LMFDB - Embedded newform 115.2.g.c.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.3
Character	$\chi$	$=$	115.6
Dual form			115.2.g.c.96.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366526 + 0.802579i) q^{2} +(0.817387 + 0.240007i) q^{3} +(0.799929 + 0.923167i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.492218 + 0.568049i) q^{6} +(0.192580 - 1.33943i) q^{7} +(-2.72725 + 0.800794i) q^{8} +(-1.91324 - 1.22957i) q^{9} +O(q^{10})$	\(q+(-0.366526 + 0.802579i) q^{2} +(0.817387 + 0.240007i) q^{3} +(0.799929 + 0.923167i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.492218 + 0.568049i) q^{6} +(0.192580 - 1.33943i) q^{7} +(-2.72725 + 0.800794i) q^{8} +(-1.91324 - 1.22957i) q^{9} +(0.125566 + 0.873331i) q^{10} +(2.43729 + 5.33691i) q^{11} +(0.432286 + 0.946573i) q^{12} +(-0.441451 - 3.07036i) q^{13} +(1.00441 + 0.645495i) q^{14} +(0.817387 - 0.240007i) q^{15} +(0.00922548 - 0.0641646i) q^{16} +(-0.255004 + 0.294291i) q^{17} +(1.68808 - 1.08486i) q^{18} +(-2.98969 - 3.45029i) q^{19} +(1.17205 + 0.344144i) q^{20} +(0.478884 - 1.04861i) q^{21} -5.17662 q^{22} +(-2.42636 - 4.13676i) q^{23} -2.42142 q^{24} +(0.415415 - 0.909632i) q^{25} +(2.62601 + 0.771067i) q^{26} +(-2.94237 - 3.39568i) q^{27} +(1.39056 - 0.893662i) q^{28} +(-0.942838 + 1.08809i) q^{29} +(-0.106969 + 0.743987i) q^{30} +(9.51592 - 2.79413i) q^{31} +(-4.73423 - 3.04250i) q^{32} +(0.711313 + 4.94729i) q^{33} +(-0.142726 - 0.312526i) q^{34} +(-0.562139 - 1.23091i) q^{35} +(-0.395363 - 2.74981i) q^{36} +(-2.91085 - 1.87069i) q^{37} +(3.86493 - 1.13485i) q^{38} +(0.376070 - 2.61563i) q^{39} +(-1.86137 + 2.14814i) q^{40} +(-5.78939 + 3.72061i) q^{41} +(0.666069 + 0.768684i) q^{42} +(0.0590243 + 0.0173311i) q^{43} +(-2.97721 + 6.51917i) q^{44} -2.27428 q^{45} +(4.20940 - 0.431116i) q^{46} +5.78228 q^{47} +(0.0229407 - 0.0502332i) q^{48} +(4.95948 + 1.45623i) q^{49} +(0.577791 + 0.666807i) q^{50} +(-0.279069 + 0.179347i) q^{51} +(2.48133 - 2.86361i) q^{52} +(-2.00938 + 13.9755i) q^{53} +(3.80376 - 1.11688i) q^{54} +(4.93573 + 3.17200i) q^{55} +(0.547389 + 3.80717i) q^{56} +(-1.61564 - 3.53777i) q^{57} +(-0.527707 - 1.15552i) q^{58} +(0.0218917 + 0.152260i) q^{59} +(0.875418 + 0.562597i) q^{60} +(-4.20259 + 1.23399i) q^{61} +(-1.24532 + 8.66140i) q^{62} +(-2.01537 + 2.32586i) q^{63} +(4.28613 - 2.75453i) q^{64} +(-2.03134 - 2.34429i) q^{65} +(-4.23131 - 1.24242i) q^{66} +(-5.59921 + 12.2606i) q^{67} -0.475665 q^{68} +(-0.990425 - 3.96368i) q^{69} +1.19394 q^{70} +(2.69555 - 5.90243i) q^{71} +(6.20253 + 1.82123i) q^{72} +(-3.21329 - 3.70834i) q^{73} +(2.56828 - 1.65053i) q^{74} +(0.557873 - 0.643819i) q^{75} +(0.793652 - 5.51997i) q^{76} +(7.61777 - 2.23678i) q^{77} +(1.96141 + 1.26052i) q^{78} +(1.13725 + 7.90977i) q^{79} +(-0.0269290 - 0.0589664i) q^{80} +(1.24423 + 2.72449i) q^{81} +(-0.864128 - 6.01014i) q^{82} +(7.23936 + 4.65246i) q^{83} +(1.35111 - 0.396723i) q^{84} +(-0.0554177 + 0.385439i) q^{85} +(-0.0355435 + 0.0410194i) q^{86} +(-1.03181 + 0.663106i) q^{87} +(-10.9209 - 12.6034i) q^{88} +(-13.9961 - 4.10963i) q^{89} +(0.833580 - 1.82529i) q^{90} -4.19754 q^{91} +(1.87801 - 5.54905i) q^{92} +8.44880 q^{93} +(-2.11936 + 4.64074i) q^{94} +(-4.38046 - 1.28622i) q^{95} +(-3.13948 - 3.62315i) q^{96} +(4.05860 - 2.60830i) q^{97} +(-2.98652 + 3.44663i) q^{98} +(1.89897 - 13.2076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.366526	+	0.802579i	−0.259173	+	0.567509i	−0.993828	−	0.110931i	$-0.964617\pi$
$2$	−0.366526	+	0.802579i	−0.259173	+	0.567509i	0.734655	+	0.678441i	$0.237344\pi$
$3$	0.817387	+	0.240007i	0.471919	+	0.138568i	0.509040	−	0.860743i	$-0.330001\pi$
$3$	0.817387	+	0.240007i	0.471919	+	0.138568i	−0.0371212	+	0.999311i	$0.511819\pi$
$4$	0.799929	+	0.923167i	0.399965	+	0.461584i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	−0.492218	+	0.568049i	−0.200947	+	0.231905i
$7$	0.192580	−	1.33943i	0.0727885	−	0.506255i	−0.920514	−	0.390710i	$-0.872229\pi$
$7$	0.192580	−	1.33943i	0.0727885	−	0.506255i	0.993302	−	0.115545i	$-0.0368615\pi$
$8$	−2.72725	+	0.800794i	−0.964230	+	0.283123i
$9$	−1.91324	−	1.22957i	−0.637747	−	0.409855i
$10$	0.125566	+	0.873331i	0.0397075	+	0.276172i
$11$	2.43729	+	5.33691i	0.734869	+	1.60914i	0.791814	+	0.610762i	$0.209137\pi$
$11$	2.43729	+	5.33691i	0.734869	+	1.60914i	−0.0569446	+	0.998377i	$0.518136\pi$
$12$	0.432286	+	0.946573i	0.124790	+	0.273252i
$13$	−0.441451	−	3.07036i	−0.122437	−	0.851565i	−0.954782	−	0.297308i	$-0.903911\pi$
$13$	−0.441451	−	3.07036i	−0.122437	−	0.851565i	0.832345	−	0.554258i	$-0.186998\pi$
$14$	1.00441	+	0.645495i	0.268440	+	0.172516i
$15$	0.817387	−	0.240007i	0.211048	−	0.0619694i
$16$	0.00922548	−	0.0641646i	0.00230637	−	0.0160412i
$17$	−0.255004	+	0.294291i	−0.0618476	+	0.0713760i	−0.785830	−	0.618442i	$-0.787764\pi$
$17$	−0.255004	+	0.294291i	−0.0618476	+	0.0713760i	0.723983	+	0.689818i	$0.242310\pi$
$18$	1.68808	−	1.08486i	0.397883	−	0.255704i
$19$	−2.98969	−	3.45029i	−0.685882	−	0.791550i	0.300891	−	0.953659i	$-0.402716\pi$
$19$	−2.98969	−	3.45029i	−0.685882	−	0.791550i	−0.986773	+	0.162108i	$0.948171\pi$
$20$	1.17205	+	0.344144i	0.262077	+	0.0769528i
$21$	0.478884	−	1.04861i	0.104501	−	0.228825i
$22$	−5.17662			−1.10366
$23$	−2.42636	−	4.13676i	−0.505931	−	0.862574i
$23$	−2.42636	−	4.13676i	−0.505931	−	0.862574i
$24$	−2.42142			−0.494270
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	2.62601	+	0.771067i	0.515003	+	0.151219i
$27$	−2.94237	−	3.39568i	−0.566260	−	0.653499i
$28$	1.39056	−	0.893662i	0.262792	−	0.168886i
$29$	−0.942838	+	1.08809i	−0.175081	+	0.202054i	−0.836507	−	0.547956i	$-0.815406\pi$
$29$	−0.942838	+	1.08809i	−0.175081	+	0.202054i	0.661426	+	0.750010i	$0.269951\pi$
$30$	−0.106969	+	0.743987i	−0.0195298	+	0.135833i
$31$	9.51592	−	2.79413i	1.70911	−	0.501840i	0.726443	−	0.687226i	$-0.241172\pi$
$31$	9.51592	−	2.79413i	1.70911	−	0.501840i	0.982666	+	0.185386i	$0.0593537\pi$
$32$	−4.73423	−	3.04250i	−0.836901	−	0.537844i
$33$	0.711313	+	4.94729i	0.123824	+	0.861212i
$34$	−0.142726	−	0.312526i	−0.0244773	−	0.0535978i
$35$	−0.562139	−	1.23091i	−0.0950189	−	0.208062i
$36$	−0.395363	−	2.74981i	−0.0658938	−	0.458301i
$37$	−2.91085	−	1.87069i	−0.478540	−	0.307539i	0.279042	−	0.960279i	$-0.409983\pi$
$37$	−2.91085	−	1.87069i	−0.478540	−	0.307539i	−0.757582	+	0.652740i	$0.773620\pi$
$38$	3.86493	−	1.13485i	0.626974	−	0.184096i
$39$	0.376070	−	2.61563i	0.0602194	−	0.418835i
$40$	−1.86137	+	2.14814i	−0.294308	+	0.339650i
$41$	−5.78939	+	3.72061i	−0.904150	+	0.581062i	−0.908018	−	0.418930i	$-0.862405\pi$
$41$	−5.78939	+	3.72061i	−0.904150	+	0.581062i	0.00386813	+	0.999993i	$0.498769\pi$
$42$	0.666069	+	0.768684i	0.102777	+	0.118611i
$43$	0.0590243	+	0.0173311i	0.00900111	+	0.00264297i	0.286230	−	0.958161i	$-0.407598\pi$
$43$	0.0590243	+	0.0173311i	0.00900111	+	0.00264297i	−0.277229	+	0.960804i	$0.589416\pi$
$44$	−2.97721	+	6.51917i	−0.448831	+	0.982803i
$45$	−2.27428			−0.339029
$46$	4.20940	−	0.431116i	0.620642	−	0.0635646i
$47$	5.78228			0.843433			0.421716	−	0.906728i	$-0.361428\pi$
$47$	5.78228			0.843433			0.421716	+	0.906728i	$0.361428\pi$
$48$	0.0229407	−	0.0502332i	0.00331121	−	0.00725053i
$49$	4.95948	+	1.45623i	0.708497	+	0.208033i
$50$	0.577791	+	0.666807i	0.0817121	+	0.0943007i
$51$	−0.279069	+	0.179347i	−0.0390775	+	0.0251136i
$52$	2.48133	−	2.86361i	0.344098	−	0.397111i
$53$	−2.00938	+	13.9755i	−0.276009	+	1.91968i	0.103758	+	0.994603i	$0.466913\pi$
$53$	−2.00938	+	13.9755i	−0.276009	+	1.91968i	−0.379767	+	0.925082i	$0.623996\pi$
$54$	3.80376	−	1.11688i	0.517626	−	0.151989i
$55$	4.93573	+	3.17200i	0.665533	+	0.427712i
$56$	0.547389	+	3.80717i	0.0731479	+	0.508755i
$57$	−1.61564	−	3.53777i	−0.213997	−	0.468589i
$58$	−0.527707	−	1.15552i	−0.0692913	−	0.151727i
$59$	0.0218917	+	0.152260i	0.00285006	+	0.0198226i	0.991197	−	0.132396i	$-0.0422672\pi$
$59$	0.0218917	+	0.152260i	0.00285006	+	0.0198226i	−0.988347	+	0.152219i	$0.951358\pi$
$60$	0.875418	+	0.562597i	0.113016	+	0.0726310i
$61$	−4.20259	+	1.23399i	−0.538087	+	0.157997i	−0.539474	−	0.842002i	$-0.681377\pi$
$61$	−4.20259	+	1.23399i	−0.538087	+	0.157997i	0.00138682	+	0.999999i	$0.499559\pi$
$62$	−1.24532	+	8.66140i	−0.158156	+	1.10000i
$63$	−2.01537	+	2.32586i	−0.253912	+	0.293030i
$64$	4.28613	−	2.75453i	0.535767	−	0.344316i
$65$	−2.03134	−	2.34429i	−0.251956	−	0.290773i
$66$	−4.23131	−	1.24242i	−0.520838	−	0.152932i
$67$	−5.59921	+	12.2606i	−0.684052	+	1.49787i	0.174239	+	0.984703i	$0.444253\pi$
$67$	−5.59921	+	12.2606i	−0.684052	+	1.49787i	−0.858292	+	0.513162i	$0.828474\pi$
$68$	−0.475665			−0.0576828
$69$	−0.990425	−	3.96368i	−0.119233	−	0.477171i
$70$	1.19394			0.142704
$71$	2.69555	−	5.90243i	0.319903	−	0.700489i	−0.679548	−	0.733631i	$-0.737824\pi$
$71$	2.69555	−	5.90243i	0.319903	−	0.700489i	0.999451	+	0.0331420i	$0.0105514\pi$
$72$	6.20253	+	1.82123i	0.730975	+	0.214634i
$73$	−3.21329	−	3.70834i	−0.376087	−	0.434028i	0.535878	−	0.844296i	$-0.319981\pi$
$73$	−3.21329	−	3.70834i	−0.376087	−	0.434028i	−0.911965	+	0.410268i	$0.865435\pi$
$74$	2.56828	−	1.65053i	0.298556	−	0.191870i
$75$	0.557873	−	0.643819i	0.0644176	−	0.0743418i
$76$	0.793652	−	5.51997i	0.0910381	−	0.633184i
$77$	7.61777	−	2.23678i	0.868126	−	0.254905i
