LMFDB - Embedded newform 207.2.o.a.113.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.28767 - 0.108975i) q^{2} +(1.58319 + 0.702495i) q^{3} +(3.23063 + 0.308488i) q^{4} +(-0.595980 + 0.568266i) q^{5} +(-3.54528 - 1.77961i) q^{6} +(-0.645310 + 3.34819i) q^{7} +(-2.82310 - 0.405901i) q^{8} +(2.01300 + 2.22437i) q^{9} +(1.42534 - 1.23506i) q^{10} +(-3.24423 - 1.67252i) q^{11} +(4.89800 + 2.75790i) q^{12} +(1.19920 - 0.231127i) q^{13} +(1.84113 - 7.58924i) q^{14} +(-1.34276 + 0.481002i) q^{15} +(0.0407460 + 0.00785315i) q^{16} +(-1.97606 + 4.32697i) q^{17} +(-4.36269 - 5.30800i) q^{18} +(1.51046 - 0.689803i) q^{19} +(-2.10070 + 1.65201i) q^{20} +(-3.37373 + 4.84750i) q^{21} +(7.23948 + 4.17971i) q^{22} +(4.57336 + 1.44374i) q^{23} +(-4.18437 - 2.62583i) q^{24} +(-0.205643 + 4.31699i) q^{25} +(-2.76857 + 0.398061i) q^{26} +(1.62436 + 4.93573i) q^{27} +(-3.11764 + 10.6177i) q^{28} +(0.595424 + 6.23556i) q^{29} +(3.12420 - 0.954048i) q^{30} +(-1.18134 - 0.929013i) q^{31} +(5.45112 + 1.32243i) q^{32} +(-3.96131 - 4.92697i) q^{33} +(4.99212 - 9.68335i) q^{34} +(-1.51807 - 2.36216i) q^{35} +(5.81708 + 7.80711i) q^{36} +(-2.51221 - 8.55582i) q^{37} +(-3.53060 + 1.41344i) q^{38} +(2.06094 + 0.476515i) q^{39} +(1.91317 - 1.36236i) q^{40} +(-1.38614 - 1.45375i) q^{41} +(8.24626 - 10.7218i) q^{42} +(1.04336 + 1.32674i) q^{43} +(-9.96496 - 6.40409i) q^{44} +(-2.46374 - 0.181760i) q^{45} +(-10.3050 - 3.80119i) q^{46} +(9.52963 - 5.50193i) q^{47} +(0.0589920 + 0.0410569i) q^{48} +(-4.29535 - 1.71960i) q^{49} +(0.940890 - 9.85345i) q^{50} +(-6.16816 + 5.46226i) q^{51} +(3.94548 - 0.376748i) q^{52} +(4.16607 - 4.80790i) q^{53} +(-3.17814 - 11.4684i) q^{54} +(2.88393 - 0.846798i) q^{55} +(3.18081 - 9.19035i) q^{56} +(2.87593 - 0.0310027i) q^{57} +(-0.682614 - 14.3298i) q^{58} +(0.504712 + 2.61869i) q^{59} +(-4.48633 + 1.13972i) q^{60} +(-4.17874 - 10.4380i) q^{61} +(2.60127 + 2.25402i) q^{62} +(-8.74662 + 5.30450i) q^{63} +(-12.4059 - 3.64270i) q^{64} +(-0.583360 + 0.819214i) q^{65} +(8.52526 + 11.7030i) q^{66} +(-3.30135 - 6.40373i) q^{67} +(-7.71875 + 13.3693i) q^{68} +(6.22629 + 5.49848i) q^{69} +(3.21543 + 5.56929i) q^{70} +(6.72112 - 10.4583i) q^{71} +(-4.78004 - 7.09671i) q^{72} +(5.56880 + 12.1940i) q^{73} +(4.81475 + 19.8467i) q^{74} +(-3.35823 + 6.69016i) q^{75} +(5.09253 - 1.76254i) q^{76} +(7.69343 - 9.78299i) q^{77} +(-4.66282 - 1.31470i) q^{78} +(8.56154 + 2.96318i) q^{79} +(-0.0287465 + 0.0184742i) q^{80} +(-0.895644 + 8.95532i) q^{81} +(3.01262 + 3.47675i) q^{82} +(-4.58096 - 4.36793i) q^{83} +(-12.3947 + 14.6197i) q^{84} +(-1.28118 - 3.70172i) q^{85} +(-2.24229 - 3.14886i) q^{86} +(-3.43778 + 10.2904i) q^{87} +(8.47992 + 6.03852i) q^{88} +(-0.898270 - 6.24760i) q^{89} +(5.61643 + 0.684295i) q^{90} +4.16431i q^{91} +(14.3295 + 6.07502i) q^{92} +(-1.21766 - 2.30069i) q^{93} +(-22.4003 + 11.5481i) q^{94} +(-0.508211 + 1.26945i) q^{95} +(7.70117 + 5.92304i) q^{96} +(13.9326 - 3.38001i) q^{97} +(9.63898 + 4.40197i) q^{98} +(-2.81034 - 10.5831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.28767	−	0.108975i	−1.61763	−	0.0770572i	−0.780894	−	0.624664i	$-0.785236\pi$
$2$	−2.28767	−	0.108975i	−1.61763	−	0.0770572i	−0.836736	+	0.547607i	$0.815539\pi$
$3$	1.58319	+	0.702495i	0.914057	+	0.405586i
$3$	1.58319	+	0.702495i	0.914057	+	0.405586i
$4$	3.23063	+	0.308488i	1.61532	+	0.154244i
$5$	−0.595980	+	0.568266i	−0.266530	+	0.254136i	−0.811544	−	0.584291i	$-0.801373\pi$
$5$	−0.595980	+	0.568266i	−0.266530	+	0.254136i	0.545014	+	0.838427i	$0.316524\pi$
$6$	−3.54528	−	1.77961i	−1.44735	−	0.726522i
$7$	−0.645310	+	3.34819i	−0.243904	+	1.26550i	0.628923	+	0.777467i	$0.283496\pi$
$7$	−0.645310	+	3.34819i	−0.243904	+	1.26550i	−0.872828	+	0.488028i	$0.837716\pi$
$8$	−2.82310	−	0.405901i	−0.998118	−	0.143508i
$9$	2.01300	+	2.22437i	0.671001	+	0.741457i
$10$	1.42534	−	1.23506i	0.450731	−	0.390560i
$11$	−3.24423	−	1.67252i	−0.978172	−	0.504283i	−0.106468	−	0.994316i	$-0.533954\pi$
$11$	−3.24423	−	1.67252i	−0.978172	−	0.504283i	−0.871704	+	0.490033i	$0.836985\pi$
$12$	4.89800	+	2.75790i	1.41393	+	0.796137i
$13$	1.19920	−	0.231127i	0.332599	−	0.0641032i	−0.0202178	−	0.999796i	$-0.506436\pi$
$13$	1.19920	−	0.231127i	0.332599	−	0.0641032i	0.352817	+	0.935692i	$0.385224\pi$
$14$	1.84113	−	7.58924i	0.492062	−	2.02831i
$15$	−1.34276	+	0.481002i	−0.346698	+	0.124194i
$16$	0.0407460	+	0.00785315i	0.0101865	+	0.00196329i
$17$	−1.97606	+	4.32697i	−0.479265	+	1.04944i	0.503400	+	0.864054i	$0.332082\pi$
$17$	−1.97606	+	4.32697i	−0.479265	+	1.04944i	−0.982665	+	0.185391i	$0.940645\pi$
$18$	−4.36269	−	5.30800i	−1.02830	−	1.25111i
$19$	1.51046	−	0.689803i	0.346523	−	0.158252i	−0.234548	−	0.972104i	$-0.575361\pi$
$19$	1.51046	−	0.689803i	0.346523	−	0.158252i	0.581071	+	0.813853i	$0.302634\pi$
$20$	−2.10070	+	1.65201i	−0.469730	+	0.369400i
$21$	−3.37373	+	4.84750i	−0.736209	+	1.05781i
$22$	7.23948	+	4.17971i	1.54346	+	0.891118i
$23$	4.57336	+	1.44374i	0.953611	+	0.301041i
$23$	4.57336	+	1.44374i	0.953611	+	0.301041i
$24$	−4.18437	−	2.62583i	−0.854132	−	0.535996i
$25$	−0.205643	+	4.31699i	−0.0411287	+	0.863397i
$26$	−2.76857	+	0.398061i	−0.542962	+	0.0780661i
$27$	1.62436	+	4.93573i	0.312609	+	0.949882i
$28$	−3.11764	+	10.6177i	−0.589178	+	2.00655i
$29$	0.595424	+	6.23556i	0.110567	+	1.15792i	0.865082	+	0.501631i	$0.167267\pi$
$29$	0.595424	+	6.23556i	0.110567	+	1.15792i	−0.754514	+	0.656284i	$0.772127\pi$
$30$	3.12420	−	0.954048i	0.570399	−	0.174185i
$31$	−1.18134	−	0.929013i	−0.212174	−	0.166856i	0.506416	−	0.862289i	$-0.330970\pi$
$31$	−1.18134	−	0.929013i	−0.212174	−	0.166856i	−0.718590	+	0.695433i	$0.755212\pi$
$32$	5.45112	+	1.32243i	0.963630	+	0.233774i
$33$	−3.96131	−	4.92697i	−0.689575	−	0.857675i
$34$	4.99212	−	9.68335i	0.856141	−	1.66068i
$35$	−1.51807	−	2.36216i	−0.256600	−	0.399278i
$36$	5.81708	+	7.80711i	0.969513	+	1.30118i
$37$	−2.51221	−	8.55582i	−0.413006	−	1.40657i	−0.859204	−	0.511634i	$-0.829041\pi$
$37$	−2.51221	−	8.55582i	−0.413006	−	1.40657i	0.446198	−	0.894934i	$-0.352778\pi$
$38$	−3.53060	+	1.41344i	−0.572740	+	0.229290i
$39$	2.06094	+	0.476515i	0.330014	+	0.0763034i
$40$	1.91317	−	1.36236i	0.302499	−	0.215409i
$41$	−1.38614	−	1.45375i	−0.216479	−	0.227037i	0.606536	−	0.795056i	$-0.292559\pi$
$41$	−1.38614	−	1.45375i	−0.216479	−	0.227037i	−0.823015	+	0.568019i	$0.807710\pi$
$42$	8.24626	−	10.7218i	1.27243	−	1.65442i
$43$	1.04336	+	1.32674i	0.159111	+	0.202326i	0.859072	−	0.511855i	$-0.171042\pi$
$43$	1.04336	+	1.32674i	0.159111	+	0.202326i	−0.699961	+	0.714181i	$0.746799\pi$
$44$	−9.96496	−	6.40409i	−1.50227	−	0.965453i
$45$	−2.46374	−	0.181760i	−0.367273	−	0.0270952i
$46$	−10.3050	−	3.80119i	−1.51939	−	0.560455i
$47$	9.52963	−	5.50193i	1.39004	−	0.802539i	0.396720	−	0.917940i	$-0.370148\pi$
$47$	9.52963	−	5.50193i	1.39004	−	0.802539i	0.993319	+	0.115400i	$0.0368151\pi$
$48$	0.0589920	+	0.0410569i	0.00851476	+	0.00592605i
$49$	−4.29535	−	1.71960i	−0.613622	−	0.245657i
$50$	0.940890	−	9.85345i	0.133062	−	1.39349i
$51$	−6.16816	+	5.46226i	−0.863715	+	0.764869i
$52$	3.94548	−	0.376748i	0.547140	−	0.0522456i
$53$	4.16607	−	4.80790i	0.572254	−	0.660416i	−0.393667	−	0.919253i	$-0.628794\pi$
$53$	4.16607	−	4.80790i	0.572254	−	0.660416i	0.965921	+	0.258837i	$0.0833393\pi$
$54$	−3.17814	−	11.4684i	−0.432490	−	1.56065i
$55$	2.88393	−	0.846798i	0.388869	−	0.114182i
$56$	3.18081	−	9.19035i	0.425054	−	1.22811i
$57$	2.87593	−	0.0310027i	0.380926	−	0.00410641i
$58$	−0.682614	−	14.3298i	−0.0896316	−	1.88160i
$59$	0.504712	+	2.61869i	0.0657079	+	0.340925i	0.999873	−	0.0159153i	$-0.00506621\pi$
$59$	0.504712	+	2.61869i	0.0657079	+	0.340925i	−0.934165	+	0.356840i	$0.883854\pi$
$60$	−4.48633	+	1.13972i	−0.579183	+	0.147137i
$61$	−4.17874	−	10.4380i	−0.535033	−	1.33645i	−0.911988	−	0.410216i	$-0.865453\pi$
$61$	−4.17874	−	10.4380i	−0.535033	−	1.33645i	0.376955	−	0.926232i	$-0.376971\pi$
$62$	2.60127	+	2.25402i	0.330362	+	0.286260i
$63$	−8.74662	+	5.30450i	−1.10197	+	0.668304i
$64$	−12.4059	−	3.64270i	−1.55074	−	0.455337i
$65$	−0.583360	+	0.819214i	−0.0723568	+	0.101611i
$66$	8.52526	+	11.7030i	1.04939	+	1.44054i
$67$	−3.30135	−	6.40373i	−0.403324	−	0.782340i	0.596470	−	0.802636i	$-0.296570\pi$
$67$	−3.30135	−	6.40373i	−0.403324	−	0.782340i	−0.999794	+	0.0202956i	$0.993539\pi$
$68$	−7.71875	+	13.3693i	−0.936035	+	1.62126i
$69$	6.22629	+	5.49848i	0.749557	+	0.661939i
$70$	3.21543	+	5.56929i	0.384317	+	0.665657i
$71$	6.72112	−	10.4583i	0.797651	−	1.24117i	−0.169138	−	0.985592i	$-0.554098\pi$
$71$	6.72112	−	10.4583i	0.797651	−	1.24117i	0.966789	−	0.255576i	$-0.0822652\pi$
$72$	−4.78004	−	7.09671i	−0.563333	−	0.836355i
$73$	5.56880	+	12.1940i	0.651778	+	1.42720i	0.889989	+	0.455982i	$0.150712\pi$
$73$	5.56880	+	12.1940i	0.651778	+	1.42720i	−0.238211	+	0.971213i	$0.576561\pi$
$74$	4.81475	+	19.8467i	0.559704	+	2.30713i
$75$	−3.35823	+	6.69016i	−0.387775	+	0.772513i
$76$	5.09253	−	1.76254i	0.584153	−	0.202177i
$77$	7.69343	−	9.78299i	0.876748	−	1.11488i
$78$	−4.66282	−	1.31470i	−0.527961	−	0.148861i
$79$	8.56154	+	2.96318i	0.963248	+	0.333383i	0.763026	−	0.646367i	$-0.223713\pi$
$79$	8.56154	+	2.96318i	0.963248	+	0.333383i	0.200222	+	0.979751i	$0.435834\pi$
$80$	−0.0287465	+	0.0184742i	−0.00321395	+	0.00206548i
