LMFDB - Embedded newform 261.2.x.a.2.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29500 - 0.955756i) q^{2} +(1.12961 + 1.31300i) q^{3} +(0.174054 + 0.564270i) q^{4} +(-0.633409 + 1.61390i) q^{5} +(-0.207940 - 2.77998i) q^{6} +(-4.42538 - 1.36505i) q^{7} +(-0.749268 + 2.14128i) q^{8} +(-0.447956 + 2.96637i) q^{9} +O(q^{10})$	\(q+(-1.29500 - 0.955756i) q^{2} +(1.12961 + 1.31300i) q^{3} +(0.174054 + 0.564270i) q^{4} +(-0.633409 + 1.61390i) q^{5} +(-0.207940 - 2.77998i) q^{6} +(-4.42538 - 1.36505i) q^{7} +(-0.749268 + 2.14128i) q^{8} +(-0.447956 + 2.96637i) q^{9} +(2.36276 - 1.48462i) q^{10} +(1.23115 + 0.232947i) q^{11} +(-0.544275 + 0.865940i) q^{12} +(-5.47821 + 0.410535i) q^{13} +(4.42623 + 5.99733i) q^{14} +(-2.83456 + 0.991411i) q^{15} +(3.99264 - 2.72214i) q^{16} +(-2.64269 - 2.64269i) q^{17} +(3.41523 - 3.41332i) q^{18} +(-2.42927 - 3.86616i) q^{19} +(-1.02092 - 0.0765075i) q^{20} +(-3.20665 - 7.35251i) q^{21} +(-1.37171 - 1.47835i) q^{22} +(-0.986324 + 6.54383i) q^{23} +(-3.65789 + 1.43503i) q^{24} +(1.46180 + 1.35635i) q^{25} +(7.48668 + 4.70419i) q^{26} +(-4.40087 + 2.76267i) q^{27} -2.73470i q^{28} +(3.16520 + 4.35678i) q^{29} +(4.61831 + 1.42527i) q^{30} +(1.11658 + 2.55923i) q^{31} +(-3.23818 - 0.121164i) q^{32} +(1.08487 + 1.87965i) q^{33} +(0.896525 + 5.94806i) q^{34} +(5.00613 - 6.27748i) q^{35} +(-1.75180 + 0.263540i) q^{36} +(3.05710 + 1.06973i) q^{37} +(-0.549194 + 7.32848i) q^{38} +(-6.72729 - 6.72917i) q^{39} +(-2.98122 - 2.56555i) q^{40} +(0.119067 + 0.0319038i) q^{41} +(-2.87459 + 12.5863i) q^{42} +(-2.87436 - 1.25407i) q^{43} +(0.0828427 + 0.735249i) q^{44} +(-4.50368 - 2.60188i) q^{45} +(7.53160 - 7.53160i) q^{46} +(0.540852 - 2.85847i) q^{47} +(8.08431 + 2.16740i) q^{48} +(11.9370 + 8.13848i) q^{49} +(-0.596693 - 3.15360i) q^{50} +(0.484648 - 6.45507i) q^{51} +(-1.18516 - 3.01974i) q^{52} +(-5.43975 + 4.33805i) q^{53} +(8.33958 + 0.628483i) q^{54} +(-1.15578 + 1.83941i) q^{55} +(6.23875 - 8.45321i) q^{56} +(2.33215 - 7.55690i) q^{57} +(0.0650747 - 8.66720i) q^{58} +(-6.86977 + 3.96626i) q^{59} +(-1.05279 - 1.42690i) q^{60} +(3.31669 - 1.75292i) q^{61} +(1.00002 - 4.38139i) q^{62} +(6.03161 - 12.5158i) q^{63} +(-3.47845 - 2.77397i) q^{64} +(2.80738 - 9.10132i) q^{65} +(0.391582 - 3.47102i) q^{66} +(6.01793 - 8.82668i) q^{67} +(1.03122 - 1.95116i) q^{68} +(-9.70624 + 6.09694i) q^{69} +(-12.4827 + 3.34473i) q^{70} +(-4.37545 - 2.10711i) q^{71} +(-6.01619 - 3.18180i) q^{72} +(-0.356699 + 0.0401903i) q^{73} +(-2.93656 - 4.30714i) q^{74} +(-0.129629 + 3.45149i) q^{75} +(1.75873 - 2.04369i) q^{76} +(-5.13034 - 2.71147i) q^{77} +(2.28042 + 15.1439i) q^{78} +(6.08525 + 7.07119i) q^{79} +(1.86428 + 8.16795i) q^{80} +(-8.59867 - 2.65761i) q^{81} +(-0.123699 - 0.155114i) q^{82} +(9.36935 - 10.0978i) q^{83} +(3.59067 - 3.08915i) q^{84} +(5.93893 - 2.59113i) q^{85} +(2.52373 + 4.37122i) q^{86} +(-2.14502 + 9.07738i) q^{87} +(-1.42127 + 2.46171i) q^{88} +(1.20741 - 10.7160i) q^{89} +(3.34552 + 7.67386i) q^{90} +(24.8036 + 5.66125i) q^{91} +(-3.86416 + 0.582429i) q^{92} +(-2.09897 + 4.35701i) q^{93} +(-3.43241 + 3.18481i) q^{94} +(7.77831 - 1.47174i) q^{95} +(-3.49880 - 4.38862i) q^{96} +(0.471450 + 12.5998i) q^{97} +(-7.68000 - 21.9482i) q^{98} +(-1.24251 + 3.54771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.29500	−	0.955756i	−0.915706	−	0.675822i	0.0304489	−	0.999536i	$-0.490306\pi$
$2$	−1.29500	−	0.955756i	−0.915706	−	0.675822i	−0.946155	+	0.323715i	$0.895068\pi$
$3$	1.12961	+	1.31300i	0.652181	+	0.758063i
$3$	1.12961	+	1.31300i	0.652181	+	0.758063i
$4$	0.174054	+	0.564270i	0.0870271	+	0.282135i
$5$	−0.633409	+	1.61390i	−0.283269	+	0.721758i	0.716440	+	0.697648i	$0.245770\pi$
$5$	−0.633409	+	1.61390i	−0.283269	+	0.721758i	−0.999709	+	0.0241092i	$0.992325\pi$
$6$	−0.207940	−	2.77998i	−0.0848910	−	1.13492i
$7$	−4.42538	−	1.36505i	−1.67264	−	0.515940i	−0.693728	−	0.720237i	$-0.744033\pi$
$7$	−4.42538	−	1.36505i	−1.67264	−	0.515940i	−0.978909	+	0.204297i	$0.934509\pi$
$8$	−0.749268	+	2.14128i	−0.264906	+	0.757058i
$9$	−0.447956	+	2.96637i	−0.149319	+	0.988789i
$10$	2.36276	−	1.48462i	0.747170	−	0.469478i
$11$	1.23115	+	0.232947i	0.371207	+	0.0702362i	0.368168	−	0.929759i	$-0.379985\pi$
$11$	1.23115	+	0.232947i	0.371207	+	0.0702362i	0.00303892	+	0.999995i	$0.499033\pi$
$12$	−0.544275	+	0.865940i	−0.157119	+	0.249975i
$13$	−5.47821	+	0.410535i	−1.51938	+	0.113862i	−0.808101	−	0.589044i	$-0.799504\pi$
$13$	−5.47821	+	0.410535i	−1.51938	+	0.113862i	−0.711282	+	0.702907i	$0.751885\pi$
$14$	4.42623	+	5.99733i	1.18296	+	1.60285i
$15$	−2.83456	+	0.991411i	−0.731880	+	0.255981i
$16$	3.99264	−	2.72214i	0.998161	−	0.680535i
$17$	−2.64269	−	2.64269i	−0.640946	−	0.640946i	0.309842	−	0.950788i	$-0.399724\pi$
$17$	−2.64269	−	2.64269i	−0.640946	−	0.640946i	−0.950788	+	0.309842i	$0.899724\pi$
$18$	3.41523	−	3.41332i	0.804977	−	0.804527i
$19$	−2.42927	−	3.86616i	−0.557313	−	0.886958i	0.442640	−	0.896699i	$-0.354042\pi$
$19$	−2.42927	−	3.86616i	−0.557313	−	0.886958i	−0.999953	+	0.00974144i	$0.996899\pi$
$20$	−1.02092	−	0.0765075i	−0.228285	−	0.0171076i
$21$	−3.20665	−	7.35251i	−0.699747	−	1.60445i
$22$	−1.37171	−	1.47835i	−0.292449	−	0.315185i
$23$	−0.986324	+	6.54383i	−0.205663	+	1.36448i	0.612943	+	0.790127i	$0.289986\pi$
$23$	−0.986324	+	6.54383i	−0.205663	+	1.36448i	−0.818606	+	0.574356i	$0.805253\pi$
$24$	−3.65789	+	1.43503i	−0.746665	+	0.292924i
$25$	1.46180	+	1.35635i	0.292359	+	0.271270i
$26$	7.48668	+	4.70419i	1.46826	+	0.922568i
$27$	−4.40087	+	2.76267i	−0.846947	+	0.531677i
$28$		−	2.73470i		−	0.516810i
$29$	3.16520	+	4.35678i	0.587763	+	0.809033i
$29$	3.16520	+	4.35678i	0.587763	+	0.809033i
$30$	4.61831	+	1.42527i	0.843185	+	0.260217i
$31$	1.11658	+	2.55923i	0.200544	+	0.459651i	0.987552	−	0.157291i	$-0.0502761\pi$
$31$	1.11658	+	2.55923i	0.200544	+	0.459651i	−0.787009	+	0.616942i	$0.788371\pi$
$32$	−3.23818	−	0.121164i	−0.572436	−	0.0214190i
$33$	1.08487	+	1.87965i	0.188851	+	0.327205i
$34$	0.896525	+	5.94806i	0.153753	+	1.02008i
$35$	5.00613	−	6.27748i	0.846190	−	1.06109i
$36$	−1.75180	+	0.263540i	−0.291967	+	0.0439234i
$37$	3.05710	+	1.06973i	0.502584	+	0.175862i	0.569651	−	0.821887i	$-0.307078\pi$
$37$	3.05710	+	1.06973i	0.502584	+	0.175862i	−0.0670669	+	0.997748i	$0.521364\pi$
$38$	−0.549194	+	7.32848i	−0.0890910	+	1.18884i
$39$	−6.72729	−	6.72917i	−1.07723	−	1.07753i
$40$	−2.98122	−	2.56555i	−0.471373	−	0.405649i
$41$	0.119067	+	0.0319038i	0.0185951	+	0.00498253i	0.268105	−	0.963390i	$-0.413603\pi$
$41$	0.119067	+	0.0319038i	0.0185951	+	0.00498253i	−0.249510	+	0.968372i	$0.580269\pi$
$42$	−2.87459	+	12.5863i	−0.443559	+	1.94211i
$43$	−2.87436	−	1.25407i	−0.438337	−	0.191244i	0.169123	−	0.985595i	$-0.445907\pi$
$43$	−2.87436	−	1.25407i	−0.438337	−	0.191244i	−0.607459	+	0.794351i	$0.707811\pi$
$44$	0.0828427	+	0.735249i	0.0124890	+	0.110843i
$45$	−4.50368	−	2.60188i	−0.671369	−	0.387865i
$46$	7.53160	−	7.53160i	1.11047	−	1.11047i
$47$	0.540852	−	2.85847i	0.0788914	−	0.416951i	−0.920750	−	0.390154i	$-0.872422\pi$
$47$	0.540852	−	2.85847i	0.0788914	−	0.416951i	0.999641	−	0.0267968i	$-0.00853071\pi$
$48$	8.08431	+	2.16740i	1.16687	+	0.312837i
$49$	11.9370	+	8.13848i	1.70528	+	1.16264i
$50$	−0.596693	−	3.15360i	−0.0843851	−	0.445986i
$51$	0.484648	−	6.45507i	0.0678643	−	0.903891i
$52$	−1.18516	−	3.01974i	−0.164352	−	0.418762i
$53$	−5.43975	+	4.33805i	−0.747207	+	0.595877i	−0.921300	−	0.388852i	$-0.872872\pi$
$53$	−5.43975	+	4.33805i	−0.747207	+	0.595877i	0.174094	+	0.984729i	$0.444300\pi$
$54$	8.33958	+	0.628483i	1.13487	+	0.0855258i
$55$	−1.15578	+	1.83941i	−0.155845	+	0.248026i
$56$	6.23875	−	8.45321i	0.833688	−	1.12961i
$57$	2.33215	−	7.55690i	0.308901	−	1.00094i
$58$	0.0650747	−	8.66720i	0.00854473	−	1.13806i
$59$	−6.86977	+	3.96626i	−0.894368	+	0.516363i	−0.875369	−	0.483456i	$-0.839381\pi$
$59$	−6.86977	+	3.96626i	−0.894368	+	0.516363i	−0.0189990	+	0.999820i	$0.506048\pi$
$60$	−1.05279	−	1.42690i	−0.135915	−	0.184212i
$61$	3.31669	−	1.75292i	0.424659	−	0.224439i	−0.241264	−	0.970460i	$-0.577562\pi$
$61$	3.31669	−	1.75292i	0.424659	−	0.224439i	0.665923	+	0.746021i	$0.268038\pi$
$62$	1.00002	−	4.38139i	0.127003	−	0.556437i
$63$	6.03161	−	12.5158i	0.759912	−	1.57685i
$64$	−3.47845	−	2.77397i	−0.434806	−	0.346747i
$65$	2.80738	−	9.10132i	0.348213	−	1.12888i
$66$	0.391582	−	3.47102i	0.0482004	−	0.427253i
$67$	6.01793	−	8.82668i	0.735207	−	1.07835i	−0.258464	−	0.966021i	$-0.583216\pi$
$67$	6.01793	−	8.82668i	0.735207	−	1.07835i	0.993671	−	0.112330i	$-0.0358313\pi$
$68$	1.03122	−	1.95116i	0.125054	−	0.236613i
$69$	−9.70624	+	6.09694i	−1.16849	+	0.733985i
$70$	−12.4827	+	3.34473i	−1.49197	+	0.399771i
$71$	−4.37545	−	2.10711i	−0.519271	−	0.250068i	0.155842	−	0.987782i	$-0.450191\pi$
$71$	−4.37545	−	2.10711i	−0.519271	−	0.250068i	−0.675113	+	0.737714i	$0.735905\pi$
$72$	−6.01619	−	3.18180i	−0.709015	−	0.374979i
$73$	−0.356699	+	0.0401903i	−0.0417484	+	0.00470392i	−0.132814	−	0.991141i	$-0.542401\pi$
$73$	−0.356699	+	0.0401903i	−0.0417484	+	0.00470392i	0.0910655	+	0.995845i	$0.470973\pi$
$74$	−2.93656	−	4.30714i	−0.341368	−	0.500695i
$75$	−0.129629	+	3.45149i	−0.0149683	+	0.398544i
$76$	1.75873	−	2.04369i	0.201741	−	0.234427i
$77$	−5.13034	−	2.71147i	−0.584657	−	0.309000i
$78$	2.28042	+	15.1439i	0.258206	+	1.71471i
$79$	6.08525	+	7.07119i	0.684644	+	0.795571i	0.987526	−	0.157457i	$-0.0503297\pi$