$78$	1.96141	+	1.26052i	0.222086	+	0.142726i
$79$	1.13725	+	7.90977i	0.127951	+	0.889919i	0.948146	+	0.317835i	$0.102956\pi$
$79$	1.13725	+	7.90977i	0.127951	+	0.889919i	−0.820195	+	0.572084i	$0.806135\pi$
$80$	−0.0269290	−	0.0589664i	−0.00301076	−	0.00659264i
$81$	1.24423	+	2.72449i	0.138248	+	0.302721i
$82$	−0.864128	−	6.01014i	−0.0954270	−	0.663709i
$83$	7.23936	+	4.65246i	0.794624	+	0.510674i	0.873857	−	0.486183i	$-0.161611\pi$
$83$	7.23936	+	4.65246i	0.794624	+	0.510674i	−0.0792337	+	0.996856i	$0.525247\pi$
$84$	1.35111	−	0.396723i	0.147419	−	0.0432860i
$85$	−0.0554177	+	0.385439i	−0.00601090	+	0.0418067i
$86$	−0.0355435	+	0.0410194i	−0.00383275	+	0.00442323i
$87$	−1.03181	+	0.663106i	−0.110622	+	0.0710924i
$88$	−10.9209	−	12.6034i	−1.16417	−	1.34352i
$89$	−13.9961	−	4.10963i	−1.48358	−	0.435619i	−0.563096	−	0.826391i	$-0.690390\pi$
$89$	−13.9961	−	4.10963i	−1.48358	−	0.435619i	−0.920488	+	0.390772i	$0.872208\pi$
$90$	0.833580	−	1.82529i	0.0878671	−	0.192402i
$91$	−4.19754			−0.440021
$92$	1.87801	−	5.54905i	0.195796	−	0.578528i
$93$	8.44880			0.876099
$94$	−2.11936	+	4.64074i	−0.218595	+	0.478656i
$95$	−4.38046	−	1.28622i	−0.449425	−	0.131963i
$96$	−3.13948	−	3.62315i	−0.320421	−	0.369786i
$97$	4.05860	−	2.60830i	0.412088	−	0.264833i	−0.318130	−	0.948047i	$-0.603055\pi$
$97$	4.05860	−	2.60830i	0.412088	−	0.264833i	0.730218	+	0.683214i	$0.239418\pi$
$98$	−2.98652	+	3.44663i	−0.301684	+	0.348162i
$99$	1.89897	−	13.2076i	0.190853	−	1.32741i
$100$	1.17205	−	0.344144i	0.117205	−	0.0344144i
$101$	−3.37074	−	2.16625i	−0.335401	−	0.215549i	0.362089	−	0.932144i	$-0.382064\pi$
$101$	−3.37074	−	2.16625i	−0.335401	−	0.215549i	−0.697490	+	0.716594i	$0.745700\pi$
$102$	−0.0416540	−	0.289710i	−0.00412436	−	0.0286856i
$103$	1.67947	+	3.67753i	0.165483	+	0.362358i	0.974148	−	0.225913i	$-0.0725364\pi$
$103$	1.67947	+	3.67753i	0.165483	+	0.362358i	−0.808664	+	0.588270i	$0.799809\pi$
$104$	3.66268	+	8.02014i	0.359155	+	0.786440i
$105$	−0.164058	−	1.14105i	−0.0160104	−	0.111355i
$106$	−10.4800	−	6.73507i	−1.01790	−	0.654168i
$107$	13.3348	−	3.91546i	1.28913	−	0.378522i	0.435868	−	0.900011i	$-0.356441\pi$
$107$	13.3348	−	3.91546i	1.28913	−	0.378522i	0.853258	+	0.521489i	$0.174623\pi$
$108$	0.781091	−	5.43261i	0.0751605	−	0.522753i
$109$	−1.45129	+	1.67488i	−0.139008	+	0.160424i	−0.820985	−	0.570950i	$-0.806575\pi$
$109$	−1.45129	+	1.67488i	−0.139008	+	0.160424i	0.681977	+	0.731374i	$0.261121\pi$
$110$	−4.35485	+	2.79869i	−0.415219	+	0.266845i
$111$	−1.93031	−	2.22770i	−0.183217	−	0.211444i
$112$	−0.0841671	−	0.0247137i	−0.00795304	−	0.00233522i
$113$	−0.309621	+	0.677975i	−0.0291267	+	0.0637785i	−0.923636	−	0.383270i	$-0.874798\pi$
$113$	−0.309621	+	0.677975i	−0.0291267	+	0.0637785i	0.894510	+	0.447049i	$0.147525\pi$
$114$	3.43151			0.321391
$115$	−4.27768	−	2.16828i	−0.398896	−	0.202193i
$116$	−1.75870			−0.163291
$117$	−2.93061	+	6.41714i	−0.270935	+	0.593265i
$118$	−0.130225	−	0.0382374i	−0.0119882	−	0.00352004i
$119$	0.345072	+	0.398234i	0.0316327	+	0.0365060i
$120$	−2.03703	+	1.30912i	−0.185954	+	0.119506i
$121$	−15.3388	+	17.7019i	−1.39444	+	1.60927i
$122$	0.549981	−	3.82520i	0.0497930	−	0.346318i
$123$	−5.62514	+	1.65169i	−0.507202	+	0.148928i
$124$	10.1915	+	6.54968i	0.915224	+	0.588179i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	−1.12800	−	2.46998i	−0.100490	−	0.220043i
$127$	2.86150	+	6.26582i	0.253917	+	0.556001i	0.993068	−	0.117538i	$-0.0375003\pi$
$127$	2.86150	+	6.26582i	0.253917	+	0.556001i	−0.739151	+	0.673540i	$0.764773\pi$
$128$	−0.962027	−	6.69104i	−0.0850320	−	0.591410i
$129$	0.0440861	+	0.0283324i	0.00388156	+	0.00249453i
$130$	2.62601	−	0.771067i	0.230316	−	0.0676270i
$131$	0.836276	−	5.81643i	0.0730658	−	0.508184i	−0.920119	−	0.391638i	$-0.871909\pi$
$131$	0.836276	−	5.81643i	0.0730658	−	0.508184i	0.993185	−	0.116546i	$-0.0371823\pi$
$132$	−3.99818	+	4.61414i	−0.347996	+	0.401609i
$133$	−5.19716	+	3.34001i	−0.450651	+	0.289616i
$134$	−7.78781	−	8.98762i	−0.672765	−	0.776412i
$135$	−4.31112	−	1.26586i	−0.371043	−	0.108948i
$136$	0.459795	−	1.00681i	0.0394271	−	0.0863334i
$137$	−0.562239			−0.0480353			−0.0240177	−	0.999712i	$-0.507646\pi$
$137$	−0.562239			−0.0480353			−0.0240177	+	0.999712i	$0.507646\pi$
$138$	3.54418	+	0.657895i	0.301701	+	0.0560037i
$139$	3.23895			0.274724			0.137362	−	0.990521i	$-0.456138\pi$
$139$	3.23895			0.274724			0.137362	+	0.990521i	$0.456138\pi$
$140$	0.686668	−	1.50359i	0.0580340	−	0.127077i
$141$	4.72636	+	1.38779i	0.398032	+	0.116873i
$142$	3.74918	+	4.32678i	0.314624	+	0.363095i
$143$	15.3103	−	9.83934i	1.28031	−	0.822807i
$144$	−0.0965452	+	0.111419i	−0.00804544	+	0.00928493i
$145$	−0.204898	+	1.42510i	−0.0170159	+	0.118348i
$146$	4.15399	−	1.21972i	0.343787	−	0.100945i
$147$	3.70431	+	2.38061i	0.305526	+	0.196350i
$148$	−0.601513	−	4.18362i	−0.0494441	−	0.343891i
$149$	1.56789	+	3.43319i	0.128446	+	0.281258i	0.962919	−	0.269791i	$-0.0869548\pi$
$149$	1.56789	+	3.43319i	0.128446	+	0.281258i	−0.834472	+	0.551050i	$0.814227\pi$
$150$	0.312241	+	0.683713i	0.0254944	+	0.0558249i
$151$	−2.04284	−	14.2083i	−0.166244	−	1.15625i	−0.886563	−	0.462608i	$-0.846914\pi$
$151$	−2.04284	−	14.2083i	−0.166244	−	1.15625i	0.720319	−	0.693643i	$-0.243995\pi$
$152$	10.9166	+	7.01568i	0.885455	+	0.569047i
$153$	0.849735	−	0.249505i	0.0686970	−	0.0201713i
$154$	−0.996916	+	6.93370i	−0.0803338	+	0.558734i
$155$	6.49468	−	7.49526i	0.521665	−	0.602034i
$156$	2.71549	−	1.74514i	0.217413	−	0.139723i
$157$	5.67673	+	6.55130i	0.453053	+	0.522851i	0.935620	−	0.353008i	$-0.114841\pi$
$157$	5.67673	+	6.55130i	0.453053	+	0.522851i	−0.482568	+	0.875859i	$0.660296\pi$
$158$	−6.76505	−	1.98640i	−0.538198	−	0.158029i
$159$	−4.99665	+	10.9411i	−0.396260	+	0.867689i
$160$	−5.62759			−0.444900
$161$	−6.00815	+	2.45327i	−0.473509	+	0.193345i
$162$	−2.64266			−0.207627
$163$	2.43749	−	5.33736i	0.190919	−	0.418054i	−0.789830	−	0.613325i	$-0.789831\pi$
$163$	2.43749	−	5.33736i	0.190919	−	0.418054i	0.980749	+	0.195271i	$0.0625588\pi$
$164$	−8.06585	−	2.36835i	−0.629837	−	0.184937i
$165$	3.27310	+	3.77736i	0.254810	+	0.294067i
$166$	−6.38738	+	4.10492i	−0.495757	+	0.318604i
$167$	−7.76508	+	8.96137i	−0.600880	+	0.693452i	−0.971959	−	0.235149i	$-0.924442\pi$
$167$	−7.76508	+	8.96137i	−0.600880	+	0.693452i	0.371080	+	0.928601i	$0.378988\pi$
$168$	−0.466318	+	3.24331i	−0.0359772	+	0.250227i
$169$	3.24117	−	0.951692i	0.249320	−	0.0732071i
$170$	−0.289033	−	0.185750i	−0.0221678	−	0.0142464i
$171$	1.47765	+	10.2773i	0.112998	+	0.785922i
$172$	0.0312157	+	0.0683529i	0.00238018	+	0.00521186i
$173$	8.78877	+	19.2447i	0.668198	+	1.46315i	0.874681	+	0.484699i	$0.161071\pi$
$173$	8.78877	+	19.2447i	0.668198	+	1.46315i	−0.206483	+	0.978450i	$0.566202\pi$
$174$	−0.154009	−	1.07116i	−0.0116754	−	0.0812042i
$175$	−1.13838	−	0.731595i	−0.0860537	−	0.0553034i
$176$	0.364926	−	0.107152i	0.0275073	−	0.00807688i
$177$	−0.0186494	+	0.129710i	−0.00140178	+	0.00974958i
$178$	8.42823	−	9.72670i	0.631723	−	0.729047i
$179$	12.9451	−	8.31931i	0.967562	−	0.621815i	0.0414814	−	0.999139i	$-0.486792\pi$
$179$	12.9451	−	8.31931i	0.967562	−	0.621815i	0.926081	+	0.377325i	$0.123156\pi$
$180$	−1.81926	−	2.09954i	−0.135600	−	0.156490i
$181$	17.6483	+	5.18201i	1.31179	+	0.385176i	0.861523	−	0.507719i	$-0.169511\pi$
$181$	17.6483	+	5.18201i	1.31179	+	0.385176i	0.450265	+	0.892895i	$0.351329\pi$
$182$	1.53850	−	3.36886i	0.114042	−	0.249716i
$183$	−3.73131			−0.275826
$184$	9.92999	+	9.33898i	0.732048	+	0.688479i
$185$	−3.46013			−0.254394
$186$	−3.09670	+	6.78083i	−0.227061	+	0.497194i
$187$	−2.19212	−	0.643665i	−0.160304	−	0.0470695i
$188$	4.62542	+	5.33802i	0.337343	+	0.389315i
$189$	−5.11490	+	3.28715i	−0.372055	+	0.239105i
$190$	2.63784	−	3.04423i	0.191369	−	0.220852i
$191$	0.142979	−	0.994443i	0.0103456	−	0.0719554i	−0.983995	−	0.178198i	$-0.942973\pi$
$191$	0.142979	−	0.994443i	0.0103456	−	0.0719554i	0.994340	+	0.106243i	$0.0338822\pi$
$192$	4.16453	−	1.22282i	0.300549	−	0.0882493i
$193$	−21.2341	−	13.6463i	−1.52847	−	0.982286i	−0.990223	−	0.139496i	$-0.955452\pi$
$193$	−21.2341	−	13.6463i	−1.52847	−	0.982286i	−0.538244	−	0.842789i	$-0.680912\pi$
$194$	0.605789	+	4.21335i	0.0434931	+	0.302501i
$195$	−1.09774	−	2.40372i	−0.0786110	−	0.172134i
$196$	2.62288	+	5.74331i	0.187349	+	0.410236i
$197$	−3.65053	−	25.3900i	−0.260090	−	1.80896i	−0.532115	−	0.846672i	$-0.678602\pi$
$197$	−3.65053	−	25.3900i	−0.260090	−	1.80896i	0.272025	−	0.962290i	$-0.412307\pi$
$198$	9.90413	+	6.36500i	0.703856	+	0.452341i
$199$	12.7698	−	3.74955i	0.905226	−	0.265798i	0.204196	−	0.978930i	$-0.434542\pi$
$199$	12.7698	−	3.74955i	0.905226	−	0.265798i	0.701030	+	0.713132i	$0.252724\pi$
$200$	−0.404514	+	2.81346i	−0.0286035	+	0.198942i
$201$	−7.51933	+	8.67778i	−0.530373	+	0.612083i
$202$	2.97405	−	1.91130i	0.209253	−	0.134479i
$203$	1.27585	+	1.47241i	0.0895470	+	0.103343i
$204$	−0.388802	−	0.114163i	−0.0272216	−	0.00799299i
$205$	−2.85883	+	6.25996i	−0.199669	+	0.437214i
$206$	−3.56708			−0.248530
$207$	−0.444209	+	10.8980i	−0.0308747	+	0.757463i
$208$	−0.201081			−0.0139425
$209$	11.1272	−	24.3651i	0.769681	−	1.68537i
$210$	0.975915	+	0.286554i	0.0673445	+	0.0197741i
$211$	−10.2279	−	11.8037i	−0.704119	−	0.812597i	0.285184	−	0.958473i	$-0.407945\pi$
