LMFDB - Embedded newform 574.2.s.a.387.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(37,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 24]))

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

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

chi := DirichletCharacter("574.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.s (of order $15$, 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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			387.7
Character	$\chi$	$=$	574.387
Dual form			574.2.s.a.221.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(0.0198289 + 0.0343446i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.313002 - 2.97801i) q^{5} +(0.0122549 + 0.0377167i) q^{6} +(-0.713008 + 2.54787i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.49921 - 2.59671i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(0.0198289 + 0.0343446i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.313002 - 2.97801i) q^{5} +(0.0122549 + 0.0377167i) q^{6} +(-0.713008 + 2.54787i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.49921 - 2.59671i) q^{9} +(0.313002 - 2.97801i) q^{10} +(0.506863 - 4.82248i) q^{11} +(0.00414536 + 0.0394405i) q^{12} +(-0.795336 - 2.44779i) q^{13} +(-1.22716 + 2.34395i) q^{14} +(0.0960722 - 0.0698006i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.268505 + 2.55465i) q^{17} +(2.00634 - 2.22827i) q^{18} +(-0.0373253 - 0.0414540i) q^{19} +(0.925326 - 2.84786i) q^{20} +(-0.101644 + 0.0260333i) q^{21} +(1.49844 - 4.61171i) q^{22} +(6.14437 + 1.30603i) q^{23} +(-0.00414536 + 0.0394405i) q^{24} +(-3.87986 + 0.824690i) q^{25} +(-0.269031 - 2.55966i) q^{26} +0.237884 q^{27} +(-1.68768 + 2.03758i) q^{28} +(1.43349 - 1.04149i) q^{29} +(0.108485 - 0.0483007i) q^{30} +(-0.289057 + 2.75020i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.175677 - 0.0782163i) q^{33} +(-0.793779 + 2.44300i) q^{34} +(7.81075 + 1.32586i) q^{35} +(2.42578 - 1.76243i) q^{36} +(-0.655266 - 6.23444i) q^{37} +(-0.0278909 - 0.0483085i) q^{38} +(0.0682978 - 0.0758524i) q^{39} +(1.49721 - 2.59324i) q^{40} +(-5.54954 + 3.19416i) q^{41} +(-0.104835 + 0.00433153i) q^{42} +(1.17906 + 3.62879i) q^{43} +(2.42452 - 4.19939i) q^{44} +(-8.20231 - 3.65190i) q^{45} +(5.73857 + 2.55497i) q^{46} +(2.56327 + 0.544840i) q^{47} +(-0.0122549 + 0.0377167i) q^{48} +(-5.98324 - 3.63330i) q^{49} -3.96654 q^{50} +(-0.0930626 + 0.0414341i) q^{51} +(0.269031 - 2.55966i) q^{52} +(3.95519 + 1.76097i) q^{53} +(0.232686 + 0.0494589i) q^{54} -14.5201 q^{55} +(-2.07443 + 1.64217i) q^{56} +(0.000683601 - 0.00210391i) q^{57} +(1.61871 - 0.720694i) q^{58} +(-3.32047 + 3.68776i) q^{59} +(0.116157 - 0.0246899i) q^{60} +(1.11890 + 1.24267i) q^{61} +(-0.854538 + 2.63000i) q^{62} +(5.54713 + 5.67127i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-7.04062 + 3.13468i) q^{65} +(0.188100 - 0.0399818i) q^{66} +(-7.27149 - 3.23748i) q^{67} +(-1.28436 + 2.22458i) q^{68} +(0.0769810 + 0.236923i) q^{69} +(7.36441 + 2.92084i) q^{70} +(10.8876 + 7.91034i) q^{71} +(2.73920 - 1.21957i) q^{72} +(4.56916 + 7.91402i) q^{73} +(0.655266 - 6.23444i) q^{74} +(-0.105257 - 0.116900i) q^{75} +(-0.0172375 - 0.0530517i) q^{76} +(11.9256 + 4.72988i) q^{77} +(0.0825759 - 0.0599949i) q^{78} +(-8.64082 + 14.9663i) q^{79} +(2.00366 - 2.22529i) q^{80} +(-4.49292 - 7.78197i) q^{81} +(-6.09237 + 1.97055i) q^{82} +16.1140 q^{83} +(-0.103445 - 0.0175595i) q^{84} +7.69183 q^{85} +(0.398832 + 3.79463i) q^{86} +(0.0641942 + 0.0285811i) q^{87} +(3.24464 - 3.60354i) q^{88} +(-2.70452 - 3.00368i) q^{89} +(-7.26380 - 5.27746i) q^{90} +(6.80372 - 0.281114i) q^{91} +(5.08196 + 3.69226i) q^{92} +(-0.100186 + 0.0446057i) q^{93} +(2.39398 + 1.06587i) q^{94} +(-0.111768 + 0.124131i) q^{95} +(-0.0198289 + 0.0343446i) q^{96} +(-11.0492 + 8.02770i) q^{97} +(-5.09709 - 4.79789i) q^{98} +(-11.7627 - 8.54610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) $ 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	0.0198289	+	0.0343446i	0.0114482	+	0.0198289i	0.871693	−	0.490053i	$-0.163023\pi$
$3$	0.0198289	+	0.0343446i	0.0114482	+	0.0198289i	−0.860245	+	0.509882i	$0.829689\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−0.313002	−	2.97801i	−0.139979	−	1.33181i	−0.808667	−	0.588266i	$-0.799811\pi$
$5$	−0.313002	−	2.97801i	−0.139979	−	1.33181i	0.668689	−	0.743543i	$-0.266856\pi$
$6$	0.0122549	+	0.0377167i	0.00500305	+	0.0153978i
$7$	−0.713008	+	2.54787i	−0.269492	+	0.963003i
$7$	−0.713008	+	2.54787i	−0.269492	+	0.963003i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.49921	−	2.59671i	0.499738	−	0.865571i
$10$	0.313002	−	2.97801i	0.0989799	−	0.941731i
$11$	0.506863	−	4.82248i	0.152825	−	1.45403i	−0.602205	−	0.798342i	$-0.705711\pi$
$11$	0.506863	−	4.82248i	0.152825	−	1.45403i	0.755030	−	0.655690i	$-0.227622\pi$
$12$	0.00414536	+	0.0394405i	0.00119666	+	0.0113855i
$13$	−0.795336	−	2.44779i	−0.220586	−	0.678895i	−0.998710	−	0.0507836i	$-0.983828\pi$
$13$	−0.795336	−	2.44779i	−0.220586	−	0.678895i	0.778123	−	0.628112i	$-0.216172\pi$
$14$	−1.22716	+	2.34395i	−0.327972	+	0.626446i
$15$	0.0960722	−	0.0698006i	0.0248057	−	0.0180224i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.268505	+	2.55465i	−0.0651219	+	0.619594i	0.912479	+	0.409125i	$0.134166\pi$
$17$	−0.268505	+	2.55465i	−0.0651219	+	0.619594i	−0.977600	+	0.210469i	$0.932501\pi$
$18$	2.00634	−	2.22827i	0.472899	−	0.525207i
$19$	−0.0373253	−	0.0414540i	−0.00856302	−	0.00951019i	0.738848	−	0.673872i	$-0.235370\pi$
$19$	−0.0373253	−	0.0414540i	−0.00856302	−	0.00951019i	−0.747411	+	0.664362i	$0.768703\pi$
$20$	0.925326	−	2.84786i	0.206909	−	0.636801i
$21$	−0.101644	+	0.0260333i	−0.0221804	+	0.00568093i
$22$	1.49844	−	4.61171i	0.319468	−	0.983221i
$23$	6.14437	+	1.30603i	1.28119	+	0.272325i	0.797716	−	0.603033i	$-0.206041\pi$
$23$	6.14437	+	1.30603i	1.28119	+	0.272325i	0.483474	+	0.875359i	$0.339375\pi$
$24$	−0.00414536	+	0.0394405i	−0.000846168	+	0.00805075i
$25$	−3.87986	+	0.824690i	−0.775973	+	0.164938i
$26$	−0.269031	−	2.55966i	−0.0527614	−	0.501991i
$27$	0.237884			0.0457808
$28$	−1.68768	+	2.03758i	−0.318941	+	0.385067i
$29$	1.43349	−	1.04149i	0.266193	−	0.193400i	−0.446680	−	0.894694i	$-0.647394\pi$
$29$	1.43349	−	1.04149i	0.266193	−	0.193400i	0.712873	+	0.701293i	$0.247394\pi$
$30$	0.108485	−	0.0483007i	0.0198066	−	0.00881846i
$31$	−0.289057	+	2.75020i	−0.0519162	+	0.493950i	0.937410	+	0.348229i	$0.113217\pi$
$31$	−0.289057	+	2.75020i	−0.0519162	+	0.493950i	−0.989326	+	0.145721i	$0.953450\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.175677	−	0.0782163i	0.0305814	−	0.0136157i
$34$	−0.793779	+	2.44300i	−0.136132	+	0.418971i
$35$	7.81075	+	1.32586i	1.32026	+	0.224111i
$36$	2.42578	−	1.76243i	0.404296	−	0.293739i
$37$	−0.655266	−	6.23444i	−0.107725	−	1.02494i	−0.906183	−	0.422885i	$-0.861017\pi$
$37$	−0.655266	−	6.23444i	−0.107725	−	1.02494i	0.798458	−	0.602050i	$-0.205649\pi$
$38$	−0.0278909	−	0.0483085i	−0.00452450	−	0.00783667i
$39$	0.0682978	−	0.0758524i	0.0109364	−	0.0121461i
$40$	1.49721	−	2.59324i	0.236730	−	0.410028i
$41$	−5.54954	+	3.19416i	−0.866692	+	0.498844i
$41$	−5.54954	+	3.19416i	−0.866692	+	0.498844i
$42$	−0.104835	+	0.00433153i	−0.0161764	+	0.000668370i
$43$	1.17906	+	3.62879i	0.179806	+	0.553385i	0.999820	−	0.0189576i	$-0.00603475\pi$
$43$	1.17906	+	3.62879i	0.179806	+	0.553385i	−0.820015	+	0.572343i	$0.806035\pi$
$44$	2.42452	−	4.19939i	0.365510	−	0.633082i
$45$	−8.20231	−	3.65190i	−1.22273	−	0.544394i
$46$	5.73857	+	2.55497i	0.846105	+	0.376710i
$47$	2.56327	+	0.544840i	0.373892	+	0.0794731i	0.391025	−	0.920380i	$-0.372121\pi$
$47$	2.56327	+	0.544840i	0.373892	+	0.0794731i	−0.0171333	+	0.999853i	$0.505454\pi$
$48$	−0.0122549	+	0.0377167i	−0.00176884	+	0.00544394i
$49$	−5.98324	−	3.63330i	−0.854748	−	0.519042i
$50$	−3.96654			−0.560954
$51$	−0.0930626	+	0.0414341i	−0.0130314	+	0.00580194i
$52$	0.269031	−	2.55966i	0.0373079	−	0.354961i
$53$	3.95519	+	1.76097i	0.543288	+	0.241887i	0.659983	−	0.751280i	$-0.270563\pi$
$53$	3.95519	+	1.76097i	0.543288	+	0.241887i	−0.116695	+	0.993168i	$0.537230\pi$
$54$	0.232686	+	0.0494589i	0.0316645	+	0.00673050i
$55$	−14.5201			−1.95788
$56$	−2.07443	+	1.64217i	−0.277208	+	0.219444i
$57$	0.000683601	−	0.00210391i	9.05452e−5	−	0.000278669i
$58$	1.61871	−	0.720694i	0.212546	−	0.0946318i
$59$	−3.32047	+	3.68776i	−0.432288	+	0.480105i	−0.919450	−	0.393207i	$-0.871366\pi$
$59$	−3.32047	+	3.68776i	−0.432288	+	0.480105i	0.487162	+	0.873312i	$0.338032\pi$
$60$	0.116157	−	0.0246899i	0.0149958	−	0.00318745i
$61$	1.11890	+	1.24267i	0.143261	+	0.159107i	0.810505	−	0.585732i	$-0.199193\pi$
$61$	1.11890	+	1.24267i	0.143261	+	0.159107i	−0.667244	+	0.744839i	$0.732526\pi$
$62$	−0.854538	+	2.63000i	−0.108526	+	0.334010i
$63$	5.54713	+	5.67127i	0.698872	+	0.714513i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−7.04062	+	3.13468i	−0.873281	+	0.388810i
$66$	0.188100	−	0.0399818i	0.0231535	−	0.00492142i
$67$	−7.27149	−	3.23748i	−0.888354	−	0.395521i	−0.0887537	−	0.996054i	$-0.528288\pi$
$67$	−7.27149	−	3.23748i	−0.888354	−	0.395521i	−0.799600	+	0.600533i	$0.794955\pi$
$68$	−1.28436	+	2.22458i	−0.155752	+	0.269770i
$69$	0.0769810	+	0.236923i	0.00926742	+	0.0285222i
$70$	7.36441	+	2.92084i	0.880215	+	0.349107i
$71$	10.8876	+	7.91034i	1.29213	+	0.938784i	0.999846	−	0.0175487i	$-0.00558621\pi$
$71$	10.8876	+	7.91034i	1.29213	+	0.938784i	0.292280	+	0.956333i	$0.405586\pi$
$72$	2.73920	−	1.21957i	0.322818	−	0.143728i
