LMFDB - Embedded newform 175.2.x.a.33.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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: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:	$1.39738203537$
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			33.3
Character	$\chi$	$=$	175.33
Dual form			175.2.x.a.122.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05690 + 1.33577i) q^{2} +(-2.80061 + 1.07506i) q^{3} +(1.63309 - 3.66797i) q^{4} +(2.23023 - 0.161449i) q^{5} +(4.32456 - 5.95224i) q^{6} +(2.18242 - 1.49568i) q^{7} +(0.773125 + 4.88132i) q^{8} +(4.45826 - 4.01424i) q^{9} +(-4.37170 + 3.31115i) q^{10} +(-2.26620 + 2.51687i) q^{11} +(-0.630373 + 12.0282i) q^{12} +(-0.306584 - 0.601706i) q^{13} +(-2.49113 + 5.99166i) q^{14} +(-6.07245 + 2.84978i) q^{15} +(-2.73729 - 3.04006i) q^{16} +(2.21216 - 1.79137i) q^{17} +(-3.80811 + 14.2121i) q^{18} +(2.91018 - 1.29570i) q^{19} +(3.04997 - 8.44409i) q^{20} +(-4.50417 + 6.53504i) q^{21} +(1.29940 - 8.20407i) q^{22} +(2.89634 + 4.45997i) q^{23} +(-7.41291 - 12.8395i) q^{24} +(4.94787 - 0.720139i) q^{25} +(1.43435 + 0.828123i) q^{26} +(-4.08462 + 8.01652i) q^{27} +(-1.92203 - 10.4476i) q^{28} +(5.40952 + 7.44556i) q^{29} +(8.68378 - 13.9731i) q^{30} +(-5.49728 - 0.577787i) q^{31} +(0.143600 + 0.0384776i) q^{32} +(3.64098 - 9.48509i) q^{33} +(-2.15734 + 6.63961i) q^{34} +(4.62582 - 3.68806i) q^{35} +(-7.44339 - 22.9084i) q^{36} +(1.66879 + 0.0874574i) q^{37} +(-4.25520 + 6.55243i) q^{38} +(1.50549 + 1.35555i) q^{39} +(2.51233 + 10.7617i) q^{40} +(0.985611 + 0.320244i) q^{41} +(0.535343 - 19.4584i) q^{42} +(3.97930 + 3.97930i) q^{43} +(5.53092 + 12.4227i) q^{44} +(9.29487 - 9.67247i) q^{45} +(-11.9149 - 5.30487i) q^{46} +(1.73333 - 2.14048i) q^{47} +(10.9343 + 5.57132i) q^{48} +(2.52589 - 6.52839i) q^{49} +(-9.21532 + 8.09044i) q^{50} +(-4.26959 + 7.39515i) q^{51} +(-2.70772 + 0.141906i) q^{52} +(-1.43467 - 3.73744i) q^{53} +(-2.30654 - 21.9453i) q^{54} +(-4.64781 + 5.97909i) q^{55} +(8.98817 + 9.49673i) q^{56} +(-6.75735 + 6.75735i) q^{57} +(-21.0724 - 8.08892i) q^{58} +(1.16618 - 0.247880i) q^{59} +(0.536074 + 26.9275i) q^{60} +(-1.21778 + 5.72922i) q^{61} +(12.0791 - 6.15462i) q^{62} +(3.72578 - 15.4289i) q^{63} +(7.43442 - 2.41559i) q^{64} +(-0.780899 - 1.29245i) q^{65} +(5.18072 + 24.3734i) q^{66} +(4.70495 + 5.81013i) q^{67} +(-2.95806 - 11.0396i) q^{68} +(-12.9062 - 9.37692i) q^{69} +(-4.58845 + 13.7650i) q^{70} +(7.96131 - 5.78423i) q^{71} +(23.0416 + 18.6587i) q^{72} +(-0.270517 - 5.16177i) q^{73} +(-3.54935 + 2.04922i) q^{74} +(-13.0829 + 7.33606i) q^{75} -12.7904i q^{76} +(-1.18137 + 8.88238i) q^{77} +(-4.90734 - 0.777246i) q^{78} +(3.95313 - 0.415491i) q^{79} +(-6.59560 - 6.33812i) q^{80} +(0.939990 - 8.94341i) q^{81} +(-2.45507 + 0.657835i) q^{82} +(-7.87661 + 1.24753i) q^{83} +(16.6146 + 27.1935i) q^{84} +(4.64442 - 4.35233i) q^{85} +(-13.5004 - 2.86961i) q^{86} +(-23.1544 - 15.0366i) q^{87} +(-14.0377 - 9.11621i) q^{88} +(-12.1194 - 2.57605i) q^{89} +(-6.19844 + 32.3110i) q^{90} +(-1.56905 - 0.854621i) q^{91} +(21.0890 - 3.34017i) q^{92} +(16.0169 - 4.29172i) q^{93} +(-0.706097 + 6.71806i) q^{94} +(6.28119 - 3.35955i) q^{95} +(-0.443535 + 0.0466174i) q^{96} +(16.7616 + 2.65478i) q^{97} +(3.52490 + 16.8022i) q^{98} +20.3180i 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} - 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}+ \cdots + 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

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 $

$2$	−2.05690	+	1.33577i	−1.45445	+	0.944529i	−0.455933	+	0.890014i	$0.650695\pi$
$2$	−2.05690	+	1.33577i	−1.45445	+	0.944529i	−0.998513	+	0.0545147i	$0.982639\pi$
$3$	−2.80061	+	1.07506i	−1.61694	+	0.620683i	−0.987676	−	0.156512i	$-0.949975\pi$
$3$	−2.80061	+	1.07506i	−1.61694	+	0.620683i	−0.629259	+	0.777195i	$0.716642\pi$
$4$	1.63309	−	3.66797i	0.816544	−	1.83399i
$5$	2.23023	−	0.161449i	0.997390	−	0.0722024i
$5$	2.23023	−	0.161449i	0.997390	−	0.0722024i
$6$	4.32456	−	5.95224i	1.76549	−	2.42999i
$7$	2.18242	−	1.49568i	0.824876	−	0.565314i
$7$	2.18242	−	1.49568i	0.824876	−	0.565314i
$8$	0.773125	+	4.88132i	0.273341	+	1.72581i
$9$	4.45826	−	4.01424i	1.48609	−	1.33808i
$10$	−4.37170	+	3.31115i	−1.38245	+	1.04708i
$11$	−2.26620	+	2.51687i	−0.683286	+	0.758866i	−0.980623	−	0.195907i	$-0.937235\pi$
$11$	−2.26620	+	2.51687i	−0.683286	+	0.758866i	0.297336	+	0.954773i	$0.403902\pi$
$12$	−0.630373	+	12.0282i	−0.181973	+	3.47225i
$13$	−0.306584	−	0.601706i	−0.0850312	−	0.166883i	0.844575	−	0.535437i	$-0.179853\pi$
$13$	−0.306584	−	0.601706i	−0.0850312	−	0.166883i	−0.929606	+	0.368554i	$0.879853\pi$
$14$	−2.49113	+	5.99166i	−0.665783	+	1.60134i
$15$	−6.07245	+	2.84978i	−1.56790	+	0.735810i
$16$	−2.73729	−	3.04006i	−0.684322	−	0.760016i
$17$	2.21216	−	1.79137i	0.536528	−	0.434472i	−0.322373	−	0.946613i	$-0.604481\pi$
$17$	2.21216	−	1.79137i	0.536528	−	0.434472i	0.858902	+	0.512140i	$0.171147\pi$
$18$	−3.80811	+	14.2121i	−0.897581	+	3.34982i
$19$	2.91018	−	1.29570i	0.667641	−	0.297253i	−0.0447886	−	0.998996i	$-0.514261\pi$
$19$	2.91018	−	1.29570i	0.667641	−	0.297253i	0.712430	+	0.701744i	$0.247595\pi$
$20$	3.04997	−	8.44409i	0.681994	−	1.88816i
$21$	−4.50417	+	6.53504i	−0.982891	+	1.42606i
$22$	1.29940	−	8.20407i	0.277032	−	1.74911i
$23$	2.89634	+	4.45997i	0.603928	+	0.929967i	0.999931	+	0.0117182i	$0.00373012\pi$
$23$	2.89634	+	4.45997i	0.603928	+	0.929967i	−0.396004	+	0.918249i	$0.629603\pi$
$24$	−7.41291	−	12.8395i	−1.51315	−	2.62086i
$25$	4.94787	−	0.720139i	0.989574	−	0.144028i
$26$	1.43435	+	0.828123i	0.281299	+	0.162408i
$27$	−4.08462	+	8.01652i	−0.786086	+	1.54278i
$28$	−1.92203	−	10.4476i	−0.363230	−	1.97442i
$29$	5.40952	+	7.44556i	1.00452	+	1.38261i	0.922509	+	0.385975i	$0.126135\pi$
$29$	5.40952	+	7.44556i	1.00452	+	1.38261i	0.0820132	+	0.996631i	$0.473865\pi$
$30$	8.68378	−	13.9731i	1.58543	−	2.55112i
$31$	−5.49728	−	0.577787i	−0.987340	−	0.103774i	−0.402929	−	0.915231i	$-0.632008\pi$
$31$	−5.49728	−	0.577787i	−0.987340	−	0.103774i	−0.584411	+	0.811458i	$0.698674\pi$
$32$	0.143600	+	0.0384776i	0.0253852	+	0.00680194i
$33$	3.64098	−	9.48509i	0.633814	−	1.65114i
$34$	−2.15734	+	6.63961i	−0.369981	+	1.13868i
$35$	4.62582	−	3.68806i	0.781906	−	0.623396i
$36$	−7.44339	−	22.9084i	−1.24056	−	3.81807i
$37$	1.66879	+	0.0874574i	0.274347	+	0.0143779i	0.189013	−	0.981975i	$-0.439471\pi$
$37$	1.66879	+	0.0874574i	0.274347	+	0.0143779i	0.0853336	+	0.996352i	$0.472804\pi$
$38$	−4.25520	+	6.55243i	−0.690284	+	1.06294i
$39$	1.50549	+	1.35555i	0.241072	+	0.217062i
$40$	2.51233	+	10.7617i	0.397235	+	1.70157i
$41$	0.985611	+	0.320244i	0.153927	+	0.0500138i	0.384967	−	0.922930i	$-0.374213\pi$
$41$	0.985611	+	0.320244i	0.153927	+	0.0500138i	−0.231040	+	0.972944i	$0.574213\pi$
$42$	0.535343	−	19.4584i	0.0826052	−	3.00250i
$43$	3.97930	+	3.97930i	0.606838	+	0.606838i	0.942118	−	0.335280i	$-0.108831\pi$
$43$	3.97930	+	3.97930i	0.606838	+	0.606838i	−0.335280	+	0.942118i	$0.608831\pi$
$44$	5.53092	+	12.4227i	0.833818	+	1.87279i
$45$	9.29487	−	9.67247i	1.38560	−	1.44189i
$46$	−11.9149	−	5.30487i	−1.75676	−	0.782160i
$47$	1.73333	−	2.14048i	0.252832	−	0.312221i	−0.634889	−	0.772603i	$-0.718954\pi$
$47$	1.73333	−	2.14048i	0.252832	−	0.312221i	0.887721	+	0.460382i	$0.152288\pi$
$48$	10.9343	+	5.57132i	1.57823	+	0.804150i
$49$	2.52589	−	6.52839i	0.360841	−	0.932627i
$50$	−9.21532	+	8.09044i	−1.30324	+	1.14416i
$51$	−4.26959	+	7.39515i	−0.597862	+	1.03553i
$52$	−2.70772	+	0.141906i	−0.375493	+	0.0196788i
$53$	−1.43467	−	3.73744i	−0.197067	−	0.513377i	0.799065	−	0.601245i	$-0.205328\pi$
$53$	−1.43467	−	3.73744i	−0.197067	−	0.513377i	−0.996132	+	0.0878672i	$0.971995\pi$
$54$	−2.30654	−	21.9453i	−0.313880	−	2.98637i
$55$	−4.64781	+	5.97909i	−0.626711	+	0.806220i
$56$	8.98817	+	9.49673i	1.20109	+	1.26905i
$57$	−6.75735	+	6.75735i	−0.895033	+	0.895033i
$58$	−21.0724	−	8.08892i	−2.76694	−	1.06213i
$59$	1.16618	−	0.247880i	0.151824	−	0.0322713i	−0.131372	−	0.991333i	$-0.541938\pi$
$59$	1.16618	−	0.247880i	0.151824	−	0.0322713i	0.283197	+	0.959062i	$0.408605\pi$
$60$	0.536074	+	26.9275i	0.0692069	+	3.47633i
$61$	−1.21778	+	5.72922i	−0.155921	+	0.733551i	0.828819	+	0.559517i	$0.189013\pi$
$61$	−1.21778	+	5.72922i	−0.155921	+	0.733551i	−0.984740	+	0.174034i	$0.944320\pi$
$62$	12.0791	−	6.15462i	1.53405	−	0.781638i
$63$	3.72578	−	15.4289i	0.469404	−	1.94386i
$64$	7.43442	−	2.41559i	0.929302	−	0.301949i
$65$	−0.780899	−	1.29245i	−0.0968587	−	0.160308i
$66$	5.18072	+	24.3734i	0.637702	+	3.00015i
$67$	4.70495	+	5.81013i	0.574801	+	0.709820i	0.978772	−	0.204952i	$-0.0657038\pi$
$67$	4.70495	+	5.81013i	0.574801	+	0.709820i	−0.403971	+	0.914772i	$0.632370\pi$
$68$	−2.95806	−	11.0396i	−0.358717	−	1.33875i
$69$	−12.9062	−	9.37692i	−1.55373	−	1.12885i
$70$	−4.58845	+	13.7650i	−0.548425	+	1.64523i
$71$	7.96131	−	5.78423i	0.944833	−	0.686462i	−0.00474583	−	0.999989i	$-0.501511\pi$
$71$	7.96131	−	5.78423i	0.944833	−	0.686462i	0.949579	+	0.313527i	$0.101511\pi$
$72$	23.0416	+	18.6587i	2.71548	+	2.19895i
$73$	−0.270517	−	5.16177i	−0.0316616	−	0.604140i	−0.967679	−	0.252186i	$-0.918851\pi$
$73$	−0.270517	−	5.16177i	−0.0316616	−	0.604140i	0.936017	−	0.351954i	$-0.114483\pi$
$74$	−3.54935	+	2.04922i	−0.412603	+	0.238217i
$75$	−13.0829	+	7.33606i	−1.51068	+	0.847096i
$76$		−	12.7904i		−	1.46716i