$211$	−10.2279	−	11.8037i	−0.704119	−	0.812597i	−0.989303	+	0.145876i	$0.953400\pi$
$212$	−14.5091	+	9.32443i	−0.996489	+	0.640405i
$213$	3.61993	−	4.17762i	0.248033	−	0.286246i
$214$	−1.74509	+	12.1374i	−0.119292	+	0.829693i
$215$	0.0590243	−	0.0173311i	0.00402542	−	0.00118197i
$216$	10.7438	+	6.90465i	0.731026	+	0.469802i
$217$	−1.90994	−	13.2840i	−0.129656	−	0.901774i
$218$	−0.812286	−	1.77866i	−0.0550150	−	0.120466i
$219$	−1.73648	−	3.80236i	−0.117340	−	0.256940i
$220$	1.01995	+	7.09388i	0.0687647	+	0.478269i
$221$	1.01615	+	0.653041i	0.0683537	+	0.0439283i
$222$	2.49541	−	0.732719i	0.167481	−	0.0491769i
$223$	−3.18659	+	22.1632i	−0.213390	+	1.48416i	0.548337	+	0.836258i	$0.315261\pi$
$223$	−3.18659	+	22.1632i	−0.213390	+	1.48416i	−0.761726	+	0.647899i	$0.775648\pi$
$224$	−4.98693	+	5.75522i	−0.333203	+	0.384537i
$225$	−1.91324	+	1.22957i	−0.127549	+	0.0819711i
$226$	−0.430644	−	0.496990i	−0.0286460	−	0.0330593i
$227$	−12.8589	−	3.77571i	−0.853473	−	0.250602i	−0.174402	−	0.984675i	$-0.555799\pi$
$227$	−12.8589	−	3.77571i	−0.853473	−	0.250602i	−0.679072	+	0.734072i	$0.737617\pi$
$228$	1.97355	−	4.32147i	0.130702	−	0.286196i
$229$	−6.77274			−0.447555			−0.223778	−	0.974640i	$-0.571839\pi$
$229$	−6.77274			−0.447555			−0.223778	+	0.974640i	$0.571839\pi$
$230$	3.30809	−	2.63845i	0.218129	−	0.173974i
$231$	6.76351			0.445006
$232$	1.70002	−	3.72253i	0.111612	−	0.244396i
$233$	−13.7746	−	4.04457i	−0.902401	−	0.264969i	−0.202562	−	0.979269i	$-0.564927\pi$
$233$	−13.7746	−	4.04457i	−0.902401	−	0.264969i	−0.699839	+	0.714301i	$0.746745\pi$
$234$	−4.07612	−	4.70409i	−0.266464	−	0.307516i
$235$	4.86437	−	3.12614i	0.317316	−	0.203927i
$236$	−0.123050	+	0.142007i	−0.00800986	+	0.00924388i
$237$	−0.968820	+	6.73829i	−0.0629316	+	0.437699i
$238$	−0.446092	+	0.130984i	−0.0289158	+	0.00849046i
$239$	−7.54382	−	4.84812i	−0.487969	−	0.313599i	0.273419	−	0.961895i	$-0.411845\pi$
$239$	−7.54382	−	4.84812i	−0.487969	−	0.313599i	−0.761388	+	0.648296i	$0.775482\pi$
$240$	−0.00785914	−	0.0546615i	−0.000507305	−	0.00352839i
$241$	−7.60504	−	16.6527i	−0.489884	−	1.07270i	−0.979626	−	0.200829i	$-0.935636\pi$
$241$	−7.60504	−	16.6527i	−0.489884	−	1.07270i	0.489743	−	0.871867i	$-0.337091\pi$
$242$	−8.58513	−	18.7988i	−0.551873	−	1.20843i
$243$	2.28144	+	15.8678i	0.146354	+	1.01792i
$244$	−4.50096	−	2.89259i	−0.288144	−	0.185179i
$245$	4.95948	−	1.45623i	0.316849	−	0.0930354i
$246$	0.736146	−	5.12001i	0.0469350	−	0.326440i
$247$	−9.27383	+	10.7026i	−0.590080	+	0.680988i
$248$	−23.7148	+	15.2406i	−1.50589	+	0.967778i
$249$	4.80074	+	5.54035i	0.304235	+	0.351106i
$250$	0.846572	+	0.248576i	0.0535419	+	0.0157213i
$251$	3.70970	−	8.12310i	0.234154	−	0.512725i	−0.755682	−	0.654938i	$-0.772695\pi$
$251$	3.70970	−	8.12310i	0.234154	−	0.512725i	0.989836	+	0.142213i	$0.0454218\pi$
$252$	−3.75930			−0.236814
$253$	16.1638	−	23.0317i	1.01621	−	1.44799i
$254$	−6.07763			−0.381344
$255$	−0.137806	+	0.301752i	−0.00862972	+	0.0188965i
$256$	15.4998	+	4.55115i	0.968738	+	0.284447i
$257$	−6.87316	−	7.93204i	−0.428736	−	0.494787i	0.499743	−	0.866174i	$-0.333428\pi$
$257$	−6.87316	−	7.93204i	−0.428736	−	0.494787i	−0.928478	+	0.371387i	$0.878882\pi$
$258$	−0.0388977	+	0.0249980i	−0.00242166	+	0.00155631i
$259$	−3.06622	+	3.53861i	−0.190526	+	0.219878i
$260$	0.539244	−	3.75053i	0.0334425	−	0.232598i
$261$	3.14176	−	0.922504i	0.194470	−	0.0571016i
$262$	4.36163	+	2.80305i	0.269462	+	0.173173i
$263$	−2.65357	−	18.4560i	−0.163626	−	1.13804i	−0.891727	−	0.452573i	$-0.850506\pi$
$263$	−2.65357	−	18.4560i	−0.163626	−	1.13804i	0.728101	−	0.685470i	$-0.240403\pi$
$264$	−5.90169	−	12.9229i	−0.363224	−	0.795349i
$265$	5.86534	+	12.8433i	0.360305	+	0.788958i
$266$	−0.775732	−	5.39533i	−0.0475632	−	0.330809i
$267$	−10.4539	−	6.71831i	−0.639768	−	0.411154i
$268$	−15.7975	+	4.63857i	−0.964987	+	0.283346i
$269$	2.51749	−	17.5095i	0.153494	−	1.06757i	−0.756810	−	0.653635i	$-0.773243\pi$
$269$	2.51749	−	17.5095i	0.153494	−	1.06757i	0.910304	−	0.413940i	$-0.135848\pi$
$270$	2.59609	−	2.99605i	0.157993	−	0.182334i
$271$	22.9580	−	14.7542i	1.39460	−	0.896255i	0.394854	−	0.918744i	$-0.370795\pi$
$271$	22.9580	−	14.7542i	1.39460	−	0.896255i	0.999747	+	0.0224887i	$0.00715896\pi$
$272$	0.0165305	+	0.0190772i	0.00100231	+	0.00115673i
$273$	−3.43101	−	1.00744i	−0.207654	−	0.0609728i
$274$	0.206075	−	0.451241i	0.0124494	−	0.0272605i
$275$	5.86711			0.353800
$276$	2.86687	−	4.08499i	0.172565	−	0.245887i
$277$	19.7171			1.18469			0.592343	−	0.805686i	$-0.298203\pi$
$277$	19.7171			1.18469			0.592343	+	0.805686i	$0.298203\pi$
$278$	−1.18716	+	2.59951i	−0.0712010	+	0.155908i
$279$	−21.6418	−	6.35461i	−1.29566	−	0.380441i
$280$	2.51880	+	2.90686i	0.150527	+	0.173718i
$281$	−6.40350	+	4.11528i	−0.382001	+	0.245497i	−0.717522	−	0.696536i	$-0.754724\pi$
$281$	−6.40350	+	4.11528i	−0.382001	+	0.245497i	0.335522	+	0.942033i	$0.391087\pi$
$282$	−2.84614	+	3.28462i	−0.169485	+	0.195596i
$283$	−2.76418	+	19.2253i	−0.164314	+	1.14283i	0.726072	+	0.687619i	$0.241344\pi$
$283$	−2.76418	+	19.2253i	−0.164314	+	1.14283i	−0.890385	+	0.455207i	$0.849565\pi$
$284$	7.60517	−	2.23308i	0.451284	−	0.132509i
$285$	−3.27183	−	2.10268i	−0.193806	−	0.124552i
$286$	2.28523	+	15.8941i	0.135128	+	0.939838i
$287$	3.86856	+	8.47097i	0.228354	+	0.500026i
$288$	5.31676	+	11.6421i	0.313293	+	0.686017i
$289$	2.39777	+	16.6769i	0.141045	+	0.980993i
$290$	−1.06865	−	0.686782i	−0.0627535	−	0.0403293i
$291$	3.94345	−	1.15790i	0.231169	−	0.0678774i
$292$	0.853010	−	5.93281i	0.0499186	−	0.347192i
$293$	16.1479	−	18.6357i	0.943372	−	1.08871i	−0.0525610	−	0.998618i	$-0.516738\pi$
$293$	16.1479	−	18.6357i	0.943372	−	1.08871i	0.995933	−	0.0900921i	$-0.0287161\pi$
$294$	−3.26835	+	2.10044i	−0.190614	+	0.122500i
$295$	0.100735	+	0.116254i	0.00586499	+	0.00676856i
$296$	9.43665	+	2.77085i	0.548494	+	0.161052i
$297$	10.9510	−	23.9794i	0.635444	−	1.39143i
$298$	−3.33008			−0.192906
$299$	−11.6302	+	9.27598i	−0.672594	+	0.536444i
$300$	1.04061			0.0600797
$301$	0.0345806	−	0.0757210i	0.00199319	−	0.00436449i
$302$	12.1520	+	3.56815i	0.699269	+	0.205324i
$303$	−2.23529	−	2.57966i	−0.128414	−	0.148198i
$304$	−0.248968	+	0.160002i	−0.0142793	+	0.00917674i
$305$	−2.86830	+	3.31019i	−0.164238	+	0.189541i
$306$	−0.111202	+	0.773429i	−0.00635702	+	0.0442140i
$307$	−20.6069	+	6.05075i	−1.17610	+	0.345334i	−0.810669	−	0.585504i	$-0.800897\pi$
$307$	−20.6069	+	6.05075i	−1.17610	+	0.345334i	−0.365431	+	0.930838i	$0.619078\pi$
$308$	8.15860	+	5.24321i	0.464879	+	0.298760i
$309$	0.490147	+	3.40905i	0.0278835	+	0.193934i
$310$	3.63507	+	7.95970i	0.206458	+	0.452081i
$311$	0.263278	+	0.576497i	0.0149291	+	0.0326902i	0.916950	−	0.399003i	$-0.130644\pi$
$311$	0.263278	+	0.576497i	0.0149291	+	0.0326902i	−0.902021	+	0.431693i	$0.857916\pi$
$312$	1.06894	+	7.43463i	0.0605167	+	0.420903i
$313$	16.1431	+	10.3745i	0.912462	+	0.586403i	0.910461	−	0.413595i	$-0.135727\pi$
$313$	16.1431	+	10.3745i	0.912462	+	0.586403i	0.00200038	+	0.999998i	$0.499363\pi$
$314$	−7.33861	+	2.15481i	−0.414142	+	0.121603i
$315$	−0.437981	+	3.04622i	−0.0246774	+	0.171635i
$316$	−6.39232	+	7.37713i	−0.359596	+	0.414996i
$317$	11.2681	−	7.24156i	0.632879	−	0.406726i	−0.184496	−	0.982833i	$-0.559065\pi$
$317$	11.2681	−	7.24156i	0.632879	−	0.406726i	0.817374	+	0.576107i	$0.195429\pi$
$318$	−6.94973	−	8.02042i	−0.389722	−	0.449763i
$319$	−8.10502	−	2.37985i	−0.453794	−	0.133246i
$320$	2.11651	−	4.63452i	0.118317	−	0.259077i
$321$	11.8394			0.660814
$322$	0.233200	−	5.72120i	0.0129957	−	0.318830i
$323$	1.77777			0.0989179
$324$	−1.51986	+	3.32803i	−0.0844367	+	0.184891i
$325$	−2.97628	−	0.873916i	−0.165095	−	0.0484761i
$326$	3.39025	+	3.91256i	0.187769	+	0.216696i
$327$	−1.58825	+	1.02070i	−0.0878302	+	0.0564450i
$328$	12.8097	−	14.7832i	0.707296	−	0.816263i
$329$	1.11355	−	7.74494i	0.0613922	−	0.426992i
$330$	−4.23131	+	1.24242i	−0.232926	+	0.0683931i
$331$	−1.49785	−	0.962612i	−0.0823294	−	0.0529099i	0.498828	−	0.866701i	$-0.333764\pi$
$331$	−1.49785	−	0.962612i	−0.0823294	−	0.0529099i	−0.581158	+	0.813791i	$0.697400\pi$
$332$	1.49598	+	10.4048i	0.0821027	+	0.571037i
$333$	3.26902	+	7.15816i	0.179141	+	0.392265i
$334$	−4.34611	−	9.51666i	−0.237809	−	0.520729i
$335$	1.91820	+	13.3414i	0.104803	+	0.728918i
$336$	−0.0628657	−	0.0404013i	−0.00342960	−	0.00220407i
$337$	−30.0419	+	8.82109i	−1.63648	+	0.480515i	−0.965380	−	0.260847i	$-0.915998\pi$
$337$	−30.0419	+	8.82109i	−1.63648	+	0.480515i	−0.671105	+	0.741363i	$0.734180\pi$
$338$	−0.424162	+	2.95011i	−0.0230714	+	0.160465i
$339$	−0.415798	+	0.479857i	−0.0225831	+	0.0260622i
$340$	−0.400155	+	0.257164i	−0.0217014	+	0.0139467i
$341$	38.1050	+	43.9755i	2.06350	+	2.38141i
$342$	−8.78991	−	2.58095i	−0.475304	−	0.139562i
$343$	6.84059	−	14.9788i	0.369357	−	0.808779i
$344$	−0.174853			−0.00942743
$345$	−2.97612	−	2.79899i	−0.160229	−	0.150693i
$346$	−18.6667			−1.00353
$347$	−7.34180	+	16.0763i	−0.394129	+	0.863021i	0.603703	+	0.797209i	$0.293691\pi$
$347$	−7.34180	+	16.0763i	−0.394129	+	0.863021i	−0.997832	+	0.0658123i	$0.979036\pi$
$348$	−1.43754	−	0.422098i	−0.0770600	−	0.0226269i
$349$	17.5443	+	20.2472i	0.939123	+	1.08381i	0.996343	+	0.0854437i	$0.0272308\pi$
