LMFDB - Embedded newform 115.2.l.a.38.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,2,Mod(7,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			38.8
Character	$\chi$	$=$	115.38
Dual form			115.2.l.a.112.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.927048 + 1.23839i) q^{2} +(0.547968 - 1.46916i) q^{3} +(-0.110730 + 0.377111i) q^{4} +(-1.20451 - 1.88392i) q^{5} +(2.32738 - 0.683382i) q^{6} +(0.876587 + 4.02961i) q^{7} +(2.32915 - 0.868729i) q^{8} +(0.409093 + 0.354481i) q^{9} +(1.21639 - 3.23814i) q^{10} +(-4.51811 + 0.649606i) q^{11} +(0.493360 + 0.369324i) q^{12} +(-3.88221 - 0.844524i) q^{13} +(-4.17759 + 4.82120i) q^{14} +(-3.42781 + 0.737293i) q^{15} +(3.89634 + 2.50403i) q^{16} +(-0.258676 - 0.141248i) q^{17} +(-0.0597374 + 0.835238i) q^{18} +(-3.49008 - 1.02478i) q^{19} +(0.843823 - 0.245629i) q^{20} +(6.40047 + 0.920248i) q^{21} +(-4.99297 - 4.99297i) q^{22} +(4.78688 - 0.292826i) q^{23} -3.89793i q^{24} +(-2.09830 + 4.53841i) q^{25} +(-2.55315 - 5.59062i) q^{26} +(4.87362 - 2.66120i) q^{27} +(-1.61667 - 0.115627i) q^{28} +(-0.403824 - 1.37530i) q^{29} +(-4.09080 - 3.56146i) q^{30} +(-2.77678 + 6.08030i) q^{31} +(0.156449 + 2.18744i) q^{32} +(-1.52140 + 6.99378i) q^{33} +(-0.0648851 - 0.451286i) q^{34} +(6.53559 - 6.50513i) q^{35} +(-0.178977 + 0.115022i) q^{36} +(3.08799 - 0.220858i) q^{37} +(-1.96640 - 5.27211i) q^{38} +(-3.36807 + 5.24081i) q^{39} +(-4.44211 - 3.34154i) q^{40} +(-6.08818 - 7.02614i) q^{41} +(4.79391 + 8.77940i) q^{42} +(1.29382 + 0.482569i) q^{43} +(0.255316 - 1.77576i) q^{44} +(0.175056 - 1.19767i) q^{45} +(4.80030 + 5.65657i) q^{46} +(9.04049 - 9.04049i) q^{47} +(5.81388 - 4.35221i) q^{48} +(-9.10189 + 4.15669i) q^{49} +(-7.56555 + 1.60881i) q^{50} +(-0.349262 + 0.302637i) q^{51} +(0.748357 - 1.37051i) q^{52} +(0.847638 - 0.184392i) q^{53} +(7.81368 + 3.56839i) q^{54} +(6.66592 + 7.72929i) q^{55} +(5.54234 + 8.62405i) q^{56} +(-3.41802 + 4.56593i) q^{57} +(1.32879 - 1.77506i) q^{58} +(2.33805 + 3.63807i) q^{59} +(0.101519 - 1.37431i) q^{60} +(-3.31298 - 1.51299i) q^{61} +(-10.1040 + 2.19799i) q^{62} +(-1.06981 + 1.95921i) q^{63} +(4.43677 - 3.84448i) q^{64} +(3.08516 + 8.33102i) q^{65} +(-10.0714 + 4.59948i) q^{66} +(0.361592 - 0.270684i) q^{67} +(0.0819094 - 0.0819094i) q^{68} +(2.19285 - 7.19315i) q^{69} +(14.1147 + 2.06305i) q^{70} +(-0.537154 + 3.73599i) q^{71} +(1.26079 + 0.470249i) q^{72} +(-2.09543 - 3.83749i) q^{73} +(3.13623 + 3.61940i) q^{74} +(5.51784 + 5.56963i) q^{75} +(0.772913 - 1.20268i) q^{76} +(-6.57817 - 17.6368i) q^{77} +(-9.61254 + 0.687502i) q^{78} +(8.40008 - 5.39840i) q^{79} +(0.0241893 - 10.3565i) q^{80} +(-1.00803 - 7.01097i) q^{81} +(3.05707 - 14.0531i) q^{82} +(0.0672048 + 0.939647i) q^{83} +(-1.05576 + 2.31179i) q^{84} +(0.0454792 + 0.657460i) q^{85} +(0.601822 + 2.04962i) q^{86} +(-2.24181 - 0.160338i) q^{87} +(-9.95903 + 5.43804i) q^{88} +(-1.99112 - 4.35995i) q^{89} +(1.64547 - 0.893514i) q^{90} -16.3841i q^{91} +(-0.419623 + 1.83761i) q^{92} +(7.41134 + 7.41134i) q^{93} +(19.5766 + 2.81470i) q^{94} +(2.27325 + 7.80939i) q^{95} +(3.29943 + 0.968799i) q^{96} +(-0.556423 + 7.77981i) q^{97} +(-13.5855 - 7.41825i) q^{98} +(-2.07860 - 1.33583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.927048	+	1.23839i	0.655522	+	0.875675i	0.997958	−	0.0638660i	$-0.0203430\pi$
$2$	0.927048	+	1.23839i	0.655522	+	0.875675i	−0.342436	+	0.939541i	$0.611252\pi$
$3$	0.547968	−	1.46916i	0.316369	−	0.848219i	−0.677283	−	0.735723i	$-0.736843\pi$
$3$	0.547968	−	1.46916i	0.316369	−	0.848219i	0.993652	−	0.112496i	$-0.0358846\pi$
$4$	−0.110730	+	0.377111i	−0.0553649	+	0.188556i
$5$	−1.20451	−	1.88392i	−0.538674	−	0.842514i
$5$	−1.20451	−	1.88392i	−0.538674	−	0.842514i
$6$	2.32738	−	0.683382i	0.950151	−	0.278989i
$7$	0.876587	+	4.02961i	0.331319	+	1.52305i	0.777948	+	0.628329i	$0.216261\pi$
$7$	0.876587	+	4.02961i	0.331319	+	1.52305i	−0.446629	+	0.894719i	$0.647376\pi$
$8$	2.32915	−	0.868729i	0.823480	−	0.307142i
$9$	0.409093	+	0.354481i	0.136364	+	0.118160i
$10$	1.21639	−	3.23814i	0.384655	−	1.02399i
$11$	−4.51811	+	0.649606i	−1.36226	+	0.195864i	−0.784392	−	0.620266i	$-0.787025\pi$
$11$	−4.51811	+	0.649606i	−1.36226	+	0.195864i	−0.577869	+	0.816129i	$0.696116\pi$
$12$	0.493360	+	0.369324i	0.142421	+	0.106615i
$13$	−3.88221	−	0.844524i	−1.07673	−	0.234229i	−0.360973	−	0.932576i	$-0.617556\pi$
$13$	−3.88221	−	0.844524i	−1.07673	−	0.234229i	−0.715759	+	0.698347i	$0.753919\pi$
$14$	−4.17759	+	4.82120i	−1.11651	+	1.28852i
$15$	−3.42781	+	0.737293i	−0.885056	+	0.190368i
$16$	3.89634	+	2.50403i	0.974085	+	0.626007i
$17$	−0.258676	−	0.141248i	−0.0627382	−	0.0342576i	0.447574	−	0.894247i	$-0.352288\pi$
$17$	−0.258676	−	0.141248i	−0.0627382	−	0.0342576i	−0.510312	+	0.859989i	$0.670470\pi$
$18$	−0.0597374	+	0.835238i	−0.0140802	+	0.196867i
$19$	−3.49008	−	1.02478i	−0.800680	−	0.235101i	−0.144303	−	0.989534i	$-0.546094\pi$
$19$	−3.49008	−	1.02478i	−0.800680	−	0.235101i	−0.656377	+	0.754433i	$0.727912\pi$
$20$	0.843823	−	0.245629i	0.188684	−	0.0549244i
$21$	6.40047	+	0.920248i	1.39670	+	0.200815i
$22$	−4.99297	−	4.99297i	−1.06450	−	1.06450i
$23$	4.78688	−	0.292826i	0.998134	−	0.0610583i
$23$	4.78688	−	0.292826i	0.998134	−	0.0610583i
$24$		−	3.89793i		−	0.795661i
$25$	−2.09830	+	4.53841i	−0.419660	+	0.907682i
$26$	−2.55315	−	5.59062i	−0.500714	−	1.09641i
$27$	4.87362	−	2.66120i	0.937928	−	0.512147i
$28$	−1.61667	−	0.115627i	−0.305523	−	0.0218514i
$29$	−0.403824	−	1.37530i	−0.0749882	−	0.255386i	0.913464	−	0.406920i	$-0.133397\pi$
$29$	−0.403824	−	1.37530i	−0.0749882	−	0.255386i	−0.988452	+	0.151533i	$0.951579\pi$
$30$	−4.09080	−	3.56146i	−0.746875	−	0.650231i
$31$	−2.77678	+	6.08030i	−0.498724	+	1.09205i	0.478157	+	0.878274i	$0.341305\pi$
$31$	−2.77678	+	6.08030i	−0.498724	+	1.09205i	−0.976882	+	0.213780i	$0.931422\pi$
$32$	0.156449	+	2.18744i	0.0276565	+	0.386689i
$33$	−1.52140	+	6.99378i	−0.264842	+	1.21746i
$34$	−0.0648851	−	0.451286i	−0.0111277	−	0.0773949i
$35$	6.53559	−	6.50513i	1.10472	−	1.09957i
$36$	−0.178977	+	0.115022i	−0.0298296	+	0.0191703i
$37$	3.08799	−	0.220858i	0.507663	−	0.0363088i	0.184841	−	0.982768i	$-0.440823\pi$
$37$	3.08799	−	0.220858i	0.507663	−	0.0363088i	0.322822	+	0.946460i	$0.395369\pi$
$38$	−1.96640	−	5.27211i	−0.318991	−	0.855249i
$39$	−3.36807	+	5.24081i	−0.539322	+	0.839202i
$40$	−4.44211	−	3.34154i	−0.702359	−	0.528343i
$41$	−6.08818	−	7.02614i	−0.950814	−	1.09730i	−0.995159	−	0.0982818i	$-0.968665\pi$
$41$	−6.08818	−	7.02614i	−0.950814	−	1.09730i	0.0443444	−	0.999016i	$-0.485880\pi$
$42$	4.79391	+	8.77940i	0.739717	+	1.35469i
$43$	1.29382	+	0.482569i	0.197305	+	0.0735911i	0.446174	−	0.894946i	$-0.352786\pi$
$43$	1.29382	+	0.482569i	0.197305	+	0.0735911i	−0.248869	+	0.968537i	$0.580059\pi$
$44$	0.255316	−	1.77576i	0.0384903	−	0.267706i
$45$	0.175056	−	1.19767i	0.0260958	−	0.178539i
$46$	4.80030	+	5.65657i	0.707766	+	0.834016i
$47$	9.04049	−	9.04049i	1.31869	−	1.31869i	0.403879	−	0.914812i	$-0.367662\pi$
$47$	9.04049	−	9.04049i	1.31869	−	1.31869i	0.914812	−	0.403879i	$-0.132338\pi$
$48$	5.81388	−	4.35221i	0.839161	−	0.628188i
$49$	−9.10189	+	4.15669i	−1.30027	+	0.593813i
$50$	−7.56555	+	1.60881i	−1.06993	+	0.227520i
$51$	−0.349262	+	0.302637i	−0.0489064	+	0.0423776i
$52$	0.748357	−	1.37051i	0.103778	−	0.190056i
$53$	0.847638	−	0.184392i	0.116432	−	0.0253282i	−0.153972	−	0.988075i	$-0.549206\pi$
$53$	0.847638	−	0.184392i	0.116432	−	0.0253282i	0.270404	+	0.962747i	$0.412843\pi$
$54$	7.81368	+	3.56839i	1.06331	+	0.485596i
$55$	6.66592	+	7.72929i	0.898833	+	1.04222i
$56$	5.54234	+	8.62405i	0.740626	+	1.15244i
$57$	−3.41802	+	4.56593i	−0.452727	+	0.604773i
$58$	1.32879	−	1.77506i	0.174479	−	0.233077i
$59$	2.33805	+	3.63807i	0.304388	+	0.473636i	0.959427	−	0.281959i	$-0.0909841\pi$
$59$	2.33805	+	3.63807i	0.304388	+	0.473636i	−0.655039	+	0.755595i	$0.727348\pi$
$60$	0.101519	−	1.37431i	0.0131061	−	0.177422i
$61$	−3.31298	−	1.51299i	−0.424184	−	0.193718i	0.191873	−	0.981420i	$-0.438544\pi$
$61$	−3.31298	−	1.51299i	−0.424184	−	0.193718i	−0.616057	+	0.787701i	$0.711271\pi$
$62$	−10.1040	+	2.19799i	−1.28321	+	0.279145i
$63$	−1.06981	+	1.95921i	−0.134784	+	0.246838i
$64$	4.43677	−	3.84448i	0.554596	−	0.480561i
$65$	3.08516	+	8.33102i	0.382667	+	1.03334i
$66$	−10.0714	+	4.59948i	−1.23971	+	0.566156i
$67$	0.361592	−	0.270684i	0.0441755	−	0.0330694i	−0.576962	−	0.816771i	$-0.695762\pi$
$67$	0.361592	−	0.270684i	0.0441755	−	0.0330694i	0.621137	+	0.783702i	$0.286671\pi$
$68$	0.0819094	−	0.0819094i	0.00993297	−	0.00993297i
$69$	2.19285	−	7.19315i	0.263988	−	0.865953i
$70$	14.1147	+	2.06305i	1.68703	+	0.246581i
$71$	−0.537154	+	3.73599i	−0.0637485	+	0.443380i	0.932802	+	0.360390i	$0.117356\pi$
$71$	−0.537154	+	3.73599i	−0.0637485	+	0.443380i	−0.996550	+	0.0829907i	$0.973553\pi$
$72$	1.26079	+	0.470249i	0.148585	+	0.0554194i
$73$	−2.09543	−	3.83749i	−0.245252	−	0.449145i	0.725836	−	0.687868i	$-0.241453\pi$
$73$	−2.09543	−	3.83749i	−0.245252	−	0.449145i	−0.971088	+	0.238723i	$0.923271\pi$
$74$	3.13623	+	3.61940i	0.364579	+	0.420746i
$75$	5.51784	+	5.56963i	0.637145	+	0.643126i
$76$	0.772913	−	1.20268i	0.0886592	−	0.137956i
$77$	−6.57817	−	17.6368i	−0.749652	−	2.00989i
$78$	−9.61254	+	0.687502i	−1.08841	+	0.0778443i
$79$	8.40008	−	5.39840i	0.945083	−	0.607368i	0.0252511	−	0.999681i	$-0.491961\pi$
