	4.53496i	0.0961682	−	0.147993i
$940$	2.56773	+	20.2083i	0.0837502	+	0.659123i
$941$	0.429427	+	23.7816i	0.0139989	+	0.775259i	0.928638	+	0.370987i	$0.120981\pi$
$941$	0.429427	+	23.7816i	0.0139989	+	0.775259i	−0.914639	+	0.404272i	$0.867525\pi$
$942$	−1.99841	+	0.884741i	−0.0651116	+	0.0288264i
$943$	−24.1468	−	41.8235i	−0.786328	−	1.36196i
$944$	59.5783	+	45.7693i	1.93911	+	1.48966i
$945$	13.4585	−	3.80285i	0.437806	−	0.123707i
$946$	−34.7771	+	11.7178i	−1.13070	+	0.380978i
$947$	−12.0255	−	6.65638i	−0.390776	−	0.216303i	0.276664	−	0.960967i	$-0.410771\pi$
$947$	−12.0255	−	6.65638i	−0.390776	−	0.216303i	−0.667440	+	0.744663i	$0.732610\pi$
$948$	22.2444	−	20.3838i	0.722466	−	0.662036i
$949$	6.56091	+	0.954310i	0.212976	+	0.0309782i
$950$	3.13175	+	8.76826i	0.101608	+	0.284480i
$951$	7.69817	+	41.8132i	0.249630	+	1.35589i
$952$	43.8582	+	3.17298i	1.42145	+	0.102837i
$953$	−2.53673	+	4.78477i	−0.0821727	+	0.154994i	−0.921193	−	0.389106i	$-0.872784\pi$
$953$	−2.53673	+	4.78477i	−0.0821727	+	0.154994i	0.839020	+	0.544100i	$0.183129\pi$
$954$	−3.94520	+	24.5309i	−0.127730	+	0.794218i
$955$	−2.75323	−	9.91623i	−0.0890924	−	0.320882i
$956$	−80.3769	+	11.6911i	−2.59958	+	0.378119i
$957$	21.7243	−	1.21094i	0.702248	−	0.0391441i
$958$	−13.5905	+	18.5644i	−0.439089	+	0.599787i
$959$	2.30899	−	0.968650i	0.0745613	−	0.0312793i
$960$	−11.6733	−	9.88494i	−0.376755	−	0.319035i
$961$	16.8207	+	11.8536i	0.542605	+	0.382374i
$962$	−6.66375	+	40.6471i	−0.214848	+	1.31051i
$963$	25.3235	+	0.837856i	0.816039	+	0.0269995i
$964$	−24.5885	−	14.7944i	−0.791943	−	0.476496i
$965$	−9.78648	−	13.3681i	−0.315038	−	0.430336i
$966$	24.7787	−	65.9132i	0.797240	−	2.12072i
$967$	48.1856	+	18.1979i	1.54955	+	0.585205i	0.972785	−	0.231709i	$-0.0744317\pi$
$967$	48.1856	+	18.1979i	1.54955	+	0.585205i	0.576760	+	0.816914i	$0.304317\pi$
$968$	58.5456	+	38.1704i	1.88173	+	1.22684i
$969$	−2.39067	+	2.72198i	−0.0767994	+	0.0874425i
$970$	5.30900	−	22.2018i	0.170462	−	0.712858i
$971$	−0.974969	−	17.9823i	−0.0312883	−	0.577078i	−0.971580	−	0.236710i	$-0.923931\pi$
$971$	−0.974969	−	17.9823i	−0.0312883	−	0.577078i	0.940292	−	0.340368i	$-0.110552\pi$
$972$	11.4372	+	74.6488i	0.366850	+	2.39436i
$973$	44.5591	+	15.0137i	1.42850	+	0.481317i
$974$	8.06470	+	40.0711i	0.258410	+	1.28396i
$975$	27.5311	−	8.77212i	0.881702	−	0.280933i
$976$	−2.47335	−	1.25461i	−0.0791700	−	0.0401592i
$977$	26.0664	−	7.74683i	0.833939	−	0.247843i	0.160453	−	0.987043i	$-0.448704\pi$
$977$	26.0664	−	7.74683i	0.833939	−	0.247843i	0.673485	+	0.739200i	$0.264796\pi$
$978$	79.5550	+	15.8856i	2.54389	+	0.507965i
