LMFDB - Embedded newform 669.2.i.b.4.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [720] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$20$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.8
Character	$\chi$	$=$	669.4
Dual form			669.2.i.b.502.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.647316 + 0.228711i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-1.18936 + 0.960343i) q^{4} +(-0.504580 - 0.819490i) q^{5} +(-0.0291373 + 0.685914i) q^{6} +(-0.0340902 + 0.266216i) q^{7} +(1.27016 - 2.06287i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(0.514050 + 0.415066i) q^{10} +(-0.177691 + 4.18300i) q^{11} +(0.447630 + 1.46167i) q^{12} +(-0.137295 - 0.341671i) q^{13} +(-0.0388194 - 0.180123i) q^{14} +(-0.948532 + 0.162642i) q^{15} +(0.293726 - 1.36289i) q^{16} +(-0.117177 + 2.75844i) q^{17} +(0.625588 + 0.282784i) q^{18} +(1.53243 - 0.399013i) q^{19} +(1.38712 + 0.490101i) q^{20} +(0.234308 + 0.130892i) q^{21} +(-0.841676 - 2.74836i) q^{22} +(2.95993 + 4.80723i) q^{23} +(-1.44053 - 1.94772i) q^{24} +(1.83406 - 3.63763i) q^{25} +(0.167017 + 0.189768i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(-0.215113 - 0.349365i) q^{28} +(0.163079 - 0.756688i) q^{29} +(0.576802 - 0.322221i) q^{30} +(9.25084 - 0.787362i) q^{31} +(0.736990 + 5.75526i) q^{32} +(3.81510 + 1.72454i) q^{33} +(-0.555037 - 1.81239i) q^{34} +(0.235362 - 0.106390i) q^{35} +(1.52317 + 0.129640i) q^{36} +(0.357252 + 8.40998i) q^{37} +(-0.900707 + 0.608772i) q^{38} -0.368224 q^{39} -2.33140 q^{40} +(-1.44596 + 0.977296i) q^{41} +(-0.181608 - 0.0311398i) q^{42} +(4.56352 + 9.05121i) q^{43} +(-3.80577 - 5.14574i) q^{44} +(-0.202752 + 0.940774i) q^{45} +(-3.01548 - 2.43483i) q^{46} +(-5.97525 - 1.55584i) q^{47} +(-1.15510 - 0.780708i) q^{48} +(6.70442 + 1.74570i) q^{49} +(-0.355246 + 2.77417i) q^{50} +(2.51584 + 1.13723i) q^{51} +(0.491414 + 0.274520i) q^{52} +(6.39730 - 7.26874i) q^{53} +(0.495647 - 0.475039i) q^{54} +(3.51758 - 1.96504i) q^{55} +(0.505869 + 0.408460i) q^{56} +(0.201136 - 1.57070i) q^{57} +(0.0674997 + 0.527115i) q^{58} +(-3.23942 + 10.5778i) q^{59} +(0.971955 - 1.10436i) q^{60} +(2.92051 + 7.26796i) q^{61} +(-5.80814 + 2.62545i) q^{62} +(0.208817 - 0.168608i) q^{63} +(-0.538024 - 1.06711i) q^{64} +(-0.210720 + 0.284912i) q^{65} +(-2.86400 - 0.243762i) q^{66} +(9.07005 - 7.32356i) q^{67} +(-2.50968 - 3.39332i) q^{68} +(5.56420 - 0.954079i) q^{69} +(-0.128021 + 0.122698i) q^{70} +(-2.90479 + 9.48513i) q^{71} +(-2.34438 + 0.610429i) q^{72} +(-12.7087 - 7.09948i) q^{73} +(-2.15471 - 5.36221i) q^{74} +(-2.69148 - 3.05812i) q^{75} +(-1.43942 + 1.94623i) q^{76} +(-1.10752 - 0.189904i) q^{77} +(0.238357 - 0.0842170i) q^{78} +(5.57203 - 3.76604i) q^{79} +(-1.26509 + 0.446983i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(0.712473 - 0.963327i) q^{82} +(7.56283 - 15.0000i) q^{83} +(-0.404378 + 0.0693376i) q^{84} +(2.31964 - 1.29583i) q^{85} +(-5.02416 - 4.81526i) q^{86} +(-0.641318 - 0.433455i) q^{87} +(8.40329 + 5.67963i) q^{88} +(-7.68598 + 12.4828i) q^{89} +(-0.0839209 - 0.655350i) q^{90} +(0.0956385 - 0.0249023i) q^{91} +(-8.13701 - 2.87499i) q^{92} +(2.71865 - 8.87733i) q^{93} +(4.22372 - 0.359491i) q^{94} +(-1.10022 - 1.05448i) q^{95} +(5.61503 + 1.46204i) q^{96} +(2.42365 - 3.93626i) q^{97} +(-4.73914 + 0.403361i) q^{98} +(3.02266 - 2.89699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) $ 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

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 $

$2$	−0.647316	+	0.228711i	−0.457722	+	0.161723i	−0.552038	−	0.833819i	$-0.686150\pi$
$2$	−0.647316	+	0.228711i	−0.457722	+	0.161723i	0.0943163	+	0.995542i	$0.469934\pi$
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$4$	−1.18936	+	0.960343i	−0.594681	+	0.480171i
$5$	−0.504580	−	0.819490i	−0.225655	−	0.366487i	0.718752	−	0.695267i	$-0.244714\pi$
$5$	−0.504580	−	0.819490i	−0.225655	−	0.366487i	−0.944407	+	0.328780i	$0.893363\pi$
$6$	−0.0291373	+	0.685914i	−0.0118952	+	0.280023i
$7$	−0.0340902	+	0.266216i	−0.0128849	+	0.100620i	−0.997066	−	0.0765443i	$-0.975611\pi$
$7$	−0.0340902	+	0.266216i	−0.0128849	+	0.100620i	0.984181	+	0.177164i	$0.0566924\pi$
$8$	1.27016	−	2.06287i	0.449070	−	0.729335i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	0.514050	+	0.415066i	0.162557	+	0.131255i
$11$	−0.177691	+	4.18300i	−0.0535760	+	1.26122i	0.748150	+	0.663529i	$0.230942\pi$
$11$	−0.177691	+	4.18300i	−0.0535760	+	1.26122i	−0.801726	+	0.597691i	$0.796085\pi$
$12$	0.447630	+	1.46167i	0.129220	+	0.421947i
$13$	−0.137295	−	0.341671i	−0.0380787	−	0.0947624i	0.907639	−	0.419751i	$-0.137883\pi$
$13$	−0.137295	−	0.341671i	−0.0380787	−	0.0947624i	−0.945718	+	0.324989i	$0.894639\pi$
$14$	−0.0388194	−	0.180123i	−0.0103749	−	0.0481398i
$15$	−0.948532	+	0.162642i	−0.244910	+	0.0419940i
$16$	0.293726	−	1.36289i	0.0734315	−	0.340723i
$17$	−0.117177	+	2.75844i	−0.0284197	+	0.669021i	0.927226	+	0.374502i	$0.122186\pi$
$17$	−0.117177	+	2.75844i	−0.0284197	+	0.669021i	−0.955646	+	0.294519i	$0.904841\pi$
$18$	0.625588	+	0.282784i	0.147453	+	0.0666528i
$19$	1.53243	−	0.399013i	0.351563	−	0.0915399i	−0.0720047	−	0.997404i	$-0.522940\pi$
$19$	1.53243	−	0.399013i	0.351563	−	0.0915399i	0.423568	+	0.905864i	$0.360777\pi$
$20$	1.38712	+	0.490101i	0.310169	+	0.109590i
$21$	0.234308	+	0.130892i	0.0511301	+	0.0285630i
$22$	−0.841676	−	2.74836i	−0.179446	−	0.585953i
$23$	2.95993	+	4.80723i	0.617188	+	1.00238i	0.997007	+	0.0773158i	$0.0246350\pi$
$23$	2.95993	+	4.80723i	0.617188	+	1.00238i	−0.379819	+	0.925061i	$0.624014\pi$
$24$	−1.44053	−	1.94772i	−0.294047	−	0.397577i
$25$	1.83406	−	3.63763i	0.366811	−	0.727527i
$26$	0.167017	+	0.189768i	0.0327547	+	0.0372166i
$27$	−0.911228	+	0.411901i	−0.175366	+	0.0792704i
$28$	−0.215113	−	0.349365i	−0.0406524	−	0.0660238i
$29$	0.163079	−	0.756688i	0.0302830	−	0.140513i	−0.959886	−	0.280391i	$-0.909536\pi$
$29$	0.163079	−	0.756688i	0.0302830	−	0.140513i	0.990169	+	0.139878i	$0.0446709\pi$
$30$	0.576802	−	0.322221i	0.105309	−	0.0588292i
$31$	9.25084	−	0.787362i	1.66150	−	0.141414i	0.783925	−	0.620855i	$-0.213214\pi$
$31$	9.25084	−	0.787362i	1.66150	−	0.141414i	0.877574	+	0.479441i	$0.159160\pi$
$32$	0.736990	+	5.75526i	0.130283	+	1.01740i
$33$	3.81510	+	1.72454i	0.664124	+	0.300203i
$34$	−0.555037	−	1.81239i	−0.0951880	−	0.310822i
$35$	0.235362	−	0.106390i	0.0397835	−	0.0179833i
$36$	1.52317	+	0.129640i	0.253861	+	0.0216067i
$37$	0.357252	+	8.40998i	0.0587318	+	1.38259i	0.750690	+	0.660655i	$0.229721\pi$
$37$	0.357252	+	8.40998i	0.0587318	+	1.38259i	−0.691958	+	0.721937i	$0.743252\pi$
$38$	−0.900707	+	0.608772i	−0.146114	+	0.0987558i
$39$	−0.368224			−0.0589630
$40$	−2.33140			−0.368627
$41$	−1.44596	+	0.977296i	−0.225820	+	0.152628i	−0.667661	−	0.744466i	$-0.732704\pi$
$41$	−1.44596	+	0.977296i	−0.225820	+	0.152628i	0.441840	+	0.897094i	$0.354326\pi$
$42$	−0.181608	−	0.0311398i	−0.0280227	−	0.00480497i
$43$	4.56352	+	9.05121i	0.695931	+	1.38030i	0.914545	+	0.404485i	$0.132549\pi$
$43$	4.56352	+	9.05121i	0.695931	+	1.38030i	−0.218614	+	0.975811i	$0.570154\pi$
$44$	−3.80577	−	5.14574i	−0.573741	−	0.775750i
$45$	−0.202752	+	0.940774i	−0.0302245	+	0.140242i
$46$	−3.01548	−	2.43483i	−0.444608	−	0.358996i
$47$	−5.97525	−	1.55584i	−0.871580	−	0.226942i	−0.210807	−	0.977528i	$-0.567609\pi$
$47$	−5.97525	−	1.55584i	−0.871580	−	0.226942i	−0.660773	+	0.750586i	$0.729771\pi$
$48$	−1.15510	−	0.780708i	−0.166724	−	0.112686i
$49$	6.70442	+	1.74570i	0.957775	+	0.249385i
$50$	−0.355246	+	2.77417i	−0.0502394	+	0.392327i
$51$	2.51584	+	1.13723i	0.352288	+	0.159244i
$52$	0.491414	+	0.274520i	0.0681469	+	0.0380691i
$53$	6.39730	−	7.26874i	0.878736	−	0.998438i	−0.121247	−	0.992622i	$-0.538689\pi$
$53$	6.39730	−	7.26874i	0.878736	−	0.998438i	0.999983	−	0.00581583i	$-0.00185125\pi$
$54$	0.495647	−	0.475039i	0.0674490	−	0.0646446i
$55$	3.51758	−	1.96504i	0.474311	−	0.264966i
$56$	0.505869	+	0.408460i	0.0675995	+	0.0545828i
$57$	0.201136	−	1.57070i	0.0266411	−	0.208044i
$58$	0.0674997	+	0.527115i	0.00886314	+	0.0692136i
$59$	−3.23942	+	10.5778i	−0.421737	+	1.37712i	0.452564	+	0.891732i	$0.350509\pi$
$59$	−3.23942	+	10.5778i	−0.421737	+	1.37712i	−0.874301	+	0.485384i	$0.838680\pi$
$60$	0.971955	−	1.10436i	0.125479	−	0.142572i
$61$	2.92051	+	7.26796i	0.373933	+	0.930567i	0.989767	+	0.142692i	$0.0455757\pi$
$61$	2.92051	+	7.26796i	0.373933	+	0.930567i	−0.615835	+	0.787875i	$0.711181\pi$
$62$	−5.80814	+	2.62545i	−0.737635	+	0.333432i
$63$	0.208817	−	0.168608i	0.0263084	−	0.0212426i
$64$	−0.538024	−	1.06711i	−0.0672530	−	0.133388i
$65$	−0.210720	+	0.284912i	−0.0261366	+	0.0353390i
$66$	−2.86400	−	0.243762i	−0.352534	−	0.0300051i
$67$	9.07005	−	7.32356i	1.10808	−	0.894715i	0.112984	−	0.993597i	$-0.463959\pi$
$67$	9.07005	−	7.32356i	1.10808	−	0.894715i	0.995099	+	0.0988818i	$0.0315266\pi$
$68$	−2.50968	−	3.39332i	−0.304344	−	0.411500i
$69$	5.56420	−	0.954079i	0.669851	−	0.114858i
$70$	−0.128021	+	0.122698i	−0.0153015	+	0.0146653i
$71$	−2.90479	+	9.48513i	−0.344735	+	1.12568i	0.600593	+	0.799555i	$0.294931\pi$
$71$	−2.90479	+	9.48513i	−0.344735	+	1.12568i	−0.945328	+	0.326122i	$0.894258\pi$
$72$	−2.34438	+	0.610429i	−0.276288	+	0.0719398i
$73$	−12.7087	−	7.09948i	−1.48744	−	0.830932i	−0.488308	−	0.872671i	$-0.662386\pi$
$73$	−12.7087	−	7.09948i	−1.48744	−	0.830932i	−0.999129	+	0.0417396i	$0.986710\pi$
$74$	−2.15471	−	5.36221i	−0.250480	−	0.623344i