$77$	−1.18137	+	8.88238i	−0.134629	+	1.01224i
$78$	−4.90734	−	0.777246i	−0.555647	−	0.0880058i
$79$	3.95313	−	0.415491i	0.444762	−	0.0467464i	0.120499	−	0.992713i	$-0.461550\pi$
$79$	3.95313	−	0.415491i	0.444762	−	0.0467464i	0.324263	+	0.945967i	$0.394884\pi$
$80$	−6.59560	−	6.33812i	−0.737411	−	0.708623i
$81$	0.939990	−	8.94341i	0.104443	−	0.993712i
$82$	−2.45507	+	0.657835i	−0.271117	+	0.0726457i
$83$	−7.87661	+	1.24753i	−0.864570	+	0.136934i	−0.572941	−	0.819597i	$-0.694197\pi$
$83$	−7.87661	+	1.24753i	−0.864570	+	0.136934i	−0.291629	+	0.956531i	$0.594197\pi$
$84$	16.6146	+	27.1935i	1.81281	+	2.96705i
$85$	4.64442	−	4.35233i	0.503758	−	0.472077i
$86$	−13.5004	−	2.86961i	−1.45579	−	0.309438i
$87$	−23.1544	−	15.0366i	−2.48241	−	1.61210i
$88$	−14.0377	−	9.11621i	−1.49643	−	0.971791i
$89$	−12.1194	−	2.57605i	−1.28465	−	0.273061i	−0.485523	−	0.874224i	$-0.661371\pi$
$89$	−12.1194	−	2.57605i	−1.28465	−	0.273061i	−0.799126	+	0.601163i	$0.794704\pi$
$90$	−6.19844	+	32.3110i	−0.653373	+	3.40588i
$91$	−1.56905	−	0.854621i	−0.164482	−	0.0895886i
$92$	21.0890	−	3.34017i	2.19868	−	0.348237i
$93$	16.0169	−	4.29172i	1.66088	−	0.445030i
$94$	−0.706097	+	6.71806i	−0.0728283	+	0.692915i
$95$	6.28119	−	3.35955i	0.644436	−	0.344682i
$96$	−0.443535	+	0.0466174i	−0.0452681	+	0.00475786i
$97$	16.7616	+	2.65478i	1.70189	+	0.269552i	0.930361	−	0.366646i	$-0.119494\pi$
$97$	16.7616	+	2.65478i	1.70189	+	0.269552i	0.771526	+	0.636198i	$0.219494\pi$
$98$	3.52490	+	16.8022i	0.356069	+	1.69728i
$99$			20.3180i			2.04203i
$100$	5.43885	−	19.3247i	0.543885	−	1.93247i
$101$	1.88364	−	1.08752i	0.187429	−	0.108212i	−0.403349	−	0.915046i	$-0.632154\pi$
$101$	1.88364	−	1.08752i	0.187429	−	0.108212i	0.590778	+	0.806834i	$0.298821\pi$
$102$	−1.09607	−	20.9142i	−0.108527	−	2.07082i
$103$	−1.91991	−	1.55471i	−0.189175	−	0.153191i	0.530054	−	0.847964i	$-0.322171\pi$
$103$	−1.91991	−	1.55471i	−0.189175	−	0.153191i	−0.719229	+	0.694773i	$0.755505\pi$
$104$	2.70009	−	1.96173i	0.264766	−	0.192363i
$105$	−8.99027	+	15.3018i	−0.877360	+	1.49331i
$106$	7.94332	+	5.77116i	0.771523	+	0.560544i
$107$	0.463175	+	1.72859i	0.0447768	+	0.167109i	0.984694	−	0.174294i	$-0.0557644\pi$
$107$	0.463175	+	1.72859i	0.0447768	+	0.167109i	−0.939917	+	0.341404i	$0.889098\pi$
$108$	22.7338	+	28.0740i	2.18756	+	2.70142i
$109$	−0.511076	−	2.40442i	−0.0489522	−	0.230302i	0.946870	−	0.321617i	$-0.104226\pi$
$109$	−0.511076	−	2.40442i	−0.0489522	−	0.230302i	−0.995822	+	0.0913149i	$0.970893\pi$
$110$	1.57341	−	18.5068i	0.150019	−	1.76455i
$111$	−4.76765	+	1.54910i	−0.452525	+	0.147034i
$112$	−10.5209	−	2.54059i	−0.994128	−	0.240063i
$113$	−1.65922	+	0.845414i	−0.156086	+	0.0795298i	−0.530289	−	0.847817i	$-0.677916\pi$
$113$	−1.65922	+	0.845414i	−0.156086	+	0.0795298i	0.374203	+	0.927347i	$0.377916\pi$
$114$	4.87294	−	22.9254i	0.456393	−	2.14716i
$115$	7.17956	+	9.47915i	0.669497	+	0.883935i
$116$	36.1443	−	7.68272i	3.35592	−	0.713322i
$117$	−3.78222	−	1.45186i	−0.349667	−	0.134225i
$118$	−2.06761	+	2.06761i	−0.190339	+	0.190339i
$119$	2.14854	−	7.21821i	0.196956	−	0.661693i
$120$	−18.6055	−	27.4383i	−1.69844	−	2.50477i
$121$	−0.0491635	−	0.467760i	−0.00446941	−	0.0425236i
$122$	−5.14803	−	13.4111i	−0.466081	−	1.21418i
$123$	−3.10460	+	0.162705i	−0.279932	+	0.0146706i
$124$	−11.0968	+	19.2203i	−0.996526	+	1.72603i
$125$	10.9186	−	2.40491i	0.976592	−	0.215102i
$126$	12.9458	+	36.7124i	1.15330	+	3.27060i
$127$	−10.4896	−	5.34472i	−0.930802	−	0.474268i	−0.0782643	−	0.996933i	$-0.524938\pi$
$127$	−10.4896	−	5.34472i	−0.930802	−	0.474268i	−0.852538	+	0.522665i	$0.824938\pi$
$128$	−12.2523	+	15.1303i	−1.08296	+	1.33734i
$129$	−15.4225	−	6.86652i	−1.35787	−	0.604564i
$130$	3.33263	+	1.61533i	0.292291	+	0.141674i
$131$	−5.57632	−	12.5246i	−0.487206	−	1.09428i	−0.975178	−	0.221423i	$-0.928930\pi$
$131$	−5.57632	−	12.5246i	−0.487206	−	1.09428i	0.487972	−	0.872859i	$-0.337737\pi$
$132$	−28.8450	−	28.8450i	−2.51064	−	2.51064i
$133$	4.41328	−	7.18044i	0.382680	−	0.622623i
$134$	−17.4386	−	5.66613i	−1.50646	−	0.489479i
$135$	−7.81539	+	18.5382i	−0.672642	+	1.59551i
$136$	10.4546	+	9.41332i	0.896470	+	0.807186i
$137$	−7.30590	+	11.2501i	−0.624185	+	0.961160i	0.375229	+	0.926932i	$0.377564\pi$
$137$	−7.30590	+	11.2501i	−0.624185	+	0.961160i	−0.999414	+	0.0342283i	$0.989103\pi$
$138$	39.0722	+	2.04769i	3.32604	+	0.174311i
$139$	−3.08285	−	9.48803i	−0.261484	−	0.804764i	−0.992483	−	0.122385i	$-0.960946\pi$
$139$	−3.08285	−	9.48803i	−0.261484	−	0.804764i	0.730999	−	0.682379i	$-0.239054\pi$
$140$	−5.97335	−	22.9903i	−0.504840	−	1.94304i
$141$	−2.55324	+	7.85808i	−0.215022	+	0.661770i
$142$	−8.64923	+	22.5320i	−0.725827	+	1.89084i
$143$	2.20920	+	0.591954i	0.184743	+	0.0495016i
$144$	−24.4071	−	2.56529i	−2.03392	−	0.213774i
$145$	13.2666	+	15.7320i	1.10173	+	1.30647i
$146$	7.45134	+	10.2559i	0.616678	+	0.848784i
$147$	−0.0556580	+	20.9990i	−0.00459060	+	1.73197i
$148$	3.04607	−	5.97824i	0.250385	−	0.491408i
$149$	−20.0681	−	11.5863i	−1.64404	−	0.949187i	−0.979376	−	0.202044i	$-0.935242\pi$
$149$	−20.0681	−	11.5863i	−1.64404	−	0.949187i	−0.664663	−	0.747143i	$-0.731425\pi$
$150$	17.1109	−	32.5652i	1.39710	−	2.65894i
$151$	−4.39641	−	7.61480i	−0.357775	−	0.619684i	0.629814	−	0.776746i	$-0.283131\pi$
$151$	−4.39641	−	7.61480i	−0.357775	−	0.619684i	−0.987589	+	0.157062i	$0.949798\pi$
$152$	8.57464	+	13.2038i	0.695495	+	1.07097i
$153$	2.67140	−	16.8666i	0.215970	−	1.36358i
$154$	−9.43483	−	19.8482i	−0.760280	−	1.59941i
$155$	−12.3535	−	0.401067i	−0.992256	−	0.0322145i
$156$	7.43072	−	3.30837i	0.594934	−	0.264882i
$157$	3.42049	−	12.7655i	0.272985	−	1.01879i	−0.684195	−	0.729299i	$-0.739846\pi$
$157$	3.42049	−	12.7655i	0.272985	−	1.01879i	0.957180	−	0.289495i	$-0.0934872\pi$
$158$	−7.57619	+	6.13508i	−0.602729	+	0.488080i
$159$	8.03592	+	8.92479i	0.637290	+	0.707782i
$160$	0.326474	+	0.0626297i	0.0258100	+	0.00495131i
$161$	12.9917	+	5.40152i	1.02389	+	0.425699i
$162$	10.0128	+	19.6513i	0.786682	+	1.54395i
$163$	−0.627122	+	11.9662i	−0.0491200	+	0.937264i	0.857282	+	0.514848i	$0.172151\pi$
$163$	−0.627122	+	11.9662i	−0.0491200	+	0.937264i	−0.906402	+	0.422417i	$0.861182\pi$
$164$	2.78424	−	3.09221i	0.217412	−	0.241461i
$165$	6.58888	−	21.7418i	0.512943	−	1.69260i
$166$	14.5350	−	13.0873i	1.12813	−	1.01577i
$167$	−3.54656	−	22.3921i	−0.274441	−	1.73275i	−0.611480	−	0.791260i	$-0.709425\pi$
$167$	−3.54656	−	22.3921i	−0.274441	−	1.73275i	0.337039	−	0.941491i	$-0.390575\pi$
$168$	−35.3819	−	16.9339i	−2.72977	−	1.30648i
$169$	7.37315	−	10.1483i	0.567166	−	0.780636i
$170$	−3.73940	+	15.1562i	−0.286799	+	1.16242i
$171$	7.77312	−	17.4587i	0.594425	−	1.33510i
$172$	21.0945	−	8.09743i	1.60844	−	0.617423i
$173$	−3.53491	+	2.29560i	−0.268754	+	0.174531i	−0.671980	−	0.740570i	$-0.734556\pi$
$173$	−3.53491	+	2.29560i	−0.268754	+	0.174531i	0.403225	+	0.915101i	$0.367889\pi$
$174$	67.7116			5.13320
$175$	9.72121	−	8.97207i	0.734855	−	0.678225i
$176$	13.8547			1.04434
$177$	−2.99955	+	1.94793i	−0.225460	+	0.146415i
$178$	28.3693	−	10.8899i	2.12637	−	0.816236i
$179$	1.77870	−	3.99502i	0.132946	−	0.298602i	−0.834790	−	0.550569i	$-0.814411\pi$
$179$	1.77870	−	3.99502i	0.132946	−	0.298602i	0.967736	+	0.251967i	$0.0810775\pi$
$180$	−20.2990	−	49.8893i	−1.51300	−	3.71853i
$181$	−14.5835	+	20.0725i	−1.08399	+	1.49198i	−0.228931	+	0.973443i	$0.573523\pi$
$181$	−14.5835	+	20.0725i	−1.08399	+	1.49198i	−0.855056	+	0.518536i	$0.826477\pi$
$182$	4.36896	−	0.338019i	0.323849	−	0.0250556i
$183$	−2.74868	−	17.3545i	−0.203189	−	1.28288i
$184$	−19.5313	+	17.5861i	−1.43987	+	1.29646i
$185$	3.73590	−	0.0743745i	0.274669	−	0.00546812i
$186$	−27.2124	+	30.2225i	−1.99531	+	2.21602i
$187$	−0.504548	+	9.62736i	−0.0368962	+	0.704022i
$188$	−5.02055	−	9.85338i	−0.366161	−	0.718632i
$189$	3.07579	+	23.6047i	0.223731	+	1.71699i
$190$	−8.43219	+	15.3004i	−0.611735	+	1.11001i
$191$	−10.4526	−	11.6088i	−0.756327	−	0.839986i	0.234919	−	0.972015i	$-0.424517\pi$
$191$	−10.4526	−	11.6088i	−0.756327	−	0.839986i	−0.991246	+	0.132029i	$0.957851\pi$
$192$	−18.2240	+	14.7575i	−1.31521	+	1.06503i
$193$	−5.29344	+	19.7554i	−0.381030	+	1.42202i	0.463301	+	0.886201i	$0.346665\pi$
$193$	−5.29344	+	19.7554i	−0.381030	+	1.42202i	−0.844331	+	0.535822i	$0.820002\pi$
$194$	−38.0231	+	16.9290i	−2.72990	+	1.21543i
$195$	3.57645	+	2.78013i	0.256115	+	0.199089i
$196$	−19.8210	−	19.9263i	−1.41578	−	1.42331i
$197$	−2.13257	+	13.4645i	−0.151939	+	0.959306i	0.787431	+	0.616402i	$0.211410\pi$
$197$	−2.13257	+	13.4645i	−0.151939	+	0.959306i	−0.939371	+	0.342904i	$0.888590\pi$
$198$	−27.1400	−	41.7920i	−1.92876	−	2.97003i
$199$	10.9166	+	18.9082i	0.773859	+	1.34036i	0.935434	+	0.353503i	$0.115009\pi$
$199$	10.9166	+	18.9082i	0.773859	+	1.34036i	−0.161574	+	0.986861i	$0.551657\pi$
$200$	7.34055	+	23.5954i	0.519055	+	1.66844i
$201$	−19.4229	−	11.2138i	−1.36999	−	0.790964i
$202$	−2.42178	+	4.75301i	−0.170396	+	0.334421i
$203$	22.9420	+	8.15842i	1.61021	+	0.572609i
$204$	20.1526	+	27.7377i	1.41096	+	1.94203i
$205$	2.24984	+	0.555093i	0.157136	+	0.0387694i
$206$	6.02580	+	0.633337i	0.419837	+	0.0441267i
$207$	30.8160	+	8.25712i	2.14186	+	0.573910i
$208$	−0.990015	+	2.57908i	−0.0686452	+	0.178827i
$209$	−3.33396	+	10.2609i	−0.230615	+	0.709759i
$210$	−1.94761	−	43.4832i	−0.134398	−	3.00063i