$79$	8.40008	−	5.39840i	0.945083	−	0.607368i	0.919832	+	0.392313i	$0.128325\pi$
$80$	0.0241893	−	10.3565i	0.00270445	−	1.15789i
$81$	−1.00803	−	7.01097i	−0.112003	−	0.778997i
$82$	3.05707	−	14.0531i	0.337597	−	1.55191i
$83$	0.0672048	+	0.939647i	0.00737669	+	0.103140i	0.999806	−	0.0196740i	$-0.00626282\pi$
$83$	0.0672048	+	0.939647i	0.00737669	+	0.103140i	−0.992430	+	0.122814i	$0.960808\pi$
$84$	−1.05576	+	2.31179i	−0.115193	+	0.252237i
$85$	0.0454792	+	0.657460i	0.00493292	+	0.0713115i
$86$	0.601822	+	2.04962i	0.0648961	+	0.221016i
$87$	−2.24181	−	0.160338i	−0.240347	−	0.0171900i
$88$	−9.95903	+	5.43804i	−1.06164	+	0.579697i
$89$	−1.99112	−	4.35995i	−0.211058	−	0.462153i	0.774263	−	0.632864i	$-0.218121\pi$
$89$	−1.99112	−	4.35995i	−0.211058	−	0.462153i	−0.985321	+	0.170711i	$0.945394\pi$
$90$	1.64547	−	0.893514i	0.173448	−	0.0941846i
$91$		−	16.3841i		−	1.71752i
$92$	−0.419623	+	1.83761i	−0.0437487	+	0.191584i
$93$	7.41134	+	7.41134i	0.768520	+	0.768520i
$94$	19.5766	+	2.81470i	2.01918	+	0.290314i
$95$	2.27325	+	7.80939i	0.233230	+	0.801227i
$96$	3.29943	+	0.968799i	0.336746	+	0.0988776i
$97$	−0.556423	+	7.77981i	−0.0564962	+	0.789920i	0.887676	+	0.460468i	$0.152318\pi$
$97$	−0.556423	+	7.77981i	−0.0564962	+	0.789920i	−0.944172	+	0.329452i	$0.893136\pi$
$98$	−13.5855	−	7.41825i	−1.37234	−	0.749356i
$99$	−2.07860	−	1.33583i	−0.208907	−	0.134256i
$100$	−1.47914	−	1.29383i	−0.147914	−	0.129383i
$101$	−2.33404	+	2.69363i	−0.232246	+	0.268026i	−0.859896	−	0.510470i	$-0.829472\pi$
$101$	−2.33404	+	2.69363i	−0.232246	+	0.268026i	0.627650	+	0.778496i	$0.284017\pi$
$102$	−0.698565	−	0.151964i	−0.0691683	−	0.0150466i
$103$	10.6765	+	7.99235i	1.05199	+	0.787510i	0.977759	−	0.209731i	$-0.0672588\pi$
$103$	10.6765	+	7.99235i	1.05199	+	0.787510i	0.0742312	+	0.997241i	$0.476350\pi$
$104$	−9.77593	+	1.40557i	−0.958609	+	0.137827i
$105$	−5.97577	−	13.1664i	−0.583176	−	1.28491i
$106$	1.01415	+	0.878767i	0.0985031	+	0.0853534i
$107$	−14.0243	+	5.23079i	−1.35578	+	0.505680i	−0.919131	−	0.393953i	$-0.871107\pi$
$107$	−14.0243	+	5.23079i	−1.35578	+	0.505680i	−0.436649	+	0.899632i	$0.643835\pi$
$108$	0.463912	+	2.13257i	0.0446400	+	0.205207i
$109$	−4.81925	+	1.41506i	−0.461600	+	0.135538i	−0.504260	−	0.863552i	$-0.668235\pi$
$109$	−4.81925	+	1.41506i	−0.461600	+	0.135538i	0.0426604	+	0.999090i	$0.486417\pi$
$110$	−3.39225	+	15.4204i	−0.323439	+	1.47028i
$111$	1.36764	−	4.65777i	0.129811	−	0.442096i
$112$	−6.67476	+	17.8957i	−0.630705	+	1.69099i
$113$	−5.83014	−	7.78815i	−0.548453	−	0.732647i	0.437583	−	0.899178i	$-0.355835\pi$
$113$	−5.83014	−	7.78815i	−0.548453	−	0.732647i	−0.986036	+	0.166530i	$0.946744\pi$
$114$	−8.82308			−0.826357
$115$	−6.31752	−	8.66539i	−0.589112	−	0.808051i
$116$	0.563356			0.0523063
$117$	−1.28882	−	1.72166i	−0.119151	−	0.159167i
$118$	−2.33787	+	6.26808i	−0.215219	+	0.577024i
$119$	0.342421	−	1.16618i	0.0313897	−	0.106903i
$120$	−7.34338	+	4.69510i	−0.670355	+	0.428602i
$121$	9.43689	−	2.77092i	0.857899	−	0.251902i
$122$	−1.19762	−	5.50538i	−0.108428	−	0.498434i
$123$	−13.6586	+	5.09440i	−1.23156	+	0.459347i
$124$	−1.98548	−	1.72043i	−0.178301	−	0.154499i
$125$	11.0774	−	1.51355i	0.990794	−	0.135376i
$126$	−3.41804	+	0.491440i	−0.304503	+	0.0437810i
$127$	11.1968	+	8.38185i	0.993559	+	0.743769i	0.966711	−	0.255870i	$-0.0823620\pi$
$127$	11.1968	+	8.38185i	0.993559	+	0.743769i	0.0268482	+	0.999640i	$0.491453\pi$
$128$	13.1599	+	2.86276i	1.16318	+	0.253035i
$129$	1.41794	−	1.63639i	0.124843	−	0.144076i
$130$	−7.45697	+	11.5439i	−0.654019	+	1.01247i
$131$	−1.30313	−	0.837474i	−0.113855	−	0.0731704i	0.482474	−	0.875910i	$-0.339738\pi$
$131$	−1.30313	−	0.837474i	−0.113855	−	0.0731704i	−0.596329	+	0.802740i	$0.703375\pi$
$132$	−2.46897	−	1.34816i	−0.214896	−	0.117342i
$133$	1.07010	−	14.9620i	0.0927895	−	1.29737i
$134$	0.670426	+	0.196855i	0.0579160	+	0.0170057i
$135$	−10.8838	−	5.97605i	−0.936729	−	0.514337i
$136$	−0.725202	−	0.104268i	−0.0621856	−	0.00894094i
$137$	0.536442	+	0.536442i	0.0458314	+	0.0458314i	0.729651	−	0.683820i	$-0.239683\pi$
$137$	0.536442	+	0.536442i	0.0458314	+	0.0458314i	−0.683820	+	0.729651i	$0.739683\pi$
$138$	10.9408	−	3.95279i	0.931343	−	0.336484i
$139$			1.53231i			0.129969i	0.997886	+	0.0649844i	$0.0206998\pi$
$139$			1.53231i			0.129969i	−0.997886	+	0.0649844i	$0.979300\pi$
$140$	1.72947	+	3.18496i	0.146167	+	0.269178i
$141$	−8.32801	−	18.2358i	−0.701345	−	1.53573i
$142$	−5.12458	+	2.79823i	−0.430046	+	0.234823i
$143$	18.0889	+	1.29374i	1.51267	+	0.108188i
$144$	0.706335	+	2.40556i	0.0588613	+	0.200463i
$145$	−2.10454	+	2.41733i	−0.174772	+	0.200749i
$146$	2.80975	−	6.15250i	0.232537	−	0.509185i
$147$	1.11930	+	15.6498i	0.0923182	+	1.29078i
$148$	−0.258645	+	1.18897i	−0.0212605	+	0.0977329i
$149$	−1.08165	−	7.52305i	−0.0886123	−	0.616312i	−0.984937	−	0.172914i	$-0.944682\pi$
$149$	−1.08165	−	7.52305i	−0.0886123	−	0.616312i	0.896325	−	0.443398i	$-0.146227\pi$
$150$	−1.78208	+	11.9966i	−0.145506	+	0.979515i
$151$	−1.59008	+	1.02188i	−0.129399	+	0.0831597i	−0.603739	−	0.797182i	$-0.706323\pi$
$151$	−1.59008	+	1.02188i	−0.129399	+	0.0831597i	0.474340	+	0.880342i	$0.342687\pi$
$152$	−9.01919	+	0.645065i	−0.731553	+	0.0523217i
$153$	−0.0557529	−	0.149479i	−0.00450735	−	0.0120847i
$154$	15.7429	−	24.4965i	1.26860	−	1.97398i
$155$	14.7995	−	2.09257i	1.18872	−	0.168079i
$156$	−1.60342	−	1.85045i	−0.128377	−	0.148155i
$157$	−1.83862	−	3.36717i	−0.146738	−	0.268730i	0.793964	−	0.607964i	$-0.208014\pi$
$157$	−1.83862	−	3.36717i	−0.146738	−	0.268730i	−0.940702	+	0.339235i	$0.889832\pi$
$158$	14.4726	+	5.39801i	1.15138	+	0.429442i
$159$	0.193577	−	1.34635i	0.0153516	−	0.106773i
$160$	3.93252	−	2.92954i	0.310893	−	0.231600i
$161$	5.37609	+	19.0326i	0.423695	+	1.49998i
$162$	7.74784	−	7.74784i	0.608728	−	0.608728i
$163$	−18.2741	+	13.6798i	−1.43134	+	1.07149i	−0.447129	+	0.894470i	$0.647553\pi$
$163$	−18.2741	+	13.6798i	−1.43134	+	1.07149i	−0.984208	+	0.177016i	$0.943356\pi$
$164$	3.32378	−	1.51792i	0.259544	−	0.118530i
$165$	15.0083	−	5.55789i	1.16839	−	0.432681i
$166$	−1.10135	+	0.954324i	−0.0854812	+	0.0740699i
$167$	1.36796	−	2.50524i	0.105856	−	0.193861i	−0.819382	−	0.573248i	$-0.805683\pi$
$167$	1.36796	−	2.50524i	0.105856	−	0.193861i	0.925238	+	0.379387i	$0.123865\pi$
$168$	15.7071	−	3.41687i	1.21183	−	0.263617i
$169$	2.53315	+	1.15685i	0.194858	+	0.0889887i
$170$	−0.772031	+	0.665818i	−0.0592121	+	0.0510659i
$171$	−1.06450	−	1.65640i	−0.0814045	−	0.126668i
$172$	−0.325246	+	0.434478i	−0.0247998	+	0.0331287i
$173$	−7.95803	+	10.6307i	−0.605038	+	0.808236i	−0.993572	−	0.113198i	$-0.963891\pi$
$173$	−7.95803	+	10.6307i	−0.605038	+	0.808236i	0.388534	+	0.921434i	$0.372981\pi$
$174$	−1.87971	−	2.92488i	−0.142500	−	0.221735i
$175$	−20.1273	−	4.47700i	−1.52148	−	0.338430i
$176$	−19.2307	−	8.78238i	−1.44957	−	0.661997i
$177$	6.62607	−	1.44141i	0.498046	−	0.108343i
$178$	3.55345	−	6.50767i	0.266343	−	0.487770i
$179$	1.30949	−	1.13468i	0.0978757	−	0.0848098i	−0.604548	−	0.796568i	$-0.706646\pi$
$179$	1.30949	−	1.13468i	0.0978757	−	0.0848098i	0.702424	+	0.711759i	$0.252101\pi$
$180$	0.432272	+	0.198634i	0.0322197	+	0.0148053i
$181$	22.3917	−	10.2259i	1.66436	−	0.760089i	0.664444	−	0.747338i	$-0.268669\pi$
$181$	22.3917	−	10.2259i	1.66436	−	0.760089i	0.999919	−	0.0127505i	$-0.00405872\pi$
$182$	20.2899	−	15.1888i	1.50399	−	1.12587i
$183$	−4.03822	+	4.03822i	−0.298514	+	0.298514i
$184$	10.8950	−	4.84054i	0.803189	−	0.356849i
$185$	−4.13560	−	5.55150i	−0.304056	−	0.408154i
$186$	−2.30747	+	16.0488i	−0.169192	+	1.17676i
$187$	1.26048	+	0.470136i	0.0921756	+	0.0343797i
$188$	2.40822	+	4.41032i	0.175637	+	0.321656i
$189$	14.9957	+	17.3060i	1.09078	+	1.25883i
$190$	−7.56368	+	10.0549i	−0.548727	+	0.729456i
$191$	−3.32253	+	5.16996i	−0.240410	+	0.374085i	−0.940402	−	0.340066i	$-0.889551\pi$
$191$	−3.32253	+	5.16996i	−0.240410	+	0.374085i	0.699992	+	0.714151i	$0.253187\pi$
$192$	−3.21695	−	8.62497i	−0.232163	−	0.622454i
$193$	3.65231	−	0.261218i	0.262899	−	0.0188029i	0.0607326	−	0.998154i	$-0.480656\pi$
$193$	3.65231	−	0.261218i	0.262899	−	0.0188029i	0.202167	+	0.979351i	$0.435202\pi$
$194$	−10.1503	+	6.52319i	−0.728748	+	0.468338i
$195$	13.9301	+	0.0325361i	0.997558	+	0.00232996i
$196$	−0.559685	−	3.89270i	−0.0399775	−	0.278050i
$197$	−4.30500	+	19.7898i	−0.306719	+	1.40996i	0.523262	+	0.852172i	$0.324715\pi$
$197$	−4.30500	+	19.7898i	−0.306719	+	1.40996i	−0.829981	+	0.557792i	$0.811649\pi$
$198$	−0.272675	−	3.81250i	−0.0193782	−	0.270943i
$199$	−2.56663	+	5.62014i	−0.181944	+	0.398401i	−0.978524	−	0.206131i	$-0.933913\pi$
$199$	−2.56663	+	5.62014i	−0.181944	+	0.398401i	0.796581	+	0.604532i	$0.206640\pi$
$200$	−0.944610	+	12.3935i	−0.0667940	+	0.876352i
$201$	−0.199537	−	0.679562i	−0.0140743	−	0.0479326i
$202$	−5.49954	−	0.393335i	−0.386946	−	0.0276749i
$203$	5.18792	−	2.83282i	0.364121	−	0.198825i
$204$	−0.0754541	−	0.165221i	−0.00528284	−	0.0115678i
$205$	−5.90338	+	19.9327i	−0.412310	+	1.39216i
$206$			20.6310i			1.43743i
$207$	2.06208	+	1.57707i	0.143324	+	0.109614i
$208$	−13.0117	−	13.0117i	−0.902201	−	0.902201i
$209$	16.4343	+	2.36289i	1.13678	+	0.163445i
$210$	10.7653	−	19.6062i	0.742879	−	1.35296i
$211$	16.0626	+	4.71640i	1.10579	+	0.324690i	0.783152	−	0.621831i	$-0.213611\pi$
