LMFDB - Embedded newform 175.2.x.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	175.33
Dual form			175.2.x.a.122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22811 + 1.44695i) q^{2} +(0.206163 - 0.0791387i) q^{3} +(2.05732 - 4.62083i) q^{4} +(-0.963847 - 2.01767i) q^{5} +(-0.344844 + 0.474637i) q^{6} +(-0.932359 + 2.47603i) q^{7} +(1.27096 + 8.02453i) q^{8} +(-2.19319 + 1.97476i) q^{9} +O(q^{10})$	\(q+(-2.22811 + 1.44695i) q^{2} +(0.206163 - 0.0791387i) q^{3} +(2.05732 - 4.62083i) q^{4} +(-0.963847 - 2.01767i) q^{5} +(-0.344844 + 0.474637i) q^{6} +(-0.932359 + 2.47603i) q^{7} +(1.27096 + 8.02453i) q^{8} +(-2.19319 + 1.97476i) q^{9} +(5.06702 + 3.10095i) q^{10} +(-2.00112 + 2.22247i) q^{11} +(0.0584587 - 1.11546i) q^{12} +(2.23475 + 4.38594i) q^{13} +(-1.50529 - 6.86593i) q^{14} +(-0.358386 - 0.339692i) q^{15} +(-7.67383 - 8.52265i) q^{16} +(-3.73417 + 3.02387i) q^{17} +(2.02929 - 7.57342i) q^{18} +(3.29351 - 1.46636i) q^{19} +(-11.3063 + 0.302763i) q^{20} +(0.00373135 + 0.584251i) q^{21} +(1.24291 - 7.84742i) q^{22} +(-1.77983 - 2.74069i) q^{23} +(0.897076 + 1.55378i) q^{24} +(-3.14200 + 3.88945i) q^{25} +(-11.3255 - 6.53878i) q^{26} +(-0.596641 + 1.17097i) q^{27} +(9.52312 + 9.40225i) q^{28} +(2.87272 + 3.95395i) q^{29} +(1.29004 + 0.238305i) q^{30} +(-1.60762 - 0.168967i) q^{31} +(13.7345 + 3.68016i) q^{32} +(-0.236674 + 0.616558i) q^{33} +(3.94475 - 12.1407i) q^{34} +(5.89446 - 0.505317i) q^{35} +(4.61291 + 14.1971i) q^{36} +(1.34111 + 0.0702847i) q^{37} +(-5.21653 + 8.03276i) q^{38} +(0.807821 + 0.727365i) q^{39} +(14.9659 - 10.2988i) q^{40} +(4.99103 + 1.62168i) q^{41} +(-0.853696 - 1.29638i) q^{42} +(-8.43891 - 8.43891i) q^{43} +(6.15269 + 13.8192i) q^{44} +(6.09832 + 2.52178i) q^{45} +(7.93128 + 3.53123i) q^{46} +(-2.10386 + 2.59805i) q^{47} +(-2.25653 - 1.14976i) q^{48} +(-5.26142 - 4.61709i) q^{49} +(1.37287 - 13.2124i) q^{50} +(-0.530544 + 0.918929i) q^{51} +(24.8643 - 1.30308i) q^{52} +(-1.53215 - 3.99138i) q^{53} +(-0.364960 - 3.47237i) q^{54} +(6.41299 + 1.89548i) q^{55} +(-21.0539 - 4.33481i) q^{56} +(0.562954 - 0.562954i) q^{57} +(-12.1219 - 4.65316i) q^{58} +(0.547410 - 0.116356i) q^{59} +(-2.30697 + 0.957180i) q^{60} +(-2.08141 + 9.79226i) q^{61} +(3.82643 - 1.94966i) q^{62} +(-2.84472 - 7.27159i) q^{63} +(-14.1129 + 4.58555i) q^{64} +(6.69544 - 8.73637i) q^{65} +(-0.364792 - 1.71621i) q^{66} +(5.88015 + 7.26138i) q^{67} +(6.29039 + 23.4761i) q^{68} +(-0.583829 - 0.424177i) q^{69} +(-12.4023 + 9.65489i) q^{70} +(-0.293741 + 0.213415i) q^{71} +(-18.6340 - 15.0895i) q^{72} +(-0.153215 - 2.92351i) q^{73} +(-3.08984 + 1.78392i) q^{74} +(-0.339959 + 1.05052i) q^{75} -18.2355i q^{76} +(-3.63713 - 7.02697i) q^{77} +(-2.85237 - 0.451771i) q^{78} +(-5.20577 + 0.547148i) q^{79} +(-9.79952 + 23.6978i) q^{80} +(0.895128 - 8.51657i) q^{81} +(-13.4670 + 3.60848i) q^{82} +(-0.898387 + 0.142291i) q^{83} +(2.70740 + 1.18475i) q^{84} +(9.70036 + 4.61979i) q^{85} +(31.0135 + 6.59212i) q^{86} +(0.905159 + 0.587817i) q^{87} +(-20.3776 - 13.2334i) q^{88} +(8.84258 + 1.87955i) q^{89} +(-17.2366 + 3.20517i) q^{90} +(-12.9433 + 1.44403i) q^{91} +(-16.3259 + 2.58577i) q^{92} +(-0.344803 + 0.0923897i) q^{93} +(0.928377 - 8.83292i) q^{94} +(-6.13308 - 5.23187i) q^{95} +(3.12280 - 0.328219i) q^{96} +(7.15230 + 1.13281i) q^{97} +(18.4037 + 2.67437i) q^{98} -8.82604i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−2.22811	+	1.44695i	−1.57551	+	1.02315i	−0.600876	+	0.799343i	$0.705181\pi$
$2$	−2.22811	+	1.44695i	−1.57551	+	1.02315i	−0.974634	+	0.223805i	$0.928152\pi$
$3$	0.206163	−	0.0791387i	0.119028	−	0.0456907i	−0.298125	−	0.954527i	$-0.596361\pi$
$3$	0.206163	−	0.0791387i	0.119028	−	0.0456907i	0.417153	+	0.908836i	$0.363028\pi$
$4$	2.05732	−	4.62083i	1.02866	−	2.31041i
$5$	−0.963847	−	2.01767i	−0.431045	−	0.902330i
$5$	−0.963847	−	2.01767i	−0.431045	−	0.902330i
$6$	−0.344844	+	0.474637i	−0.140782	+	0.193770i
$7$	−0.932359	+	2.47603i	−0.352398	+	0.935850i
$7$	−0.932359	+	2.47603i	−0.352398	+	0.935850i
$8$	1.27096	+	8.02453i	0.449352	+	2.83710i
$9$	−2.19319	+	1.97476i	−0.731065	+	0.658254i
$10$	5.06702	+	3.10095i	1.60233	+	0.980607i
$11$	−2.00112	+	2.22247i	−0.603361	+	0.670100i	−0.965010	−	0.262214i	$-0.915547\pi$
$11$	−2.00112	+	2.22247i	−0.603361	+	0.670100i	0.361649	+	0.932314i	$0.382214\pi$
$12$	0.0584587	−	1.11546i	0.0168756	−	0.322005i
$13$	2.23475	+	4.38594i	0.619808	+	1.21644i	0.961026	+	0.276458i	$0.0891605\pi$
$13$	2.23475	+	4.38594i	0.619808	+	1.21644i	−0.341218	+	0.939984i	$0.610839\pi$
$14$	−1.50529	−	6.86593i	−0.402306	−	1.83500i
$15$	−0.358386	−	0.339692i	−0.0925348	−	0.0877082i
$16$	−7.67383	−	8.52265i	−1.91846	−	2.13066i
$17$	−3.73417	+	3.02387i	−0.905670	+	0.733397i	−0.964280	−	0.264884i	$-0.914666\pi$
$17$	−3.73417	+	3.02387i	−0.905670	+	0.733397i	0.0586101	+	0.998281i	$0.481333\pi$
$18$	2.02929	−	7.57342i	0.478309	−	1.78507i
$19$	3.29351	−	1.46636i	0.755583	−	0.336407i	0.00746418	−	0.999972i	$-0.497624\pi$
$19$	3.29351	−	1.46636i	0.755583	−	0.336407i	0.748119	+	0.663565i	$0.230957\pi$
$20$	−11.3063	+	0.302763i	−2.52816	+	0.0676999i
$21$	0.00373135	+	0.584251i	0.000814247	+	0.127494i
$22$	1.24291	−	7.84742i	0.264989	−	1.67308i
$23$	−1.77983	−	2.74069i	−0.371119	−	0.571473i	0.602934	−	0.797791i	$-0.293998\pi$
$23$	−1.77983	−	2.74069i	−0.371119	−	0.571473i	−0.974054	+	0.226317i	$0.927331\pi$
$24$	0.897076	+	1.55378i	0.183115	+	0.317164i
$25$	−3.14200	+	3.88945i	−0.628400	+	0.777891i
$26$	−11.3255	−	6.53878i	−2.22111	−	1.28236i
$27$	−0.596641	+	1.17097i	−0.114824	+	0.225354i
$28$	9.52312	+	9.40225i	1.79970	+	1.77686i
$29$	2.87272	+	3.95395i	0.533450	+	0.734231i	0.987651	−	0.156668i	$-0.0500753\pi$
$29$	2.87272	+	3.95395i	0.533450	+	0.734231i	−0.454201	+	0.890899i	$0.650075\pi$
$30$	1.29004	+	0.238305i	0.235528	+	0.0435083i
$31$	−1.60762	−	0.168967i	−0.288736	−	0.0303474i	−0.0409469	−	0.999161i	$-0.513037\pi$
$31$	−1.60762	−	0.168967i	−0.288736	−	0.0303474i	−0.247789	+	0.968814i	$0.579704\pi$
$32$	13.7345	+	3.68016i	2.42794	+	0.650566i
$33$	−0.236674	+	0.616558i	−0.0411997	+	0.107329i
$34$	3.94475	−	12.1407i	0.676518	−	2.08211i
$35$	5.89446	−	0.505317i	0.996346	−	0.0854141i
$36$	4.61291	+	14.1971i	0.768819	+	2.36618i
$37$	1.34111	+	0.0702847i	0.220477	+	0.0115547i	0.162255	−	0.986749i	$-0.448123\pi$
$37$	1.34111	+	0.0702847i	0.220477	+	0.0115547i	0.0582226	+	0.998304i	$0.481457\pi$
$38$	−5.21653	+	8.03276i	−0.846234	+	1.30309i
$39$	0.807821	+	0.727365i	0.129355	+	0.116472i
$40$	14.9659	−	10.2988i	2.36631	−	1.62838i
$41$	4.99103	+	1.62168i	0.779468	+	0.253264i	0.671613	−	0.740902i	$-0.265602\pi$
$41$	4.99103	+	1.62168i	0.779468	+	0.253264i	0.107855	+	0.994167i	$0.465602\pi$
$42$	−0.853696	−	1.29638i	−0.131728	−	0.200035i
$43$	−8.43891	−	8.43891i	−1.28692	−	1.28692i	−0.936647	−	0.350276i	$-0.886088\pi$
$43$	−8.43891	−	8.43891i	−1.28692	−	1.28692i	−0.350276	−	0.936647i	$-0.613912\pi$
$44$	6.15269	+	13.8192i	0.927553	+	2.08332i
$45$	6.09832	+	2.52178i	0.909084	+	0.375925i
$46$	7.93128	+	3.53123i	1.16940	+	0.520652i
$47$	−2.10386	+	2.59805i	−0.306880	+	0.378965i	−0.907132	−	0.420846i	$-0.861733\pi$
$47$	−2.10386	+	2.59805i	−0.306880	+	0.378965i	0.600253	+	0.799810i	$0.295067\pi$
$48$	−2.25653	−	1.14976i	−0.325703	−	0.165954i
$49$	−5.26142	−	4.61709i	−0.751631	−	0.659584i
$50$	1.37287	−	13.2124i	0.194153	−	1.86852i
$51$	−0.530544	+	0.918929i	−0.0742910	+	0.128676i