$211$	2.71073	+	8.34277i	0.186614	+	0.574340i	0.999972	−	0.00742360i	$-0.00236303\pi$
$211$	2.71073	+	8.34277i	0.186614	+	0.574340i	−0.813358	+	0.581763i	$0.802363\pi$
$212$	−16.0518	−	0.841238i	−1.10244	−	0.0577765i
$213$	−16.0782	+	24.7582i	−1.10166	+	1.69641i
$214$	−3.26170	−	2.93685i	−0.222965	−	0.200759i
$215$	9.51723	+	8.23231i	0.649069	+	0.561439i
$216$	−42.2891	−	13.7406i	−2.87741	−	0.934927i
$217$	−12.8615	+	6.96119i	−0.873098	+	0.472556i
$218$	4.26298	+	4.26298i	0.288725	+	0.288725i
$219$	6.30681	+	14.1653i	0.426174	+	0.957204i
$220$	14.3409	+	26.8124i	0.966861	+	1.80769i
$221$	−1.75610	−	0.781864i	−0.118128	−	0.0525939i
$222$	7.73733	−	9.55481i	0.519296	−	0.641277i
$223$	7.97499	+	4.06346i	0.534045	+	0.272109i	0.700146	−	0.713999i	$-0.253118\pi$
$223$	7.97499	+	4.06346i	0.534045	+	0.272109i	−0.166102	+	0.986109i	$0.553118\pi$
$224$	0.370946	−	0.130806i	0.0247849	−	0.00873983i
$225$	19.1681	−	23.0725i	1.27787	−	1.53817i
$226$	2.28357	−	3.95525i	0.151901	−	0.263100i
$227$	16.8189	−	0.881441i	1.11631	−	0.0585033i	0.514756	−	0.857336i	$-0.327882\pi$
$227$	16.8189	−	0.881441i	1.11631	−	0.0585033i	0.601553	+	0.798833i	$0.294549\pi$
$228$	13.7504	+	35.8211i	0.910645	+	2.37231i
$229$	−0.00668509	−	0.0636044i	−0.000441763	−	0.00420309i	0.994299	−	0.106630i	$-0.0340060\pi$
$229$	−0.00668509	−	0.0636044i	−0.000441763	−	0.00420309i	−0.994741	+	0.102427i	$0.967339\pi$
$230$	−27.4295	−	9.90743i	−1.80865	−	0.653277i
$231$	−6.24050	−	26.1462i	−0.410595	−	1.72029i
$232$	−32.1619	+	32.1619i	−2.11153	+	2.11153i
$233$	−17.3318	−	6.65304i	−1.13544	−	0.435855i	−0.283230	−	0.959052i	$-0.591406\pi$
$233$	−17.3318	−	6.65304i	−1.13544	−	0.435855i	−0.852212	+	0.523197i	$0.824739\pi$
$234$	9.71899	−	2.06584i	0.635351	−	0.135048i
$235$	3.52014	−	5.05361i	0.229629	−	0.329661i
$236$	0.995263	−	4.68234i	0.0647861	−	0.304795i
$237$	−10.6245	+	5.41346i	−0.690137	+	0.351642i
$238$	5.22251	+	17.7171i	0.338525	+	1.14843i
$239$	−6.24077	+	2.02775i	−0.403682	+	0.131164i	−0.503819	−	0.863810i	$-0.668072\pi$
$239$	−6.24077	+	2.02775i	−0.403682	+	0.131164i	0.100137	+	0.994974i	$0.468072\pi$
$240$	25.2856	+	10.6600i	1.63218	+	0.688099i
$241$	−0.917290	−	4.31551i	−0.0590879	−	0.277987i	0.938678	−	0.344795i	$-0.112052\pi$
$241$	−0.917290	−	4.31551i	−0.0590879	−	0.277987i	−0.997766	+	0.0668086i	$0.978718\pi$
$242$	0.725941	+	0.896463i	0.0466653	+	0.0576268i
$243$	−0.00379321	−	0.0141564i	−0.000243334	−	0.000908136i
$244$	19.0259	+	13.8231i	1.21801	+	0.884933i
$245$	4.57931	−	14.9676i	0.292561	−	0.956247i
$246$	6.16850	−	4.48168i	0.393289	−	0.285741i
$247$	−1.67184	−	1.35383i	−0.106377	−	0.0861423i
$248$	−1.42972	−	27.2807i	−0.0907873	−	1.73232i
$249$	20.7182	−	11.9616i	1.31296	−	0.758038i
$250$	−19.2461	+	19.5314i	−1.21723	+	1.23527i
$251$			4.66639i			0.294540i	0.989096	+	0.147270i	$0.0470486\pi$
$251$			4.66639i			0.294540i	−0.989096	+	0.147270i	$0.952951\pi$
$252$	−50.5082	−	38.8628i	−3.18172	−	2.44812i
$253$	−17.7889	−	2.81748i	−1.11838	−	0.177133i
$254$	28.7154	−	3.01811i	1.80176	−	0.189373i
$255$	−8.32823	+	17.1822i	−0.521534	+	1.07599i
$256$	3.35696	−	31.9393i	0.209810	−	1.99621i
$257$	−7.00253	+	1.87632i	−0.436806	+	0.117042i	−0.470519	−	0.882390i	$-0.655933\pi$
$257$	−7.00253	+	1.87632i	−0.436806	+	0.117042i	0.0337134	+	0.999432i	$0.489267\pi$
$258$	40.8945	−	6.47705i	2.54598	−	0.403244i
$259$	3.77280	−	2.30510i	0.234430	−	0.143232i
$260$	−6.01593	+	0.753642i	−0.373092	+	0.0467389i
$261$	54.0053	+	11.4792i	3.34285	+	0.710544i
$262$	28.1999	+	18.3132i	1.74220	+	1.13139i
$263$	−9.39360	−	6.10027i	−0.579234	−	0.376159i	0.221517	−	0.975157i	$-0.428899\pi$
$263$	−9.39360	−	6.10027i	−0.579234	−	0.376159i	−0.800751	+	0.598998i	$0.795566\pi$
$264$	49.1147	+	10.4396i	3.02280	+	0.642516i
$265$	−3.80306	−	8.10374i	−0.233620	−	0.497809i
$266$	0.513717	+	20.6645i	0.0314980	+	1.26702i
$267$	36.7110	−	5.81446i	2.24668	−	0.355839i
$268$	28.9950	−	7.76918i	1.77115	−	0.474578i
$269$	−0.746059	+	7.09828i	−0.0454880	+	0.432790i	0.947950	+	0.318419i	$0.103152\pi$
$269$	−0.746059	+	7.09828i	−0.0454880	+	0.432790i	−0.993438	+	0.114371i	$0.963515\pi$
$270$	−8.68717	−	48.5706i	−0.528684	−	2.95591i
$271$	17.2157	−	1.80944i	1.04578	−	0.109916i	0.433975	−	0.900925i	$-0.357111\pi$
$271$	17.2157	−	1.80944i	1.04578	−	0.109916i	0.611804	+	0.791009i	$0.290444\pi$
$272$	−11.5012	−	1.82161i	−0.697364	−	0.110452i
$273$	5.31308	+	0.706645i	0.321562	+	0.0427681i
$274$		−	32.8993i		−	1.98752i
$275$	−9.40038	+	14.0851i	−0.566864	+	0.849366i
$276$	−55.4713	+	32.0264i	−3.33898	+	1.92776i
$277$	−0.740253	−	14.1249i	−0.0444775	−	0.848681i	−0.926228	−	0.376964i	$-0.876968\pi$
$277$	−0.740253	−	14.1249i	−0.0444775	−	0.848681i	0.881750	−	0.471717i	$-0.156365\pi$
$278$	19.0149	+	15.3979i	1.14044	+	0.923507i
$279$	−26.8277	+	19.4915i	−1.60613	+	1.16692i
$280$	21.5789	+	19.7288i	1.28959	+	1.17902i
$281$	8.33513	+	6.05583i	0.497232	+	0.361260i	0.807959	−	0.589239i	$-0.200572\pi$
$281$	8.33513	+	6.05583i	0.497232	+	0.361260i	−0.310727	+	0.950499i	$0.600572\pi$
$282$	−5.24478	−	19.5738i	−0.312322	−	1.16560i
$283$	−1.85478	−	2.29046i	−0.110255	−	0.136154i	0.719031	−	0.694978i	$-0.244586\pi$
$283$	−1.85478	−	2.29046i	−0.110255	−	0.136154i	−0.829286	+	0.558824i	$0.811253\pi$
$284$	−8.21489	−	38.6480i	−0.487464	−	2.29334i
$285$	−13.9795	+	16.1614i	−0.828073	+	0.957320i
$286$	−5.33481	+	1.73339i	−0.315454	+	0.102497i
$287$	2.63000	−	0.775251i	0.155244	−	0.0457616i
$288$	0.794666	−	0.404903i	0.0468261	−	0.0238591i
$289$	−1.84985	+	8.70288i	−0.108815	+	0.511934i
$290$	−48.3022	−	14.6380i	−2.83640	−	0.859575i
$291$	−49.7969	+	10.5847i	−2.91915	+	0.620484i
$292$	−19.3750	−	7.43738i	−1.13384	−	0.435240i
$293$	7.38784	−	7.38784i	0.431602	−	0.431602i	−0.457571	−	0.889173i	$-0.651280\pi$
$293$	7.38784	−	7.38784i	0.431602	−	0.431602i	0.889173	+	0.457571i	$0.151280\pi$
$294$	−27.9352	−	43.2671i	−1.62921	−	2.52339i
$295$	2.56084	−	0.741110i	0.149098	−	0.0431491i
$296$	0.863273	+	8.21350i	0.0501767	+	0.477400i
$297$	−10.9200	−	28.4475i	−0.633642	−	1.65069i
$298$	56.7545	−	2.97438i	3.28770	−	0.172301i
$299$	1.79562	−	3.11010i	0.103843	−	0.179862i
$300$	5.54301	+	59.9681i	0.320026	+	3.46226i
$301$	14.6363	+	2.73274i	0.843620	+	0.157512i
$302$	19.2145	+	9.79030i	1.10567	+	0.563368i
$303$	−4.10620	+	5.07074i	−0.235895	+	0.291306i
$304$	−11.9050	−	5.30044i	−0.682798	−	0.304001i
$305$	−1.79096	+	12.9741i	−0.102550	+	0.742894i
$306$	17.0350	+	38.2612i	0.973825	+	2.18725i
$307$	−19.3045	−	19.3045i	−1.10176	−	1.10176i	−0.994198	−	0.107567i	$-0.965694\pi$
$307$	−19.3045	−	19.3045i	−1.10176	−	1.10176i	−0.107567	−	0.994198i	$-0.534306\pi$
$308$	30.6511	+	18.8389i	1.74651	+	1.07345i
$309$	7.04834	+	2.29014i	0.400966	+	0.130282i
$310$	25.9456	−	15.6764i	1.47361	−	0.890360i
$311$	0.971602	+	0.874834i	0.0550945	+	0.0496073i	0.696218	−	0.717830i	$-0.254865\pi$
$311$	0.971602	+	0.874834i	0.0550945	+	0.0496073i	−0.641123	+	0.767438i	$0.721531\pi$
$312$	−5.45294	+	8.39680i	−0.308712	+	0.475375i
$313$	−14.0218	−	0.734854i	−0.792562	−	0.0415364i	−0.348242	−	0.937405i	$-0.613221\pi$
$313$	−14.0218	−	0.734854i	−0.792562	−	0.0415364i	−0.444320	+	0.895868i	$0.646555\pi$
$314$	10.0160	+	30.8262i	0.565238	+	1.73962i
$315$	5.81836	−	35.0115i	0.327828	−	1.97267i
$316$	4.93180	−	15.1785i	0.277435	−	0.853858i
$317$	10.4456	−	27.2117i	0.586684	−	1.52836i	−0.242940	−	0.970041i	$-0.578112\pi$
$317$	10.4456	−	27.2117i	0.586684	−	1.52836i	0.829624	−	0.558323i	$-0.188555\pi$
$318$	−28.4505	−	7.62328i	−1.59542	−	0.427492i
$319$	−30.9986	−	3.25809i	−1.73559	−	0.182418i
$320$	16.1905	−	6.58760i	0.905075	−	0.368258i
$321$	−3.15551	−	4.34318i	−0.176123	−	0.242413i
$322$	−33.9377	+	6.24348i	−1.89128	+	0.347935i
$323$	4.11672	−	8.07951i	0.229060	−	0.449556i
$324$	−31.2691	−	18.0532i	−1.73717	−	1.00296i
$325$	−1.95025	−	2.75638i	−0.108180	−	0.152896i
$326$	−14.6941	−	25.4509i	−0.813831	−	1.40960i
$327$	4.01622	+	6.18443i	0.222097	+	0.342000i
$328$	−0.801215	+	5.05867i	−0.0442397	+	0.279318i
$329$	0.581370	−	7.26392i	0.0320520	−	0.400473i
$330$	15.4893	+	53.5218i	0.852656	+	2.94628i
$331$	−7.70814	+	3.43189i	−0.423678	+	0.188634i	−0.607489	−	0.794328i	$-0.707823\pi$
$331$	−7.70814	+	3.43189i	−0.423678	+	0.188634i	0.183811	+	0.982962i	$0.441157\pi$
$332$	−8.28727	+	30.9285i	−0.454823	+	1.69742i
$333$	7.79097	−	6.30900i	0.426942	−	0.345731i
$334$	37.2055	+	41.3208i	2.03579	+	2.26098i
$335$	11.4312	+	12.1983i	0.624551	+	0.666465i
$336$	32.1962	−	4.19530i	1.75644	−	0.228873i
$337$	−10.0363	−	19.6973i	−0.546710	−	1.07298i	−0.984742	−	0.174019i	$-0.944324\pi$
$337$	−10.0363	−	19.6973i	−0.546710	−	1.07298i	0.438032	−	0.898959i	$-0.355676\pi$
$338$	−1.61011	+	30.7228i	−0.0875785	+	1.67110i
$339$	3.73796	−	4.15143i	0.203018	−	0.225475i
$340$	−8.37950	−	24.1434i	−0.454442	−	1.30936i
$341$	13.9122	−	12.5266i	0.753386	−	0.678352i
$342$	7.33222	+	46.2938i	0.396481	+	2.50328i
$343$	−4.25184	−	18.0256i	−0.229578	−	0.973290i
$344$	−16.3478	+	22.5008i	−0.881412	+	1.21316i
$345$	−30.2978	−	18.8290i	−1.63118	−	1.01372i
$346$	4.20457	−	9.44361i	0.226039	−	0.507692i
$347$	−17.2043	+	6.60411i	−0.923575	+	0.354527i	−0.773244	−	0.634109i	$-0.781367\pi$
$347$	−17.2043	+	6.60411i	−0.923575	+	0.354527i	−0.150331	+	0.988636i	$0.548034\pi$
$348$	−92.9670	+	60.3735i	−4.98356	+	3.23636i
$349$	−30.5633			−1.63602			−0.818008	−	0.575207i	$-0.804922\pi$