$73$	4.56916	+	7.91402i	0.534780	+	0.926266i	0.999174	+	0.0406376i	$0.0129389\pi$
$73$	4.56916	+	7.91402i	0.534780	+	0.926266i	−0.464394	+	0.885629i	$0.653728\pi$
$74$	0.655266	−	6.23444i	0.0761731	−	0.724739i
$75$	−0.105257	−	0.116900i	−0.0121540	−	0.0134984i
$76$	−0.0172375	−	0.0530517i	−0.00197728	−	0.00608544i
$77$	11.9256	+	4.72988i	1.35905	+	0.539020i
$78$	0.0825759	−	0.0599949i	0.00934988	−	0.00679309i
$79$	−8.64082	+	14.9663i	−0.972169	+	1.68385i	−0.283189	+	0.959064i	$0.591393\pi$
$79$	−8.64082	+	14.9663i	−0.972169	+	1.68385i	−0.688979	+	0.724781i	$0.741941\pi$
$80$	2.00366	−	2.22529i	0.224016	−	0.248795i
$81$	−4.49292	−	7.78197i	−0.499214	−	0.864664i
$82$	−6.09237	+	1.97055i	−0.672789	+	0.217610i
$83$	16.1140			1.76874			0.884372	−	0.466783i	$-0.154587\pi$
$83$	16.1140			1.76874			0.884372	+	0.466783i	$0.154587\pi$
$84$	−0.103445	−	0.0175595i	−0.0112867	−	0.00191590i
$85$	7.69183			0.834296
$86$	0.398832	+	3.79463i	0.0430071	+	0.409186i
$87$	0.0641942	+	0.0285811i	0.00688234	+	0.00306421i
$88$	3.24464	−	3.60354i	0.345880	−	0.384139i
$89$	−2.70452	−	3.00368i	−0.286679	−	0.318389i	0.582554	−	0.812792i	$-0.302053\pi$
$89$	−2.70452	−	3.00368i	−0.286679	−	0.318389i	−0.869233	+	0.494403i	$0.835387\pi$
$90$	−7.26380	−	5.27746i	−0.765671	−	0.556293i
$91$	6.80372	−	0.281114i	0.713224	−	0.0294687i
$92$	5.08196	+	3.69226i	0.529830	+	0.384944i
$93$	−0.100186	+	0.0446057i	−0.0103888	+	0.00462539i
$94$	2.39398	+	1.06587i	0.246920	+	0.109936i
$95$	−0.111768	+	0.124131i	−0.0114671	+	0.0127355i
$96$	−0.0198289	+	0.0343446i	−0.00202377	+	0.00350528i
$97$	−11.0492	+	8.02770i	−1.12187	+	0.815089i	−0.984492	−	0.175429i	$-0.943869\pi$
$97$	−11.0492	+	8.02770i	−1.12187	+	0.815089i	−0.137382	+	0.990518i	$0.543869\pi$
$98$	−5.09709	−	4.79789i	−0.514883	−	0.484660i
$99$	−11.7627	−	8.54610i	−1.18220	−	0.858916i
$100$	−3.87986	−	0.824690i	−0.387986	−	0.0824690i
$101$	−18.2360	+	3.87618i	−1.81455	+	0.385694i	−0.984974	−	0.172702i	$-0.944750\pi$
$101$	−18.2360	+	3.87618i	−1.81455	+	0.385694i	−0.829575	+	0.558396i	$0.811417\pi$
$102$	−0.0996436	+	0.0211799i	−0.00986619	+	0.00209712i
$103$	−2.55621	−	2.83896i	−0.251871	−	0.279731i	0.603929	−	0.797038i	$-0.293601\pi$
$103$	−2.55621	−	2.83896i	−0.251871	−	0.279731i	−0.855800	+	0.517307i	$0.826934\pi$
$104$	0.795336	−	2.44779i	0.0779891	−	0.240026i
$105$	0.109342	+	0.294548i	0.0106707	+	0.0287449i
$106$	3.50264	+	2.54482i	0.340206	+	0.247174i
$107$	−3.22659	−	3.58350i	−0.311927	−	0.346430i	0.566713	−	0.823915i	$-0.308215\pi$
$107$	−3.22659	−	3.58350i	−0.311927	−	0.346430i	−0.878639	+	0.477486i	$0.841548\pi$
$108$	0.217318	+	0.0967561i	0.0209114	+	0.00931036i
$109$	3.53236	+	6.11823i	0.338339	+	0.586020i	0.984120	−	0.177502i	$-0.0568017\pi$
$109$	3.53236	+	6.11823i	0.338339	+	0.586020i	−0.645782	+	0.763522i	$0.723468\pi$
$110$	−14.2028	−	3.01889i	−1.35418	−	0.287840i
$111$	0.201126	−	0.146127i	0.0190901	−	0.0138697i
$112$	−2.37053	+	1.17499i	−0.223994	+	0.111026i
$113$	3.89793	+	2.83201i	0.366686	+	0.266413i	0.755836	−	0.654762i	$-0.227231\pi$
$113$	3.89793	+	2.83201i	0.366686	+	0.266413i	−0.389149	+	0.921175i	$0.627231\pi$
$114$	0.00110609	−	0.00191580i	0.000103595	−	0.000179432i
$115$	1.96617	−	18.7068i	0.183346	−	1.74442i
$116$	1.73317	−	0.368397i	0.160921	−	0.0342048i
$117$	−7.54859	−	1.60450i	−0.697868	−	0.148336i
$118$	−4.01464	+	2.91681i	−0.369577	+	0.268514i
$119$	−6.31746	−	2.50560i	−0.579121	−	0.229688i
$120$	0.118752			0.0108405
$121$	−12.2398	−	2.60164i	−1.11271	−	0.236513i
$122$	0.836086	+	1.44814i	0.0756956	+	0.131109i
$123$	−0.219743	−	0.127260i	−0.0198136	−	0.0114746i
$124$	−1.38267	+	2.39486i	−0.124168	+	0.215065i
$125$	−0.956286	−	2.94315i	−0.0855328	−	0.263243i
$126$	4.24679	+	6.70065i	0.378334	+	0.596942i
$127$	7.19854	−	5.23005i	0.638767	−	0.464092i	−0.220659	−	0.975351i	$-0.570821\pi$
$127$	7.19854	−	5.23005i	0.638767	−	0.464092i	0.859427	+	0.511259i	$0.170821\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.101250	+	0.112449i	−0.00891454	+	0.00990060i
$130$	−7.53850	+	1.60236i	−0.661170	+	0.140536i
$131$	−11.8795	+	5.28909i	−1.03792	+	0.462110i	−0.853694	−	0.520775i	$-0.825643\pi$
$131$	−11.8795	+	5.28909i	−1.03792	+	0.462110i	−0.184222	+	0.982885i	$0.558976\pi$
$132$	0.192302			0.0167377
$133$	0.132232	−	0.0655429i	0.0114660	−	0.00568329i
$134$	−6.43948	−	4.67856i	−0.556286	−	0.404166i
$135$	−0.0744581	−	0.708422i	−0.00640834	−	0.0609713i
$136$	−1.71881	+	1.90893i	−0.147387	+	0.163690i
$137$	3.32952	+	5.76689i	0.284460	+	0.492699i	0.972478	−	0.232995i	$-0.0748524\pi$
$137$	3.32952	+	5.76689i	0.284460	+	0.492699i	−0.688018	+	0.725693i	$0.741519\pi$
$138$	0.0260397	+	0.247751i	0.00221664	+	0.0210900i
$139$	4.74702	−	14.6098i	0.402637	−	1.23919i	−0.520215	−	0.854036i	$-0.674148\pi$
$139$	4.74702	−	14.6098i	0.402637	−	1.23919i	0.922852	−	0.385155i	$-0.125852\pi$
$140$	6.59620	+	4.38815i	0.557481	+	0.370867i
$141$	0.0321144	+	0.0988381i	0.00270452	+	0.00832367i
$142$	9.00507	+	10.0011i	0.755689	+	0.839277i
$143$	−12.2075	+	2.59479i	−1.02085	+	0.216988i
$144$	2.93290	−	0.623408i	0.244409	−	0.0519507i
$145$	−3.55027	−	3.94297i	−0.294834	−	0.327446i
$146$	2.82390	+	8.69107i	0.233708	+	0.719278i
$147$	0.00614329	−	0.277536i	0.000506690	−	0.0228908i
$148$	1.93716	−	5.96197i	0.159234	−	0.490071i
$149$	2.46288	+	23.4328i	0.201767	+	1.91969i	0.361219	+	0.932481i	$0.382361\pi$
$149$	2.46288	+	23.4328i	0.201767	+	1.91969i	−0.159452	+	0.987206i	$0.550973\pi$
$150$	−0.0786520	−	0.136229i	−0.00642191	−	0.0111231i
$151$	−0.400219	+	0.444488i	−0.0325694	+	0.0361720i	−0.759209	−	0.650846i	$-0.774414\pi$
$151$	−0.400219	+	0.444488i	−0.0325694	+	0.0361720i	0.726640	+	0.687018i	$0.241081\pi$
$152$	−0.00583079	−	0.0554763i	−0.000472939	−	0.00449972i
$153$	6.23115	+	4.52720i	0.503759	+	0.366002i
$154$	10.6816	+	7.10600i	0.860750	+	0.572618i
$155$	8.28060			0.665114
$156$	0.0932451	−	0.0415154i	0.00746558	−	0.00332389i
$157$	3.13627	−	0.666634i	0.250301	−	0.0532032i	−0.0810522	−	0.996710i	$-0.525828\pi$
$157$	3.13627	−	0.666634i	0.250301	−	0.0532032i	0.331354	+	0.943507i	$0.392495\pi$
$158$	−11.5637	+	12.8428i	−0.919957	+	1.02172i
$159$	0.0179473	+	0.170757i	0.00142332	+	0.0135420i
$160$	2.42254	−	1.76007i	0.191518	−	0.139146i
$161$	−7.70857	+	14.7238i	−0.607520	+	1.16040i
$162$	−2.77678	−	8.54605i	−0.218164	−	0.671441i
$163$	−3.54719	+	6.14392i	−0.277838	+	0.481229i	−0.970847	−	0.239700i	$-0.922951\pi$
$163$	−3.54719	+	6.14392i	−0.277838	+	0.481229i	0.693010	+	0.720928i	$0.256284\pi$
$164$	−6.36893	+	0.660811i	−0.497330	+	0.0516007i
$165$	−0.287916	−	0.498686i	−0.0224143	−	0.0388226i
$166$	15.7619	+	3.35029i	1.22336	+	0.260033i
$167$	22.3550			1.72988			0.864939	−	0.501876i	$-0.167357\pi$
$167$	22.3550			1.72988			0.864939	+	0.501876i	$0.167357\pi$
$168$	−0.0975334	−	0.0386832i	−0.00752486	−	0.00298447i
$169$	5.15810	−	3.74758i	0.396777	−	0.288275i
$170$	7.52375	+	1.59922i	0.577045	+	0.122655i
$171$	−0.163603	+	0.0347748i	−0.0125110	+	0.00265930i
$172$	−0.398832	+	3.79463i	−0.0304106	+	0.289338i
$173$	11.9653	−	20.7245i	0.909705	−	1.57566i	0.0952309	−	0.995455i	$-0.469641\pi$
$173$	11.9653	−	20.7245i	0.909705	−	1.57566i	0.814474	−	0.580200i	$-0.197026\pi$
$174$	0.0568490	+	0.0413032i	0.00430971	+	0.00313119i
$175$	0.665173	−	10.4734i	0.0502824	−	0.791713i
$176$	3.92296	−	2.85020i	0.295704	−	0.214842i
$177$	−0.192496	−	0.0409162i	−0.0144689	−	0.00307545i
$178$	−2.02092	−	3.50034i	−0.151475	−	0.262362i
$179$	−1.09253	−	0.486424i	−0.0816593	−	0.0363571i	0.365501	−	0.930811i	$-0.380898\pi$
$179$	−1.09253	−	0.486424i	−0.0816593	−	0.0363571i	−0.447160	+	0.894454i	$0.647564\pi$
$180$	−6.00782	−	6.67236i	−0.447796	−	0.497328i
$181$	2.00378	+	1.45583i	0.148940	+	0.108211i	0.659760	−	0.751477i	$-0.270658\pi$
$181$	2.00378	+	1.45583i	0.148940	+	0.108211i	−0.510820	+	0.859688i	$0.670658\pi$
$182$	6.71349	+	1.13960i	0.497637	+	0.0844730i
$183$	−0.0204923	+	0.0630688i	−0.00151483	+	0.00466218i
$184$	4.20324	+	4.66817i	0.309867	+	0.344142i
$185$	−18.3612	+	3.90278i	−1.34994	+	0.286938i
$186$	−0.107271	+	0.0228011i	−0.00786547	+	0.00167186i
$187$	12.1837	+	2.58972i	0.890957	+	0.189379i
$188$	2.12006	+	1.54031i	0.154621	+	0.112339i
$189$	−0.169613	+	0.606096i	−0.0123375	+	0.0440870i
$190$	−0.135133	+	0.0981802i	−0.00980361	+	0.00712274i
$191$	−8.33751	+	14.4410i	−0.603281	+	1.04491i	0.389040	+	0.921221i	$0.372807\pi$
$191$	−8.33751	+	14.4410i	−0.603281	+	1.04491i	−0.992321	+	0.123692i	$0.960526\pi$
$192$	−0.0265362	+	0.0294714i	−0.00191508	+	0.00212692i
$193$	9.51603	+	4.23681i	0.684979	+	0.304972i	0.719561	−	0.694430i	$-0.244343\pi$
$193$	9.51603	+	4.23681i	0.684979	+	0.304972i	−0.0345816	+	0.999402i	$0.511010\pi$
$194$	−12.4768	+	5.55502i	−0.895781	+	0.398827i
$195$	−0.247267	−	0.179650i	−0.0177071	−	0.0128650i
$196$	−3.98817	−	5.75278i	−0.284869	−	0.410913i
$197$	1.06053	+	0.770519i	0.0755595	+	0.0548972i	0.624924	−	0.780686i	$-0.285130\pi$
$197$	1.06053	+	0.770519i	0.0755595	+	0.0548972i	−0.549364	+	0.835583i	$0.685130\pi$
$198$	−9.72882	−	10.8050i	−0.691397	−	0.767875i
$199$	17.2850	−	19.1969i	1.22530	−	1.36083i	0.313825	−	0.949481i	$-0.398390\pi$
$199$	17.2850	−	19.1969i	1.22530	−	1.36083i	0.911476	−	0.411353i	$-0.134944\pi$
$200$	−3.62362	−	1.61334i	−0.256228	−	0.114080i
$201$	−0.0329956	−	0.313932i	−0.00232733	−	0.0221430i
$202$	−18.6434			−1.31174
$203$	1.63149	+	4.39494i	0.114508	+	0.308464i
$204$	−0.101870			−0.00713231
$205$	11.2493	+	15.5268i	0.785683	+	1.08444i
$206$	−1.91010	−	3.30839i	−0.133083	−	0.230506i
