LMFDB - Embedded newform 803.2.bk.a.268.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [803,2,Mod(3,803)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(803, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([48, 5]))

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

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

chi := DirichletCharacter("803.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 803 = 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	803.bk (of order $60$, degree $16$, 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:	$6.41198728231$
Analytic rank:	$0$
Dimension:	$1152$
Relative dimension:	$72$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			268.18
Character	$\chi$	$=$	803.268
Dual form			803.2.bk.a.3.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.153529 + 1.46073i) q^{2} +(1.53227 + 0.497863i) q^{3} +(-0.153864 - 0.0327049i) q^{4} +(-0.726055 + 0.896603i) q^{5} +(-0.962490 + 2.16179i) q^{6} +(0.389717 - 0.764864i) q^{7} +(-0.836358 + 2.57404i) q^{8} +(-0.327082 - 0.237639i) q^{9} +O(q^{10})$	\(q+(-0.153529 + 1.46073i) q^{2} +(1.53227 + 0.497863i) q^{3} +(-0.153864 - 0.0327049i) q^{4} +(-0.726055 + 0.896603i) q^{5} +(-0.962490 + 2.16179i) q^{6} +(0.389717 - 0.764864i) q^{7} +(-0.836358 + 2.57404i) q^{8} +(-0.327082 - 0.237639i) q^{9} +(-1.19822 - 1.19822i) q^{10} +(-1.45542 + 2.98023i) q^{11} +(-0.219479 - 0.126716i) q^{12} +(3.97455 + 4.90817i) q^{13} +(1.05743 + 0.686700i) q^{14} +(-1.55889 + 1.01236i) q^{15} +(-3.91898 - 1.74484i) q^{16} +(-0.302460 - 0.0479050i) q^{17} +(0.397342 - 0.441293i) q^{18} +(-1.38101 - 6.49712i) q^{19} +(0.141037 - 0.114210i) q^{20} +(0.977948 - 0.977948i) q^{21} +(-4.12986 - 2.58352i) q^{22} +(2.54900 + 1.47166i) q^{23} +(-2.56304 + 3.52773i) q^{24} +(0.762817 + 3.58877i) q^{25} +(-7.77971 + 5.05220i) q^{26} +(-3.22384 - 4.43724i) q^{27} +(-0.0849784 + 0.104940i) q^{28} +(0.185633 + 3.54209i) q^{29} +(-1.23945 - 2.43255i) q^{30} +(1.81672 + 2.24346i) q^{31} +(0.443911 - 0.768876i) q^{32} +(-3.71383 + 3.84190i) q^{33} +(0.116413 - 0.434458i) q^{34} +(0.402823 + 0.904754i) q^{35} +(0.0425543 + 0.0472613i) q^{36} +(-10.8606 - 2.30850i) q^{37} +(9.70256 - 1.01978i) q^{38} +(3.64648 + 9.49940i) q^{39} +(-1.70065 - 2.61878i) q^{40} +(2.88197 + 3.20076i) q^{41} +(1.27837 + 1.57866i) q^{42} +(7.61745 - 7.61745i) q^{43} +(0.321405 - 0.410952i) q^{44} +(0.450547 - 0.120724i) q^{45} +(-2.54105 + 3.49745i) q^{46} +(-3.92672 - 0.205791i) q^{47} +(-5.13623 - 4.62468i) q^{48} +(3.68136 + 5.06696i) q^{49} +(-5.35934 + 0.563289i) q^{50} +(-0.439599 - 0.223987i) q^{51} +(-0.451022 - 0.885180i) q^{52} +(0.967241 - 0.783256i) q^{53} +(6.97655 - 4.02792i) q^{54} +(-1.61537 - 3.46874i) q^{55} +(1.64285 + 1.64285i) q^{56} +(1.11861 - 10.6429i) q^{57} +(-5.20253 - 0.272653i) q^{58} +(8.41276 - 0.440894i) q^{59} +(0.272967 - 0.104782i) q^{60} +(-0.807560 + 0.0848779i) q^{61} +(-3.55600 + 2.30929i) q^{62} +(-0.309231 + 0.157561i) q^{63} +(-5.88617 - 4.27655i) q^{64} -7.28642 q^{65} +(-5.04179 - 6.01475i) q^{66} +(0.419495 - 0.242196i) q^{67} +(0.0449712 + 0.0172628i) q^{68} +(3.17305 + 3.52403i) q^{69} +(-1.38345 + 0.449509i) q^{70} +(1.12945 + 0.502866i) q^{71} +(0.885250 - 0.643172i) q^{72} +(6.34051 - 5.72695i) q^{73} +(5.03951 - 15.5100i) q^{74} +(-0.617880 + 5.87873i) q^{75} +1.04484i q^{76} +(1.71227 + 2.27464i) q^{77} +(-14.4359 + 3.86809i) q^{78} +(7.87661 + 0.827865i) q^{79} +(4.40983 - 2.24692i) q^{80} +(-2.35584 - 7.25053i) q^{81} +(-5.11791 + 3.71838i) q^{82} +(4.27294 + 0.676768i) q^{83} +(-0.182455 + 0.118488i) q^{84} +(0.262554 - 0.236405i) q^{85} +(9.95753 + 12.2965i) q^{86} +(-1.47904 + 5.51984i) q^{87} +(-6.45399 - 6.23885i) q^{88} +(0.930778 + 1.61215i) q^{89} +(0.107173 + 0.676661i) q^{90} +(5.30303 - 1.12719i) q^{91} +(-0.344069 - 0.309801i) q^{92} +(1.66676 + 4.34205i) q^{93} +(0.903469 - 5.70428i) q^{94} +(6.82802 + 3.47905i) q^{95} +(1.06298 - 0.957115i) q^{96} +(-5.30827 + 7.30620i) q^{97} +(-7.96665 + 4.59955i) q^{98} +(1.18426 - 0.628914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1152 q - 2 q^{2} + 134 q^{4} - 8 q^{5} - 42 q^{6} - 8 q^{7} - 64 q^{8} + 272 q^{9}+O(q^{10}) $ 1152 * q - 2 * q^2 + 134 * q^4 - 8 * q^5 - 42 * q^6 - 8 * q^7 - 64 * q^8 + 272 * q^9	\( 1152 q - 2 q^{2} + 134 q^{4} - 8 q^{5} - 42 q^{6} - 8 q^{7} - 64 q^{8} + 272 q^{9} - 32 q^{10} - 14 q^{11} - 84 q^{12} - 12 q^{13} - 12 q^{14} - 36 q^{15} + 134 q^{16} - 42 q^{17} - 28 q^{18} - 18 q^{19} - 2 q^{20} - 64 q^{21} - 28 q^{22} - 48 q^{23} + 42 q^{25} - 34 q^{26} - 92 q^{28} - 4 q^{29} + 36 q^{30} - 36 q^{31} - 148 q^{32} - 84 q^{33} + 54 q^{35} - 70 q^{36} - 18 q^{37} + 42 q^{38} + 76 q^{39} + 136 q^{40} - 38 q^{41} + 96 q^{42} - 40 q^{43} - 72 q^{44} - 68 q^{45} + 8 q^{47} - 6 q^{48} - 90 q^{50} - 78 q^{51} - 98 q^{52} + 10 q^{53} - 36 q^{54} + 4 q^{55} + 24 q^{56} - 78 q^{57} + 116 q^{58} + 76 q^{59} - 250 q^{60} + 6 q^{61} - 68 q^{62} + 12 q^{63} - 264 q^{64} - 272 q^{65} - 70 q^{66} - 48 q^{67} - 12 q^{68} + 12 q^{69} + 54 q^{71} - 16 q^{72} - 36 q^{73} - 104 q^{74} - 76 q^{75} + 2 q^{77} + 336 q^{78} - 66 q^{79} - 248 q^{80} - 268 q^{81} - 40 q^{82} - 114 q^{83} - 70 q^{84} - 180 q^{85} - 2 q^{86} - 116 q^{87} - 46 q^{88} - 64 q^{89} - 148 q^{90} - 18 q^{91} + 36 q^{92} - 112 q^{93} + 84 q^{94} + 158 q^{95} - 156 q^{96} - 72 q^{98} + 112 q^{99}+O(q^{100}) \) 1152 * q - 2 * q^2 + 134 * q^4 - 8 * q^5 - 42 * q^6 - 8 * q^7 - 64 * q^8 + 272 * q^9 - 32 * q^10 - 14 * q^11 - 84 * q^12 - 12 * q^13 - 12 * q^14 - 36 * q^15 + 134 * q^16 - 42 * q^17 - 28 * q^18 - 18 * q^19 - 2 * q^20 - 64 * q^21 - 28 * q^22 - 48 * q^23 + 42 * q^25 - 34 * q^26 - 92 * q^28 - 4 * q^29 + 36 * q^30 - 36 * q^31 - 148 * q^32 - 84 * q^33 + 54 * q^35 - 70 * q^36 - 18 * q^37 + 42 * q^38 + 76 * q^39 + 136 * q^40 - 38 * q^41 + 96 * q^42 - 40 * q^43 - 72 * q^44 - 68 * q^45 + 8 * q^47 - 6 * q^48 - 90 * q^50 - 78 * q^51 - 98 * q^52 + 10 * q^53 - 36 * q^54 + 4 * q^55 + 24 * q^56 - 78 * q^57 + 116 * q^58 + 76 * q^59 - 250 * q^60 + 6 * q^61 - 68 * q^62 + 12 * q^63 - 264 * q^64 - 272 * q^65 - 70 * q^66 - 48 * q^67 - 12 * q^68 + 12 * q^69 + 54 * q^71 - 16 * q^72 - 36 * q^73 - 104 * q^74 - 76 * q^75 + 2 * q^77 + 336 * q^78 - 66 * q^79 - 248 * q^80 - 268 * q^81 - 40 * q^82 - 114 * q^83 - 70 * q^84 - 180 * q^85 - 2 * q^86 - 116 * q^87 - 46 * q^88 - 64 * q^89 - 148 * q^90 - 18 * q^91 + 36 * q^92 - 112 * q^93 + 84 * q^94 + 158 * q^95 - 156 * q^96 - 72 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/803\mathbb{Z}\right)^\times$.

$n$	$78$	$585$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.153529	+	1.46073i	−0.108561	+	1.03289i	0.795635	+	0.605776i	$0.207137\pi$
$2$	−0.153529	+	1.46073i	−0.108561	+	1.03289i	−0.904197	+	0.427116i	$0.859530\pi$
$3$	1.53227	+	0.497863i	0.884654	+	0.287441i	0.715888	−	0.698215i	$-0.246022\pi$
$3$	1.53227	+	0.497863i	0.884654	+	0.287441i	0.168765	+	0.985656i	$0.446022\pi$
$4$	−0.153864	−	0.0327049i	−0.0769322	−	0.0163524i
$5$	−0.726055	+	0.896603i	−0.324701	+	0.400973i	−0.913191	−	0.407532i	$-0.866390\pi$
$5$	−0.726055	+	0.896603i	−0.324701	+	0.400973i	0.588489	+	0.808505i	$0.299723\pi$
$6$	−0.962490	+	2.16179i	−0.392935	+	0.882547i
$7$	0.389717	−	0.764864i	0.147299	−	0.289091i	−0.805554	−	0.592522i	$-0.798132\pi$
$7$	0.389717	−	0.764864i	0.147299	−	0.289091i	0.952853	+	0.303431i	$0.0981322\pi$
$8$	−0.836358	+	2.57404i	−0.295697	+	0.910062i
$9$	−0.327082	−	0.237639i	−0.109027	−	0.0792129i
$10$	−1.19822	−	1.19822i	−0.378912	−	0.378912i
$11$	−1.45542	+	2.98023i	−0.438825	+	0.898572i
$11$	−1.45542	+	2.98023i	−0.438825	+	0.898572i
$12$	−0.219479	−	0.126716i	−0.0633580	−	0.0365798i
$13$	3.97455	+	4.90817i	1.10234	+	1.36128i	0.926251	+	0.376907i	$0.123012\pi$
$13$	3.97455	+	4.90817i	1.10234	+	1.36128i	0.176092	+	0.984374i	$0.443654\pi$
$14$	1.05743	+	0.686700i	0.282609	+	0.183528i
$15$	−1.55889	+	1.01236i	−0.402505	+	0.261390i
$16$	−3.91898	−	1.74484i	−0.979745	−	0.436211i
$17$	−0.302460	−	0.0479050i	−0.0733574	−	0.0116187i	0.119648	−	0.992816i	$-0.461823\pi$
$17$	−0.302460	−	0.0479050i	−0.0733574	−	0.0116187i	−0.193005	+	0.981198i	$0.561823\pi$
$18$	0.397342	−	0.441293i	0.0936545	−	0.104014i
$19$	−1.38101	−	6.49712i	−0.316824	−	1.49054i	−0.791929	−	0.610613i	$-0.790923\pi$
$19$	−1.38101	−	6.49712i	−0.316824	−	1.49054i	0.475105	−	0.879929i	$-0.342410\pi$
$20$	0.141037	−	0.114210i	0.0315369	−	0.0255381i
$21$	0.977948	−	0.977948i	0.213406	−	0.213406i
$22$	−4.12986	−	2.58352i	−0.880488	−	0.550809i
$23$	2.54900	+	1.47166i	0.531502	+	0.306863i	0.741628	−	0.670811i	$-0.234054\pi$
$23$	2.54900	+	1.47166i	0.531502	+	0.306863i	−0.210126	+	0.977674i	$0.567387\pi$
$24$	−2.56304	+	3.52773i	−0.523179	+	0.720094i
$25$	0.762817	+	3.58877i	0.152563	+	0.717755i
$26$	−7.77971	+	5.05220i	−1.52573	+	0.990819i
$27$	−3.22384	−	4.43724i	−0.620428	−	0.853946i
$28$	−0.0849784	+	0.104940i	−0.0160594	+	0.0198317i
$29$	0.185633	+	3.54209i	0.0344712	+	0.657749i	0.960158	+	0.279458i	$0.0901548\pi$
$29$	0.185633	+	3.54209i	0.0344712	+	0.657749i	−0.925687	+	0.378291i	$0.876512\pi$
$30$	−1.23945	−	2.43255i	−0.226291	−	0.444121i
$31$	1.81672	+	2.24346i	0.326292	+	0.402937i	0.913723	−	0.406337i	$-0.133194\pi$
$31$	1.81672	+	2.24346i	0.326292	+	0.402937i	−0.587431	+	0.809274i	$0.699861\pi$
$32$	0.443911	−	0.768876i	0.0784731	−	0.135919i
$33$	−3.71383	+	3.84190i	−0.646496	+	0.668789i
$34$	0.116413	−	0.434458i	0.0199646	−	0.0745089i
$35$	0.402823	+	0.904754i	0.0680895	+	0.152931i
$36$	0.0425543	+	0.0472613i	0.00709238	+	0.00787689i
$37$	−10.8606	−	2.30850i	−1.78548	−	0.379515i	−0.807772	−	0.589496i	$-0.799327\pi$
$37$	−10.8606	−	2.30850i	−1.78548	−	0.379515i	−0.977706	+	0.209981i	$0.932660\pi$
$38$	9.70256	−	1.01978i	1.57396	−	0.165430i
$39$	3.64648	+	9.49940i	0.583904	+	1.52112i
$40$	−1.70065	−	2.61878i	−0.268897	−	0.414065i
$41$	2.88197	+	3.20076i	0.450089	+	0.499874i	0.924898	−	0.380214i	$-0.124150\pi$
$41$	2.88197	+	3.20076i	0.450089	+	0.499874i	−0.474810	+	0.880089i	$0.657483\pi$
$42$	1.27837	+	1.57866i	0.197257	+	0.243593i
$43$	7.61745	−	7.61745i	1.16165	−	1.16165i	0.177535	−	0.984114i	$-0.443188\pi$