$79$	6.08525	+	7.07119i	0.684644	+	0.795571i	−0.302882	+	0.953028i	$0.597949\pi$
$80$	1.86428	+	8.16795i	0.208433	+	0.913205i
$81$	−8.59867	−	2.65761i	−0.955408	−	0.295290i
$82$	−0.123699	−	0.155114i	−0.0136603	−	0.0171295i
$83$	9.36935	−	10.0978i	1.02842	−	1.10837i	0.0343743	−	0.999409i	$-0.489056\pi$
$83$	9.36935	−	10.0978i	1.02842	−	1.10837i	0.994046	−	0.108964i	$-0.0347534\pi$
$84$	3.59067	−	3.08915i	0.391775	−	0.337054i
$85$	5.93893	−	2.59113i	0.644168	−	0.281048i
$86$	2.52373	+	4.37122i	0.272140	+	0.471361i
$87$	−2.14502	+	9.07738i	−0.229970	+	0.973198i
$88$	−1.42127	+	2.46171i	−0.151508	+	0.262419i
$89$	1.20741	−	10.7160i	0.127985	−	1.13590i	−0.751421	−	0.659824i	$-0.770631\pi$
$89$	1.20741	−	10.7160i	0.127985	−	1.13590i	0.879405	−	0.476074i	$-0.157940\pi$
$90$	3.34552	+	7.67386i	0.352648	+	0.808896i
$91$	24.8036	+	5.66125i	2.60012	+	0.593461i
$92$	−3.86416	+	0.582429i	−0.402867	+	0.0607224i
$93$	−2.09897	+	4.35701i	−0.217653	+	0.451800i
$94$	−3.43241	+	3.18481i	−0.354026	+	0.328488i
$95$	7.77831	−	1.47174i	0.798038	−	0.150997i
$96$	−3.49880	−	4.38862i	−0.357095	−	0.447911i
$97$	0.471450	+	12.5998i	0.0478684	+	1.27931i	0.791686	+	0.610928i	$0.209204\pi$
$97$	0.471450	+	12.5998i	0.0478684	+	1.27931i	−0.743817	+	0.668383i	$0.766987\pi$
$98$	−7.68000	−	21.9482i	−0.775797	−	2.21710i
$99$	−1.24251	+	3.54771i	−0.124877	+	0.356558i
$100$	−0.510915	+	1.06093i	−0.0510915	+	0.106093i
$101$	−7.12192	+	16.3236i	−0.708658	+	1.62426i	0.0705606	+	0.997507i	$0.477521\pi$
$101$	−7.12192	+	16.3236i	−0.708658	+	1.62426i	−0.779218	+	0.626753i	$0.784384\pi$
$102$	−6.79709	+	7.89613i	−0.673013	+	0.781834i
$103$	−1.38277	−	18.4518i	−0.136248	−	1.81811i	−0.478045	−	0.878335i	$-0.658654\pi$
$103$	−1.38277	−	18.4518i	−0.136248	−	1.81811i	0.341796	−	0.939774i	$-0.388965\pi$
$104$	3.22557	−	12.0380i	0.316294	−	1.18042i
$105$	13.8973	−	0.518056i	1.35624	−	0.0505570i
$106$	11.1906	−	0.418723i	1.08693	−	0.0406700i
$107$	6.65493	+	13.8191i	0.643356	+	1.33594i	0.926293	+	0.376805i	$0.122977\pi$
$107$	6.65493	+	13.8191i	0.643356	+	1.33594i	−0.282936	+	0.959139i	$0.591308\pi$
$108$	−2.32488	−	2.00242i	−0.223712	−	0.192683i
$109$	−14.4994	+	3.30939i	−1.38879	+	0.316982i	−0.850587	−	0.525834i	$-0.823753\pi$
$109$	−14.4994	+	3.30939i	−1.38879	+	0.316982i	−0.538202	+	0.842816i	$0.680896\pi$
$110$	3.25476	−	1.27740i	0.310329	−	0.121795i
$111$	2.04878	+	5.22236i	0.194462	+	0.495684i
$112$	−21.3848	+	6.59634i	−2.02068	+	0.623296i
$113$	−0.115505	+	3.08692i	−0.0108658	+	0.290393i	0.983263	+	0.182191i	$0.0583190\pi$
$113$	−0.115505	+	3.08692i	−0.0108658	+	0.290393i	−0.994129	+	0.108202i	$0.965491\pi$
$114$	−10.2427	+	7.55724i	−0.959316	+	0.707801i
$115$	−9.93634	−	5.73675i	−0.926568	−	0.534954i
$116$	−1.90748	+	2.54434i	−0.177105	+	0.236236i
$117$	1.23620	−	16.4343i	0.114287	−	1.51935i
$118$	12.6872	+	1.42950i	1.16795	+	0.131596i
$119$	8.08750	+	15.3023i	0.741380	+	1.40276i
$120$	0.000952584	−	6.81243i	8.69586e−5	−	0.621887i
$121$	−8.77813	−	3.44516i	−0.798012	−	0.313197i
$122$	−5.97050	−	0.899908i	−0.540544	−	0.0814738i
$123$	0.0926091	+	0.192374i	0.00835029	+	0.0173457i
$124$	−1.24975	+	1.07550i	−0.112231	+	0.0965825i
$125$	−10.9252	+	5.26129i	−0.977178	+	0.470584i
$126$	−19.7730	+	10.4433i	−1.76152	+	0.930361i
$127$	−7.91093	+	2.76815i	−0.701982	+	0.245634i	−0.657585	−	0.753380i	$-0.728422\pi$
$127$	−7.91093	+	2.76815i	−0.701982	+	0.245634i	−0.0443962	+	0.999014i	$0.514136\pi$
$128$	3.53075	+	13.1769i	0.312077	+	1.16469i
$129$	−1.60031	−	5.19067i	−0.140900	−	0.457013i
$130$	−12.3342	+	9.10307i	−1.08178	+	0.798392i
$131$	−0.393906	+	0.290716i	−0.0344157	+	0.0253999i	−0.610892	−	0.791714i	$-0.709189\pi$
$131$	−0.393906	+	0.290716i	−0.0344157	+	0.0253999i	0.576477	+	0.817114i	$0.304427\pi$
$132$	−0.871805	+	0.939318i	−0.0758808	+	0.0817572i
$133$	5.47294	+	20.4253i	0.474564	+	1.77110i
$134$	−16.2294	+	5.67891i	−1.40201	+	0.490583i
$135$	−1.67113	−	8.85246i	−0.143828	−	0.761898i
$136$	7.63883	−	3.67866i	0.655024	−	0.315443i
$137$	1.85215	−	1.59390i	0.158240	−	0.136176i	−0.569604	−	0.821919i	$-0.692903\pi$
$137$	1.85215	−	1.59390i	0.158240	−	0.136176i	0.727844	+	0.685743i	$0.240523\pi$
$138$	18.3968	+	1.38124i	1.56604	+	0.117579i
$139$	7.07783	+	1.06681i	0.600334	+	0.0904857i	0.442176	−	0.896928i	$-0.354207\pi$
$139$	7.07783	+	1.06681i	0.600334	+	0.0904857i	0.158157	+	0.987414i	$0.449445\pi$
$140$	4.41353	+	1.73218i	0.373012	+	0.146396i
$141$	4.36414	−	2.51882i	0.367527	−	0.212123i
$142$	3.65235	+	6.91058i	0.306498	+	0.579923i
$143$	−6.84016	−	0.770701i	−0.572003	−	0.0644493i
$144$	6.28633	+	13.0631i	0.523861	+	1.08859i
$145$	−9.03626	+	2.34869i	−0.750421	+	0.195048i
$146$	0.500338	+	0.288871i	0.0414083	+	0.0239071i
$147$	2.79827	+	24.8666i	0.230797	+	2.05096i
$148$	−0.0715128	+	1.91122i	−0.00587832	+	0.157101i
$149$	−11.5507	+	3.56293i	−0.946274	+	0.291887i	−0.729225	−	0.684274i	$-0.760119\pi$
$149$	−11.5507	+	3.56293i	−0.946274	+	0.291887i	−0.217049	+	0.976161i	$0.569643\pi$
$150$	3.46665	−	4.34580i	0.283051	−	0.354833i
$151$	0.868062	−	0.340689i	0.0706419	−	0.0277249i	−0.329757	−	0.944066i	$-0.606967\pi$
$151$	0.868062	−	0.340689i	0.0706419	−	0.0277249i	0.400399	+	0.916341i	$0.368872\pi$
$152$	10.0987	−	2.30497i	0.819114	−	0.186957i
$153$	9.02299	−	6.65537i	0.729466	−	0.538055i
$154$	4.05231	+	8.41472i	0.326545	+	0.678077i
$155$	−4.83759	+	0.181010i	−0.388564	+	0.0145391i
$156$	2.62615	−	4.96725i	0.210261	−	0.397698i
$157$	−4.65832	+	17.3851i	−0.371775	+	1.38748i	0.486226	+	0.873833i	$0.338373\pi$
$157$	−4.65832	+	17.3851i	−0.371775	+	1.38748i	−0.858000	+	0.513649i	$0.828293\pi$
$158$	−1.12209	−	14.9732i	−0.0892686	−	1.19121i
$159$	−11.8407	−	2.24209i	−0.939027	−	0.177809i
$160$	2.24664	−	5.14936i	0.177613	−	0.407092i
$161$	13.2975	−	27.6126i	1.04799	−	2.17617i
$162$	8.59529	+	11.6598i	0.675309	+	0.916084i
$163$	−2.54461	−	7.27207i	−0.199309	−	0.569592i	0.800238	−	0.599682i	$-0.204706\pi$
$163$	−2.54461	−	7.27207i	−0.199309	−	0.569592i	−0.999547	+	0.0300898i	$0.990421\pi$
$164$	0.00272169	+	0.0727387i	0.000212528	+	0.00567994i
$165$	−3.72073	+	0.560278i	−0.289658	+	0.0436175i
$166$	−21.7843	+	4.12182i	−1.69079	+	0.319915i
$167$	−3.91595	+	3.63347i	−0.303026	+	0.281167i	−0.816999	−	0.576640i	$-0.804364\pi$
$167$	−3.91595	+	3.63347i	−0.303026	+	0.281167i	0.513973	+	0.857806i	$0.328173\pi$
$168$	18.1465	−	1.35734i	1.40003	−	0.104721i
$169$	16.9875	−	2.56045i	1.30673	−	0.196958i
$170$	−10.1674	−	2.32065i	−0.779806	−	0.177986i
$171$	12.5567	−	5.47423i	0.960232	−	0.418625i
$172$	0.207340	−	1.84019i	0.0158095	−	0.140314i
$173$	0.300046	−	0.519695i	0.0228121	−	0.0395117i	−0.854394	−	0.519626i	$-0.826071\pi$
$173$	0.300046	−	0.519695i	0.0228121	−	0.0395117i	0.877206	+	0.480114i	$0.159405\pi$
$174$	11.4536	−	9.70513i	0.868293	−	0.735744i
$175$	−4.61752	−	7.99778i	−0.349052	−	0.604575i
$176$	5.54968	−	2.42130i	0.418323	−	0.182512i
$177$	−12.9679	−	4.53969i	−0.974726	−	0.341224i
$178$	−11.8055	+	12.7233i	−0.884860	+	0.953653i
$179$	4.54611	+	5.70064i	0.339792	+	0.426086i	0.922142	−	0.386853i	$-0.126438\pi$
$179$	4.54611	+	5.70064i	0.339792	+	0.426086i	−0.582349	+	0.812939i	$0.697866\pi$
$180$	0.684278	−	2.99416i	0.0510031	−	0.223171i
$181$	1.17455	+	5.14606i	0.0873039	+	0.382504i	0.999637	−	0.0269456i	$-0.00857807\pi$
$181$	1.17455	+	5.14606i	0.0873039	+	0.382504i	−0.912333	+	0.409449i	$0.865721\pi$
$182$	−26.7099	−	31.0375i	−1.97987	−	2.30065i
$183$	6.04817	+	2.37471i	0.447094	+	0.175543i
$184$	−13.2732	−	7.01508i	−0.978512	−	0.517159i
$185$	−3.66282	+	4.25628i	−0.269296	+	0.312928i
$186$	6.88241	−	3.63623i	0.504643	−	0.266621i
$187$	−2.63795	−	3.86916i	−0.192906	−	0.282941i
$188$	1.70709	−	0.192343i	0.124502	−	0.0140280i
$189$	23.2467	−	6.21848i	1.69095	−	0.452328i
$190$	−11.4796	−	5.52827i	−0.832815	−	0.401063i
$191$	−8.60041	+	2.30447i	−0.622304	+	0.166746i	−0.556175	−	0.831065i	$-0.687732\pi$
$191$	−8.60041	+	2.30447i	−0.622304	+	0.166746i	−0.0661290	+	0.997811i	$0.521065\pi$
$192$	−0.287063	−	7.70073i	−0.0207170	−	0.555752i
$193$	−11.0880	+	20.9796i	−0.798133	+	1.51014i	0.0608551	+	0.998147i	$0.480617\pi$
$193$	−11.0880	+	20.9796i	−0.798133	+	1.51014i	−0.858988	+	0.511995i	$0.828907\pi$
$194$	11.4318	−	16.7673i	0.820753	−	1.20382i
$195$	15.1213	−	6.59485i	1.08286	−	0.472267i
$196$	−2.51462	+	8.15221i	−0.179616	+	0.582300i
$197$	6.91584	+	5.51520i	0.492733	+	0.392941i	0.838092	−	0.545529i	$-0.183671\pi$
$197$	6.91584	+	5.51520i	0.492733	+	0.392941i	−0.345359	+	0.938471i	$0.612243\pi$
$198$	4.99980	−	3.40676i	0.355320	−	0.242108i
$199$	2.06301	−	9.03862i	0.146243	−	0.640731i	−0.847667	−	0.530529i	$-0.821993\pi$
$199$	2.06301	−	9.03862i	0.146243	−	0.640731i	0.993909	−	0.110202i	$-0.0351497\pi$
$200$	−3.99960	+	2.11385i	−0.282815	+	0.149472i
$201$	18.3874	−	2.06916i	1.29695	−	0.145947i
$202$	24.8243	−	14.3323i	1.74663	−	1.00842i
$203$	−8.05999	−	23.6011i	−0.565700	−	1.65647i
$204$	3.72676	−	0.850060i	0.260925	−	0.0595161i
$205$	−0.126907	+	0.171953i	−0.00886359	+	0.0120097i
$206$	−15.8447	+	25.2167i	−1.10395	+	1.75693i
$207$	−18.9696	−	5.85715i	−1.31848	−	0.407100i
$208$	−20.7550	+	16.5516i	−1.43910	+	1.14765i
$209$	−2.09020	−	5.32573i	−0.144582	−	0.368389i
$210$	−18.4922	−	12.6116i	−1.27609	−	0.870282i
$211$	1.19004	+	6.28950i	0.0819256	+	0.432987i	0.999382	+	0.0351508i	$0.0111912\pi$