$207$	12.6031	−	13.9972i	0.875976	−	0.972870i
$208$	1.28688	−	2.22894i	0.0892291	−	0.154549i
$209$	−0.218830	+	0.158989i	−0.0151368	+	0.0109975i
$210$	0.0457129	+	0.310844i	0.00315449	+	0.0214503i
$211$	−4.36109	−	13.4221i	−0.300230	−	0.924012i	−0.981414	−	0.191901i	$-0.938535\pi$
$211$	−4.36109	−	13.4221i	−0.300230	−	0.924012i	0.681185	−	0.732112i	$-0.261465\pi$
$212$	2.89700	+	3.21744i	0.198967	+	0.220975i
$213$	−0.0557877	+	0.530785i	−0.00382251	+	0.0363688i
$214$	−2.41103	−	4.17603i	−0.164815	−	0.285468i
$215$	10.4375	−	4.64709i	0.711834	−	0.316929i
$216$	0.192452	+	0.139825i	0.0130947	+	0.00951386i
$217$	−6.80103	−	2.69739i	−0.461684	−	0.183111i
$218$	2.18312	+	6.71895i	0.147859	+	0.455065i
$219$	−0.181203	+	0.313852i	−0.0122445	+	0.0212082i
$220$	−13.2647	−	5.90584i	−0.894308	−	0.398172i
$221$	6.46680	−	1.37456i	0.435004	−	0.0924630i
$222$	0.227113	−	0.101117i	0.0152428	−	0.00678653i
$223$	2.00806	+	6.18019i	0.134470	+	0.413856i	0.995507	−	0.0946859i	$-0.0301847\pi$
$223$	2.00806	+	6.18019i	0.134470	+	0.413856i	−0.861037	+	0.508542i	$0.830185\pi$
$224$	−2.56302	+	0.656450i	−0.171249	+	0.0438609i
$225$	−3.67526	+	11.3113i	−0.245017	+	0.754086i
$226$	3.22394	+	3.58055i	0.214453	+	0.238175i
$227$	−3.70519	+	0.787562i	−0.245922	+	0.0522723i	−0.329223	−	0.944252i	$-0.606787\pi$
$227$	−3.70519	+	0.787562i	−0.245922	+	0.0522723i	0.0833014	+	0.996524i	$0.473454\pi$
$228$	0.00148024	−	0.00164397i	9.80311e−5	−	0.000108875i
$229$	−3.79829	+	1.69111i	−0.250998	+	0.111752i	−0.528379	−	0.849008i	$-0.677200\pi$
$229$	−3.79829	+	1.69111i	−0.250998	+	0.111752i	0.277381	+	0.960760i	$0.410533\pi$
$230$	5.81257	−	17.8892i	0.383269	−	1.17958i
$231$	0.0740257	+	0.503369i	0.00487053	+	0.0331193i
$232$	1.77189			0.116330
$233$	−24.9887	−	5.31150i	−1.63706	−	0.347968i	−0.704703	−	0.709502i	$-0.748920\pi$
$233$	−24.9887	−	5.31150i	−1.63706	−	0.347968i	−0.932359	+	0.361534i	$0.882253\pi$
$234$	−7.05004	−	3.13888i	−0.460876	−	0.205195i
$235$	0.820233	−	7.80400i	0.0535061	−	0.509077i
$236$	−4.53335	+	2.01838i	−0.295096	+	0.131385i
$237$	−0.685351			−0.0445183
$238$	−5.65847	−	3.76432i	−0.366784	−	0.244005i
$239$	5.64576	−	17.3759i	0.365194	−	1.12395i	−0.584665	−	0.811275i	$-0.698774\pi$
$239$	5.64576	−	17.3759i	0.365194	−	1.12395i	0.949859	−	0.312677i	$-0.101226\pi$
$240$	0.116157	+	0.0246899i	0.00749789	+	0.00159373i
$241$	−7.44226	−	3.31351i	−0.479398	−	0.213442i	0.152787	−	0.988259i	$-0.451175\pi$
$241$	−7.44226	−	3.31351i	−0.479398	−	0.213442i	−0.632185	+	0.774817i	$0.717842\pi$
$242$	−11.4314	−	5.08958i	−0.734837	−	0.327171i
$243$	0.535005	−	0.926656i	0.0343206	−	0.0594450i
$244$	0.516729	+	1.59033i	0.0330802	+	0.101810i
$245$	−8.94725	+	18.9554i	−0.571619	+	1.21102i
$246$	−0.188482	−	0.170166i	−0.0120172	−	0.0108494i
$247$	−0.0717845	+	0.124334i	−0.00456754	+	0.00791121i
$248$	−1.85038	+	2.05505i	−0.117499	+	0.130496i
$249$	0.319523	+	0.553430i	0.0202489	+	0.0350722i
$250$	−0.323474	−	3.07765i	−0.0204583	−	0.194648i
$251$	2.13056	−	1.54794i	0.134480	−	0.0977054i	−0.518512	−	0.855071i	$-0.673514\pi$
$251$	2.13056	−	1.54794i	0.134480	−	0.0977054i	0.652992	+	0.757365i	$0.273514\pi$
$252$	2.76084	+	7.43719i	0.173917	+	0.468499i
$253$	9.41264	−	28.9691i	0.591768	−	1.82127i
$254$	8.12863	−	3.61910i	0.510035	−	0.227082i
$255$	0.152520	+	0.264173i	0.00955119	+	0.0165431i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−0.358536	+	0.159630i	−0.0223648	+	0.00995747i	−0.417889	−	0.908498i	$-0.637230\pi$
$257$	−0.358536	+	0.159630i	−0.0223648	+	0.00995747i	0.395524	+	0.918456i	$0.370563\pi$
$258$	−0.122417	+	0.0889409i	−0.00762133	+	0.00553722i
$259$	16.3517	+	2.77568i	1.01605	+	0.172472i
$260$	−7.70691			−0.477963
$261$	−0.555349	−	5.28379i	−0.0343752	−	0.327058i
$262$	−12.7196	+	2.70363i	−0.785817	+	0.167031i
$263$	0.129717	−	1.23418i	0.00799872	−	0.0761027i	−0.989794	−	0.142503i	$-0.954485\pi$
$263$	0.129717	−	1.23418i	0.00799872	−	0.0761027i	0.997793	+	0.0664006i	$0.0211515\pi$
$264$	0.188100	+	0.0399818i	0.0115767	+	0.00246071i
$265$	4.00620	−	12.3298i	0.246099	−	0.757414i
$266$	0.142970	−	0.0366180i	0.00876605	−	0.00224519i
$267$	0.0495324	−	0.152445i	0.00303134	−	0.00932949i
$268$	−5.32604	−	5.91516i	−0.325339	−	0.361326i
$269$	1.38767	−	1.54116i	0.0846075	−	0.0939661i	−0.699354	−	0.714775i	$-0.746529\pi$
$269$	1.38767	−	1.54116i	0.0846075	−	0.0939661i	0.783962	+	0.620809i	$0.213196\pi$
$270$	0.0744581	−	0.708422i	0.00453138	−	0.0431132i
$271$	10.9214	+	12.1294i	0.663428	+	0.736811i	0.977114	−	0.212716i	$-0.0682308\pi$
$271$	10.9214	+	12.1294i	0.663428	+	0.736811i	−0.313687	+	0.949527i	$0.601564\pi$
$272$	−2.07814	+	1.50986i	−0.126006	+	0.0915486i
$273$	0.144565	+	0.228097i	0.00874946	+	0.0138051i
$274$	2.05775	+	6.33312i	0.124313	+	0.382598i
$275$	2.01049	+	19.1286i	0.121237	+	1.15350i
$276$	−0.0260397	+	0.247751i	−0.00156740	+	0.0149129i
$277$	2.04753	−	19.4810i	0.123024	−	1.17050i	−0.742576	−	0.669762i	$-0.766396\pi$
$277$	2.04753	−	19.4810i	0.123024	−	1.17050i	0.865600	−	0.500736i	$-0.166937\pi$
$278$	7.68085	−	13.3036i	0.460667	−	0.797898i
$279$	6.70811	+	4.87373i	0.401604	+	0.291783i
$280$	5.53971	+	5.66369i	0.331061	+	0.338470i
$281$	4.80100	+	14.7760i	0.286404	+	0.881461i	0.985974	+	0.166897i	$0.0533747\pi$
$281$	4.80100	+	14.7760i	0.286404	+	0.881461i	−0.699570	+	0.714564i	$0.746625\pi$
$282$	0.0108631	+	0.103355i	0.000646886	+	0.00615471i
$283$	4.19953	+	1.86975i	0.249636	+	0.111145i	0.527740	−	0.849406i	$-0.323039\pi$
$283$	4.19953	+	1.86975i	0.249636	+	0.111145i	−0.278104	+	0.960551i	$0.589706\pi$
$284$	6.72893	+	11.6549i	0.399289	+	0.691588i
$285$	−0.00647944	−	0.00137725i	−0.000383809	−	8.15811e-5i
$286$	−12.4803			−0.737974
$287$	−4.18143	−	16.4169i	−0.246822	−	0.969061i
$288$	2.99843			0.176684
$289$	10.1744	+	2.16263i	0.598492	+	0.127213i
$290$	−2.65290	−	4.59495i	−0.155783	−	0.269825i
$291$	−0.494801	−	0.220299i	−0.0290057	−	0.0129142i
$292$	0.955215	+	9.08827i	0.0558998	+	0.531851i
$293$	2.23101	+	6.86634i	0.130337	+	0.401136i	0.994836	−	0.101499i	$-0.0323639\pi$
$293$	2.23101	+	6.86634i	0.130337	+	0.401136i	−0.864499	+	0.502635i	$0.832364\pi$
$294$	0.0637120	−	0.270194i	0.00371576	−	0.0157580i
$295$	12.0215	+	8.73414i	0.699919	+	0.508521i
$296$	3.13439	−	5.42892i	0.182183	−	0.315550i
$297$	0.120575	−	1.14719i	0.00699645	−	0.0665667i
$298$	−2.46288	+	23.4328i	−0.142671	+	1.35742i
$299$	−1.68996	−	16.0789i	−0.0977328	−	0.929865i
$300$	−0.0486096	−	0.149605i	−0.00280648	−	0.00863745i
$301$	−10.0863	+	0.416744i	−0.581367	+	0.0240207i
$302$	−0.483888	+	0.351565i	−0.0278446	+	0.0202303i
$303$	−0.494725	−	0.549447i	−0.0284212	−	0.0315649i
$304$	0.00583079	−	0.0554763i	0.000334419	−	0.00318178i
$305$	3.35046	−	3.72106i	0.191847	−	0.213067i
$306$	5.15373	+	5.72380i	0.294619	+	0.327208i
$307$	−9.78842	+	30.1256i	−0.558654	+	1.71936i	0.127438	+	0.991847i	$0.459325\pi$
$307$	−9.78842	+	30.1256i	−0.558654	+	1.71936i	−0.686092	+	0.727515i	$0.740675\pi$
$308$	8.97079	+	9.17156i	0.511158	+	0.522598i
$309$	0.0468162	−	0.144085i	0.00266328	−	0.00819673i
$310$	8.09965	+	1.72163i	0.460029	+	0.0977822i
$311$	2.63335	−	25.0546i	0.149323	−	1.42072i	−0.621373	−	0.783515i	$-0.713425\pi$
$311$	2.63335	−	25.0546i	0.149323	−	1.42072i	0.770697	−	0.637202i	$-0.219908\pi$
$312$	0.0998390	−	0.0212214i	0.00565227	−	0.00120143i
$313$	−1.60528	−	15.2733i	−0.0907360	−	0.863295i	−0.941333	−	0.337478i	$-0.890426\pi$
$313$	−1.60528	−	15.2733i	−0.0907360	−	0.863295i	0.850597	−	0.525817i	$-0.176240\pi$
$314$	3.20633			0.180944
$315$	15.1529	−	18.2945i	0.853768	−	1.03078i
$316$	−13.9811	+	10.1579i	−0.786501	+	0.571426i
$317$	20.6585	−	9.19775i	1.16030	−	0.516597i	0.265956	−	0.963985i	$-0.414312\pi$
$317$	20.6585	−	9.19775i	1.16030	−	0.516597i	0.894340	+	0.447388i	$0.147646\pi$
$318$	−0.0179473	+	0.170757i	−0.00100644	+	0.00957561i
$319$	−4.29599	−	7.44088i	−0.240529	−	0.416609i
$320$	2.73554	−	1.21794i	0.152921	−	0.0680849i
$321$	0.0590940	−	0.181873i	0.00329831	−	0.0101511i
$322$	−10.6014	+	12.7994i	−0.590791	+	0.713281i
$323$	0.115922	−	0.0842226i	0.00645010	−	0.00468627i
$324$	−0.939277	−	8.93662i	−0.0521820	−	0.496479i
$325$	5.10446	+	8.84119i	0.283145	+	0.490421i
$326$	−4.74707	+	5.27215i	−0.262916	+	0.291998i
$327$	−0.140085	+	0.242635i	−0.00774674	+	0.0134177i
$328$	−6.36715	−	0.677805i	−0.351567	−	0.0374255i
$329$	−3.21581	+	6.14240i	−0.177293	+	0.338641i
$330$	−0.177942	−	0.547649i	−0.00979539	−	0.0301471i
$331$	−13.3755	+	23.1671i	−0.735185	+	1.27338i	0.219457	+	0.975622i	$0.429572\pi$
$331$	−13.3755	+	23.1671i	−0.735185	+	1.27338i	−0.954642	+	0.297756i	$0.903762\pi$
$332$	14.7209	+	6.55416i	0.807914	+	0.359706i
$333$	−17.1714	−	7.64522i	−0.940989	−	0.418956i
$334$	21.8665	+	4.64786i	1.19648	+	0.254319i
$335$	−7.36526	+	22.6679i	−0.402407	+	1.23848i
$336$	−0.0873593	−	0.0581162i	−0.00476584	−	0.00317050i
$337$	2.38003			0.129648			0.0648242	−	0.997897i	$-0.479351\pi$
$337$	2.38003			0.129648			0.0648242	+	0.997897i	$0.479351\pi$
$338$	5.82455	−	2.59325i	0.316814	−	0.141054i
$339$	−0.0199728	+	0.190028i	−0.00108477	+	0.0103209i
$340$	7.02684	+	3.12855i	0.381084	+	0.169669i
$341$	13.1162	+	2.78794i	0.710285	+	0.150976i
$342$	−0.167258			−0.00904426
$343$	13.5233	−	12.6539i	0.730187	−	0.683247i
$344$	−1.17906	+	3.62879i	−0.0635709	+	0.195651i
$345$	0.681465	−	0.303408i	0.0366888	−	0.0163349i
$346$	16.0127	−	17.7839i	0.860848	−	0.956069i
$347$	−11.6484	+	2.47594i	−0.625317	+	0.132915i	−0.509663	−	0.860374i	$-0.670230\pi$
