LMFDB - Embedded newform 99.2.p.a.74.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(2,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			74.3
Character	$\chi$	$=$	99.74
Dual form			99.2.p.a.95.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.189668 - 1.80457i) q^{2} +(1.02180 + 1.39855i) q^{3} +(-1.26420 + 0.268714i) q^{4} +(-1.19507 - 0.125607i) q^{5} +(2.32997 - 2.10916i) q^{6} +(3.59771 - 3.23939i) q^{7} +(-0.396737 - 1.22103i) q^{8} +(-0.911868 + 2.85806i) q^{9} +2.18041i q^{10} +(-1.93170 + 2.69602i) q^{11} +(-1.66756 - 1.49347i) q^{12} +(-1.24460 + 2.79542i) q^{13} +(-6.52808 - 5.87791i) q^{14} +(-1.04545 - 1.79971i) q^{15} +(-4.48960 + 1.99890i) q^{16} +(1.80866 + 1.31407i) q^{17} +(5.33052 + 1.10345i) q^{18} +(-4.34428 + 1.41154i) q^{19} +(1.54456 - 0.162340i) q^{20} +(8.20657 + 1.72157i) q^{21} +(5.23153 + 2.97455i) q^{22} +(1.72112 - 0.993689i) q^{23} +(1.30229 - 1.80250i) q^{24} +(-3.47832 - 0.739340i) q^{25} +(5.28060 + 1.71577i) q^{26} +(-4.92887 + 1.64506i) q^{27} +(-3.67776 + 5.06200i) q^{28} +(-1.13479 - 1.26031i) q^{29} +(-3.04941 + 2.22793i) q^{30} +(4.85274 + 2.16058i) q^{31} +(3.17481 + 5.49894i) q^{32} +(-5.74432 + 0.0531993i) q^{33} +(2.02828 - 3.51308i) q^{34} +(-4.70641 + 3.41941i) q^{35} +(0.384784 - 3.85819i) q^{36} +(0.344857 - 1.06136i) q^{37} +(3.37119 + 7.57182i) q^{38} +(-5.18126 + 1.11572i) q^{39} +(0.320759 + 1.50905i) q^{40} +(7.11427 - 7.90120i) q^{41} +(1.55017 - 15.1358i) q^{42} +(-3.28272 - 1.89528i) q^{43} +(1.71760 - 3.92738i) q^{44} +(1.44874 - 3.30104i) q^{45} +(-2.11962 - 2.91741i) q^{46} +(-0.678872 + 3.19384i) q^{47} +(-7.38300 - 4.23645i) q^{48} +(1.71815 - 16.3471i) q^{49} +(-0.674464 + 6.41710i) q^{50} +(0.0102939 + 3.87220i) q^{51} +(0.822258 - 3.86842i) q^{52} +(-0.749954 - 1.03222i) q^{53} +(3.90347 + 8.58247i) q^{54} +(2.64716 - 2.97930i) q^{55} +(-5.38274 - 3.10773i) q^{56} +(-6.41307 - 4.63337i) q^{57} +(-2.05908 + 2.28684i) q^{58} +(-0.00657007 - 0.0309097i) q^{59} +(1.80527 + 1.99426i) q^{60} +(-0.482921 - 1.08466i) q^{61} +(2.97851 - 9.16690i) q^{62} +(5.97773 + 13.2364i) q^{63} +(1.36926 - 0.994827i) q^{64} +(1.83851 - 3.18440i) q^{65} +(1.18551 + 10.3559i) q^{66} +(1.05277 + 1.82345i) q^{67} +(-2.63961 - 1.17523i) q^{68} +(3.14835 + 1.39172i) q^{69} +(7.06321 + 7.84449i) q^{70} +(-2.26013 + 3.11080i) q^{71} +(3.85155 - 0.0204781i) q^{72} +(6.69980 + 2.17690i) q^{73} +(-1.98070 - 0.421012i) q^{74} +(-2.52013 - 5.62005i) q^{75} +(5.11273 - 2.95184i) q^{76} +(1.78375 + 15.9570i) q^{77} +(2.99610 + 9.13833i) q^{78} +(3.80026 - 0.399424i) q^{79} +(5.61646 - 1.82490i) q^{80} +(-7.33699 - 5.21234i) q^{81} +(-15.6076 - 11.3396i) q^{82} +(6.64079 - 2.95667i) q^{83} +(-10.8374 + 0.0288101i) q^{84} +(-1.99642 - 1.79758i) q^{85} +(-2.79753 + 6.28336i) q^{86} +(0.603082 - 2.87484i) q^{87} +(4.05830 + 1.28906i) q^{88} +10.2875i q^{89} +(-6.23174 - 1.98825i) q^{90} +(4.57775 + 14.0889i) q^{91} +(-1.90882 + 1.71871i) q^{92} +(1.93684 + 8.99446i) q^{93} +(5.89227 + 0.619302i) q^{94} +(5.36902 - 1.14122i) q^{95} +(-4.44651 + 10.0589i) q^{96} +(-1.51615 - 14.4252i) q^{97} -29.8254 q^{98} +(-5.94392 - 7.97934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.189668	−	1.80457i	−0.134115	−	1.27602i	−0.829957	−	0.557828i	$-0.811635\pi$
$2$	−0.189668	−	1.80457i	−0.134115	−	1.27602i	0.695841	−	0.718195i	$-0.255032\pi$
$3$	1.02180	+	1.39855i	0.589934	+	0.807452i
$3$	1.02180	+	1.39855i	0.589934	+	0.807452i
$4$	−1.26420	+	0.268714i	−0.632100	+	0.134357i
$5$	−1.19507	−	0.125607i	−0.534452	−	0.0561731i	−0.166542	−	0.986034i	$-0.553260\pi$
$5$	−1.19507	−	0.125607i	−0.534452	−	0.0561731i	−0.367910	+	0.929861i	$0.619927\pi$
$6$	2.32997	−	2.10916i	0.951208	−	0.861061i
$7$	3.59771	−	3.23939i	1.35981	−	1.22438i	0.409788	−	0.912181i	$-0.365603\pi$
$7$	3.59771	−	3.23939i	1.35981	−	1.22438i	0.950018	−	0.312195i	$-0.101064\pi$
$8$	−0.396737	−	1.22103i	−0.140268	−	0.431700i
$9$	−0.911868	+	2.85806i	−0.303956	+	0.952686i
$10$			2.18041i			0.689506i
$11$	−1.93170	+	2.69602i	−0.582431	+	0.812880i
$11$	−1.93170	+	2.69602i	−0.582431	+	0.812880i
$12$	−1.66756	−	1.49347i	−0.481384	−	0.431128i
$13$	−1.24460	+	2.79542i	−0.345191	+	0.775311i	0.654622	+	0.755956i	$0.272828\pi$
$13$	−1.24460	+	2.79542i	−0.345191	+	0.775311i	−0.999813	+	0.0193546i	$0.993839\pi$
$14$	−6.52808	−	5.87791i	−1.74470	−	1.57094i
$15$	−1.04545	−	1.79971i	−0.269934	−	0.464682i
$16$	−4.48960	+	1.99890i	−1.12240	+	0.499724i
$17$	1.80866	+	1.31407i	0.438664	+	0.318708i	0.785104	−	0.619364i	$-0.212610\pi$
$17$	1.80866	+	1.31407i	0.438664	+	0.318708i	−0.346440	+	0.938072i	$0.612610\pi$
$18$	5.33052	+	1.10345i	1.25641	+	0.260085i
$19$	−4.34428	+	1.41154i	−0.996645	+	0.323830i	−0.761524	−	0.648136i	$-0.775549\pi$
$19$	−4.34428	+	1.41154i	−0.996645	+	0.323830i	−0.235121	+	0.971966i	$0.575549\pi$
$20$	1.54456	−	0.162340i	0.345374	−	0.0363003i
$21$	8.20657	+	1.72157i	1.79082	+	0.375677i
$22$	5.23153	+	2.97455i	1.11537	+	0.634175i
$23$	1.72112	−	0.993689i	0.358878	−	0.207199i	−0.309710	−	0.950831i	$-0.600232\pi$
$23$	1.72112	−	0.993689i	0.358878	−	0.207199i	0.668589	+	0.743632i	$0.266899\pi$
$24$	1.30229	−	1.80250i	0.265828	−	0.367934i
$25$	−3.47832	−	0.739340i	−0.695664	−	0.147868i
$26$	5.28060	+	1.71577i	1.03561	+	0.336490i
$27$	−4.92887	+	1.64506i	−0.948562	+	0.316592i
$28$	−3.67776	+	5.06200i	−0.695030	+	0.956627i
$29$	−1.13479	−	1.26031i	−0.210725	−	0.234034i	0.628512	−	0.777800i	$-0.283664\pi$
$29$	−1.13479	−	1.26031i	−0.210725	−	0.234034i	−0.839237	+	0.543766i	$0.816998\pi$
$30$	−3.04941	+	2.22793i	−0.556743	+	0.406763i
$31$	4.85274	+	2.16058i	0.871579	+	0.388052i	0.793265	−	0.608877i	$-0.208380\pi$
$31$	4.85274	+	2.16058i	0.871579	+	0.388052i	0.0783139	+	0.996929i	$0.475046\pi$
$32$	3.17481	+	5.49894i	0.561233	+	0.972084i
$33$	−5.74432	+	0.0531993i	−0.999957	+	0.00926081i
$34$	2.02828	−	3.51308i	0.347847	−	0.602489i
$35$	−4.70641	+	3.41941i	−0.795528	+	0.577985i
$36$	0.384784	−	3.85819i	0.0641306	−	0.643032i
$37$	0.344857	−	1.06136i	0.0566941	−	0.174486i	−0.918699	−	0.394957i	$-0.870759\pi$
$37$	0.344857	−	1.06136i	0.0566941	−	0.174486i	0.975394	+	0.220471i	$0.0707594\pi$
$38$	3.37119	+	7.57182i	0.546880	+	1.22831i
$39$	−5.18126	+	1.11572i	−0.829666	+	0.178657i
$40$	0.320759	+	1.50905i	0.0507164	+	0.238602i
$41$	7.11427	−	7.90120i	1.11106	−	1.23396i	0.141285	−	0.989969i	$-0.454877\pi$
$41$	7.11427	−	7.90120i	1.11106	−	1.23396i	0.969778	−	0.243991i	$-0.0784567\pi$
$42$	1.55017	−	15.1358i	0.239197	−	2.33551i
$43$	−3.28272	−	1.89528i	−0.500609	−	0.289027i	0.228356	−	0.973578i	$-0.426665\pi$
$43$	−3.28272	−	1.89528i	−0.500609	−	0.289027i	−0.728965	+	0.684551i	$0.759998\pi$
$44$	1.71760	−	3.92738i	0.258938	−	0.592075i
$45$	1.44874	−	3.30104i	0.215965	−	0.492091i
$46$	−2.11962	−	2.91741i	−0.312521	−	0.430149i
$47$	−0.678872	+	3.19384i	−0.0990236	+	0.465870i	0.900496	+	0.434865i	$0.143204\pi$
$47$	−0.678872	+	3.19384i	−0.0990236	+	0.465870i	−0.999519	+	0.0310045i	$0.990129\pi$
$48$	−7.38300	−	4.23645i	−1.06564	−	0.611479i
$49$	1.71815	−	16.3471i	0.245450	−	2.33530i
$50$	−0.674464	+	6.41710i	−0.0953837	+	0.907515i
$51$	0.0102939	+	3.87220i	0.00144143	+	0.542216i
$52$	0.822258	−	3.86842i	0.114027	−	0.536453i
$53$	−0.749954	−	1.03222i	−0.103014	−	0.141787i	0.754398	−	0.656417i	$-0.227929\pi$
$53$	−0.749954	−	1.03222i	−0.103014	−	0.141787i	−0.857412	+	0.514631i	$0.827929\pi$
$54$	3.90347	+	8.58247i	0.531195	+	1.16793i
$55$	2.64716	−	2.97930i	0.356943	−	0.401728i
$56$	−5.38274	−	3.10773i	−0.719299	−	0.415288i
$57$	−6.41307	−	4.63337i	−0.849432	−	0.613705i
$58$	−2.05908	+	2.28684i	−0.270371	+	0.300277i
$59$	−0.00657007	−	0.0309097i	−0.000855350	−	0.00402410i	0.977718	−	0.209923i	$-0.0673214\pi$
$59$	−0.00657007	−	0.0309097i	−0.000855350	−	0.00402410i	−0.978573	+	0.205899i	$0.933988\pi$
$60$	1.80527	+	1.99426i	0.233059	+	0.257458i
$61$	−0.482921	−	1.08466i	−0.0618317	−	0.138876i	0.879987	−	0.474998i	$-0.157551\pi$
$61$	−0.482921	−	1.08466i	−0.0618317	−	0.138876i	−0.941818	+	0.336122i	$0.890885\pi$
$62$	2.97851	−	9.16690i	0.378271	−	1.16420i
$63$	5.97773	+	13.2364i	0.753124	+	1.66762i
$64$	1.36926	−	0.994827i	0.171158	−	0.124353i
$65$	1.83851	−	3.18440i	0.228039	−	0.394976i
$66$	1.18551	+	10.3559i	0.145927	+	1.27473i
$67$	1.05277	+	1.82345i	0.128617	+	0.222770i	0.923141	−	0.384462i	$-0.125613\pi$
$67$	1.05277	+	1.82345i	0.128617	+	0.222770i	−0.794524	+	0.607232i	$0.792280\pi$
$68$	−2.63961	−	1.17523i	−0.320100	−	0.142518i
$69$	3.14835	+	1.39172i	0.379017	+	0.167543i
$70$	7.06321	+	7.84449i	0.844215	+	0.937595i
$71$	−2.26013	+	3.11080i	−0.268228	+	0.369184i	−0.921790	−	0.387688i	$-0.873274\pi$
$71$	−2.26013	+	3.11080i	−0.268228	+	0.369184i	0.653563	+	0.756873i	$0.273274\pi$
$72$	3.85155	−	0.0204781i	0.453910	−	0.00241337i
$73$	6.69980	+	2.17690i	0.784152	+	0.254786i	0.673612	−	0.739085i	$-0.264742\pi$
$73$	6.69980	+	2.17690i	0.784152	+	0.254786i	0.110540	+	0.993872i	$0.464742\pi$
$74$	−1.98070	−	0.421012i	−0.230252	−	0.0489416i
$75$	−2.52013	−	5.62005i	−0.291000	−	0.648948i
$76$	5.11273	−	2.95184i	0.586471	−	0.338599i
$77$	1.78375	+	15.9570i	0.203277	+	1.81847i
$78$	2.99610	+	9.13833i	0.339242	+	1.03471i
$79$	3.80026	−	0.399424i	0.427563	−	0.0449387i	0.111697	−	0.993742i	$-0.464372\pi$