$211$	16.0626	+	4.71640i	1.10579	+	0.324690i	0.322642	+	0.946521i	$0.395429\pi$
$212$	−0.0243224	+	0.340072i	−0.00167047	+	0.0233562i
$213$	5.19441	+	2.83636i	0.355915	+	0.194344i
$214$	−19.4790	−	12.5184i	−1.33155	−	0.855738i
$215$	−0.649299	−	3.01871i	−0.0442818	−	0.205874i
$216$	9.03954	−	10.4322i	0.615063	−	0.709820i
$217$	−26.9353	−	5.85942i	−1.82849	−	0.397763i
$218$	−6.22007	−	4.65629i	−0.421276	−	0.315363i
$219$	−6.78611	+	0.975695i	−0.458563	+	0.0659314i
$220$	−3.65292	+	1.65793i	−0.246280	+	0.111778i
$221$	0.884949	+	0.766813i	0.0595281	+	0.0515814i
$222$	7.03601	−	2.62430i	0.472226	−	0.176131i
$223$	−2.35231	−	10.8134i	−0.157523	−	0.724119i	−0.986356	−	0.164625i	$-0.947359\pi$
$223$	−2.35231	−	10.8134i	−0.157523	−	0.724119i	0.828834	−	0.559495i	$-0.189005\pi$
$224$	−8.67738	+	2.54791i	−0.579782	+	0.170239i
$225$	−2.46718	+	1.11282i	−0.164478	+	0.0741882i
$226$	4.23996	−	14.4400i	0.282038	−	0.960533i
$227$	−5.18363	+	13.8979i	−0.344050	+	0.922433i	0.643545	+	0.765408i	$0.277463\pi$
$227$	−5.18363	+	13.8979i	−0.344050	+	0.922433i	−0.987595	+	0.157025i	$0.949810\pi$
$228$	−1.34339	−	1.79456i	−0.0889681	−	0.118848i
$229$	−5.58663			−0.369175			−0.184588	−	0.982816i	$-0.559095\pi$
$229$	−5.58663			−0.369175			−0.184588	+	0.982816i	$0.559095\pi$
$230$	4.87449	−	15.8568i	0.321415	−	1.04557i
$231$	−29.5158			−1.94200
$232$	−2.13533	−	2.85246i	−0.140191	−	0.187273i
$233$	−4.73869	+	12.7049i	−0.310442	+	0.832327i	0.684233	+	0.729264i	$0.260137\pi$
$233$	−4.73869	+	12.7049i	−0.310442	+	0.832327i	−0.994675	+	0.103064i	$0.967135\pi$
$234$	0.937292	−	3.19212i	0.0612727	−	0.208676i
$235$	−27.9209	−	6.14216i	−1.82136	−	0.400671i
$236$	−1.63085	+	0.478861i	−0.106159	+	0.0311712i
$237$	−3.32814	−	15.2992i	−0.216186	−	0.993789i
$238$	1.76163	−	0.657053i	0.114189	−	0.0425904i
$239$	−17.9625	−	15.5646i	−1.16190	−	1.00679i	−0.999800	−	0.0200143i	$-0.993629\pi$
$239$	−17.9625	−	15.5646i	−1.16190	−	1.00679i	−0.162097	−	0.986775i	$-0.551826\pi$
$240$	−15.2021	−	5.71058i	−0.981292	−	0.368616i
$241$	−24.0576	+	3.45897i	−1.54969	+	0.222812i	−0.863401	−	0.504519i	$-0.831670\pi$
$241$	−24.0576	+	3.45897i	−1.54969	+	0.222812i	−0.686288	+	0.727330i	$0.740761\pi$
$242$	12.1799	+	9.11779i	0.782956	+	0.586114i
$243$	5.42526	+	1.18019i	0.348030	+	0.0757094i
$244$	0.937411	−	1.08183i	0.0600116	−	0.0692570i
$245$	18.7942	+	12.1404i	1.20072	+	0.775624i
$246$	−18.9711	−	12.1920i	−1.20955	−	0.777332i
$247$	12.6838	+	6.92588i	0.807051	+	0.440683i
$248$	−1.18541	+	16.5742i	−0.0752737	+	1.05246i
$249$	1.41732	+	0.416161i	0.0898187	+	0.0263731i
$250$	12.1437	+	12.3150i	0.768033	+	0.778872i
$251$	21.9423	+	3.15483i	1.38499	+	0.199131i	0.794181	−	0.607681i	$-0.207900\pi$
$251$	21.9423	+	3.15483i	1.38499	+	0.199131i	0.590807	+	0.806813i	$0.298809\pi$
$252$	−0.620382	−	0.620382i	−0.0390804	−	0.0390804i
$253$	−21.4374	+	4.43261i	−1.34776	+	0.278676i
$254$			21.6365i			1.35759i
$255$	0.990833	+	0.293450i	0.0620484	+	0.0183766i
$256$	3.77710	+	8.27069i	0.236069	+	0.516918i
$257$	9.71040	−	5.30228i	0.605718	−	0.330747i	−0.146953	−	0.989143i	$-0.546947\pi$
$257$	9.71040	−	5.30228i	0.605718	−	0.330747i	0.752671	+	0.658396i	$0.228765\pi$
$258$	3.34099	+	0.238952i	0.208001	+	0.0148765i
$259$	3.59686	+	12.2498i	0.223498	+	0.761165i
$260$	−3.48334	+	0.240957i	−0.216028	+	0.0149435i
$261$	0.322315	−	0.705772i	0.0199508	−	0.0436862i
$262$	−0.170948	−	2.39017i	−0.0105612	−	0.147665i
$263$	5.63125	−	25.8864i	0.347238	−	1.59623i	−0.390147	−	0.920753i	$-0.627576\pi$
$263$	5.63125	−	25.8864i	0.347238	−	1.59623i	0.737384	−	0.675473i	$-0.236061\pi$
$264$	2.53212	+	17.6113i	0.155841	+	1.08390i
$265$	−1.36837	−	1.37478i	−0.0840584	−	0.0844519i
$266$	19.5208	−	12.5453i	1.19690	−	0.769199i
$267$	−7.49652	+	0.536161i	−0.458779	+	0.0328125i
$268$	0.0620391	+	0.166333i	0.00378964	+	0.0101604i
$269$	−12.9958	+	20.2218i	−0.792366	+	1.23295i	0.176240	+	0.984347i	$0.443606\pi$
$269$	−12.9958	+	20.2218i	−0.792366	+	1.23295i	−0.968607	+	0.248599i	$0.920030\pi$
$270$	−2.68912	−	19.0185i	−0.163655	−	1.15743i
$271$	13.9638	+	16.1151i	0.848239	+	0.978920i	0.999955	−	0.00950404i	$-0.00302527\pi$
$271$	13.9638	+	16.1151i	0.848239	+	0.978920i	−0.151716	+	0.988424i	$0.548480\pi$
$272$	−0.654202	−	1.19808i	−0.0396668	−	0.0726444i
$273$	−24.0708	−	8.97795i	−1.45683	−	0.543370i
$274$	−0.167018	+	1.16163i	−0.0100899	+	0.0701768i
$275$	6.53216	−	21.8681i	0.393904	−	1.31870i
$276$	2.46980	+	1.62344i	0.148665	+	0.0977199i
$277$	8.95749	−	8.95749i	0.538203	−	0.538203i	−0.384798	−	0.923001i	$-0.625729\pi$
$277$	8.95749	−	8.95749i	0.538203	−	0.538203i	0.923001	+	0.384798i	$0.125729\pi$
$278$	−1.89760	+	1.42052i	−0.113810	+	0.0851974i
$279$	−3.29131	+	1.50309i	−0.197046	+	0.0899877i
$280$	9.57118	−	20.8291i	0.571988	−	1.24478i
$281$	−18.3424	+	15.8938i	−1.09422	+	0.948143i	−0.998881	−	0.0473018i	$-0.984938\pi$
$281$	−18.3424	+	15.8938i	−1.09422	+	0.948143i	−0.0953352	+	0.995445i	$0.530392\pi$
$282$	14.8626	−	27.2188i	0.885055	−	1.62086i
$283$	−1.32752	+	0.288784i	−0.0789127	+	0.0171664i	−0.251848	−	0.967767i	$-0.581038\pi$
$283$	−1.32752	+	0.288784i	−0.0789127	+	0.0171664i	0.172936	+	0.984933i	$0.444675\pi$
$284$	−1.34940	−	0.616252i	−0.0800724	−	0.0365679i
$285$	12.7189	+	0.939537i	0.753402	+	0.0556534i
$286$	15.1671	+	23.6005i	0.896849	+	1.39552i
$287$	22.9757	−	30.6920i	1.35621	−	1.81169i
$288$	−0.711404	+	0.950324i	−0.0419199	+	0.0559984i
$289$	−9.14393	−	14.2282i	−0.537878	−	0.836955i
$290$	−4.94461	−	0.365256i	−0.290358	−	0.0214486i
$291$	11.1249	+	5.08056i	0.652151	+	0.297827i
$292$	1.67919	−	0.365285i	0.0982671	−	0.0213767i
$293$	0.917604	−	1.68047i	0.0536070	−	0.0981738i	−0.849502	−	0.527586i	$-0.823097\pi$
$293$	0.917604	−	1.68047i	0.0536070	−	0.0981738i	0.903109	+	0.429412i	$0.141279\pi$
$294$	−18.3430	+	15.8943i	−1.06978	+	0.926974i
$295$	4.03762	−	8.78679i	0.235079	−	0.511587i
$296$	7.00054	−	3.19704i	0.406898	−	0.185824i
$297$	−20.2908	+	15.1895i	−1.17739	+	0.881384i
$298$	8.31374	−	8.31374i	0.481602	−	0.481602i
$299$	−18.8310	−	2.90583i	−1.08903	−	0.168048i
$300$	−2.71136	+	1.46411i	−0.156540	+	0.0845307i
$301$	−0.810419	+	5.63659i	−0.0467118	+	0.324887i
$302$	−2.73957	−	1.02181i	−0.157645	−	0.0587984i
$303$	2.67839	+	4.90510i	0.153869	+	0.281790i
$304$	−11.0325	−	12.7322i	−0.632756	−	0.730239i
$305$	1.14018	+	8.06380i	0.0652866	+	0.461732i
$306$	0.133428	−	0.207618i	0.00762758	−	0.0118687i
$307$	2.82114	+	7.56378i	0.161011	+	0.431688i	0.992255	−	0.124221i	$-0.0396432\pi$
$307$	2.82114	+	7.56378i	0.161011	+	0.431688i	−0.831243	+	0.555909i	$0.812370\pi$
$308$	7.37942	−	0.527787i	0.420482	−	0.0300734i
$309$	17.5924	−	11.3060i	1.00080	−	0.643174i
$310$	16.3112	+	16.3876i	0.926416	+	0.930754i
$311$	−0.592979	−	4.12426i	−0.0336248	−	0.233865i	0.966078	−	0.258251i	$-0.0831462\pi$
$311$	−0.592979	−	4.12426i	−0.0336248	−	0.233865i	−0.999703	+	0.0243856i	$0.992237\pi$
$312$	−3.29189	+	15.1326i	−0.186367	+	0.856714i
$313$	−1.34420	−	18.7944i	−0.0759788	−	1.06232i	−0.882251	−	0.470778i	$-0.843973\pi$
$313$	−1.34420	−	18.7944i	−0.0759788	−	1.06232i	0.806273	−	0.591544i	$-0.201481\pi$
$314$	2.46539	−	5.39846i	0.139130	−	0.304653i
$315$	4.97960	−	0.344460i	0.280569	−	0.0194081i
$316$	1.10566	+	3.76553i	0.0621982	+	0.211828i
$317$	20.5464	+	1.46950i	1.15400	+	0.0825356i	0.635191	−	0.772355i	$-0.280922\pi$
$317$	20.5464	+	1.46950i	1.15400	+	0.0825356i	0.518808	+	0.854891i	$0.326376\pi$
$318$	1.84677	−	1.00841i	0.103562	−	0.0565490i
$319$	2.71792	+	5.95142i	0.152174	+	0.333215i
$320$	−12.5868	−	3.72779i	−0.703626	−	0.208390i
$321$			23.4702i			1.30998i
$322$	−18.5859	+	24.3018i	−1.03575	+	1.35429i
$323$	0.758053	+	0.758053i	0.0421792	+	0.0421792i
$324$	2.75553	+	0.396186i	0.153085	+	0.0220103i
$325$	11.9788	−	15.8470i	0.664466	−	0.879034i
$326$	−33.8819	−	9.94863i	−1.87655	−	0.551004i
$327$	−0.561846	+	7.85564i	−0.0310702	+	0.434418i
$328$	−20.2841	−	11.0760i	−1.12000	−	0.611568i
$329$	44.3544	+	28.5048i	2.44534	+	1.57152i
$330$	20.7962	+	13.4337i	1.14479	+	0.739499i
$331$	1.39492	−	1.60982i	0.0766715	−	0.0884836i	−0.716118	−	0.697979i	$-0.754083\pi$
$331$	1.39492	−	1.60982i	0.0766715	−	0.0884836i	0.792789	+	0.609496i	$0.208628\pi$
$332$	−0.361793	−	0.0787032i	−0.0198560	−	0.00431940i
$333$	1.34156	+	1.00428i	0.0735173	+	0.0550343i
$334$	4.37063	−	0.628402i	0.239150	−	0.0343847i
$335$	−0.945489	−	0.355167i	−0.0516576	−	0.0194048i
$336$	22.6341	+	19.6125i	1.23479	+	1.06995i
$337$	9.36970	−	3.49472i	0.510400	−	0.190369i	−0.0810514	−	0.996710i	$-0.525828\pi$
$337$	9.36970	−	3.49472i	0.510400	−	0.190369i	0.591452	+	0.806340i	$0.298555\pi$
$338$	0.915719	+	4.20949i	0.0498086	+	0.228966i
$339$	−14.6367	+	4.29774i	−0.794959	+	0.233421i
$340$	−0.252971	−	0.0556497i	−0.0137193	−	0.00301803i
$341$	8.59599	−	29.2753i	0.465499	−	1.58534i
$342$	1.06442	−	2.85383i	0.0575574	−	0.154317i
$343$	−7.42912	−	9.92415i	−0.401135	−	0.535854i
$344$	3.43272			0.185080
$345$	−16.1926	+	4.53309i	−0.871781	+	0.244053i
$346$	−20.5424			−1.10437
$347$	−8.94725	−	11.9521i	−0.480313	−	0.641624i	0.493291	−	0.869864i	$-0.335794\pi$
$347$	−8.94725	−	11.9521i	−0.480313	−	0.641624i	−0.973605	+	0.228241i	$0.926703\pi$
$348$	0.308701	−	0.827658i	0.0165481	−	0.0443671i
$349$	−9.92356	+	33.7965i	−0.531196	+	1.80909i	0.0544443	+	0.998517i	$0.482661\pi$