$347$	−11.6484	+	2.47594i	−0.625317	+	0.132915i	−0.115654	+	0.993290i	$0.536896\pi$
$348$	0.0470193	+	0.0522202i	0.00252050	+	0.00279930i
$349$	1.20722	−	3.71545i	0.0646211	−	0.198883i	−0.913533	−	0.406765i	$-0.866657\pi$
$349$	1.20722	−	3.71545i	0.0646211	−	0.198883i	0.978154	+	0.207882i	$0.0666569\pi$
$350$	2.82818	−	10.1062i	0.151172	−	0.540200i
$351$	−0.189198	−	0.582290i	−0.0100986	−	0.0310804i
$352$	4.42982	−	1.97228i	0.236110	−	0.105123i
$353$	−12.5183	+	2.66085i	−0.666282	+	0.141623i	−0.528622	−	0.848857i	$-0.677291\pi$
$353$	−12.5183	+	2.66085i	−0.666282	+	0.141623i	−0.137659	+	0.990480i	$0.543958\pi$
$354$	−0.179782	−	0.0800442i	−0.00955532	−	0.00425430i
$355$	20.1492	−	34.8995i	1.06941	−	1.85227i
$356$	−1.24900	−	3.84402i	−0.0661968	−	0.203733i
$357$	−0.0392143	−	0.266654i	−0.00207544	−	0.0141128i
$358$	−0.967519	−	0.702944i	−0.0511350	−	0.0371517i
$359$	24.9606	−	11.1132i	1.31737	−	0.586531i	0.376852	−	0.926273i	$-0.377006\pi$
$359$	24.9606	−	11.1132i	1.31737	−	0.586531i	0.940519	+	0.339742i	$0.110340\pi$
$360$	−4.48927	−	7.77565i	−0.236605	−	0.409813i
$361$	1.98572	−	18.8928i	0.104511	−	0.994359i
$362$	1.65731	+	1.84063i	0.0871063	+	0.0967414i
$363$	−0.153348	−	0.471957i	−0.00804870	−	0.0247713i
$364$	6.32985	+	2.51051i	0.331774	+	0.131587i
$365$	22.1379	−	16.0841i	1.15875	−	0.841883i
$366$	−0.0331572	+	0.0574300i	−0.00173316	+	0.00300192i
$367$	−15.5593	+	17.2804i	−0.812191	+	0.902029i	−0.996731	−	0.0807958i	$-0.974254\pi$
$367$	−15.5593	+	17.2804i	−0.812191	+	0.902029i	0.184540	+	0.982825i	$0.440921\pi$
$368$	3.14082	+	5.44006i	0.163727	+	0.283583i
$369$	−0.0256183	+	19.1993i	−0.00133364	+	0.999475i
$370$	−18.7714			−0.975876
$371$	−7.30679	+	8.82172i	−0.379350	+	0.458001i
$372$	−0.109667			−0.00568598
$373$	−3.15150	−	29.9845i	−0.163178	−	1.55254i	−0.703265	−	0.710928i	$-0.748275\pi$
$373$	−3.15150	−	29.9845i	−0.163178	−	1.55254i	0.540087	−	0.841609i	$-0.318391\pi$
$374$	11.3790	+	5.06625i	0.588393	+	0.261969i
$375$	0.0821191	−	0.0912025i	0.00424061	−	0.00470968i
$376$	1.75348	+	1.94744i	0.0904289	+	0.100431i
$377$	−3.68946	−	2.68055i	−0.190017	−	0.138055i
$378$	−0.291921	+	0.557587i	−0.0150148	+	0.0286792i
$379$	−9.67484	−	7.02919i	−0.496963	−	0.361065i	0.310893	−	0.950445i	$-0.399372\pi$
$379$	−9.67484	−	7.02919i	−0.496963	−	0.361065i	−0.807856	+	0.589380i	$0.799372\pi$
$380$	−0.152593	+	0.0679389i	−0.00782787	+	0.00348519i
$381$	0.322363	+	0.143525i	0.0165151	+	0.00735302i
$382$	−11.1578	+	12.3920i	−0.570881	+	0.634027i
$383$	−14.7479	+	25.5442i	−0.753585	+	1.30525i	0.192490	+	0.981299i	$0.438344\pi$
$383$	−14.7479	+	25.5442i	−0.753585	+	1.30525i	−0.946075	+	0.323948i	$0.894990\pi$
$384$	−0.0320838	+	0.0233102i	−0.00163727	+	0.00118954i
$385$	10.3529	−	36.9952i	0.527634	−	1.88545i
$386$	8.42720	+	6.12272i	0.428933	+	0.311638i
$387$	11.1906	+	2.37863i	0.568850	+	0.120913i
$388$	−13.3591	+	2.83956i	−0.678205	+	0.144157i
$389$	−38.3577	+	8.15318i	−1.94481	+	0.413383i	−0.949912	+	0.312518i	$0.898827\pi$
$389$	−38.3577	+	8.15318i	−1.94481	+	0.413383i	−0.994900	+	0.100864i	$0.967839\pi$
$390$	−0.204512	−	0.227134i	−0.0103559	−	0.0115014i
$391$	−4.98624	+	15.3461i	−0.252165	+	0.776083i
$392$	−2.70494	−	6.45626i	−0.136620	−	0.326090i
$393$	−0.417208	−	0.303120i	−0.0210454	−	0.0152904i
$394$	0.877154	+	0.974178i	0.0441904	+	0.0490784i
$395$	47.2746	+	21.0480i	2.37864	+	1.05904i
$396$	−7.26975	−	12.5916i	−0.365319	−	0.632751i
$397$	−22.8709	−	4.86136i	−1.14786	−	0.243985i	−0.405569	−	0.914065i	$-0.632926\pi$
$397$	−22.8709	−	4.86136i	−1.14786	−	0.243985i	−0.742289	+	0.670080i	$0.766260\pi$
$398$	20.8985	−	15.1837i	1.04755	−	0.761089i
$399$	0.00487306	+	0.00324183i	0.000243958	+	0.000162294i
$400$	−3.20900	−	2.33147i	−0.160450	−	0.116574i
$401$	−7.42672	+	12.8635i	−0.370873	+	0.642370i	−0.989700	−	0.143157i	$-0.954275\pi$
$401$	−7.42672	+	12.8635i	−0.370873	+	0.642370i	0.618827	+	0.785527i	$0.287608\pi$
$402$	0.0329956	−	0.313932i	0.00164567	−	0.0156575i
$403$	6.96180	−	1.47978i	0.346792	−	0.0737129i
$404$	−18.2360	−	3.87618i	−0.907274	−	0.192847i
$405$	−21.7685	+	15.8158i	−1.08169	+	0.785892i
$406$	0.682082	+	4.63810i	0.0338512	+	0.230185i
$407$	−30.3976			−1.50675
$408$	−0.0996436	−	0.0211799i	−0.00493309	−	0.00104856i
$409$	0.918416	+	1.59074i	0.0454128	+	0.0786572i	0.887838	−	0.460156i	$-0.152206\pi$
$409$	0.918416	+	1.59074i	0.0454128	+	0.0786572i	−0.842426	+	0.538813i	$0.818873\pi$
$410$	7.77524	+	17.5264i	0.383992	+	0.865566i
$411$	−0.132041	+	0.228702i	−0.00651310	+	0.0112810i
$412$	−1.18051	−	3.63322i	−0.0581593	−	0.178996i
$413$	−7.02839	−	11.0895i	−0.345844	−	0.545679i
$414$	15.2379	−	11.0710i	0.748901	−	0.544108i
$415$	−5.04372	−	47.9878i	−0.247587	−	2.35563i
$416$	1.72218	−	1.91268i	0.0844369	−	0.0937767i
$417$	0.595897	−	0.126662i	0.0291812	−	0.00620266i
$418$	−0.247103	+	0.110018i	−0.0120862	+	0.00538113i
$419$	18.8988			0.923265			0.461633	−	0.887071i	$-0.347264\pi$
$419$	18.8988			0.923265			0.461633	+	0.887071i	$0.347264\pi$
$420$	−0.0199142	+	0.313556i	−0.000971713	+	0.0153000i
$421$	18.1706	+	13.2017i	0.885583	+	0.643413i	0.934722	−	0.355378i	$-0.115648\pi$
$421$	18.1706	+	13.2017i	0.885583	+	0.643413i	−0.0491399	+	0.998792i	$0.515648\pi$
$422$	−1.47519	−	14.0355i	−0.0718110	−	0.683236i
$423$	5.25768	−	5.83925i	0.255637	−	0.283914i
$424$	2.16475	+	3.74946i	0.105130	+	0.182090i
$425$	−1.06503	−	10.1331i	−0.0516618	−	0.491529i
$426$	−0.164925	+	0.507587i	−0.00799064	+	0.0245927i
$427$	−3.96393	+	1.96478i	−0.191828	+	0.0950823i
$428$	−1.49010	−	4.58606i	−0.0720268	−	0.221676i
$429$	−0.331179	−	0.367811i	−0.0159895	−	0.0177581i
$430$	11.1756	−	2.37545i	0.538937	−	0.114555i
$431$	14.8926	−	3.16552i	0.717351	−	0.152478i	0.165246	−	0.986252i	$-0.447158\pi$
$431$	14.8926	−	3.16552i	0.717351	−	0.152478i	0.552105	+	0.833775i	$0.313825\pi$
$432$	0.159175	+	0.176782i	0.00765833	+	0.00850544i
$433$	−1.74823	−	5.38049i	−0.0840144	−	0.258570i	0.900221	−	0.435433i	$-0.143405\pi$
$433$	−1.74823	−	5.38049i	−0.0840144	−	0.258570i	−0.984235	+	0.176864i	$0.943405\pi$
$434$	−6.09159	−	4.05246i	−0.292406	−	0.194524i
$435$	0.0650220	−	0.200117i	0.00311757	−	0.00959488i
$436$	0.738464	+	7.02602i	0.0353660	+	0.336485i
$437$	−0.175201	−	0.303457i	−0.00838099	−	0.0145163i
$438$	−0.242496	+	0.269320i	−0.0115869	+	0.0128686i
$439$	−0.491250	−	4.67393i	−0.0234461	−	0.223075i	−0.999971	−	0.00766827i	$-0.997559\pi$
$439$	−0.491250	−	4.67393i	−0.0234461	−	0.223075i	0.976525	−	0.215406i	$-0.0691076\pi$
$440$	−11.7470	−	8.53468i	−0.560015	−	0.406875i
$441$	−18.4048	+	10.0897i	−0.876418	+	0.480461i
$442$	6.61128			0.314466
$443$	−15.5149	+	6.90769i	−0.737136	+	0.328194i	−0.740733	−	0.671799i	$-0.765522\pi$
$443$	−15.5149	+	6.90769i	−0.737136	+	0.328194i	0.00359715	+	0.999994i	$0.498855\pi$
$444$	0.243173	−	0.0516880i	0.0115405	−	0.00245300i
$445$	−8.09847	+	8.99426i	−0.383904	+	0.426369i
$446$	0.679250	+	6.46264i	0.0321634	+	0.306015i
$447$	−0.755953	+	0.549232i	−0.0357553	+	0.0259778i
$448$	−2.64350	+	0.109223i	−0.124893	+	0.00516030i
$449$	−11.8149	−	36.3625i	−0.557579	−	1.71605i	−0.689032	−	0.724731i	$-0.741964\pi$
$449$	−11.8149	−	36.3625i	−0.557579	−	1.71605i	0.131453	−	0.991322i	$-0.458036\pi$
$450$	−5.94669	+	10.3000i	−0.280330	+	0.485545i
$451$	12.5909	+	28.3815i	0.592883	+	1.33643i
$452$	2.40905	+	4.17260i	0.113312	+	0.196263i
$453$	−0.0232017	−	0.00493167i	−0.00109011	−	0.000231710i
$454$	−3.78796			−0.177778
$455$	−2.96674	−	20.1736i	−0.139083	−	0.945753i
$456$	0.00178969	−	0.00130029i	8.38100e−5	−	6.08915e-5i
$457$	−20.2734	−	4.30924i	−0.948348	−	0.201578i	−0.292325	−	0.956319i	$-0.594429\pi$
$457$	−20.2734	−	4.30924i	−0.948348	−	0.201578i	−0.656022	+	0.754741i	$0.727762\pi$
$458$	−4.06689	+	0.864444i	−0.190033	+	0.0403928i
$459$	−0.0638730	+	0.607711i	−0.00298133	+	0.0283655i
$460$	9.40493	−	16.2898i	0.438507	−	0.759517i
$461$	11.2258	+	8.15603i	0.522838	+	0.379864i	0.817672	−	0.575684i	$-0.195264\pi$
$461$	11.2258	+	8.15603i	0.522838	+	0.379864i	−0.294834	+	0.955549i	$0.595264\pi$
$462$	−0.0322483	+	0.507760i	−0.00150032	+	0.0236231i
$463$	5.36981	−	3.90140i	0.249556	−	0.181313i	−0.455974	−	0.889993i	$-0.650709\pi$
$463$	5.36981	−	3.90140i	0.249556	−	0.181313i	0.705530	+	0.708680i	$0.250709\pi$
$464$	1.73317	+	0.368397i	0.0804605	+	0.0171024i
$465$	0.164195	+	0.284394i	0.00761435	+	0.0131884i
$466$	−23.3383	−	10.3909i	−1.08112	−	0.481348i
$467$	21.0969	+	23.4305i	0.976248	+	1.08423i	0.996429	+	0.0844373i	$0.0269093\pi$
$467$	21.0969	+	23.4305i	0.976248	+	1.08423i	−0.0201805	+	0.999796i	$0.506424\pi$
$468$	−6.24337	−	4.53608i	−0.288600	−	0.209680i
$469$	13.4333	−	16.2184i	0.620291	−	0.748897i
$470$	2.42485	−	7.46292i	0.111850	−	0.344239i
$471$	0.0850839	+	0.0944952i	0.00392046	+	0.00435411i
$472$	−4.85393	+	1.03173i	−0.223420	+	0.0474894i
$473$	18.0974	−	3.84672i	0.832118	−	0.176872i
$474$	−0.670374	−	0.142492i	−0.0307913	−	0.00654489i
$475$	0.179004	+	0.130054i	0.00821326	+	0.00596728i
$476$	−4.75217	−	4.85852i	−0.217815	−	0.222690i
$477$	10.5024	−	7.63045i	0.480872	−	0.349374i
$478$	9.13504	−	15.8224i	0.417827	−	0.723697i
$479$	−8.46155	+	9.39750i	−0.386618	+	0.429383i	−0.904767	−	0.425908i	$-0.859955\pi$
$479$	−8.46155	+	9.39750i	−0.386618	+	0.429383i	0.518149	+	0.855291i	$0.326621\pi$
$480$	0.108485	+	0.0483007i	0.00495165	+	0.00220462i
$481$	−14.7395	+	6.56243i	−0.672061	+	0.299221i
$482$	−6.59071	−	4.78843i	−0.300199	−	0.218107i
$483$	−0.658536	+	0.0272091i	−0.0299644	+	0.00123806i
