LMFDB - Embedded newform 224.2.bd.a.109.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.13
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.436149 - 1.34528i) q^{2} +(0.756979 + 0.986515i) q^{3} +(-1.61955 + 1.17348i) q^{4} +(-2.52010 - 1.93374i) q^{5} +(0.996981 - 1.44862i) q^{6} +(-0.259491 - 2.63300i) q^{7} +(2.28503 + 1.66693i) q^{8} +(0.376264 - 1.40424i) q^{9} +O(q^{10})$	\(q+(-0.436149 - 1.34528i) q^{2} +(0.756979 + 0.986515i) q^{3} +(-1.61955 + 1.17348i) q^{4} +(-2.52010 - 1.93374i) q^{5} +(0.996981 - 1.44862i) q^{6} +(-0.259491 - 2.63300i) q^{7} +(2.28503 + 1.66693i) q^{8} +(0.376264 - 1.40424i) q^{9} +(-1.50228 + 4.23364i) q^{10} +(0.371867 + 0.0489572i) q^{11} +(-2.38362 - 0.709405i) q^{12} +(-5.81297 - 2.40781i) q^{13} +(-3.42893 + 1.49747i) q^{14} -3.94992i q^{15} +(1.24587 - 3.80103i) q^{16} +(2.99322 + 1.72814i) q^{17} +(-2.05319 + 0.106276i) q^{18} +(-0.790086 - 6.00130i) q^{19} +(6.35065 + 0.174490i) q^{20} +(2.40106 - 2.24911i) q^{21} +(-0.0963282 - 0.521617i) q^{22} +(-0.841254 + 3.13960i) q^{23} +(0.0852674 + 3.51604i) q^{24} +(1.31746 + 4.91684i) q^{25} +(-0.703855 + 8.87022i) q^{26} +(5.11658 - 2.11936i) q^{27} +(3.51004 + 3.95975i) q^{28} +(-1.74109 + 4.20337i) q^{29} +(-5.31375 + 1.72276i) q^{30} +(1.58784 - 2.75022i) q^{31} +(-5.65682 - 0.0182315i) q^{32} +(0.233198 + 0.403911i) q^{33} +(1.01934 - 4.78045i) q^{34} +(-4.43759 + 7.13721i) q^{35} +(1.03847 + 2.71577i) q^{36} +(4.70183 + 3.60784i) q^{37} +(-7.72883 + 3.68035i) q^{38} +(-2.02496 - 7.55724i) q^{39} +(-2.53509 - 8.61949i) q^{40} +(3.47792 + 3.47792i) q^{41} +(-4.07290 - 2.24914i) q^{42} +(0.953485 + 2.30192i) q^{43} +(-0.659706 + 0.357091i) q^{44} +(-3.66366 + 2.81122i) q^{45} +(4.59055 - 0.237613i) q^{46} +(5.59518 - 3.23038i) q^{47} +(4.69287 - 1.64823i) q^{48} +(-6.86533 + 1.36648i) q^{49} +(6.03991 - 3.91683i) q^{50} +(0.560974 + 4.26102i) q^{51} +(12.2399 - 2.92186i) q^{52} +(11.6032 + 1.52759i) q^{53} +(-5.08272 - 5.95887i) q^{54} +(-0.842472 - 0.842472i) q^{55} +(3.79607 - 6.44902i) q^{56} +(5.32229 - 5.32229i) q^{57} +(6.41408 + 0.508959i) q^{58} +(0.794692 - 6.03629i) q^{59} +(4.63517 + 6.39709i) q^{60} +(-8.43592 + 1.11061i) q^{61} +(-4.39234 - 0.936581i) q^{62} +(-3.79498 - 0.626314i) q^{63} +(2.44269 + 7.61796i) q^{64} +(9.99320 + 17.3087i) q^{65} +(0.441664 - 0.489882i) q^{66} +(-7.97415 - 10.3921i) q^{67} +(-6.87561 + 0.713695i) q^{68} +(-3.73407 + 1.54670i) q^{69} +(11.5370 + 2.85691i) q^{70} +(3.32452 - 3.32452i) q^{71} +(3.20053 - 2.58151i) q^{72} +(6.25354 - 1.67563i) q^{73} +(2.80286 - 7.89883i) q^{74} +(-3.85324 + 5.02165i) q^{75} +(8.32201 + 8.79224i) q^{76} +(0.0324079 - 0.991827i) q^{77} +(-9.28341 + 6.02021i) q^{78} +(10.0098 - 5.77915i) q^{79} +(-10.4899 + 7.16978i) q^{80} +(2.18692 + 1.26262i) q^{81} +(3.16188 - 6.19566i) q^{82} +(-2.66146 - 1.10241i) q^{83} +(-1.24933 + 6.46015i) q^{84} +(-4.20146 - 10.1432i) q^{85} +(2.68086 - 2.28668i) q^{86} +(-5.46465 + 1.46425i) q^{87} +(0.768117 + 0.731744i) q^{88} +(-11.4398 - 3.06527i) q^{89} +(5.37978 + 3.70253i) q^{90} +(-4.83134 + 15.9303i) q^{91} +(-2.32182 - 6.07193i) q^{92} +(3.91509 - 0.515431i) q^{93} +(-6.78609 - 6.11815i) q^{94} +(-9.61388 + 16.6517i) q^{95} +(-4.26411 - 5.59434i) q^{96} -4.79566 q^{97} +(4.83260 + 8.63979i) q^{98} +(0.208667 - 0.503767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.436149	−	1.34528i	−0.308404	−	0.951256i
$2$	−0.436149	−	1.34528i	−0.308404	−	0.951256i
$3$	0.756979	+	0.986515i	0.437042	+	0.569564i	0.959000	−	0.283407i	$-0.0914647\pi$
$3$	0.756979	+	0.986515i	0.437042	+	0.569564i	−0.521958	+	0.852971i	$0.674798\pi$
$4$	−1.61955	+	1.17348i	−0.809774	+	0.586742i
$5$	−2.52010	−	1.93374i	−1.12702	−	0.864797i	−0.135001	−	0.990845i	$-0.543104\pi$
$5$	−2.52010	−	1.93374i	−1.12702	−	0.864797i	−0.992024	+	0.126049i	$0.959770\pi$
$6$	0.996981	−	1.44862i	0.407016	−	0.591395i
$7$	−0.259491	−	2.63300i	−0.0980785	−	0.995179i
$7$	−0.259491	−	2.63300i	−0.0980785	−	0.995179i
$8$	2.28503	+	1.66693i	0.807879	+	0.589349i
$9$	0.376264	−	1.40424i	0.125421	−	0.468078i
$10$	−1.50228	+	4.23364i	−0.475064	+	1.33880i
$11$	0.371867	+	0.0489572i	0.112122	+	0.0147611i	0.186378	−	0.982478i	$-0.440325\pi$
$11$	0.371867	+	0.0489572i	0.112122	+	0.0147611i	−0.0742564	+	0.997239i	$0.523658\pi$
$12$	−2.38362	−	0.709405i	−0.688093	−	0.204788i
$13$	−5.81297	−	2.40781i	−1.61223	−	0.667806i	−0.619150	−	0.785273i	$-0.712523\pi$
$13$	−5.81297	−	2.40781i	−1.61223	−	0.667806i	−0.993077	+	0.117466i	$0.962523\pi$
$14$	−3.42893	+	1.49747i	−0.916421	+	0.400215i
$15$		−	3.94992i		−	1.01987i
$16$	1.24587	−	3.80103i	0.311468	−	0.950257i
$17$	2.99322	+	1.72814i	0.725963	+	0.419135i	0.816944	−	0.576718i	$-0.195667\pi$
$17$	2.99322	+	1.72814i	0.725963	+	0.419135i	−0.0909802	+	0.995853i	$0.529000\pi$
$18$	−2.05319	+	0.106276i	−0.483943	+	0.0250496i
$19$	−0.790086	−	6.00130i	−0.181258	−	1.37679i	−0.804123	−	0.594463i	$-0.797365\pi$
$19$	−0.790086	−	6.00130i	−0.181258	−	1.37679i	0.622865	−	0.782330i	$-0.285969\pi$
$20$	6.35065	+	0.174490i	1.42005	+	0.0390172i
$21$	2.40106	−	2.24911i	0.523954	−	0.490797i
$22$	−0.0963282	−	0.521617i	−0.0205372	−	0.111209i
$23$	−0.841254	+	3.13960i	−0.175413	+	0.654652i	0.821067	+	0.570831i	$0.193379\pi$
$23$	−0.841254	+	3.13960i	−0.175413	+	0.654652i	−0.996481	+	0.0838207i	$0.973288\pi$
$24$	0.0852674	+	3.51604i	0.0174051	+	0.717709i
$25$	1.31746	+	4.91684i	0.263493	+	0.983369i
$26$	−0.703855	+	8.87022i	−0.138037	+	1.73959i
$27$	5.11658	−	2.11936i	0.984687	−	0.407871i
$28$	3.51004	+	3.95975i	0.663334	+	0.748323i
$29$	−1.74109	+	4.20337i	−0.323313	+	0.780546i	0.675745	+	0.737136i	$0.263822\pi$
$29$	−1.74109	+	4.20337i	−0.323313	+	0.780546i	−0.999057	+	0.0434100i	$0.986178\pi$
$30$	−5.31375	+	1.72276i	−0.970153	+	0.314531i
$31$	1.58784	−	2.75022i	0.285184	−	0.493954i	−0.687470	−	0.726213i	$-0.741279\pi$
$31$	1.58784	−	2.75022i	0.285184	−	0.493954i	0.972654	+	0.232260i	$0.0746119\pi$
$32$	−5.65682	−	0.0182315i	−0.999995	−	0.00322290i
$33$	0.233198	+	0.403911i	0.0405946	+	0.0703119i
$34$	1.01934	−	4.78045i	0.174815	−	0.819840i
$35$	−4.43759	+	7.13721i	−0.750090	+	1.20641i
$36$	1.03847	+	2.71577i	0.173078	+	0.452628i
$37$	4.70183	+	3.60784i	0.772977	+	0.593126i	0.918128	−	0.396283i	$-0.129700\pi$
$37$	4.70183	+	3.60784i	0.772977	+	0.593126i	−0.145151	+	0.989409i	$0.546367\pi$
$38$	−7.72883	+	3.68035i	−1.25378	+	0.597031i
$39$	−2.02496	−	7.55724i	−0.324252	−	1.21013i
$40$	−2.53509	−	8.61949i	−0.400833	−	1.36286i
$41$	3.47792	+	3.47792i	0.543160	+	0.543160i	0.924454	−	0.381294i	$-0.124521\pi$
$41$	3.47792	+	3.47792i	0.543160	+	0.543160i	−0.381294	+	0.924454i	$0.624521\pi$
$42$	−4.07290	−	2.24914i	−0.628463	−	0.347050i
$43$	0.953485	+	2.30192i	0.145405	+	0.351039i	0.979756	−	0.200194i	$-0.0641574\pi$
$43$	0.953485	+	2.30192i	0.145405	+	0.351039i	−0.834351	+	0.551233i	$0.814157\pi$
$44$	−0.659706	+	0.357091i	−0.0994545	+	0.0538335i
$45$	−3.66366	+	2.81122i	−0.546146	+	0.419072i
$46$	4.59055	−	0.237613i	0.676840	−	0.0350342i
$47$	5.59518	−	3.23038i	0.816141	−	0.471199i	−0.0329428	−	0.999457i	$-0.510488\pi$
$47$	5.59518	−	3.23038i	0.816141	−	0.471199i	0.849084	+	0.528258i	$0.177155\pi$
$48$	4.69287	−	1.64823i	0.677357	−	0.237901i
$49$	−6.86533	+	1.36648i	−0.980761	+	0.195211i
$50$	6.03991	−	3.91683i	0.854173	−	0.553924i
$51$	0.560974	+	4.26102i	0.0785521	+	0.596663i
$52$	12.2399	−	2.92186i	1.69737	−	0.405189i
$53$	11.6032	+	1.52759i	1.59382	+	0.209831i	0.874563	−	0.484912i	$-0.161148\pi$
$53$	11.6032	+	1.52759i	1.59382	+	0.209831i	0.719259	+	0.694742i	$0.244482\pi$
$54$	−5.08272	−	5.95887i	−0.691671	−	0.810900i
$55$	−0.842472	−	0.842472i	−0.113599	−	0.113599i
$56$	3.79607	−	6.44902i	0.507272	−	0.861786i
$57$	5.32229	−	5.32229i	0.704955	−	0.704955i
$58$	6.41408	+	0.508959i	0.842209	+	0.0668296i
$59$	0.794692	−	6.03629i	0.103460	−	0.785858i	−0.858528	−	0.512767i	$-0.828621\pi$
$59$	0.794692	−	6.03629i	0.103460	−	0.785858i	0.961988	−	0.273091i	$-0.0880461\pi$
$60$	4.63517	+	6.39709i	0.598398	+	0.825861i
$61$	−8.43592	+	1.11061i	−1.08011	+	0.142199i	−0.649517	−	0.760347i	$-0.725029\pi$
$61$	−8.43592	+	1.11061i	−1.08011	+	0.142199i	−0.430592	+	0.902546i	$0.641695\pi$
$62$	−4.39234	−	0.936581i	−0.557828	−	0.118946i
$63$	−3.79498	−	0.626314i	−0.478123	−	0.0789081i
$64$	2.44269	+	7.61796i	0.305336	+	0.952245i
$65$	9.99320	+	17.3087i	1.23950	+	2.14688i
$66$	0.441664	−	0.489882i	0.0543651	−	0.0603003i
$67$	−7.97415	−	10.3921i	−0.974197	−	1.26960i	−0.962955	−	0.269662i	$-0.913088\pi$
$67$	−7.97415	−	10.3921i	−0.974197	−	1.26960i	−0.0112420	−	0.999937i	$-0.503579\pi$
$68$	−6.87561	+	0.713695i	−0.833790	+	0.0865483i
$69$	−3.73407	+	1.54670i	−0.449530	+	0.186201i
$70$	11.5370	+	2.85691i	1.37893	+	0.341466i
$71$	3.32452	−	3.32452i	0.394548	−	0.394548i	−0.481757	−	0.876305i	$-0.660001\pi$
$71$	3.32452	−	3.32452i	0.394548	−	0.394548i	0.876305	+	0.481757i	$0.160001\pi$
$72$	3.20053	−	2.58151i	0.377187	−	0.304234i
$73$	6.25354	−	1.67563i	0.731921	−	0.196118i	0.126437	−	0.991975i	$-0.459646\pi$
$73$	6.25354	−	1.67563i	0.731921	−	0.196118i	0.605485	+	0.795857i	$0.292979\pi$
$74$	2.80286	−	7.89883i	0.325825	−	0.918221i
$75$	−3.85324	+	5.02165i	−0.444934	+	0.579850i
$76$	8.32201	+	8.79224i	0.954600	+	1.00854i
$77$	0.0324079	−	0.991827i	0.00369322	−	0.113029i