$211$	1.19004	+	6.28950i	0.0819256	+	0.432987i	−0.917456	+	0.397836i	$0.869761\pi$
$212$	−3.39464	−	2.31443i	−0.233145	−	0.158956i
$213$	−2.17592	−	8.12520i	−0.149092	−	0.556729i
$214$	4.58954	−	24.2563i	0.313734	−	1.65813i
$215$	3.84459	−	3.84459i	0.262199	−	0.262199i
$216$	−2.61824	−	11.4935i	−0.178149	−	0.782033i
$217$	−1.44782	−	12.8497i	−0.0982843	−	0.872297i
$218$	21.9397	+	9.57221i	1.48595	+	0.648312i
$219$	−0.455701	−	0.422947i	−0.0307934	−	0.0285801i
$220$	−1.23909	−	0.332013i	−0.0835395	−	0.0223843i
$221$	15.5621	+	13.3923i	1.04682	+	0.900863i
$222$	2.33812	−	8.72111i	0.156924	−	0.585322i
$223$	1.76178	−	23.5094i	0.117978	−	1.57430i	−0.553226	−	0.833031i	$-0.686603\pi$
$223$	1.76178	−	23.5094i	0.117978	−	1.57430i	0.671204	−	0.741273i	$-0.265778\pi$
$224$	14.1648	+	4.95648i	0.946426	+	0.331169i
$225$	−4.67825	+	3.72864i	−0.311883	+	0.248576i
$226$	3.09993	−	3.88718i	0.206204	−	0.258572i
$227$	0.228723	+	1.51748i	0.0151809	+	0.100718i	0.995138	−	0.0984896i	$-0.0314011\pi$
$227$	0.228723	+	1.51748i	0.0151809	+	0.100718i	−0.979957	+	0.199208i	$0.936163\pi$
$228$	4.67005		0.000653014i	0.309282		4.32469e-5i
$229$	1.98856	+	0.0744068i	0.131408	+	0.00491694i	0.103014	−	0.994680i	$-0.467151\pi$
$229$	1.98856	+	0.0744068i	0.131408	+	0.00491694i	0.0283937	+	0.999597i	$0.490961\pi$
$230$	7.38466	+	16.9258i	0.486930	+	1.11606i
$231$	−2.23513	−	9.79906i	−0.147061	−	0.644731i
$232$	−11.7007	+	3.51319i	−0.768187	+	0.230653i
$233$			2.88140i			0.188767i	0.995536	+	0.0943835i	$0.0300880\pi$
$233$			2.88140i			0.188767i	−0.995536	+	0.0943835i	$0.969912\pi$
$234$	−17.3081	+	20.1010i	−1.13146	+	1.31404i
$235$	4.27071	+	2.68346i	0.278590	+	0.175050i
$236$	−3.43375	−	3.18606i	−0.223518	−	0.207395i
$237$	−2.41053	+	15.9776i	−0.156581	+	1.03786i
$238$	4.15192	−	27.5462i	0.269129	−	1.78556i
$239$	15.6452	+	16.8615i	1.01200	+	1.09068i	0.995868	+	0.0908088i	$0.0289452\pi$
$239$	15.6452	+	16.8615i	1.01200	+	1.09068i	0.0161335	+	0.999870i	$0.494864\pi$
$240$	−8.61864	+	11.6744i	−0.556331	+	0.753581i
$241$	1.32524	+	0.0993129i	0.0853661	+	0.00639730i	0.117345	−	0.993091i	$-0.462562\pi$
$241$	1.32524	+	0.0993129i	0.0853661	+	0.00639730i	−0.0319786	+	0.999489i	$0.510181\pi$
$242$	8.07498	+	12.8513i	0.519079	+	0.826110i
$243$	−6.22371	−	14.2921i	−0.399251	−	0.916842i
$244$	1.56641	+	1.56641i	0.100279	+	0.100279i
$245$	−20.6957	+	14.1101i	−1.32220	+	0.901459i
$246$	0.0639332	−	0.337636i	0.00407623	−	0.0215269i
$247$	14.8953	+	20.1823i	0.947762	+	1.28417i
$248$	−6.31665	+	0.473367i	−0.401108	+	0.0300589i
$249$	23.8421	+	0.895448i	1.51093	+	0.0567467i
$250$	19.1767	+	3.62842i	1.21284	+	0.229481i
$251$	−0.667636	+	0.419503i	−0.0421408	+	0.0264788i	−0.552938	−	0.833223i	$-0.686493\pi$
$251$	−0.667636	+	0.419503i	−0.0421408	+	0.0264788i	0.510797	+	0.859701i	$0.329350\pi$
$252$	8.11213	+	1.22503i	0.511016	+	0.0771695i
$253$	−2.73868	+	7.82671i	−0.172180	+	0.492061i
$254$	12.8904	+	3.97615i	0.808813	+	0.249486i
$255$	10.1108	+	4.87087i	0.633166	+	0.305026i
$256$	4.77072	−	12.1556i	0.298170	−	0.759724i
$257$	1.77982	+	5.77003i	0.111022	+	0.359925i	0.993985	−	0.109519i	$-0.0349309\pi$
$257$	1.77982	+	5.77003i	0.111022	+	0.359925i	−0.882963	+	0.469443i	$0.844455\pi$
$258$	−2.88860	+	8.25144i	−0.179836	+	0.513712i
$259$	−12.0686	−	8.90703i	−0.749906	−	0.553456i
$260$	5.62424			0.348800
$261$	−14.3417	+	7.43749i	−0.887727	+	0.460369i
$262$	0.787963			0.0486805
$263$	−8.04816	−	5.93981i	−0.496271	−	0.366264i	0.316741	−	0.948512i	$-0.397411\pi$
$263$	−8.04816	−	5.93981i	−0.496271	−	0.366264i	−0.813011	+	0.582248i	$0.802173\pi$
$264$	−4.83772	+	0.914645i	−0.297741	+	0.0562925i
$265$	−3.55560	−	11.5270i	−0.218419	−	0.708096i
$266$	12.4341	−	31.6816i	0.762385	−	1.94253i
$267$	15.4341	−	10.5196i	0.944551	−	0.643790i
$268$	6.02808	+	1.85942i	0.368223	+	0.113582i
$269$	−0.347949	+	0.994380i	−0.0212148	+	0.0606284i	−0.954004	−	0.299794i	$-0.903082\pi$
$269$	−0.347949	+	0.994380i	−0.0212148	+	0.0606284i	0.932789	+	0.360423i	$0.117368\pi$
$270$	−6.29667	+	13.0612i	−0.383203	+	0.794877i
$271$	19.1106	−	12.0080i	1.16089	−	0.729433i	0.193093	−	0.981181i	$-0.438148\pi$
$271$	19.1106	−	12.0080i	1.16089	−	0.729433i	0.967793	+	0.251748i	$0.0810053\pi$
$272$	−17.7451	−	3.35755i	−1.07595	−	0.203581i
$273$	20.5852	+	38.9622i	1.24587	+	2.35810i
$274$	−3.92192	+	0.293908i	−0.236932	+	0.0177556i
$275$	1.48374	+	2.01040i	0.0894729	+	0.121231i
$276$	−5.12973	−	4.41574i	−0.308774	−	0.265796i
$277$	−7.29029	+	4.97044i	−0.438031	+	0.298645i	−0.762184	−	0.647360i	$-0.775873\pi$
$277$	−7.29029	+	4.97044i	−0.438031	+	0.298645i	0.324153	+	0.946005i	$0.394921\pi$
$278$	−8.14620	−	8.14620i	−0.488577	−	0.488577i
$279$	−8.09179	+	2.16576i	−0.484443	+	0.129661i
$280$	9.69094	+	15.4230i	0.579145	+	0.921703i
$281$	−15.1183	−	1.13296i	−0.901882	−	0.0675867i	−0.384288	−	0.923213i	$-0.625553\pi$
$281$	−15.1183	−	1.13296i	−0.901882	−	0.0675867i	−0.517594	+	0.855626i	$0.673172\pi$
$282$	−8.05895	−	0.909167i	−0.479904	−	0.0541401i
$283$	−2.94095	−	3.16959i	−0.174822	−	0.188413i	0.639563	−	0.768739i	$-0.279116\pi$
$283$	−2.94095	−	3.16959i	−0.174822	−	0.188413i	−0.814384	+	0.580326i	$0.802925\pi$
$284$	0.427411	−	2.83569i	0.0253622	−	0.168267i
$285$	10.7189	+	8.55046i	0.634931	+	0.506486i
$286$	8.12143	+	7.53559i	0.480230	+	0.445589i
$287$	−0.483365	−	0.303718i	−0.0285321	−	0.0179279i
$288$	1.80998	−	9.55137i	0.106654	−	0.562820i
$289$		−	3.03240i		−	0.178376i
$290$	13.9468	+	5.59490i	0.818983	+	0.328544i
$291$	−16.0110	+	14.8518i	−0.938579	+	0.870630i
$292$	−0.0847631	−	0.194279i	−0.00496039	−	0.0113693i
$293$	−3.06548	−	0.114702i	−0.179087	−	0.00670097i	−0.0523029	−	0.998631i	$-0.516656\pi$
$293$	−3.06548	−	0.114702i	−0.179087	−	0.00670097i	−0.126784	+	0.991930i	$0.540466\pi$
$294$	20.1426	−	34.8768i	1.17474	−	2.03406i
$295$	−2.04978	−	13.5994i	−0.119343	−	0.791786i
$296$	−4.58117	+	5.74461i	−0.266275	+	0.333899i
$297$	−6.06171	+	2.37611i	−0.351736	+	0.137876i
$298$	18.3636	+	6.42569i	1.06377	+	0.372230i
$299$	2.71682	−	36.2534i	0.157118	−	2.09659i
$300$	−1.97013	+	0.527601i	−0.113746	+	0.0304610i
$301$	11.0083	+	9.47340i	0.634507	+	0.546038i
$302$	−1.44976	−	0.388462i	−0.0834243	−	0.0223535i
$303$	−29.4780	+	9.08823i	−1.69346	+	0.522105i
$304$	−20.2234	−	8.82340i	−1.15989	−	0.506056i
$305$	0.728219	+	6.46313i	0.0416977	+	0.370078i
$306$	−18.0457	−	0.00504668i	−1.03161	−	0.000288499i
$307$	−19.7708	+	19.7708i	−1.12838	+	1.12838i	−0.137938	+	0.990441i	$0.544048\pi$
$307$	−19.7708	+	19.7708i	−1.12838	+	1.12838i	−0.990441	+	0.137938i	$0.955952\pi$
$308$	0.637041	−	3.36684i	0.0362988	−	0.191844i
$309$	22.6653	−	22.6589i	1.28938	−	1.28902i
$310$	6.43769	+	4.38915i	0.365636	+	0.249287i
$311$	−5.19624	−	27.4628i	−0.294652	−	1.55727i	−0.746628	−	0.665242i	$-0.768329\pi$
$311$	−5.19624	−	27.4628i	−0.294652	−	1.55727i	0.451977	−	0.892030i	$-0.350719\pi$
$312$	19.4496	−	9.36308i	1.10112	−	0.530080i
$313$	11.6290	+	29.6303i	0.657312	+	1.67480i	0.735207	+	0.677843i	$0.237085\pi$
$313$	11.6290	+	29.6303i	0.657312	+	1.67480i	−0.0778944	+	0.996962i	$0.524820\pi$
$314$	22.6485	−	18.0616i	1.27813	−	1.01927i
$315$	16.3788	+	17.6620i	0.922840	+	0.995144i
$316$	−2.93090	+	4.66449i	−0.164876	+	0.262398i
$317$	−6.29271	+	8.52631i	−0.353434	+	0.478885i	−0.944860	−	0.327473i	$-0.893803\pi$
$317$	−6.29271	+	8.52631i	−0.353434	+	0.478885i	0.591427	+	0.806359i	$0.298565\pi$
$318$	13.1908	+	14.2203i	0.739705	+	0.797436i
$319$	2.88195	+	6.10119i	0.161358	+	0.341601i
$320$	6.68019	−	3.85681i	0.373434	−	0.215602i
$321$	−10.6270	+	24.3482i	−0.593144	+	1.35898i
$322$	−43.6112	+	23.0492i	−2.43036	+	1.28448i
$323$	−3.79725	+	16.6369i	−0.211285	+	0.925700i
$324$	0.00297253	−	5.31454i	0.000165141	−	0.295252i
$325$	−8.56486	−	6.83025i	−0.475093	−	0.378874i
$326$	−3.65505	+	11.8494i	−0.202435	+	0.656277i
$327$	−20.7239	−	15.2994i	−1.14603	−	0.846060i
$328$	−0.157528	+	0.231051i	−0.00869802	+	0.0127576i
$329$	−6.29543	+	11.9115i	−0.347078	+	0.656704i
$330$	5.35385	+	2.83055i	0.294720	+	0.155817i
$331$	−6.56862	+	1.76006i	−0.361044	+	0.0967415i	−0.434781	−	0.900536i	$-0.643174\pi$
$331$	−6.56862	+	1.76006i	−0.361044	+	0.0967415i	0.0737369	+	0.997278i	$0.476508\pi$
$332$	7.32864	+	3.52929i	0.402211	+	0.193695i
$333$	−4.54265	+	8.58929i	−0.248935	+	0.470690i
$334$	8.54389	−	0.962665i	0.467501	−	0.0526747i
$335$	10.4336	+	15.3032i	0.570046	+	0.836105i
$336$	−32.8176	−	20.6270i	−1.79034	−	1.12530i
$337$	7.56142	−	8.78653i	0.411897	−	0.478633i	−0.513252	−	0.858238i	$-0.671559\pi$
$337$	7.56142	−	8.78653i	0.411897	−	0.478633i	0.925148	+	0.379605i	$0.123940\pi$
$338$	−24.4460	−	12.9201i	−1.32969	−	0.702760i
$339$	−4.18362	+	3.33537i	−0.227223	+	0.181152i
$340$	2.49579	+	2.90016i	0.135353	+	0.157283i
$341$	0.778518	+	3.41091i	0.0421591	+	0.184711i
$342$	−21.4930	−	4.91195i	−1.16221	−	0.265608i
$343$	−21.5039	−	26.9651i	−1.16110	−	1.45598i
$344$	4.83899	−	5.21519i	0.260901	−	0.281184i
$345$	−3.69183	−	19.5267i	−0.198761	−	1.05128i
$346$	−0.885262	+	0.386236i	−0.0475920	+	0.0207642i
$347$	1.95903	+	3.39315i	0.105166	+	0.182154i	0.913806	−	0.406151i	$-0.133129\pi$
$347$	1.95903	+	3.39315i	0.105166	+	0.182154i	−0.808640	+	0.588304i	$0.799796\pi$
$348$	−5.49544	+	0.369586i	−0.294587	+	0.0198119i
$349$	15.4401	−	26.7430i	0.826490	−	1.43152i	−0.0742860	−	0.997237i	$-0.523668\pi$
$349$	15.4401	−	26.7430i	0.826490	−	1.43152i	0.900776	−	0.434285i	$-0.142999\pi$