$484$	−10.1234	−	7.35508i	−0.460155	−	0.334322i
$485$	27.3650	+	30.3919i	1.24258	+	1.38003i
$486$	0.715977	−	0.795173i	0.0324774	−	0.0360698i
$487$	−8.40298	−	3.74125i	−0.380775	−	0.169532i	0.207418	−	0.978252i	$-0.433494\pi$
$487$	−8.40298	−	3.74125i	−0.380775	−	0.169532i	−0.588193	+	0.808720i	$0.700161\pi$
$488$	0.174789	+	1.66301i	0.00791235	+	0.0752810i
$489$	−0.281347			−0.0127230
$490$	−12.6928	+	16.6809i	−0.573401	+	0.753568i
$491$	−9.33166			−0.421132			−0.210566	−	0.977580i	$-0.567531\pi$
$491$	−9.33166			−0.421132			−0.210566	+	0.977580i	$0.567531\pi$
$492$	−0.148984	−	0.205635i	−0.00671672	−	0.00927076i
$493$	2.27575	+	3.94172i	0.102495	+	0.177526i
$494$	−0.0960664	+	0.106693i	−0.00432223	+	0.00480033i
$495$	−21.7687	+	37.7044i	−0.978429	+	1.69469i
$496$	−2.23721	+	1.62543i	−0.100454	+	0.0729839i
$497$	−27.9175	+	22.1001i	−1.25227	+	0.991326i
$498$	0.197476	+	0.607768i	0.00884911	+	0.0272347i
$499$	−5.16907	−	5.74083i	−0.231399	−	0.256995i	0.616252	−	0.787549i	$-0.288650\pi$
$499$	−5.16907	−	5.74083i	−0.231399	−	0.256995i	−0.847651	+	0.530554i	$0.821984\pi$
$500$	0.323474	−	3.07765i	0.0144662	−	0.137637i
$501$	0.443273	+	0.767772i	0.0198040	+	0.0343015i
$502$	2.40584	−	1.07115i	0.107378	−	0.0478077i
$503$	0.445409	+	0.323608i	0.0198598	+	0.0144290i	0.597671	−	0.801742i	$-0.296093\pi$
$503$	0.445409	+	0.323608i	0.0198598	+	0.0144290i	−0.577811	+	0.816171i	$0.696093\pi$
$504$	1.15423	+	7.84868i	0.0514135	+	0.349608i
$505$	17.2512	+	53.0938i	0.767669	+	2.36264i
$506$	15.2300	−	26.3791i	0.677055	−	1.17269i
$507$	0.230988	+	0.102843i	0.0102585	+	0.00456740i
$508$	8.70345	−	1.84998i	0.386153	−	0.0820794i
$509$	35.4347	−	15.7765i	1.57061	−	0.699283i	0.577496	−	0.816394i	$-0.304030\pi$
$509$	35.4347	−	15.7765i	1.57061	−	0.699283i	0.993119	+	0.117111i	$0.0373634\pi$
$510$	0.0942627	+	0.290111i	0.00417402	+	0.0128463i
$511$	−23.4217	+	5.99885i	−1.03612	+	0.265374i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−0.00887910	−	0.00986124i	−0.000392022	−	0.000435384i
$514$	−0.383890	+	0.0815983i	−0.0169327	+	0.00359915i
$515$	−7.65436	+	8.50103i	−0.337291	+	0.374600i
$516$	−0.138233	+	0.0615455i	−0.00608539	+	0.00270939i
$517$	3.92671	−	12.0852i	0.172696	−	0.531505i
$518$	15.4173	+	6.11474i	0.677398	+	0.268666i
$519$	0.949033			0.0416579
$520$	−7.53850	−	1.60236i	−0.330585	−	0.0702680i
$521$	19.6147	+	8.73304i	0.859337	+	0.382601i	0.788609	−	0.614894i	$-0.210801\pi$
$521$	19.6147	+	8.73304i	0.859337	+	0.382601i	0.0707271	+	0.997496i	$0.477468\pi$
$522$	0.555349	−	5.28379i	0.0243069	−	0.231265i
$523$	−20.1531	+	8.97274i	−0.881234	+	0.392351i	−0.796917	−	0.604088i	$-0.793537\pi$
$523$	−20.1531	+	8.97274i	−0.881234	+	0.392351i	−0.0843166	+	0.996439i	$0.526871\pi$
$524$	−13.0037			−0.568070
$525$	0.372894	−	0.184830i	0.0162744	−	0.00806665i
$526$	0.383483	−	1.18024i	0.0167207	−	0.0514609i
$527$	−6.94818	−	1.47688i	−0.302667	−	0.0643339i
$528$	0.175677	+	0.0782163i	0.00764534	+	0.00340393i
$529$	15.0361	+	6.69449i	0.653742	+	0.291065i
$530$	6.48217	−	11.2274i	0.281567	−	0.487689i
$531$	4.59795	+	14.1510i	0.199534	+	0.614103i
$532$	0.147459	−	0.00609266i	0.00639316	−	0.000264150i
$533$	12.2324	+	11.0437i	0.529843	+	0.478355i
$534$	0.0801452	−	0.138816i	0.00346822	−	0.00600714i
$535$	−9.66177	+	10.7305i	−0.417715	+	0.463919i
$536$	−3.97982	−	6.89325i	−0.171902	−	0.297743i
$537$	−0.00495752	−	0.0471676i	−0.000213933	−	0.00203543i
$538$	1.67777	−	1.21897i	0.0723337	−	0.0525535i
$539$	−20.5542	+	27.0125i	−0.885331	+	1.16351i
$540$	0.220120	−	0.677461i	0.00947247	−	0.0291533i
$541$	−37.7751	+	16.8186i	−1.62408	+	0.723086i	−0.998376	−	0.0569747i	$-0.981855\pi$
$541$	−37.7751	+	16.8186i	−1.62408	+	0.723086i	−0.625703	+	0.780061i	$0.715188\pi$
$542$	8.16089	+	14.1351i	0.350540	+	0.607153i
$543$	−0.0102673	+	0.0976866i	−0.000440611	+	0.00419213i
$544$	−2.34665	+	1.04479i	−0.100612	+	0.0447952i
$545$	17.1145	−	12.4344i	0.733106	−	0.532633i
$546$	0.0939817	+	0.253169i	0.00402205	+	0.0108346i
$547$	−40.7299			−1.74148			−0.870742	−	0.491741i	$-0.836361\pi$
$547$	−40.7299			−1.74148			−0.870742	+	0.491741i	$0.836361\pi$
$548$	0.696059	+	6.62255i	0.0297341	+	0.282902i
$549$	4.90432	−	1.04244i	0.209311	−	0.0444905i
$550$	−2.01049	+	19.1286i	−0.0857277	+	0.815645i
$551$	−0.0966796	−	0.0205499i	−0.00411869	−	0.000875454i
$552$	−0.0769810	+	0.236923i	−0.00327653	+	0.0100841i
$553$	−31.9713	−	32.6868i	−1.35956	−	1.38998i
$554$	6.05311	−	18.6296i	0.257172	−	0.791494i
$555$	−0.498120	−	0.553219i	−0.0211440	−	0.0234828i
$556$	10.2790	−	11.4160i	0.435926	−	0.484145i
$557$	−1.57304	+	14.9664i	−0.0666517	+	0.634149i	0.909297	+	0.416148i	$0.136620\pi$
$557$	−1.57304	+	14.9664i	−0.0666517	+	0.634149i	−0.975949	+	0.218001i	$0.930046\pi$
$558$	5.54822	+	6.16192i	0.234875	+	0.260855i
$559$	7.94476	−	5.77221i	0.336028	−	0.244138i
$560$	4.24111	+	6.69170i	0.179220	+	0.282776i
$561$	0.152645	+	0.469794i	0.00644469	+	0.0198347i
$562$	1.62399	+	15.4513i	0.0685040	+	0.651772i
$563$	0.999241	−	9.50714i	0.0421130	−	0.400678i	−0.953078	−	0.302725i	$-0.902104\pi$
$563$	0.999241	−	9.50714i	0.0421130	−	0.400678i	0.995191	−	0.0979535i	$-0.0312296\pi$
$564$	−0.0108631	+	0.103355i	−0.000457418	+	0.00435204i
$565$	7.21371	−	12.4945i	0.303483	−	0.525648i
$566$	3.71902	+	2.70203i	0.156322	+	0.113575i
$567$	23.0309	−	5.89876i	0.967207	−	0.247725i
$568$	4.15871	+	12.7992i	0.174496	+	0.537042i
$569$	1.13032	+	10.7543i	0.0473854	+	0.450842i	0.992330	+	0.123613i	$0.0394482\pi$
$569$	1.13032	+	10.7543i	0.0473854	+	0.450842i	−0.944945	+	0.327229i	$0.893885\pi$
$570$	−0.00605150	−	0.00269430i	−0.000253470	−	0.000112852i
$571$	13.3803	+	23.1753i	0.559946	+	0.969855i	0.997500	+	0.0706632i	$0.0225115\pi$
$571$	13.3803	+	23.1753i	0.559946	+	0.969855i	−0.437554	+	0.899192i	$0.644155\pi$
$572$	−12.2075	−	2.59479i	−0.510423	−	0.108494i
$573$	−0.661293			−0.0276259
$574$	−0.676782	−	16.9276i	−0.0282483	−	0.706542i
$575$	−24.9164			−1.03909
$576$	2.93290	+	0.623408i	0.122204	+	0.0259753i
$577$	−7.14409	−	12.3739i	−0.297412	−	0.515133i	0.678131	−	0.734941i	$-0.262790\pi$
$577$	−7.14409	−	12.3739i	−0.297412	−	0.515133i	−0.975543	+	0.219808i	$0.929457\pi$
$578$	9.50239	+	4.23074i	0.395247	+	0.175975i
$579$	0.0431806	+	0.410836i	0.00179452	+	0.0170737i
$580$	−1.63958	−	5.04611i	−0.0680798	−	0.209528i
$581$	−11.4894	+	41.0564i	−0.476662	+	1.70331i
$582$	−0.438185	−	0.318360i	−0.0181634	−	0.0131965i
$583$	10.4970	−	18.1813i	0.434740	−	0.752991i
$584$	−0.955215	+	9.08827i	−0.0395271	+	0.376075i
$585$	−2.41551	+	22.9820i	−0.0998690	+	0.950190i
$586$	0.754664	+	7.18015i	0.0311749	+	0.296609i
$587$	6.69512	+	20.6055i	0.276337	+	0.850479i	0.988862	+	0.148832i	$0.0475514\pi$
$587$	6.69512	+	20.6055i	0.276337	+	0.850479i	−0.712525	+	0.701646i	$0.752449\pi$
$588$	0.118496	−	0.251043i	0.00488670	−	0.0103528i
$589$	0.124796	−	0.0906694i	0.00514212	−	0.00373597i
$590$	9.94288	+	11.0427i	0.409342	+	0.454620i
$591$	−0.00543409	+	0.0517020i	−0.000223529	+	0.00212673i
$592$	4.19463	−	4.65861i	0.172398	−	0.191468i
$593$	18.8192	+	20.9009i	0.772813	+	0.858296i	0.993116	−	0.117136i	$-0.0373712\pi$
$593$	18.8192	+	20.9009i	0.772813	+	0.858296i	−0.220303	+	0.975432i	$0.570705\pi$
$594$	0.356454	−	1.09705i	0.0146255	−	0.0450126i
$595$	−5.48434	+	19.5978i	−0.224836	+	0.803430i
$596$	−7.28101	+	22.4086i	−0.298242	+	0.917894i
$597$	1.00205	+	0.212993i	0.0410113	+	0.00871722i
$598$	1.68996	−	16.0789i	0.0691075	−	0.657514i
$599$	−22.2918	+	4.73828i	−0.910820	+	0.193601i	−0.639413	−	0.768864i	$-0.720822\pi$
$599$	−22.2918	+	4.73828i	−0.910820	+	0.193601i	−0.271407	+	0.962465i	$0.587489\pi$
$600$	−0.0164427	−	0.156442i	−0.000671272	−	0.00638673i
$601$	−37.9598			−1.54841			−0.774207	−	0.632933i	$-0.781851\pi$
$601$	−37.9598			−1.54841			−0.774207	+	0.632933i	$0.781851\pi$
$602$	−9.95258	−	1.68943i	−0.405637	−	0.0688561i
$603$	−19.3083	+	14.0283i	−0.786295	+	0.571277i
$604$	−0.546408	+	0.243277i	−0.0222330	+	0.00989878i
$605$	−3.91666	+	37.2645i	−0.159235	+	1.51502i
$606$	−0.369677	−	0.640300i	−0.0150171	−	0.0260104i
$607$	−9.79221	+	4.35977i	−0.397454	+	0.176958i	−0.595723	−	0.803190i	$-0.703135\pi$
$607$	−9.79221	+	4.35977i	−0.397454	+	0.176958i	0.198270	+	0.980148i	$0.436468\pi$
$608$	0.0172375	−	0.0530517i	0.000699074	−	0.00215153i
$609$	−0.118592	+	0.143180i	−0.00480558	+	0.00580193i
$610$	4.05089	−	2.94315i	0.164016	−	0.119165i
$611$	−0.705006	−	6.70768i	−0.0285215	−	0.271364i
$612$	3.85106	+	6.67024i	0.155670	+	0.269628i
$613$	−2.12955	+	2.36510i	−0.0860115	+	0.0955255i	−0.784614	−	0.619984i	$-0.787139\pi$
$613$	−2.12955	+	2.36510i	−0.0860115	+	0.0955255i	0.698603	+	0.715510i	$0.253806\pi$
$614$	−15.8380	+	27.4322i	−0.639169	+	1.10707i
$615$	−0.310202	+	0.694231i	−0.0125086	+	0.0279941i
$616$	6.86788	+	10.8363i	0.276715	+	0.436606i
$617$	−10.9779	−	33.7864i	−0.441953	−	1.36019i	−0.885791	−	0.464084i	$-0.846384\pi$
$617$	−10.9779	−	33.7864i	−0.441953	−	1.36019i	0.443839	−	0.896107i	$-0.353616\pi$
$618$	0.0757501	−	0.131203i	0.00304712	−	0.00527776i
$619$	−26.2950	−	11.7073i	−1.05689	−	0.470556i	−0.196662	−	0.980471i	$-0.563010\pi$
$619$	−26.2950	−	11.7073i	−1.05689	−	0.470556i	−0.860225	+	0.509915i	$0.829677\pi$
$620$	7.56470	+	3.36802i	0.303806	+	0.135263i
$621$	1.46165	+	0.310683i	0.0586539	+	0.0124673i
$622$	7.78495	−	23.9596i	0.312148	−	0.960693i
$623$	9.58131	−	4.74911i	0.383867	−	0.190269i
$624$	0.102069			0.00408605
$625$	−26.5835	+	11.8357i	−1.06334	+	0.473429i