$979$	13.3908	−	6.79254i	0.427973	−	0.217091i
$980$	−0.308439	−	1.88139i	−0.00985271	−	0.0600989i
$981$	22.8588	+	23.1344i	0.729827	+	0.738625i
$982$	−20.9033	+	2.27337i	−0.667051	+	0.0725462i
$983$	−0.394801	+	21.8640i	−0.0125922	+	0.697355i	0.930773	+	0.365598i	$0.119136\pi$
$983$	−0.394801	+	21.8640i	−0.0125922	+	0.697355i	−0.943365	+	0.331757i	$0.892359\pi$
$984$	−62.2683	+	82.1712i	−1.98504	+	2.61952i
$985$	4.23691	+	3.46915i	0.134999	+	0.110536i
$986$	5.36276	−	59.2428i	0.170785	−	1.88668i
$987$	13.6780	+	11.5825i	0.435375	+	0.368674i
$988$	−2.37594	+	18.6989i	−0.0755888	+	0.594891i
$989$	66.3812	+	7.21939i	2.11080	+	0.229563i
$990$	−3.82423	+	9.68349i	−0.121542	+	0.307762i
$991$	11.7632	−	29.5235i	0.373671	−	0.937844i	−0.615106	−	0.788445i	$-0.710887\pi$
$991$	11.7632	−	29.5235i	0.373671	−	0.937844i	0.988777	−	0.149399i	$-0.0477340\pi$
$992$	−24.2156	+	24.6568i	−0.768847	+	0.782855i
$993$	−8.97883	+	34.9809i	−0.284934	+	1.11009i
$994$	37.9849	+	60.6261i	1.20481	+	1.92294i
$995$	7.02428	+	14.4903i	0.222685	+	0.459375i
$996$	109.198	+	38.8155i	3.46008	+	1.22992i
$997$	31.0506	+	5.66795i	0.983383	+	0.179506i	0.647224	−	0.762300i	$-0.275930\pi$
$997$	31.0506	+	5.66795i	0.983383	+	0.179506i	0.336158	+	0.941805i	$0.390872\pi$
$998$	−4.53064	−	11.3710i	−0.143415	−	0.359944i
$999$	11.5231	−	15.3026i	0.364575	−	0.484151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.m.a.130.4	✓	3248
9.7	even	3	inner	531.2.m.a.484.4	yes	3248
59.5	even	29	inner	531.2.m.a.418.4	yes	3248
531.241	even	87	inner	531.2.m.a.241.4	yes	3248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.2.m.a.130.4	✓	3248	1.1	even	1	trivial
531.2.m.a.241.4	yes	3248	531.241	even	87	inner
531.2.m.a.418.4	yes	3248	59.5	even	29	inner
531.2.m.a.484.4	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)

\(f(q)\)	\(=\)	\(q+(-1.96308 - 1.72943i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(0.610661 + 4.80597i) q^{4} +(-1.03490 - 0.150531i) q^{5} +(4.51359 + 0.401670i) q^{6} +(0.232023 + 2.56317i) q^{7} +(4.17642 - 6.15976i) q^{8} +(0.897734 - 2.86253i) q^{9} +O(q^{10})\)	\(q+(-1.96308 - 1.72943i) q^{2} +(-1.39602 + 1.02525i) q^{3} +(0.610661 + 4.80597i) q^{4} +(-1.03490 - 0.150531i) q^{5} +(4.51359 + 0.401670i) q^{6} +(0.232023 + 2.56317i) q^{7} +(4.17642 - 6.15976i) q^{8} +(0.897734 - 2.86253i) q^{9} +(1.77126 + 2.08529i) q^{10} +(-0.888776 + 0.904969i) q^{11} +(-5.77980 - 6.08314i) q^{12} +(4.26785 + 0.154180i) q^{13} +(3.97735 - 5.43298i) q^{14} +(1.59907 - 0.850887i) q^{15} +(-9.47019 + 2.44612i) q^{16} +(2.08363 - 0.963988i) q^{17} +(-6.71286 + 4.06681i) q^{18} +(0.889752 + 0.195849i) q^{19} +(0.0914704 - 5.06562i) q^{20} +(-2.95180 - 3.34036i) q^{21} +(3.30982 - 0.239453i) q^{22} +(-5.64858 - 2.13325i) q^{23} +(0.484920 + 12.8810i) q^{24} +(-3.74445 - 1.11284i) q^{25} +(-8.11149 - 7.68361i) q^{26} +(1.68155 + 4.91654i) q^{27} +(-12.1768 + 2.68033i) q^{28} +(1.95403 + 9.70899i) q^{29} +(-4.61065 - 1.09512i) q^{30} +(-0.975413 + 3.07746i) q^{31} +(9.54699 + 4.84274i) q^{32} +(0.312929 - 2.17457i) q^{33} +(-5.75748 - 1.71110i) q^{34} +(0.145715 - 2.68756i) q^{35} +(14.3054 + 2.56644i) q^{36} +(-2.06885 - 3.05133i) q^{37} +(-1.40795 - 1.92323i) q^{38} +(-6.11607 + 4.16037i) q^{39} +(-5.24941 + 5.74606i) q^{40} +(6.18850 + 5.06709i) q^{41} +(0.0177049 + 11.6623i) q^{42} +(-10.7074 + 2.76567i) q^{43} +(-4.89199 - 3.71880i) q^{44} +(-1.35996 + 2.82730i) q^{45} +(7.39930 + 13.9566i) q^{46} +(-3.97886 + 0.578741i) q^{47} +(10.7127 - 13.1241i) q^{48} +(0.370184 - 0.0675730i) q^{49} +(5.42609 + 8.66035i) q^{50} +(-1.92045 + 3.48198i) q^{51} +(1.86523 + 20.6053i) q^{52} +(2.04940 - 2.41274i) q^{53} +(5.20179 - 12.5597i) q^{54} +(1.05602 - 0.802766i) q^{55} +(16.7576 + 9.27569i) q^{56} +(-1.44290 + 0.638807i) q^{57} +(12.9551 - 22.4389i) q^{58} +(-4.72741 - 6.05406i) q^{59} +(5.06582 + 7.16548i) q^{60} +(0.212758 + 0.187435i) q^{61} +(7.23707 - 4.35440i) q^{62} +(7.54546 + 1.63688i) q^{63} +(-3.12569 - 7.84489i) q^{64} +(-4.39360 - 0.802003i) q^{65} +(-4.37507 + 3.72766i) q^{66} +(-0.858840 - 1.77170i) q^{67} +(5.90529 + 9.42517i) q^{68} +(10.0726 - 2.81313i) q^{69} +(-4.93399 + 5.02389i) q^{70} +(-3.93283 + 9.87066i) q^{71} +(-13.8832 - 17.4849i) q^{72} +(1.54335 + 0.167849i) q^{73} +(-1.21573 + 9.56793i) q^{74} +(6.36826 - 2.28545i) q^{75} +(-0.397908 + 4.39571i) q^{76} +(-2.52581 - 2.06811i) q^{77} +(19.2014 + 2.41017i) q^{78} +(-0.0649163 + 3.59506i) q^{79} +(10.1689 - 1.10594i) q^{80} +(-7.38815 - 5.13958i) q^{81} +(-3.38534 - 20.6497i) q^{82} +(-12.3172 + 6.24796i) q^{83} +(14.2511 - 16.2261i) q^{84} +(-2.30146 + 0.683983i) q^{85} +(25.8024 + 13.0884i) q^{86} +(-12.6820 - 11.5506i) q^{87} +(1.86249 + 9.25417i) q^{88} +(-11.2180 - 3.77977i) q^{89} +(7.55933 - 3.19825i) q^{90} +(0.595048 + 10.9750i) q^{91} +(6.80298 - 28.4496i) q^{92} +(-1.79347 - 5.29624i) q^{93} +(8.81170 + 5.74503i) q^{94} +(-0.891324 - 0.336619i) q^{95} +(-18.2928 + 3.02747i) q^{96} +(-4.92848 - 6.73222i) q^{97} +(-0.843563 - 0.507555i) q^{98} +(1.79262 + 3.35657i) 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

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Database

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