$78$	−9.28341	+	6.02021i	−1.05114	+	0.681655i
$79$	10.0098	−	5.77915i	1.12619	−	0.650205i	0.183215	−	0.983073i	$-0.441350\pi$
$79$	10.0098	−	5.77915i	1.12619	−	0.650205i	0.942974	+	0.332867i	$0.108016\pi$
$80$	−10.4899	+	7.16978i	−1.17281	+	0.801606i
$81$	2.18692	+	1.26262i	0.242991	+	0.140291i
$82$	3.16188	−	6.19566i	0.349171	−	0.684197i
$83$	−2.66146	−	1.10241i	−0.292133	−	0.121005i	0.231804	−	0.972763i	$-0.425537\pi$
$83$	−2.66146	−	1.10241i	−0.292133	−	0.121005i	−0.523937	+	0.851757i	$0.675537\pi$
$84$	−1.24933	+	6.46015i	−0.136313	+	0.704860i
$85$	−4.20146	−	10.1432i	−0.455712	−	1.10019i
$86$	2.68086	−	2.28668i	0.289084	−	0.246579i
$87$	−5.46465	+	1.46425i	−0.585872	+	0.156984i
$88$	0.768117	+	0.731744i	0.0818815	+	0.0780041i
$89$	−11.4398	−	3.06527i	−1.21261	−	0.324918i	−0.404826	−	0.914394i	$-0.632668\pi$
$89$	−11.4398	−	3.06527i	−1.21261	−	0.324918i	−0.807786	+	0.589475i	$0.799335\pi$
$90$	5.37978	+	3.70253i	0.567078	+	0.390280i
$91$	−4.83134	+	15.9303i	−0.506462	+	1.66995i
$92$	−2.32182	−	6.07193i	−0.242066	−	0.633043i
$93$	3.91509	−	0.515431i	0.405976	−	0.0534477i
$94$	−6.78609	−	6.11815i	−0.699932	−	0.631039i
$95$	−9.61388	+	16.6517i	−0.986363	+	1.70843i
$96$	−4.26411	−	5.59434i	−0.435204	−	0.570970i
$97$	−4.79566			−0.486926			−0.243463	−	0.969910i	$-0.578283\pi$
$97$	−4.79566			−0.486926			−0.243463	+	0.969910i	$0.578283\pi$
$98$	4.83260	+	8.63979i	0.488166	+	0.872751i
$99$	0.208667	−	0.503767i	0.0209719	−	0.0506305i
$100$	−7.90353	−	6.41704i	−0.790353	−	0.641704i
$101$	1.15349	−	8.76166i	0.114777	−	0.871818i	−0.833087	−	0.553142i	$-0.813429\pi$
$101$	1.15349	−	8.76166i	0.114777	−	0.871818i	0.947864	−	0.318676i	$-0.103238\pi$
$102$	5.48759	−	2.61311i	0.543353	−	0.258736i
$103$	6.70108	+	1.79555i	0.660277	+	0.176921i	0.573371	−	0.819296i	$-0.305635\pi$
$103$	6.70108	+	1.79555i	0.660277	+	0.176921i	0.0869061	+	0.996217i	$0.472302\pi$
$104$	−9.26913	−	15.1917i	−0.908913	−	1.48967i
$105$	−10.4001	+	1.02497i	−1.01495	+	0.100027i
$106$	−3.00569	−	16.2758i	−0.291938	−	1.58084i
$107$	−6.95900	+	9.06914i	−0.672752	+	0.876747i	−0.997616	−	0.0690137i	$-0.978015\pi$
$107$	−6.95900	+	9.06914i	−0.672752	+	0.876747i	0.324864	+	0.945761i	$0.394681\pi$
$108$	−5.79952	+	9.43663i	−0.558059	+	0.908040i
$109$	−6.14837	+	4.71781i	−0.588907	+	0.451884i	−0.859733	−	0.510744i	$-0.829370\pi$
$109$	−6.14837	+	4.71781i	−0.588907	+	0.451884i	0.270826	+	0.962628i	$0.412703\pi$
$110$	−0.765916	+	1.50080i	−0.0730272	+	0.143096i
$111$			7.36949i			0.699481i
$112$	−10.3314	−	2.29404i	−0.976223	−	0.216767i
$113$		−	5.24640i		−	0.493540i	−0.969074	−	0.246770i	$-0.920631\pi$
$113$		−	5.24640i		−	0.493540i	0.969074	−	0.246770i	$-0.0793693\pi$
$114$	−9.48128	−	4.83865i	−0.888003	−	0.453181i
$115$	8.19123	−	6.28535i	0.763836	−	0.586112i
$116$	−2.11280	−	8.85070i	−0.196169	−	0.821767i
$117$	−5.56834	+	7.25680i	−0.514793	+	0.670892i
$118$	−8.46709	+	1.56364i	−0.779459	+	0.143945i
$119$	3.77347	−	8.32958i	0.345913	−	0.763571i
$120$	6.58424	−	9.02568i	0.601056	−	0.823928i
$121$	−10.4893	−	2.81060i	−0.953572	−	0.255509i
$122$	5.17340	+	10.8643i	0.468377	+	0.983605i
$123$	−0.798306	+	6.06373i	−0.0719808	+	0.546748i
$124$	0.655754	+	6.31741i	0.0588884	+	0.567320i
$125$	0.109757	−	0.264978i	0.00981700	−	0.0237003i
$126$	0.812611	+	5.37847i	0.0723931	+	0.479153i
$127$	21.1168			1.87381			0.936906	−	0.349581i	$-0.113676\pi$
$127$	21.1168			1.87381			0.936906	+	0.349581i	$0.113676\pi$
$128$	9.18289	−	6.60866i	0.811661	−	0.584129i
$129$	−1.54911	+	2.68313i	−0.136391	+	0.236236i
$130$	18.9265	−	20.9928i	1.65997	−	1.84119i
$131$	2.08472	−	0.274458i	0.182143	−	0.0239795i	−0.0389030	−	0.999243i	$-0.512386\pi$
$131$	2.08472	−	0.274458i	0.182143	−	0.0239795i	0.221046	+	0.975263i	$0.429053\pi$
$132$	−0.851659	−	0.380499i	−0.0741274	−	0.0331182i
$133$	−15.5964	+	3.63758i	−1.35238	+	0.315418i
$134$	−10.5024	+	15.2600i	−0.907266	+	1.31826i
$135$	−16.9926	−	4.55316i	−1.46249	−	0.391874i
$136$	3.95891	+	8.93834i	0.339474	+	0.766456i
$137$	2.61816	−	0.701533i	0.223684	−	0.0599360i	−0.145236	−	0.989397i	$-0.546394\pi$
$137$	2.61816	−	0.701533i	0.223684	−	0.0599360i	0.368920	+	0.929461i	$0.379728\pi$
$138$	3.70936	+	4.34878i	0.315762	+	0.370192i
$139$	4.57345	+	11.0413i	0.387915	+	0.936510i	0.990381	+	0.138365i	$0.0441848\pi$
$139$	4.57345	+	11.0413i	0.387915	+	0.936510i	−0.602466	+	0.798144i	$0.705815\pi$
$140$	−1.18850	−	16.7665i	−0.100447	−	1.41703i
$141$	7.42225	+	3.07440i	0.625066	+	0.258911i
$142$	−5.92239	−	3.02242i	−0.496996	−	0.253636i
$143$	−2.04377	−	1.17997i	−0.170909	−	0.0986741i
$144$	−4.86876	−	3.17969i	−0.405730	−	0.264974i
$145$	12.5160	−	7.22610i	1.03939	−	0.600095i
$146$	−4.98166	−	7.68192i	−0.412285	−	0.635761i
$147$	−6.54496	−	5.73835i	−0.539819	−	0.473291i
$148$	−11.8486	−	0.325552i	−0.973948	−	0.0267602i
$149$	8.25492	−	10.7580i	0.676269	−	0.881331i	−0.321580	−	0.946882i	$-0.604214\pi$
$149$	8.25492	−	10.7580i	0.676269	−	0.881331i	0.997849	+	0.0655512i	$0.0208806\pi$
$150$	8.43610	+	2.99350i	0.688805	+	0.244418i
$151$	1.73237	−	0.464188i	0.140979	−	0.0377751i	−0.187640	−	0.982238i	$-0.560084\pi$
$151$	1.73237	−	0.464188i	0.140979	−	0.0377751i	0.328618	+	0.944463i	$0.393417\pi$
$152$	8.19838	−	15.0302i	0.664976	−	1.21911i
$153$	3.55295	−	3.55295i	0.287239	−	0.287239i
$154$	−1.34842	+	0.388987i	−0.108659	+	0.0313454i
$155$	−9.31973	+	3.86036i	−0.748579	+	0.310072i
$156$	12.1478	+	9.86306i	0.972603	+	0.789677i
$157$	1.49146	+	1.94371i	0.119032	+	0.155125i	0.849069	−	0.528283i	$-0.177164\pi$
$157$	1.49146	+	1.94371i	0.119032	+	0.155125i	−0.730037	+	0.683408i	$0.760497\pi$
$158$	−12.1403	−	10.9454i	−0.965832	−	0.870767i
$159$	7.27639	+	12.6031i	0.577055	+	0.999489i
$160$	14.2205	+	10.9848i	1.12423	+	0.868424i
$161$	8.48485	+	1.40032i	0.668700	+	0.110361i
$162$	0.744750	−	3.49270i	0.0585131	−	0.274412i
$163$	12.5454	−	1.65163i	0.982630	−	0.129366i	0.377943	−	0.925829i	$-0.376632\pi$
$163$	12.5454	−	1.65163i	0.982630	−	0.129366i	0.604687	+	0.796463i	$0.293298\pi$
$164$	−9.71394	−	1.55138i	−0.758531	−	0.121142i
$165$	0.193377	−	1.46884i	0.0150544	−	0.114349i
$166$	−0.322259	+	4.06122i	−0.0250121	+	0.315211i
$167$	−5.47705	+	5.47705i	−0.423827	+	0.423827i	−0.886519	−	0.462692i	$-0.846883\pi$
$167$	−5.47705	+	5.47705i	−0.423827	+	0.423827i	0.462692	+	0.886519i	$0.346883\pi$
$168$	9.23560	−	1.13689i	0.712542	−	0.0877130i
$169$	18.8007	+	18.8007i	1.44620	+	1.44620i
$170$	−11.8130	+	10.0761i	−0.906015	+	0.772800i
$171$	−8.72452	−	1.14861i	−0.667181	−	0.0878360i
$172$	−4.24548	−	2.60916i	−0.323714	−	0.198947i
$173$	3.17450	+	24.1127i	0.241353	+	1.83325i	0.498509	+	0.866885i	$0.333881\pi$
$173$	3.17450	+	24.1127i	0.241353	+	1.83325i	−0.257156	+	0.966370i	$0.582785\pi$
$174$	4.35323	+	6.71285i	0.330017	+	0.508900i
$175$	12.6042	−	4.74475i	0.952785	−	0.358670i
$176$	0.649386	−	1.35248i	0.0489493	−	0.101947i
$177$	6.55645	−	3.78537i	0.492813	−	0.284526i
$178$	0.865792	+	16.7266i	0.0648939	+	1.25371i
$179$	8.04970	−	6.17676i	0.601663	−	0.461672i	−0.262467	−	0.964941i	$-0.584536\pi$
$179$	8.04970	−	6.17676i	0.601663	−	0.461672i	0.864130	+	0.503269i	$0.167869\pi$
$180$	2.63454	−	8.85215i	0.196367	−	0.659800i
$181$	−9.45866	−	22.8352i	−0.703057	−	1.69733i	−0.716660	−	0.697422i	$-0.754330\pi$
$181$	−9.45866	−	22.8352i	−0.703057	−	1.69733i	0.0136035	−	0.999907i	$-0.495670\pi$
$182$	23.5379	−	0.448498i	1.74475	−	0.0332449i
$183$	−7.48145	−	7.48145i	−0.553045	−	0.553045i
$184$	−7.15578	+	5.77176i	−0.527531	+	0.425500i
$185$	−4.87247	−	18.1843i	−0.358231	−	1.33694i
$186$	−2.40096	−	5.04208i	−0.176047	−	0.369703i
$187$	1.02848	+	0.789177i	0.0752095	+	0.0577103i
$188$	−5.27087	+	11.7976i	−0.384418	+	0.860429i
$189$	−6.90797	−	12.9220i	−0.502481	−	0.939936i
$190$	26.5943	+	5.67071i	1.92935	+	0.411397i
$191$	−7.65221	−	13.2540i	−0.553694	−	0.959027i	−0.998004	−	0.0631533i	$-0.979884\pi$
$191$	−7.65221	−	13.2540i	−0.553694	−	0.959027i	0.444310	−	0.895873i	$-0.353449\pi$
$192$	−5.66616	+	8.17639i	−0.408920	+	0.590080i
$193$	3.37960	−	5.85364i	0.243269	−	0.421354i	−0.718374	−	0.695657i	$-0.755114\pi$
$193$	3.37960	−	5.85364i	0.243269	−	0.421354i	0.961644	+	0.274302i	$0.0884469\pi$
$194$	2.09162	+	6.45150i	0.150170	+	0.463191i
$195$	−9.51066	+	22.9608i	−0.681073	+	1.64426i
$196$	9.51519	−	10.2694i	0.679656	−	0.733531i
$197$	−8.19378	+	3.39398i	−0.583783	+	0.241811i	−0.654973	−	0.755652i	$-0.727320\pi$
$197$	−8.19378	+	3.39398i	−0.583783	+	0.241811i	0.0711905	+	0.997463i	$0.477320\pi$
$198$	−0.768717	−	0.0609980i	−0.0546304	−	0.00433494i
$199$	−2.56836	−	9.58524i	−0.182066	−	0.679480i	−0.995240	−	0.0974584i	$-0.968929\pi$
$199$	−2.56836	−	9.58524i	−0.182066	−	0.679480i	0.813174	−	0.582021i	$-0.197738\pi$
$200$	−5.18559	+	13.4312i	−0.366677	+	0.949732i
$201$	4.21570	−	15.7332i	0.297353	−	1.10974i
$202$	−12.2900	+	2.26962i	−0.864719	+	0.159690i
$203$	11.5192	+	3.49355i	0.808493	+	0.245199i
$204$	−5.90877	−	6.24264i	−0.413696	−	0.437072i
$205$	−2.03931	−	15.4901i	−0.142432	−	1.08188i
$206$	−0.507156	−	9.79795i	−0.0353352	−	0.682655i
$207$	4.09221	+	2.36264i	0.284428	+	0.164215i
$208$	−16.3944	+	19.0954i	−1.13674	+	1.32403i
$209$		−	2.27036i		−	0.157044i
$210$	5.91488	+	13.5440i	0.408165	+	0.934627i
$211$	6.18184	+	2.56060i	0.425576	+	0.176279i	0.585183	−	0.810901i	$-0.301023\pi$