$349$	17.5443	+	20.2472i	0.939123	+	1.08381i	−0.0572204	+	0.998362i	$0.518224\pi$
$350$	1.00441	−	0.645495i	0.0536880	−	0.0345032i
$351$	−9.12705	+	10.5332i	−0.487166	+	0.562219i
$352$	4.69890	−	32.6816i	0.250452	−	1.74194i
$353$	−3.32308	+	0.975745i	−0.176870	+	0.0519337i	−0.368968	−	0.929442i	$-0.620289\pi$
$353$	−3.32308	+	0.975745i	−0.176870	+	0.0519337i	0.192098	+	0.981376i	$0.438471\pi$
$354$	−0.0972668	−	0.0625096i	−0.00516967	−	0.00332235i
$355$	−0.923453	−	6.42276i	−0.0490118	−	0.340885i
$356$	−7.40202	−	16.2082i	−0.392306	−	0.859030i
$357$	0.186478	+	0.408331i	0.00986948	+	0.0216112i
$358$	1.93220	+	13.4387i	0.102120	+	0.710258i
$359$	−2.01571	−	1.29542i	−0.106385	−	0.0683697i	0.486366	−	0.873755i	$-0.338322\pi$
$359$	−2.01571	−	1.29542i	−0.106385	−	0.0683697i	−0.592752	+	0.805385i	$0.701958\pi$
$360$	6.20253	−	1.82123i	0.326902	−	0.0959870i
$361$	−0.262250	+	1.82399i	−0.0138026	+	0.0959994i
$362$	−10.6275	+	12.2648i	−0.558571	+	0.644625i
$363$	−16.7863	+	10.7879i	−0.881053	+	0.566218i
$364$	−3.35773	−	3.87503i	−0.175993	−	0.203107i
$365$	−4.70807	−	1.38241i	−0.246432	−	0.0723589i
$366$	1.36762	−	2.99467i	0.0714867	−	0.156534i
$367$	−2.95953			−0.154486			−0.0772430	−	0.997012i	$-0.524612\pi$
$367$	−2.95953			−0.154486			−0.0772430	+	0.997012i	$0.524612\pi$
$368$	−0.287818	+	0.117523i	−0.0150036	+	0.00612630i
$369$	15.6512			0.814771
$370$	1.26823	−	2.77703i	0.0659320	−	0.144371i
$371$	18.3322	+	5.38282i	0.951760	+	0.279462i
$372$	6.75844	+	7.79965i	0.350409	+	0.404393i
$373$	−7.43641	+	4.77909i	−0.385043	+	0.247452i	−0.718814	−	0.695202i	$-0.755315\pi$
$373$	−7.43641	+	4.77909i	−0.385043	+	0.247452i	0.333772	+	0.942654i	$0.391679\pi$
$374$	1.32006	−	1.52343i	0.0682587	−	0.0787748i
$375$	0.121237	−	0.843224i	0.00626067	−	0.0435439i
$376$	−15.7698	+	4.63042i	−0.813263	+	0.238796i
$377$	3.75706	+	2.41451i	0.193498	+	0.124354i
$378$	−0.763454	−	5.30994i	−0.0392678	−	0.273114i
$379$	9.72306	+	21.2905i	0.499440	+	1.09362i	0.976651	+	0.214832i	$0.0689204\pi$
$379$	9.72306	+	21.2905i	0.499440	+	1.09362i	−0.477211	+	0.878789i	$0.658352\pi$
$380$	−2.31666	−	5.07278i	−0.118842	−	0.260228i
$381$	0.835118	+	5.80838i	0.0427844	+	0.297572i
$382$	0.745714	+	0.479241i	0.0381540	+	0.0245201i
$383$	−5.56414	+	1.63378i	−0.284314	+	0.0834823i	−0.420780	−	0.907162i	$-0.638244\pi$
$383$	−5.56414	+	1.63378i	−0.284314	+	0.0834823i	0.136466	+	0.990645i	$0.456426\pi$
$384$	0.819546	−	5.70007i	0.0418223	−	0.290880i
$385$	5.19918	−	6.00018i	0.264975	−	0.305797i
$386$	18.7351	−	12.0403i	0.953593	−	0.612837i
$387$	−0.0916180	−	0.105733i	−0.00465720	−	0.00537470i
$388$	5.65449	+	1.66031i	0.287063	+	0.0842893i
$389$	−4.69526	+	10.2812i	−0.238059	+	0.521277i	−0.990521	−	0.137358i	$-0.956139\pi$
$389$	−4.69526	+	10.2812i	−0.238059	+	0.521277i	0.752462	+	0.658636i	$0.228866\pi$
$390$	2.33153			0.118062
$391$	1.83614	+	0.340837i	0.0928577	+	0.0172369i
$392$	−14.6919			−0.742053
$393$	2.07954	−	4.55356i	0.104899	−	0.229697i
$394$	21.7155	+	6.37625i	1.09401	+	0.321231i
$395$	5.23306	+	6.03928i	0.263304	+	0.303869i
$396$	13.7119	−	8.81209i	0.689048	−	0.442824i
$397$	2.00993	−	2.31959i	0.100876	−	0.116417i	−0.703067	−	0.711124i	$-0.748187\pi$
$397$	2.00993	−	2.31959i	0.100876	−	0.116417i	0.803942	+	0.594707i	$0.202732\pi$
$398$	−1.67114	+	11.6231i	−0.0837669	+	0.582612i
$399$	−5.04972	+	1.48273i	−0.252802	+	0.0742294i
$400$	−0.0545338	−	0.0350467i	−0.00272669	−	0.00175234i
$401$	−2.50209	−	17.4024i	−0.124948	−	0.869035i	−0.951823	−	0.306649i	$-0.900792\pi$
$401$	−2.50209	−	17.4024i	−0.124948	−	0.869035i	0.826874	−	0.562387i	$-0.190117\pi$
$402$	−4.20857	−	9.21549i	−0.209905	−	0.459627i
$403$	−12.7798	−	27.9838i	−0.636607	−	1.39397i
$404$	−0.696549	−	4.84460i	−0.0346546	−	0.241028i
$405$	2.51968	+	1.61930i	0.125204	+	0.0804638i
$406$	−1.64935	+	0.484294i	−0.0818561	+	0.0240351i
$407$	2.88913	−	20.0943i	0.143209	−	0.996039i
$408$	0.617472	−	0.712601i	0.0305694	−	0.0352790i
$409$	6.11617	−	3.93062i	0.302425	−	0.194357i	−0.380623	−	0.924730i	$-0.624290\pi$
$409$	6.11617	−	3.93062i	0.302425	−	0.194357i	0.683048	+	0.730374i	$0.260654\pi$
$410$	−3.97628	−	4.58887i	−0.196374	−	0.226628i
$411$	−0.459567	−	0.134941i	−0.0226688	−	0.00665615i
$412$	−2.05152	+	4.49220i	−0.101071	+	0.221315i
$413$	0.208157			0.0102427
$414$	−8.58369	−	4.35091i	−0.421865	−	0.213835i
$415$	8.60545			0.422425
$416$	−7.25165	+	15.8789i	−0.355542	+	0.778527i
$417$	2.64747	+	0.777368i	0.129647	+	0.0380679i
$418$	15.4765	+	17.8608i	0.756981	+	0.873602i
$419$	−17.9543	+	11.5386i	−0.877127	+	0.563696i	−0.899925	−	0.436045i	$-0.856379\pi$
$419$	−17.9543	+	11.5386i	−0.877127	+	0.563696i	0.0227977	+	0.999740i	$0.492743\pi$
$420$	0.922145	−	1.06421i	0.0449961	−	0.0519282i
$421$	1.63073	−	11.3420i	0.0794771	−	0.552776i	−0.910712	−	0.413042i	$-0.864466\pi$
$421$	1.63073	−	11.3420i	0.0794771	−	0.552776i	0.990189	−	0.139734i	$-0.0446246\pi$
$422$	13.2222	−	3.88238i	0.643645	−	0.188991i
$423$	−11.0629	−	7.10970i	−0.537897	−	0.345685i
$424$	−5.71143	−	39.7239i	−0.277372	−	1.92916i
$425$	0.161764	+	0.354213i	0.00784669	+	0.0171818i
$426$	2.02607	+	4.43648i	0.0981636	+	0.214948i
$427$	0.843505	+	5.86670i	0.0408200	+	0.283910i
$428$	14.2815	+	9.17819i	0.690324	+	0.443644i
$429$	14.8760	−	4.36797i	0.718218	−	0.210888i
$430$	−0.00772434	+	0.0537239i	−0.000372501	+	0.00259080i
$431$	−15.2095	+	17.5527i	−0.732618	+	0.845486i	−0.992764	−	0.120083i	$-0.961684\pi$
$431$	−15.2095	+	17.5527i	−0.732618	+	0.845486i	0.260146	+	0.965569i	$0.416229\pi$
$432$	−0.245027	+	0.157469i	−0.0117889	+	0.00757625i
$433$	−19.2783	−	22.2484i	−0.926457	−	1.06919i	−0.997426	−	0.0717096i	$-0.977155\pi$
$433$	−19.2783	−	22.2484i	−0.926457	−	1.06919i	0.0709688	−	0.997479i	$-0.477391\pi$
$434$	11.3615	+	3.33603i	0.545368	+	0.160135i
$435$	−0.509514	+	1.11568i	−0.0244293	+	0.0534928i
$436$	−2.70712			−0.129647
$437$	−7.01895	+	20.7393i	−0.335762	+	0.992094i
$438$	3.68816			0.176227
$439$	3.60492	−	7.89368i	0.172054	−	0.376745i	−0.803887	−	0.594782i	$-0.797238\pi$
$439$	3.60492	−	7.89368i	0.172054	−	0.376745i	0.975940	+	0.218038i	$0.0699655\pi$
$440$	−16.0011	−	4.69835i	−0.762823	−	0.223985i
$441$	−7.69814	−	8.88413i	−0.366578	−	0.423054i
$442$	−0.896562	+	0.576185i	−0.0426451	+	0.0274063i
$443$	13.4867	−	15.5645i	0.640773	−	0.739491i	−0.338739	−	0.940881i	$-0.610000\pi$
$443$	13.4867	−	15.5645i	0.640773	−	0.739491i	0.979511	+	0.201390i	$0.0645457\pi$
$444$	0.512426	−	3.56400i	0.0243187	−	0.169140i
$445$	−13.9961	+	4.10963i	−0.663479	+	0.194815i
$446$	−16.6198	−	10.6809i	−0.786968	−	0.505754i
$447$	0.457582	+	3.18255i	0.0216429	+	0.150530i
$448$	−2.86406	−	6.27142i	−0.135314	−	0.296297i
$449$	−8.95607	−	19.6111i	−0.422663	−	0.925503i	−0.994461	−	0.105108i	$-0.966481\pi$
$449$	−8.95607	−	19.6111i	−0.422663	−	0.925503i	0.571798	−	0.820395i	$-0.306246\pi$
$450$	−0.285572	−	1.98620i	−0.0134620	−	0.0936302i
$451$	−33.9670	−	21.8292i	−1.59944	−	1.02790i
$452$	−0.873558	+	0.256500i	−0.0410887	+	0.0120647i
$453$	1.74028	−	12.1039i	0.0817656	−	0.568693i
$454$	7.74341	−	8.93637i	0.363416	−	0.419405i
$455$	−3.53119	+	2.26936i	−0.165545	+	0.106389i
$456$	7.23929	+	8.35459i	0.339011	+	0.391240i
$457$	28.0231	+	8.22834i	1.31087	+	0.384905i	0.861189	−	0.508285i	$-0.169720\pi$
$457$	28.0231	+	8.22834i	1.31087	+	0.384905i	0.449679	+	0.893190i	$0.351539\pi$
$458$	2.48238	−	5.43566i	0.115994	−	0.253992i
$459$	1.74963			0.0816660
$460$	−1.42016	−	5.68349i	−0.0662154	−	0.264994i
$461$	−38.5214			−1.79412			−0.897060	−	0.441909i	$-0.854301\pi$
$461$	−38.5214			−1.79412			−0.897060	+	0.441909i	$0.854301\pi$
$462$	−2.47900	+	5.42825i	−0.115334	+	0.252545i
$463$	−31.3471	−	9.20435i	−1.45682	−	0.427762i	−0.545033	−	0.838415i	$-0.683483\pi$
$463$	−31.3471	−	9.20435i	−1.45682	−	0.427762i	−0.911792	+	0.410652i	$0.865301\pi$
$464$	0.0611190	+	0.0705350i	0.00283738	+	0.00327451i
$465$	7.10758	−	4.56776i	0.329606	−	0.211825i
$466$	8.29482	−	9.57273i	0.384250	−	0.443448i
$467$	−1.94038	+	13.4956i	−0.0897899	+	0.624503i	0.894384	+	0.447299i	$0.147614\pi$
$467$	−1.94038	+	13.4956i	−0.0897899	+	0.624503i	−0.984174	+	0.177203i	$0.943295\pi$
$468$	−8.26837	+	2.42781i	−0.382206	+	0.112226i
$469$	15.3438	+	9.86087i	0.708511	+	0.455333i
$470$	0.726059	+	5.04985i	0.0334906	+	0.232932i
$471$	3.06773	+	6.71740i	0.141354	+	0.309522i
$472$	−0.181633	−	0.397722i	−0.00836035	−	0.0183066i
$473$	0.0513645	+	0.357248i	0.00236174	+	0.0164263i
$474$	−5.05292	−	3.24731i	−0.232088	−	0.149154i
$475$	−4.38046	+	1.28622i	−0.200989	+	0.0590157i
$476$	−0.0916037	+	0.637118i	−0.00419865	+	0.0292022i
$477$	21.0282	−	24.2679i	0.962817	−	1.11115i
$478$	6.65600	−	4.27755i	0.304439	−	0.195651i
$479$	16.6081	+	19.1667i	0.758842	+	0.875751i	0.995394	−	0.0958680i	$-0.0305627\pi$
$479$	16.6081	+	19.1667i	0.758842	+	0.875751i	−0.236552	+	0.971619i	$0.576017\pi$
$480$	−4.59992	−	1.35066i	−0.209956	−	0.0616488i
$481$	−4.45869	+	9.76317i	−0.203299	+	0.445162i
$482$	16.1526			0.735729
$483$	−5.49979	+	0.563274i	−0.250249	+	0.0256299i
$484$	−28.6118			−1.30054
$485$	2.00415	−	4.38849i	0.0910039	−	0.199271i
$486$	−13.5713	−	3.98491i	−0.615609	−	0.180759i
$487$	−9.49596	−	10.9589i	−0.430303	−	0.496596i	0.498645	−	0.866806i	$-0.333831\pi$
$487$	−9.49596	−	10.9589i	−0.430303	−	0.496596i	−0.928948	+	0.370210i	$0.879286\pi$