$52$	24.8643	−	1.30308i	3.44805	−	0.180705i
$53$	−1.53215	−	3.99138i	−0.210456	−	0.548258i	0.787199	−	0.616699i	$-0.211531\pi$
$53$	−1.53215	−	3.99138i	−0.210456	−	0.548258i	−0.997655	+	0.0684418i	$0.978197\pi$
$54$	−0.364960	−	3.47237i	−0.0496648	−	0.472529i
$55$	6.41299	+	1.89548i	0.864727	+	0.255587i
$56$	−21.0539	−	4.33481i	−2.81345	−	0.579263i
$57$	0.562954	−	0.562954i	0.0745651	−	0.0745651i
$58$	−12.1219	−	4.65316i	−1.59168	−	0.610990i
$59$	0.547410	−	0.116356i	0.0712667	−	0.0151482i	−0.172140	−	0.985072i	$-0.555068\pi$
$59$	0.547410	−	0.116356i	0.0712667	−	0.0151482i	0.243407	+	0.969924i	$0.421735\pi$
$60$	−2.30697	+	0.957180i	−0.297829	+	0.123571i
$61$	−2.08141	+	9.79226i	−0.266497	+	1.25377i	0.617609	+	0.786485i	$0.288101\pi$
$61$	−2.08141	+	9.79226i	−0.266497	+	1.25377i	−0.884106	+	0.467286i	$0.845232\pi$
$62$	3.82643	−	1.94966i	0.485957	−	0.247607i
$63$	−2.84472	−	7.27159i	−0.358401	−	0.916134i
$64$	−14.1129	+	4.58555i	−1.76411	+	0.573194i
$65$	6.69544	−	8.73637i	0.830467	−	1.08361i
$66$	−0.364792	−	1.71621i	−0.0449028	−	0.211251i
$67$	5.88015	+	7.26138i	0.718375	+	0.887119i	0.997318	−	0.0731888i	$-0.0233176\pi$
$67$	5.88015	+	7.26138i	0.718375	+	0.887119i	−0.278944	+	0.960308i	$0.589984\pi$
$68$	6.29039	+	23.4761i	0.762822	+	2.84689i
$69$	−0.583829	−	0.424177i	−0.0702848	−	0.0510649i
$70$	−12.4023	+	9.65489i	−1.48236	+	1.15398i
$71$	−0.293741	+	0.213415i	−0.0348607	+	0.0253278i	−0.605079	−	0.796165i	$-0.706859\pi$
$71$	−0.293741	+	0.213415i	−0.0348607	+	0.0253278i	0.570218	+	0.821493i	$0.306859\pi$
$72$	−18.6340	−	15.0895i	−2.19604	−	1.77832i
$73$	−0.153215	−	2.92351i	−0.0179324	−	0.342171i	−0.992831	−	0.119523i	$-0.961863\pi$
$73$	−0.153215	−	2.92351i	−0.0179324	−	0.342171i	0.974899	−	0.222648i	$-0.0714700\pi$
$74$	−3.08984	+	1.78392i	−0.359186	+	0.207376i
$75$	−0.339959	+	1.05052i	−0.0392550	+	0.121303i
$76$		−	18.2355i		−	2.09176i
$77$	−3.63713	−	7.02697i	−0.414490	−	0.800797i
$78$	−2.85237	−	0.451771i	−0.322968	−	0.0511530i
$79$	−5.20577	+	0.547148i	−0.585694	+	0.0615590i	−0.392741	−	0.919649i	$-0.628473\pi$
$79$	−5.20577	+	0.547148i	−0.585694	+	0.0615590i	−0.192953	+	0.981208i	$0.561807\pi$
$80$	−9.79952	+	23.6978i	−1.09562	+	2.64950i
$81$	0.895128	−	8.51657i	0.0994586	−	0.946286i
$82$	−13.4670	+	3.60848i	−1.48719	+	0.398490i
$83$	−0.898387	+	0.142291i	−0.0986108	+	0.0156184i	−0.205545	−	0.978648i	$-0.565897\pi$
$83$	−0.898387	+	0.142291i	−0.0986108	+	0.0156184i	0.106934	+	0.994266i	$0.465897\pi$
$84$	2.70740	+	1.18475i	0.295402	+	0.129267i
$85$	9.70036	+	4.61979i	1.05215	+	0.501086i
$86$	31.0135	+	6.59212i	3.34427	+	0.710847i
$87$	0.905159	+	0.587817i	0.0970432	+	0.0630206i
$88$	−20.3776	−	13.2334i	−2.17226	−	1.41068i
$89$	8.84258	+	1.87955i	0.937312	+	0.199232i	0.651150	−	0.758949i	$-0.274287\pi$
$89$	8.84258	+	1.87955i	0.937312	+	0.199232i	0.286162	+	0.958181i	$0.407620\pi$
$90$	−17.2366	+	3.20517i	−1.81690	+	0.337855i
$91$	−12.9433	+	1.44403i	−1.35683	+	0.151375i
$92$	−16.3259	+	2.58577i	−1.70210	+	0.269585i
$93$	−0.344803	+	0.0923897i	−0.0357544	+	0.00958037i
$94$	0.928377	−	8.83292i	0.0957548	−	0.911046i
$95$	−6.13308	−	5.23187i	−0.629241	−	0.536778i
$96$	3.12280	−	0.328219i	0.318719	−	0.0334987i
$97$	7.15230	+	1.13281i	0.726206	+	0.115020i	0.508583	−	0.861013i	$-0.330170\pi$
$97$	7.15230	+	1.13281i	0.726206	+	0.115020i	0.217624	+	0.976033i	$0.430170\pi$
$98$	18.4037	+	2.67437i	1.85905	+	0.270152i
$99$		−	8.82604i		−	0.887051i
$100$	11.5084	+	22.5205i	1.15084	+	2.25205i
$101$	2.36935	−	1.36795i	0.235759	−	0.136116i	−0.377467	−	0.926023i	$-0.623205\pi$
$101$	2.36935	−	1.36795i	0.235759	−	0.136116i	0.613226	+	0.789907i	$0.289871\pi$
$102$	−0.147535	−	2.81514i	−0.0146082	−	0.278741i
$103$	0.518795	+	0.420112i	0.0511184	+	0.0413949i	0.654539	−	0.756028i	$-0.272863\pi$
$103$	0.518795	+	0.420112i	0.0511184	+	0.0413949i	−0.603421	+	0.797423i	$0.706196\pi$
$104$	−32.3548	+	23.5072i	−3.17265	+	2.30507i
$105$	1.17523	−	0.570657i	0.114691	−	0.0556905i
$106$	9.18910	+	6.67627i	0.892524	+	0.648457i
$107$	−0.699970	−	2.61232i	−0.0676686	−	0.252543i	0.923802	−	0.382869i	$-0.125064\pi$
$107$	−0.699970	−	2.61232i	−0.0676686	−	0.252543i	−0.991471	+	0.130327i	$0.958397\pi$
$108$	4.18338	+	5.16605i	0.402546	+	0.497103i
$109$	−0.966861	−	4.54872i	−0.0926085	−	0.435689i	−0.999885	−	0.0151544i	$-0.995176\pi$
$109$	−0.966861	−	4.54872i	−0.0926085	−	0.435689i	0.907277	−	0.420534i	$-0.138157\pi$
$110$	−17.0315	+	5.05593i	−1.62389	+	0.482064i
$111$	0.282050	−	0.0916436i	0.0267710	−	0.00869843i
$112$	28.2571	−	11.0544i	2.67004	−	1.04455i
$113$	15.5844	−	7.94063i	1.46605	−	0.746991i	0.474941	−	0.880018i	$-0.342470\pi$
$113$	15.5844	−	7.94063i	1.46605	−	0.746991i	0.991112	+	0.133026i	$0.0424695\pi$
$114$	−0.439756	+	2.06889i	−0.0411869	+	0.193769i
$115$	−3.81433	+	6.23271i	−0.355689	+	0.581203i
$116$	24.1806	−	5.13975i	2.24512	−	0.477214i
$117$	−13.5624	−	5.20613i	−1.25385	−	0.481307i
$118$	−1.05133	+	1.05133i	−0.0967825	+	0.0967825i
$119$	−4.00560	−	12.0653i	−0.367193	−	1.10602i
$120$	2.27038	−	3.30761i	0.207256	−	0.301942i
$121$	0.214925	+	2.04488i	0.0195387	+	0.185898i
$122$	−9.53131	−	24.8299i	−0.862924	−	2.24799i
$123$	1.15730	−	0.0606518i	0.104351	−	0.00546879i
$124$	−4.08816	+	7.08089i	−0.367127	+	0.635883i
$125$	10.8760	+	2.59069i	0.972783	+	0.231718i
$126$	16.8600	+	12.0857i	1.50200	+	1.07668i
$127$	−4.64631	−	2.36741i	−0.412293	−	0.210074i	0.235526	−	0.971868i	$-0.424319\pi$
$127$	−4.64631	−	2.36741i	−0.412293	−	0.210074i	−0.647819	+	0.761794i	$0.724319\pi$
$128$	6.91329	−	8.53721i	0.611055	−	0.754589i
$129$	−2.40764	−	1.07195i	−0.211981	−	0.0943799i
$130$	−2.27707	+	29.1535i	−0.199712	+	2.55693i
$131$	1.53042	+	3.43738i	0.133714	+	0.300325i	0.967976	−	0.251042i	$-0.0807731\pi$
$131$	1.53042	+	3.43738i	0.133714	+	0.300325i	−0.834263	+	0.551367i	$0.814106\pi$
$132$	2.36209	+	2.36209i	0.205594	+	0.205594i
$133$	0.560027	+	9.52199i	0.0485605	+	0.825662i
$134$	−23.6085	−	7.67085i	−2.03946	−	0.662661i
$135$	2.93771	+	0.0751863i	0.252838	+	0.00647100i
$136$	−29.0112	−	26.1218i	−2.48769	−	2.23992i
$137$	−2.17586	+	3.35053i	−0.185896	+	0.286255i	−0.919315	−	0.393522i	$-0.871257\pi$
$137$	−2.17586	+	3.35053i	−0.185896	+	0.286255i	0.733419	+	0.679777i	$0.237923\pi$
$138$	1.91460	+	0.100340i	0.162981	+	0.00854148i
$139$	2.53686	+	7.80766i	0.215174	+	0.662237i	0.999141	+	0.0414349i	$0.0131929\pi$
$139$	2.53686	+	7.80766i	0.215174	+	0.662237i	−0.783967	+	0.620802i	$0.786807\pi$
$140$	9.79183	−	28.2769i	0.827561	−	2.38983i
$141$	−0.228132	+	0.702119i	−0.0192122	+	0.0591291i
$142$	0.345685	−	0.900541i	0.0290093	−	0.0755717i
$143$	−14.2196	−	3.81014i	−1.18911	−	0.318620i
$144$	33.6604	+	3.53785i	2.80503	+	0.294821i
$145$	5.20892	−	9.60720i	0.432578	−	0.797835i
$146$	4.57155	+	6.29220i	0.378344	+	0.520746i
$147$	−1.45010	−	0.535493i	−0.119602	−	0.0441667i
$148$	3.08387	−	6.05244i	0.253493	−	0.497508i
$149$	18.8977	+	10.9106i	1.54816	+	0.893830i	0.998282	+	0.0585846i	$0.0186588\pi$
$149$	18.8977	+	10.9106i	1.54816	+	0.893830i	0.549877	+	0.835246i	$0.314675\pi$
$150$	−0.762579	−	2.83256i	−0.0622643	−	0.231278i
$151$	1.20290	+	2.08349i	0.0978908	+	0.169552i	0.910811	−	0.412823i	$-0.135457\pi$
$151$	1.20290	+	2.08349i	0.0978908	+	0.169552i	−0.812921	+	0.582375i	$0.802124\pi$
$152$	15.9528	+	24.5652i	1.29394	+	1.99250i
$153$	2.21834	−	14.0060i	0.179342	−	1.13232i