$79$	3.80026	−	0.399424i	0.427563	−	0.0449387i	0.315866	+	0.948804i	$0.397705\pi$
$80$	5.61646	−	1.82490i	0.627940	−	0.204030i
$81$	−7.33699	−	5.21234i	−0.815221	−	0.579149i
$82$	−15.6076	−	11.3396i	−1.72357	−	1.25225i
$83$	6.64079	−	2.95667i	0.728922	−	0.324537i	−0.00850508	−	0.999964i	$-0.502707\pi$
$83$	6.64079	−	2.95667i	0.728922	−	0.324537i	0.737427	+	0.675427i	$0.236041\pi$
$84$	−10.8374	+	0.0288101i	−1.18245	+	0.00314344i
$85$	−1.99642	−	1.79758i	−0.216542	−	0.194975i
$86$	−2.79753	+	6.28336i	−0.301666	+	0.677552i
$87$	0.603082	−	2.87484i	0.0646572	−	0.308215i
$88$	4.05830	+	1.28906i	0.432616	+	0.137414i
$89$			10.2875i			1.09048i	0.838281	+	0.545238i	$0.183561\pi$
$89$			10.2875i			1.09048i	−0.838281	+	0.545238i	$0.816439\pi$
$90$	−6.23174	−	1.98825i	−0.656883	−	0.209580i
$91$	4.57775	+	14.0889i	0.479879	+	1.47692i
$92$	−1.90882	+	1.71871i	−0.199009	+	0.179188i
$93$	1.93684	+	8.99446i	0.200841	+	0.932682i
$94$	5.89227	+	0.619302i	0.607741	+	0.0638761i
$95$	5.36902	−	1.14122i	0.550849	−	0.117087i
$96$	−4.44651	+	10.0589i	−0.453820	+	1.02663i
$97$	−1.51615	−	14.4252i	−0.153941	−	1.46465i	−0.749853	−	0.661605i	$-0.769876\pi$
$97$	−1.51615	−	14.4252i	−0.153941	−	1.46465i	0.595912	−	0.803050i	$-0.296791\pi$
$98$	−29.8254			−3.01282
$99$	−5.94392	−	7.97934i	−0.597386	−	0.801954i
$100$	4.59597			0.459597
$101$	−1.68141	−	15.9976i	−0.167307	−	1.59182i	−0.679977	−	0.733234i	$-0.738010\pi$
$101$	−1.68141	−	15.9976i	−0.167307	−	1.59182i	0.512670	−	0.858586i	$-0.328657\pi$
$102$	6.98570	−	0.753008i	0.691687	−	0.0745589i
$103$	2.03569	−	0.432699i	0.200582	−	0.0426351i	−0.106525	−	0.994310i	$-0.533972\pi$
$103$	2.03569	−	0.432699i	0.200582	−	0.0426351i	0.307107	+	0.951675i	$0.400639\pi$
$104$	3.90708	+	0.410651i	0.383121	+	0.0402676i
$105$	−9.59118	−	3.08820i	−0.936004	−	0.301377i
$106$	−1.72047	+	1.54912i	−0.167107	+	0.150464i
$107$	0.129361	+	0.398133i	0.0125058	+	0.0384889i	0.957115	−	0.289709i	$-0.0935586\pi$
$107$	0.129361	+	0.398133i	0.0125058	+	0.0384889i	−0.944609	+	0.328198i	$0.893559\pi$
$108$	5.78903	−	3.40414i	0.557050	−	0.327564i
$109$		−	14.6788i		−	1.40597i	−0.711205	−	0.702985i	$-0.751850\pi$
$109$		−	14.6788i		−	1.40597i	0.711205	−	0.702985i	$-0.248150\pi$
$110$	−5.87843	−	4.21191i	−0.560486	−	0.401590i
$111$	1.83673	−	0.602194i	0.174335	−	0.0571577i
$112$	−9.67706	+	21.7350i	−0.914396	+	2.05377i
$113$	2.37557	+	2.13897i	0.223475	+	0.201218i	0.773261	−	0.634088i	$-0.218624\pi$
$113$	2.37557	+	2.13897i	0.223475	+	0.201218i	−0.549786	+	0.835305i	$0.685291\pi$
$114$	−7.14488	+	12.4516i	−0.669179	+	1.16620i
$115$	−2.18167	+	0.971344i	−0.203442	+	0.0905783i
$116$	1.77326	+	1.28835i	0.164643	+	0.119620i
$117$	−6.85457	−	6.10621i	−0.633705	−	0.564519i
$118$	−0.0545326	+	0.0177187i	−0.00502013	+	0.00163114i
$119$	10.7638	−	1.13132i	0.986716	−	0.103708i
$120$	−1.78273	+	1.99054i	−0.162740	+	0.181710i
$121$	−3.53703	−	10.4158i	−0.321548	−	0.946893i
$122$	−1.86575	+	1.07719i	−0.168917	+	0.0975241i
$123$	18.3195	+	1.87623i	1.65182	+	0.169174i
$124$	−6.71542	−	1.42741i	−0.603062	−	0.128185i
$125$	9.77817	+	3.17712i	0.874587	+	0.284170i
$126$	22.7521	−	13.2977i	2.02692	−	1.18466i
$127$	−13.1088	+	18.0428i	−1.16322	+	1.60104i	−0.464654	+	0.885492i	$0.653821\pi$
$127$	−13.1088	+	18.0428i	−1.16322	+	1.60104i	−0.698567	+	0.715545i	$0.746179\pi$
$128$	6.44252	+	7.15514i	0.569444	+	0.632431i
$129$	−0.703630	−	6.52762i	−0.0619512	−	0.574725i
$130$	−6.09517	−	2.71375i	−0.534582	−	0.238011i
$131$	−7.74960	−	13.4227i	−0.677086	−	1.17275i	−0.975855	−	0.218421i	$-0.929909\pi$
$131$	−7.74960	−	13.4227i	−0.677086	−	1.17275i	0.298769	−	0.954326i	$-0.403424\pi$
$132$	7.24767	−	1.61083i	0.630829	−	0.140205i
$133$	−11.0569	+	19.1511i	−0.958756	+	1.66061i
$134$	3.09087	−	2.24565i	0.267011	−	0.193995i
$135$	6.09698	−	1.34686i	0.524745	−	0.115919i
$136$	0.886955	−	2.72977i	0.0760557	−	0.234075i
$137$	6.97178	+	15.6589i	0.595639	+	1.33783i	0.920009	+	0.391897i	$0.128181\pi$
$137$	6.97178	+	15.6589i	0.595639	+	1.33783i	−0.324370	+	0.945930i	$0.605152\pi$
$138$	1.91431	−	5.94539i	0.162957	−	0.506105i
$139$	2.15559	+	10.1413i	0.182835	+	0.860172i	0.969938	+	0.243350i	$0.0782465\pi$
$139$	2.15559	+	10.1413i	0.182835	+	0.860172i	−0.787103	+	0.616821i	$0.788420\pi$
$140$	5.03100	−	5.58749i	0.425197	−	0.472229i
$141$	−5.16041	+	2.31402i	−0.434585	+	0.194875i
$142$	6.04233	+	3.48854i	0.507061	+	0.292752i
$143$	−5.13231	−	8.75541i	−0.429185	−	0.732164i
$144$	−1.61904	−	14.6543i	−0.134920	−	1.22119i
$145$	1.19785	+	1.64870i	0.0994759	+	0.136917i
$146$	2.65762	−	12.5031i	0.219946	−	1.03477i
$147$	24.6178	−	14.3005i	2.03045	−	1.17949i
$148$	−0.150766	+	1.43444i	−0.0123929	+	0.117910i
$149$	−0.00422899	+	0.0402361i	−0.000346452	+	0.00329627i	−0.994694	−	0.102880i	$-0.967194\pi$
$149$	−0.00422899	+	0.0402361i	−0.000346452	+	0.00329627i	0.994347	+	0.106176i	$0.0338608\pi$
$150$	−9.66378	+	5.61369i	−0.789044	+	0.458356i
$151$	−0.572095	+	2.69150i	−0.0465564	+	0.219031i	−0.995276	−	0.0970890i	$-0.969047\pi$
$151$	−0.572095	+	2.69150i	−0.0465564	+	0.219031i	0.948719	+	0.316120i	$0.102380\pi$
$152$	3.44707	+	4.74449i	0.279594	+	0.384829i
$153$	−5.40493	+	3.97099i	−0.436963	+	0.321036i
$154$	28.4573	−	6.24544i	2.29315	−	0.503272i
$155$	−5.52799	−	3.19159i	−0.444019	−	0.256354i
$156$	6.25034	−	2.80277i	0.500428	−	0.224401i
$157$	1.41178	−	1.56794i	0.112672	−	0.125135i	−0.684170	−	0.729322i	$-0.739835\pi$
$157$	1.41178	−	1.56794i	0.112672	−	0.125135i	0.796842	+	0.604187i	$0.206502\pi$
$158$	−1.44158	−	6.78208i	−0.114686	−	0.539553i
$159$	0.677313	−	2.10357i	0.0537144	−	0.166824i
$160$	−3.10342	−	6.97040i	−0.245347	−	0.551058i
$161$	2.97314	−	9.15039i	0.234316	−	0.721152i
$162$	−8.01444	+	14.2287i	−0.629674	+	1.11791i
$163$	−11.8085	+	8.57941i	−0.924917	+	0.671991i	−0.944743	−	0.327812i	$-0.893689\pi$
$163$	−11.8085	+	8.57941i	−0.924917	+	0.671991i	0.0198264	+	0.999803i	$0.493689\pi$
$164$	−6.87070	+	11.9004i	−0.536512	+	0.929265i
$165$	6.87155	+	0.657949i	0.534949	+	0.0512213i
$166$	−6.59506	−	11.4230i	−0.511876	−	0.886596i
$167$	0.815131	+	0.362920i	0.0630767	+	0.0280836i	0.438033	−	0.898959i	$-0.355675\pi$
$167$	0.815131	+	0.362920i	0.0630767	+	0.0280836i	−0.374956	+	0.927043i	$0.622342\pi$
$168$	−1.15376	−	10.7035i	−0.0890144	−	0.825792i
$169$	2.43334	+	2.70250i	0.187180	+	0.207884i
$170$	−2.86520	+	3.94362i	−0.219751	+	0.302461i
$171$	−0.0728586	−	13.7033i	−0.00557164	−	1.04792i
$172$	4.65930	+	1.51390i	0.355268	+	0.115434i
$173$	−12.9579	−	2.75430i	−0.985175	−	0.209405i	−0.312964	−	0.949765i	$-0.601322\pi$
$173$	−12.9579	−	2.75430i	−0.985175	−	0.209405i	−0.672211	+	0.740360i	$0.734655\pi$
$174$	−5.30222	−	0.543039i	−0.401961	−	0.0411677i
$175$	−14.9090	+	8.60772i	−1.12701	+	0.650682i
$176$	3.28351	−	15.9653i	0.247504	−	1.20343i
$177$	0.0365155	−	0.0407720i	0.00274467	−	0.00306461i
$178$	18.5646	−	1.95121i	1.39147	−	0.146250i
$179$	−19.1587	+	6.22502i	−1.43199	+	0.465280i	−0.919389	−	0.393350i	$-0.871316\pi$
$179$	−19.1587	+	6.22502i	−1.43199	+	0.465280i	−0.512596	+	0.858630i	$0.671316\pi$
$180$	−0.944459	+	4.56248i	−0.0703958	+	0.340067i
$181$	3.63758	+	2.64286i	0.270379	+	0.196442i	0.714710	−	0.699421i	$-0.246559\pi$
$181$	3.63758	+	2.64286i	0.270379	+	0.196442i	−0.444331	+	0.895863i	$0.646559\pi$
$182$	24.5561	−	10.9331i	1.82022	−	0.810414i
$183$	1.02350	−	1.78369i	0.0756592	−	0.131854i
$184$	−1.89616	−	1.70731i	−0.139787	−	0.125864i
$185$	−0.545442	+	1.22508i	−0.0401017	+	0.0900699i
$186$	15.8638	−	5.20112i	1.16319	−	0.381364i
$187$	−7.03654	+	2.33778i	−0.514563	+	0.170956i
$188$		−	4.22008i		−	0.307781i
$189$	−12.4037	+	21.8850i	−0.902233	+	1.59190i
$190$	−3.07774	−	9.47231i	−0.223283	−	0.687193i
$191$	−13.2086	+	11.8931i	−0.955742	+	0.860554i	−0.990314	−	0.138849i	$-0.955660\pi$
$191$	−13.2086	+	11.8931i	−0.955742	+	0.860554i	0.0345721	+	0.999402i	$0.488993\pi$
$192$	2.79042	+	0.898468i	0.201381	+	0.0648413i
$193$	−6.12522	−	0.643787i	−0.440903	−	0.0463408i	−0.118523	−	0.992951i	$-0.537816\pi$
$193$	−6.12522	−	0.643787i	−0.440903	−	0.0463408i	−0.322380	+	0.946610i	$0.604483\pi$
$194$	−25.7437	+	5.47198i	−1.84829	+	0.392866i
$195$	6.33211	−	0.682556i	0.453452	−	0.0488789i
$196$	2.22062	+	21.1277i	0.158615	+	1.50912i
$197$	22.5100			1.60377			0.801886	−	0.597477i	$-0.203830\pi$
$197$	22.5100			1.60377			0.801886	+	0.597477i	$0.203830\pi$
$198$	−13.2719	+	12.2396i	−0.943193	+	0.869833i
$199$	9.30680			0.659742			0.329871	−	0.944026i	$-0.392995\pi$
$199$	9.30680			0.659742			0.329871	+	0.944026i	$0.392995\pi$
$200$	0.477222	+	4.54046i	0.0337447	+	0.321059i
$201$	−1.47447	+	3.33555i	−0.104001	+	0.235271i
$202$	−28.5498	+	6.06846i	−2.00876	+	0.426975i
$203$	−8.16528	−	0.858206i	−0.573090	−	0.0602342i
$204$	−1.05353	−	4.89247i	−0.0737617	−	0.342541i
$205$	−9.49450	+	8.54889i	−0.663125	+	0.597080i
$206$	−1.16694	−	3.59147i	−0.0813046	−	0.250230i
$207$	1.27059	+	5.82518i	0.0883119	+	0.404878i
$208$		−	15.0382i		−	1.04271i
$209$	4.58632	−	14.4389i	0.317242	−	0.998762i
$210$	−3.75373	+	17.8937i	−0.259032	+	1.23478i
$211$	5.69884	−	12.7998i	0.392325	−	0.881175i	−0.604118	−	0.796895i	$-0.706474\pi$
$211$	5.69884	−	12.7998i	0.392325	−	0.881175i	0.996442	−	0.0842801i	$-0.0268591\pi$
$212$	1.22546	+	1.10341i	0.0841652	+	0.0757827i
$213$	−6.65999	+	0.0177050i	−0.456335	+	0.00121313i