$81$	−0.895644	+	8.95532i	−0.0995160	+	0.995036i
$82$	3.01262	+	3.47675i	0.332688	+	0.383943i
$83$	−4.58096	−	4.36793i	−0.502825	−	0.479443i	0.395691	−	0.918384i	$-0.370505\pi$
$83$	−4.58096	−	4.36793i	−0.502825	−	0.479443i	−0.898516	+	0.438941i	$0.855354\pi$
$84$	−12.3947	+	14.6197i	−1.35237	+	1.59514i
$85$	−1.28118	−	3.70172i	−0.138963	−	0.401508i
$86$	−2.24229	−	3.14886i	−0.241792	−	0.339550i
$87$	−3.43778	+	10.2904i	−0.368569	+	1.10325i
$88$	8.47992	+	6.03852i	0.903962	+	0.643709i
$89$	−0.898270	−	6.24760i	−0.0952164	−	0.662245i	−0.980402	−	0.197007i	$-0.936878\pi$
$89$	−0.898270	−	6.24760i	−0.0952164	−	0.662245i	0.885186	−	0.465238i	$-0.154031\pi$
$90$	5.61643	+	0.684295i	0.592024	+	0.0721310i
$91$			4.16431i			0.436538i
$92$	14.3295	+	6.07502i	1.49395	+	0.633365i
$93$	−1.21766	−	2.30069i	−0.126265	−	0.238570i
$94$	−22.4003	+	11.5481i	−2.31041	+	1.19110i
$95$	−0.508211	+	1.26945i	−0.0521414	+	0.130243i
$96$	7.70117	+	5.92304i	0.785998	+	0.604517i
$97$	13.9326	−	3.38001i	1.41464	−	0.343188i	0.545649	−	0.838014i	$-0.316283\pi$
$97$	13.9326	−	3.38001i	1.41464	−	0.343188i	0.868992	+	0.494826i	$0.164768\pi$
$98$	9.63898	+	4.40197i	0.973684	+	0.444666i
$99$	−2.81034	−	10.5831i	−0.282450	−	1.06365i
$100$	−1.99610	+	13.8832i	−0.199610	+	1.38832i
$101$	−9.46068	+	9.92208i	−0.941373	+	0.987284i	−0.999940	−	0.0109996i	$-0.996499\pi$
$101$	−9.46068	+	9.92208i	−0.941373	+	0.987284i	0.0585662	+	0.998284i	$0.481347\pi$
$102$	14.7060	−	11.8237i	1.45611	−	1.17072i
$103$	−0.838685	+	0.0399515i	−0.0826381	+	0.00393654i	−0.0888602	−	0.996044i	$-0.528322\pi$
$103$	−0.838685	+	0.0399515i	−0.0826381	+	0.00393654i	0.00622215	+	0.999981i	$0.498019\pi$
$104$	−3.47929	+	0.165739i	−0.341172	+	0.0162520i
$105$	−0.743990	−	4.80619i	−0.0726060	−	0.469036i
$106$	−10.0546	+	10.5449i	−0.976584	+	1.02421i
$107$	0.225373	−	1.56751i	0.0217877	−	0.151537i	−0.976023	−	0.217666i	$-0.930156\pi$
$107$	0.225373	−	1.56751i	0.0217877	−	0.151537i	0.997811	+	0.0661290i	$0.0210649\pi$
$108$	3.72511	+	16.4466i	0.358449	+	1.58258i
$109$	−14.0826	−	6.43130i	−1.34887	−	0.616006i	−0.395679	−	0.918389i	$-0.629491\pi$
$109$	−14.0826	−	6.43130i	−1.34887	−	0.616006i	−0.953187	+	0.302382i	$0.902218\pi$
$110$	−6.68977	+	1.62292i	−0.637845	+	0.154739i
$111$	2.03310	−	15.3103i	0.192973	−	1.45319i
$112$	−0.0525876	+	0.131357i	−0.00496906	+	0.0124121i
$113$	−4.08845	+	2.10774i	−0.384609	+	0.198279i	−0.639678	−	0.768643i	$-0.720932\pi$
$113$	−4.08845	+	2.10774i	−0.384609	+	0.198279i	0.255069	+	0.966923i	$0.417902\pi$
$114$	−6.58257	−	0.242481i	−0.616514	−	0.0227104i
$115$	−3.54606	+	1.73844i	−0.330672	+	0.162111i
$116$			20.3285i			1.88745i
$117$	2.92811	+	2.20221i	0.270704	+	0.203595i
$118$	−0.869243	−	6.04572i	−0.0800203	−	0.556553i
$119$	−13.2123	−	9.40846i	−1.21117	−	0.862472i
$120$	3.98598	−	0.812892i	0.363868	−	0.0742066i
$121$	1.34709	+	1.89172i	0.122462	+	0.171974i
$122$	8.42211	+	24.3341i	0.762502	+	2.20311i
$123$	−1.17328	−	3.27532i	−0.105792	−	0.295326i
$124$	−3.52987	−	3.36573i	−0.316992	−	0.302251i
$125$	−5.02696	−	5.80142i	−0.449625	−	0.518895i
$126$	20.5875	−	11.1818i	1.83408	−	0.996154i
$127$	8.43831	−	5.42297i	0.748779	−	0.481211i	−0.109761	−	0.993958i	$-0.535008\pi$
$127$	8.43831	−	5.42297i	0.748779	−	0.481211i	0.858540	+	0.512747i	$0.171372\pi$
$128$	17.3822	+	6.01604i	1.53639	+	0.531748i
$129$	0.719814	+	2.83345i	0.0633761	+	0.249471i
$130$	1.42381	−	1.81052i	0.124876	−	0.158793i
$131$	11.3990	−	3.94523i	0.995936	−	0.344697i	0.219994	−	0.975501i	$-0.429396\pi$
$131$	11.3990	−	3.94523i	0.995936	−	0.344697i	0.775942	+	0.630805i	$0.217275\pi$
$132$	−11.2776	−	17.1392i	−0.981591	−	1.49178i
$133$	1.33487	+	5.50243i	0.115748	+	0.477121i
$134$	6.85457	+	15.0094i	0.592144	+	1.29662i
$135$	−3.77290	−	2.01853i	−0.324719	−	0.173727i
$136$	7.33495	−	11.4134i	0.628966	−	0.978691i
$137$	8.50971	+	14.7392i	0.727033	+	1.25926i	0.958132	+	0.286328i	$0.0924348\pi$
$137$	8.50971	+	14.7392i	0.727033	+	1.25926i	−0.231098	+	0.972930i	$0.574232\pi$
$138$	−13.6445	−	13.2572i	−1.16150	−	1.12853i
$139$	0.953387	−	1.65131i	0.0808652	−	0.140063i	−0.822757	−	0.568394i	$-0.807565\pi$
$139$	0.953387	−	1.65131i	0.0808652	−	0.140063i	0.903622	+	0.428331i	$0.140898\pi$
$140$	−4.17562	−	8.09958i	−0.352905	−	0.684539i
$141$	18.9523	−	2.01611i	1.59607	−	0.169787i
$142$	−16.5154	+	23.1927i	−1.38594	+	1.94629i
$143$	−4.27705	−	1.25586i	−0.357665	−	0.105020i
$144$	0.0645535	+	0.106443i	0.00537945	+	0.00887021i
$145$	−3.89832	−	3.37791i	−0.323738	−	0.280520i
$146$	−11.4107	−	28.5027i	−0.944360	−	2.35890i
$147$	−5.59237	−	5.73992i	−0.461251	−	0.473421i
$148$	−5.47668	−	28.4157i	−0.450180	−	2.33576i
$149$	1.06520	+	22.3613i	0.0872645	+	1.83191i	0.442086	+	0.896973i	$0.354239\pi$
$149$	1.06520	+	22.3613i	0.0872645	+	1.83191i	−0.354821	+	0.934934i	$0.615458\pi$
$150$	8.41161	−	14.9389i	0.686805	−	1.21976i
$151$	5.81654	−	16.8058i	0.473343	−	1.36764i	−0.415570	−	0.909561i	$-0.636418\pi$
$151$	5.81654	−	16.8058i	0.473343	−	1.36764i	0.888914	−	0.458075i	$-0.151461\pi$
$152$	−4.54417	+	1.33429i	−0.368581	+	0.108225i
$153$	−13.6026	+	4.31471i	−1.09970	+	0.348824i
$154$	−18.6662	+	21.5419i	−1.50416	+	1.73590i
$155$	1.23198	−	0.117640i	0.0989550	−	0.00944906i
$156$	6.51113	+	2.17522i	0.521308	+	0.174157i
$157$	−0.739777	+	7.74729i	−0.0590406	+	0.618301i	0.916730	+	0.399507i	$0.130819\pi$
$157$	−0.739777	+	7.74729i	−0.0590406	+	0.618301i	−0.975771	+	0.218795i	$0.929787\pi$
$158$	−19.2631	−	7.71178i	−1.53249	−	0.613516i
$159$	9.97322	−	4.68519i	0.790928	−	0.371560i
$160$	−4.00025	+	2.30954i	−0.316247	+	0.182585i
$161$	−7.78515	+	14.3808i	−0.613556	+	1.13337i
$162$	3.02485	−	20.3893i	0.237655	−	1.60193i
$163$	12.3097	+	7.91093i	0.964167	+	0.619632i	0.925148	−	0.379606i	$-0.123941\pi$
$163$	12.3097	+	7.91093i	0.964167	+	0.619632i	0.0390184	+	0.999238i	$0.487577\pi$
$164$	−4.02966	−	5.12413i	−0.314663	−	0.400127i
$165$	5.16069	+	0.685301i	0.401759	+	0.0533506i
$166$	10.0037	+	10.4916i	0.776441	+	0.814308i
$167$	−2.00521	+	1.42790i	−0.155168	+	0.110494i	−0.655004	−	0.755626i	$-0.727333\pi$
$167$	−2.00521	+	1.42790i	−0.155168	+	0.110494i	0.499836	+	0.866120i	$0.333394\pi$
$168$	11.4920	−	12.3156i	0.886627	−	0.950168i
$169$	−10.6841	+	4.27727i	−0.821855	+	0.329021i
$170$	2.52752	+	8.60794i	0.193852	+	0.660199i
$171$	4.57493	+	1.97124i	0.349854	+	0.150745i
$172$	2.96144	+	4.60808i	0.225807	+	0.351363i
$173$	8.93927	−	17.3398i	0.679640	−	1.31832i	−0.256450	−	0.966557i	$-0.582553\pi$
$173$	8.93927	−	17.3398i	0.679640	−	1.31832i	0.936090	−	0.351760i	$-0.114417\pi$
$174$	8.98592	−	23.1664i	0.681221	−	1.75624i
$175$	−14.3214	−	3.47433i	−1.08259	−	0.262634i
$176$	−0.119055	−	0.0936257i	−0.00897409	−	0.00705730i
$177$	−1.04056	+	4.50046i	−0.0782134	+	0.338275i
$178$	1.37411	+	14.3904i	0.102994	+	1.07860i
$179$	4.02968	−	13.7238i	0.301193	−	1.02577i	−0.660315	−	0.750989i	$-0.729577\pi$
$179$	4.02968	−	13.7238i	0.301193	−	1.02577i	0.961507	−	0.274779i	$-0.0886047\pi$
$180$	−7.90338	−	1.34723i	−0.589083	−	0.100417i
$181$	9.25811	−	1.33111i	0.688150	−	0.0989410i	0.210635	−	0.977565i	$-0.432447\pi$
$181$	9.25811	−	1.33111i	0.688150	−	0.0989410i	0.477515	+	0.878624i	$0.341538\pi$
$182$	0.453807	−	9.52657i	0.0336384	−	0.706157i
$183$	0.716879	−	19.4609i	0.0529932	−	1.43859i
$184$	−12.3250	−	5.93216i	−0.908615	−	0.437325i
$185$	6.35921	+	3.67149i	0.467538	+	0.269933i
$186$	2.53488	+	5.39592i	0.185867	+	0.395648i
$187$	13.6477	−	10.7327i	0.998020	−	0.784852i
$188$	32.4840	−	14.8349i	2.36914	−	1.08195i
$189$	−17.5740	+	2.25359i	−1.27832	+	0.163925i
$190$	1.30096	−	2.84871i	0.0943816	−	0.206667i
$191$	−11.7370	−	2.26212i	−0.849259	−	0.163681i	−0.253989	−	0.967207i	$-0.581743\pi$
$191$	−11.7370	−	2.26212i	−0.849259	−	0.163681i	−0.595270	+	0.803526i	$0.702955\pi$
$192$	−17.0820	−	14.4822i	−1.23278	−	1.04516i
$193$	−5.78344	+	23.8397i	−0.416301	+	1.71602i	0.248183	+	0.968713i	$0.420167\pi$
$193$	−5.78344	+	23.8397i	−0.416301	+	1.71602i	−0.664484	+	0.747303i	$0.731349\pi$
$194$	−32.2416	+	6.21405i	−2.31481	+	0.446143i
$195$	−1.49906	+	0.887167i	−0.107350	+	0.0635313i
$196$	−13.3462	−	6.88046i	−0.953302	−	0.491462i
$197$	−1.35838	+	1.17704i	−0.0967802	+	0.0838605i	−0.701907	−	0.712269i	$-0.747668\pi$
$197$	−1.35838	+	1.17704i	−0.0967802	+	0.0838605i	0.605127	+	0.796129i	$0.293122\pi$
$198$	5.27585	+	24.5170i	0.374938	+	1.74235i
$199$	19.1909	+	2.75924i	1.36041	+	0.195597i	0.783591	−	0.621276i	$-0.213386\pi$
$199$	19.1909	+	2.75924i	1.36041	+	0.195597i	0.576817	+	0.816874i	$0.304295\pi$
$200$	2.33282	−	12.1038i	0.164955	−	0.855870i
$201$	−0.728092	−	12.4575i	−0.0513556	−	0.878686i
$202$	22.7242	−	21.6675i	1.59887	−	1.52452i
$203$	−21.2621	−	2.03028i	−1.49230	−	0.142498i
$204$	−21.6121	+	15.7437i	−1.51315	+	1.10228i
$205$	1.65223	+	0.0787053i	0.115397	+	0.00549702i
$206$	1.92299			0.133981
$207$	5.99477	+	13.0791i	0.416665	+	0.909060i
$208$	0.0506778			0.00351387
$209$	−6.05398	−	0.288386i	−0.418762	−	0.0199481i
$210$	1.17825	+	11.0761i	0.0813070	+	0.764322i
$211$	1.75455	+	0.167539i	0.120788	+	0.0115338i	0.155275	−	0.987871i	$-0.450374\pi$
$211$	1.75455	+	0.167539i	0.120788	+	0.0115338i	−0.0344870	+	0.999405i	$0.510980\pi$
$212$	14.9422	−	14.2474i	1.02624	−	0.978514i
$213$	17.9877	−	11.8359i	1.23250	−	0.810983i