$154$	18.2716	+	10.3941i	1.47237	+	0.837580i
$155$	1.20858	+	3.40650i	0.0970751	+	0.273617i
$156$	5.02298	−	2.23637i	0.402160	−	0.179053i
$157$	−5.67894	+	21.1941i	−0.453229	+	1.69147i	0.240016	+	0.970769i	$0.422847\pi$
$157$	−5.67894	+	21.1941i	−0.453229	+	1.69147i	−0.693244	+	0.720703i	$0.743819\pi$
$158$	10.8073	−	8.75158i	0.859783	−	0.696239i
$159$	−0.631744	−	0.701623i	−0.0501006	−	0.0556423i
$160$	−5.81264	−	31.2589i	−0.459529	−	2.47123i
$161$	8.44546	−	1.85159i	0.665595	−	0.145926i
$162$	10.3286	+	20.2710i	0.811492	+	1.59264i
$163$	0.464753	−	8.86802i	0.0364023	−	0.694597i	−0.918092	−	0.396368i	$-0.870271\pi$
$163$	0.464753	−	8.86802i	0.0364023	−	0.694597i	0.954494	−	0.298230i	$-0.0963961\pi$
$164$	17.7617	−	19.7263i	1.38695	−	1.54037i
$165$	1.47213	−	0.116736i	0.114605	−	0.00908789i
$166$	1.79582	−	1.61696i	0.139382	−	0.125500i
$167$	1.64313	+	10.3743i	0.127149	+	0.802786i	0.966022	+	0.258460i	$0.0832149\pi$
$167$	1.64313	+	10.3743i	0.127149	+	0.802786i	−0.838873	+	0.544327i	$0.816785\pi$
$168$	−4.68360	+	0.772502i	−0.361347	+	0.0595999i
$169$	−6.60118	+	9.08574i	−0.507783	+	0.698903i
$170$	−28.2980	+	3.74255i	−2.17036	+	0.287041i
$171$	−4.32759	+	9.71992i	−0.330939	+	0.743301i
$172$	−56.3563	+	21.6332i	−4.29713	+	1.64951i
$173$	−15.1058	+	9.80981i	−1.14847	+	0.745826i	−0.971183	−	0.238333i	$-0.923399\pi$
$173$	−15.1058	+	9.80981i	−1.14847	+	0.745826i	−0.177288	+	0.984159i	$0.556732\pi$
$174$	−2.86733			−0.217372
$175$	−6.70092	−	11.4060i	−0.506542	−	0.862215i
$176$	34.2976			2.58528
$177$	0.103648	−	0.0673095i	0.00779063	−	0.00505929i
$178$	−22.4218	+	8.60693i	−1.68059	+	0.645117i
$179$	−2.64040	+	5.93043i	−0.197353	+	0.443261i	−0.984930	−	0.172955i	$-0.944668\pi$
$179$	−2.64040	+	5.93043i	−0.197353	+	0.443261i	0.787577	+	0.616216i	$0.211335\pi$
$180$	24.1989	−	22.9912i	1.80368	−	1.71366i
$181$	−10.3669	+	14.2688i	−0.770563	+	1.06059i	0.225698	+	0.974197i	$0.427534\pi$
$181$	−10.3669	+	14.2688i	−0.770563	+	1.06059i	−0.996261	+	0.0863916i	$0.972466\pi$
$182$	26.7496	−	21.9457i	1.98281	−	1.62673i
$183$	0.345836	+	2.18352i	0.0255650	+	0.161411i
$184$	19.7307	−	17.7656i	1.45456	−	1.30969i
$185$	−1.15081	−	2.77367i	−0.0846096	−	0.203924i
$186$	0.634575	−	0.704767i	0.0465293	−	0.0516760i
$187$	0.752064	−	14.3502i	0.0549963	−	1.04939i
$188$	7.67682	+	15.0666i	0.559890	+	1.09885i
$189$	−2.34308	−	2.56907i	−0.170434	−	0.186872i
$190$	21.2354	+	2.78291i	1.54058	+	0.201893i
$191$	−8.10613	−	9.00277i	−0.586539	−	0.651418i	0.374696	−	0.927148i	$-0.377747\pi$
$191$	−8.10613	−	9.00277i	−0.586539	−	0.651418i	−0.961235	+	0.275730i	$0.911080\pi$
$192$	−2.54666	+	2.06225i	−0.183790	+	0.148830i
$193$	2.22173	−	8.29161i	0.159924	−	0.596843i	−0.838710	−	0.544579i	$-0.816689\pi$
$193$	2.22173	−	8.29161i	0.159924	−	0.596843i	0.998633	−	0.0522644i	$-0.0166439\pi$
$194$	−17.5752	+	7.82499i	−1.26183	+	0.561802i
$195$	0.688969	−	2.33099i	0.0493381	−	0.166925i
$196$	−32.1592	+	14.8132i	−2.29709	+	1.05809i
$197$	0.621240	−	3.92235i	0.0442615	−	0.279456i	−0.955624	−	0.294589i	$-0.904817\pi$
$197$	0.621240	−	3.92235i	0.0442615	−	0.279456i	0.999885	+	0.0151331i	$0.00481720\pi$
$198$	12.7708	+	19.6654i	0.907584	+	1.39756i
$199$	−6.13171	−	10.6204i	−0.434666	−	0.752863i	0.562603	−	0.826727i	$-0.309800\pi$
$199$	−6.13171	−	10.6204i	−0.434666	−	0.752863i	−0.997268	+	0.0738644i	$0.976467\pi$
$200$	−35.2044	−	20.2697i	−2.48933	−	1.43329i
$201$	1.78693	+	1.03168i	0.126040	+	0.0727693i
$202$	−3.29982	+	6.47626i	−0.232174	+	0.455668i
$203$	−12.4685	+	3.42642i	−0.875117	+	0.240487i
$204$	3.15471	+	4.34209i	0.220874	+	0.304007i
$205$	−1.53856	−	11.6333i	−0.107458	−	0.812506i
$206$	−1.76381	−	0.185384i	−0.122891	−	0.0129163i
$207$	9.31571	+	2.49614i	0.647487	+	0.173494i
$208$	20.2308	−	52.7030i	1.40275	−	3.65429i
$209$	−3.33176	+	10.2541i	−0.230463	+	0.709291i
$210$	−1.79283	+	2.97199i	−0.123717	+	0.205086i
$211$	−6.78037	−	20.8678i	−0.466780	−	1.43660i	−0.856730	−	0.515765i	$-0.827508\pi$
$211$	−6.78037	−	20.8678i	−0.466780	−	1.43660i	0.389950	−	0.920836i	$-0.372492\pi$
$212$	−21.5956	−	1.13178i	−1.48319	−	0.0777307i
$213$	−0.0436692	+	0.0672447i	−0.00299217	+	0.00460753i
$214$	5.33951	+	4.80771i	0.365001	+	0.328649i
$215$	−8.89314	+	25.1608i	−0.606507	+	1.71595i
$216$	−10.1548	−	3.29950i	−0.690948	−	0.224503i
$217$	1.91724	−	3.82296i	0.130151	−	0.259520i
$218$	8.73604	+	8.73604i	0.591679	+	0.591679i
$219$	−0.262950	−	0.590595i	−0.0177685	−	0.0399087i
$220$	21.9523	−	25.7337i	1.48002	−	1.73496i
$221$	−21.6075	−	9.62027i	−1.45348	−	0.647130i
$222$	−0.495834	+	0.612304i	−0.0332782	+	0.0410952i
$223$	−1.26491	−	0.644506i	−0.0847049	−	0.0431593i	0.411125	−	0.911579i	$-0.365136\pi$
$223$	−1.26491	−	0.644506i	−0.0847049	−	0.0431593i	−0.495830	+	0.868420i	$0.665136\pi$
$224$	−21.9177	+	30.5758i	−1.46444	+	2.04293i
$225$	−0.789727	−	14.7350i	−0.0526484	−	0.982335i
$226$	−23.2339	+	40.2423i	−1.54550	+	2.67688i
$227$	28.3058	−	1.48345i	1.87872	−	0.0984598i	0.921601	−	0.388139i	$-0.126882\pi$
$227$	28.3058	−	1.48345i	1.87872	−	0.0984598i	0.957124	+	0.289679i	$0.0935487\pi$
$228$	−1.44313	−	3.75949i	−0.0955739	−	0.248979i
$229$	0.0633876	+	0.603092i	0.00418877	+	0.0398535i	0.996417	−	0.0845807i	$-0.0269551\pi$
$229$	0.0633876	+	0.603092i	0.00418877	+	0.0398535i	−0.992228	+	0.124434i	$0.960288\pi$
$230$	−0.519669	−	19.4063i	−0.0342660	−	1.27961i
$231$	−1.30595	−	1.16086i	−0.0859251	−	0.0763793i
$232$	−28.0775	+	28.0775i	−1.84338	+	1.84338i
$233$	−4.20111	−	1.61266i	−0.275224	−	0.105649i	0.216841	−	0.976207i	$-0.430425\pi$
$233$	−4.20111	−	1.61266i	−0.275224	−	0.105649i	−0.492065	+	0.870558i	$0.663758\pi$
$234$	37.7515	−	8.02434i	2.46790	−	0.524567i
$235$	7.26981	+	1.74078i	0.474230	+	0.113556i
$236$	0.588541	−	2.76887i	0.0383107	−	0.180238i
$237$	−1.02994	+	0.524779i	−0.0669016	+	0.0340881i
$238$	26.3827	+	21.0868i	1.71014	+	1.36685i
$239$	−12.4990	+	4.06118i	−0.808494	+	0.262696i	−0.683960	−	0.729520i	$-0.739744\pi$
$239$	−12.4990	+	4.06118i	−0.808494	+	0.262696i	−0.124534	+	0.992215i	$0.539744\pi$
$240$	−0.144888	+	5.66114i	−0.00935249	+	0.365425i
$241$	3.44513	+	16.2081i	0.221920	+	1.04405i	0.938161	+	0.346200i	$0.112528\pi$
$241$	3.44513	+	16.2081i	0.221920	+	1.04405i	−0.716241	+	0.697853i	$0.754139\pi$
$242$	−3.43771	−	4.24522i	−0.220984	−	0.272893i
$243$	−1.50988	−	5.63495i	−0.0968588	−	0.361482i
$244$	40.9662	+	29.7637i	2.62259	+	1.90542i
$245$	−4.24457	+	15.0660i	−0.271176	+	0.962530i
$246$	−2.49084	+	1.80970i	−0.158810	+	0.115382i
$247$	13.7916	+	11.1682i	0.877536	+	0.710615i
$248$	−0.687334	−	13.1151i	−0.0436457	−	0.832810i
$249$	−0.173954	+	0.100432i	−0.0110239	+	0.00636464i
$250$	−27.9816	+	9.96476i	−1.76971	+	0.630227i
$251$		−	21.3400i		−	1.34697i	−0.739200	−	0.673486i	$-0.764796\pi$
$251$		−	21.3400i		−	1.34697i	0.739200	−	0.673486i	$-0.235204\pi$
$252$	−39.4533	−	1.81508i	−2.48532	−	0.114339i
$253$	9.65275	+	1.52885i	0.606863	+	0.0961177i
$254$	13.7780	−	1.44813i	0.864508	−	0.0908635i
$255$	2.36546	+	0.184757i	0.148131	+	0.0115699i
$256$	0.0515804	−	0.490755i	0.00322378	−	0.0306722i
$257$	21.6223	−	5.79368i	1.34876	−	0.361400i	0.489085	−	0.872236i	$-0.337331\pi$
$257$	21.6223	−	5.79368i	1.34876	−	0.361400i	0.859678	+	0.510836i	$0.170664\pi$
$258$	6.91553	−	1.09531i	0.430542	−	0.0681912i
$259$	−1.42442	+	3.25510i	−0.0885094	+	0.202262i
$260$	−26.5945	−	48.9120i	−1.64932	−	3.03339i