$75$	−2.69148	−	3.05812i	−0.310785	−	0.353121i
$76$	−1.43942	+	1.94623i	−0.165113	+	0.223248i
$77$	−1.10752	−	0.189904i	−0.126214	−	0.0216415i
$78$	0.238357	−	0.0842170i	0.0269886	−	0.00953570i
$79$	5.57203	−	3.76604i	0.626902	−	0.423712i	−0.204901	−	0.978783i	$-0.565687\pi$
$79$	5.57203	−	3.76604i	0.626902	−	0.423712i	0.831803	+	0.555071i	$0.187309\pi$
$80$	−1.26509	+	0.446983i	−0.141441	+	0.0499742i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	0.712473	−	0.963327i	0.0786794	−	0.106382i
$83$	7.56283	−	15.0000i	0.830129	−	1.64646i	0.0692219	−	0.997601i	$-0.477948\pi$
$83$	7.56283	−	15.0000i	0.830129	−	1.64646i	0.760907	−	0.648861i	$-0.224754\pi$
$84$	−0.404378	+	0.0693376i	−0.0441213	+	0.00756535i
$85$	2.31964	−	1.29583i	0.251601	−	0.140552i
$86$	−5.02416	−	4.81526i	−0.541769	−	0.519243i
$87$	−0.641318	−	0.433455i	−0.0687565	−	0.0464713i
$88$	8.40329	+	5.67963i	0.895794	+	0.605451i
$89$	−7.68598	+	12.4828i	−0.814712	+	1.32318i	0.128744	+	0.991678i	$0.458905\pi$
$89$	−7.68598	+	12.4828i	−0.814712	+	1.32318i	−0.943456	+	0.331498i	$0.892446\pi$
$90$	−0.0839209	−	0.655350i	−0.00884604	−	0.0690800i
$91$	0.0956385	−	0.0249023i	0.0100256	−	0.00261047i
$92$	−8.13701	−	2.87499i	−0.848342	−	0.299738i
$93$	2.71865	−	8.87733i	0.281911	−	0.920536i
$94$	4.22372	−	0.359491i	0.435643	−	0.0370787i
$95$	−1.10022	−	1.05448i	−0.112880	−	0.108187i
$96$	5.61503	+	1.46204i	0.573082	+	0.149219i
$97$	2.42365	−	3.93626i	0.246084	−	0.399666i	−0.704707	−	0.709499i	$-0.748921\pi$
$97$	2.42365	−	3.93626i	0.246084	−	0.399666i	0.950791	+	0.309832i	$0.100273\pi$
$98$	−4.73914	+	0.403361i	−0.478726	+	0.0407456i
$99$	3.02266	−	2.89699i	0.303789	−	0.291158i
$100$	1.31202	+	6.08778i	0.131202	+	0.608778i
$101$	6.17095	+	7.01156i	0.614033	+	0.697677i	0.971712	−	0.236168i	$-0.0758915\pi$
$101$	6.17095	+	7.01156i	0.614033	+	0.697677i	−0.357680	+	0.933844i	$0.616432\pi$
$102$	−1.88864	−	0.160747i	−0.187003	−	0.0159163i
$103$	−4.28013	+	10.6515i	−0.421734	+	1.04952i	0.554380	+	0.832264i	$0.312955\pi$
$103$	−4.28013	+	10.6515i	−0.421734	+	1.04952i	−0.976114	+	0.217261i	$0.930288\pi$
$104$	−0.879209	−	0.150756i	−0.0862136	−	0.0147828i
$105$	−0.0109622	−	0.258058i	−0.00106980	−	0.0251839i
$106$	−2.47863	+	6.16831i	−0.240746	+	0.599119i
$107$	−5.67911	−	11.2638i	−0.549020	−	1.08892i	−0.982240	−	0.187628i	$-0.939920\pi$
$107$	−5.67911	−	11.2638i	−0.549020	−	1.08892i	0.433220	−	0.901288i	$-0.357377\pi$
$108$	0.688214	−	1.36499i	0.0662234	−	0.131346i
$109$	−2.82624	−	13.1138i	−0.270705	−	1.25608i	−0.884474	−	0.466589i	$-0.845483\pi$
$109$	−2.82624	−	13.1138i	−0.270705	−	1.25608i	0.613769	−	0.789486i	$-0.289653\pi$
$110$	−1.82756	+	2.07651i	−0.174251	+	0.197988i
$111$	7.93673	+	2.80423i	0.753321	+	0.266165i
$112$	0.352810	+	0.124656i	0.0333374	+	0.0117789i
$113$	−9.46210	+	10.7510i	−0.890119	+	1.01137i	0.109729	+	0.993962i	$0.465002\pi$
$113$	−9.46210	+	10.7510i	−0.890119	+	1.01137i	−0.999848	+	0.0174105i	$0.994458\pi$
$114$	0.229038	+	1.06274i	0.0214514	+	0.0995348i
$115$	2.44596	−	4.85126i	0.228087	−	0.452383i
$116$	0.532720	+	1.05659i	0.0494618	+	0.0981017i
$117$	−0.137295	+	0.341671i	−0.0126929	+	0.0315875i
$118$	−0.322338	−	7.58809i	−0.0296736	−	0.698541i
$119$	−0.730346	−	0.125230i	−0.0669507	−	0.0114799i
$120$	−0.869278	+	2.16328i	−0.0793538	+	0.197480i
$121$	−6.50551	−	0.553700i	−0.591410	−	0.0503364i
$122$	−3.55276	−	4.03672i	−0.321652	−	0.365467i
$123$	0.367688	+	1.70608i	0.0331533	+	0.153832i
$124$	−10.2465	+	9.82043i	−0.920159	+	0.881901i
$125$	−8.70097	+	0.740562i	−0.778238	+	0.0662379i
$126$	−0.0966079	+	0.156901i	−0.00860652	+	0.0139779i
$127$	−9.11144	−	2.37243i	−0.808509	−	0.210519i	−0.175315	−	0.984512i	$-0.556094\pi$
$127$	−9.11144	−	2.37243i	−0.808509	−	0.210519i	−0.633194	+	0.773993i	$0.718257\pi$
$128$	−7.78561	−	7.46191i	−0.688157	−	0.659546i
$129$	10.1001	−	0.859641i	0.889260	−	0.0756872i
$130$	0.0712397	−	0.232622i	0.00624814	−	0.0204023i
$131$	7.54219	+	2.66483i	0.658964	+	0.232827i	0.641620	−	0.767023i	$-0.278263\pi$
$131$	7.54219	+	2.66483i	0.658964	+	0.232827i	0.0173443	+	0.999850i	$0.494479\pi$
$132$	−6.19368	+	1.61271i	−0.539091	+	0.140368i
$133$	0.0539827	+	0.421559i	0.00468089	+	0.0365538i
$134$	−4.19621	+	6.81508i	−0.362498	+	0.588734i
$135$	0.797337	+	0.538906i	0.0686238	+	0.0463816i
$136$	5.54148	+	3.74539i	0.475178	+	0.321164i
$137$	−1.75807	−	1.68497i	−0.150202	−	0.143957i	0.613084	−	0.790018i	$-0.289929\pi$
$137$	−1.75807	−	1.68497i	−0.150202	−	0.143957i	−0.763286	+	0.646061i	$0.776415\pi$
$138$	−3.38359	+	1.89019i	−0.288030	+	0.160903i
$139$	−8.85010	+	1.51750i	−0.750656	+	0.128713i	−0.531595	−	0.846998i	$-0.678407\pi$
$139$	−8.85010	+	1.51750i	−0.750656	+	0.128713i	−0.219060	+	0.975711i	$0.570299\pi$
$140$	−0.177760	+	0.352565i	−0.0150234	+	0.0297972i
$141$	−3.67155	+	4.96427i	−0.309201	+	0.418067i
$142$	−0.289040	−	6.80424i	−0.0242557	−	0.570999i
$143$	1.45360	−	0.513591i	0.121556	−	0.0429486i
$144$	−1.15510	+	0.780708i	−0.0962580	+	0.0650590i
$145$	−0.702385	+	0.248168i	−0.0583299	+	0.0206093i
$146$	9.85026	+	1.68900i	0.815213	+	0.139782i
$147$	4.11960	−	5.57007i	0.339779	−	0.459411i
$148$	−8.50136	−	9.65942i	−0.698808	−	0.794000i
$149$	2.30140	+	5.72724i	0.188538	+	0.469194i	0.992012	−	0.126146i	$-0.0402607\pi$
$149$	2.30140	+	5.72724i	0.188538	+	0.469194i	−0.803474	+	0.595340i	$0.797017\pi$
$150$	2.44167	+	1.36400i	0.199361	+	0.111370i
$151$	−3.49562	+	0.910188i	−0.284469	+	0.0740701i	−0.391476	−	0.920188i	$-0.628035\pi$
$151$	−3.49562	+	0.910188i	−0.284469	+	0.0740701i	0.107007	+	0.994258i	$0.465873\pi$
$152$	1.12332	−	3.66801i	0.0911130	−	0.297515i
$153$	1.99327	−	1.91040i	0.161146	−	0.154446i
$154$	0.760350	−	0.130375i	0.0612707	−	0.0105059i
$155$	−5.31302	−	7.18368i	−0.426752	−	0.577007i
$156$	0.437951	−	0.353621i	0.0350642	−	0.0283123i
$157$	4.29716	+	0.365742i	0.342950	+	0.0291894i	0.255016	−	0.966937i	$-0.417919\pi$
$157$	4.29716	+	0.365742i	0.342950	+	0.0291894i	0.0879346	+	0.996126i	$0.471973\pi$
$158$	−2.74553	+	3.71220i	−0.218423	+	0.295327i
$159$	−4.35931	−	8.64618i	−0.345716	−	0.685686i
$160$	4.34451	−	3.50794i	0.343463	−	0.277327i
$161$	−1.38066	+	0.624099i	−0.108812	+	0.0491859i
$162$	−0.255978	−	0.637026i	−0.0201116	−	0.0500495i
$163$	9.15825	−	10.4058i	0.717329	−	0.815044i	−0.271760	−	0.962365i	$-0.587606\pi$
$163$	9.15825	−	10.4058i	0.717329	−	0.815044i	0.989089	+	0.147321i	$0.0470650\pi$
$164$	0.781227	−	2.55097i	0.0610035	−	0.199197i
$165$	−0.511785	−	3.99660i	−0.0398424	−	0.311135i
$166$	−1.46488	+	11.4394i	−0.113697	+	0.887873i
$167$	0.699145	+	0.564520i	0.0541015	+	0.0436839i	0.654891	−	0.755723i	$-0.272715\pi$
$167$	0.699145	+	0.564520i	0.0541015	+	0.0436839i	−0.600789	+	0.799407i	$0.705147\pi$
$168$	0.567622	−	0.317093i	0.0437930	−	0.0244642i
$169$	9.28754	−	8.90139i	0.714426	−	0.684722i
$170$	−1.20517	+	1.36934i	−0.0924324	+	0.105024i
$171$	−1.38244	−	0.772277i	−0.105718	−	0.0590575i
$172$	−14.1199	−	6.38261i	−1.07664	−	0.486670i
$173$	−0.770340	+	6.01570i	−0.0585679	+	0.457365i	0.935895	+	0.352279i	$0.114593\pi$
$173$	−0.770340	+	6.01570i	−0.0585679	+	0.457365i	−0.994463	+	0.105086i	$0.966488\pi$
$174$	0.514272	+	0.133906i	0.0389868	+	0.0101514i
$175$	0.905871	+	0.612262i	0.0684774	+	0.0462827i
$176$	5.64878	+	1.47083i	0.425793	+	0.110868i
$177$	8.60721	+	6.94984i	0.646957	+	0.522382i
$178$	2.12030	−	9.83820i	0.158923	−	0.737405i
$179$	−8.61983	−	11.6548i	−0.644277	−	0.871120i	0.353657	−	0.935375i	$-0.384938\pi$
$179$	−8.61983	−	11.6548i	−0.644277	−	0.871120i	−0.997933	+	0.0642557i	$0.979533\pi$
$180$	−0.662320	−	1.31363i	−0.0493664	−	0.0979124i
$181$	−17.9421	−	3.07648i	−1.33362	−	0.228673i	−0.542359	−	0.840147i	$-0.682469\pi$
$181$	−17.9421	−	3.07648i	−1.33362	−	0.228673i	−0.791265	+	0.611474i	$0.790577\pi$
$182$	−0.0562129	+	0.0379933i	−0.00416678	+	0.00281625i
$183$	7.83279			0.579017
$184$	13.6763			1.00823
$185$	6.71163	−	4.53627i	0.493449	−	0.333513i
$186$	0.270519	+	6.36822i	0.0198354	+	0.466941i
$187$	−11.5177	−	0.980304i	−0.842260	−	0.0716869i
$188$	8.60087	−	3.88784i	0.627283	−	0.283550i
$189$	−0.0785905	−	0.256625i	−0.00571662	−	0.0186667i
$190$	0.953361	+	0.430946i	0.0691641	+	0.0312641i
$191$	−0.563060	−	4.39702i	−0.0407416	−	0.318157i	−0.999432	−	0.0337049i	$-0.989269\pi$
$191$	−0.563060	−	4.39702i	−0.0407416	−	0.318157i	0.958690	−	0.284452i	$-0.0918117\pi$
$192$	−1.19076	+	0.101349i	−0.0859359	+	0.00731423i
$193$	10.5862	−	5.91381i	0.762012	−	0.425685i	−0.0577930	−	0.998329i	$-0.518406\pi$
$193$	10.5862	−	5.91381i	0.762012	−	0.425685i	0.819805	+	0.572643i	$0.194082\pi$
$194$	−0.668601	+	3.10232i	−0.0480028	+	0.222734i
$195$	0.185798	+	0.301756i	0.0133053	+	0.0216092i
$196$	−9.65045	+	4.36228i	−0.689318	+	0.311591i
$197$	−10.9357	−	12.4254i	−0.779140	−	0.885275i	0.216715	−	0.976235i	$-0.430466\pi$
$197$	−10.9357	−	12.4254i	−0.779140	−	0.885275i	−0.995855	+	0.0909601i	$0.971006\pi$
$198$	−1.29405	+	2.56659i	−0.0919638	+	0.182399i
$199$	−10.7964	−	14.5977i	−0.765334	−	1.03480i	−0.998060	−	0.0622580i	$-0.980170\pi$
$199$	−10.7964	−	14.5977i	−0.765334	−	1.03480i	0.232726	−	0.972542i	$-0.425236\pi$
$200$	−5.17442	−	8.40380i	−0.365887	−	0.594238i
$201$	−3.41362	−	11.1466i	−0.240778	−	0.786223i
$202$	−5.59818	−	3.12733i	−0.393887	−	0.220038i
$203$	0.195883	+	0.0692098i	0.0137483	+	0.00485758i
$204$	−4.08437	+	1.06349i	−0.285963	+	0.0744591i