$349$	−9.92356	+	33.7965i	−0.531196	+	1.80909i	−0.585640	+	0.810571i	$0.699157\pi$
$350$	−13.1147	−	29.0759i	−0.701011	−	1.55417i
$351$	−21.1679	+	6.21545i	−1.12986	+	0.331756i
$352$	−2.12783	−	9.78147i	−0.113414	−	0.521354i
$353$	−4.00481	+	1.49372i	−0.213154	+	0.0795025i	−0.453773	−	0.891117i	$-0.649922\pi$
$353$	−4.00481	+	1.49372i	−0.213154	+	0.0795025i	0.240619	+	0.970620i	$0.422650\pi$
$354$	7.92772	+	6.86941i	0.421354	+	0.365105i
$355$	7.68531	−	3.48809i	0.407894	−	0.185129i
$356$	1.86466	−	0.268098i	0.0988268	−	0.0142092i
$357$	−1.52567	−	1.14210i	−0.0807468	−	0.0604463i
$358$	2.61913	+	0.569758i	0.138426	+	0.0301126i
$359$	11.5833	−	13.3679i	0.611344	−	0.705529i	−0.362695	−	0.931908i	$-0.618143\pi$
$359$	11.5833	−	13.3679i	0.611344	−	0.705529i	0.974039	+	0.226379i	$0.0726888\pi$
$360$	−0.632722	−	2.94164i	−0.0333474	−	0.155038i
$361$	−4.85332	−	3.11904i	−0.255438	−	0.164160i
$362$	33.4219	+	18.2497i	1.75662	+	0.959186i
$363$	1.10019	−	15.3827i	0.0577450	−	0.807380i
$364$	6.17863	+	1.81421i	0.323848	+	0.0950904i
$365$	−4.70555	+	8.56993i	−0.246300	+	0.448571i
$366$	−8.74453	−	1.25727i	−0.457084	−	0.0657187i
$367$	6.48917	+	6.48917i	0.338732	+	0.338732i	0.855890	−	0.517158i	$-0.173010\pi$
$367$	6.48917	+	6.48917i	0.338732	+	0.338732i	−0.517158	+	0.855890i	$0.673010\pi$
$368$	19.3846	+	10.8455i	1.01049	+	0.565363i
$369$		−	5.03248i		−	0.261981i
$370$	3.04103	−	10.2680i	0.158095	−	0.533808i
$371$	1.48606	+	3.25401i	0.0771522	+	0.168940i
$372$	−3.61555	+	1.97424i	−0.187458	+	0.102360i
$373$	34.8417	+	2.49193i	1.80404	+	0.129027i	0.932469	−	0.361250i	$-0.117650\pi$
$373$	34.8417	+	2.49193i	1.80404	+	0.129027i	0.871567	+	0.490277i	$0.163104\pi$
$374$	0.586316	+	1.99681i	0.0303177	+	0.103253i
$375$	3.84643	−	17.1038i	0.198629	−	0.883239i
$376$	13.2029	−	28.9104i	0.680890	−	1.49094i
$377$	0.406259	+	5.68024i	0.0209234	+	0.292547i
$378$	−7.52983	+	34.6141i	−0.387292	+	1.78035i
$379$	−3.53302	−	24.5727i	−0.181479	−	1.26221i	−0.853268	−	0.521472i	$-0.825383\pi$
$379$	−3.53302	−	24.5727i	−0.181479	−	1.26221i	0.671789	−	0.740742i	$-0.265526\pi$
$380$	−3.19673	−	0.00746647i	−0.163989	−	0.000383022i
$381$	18.4498	−	11.8569i	0.945210	−	0.607450i
$382$	−9.48258	+	0.678207i	−0.485171	+	0.0347001i
$383$	4.86987	+	13.0566i	0.248839	+	0.667162i	0.999975	+	0.00701537i	$0.00223308\pi$
$383$	4.86987	+	13.0566i	0.248839	+	0.667162i	−0.751137	+	0.660146i	$0.770494\pi$
$384$	11.4170	−	17.7653i	0.582624	−	0.906580i
$385$	−25.3027	+	33.6364i	−1.28955	+	1.71427i
$386$	3.70936	+	4.28083i	0.188801	+	0.217888i
$387$	0.358230	+	0.656049i	0.0182098	+	0.0333488i
$388$	−2.87224	−	1.07129i	−0.145816	−	0.0543865i
$389$	−0.192013	+	1.33548i	−0.00973544	+	0.0677115i	−0.994110	−	0.108376i	$-0.965435\pi$
$389$	−0.192013	+	1.33548i	−0.00973544	+	0.0677115i	0.984375	+	0.176087i	$0.0563441\pi$
$390$	12.8736	+	17.2811i	0.651881	+	0.875064i
$391$	−1.27961	−	0.600390i	−0.0647129	−	0.0303630i
$392$	−17.5886	+	17.5886i	−0.888361	+	0.888361i
$393$	−1.94446	+	1.45560i	−0.0980849	+	0.0734254i
$394$	−28.4984	+	13.0148i	−1.43573	+	0.655676i
$395$	−20.2882	−	9.32262i	−1.02081	−	0.469072i
$396$	0.733921	−	0.635946i	0.0368809	−	0.0319575i
$397$	2.87009	−	5.25618i	0.144046	−	0.263800i	−0.795688	−	0.605706i	$-0.792891\pi$
$397$	2.87009	−	5.25618i	0.144046	−	0.263800i	0.939734	+	0.341906i	$0.111072\pi$
$398$	−9.33933	+	2.03165i	−0.468138	+	0.101837i
$399$	−21.3951	−	9.77082i	−1.07109	−	0.489153i
$400$	−19.5400	+	12.4290i	−0.976999	+	0.621450i
$401$	5.04254	+	7.84635i	0.251813	+	0.391828i	0.944029	−	0.329862i	$-0.107002\pi$
$401$	5.04254	+	7.84635i	0.251813	+	0.391828i	−0.692217	+	0.721690i	$0.743366\pi$
$402$	0.656583	−	0.877092i	0.0327474	−	0.0437454i
$403$	15.9150	−	21.2600i	0.792783	−	1.05903i
$404$	−0.757350	−	1.17846i	−0.0376795	−	0.0586305i
$405$	−11.9939	+	10.3438i	−0.595983	+	0.513990i
$406$	8.31759	+	3.79852i	0.412795	+	0.188517i
$407$	−13.8084	+	3.00384i	−0.684457	+	0.148895i
$408$	−0.550574	+	1.00830i	−0.0272575	+	0.0499183i
$409$	22.9218	−	19.8618i	1.13341	−	0.982104i	0.133448	−	0.991056i	$-0.457395\pi$
$409$	22.9218	−	19.8618i	1.13341	−	0.982104i	0.999960	+	0.00895179i	$0.00284948\pi$
$410$	−30.1572	+	11.1679i	−1.48936	+	0.551543i
$411$	1.08207	−	0.494165i	0.0533746	−	0.0243754i
$412$	−4.19622	+	3.14125i	−0.206733	+	0.154758i
$413$	−12.6105	+	12.6105i	−0.620522	+	0.620522i
$414$	−0.0413769	+	4.01568i	−0.00203357	+	0.197360i
$415$	1.68927	−	1.25842i	0.0829229	−	0.0617736i
$416$	1.23998	−	8.62424i	0.0607950	−	0.422838i
$417$	2.25120	+	0.839656i	0.110242	+	0.0411181i
$418$	12.3092	+	22.5426i	0.602062	+	1.10259i
$419$	1.71447	+	1.97861i	0.0837575	+	0.0966613i	0.796081	−	0.605190i	$-0.206903\pi$
$419$	1.71447	+	1.97861i	0.0837575	+	0.0966613i	−0.712324	+	0.701851i	$0.752357\pi$
$420$	5.62690	−	0.795616i	0.274565	−	0.0388221i
$421$	11.2076	−	17.4394i	0.546225	−	0.849942i	−0.452909	−	0.891557i	$-0.649614\pi$
$421$	11.2076	−	17.4394i	0.546225	−	0.849942i	0.999134	+	0.0416143i	$0.0132501\pi$
$422$	9.05004	+	24.2641i	0.440549	+	1.18116i
$423$	6.90308	−	0.493718i	0.335639	−	0.0240054i
$424$	1.81409	−	1.16585i	0.0881000	−	0.0566185i
$425$	1.18382	−	0.877598i	0.0574237	−	0.0425697i
$426$	1.30294	+	9.06216i	0.0631278	+	0.439063i
$427$	3.19263	−	14.6763i	0.154502	−	0.710234i
$428$	−0.419682	−	5.86792i	−0.0202861	−	0.283637i
$429$	11.8128	−	25.8665i	0.570329	−	1.24885i
$430$	3.13641	−	3.60257i	0.151251	−	0.173732i
$431$	−10.0073	−	34.0817i	−0.482034	−	1.64166i	−0.737875	−	0.674937i	$-0.764171\pi$
$431$	−10.0073	−	34.0817i	−0.482034	−	1.64166i	0.255842	−	0.966719i	$-0.417647\pi$
$432$	25.6530	+	1.83474i	1.23423	+	0.0882739i
$433$	31.1559	−	17.0124i	1.49726	−	0.817565i	0.498477	−	0.866903i	$-0.333893\pi$
$433$	31.1559	−	17.0124i	1.49726	−	0.817565i	0.998782	+	0.0493377i	$0.0157110\pi$
$434$	−17.7141	−	38.7884i	−0.850303	−	1.86190i
$435$	2.39823	+	4.41652i	0.114986	+	0.211756i
$436$		−	1.97408i		−	0.0945413i
$437$	−17.0067	−	3.88352i	−0.813541	−	0.185774i
$438$	−7.49935	−	7.49935i	−0.358333	−	0.358333i
$439$	−26.4790	−	3.80711i	−1.26378	−	0.181703i	−0.522346	−	0.852734i	$-0.674943\pi$
$439$	−26.4790	−	3.80711i	−1.26378	−	0.181703i	−0.741430	+	0.671030i	$0.765852\pi$
$440$	22.2406	+	12.2118i	1.06028	+	0.582175i
$441$	−5.19698	−	1.52597i	−0.247475	−	0.0726653i
$442$	−0.129224	+	1.80679i	−0.00614655	+	0.0859401i
$443$	−13.4213	−	7.32859i	−0.637665	−	0.348192i	0.127676	−	0.991816i	$-0.459248\pi$
$443$	−13.4213	−	7.32859i	−0.637665	−	0.348192i	−0.765342	+	0.643624i	$0.777430\pi$
$444$	1.60506	+	1.03151i	0.0761727	+	0.0489532i
$445$	−5.81545	+	9.00272i	−0.275679	+	0.426770i
$446$	11.2105	−	12.9376i	0.530834	−	0.612615i
$447$	−11.6453	−	2.53327i	−0.550802	−	0.119820i
$448$	19.3810	+	14.5084i	0.915665	+	0.685458i
$449$	−12.7619	+	1.83489i	−0.602272	+	0.0865937i	−0.436705	−	0.899605i	$-0.643855\pi$
$449$	−12.7619	+	1.83489i	−0.602272	+	0.0865937i	−0.165567	+	0.986198i	$0.552946\pi$
$450$	−3.66530	−	2.02369i	−0.172784	−	0.0953977i
$451$	32.0713	+	27.7899i	1.51018	+	1.30858i
$452$	3.58257	−	1.33623i	0.168510	−	0.0628509i
$453$	0.629995	+	2.89604i	0.0295997	+	0.136068i
$454$	−22.0165	+	6.46462i	−1.03328	+	0.303400i
$455$	−30.8663	+	19.7348i	−1.44703	+	0.925184i
$456$	−3.99452	+	13.6041i	−0.187061	+	0.637070i
$457$	11.9160	−	31.9481i	0.557408	−	1.49447i	−0.286554	−	0.958064i	$-0.592510\pi$
$457$	11.9160	−	31.9481i	0.557408	−	1.49447i	0.843962	−	0.536404i	$-0.180218\pi$
$458$	−5.17908	−	6.91844i	−0.242002	−	0.323277i
$459$	−1.63658			−0.0763889
$460$	3.96735	−	1.42289i	0.184979	−	0.0663427i
$461$	−0.104891			−0.00488528			−0.00244264	−	0.999997i	$-0.500778\pi$
$461$	−0.104891			−0.00488528			−0.00244264	+	0.999997i	$0.500778\pi$
$462$	−27.3626	−	36.5521i	−1.27302	−	1.70056i
$463$	−12.6136	+	33.8185i	−0.586206	+	1.57168i	0.217123	+	0.976144i	$0.430333\pi$
$463$	−12.6136	+	33.8185i	−0.586206	+	1.57168i	−0.803329	+	0.595535i	$0.796940\pi$
$464$	1.87035	−	6.36981i	0.0868286	−	0.295711i
$465$	5.03530	−	22.8894i	0.233507	−	1.06147i
$466$	−20.1267	+	5.90972i	−0.932350	+	0.273763i
$467$	6.53100	+	30.0225i	0.302219	+	1.38928i	0.838346	+	0.545139i	$0.183523\pi$
$467$	6.53100	+	30.0225i	0.302219	+	1.38928i	−0.536127	+	0.844137i	$0.680113\pi$
$468$	0.791968	−	0.295389i	0.0366087	−	0.0136543i
$469$	1.40772	+	1.21979i	0.0650024	+	0.0563249i
$470$	−18.2777	−	40.2711i	−0.843085	−	1.85757i
$471$	−5.95441	+	0.856115i	−0.274365	+	0.0394477i
$472$	8.60616	+	6.44249i	0.396131	+	0.296540i
$473$	−6.15909	−	1.33983i	−0.283195	−	0.0616053i
$474$	15.8610	−	18.3046i	0.728522	−	0.840759i
$475$	11.9741	−	13.6891i	0.549410	−	0.628100i
$476$	0.401863	+	0.258262i	0.0184194	+	0.0118374i
$477$	0.412126	+	0.225038i	0.0188700	+	0.0103038i
$478$	2.62296	−	36.6737i	0.119971	−	1.67742i
$479$	−20.2802	−	5.95481i	−0.926627	−	0.272082i	−0.216603	−	0.976260i	$-0.569498\pi$
$479$	−20.2802	−	5.95481i	−0.926627	−	0.272082i	−0.710024	+	0.704178i	$0.751316\pi$
$480$	−2.14906	−	7.38278i	−0.0980908	−	0.336976i
$481$	−12.1748	−	1.75047i	−0.555122	−	0.0798144i
$482$	−26.5861	−	26.5861i	−1.21097	−	1.21097i
$483$	30.9078	+	2.53090i	1.40635	+	0.115160i
$484$			3.86558i			0.175708i
$485$	15.3267	−	8.32262i	0.695952	−	0.377911i
$486$	3.56793	+	7.81269i	0.161845	+	0.354391i
$487$	−7.28517	+	3.97800i	−0.330122	+	0.180260i	−0.635759	−	0.771888i	$-0.719313\pi$