$488$	10.4734	−	6.73082i	0.474107	−	0.304690i
$489$	3.27337	−	3.77767i	0.148027	−	0.170832i
$490$	−0.649032	+	4.51412i	−0.0293203	+	0.203927i
$491$	24.6784	−	7.24623i	1.11372	−	0.327018i	0.327430	−	0.944875i	$-0.393817\pi$
$491$	24.6784	−	7.24623i	1.11372	−	0.327018i	0.786290	+	0.617858i	$0.211999\pi$
$492$	−6.02450	−	3.87171i	−0.271605	−	0.174550i
$493$	−0.0797879	−	0.554937i	−0.00359347	−	0.0249931i
$494$	−5.19056	−	11.3657i	−0.233535	−	0.511369i
$495$	−5.54306	−	12.1376i	−0.249142	−	0.545545i
$496$	−0.0914951	−	0.636362i	−0.00410825	−	0.0285735i
$497$	−7.38675	−	4.74718i	−0.331341	−	0.212940i
$498$	−6.20617	+	1.82230i	−0.278105	+	0.0816590i
$499$	−5.98164	+	41.6032i	−0.267775	+	1.86242i	0.201667	+	0.979454i	$0.435364\pi$
$499$	−5.98164	+	41.6032i	−0.267775	+	1.86242i	−0.469443	+	0.882963i	$0.655545\pi$
$500$	0.799929	−	0.923167i	0.0357739	−	0.0412853i
$501$	−8.49786	+	5.46124i	−0.379656	+	0.243990i
$502$	5.15973	+	5.95465i	0.230290	+	0.265769i
$503$	32.9635	+	9.67896i	1.46977	+	0.431563i	0.916024	−	0.401122i	$-0.131380\pi$
$503$	32.9635	+	9.67896i	1.46977	+	0.431563i	0.553746	+	0.832686i	$0.313198\pi$
$504$	3.63388	−	7.95709i	0.161866	−	0.354437i
$505$	−4.00681			−0.178301
$506$	12.5603	+	21.4144i	0.558375	+	0.951988i
$507$	2.87770			0.127803
$508$	−3.49540	+	7.65385i	−0.155083	+	0.339585i
$509$	−11.7572	−	3.45222i	−0.521128	−	0.153017i	0.0105809	−	0.999944i	$-0.496632\pi$
$509$	−11.7572	−	3.45222i	−0.521128	−	0.153017i	−0.531709	+	0.846927i	$0.678450\pi$
$510$	−0.191671	−	0.221200i	−0.00848732	−	0.00979489i
$511$	−5.58586	+	3.58981i	−0.247104	+	0.158804i
$512$	−0.480221	+	0.554205i	−0.0212230	+	0.0244926i
$513$	−2.91928	+	20.3041i	−0.128890	+	0.896447i
$514$	8.88528	−	2.60895i	0.391913	−	0.115076i
$515$	3.40108	+	2.18574i	0.149870	+	0.0963154i
$516$	0.00911019	+	0.0633628i	0.000401054	+	0.00278939i
$517$	14.0931	+	30.8595i	0.619813	+	1.35720i
$518$	−1.71616	−	3.75787i	−0.0754039	−	0.165112i
$519$	2.56497	+	17.8397i	0.112590	+	0.783078i
$520$	7.41726	+	4.76678i	0.325268	+	0.209037i
$521$	−37.4109	+	10.9848i	−1.63900	+	0.481254i	−0.966033	−	0.258418i	$-0.916799\pi$
$521$	−37.4109	+	10.9848i	−1.63900	+	0.481254i	−0.672968	+	0.739672i	$0.734981\pi$
$522$	−0.411153	+	2.85963i	−0.0179957	+	0.125163i
$523$	6.22155	−	7.18006i	0.272050	−	0.313962i	−0.603241	−	0.797559i	$-0.706124\pi$
$523$	6.22155	−	7.18006i	0.272050	−	0.313962i	0.875291	+	0.483597i	$0.160670\pi$
$524$	6.03850	−	3.88071i	0.263793	−	0.169530i
$525$	−0.754913	−	0.871216i	−0.0329471	−	0.0380230i
$526$	15.7850	+	4.63488i	0.688257	+	0.202091i
$527$	−1.60431	+	3.51296i	−0.0698851	+	0.153027i
$528$	0.324003			0.0141004
$529$	−11.2256	+	20.0745i	−0.488068	+	0.872805i
$530$	−12.4576			−0.541122
$531$	0.145330	−	0.318228i	0.00630678	−	0.0138099i
$532$	−7.24075	−	2.12608i	−0.313926	−	0.0921771i
$533$	13.9794	+	16.1330i	0.605513	+	0.698800i
$534$	9.22360	−	5.92765i	0.399144	−	0.256514i
$535$	9.10111	−	10.5032i	0.393475	−	0.454095i
$536$	5.45228	−	37.9215i	0.235503	−	1.63796i
$537$	12.5779	−	3.69319i	0.542774	−	0.159373i
$538$	13.1301	+	8.43817i	0.566077	+	0.363795i
$539$	4.31587	+	30.0175i	0.185898	+	1.29295i
$540$	−2.27999	−	4.99249i	−0.0981153	−	0.214842i
$541$	−13.7275	−	30.0591i	−0.590192	−	1.29234i	−0.935326	−	0.353787i	$-0.884894\pi$
$541$	−13.7275	−	30.0591i	−0.590192	−	1.29234i	0.345134	−	0.938553i	$-0.387833\pi$
$542$	3.42673	+	23.8334i	0.147191	+	1.02373i
$543$	13.1818	+	8.47142i	0.565684	+	0.363543i
$544$	2.10263	−	0.617387i	0.0901495	−	0.0264703i
$545$	−0.315395	+	2.19362i	−0.0135100	+	0.0939644i
$546$	2.06610	−	2.38441i	0.0884210	−	0.102043i
$547$	9.84579	−	6.32751i	0.420976	−	0.270545i	−0.312956	−	0.949767i	$-0.601319\pi$
$547$	9.84579	−	6.32751i	0.420976	−	0.270545i	0.733932	+	0.679223i	$0.237683\pi$
$548$	−0.449751	−	0.519041i	−0.0192124	−	0.0221723i
$549$	9.55785	+	2.80644i	0.407919	+	0.119776i
$550$	−2.15045	+	4.70882i	−0.0916954	+	0.200785i
$551$	6.57303			0.280021
$552$	5.87523	+	10.0168i	0.250066	+	0.426344i
$553$	10.8136			0.459839
$554$	−7.22683	+	15.8245i	−0.307038	+	0.672320i
$555$	−2.82827	−	0.830454i	−0.120053	−	0.0352508i
$556$	2.59093	+	2.99009i	0.109880	+	0.126808i
$557$	−7.90744	+	5.08181i	−0.335049	+	0.215323i	−0.697337	−	0.716743i	$-0.745632\pi$
$557$	−7.90744	+	5.08181i	−0.335049	+	0.215323i	0.362288	+	0.932066i	$0.381996\pi$
$558$	13.0324	−	15.0401i	0.551704	−	0.636700i
$559$	0.0271564	−	0.188877i	0.00114859	−	0.00798863i
$560$	−0.0841671	+	0.0247137i	−0.00355671	+	0.00104434i
$561$	−1.63733	−	1.05225i	−0.0691281	−	0.0444259i
$562$	−0.955791	−	6.64767i	−0.0403176	−	0.280415i
$563$	−1.74692	−	3.82522i	−0.0736240	−	0.161214i	0.869241	−	0.494388i	$-0.164608\pi$
$563$	−1.74692	−	3.82522i	−0.0736240	−	0.161214i	−0.942865	+	0.333174i	$0.891880\pi$
$564$	2.49960	+	5.47336i	0.105252	+	0.230470i
$565$	0.106071	+	0.737742i	0.00446245	+	0.0310370i
$566$	−14.4167	−	9.26504i	−0.605979	−	0.389439i
$567$	3.88886	−	1.14187i	0.163317	−	0.0479542i
$568$	−2.62482	+	18.2560i	−0.110135	+	0.766004i
$569$	13.6315	−	15.7316i	0.571463	−	0.659504i	−0.394284	−	0.918989i	$-0.629007\pi$
$569$	13.6315	−	15.7316i	0.571463	−	0.659504i	0.965747	+	0.259485i	$0.0835527\pi$
$570$	2.88677	−	1.85522i	0.120914	−	0.0777064i
$571$	−1.80116	−	2.07865i	−0.0753762	−	0.0869887i	0.716809	−	0.697270i	$-0.245602\pi$
$571$	−1.80116	−	2.07865i	−0.0753762	−	0.0869887i	−0.792185	+	0.610281i	$0.791057\pi$
$572$	21.3305	+	6.26320i	0.891874	+	0.261878i
$573$	0.355542	−	0.778529i	0.0148530	−	0.0325235i
$574$	−8.21655			−0.342952
$575$	−4.77088	+	0.488621i	−0.198959	+	0.0203769i
$576$	−11.5873			−0.482804
$577$	14.1970	−	31.0871i	0.591028	−	1.29417i	−0.343791	−	0.939046i	$-0.611711\pi$
$577$	14.1970	−	31.0871i	0.591028	−	1.29417i	0.934819	−	0.355125i	$-0.115562\pi$
$578$	−14.2634	−	4.18810i	−0.593277	−	0.174202i
$579$	−14.0813	−	16.2507i	−0.585199	−	0.675355i
$580$	−1.47951	+	0.950823i	−0.0614333	+	0.0394808i
$581$	7.62578	−	8.80062i	0.316371	−	0.365111i
$582$	−0.516068	+	3.58933i	−0.0213917	+	0.148783i
$583$	−79.4835	+	23.3385i	−3.29187	+	0.966581i
$584$	11.7331	+	7.54039i	0.485518	+	0.312024i
$585$	1.00398	+	6.98285i	0.0415095	+	0.288705i
$586$	9.03800	+	19.7905i	0.373356	+	0.817537i
$587$	6.19358	+	13.5620i	0.255636	+	0.559765i	0.993321	−	0.115379i	$-0.0368084\pi$
$587$	6.19358	+	13.5620i	0.255636	+	0.559765i	−0.737685	+	0.675145i	$0.764081\pi$
$588$	0.765478	+	5.32402i	0.0315678	+	0.219559i
$589$	−38.0902	−	24.4791i	−1.56948	−	1.00864i
$590$	−0.130225	+	0.0382374i	−0.00536127	+	0.00157421i
$591$	3.10987	−	21.6296i	0.127923	−	0.889723i
$592$	−0.146886	+	0.169515i	−0.00603698	+	0.00696704i
$593$	−21.3797	+	13.7399i	−0.877959	+	0.564230i	−0.900178	−	0.435523i	$-0.856563\pi$
$593$	−21.3797	+	13.7399i	−0.877959	+	0.564230i	0.0222186	+	0.999753i	$0.492927\pi$
$594$	15.2316	+	17.5782i	0.624958	+	0.721240i
$595$	0.505594	+	0.148456i	0.0207273	+	0.00608610i
$596$	−1.91521	+	4.19373i	−0.0784502	+	0.171782i
$597$	11.3378			0.464024
$598$	−3.18193	−	12.7341i	−0.130119	−	0.520735i
$599$	26.2447			1.07233			0.536166	−	0.844113i	$-0.319872\pi$
$599$	26.2447			1.07233			0.536166	+	0.844113i	$0.319872\pi$
$600$	−1.00589	+	2.20260i	−0.0410654	+	0.0899207i
$601$	28.5265	+	8.37613i	1.16362	+	0.341669i	0.805838	−	0.592136i	$-0.201715\pi$
$601$	28.5265	+	8.37613i	1.16362	+	0.341669i	0.357781	+	0.933806i	$0.383533\pi$
$602$	0.0480974	+	0.0555074i	0.00196030	+	0.00226231i
$603$	25.7878	−	16.5728i	1.05016	−	0.674897i
$604$	11.4825	−	13.2515i	0.467215	−	0.539195i
$605$	−3.33344	+	23.1846i	−0.135524	+	0.942587i
$606$	2.88967	−	0.848485i	0.117385	−	0.0344673i
$607$	0.883086	+	0.567525i	0.0358433	+	0.0230351i	0.558440	−	0.829545i	$-0.311400\pi$
$607$	0.883086	+	0.567525i	0.0358433	+	0.0230351i	−0.522596	+	0.852580i	$0.675037\pi$
$608$	3.65637	+	25.4306i	0.148285	+	1.03135i
$609$	0.689474	+	1.50974i	0.0279389	+	0.0611777i
$610$	−1.60539	−	3.51531i	−0.0650002	−	0.142331i
$611$	−2.55260	−	17.7537i	−0.103267	−	0.718238i
$612$	0.910062	+	0.584861i	0.0367871	+	0.0236416i
$613$	45.2053	−	13.2735i	1.82583	−	0.536111i	0.826198	−	0.563380i	$-0.190499\pi$
$613$	45.2053	−	13.2735i	1.82583	−	0.536111i	0.999628	+	0.0272688i	$0.00868100\pi$
$614$	2.69677	−	18.7565i	0.108833	−	0.756949i
$615$	−3.83920	+	4.43067i	−0.154811	+	0.178662i
$616$	−18.9844	+	12.2005i	−0.764903	+	0.491573i
$617$	11.3328	+	13.0788i	0.456243	+	0.526532i	0.936534	−	0.350577i	$-0.114015\pi$
$617$	11.3328	+	13.0788i	0.456243	+	0.526532i	−0.480291	+	0.877109i	$0.659469\pi$
$618$	−2.91568	−	0.856122i	−0.117286	−	0.0344383i
$619$	6.84968	−	14.9987i	0.275312	−	0.602849i	−0.720583	−	0.693369i	$-0.756126\pi$
$619$	6.84968	−	14.9987i	0.275312	−	0.602849i	0.995895	+	0.0905200i	$0.0288529\pi$
$620$	12.1147			0.486537
$621$	−6.90786	+	20.4110i	−0.277203	+	0.819066i
$622$	−0.559183			−0.0224212
$623$	−8.19991	+	17.9553i	−0.328523	+	0.719364i
$624$	−0.164361	−	0.0482608i	−0.00657971	−	0.00193198i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−14.2432	+	9.15358i	−0.569275	+	0.365851i
$627$	14.9430	−	17.2451i	0.596764	−	0.688703i
$628$	−1.50696	+	10.4812i	−0.0601343	+	0.418243i
$629$	1.29280	−	0.379602i	0.0515475	−	0.0151357i
$630$	−2.28430	−	1.46803i	−0.0910088	−	0.0584878i