$214$	0.693922	−	0.308954i	0.0474355	−	0.0211197i
$215$	3.68502	+	2.67732i	0.251316	+	0.182592i
$216$	3.96414	+	5.36565i	0.269725	+	0.365086i
$217$	24.4577	−	7.94680i	1.66030	−	0.539464i
$218$	−26.4888	+	2.78409i	−1.79405	+	0.188562i
$219$	3.80133	+	11.5943i	0.256870	+	0.783472i
$220$	−2.54596	+	4.47776i	−0.171649	+	0.301890i
$221$	−5.92443	+	3.42047i	−0.398520	+	0.230086i
$222$	−1.43507	−	3.20030i	−0.0963156	−	0.214790i
$223$	15.7802	+	3.35419i	1.05672	+	0.224613i	0.703331	−	0.710863i	$-0.251695\pi$
$223$	15.7802	+	3.35419i	1.05672	+	0.224613i	0.353391	+	0.935476i	$0.385029\pi$
$224$	29.2353	+	9.49912i	1.95336	+	0.634686i
$225$	5.28485	−	9.26706i	0.352323	−	0.617804i
$226$	3.40936	−	4.69258i	0.226787	−	0.312146i
$227$	−9.84619	−	10.9353i	−0.653515	−	0.725802i	0.321754	−	0.946823i	$-0.395728\pi$
$227$	−9.84619	−	10.9353i	−0.653515	−	0.725802i	−0.975269	+	0.221022i	$0.929061\pi$
$228$	9.35245	+	4.13422i	0.619381	+	0.273796i
$229$	20.2798	+	9.02915i	1.34013	+	0.596663i	0.946529	−	0.322620i	$-0.104564\pi$
$229$	20.2798	+	9.02915i	1.34013	+	0.596663i	0.393598	+	0.919283i	$0.371230\pi$
$230$	2.16665	+	3.75275i	0.142865	+	0.247449i
$231$	−20.4940	+	18.7995i	−1.34841	+	1.23692i
$232$	−1.08867	+	1.88562i	−0.0714744	+	0.123797i
$233$	4.18134	−	3.03792i	0.273929	−	0.199021i	−0.442336	−	0.896849i	$-0.645850\pi$
$233$	4.18134	−	3.03792i	0.273929	−	0.199021i	0.716265	+	0.697828i	$0.245850\pi$
$234$	−9.71898	+	13.5277i	−0.635349	+	0.884333i
$235$	1.21247	−	3.73159i	0.0790927	−	0.243422i
$236$	0.0166118	+	0.0373106i	0.00108133	+	0.00242871i
$237$	4.44170	+	4.90672i	0.288520	+	0.318726i
$238$	−4.08309	−	19.2094i	−0.264668	−	1.24516i
$239$	−9.14380	+	10.1552i	−0.591463	+	0.656886i	−0.962357	−	0.271789i	$-0.912385\pi$
$239$	−9.14380	+	10.1552i	−0.591463	+	0.656886i	0.370894	+	0.928675i	$0.379051\pi$
$240$	8.29108	+	5.99021i	0.535187	+	0.386667i
$241$	−6.10765	−	3.52625i	−0.393428	−	0.227146i	0.290216	−	0.956961i	$-0.406273\pi$
$241$	−6.10765	−	3.52625i	−0.393428	−	0.227146i	−0.683645	+	0.729815i	$0.739606\pi$
$242$	−18.1252	+	8.35837i	−1.16513	+	0.537296i
$243$	−0.207196	−	15.5871i	−0.0132916	−	0.999912i
$244$	0.901971	+	1.24146i	0.0577428	+	0.0794761i
$245$	−4.10663	+	19.3202i	−0.262363	+	1.23432i
$246$	−0.0888300	−	33.4147i	−0.00566359	−	2.13044i
$247$	1.46104	−	13.9009i	0.0929640	−	0.884493i
$248$	0.712873	−	6.78253i	0.0452675	−	0.430691i
$249$	10.9206	+	6.26635i	0.692064	+	0.397114i
$250$	3.87873	−	18.2480i	0.245312	−	1.15410i
$251$	3.95496	+	5.44354i	0.249635	+	0.343593i	0.915383	−	0.402583i	$-0.131888\pi$
$251$	3.95496	+	5.44354i	0.249635	+	0.343593i	−0.665748	+	0.746176i	$0.731888\pi$
$252$	−11.1139	−	15.1271i	−0.700107	−	0.952918i
$253$	−0.645692	+	6.55969i	−0.0405943	+	0.412404i
$254$	35.0457	+	20.2337i	2.19897	+	1.26957i
$255$	0.474073	−	4.62884i	0.0296876	−	0.289869i
$256$	13.9550	−	15.4986i	0.872189	−	0.968664i
$257$	−2.94227	−	13.8423i	−0.183534	−	0.863457i	−0.969481	−	0.245165i	$-0.921158\pi$
$257$	−2.94227	−	13.8423i	−0.183534	−	0.863457i	0.785948	−	0.618293i	$-0.212175\pi$
$258$	−11.6461	+	2.50783i	−0.725053	+	0.156131i
$259$	−2.19747	−	4.93559i	−0.136544	−	0.306683i
$260$	−1.46856	+	4.51975i	−0.0910760	+	0.280303i
$261$	4.63682	−	2.09406i	0.287012	−	0.129619i
$262$	−22.7523	+	16.5305i	−1.40564	+	1.02126i
$263$	−3.47292	+	6.01527i	−0.214149	+	0.370917i	−0.953009	−	0.302942i	$-0.902031\pi$
$263$	−3.47292	+	6.01527i	−0.214149	+	0.370917i	0.738860	+	0.673859i	$0.235365\pi$
$264$	2.34394	+	6.99288i	0.144260	+	0.430382i
$265$	0.766593	+	1.32778i	0.0470914	+	0.0815648i
$266$	36.6567	+	16.3206i	2.24757	+	1.00068i
$267$	−14.3876	+	10.5117i	−0.880506	+	0.643309i
$268$	−1.82090	−	2.02232i	−0.111229	−	0.123533i
$269$	−4.05850	+	5.58605i	−0.247451	+	0.340587i	−0.914617	−	0.404322i	$-0.867507\pi$
$269$	−4.05850	+	5.58605i	−0.247451	+	0.340587i	0.667165	+	0.744910i	$0.267507\pi$
$270$	−3.58691	−	10.7470i	−0.218292	−	0.654040i
$271$	−12.9581	−	4.21033i	−0.787146	−	0.255759i	−0.112258	−	0.993679i	$-0.535808\pi$
$271$	−12.9581	−	4.21033i	−0.787146	−	0.255759i	−0.674888	+	0.737920i	$0.735808\pi$
$272$	−10.7468	−	2.28431i	−0.651622	−	0.138507i
$273$	−15.0264	+	20.7982i	−0.909441	+	1.25876i
$274$	26.9352	−	15.5510i	1.62721	−	0.939473i
$275$	8.71236	−	7.94943i	0.525375	−	0.479369i
$276$	−4.35413	−	0.913407i	−0.262088	−	0.0549806i
$277$	11.5914	−	1.21831i	0.696461	−	0.0732010i	0.250319	−	0.968163i	$-0.419464\pi$
$277$	11.5914	−	1.21831i	0.696461	−	0.0732010i	0.446142	+	0.894962i	$0.352798\pi$
$278$	17.8918	−	5.81339i	1.07308	−	0.348664i
$279$	−10.6001	+	11.8993i	−0.634613	+	0.712390i
$280$	6.04241	+	4.39007i	0.361103	+	0.262357i
$281$	−19.9523	+	8.88333i	−1.19025	+	0.529935i	−0.903715	−	0.428134i	$-0.859171\pi$
$281$	−19.9523	+	8.88333i	−1.19025	+	0.529935i	−0.286538	+	0.958069i	$0.592505\pi$
$282$	5.15457	+	8.87341i	0.306950	+	0.528404i
$283$	17.4451	+	15.7076i	1.03700	+	0.933722i	0.997852	−	0.0655115i	$-0.0208679\pi$
$283$	17.4451	+	15.7076i	1.03700	+	0.933722i	0.0391513	+	0.999233i	$0.487535\pi$
$284$	2.02134	−	4.54000i	0.119944	−	0.269400i
$285$	7.08209	+	6.34273i	0.419507	+	0.375711i
$286$	−14.8263	+	10.9222i	−0.876698	+	0.645845i
$287$		−	51.4721i		−	3.03830i
$288$	−18.6113	+	4.05949i	−1.09668	+	0.239208i
$289$	−3.70882	−	11.4146i	−0.218166	−	0.671445i
$290$	2.74799	−	2.47431i	0.161368	−	0.145296i
$291$	18.6251	−	16.8600i	1.09182	−	0.988350i
$292$	−9.05485	−	0.951703i	−0.529895	−	0.0556942i
$293$	1.65959	−	0.352756i	0.0969542	−	0.0206082i	−0.159179	−	0.987250i	$-0.550885\pi$
$293$	1.65959	−	0.352756i	0.0969542	−	0.0206082i	0.256133	+	0.966641i	$0.417551\pi$
$294$	−30.4755	−	41.7122i	−1.77737	−	2.43271i
$295$	0.00396922	+	0.0377646i	0.000231097	+	0.00219874i
$296$	−1.43277			−0.0832781
$297$	5.08601	−	16.4661i	0.295120	−	0.955460i
$298$	0.0734110			0.00425258
$299$	0.635671	+	6.04801i	0.0367618	+	0.349765i
$300$	4.69614	+	6.42767i	0.271132	+	0.371102i
$301$	−17.9498	+	3.81535i	−1.03461	+	0.219913i
$302$	4.96550	+	0.521895i	0.285732	+	0.0300317i
$303$	20.6553	−	18.6978i	1.18662	−	1.07416i
$304$	16.6825	−	15.0210i	0.956809	−	0.861514i
$305$	0.440884	+	1.35690i	0.0252449	+	0.0776959i
$306$	8.19107	+	9.00041i	0.468252	+	0.514519i
$307$			2.35281i			0.134282i	0.997743	+	0.0671410i	$0.0213877\pi$
$307$			2.35281i			0.134282i	−0.997743	+	0.0671410i	$0.978612\pi$
$308$	−6.54290	−	19.6936i	−0.372816	−	1.12215i
$309$	2.68521	+	2.40488i	0.152756	+	0.136809i
$310$	−4.71095	+	10.5810i	−0.267564	+	0.600959i
$311$	7.88205	+	7.09703i	0.446950	+	0.402436i	0.861634	−	0.507530i	$-0.169441\pi$
$311$	7.88205	+	7.09703i	0.446950	+	0.402436i	−0.414684	+	0.909965i	$0.636108\pi$
$312$	3.41792	+	5.88384i	0.193502	+	0.333107i
$313$	−23.1439	+	10.3043i	−1.30817	+	0.582435i	−0.938034	−	0.346543i	$-0.887355\pi$
$313$	−23.1439	+	10.3043i	−1.30817	+	0.582435i	−0.370136	+	0.928978i	$0.620689\pi$
$314$	−3.09722	−	2.25026i	−0.174786	−	0.126990i
$315$	−5.48124	−	16.5692i	−0.308833	−	0.933571i
$316$	−4.69696	+	1.52614i	−0.264225	+	0.0858518i
$317$	26.6656	−	2.80266i	1.49769	−	0.157413i	0.680058	−	0.733158i	$-0.261955\pi$
$317$	26.6656	−	2.80266i	1.49769	−	0.157413i	0.817629	+	0.575745i	$0.195288\pi$
$318$	−3.92449	−	0.823279i	−0.220075	−	0.0461672i
$319$	5.58990	−	0.624864i	0.312974	−	0.0349856i
$320$	−1.76132	+	1.01690i	−0.0984609	+	0.0568464i
$321$	−0.424627	+	0.587728i	−0.0237003	+	0.0328038i
$322$	−17.0764	−	3.62971i	−0.951632	−	0.202276i
$323$	−9.71216	−	3.15567i	−0.540399	−	0.175586i
$324$	10.6761	+	4.61789i	0.593114	+	0.256550i
$325$	6.39590	−	8.80320i	0.354781	−	0.488314i
$326$	17.7218	+	19.6821i	0.981522	+	1.09009i
$327$	20.5289	−	14.9987i	1.13525	−	0.829429i
$328$	−12.4701	−	5.55205i	−0.688546	−	0.306561i
$329$	7.90372	+	13.6896i	0.435746	+	0.754735i
$330$	−0.115996	−	12.5250i	−0.00638539	−	0.689477i
$331$	8.66186	−	15.0028i	0.476099	−	0.824627i	−0.523526	−	0.852010i	$-0.675384\pi$
$331$	8.66186	−	15.0028i	0.476099	−	0.824627i	0.999625	+	0.0273822i	$0.00871710\pi$
$332$	−7.60079	+	5.52230i	−0.417148	+	0.303076i
$333$	2.71896	+	1.95344i	0.148998	+	0.107048i
$334$	0.500309	−	1.53979i	0.0273757	−	0.0842538i
$335$	−1.02910	−	2.31139i	−0.0562256	−	0.126285i
$336$	−40.2854	+	8.67493i	−2.19775	+	0.473256i
$337$	2.70366	+	12.7197i	0.147278	+	0.692887i	0.988379	+	0.152009i	$0.0485743\pi$
$337$	2.70366	+	12.7197i	0.147278	+	0.692887i	−0.841101	+	0.540877i	$0.818092\pi$
$338$	4.41532	−	4.90371i	0.240162	−	0.266727i
$339$	−0.564108	+	5.50794i	−0.0306382	+	0.299150i
$340$	3.00691	+	1.73604i	0.163072	+	0.0941499i
$341$	−15.1990	+	8.90948i	−0.823074	+	0.482476i
$342$	−24.7148	+	2.73056i	−1.33642	+	0.147652i
$343$	−26.8543	−	36.9618i	−1.45000	−	1.99575i
$344$	−1.01182	+	4.76023i	−0.0545535	+	0.256654i
$345$	−3.58770	−	2.05866i	−0.193155	−	0.110835i
$346$	−2.51261	+	23.9059i	−0.135079	+	1.28519i
$347$	−2.22189	+	21.1399i	−0.119277	+	1.13485i	0.757126	+	0.653269i	$0.226603\pi$
$347$	−2.22189	+	21.1399i	−0.119277	+	1.13485i	−0.876403	+	0.481578i	$0.840064\pi$
$348$	0.0100924	+	3.79642i	0.000541012	+	0.203510i
$349$	−1.94002	+	9.12708i	−0.103847	+	0.488562i	0.895230	+	0.445604i	$0.147011\pi$
$349$	−1.94002	+	9.12708i	−0.103847	+	0.488562i	−0.999077	+	0.0429571i	$0.986322\pi$
$350$	18.3610	+	25.2717i	0.981436	+	1.35083i
$351$	1.53585	−	15.8257i	0.0819775	−	0.844715i