$211$	6.18184	+	2.56060i	0.425576	+	0.176279i	−0.159607	+	0.987181i	$0.551023\pi$
$212$	−20.5845	+	11.1422i	−1.41375	+	0.765247i
$213$	5.79628	+	0.763095i	0.397155	+	0.0522864i
$214$	15.2357	+	5.40629i	1.04149	+	0.369566i
$215$	2.04843	−	7.64486i	0.139702	−	0.521375i
$216$	15.2244	+	3.68619i	1.03589	+	0.250814i
$217$	−7.65334	−	3.46711i	−0.519542	−	0.235363i
$218$	9.02837	+	6.21360i	0.611478	+	0.420838i
$219$	6.38683	+	4.90079i	0.431582	+	0.331165i
$220$	2.35305	+	0.375797i	0.158643	+	0.0253362i
$221$	−13.2385	−	17.2527i	−0.890517	−	1.16054i
$222$	9.91402	−	3.21420i	0.665385	−	0.215723i
$223$	−10.4443			−0.699401			−0.349700	−	0.936862i	$-0.613717\pi$
$223$	−10.4443			−0.699401			−0.349700	+	0.936862i	$0.613717\pi$
$224$	1.41989	+	14.8991i	0.0948706	+	0.995490i
$225$	7.40012			0.493341
$226$	−7.05788	+	2.28821i	−0.469483	+	0.152210i
$227$	9.62947	+	12.5494i	0.639131	+	0.832931i	0.994818	−	0.101674i	$-0.0324198\pi$
$227$	9.62947	+	12.5494i	0.639131	+	0.832931i	−0.355687	+	0.934605i	$0.615753\pi$
$228$	−2.37409	+	14.8653i	−0.157228	+	0.984481i
$229$	10.7853	+	8.27584i	0.712711	+	0.546883i	0.900249	−	0.435375i	$-0.143384\pi$
$229$	10.7853	+	8.27584i	0.712711	+	0.546883i	−0.187538	+	0.982257i	$0.560051\pi$
$230$	−12.0281	−	8.27814i	−0.793112	−	0.545844i
$231$	1.00298	−	0.718822i	0.0659915	−	0.0472950i
$232$	−10.9852	+	6.70253i	−0.721211	+	0.440043i
$233$	−1.14913	+	4.28861i	−0.0752820	+	0.280956i	−0.993297	−	0.115589i	$-0.963124\pi$
$233$	−1.14913	+	4.28861i	−0.0752820	+	0.280956i	0.918015	+	0.396545i	$0.129791\pi$
$234$	12.1910	+	4.32592i	0.796954	+	0.282794i
$235$	−20.3472	−	2.67876i	−1.32730	−	0.174743i
$236$	5.79644	+	10.7086i	0.377316	+	0.697072i
$237$	13.2784	+	5.50010i	0.862526	+	0.357270i
$238$	−12.8514	−	1.44342i	−0.833032	−	0.0935632i
$239$		−	0.341372i		−	0.0220815i	−0.999939	−	0.0110408i	$-0.996486\pi$
$239$		−	0.341372i		−	0.0220815i	0.999939	−	0.0110408i	$-0.00351446\pi$
$240$	−15.0138	−	4.92110i	−0.969134	−	0.317656i
$241$	−4.79262	−	2.76702i	−0.308720	−	0.178239i	0.337634	−	0.941278i	$-0.390374\pi$
$241$	−4.79262	−	2.76702i	−0.308720	−	0.178239i	−0.646353	+	0.763038i	$0.723707\pi$
$242$	0.793858	+	15.3369i	0.0510311	+	0.985891i
$243$	−1.75876	−	13.3591i	−0.112825	−	0.856988i
$244$	12.3591	−	11.6981i	0.791210	−	0.748894i
$245$	19.9438	+	9.83212i	1.27416	+	0.628151i
$246$	8.50559	−	1.57075i	0.542297	−	0.100147i
$247$	−9.85725	+	36.7877i	−0.627202	+	2.34075i
$248$	8.21267	−	3.63750i	0.521505	−	0.230982i
$249$	−0.927122	−	3.46007i	−0.0587540	−	0.219273i
$250$	−0.404340	−	0.0320845i	−0.0255727	−	0.00202920i
$251$	4.79096	−	1.98448i	0.302402	−	0.125259i	−0.226322	−	0.974052i	$-0.572670\pi$
$251$	4.79096	−	1.98448i	0.302402	−	0.125259i	0.528725	+	0.848793i	$0.322670\pi$
$252$	6.88113	−	3.43900i	0.433470	−	0.216637i
$253$	−0.466540	+	1.12633i	−0.0293311	+	0.0708116i
$254$	−9.21007	−	28.4080i	−0.577891	−	1.78247i
$255$	6.82601	−	11.8230i	0.427462	−	0.740385i
$256$	−12.8956	−	9.47119i	−0.805975	−	0.591949i
$257$	0.182664	+	0.316383i	0.0113943	+	0.0197354i	0.871666	−	0.490100i	$-0.163040\pi$
$257$	0.182664	+	0.316383i	0.0113943	+	0.0197354i	−0.860272	+	0.509835i	$0.829706\pi$
$258$	4.28520	+	0.913734i	0.266785	+	0.0568866i
$259$	8.27935	−	13.3161i	0.514454	−	0.827423i
$260$	−36.4960	−	16.3055i	−2.26338	−	1.01122i
$261$	5.24741	+	4.02648i	0.324806	+	0.249233i
$262$	−1.27847	−	2.68482i	−0.0789842	−	0.165869i
$263$	6.89813	+	25.7442i	0.425357	+	1.58745i	0.763143	+	0.646230i	$0.223655\pi$
$263$	6.89813	+	25.7442i	0.425357	+	1.58745i	−0.337786	+	0.941223i	$0.609678\pi$
$264$	−0.140427	+	1.31167i	−0.00864271	+	0.0807279i
$265$	−26.2873	−	26.2873i	−1.61482	−	1.61482i
$266$	11.6959	+	19.3949i	0.717122	+	1.18918i
$267$	−5.63572	−	13.6058i	−0.344901	−	0.832664i
$268$	25.1095	+	7.47299i	1.53381	+	0.456486i
$269$	2.08381	−	1.59896i	0.127052	−	0.0974906i	−0.543281	−	0.839551i	$-0.682818\pi$
$269$	2.08381	−	1.59896i	0.127052	−	0.0974906i	0.670333	+	0.742061i	$0.266151\pi$
$270$	1.28605	+	24.8457i	0.0782664	+	1.51206i
$271$	3.30653	−	1.90903i	0.200857	−	0.115965i	−0.396198	−	0.918165i	$-0.629671\pi$
$271$	3.30653	−	1.90903i	0.200857	−	0.115965i	0.597055	+	0.802200i	$0.296337\pi$
$272$	10.2979	−	9.22428i	0.624400	−	0.559304i
$273$	−19.3727	+	7.29274i	−1.17249	+	0.441377i
$274$	−2.08566	−	3.21618i	−0.126000	−	0.194296i
$275$	0.249206	+	1.89291i	0.0150277	+	0.114147i
$276$	4.23248	−	6.88684i	0.254765	−	0.414539i
$277$	7.67168	+	1.01000i	0.460947	+	0.0606848i	0.357424	−	0.933942i	$-0.383655\pi$
$277$	7.67168	+	1.01000i	0.460947	+	0.0606848i	0.103523	+	0.994627i	$0.466989\pi$
$278$	12.8589	−	10.9682i	0.771225	−	0.657829i
$279$	−3.26451	−	3.26451i	−0.195441	−	0.195441i
$280$	−22.0372	+	8.91156i	−1.31698	+	0.532568i
$281$	−19.8264	+	19.8264i	−1.18274	+	1.18274i	−0.203710	+	0.979031i	$0.565300\pi$
$281$	−19.8264	+	19.8264i	−1.18274	+	1.18274i	−0.979031	+	0.203710i	$0.934700\pi$
$282$	0.898713	−	11.3259i	0.0535176	−	0.674447i
$283$	−1.44667	+	10.9886i	−0.0859958	+	0.653203i	0.893108	+	0.449842i	$0.148520\pi$
$283$	−1.44667	+	10.9886i	−0.0859958	+	0.653203i	−0.979104	+	0.203361i	$0.934814\pi$
$284$	−1.48295	+	9.28550i	−0.0879970	+	0.550993i
$285$	−23.7047	+	3.12078i	−1.40414	+	0.184859i
$286$	−0.696001	+	3.26408i	−0.0411554	+	0.193009i
$287$	8.25486	−	10.0598i	0.487269	−	0.593813i
$288$	−2.15406	+	7.93665i	−0.126929	+	0.467672i
$289$	−2.52707	−	4.37702i	−0.148651	−	0.257472i
$290$	−15.1799	−	13.6858i	−0.891397	−	0.803658i
$291$	−3.63022	−	4.73099i	−0.212807	−	0.277336i
$292$	−8.16158	+	10.0522i	−0.477620	+	0.588260i
$293$	12.9244	−	5.35348i	0.755054	−	0.312754i	0.0282521	−	0.999601i	$-0.491006\pi$
$293$	12.9244	−	5.35348i	0.755054	−	0.312754i	0.726802	+	0.686847i	$0.241006\pi$
$294$	−4.86510	+	11.3076i	−0.283738	+	0.659471i
$295$	−13.6753	+	13.6753i	−0.796209	+	0.796209i
$296$	4.72979	+	16.0816i	0.274914	+	0.934727i
$297$	2.00644	−	0.537625i	0.116426	−	0.0311962i
$298$	−18.0729	−	6.41306i	−1.04694	−	0.371499i
$299$	12.4497	−	16.2248i	0.719987	−	0.938306i
$300$	0.347696	−	12.6545i	0.0200742	−	0.730609i
$301$	5.81351	−	3.10785i	0.335085	−	0.179133i
$302$	−1.38004	−	2.12807i	−0.0794121	−	0.122457i
$303$	9.51668	−	5.49446i	0.546719	−	0.315648i
$304$	−23.7955	−	4.47372i	−1.36476	−	0.256585i
$305$	23.4070	+	13.5141i	1.34028	+	0.773813i
$306$	−6.32933	−	3.23010i	−0.361824	−	0.184652i
$307$	−7.18125	−	2.97457i	−0.409856	−	0.169768i	0.168223	−	0.985749i	$-0.446197\pi$
$307$	−7.18125	−	2.97457i	−0.409856	−	0.169768i	−0.578078	+	0.815981i	$0.696197\pi$
$308$	1.11141	+	1.64434i	0.0633283	+	0.0936951i
$309$	3.30124	+	7.96991i	0.187801	+	0.453392i
$310$	9.25805	+	10.8539i	0.525822	+	0.616463i
$311$	12.5603	−	3.36552i	0.712230	−	0.190841i	0.115528	−	0.993304i	$-0.463144\pi$
$311$	12.5603	−	3.36552i	0.712230	−	0.190841i	0.596702	+	0.802463i	$0.296477\pi$
$312$	7.97031	−	20.6440i	0.451230	−	1.16873i
$313$	7.79717	+	2.08925i	0.440722	+	0.118091i	0.472355	−	0.881408i	$-0.343404\pi$
$313$	7.79717	+	2.08925i	0.440722	+	0.118091i	−0.0316327	+	0.999500i	$0.510071\pi$
$314$	1.96433	−	2.85418i	0.110854	−	0.161071i
$315$	8.35262	+	8.91690i	0.470617	+	0.502410i
$316$	−9.42959	+	21.1059i	−0.530456	+	1.18730i
$317$	17.7279	−	2.33392i	0.995698	−	0.131086i	0.384972	−	0.922928i	$-0.374211\pi$
$317$	17.7279	−	2.33392i	0.995698	−	0.131086i	0.610726	+	0.791842i	$0.290878\pi$
$318$	13.7811	−	15.2856i	0.772803	−	0.857173i
$319$	−0.853239	+	1.47785i	−0.0477722	+	0.0827439i
$320$	8.57534	−	23.9216i	0.479376	−	1.33726i
$321$	−14.2147			−0.793385
$322$	−1.81684	−	12.0252i	−0.101249	−	0.670140i
$323$	8.00618	−	19.3286i	0.445475	−	1.07547i
$324$	−5.02348	+	0.521442i	−0.279082	+	0.0289690i
$325$	4.18045	−	31.7537i	0.231890	−	1.76138i
$326$	−7.69356	−	16.1567i	−0.426107	−	0.894835i
$327$	−9.30837	−	2.49417i	−0.514754	−	0.137928i
$328$	2.14969	+	13.7446i	0.118697	+	0.758918i
$329$	−9.95748	−	13.8938i	−0.548973	−	0.765992i
$330$	−2.06035	+	0.380489i	−0.113418	+	0.0209452i
$331$	7.33144	−	9.55452i	0.402973	−	0.525164i	−0.547153	−	0.837033i	$-0.684288\pi$
$331$	7.33144	−	9.55452i	0.402973	−	0.525164i	0.950125	+	0.311869i	$0.100955\pi$
$332$	5.60402	−	1.33777i	0.307560	−	0.0734195i
$333$	6.83539	−	5.24498i	0.374577	−	0.287423i
$334$	9.75696	+	4.97934i	0.533877	+	0.272458i
$335$			41.6092i			2.27335i
$336$	−5.55753	−	11.9286i	−0.303188	−	0.650758i
$337$			6.60738i			0.359927i	0.983673	+	0.179963i	$0.0575979\pi$
$337$			6.60738i			0.359927i	−0.983673	+	0.179963i	$0.942402\pi$
$338$	17.0922	−	33.4920i	0.929695	−	1.82172i
$339$	5.17565	−	3.97142i	0.281103	−	0.215698i
$340$	18.7074	+	11.4971i	1.01455	+	0.623517i
$341$	0.725107	−	0.944978i	0.0392667	−	0.0511734i
$342$	2.26000	+	12.2379i	0.122207	+	0.661748i
$343$	5.37942	+	17.7218i	0.290462	+	0.956887i
$344$	−1.65839	+	6.84933i	−0.0894146	+	0.369291i
$345$	12.4012	+	3.32289i	0.667657	+	0.178898i
$346$	31.0537	−	14.7873i	1.66946	−	0.794971i
$347$	2.86524	−	21.7637i	0.153814	−	1.16833i	−0.724162	−	0.689630i	$-0.757773\pi$
$347$	2.86524	−	21.7637i	0.153814	−	1.16833i	0.877976	−	0.478705i	$-0.158894\pi$
$348$	7.13200	−	8.78410i	0.382315	−	0.470877i
$349$	0.537281	−	1.29711i	0.0287600	−	0.0694328i	−0.908847	−	0.417130i	$-0.863036\pi$
$349$	0.537281	−	1.29711i	0.0287600	−	0.0694328i	0.937607	+	0.347697i	$0.113036\pi$
