LMFDB - Embedded newform 547.2.m.a.10.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(10,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(182))

chi = DirichletCharacter(H, H._module([60]))

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

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

chi := DirichletCharacter("547.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.m (of order $91$, degree $72$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$44$ over $\Q(\zeta_{91})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{91}]$

Embedding invariants

Embedding label			10.14
Character	$\chi$	$=$	547.10
Dual form			547.2.m.a.383.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607931 - 1.02553i) q^{2} +(0.696260 + 3.05052i) q^{3} +(0.277745 - 0.507704i) q^{4} +(-0.411634 - 0.0142165i) q^{5} +(2.70512 - 2.56854i) q^{6} +(3.12156 - 0.433823i) q^{7} +(-3.07245 + 0.106112i) q^{8} +(-6.11797 + 2.94626i) q^{9} +O(q^{10})$	\(q+(-0.607931 - 1.02553i) q^{2} +(0.696260 + 3.05052i) q^{3} +(0.277745 - 0.507704i) q^{4} +(-0.411634 - 0.0142165i) q^{5} +(2.70512 - 2.56854i) q^{6} +(3.12156 - 0.433823i) q^{7} +(-3.07245 + 0.106112i) q^{8} +(-6.11797 + 2.94626i) q^{9} +(0.235665 + 0.430785i) q^{10} +(3.33735 + 0.822584i) q^{11} +(1.74214 + 0.493770i) q^{12} +(1.64225 + 2.05932i) q^{13} +(-2.34259 - 2.93751i) q^{14} +(-0.243237 - 1.26559i) q^{15} +(1.35244 + 2.11172i) q^{16} +(1.98549 - 1.64023i) q^{17} +(6.74077 + 4.48303i) q^{18} +(3.31223 - 2.04155i) q^{19} +(-0.121547 + 0.205039i) q^{20} +(3.49680 + 9.22031i) q^{21} +(-1.18530 - 3.92263i) q^{22} +(-1.40624 + 4.65381i) q^{23} +(-2.46292 - 9.29868i) q^{24} +(-4.81885 - 0.333252i) q^{25} +(1.11352 - 2.93611i) q^{26} +(-7.39467 - 9.27262i) q^{27} +(0.646742 - 1.70532i) q^{28} +(-6.79870 + 3.87325i) q^{29} +(-1.15003 + 1.01884i) q^{30} +(8.86290 - 3.18739i) q^{31} +(-1.41955 + 2.82205i) q^{32} +(-0.185638 + 10.7534i) q^{33} +(-2.88915 - 1.03903i) q^{34} +(-1.29111 + 0.134199i) q^{35} +(-0.203406 + 3.92442i) q^{36} +(-1.54695 + 9.87738i) q^{37} +(-4.10728 - 2.15567i) q^{38} +(-5.13856 + 6.44355i) q^{39} +1.26623 q^{40} +8.98318 q^{41} +(7.32988 - 9.19138i) q^{42} +(5.06450 - 3.62641i) q^{43} +(1.34456 - 1.46592i) q^{44} +(2.56025 - 1.12580i) q^{45} +(5.62751 - 1.38706i) q^{46} +(-4.05712 + 5.87776i) q^{47} +(-5.50017 + 5.59594i) q^{48} +(2.82120 - 0.799604i) q^{49} +(2.58777 + 5.14446i) q^{50} +(6.38597 + 4.91474i) q^{51} +(1.50165 - 0.261813i) q^{52} +(-2.08691 - 10.8585i) q^{53} +(-5.01390 + 13.2206i) q^{54} +(-1.36207 - 0.386048i) q^{55} +(-9.54480 + 1.66414i) q^{56} +(8.53397 + 8.68256i) q^{57} +(8.10527 + 4.61760i) q^{58} +(0.313907 + 2.58526i) q^{59} +(-0.710104 - 0.228020i) q^{60} +(-0.0191293 - 0.221090i) q^{61} +(-8.65679 - 7.15146i) q^{62} +(-17.8194 + 11.8510i) q^{63} +(8.76048 - 0.605839i) q^{64} +(-0.646731 - 0.871033i) q^{65} +(11.1408 - 6.34694i) q^{66} +(-14.3946 - 4.07983i) q^{67} +(-0.281293 - 1.46361i) q^{68} +(-15.1756 - 1.04948i) q^{69} +(0.922527 + 1.24248i) q^{70} +(-0.654358 - 1.92313i) q^{71} +(18.4845 - 9.70142i) q^{72} +(-1.05759 + 5.50277i) q^{73} +(11.0700 - 4.41832i) q^{74} +(-2.33858 - 14.9320i) q^{75} +(-0.116550 - 2.24866i) q^{76} +(10.7746 + 1.11992i) q^{77} +(9.73194 + 1.35251i) q^{78} +(13.5742 - 9.71976i) q^{79} +(-0.526688 - 0.888480i) q^{80} +(10.4364 - 13.0868i) q^{81} +(-5.46115 - 9.21251i) q^{82} +(-5.77982 - 3.03349i) q^{83} +(5.65240 + 0.785551i) q^{84} +(-0.840613 + 0.646948i) q^{85} +(-6.79785 - 2.98918i) q^{86} +(-16.5491 - 18.0428i) q^{87} +(-10.3411 - 2.17321i) q^{88} +(0.825438 - 9.54016i) q^{89} +(-2.71100 - 1.94120i) q^{90} +(6.01977 + 5.71585i) q^{91} +(1.97218 + 2.00652i) q^{92} +(15.8941 + 24.8172i) q^{93} +(8.49426 + 0.587428i) q^{94} +(-1.39245 + 0.793284i) q^{95} +(-9.59709 - 2.36547i) q^{96} +(1.38248 + 1.06398i) q^{97} +(-2.53511 - 2.40712i) q^{98} +(-22.8414 + 4.80016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) $ 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{30}{91}\right)$

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 $

$2$	−0.607931	−	1.02553i	−0.429872	−	0.725159i	0.565131	−	0.825001i	$-0.308826\pi$
$2$	−0.607931	−	1.02553i	−0.429872	−	0.725159i	−0.995003	+	0.0998423i	$0.968166\pi$
$3$	0.696260	+	3.05052i	0.401986	+	1.76122i	0.619339	+	0.785123i	$0.287401\pi$
$3$	0.696260	+	3.05052i	0.401986	+	1.76122i	−0.217353	+	0.976093i	$0.569742\pi$
$4$	0.277745	−	0.507704i	0.138872	−	0.253852i
$5$	−0.411634	−	0.0142165i	−0.184088	−	0.00635780i	−0.0576746	−	0.998335i	$-0.518369\pi$
$5$	−0.411634	−	0.0142165i	−0.184088	−	0.00635780i	−0.126414	+	0.991978i	$0.540347\pi$
$6$	2.70512	−	2.56854i	1.10436	−	1.04860i
$7$	3.12156	−	0.433823i	1.17984	−	0.163970i	0.479343	−	0.877627i	$-0.340875\pi$
$7$	3.12156	−	0.433823i	1.17984	−	0.163970i	0.700495	+	0.713658i	$0.252963\pi$
$8$	−3.07245	+	0.106112i	−1.08628	+	0.0375164i
$9$	−6.11797	+	2.94626i	−2.03932	+	0.982086i
$10$	0.235665	+	0.430785i	0.0745239	+	0.136226i
$11$	3.33735	+	0.822584i	1.00625	+	0.248018i	0.707804	−	0.706408i	$-0.249686\pi$
$11$	3.33735	+	0.822584i	1.00625	+	0.248018i	0.298445	+	0.954427i	$0.403532\pi$
$12$	1.74214	+	0.493770i	0.502913	+	0.142539i
$13$	1.64225	+	2.05932i	0.455480	+	0.571153i	0.955549	−	0.294832i	$-0.0952637\pi$
$13$	1.64225	+	2.05932i	0.455480	+	0.571153i	−0.500070	+	0.865985i	$0.666692\pi$
$14$	−2.34259	−	2.93751i	−0.626083	−	0.785084i
$15$	−0.243237	−	1.26559i	−0.0628034	−	0.326775i
$16$	1.35244	+	2.11172i	0.338110	+	0.527929i
$17$	1.98549	−	1.64023i	0.481552	−	0.397815i	−0.364259	−	0.931298i	$-0.618678\pi$
$17$	1.98549	−	1.64023i	0.481552	−	0.397815i	0.845811	+	0.533483i	$0.179117\pi$
$18$	6.74077	+	4.48303i	1.58882	+	1.05666i
$19$	3.31223	−	2.04155i	0.759878	−	0.468364i	−0.0896070	−	0.995977i	$-0.528561\pi$
$19$	3.31223	−	2.04155i	0.759878	−	0.468364i	0.849485	+	0.527613i	$0.176913\pi$
$20$	−0.121547	+	0.205039i	−0.0271787	+	0.0458482i
$21$	3.49680	+	9.22031i	0.763065	+	2.01204i
$22$	−1.18530	−	3.92263i	−0.252706	−	0.836307i
$23$	−1.40624	+	4.65381i	−0.293220	+	0.970386i	0.678569	+	0.734536i	$0.262600\pi$
$23$	−1.40624	+	4.65381i	−0.293220	+	0.970386i	−0.971790	+	0.235849i	$0.924213\pi$
$24$	−2.46292	−	9.29868i	−0.502742	−	1.89809i
$25$	−4.81885	−	0.333252i	−0.963769	−	0.0666504i
$26$	1.11352	−	2.93611i	0.218379	−	0.575818i
$27$	−7.39467	−	9.27262i	−1.42310	−	1.78452i
$28$	0.646742	−	1.70532i	0.122223	−	0.322275i
$29$	−6.79870	+	3.87325i	−1.26249	+	0.719244i	−0.971399	−	0.237453i	$-0.923688\pi$
$29$	−6.79870	+	3.87325i	−1.26249	+	0.719244i	−0.291088	+	0.956696i	$0.594017\pi$
$30$	−1.15003	+	1.01884i	−0.209966	+	0.186014i
$31$	8.86290	−	3.18739i	1.59182	−	0.572471i	0.615378	−	0.788232i	$-0.289003\pi$
$31$	8.86290	−	3.18739i	1.59182	−	0.572471i	0.976446	+	0.215761i	$0.0692231\pi$
$32$	−1.41955	+	2.82205i	−0.250943	+	0.498873i
$33$	−0.185638	+	10.7534i	−0.0323154	+	1.87192i
$34$	−2.88915	−	1.03903i	−0.495485	−	0.178192i
$35$	−1.29111	+	0.134199i	−0.218237	+	0.0226837i
$36$	−0.203406	+	3.92442i	−0.0339010	+	0.654070i
$37$	−1.54695	+	9.87738i	−0.254317	+	1.62383i	0.435737	+	0.900074i	$0.356488\pi$
$37$	−1.54695	+	9.87738i	−0.254317	+	1.62383i	−0.690054	+	0.723758i	$0.742413\pi$
$38$	−4.10728	−	2.15567i	−0.666289	−	0.349695i
$39$	−5.13856	+	6.44355i	−0.822828	+	1.03179i
$40$	1.26623			0.200209
$41$	8.98318			1.40294			0.701468	−	0.712701i	$-0.252528\pi$
$41$	8.98318			1.40294			0.701468	+	0.712701i	$0.252528\pi$
$42$	7.32988	−	9.19138i	1.13103	−	1.41826i
$43$	5.06450	−	3.62641i	0.772328	−	0.553022i	−0.126165	−	0.992009i	$-0.540267\pi$
$43$	5.06450	−	3.62641i	0.772328	−	0.553022i	0.898494	+	0.438987i	$0.144663\pi$
$44$	1.34456	−	1.46592i	0.202700	−	0.220995i
$45$	2.56025	−	1.12580i	0.381659	−	0.167825i
$46$	5.62751	−	1.38706i	0.829731	−	0.204510i
$47$	−4.05712	+	5.87776i	−0.591792	+	0.857359i	−0.998417	−	0.0562361i	$-0.982090\pi$
$47$	−4.05712	+	5.87776i	−0.591792	+	0.857359i	0.406625	+	0.913595i	$0.366705\pi$
$48$	−5.50017	+	5.59594i	−0.793882	+	0.807705i
$49$	2.82120	−	0.799604i	0.403028	−	0.114229i
$50$	2.58777	+	5.14446i	0.365965	+	0.727537i
$51$	6.38597	+	4.91474i	0.894215	+	0.688201i
$52$	1.50165	−	0.261813i	0.208242	−	0.0363070i
$53$	−2.08691	−	10.8585i	−0.286660	−	1.49153i	−0.782245	−	0.622971i	$-0.785926\pi$
$53$	−2.08691	−	10.8585i	−0.286660	−	1.49153i	0.495586	−	0.868559i	$-0.334953\pi$
$54$	−5.01390	+	13.2206i	−0.682305	+	1.79909i
$55$	−1.36207	−	0.386048i	−0.183662	−	0.0520548i
$56$	−9.54480	+	1.66414i	−1.27548	+	0.222380i
$57$	8.53397	+	8.68256i	1.13035	+	1.15003i
$58$	8.10527	+	4.61760i	1.06427	+	0.606321i
$59$	0.313907	+	2.58526i	0.0408672	+	0.336572i	0.998774	+	0.0494939i	$0.0157608\pi$
$59$	0.313907	+	2.58526i	0.0408672	+	0.336572i	−0.957907	+	0.287078i	$0.907316\pi$
$60$	−0.710104	−	0.228020i	−0.0916740	−	0.0294372i
$61$	−0.0191293	−	0.221090i	−0.00244925	−	0.0283077i	0.994953	−	0.100346i	$-0.0319948\pi$
$61$	−0.0191293	−	0.221090i	−0.00244925	−	0.0283077i	−0.997402	+	0.0720378i	$0.977050\pi$
$62$	−8.65679	−	7.15146i	−1.09941	−	0.908236i
$63$	−17.8194	+	11.8510i	−2.24504	+	1.49309i
$64$	8.76048	−	0.605839i	1.09506	−	0.0757299i
$65$	−0.646731	−	0.871033i	−0.0802171	−	0.108038i
$66$	11.1408	−	6.34694i	1.37133	−	0.781254i
$67$	−14.3946	−	4.07983i	−1.75858	−	0.498430i	−0.768614	−	0.639713i	$-0.779053\pi$
$67$	−14.3946	−	4.07983i	−1.75858	−	0.498430i	−0.989969	+	0.141283i	$0.954877\pi$
$68$	−0.281293	−	1.46361i	−0.0341118	−	0.177488i
$69$	−15.1756	−	1.04948i	−1.82693	−	0.126343i
$70$	0.922527	+	1.24248i	0.110263	+	0.148505i
$71$	−0.654358	−	1.92313i	−0.0776580	−	0.228234i	0.900967	−	0.433888i	$-0.142859\pi$