$352$	−20.9580	−	2.06297i	−1.11707	−	0.109957i
$353$	7.89937	+	4.56070i	0.420441	+	0.242742i	0.695266	−	0.718753i	$-0.255287\pi$
$353$	7.89937	+	4.56070i	0.420441	+	0.242742i	−0.274825	+	0.961494i	$0.588620\pi$
$354$	−0.0805016	−	0.0581615i	−0.00427861	−	0.00309125i
$355$	3.09175	−	3.43374i	0.164093	−	0.182244i
$356$	−2.76440	−	13.0055i	−0.146513	−	0.689290i
$357$	12.5806	+	13.8977i	0.665836	+	0.735544i
$358$	14.8673	+	33.3924i	0.785760	+	1.76484i
$359$	2.41692	−	7.43851i	0.127560	−	0.392589i	−0.866799	−	0.498658i	$-0.833826\pi$
$359$	2.41692	−	7.43851i	0.127560	−	0.392589i	0.994359	+	0.106069i	$0.0338263\pi$
$360$	−4.60545	−	0.459309i	−0.242728	−	0.0242077i
$361$	1.50897	−	1.09633i	0.0794193	−	0.0577015i
$362$	4.07929	−	7.06553i	0.214402	−	0.371356i
$363$	10.9529	−	15.5895i	0.574878	−	0.818239i
$364$	−9.57308	−	16.5811i	−0.501766	−	0.869084i
$365$	−7.73330	−	3.44309i	−0.404779	−	0.180219i
$366$	−3.41291	−	1.50867i	−0.178396	−	0.0788593i
$367$	16.3966	+	18.2102i	0.855894	+	0.950567i	0.999235	−	0.0391068i	$-0.0124513\pi$
$367$	16.3966	+	18.2102i	0.855894	+	0.950567i	−0.143341	+	0.989673i	$0.545785\pi$
$368$	−5.74086	+	7.90161i	−0.299263	+	0.411900i
$369$	16.0948	+	27.5379i	0.837862	+	1.43356i
$370$	2.31420	+	0.751929i	0.120310	+	0.0390909i
$371$	−6.04189	−	1.28424i	−0.313679	−	0.0666746i
$372$	−4.86549	−	10.8503i	−0.252264	−	0.562564i
$373$	2.47795	−	1.43065i	0.128303	−	0.0740760i	−0.434475	−	0.900684i	$-0.643066\pi$
$373$	2.47795	−	1.43065i	0.128303	−	0.0740760i	0.562778	+	0.826608i	$0.309733\pi$
$374$	5.55330	+	12.2545i	0.287154	+	0.633666i
$375$	5.54794	+	16.9216i	0.286494	+	0.873828i
$376$	4.16911	−	0.438191i	0.215006	−	0.0225980i
$377$	4.93546	−	1.60363i	0.254189	−	0.0825911i
$378$	41.8456	+	18.2324i	2.15230	+	0.937772i
$379$	23.6747	+	17.2007i	1.21609	+	0.883540i	0.995769	−	0.0918872i	$-0.0292899\pi$
$379$	23.6747	+	17.2007i	1.21609	+	0.883540i	0.220320	+	0.975428i	$0.429290\pi$
$380$	−6.48085	+	2.88546i	−0.332461	+	0.148021i
$381$	−38.6282	+	0.102690i	−1.97898	+	0.00526095i
$382$	23.9671	+	21.5801i	1.22627	+	1.10413i
$383$	11.5755	−	25.9990i	0.591480	−	1.32849i	−0.331434	−	0.943478i	$-0.607532\pi$
$383$	11.5755	−	25.9990i	0.591480	−	1.32849i	0.922914	−	0.385007i	$-0.125801\pi$
$384$	−3.42387	+	16.3213i	−0.174724	+	0.832891i
$385$	−0.127390	−	19.2938i	−0.00649240	−	0.983305i
$386$			11.1755i			0.568818i
$387$	8.41022	−	7.65395i	0.427515	−	0.389072i
$388$	5.79296	+	17.8289i	0.294093	+	0.905125i
$389$	10.6132	−	9.55615i	0.538110	−	0.484516i	−0.354681	−	0.934987i	$-0.615411\pi$
$389$	10.6132	−	9.55615i	0.538110	−	0.484516i	0.892791	+	0.450471i	$0.148744\pi$
$390$	−2.43272	−	11.2973i	−0.123185	−	0.572060i
$391$	4.41869	+	0.464423i	0.223463	+	0.0234869i
$392$	−20.6420	+	4.38760i	−1.04258	+	0.221607i
$393$	10.8538	−	24.5534i	0.547501	−	1.23856i
$394$	−4.26943	−	40.6209i	−0.215091	−	2.04645i
$395$	−4.59175			−0.231036
$396$	9.65846	+	8.49027i	0.485356	+	0.426652i
$397$	2.20687			0.110760			0.0553798	−	0.998465i	$-0.482363\pi$
$397$	2.20687			0.110760			0.0553798	+	0.998465i	$0.482363\pi$
$398$	−1.76520	−	16.7948i	−0.0884815	−	0.841845i
$399$	−38.0817	+	4.10493i	−1.90647	+	0.205503i
$400$	17.0941	−	3.63347i	0.854707	−	0.181673i
$401$	−31.3702	−	3.29714i	−1.56655	−	0.164651i	−0.718866	−	0.695148i	$-0.755339\pi$
$401$	−31.3702	−	3.29714i	−1.56655	−	0.164651i	−0.847687	+	0.530497i	$0.822005\pi$
$402$	6.29889	+	2.02814i	0.314160	+	0.101154i
$403$	−12.0795	+	10.8764i	−0.601722	+	0.541793i
$404$	6.42442	+	19.7723i	0.319627	+	0.983710i
$405$	8.11352	+	7.15070i	0.403164	+	0.355321i
$406$			14.8976i			0.739355i
$407$	2.19528	+	2.97997i	0.108816	+	0.147712i
$408$	4.72399	−	1.54881i	0.233872	−	0.0766777i
$409$	−2.75694	+	6.19219i	−0.136322	+	0.306184i	−0.968788	−	0.247893i	$-0.920262\pi$
$409$	−2.75694	+	6.19219i	−0.136322	+	0.306184i	0.832466	+	0.554077i	$0.186929\pi$
$410$	17.2279	+	15.5120i	0.850823	+	0.766085i
$411$	−14.7759	+	25.7505i	−0.728843	+	1.27018i
$412$	−2.45725	+	1.09404i	−0.121060	+	0.0538993i
$413$	−0.123766	−	0.0899212i	−0.00609012	−	0.00442473i
$414$	10.2709	−	3.39771i	0.504789	−	0.166988i
$415$	−8.30760	+	2.69930i	−0.407804	+	0.132504i
$416$	−19.3232	+	2.03095i	−0.947400	+	0.0995757i
$417$	−11.9805	+	13.3770i	−0.586686	+	0.655075i
$418$	−26.9259	−	5.53773i	−1.31699	−	0.270859i
$419$	−24.7759	+	14.3044i	−1.21038	+	0.698815i	−0.962843	−	0.270062i	$-0.912956\pi$
$419$	−24.7759	+	14.3044i	−1.21038	+	0.698815i	−0.247541	+	0.968877i	$0.579622\pi$
$420$	12.9550	+	1.32682i	0.632140	+	0.0647420i
$421$	5.47106	+	1.16291i	0.266643	+	0.0566768i	0.339293	−	0.940681i	$-0.389812\pi$
$421$	5.47106	+	1.16291i	0.266643	+	0.0566768i	−0.0726497	+	0.997358i	$0.523146\pi$
$422$	−24.1790	−	7.85624i	−1.17702	−	0.382436i
$423$	−8.50914	−	4.85262i	−0.413729	−	0.235942i
$424$	−0.962842	+	1.32524i	−0.0467597	+	0.0643592i
$425$	−5.31955	−	5.90796i	−0.258036	−	0.286578i
$426$	1.29514	+	12.0151i	0.0627495	+	0.582131i
$427$	−5.25104	−	2.33791i	−0.254116	−	0.113140i
$428$	−0.270522	−	0.468558i	−0.0130762	−	0.0226486i
$429$	7.00068	−	16.1240i	0.337996	−	0.778475i
$430$	4.13248	−	7.15767i	0.199286	−	0.345173i
$431$	−15.7825	+	11.4667i	−0.760216	+	0.552329i	−0.898977	−	0.437997i	$-0.855688\pi$
$431$	−15.7825	+	11.4667i	−0.760216	+	0.552329i	0.138760	+	0.990326i	$0.455688\pi$
$432$	18.8403	−	17.2380i	0.906457	−	0.829362i
$433$	−6.96921	+	21.4490i	−0.334919	+	1.03077i	0.631843	+	0.775096i	$0.282299\pi$
$433$	−6.96921	+	21.4490i	−0.334919	+	1.03077i	−0.966762	+	0.255678i	$0.917701\pi$
$434$	−18.9794	−	42.6284i	−0.911040	−	2.04623i
$435$	−1.08182	+	3.35988i	−0.0518695	+	0.161094i
$436$	3.94439	+	18.5569i	0.188902	+	0.888714i
$437$	−6.07439	+	6.74629i	−0.290577	+	0.322719i
$438$	20.2018	−	9.05883i	0.965278	−	0.432848i
$439$	−25.9695	−	14.9935i	−1.23946	−	0.715601i	−0.270474	−	0.962727i	$-0.587181\pi$
$439$	−25.9695	−	14.9935i	−1.23946	−	0.715601i	−0.968983	+	0.247126i	$0.920514\pi$
$440$	−4.68804	−	2.05027i	−0.223494	−	0.0977428i
$441$	45.1543	+	19.8170i	2.15021	+	0.943667i
$442$	7.29615	+	10.0423i	0.347043	+	0.477663i
$443$	6.55910	−	30.8582i	0.311632	−	1.46612i	−0.491794	−	0.870711i	$-0.663659\pi$
$443$	6.55910	−	30.8582i	0.311632	−	1.46612i	0.803427	−	0.595404i	$-0.203008\pi$
$444$	−2.16018	+	1.25485i	−0.102518	+	0.0595526i
$445$	1.29219	−	12.2943i	0.0612555	−	0.582807i
$446$	3.05986	−	29.1127i	0.144889	−	1.37852i
$447$	−0.0605933	+	0.0351987i	−0.00286596	+	0.00166484i
$448$	1.70357	−	8.01468i	0.0804862	−	0.378658i
$449$	−22.3362	−	30.7432i	−1.05411	−	1.45086i	−0.885190	−	0.465229i	$-0.845972\pi$
$449$	−22.3362	−	30.7432i	−1.05411	−	1.45086i	−0.168921	−	0.985630i	$-0.554028\pi$
$450$	−17.7254	−	7.77921i	−0.835584	−	0.366715i
$451$	7.55911	+	34.4430i	0.355944	+	1.62186i
$452$	−3.57797	−	2.06574i	−0.168294	−	0.0971644i
$453$	−4.34875	+	1.95006i	−0.204322	+	0.0916216i
$454$	−17.8660	+	19.8422i	−0.838493	+	0.931241i
$455$	−3.70108	−	17.4122i	−0.173509	−	0.816297i
$456$	−3.11319	+	9.66879i	−0.145788	+	0.452782i
$457$	−15.9546	−	35.8347i	−0.746327	−	1.67628i	−0.736603	−	0.676325i	$-0.763571\pi$
$457$	−15.9546	−	35.8347i	−0.746327	−	1.67628i	−0.00972362	−	0.999953i	$-0.503095\pi$
$458$	12.4473	−	38.3088i	0.581624	−	1.79005i
$459$	−11.0764	−	3.50151i	−0.517000	−	0.163437i
$460$	2.49706	−	1.81422i	0.116426	−	0.0845885i
$461$	8.77604	−	15.2006i	0.408741	−	0.707960i	−0.586008	−	0.810305i	$-0.699301\pi$
$461$	8.77604	−	15.2006i	0.408741	−	0.707960i	0.994749	+	0.102345i	$0.0326346\pi$
$462$	37.8120	+	33.4173i	1.75918	+	1.55471i
$463$	−2.53619	−	4.39282i	−0.117867	−	0.204151i	0.801055	−	0.598590i	$-0.204272\pi$
$463$	−2.53619	−	4.39282i	−0.117867	−	0.204151i	−0.918922	+	0.394439i	$0.870939\pi$
$464$	7.61398	+	3.38996i	0.353470	+	0.157375i
$465$	−1.18489	−	10.9923i	−0.0549480	−	0.509756i
$466$	−6.27521	−	6.96932i	−0.290693	−	0.322848i
$467$	9.96792	−	13.7197i	0.461260	−	0.634870i	−0.513509	−	0.858084i	$-0.671655\pi$
$467$	9.96792	−	13.7197i	0.461260	−	0.634870i	0.974770	+	0.223214i	$0.0716548\pi$
$468$	10.3064	+	5.87755i	0.476412	+	0.271690i
$469$	9.69445	+	3.14992i	0.447648	+	0.145450i
$470$	−6.96389	−	1.48022i	−0.321220	−	0.0682774i
$471$	3.63538	+	0.372326i	0.167510	+	0.0171559i
$472$	−0.0351352	+	0.0202853i	−0.00161723	+	0.000933706i
$473$	11.4509	−	5.18915i	0.526515	−	0.238597i
$474$	8.01206	−	8.94601i	0.368006	−	0.410904i
$475$	16.1544	−	1.69790i	0.741215	−	0.0779048i
$476$	−13.3036	+	4.32260i	−0.609769	+	0.198126i
$477$	3.63401	−	1.20216i	0.166390	−	0.0550431i
$478$	20.0601	+	14.5745i	0.917526	+	0.666622i
$479$	16.5165	−	7.35362i	0.754658	−	0.335996i	0.00690859	−	0.999976i	$-0.497801\pi$
$479$	16.5165	−	7.35362i	0.754658	−	0.335996i	0.747750	+	0.663981i	$0.231134\pi$
$480$	6.57737	−	11.4626i	0.300214	−	0.523194i
$481$	2.53774	+	2.28499i	0.115711	+	0.104187i
$482$	−5.20495	+	11.6905i	−0.237079	+	0.532488i
$483$	15.8352	−	5.19175i	0.720526	−	0.236233i
$484$	7.27040	+	12.2172i	0.330473	+	0.555329i
$485$			17.4295i			0.791435i
$486$	−28.0887	+	3.33027i	−1.27413	+	0.151064i
$487$	−8.03498	−	24.7291i	−0.364100	−	1.12058i	−0.950543	−	0.310594i	$-0.899472\pi$
$487$	−8.03498	−	24.7291i	−0.364100	−	1.12058i	0.586443	−	0.809991i	$-0.300528\pi$
$488$	−1.13281	+	1.01999i	−0.0512798	+	0.0461726i
$489$	−24.0646	−	7.74840i	−1.08824	−	0.350395i