$350$	−1.66422	+	14.7704i	−0.0889564	+	0.789510i
$351$	22.9747	−	16.9412i	1.22630	−	0.904256i
$352$	−3.95848	−	0.903498i	−0.210988	−	0.0481566i
$353$	−19.1534	+	2.88691i	−1.01943	+	0.153655i	−0.637431	−	0.770508i	$-0.720003\pi$
$353$	−19.1534	+	2.88691i	−1.01943	+	0.153655i	−0.382000	+	0.924162i	$0.624765\pi$
$354$	12.4546	+	18.2731i	0.661955	+	0.971202i
$355$	6.17211	−	5.72688i	0.327582	−	0.303951i
$356$	6.25689	−	1.18387i	0.331614	−	0.0627448i
$357$	−10.9562	+	27.9046i	−0.579866	+	1.47687i
$358$	−0.438806	−	11.7273i	−0.0231916	−	0.619809i
$359$	−0.761387	−	2.17592i	−0.0401845	−	0.114841i	0.922043	−	0.387088i	$-0.126519\pi$
$359$	−0.761387	−	2.17592i	−0.0401845	−	0.114841i	−0.962227	+	0.272247i	$0.912233\pi$
$360$	8.94582	−	7.69415i	0.471486	−	0.405517i
$361$	−0.802054	+	1.66548i	−0.0422134	+	0.0876570i
$362$	3.39733	−	7.78675i	0.178559	−	0.409263i
$363$	−5.39237	−	15.4174i	−0.283026	−	0.809204i
$364$	1.12269	+	14.9813i	0.0588450	+	0.785232i
$365$	0.161073	−	0.601133i	0.00843095	−	0.0314647i
$366$	−5.56276	−	8.85583i	−0.290770	−	0.462902i
$367$	8.08502	−	0.302520i	0.422035	−	0.0157914i	0.174469	−	0.984663i	$-0.444179\pi$
$367$	8.08502	−	0.302520i	0.422035	−	0.0157914i	0.247565	+	0.968871i	$0.420369\pi$
$368$	13.8752	+	28.8121i	0.723294	+	1.50193i
$369$	−0.147975	+	0.338904i	−0.00770327	+	0.0176426i
$370$	8.81133	−	2.01113i	0.458079	−	0.104554i
$371$	29.9946	−	11.7720i	1.55724	−	0.611173i
$372$	−2.82386	−	0.426033i	−0.146410	−	0.0220888i
$373$	31.5627	−	9.73580i	1.63425	−	0.504101i	0.664316	−	0.747451i	$-0.268723\pi$
$373$	31.5627	−	9.73580i	1.63425	−	0.504101i	0.969938	+	0.243351i	$0.0782465\pi$
$374$	−0.281821	+	7.53182i	−0.0145726	+	0.389461i
$375$	−19.2493	−	8.40159i	−0.994030	−	0.433856i
$376$	5.71556	+	3.29988i	0.294757	+	0.170178i
$377$	−19.1282	−	22.5679i	−0.985155	−	1.16231i
$378$	−36.0479	−	14.1652i	−1.85410	−	0.728580i
$379$	8.75453	+	0.986399i	0.449690	+	0.0506679i	0.333906	−	0.942606i	$-0.391633\pi$
$379$	8.75453	+	0.986399i	0.449690	+	0.0506679i	0.115784	+	0.993274i	$0.463062\pi$
$380$	2.18430	+	4.13291i	0.112052	+	0.212014i
$381$	−12.5709	−	7.26014i	−0.644025	−	0.371948i
$382$	13.3401	+	5.23560i	0.682538	+	0.267876i
$383$	8.04776	+	1.21300i	0.411221	+	0.0619816i	0.351395	−	0.936227i	$-0.385707\pi$
$383$	8.04776	+	1.21300i	0.411221	+	0.0619816i	0.0598259	+	0.998209i	$0.480945\pi$
$384$	−13.3130	+	19.5207i	−0.679375	+	0.996161i
$385$	7.62564	−	6.56239i	0.388638	−	0.334450i
$386$	34.4104	−	16.5712i	1.75144	−	0.843450i
$387$	5.00763	−	7.96465i	0.254552	−	0.404866i
$388$	−7.02760	+	2.45907i	−0.356773	+	0.124840i
$389$	3.24745	+	12.1196i	0.164652	+	0.614491i	0.998084	+	0.0618686i	$0.0197060\pi$
$389$	3.24745	+	12.1196i	0.164652	+	0.614491i	−0.833432	+	0.552622i	$0.813627\pi$
$390$	−25.8852	−	5.91194i	−1.31075	−	0.299363i
$391$	19.8999	−	14.6868i	1.00638	−	0.742741i
$392$	−26.3708	+	19.4625i	−1.33193	+	0.983006i
$393$	−0.826671	−	0.188804i	−0.0417000	−	0.00952390i
$394$	−3.68485	−	13.7521i	−0.185640	−	0.692818i
$395$	−15.2666	+	5.34203i	−0.768148	+	0.268787i
$396$	−2.21813	−	0.0836177i	−0.111465	−	0.00420195i
$397$	12.5605	−	6.04881i	0.630392	−	0.303581i	−0.0912700	−	0.995826i	$-0.529093\pi$
$397$	12.5605	−	6.04881i	0.630392	−	0.303581i	0.721662	+	0.692245i	$0.243378\pi$
$398$	−11.3103	+	9.73332i	−0.566935	+	0.487887i
$399$	−20.6362	+	30.2586i	−1.03310	+	1.51483i
$400$	9.52860	+	1.43621i	0.476430	+	0.0718103i
$401$	9.77268	+	3.83549i	0.488024	+	0.191535i	0.596578	−	0.802555i	$-0.296527\pi$
$401$	9.77268	+	3.83549i	0.488024	+	0.191535i	−0.108554	+	0.994091i	$0.534622\pi$
$402$	−25.7893	−	14.8943i	−1.28626	−	0.742860i
$403$	−7.16751	−	13.5616i	−0.357039	−	0.675551i
$404$	−10.4505	−	1.17749i	−0.519933	−	0.0585824i
$405$	9.73558	−	12.1940i	0.483765	−	0.605926i
$406$	−12.1191	+	38.2668i	−0.601463	+	1.89915i
$407$	3.51457	+	2.02914i	0.174211	+	0.100581i
$408$	13.4590	+	5.87434i	0.666320	+	0.290823i
$409$	−1.25641	+	33.5783i	−0.0621256	+	1.66034i	0.525191	+	0.850984i	$0.323994\pi$
$409$	−1.25641	+	33.5783i	−0.0621256	+	1.66034i	−0.587317	+	0.809357i	$0.699816\pi$
$410$	0.328691	−	0.101388i	0.0162329	−	0.00500718i
$411$	4.18501	+	0.631387i	0.206431	+	0.0311440i
$412$	10.1711	−	3.99187i	0.501095	−	0.196665i
$413$	35.8155	−	8.17465i	1.76236	−	0.402248i
$414$	18.9677	+	25.7153i	0.932210	+	1.26384i
$415$	10.3621	+	21.5172i	0.508657	+	1.05624i
$416$	17.7892	−	0.665625i	0.872188	−	0.0326350i
$417$	6.59447	+	10.4983i	0.322933	+	0.514104i
$418$	−2.38329	+	8.89456i	−0.116571	+	0.435047i
$419$	−1.36045	−	18.1539i	−0.0664622	−	0.886876i	−0.926415	−	0.376503i	$-0.877126\pi$
$419$	−1.36045	−	18.1539i	−0.0664622	−	0.886876i	0.859953	−	0.510373i	$-0.170493\pi$
$420$	2.71121	+	7.75168i	0.132294	+	0.378243i
$421$	4.31465	−	9.88927i	0.210283	−	0.481974i	−0.779173	−	0.626809i	$-0.784361\pi$
$421$	4.31465	−	9.88927i	0.210283	−	0.481974i	0.989456	+	0.144835i	$0.0462653\pi$
$422$	4.47013	−	9.28231i	0.217602	−	0.451856i
$423$	8.23700	+	2.88484i	0.400497	+	0.140266i
$424$	−5.21318	−	14.8984i	−0.253174	−	0.723530i
$425$	−0.278665	−	7.44748i	−0.0135172	−	0.361256i
$426$	−4.94788	+	12.6018i	−0.239726	+	0.610560i
$427$	−17.0705	+	3.22991i	−0.826097	+	0.156306i
$428$	−6.63939	+	6.16045i	−0.320927	+	0.297777i
$429$	−6.71479	−	9.85175i	−0.324193	−	0.475647i
$430$	−8.65326	+	1.30427i	−0.417297	+	0.0628974i
$431$	−33.9613	−	7.75145i	−1.63586	−	0.373374i	−0.696836	−	0.717230i	$-0.745410\pi$
$431$	−33.9613	−	7.75145i	−1.63586	−	0.373374i	−0.939022	+	0.343856i	$0.888267\pi$
$432$	−10.0507	+	23.0101i	−0.483565	+	1.10708i
$433$	3.73046	−	33.1088i	0.179275	−	1.59111i	−0.505812	−	0.862644i	$-0.668807\pi$
$433$	3.73046	−	33.1088i	0.179275	−	1.59111i	0.685087	−	0.728462i	$-0.259764\pi$
$434$	−10.4063	+	18.0242i	−0.499518	+	0.865191i
$435$	−13.2913	−	9.21154i	−0.637269	−	0.441660i
$436$	−4.39107	−	7.60555i	−0.210294	−	0.364240i
$437$	27.6955	−	12.0834i	1.32486	−	0.578029i
$438$	0.185900	+	0.983258i	0.00888264	+	0.0469819i
$439$	12.0697	−	13.0081i	0.576056	−	0.620841i	−0.376053	−	0.926598i	$-0.622719\pi$
$439$	12.0697	−	13.0081i	0.576056	−	0.620841i	0.952110	+	0.305757i	$0.0989095\pi$
$440$	−3.07271	−	3.85306i	−0.146486	−	0.183687i
$441$	−29.4890	+	31.7637i	−1.40424	+	1.51256i
$442$	−7.35324	−	32.2167i	−0.349758	−	1.53239i
$443$	7.15877	+	8.31864i	0.340123	+	0.395231i	0.901819	−	0.432113i	$-0.142232\pi$
$443$	7.15877	+	8.31864i	0.340123	+	0.395231i	−0.561696	+	0.827344i	$0.689851\pi$
$444$	−2.59022	+	2.06504i	−0.122926	+	0.0980024i
$445$	16.5298	+	8.73626i	0.783588	+	0.414138i
$446$	−24.7507	+	28.7609i	−1.17198	+	1.36187i
$447$	−17.7260	−	11.1414i	−0.838411	−	0.526972i
$448$	11.6069	+	17.0241i	0.548373	+	0.804315i
$449$	−19.8185	+	2.23300i	−0.935291	+	0.105382i	−0.566437	−	0.824105i	$-0.691678\pi$
$449$	−19.8185	+	2.23300i	−0.935291	+	0.105382i	−0.368854	+	0.929487i	$0.620250\pi$
$450$	9.62202	−	0.357336i	0.453586	−	0.0168450i
$451$	0.139157	+	0.0670147i	0.00655267	+	0.00315560i
$452$	−1.76196	+	0.472117i	−0.0828758	+	0.0222065i
$453$	1.42790	+	0.754922i	0.0670885	+	0.0354693i
$454$	1.15414	−	2.18374i	0.0541665	−	0.102488i
$455$	−24.8475	+	36.4446i	−1.16487	+	1.70855i
$456$	14.4341	+	10.6559i	0.675937	+	0.499010i
$457$	−1.26068	+	4.08704i	−0.0589723	+	0.191183i	−0.980266	−	0.197685i	$-0.936658\pi$
$457$	−1.26068	+	4.08704i	−0.0589723	+	0.191183i	0.921293	+	0.388868i	$0.127134\pi$
$458$	−2.50408	−	1.99694i	−0.117008	−	0.0933108i
$459$	18.9310	+	4.32923i	0.883624	+	0.202071i
$460$	1.50761	−	6.60528i	0.0702928	−	0.307973i
$461$	3.36772	−	1.77989i	0.156850	−	0.0828978i	−0.387002	−	0.922079i	$-0.626489\pi$
$461$	3.36772	−	1.77989i	0.156850	−	0.0828978i	0.543852	+	0.839181i	$0.316965\pi$
$462$	−6.47101	+	14.8261i	−0.301059	+	0.689771i
$463$	−12.1828	+	7.03376i	−0.566184	+	0.326887i	−0.755624	−	0.655006i	$-0.772666\pi$
$463$	−12.1828	+	7.03376i	−0.566184	+	0.326887i	0.189440	+	0.981892i	$0.439333\pi$
$464$	24.4973	+	8.77896i	1.13726	+	0.407553i
$465$	−5.70226	−	6.14730i	−0.264436	−	0.285074i
$466$	2.75392	−	3.73143i	0.127573	−	0.172855i
$467$	4.84070	−	7.70393i	0.224001	−	0.356495i	−0.715749	−	0.698357i	$-0.753915\pi$
$467$	4.84070	−	7.70393i	0.224001	−	0.356495i	0.939750	+	0.341862i	$0.111058\pi$
$468$	9.48854	−	2.16291i	0.438608	−	0.0999804i
$469$	−38.6805	+	30.8467i	−1.78610	+	1.42437i
$470$	−2.96584	−	7.55685i	−0.136804	−	0.348571i
$471$	−28.0888	+	13.5220i	−1.29426	+	0.623062i
$472$	−3.34560	−	17.6819i	−0.153994	−	0.813876i
$473$	−3.24666	−	2.21353i	−0.149281	−	0.101778i
$474$	18.3924	−	18.3872i	0.844790	−	0.844554i
$475$	1.69276	−	8.94647i	0.0776694	−	0.410492i
$476$	−7.22696	+	7.22696i	−0.331247	+	0.331247i
$477$	−10.4315	−	18.0795i	−0.477625	−	0.827805i
$478$	−4.14509	−	36.7886i	−0.189592	−	1.68267i
$479$	−19.2829	−	8.41304i	−0.881058	−	0.384402i	−0.0898547	−	0.995955i	$-0.528640\pi$
$479$	−19.2829	−	8.41304i	−0.881058	−	0.384402i	−0.791203	+	0.611553i	$0.790545\pi$
$480$	9.29895	−	2.86692i	0.424437	−	0.130857i
$481$	−17.1866	−	4.60514i	−0.783642	−	0.209976i
$482$	−1.62127	−	1.39522i	−0.0738468	−	0.0635503i
$483$	51.2764	−	13.7318i	2.33316	−	0.624818i
$484$	0.416131	−	5.55288i	0.0189150	−	0.252404i
$485$	−20.6333	−	7.21992i	−0.936912	−	0.327840i
$486$	−5.60008	+	24.4567i	−0.254025	+	1.10938i
$487$	−11.6305	+	14.5842i	−0.527028	+	0.660872i	−0.972085	−	0.234630i	$-0.924612\pi$
$487$	−11.6305	+	14.5842i	−0.527028	+	0.660872i	0.445057	+	0.895502i	$0.353184\pi$