$205$	1.53049	+	0.691823i	0.106894	+	0.0483190i
$206$	0.334475	−	7.87381i	0.0233040	−	0.548594i
$207$	1.18937	−	5.51870i	0.0826670	−	0.383576i
$208$	−0.505988	+	0.0867603i	−0.0350839	+	0.00601574i
$209$	1.39677	+	6.48104i	0.0966167	+	0.448303i
$210$	0.0661169	+	0.164538i	0.00456250	+	0.0113542i
$211$	−2.35133	−	7.67790i	−0.161872	−	0.528569i	0.837981	−	0.545700i	$-0.183736\pi$
$211$	−2.35133	−	7.67790i	−0.161872	−	0.528569i	−0.999853	+	0.0171308i	$0.994547\pi$
$212$	−0.628219	+	14.7888i	−0.0431462	+	1.01570i
$213$	7.71808	+	6.23191i	0.528834	+	0.427004i
$214$	6.25235	+	5.99239i	0.427402	+	0.409631i
$215$	5.11471	−	8.30682i	0.348820	−	0.566520i
$216$	−0.307707	+	2.40293i	−0.0209368	+	0.163499i
$217$	−0.105755	+	2.48956i	−0.00717913	+	0.169002i
$218$	4.82875	+	7.84239i	0.327044	+	0.531154i
$219$	−11.3260	+	9.14514i	−0.765343	+	0.617971i
$220$	−2.29657	+	5.71523i	−0.154835	+	0.385321i
$221$	0.958567	−	0.338683i	0.0644802	−	0.0227823i
$222$	−5.77893			−0.387857
$223$	14.6454	+	2.91744i	0.980730	+	0.195367i
$223$	14.6454	+	2.91744i	0.980730	+	0.195367i
$224$	−1.55726			−0.104049
$225$	−3.84113	+	1.35716i	−0.256075	+	0.0904771i
$226$	3.66609	−	9.12341i	0.243865	−	0.606880i
$227$	−15.5449	+	12.5516i	−1.03175	+	0.833081i	−0.986146	−	0.165878i	$-0.946954\pi$
$227$	−15.5449	+	12.5516i	−1.03175	+	0.833081i	−0.0456055	+	0.998960i	$0.514522\pi$
$228$	1.26919	+	2.06129i	0.0840539	+	0.136512i
$229$	−0.632844	+	14.8976i	−0.0418195	+	0.984464i	0.848519	+	0.529165i	$0.177495\pi$
$229$	−0.632844	+	14.8976i	−0.0418195	+	0.984464i	−0.890338	+	0.455299i	$0.849532\pi$
$230$	−0.473768	+	3.69972i	−0.0312393	+	0.243952i
$231$	−0.589156	+	0.956850i	−0.0387636	+	0.0629561i
$232$	−1.35381	−	1.29753i	−0.0888823	−	0.0851868i
$233$	14.1434	+	11.4200i	0.926562	+	0.748146i	0.967988	−	0.250995i	$-0.0807578\pi$
$233$	14.1434	+	11.4200i	0.926562	+	0.748146i	−0.0414266	+	0.999142i	$0.513190\pi$
$234$	0.0107290	−	0.252570i	0.000701379	−	0.0165110i
$235$	1.74000	+	5.68170i	0.113505	+	0.370634i
$236$	−6.30549	−	15.6918i	−0.410453	−	1.02145i
$237$	−1.41690	−	6.57442i	−0.0920372	−	0.427054i
$238$	0.501407	−	0.0859748i	0.0325014	−	0.00557292i
$239$	−2.09650	+	9.72779i	−0.135611	+	0.629238i	0.857737	+	0.514089i	$0.171870\pi$
$239$	−2.09650	+	9.72779i	−0.135611	+	0.629238i	−0.993348	+	0.115149i	$0.963265\pi$
$240$	−0.0569446	+	1.34052i	−0.00367576	+	0.0865301i
$241$	−5.73444	−	2.59213i	−0.369388	−	0.166974i	0.218658	−	0.975802i	$-0.429832\pi$
$241$	−5.73444	−	2.59213i	−0.369388	−	0.166974i	−0.588046	+	0.808828i	$0.700102\pi$
$242$	4.33776	−	1.12947i	0.278842	−	0.0726048i
$243$	0.942877	+	0.333140i	0.0604856	+	0.0213709i
$244$	−10.4533	−	5.83955i	−0.669202	−	0.373839i
$245$	−1.95234	−	6.37505i	−0.124730	−	0.407287i
$246$	−0.628210	−	1.02028i	−0.0400532	−	0.0650506i
$247$	−0.346725	−	0.468804i	−0.0220616	−	0.0298293i
$248$	10.1258	−	20.0834i	0.642990	−	1.27530i
$249$	−11.0985	−	12.6103i	−0.703337	−	0.799146i
$250$	5.46291	−	2.46939i	0.345504	−	0.156178i
$251$	−7.21810	−	11.7229i	−0.455603	−	0.739946i	0.539155	−	0.842207i	$-0.318744\pi$
$251$	−7.21810	−	11.7229i	−0.455603	−	0.739946i	−0.994758	+	0.102261i	$0.967392\pi$
$252$	−0.0864374	+	0.401071i	−0.00544504	+	0.0252651i
$253$	−20.6346	+	11.5272i	−1.29728	+	0.724707i
$254$	6.44059	−	0.548175i	0.404118	−	0.0343955i
$255$	−0.337493	−	2.63553i	−0.0211346	−	0.165043i
$256$	8.92434	+	4.03406i	0.557771	+	0.252128i
$257$	5.58227	+	18.2280i	0.348212	+	1.13703i	0.942900	+	0.333076i	$0.108086\pi$
$257$	5.58227	+	18.2280i	0.348212	+	1.13703i	−0.594688	+	0.803957i	$0.702724\pi$
$258$	−6.34132	+	2.86646i	−0.394793	+	0.178458i
$259$	−2.25105	−	0.191592i	−0.139873	−	0.0119050i
$260$	−0.0229910	−	0.541226i	−0.00142584	−	0.0335654i
$261$	−0.641318	+	0.433455i	−0.0396966	+	0.0268302i
$262$	−5.49166			−0.339276
$263$	25.9745			1.60166			0.800829	−	0.598893i	$-0.204393\pi$
$263$	25.9745			1.60166			0.800829	+	0.598893i	$0.204393\pi$
$264$	8.40329	−	5.67963i	0.517187	−	0.349557i
$265$	−9.18461	−	1.57486i	−0.564206	−	0.0967428i
$266$	−0.131359	−	0.260535i	−0.00805415	−	0.0159745i
$267$	8.71690	+	11.7860i	0.533466	+	0.721293i
$268$	−3.75445	+	17.4207i	−0.229340	+	1.06414i
$269$	5.84578	+	4.72014i	0.356424	+	0.287792i	0.789730	−	0.613455i	$-0.210221\pi$
$269$	5.84578	+	4.72014i	0.356424	+	0.287792i	−0.433306	+	0.901247i	$0.642653\pi$
$270$	−0.639383	−	0.166482i	−0.0389116	−	0.0101318i
$271$	20.9398	+	14.1529i	1.27200	+	0.859725i	0.994875	−	0.101108i	$-0.0322389\pi$
$271$	20.9398	+	14.1529i	1.27200	+	0.859725i	0.277128	+	0.960833i	$0.410617\pi$
$272$	3.72504	+	0.969926i	0.225864	+	0.0588104i
$273$	0.0125528	−	0.0980269i	0.000759732	−	0.00593286i
$274$	1.52340	+	0.688620i	0.0920320	+	0.0416011i
$275$	14.8903	+	8.31822i	0.897919	+	0.501608i
$276$	−5.70161	+	6.47829i	−0.343197	+	0.389947i
$277$	−15.9054	+	15.2441i	−0.955661	+	0.915927i	−0.996530	−	0.0832377i	$-0.973474\pi$
$277$	−15.9054	+	15.2441i	−0.955661	+	0.915927i	0.0408687	+	0.999165i	$0.486987\pi$
$278$	5.38175	−	3.00642i	0.322776	−	0.180313i
$279$	−7.22351	−	5.83257i	−0.432460	−	0.349187i
$280$	0.0794780	−	0.620655i	0.00474972	−	0.0370912i
$281$	1.68881	+	13.1881i	0.100746	+	0.786739i	0.960937	+	0.276767i	$0.0892631\pi$
$281$	1.68881	+	13.1881i	0.100746	+	0.786739i	−0.860191	+	0.509972i	$0.829656\pi$
$282$	1.24127	−	4.05318i	0.0739167	−	0.241363i
$283$	0.948617	−	1.07784i	0.0563894	−	0.0640708i	−0.721794	−	0.692108i	$-0.756682\pi$
$283$	0.948617	−	1.07784i	0.0563894	−	0.0640708i	0.778183	+	0.628037i	$0.216142\pi$
$284$	−5.65413	−	14.0708i	−0.335511	−	0.834951i
$285$	−1.38866	+	0.627714i	−0.0822572	+	0.0371826i
$286$	−0.823477	+	0.664912i	−0.0486932	+	0.0393170i
$287$	−0.210878	−	0.418252i	−0.0124478	−	0.0246887i
$288$	3.45021	−	4.66500i	0.203306	−	0.274887i
$289$	9.34348	+	0.795247i	0.549616	+	0.0467792i
$290$	0.397906	−	0.321287i	0.0233659	−	0.0188666i
$291$	−2.74874	−	3.71654i	−0.161134	−	0.217867i
$292$	21.9331	−	3.76081i	1.28354	−	0.220085i
$293$	23.7002	−	22.7148i	1.38458	−	1.32701i	0.495977	−	0.868336i	$-0.334810\pi$
$293$	23.7002	−	22.7148i	1.38458	−	1.32701i	0.888603	−	0.458677i	$-0.151676\pi$
$294$	−1.39275	+	4.54779i	−0.0812266	+	0.265233i
$295$	10.3030	−	2.68269i	0.599862	−	0.156192i
$296$	17.8025	+	9.94506i	1.03475	+	0.578045i
$297$	−1.56106	−	3.88486i	−0.0905821	−	0.225422i
$298$	−2.79962	−	3.18098i	−0.162177	−	0.184269i
$299$	1.23611	−	1.67133i	0.0714859	−	0.0966554i
$300$	6.13798	+	1.05246i	0.354377	+	0.0607640i
$301$	−2.56514	+	0.906323i	−0.147852	+	0.0522396i
$302$	2.05460	−	1.38867i	0.118229	−	0.0799088i
$303$	8.80683	−	3.11165i	0.505939	−	0.178760i
$304$	−0.0936985	−	2.20574i	−0.00537398	−	0.126508i
$305$	4.48239	−	6.06059i	0.256661	−	0.347029i
$306$	−0.853348	+	1.69251i	−0.0487826	+	0.0967546i
$307$	10.3038	−	1.76677i	0.588069	−	0.100835i	0.132729	−	0.991152i	$-0.457626\pi$
$307$	10.3038	−	1.76677i	0.588069	−	0.100835i	0.455340	+	0.890318i	$0.349518\pi$
$308$	1.49962	−	0.837736i	0.0854485	−	0.0477344i
$309$	8.28754	+	7.94297i	0.471462	+	0.451860i
$310$	5.08220	+	3.43497i	0.288649	+	0.195093i
$311$	−9.12923	−	6.17028i	−0.517671	−	0.349885i	0.273111	−	0.961983i	$-0.411947\pi$
$311$	−9.12923	−	6.17028i	−0.517671	−	0.349885i	−0.790782	+	0.612098i	$0.790326\pi$
$312$	−0.467703	+	0.759598i	−0.0264785	+	0.0430038i
$313$	2.91125	+	22.7343i	0.164553	+	1.28502i	0.837953	+	0.545742i	$0.183752\pi$
$313$	2.91125	+	22.7343i	0.164553	+	1.28502i	−0.673400	+	0.739279i	$0.735167\pi$
$314$	−2.86527	+	0.746058i	−0.161697	+	0.0421025i
$315$	−0.243537	−	0.0860471i	−0.0137218	−	0.00484820i
$316$	−3.01048	+	9.83024i	−0.169353	+	0.552994i
$317$	−15.2445	+	1.29750i	−0.856215	+	0.0728746i	−0.504687	−	0.863303i	$-0.668392\pi$
$317$	−15.2445	+	1.29750i	−0.856215	+	0.0728746i	−0.351528	+	0.936177i	$0.614338\pi$
$318$	4.79933	+	4.59979i	0.269133	+	0.257943i
$319$	3.13625	+	0.816615i	0.175596	+	0.0457217i
$320$	−0.603008	+	0.979347i	−0.0337092	+	0.0547471i
$321$	−12.5691	+	1.06979i	−0.701538	+	0.0597097i
$322$	0.750988	−	0.719763i	0.0418509	−	0.0401109i
$323$	0.921090	+	4.27387i	0.0512508	+	0.237805i
$324$	−1.00996	−	1.14753i	−0.0561086	−	0.0637518i
$325$	−1.49468	−	0.127216i	−0.0829099	−	0.00705667i
$326$	−3.54836	+	8.83043i	−0.196525	+	0.489072i
$327$	−13.2219	−	2.26713i	−0.731175	−	0.125373i
$328$	0.179440	+	4.22415i	0.00990789	+	0.233239i
$329$	0.617885	−	1.53767i	0.0340651	−	0.0847743i
$330$	1.24536	+	2.47002i	0.0685546	+	0.135970i
$331$	10.4030	−	20.6332i	0.571802	−	1.13410i	−0.403860	−	0.914821i	$-0.632332\pi$
$331$	10.4030	−	20.6332i	0.571802	−	1.13410i	0.975662	−	0.219280i	$-0.0703709\pi$
$332$	5.41018	+	25.1033i	0.296922	+	1.37772i
$333$	5.56127	−	6.31883i	0.304756	−	0.346270i
$334$	−0.581680	−	0.205521i	−0.0318281	−	0.0112456i
$335$	−10.5782	−	3.73750i	−0.577946	−	0.204201i
$336$	0.247214	−	0.280890i	0.0134866	−	0.0153238i
$337$	−3.85192	−	17.8730i	−0.209827	−	0.973603i	−0.952639	−	0.304102i	$-0.901643\pi$
$337$	−3.85192	−	17.8730i	−0.209827	−	0.973603i	0.742812	−	0.669500i	$-0.233492\pi$
$338$	−3.97613	+	7.88618i	−0.216273	+	0.428952i
$339$	6.44776	+	12.7884i	0.350194	+	0.694569i
$340$	−1.51445	+	3.76886i	−0.0821328	+	0.204395i
$341$	1.64974	+	38.8361i	0.0893384	+	2.10309i
$342$	1.07150	+	0.183728i	0.0579403	+	0.00993486i
$343$	−1.39378	+	3.46856i	−0.0752571	+	0.187285i
$344$	24.4679	+	2.08252i	1.31922	+	0.112282i
$345$	−3.58944	−	4.07840i	−0.193249	−	0.219574i
$346$	−0.877205	−	4.07025i	−0.0471588	−	0.218818i