$71$	−0.654358	−	1.92313i	−0.0776580	−	0.228234i	−0.978625	+	0.205655i	$0.934068\pi$
$72$	18.4845	−	9.70142i	2.17842	−	1.14332i
$73$	−1.05759	+	5.50277i	−0.123781	+	0.644050i	0.865837	+	0.500327i	$0.166787\pi$
$73$	−1.05759	+	5.50277i	−0.123781	+	0.644050i	−0.989618	+	0.143724i	$0.954092\pi$
$74$	11.0700	−	4.41832i	1.28686	−	0.513620i
$75$	−2.33858	−	14.9320i	−0.270036	−	1.72420i
$76$	−0.116550	−	2.24866i	−0.0133692	−	0.257939i
$77$	10.7746	+	1.11992i	1.22788	+	0.127627i
$78$	9.73194	+	1.35251i	1.10192	+	0.153142i
$79$	13.5742	−	9.71976i	1.52722	−	1.09356i	0.563678	−	0.825994i	$-0.309386\pi$
$79$	13.5742	−	9.71976i	1.52722	−	1.09356i	0.963540	−	0.267564i	$-0.0862186\pi$
$80$	−0.526688	−	0.888480i	−0.0588856	−	0.0993351i
$81$	10.4364	−	13.0868i	1.15960	−	1.45409i
$82$	−5.46115	−	9.21251i	−0.603083	−	1.01735i
$83$	−5.77982	−	3.03349i	−0.634418	−	0.332968i	0.116670	−	0.993171i	$-0.462778\pi$
$83$	−5.77982	−	3.03349i	−0.634418	−	0.332968i	−0.751088	+	0.660202i	$0.770470\pi$
$84$	5.65240	+	0.785551i	0.616728	+	0.0857107i
$85$	−0.840613	+	0.646948i	−0.0911772	+	0.0701714i
$86$	−6.79785	−	2.98918i	−0.733031	−	0.322332i
$87$	−16.5491	−	18.0428i	−1.77425	−	1.93439i
$88$	−10.3411	−	2.17321i	−1.10237	−	0.231665i
$89$	0.825438	−	9.54016i	0.0874963	−	1.01126i	−0.814687	−	0.579901i	$-0.803091\pi$
$89$	0.825438	−	9.54016i	0.0874963	−	1.01126i	0.902183	−	0.431354i	$-0.141964\pi$
$90$	−2.71100	−	1.94120i	−0.285764	−	0.204620i
$91$	6.01977	+	5.71585i	0.631044	+	0.599183i
$92$	1.97218	+	2.00652i	0.205614	+	0.209194i
$93$	15.8941	+	24.8172i	1.64814	+	2.57342i
$94$	8.49426	+	0.587428i	0.876116	+	0.0605886i
$95$	−1.39245	+	0.793284i	−0.142862	+	0.0813892i
$96$	−9.59709	−	2.36547i	−0.979499	−	0.241425i
$97$	1.38248	+	1.06398i	0.140370	+	0.108031i	0.677690	−	0.735347i	$-0.262981\pi$
$97$	1.38248	+	1.06398i	0.140370	+	0.108031i	−0.537320	+	0.843378i	$0.680563\pi$
$98$	−2.53511	−	2.40712i	−0.256085	−	0.243156i
$99$	−22.8414	+	4.80016i	−2.29564	+	0.482434i
$100$	−1.50760	+	2.35399i	−0.150760	+	0.235399i
$101$	4.78005	−	6.43789i	0.475633	−	0.640594i	−0.498414	−	0.866939i	$-0.666084\pi$
$101$	4.78005	−	6.43789i	0.475633	−	0.640594i	0.974047	+	0.226345i	$0.0726775\pi$
$102$	1.15798	−	9.53683i	0.114657	−	0.944286i
$103$	4.39140	−	9.53651i	0.432698	−	0.939660i	−0.561026	−	0.827798i	$-0.689593\pi$
$103$	4.39140	−	9.53651i	0.432698	−	0.939660i	0.993724	−	0.111862i	$-0.0356815\pi$
$104$	−5.26427	−	6.15290i	−0.516204	−	0.603342i
$105$	−1.30832	−	3.84510i	−0.127679	−	0.375243i
$106$	−9.86701	+	8.74141i	−0.958369	+	0.849041i
$107$	3.90360	+	0.962151i	0.377375	+	0.0930146i	0.423441	−	0.905924i	$-0.360822\pi$
$107$	3.90360	+	0.962151i	0.377375	+	0.0930146i	−0.0460657	+	0.998938i	$0.514668\pi$
$108$	−6.76157	+	1.17888i	−0.650633	+	0.113438i
$109$	−6.94715	−	10.8474i	−0.665416	−	1.03899i	−0.995475	−	0.0950281i	$-0.969706\pi$
$109$	−6.94715	−	10.8474i	−0.665416	−	1.03899i	0.330059	−	0.943960i	$-0.392931\pi$
$110$	0.432142	+	1.63154i	0.0412031	+	0.155561i
$111$	−31.2082	+	2.15823i	−2.96215	+	0.204850i
$112$	5.13783	+	6.00512i	0.485479	+	0.567431i
$113$	−6.49354	−	4.00241i	−0.610861	−	0.376515i	0.184339	−	0.982863i	$-0.440986\pi$
$113$	−6.49354	−	4.00241i	−0.610861	−	0.376515i	−0.795200	+	0.606348i	$0.792634\pi$
$114$	3.71616	−	14.0302i	0.348050	−	1.31405i
$115$	0.645015	−	1.89567i	0.0601479	−	0.176772i
$116$	0.0781592	+	4.52750i	0.00725690	+	0.420368i
$117$	−16.1146	−	7.76036i	−1.48979	−	0.717445i
$118$	2.46042	−	1.89358i	0.226500	−	0.174318i
$119$	5.48625	−	5.98143i	0.502924	−	0.548317i
$120$	0.881628	+	3.86266i	0.0804812	+	0.352611i
$121$	0.721266	+	0.378549i	0.0655696	+	0.0344136i
$122$	−0.215105	+	0.154025i	−0.0194747	+	0.0139448i
$123$	6.25463	+	27.4033i	0.563961	+	2.47088i
$124$	0.843375	−	5.38501i	0.0757374	−	0.483588i
$125$	4.02722	+	0.418593i	0.360206	+	0.0374401i
$126$	22.9866	+	11.0697i	2.04780	+	0.986171i
$127$	5.78928	+	1.00936i	0.513716	+	0.0895664i	0.422676	−	0.906281i	$-0.361091\pi$
$127$	5.78928	+	1.00936i	0.513716	+	0.0895664i	0.0910397	+	0.995847i	$0.470981\pi$
$128$	−2.35808	−	3.41626i	−0.208426	−	0.301958i
$129$	14.5886	+	12.9244i	1.28446	+	1.13793i
$130$	−0.500103	+	1.19277i	−0.0438619	+	0.104613i
$131$	−10.2158	+	2.14688i	−0.892560	+	0.187573i	−0.629310	−	0.777154i	$-0.716662\pi$
$131$	−10.2158	+	2.14688i	−0.892560	+	0.187573i	−0.263250	+	0.964728i	$0.584794\pi$
$132$	5.40797	+	3.08094i	0.470704	+	0.268162i
$133$	9.45365	−	7.80975i	0.819735	−	0.677191i
$134$	4.56695	+	17.2424i	0.394525	+	1.48951i
$135$	2.91207	+	3.92205i	0.250631	+	0.337556i
$136$	−5.92627	+	5.25022i	−0.508174	+	0.450203i
$137$	0.402969	+	0.736607i	0.0344279	+	0.0629326i	0.893952	−	0.448162i	$-0.147921\pi$
$137$	0.402969	+	0.736607i	0.0344279	+	0.0629326i	−0.859524	+	0.511095i	$0.829240\pi$
$138$	8.14945	+	16.2011i	0.693727	+	1.37913i
$139$	−2.99177	−	2.14224i	−0.253758	−	0.181703i	0.448174	−	0.893947i	$-0.352075\pi$
$139$	−2.99177	−	2.14224i	−0.253758	−	0.181703i	−0.701932	+	0.712244i	$0.747679\pi$
$140$	−0.290464	+	0.692772i	−0.0245487	+	0.0585499i
$141$	−20.7550	−	8.28387i	−1.74789	−	0.697628i
$142$	−1.57442	+	1.84019i	−0.132123	+	0.154426i
$143$	3.78682	+	8.22358i	0.316670	+	0.687690i
$144$	−14.4958	−	8.93477i	−1.20799	−	0.744564i
$145$	2.85364	−	1.49770i	0.236982	−	0.124378i
$146$	6.28619	−	2.26072i	0.520249	−	0.187098i
$147$	4.40350	+	8.04938i	0.363194	+	0.663902i
$148$	4.58513	+	3.52878i	0.376895	+	0.290064i
$149$	−5.87869	−	5.98105i	−0.481601	−	0.489987i	0.428982	−	0.903313i	$-0.358872\pi$
$149$	−5.87869	−	5.98105i	−0.481601	−	0.489987i	−0.910583	+	0.413326i	$0.864367\pi$
$150$	−13.8915	+	11.4759i	−1.13424	+	0.937004i
$151$	0.630261	−	2.08579i	0.0512899	−	0.169739i	−0.927838	−	0.372983i	$-0.878335\pi$
$151$	0.630261	−	2.08579i	0.0512899	−	0.169739i	0.979128	+	0.203243i	$0.0651483\pi$
$152$	−9.96004	+	6.62404i	−0.807866	+	0.537281i
$153$	−7.31461	+	15.8846i	−0.591351	+	1.28420i
$154$	−5.40170	−	11.7305i	−0.435281	−	0.945270i
$155$	−3.69358	+	1.18604i	−0.296676	+	0.0952647i
$156$	1.84421	+	4.39853i	0.147655	+	0.352164i
$157$	−4.39838	−	0.766858i	−0.351029	−	0.0612019i	−0.00650329	−	0.999979i	$-0.502070\pi$
$157$	−4.39838	−	0.766858i	−0.351029	−	0.0612019i	−0.344526	+	0.938777i	$0.611960\pi$
$158$	−18.2201	−	8.01181i	−1.44951	−	0.637386i
$159$	31.6710	−	13.9265i	2.51167	−	1.10444i
$160$	0.624453	−	1.14147i	0.0493673	−	0.0902411i
$161$	−2.37072	+	15.1372i	−0.186839	+	1.19298i
$162$	−19.7655	−	2.74694i	−1.55292	−	0.215820i
$163$	6.42267	−	7.00237i	0.503062	−	0.548468i	−0.432498	−	0.901635i	$-0.642368\pi$
$163$	6.42267	−	7.00237i	0.503062	−	0.548468i	0.935560	+	0.353167i	$0.114895\pi$
$164$	2.49503	−	4.56079i	0.194829	−	0.356138i
$165$	0.229290	−	4.42381i	0.0178502	−	0.344394i
$166$	0.402805	+	7.77153i	0.0312637	+	0.603188i
$167$	−0.169394	−	9.81244i	−0.0131081	−	0.759309i	−0.931521	−	0.363687i	$-0.881518\pi$
$167$	−0.169394	−	9.81244i	−0.0131081	−	0.759309i	0.918413	−	0.395622i	$-0.129471\pi$
$168$	−11.7221	−	27.9579i	−0.904383	−	2.15700i
$169$	1.34896	−	5.91020i	0.103766	−	0.454631i
$170$	1.17450	+	0.468773i	0.0900799	+	0.0359533i
$171$	−14.2492	+	22.2488i	−1.08966	+	1.70141i
$172$	−0.434506	−	3.57848i	−0.0331308	−	0.272856i
$173$	−2.03218	−	1.35153i	−0.154504	−	0.102755i	0.474135	−	0.880452i	$-0.342761\pi$
$173$	−2.03218	−	1.35153i	−0.154504	−	0.102755i	−0.628638	+	0.777698i	$0.716387\pi$
$174$	−8.44269	+	27.9403i	−0.640039	+	2.11815i
$175$	−15.1869	+	1.05026i	−1.14802	+	0.0793924i
$176$	2.77651	+	8.16004i	0.209287	+	0.615086i
$177$	−7.66781	+	2.75759i	−0.576348	+	0.207273i
$178$	−10.2855	+	4.95325i	−0.770933	+	0.371262i
$179$	−23.0079	+	6.52106i	−1.71969	+	0.487407i	−0.982182	−	0.187931i	$-0.939822\pi$
$179$	−23.0079	+	6.52106i	−1.71969	+	0.487407i	−0.737508	+	0.675338i	$0.763998\pi$
$180$	0.139520	−	1.61253i	0.0103992	−	0.120191i
$181$	−15.4507	−	13.6882i	−1.14845	−	1.01743i	−0.999592	−	0.0285744i	$-0.990903\pi$
$181$	−15.4507	−	13.6882i	−1.14845	−	1.01743i	−0.148853	−	0.988859i	$-0.547558\pi$
$182$	2.20216	−	9.64829i	0.163235	−	0.715179i
$183$	0.661121	−	0.212291i	0.0488715	−	0.0156930i
$184$	3.82676	−	14.4478i	0.282113	−	1.06511i
$185$	0.777199	−	4.04387i	0.0571408	−	0.297311i
$186$	15.7883	−	31.3870i	1.15765	−	2.30140i
$187$	7.97551	−	3.84080i	0.583227	−	0.280867i
$188$	1.85731	+	3.69233i	0.135459	+	0.269291i
$189$	−27.1056	−	25.7370i	−1.97164	−	1.87209i
$190$	1.66005	+	0.945736i	0.120433	+	0.0686109i
$191$	7.98760	+	5.31225i	0.577962	+	0.384381i	0.808336	−	0.588721i	$-0.200369\pi$
$191$	7.98760	+	5.31225i	0.577962	+	0.384381i	−0.230374	+	0.973102i	$0.573995\pi$
$192$	7.94770	+	26.3022i	0.573576	+	1.89820i
$193$	−2.44141	−	2.01687i	−0.175736	−	0.145177i	0.544874	−	0.838518i	$-0.316578\pi$
$193$	−2.44141	−	2.01687i	−0.175736	−	0.145177i	−0.720610	+	0.693341i	$0.756138\pi$
$194$	0.250688	−	2.06460i	0.0179984	−	0.148230i
$195$	2.20681	−	2.57933i	0.158033	−	0.184710i
$196$	0.377610	−	1.65442i	0.0269722	−	0.118173i
$197$	0.969999	+	1.40529i	0.0691096	+	0.100123i	0.856015	−	0.516952i	$-0.172933\pi$
$197$	0.969999	+	1.40529i	0.0691096	+	0.100123i	−0.786905	+	0.617074i	$0.788318\pi$
$198$	18.8087	+	20.5063i	1.33667	+	1.45732i
$199$	−13.3145	+	3.28173i	−0.943841	+	0.232636i	−0.681066	−	0.732222i	$-0.738484\pi$
$199$	−13.3145	+	3.28173i	−0.943841	+	0.232636i	−0.262774	+	0.964857i	$0.584637\pi$
$200$	14.8410	+	0.512561i	1.04942	+	0.0362435i
$201$	2.42318	−	46.7517i	0.170918	−	3.29761i
$202$	−9.50819	−	0.988290i	−0.668994	−	0.0695358i
$203$	−19.5422	+	15.0400i	−1.37160	+	1.05560i
$204$	4.26890	−	1.87714i	0.298883	−	0.131426i
$205$	−3.69778	−	0.127709i	−0.258264	−	0.00891959i