$214$	−0.686400	+	3.56138i	−0.0469214	+	0.243451i
$215$	−1.37577	−	0.197805i	−0.0938265	−	0.0134902i
$216$	−2.58233	−	14.5934i	−0.175705	−	0.992956i
$217$	3.87284	−	3.35583i	0.262905	−	0.227809i
$218$	31.5155	+	16.2474i	2.13450	+	1.10041i
$219$	0.250286	+	23.2174i	0.0169128	+	1.56889i
$220$	9.57815	−	1.84604i	0.645759	−	0.124460i
$221$	−1.36962	+	5.64564i	−0.0921304	+	0.379767i
$222$	−6.31951	+	34.8035i	−0.424138	+	2.33586i
$223$	−13.9573	−	2.69005i	−0.934650	−	0.180139i	−0.300881	−	0.953662i	$-0.597281\pi$
$223$	−13.9573	−	2.69005i	−0.934650	−	0.180139i	−0.633769	+	0.773523i	$0.718493\pi$
$224$	−7.94539	+	17.3980i	−0.530874	+	1.16245i
$225$	−10.0165	+	8.23268i	−0.667769	+	0.548845i
$226$	9.58272	−	4.37628i	0.637433	−	0.291106i
$227$	−11.2166	+	8.82086i	−0.744474	+	0.585461i	−0.916690	−	0.399598i	$-0.869150\pi$
$227$	−11.2166	+	8.82086i	−0.744474	+	0.585461i	0.172216	+	0.985059i	$0.444907\pi$
$228$	9.30063	+	0.787031i	0.615949	+	0.0521224i
$229$	17.0418	+	9.83909i	1.12615	+	0.650185i	0.942965	−	0.332893i	$-0.108025\pi$
$229$	17.0418	+	9.83909i	1.12615	+	0.650185i	0.183189	+	0.983078i	$0.441358\pi$
$230$	8.30168	−	3.59056i	0.547396	−	0.236754i
$231$	19.0527	−	10.0838i	1.25357	−	0.663464i
$232$	0.850078	−	17.8453i	0.0558103	−	1.17160i
$233$	12.5399	−	1.80297i	0.821517	−	0.118116i	0.281276	−	0.959627i	$-0.409242\pi$
$233$	12.5399	−	1.80297i	0.821517	−	0.118116i	0.540241	+	0.841511i	$0.318333\pi$
$234$	−6.45858	−	5.35703i	−0.422210	−	0.350200i
$235$	−2.55291	+	8.69441i	−0.166533	+	0.567160i
$236$	0.822703	+	8.61573i	0.0535534	+	0.560836i
$237$	11.4730	+	10.7057i	0.745248	+	0.695411i
$238$	29.2002	+	22.9633i	1.89277	+	1.48849i
$239$	−21.2745	−	5.16114i	−1.37613	−	0.333846i	−0.521577	−	0.853204i	$-0.674656\pi$
$239$	−21.2745	−	5.16114i	−1.37613	−	0.333846i	−0.854557	+	0.519358i	$0.826171\pi$
$240$	−0.0584893	+	0.00905404i	−0.00377547	+	0.000584436i
$241$	−11.4411	+	22.1927i	−0.736988	+	1.42956i	0.159824	+	0.987145i	$0.448907\pi$
$241$	−11.4411	+	22.1927i	−0.736988	+	1.42956i	−0.896812	+	0.442412i	$0.854123\pi$
$242$	−2.87554	−	4.47443i	−0.184847	−	0.287627i
$243$	−7.70905	+	13.5488i	−0.494536	+	0.869157i
$244$	−10.2800	−	35.0104i	−0.658108	−	2.24131i
$245$	3.53714	−	1.41606i	0.225979	−	0.0904685i
$246$	2.32716	+	7.62072i	0.148375	+	0.485879i
$247$	1.65191	−	1.17632i	0.105109	−	0.0748476i
$248$	2.95795	+	3.10221i	0.187830	+	0.196990i
$249$	−4.18409	−	10.1334i	−0.265156	−	0.642177i
$250$	10.8678	+	13.8196i	0.687342	+	0.874027i
$251$	−6.71604	−	4.31613i	−0.423912	−	0.272432i	0.311243	−	0.950330i	$-0.399255\pi$
$251$	−6.71604	−	4.31613i	−0.423912	−	0.272432i	−0.735156	+	0.677898i	$0.762891\pi$
$252$	−29.8935	+	14.4387i	−1.88311	+	0.909550i
$253$	−12.4223	−	12.3328i	−0.780986	−	0.775359i
$254$	−19.8951	+	11.4864i	−1.24833	+	0.720723i
$255$	0.572086	−	6.76055i	0.0358254	−	0.423362i
$256$	−15.1023	−	6.04606i	−0.943896	−	0.377879i
$257$	0.567957	−	5.94792i	0.0354282	−	0.371021i	−0.960320	−	0.278901i	$-0.910030\pi$
$257$	0.567957	−	5.94792i	0.0354282	−	0.371021i	0.995748	−	0.0921196i	$-0.0293642\pi$
$258$	−1.33792	−	6.56044i	−0.0832955	−	0.408435i
$259$	30.2676	−	2.89021i	1.88074	−	0.179589i
$260$	−2.13734	+	2.46662i	−0.132552	+	0.152973i
$261$	−12.6716	+	13.8766i	−0.784353	+	0.858943i
$262$	−26.5071	+	7.78320i	−1.63762	+	0.480848i
$263$	1.03881	−	3.00146i	0.0640560	−	0.185078i	−0.908431	−	0.418035i	$-0.862719\pi$
$263$	1.03881	−	3.00146i	0.0640560	−	0.185078i	0.972487	+	0.232957i	$0.0748402\pi$
$264$	9.18332	+	15.5172i	0.565194	+	0.955020i
$265$	0.249271	+	5.23285i	0.0153126	+	0.321451i
$266$	−2.45413	−	12.7332i	−0.150472	−	0.780725i
$267$	2.96677	−	10.5222i	0.181564	−	0.643948i
$268$	−8.68998	−	21.7065i	−0.530825	−	1.32594i
$269$	−15.9594	−	13.8289i	−0.973061	−	0.843162i	0.0145802	−	0.999894i	$-0.495359\pi$
$269$	−15.9594	−	13.8289i	−0.973061	−	0.843162i	−0.987641	+	0.156731i	$0.949904\pi$
$270$	8.41119	+	5.02889i	0.511889	+	0.306048i
$271$	0.594331	+	0.174511i	0.0361031	+	0.0106008i	0.299734	−	0.954023i	$-0.403102\pi$
$271$	0.594331	+	0.174511i	0.0361031	+	0.0106008i	−0.263631	+	0.964624i	$0.584920\pi$
$272$	−0.114497	+	0.160788i	−0.00694239	+	0.00974923i
$273$	−2.92540	+	6.59290i	−0.177053	+	0.399020i
$274$	−17.8612	−	34.6459i	−1.07904	−	2.09304i
$275$	7.88738	−	13.6613i	0.475627	−	0.823810i
$276$	18.4186	+	19.6843i	1.10867	+	1.18486i
$277$	−11.5102	−	19.9362i	−0.691578	−	1.19785i	−0.971321	−	0.237773i	$-0.923582\pi$
$277$	−11.5102	−	19.9362i	−0.691578	−	1.19785i	0.279743	−	0.960075i	$-0.409751\pi$
$278$	−2.36099	+	3.67377i	−0.141603	+	0.220338i
$279$	−0.311564	−	4.49783i	−0.0186528	−	0.269278i
$280$	3.32686	+	7.28481i	0.198818	+	0.435351i
$281$	−5.73956	−	23.6588i	−0.342393	−	1.41136i	−0.839351	−	0.543589i	$-0.817065\pi$
$281$	−5.73956	−	23.6588i	−0.342393	−	1.41136i	0.496958	−	0.867774i	$-0.334450\pi$
$282$	−43.5764	+	2.54687i	−2.59494	+	0.151664i
$283$	−4.28851	+	1.48427i	−0.254925	+	0.0882305i	−0.451542	−	0.892250i	$-0.649126\pi$
$283$	−4.28851	+	1.48427i	−0.254925	+	0.0882305i	0.196617	+	0.980480i	$0.437005\pi$
$284$	24.9397	−	31.7134i	1.47990	−	1.88185i
$285$	−1.69638	+	1.65277i	−0.100485	+	0.0979016i
$286$	9.64765	+	3.33908i	0.570477	+	0.197444i
$287$	5.76190	−	3.70295i	0.340114	−	0.218578i
$288$	8.03154	+	14.7873i	0.473263	+	0.871353i
$289$	−3.68522	−	4.25297i	−0.216778	−	0.250175i
$290$	8.54998	+	8.15239i	0.502072	+	0.478725i
$291$	24.4324	+	4.43636i	1.43225	+	0.260064i
$292$	14.2290	+	41.1121i	0.832692	+	2.40590i
$293$	12.8860	+	18.0959i	0.752811	+	1.05717i	0.996187	+	0.0872427i	$0.0278056\pi$
$293$	12.8860	+	18.0959i	0.752811	+	1.05717i	−0.243376	+	0.969932i	$0.578255\pi$
$294$	12.1680	+	13.7405i	0.709652	+	0.801362i
$295$	−1.78891	−	1.27388i	−0.104155	−	0.0741681i
$296$	3.61943	+	25.1737i	0.210375	+	1.46319i
$297$	2.98528	−	18.7294i	0.173224	−	1.08679i
$298$		−	51.2714i		−	2.97007i
$299$	5.81808	+	0.674310i	0.336468	+	0.0389963i
$300$	−12.9131	+	20.5775i	−0.745535	+	1.18804i
$301$	−5.11547	+	2.63721i	−0.294851	+	0.152006i
$302$	−15.1378	+	37.8123i	−0.871081	+	2.17585i
$303$	−21.9483	+	9.06249i	−1.26090	+	0.520626i
$304$	0.0669622	−	0.0162449i	0.00384054	−	0.000931706i
$305$	8.42200	+	3.84620i	0.482243	+	0.220233i
$306$	31.5885	−	8.38830i	1.80579	−	0.479527i
$307$	−2.89633	+	20.1444i	−0.165302	+	1.14970i	0.723135	+	0.690706i	$0.242700\pi$
$307$	−2.89633	+	20.1444i	−0.165302	+	1.14970i	−0.888438	+	0.458997i	$0.848209\pi$
$308$	27.8726	−	29.2319i	1.58819	−	1.66564i
$309$	−1.35587	−	0.525921i	−0.0771325	−	0.0299186i
$310$	−2.83119	+	0.134866i	−0.160801	+	0.00765988i
$311$	−0.890115	+	0.0424014i	−0.0504738	+	0.00240436i	−0.0728036	−	0.997346i	$-0.523195\pi$
$311$	−0.890115	+	0.0424014i	−0.0504738	+	0.00240436i	0.0223298	+	0.999751i	$0.492892\pi$
$312$	−5.62482	−	2.18179i	−0.318443	−	0.123519i
$313$	−7.32734	+	7.68470i	−0.414166	+	0.434365i	−0.897462	−	0.441092i	$-0.854591\pi$
$313$	−7.32734	+	7.68470i	−0.414166	+	0.434365i	0.483296	+	0.875457i	$0.339440\pi$
$314$	2.53663	−	17.6427i	0.143150	−	0.995633i
$315$	2.19844	−	8.13178i	0.123868	−	0.458174i
$316$	26.7451	+	12.2141i	1.50453	+	0.687095i
$317$	7.39060	−	1.79294i	0.415097	−	0.100702i	−0.0227708	−	0.999741i	$-0.507249\pi$
$317$	7.39060	−	1.79294i	0.415097	−	0.100702i	0.437868	+	0.899039i	$0.355734\pi$
$318$	−23.3260	+	9.63136i	−1.30806	+	0.540100i
$319$	8.49739	−	21.2255i	0.475762	−	1.18840i
$320$	9.46369	−	4.87887i	0.529036	−	0.272737i
$321$	1.45797	−	2.32334i	0.0813762	−	0.129676i
$322$	19.3770	−	32.0502i	1.07984	−	1.78609i
$323$			7.89880i			0.439501i
$324$	−5.65611	+	28.6551i	−0.314228	+	1.59195i
$325$	0.751166	+	5.22447i	0.0416672	+	0.289802i
$326$	−27.2984	−	19.4391i	−1.51192	−	1.07663i
$327$	−17.7775	−	20.0749i	−0.983097	−	1.11015i
$328$	3.32315	+	4.66671i	0.183490	+	0.257676i
$329$	12.2719	+	35.4574i	0.676574	+	1.95483i
$330$	−11.7313	−	2.13013i	−0.645787	−	0.117260i
$331$	−11.3562	−	10.8281i	−0.624195	−	0.595168i	0.310520	−	0.950567i	$-0.399497\pi$
$331$	−11.3562	−	10.8281i	−0.624195	−	0.595168i	−0.934715	+	0.355398i	$0.884345\pi$
$332$	−13.4519	−	15.5244i	−0.738271	−	0.852010i
$333$	13.9742	−	22.8110i	0.765782	−	1.25003i
$334$	4.74287	−	3.04806i	0.259518	−	0.166782i
$335$	5.60656	+	1.94045i	0.306319	+	0.106018i
$336$	−0.175534	+	0.171022i	−0.00957618	+	0.00933000i
$337$	−7.10882	+	9.03960i	−0.387242	+	0.492418i	−0.940120	−	0.340844i	$-0.889287\pi$
$337$	−7.10882	+	9.03960i	−0.387242	+	0.492418i	0.552878	+	0.833262i	$0.313530\pi$
$338$	24.9079	−	8.62070i	1.35481	−	0.468904i
$339$	−7.95348	+	0.464848i	−0.431973	+	0.0252471i
$340$	−2.99708	−	12.3541i	−0.162539	−	0.669996i
$341$	2.27874	+	4.98974i	0.123400	+	0.270209i
$342$	−10.2511	−	5.00811i	−0.554318	−	0.270808i
$343$	−4.37498	+	6.80761i	−0.236227	+	0.367576i
$344$	−2.40699	−	4.16903i	−0.129776	−	0.224779i
$345$	−6.83535	+	0.261203i	−0.368003	+	0.0140627i
$346$	−22.3397	+	38.6936i	−1.20099	+	2.08018i
$347$	−1.96109	−	3.80399i	−0.105277	−	0.204209i	0.830313	−	0.557298i	$-0.188162\pi$
$347$	−1.96109	−	3.80399i	−0.105277	−	0.204209i	−0.935590	+	0.353089i	$0.885131\pi$
$348$	−14.2807	+	32.1839i	−0.765524	+	1.72524i
$349$	17.9279	−	25.1762i	0.959659	−	1.34765i	0.0221258	−	0.999755i	$-0.492957\pi$
$349$	17.9279	−	25.1762i	0.959659	−	1.34765i	0.937533	−	0.347897i	$-0.113104\pi$
$350$	32.3840	+	9.50880i	1.73100	+	0.508267i