$347$	11.1847	−	10.7196i	0.600424	−	0.575460i	−0.329066	−	0.944307i	$-0.606734\pi$
$347$	11.1847	−	10.7196i	0.600424	−	0.575460i	0.929490	+	0.368847i	$0.120247\pi$
$348$	1.17902	−	0.100350i	0.0632023	−	0.00537931i
$349$	−13.7796	+	22.3795i	−0.737605	+	1.19795i	0.236452	+	0.971643i	$0.424015\pi$
$349$	−13.7796	+	22.3795i	−0.737605	+	1.19795i	−0.974057	+	0.226303i	$0.927336\pi$
$350$	−0.726417	−	0.189144i	−0.0388286	−	0.0101102i
$351$	0.265841	+	0.254788i	0.0141896	+	0.0135996i
$352$	−24.2052	+	2.06016i	−1.29014	+	0.109807i
$353$	−4.95687	+	16.1859i	−0.263828	+	0.861487i	0.721734	+	0.692170i	$0.243345\pi$
$353$	−4.95687	+	16.1859i	−0.263828	+	0.861487i	−0.985562	+	0.169317i	$0.945844\pi$
$354$	−7.16109	−	2.53018i	−0.380608	−	0.134477i
$355$	9.23867	−	2.40556i	0.490337	−	0.127674i
$356$	−2.84638	−	22.2278i	−0.150858	−	1.17807i
$357$	−0.388514	+	0.630987i	−0.0205623	+	0.0333954i
$358$	8.24534	+	5.57288i	0.435780	+	0.294536i
$359$	14.1673	+	9.57541i	0.747720	+	0.505371i	0.873582	−	0.486677i	$-0.161791\pi$
$359$	14.1673	+	9.57541i	0.747720	+	0.505371i	−0.125862	+	0.992048i	$0.540170\pi$
$360$	1.68317	+	1.61319i	0.0887108	+	0.0850224i
$361$	−14.3981	+	8.04329i	−0.757797	+	0.423331i
$362$	12.3178	−	2.11210i	0.647411	−	0.111010i
$363$	−2.93939	+	5.82994i	−0.154278	+	0.305993i
$364$	−0.0898340	+	0.121464i	−0.00470858	+	0.00636642i
$365$	0.594580	+	13.9969i	0.0311217	+	0.732630i
$366$	−5.07029	+	1.79145i	−0.265029	+	0.0936405i
$367$	3.25663	−	2.20110i	0.169995	−	0.114896i	−0.472023	−	0.881586i	$-0.656476\pi$
$367$	3.25663	−	2.20110i	0.169995	−	0.114896i	0.642018	+	0.766690i	$0.278098\pi$
$368$	7.42115	−	2.62206i	0.386854	−	0.136684i
$369$	1.72015	+	0.294949i	0.0895472	+	0.0153544i
$370$	−3.30705	+	4.47143i	−0.171925	+	0.232459i
$371$	1.71697	+	1.95085i	0.0891405	+	0.101283i
$372$	5.29182	+	13.1692i	0.274368	+	0.682791i
$373$	7.17587	+	4.00868i	0.371552	+	0.207562i	0.662301	−	0.749238i	$-0.269580\pi$
$373$	7.17587	+	4.00868i	0.371552	+	0.207562i	−0.290749	+	0.956799i	$0.593904\pi$
$374$	7.67983	−	1.99967i	0.397114	−	0.103401i
$375$	−2.55705	+	8.34966i	−0.132046	+	0.431174i
$376$	−10.7990	+	10.3500i	−0.556917	+	0.533762i
$377$	−0.280928	+	0.0481700i	−0.0144685	+	0.00248088i
$378$	0.109566	+	0.148143i	0.00563547	+	0.00761966i
$379$	−5.33538	+	4.30802i	−0.274060	+	0.221288i	−0.755430	−	0.655230i	$-0.772572\pi$
$379$	−5.33538	+	4.30802i	−0.274060	+	0.221288i	0.481370	+	0.876518i	$0.340139\pi$
$380$	2.32122	+	0.197565i	0.119076	+	0.0101349i
$381$	−5.59861	+	7.56983i	−0.286826	+	0.387814i
$382$	1.37013	+	2.71748i	0.0701018	+	0.139039i
$383$	16.9477	−	13.6843i	0.865988	−	0.699236i	−0.0889521	−	0.996036i	$-0.528352\pi$
$383$	16.9477	−	13.6843i	0.865988	−	0.699236i	0.954940	+	0.296800i	$0.0959194\pi$
$384$	−9.82674	+	4.44196i	−0.501469	+	0.226678i
$385$	0.403209	+	1.00342i	0.0205494	+	0.0511392i
$386$	−5.50007	+	6.24929i	−0.279946	+	0.318080i
$387$	2.96822	−	9.69225i	0.150883	−	0.492685i
$388$	0.897559	+	7.00917i	0.0455667	+	0.355837i
$389$	−3.06347	+	23.9231i	−0.155324	+	1.21295i	0.707230	+	0.706984i	$0.249945\pi$
$389$	−3.06347	+	23.9231i	−0.155324	+	1.21295i	−0.862554	+	0.505965i	$0.831136\pi$
$390$	−0.189285	−	0.152837i	−0.00958483	−	0.00773921i
$391$	−13.6073	+	7.60150i	−0.688151	+	0.384424i
$392$	12.1168	−	11.6130i	0.611993	−	0.586548i
$393$	5.28482	−	6.00472i	0.266584	−	0.302898i
$394$	9.92073	+	5.54205i	0.499799	+	0.279204i
$395$	−5.89776	−	2.66596i	−0.296749	−	0.134139i
$396$	−0.812939	+	6.34836i	−0.0408517	+	0.319017i
$397$	13.0314	+	3.39311i	0.654026	+	0.170295i	0.564169	−	0.825659i	$-0.309197\pi$
$397$	13.0314	+	3.39311i	0.654026	+	0.170295i	0.0898574	+	0.995955i	$0.471359\pi$
$398$	10.3273	+	6.98005i	0.517662	+	0.349878i
$399$	0.411288	+	0.107091i	0.0205901	+	0.00536125i
$400$	−4.41899	−	3.56809i	−0.220950	−	0.178404i
$401$	5.89396	−	27.3481i	0.294330	−	1.36570i	−0.552357	−	0.833607i	$-0.686272\pi$
$401$	5.89396	−	27.3481i	0.294330	−	1.36570i	0.846688	−	0.532090i	$-0.178593\pi$
$402$	4.75906	+	6.43467i	0.237360	+	0.320932i
$403$	−1.53911	−	3.05264i	−0.0766685	−	0.152063i
$404$	−14.0730	−	2.41306i	−0.700158	−	0.120054i
$405$	0.797337	−	0.538906i	0.0396200	−	0.0267784i
$406$	−0.142627			−0.00707847
$407$	−35.2424			−1.74690
$408$	5.54148	−	3.74539i	0.274344	−	0.185424i
$409$	1.31909	+	31.0525i	0.0652249	+	1.53545i	0.671987	+	0.740563i	$0.265441\pi$
$409$	1.31909	+	31.0525i	0.0652249	+	1.53545i	−0.606762	+	0.794883i	$0.707532\pi$
$410$	−1.14894	−	0.0977889i	−0.0567419	−	0.00482945i
$411$	−2.21898	+	1.00304i	−0.109454	+	0.0494763i
$412$	−5.13848	−	16.7789i	−0.253155	−	0.826637i
$413$	−2.70555	−	1.22299i	−0.133131	−	0.0601792i
$414$	0.492290	+	3.84437i	0.0241948	+	0.188940i
$415$	−16.1084	+	1.37103i	−0.790730	+	0.0673010i
$416$	1.86522	−	1.04197i	0.0914499	−	0.0510870i
$417$	−1.89174	+	8.77772i	−0.0926391	+	0.429847i
$418$	−2.38644	−	3.87583i	−0.116725	−	0.189573i
$419$	−2.18377	+	0.987127i	−0.106684	+	0.0482243i	−0.464537	−	0.885554i	$-0.653779\pi$
$419$	−2.18377	+	0.987127i	−0.106684	+	0.0482243i	0.357853	+	0.933778i	$0.383509\pi$
$420$	0.260863	+	0.296397i	0.0127288	+	0.0144627i
$421$	12.3531	−	24.5010i	0.602055	−	1.19410i	−0.362935	−	0.931815i	$-0.618225\pi$
$421$	12.3531	−	24.5010i	0.602055	−	1.19410i	0.964989	−	0.262289i	$-0.0844775\pi$
$422$	3.27808	+	4.43226i	0.159574	+	0.215759i
$423$	3.23733	+	5.25775i	0.157404	+	0.255641i
$424$	−6.86889	−	22.4293i	−0.333583	−	1.08926i
$425$	9.81929	+	5.48539i	0.476306	+	0.266080i
$426$	−6.42135	−	2.26881i	−0.311115	−	0.109924i
$427$	−2.03441	+	0.529718i	−0.0984518	+	0.0256348i
$428$	17.5717	+	7.94289i	0.849358	+	0.383934i
$429$	0.0654302	−	1.54028i	0.00315900	−	0.0743653i
$430$	−1.41097	+	6.54693i	−0.0680431	+	0.315721i
$431$	20.2264	−	3.46816i	0.974269	−	0.167055i	0.340218	−	0.940347i	$-0.389499\pi$
$431$	20.2264	−	3.46816i	0.974269	−	0.167055i	0.634051	+	0.773291i	$0.281391\pi$
$432$	0.293726	+	1.36289i	0.0141319	+	0.0655722i
$433$	−11.6323	−	28.9482i	−0.559015	−	1.39116i	−0.893629	−	0.448806i	$-0.851849\pi$
$433$	−11.6323	−	28.9482i	−0.559015	−	1.39116i	0.334615	−	0.942355i	$-0.391394\pi$
$434$	−0.500934	−	1.63572i	−0.0240456	−	0.0785171i
$435$	−0.0316160	+	0.744266i	−0.00151587	+	0.0356848i
$436$	15.9552	+	12.8829i	0.764114	+	0.616979i
$437$	6.45403	+	6.18568i	0.308738	+	0.295901i
$438$	5.23993	−	8.51019i	0.250374	−	0.406633i
$439$	−2.95436	+	23.0710i	−0.141004	+	1.10112i	0.754574	+	0.656214i	$0.227843\pi$
$439$	−2.95436	+	23.0710i	−0.141004	+	1.10112i	−0.895578	+	0.444904i	$0.853238\pi$
$440$	0.414270	−	9.75224i	0.0197495	−	0.464920i
$441$	−3.63238	−	5.89937i	−0.172971	−	0.280922i
$442$	−0.543036	+	0.438471i	−0.0258296	+	0.0208559i
$443$	10.2949	−	25.6197i	0.489123	−	1.21723i	−0.455842	−	0.890061i	$-0.650662\pi$
$443$	10.2949	−	25.6197i	0.489123	−	1.21723i	0.944966	−	0.327170i	$-0.106095\pi$
$444$	−12.1327	+	4.28674i	−0.575791	+	0.203440i
$445$	14.1077			0.668771
$446$	−10.1475	+	1.46107i	−0.480497	+	0.0691835i
$447$	6.17234			0.291941
$448$	0.302422	−	0.106852i	0.0142881	−	0.00504831i
$449$	8.81925	−	21.9475i	0.416206	−	1.03577i	−0.561815	−	0.827263i	$-0.689897\pi$
$449$	8.81925	−	21.9475i	0.416206	−	1.03577i	0.978021	−	0.208506i	$-0.0668600\pi$
$450$	2.17603	−	1.75702i	0.102579	−	0.0828267i
$451$	−3.83109	−	6.22209i	−0.180399	−	0.292987i
$452$	0.929184	−	21.8737i	0.0437052	−	1.02885i
$453$	−0.458810	+	3.58291i	−0.0215568	+	0.168340i
$454$	7.19177	−	11.6802i	0.337527	−	0.548178i
$455$	−0.0686645	−	0.0658096i	−0.00321904	−	0.00308520i
$456$	−2.98467	−	2.40996i	−0.139770	−	0.112857i
$457$	0.200787	−	4.72667i	0.00939240	−	0.221104i	−0.988268	−	0.152733i	$-0.951193\pi$
$457$	0.200787	−	4.72667i	0.00939240	−	0.221104i	0.997660	−	0.0683716i	$-0.0217803\pi$
$458$	−2.99761	−	9.78823i	−0.140069	−	0.457374i
$459$	−1.02943	−	2.56184i	−0.0480497	−	0.119576i
$460$	1.74975	+	8.11886i	0.0815825	+	0.378544i
$461$	−22.3829	+	3.83793i	−1.04247	+	0.178750i	−0.664671	−	0.747136i	$-0.731428\pi$
$461$	−22.3829	+	3.83793i	−1.04247	+	0.178750i	−0.377803	+	0.925886i	$0.623320\pi$
$462$	0.162528	−	0.754131i	0.00756147	−	0.0350854i
$463$	−0.272702	+	6.41961i	−0.0126735	+	0.298345i	0.981563	+	0.191138i	$0.0612177\pi$
$463$	−0.272702	+	6.41961i	−0.0126735	+	0.298345i	−0.994237	+	0.107207i	$0.965809\pi$
$464$	−0.983384	−	0.444518i	−0.0456525	−	0.0206362i
$465$	−8.64666	+	2.25141i	−0.400979	+	0.104407i
$466$	−11.7671	−	4.15758i	−0.545100	−	0.192596i
$467$	7.89620	+	4.41108i	0.365393	+	0.204121i	0.659593	−	0.751623i	$-0.270729\pi$
$467$	7.89620	+	4.41108i	0.365393	+	0.204121i	−0.294200	+	0.955744i	$0.595053\pi$
$468$	−0.164828	−	0.538220i	−0.00761918	−	0.0248792i
$469$	1.64044	+	2.66425i	0.0757487	+	0.123024i
$470$	−2.42580	−	3.27990i	−0.111894	−	0.151291i
$471$	1.94159	−	3.85092i	0.0894638	−	0.177441i
$472$	17.7061	+	20.1181i	0.814990	+	0.926008i
$473$	−38.6721	+	17.4809i	−1.77814	+	0.803771i
$474$	2.42082	+	3.93167i	0.111192	+	0.180587i
$475$	1.35910	−	6.30622i	0.0623596	−	0.289349i
$476$	0.988910	−	0.552438i	0.0453266	−	0.0253210i
$477$	−9.64809	+	0.821173i	−0.441756	+	0.0375990i
$478$	−0.867758	−	6.77645i	−0.0396903	−	0.309948i
$479$	−19.0105	−	8.59330i	−0.868613	−	0.392638i	−0.0721992	−	0.997390i	$-0.523002\pi$
$479$	−19.0105	−	8.59330i	−0.868613	−	0.392638i	−0.796413	+	0.604753i	$0.793272\pi$
$480$	−1.63511	−	5.33918i	−0.0746320	−	0.243699i
$481$	2.82440	−	1.27671i	0.128781	−	0.0582128i