$631$	−3.04048	−	21.1470i	−0.121040	−	0.841850i	−0.956382	−	0.292120i	$-0.905639\pi$
$631$	−3.04048	−	21.1470i	−0.121040	−	0.841850i	0.835342	−	0.549731i	$-0.185270\pi$
$632$	−9.43568	−	20.6612i	−0.375331	−	0.821860i
$633$	−5.52722	−	12.1029i	−0.219687	−	0.481048i
$634$	1.68188	+	11.6977i	0.0667961	+	0.464577i
$635$	5.79480	+	3.72409i	0.229960	+	0.147786i
$636$	−14.0975	+	4.13939i	−0.559001	+	0.164138i
$637$	2.28180	−	15.8702i	0.0904081	−	0.628802i
$638$	4.88072	−	5.63265i	0.193229	−	0.222999i
$639$	−12.4147	+	7.97842i	−0.491116	+	0.315621i
$640$	−4.42676	−	5.10875i	−0.174983	−	0.201941i
$641$	−33.1459	−	9.73250i	−1.30918	−	0.384411i	−0.448605	−	0.893730i	$-0.648079\pi$
$641$	−33.1459	−	9.73250i	−1.30918	−	0.384411i	−0.860577	+	0.509320i	$0.829897\pi$
$642$	−4.33946	+	9.50210i	−0.171265	+	0.375018i
$643$	47.7535			1.88321			0.941607	−	0.336715i	$-0.109316\pi$
$643$	47.7535			1.88321			0.941607	+	0.336715i	$0.109316\pi$
$644$	−7.07087	−	3.58409i	−0.278631	−	0.141233i
$645$	0.0524052			0.00206345
$646$	−0.651599	+	1.42680i	−0.0256368	+	0.0561368i
$647$	19.0492	+	5.59335i	0.748901	+	0.219897i	0.633843	−	0.773462i	$-0.281476\pi$
$647$	19.0492	+	5.59335i	0.748901	+	0.219897i	0.115058	+	0.993359i	$0.463295\pi$
$648$	−5.57509	−	6.43399i	−0.219010	−	0.252751i
$649$	−0.759243	+	0.487936i	−0.0298029	+	0.0191532i
$650$	1.79227	−	2.06839i	0.0702987	−	0.0811290i
$651$	1.62707	−	11.3165i	0.0637700	−	0.443530i
$652$	6.87709	−	2.01930i	0.269328	−	0.0790817i
$653$	6.88045	+	4.42180i	0.269253	+	0.173038i	0.668300	−	0.743892i	$-0.267022\pi$
$653$	6.88045	+	4.42180i	0.269253	+	0.173038i	−0.399047	+	0.916931i	$0.630659\pi$
$654$	−0.237063	−	1.64881i	−0.00926988	−	0.0644734i
$655$	−2.44108	−	5.34522i	−0.0953808	−	0.208855i
$656$	0.185322	+	0.405798i	0.00723560	+	0.0158438i
$657$	1.58816	+	11.0459i	0.0619601	+	0.430942i
$658$	5.80778	+	3.73243i	0.226411	+	0.145505i
$659$	−22.7883	+	6.69125i	−0.887706	+	0.260654i	−0.693629	−	0.720332i	$-0.743989\pi$
$659$	−22.7883	+	6.69125i	−0.887706	+	0.260654i	−0.194077	+	0.980986i	$0.562171\pi$
$660$	−0.868887	+	6.04324i	−0.0338214	+	0.235233i
$661$	8.60620	−	9.93208i	0.334742	−	0.386313i	−0.563278	−	0.826268i	$-0.690460\pi$
$661$	8.60620	−	9.93208i	0.334742	−	0.386313i	0.898020	+	0.439954i	$0.145005\pi$
$662$	1.32157	−	0.849324i	0.0513644	−	0.0330099i
$663$	0.673855	+	0.777670i	0.0261703	+	0.0302022i
$664$	−23.4692	−	6.89119i	−0.910783	−	0.267430i
$665$	−2.56638	+	5.61959i	−0.0995201	+	0.217919i
$666$	−6.94317			−0.269042
$667$	6.78884	+	1.26019i	0.262865	+	0.0487948i
$668$	−14.4844			−0.560417
$669$	−7.92398	+	17.3511i	−0.306359	+	0.670832i
$670$	−11.4106	−	3.35045i	−0.440830	−	0.129439i
$671$	−16.8286	−	19.4213i	−0.649662	−	0.749750i
$672$	−5.45754	+	3.50735i	−0.210529	+	0.135299i
$673$	−7.56701	+	8.73279i	−0.291687	+	0.336624i	−0.882612	−	0.470102i	$-0.844217\pi$
$673$	−7.56701	+	8.73279i	−0.291687	+	0.336624i	0.590926	+	0.806726i	$0.298763\pi$
$674$	3.93149	−	27.3441i	0.151435	−	1.05326i
$675$	−4.31112	+	1.26586i	−0.165935	+	0.0487230i
$676$	3.47127	+	2.23085i	0.133511	+	0.0858020i
$677$	−3.47079	−	24.1398i	−0.133393	−	0.927770i	−0.941086	−	0.338167i	$-0.890193\pi$
$677$	−3.47079	−	24.1398i	−0.133393	−	0.927770i	0.807693	−	0.589603i	$-0.200716\pi$
$678$	−0.232722	−	0.509591i	−0.00893765	−	0.0195707i
$679$	−2.71202	−	5.93850i	−0.104078	−	0.227899i
$680$	−0.157519	−	1.09557i	−0.00604057	−	0.0420131i
$681$	−9.60448	−	6.17243i	−0.368045	−	0.236528i
$682$	−49.2603	+	14.4641i	−1.88627	+	0.553860i
$683$	0.497370	−	3.45929i	0.0190313	−	0.132366i	−0.978091	−	0.208179i	$-0.933246\pi$
$683$	0.497370	−	3.45929i	0.0190313	−	0.132366i	0.997122	+	0.0758134i	$0.0241553\pi$
$684$	−8.30562	+	9.58519i	−0.317573	+	0.366499i
$685$	−0.472986	+	0.303969i	−0.0180718	+	0.0116141i
$686$	9.51442	+	10.9802i	0.363262	+	0.419227i
$687$	−5.53595	−	1.62550i	−0.211210	−	0.0620167i
$688$	0.00165657	−	0.00362738i	6.31561e−5	−	0.000138293i
$689$	43.7969			1.66853
$690$	3.33724	−	1.36267i	0.127047	−	0.0518760i
$691$	46.6961			1.77640			0.888201	−	0.459455i	$-0.151955\pi$
$691$	46.6961			1.77640			0.888201	+	0.459455i	$0.151955\pi$
$692$	−10.7357	+	23.5079i	−0.408110	+	0.893637i
$693$	−17.3249	−	5.08705i	−0.658119	−	0.193241i
$694$	−10.2116	−	11.7848i	−0.387625	−	0.447343i
$695$	2.72478	−	1.75111i	0.103357	−	0.0664233i
$696$	2.28301	−	2.63473i	0.0865371	−	0.0998691i
$697$	0.381377	−	2.65253i	0.0144457	−	0.100472i
$698$	−22.6804	+	6.65956i	−0.858465	+	0.252068i
$699$	−10.2884	−	6.61196i	−0.389144	−	0.250087i
$700$	−0.235242	−	1.63614i	−0.00889130	−	0.0618404i
$701$	9.70151	+	21.2433i	0.366421	+	0.802350i	0.999598	+	0.0283430i	$0.00902307\pi$
$701$	9.70151	+	21.2433i	0.366421	+	0.802350i	−0.633177	+	0.774007i	$0.718250\pi$
$702$	−5.10841	−	11.1859i	−0.192805	−	0.422183i
$703$	2.24812	+	15.6360i	0.0847896	+	0.589724i
$704$	25.1472	+	16.1611i	0.947771	+	0.609096i
$705$	4.72636	−	1.38779i	0.178005	−	0.0522670i
$706$	0.434882	−	3.02467i	0.0163670	−	0.113835i
$707$	−3.55066	+	4.09768i	−0.133536	+	0.154109i
$708$	−0.134662	+	0.0865420i	−0.00506091	+	0.00325245i
$709$	−5.05759	−	5.83678i	−0.189942	−	0.219205i	0.652789	−	0.757540i	$-0.273599\pi$
$709$	−5.05759	−	5.83678i	−0.189942	−	0.219205i	−0.842731	+	0.538335i	$0.819053\pi$
$710$	5.49324	+	1.61296i	0.206158	+	0.0605334i
$711$	7.54974	−	16.5316i	0.283138	−	0.619985i
$712$	41.4619			1.55385
$713$	−34.6477	−	32.5855i	−1.29756	−	1.22034i
$714$	−0.396067			−0.0148224
$715$	7.56030	−	16.5548i	0.282739	−	0.619113i
$716$	18.0353	+	5.29564i	0.674010	+	0.197907i
$717$	−5.00264	−	5.77336i	−0.186827	−	0.215610i
$718$	1.77849	−	1.14297i	0.0663726	−	0.0426551i
$719$	−2.49619	+	2.88076i	−0.0930923	+	0.107434i	−0.800384	−	0.599487i	$-0.795371\pi$
$719$	−2.49619	+	2.88076i	−0.0930923	+	0.107434i	0.707292	+	0.706922i	$0.249917\pi$
$720$	−0.0209813	+	0.145928i	−0.000781926	+	0.00543842i
$721$	5.24921	−	1.54131i	0.195491	−	0.0574013i
$722$	−1.36777	−	0.879015i	−0.0509033	−	0.0327135i
$723$	−2.21950	−	15.4370i	−0.0825442	−	0.574107i
$724$	9.33353	+	20.4376i	0.346878	+	0.759557i
$725$	0.598095	+	1.30965i	0.0222127	+	0.0486390i
$726$	−2.50554	−	17.4264i	−0.0929892	−	0.646754i
$727$	−37.9763	−	24.4059i	−1.40846	−	0.905163i	−0.408490	−	0.912763i	$-0.633945\pi$
$727$	−37.9763	−	24.4059i	−1.40846	−	0.905163i	−0.999971	+	0.00759945i	$0.997581\pi$
$728$	11.4477	−	3.36136i	0.424282	−	0.124580i
$729$	−0.664783	+	4.62367i	−0.0246216	+	0.171247i
$730$	2.83513	−	3.27191i	0.104933	−	0.121099i
$731$	−0.0201518	+	0.0129508i	−0.000745342	+	0.000479002i
$732$	−2.98478	−	3.44462i	−0.110321	−	0.127317i
$733$	−1.53779	−	0.451536i	−0.0567996	−	0.0166779i	0.253209	−	0.967412i	$-0.418514\pi$
$733$	−1.53779	−	0.451536i	−0.0567996	−	0.0166779i	−0.310009	+	0.950734i	$0.600332\pi$
$734$	1.08474	−	2.37525i	0.0400386	−	0.0876722i
$735$	4.40332			0.162419
$736$	−1.09917	+	26.9666i	−0.0405161	+	0.994001i
$737$	−79.0804			−2.91296
$738$	−5.73658	+	12.5614i	−0.211166	+	0.462390i
$739$	24.7668	+	7.27218i	0.911061	+	0.267512i	0.703487	−	0.710708i	$-0.251625\pi$
$739$	24.7668	+	7.27218i	0.911061	+	0.267512i	0.207573	+	0.978219i	$0.433443\pi$
$740$	−2.76786	−	3.19428i	−0.101749	−	0.117424i
$741$	−10.1490	+	6.52236i	−0.372833	+	0.239605i
$742$	−11.0394	+	12.7401i	−0.405268	+	0.467704i
$743$	−1.24686	+	8.67210i	−0.0457428	+	0.318148i	0.954084	+	0.299539i	$0.0968329\pi$
$743$	−1.24686	+	8.67210i	−0.0457428	+	0.318148i	−0.999827	+	0.0186092i	$0.994076\pi$
$744$	−23.0420	+	6.76575i	−0.844761	+	0.248044i
$745$	3.17512	+	2.04052i	0.116327	+	0.0747590i
$746$	−1.10996	−	7.71997i	−0.0406387	−	0.282648i
$747$	−8.13015	−	17.8026i	−0.297467	−	0.651361i
$748$	−1.15933	−	2.53858i	−0.0423894	−	0.0928198i
$749$	−2.67644	−	18.6150i	−0.0977950	−	0.680179i
$750$	0.632317	+	0.406366i	0.0230890	+	0.0148384i
$751$	−7.20428	+	2.11537i	−0.262888	+	0.0771908i	−0.410520	−	0.911851i	$-0.634653\pi$
$751$	−7.20428	+	2.11537i	−0.262888	+	0.0771908i	0.147632	+	0.989042i	$0.452835\pi$
$752$	0.0533443	−	0.371018i	0.00194527	−	0.0135296i
$753$	4.98185	−	5.74937i	0.181549	−	0.209519i
$754$	−3.31490	+	2.13035i	−0.120721	+	0.0775829i
$755$	−9.40011	−	10.8483i	−0.342105	−	0.394810i
$756$	−7.12615	−	2.09243i	−0.259176	−	0.0761008i
$757$	−6.30560	+	13.8073i	−0.229181	+	0.501836i	−0.988930	−	0.148380i	$-0.952594\pi$
$757$	−6.30560	+	13.8073i	−0.229181	+	0.501836i	0.759750	+	0.650216i	$0.225322\pi$
$758$	−20.6511			−0.750081
$759$	18.7398	−	14.9464i	0.680213	−	0.542521i
$760$	12.9766			0.470711
$761$	−3.34608	+	7.32690i	−0.121295	+	0.265600i	−0.960534	−	0.278164i	$-0.910274\pi$
$761$	−3.34608	+	7.32690i	−0.121295	+	0.265600i	0.839238	+	0.543764i	$0.183001\pi$
$762$	−4.96777	−	1.45867i	−0.179963	−	0.0528420i
$763$	1.96388	+	2.26644i	0.0710973	+	0.0820507i
$764$	1.03241	−	0.663490i	0.0373513	−	0.0240042i
$765$	0.579950	−	0.669298i	0.0209681	−	0.0241985i
$766$	0.728164	−	5.06449i	0.0263096	−	0.182987i
$767$	0.457830	−	0.134431i	0.0165313	−	0.00485402i
$768$	11.5770	+	7.44011i	0.417750	+	0.268472i
$769$	−3.81149	−	26.5095i	−0.137446	−	0.955957i	−0.935489	−	0.353356i	$-0.885040\pi$
$769$	−3.81149	−	26.5095i	−0.137446	−	0.955957i	0.798043	−	0.602601i	$-0.205869\pi$
$770$	2.90998	+	6.37197i	0.104869	+	0.229630i
$771$	−3.71429	−	8.13315i	−0.133767	−	0.292908i