$351$	3.08872	+	5.54351i	0.164864	+	0.295891i
$352$	−15.4729	−	13.4073i	−0.824708	−	0.714613i
$353$	−1.16049	−	2.89876i	−0.0617666	−	0.154286i	0.894274	−	0.447520i	$-0.147693\pi$
$353$	−1.16049	−	2.89876i	−0.0617666	−	0.154286i	−0.956041	+	0.293234i	$0.905268\pi$
$354$	2.87091	−	10.1822i	0.152587	−	0.541177i
$355$	1.93742	+	10.0523i	0.102828	+	0.533521i
$356$	−0.974669	−	20.4608i	−0.0516573	−	1.08442i
$357$	−14.3083	−	24.1770i	−0.757275	−	1.27958i
$358$	−10.7142	+	30.9565i	−0.566261	+	1.63610i
$359$	−2.62796	+	0.771639i	−0.138698	+	0.0407255i	−0.350345	−	0.936621i	$-0.613936\pi$
$359$	−2.62796	+	0.771639i	−0.138698	+	0.0407255i	0.211647	+	0.977346i	$0.432117\pi$
$360$	6.88163	+	1.51316i	0.362694	+	0.0797507i
$361$	−10.6367	+	12.2754i	−0.559826	+	0.646074i
$362$	−21.3246	+	2.03625i	−1.12080	+	0.107023i
$363$	0.803775	+	3.94127i	0.0421873	+	0.206863i
$364$	−1.28464	+	13.4533i	−0.0673333	+	0.705147i
$365$	−10.2483	−	4.10280i	−0.536421	−	0.214750i
$366$	−3.76074	+	44.4421i	−0.196577	+	2.32302i
$367$	9.16318	−	5.29037i	0.478314	−	0.276155i	−0.241399	−	0.970426i	$-0.577606\pi$
$367$	9.16318	−	5.29037i	0.478314	−	0.276155i	0.719714	+	0.694271i	$0.244273\pi$
$368$	0.175008	+	0.0947419i	0.00912293	+	0.00493876i
$369$	0.443358	−	6.00969i	0.0230803	−	0.312852i
$370$	−14.1477	−	9.09217i	−0.735504	−	0.472680i
$371$	13.4093	+	17.0514i	0.696178	+	0.885263i
$372$	−3.22407	−	7.80832i	−0.167160	−	0.404842i
$373$	6.42026	+	6.73338i	0.332429	+	0.348641i	0.868641	−	0.495442i	$-0.164994\pi$
$373$	6.42026	+	6.73338i	0.332429	+	0.348641i	−0.536212	+	0.844083i	$0.680145\pi$
$374$	−32.3911	+	23.0656i	−1.67491	+	1.19270i
$375$	−3.88318	−	12.7162i	−0.200527	−	0.656661i
$376$	−29.1364	+	11.6644i	−1.50259	+	0.601548i
$377$	2.15524	+	7.34009i	0.111001	+	0.378034i
$378$	40.4491	−	3.24036i	2.08048	−	0.166666i
$379$	0.632891	+	0.984798i	0.0325094	+	0.0505857i	0.857128	−	0.515104i	$-0.172247\pi$
$379$	0.632891	+	0.984798i	0.0325094	+	0.0505857i	−0.824619	+	0.565689i	$0.808610\pi$
$380$	−2.03345	+	3.94435i	−0.104314	+	0.202341i
$381$	17.1691	−	2.65775i	0.879599	−	0.136160i
$382$	26.6039	+	6.45403i	1.36117	+	0.330217i
$383$	−12.4534	−	9.79345i	−0.636338	−	0.500422i	0.247087	−	0.968993i	$-0.420527\pi$
$383$	−12.4534	−	9.79345i	−0.636338	−	0.500422i	−0.883426	+	0.468571i	$0.844769\pi$
$384$	23.2932	+	21.7355i	1.18867	+	1.10918i
$385$	0.974210	+	10.2024i	0.0496503	+	0.519962i
$386$	15.8286	−	53.9071i	0.805652	−	2.74380i
$387$	−0.850877	+	4.99156i	−0.0432525	+	0.253735i
$388$	46.0538	−	6.62154i	2.33803	−	0.336158i
$389$	−0.733287	+	15.3936i	−0.0371791	+	0.780486i	0.900892	+	0.434043i	$0.142914\pi$
$389$	−0.733287	+	15.3936i	−0.0371791	+	0.780486i	−0.938071	+	0.346443i	$0.887389\pi$
$390$	3.52605	−	1.86619i	0.178548	−	0.0944981i
$391$	−15.2843	+	16.9359i	−0.772958	+	0.856484i
$392$	11.4282	+	6.59810i	0.577213	+	0.333254i
$393$	20.8183	+	1.76167i	1.05015	+	0.0888647i
$394$	3.23579	−	2.54465i	0.163017	−	0.128198i
$395$	−6.78638	+	3.09924i	−0.341460	+	0.155939i
$396$	−5.81442	−	35.0572i	−0.292186	−	1.76169i
$397$	−8.76579	+	19.1944i	−0.439942	+	0.963339i	0.551667	+	0.834065i	$0.313992\pi$
$397$	−8.76579	+	19.1944i	−0.439942	+	0.963339i	−0.991609	+	0.129274i	$0.958735\pi$
$398$	−43.6019	−	8.40357i	−2.18556	−	0.421233i
$399$	−1.75206	+	9.64915i	−0.0877129	+	0.483062i
$400$	−0.0422811	+	0.174285i	−0.00211405	+	0.00871425i
$401$	−5.95942	+	1.14858i	−0.297599	+	0.0573575i	−0.335865	−	0.941910i	$-0.609029\pi$
$401$	−5.95942	+	1.14858i	−0.297599	+	0.0573575i	0.0382661	+	0.999268i	$0.487817\pi$
$402$	0.308074	+	28.5781i	0.0153653	+	1.42535i
$403$	−1.63138	−	0.841036i	−0.0812650	−	0.0418950i
$404$	−33.6248	+	29.1361i	−1.67290	+	1.44957i
$405$	−4.55522	−	5.84616i	−0.226351	−	0.290498i
$406$	48.4194	+	6.96166i	2.40302	+	0.345501i
$407$	−6.15954	+	31.9588i	−0.305317	+	1.58414i
$408$	19.6305	−	12.9169i	0.971854	−	0.639480i
$409$	5.01382	−	4.78067i	0.247917	−	0.236389i	−0.555923	−	0.831234i	$-0.687635\pi$
$409$	5.01382	−	4.78067i	0.247917	−	0.236389i	0.803840	+	0.594845i	$0.202787\pi$
$410$	−3.77118	−	0.360104i	−0.186245	−	0.0177843i
$411$	3.11827	+	29.3131i	0.153813	+	1.44591i
$412$	−2.72181	−	0.129656i	−0.134094	−	0.00638768i
$413$	−9.09357			−0.447465
$414$	−12.2888	−	30.5740i	−0.603960	−	1.50263i
$415$	5.21231			0.255862
$416$	6.84264	+	0.325955i	0.335488	+	0.0159813i
$417$	2.66944	−	1.94460i	0.130723	−	0.0952275i
$418$	13.8181	+	1.31947i	0.675865	+	0.0645373i
$419$	18.8812	−	18.0032i	0.922409	−	0.879515i	−0.0706057	−	0.997504i	$-0.522493\pi$
$419$	18.8812	−	18.0032i	0.922409	−	0.879515i	0.993015	+	0.117989i	$0.0376447\pi$
$420$	−0.920907	−	15.7566i	−0.0449357	−	0.768841i
$421$	−1.63350	+	8.47540i	−0.0796119	+	0.413066i	0.920157	+	0.391550i	$0.128061\pi$
$421$	−1.63350	+	8.47540i	−0.0796119	+	0.413066i	−0.999769	+	0.0215152i	$0.993151\pi$
$422$	−3.99557	−	0.574476i	−0.194501	−	0.0279651i
$423$	31.4215	+	10.1220i	1.52777	+	0.492149i
$424$	−13.7128	+	11.8822i	−0.665951	+	0.577050i
$425$	−18.2731	−	9.42044i	−0.886376	−	0.456959i
$426$	−42.4399	+	25.1165i	−2.05622	+	1.21690i
$427$	37.6449	−	7.25547i	1.82177	−	0.351117i
$428$	1.21166	−	4.99451i	0.0585676	−	0.241419i
$429$	−5.88917	−	4.99287i	−0.284332	−	0.241058i
$430$	3.12575	+	0.602439i	0.150737	+	0.0290522i
$431$	4.48180	−	9.81378i	0.215881	−	0.472713i	−0.770448	−	0.637503i	$-0.779967\pi$
$431$	4.48180	−	9.81378i	0.215881	−	0.472713i	0.986329	+	0.164790i	$0.0526946\pi$
$432$	0.0274253	+	0.213868i	0.00131950	+	0.0102897i
$433$	8.19641	−	3.74317i	0.393894	−	0.179886i	−0.208614	−	0.977998i	$-0.566895\pi$
$433$	8.19641	−	3.74317i	0.393894	−	0.179886i	0.602508	+	0.798113i	$0.294168\pi$
$434$	−9.22549	+	7.25501i	−0.442838	+	0.348252i
$435$	−3.79883	−	8.08644i	−0.182140	−	0.387715i
$436$	−43.5116	−	25.1215i	−2.08383	−	1.20310i
$437$	7.90376	−	0.974007i	0.378088	−	0.0465931i
$438$	1.95756	−	53.1412i	0.0935357	−	2.53919i
$439$	0.269055	−	5.64817i	0.0128413	−	0.269572i	−0.983311	−	0.181933i	$-0.941765\pi$
$439$	0.269055	−	5.64817i	0.0128413	−	0.269572i	0.996152	−	0.0876395i	$-0.0279324\pi$
$440$	−8.48535	+	1.22001i	−0.404523	+	0.0581617i
$441$	−4.82153	−	13.0160i	−0.229597	−	0.619810i
$442$	3.74847	−	12.7661i	0.178297	−	0.607223i
$443$	−2.05179	−	21.4873i	−0.0974833	−	1.02089i	−0.903382	−	0.428838i	$-0.858923\pi$
$443$	−2.05179	−	21.4873i	−0.0974833	−	1.02089i	0.805898	−	0.592054i	$-0.201683\pi$
$444$	11.2912	−	48.8349i	0.535858	−	2.31760i
$445$	4.08565	+	3.21299i	0.193678	+	0.152310i
$446$	31.6366	+	7.67496i	1.49804	+	0.363420i
$447$	−14.0223	+	36.1505i	−0.663230	+	1.70986i
$448$	20.2021	−	39.1866i	0.954459	−	1.85139i
$449$	12.1697	+	18.9363i	0.574321	+	0.893662i	0.999937	−	0.0112426i	$-0.00357871\pi$
$449$	12.1697	+	18.9363i	0.574321	+	0.893662i	−0.425615	+	0.904904i	$0.639942\pi$
$450$	23.8117	−	17.7421i	1.12250	−	0.836372i
$451$	2.06555	+	7.03463i	0.0972631	+	0.331248i
$452$	−13.8585	+	5.54810i	−0.651848	+	0.260961i
$453$	21.0147	−	22.5207i	0.987356	−	1.05812i
$454$	26.6213	−	18.9569i	1.24940	−	0.889692i
$455$	−2.36643	−	2.48184i	−0.110940	−	0.116351i
$456$	−8.13163	−	1.07982i	−0.380798	−	0.0505671i
$457$	−11.3475	−	14.4295i	−0.530812	−	0.674983i	0.444509	−	0.895775i	$-0.353378\pi$
$457$	−11.3475	−	14.4295i	−0.530812	−	0.674983i	−0.975321	+	0.220792i	$0.929136\pi$
$458$	−37.9139	−	24.3658i	−1.77160	−	1.13854i
$459$	−24.5666	−	2.72473i	−1.14667	−	0.127180i
$460$	−11.9923	+	4.52235i	−0.559144	+	0.210856i
$461$	−8.01373	+	4.62673i	−0.373236	+	0.215488i	−0.674871	−	0.737935i	$-0.735801\pi$
$461$	−8.01373	+	4.62673i	−0.373236	+	0.215488i	0.301635	+	0.953423i	$0.402468\pi$
$462$	−44.6852	+	20.9921i	−2.07894	+	0.976642i
$463$	−24.3098	−	9.73218i	−1.12977	−	0.452293i	−0.269944	−	0.962876i	$-0.587005\pi$
$463$	−24.3098	−	9.73218i	−1.12977	−	0.452293i	−0.859828	+	0.510583i	$0.829430\pi$
$464$	−0.0247076	+	0.258750i	−0.00114702	+	0.0120122i
$465$	2.03310	+	0.679213i	0.0942829	+	0.0314977i
$466$	−28.8837	+	2.75806i	−1.33801	+	0.127765i
$467$	−14.9393	+	17.2409i	−0.691308	+	0.797812i	−0.987551	−	0.157301i	$-0.949721\pi$
$467$	−14.9393	+	17.2409i	−0.691308	+	0.797812i	0.296243	+	0.955113i	$0.404266\pi$
$468$	8.78030	+	8.01782i	0.405869	+	0.370624i
$469$	23.5713	−	6.92115i	1.08842	−	0.319589i
$470$	6.78770	−	19.6118i	0.313093	−	0.904623i
$471$	−6.61364	+	11.7458i	−0.304741	+	0.541217i
$472$	−0.361923	−	7.59770i	−0.0166589	−	0.349713i
$473$	−1.16591	−	6.04930i	−0.0536084	−	0.278147i
$474$	−25.0797	−	25.7415i	−1.15195	−	1.18234i
$475$	2.66725	+	6.66248i	0.122382	+	0.305695i
$476$	−39.7818	−	34.4711i	−1.82340	−	1.57998i
$477$	19.0809	−	0.411434i	0.873652	−	0.0188383i
$478$	48.1067	+	14.1254i	2.20035	+	0.646081i
$479$	−3.01132	+	4.22880i	−0.137591	+	0.193219i	−0.877622	−	0.479353i	$-0.840871\pi$
$479$	−3.01132	+	4.22880i	−0.137591	+	0.193219i	0.740031	+	0.672572i	$0.234811\pi$
$480$	−7.95561	+	0.846302i	−0.363122	+	0.0386282i
$481$	−4.99014	−	9.67952i	−0.227531	−	0.441348i
$482$	28.5920	−	49.5228i	1.30233	−	2.25570i
$483$	−22.4278	+	17.2986i	−1.02050	+	0.787112i
$484$	3.76837	+	6.52700i	0.171289	+	0.296682i
$485$	−6.38281	+	9.93184i	−0.289828	+	0.450982i
$486$	19.1123	−	30.1552i	0.866950	−	1.36787i
$487$	10.1403	+	22.2042i	0.459501	+	1.00617i	0.987601	+	0.156985i	$0.0501773\pi$