$487$	−7.28517	+	3.97800i	−0.330122	+	0.180260i	0.305636	+	0.952148i	$0.401131\pi$
$488$	−9.03081	−	0.645896i	−0.408806	−	0.0292384i
$489$	10.0842	+	34.3436i	0.456023	+	1.55307i
$490$	2.38854	+	34.5294i	0.107903	+	1.55988i
$491$	−10.6070	+	23.2262i	−0.478689	+	1.04818i	0.504133	+	0.863626i	$0.331812\pi$
$491$	−10.6070	+	23.2262i	−0.478689	+	1.04818i	−0.982822	+	0.184556i	$0.940915\pi$
$492$	−0.408740	−	5.71493i	−0.0184274	−	0.257649i
$493$	−0.0897983	+	0.412796i	−0.00404431	+	0.0185914i
$494$	3.18154	+	22.1281i	0.143144	+	0.995592i
$495$	−0.0129044	+	5.52494i	−0.000580009	+	0.248327i
$496$	−26.0445	+	16.7378i	−1.16943	+	0.751549i
$497$	−15.5254	+	1.11040i	−0.696410	+	0.0498083i
$498$	0.798549	+	2.14099i	0.0357838	+	0.0959402i
$499$	−15.2280	+	23.6952i	−0.681699	+	1.06074i	0.312153	+	0.950032i	$0.398950\pi$
$499$	−15.2280	+	23.6952i	−0.681699	+	1.06074i	−0.993852	+	0.110713i	$0.964687\pi$
$500$	−0.655825	+	4.34501i	−0.0293294	+	0.194315i
$501$	−2.93099	−	3.38254i	−0.130947	−	0.151121i
$502$	16.4347	+	30.0979i	0.733516	+	1.34333i
$503$	−8.48288	−	3.16395i	−0.378233	−	0.141074i	0.153155	−	0.988202i	$-0.451057\pi$
$503$	−8.48288	−	3.16395i	−0.378233	−	0.141074i	−0.531388	+	0.847129i	$0.678329\pi$
$504$	−0.789729	+	5.49269i	−0.0351773	+	0.244664i
$505$	7.88596	+	1.15264i	0.350921	+	0.0512916i
$506$	−25.3628	−	22.4387i	−1.12752	−	0.997522i
$507$	3.08769	−	3.08769i	0.137129	−	0.137129i
$508$	−4.40072	+	3.29434i	−0.195250	+	0.146162i
$509$	38.1610	−	17.4276i	1.69146	−	0.772463i	0.692775	−	0.721154i	$-0.256388\pi$
$509$	38.1610	−	17.4276i	1.69146	−	0.772463i	0.998683	−	0.0513092i	$-0.0163394\pi$
$510$	0.555144	+	1.49908i	0.0245822	+	0.0663805i
$511$	13.6268	−	11.8077i	0.602812	−	0.522340i
$512$	6.16794	−	11.2957i	0.272587	−	0.499206i
$513$	−19.7365	+	4.29341i	−0.871386	+	0.189559i
$514$	15.5683	+	7.10981i	0.686689	+	0.313600i
$515$	2.19692	−	29.7406i	0.0968079	−	1.31053i
$516$	0.460093	+	0.715918i	0.0202545	+	0.0315165i
$517$	−34.9732	+	46.7187i	−1.53812	+	2.05469i
$518$	−11.8356	+	15.8105i	−0.520025	+	0.694672i
$519$	11.2574	+	17.5169i	0.494146	+	0.768905i
$520$	14.4232	+	16.7240i	0.632499	+	0.733397i
$521$	−11.9238	−	5.44540i	−0.522389	−	0.238567i	0.136726	−	0.990609i	$-0.456342\pi$
$521$	−11.9238	−	5.44540i	−0.522389	−	0.238567i	−0.659115	+	0.752042i	$0.729069\pi$
$522$	1.17282	−	0.255132i	0.0513331	−	0.0111668i
$523$	0.652242	−	1.19449i	0.0285205	−	0.0522315i	−0.863030	−	0.505153i	$-0.831436\pi$
$523$	0.652242	−	1.19449i	0.0285205	−	0.0522315i	0.891551	+	0.452921i	$0.149618\pi$
$524$	0.460117	−	0.398694i	0.0201003	−	0.0174170i
$525$	−17.6066	+	27.1170i	−0.768413	+	1.18348i
$526$	37.2780	−	17.0243i	1.62540	−	0.742294i
$527$	1.57712	−	1.18061i	0.0687003	−	0.0514284i
$528$	−23.4405	+	23.4405i	−1.02012	+	1.02012i
$529$	22.8285	−	2.80344i	0.992544	−	0.121889i
$530$	0.433967	−	2.96906i	0.0188503	−	0.128968i
$531$	−0.333149	+	2.31710i	−0.0144574	+	0.100554i
$532$	5.52383	+	2.06028i	0.239489	+	0.0893246i
$533$	17.7019	+	32.4186i	0.766754	+	1.40420i
$534$	−7.61361	−	8.78657i	−0.329473	−	0.380232i
$535$	26.7468	+	20.1201i	1.15637	+	0.869866i
$536$	0.607051	−	0.944590i	0.0262206	−	0.0408001i
$537$	−0.949464	−	2.54561i	−0.0409724	−	0.109851i
$538$	−37.0902	+	2.65275i	−1.59907	+	0.114368i
$539$	38.4231	−	24.6930i	1.65500	−	1.06360i
$540$	3.45880	−	3.44268i	0.148843	−	0.148149i
$541$	−1.96647	−	13.6771i	−0.0845453	−	0.588025i	−0.987420	−	0.158121i	$-0.949456\pi$
$541$	−1.96647	−	13.6771i	−0.0845453	−	0.588025i	0.902874	−	0.429904i	$-0.141453\pi$
$542$	−7.01166	+	32.2321i	−0.301176	+	1.38449i
$543$	−2.75361	−	38.5004i	−0.118169	−	1.65221i
$544$	0.268502	−	0.587937i	0.0115119	−	0.0252076i
$545$	8.47070	+	7.37461i	0.362845	+	0.315894i
$546$	−11.1966	−	38.1321i	−0.479170	−	1.63190i
$547$	−8.35972	−	0.597899i	−0.357436	−	0.0255643i	−0.108533	−	0.994093i	$-0.534615\pi$
$547$	−8.35972	−	0.597899i	−0.357436	−	0.0255643i	−0.248903	+	0.968528i	$0.580070\pi$
$548$	−0.261699	+	0.142898i	−0.0111792	+	0.00610431i
$549$	−0.818991	−	1.79334i	−0.0349537	−	0.0765379i
$550$	33.1369	−	12.1834i	1.41296	−	0.519502i
$551$			5.21373i			0.222112i
$552$	−1.14141	−	18.6589i	−0.0485817	−	0.794176i
$553$	29.1168	+	29.1168i	1.23817	+	1.23817i
$554$	19.3969	+	2.78885i	0.824095	+	0.118487i
$555$	−10.4222	+	3.03381i	−0.442398	+	0.128778i
$556$	−0.577851	−	0.169672i	−0.0245063	−	0.00719571i
$557$	1.98924	−	27.8131i	0.0842866	−	1.17848i	−0.762659	−	0.646801i	$-0.776106\pi$
$557$	1.98924	−	27.8131i	0.0842866	−	1.17848i	0.846945	−	0.531680i	$-0.178439\pi$
$558$	−4.91262	−	2.68249i	−0.207968	−	0.113559i
$559$	−4.61534	−	2.96610i	−0.195208	−	0.125453i
$560$	41.7539	−	8.98092i	1.76442	−	0.379513i
$561$	1.38141	−	1.59423i	0.0583230	−	0.0673084i
$562$	−36.6870	−	7.98077i	−1.54755	−	0.336648i
$563$	−25.7007	−	19.2393i	−1.08316	−	0.810840i	−0.100253	−	0.994962i	$-0.531965\pi$
$563$	−25.7007	−	19.2393i	−1.08316	−	0.810840i	−0.982903	+	0.184122i	$0.941056\pi$
$564$	7.79909	−	1.12134i	0.328401	−	0.0472169i
$565$	−7.64977	+	20.3644i	−0.321828	+	0.856738i
$566$	−1.58830	−	1.37627i	−0.0667612	−	0.0578489i
$567$	27.3678	−	10.2077i	1.14934	−	0.428682i
$568$	1.99445	+	9.16833i	0.0836851	+	0.384694i
$569$	26.3665	−	7.74190i	1.10534	−	0.324557i	0.322368	−	0.946614i	$-0.395521\pi$
$569$	26.3665	−	7.74190i	1.10534	−	0.324557i	0.782972	+	0.622057i	$0.213703\pi$
$570$	10.6275	+	16.6220i	0.445138	+	0.696218i
$571$	−1.99692	+	6.80090i	−0.0835686	+	0.284609i	−0.990666	−	0.136312i	$-0.956475\pi$
$571$	−1.99692	+	6.80090i	−0.0835686	+	0.284609i	0.907097	+	0.420921i	$0.138293\pi$
$572$	−2.49086	+	6.67826i	−0.104148	+	0.279232i
$573$	5.77484	+	7.71429i	0.241248	+	0.322269i
$574$	59.3083			2.47548
$575$	−8.71535	+	22.3393i	−0.363455	+	0.931612i
$576$	3.17785			0.132410
$577$	−21.6175	−	28.8776i	−0.899949	−	1.20219i	−0.978700	−	0.205297i	$-0.934184\pi$
$577$	−21.6175	−	28.8776i	−0.899949	−	1.20219i	0.0787505	−	0.996894i	$-0.474907\pi$
$578$	9.14326	−	24.5140i	0.380309	−	1.01965i
$579$	1.61758	−	5.50896i	0.0672242	−	0.228945i
$580$	−0.678569	−	1.06132i	−0.0281760	−	0.0440688i
$581$	−3.72749	+	1.09449i	−0.154643	+	0.0454071i
$582$	4.02157	+	18.4869i	0.166699	+	0.766305i
$583$	−3.70994	+	1.38374i	−0.153650	+	0.0573085i
$584$	−8.21432	−	7.11774i	−0.339911	−	0.294534i
$585$	−1.69107	+	4.50179i	−0.0699171	+	0.186126i
$586$	2.93174	−	0.421520i	0.121109	−	0.0174128i
$587$	2.86767	+	2.14671i	0.118361	+	0.0886043i	0.656819	−	0.754049i	$-0.271902\pi$
$587$	2.86767	+	2.14671i	0.118361	+	0.0886043i	−0.538457	+	0.842653i	$0.680993\pi$
$588$	−6.02567	−	1.31081i	−0.248495	−	0.0540567i
$589$	15.9222	−	18.3752i	0.656061	−	0.757135i
$590$	14.6246	−	3.14562i	0.602083	−	0.129503i
$591$	26.7153	+	17.1689i	1.09892	+	0.706234i
$592$	12.5849	+	6.87188i	0.517236	+	0.282432i
$593$	−0.187734	+	2.62487i	−0.00770933	+	0.107790i	−0.999850	−	0.0173397i	$-0.994480\pi$
$593$	−0.187734	+	2.62487i	−0.00770933	+	0.107790i	0.992140	+	0.125130i	$0.0399349\pi$
$594$	−37.6211	−	11.0466i	−1.54361	−	0.453246i
$595$	−2.60944	+	0.759584i	−0.106976	+	0.0311399i
$596$	2.95680	+	0.425123i	0.121115	+	0.0174137i
$597$	6.85044	+	6.85044i	0.280370	+	0.280370i
$598$	−13.8587	−	26.0140i	−0.566724	−	1.06379i
$599$			30.0749i			1.22883i	0.788984	+	0.614413i	$0.210607\pi$
$599$			30.0749i			1.22883i	−0.788984	+	0.614413i	$0.789393\pi$
$600$	17.6904	+	8.17901i	0.722207	+	0.333907i
$601$	1.25891	+	2.75664i	0.0513522	+	0.112446i	0.933569	−	0.358398i	$-0.116677\pi$
$601$	1.25891	+	2.75664i	0.0513522	+	0.112446i	−0.882217	+	0.470844i	$0.843950\pi$
$602$	−7.73160	+	4.22177i	−0.315116	+	0.172067i
$603$	0.243877	+	0.0174424i	0.00993144	+	0.000710310i
$604$	−0.209294	−	0.712791i	−0.00851606	−	0.0290030i
$605$	−16.5870	−	14.4407i	−0.674359	−	0.587099i
$606$	−3.59144	+	7.86415i	−0.145892	+	0.319459i
$607$	−1.48672	−	20.7870i	−0.0603440	−	0.843719i	−0.934022	−	0.357215i	$-0.883726\pi$
$607$	−1.48672	−	20.7870i	−0.0603440	−	0.843719i	0.873678	−	0.486504i	$-0.161728\pi$
$608$	1.69563	−	7.79468i	0.0687668	−	0.316116i
$609$	−1.31905	−	9.17416i	−0.0534504	−	0.371756i
$610$	−8.92914	+	8.88752i	−0.361530	+	0.359845i
$611$	−42.7320	+	27.4622i	−1.72875	+	1.11100i
$612$	0.0625438	−	0.00447322i	0.00252818	−	0.000180819i
$613$	−10.5836	−	28.3756i	−0.427466	−	1.14608i	−0.955015	−	0.296556i	$-0.904162\pi$
$613$	−10.5836	−	28.3756i	−0.427466	−	1.14608i	0.527549	−	0.849524i	$-0.323111\pi$
$614$	−6.75158	+	10.5057i	−0.272472	+	0.423974i
$615$	26.0494	+	19.5955i	1.05041	+	0.790166i
$616$	−30.6431	−	35.3640i	−1.23465	−	1.42486i
$617$	12.4425	+	22.7868i	0.500917	+	0.917361i	0.998745	+	0.0500850i	$0.0159492\pi$
$617$	12.4425	+	22.7868i	0.500917	+	0.917361i	−0.497828	+	0.867276i	$0.665869\pi$
$618$	30.3102	+	11.3051i	1.21926	+	0.454759i
$619$	2.74672	−	19.1039i	0.110400	−	0.767849i	−0.857131	−	0.515098i	$-0.827756\pi$
$619$	2.74672	−	19.1039i	0.110400	−	0.767849i	0.967531	−	0.252751i	$-0.0813353\pi$
$620$	−0.849610	+	5.81275i	−0.0341211	+	0.233446i
$621$	22.5502	−	14.1660i	0.904907	−	0.568460i
$622$	4.55773	−	4.55773i	0.182748	−	0.182748i
$623$	15.8235	−	11.8453i	0.633954	−	0.474572i
$624$	−26.2463	+	11.9863i	−1.05069	+	0.479835i
$625$	−16.1943	−	19.0459i	−0.647772	−	0.761835i
$626$	22.0287	−	19.0880i	0.880444	−	0.762909i
$627$	12.4769	−	22.8498i	0.498280	−	0.912531i
$628$	1.47339	−	0.320516i	0.0587946	−	0.0127900i