$43$	7.61745	−	7.61745i	1.16165	−	1.16165i	0.984114	−	0.177535i	$-0.0568124\pi$
$44$	0.321405	−	0.410952i	0.0484537	−	0.0619533i
$45$	0.450547	−	0.120724i	0.0671635	−	0.0179964i
$46$	−2.54105	+	3.49745i	−0.374657	+	0.515671i
$47$	−3.92672	−	0.205791i	−0.572771	−	0.0300176i	−0.236248	−	0.971693i	$-0.575918\pi$
$47$	−3.92672	−	0.205791i	−0.572771	−	0.0300176i	−0.336523	+	0.941675i	$0.609251\pi$
$48$	−5.13623	−	4.62468i	−0.741351	−	0.667515i
$49$	3.68136	+	5.06696i	0.525909	+	0.723851i
$50$	−5.35934	+	0.563289i	−0.757925	+	0.0796612i
$51$	−0.439599	−	0.223987i	−0.0615562	−	0.0313645i
$52$	−0.451022	−	0.885180i	−0.0625454	−	0.122752i
$53$	0.967241	−	0.783256i	0.132861	−	0.107589i	−0.560587	−	0.828096i	$-0.689424\pi$
$53$	0.967241	−	0.783256i	0.132861	−	0.107589i	0.693447	+	0.720507i	$0.256091\pi$
$54$	6.97655	−	4.02792i	0.949389	−	0.548130i
$55$	−1.61537	−	3.46874i	−0.217816	−	0.467725i
$56$	1.64285	+	1.64285i	0.219535	+	0.219535i
$57$	1.11861	−	10.6429i	0.148164	−	1.40968i
$58$	−5.20253	−	0.272653i	−0.683126	−	0.0358011i
$59$	8.41276	−	0.440894i	1.09525	−	0.0573995i	0.503859	−	0.863786i	$-0.331913\pi$
$59$	8.41276	−	0.440894i	1.09525	−	0.0573995i	0.591389	+	0.806386i	$0.298580\pi$
$60$	0.272967	−	0.104782i	0.0352399	−	0.0135273i
$61$	−0.807560	+	0.0848779i	−0.103397	+	0.0108675i	−0.156086	−	0.987743i	$-0.549888\pi$
$61$	−0.807560	+	0.0848779i	−0.103397	+	0.0108675i	0.0526884	+	0.998611i	$0.483221\pi$
$62$	−3.55600	+	2.30929i	−0.451613	+	0.293281i
$63$	−0.309231	+	0.157561i	−0.0389594	+	0.0198508i
$64$	−5.88617	−	4.27655i	−0.735772	−	0.534569i
$65$	−7.28642			−0.903769
$66$	−5.04179	−	6.01475i	−0.620602	−	0.740364i
$67$	0.419495	−	0.242196i	0.0512495	−	0.0295889i	−0.474156	−	0.880441i	$-0.657247\pi$
$67$	0.419495	−	0.242196i	0.0512495	−	0.0295889i	0.525406	+	0.850852i	$0.323914\pi$
$68$	0.0449712	+	0.0172628i	0.00545355	+	0.00209342i
$69$	3.17305	+	3.52403i	0.381990	+	0.424243i
$70$	−1.38345	+	0.449509i	−0.165353	+	0.0537266i
$71$	1.12945	+	0.502866i	0.134042	+	0.0596792i	0.472661	−	0.881244i	$-0.343293\pi$
$71$	1.12945	+	0.502866i	0.134042	+	0.0596792i	−0.338620	+	0.940923i	$0.609960\pi$
$72$	0.885250	−	0.643172i	0.104328	−	0.0757985i
$73$	6.34051	−	5.72695i	0.742100	−	0.670289i
$73$	6.34051	−	5.72695i	0.742100	−	0.670289i
$74$	5.03951	−	15.5100i	0.585832	−	1.80300i
$75$	−0.617880	+	5.87873i	−0.0713466	+	0.678817i
$76$			1.04484i			0.119852i
$77$	1.71227	+	2.27464i	0.195131	+	0.259220i
$78$	−14.4359	+	3.86809i	−1.63454	+	0.437974i
$79$	7.87661	+	0.827865i	0.886188	+	0.0931421i	0.536675	−	0.843789i	$-0.319680\pi$
$79$	7.87661	+	0.827865i	0.886188	+	0.0931421i	0.349513	+	0.936931i	$0.386347\pi$
$80$	4.40983	−	2.24692i	0.493034	−	0.251213i
$81$	−2.35584	−	7.25053i	−0.261760	−	0.805615i
$82$	−5.11791	+	3.71838i	−0.565178	+	0.410626i
$83$	4.27294	+	0.676768i	0.469017	+	0.0742849i	0.386469	−	0.922302i	$-0.373694\pi$
$83$	4.27294	+	0.676768i	0.469017	+	0.0742849i	0.0825472	+	0.996587i	$0.473694\pi$
$84$	−0.182455	+	0.118488i	−0.0199075	+	0.0129281i
$85$	0.262554	−	0.236405i	0.0284780	−	0.0256417i
$86$	9.95753	+	12.2965i	1.07375	+	1.32597i
$87$	−1.47904	+	5.51984i	−0.158569	+	0.591789i
$88$	−6.45399	−	6.23885i	−0.687997	−	0.665064i
$89$	0.930778	+	1.61215i	0.0986622	+	0.170888i	0.911131	−	0.412116i	$-0.135210\pi$
$89$	0.930778	+	1.61215i	0.0986622	+	0.170888i	−0.812469	+	0.583005i	$0.801877\pi$
$90$	0.107173	+	0.676661i	0.0112970	+	0.0713264i
$91$	5.30303	−	1.12719i	0.555909	−	0.118162i
$92$	−0.344069	−	0.309801i	−0.0358717	−	0.0322990i
$93$	1.66676	+	4.34205i	0.172834	+	0.450249i
$94$	0.903469	−	5.70428i	0.0931857	−	0.588351i
$95$	6.82802	+	3.47905i	0.700540	+	0.356943i
$96$	1.06298	−	0.957115i	0.108490	−	0.0976851i
$97$	−5.30827	+	7.30620i	−0.538973	+	0.741832i	−0.988465	−	0.151452i	$-0.951605\pi$
$97$	−5.30827	+	7.30620i	−0.538973	+	0.741832i	0.449492	+	0.893284i	$0.351605\pi$
$98$	−7.96665	+	4.59955i	−0.804753	+	0.464624i
$99$	1.18426	−	0.628914i	0.119022	−	0.0632082i
$100$		−	0.577132i		−	0.0577132i
$101$	10.2732	+	3.94350i	1.02222	+	0.392393i	0.811000	−	0.585046i	$-0.198924\pi$
$101$	10.2732	+	3.94350i	1.02222	+	0.392393i	0.211218	+	0.977439i	$0.432257\pi$
$102$	0.394676	−	0.607747i	0.0390787	−	0.0601759i
$103$	−4.06786	−	2.07268i	−0.400818	−	0.204227i	0.241948	−	0.970289i	$-0.422214\pi$
$103$	−4.06786	−	2.07268i	−0.400818	−	0.204227i	−0.642767	+	0.766062i	$0.722214\pi$
$104$	−15.9580	+	6.12570i	−1.56481	+	0.600674i
$105$	0.166787	+	1.58687i	0.0162768	+	0.154863i
$106$	0.995626	+	1.53313i	0.0967038	+	0.148911i
$107$	−10.5131	−	6.82730i	−1.01634	−	0.660020i	−0.0748984	−	0.997191i	$-0.523863\pi$
$107$	−10.5131	−	6.82730i	−1.01634	−	0.660020i	−0.941443	+	0.337171i	$0.890530\pi$
$108$	0.350915	+	0.788168i	0.0337668	+	0.0758415i
$109$	9.31458	−	16.1333i	0.892175	−	1.54529i	0.0549129	−	0.998491i	$-0.482512\pi$
$109$	9.31458	−	16.1333i	0.892175	−	1.54529i	0.837262	−	0.546802i	$-0.184155\pi$
$110$	5.31490	−	1.82706i	0.506756	−	0.174203i
$111$	−15.4921	−	8.94434i	−1.47044	−	0.848959i
$112$	−2.86186	+	2.31749i	−0.270421	+	0.218982i
$113$	0.394405	−	7.52569i	0.0371025	−	0.707957i	−0.915237	−	0.402916i	$-0.867997\pi$
$113$	0.394405	−	7.52569i	0.0371025	−	0.707957i	0.952339	−	0.305041i	$-0.0986701\pi$
$114$	15.3746	+	3.26797i	1.43996	+	0.306074i
$115$	−3.17021	+	1.21693i	−0.295623	+	0.113479i
$116$	0.0872813	−	0.551072i	0.00810386	−	0.0511658i
$117$	−0.133634	−	2.54988i	−0.0123544	−	0.235736i
$118$	−0.647574	+	12.3565i	−0.0596141	+	1.13750i
$119$	−0.154515	+	0.212671i	−0.0141644	+	0.0194956i
$120$	−1.30206	−	4.85935i	−0.118861	−	0.443596i
$121$	−6.76351	−	8.67496i	−0.614864	−	0.788633i
$122$		−	1.19266i		−	0.107978i
$123$	2.82241	+	6.33924i	0.254488	+	0.571590i
$124$	−0.206156	−	0.404604i	−0.0185133	−	0.0363345i
$125$	−8.91138	−	4.54057i	−0.797058	−	0.406121i
$126$	−0.182678	−	0.475892i	−0.0162743	−	0.0423959i
$127$	0.245243	−	0.550824i	0.0217618	−	0.0488777i	−0.902338	−	0.431030i	$-0.858150\pi$
$127$	0.245243	−	0.550824i	0.0217618	−	0.0488777i	0.924099	+	0.382152i	$0.124817\pi$
$128$	8.33872	−	9.26109i	0.737046	−	0.818573i
$129$	15.4644	−	7.87950i	1.36156	−	0.693752i
$130$	1.11868	−	10.6435i	0.0981143	−	0.933496i
$131$	−0.935616	−	3.49177i	−0.0817452	−	0.305077i	0.912933	−	0.408110i	$-0.133812\pi$
$131$	−0.935616	−	3.49177i	−0.0817452	−	0.305077i	−0.994678	+	0.103033i	$0.967145\pi$
$132$	0.697076	−	0.469671i	0.0606727	−	0.0408796i
$133$	−5.50761	−	1.47576i	−0.477571	−	0.127965i
$134$	0.289378	+	0.649953i	0.0249984	+	0.0561474i
$135$	6.31912	+	0.331171i	0.543863	+	0.0285027i
$136$	0.376275	−	0.738480i	0.0322653	−	0.0633242i
$137$	1.20629	−	0.876419i	0.103060	−	0.0748775i	−0.535062	−	0.844813i	$-0.679712\pi$
$137$	1.20629	−	0.876419i	0.103060	−	0.0748775i	0.638122	+	0.769935i	$0.279712\pi$
$138$	−5.63481	+	4.09393i	−0.479667	+	0.348498i
$139$	7.69231	−	15.0970i	0.652453	−	1.28051i	−0.293423	−	0.955983i	$-0.594794\pi$
$139$	7.69231	−	15.0970i	0.652453	−	1.28051i	0.945876	−	0.324529i	$-0.105206\pi$
$140$	−0.0323902	−	0.152384i	−0.00273747	−	0.0128788i
$141$	−5.91432	−	2.27029i	−0.498075	−	0.191193i
$142$	−0.907955	+	1.57262i	−0.0761939	+	0.131972i
$143$	−20.4121	+	4.70164i	−1.70695	+	0.393171i
$144$	0.867185	+	1.50201i	0.0722654	+	0.125167i
$145$	−3.31062	−	2.40531i	−0.274932	−	0.199750i
$146$	7.39207	+	10.1410i	0.611772	+	0.839277i
$147$	3.11817	+	9.59674i	0.257182	+	0.791526i
$148$	1.59557	+	0.710392i	0.131155	+	0.0583938i
$149$	1.53739	+	2.11603i	0.125948	+	0.173352i	0.867334	−	0.497726i	$-0.165831\pi$
$149$	1.53739	+	2.11603i	0.125948	+	0.173352i	−0.741387	+	0.671078i	$0.765831\pi$
$150$	−8.49237	−	1.80511i	−0.693399	−	0.147387i
$151$	−0.308419	+	5.88498i	−0.0250988	+	0.478913i	0.956946	+	0.290266i	$0.0937436\pi$
$151$	−0.308419	+	5.88498i	−0.0250988	+	0.478913i	−0.982045	+	0.188647i	$0.939590\pi$
$152$	17.8789	+	1.87915i	1.45017	+	0.152419i
$153$	0.0875451	+	0.0875451i	0.00707760	+	0.00707760i
$154$	−3.58552	+	2.15193i	−0.288930	+	0.173408i
$155$	−3.33052			−0.267514
$156$	−0.250386	−	1.58088i	−0.0200470	−	0.126571i
$157$	12.9808	+	0.680297i	1.03598	+	0.0542936i	0.562736	−	0.826636i	$-0.309749\pi$
$157$	12.9808	+	0.680297i	1.03598	+	0.0542936i	0.473247	+	0.880930i	$0.343082\pi$
$158$	−2.41857	+	11.3785i	−0.192411	+	0.905224i
$159$	1.87202	−	0.718603i	0.148461	−	0.0569889i
$160$	0.367073	+	0.956257i	0.0290197	+	0.0755988i
$161$	2.11901	−	1.37610i	0.167001	−	0.108452i
$162$	10.9528	−	2.32808i	0.860530	−	0.182911i
$163$	−1.28302	−	8.10070i	−0.100494	−	0.634496i	−0.985598	−	0.169103i	$-0.945913\pi$
$163$	−1.28302	−	8.10070i	−0.100494	−	0.634496i	0.885104	−	0.465393i	$-0.154087\pi$
$164$	−0.338753	−	0.586737i	−0.0264522	−	0.0458165i
$165$	−0.748211	−	6.11926i	−0.0582482	−	0.476384i
$166$	−1.64460	+	6.13771i	−0.127645	+	0.476379i
$167$	13.2381	−	2.09670i	1.02439	−	0.162248i	0.378440	−	0.925626i	$-0.376461\pi$
$167$	13.2381	−	2.09670i	1.02439	−	0.162248i	0.645952	+	0.763378i	$0.276461\pi$
$168$	1.69937	+	3.33520i	0.131109	+	0.257316i
$169$	−5.59016	+	26.2996i	−0.430012	+	2.02305i
$170$	0.305014	+	0.419816i	0.0233935	+	0.0321984i
$171$	−1.09227	+	2.45327i	−0.0835277	+	0.187606i
$172$	−1.42118	+	0.922926i	−0.108364	+	0.0703725i
$173$	15.7746	+	5.12548i	1.19932	+	0.389683i	0.839511	−	0.543343i	$-0.182842\pi$
$173$	15.7746	+	5.12548i	1.19932	+	0.389683i	0.359810	+	0.933026i	$0.382842\pi$
$174$	−7.83591	−	3.00793i	−0.594039	−	0.228030i
$175$	3.04221	+	0.815156i	0.229969	+	0.0616200i
$176$	10.9038	−	9.13998i	0.821904	−	0.688952i
$177$	13.1101	+	3.51284i	0.985414	+	0.264041i
$178$	−2.49782	+	1.11210i	−0.187220	+	0.0833556i
$179$	−1.17277	+	22.3779i	−0.0876573	+	1.67260i	0.501939	+	0.864903i	$0.332620\pi$
$179$	−1.17277	+	22.3779i	−0.0876573	+	1.67260i	−0.589597	+	0.807698i	$0.700713\pi$
$180$	−0.0732714	+	0.00383999i	−0.00546132	+	0.000286216i
$181$	20.3157	−	2.13527i	1.51006	−	0.158713i	0.686994	−	0.726663i	$-0.258930\pi$
$181$	20.3157	−	2.13527i	1.51006	−	0.158713i	0.823063	+	0.567950i	$0.192263\pi$
$182$	0.832357	+	7.91935i	0.0616984	+	0.587021i
$183$	−1.27965	−	0.271999i	−0.0945947	−	0.0201067i
$184$	−5.92000	+	5.33039i	−0.436428	+	0.392962i