$487$	10.1403	+	22.2042i	0.459501	+	1.00617i	−0.528100	+	0.849182i	$0.677095\pi$
$488$	7.56023	+	31.1637i	0.342235	+	1.41071i
$489$	13.9312	+	21.1720i	0.629989	+	0.957431i
$490$	−8.24613	+	2.85401i	−0.372522	+	0.128931i
$491$	9.28904	−	11.8120i	0.419209	−	0.533067i	−0.529882	−	0.848072i	$-0.677764\pi$
$491$	9.28904	−	11.8120i	0.419209	−	0.533067i	0.949090	+	0.315005i	$0.102006\pi$
$492$	−2.78005	−	10.9433i	−0.125335	−	0.493362i
$493$	−28.1577	−	9.74547i	−1.26816	−	0.438914i
$494$	−3.90723	+	2.51102i	−0.175794	+	0.112976i
$495$	7.68895	+	4.71032i	0.345593	+	0.211713i
$496$	−0.0408390	−	0.0471308i	−0.00183373	−	0.00211623i
$497$	30.6790	+	29.2524i	1.37614	+	1.31215i
$498$	8.46755	+	23.6378i	0.379440	+	1.05924i
$499$	−13.3525	−	38.5794i	−0.597738	−	1.72705i	−0.682731	−	0.730669i	$-0.739208\pi$
$499$	−13.3525	−	38.5794i	−0.597738	−	1.72705i	0.0849932	−	0.996382i	$-0.472913\pi$
$500$	−14.4506	−	20.2930i	−0.646250	−	0.907531i
$501$	−4.17773	+	0.851998i	−0.186647	+	0.0380644i
$502$	14.8937	+	10.6058i	0.664740	+	0.473360i
$503$	−1.35192	−	9.40282i	−0.0602792	−	0.419251i	−0.997509	−	0.0705387i	$-0.977528\pi$
$503$	−1.35192	−	9.40282i	−0.0602792	−	0.419251i	0.937230	−	0.348712i	$-0.113381\pi$
$504$	26.8457	−	11.4249i	1.19580	−	0.508905i
$505$		−	11.2895i		−	0.502378i
$506$	27.0743	+	29.5673i	1.20360	+	1.31442i
$507$	−19.9198	−	0.733783i	−0.884669	−	0.0325884i
$508$	28.9340	−	14.9165i	1.28374	−	0.661813i
$509$	2.57133	−	6.42286i	0.113972	−	0.284688i	−0.860404	−	0.509612i	$-0.829789\pi$
$509$	2.57133	−	6.42286i	0.113972	−	0.284688i	0.974376	+	0.224923i	$0.0722132\pi$
$510$	−2.04548	+	15.4036i	−0.0905754	+	0.682083i
$511$	−44.4213	+	10.7765i	−1.96508	+	0.476723i
$512$	0.427039	+	0.195022i	0.0188726	+	0.00861884i
$513$	5.85821	+	6.33472i	0.258646	+	0.279685i
$514$	−1.94748	+	13.5450i	−0.0858996	+	0.597445i
$515$	0.477137	−	0.500406i	0.0210251	−	0.0220505i
$516$	1.45137	+	9.37588i	0.0638930	+	0.412750i
$517$	−40.1184	+	1.91107i	−1.76440	+	0.0840489i
$518$	−69.5574	+	3.31343i	−3.05618	+	0.145584i
$519$	26.3337	−	21.1724i	1.15592	−	0.929366i
$520$	1.97940	−	2.07594i	0.0868026	−	0.0910359i
$521$	4.26639	−	29.6734i	0.186914	−	1.30001i	−0.653026	−	0.757335i	$-0.726501\pi$
$521$	4.26639	−	29.6734i	0.186914	−	1.30001i	0.839940	−	0.542679i	$-0.182590\pi$
$522$	30.5007	−	30.3644i	1.33498	−	1.32901i
$523$	0.126289	+	0.0576744i	0.00552225	+	0.00252193i	0.418174	−	0.908367i	$-0.362670\pi$
$523$	0.126289	+	0.0576744i	0.00552225	+	0.00252193i	−0.412652	+	0.910889i	$0.635397\pi$
$524$	38.0431	−	9.22914i	1.66192	−	0.403177i
$525$	−20.2328	−	15.5612i	−0.883032	−	0.679147i
$526$	−2.70355	+	6.75315i	−0.117880	+	0.294451i
$527$	6.35420	−	3.27582i	0.276794	−	0.142697i
$528$	−0.122715	−	0.231863i	−0.00534049	−	0.0100905i
$529$	18.8312	+	13.2055i	0.818749	+	0.574152i
$530$		−	11.9982i		−	0.521169i
$531$	−4.80896	+	6.39410i	−0.208691	+	0.277480i
$532$	2.61506	+	18.1881i	0.113377	+	0.788555i
$533$	−1.99827	−	1.42296i	−0.0865546	−	0.0616353i
$534$	−7.93367	+	23.7480i	−0.343324	+	1.02768i
$535$	0.756442	+	1.06227i	0.0327039	+	0.0459261i
$536$	6.72078	+	19.4184i	0.290293	+	0.838748i
$537$	16.0207	−	18.8967i	0.691344	−	0.815451i
$538$	35.0029	+	33.3752i	1.50908	+	1.43891i
$539$	11.0591	+	12.7628i	0.476347	+	0.549734i
$540$	−11.5662	−	7.68501i	−0.497728	−	0.330710i
$541$	17.1010	−	10.9902i	0.735231	−	0.472504i	−0.118674	−	0.992933i	$-0.537864\pi$
$541$	17.1010	−	10.9902i	0.735231	−	0.472504i	0.853905	+	0.520429i	$0.174228\pi$
$542$	−1.34062	−	0.463993i	−0.0575845	−	0.0199302i
$543$	15.5925	+	4.39636i	0.669137	+	0.188666i
$544$	−16.4938	+	20.9736i	−0.707167	+	0.899237i
$545$	12.0476	−	4.16972i	0.516063	−	0.178611i
$546$	7.41083	−	14.7636i	0.317154	−	0.631824i
$547$	2.78652	+	11.4862i	0.119143	+	0.491114i	0.999848	+	0.0174484i	$0.00555429\pi$
$547$	2.78652	+	11.4862i	0.119143	+	0.491114i	−0.880705	+	0.473666i	$0.842931\pi$
$548$	22.9449	+	50.2422i	0.980156	+	2.14624i
$549$	14.8061	−	30.3068i	0.631911	−	1.29346i
$550$	−19.5325	+	30.3932i	−0.832869	+	1.29597i
$551$	5.20067	+	9.00783i	0.221556	+	0.383746i
$552$	−15.3456	−	18.0500i	−0.653153	−	0.768261i
$553$	−15.4461	+	26.7535i	−0.656836	+	1.13767i
$554$	24.1589	+	46.8618i	1.02641	+	1.99097i
$555$	7.48866	+	10.2800i	0.317876	+	0.436361i
$556$	3.58945	−	5.04068i	0.152227	−	0.213772i
$557$	−24.6668	−	7.24284i	−1.04517	−	0.306889i	−0.286304	−	0.958139i	$-0.592427\pi$
$557$	−24.6668	−	7.24284i	−1.04517	−	0.306889i	−0.758863	+	0.651250i	$0.774245\pi$
$558$	0.222603	+	10.3235i	0.00942353	+	0.437030i
$559$	1.55785	+	1.34988i	0.0658900	+	0.0570940i
$560$	−0.0433048	−	0.108170i	−0.00182996	−	0.00457102i
$561$	29.1466	−	7.40447i	1.23057	−	0.312617i
$562$	10.5520	+	54.7490i	0.445110	+	2.30945i
$563$	0.867469	+	18.2104i	0.0365595	+	0.767477i	0.940495	+	0.339808i	$0.110362\pi$
$563$	0.867469	+	18.2104i	0.0365595	+	0.767477i	−0.903935	+	0.427669i	$0.859335\pi$
$564$	61.8499	−	0.666747i	2.60435	−	0.0280751i
$565$	1.23888	−	3.57950i	0.0521199	−	0.150591i
$566$	9.97245	−	2.92818i	0.419174	−	0.123080i
$567$	−29.4061	−	8.77775i	−1.23494	−	0.368631i
$568$	−23.2194	+	26.7967i	−0.974266	+	1.12436i
$569$	6.86408	−	0.655440i	0.287757	−	0.0274775i	0.0498206	−	0.998758i	$-0.484135\pi$
$569$	6.86408	−	0.655440i	0.287757	−	0.0274775i	0.237936	+	0.971281i	$0.423529\pi$
$570$	4.06087	−	3.59613i	0.170091	−	0.150625i
$571$	2.57253	−	26.9408i	0.107657	−	1.12744i	−0.766651	−	0.642064i	$-0.778078\pi$
$571$	2.57253	−	26.9408i	0.107657	−	1.12744i	0.874308	−	0.485371i	$-0.161316\pi$
$572$	−13.4302	−	5.37663i	−0.561544	−	0.224808i
$573$	−16.9928	−	11.8265i	−0.709884	−	0.494061i
$574$	−13.5849	+	7.84324i	−0.567022	+	0.327370i
$575$	−7.17309	+	19.4462i	−0.299139	+	0.810964i
$576$	−16.8704	−	34.9281i	−0.702932	−	1.45534i
$577$	−39.4310	−	25.3408i	−1.64153	−	1.05495i	−0.939353	−	0.342953i	$-0.888573\pi$
$577$	−39.4310	−	25.3408i	−1.64153	−	1.05495i	−0.702182	−	0.711998i	$-0.747791\pi$
$578$	7.96711	+	10.1310i	0.331388	+	0.421394i
$579$	−25.9035	+	33.6799i	−1.07651	+	1.39969i
$580$	−11.5520	−	12.1154i	−0.479670	−	0.503064i
$581$	17.5808	−	12.5192i	0.729374	−	0.519385i
$582$	−55.4100	−	12.8115i	−2.29682	−	0.531053i
$583$	−21.5570	+	8.63011i	−0.892799	+	0.357423i
$584$	−10.7717	−	36.6852i	−0.445738	−	1.51804i
$585$	−2.99654	+	0.351472i	−0.123892	+	0.0145316i
$586$	−27.5071	−	42.8018i	−1.13631	−	1.76813i
$587$	−8.12137	+	15.7533i	−0.335205	+	0.650207i	−0.994849	−	0.101372i	$-0.967677\pi$
$587$	−8.12137	+	15.7533i	−0.335205	+	0.650207i	0.659644	+	0.751578i	$0.270707\pi$
$588$	−16.2962	−	20.2688i	−0.672043	−	0.835870i
$589$	−2.42519	−	0.588346i	−0.0999284	−	0.0242424i
$590$	3.95363	+	3.10917i	0.162768	+	0.128002i
$591$	−2.97743	+	0.909229i	−0.122475	+	0.0374007i
$592$	−0.0351726	−	0.368344i	−0.00144558	−	0.0151388i
$593$	−9.55874	+	32.5541i	−0.392531	+	1.33684i	0.492098	+	0.870540i	$0.336230\pi$
$593$	−9.55874	+	32.5541i	−0.392531	+	1.33684i	−0.884628	+	0.466297i	$0.845588\pi$
$594$	−8.87040	+	42.5215i	−0.363957	+	1.74468i
$595$	13.2208	−	1.90086i	0.542000	−	0.0779278i
$596$	−3.45692	+	72.5697i	−0.141601	+	2.97257i
$597$	28.4446	+	17.8499i	1.16416	+	0.730549i
$598$	−13.2364	−	2.17663i	−0.541276	−	0.0890089i
$599$	4.49961	+	2.59785i	0.183849	+	0.106145i	0.589100	−	0.808060i	$-0.299482\pi$
$599$	4.49961	+	2.59785i	0.183849	+	0.106145i	−0.405251	+	0.914206i	$0.632816\pi$
$600$	12.1962	−	17.5239i	0.497907	−	0.715410i
$601$	9.54259	−	7.50437i	0.389250	−	0.306110i	−0.404286	−	0.914633i	$-0.632480\pi$
$601$	9.54259	−	7.50437i	0.389250	−	0.306110i	0.793536	+	0.608523i	$0.208238\pi$
$602$	11.9899	−	5.47562i	0.488673	−	0.223169i
$603$	7.59863	−	20.2341i	0.309440	−	0.823998i
$604$	23.9755	−	52.4990i	0.975549	−	2.13615i
$605$	−1.87783	−	0.361923i	−0.0763448	−	0.0147143i
$606$	51.1981	−	18.3402i	2.07978	−	0.745020i
$607$	4.22514	−	17.4162i	0.171493	−	0.706904i	−0.819510	−	0.573065i	$-0.805754\pi$
$607$	4.22514	−	17.4162i	0.171493	−	0.706904i	0.991003	−	0.133839i	$-0.0427305\pi$
$608$	9.14589	−	1.76273i	0.370915	−	0.0714880i
$609$	−32.2357	−	18.1508i	−1.30626	−	0.735508i
$610$	−18.8477	−	9.71664i	−0.763119	−	0.393415i
$611$	10.1563	−	8.80049i	0.410880	−	0.356030i
$612$	−45.2760	+	9.74300i	−1.83018	+	0.393838i
$613$	−30.5912	−	4.39836i	−1.23557	−	0.177648i	−0.506591	−	0.862186i	$-0.669095\pi$
$613$	−30.5912	−	4.39836i	−1.23557	−	0.177648i	−0.728977	+	0.684538i	$0.760004\pi$
$614$	8.82111	−	45.7683i	0.355991	−	1.84706i
$615$	2.56051	+	1.28529i	0.103250	+	0.0518278i
$616$	−25.6903	+	24.4956i	−1.03509	+	0.986957i
$617$	6.20202	+	0.592221i	0.249684	+	0.0238419i	0.219147	−	0.975692i	$-0.429672\pi$
$617$	6.20202	+	0.592221i	0.249684	+	0.0238419i	0.0305363	+	0.999534i	$0.490278\pi$
$618$	3.04447	+	1.35089i	0.122466	+	0.0543408i
$619$	45.2187	+	2.15403i	1.81749	+	0.0865779i	0.928498	−	0.371338i	$-0.121101\pi$
$619$	45.2187	+	2.15403i	1.81749	+	0.0865779i	0.888995	+	0.457916i	$0.151404\pi$
$620$	4.01636			0.161301
$621$	0.302880	+	24.9180i	0.0121542	+	0.999926i
$622$	2.04091			0.0818332
$623$	21.4978	+	1.02407i	0.861292	+	0.0410284i
$624$	0.0802327	+	0.0356009i	0.00321188	+	0.00142518i
$625$	−15.2188	−	1.45322i	−0.608754	−	0.0581289i
$626$	17.6000	−	16.7816i	0.703438	−	0.670727i
$627$	−9.38202	−	4.70946i	−0.374682	−	0.188078i
$628$	−4.77989	+	24.8004i	−0.190739	+	0.989646i