$350$	−11.8803	−	14.8867i	−0.635029	−	0.795726i
$351$	−34.8455			−1.85992
$352$	−2.10269	−	0.283722i	−0.112074	−	0.0151224i
$353$	−14.4794	+	25.0790i	−0.770659	+	1.33482i	0.166543	+	0.986034i	$0.446739\pi$
$353$	−14.4794	+	25.0790i	−0.770659	+	1.33482i	−0.937202	+	0.348786i	$0.886594\pi$
$354$	−7.95197	−	7.16927i	−0.422642	−	0.381042i
$355$	−14.8069	+	1.94937i	−0.785870	+	0.103462i
$356$	22.1243	−	8.46001i	1.17259	−	0.448380i
$357$	11.0737	−	2.58274i	0.586082	−	0.136693i
$358$	−11.8203	−	8.13511i	−0.624724	−	0.429954i
$359$	−14.8064	−	3.96737i	−0.781453	−	0.209390i	−0.154028	−	0.988066i	$-0.549225\pi$
$359$	−14.8064	−	3.96737i	−0.781453	−	0.209390i	−0.627425	+	0.778677i	$0.715891\pi$
$360$	−13.0577	+	0.316661i	−0.688199	+	0.0166895i
$361$	−17.0388	+	4.56553i	−0.896779	+	0.240291i
$362$	−26.5944	+	22.6841i	−1.39777	+	1.19225i
$363$	−5.16748	−	12.4754i	−0.271223	−	0.654789i
$364$	−10.8694	−	31.4694i	−0.569711	−	1.64945i
$365$	−18.9998	−	7.86998i	−0.994495	−	0.411933i
$366$	−6.80161	+	13.3277i	−0.355526	+	0.696648i
$367$	−29.1816	−	16.8480i	−1.52327	−	0.879458i	−0.999621	−	0.0275203i	$-0.991239\pi$
$367$	−29.1816	−	16.8480i	−1.52327	−	0.879458i	−0.523644	−	0.851937i	$-0.675428\pi$
$368$	10.8856	+	7.10917i	0.567452	+	0.370591i
$369$	6.19243	−	3.57520i	0.322365	−	0.186118i
$370$	−22.3378	+	14.4859i	−1.16129	+	0.753085i
$371$	1.01121	−	30.9476i	0.0524994	−	1.60672i
$372$	−5.73583	+	5.42906i	−0.297389	+	0.281484i
$373$	−20.5591	+	26.7931i	−1.06451	+	1.38729i	−0.147204	+	0.989106i	$0.547028\pi$
$373$	−20.5591	+	26.7931i	−1.06451	+	1.38729i	−0.917304	+	0.398188i	$0.869639\pi$
$374$	0.613094	−	1.72778i	0.0317023	−	0.0893416i
$375$	0.344489	−	0.0923054i	0.0177893	−	0.00476663i
$376$	18.1700	+	1.94527i	0.937044	+	0.100320i
$377$	20.2418	−	20.2418i	1.04251	−	1.04251i
$378$	−14.3708	+	14.9291i	−0.739152	+	0.767868i
$379$	27.9121	−	11.5616i	1.43375	−	0.593877i	0.475473	−	0.879731i	$-0.342277\pi$
$379$	27.9121	−	11.5616i	1.43375	−	0.593877i	0.958273	+	0.285853i	$0.0922771\pi$
$380$	−3.97039	−	38.2500i	−0.203677	−	1.96218i
$381$	15.9850	+	20.8320i	0.818935	+	1.06726i
$382$	−14.4928	+	16.0751i	−0.741518	+	0.822472i
$383$	11.6683	+	20.2100i	0.596221	+	1.03268i	0.993373	+	0.114932i	$0.0366650\pi$
$383$	11.6683	+	20.2100i	0.596221	+	1.03268i	−0.397153	+	0.917752i	$0.630002\pi$
$384$	13.4708	+	4.05644i	0.687429	+	0.207004i
$385$	−1.99961	+	2.43684i	−0.101910	+	0.124193i
$386$	−9.34879	−	1.99345i	−0.475841	−	0.101464i
$387$	3.59119	−	0.472790i	0.182551	−	0.0240332i
$388$	7.76680	−	5.62763i	0.394300	−	0.285700i
$389$	−4.07539	+	30.9556i	−0.206630	+	1.56951i	0.502590	+	0.864525i	$0.332381\pi$
$389$	−4.07539	+	30.9556i	−0.206630	+	1.56951i	−0.709220	+	0.704987i	$0.750953\pi$
$390$	35.0367	+	2.78017i	1.77415	+	0.140780i
$391$	−7.94373	+	7.94373i	−0.401731	+	0.401731i
$392$	−17.9653	−	8.32158i	−0.907384	−	0.420303i
$393$	1.84885	+	1.84885i	0.0932619	+	0.0932619i
$394$	8.13955	+	9.54264i	0.410065	+	0.480751i
$395$	−36.4011	−	4.79230i	−1.83154	−	0.241127i
$396$	0.253216	+	1.06074i	0.0127246	+	0.0533044i
$397$	2.19735	+	16.6905i	0.110282	+	0.837674i	0.953772	+	0.300530i	$0.0971636\pi$
$397$	2.19735	+	16.6905i	0.110282	+	0.837674i	−0.843490	+	0.537144i	$0.819503\pi$
$398$	−11.7746	+	7.63575i	−0.590209	+	0.382746i
$399$	−15.3947	−	12.6325i	−0.770697	−	0.632415i
$400$	20.3304	+	1.11804i	1.01652	+	0.0559021i
$401$	−3.21196	+	1.85442i	−0.160397	+	0.0926055i	−0.578050	−	0.816001i	$-0.696186\pi$
$401$	−3.21196	+	1.85442i	−0.160397	+	0.0926055i	0.417653	+	0.908607i	$0.362853\pi$
$402$	−23.0042	+	1.19073i	−1.14735	+	0.0593884i
$403$	−15.8521	+	12.1637i	−0.789647	+	0.605917i
$404$	8.41353	+	15.5435i	0.418589	+	0.773320i
$405$	−3.06968	−	7.41086i	−0.152534	−	0.368249i
$406$	−0.324310	−	17.0203i	−0.0160952	−	0.844703i
$407$	1.57183	+	1.57183i	0.0779125	+	0.0779125i
$408$	−5.82098	+	10.6717i	−0.288182	+	0.528326i
$409$	2.91070	+	10.8629i	0.143925	+	0.537134i	0.999801	+	0.0199534i	$0.00635178\pi$
$409$	2.91070	+	10.8629i	0.143925	+	0.537134i	−0.855876	+	0.517181i	$0.826982\pi$
$410$	−19.9491	+	9.49945i	−0.985215	+	0.469144i
$411$	2.67396	+	2.05180i	0.131897	+	0.101208i
$412$	−12.9598	+	4.95563i	−0.638482	+	0.244146i
$413$	−16.0997	−	0.526058i	−0.792216	−	0.0258856i
$414$	1.39359	−	6.53562i	0.0684913	−	0.321208i
$415$	4.57537	+	7.92477i	0.224596	+	0.389012i
$416$	32.8390	+	13.7265i	1.61007	+	0.672999i
$417$	−7.43038	+	12.8698i	−0.363867	+	0.630237i
$418$	−3.05427	+	0.990217i	−0.149389	+	0.0484331i
$419$	1.89310	−	4.57034i	0.0924838	−	0.223276i	−0.870868	−	0.491517i	$-0.836443\pi$
$419$	1.89310	−	4.57034i	0.0924838	−	0.223276i	0.963352	+	0.268242i	$0.0864425\pi$
$420$	15.6407	−	13.8644i	0.763189	−	0.676512i
$421$	1.26507	−	0.524008i	0.0616556	−	0.0255386i	−0.351643	−	0.936134i	$-0.614377\pi$
$421$	1.26507	−	0.524008i	0.0616556	−	0.0255386i	0.413298	+	0.910596i	$0.364377\pi$
$422$	0.748520	−	9.43311i	0.0364374	−	0.459196i
$423$	−2.43095	−	9.07243i	−0.118197	−	0.441117i
$424$	23.9672	+	22.8323i	1.16395	+	1.10883i
$425$	−4.55352	+	16.9940i	−0.220878	+	0.824329i
$426$	−1.50147	−	8.13044i	−0.0727463	−	0.393921i
$427$	5.11328	+	21.9235i	0.247449	+	1.06095i
$428$	0.627942	−	22.8542i	0.0303527	−	1.10470i
$429$	−0.383032	−	2.90942i	−0.0184930	−	0.140468i
$430$	−11.1779	+	0.578584i	−0.539046	+	0.0279018i
$431$	−5.49609	−	3.17317i	−0.264737	−	0.152846i	0.361756	−	0.932273i	$-0.382177\pi$
$431$	−5.49609	−	3.17317i	−0.264737	−	0.152846i	−0.626494	+	0.779427i	$0.715511\pi$
$432$	−1.68113	−	22.0887i	−0.0808833	−	1.06274i
$433$			16.1671i			0.776941i	0.921461	+	0.388470i	$0.126996\pi$
$433$			16.1671i			0.776941i	−0.921461	+	0.388470i	$0.873004\pi$
$434$	−1.32624	+	11.8080i	−0.0636615	+	0.566805i
$435$	16.6030	+	6.87718i	0.796052	+	0.329736i
$436$	4.42131	−	14.8557i	0.211742	−	0.711460i
$437$	19.5064	+	2.56806i	0.933116	+	0.122847i
$438$	3.80731	−	10.7295i	0.181921	−	0.512677i
$439$	−0.895877	+	3.34346i	−0.0427579	+	0.159575i	−0.984004	−	0.178147i	$-0.942990\pi$
$439$	−0.895877	+	3.34346i	−0.0427579	+	0.159575i	0.941246	+	0.337722i	$0.109656\pi$
$440$	−0.520729	−	3.32941i	−0.0248248	−	0.158723i
$441$	−0.664317	+	10.1547i	−0.0316341	+	0.483557i
$442$	−17.4358	+	25.3342i	−0.829335	+	1.20503i
$443$	−19.0134	−	14.5895i	−0.903354	−	0.693168i	0.0487928	−	0.998809i	$-0.484463\pi$
$443$	−19.0134	−	14.5895i	−0.903354	−	0.693168i	−0.952147	+	0.305641i	$0.901129\pi$
$444$	−8.64798	−	11.9352i	−0.410415	−	0.566422i
$445$	22.9019	+	29.8464i	1.08566	+	1.41485i
$446$	4.55526	+	14.0505i	0.215698	+	0.665309i
$447$	16.8617			0.797533
$448$	19.4242	−	8.40839i	0.917707	−	0.397259i
$449$	−6.58655			−0.310838			−0.155419	−	0.987849i	$-0.549673\pi$
$449$	−6.58655			−0.310838			−0.155419	+	0.987849i	$0.549673\pi$
$450$	−3.22755	−	9.95522i	−0.152148	−	0.469294i
$451$	1.12305	+	1.46359i	0.0528825	+	0.0689178i
$452$	6.15657	+	8.49681i	0.289581	+	0.399656i
$453$	1.76930	+	1.35763i	0.0831290	+	0.0637871i
$454$	12.6825	−	18.4277i	0.595220	−	0.864856i
$455$	42.9806	−	30.8035i	2.01496	−	1.44409i
$456$	21.0335	−	3.28969i	0.984982	−	0.154054i
$457$	4.39682	−	16.4091i	0.205674	−	0.767587i	−0.783569	−	0.621305i	$-0.786603\pi$
$457$	4.39682	−	16.4091i	0.205674	−	0.767587i	0.989243	−	0.146282i	$-0.0467307\pi$
$458$	6.42931	−	18.1187i	0.300422	−	0.846631i
$459$	18.9776	+	2.49845i	0.885800	+	0.116618i
$460$	−5.89033	+	19.7917i	−0.274638	+	0.922793i
$461$	7.23732	+	2.99780i	0.337076	+	0.139621i	0.544800	−	0.838566i	$-0.316606\pi$
$461$	7.23732	+	2.99780i	0.337076	+	0.139621i	−0.207724	+	0.978187i	$0.566606\pi$
$462$	−1.40447	−	1.03578i	−0.0653416	−	0.0481888i
$463$			22.8395i			1.06144i	0.847546	+	0.530721i	$0.178079\pi$
$463$			22.8395i			1.06144i	−0.847546	+	0.530721i	$0.821921\pi$
$464$	13.8079	+	11.8548i	0.641017	+	0.550345i
$465$	−10.8631	−	6.27184i	−0.503766	−	0.290850i
$466$	6.27057	−	0.324574i	0.290479	−	0.0150356i
$467$	2.23063	+	16.9433i	0.103221	+	0.784042i	0.962260	+	0.272132i	$0.0877286\pi$
$467$	2.23063	+	16.9433i	0.103221	+	0.784042i	−0.859039	+	0.511910i	$0.828938\pi$
$468$	0.502457	−	18.2871i	0.0232261	−	0.845321i
$469$	−25.2932	+	23.6926i	−1.16793	+	1.09402i
$470$	5.27072	+	28.5409i	0.243120	+	1.31650i
$471$	−0.788493	+	2.94270i	−0.0363318	+	0.135592i
$472$	11.8780	−	12.4684i	0.546727	−	0.573904i
$473$	0.241874	+	0.902685i	0.0111214	+	0.0415055i
$474$	1.60780	−	20.2620i	0.0738486	−	0.930666i
$475$	28.4665	−	11.7912i	1.30613	−	0.541019i
$476$	3.66332	+	17.9183i	0.167908	+	0.821282i
$477$	6.51096	−	15.7188i	0.298116	−	0.719717i
$478$	−0.459241	+	0.148889i	−0.0210052	+	0.00681003i
$479$	−8.59756	+	14.8914i	−0.392832	+	0.680406i	−0.992822	−	0.119602i	$-0.961838\pi$
$479$	−8.59756	+	14.8914i	−0.392832	+	0.680406i	0.599989	+	0.800008i	$0.295171\pi$
$480$	−0.0720129	+	22.3440i	−0.00328692	+	1.01986i
$481$	−18.6446	−	32.2934i	−0.850121	−	1.47245i
$482$	−1.63212	+	7.65424i	−0.0743409	+	0.348641i
$483$	5.04142	+	9.43044i	0.229393	+	0.429100i
$484$	20.2861	−	7.75712i	0.922096	−	0.352596i
$485$	12.0856	+	9.27358i	0.548777	+	0.421092i
$486$	−17.2046	+	8.19259i	−0.780419	+	0.371623i
$487$	−6.98677	−	26.0750i	−0.316601	−	1.18157i	−0.922490	−	0.386021i	$-0.873849\pi$
$487$	−6.98677	−	26.0750i	−0.316601	−	1.18157i	0.605889	−	0.795549i	$-0.292817\pi$
$488$	−21.1276	−	11.5243i	−0.956402	−	0.521681i