$261$	−14.1085	−	2.99886i	−0.873297	−	0.185625i
$262$	−8.38366	−	5.44441i	−0.517944	−	0.336357i
$263$	20.5982	+	13.3766i	1.27014	+	0.824837i	0.990797	−	0.135355i	$-0.0432174\pi$
$263$	20.5982	+	13.3766i	1.27014	+	0.824837i	0.279341	+	0.960192i	$0.409884\pi$
$264$	−5.24839	−	1.11558i	−0.323016	−	0.0686592i
$265$	−6.57653	+	6.93844i	−0.403993	+	0.426225i
$266$	−15.0256	−	20.4057i	−0.921281	−	1.25115i
$267$	1.97176	−	0.312296i	0.120670	−	0.0191122i
$268$	45.6509	−	12.2321i	2.78857	−	0.747196i
$269$	−2.48896	+	23.6809i	−0.151755	+	1.44385i	0.608154	+	0.793819i	$0.291910\pi$
$269$	−2.48896	+	23.6809i	−0.151755	+	1.44385i	−0.759909	+	0.650029i	$0.774757\pi$
$270$	−6.65433	+	4.08320i	−0.404970	+	0.248496i
$271$	28.2620	−	2.97045i	1.71679	−	0.180442i	0.805610	−	0.592446i	$-0.201838\pi$
$271$	28.2620	−	2.97045i	1.71679	−	0.180442i	0.911182	+	0.412004i	$0.135171\pi$
$272$	54.4269	+	8.62037i	3.30011	+	0.522687i
$273$	−2.55415	+	1.32202i	−0.154584	+	0.0800123i
$274$		−	10.6137i		−	0.641196i
$275$	−2.35667	−	14.7663i	−0.142113	−	0.890439i
$276$	−3.16117	+	1.82510i	−0.190280	+	0.109858i
$277$	0.631417	+	12.0482i	0.0379382	+	0.723904i	0.949696	+	0.313175i	$0.101393\pi$
$277$	0.631417	+	12.0482i	0.0379382	+	0.723904i	−0.911757	+	0.410729i	$0.865274\pi$
$278$	−16.9497	−	13.7256i	−1.01657	−	0.823206i
$279$	3.85948	−	2.80408i	0.231061	−	0.167876i
$280$	11.5466	+	46.6580i	0.690038	+	2.78835i
$281$	5.98822	+	4.35069i	0.357227	+	0.259541i	0.751895	−	0.659283i	$-0.229140\pi$
$281$	5.98822	+	4.35069i	0.357227	+	0.259541i	−0.394668	+	0.918824i	$0.629140\pi$
$282$	−0.507628	−	1.89449i	−0.0302288	−	0.112815i
$283$	16.0965	+	19.8775i	0.956835	+	1.18159i	0.983309	+	0.181944i	$0.0582389\pi$
$283$	16.0965	+	19.8775i	0.956835	+	1.18159i	−0.0264736	+	0.999650i	$0.508428\pi$
$284$	0.381835	+	1.79639i	0.0226577	+	0.106596i
$285$	−1.67846	−	0.593255i	−0.0994233	−	0.0351414i
$286$	37.1959	−	12.0857i	2.19944	−	0.714642i
$287$	−8.66876	+	10.8459i	−0.511701	+	0.640215i
$288$	−37.3899	+	19.0511i	−2.20322	+	1.12260i
$289$	1.26574	−	5.95484i	0.0744553	−	0.350285i
$290$	2.29510	+	28.9429i	0.134773	+	1.69959i
$291$	1.56419	−	0.332479i	0.0916945	−	0.0194903i
$292$	−13.8242	−	5.30663i	−0.809003	−	0.310547i
$293$	1.98458	−	1.98458i	0.115941	−	0.115941i	−0.646756	−	0.762697i	$-0.723875\pi$
$293$	1.98458	−	1.98458i	0.115941	−	0.115941i	0.762697	+	0.646756i	$0.223875\pi$
$294$	4.00581	−	0.905087i	0.233624	−	0.0527858i
$295$	−0.762387	−	0.992345i	−0.0443879	−	0.0577765i
$296$	1.14050	+	10.8511i	0.0662901	+	0.630708i
$297$	−1.40850	−	3.66928i	−0.0817297	−	0.212913i
$298$	−57.8932	+	3.03405i	−3.35366	+	0.175758i
$299$	8.04305	−	13.9310i	0.465141	−	0.805649i
$300$	4.15485	+	3.73214i	0.239880	+	0.215475i
$301$	28.7631	−	13.0269i	1.65788	−	0.750857i
$302$	−5.69490	−	2.90170i	−0.327705	−	0.166974i
$303$	0.380216	−	0.469527i	0.0218428	−	0.0269736i
$304$	−37.7712	−	16.8168i	−2.16632	−	0.964510i
$305$	21.7637	−	5.23864i	1.24619	−	0.299964i
$306$	15.3233	+	34.4168i	0.875977	+	1.96748i
$307$	−17.0423	−	17.0423i	−0.972656	−	0.972656i	0.0269795	−	0.999636i	$-0.491411\pi$
$307$	−17.0423	−	17.0423i	−0.972656	−	0.972656i	−0.999636	+	0.0269795i	$0.991411\pi$
$308$	−39.9532	+	2.34981i	−2.27654	+	0.133893i
$309$	0.140204	+	0.0455549i	0.00797590	+	0.00259153i
$310$	−7.62187	−	5.84130i	−0.432893	−	0.331763i
$311$	−21.0651	−	18.9671i	−1.19449	−	1.07552i	−0.995426	−	0.0955378i	$-0.969543\pi$
$311$	−21.0651	−	18.9671i	−1.19449	−	1.07552i	−0.199065	−	0.979986i	$-0.563790\pi$
$312$	−4.81005	+	7.40683i	−0.272316	+	0.419329i
$313$	21.5100	+	1.12729i	1.21582	+	0.0637183i	0.649431	−	0.760421i	$-0.275007\pi$
$313$	21.5100	+	1.12729i	1.21582	+	0.0637183i	0.566387	+	0.824139i	$0.308341\pi$
$314$	−18.0135	−	55.4398i	−1.01656	−	3.12865i
$315$	−11.9298	+	12.7484i	−0.672169	+	0.718291i
$316$	−8.18167	+	25.1806i	−0.460255	+	1.41652i
$317$	0.0809595	−	0.210907i	0.00454714	−	0.0118457i	−0.931288	−	0.364284i	$-0.881314\pi$
$317$	0.0809595	−	0.210907i	0.00454714	−	0.0118457i	0.935835	+	0.352438i	$0.114647\pi$
$318$	2.42281	+	0.649189i	0.135864	+	0.0364047i
$319$	−14.5362	−	1.52782i	−0.813871	−	0.0855413i
$320$	22.8548	+	24.0554i	1.27762	+	1.34474i
$321$	−0.351044	−	0.483170i	−0.0195934	−	0.0269679i
$322$	−16.1382	+	16.3457i	−0.899348	+	0.910909i
$323$	−7.86443	+	15.4348i	−0.437589	+	0.858816i
$324$	−37.5120	−	21.6576i	−2.08400	−	1.20320i
$325$	−24.0805	−	5.08867i	−1.33575	−	0.282269i
$326$	11.7961	+	20.4314i	0.653323	+	1.13159i
$327$	−0.559311	−	0.861263i	−0.0309300	−	0.0476280i
$328$	−6.66985	+	42.1118i	−0.368281	+	2.32523i
$329$	−4.47129	−	7.63153i	−0.246510	−	0.420740i
$330$	−3.11115	+	2.39020i	−0.171263	+	0.131576i
$331$	−17.4658	+	7.77627i	−0.960007	+	0.427423i	−0.826070	−	0.563567i	$-0.809429\pi$
$331$	−17.4658	+	7.77627i	−0.960007	+	0.427423i	−0.133937	+	0.990990i	$0.542762\pi$
$332$	−1.19077	+	4.44403i	−0.0653522	+	0.243898i
$333$	−3.08011	+	2.49423i	−0.168789	+	0.136683i
$334$	−18.6721	−	20.7375i	−1.02169	−	1.13471i
$335$	8.98352	−	18.8631i	0.490822	−	1.03060i
$336$	4.95074	−	4.51525i	0.270085	−	0.246327i
$337$	−0.693845	−	1.36175i	−0.0377961	−	0.0741791i	0.871336	−	0.490687i	$-0.163254\pi$
$337$	−0.693845	−	1.36175i	−0.0377961	−	0.0741791i	−0.909132	+	0.416507i	$0.863254\pi$
$338$	1.56152	−	29.7956i	0.0849355	−	1.62067i
$339$	2.58451	−	2.87039i	0.140371	−	0.155898i
$340$	41.3040	−	35.3193i	2.24002	−	1.91546i
$341$	3.59256	−	3.23475i	0.194548	−	0.175172i
$342$	−4.42190	−	27.9188i	−0.239109	−	1.50968i
$343$	16.3376	−	8.72262i	0.882145	−	0.470977i
$344$	56.9928	−	78.4438i	3.07284	−	4.22941i
$345$	−0.293127	+	1.58682i	−0.0157815	+	0.0854313i
$346$	19.4630	−	43.7146i	1.04634	−	2.35011i
$347$	−18.5250	+	7.11107i	−0.994473	+	0.381742i	−0.800545	−	0.599273i	$-0.795456\pi$
$347$	−18.5250	+	7.11107i	−0.994473	+	0.381742i	−0.193928	+	0.981016i	$0.562123\pi$
$348$	4.57841	−	2.97325i	0.245428	−	0.159383i
$349$	−7.02028			−0.375787			−0.187894	−	0.982189i	$-0.560166\pi$
$349$	−7.02028			−0.375787			−0.187894	+	0.982189i	$0.560166\pi$
$350$	31.4343	+	15.7180i	1.68024	+	0.840161i
$351$	−6.46917			−0.345299
$352$	−35.6635	+	23.1601i	−1.90087	+	1.23444i
$353$	25.1898	−	9.66944i	1.34072	−	0.514653i	0.420937	−	0.907090i	$-0.361701\pi$
$353$	25.1898	−	9.66944i	1.34072	−	0.514653i	0.919779	+	0.392437i	$0.128368\pi$
$354$	−0.133544	+	0.299946i	−0.00709781	+	0.0159419i
$355$	0.713724	+	0.386973i	0.0378805	+	0.0205384i
$356$	26.8771	−	36.9932i	1.42448	−	1.96063i
$357$	−1.78064	−	2.17041i	−0.0942413	−	0.114870i
$358$	−2.69794	−	17.0341i	−0.142591	−	0.900283i
$359$	−10.3780	+	9.34436i	−0.547728	+	0.493176i	−0.895901	−	0.444254i	$-0.853469\pi$
$359$	−10.3780	+	9.34436i	−0.547728	+	0.493176i	0.348173	+	0.937430i	$0.386802\pi$
$360$	−12.4854	+	52.1412i	−0.658036	+	2.74808i
$361$	−4.01650	+	4.46078i	−0.211395	+	0.234778i
$362$	2.45230	−	46.7927i	0.128890	−	2.45937i
$363$	0.206138	+	0.404570i	0.0108195	+	0.0212344i
$364$	−19.9560	+	62.7796i	−1.04598	+	3.29054i
$365$	−5.75101	+	3.12695i	−0.301022	+	0.163672i
$366$	−3.93001	−	4.36472i	−0.205425	−	0.228147i
$367$	22.0904	−	17.8884i	1.15311	−	0.933769i	0.154580	−	0.987980i	$-0.450598\pi$
$367$	22.0904	−	17.8884i	1.15311	−	0.933769i	0.998529	+	0.0542111i	$0.0172644\pi$
$368$	−9.69987	+	36.2004i	−0.505641	+	1.88708i
$369$	−14.1487	+	6.29942i	−0.736554	+	0.327935i
$370$	6.57749	+	4.51485i	0.341948	+	0.234716i
$371$	11.3113	−	0.0722399i	0.587251	−	0.00375051i