$629$	41.9851	+	6.03654i	1.67405	+	0.240693i
$630$	−5.91549	+	18.3633i	−0.235679	+	0.731611i
$631$	−13.1130	+	11.3625i	−0.522021	+	0.452333i	−0.875576	−	0.483080i	$-0.839518\pi$
$631$	−13.1130	+	11.3625i	−0.522021	+	0.452333i	0.353556	+	0.935414i	$0.384973\pi$
$632$	−22.9673	−	11.8405i	−0.913592	−	0.470989i
$633$	2.66009	+	1.49780i	0.105729	+	0.0595324i
$634$	−17.1027	+	3.29627i	−0.679234	+	0.130912i
$635$	−1.94738	+	8.02719i	−0.0772792	+	0.318549i
$636$	33.6651	−	12.0595i	1.33491	−	0.478191i
$637$	−5.54845	−	1.06938i	−0.219838	−	0.0423702i
$638$	−21.7523	+	47.6309i	−0.861182	+	1.88573i
$639$	36.7927	−	6.10226i	1.45550	−	0.241402i
$640$	−13.7782	+	6.29228i	−0.544630	+	0.248724i
$641$	−12.4186	+	9.76607i	−0.490504	+	0.385737i	−0.832553	−	0.553946i	$-0.813122\pi$
$641$	−12.4186	+	9.76607i	−0.490504	+	0.385737i	0.342049	+	0.939682i	$0.388879\pi$
$642$	−3.58856	+	5.15616i	−0.141629	+	0.203498i
$643$	2.88529	+	1.66582i	0.113785	+	0.0656937i	0.555812	−	0.831308i	$-0.312407\pi$
$643$	2.88529	+	1.66582i	0.113785	+	0.0656937i	−0.442028	+	0.897001i	$0.645741\pi$
$644$	−29.5873	+	44.0575i	−1.16590	+	1.73611i
$645$	−2.03915	−	1.27963i	−0.0802913	−	0.0503855i
$646$	0.860774	−	18.0699i	0.0338667	−	0.710949i
$647$	40.0121	−	5.75287i	1.57304	−	0.226168i	0.700115	−	0.714030i	$-0.253132\pi$
$647$	40.0121	−	5.75287i	1.57304	−	0.226168i	0.872921	+	0.487861i	$0.162223\pi$
$648$	6.16347	−	24.9183i	0.242124	−	0.978882i
$649$	2.74241	−	9.33978i	0.107649	−	0.366618i
$650$	−1.14908	−	12.0338i	−0.0450708	−	0.472003i
$651$	8.48891	−	2.59228i	0.332706	−	0.101600i
$652$	37.3275	+	29.3547i	1.46186	+	1.14962i
$653$	20.7896	+	5.04351i	0.813561	+	0.197368i	0.620892	−	0.783896i	$-0.286771\pi$
$653$	20.7896	+	5.04351i	0.813561	+	0.197368i	0.192669	+	0.981264i	$0.438286\pi$
$654$	38.4814	+	47.8622i	1.50474	+	1.87156i
$655$	−4.55164	+	8.82895i	−0.177847	+	0.344976i
$656$	−0.0450633	−	0.0701199i	−0.00175943	−	0.00273772i
$657$	−15.9139	+	36.9335i	−0.620860	+	1.44091i
$658$	−24.2102	−	82.4524i	−0.943812	−	3.21433i
$659$	−2.34651	+	0.939400i	−0.0914070	+	0.0365938i	−0.416915	−	0.908945i	$-0.636889\pi$
$659$	−2.34651	+	0.939400i	−0.0914070	+	0.0365938i	0.325508	+	0.945539i	$0.394465\pi$
$660$	16.4609	+	3.80597i	0.640739	+	0.148147i
$661$	2.68296	−	1.91053i	0.104355	−	0.0743110i	−0.526688	−	0.850059i	$-0.676566\pi$
$661$	2.68296	−	1.91053i	0.104355	−	0.0743110i	0.631043	+	0.775748i	$0.282627\pi$
$662$	24.7993	+	26.0088i	0.963854	+	1.01086i
$663$	−6.13440	+	7.97599i	−0.238240	+	0.309762i
$664$	11.1596	+	14.1905i	0.433075	+	0.550700i
$665$	−3.92240	−	2.52078i	−0.152104	−	0.0977515i
$666$	−34.4543	+	50.6612i	−1.33508	+	1.96308i
$667$	−6.27945	+	29.3771i	−0.243141	+	1.13749i
$668$	−6.91859	+	3.99445i	−0.267688	+	0.154550i
$669$	−20.2074	−	14.0638i	−0.781262	−	0.543738i
$670$	−12.6145	−	5.05009i	−0.487342	−	0.195102i
$671$	−3.90092	+	40.8523i	−0.150593	+	1.57708i
$672$	−24.8011	+	21.9628i	−0.956722	+	0.847232i
$673$	−4.58002	+	0.437339i	−0.176547	+	0.0168582i	−0.182955	−	0.983121i	$-0.558566\pi$
$673$	−4.58002	+	0.437339i	−0.176547	+	0.0168582i	0.00640810	+	0.999979i	$0.497960\pi$
$674$	17.2477	−	19.9050i	0.664358	−	0.766710i
$675$	−21.6415	+	5.99735i	−0.832983	+	0.230838i
$676$	−35.8359	+	10.5224i	−1.37831	+	0.404707i
$677$	10.1525	−	29.3338i	0.390193	−	1.12739i	−0.563373	−	0.826203i	$-0.690497\pi$
$677$	10.1525	−	29.3338i	0.390193	−	1.12739i	0.953566	−	0.301185i	$-0.0973822\pi$
$678$	18.2456	−	0.196689i	0.700719	−	0.00755380i
$679$	2.32606	+	48.8301i	0.0892661	+	1.87393i
$680$	2.11436	+	10.9704i	0.0810821	+	0.420694i
$681$	−23.9547	+	6.08550i	−0.917947	+	0.233197i
$682$	−4.66925	−	11.6632i	−0.178795	−	0.446608i
$683$	3.80767	+	3.29936i	0.145696	+	0.126247i	0.724660	−	0.689107i	$-0.241997\pi$
$683$	3.80767	+	3.29936i	0.145696	+	0.126247i	−0.578963	+	0.815354i	$0.696542\pi$
$684$	14.1718	+	7.77967i	0.541873	+	0.297463i
$685$	−13.4474	−	3.94852i	−0.513800	−	0.150865i
$686$	10.7504	−	15.0968i	0.410452	−	0.576399i
$687$	20.0686	+	27.5489i	0.765663	+	1.05106i
$688$	0.0320937	+	0.0622531i	0.00122356	+	0.00237338i
$689$	3.88473	−	6.72854i	0.147996	−	0.256337i
$690$	15.6655	+	0.147336i	0.596376	+	0.00560900i
$691$	−2.89867	−	5.02064i	−0.110271	−	0.190994i	0.805609	−	0.592448i	$-0.201838\pi$
$691$	−2.89867	−	5.02064i	−0.110271	−	0.190994i	−0.915879	+	0.401454i	$0.868505\pi$
$692$	34.2286	−	53.2607i	1.30118	−	2.02467i
$693$	37.2479	−	2.58015i	1.41493	−	0.0980118i
$694$	4.07180	+	8.91601i	0.154564	+	0.338447i
$695$	0.370186	+	1.52593i	0.0140420	+	0.0578817i
$696$	13.8821	−	27.6554i	0.526199	−	1.04828i
$697$	9.02942	−	3.12511i	0.342014	−	0.118372i
$698$	−43.7568	+	55.6413i	−1.65622	+	2.10605i
$699$	21.1197	+	5.95478i	0.798820	+	0.225230i
$700$	−45.1953	−	15.6422i	−1.70822	−	0.591221i
$701$	10.1837	−	6.54467i	0.384633	−	0.247189i	−0.334007	−	0.942570i	$-0.608401\pi$
$701$	10.1837	−	6.54467i	0.384633	−	0.247189i	0.718641	+	0.695382i	$0.244765\pi$
$702$	−6.46189	−	13.0183i	−0.243888	−	0.491346i
$703$	−9.69642	−	11.1903i	−0.365707	−	0.422049i
$704$	34.1551	+	32.5668i	1.28727	+	1.22741i
$705$	−10.1495	+	11.9715i	−0.382253	+	0.450874i
$706$	2.33893	+	6.75789i	0.0880267	+	0.254337i
$707$	−27.1159	−	38.0790i	−1.01980	−	1.43211i
$708$	−4.75001	+	14.2183i	−0.178516	+	0.534357i
$709$	−30.0293	−	21.3837i	−1.12777	−	0.803083i	−0.145281	−	0.989390i	$-0.546409\pi$
$709$	−30.0293	−	21.3837i	−1.12777	−	0.803083i	−0.982492	+	0.186307i	$0.940348\pi$
$710$	−3.33674	−	23.2075i	−0.125226	−	0.870963i
$711$	10.6432	+	25.0089i	0.399151	+	0.937907i
$712$			18.0022i			0.674662i
$713$	−4.06142	−	5.95425i	−0.152101	−	0.222989i
$714$	30.0980	+	56.8684i	1.12639	+	2.12824i
$715$	3.26270	−	1.68204i	0.122018	−	0.0629047i
$716$	17.2521	−	43.0936i	0.644740	−	1.61048i
$717$	−30.0560	−	23.1163i	−1.12246	−	0.863295i
$718$	6.09600	−	1.47887i	0.227501	−	0.0551911i
$719$	31.4071	+	14.3431i	1.17129	+	0.534909i	0.903508	−	0.428572i	$-0.140983\pi$
$719$	31.4071	+	14.3431i	1.17129	+	0.534909i	0.267779	+	0.963480i	$0.413710\pi$
$720$	−0.0989603	−	0.0267541i	−0.00368803	−	0.000997067i
$721$	0.407447	−	2.83385i	0.0151741	−	0.105538i
$722$	25.6710	−	26.9230i	0.955376	−	1.00197i
$723$	−33.7038	+	27.0980i	−1.25346	+	1.00779i
$724$	30.3202	−	1.44433i	1.12684	−	0.0536780i
$725$	−27.0413	+	1.28814i	−1.00429	+	0.0478401i
$726$	−1.40927	−	9.10394i	−0.0523031	−	0.337879i
$727$	7.79060	−	8.17055i	0.288938	−	0.303029i	−0.563228	−	0.826302i	$-0.690441\pi$
$727$	7.79060	−	8.17055i	0.288938	−	0.303029i	0.852165	+	0.523273i	$0.175289\pi$
$728$	1.69030	−	11.7563i	0.0626465	−	0.435716i
$729$	−21.7229	+	16.0348i	−0.804551	+	0.593883i
$730$	22.9977	+	10.5027i	0.851182	+	0.388722i
$731$	−7.80252	+	1.89287i	−0.288587	+	0.0700104i
$732$	8.31943	−	62.6499i	0.307495	−	2.31561i
$733$	11.8323	−	29.5555i	0.437034	−	1.09166i	−0.532441	−	0.846467i	$-0.678725\pi$
$733$	11.8323	−	29.5555i	0.437034	−	1.09166i	0.969475	−	0.245191i	$-0.0788507\pi$
$734$	−21.5389	+	11.1041i	−0.795015	+	0.409859i
$735$	6.59474	+	0.242930i	0.243251	+	0.00896060i
$736$	23.0207	+	13.9179i	0.848553	+	0.513022i
$737$			26.2967i			0.968652i
$738$	−1.66917	+	13.6999i	−0.0614429	+	0.504300i
$739$	0.777887	+	5.41032i	0.0286150	+	0.199022i	0.999114	−	0.0420828i	$-0.0133993\pi$
$739$	0.777887	+	5.41032i	0.0286150	+	0.199022i	−0.970499	+	0.241105i	$0.922490\pi$
$740$	19.4117	+	13.8230i	0.713587	+	0.508143i
$741$	3.44166	−	0.701885i	0.126432	−	0.0257844i
$742$	−28.8180	−	40.4693i	−1.05794	−	1.48567i
$743$	−8.68354	−	25.0895i	−0.318568	−	0.920443i	−0.984646	−	0.174561i	$-0.944149\pi$
$743$	−8.68354	−	25.0895i	−0.318568	−	0.920443i	0.666078	−	0.745882i	$-0.267972\pi$
$744$	2.50372	+	6.98933i	0.0917908	+	0.256241i
$745$	−13.3420	−	12.7216i	−0.488813	−	0.466082i
$746$	−13.9537	−	16.1034i	−0.510881	−	0.589588i
$747$	0.494425	−	18.9824i	0.0180900	−	0.694530i
$748$	47.4017	−	30.4632i	1.73318	−	1.11385i
$749$	5.10287	+	1.76612i	0.186455	+	0.0645326i
$750$	7.49770	+	29.5136i	0.273777	+	1.07769i
$751$	−3.13001	+	3.98013i	−0.114216	+	0.145237i	−0.839799	−	0.542897i	$-0.817327\pi$
$751$	−3.13001	+	3.98013i	−0.114216	+	0.145237i	0.725584	+	0.688134i	$0.241570\pi$
$752$	0.431502	−	0.149344i	0.0157352	−	0.00544602i
$753$	−7.60072	−	11.5513i	−0.276986	−	0.420951i
$754$	−4.13061	−	17.0266i	−0.150428	−	0.620072i
$755$	6.08362	+	13.3213i	0.221406	+	0.484810i
$756$	−57.4702	+	1.85918i	−2.09017	+	0.0676176i
$757$	18.0026	−	28.0126i	0.654315	−	1.01813i	−0.342587	−	0.939486i	$-0.611303\pi$
$757$	18.0026	−	28.0126i	0.654315	−	1.01813i	0.996902	−	0.0786481i	$-0.0250603\pi$
$758$	−1.34053	−	2.32187i	−0.0486902	−	0.0843340i
$759$	−11.0032	−	28.2519i	−0.399391	−	1.02548i
$760$	1.95000	−	3.37751i	0.0707341	−	0.122515i
$761$	2.72885	+	5.29322i	0.0989206	+	0.191879i	0.933103	−	0.359610i	$-0.117090\pi$
$761$	2.72885	+	5.29322i	0.0989206	+	0.191879i	−0.834182	+	0.551489i	$0.814060\pi$
$762$	−39.5669	+	4.20905i	−1.43336	+	0.152478i
$763$	30.6208	−	43.0009i	1.10855	−	1.55674i
$764$	−37.2201	−	10.9288i	−1.34657	−	0.395390i
$765$	5.65498	−	10.3014i	0.204456	−	0.372447i
$766$	27.4220	+	23.7613i	0.990799	+	0.858532i
$767$	1.21050	+	3.02369i	0.0437088	+	0.109179i
$768$	−19.6626	−	20.1814i	−0.709512	−	0.728233i
$769$	−9.77905	−	50.7385i	−0.352641	−	1.82968i	−0.533047	−	0.846085i	$-0.678953\pi$