$629$	−0.829986	−	0.379042i	−0.0330937	−	0.0151134i
$630$	5.04291	+	5.84737i	0.200914	+	0.232965i
$631$	11.9260	+	18.5573i	0.474768	+	0.738753i	0.993207	−	0.116361i	$-0.0371230\pi$
$631$	11.9260	+	18.5573i	0.474768	+	0.738753i	−0.518439	+	0.855115i	$0.673487\pi$
$632$	14.8753	−	19.8711i	0.591708	−	0.790430i
$633$	15.7309	−	21.0140i	0.625248	−	0.835233i
$634$	17.2276	+	26.8067i	0.684197	+	1.06463i
$635$	2.30399	−	31.1900i	0.0914309	−	1.23774i
$636$	0.486291	+	0.222082i	0.0192827	+	0.00880611i
$637$	38.8459	−	8.45041i	1.53913	−	0.334818i
$638$	−4.85054	+	8.88310i	−0.192035	+	0.351685i
$639$	−1.54408	+	1.33795i	−0.0610829	+	0.0529287i
$640$	−10.4581	−	28.2404i	−0.413391	−	1.11630i
$641$	−23.3854	+	10.6797i	−0.923667	+	0.421824i	−0.819724	−	0.572759i	$-0.805873\pi$
$641$	−23.3854	+	10.6797i	−0.923667	+	0.421824i	−0.103943	+	0.994583i	$0.533146\pi$
$642$	−29.0653	+	21.7580i	−1.14712	+	0.858720i
$643$	−9.34906	+	9.34906i	−0.368691	+	0.368691i	−0.867000	−	0.498309i	$-0.833955\pi$
$643$	−9.34906	+	9.34906i	−0.368691	+	0.368691i	0.498309	+	0.867000i	$0.333955\pi$
$644$	−7.77269	−	0.0800886i	−0.306287	−	0.00315593i
$645$	−4.79075	−	0.700231i	−0.188636	−	0.0275716i
$646$	−0.236015	+	1.64152i	−0.00928587	+	0.0645847i
$647$	−28.6226	−	10.6757i	−1.12527	−	0.419705i	−0.283195	−	0.959062i	$-0.591394\pi$
$647$	−28.6226	−	10.6757i	−1.12527	−	0.419705i	−0.842077	+	0.539357i	$0.818667\pi$
$648$	−8.43847	−	15.4539i	−0.331495	−	0.607087i
$649$	−12.9269	−	14.9184i	−0.507424	−	0.585598i
$650$	30.7298	+	0.143549i	1.20532	+	0.00563047i
$651$	−23.3681	+	36.3614i	−0.915867	+	1.42512i
$652$	−3.13532	−	8.40613i	−0.122789	−	0.329209i
$653$	5.01593	−	0.358746i	0.196288	−	0.0140388i	0.0271512	−	0.999631i	$-0.491356\pi$
$653$	5.01593	−	0.358746i	0.196288	−	0.0140388i	0.169137	+	0.985593i	$0.445902\pi$
$654$	−10.2492	+	6.58677i	−0.400776	+	0.257563i
$655$	−0.00809014	+	3.46375i	−0.000316108	+	0.135340i
$656$	−6.12800	−	42.6212i	−0.239258	−	1.66408i
$657$	0.503093	−	2.31268i	0.0196275	−	0.0902262i
$658$	5.81851	+	81.3535i	0.226829	+	3.17149i
$659$	−9.90689	+	21.6931i	−0.385918	+	0.845042i	0.612588	+	0.790402i	$0.290128\pi$
$659$	−9.90689	+	21.6931i	−0.385918	+	0.845042i	−0.998506	+	0.0546397i	$0.982599\pi$
$660$	0.434082	+	6.27521i	0.0168966	+	0.244262i
$661$	4.03122	+	13.7291i	0.156796	+	0.533999i	0.999994	−	0.00360508i	$-0.00114754\pi$
$661$	4.03122	+	13.7291i	0.156796	+	0.533999i	−0.843197	+	0.537605i	$0.819329\pi$
$662$	3.28674	+	0.235072i	0.127743	+	0.00913634i
$663$	1.61149	−	0.879942i	0.0625852	−	0.0341741i
$664$	0.972828	+	2.13020i	0.0377531	+	0.0826677i
$665$	−29.4761	+	16.0059i	−1.14303	+	0.620682i
$666$			2.59240i			0.100453i
$667$	−2.33578	−	6.46514i	−0.0904418	−	0.250331i
$668$	0.793279	+	0.793279i	0.0306929	+	0.0306929i
$669$	−17.1756	−	2.46948i	−0.664047	−	0.0954755i
$670$	−0.436678	−	1.50014i	−0.0168704	−	0.0579556i
$671$	15.9513	+	4.68371i	0.615791	+	0.180813i
$672$	−1.01164	+	14.1446i	−0.0390250	+	0.545640i
$673$	−0.486570	−	0.265687i	−0.0187559	−	0.0102415i	0.469844	−	0.882750i	$-0.344310\pi$
$673$	−0.486570	−	0.265687i	−0.0187559	−	0.0102415i	−0.488600	+	0.872508i	$0.662492\pi$
$674$	13.0140	+	8.36359i	0.501280	+	0.322153i
$675$	1.85129	+	27.7024i	0.0712563	+	1.06627i
$676$	−0.716758	+	0.827183i	−0.0275676	+	0.0318147i
$677$	−26.1995	−	5.69936i	−1.00693	−	0.219044i	−0.321287	−	0.946982i	$-0.604115\pi$
$677$	−26.1995	−	5.69936i	−1.00693	−	0.219044i	−0.685643	+	0.727938i	$0.740479\pi$
$678$	−18.8912	−	14.1418i	−0.725514	−	0.543113i
$679$	−31.8373	+	4.57751i	−1.22180	+	0.175669i
$680$	0.677082	+	1.49181i	0.0259649	+	0.0572085i
$681$	17.5777	+	15.2312i	0.673578	+	0.583659i
$682$	44.2231	−	16.4944i	1.69339	−	0.631602i
$683$	1.60531	+	7.37951i	0.0614256	+	0.282369i	0.997606	−	0.0691502i	$-0.0220288\pi$
$683$	1.60531	+	7.37951i	0.0614256	+	0.282369i	−0.936181	+	0.351519i	$0.885665\pi$
$684$	0.742518	−	0.218023i	0.0283909	−	0.00833632i
$685$	0.364462	−	1.65677i	0.0139254	−	0.0633017i
$686$	5.40282	−	18.4003i	0.206281	−	0.702528i
$687$	−3.06129	+	8.20765i	−0.116796	+	0.313141i
$688$	3.83279	+	5.12001i	0.146124	+	0.195198i
$689$	−3.44644			−0.131299
$690$	−20.6251	−	15.8504i	−0.785183	−	0.603415i
$691$	−29.9436			−1.13911			−0.569555	−	0.821953i	$-0.692884\pi$
$691$	−29.9436			−1.13911			−0.569555	+	0.821953i	$0.692884\pi$
$692$	−3.12776	−	4.17820i	−0.118900	−	0.158831i
$693$	3.56081	−	9.54690i	0.135264	−	0.362657i
$694$	6.50688	−	22.1604i	0.246998	−	0.841197i
$695$	2.88675	−	1.84569i	0.109500	−	0.0700108i
$696$	−5.36081	+	1.57408i	−0.203201	+	0.0596652i
$697$	0.582441	+	2.67744i	0.0220615	+	0.101415i
$698$	−51.0530	+	19.0418i	−1.93238	+	0.720742i
$699$	16.0689	+	13.9238i	0.607781	+	0.526645i
$700$	3.91703	−	7.09451i	0.148050	−	0.268147i
$701$	−12.9369	+	1.86004i	−0.488620	+	0.0702529i	−0.382222	−	0.924071i	$-0.624841\pi$
$701$	−12.9369	+	1.86004i	−0.488620	+	0.0702529i	−0.106398	+	0.994324i	$0.533932\pi$
$702$	−27.3208	−	20.4521i	−1.03116	−	0.771915i
$703$	−11.0037	−	2.39370i	−0.415011	−	0.0902802i
$704$	−17.5484	+	20.2519i	−0.661381	+	0.763274i
$705$	−24.3236	+	37.6546i	−0.916079	+	1.41815i
$706$	−5.56246	−	3.57477i	−0.209346	−	0.134538i
$707$	−12.9002	−	7.04407i	−0.485164	−	0.264919i
$708$	−0.190131	+	2.65837i	−0.00714555	+	0.0999078i
$709$	3.21911	+	0.945215i	0.120896	+	0.0354983i	0.341621	−	0.939838i	$-0.389024\pi$
$709$	3.21911	+	0.945215i	0.120896	+	0.0354983i	−0.220725	+	0.975336i	$0.570842\pi$
$710$	11.4443	+	6.28379i	0.429496	+	0.235826i
$711$	5.35004	+	0.769220i	0.200642	+	0.0288480i
$712$	−8.42523	−	8.42523i	−0.315749	−	0.315749i
$713$	−11.5117	+	29.9188i	−0.431115	+	1.12047i
$714$		−	2.94815i		−	0.110332i
$715$	−19.3510	−	35.6363i	−0.723685	−	1.33272i
$716$	0.282900	+	0.619465i	0.0105725	+	0.0231505i
$717$	−32.7097	+	17.8608i	−1.22157	+	0.667025i
$718$	27.2929	+	1.95203i	1.01856	+	0.0728491i
$719$	−12.1438	−	41.3579i	−0.452887	−	1.54239i	−0.797306	−	0.603575i	$-0.793742\pi$
$719$	−12.1438	−	41.3579i	−0.452887	−	1.54239i	0.344420	−	0.938816i	$-0.388076\pi$
$720$	3.68108	−	4.22820i	0.137186	−	0.157576i
$721$	−22.8471	+	50.0282i	−0.850871	+	1.86315i
$722$	−0.636670	−	8.90181i	−0.0236944	−	0.331291i
$723$	−8.10103	+	37.2399i	−0.301281	+	1.38497i
$724$	1.37689	+	9.57648i	0.0511717	+	0.355907i
$725$	7.08900	+	1.05307i	0.263279	+	0.0391099i
$726$	20.0697	−	12.8980i	0.744856	−	0.478690i
$727$	−2.24270	+	0.160401i	−0.0831772	+	0.00594895i	−0.112866	−	0.993610i	$-0.536003\pi$
$727$	−2.24270	+	0.160401i	−0.0831772	+	0.00594895i	0.0296885	+	0.999559i	$0.490548\pi$
$728$	−14.2333	−	38.1610i	−0.527522	−	1.41434i
$729$	16.1949	−	25.1998i	0.599812	−	0.933326i
$730$	−14.9752	+	2.11742i	−0.554257	+	0.0783693i
$731$	−0.266518	−	0.307578i	−0.00985752	−	0.0113762i
$732$	−1.07571	−	1.97001i	−0.0397593	−	0.0728137i
$733$	−6.63893	−	2.47619i	−0.245215	−	0.0914603i	0.223852	−	0.974623i	$-0.428137\pi$
$733$	−6.63893	−	2.47619i	−0.245215	−	0.0914603i	−0.469066	+	0.883163i	$0.655410\pi$
$734$	−2.02036	+	14.0519i	−0.0745728	+	0.518665i
$735$	28.1348	−	20.9591i	1.03777	−	0.773088i
$736$	1.38944	+	10.4252i	0.0512155	+	0.384278i
$737$	−1.45787	+	1.45787i	−0.0537015	+	0.0537015i
$738$	6.23219	−	4.66536i	0.229410	−	0.171734i
$739$	30.6945	−	14.0177i	1.12912	−	0.515650i	0.238834	−	0.971060i	$-0.423235\pi$
$739$	30.6945	−	14.0177i	1.12912	−	0.515650i	0.890282	+	0.455411i	$0.150508\pi$
$740$	2.55147	−	0.944866i	0.0937938	−	0.0347340i
$741$	17.1255	−	14.8393i	0.629121	−	0.545137i
$742$	−2.65209	+	4.85695i	−0.0973614	+	0.178304i
$743$	1.77648	−	0.386449i	0.0651726	−	0.0141774i	−0.179861	−	0.983692i	$-0.557565\pi$
$743$	1.77648	−	0.386449i	0.0651726	−	0.0141774i	0.245033	+	0.969515i	$0.421201\pi$
$744$	23.7006	+	10.8237i	0.868905	+	0.396816i
$745$	−12.8700	+	11.0994i	−0.471518	+	0.406649i
$746$	29.2140	+	45.4578i	1.06960	+	1.66433i
$747$	−0.305594	+	0.408225i	−0.0111811	+	0.0149362i
$748$	−0.316867	+	0.423284i	−0.0115858	+	0.0154768i
$749$	−33.3715	−	51.9271i	−1.21937	−	1.89738i
$750$	24.7471	−	11.0927i	0.903636	−	0.405049i
$751$	−14.4073	−	6.57958i	−0.525729	−	0.240092i	0.134827	−	0.990869i	$-0.456952\pi$
$751$	−14.4073	−	6.57958i	−0.525729	−	0.240092i	−0.660556	+	0.750777i	$0.729679\pi$
$752$	57.8625	−	12.5872i	2.11003	−	0.459008i
$753$	16.6586	−	30.5080i	0.607074	−	1.11177i
$754$	−6.65774	+	5.76896i	−0.242461	+	0.210093i
$755$	3.84042	+	1.76471i	0.139767	+	0.0642245i
$756$	−8.18676	+	3.73877i	−0.297749	+	0.135978i
$757$	12.6944	−	9.50293i	0.461387	−	0.345390i	−0.343162	−	0.939276i	$-0.611498\pi$
$757$	12.6944	−	9.50293i	0.461387	−	0.345390i	0.804549	+	0.593886i	$0.202407\pi$
$758$	27.1553	−	27.1553i	0.986326	−	0.986326i
$759$	−5.23482	+	33.9239i	−0.190012	+	1.23136i
$760$	12.0790	+	16.2144i	0.438151	+	0.588159i
$761$	2.43263	−	16.9193i	0.0881826	−	0.613324i	−0.897028	−	0.441974i	$-0.854278\pi$
$761$	2.43263	−	16.9193i	0.0881826	−	0.613324i	0.985210	−	0.171349i	$-0.0548127\pi$
$762$	31.7874	+	11.8561i	1.15153	+	0.429500i
$763$	−9.92661	−	18.1792i	−0.359368	−	0.658133i
$764$	−1.58175	−	1.82543i	−0.0572256	−	0.0660418i
$765$	−0.214452	+	0.285083i	−0.00775351	+	0.0103072i
$766$	−11.6546	+	18.1349i	−0.421098	+	0.655241i
$767$	−6.00436	−	16.0983i	−0.216805	−	0.581276i
$768$	14.2207	−	1.01708i	0.513144	−	0.0367008i
$769$	−36.9331	+	23.7355i	−1.33184	+	0.855924i	−0.996287	−	0.0860967i	$-0.972561\pi$