$489$	11.1259	+	11.1259i	0.503133	+	0.503133i
$490$	4.52849	−	31.1182i	0.204576	−	1.40578i
$491$	−1.43745	−	3.47031i	−0.0648712	−	0.156613i	0.888119	−	0.459613i	$-0.152012\pi$
$491$	−1.43745	−	3.47031i	−0.0648712	−	0.156613i	−0.952991	+	0.303000i	$0.902012\pi$
$492$	−5.82280	−	10.7573i	−0.262512	−	0.484977i
$493$	−12.4755	+	9.57277i	−0.561867	+	0.431136i
$494$	53.7890	−	2.78420i	2.42008	−	0.125267i
$495$	−1.50002	+	0.866037i	−0.0674209	+	0.0389255i
$496$	−8.47540	−	9.46184i	−0.380557	−	0.424849i
$497$	−9.61614	−	7.89077i	−0.431343	−	0.353949i
$498$	−4.25039	+	2.75634i	−0.190465	+	0.123515i
$499$	4.76801	+	36.2166i	0.213445	+	1.62128i	0.677536	+	0.735490i	$0.263048\pi$
$499$	4.76801	+	36.2166i	0.213445	+	1.62128i	−0.464091	+	0.885788i	$0.653619\pi$
$500$	0.133190	+	0.557943i	0.00595643	+	0.0249520i
$501$	−9.54919	−	1.25718i	−0.426627	−	0.0561665i
$502$	−4.75925	−	5.57964i	−0.212416	−	0.249032i
$503$	11.4983	+	11.4983i	0.512683	+	0.512683i	0.915348	−	0.402664i	$-0.131916\pi$
$503$	11.4983	+	11.4983i	0.512683	+	0.512683i	−0.402664	+	0.915348i	$0.631916\pi$
$504$	−7.62761	−	7.75711i	−0.339761	−	0.345529i
$505$	−19.8497	+	19.8497i	−0.883302	+	0.883302i
$506$	1.71870	+	0.136380i	0.0764057	+	0.00606282i
$507$	−4.31541	+	32.7788i	−0.191654	+	1.45576i
$508$	−34.1997	+	24.7802i	−1.51736	+	1.09944i
$509$	21.4112	−	2.81884i	0.949037	−	0.124943i	0.359913	−	0.932986i	$-0.382806\pi$
$509$	21.4112	−	2.81884i	0.949037	−	0.124943i	0.589124	+	0.808043i	$0.299473\pi$
$510$	−18.8824	−	4.02630i	−0.836126	−	0.178288i
$511$	−6.03466	−	16.0307i	−0.266958	−	0.709157i
$512$	−7.11698	+	21.4790i	−0.314529	+	0.949248i
$513$	−16.7615	−	29.0317i	−0.740036	−	1.28178i
$514$	0.345955	−	0.383724i	0.0152594	−	0.0169253i
$515$	−13.4153	−	17.4831i	−0.591148	−	0.770400i
$516$	−0.639757	−	6.16331i	−0.0281637	−	0.271324i
$517$	2.23881	−	0.927346i	0.0984628	−	0.0407846i
$518$	−21.5249	−	5.33023i	−0.945750	−	0.234197i
$519$	−21.3845	+	21.3845i	−0.938675	+	0.938675i
$520$	−6.01770	+	56.2088i	−0.263894	+	2.46492i
$521$	9.31869	−	2.49694i	0.408259	−	0.109393i	−0.0488438	−	0.998806i	$-0.515554\pi$
$521$	9.31869	−	2.49694i	0.408259	−	0.109393i	0.457103	+	0.889414i	$0.348887\pi$
$522$	3.12808	−	8.81537i	0.136912	−	0.385838i
$523$	2.89302	−	3.77026i	0.126503	−	0.164862i	−0.725808	−	0.687898i	$-0.758534\pi$
$523$	2.89302	−	3.77026i	0.126503	−	0.164862i	0.852311	+	0.523036i	$0.175201\pi$
$524$	−3.05423	+	2.89088i	−0.133425	+	0.126289i
$525$	14.2219	+	8.84250i	0.620693	+	0.385918i
$526$	31.6245	−	20.5082i	1.37889	−	0.894200i
$527$	9.50551	−	5.48801i	0.414067	−	0.239061i
$528$	1.82581	−	0.383171i	0.0794583	−	0.0166754i
$529$	10.7692	+	6.21760i	0.468226	+	0.270330i
$530$	−23.8986	+	46.8289i	−1.03809	+	2.03412i
$531$	−8.17736	−	3.38717i	−0.354867	−	0.146991i
$532$	20.9904	−	24.1933i	0.910051	−	1.04891i
$533$	−11.8429	−	28.5912i	−0.512972	−	1.23842i
$534$	−15.8456	+	13.5158i	−0.685707	+	0.584885i
$535$	35.0748	−	9.39826i	1.51642	−	0.406322i
$536$	−0.898221	−	37.0386i	−0.0387972	−	1.59982i
$537$	12.1869	+	3.26547i	0.525904	+	0.140916i
$538$	−3.05990	−	2.10592i	−0.131922	−	0.0907926i
$539$	−2.61989	+	0.172041i	−0.112846	+	0.00741031i
$540$	32.8634	−	12.5665i	1.41422	−	0.540776i
$541$	−40.9773	+	5.39477i	−1.76175	+	0.231939i	−0.940778	−	0.339024i	$-0.889903\pi$
$541$	−40.9773	+	5.39477i	−1.76175	+	0.231939i	−0.820976	+	0.570963i	$0.806570\pi$
$542$	−4.01031	−	3.61558i	−0.172258	−	0.155303i
$543$	15.3673	−	26.6169i	0.659473	−	1.14224i
$544$	−16.9006	−	9.83035i	−0.724609	−	0.421473i
$545$	24.6176			1.05450
$546$	18.2602	+	22.8810i	0.781462	+	0.979215i
$547$	14.7655	−	35.6471i	0.631328	−	1.52416i	−0.206627	−	0.978420i	$-0.566249\pi$
$547$	14.7655	−	35.6471i	0.631328	−	1.52416i	0.837955	−	0.545740i	$-0.183751\pi$
$548$	−3.41699	+	4.20853i	−0.145967	+	0.179780i
$549$	−1.61457	+	12.2639i	−0.0689083	+	0.523411i
$550$	2.43780	−	1.16084i	0.103948	−	0.0494985i
$551$	26.6013	+	7.12779i	1.13325	+	0.303654i
$552$	−11.1107	−	2.69018i	−0.472903	−	0.114502i
$553$	−17.8139	−	24.8561i	−0.757525	−	1.05699i
$554$	−1.98727	−	10.7611i	−0.0844310	−	0.457193i
$555$	14.2507	−	18.5719i	0.604909	−	0.788333i
$556$	−20.3637	−	12.5150i	−0.863613	−	0.530755i
$557$	10.0135	−	7.68365i	0.424287	−	0.325567i	−0.374450	−	0.927247i	$-0.622169\pi$
$557$	10.0135	−	7.68365i	0.424287	−	0.325567i	0.798737	+	0.601680i	$0.205502\pi$
$558$	−2.96786	+	5.81548i	−0.125639	+	0.246189i
$559$		−	15.6768i		−	0.663057i
$560$	21.6001	+	25.7595i	0.912769	+	1.08854i
$561$			1.61200i			0.0680585i
$562$	35.3192	+	18.0247i	1.48985	+	0.760327i
$563$	−14.1453	+	10.8540i	−0.596152	+	0.457444i	−0.862236	−	0.506506i	$-0.830937\pi$
$563$	−14.1453	+	10.8540i	−0.596152	+	0.457444i	0.266084	+	0.963950i	$0.414270\pi$
$564$	−15.6285	+	3.73076i	−0.658077	+	0.157093i
$565$	−10.1452	+	13.2215i	−0.426812	+	0.556232i
$566$	15.4137	−	2.84648i	0.647884	−	0.119646i
$567$	2.75698	−	6.08578i	0.115782	−	0.255579i
$568$	13.1384	−	2.05488i	0.551274	−	0.0862207i
$569$	−37.1117	−	9.94404i	−1.55580	−	0.416876i	−0.624470	−	0.781049i	$-0.714685\pi$
$569$	−37.1117	−	9.94404i	−1.55580	−	0.416876i	−0.931331	+	0.364173i	$0.881352\pi$
$570$	14.5371	+	30.5283i	0.608892	+	1.27869i
$571$	1.47638	−	11.2142i	0.0617847	−	0.469301i	−0.932384	−	0.361468i	$-0.882276\pi$
$571$	1.47638	−	11.2142i	0.0617847	−	0.469301i	0.994169	−	0.107833i	$-0.0343911\pi$
$572$	4.69466	−	0.487310i	0.196294	−	0.0203755i
$573$	7.28271	−	17.5820i	0.304240	−	0.734500i
$574$	−17.1336	−	6.71750i	−0.715144	−	0.280383i
$575$	−16.5452			−0.689984
$576$	11.6165	−	0.563754i	0.484021	−	0.0234897i
$577$	4.87229	−	8.43905i	0.202836	−	0.351322i	−0.746605	−	0.665267i	$-0.768317\pi$
$577$	4.87229	−	8.43905i	0.202836	−	0.351322i	0.949441	+	0.313945i	$0.101651\pi$
$578$	−4.78613	+	5.30865i	−0.199077	+	0.220811i
$579$	8.33299	−	1.09706i	0.346307	−	0.0455922i
$580$	−11.7905	+	26.3903i	−0.489574	+	1.09580i
$581$	−2.21202	+	7.29367i	−0.0917700	+	0.302592i
$582$	−4.78118	+	6.94707i	−0.198186	+	0.287965i
$583$	4.24006	+	1.13612i	0.175605	+	0.0470533i
$584$	17.0827	+	6.59535i	0.706885	+	0.272917i
$585$	28.0656	−	7.52015i	1.16037	−	0.310920i
$586$	−12.8389	−	15.0521i	−0.530370	−	0.621795i
$587$	7.17747	+	17.3280i	0.296246	+	0.715201i	0.999989	+	0.00474619i	$0.00151077\pi$
$587$	7.17747	+	17.3280i	0.296246	+	0.715201i	−0.703743	+	0.710455i	$0.748489\pi$
$588$	17.3337	+	1.61313i	0.714831	+	0.0665244i
$589$	−17.7594	−	7.35619i	−0.731764	−	0.303106i
$590$	24.3616	+	12.4327i	1.00295	+	0.511844i
$591$	−9.55073	−	5.51412i	−0.392865	−	0.226820i
$592$	19.5714	−	13.3769i	0.804380	−	0.549787i
$593$	−7.23529	+	4.17730i	−0.297118	+	0.171541i	−0.641147	−	0.767418i	$-0.721541\pi$
$593$	−7.23529	+	4.17730i	−0.297118	+	0.171541i	0.344030	+	0.938959i	$0.388208\pi$
$594$	−1.59836	−	2.46474i	−0.0655817	−	0.101130i
$595$	−25.6168	+	13.6945i	−1.05019	+	0.561420i
$596$	−0.744879	+	27.1101i	−0.0305114	+	1.11047i
$597$	7.51179	−	9.78955i	0.307437	−	0.400660i
$598$	−27.2568	−	9.67193i	−1.11462	−	0.395515i
$599$	−26.8646	+	7.19836i	−1.09766	+	0.294117i	−0.761811	−	0.647799i	$-0.775690\pi$
$599$	−26.8646	+	7.19836i	−1.09766	+	0.294117i	−0.335848	+	0.941916i	$0.609023\pi$
$600$	−17.1755	+	5.05151i	−0.701187	+	0.206227i
$601$	−5.37678	+	5.37678i	−0.219324	+	0.219324i	−0.808213	−	0.588890i	$-0.799565\pi$
$601$	−5.37678	+	5.37678i	−0.219324	+	0.219324i	0.588890	+	0.808213i	$0.299565\pi$
$602$	−6.71648	−	6.46531i	−0.273743	−	0.263506i
$603$	−17.5934	+	7.28741i	−0.716457	+	0.296766i
$604$	−2.26095	+	2.78469i	−0.0919966	+	0.113307i
$605$	20.9991	+	27.3666i	0.853736	+	1.11261i
$606$	−11.5423	−	10.4062i	−0.468873	−	0.422722i
$607$	−8.06089	−	13.9619i	−0.327181	−	0.566695i	0.654770	−	0.755828i	$-0.272765\pi$
$607$	−8.06089	−	13.9619i	−0.327181	−	0.566695i	−0.981951	+	0.189133i	$0.939432\pi$
$608$	4.35997	+	33.9627i	0.176820	+	1.37737i
$609$	5.27339	+	14.0084i	0.213689	+	0.567651i
$610$	7.97122	−	37.3831i	0.322745	−	1.51360i
$611$	−40.3028	+	5.30596i	−1.63047	+	0.214656i
$612$	−1.58485	+	9.92352i	−0.0640636	+	0.401134i
$613$	1.20131	−	9.12487i	0.0485205	−	0.368550i	−0.949909	−	0.312527i	$-0.898825\pi$
$613$	1.20131	−	9.12487i	0.0485205	−	0.368550i	0.998429	−	0.0560233i	$-0.0178421\pi$
$614$	−0.869532	+	10.9581i	−0.0350915	+	0.442235i
$615$	13.7375	−	13.7375i	0.553950	−	0.553950i
$616$	1.72736	−	2.21233i	0.0695973	−	0.0891373i
$617$	30.2880	+	30.2880i	1.21935	+	1.21935i	0.967860	+	0.251491i	$0.0809209\pi$
$617$	30.2880	+	30.2880i	1.21935	+	1.21935i	0.251491	+	0.967860i	$0.419079\pi$
$618$	9.28191	−	7.91716i	0.373373	−	0.318475i
$619$	45.9581	+	6.05050i	1.84721	+	0.243190i	0.971058	−	0.238843i	$-0.0767682\pi$
$619$	45.9581	+	6.05050i	1.84721	+	0.243190i	0.876153	+	0.482033i	$0.160101\pi$
$620$	10.5637	−	17.1886i	0.424248	−	0.690311i
$621$	2.34960	+	17.8470i	0.0942860	+	0.716173i
$622$	−10.0057	−	15.4292i	−0.401193	−	0.618656i
$623$	−5.10234	+	30.9162i	−0.204421	+	1.23863i
$624$	−31.2481	−	1.71844i	−1.25093	−	0.0687928i
$625$	21.2526	−	12.2702i	0.850104	−	0.490808i
$626$	−0.590111	−	11.4006i	−0.0235856	−	0.455659i
$627$	2.23975	−	1.71862i	0.0894469	−	0.0686350i
$628$	−4.69640	−	1.39773i	−0.187407	−	0.0557754i
$629$	7.83879	+	18.9245i	0.312553	+	0.754570i
$630$	8.35273	−	15.1257i	0.332781	−	0.602622i