$769$	−9.77905	−	50.7385i	−0.352641	−	1.82968i	0.180406	−	0.983592i	$-0.442259\pi$
$770$	−1.11687	−	23.4459i	−0.0402490	−	0.844931i
$771$	5.07757	−	9.01772i	0.182864	−	0.324765i
$772$	−26.0384	+	75.2330i	−0.937143	+	2.70770i
$773$	−4.77710	+	1.40268i	−0.171820	+	0.0504510i	−0.366511	−	0.930414i	$-0.619448\pi$
$773$	−4.77710	+	1.40268i	−0.171820	+	0.0504510i	0.194691	+	0.980865i	$0.437630\pi$
$774$	2.49049	−	11.3263i	0.0895187	−	0.407117i
$775$	4.25347	−	4.90877i	0.152789	−	0.176328i
$776$	−40.7051	+	3.88687i	−1.46123	+	0.139530i
$777$	49.9499	+	16.6871i	1.79194	+	0.598646i
$778$	3.35504	−	35.1356i	0.120284	−	1.25967i
$779$	−3.09651	−	1.23965i	−0.110944	−	0.0444152i
$780$	−5.11661	+	2.40367i	−0.183204	+	0.0860651i
$781$	−39.2965	+	22.6878i	−1.40614	+	0.811835i
$782$	36.8110	−	37.0781i	1.31636	−	1.32591i
$783$	−29.8099	+	13.0677i	−1.06532	+	0.467001i
$784$	−0.161514	−	0.103799i	−0.00576836	−	0.00370710i
$785$	−3.96163	−	5.03762i	−0.141397	−	0.179801i
$786$	−47.4336	−	6.29882i	−1.69190	−	0.224671i
$787$	35.9788	+	37.7335i	1.28251	+	1.34505i	0.908646	+	0.417568i	$0.137117\pi$
$787$	35.9788	+	37.7335i	1.28251	+	1.34505i	0.373860	+	0.927485i	$0.378034\pi$
$788$	−4.75151	+	3.38354i	−0.169266	+	0.120534i
$789$	3.75315	−	4.02212i	0.133616	−	0.143191i
$790$	15.8628	−	6.35049i	0.564372	−	0.225940i
$791$	−4.41879	−	15.0490i	−0.157114	−	0.535082i
$792$	3.63819	+	31.0180i	0.129277	+	1.10218i
$793$	−7.42367	−	11.5515i	−0.263622	−	0.410204i
$794$	22.1450	−	42.9553i	0.785896	−	1.52443i
$795$	−3.28140	+	8.45972i	−0.116379	+	0.300035i
$796$	61.1476	+	14.8343i	2.16732	+	0.525786i
$797$	−21.8460	−	17.1799i	−0.773824	−	0.608542i	0.151177	−	0.988507i	$-0.451694\pi$
$797$	−21.8460	−	17.1799i	−0.773824	−	0.608542i	−0.925001	+	0.379965i	$0.875936\pi$
$798$	5.05967	−	21.8832i	0.179110	−	0.774656i
$799$	4.97557	+	52.1066i	0.176023	+	1.84340i
$800$	−6.82988	+	23.2604i	−0.241473	+	0.822381i
$801$	12.0888	−	14.5745i	0.427135	−	0.514966i
$802$	13.7584	−	1.97815i	0.485825	−	0.0698511i
$803$	2.32815	−	48.8739i	0.0821587	−	1.72472i
$804$	1.49080	−	40.4703i	0.0525764	−	1.42728i
$805$	−3.53232	−	12.9947i	−0.124498	−	0.458003i
$806$	3.64042	+	2.10180i	0.128228	+	0.0740327i
$807$	−15.5521	−	33.1052i	−0.547459	−	1.16536i
$808$	30.7359	−	24.1710i	1.08128	−	0.850331i
$809$	1.18423	−	0.540818i	0.0416352	−	0.0190142i	−0.394489	−	0.918901i	$-0.629078\pi$
$809$	1.18423	−	0.540818i	0.0416352	−	0.0190142i	0.436124	+	0.899887i	$0.356351\pi$
$810$	9.78377	+	13.8705i	0.343767	+	0.487360i
$811$	8.72972	−	19.1154i	0.306542	−	0.671233i	−0.692183	−	0.721722i	$-0.743351\pi$
$811$	8.72972	−	19.1154i	0.306542	−	0.671233i	0.998725	+	0.0504893i	$0.0160781\pi$
$812$	−68.0636	−	13.1182i	−2.38856	−	0.460358i
$813$	0.818348	+	0.693800i	0.0287007	+	0.0243326i
$814$	17.5737	−	72.4400i	0.615959	−	2.53902i
$815$	−11.8318	+	2.28040i	−0.414451	+	0.0798788i
$816$	−0.294224	+	0.174126i	−0.0102999	+	0.00609562i
$817$	2.49114	+	1.28427i	0.0871541	+	0.0449311i
$818$	−11.9910	+	10.3902i	−0.419254	+	0.363286i
$819$	−9.26296	+	8.38276i	−0.323674	+	0.292917i
$820$	5.31346	+	0.763961i	0.185554	+	0.0266787i
$821$	1.63050	−	8.45983i	0.0569048	−	0.295250i	−0.942316	−	0.334725i	$-0.891356\pi$
$821$	1.63050	−	8.45983i	0.0569048	−	0.295250i	0.999221	+	0.0394752i	$0.0125686\pi$
$822$	−3.93918	−	67.3986i	−0.137395	−	2.35080i
$823$	−15.1253	+	14.4219i	−0.527234	+	0.502717i	−0.906290	−	0.422657i	$-0.861098\pi$
$823$	−15.1253	+	14.4219i	−0.527234	+	0.502717i	0.379055	+	0.925374i	$0.376249\pi$
$824$	2.38391	+	0.227636i	0.0830475	+	0.00793007i
$825$	22.0843	−	16.0877i	0.768876	−	0.560102i
$826$	20.8031	+	0.990975i	0.723833	+	0.0344804i
$827$	0.162395			0.00564701			0.00282351	−	0.999996i	$-0.499101\pi$
$827$	0.162395			0.00564701			0.00282351	+	0.999996i	$0.499101\pi$
$828$	15.3321	+	44.1031i	0.532829	+	1.53269i
$829$	51.8376			1.80039			0.900197	−	0.435482i	$-0.143422\pi$
$829$	51.8376			1.80039			0.900197	+	0.435482i	$0.143422\pi$
$830$	−11.9241	−	0.568013i	−0.413890	−	0.0197160i
$831$	−4.21774	−	39.6486i	−0.146312	−	1.37540i
$832$	−15.7191	−	1.50099i	−0.544962	−	0.0520376i
$833$	15.9285	−	15.1878i	0.551891	−	0.526227i
$834$	−6.31871	+	4.15771i	−0.218799	+	0.143970i
$835$	0.383636	−	1.99049i	0.0132763	−	0.0688839i
$836$	−19.4692	−	2.79925i	−0.673357	−	0.0968141i
$837$	2.66644	−	7.33981i	0.0921657	−	0.253701i
$838$	−45.1560	+	39.1279i	−1.55989	+	1.35165i
$839$	8.64645	+	4.45756i	0.298509	+	0.153892i	0.600974	−	0.799268i	$-0.294779\pi$
$839$	8.64645	+	4.45756i	0.298509	+	0.153892i	−0.302466	+	0.953160i	$0.597810\pi$
$840$	0.149524	+	13.8704i	0.00515905	+	0.478573i
$841$	−10.0518	+	1.93732i	−0.346614	+	0.0668043i
$842$	4.66052	−	19.2109i	0.160612	−	0.662052i
$843$	7.53334	−	41.4884i	0.259462	−	1.42894i
$844$	5.61661	+	1.08251i	0.193332	+	0.0372616i
$845$	3.93689	−	8.62059i	0.135433	−	0.296557i
$846$	−70.7791	−	26.5800i	−2.43343	−	0.913840i
$847$	−7.20311	+	3.28955i	−0.247502	+	0.113030i
$848$	0.207508	−	0.163186i	0.00712584	−	0.00560383i
$849$	−7.83223	−	0.662773i	−0.268801	−	0.0227463i
$850$	40.7763	+	23.5422i	1.39862	+	0.807491i
$851$	0.863123	−	42.7558i	0.0295875	−	1.46565i
$852$	61.7629	−	32.6885i	2.11596	−	1.11989i
$853$	1.00923	−	21.1863i	0.0345553	−	0.725405i	−0.913412	−	0.407037i	$-0.866562\pi$
$853$	1.00923	−	21.1863i	0.0345553	−	0.725405i	0.947967	−	0.318368i	$-0.103135\pi$
$854$	−86.9100	+	12.4958i	−2.97400	+	0.427596i
$855$	−3.84676	+	1.42496i	−0.131556	+	0.0487325i
$856$	−1.27250	+	4.33375i	−0.0434933	+	0.148125i
$857$	−2.70085	−	28.2846i	−0.0922593	−	0.966183i	−0.916524	−	0.399979i	$-0.869017\pi$
$857$	−2.70085	−	28.2846i	−0.0922593	−	0.966183i	0.824265	−	0.566204i	$-0.191589\pi$
$858$	12.9284	+	12.0638i	0.441368	+	0.411853i
$859$	−15.9310	−	12.5283i	−0.543559	−	0.427460i	0.308255	−	0.951304i	$-0.400255\pi$
$859$	−15.9310	−	12.5283i	−0.543559	−	0.427460i	−0.851814	+	0.523844i	$0.824497\pi$
$860$	−4.38357	−	1.06344i	−0.149479	−	0.0362631i
$861$	11.7235	−	1.81478i	0.399536	−	0.0618475i
$862$	−11.3224	+	21.9623i	−0.385641	+	0.748040i
$863$	20.4029	+	31.7475i	0.694521	+	1.08070i	0.992033	+	0.125978i	$0.0402070\pi$
$863$	20.4029	+	31.7475i	0.694521	+	1.08070i	−0.297512	+	0.954718i	$0.596157\pi$
$864$	2.32745	+	29.0533i	0.0791815	+	0.988415i
$865$	4.52597	+	15.4140i	0.153888	+	0.524093i
$866$	−19.1586	+	7.66996i	−0.651037	+	0.260636i
$867$	−2.84673	−	9.32212i	−0.0966799	−	0.316596i
$868$	13.5470	−	9.64674i	0.459813	−	0.327432i
$869$	−22.8196	−	23.9325i	−0.774103	−	0.811856i
$870$	7.80926	+	18.9131i	0.264759	+	0.641215i
$871$	−5.43907	−	6.91634i	−0.184296	−	0.234351i
$872$	37.1461	+	23.8723i	1.25793	+	0.808420i
$873$	35.5647	+	24.1873i	1.20368	+	0.818615i
$874$	−18.1874	+	1.36689i	−0.615197	+	0.0462359i
$875$	22.6682	−	13.0875i	0.766325	−	0.442438i
$876$	−6.35372	+	75.0842i	−0.214672	+	2.53686i
$877$	10.1756	+	4.07368i	0.343604	+	0.137558i	0.537045	−	0.843554i	$-0.319541\pi$
$877$	10.1756	+	4.07368i	0.343604	+	0.137558i	−0.193441	+	0.981112i	$0.561965\pi$
$878$	−1.23102	+	12.8919i	−0.0415450	+	0.435079i
$879$	7.68881	+	37.7017i	0.259337	+	1.27165i
$880$	0.124159	−	0.0118557i	0.00418539	−	0.000399656i
$881$	−5.30482	+	6.12209i	−0.178724	+	0.206259i	−0.838042	−	0.545606i	$-0.816300\pi$
$881$	−5.30482	+	6.12209i	−0.178724	+	0.206259i	0.659318	+	0.751864i	$0.270845\pi$
$882$	9.61166	+	30.3018i	0.323642	+	1.02032i
$883$	−53.2966	+	15.6493i	−1.79357	+	0.526641i	−0.996965	−	0.0778554i	$-0.975193\pi$
$883$	−53.2966	+	15.6493i	−1.79357	+	0.526641i	−0.796608	+	0.604496i	$0.793375\pi$
$884$	−6.16634	+	17.8165i	−0.207396	+	0.599233i
$885$	−1.93730	−	3.27350i	−0.0651217	−	0.110037i
$886$	2.35224	+	49.3795i	0.0790249	+	1.65894i
$887$	−2.78842	−	14.4677i	−0.0936259	−	0.485777i	−0.998227	−	0.0595186i	$-0.981043\pi$
$887$	−2.78842	−	14.4677i	−0.0936259	−	0.485777i	0.904601	−	0.426259i	$-0.140169\pi$
$888$	−11.9541	+	42.3974i	−0.401154	+	1.42276i
$889$	12.7118	+	31.7525i	0.426340	+	1.06495i
$890$	−8.99650	−	7.79551i	−0.301563	−	0.261306i
$891$	17.8836	−	27.5551i	0.599123	−	0.923132i
$892$	−44.2611	−	12.9962i	−1.48197	−	0.435146i
$893$	10.5988	−	14.8840i	0.354677	−	0.498074i
$894$	36.0179	−	81.1725i	1.20462	−	2.71481i
$895$	5.39718	+	10.4691i	0.180408	+	0.349942i
$896$	−31.3598	+	54.3167i	−1.04766	+	1.81459i
$897$	8.73744	+	5.15473i	0.291735	+	0.172111i
$898$	−25.7766	−	44.6464i	−0.860176	−	1.48987i
$899$	5.08952	−	7.91946i	0.169745	−	0.264129i
$900$	−34.8994	+	23.5068i	−1.16331	+	0.783559i
$901$	12.5712	+	27.5272i	0.418809	+	0.917063i
$902$	−3.95871	−	16.3180i	−0.131811	−	0.543331i
$903$	−9.95141	+	0.581620i	−0.331162	+	0.0193551i
$904$	12.3976	−	4.29086i	0.412339	−	0.142712i
$905$	−4.76122	+	6.05439i	−0.158268	+	0.201255i
$906$	−50.5290	+	49.2300i	−1.67871	+	1.63556i
$907$	0.681309	+	0.235803i	0.0226225	+	0.00782972i	0.338356	−	0.941018i	$-0.390129\pi$
$907$	0.681309	+	0.235803i	0.0226225	+	0.00782972i	−0.315733	+	0.948848i	$0.602250\pi$
$908$	−38.9580	+	25.0368i	−1.29287	+	0.830874i
$909$	−41.1148	−	1.07089i	−1.36369	−	0.0355193i
$910$	5.14317	+	5.93553i	0.170494	+	0.196761i
$911$	18.0177	+	17.1799i	0.596954	+	0.569195i	0.927137	−	0.374722i	$-0.122262\pi$
$911$	18.0177	+	17.1799i	0.596954	+	0.569195i	−0.330183	+	0.943917i	$0.607110\pi$
$912$	0.117426	+	0.0213218i	0.00388836	+	0.000706037i