$769$	−36.9331	+	23.7355i	−1.33184	+	0.855924i	−0.335556	+	0.942020i	$0.608924\pi$
$770$	−65.1119	−	0.152079i	−2.34647	−	0.00548056i
$771$	−2.46890	−	17.1716i	−0.0889153	−	0.618420i
$772$	−0.305912	+	1.40625i	−0.0110100	+	0.0506121i
$773$	2.07562	+	29.0209i	0.0746548	+	1.04381i	0.887343	+	0.461111i	$0.152549\pi$
$773$	2.07562	+	29.0209i	0.0746548	+	1.04381i	−0.812688	+	0.582699i	$0.801997\pi$
$774$	−0.480349	+	1.05182i	−0.0172658	+	0.0378068i
$775$	−21.7684	−	25.3604i	−0.781943	−	0.910974i
$776$	5.46255	+	18.6037i	0.196094	+	0.667835i
$777$	19.9678	+	1.42813i	0.716342	+	0.0512338i
$778$	−1.83185	+	1.00027i	−0.0656751	+	0.0358613i
$779$	14.0480	+	30.7608i	0.503322	+	1.10212i
$780$	−1.55475	+	5.24961i	−0.0556691	+	0.187966i
$781$		−	17.2285i		−	0.616486i
$782$	−0.442746	−	2.14125i	−0.0158326	−	0.0765711i
$783$	−5.62802	−	5.62802i	−0.201129	−	0.201129i
$784$	−45.8725	−	6.59548i	−1.63830	−	0.235553i
$785$	−4.12884	+	7.51961i	−0.147365	+	0.268386i
$786$	−3.60521	−	1.05859i	−0.128594	−	0.0377585i
$787$	−1.83894	+	25.7117i	−0.0655510	+	0.916523i	0.853174	+	0.521626i	$0.174674\pi$
$787$	−1.83894	+	25.7117i	−0.0655510	+	0.916523i	−0.918725	+	0.394897i	$0.870780\pi$
$788$	−6.98626	−	3.81479i	−0.248875	−	0.135896i
$789$	−34.9455	−	22.4581i	−1.24409	−	0.799530i
$790$	−7.26304	−	33.7672i	−0.258408	−	1.20138i
$791$	26.2725	−	30.3201i	0.934144	−	1.07806i
$792$	−6.00185	−	1.30562i	−0.213266	−	0.0463932i
$793$	11.5839	+	8.67163i	0.411358	+	0.307939i
$794$	9.16993	−	1.31844i	0.325429	−	0.0467896i
$795$	−2.76959	+	1.25702i	−0.0982272	+	0.0445819i
$796$	−1.83522	−	1.59022i	−0.0650475	−	0.0563640i
$797$	26.7757	−	9.98681i	0.948443	−	0.353751i	0.172825	−	0.984953i	$-0.444711\pi$
$797$	26.7757	−	9.98681i	0.948443	−	0.353751i	0.775619	+	0.631201i	$0.217438\pi$
$798$	−7.73420	−	35.5535i	−0.273788	−	1.25858i
$799$	−3.61551	+	1.06161i	−0.127908	+	0.0375571i
$800$	−10.2558	−	3.87988i	−0.362596	−	0.137174i
$801$	0.730964	−	2.48944i	0.0258273	−	0.0879599i
$802$	−5.04217	+	13.5186i	−0.178045	+	0.477358i
$803$	11.9602	+	15.9770i	0.422068	+	0.563816i
$804$	0.278365			0.00981718
$805$	29.3802	−	33.0531i	1.03552	−	1.16497i
$806$	41.0822			1.44706
$807$	22.5878	+	30.1737i	0.795127	+	1.06217i
$808$	−3.09631	+	8.30152i	−0.108928	+	0.292046i
$809$	3.72336	−	12.6806i	0.130906	−	0.445826i	−0.867787	−	0.496937i	$-0.834458\pi$
$809$	3.72336	−	12.6806i	0.130906	−	0.445826i	0.998693	+	0.0511109i	$0.0162762\pi$
$810$	−23.9287	−	5.26393i	−0.840768	−	0.184955i
$811$	12.9426	−	3.80030i	0.454477	−	0.133447i	−0.0464788	−	0.998919i	$-0.514800\pi$
$811$	12.9426	−	3.80030i	0.454477	−	0.133447i	0.500956	+	0.865473i	$0.332982\pi$
$812$	0.493830	+	2.27010i	0.0173300	+	0.0796649i
$813$	31.3273	−	11.6845i	1.09870	−	0.409792i
$814$	−16.5210	−	14.3155i	−0.579060	−	0.501759i
$815$	47.7830	+	17.9494i	1.67377	+	0.628740i
$816$	−2.11865	+	0.304616i	−0.0741677	+	0.0106637i
$817$	−4.02100	−	3.01008i	−0.140677	−	0.105310i
$818$	45.8463	+	9.97325i	1.60298	+	0.348707i
$819$	5.80785	−	6.70261i	0.202943	−	0.234208i
$820$	−6.86317	−	4.43338i	−0.239672	−	0.154820i
$821$	28.1910	+	18.1172i	0.983871	+	0.632296i	0.930505	−	0.366279i	$-0.119369\pi$
$821$	28.1910	+	18.1172i	0.983871	+	0.632296i	0.0533664	+	0.998575i	$0.483005\pi$
$822$	1.61510	+	0.881913i	0.0563332	+	0.0307602i
$823$	0.989507	−	13.8351i	0.0344921	−	0.482262i	−0.950621	−	0.310354i	$-0.899552\pi$
$823$	0.989507	−	13.8351i	0.0344921	−	0.482262i	0.985113	−	0.171908i	$-0.0549931\pi$
$824$	31.8105	+	9.34039i	1.10817	+	0.325388i
$825$	−28.5483	−	21.5798i	−0.993923	−	0.751311i
$826$	−27.3073	−	3.92619i	−0.950141	−	0.136610i
$827$	1.92931	+	1.92931i	0.0670885	+	0.0670885i	0.739855	−	0.672766i	$-0.234894\pi$
$827$	1.92931	+	1.92931i	0.0670885	+	0.0670885i	−0.672766	+	0.739855i	$0.734894\pi$
$828$	−0.823063	+	0.603005i	−0.0286034	+	0.0209559i
$829$		−	13.4993i		−	0.468849i	−0.972134	−	0.234424i	$-0.924679\pi$
$829$		−	13.4993i		−	0.468849i	0.972134	−	0.234424i	$-0.0753205\pi$
$830$	3.12446	+	0.925355i	0.108451	+	0.0321196i
$831$	−8.25155	−	18.0684i	−0.286243	−	0.626785i
$832$	−20.4713	+	11.1782i	−0.709713	+	0.387533i
$833$	2.94157	+	0.210385i	0.101919	+	0.00728941i
$834$	1.04715	+	3.56627i	0.0362599	+	0.123490i
$835$	−6.36740	+	0.440459i	−0.220353	+	0.0152427i
$836$	−2.71084	+	5.93591i	−0.0937563	+	0.205298i
$837$	2.64791	+	37.0226i	0.0915251	+	1.27969i
$838$	−0.860892	+	3.95746i	−0.0297390	+	0.136708i
$839$	5.83579	+	40.5888i	0.201474	+	1.40128i	0.799914	+	0.600114i	$0.204878\pi$
$839$	5.83579	+	40.5888i	0.201474	+	1.40128i	−0.598441	+	0.801167i	$0.704213\pi$
$840$	−25.3565	−	25.4752i	−0.874883	−	0.878979i
$841$	22.6680	−	14.5678i	0.781655	−	0.502339i
$842$	31.9867	−	2.28774i	1.10234	−	0.0788406i
$843$	13.2994	+	35.6572i	0.458057	+	1.22810i
$844$	−3.55722	+	5.53514i	−0.122444	+	0.190527i
$845$	−0.871800	−	6.16570i	−0.0299908	−	0.212107i
$846$	7.01090	+	8.09101i	0.241040	+	0.278175i
$847$	19.4380	+	35.5980i	0.667897	+	1.22316i
$848$	3.76441	+	1.40405i	0.129270	+	0.0482154i
$849$	−0.303167	+	2.10857i	−0.0104047	+	0.0723661i
$850$	2.18427	+	0.652457i	0.0749198	+	0.0223791i
$851$	14.7172	−	1.96146i	0.504499	−	0.0672381i
$852$	−1.64480	+	1.64480i	−0.0563500	+	0.0563500i
$853$	−22.6859	+	16.9825i	−0.776751	+	0.581469i	−0.912405	−	0.409288i	$-0.865777\pi$
$853$	−22.6859	+	16.9825i	−0.776751	+	0.581469i	0.135654	+	0.990756i	$0.456686\pi$
$854$	21.1347	−	9.65189i	0.723214	−	0.330281i
$855$	−1.83831	+	4.00059i	−0.0628689	+	0.136817i
$856$	−28.1206	+	24.3666i	−0.961141	+	0.832833i
$857$	−0.366015	+	0.670306i	−0.0125028	+	0.0228972i	−0.883856	−	0.467760i	$-0.845061\pi$
$857$	−0.366015	+	0.670306i	−0.0125028	+	0.0228972i	0.871353	+	0.490657i	$0.163243\pi$
$858$	42.9839	−	9.35057i	1.46745	−	0.319223i
$859$	4.96348	+	2.26675i	0.169352	+	0.0773404i	0.498287	−	0.867012i	$-0.333963\pi$
$859$	4.96348	+	2.26675i	0.169352	+	0.0773404i	−0.328935	+	0.944352i	$0.606690\pi$
$860$	1.21029	+	0.0894031i	0.0412704	+	0.00304862i
$861$	−32.5014	−	50.5732i	−1.10765	−	1.72353i
$862$	32.9292	−	43.9883i	1.12157	−	1.49825i
$863$	21.1231	−	28.2172i	0.719039	−	0.960524i	−0.280961	−	0.959719i	$-0.590653\pi$
$863$	21.1231	−	28.2172i	0.719039	−	0.960524i	1.00000		0.000804477i	$-0.000256073\pi$
$864$	6.58368	+	10.2444i	0.223981	+	0.348522i
$865$	29.6129	+	2.18749i	1.00687	+	0.0743768i
$866$	49.9511	+	22.8119i	1.69741	+	0.775180i
$867$	−25.9141	+	5.63727i	−0.880089	+	0.191452i
$868$	5.19219	−	9.50879i	0.176235	−	0.322750i
$869$	−34.4456	+	29.8473i	−1.16849	+	1.01250i
$870$	−3.24611	+	7.06427i	−0.110053	+	0.239501i
$871$	−1.63238	+	0.745482i	−0.0553110	+	0.0252597i
$872$	−9.99545	+	7.48250i	−0.338489	+	0.253389i
$873$	−2.98542	+	2.98542i	−0.101041	+	0.101041i
$874$	−10.9567	−	24.6612i	−0.370616	−	0.834176i
$875$	15.8093	+	43.3109i	0.534452	+	1.46417i
$876$	0.383479	−	2.66716i	0.0129566	−	0.0901149i
$877$	41.6214	+	15.5240i	1.40545	+	0.524208i	0.933870	−	0.357613i	$-0.116409\pi$
$877$	41.6214	+	15.5240i	1.40545	+	0.524208i	0.471585	+	0.881821i	$0.343682\pi$
$878$	−19.8326	−	36.3208i	−0.669319	−	1.22577i
$879$	−1.96605	−	2.26894i	−0.0663133	−	0.0765296i
$880$	6.61837	+	46.8076i	0.223105	+	1.57788i
$881$	7.42462	−	11.5529i	0.250142	−	0.389228i	−0.693362	−	0.720589i	$-0.743871\pi$
$881$	7.42462	−	11.5529i	0.250142	−	0.389228i	0.943504	+	0.331361i	$0.107508\pi$
$882$	−2.92810	−	7.85055i	−0.0985944	−	0.264342i
$883$	41.2280	−	2.94868i	1.38743	−	0.0992310i	0.642456	−	0.766323i	$-0.277916\pi$
$883$	41.2280	−	2.94868i	1.38743	−	0.0992310i	0.744976	+	0.667092i	$0.232461\pi$
$884$	−0.387164	+	0.248815i	−0.0130217	+	0.00836856i
$885$	−10.6967	−	10.7468i	−0.359565	−	0.361249i
$886$	−3.36654	−	23.4148i	−0.113101	−	0.786635i
$887$	−9.83907	+	45.2295i	−0.330364	+	1.51866i	0.449827	+	0.893116i	$0.351486\pi$
$887$	−9.83907	+	45.2295i	−0.330364	+	1.51866i	−0.780191	+	0.625542i	$0.784878\pi$
$888$	−0.860886	−	12.0368i	−0.0288895	−	0.403927i
$889$	−23.9605	+	52.4663i	−0.803611	+	1.75966i
$890$	−16.5401	+	1.14415i	−0.554425	+	0.0383519i
$891$	9.10873	+	31.0215i	0.305154	+	1.03926i
$892$	4.33833	+	0.310284i	0.145258	+	0.0103891i
$893$	−40.8166	+	22.2875i	−1.36587	+	0.745824i
$894$	−7.65853	−	16.7699i	−0.256140	−	0.560868i
$895$	−3.71494	−	1.10023i	−0.124177	−	0.0367768i
$896$			55.5387i			1.85542i
$897$	−14.5879	+	26.0734i	−0.487076	+	0.870566i
$898$	−14.1032	−	14.1032i	−0.470631	−	0.470631i
$899$	9.48355	+	1.36353i	0.316294	+	0.0454762i
$900$	−0.146468	−	1.05362i	−0.00488226	−	0.0351208i
$901$	−0.245309	−	0.0720292i	−0.00817242	−	0.00239964i
$902$	−4.68318	+	65.4794i	−0.155933	+	2.18023i
$903$	7.83695	+	4.27930i	0.260797	+	0.142406i
$904$	−20.3451	−	13.0750i	−0.676667	−	0.434867i
$905$	−46.2360	−	29.8669i	−1.53693	−	0.992808i
$906$	−3.00239	+	3.46495i	−0.0997479	+	0.115115i
$907$	2.73055	+	0.593994i	0.0906664	+	0.0197233i	0.257670	−	0.966233i	$-0.417045\pi$
$907$	2.73055	+	0.593994i	0.0906664	+	0.0197233i	−0.167003	+	0.985956i	$0.553409\pi$
$908$	−4.66706	−	3.49372i	−0.154882	−	0.115943i
$909$	−1.90968	+	0.274570i	−0.0633400	+	0.00910692i
$910$	−53.0540	−	19.9294i	−1.75872	−	0.660653i
$911$	−35.2034	−	30.5039i	−1.16634	−	1.01064i	−0.999697	−	0.0246230i	$-0.992161\pi$
$911$	−35.2034	−	30.5039i	−1.16634	−	1.01064i	−0.166644	−	0.986017i	$-0.553293\pi$
$912$	−24.7510	+	9.23164i	−0.819587	+	0.305690i