$185$	9.95522	−	8.06158i	0.731922	−	0.592699i
$186$	−6.59845	+	1.76805i	−0.483822	+	0.129640i
$187$	0.582974	−	0.831679i	0.0426313	−	0.0608184i
$188$	0.597452	+	0.160087i	0.0435737	+	0.0116755i
$189$	−4.65027	+	0.736530i	−0.338257	+	0.0535747i
$190$	−6.13025	+	9.43976i	−0.444735	+	0.684832i
$191$	−3.07458	−	4.73443i	−0.222469	−	0.342572i	0.709759	−	0.704445i	$-0.248804\pi$
$191$	−3.07458	−	4.73443i	−0.222469	−	0.342572i	−0.932227	+	0.361873i	$0.882137\pi$
$192$	−6.89004	−	9.48333i	−0.497246	−	0.684400i
$193$	−1.46458	−	1.18599i	−0.105423	−	0.0853697i	0.575160	−	0.818041i	$-0.304940\pi$
$193$	−1.46458	−	1.18599i	−0.105423	−	0.0853697i	−0.680583	+	0.732671i	$0.738273\pi$
$194$	−9.85741	−	8.87565i	−0.707721	−	0.637235i
$195$	−11.1647	−	3.62764i	−0.799523	−	0.259781i
$196$	−0.400716	−	0.900023i	−0.0286226	−	0.0642874i
$197$	−14.1216	+	14.1216i	−1.00613	+	1.00613i	−0.00614422	+	0.999981i	$0.501956\pi$
$197$	−14.1216	+	14.1216i	−1.00613	+	1.00613i	−0.999981	+	0.00614422i	$0.998044\pi$
$198$	0.736855	+	1.82644i	0.0523660	+	0.129799i
$199$	0.270294	−	1.00875i	0.0191607	−	0.0715086i	−0.955684	−	0.294396i	$-0.904882\pi$
$199$	0.270294	−	1.00875i	0.0191607	−	0.0715086i	0.974844	+	0.222887i	$0.0715482\pi$
$200$	−9.87565	−	1.03797i	−0.698314	−	0.0733957i
$201$	0.763359	−	0.162257i	0.0538432	−	0.0114447i
$202$	−7.33762	+	14.4009i	−0.516273	+	1.01324i
$203$	2.78156	+	1.23843i	0.195227	+	0.0869207i
$204$	0.0603132	+	0.0488407i	0.00422277	+	0.00341953i
$205$	−4.96228	+	0.260062i	−0.346581	+	0.0181635i
$206$	3.65216	−	5.62383i	0.254458	−	0.391831i
$207$	−0.484006	−	1.08709i	−0.0336407	−	0.0755583i
$208$	−7.01223	−	26.1700i	−0.486211	−	1.81456i
$209$	21.3728	+	5.34032i	1.47839	+	0.369398i
$210$	−2.34360			−0.161724
$211$	16.8355	+	12.2317i	1.15900	+	0.842064i	0.989651	−	0.143492i	$-0.0458333\pi$
$211$	16.8355	+	12.2317i	1.15900	+	0.842064i	0.169350	+	0.985556i	$0.445833\pi$
$212$	−0.174440	+	0.0888818i	−0.0119806	+	0.00610443i
$213$	1.48027	+	1.33284i	0.101426	+	0.0913245i
$214$	11.5869	−	14.3086i	0.792065	−	0.978118i
$215$	1.29914	+	12.3605i	0.0886007	+	0.842980i
$216$	14.1179	−	4.58719i	0.960603	−	0.312119i
$217$	2.42394	−	0.515225i	0.164548	−	0.0349758i
$218$	22.1364	+	16.0830i	1.49926	+	1.08928i
$219$	12.5666	−	5.61850i	0.849171	−	0.379663i
$220$	0.135103	+	0.586546i	0.00910861	+	0.0395449i
$221$	−0.967019	−	1.67493i	−0.0650488	−	0.112668i
$222$	15.4437	−	21.2565i	1.03652	−	1.42664i
$223$	2.79380	+	3.10282i	0.187086	+	0.207781i	0.829390	−	0.558670i	$-0.188688\pi$
$223$	2.79380	+	3.10282i	0.187086	+	0.207781i	−0.642304	+	0.766450i	$0.722021\pi$
$224$	−0.415085	−	0.639175i	−0.0277341	−	0.0427067i
$225$	0.603328	−	1.35510i	0.0402219	−	0.0903398i
$226$	10.9324	+	1.73153i	0.727215	+	0.115180i
$227$	−1.43480	−	4.41587i	−0.0952312	−	0.293092i	0.892083	−	0.451872i	$-0.149244\pi$
$227$	−1.43480	−	4.41587i	−0.0952312	−	0.293092i	−0.987314	+	0.158781i	$0.949244\pi$
$228$	−0.520188	+	1.60097i	−0.0344503	+	0.106027i
$229$	0.977045	+	6.16882i	0.0645649	+	0.407647i	0.998711	+	0.0507562i	$0.0161631\pi$
$229$	0.977045	+	6.16882i	0.0645649	+	0.407647i	−0.934146	+	0.356891i	$0.883837\pi$
$230$	−1.29089	−	4.81765i	−0.0851185	−	0.317666i
$231$	1.49118	+	4.33783i	0.0981126	+	0.285408i
$232$	−9.27274	−	2.48462i	−0.608785	−	0.163124i
$233$	22.1419	−	17.9302i	1.45057	−	1.17465i	0.499240	−	0.866464i	$-0.333613\pi$
$233$	22.1419	−	17.9302i	1.45057	−	1.17465i	0.951327	−	0.308182i	$-0.0997206\pi$
$234$	3.74520	+	0.196278i	0.244831	+	0.0128311i
$235$	3.03552	−	3.37129i	0.198016	−	0.219919i
$236$	−1.30884	−	0.207301i	−0.0851985	−	0.0134941i
$237$	11.6569	+	5.18998i	0.757196	+	0.337126i
$238$	−0.286933	−	0.258356i	−0.0185991	−	0.0167467i
$239$	−1.73555	−	1.12708i	−0.112263	−	0.0729047i	0.487286	−	0.873242i	$-0.337987\pi$
$239$	−1.73555	−	1.12708i	−0.112263	−	0.0729047i	−0.599550	+	0.800338i	$0.704654\pi$
$240$	7.87568	−	1.24739i	0.508373	−	0.0805184i
$241$	−5.38347	+	5.38347i	−0.346780	+	0.346780i	−0.858909	−	0.512129i	$-0.828857\pi$
$241$	−5.38347	+	5.38347i	−0.346780	+	0.346780i	0.512129	+	0.858909i	$0.328857\pi$
$242$	13.7102	−	8.54780i	0.881323	−	0.549473i
$243$			4.17155i			0.267605i
$244$	0.127031	+	0.0133515i	0.00813230	+	0.000854739i
$245$	−7.21592	−	0.378170i	−0.461008	−	0.0241604i
$246$	−9.69324	+	3.14952i	−0.618018	+	0.200806i
$247$	26.4001	−	32.6014i	1.67980	−	2.07438i
$248$	−7.29418	+	2.79997i	−0.463181	+	0.177798i
$249$	6.21035	+	3.16433i	0.393565	+	0.200531i
$250$	8.00070	−	12.3200i	0.506009	−	0.779185i
$251$	−16.7210	+	7.44468i	−1.05542	+	0.469904i	−0.859723	−	0.510760i	$-0.829364\pi$
$251$	−16.7210	+	7.44468i	−1.05542	+	0.469904i	−0.195698	+	0.980664i	$0.562697\pi$
$252$	0.0527326	−	0.0141297i	0.00332184	−	0.000890085i
$253$	−8.09575	+	5.45470i	−0.508975	+	0.342934i
$254$	0.766953	+	0.442801i	0.0481229	+	0.0277838i
$255$	0.520000	−	0.231519i	0.0325637	−	0.0144983i
$256$	2.51091	+	2.78865i	0.156932	+	0.174291i
$257$	0.152403	−	0.717000i	0.00950664	−	0.0447252i	−0.973139	−	0.230220i	$-0.926055\pi$
$257$	0.152403	−	0.717000i	0.00950664	−	0.0447252i	0.982645	+	0.185495i	$0.0593888\pi$
$258$	9.13559	+	23.7990i	0.568757	+	1.48166i
$259$	−5.99827	+	7.40724i	−0.372714	+	0.460264i
$260$	1.12112	+	0.238302i	0.0695290	+	0.0147788i
$261$	0.781020	−	1.20267i	0.0483439	−	0.0744431i
$262$	5.24417	−	0.830595i	0.323986	−	0.0513143i
$263$	−9.61219	−	2.57558i	−0.592713	−	0.158817i	−0.0500201	−	0.998748i	$-0.515929\pi$
$263$	−9.61219	−	2.57558i	−0.592713	−	0.158817i	−0.542693	+	0.839931i	$0.682595\pi$
$264$	−6.78312	−	12.7728i	−0.417472	−	0.786110i
$265$			1.43592i			0.0882077i
$266$	3.00126	−	7.81856i	0.184019	−	0.479387i
$267$	0.623566	+	2.93365i	0.0381616	+	0.179536i
$268$	−0.0724664	+	0.0235458i	−0.00442659	+	0.00143829i
$269$	−8.09709	+	0.851038i	−0.493688	+	0.0518887i	−0.348102	−	0.937457i	$-0.613174\pi$
$269$	−8.09709	+	0.851038i	−0.493688	+	0.0518887i	−0.145587	+	0.989346i	$0.546507\pi$
$270$	−1.45392	+	9.17968i	−0.0884827	+	0.558658i
$271$	−17.7340	−	9.03592i	−1.07726	−	0.548893i	−0.176987	−	0.984213i	$-0.556635\pi$
$271$	−17.7340	−	9.03592i	−1.07726	−	0.548893i	−0.900276	+	0.435320i	$0.856635\pi$
$272$	1.10175	+	0.715485i	0.0668034	+	0.0433826i
$273$	8.68684	+	0.913024i	0.525751	+	0.0552587i
$274$	1.09501	+	1.89662i	0.0661521	+	0.114579i
$275$	−11.8056	−	2.94980i	−0.711903	−	0.177880i
$276$	−0.372967	−	0.645997i	−0.0224500	−	0.0388845i
$277$	−8.26216	+	21.5237i	−0.496425	+	1.29323i	0.425182	+	0.905108i	$0.360210\pi$
$277$	−8.26216	+	21.5237i	−0.496425	+	1.29323i	−0.921607	+	0.388124i	$0.873123\pi$
$278$	20.8717	+	13.5542i	1.25180	+	0.812927i
$279$	−0.0610821	−	1.16552i	−0.00365689	−	0.0697776i
$280$	−2.66578	+	0.280185i	−0.159311	+	0.0167443i
$281$	−19.6480	−	15.9106i	−1.17210	−	0.949149i	−0.172743	−	0.984967i	$-0.555263\pi$
$281$	−19.6480	−	15.9106i	−1.17210	−	0.949149i	−0.999358	+	0.0358178i	$0.988596\pi$
$282$	4.22430	−	8.29066i	0.251554	−	0.493702i
$283$	−3.22142	+	9.91451i	−0.191494	+	0.589357i	0.808506	+	0.588488i	$0.200277\pi$
$283$	−3.22142	+	9.91451i	−0.191494	+	0.589357i	−1.00000		0.000868772i	$0.999723\pi$
$284$	−0.157337	−	0.114312i	−0.00933622	−	0.00678316i
$285$	8.73025	+	8.73025i	0.517135	+	0.517135i
$286$	−3.73397	−	30.5384i	−0.220794	−	1.80577i
$287$	3.57130	−	0.956927i	0.210807	−	0.0564856i
$288$	−0.327910	+	0.145995i	−0.0193223	+	0.00860283i
$289$	−16.0788	−	5.22431i	−0.945810	−	0.307312i
$290$	4.02178	−	4.46664i	0.236167	−	0.262290i
$291$	−11.7712	+	8.55225i	−0.690038	+	0.501342i
$292$	−1.16288	+	0.673808i	−0.0680523	+	0.0394316i
$293$	−2.29071	−	7.05008i	−0.133825	−	0.411870i	0.861581	−	0.507621i	$-0.169475\pi$
$293$	−2.29071	−	7.05008i	−0.133825	−	0.411870i	−0.995405	+	0.0957507i	$0.969475\pi$
$294$	−14.4970	+	3.08143i	−0.845480	+	0.179712i
$295$	−5.71282	+	7.86302i	−0.332613	+	0.457803i
$296$	15.0256	−	26.0250i	0.873342	−	1.51267i
$297$	17.9160	−	3.14974i	1.03959	−	0.182766i
$298$	−3.32699	+	1.92084i	−0.192727	+	0.111271i
$299$	2.90795	+	18.3601i	0.168171	+	1.06179i
$300$	0.287333	−	0.884320i	0.0165892	−	0.0510562i
$301$	−2.85766	−	8.79496i	−0.164713	−	0.506933i
$302$	−8.54901	−	1.35403i	−0.491940	−	0.0779157i
$303$	13.7779	+	11.1571i	0.791520	+	0.640960i
$304$	−5.92432	+	27.8717i	−0.339783	+	1.59855i
$305$	0.510231	−	0.785686i	0.0292157	−	0.0449883i
$306$	−0.141320	+	0.114439i	−0.00807875	+	0.00654205i
$307$	2.97289	+	11.0950i	0.169672	+	0.633223i	0.997398	+	0.0720910i	$0.0229672\pi$
$307$	2.97289	+	11.0950i	0.169672	+	0.633223i	−0.827727	+	0.561132i	$0.810366\pi$
$308$	−0.189065	−	0.405986i	−0.0107730	−	0.0231332i
$309$	−5.20113	−	5.20113i	−0.295882	−	0.295882i
$310$	0.511332	−	4.86499i	0.0290417	−	0.276313i
$311$	−5.44449	−	25.6143i	−0.308729	−	1.45246i	−0.809625	−	0.586948i	$-0.800329\pi$
$311$	−5.44449	−	25.6143i	−0.308729	−	1.45246i	0.500896	−	0.865507i	$-0.333004\pi$
$312$	−27.5016	+	1.44130i	−1.55697	+	0.0815975i
$313$	0.108292	−	0.683727i	0.00612101	−	0.0386465i	−0.984439	−	0.175728i	$-0.943772\pi$
$313$	0.108292	−	0.683727i	0.00612101	−	0.0386465i	0.990560	+	0.137081i	$0.0437721\pi$
$314$	−2.98666	+	18.8570i	−0.168547	+	1.06416i
$315$	0.0832488	−	0.391655i	0.00469054	−	0.0220673i
$316$	−1.18485	−	0.384983i	−0.0666533	−	0.0216570i
$317$	−24.4062	−	2.56520i	−1.37079	−	0.144076i	−0.609653	−	0.792668i	$-0.708691\pi$
$317$	−24.4062	−	2.56520i	−1.37079	−	0.144076i	−0.761136	+	0.648592i	$0.775358\pi$
$318$	0.762275	+	2.84485i	0.0427462	+	0.159531i
$319$	−10.8264	−	4.60199i	−0.606162	−	0.257662i
$320$	8.10805	−	2.17255i	0.453254	−	0.121449i
$321$	−12.7098	−	15.6953i	−0.709394	−	0.876028i
$322$	1.68478	+	3.30657i	0.0938893	+	0.184268i
$323$	0.106455	+	2.03128i	0.00592330	+	0.113023i
$324$	0.125352	+	1.19265i	0.00696401	+	0.0662581i
$325$	−14.5824	+	18.0078i	−0.808888	+	0.998894i
$326$	12.0299	−	0.630461i	0.666275	−	0.0349180i
$327$	22.3046	−	20.0832i	1.23345	−	1.11060i
$328$	−10.6493	+	4.74135i	−0.588007	+	0.261797i
$329$	−1.68771	+	2.92320i	−0.0930466	+	0.161161i
$330$	9.05346	−	0.153451i	0.498377	−	0.00844719i
$331$	3.33505	−	12.4466i	0.183311	−	0.684125i	−0.811675	−	0.584109i	$-0.801444\pi$
$331$	3.33505	−	12.4466i	0.183311	−	0.684125i	0.994986	−	0.100016i	$-0.0318894\pi$