$206$	−12.4496	+	1.29403i	−0.867408	+	0.0901591i
$207$	−5.10801	−	32.6150i	−0.355031	−	2.26690i
$208$	−2.12765	+	6.25308i	−0.147526	+	0.433573i
$209$	12.7334	−	4.08880i	0.880790	−	0.282828i
$210$	−3.14790	+	3.67928i	−0.217225	+	0.253894i
$211$	−4.13887	+	5.57433i	−0.284931	+	0.383753i	−0.922087	−	0.386982i	$-0.873517\pi$
$211$	−4.13887	+	5.57433i	−0.284931	+	0.383753i	0.637156	+	0.770735i	$0.280111\pi$
$212$	−6.09253	−	1.95635i	−0.418437	−	0.134363i
$213$	5.41094	−	3.33513i	0.370751	−	0.228519i
$214$	−1.38640	−	4.58818i	−0.0947726	−	0.313641i
$215$	−2.13627	+	1.42075i	−0.145693	+	0.0968946i
$216$	23.7037	+	27.7050i	1.61283	+	1.88509i
$217$	26.2833	−	13.7945i	1.78423	−	0.936434i
$218$	−6.90090	+	13.7189i	−0.467388	+	0.929164i
$219$	−17.5226	+	0.605174i	−1.18407	+	0.0408939i
$220$	−0.574306	+	0.584306i	−0.0387197	+	0.0393939i
$221$	6.63845	+	1.39508i	0.446550	+	0.0938435i
$222$	21.1858	+	30.6929i	1.42190	+	2.05997i
$223$	0.0972041	+	0.231837i	0.00650927	+	0.0155249i	0.925441	−	0.378891i	$-0.123694\pi$
$223$	0.0972041	+	0.231837i	0.00650927	+	0.0155249i	−0.918932	+	0.394416i	$0.870947\pi$
$224$	−3.20693	+	9.42503i	−0.214272	+	0.629736i
$225$	30.4634	−	12.1587i	2.03089	−	0.810582i
$226$	−0.156966	+	9.09251i	−0.0104412	+	0.604824i
$227$	−8.38418	+	0.289562i	−0.556477	+	0.0192189i	−0.311390	−	0.950282i	$-0.600795\pi$
$227$	−8.38418	+	0.289562i	−0.556477	+	0.0192189i	−0.245087	+	0.969501i	$0.578817\pi$
$228$	6.77843	−	1.92119i	0.448913	−	0.127234i
$229$	20.8075	+	14.8991i	1.37500	+	0.984562i	0.998303	+	0.0582252i	$0.0185441\pi$
$229$	20.8075	+	14.8991i	1.37500	+	0.984562i	0.376696	+	0.926337i	$0.377060\pi$
$230$	−2.33619	+	0.490956i	−0.154044	+	0.0323727i
$231$	4.08559	+	33.6478i	0.268812	+	2.21387i
$232$	20.4777	−	12.6218i	1.34443	−	0.828661i
$233$	−0.457096	−	1.20526i	−0.0299453	−	0.0789594i	0.919210	−	0.393768i	$-0.128829\pi$
$233$	−0.457096	−	1.20526i	−0.0299453	−	0.0789594i	−0.949155	+	0.314809i	$0.898060\pi$
$234$	1.83806	+	21.2437i	0.120158	+	1.38874i
$235$	1.75361	−	2.36180i	0.114393	−	0.154067i
$236$	1.39973	+	0.558669i	0.0911147	+	0.0363663i
$237$	39.1015	+	34.6409i	2.53991	+	2.25017i
$238$	−9.46939	−	1.99001i	−0.613810	−	0.128993i
$239$	7.02907	−	10.1834i	0.454673	−	0.658707i	−0.526871	−	0.849945i	$-0.676635\pi$
$239$	7.02907	−	10.1834i	0.454673	−	0.658707i	0.981544	+	0.191238i	$0.0612503\pi$
$240$	2.34361	−	2.22529i	0.151279	−	0.143642i
$241$	15.2645	−	1.58660i	0.983271	−	0.102202i	0.401764	−	0.915743i	$-0.368397\pi$
$241$	15.2645	−	1.58660i	0.983271	−	0.102202i	0.581507	+	0.813541i	$0.302463\pi$
$242$	−0.0502661	−	0.969811i	−0.00323123	−	0.0623418i
$243$	15.1311	+	7.28676i	0.970662	+	0.467446i
$244$	−0.117561	−	0.0516947i	−0.00752610	−	0.00330941i
$245$	−1.17267	+	0.289037i	−0.0749190	+	0.0184659i
$246$	24.3005	−	23.0736i	1.54935	−	1.47112i
$247$	9.64374	+	3.46820i	0.613617	+	0.220676i
$248$	−26.8926	+	10.7336i	−1.70768	+	0.681581i
$249$	5.22944	−	19.7435i	0.331402	−	1.25120i
$250$	−2.01899	−	4.38451i	−0.127692	−	0.277301i
$251$	−1.37384	+	11.3146i	−0.0867158	+	0.714169i	0.882904	+	0.469553i	$0.155585\pi$
$251$	−1.37384	+	11.3146i	−0.0867158	+	0.714169i	−0.969620	+	0.244616i	$0.921338\pi$
$252$	1.06756	+	12.3385i	0.0672500	+	0.777255i
$253$	−8.52125	+	14.3746i	−0.535726	+	0.903726i
$254$	−2.48435	−	6.55070i	−0.155882	−	0.411027i
$255$	−2.55881	−	2.11386i	−0.160239	−	0.132375i
$256$	5.27603	−	11.4576i	0.329752	−	0.716100i
$257$	13.5711	+	8.36478i	0.846541	+	0.521781i	0.878519	−	0.477708i	$-0.158532\pi$
$257$	13.5711	+	8.36478i	0.846541	+	0.521781i	−0.0319779	+	0.999489i	$0.510181\pi$
$258$	4.38547	−	22.8182i	0.273028	−	1.42060i
$259$	−0.543859	+	31.5039i	−0.0337938	+	1.95756i
$260$	−0.621853	+	0.0864229i	−0.0385657	+	0.00535972i
$261$	30.1826	−	43.7271i	1.86826	−	2.70664i
$262$	8.41219	+	9.17146i	0.519707	+	0.566615i
$263$	31.0481	+	5.41323i	1.91451	+	0.333794i	0.997830	−	0.0658376i	$-0.0209719\pi$
$263$	31.0481	+	5.41323i	1.91451	+	0.333794i	0.916676	+	0.399632i	$0.130862\pi$
$264$	−0.570704	−	33.0589i	−0.0351244	−	2.03464i
$265$	0.704674	+	4.49939i	0.0432878	+	0.276395i
$266$	−13.7563	−	4.94721i	−0.843452	−	0.303333i
$267$	29.6771	−	4.12443i	1.81621	−	0.252411i
$268$	−6.06937	+	6.17505i	−0.370746	+	0.377201i
$269$	2.51205	−	29.0335i	0.153163	−	1.77021i	−0.380761	−	0.924674i	$-0.624338\pi$
$269$	2.51205	−	29.0335i	0.153163	−	1.77021i	0.533923	−	0.845533i	$-0.320717\pi$
$270$	2.25184	−	5.37075i	0.137043	−	0.326853i
$271$	11.5149	−	17.9795i	0.699479	−	1.09217i	−0.291293	−	0.956634i	$-0.594086\pi$
$271$	11.5149	−	17.9795i	0.699479	−	1.09217i	0.990772	−	0.135540i	$-0.0432771\pi$
$272$	6.14896	+	1.97448i	0.372835	+	0.119720i
$273$	−13.2449	+	22.3431i	−0.801621	+	1.35227i
$274$	0.510435	−	0.861062i	0.0308365	−	0.0520187i
$275$	−15.8081	−	5.07608i	−0.953262	−	0.306099i
$276$	−4.74777	+	7.41323i	−0.285782	+	0.446224i
$277$	0.0656667	−	0.156618i	0.00394553	−	0.00941029i	−0.920235	−	0.391367i	$-0.872002\pi$
$277$	0.0656667	−	0.156618i	0.00394553	−	0.00941029i	0.924180	+	0.381957i	$0.124750\pi$
$278$	−0.378145	+	4.37048i	−0.0226796	+	0.262124i
$279$	−44.8321	+	45.6127i	−2.68403	+	2.73076i
$280$	3.95262	−	0.549321i	0.236214	−	0.0328282i
$281$	−28.0744	−	10.0965i	−1.67478	−	0.602305i	−0.683019	−	0.730400i	$-0.739334\pi$
$281$	−28.0744	−	10.0965i	−1.67478	−	0.602305i	−0.991762	+	0.128095i	$0.959114\pi$
$282$	4.12226	+	26.3209i	0.245477	+	1.56739i
$283$	0.357336	+	20.6993i	0.0212414	+	1.23044i	0.798785	+	0.601616i	$0.205476\pi$
$283$	0.357336	+	20.6993i	0.0212414	+	1.23044i	−0.777544	+	0.628829i	$0.783535\pi$
$284$	−1.15813	−	0.201919i	−0.0687221	−	0.0119817i
$285$	−3.38943	−	3.69536i	−0.200773	−	0.218894i
$286$	6.13140	−	8.88286i	0.362557	−	0.525255i
$287$	28.0415	−	3.89711i	1.65524	−	0.230039i
$288$	0.370254	−	21.4476i	0.0218174	−	1.26381i
$289$	−1.95673	+	10.1811i	−0.115102	+	0.598891i
$290$	−3.27075	−	2.01599i	−0.192065	−	0.118383i
$291$	−2.28312	+	4.95810i	−0.133839	+	0.290649i
$292$	2.50004	+	2.06530i	0.146304	+	0.120863i
$293$	1.02369	+	2.69925i	0.0598045	+	0.157692i	0.961588	−	0.274496i	$-0.0885110\pi$
$293$	1.02369	+	2.69925i	0.0598045	+	0.157692i	−0.901784	+	0.432188i	$0.857742\pi$
$294$	5.57785	−	9.40938i	0.325307	−	0.548766i
$295$	−0.0924615	−	1.06864i	−0.00538331	−	0.0622187i
$296$	3.70482	−	30.5119i	0.215338	−	1.77347i
$297$	−17.0511	−	37.0287i	−0.989406	−	2.14863i
$298$	−2.55991	+	9.66484i	−0.148291	+	0.559869i
$299$	−11.8931	+	4.74684i	−0.687795	+	0.274517i
$300$	−8.23056	−	2.95997i	−0.475192	−	0.170894i
$301$	14.2359	−	13.5171i	0.820543	−	0.779115i
$302$	−2.52219	+	0.621665i	−0.145136	+	0.0357728i
$303$	22.9671	+	10.0992i	1.31942	+	0.580183i
$304$	8.79077	+	4.23341i	0.504185	+	0.242803i
$305$	0.00473113	+	0.0912802i	0.000270904	+	0.00522669i
$306$	20.7370	−	2.15542i	1.18545	−	0.123217i
$307$	−25.2730	+	23.9970i	−1.44241	+	1.36958i	−0.649218	+	0.760603i	$0.724904\pi$
$307$	−25.2730	+	23.9970i	−1.44241	+	1.36958i	−0.793187	+	0.608978i	$0.791580\pi$
$308$	3.56117	−	5.15925i	0.202917	−	0.293976i
$309$	32.1488	+	6.75615i	1.82888	+	0.384344i
$310$	3.46176	+	3.06685i	0.196615	+	0.174185i
$311$	−14.1182	−	5.63493i	−0.800567	−	0.319527i	−0.0657878	−	0.997834i	$-0.520956\pi$
$311$	−14.1182	−	5.63493i	−0.800567	−	0.319527i	−0.734779	+	0.678306i	$0.762714\pi$
$312$	15.1042	−	20.3428i	0.855109	−	1.15168i
$313$	1.15091	+	13.3019i	0.0650535	+	0.751869i	0.955155	+	0.296106i	$0.0956883\pi$
$313$	1.15091	+	13.3019i	0.0650535	+	0.751869i	−0.890101	+	0.455763i	$0.849367\pi$
$314$	1.88747	+	4.97686i	0.106516	+	0.280861i
$315$	7.50355	−	4.62495i	0.422777	−	0.260586i
$316$	−1.16459	−	9.59129i	−0.0655135	−	0.539552i
$317$	14.4869	−	3.04445i	0.813665	−	0.170994i	0.219786	−	0.975548i	$-0.429464\pi$
$317$	14.4869	−	3.04445i	0.813665	−	0.170994i	0.593879	+	0.804554i	$0.297596\pi$
$318$	−33.5358	−	24.0132i	−1.88060	−	1.34659i
$319$	−25.8757	+	7.33389i	−1.44876	+	0.410619i
$320$	−3.61472	+	0.124841i	−0.202069	+	0.00697880i
$321$	−0.217135	+	12.5779i	−0.0121193	+	0.702030i
$322$	16.9649	−	6.77112i	0.945414	−	0.377340i
$323$	3.22778	−	9.48631i	0.179598	−	0.527833i
$324$	−3.74557	−	8.93337i	−0.208087	−	0.496298i
$325$	−7.22750	−	10.4708i	−0.400910	−	0.580818i
$326$	−11.0857	−	2.32968i	−0.613979	−	0.129029i
$327$	28.2530	−	28.7450i	1.56240	−	1.58960i
$328$	−27.6004	+	0.953226i	−1.52398	+	0.0526331i
$329$	−10.1146	+	20.1078i	−0.557638	+	1.10858i
$330$	−4.67614	+	2.45423i	−0.257413	+	0.135101i
$331$	15.5633	+	18.1905i	0.855436	+	0.999838i	0.999947	+	0.0103347i	$0.00328971\pi$
$331$	15.5633	+	18.1905i	0.855436	+	0.999838i	−0.144511	+	0.989503i	$0.546161\pi$
$332$	−3.14543	+	2.09190i	−0.172628	+	0.114808i
$333$	−19.6371	−	64.9872i	−1.07611	−	3.56128i
$334$	−9.95996	+	6.13900i	−0.544985	+	0.335911i
$335$	5.86731	+	1.88404i	0.320565	+	0.102936i
$336$	−14.7415	+	19.8542i	−0.804212	+	1.08313i
$337$	−20.9280	+	24.4607i	−1.14002	+	1.33246i	−0.204632	+	0.978839i	$0.565600\pi$
$337$	−20.9280	+	24.4607i	−1.14002	+	1.33246i	−0.935388	+	0.353623i	$0.884950\pi$
$338$	−6.88116	+	2.20959i	−0.374286	+	0.120186i
$339$	7.68822	−	22.5954i	0.417567	−	1.22721i
$340$	0.0949823	+	0.606468i	0.00515114	+	0.0328904i
$341$	32.2005	−	3.34695i	1.74376	−	0.181248i
$342$	31.4794	+	1.08719i	1.70221	+	0.0587887i
$343$	−11.7351	+	5.16021i	−0.633635	+	0.278625i
$344$	−15.1756	+	11.6794i	−0.818214	+	0.629710i
$345$	6.23187	+	0.647747i	0.335513	+	0.0348735i
$346$	−0.150605	+	2.90570i	−0.00809655	+	0.156211i
$347$	7.27049	+	0.251099i	0.390300	+	0.0134797i	0.229002	−	0.973426i	$-0.426454\pi$
$347$	7.27049	+	0.251099i	0.390300	+	0.0134797i	0.161299	+	0.986906i	$0.448432\pi$
$348$	−13.7568	+	3.39074i	−0.737441	+	0.181763i