$490$	35.6435	+	3.74628i	1.61021	+	0.169240i
$491$	7.17172	−	1.52440i	0.323655	−	0.0687950i	−0.0432191	−	0.999066i	$-0.513761\pi$
$491$	7.17172	−	1.52440i	0.323655	−	0.0687950i	0.366874	+	0.930271i	$0.380428\pi$
$492$	−23.6637	+	2.55078i	−1.06684	+	0.114998i
$493$	−0.396312	−	3.77066i	−0.0178490	−	0.169822i
$494$	−25.3622			−1.14110
$495$	6.10114	+	10.2825i	0.274226	+	0.462163i
$496$	−26.1057			−1.17218
$497$	1.94582	+	18.5132i	0.0872818	+	0.830431i
$498$	9.23678	−	20.8955i	0.413910	−	0.936348i
$499$	9.21321	−	1.95833i	0.412440	−	0.0876668i	0.00298137	−	0.999996i	$-0.499051\pi$
$499$	9.21321	−	1.95833i	0.412440	−	0.0876668i	0.409458	+	0.912329i	$0.365718\pi$
$500$	−13.2153	−	1.38898i	−0.591007	−	0.0621173i
$501$	0.325337	+	1.51083i	0.0145350	+	0.0674988i
$502$	9.07311	−	8.16946i	0.404953	−	0.364621i
$503$	10.3211	+	31.7652i	0.460196	+	1.41634i	0.864925	+	0.501902i	$0.167366\pi$
$503$	10.3211	+	31.7652i	0.460196	+	1.41634i	−0.404728	+	0.914437i	$0.632634\pi$
$504$	13.7904	−	12.5504i	0.614274	−	0.559037i
$505$			19.3294i			0.860149i
$506$	11.9599	−	0.0789666i	0.531681	−	0.00351050i
$507$	−1.29320	+	6.16454i	−0.0574328	+	0.273777i
$508$	11.7239	−	26.3322i	0.520162	−	1.16830i
$509$	15.2373	+	13.7197i	0.675379	+	0.608114i	0.933748	−	0.357932i	$-0.116518\pi$
$509$	15.2373	+	13.7197i	0.675379	+	0.608114i	−0.258368	+	0.966047i	$0.583185\pi$
$510$	−8.44298	+	0.0224449i	−0.373862	+	0.000993877i
$511$	31.1557	−	13.8714i	1.37825	−	0.613636i
$512$	−15.0364	−	10.9246i	−0.664521	−	0.482803i
$513$	19.0903	−	14.1039i	0.842858	−	0.622702i
$514$	−24.4213	+	7.93496i	−1.07718	+	0.349996i
$515$	−2.48714	+	0.261409i	−0.109597	+	0.0115191i
$516$	2.64359	+	8.06314i	0.116378	+	0.354960i
$517$	−7.29928	−	7.99981i	−0.321022	−	0.351831i
$518$	−8.48982	+	4.90160i	−0.373021	+	0.215364i
$519$	−9.38836	−	20.9366i	−0.412103	−	0.919016i
$520$	−4.61766	−	0.981513i	−0.202498	−	0.0430422i
$521$	12.4115	+	4.03273i	0.543757	+	0.176677i	0.568000	−	0.823029i	$-0.307718\pi$
$521$	12.4115	+	4.03273i	0.543757	+	0.176677i	−0.0242430	+	0.999706i	$0.507718\pi$
$522$	−4.65832	−	7.97028i	−0.203889	−	0.348850i
$523$	−4.85832	+	6.68690i	−0.212439	+	0.292398i	−0.901917	−	0.431909i	$-0.857840\pi$
$523$	−4.85832	+	6.68690i	−0.212439	+	0.292398i	0.689478	+	0.724307i	$0.257840\pi$
$524$	13.4039	+	14.8866i	0.585553	+	0.650322i
$525$	−27.2723	−	12.0556i	−1.19026	−	0.526150i
$526$	11.5137	+	5.12621i	0.502020	+	0.223514i
$527$	5.93780	+	10.2846i	0.258655	+	0.448003i
$528$	25.6833	−	11.7211i	1.11772	−	0.510097i
$529$	−9.52516	+	16.4981i	−0.414138	+	0.717307i
$530$	2.25067	−	1.63521i	0.0977628	−	0.0710289i
$531$	0.0943329	+	0.00940797i	0.00409370	+	0.000408271i
$532$	8.83197	−	27.1820i	0.382915	−	1.17849i
$533$	13.2328	+	29.7213i	0.573174	+	1.28737i
$534$	21.6980	+	23.9697i	0.938966	+	1.03727i
$535$	−0.104587	−	0.492045i	−0.00452171	−	0.0212730i
$536$	1.80882	−	2.00890i	0.0781292	−	0.0867712i
$537$	−28.2822	−	20.4336i	−1.22047	−	0.881774i
$538$	10.8502	+	6.26435i	0.467784	+	0.270075i
$539$	40.7532	+	36.2100i	1.75537	+	1.55968i
$540$	−7.34588	+	3.34105i	−0.316117	+	0.143776i
$541$	5.73469	+	7.89312i	0.246554	+	0.339352i	0.914301	−	0.405036i	$-0.132741\pi$
$541$	5.73469	+	7.89312i	0.246554	+	0.339352i	−0.667747	+	0.744388i	$0.732741\pi$
$542$	−5.14010	+	24.1823i	−0.220786	+	1.03872i
$543$	0.0207031	+	7.78779i	0.000888456	+	0.334206i
$544$	−1.48382	+	14.1176i	−0.0636183	+	0.605287i
$545$	−1.84375	+	17.5421i	−0.0789777	+	0.751423i
$546$	40.3817	+	23.1715i	1.72818	+	0.991648i
$547$	−1.61861	+	7.61497i	−0.0692068	+	0.325592i	−0.999109	−	0.0422157i	$-0.986558\pi$
$547$	−1.61861	+	7.61497i	−0.0692068	+	0.325592i	0.929902	+	0.367808i	$0.119892\pi$
$548$	−13.0215	−	17.9225i	−0.556250	−	0.765613i
$549$	3.54038	−	0.391151i	0.151100	−	0.0166939i
$550$	−15.9978	−	14.2143i	−0.682147	−	0.606100i
$551$	6.70882	+	3.87334i	0.285805	+	0.165010i
$552$	0.450266	−	4.39639i	0.0191646	−	0.187123i
$553$	12.3784	−	13.7476i	0.526381	−	0.584605i
$554$	−4.39704	−	20.6864i	−0.186812	−	0.878883i
$555$	−2.27067	+	0.488958i	−0.0963845	+	0.0207551i
$556$	−5.45021	−	12.2414i	−0.231140	−	0.519149i
$557$	−1.09093	+	3.35755i	−0.0462244	+	0.142264i	−0.971505	−	0.237019i	$-0.923829\pi$
$557$	−1.09093	+	3.35755i	−0.0462244	+	0.142264i	0.925281	+	0.379283i	$0.123829\pi$
$558$	23.4835	+	16.8718i	0.994137	+	0.714238i
$559$	9.38378	−	6.81772i	0.396892	−	0.288359i
$560$	14.2948	−	24.7594i	0.604067	−	1.04627i
$561$	−10.4594	−	7.45219i	−0.441596	−	0.314632i
$562$	19.8149	+	34.3204i	0.835841	+	1.44772i
$563$	−1.37274	−	0.611183i	−0.0578540	−	0.0257583i	0.377606	−	0.925966i	$-0.376747\pi$
$563$	−1.37274	−	0.611183i	−0.0578540	−	0.0257583i	−0.435460	+	0.900208i	$0.643414\pi$
$564$	5.90198	−	4.31206i	0.248518	−	0.181570i
$565$	−2.57031	−	2.85461i	−0.108134	−	0.120095i
$566$	25.0367	−	34.4601i	1.05237	−	1.44847i
$567$	−43.2812	+	5.01490i	−1.81764	+	0.210606i
$568$	4.69506	+	1.52552i	0.197000	+	0.0640093i
$569$	−14.5137	−	3.08499i	−0.608447	−	0.129329i	−0.106624	−	0.994299i	$-0.534004\pi$
$569$	−14.5137	−	3.08499i	−0.608447	−	0.129329i	−0.501823	+	0.864970i	$0.667337\pi$
$570$	10.1026	−	13.9831i	0.423153	−	0.585689i
$571$	−25.8594	+	14.9299i	−1.08218	+	0.624798i	−0.931484	−	0.363782i	$-0.881485\pi$
$571$	−25.8594	+	14.9299i	−1.08218	+	0.624798i	−0.150697	+	0.988580i	$0.548152\pi$
$572$	8.84097	+	9.68946i	0.369659	+	0.405137i
$573$	−30.1295	−	6.32056i	−1.25868	−	0.264045i
$574$	−92.8850	+	9.76261i	−3.87695	+	0.407483i
$575$	−6.72128	+	2.18388i	−0.280297	+	0.0910740i
$576$	1.59469	+	4.82058i	0.0664453	+	0.200858i
$577$	−20.6394	−	14.9954i	−0.859228	−	0.624266i	0.0684465	−	0.997655i	$-0.478196\pi$
$577$	−20.6394	−	14.9954i	−0.859228	−	0.624266i	−0.927675	+	0.373389i	$0.878196\pi$
$578$	−19.8949	+	8.85780i	−0.827520	+	0.368436i
$579$	−5.35836	−	9.22423i	−0.222686	−	0.383346i
$580$	−1.95735	−	1.76240i	−0.0812745	−	0.0731799i
$581$	14.3138	−	32.1494i	0.593838	−	1.33378i
$582$	−33.9576	−	30.4125i	−1.40759	−	1.26064i
$583$	4.23158	−	0.0279396i	0.175254	−	0.00115714i
$584$		−	9.04432i		−	0.374256i
$585$	7.42471	+	8.15833i	0.306974	+	0.337305i
$586$	−0.951344	−	2.92793i	−0.0392996	−	0.120952i
$587$	−17.5588	+	15.8100i	−0.724731	+	0.652550i	−0.946557	−	0.322536i	$-0.895465\pi$
$587$	−17.5588	+	15.8100i	−0.724731	+	0.652550i	0.221827	+	0.975086i	$0.428798\pi$
$588$	−27.2791	+	24.6939i	−1.12497	+	1.01836i
$589$	−24.1314	−	2.53631i	−0.994317	−	0.104507i
$590$	0.0673959	−	0.0143254i	0.00277465	−	0.000589769i
$591$	23.0006	+	31.4813i	0.946120	+	1.29497i
$592$	0.573282	+	5.45441i	0.0235617	+	0.224175i
$593$	10.1681			0.417553			0.208777	−	0.977963i	$-0.433052\pi$
$593$	10.1681			0.417553			0.208777	+	0.977963i	$0.433052\pi$
$594$	−30.6789	−	6.05497i	−1.25877	−	0.248438i
$595$	−13.0056			−0.533178
$596$	−0.00546573	−	0.0520029i	−0.000223885	−	0.00213012i
$597$	9.50965	+	13.0160i	0.389204	+	0.532709i
$598$	10.7935	−	2.29423i	0.441378	−	0.0938179i
$599$	6.06202	+	0.637144i	0.247687	+	0.0260330i	0.227559	−	0.973764i	$-0.426926\pi$
$599$	6.06202	+	0.637144i	0.247687	+	0.0260330i	0.0201288	+	0.999797i	$0.493592\pi$
$600$	−5.86243	+	5.30684i	−0.239333	+	0.216651i
$601$	−10.4219	+	9.38389i	−0.425117	+	0.382777i	−0.853734	−	0.520709i	$-0.825667\pi$
$601$	−10.4219	+	9.38389i	−0.425117	+	0.382777i	0.428617	+	0.903486i	$0.359001\pi$
$602$	10.2896	+	31.6680i	0.419371	+	1.29069i
$603$	−6.17153	+	1.34613i	−0.251324	+	0.0548188i
$604$		−	3.55632i		−	0.144705i
$605$	2.91870	+	12.8919i	0.118662	+	0.524131i
$606$	−37.6591	−	33.7276i	−1.52980	−	1.37009i
$607$	−0.344302	+	0.773316i	−0.0139748	+	0.0313879i	−0.920398	−	0.390983i	$-0.872135\pi$
$607$	−0.344302	+	0.773316i	−0.0139748	+	0.0313879i	0.906423	+	0.422371i	$0.138802\pi$
$608$	−21.5542	−	19.4075i	−0.874140	−	0.787079i
$609$	−7.14301	−	12.2964i	−0.289449	−	0.498277i
$610$	2.36500	−	1.05297i	0.0957560	−	0.0426333i
$611$	−8.08321	−	5.87280i	−0.327012	−	0.237588i
$612$	5.76586	−	6.47251i	0.233071	−	0.261636i
$613$	−24.1513	+	7.84724i	−0.975462	+	0.316947i	−0.753019	−	0.657999i	$-0.771403\pi$
$613$	−24.1513	+	7.84724i	−0.975462	+	0.316947i	−0.222443	+	0.974946i	$0.571403\pi$
$614$	4.24581	−	0.446253i	0.171347	−	0.0180093i
$615$	−21.6575	−	4.54329i	−0.873313	−	0.183203i
$616$	18.7764	−	8.50876i	0.756521	−	0.342828i
$617$	8.73291	−	5.04195i	0.351574	−	0.202981i	−0.313805	−	0.949488i	$-0.601604\pi$
$617$	8.73291	−	5.04195i	0.351574	−	0.202981i	0.665378	+	0.746507i	$0.268270\pi$
$618$	3.83047	−	5.30177i	0.154084	−	0.213269i
$619$	25.4818	+	5.41633i	1.02420	+	0.217701i	0.689241	−	0.724532i	$-0.257944\pi$
$619$	25.4818	+	5.41633i	1.02420	+	0.217701i	0.334960	+	0.942232i	$0.391277\pi$
$620$	7.84611	+	2.54935i	0.315107	+	0.102385i
$621$	−6.84850	+	7.72911i	−0.274821	+	0.310159i
$622$	11.3121	−	15.5698i	0.453574	−	0.624291i
$623$	33.3253	+	37.0115i	1.33515	+	1.48284i
$624$	21.0316	−	15.3659i	0.841937	−	0.615129i
$625$	4.95643	+	2.20675i	0.198257	+	0.0882698i
$626$	22.9845	+	39.8103i	0.918646	+	1.59114i
$627$	24.8798	−	8.33945i	0.993604	−	0.333046i
$628$	−1.36344	+	2.36155i	−0.0544073	+	0.0942362i
$629$	2.01842	−	1.46647i	0.0804798	−	0.0584720i
$630$	−28.8607	+	13.0339i	−1.14984	+	0.519284i
$631$	3.44605	−	10.6058i	0.137185	−	0.422212i	−0.858739	−	0.512414i	$-0.828751\pi$
$631$	3.44605	−	10.6058i	0.137185	−	0.422212i	0.995923	+	0.0902022i	$0.0287513\pi$