$332$	−0.635321	−	0.243877i	−0.0348677	−	0.0133845i
$333$	3.00373	+	3.33597i	0.164603	+	0.182810i
$334$	1.03029	+	19.6591i	0.0563750	+	1.07570i
$335$	−0.0874231	+	0.551968i	−0.00477644	+	0.0301572i
$336$	−5.53893	+	2.12619i	−0.302173	+	0.115993i
$337$	−17.7527	−	27.3368i	−0.967051	−	1.48913i	−0.869521	−	0.493896i	$-0.835572\pi$
$337$	−17.7527	−	27.3368i	−0.967051	−	1.48913i	−0.0975306	−	0.995233i	$-0.531094\pi$
$338$	−37.5584	−	12.2035i	−2.04291	−	0.663781i
$339$	4.35110	−	11.3350i	0.236319	−	0.615632i
$340$	−0.0481294	+	0.0277875i	−0.00261018	+	0.00150699i
$341$	−9.33009	+	2.14905i	−0.505253	+	0.116378i
$342$	−3.41587	−	1.97215i	−0.184709	−	0.106642i
$343$	11.2452	−	1.78107i	0.607185	−	0.0961687i
$344$	13.2367	+	25.9786i	0.713677	+	1.40067i
$345$	−5.46346	+	0.286328i	−0.294143	+	0.0154154i
$346$	−9.90879	+	22.2555i	−0.532700	+	1.19646i
$347$	26.2862	+	11.7034i	1.41112	+	0.628270i	0.963926	−	0.266169i	$-0.0857579\pi$
$347$	26.2862	+	11.7034i	1.41112	+	0.628270i	0.447191	+	0.894439i	$0.352425\pi$
$348$	0.408097	−	0.800935i	0.0218763	−	0.0429346i
$349$	10.2096	−	2.17012i	0.546507	−	0.116164i	0.0736197	−	0.997286i	$-0.476545\pi$
$349$	10.2096	−	2.17012i	0.546507	−	0.116164i	0.472888	+	0.881123i	$0.343212\pi$
$350$	−1.65779	+	4.31869i	−0.0886126	+	0.230844i
$351$	8.96536	−	33.4592i	0.478536	−	1.78592i
$352$	1.64535	+	2.44199i	0.0876974	+	0.130159i
$353$	−12.7007	−	7.33273i	−0.675988	−	0.390282i	0.122354	−	0.992487i	$-0.460956\pi$
$353$	−12.7007	−	7.33273i	−0.675988	−	0.390282i	−0.798342	+	0.602205i	$0.794289\pi$
$354$	−7.14408	+	18.6110i	−0.379704	+	0.989162i
$355$	−1.27092	+	0.647564i	−0.0674533	+	0.0343692i
$356$	−0.0904883	−	0.278494i	−0.00479587	−	0.0147602i
$357$	−0.342639	+	0.248942i	−0.0181344	+	0.0131754i
$358$	−32.5080	−	5.14876i	−1.71810	−	0.272120i
$359$	26.4588	+	23.8236i	1.39644	+	1.25736i	0.927341	+	0.374216i	$0.122088\pi$
$359$	26.4588	+	23.8236i	1.39644	+	1.25736i	0.469100	+	0.883145i	$0.344578\pi$
$360$	−0.0660702	+	1.26070i	−0.00348221	+	0.0664445i
$361$	−22.9480	+	10.2171i	−1.20779	+	0.537743i
$362$			30.0036i			1.57696i
$363$	−6.04455	−	16.6596i	−0.317256	−	0.874405i
$364$	−0.852813			−0.0446995
$365$	0.531244	+	9.84300i	0.0278066	+	0.515206i
$366$	0.593780	−	1.82747i	0.0310374	−	0.0955233i
$367$	4.53577	−	5.03748i	0.236765	−	0.262955i	−0.613039	−	0.790052i	$-0.710053\pi$
$367$	4.53577	−	5.03748i	0.236765	−	0.262955i	0.849805	+	0.527098i	$0.176720\pi$
$368$	−7.42165	−	10.2150i	−0.386880	−	0.532495i
$369$	−0.182017	−	1.73178i	−0.00947544	−	0.0901528i
$370$	10.2474	+	15.7796i	0.532735	+	0.820341i
$371$	−0.222134	−	1.04506i	−0.0115326	−	0.0542566i
$372$	−0.114448	−	0.722598i	−0.00593386	−	0.0374649i
$373$	−26.2536			−1.35936			−0.679679	−	0.733510i	$-0.737881\pi$
$373$	−26.2536			−1.35936			−0.679679	+	0.733510i	$0.737881\pi$
$374$	1.12535	+	0.979254i	0.0581907	+	0.0506360i
$375$	−11.3940	−	11.3940i	−0.588384	−	0.588384i
$376$	3.81385	−	9.93543i	0.196685	−	0.512381i
$377$	−16.6473	+	14.9893i	−0.857382	+	0.771990i
$378$	−0.361921	−	6.90586i	−0.0186152	−	0.355199i
$379$	−11.4322	−	29.7819i	−0.587233	−	1.52979i	−0.828878	−	0.559429i	$-0.811020\pi$
$379$	−11.4322	−	29.7819i	−0.587233	−	1.52979i	0.241645	−	0.970365i	$-0.422313\pi$
$380$	−0.936808	−	0.758612i	−0.0480572	−	0.0389160i
$381$	0.650012	−	0.721911i	0.0333011	−	0.0369846i
$382$	7.38776	−	3.76425i	0.377991	−	0.192596i
$383$	0.598474	−	5.69410i	0.0305806	−	0.290955i	−0.968534	−	0.248882i	$-0.919937\pi$
$383$	0.598474	−	5.69410i	0.0305806	−	0.290955i	0.999115	−	0.0420734i	$-0.0133963\pi$
$384$	17.3879	−	10.0389i	0.887322	−	0.512296i
$385$	−3.28265	−	0.116294i	−0.167299	−	0.00592690i
$386$	1.95727	−	1.95727i	0.0996225	−	0.0996225i
$387$	−4.30173	+	0.681327i	−0.218669	+	0.0346338i
$388$	1.05570	−	0.950558i	0.0535951	−	0.0482573i
$389$	24.0722	−	7.82152i	1.22051	−	0.396567i	0.373240	−	0.927735i	$-0.378247\pi$
$389$	24.0722	−	7.82152i	1.22051	−	0.396567i	0.847267	+	0.531168i	$0.178247\pi$
$390$	7.01311	−	15.7517i	0.355123	−	0.797618i
$391$	−0.700470	−	0.567229i	−0.0354243	−	0.0286860i
$392$	−16.1215	+	5.23819i	−0.814259	+	0.264569i
$393$	0.304810	−	5.81612i	0.0153756	−	0.293385i
$394$	−18.4598	−	22.7960i	−0.929992	−	1.14844i
$395$	−6.46111	+	6.46111i	−0.325094	+	0.325094i
$396$	−0.202784	+	0.0580364i	−0.0101903	+	0.00291644i
$397$	−11.3391	+	19.6400i	−0.569095	+	0.985701i	0.427561	+	0.903987i	$0.359373\pi$
$397$	−11.3391	+	19.6400i	−0.569095	+	0.985701i	−0.996656	+	0.0817146i	$0.973960\pi$
$398$	1.43202	+	0.549700i	0.0717805	+	0.0275540i
$399$	−7.70440	−	5.00329i	−0.385702	−	0.250478i
$400$	3.27238	−	15.3953i	0.163619	−	0.769767i
$401$	1.03430	+	9.84070i	0.0516504	+	0.491421i	0.989516	+	0.144422i	$0.0461324\pi$
$401$	1.03430	+	9.84070i	0.0516504	+	0.491421i	−0.937866	+	0.346998i	$0.887201\pi$
$402$	0.119816	+	1.13997i	0.00597587	+	0.0568566i
$403$	−3.79062	+	17.8335i	−0.188824	+	0.888349i
$404$	−1.45170	−	0.942747i	−0.0722250	−	0.0469034i
$405$	8.21132	+	3.15203i	0.408024	+	0.156626i
$406$	−2.23606	+	3.87297i	−0.110974	+	0.192212i
$407$	22.6866	−	29.0073i	1.12453	−	1.43784i
$408$	0.944215	−	0.944215i	0.0467456	−	0.0467456i
$409$	−17.7830	−	21.9602i	−0.879314	−	1.08586i	−0.995698	−	0.0926576i	$-0.970464\pi$
$409$	−17.7830	−	21.9602i	−0.879314	−	1.08586i	0.116384	−	0.993204i	$-0.462870\pi$
$410$	0.381973	−	7.28847i	0.0188643	−	0.359952i
$411$	2.28469	−	0.742341i	0.112695	−	0.0366170i
$412$	0.558113	+	0.451951i	0.0274962	+	0.0222660i
$413$	2.94138	−	6.60644i	0.144736	−	0.325082i
$414$	1.66226	−	0.540101i	0.0816956	−	0.0265445i
$415$	−3.70918	+	3.33976i	−0.182077	+	0.163943i
$416$	5.53812	−	0.877152i	0.271529	−	0.0430059i
$417$	19.3029	−	19.3029i	0.945267	−	0.945267i
$418$	−11.0821	+	30.4000i	−0.542044	+	1.48691i
$419$	−25.8003	+	14.8958i	−1.26043	+	0.727708i	−0.973157	−	0.230142i	$-0.926081\pi$
$419$	−25.8003	+	14.8958i	−1.26043	+	0.727708i	−0.287270	+	0.957850i	$0.592748\pi$
$420$	0.0262359	−	0.249618i	0.00128018	−	0.0121801i
$421$	−18.4357	+	9.39346i	−0.898501	+	0.457809i	−0.841309	−	0.540554i	$-0.818215\pi$
$421$	−18.4357	+	9.39346i	−0.898501	+	0.457809i	−0.0571919	+	0.998363i	$0.518215\pi$
$422$	−20.4519	+	22.7141i	−0.995583	+	1.10571i
$423$	1.23545	+	1.00045i	0.0600698	+	0.0486436i
$424$	1.20718	+	3.14480i	0.0586257	+	0.152725i
$425$	−0.0588017	−	1.12200i	−0.00285230	−	0.0544252i
$426$	−2.17418	+	1.95764i	−0.105339	+	0.0948480i
$427$	−0.249800	+	0.650751i	−0.0120887	+	0.0314921i
$428$	1.39431	+	1.39431i	0.0673965	+	0.0673965i
$429$	−33.6175	−	2.95828i	−1.62307	−	0.142827i
$430$	−18.2548			−0.880325
$431$	1.45303	+	9.17409i	0.0699901	+	0.441900i	0.997652	+	0.0684802i	$0.0218150\pi$
$431$	1.45303	+	9.17409i	0.0699901	+	0.441900i	−0.927662	+	0.373420i	$0.878185\pi$
$432$	4.89189	+	23.0145i	0.235361	+	1.10729i
$433$	−2.56524	−	3.95012i	−0.123277	−	0.189831i	0.771644	−	0.636055i	$-0.219435\pi$
$433$	−2.56524	−	3.95012i	−0.123277	−	0.189831i	−0.894921	+	0.446225i	$0.852768\pi$
$434$	0.380459	+	3.61983i	0.0182626	+	0.173757i
$435$	−3.87524	−	5.33381i	−0.185804	−	0.255737i
$436$	−1.96082	+	2.17771i	−0.0939063	+	0.104294i
$437$	6.04140	−	18.5935i	0.288999	−	0.889448i
$438$	6.27778	+	19.2190i	0.299964	+	0.918318i
$439$	10.6901			0.510212			0.255106	−	0.966913i	$-0.417890\pi$
$439$	10.6901			0.510212			0.255106	+	0.966913i	$0.417890\pi$
$440$	10.2797	−	1.25692i	0.490066	−	0.0599211i
$441$		−	2.53214i		−	0.120578i
$442$	2.59508	−	1.15540i	0.123435	−	0.0549570i
$443$	−0.455568	+	8.69275i	−0.0216447	+	0.413005i	0.966223	+	0.257707i	$0.0829670\pi$
$443$	−0.455568	+	8.69275i	−0.0216447	+	0.413005i	−0.987868	+	0.155298i	$0.950366\pi$
$444$	2.09115	+	1.88288i	0.0992417	+	0.0893576i
$445$	−2.12126	−	0.335974i	−0.100557	−	0.0159267i
$446$	−4.96132	+	3.60461i	−0.234925	+	0.170683i
$447$	1.30219	+	4.00774i	0.0615916	+	0.189559i
$448$	−5.56493	+	2.83547i	−0.262918	+	0.133963i
$449$	−3.12763	+	8.14774i	−0.147602	+	0.384516i	−0.987370	−	0.158429i	$-0.949357\pi$
$449$	−3.12763	+	8.14774i	−0.147602	+	0.384516i	0.839769	+	0.542944i	$0.182691\pi$
$450$	1.88680	+	1.08935i	0.0889447	+	0.0513522i
$451$	−13.7335	+	3.93050i	−0.646684	+	0.185080i
$452$	−0.306812	+	1.14504i	−0.0144312	+	0.0538580i
$453$	−3.40249	+	8.86380i	−0.159863	+	0.416458i
$454$	6.67068	−	1.41790i	0.313070	−	0.0665452i
$455$	−2.83964	+	5.57312i	−0.133125	+	0.261272i
$456$	26.4596	+	11.7806i	1.23909	+	0.551677i
$457$	−7.74156	+	17.3878i	−0.362135	+	0.813368i	0.636963	+	0.770895i	$0.280191\pi$
$457$	−7.74156	+	17.3878i	−0.362135	+	0.813368i	−0.999098	+	0.0424737i	$0.986476\pi$
$458$	−9.16098	+	0.480107i	−0.428064	+	0.0224339i
$459$	0.762518	+	1.49653i	0.0355913	+	0.0698518i
$460$	0.527582	−	0.0835607i	0.0245986	−	0.00389604i
$461$	−16.2791	−	9.39877i	−0.758195	−	0.437744i	0.0704521	−	0.997515i	$-0.477556\pi$
$461$	−16.2791	−	9.39877i	−0.758195	−	0.437744i	−0.828647	+	0.559771i	$0.810889\pi$
$462$	−6.56534	+	1.51223i	−0.305447	+	0.0703554i
$463$	−12.8514	+	7.41979i	−0.597257	+	0.344827i	−0.767962	−	0.640496i	$-0.778729\pi$
$463$	−12.8514	+	7.41979i	−0.597257	+	0.344827i	0.170705	+	0.985322i	$0.445396\pi$
$464$	5.45289	−	14.2053i	0.253144	−	0.659463i
$465$	−5.10325	−	1.65815i	−0.236657	−	0.0768946i
$466$	22.7917	+	35.0962i	1.05581	+	1.62580i
$467$	−18.5699	+	7.12830i	−0.859310	+	0.329858i	−0.747815	−	0.663907i	$-0.768897\pi$
$467$	−18.5699	+	7.12830i	−0.859310	+	0.329858i	−0.111495	+	0.993765i	$0.535564\pi$
$468$	−0.0628321	+	0.396706i	−0.00290441	+	0.0183378i
$469$	−0.0217620	−	0.415245i	−0.00100488	−	0.0191742i
$470$	4.45850	+	4.95167i	0.205655	+	0.228404i
$471$	19.5514	+	7.50507i	0.900880	+	0.345816i
$472$	−5.90120	+	22.0236i	−0.271625	+	1.01372i
$473$	11.6151	+	33.7883i	0.534065	+	1.55359i
$474$	−9.37083	+	16.2308i	−0.430416	+	0.745503i
$475$	22.2632	−	9.91223i	1.02151	−	0.454804i
$476$	0.0307297	−	0.0276692i	0.00140850	−	0.00126821i
$477$	−0.502499	+	0.0263349i	−0.0230078	+	0.00120579i
$478$	1.91282	−	2.36213i	0.0874902	−	0.108041i
$479$	−2.23067	−	21.2234i	−0.101922	−	0.969723i	−0.919283	−	0.393597i	$-0.871231\pi$
$479$	−2.23067	−	21.2234i	−0.101922	−	0.969723i	0.817361	−	0.576126i	$-0.195436\pi$
$480$	0.0863676	+	1.64799i	0.00394212	+	0.0752202i