$488$	1.26842	+	8.41539i	0.0574185	+	0.380947i
$489$	6.67384	−	11.5557i	0.301801	−	0.522566i
$490$	40.2867	+	1.50742i	1.81997	+	0.0680984i
$491$	15.1647	+	34.7579i	0.684375	+	1.56860i	0.816484	+	0.577368i	$0.195920\pi$
$491$	15.1647	+	34.7579i	0.684375	+	1.56860i	−0.132109	+	0.991235i	$0.542175\pi$
$492$	−0.0924317	+	0.0857400i	−0.00416714	+	0.00386546i
$493$	3.14898	−	19.8782i	0.141823	−	0.895271i
$494$		−	40.3724i		−	1.81644i
$495$	−4.93862	−	4.25243i	−0.221975	−	0.191133i
$496$	11.4247	+	7.17860i	0.512983	+	0.322329i
$497$	16.4867	+	15.2975i	0.739531	+	0.686185i
$498$	−30.0198	−	23.9469i	−1.34522	−	1.07308i
$499$	−4.65984	+	30.9160i	−0.208603	+	1.38399i	0.602047	+	0.798461i	$0.294352\pi$
$499$	−4.65984	+	30.9160i	−0.208603	+	1.38399i	−0.810650	+	0.585531i	$0.800886\pi$
$500$	−4.87036	−	5.24900i	−0.217809	−	0.234742i
$501$	−9.19427	−	1.03725i	−0.410770	−	0.0463408i
$502$	1.26553	+	0.0948386i	0.0564835	+	0.00423285i
$503$	19.1431	+	30.4661i	0.853549	+	1.35842i	0.932362	+	0.361526i	$0.117744\pi$
$503$	19.1431	+	30.4661i	0.853549	+	1.35842i	−0.0788131	+	0.996889i	$0.525113\pi$
$504$	22.2806	+	22.2931i	0.992458	+	0.993013i
$505$	−21.8336	−	21.8336i	−0.971581	−	0.971581i
$506$	11.0270	−	7.51810i	0.490211	−	0.334220i
$507$	22.5511	+	19.4123i	1.00153	+	0.862131i
$508$	−2.93892	−	3.98209i	−0.130393	−	0.176677i
$509$	0.246346	−	0.0184611i	0.0109191	−	0.000818273i	−0.0692694	−	0.997598i	$-0.522067\pi$
$509$	0.246346	−	0.0184611i	0.0109191	−	0.000818273i	0.0801885	+	0.996780i	$0.474448\pi$
$510$	−8.43822	−	15.9713i	−0.373651	−	0.707221i
$511$	1.63339	+	0.309054i	0.0722569	+	0.0136717i
$512$	5.30574	−	3.33382i	0.234483	−	0.147335i
$513$	21.3718	+	10.3032i	0.943589	+	0.454896i
$514$	3.20987	−	9.17328i	0.141581	−	0.404616i
$515$	30.6552	+	9.45587i	1.35083	+	0.416676i
$516$	2.65040	−	1.80647i	0.116677	−	0.0795252i
$517$	1.33175	−	3.39323i	0.0585701	−	0.149234i
$518$	7.11593	+	23.0693i	0.312656	+	1.01361i
$519$	1.02130	−	0.193092i	0.0448299	−	0.00847579i
$520$	17.3850	+	12.8307i	0.762384	+	0.562665i
$521$	−8.90558			−0.390160			−0.195080	−	0.980787i	$-0.562497\pi$
$521$	−8.90558			−0.390160			−0.195080	+	0.980787i	$0.562497\pi$
$522$	25.6810	+	4.07556i	1.12402	+	0.178383i
$523$	44.4324			1.94289			0.971447	−	0.237257i	$-0.0762485\pi$
$523$	44.4324			1.94289			0.971447	+	0.237257i	$0.0762485\pi$
$524$	−0.232603	−	0.171669i	−0.0101613	−	0.00749939i
$525$	5.28511	−	15.0972i	0.230661	−	0.658896i
$526$	4.74538	+	15.3841i	0.206908	+	0.670781i
$527$	3.81247	−	9.71401i	0.166074	−	0.423149i
$528$	9.44815	+	4.55162i	0.411178	+	0.198084i
$529$	−19.8707	−	6.12930i	−0.863944	−	0.266491i
$530$	−6.41245	+	18.3257i	−0.278539	+	0.796019i
$531$	−8.68803	−	22.1550i	−0.377029	−	0.961444i
$532$	−10.5728	+	6.64333i	−0.458389	+	0.288025i
$533$	−0.665370	−	0.125895i	−0.0288204	−	0.00545311i
$534$	−30.0414	−	1.12828i	−1.30002	−	0.0488253i
$535$	−26.5179	+	1.98724i	−1.14647	+	0.0859161i
$536$	14.3914	+	19.4996i	0.621613	+	0.842256i
$537$	−2.34963	+	12.4086i	−0.101394	+	0.535469i
$538$	1.40098	−	0.955172i	0.0604005	−	0.0411804i
$539$	12.8004	+	12.8004i	0.551353	+	0.551353i
$540$	4.70431	−	2.48378i	0.202441	−	0.106885i
$541$	7.62335	+	12.1325i	0.327753	+	0.521616i	0.969433	−	0.245356i	$-0.0789050\pi$
$541$	7.62335	+	12.1325i	0.327753	+	0.521616i	−0.641680	+	0.766973i	$0.721762\pi$
$542$	−36.2250	−	2.71469i	−1.55600	−	0.116606i
$543$	−5.43000	+	7.35524i	−0.233024	+	0.315644i
$544$	8.23731	+	8.87771i	0.353172	+	0.380629i
$545$	3.84302	−	25.4967i	0.164617	−	1.09216i
$546$	10.5805	−	70.1306i	0.452804	−	3.00131i
$547$	−22.2518	−	20.6466i	−0.951418	−	0.882787i	0.0417917	−	0.999126i	$-0.486693\pi$
$547$	−22.2518	−	20.6466i	−0.951418	−	0.882787i	−0.993209	+	0.116340i	$0.962884\pi$
$548$	1.22177	+	0.767687i	0.0521913	+	0.0327940i
$549$	3.71408	+	10.6238i	0.158513	+	0.453411i
$550$		−	4.02156i		−	0.171480i
$551$	9.15488	−	22.8210i	0.390011	−	0.972205i
$552$	−5.78271	−	25.3520i	−0.246128	−	1.07905i
$553$	−17.2770	−	39.5994i	−0.734694	−	1.68394i
$554$	14.1915	+	0.531008i	0.602938	+	0.0225604i
$555$	−9.72607	−	0.00136000i	−0.412849	−	5.77287e-5i
$556$	0.629957	+	4.17949i	0.0267161	+	0.177250i
$557$	23.7997	−	29.8439i	1.00843	−	1.26453i	0.0443197	−	0.999017i	$-0.485888\pi$
$557$	23.7997	−	29.8439i	1.00843	−	1.26453i	0.964108	−	0.265511i	$-0.0855406\pi$
$558$	12.5488	+	4.92911i	0.531235	+	0.208666i
$559$	16.2612	+	5.69005i	0.687776	+	0.240663i
$560$	2.89950	−	38.6911i	0.122526	−	1.63500i
$561$	2.10037	−	7.83429i	0.0886775	−	0.330764i
$562$	18.4954	+	15.9166i	0.780182	+	0.671401i
$563$	−30.1537	−	8.07965i	−1.27083	−	0.340517i	−0.440479	−	0.897763i	$-0.645191\pi$
$563$	−30.1537	−	8.07965i	−1.27083	−	0.340517i	−0.830347	+	0.557246i	$0.811858\pi$
$564$	2.18089	+	2.02414i	0.0918321	+	0.0852317i
$565$	−4.90882	−	2.14170i	−0.206516	−	0.0901019i
$566$	0.779186	+	6.91547i	0.0327516	+	0.290679i
$567$	34.4246	+	23.4985i	1.44570	+	0.986845i
$568$	7.79030	−	7.79030i	0.326874	−	0.326874i
$569$	4.22320	−	22.3202i	0.177046	−	0.935710i	−0.775508	−	0.631338i	$-0.782506\pi$
$569$	4.22320	−	22.3202i	0.177046	−	0.935710i	0.952553	−	0.304372i	$-0.0984464\pi$
$570$	−5.70881	−	21.3175i	−0.239116	−	0.892892i
$571$	7.35435	+	5.01411i	0.307770	+	0.209834i	0.707349	−	0.706865i	$-0.249891\pi$
$571$	7.35435	+	5.01411i	0.307770	+	0.209834i	−0.399578	+	0.916699i	$0.630843\pi$
$572$	−0.755675	−	3.99384i	−0.0315964	−	0.166991i
$573$	−12.7409	−	8.68921i	−0.532259	−	0.362997i
$574$	0.335678	+	0.855295i	0.0140109	+	0.0356993i
$575$	−10.3175	+	8.22795i	−0.430270	+	0.343129i
$576$	9.78682	−	9.07575i	0.407784	−	0.378156i
$577$	1.03792	−	1.65184i	0.0432093	−	0.0687672i	−0.824421	−	0.565977i	$-0.808499\pi$
$577$	1.03792	−	1.65184i	0.0432093	−	0.0687672i	0.867630	+	0.497210i	$0.165642\pi$
$578$	−2.89823	+	3.92697i	−0.120551	+	0.163340i
$579$	−40.0714	+	9.14014i	−1.66531	+	0.379851i
$580$	−2.89809	−	4.69009i	−0.120337	−	0.194746i
$581$	−55.2469	+	31.8968i	−2.29203	+	1.32330i
$582$	34.9290	−	3.93061i	1.44785	−	0.162929i
$583$	−7.70771	+	4.07364i	−0.319221	+	0.168713i
$584$	0.181204	−	0.793907i	0.00749828	−	0.0328521i
$585$	25.7403	+	12.4047i	1.06423	+	0.512872i
$586$	3.86018	+	3.07839i	0.159463	+	0.127167i
$587$	5.98310	−	19.3967i	0.246949	−	0.800588i	−0.744214	−	0.667941i	$-0.767176\pi$
$587$	5.98310	−	19.3967i	0.246949	−	0.800588i	0.991163	−	0.132648i	$-0.0423478\pi$
$588$	−13.5444	+	5.90712i	−0.558562	+	0.243605i
$589$	7.18191	−	10.5339i	0.295926	−	0.434043i
$590$	−10.3432	+	19.5703i	−0.425824	+	0.805698i
$591$	0.570736	+	15.3105i	0.0234770	+	0.629792i
$592$	15.1179	−	4.05082i	0.621340	−	0.166488i
$593$	32.5033	+	15.6528i	1.33475	+	0.642782i	0.958859	−	0.283883i	$-0.0916226\pi$
$593$	32.5033	+	15.6528i	1.33475	+	0.642782i	0.375891	+	0.926664i	$0.377337\pi$
$594$	10.1209	+	2.71644i	0.415266	+	0.111457i
$595$	−29.8191	+	3.35980i	−1.22246	+	0.137738i
$596$	−4.02091	−	5.89760i	−0.164703	−	0.241575i
$597$	14.1981	−	7.50140i	0.581091	−	0.307012i
$598$	−38.1677	+	44.3517i	−1.56079	+	1.81368i
$599$	−9.65481	−	5.10271i	−0.394485	−	0.208491i	0.258250	−	0.966078i	$-0.416854\pi$
$599$	−9.65481	−	5.10271i	−0.394485	−	0.208491i	−0.652734	+	0.757587i	$0.726378\pi$
$600$	−7.29349	−	2.86366i	−0.297756	−	0.116909i
$601$	10.1018	+	11.7386i	0.412063	+	0.478826i	0.925199	−	0.379481i	$-0.123898\pi$
$601$	10.1018	+	11.7386i	0.412063	+	0.478826i	−0.513137	+	0.858307i	$0.671517\pi$
$602$	−5.20151	−	22.7893i	−0.211998	−	0.928823i
$603$	23.4874	+	21.8054i	0.956481	+	0.887983i
$604$	0.343331	+	0.430523i	0.0139699	+	0.0175177i
$605$	11.1203	−	11.9848i	0.452104	−	0.487252i
$606$	46.8602	+	16.4045i	1.90357	+	0.666385i
$607$	−38.1143	+	16.6291i	−1.54701	+	0.674954i	−0.988035	−	0.154229i	$-0.950711\pi$
$607$	−38.1143	+	16.6291i	−1.54701	+	0.674954i	−0.558977	+	0.829183i	$0.688806\pi$
$608$	7.39798	+	12.8137i	0.300028	+	0.519663i
$609$	21.8836	−	37.2428i	0.886769	−	1.50915i
$610$	5.23413	−	9.06577i	0.211924	−	0.367062i
$611$	−1.78940	+	15.8814i	−0.0723914	+	0.642491i
$612$	5.32592	+	3.93301i	0.215287	+	0.158982i
$613$	−26.0889	−	5.95462i	−1.05372	−	0.240505i	−0.339631	−	0.940559i	$-0.610302\pi$
$613$	−26.0889	−	5.95462i	−1.05372	−	0.240505i	−0.714090	+	0.700054i	$0.753159\pi$
$614$	44.4993	−	6.70719i	1.79585	−	0.270680i
$615$	−0.369131	+	0.0276106i	−0.0148848	+	0.00111337i
$616$	9.65002	−	8.95391i	0.388810	−	0.360763i
$617$	−9.13581	+	1.72859i	−0.367794	+	0.0695904i	−0.366523	−	0.930409i	$-0.619452\pi$
$617$	−9.13581	+	1.72859i	−0.367794	+	0.0695904i	−0.00127055	+	0.999999i	$0.500404\pi$
$618$	−51.0080	+	7.68093i	−2.05184	+	0.308972i
$619$	0.554331	+	14.8148i	0.0222804	+	0.595457i	0.965058	+	0.262035i	$0.0843937\pi$
$619$	0.554331	+	14.8148i	0.0222804	+	0.595457i	−0.942778	+	0.333422i	$0.891797\pi$
$620$	−0.944141	−	2.69820i	−0.0379176	−	0.108362i
$621$	−13.7378	−	31.5234i	−0.551279	−	1.26499i
$622$	−19.5186	+	40.5307i	−0.782623	+	1.62513i
$623$	−19.9711	+	45.7744i	−0.800127	+	1.83391i
$624$	−45.1774	−	8.55457i	−1.80854	−	0.342457i
$625$	−0.825981	−	11.0219i	−0.0330392	−	0.440878i
$626$	13.2597	−	49.4859i	0.529964	−	1.97785i
$627$	4.63160	−	8.76044i	0.184968	−	0.349858i
$628$	−10.6207	+	0.397398i	−0.423812	+	0.0158579i
$629$	−5.25201	−	10.9059i	−0.209411	−	0.434847i
$630$	−4.32999	−	38.5265i	−0.172511	−	1.53493i
$631$	5.69271	−	1.29932i	0.226623	−	0.0517253i	−0.107701	−	0.994183i	$-0.534349\pi$