$372$	−0.282455	+	1.78335i	−0.0146446	+	0.0924624i
$373$	−12.0465	−	18.5499i	−0.623742	−	0.960478i	−0.999431	−	0.0337325i	$-0.989261\pi$
$373$	−12.0465	−	18.5499i	−0.623742	−	0.960478i	0.375689	−	0.926746i	$-0.377406\pi$
$374$	19.0884	+	33.0620i	0.987037	+	1.70960i
$375$	2.44726	−	0.326612i	0.126376	−	0.0168661i
$376$	−23.5221	−	13.5805i	−1.21306	−	0.700359i
$377$	−10.9220	+	21.4357i	−0.562512	+	1.10399i
$378$	8.93794	+	2.33384i	0.459718	+	0.120040i
$379$	19.8453	+	27.3147i	1.01938	+	1.40306i	0.912636	+	0.408774i	$0.134044\pi$
$379$	19.8453	+	27.3147i	1.01938	+	1.40306i	0.106747	+	0.994286i	$0.465956\pi$
$380$	−36.7933	+	17.5762i	−1.88746	+	0.901642i
$381$	−1.14525	−	0.120371i	−0.0586730	−	0.00616678i
$382$	31.0879	+	8.32997i	1.59059	+	0.426199i
$383$	−13.5801	+	35.3775i	−0.693913	+	1.80770i	−0.113238	+	0.993568i	$0.536122\pi$
$383$	−13.5801	+	35.3775i	−0.693913	+	1.80770i	−0.580674	+	0.814136i	$0.697211\pi$
$384$	0.749644	−	2.30717i	0.0382551	−	0.117737i
$385$	−10.6725	+	14.1115i	−0.543920	+	0.719187i
$386$	7.04729	+	21.6893i	0.358698	+	1.10396i
$387$	35.1730	+	1.84334i	1.78794	+	0.0937022i
$388$	19.9491	−	30.7190i	1.01276	−	1.55952i
$389$	9.43110	+	8.49180i	0.478176	+	0.430552i	0.872643	−	0.488359i	$-0.162404\pi$
$389$	9.43110	+	8.49180i	0.478176	+	0.430552i	−0.394467	+	0.918910i	$0.629071\pi$
$390$	1.83772	+	6.19059i	0.0930567	+	0.313473i
$391$	14.9337	+	4.85225i	0.755229	+	0.245389i
$392$	30.3629	−	48.0885i	1.53356	−	2.42884i
$393$	0.587546	+	0.587546i	0.0296378	+	0.0296378i
$394$	4.29126	+	9.63832i	0.216190	+	0.485572i
$395$	6.12153	+	9.97616i	0.308007	+	0.501955i
$396$	−40.7836	−	18.1580i	−2.04945	−	0.912475i
$397$	16.8978	−	20.8670i	0.848075	−	1.04729i	−0.150205	−	0.988655i	$-0.547993\pi$
$397$	16.8978	−	20.8670i	0.848075	−	1.04729i	0.998280	−	0.0586306i	$-0.0186734\pi$
$398$	29.0294	+	14.7912i	1.45511	+	0.741416i
$399$	0.869015	+	1.91877i	0.0435052	+	0.0960584i
$400$	57.2596	−	3.06884i	2.86298	−	0.153442i
$401$	1.13896	−	1.97273i	0.0568769	−	0.0985137i	−0.836185	−	0.548447i	$-0.815219\pi$
$401$	1.13896	−	1.97273i	0.0568769	−	0.0985137i	0.893062	+	0.449934i	$0.148552\pi$
$402$	−5.47426	+	0.286894i	−0.273031	+	0.0143090i
$403$	−2.85154	−	7.42851i	−0.142045	−	0.370041i
$404$	−1.44651	−	13.7627i	−0.0719668	−	0.684718i
$405$	−18.0464	+	6.40260i	−0.896733	+	0.318148i
$406$	22.8233	−	25.6757i	1.13270	−	1.27426i
$407$	−2.83993	+	2.83993i	−0.140770	+	0.140770i
$408$	−8.04827	−	3.08944i	−0.398449	−	0.152950i
$409$	−28.3811	+	6.03258i	−1.40335	+	0.298292i	−0.846531	−	0.532339i	$-0.821313\pi$
$409$	−28.3811	+	6.03258i	−1.40335	+	0.298292i	−0.556823	+	0.830631i	$0.687980\pi$
$410$	20.2609	+	23.6940i	1.00061	+	1.17017i
$411$	−0.183426	+	0.862950i	−0.00904772	+	0.0425662i
$412$	3.00859	−	1.53295i	0.148223	−	0.0755233i
$413$	−0.222283	+	1.46389i	−0.0109378	+	0.0720332i
$414$	−24.3682	+	7.91770i	−1.19763	+	0.389134i
$415$	1.15300	+	1.67550i	0.0565987	+	0.0822473i
$416$	14.5523	+	68.4631i	0.713484	+	3.35668i
$417$	1.14090	+	1.40889i	0.0558699	+	0.0689935i
$418$	−7.41365	−	27.6681i	−0.362613	−	1.35329i
$419$	4.33888	+	3.15238i	0.211968	+	0.154004i	0.688704	−	0.725043i	$-0.258180\pi$
$419$	4.33888	+	3.15238i	0.211968	+	0.154004i	−0.476736	+	0.879047i	$0.658180\pi$
$420$	−0.219077	−	6.60456i	−0.0106899	−	0.322270i
$421$	−15.3126	+	11.1253i	−0.746290	+	0.542212i	−0.894675	−	0.446718i	$-0.852593\pi$
$421$	−15.3126	+	11.1253i	−0.746290	+	0.542212i	0.148385	+	0.988930i	$0.452593\pi$
$422$	45.3021	+	36.6849i	2.20527	+	1.78579i
$423$	−0.516356	−	9.85265i	−0.0251061	−	0.479052i
$424$	30.0816	−	17.3676i	1.46089	−	0.843446i
$425$	−0.0284479	−	24.0249i	−0.00137993	−	1.16538i
$426$		−	0.213016i		−	0.0103206i
$427$	−22.3053	−	14.2835i	−1.07943	−	0.691228i
$428$	−13.5112	−	2.13996i	−0.653086	−	0.103439i
$429$	−3.23309	+	0.339812i	−0.156095	+	0.0164063i
$430$	−16.5915	−	68.9288i	−0.800114	−	3.32404i
$431$	2.43244	−	23.1431i	0.117166	−	1.11476i	−0.765067	−	0.643951i	$-0.777294\pi$
$431$	2.43244	−	23.1431i	0.117166	−	1.11476i	0.882233	−	0.470813i	$-0.156039\pi$
$432$	14.5583	−	3.90089i	0.700438	−	0.187682i
$433$	5.95872	−	0.943769i	0.286358	−	0.0453546i	−0.0116031	−	0.999933i	$-0.503693\pi$
$433$	5.95872	−	0.943769i	0.286358	−	0.0453546i	0.297961	+	0.954578i	$0.403693\pi$
$434$	1.25981	+	11.2921i	0.0604730	+	0.542039i
$435$	0.313587	−	2.39288i	0.0150354	−	0.114730i
$436$	−23.0080	−	4.89050i	−1.10188	−	0.234213i
$437$	−9.88072	−	6.41662i	−0.472659	−	0.306948i
$438$	1.44044	+	0.935434i	0.0688270	+	0.0446968i
$439$	34.9553	+	7.42998i	1.66833	+	0.354614i	0.942743	−	0.333520i	$-0.108236\pi$
$439$	34.9553	+	7.42998i	1.66833	+	0.354614i	0.725584	+	0.688134i	$0.241570\pi$
$440$	−7.05971	+	53.8703i	−0.336559	+	2.56817i
$441$	20.6570	−	0.263864i	0.983664	−	0.0125650i
$442$	62.0638	−	9.82995i	2.95208	−	0.467563i
$443$	−20.3219	+	5.44524i	−0.965523	+	0.258711i	−0.706936	−	0.707277i	$-0.749923\pi$
$443$	−20.3219	+	5.44524i	−0.965523	+	0.258711i	−0.258586	+	0.965988i	$0.583257\pi$
$444$	0.156799	−	1.49185i	0.00744136	−	0.0707998i
$445$	−4.73058	−	19.6530i	−0.224251	−	0.931643i
$446$	3.75093	−	0.394239i	0.177612	−	0.0186677i
$447$	4.75946	+	0.753824i	0.225115	+	0.0356547i
$448$	1.80431	−	39.2193i	0.0852458	−	1.85294i
$449$			17.1662i			0.810122i	0.914290	+	0.405061i	$0.132750\pi$
$449$			17.1662i			0.810122i	−0.914290	+	0.405061i	$0.867250\pi$
$450$	23.0804	+	31.6885i	1.08802	+	1.49381i
$451$	−13.5918	+	7.84723i	−0.640013	+	0.369512i
$452$	−4.63018	−	88.3490i	−0.217785	−	4.15559i
$453$	0.412879	+	0.334343i	0.0193987	+	0.0157088i
$454$	−60.9220	+	44.2624i	−2.85921	+	2.07734i
$455$	15.3889	+	24.7235i	0.721444	+	1.15906i
$456$	5.23294	+	3.80195i	0.245055	+	0.178043i
$457$	−6.00543	−	22.4126i	−0.280922	−	1.04842i	−0.951768	−	0.306819i	$-0.900735\pi$
$457$	−6.00543	−	22.4126i	−0.280922	−	1.04842i	0.670845	−	0.741597i	$-0.265931\pi$
$458$	−1.01388	−	1.25204i	−0.0473754	−	0.0585038i
$459$	−1.31292	−	6.17679i	−0.0612817	−	0.288308i
$460$	20.9529	+	30.4481i	0.976936	+	1.41965i
$461$	−15.9507	+	5.18270i	−0.742899	+	0.241383i	−0.655923	−	0.754828i	$-0.727720\pi$
$461$	−15.9507	+	5.18270i	−0.742899	+	0.241383i	−0.0869763	+	0.996210i	$0.527720\pi$
$462$	4.58950	+	0.696890i	0.213523	+	0.0324223i
$463$	−25.0376	+	12.7573i	−1.16360	+	0.592882i	−0.925644	−	0.378395i	$-0.876476\pi$
$463$	−25.0376	+	12.7573i	−1.16360	+	0.592882i	−0.237952	+	0.971277i	$0.576476\pi$
$464$	11.6534	−	54.8251i	0.540998	−	2.54519i
$465$	0.518750	+	0.606650i	0.0240564	+	0.0281327i
$466$	11.6940	−	2.48563i	0.541712	−	0.115144i
$467$	5.32801	+	2.04523i	0.246551	+	0.0946420i	0.478505	−	0.878085i	$-0.341179\pi$
$467$	5.32801	+	2.04523i	0.246551	+	0.0946420i	−0.231955	+	0.972727i	$0.574512\pi$
$468$	−51.9589	+	51.9589i	−2.40180	+	2.40180i
$469$	−23.4618	+	7.78920i	−1.08336	+	0.359672i
$470$	−18.7167	+	6.64042i	−0.863339	+	0.306300i
$471$	0.506483	+	4.81886i	0.0233375	+	0.222042i
$472$	1.62943	+	4.24482i	0.0750008	+	0.195384i
$473$	35.6425	−	1.86795i	1.63885	−	0.0858882i
$474$	1.53548	−	2.65953i	0.0705270	−	0.122156i
$475$	−4.64484	+	17.4173i	−0.213120	+	0.799159i
$476$	−63.9922	−	6.31293i	−2.93308	−	0.289353i
$477$	11.2423	+	5.72824i	0.514750	+	0.262278i
$478$	21.9728	−	27.1342i	1.00501	−	1.24109i
$479$	17.1076	+	7.61681i	0.781668	+	0.348021i	0.758468	−	0.651710i	$-0.225948\pi$
$479$	17.1076	+	7.61681i	0.781668	+	0.348021i	0.0231993	+	0.999731i	$0.492615\pi$