$349$	−30.5633			−1.63602			−0.818008	+	0.575207i	$0.804922\pi$
$350$	−8.01097	+	31.4399i	−0.428204	+	1.68053i
$351$	6.07587			0.324306
$352$	−0.422271	+	0.274226i	−0.0225071	+	0.0146163i
$353$	−23.5980	+	9.05843i	−1.25600	+	0.482131i	−0.893167	−	0.449725i	$-0.851522\pi$
$353$	−23.5980	+	9.05843i	−1.25600	+	0.482131i	−0.362828	+	0.931856i	$0.618189\pi$
$354$	3.56779	−	8.01339i	0.189626	−	0.425907i
$355$	16.8217	−	14.1855i	0.892803	−	0.752889i
$356$	−29.2408	+	40.2466i	−1.54976	+	2.13306i
$357$	1.74274	+	22.5252i	0.0922356	+	1.19216i
$358$	1.67781	+	10.5933i	0.0886749	+	0.559872i
$359$	26.1396	−	23.5362i	1.37960	−	1.24220i	0.440854	−	0.897579i	$-0.354676\pi$
$359$	26.1396	−	23.5362i	1.37960	−	1.24220i	0.938743	−	0.344617i	$-0.111991\pi$
$360$	54.4005	+	37.8932i	2.86716	+	1.99715i
$361$	−5.92316	+	6.57834i	−0.311745	+	0.346228i
$362$	3.18468	−	60.7673i	0.167383	−	3.19386i
$363$	0.640556	+	1.25716i	0.0336205	+	0.0659839i
$364$	−5.69713	+	4.35958i	−0.298611	+	0.228504i
$365$	−1.43668	−	11.4683i	−0.0751994	−	0.600277i
$366$	28.8353	+	32.0249i	1.50725	+	1.67397i
$367$	−1.78783	+	1.44775i	−0.0933237	+	0.0755721i	−0.674847	−	0.737958i	$-0.735790\pi$
$367$	−1.78783	+	1.44775i	−0.0933237	+	0.0755721i	0.581523	+	0.813530i	$0.302457\pi$
$368$	5.63048	−	21.0133i	0.293509	−	1.09539i
$369$	5.67965	−	2.52874i	0.295671	−	0.131641i
$370$	−7.58502	+	5.14327i	−0.394327	+	0.267386i
$371$	−8.72106	−	6.01085i	−0.452775	−	0.312068i
$372$	10.4151	−	65.7584i	0.539998	−	3.40941i
$373$	7.12428	+	10.9704i	0.368881	+	0.568028i	0.973557	−	0.228444i	$-0.0733639\pi$
$373$	7.12428	+	10.9704i	0.368881	+	0.568028i	−0.604676	+	0.796472i	$0.706697\pi$
$374$	−11.8221	−	20.4764i	−0.611305	−	1.05881i
$375$	−27.9935	+	18.4733i	−1.44558	+	0.953960i
$376$	11.7884	+	6.80606i	0.607942	+	0.350996i
$377$	2.82156	−	5.53763i	0.145318	−	0.285203i
$378$	−37.8569	−	44.4439i	−1.94715	−	2.28595i
$379$	−11.2000	−	15.4155i	−0.575307	−	0.791842i	0.417864	−	0.908510i	$-0.362779\pi$
$379$	−11.2000	−	15.4155i	−0.575307	−	0.791842i	−0.993171	+	0.116667i	$0.962779\pi$
$380$	−2.06501	−	28.5257i	−0.105933	−	1.46334i
$381$	35.1232	+	3.69160i	1.79942	+	0.189126i
$382$	37.0067	+	9.91592i	1.89343	+	0.507342i
$383$	−7.36088	+	19.1758i	−0.376124	+	0.979836i	0.606641	+	0.794976i	$0.292516\pi$
$383$	−7.36088	+	19.1758i	−0.376124	+	0.979836i	−0.982765	+	0.184860i	$0.940817\pi$
$384$	18.0480	−	55.5461i	0.921009	−	2.83457i
$385$	−1.20066	+	20.0005i	−0.0611914	+	1.01932i
$386$	−15.5005	−	47.7056i	−0.788954	−	2.42815i
$387$	33.7147	+	1.76691i	1.71381	+	0.0898171i
$388$	37.1109	−	57.1458i	1.88402	−	2.90114i
$389$	29.1119	+	26.2125i	1.47603	+	1.32903i	0.816491	+	0.577357i	$0.195916\pi$
$389$	29.1119	+	26.2125i	1.47603	+	1.32903i	0.659541	+	0.751668i	$0.270751\pi$
$390$	−11.0700	−	0.941152i	−0.560551	−	0.0476571i
$391$	14.3966	+	4.67775i	0.728069	+	0.236564i
$392$	33.8200	+	7.28240i	1.70817	+	0.367817i
$393$	29.0818	+	29.0818i	1.46698	+	1.46698i
$394$	−13.5989	−	30.5437i	−0.685105	−	1.53877i
$395$	8.74932	−	1.56487i	0.440226	−	0.0787372i
$396$	74.5258	+	33.1810i	3.74506	+	1.66741i
$397$	−9.52845	+	11.7667i	−0.478219	+	0.590552i	−0.957975	−	0.286850i	$-0.907392\pi$
$397$	−9.52845	+	11.7667i	−0.478219	+	0.590552i	0.479756	+	0.877402i	$0.340725\pi$
$398$	−47.7112	−	24.3101i	−2.39155	−	1.21855i
$399$	−4.64053	+	24.8542i	−0.232317	+	1.24427i
$400$	−15.7330	−	13.0706i	−0.786650	−	0.653531i
$401$	11.4812	−	19.8860i	0.573343	−	0.993059i	−0.422877	−	0.906187i	$-0.638980\pi$
$401$	11.4812	−	19.8860i	0.573343	−	0.993059i	0.996220	−	0.0868716i	$-0.0276870\pi$
$402$	54.9301	−	2.87876i	2.73966	−	0.143580i
$403$	1.33772	+	3.48488i	0.0666367	+	0.173594i
$404$	−0.912846	−	8.68515i	−0.0454158	−	0.432102i
$405$	0.652487	−	20.0976i	0.0324224	−	0.998660i
$406$	−58.0871	+	13.8641i	−2.88281	+	0.688063i
$407$	−4.00193	+	4.00193i	−0.198368	+	0.198368i
$408$	−39.3990	−	15.1239i	−1.95054	−	0.748743i
$409$	−22.4108	+	4.76357i	−1.10814	+	0.235543i	−0.725411	−	0.688315i	$-0.758350\pi$
$409$	−22.4108	+	4.76357i	−1.10814	+	0.235543i	−0.382733	+	0.923859i	$0.625017\pi$
$410$	−5.36917	+	1.86349i	−0.265165	+	0.0920314i
$411$	8.36653	−	39.3614i	0.412690	−	1.94156i
$412$	−8.83804	+	4.50320i	−0.435419	+	0.221857i
$413$	2.17435	−	2.28522i	0.106993	−	0.112448i
$414$	−74.4149	+	24.1789i	−3.65729	+	1.18833i
$415$	−17.3652	+	4.05396i	−0.852427	+	0.199001i
$416$	−0.0208734	−	0.0982017i	−0.00102340	−	0.00481474i
$417$	18.8340	+	23.2581i	0.922306	+	1.13895i
$418$	−6.84850	−	25.5589i	−0.334971	−	1.25013i
$419$	25.0790	+	18.2210i	1.22519	+	0.890153i	0.996520	−	0.0833506i	$-0.0265621\pi$
$419$	25.0790	+	18.2210i	1.22519	+	0.890153i	0.228671	+	0.973504i	$0.426562\pi$
$420$	41.4449	+	57.9653i	2.02230	+	2.82842i
$421$	−18.7028	+	13.5884i	−0.911518	+	0.662257i	−0.941398	−	0.337297i	$-0.890487\pi$
$421$	−18.7028	+	13.5884i	−0.911518	+	0.662257i	0.0298801	+	0.999553i	$0.490487\pi$
$422$	−16.7197	−	13.5393i	−0.813901	−	0.659084i
$423$	−0.864771	−	16.5008i	−0.0420466	−	0.802297i
$424$	17.1345	−	9.89259i	0.832124	−	0.480427i
$425$	9.65545	−	10.4566i	0.468358	−	0.507217i
$426$		−	72.4019i		−	3.50788i
$427$	5.91136	+	14.3249i	0.286071	+	0.693233i
$428$	7.09684	+	1.12403i	0.343039	+	0.0543320i
$429$	−6.82350	+	0.717179i	−0.329442	+	0.0346257i
$430$	−30.5724	−	4.22025i	−1.47433	−	0.203518i
$431$	0.463434	−	4.40928i	0.0223228	−	0.212387i	−0.977675	−	0.210125i	$-0.932613\pi$
$431$	0.463434	−	4.40928i	0.0223228	−	0.212387i	0.999997	−	0.00226281i	$-0.000720274\pi$
$432$	35.5515	−	9.52600i	1.71047	−	0.458320i
$433$	23.2113	−	3.67631i	1.11546	−	0.176672i	0.428626	−	0.903482i	$-0.358998\pi$
$433$	23.2113	−	3.67631i	1.11546	−	0.176672i	0.686839	+	0.726810i	$0.258998\pi$
$434$	17.1564	−	31.4984i	0.823531	−	1.51197i
$435$	−54.0673	−	29.7969i	−2.59233	−	1.42865i
$436$	−9.65400	−	2.05202i	−0.462343	−	0.0982740i
$437$	14.2076	+	9.22653i	0.679642	+	0.441365i
$438$	−31.8940	−	20.7122i	−1.52395	−	0.989667i
$439$	−31.8882	−	6.77804i	−1.52194	−	0.323498i	−0.630339	−	0.776320i	$-0.717084\pi$
$439$	−31.8882	−	6.77804i	−1.52194	−	0.323498i	−0.891601	+	0.452822i	$0.850417\pi$
$440$	−32.7792	−	18.0649i	−1.56269	−	0.861209i
$441$	−14.9454	−	39.2448i	−0.711688	−	1.86880i
$442$	4.65650	−	0.737516i	0.221487	−	0.0350801i
$443$	5.94509	−	1.59298i	0.282460	−	0.0756849i	−0.114808	−	0.993388i	$-0.536625\pi$
$443$	5.94509	−	1.59298i	0.282460	−	0.0756849i	0.397267	+	0.917703i	$0.369959\pi$
$444$	−2.10392	+	20.0174i	−0.0998475	+	0.949986i
$445$	−27.4449	−	3.78852i	−1.30101	−	0.179593i
$446$	−21.8316	+	2.29459i	−1.03375	+	0.108652i
$447$	68.6588	+	10.8745i	3.24745	+	0.514346i
$448$	12.6121	−	16.3913i	0.595863	−	0.774417i
$449$		−	11.7708i		−	0.555497i	−0.960654	−	0.277748i	$-0.910412\pi$
$449$		−	11.7708i		−	0.555497i	0.960654	−	0.277748i	$-0.0895882\pi$
$450$	−8.60737	+	73.0618i	−0.405755	+	3.44417i
$451$	−3.03961	+	1.75492i	−0.143130	+	0.0826359i
$452$	0.391308	+	7.46660i	0.0184056	+	0.351199i
$453$	20.4990	+	16.5997i	0.963126	+	0.779924i
$454$	−33.4173	+	24.2791i	−1.56835	+	1.13948i
$455$	−3.63733	−	1.65268i	−0.170521	−	0.0774788i
$456$	−38.2090	−	27.7605i	−1.78930	−	1.30000i
$457$	2.10064	+	7.83968i	0.0982637	+	0.366725i	0.997494	−	0.0707504i	$-0.0225394\pi$
$457$	2.10064	+	7.83968i	0.0982637	+	0.366725i	−0.899230	+	0.437475i	$0.855873\pi$
$458$	0.0987110	+	0.121898i	0.00461246	+	0.00569592i
$459$	5.32474	+	25.0509i	0.248538	+	1.16928i
$460$	46.4941	−	10.8542i	2.16780	−	0.506078i
$461$	−10.6651	+	3.46531i	−0.496724	+	0.161395i	−0.546656	−	0.837357i	$-0.684100\pi$
$461$	−10.6651	+	3.46531i	−0.496724	+	0.161395i	0.0499320	+	0.998753i	$0.484100\pi$
$462$	47.7612	+	45.4441i	2.22205	+	2.11425i
$463$	4.85570	−	2.47410i	0.225664	−	0.114981i	−0.337504	−	0.941324i	$-0.609583\pi$
$463$	4.85570	−	2.47410i	0.225664	−	0.114981i	0.563167	+	0.826343i	$0.309583\pi$
$464$	7.82759	−	36.8259i	0.363387	−	1.70960i
$465$	35.0285	−	12.1574i	1.62441	−	0.563788i
$466$	44.5366	−	9.46654i	2.06312	−	0.438529i
$467$	−6.88299	−	2.64213i	−0.318507	−	0.122263i	0.193862	−	0.981029i	$-0.437899\pi$
$467$	−6.88299	−	2.64213i	−0.318507	−	0.122263i	−0.512369	+	0.858766i	$0.671232\pi$
$468$	−11.5021	+	11.5021i	−0.531684	+	0.531684i
$469$	18.9582	+	5.64303i	0.875410	+	0.260571i
$470$	−0.490132	+	15.0968i	−0.0226081	+	0.696365i
$471$	4.14408	+	39.4283i	0.190949	+	1.81676i
$472$	2.11159	+	5.50088i	0.0971938	+	0.253198i
$473$	−19.0333	+	0.997494i	−0.875153	+	0.0458648i
$474$	14.6224	−	25.3268i	0.671631	−	1.16330i
$475$	13.4661	−	8.50667i	0.617867	−	0.390313i
$476$	−22.9675	−	19.6688i	−1.05271	−	0.901516i
$477$	−21.3991	−	10.9034i	−0.979799	−	0.499232i
$478$	10.1280	−	12.5071i	0.463245	−	0.572060i
$479$	−9.15177	−	4.07463i	−0.418155	−	0.186175i	0.186864	−	0.982386i	$-0.440168\pi$
$479$	−9.15177	−	4.07463i	−0.418155	−	0.186175i	−0.605019	+	0.796211i	$0.706834\pi$
$480$	−0.981658	+	0.175576i	−0.0448064	+	0.00801391i
$481$	−0.459000	−	1.03093i	−0.0209286	−	0.0470064i
$482$	7.65128	+	7.65128i	0.348506	+	0.348506i
$483$	−42.1916	−	1.16078i	−1.91979	−	0.0528174i
$484$	−1.79602	−	0.583562i	−0.0816372	−	0.0265255i
$485$	37.8110	+	3.21462i	1.71691	+	0.145969i
$486$	0.0267119	+	0.0240515i	0.00121168	+	0.00109100i
$487$	10.1413	−	15.6162i	0.459544	−	0.707636i	−0.530610	−	0.847616i	$-0.678037\pi$
$487$	10.1413	−	15.6162i	0.459544	−	0.707636i	0.990154	+	0.139980i	$0.0447039\pi$
$488$	−28.9076	−	1.51498i	−1.30859	−	0.0685801i