$349$	−3.35028	−	3.65267i	−0.179336	−	0.195523i	0.640772	−	0.767731i	$-0.278614\pi$
$349$	−3.35028	−	3.65267i	−0.179336	−	0.195523i	−0.820108	+	0.572208i	$0.806087\pi$
$350$	10.3096	+	14.9361i	0.551074	+	0.798368i
$351$	6.95139	−	30.4560i	0.371037	−	1.62562i
$352$	−7.05890	+	8.25048i	−0.376241	+	0.439752i
$353$	−0.990594	+	8.15827i	−0.0527240	+	0.434221i	0.942314	+	0.334729i	$0.108645\pi$
$353$	−0.990594	+	8.15827i	−0.0527240	+	0.434221i	−0.995038	+	0.0994919i	$0.968278\pi$
$354$	7.48949	+	6.18714i	0.398062	+	0.328843i
$355$	0.242016	+	0.800928i	0.0128449	+	0.0425088i
$356$	−4.61431	−	3.06881i	−0.244558	−	0.162646i
$357$	22.0663	+	12.5713i	1.16787	+	0.665342i
$358$	20.6747	+	19.6309i	1.09269	+	1.03753i
$359$	11.1225	+	22.1114i	0.587023	+	1.16700i	0.969969	+	0.243227i	$0.0782059\pi$
$359$	11.1225	+	22.1114i	0.587023	+	1.16700i	−0.382947	+	0.923770i	$0.625091\pi$
$360$	−7.74677	+	3.73065i	−0.408291	+	0.196622i
$361$	−1.73510	+	3.44937i	−0.0913211	+	0.181546i
$362$	−4.64463	+	24.1667i	−0.244116	+	1.27017i
$363$	−0.652582	+	2.46380i	−0.0342517	+	0.129316i
$364$	4.57391	−	1.46872i	0.239738	−	0.0769817i
$365$	0.513568	−	2.25009i	0.0268814	−	0.117775i
$366$	−0.619626	−	0.548941i	−0.0323884	−	0.0286936i
$367$	−0.232497	+	2.68713i	−0.0121363	+	0.140267i	−0.999874	−	0.0158529i	$-0.994954\pi$
$367$	−0.232497	+	2.68713i	−0.0121363	+	0.140267i	0.987738	+	0.156120i	$0.0498987\pi$
$368$	−11.7294	+	3.32442i	−0.611435	+	0.173297i
$369$	−54.9588	+	26.4667i	−2.86104	+	1.37780i
$370$	−4.61959	+	1.66135i	−0.240161	+	0.0863697i
$371$	−11.2251	−	32.9901i	−0.582778	−	1.71276i
$372$	17.0143	−	1.17664i	0.882148	−	0.0610058i
$373$	2.93843	−	9.72446i	0.152146	−	0.503513i	−0.847481	−	0.530826i	$-0.821882\pi$
$373$	2.93843	−	9.72446i	0.152146	−	0.503513i	0.999627	+	0.0273126i	$0.00869494\pi$
$374$	−8.78741	−	5.84418i	−0.454386	−	0.302195i
$375$	1.52707	+	12.5766i	0.0788576	+	0.649450i
$376$	11.8416	−	18.4896i	0.610684	−	0.953530i
$377$	−19.1415	−	7.63986i	−0.985835	−	0.393473i
$378$	−9.91578	+	43.4439i	−0.510013	+	2.23451i
$379$	−3.29124	−	7.84978i	−0.169060	−	0.403216i	0.815383	−	0.578922i	$-0.196526\pi$
$379$	−3.29124	−	7.84978i	−0.169060	−	0.403216i	−0.984443	+	0.175706i	$0.943779\pi$
$380$	0.0160079	+	0.927282i	0.000821186	+	0.0475686i
$381$	0.951774	+	18.3631i	0.0487608	+	0.940769i
$382$	0.591960	−	11.4210i	0.0302873	−	0.584349i
$383$	16.7755	−	30.6649i	0.857190	−	1.56690i	0.0337976	−	0.999429i	$-0.489240\pi$
$383$	16.7755	−	30.6649i	0.857190	−	1.56690i	0.823392	−	0.567473i	$-0.192079\pi$
$384$	8.77953	−	9.57196i	0.448029	−	0.488467i
$385$	−4.41926	−	0.614174i	−0.225227	−	0.0313012i
$386$	−0.584152	+	3.72985i	−0.0297326	+	0.189844i
$387$	−20.3001	+	37.1076i	−1.03191	+	1.88628i
$388$	0.924164	−	0.406377i	0.0469173	−	0.0206307i
$389$	−0.113124	−	0.0497432i	−0.00573559	−	0.00252208i	0.399657	−	0.916665i	$-0.369129\pi$
$389$	−0.113124	−	0.0497432i	−0.00573559	−	0.00252208i	−0.405393	+	0.914142i	$0.632865\pi$
$390$	−3.98676	−	0.695093i	−0.201878	−	0.0351974i
$391$	4.84126	+	11.5466i	0.244833	+	0.583939i
$392$	−8.58315	+	2.75611i	−0.433514	+	0.139205i
$393$	−13.6619	−	29.6687i	−0.689154	−	1.49659i
$394$	0.851470	−	1.84908i	0.0428965	−	0.0931553i
$395$	−5.72578	+	3.80800i	−0.288095	+	0.191601i
$396$	−3.90700	+	12.9299i	−0.196334	+	0.649750i
$397$	2.95339	−	2.43982i	0.148226	−	0.122451i	−0.559829	−	0.828608i	$-0.689133\pi$
$397$	2.95339	−	2.43982i	0.148226	−	0.122451i	0.708055	+	0.706157i	$0.249573\pi$
$398$	11.4598	+	11.6594i	0.574429	+	0.584431i
$399$	30.4060	+	23.4009i	1.52220	+	1.17151i
$400$	−5.81347	−	10.6267i	−0.290673	−	0.531337i
$401$	−22.9529	+	8.25459i	−1.14621	+	0.412215i	−0.841515	−	0.540234i	$-0.818336\pi$
$401$	−22.9529	+	8.25459i	−1.14621	+	0.412215i	−0.304697	+	0.952449i	$0.598555\pi$
$402$	−49.4183	+	25.9367i	−2.46476	+	1.29361i
$403$	21.1190	+	13.0171i	1.05201	+	0.648427i
$404$	−1.94091	−	4.21494i	−0.0965638	−	0.209701i
$405$	−4.48201	+	5.23860i	−0.222713	+	0.260308i
$406$	27.3043	+	10.8979i	1.35509	+	0.540852i
$407$	−13.2877	+	31.6918i	−0.658647	+	1.57091i
$408$	−20.1421	−	14.4227i	−0.997183	−	0.714029i
$409$	7.80318	+	15.5127i	0.385842	+	0.767052i	0.999751	−	0.0223252i	$-0.00710691\pi$
$409$	7.80318	+	15.5127i	0.385842	+	0.767052i	−0.613908	+	0.789377i	$0.710404\pi$
$410$	2.11702	+	3.86982i	0.104552	+	0.191117i
$411$	−1.96646	+	1.74213i	−0.0969984	+	0.0859331i
$412$	−3.62203	−	4.87824i	−0.178445	−	0.240334i
$413$	2.10142	+	7.93385i	0.103404	+	0.390399i
$414$	−30.3423	+	25.0661i	−1.49124	+	1.23193i
$415$	2.33604	+	1.33085i	0.114672	+	0.0653290i
$416$	−8.14277	+	1.71122i	−0.399232	+	0.0838995i
$417$	4.45190	−	10.6180i	0.218010	−	0.519965i
$418$	−11.9342	−	10.5728i	−0.583722	−	0.517133i
$419$	2.22959	+	3.23012i	0.108923	+	0.157802i	0.873654	−	0.486547i	$-0.161744\pi$
$419$	2.22959	+	3.23012i	0.108923	+	0.157802i	−0.764732	+	0.644349i	$0.777128\pi$
$420$	−2.31555	−	0.403716i	−0.112987	−	0.0196993i
$421$	4.33392	+	2.08711i	0.211222	+	0.101719i	0.536504	−	0.843898i	$-0.319745\pi$
$421$	4.33392	+	2.08711i	0.211222	+	0.101719i	−0.325281	+	0.945617i	$0.605459\pi$
$422$	8.23279	+	0.855723i	0.400766	+	0.0416559i
$423$	7.50395	−	47.9132i	0.364855	−	2.32962i
$424$	7.56416	+	33.1408i	0.367348	+	1.60946i
$425$	−10.1144	+	7.24236i	−0.490620	+	0.351306i
$426$	−6.70975	−	3.52155i	−0.325088	−	0.170620i
$427$	−0.155627	−	0.681848i	−0.00753133	−	0.0329969i
$428$	1.57269	−	1.71464i	0.0760189	−	0.0828802i
$429$	−22.4495	+	17.2775i	−1.08387	+	0.834166i
$430$	2.75573	+	1.32709i	0.132893	+	0.0639979i
$431$	−0.233764	−	13.5412i	−0.0112600	−	0.652255i	−0.950798	−	0.309811i	$-0.899734\pi$
$431$	−0.233764	−	13.5412i	−0.0112600	−	0.652255i	0.939538	−	0.342444i	$-0.111255\pi$
$432$	9.58030	−	28.1561i	0.460932	−	1.35466i
$433$	6.68539	−	25.2405i	0.321279	−	1.21298i	−0.592098	−	0.805866i	$-0.701700\pi$
$433$	6.68539	−	25.2405i	0.321279	−	1.21298i	0.913378	−	0.407113i	$-0.133465\pi$
$434$	−30.1251	−	18.5682i	−1.44605	−	0.891301i
$435$	6.55565	+	7.66228i	0.314319	+	0.367378i
$436$	−7.43678	+	0.514297i	−0.356157	+	0.0246304i
$437$	4.84322	+	18.2854i	0.231682	+	0.874709i
$438$	11.2732	+	17.6021i	0.538653	+	0.841060i
$439$	−4.66203	+	0.812826i	−0.222507	+	0.0387940i	−0.281914	−	0.959440i	$-0.590969\pi$
$439$	−4.66203	+	0.812826i	−0.222507	+	0.0387940i	0.0594069	+	0.998234i	$0.481079\pi$
$440$	4.22587	+	1.04158i	0.201460	+	0.0496555i
$441$	−14.9042	+	13.2039i	−0.709722	+	0.628758i
$442$	−2.60502	−	7.65604i	−0.123908	−	0.364161i
$443$	−4.70848	−	5.50330i	−0.223707	−	0.261470i	0.636660	−	0.771144i	$-0.280315\pi$
$443$	−4.70848	−	5.50330i	−0.223707	−	0.261470i	−0.860367	+	0.509674i	$0.829766\pi$
$444$	−7.57217	+	16.4440i	−0.359359	+	0.780396i
$445$	−0.475406	+	3.91532i	−0.0225364	+	0.185604i
$446$	0.178662	−	0.240626i	0.00845988	−	0.0113940i
$447$	14.1522	−	22.0974i	0.669376	−	1.04517i
$448$	27.0835	−	5.69166i	1.27958	−	0.268906i
$449$	2.63450	+	2.50149i	0.124330	+	0.118052i	0.748193	−	0.663481i	$-0.230922\pi$
$449$	2.63450	+	2.50149i	0.124330	+	0.118052i	−0.623864	+	0.781533i	$0.714438\pi$
$450$	−30.9888	−	23.8494i	−1.46082	−	1.12427i
$451$	29.9800	+	7.38941i	1.41170	+	0.347954i
$452$	−3.83558	+	2.18515i	−0.180411	+	0.102781i
$453$	6.80156	+	0.470368i	0.319565	+	0.0220998i
$454$	5.39395	+	8.42218i	0.253151	+	0.395273i
$455$	−2.39668	−	2.43841i	−0.112358	−	0.114315i
$456$	−27.1415	−	25.7712i	−1.27102	−	1.20685i
$457$	−4.72010	−	3.37981i	−0.220797	−	0.158101i	0.466395	−	0.884577i	$-0.345553\pi$
$457$	−4.72010	−	3.37981i	−0.220797	−	0.158101i	−0.687192	+	0.726476i	$0.741157\pi$
$458$	2.62997	−	30.3964i	0.122890	−	1.42033i
$459$	−29.8913	−	6.28172i	−1.39521	−	0.293206i
$460$	−0.783290	−	0.853989i	−0.0365211	−	0.0398174i
$461$	−17.8704	−	7.85804i	−0.832306	−	0.365985i	−0.0576255	−	0.998338i	$-0.518353\pi$
$461$	−17.8704	−	7.85804i	−0.832306	−	0.365985i	−0.774680	+	0.632353i	$0.782089\pi$
$462$	32.0231	−	24.6454i	1.48985	−	1.14661i
$463$	13.0775	+	1.81747i	0.607764	+	0.0844650i	0.434897	−	0.900480i	$-0.356785\pi$
$463$	13.0775	+	1.81747i	0.607764	+	0.0844650i	0.172867	+	0.984945i	$0.444697\pi$
$464$	−17.3740	−	9.11859i	−0.806569	−	0.423320i
$465$	−6.18972	−	10.4415i	−0.287041	−	0.484215i
$466$	−0.958150	+	1.20148i	−0.0443854	+	0.0556576i
$467$	10.1182	+	17.0686i	0.468214	+	0.789838i	0.998311	−	0.0580987i	$-0.0185038\pi$
$467$	10.1182	+	17.0686i	0.468214	+	0.789838i	−0.530097	+	0.847937i	$0.677844\pi$
$468$	−8.41569	+	6.02602i	−0.389015	+	0.278553i
$469$	−46.7036	−	6.49070i	−2.15657	−	0.299713i
$470$	−3.48817	−	0.362564i	−0.160897	−	0.0167238i
$471$	−0.723105	−	13.9513i	−0.0333189	−	0.642840i
$472$	−1.23879	−	7.90977i	−0.0570200	−	0.364077i
$473$	19.8850	−	7.93664i	0.914315	−	0.364927i
$474$	11.7542	−	61.1590i	0.539891	−	2.80912i
$475$	−16.6415	+	8.73413i	−0.763564	+	0.400749i
$476$	−1.51302	−	4.44670i	−0.0693491	−	0.203814i
$477$	44.7596	+	60.2833i	2.04940	+	2.76018i
$478$	−14.7165	−	1.01773i	−0.673118	−	0.0465501i
$479$	3.99119	+	20.7667i	0.182362	+	0.948855i	0.951005	+	0.309176i	$0.100053\pi$
$479$	3.99119	+	20.7667i	0.182362	+	0.948855i	−0.768643	+	0.639678i	$0.779068\pi$
$480$	3.91685	+	1.11014i	0.178779	+	0.0506709i
$481$	−22.8812	+	13.0355i	−1.04329	+	0.594368i
$482$	−10.9069	−	14.6896i	−0.496794	−	0.669094i
$483$	−47.8269	+	3.30751i	−2.17620	+	0.150497i
$484$	0.392519	−	0.261049i	0.0178418	−	0.0118659i
$485$	−0.553951	−	0.457624i	−0.0251536	−	0.0207796i
$486$	−1.72589	−	19.9473i	−0.0782877	−	0.904826i
$487$	−20.0046	−	6.42363i	−0.906496	−	0.291082i	−0.184380	−	0.982855i	$-0.559028\pi$
$487$	−20.0046	−	6.42363i	−0.906496	−	0.291082i	−0.722115	+	0.691773i	$0.756830\pi$