$482$	4.30485	+	0.366396i	0.196080	+	0.0166889i
$483$	0.0643055	+	1.51380i	0.00292600	+	0.0688804i
$484$	8.26915	−	5.58897i	0.375870	−	0.254044i
$485$	−4.44865			−0.202003
$486$	−0.686533			−0.0311418
$487$	5.40629	−	3.65401i	0.244982	−	0.165579i	−0.431330	−	0.902194i	$-0.641955\pi$
$487$	5.40629	−	3.65401i	0.244982	−	0.165579i	0.676312	+	0.736615i	$0.263577\pi$
$488$	18.7024	+	3.20685i	0.846617	+	0.145167i
$489$	−6.24071	−	12.3777i	−0.282214	−	0.559739i
$490$	2.72183	+	3.68015i	0.122960	+	0.166252i
$491$	4.04091	−	18.7499i	0.182364	−	0.846171i	−0.790074	−	0.613011i	$-0.789958\pi$
$491$	4.04091	−	18.7499i	0.182364	−	0.846171i	0.972438	−	0.233160i	$-0.0749067\pi$
$492$	−2.07573	−	1.67604i	−0.0935813	−	0.0755616i
$493$	2.06817	+	0.538510i	0.0931458	+	0.0242533i
$494$	0.331662	+	0.224164i	0.0149222	+	0.0100856i
$495$	−3.89923	−	1.01528i	−0.175257	−	0.0456334i
$496$	1.64412	−	12.8392i	0.0738232	−	0.576496i
$497$	−2.42606	−	1.09665i	−0.108824	−	0.0491915i
$498$	10.0683	+	5.62451i	0.451173	+	0.252041i
$499$	2.99660	−	3.40480i	0.134146	−	0.152420i	−0.679721	−	0.733471i	$-0.737899\pi$
$499$	2.99660	−	3.40480i	0.134146	−	0.152420i	0.813867	+	0.581051i	$0.197358\pi$
$500$	9.63741	−	9.23671i	0.430998	−	0.413078i
$501$	0.784493	−	0.438244i	0.0350485	−	0.0195793i
$502$	7.35357	+	5.93759i	0.328206	+	0.265008i
$503$	4.79952	−	37.4802i	0.214000	−	1.67116i	−0.427485	−	0.904023i	$-0.640600\pi$
$503$	4.79952	−	37.4802i	0.214000	−	1.67116i	0.641485	−	0.767136i	$-0.278319\pi$
$504$	−0.0825853	−	0.644920i	−0.00367864	−	0.0287270i
$505$	2.63217	−	8.59493i	0.117130	−	0.382469i
$506$	10.7207	−	12.1811i	0.476593	−	0.541515i
$507$	−4.79658	−	11.9367i	−0.213024	−	0.530130i
$508$	13.1151	−	5.92842i	0.581891	−	0.263031i
$509$	−10.7479	+	8.67834i	−0.476393	+	0.384661i	−0.836251	−	0.548346i	$-0.815258\pi$
$509$	−10.7479	+	8.67834i	−0.476393	+	0.384661i	0.359858	+	0.933007i	$0.382825\pi$
$510$	0.821240	+	1.62883i	0.0363651	+	0.0721259i
$511$	2.32323	−	3.14122i	0.102774	−	0.138959i
$512$	14.7909	+	1.25889i	0.653672	+	0.0556357i
$513$	−1.23204	+	0.994802i	−0.0543958	+	0.0439216i
$514$	−7.78245	−	10.5226i	−0.343269	−	0.464130i
$515$	10.8885	−	1.86702i	0.479803	−	0.0822706i
$516$	−11.1871	+	10.7219i	−0.492483	+	0.472007i
$517$	7.56980	−	24.7180i	0.332920	−	1.08710i
$518$	1.50096	−	0.390819i	0.0659483	−	0.0171716i
$519$	5.29467	+	2.95778i	0.232410	+	0.129832i
$520$	0.320089	+	0.796571i	0.0140368	+	0.0349320i
$521$	−12.8795	−	14.6340i	−0.564262	−	0.641126i	0.396653	−	0.917968i	$-0.370171\pi$
$521$	−12.8795	−	14.6340i	−0.564262	−	0.641126i	−0.960915	+	0.276842i	$0.910712\pi$
$522$	0.315999	−	0.427259i	0.0138309	−	0.0187006i
$523$	−5.54850	−	0.951386i	−0.242619	−	0.0416012i	0.0464063	−	0.998923i	$-0.485223\pi$
$523$	−5.54850	−	0.951386i	−0.242619	−	0.0416012i	−0.289025	+	0.957321i	$0.593331\pi$
$524$	−11.5295	+	4.07365i	−0.503670	+	0.177958i
$525$	0.905871	−	0.612262i	0.0395355	−	0.0267213i
$526$	−16.8137	+	5.94067i	−0.733114	+	0.259025i
$527$	1.08791	+	25.6102i	0.0473900	+	1.11560i
$528$	3.47095	−	4.69303i	0.151054	−	0.204238i
$529$	−3.99359	+	7.92082i	−0.173634	+	0.344383i
$530$	6.30554	−	1.08119i	0.273895	−	0.0469640i
$531$	9.65793	−	5.39524i	0.419118	−	0.234134i
$532$	−0.469046	−	0.449544i	−0.0203357	−	0.0194902i
$533$	0.532436	+	0.359864i	0.0230623	+	0.0155874i
$534$	−8.33820	−	5.63564i	−0.360829	−	0.243878i
$535$	−6.36504	+	10.3375i	−0.275185	+	0.446928i
$536$	−3.58714	−	28.0125i	−0.154941	−	1.20995i
$537$	−14.0283	+	3.65269i	−0.605366	+	0.157625i
$538$	−4.86362	−	1.71843i	−0.209686	−	0.0740866i
$539$	−8.49356	+	27.7344i	−0.365843	+	1.19460i
$540$	−1.46586	+	0.124763i	−0.0630804	+	0.00536893i
$541$	−20.6739	−	19.8143i	−0.888839	−	0.851883i	0.100881	−	0.994898i	$-0.467834\pi$
$541$	−20.6739	−	19.8143i	−0.888839	−	0.851883i	−0.989720	+	0.143015i	$0.954320\pi$
$542$	−16.7916	−	4.37220i	−0.721261	−	0.187802i
$543$	−9.54445	+	15.5012i	−0.409592	+	0.665219i
$544$	−15.9619	+	1.35856i	−0.684361	+	0.0582477i
$545$	−9.32057	+	8.93304i	−0.399249	+	0.382650i
$546$	0.0142942	+	0.0663254i	0.000611736	+	0.00283846i
$547$	−11.3240	−	12.8666i	−0.484180	−	0.550136i	0.456370	−	0.889790i	$-0.349149\pi$
$547$	−11.3240	−	12.8666i	−0.484180	−	0.550136i	−0.940550	+	0.339654i	$0.889690\pi$
$548$	3.70913	+	0.315694i	0.158446	+	0.0134858i
$549$	2.92051	−	7.26796i	0.124644	−	0.310189i
$550$	−11.5412	−	1.97894i	−0.492119	−	0.0843823i
$551$	−0.0520221	−	1.22464i	−0.00221622	−	0.0521715i
$552$	5.09929	−	12.6901i	0.217040	−	0.540125i
$553$	0.812625	+	1.61175i	0.0345563	+	0.0685384i
$554$	6.80932	−	13.5055i	0.289300	−	0.573792i
$555$	−1.70668	−	7.91903i	−0.0724446	−	0.336144i
$556$	9.06865	−	10.3040i	0.384596	−	0.436986i
$557$	−35.4853	−	12.5378i	−1.50356	−	0.531242i	−0.550715	−	0.834693i	$-0.685645\pi$
$557$	−35.4853	−	12.5378i	−1.50356	−	0.531242i	−0.952847	+	0.303451i	$0.901861\pi$
$558$	6.00987	+	2.12342i	0.254418	+	0.0898916i
$559$	2.46599	−	2.80190i	0.104300	−	0.118508i
$560$	−0.0758668	−	0.352023i	−0.00320596	−	0.0148757i
$561$	−5.20408	+	10.3217i	−0.219716	+	0.435781i
$562$	−4.10947	−	8.15065i	−0.173348	−	0.343815i
$563$	5.78585	−	14.3986i	0.243844	−	0.606830i	−0.754957	−	0.655774i	$-0.772342\pi$
$563$	5.78585	−	14.3986i	0.243844	−	0.606830i	0.998802	+	0.0489441i	$0.0155856\pi$
$564$	−0.400593	−	9.43026i	−0.0168680	−	0.397086i
$565$	13.5848	+	2.32934i	0.571515	+	0.0979960i
$566$	−0.367541	+	0.914662i	−0.0154489	+	0.0384461i
$567$	−0.267423	−	0.0227610i	−0.0112307	−	0.000955873i
$568$	15.8771	+	18.0398i	0.666187	+	0.756935i
$569$	−1.66794	−	7.73925i	−0.0699235	−	0.324446i	0.929039	−	0.369981i	$-0.120636\pi$
$569$	−1.66794	−	7.73925i	−0.0699235	−	0.324446i	−0.998963	+	0.0455349i	$0.985501\pi$
$570$	0.755337	−	0.723932i	0.0316376	−	0.0303222i
$571$	31.4393	−	2.67588i	1.31569	−	0.111982i	0.594151	−	0.804353i	$-0.297488\pi$
$571$	31.4393	−	2.67588i	1.31569	−	0.111982i	0.721541	+	0.692372i	$0.243434\pi$
$572$	−1.23564	+	2.00680i	−0.0516646	+	0.0839086i
$573$	−4.28989	−	1.11700i	−0.179213	−	0.0466633i
$574$	0.232164	+	0.222511i	0.00969035	+	0.00928744i
$575$	22.9156	−	1.95041i	0.955647	−	0.0813375i
$576$	−0.349943	+	1.14268i	−0.0145810	+	0.0476119i
$577$	−23.1629	−	8.18398i	−0.964286	−	0.340704i	−0.195852	−	0.980633i	$-0.562747\pi$
$577$	−23.1629	−	8.18398i	−0.964286	−	0.340704i	−0.768433	+	0.639930i	$0.778963\pi$
$578$	−6.23007	+	1.62218i	−0.259137	+	0.0674739i
$579$	−1.54022	−	12.0278i	−0.0640095	−	0.499859i
$580$	0.597063	−	0.969692i	0.0247917	−	0.0402643i
$581$	3.73541	+	2.52470i	0.154971	+	0.104742i
$582$	2.62932	+	1.77711i	0.108989	+	0.0736635i
$583$	29.2684	+	28.0515i	1.21217	+	1.16177i
$584$	−30.7874	+	17.1989i	−1.27399	+	0.711694i
$585$	0.349272	−	0.0598887i	0.0144406	−	0.00247609i
$586$	−10.1464	+	20.1242i	−0.419144	+	0.831322i
$587$	5.84180	−	7.89864i	0.241117	−	0.326012i	−0.666741	−	0.745289i	$-0.732311\pi$
$587$	5.84180	−	7.89864i	0.241117	−	0.326012i	0.907858	+	0.419278i	$0.137717\pi$
$588$	0.449478	+	10.5811i	0.0185361	+	0.436355i
$589$	13.8621	−	4.89778i	0.571177	−	0.201810i
$590$	−6.05572	+	4.09295i	−0.249310	+	0.168504i
$591$	−15.6069	+	5.51426i	−0.641981	+	0.226826i
$592$	11.5668	+	1.98333i	0.475394	+	0.0815145i
$593$	0.659703	−	0.891977i	0.0270908	−	0.0366291i	−0.790243	−	0.612793i	$-0.790046\pi$
$593$	0.659703	−	0.891977i	0.0270908	−	0.0366291i	0.817334	+	0.576164i	$0.195451\pi$
$594$	1.89901	+	2.15770i	0.0779175	+	0.0885314i
$595$	0.265893	+	0.661700i	0.0109005	+	0.0271271i
$596$	−8.23731	−	4.60164i	−0.337413	−	0.188490i
$597$	−17.5705	+	4.57500i	−0.719113	+	0.187242i
$598$	−0.417901	+	1.36459i	−0.0170892	+	0.0558022i
$599$	9.44657	−	9.05380i	0.385976	−	0.369928i	−0.473771	−	0.880648i	$-0.657108\pi$
$599$	9.44657	−	9.05380i	0.385976	−	0.369928i	0.859747	+	0.510720i	$0.170621\pi$
$600$	−9.72711	+	1.66788i	−0.397108	+	0.0680909i
$601$	18.4474	+	24.9426i	0.752486	+	1.01743i	0.998835	+	0.0482475i	$0.0153636\pi$
$601$	18.4474	+	24.9426i	0.752486	+	1.01743i	−0.246349	+	0.969181i	$0.579231\pi$
$602$	1.45317	−	1.17336i	0.0592269	−	0.0478224i
$603$	−11.6156	−	0.988636i	−0.473025	−	0.0402604i
$604$	3.28346	−	4.43953i	0.133602	−	0.180642i
$605$	2.82880	+	5.61059i	0.115007	+	0.228103i
$606$	−4.98914	+	4.02845i	−0.202670	+	0.163644i
$607$	−4.23213	+	1.91304i	−0.171777	+	0.0776480i	−0.495956	−	0.868348i	$-0.665182\pi$
$607$	−4.23213	+	1.91304i	−0.171777	+	0.0776480i	0.324179	+	0.945996i	$0.394912\pi$
$608$	3.42581	+	8.52545i	0.138935	+	0.345753i
$609$	0.137255	−	0.155952i	0.00556186	−	0.00631950i
$610$	−1.51540	+	4.94830i	−0.0613567	+	0.200351i
$611$	0.288787	+	2.25518i	0.0116831	+	0.0912347i
$612$	−0.536086	+	4.18638i	−0.0216700	+	0.169224i
$613$	−27.2239	−	21.9818i	−1.09956	−	0.887837i	−0.105264	−	0.994444i	$-0.533569\pi$
$613$	−27.2239	−	21.9818i	−1.09956	−	0.887837i	−0.994301	+	0.106608i	$0.966001\pi$
$614$	−6.26574	+	3.50026i	−0.252865	+	0.141259i
$615$	1.21259	−	1.16217i	0.0488962	−	0.0468632i
$616$	−1.79848	+	2.04347i	−0.0724627	+	0.0823336i
$617$	13.8566	+	7.74075i	0.557845	+	0.311631i	0.741057	−	0.671443i	$-0.234325\pi$
$617$	13.8566	+	7.74075i	0.557845	+	0.311631i	−0.183212	+	0.983074i	$0.558649\pi$
$618$	−7.18131	−	3.24616i	−0.288875	−	0.130580i
$619$	−0.161516	+	1.26130i	−0.00649189	+	0.0506961i	−0.994822	−	0.101628i	$-0.967595\pi$
$619$	−0.161516	+	1.26130i	−0.00649189	+	0.0506961i	0.988331	+	0.152324i	$0.0486758\pi$
$620$	13.2179	+	3.44168i	0.530844	+	0.138221i