$489$	−11.1080	−	34.1869i	−0.502321	−	1.54598i
$490$	10.5741	+	36.9038i	0.477687	+	1.66714i
$491$	3.16161	−	9.73045i	0.142682	−	0.439129i	−0.854024	−	0.520234i	$-0.825845\pi$
$491$	3.16161	−	9.73045i	0.142682	−	0.439129i	0.996706	+	0.0811048i	$0.0258448\pi$
$492$	−4.47328	+	11.6533i	−0.201671	+	0.525371i
$493$	25.3045	+	6.78033i	1.13966	+	0.305371i
$494$	5.24721	+	0.551504i	0.236083	+	0.0248133i
$495$	3.28033	+	45.3138i	0.147440	+	2.03670i
$496$	13.2911	+	18.2936i	0.596789	+	0.821409i
$497$	8.72354	−	24.5312i	0.391304	−	1.10037i
$498$	−26.6372	+	52.2785i	−1.19364	+	2.34266i
$499$	8.93457	+	5.15838i	0.399966	+	0.230921i	0.686470	−	0.727159i	$-0.259160\pi$
$499$	8.93457	+	5.15838i	0.399966	+	0.230921i	−0.286503	+	0.958079i	$0.592493\pi$
$500$	9.00993	−	43.9767i	0.402936	−	1.96670i
$501$	34.0053	+	58.8988i	1.51924	+	2.63141i
$502$	−6.23320	−	9.59829i	−0.278201	−	0.428393i
$503$	−4.07688	+	25.7404i	−0.181779	+	1.14771i	0.712989	+	0.701176i	$0.247341\pi$
$503$	−4.07688	+	25.7404i	−0.181779	+	1.14771i	−0.894768	+	0.446532i	$0.852659\pi$
$504$	78.1938	+	6.25826i	3.48303	+	0.278765i
$505$	4.02537	−	2.72953i	0.179127	−	0.121463i
$506$	40.3534	−	17.9665i	1.79393	−	0.798707i
$507$	−9.73940	+	36.3479i	−0.432542	+	1.61427i
$508$	−36.7348	+	29.7472i	−1.62984	+	1.31982i
$509$	−7.29745	−	8.10464i	−0.323454	−	0.359232i	0.559385	−	0.828908i	$-0.311037\pi$
$509$	−7.29745	−	8.10464i	−0.323454	−	0.359232i	−0.882839	+	0.469676i	$0.844371\pi$
$510$	−5.82108	−	46.4666i	−0.257762	−	2.05758i
$511$	−8.31074	−	10.8605i	−0.367645	−	0.480442i
$512$	18.0810	+	35.4859i	0.799074	+	1.56827i
$513$	−1.50001	+	28.6219i	−0.0662272	+	1.26369i
$514$	11.8972	−	13.2131i	0.524761	−	0.582806i
$515$	−4.53286	−	3.15740i	−0.199742	−	0.139132i
$516$	−50.3725	+	45.3556i	−2.21752	+	1.99667i
$517$	1.45925	+	9.21333i	0.0641776	+	0.405202i
$518$	−4.68119	+	9.78093i	−0.205679	+	0.429749i
$519$	7.43202	−	10.2293i	0.326230	−	0.449017i
$520$	5.70511	−	4.81104i	0.250185	−	0.210978i
$521$	−8.43887	+	18.9540i	−0.369713	+	0.830390i	0.628887	+	0.777497i	$0.283511\pi$
$521$	−8.43887	+	18.9540i	−0.369713	+	0.830390i	−0.998600	+	0.0528931i	$0.983156\pi$
$522$	−126.417	+	48.5269i	−5.53312	+	2.12397i
$523$	3.49427	−	2.26921i	0.152794	−	0.0992255i	−0.465978	−	0.884796i	$-0.654297\pi$
$523$	3.49427	−	2.26921i	0.152794	−	0.0992255i	0.618772	+	0.785571i	$0.287631\pi$
$524$	−55.0466			−2.40472
$525$	−17.5799	+	35.5781i	−0.767250	+	1.55276i
$526$	27.4702			1.19776
$527$	−13.1959	+	8.56952i	−0.574823	+	0.373294i
$528$	−38.8017	+	14.8946i	−1.68863	+	0.648203i
$529$	−2.14759	+	4.82357i	−0.0933736	+	0.209721i
$530$	18.6472	+	11.5886i	0.809982	+	0.503375i
$531$	4.20411	−	5.78646i	0.182443	−	0.251111i
$532$	−19.1304	−	27.9141i	−0.829408	−	1.21023i
$533$	−0.109480	−	0.691230i	−0.00474211	−	0.0299405i
$534$	−67.7441	+	60.9971i	−2.93157	+	2.63960i
$535$	1.31207	+	3.78038i	0.0567256	+	0.163440i
$536$	−24.7236	+	27.4583i	−1.06790	+	1.18602i
$537$	−0.686579	+	13.1007i	−0.0296281	+	0.565337i
$538$	−7.94707	−	15.5970i	−0.342622	−	0.672434i
$539$	10.7070	+	21.1520i	0.461182	+	0.911081i
$540$	55.2343	+	58.9411i	2.37690	+	2.53642i
$541$	−1.25255	−	1.39110i	−0.0538515	−	0.0598081i	0.715617	−	0.698493i	$-0.246146\pi$
$541$	−1.25255	−	1.39110i	−0.0538515	−	0.0598081i	−0.769469	+	0.638685i	$0.779479\pi$
$542$	−32.9940	+	26.7180i	−1.41721	+	1.14764i
$543$	19.2638	−	71.8935i	0.826689	−	3.08525i
$544$	0.386595	−	0.172123i	0.0165751	−	0.00737972i
$545$	−1.52801	−	5.27991i	−0.0654528	−	0.226167i
$546$	−11.8724	+	5.64353i	−0.508091	+	0.241521i
$547$	−1.28862	+	8.13603i	−0.0550974	+	0.347871i	0.944704	+	0.327925i	$0.106349\pi$
$547$	−1.28862	+	8.13603i	−0.0550974	+	0.347871i	−0.999801	+	0.0199460i	$0.993651\pi$
$548$	29.3339	+	45.1702i	1.25308	+	1.92958i
$549$	17.5692	+	30.4308i	0.749837	+	1.29876i
$550$	0.521170	−	41.5284i	0.0222228	−	1.77078i
$551$	25.3899	+	14.6588i	1.08164	+	0.624488i
$552$	35.7936	−	70.2490i	1.52348	−	2.98999i
$553$	8.00594	−	6.81939i	0.340447	−	0.289990i
$554$	20.3901	+	28.0646i	0.866294	+	1.19235i
$555$	−10.3829	+	4.22460i	−0.440728	+	0.179324i
$556$	−39.8364	−	4.18697i	−1.68944	−	0.177567i
$557$	1.88967	+	0.506336i	0.0800679	+	0.0214541i	0.298631	−	0.954369i	$-0.403470\pi$
$557$	1.88967	+	0.506336i	0.0800679	+	0.0214541i	−0.218563	+	0.975823i	$0.570137\pi$
$558$	29.1458	−	75.9274i	1.23384	−	3.21426i
$559$	1.17438	−	3.61436i	0.0496709	−	0.152871i
$560$	−23.8741	−	3.96751i	−1.00887	−	0.167658i
$561$	−8.93690	−	27.5049i	−0.377316	−	1.16126i
$562$	−25.2337	−	1.32244i	−1.06442	−	0.0557838i
$563$	−18.0191	+	27.7470i	−0.759414	+	1.16940i	0.221539	+	0.975151i	$0.428892\pi$
$563$	−18.0191	+	27.7470i	−0.759414	+	1.16940i	−0.980953	+	0.194244i	$0.937775\pi$
$564$	24.6536	+	22.1982i	1.03810	+	0.934711i
$565$	−3.56395	+	2.15335i	−0.149936	+	0.0905920i
$566$	6.87462	+	2.23370i	0.288962	+	0.0938894i
$567$	−11.3250	−	20.9242i	−0.475606	−	0.878733i
$568$	34.3898	+	34.3898i	1.44296	+	1.44296i
$569$	−9.37312	−	21.0524i	−0.392942	−	0.882561i	−0.996369	−	0.0851431i	$-0.972865\pi$
$569$	−9.37312	−	21.0524i	−0.392942	−	0.882561i	0.603427	−	0.797418i	$-0.293801\pi$
$570$	7.16650	−	51.9157i	0.300172	−	2.17451i
$571$	−16.8963	−	7.52274i	−0.707090	−	0.314817i	0.0214980	−	0.999769i	$-0.493156\pi$
$571$	−16.8963	−	7.52274i	−0.707090	−	0.314817i	−0.728588	+	0.684952i	$0.759823\pi$
$572$	5.77909	−	7.13658i	0.241636	−	0.298395i
$573$	41.7540	+	21.2747i	1.74430	+	0.888764i
$574$	−4.37408	+	5.10767i	−0.182571	+	0.213190i
$575$	17.5425	+	19.9816i	0.731572	+	0.833289i
$576$	23.4478	−	40.6129i	0.976993	−	1.69220i
$577$	26.8226	−	1.40571i	1.11664	−	0.0585206i	0.514928	−	0.857233i	$-0.327819\pi$
$577$	26.8226	−	1.40571i	1.11664	−	0.0585206i	0.601712	+	0.798713i	$0.294485\pi$
$578$	−7.82004	−	20.3719i	−0.325271	−	0.847360i
$579$	−6.41325	−	61.0180i	−0.266525	−	2.53582i
$580$	79.3699	−	22.9697i	3.29566	−	0.953766i
$581$	−15.3241	+	14.5035i	−0.635752	+	0.601707i
$582$	88.2886	−	88.2886i	3.65968	−	3.65968i
$583$	12.6579	+	4.85892i	0.524238	+	0.201236i
$584$	24.9871	−	5.31118i	1.03397	−	0.219778i
$585$	−8.66964	−	2.62735i	−0.358446	−	0.108627i
$586$	−5.32761	+	25.0645i	−0.220082	+	1.03540i
$587$	−0.477303	+	0.243198i	−0.0197004	+	0.0100379i	−0.463813	−	0.885933i	$-0.653519\pi$
$587$	−0.477303	+	0.243198i	−0.0197004	+	0.0100379i	0.444113	+	0.895971i	$0.353519\pi$
$588$	76.9328	+	34.4973i	3.17266	+	1.42265i
$589$	−16.7467	+	5.44133i	−0.690036	+	0.224206i
$590$	−4.27744	+	4.94507i	−0.176099	+	0.203585i
$591$	−8.50258	−	40.0015i	−0.349750	−	1.64544i
$592$	−4.30207	−	5.31262i	−0.176814	−	0.218347i
$593$	4.46701	+	16.6711i	0.183438	+	0.684600i	0.994960	+	0.100277i	$0.0319731\pi$
$593$	4.46701	+	16.6711i	0.183438	+	0.684600i	−0.811521	+	0.584323i	$0.801360\pi$
$594$	60.4605	+	43.9272i	2.48073	+	1.80235i
$595$	3.62637	−	16.4452i	0.148667	−	0.674186i
$596$	−75.2712	+	54.6877i	−3.08323	+	2.24010i
$597$	−50.9006	−	41.2185i	−2.08322	−	1.68696i
$598$	0.460962	+	8.79568i	0.0188501	+	0.359682i
$599$	−8.98779	+	5.18910i	−0.367231	+	0.212021i	−0.672248	−	0.740326i	$-0.734671\pi$
$599$	−8.98779	+	5.18910i	−0.367231	+	0.212021i	0.305017	+	0.952347i	$0.401338\pi$
$600$	−45.9244	−	58.1900i	−1.87485	−	2.37560i
$601$			15.2610i			0.622508i	0.950327	+	0.311254i	$0.100749\pi$
$601$			15.2610i			0.622508i	−0.950327	+	0.311254i	$0.899251\pi$
$602$	−33.7556	+	13.9296i	−1.37578	+	0.567730i
$603$	44.2991	+	7.01629i	1.80400	+	0.285726i
$604$	−35.1106	+	3.69027i	−1.42863	+	0.150155i
$605$	−0.185166	−	1.03528i	−0.00752805	−	0.0420899i
$606$	1.67272	−	15.9149i	0.0679498	−	0.646499i
$607$	−8.65699	+	2.31963i	−0.351376	+	0.0941510i	−0.430190	−	0.902738i	$-0.641553\pi$
$607$	−8.65699	+	2.31963i	−0.351376	+	0.0941510i	0.0788137	+	0.996889i	$0.474887\pi$
$608$	0.467758	−	0.0740856i	0.0189701	−	0.00300457i
$609$	−73.0224	+	1.81532i	−2.95902	+	0.0735606i
$610$	−13.6465	−	29.0787i	−0.552531	−	1.17736i
$611$	−1.81935	−	0.386715i	−0.0736030	−	0.0156448i
$612$	−57.5035	−	37.3432i	−2.32444	−	1.50951i
$613$	−13.8752	−	9.01065i	−0.560413	−	0.363937i	0.233135	−	0.972444i	$-0.425102\pi$
$613$	−13.8752	−	9.01065i	−0.560413	−	0.363937i	−0.793548	+	0.608508i	$0.791768\pi$
$614$	65.4936	+	13.9211i	2.64311	+	0.561809i
$615$	−6.89770	+	0.864105i	−0.278142	+	0.0348441i
$616$	−44.2711	+	1.10057i	−1.78373	+	0.0443433i
$617$	−20.5016	+	3.24713i	−0.825362	+	0.130725i	−0.554806	−	0.831980i	$-0.687208\pi$
$617$	−20.5016	+	3.24713i	−0.825362	+	0.130725i	−0.270556	+	0.962704i	$0.587208\pi$
$618$	−17.5568	+	4.70433i	−0.706238	+	0.189236i
$619$	4.63534	−	44.1024i	0.186310	−	1.77262i	−0.357983	−	0.933728i	$-0.616535\pi$
$619$	4.63534	−	44.1024i	0.186310	−	1.77262i	0.544293	−	0.838895i	$-0.316798\pi$
$620$	−21.6454	+	44.6573i	−0.869301	+	1.79348i
$621$	−47.5838	+	5.00126i	−1.90947	+	0.200694i
$622$	−3.16706	−	0.501613i	−0.126988	−	0.0201128i
$623$	−30.3024	+	12.5047i	−1.21404	+	0.500988i
$624$		−	8.28732i		−	0.331758i
$625$	23.9628	−	7.12631i	0.958512	−	0.285052i
$626$	29.8231	−	17.2184i	1.19197	−	0.688185i
$627$	−1.69387	−	32.3209i	−0.0676466	−	1.29077i
$628$	−41.2374	−	33.3934i	−1.64555	−	1.33254i
$629$	3.84830	−	2.79595i	0.153442	−	0.111482i
$630$	34.7993	+	79.7870i	1.38644	+	3.17879i
$631$	39.2726	+	28.5332i	1.56342	+	1.13589i	0.933136	+	0.359523i	$0.117060\pi$
$631$	39.2726	+	28.5332i	1.56342	+	1.13589i	0.630281	+	0.776367i	$0.282940\pi$