$488$	0.0822342	+	0.677260i	0.00372257	+	0.0306581i
$489$	25.8327	+	14.7170i	1.16819	+	0.665525i
$490$	1.00932	+	1.02689i	0.0455963	+	0.0463902i
$491$	17.7418	−	3.09329i	0.800677	−	0.139598i	0.243402	−	0.969926i	$-0.421737\pi$
$491$	17.7418	−	3.09329i	0.800677	−	0.139598i	0.557276	+	0.830327i	$0.311847\pi$
$492$	15.6500	+	4.43563i	0.705555	+	0.199973i
$493$	−7.14573	+	18.8417i	−0.321827	+	0.848589i
$494$	−2.30599	−	11.9984i	−0.103751	−	0.539832i
$495$	9.47051	−	1.65118i	0.425668	−	0.0742152i
$496$	18.7174	+	14.4052i	0.840436	+	0.646812i
$497$	−2.87692	−	5.71929i	−0.129047	−	0.256545i
$498$	−23.4267	+	6.63977i	−1.04978	+	0.297535i
$499$	26.4517	−	26.9122i	1.18414	−	1.20476i	0.210271	−	0.977643i	$-0.432565\pi$
$499$	26.4517	−	26.9122i	1.18414	−	1.20476i	0.973868	−	0.227114i	$-0.0729291\pi$
$500$	1.33106	−	1.92837i	0.0595268	−	0.0862395i
$501$	29.8151	−	7.34875i	1.33204	−	0.328318i
$502$	12.4386	−	5.46956i	0.555162	−	0.244118i
$503$	−28.9963	+	31.6134i	−1.29288	+	1.40957i	−0.431088	+	0.902310i	$0.641870\pi$
$503$	−28.9963	+	31.6134i	−1.29288	+	1.40957i	−0.861791	+	0.507263i	$0.830657\pi$
$504$	53.4918	−	38.3026i	2.38271	−	1.70613i
$505$	−2.05915	+	2.58210i	−0.0916312	+	0.114902i
$506$	19.9220			0.885639
$507$	18.9684			0.842416
$508$	2.12040	−	2.65889i	0.0940774	−	0.117969i
$509$	−7.10720	−	3.73014i	−0.315021	−	0.165336i	0.299801	−	0.954002i	$-0.403080\pi$
$509$	−7.10720	−	3.73014i	−0.315021	−	0.165336i	−0.614822	+	0.788666i	$0.710772\pi$
$510$	−0.612244	+	3.90922i	−0.0271106	+	0.173103i
$511$	−0.914089	+	17.6360i	−0.0404369	+	0.780171i
$512$	−23.2152	+	2.41301i	−1.02598	+	0.106641i
$513$	−43.4234	−	15.6165i	−1.91719	−	0.689483i
$514$	0.328049	−	19.0028i	0.0144696	−	0.838175i
$515$	−1.94322	+	3.86312i	−0.0856287	+	0.170229i
$516$	10.6137	−	3.81702i	0.467241	−	0.168035i
$517$	−18.3750	+	16.2788i	−0.808131	+	0.715942i
$518$	32.6388	−	18.5945i	1.43407	−	0.816994i
$519$	2.70793	−	7.14021i	0.118865	−	0.313421i
$520$	2.07948	+	2.60758i	0.0911911	+	0.114350i
$521$	−7.29367	+	19.2318i	−0.319541	+	0.842561i	0.674962	+	0.737853i	$0.264160\pi$
$521$	−7.29367	+	19.2318i	−0.319541	+	0.842561i	−0.994503	+	0.104708i	$0.966609\pi$
$522$	−63.1924	−	4.37013i	−2.76586	−	0.191275i
$523$	10.1488	+	38.3165i	0.443776	+	1.67546i	0.704227	+	0.709975i	$0.251294\pi$
$523$	10.1488	+	38.3165i	0.443776	+	1.67546i	−0.260451	+	0.965487i	$0.583871\pi$
$524$	−1.74741	+	5.78289i	−0.0763359	+	0.252627i
$525$	−13.7779	−	45.5966i	−0.601315	−	1.99000i
$526$	−13.3237	−	35.1316i	−0.580939	−	1.53181i
$527$	12.3692	−	20.8657i	0.538809	−	0.908926i
$528$	−22.9592	+	14.1513i	−0.999169	+	0.615856i
$529$	−0.529087	−	0.351876i	−0.0230038	−	0.0152989i
$530$	4.18586	−	3.45798i	0.181822	−	0.150205i
$531$	−9.53731	−	14.8917i	−0.413884	−	0.646243i
$532$	−1.33934	−	6.96877i	−0.0580677	−	0.302134i
$533$	14.7527	+	18.4993i	0.639009	+	0.801292i
$534$	−22.2714	−	27.9274i	−0.963776	−	1.20854i
$535$	−1.59317	−	0.451549i	−0.0688789	−	0.0195222i
$536$	44.6597	+	11.0076i	1.92901	+	0.475457i
$537$	−35.9121	−	65.6456i	−1.54972	−	2.83282i
$538$	−31.3019	+	15.0742i	−1.34952	+	0.649895i
$539$	10.0731	−	0.347891i	0.433878	−	0.0149847i
$540$	2.80005	−	0.389141i	0.120495	−	0.0167460i
$541$	−12.5677	+	11.9331i	−0.540326	+	0.513046i	−0.909158	−	0.416450i	$-0.863274\pi$
$541$	−12.5677	+	11.9331i	−0.540326	+	0.513046i	0.368833	+	0.929496i	$0.379758\pi$
$542$	−25.4387	−	0.878569i	−1.09269	−	0.0377378i
$543$	30.9982	−	56.6633i	1.33026	−	2.43165i
$544$	1.81032	+	7.93154i	0.0776169	+	0.340062i
$545$	2.70547	+	4.56390i	0.115890	+	0.195496i
$546$	30.9656			1.32520
$547$	−23.1687	−	3.19553i	−0.990622	−	0.136631i
$547$	−23.1687	−	3.19553i	−0.990622	−	0.136631i
$548$	0.485900			0.0207566
$549$	0.768422	+	1.29626i	0.0327954	+	0.0553232i
$550$	4.40454	+	19.2975i	0.187810	+	0.822850i
$551$	−14.6114	+	26.7090i	−0.622468	+	1.13784i
$552$	46.7377	+	1.61417i	1.98929	+	0.0687035i
$553$	38.1560	−	36.2296i	1.62256	−	1.54064i
$554$	−0.200538	+	0.0278700i	−0.00852003	+	0.00118408i
$555$	12.8770	−	0.444730i	0.546599	−	0.0188777i
$556$	−1.91857	+	0.923935i	−0.0813656	+	0.0391836i
$557$	13.8556	+	25.3274i	0.587081	+	1.07316i	0.987618	+	0.156875i	$0.0501420\pi$
$557$	13.8556	+	25.3274i	0.587081	+	1.07316i	−0.400538	+	0.916280i	$0.631177\pi$
$558$	74.0320	+	18.2472i	3.13402	+	0.772467i
$559$	15.7851	+	4.47394i	0.667640	+	0.189227i
$560$	−2.02953	−	2.54495i	−0.0857634	−	0.107544i
$561$	17.2695	+	21.6552i	0.729117	+	0.914284i
$562$	6.71309	+	34.9291i	0.283175	+	1.47340i
$563$	−2.35810	−	3.68197i	−0.0993822	−	0.155177i	0.788828	−	0.614614i	$-0.210688\pi$
$563$	−2.35810	−	3.68197i	−0.0993822	−	0.155177i	−0.888210	+	0.459438i	$0.848051\pi$
$564$	−9.97034	+	8.23659i	−0.419827	+	0.346823i
$565$	2.61606	+	1.73984i	0.110058	+	0.0731957i
$566$	21.0105	−	12.9502i	0.883137	−	0.544337i
$567$	26.9004	−	45.3787i	1.12971	−	1.90573i
$568$	2.21455	+	5.83929i	0.0929205	+	0.245011i
$569$	−1.57155	−	5.20091i	−0.0658830	−	0.218034i	0.918084	−	0.396387i	$-0.129736\pi$
$569$	−1.57155	−	5.20091i	−0.0658830	−	0.218034i	−0.983966	+	0.178353i	$0.942923\pi$
$570$	−1.72916	+	5.72248i	−0.0724264	+	0.239689i
$571$	−0.442048	−	1.66894i	−0.0184991	−	0.0698428i	0.956786	−	0.290793i	$-0.0939192\pi$
$571$	−0.442048	−	1.66894i	−0.0184991	−	0.0698428i	−0.975285	+	0.220951i	$0.929084\pi$
$572$	5.22691	+	0.361472i	0.218548	+	0.0151139i
$573$	−10.6437	+	28.0650i	−0.444645	+	1.17243i
$574$	−21.0439	−	26.3882i	−0.878355	−	1.10142i
$575$	8.32732	−	21.9573i	0.347273	−	0.915685i
$576$	−51.8114	+	29.5171i	−2.15881	+	1.22988i
$577$	16.3430	−	14.4787i	0.680369	−	0.602754i	−0.250496	−	0.968118i	$-0.580594\pi$
$577$	16.3430	−	14.4787i	0.680369	−	0.602754i	0.930865	+	0.365363i	$0.119055\pi$
$578$	11.6306	−	4.18274i	0.483770	−	0.173979i
$579$	4.45264	−	8.85181i	0.185045	−	0.367869i
$580$	0.0321921	−	1.86478i	0.00133671	−	0.0774308i
$581$	−19.3581	−	6.96178i	−0.803107	−	0.288823i
$582$	6.47265	−	0.672773i	0.268300	−	0.0278873i
$583$	1.96726	−	37.9553i	0.0814754	−	1.57195i
$584$	2.66547	−	17.0192i	0.110298	−	0.704260i
$585$	6.52297	+	3.42352i	0.269691	+	0.141545i
$586$	2.14582	−	2.69078i	0.0886431	−	0.111155i
$587$	19.8707			0.820152			0.410076	−	0.912051i	$-0.365502\pi$
$587$	19.8707			0.820152			0.410076	+	0.912051i	$0.365502\pi$
$588$	5.30975			0.218970
$589$	22.8488	−	28.6515i	0.941467	−	1.18056i
$590$	−1.03971	+	0.744482i	−0.0428043	+	0.0306498i
$591$	−3.61148	+	3.93745i	−0.148556	+	0.161965i
$592$	−22.9504	+	10.0918i	−0.943255	+	0.414772i
$593$	33.3891	−	8.22968i	1.37113	−	0.337952i	0.516097	−	0.856530i	$-0.327385\pi$
$593$	33.3891	−	8.22968i	1.37113	−	0.337952i	0.855030	+	0.518578i	$0.173538\pi$
$594$	−27.6082	+	39.9973i	−1.13278	+	1.64111i
$595$	−2.34336	+	2.38416i	−0.0960684	+	0.0977411i
$596$	−4.66938	+	1.32343i	−0.191265	+	0.0542098i
$597$	−19.2813	−	38.3312i	−0.789133	−	1.56879i
$598$	12.0982	+	9.31095i	0.494732	+	0.380753i
$599$	6.09746	−	1.06309i	0.249136	−	0.0434368i	−0.0458126	−	0.998950i	$-0.514588\pi$
$599$	6.09746	−	1.06309i	0.249136	−	0.0434368i	0.294948	+	0.955513i	$0.404698\pi$
$600$	8.76965	+	45.6297i	0.358019	+	1.86282i
$601$	−2.94917	+	7.77632i	−0.120299	+	0.317203i	−0.981616	−	0.190865i	$-0.938871\pi$
$601$	−2.94917	+	7.77632i	−0.120299	+	0.317203i	0.861317	+	0.508068i	$0.169640\pi$
$602$	−22.5167	−	6.38184i	−0.917711	−	0.260104i
$603$	100.086	−	17.4500i	4.07582	−	0.710619i
$604$	−0.883911	−	0.899302i	−0.0359658	−	0.0365921i
$605$	−0.291516	−	0.166078i	−0.0118518	−	0.00675201i
$606$	−3.60538	−	29.6930i	−0.146459	−	1.20620i
$607$	−38.9132	−	12.4953i	−1.57944	−	0.507169i	−0.618935	−	0.785442i	$-0.712436\pi$
$607$	−38.9132	−	12.4953i	−1.57944	−	0.507169i	−0.960502	+	0.278274i	$0.910238\pi$
$608$	1.05950	+	12.2454i	0.0429684	+	0.496615i
$609$	−59.4862	−	49.1422i	−2.41050	−	1.99134i
$610$	0.0907343	−	0.0603440i	0.00367373	−	0.00244326i
$611$	−18.7670	+	1.29785i	−0.759232	+	0.0525054i
$612$	6.03310	+	8.12553i	0.243874	+	0.328455i
$613$	−23.3815	+	13.3205i	−0.944368	+	0.538010i	−0.887720	−	0.460384i	$-0.847712\pi$
$613$	−23.3815	+	13.3205i	−0.944368	+	0.538010i	−0.0566485	+	0.998394i	$0.518041\pi$
$614$	39.9738	+	11.3297i	1.61321	+	0.457228i
$615$	−2.18504	−	11.3691i	−0.0881092	−	0.458444i
$616$	−33.2233	−	2.29759i	−1.33860	−	0.0925723i
$617$	12.6201	+	16.9970i	0.508065	+	0.684274i	0.980371	−	0.197160i	$-0.0631719\pi$
$617$	12.6201	+	16.9970i	0.508065	+	0.684274i	−0.472307	+	0.881434i	$0.656578\pi$
$618$	−12.6156	−	37.0769i	−0.507476	−	1.49145i
$619$	−23.5254	+	12.3471i	−0.945568	+	0.496272i	−0.865717	−	0.500535i	$-0.833137\pi$
$619$	−23.5254	+	12.3471i	−0.945568	+	0.496272i	−0.0798511	+	0.996807i	$0.525444\pi$
$620$	−0.423717	+	2.20466i	−0.0170169	+	0.0885413i
$621$	53.5516	−	21.3739i	2.14895	−	0.857704i
$622$	2.80408	+	17.9042i	0.112433	+	0.717894i
$623$	−1.56209	−	30.1383i	−0.0625839	−	1.20746i
$624$	−20.5565	−	2.13666i	−0.822920	−	0.0855351i
$625$	22.2701	+	3.09502i	0.890803	+	0.123801i
$626$	12.9418	−	9.26694i	0.517260	−	0.370382i
$627$	21.3387	+	35.9967i	0.852187	+	1.43757i
$628$	−1.61096	+	2.02008i	−0.0642844	+	0.0806101i
$629$	13.1297	+	22.1488i	0.523517	+	0.883131i
$630$	−9.30467	−	4.88347i	−0.370707	−	0.194562i
$631$	−35.1376	−	4.88331i	−1.39881	−	0.194401i	−0.601933	−	0.798546i	$-0.705603\pi$
$631$	−35.1376	−	4.88331i	−1.39881	−	0.194401i	−0.796874	+	0.604145i	$0.793515\pi$
$632$	−40.6747	+	31.3039i	−1.61795	+	1.24520i
$633$	−19.8863	−	8.74450i	−0.790410	−	0.347563i
$634$	−11.9292	−	13.0059i	−0.473769	−	0.516531i
$635$	−2.36871	−	0.497790i	−0.0939995	−	0.0197542i
$636$	1.72591	−	19.9475i	0.0684366	−	0.790970i
$637$	6.27977	+	4.49660i	0.248814	+	0.178162i