$480$	−3.67214	−	5.98443i	−0.167609	−	0.273151i
$481$	2.68878	+	6.03911i	0.122598	+	0.275360i
$482$	−31.1284	−	31.1284i	−1.41786	−	1.41786i
$483$	1.59461	−	1.05009i	0.0725573	−	0.0477808i
$484$	9.89119	+	3.21384i	0.449599	+	0.146084i
$485$	−4.60808	−	15.5229i	−0.209242	−	0.704857i
$486$	11.5177	+	10.3705i	0.522451	+	0.470417i
$487$	−12.4178	+	19.1217i	−0.562705	+	0.866489i	−0.999452	−	0.0330949i	$-0.989464\pi$
$487$	−12.4178	+	19.1217i	−0.562705	+	0.866489i	0.436748	+	0.899584i	$0.356130\pi$
$488$	−81.2237	−	4.25675i	−3.67682	−	0.192694i
$489$	−0.605988	−	1.86504i	−0.0274037	−	0.0843400i
$490$	−12.3423	−	39.7103i	−0.557570	−	1.79393i
$491$	3.66657	−	11.2845i	0.165470	−	0.509264i	−0.833601	−	0.552368i	$-0.813724\pi$
$491$	3.66657	−	11.2845i	0.165470	−	0.509264i	0.999071	+	0.0431034i	$0.0137245\pi$
$492$	2.10069	−	5.47248i	0.0947064	−	0.246719i
$493$	−22.6835	−	6.07802i	−1.02161	−	0.273740i
$494$	−46.8889	−	4.92822i	−2.10963	−	0.221731i
$495$	−17.8081	+	8.50695i	−0.800413	+	0.382359i
$496$	10.8965	+	14.9978i	0.489268	+	0.673420i
$497$	−0.254550	−	0.926291i	−0.0114181	−	0.0415498i
$498$	0.242267	−	0.475476i	0.0108563	−	0.0213066i
$499$	8.20677	+	4.73818i	0.367385	+	0.212110i	0.672316	−	0.740265i	$-0.265300\pi$
$499$	8.20677	+	4.73818i	0.367385	+	0.212110i	−0.304930	+	0.952375i	$0.598633\pi$
$500$	34.3466	−	44.9264i	1.53603	−	2.00917i
$501$	1.15976	+	2.00876i	0.0518142	+	0.0897449i
$502$	30.8780	+	47.5479i	1.37815	+	2.12217i
$503$	−3.15307	+	19.9077i	−0.140588	+	0.887640i	0.812062	+	0.583572i	$0.198345\pi$
$503$	−3.15307	+	19.9077i	−0.140588	+	0.887640i	−0.952650	+	0.304069i	$0.901655\pi$
$504$	54.7356	−	32.0694i	2.43812	−	1.42849i
$505$	−5.04376	−	3.46208i	−0.224444	−	0.154061i
$506$	−23.7195	+	10.5606i	−1.05446	+	0.469476i
$507$	−0.641887	+	2.39556i	−0.0285072	+	0.106390i
$508$	−20.4984	+	16.5992i	−0.909468	+	0.736472i
$509$	−11.8798	−	13.1938i	−0.526561	−	0.584805i	0.419922	−	0.907560i	$-0.362058\pi$
$509$	−11.8798	−	13.1938i	−0.526561	−	0.584805i	−0.946482	+	0.322755i	$0.895391\pi$
$510$	−5.53783	+	3.01105i	−0.245219	+	0.133331i
$511$	7.38154	+	2.34640i	0.326540	+	0.103798i
$512$	10.5696	+	20.7441i	0.467117	+	0.916768i
$513$	−0.247968	+	4.73151i	−0.0109480	+	0.208901i
$514$	−39.7937	+	44.1954i	−1.75522	+	1.94937i
$515$	0.347609	−	1.45168i	0.0153175	−	0.0639687i
$516$	−9.90658	+	8.91993i	−0.436113	+	0.392678i
$517$	−1.56401	−	9.87478i	−0.0687852	−	0.434292i
$518$	−1.53619	−	9.31377i	−0.0674965	−	0.409224i
$519$	−2.33792	+	3.21787i	−0.102623	+	0.141249i
$520$	78.6149	+	42.6241i	3.44749	+	1.86919i
$521$	5.99662	−	13.4686i	0.262717	−	0.590072i	−0.733233	−	0.679977i	$-0.761990\pi$
$521$	5.99662	−	13.4686i	0.262717	−	0.590072i	0.995950	+	0.0899053i	$0.0286564\pi$
$522$	35.7745	−	13.7326i	1.56581	−	0.601058i
$523$	3.48231	−	2.26144i	0.152271	−	0.0988859i	−0.466255	−	0.884651i	$-0.654397\pi$
$523$	3.48231	−	2.26144i	0.152271	−	0.0988859i	0.618526	+	0.785765i	$0.287730\pi$
$524$	19.0321			0.831422
$525$	−2.28414	−	1.82120i	−0.0996881	−	0.0794839i
$526$	−65.2502			−2.84504
$527$	6.51405	−	4.23028i	0.283757	−	0.184274i
$528$	7.07091	−	2.71427i	0.307722	−	0.118123i
$529$	5.01134	−	11.2556i	0.217884	−	0.489376i
$530$	4.61364	−	24.9755i	0.200404	−	1.08487i
$531$	−0.970802	+	1.33619i	−0.0421292	+	0.0579859i
$532$	45.1516	+	17.0020i	1.95757	+	0.737132i
$533$	4.04109	+	25.5144i	0.175039	+	1.10515i
$534$	−3.94142	+	3.54887i	−0.170562	+	0.153574i
$535$	−4.59615	+	3.93019i	−0.198709	+	0.169917i
$536$	−50.7957	+	56.4143i	−2.19404	+	2.43673i
$537$	−0.0750267	+	1.43159i	−0.00323764	+	0.0617778i
$538$	−28.7194	−	56.3649i	−1.23818	−	2.43006i
$539$	20.7901	−	2.45398i	0.895492	−	0.105701i
$540$	6.39125	−	13.4200i	0.275036	−	0.577504i
$541$	20.2170	+	22.4533i	0.869197	+	0.965342i	0.999659	−	0.0261118i	$-0.00831259\pi$
$541$	20.2170	+	22.4533i	0.869197	+	0.965342i	−0.130462	+	0.991453i	$0.541646\pi$
$542$	−58.6726	+	47.5121i	−2.52020	+	2.04082i
$543$	−1.00806	+	3.76211i	−0.0432598	+	0.161448i
$544$	−62.4155	+	27.7892i	−2.67604	+	1.19145i
$545$	−8.24592	+	6.33508i	−0.353217	+	0.271365i
$546$	3.77803	−	6.64134i	0.161685	−	0.284223i
$547$	−1.01423	+	6.40362i	−0.0433655	+	0.273799i	−0.999838	−	0.0180249i	$-0.994262\pi$
$547$	−1.01423	+	6.40362i	−0.0433655	+	0.273799i	0.956472	+	0.291824i	$0.0942622\pi$
$548$	11.0057	+	16.9474i	0.470142	+	0.723956i
$549$	−14.7724	−	25.5866i	−0.630472	−	1.09201i
$550$	26.6170	+	29.4908i	1.13495	+	1.25749i
$551$	15.2593	+	8.80994i	0.650066	+	0.375316i
$552$	2.66179	−	5.22406i	0.113293	−	0.222351i
$553$	3.49889	−	13.3998i	0.148788	−	0.569815i
$554$	−18.8399	−	25.9310i	−0.800433	−	1.10170i
$555$	−0.456760	−	0.480754i	−0.0193884	−	0.0204069i
$556$	41.2970	+	4.34049i	1.75138	+	0.184078i
$557$	−11.8915	−	3.18632i	−0.503860	−	0.135009i	−0.00206894	−	0.999998i	$-0.500659\pi$
$557$	−11.8915	−	3.18632i	−0.503860	−	0.135009i	−0.501791	+	0.864989i	$0.667325\pi$
$558$	−4.54198	+	11.8323i	−0.192277	+	0.500900i
$559$	18.1537	−	55.8715i	0.767821	−	2.36311i
$560$	−49.5397	−	46.3587i	−2.09344	−	1.95901i
$561$	−0.980610	−	3.01801i	−0.0414014	−	0.127420i
$562$	−19.6376	−	1.02916i	−0.828363	−	0.0434127i
$563$	4.64447	−	7.15185i	0.195741	−	0.301415i	−0.727148	−	0.686481i	$-0.759155\pi$
$563$	4.64447	−	7.15185i	0.195741	−	0.301415i	0.922889	+	0.385066i	$0.125821\pi$
$564$	2.77503	+	2.49865i	0.116850	+	0.105212i
$565$	−31.0425	−	23.7906i	−1.30597	−	1.00088i
$566$	−64.6263	−	20.9984i	−2.71645	−	0.882627i
$567$	20.2527	+	10.1569i	0.850532	+	0.426548i
$568$	−2.08589	−	2.08589i	−0.0875221	−	0.0875221i
$569$	12.7114	+	28.5502i	0.532889	+	1.19689i	0.956684	+	0.291130i	$0.0940311\pi$
$569$	12.7114	+	28.5502i	0.532889	+	1.19689i	−0.423795	+	0.905758i	$0.639302\pi$
$570$	4.59820	−	1.10681i	0.192597	−	0.0463591i
$571$	7.71715	+	3.43590i	0.322953	+	0.143788i	0.561809	−	0.827267i	$-0.310106\pi$
$571$	7.71715	+	3.43590i	0.322953	+	0.143788i	−0.238856	+	0.971055i	$0.576772\pi$
$572$	−46.8604	+	57.8677i	−1.95933	+	2.41957i
$573$	−2.38365	−	1.21453i	−0.0995786	−	0.0507378i
$574$	3.62141	−	36.7092i	0.151155	−	1.53221i
$575$	16.2520	+	1.68870i	0.677755	+	0.0704236i
$576$	21.8969	−	37.9266i	0.912372	−	1.58027i
$577$	−14.0205	+	0.734783i	−0.583681	+	0.0305894i	−0.341892	−	0.939739i	$-0.611068\pi$
$577$	−14.0205	+	0.734783i	−0.583681	+	0.0305894i	−0.241789	+	0.970329i	$0.577734\pi$
$578$	5.79615	+	15.0995i	0.241088	+	0.628056i
$579$	−0.198148	−	1.88525i	−0.00823474	−	0.0783484i
$580$	−33.6768	−	43.8347i	−1.39835	−	1.82014i
$581$	0.485304	−	2.35710i	0.0201338	−	0.0977889i
$582$	−3.00411	+	3.00411i	−0.124524	+	0.124524i
$583$	11.9367	+	4.58208i	0.494368	+	0.189770i
$584$	23.2651	−	4.94514i	0.962715	−	0.204631i
$585$	2.56784	+	32.3824i	0.106167	+	1.33885i
$586$	−1.55027	+	7.29346i	−0.0640412	+	0.301290i
$587$	−17.5353	+	8.93468i	−0.723759	+	0.368774i	−0.776740	−	0.629822i	$-0.783128\pi$
$587$	−17.5353	+	8.93468i	−0.723759	+	0.368774i	0.0529805	+	0.998596i	$0.483128\pi$
$588$	−5.45775	+	5.59898i	−0.225074	+	0.230898i
$589$	−5.54247	+	1.80086i	−0.228373	+	0.0742030i
$590$	3.13455	+	1.10791i	0.129047	+	0.0456121i
$591$	−0.182333	−	0.857809i	−0.00750018	−	0.0352856i
$592$	−9.69245	−	11.9692i	−0.398357	−	0.491930i
$593$	−1.08028	−	4.03167i	−0.0443619	−	0.165561i	0.940191	−	0.340647i	$-0.110646\pi$
$593$	−1.08028	−	4.03167i	−0.0443619	−	0.165561i	−0.984553	+	0.175086i	$0.943980\pi$
$594$	8.44756	+	6.13751i	0.346608	+	0.251825i