$481$	−31.8357	−	62.4811i	−1.45158	−	2.84889i
$482$	−7.03728	−	8.69031i	−0.320539	−	0.395833i
$483$	3.93200	−	1.05358i	0.178912	−	0.0479393i
$484$	0.756950	+	1.55597i	0.0344068	+	0.0707258i
$485$	−2.69667	−	10.0641i	−0.122449	−	0.456987i
$486$	−6.09351	−	0.640453i	−0.276407	−	0.0290516i
$487$	−19.4847	−	6.33097i	−0.882937	−	0.286884i	−0.167761	−	0.985828i	$-0.553654\pi$
$487$	−19.4847	−	6.33097i	−0.882937	−	0.286884i	−0.715176	+	0.698944i	$0.753654\pi$
$488$	0.456929	−	2.14968i	0.0206842	−	0.0973115i
$489$	2.06711	−	13.0512i	0.0934777	−	0.590195i
$490$	1.66026	−	10.4824i	0.0750027	−	0.473548i
$491$	−4.78185	+	0.250606i	−0.215802	+	0.0113097i	−0.159930	−	0.987128i	$-0.551127\pi$
$491$	−4.78185	+	0.250606i	−0.215802	+	0.0113097i	−0.0558713	+	0.998438i	$0.517794\pi$
$492$	−0.226945	−	1.06769i	−0.0102314	−	0.0481352i
$493$	0.113537	−	1.08023i	0.00511345	−	0.0486513i
$494$	43.5686	+	43.5686i	1.96024	+	1.96024i
$495$	−0.295951	+	1.51843i	−0.0133020	+	0.0682486i
$496$	−3.20519	−	11.9619i	−0.143917	−	0.537107i
$497$	0.824792	−	0.667903i	0.0369970	−	0.0299596i
$498$	−5.57570	+	8.58582i	−0.249853	+	0.384740i
$499$	−3.57650	+	16.8261i	−0.160106	+	0.753241i	0.822681	+	0.568503i	$0.192477\pi$
$499$	−3.57650	+	16.8261i	−0.160106	+	0.753241i	−0.982788	+	0.184738i	$0.940856\pi$
$500$	1.22264	+	0.990078i	0.0546783	+	0.0442776i
$501$	21.3281	+	3.37804i	0.952869	+	0.150920i
$502$	−8.30750	−	25.5679i	−0.370782	−	1.14115i
$503$	−2.80822	+	8.64282i	−0.125213	+	0.385365i	−0.993940	−	0.109926i	$-0.964939\pi$
$503$	−2.80822	+	8.64282i	−0.125213	+	0.385365i	0.868727	+	0.495291i	$0.164939\pi$
$504$	−0.146941	−	0.927751i	−0.00654528	−	0.0413253i
$505$	−10.9946	+	6.34776i	−0.489255	+	0.282471i
$506$	−6.72491	−	12.6632i	−0.298959	−	0.562946i
$507$	−21.6592	+	37.5149i	−0.961920	+	1.66609i
$508$	−0.0557488	+	0.0767316i	−0.00247345	+	0.00340441i
$509$	13.9214	−	2.95909i	0.617056	−	0.131159i	0.111230	−	0.993795i	$-0.464521\pi$
$509$	13.9214	−	2.95909i	0.617056	−	0.131159i	0.505826	+	0.862636i	$0.331188\pi$
$510$	0.258352	+	0.795125i	0.0114400	+	0.0352087i
$511$	−1.90933	−	7.08152i	−0.0844637	−	0.313268i
$512$	15.7050	−	11.4104i	0.694070	−	0.504272i
$513$	−24.3771	+	27.0735i	−1.07628	+	1.19533i
$514$	1.02394	+	0.332700i	0.0451642	+	0.0146748i
$515$	4.81186	−	2.14238i	0.212036	−	0.0944045i
$516$	−2.63712	+	0.706614i	−0.116093	+	0.0311069i
$517$	6.32832	−	11.4030i	0.278319	−	0.501503i
$518$	−9.89907	−	9.89907i	−0.434940	−	0.434940i
$519$	21.6191	+	15.7072i	0.948972	+	0.689469i
$520$	6.09405	−	18.7556i	0.267242	−	0.822486i
$521$	20.0416	−	39.3339i	0.878040	−	1.72325i	0.212096	−	0.977249i	$-0.431971\pi$
$521$	20.0416	−	39.3339i	0.878040	−	1.72325i	0.665944	−	0.746002i	$-0.268029\pi$
$522$	1.63686	+	1.32550i	0.0716434	+	0.0580157i
$523$	12.4336	−	1.30682i	0.543683	−	0.0571434i	0.171294	−	0.985220i	$-0.445205\pi$
$523$	12.4336	−	1.30682i	0.543683	−	0.0571434i	0.372389	+	0.928077i	$0.378539\pi$
$524$	0.0297602	+	0.567858i	0.00130008	+	0.0248070i
$525$	4.25563	+	2.76364i	0.185731	+	0.120615i
$526$	5.23797	−	13.6454i	0.228386	−	0.594967i
$527$	−0.442011	−	0.765586i	−0.0192543	−	0.0333495i
$528$	21.2580	−	8.57628i	0.925134	−	0.373235i
$529$	−7.16841	−	12.4161i	−0.311670	−	0.539829i
$530$	−2.09749	−	0.220455i	−0.0911091	−	0.00957595i
$531$	−2.85643	−	1.85499i	−0.123959	−	0.0804997i
$532$	0.799161	+	0.407193i	0.0346480	+	0.0176541i
$533$	−4.25528	+	26.8668i	−0.184317	+	1.16373i
$534$	−4.38100	+	0.460462i	−0.189585	+	0.0199261i
$535$	13.7545	−	4.46910i	0.594658	−	0.193216i
$536$	0.272574	+	1.28236i	0.0117734	+	0.0553896i
$537$	−12.9381	+	33.7050i	−0.558321	+	1.45448i
$538$		−	11.9583i		−	0.515559i
$539$	−20.4586	+	3.59674i	−0.881215	+	0.154923i
$540$	−0.961457	−	0.257622i	−0.0413745	−	0.0110863i
$541$	32.8574	−	5.20410i	1.41265	−	0.223742i	0.596978	−	0.802258i	$-0.296368\pi$
$541$	32.8574	−	5.20410i	1.41265	−	0.223742i	0.815671	+	0.578516i	$0.196368\pi$
$542$	15.9217	−	24.5173i	0.683896	−	1.05311i
$543$	32.1922	+	6.84266i	1.38150	+	0.293647i
$544$	−0.171098	+	0.211289i	−0.00733578	+	0.00905894i
$545$	7.70229	+	20.0652i	0.329930	+	0.859497i
$546$	−2.66736	+	12.5489i	−0.114153	+	0.537045i
$547$	−3.76689	−	4.18355i	−0.161060	−	0.178876i	0.657213	−	0.753705i	$-0.271735\pi$
$547$	−3.76689	−	4.18355i	−0.161060	−	0.178876i	−0.818273	+	0.574829i	$0.805069\pi$
$548$	−0.214268	+	0.0953982i	−0.00915307	+	0.00407521i
$549$	0.284308	+	0.164145i	0.0121340	+	0.00700556i
$550$	6.12136	−	16.7919i	0.261016	−	0.716008i
$551$	22.7570	−	6.09772i	0.969481	−	0.259772i
$552$	−11.7248	+	5.22022i	−0.499041	+	0.222187i
$553$	3.70286	−	5.70190i	0.157461	−	0.242469i
$554$	−30.1718	−	15.3733i	−1.28188	−	0.653148i
$555$	19.2676	−	7.39614i	0.817864	−	0.313949i
$556$	−1.67732	+	2.07132i	−0.0711342	+	0.0878434i
$557$	5.82571	−	1.89289i	0.246843	−	0.0802043i	−0.182982	−	0.983116i	$-0.558575\pi$
$557$	5.82571	−	1.89289i	0.246843	−	0.0802043i	0.429826	+	0.902912i	$0.358575\pi$
$558$	1.71188	+	0.0897159i	0.0724697	+	0.00379798i
$559$	67.6637	+	7.11174i	2.86187	+	0.300794i
$560$		−	4.24858i		−	0.179535i
$561$	1.30733	−	0.984111i	0.0551957	−	0.0415492i
$562$	26.2577	−	26.2577i	1.10761	−	1.10761i
$563$	−29.8065	+	4.72089i	−1.25619	+	0.198962i	−0.748826	−	0.662767i	$-0.769382\pi$
$563$	−29.8065	+	4.72089i	−1.25619	+	0.198962i	−0.507369	+	0.861729i	$0.669382\pi$
$564$	0.835754	+	0.542745i	0.0351916	+	0.0228537i
$565$	6.46119	+	5.81768i	0.271824	+	0.244752i
$566$	−13.9878	−	6.22779i	−0.587953	−	0.261773i
$567$	−6.46378	−	1.02376i	−0.271453	−	0.0429940i
$568$	−2.23903	+	2.48669i	−0.0939475	+	0.104339i
$569$	−41.6584	−	2.18322i	−1.74641	−	0.0915254i	−0.847811	−	0.530298i	$-0.822080\pi$
$569$	−41.6584	−	2.18322i	−1.74641	−	0.0915254i	−0.898598	+	0.438772i	$0.855413\pi$
$570$	−14.0929	+	11.4122i	−0.590286	+	0.478004i
$571$	34.6292	+	9.27886i	1.44919	+	0.388308i	0.895741	−	0.444577i	$-0.146646\pi$
$571$	34.6292	+	9.27886i	1.44919	+	0.388308i	0.553446	+	0.832885i	$0.313313\pi$
$572$	3.29446	−	0.0558392i	0.137748	−	0.00233475i
$573$	−2.35397	−	8.78513i	−0.0983384	−	0.367004i
$574$	0.849514	+	5.36362i	0.0354580	+	0.223873i
$575$	−3.33705	+	10.2704i	−0.139165	+	0.428304i
$576$	0.908984	+	2.79757i	0.0378743	+	0.116565i
$577$	−35.9421	−	5.69267i	−1.49629	−	0.236989i	−0.646014	−	0.763326i	$-0.723565\pi$
$577$	−35.9421	−	5.69267i	−1.49629	−	0.236989i	−0.850276	+	0.526337i	$0.823565\pi$
$578$	10.0999	−	22.6847i	0.420099	−	0.943557i
$579$	−1.65366	−	2.54642i	−0.0687239	−	0.105826i
$580$	0.430722	+	0.478365i	0.0178848	+	0.0198630i
$581$	2.18288	−	3.00447i	0.0905610	−	0.124646i
$582$	−10.6853	−	18.5075i	−0.442920	−	0.767160i
$583$	0.926541	+	4.02257i	0.0383734	+	0.166598i
$584$	9.43849	+	21.1105i	0.390567	+	0.873560i
$585$	2.38325	+	1.73154i	0.0985354	+	0.0715902i
$586$	10.6499	−	2.26372i	0.439945	−	0.0935133i
$587$	21.6754	−	7.04277i	0.894641	−	0.290686i	0.174617	−	0.984636i	$-0.444131\pi$
$587$	21.6754	−	7.04277i	0.894641	−	0.290686i	0.720023	+	0.693950i	$0.244131\pi$
$588$	−0.165915	−	1.57858i	−0.00684222	−	0.0650994i
$589$	12.0671	−	14.9016i	0.497217	−	0.614012i
$590$	−10.6087	−	9.55208i	−0.436752	−	0.393253i
$591$	−28.6687	+	14.6075i	−1.17927	+	0.600870i
$592$	38.5347	+	27.9971i	1.58376	+	1.15067i
$593$	−42.1036			−1.72899			−0.864493	−	0.502645i	$-0.832360\pi$
$593$	−42.1036			−1.72899			−0.864493	+	0.502645i	$0.832360\pi$
$594$	1.85029	+	26.6540i	0.0759184	+	1.09363i
$595$	−0.0784956	−	0.292950i	−0.00321801	−	0.0120098i
$596$	−0.167345	−	0.375863i	−0.00685471	−	0.0153959i
$597$	0.916383	−	1.41111i	0.0375051	−	0.0577528i
$598$	−27.2656	+	1.42893i	−1.11497	+	0.0584333i
$599$	14.5364	+	11.7713i	0.593940	+	0.480963i	0.878531	−	0.477686i	$-0.158524\pi$
$599$	14.5364	+	11.7713i	0.593940	+	0.480963i	−0.284591	+	0.958649i	$0.591858\pi$
$600$	−14.6153	−	6.50717i	−0.596669	−	0.265654i
$601$	9.43650	−	18.5202i	0.384923	−	0.755454i	−0.614518	−	0.788903i	$-0.710649\pi$
$601$	9.43650	−	18.5202i	0.384923	−	0.755454i	0.999440	+	0.0334496i	$0.0106493\pi$
$602$	13.2858	−	2.82398i	0.541488	−	0.115097i
$603$	−0.194764	−	0.0204706i	−0.00793142	−	0.000833625i
$604$	0.239922	−	0.895402i	0.00976230	−	0.0364334i
$605$	12.6887	+	0.234314i	0.515868	+	0.00952622i
$606$	−18.4128	+	18.4128i	−0.747971	+	0.747971i
$607$	9.67362	+	21.7273i	0.392640	+	0.881884i	0.996405	+	0.0847213i	$0.0270000\pi$
$607$	9.67362	+	21.7273i	0.392640	+	0.881884i	−0.603765	+	0.797163i	$0.706333\pi$
$608$	−5.60852	−	1.82232i	−0.227456	−	0.0739048i
$609$	3.64552	+	3.28244i	0.147724	+	0.133011i
$610$	1.06934	+	0.865934i	0.0432963	+	0.0350607i
$611$	−14.5969	−	20.0909i	−0.590527	−	0.812791i
$612$	−0.0106069	−	0.0163332i	−0.000428760	−	0.000660232i
$613$	8.20765	−	12.6387i	0.331504	−	0.510471i	−0.633137	−	0.774040i	$-0.718233\pi$
$613$	8.20765	−	12.6387i	0.331504	−	0.510471i	0.964641	+	0.263569i	$0.0848996\pi$
$614$	−16.6632	+	2.63918i	−0.672470	+	0.106509i
$615$	−7.73300	−	2.07205i	−0.311825	−	0.0835532i
$616$	−7.28710	+	2.50503i	−0.293606	+	0.100931i
$617$	−15.7862	+	4.22991i	−0.635530	+	0.170290i	−0.562178	−	0.827016i	$-0.690036\pi$
$617$	−15.7862	+	4.22991i	−0.635530	+	0.170290i	−0.0733521	+	0.997306i	$0.523370\pi$
$618$	8.39597	−	6.79893i	0.337736	−	0.273493i
$619$	−34.4714	+	31.0382i	−1.38552	+	1.24753i	−0.450578	+	0.892737i	$0.648782\pi$
$619$	−34.4714	+	31.0382i	−1.38552	+	1.24753i	−0.934945	+	0.354793i	$0.884551\pi$
$620$	0.512449	+	0.108924i	0.0205805	+	0.00437451i
$621$	−1.68744	−	16.0549i	−0.0677146	−	0.644261i
$622$	38.2515	−	4.02039i	1.53374	−	0.161203i
$623$	1.59582	−	0.0836333i	0.0639351	−	0.00335070i
$624$	2.28448	−	43.5905i	0.0914524	−	1.74502i
$625$	−6.21752	+	2.76822i	−0.248701	+	0.110729i
$626$	0.982114	+	0.263157i	0.0392532	+	0.0105179i
$627$	30.0901	+	18.8235i	1.20168	+	0.751740i
$628$	−1.97504	−	0.529210i	−0.0788126	−	0.0211178i
$629$	3.17432	+	1.21851i	0.126568	+	0.0485851i
$630$	0.559321	+	0.181734i	0.0222839	+	0.00724047i
$631$	22.7309	−	14.7616i	0.904904	−	0.587652i	−0.00613041	−	0.999981i	$-0.501951\pi$
$631$	22.7309	−	14.7616i	0.904904	−	0.587652i	0.911035	+	0.412329i	$0.135285\pi$
$632$	−8.71862	+	19.5823i	−0.346808	+	0.778944i