$638$	23.2518	+	22.0778i	0.920547	+	0.874070i
$639$	9.66938	+	9.83774i	0.382515	+	0.389175i
$640$	0.922096	+	1.43977i	0.0364490	+	0.0569120i
$641$	15.9017	+	1.09970i	0.628081	+	0.0434355i	0.379524	−	0.925182i	$-0.376088\pi$
$641$	15.9017	+	1.09970i	0.628081	+	0.0434355i	0.248557	+	0.968617i	$0.420044\pi$
$642$	13.0310	−	7.42381i	0.514293	−	0.292995i
$643$	−21.3630	−	5.26550i	−0.842473	−	0.207651i	−0.205616	−	0.978633i	$-0.565920\pi$
$643$	−21.3630	−	5.26550i	−0.842473	−	0.207651i	−0.636857	+	0.770982i	$0.719766\pi$
$644$	7.02675	+	5.40789i	0.276893	+	0.213101i
$645$	−5.82143	−	5.52752i	−0.229219	−	0.217646i
$646$	−11.6908	+	2.45684i	−0.459967	+	0.0966630i
$647$	12.5526	−	19.5997i	0.493492	−	0.770544i	−0.502053	−	0.864837i	$-0.667422\pi$
$647$	12.5526	−	19.5997i	0.493492	−	0.770544i	0.995544	+	0.0942929i	$0.0300590\pi$
$648$	−30.6766	+	41.3160i	−1.20509	+	1.62305i
$649$	−1.07897	+	8.88613i	−0.0423533	+	0.348811i
$650$	−6.34433	+	13.7776i	−0.248845	+	0.540400i
$651$	60.3805	+	70.5731i	2.36650	+	2.76598i
$652$	−1.77127	−	5.20568i	−0.0693682	−	0.203870i
$653$	21.4268	−	18.9825i	0.838496	−	0.742842i	−0.130095	−	0.991501i	$-0.541528\pi$
$653$	21.4268	−	18.9825i	0.838496	−	0.742842i	0.968591	+	0.248659i	$0.0799899\pi$
$654$	−46.6547	−	11.4993i	−1.82434	−	0.449660i
$655$	4.23569	−	0.738493i	0.165502	−	0.0288553i
$656$	12.1492	+	18.9699i	0.474347	+	0.740651i
$657$	−9.74229	−	36.7817i	−0.380083	−	1.43499i
$658$	26.7702	−	1.85132i	1.04361	−	0.0721718i
$659$	−21.2333	−	24.8176i	−0.827131	−	0.966756i	0.172703	−	0.984974i	$-0.444750\pi$
$659$	−21.2333	−	24.8176i	−0.827131	−	0.966756i	−0.999834	+	0.0182184i	$0.994201\pi$
$660$	−2.18230	−	1.34510i	−0.0849460	−	0.0523580i
$661$	−8.50140	+	32.0967i	−0.330666	+	1.24842i	0.572777	+	0.819711i	$0.305866\pi$
$661$	−8.50140	+	32.0967i	−0.330666	+	1.24842i	−0.903443	+	0.428707i	$0.858969\pi$
$662$	9.19344	−	27.0191i	0.357313	−	1.05013i
$663$	0.366361	+	21.2220i	0.0142283	+	0.824196i
$664$	18.0801	+	8.70693i	0.701645	+	0.337894i
$665$	−4.00247	+	3.08036i	−0.155209	+	0.119451i
$666$	−54.7083	+	59.6462i	−2.11990	+	2.31124i
$667$	−8.46476	−	37.0865i	−0.327757	−	1.43600i
$668$	−5.02886	−	2.63935i	−0.194572	−	0.102119i
$669$	−0.639542	+	0.457941i	−0.0247261	+	0.0177050i
$670$	−1.63479	−	7.16246i	−0.0631573	−	0.276710i
$671$	0.118024	−	0.753592i	0.00455627	−	0.0290921i
$672$	−30.9841	−	3.22051i	−1.19524	−	0.124234i
$673$	−30.6825	−	14.7759i	−1.18272	−	0.569570i	−0.264020	−	0.964517i	$-0.585049\pi$
$673$	−30.6825	−	14.7759i	−1.18272	−	0.569570i	−0.918704	+	0.394947i	$0.870763\pi$
$674$	37.8080	+	6.59183i	1.45631	+	0.253908i
$675$	32.5437	+	47.1476i	1.25261	+	1.81471i
$676$	−2.62596	−	2.32640i	−0.100999	−	0.0894769i
$677$	3.77247	−	8.99753i	0.144988	−	0.345803i	−0.833372	−	0.552712i	$-0.813593\pi$
$677$	3.77247	−	8.99753i	0.144988	−	0.345803i	0.978360	+	0.206909i	$0.0663403\pi$
$678$	−27.8461	+	5.85193i	−1.06942	+	0.224742i
$679$	4.77708	+	2.72152i	0.183328	+	0.104442i
$680$	2.51409	−	2.07692i	0.0964110	−	0.0796461i
$681$	−6.72088	−	25.3745i	−0.257545	−	0.972351i
$682$	−23.0081	−	30.9879i	−0.881025	−	1.18659i
$683$	−2.75896	+	2.44422i	−0.105569	+	0.0935256i	−0.714256	−	0.699884i	$-0.753235\pi$
$683$	−2.75896	+	2.44422i	−0.105569	+	0.0935256i	0.608687	+	0.793410i	$0.291696\pi$
$684$	7.33819	+	13.4139i	0.280583	+	0.512891i
$685$	−0.155403	−	0.308941i	−0.00593766	−	0.0118040i
$686$	12.4261	+	8.89763i	0.474429	+	0.339713i
$687$	−30.9626	+	73.8473i	−1.18130	+	2.81745i
$688$	14.5074	+	5.79027i	0.553088	+	0.220752i
$689$	18.9339	−	22.1301i	0.721324	−	0.843088i
$690$	−3.12427	−	6.78476i	−0.118939	−	0.258291i
$691$	17.8777	+	11.0192i	0.680099	+	0.419191i	0.821074	−	0.570822i	$-0.193375\pi$
$691$	17.8777	+	11.0192i	0.680099	+	0.419191i	−0.140975	+	0.990013i	$0.545024\pi$
$692$	−1.25060	+	0.656366i	−0.0475407	+	0.0249513i
$693$	−69.2182	+	24.8931i	−2.62938	+	0.945610i
$694$	−4.16245	−	7.60875i	−0.158004	−	0.288824i
$695$	1.20106	+	0.924351i	0.0455587	+	0.0350626i
$696$	52.7608	+	53.6794i	1.99989	+	2.03471i
$697$	17.8360	−	14.7345i	0.675587	−	0.558109i
$698$	−1.70918	+	5.65637i	−0.0646934	+	0.214097i
$699$	3.35842	−	2.23356i	0.127027	−	0.0844808i
$700$	−3.68485	+	8.00214i	−0.139274	+	0.302452i
$701$	−6.96394	−	15.1231i	−0.263025	−	0.571192i	0.730745	−	0.682651i	$-0.239173\pi$
$701$	−6.96394	−	15.1231i	−0.263025	−	0.571192i	−0.993769	+	0.111459i	$0.964448\pi$
$702$	−35.4595	+	11.3863i	−1.33833	+	0.429748i
$703$	15.0413	+	35.8744i	0.567295	+	1.35303i
$704$	29.7352	+	5.18433i	1.12069	+	0.195392i
$705$	8.42569	+	3.70498i	0.317330	+	0.139538i
$706$	8.96876	−	3.94378i	0.337544	−	0.148426i
$707$	12.1283	−	22.1700i	0.456132	−	0.833787i
$708$	−0.729653	+	4.65888i	−0.0274220	+	0.175091i
$709$	−49.3106	−	6.85301i	−1.85190	−	0.257370i	−0.877075	−	0.480353i	$-0.840509\pi$
$709$	−49.3106	−	6.85301i	−1.85190	−	0.257370i	−0.974822	+	0.222983i	$0.928421\pi$
$710$	0.674246	−	0.735103i	0.0253040	−	0.0275879i
$711$	−54.4097	+	99.4583i	−2.04052	+	3.72998i
$712$	−1.52379	+	29.3993i	−0.0571064	+	1.10178i
$713$	2.37014	+	45.7285i	0.0887626	+	1.71254i
$714$	−0.522594	−	30.2721i	−0.0195576	−	1.13291i
$715$	−1.44187	−	3.43894i	−0.0539229	−	0.128609i
$716$	−3.07955	+	13.4924i	−0.115088	+	0.504234i
$717$	35.9586	+	14.3520i	1.34290	+	0.535986i
$718$	15.9142	−	24.8487i	0.593914	−	0.927344i
$719$	−4.90298	−	40.3797i	−0.182850	−	1.50591i	−0.738365	−	0.674402i	$-0.764402\pi$
$719$	−4.90298	−	40.3797i	−0.182850	−	1.50591i	0.555514	−	0.831507i	$-0.312521\pi$
$720$	5.83995	+	3.88393i	0.217642	+	0.144746i
$721$	9.57086	−	31.6739i	0.356437	−	1.17960i
$722$	4.59225	−	0.317581i	0.170906	−	0.0118192i
$723$	15.4680	+	45.4598i	0.575261	+	1.69067i
$724$	−11.2409	+	4.04259i	−0.417765	+	0.150242i
$725$	34.0527	−	16.3989i	1.26468	−	0.609040i
$726$	2.92343	−	0.828579i	0.108499	−	0.0307514i
$727$	0.421839	−	4.87548i	0.0156451	−	0.180822i	−0.984344	−	0.176256i	$-0.943601\pi$
$727$	0.421839	−	4.87548i	0.0156451	−	0.180822i	0.999990	−	0.00456616i	$-0.00145346\pi$
$728$	−19.1020	−	16.9229i	−0.707967	−	0.627204i
$729$	−0.519095	+	2.27430i	−0.0192257	+	0.0842335i
$730$	−2.61975	+	0.841219i	−0.0969611	+	0.0311349i
$731$	4.10735	−	15.5072i	0.151916	−	0.573553i
$732$	0.0758420	−	0.394616i	0.00280320	−	0.0145854i
$733$	9.15523	−	18.2005i	0.338156	−	0.672252i	−0.658621	−	0.752475i	$-0.728860\pi$
$733$	9.15523	−	18.2005i	0.338156	−	0.672252i	0.996777	+	0.0802226i	$0.0255631\pi$
$734$	2.89708	−	1.39516i	0.106933	−	0.0514962i
$735$	−1.69819	−	3.37600i	−0.0626388	−	0.124526i
$736$	−11.1371	−	10.5748i	−0.410517	−	0.389791i
$737$	−44.6839	−	25.4566i	−1.64595	−	0.937706i
$738$	60.5536	+	40.2719i	2.22901	+	1.48243i
$739$	−0.932195	−	3.08501i	−0.0342913	−	0.113484i	0.938424	−	0.345485i	$-0.112286\pi$
$739$	−0.932195	−	3.08501i	−0.0342913	−	0.113484i	−0.972715	+	0.232002i	$0.925473\pi$
$740$	−1.83723	−	1.51775i	−0.0675378	−	0.0557936i
$741$	−3.86525	+	31.8332i	−0.141993	+	1.16942i
$742$	−27.0082	+	31.5673i	−0.991503	+	1.15887i
$743$	7.85831	−	34.4295i	0.288293	−	1.26310i	−0.598572	−	0.801069i	$-0.704265\pi$
$743$	7.85831	−	34.4295i	0.288293	−	1.26310i	0.886866	−	0.462027i	$-0.152878\pi$
$744$	−51.4671	−	74.5630i	−1.88688	−	2.73361i
$745$	2.33484	+	2.54558i	0.0855418	+	0.0932627i
$746$	−11.7591	+	2.89835i	−0.430531	+	0.106116i
$747$	44.2982	+	1.52991i	1.62079	+	0.0559766i
$748$	0.265164	−	5.11596i	0.00969537	−	0.187058i
$749$	12.6027	+	1.30994i	0.460493	+	0.0478641i
$750$	11.9693	−	9.21173i	0.437056	−	0.336365i
$751$	21.9601	−	9.65638i	0.801335	−	0.352366i	0.0387451	−	0.999249i	$-0.487664\pi$
$751$	21.9601	−	9.65638i	0.801335	−	0.352366i	0.762589	+	0.646883i	$0.223928\pi$
$752$	−17.8992	−	0.618178i	−0.652715	−	0.0225426i
$753$	−35.4718	+	3.68697i	−1.29266	+	0.134361i
$754$	3.80178	+	24.2746i	0.138453	+	0.884030i
$755$	−0.289089	+	0.849621i	−0.0105210	+	0.0309209i
$756$	−20.5952	+	6.61327i	−0.749041	+	0.240522i
$757$	−3.59549	+	4.20243i	−0.130680	+	0.152740i	−0.821338	−	0.570442i	$-0.806772\pi$
$757$	−3.59549	+	4.20243i	−0.130680	+	0.152740i	0.690657	+	0.723182i	$0.257321\pi$
$758$	−6.04933	+	8.14739i	−0.219722	+	0.295927i
$759$	−49.7831	−	15.9857i	−1.80701	−	0.580245i
$760$	4.19406	−	2.58508i	0.152134	−	0.0937708i
$761$	−2.04648	−	6.77263i	−0.0741848	−	0.245508i	0.912257	−	0.409618i	$-0.134338\pi$
$761$	−2.04648	−	6.77263i	−0.0741848	−	0.245508i	−0.986442	+	0.164110i	$0.947525\pi$
$762$	18.2533	−	12.1396i	0.661246	−	0.439770i
$763$	−26.3918	−	30.8468i	−0.955446	−	1.11673i
$764$	4.91556	−	2.57988i	0.177839	−	0.0933369i
$765$	3.23676	−	6.43467i	0.117025	−	0.232646i
$766$	−41.6461	+	1.43832i	−1.50473	+	0.0519686i
$767$	−4.80836	+	4.89209i	−0.173620	+	0.176643i
$768$	38.6251	+	8.11714i	1.39376	+	0.292902i
$769$	7.36952	+	10.6766i	0.265752	+	0.385008i	0.933029	−	0.359802i	$-0.117156\pi$
$769$	7.36952	+	10.6766i	0.265752	+	0.385008i	−0.667277	+	0.744810i	$0.732540\pi$
$770$	2.05675	+	4.90546i	0.0741203	+	0.176781i
$771$	−16.0679	+	47.2229i	−0.578671	+	1.70069i
$772$	−1.70206	+	0.679336i	−0.0612584	+	0.0244498i
$773$	−0.332021	+	19.2329i	−0.0119420	+	0.691758i	0.932149	+	0.362074i	$0.117931\pi$
$773$	−0.332021	+	19.2329i	−0.0119420	+	0.691758i	−0.944091	+	0.329684i	$0.893058\pi$
$774$	50.3959	−	1.74051i	1.81144	−	0.0625614i
$775$	−43.7712	+	12.4059i	−1.57231	+	0.445635i
$776$	−4.36051	−	3.12233i	−0.156533	−	0.112085i
$777$	−96.4819	+	20.2759i	−3.46127	+	0.727393i
$778$	0.0177582	+	0.146252i	0.000636662	+	0.00524338i
$779$	29.7544	−	18.3396i	1.06606	−	0.657086i
$780$	−0.696606	−	1.83680i	−0.0249425	−	0.0657680i
$781$	−0.601887	−	6.95643i	−0.0215372	−	0.248921i
$782$	8.89827	−	11.9844i	0.318201	−	0.428562i