$626$	1.60528	−	15.2733i	0.0641600	−	0.610442i
$627$	−0.00979956	−	0.00436305i	−0.000391357	−	0.000174243i
$628$	3.13627	+	0.666634i	0.125151	+	0.0266016i
$629$	16.1028			0.642059
$630$	18.6254	−	14.7443i	0.742054	−	0.587427i
$631$	−6.63594	+	20.4233i	−0.264173	+	0.813040i	0.727710	+	0.685885i	$0.240585\pi$
$631$	−6.63594	+	20.4233i	−0.264173	+	0.813040i	−0.991883	+	0.127155i	$0.959415\pi$
$632$	−15.7876	+	7.02908i	−0.627996	+	0.279602i
$633$	0.374500	−	0.415924i	0.0148850	−	0.0165315i
$634$	22.1194	−	4.70162i	0.878472	−	0.186725i
$635$	−17.8283	−	19.8004i	−0.707495	−	0.785753i
$636$	−0.0530576	+	0.163295i	−0.00210387	+	0.00647505i
$637$	−4.13487	+	17.5354i	−0.163829	+	0.694778i
$638$	−2.65507	−	8.17146i	−0.105115	−	0.323511i
$639$	36.8638	−	16.4128i	1.45831	−	0.649281i
$640$	2.92898	−	0.622575i	0.115778	−	0.0246094i
$641$	−38.2406	−	17.0258i	−1.51041	−	0.672479i	−0.526344	−	0.850272i	$-0.676438\pi$
$641$	−38.2406	−	17.0258i	−1.51041	−	0.672479i	−0.984068	+	0.177793i	$0.943104\pi$
$642$	0.0956161	−	0.165612i	0.00377367	−	0.00653618i
$643$	−9.24038	−	28.4390i	−0.364405	−	1.12152i	−0.950353	−	0.311175i	$-0.899278\pi$
$643$	−9.24038	−	28.4390i	−0.364405	−	1.12152i	0.585948	−	0.810349i	$-0.300722\pi$
$644$	−13.0308	+	10.3155i	−0.513487	+	0.406489i
$645$	0.366567	+	0.266326i	0.0144336	+	0.0104866i
$646$	0.130900	−	0.0582805i	0.00515020	−	0.00229302i
$647$	−11.3312	−	19.6263i	−0.445477	−	0.771589i	0.552608	−	0.833441i	$-0.313633\pi$
$647$	−11.3312	−	19.6263i	−0.445477	−	0.771589i	−0.998085	+	0.0618520i	$0.980299\pi$
$648$	0.939277	−	8.93662i	0.0368983	−	0.351064i
$649$	16.1011	+	17.8821i	0.632024	+	0.701933i
$650$	3.15473	+	9.70927i	0.123739	+	0.380829i
$651$	−0.0422159	−	0.287065i	−0.00165457	−	0.0112510i
$652$	−5.73948	+	4.16997i	−0.224775	+	0.163309i
$653$	18.2954	−	31.6885i	0.715953	−	1.24007i	−0.246638	−	0.969108i	$-0.579326\pi$
$653$	18.2954	−	31.6885i	0.715953	−	1.24007i	0.962591	−	0.270959i	$-0.0873409\pi$
$654$	−0.187471	+	0.208207i	−0.00733069	+	0.00814155i
$655$	19.4693	+	33.7218i	0.760728	+	1.31762i
$656$	−6.08709	−	1.98680i	−0.237661	−	0.0775714i
$657$	27.4006			1.06900
$658$	−4.42261	+	5.33956i	−0.172411	+	0.208158i
$659$	−29.8721			−1.16365			−0.581825	−	0.813314i	$-0.697661\pi$
$659$	−29.8721			−1.16365			−0.581825	+	0.813314i	$0.697661\pi$
$660$	−0.0601909	−	0.572678i	−0.00234293	−	0.0222915i
$661$	−29.3651	−	13.0742i	−1.14217	−	0.508526i	−0.253618	−	0.967304i	$-0.581621\pi$
$661$	−29.3651	−	13.0742i	−1.14217	−	0.508526i	−0.888551	+	0.458778i	$0.848287\pi$
$662$	−17.8999	+	19.8799i	−0.695701	+	0.772654i
$663$	0.175438	+	0.194844i	0.00681345	+	0.00756711i
$664$	13.0365	+	9.47158i	0.505915	+	0.367569i
$665$	−0.236577	−	0.373275i	−0.00917405	−	0.0144750i
$666$	−15.2067	−	11.0483i	−0.589247	−	0.428113i
$667$	10.1681	−	4.52714i	0.393711	−	0.175292i
$668$	20.4223	+	9.09258i	0.790162	+	0.351803i
$669$	−0.172438	+	0.191512i	−0.00666685	+	0.00740429i
$670$	−11.9172	+	20.6413i	−0.460403	+	0.797442i
$671$	6.55986	−	4.76601i	0.253240	−	0.183990i
$672$	−0.0733673	−	0.0750092i	−0.00283020	−	0.00289354i
$673$	−0.298357	−	0.216769i	−0.0115008	−	0.00835584i	0.582020	−	0.813174i	$-0.302263\pi$
$673$	−0.298357	−	0.216769i	−0.0115008	−	0.00835584i	−0.593521	+	0.804819i	$0.702263\pi$
$674$	2.32802	+	0.494836i	0.0896720	+	0.0190604i
$675$	−0.922957	+	0.196181i	−0.0355246	+	0.00755100i
$676$	6.23643	−	1.32559i	0.239863	−	0.0509844i
$677$	24.5009	+	27.2110i	0.941647	+	1.04580i	0.998874	+	0.0474435i	$0.0151074\pi$
$677$	24.5009	+	27.2110i	0.941647	+	1.04580i	−0.0572272	+	0.998361i	$0.518226\pi$
$678$	−0.0590455	+	0.181723i	−0.00226763	+	0.00697904i
$679$	−12.5753	−	33.8756i	−0.482597	−	1.30003i
$680$	6.22282	+	4.52115i	0.238634	+	0.173378i
$681$	−0.100518	−	0.111637i	−0.00385186	−	0.00427793i
$682$	12.2500	+	5.45404i	0.469076	+	0.208846i
$683$	−10.2032	−	17.6724i	−0.390414	−	0.676216i	0.602090	−	0.798428i	$-0.294335\pi$
$683$	−10.2032	−	17.6724i	−0.390414	−	0.676216i	−0.992504	+	0.122212i	$0.961001\pi$
$684$	−0.163603	−	0.0347748i	−0.00625551	−	0.00132965i
$685$	16.1317	−	11.7204i	0.616362	−	0.447813i
$686$	15.8586	−	9.56576i	0.605485	−	0.365222i
$687$	−0.133396	−	0.0969180i	−0.00508938	−	0.00369765i
$688$	−1.90777	+	3.30435i	−0.0727329	+	0.125977i
$689$	1.16477	−	11.0820i	0.0443742	−	0.422192i
$690$	0.729655	−	0.155093i	0.0277775	−	0.00590429i
$691$	−18.8729	−	4.01155i	−0.717958	−	0.152607i	−0.165575	−	0.986197i	$-0.552948\pi$
$691$	−18.8729	−	4.01155i	−0.717958	−	0.152607i	−0.552383	+	0.833591i	$0.686281\pi$
$692$	19.3603	−	14.0661i	0.735967	−	0.534711i
$693$	30.1612	−	23.8763i	1.14573	−	0.906987i
$694$	−11.9086			−0.452044
$695$	−44.9941	−	9.56380i	−1.70672	−	0.362776i
$696$	0.0351346	+	0.0608550i	0.00133177	+	0.00230670i
$697$	−6.66989	−	15.0348i	−0.252640	−	0.569483i
$698$	1.95333	−	3.38326i	0.0739344	−	0.128058i
$699$	−0.313075	−	0.963547i	−0.0118416	−	0.0364447i
$700$	4.86757	−	9.29736i	0.183977	−	0.351407i
$701$	−17.4623	+	12.6871i	−0.659540	+	0.479184i	−0.866508	−	0.499164i	$-0.833641\pi$
$701$	−17.4623	+	12.6871i	−0.659540	+	0.479184i	0.206967	+	0.978348i	$0.433641\pi$
$702$	−0.0639982	−	0.608902i	−0.00241546	−	0.0229815i
$703$	−0.233984	+	0.259866i	−0.00882489	+	0.00980103i
$704$	4.74308	−	1.00817i	0.178762	−	0.0379969i
$705$	0.284289	−	0.126574i	0.0107070	−	0.00476704i
$706$	−12.7980			−0.481658
$707$	3.12642	−	49.2266i	0.117581	−	1.85136i
$708$	−0.159211	−	0.115674i	−0.00598353	−	0.00434729i
$709$	1.53593	+	14.6134i	0.0576832	+	0.548819i	0.984756	+	0.173939i	$0.0556495\pi$
$709$	1.53593	+	14.6134i	0.0576832	+	0.548819i	−0.927073	+	0.374880i	$0.877684\pi$
$710$	26.9650	−	29.9476i	1.01198	−	1.12391i
$711$	25.9089	+	44.8755i	0.971659	+	1.68296i
$712$	−0.422488	−	4.01970i	−0.0158334	−	0.150645i
$713$	−5.36790	+	16.5207i	−0.201030	+	0.618705i
$714$	0.0170831	−	0.268980i	0.000639320	−	0.0100663i
$715$	11.5483	+	35.5421i	0.431883	+	1.32920i
$716$	−0.800226	−	0.888741i	−0.0299059	−	0.0332138i
$717$	0.708716	−	0.150642i	0.0264675	−	0.00562584i
$718$	26.7257	−	5.68073i	0.997395	−	0.212003i
$719$	−0.443525	−	0.492585i	−0.0165407	−	0.0183703i	0.734818	−	0.678265i	$-0.237268\pi$
$719$	−0.443525	−	0.492585i	−0.0165407	−	0.0183703i	−0.751358	+	0.659894i	$0.770601\pi$
$720$	−2.77452	−	8.53910i	−0.103400	−	0.318234i
$721$	9.05588	−	4.48868i	0.337259	−	0.167167i
$722$	5.87036	−	18.0671i	0.218472	−	0.672388i
$723$	−0.0337704	−	0.321304i	−0.00125594	−	0.0119494i
$724$	1.23841	+	2.14498i	0.0460250	+	0.0797176i
$725$	−4.70284	+	5.22304i	−0.174659	+	0.193979i
$726$	−0.0518718	−	0.493527i	−0.00192514	−	0.0183165i
$727$	−18.5554	−	13.4813i	−0.688183	−	0.499994i	0.187879	−	0.982192i	$-0.439839\pi$
$727$	−18.5554	−	13.4813i	−0.688183	−	0.499994i	−0.876062	+	0.482198i	$0.839839\pi$
$728$	5.66956	+	3.77170i	0.210128	+	0.139789i
$729$	−26.9151			−0.996856
$730$	24.9982	−	11.1299i	0.925226	−	0.411937i
$731$	−9.58687	+	2.03775i	−0.354583	+	0.0753690i
$732$	−0.0443731	+	0.0492813i	−0.00164008	+	0.00182149i
$733$	−1.23356	−	11.7366i	−0.0455627	−	0.433500i	−0.993396	−	0.114734i	$-0.963398\pi$
$733$	−1.23356	−	11.7366i	−0.0455627	−	0.433500i	0.947834	−	0.318766i	$-0.103268\pi$
$734$	−18.8121	+	13.6678i	−0.694368	+	0.504488i
$735$	−0.828429	+	0.0685745i	−0.0305571	+	0.00252941i
$736$	1.94113	+	5.97420i	0.0715512	+	0.220212i
$737$	−19.2983	+	33.4256i	−0.710862	+	1.23125i
$738$	−4.01681	+	18.7744i	−0.147861	+	0.691096i
$739$	5.34346	+	9.25514i	0.196562	+	0.340456i	0.947412	−	0.320018i	$-0.103689\pi$
$739$	5.34346	+	9.25514i	0.196562	+	0.340456i	−0.750849	+	0.660474i	$0.770356\pi$
$740$	−18.3612	−	3.90278i	−0.674970	−	0.143469i
$741$	−0.00569362			−0.000209160
$742$	−8.98126	+	7.10978i	−0.329712	+	0.261008i
$743$	25.6238	−	18.6168i	0.940046	−	0.682984i	−0.00838556	−	0.999965i	$-0.502669\pi$
$743$	25.6238	−	18.6168i	0.940046	−	0.682984i	0.948432	+	0.316981i	$0.102669\pi$
$744$	−0.107271	−	0.0228011i	−0.00393274	−	0.000835929i
$745$	69.0122	−	14.6690i	2.52841	−	0.537431i
$746$	3.15150	−	29.9845i	0.115384	−	1.09781i
$747$	24.1584	−	41.8435i	0.883908	−	1.53097i
$748$	10.0770	+	7.32136i	0.368451	+	0.267696i
$749$	11.4309	−	5.66587i	0.417674	−	0.207026i
$750$	0.0992866	−	0.0721360i	0.00362544	−	0.00263403i
$751$	−20.7500	−	4.41054i	−0.757177	−	0.160943i	−0.186882	−	0.982382i	$-0.559838\pi$
$751$	−20.7500	−	4.41054i	−0.757177	−	0.160943i	−0.570296	+	0.821439i	$0.693171\pi$
$752$	1.31027	+	2.26945i	0.0477806	+	0.0827584i
$753$	0.0954101	+	0.0424793i	0.00347694	+	0.00154803i
$754$	−3.05152	−	3.38906i	−0.111130	−	0.123422i
$755$	1.44896	+	1.05273i	0.0527331	+	0.0383129i
$756$	−0.401471	+	0.484709i	−0.0146014	+	0.0176287i
$757$	−3.57767	+	11.0109i	−0.130033	+	0.400200i	−0.994784	−	0.102000i	$-0.967476\pi$
$757$	−3.57767	+	11.0109i	−0.130033	+	0.400200i	0.864752	+	0.502200i	$0.167476\pi$
$758$	−8.00198	−	8.88709i	−0.290645	−	0.322794i
$759$	1.18158	−	0.251152i	0.0428885	−	0.00911622i
$760$	−0.163384	+	0.0347283i	−0.00592656	+	0.00125973i
$761$	−1.70986	−	0.363442i	−0.0619824	−	0.0131748i	0.176816	−	0.984244i	$-0.443420\pi$
$761$	−1.70986	−	0.363442i	−0.0619824	−	0.0131748i	−0.238799	+	0.971069i	$0.576754\pi$
$762$	0.285478	+	0.207412i	0.0103418	+	0.00751374i
$763$	−18.1070	+	4.63763i	−0.655518	+	0.167894i
$764$	−13.4904	+	9.80133i	−0.488064	+	0.354600i
$765$	11.5317	−	19.9735i	0.416929	−	0.722143i
$766$	−19.7366	+	21.9197i	−0.713112	+	0.791992i
$767$	11.6677	+	5.19482i	0.421298	+	0.187574i
$768$	−0.0362291	+	0.0161302i	−0.00130731	+	0.000582050i