$633$	19.7067	+	27.1239i	0.783271	+	1.07808i
$634$	7.49412	−	35.2570i	0.297629	−	1.40024i
$635$	0.315811	+	0.619814i	0.0125326	+	0.0245966i
$636$	−0.311540	+	0.0493431i	−0.0123534	+	0.00195658i
$637$	−10.2377	+	38.2076i	−0.405633	+	1.51384i
$638$	8.38443	−	15.1079i	0.331943	−	0.598128i
$639$	−0.249924	−	0.432880i	−0.00988683	−	0.0171245i
$640$	2.24915	+	14.2006i	0.0889055	+	0.561327i
$641$	−31.2036	+	6.63254i	−1.23247	+	0.261969i	−0.777698	−	0.628639i	$-0.783613\pi$
$641$	−31.2036	+	6.63254i	−1.23247	+	0.261969i	−0.454772	+	0.890608i	$0.650279\pi$
$642$	24.8780	−	16.1559i	0.981855	−	0.637624i
$643$	−11.4248	−	29.7627i	−0.450551	−	1.17372i	−0.951337	−	0.308153i	$-0.900289\pi$
$643$	−11.4248	−	29.7627i	−0.450551	−	1.17372i	0.500786	−	0.865571i	$-0.333044\pi$
$644$	−0.371046	+	0.142431i	−0.0146212	+	0.00561257i
$645$	−4.16321	+	19.5864i	−0.163926	+	0.771213i
$646$	−2.98349	−	0.156358i	−0.117384	−	0.00615183i
$647$	−6.86847	−	43.3658i	−0.270027	−	1.70488i	−0.633882	−	0.773429i	$-0.718540\pi$
$647$	−6.86847	−	43.3658i	−0.270027	−	1.70488i	0.363855	−	0.931456i	$-0.381460\pi$
$648$	20.6335			0.810561
$649$	−10.9301	+	25.7136i	−0.429045	+	1.00935i
$650$	−24.0657	−	24.0657i	−0.943935	−	0.943935i
$651$	3.97064	+	0.417331i	0.155622	+	0.0163565i
$652$	−0.0675206	+	1.28837i	−0.00264431	+	0.0504565i
$653$	35.3110	+	7.50559i	1.38183	+	0.293717i	0.838087	−	0.545537i	$-0.183674\pi$
$653$	35.3110	+	7.50559i	1.38183	+	0.293717i	0.543741	+	0.839253i	$0.317007\pi$
$654$	25.9117	+	35.6643i	1.01323	+	1.39459i
$655$	3.81004	+	1.69634i	0.148870	+	0.0662814i
$656$	−5.70959	−	17.5723i	−0.222922	−	0.686083i
$657$	−3.43481	+	0.366430i	−0.134005	+	0.0142958i
$658$	−4.01090	−	2.91409i	−0.156361	−	0.113603i
$659$	−1.92116	−	3.32755i	−0.0748378	−	0.129623i	0.826178	−	0.563409i	$-0.190511\pi$
$659$	−1.92116	−	3.32755i	−0.0748378	−	0.129623i	−0.901016	+	0.433786i	$0.857177\pi$
$660$	−0.0850067	+	0.966007i	−0.00330888	+	0.0376018i
$661$	−4.59761	+	7.96329i	−0.178826	+	0.309736i	−0.941479	−	0.337072i	$-0.890563\pi$
$661$	−4.59761	+	7.96329i	−0.178826	+	0.309736i	0.762653	+	0.646808i	$0.223897\pi$
$662$	17.6690	+	6.78251i	0.686727	+	0.263610i
$663$	−0.647846	−	3.04788i	−0.0251602	−	0.118370i
$664$	−5.31574	+	10.4327i	−0.206291	+	0.404868i
$665$	5.32200	−	3.86666i	0.206378	−	0.149943i
$666$	−5.33412	+	3.87546i	−0.206693	+	0.150171i
$667$	−4.73958	+	9.30195i	−0.183517	+	0.360173i
$668$	−2.10544	−	0.110341i	−0.0814619	−	0.00426924i
$669$	2.73605	+	6.14528i	0.105782	+	0.237590i
$670$	−0.792854	−	0.212445i	−0.0306306	−	0.00820745i
$671$	0.922382	−	2.53024i	0.0356082	−	0.0976790i
$672$	−0.317799	−	1.18604i	−0.0122594	−	0.0457526i
$673$	0.273072	−	2.59811i	0.0105262	−	0.100150i	−0.987997	−	0.154471i	$-0.950633\pi$
$673$	0.273072	−	2.59811i	0.0105262	−	0.100150i	0.998524	+	0.0543210i	$0.0172994\pi$
$674$	42.6572	−	21.7349i	1.64309	−	0.837198i
$675$	13.4650	−	14.9544i	0.518269	−	0.575596i
$676$	1.72025	−	3.86375i	0.0661636	−	0.148606i
$677$	−5.63787	−	14.6872i	−0.216681	−	0.564473i	0.781555	−	0.623836i	$-0.214427\pi$
$677$	−5.63787	−	14.6872i	−0.216681	−	0.564473i	−0.998236	+	0.0593624i	$0.981093\pi$
$678$	15.8893	+	8.09602i	0.610226	+	0.310926i
$679$	3.51952	+	6.90745i	0.135067	+	0.265084i
$680$	0.388928	+	0.873546i	0.0149147	+	0.0334990i
$681$		−	7.48062i		−	0.286658i
$682$	−1.70675	−	13.9587i	−0.0653548	−	0.534506i
$683$	7.43505	+	27.7480i	0.284494	+	1.06175i	0.949208	+	0.314649i	$0.101887\pi$
$683$	7.43505	+	27.7480i	0.284494	+	1.06175i	−0.664714	+	0.747098i	$0.731447\pi$
$684$	0.248295	−	0.341748i	0.00949379	−	0.0130671i
$685$	−0.0900307	+	1.71789i	−0.00343990	+	0.0656372i
$686$	0.875193	+	16.6997i	0.0334150	+	0.637597i
$687$	−1.57414	+	9.93870i	−0.0600570	+	0.379185i
$688$	−43.1439	+	16.5614i	−1.64485	+	0.631397i
$689$	7.68871	+	1.63428i	0.292916	+	0.0622613i
$690$	0.420552	−	8.02460i	0.0160101	−	0.305491i
$691$	19.8178	−	16.0481i	0.753905	−	0.610500i	−0.173381	−	0.984855i	$-0.555469\pi$
$691$	19.8178	−	16.0481i	0.753905	−	0.610500i	0.927286	+	0.374355i	$0.122136\pi$
$692$	−2.25952	−	1.30454i	−0.0858941	−	0.0495910i
$693$	−0.0195070	−	1.15089i	−0.000741009	−	0.0437189i
$694$	−21.1311	+	36.6002i	−0.802127	+	1.38933i
$695$	7.95098	+	17.8582i	0.301598	+	0.677400i
$696$	−12.9713	−	8.42366i	−0.491676	−	0.319298i
$697$	−0.718351	−	1.10616i	−0.0272095	−	0.0418989i
$698$	1.60249	+	15.2466i	0.0606550	+	0.577094i
$699$	42.8541	−	16.4502i	1.62089	−	0.622202i
$700$	−0.441428	−	0.224919i	−0.0166844	−	0.00850112i
$701$	25.7444	−	39.6429i	0.972353	−	1.49729i	0.108160	−	0.994134i	$-0.465504\pi$
$701$	25.7444	−	39.6429i	0.972353	−	1.49729i	0.864194	−	0.503159i	$-0.167829\pi$
$702$	47.4984	+	18.2329i	1.79271	+	0.688157i
$703$			73.7509i			2.78157i
$704$	21.3120	−	11.3180i	0.803224	−	0.426561i
$705$	6.32967	−	3.65444i	0.238389	−	0.137634i
$706$	12.6611	−	17.4264i	0.476505	−	0.655853i
$707$	7.01987	−	6.32072i	0.264010	−	0.237715i
$708$	−1.90229	−	0.969265i	−0.0714924	−	0.0364272i
$709$	0.242218	−	1.52930i	0.00909669	−	0.0574342i	−0.982722	−	0.185085i	$-0.940744\pi$
$709$	0.242218	−	1.52930i	0.00909669	−	0.0574342i	0.991819	+	0.127651i	$0.0407438\pi$
$710$	−0.750794	−	1.95589i	−0.0281768	−	0.0734031i
$711$	−2.37956	−	2.14257i	−0.0892405	−	0.0803525i
$712$	−4.92822	+	1.04753i	−0.184693	+	0.0392577i
$713$	1.32919	+	8.39215i	0.0497784	+	0.314289i
$714$	−0.311032	−	0.538723i	−0.0116401	−	0.0201612i
$715$	10.6048	−	21.7152i	0.396597	−	0.812102i
$716$	0.912314	−	3.40480i	0.0340948	−	0.127243i
$717$	−2.09819	−	2.59105i	−0.0783584	−	0.0967646i
$718$	−38.8620	+	34.9915i	−1.45032	+	1.30587i
$719$	41.7195	−	27.0930i	1.55587	−	1.01040i	0.574452	−	0.818538i	$-0.305215\pi$
$719$	41.7195	−	27.0930i	1.55587	−	1.01040i	0.981423	−	0.191859i	$-0.0614515\pi$
$720$	−1.97633	−	0.313020i	−0.0736534	−	0.0116656i
$721$	−3.17063	+	2.30360i	−0.118081	+	0.0857906i
$722$	−11.4013	−	35.0895i	−0.424311	−	1.30590i
$723$	−10.9291	+	5.56867i	−0.406459	+	0.207101i
$724$	−3.19570	−	0.335882i	−0.118767	−	0.0124830i
$725$	−12.5701	+	3.36816i	−0.466843	+	0.125090i
$726$	25.2632	−	6.27171i	0.937607	−	0.232765i
$727$		−	13.3288i		−	0.494337i	−0.968972	−	0.247169i	$-0.920500\pi$
$727$		−	13.3288i		−	0.494337i	0.968972	−	0.247169i	$-0.0795002\pi$
$728$	−1.53378	+	14.5930i	−0.0568458	+	0.540852i
$729$	−9.14438	+	28.1435i	−0.338681	+	1.04235i
$730$	−14.4595	−	0.735180i	−0.535171	−	0.0272102i
$731$	−2.66889	+	1.93906i	−0.0987124	+	0.0717188i
$732$	0.187997	+	0.0837018i	0.00694858	+	0.00309371i
$733$	−13.8765	+	4.50876i	−0.512541	+	0.166535i	−0.553858	−	0.832611i	$-0.686845\pi$
$733$	−13.8765	+	4.50876i	−0.512541	+	0.166535i	0.0413163	+	0.999146i	$0.486845\pi$
$734$	6.66203	+	7.39893i	0.245900	+	0.273100i
$735$	−10.8684	−	4.17200i	−0.400888	−	0.153886i
$736$	2.26305	−	1.30657i	0.0834172	−	0.0481610i
$737$	0.111257	+	1.60269i	0.00409819	+	0.0590358i
$738$	2.55760			0.0941467
$739$	−16.5529	−	12.0264i	−0.608909	−	0.442398i	0.240121	−	0.970743i	$-0.422813\pi$
$739$	−16.5529	−	12.0264i	−0.608909	−	0.442398i	−0.849030	+	0.528345i	$0.822813\pi$
$740$	−1.79541	+	0.914806i	−0.0660005	+	0.0336289i
$741$	56.6829	−	36.8103i	2.08230	−	1.35226i
$742$	1.56065	−	0.164031i	0.0572932	−	0.00602176i
$743$	10.7897	−	4.14179i	0.395836	−	0.151947i	−0.152304	−	0.988334i	$-0.548669\pi$
$743$	10.7897	−	4.14179i	0.395836	−	0.151947i	0.548140	+	0.836386i	$0.315336\pi$
$744$	−12.5706	+	0.658798i	−0.460861	+	0.0241527i
$745$	−3.01347	−	0.157929i	−0.110405	−	0.00578608i
$746$	4.03068	−	38.3493i	0.147574	−	1.40407i
$747$	−1.23678	−	1.23678i	−0.0452512	−	0.0452512i
$748$	−0.116899	+	0.108900i	−0.00427425	+	0.00398176i
$749$	−9.31910	+	5.38039i	−0.340513	+	0.196595i
$750$	18.3929	−	14.8943i	0.671613	−	0.543861i
$751$	2.50452	+	4.91539i	0.0913912	+	0.179365i	0.932177	−	0.362002i	$-0.117907\pi$
$751$	2.50452	+	4.91539i	0.0913912	+	0.179365i	−0.840786	+	0.541368i	$0.817907\pi$
$752$	15.0297	+	7.65800i	0.548075	+	0.279258i
$753$	−29.3275	+	3.08244i	−1.06875	+	0.112330i
$754$	−19.3395	−	26.6186i	−0.704304	−	0.969391i
$755$	−5.05256	−	4.54934i	−0.183881	−	0.165568i
$756$	0.739599	+	0.0387607i	0.0268990	+	0.00140971i
$757$	−8.36267	+	11.5102i	−0.303947	+	0.418346i	−0.933481	−	0.358626i	$-0.883245\pi$
$757$	−8.36267	+	11.5102i	−0.303947	+	0.418346i	0.629535	+	0.776972i	$0.283245\pi$
$758$	45.2585	−	12.1270i	1.64386	−	0.440472i
$759$	−15.1205	+	4.32747i	−0.548840	+	0.157077i
$760$	−14.6659	+	14.6659i	−0.531988	+	0.531988i
$761$	0.895022	+	1.10526i	0.0324445	+	0.0400656i	0.793110	−	0.609078i	$-0.208461\pi$
$761$	0.895022	+	1.10526i	0.0324445	+	0.0400656i	−0.760665	+	0.649144i	$0.775127\pi$
$762$	0.954722	+	1.06033i	0.0345859	+	0.0384115i
$763$	−8.70974	−	13.4118i	−0.315314	−	0.485541i
$764$	0.318229	+	0.829015i	0.0115131	+	0.0299927i
$765$	−0.142056	+	0.0149307i	−0.00513604	+	0.000539819i
$766$	8.22566	+	1.74842i	0.297205	+	0.0631729i
$767$	35.6010	+	39.5389i	1.28548	+	1.42767i
$768$	2.45902	+	5.52305i	0.0887322	+	0.199296i
$769$	−4.60203	+	17.1750i	−0.165954	+	0.619347i	0.831963	+	0.554831i	$0.187217\pi$
$769$	−4.60203	+	17.1750i	−0.165954	+	0.619347i	−0.997917	+	0.0645161i	$0.979450\pi$
$770$	0.673856	−	4.77721i	0.0242841	−	0.172159i
$771$	0.590490	−	1.02276i	0.0212660	−	0.0368337i
$772$	0.186559	+	0.230381i	0.00671441	+	0.00829160i
$773$	15.8224	+	31.0533i	0.569093	+	1.11691i	0.978824	+	0.204702i	$0.0656226\pi$
$773$	15.8224	+	31.0533i	0.569093	+	1.11691i	−0.409731	+	0.912206i	$0.634377\pi$
$774$	−0.334795	−	6.38826i	−0.0120339	−	0.229621i
$775$	−6.66543	+	8.23113i	−0.239429	+	0.295671i
$776$	−14.3669	−	19.7743i	−0.515741	−	0.709856i
$777$	−12.8787	+	8.36354i	−0.462022	+	0.300040i
$778$	7.72935	+	36.3637i	0.277111	+	1.30370i
$779$	16.8157	−	23.1448i	0.602484	−	0.829249i
$780$	1.59921	+	0.923306i	0.0572610	+	0.0330597i
$781$	−3.14248	+	2.63415i	−0.112447	+	0.0942574i
$782$	0.936111	−	0.936111i	0.0334753	−	0.0334753i
$783$	15.1186	−	12.2428i	0.540296	−	0.437523i
$784$	−5.58614	−	26.2807i	−0.199505	−	0.938597i
$785$	−10.0347	+	11.1447i	−0.358156	+	0.397772i
$786$	8.44899	+	1.33819i	0.301365	+	0.0477316i
$787$	17.9709	+	8.00118i	0.640595	+	0.285211i	0.701215	−	0.712950i	$-0.252641\pi$