$632$	−1.99541	−	4.48177i	−0.0793733	−	0.178275i
$633$	23.7242	−	5.10869i	0.942952	−	0.203052i
$634$	−10.1152	−	47.5883i	−0.401726	−	1.88997i
$635$	17.9323	−	19.9158i	0.711621	−	0.790335i
$636$	−0.291001	+	2.84133i	−0.0115390	+	0.112666i
$637$	43.5588	+	25.1487i	1.72586	+	0.996426i
$638$	−2.18783	−	9.96884i	−0.0866172	−	0.394670i
$639$	−6.82991	−	9.29622i	−0.270187	−	0.367753i
$640$	−6.80053	−	9.36013i	−0.268815	−	0.369991i
$641$	2.29516	−	10.7979i	0.0906534	−	0.426491i	−0.909293	−	0.416156i	$-0.863377\pi$
$641$	2.29516	−	10.7979i	0.0906534	−	0.426491i	0.999947	−	0.0103346i	$-0.00328968\pi$
$642$	1.14113	+	0.654795i	0.0450369	+	0.0258427i
$643$	−3.84039	+	36.5389i	−0.151450	+	1.44095i	0.609831	+	0.792532i	$0.291237\pi$
$643$	−3.84039	+	36.5389i	−0.151450	+	1.44095i	−0.761281	+	0.648422i	$0.775429\pi$
$644$	−1.29981	+	12.3669i	−0.0512196	+	0.487322i
$645$	0.0209731	+	7.88935i	0.000825815	+	0.310643i
$646$	−3.85255	+	18.1248i	−0.151576	+	0.713111i
$647$	−1.59821	−	2.19975i	−0.0628321	−	0.0864810i	0.776445	−	0.630186i	$-0.217021\pi$
$647$	−1.59821	−	2.19975i	−0.0628321	−	0.0864810i	−0.839277	+	0.543705i	$0.817021\pi$
$648$	−3.45358	+	11.0266i	−0.135669	+	0.433167i
$649$	0.0960246	+	0.0419955i	0.00376930	+	0.00164847i
$650$	−17.0991	−	9.87215i	−0.670681	−	0.387218i
$651$	36.1048	+	26.0853i	1.41506	+	1.02236i
$652$	12.6230	−	14.0192i	0.494353	−	0.549035i
$653$	9.19912	+	43.2784i	0.359989	+	1.69362i	0.669575	+	0.742745i	$0.266476\pi$
$653$	9.19912	+	43.2784i	0.359989	+	1.69362i	−0.309586	+	0.950872i	$0.600190\pi$
$654$	−30.9598	−	34.2011i	−1.21063	−	1.33737i
$655$	7.57534	+	17.0145i	0.295993	+	0.664811i
$656$	−16.1465	+	49.6939i	−0.630416	+	1.94022i
$657$	−12.3310	+	17.1634i	−0.481079	+	0.669607i
$658$	23.2048	−	16.8593i	0.904618	−	0.657244i
$659$	−4.58714	+	7.94516i	−0.178690	+	0.309499i	−0.941432	−	0.337203i	$-0.890519\pi$
$659$	−4.58714	+	7.94516i	−0.178690	+	0.309499i	0.762742	+	0.646702i	$0.223852\pi$
$660$	−8.86381	+	1.01470i	−0.345023	+	0.0394972i
$661$	4.94816	+	8.57046i	0.192461	+	0.333352i	0.946065	−	0.323976i	$-0.105020\pi$
$661$	4.94816	+	8.57046i	0.192461	+	0.333352i	−0.753604	+	0.657328i	$0.771686\pi$
$662$	−28.7164	−	12.7854i	−1.11610	−	0.496918i
$663$	−10.8372	−	4.79057i	−0.420884	−	0.186050i
$664$	−6.24484	−	6.93560i	−0.242347	−	0.269153i
$665$	15.6193	−	21.4981i	0.605691	−	0.833662i
$666$	3.00942	−	5.27706i	0.116613	−	0.204482i
$667$	−3.20547	−	1.04152i	−0.124116	−	0.0403278i
$668$	−1.12801	−	0.239766i	−0.0436440	−	0.00927682i
$669$	11.4332	+	25.4967i	0.442031	+	0.985758i
$670$	−3.97588	+	2.29547i	−0.153602	+	0.0886819i
$671$	3.85712	+	0.793275i	0.148902	+	0.0306241i
$672$	16.5875	+	50.5931i	0.639877	+	1.95167i
$673$	17.5860	−	1.84836i	0.677891	−	0.0712492i	0.240675	−	0.970606i	$-0.422631\pi$
$673$	17.5860	−	1.84836i	0.677891	−	0.0712492i	0.437216	+	0.899357i	$0.355965\pi$
$674$	22.4408	−	7.29146i	0.864387	−	0.280856i
$675$	18.3605	−	2.07794i	0.706694	−	0.0799798i
$676$	−3.80243	−	2.76263i	−0.146247	−	0.106255i
$677$	−10.8673	+	4.83844i	−0.417665	+	0.185956i	−0.604799	−	0.796378i	$-0.706747\pi$
$677$	−10.8673	+	4.83844i	−0.417665	+	0.185956i	0.187134	+	0.982334i	$0.440080\pi$
$678$	10.0465	−	0.0267076i	0.385832	−	0.00102570i
$679$	−52.1835	−	46.9862i	−2.00262	−	1.80316i
$680$	−1.40285	+	3.15085i	−0.0537969	+	0.120830i
$681$	5.23274	−	24.9440i	0.200519	−	0.955856i
$682$	18.9605	+	25.7379i	0.726037	+	0.985554i
$683$		−	18.2564i		−	0.698561i	−0.937018	−	0.349280i	$-0.886426\pi$
$683$		−	18.2564i		−	0.698561i	0.937018	−	0.349280i	$-0.113574\pi$
$684$	3.77439	+	17.3042i	0.144317	+	0.661642i
$685$	−6.36490	−	19.5892i	−0.243190	−	0.748463i
$686$	−61.6066	+	55.4709i	−2.35215	+	2.11789i
$687$	8.09412	+	37.5882i	0.308810	+	1.43408i
$688$	18.5265	+	1.94722i	0.706318	+	0.0742370i
$689$	3.81889	−	0.811731i	0.145488	−	0.0309245i
$690$	−3.03452	+	6.86471i	−0.115522	+	0.261335i
$691$	−1.88403	−	17.9254i	−0.0716720	−	0.681914i	−0.970086	−	0.242763i	$-0.921946\pi$
$691$	−1.88403	−	17.9254i	−0.0716720	−	0.681914i	0.898414	−	0.439150i	$-0.144721\pi$
$692$	17.1216			0.650864
$693$	−47.2327	−	9.45266i	−1.79422	−	0.359077i
$694$	38.5698			1.46409
$695$	−1.30227	−	12.3903i	−0.0493980	−	0.469991i
$696$	−3.74953	+	0.404172i	−0.142126	+	0.0153201i
$697$	23.2500	−	4.94193i	0.880655	−	0.187189i
$698$	16.8384	+	1.76979i	0.637343	+	0.0669875i
$699$	8.52115	+	2.74367i	0.322300	+	0.103775i
$700$	16.5350	−	14.8881i	0.624962	−	0.562719i
$701$	2.60431	+	8.01524i	0.0983635	+	0.302732i	0.988116	−	0.153712i	$-0.0491229\pi$
$701$	2.60431	+	8.01524i	0.0983635	+	0.302732i	−0.889752	+	0.456444i	$0.849123\pi$
$702$	−28.8499	+	0.230089i	−1.08887	+	0.00868415i
$703$			5.09762i			0.192260i
$704$	0.0370623	+	5.61327i	0.00139684	+	0.211558i
$705$	6.45771	−	2.11723i	0.243211	−	0.0797396i
$706$	6.73185	−	15.1200i	0.253356	−	0.569048i
$707$	−57.8717	−	52.1079i	−2.17649	−	1.95972i
$708$	−0.0352068	+	0.0613562i	−0.00132315	+	0.00230591i
$709$	18.9224	−	8.42480i	0.710646	−	0.316400i	−0.0193869	−	0.999812i	$-0.506171\pi$
$709$	18.9224	−	8.42480i	0.710646	−	0.316400i	0.730033	+	0.683412i	$0.239505\pi$
$710$	−6.78282	−	4.92801i	−0.254555	−	0.184945i
$711$	−2.32376	+	11.2256i	−0.0871479	+	0.420993i
$712$	12.5614	−	4.08144i	0.470758	−	0.152959i
$713$	10.4991	−	1.10350i	0.393194	−	0.0413264i
$714$	22.6932	−	25.3385i	0.849273	−	0.948270i
$715$	5.03373	+	11.1080i	0.188251	+	0.415415i
$716$	22.5476	−	13.0179i	0.842644	−	0.486501i
$717$	−23.5456	−	2.41148i	−0.879328	−	0.0900583i
$718$	−13.8817	−	2.95065i	−0.518061	−	0.110117i
$719$	34.3009	+	11.1450i	1.27921	+	0.415640i	0.868301	−	0.496038i	$-0.165212\pi$
$719$	34.3009	+	11.1450i	1.27921	+	0.415640i	0.410906	+	0.911678i	$0.365212\pi$
$720$	0.0941947	+	17.7162i	0.00351043	+	0.660245i
$721$	5.92214	−	8.15112i	0.220552	−	0.303564i
$722$	−2.26460	−	2.51510i	−0.0842798	−	0.0936022i
$723$	−1.30914	−	12.1450i	−0.0486874	−	0.451676i
$724$	−5.30880	−	2.36363i	−0.197300	−	0.0878437i
$725$	3.01536	+	5.22276i	0.111988	+	0.193968i
$726$	−30.2098	−	16.8084i	−1.12119	−	0.623819i
$727$	10.4928	−	18.1741i	0.389158	−	0.674042i	−0.603178	−	0.797606i	$-0.706099\pi$
$727$	10.4928	−	18.1741i	0.389158	−	0.674042i	0.992337	+	0.123565i	$0.0394327\pi$
$728$	15.3868	−	11.1792i	0.570273	−	0.414327i
$729$	21.5876	−	16.2166i	0.799539	−	0.600614i
$730$	−4.74653	+	14.6083i	−0.175677	+	0.540678i
$731$	−3.44679	−	7.74161i	−0.127484	−	0.286334i
$732$	−0.814606	+	2.52996i	−0.0301087	+	0.0935102i
$733$	−8.44604	−	39.7355i	−0.311962	−	1.46766i	−0.802714	−	0.596364i	$-0.796611\pi$
$733$	−8.44604	−	39.7355i	−0.311962	−	1.46766i	0.490752	−	0.871299i	$-0.336722\pi$
$734$	29.7517	−	33.0426i	1.09816	−	1.21963i
$735$	−31.2163	+	13.9979i	−1.15143	+	0.516322i
$736$	10.9285	+	6.30956i	0.402829	+	0.232573i
$737$	−6.94971	−	0.684083i	−0.255996	−	0.0251985i
$738$	46.6413	−	34.2672i	1.71689	−	1.26139i
$739$	−0.159730	−	0.219850i	−0.00587578	−	0.00808731i	0.806069	−	0.591822i	$-0.201591\pi$
$739$	−0.159730	−	0.219850i	−0.00587578	−	0.00808731i	−0.811945	+	0.583734i	$0.801591\pi$
$740$	0.360351	−	1.69532i	0.0132468	−	0.0623212i
$741$	20.9340	−	12.1605i	0.769028	−	0.446729i
$742$	−1.17155	+	11.1466i	−0.0430091	+	0.409204i
$743$	−2.14939	+	20.4500i	−0.0788533	+	0.750239i	0.881637	+	0.471927i	$0.156442\pi$
$743$	−2.14939	+	20.4500i	−0.0788533	+	0.750239i	−0.960491	+	0.278312i	$0.910225\pi$
$744$	10.2141	−	5.93338i	0.374467	−	0.217528i
$745$	0.0101079	−	0.0475538i	0.000370324	−	0.00174224i
$746$	−3.05169	−	4.20029i	−0.111730	−	0.153783i
$747$	2.39481	+	21.6759i	0.0876216	+	0.793079i
$748$	8.26740	−	4.84624i	0.302286	−	0.177196i
$749$	1.75511	+	1.01331i	0.0641304	+	0.0370257i
$750$	29.4839	−	13.2211i	1.07660	−	0.482767i
$751$	−34.8745	+	38.7320i	−1.27259	+	1.41335i	−0.406351	+	0.913717i	$0.633199\pi$
$751$	−34.8745	+	38.7320i	−1.27259	+	1.41335i	−0.866237	+	0.499634i	$0.833468\pi$
$752$	−3.33630	−	15.6961i	−0.121662	−	0.572376i
$753$	−3.57188	+	11.0934i	−0.130167	+	0.404265i
$754$	−3.82996	−	8.60223i	−0.139479	−	0.313275i
$755$	1.02176	−	3.14467i	0.0371858	−	0.114446i
$756$	9.79990	−	31.0001i	0.356419	−	1.12746i
$757$	30.2153	−	21.9527i	1.09819	−	0.797884i	0.117429	−	0.993081i	$-0.462535\pi$
$757$	30.2153	−	21.9527i	1.09819	−	0.797884i	0.980764	+	0.195197i	$0.0625347\pi$
$758$	26.5495	−	45.9851i	0.964322	−	1.67025i
$759$	−9.83380	+	5.79963i	−0.356944	+	0.210513i
$760$	−3.52355	−	6.10297i	−0.127813	−	0.221378i
$761$	−40.7814	−	18.1571i	−1.47833	−	0.658193i	−0.500144	−	0.865942i	$-0.666720\pi$
$761$	−40.7814	−	18.1571i	−1.47833	−	0.658193i	−0.978182	+	0.207749i	$0.933386\pi$
$762$	7.51184	+	69.6878i	0.272125	+	2.52452i
$763$	−47.5502	−	52.8099i	−1.72143	−	1.91185i
$764$	13.5025	−	18.5846i	0.488503	−	0.672367i
$765$	6.95806	−	4.06672i	0.251569	−	0.147032i
$766$	−49.1124	−	15.9576i	−1.77450	−	0.576571i
$767$	0.0945829	+	0.0201042i	0.00341519	+	0.000725921i
$768$	35.9347	+	3.68033i	1.29668	+	0.132803i
$769$	−19.3337	+	11.1623i	−0.697192	+	0.402524i	−0.806301	−	0.591506i	$-0.798534\pi$
$769$	−19.3337	+	11.1623i	−0.697192	+	0.402524i	0.109109	+	0.994030i	$0.465200\pi$
$770$	−34.7929	+	3.88931i	−1.25385	+	0.140161i
$771$	16.3527	−	18.2589i	0.588927	−	0.657577i
$772$	7.91650	−	0.832058i	0.284921	−	0.0299464i