$783$	86.1893	+	34.4004i	3.08015	+	1.22937i
$784$	5.50404	+	4.87615i	0.196573	+	0.174148i
$785$	1.79962	+	0.378194i	0.0642311	+	0.0134983i
$786$	−22.1206	+	32.0473i	−0.789017	+	1.14309i
$787$	6.70258	−	6.36418i	0.238921	−	0.226858i	−0.559696	−	0.828698i	$-0.689082\pi$
$787$	6.70258	−	6.36418i	0.238921	−	0.226858i	0.798617	+	0.601840i	$0.205565\pi$
$788$	0.982881	−	0.102162i	0.0350137	−	0.00363936i
$789$	5.10439	+	98.4817i	0.181721	+	3.50604i
$790$	7.38610	+	3.55696i	0.262786	+	0.126551i
$791$	−22.0063	−	9.67671i	−0.782454	−	0.344064i
$792$	69.6696	−	17.1720i	2.47560	−	0.610181i
$793$	0.423881	−	0.402480i	0.0150525	−	0.0142925i
$794$	−4.29757	−	1.54554i	−0.152515	−	0.0548493i
$795$	−13.2348	+	5.28237i	−0.469391	+	0.187346i
$796$	−2.03188	+	7.67131i	−0.0720182	+	0.271902i
$797$	−0.890722	−	1.93432i	−0.0315510	−	0.0685172i	0.891902	−	0.452229i	$-0.149371\pi$
$797$	−0.890722	−	1.93432i	−0.0315510	−	0.0685172i	−0.923453	+	0.383712i	$0.874646\pi$
$798$	5.51357	−	45.4083i	0.195178	−	1.60744i
$799$	1.58551	+	18.3248i	0.0560913	+	0.648287i
$800$	7.78103	−	13.1260i	0.275101	−	0.464073i
$801$	23.0578	+	60.7983i	0.814706	+	2.14820i
$802$	22.4191	+	18.5206i	0.791646	+	0.653986i
$803$	−8.05603	+	17.4947i	−0.284291	+	0.617375i
$804$	−23.0630	−	14.2153i	−0.813368	−	0.501334i
$805$	1.19106	−	6.19727i	0.0419795	−	0.218425i
$806$	0.510501	−	29.5716i	0.0179816	−	1.04162i
$807$	90.3164	−	12.5519i	3.17929	−	0.441846i
$808$	−14.0033	+	20.2873i	−0.492636	+	0.713706i
$809$	−18.6285	−	20.3099i	−0.654945	−	0.714059i	0.317222	−	0.948351i	$-0.397250\pi$
$809$	−18.6285	−	20.3099i	−0.654945	−	0.714059i	−0.972166	+	0.234293i	$0.924723\pi$
$810$	8.09709	+	1.41173i	0.284503	+	0.0496031i
$811$	−0.0250069	−	1.44857i	−0.000878111	−	0.0508660i	−0.999967	−	0.00817795i	$-0.997397\pi$
$811$	−0.0250069	−	1.44857i	−0.000878111	−	0.0508660i	0.999088	−	0.0426881i	$-0.0135922\pi$
$812$	2.20811	+	14.0989i	0.0774895	+	0.494776i
$813$	62.8640	+	22.6079i	2.20474	+	0.792894i
$814$	40.5789	−	5.63951i	1.42229	−	0.197665i
$815$	−2.74334	+	2.79110i	−0.0960948	+	0.0977681i
$816$	−1.74189	+	20.1323i	−0.0609784	+	0.704770i
$817$	9.37127	−	22.3510i	0.327859	−	0.781961i
$818$	11.1649	−	17.4330i	0.390372	−	0.609531i
$819$	−53.6691	−	17.2335i	−1.87535	−	0.602189i
$820$	−1.09188	+	1.84190i	−0.0381300	+	0.0643221i
$821$	17.2683	−	29.1302i	0.602668	−	1.01665i	−0.392621	−	0.919700i	$-0.628432\pi$
$821$	17.2683	−	29.1302i	0.602668	−	1.01665i	0.995289	−	0.0969511i	$-0.0309090\pi$
$822$	2.98208	+	0.957567i	0.104012	+	0.0333990i
$823$	19.8963	−	31.0664i	0.693543	−	1.08291i	−0.298180	−	0.954510i	$-0.596380\pi$
$823$	19.8963	−	31.0664i	0.693543	−	1.08291i	0.991723	−	0.128396i	$-0.0409830\pi$
$824$	−12.4804	+	29.7664i	−0.434776	+	1.03696i
$825$	4.47814	−	51.7570i	0.155909	−	1.80195i
$826$	6.85888	−	6.97830i	0.238651	−	0.242806i
$827$	21.3592	−	2.96842i	0.742731	−	0.103222i	0.243754	−	0.969837i	$-0.421621\pi$
$827$	21.3592	−	2.96842i	0.742731	−	0.103222i	0.498977	+	0.866615i	$0.333709\pi$
$828$	−17.9775	−	6.46527i	−0.624760	−	0.224684i
$829$	3.05375	+	19.4984i	0.106061	+	0.677207i	0.981150	+	0.193245i	$0.0619013\pi$
$829$	3.05375	+	19.4984i	0.106061	+	0.677207i	−0.875089	+	0.483961i	$0.839198\pi$
$830$	−0.0553243	−	3.20475i	−0.00192033	−	0.111238i
$831$	0.523488	+	0.0912702i	0.0181596	+	0.00316613i
$832$	15.6346	+	17.0457i	0.542031	+	0.590954i
$833$	4.28992	−	6.21503i	0.148637	−	0.215338i
$834$	−13.5955	+	1.88946i	−0.470774	+	0.0654265i
$835$	−0.0697699	+	4.04154i	−0.00241449	+	0.139863i
$836$	1.46074	−	7.60045i	0.0505209	−	0.262867i
$837$	−95.0936	−	58.6127i	−3.28692	−	2.02595i
$838$	1.95714	−	4.25020i	0.0676084	−	0.146821i
$839$	−40.2425	−	33.2447i	−1.38932	−	1.14773i	−0.970901	−	0.239483i	$-0.923022\pi$
$839$	−40.2425	−	33.2447i	−1.38932	−	1.14773i	−0.418424	−	0.908252i	$-0.637417\pi$
$840$	4.42776	+	11.6751i	0.152772	+	0.402828i
$841$	16.4323	−	27.7199i	0.566630	−	0.955857i
$842$	−0.494336	−	5.71338i	−0.0170359	−	0.196896i
$843$	11.2523	−	92.6713i	0.387551	−	3.19177i
$844$	1.68056	+	3.64956i	0.0578473	+	0.125623i
$845$	−0.639301	+	2.41366i	−0.0219926	+	0.0830324i
$846$	−53.6983	+	21.4324i	−1.84619	+	0.736861i
$847$	2.41570	+	0.868762i	0.0830043	+	0.0298510i
$848$	20.1076	−	19.0924i	0.690499	−	0.655637i
$849$	−62.8947	+	15.5022i	−2.15854	+	0.532032i
$850$	13.5761	+	5.96974i	0.465656	+	0.204760i
$851$	−43.7921	−	21.0891i	−1.50117	−	0.722927i
$852$	−0.190399	−	3.67347i	−0.00652296	−	0.125851i
$853$	22.2871	−	2.31655i	0.763097	−	0.0793170i	0.286074	−	0.958208i	$-0.407650\pi$
$853$	22.2871	−	2.31655i	0.763097	−	0.0793170i	0.477024	+	0.878891i	$0.341716\pi$
$854$	−0.604644	+	0.574117i	−0.0206905	+	0.0196459i
$855$	6.18174	−	8.95580i	0.211411	−	0.306282i
$856$	−12.0957	−	2.54194i	−0.413423	−	0.0868817i
$857$	2.05928	+	1.82437i	0.0703438	+	0.0623192i	0.697562	−	0.716524i	$-0.254268\pi$
$857$	2.05928	+	1.82437i	0.0703438	+	0.0623192i	−0.627218	+	0.778844i	$0.715807\pi$
$858$	31.3664	+	12.5191i	1.07083	+	0.427396i
$859$	−4.56990	+	6.15486i	−0.155923	+	0.210001i	−0.873952	−	0.486012i	$-0.838451\pi$
$859$	−4.56990	+	6.15486i	−0.155923	+	0.210001i	0.718029	+	0.696013i	$0.245045\pi$
$860$	0.127984	+	1.47920i	0.00436422	+	0.0504403i
$861$	31.4124	+	82.8277i	1.07053	+	2.82276i
$862$	−13.7447	+	8.47182i	−0.468148	+	0.288551i
$863$	5.78695	+	47.6598i	0.196990	+	1.62236i	0.670736	+	0.741696i	$0.265979\pi$
$863$	5.78695	+	47.6598i	0.196990	+	1.62236i	−0.473746	+	0.880662i	$0.657098\pi$
$864$	36.6649	−	7.70521i	1.24736	−	0.262136i
$865$	0.817300	+	0.585224i	0.0277890	+	0.0198982i
$866$	−29.9491	+	8.48839i	−1.01771	+	0.288447i
$867$	−32.4201	+	1.11968i	−1.10105	+	0.0380265i
$868$	0.296504	−	17.1755i	0.0100640	−	0.582974i
$869$	53.2973	−	21.2723i	1.80799	−	0.721615i
$870$	3.87251	−	11.3811i	0.131290	−	0.385857i
$871$	−15.2380	−	36.3433i	−0.516318	−	1.23145i
$872$	22.4958	+	32.5908i	0.761804	+	1.10366i
$873$	−11.5927	−	2.43624i	−0.392355	−	0.0824543i
$874$	15.8079	−	16.0831i	0.534709	−	0.544019i
$875$	12.7528	−	0.440440i	0.431123	−	0.0148896i
$876$	−4.55957	+	9.06439i	−0.154054	+	0.306257i
$877$	25.3619	−	13.3110i	0.856412	−	0.449480i	0.0214387	−	0.999770i	$-0.493175\pi$
$877$	25.3619	−	13.3110i	0.856412	−	0.449480i	0.834973	+	0.550290i	$0.185483\pi$
$878$	3.66777	+	4.28691i	0.123781	+	0.144676i
$879$	−7.52134	+	5.00216i	−0.253688	+	0.168719i
$880$	−1.02690	−	3.39842i	−0.0346167	−	0.114561i
$881$	36.5309	−	22.5165i	1.23076	−	0.758599i	0.252823	−	0.967513i	$-0.418641\pi$
$881$	36.5309	−	22.5165i	1.23076	−	0.758599i	0.977934	+	0.208913i	$0.0669926\pi$
$882$	22.6017	+	7.25757i	0.761039	+	0.244375i
$883$	−14.7304	+	19.8393i	−0.495718	+	0.667645i	−0.978057	−	0.208339i	$-0.933194\pi$
$883$	−14.7304	+	19.8393i	−0.495718	+	0.667645i	0.482338	+	0.875985i	$0.339788\pi$
$884$	2.55208	−	2.98289i	0.0858358	−	0.100325i
$885$	3.19553	−	1.02611i	0.107417	−	0.0344922i
$886$	−2.78136	+	8.17432i	−0.0934418	+	0.274622i
$887$	−2.42176	−	15.4631i	−0.0813147	−	0.519200i	−0.993897	−	0.110308i	$-0.964816\pi$
$887$	−2.42176	−	15.4631i	−0.0813147	−	0.519200i	0.912583	−	0.408892i	$-0.134085\pi$
$888$	95.6567	−	9.94264i	3.21003	−	0.333653i
$889$	18.5095	+	0.639256i	0.620787	+	0.0214400i
$890$	4.30429	−	1.89270i	0.144280	−	0.0634434i
$891$	45.5949	−	35.0905i	1.52749	−	1.17558i
$892$	0.144702	+	0.0150405i	0.00484499	+	0.000503592i
$893$	−1.43837	+	27.7513i	−0.0481334	+	0.928663i
$894$	−31.2651	−	1.07979i	−1.04566	−	0.0361137i
$895$	9.56353	−	2.35720i	0.319673	−	0.0787924i
$896$	−8.84292	−	9.64107i	−0.295421	−	0.322086i
$897$	−22.7610	−	32.9750i	−0.759968	−	1.10100i
$898$	0.963755	−	4.22249i	0.0321609	−	0.140906i
$899$	−47.9107	+	55.9983i	−1.59791	+	1.86765i
$900$	2.28800	−	18.8434i	0.0762667	−	0.628113i
$901$	−21.9540	−	18.1364i	−0.731394	−	0.604212i
$902$	−10.6477	−	35.2377i	−0.354530	−	1.17329i
$903$	51.1462	+	34.0154i	1.70204	+	1.13196i
$904$	20.3758	+	11.6082i	0.677689	+	0.386082i
$905$	6.16545	+	5.85417i	0.204946	+	0.194599i
$906$	−3.65250	−	7.26115i	−0.121346	−	0.241236i
$907$	−5.48108	+	2.63955i	−0.181996	+	0.0876449i	−0.522663	−	0.852539i	$-0.675061\pi$
$907$	−5.48108	+	2.63955i	−0.181996	+	0.0876449i	0.340667	+	0.940184i	$0.389347\pi$
$908$	−2.18165	+	4.33710i	−0.0724005	+	0.143932i
$909$	−10.2765	+	53.4701i	−0.340850	+	1.77349i
$910$	−1.04365	+	3.94025i	−0.0345966	+	0.130618i
$911$	−6.98448	+	2.24277i	−0.231406	+	0.0743062i	−0.419169	−	0.907908i	$-0.637679\pi$
$911$	−6.98448	+	2.24277i	−0.231406	+	0.0743062i	0.187763	+	0.982214i	$0.439876\pi$
$912$	−6.79343	+	29.7640i	−0.224953	+	0.985583i
$913$	−16.7940	−	14.8782i	−0.555801	−	0.492397i
$914$	−0.596597	+	6.89529i	−0.0197337	+	0.228076i
$915$	−0.275158	+	0.0779872i	−0.00909643	+	0.00257818i
$916$	13.3435	−	6.42590i	0.440882	−	0.212318i
$917$	−30.9579	+	11.1335i	−1.02232	+	0.367659i
$918$	11.7297	+	34.4732i	0.387139	+	1.13779i
$919$	−9.89259	+	0.684131i	−0.326327	+	0.0225674i	−0.231225	−	0.972900i	$-0.574273\pi$
$919$	−9.89259	+	0.684131i	−0.326327	+	0.0225674i	−0.0951011	+	0.995468i	$0.530317\pi$
$920$	−1.78062	+	5.89280i	−0.0587054	+	0.194280i
$921$	−90.7998	−	60.3875i	−2.99195	−	1.98984i
$922$	2.80530	+	23.1037i	0.0923876	+	0.760881i
$923$	2.88572	−	4.50581i	0.0949848	−	0.148310i
$924$	18.2179	+	7.27124i	0.599324	+	0.239206i
$925$	10.7462	−	47.0821i	0.353332	−	1.54805i
$926$	−6.08637	−	14.5163i	−0.200010	−	0.477035i
$927$	1.23056	+	71.2822i	0.0404169	+	2.34122i
$928$	−1.27942	−	24.6845i	−0.0419990	−	0.810309i
$929$	−2.38800	+	46.0729i	−0.0783477	+	1.51160i	0.613577	+	0.789635i	$0.289730\pi$
$929$	−2.38800	+	46.0729i	−0.0783477	+	1.51160i	−0.691925	+	0.721969i	$0.743237\pi$