$769$	−33.2322	−	24.1446i	−1.19838	−	0.870677i	−0.204260	−	0.978917i	$-0.565479\pi$
$769$	−33.2322	−	24.1446i	−1.19838	−	0.870677i	−0.994125	+	0.108239i	$0.965479\pi$
$770$	17.8184	−	34.0342i	0.642131	−	1.22651i
$771$	−0.0125918	−	0.00914848i	−0.000453482	−	0.000329474i
$772$	6.97006	+	7.74104i	0.250858	+	0.278606i
$773$	−8.19048	+	9.09644i	−0.294591	+	0.327176i	−0.872211	−	0.489129i	$-0.837315\pi$
$773$	−8.19048	+	9.09644i	−0.294591	+	0.327176i	0.577620	+	0.816305i	$0.303981\pi$
$774$	10.4515	+	4.65331i	0.375672	+	0.167260i
$775$	−1.14656	−	10.9088i	−0.0411856	−	0.391854i
$776$	−13.6575			−0.490277
$777$	0.228907	+	0.616632i	0.00821198	+	0.0221216i
$778$	−39.2146			−1.40591
$779$	0.339549	+	0.110827i	0.0121656	+	0.00397080i
$780$	−0.152819	−	0.264691i	−0.00547181	−	0.00947745i
$781$	43.6660	−	48.4960i	1.56249	−	1.73532i
$782$	−8.06790	+	13.9740i	−0.288507	+	0.499710i
$783$	0.341005	−	0.247754i	0.0121865	−	0.00885402i
$784$	−1.30350	−	6.87756i	−0.0465537	−	0.245627i
$785$	−2.96690	−	9.13119i	−0.105893	−	0.325906i
$786$	−0.345069	−	0.383238i	−0.0123082	−	0.0136697i
$787$	−1.82222	+	17.3372i	−0.0649550	+	0.618006i	0.912822	+	0.408358i	$0.133898\pi$
$787$	−1.82222	+	17.3372i	−0.0649550	+	0.618006i	−0.977777	+	0.209648i	$0.932768\pi$
$788$	0.655443	+	1.13526i	0.0233492	+	0.0404420i
$789$	0.0449595	−	0.0200173i	0.00160060	−	0.000712634i
$790$	41.8654	+	30.4170i	1.48950	+	1.08219i
$791$	−9.99484	+	7.91215i	−0.355376	+	0.281324i
$792$	−4.49295	−	13.8279i	−0.159650	−	0.491353i
$793$	2.15188	−	3.72717i	0.0764156	−	0.132356i
$794$	−21.3604	−	9.51026i	−0.758052	−	0.337506i
$795$	0.502901	−	0.106895i	0.0178361	−	0.00379117i
$796$	23.5987	−	10.5068i	0.836434	−	0.372405i
$797$	10.2971	+	31.6912i	0.364742	+	1.12256i	0.950143	+	0.311816i	$0.100937\pi$
$797$	10.2971	+	31.6912i	0.364742	+	1.12256i	−0.585401	+	0.810744i	$0.699063\pi$
$798$	0.00409256	+	0.00418415i	0.000144875	+	0.000148117i
$799$	−2.08013	+	6.40197i	−0.0735896	+	0.226485i
$800$	−2.65413	−	2.94771i	−0.0938378	−	0.104217i
$801$	−11.8543	+	2.51972i	−0.418853	+	0.0890299i
$802$	−9.93889	+	11.0383i	−0.350954	+	0.389774i
$803$	40.4812	−	18.0234i	1.42855	−	0.636031i
$804$	0.0975446	−	0.300211i	0.00344013	−	0.0105876i
$805$	46.2606	+	18.3476i	1.63047	+	0.646669i
$806$	7.11733			0.250697
$807$	0.0804463	+	0.0170994i	0.00283184	+	0.000601927i
$808$	−17.0316	−	7.58295i	−0.599169	−	0.266767i
$809$	2.21316	−	21.0568i	0.0778106	−	0.740319i	−0.884163	−	0.467178i	$-0.845271\pi$
$809$	2.21316	−	21.0568i	0.0778106	−	0.740319i	0.961974	−	0.273141i	$-0.0880625\pi$
$810$	−24.5811	+	10.9442i	−0.863693	+	0.384541i
$811$	45.2396			1.58858			0.794289	−	0.607540i	$-0.207843\pi$
$811$	45.2396			1.58858			0.794289	+	0.607540i	$0.207843\pi$
$812$	−0.297139	+	4.67856i	−0.0104275	+	0.164185i
$813$	−0.200022	+	0.615604i	−0.00701507	+	0.0215902i
$814$	−29.7333	−	6.32001i	−1.04215	−	0.221516i
$815$	19.4070	+	8.64053i	0.679796	+	0.302665i
$816$	−0.0930626	−	0.0414341i	−0.00325784	−	0.00145049i
$817$	0.106419	−	0.184323i	0.00372312	−	0.00644863i
$818$	0.567612	+	1.74693i	0.0198461	+	0.0610800i
$819$	9.47026	−	18.0888i	0.330918	−	0.632073i
$820$	3.96139	+	18.7599i	0.138338	+	0.655126i
$821$	−12.5412	+	21.7219i	−0.437690	+	0.758101i	−0.997511	−	0.0705126i	$-0.977536\pi$
$821$	−12.5412	+	21.7219i	−0.437690	+	0.758101i	0.559821	+	0.828613i	$0.310870\pi$
$822$	−0.176705	+	0.196251i	−0.00616331	+	0.00684505i
$823$	20.8950	+	36.1912i	0.728353	+	1.26154i	0.957579	+	0.288171i	$0.0930472\pi$
$823$	20.8950	+	36.1912i	0.728353	+	1.26154i	−0.229226	+	0.973373i	$0.573620\pi$
$824$	−0.399319	−	3.79927i	−0.0139109	−	0.132354i
$825$	−0.617097	+	0.448347i	−0.0214846	+	0.0156094i
$826$	−4.56916	−	12.3085i	−0.158981	−	0.428266i
$827$	−10.1700	+	31.3000i	−0.353646	+	1.08841i	0.603145	+	0.797631i	$0.293914\pi$
$827$	−10.1700	+	31.3000i	−0.353646	+	1.08841i	−0.956791	+	0.290778i	$0.906086\pi$
$828$	17.2067	−	7.66090i	0.597973	−	0.266235i
$829$	−26.8089	−	46.4343i	−0.931111	−	1.61273i	−0.781426	−	0.623998i	$-0.785507\pi$
$829$	−26.8089	−	46.4343i	−0.931111	−	1.61273i	−0.149685	−	0.988734i	$-0.547826\pi$
$830$	5.04372	−	47.9878i	0.175070	−	1.66568i
$831$	0.709667	−	0.315964i	0.0246181	−	0.0109607i
$832$	2.08222	−	1.51282i	0.0721878	−	0.0524475i
$833$	10.8883	−	14.3095i	0.377258	−	0.495796i
$834$	0.609210			0.0210952
$835$	−6.99715	−	66.5734i	−0.242146	−	2.30387i
$836$	−0.264578	+	0.0562377i	−0.00915061	+	0.00194502i
$837$	−0.0687621	+	0.654227i	−0.00237676	+	0.0226134i
$838$	18.4858	+	3.92927i	0.638581	+	0.135735i
$839$	7.23293	−	22.2607i	0.249709	−	0.768524i	−0.745118	−	0.666933i	$-0.767607\pi$
$839$	7.23293	−	22.2607i	0.249709	−	0.768524i	0.994826	−	0.101591i	$-0.0323933\pi$
$840$	−0.0846710	+	0.302564i	−0.00292143	+	0.0104394i
$841$	−7.99130	+	24.5947i	−0.275562	+	0.848093i
$842$	15.0288	+	16.6911i	0.517926	+	0.575215i
$843$	−0.412276	+	0.457879i	−0.0141996	+	0.0157702i
$844$	1.47519	−	14.0355i	0.0507780	−	0.483121i
$845$	−12.7748	−	14.1879i	−0.439468	−	0.488078i
$846$	6.35684	−	4.61851i	0.218553	−	0.158788i
$847$	15.3557	−	29.3303i	0.527628	−	1.00780i
$848$	1.33789	+	4.11760i	0.0459433	+	0.141399i
$849$	0.0190561	+	0.181306i	0.000654002	+	0.00622242i
$850$	1.06503	−	10.1331i	0.0365304	−	0.347564i
$851$	4.11615	−	39.1625i	0.141100	−	1.34247i
$852$	−0.266854	+	0.462205i	−0.00914227	+	0.0158349i
$853$	33.0927	+	24.0432i	1.13307	+	0.823225i	0.986139	−	0.165922i	$-0.0530600\pi$
$853$	33.0927	+	24.0432i	1.13307	+	0.823225i	0.146932	+	0.989147i	$0.453060\pi$
$854$	−4.28581	+	1.09770i	−0.146657	+	0.0375624i
$855$	0.154768	+	0.476327i	0.00529295	+	0.0162900i
$856$	−0.504043	−	4.79565i	−0.0172278	−	0.163912i
$857$	37.0403	+	16.4914i	1.26527	+	0.563336i	0.926061	−	0.377374i	$-0.123173\pi$
$857$	37.0403	+	16.4914i	1.26527	+	0.563336i	0.339212	+	0.940710i	$0.389840\pi$
$858$	−0.247470	−	0.428630i	−0.00844847	−	0.0146332i
$859$	16.2052	+	3.44452i	0.552914	+	0.117525i	0.475892	−	0.879504i	$-0.342125\pi$
$859$	16.2052	+	3.44452i	0.552914	+	0.117525i	0.0770223	+	0.997029i	$0.475459\pi$
$860$	11.4253			0.389600
$861$	0.480920	−	0.469139i	0.0163897	−	0.0159882i
$862$	15.2253			0.518576
$863$	−11.2549	−	2.39229i	−0.383120	−	0.0814346i	0.0123259	−	0.999924i	$-0.496076\pi$
$863$	−11.2549	−	2.39229i	−0.383120	−	0.0814346i	−0.395445	+	0.918489i	$0.629410\pi$
$864$	0.118942	+	0.206014i	0.00404649	+	0.00700872i
$865$	−65.4631	−	29.1460i	−2.22581	−	0.990995i
$866$	−0.591357	−	5.62639i	−0.0200951	−	0.191192i
$867$	0.127471	+	0.392317i	0.00432916	+	0.0133238i
$868$	−5.11592	−	5.23042i	−0.173646	−	0.177532i
$869$	67.7952	+	49.2561i	2.29979	+	1.67090i
$870$	0.105208	−	0.182225i	0.00356688	−	0.00617801i
$871$	−2.14139	+	20.3740i	−0.0725582	+	0.690345i
$872$	−0.738464	+	7.02602i	−0.0250076	+	0.237931i
$873$	4.28056	+	40.7268i	0.144875	+	1.37839i
$874$	−0.108280	−	0.333252i	−0.00366263	−	0.0112724i
$875$	8.18058	−	0.338002i	0.276554	−	0.0114266i
$876$	−0.293192	+	0.213016i	−0.00990604	+	0.00719716i
$877$	5.90497	+	6.55813i	0.199397	+	0.221452i	0.834548	−	0.550935i	$-0.185729\pi$
$877$	5.90497	+	6.55813i	0.199397	+	0.221452i	−0.635151	+	0.772388i	$0.719062\pi$
$878$	0.491250	−	4.67393i	0.0165789	−	0.157738i
$879$	−0.191583	+	0.212775i	−0.00646195	+	0.00717672i
$880$	−9.71582	−	10.7905i	−0.327520	−	0.363748i
$881$	16.6484	−	51.2384i	0.560898	−	1.72627i	−0.118937	−	0.992902i	$-0.537949\pi$
$881$	16.6484	−	51.2384i	0.560898	−	1.72627i	0.679835	−	0.733365i	$-0.262051\pi$
$882$	−20.1004	+	6.04262i	−0.676814	+	0.203466i
$883$	−3.64115	+	11.2063i	−0.122534	+	0.377122i	−0.993444	−	0.114321i	$-0.963531\pi$
$883$	−3.64115	+	11.2063i	−0.122534	+	0.377122i	0.870909	+	0.491444i	$0.163531\pi$
$884$	6.46680	+	1.37456i	0.217502	+	0.0462315i
$885$	−0.0615976	+	0.586062i	−0.00207058	+	0.0197002i
$886$	−16.6121	+	3.53100i	−0.558093	+	0.118626i
$887$	3.94699	+	37.5531i	0.132527	+	1.26091i	0.835420	+	0.549613i	$0.185225\pi$
$887$	3.94699	+	37.5531i	0.132527	+	1.26091i	−0.702893	+	0.711296i	$0.748109\pi$
$888$	0.248606			0.00834266
$889$	8.19284	+	22.0700i	0.274779	+	0.740204i
$890$	−9.79151	+	7.11395i	−0.328212	+	0.238460i
$891$	−39.8057	+	17.7226i	−1.33354	+	0.593731i
$892$	−0.679250	+	6.46264i	−0.0227430	+	0.216385i
$893$	−0.0730891	−	0.126594i	−0.00244584	−	0.00423631i
$894$	−0.853625	+	0.380058i	−0.0285495	+	0.0127111i
$895$	−1.10662	+	3.40581i	−0.0369901	+	0.113844i
$896$	−2.60844	−	0.442778i	−0.0871418	−	0.0147922i
$897$	0.518712	−	0.376867i	0.0173193	−	0.0125832i
$898$	−3.99652	−	38.0244i	−0.133366	−	1.26889i
$899$	2.44995	+	4.24343i	0.0817103	+	0.141526i
$900$	−7.95823	+	8.83851i	−0.265274	+	0.294617i
$901$	−5.56064	+	9.63131i	−0.185252	+	0.320866i
$902$	6.41492	+	30.3791i	0.213594	+	1.01151i
$903$	−0.214314	−	0.338148i	−0.00713191	−	0.0112529i
$904$	1.48888	+	4.58229i	0.0495193	+	0.152405i
$905$	3.70831	−	6.42297i	0.123268	−	0.213507i
$906$	−0.0216693	−	0.00964780i	−0.000719914	−	0.000320527i
$907$	38.9499	+	17.3416i	1.29331	+	0.575819i	0.933958	−	0.357383i	$-0.116331\pi$
$907$	38.9499	+	17.3416i	1.29331	+	0.575819i	0.359352	+	0.933202i	$0.382998\pi$
$908$	−3.70519	−	0.787562i	−0.122961	−	0.0261362i
$909$	−17.2743	+	53.1649i	−0.572953	+	1.76337i
$910$	1.29242	−	20.3496i	0.0428433	−	0.674582i
$911$	−40.8909			−1.35477			−0.677387	−	0.735626i	$-0.736888\pi$
$911$	−40.8909			−1.35477			−0.677387	+	0.735626i	$0.736888\pi$
$912$	0.00202093		0.000899775i	6.69196e−5		2.97945e-5i
$913$	8.16760	−	77.7095i	0.270308	−	2.57181i
$914$	−18.9344	−	8.43014i	−0.626294	−	0.278844i