$773$	−19.1268	+	6.21468i	−0.687944	+	0.223526i	−0.632070	−	0.774911i	$-0.717794\pi$
$773$	−19.1268	+	6.21468i	−0.687944	+	0.223526i	−0.0558738	+	0.998438i	$0.517794\pi$
$774$	−15.4072	−	13.7251i	−0.553801	−	0.493339i
$775$	−15.2820	−	11.1030i	−0.548946	−	0.398832i
$776$	−17.0121	+	7.57426i	−0.610698	+	0.271900i
$777$	4.65729	−	8.11642i	0.167080	−	0.291175i
$778$	−19.2577	−	17.3397i	−0.690423	−	0.621659i
$779$	−19.7535	+	44.3671i	−0.707742	+	1.58962i
$780$	−7.82165	+	2.56442i	−0.280060	+	0.0918208i
$781$	−4.02087	−	12.1025i	−0.143878	−	0.433061i
$782$		−	8.06192i		−	0.288294i
$783$	7.66651	+	4.34511i	0.273979	+	0.155282i
$784$	24.9624	+	76.8265i	0.891516	+	2.74380i
$785$	−1.88412	+	1.69647i	−0.0672471	+	0.0605495i
$786$	−46.3670	−	14.9294i	−1.65386	−	0.532514i
$787$	34.6278	+	3.63953i	1.23435	+	0.129735i	0.699139	−	0.714985i	$-0.253567\pi$
$787$	34.6278	+	3.63953i	1.23435	+	0.129735i	0.535208	+	0.844721i	$0.320233\pi$
$788$	−28.4572	+	6.04876i	−1.01374	+	0.215478i
$789$	−11.9612	+	1.28934i	−0.425832	+	0.0459016i
$790$	0.870908	+	8.28613i	0.0309855	+	0.294807i
$791$	15.4756			0.550249
$792$	−7.38485	+	10.4234i	−0.262409	+	0.370380i
$793$	3.63312			0.129016
$794$	−0.418572	−	3.98245i	−0.0148546	−	0.141332i
$795$	−1.07366	+	2.42883i	−0.0380788	+	0.0861419i
$796$	−11.7657	+	2.50087i	−0.417023	+	0.0886409i
$797$	0.782420	+	0.0822356i	0.0277147	+	0.00291294i	0.118376	−	0.992969i	$-0.462231\pi$
$797$	0.782420	+	0.0822356i	0.0277147	+	0.00291294i	−0.0906609	+	0.995882i	$0.528898\pi$
$798$	14.6305	+	67.9424i	0.517914	+	2.40514i
$799$	−5.42477	+	4.88448i	−0.191914	+	0.172800i
$800$	−6.97744	−	21.4743i	−0.246690	−	0.759233i
$801$	−29.4024	−	9.38087i	−1.03888	−	0.331457i
$802$			57.2351i			2.02104i
$803$	−18.8110	+	13.8577i	−0.663825	+	0.489026i
$804$	0.967716	−	4.61301i	0.0341287	−	0.162688i
$805$	−4.70247	+	10.5619i	−0.165740	+	0.372259i
$806$	21.9183	+	19.7353i	0.772040	+	0.695148i
$807$	−11.9593	+	0.0317927i	−0.420987	+	0.00111916i
$808$	−18.8665	+	8.39990i	−0.663720	+	0.295507i
$809$	−24.9035	−	18.0934i	−0.875560	−	0.636131i	0.0565132	−	0.998402i	$-0.482002\pi$
$809$	−24.9035	−	18.0934i	−0.875560	−	0.636131i	−0.932073	+	0.362270i	$0.882002\pi$
$810$	11.3651	−	15.9977i	0.399327	−	0.562100i
$811$	41.4535	−	13.4691i	1.45563	−	0.472963i	0.528898	−	0.848686i	$-0.322606\pi$
$811$	41.4535	−	13.4691i	1.45563	−	0.472963i	0.926732	+	0.375723i	$0.122606\pi$
$812$	10.5532	−	1.10918i	0.370343	−	0.0389247i
$813$	−7.35214	−	22.4246i	−0.257851	−	0.786463i
$814$	4.96119	−	4.52675i	0.173890	−	0.158662i
$815$	15.1897	−	8.76976i	0.532071	−	0.307191i
$816$	−7.78635	−	17.3640i	−0.272577	−	0.607863i
$817$	16.9363	+	3.59992i	0.592526	+	0.125945i
$818$	11.6971	+	3.80063i	0.408981	+	0.132886i
$819$	−44.4411	+	0.236287i	−1.55290	+	0.00825654i
$820$	9.70574	−	13.3588i	0.338939	−	0.466510i
$821$	−26.0695	−	28.9531i	−0.909833	−	1.01047i	−0.999894	−	0.0145354i	$-0.995373\pi$
$821$	−26.0695	−	28.9531i	−0.909833	−	1.01047i	0.0900617	−	0.995936i	$-0.471294\pi$
$822$	49.2711	+	21.7802i	1.71853	+	0.759670i
$823$	34.3311	+	15.2852i	1.19671	+	0.532809i	0.905703	−	0.423913i	$-0.139344\pi$
$823$	34.3311	+	15.2852i	1.19671	+	0.532809i	0.291005	+	0.956721i	$0.406010\pi$
$824$	−1.33597	−	2.31397i	−0.0465408	−	0.0806111i
$825$	20.0199	+	4.06196i	0.697004	+	0.141419i
$826$	−0.138795	+	0.240399i	−0.00482928	+	0.00836456i
$827$	−36.8905	+	26.8025i	−1.28281	+	0.932015i	−0.999634	−	0.0270532i	$-0.991388\pi$
$827$	−36.8905	+	26.8025i	−1.28281	+	0.932015i	−0.283175	+	0.959068i	$0.591388\pi$
$828$	−3.17158	−	7.02276i	−0.110220	−	0.244058i
$829$	8.83146	−	27.1804i	0.306729	−	0.944016i	−0.672297	−	0.740282i	$-0.734692\pi$
$829$	8.83146	−	27.1804i	0.306729	−	0.944016i	0.979026	−	0.203734i	$-0.0653078\pi$
$830$	6.44676	+	14.4797i	0.223770	+	0.502596i
$831$	13.5479	+	14.9663i	0.469972	+	0.519175i
$832$	1.07678	+	5.06583i	0.0373305	+	0.175626i
$833$	24.5888	−	27.3086i	0.851950	−	0.946187i
$834$	26.4120	+	19.0824i	0.914574	+	0.660770i
$835$	−0.928554	−	0.536101i	−0.0321339	−	0.0185525i
$836$	−1.91808	+	19.4861i	−0.0663382	+	0.673941i
$837$	−27.4728	−	2.66617i	−0.949600	−	0.0921563i
$838$	30.5125	+	41.9968i	1.05404	+	1.45076i
$839$	−1.18333	+	5.56715i	−0.0408532	+	0.192199i	−0.993842	−	0.110806i	$-0.964657\pi$
$839$	−1.18333	+	5.56715i	−0.0408532	+	0.192199i	0.952989	+	0.303005i	$0.0979900\pi$
$840$	0.0343901	+	12.9363i	0.00118657	+	0.446346i
$841$	2.73069	−	25.9808i	0.0941617	−	0.895888i
$842$	1.06087	−	10.0935i	0.0365599	−	0.347844i
$843$	−32.8109	−	18.8273i	−1.13007	−	0.648446i
$844$	−3.76499	+	17.7129i	−0.129596	+	0.609703i
$845$	−2.56856	−	3.53532i	−0.0883612	−	0.121619i
$846$	−7.14297	+	16.2757i	−0.245580	+	0.559571i
$847$	−46.4662	−	26.0153i	−1.59660	−	0.893895i
$848$	5.43030	+	3.13518i	0.186477	+	0.107663i
$849$	−4.14255	+	40.4478i	−0.142172	+	1.38816i
$850$	−9.65237	+	10.7200i	−0.331074	+	0.367694i
$851$	−0.461122	−	2.16941i	−0.0158071	−	0.0743664i
$852$	8.41480	−	1.81202i	0.288286	−	0.0620786i
$853$	10.1942	+	22.8965i	0.349042	+	0.783962i	0.999698	+	0.0245888i	$0.00782763\pi$
$853$	10.1942	+	22.8965i	0.349042	+	0.783962i	−0.650655	+	0.759373i	$0.725506\pi$
$854$	−3.22297	+	9.91929i	−0.110288	+	0.339431i
$855$	−1.63416	+	16.3856i	−0.0558872	+	0.560376i
$856$	0.434810	−	0.315908i	0.0148615	−	0.0107975i
$857$	17.9582	−	31.1045i	0.613440	−	1.06251i	−0.377216	−	0.926126i	$-0.623118\pi$
$857$	17.9582	−	31.1045i	0.613440	−	1.06251i	0.990656	−	0.136385i	$-0.0435483\pi$
$858$	−30.4247	−	9.57500i	−1.03868	−	0.326885i
$859$	7.86620	+	13.6247i	0.268391	+	0.464868i	0.968447	−	0.249221i	$-0.0801746\pi$
$859$	7.86620	+	13.6247i	0.268391	+	0.464868i	−0.700055	+	0.714089i	$0.746841\pi$
$860$	−5.37803	−	2.39445i	−0.183389	−	0.0816502i
$861$	71.9862	−	52.5940i	2.45328	−	1.79240i
$862$	23.6858	+	26.3058i	0.806742	+	0.895978i
$863$	−16.0883	+	22.1436i	−0.547652	+	0.753778i	−0.989691	−	0.143217i	$-0.954255\pi$
$863$	−16.0883	+	22.1436i	−0.547652	+	0.753778i	0.442039	+	0.896996i	$0.354255\pi$
$864$	−24.6943	−	21.8808i	−0.840118	−	0.744400i
$865$	15.1397	+	4.91919i	0.514765	+	0.167257i
$866$	40.0281	+	8.50823i	1.36021	+	0.289121i
$867$	12.1742	−	16.8503i	0.413456	−	0.572267i
$868$	−28.7841	+	16.6185i	−0.976995	+	0.564068i
$869$	−6.26413	+	11.0171i	−0.212496	+	0.373731i
$870$	6.26832	+	1.31497i	0.212516	+	0.0445815i
$871$	−6.40761	+	0.673467i	−0.217114	+	0.0228196i
$872$	−17.9232	+	5.82361i	−0.606957	+	0.197212i
$873$	42.6105	+	8.82062i	1.44215	+	0.298533i
$874$	13.3263	+	9.68210i	0.450768	+	0.327502i
$875$	45.4710	−	20.2450i	1.53720	−	0.684405i
$876$	−7.92120	−	13.6361i	−0.267633	−	0.460720i
$877$	−38.6754	−	34.8235i	−1.30597	−	1.17590i	−0.972437	−	0.233168i	$-0.925091\pi$
$877$	−38.6754	−	34.8235i	−1.30597	−	1.17590i	−0.333538	−	0.942737i	$-0.608242\pi$
$878$	−22.1312	+	49.7076i	−0.746893	+	1.67755i
$879$	2.18911	+	1.96057i	0.0738367	+	0.0661283i
$880$	−5.92938	+	18.6673i	−0.199880	+	0.629273i
$881$			39.9758i			1.34682i	0.739270	+	0.673409i	$0.235171\pi$
$881$			39.9758i			1.34682i	−0.739270	+	0.673409i	$0.764829\pi$
$882$	27.1968	−	85.2428i	0.915765	−	2.87027i
$883$	−5.74452	−	17.6798i	−0.193318	−	0.594973i	−0.999992	−	0.00397571i	$-0.998734\pi$
$883$	−5.74452	−	17.6798i	−0.193318	−	0.594973i	0.806674	−	0.590997i	$-0.201266\pi$
$884$	6.57054	−	5.91614i	0.220991	−	0.198981i
$885$	−0.0487598	+	0.0441388i	−0.00163904	+	0.00148371i
$886$	−56.9297	−	5.98356i	−1.91259	−	0.201021i
$887$	53.3355	−	11.3368i	1.79083	−	0.380653i	0.811731	−	0.584032i	$-0.198526\pi$
$887$	53.3355	−	11.3368i	1.79083	−	0.380653i	0.979100	+	0.203379i	$0.0651922\pi$
$888$	−1.46400	−	2.00380i	−0.0491286	−	0.0672430i
$889$	11.2858	+	107.377i	0.378514	+	3.60132i
$890$	−22.4310			−0.751890
$891$	28.2255	−	9.71196i	0.945589	−	0.325363i
$892$	−20.8507			−0.698132
$893$	−1.55903	−	14.8332i	−0.0521710	−	0.496374i
$894$	0.0750110	+	0.102669i	0.00250874	+	0.00343376i
$895$	23.6779	−	5.03288i	0.791463	−	0.168231i
$896$	46.3566	+	4.87228i	1.54867	+	0.162771i
$897$	−7.80890	+	7.06884i	−0.260732	+	0.236022i
$898$	−51.2417	+	46.1382i	−1.70996	+	1.53965i
$899$	−2.78384	−	8.56777i	−0.0928461	−	0.285751i
$900$	−4.19092	+	13.1355i	−0.139697	+	0.437851i
$901$		−	2.85243i		−	0.0950281i
$902$	60.7210	−	20.1737i	2.02179	−	0.671709i
$903$	−23.6770	−	21.2051i	−0.787920	−	0.705663i
$904$	1.66928	−	3.74926i	0.0555193	−	0.124698i
$905$	−4.01520	−	3.61531i	−0.133470	−	0.120177i
$906$	4.34383	+	7.47775i	0.144314	+	0.248432i
$907$	−11.3582	+	5.05700i	−0.377143	+	0.167915i	−0.586549	−	0.809914i	$-0.699514\pi$
$907$	−11.3582	+	5.05700i	−0.377143	+	0.167915i	0.209406	+	0.977829i	$0.432847\pi$
$908$	15.3860	+	11.1786i	0.510603	+	0.370975i
$909$	47.2553	+	9.78211i	1.56736	+	0.324452i
$910$	−30.7195	+	9.98139i	−1.01834	+	0.330880i
$911$	−44.7416	+	4.70253i	−1.48235	+	0.155802i	−0.810874	−	0.585220i	$-0.801008\pi$
$911$	−44.7416	+	4.70253i	−1.48235	+	0.155802i	−0.671481	+	0.741022i	$0.734341\pi$
$912$	38.0537	+	7.98290i	1.26008	+	0.264340i
$913$	−4.85681	+	23.6151i	−0.160737	+	0.781546i
$914$	−61.6402	+	35.5880i	−2.03887	+	1.17715i
$915$	−1.44720	+	2.00307i	−0.0478428	+	0.0662195i
$916$	−28.0640	−	5.96518i	−0.927260	−	0.197095i
$917$	−71.3622	−	23.1870i	−2.35659	−	0.765702i
$918$	−4.21790	+	20.6522i	−0.139211	+	0.681623i
$919$	13.6185	−	18.7442i	0.449232	−	0.618315i	−0.523000	−	0.852333i	$-0.675187\pi$