$913$	7.55624	+	21.8323i	0.250075	+	0.722544i
$914$	24.3869	+	34.2465i	0.806646	+	1.13278i
$915$	10.6317	+	12.0057i	0.351474	+	0.396896i
$916$	52.0205	+	37.0437i	1.71881	+	1.22396i
$917$	5.85349	+	40.7119i	0.193299	+	1.34443i
$918$	55.9034	+	8.91046i	1.84509	+	0.294089i
$919$			1.33479i			0.0440305i	0.999758	+	0.0220153i	$0.00700825\pi$
$919$			1.33479i			0.0440305i	−0.999758	+	0.0220153i	$0.992992\pi$
$920$	10.7165	−	3.46846i	0.353314	−	0.114352i
$921$	−18.7368	+	29.8579i	−0.617399	+	0.983850i
$922$	18.8370	−	9.71114i	0.620363	−	0.319819i
$923$	5.64280	−	14.0950i	0.185735	−	0.463944i
$924$	64.6630	−	26.6994i	2.12726	−	0.878347i
$925$	37.4520	−	9.08575i	1.23141	−	0.298738i
$926$	54.5524	+	24.9132i	1.79270	+	0.818700i
$927$	−1.77714	−	1.78512i	−0.0583690	−	0.0586311i
$928$	−5.00035	+	34.7782i	−0.164144	+	1.14165i
$929$	−24.7251	+	25.9310i	−0.811205	+	0.850767i	−0.991128	−	0.132914i	$-0.957567\pi$
$929$	−24.7251	+	25.9310i	−0.811205	+	0.850767i	0.179923	+	0.983681i	$0.442415\pi$
$930$	−4.57706	−	1.77538i	−0.150088	−	0.0582169i
$931$	−7.67413	+	0.365564i	−0.251510	+	0.0119809i
$932$	41.0680	−	1.95631i	1.34523	−	0.0640811i
$933$	−1.43901	−	0.558172i	−0.0471111	−	0.0182737i
$934$	36.0550	−	37.8134i	1.17976	−	1.23729i
$935$	−2.03475	+	14.1520i	−0.0665435	+	0.462820i
$936$	−7.37248	−	7.40559i	−0.240977	−	0.242059i
$937$	−14.8468	−	6.78029i	−0.485022	−	0.221502i	0.157868	−	0.987460i	$-0.449538\pi$
$937$	−14.8468	−	6.78029i	−0.485022	−	0.221502i	−0.642891	+	0.765958i	$0.722265\pi$
$938$	−54.6776	+	13.2646i	−1.78529	+	0.433106i
$939$	−16.9991	+	7.01894i	−0.554743	+	0.229054i
$940$	−10.9296	+	27.3009i	−0.356485	+	0.890457i
$941$	13.4427	−	6.93021i	0.438221	−	0.225919i	−0.224975	−	0.974365i	$-0.572230\pi$
$941$	13.4427	−	6.93021i	0.438221	−	0.225919i	0.663196	+	0.748446i	$0.269200\pi$
$942$	16.4099	−	26.1498i	0.534662	−	0.852006i
$943$	−4.24050	−	8.64973i	−0.138090	−	0.281674i
$944$			0.110665i			0.00360183i
$945$	9.19310	−	11.3298i	0.299051	−	0.368558i
$946$	2.00799	+	13.9659i	0.0652854	+	0.454070i
$947$	−4.02585	−	2.86680i	−0.130823	−	0.0931584i	0.512772	−	0.858525i	$-0.328618\pi$
$947$	−4.02585	−	2.86680i	−0.130823	−	0.0931584i	−0.643595	+	0.765366i	$0.722558\pi$
$948$	33.7623	+	38.1255i	1.09655	+	1.23826i
$949$	9.49648	+	13.3359i	0.308269	+	0.432903i
$950$	−5.37576	−	15.5322i	−0.174413	−	0.503932i
$951$	12.9603	+	2.35329i	0.420266	+	0.0763106i
$952$	33.4809	+	31.9239i	1.08512	+	1.03466i
$953$	8.32954	+	9.61281i	0.269820	+	0.311389i	0.874448	−	0.485119i	$-0.161224\pi$
$953$	8.32954	+	9.61281i	0.269820	+	0.311389i	−0.604628	+	0.796508i	$0.706678\pi$
$954$	−43.6956	−	1.13812i	−1.41470	−	0.0368479i
$955$	8.28050	−	5.32155i	0.267951	−	0.172201i
$956$	−67.1380	−	23.2367i	−2.17140	−	0.751528i
$957$	28.3638	−	27.6346i	0.916871	−	0.893301i
$958$	7.34974	−	9.34596i	0.237459	−	0.301954i
$959$	−54.8411	+	18.9807i	−1.77091	+	0.612919i
$960$	18.4102	−	1.07600i	0.594188	−	0.0347279i
$961$	−6.77604	−	27.9312i	−0.218582	−	0.901007i
$962$	10.3610	+	22.6874i	0.334052	+	0.731471i
$963$	3.94039	−	2.65408i	0.126977	−	0.0855265i
$964$	−43.8083	+	68.1670i	−1.41097	+	2.19551i
$965$	−10.1004	−	17.4945i	−0.325145	−	0.563168i
$966$	53.1927	−	37.1294i	1.71145	−	1.19462i
$967$	11.6905	−	20.2486i	0.375941	−	0.651150i	−0.614526	−	0.788897i	$-0.710653\pi$
$967$	11.6905	−	20.2486i	0.375941	−	0.651150i	0.990467	+	0.137747i	$0.0439860\pi$
$968$	−3.03511	−	5.88729i	−0.0975522	−	0.189225i
$969$	−5.54886	+	12.5053i	−0.178255	+	0.401729i
$970$	15.6841	−	22.0252i	0.503586	−	0.707188i
$971$	−49.4889	−	14.5313i	−1.58817	−	0.466330i	−0.635950	−	0.771730i	$-0.719392\pi$
$971$	−49.4889	−	14.5313i	−1.58817	−	0.466330i	−0.952224	+	0.305400i	$0.901210\pi$
$972$	−29.0847	+	41.3931i	−0.932894	+	1.32768i
$973$	4.91368	+	4.25773i	0.157525	+	0.136496i
$974$	−20.7780	−	51.9009i	−0.665770	−	1.66301i
$975$	−2.48092	+	8.79904i	−0.0794532	+	0.281795i
$976$	−0.0882959	−	0.458123i	−0.00282628	−	0.0146641i
$977$	2.82620	+	59.3292i	0.0904180	+	1.89811i	0.356709	+	0.934216i	$0.383899\pi$
$977$	2.82620	+	59.3292i	0.0904180	+	1.89811i	−0.266291	+	0.963893i	$0.585798\pi$
$978$	−29.5628	−	49.9528i	−0.945313	−	1.59731i
$979$	−7.53503	+	21.7710i	−0.240820	+	0.695805i
$980$	11.8640	−	3.48359i	0.378982	−	0.111279i
$981$	−14.0427	−	44.2711i	−0.448348	−	1.41347i
$982$	−22.5375	+	26.0097i	−0.719201	+	0.830002i
$983$	16.0347	−	1.53113i	0.511429	−	0.0488355i	0.163848	−	0.986486i	$-0.447609\pi$
$983$	16.0347	−	1.53113i	0.511429	−	0.0488355i	0.347581	+	0.937650i	$0.387003\pi$
$984$	1.98285	+	9.72280i	0.0632109	+	0.309952i
$985$	0.140694	−	1.47341i	0.00448287	−	0.0469468i
$986$	63.3536	+	25.3630i	2.01759	+	0.807721i
$987$	−5.47981	+	64.7569i	−0.174424	+	2.06124i
$988$	5.69960	−	3.29067i	0.181329	−	0.104690i
$989$	2.85620	+	7.57402i	0.0908218	+	0.240840i
$990$	−17.0765	−	11.6136i	−0.542727	−	0.369104i
$991$	16.2185	+	10.4230i	0.515197	+	0.331097i	0.772269	−	0.635295i	$-0.219122\pi$
$991$	16.2185	+	10.4230i	0.515197	+	0.331097i	−0.257072	+	0.966392i	$0.582758\pi$
$992$	−5.21105	−	6.62639i	−0.165451	−	0.210388i
$993$	−10.3724	−	25.1207i	−0.329158	−	0.797182i
$994$	−66.9958	−	70.2632i	−2.12498	−	2.22861i
$995$	−13.0054	+	9.26110i	−0.412299	+	0.293596i
$996$	−10.3912	−	34.0280i	−0.329259	−	1.07822i
$997$	10.6261	−	4.25405i	0.336532	−	0.134727i	−0.197241	−	0.980355i	$-0.563198\pi$
$997$	10.6261	−	4.25405i	0.336532	−	0.134727i	0.533773	+	0.845628i	$0.320774\pi$
$998$	26.3419	+	89.7122i	0.833837	+	2.83979i
$999$	38.1485	−	26.2974i	1.20696	−	0.832012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.4	yes	440
3.2	odd	2		621.2.s.a.44.19		440
9.2	odd	6	inner	207.2.o.a.182.4	yes	440
9.7	even	3		621.2.s.a.251.19		440
23.11	odd	22	inner	207.2.o.a.149.4	yes	440
69.11	even	22		621.2.s.a.287.19		440
207.11	even	66	inner	207.2.o.a.11.4	✓	440
207.34	odd	66		621.2.s.a.494.19		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.4	✓	440	207.11	even	66	inner
207.2.o.a.113.4	yes	440	1.1	even	1	trivial
207.2.o.a.149.4	yes	440	23.11	odd	22	inner
207.2.o.a.182.4	yes	440	9.2	odd	6	inner
621.2.s.a.44.19		440	3.2	odd	2
621.2.s.a.251.19		440	9.7	even	3
621.2.s.a.287.19		440	69.11	even	22
621.2.s.a.494.19		440	207.34	odd	66

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.28767 - 0.108975i) q^{2} +(1.58319 + 0.702495i) q^{3} +(3.23063 + 0.308488i) q^{4} +(-0.595980 + 0.568266i) q^{5} +(-3.54528 - 1.77961i) q^{6} +(-0.645310 + 3.34819i) q^{7} +(-2.82310 - 0.405901i) q^{8} +(2.01300 + 2.22437i) q^{9} +(1.42534 - 1.23506i) q^{10} +(-3.24423 - 1.67252i) q^{11} +(4.89800 + 2.75790i) q^{12} +(1.19920 - 0.231127i) q^{13} +(1.84113 - 7.58924i) q^{14} +(-1.34276 + 0.481002i) q^{15} +(0.0407460 + 0.00785315i) q^{16} +(-1.97606 + 4.32697i) q^{17} +(-4.36269 - 5.30800i) q^{18} +(1.51046 - 0.689803i) q^{19} +(-2.10070 + 1.65201i) q^{20} +(-3.37373 + 4.84750i) q^{21} +(7.23948 + 4.17971i) q^{22} +(4.57336 + 1.44374i) q^{23} +(-4.18437 - 2.62583i) q^{24} +(-0.205643 + 4.31699i) q^{25} +(-2.76857 + 0.398061i) q^{26} +(1.62436 + 4.93573i) q^{27} +(-3.11764 + 10.6177i) q^{28} +(0.595424 + 6.23556i) q^{29} +(3.12420 - 0.954048i) q^{30} +(-1.18134 - 0.929013i) q^{31} +(5.45112 + 1.32243i) q^{32} +(-3.96131 - 4.92697i) q^{33} +(4.99212 - 9.68335i) q^{34} +(-1.51807 - 2.36216i) q^{35} +(5.81708 + 7.80711i) q^{36} +(-2.51221 - 8.55582i) q^{37} +(-3.53060 + 1.41344i) q^{38} +(2.06094 + 0.476515i) q^{39} +(1.91317 - 1.36236i) q^{40} +(-1.38614 - 1.45375i) q^{41} +(8.24626 - 10.7218i) q^{42} +(1.04336 + 1.32674i) q^{43} +(-9.96496 - 6.40409i) q^{44} +(-2.46374 - 0.181760i) q^{45} +(-10.3050 - 3.80119i) q^{46} +(9.52963 - 5.50193i) q^{47} +(0.0589920 + 0.0410569i) q^{48} +(-4.29535 - 1.71960i) q^{49} +(0.940890 - 9.85345i) q^{50} +(-6.16816 + 5.46226i) q^{51} +(3.94548 - 0.376748i) q^{52} +(4.16607 - 4.80790i) q^{53} +(-3.17814 - 11.4684i) q^{54} +(2.88393 - 0.846798i) q^{55} +(3.18081 - 9.19035i) q^{56} +(2.87593 - 0.0310027i) q^{57} +(-0.682614 - 14.3298i) q^{58} +(0.504712 + 2.61869i) q^{59} +(-4.48633 + 1.13972i) q^{60} +(-4.17874 - 10.4380i) q^{61} +(2.60127 + 2.25402i) q^{62} +(-8.74662 + 5.30450i) q^{63} +(-12.4059 - 3.64270i) q^{64} +(-0.583360 + 0.819214i) q^{65} +(8.52526 + 11.7030i) q^{66} +(-3.30135 - 6.40373i) q^{67} +(-7.71875 + 13.3693i) q^{68} +(6.22629 + 5.49848i) q^{69} +(3.21543 + 5.56929i) q^{70} +(6.72112 - 10.4583i) q^{71} +(-4.78004 - 7.09671i) q^{72} +(5.56880 + 12.1940i) q^{73} +(4.81475 + 19.8467i) q^{74} +(-3.35823 + 6.69016i) q^{75} +(5.09253 - 1.76254i) q^{76} +(7.69343 - 9.78299i) q^{77} +(-4.66282 - 1.31470i) q^{78} +(8.56154 + 2.96318i) q^{79} +(-0.0287465 + 0.0184742i) q^{80} +(-0.895644 + 8.95532i) q^{81} +(3.01262 + 3.47675i) q^{82} +(-4.58096 - 4.36793i) q^{83} +(-12.3947 + 14.6197i) q^{84} +(-1.28118 - 3.70172i) q^{85} +(-2.24229 - 3.14886i) q^{86} +(-3.43778 + 10.2904i) q^{87} +(8.47992 + 6.03852i) q^{88} +(-0.898270 - 6.24760i) q^{89} +(5.61643 + 0.684295i) q^{90} +4.16431i q^{91} +(14.3295 + 6.07502i) q^{92} +(-1.21766 - 2.30069i) q^{93} +(-22.4003 + 11.5481i) q^{94} +(-0.508211 + 1.26945i) q^{95} +(7.70117 + 5.92304i) q^{96} +(13.9326 - 3.38001i) q^{97} +(9.63898 + 4.40197i) q^{98} +(-2.81034 - 10.5831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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