$631$	−26.3453	−	26.3453i	−1.04879	−	1.04879i	−0.998747	−	0.0500421i	$-0.984064\pi$
$631$	−26.3453	−	26.3453i	−1.04879	−	1.04879i	−0.0500421	−	0.998747i	$-0.515936\pi$
$632$	32.5061	+	3.48009i	1.29302	+	0.138431i
$633$	2.15345	+	8.03680i	0.0855921	+	0.319434i
$634$	−10.8718	−	22.8310i	−0.431774	−	0.906736i
$635$	−53.2165	−	40.8345i	−2.11183	−	1.62047i
$636$	−26.5740	−	11.8726i	−1.05373	−	0.470778i
$637$	43.1982	+	8.58711i	1.71157	+	0.340234i
$638$	2.36026	+	0.503280i	0.0934437	+	0.0199250i
$639$	−3.41751	−	5.91931i	−0.135195	−	0.234164i
$640$	−35.9213	−	1.10284i	−1.41991	−	0.0435937i
$641$	8.17018	−	14.1512i	0.322703	−	0.558937i	−0.658342	−	0.752719i	$-0.728742\pi$
$641$	8.17018	−	14.1512i	0.322703	−	0.558937i	0.981045	+	0.193782i	$0.0620753\pi$
$642$	6.19971	+	19.1227i	0.244683	+	0.754712i
$643$	4.24848	−	10.2567i	0.167544	−	0.404486i	−0.817700	−	0.575645i	$-0.804751\pi$
$643$	4.24848	−	10.2567i	0.167544	−	0.404486i	0.985243	+	0.171159i	$0.0547510\pi$
$644$	−15.3849	+	7.68895i	−0.606249	+	0.302987i
$645$	9.09239	−	3.76619i	0.358013	−	0.148294i
$646$	−29.4943	−	2.34038i	−1.16044	−	0.0920810i
$647$	9.07915	+	33.8838i	0.356938	+	1.33211i	0.878028	+	0.478609i	$0.158859\pi$
$647$	9.07915	+	33.8838i	0.356938	+	1.33211i	−0.521090	+	0.853502i	$0.674474\pi$
$648$	2.89247	+	6.53055i	0.113627	+	0.256544i
$649$	0.591039	−	2.20579i	0.0232003	−	0.0865848i
$650$	−44.5408	+	8.22546i	−1.74703	+	0.322629i
$651$	−2.37306	−	10.1747i	−0.0930075	−	0.398776i
$652$	−18.3797	+	17.3967i	−0.719804	+	0.681307i
$653$	−5.23135	−	39.7360i	−0.204718	−	1.55499i	−0.717553	−	0.696504i	$-0.754738\pi$
$653$	−5.23135	−	39.7360i	−0.204718	−	1.55499i	0.512835	−	0.858487i	$-0.328595\pi$
$654$	0.704483	+	13.6102i	0.0275475	+	0.532200i
$655$	−5.78444	−	3.33965i	−0.226017	−	0.130491i
$656$	17.5527	−	8.88662i	0.685318	−	0.346964i
$657$		−	9.41192i		−	0.367194i
$658$	−14.3481	+	19.4554i	−0.559348	+	0.758449i
$659$	7.00413	+	2.90121i	0.272842	+	0.113015i	0.514910	−	0.857244i	$-0.327825\pi$
$659$	7.00413	+	2.90121i	0.272842	+	0.113015i	−0.242067	+	0.970259i	$0.577825\pi$
$660$	1.41048	+	2.60579i	0.0549029	+	0.101430i
$661$	18.4718	+	2.43186i	0.718471	+	0.0945885i	0.480892	−	0.876780i	$-0.340313\pi$
$661$	18.4718	+	2.43186i	0.718471	+	0.0945885i	0.237579	+	0.971368i	$0.423646\pi$
$662$	−16.0511	−	5.69564i	−0.623844	−	0.221367i
$663$	6.99881	−	26.1199i	0.271811	−	1.01441i
$664$	−4.24386	−	6.95550i	−0.164694	−	0.269926i
$665$	46.3386	+	20.9923i	1.79694	+	0.814047i
$666$	−10.0372	−	6.90791i	−0.388934	−	0.267676i
$667$	−11.7322	−	9.00243i	−0.454273	−	0.348576i
$668$	2.44312	−	15.2976i	0.0945270	−	0.591880i
$669$	−7.90611	−	10.3034i	−0.305668	−	0.398354i
$670$	55.9759	−	18.1478i	2.16254	−	0.701110i
$671$	−3.19141			−0.123203
$672$	−13.6234	+	12.6791i	−0.525533	+	0.489106i
$673$	0.130380			0.00502578			0.00251289	−	0.999997i	$-0.499200\pi$
$673$	0.130380			0.00502578			0.00251289	+	0.999997i	$0.499200\pi$
$674$	8.88876	−	2.88180i	0.342382	−	0.111003i
$675$	17.1615	+	22.3653i	0.660545	+	0.860839i
$676$	−52.5108	−	8.38630i	−2.01965	−	0.322550i
$677$	−24.2622	−	18.6171i	−0.932474	−	0.715512i	0.0263086	−	0.999654i	$-0.491625\pi$
$677$	−24.2622	−	18.6171i	−0.932474	−	0.715512i	−0.958782	+	0.284142i	$0.908291\pi$
$678$	−7.60002	−	5.23057i	−0.291877	−	0.200879i
$679$	1.24443	+	12.6270i	0.0477569	+	0.484578i
$680$	7.30759	−	30.1811i	0.280233	−	1.15739i
$681$	−5.09083	+	18.9992i	−0.195081	+	0.728052i
$682$	−1.58751	−	0.563320i	−0.0607890	−	0.0215706i
$683$	−16.1487	−	2.12602i	−0.617915	−	0.0813500i	−0.184931	−	0.982752i	$-0.559206\pi$
$683$	−16.1487	−	2.12602i	−0.617915	−	0.0813500i	−0.432984	+	0.901402i	$0.642539\pi$
$684$	15.4777	−	8.37786i	0.591803	−	0.320336i
$685$	−7.95461	−	3.29491i	−0.303930	−	0.125892i
$686$	21.4945	−	14.9662i	0.820664	−	0.571411i
$687$			16.9045i			0.644946i
$688$	9.93756	−	0.756327i	0.378866	−	0.0288347i
$689$	−63.7709	−	36.8181i	−2.42948	−	1.40266i
$690$	−0.938555	−	18.1323i	−0.0357302	−	0.690286i
$691$	−0.0938931	−	0.713189i	−0.00357186	−	0.0271310i	0.989566	−	0.144079i	$-0.0460221\pi$
$691$	−0.0938931	−	0.713189i	−0.00357186	−	0.0271310i	−0.993138	+	0.116948i	$0.962689\pi$
$692$	−33.4371	−	35.3265i	−1.27109	−	1.34291i
$693$	−1.38056	−	0.418697i	−0.0524433	−	0.0159050i
$694$	−30.5279	+	5.63765i	−1.15882	+	0.214002i
$695$	9.82545	−	36.6691i	0.372700	−	1.39094i
$696$	−14.9277	−	5.76334i	−0.565832	−	0.218459i
$697$	4.39987	+	16.4205i	0.166657	+	0.621972i
$698$	−1.97931	−	0.157059i	−0.0749180	−	0.00594477i
$699$	−5.10065	+	2.11276i	−0.192924	+	0.0799118i
$700$	−14.8451	+	22.4751i	−0.561094	+	0.849480i
$701$	9.54600	−	23.0461i	0.360547	−	0.870438i	−0.634673	−	0.772781i	$-0.718865\pi$
$701$	9.54600	−	23.0461i	0.360547	−	0.870438i	0.995220	−	0.0976572i	$-0.0311349\pi$
$702$	15.1979	+	46.8770i	0.573606	+	1.76926i
$703$	17.9369	−	31.0676i	0.676503	−	1.17174i
$704$	0.535402	+	2.95245i	0.0201787	+	0.111275i
$705$	−12.7598	−	22.1005i	−0.480560	−	0.832354i
$706$	40.0534	+	8.54060i	1.50743	+	0.321430i
$707$	−23.3687	−	0.763572i	−0.878872	−	0.0287171i
$708$	−6.17642	+	13.8245i	−0.232124	+	0.519556i
$709$	−4.20308	−	3.22513i	−0.157850	−	0.121122i	0.526817	−	0.849979i	$-0.323385\pi$
$709$	−4.20308	−	3.22513i	−0.157850	−	0.121122i	−0.684666	+	0.728857i	$0.740052\pi$
$710$	9.08046	+	19.0692i	0.340784	+	0.715655i
$711$	−4.34897	−	16.2306i	−0.163099	−	0.608694i
$712$	−21.0306	−	26.0735i	−0.788154	−	0.977146i
$713$	7.29881	+	7.29881i	0.273343	+	0.273343i
$714$	−8.30428	−	13.7707i	−0.310780	−	0.515357i
$715$	2.86875	+	6.92577i	0.107285	+	0.259009i
$716$	−5.78856	+	19.4497i	−0.216329	+	0.726871i
$717$	0.336769	−	0.258412i	0.0125769	−	0.00965056i
$718$	1.12059	+	21.6491i	0.0418201	+	0.807938i
$719$	37.7629	−	21.8024i	1.40832	−	0.813094i	0.413094	−	0.910688i	$-0.364448\pi$
$719$	37.7629	−	21.8024i	1.40832	−	0.813094i	0.995226	+	0.0975942i	$0.0311147\pi$
$720$	6.12108	+	17.4281i	0.228119	+	0.649506i
$721$	2.98880	−	18.1098i	0.111309	−	0.674446i
$722$	13.5734	+	20.9307i	0.505148	+	0.778959i
$723$	−0.898208	−	6.82257i	−0.0334047	−	0.253734i
$724$	42.1155	+	25.8832i	1.56521	+	0.961941i
$725$	−22.9611	−	3.02289i	−0.852755	−	0.112267i
$726$	−14.5291	+	12.3928i	−0.539226	+	0.459941i
$727$	−21.0735	−	21.0735i	−0.781573	−	0.781573i	0.198523	−	0.980096i	$-0.436385\pi$
$727$	−21.0735	−	21.0735i	−0.781573	−	0.781573i	−0.980096	+	0.198523i	$0.936385\pi$
$728$	−37.5945	+	28.3477i	−1.39334	+	1.05064i
$729$	17.2044	−	17.2044i	0.637202	−	0.637202i
$730$	−2.30056	+	28.9925i	−0.0851477	+	1.07306i
$731$	−1.12404	+	8.53790i	−0.0415740	+	0.315786i
$732$	20.8959	+	3.33721i	0.772336	+	0.123347i
$733$	−19.0528	+	2.50835i	−0.703731	+	0.0926479i	−0.473895	−	0.880581i	$-0.657152\pi$
$733$	−19.0528	+	2.50835i	−0.703731	+	0.0926479i	−0.229836	+	0.973229i	$0.573819\pi$
$734$	−9.93772	+	46.6056i	−0.366808	+	1.72024i
$735$	5.39748	+	27.1175i	0.199089	+	1.00024i
$736$	4.81606	−	17.7448i	0.177522	−	0.654083i
$737$	−2.45655	−	4.25487i	−0.0904882	−	0.156730i
$738$	−7.51047	−	6.77123i	−0.276464	−	0.249252i
$739$	22.5773	+	29.4233i	0.830520	+	1.08235i	0.995378	+	0.0960372i	$0.0306168\pi$
$739$	22.5773	+	29.4233i	0.830520	+	1.08235i	−0.164858	+	0.986317i	$0.552717\pi$
$740$	29.2302	+	23.7326i	1.07452	+	0.872427i
$741$	−43.7534	+	18.1232i	−1.60732	+	0.665774i
$742$	−42.0741	+	12.1374i	−1.54459	+	0.445578i
$743$	−4.82781	+	4.82781i	−0.177115	+	0.177115i	−0.790097	−	0.612982i	$-0.789970\pi$
$743$	−4.82781	+	4.82781i	−0.177115	+	0.177115i	0.612982	+	0.790097i	$0.289970\pi$
$744$	9.80527	+	5.34840i	0.359479	+	0.196082i
$745$	−41.6065	+	11.1484i	−1.52434	+	0.408447i
$746$	45.0110	+	15.9719i	1.64797	+	0.584772i
$747$	−2.54945	+	3.32251i	−0.0932797	+	0.121564i
$748$	−2.59175	−	0.0712110i	−0.0947638	−	0.00260373i
$749$	25.6848	+	15.9696i	0.938502	+	0.583518i
$750$	−0.274425	−	0.423174i	−0.0100206	−	0.0154521i
$751$	−38.6912	+	22.3384i	−1.41186	+	0.815139i	−0.995564	−	0.0940891i	$-0.970006\pi$
$751$	−38.6912	+	22.3384i	−1.41186	+	0.815139i	−0.416298	+	0.909228i	$0.636673\pi$
$752$	−5.30788	−	25.2921i	−0.193558	−	0.922307i
$753$	5.58437	+	3.22414i	0.203506	+	0.117494i
$754$	−36.0593	−	18.4024i	−1.31320	−	0.670177i
$755$	−5.26339	−	2.18017i	−0.191554	−	0.0793443i
$756$	26.3515	+	12.8214i	0.958396	+	0.466309i
$757$	−7.00128	−	16.9026i	−0.254466	−	0.614335i	0.744089	−	0.668081i	$-0.232884\pi$
$757$	−7.00128	−	16.9026i	−0.254466	−	0.614335i	−0.998555	+	0.0537460i	$0.982884\pi$
$758$	−27.7273	−	32.5069i	−1.00710	−	1.18070i
$759$	−1.46430	+	0.392358i	−0.0531507	+	0.0142417i
$760$	−49.7252	+	22.0240i	−1.80372	+	0.798894i
$761$	−20.1463	−	5.39820i	−0.730304	−	0.195684i	−0.125540	−	0.992089i	$-0.540066\pi$
$761$	−20.1463	−	5.39820i	−0.730304	−	0.195684i	−0.604765	+	0.796404i	$0.706733\pi$
$762$	21.0530	−	30.5901i	0.762671	−	1.10816i
$763$	14.0174	+	14.9644i	0.507464	+	0.541747i
$764$	27.9465	+	12.4858i	1.01107	+	0.451719i
$765$	−15.8243	+	2.08331i	−0.572130	+	0.0753223i
$766$	22.0990	−	24.5117i	0.798470	−	0.885642i
$767$	−19.1538	+	33.1753i	−0.691602	+	1.19789i
$768$	−0.418240	−	19.8912i	−0.0150919	−	0.717762i
$769$	25.1487			0.906887			0.453443	−	0.891285i	$-0.350195\pi$
$769$	25.1487			0.906887			0.453443	+	0.891285i	$0.350195\pi$
$770$	4.15035	+	1.62721i	0.149568	+	0.0586405i
$771$	−0.173844	+	0.419696i	−0.00626083	+	0.0151150i