$913$	−0.914039	−	4.20177i	−0.0302503	−	0.139058i
$914$	50.6109	−	14.8607i	1.67406	−	0.491549i
$915$	12.4718	+	2.74359i	0.412304	+	0.0907004i
$916$	0.618607	−	2.10678i	0.0204394	−	0.0696101i
$917$	2.23238	−	5.98524i	0.0737196	−	0.197650i
$918$	−1.51719	−	2.02672i	−0.0500746	−	0.0668918i
$919$	48.5619			1.60191			0.800955	−	0.598725i	$-0.204326\pi$
$919$	48.5619			1.60191			0.800955	+	0.598725i	$0.204326\pi$
$920$	−22.2423	−	14.6948i	−0.733308	−	0.484473i
$921$	12.6583			0.417105
$922$	−0.0972393	−	0.129897i	−0.00320241	−	0.00427791i
$923$	5.24048	−	14.0503i	0.172492	−	0.462470i
$924$	3.26828	−	11.1307i	0.107519	−	0.366175i
$925$	−5.47719	+	14.4780i	−0.180089	+	0.476033i
$926$	−53.5740	+	15.7307i	−1.76055	+	0.516944i
$927$	1.53456	+	7.05424i	0.0504014	+	0.231692i
$928$	2.94520	−	1.09850i	0.0966811	−	0.0360602i
$929$	−15.1725	−	13.1470i	−0.497793	−	0.431340i	0.369431	−	0.929258i	$-0.379553\pi$
$929$	−15.1725	−	13.1470i	−0.497793	−	0.431340i	−0.867224	+	0.497918i	$0.834098\pi$
$930$	33.0140	−	14.9839i	1.08257	−	0.491341i
$931$	36.0260	−	5.17976i	1.18071	−	0.169760i
$932$	−4.26646	−	3.19383i	−0.139752	−	0.104617i
$933$	−6.38413	−	1.38878i	−0.209007	−	0.0454667i
$934$	−31.1251	+	35.9202i	−1.01844	+	1.17535i
$935$	−0.632570	−	2.94093i	−0.0206872	−	0.0961787i
$936$	−4.49751	−	2.89037i	−0.147006	−	0.0944748i
$937$	−41.7992	−	22.8241i	−1.36552	−	0.745631i	−0.381615	−	0.924321i	$-0.624632\pi$
$937$	−41.7992	−	22.8241i	−1.36552	−	0.745631i	−0.983905	+	0.178691i	$0.942814\pi$
$938$	−0.205561	+	2.87411i	−0.00671179	+	0.0938431i
$939$	−28.3485	−	8.32388i	−0.925119	−	0.271639i
$940$	5.40796	−	9.84918i	0.176388	−	0.321245i
$941$	15.8119	+	2.27341i	0.515453	+	0.0741110i	0.395133	−	0.918624i	$-0.370699\pi$
$941$	15.8119	+	2.27341i	0.515453	+	0.0741110i	0.120321	+	0.992735i	$0.461608\pi$
$942$	−6.58023	−	6.58023i	−0.214396	−	0.214396i
$943$	−31.2008	−	31.8505i	−1.01604	−	1.03720i
$944$			20.0297i			0.651911i
$945$	14.5405	−	49.0960i	0.473003	−	1.59709i
$946$	−4.05054	−	8.86944i	−0.131694	−	0.288371i
$947$	−9.93973	+	5.42750i	−0.322998	+	0.176370i	−0.632565	−	0.774508i	$-0.717998\pi$
$947$	−9.93973	+	5.42750i	−0.322998	+	0.176370i	0.309567	+	0.950878i	$0.399816\pi$
$948$	6.13802	+	0.439000i	0.199354	+	0.0142581i
$949$	4.89405	+	16.6676i	0.158868	+	0.541054i
$950$	28.0531	+	2.13815i	0.910162	+	0.0693709i
$951$	13.4177	−	29.3806i	0.435098	−	0.952731i
$952$	−0.215543	−	3.01368i	−0.00698577	−	0.0976739i
$953$	−7.87966	+	36.2222i	−0.255247	+	1.17335i	0.653802	+	0.756665i	$0.273173\pi$
$953$	−7.87966	+	36.2222i	−0.255247	+	1.17335i	−0.909050	+	0.416688i	$0.863191\pi$
$954$	0.103376	+	0.718994i	0.00334691	+	0.0232783i
$955$	13.7418	+	0.0320962i	0.444674	+	0.00103861i
$956$	7.85856	−	5.05039i	0.254164	−	0.163341i
$957$	10.2329	−	0.731872i	0.330783	−	0.0236581i
$958$	−11.4264	−	30.6352i	−0.369169	−	0.989780i
$959$	−1.69141	+	2.63189i	−0.0546186	+	0.0849881i
$960$	−12.3739	+	16.4494i	−0.399365	+	0.530901i
$961$	−8.95886	−	10.3391i	−0.288996	−	0.333519i
$962$	−9.11883	−	16.6999i	−0.294003	−	0.538426i
$963$	−7.59145	−	2.83146i	−0.244631	−	0.0912426i
$964$	1.35948	−	9.45542i	0.0437860	−	0.304538i
$965$	−4.89137	−	6.56602i	−0.157459	−	0.211368i
$966$	25.5187	+	40.6222i	0.821052	+	1.30700i
$967$	18.9542	−	18.9542i	0.609525	−	0.609525i	−0.333297	−	0.942822i	$-0.608161\pi$
$967$	18.9542	−	18.9542i	0.609525	−	0.609525i	0.942822	+	0.333297i	$0.108161\pi$
$968$	19.5728	−	14.6520i	0.629093	−	0.470933i
$969$	1.52909	−	0.698311i	0.0491214	−	0.0224330i
$970$	24.5153	+	11.2650i	0.787139	+	0.361699i
$971$	40.0798	−	34.7294i	1.28622	−	1.11452i	0.299158	−	0.954204i	$-0.403294\pi$
$971$	40.0798	−	34.7294i	1.28622	−	1.11452i	0.987066	−	0.160315i	$-0.0512511\pi$
$972$	−1.04580	+	1.91524i	−0.0335441	+	0.0614314i
$973$	−6.17460	+	1.34320i	−0.197949	+	0.0430611i
$974$	−11.6800	−	5.33409i	−0.374252	−	0.170915i
$975$	−16.7177	−	26.2825i	−0.535396	−	0.841712i
$976$	−9.11994	−	14.1909i	−0.291922	−	0.454240i
$977$	20.1751	−	26.9507i	0.645457	−	0.862230i	−0.351813	−	0.936070i	$-0.614435\pi$
$977$	20.1751	−	26.9507i	0.645457	−	0.862230i	0.997270	+	0.0738405i	$0.0235256\pi$
$978$	−33.1823	+	44.3264i	−1.06105	+	1.41740i
$979$	11.8283	+	18.4053i	0.378035	+	0.588235i
$980$	−6.65937	+	5.74320i	−0.212726	+	0.183460i
$981$	−2.47313	−	1.12944i	−0.0789609	−	0.0360602i
$982$	−38.5963	+	8.39611i	−1.23166	+	0.267931i
$983$	−1.40127	+	2.56624i	−0.0446936	+	0.0818503i	−0.899071	−	0.437803i	$-0.855757\pi$
$983$	−1.40127	+	2.56624i	−0.0446936	+	0.0818503i	0.854378	+	0.519653i	$0.173939\pi$
$984$	−27.3874	+	23.7313i	−0.873077	+	0.756526i
$985$	42.4678	−	15.7268i	1.35314	−	0.501097i
$986$	−0.594450	+	0.271476i	−0.0189312	+	0.00864557i
$987$	66.1829	−	49.5439i	2.10662	−	1.57700i
$988$	−4.01630	+	4.01630i	−0.127776	+	0.127776i
$989$	6.33466	+	1.93114i	0.201431	+	0.0614066i
$990$	−6.85400	+	5.10590i	−0.217834	+	0.162276i
$991$	−5.16058	+	35.8926i	−0.163931	+	1.14017i	0.727202	+	0.686424i	$0.240820\pi$
$991$	−5.16058	+	35.8926i	−0.163931	+	1.14017i	−0.891133	+	0.453742i	$0.850089\pi$
$992$	−13.7347	−	5.12279i	−0.436078	−	0.162649i
$993$	−1.60071	−	2.93148i	−0.0507969	−	0.0930276i
$994$	−15.7679	−	18.1972i	−0.500128	−	0.577179i
$995$	13.6794	−	1.93421i	0.433667	−	0.0613184i
$996$	−0.313878	+	0.488404i	−0.00994561	+	0.0154757i
$997$	−10.7021	−	28.6935i	−0.338940	−	0.908733i	−0.988876	−	0.148744i	$-0.952477\pi$
$997$	−10.7021	−	28.6935i	−0.338940	−	0.908733i	0.649936	−	0.759989i	$-0.274796\pi$
$998$	−43.4611	+	3.10840i	−1.37574	+	0.0983946i
$999$	14.4619	−	9.29413i	0.457556	−	0.294053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.38.8	✓	200
5.2	odd	4	inner	115.2.l.a.107.3	yes	200
5.3	odd	4		575.2.r.b.107.8		200
5.4	even	2		575.2.r.b.268.3		200
23.20	odd	22	inner	115.2.l.a.43.3	yes	200
115.43	even	44		575.2.r.b.457.3		200
115.89	odd	22		575.2.r.b.43.8		200
115.112	even	44	inner	115.2.l.a.112.8	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.38.8	✓	200	1.1	even	1	trivial
115.2.l.a.43.3	yes	200	23.20	odd	22	inner
115.2.l.a.107.3	yes	200	5.2	odd	4	inner
115.2.l.a.112.8	yes	200	115.112	even	44	inner
575.2.r.b.43.8		200	115.89	odd	22
575.2.r.b.107.8		200	5.3	odd	4
575.2.r.b.268.3		200	5.4	even	2
575.2.r.b.457.3		200	115.43	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.927048 + 1.23839i) q^{2} +(0.547968 - 1.46916i) q^{3} +(-0.110730 + 0.377111i) q^{4} +(-1.20451 - 1.88392i) q^{5} +(2.32738 - 0.683382i) q^{6} +(0.876587 + 4.02961i) q^{7} +(2.32915 - 0.868729i) q^{8} +(0.409093 + 0.354481i) q^{9} +(1.21639 - 3.23814i) q^{10} +(-4.51811 + 0.649606i) q^{11} +(0.493360 + 0.369324i) q^{12} +(-3.88221 - 0.844524i) q^{13} +(-4.17759 + 4.82120i) q^{14} +(-3.42781 + 0.737293i) q^{15} +(3.89634 + 2.50403i) q^{16} +(-0.258676 - 0.141248i) q^{17} +(-0.0597374 + 0.835238i) q^{18} +(-3.49008 - 1.02478i) q^{19} +(0.843823 - 0.245629i) q^{20} +(6.40047 + 0.920248i) q^{21} +(-4.99297 - 4.99297i) q^{22} +(4.78688 - 0.292826i) q^{23} -3.89793i q^{24} +(-2.09830 + 4.53841i) q^{25} +(-2.55315 - 5.59062i) q^{26} +(4.87362 - 2.66120i) q^{27} +(-1.61667 - 0.115627i) q^{28} +(-0.403824 - 1.37530i) q^{29} +(-4.09080 - 3.56146i) q^{30} +(-2.77678 + 6.08030i) q^{31} +(0.156449 + 2.18744i) q^{32} +(-1.52140 + 6.99378i) q^{33} +(-0.0648851 - 0.451286i) q^{34} +(6.53559 - 6.50513i) q^{35} +(-0.178977 + 0.115022i) q^{36} +(3.08799 - 0.220858i) q^{37} +(-1.96640 - 5.27211i) q^{38} +(-3.36807 + 5.24081i) q^{39} +(-4.44211 - 3.34154i) q^{40} +(-6.08818 - 7.02614i) q^{41} +(4.79391 + 8.77940i) q^{42} +(1.29382 + 0.482569i) q^{43} +(0.255316 - 1.77576i) q^{44} +(0.175056 - 1.19767i) q^{45} +(4.80030 + 5.65657i) q^{46} +(9.04049 - 9.04049i) q^{47} +(5.81388 - 4.35221i) q^{48} +(-9.10189 + 4.15669i) q^{49} +(-7.56555 + 1.60881i) q^{50} +(-0.349262 + 0.302637i) q^{51} +(0.748357 - 1.37051i) q^{52} +(0.847638 - 0.184392i) q^{53} +(7.81368 + 3.56839i) q^{54} +(6.66592 + 7.72929i) q^{55} +(5.54234 + 8.62405i) q^{56} +(-3.41802 + 4.56593i) q^{57} +(1.32879 - 1.77506i) q^{58} +(2.33805 + 3.63807i) q^{59} +(0.101519 - 1.37431i) q^{60} +(-3.31298 - 1.51299i) q^{61} +(-10.1040 + 2.19799i) q^{62} +(-1.06981 + 1.95921i) q^{63} +(4.43677 - 3.84448i) q^{64} +(3.08516 + 8.33102i) q^{65} +(-10.0714 + 4.59948i) q^{66} +(0.361592 - 0.270684i) q^{67} +(0.0819094 - 0.0819094i) q^{68} +(2.19285 - 7.19315i) q^{69} +(14.1147 + 2.06305i) q^{70} +(-0.537154 + 3.73599i) q^{71} +(1.26079 + 0.470249i) q^{72} +(-2.09543 - 3.83749i) q^{73} +(3.13623 + 3.61940i) q^{74} +(5.51784 + 5.56963i) q^{75} +(0.772913 - 1.20268i) q^{76} +(-6.57817 - 17.6368i) q^{77} +(-9.61254 + 0.687502i) q^{78} +(8.40008 - 5.39840i) q^{79} +(0.0241893 - 10.3565i) q^{80} +(-1.00803 - 7.01097i) q^{81} +(3.05707 - 14.0531i) q^{82} +(0.0672048 + 0.939647i) q^{83} +(-1.05576 + 2.31179i) q^{84} +(0.0454792 + 0.657460i) q^{85} +(0.601822 + 2.04962i) q^{86} +(-2.24181 - 0.160338i) q^{87} +(-9.95903 + 5.43804i) q^{88} +(-1.99112 - 4.35995i) q^{89} +(1.64547 - 0.893514i) q^{90} -16.3841i q^{91} +(-0.419623 + 1.83761i) q^{92} +(7.41134 + 7.41134i) q^{93} +(19.5766 + 2.81470i) q^{94} +(2.27325 + 7.80939i) q^{95} +(3.29943 + 0.968799i) q^{96} +(-0.556423 + 7.77981i) q^{97} +(-13.5855 - 7.41825i) q^{98} +(-2.07860 - 1.33583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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