$595$	−20.4829	+	19.7110i	−0.839718	+	0.808074i
$596$	89.2946	−	64.8763i	3.65765	−	2.65744i
$597$	−2.10462	−	1.70429i	−0.0861364	−	0.0697519i
$598$	2.23664	+	42.6776i	0.0914629	+	1.74522i
$599$	0.232901	−	0.134465i	0.00951606	−	0.00549410i	−0.495234	−	0.868759i	$-0.664918\pi$
$599$	0.232901	−	0.134465i	0.00951606	−	0.00549410i	0.504750	+	0.863265i	$0.331584\pi$
$600$	−8.86197	−	1.39284i	−0.361788	−	0.0568626i
$601$		−	10.5831i		−	0.431694i	−0.976427	−	0.215847i	$-0.930749\pi$
$601$		−	10.5831i		−	0.431694i	0.976427	−	0.215847i	$-0.0692513\pi$
$602$	−45.2380	+	70.6440i	−1.84376	+	2.87923i
$603$	−27.2358	−	4.31373i	−1.10913	−	0.175669i
$604$	12.1022	−	1.27199i	0.492431	−	0.0517566i
$605$	3.91873	−	2.40460i	0.159319	−	0.0977607i
$606$	−0.167779	+	1.59631i	−0.00681555	+	0.0648457i
$607$	−1.20593	+	0.323127i	−0.0489470	+	0.0131153i	−0.283209	−	0.959058i	$-0.591399\pi$
$607$	−1.20593	+	0.323127i	−0.0489470	+	0.0131153i	0.234262	+	0.972173i	$0.424732\pi$
$608$	50.6313	−	8.01920i	2.05337	−	0.325222i
$609$	−2.29938	+	1.69314i	−0.0931757	+	0.0686096i
$610$	−40.9119	+	43.1633i	−1.65647	+	1.74763i
$611$	−16.0965	−	3.42142i	−0.651195	−	0.138416i
$612$	−60.1556	−	39.0655i	−2.43165	−	1.57913i
$613$	22.5163	+	14.6222i	0.909424	+	0.590587i	0.912351	−	0.409409i	$-0.134265\pi$
$613$	22.5163	+	14.6222i	0.909424	+	0.590587i	−0.00292696	+	0.999996i	$0.500932\pi$
$614$	62.6315	+	13.3127i	2.52760	+	0.537258i
$615$	−1.23784	−	2.27660i	−0.0499145	−	0.0918015i
$616$	51.7654	−	38.1173i	2.08569	−	1.53579i
$617$	−9.11291	+	1.44334i	−0.366872	+	0.0581068i	−0.337149	−	0.941451i	$-0.609463\pi$
$617$	−9.11291	+	1.44334i	−0.366872	+	0.0581068i	−0.0297232	+	0.999558i	$0.509463\pi$
$618$	−0.378304	+	0.101366i	−0.0152176	+	0.00407755i
$619$	0.850251	−	8.08960i	0.0341745	−	0.325149i	−0.964057	−	0.265697i	$-0.914398\pi$
$619$	0.850251	−	8.08960i	0.0341745	−	0.325149i	0.998231	−	0.0594519i	$-0.0189353\pi$
$620$	18.2273	+	1.42366i	0.732025	+	0.0571755i
$621$	4.27120	−	0.448921i	0.171397	−	0.0180146i
$622$	74.3796	+	11.7806i	2.98235	+	0.472358i
$623$	−12.8983	+	20.1421i	−0.516758	+	0.806974i
$624$		−	12.4665i		−	0.499058i
$625$	−5.25569	−	24.4413i	−0.210228	−	0.977652i
$626$	−49.5578	+	28.6122i	−1.98073	+	1.14357i
$627$	0.124609	+	2.37769i	0.00497642	+	0.0949558i
$628$	86.2507	+	69.8445i	3.44178	+	2.78710i
$629$	−5.22048	+	3.79290i	−0.208154	+	0.151233i
$630$	8.13460	−	45.6666i	0.324090	−	1.81940i
$631$	−26.1031	−	18.9650i	−1.03915	−	0.754985i	−0.0690289	−	0.997615i	$-0.521990\pi$
$631$	−26.1031	−	18.9650i	−1.03915	−	0.754985i	−0.970119	+	0.242629i	$0.921990\pi$
$632$	−11.0069	−	41.0784i	−0.437832	−	1.63401i
$633$	−3.04932	−	3.76559i	−0.121199	−	0.149669i
$634$	0.124785	+	0.587067i	0.00495585	+	0.0233154i
$635$	−0.298332	+	11.6565i	−0.0118389	+	0.462576i
$636$	−4.54178	+	1.47571i	−0.180093	+	0.0585158i
$637$	8.49234	−	33.3943i	0.336479	−	1.32313i
$638$	34.5989	−	17.6290i	1.36978	−	0.697939i
$639$	0.222787	−	1.04813i	0.00881331	−	0.0414634i
$640$	−23.8886	−	5.72020i	−0.944281	−	0.226111i
$641$	−28.7012	+	6.10064i	−1.13363	+	0.240961i	−0.736261	−	0.676698i	$-0.763410\pi$
$641$	−28.7012	+	6.10064i	−1.13363	+	0.240961i	−0.397370	+	0.917658i	$0.630077\pi$
$642$	1.48129	+	0.568613i	0.0584617	+	0.0224413i
$643$	23.5100	−	23.5100i	0.927145	−	0.927145i	−0.0703751	−	0.997521i	$-0.522420\pi$
$643$	23.5100	−	23.5100i	0.927145	−	0.927145i	0.997521	+	0.0703751i	$0.0224196\pi$
$644$	8.81918	−	42.8343i	0.347524	−	1.68791i
$645$	0.157752	+	5.89102i	0.00621148	+	0.231959i
$646$	−4.81061	−	45.7699i	−0.189271	−	1.80079i
$647$	−0.606120	−	1.57900i	−0.0238290	−	0.0620768i	0.921150	−	0.389208i	$-0.127251\pi$
$647$	−0.606120	−	1.57900i	−0.0238290	−	0.0620768i	−0.944979	+	0.327131i	$0.893918\pi$
$648$	69.4791	−	3.64125i	2.72940	−	0.143042i
$649$	−0.836837	+	1.44944i	−0.0328487	+	0.0568956i
$650$	61.0170	−	23.5052i	2.39328	−	0.921948i
$651$	0.0927208	−	0.939882i	0.00363401	−	0.0368369i
$652$	−40.0214	−	20.3919i	−1.56736	−	0.798610i
$653$	−11.0503	+	13.6459i	−0.432430	+	0.534007i	−0.946054	−	0.324008i	$-0.894969\pi$
$653$	−11.0503	+	13.6459i	−0.432430	+	0.534007i	0.513624	+	0.858016i	$0.328303\pi$
$654$	2.49241	+	1.10969i	0.0974609	+	0.0433924i
$655$	5.46042	−	6.40100i	0.213356	−	0.250108i
$656$	−24.4793	−	54.9813i	−0.955755	−	2.14666i
$657$	6.10926	+	6.10926i	0.238345	+	0.238345i
$658$	21.0050	+	10.5341i	0.818858	+	0.410663i
$659$	−12.1353	−	3.94299i	−0.472724	−	0.153597i	0.0629598	−	0.998016i	$-0.479946\pi$
$659$	−12.1353	−	3.94299i	−0.472724	−	0.153597i	−0.535684	+	0.844419i	$0.679946\pi$
$660$	2.48923	−	7.04261i	0.0968931	−	0.274133i
$661$	34.1996	+	30.7934i	1.33021	+	1.19773i	0.963600	+	0.267350i	$0.0861479\pi$
$661$	34.1996	+	30.7934i	1.33021	+	1.19773i	0.366609	+	0.930375i	$0.380519\pi$
$662$	27.6638	−	42.5985i	1.07518	−	1.65564i
$663$	−5.21600	−	0.273359i	−0.202573	−	0.0106164i
$664$	−2.28363	−	7.02829i	−0.0886220	−	0.272751i
$665$	18.6725	−	10.3077i	0.724088	−	0.399715i
$666$	3.25380	−	10.0142i	0.126082	−	0.388041i
$667$	5.72363	−	14.9106i	0.221620	−	0.577340i
$668$	51.3182	+	13.7507i	1.98556	+	0.532029i
$669$	−0.311784	−	0.0327698i	−0.0120543	−	0.00126695i
$670$	7.27767	+	55.0276i	0.281161	+	2.12590i
$671$	−17.5979	−	24.2214i	−0.679358	−	0.935056i
$672$	−2.09889	+	8.03815i	−0.0809664	+	0.310078i
$673$	13.5468	−	26.5870i	0.522189	−	1.02485i	−0.467816	−	0.883826i	$-0.654959\pi$
$673$	13.5468	−	26.5870i	0.522189	−	1.02485i	0.990006	−	0.141028i	$-0.0450409\pi$
$674$	3.51634	+	2.03016i	0.135444	+	0.0781988i
$675$	−2.67980	−	5.99981i	−0.103146	−	0.230933i
$676$	28.4029	+	49.1952i	1.09242	+	1.89212i
$677$	−15.7205	−	24.2075i	−0.604189	−	0.930369i	−0.999928	−	0.0120061i	$-0.996178\pi$
$677$	−15.7205	−	24.2075i	−0.604189	−	0.930369i	0.395739	−	0.918363i	$-0.370488\pi$
$678$	−1.60526	+	10.1352i	−0.0616495	+	0.389240i
$679$	−9.47339	+	16.6531i	−0.363555	+	0.639088i
$680$	−24.7428	+	83.7124i	−0.948844	+	3.21022i
$681$	5.71823	−	2.54592i	0.219123	−	0.0975598i
$682$	−3.32408	+	12.4056i	−0.127286	+	0.475036i
$683$	12.3270	−	9.98225i	0.471681	−	0.381960i	−0.363802	−	0.931476i	$-0.618521\pi$
$683$	12.3270	−	9.98225i	0.471681	−	0.381960i	0.835483	+	0.549516i	$0.185188\pi$
$684$	36.0108	+	39.9940i	1.37691	+	1.52921i
$685$	8.85745	+	1.16077i	0.338426	+	0.0443508i
$686$	−23.7806	+	43.0746i	−0.907949	+	1.64459i
$687$	0.0607961	+	0.119319i	0.00231952	+	0.00455231i
$688$	−7.16313	+	136.681i	−0.273092	+	5.21090i
$689$	14.0820	−	15.6396i	0.536481	−	0.595822i
$690$	−1.64292	−	3.95974i	−0.0625451	−	0.150745i
$691$	−0.882689	+	0.794776i	−0.0335791	+	0.0302347i	−0.685749	−	0.727838i	$-0.740525\pi$
$691$	−0.882689	+	0.794776i	−0.0335791	+	0.0302347i	0.652170	+	0.758073i	$0.273859\pi$
$692$	14.2519	+	89.9831i	0.541777	+	3.42064i
$693$	21.8535	+	8.22904i	0.830147	+	0.312595i
$694$	30.9863	−	42.6489i	1.17622	−	1.61893i
$695$	13.3081	−	12.6439i	0.504807	−	0.479612i
$696$	−3.56653	+	8.01057i	−0.135189	+	0.303640i
$697$	−23.5411	+	9.03660i	−0.891684	+	0.342286i
$698$	15.6419	−	10.1580i	0.592056	−	0.384486i
$699$	−0.993738			−0.0375866
$700$	−66.4913	+	7.49787i	−2.51313	+	0.283393i
$701$	8.69736			0.328495			0.164247	−	0.986419i	$-0.447480\pi$
$701$	8.69736			0.328495			0.164247	+	0.986419i	$0.447480\pi$
$702$	14.4140	−	9.36056i	0.544021	−	0.353292i
$703$	4.52003	−	1.73508i	0.170476	−	0.0654396i
$704$	18.0503	−	40.5417i	0.680298	−	1.52797i