$787$	17.9709	+	8.00118i	0.640595	+	0.285211i	−0.0606204	+	0.998161i	$0.519308\pi$
$788$	2.63467	−	1.71097i	0.0938561	−	0.0609508i
$789$	−13.4461	−	8.73202i	−0.478695	−	0.310868i
$790$	−8.44597	−	10.4299i	−0.300494	−	0.371079i
$791$	−5.60242	−	3.23456i	−0.199199	−	0.115008i
$792$	0.628388	+	3.57433i	0.0223288	+	0.127008i
$793$	−3.62628	−	3.62628i	−0.128773	−	0.128773i
$794$	−26.9478	−	19.5787i	−0.956341	−	0.694822i
$795$	−0.714891	+	2.20021i	−0.0253546	+	0.0780333i
$796$	−0.0745798	+	0.146371i	−0.00264341	+	0.00518799i
$797$	−1.02592	+	2.30425i	−0.0363399	+	0.0816206i	−0.930803	−	0.365520i	$-0.880891\pi$
$797$	−1.02592	+	2.30425i	−0.0363399	+	0.0816206i	0.894464	+	0.447141i	$0.147558\pi$
$798$	8.49131	−	10.4859i	0.300589	−	0.371197i
$799$	1.17782	+	0.250353i	0.0416682	+	0.00885685i
$800$	3.09794	+	1.00658i	0.109529	+	0.0355881i
$801$	0.0786700	−	0.748495i	0.00277967	−	0.0264468i
$802$	−14.5334			−0.513192
$803$	7.83951	+	27.2313i	0.276650	+	0.960971i
$804$	−0.122760			−0.00432942
$805$	−0.304701	+	2.89903i	−0.0107393	+	0.102178i
$806$	−25.4679	−	8.27503i	−0.897069	−	0.291476i
$807$	−12.8306	−	2.72723i	−0.451658	−	0.0960029i
$808$	−18.7428	+	23.1454i	−0.659369	+	0.814253i
$809$	−5.67979	+	12.7570i	−0.199691	+	0.448513i	−0.985438	−	0.170035i	$-0.945612\pi$
$809$	−5.67979	+	12.7570i	−0.199691	+	0.448513i	0.785747	+	0.618548i	$0.212279\pi$
$810$	−5.86493	+	11.5106i	−0.206073	+	0.404441i
$811$	−15.6122	+	48.0494i	−0.548218	+	1.68724i	0.164994	+	0.986295i	$0.447240\pi$
$811$	−15.6122	+	48.0494i	−0.548218	+	1.68724i	−0.713212	+	0.700948i	$0.752760\pi$
$812$	−0.387480	−	0.281521i	−0.0135979	−	0.00987944i
$813$	−22.6745	−	22.6745i	−0.795230	−	0.795230i
$814$	38.8888	+	37.5925i	1.36305	+	1.31762i
$815$	8.19465	+	4.73119i	0.287046	+	0.165726i
$816$	1.33196	+	1.64483i	0.0466279	+	0.0575807i
$817$	−60.0112	−	38.9717i	−2.09953	−	1.36345i
$818$	34.8081	−	22.6047i	1.21704	−	0.790353i
$819$	−2.00239	−	0.891521i	−0.0699691	−	0.0311523i
$820$	0.772024	+	0.122277i	0.0269602	+	0.00427008i
$821$	22.5546	−	25.0494i	0.787160	−	0.874230i	−0.207415	−	0.978253i	$-0.566505\pi$
$821$	22.5546	−	25.0494i	0.787160	−	0.874230i	0.994575	+	0.104023i	$0.0331717\pi$
$822$	0.733593	+	3.45128i	0.0255870	+	0.120377i
$823$	32.5598	−	26.3664i	1.13496	−	0.919076i	0.137518	−	0.990499i	$-0.456087\pi$
$823$	32.5598	−	26.3664i	1.13496	−	0.919076i	0.997446	+	0.0714230i	$0.0227540\pi$
$824$	8.73736	−	8.73736i	0.304380	−	0.304380i
$825$	−16.6207	−	10.3974i	−0.578658	−	0.361992i
$826$	9.19863	+	5.31083i	0.320061	+	0.184788i
$827$	2.48679	−	3.42277i	0.0864742	−	0.119022i	−0.763588	−	0.645704i	$-0.776564\pi$
$827$	2.48679	−	3.42277i	0.0864742	−	0.119022i	0.850062	+	0.526682i	$0.176564\pi$
$828$	0.0389179	+	0.183094i	0.00135249	+	0.00636297i
$829$	4.42490	−	2.87357i	0.153683	−	0.0998031i	−0.465507	−	0.885044i	$-0.654128\pi$
$829$	4.42490	−	2.87357i	0.153683	−	0.0998031i	0.619190	+	0.785241i	$0.287461\pi$
$830$	−4.30902	−	5.93086i	−0.149568	−	0.205863i
$831$	−23.3757	+	28.8665i	−0.810893	+	1.00137i
$832$	−2.40487	−	45.8877i	−0.0833740	−	1.59087i
$833$	−0.870733	−	1.70891i	−0.0301691	−	0.0592102i
$834$	25.2328	+	31.1599i	0.873739	+	1.07898i
$835$	−7.73165	+	13.3916i	−0.267565	+	0.463436i
$836$	−3.11386	−	1.52068i	−0.107695	−	0.0525939i
$837$	4.09795	−	15.2937i	0.141646	−	0.528629i
$838$	−17.7977	−	39.9742i	−0.614810	−	1.38089i
$839$	−25.3797	−	28.1871i	−0.876206	−	0.973125i	0.123609	−	0.992331i	$-0.460553\pi$
$839$	−25.3797	−	28.1871i	−0.876206	−	0.973125i	−0.999816	+	0.0192055i	$0.993886\pi$
$840$	−4.22418	−	0.897877i	−0.145748	−	0.0309797i
$841$	16.3292	−	1.71627i	0.563076	−	0.0591817i
$842$	−10.8909	−	28.3717i	−0.375325	−	0.977755i
$843$	−22.1846	−	34.1613i	−0.764079	−	1.17658i
$844$	−2.19034	−	2.43262i	−0.0753947	−	0.0837343i
$845$	−19.5216	−	24.1071i	−0.671562	−	0.829310i
$846$	−1.65107	+	1.65107i	−0.0567648	+	0.0567648i
$847$	−9.27102	+	1.79238i	−0.318556	+	0.0615868i
$848$	−5.15726	+	1.38188i	−0.177101	+	0.0474541i
$849$	−9.87214	+	13.5878i	−0.338811	+	0.466333i
$850$	1.64797	+	0.0863666i	0.0565250	+	0.00296235i
$851$	−24.2864	−	21.8676i	−0.832526	−	0.749610i
$852$	−0.184170	−	0.253488i	−0.00630956	−	0.00868437i
$853$	−16.8960	+	1.77584i	−0.578507	+	0.0608036i	−0.389263	−	0.921127i	$-0.627270\pi$
$853$	−16.8960	+	1.77584i	−0.578507	+	0.0608036i	−0.189244	+	0.981930i	$0.560604\pi$
$854$	−0.912220	−	0.464799i	−0.0312155	−	0.0159051i
$855$	−1.40656	−	2.76054i	−0.0481035	−	0.0944083i
$856$	26.3665	−	21.3512i	0.901189	−	0.729768i
$857$	−12.1625	+	7.02202i	−0.415463	+	0.239868i	−0.693134	−	0.720809i	$-0.743771\pi$
$857$	−12.1625	+	7.02202i	−0.415463	+	0.239868i	0.277671	+	0.960676i	$0.410437\pi$
$858$	9.48250	−	48.6519i	0.323727	−	1.66095i
$859$	36.6621	+	36.6621i	1.25089	+	1.25089i	0.955320	+	0.295575i	$0.0955112\pi$
$859$	36.6621	+	36.6621i	1.25089	+	1.25089i	0.295575	+	0.955320i	$0.404489\pi$
$860$	0.204357	−	1.94433i	0.00696853	−	0.0663011i
$861$	5.94860	+	0.311753i	0.202728	+	0.0106245i
$862$	−13.6239	+	0.714001i	−0.464033	+	0.0243190i
$863$	2.07134	−	0.795113i	0.0705092	−	0.0270659i	−0.322858	−	0.946448i	$-0.604644\pi$
$863$	2.07134	−	0.795113i	0.0705092	−	0.0270659i	0.393367	+	0.919382i	$0.371310\pi$
$864$	−4.84278	+	0.508997i	−0.164755	+	0.0173164i
$865$	−16.0487	+	10.4222i	−0.545673	+	0.354364i
$866$	6.16390	−	3.14066i	0.209458	−	0.106724i
$867$	−22.0360	−	16.0101i	−0.748380	−	0.543730i
$868$	−0.389809			−0.0132310
$869$	−13.9310	+	22.2692i	−0.472577	+	0.755431i
$870$	8.38622	−	4.84178i	0.284319	−	0.164152i
$871$	2.85604	+	1.09633i	0.0967734	+	0.0371478i
$872$	33.7376	+	37.4694i	1.14250	+	1.26887i
$873$	3.47247	−	1.12827i	0.117525	−	0.0381863i
$874$	26.2326	+	11.6795i	0.887330	+	0.395065i
$875$	−6.94584	+	5.04645i	−0.234812	+	0.170601i
$876$	−2.11730	+	0.453499i	−0.0715370	+	0.0153223i
$877$	−10.5237	+	32.3885i	−0.355359	+	1.09368i	0.600442	+	0.799668i	$0.294991\pi$
$877$	−10.5237	+	32.3885i	−0.355359	+	1.09368i	−0.955801	+	0.294014i	$0.905009\pi$
$878$	−1.64124	+	15.6154i	−0.0553893	+	0.526994i
$879$		−	11.9431i		−	0.402829i
$880$	0.278182	+	16.4125i	0.00937751	+	0.553265i
$881$	13.1610	−	3.52648i	0.443406	−	0.118810i	−0.0302064	−	0.999544i	$-0.509616\pi$
$881$	13.1610	−	3.52648i	0.443406	−	0.118810i	0.473612	+	0.880733i	$0.342950\pi$
$882$	3.69878	+	0.388757i	0.124544	+	0.0130901i
$883$	31.8761	−	16.2417i	1.07272	−	0.546576i	0.173837	−	0.984774i	$-0.444383\pi$
$883$	31.8761	−	16.2417i	1.07272	−	0.546576i	0.898878	+	0.438198i	$0.144383\pi$
$884$	0.0940116	+	0.289338i	0.00316195	+	0.00973149i
$885$	−12.6683	+	9.20403i	−0.425839	+	0.309390i
$886$	−12.6278	−	2.00005i	−0.424240	−	0.0671930i
$887$	−30.7483	+	19.9682i	−1.03243	+	0.670466i	−0.945458	−	0.325745i	$-0.894385\pi$
$887$	−30.7483	+	19.9682i	−1.03243	+	0.670466i	−0.0869697	+	0.996211i	$0.527718\pi$
$888$	35.9800	−	32.3966i	1.20741	−	1.08716i
$889$	−0.325730	−	0.402243i	−0.0109246	−	0.0134908i
$890$	0.816442	−	3.04700i	0.0273672	−	0.102136i
$891$	25.0370	+	3.53162i	0.838770	+	0.118314i
$892$	−0.328388	−	0.568785i	−0.0109953	−	0.0190443i
$893$	4.08577	+	25.7966i	0.136725	+	0.863249i
$894$	−6.05414	+	1.28685i	−0.202481	+	0.0430386i
$895$	−19.2126	−	17.2991i	−0.642205	−	0.578244i
$896$	−3.83373	−	9.98720i	−0.128076	−	0.333649i
$897$	−4.68506	+	29.5803i	−0.156430	+	0.987658i
$898$	−11.4215	−	5.81953i	−0.381139	−	0.194200i
$899$	−7.60928	+	6.85142i	−0.253784	+	0.228508i
$900$	−0.137149	+	0.188769i	−0.00457163	+	0.00629231i
$901$	−0.330074	+	0.190568i	−0.0109964	+	0.00634875i
$902$	−3.63291	−	20.6643i	−0.120963	−	0.688047i
$903$		−	14.8989i		−	0.495806i
$904$	19.0416	+	7.30938i	0.633314	+	0.243106i
$905$	−12.8358	+	19.7655i	−0.426678	+	0.657027i
$906$	−12.4252	−	6.33097i	−0.412801	−	0.210332i
$907$	21.0371	−	8.07538i	0.698525	−	0.268139i	0.0169179	−	0.999857i	$-0.494615\pi$
$907$	21.0371	−	8.07538i	0.698525	−	0.268139i	0.681607	+	0.731718i	$0.261281\pi$
$908$	0.0763446	+	0.726371i	0.00253359	+	0.0241055i
$909$	−2.42304	−	3.73115i	−0.0803671	−	0.123754i
$910$	−7.70485	−	5.00359i	−0.255413	−	0.165867i
$911$	−8.55279	−	19.2099i	−0.283367	−	0.636452i	0.714645	−	0.699488i	$-0.246588\pi$
$911$	−8.55279	−	19.2099i	−0.283367	−	0.636452i	−0.998011	+	0.0630357i	$0.979922\pi$
$912$	−22.9539	+	39.7574i	−0.760081	+	1.31650i
$913$	−8.23585	+	11.7494i	−0.272567	+	0.388847i
$914$	−24.2104	−	13.9779i	−0.800808	−	0.462346i
$915$	1.17297	−	0.949855i	0.0387773	−	0.0314012i
$916$	0.0514181	−	0.981116i	0.00169890	−	0.0324170i
$917$	−3.03535	−	0.645184i	−0.100236	−	0.0213059i
$918$	−2.30309	+	0.884073i	−0.0760132	+	0.0291787i
$919$	1.46502	−	9.24975i	0.0483264	−	0.305121i	−0.951672	−	0.307118i	$-0.900636\pi$
$919$	1.46502	−	9.24975i	0.0483264	−	0.305121i	0.999998	+	0.00199653i	$0.000635517\pi$
$920$	−0.481001	−	9.17804i	−0.0158581	−	0.302591i
$921$	−0.968522	+	18.4805i	−0.0319139	+	0.608953i
$922$	16.2284	−	22.3364i	0.534453	−	0.735612i
$923$	2.02093	+	7.54222i	0.0665198	+	0.248255i
$924$	−0.0875717	−	0.716207i	−0.00288090	−	0.0235615i
$925$		−	40.7373i		−	1.33943i
$926$	−8.86523	−	19.9116i	−0.291330	−	0.654337i
$927$	0.837974	+	1.64462i	0.0275227	+	0.0540163i
$928$	2.80583	+	1.42964i	0.0921059	+	0.0469303i
$929$	−18.4884	−	48.1638i	−0.606583	−	1.58020i	−0.800596	−	0.599205i	$-0.795484\pi$
$929$	−18.4884	−	48.1638i	−0.606583	−	1.58020i	0.194012	−	0.980999i	$-0.437850\pi$
$930$	3.20560	−	7.19989i	0.105116	−	0.236094i
$931$	27.8367	−	30.9157i	0.912310	−	1.01322i
$932$	−3.99326	+	2.03467i	−0.130804	+	0.0666478i
$933$	4.41002	−	41.9586i	0.144378	−	1.37366i
$934$	−7.56151	−	28.2199i	−0.247420	−	0.923384i
$935$	0.322414	+	1.12654i	0.0105441	+	0.0368418i
$936$	6.67527	+	1.78863i	0.218188	+	0.0584633i
$937$	21.7170	+	48.7772i	0.709463	+	1.59348i	0.801688	+	0.597742i	$0.203935\pi$
$937$	21.7170	+	48.7772i	0.709463	+	1.59348i	−0.0922249	+	0.995738i	$0.529398\pi$
$938$	0.609901	+	0.0319636i	0.0199140	+	0.00104365i
$939$	0.506334	−	0.993736i	0.0165236	−	0.0324294i
$940$	−0.577317	+	0.419445i	−0.0188300	+	0.0136808i
$941$	−29.2265	+	21.2343i	−0.952756	+	0.692218i	−0.951457	−	0.307781i	$-0.900414\pi$
$941$	−29.2265	+	21.2343i	−0.952756	+	0.692218i	−0.00129921	+	0.999999i	$0.500414\pi$