$772$	−4.38794	−	30.5188i	−0.157925	−	1.09839i
$773$	2.90117	+	1.86447i	0.104348	+	0.0670603i	0.591774	−	0.806104i	$-0.298428\pi$
$773$	2.90117	+	1.86447i	0.104348	+	0.0670603i	−0.487426	+	0.873164i	$0.662064\pi$
$774$	0.118439	−	0.0347769i	0.00425721	−	0.00125003i
$775$	1.41143	−	9.81670i	0.0507000	−	0.352626i
$776$	−8.98011	+	10.3636i	−0.322367	+	0.372032i
$777$	−3.35558	+	2.15650i	−0.120381	+	0.0773639i
$778$	−6.53054	−	7.53664i	−0.234131	−	0.270202i
$779$	30.1457	+	8.85157i	1.08008	+	0.317140i
$780$	1.34092	−	2.93621i	0.0480127	−	0.105133i
$781$	38.0705			1.36227
$782$	−0.946542	+	1.34872i	−0.0338483	+	0.0482303i
$783$	6.46900			0.231183
$784$	0.139192	−	0.304789i	0.00497115	−	0.0108853i
$785$	8.31747	+	2.44223i	0.296863	+	0.0871669i
$786$	2.89239	+	3.33800i	0.103168	+	0.119062i
$787$	7.32293	−	4.70616i	0.261034	−	0.167756i	−0.403577	−	0.914945i	$-0.632233\pi$
$787$	7.32293	−	4.70616i	0.261034	−	0.167756i	0.664612	+	0.747189i	$0.268597\pi$
$788$	20.5191	−	23.6802i	0.730961	−	0.843574i
$789$	2.26056	−	15.7225i	0.0804780	−	0.559737i
$790$	−6.76505	+	1.98640i	−0.240690	+	0.0706729i
$791$	0.848470	+	0.545278i	0.0301681	+	0.0193879i
$792$	5.39761	+	37.5412i	0.191796	+	1.33397i
$793$	5.64404	+	12.3587i	0.200426	+	0.438871i
$794$	1.12496	+	2.46332i	0.0399234	+	0.0874200i
$795$	1.71178	+	11.9057i	0.0607105	+	0.422251i
$796$	13.6764	+	8.78927i	0.484746	+	0.311527i
$797$	29.1188	−	8.55006i	1.03144	−	0.302859i	0.278145	−	0.960539i	$-0.410281\pi$
$797$	29.1188	−	8.55006i	1.03144	−	0.302859i	0.753297	+	0.657681i	$0.228462\pi$
$798$	0.660842	−	4.59626i	0.0233936	−	0.162706i
$799$	−1.47451	+	1.70167i	−0.0521643	+	0.0602008i
$800$	−4.73423	+	3.04250i	−0.167380	+	0.107569i
$801$	21.7249	+	25.0718i	0.767611	+	0.885870i
$802$	14.8839	+	4.37031i	0.525569	+	0.154321i
$803$	11.9594	−	26.1873i	0.422037	−	0.924131i
$804$	−14.0260			−0.494658
$805$	−3.72804	+	5.31207i	−0.131396	+	0.187226i
$806$	27.1434			0.956084
$807$	6.26016	−	13.7078i	0.220368	−	0.482539i
$808$	10.9276	+	3.20863i	0.384431	+	0.112879i
$809$	21.5444	+	24.8635i	0.757460	+	0.874155i	0.995269	−	0.0971569i	$-0.0309748\pi$
$809$	21.5444	+	24.8635i	0.757460	+	0.874155i	−0.237809	+	0.971312i	$0.576429\pi$
$810$	−2.22315	+	1.42873i	−0.0781134	+	0.0502004i
$811$	−19.6536	+	22.6815i	−0.690132	+	0.796454i	−0.987384	−	0.158345i	$-0.949384\pi$
$811$	−19.6536	+	22.6815i	−0.690132	+	0.796454i	0.297252	+	0.954799i	$0.403930\pi$
$812$	−0.338690	+	2.35564i	−0.0118857	+	0.0826668i
$813$	22.3067	−	6.54984i	0.782330	−	0.229713i
$814$	15.0684	+	9.68385i	0.528146	+	0.339419i
$815$	−0.835046	−	5.80787i	−0.0292504	−	0.203441i
$816$	0.00893317	+	0.0195609i	0.000312724	+	0.000684769i
$817$	−0.116667	−	0.255465i	−0.00408166	−	0.00893760i
$818$	0.912903	+	6.34938i	0.0319189	+	0.222001i
$819$	8.03090	+	5.16115i	0.280622	+	0.180345i
$820$	−8.06585	+	2.36835i	−0.281672	+	0.0827062i
$821$	−2.06759	+	14.3804i	−0.0721593	+	0.501879i	0.921405	+	0.388605i	$0.127043\pi$
$821$	−2.06759	+	14.3804i	−0.0721593	+	0.501879i	−0.993564	+	0.113274i	$0.963866\pi$
$822$	0.276744	−	0.319380i	0.00965255	−	0.0111396i
$823$	−22.7177	+	14.5998i	−0.791889	+	0.508916i	−0.872960	−	0.487792i	$-0.837802\pi$
$823$	−22.7177	+	14.5998i	−0.791889	+	0.508916i	0.0810709	+	0.996708i	$0.474166\pi$
$824$	−7.52529	−	8.68465i	−0.262156	−	0.302544i
$825$	4.79570	+	1.40814i	0.166965	+	0.0490253i
$826$	−0.0762950	+	0.167063i	−0.00265464	+	0.00581285i
$827$	−26.7426			−0.929933			−0.464966	−	0.885328i	$-0.653934\pi$
$827$	−26.7426			−0.929933			−0.464966	+	0.885328i	$0.653934\pi$
$828$	−10.4160	+	8.30754i	−0.361981	+	0.288707i
$829$	−36.5956			−1.27102			−0.635508	−	0.772094i	$-0.719209\pi$
$829$	−36.5956			−1.27102			−0.635508	+	0.772094i	$0.719209\pi$
$830$	−3.15412	+	6.90656i	−0.109481	+	0.239730i
$831$	16.1165	+	4.73223i	0.559076	+	0.164159i
$832$	−10.3495	−	11.9440i	−0.358805	−	0.414083i
$833$	−1.69324	+	1.08818i	−0.0586674	+	0.0377033i
$834$	−1.59427	+	1.83988i	−0.0552049	+	0.0637099i
$835$	−1.68751	+	11.7369i	−0.0583988	+	0.406172i
$836$	31.3940	−	9.21810i	1.08578	−	0.318815i
$837$	−37.4873	−	24.0916i	−1.29575	−	0.832729i
$838$	−2.67988	−	18.6390i	−0.0925749	−	0.643872i
$839$	−14.9213	−	32.6730i	−0.515139	−	1.12800i	−0.971247	−	0.238073i	$-0.923484\pi$
$839$	−14.9213	−	32.6730i	−0.515139	−	1.12800i	0.456108	−	0.889924i	$-0.349243\pi$
$840$	1.36117	+	2.98056i	0.0469650	+	0.102839i
$841$	3.83213	+	26.6530i	0.132142	+	0.919070i
$842$	8.50515	+	5.46593i	0.293107	+	0.188368i
$843$	−6.22183	+	1.82689i	−0.214291	+	0.0629216i
$844$	2.71513	−	18.8842i	0.0934588	−	0.650020i
$845$	2.21212	−	2.55292i	0.0760992	−	0.0878232i
$846$	9.76094	−	6.27297i	0.335588	−	0.215669i
$847$	20.7565	+	23.9542i	0.713200	+	0.823077i
$848$	0.878196	+	0.257862i	0.0301574	+	0.00885501i
$849$	−6.87361	+	15.0511i	−0.235902	+	0.516552i
$850$	−0.343574			−0.0117845
$851$	−0.675829	+	16.5804i	−0.0231671	+	0.568370i
$852$	6.75233			0.231331
$853$	12.8601	−	28.1596i	0.440320	−	0.964167i	−0.551219	−	0.834361i	$-0.685837\pi$
$853$	12.8601	−	28.1596i	0.440320	−	0.964167i	0.991539	−	0.129806i	$-0.0414356\pi$
$854$	−5.01766	−	1.47332i	−0.171701	−	0.0504159i
$855$	6.79938	+	7.84690i	0.232534	+	0.268358i
$856$	−33.2320	+	21.3569i	−1.13585	+	0.729964i
$857$	5.32735	−	6.14809i	0.181979	−	0.210015i	−0.657430	−	0.753516i	$-0.728356\pi$
$857$	5.32735	−	6.14809i	0.181979	−	0.210015i	0.839408	+	0.543501i	$0.182902\pi$
$858$	−1.94677	+	13.5401i	−0.0664617	+	0.462252i
$859$	−41.5229	+	12.1922i	−1.41674	+	0.415993i	−0.898400	−	0.439179i	$-0.855269\pi$
$859$	−41.5229	+	12.1922i	−1.41674	+	0.415993i	−0.518344	+	0.855172i	$0.673451\pi$
$860$	0.0632147	+	0.0406256i	0.00215560	+	0.00138532i
$861$	1.12903	+	7.85254i	0.0384771	+	0.267614i
$862$	−8.51278	−	18.6404i	−0.289947	−	0.634894i
$863$	1.19405	+	2.61462i	0.0406461	+	0.0890026i	0.928866	−	0.370416i	$-0.120785\pi$
$863$	1.19405	+	2.61462i	0.0406461	+	0.0890026i	−0.888220	+	0.459419i	$0.848058\pi$
$864$	3.59850	+	25.0281i	0.122423	+	0.851473i
$865$	17.7981	+	11.4381i	0.605152	+	0.388908i
$866$	24.9221	−	7.31778i	0.846886	−	0.248668i
$867$	−2.04265	+	14.2069i	−0.0693720	+	0.482493i
$868$	10.7355	−	12.3894i	0.364386	−	0.420524i
$869$	−39.4419	+	25.3478i	−1.33798	+	0.859865i
$870$	−0.708672	−	0.817851i	−0.0240262	−	0.0277278i
$871$	40.1161	+	11.7792i	1.35928	+	0.399122i
$872$	2.61680	−	5.72999i	0.0886161	−	0.194042i
$873$	−10.9722			−0.371351
$874$	−14.0723	−	13.2347i	−0.476002	−	0.447672i
$875$	−1.35320			−0.0457465
$876$	2.12115	−	4.64468i	0.0716671	−	0.156929i
$877$	26.9041	+	7.89977i	0.908488	+	0.266756i	0.702404	−	0.711778i	$-0.252110\pi$
$877$	26.9041	+	7.89977i	0.908488	+	0.266756i	0.206084	+	0.978534i	$0.433928\pi$
$878$	5.01401	+	5.78647i	0.169214	+	0.195284i
$879$	17.6718	−	11.3570i	0.596055	−	0.383061i
$880$	0.249065	−	0.287436i	0.00839597	−	0.00968946i
$881$	0.600428	−	4.17607i	0.0202289	−	0.140695i	−0.977204	−	0.212303i	$-0.931904\pi$
$881$	0.600428	−	4.17607i	0.0202289	−	0.140695i	0.997433	+	0.0716073i	$0.0228128\pi$
$882$	9.95179	−	2.92211i	0.335094	−	0.0983925i
$883$	8.19728	+	5.26807i	0.275861	+	0.177285i	0.671255	−	0.741227i	$-0.265756\pi$
$883$	8.19728	+	5.26807i	0.275861	+	0.177285i	−0.395394	+	0.918512i	$0.629392\pi$
$884$	0.209983	+	1.46046i	0.00706249	+	0.0491207i
$885$	0.0544375	+	0.119201i	0.00182990	+	0.00400691i
$886$	7.54851	+	16.5289i	0.253597	+	0.555300i
$887$	4.75906	+	33.1000i	0.159794	+	1.11139i	0.899012	+	0.437923i	$0.144286\pi$
$887$	4.75906	+	33.1000i	0.159794	+	1.11139i	−0.739219	+	0.673465i	$0.764805\pi$
$888$	7.04838	+	4.52972i	0.236528	+	0.152007i
$889$	8.94366	−	2.62610i	0.299961	−	0.0880764i
$890$	1.83163	−	12.7393i	0.0613964	−	0.427021i
$891$	−11.5078	+	13.2807i	−0.385526	+	0.444920i
$892$	−23.0094	+	14.7872i	−0.770411	+	0.495113i
$893$	−17.2872	−	19.9505i	−0.578496	−	0.667620i
$894$	−2.72197	−	0.799241i	−0.0910362	−	0.0267306i
$895$	6.39235	−	13.9973i	0.213673	−	0.467878i
$896$	−9.14742			−0.305594
$897$	−11.7327	+	4.79073i	−0.391743	+	0.159958i
$898$	19.0221			0.634774
$899$	−5.93170	+	12.9886i	−0.197833	+	0.433194i
$900$	−2.66555	−	0.782677i	−0.0888518	−	0.0260892i
$901$	−3.60046	−	4.15516i	−0.119949	−	0.138428i
$902$	29.9695	−	19.2602i	0.997874	−	0.641295i
$903$	0.0464393	−	0.0535938i	0.00154540	−	0.00178349i
$904$	0.301496	−	2.09695i	0.0100276	−	0.0697436i
$905$	17.6483	−	5.18201i	0.586649	−	0.172256i
$906$	9.07651	+	5.83312i	0.301547	+	0.193792i
$907$	6.43151	+	44.7321i	0.213555	+	1.48531i	0.761158	+	0.648567i	$0.224631\pi$
$907$	6.43151	+	44.7321i	0.213555	+	1.48531i	−0.547603	+	0.836738i	$0.684460\pi$
$908$	−6.80058	−	14.8912i	−0.225685	−	0.494182i
$909$	3.78551	+	8.28910i	0.125557	+	0.274932i
$910$	−0.527068	−	3.66584i	−0.0174721	−	0.121521i
$911$	32.2670	+	20.7367i	1.06905	+	0.687039i	0.952004	−	0.306087i	$-0.0990199\pi$
$911$	32.2670	+	20.7367i	1.06905	+	0.687039i	0.117050	+	0.993126i	$0.462656\pi$
$912$	−0.241905	+	0.0710296i	−0.00801026	+	0.00235202i
$913$	−7.18535	+	49.9752i	−0.237800	+	1.65394i
$914$	−16.8751	+	19.4749i	−0.558179	+	0.644172i
$915$	−3.13898	+	2.01730i	−0.103771	+	0.0666899i
$916$	−5.41771	−	6.25237i	−0.179006	−	0.206584i
$917$	−7.62963	−	2.24026i	−0.251952	−	0.0739799i
$918$	−0.641286	+	1.40422i	−0.0211656	+	0.0463462i