$632$	5.08441	+	18.9753i	0.202247	+	0.754796i
$633$	−16.5606	−	20.4507i	−0.658226	−	0.812842i
$634$	14.8629	+	69.9247i	0.590283	+	2.77706i
$635$	−24.2572	−	10.2264i	−0.962616	−	0.405824i
$636$	45.8592	−	14.9006i	1.81844	−	0.590846i
$637$	−4.70257	+	0.481661i	−0.186323	+	0.0190841i
$638$	68.1130	−	34.7053i	2.69662	−	1.37400i
$639$	12.2743	−	57.7462i	0.485565	−	2.28440i
$640$	−24.8827	+	35.7223i	−0.983574	+	1.41205i
$641$	24.9930	−	5.31242i	0.987162	−	0.209828i	0.314081	−	0.949396i	$-0.398304\pi$
$641$	24.9930	−	5.31242i	0.987162	−	0.209828i	0.673081	+	0.739568i	$0.264970\pi$
$642$	12.2920	+	4.71847i	0.485128	+	0.186223i
$643$	−8.37217	+	8.37217i	−0.330166	+	0.330166i	−0.852650	−	0.522483i	$-0.825006\pi$
$643$	−8.37217	+	8.37217i	−0.330166	+	0.330166i	0.522483	+	0.852650i	$0.325006\pi$
$644$	41.0292	−	38.8320i	1.61678	−	1.53020i
$645$	−35.5043	−	12.8240i	−1.39798	−	0.504944i
$646$	2.32466	+	22.1177i	0.0914627	+	0.870209i
$647$	8.40167	+	21.8871i	0.330304	+	0.860471i	0.993687	+	0.112191i	$0.0357867\pi$
$647$	8.40167	+	21.8871i	0.330304	+	0.860471i	−0.663383	+	0.748280i	$0.730880\pi$
$648$	44.3824	−	2.32598i	1.74350	−	0.0913732i
$649$	−2.01893	+	3.49689i	−0.0792499	+	0.137265i
$650$	7.69334	+	3.06451i	0.301758	+	0.120200i
$651$	28.5365	−	33.3225i	1.11844	−	1.30601i
$652$	42.8675	+	21.8421i	1.67882	+	0.855403i
$653$	−11.6229	+	14.3531i	−0.454840	+	0.561680i	−0.952047	−	0.305951i	$-0.901025\pi$
$653$	−11.6229	+	14.3531i	−0.454840	+	0.561680i	0.497207	+	0.867632i	$0.334359\pi$
$654$	−16.5219	−	7.35602i	−0.646057	−	0.287643i
$655$	−14.4586	−	27.0325i	−0.564944	−	1.05625i
$656$	−1.72434	−	3.87292i	−0.0673240	−	0.151212i
$657$	−21.9266	−	21.9266i	−0.855439	−	0.855439i
$658$	8.50707	+	15.7177i	0.331640	+	0.612740i
$659$	41.0738	+	13.3457i	1.60001	+	0.519875i	0.967110	−	0.254359i	$-0.0818646\pi$
$659$	41.0738	+	13.3457i	1.60001	+	0.519875i	0.632899	+	0.774234i	$0.281865\pi$
$660$	−68.9881	−	59.6741i	−2.68536	−	2.32281i
$661$	2.78901	+	2.51124i	0.108480	+	0.0976758i	0.721586	−	0.692325i	$-0.243413\pi$
$661$	2.78901	+	2.51124i	0.108480	+	0.0976758i	−0.613106	+	0.790001i	$0.710080\pi$
$662$	11.2707	−	17.3553i	0.438047	−	0.674533i
$663$	5.75869	+	0.301800i	0.223649	+	0.0117210i
$664$	−12.1792	−	37.4837i	−0.472645	−	1.45465i
$665$	8.68336	−	16.7266i	0.336726	−	0.648629i
$666$	−7.59788	+	23.3839i	−0.294412	+	0.906107i
$667$	−17.5392	+	45.6911i	−0.679120	+	1.76917i
$668$	−87.9254	−	23.5595i	−3.40194	−	0.911546i
$669$	−26.7033	−	2.80663i	−1.03241	−	0.108511i
$670$	−39.8068	−	9.82134i	−1.53787	−	0.379431i
$671$	−11.6600	−	16.0486i	−0.450128	−	0.619548i
$672$	−0.898253	+	0.765124i	−0.0346508	+	0.0295153i
$673$	13.3247	−	26.1511i	0.513628	−	1.00805i	−0.477931	−	0.878397i	$-0.658613\pi$
$673$	13.3247	−	26.1511i	0.513628	−	1.00805i	0.991559	−	0.129654i	$-0.0413868\pi$
$674$	46.9545	+	27.1092i	1.80862	+	1.04421i
$675$	−14.4372	+	42.6062i	−0.555686	+	1.63991i
$676$	−25.1826	−	43.6175i	−0.968562	−	1.67760i
$677$	5.27903	+	8.12900i	0.202890	+	0.312423i	0.925439	−	0.378897i	$-0.123696\pi$
$677$	5.27903	+	8.12900i	0.202890	+	0.312423i	−0.722549	+	0.691319i	$0.757030\pi$
$678$	−2.14327	+	13.5321i	−0.0823120	+	0.519697i
$679$	40.5516	−	19.2762i	1.55623	−	0.739752i
$680$	24.8358	+	19.3060i	0.952411	+	0.740351i
$681$	−46.1556	+	20.5498i	−1.76869	+	0.787471i
$682$	−11.8834	+	44.3493i	−0.455037	+	1.69822i
$683$	18.2459	−	14.7752i	0.698159	−	0.565358i	−0.213181	−	0.977013i	$-0.568382\pi$
$683$	18.2459	−	14.7752i	0.698159	−	0.565358i	0.911340	+	0.411655i	$0.135049\pi$
$684$	−51.3439	−	57.0232i	−1.96318	−	2.18034i
$685$	−14.4775	+	26.2698i	−0.553158	+	1.00372i
$686$	32.8235	+	31.3973i	1.25321	+	1.19876i
$687$	0.0871006	+	0.170944i	0.00332309	+	0.00652194i
$688$	1.20485	−	22.9898i	0.0459343	−	0.876479i
$689$	−1.80899	+	2.00909i	−0.0689172	+	0.0765403i
$690$	87.4706	−	1.74137i	3.32995	−	0.0662927i
$691$	−22.1618	+	19.9546i	−0.843075	+	0.759108i	−0.972604	−	0.232467i	$-0.925320\pi$
$691$	−22.1618	+	19.9546i	−0.843075	+	0.759108i	0.129529	+	0.991576i	$0.458653\pi$
$692$	2.64737	+	16.7149i	0.100638	+	0.635404i
$693$	30.3892	+	44.3423i	1.15439	+	1.68442i
$694$	26.5659	−	36.5649i	1.00843	−	1.38798i
$695$	−8.40730	−	20.6628i	−0.318907	−	0.783784i
$696$	55.4973	−	124.649i	2.10362	−	4.72481i
$697$	2.75401	−	1.05717i	0.104316	−	0.0400430i
$698$	62.8656	−	40.8254i	2.37950	−	1.54526i
$699$	55.6920			2.10646
$700$	−17.0337	−	50.3093i	−0.643814	−	1.90151i
$701$	−51.6850			−1.95212			−0.976058	−	0.217508i	$-0.930207\pi$
$701$	−51.6850			−1.95212			−0.976058	+	0.217508i	$0.930207\pi$
$702$	−12.4974	+	8.11593i	−0.471685	+	0.306316i
$703$	4.96979	−	1.90772i	0.187439	−	0.0719511i
$704$	−10.7682	+	24.1857i	−0.405841	+	0.911533i
$705$	−4.42564	+	17.9376i	−0.166679	+	0.675567i
$706$	36.4388	−	50.1537i	1.37139	−	1.88756i
$707$	2.48430	−	5.19074i	0.0934319	−	0.195218i
$708$	2.24643	+	14.1834i	0.0844260	+	0.533045i
$709$	5.60416	−	5.04601i	0.210469	−	0.189507i	−0.557153	−	0.830410i	$-0.688106\pi$
$709$	5.60416	−	5.04601i	0.210469	−	0.189507i	0.767622	+	0.640903i	$0.221440\pi$
$710$	−15.6520	+	51.6480i	−0.587409	+	1.93832i
$711$	15.9562	−	17.7212i	0.598405	−	0.664596i
$712$	3.20474	−	61.1501i	0.120103	−	2.29170i
$713$	−13.3451	−	26.1911i	−0.499776	−	0.980866i
$714$	−33.6731	−	44.0042i	−1.26018	−	1.64682i
$715$	5.02260	+	0.963519i	0.187835	+	0.0360336i
$716$	−11.7489	−	13.0484i	−0.439075	−	0.487643i
$717$	15.2980	−	12.3881i	0.571316	−	0.462643i
$718$	−22.3277	+	83.3281i	−0.833262	+	3.10978i
$719$	11.6204	−	5.17372i	0.433367	−	0.192947i	−0.178446	−	0.983950i	$-0.557107\pi$
$719$	11.6204	−	5.17372i	0.433367	−	0.192947i	0.611813	+	0.791002i	$0.290440\pi$
$720$	−54.8476	−	1.78068i	−2.04405	−	0.0663619i
$721$	−6.51540	−	0.521462i	−0.242646	−	0.0194203i
$722$	3.39623	−	21.4429i	0.126394	−	0.798023i
$723$	7.20839	+	11.0999i	0.268083	+	0.412811i
$724$	49.8093	+	86.2722i	1.85115	+	3.20628i
$725$	32.1274	+	32.9441i	1.19318	+	1.22351i
$726$	−2.99683	−	1.73022i	−0.111223	−	0.0642145i
$727$	2.99184	−	5.87181i	0.110961	−	0.217774i	−0.828848	−	0.559474i	$-0.811003\pi$
$727$	2.99184	−	5.87181i	0.110961	−	0.217774i	0.939809	+	0.341701i	$0.111003\pi$
$728$	2.95860	−	8.31978i	0.109653	−	0.308352i
$729$	15.8831	+	21.8612i	0.588264	+	0.809676i
$730$	18.2740	+	21.6700i	0.676352	+	0.802043i
$731$	15.9313	+	1.67445i	0.589240	+	0.0619316i
$732$	−68.1447	−	18.2593i	−2.51870	−	0.674884i
$733$	−14.2939	+	37.2370i	−0.527959	+	1.37538i	0.367412	+	0.930058i	$0.380244\pi$
$733$	−14.2939	+	37.2370i	−0.527959	+	1.37538i	−0.895371	+	0.445322i	$0.853089\pi$
$734$	1.74352	−	5.36599i	0.0643544	−	0.198062i
$735$	3.26614	+	46.8416i	0.120474	+	1.72778i
$736$	0.244306	+	0.751896i	0.00900524	+	0.0277153i
$737$	−25.2857	−	1.32517i	−0.931412	−	0.0488132i
$738$	−8.30465	+	12.7880i	−0.305699	+	0.470735i
$739$	−24.1854	−	21.7767i	−0.889675	−	0.801067i	0.0911743	−	0.995835i	$-0.470938\pi$
$739$	−24.1854	−	21.7767i	−0.889675	−	0.801067i	−0.980849	+	0.194768i	$0.937605\pi$
$740$	5.82825	−	13.8247i	0.214251	−	0.508204i
$741$	6.13763	+	1.99424i	0.225472	+	0.0732602i
$742$	25.9674	+	0.714419i	0.953294	+	0.0262272i
$743$	−30.1810	−	30.1810i	−1.10723	−	1.10723i	−0.993513	−	0.113722i	$-0.963723\pi$
$743$	−30.1810	−	30.1810i	−1.10723	−	1.10723i	−0.113722	−	0.993513i	$-0.536277\pi$
$744$	33.3323	+	74.8656i	1.22202	+	2.74471i
$745$	−46.6270	−	22.6002i	−1.70828	−	0.828006i
$746$	−29.3078	−	13.0487i	−1.07304	−	0.477747i
$747$	−30.1081	+	37.1804i	−1.10160	+	1.36036i
$748$	34.4889	+	17.5730i	1.26104	+	0.642532i
$749$	3.59626	+	3.07975i	0.131405	+	0.112532i
$750$	32.9036	−	75.3905i	1.20147	−	2.75287i
$751$	−3.97735	+	6.88897i	−0.145136	+	0.251382i	−0.929424	−	0.369015i	$-0.879695\pi$
$751$	−3.97735	+	6.88897i	−0.145136	+	0.251382i	0.784288	+	0.620397i	$0.213028\pi$
$752$	−11.2518	+	0.589682i	−0.410311	+	0.0215035i
$753$	−5.01663	−	13.0688i	−0.182816	−	0.476252i
$754$	1.59331	+	15.1593i	0.0580248	+	0.552069i
$755$	−11.0344	−	16.2730i	−0.401583	−	0.592234i
$756$	91.6043	+	27.2665i	3.33162	+	0.991675i
$757$	−13.7537	+	13.7537i	−0.499888	+	0.499888i	−0.911403	−	0.411515i	$-0.865000\pi$
$757$	−13.7537	+	13.7537i	−0.499888	+	0.499888i	0.411515	+	0.911403i	$0.365000\pi$
$758$	43.6289	+	16.7475i	1.58467	+	0.608298i
$759$	52.8487	−	11.2333i	1.91829	−	0.407744i
$760$	21.2552	+	28.0631i	0.771006	+	1.01796i
$761$	7.56356	−	35.5837i	0.274179	−	1.28991i	−0.598306	−	0.801268i	$-0.704159\pi$
$761$	7.56356	−	35.5837i	0.274179	−	1.28991i	0.872485	−	0.488642i	$-0.162507\pi$
$762$	−77.1760	+	39.3231i	−2.79579	+	1.42453i
$763$	−4.71163	−	4.48305i	−0.170572	−	0.162297i
$764$	−59.6510	+	19.3818i	−2.15810	+	0.701208i
$765$	3.23475	−	38.0477i	0.116953	−	1.37562i
$766$	−10.4737	−	49.2750i	−0.378431	−	1.78038i
$767$	−0.506685	−	0.625704i	−0.0182953	−	0.0225929i
$768$	24.9350	+	93.0587i	0.899764	+	3.35797i
$769$	22.4668	+	16.3231i	0.810173	+	0.588625i	0.913881	−	0.405983i	$-0.133071\pi$
$769$	22.4668	+	16.3231i	0.810173	+	0.588625i	−0.103708	+	0.994608i	$0.533071\pi$
$770$	−24.2463	−	42.7428i	−0.873777	−	1.54034i
$771$	17.5942	−	12.7830i	0.633641	−	0.460367i
$772$	63.8176	+	51.6785i	2.29685	+	1.85995i
$773$	−1.69966	−	32.4314i	−0.0611325	−	1.16648i	−0.841179	−	0.540756i	$-0.818138\pi$
$773$	−1.69966	−	32.4314i	−0.0611325	−	1.16648i	0.780047	−	0.625721i	$-0.215195\pi$
$774$	−71.7078	+	41.4005i	−2.57748	+	1.48811i