$705$	1.63653	−	0.216439i	0.0616353	−	0.00815157i
$706$	−42.1343	+	57.9929i	−1.58574	+	2.18259i
$707$	1.17798	+	7.14199i	0.0443027	+	0.268602i
$708$	−0.0977889	−	0.617415i	−0.00367513	−	0.0232039i
$709$	12.7518	−	11.4818i	0.478905	−	0.431208i	−0.393991	−	0.919114i	$-0.628906\pi$
$709$	12.7518	−	11.4818i	0.478905	−	0.431208i	0.872896	+	0.487906i	$0.162239\pi$
$710$	−2.15018	+	0.170504i	−0.0806950	+	0.00639891i
$711$	10.3368	−	11.4801i	0.387659	−	0.430539i
$712$	−3.84392	+	73.3464i	−0.144057	+	2.74877i
$713$	2.39819	+	4.70671i	0.0898129	+	0.176268i
$714$	7.10793	+	2.25942i	0.266007	+	0.0845567i
$715$	6.01794	+	32.3629i	0.225058	+	1.21031i
$716$	21.9713	+	24.4016i	0.821107	+	0.911931i
$717$	−2.25544	+	1.82642i	−0.0842310	+	0.0682090i
$718$	9.60239	−	35.8366i	0.358358	−	1.33741i
$719$	29.7684	−	13.2537i	1.11017	−	0.494281i	0.232044	−	0.972705i	$-0.425459\pi$
$719$	29.7684	−	13.2537i	1.11017	−	0.494281i	0.878129	+	0.478425i	$0.158792\pi$
$720$	−25.3052	−	71.3256i	−0.943071	−	2.65815i
$721$	−1.52391	+	0.892855i	−0.0567534	+	0.0332517i
$722$	2.49468	−	15.7508i	0.0928423	−	0.586183i
$723$	1.99294	+	3.06886i	0.0741184	+	0.114132i
$724$	44.6055	+	77.2589i	1.65775	+	2.87131i
$725$	−24.4048	−	1.25003i	−0.906371	−	0.0464248i
$726$	−1.04469	−	0.603152i	−0.0387721	−	0.0223851i
$727$	10.8247	−	21.2447i	0.401466	−	0.787922i	−0.598446	−	0.801163i	$-0.704215\pi$
$727$	10.8247	−	21.2447i	0.401466	−	0.787922i	0.999912	+	0.0132413i	$0.00421495\pi$
$728$	−28.0381	−	102.029i	−1.03916	−	3.78143i
$729$	14.3432	+	19.7418i	0.531231	+	0.731177i
$730$	8.28932	−	15.2886i	0.306801	−	0.565857i
$731$	57.0306	+	5.99416i	2.10935	+	0.221702i
$732$	10.8012	+	2.89417i	0.399223	+	0.106972i
$733$	−11.6517	+	30.3537i	−0.430366	+	1.12114i	0.531364	+	0.847143i	$0.321679\pi$
$733$	−11.6517	+	30.3537i	−0.430366	+	1.12114i	−0.961730	+	0.273998i	$0.911654\pi$
$734$	−23.3361	+	71.8210i	−0.861350	+	2.65096i
$735$	0.317226	+	3.44196i	0.0117011	+	0.126959i
$736$	−14.3589	−	44.1921i	−0.529276	−	1.62894i
$737$	−27.9051	−	1.46244i	−1.02790	−	0.0538698i
$738$	22.4099	−	34.5083i	0.824922	−	1.27027i
$739$	−39.4458	−	35.5172i	−1.45104	−	1.30652i	−0.870388	−	0.492366i	$-0.836132\pi$
$739$	−39.4458	−	35.5172i	−1.45104	−	1.30652i	−0.580649	−	0.814154i	$-0.697201\pi$
$740$	−15.1842	−	0.388617i	−0.558183	−	0.0142858i
$741$	3.72715	+	1.21102i	0.136920	+	0.0444881i
$742$	−25.0982	+	16.5278i	−0.921383	+	0.606754i
$743$	−35.7302	−	35.7302i	−1.31082	−	1.31082i	−0.920814	−	0.390001i	$-0.872474\pi$
$743$	−35.7302	−	35.7302i	−1.31082	−	1.31082i	−0.390001	−	0.920814i	$-0.627526\pi$
$744$	−1.17962	−	2.64946i	−0.0432468	−	0.0971339i
$745$	3.79950	−	48.6455i	0.139203	−	1.78223i
$746$	53.6816	+	23.9006i	1.96542	+	0.875062i
$747$	1.68935	−	2.08617i	0.0618100	−	0.0763290i
$748$	−64.7627	−	32.9982i	−2.36796	−	1.20653i
$749$	7.12080	+	0.702478i	0.260189	+	0.0256680i
$750$	−4.98018	+	4.26879i	−0.181850	+	0.155874i
$751$	20.8809	−	36.1668i	0.761956	−	1.31975i	−0.179886	−	0.983688i	$-0.557573\pi$
$751$	20.8809	−	36.1668i	0.761956	−	1.31975i	0.941841	−	0.336058i	$-0.109094\pi$
$752$	38.2870	−	2.00653i	1.39618	−	0.0731708i
$753$	−1.68882	−	4.39953i	−0.0615441	−	0.160328i
$754$	−6.68090	−	63.5646i	−0.243304	−	2.31488i
$755$	3.04438	−	4.43523i	0.110796	−	0.161414i
$756$	−16.6917	+	5.54156i	−0.607071	+	0.201545i
$757$	−22.3878	+	22.3878i	−0.813699	+	0.813699i	−0.985186	−	0.171487i	$-0.945143\pi$
$757$	−22.3878	+	22.3878i	−0.813699	+	0.813699i	0.171487	+	0.985186i	$0.445143\pi$
$758$	−83.7403	−	32.1449i	−3.04158	−	1.16756i
$759$	2.11103	−	0.448714i	0.0766256	−	0.0162873i
$760$	34.1884	−	55.8646i	1.24014	−	2.02642i
$761$	5.71569	−	26.8902i	0.207194	−	0.974770i	−0.744477	−	0.667648i	$-0.767301\pi$
$761$	5.71569	−	26.8902i	0.207194	−	0.974770i	0.951670	−	0.307121i	$-0.0993657\pi$
$762$	2.72591	−	1.38892i	0.0987494	−	0.0503154i
$763$	12.1642	+	1.84707i	0.440374	+	0.0668683i
$764$	−58.2772	+	18.9354i	−2.10839	+	0.685059i
$765$	−30.3977	+	9.02380i	−1.09903	+	0.326256i
$766$	−20.9314	−	98.4745i	−0.756283	−	3.55803i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22811 + 1.44695i) q^{2} +(0.206163 - 0.0791387i) q^{3} +(2.05732 - 4.62083i) q^{4} +(-0.963847 - 2.01767i) q^{5} +(-0.344844 + 0.474637i) q^{6} +(-0.932359 + 2.47603i) q^{7} +(1.27096 + 8.02453i) q^{8} +(-2.19319 + 1.97476i) q^{9} +O(q^{10})\)	\(q+(-2.22811 + 1.44695i) q^{2} +(0.206163 - 0.0791387i) q^{3} +(2.05732 - 4.62083i) q^{4} +(-0.963847 - 2.01767i) q^{5} +(-0.344844 + 0.474637i) q^{6} +(-0.932359 + 2.47603i) q^{7} +(1.27096 + 8.02453i) q^{8} +(-2.19319 + 1.97476i) q^{9} +(5.06702 + 3.10095i) q^{10} +(-2.00112 + 2.22247i) q^{11} +(0.0584587 - 1.11546i) q^{12} +(2.23475 + 4.38594i) q^{13} +(-1.50529 - 6.86593i) q^{14} +(-0.358386 - 0.339692i) q^{15} +(-7.67383 - 8.52265i) q^{16} +(-3.73417 + 3.02387i) q^{17} +(2.02929 - 7.57342i) q^{18} +(3.29351 - 1.46636i) q^{19} +(-11.3063 + 0.302763i) q^{20} +(0.00373135 + 0.584251i) q^{21} +(1.24291 - 7.84742i) q^{22} +(-1.77983 - 2.74069i) q^{23} +(0.897076 + 1.55378i) q^{24} +(-3.14200 + 3.88945i) q^{25} +(-11.3255 - 6.53878i) q^{26} +(-0.596641 + 1.17097i) q^{27} +(9.52312 + 9.40225i) q^{28} +(2.87272 + 3.95395i) q^{29} +(1.29004 + 0.238305i) q^{30} +(-1.60762 - 0.168967i) q^{31} +(13.7345 + 3.68016i) q^{32} +(-0.236674 + 0.616558i) q^{33} +(3.94475 - 12.1407i) q^{34} +(5.89446 - 0.505317i) q^{35} +(4.61291 + 14.1971i) q^{36} +(1.34111 + 0.0702847i) q^{37} +(-5.21653 + 8.03276i) q^{38} +(0.807821 + 0.727365i) q^{39} +(14.9659 - 10.2988i) q^{40} +(4.99103 + 1.62168i) q^{41} +(-0.853696 - 1.29638i) q^{42} +(-8.43891 - 8.43891i) q^{43} +(6.15269 + 13.8192i) q^{44} +(6.09832 + 2.52178i) q^{45} +(7.93128 + 3.53123i) q^{46} +(-2.10386 + 2.59805i) q^{47} +(-2.25653 - 1.14976i) q^{48} +(-5.26142 - 4.61709i) q^{49} +(1.37287 - 13.2124i) q^{50} +(-0.530544 + 0.918929i) q^{51} +(24.8643 - 1.30308i) q^{52} +(-1.53215 - 3.99138i) q^{53} +(-0.364960 - 3.47237i) q^{54} +(6.41299 + 1.89548i) q^{55} +(-21.0539 - 4.33481i) q^{56} +(0.562954 - 0.562954i) q^{57} +(-12.1219 - 4.65316i) q^{58} +(0.547410 - 0.116356i) q^{59} +(-2.30697 + 0.957180i) q^{60} +(-2.08141 + 9.79226i) q^{61} +(3.82643 - 1.94966i) q^{62} +(-2.84472 - 7.27159i) q^{63} +(-14.1129 + 4.58555i) q^{64} +(6.69544 - 8.73637i) q^{65} +(-0.364792 - 1.71621i) q^{66} +(5.88015 + 7.26138i) q^{67} +(6.29039 + 23.4761i) q^{68} +(-0.583829 - 0.424177i) q^{69} +(-12.4023 + 9.65489i) q^{70} +(-0.293741 + 0.213415i) q^{71} +(-18.6340 - 15.0895i) q^{72} +(-0.153215 - 2.92351i) q^{73} +(-3.08984 + 1.78392i) q^{74} +(-0.339959 + 1.05052i) q^{75} -18.2355i q^{76} +(-3.63713 - 7.02697i) q^{77} +(-2.85237 - 0.451771i) q^{78} +(-5.20577 + 0.547148i) q^{79} +(-9.79952 + 23.6978i) q^{80} +(0.895128 - 8.51657i) q^{81} +(-13.4670 + 3.60848i) q^{82} +(-0.898387 + 0.142291i) q^{83} +(2.70740 + 1.18475i) q^{84} +(9.70036 + 4.61979i) q^{85} +(31.0135 + 6.59212i) q^{86} +(0.905159 + 0.587817i) q^{87} +(-20.3776 - 13.2334i) q^{88} +(8.84258 + 1.87955i) q^{89} +(-17.2366 + 3.20517i) q^{90} +(-12.9433 + 1.44403i) q^{91} +(-16.3259 + 2.58577i) q^{92} +(-0.344803 + 0.0923897i) q^{93} +(0.928377 - 8.83292i) q^{94} +(-6.13308 - 5.23187i) q^{95} +(3.12280 - 0.328219i) q^{96} +(7.15230 + 1.13281i) q^{97} +(18.4037 + 2.67437i) q^{98} -8.82604i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

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