$621$	−4.67728	−	3.16129i	−0.187693	−	0.126858i
$622$	7.32071	+	1.90617i	0.293534	+	0.0764303i
$623$	−3.06110	−	2.47167i	−0.122641	−	0.0990253i
$624$	−0.108157	+	0.501849i	−0.00432974	+	0.0200901i
$625$	−7.11497	−	9.62007i	−0.284599	−	0.384803i
$626$	−7.08410	−	14.0505i	−0.283138	−	0.561570i
$627$	6.53448	+	1.12045i	0.260962	+	0.0447465i
$628$	−5.46211	+	3.69174i	−0.217962	+	0.147317i
$629$	−23.2403			−0.926652
$630$	0.177325			0.00706481
$631$	−21.5832	+	14.5877i	−0.859214	+	0.580727i	−0.908419	−	0.418062i	$-0.862710\pi$
$631$	−21.5832	+	14.5877i	−0.859214	+	0.580727i	0.0492049	+	0.998789i	$0.484331\pi$
$632$	−0.691475	−	16.2779i	−0.0275054	−	0.647498i
$633$	−8.00095	−	0.680981i	−0.318009	−	0.0270666i
$634$	9.57124	−	4.32648i	0.380123	−	0.171826i
$635$	2.65326	+	8.66382i	0.105292	+	0.343813i
$636$	13.4881	+	6.09700i	0.534838	+	0.241762i
$637$	−0.324028	−	2.53038i	−0.0128384	−	0.100257i
$638$	−2.21691	+	0.188687i	−0.0877684	+	0.00747019i
$639$	8.66026	−	4.83791i	0.342595	−	0.191385i
$640$	−2.18649	+	10.1454i	−0.0864287	+	0.401031i
$641$	−7.54996	−	12.2619i	−0.298206	−	0.484317i	0.667268	−	0.744818i	$-0.267464\pi$
$641$	−7.54996	−	12.2619i	−0.298206	−	0.484317i	−0.965474	+	0.260501i	$0.916112\pi$
$642$	7.89150	−	3.56718i	0.311453	−	0.140785i
$643$	4.47809	+	5.08810i	0.176599	+	0.200655i	0.832237	−	0.554420i	$-0.187060\pi$
$643$	4.47809	+	5.08810i	0.176599	+	0.200655i	−0.655638	+	0.755075i	$0.727600\pi$
$644$	1.04276	−	2.06819i	0.0410905	−	0.0814981i
$645$	−5.80075	−	7.84314i	−0.228404	−	0.308823i
$646$	−1.57372	−	2.55588i	−0.0619172	−	0.100560i
$647$	11.4486	+	37.3836i	0.450091	+	1.46970i	0.836805	+	0.547502i	$0.184421\pi$
$647$	11.4486	+	37.3836i	0.450091	+	1.46970i	−0.386714	+	0.922200i	$0.626390\pi$
$648$	2.11492	+	1.18147i	0.0830819	+	0.0464123i
$649$	−43.6714	−	15.4301i	−1.71425	−	0.605684i
$650$	0.996626	−	0.259501i	0.0390909	−	0.0101785i
$651$	2.27060	+	1.02638i	0.0889919	+	0.0402269i
$652$	−0.899346	+	21.1713i	−0.0352211	+	0.829132i
$653$	0.541040	−	2.51044i	0.0211725	−	0.0982409i	−0.965734	−	0.259534i	$-0.916431\pi$
$653$	0.541040	−	2.51044i	0.0211725	−	0.0982409i	0.986907	+	0.161293i	$0.0515663\pi$
$654$	9.07730	−	1.55646i	0.354950	−	0.0608624i
$655$	−1.62184	−	7.52537i	−0.0633706	−	0.294040i
$656$	0.907235	+	2.25774i	0.0354216	+	0.0881500i
$657$	4.26269	+	13.9191i	0.166303	+	0.543037i
$658$	−0.0482853	+	1.13667i	−0.00188236	+	0.0443122i
$659$	−13.1315	−	10.6030i	−0.511531	−	0.413033i	0.337540	−	0.941311i	$-0.390405\pi$
$659$	−13.1315	−	10.6030i	−0.511531	−	0.413033i	−0.849071	+	0.528279i	$0.822838\pi$
$660$	4.44681	+	4.26192i	0.173092	+	0.165895i
$661$	−19.1711	+	31.1359i	−0.745671	+	1.21105i	0.225867	+	0.974158i	$0.427479\pi$
$661$	−19.1711	+	31.1359i	−0.745671	+	1.21105i	−0.971537	+	0.236888i	$0.923873\pi$
$662$	−2.01501	+	15.7355i	−0.0783154	+	0.611577i
$663$	0.0431474	−	1.01572i	0.00167571	−	0.0394475i
$664$	−21.3370	−	34.6535i	−0.828038	−	1.34482i
$665$	0.318225	−	0.256948i	0.0123402	−	0.00996403i
$666$	−2.15471	+	5.36221i	−0.0834934	+	0.207781i
$667$	4.12028	−	1.45579i	0.159538	−	0.0563683i
$668$	−1.37367			−0.0531489
$669$	8.16771	−	12.5015i	0.315782	−	0.483338i
$670$	7.70222			0.297563
$671$	−30.9208	+	10.9250i	−1.19368	+	0.421756i
$672$	−0.580636	+	1.44497i	−0.0223985	+	0.0557408i
$673$	28.5891	−	23.0841i	1.10203	−	0.889827i	0.107492	−	0.994206i	$-0.465718\pi$
$673$	28.5891	−	23.0841i	1.10203	−	0.889827i	0.994538	+	0.104379i	$0.0332855\pi$
$674$	6.58116	+	10.6885i	0.253497	+	0.411705i
$675$	−0.172898	+	4.07016i	−0.00665486	+	0.156661i
$676$	−2.49787	+	19.5062i	−0.0960717	+	0.750238i
$677$	6.50951	−	10.5721i	0.250181	−	0.406319i	−0.701849	−	0.712326i	$-0.747642\pi$
$677$	6.50951	−	10.5721i	0.250181	−	0.406319i	0.952029	+	0.306007i	$0.0989931\pi$
$678$	−7.09859	−	6.80345i	−0.272620	−	0.261285i
$679$	0.965270	+	0.779401i	0.0370437	+	0.0299107i
$680$	0.273187	−	6.43104i	0.0104762	−	0.246619i
$681$	5.85051	+	19.1039i	0.224192	+	0.732063i
$682$	−9.95017	−	24.7620i	−0.381012	−	0.948184i
$683$	3.78880	+	17.5801i	0.144975	+	0.672684i	0.990359	+	0.138526i	$0.0442364\pi$
$683$	3.78880	+	17.5801i	0.144975	+	0.672684i	−0.845384	+	0.534159i	$0.820628\pi$
$684$	2.38587	−	0.409099i	0.0912260	−	0.0156423i
$685$	−0.493732	+	2.29092i	−0.0188645	+	0.0875317i
$686$	0.108919	−	2.56403i	0.00415853	−	0.0978951i
$687$	13.5874	+	6.14189i	0.518392	+	0.234328i
$688$	13.6762	−	3.56102i	0.521402	−	0.135763i
$689$	−3.36183	−	1.18781i	−0.128076	−	0.0452520i
$690$	3.25628	+	1.81907i	0.123965	+	0.0692508i
$691$	−5.41531	−	17.6828i	−0.206008	−	0.672687i	−0.998062	−	0.0622350i	$-0.980177\pi$
$691$	−5.41531	−	17.6828i	−0.206008	−	0.672687i	0.792054	−	0.610452i	$-0.209012\pi$
$692$	−4.86092	−	7.89463i	−0.184784	−	0.300109i
$693$	0.668180	+	0.903439i	0.0253821	+	0.0343188i
$694$	−4.78832	+	9.49706i	−0.181762	+	0.360503i
$695$	5.70916	+	6.48687i	0.216561	+	0.246061i
$696$	−1.70874	+	0.772399i	−0.0647696	+	0.0292777i
$697$	−2.52638	−	4.10311i	−0.0956936	−	0.155416i
$698$	3.80131	−	17.6382i	0.143882	−	0.667614i
$699$	15.8699	−	8.86546i	0.600255	−	0.335322i
$700$	−1.66539	+	0.141746i	−0.0629458	+	0.00535748i
$701$	0.0866632	+	0.676766i	0.00327323	+	0.0255611i	0.993455	−	0.114227i	$-0.0364390\pi$
$701$	0.0866632	+	0.676766i	0.00327323	+	0.0255611i	−0.990181	+	0.139788i	$0.955358\pi$
$702$	−0.230356	−	0.104128i	−0.00869425	−	0.00393005i
$703$	3.90316	+	12.7451i	0.147210	+	0.480692i
$704$	4.55931	−	2.06094i	0.171835	−	0.0776745i
$705$	5.92076	+	0.503931i	0.222989	+	0.0189791i
$706$	−0.493232	−	11.6111i	−0.0185630	−	0.436989i
$707$	−2.07696	+	1.40378i	−0.0781120	+	0.0527945i
$708$	−16.9113			−0.635566
$709$	−44.9646			−1.68868			−0.844340	−	0.535808i	$-0.820007\pi$
$709$	−44.9646			−1.68868			−0.844340	+	0.535808i	$0.820007\pi$
$710$	−5.43016	+	3.67015i	−0.203790	+	0.137738i
$711$	−6.62863	−	1.13659i	−0.248593	−	0.0426255i
$712$	15.9880	+	31.7104i	0.599177	+	1.18840i
$713$	31.1669	+	42.1404i	1.16721	+	1.57817i
$714$	0.107178	−	0.497306i	0.00401102	−	0.0186112i
$715$	−1.15434	−	0.932066i	−0.0431699	−	0.0348573i
$716$	21.4447	+	5.58376i	0.801426	+	0.208675i
$717$	8.24461	+	5.57239i	0.307901	+	0.208105i
$718$	−11.3607	−	2.95810i	−0.423978	−	0.110395i
$719$	1.29807	−	10.1368i	0.0484097	−	0.378038i	−0.949519	−	0.313709i	$-0.898428\pi$
$719$	1.29807	−	10.1368i	0.0484097	−	0.378038i	0.997929	−	0.0643289i	$-0.0204907\pi$
$720$	1.22262	+	0.552659i	0.0455644	+	0.0205964i
$721$	−2.68969	−	1.50255i	−0.100169	−	0.0559579i
$722$	7.48056	−	8.49957i	0.278398	−	0.316321i
$723$	−4.54333	+	4.35443i	−0.168968	+	0.161943i
$724$	24.2941	−	13.5715i	0.902883	−	0.504381i
$725$	−2.45346	−	1.98103i	−0.0911192	−	0.0735736i
$726$	0.569344	−	4.44609i	0.0211303	−	0.165010i
$727$	−0.505295	−	3.94592i	−0.0187403	−	0.146346i	0.979828	−	0.199845i	$-0.0640438\pi$
$727$	−0.505295	−	3.94592i	−0.0187403	−	0.146346i	−0.998568	+	0.0534987i	$0.982963\pi$
$728$	0.0701059	−	0.228920i	0.00259830	−	0.00848434i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	−3.58613	−	8.92442i	−0.132729	−	0.330308i
$731$	−25.5020	+	11.5276i	−0.943225	+	0.426365i
$732$	−9.31602	+	7.52216i	−0.344330	+	0.278027i
$733$	−20.4566	−	40.5733i	−0.755583	−	1.49861i	−0.863444	−	0.504444i	$-0.831697\pi$
$733$	−20.4566	−	40.5733i	−0.755583	−	1.49861i	0.107861	−	0.994166i	$-0.465600\pi$
$734$	−1.60465	+	2.16964i	−0.0592289	+	0.0800827i
$735$	−6.64328	−	0.565427i	−0.245041	−	0.0208561i
$736$	−25.4854	+	20.5780i	−0.939405	+	0.758516i
$737$	29.0227	+	39.2413i	1.06907	+	1.44547i
$738$	−1.18094	+	0.202492i	−0.0434709	+	0.00745383i
$739$	18.0217	−	17.2724i	0.662940	−	0.635377i	−0.283228	−	0.959053i	$-0.591405\pi$
$739$	18.0217	−	17.2724i	0.662940	−	0.635377i	0.946168	+	0.323676i	$0.104919\pi$
$740$	−3.62618	+	11.8407i	−0.133301	+	0.435274i
$741$	−0.564277	+	0.146926i	−0.0207292	+	0.00539747i
$742$	−1.55760	−	0.870129i	−0.0571814	−	0.0319434i
$743$	1.93034	+	4.80384i	0.0708173	+	0.176236i	0.959104	−	0.283054i	$-0.0913474\pi$
$743$	1.93034	+	4.80384i	0.0708173	+	0.176236i	−0.888287	+	0.459289i	$0.848104\pi$
$744$	−14.8597	−	16.8839i	−0.544782	−	0.618992i
$745$	3.53218	−	4.77582i	0.129409	−	0.174973i
$746$	−5.56189	−	0.953681i	−0.203635	−	0.0349167i
$747$	−15.8391	+	5.59631i	−0.579523	+	0.204758i
$748$	14.6402	−	9.89504i	0.535298	−	0.361798i
$749$	3.19221	−	1.12788i	0.116641	−	0.0412118i
$750$	−0.254439	−	5.98970i	−0.00929081	−	0.218713i
$751$	−30.3179	+	40.9925i	−1.10632	+	1.49584i	−0.258154	+	0.966104i	$0.583114\pi$
$751$	−30.3179	+	40.9925i	−1.10632	+	1.49584i	−0.848163	+	0.529735i	$0.822291\pi$
$752$	−3.87552	+	7.68664i	−0.141326	+	0.280303i
$753$	−13.5689	+	2.32662i	−0.494478	+	0.0847868i
$754$	0.170832	−	0.0954327i	0.00622135	−	0.00347545i
$755$	2.50971	+	2.40536i	0.0913377	+	0.0875401i
$756$	0.339921	+	0.229746i	0.0123628	+	0.00835579i
$757$	−20.2608	−	13.6939i	−0.736391	−	0.497714i	0.133444	−	0.991056i	$-0.457396\pi$
$757$	−20.2608	−	13.6939i	−0.736391	−	0.497714i	−0.869835	+	0.493343i	$0.835775\pi$
$758$	2.46839	−	4.00892i	0.0896559	−	0.145610i
$759$	3.00220	+	23.4446i	0.108973	+	0.850984i
$760$	−3.57270	+	0.930260i	−0.129596	+	0.0337441i
$761$	4.71113	+	1.66455i	0.170778	+	0.0603398i	0.417160	−	0.908833i	$-0.363025\pi$
$761$	4.71113	+	1.66455i	0.170778	+	0.0603398i	−0.246382	+	0.969173i	$0.579242\pi$
$762$	1.89277	−	6.18054i	0.0685678	−	0.223897i
$763$	3.58745	−	0.305337i	0.129874	−	0.0110539i