$775$	−27.6159	+	1.09999i	−0.991992	+	0.0395129i
$776$			83.8714i			3.01081i
$777$	−8.08804	+	10.5117i	−0.290157	+	0.377104i
$778$	−94.8940	−	15.0297i	−3.40211	−	0.538842i
$779$	3.28324	−	0.345083i	0.117634	−	0.0123639i
$780$	16.0381	−	8.57812i	0.574256	−	0.307146i
$781$	−3.48377	+	33.1459i	−0.124659	+	1.18605i
$782$	−35.8608	+	9.60887i	−1.28238	+	0.343612i
$783$	−81.7833	+	12.9532i	−2.92270	+	0.462910i
$784$	−26.7608	+	10.1912i	−0.955743	+	0.363972i
$785$	5.56752	−	29.0222i	0.198713	−	1.03585i
$786$	−98.6648	−	20.9718i	−3.51926	−	0.748041i
$787$	−15.2828	−	9.92475i	−0.544772	−	0.353779i	0.242727	−	0.970095i	$-0.421958\pi$
$787$	−15.2828	−	9.92475i	−0.544772	−	0.353779i	−0.787499	+	0.616316i	$0.788625\pi$
$788$	45.9048	+	29.8109i	1.63529	+	1.06197i
$789$	32.8660	+	6.98588i	1.17006	+	0.248704i
$790$	−15.9062	+	14.9058i	−0.565915	+	0.530325i
$791$	−2.35664	+	4.32670i	−0.0837924	+	0.153840i
$792$	−99.1785	+	15.7083i	−3.52416	+	0.558171i
$793$	3.82066	−	1.02374i	0.135675	−	0.0363541i
$794$	3.88156	−	36.9306i	0.137751	−	1.31062i
$795$	19.3629	+	18.6070i	0.686730	+	0.659921i
$796$	87.1824	−	9.16324i	3.09010	−	0.324782i
$797$	14.1304	+	2.23804i	0.500525	+	0.0792753i	0.401592	−	0.915819i	$-0.368457\pi$
$797$	14.1304	+	2.23804i	0.500525	+	0.0792753i	0.0989330	+	0.995094i	$0.468457\pi$
$798$	−23.6542	−	57.3212i	−0.837351	−	2.02915i
$799$		−	7.84013i		−	0.277364i
$800$	0.738224	+	0.0869697i	0.0261002	+	0.00307484i
$801$	−64.3722	+	37.1653i	−2.27448	+	1.31317i
$802$	2.94739	+	56.2396i	0.104076	+	1.98589i
$803$	13.6046	+	11.0168i	0.480095	+	0.388774i
$804$	−72.8515	+	52.9297i	−2.56927	+	1.86669i
$805$	29.8466	+	9.94913i	1.05195	+	0.350661i
$806$	−7.40654	−	5.38117i	−0.260884	−	0.189544i
$807$	−5.54162	−	20.6816i	−0.195074	−	0.728027i
$808$	6.76482	+	8.35385i	0.237985	+	0.293888i
$809$	0.0647150	+	0.304460i	0.00227526	+	0.0107043i	0.979271	−	0.202556i	$-0.0649250\pi$
$809$	0.0647150	+	0.304460i	0.00227526	+	0.0107043i	−0.976995	+	0.213261i	$0.931592\pi$
$810$	25.5036	+	42.2104i	0.896106	+	1.48312i
$811$	3.46924	−	1.12722i	0.121822	−	0.0395822i	−0.247472	−	0.968895i	$-0.579600\pi$
$811$	3.46924	−	1.12722i	0.121822	−	0.0395822i	0.369293	+	0.929313i	$0.379600\pi$
$812$	67.3912	−	70.8272i	2.36497	−	2.48555i
$813$	−46.2693	+	23.5754i	−1.62274	+	0.826825i
$814$	2.88592	−	13.5772i	0.101152	−	0.475881i
$815$	0.533309	+	26.7886i	0.0186810	+	0.938365i
$816$	34.1688	−	7.26281i	1.19615	−	0.254249i
$817$	16.7365	+	6.42452i	0.585534	+	0.224766i
$818$	39.7338	−	39.7338i	1.38926	−	1.38926i
$819$	−10.4259	+	2.48843i	−0.364311	+	0.0869528i
$820$	5.71026	−	7.34585i	0.199411	−	0.256528i
$821$	3.00615	+	28.6016i	0.104915	+	0.998204i	0.912673	+	0.408690i	$0.134014\pi$
$821$	3.00615	+	28.6016i	0.104915	+	0.998204i	−0.807758	+	0.589514i	$0.799319\pi$
$822$	35.3685	+	92.1381i	1.23362	+	3.21369i
$823$	−25.5418	+	1.33859i	−0.890331	+	0.0466603i	−0.492014	−	0.870587i	$-0.663739\pi$
$823$	−25.5418	+	1.33859i	−0.890331	+	0.0466603i	−0.398317	+	0.917248i	$0.630406\pi$
$824$	6.10473	−	10.5737i	0.212668	−	0.368352i
$825$	11.1845	−	49.5530i	0.389395	−	1.72521i
$826$	−1.41991	+	7.60488i	−0.0494049	+	0.264608i
$827$	−19.3175	−	9.84275i	−0.671735	−	0.342266i	0.0846335	−	0.996412i	$-0.473028\pi$
$827$	−19.3175	−	9.84275i	−0.671735	−	0.342266i	−0.756368	+	0.654146i	$0.773028\pi$
$828$	80.6121	−	99.5477i	2.80146	−	3.45952i
$829$	18.7960	+	8.36852i	0.652812	+	0.290651i	0.706295	−	0.707918i	$-0.250365\pi$
$829$	18.7960	+	8.36852i	0.652812	+	0.290651i	−0.0534822	+	0.998569i	$0.517032\pi$
$830$	30.3034	−	31.5345i	1.05185	−	1.09458i
$831$	17.2582	+	38.7625i	0.598680	+	1.34466i
$832$	−3.73275	−	3.73275i	−0.129410	−	0.129410i
$833$	−6.10712	−	18.9667i	−0.211599	−	0.657157i
$834$	−69.8070	−	22.6817i	−2.41722	−	0.785402i
$835$	−11.5248	−	49.3669i	−0.398833	−	1.70841i
$836$	32.1919	+	28.9858i	1.11338	+	1.00249i
$837$	27.0861	−	41.7090i	0.936234	−	1.44167i
$838$	−75.9240	−	3.97901i	−2.62275	−	0.137452i
$839$	10.5057	+	32.3333i	0.362698	+	1.11627i	0.951410	+	0.307926i	$0.0996350\pi$
$839$	10.5057	+	32.3333i	0.362698	+	1.11627i	−0.588713	+	0.808342i	$0.700365\pi$
$840$	−81.6438	−	32.0541i	−2.81698	−	1.10597i
$841$	−17.2120	+	52.9732i	−0.593518	+	1.82666i
$842$	20.3189	−	52.9324i	0.700234	−	1.82417i
$843$	−29.8538	−	7.99931i	−1.02822	−	0.275511i
$844$	35.0279	+	3.68158i	1.20571	+	0.126725i
$845$	14.8054	−	23.8234i	0.509321	−	0.819550i
$846$	23.8199	+	32.7853i	0.818947	+	1.12718i
$847$	−0.806914	−	0.947314i	−0.0277259	−	0.0325501i
$848$	−7.43497	+	14.5919i	−0.255318	+	0.501089i
$849$	7.65690	+	4.42072i	0.262784	+	0.151719i
$850$	−5.89278	+	34.4055i	−0.202121	+	1.18010i
$851$	4.44331	+	7.69604i	0.152315	+	0.263817i
$852$	64.5555	+	99.4067i	2.21163	+	3.40562i
$853$	2.16517	−	13.6703i	0.0741339	−	0.468063i	−0.922494	−	0.386011i	$-0.873853\pi$
$853$	2.16517	−	13.6703i	0.0741339	−	0.468063i	0.996628	−	0.0820518i	$-0.0261473\pi$
$854$	−31.2938	−	21.5688i	−1.07085	−	0.738068i
$855$	14.5172	−	40.1919i	0.496476	−	1.37454i
$856$	−8.07972	+	3.59732i	−0.276159	+	0.122954i
$857$	10.9620	−	40.9109i	0.374456	−	1.39749i	−0.479681	−	0.877443i	$-0.659248\pi$
$857$	10.9620	−	40.9109i	0.374456	−	1.39749i	0.854137	−	0.520047i	$-0.174086\pi$
$858$	13.0773	−	10.5898i	0.446450	−	0.361528i
$859$	−29.4321	−	32.6877i	−1.00421	−	1.11529i	−0.993325	−	0.115348i	$-0.963202\pi$
$859$	−29.4321	−	32.6877i	−1.00421	−	1.11529i	−0.0108856	−	0.999941i	$-0.503465\pi$
$860$	45.7384	−	21.4648i	1.55967	−	0.731945i
$861$	−6.53217	+	4.99857i	−0.222616	+	0.170351i
$862$	4.93652	+	9.68847i	0.168139	+	0.329991i
$863$	1.51176	−	28.8460i	0.0514608	−	0.981930i	−0.843875	−	0.536539i	$-0.819731\pi$
$863$	1.51176	−	28.8460i	0.0514608	−	0.981930i	0.895336	−	0.445391i	$-0.146935\pi$
$864$	−0.895009	+	0.994008i	−0.0304488	+	0.0338168i
$865$	−7.51304	+	5.69042i	−0.255451	+	0.193480i
$866$	−42.8326	+	38.5667i	−1.45551	+	1.31055i
$867$	−4.17535	−	26.3621i	−0.141802	−	0.895304i
$868$	4.52946	+	58.5440i	0.153740	+	1.98711i
$869$	−7.91286	+	10.8911i	−0.268425	+	0.369456i
$870$	151.012	−	10.9320i	5.11980	−	0.370629i
$871$	2.05352	−	4.61229i	0.0695810	−	0.156281i
$872$	11.3416	−	4.35365i	0.384076	−	0.147433i
$873$	85.3847	−	55.4495i	2.88984	−	1.87668i
$874$	−41.5481			−1.40539
$875$	20.2320	−	21.5793i	0.683967	−	0.729513i
$876$	62.2576			2.10349
$877$	23.2176	−	15.0777i	0.784003	−	0.509138i	−0.0894819	−	0.995988i	$-0.528521\pi$
$877$	23.2176	−	15.0777i	0.784003	−	0.509138i	0.873485	+	0.486851i	$0.161854\pi$
$878$	74.6446	−	28.6534i	2.51913	−	0.967005i
$879$	−12.7482	+	28.6328i	−0.429985	+	0.965761i
$880$	30.8992	−	2.23684i	1.04161	−	0.0754037i
$881$	21.9771	−	30.2489i	0.740427	−	1.01911i	−0.258167	−	0.966100i	$-0.583119\pi$
$881$	21.9771	−	30.2489i	0.740427	−	1.01911i	0.998594	−	0.0530096i	$-0.0168814\pi$
$882$	83.1631	+	60.7590i	2.80025	+	2.04586i
$883$	1.16366	+	7.34708i	0.0391604	+	0.247249i	0.999501	−	0.0315798i	$-0.0100538\pi$
$883$	1.16366	+	7.34708i	0.0391604	+	0.247249i	−0.960341	+	0.278829i	$0.910054\pi$
$884$	−5.73571	+	5.16446i	−0.192913	+	0.173700i
$885$	−6.37520	+	4.82861i	−0.214300	+	0.162312i
$886$	−10.1006	+	11.2178i	−0.339336	+	0.376871i
$887$	0.00661726	−	0.126265i	0.000222186	−	0.00423956i	−0.998516	−	0.0544556i	$-0.982658\pi$
$887$	0.00661726	−	0.126265i	0.000222186	−	0.00423956i	0.998738	+	0.0502161i	$0.0159910\pi$
$888$	−11.2477	−	22.0748i	−0.377447	−	0.740781i
$889$	−30.8867	+	4.02468i	−1.03591	+	0.134983i
$890$	61.5119	−	28.8673i	2.06188	−	0.967634i
$891$	20.3792	+	22.6334i	0.682730	+	0.758248i
$892$	27.9285	−	22.6161i	0.935115	−	0.757242i
$893$	2.27088	−	8.47504i	0.0759921	−	0.283606i
$894$	−155.750	+	69.3443i	−5.20906	+	2.31922i
$895$	3.32191	−	9.19699i	0.111039	−	0.307421i
$896$	−4.10951	+	51.3462i	−0.137289	+	1.71536i
$897$	−1.68530	+	10.6406i	−0.0562706	+	0.355278i
$898$	15.7230	+	24.2113i	0.524683	+	0.807941i
$899$	−25.4357	−	44.0559i	−0.848327	−	1.46935i
$900$	−53.3261	−	107.987i	−1.77754	−	3.59958i
$901$	−9.86889	−	5.69780i	−0.328780	−	0.189821i
$902$	3.90801	−	7.66990i	0.130122	−	0.255380i
$903$	−43.9284	+	8.08144i	−1.46184	+	0.268934i
$904$	−5.40952	−	7.44556i	−0.179918	−	0.247636i
$905$	−29.2840	+	47.1209i	−0.973433	+	1.56635i
$906$	−64.3376	−	6.76216i	−2.13748	−	0.224658i
$907$	40.0873	+	10.7414i	1.33108	+	0.356661i	0.853117	−	0.521720i	$-0.174710\pi$
$907$	40.0873	+	10.7414i	1.33108	+	0.356661i	0.477960	+	0.878381i	$0.341376\pi$
$908$	24.2336	−	63.1307i	0.804221	−	2.09507i
$909$	4.03220	−	12.4098i	0.133739	−	0.411608i
$910$	9.68921	−	1.45923i	0.321194	−	0.0483729i
$911$	10.0535	+	30.9415i	0.333087	+	1.02514i	0.967656	+	0.252272i	$0.0811776\pi$
$911$	10.0535	+	30.9415i	0.333087	+	1.02514i	−0.634569	+	0.772866i	$0.718822\pi$
$912$	39.0396	+	2.04598i	1.29273	+	0.0677491i
$913$	14.7101	−	22.6516i	0.486834	−	0.749658i
$914$	−14.7928	−	13.3195i	−0.489301	−	0.440569i
$915$	−8.93208	−	38.2608i	−0.295285	−	1.26486i
$916$	−0.244216	−	0.0793507i	−0.00806914	−	0.00262182i
$917$	−30.9027	−	18.9936i	−1.02050	−	0.627223i
$918$	−44.4146	−	44.4146i	−1.46590	−	1.46590i
$919$	10.6182	+	23.8488i	0.350261	+	0.786699i	0.999655	+	0.0262472i	$0.00835572\pi$
$919$	10.6182	+	23.8488i	0.350261	+	0.786699i	−0.649395	+	0.760452i	$0.724978\pi$
$920$	−40.7200	+	42.3743i	−1.34250	+	1.39704i
$921$	74.8178	+	33.3110i	2.46533	+	1.09764i
$922$	17.3082	−	21.3739i	0.570016	−	0.703911i