$631$	5.69271	−	1.29932i	0.226623	−	0.0517253i	0.334325	+	0.942458i	$0.391492\pi$
$632$	−19.7009	+	7.73203i	−0.783660	+	0.307564i
$633$	−6.91386	+	8.66721i	−0.274801	+	0.344491i
$634$	16.2982	−	5.02731i	0.647282	−	0.199660i
$635$	0.543331	−	14.5208i	0.0215614	−	0.576241i
$636$	−0.795775	−	7.07158i	−0.0315545	−	0.280407i
$637$	−68.7343	−	39.6838i	−2.72335	−	1.57233i
$638$	2.09912	−	10.6555i	0.0831048	−	0.421856i
$639$	8.21047	−	12.0353i	0.324801	−	0.476110i
$640$	−23.5026	−	2.64811i	−0.929023	−	0.104676i
$641$	4.85379	+	9.18381i	0.191713	+	0.362739i	0.961169	−	0.275961i	$-0.0889962\pi$
$641$	4.85379	+	9.18381i	0.191713	+	0.362739i	−0.769456	+	0.638700i	$0.779472\pi$
$642$	37.0330	−	21.3741i	1.46158	−	0.843568i
$643$	16.4220	+	6.44517i	0.647622	+	0.254173i	0.666335	−	0.745652i	$-0.267862\pi$
$643$	16.4220	+	6.44517i	0.647622	+	0.254173i	−0.0187138	+	0.999825i	$0.505957\pi$
$644$	17.8954	+	2.69730i	0.705179	+	0.106289i
$645$	9.39086	+	0.705068i	0.369765	+	0.0277620i
$646$	20.8182	−	17.9155i	0.819083	−	0.704878i
$647$	41.7098	−	20.0864i	1.63978	−	0.789677i	0.640007	−	0.768369i	$-0.278931\pi$
$647$	41.7098	−	20.0864i	1.63978	−	0.789677i	0.999773	−	0.0213078i	$-0.00678301\pi$
$648$	12.1334	−	16.4209i	0.476645	−	0.645075i
$649$	−9.38168	+	3.28279i	−0.368263	+	0.128861i
$650$	4.56347	+	17.0311i	0.178994	+	0.668015i
$651$	15.2363	−	16.4162i	0.597157	−	0.643402i
$652$	3.66051	−	2.70158i	0.143357	−	0.105802i
$653$	9.89999	−	7.30652i	0.387417	−	0.285926i	−0.382646	−	0.923895i	$-0.624987\pi$
$653$	9.89999	−	7.30652i	0.387417	−	0.285926i	0.770062	+	0.637969i	$0.220225\pi$
$654$	12.2150	+	39.6198i	0.477645	+	1.54926i
$655$	−0.219682	−	0.819866i	−0.00858370	−	0.0320348i
$656$	0.562237	−	0.196735i	0.0219517	−	0.00768122i
$657$	0.0405663	−	1.07610i	0.00158264	−	0.0419828i
$658$	19.5371	−	9.40859i	0.761637	−	0.366785i
$659$	−27.6657	+	23.8082i	−1.07770	+	0.927438i	−0.997592	−	0.0693485i	$-0.977908\pi$
$659$	−27.6657	+	23.8082i	−1.07770	+	0.927438i	−0.0801095	+	0.996786i	$0.525527\pi$
$660$	−0.963756	−	2.00198i	−0.0375142	−	0.0779268i
$661$	5.24367	+	0.790355i	0.203955	+	0.0307413i	0.250225	−	0.968188i	$-0.419495\pi$
$661$	5.24367	+	0.790355i	0.203955	+	0.0307413i	−0.0462701	+	0.998929i	$0.514733\pi$
$662$	10.1886	+	3.99872i	0.395990	+	0.155415i
$663$	−0.00497253	+	35.5612i	−0.000193117	+	1.38108i
$664$	14.6020	+	27.6284i	0.566668	+	1.07219i
$665$	−36.4310	−	4.10479i	−1.41273	−	0.159177i
$666$	14.0920	−	6.78150i	0.546054	−	0.262778i
$667$	−31.6319	+	16.4153i	−1.22479	+	0.635604i
$668$	−2.73185	−	1.57723i	−0.105698	−	0.0610250i
$669$	32.8580	−	24.2432i	1.27036	−	0.937297i
$670$	1.11465	−	29.7897i	0.0430627	−	1.15088i
$671$	4.49170	−	1.38551i	0.173400	−	0.0534869i
$672$	9.49285	+	24.1973i	0.366195	+	0.933432i
$673$	−2.54027	+	0.996982i	−0.0979201	+	0.0384308i	−0.413795	−	0.910370i	$-0.635797\pi$
$673$	−2.54027	+	0.996982i	−0.0979201	+	0.0384308i	0.315875	+	0.948801i	$0.397702\pi$
$674$	−18.1898	+	4.15171i	−0.700647	+	0.159918i
$675$	−10.1803	−	1.93064i	−0.391841	−	0.0743105i
$676$	4.40153	+	9.13986i	0.169289	+	0.351533i
$677$	44.3786	−	1.66053i	1.70561	−	0.0638194i	0.833315	−	0.552799i	$-0.186440\pi$
$677$	44.3786	−	1.66053i	1.70561	−	0.0638194i	0.872295	+	0.488980i	$0.162631\pi$
$678$	8.60560	−	0.320794i	0.330496	−	0.0123200i
$679$	15.1129	−	56.4023i	0.579981	−	2.16452i
$680$	1.09849	+	14.6584i	0.0421253	+	0.562124i
$681$	−1.73408	+	2.01447i	−0.0664503	+	0.0771948i
$682$	2.25181	−	5.16121i	0.0862264	−	0.197633i
$683$	3.00361	−	6.23707i	0.114930	−	0.238655i	−0.835567	−	0.549389i	$-0.814861\pi$
$683$	3.00361	−	6.23707i	0.114930	−	0.238655i	0.950497	+	0.310734i	$0.100575\pi$
$684$	5.27449	+	6.13253i	0.201675	+	0.234483i
$685$	1.39923	+	3.99877i	0.0534619	+	0.152785i
$686$	2.07563	+	55.4724i	0.0792479	+	2.11795i
$687$	2.14861	+	2.69504i	0.0819745	+	0.102822i
$688$	−14.8901	+	2.81735i	−0.567679	+	0.107411i
$689$	28.0192	−	25.9980i	1.06745	−	0.990444i
$690$	−13.8819	+	28.8157i	−0.528474	+	1.09699i
$691$	−3.57541	+	0.538906i	−0.136015	+	0.0205010i	−0.216697	−	0.976239i	$-0.569528\pi$
$691$	−3.57541	+	0.538906i	−0.136015	+	0.0205010i	0.0806819	+	0.996740i	$0.474290\pi$
$692$	0.345472	+	0.0788518i	0.0131329	+	0.00299750i
$693$	10.3414	−	14.0039i	0.392836	−	0.531963i
$694$	0.706064	−	6.26650i	0.0268018	−	0.237873i
$695$	−6.20488	+	10.7472i	−0.235365	+	0.407663i
$696$	−17.8301	−	11.3945i	−0.675847	−	0.431907i
$697$	−0.230344	−	0.398968i	−0.00872490	−	0.0151120i
$698$	−45.5548	+	19.8754i	−1.72427	+	0.752293i
$699$	−3.78329	+	3.25487i	−0.143097	+	0.123110i
$700$	3.70921	−	3.99758i	0.140195	−	0.151094i
$701$	−11.3620	−	14.2474i	−0.429135	−	0.538118i	0.519509	−	0.854465i	$-0.326115\pi$
$701$	−11.3620	−	14.2474i	−0.429135	−	0.538118i	−0.948644	+	0.316347i	$0.897544\pi$
$702$	−45.9440	−	0.0192731i	−1.73405	−	0.000727416i
$703$	−3.29079	−	14.4179i	−0.124114	−	0.543781i
$704$	−3.63632	−	4.22548i	−0.137049	−	0.159254i
$705$	1.30084	+	8.63872i	0.0489926	+	0.325353i
$706$	27.5629	+	14.5674i	1.03734	+	0.548251i
$707$	53.7997	−	62.5164i	2.02335	−	2.35117i
$708$	0.304498	−	8.10754i	0.0114437	−	0.304700i
$709$	7.94510	+	11.6533i	0.298384	+	0.437649i	0.945927	−	0.324380i	$-0.105156\pi$
$709$	7.94510	+	11.6533i	0.298384	+	0.437649i	−0.647543	+	0.762029i	$0.724203\pi$
$710$	−13.4664	+	1.51730i	−0.505385	+	0.0569432i
$711$	−23.7017	+	14.8835i	−0.888882	+	0.558175i
$712$	22.0414	+	10.6146i	0.826036	+	0.397798i
$713$	−17.8485	+	4.78248i	−0.668430	+	0.179105i
$714$	40.8583	−	25.6650i	1.52908	−	0.960489i
$715$	5.57645	−	10.5512i	0.208547	−	0.394591i
$716$	−2.42543	+	3.55746i	−0.0906426	+	0.132948i
$717$	−4.46622	+	39.5891i	−0.166794	+	1.47848i
$718$	−1.09365	+	3.54552i	−0.0408146	+	0.132318i
$719$	11.0943	+	8.84745i	0.413749	+	0.329954i	0.808142	−	0.588988i	$-0.200474\pi$
$719$	11.0943	+	8.84745i	0.413749	+	0.329954i	−0.394392	+	0.918942i	$0.629045\pi$
$720$	−25.0643	+	1.87126i	−0.934090	+	0.0697377i
$721$	−19.0683	+	83.5438i	−0.710141	+	3.11133i
$722$	2.63046	−	1.39024i	0.0978956	−	0.0517393i
$723$	1.36661	+	1.85223i	0.0508246	+	0.0688851i
$724$	−2.69933	+	1.55846i	−0.100320	+	0.0579197i
$725$	−1.28244	+	10.6618i	−0.0476285	+	0.395971i
$726$	−7.75216	+	25.1194i	−0.287709	+	0.932268i
$727$	−10.9814	+	14.8793i	−0.407277	+	0.551841i	−0.959446	−	0.281891i	$-0.909038\pi$
$727$	−10.9814	+	14.8793i	−0.407277	+	0.551841i	0.552169	+	0.833732i	$0.313800\pi$
$728$	−30.7069	+	48.8697i	−1.13807	+	1.81123i
$729$	11.7353	−	24.3163i	0.434639	−	0.900605i
$730$	−0.783127	+	0.624523i	−0.0289848	+	0.0231146i
$731$	4.28193	+	10.9102i	0.158373	+	0.403527i
$732$	−0.287267	+	3.82613i	−0.0106177	+	0.141418i
$733$	4.52753	+	23.9286i	0.167228	+	0.883823i	0.961197	+	0.275864i	$0.0889638\pi$
$733$	4.52753	+	23.9286i	0.167228	+	0.883823i	−0.793969	+	0.607959i	$0.791989\pi$
$734$	−10.7593	−	7.33555i	−0.397132	−	0.270760i
$735$	−41.9046	−	11.2346i	−1.54568	−	0.414394i
$736$	3.98678	−	21.0706i	0.146955	−	0.776674i
$737$	9.46515	−	9.46515i	0.348653	−	0.348653i
$738$	0.515537	−	0.297453i	0.0189772	−	0.0109494i
$739$	−0.807158	−	7.16372i	−0.0296918	−	0.263522i	−0.999784	−	0.0207851i	$-0.993383\pi$
$739$	−0.807158	−	7.16372i	−0.0296918	−	0.263522i	0.970092	−	0.242737i	$-0.0780451\pi$
$740$	−3.03922	−	1.32600i	−0.111724	−	0.0487446i
$741$	−9.67365	+	42.3557i	−0.355370	+	1.55598i
$742$	−50.0943	−	13.4227i	−1.83902	−	0.492764i
$743$	20.0830	+	17.2828i	0.736772	+	0.634044i	0.938453	−	0.345407i	$-0.112259\pi$
$743$	20.0830	+	17.2828i	0.736772	+	0.634044i	−0.201680	+	0.979451i	$0.564640\pi$
$744$	−7.75689	−	7.75906i	−0.284381	−	0.284461i
$745$	1.56613	−	20.8985i	0.0573785	−	0.765663i
$746$	−50.1789	−	17.5583i	−1.83718	−	0.642857i
$747$	25.7566	+	32.3163i	0.942385	+	1.18239i
$748$	1.72411	−	2.16196i	0.0630396	−	0.0790491i
$749$	−10.5868	−	70.2391i	−0.386835	−	2.56648i
$750$	16.8980	+	29.2777i	0.617029	+	1.06907i
$751$	−22.4848	−	0.841322i	−0.820482	−	0.0307003i	−0.376146	−	0.926560i	$-0.622751\pi$
$751$	−22.4848	−	0.841322i	−0.820482	−	0.0307003i	−0.444336	+	0.895860i	$0.646560\pi$
$752$	−5.62173	−	12.8851i	−0.205003	−	0.469873i
$753$	−1.30498	−	0.402732i	−0.0475560	−	0.0146764i
$754$	3.20170	+	47.5075i	0.116599	+	1.73012i
$755$			1.61676i			0.0588399i
$756$	7.55509	+	12.0351i	0.274776	+	0.437711i
$757$	11.9176	+	7.48833i	0.433153	+	0.272168i	0.730910	−	0.682474i	$-0.239096\pi$
$757$	11.9176	+	7.48833i	0.433153	+	0.272168i	−0.297757	+	0.954642i	$0.596239\pi$
$758$	−10.3944	−	9.64459i	−0.377541	−	0.350307i
$759$	−13.3701	+	5.24524i	−0.485305	+	0.190390i
$760$	−2.67663	+	17.7583i	−0.0970917	+	0.644161i
$761$	−26.6803	−	28.7545i	−0.967161	−	1.04235i	−0.999081	−	0.0428608i	$-0.986353\pi$
$761$	−26.6803	−	28.7545i	−0.967161	−	1.04235i	0.0319205	−	0.999490i	$-0.489838\pi$
$762$	9.34040	+	21.4166i	0.338367	+	0.775841i
$763$	68.6828	+	5.14706i	2.48648	+	0.186336i
$764$	−2.79728	−	4.45185i	−0.101202	−	0.161062i
$765$	5.02586	+	18.7778i	0.181710	+	0.678912i
$766$	−9.26254	−	9.26254i	−0.334669	−	0.334669i
$767$	36.0058	−	24.5483i	1.30009	−	0.886388i
$768$	21.3494	−	7.46712i	0.770380	−	0.269447i
$769$	16.0250	+	21.7131i	0.577877	+	0.782995i	0.991866	−	0.127287i	$-0.0406268\pi$
$769$	16.0250	+	21.7131i	0.577877	+	0.782995i	−0.413989	+	0.910282i	$0.635865\pi$
$770$	−16.1473	+	1.21007i	−0.581907	+	0.0436079i
$771$	−5.56557	+	8.85480i	−0.200439	+	0.318898i
$772$	−13.7681	−	2.60506i	−0.495523	−	0.0937580i