$764$	4.89233	+	4.68892i	0.176998	+	0.169639i
$765$	−2.57132	−	0.669518i	−0.0929661	−	0.0242065i
$766$	−7.84077	+	12.7342i	−0.283299	+	0.460106i
$767$	4.05889	−	0.345462i	0.146558	−	0.0124739i
$768$	7.07065	−	6.77667i	0.255140	−	0.244532i
$769$	0.159618	+	0.740631i	0.00575598	+	0.0267078i	0.980342	−	0.197306i	$-0.0632192\pi$
$769$	0.159618	+	0.740631i	0.00575598	+	0.0267078i	−0.974586	+	0.224014i	$0.928084\pi$
$770$	−0.490498	−	0.557314i	−0.0176763	−	0.0200842i
$771$	18.9950	+	1.61671i	0.684087	+	0.0582244i
$772$	−6.91154	+	17.2000i	−0.248752	+	0.619043i
$773$	−33.6032	−	5.76184i	−1.20862	−	0.207239i	−0.470804	−	0.882238i	$-0.656036\pi$
$773$	−33.6032	−	5.76184i	−1.20862	−	0.207239i	−0.737819	+	0.674999i	$0.764144\pi$
$774$	0.295352	+	6.95282i	0.0106162	+	0.249914i
$775$	14.1024	−	35.0952i	0.506574	−	1.26066i
$776$	−5.04157	−	9.99936i	−0.180982	−	0.358956i
$777$	−1.01709	+	2.01728i	−0.0364880	+	0.0723697i
$778$	−3.48845	−	16.1865i	−0.125067	−	0.580313i
$779$	−1.82587	+	2.07459i	−0.0654186	+	0.0743300i
$780$	−0.510770	−	0.180467i	−0.0182885	−	0.00646174i
$781$	−39.1601	−	13.8361i	−1.40126	−	0.495096i
$782$	7.06968	−	8.03272i	0.252811	−	0.287250i
$783$	0.163079	+	0.756688i	0.00582796	+	0.0270418i
$784$	4.34846	−	8.62465i	0.155302	−	0.308023i
$785$	−1.86854	−	3.70602i	−0.0666910	−	0.132274i
$786$	−2.04760	+	5.09565i	−0.0730355	+	0.181756i
$787$	−0.761504	−	17.9264i	−0.0271447	−	0.639007i	−0.960207	−	0.279291i	$-0.909901\pi$
$787$	−0.761504	−	17.9264i	−0.0271447	−	0.639007i	0.933062	−	0.359716i	$-0.117126\pi$
$788$	24.9392	+	4.27626i	0.888423	+	0.152335i
$789$	9.68477	−	24.1015i	0.344787	−	0.858035i
$790$	4.42745	+	0.376832i	0.157522	+	0.0134071i
$791$	−2.53953	−	2.88546i	−0.0902952	−	0.102595i
$792$	−2.13685	−	9.91501i	−0.0759296	−	0.352314i
$793$	2.08228	−	1.99570i	0.0739439	−	0.0708695i
$794$	−9.21147	+	0.784012i	−0.326903	+	0.0278235i
$795$	−4.88583	+	7.93510i	−0.173283	+	0.281429i
$796$	26.8595	+	6.99368i	0.952011	+	0.247884i
$797$	0.745079	+	0.714100i	0.0263920	+	0.0252947i	0.705019	−	0.709188i	$-0.250938\pi$
$797$	0.745079	+	0.714100i	0.0263920	+	0.0252947i	−0.678627	+	0.734483i	$0.737425\pi$
$798$	−0.290726	+	0.0247444i	−0.0102916	+	0.000875944i
$799$	4.99185	−	16.3001i	0.176599	−	0.576656i
$800$	22.2872	+	7.87457i	0.787971	+	0.278408i
$801$	14.1863	−	3.69382i	0.501248	−	0.130515i
$802$	2.43956	+	19.0509i	0.0861438	+	0.672710i
$803$	31.9553	−	51.8988i	1.12768	−	1.83147i
$804$	14.7646	+	9.97914i	0.520708	+	0.351937i
$805$	1.20810	+	0.816532i	0.0425799	+	0.0287790i
$806$	1.69446	+	1.62401i	0.0596850	+	0.0572034i
$807$	6.55940	−	3.66430i	0.230902	−	0.128990i
$808$	22.3021	−	3.82407i	0.784584	−	0.134530i
$809$	8.75013	−	17.3548i	0.307638	−	0.610164i	−0.685372	−	0.728193i	$-0.740360\pi$
$809$	8.75013	−	17.3548i	0.307638	−	0.610164i	0.993010	+	0.118029i	$0.0376577\pi$
$810$	−0.392875	+	0.531202i	−0.0138042	+	0.0186646i
$811$	−0.906169	−	21.3319i	−0.0318199	−	0.749065i	−0.942152	−	0.335186i	$-0.891201\pi$
$811$	−0.906169	−	21.3319i	−0.0318199	−	0.749065i	0.910332	−	0.413879i	$-0.135826\pi$
$812$	−0.299441	+	0.105799i	−0.0105083	+	0.00371282i
$813$	20.9398	−	14.1529i	0.734392	−	0.496362i
$814$	22.8130	−	8.06034i	0.799594	−	0.282515i
$815$	−13.1485	−	2.25454i	−0.460572	−	0.0789730i
$816$	2.28889	−	3.09478i	0.0801272	−	0.108339i
$817$	10.6048	+	12.0494i	0.371016	+	0.421556i
$818$	−7.95593	−	19.7991i	−0.278172	−	0.692259i
$819$	−0.0862777	−	0.0481976i	−0.00301479	−	0.00168416i
$820$	−2.48469	+	0.646962i	−0.0867691	+	0.0225929i
$821$	0.581048	−	1.89732i	0.0202787	−	0.0662169i	−0.945454	−	0.325756i	$-0.894381\pi$
$821$	0.581048	−	1.89732i	0.0202787	−	0.0662169i	0.965733	+	0.259539i	$0.0835705\pi$
$822$	1.20697	−	1.15679i	0.0420980	−	0.0403477i
$823$	19.3541	−	3.31859i	0.674641	−	0.115679i	0.178525	−	0.983935i	$-0.442867\pi$
$823$	19.3541	−	3.31859i	0.674641	−	0.115679i	0.496115	+	0.868257i	$0.334759\pi$
$824$	16.5362	+	22.3585i	0.576067	+	0.778895i
$825$	13.2703	−	10.7150i	0.462014	−	0.373050i
$826$	2.03106	+	0.172868i	0.0706695	+	0.00601486i
$827$	16.3934	−	22.1653i	0.570054	−	0.770764i	−0.420587	−	0.907252i	$-0.638176\pi$
$827$	16.3934	−	22.1653i	0.570054	−	0.770764i	0.990642	+	0.136488i	$0.0435814\pi$
$828$	3.88525	+	7.70593i	0.135022	+	0.267800i
$829$	−21.0208	+	16.9731i	−0.730081	+	0.589499i	−0.919822	−	0.392335i	$-0.871667\pi$
$829$	−21.0208	+	16.9731i	−0.730081	+	0.589499i	0.189741	+	0.981834i	$0.439235\pi$
$830$	10.1137	−	4.57166i	0.351050	−	0.158685i
$831$	8.21438	+	20.4423i	0.284954	+	0.709134i
$832$	−0.290732	+	0.330335i	−0.0100793	+	0.0114523i
$833$	−5.60101	+	18.2892i	−0.194063	+	0.633684i
$834$	−0.783009	−	6.11463i	−0.0271134	−	0.211732i
$835$	0.109844	−	0.857788i	0.00380131	−	0.0296850i
$836$	−7.88529	−	6.36693i	−0.272718	−	0.220205i
$837$	−8.10531	+	4.52790i	−0.280161	+	0.156507i
$838$	1.18782	−	1.13844i	0.0410327	−	0.0393267i
$839$	−13.7882	+	15.6664i	−0.476020	+	0.540864i	−0.938278	−	0.345882i	$-0.887580\pi$
$839$	−13.7882	+	15.6664i	−0.476020	+	0.540864i	0.462258	+	0.886745i	$0.347039\pi$
$840$	−0.546265	−	0.305162i	−0.0188479	−	0.0105291i
$841$	25.8796	+	11.6983i	0.892402	+	0.403391i
$842$	−2.39273	+	18.6852i	−0.0824589	+	0.643934i
$843$	12.8668	+	3.35026i	0.443157	+	0.115389i
$844$	10.1700	+	6.87372i	0.350066	+	0.236603i
$845$	−11.9809	−	3.11958i	−0.412156	−	0.107317i
$846$	−3.29808	−	2.66302i	−0.113390	−	0.0915564i
$847$	0.369178	−	1.71299i	0.0126851	−	0.0588591i
$848$	−8.02746	−	10.8538i	−0.275664	−	0.372723i
$849$	−0.646416	−	1.28209i	−0.0221849	−	0.0440012i
$850$	−7.61076	−	1.30500i	−0.261047	−	0.0447610i
$851$	−39.3713	+	26.6103i	−1.34963	+	0.912190i
$852$	−15.1644			−0.519522
$853$	−4.87683			−0.166980			−0.0834898	−	0.996509i	$-0.526607\pi$
$853$	−4.87683			−0.166980			−0.0834898	+	0.996509i	$0.526607\pi$
$854$	1.19575	−	0.808187i	0.0409178	−	0.0276556i
$855$	0.0646780	+	1.52257i	0.00221194	+	0.0520708i
$856$	−30.4492	−	2.59161i	−1.04073	−	0.0885794i
$857$	1.34890	−	0.609742i	0.0460776	−	0.0208284i	−0.388731	−	0.921351i	$-0.627086\pi$
$857$	1.34890	−	0.609742i	0.0460776	−	0.0208284i	0.434808	+	0.900523i	$0.356816\pi$
$858$	0.309925	+	1.01201i	0.0105807	+	0.0345495i
$859$	2.42585	+	1.09655i	0.0827689	+	0.0374139i	0.452861	−	0.891581i	$-0.350403\pi$
$859$	2.42585	+	1.09655i	0.0827689	+	0.0374139i	−0.370092	+	0.928995i	$0.620674\pi$
$860$	1.89415	+	14.7917i	0.0645900	+	0.504392i
$861$	−0.466719	+	0.0397237i	−0.0159057	+	0.00135378i
$862$	−12.2996	+	6.87099i	−0.418928	+	0.234027i
$863$	8.99754	−	41.7487i	0.306280	−	1.42114i	−0.518204	−	0.855257i	$-0.673399\pi$
$863$	8.99754	−	41.7487i	0.306280	−	1.42114i	0.824484	−	0.565886i	$-0.191466\pi$
$864$	−3.04216	−	4.94079i	−0.103497	−	0.168089i
$865$	5.31850	−	2.40411i	0.180835	−	0.0817424i
$866$	14.1506	+	16.0782i	0.480856	+	0.546359i
$867$	4.22168	−	8.37320i	0.143376	−	0.284369i
$868$	−2.26505	−	3.06255i	−0.0768807	−	0.103950i
$869$	14.7632	+	23.9770i	0.500808	+	0.813363i
$870$	−0.149757	−	0.489007i	−0.00507723	−	0.0165789i
$871$	−3.74752	−	2.09349i	−0.126980	−	0.0709351i
$872$	−30.6419	−	10.8265i	−1.03767	−	0.366630i
$873$	−4.47342	+	1.16479i	−0.151402	+	0.0394221i
$874$	−5.59253	−	2.52799i	−0.189170	−	0.0855104i
$875$	0.0994691	−	2.34158i	0.00336267	−	0.0791598i
$876$	4.68829	−	21.7538i	0.158403	−	0.734991i
$877$	35.0358	−	6.00749i	1.18307	−	0.202858i	0.456358	−	0.889796i	$-0.349154\pi$
$877$	35.0358	−	6.00749i	1.18307	−	0.202858i	0.726716	+	0.686938i	$0.241046\pi$
$878$	−3.36420	−	15.6099i	−0.113536	−	0.526810i
$879$	−12.2400	−	30.4605i	−0.412846	−	1.02741i
$880$	−1.64493	−	5.37127i	−0.0554507	−	0.181066i
$881$	−1.07265	+	25.2510i	−0.0361384	+	0.850726i	0.885958	+	0.463766i	$0.153502\pi$
$881$	−1.07265	+	25.2510i	−0.0361384	+	0.850726i	−0.922096	+	0.386960i	$0.873525\pi$
$882$	3.70055	+	2.98799i	0.124604	+	0.100611i
$883$	42.0312	+	40.2836i	1.41446	+	1.35565i	0.846269	+	0.532755i	$0.178843\pi$
$883$	42.0312	+	40.2836i	1.41446	+	1.35565i	0.568192	+	0.822896i	$0.307643\pi$
$884$	−0.814831	+	1.32337i	−0.0274057	+	0.0445098i
$885$	1.35230	−	10.5603i	0.0454569	−	0.354980i
$886$	−0.804503	+	18.9386i	−0.0270278	+	0.636256i
$887$	−27.1093	−	44.0283i	−0.910241	−	1.47833i	−0.877897	−	0.478849i	$-0.841054\pi$
$887$	−27.1093	−	44.0283i	−0.910241	−	1.47833i	−0.0323436	−	0.999477i	$-0.510297\pi$
$888$	15.8657	−	12.8106i	0.532417	−	0.429897i
$889$	0.942190	−	2.34473i	0.0316000	−	0.0786397i
$890$	−9.13217	+	3.22660i	−0.306111	+	0.108156i
$891$	−4.18677			−0.140262
$892$	−20.2205	+	10.5947i	−0.677031	+	0.354738i
$893$	−9.77745			−0.327190
$894$	−3.99545	+	1.41168i	−0.133628	+	0.0472138i
$895$	−5.20158	+	12.9446i	−0.173870	+	0.432692i
$896$	2.25189	−	1.81827i	0.0752303	−	0.0607442i
$897$	−1.08992	−	1.77014i	−0.0363912	−	0.0591031i
$898$	−0.689190	+	16.2241i	−0.0229986	+	0.541404i
$899$	0.912828	−	7.12840i	0.0304445	−	0.237746i
$900$	3.26515	−	5.30295i	0.108838	−	0.176765i
$901$	19.3008	+	18.4983i	0.643003	+	0.616268i
$902$	3.90299	+	3.15145i	0.129955	+	0.104932i
$903$	−0.115463	+	2.71810i	−0.00384238	+	0.0904526i
$904$	10.1596	+	33.1746i	0.337904	+	1.10337i
$905$	6.53207	+	16.2557i	0.217133	+	0.540357i
$906$	−0.522458	−	2.42421i	−0.0173575	−	0.0805391i
$907$	3.90449	−	0.669493i	0.129647	−	0.0222301i	−0.103812	−	0.994597i	$-0.533104\pi$
$907$	3.90449	−	0.669493i	0.129647	−	0.0222301i	0.233458	+	0.972367i	$0.424996\pi$
$908$	6.43465	−	29.8569i	0.213541	−	0.990835i