$772$	1.39573	+	13.4462i	0.0502333	+	0.483938i
$773$	6.22041	−	47.2487i	0.223733	−	1.69942i	−0.398973	−	0.916963i	$-0.630633\pi$
$773$	6.22041	−	47.2487i	0.223733	−	1.69942i	0.622705	−	0.782456i	$-0.286033\pi$
$774$	−2.20233	−	4.62495i	−0.0791611	−	0.166240i
$775$	15.6143	+	4.18384i	0.560882	+	0.150288i
$776$	−10.9582	−	7.99403i	−0.393377	−	0.286969i
$777$	19.4038	−	1.91232i	0.696109	−	0.0686040i
$778$	43.4214	−	8.01874i	1.55673	−	0.287486i
$779$	18.1242	−	23.6199i	0.649367	−	0.846271i
$780$	−11.5411	−	48.3467i	−0.413238	−	1.73109i
$781$	1.39904	−	1.07352i	0.0500615	−	0.0384135i
$782$	14.1512	+	7.22187i	0.506045	+	0.258254i
$783$			25.1969i			0.900463i
$784$	−3.35930	+	27.7978i	−0.119975	+	0.992777i
$785$		−	7.78246i		−	0.277768i
$786$	1.68084	−	3.29358i	0.0599536	−	0.117478i
$787$	−2.14091	+	1.64278i	−0.0763152	+	0.0585587i	−0.646215	−	0.763156i	$-0.723649\pi$
$787$	−2.14091	+	1.64278i	−0.0763152	+	0.0585587i	0.569899	+	0.821715i	$0.306982\pi$
$788$	9.28745	−	15.1120i	0.330852	−	0.538342i
$789$	−20.1753	+	26.2929i	−0.718258	+	0.936052i
$790$	9.42933	+	51.0598i	0.335481	+	1.81663i
$791$	−13.8138	+	1.36140i	−0.491161	+	0.0484057i
$792$	1.31656	−	0.803288i	0.0467817	−	0.0285436i
$793$	51.7119	+	13.8562i	1.83634	+	0.492046i
$794$	21.4951	−	10.2356i	0.762831	−	0.363248i
$795$	6.03386	−	45.8317i	0.213999	−	1.62548i
$796$	15.4077	+	12.5098i	0.546112	+	0.443399i
$797$	12.2055	−	29.4667i	0.432341	−	1.04376i	−0.546189	−	0.837662i	$-0.683922\pi$
$797$	12.2055	−	29.4667i	0.432341	−	1.04376i	0.978530	−	0.206103i	$-0.0660781\pi$
$798$	−10.2798	+	26.2197i	−0.363902	+	0.928169i
$799$	22.3302			0.789985
$800$	−7.36302	−	27.8377i	−0.260322	−	0.984213i
$801$	−8.60873	+	14.9108i	−0.304175	+	0.526846i
$802$	3.89561	+	3.51217i	0.137559	+	0.124019i
$803$	2.40752	−	0.316955i	0.0849594	−	0.0111851i
$804$	11.6351	+	30.4278i	0.410340	+	1.07310i
$805$	−18.6749	−	19.9365i	−0.658202	−	0.702669i
$806$	23.2774	+	16.0202i	0.819913	+	0.564289i
$807$	3.15480	+	0.845327i	0.111054	+	0.0297569i
$808$	17.2408	−	18.0978i	0.606531	−	0.636680i
$809$	−23.8591	+	6.39303i	−0.838842	+	0.224767i	−0.652567	−	0.757731i	$-0.726308\pi$
$809$	−23.8591	+	6.39303i	−0.838842	+	0.224767i	−0.186275	+	0.982498i	$0.559641\pi$
$810$	−8.63084	+	7.36181i	−0.303257	+	0.258668i
$811$	12.1160	+	29.2507i	0.425451	+	1.02713i	0.980713	+	0.195454i	$0.0626182\pi$
$811$	12.1160	+	29.2507i	0.425451	+	1.02713i	−0.555261	+	0.831676i	$0.687382\pi$
$812$	−22.7556	+	7.85967i	−0.798565	+	0.275820i
$813$	4.38626	+	1.81685i	0.153833	+	0.0637196i
$814$	1.42899	−	2.80009i	0.0500862	−	0.0981432i
$815$	−34.8095	−	20.0973i	−1.21932	−	0.703977i
$816$	16.8952	+	3.17641i	0.591449	+	0.111197i
$817$	13.0612	−	7.54086i	0.456952	−	0.263821i
$818$	13.3441	−	8.65352i	0.466565	−	0.302563i
$819$	20.5521	+	12.7783i	0.718147	+	0.446511i
$820$	21.4802	+	22.6939i	0.750120	+	0.792506i
$821$	16.7208	−	21.7910i	0.583561	−	0.760511i	−0.404506	−	0.914535i	$-0.632557\pi$
$821$	16.7208	−	21.7910i	0.583561	−	0.760511i	0.988067	+	0.154024i	$0.0492233\pi$
$822$	1.59400	−	4.49212i	0.0555972	−	0.156681i
$823$	19.8352	−	5.31482i	0.691411	−	0.185263i	0.104031	−	0.994574i	$-0.466826\pi$
$823$	19.8352	−	5.31482i	0.691411	−	0.185263i	0.587380	+	0.809311i	$0.300159\pi$
$824$	12.3191	+	15.2731i	0.429156	+	0.532064i
$825$	−1.67874	+	1.67874i	−0.0584462	+	0.0584462i
$826$	6.31419	+	21.8881i	0.219699	+	0.761583i
$827$	−0.704005	+	0.291608i	−0.0244807	+	0.0101402i	−0.394890	−	0.918728i	$-0.629217\pi$
$827$	−0.704005	+	0.291608i	−0.0244807	+	0.0101402i	0.370410	+	0.928869i	$0.379217\pi$
$828$	−9.40004	+	0.975734i	−0.326674	+	0.0339091i
$829$	19.3247	+	25.1844i	0.671173	+	0.874689i	0.997507	−	0.0705649i	$-0.0224802\pi$
$829$	19.3247	+	25.1844i	0.671173	+	0.874689i	−0.326334	+	0.945254i	$0.605814\pi$
$830$	8.66548	−	9.61152i	0.300783	−	0.333621i
$831$	4.81093	+	8.33277i	0.166889	+	0.289061i
$832$	4.14330	−	50.1645i	0.143643	−	1.73914i
$833$	−22.9109	−	7.77406i	−0.793817	−	0.269355i
$834$	20.5542	+	4.38278i	0.711734	+	0.151763i
$835$	24.3939	−	3.21152i	0.844187	−	0.111139i
$836$	2.66423	+	3.67696i	0.0921445	+	0.127170i
$837$	2.29561	−	17.4369i	0.0793480	−	0.602708i
$838$	−6.97405	−	0.553393i	−0.240915	−	0.0191166i
$839$	31.3843	−	31.3843i	1.08351	−	1.08351i	0.0873282	−	0.996180i	$-0.472167\pi$
$839$	31.3843	−	31.3843i	1.08351	−	1.08351i	0.996180	−	0.0873282i	$-0.0278329\pi$
$840$	−25.4731	−	14.9942i	−0.878906	−	0.517349i
$841$	5.86920	+	5.86920i	0.202386	+	0.202386i
$842$	−1.25669	−	1.47332i	−0.0433086	−	0.0507740i
$843$	−34.5671	−	4.55085i	−1.19056	−	0.156740i
$844$	−13.0166	+	3.10727i	−0.448051	+	0.106957i
$845$	−11.0240	−	83.7353i	−0.379236	−	2.88058i
$846$	−11.1447	+	7.22723i	−0.383162	+	0.248477i
$847$	−4.67841	+	28.3476i	−0.160752	+	0.974035i
$848$	20.2625	−	42.2009i	0.695818	−	1.44918i
$849$	−11.9355	+	6.89096i	−0.409625	+	0.236497i
$850$	24.8476	−	1.28615i	0.852267	−	0.0441146i
$851$	−15.2826	+	11.7268i	−0.523882	+	0.401989i
$852$	−10.2828	+	5.56597i	−0.352284	+	0.190687i
$853$	13.6261	+	32.8963i	0.466549	+	1.12635i	0.965660	+	0.259811i	$0.0836602\pi$
$853$	13.6261	+	32.8963i	0.466549	+	1.12635i	−0.499111	+	0.866538i	$0.666340\pi$
$854$	27.2631	−	16.4407i	0.932925	−	0.562590i
$855$	19.7656	+	19.7656i	0.675969	+	0.675969i
$856$	−31.0191	+	9.12307i	−1.06021	+	0.311820i
$857$	11.0762	+	41.3369i	0.378356	+	1.41204i	0.848379	+	0.529389i	$0.177579\pi$
$857$	11.0762	+	41.3369i	0.378356	+	1.41204i	−0.470024	+	0.882654i	$0.655755\pi$
$858$	−3.74692	+	1.78423i	−0.127918	+	0.0609125i
$859$	−17.3713	−	13.3294i	−0.592700	−	0.454794i	0.268346	−	0.963323i	$-0.413523\pi$
$859$	−17.3713	−	13.3294i	−0.592700	−	0.454794i	−0.861045	+	0.508528i	$0.830190\pi$
$860$	5.65358	+	14.7850i	0.192786	+	0.504165i
$861$	16.1729	+	0.528449i	0.551172	+	0.0180095i
$862$	−1.87168	+	8.77774i	−0.0637497	+	0.298971i
$863$	11.2021	+	19.4026i	0.381323	+	0.660472i	0.991252	−	0.131985i	$-0.0421351\pi$
$863$	11.2021	+	19.4026i	0.381323	+	0.660472i	−0.609928	+	0.792457i	$0.708802\pi$
$864$	−28.9823	+	11.8956i	−0.985996	+	0.404695i
$865$	38.6277	−	66.9052i	1.31338	−	2.27484i
$866$	21.7492	−	7.05126i	0.739069	−	0.239612i
$867$	2.40505	−	5.80631i	0.0816799	−	0.197193i
$868$	16.4636	−	3.36591i	0.558809	−	0.114246i
$869$	4.00524	−	1.65902i	0.135868	−	0.0562785i
$870$	2.01035	−	25.3351i	0.0681572	−	0.858941i
$871$	21.3312	+	79.6092i	0.722781	+	2.69746i
$872$	−21.9134	+	0.531422i	−0.742083	+	0.0179962i
$873$	−1.80443	+	6.73424i	−0.0610708	+	0.227919i
$874$	−5.05292	−	27.3615i	−0.170918	−	0.925518i
$875$	−0.726166	−	0.220231i	−0.0245489	−	0.00744518i
$876$	−16.0948	−	0.442220i	−0.543792	−	0.0149412i
$877$	−2.22629	−	16.9104i	−0.0751765	−	0.571023i	−0.987033	−	0.160514i	$-0.948685\pi$
$877$	−2.22629	−	16.9104i	−0.0751765	−	0.571023i	0.911857	−	0.410508i	$-0.134649\pi$
$878$	4.88862	−	0.253042i	0.164983	−	0.00853976i
$879$	15.0648	+	8.69768i	0.508124	+	0.293365i
$880$	−4.25187	+	2.15265i	−0.143331	+	0.0725657i
$881$			32.1407i			1.08285i	0.840750	+	0.541423i	$0.182114\pi$
$881$			32.1407i			1.08285i	−0.840750	+	0.541423i	$0.817886\pi$
$882$	13.9506	−	3.53527i	0.469742	−	0.119039i
$883$	23.9601	+	9.92460i	0.806321	+	0.333989i	0.747485	−	0.664278i	$-0.231261\pi$
$883$	23.9601	+	9.92460i	0.806321	+	0.333989i	0.0588361	+	0.998268i	$0.481261\pi$
$884$	41.6862	+	12.4065i	1.40206	+	0.417275i
$885$	−23.8429	−	3.13897i	−0.801470	−	0.105515i
$886$	−11.3343	+	31.9415i	−0.380782	+	1.07310i
$887$	−11.2436	+	41.9618i	−0.377524	+	1.40894i	0.472097	+	0.881546i	$0.343497\pi$
$887$	−11.2436	+	41.9618i	−0.377524	+	1.40894i	−0.849621	+	0.527393i	$0.823170\pi$
$888$	−12.2844	+	16.8395i	−0.412238	+	0.565096i
$889$	−5.47962	−	55.6004i	−0.183781	−	1.86478i
$890$	30.1630	−	43.8269i	1.01107	−	1.46908i
$891$	0.751427	+	0.576590i	0.0251738	+	0.0193165i
$892$	16.9150	−	12.2562i	0.566357	−	0.410368i
$893$	−23.8072	−	31.0261i	−0.796676	−	1.03825i
$894$	−7.35423	−	22.6837i	−0.245962	−	0.758658i
$895$	−32.2304			−1.07734
$896$	−19.7835	−	22.4636i	−0.660919	−	0.750457i
$897$	25.4302			0.849090
$898$	2.87272	+	8.86074i	0.0958637	+	0.295687i
$899$	8.79560	+	11.4626i	0.293350	+	0.382301i
$900$	−11.9848	+	8.68392i	−0.399495	+	0.289464i
$901$	32.0911	+	24.6244i	1.06911	+	0.820356i
$902$	1.47912	−	2.14916i	0.0492493	−	0.0715593i
$903$	7.46665	+	3.38254i	0.248474	+	0.112564i
$904$	8.74539	−	11.9882i	0.290867	−	0.398721i
$905$	−20.3207	+	75.8378i	−0.675482	+	2.52093i
$906$	1.05471	−	2.97233i	0.0350405	−	0.0987491i
$907$	44.3752	+	5.84211i	1.47346	+	0.193984i	0.824075	−	0.566480i	$-0.191695\pi$
$907$	44.3752	+	5.84211i	1.47346	+	0.193984i	0.649380	+	0.760464i	$0.275029\pi$
$908$	−30.3219	−	9.02429i	−1.00627	−	0.299481i
$909$	−11.8694	−	4.91647i	−0.393684	−	0.163069i
$910$	−60.1852	−	44.3860i	−1.99512	−	1.47138i
$911$		−	27.9126i		−	0.924787i	−0.886675	−	0.462394i	$-0.846991\pi$
$911$		−	27.9126i		−	0.924787i	0.886675	−	0.462394i	$-0.153009\pi$
$912$	−13.5993	−	26.8611i	−0.450317	−	0.889459i
$913$	−0.935736	−	0.540247i	−0.0309683	−	0.0178796i
$914$	−23.9925	+	1.24189i	−0.793602	+	0.0410780i
$915$	4.38682	+	33.3212i	0.145024	+	1.10157i
$916$	−27.1788	−	0.746766i	−0.898014	−	0.0246738i
$917$	−1.26361	−	5.41783i	−0.0417282	−	0.178913i
$918$	−4.91596	−	26.6199i	−0.162251	−	0.878587i