$919$	−7.06723			−0.233126			−0.116563	−	0.993183i	$-0.537188\pi$
$919$	−7.06723			−0.233126			−0.116563	+	0.993183i	$0.537188\pi$
$920$	13.4027	+	2.48790i	0.441873	+	0.0820235i
$921$	−18.2961			−0.602876
$922$	14.1191	−	30.9165i	0.464987	−	1.01818i
$923$	−19.3125	−	5.67067i	−0.635680	−	0.186652i
$924$	5.41033	+	6.24385i	0.177987	+	0.205408i
$925$	−2.91085	+	1.87069i	−0.0957081	+	0.0615078i
$926$	18.8767	−	21.7849i	0.620328	−	0.715897i
$927$	1.30853	−	9.10103i	0.0429778	−	0.298917i
$928$	7.77414	−	2.28269i	0.255199	−	0.0749330i
$929$	−37.6681	−	24.2078i	−1.23585	−	0.794232i	−0.251058	−	0.967972i	$-0.580778\pi$
$929$	−37.6681	−	24.2078i	−1.23585	−	0.794232i	−0.984792	+	0.173740i	$0.944415\pi$
$930$	1.06088	+	7.37860i	0.0347877	+	0.241954i
$931$	−9.80288	−	21.4653i	−0.321276	−	0.703497i
$932$	−7.28485	−	15.9516i	−0.238623	−	0.522512i
$933$	0.0768365	+	0.534410i	0.00251552	+	0.0174958i
$934$	−10.1201	−	6.50380i	−0.331140	−	0.212811i
$935$	−2.19212	+	0.643665i	−0.0716901	+	0.0210501i
$936$	2.85371	−	19.8480i	0.0932764	−	0.648752i
$937$	−27.4973	+	31.7336i	−0.898298	+	1.03669i	0.100829	+	0.994904i	$0.467851\pi$
$937$	−27.4973	+	31.7336i	−0.898298	+	1.03669i	−0.999127	+	0.0417870i	$0.986695\pi$
$938$	−13.5380	+	8.70036i	−0.442032	+	0.284077i
$939$	10.7052	+	12.3545i	0.349351	+	0.403173i
$940$	6.77710	+	1.98994i	0.221045	+	0.0649045i
$941$	−15.3768	+	33.6704i	−0.501268	+	1.09762i	0.474787	+	0.880101i	$0.342525\pi$
$941$	−15.3768	+	33.6704i	−0.501268	+	1.09762i	−0.976055	+	0.217523i	$0.930202\pi$
$942$	−6.51565			−0.212291
$943$	29.4384	+	14.9218i	0.958646	+	0.485919i
$944$	0.00997168			0.000324551
$945$	−2.52576	+	5.53065i	−0.0821631	+	0.179912i
$946$	−0.305546	−	0.0897165i	−0.00993417	−	0.00291693i
$947$	−22.5504	−	26.0246i	−0.732790	−	0.845684i	0.259993	−	0.965610i	$-0.416280\pi$
$947$	−22.5504	−	26.0246i	−0.732790	−	0.845684i	−0.992783	+	0.119926i	$0.961734\pi$
$948$	−6.99556	+	4.49577i	−0.227205	+	0.146016i
$949$	−9.96743	+	11.5030i	−0.323556	+	0.373404i
$950$	0.573258	−	3.98709i	0.0185989	−	0.129358i
$951$	10.9484	−	3.21474i	0.355027	−	0.104245i
$952$	−1.26000	−	0.809754i	−0.0408369	−	0.0262443i
$953$	−0.295612	−	2.05603i	−0.00957581	−	0.0666012i	0.984473	−	0.175535i	$-0.0561655\pi$
$953$	−0.295612	−	2.05603i	−0.00957581	−	0.0666012i	−0.994049	+	0.108934i	$0.965256\pi$
$954$	11.7695	+	25.7716i	0.381052	+	0.834387i
$955$	−0.417355	−	0.913879i	−0.0135053	−	0.0295724i
$956$	−1.55890	−	10.8424i	−0.0504183	−	0.350667i
$957$	−6.05376	−	3.89052i	−0.195690	−	0.125763i
$958$	−21.4701	+	6.30420i	−0.693668	+	0.203679i
$959$	−0.108276	+	0.753077i	−0.00349642	+	0.0243181i
$960$	2.84232	−	3.28022i	0.0917356	−	0.105869i
$961$	56.6667	−	36.4175i	1.82796	−	1.17476i
$962$	−6.20149	−	7.15691i	−0.199944	−	0.230748i
$963$	−30.3271	−	8.90483i	−0.977276	−	0.286954i
$964$	9.28975	−	20.3417i	0.299203	−	0.655163i
$965$	−25.2411			−0.812538
$966$	1.56374	−	4.62047i	0.0503125	−	0.148661i
$967$	−15.8673			−0.510258			−0.255129	−	0.966907i	$-0.582118\pi$
$967$	−15.8673			−0.510258			−0.255129	+	0.966907i	$0.582118\pi$
$968$	27.6572	−	60.5608i	0.888936	−	1.94650i
$969$	1.45313	+	0.426677i	0.0466812	+	0.0137068i
$970$	2.78753	+	3.21698i	0.0895023	+	0.103291i
$971$	3.02736	−	1.94556i	0.0971525	−	0.0624361i	−0.491163	−	0.871068i	$-0.663428\pi$
$971$	3.02736	−	1.94556i	0.0971525	−	0.0624361i	0.588315	+	0.808632i	$0.299792\pi$
$972$	−12.8236	+	14.7992i	−0.411318	+	0.474686i
$973$	0.623758	−	4.33833i	0.0199967	−	0.139080i
$974$	12.2759	−	3.60453i	0.393346	−	0.115497i
$975$	−2.22303	−	1.42866i	−0.0711940	−	0.0457536i
$976$	0.0404077	+	0.281042i	0.00129342	+	0.00899593i
$977$	2.44672	+	5.35756i	0.0782774	+	0.171404i	0.944724	−	0.327865i	$-0.106329\pi$
$977$	2.44672	+	5.35756i	0.0782774	+	0.171404i	−0.866447	+	0.499269i	$0.833602\pi$
$978$	1.83211	+	4.01175i	0.0585843	+	0.128282i
$979$	−12.1798	−	84.7123i	−0.389268	−	2.70742i
$980$	5.31158	+	3.41354i	0.169672	+	0.109042i
$981$	4.83604	−	1.41999i	0.154403	−	0.0453367i
$982$	−3.22959	+	22.4623i	−0.103060	+	0.716800i
$983$	26.5373	−	30.6257i	0.846409	−	0.976808i	−0.153527	−	0.988144i	$-0.549063\pi$
$983$	26.5373	−	30.6257i	0.846409	−	0.976808i	0.999936	+	0.0113367i	$0.00360867\pi$
$984$	14.0185	−	9.00916i	0.446894	−	0.287201i
$985$	−16.7979	−	19.3858i	−0.535225	−	0.617683i
$986$	0.474625	+	0.139363i	0.0151151	+	0.00443821i
$987$	2.76904	−	6.06335i	0.0881395	−	0.192999i
$988$	−17.2987			−0.550344
$989$	−0.0715195	−	0.286221i	−0.00227419	−	0.00910129i
$990$	11.7731			0.374173
$991$	−7.99375	+	17.5039i	−0.253930	+	0.556029i	−0.993070	−	0.117523i	$-0.962505\pi$
$991$	−7.99375	+	17.5039i	−0.253930	+	0.556029i	0.739140	+	0.673551i	$0.235232\pi$
$992$	−53.5516	−	15.7242i	−1.70027	−	0.499243i
$993$	−0.993293	−	1.14632i	−0.0315212	−	0.0363774i
$994$	6.51742	−	4.18849i	0.206720	−	0.132851i
$995$	8.71546	−	10.0582i	0.276299	−	0.318866i
$996$	−1.27442	+	8.86378i	−0.0403815	+	0.280860i
$997$	−27.8144	+	8.16706i	−0.880892	+	0.258653i	−0.690742	−	0.723102i	$-0.742716\pi$
$997$	−27.8144	+	8.16706i	−0.880892	+	0.258653i	−0.190151	+	0.981755i	$0.560898\pi$
$998$	−31.1975	−	20.0494i	−0.987539	−	0.634653i
$999$	2.21254	+	15.3886i	0.0700017	+	0.486873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.6.3	✓	50
5.2	odd	4		575.2.p.d.374.5		100
5.3	odd	4		575.2.p.d.374.6		100
5.4	even	2		575.2.k.d.351.3		50
23.2	even	11		2645.2.a.y.1.11		25
23.4	even	11	inner	115.2.g.c.96.3	yes	50
23.21	odd	22		2645.2.a.x.1.11		25
115.4	even	22		575.2.k.d.326.3		50
115.27	odd	44		575.2.p.d.349.6		100
115.73	odd	44		575.2.p.d.349.5		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.6.3	✓	50	1.1	even	1	trivial
115.2.g.c.96.3	yes	50	23.4	even	11	inner
575.2.k.d.326.3		50	115.4	even	22
575.2.k.d.351.3		50	5.4	even	2
575.2.p.d.349.5		100	115.73	odd	44
575.2.p.d.349.6		100	115.27	odd	44
575.2.p.d.374.5		100	5.2	odd	4
575.2.p.d.374.6		100	5.3	odd	4
2645.2.a.x.1.11		25	23.21	odd	22
2645.2.a.y.1.11		25	23.2	even	11

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366526 + 0.802579i) q^{2} +(0.817387 + 0.240007i) q^{3} +(0.799929 + 0.923167i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.492218 + 0.568049i) q^{6} +(0.192580 - 1.33943i) q^{7} +(-2.72725 + 0.800794i) q^{8} +(-1.91324 - 1.22957i) q^{9} +O(q^{10})\)	\(q+(-0.366526 + 0.802579i) q^{2} +(0.817387 + 0.240007i) q^{3} +(0.799929 + 0.923167i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.492218 + 0.568049i) q^{6} +(0.192580 - 1.33943i) q^{7} +(-2.72725 + 0.800794i) q^{8} +(-1.91324 - 1.22957i) q^{9} +(0.125566 + 0.873331i) q^{10} +(2.43729 + 5.33691i) q^{11} +(0.432286 + 0.946573i) q^{12} +(-0.441451 - 3.07036i) q^{13} +(1.00441 + 0.645495i) q^{14} +(0.817387 - 0.240007i) q^{15} +(0.00922548 - 0.0641646i) q^{16} +(-0.255004 + 0.294291i) q^{17} +(1.68808 - 1.08486i) q^{18} +(-2.98969 - 3.45029i) q^{19} +(1.17205 + 0.344144i) q^{20} +(0.478884 - 1.04861i) q^{21} -5.17662 q^{22} +(-2.42636 - 4.13676i) q^{23} -2.42142 q^{24} +(0.415415 - 0.909632i) q^{25} +(2.62601 + 0.771067i) q^{26} +(-2.94237 - 3.39568i) q^{27} +(1.39056 - 0.893662i) q^{28} +(-0.942838 + 1.08809i) q^{29} +(-0.106969 + 0.743987i) q^{30} +(9.51592 - 2.79413i) q^{31} +(-4.73423 - 3.04250i) q^{32} +(0.711313 + 4.94729i) q^{33} +(-0.142726 - 0.312526i) q^{34} +(-0.562139 - 1.23091i) q^{35} +(-0.395363 - 2.74981i) q^{36} +(-2.91085 - 1.87069i) q^{37} +(3.86493 - 1.13485i) q^{38} +(0.376070 - 2.61563i) q^{39} +(-1.86137 + 2.14814i) q^{40} +(-5.78939 + 3.72061i) q^{41} +(0.666069 + 0.768684i) q^{42} +(0.0590243 + 0.0173311i) q^{43} +(-2.97721 + 6.51917i) q^{44} -2.27428 q^{45} +(4.20940 - 0.431116i) q^{46} +5.78228 q^{47} +(0.0229407 - 0.0502332i) q^{48} +(4.95948 + 1.45623i) q^{49} +(0.577791 + 0.666807i) q^{50} +(-0.279069 + 0.179347i) q^{51} +(2.48133 - 2.86361i) q^{52} +(-2.00938 + 13.9755i) q^{53} +(3.80376 - 1.11688i) q^{54} +(4.93573 + 3.17200i) q^{55} +(0.547389 + 3.80717i) q^{56} +(-1.61564 - 3.53777i) q^{57} +(-0.527707 - 1.15552i) q^{58} +(0.0218917 + 0.152260i) q^{59} +(0.875418 + 0.562597i) q^{60} +(-4.20259 + 1.23399i) q^{61} +(-1.24532 + 8.66140i) q^{62} +(-2.01537 + 2.32586i) q^{63} +(4.28613 - 2.75453i) q^{64} +(-2.03134 - 2.34429i) q^{65} +(-4.23131 - 1.24242i) q^{66} +(-5.59921 + 12.2606i) q^{67} -0.475665 q^{68} +(-0.990425 - 3.96368i) q^{69} +1.19394 q^{70} +(2.69555 - 5.90243i) q^{71} +(6.20253 + 1.82123i) q^{72} +(-3.21329 - 3.70834i) q^{73} +(2.56828 - 1.65053i) q^{74} +(0.557873 - 0.643819i) q^{75} +(0.793652 - 5.51997i) q^{76} +(7.61777 - 2.23678i) q^{77} +(1.96141 + 1.26052i) q^{78} +(1.13725 + 7.90977i) q^{79} +(-0.0269290 - 0.0589664i) q^{80} +(1.24423 + 2.72449i) q^{81} +(-0.864128 - 6.01014i) q^{82} +(7.23936 + 4.65246i) q^{83} +(1.35111 - 0.396723i) q^{84} +(-0.0554177 + 0.385439i) q^{85} +(-0.0355435 + 0.0410194i) q^{86} +(-1.03181 + 0.663106i) q^{87} +(-10.9209 - 12.6034i) q^{88} +(-13.9961 - 4.10963i) q^{89} +(0.833580 - 1.82529i) q^{90} -4.19754 q^{91} +(1.87801 - 5.54905i) q^{92} +8.44880 q^{93} +(-2.11936 + 4.64074i) q^{94} +(-4.38046 - 1.28622i) q^{95} +(-3.13948 - 3.62315i) q^{96} +(4.05860 - 2.60830i) q^{97} +(-2.98652 + 3.44663i) q^{98} +(1.89897 - 13.2076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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