$909$	0.396417	−	9.33196i	0.0131483	−	0.309522i
$910$	0.0594990	+	0.0268953i	0.00197237	+	0.000891569i
$911$	−1.36293	+	0.354880i	−0.0451560	+	0.0117577i	−0.274487	−	0.961591i	$-0.588508\pi$
$911$	−1.36293	+	0.354880i	−0.0451560	+	0.0117577i	0.229331	+	0.973348i	$0.426346\pi$
$912$	−2.08161	−	0.735481i	−0.0689291	−	0.0243542i
$913$	61.4010	+	34.3007i	2.03208	+	1.13519i
$914$	0.951071	+	3.10557i	0.0314586	+	0.102723i
$915$	−3.95227	−	6.41889i	−0.130658	−	0.212202i
$916$	−13.5542	−	18.3264i	−0.447842	−	0.605523i
$917$	−0.966533	+	1.91700i	−0.0319177	+	0.0633051i
$918$	1.25229	+	1.42288i	0.0413317	+	0.0469619i
$919$	−45.5136	+	20.5734i	−1.50135	+	0.678655i	−0.984171	−	0.177219i	$-0.943290\pi$
$919$	−45.5136	+	20.5734i	−1.50135	+	0.678655i	−0.517184	+	0.855875i	$0.673020\pi$
$920$	−6.90078	−	11.2076i	−0.227512	−	0.369503i
$921$	2.20248	−	10.2195i	0.0725742	−	0.336745i
$922$	13.6110	−	7.60357i	0.448255	−	0.250410i
$923$	3.63960	−	0.309776i	0.119799	−	0.0101964i
$924$	−0.218184	−	1.70383i	−0.00717774	−	0.0560520i
$925$	31.2476	+	14.1248i	1.02742	+	0.464421i
$926$	−1.29171	−	4.21789i	−0.0424483	−	0.138608i
$927$	10.4603	−	4.72833i	0.343560	−	0.155299i
$928$	4.47512	+	0.380889i	0.146903	+	0.0125033i
$929$	2.09649	+	49.3531i	0.0687838	+	1.61922i	0.619822	+	0.784743i	$0.287205\pi$
$929$	2.09649	+	49.3531i	0.0687838	+	1.61922i	−0.551038	+	0.834480i	$0.685768\pi$
$930$	5.08220	−	3.43497i	0.166652	−	0.112637i
$931$	10.9706			0.359547
$932$	−27.7886			−0.910247
$933$	−9.12923	+	6.17028i	−0.298877	+	0.202006i
$934$	−6.12021	−	1.04941i	−0.200259	−	0.0343379i
$935$	5.00827	+	9.93331i	0.163788	+	0.324854i
$936$	0.530437	+	0.717198i	0.0173379	+	0.0234423i
$937$	−2.34984	+	10.9033i	−0.0767658	+	0.356195i	−0.999578	−	0.0290559i	$-0.990750\pi$
$937$	−2.34984	+	10.9033i	−0.0767658	+	0.356195i	0.922812	+	0.385251i	$0.125885\pi$
$938$	−1.67123	−	1.34943i	−0.0545676	−	0.0440603i
$939$	22.1804	+	5.77533i	0.723831	+	0.188471i
$940$	−7.52588	−	5.08660i	−0.245467	−	0.165907i
$941$	12.1498	+	3.16356i	0.396072	+	0.103129i	0.444682	−	0.895689i	$-0.353317\pi$
$941$	12.1498	+	3.16356i	0.396072	+	0.103129i	−0.0486096	+	0.998818i	$0.515479\pi$
$942$	−0.376075	+	2.93682i	−0.0122532	+	0.0956869i
$943$	−8.97801	−	4.05832i	−0.292364	−	0.132157i
$944$	13.4649	+	7.52197i	0.438246	+	0.244819i
$945$	−0.170646	+	0.193892i	−0.00555113	+	0.00630731i
$946$	21.0350	−	20.1604i	0.683906	−	0.655471i
$947$	−0.548315	+	0.306307i	−0.0178178	+	0.00995364i	−0.496578	−	0.867992i	$-0.665411\pi$
$947$	−0.548315	+	0.306307i	−0.0178178	+	0.00995364i	0.478761	+	0.877945i	$0.341086\pi$
$948$	7.99889	+	6.45866i	0.259792	+	0.209767i
$949$	−0.680856	+	5.31690i	−0.0221015	+	0.172594i
$950$	0.562541	+	4.39296i	0.0182512	+	0.142527i
$951$	−4.48007	+	14.6290i	−0.145276	+	0.474376i
$952$	−1.18599	+	1.34755i	−0.0384382	+	0.0436743i
$953$	−16.9015	−	42.0611i	−0.547495	−	1.36249i	−0.903733	−	0.428098i	$-0.859184\pi$
$953$	−16.9015	−	42.0611i	−0.547495	−	1.36249i	0.356238	−	0.934395i	$-0.384059\pi$
$954$	6.05756	−	2.73819i	0.196121	−	0.0886521i
$955$	−3.31920	+	2.68007i	−0.107407	+	0.0867250i
$956$	−6.84851	−	13.5832i	−0.221497	−	0.439313i
$957$	1.92710	−	2.60561i	0.0622942	−	0.0842274i
$958$	14.2712	+	1.21466i	0.461082	+	0.0392438i
$959$	0.508499	−	0.410584i	0.0164203	−	0.0132585i
$960$	0.683890	+	0.924680i	0.0220724	+	0.0298439i
$961$	54.4040	−	9.32850i	1.75497	−	0.300919i
$962$	−1.53628	+	1.47240i	−0.0495317	+	0.0474722i
$963$	−3.69382	+	12.0616i	−0.119032	+	0.388679i
$964$	9.30966	−	2.42405i	0.299844	−	0.0780733i
$965$	−10.1879	−	5.69130i	−0.327960	−	0.183209i
$966$	−0.387850	−	0.965202i	−0.0124789	−	0.0310549i
$967$	−1.47687	−	1.67805i	−0.0474928	−	0.0539623i	0.726441	−	0.687229i	$-0.241173\pi$
$967$	−1.47687	−	1.67805i	−0.0474928	−	0.0539623i	−0.773934	+	0.633267i	$0.781714\pi$
$968$	−9.40525	+	12.7167i	−0.302296	+	0.408732i
$969$	4.30911	+	0.738872i	0.138429	+	0.0237360i
$970$	2.87968	−	1.01746i	0.0924611	−	0.0326686i
$971$	45.6558	−	30.8579i	1.46516	−	0.990278i	0.471030	−	0.882117i	$-0.343882\pi$
$971$	45.6558	−	30.8579i	1.46516	−	0.990278i	0.994133	−	0.108160i	$-0.0344960\pi$
$972$	−1.44135	+	0.509262i	−0.0462314	+	0.0163346i
$973$	−0.102281	−	2.40777i	−0.00327897	−	0.0771895i
$974$	−2.66387	+	3.60178i	−0.0853557	+	0.115409i
$975$	−0.675343	+	1.33946i	−0.0216283	+	0.0428971i
$976$	10.7633	−	1.84555i	0.344524	−	0.0590746i
$977$	−30.6347	+	17.1136i	−0.980090	+	0.547511i	−0.893659	−	0.448747i	$-0.851871\pi$
$977$	−30.6347	+	17.1136i	−0.980090	+	0.547511i	−0.0864312	+	0.996258i	$0.527546\pi$
$978$	6.87063	+	6.58497i	0.219699	+	0.210564i
$979$	−50.8498	−	34.3685i	−1.62517	−	1.09842i
$980$	8.44427	+	5.70733i	0.269742	+	0.182314i
$981$	−7.03353	+	11.4232i	−0.224563	+	0.364714i
$982$	1.67257	+	13.0613i	0.0533738	+	0.416804i
$983$	−26.1952	+	6.82071i	−0.835498	+	0.217547i	−0.645040	−	0.764149i	$-0.723159\pi$
$983$	−26.1952	+	6.82071i	−0.835498	+	0.217547i	−0.190458	+	0.981695i	$0.560997\pi$
$984$	3.98644	+	1.40850i	0.127083	+	0.0449013i
$985$	−4.66455	+	15.2314i	−0.148625	+	0.485311i
$986$	−1.46193	+	0.124428i	−0.0465572	+	0.00396260i
$987$	−1.19640	−	1.14666i	−0.0380819	−	0.0364985i
$988$	0.862594	+	0.224602i	0.0274428	+	0.00714554i
$989$	−30.0035	+	48.7288i	−0.954057	+	1.54949i
$990$	2.75624	−	0.234591i	0.0875991	−	0.00745578i
$991$	−21.7387	+	20.8349i	−0.690553	+	0.661842i	−0.952953	−	0.303117i	$-0.901973\pi$
$991$	−21.7387	+	20.8349i	−0.690553	+	0.661842i	0.262400	+	0.964959i	$0.415486\pi$
$992$	11.3492	+	52.6607i	0.360339	+	1.67198i
$993$	−15.2664	−	17.3461i	−0.484466	−	0.550460i
$994$	1.82125	+	0.155011i	0.0577665	+	0.00491665i
$995$	−6.51500	+	16.2132i	−0.206539	+	0.513993i
$996$	25.3103	+	4.33989i	0.801988	+	0.137515i
$997$	−1.08904	−	25.6369i	−0.0344903	−	0.811929i	−0.930148	−	0.367185i	$-0.880322\pi$
$997$	−1.08904	−	25.6369i	−0.0344903	−	0.811929i	0.895658	−	0.444744i	$-0.146705\pi$
$998$	−1.16103	+	2.88934i	−0.0367518	+	0.0914604i
$999$	−3.78962	−	7.51626i	−0.119898	−	0.237804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.b.4.8	✓	720
223.56	even	37	inner	669.2.i.b.502.8	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.b.4.8	✓	720	1.1	even	1	trivial
669.2.i.b.502.8	yes	720	223.56	even	37	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647316 + 0.228711i) q^{2} +(0.372856 - 0.927889i) q^{3} +(-1.18936 + 0.960343i) q^{4} +(-0.504580 - 0.819490i) q^{5} +(-0.0291373 + 0.685914i) q^{6} +(-0.0340902 + 0.266216i) q^{7} +(1.27016 - 2.06287i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(0.514050 + 0.415066i) q^{10} +(-0.177691 + 4.18300i) q^{11} +(0.447630 + 1.46167i) q^{12} +(-0.137295 - 0.341671i) q^{13} +(-0.0388194 - 0.180123i) q^{14} +(-0.948532 + 0.162642i) q^{15} +(0.293726 - 1.36289i) q^{16} +(-0.117177 + 2.75844i) q^{17} +(0.625588 + 0.282784i) q^{18} +(1.53243 - 0.399013i) q^{19} +(1.38712 + 0.490101i) q^{20} +(0.234308 + 0.130892i) q^{21} +(-0.841676 - 2.74836i) q^{22} +(2.95993 + 4.80723i) q^{23} +(-1.44053 - 1.94772i) q^{24} +(1.83406 - 3.63763i) q^{25} +(0.167017 + 0.189768i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(-0.215113 - 0.349365i) q^{28} +(0.163079 - 0.756688i) q^{29} +(0.576802 - 0.322221i) q^{30} +(9.25084 - 0.787362i) q^{31} +(0.736990 + 5.75526i) q^{32} +(3.81510 + 1.72454i) q^{33} +(-0.555037 - 1.81239i) q^{34} +(0.235362 - 0.106390i) q^{35} +(1.52317 + 0.129640i) q^{36} +(0.357252 + 8.40998i) q^{37} +(-0.900707 + 0.608772i) q^{38} -0.368224 q^{39} -2.33140 q^{40} +(-1.44596 + 0.977296i) q^{41} +(-0.181608 - 0.0311398i) q^{42} +(4.56352 + 9.05121i) q^{43} +(-3.80577 - 5.14574i) q^{44} +(-0.202752 + 0.940774i) q^{45} +(-3.01548 - 2.43483i) q^{46} +(-5.97525 - 1.55584i) q^{47} +(-1.15510 - 0.780708i) q^{48} +(6.70442 + 1.74570i) q^{49} +(-0.355246 + 2.77417i) q^{50} +(2.51584 + 1.13723i) q^{51} +(0.491414 + 0.274520i) q^{52} +(6.39730 - 7.26874i) q^{53} +(0.495647 - 0.475039i) q^{54} +(3.51758 - 1.96504i) q^{55} +(0.505869 + 0.408460i) q^{56} +(0.201136 - 1.57070i) q^{57} +(0.0674997 + 0.527115i) q^{58} +(-3.23942 + 10.5778i) q^{59} +(0.971955 - 1.10436i) q^{60} +(2.92051 + 7.26796i) q^{61} +(-5.80814 + 2.62545i) q^{62} +(0.208817 - 0.168608i) q^{63} +(-0.538024 - 1.06711i) q^{64} +(-0.210720 + 0.284912i) q^{65} +(-2.86400 - 0.243762i) q^{66} +(9.07005 - 7.32356i) q^{67} +(-2.50968 - 3.39332i) q^{68} +(5.56420 - 0.954079i) q^{69} +(-0.128021 + 0.122698i) q^{70} +(-2.90479 + 9.48513i) q^{71} +(-2.34438 + 0.610429i) q^{72} +(-12.7087 - 7.09948i) q^{73} +(-2.15471 - 5.36221i) q^{74} +(-2.69148 - 3.05812i) q^{75} +(-1.43942 + 1.94623i) q^{76} +(-1.10752 - 0.189904i) q^{77} +(0.238357 - 0.0842170i) q^{78} +(5.57203 - 3.76604i) q^{79} +(-1.26509 + 0.446983i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(0.712473 - 0.963327i) q^{82} +(7.56283 - 15.0000i) q^{83} +(-0.404378 + 0.0693376i) q^{84} +(2.31964 - 1.29583i) q^{85} +(-5.02416 - 4.81526i) q^{86} +(-0.641318 - 0.433455i) q^{87} +(8.40329 + 5.67963i) q^{88} +(-7.68598 + 12.4828i) q^{89} +(-0.0839209 - 0.655350i) q^{90} +(0.0956385 - 0.0249023i) q^{91} +(-8.13701 - 2.87499i) q^{92} +(2.71865 - 8.87733i) q^{93} +(4.22372 - 0.359491i) q^{94} +(-1.10022 - 1.05448i) q^{95} +(5.61503 + 1.46204i) q^{96} +(2.42365 - 3.93626i) q^{97} +(-4.73914 + 0.403361i) q^{98} +(3.02266 - 2.89699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) \) 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more