$923$	−5.92122	−	3.01701i	−0.194899	−	0.0993061i
$924$	−106.095	−	19.8090i	−3.49026	−	0.651667i
$925$	8.31992	−	0.769032i	0.273557	−	0.0252856i
$926$	−6.68286	+	11.5751i	−0.219612	+	0.380380i
$927$	−14.8005	+	0.775660i	−0.486111	+	0.0254760i
$928$	0.490321	+	1.27733i	0.0160956	+	0.0419304i
$929$	4.30011	+	40.9128i	0.141082	+	1.34231i	0.804453	+	0.594016i	$0.202458\pi$
$929$	4.30011	+	40.9128i	0.141082	+	1.34231i	−0.663371	+	0.748290i	$0.730875\pi$
$930$	−55.8106	+	71.7965i	−1.83010	+	2.35430i
$931$	−1.10802	−	22.2716i	−0.0363138	−	0.729921i
$932$	−52.7075	+	52.7075i	−1.72649	+	1.72649i
$933$	−3.66158	−	1.40555i	−0.119875	−	0.0460156i
$934$	17.6869	−	3.75946i	0.578732	−	0.123013i
$935$	0.429072	+	21.5527i	0.0140321	+	0.704849i
$936$	4.16286	−	19.5847i	0.136067	−	0.640147i
$937$	−27.5551	+	14.0400i	−0.900186	+	0.458668i	−0.841901	−	0.539632i	$-0.818563\pi$
$937$	−27.5551	+	14.0400i	−0.900186	+	0.458668i	−0.0582855	+	0.998300i	$0.518563\pi$
$938$	−46.5329	+	13.7166i	−1.51935	+	0.447864i
$939$	40.0598	−	13.0162i	1.30730	−	0.424768i
$940$	−12.7878	−	21.1648i	−0.417092	−	0.690318i
$941$	3.89942	+	18.3453i	0.127117	+	0.598040i	0.994880	+	0.101062i	$0.0322239\pi$
$941$	3.89942	+	18.3453i	0.127117	+	0.598040i	−0.867763	+	0.496979i	$0.834443\pi$
$942$	−61.1909	−	75.5645i	−1.99371	−	2.46203i
$943$	1.42638	+	5.32333i	0.0464494	+	0.173351i
$944$	−3.94575	−	2.86676i	−0.128423	−	0.0933050i
$945$	10.6707	+	52.1473i	0.347118	+	1.69635i
$946$	37.8172	−	27.4758i	1.22954	−	0.893315i
$947$	−44.1116	−	35.7209i	−1.43344	−	1.16077i	−0.960019	−	0.279934i	$-0.909687\pi$
$947$	−44.1116	−	35.7209i	−1.43344	−	1.16077i	−0.473416	−	0.880839i	$-0.656979\pi$
$948$	2.50567	+	47.8111i	0.0813805	+	1.55283i
$949$	−3.02293	+	1.74529i	−0.0981286	+	0.0566545i
$950$	−16.3355	+	35.4849i	−0.529993	+	1.15128i
$951$			87.4392i			2.83541i
$952$	36.8955	+	4.90714i	1.19579	+	0.159041i
$953$	30.4878	+	4.82879i	0.987595	+	0.156420i	0.629278	−	0.777180i	$-0.283351\pi$
$953$	30.4878	+	4.82879i	0.987595	+	0.156420i	0.358317	+	0.933600i	$0.383351\pi$
$954$	58.5802	−	6.15703i	1.89660	−	0.199341i
$955$	−25.1861	−	24.2028i	−0.815002	−	0.783185i
$956$	−2.75399	+	26.2025i	−0.0890704	+	0.847449i
$957$	90.3178	−	24.2006i	2.91956	−	0.782294i
$958$	24.2670	−	3.84351i	0.784031	−	0.124178i
$959$	0.882018	+	35.4797i	0.0284818	+	1.14570i
$960$	−38.2612	+	35.8550i	−1.23488	+	1.15722i
$961$	−0.436352	−	0.0927495i	−0.0140759	−	0.00299192i
$962$	2.32120	+	1.50740i	0.0748385	+	0.0486007i
$963$	9.00394	+	5.84723i	0.290148	+	0.188424i
$964$	−17.3272	−	3.68301i	−0.558072	−	0.118622i
$965$	−8.61610	+	44.9137i	−0.277362	+	1.44582i
$966$	88.3344	−	53.9705i	2.84211	−	1.73647i
$967$	23.7132	−	3.75580i	0.762565	−	0.120778i	0.236974	−	0.971516i	$-0.423844\pi$
$967$	23.7132	−	3.75580i	0.762565	−	0.120778i	0.525591	+	0.850738i	$0.323844\pi$
$968$	2.24528	−	0.601620i	0.0721659	−	0.0193368i
$969$	−2.84342	+	27.0533i	−0.0913437	+	0.869077i
$970$	−82.0672	+	43.8944i	−2.63502	+	1.40936i
$971$	15.4953	−	1.62862i	0.497267	−	0.0522649i	0.147424	−	0.989073i	$-0.452902\pi$
$971$	15.4953	−	1.62862i	0.497267	−	0.0522649i	0.349843	+	0.936808i	$0.386235\pi$
$972$	−0.0581201	−	0.00920532i	−0.00186420	−	0.000295261i
$973$	−20.9191	−	16.0959i	−0.670636	−	0.516010i
$974$			45.6672i			1.46327i
$975$	8.42516	+	5.62292i	0.269821	+	0.180078i
$976$	20.7506	−	11.9804i	0.664211	−	0.383482i
$977$	−2.03754	−	38.8786i	−0.0651868	−	1.24384i	−0.813924	−	0.580971i	$-0.802673\pi$
$977$	−2.03754	−	38.8786i	−0.0651868	−	1.24384i	0.748737	−	0.662867i	$-0.230660\pi$
$978$	68.5136	+	55.4813i	2.19082	+	1.77409i
$979$	33.9485	−	24.6650i	1.08500	−	0.788298i
$980$	−47.4225	−	41.2402i	−1.51485	−	1.31737i
$981$	−11.9304	−	8.66798i	−0.380910	−	0.276747i
$982$	6.49448	+	24.2377i	0.207247	+	0.773456i
$983$	27.5093	+	33.9712i	0.877411	+	1.08351i	0.995891	+	0.0905558i	$0.0288643\pi$
$983$	27.5093	+	33.9712i	0.877411	+	1.08351i	−0.118481	+	0.992956i	$0.537802\pi$
$984$	−3.19446	−	15.0287i	−0.101836	−	0.479099i
$985$	−2.58228	+	30.3733i	−0.0822784	+	0.967773i
$986$	−61.1058	+	19.8545i	−1.94600	+	0.632295i
$987$	6.18092	+	20.9684i	0.196741	+	0.667433i
$988$	−7.69609	+	3.92135i	−0.244845	+	0.124755i
$989$	−6.22216	+	29.2730i	−0.197853	+	0.930826i
$990$	−67.2759	−	88.8241i	−2.13817	−	2.82301i
$991$	23.9867	−	5.09852i	0.761962	−	0.161960i	0.189488	−	0.981883i	$-0.439317\pi$
$991$	23.9867	−	5.09852i	0.761962	−	0.161960i	0.572474	+	0.819923i	$0.305984\pi$
$992$	−0.767179	−	0.294492i	−0.0243579	−	0.00935014i
$993$	17.8981	−	17.8981i	0.567978	−	0.567978i
$994$	14.8244	+	62.1107i	0.470202	+	1.97003i
$995$	27.3993	+	40.4071i	0.868617	+	1.28099i
$996$	−10.0404	−	95.5281i	−0.318143	−	3.02693i
$997$	−20.3999	−	53.1435i	−0.646071	−	1.68307i	−0.727251	−	0.686372i	$-0.759202\pi$
$997$	−20.3999	−	53.1435i	−0.646071	−	1.68307i	0.0811802	−	0.996699i	$-0.474131\pi$
$998$	−25.2679	+	1.32423i	−0.799841	+	0.0419179i
$999$	−7.51747	+	13.0206i	−0.237842	+	0.411955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.33.3	✓	288
5.2	odd	4		875.2.bb.b.607.3		288
5.3	odd	4		875.2.bb.a.607.16		288
5.4	even	2		875.2.bb.c.768.16		288
7.3	odd	6	inner	175.2.x.a.108.3	yes	288
25.3	odd	20		875.2.bb.c.257.16		288
25.4	even	10		875.2.bb.a.243.3		288
25.21	even	5		875.2.bb.b.243.16		288
25.22	odd	20	inner	175.2.x.a.47.3	yes	288
35.3	even	12		875.2.bb.a.857.3		288
35.17	even	12		875.2.bb.b.857.16		288
35.24	odd	6		875.2.bb.c.143.16		288
175.3	even	60		875.2.bb.c.507.16		288
175.122	even	60	inner	175.2.x.a.122.3	yes	288
175.129	odd	30		875.2.bb.a.493.16		288
175.171	odd	30		875.2.bb.b.493.3		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.3	✓	288	1.1	even	1	trivial
175.2.x.a.47.3	yes	288	25.22	odd	20	inner
175.2.x.a.108.3	yes	288	7.3	odd	6	inner
175.2.x.a.122.3	yes	288	175.122	even	60	inner
875.2.bb.a.243.3		288	25.4	even	10
875.2.bb.a.493.16		288	175.129	odd	30
875.2.bb.a.607.16		288	5.3	odd	4
875.2.bb.a.857.3		288	35.3	even	12
875.2.bb.b.243.16		288	25.21	even	5
875.2.bb.b.493.3		288	175.171	odd	30
875.2.bb.b.607.3		288	5.2	odd	4
875.2.bb.b.857.16		288	35.17	even	12
875.2.bb.c.143.16		288	35.24	odd	6
875.2.bb.c.257.16		288	25.3	odd	20
875.2.bb.c.507.16		288	175.3	even	60
875.2.bb.c.768.16		288	5.4	even	2

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

\(f(q)\)	\(=\)	\(q+(-2.05690 + 1.33577i) q^{2} +(-2.80061 + 1.07506i) q^{3} +(1.63309 - 3.66797i) q^{4} +(2.23023 - 0.161449i) q^{5} +(4.32456 - 5.95224i) q^{6} +(2.18242 - 1.49568i) q^{7} +(0.773125 + 4.88132i) q^{8} +(4.45826 - 4.01424i) q^{9} +(-4.37170 + 3.31115i) q^{10} +(-2.26620 + 2.51687i) q^{11} +(-0.630373 + 12.0282i) q^{12} +(-0.306584 - 0.601706i) q^{13} +(-2.49113 + 5.99166i) q^{14} +(-6.07245 + 2.84978i) q^{15} +(-2.73729 - 3.04006i) q^{16} +(2.21216 - 1.79137i) q^{17} +(-3.80811 + 14.2121i) q^{18} +(2.91018 - 1.29570i) q^{19} +(3.04997 - 8.44409i) q^{20} +(-4.50417 + 6.53504i) q^{21} +(1.29940 - 8.20407i) q^{22} +(2.89634 + 4.45997i) q^{23} +(-7.41291 - 12.8395i) q^{24} +(4.94787 - 0.720139i) q^{25} +(1.43435 + 0.828123i) q^{26} +(-4.08462 + 8.01652i) q^{27} +(-1.92203 - 10.4476i) q^{28} +(5.40952 + 7.44556i) q^{29} +(8.68378 - 13.9731i) q^{30} +(-5.49728 - 0.577787i) q^{31} +(0.143600 + 0.0384776i) q^{32} +(3.64098 - 9.48509i) q^{33} +(-2.15734 + 6.63961i) q^{34} +(4.62582 - 3.68806i) q^{35} +(-7.44339 - 22.9084i) q^{36} +(1.66879 + 0.0874574i) q^{37} +(-4.25520 + 6.55243i) q^{38} +(1.50549 + 1.35555i) q^{39} +(2.51233 + 10.7617i) q^{40} +(0.985611 + 0.320244i) q^{41} +(0.535343 - 19.4584i) q^{42} +(3.97930 + 3.97930i) q^{43} +(5.53092 + 12.4227i) q^{44} +(9.29487 - 9.67247i) q^{45} +(-11.9149 - 5.30487i) q^{46} +(1.73333 - 2.14048i) q^{47} +(10.9343 + 5.57132i) q^{48} +(2.52589 - 6.52839i) q^{49} +(-9.21532 + 8.09044i) q^{50} +(-4.26959 + 7.39515i) q^{51} +(-2.70772 + 0.141906i) q^{52} +(-1.43467 - 3.73744i) q^{53} +(-2.30654 - 21.9453i) q^{54} +(-4.64781 + 5.97909i) q^{55} +(8.98817 + 9.49673i) q^{56} +(-6.75735 + 6.75735i) q^{57} +(-21.0724 - 8.08892i) q^{58} +(1.16618 - 0.247880i) q^{59} +(0.536074 + 26.9275i) q^{60} +(-1.21778 + 5.72922i) q^{61} +(12.0791 - 6.15462i) q^{62} +(3.72578 - 15.4289i) q^{63} +(7.43442 - 2.41559i) q^{64} +(-0.780899 - 1.29245i) q^{65} +(5.18072 + 24.3734i) q^{66} +(4.70495 + 5.81013i) q^{67} +(-2.95806 - 11.0396i) q^{68} +(-12.9062 - 9.37692i) q^{69} +(-4.58845 + 13.7650i) q^{70} +(7.96131 - 5.78423i) q^{71} +(23.0416 + 18.6587i) q^{72} +(-0.270517 - 5.16177i) q^{73} +(-3.54935 + 2.04922i) q^{74} +(-13.0829 + 7.33606i) q^{75} -12.7904i q^{76} +(-1.18137 + 8.88238i) q^{77} +(-4.90734 - 0.777246i) q^{78} +(3.95313 - 0.415491i) q^{79} +(-6.59560 - 6.33812i) q^{80} +(0.939990 - 8.94341i) q^{81} +(-2.45507 + 0.657835i) q^{82} +(-7.87661 + 1.24753i) q^{83} +(16.6146 + 27.1935i) q^{84} +(4.64442 - 4.35233i) q^{85} +(-13.5004 - 2.86961i) q^{86} +(-23.1544 - 15.0366i) q^{87} +(-14.0377 - 9.11621i) q^{88} +(-12.1194 - 2.57605i) q^{89} +(-6.19844 + 32.3110i) q^{90} +(-1.56905 - 0.854621i) q^{91} +(21.0890 - 3.34017i) q^{92} +(16.0169 - 4.29172i) q^{93} +(-0.706097 + 6.71806i) q^{94} +(6.28119 - 3.35955i) q^{95} +(-0.443535 + 0.0466174i) q^{96} +(16.7616 + 2.65478i) q^{97} +(3.52490 + 16.8022i) q^{98} +20.3180i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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