$930$	−6.94519	+	12.6955i	−0.227742	+	0.416301i
$931$	7.71203	−	8.40810i	0.252751	−	0.275564i
$932$	−0.738872	−	0.102686i	−0.0242026	−	0.00336359i
$933$	7.35952	−	46.9910i	0.240940	−	1.53842i
$934$	11.3531	−	20.7530i	0.371486	−	0.679059i
$935$	−3.33759	+	1.46762i	−0.109151	+	0.0479963i
$936$	50.3346	+	22.1334i	1.64524	+	0.723452i
$937$	−13.9251	−	2.42785i	−0.454915	−	0.0793144i	−0.0603392	−	0.998178i	$-0.519218\pi$
$937$	−13.9251	−	2.42785i	−0.454915	−	0.0793144i	−0.394576	+	0.918864i	$0.629108\pi$
$938$	21.7361	+	51.8418i	0.709710	+	1.69269i
$939$	−39.7764	+	12.7725i	−1.29805	+	0.416814i
$940$	−0.712041	−	1.54629i	−0.0232242	−	0.0504345i
$941$	0.256295	−	0.556578i	0.00835497	−	0.0181439i	−0.904101	−	0.427319i	$-0.859458\pi$
$941$	0.256295	−	0.556578i	0.00835497	−	0.0181439i	0.912456	+	0.409175i	$0.134183\pi$
$942$	−13.8678	+	9.22297i	−0.451838	+	0.300500i
$943$	−12.6325	+	41.8060i	−0.411370	+	1.36139i
$944$	−5.03479	+	4.15929i	−0.163868	+	0.135373i
$945$	10.7917	+	10.9796i	0.351053	+	0.357166i
$946$	−20.2280	−	15.5678i	−0.657669	−	0.506152i
$947$	5.73235	+	10.4785i	0.186276	+	0.340504i	0.953762	−	0.300561i	$-0.0971740\pi$
$947$	5.73235	+	10.4785i	0.186276	+	0.340504i	−0.767486	+	0.641065i	$0.778493\pi$
$948$	28.4475	−	10.2306i	0.923933	−	0.332276i
$949$	−13.0688	+	6.85903i	−0.424231	+	0.222654i
$950$	19.0740	+	11.7566i	0.618841	+	0.381434i
$951$	19.3738	+	42.0728i	0.628239	+	1.36430i
$952$	−16.2215	+	18.9598i	−0.525743	+	0.614491i
$953$	24.6367	+	9.83316i	0.798062	+	0.318527i	0.733765	−	0.679403i	$-0.237761\pi$
$953$	24.6367	+	9.83316i	0.798062	+	0.318527i	0.0642967	+	0.997931i	$0.479520\pi$
$954$	34.6116	−	82.5504i	1.12059	−	2.67267i
$955$	−3.21244	−	2.30026i	−0.103952	−	0.0744345i
$956$	−3.21784	−	6.39706i	−0.104073	−	0.206896i
$957$	−40.3884	−	73.8281i	−1.30557	−	2.38652i
$958$	18.8705	−	16.7178i	0.609678	−	0.540128i
$959$	1.57745	+	2.12454i	0.0509384	+	0.0686051i
$960$	−2.89762	−	10.9398i	−0.0935202	−	0.353082i
$961$	44.4921	−	36.7553i	1.43523	−	1.18566i
$962$	27.2785	+	15.5407i	0.879494	+	0.501051i
$963$	−26.7168	+	5.61460i	−0.860938	+	0.180928i
$964$	3.43410	−	8.19050i	0.110605	−	0.263798i
$965$	0.976292	+	0.864919i	0.0314279	+	0.0278427i
$966$	32.4674	+	47.0371i	1.04462	+	1.51339i
$967$	−47.6173	−	8.30208i	−1.53127	−	0.266977i	−0.657552	−	0.753409i	$-0.728408\pi$
$967$	−47.6173	−	8.30208i	−1.53127	−	0.266977i	−0.873718	+	0.486432i	$0.838298\pi$
$968$	−2.25622	−	1.08654i	−0.0725177	−	0.0349227i
$969$	31.1855	+	3.24145i	1.00182	+	0.104130i
$970$	−0.132543	+	0.846296i	−0.00425570	+	0.0271729i
$971$	8.01966	+	35.1364i	0.257363	+	1.12758i	0.924059	+	0.382251i	$0.124851\pi$
$971$	8.01966	+	35.1364i	0.257363	+	1.12758i	−0.666696	+	0.745330i	$0.732292\pi$
$972$	7.90210	−	5.65827i	0.253460	−	0.181489i
$973$	−10.2683	−	5.38924i	−0.329188	−	0.172771i
$974$	5.57381	+	24.4204i	0.178596	+	0.782481i
$975$	26.9093	−	29.3380i	0.861786	−	0.939569i
$976$	0.441009	−	0.339407i	0.0141164	−	0.0108642i
$977$	25.0565	+	12.0666i	0.801628	+	0.386044i	0.789398	−	0.613881i	$-0.210393\pi$
$977$	25.0565	+	12.0666i	0.801628	+	0.386044i	0.0122300	+	0.999925i	$0.496107\pi$
$978$	−0.611793	−	35.4391i	−0.0195630	−	1.13322i
$979$	10.6024	−	31.1599i	0.338853	−	0.995875i
$980$	−0.178957	+	0.675646i	−0.00571657	+	0.0215827i
$981$	74.4615	+	45.8957i	2.37737	+	1.46534i
$982$	−13.9581	−	16.3143i	−0.445420	−	0.520609i
$983$	27.1994	−	1.88100i	0.867526	−	0.0599946i	0.371635	−	0.928379i	$-0.378797\pi$
$983$	27.1994	−	1.88100i	0.867526	−	0.0599946i	0.495892	+	0.868384i	$0.334841\pi$
$984$	−22.1249	−	83.5317i	−0.705315	−	2.66289i
$985$	−0.379306	−	0.592253i	−0.0120857	−	0.0188708i
$986$	23.6669	−	4.12632i	0.753707	−	0.131409i
$987$	−68.3817	−	16.8546i	−2.17661	−	0.536487i
$988$	4.43932	−	3.93289i	0.141233	−	0.125122i
$989$	9.75474	+	28.6688i	0.310183	+	0.911614i
$990$	−7.45075	−	8.70848i	−0.236800	−	0.276774i
$991$	−6.34416	+	13.7772i	−0.201529	+	0.437647i	−0.982336	−	0.187125i	$-0.940083\pi$
$991$	−6.34416	+	13.7772i	−0.201529	+	0.437647i	0.780807	+	0.624772i	$0.214808\pi$
$992$	−3.58634	+	29.5362i	−0.113867	+	0.937775i
$993$	−44.6542	+	60.1414i	−1.41706	+	1.90853i
$994$	−4.11633	+	6.42729i	−0.130562	+	0.203861i
$995$	5.52735	−	1.16159i	0.175229	−	0.0368247i
$996$	−8.57142	−	8.13867i	−0.271596	−	0.257883i
$997$	0.0871268	+	0.0670541i	0.00275933	+	0.00212362i	0.611281	−	0.791414i	$-0.290655\pi$
$997$	0.0871268	+	0.0670541i	0.00275933	+	0.00212362i	−0.608521	+	0.793537i	$0.708237\pi$
$998$	−43.6801	−	10.7662i	−1.38267	−	0.340797i
$999$	103.028	−	58.6957i	3.25968	−	1.85705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.m.a.10.14	✓	3168
547.383	even	91	inner	547.2.m.a.383.14	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.m.a.10.14	✓	3168	1.1	even	1	trivial
547.2.m.a.383.14	yes	3168	547.383	even	91	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.m (of order \(91\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.607931 - 1.02553i) q^{2} +(0.696260 + 3.05052i) q^{3} +(0.277745 - 0.507704i) q^{4} +(-0.411634 - 0.0142165i) q^{5} +(2.70512 - 2.56854i) q^{6} +(3.12156 - 0.433823i) q^{7} +(-3.07245 + 0.106112i) q^{8} +(-6.11797 + 2.94626i) q^{9} +O(q^{10})\)	\(q+(-0.607931 - 1.02553i) q^{2} +(0.696260 + 3.05052i) q^{3} +(0.277745 - 0.507704i) q^{4} +(-0.411634 - 0.0142165i) q^{5} +(2.70512 - 2.56854i) q^{6} +(3.12156 - 0.433823i) q^{7} +(-3.07245 + 0.106112i) q^{8} +(-6.11797 + 2.94626i) q^{9} +(0.235665 + 0.430785i) q^{10} +(3.33735 + 0.822584i) q^{11} +(1.74214 + 0.493770i) q^{12} +(1.64225 + 2.05932i) q^{13} +(-2.34259 - 2.93751i) q^{14} +(-0.243237 - 1.26559i) q^{15} +(1.35244 + 2.11172i) q^{16} +(1.98549 - 1.64023i) q^{17} +(6.74077 + 4.48303i) q^{18} +(3.31223 - 2.04155i) q^{19} +(-0.121547 + 0.205039i) q^{20} +(3.49680 + 9.22031i) q^{21} +(-1.18530 - 3.92263i) q^{22} +(-1.40624 + 4.65381i) q^{23} +(-2.46292 - 9.29868i) q^{24} +(-4.81885 - 0.333252i) q^{25} +(1.11352 - 2.93611i) q^{26} +(-7.39467 - 9.27262i) q^{27} +(0.646742 - 1.70532i) q^{28} +(-6.79870 + 3.87325i) q^{29} +(-1.15003 + 1.01884i) q^{30} +(8.86290 - 3.18739i) q^{31} +(-1.41955 + 2.82205i) q^{32} +(-0.185638 + 10.7534i) q^{33} +(-2.88915 - 1.03903i) q^{34} +(-1.29111 + 0.134199i) q^{35} +(-0.203406 + 3.92442i) q^{36} +(-1.54695 + 9.87738i) q^{37} +(-4.10728 - 2.15567i) q^{38} +(-5.13856 + 6.44355i) q^{39} +1.26623 q^{40} +8.98318 q^{41} +(7.32988 - 9.19138i) q^{42} +(5.06450 - 3.62641i) q^{43} +(1.34456 - 1.46592i) q^{44} +(2.56025 - 1.12580i) q^{45} +(5.62751 - 1.38706i) q^{46} +(-4.05712 + 5.87776i) q^{47} +(-5.50017 + 5.59594i) q^{48} +(2.82120 - 0.799604i) q^{49} +(2.58777 + 5.14446i) q^{50} +(6.38597 + 4.91474i) q^{51} +(1.50165 - 0.261813i) q^{52} +(-2.08691 - 10.8585i) q^{53} +(-5.01390 + 13.2206i) q^{54} +(-1.36207 - 0.386048i) q^{55} +(-9.54480 + 1.66414i) q^{56} +(8.53397 + 8.68256i) q^{57} +(8.10527 + 4.61760i) q^{58} +(0.313907 + 2.58526i) q^{59} +(-0.710104 - 0.228020i) q^{60} +(-0.0191293 - 0.221090i) q^{61} +(-8.65679 - 7.15146i) q^{62} +(-17.8194 + 11.8510i) q^{63} +(8.76048 - 0.605839i) q^{64} +(-0.646731 - 0.871033i) q^{65} +(11.1408 - 6.34694i) q^{66} +(-14.3946 - 4.07983i) q^{67} +(-0.281293 - 1.46361i) q^{68} +(-15.1756 - 1.04948i) q^{69} +(0.922527 + 1.24248i) q^{70} +(-0.654358 - 1.92313i) q^{71} +(18.4845 - 9.70142i) q^{72} +(-1.05759 + 5.50277i) q^{73} +(11.0700 - 4.41832i) q^{74} +(-2.33858 - 14.9320i) q^{75} +(-0.116550 - 2.24866i) q^{76} +(10.7746 + 1.11992i) q^{77} +(9.73194 + 1.35251i) q^{78} +(13.5742 - 9.71976i) q^{79} +(-0.526688 - 0.888480i) q^{80} +(10.4364 - 13.0868i) q^{81} +(-5.46115 - 9.21251i) q^{82} +(-5.77982 - 3.03349i) q^{83} +(5.65240 + 0.785551i) q^{84} +(-0.840613 + 0.646948i) q^{85} +(-6.79785 - 2.98918i) q^{86} +(-16.5491 - 18.0428i) q^{87} +(-10.3411 - 2.17321i) q^{88} +(0.825438 - 9.54016i) q^{89} +(-2.71100 - 1.94120i) q^{90} +(6.01977 + 5.71585i) q^{91} +(1.97218 + 2.00652i) q^{92} +(15.8941 + 24.8172i) q^{93} +(8.49426 + 0.587428i) q^{94} +(-1.39245 + 0.793284i) q^{95} +(-9.59709 - 2.36547i) q^{96} +(1.38248 + 1.06398i) q^{97} +(-2.53511 - 2.40712i) q^{98} +(-22.8414 + 4.80016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9}+O(q^{10}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9	\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99}+O(q^{100}) \) 3168 * q - 76 * q^2 - 38 * q^3 - 34 * q^4 - 75 * q^5 - 42 * q^6 - 60 * q^7 - 77 * q^8 - 550 * q^9 - 91 * q^10 - 61 * q^11 - 31 * q^12 - 72 * q^13 - 21 * q^14 - 46 * q^15 + 24 * q^16 - 91 * q^17 + 9 * q^18 - 89 * q^19 - 108 * q^20 - 81 * q^21 - 50 * q^22 - 86 * q^23 - 33 * q^24 - 15 * q^25 + 137 * q^26 + 163 * q^27 - 47 * q^28 - 12 * q^29 + 29 * q^30 - 53 * q^31 - 122 * q^32 - 21 * q^33 - 80 * q^34 - 75 * q^35 - 8 * q^36 - 49 * q^37 - 47 * q^38 + 128 * q^39 - 246 * q^40 - 686 * q^41 - 466 * q^42 - 9 * q^43 - 43 * q^44 + 156 * q^45 - 91 * q^46 - 72 * q^47 + 21 * q^48 - 8 * q^49 - 84 * q^50 + 93 * q^51 + 4 * q^52 - 32 * q^53 - 71 * q^54 - 34 * q^55 - 263 * q^56 - 61 * q^57 - 36 * q^58 - 23 * q^59 + 87 * q^60 + 38 * q^61 + 26 * q^62 + 133 * q^63 + 343 * q^64 + 143 * q^65 - 65 * q^66 - 50 * q^67 - 213 * q^68 - 140 * q^69 + 372 * q^70 - 75 * q^71 + 147 * q^72 - 18 * q^73 - 85 * q^74 + 97 * q^75 - 47 * q^76 + 11 * q^77 + 55 * q^78 - 37 * q^79 - 142 * q^80 - 532 * q^81 - 94 * q^82 - 279 * q^83 + 395 * q^84 - 75 * q^85 - 147 * q^86 + 84 * q^87 + 345 * q^88 + 8 * q^89 + 278 * q^90 - 38 * q^91 - 78 * q^92 - 83 * q^93 - 540 * q^94 + 35 * q^95 + 123 * q^96 - 735 * q^97 - 90 * q^98 + 351 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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