$919$	13.6185	−	18.7442i	0.449232	−	0.618315i	0.972232	+	0.234017i	$0.0751872\pi$
$920$	2.05159	+	2.27852i	0.0676390	+	0.0751207i
$921$	−3.29052	+	2.40409i	−0.108426	+	0.0792175i
$922$	−29.0950	−	12.9539i	−0.958192	−	0.426615i
$923$	−5.88304	−	10.1897i	−0.193643	−	0.335399i
$924$	20.8569	−	29.2734i	0.686141	−	0.963023i
$925$	−1.98423	+	3.43678i	−0.0652410	+	0.113001i
$926$	−7.44610	+	5.40991i	−0.244694	+	0.177781i
$927$	−0.619601	+	6.21268i	−0.0203504	+	0.204051i
$928$	3.32763	−	10.2414i	0.109235	−	0.336190i
$929$	−4.70492	−	10.5674i	−0.154364	−	0.346706i	0.819765	−	0.572700i	$-0.194104\pi$
$929$	−4.70492	−	10.5674i	−0.154364	−	0.346706i	−0.974129	+	0.225993i	$0.927437\pi$
$930$	−19.6116	+	4.22310i	−0.643091	+	0.138481i
$931$	15.6105	+	73.4417i	0.511614	+	2.40696i
$932$	−4.46972	+	4.96413i	−0.146411	+	0.162605i
$933$	−1.87169	+	18.2751i	−0.0612763	+	0.598301i
$934$	−26.6487	−	15.3856i	−0.871971	−	0.503433i
$935$	8.70280	−	1.90998i	0.284612	−	0.0624630i
$936$	−4.73641	+	10.7922i	−0.154814	+	0.352754i
$937$	15.1544	+	20.8582i	0.495071	+	0.681407i	0.981313	−	0.192417i	$-0.0616326\pi$
$937$	15.1544	+	20.8582i	0.495071	+	0.681407i	−0.486242	+	0.873824i	$0.661633\pi$
$938$	3.84552	−	18.0917i	0.125561	−	0.590716i
$939$	−38.0594	−	21.8389i	−1.24202	−	0.712686i
$940$	−0.530071	+	5.04329i	−0.0172890	+	0.164494i
$941$	6.18370	−	58.8340i	0.201583	−	1.91793i	−0.162756	−	0.986666i	$-0.552038\pi$
$941$	6.18370	−	58.8340i	0.201583	−	1.91793i	0.364339	−	0.931267i	$-0.381295\pi$
$942$	−0.0176277	−	6.63092i	−0.000574341	−	0.216047i
$943$	4.39318	−	20.6683i	0.143062	−	0.673052i
$944$	0.0912824	+	0.125639i	0.00297099	+	0.00408921i
$945$	17.5722	−	24.5961i	0.571622	−	0.800112i
$946$	−11.5361	−	19.6798i	−0.375069	−	0.639845i
$947$	0.104615	+	0.0603997i	0.00339954	+	0.00196272i	0.501699	−	0.865042i	$-0.332709\pi$
$947$	0.104615	+	0.0603997i	0.00339954	+	0.00196272i	−0.498299	+	0.867005i	$0.666042\pi$
$948$	−6.93371	−	5.00952i	−0.225196	−	0.162702i
$949$	−14.4239	+	16.0194i	−0.468221	+	0.520012i
$950$	−6.12794	−	28.8297i	−0.198817	−	0.935359i
$951$	31.1664	+	34.4293i	1.01064	+	1.11645i
$952$	−5.65178	−	12.6941i	−0.183175	−	0.411418i
$953$	2.50261	−	7.70223i	0.0810674	−	0.249500i	−0.902306	−	0.431097i	$-0.858127\pi$
$953$	2.50261	−	7.70223i	0.0810674	−	0.249500i	0.983373	+	0.181597i	$0.0581267\pi$
$954$	−2.85864	−	6.32981i	−0.0925518	−	0.204935i
$955$	17.2791	−	12.5540i	0.559138	−	0.406237i
$956$	8.83074	−	15.2953i	0.285607	−	0.494685i
$957$	6.58563	+	7.17925i	0.212883	+	0.232072i
$958$	−16.4028	−	28.4104i	−0.529949	−	0.917899i
$959$	75.8077	+	33.7517i	2.44796	+	1.08990i
$960$	−3.22189	−	1.42423i	−0.103986	−	0.0459668i
$961$	−1.86203	−	2.06800i	−0.0600656	−	0.0667096i
$962$	3.64210	−	5.01292i	0.117426	−	0.161623i
$963$	−1.25585	+	0.00667715i	−0.0404691	+	0.000215168i
$964$	8.66885	+	2.81668i	0.279205	+	0.0907192i
$965$	7.23921	+	1.53874i	0.233038	+	0.0495338i
$966$	−12.3723	−	27.5910i	−0.398072	−	0.887726i
$967$	8.61320	−	4.97284i	0.276982	−	0.159916i	−0.355074	−	0.934838i	$-0.615544\pi$
$967$	8.61320	−	4.97284i	0.276982	−	0.159916i	0.632056	+	0.774922i	$0.282211\pi$
$968$	−11.3148	+	8.45117i	−0.363671	+	0.271631i
$969$	−5.51049	−	16.8074i	−0.177022	−	0.539931i
$970$	31.4528	−	3.30582i	1.00989	−	0.106144i
$971$	36.6171	−	11.8976i	1.17510	−	0.381813i	0.344555	−	0.938766i	$-0.388030\pi$
$971$	36.6171	−	11.8976i	1.17510	−	0.381813i	0.830544	+	0.556953i	$0.188030\pi$
$972$	4.45040	+	19.6495i	0.142747	+	0.630258i
$973$	40.6068	+	29.5025i	1.30179	+	0.945808i
$974$	−43.1015	+	19.1900i	−1.38106	+	0.614887i
$975$	18.8470	−	0.0501030i	0.603587	−	0.00160458i
$976$	4.33624	+	3.90437i	0.138800	+	0.124976i
$977$	−8.26143	+	18.5555i	−0.264307	+	0.593642i	−0.996134	−	0.0878477i	$-0.972001\pi$
$977$	−8.26143	+	18.5555i	−0.264307	+	0.593642i	0.731827	+	0.681490i	$0.238668\pi$
$978$	−9.41824	+	44.8959i	−0.301162	+	1.43561i
$979$	−27.7354	−	19.8725i	−0.886426	−	0.635127i
$980$		−	25.5281i		−	0.815464i
$981$	41.9527	+	13.3851i	1.33945	+	0.427353i
$982$	−4.11112	−	12.6527i	−0.131191	−	0.403765i
$983$	−7.22568	+	6.50603i	−0.230464	+	0.207510i	−0.776269	−	0.630401i	$-0.782890\pi$
$983$	−7.22568	+	6.50603i	−0.230464	+	0.207510i	0.545806	+	0.837912i	$0.316224\pi$
$984$	−4.97709	−	23.1131i	−0.158664	−	0.736818i
$985$	−26.9011	−	2.82742i	−0.857139	−	0.0900889i
$986$	−6.72924	+	1.43034i	−0.214303	+	0.0455515i
$987$	−11.0696	+	25.0417i	−0.352350	+	0.797088i
$988$	1.88832	+	17.9661i	0.0600753	+	0.571579i
$989$	−7.53327			−0.239544
$990$	17.3982	−	12.9602i	0.552952	−	0.411902i
$991$	−22.9196			−0.728065			−0.364032	−	0.931386i	$-0.618600\pi$
$991$	−22.9196			−0.728065			−0.364032	+	0.931386i	$0.618600\pi$
$992$	3.52566	+	33.5444i	0.111940	+	1.06504i
$993$	29.8327	−	3.21575i	0.946714	−	0.102049i
$994$	33.0393	−	7.02272i	1.04794	−	0.222747i
$995$	−11.1223	−	1.16900i	−0.352600	−	0.0370598i
$996$	−15.4897	−	4.98741i	−0.490808	−	0.158032i
$997$	15.9789	−	14.3875i	0.506057	−	0.455656i	−0.376122	−	0.926570i	$-0.622743\pi$
$997$	15.9789	−	14.3875i	0.506057	−	0.455656i	0.882179	+	0.470914i	$0.156076\pi$
$998$	−5.28139	−	16.2544i	−0.167179	−	0.514525i
$999$	0.0462461	+	5.79862i	0.00146316	+	0.183460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.74.3	yes	80
3.2	odd	2		297.2.t.a.8.8		80
9.2	odd	6		891.2.k.a.404.16		80
9.4	even	3		297.2.t.a.206.8		80
9.5	odd	6	inner	99.2.p.a.41.3	yes	80
9.7	even	3		891.2.k.a.404.5		80
11.7	odd	10	inner	99.2.p.a.29.3	✓	80
33.29	even	10		297.2.t.a.62.8		80
99.7	odd	30		891.2.k.a.161.16		80
99.29	even	30		891.2.k.a.161.5		80
99.40	odd	30		297.2.t.a.260.8		80
99.95	even	30	inner	99.2.p.a.95.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.3	✓	80	11.7	odd	10	inner
99.2.p.a.41.3	yes	80	9.5	odd	6	inner
99.2.p.a.74.3	yes	80	1.1	even	1	trivial
99.2.p.a.95.3	yes	80	99.95	even	30	inner
297.2.t.a.8.8		80	3.2	odd	2
297.2.t.a.62.8		80	33.29	even	10
297.2.t.a.206.8		80	9.4	even	3
297.2.t.a.260.8		80	99.40	odd	30
891.2.k.a.161.5		80	99.29	even	30
891.2.k.a.161.16		80	99.7	odd	30
891.2.k.a.404.5		80	9.7	even	3
891.2.k.a.404.16		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.189668 - 1.80457i) q^{2} +(1.02180 + 1.39855i) q^{3} +(-1.26420 + 0.268714i) q^{4} +(-1.19507 - 0.125607i) q^{5} +(2.32997 - 2.10916i) q^{6} +(3.59771 - 3.23939i) q^{7} +(-0.396737 - 1.22103i) q^{8} +(-0.911868 + 2.85806i) q^{9} +2.18041i q^{10} +(-1.93170 + 2.69602i) q^{11} +(-1.66756 - 1.49347i) q^{12} +(-1.24460 + 2.79542i) q^{13} +(-6.52808 - 5.87791i) q^{14} +(-1.04545 - 1.79971i) q^{15} +(-4.48960 + 1.99890i) q^{16} +(1.80866 + 1.31407i) q^{17} +(5.33052 + 1.10345i) q^{18} +(-4.34428 + 1.41154i) q^{19} +(1.54456 - 0.162340i) q^{20} +(8.20657 + 1.72157i) q^{21} +(5.23153 + 2.97455i) q^{22} +(1.72112 - 0.993689i) q^{23} +(1.30229 - 1.80250i) q^{24} +(-3.47832 - 0.739340i) q^{25} +(5.28060 + 1.71577i) q^{26} +(-4.92887 + 1.64506i) q^{27} +(-3.67776 + 5.06200i) q^{28} +(-1.13479 - 1.26031i) q^{29} +(-3.04941 + 2.22793i) q^{30} +(4.85274 + 2.16058i) q^{31} +(3.17481 + 5.49894i) q^{32} +(-5.74432 + 0.0531993i) q^{33} +(2.02828 - 3.51308i) q^{34} +(-4.70641 + 3.41941i) q^{35} +(0.384784 - 3.85819i) q^{36} +(0.344857 - 1.06136i) q^{37} +(3.37119 + 7.57182i) q^{38} +(-5.18126 + 1.11572i) q^{39} +(0.320759 + 1.50905i) q^{40} +(7.11427 - 7.90120i) q^{41} +(1.55017 - 15.1358i) q^{42} +(-3.28272 - 1.89528i) q^{43} +(1.71760 - 3.92738i) q^{44} +(1.44874 - 3.30104i) q^{45} +(-2.11962 - 2.91741i) q^{46} +(-0.678872 + 3.19384i) q^{47} +(-7.38300 - 4.23645i) q^{48} +(1.71815 - 16.3471i) q^{49} +(-0.674464 + 6.41710i) q^{50} +(0.0102939 + 3.87220i) q^{51} +(0.822258 - 3.86842i) q^{52} +(-0.749954 - 1.03222i) q^{53} +(3.90347 + 8.58247i) q^{54} +(2.64716 - 2.97930i) q^{55} +(-5.38274 - 3.10773i) q^{56} +(-6.41307 - 4.63337i) q^{57} +(-2.05908 + 2.28684i) q^{58} +(-0.00657007 - 0.0309097i) q^{59} +(1.80527 + 1.99426i) q^{60} +(-0.482921 - 1.08466i) q^{61} +(2.97851 - 9.16690i) q^{62} +(5.97773 + 13.2364i) q^{63} +(1.36926 - 0.994827i) q^{64} +(1.83851 - 3.18440i) q^{65} +(1.18551 + 10.3559i) q^{66} +(1.05277 + 1.82345i) q^{67} +(-2.63961 - 1.17523i) q^{68} +(3.14835 + 1.39172i) q^{69} +(7.06321 + 7.84449i) q^{70} +(-2.26013 + 3.11080i) q^{71} +(3.85155 - 0.0204781i) q^{72} +(6.69980 + 2.17690i) q^{73} +(-1.98070 - 0.421012i) q^{74} +(-2.52013 - 5.62005i) q^{75} +(5.11273 - 2.95184i) q^{76} +(1.78375 + 15.9570i) q^{77} +(2.99610 + 9.13833i) q^{78} +(3.80026 - 0.399424i) q^{79} +(5.61646 - 1.82490i) q^{80} +(-7.33699 - 5.21234i) q^{81} +(-15.6076 - 11.3396i) q^{82} +(6.64079 - 2.95667i) q^{83} +(-10.8374 + 0.0288101i) q^{84} +(-1.99642 - 1.79758i) q^{85} +(-2.79753 + 6.28336i) q^{86} +(0.603082 - 2.87484i) q^{87} +(4.05830 + 1.28906i) q^{88} +10.2875i q^{89} +(-6.23174 - 1.98825i) q^{90} +(4.57775 + 14.0889i) q^{91} +(-1.90882 + 1.71871i) q^{92} +(1.93684 + 8.99446i) q^{93} +(5.89227 + 0.619302i) q^{94} +(5.36902 - 1.14122i) q^{95} +(-4.44651 + 10.0589i) q^{96} +(-1.51615 - 14.4252i) q^{97} -29.8254 q^{98} +(-5.94392 - 7.97934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27}+ \cdots + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

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Database

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