$773$	−42.8905	+	26.9499i	−1.54266	+	0.969319i	−0.551870	+	0.833930i	$0.686086\pi$
$773$	−42.8905	+	26.9499i	−1.54266	+	0.969319i	−0.990793	+	0.135389i	$0.956772\pi$
$774$	−14.0972	+	5.52818i	−0.506712	+	0.198706i
$775$	−1.83899	+	5.25554i	−0.0660586	+	0.188785i
$776$	−27.3329	−	8.43108i	−0.981194	−	0.302658i
$777$	−1.93786	−	25.9076i	−0.0695205	−	0.929430i
$778$	7.37797	−	18.7988i	0.264513	−	0.673968i
$779$	−0.165900	−	0.537833i	−0.00594397	−	0.0192699i
$780$	6.35320	+	7.38464i	0.227481	+	0.264413i
$781$	−4.89602	−	3.61342i	−0.175193	−	0.129298i
$782$	−39.8073			−1.42351
$783$	−25.9660	−	10.4292i	−0.927948	−	0.372709i
$784$	69.8141			2.49336
$785$	−25.1072	−	18.5299i	−0.896114	−	0.661362i
$786$	0.890091	+	1.03460i	0.0317485	+	0.0369029i
$787$	1.63134	+	5.28869i	0.0581511	+	0.188521i	0.979988	−	0.199057i	$-0.0637879\pi$
$787$	1.63134	+	5.28869i	0.0581511	+	0.188521i	−0.921837	+	0.387578i	$0.873312\pi$
$788$	−1.90833	+	4.86234i	−0.0679814	+	0.173214i
$789$	−1.29230	−	17.2769i	−0.0460070	−	0.615075i
$790$	24.8760	+	7.67324i	0.885049	+	0.273001i
$791$	4.72496	−	13.5031i	0.168000	−	0.480117i
$792$	−6.66567	−	5.31875i	−0.236854	−	0.188993i
$793$	−17.4499	+	10.9645i	−0.619665	+	0.389361i
$794$	−22.0471	−	4.17153i	−0.782421	−	0.148042i
$795$	11.1185	−	17.6895i	0.394332	−	0.627382i
$796$	5.45930	−	0.409118i	0.193500	−	0.0145008i
$797$	−2.14325	−	2.90400i	−0.0759177	−	0.102865i	0.764993	−	0.644038i	$-0.222742\pi$
$797$	−2.14325	−	2.90400i	−0.0759177	−	0.102865i	−0.840911	+	0.541173i	$0.817980\pi$
$798$	55.6438	−	19.4619i	1.96977	−	0.688943i
$799$	−8.98336	+	6.12475i	−0.317808	+	0.216678i
$800$	−4.56922	−	4.56922i	−0.161546	−	0.161546i
$801$	31.2468	+	8.38193i	1.10405	+	0.296161i
$802$	−8.98986	−	14.3073i	−0.317443	−	0.505208i
$803$	−0.448514	−	0.0336115i	−0.0158277	−	0.00118612i
$804$	4.36797	+	10.0153i	0.154046	+	0.353212i
$805$	36.1411	+	38.9509i	1.27381	+	1.37284i
$806$	−3.67963	+	24.4127i	−0.129609	+	0.859901i
$807$	−1.69867	+	0.666405i	−0.0597961	+	0.0234586i
$808$	−29.6173	−	27.4808i	−1.04193	−	0.966771i
$809$	−36.1315	−	22.7029i	−1.27032	−	0.798192i	−0.283333	−	0.959022i	$-0.591440\pi$
$809$	−36.1315	−	22.7029i	−1.27032	−	0.798192i	−0.986982	+	0.160830i	$0.948583\pi$
$810$	−24.2621	+	6.48648i	−0.852485	+	0.227912i
$811$			30.8812i			1.08439i	0.840254	+	0.542193i	$0.182406\pi$
$811$			30.8812i			1.08439i	−0.840254	+	0.542193i	$0.817594\pi$
$812$	11.9145	−	8.65587i	0.418117	−	0.303762i
$813$	37.3541	+	11.5279i	1.31006	+	0.404302i
$814$	−2.61202	−	5.98682i	−0.0915513	−	0.209838i
$815$	13.3482	+	0.499453i	0.467566	+	0.0174951i
$816$	−15.6366	−	27.0921i	−0.547389	−	0.948412i
$817$	2.13416	+	14.1592i	0.0746649	+	0.495369i
$818$	33.7198	−	42.2832i	1.17898	−	1.47840i
$819$	−27.9043	+	71.0405i	−0.975054	+	2.48236i
$820$	−0.119117	−	0.0416808i	−0.00415974	−	0.00145556i
$821$	−2.25674	+	30.1141i	−0.0787609	+	1.05099i	0.808128	+	0.589007i	$0.200481\pi$
$821$	−2.25674	+	30.1141i	−0.0787609	+	1.05099i	−0.886889	+	0.461983i	$0.847138\pi$
$822$	−4.81615	−	4.81750i	−0.167983	−	0.168030i
$823$	−39.7908	−	34.2428i	−1.38702	−	1.19363i	−0.956744	−	0.290930i	$-0.906035\pi$
$823$	−39.7908	−	34.2428i	−1.38702	−	1.19363i	−0.430276	−	0.902697i	$-0.641584\pi$
$824$	40.5466	+	10.8644i	1.41251	+	0.378480i
$825$	−0.963608	+	4.21912i	−0.0335485	+	0.146891i
$826$	−54.1941	−	23.6447i	−1.88566	−	0.822703i
$827$	−2.41532	−	21.4366i	−0.0839889	−	0.745422i	−0.963162	−	0.268920i	$-0.913333\pi$
$827$	−2.41532	−	21.4366i	−0.0839889	−	0.745422i	0.879174	−	0.476502i	$-0.158095\pi$
$828$	0.00327858	−	11.7234i	0.000113938	−	0.407417i
$829$	−26.2709	+	26.2709i	−0.912424	+	0.912424i	−0.996463	−	0.0840381i	$-0.973218\pi$
$829$	−26.2709	+	26.2709i	−0.912424	+	0.912424i	0.0840381	+	0.996463i	$0.473218\pi$
$830$	7.14619	−	37.7685i	0.248048	−	1.31096i
$831$	−14.7614	−	3.95752i	−0.512067	−	0.137285i
$832$	20.1945	+	13.7684i	0.700119	+	0.477333i
$833$	−10.0382	−	53.0531i	−0.347803	−	1.83818i
$834$	1.49395	−	19.8980i	0.0517312	−	0.689013i
$835$	−3.38366	−	8.62143i	−0.117096	−	0.298357i
$836$	2.64134	−	2.10640i	0.0913528	−	0.0728514i
$837$	−11.9842	−	8.17808i	−0.414236	−	0.282676i
$838$	−15.5889	+	24.8096i	−0.538510	+	0.857034i
$839$	20.0483	−	27.1645i	0.692145	−	0.937823i	−0.307762	−	0.951463i	$-0.599580\pi$
$839$	20.0483	−	27.1645i	0.692145	−	0.937823i	0.999907	+	0.0136400i	$0.00434188\pi$
$840$	−9.30352	+	30.1463i	−0.321002	+	1.04015i
$841$	−8.96304	+	27.5801i	−0.309070	+	0.951039i
$842$	−15.0392	+	8.68290i	−0.518286	+	0.299232i
$843$	−15.5902	−	21.1302i	−0.536956	−	0.727762i
$844$	−3.34185	+	1.76622i	−0.115031	+	0.0607957i
$845$	−6.62771	+	29.0379i	−0.228000	+	0.998933i
$846$	−7.90975	−	11.6084i	−0.271943	−	0.399106i
$847$	34.1438	+	27.2287i	1.17319	+	0.935591i
$848$	−9.91019	+	32.1281i	−0.340317	+	1.10328i
$849$	0.839553	−	7.44189i	0.0288134	−	0.255405i
$850$	−6.75710	+	9.91085i	−0.231767	+	0.339939i
$851$	−10.0154	+	18.9501i	−0.343323	+	0.649599i
$852$	4.20608	−	2.64203i	0.144098	−	0.0905146i
$853$	2.83740	−	0.760278i	0.0971506	−	0.0260314i	−0.209916	−	0.977719i	$-0.567319\pi$
$853$	2.83740	−	0.760278i	0.0971506	−	0.0260314i	0.307067	+	0.951688i	$0.400652\pi$
$854$	25.1933	+	12.1325i	0.862097	+	0.415164i
$855$	0.881365	+	23.7326i	0.0301421	+	0.811638i
$856$	−34.5770	+	3.89589i	−1.18182	+	0.133159i
$857$	19.8927	+	29.1773i	0.679523	+	0.996677i	0.998798	+	0.0490152i	$0.0156083\pi$
$857$	19.8927	+	29.1773i	0.679523	+	0.996677i	−0.319275	+	0.947662i	$0.603439\pi$
$858$	−0.720191	+	19.1758i	−0.0245869	+	0.654649i
$859$	−18.8514	+	21.9058i	−0.643203	+	0.747415i	−0.981043	−	0.193788i	$-0.937922\pi$
$859$	−18.8514	+	21.9058i	−0.643203	+	0.747415i	0.337841	+	0.941203i	$0.390303\pi$
$860$	2.83856	+	1.50022i	0.0967940	+	0.0511571i
$861$	−0.147231	−	0.977743i	−0.00501763	−	0.0333214i
$862$	36.5715	+	42.4969i	1.24563	+	1.44745i
$863$	0.825309	+	3.61592i	0.0280939	+	0.123087i	0.987030	−	0.160534i	$-0.0513215\pi$
$863$	0.825309	+	3.61592i	0.0280939	+	0.123087i	−0.958937	+	0.283621i	$0.908464\pi$
$864$	14.5856	−	8.41282i	0.496211	−	0.286210i
$865$	0.648683	+	0.813423i	0.0220559	+	0.0276572i
$866$	−36.4749	+	39.3105i	−1.23947	+	1.33583i
$867$	3.98155	−	3.42543i	0.135221	−	0.116334i
$868$	6.99873	−	3.05351i	0.237552	−	0.103643i
$869$	5.84467	+	10.1233i	0.198267	+	0.343408i
$870$	8.40830	+	24.6322i	0.285068	+	0.835111i
$871$	−29.3438	+	50.8250i	−0.994278	+	1.72214i
$872$	3.77758	−	33.5269i	0.127925	−	1.13536i
$873$	−37.5867	−	4.24565i	−1.27212	−	0.143693i
$874$	−47.4147	−	10.8221i	−1.60382	−	0.366063i
$875$	55.5300	−	8.36980i	1.87726	−	0.282951i
$876$	0.159340	−	0.330754i	0.00538359	−	0.0111751i
$877$	8.76050	−	8.12855i	0.295821	−	0.274482i	−0.518273	−	0.855215i	$-0.673425\pi$
$877$	8.76050	−	8.12855i	0.295821	−	0.274482i	0.814094	+	0.580734i	$0.197234\pi$
$878$	−28.0629	+	5.30978i	−0.947076	+	0.179196i
$879$	−3.31220	−	4.15456i	−0.111718	−	0.140130i
$880$	0.392519	+	10.4903i	0.0132318	+	0.353628i
$881$	14.9173	+	42.6312i	0.502577	+	1.43628i	0.863815	+	0.503809i	$0.168069\pi$
$881$	14.9173	+	42.6312i	0.502577	+	1.43628i	−0.361238	+	0.932474i	$0.617646\pi$
$882$	68.5467	−	12.9499i	2.30809	−	0.436045i
$883$	18.7768	−	38.9905i	0.631891	−	1.31213i	−0.301566	−	0.953445i	$-0.597509\pi$
$883$	18.7768	−	38.9905i	0.631891	−	1.31213i	0.933457	−	0.358690i	$-0.116776\pi$
$884$	−4.84821	+	11.1122i	−0.163063	+	0.373745i
$885$	15.5406	−	18.0534i	0.522391	−	0.606857i
$886$	−1.32004	−	17.6147i	−0.0443476	−	0.591778i
$887$	−3.36760	+	12.5681i	−0.113073	+	0.421994i	−0.999136	−	0.0415717i	$-0.986764\pi$
$887$	−3.36760	+	12.5681i	−0.113073	+	0.421994i	0.886063	+	0.463566i	$0.153430\pi$
$888$	−12.7176	+	0.474079i	−0.426776	+	0.0159091i
$889$	38.7875	−	1.45133i	1.30089	−	0.0486760i
$890$	−13.0564	−	27.1120i	−0.437653	−	0.908795i
$891$	−9.96721	−	5.27496i	−0.333914	−	0.176718i
$892$	13.5723	−	3.09778i	0.454433	−	0.103721i
$893$	−12.3652	+	4.85298i	−0.413785	+	0.162399i
$894$	12.3067	+	31.3699i	0.411599	+	1.04917i
$895$	−12.0798	+	3.72613i	−0.403783	+	0.124551i
$896$	2.36225	−	63.1326i	0.0789174	−	2.10911i
$897$	50.6698	−	37.3851i	1.69182	−	1.24825i
$898$	27.7992	+	16.0499i	0.927671	+	0.535591i
$899$	−7.61579	+	12.9652i	−0.254001	+	0.432412i
$900$	−2.91823	−	1.99081i	−0.0972743	−	0.0663603i
$901$	25.8397	+	2.91143i	0.860844	+	0.0969939i
$902$	−0.116160	−	0.219785i	−0.00386769	−	0.00731804i
$903$	−0.00351745	+	25.1552i	−0.000117054	+	0.837112i
$904$	−6.52344	−	2.56026i	−0.216966	−	0.0851530i
$905$	−9.04919	−	1.36395i	−0.300805	−	0.0453391i
$906$	−1.12761	−	2.34235i	−0.0374624	−	0.0778194i
$907$	5.71996	−	4.92243i	0.189928	−	0.163446i	−0.552184	−	0.833723i	$-0.686205\pi$
$907$	5.71996	−	4.92243i	0.189928	−	0.163446i	0.742112	+	0.670276i	$0.233824\pi$
$908$	−0.816457	+	0.393185i	−0.0270951	+	0.0130483i
$909$	−45.2315	−	28.4385i	−1.50023	−	0.943245i
$910$	67.0097	−	23.4477i	2.22135	−	0.777284i
$911$	7.91760	+	29.5489i	0.262322	+	0.978998i	0.963869	+	0.266376i	$0.0858261\pi$
$911$	7.91760	+	29.5489i	0.262322	+	0.978998i	−0.701548	+	0.712623i	$0.747507\pi$
$912$	−11.2595	−	36.5205i	−0.372838	−	1.20931i
$913$	13.8874	−	10.2493i	0.459605	−	0.339204i
$914$	5.53880	−	4.08782i	0.183207	−	0.135213i
$915$	−7.66350	+	8.25698i	−0.253348	+	0.272967i
$916$	0.304132	+	1.13504i	0.0100488	+	0.0375027i
$917$	2.14002	−	0.748827i	0.0706698	−	0.0247284i
$918$	−20.3780	−	23.6998i	−0.672575	−	0.782210i