$942$	−13.9646	+	27.4070i	−0.454991	+	0.892970i
$943$	2.63570	+	12.4000i	0.0858303	+	0.403800i
$944$	−33.7387	−	12.9511i	−1.09810	−	0.421522i
$945$	2.71597	−	4.70420i	0.0883506	−	0.153028i
$946$	−51.1388	+	11.7791i	−1.66267	+	0.382972i
$947$	−30.2098	−	52.3249i	−0.981687	−	1.70033i	−0.655822	−	0.754915i	$-0.727678\pi$
$947$	−30.2098	−	52.3249i	−0.981687	−	1.70033i	−0.325865	−	0.945416i	$-0.605655\pi$
$948$	−1.62384	−	1.17979i	−0.0527400	−	0.0383178i
$949$	53.3095	+	8.35819i	1.73050	+	0.271318i
$950$	11.0610	+	34.0424i	0.358868	+	1.10448i
$951$	−36.1197	−	16.0815i	−1.17126	−	0.521479i
$952$	−0.418196	−	0.575597i	−0.0135538	−	0.0186552i
$953$	4.80027	+	1.02033i	0.155496	+	0.0330517i	0.285002	−	0.958527i	$-0.408006\pi$
$953$	4.80027	+	1.02033i	0.155496	+	0.0330517i	−0.129506	+	0.991579i	$0.541339\pi$
$954$	0.0386800	−	0.738058i	0.00125231	−	0.0238955i
$955$	6.47722	+	0.680783i	0.209598	+	0.0220296i
$956$	0.230179	+	0.230179i	0.00744451	+	0.00744451i
$957$	−14.2978	−	12.4415i	−0.462181	−	0.402178i
$958$	31.3441			1.01268
$959$	−0.200230	−	1.26420i	−0.00646576	−	0.0408232i
$960$	13.5053	+	0.707784i	0.435882	+	0.0228436i
$961$	4.71262	−	22.1711i	0.152020	−	0.715198i
$962$	96.1556	−	36.9107i	3.10018	−	1.19005i
$963$	1.81622	+	4.73141i	0.0585268	+	0.152468i
$964$	1.00439	−	0.652259i	0.0323492	−	0.0210078i
$965$	2.12673	−	0.452051i	0.0684619	−	0.0145520i
$966$	0.935313	+	5.90534i	0.0300932	+	0.190001i
$967$	20.2901	+	35.1434i	0.652484	+	1.13014i	0.982518	+	0.186167i	$0.0596064\pi$
$967$	20.2901	+	35.1434i	0.652484	+	1.13014i	−0.330034	+	0.943969i	$0.607060\pi$
$968$	27.9864	−	10.1542i	0.899518	−	0.326368i
$969$	−0.848182	+	3.16546i	−0.0272475	+	0.101689i
$970$	15.1150	−	2.39397i	0.485312	−	0.0768659i
$971$	21.7415	+	42.6700i	0.697717	+	1.36935i	0.919047	+	0.394148i	$0.128960\pi$
$971$	21.7415	+	42.6700i	0.697717	+	1.36935i	−0.221330	+	0.975199i	$0.571040\pi$
$972$	0.136430	−	0.641853i	0.00437600	−	0.0205875i
$973$	−8.54932	−	11.7671i	−0.274079	−	0.377237i
$974$	12.2393	−	27.4899i	0.392173	−	0.880834i
$975$	−31.3096	+	20.3327i	−1.00271	+	0.651167i
$976$	3.31291	+	1.07643i	0.106044	+	0.0344557i
$977$	−9.33382	−	3.58292i	−0.298615	−	0.114628i	0.204448	−	0.978878i	$-0.434460\pi$
$977$	−9.33382	−	3.58292i	−0.298615	−	0.114628i	−0.503063	+	0.864250i	$0.667794\pi$
$978$	18.7469	+	5.02322i	0.599460	+	0.160625i
$979$	−6.15926	+	0.427569i	−0.196851	+	0.0136652i
$980$	1.09790	+	0.294183i	0.0350713	+	0.00939732i
$981$	−6.88053	+	3.06341i	−0.219679	+	0.0978072i
$982$	0.368084	−	7.02346i	0.0117460	−	0.224128i
$983$	−53.1855	+	2.78733i	−1.69635	+	0.0889021i	−0.875802	−	0.482670i	$-0.839667\pi$
$983$	−53.1855	+	2.78733i	−1.69635	+	0.0889021i	−0.820552	+	0.571573i	$0.806334\pi$
$984$	−18.6780	+	1.96314i	−0.595434	+	0.0625826i
$985$	−2.40842	−	22.9146i	−0.0767386	−	0.730119i
$986$	1.56050	+	0.331694i	0.0496964	+	0.0105633i
$987$	−4.04138	+	3.63887i	−0.128638	+	0.115827i
$988$	−5.12826	+	4.15278i	−0.163152	+	0.132118i
$989$	30.6272	−	8.20652i	0.973887	−	0.260952i
$990$	−2.17259	−	0.665427i	−0.0690493	−	0.0211487i
$991$	16.3570	+	4.38283i	0.519596	+	0.139225i	0.509080	−	0.860719i	$-0.329986\pi$
$991$	16.3570	+	4.38283i	0.519596	+	0.139225i	0.0105163	+	0.999945i	$0.496653\pi$
$992$	2.53140	−	0.400934i	0.0803720	−	0.0127297i
$993$	11.3069	−	17.4110i	0.358813	−	0.552523i
$994$	0.848997	+	1.30734i	0.0269285	+	0.0414663i
$995$	0.708202	+	0.974756i	0.0224515	+	0.0309018i
$996$	−0.852062	−	0.689987i	−0.0269986	−	0.0218631i
$997$	26.0324	+	23.4397i	0.824456	+	0.742343i	0.968975	−	0.247159i	$-0.0794968\pi$
$997$	26.0324	+	23.4397i	0.824456	+	0.742343i	−0.144519	+	0.989502i	$0.546164\pi$
$998$	−24.0293	−	7.80760i	−0.760635	−	0.247145i
$999$	24.7696	+	55.6334i	0.783675	+	1.76016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	803.2.bk.a.268.18	yes	1152
11.3	even	5	inner	803.2.bk.a.487.55	yes	1152
73.3	even	12	inner	803.2.bk.a.587.55	yes	1152
803.3	even	60	inner	803.2.bk.a.3.18	✓	1152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
803.2.bk.a.3.18	✓	1152	803.3	even	60	inner
803.2.bk.a.268.18	yes	1152	1.1	even	1	trivial
803.2.bk.a.487.55	yes	1152	11.3	even	5	inner
803.2.bk.a.587.55	yes	1152	73.3	even	12	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:	\( N \)	\(=\)	\( 803 = 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	803.bk (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.153529 + 1.46073i) q^{2} +(1.53227 + 0.497863i) q^{3} +(-0.153864 - 0.0327049i) q^{4} +(-0.726055 + 0.896603i) q^{5} +(-0.962490 + 2.16179i) q^{6} +(0.389717 - 0.764864i) q^{7} +(-0.836358 + 2.57404i) q^{8} +(-0.327082 - 0.237639i) q^{9} +O(q^{10})\)	\(q+(-0.153529 + 1.46073i) q^{2} +(1.53227 + 0.497863i) q^{3} +(-0.153864 - 0.0327049i) q^{4} +(-0.726055 + 0.896603i) q^{5} +(-0.962490 + 2.16179i) q^{6} +(0.389717 - 0.764864i) q^{7} +(-0.836358 + 2.57404i) q^{8} +(-0.327082 - 0.237639i) q^{9} +(-1.19822 - 1.19822i) q^{10} +(-1.45542 + 2.98023i) q^{11} +(-0.219479 - 0.126716i) q^{12} +(3.97455 + 4.90817i) q^{13} +(1.05743 + 0.686700i) q^{14} +(-1.55889 + 1.01236i) q^{15} +(-3.91898 - 1.74484i) q^{16} +(-0.302460 - 0.0479050i) q^{17} +(0.397342 - 0.441293i) q^{18} +(-1.38101 - 6.49712i) q^{19} +(0.141037 - 0.114210i) q^{20} +(0.977948 - 0.977948i) q^{21} +(-4.12986 - 2.58352i) q^{22} +(2.54900 + 1.47166i) q^{23} +(-2.56304 + 3.52773i) q^{24} +(0.762817 + 3.58877i) q^{25} +(-7.77971 + 5.05220i) q^{26} +(-3.22384 - 4.43724i) q^{27} +(-0.0849784 + 0.104940i) q^{28} +(0.185633 + 3.54209i) q^{29} +(-1.23945 - 2.43255i) q^{30} +(1.81672 + 2.24346i) q^{31} +(0.443911 - 0.768876i) q^{32} +(-3.71383 + 3.84190i) q^{33} +(0.116413 - 0.434458i) q^{34} +(0.402823 + 0.904754i) q^{35} +(0.0425543 + 0.0472613i) q^{36} +(-10.8606 - 2.30850i) q^{37} +(9.70256 - 1.01978i) q^{38} +(3.64648 + 9.49940i) q^{39} +(-1.70065 - 2.61878i) q^{40} +(2.88197 + 3.20076i) q^{41} +(1.27837 + 1.57866i) q^{42} +(7.61745 - 7.61745i) q^{43} +(0.321405 - 0.410952i) q^{44} +(0.450547 - 0.120724i) q^{45} +(-2.54105 + 3.49745i) q^{46} +(-3.92672 - 0.205791i) q^{47} +(-5.13623 - 4.62468i) q^{48} +(3.68136 + 5.06696i) q^{49} +(-5.35934 + 0.563289i) q^{50} +(-0.439599 - 0.223987i) q^{51} +(-0.451022 - 0.885180i) q^{52} +(0.967241 - 0.783256i) q^{53} +(6.97655 - 4.02792i) q^{54} +(-1.61537 - 3.46874i) q^{55} +(1.64285 + 1.64285i) q^{56} +(1.11861 - 10.6429i) q^{57} +(-5.20253 - 0.272653i) q^{58} +(8.41276 - 0.440894i) q^{59} +(0.272967 - 0.104782i) q^{60} +(-0.807560 + 0.0848779i) q^{61} +(-3.55600 + 2.30929i) q^{62} +(-0.309231 + 0.157561i) q^{63} +(-5.88617 - 4.27655i) q^{64} -7.28642 q^{65} +(-5.04179 - 6.01475i) q^{66} +(0.419495 - 0.242196i) q^{67} +(0.0449712 + 0.0172628i) q^{68} +(3.17305 + 3.52403i) q^{69} +(-1.38345 + 0.449509i) q^{70} +(1.12945 + 0.502866i) q^{71} +(0.885250 - 0.643172i) q^{72} +(6.34051 - 5.72695i) q^{73} +(5.03951 - 15.5100i) q^{74} +(-0.617880 + 5.87873i) q^{75} +1.04484i q^{76} +(1.71227 + 2.27464i) q^{77} +(-14.4359 + 3.86809i) q^{78} +(7.87661 + 0.827865i) q^{79} +(4.40983 - 2.24692i) q^{80} +(-2.35584 - 7.25053i) q^{81} +(-5.11791 + 3.71838i) q^{82} +(4.27294 + 0.676768i) q^{83} +(-0.182455 + 0.118488i) q^{84} +(0.262554 - 0.236405i) q^{85} +(9.95753 + 12.2965i) q^{86} +(-1.47904 + 5.51984i) q^{87} +(-6.45399 - 6.23885i) q^{88} +(0.930778 + 1.61215i) q^{89} +(0.107173 + 0.676661i) q^{90} +(5.30303 - 1.12719i) q^{91} +(-0.344069 - 0.309801i) q^{92} +(1.66676 + 4.34205i) q^{93} +(0.903469 - 5.70428i) q^{94} +(6.82802 + 3.47905i) q^{95} +(1.06298 - 0.957115i) q^{96} +(-5.30827 + 7.30620i) q^{97} +(-7.96665 + 4.59955i) q^{98} +(1.18426 - 0.628914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1152 q - 2 q^{2} + 134 q^{4} - 8 q^{5} - 42 q^{6} - 8 q^{7} - 64 q^{8} + 272 q^{9}+O(q^{10}) \) 1152 * q - 2 * q^2 + 134 * q^4 - 8 * q^5 - 42 * q^6 - 8 * q^7 - 64 * q^8 + 272 * q^9	\( 1152 q - 2 q^{2} + 134 q^{4} - 8 q^{5} - 42 q^{6} - 8 q^{7} - 64 q^{8} + 272 q^{9} - 32 q^{10} - 14 q^{11} - 84 q^{12} - 12 q^{13} - 12 q^{14} - 36 q^{15} + 134 q^{16} - 42 q^{17} - 28 q^{18} - 18 q^{19} - 2 q^{20} - 64 q^{21} - 28 q^{22} - 48 q^{23} + 42 q^{25} - 34 q^{26} - 92 q^{28} - 4 q^{29} + 36 q^{30} - 36 q^{31} - 148 q^{32} - 84 q^{33} + 54 q^{35} - 70 q^{36} - 18 q^{37} + 42 q^{38} + 76 q^{39} + 136 q^{40} - 38 q^{41} + 96 q^{42} - 40 q^{43} - 72 q^{44} - 68 q^{45} + 8 q^{47} - 6 q^{48} - 90 q^{50} - 78 q^{51} - 98 q^{52} + 10 q^{53} - 36 q^{54} + 4 q^{55} + 24 q^{56} - 78 q^{57} + 116 q^{58} + 76 q^{59} - 250 q^{60} + 6 q^{61} - 68 q^{62} + 12 q^{63} - 264 q^{64} - 272 q^{65} - 70 q^{66} - 48 q^{67} - 12 q^{68} + 12 q^{69} + 54 q^{71} - 16 q^{72} - 36 q^{73} - 104 q^{74} - 76 q^{75} + 2 q^{77} + 336 q^{78} - 66 q^{79} - 248 q^{80} - 268 q^{81} - 40 q^{82} - 114 q^{83} - 70 q^{84} - 180 q^{85} - 2 q^{86} - 116 q^{87} - 46 q^{88} - 64 q^{89} - 148 q^{90} - 18 q^{91} + 36 q^{92} - 112 q^{93} + 84 q^{94} + 158 q^{95} - 156 q^{96} - 72 q^{98} + 112 q^{99}+O(q^{100}) \) 1152 * q - 2 * q^2 + 134 * q^4 - 8 * q^5 - 42 * q^6 - 8 * q^7 - 64 * q^8 + 272 * q^9 - 32 * q^10 - 14 * q^11 - 84 * q^12 - 12 * q^13 - 12 * q^14 - 36 * q^15 + 134 * q^16 - 42 * q^17 - 28 * q^18 - 18 * q^19 - 2 * q^20 - 64 * q^21 - 28 * q^22 - 48 * q^23 + 42 * q^25 - 34 * q^26 - 92 * q^28 - 4 * q^29 + 36 * q^30 - 36 * q^31 - 148 * q^32 - 84 * q^33 + 54 * q^35 - 70 * q^36 - 18 * q^37 + 42 * q^38 + 76 * q^39 + 136 * q^40 - 38 * q^41 + 96 * q^42 - 40 * q^43 - 72 * q^44 - 68 * q^45 + 8 * q^47 - 6 * q^48 - 90 * q^50 - 78 * q^51 - 98 * q^52 + 10 * q^53 - 36 * q^54 + 4 * q^55 + 24 * q^56 - 78 * q^57 + 116 * q^58 + 76 * q^59 - 250 * q^60 + 6 * q^61 - 68 * q^62 + 12 * q^63 - 264 * q^64 - 272 * q^65 - 70 * q^66 - 48 * q^67 - 12 * q^68 + 12 * q^69 + 54 * q^71 - 16 * q^72 - 36 * q^73 - 104 * q^74 - 76 * q^75 + 2 * q^77 + 336 * q^78 - 66 * q^79 - 248 * q^80 - 268 * q^81 - 40 * q^82 - 114 * q^83 - 70 * q^84 - 180 * q^85 - 2 * q^86 - 116 * q^87 - 46 * q^88 - 64 * q^89 - 148 * q^90 - 18 * q^91 + 36 * q^92 - 112 * q^93 + 84 * q^94 + 158 * q^95 - 156 * q^96 - 72 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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