$915$	0.194234	+	0.0412857i	0.00642118	+	0.00136486i
$916$	−4.15775			−0.137376
$917$	−5.00572	−	34.0385i	−0.165303	−	1.12405i
$918$	−0.188827	+	0.581151i	−0.00623223	+	0.0191808i
$919$	17.3469	−	7.72334i	0.572222	−	0.254769i	−0.100163	−	0.994971i	$-0.531937\pi$
$919$	17.3469	−	7.72334i	0.572222	−	0.254769i	0.672385	+	0.740202i	$0.265270\pi$
$920$	12.5863	−	13.9785i	0.414957	−	0.460856i
$921$	−1.22875	+	0.261178i	−0.0404886	+	0.00860611i
$922$	9.28477	+	10.3118i	0.305778	+	0.339600i
$923$	10.7035	−	32.9421i	0.352311	−	1.08430i
$924$	−0.137113	+	0.489960i	−0.00451068	+	0.0161185i
$925$	7.68383	+	23.6484i	0.252643	+	0.777554i
$926$	6.06362	−	2.69970i	0.199263	−	0.0887175i
$927$	−11.2043	+	2.38154i	−0.367996	+	0.0782201i
$928$	1.61871	+	0.720694i	0.0531366	+	0.0236579i
$929$	9.10747	−	15.7746i	0.298806	−	0.517548i	−0.677057	−	0.735931i	$-0.736745\pi$
$929$	9.10747	−	15.7746i	0.298806	−	0.517548i	0.975863	+	0.218383i	$0.0700782\pi$
$930$	0.101478	+	0.312317i	0.00332759	+	0.0102413i
$931$	0.0727118	+	0.383643i	0.00238303	+	0.0125734i
$932$	−20.6679	−	15.0161i	−0.677000	−	0.491869i
$933$	0.912707	−	0.406363i	0.0298807	−	0.0133037i
$934$	15.7644	+	27.3048i	0.515827	+	0.893439i
$935$	3.89870	−	37.0937i	0.127501	−	1.21309i
$936$	−5.16384	−	5.73502i	−0.168785	−	0.187455i
$937$	−7.76179	−	23.8883i	−0.253567	−	0.780398i	−0.994109	−	0.108388i	$-0.965431\pi$
$937$	−7.76179	−	23.8883i	−0.253567	−	0.780398i	0.740542	−	0.672010i	$-0.234569\pi$
$938$	16.5117	−	13.0711i	0.539127	−	0.426786i
$939$	0.492723	−	0.357984i	0.0160794	−	0.0116824i
$940$	3.92349	−	6.79569i	0.127970	−	0.221651i
$941$	17.1643	−	19.0629i	0.559540	−	0.621433i	−0.395300	−	0.918552i	$-0.629359\pi$
$941$	17.1643	−	19.0629i	0.559540	−	0.621433i	0.954840	+	0.297120i	$0.0960260\pi$
$942$	0.0635779	+	0.110120i	0.00207148	+	0.00358791i
$943$	−38.2701	+	12.3783i	−1.24625	+	0.403092i
$944$	−4.96237			−0.161511
$945$	1.85805	+	0.315401i	0.0604425	+	0.0102600i
$946$	18.5017			0.601542
$947$	0.543966	+	5.17550i	0.0176765	+	0.168181i	0.999799	−	0.0200636i	$-0.00638688\pi$
$947$	0.543966	+	5.17550i	0.0176765	+	0.168181i	−0.982122	+	0.188245i	$0.939720\pi$
$948$	−0.626099	−	0.278757i	−0.0203348	−	0.00905361i
$949$	15.7379	−	17.4787i	0.510873	−	0.567381i
$950$	0.148052	+	0.164429i	0.00480346	+	0.00533478i
$951$	0.725527	+	0.527126i	0.0235268	+	0.0170932i
$952$	−3.63818	−	5.74038i	−0.117914	−	0.186047i
$953$	−11.0809	−	8.05075i	−0.358946	−	0.260789i	0.393666	−	0.919253i	$-0.371206\pi$
$953$	−11.0809	−	8.05075i	−0.358946	−	0.260789i	−0.752612	+	0.658464i	$0.771206\pi$
$954$	11.8594	−	5.28013i	0.383961	−	0.170950i
$955$	45.6151	+	20.3092i	1.47607	+	0.657189i
$956$	12.2251	−	13.5773i	0.395387	−	0.439122i
$957$	0.170369	−	0.295088i	0.00550726	−	0.00953885i
$958$	−10.2305	+	7.43289i	−0.330532	+	0.240146i
$959$	−17.0672	+	4.37132i	−0.551130	+	0.141157i
$960$	0.0960722	+	0.0698006i	0.00310072	+	0.00225280i
$961$	22.8426	+	4.85533i	0.736857	+	0.156624i
$962$	−15.7818	+	3.35452i	−0.508825	+	0.108154i
$963$	−14.1427	+	3.00612i	−0.455741	+	0.0968707i
$964$	−5.45111	−	6.05408i	−0.175569	−	0.194989i
$965$	9.63875	−	29.6650i	0.310282	−	0.954951i
$966$	−0.649803	−	0.110303i	−0.0209071	−	0.00354893i
$967$	29.9588	+	21.7663i	0.963409	+	0.699958i	0.953940	−	0.299997i	$-0.0969858\pi$
$967$	29.9588	+	21.7663i	0.963409	+	0.699958i	0.00946931	+	0.999955i	$0.496986\pi$
$968$	−8.37297	−	9.29913i	−0.269118	−	0.298885i
$969$	0.00519120	+	0.00231127i	0.000166765	+	7.42488e-5i
$970$	20.4482	+	35.4173i	0.656552	+	1.13718i
$971$	−52.8310	−	11.2296i	−1.69543	−	0.360374i	−0.743985	−	0.668197i	$-0.767066\pi$
$971$	−52.8310	−	11.2296i	−1.69543	−	0.360374i	−0.951444	+	0.307822i	$0.900400\pi$
$972$	0.865656	−	0.628936i	0.0277659	−	0.0201731i
$973$	33.8392	+	22.5117i	1.08484	+	0.721692i
$974$	−7.44150	−	5.40657i	−0.238441	−	0.173238i
$975$	−0.202431	+	0.350621i	−0.00648299	+	0.0112289i
$976$	−0.174789	+	1.66301i	−0.00559487	+	0.0532317i
$977$	44.7472	−	9.51131i	1.43159	−	0.304294i	0.574096	−	0.818788i	$-0.305354\pi$
$977$	44.7472	−	9.51131i	1.43159	−	0.304294i	0.857494	+	0.514494i	$0.172020\pi$
$978$	−0.275199	−	0.0584954i	−0.00879989	−	0.00187048i
$979$	−15.8560	+	11.5200i	−0.506760	+	0.368182i
$980$	−15.8836	+	13.6775i	−0.507382	+	0.436910i
$981$	21.1831			0.676323
$982$	−9.12774	−	1.94016i	−0.291278	−	0.0619130i
$983$	16.2673	+	28.1758i	0.518847	+	0.898669i	0.999760	+	0.0219009i	$0.00697184\pi$
$983$	16.2673	+	28.1758i	0.518847	+	0.898669i	−0.480913	+	0.876768i	$0.659695\pi$
$984$	−0.102974	−	0.232117i	−0.00328270	−	0.00739963i
$985$	1.96267	−	3.39944i	0.0625359	−	0.108315i
$986$	1.40649	+	4.32874i	0.0447918	+	0.137855i
$987$	−0.274724	+	0.0113509i	−0.00874456	+	0.000361304i
$988$	−0.116150	+	0.0843878i	−0.00369522	+	0.00268473i
$989$	2.50532	+	23.8365i	0.0796645	+	0.757957i
$990$	−29.1322	+	32.3546i	−0.925881	+	1.02830i
$991$	−0.663295	+	0.140988i	−0.0210703	+	0.00447862i	−0.218435	−	0.975852i	$-0.570095\pi$
$991$	−0.663295	+	0.140988i	−0.0210703	+	0.00447862i	0.197365	+	0.980330i	$0.436762\pi$
$992$	−2.52627	+	1.12477i	−0.0802091	+	0.0357114i
$993$	−1.06089			−0.0336662
$994$	−31.9023	+	15.8128i	−1.01188	+	0.501552i
$995$	−62.5790	−	45.4663i	−1.98389	−	1.44138i
$996$	0.0667984	+	0.635545i	0.00211659	+	0.0201380i
$997$	5.82165	−	6.46560i	0.184373	−	0.204768i	−0.643872	−	0.765134i	$-0.722673\pi$
$997$	5.82165	−	6.46560i	0.184373	−	0.204768i	0.828245	+	0.560366i	$0.189340\pi$
$998$	−3.86253	−	6.69009i	−0.122266	−	0.211771i
$999$	−0.155877	−	1.48307i	−0.00493174	−	0.0469224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.s.a.387.7	yes	112
7.4	even	3	inner	574.2.s.a.305.7	yes	112
41.16	even	5	inner	574.2.s.a.303.7	yes	112
287.221	even	15	inner	574.2.s.a.221.7	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.s.a.221.7	✓	112	287.221	even	15	inner
574.2.s.a.303.7	yes	112	41.16	even	5	inner
574.2.s.a.305.7	yes	112	7.4	even	3	inner
574.2.s.a.387.7	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.s (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.0198289 + 0.0343446i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.313002 - 2.97801i) q^{5} +(0.0122549 + 0.0377167i) q^{6} +(-0.713008 + 2.54787i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.49921 - 2.59671i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.0198289 + 0.0343446i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.313002 - 2.97801i) q^{5} +(0.0122549 + 0.0377167i) q^{6} +(-0.713008 + 2.54787i) q^{7} +(0.809017 + 0.587785i) q^{8} +(1.49921 - 2.59671i) q^{9} +(0.313002 - 2.97801i) q^{10} +(0.506863 - 4.82248i) q^{11} +(0.00414536 + 0.0394405i) q^{12} +(-0.795336 - 2.44779i) q^{13} +(-1.22716 + 2.34395i) q^{14} +(0.0960722 - 0.0698006i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.268505 + 2.55465i) q^{17} +(2.00634 - 2.22827i) q^{18} +(-0.0373253 - 0.0414540i) q^{19} +(0.925326 - 2.84786i) q^{20} +(-0.101644 + 0.0260333i) q^{21} +(1.49844 - 4.61171i) q^{22} +(6.14437 + 1.30603i) q^{23} +(-0.00414536 + 0.0394405i) q^{24} +(-3.87986 + 0.824690i) q^{25} +(-0.269031 - 2.55966i) q^{26} +0.237884 q^{27} +(-1.68768 + 2.03758i) q^{28} +(1.43349 - 1.04149i) q^{29} +(0.108485 - 0.0483007i) q^{30} +(-0.289057 + 2.75020i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.175677 - 0.0782163i) q^{33} +(-0.793779 + 2.44300i) q^{34} +(7.81075 + 1.32586i) q^{35} +(2.42578 - 1.76243i) q^{36} +(-0.655266 - 6.23444i) q^{37} +(-0.0278909 - 0.0483085i) q^{38} +(0.0682978 - 0.0758524i) q^{39} +(1.49721 - 2.59324i) q^{40} +(-5.54954 + 3.19416i) q^{41} +(-0.104835 + 0.00433153i) q^{42} +(1.17906 + 3.62879i) q^{43} +(2.42452 - 4.19939i) q^{44} +(-8.20231 - 3.65190i) q^{45} +(5.73857 + 2.55497i) q^{46} +(2.56327 + 0.544840i) q^{47} +(-0.0122549 + 0.0377167i) q^{48} +(-5.98324 - 3.63330i) q^{49} -3.96654 q^{50} +(-0.0930626 + 0.0414341i) q^{51} +(0.269031 - 2.55966i) q^{52} +(3.95519 + 1.76097i) q^{53} +(0.232686 + 0.0494589i) q^{54} -14.5201 q^{55} +(-2.07443 + 1.64217i) q^{56} +(0.000683601 - 0.00210391i) q^{57} +(1.61871 - 0.720694i) q^{58} +(-3.32047 + 3.68776i) q^{59} +(0.116157 - 0.0246899i) q^{60} +(1.11890 + 1.24267i) q^{61} +(-0.854538 + 2.63000i) q^{62} +(5.54713 + 5.67127i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-7.04062 + 3.13468i) q^{65} +(0.188100 - 0.0399818i) q^{66} +(-7.27149 - 3.23748i) q^{67} +(-1.28436 + 2.22458i) q^{68} +(0.0769810 + 0.236923i) q^{69} +(7.36441 + 2.92084i) q^{70} +(10.8876 + 7.91034i) q^{71} +(2.73920 - 1.21957i) q^{72} +(4.56916 + 7.91402i) q^{73} +(0.655266 - 6.23444i) q^{74} +(-0.105257 - 0.116900i) q^{75} +(-0.0172375 - 0.0530517i) q^{76} +(11.9256 + 4.72988i) q^{77} +(0.0825759 - 0.0599949i) q^{78} +(-8.64082 + 14.9663i) q^{79} +(2.00366 - 2.22529i) q^{80} +(-4.49292 - 7.78197i) q^{81} +(-6.09237 + 1.97055i) q^{82} +16.1140 q^{83} +(-0.103445 - 0.0175595i) q^{84} +7.69183 q^{85} +(0.398832 + 3.79463i) q^{86} +(0.0641942 + 0.0285811i) q^{87} +(3.24464 - 3.60354i) q^{88} +(-2.70452 - 3.00368i) q^{89} +(-7.26380 - 5.27746i) q^{90} +(6.80372 - 0.281114i) q^{91} +(5.08196 + 3.69226i) q^{92} +(-0.100186 + 0.0446057i) q^{93} +(2.39398 + 1.06587i) q^{94} +(-0.111768 + 0.124131i) q^{95} +(-0.0198289 + 0.0343446i) q^{96} +(-11.0492 + 8.02770i) q^{97} +(-5.09709 - 4.79789i) q^{98} +(-11.7627 - 8.54610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

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Database

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