$919$	−15.1351	+	7.28869i	−0.499262	+	0.240432i	−0.666528	−	0.745480i	$-0.732220\pi$
$919$	−15.1351	+	7.28869i	−0.499262	+	0.240432i	0.167266	+	0.985912i	$0.446506\pi$
$920$	19.7290	−	16.9782i	0.650445	−	0.559753i
$921$	−48.2925	−	3.62581i	−1.59129	−	0.119474i
$922$	−6.06235	−	0.913752i	−0.199653	−	0.0300928i
$923$	24.8347	+	9.74691i	0.817444	+	0.320823i
$924$	5.14028	−	2.96678i	0.169103	−	0.0976001i
$925$	3.01794	+	5.71021i	0.0992291	+	0.187751i
$926$	22.4994	+	2.53507i	0.739375	+	0.0833076i
$927$	55.3542	+	4.16379i	1.81807	+	0.136757i
$928$	−9.72161	−	14.4916i	−0.319128	−	0.475709i
$929$	−13.1545	−	7.59477i	−0.431586	−	0.249176i	0.268436	−	0.963298i	$-0.413493\pi$
$929$	−13.1545	−	7.59477i	−0.431586	−	0.249176i	−0.700022	+	0.714121i	$0.746827\pi$
$930$	1.50913	+	13.4107i	0.0494863	+	0.439756i
$931$	2.46658	−	65.9208i	0.0808389	−	2.16047i
$932$	−1.62589	+	0.501521i	−0.0532578	+	0.0164279i
$933$	30.1890	−	37.8449i	0.988343	−	1.23899i
$934$	−13.6318	+	5.35009i	−0.446046	+	0.175060i
$935$	7.91534	−	1.80663i	0.258859	−	0.0590830i
$936$	34.2642	+	14.9607i	1.11996	+	0.489007i
$937$	−1.25139	−	2.59855i	−0.0408813	−	0.0848909i	0.879528	−	0.475847i	$-0.157859\pi$
$937$	−1.25139	−	2.59855i	−0.0408813	−	0.0848909i	−0.920409	+	0.390957i	$0.872144\pi$
$938$	79.5732	−	2.97742i	2.59816	−	0.0972162i
$939$	−25.7684	+	48.7397i	−0.840920	+	1.59056i
$940$	−0.770863	+	2.87690i	−0.0251428	+	0.0938341i
$941$	−3.90794	−	52.1478i	−0.127395	−	1.69997i	−0.585178	−	0.810905i	$-0.698975\pi$
$941$	−3.90794	−	52.1478i	−0.127395	−	1.69997i	0.457783	−	0.889064i	$-0.348644\pi$
$942$	49.2988	+	9.33499i	1.60624	+	0.304150i
$943$	−0.326211	+	0.747684i	−0.0106229	+	0.0243479i
$944$	−16.6318	+	34.5363i	−0.541320	+	1.12406i
$945$	−4.68866	+	41.4567i	−0.152522	+	1.34859i
$946$	2.08883	+	5.96954i	0.0679138	+	0.194087i
$947$	−1.11474	−	29.7920i	−0.0362242	−	0.968111i	−0.892350	−	0.451344i	$-0.850945\pi$
$947$	−1.11474	−	29.7920i	−0.0362242	−	0.968111i	0.856126	−	0.516767i	$-0.172865\pi$
$948$	−9.43527	+	1.42079i	−0.306443	+	0.0461451i
$949$	1.93757	−	0.366609i	0.0628963	−	0.0119006i
$950$	−10.7428	+	9.96785i	−0.348542	+	0.323400i
$951$	−18.3034	+	1.36908i	−0.593528	+	0.0443953i
$952$	−38.8263	+	5.85212i	−1.25837	+	0.189668i
$953$	−22.9765	−	5.24423i	−0.744281	−	0.169877i	−0.166469	−	0.986047i	$-0.553236\pi$
$953$	−22.9765	−	5.24423i	−0.744281	−	0.169877i	−0.577813	+	0.816169i	$0.696094\pi$
$954$	−3.77082	+	33.3830i	−0.122085	+	1.08082i
$955$	1.72839	−	15.3399i	0.0559293	−	0.496386i
$956$	−6.79132	+	11.7629i	−0.219647	+	0.380440i
$957$	−4.75540	+	10.6760i	−0.153720	+	0.345106i
$958$	16.9306	+	29.3247i	0.547003	+	0.947437i
$959$	−10.3722	+	4.52535i	−0.334937	+	0.146131i
$960$	12.6100	+	4.41442i	0.406987	+	0.142475i
$961$	15.7825	−	17.0094i	0.509112	−	0.548692i
$962$	17.8553	+	22.3899i	0.575679	+	0.721878i
$963$	−43.9737	+	13.5506i	−1.41703	+	0.436662i
$964$	0.174624	+	0.765078i	0.00562426	+	0.0246415i
$965$	−26.8356	−	31.1836i	−0.863870	−	1.00383i
$966$	−79.5274	−	31.2250i	−2.55875	−	1.00465i
$967$	19.9863	+	10.5631i	0.642717	+	0.339686i	0.756667	−	0.653801i	$-0.226827\pi$
$967$	19.9863	+	10.5631i	0.642717	+	0.339686i	−0.113950	+	0.993486i	$0.536350\pi$
$968$	13.9542	−	16.2151i	0.448506	−	0.521174i
$969$	−26.1337	+	13.8074i	−0.839535	+	0.443557i
$970$	19.8198	+	29.0703i	0.636375	+	0.933390i
$971$	36.6564	−	4.13018i	1.17636	−	0.132544i	0.497935	−	0.867215i	$-0.334092\pi$
$971$	36.6564	−	4.13018i	1.17636	−	0.132544i	0.678424	+	0.734671i	$0.262663\pi$
$972$	6.98137	−	5.99946i	0.223927	−	0.192433i
$973$	−29.8658	−	14.3826i	−0.957455	−	0.461086i
$974$	29.0005	−	7.77065i	0.929235	−	0.248988i
$975$	−0.706824	−	18.9612i	−0.0226365	−	0.607245i
$976$	8.47068	−	16.0273i	0.271140	−	0.513022i
$977$	−12.9707	+	19.0245i	−0.414969	+	0.608647i	−0.975636	−	0.219394i	$-0.929592\pi$
$977$	−12.9707	+	19.0245i	−0.414969	+	0.608647i	0.560668	+	0.828041i	$0.310544\pi$
$978$	−19.6871	+	8.58610i	−0.629523	+	0.274553i
$979$	3.98277	−	12.9118i	0.127290	−	0.412664i
$980$	−11.5641	−	9.22202i	−0.369400	−	0.294587i
$981$	−3.32177	−	44.4930i	−0.106056	−	1.42055i
$982$	13.5817	−	59.5054i	0.433410	−	1.89889i
$983$	−1.94928	+	1.03022i	−0.0621724	+	0.0328591i	−0.498066	−	0.867139i	$-0.665956\pi$
$983$	−1.94928	+	1.03022i	−0.0621724	+	0.0328591i	0.435894	+	0.899998i	$0.356432\pi$
$984$	−0.481316	+	0.0541631i	−0.0153438	+	0.00172666i
$985$	−13.2815	+	7.66809i	−0.423184	+	0.244326i
$986$	−23.0767	+	22.7327i	−0.734911	+	0.723958i
$987$	−22.7513	+	5.18948i	−0.724181	+	0.165183i
$988$	−8.79571	+	11.9178i	−0.279829	+	0.379155i
$989$	11.0415	−	17.5724i	0.351099	−	0.558771i
$990$	2.33125	+	10.2270i	0.0740919	+	0.325037i
$991$	−4.14585	+	3.30621i	−0.131697	+	0.105025i	−0.687123	−	0.726541i	$-0.741127\pi$
$991$	−4.14585	+	3.30621i	−0.131697	+	0.105025i	0.555426	+	0.831566i	$0.312555\pi$
$992$	−3.30560	−	8.42254i	−0.104953	−	0.267416i
$993$	−9.73095	−	6.63644i	−0.308802	−	0.210601i
$994$	−6.72975	−	35.5676i	−0.213455	−	1.12813i
$995$	13.2807	+	9.05463i	0.421026	+	0.287051i
$996$	3.64455	+	13.6092i	0.115482	+	0.431226i
$997$	−0.409144	+	2.16238i	−0.0129577	+	0.0684831i	−0.988449	−	0.151557i	$-0.951571\pi$
$997$	−0.409144	+	2.16238i	−0.0129577	+	0.0684831i	0.975491	+	0.220040i	$0.0706189\pi$
$998$	35.5827	−	35.5827i	1.12635	−	1.12635i
$999$	−16.4092	+	3.73805i	−0.519164	+	0.118267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.7	✓	672
3.2	odd	2		783.2.be.a.89.22		672
9.4	even	3		783.2.be.a.611.22		672
9.5	odd	6	inner	261.2.x.a.176.7	yes	672
29.15	odd	28	inner	261.2.x.a.218.7	yes	672
87.44	even	28		783.2.be.a.305.22		672
261.131	even	84	inner	261.2.x.a.131.7	yes	672
261.247	odd	84		783.2.be.a.44.22		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.7	✓	672	1.1	even	1	trivial
261.2.x.a.131.7	yes	672	261.131	even	84	inner
261.2.x.a.176.7	yes	672	9.5	odd	6	inner
261.2.x.a.218.7	yes	672	29.15	odd	28	inner
783.2.be.a.44.22		672	261.247	odd	84
783.2.be.a.89.22		672	3.2	odd	2
783.2.be.a.305.22		672	87.44	even	28
783.2.be.a.611.22		672	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.29500 - 0.955756i) q^{2} +(1.12961 + 1.31300i) q^{3} +(0.174054 + 0.564270i) q^{4} +(-0.633409 + 1.61390i) q^{5} +(-0.207940 - 2.77998i) q^{6} +(-4.42538 - 1.36505i) q^{7} +(-0.749268 + 2.14128i) q^{8} +(-0.447956 + 2.96637i) q^{9} +O(q^{10})\)	\(q+(-1.29500 - 0.955756i) q^{2} +(1.12961 + 1.31300i) q^{3} +(0.174054 + 0.564270i) q^{4} +(-0.633409 + 1.61390i) q^{5} +(-0.207940 - 2.77998i) q^{6} +(-4.42538 - 1.36505i) q^{7} +(-0.749268 + 2.14128i) q^{8} +(-0.447956 + 2.96637i) q^{9} +(2.36276 - 1.48462i) q^{10} +(1.23115 + 0.232947i) q^{11} +(-0.544275 + 0.865940i) q^{12} +(-5.47821 + 0.410535i) q^{13} +(4.42623 + 5.99733i) q^{14} +(-2.83456 + 0.991411i) q^{15} +(3.99264 - 2.72214i) q^{16} +(-2.64269 - 2.64269i) q^{17} +(3.41523 - 3.41332i) q^{18} +(-2.42927 - 3.86616i) q^{19} +(-1.02092 - 0.0765075i) q^{20} +(-3.20665 - 7.35251i) q^{21} +(-1.37171 - 1.47835i) q^{22} +(-0.986324 + 6.54383i) q^{23} +(-3.65789 + 1.43503i) q^{24} +(1.46180 + 1.35635i) q^{25} +(7.48668 + 4.70419i) q^{26} +(-4.40087 + 2.76267i) q^{27} -2.73470i q^{28} +(3.16520 + 4.35678i) q^{29} +(4.61831 + 1.42527i) q^{30} +(1.11658 + 2.55923i) q^{31} +(-3.23818 - 0.121164i) q^{32} +(1.08487 + 1.87965i) q^{33} +(0.896525 + 5.94806i) q^{34} +(5.00613 - 6.27748i) q^{35} +(-1.75180 + 0.263540i) q^{36} +(3.05710 + 1.06973i) q^{37} +(-0.549194 + 7.32848i) q^{38} +(-6.72729 - 6.72917i) q^{39} +(-2.98122 - 2.56555i) q^{40} +(0.119067 + 0.0319038i) q^{41} +(-2.87459 + 12.5863i) q^{42} +(-2.87436 - 1.25407i) q^{43} +(0.0828427 + 0.735249i) q^{44} +(-4.50368 - 2.60188i) q^{45} +(7.53160 - 7.53160i) q^{46} +(0.540852 - 2.85847i) q^{47} +(8.08431 + 2.16740i) q^{48} +(11.9370 + 8.13848i) q^{49} +(-0.596693 - 3.15360i) q^{50} +(0.484648 - 6.45507i) q^{51} +(-1.18516 - 3.01974i) q^{52} +(-5.43975 + 4.33805i) q^{53} +(8.33958 + 0.628483i) q^{54} +(-1.15578 + 1.83941i) q^{55} +(6.23875 - 8.45321i) q^{56} +(2.33215 - 7.55690i) q^{57} +(0.0650747 - 8.66720i) q^{58} +(-6.86977 + 3.96626i) q^{59} +(-1.05279 - 1.42690i) q^{60} +(3.31669 - 1.75292i) q^{61} +(1.00002 - 4.38139i) q^{62} +(6.03161 - 12.5158i) q^{63} +(-3.47845 - 2.77397i) q^{64} +(2.80738 - 9.10132i) q^{65} +(0.391582 - 3.47102i) q^{66} +(6.01793 - 8.82668i) q^{67} +(1.03122 - 1.95116i) q^{68} +(-9.70624 + 6.09694i) q^{69} +(-12.4827 + 3.34473i) q^{70} +(-4.37545 - 2.10711i) q^{71} +(-6.01619 - 3.18180i) q^{72} +(-0.356699 + 0.0401903i) q^{73} +(-2.93656 - 4.30714i) q^{74} +(-0.129629 + 3.45149i) q^{75} +(1.75873 - 2.04369i) q^{76} +(-5.13034 - 2.71147i) q^{77} +(2.28042 + 15.1439i) q^{78} +(6.08525 + 7.07119i) q^{79} +(1.86428 + 8.16795i) q^{80} +(-8.59867 - 2.65761i) q^{81} +(-0.123699 - 0.155114i) q^{82} +(9.36935 - 10.0978i) q^{83} +(3.59067 - 3.08915i) q^{84} +(5.93893 - 2.59113i) q^{85} +(2.52373 + 4.37122i) q^{86} +(-2.14502 + 9.07738i) q^{87} +(-1.42127 + 2.46171i) q^{88} +(1.20741 - 10.7160i) q^{89} +(3.34552 + 7.67386i) q^{90} +(24.8036 + 5.66125i) q^{91} +(-3.86416 + 0.582429i) q^{92} +(-2.09897 + 4.35701i) q^{93} +(-3.43241 + 3.18481i) q^{94} +(7.77831 - 1.47174i) q^{95} +(-3.49880 - 4.38862i) q^{96} +(0.471450 + 12.5998i) q^{97} +(-7.68000 - 21.9482i) q^{98} +(-1.24251 + 3.54771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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