$919$	0.293434	−	1.09511i	0.00967948	−	0.0361243i	−0.960917	−	0.276836i	$-0.910714\pi$
$919$	0.293434	−	1.09511i	0.00967948	−	0.0361243i	0.970597	+	0.240712i	$0.0773808\pi$
$920$	29.1944	−	0.707992i	0.962512	−	0.0233418i
$921$	−2.50160	−	9.33610i	−0.0824305	−	0.307635i
$922$	0.876321	−	11.0437i	0.0288601	−	0.363705i
$923$	−27.3302	+	11.3205i	−0.899583	+	0.372619i
$924$	−0.780855	+	2.34115i	−0.0256882	+	0.0770182i
$925$	−11.5447	+	27.8714i	−0.379588	+	0.916406i
$926$	30.7255	−	9.96143i	1.00970	−	0.327353i
$927$	5.04275	−	8.73430i	0.165626	−	0.286872i
$928$	9.92569	−	23.7460i	0.325827	−	0.779500i
$929$	11.0269	+	19.0991i	0.361780	+	0.626622i	0.988254	−	0.152821i	$-0.0488358\pi$
$929$	11.0269	+	19.0991i	0.361780	+	0.626622i	−0.626474	+	0.779442i	$0.715502\pi$
$930$	−3.69942	+	17.3494i	−0.121309	+	0.568910i
$931$	13.6249	+	40.1213i	0.446536	+	1.31492i
$932$	−3.17154	−	8.29410i	−0.103887	−	0.271682i
$933$	12.8280	+	9.84330i	0.419971	+	0.322255i
$934$	21.8206	−	10.3906i	0.713990	−	0.339991i
$935$	−1.06580	−	3.97761i	−0.0348553	−	0.130082i
$936$	−24.8204	+	7.29996i	−0.811280	+	0.238607i
$937$	−28.4618	−	28.4618i	−0.929808	−	0.929808i	0.0678852	−	0.997693i	$-0.478375\pi$
$937$	−28.4618	−	28.4618i	−0.929808	−	0.929808i	−0.997693	+	0.0678852i	$0.978375\pi$
$938$	42.9047	+	23.6929i	1.40089	+	0.773599i
$939$	3.84123	+	9.27354i	0.125354	+	0.302631i
$940$	36.0967	−	19.5387i	1.17734	−	0.637282i
$941$	−15.9452	+	12.2352i	−0.519800	+	0.398857i	−0.835069	−	0.550146i	$-0.814572\pi$
$941$	−15.9452	+	12.2352i	−0.519800	+	0.398857i	0.315269	+	0.949003i	$0.397905\pi$
$942$	4.30265	−	0.222711i	0.140188	−	0.00725632i
$943$	−13.8451	+	7.99347i	−0.450858	+	0.260303i
$944$	−21.9540	−	10.5411i	−0.714542	−	0.343083i
$945$	−7.57901	+	45.9230i	−0.246545	+	1.49388i
$946$	1.10887	−	0.719093i	0.0360525	−	0.0233797i
$947$	5.55456	+	42.1911i	0.180499	+	1.37103i	0.806514	+	0.591215i	$0.201352\pi$
$947$	5.55456	+	42.1911i	0.180499	+	1.37103i	−0.626015	+	0.779811i	$0.715315\pi$
$948$	−27.9593	+	6.67433i	−0.908076	+	0.216772i
$949$	−40.3862	−	5.31694i	−1.31099	−	0.172595i
$950$	−28.2781	−	33.1527i	−0.917464	−	1.07562i
$951$	15.7221	+	15.7221i	0.509824	+	0.509824i
$952$	22.5073	−	12.7432i	0.729466	−	0.413010i
$953$	17.0063	−	17.0063i	0.550887	−	0.550887i	−0.375810	−	0.926697i	$-0.622635\pi$
$953$	17.0063	−	17.0063i	0.550887	−	0.550887i	0.926697	+	0.375810i	$0.122635\pi$
$954$	−23.9860	−	1.90329i	−0.776575	−	0.0616214i
$955$	−6.34551	+	48.1989i	−0.205336	+	1.55968i
$956$	0.400595	+	0.552869i	0.0129562	+	0.0178810i
$957$	−2.10381	+	0.276972i	−0.0680064	+	0.00895322i
$958$	23.7829	+	5.07124i	0.768391	+	0.163844i
$959$	−2.52652	−	6.71155i	−0.0815857	−	0.216727i
$960$	30.0903	−	9.64845i	0.971162	−	0.311402i
$961$	10.4575	+	18.1130i	0.337340	+	0.584290i
$962$	−35.3118	+	39.1669i	−1.13850	+	1.26279i
$963$	10.1168	+	13.1845i	0.326009	+	0.424863i
$964$	11.0089	−	1.14274i	0.354574	−	0.0368051i
$965$	−19.8364	+	8.21650i	−0.638556	+	0.264499i
$966$	10.4878	−	10.8952i	0.337438	−	0.350547i
$967$	−11.8288	+	11.8288i	−0.380388	+	0.380388i	−0.871242	−	0.490854i	$-0.836685\pi$
$967$	−11.8288	+	11.8288i	−0.380388	+	0.380388i	0.490854	+	0.871242i	$0.336685\pi$
$968$	−19.2832	−	23.9072i	−0.619787	−	0.768407i
$969$	25.1285	−	6.73315i	0.807243	−	0.216300i
$970$	7.20444	−	20.3031i	0.231321	−	0.651894i
$971$	−26.5581	+	34.6112i	−0.852290	+	1.11073i	0.140408	+	0.990094i	$0.455159\pi$
$971$	−26.5581	+	34.6112i	−0.852290	+	1.11073i	−0.992697	+	0.120632i	$0.961508\pi$
$972$	18.5251	+	19.5719i	0.594193	+	0.627767i
$973$	27.8849	−	14.9070i	0.893948	−	0.477896i
$974$	−32.0308	+	20.7717i	−1.02633	+	0.665569i
$975$	34.4900	−	19.9128i	1.10456	−	0.637719i
$976$	−6.28862	+	33.4488i	−0.201294	+	1.07067i
$977$	−27.7505	−	16.0217i	−0.887816	−	0.512581i	−0.0145883	−	0.999894i	$-0.504644\pi$
$977$	−27.7505	−	16.0217i	−0.887816	−	0.512581i	−0.873227	+	0.487313i	$0.837977\pi$
$978$	10.1149	−	19.8201i	0.323440	−	0.633776i
$979$	−4.10400	−	1.69993i	−0.131164	−	0.0543300i
$980$	−43.8377	+	7.48009i	−1.40034	+	0.238943i
$981$	4.31151	+	10.4089i	0.137656	+	0.332330i
$982$	−4.04159	+	3.44734i	−0.128972	+	0.110009i
$983$	−20.2831	+	5.43484i	−0.646930	+	0.173344i	−0.567341	−	0.823483i	$-0.692028\pi$
$983$	−20.2831	+	5.43484i	−0.646930	+	0.173344i	−0.0795897	+	0.996828i	$0.525361\pi$
$984$	−11.9320	+	12.5251i	−0.380377	+	0.399285i
$985$	27.2123	+	7.29150i	0.867055	+	0.232327i
$986$	18.3192	+	12.6078i	0.583403	+	0.401515i
$987$	6.16887	−	20.3405i	0.196357	−	0.647446i
$988$	−27.2055	−	71.1468i	−0.865523	−	2.26348i
$989$	−8.02922	+	1.05707i	−0.255314	+	0.0336128i
$990$	1.81929	+	1.64022i	0.0578209	+	0.0521297i
$991$	15.4597	−	26.7770i	0.491095	−	0.850601i	−0.508853	−	0.860854i	$-0.669930\pi$
$991$	15.4597	−	26.7770i	0.491095	−	0.850601i	0.999947	+	0.0102527i	$0.00326360\pi$
$992$	−9.03226	+	15.5285i	−0.286775	+	0.493032i
$993$	14.9754			0.475231
$994$	−6.42121	+	16.3779i	−0.203668	+	0.519476i
$995$	−12.0629	+	29.1224i	−0.382419	+	0.923241i
$996$	5.56185	+	4.51578i	0.176234	+	0.143088i
$997$	0.533895	−	4.05534i	0.0169086	−	0.128434i	−0.980909	−	0.194469i	$-0.937702\pi$
$997$	0.533895	−	4.05534i	0.0169086	−	0.128434i	0.997817	+	0.0660352i	$0.0210350\pi$
$998$	46.6418	−	22.2101i	1.47642	−	0.703049i
$999$	31.7036	+	8.49497i	1.00306	+	0.268769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.13	yes	240
4.3	odd	2		896.2.bh.a.529.8		240
7.2	even	3	inner	224.2.bd.a.205.9	yes	240
28.23	odd	6		896.2.bh.a.401.23		240
32.5	even	8	inner	224.2.bd.a.165.9	yes	240
32.27	odd	8		896.2.bh.a.753.23		240
224.37	even	24	inner	224.2.bd.a.37.13	✓	240
224.219	odd	24		896.2.bh.a.625.8		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.13	✓	240	224.37	even	24	inner
224.2.bd.a.109.13	yes	240	1.1	even	1	trivial
224.2.bd.a.165.9	yes	240	32.5	even	8	inner
224.2.bd.a.205.9	yes	240	7.2	even	3	inner
896.2.bh.a.401.23		240	28.23	odd	6
896.2.bh.a.529.8		240	4.3	odd	2
896.2.bh.a.625.8		240	224.219	odd	24
896.2.bh.a.753.23		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.436149 - 1.34528i) q^{2} +(0.756979 + 0.986515i) q^{3} +(-1.61955 + 1.17348i) q^{4} +(-2.52010 - 1.93374i) q^{5} +(0.996981 - 1.44862i) q^{6} +(-0.259491 - 2.63300i) q^{7} +(2.28503 + 1.66693i) q^{8} +(0.376264 - 1.40424i) q^{9} +O(q^{10})\)	\(q+(-0.436149 - 1.34528i) q^{2} +(0.756979 + 0.986515i) q^{3} +(-1.61955 + 1.17348i) q^{4} +(-2.52010 - 1.93374i) q^{5} +(0.996981 - 1.44862i) q^{6} +(-0.259491 - 2.63300i) q^{7} +(2.28503 + 1.66693i) q^{8} +(0.376264 - 1.40424i) q^{9} +(-1.50228 + 4.23364i) q^{10} +(0.371867 + 0.0489572i) q^{11} +(-2.38362 - 0.709405i) q^{12} +(-5.81297 - 2.40781i) q^{13} +(-3.42893 + 1.49747i) q^{14} -3.94992i q^{15} +(1.24587 - 3.80103i) q^{16} +(2.99322 + 1.72814i) q^{17} +(-2.05319 + 0.106276i) q^{18} +(-0.790086 - 6.00130i) q^{19} +(6.35065 + 0.174490i) q^{20} +(2.40106 - 2.24911i) q^{21} +(-0.0963282 - 0.521617i) q^{22} +(-0.841254 + 3.13960i) q^{23} +(0.0852674 + 3.51604i) q^{24} +(1.31746 + 4.91684i) q^{25} +(-0.703855 + 8.87022i) q^{26} +(5.11658 - 2.11936i) q^{27} +(3.51004 + 3.95975i) q^{28} +(-1.74109 + 4.20337i) q^{29} +(-5.31375 + 1.72276i) q^{30} +(1.58784 - 2.75022i) q^{31} +(-5.65682 - 0.0182315i) q^{32} +(0.233198 + 0.403911i) q^{33} +(1.01934 - 4.78045i) q^{34} +(-4.43759 + 7.13721i) q^{35} +(1.03847 + 2.71577i) q^{36} +(4.70183 + 3.60784i) q^{37} +(-7.72883 + 3.68035i) q^{38} +(-2.02496 - 7.55724i) q^{39} +(-2.53509 - 8.61949i) q^{40} +(3.47792 + 3.47792i) q^{41} +(-4.07290 - 2.24914i) q^{42} +(0.953485 + 2.30192i) q^{43} +(-0.659706 + 0.357091i) q^{44} +(-3.66366 + 2.81122i) q^{45} +(4.59055 - 0.237613i) q^{46} +(5.59518 - 3.23038i) q^{47} +(4.69287 - 1.64823i) q^{48} +(-6.86533 + 1.36648i) q^{49} +(6.03991 - 3.91683i) q^{50} +(0.560974 + 4.26102i) q^{51} +(12.2399 - 2.92186i) q^{52} +(11.6032 + 1.52759i) q^{53} +(-5.08272 - 5.95887i) q^{54} +(-0.842472 - 0.842472i) q^{55} +(3.79607 - 6.44902i) q^{56} +(5.32229 - 5.32229i) q^{57} +(6.41408 + 0.508959i) q^{58} +(0.794692 - 6.03629i) q^{59} +(4.63517 + 6.39709i) q^{60} +(-8.43592 + 1.11061i) q^{61} +(-4.39234 - 0.936581i) q^{62} +(-3.79498 - 0.626314i) q^{63} +(2.44269 + 7.61796i) q^{64} +(9.99320 + 17.3087i) q^{65} +(0.441664 - 0.489882i) q^{66} +(-7.97415 - 10.3921i) q^{67} +(-6.87561 + 0.713695i) q^{68} +(-3.73407 + 1.54670i) q^{69} +(11.5370 + 2.85691i) q^{70} +(3.32452 - 3.32452i) q^{71} +(3.20053 - 2.58151i) q^{72} +(6.25354 - 1.67563i) q^{73} +(2.80286 - 7.89883i) q^{74} +(-3.85324 + 5.02165i) q^{75} +(8.32201 + 8.79224i) q^{76} +(0.0324079 - 0.991827i) q^{77} +(-9.28341 + 6.02021i) q^{78} +(10.0098 - 5.77915i) q^{79} +(-10.4899 + 7.16978i) q^{80} +(2.18692 + 1.26262i) q^{81} +(3.16188 - 6.19566i) q^{82} +(-2.66146 - 1.10241i) q^{83} +(-1.24933 + 6.46015i) q^{84} +(-4.20146 - 10.1432i) q^{85} +(2.68086 - 2.28668i) q^{86} +(-5.46465 + 1.46425i) q^{87} +(0.768117 + 0.731744i) q^{88} +(-11.4398 - 3.06527i) q^{89} +(5.37978 + 3.70253i) q^{90} +(-4.83134 + 15.9303i) q^{91} +(-2.32182 - 6.07193i) q^{92} +(3.91509 - 0.515431i) q^{93} +(-6.78609 - 6.11815i) q^{94} +(-9.61388 + 16.6517i) q^{95} +(-4.26411 - 5.59434i) q^{96} -4.79566 q^{97} +(4.83260 + 8.63979i) q^{98} +(0.208667 - 0.503767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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