LMFDB - Embedded newform 115.2.j.a.4.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(4,115)]

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([11, 4]))

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

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

chi := DirichletCharacter("115.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.j (of order $22$, 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:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	115.4
Dual form			115.2.j.a.29.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04322 - 0.933106i) q^{2} +(-0.0755218 - 0.257204i) q^{3} +(1.99433 - 2.30158i) q^{4} +(-1.91428 + 1.15566i) q^{5} +(-0.394306 - 0.455053i) q^{6} +(-0.783997 + 0.112722i) q^{7} +(0.661572 - 2.25311i) q^{8} +(2.46331 - 1.58307i) q^{9} +O(q^{10})$	\(q+(2.04322 - 0.933106i) q^{2} +(-0.0755218 - 0.257204i) q^{3} +(1.99433 - 2.30158i) q^{4} +(-1.91428 + 1.15566i) q^{5} +(-0.394306 - 0.455053i) q^{6} +(-0.783997 + 0.112722i) q^{7} +(0.661572 - 2.25311i) q^{8} +(2.46331 - 1.58307i) q^{9} +(-2.83293 + 4.14748i) q^{10} +(-1.20111 + 2.63005i) q^{11} +(-0.742589 - 0.339129i) q^{12} +(-3.88010 - 0.557874i) q^{13} +(-1.49669 + 0.961867i) q^{14} +(0.441810 + 0.405081i) q^{15} +(0.116164 + 0.807941i) q^{16} +(-2.16592 + 1.87678i) q^{17} +(3.55590 - 5.53309i) q^{18} +(2.93468 - 3.38680i) q^{19} +(-1.15785 + 6.71061i) q^{20} +(0.0882013 + 0.193134i) q^{21} +6.49453i q^{22} +(4.75940 - 0.590036i) q^{23} -0.629471 q^{24} +(2.32890 - 4.42450i) q^{25} +(-8.44844 + 2.48069i) q^{26} +(-1.20097 - 1.04065i) q^{27} +(-1.30411 + 2.02923i) q^{28} +(-3.85993 - 4.45460i) q^{29} +(1.28070 + 0.415414i) q^{30} +(-0.607115 - 0.178265i) q^{31} +(3.53034 + 5.49332i) q^{32} +(0.767170 + 0.110302i) q^{33} +(-2.67421 + 5.85570i) q^{34} +(1.37052 - 1.12181i) q^{35} +(1.26908 - 8.82666i) q^{36} +(-3.20008 - 4.97942i) q^{37} +(2.83595 - 9.65834i) q^{38} +(0.149545 + 1.04011i) q^{39} +(1.33739 + 5.07762i) q^{40} +(7.81204 + 5.02049i) q^{41} +(0.360429 + 0.312313i) q^{42} +(0.636806 + 2.16876i) q^{43} +(3.65787 + 8.00963i) q^{44} +(-2.88596 + 5.87719i) q^{45} +(9.17391 - 5.64659i) q^{46} -5.56900i q^{47} +(0.199033 - 0.0908952i) q^{48} +(-6.11451 + 1.79538i) q^{49} +(0.629925 - 11.2133i) q^{50} +(0.646289 + 0.415345i) q^{51} +(-9.02218 + 7.81776i) q^{52} +(2.42492 - 0.348651i) q^{53} +(-3.42487 - 1.00563i) q^{54} +(-0.740200 - 6.42272i) q^{55} +(-0.264696 + 1.84100i) q^{56} +(-1.09273 - 0.499034i) q^{57} +(-12.0433 - 5.49998i) q^{58} +(-0.362875 + 2.52385i) q^{59} +(1.81344 - 0.208994i) q^{60} +(-12.6025 - 3.70044i) q^{61} +(-1.40681 + 0.202269i) q^{62} +(-1.75278 + 1.51879i) q^{63} +(10.9658 + 7.04726i) q^{64} +(8.07229 - 3.41615i) q^{65} +(1.67042 - 0.490479i) q^{66} +(10.4047 - 4.75166i) q^{67} +8.72794i q^{68} +(-0.511198 - 1.17957i) q^{69} +(1.75349 - 3.57095i) q^{70} +(6.24137 + 13.6667i) q^{71} +(-1.93718 - 6.59742i) q^{72} +(-0.336090 - 0.291224i) q^{73} +(-11.1848 - 7.18803i) q^{74} +(-1.31388 - 0.264856i) q^{75} +(-1.94227 - 13.5088i) q^{76} +(0.645199 - 2.19734i) q^{77} +(1.27608 + 1.98562i) q^{78} +(-1.28969 + 8.96996i) q^{79} +(-1.15608 - 1.41238i) q^{80} +(3.47222 - 7.60311i) q^{81} +(20.6463 + 2.96850i) q^{82} +(-0.0445868 - 0.0693784i) q^{83} +(0.620415 + 0.182170i) q^{84} +(1.97725 - 6.09574i) q^{85} +(3.32482 + 3.83704i) q^{86} +(-0.854230 + 1.32921i) q^{87} +(5.13118 + 4.44619i) q^{88} +(4.36696 - 1.28225i) q^{89} +(-0.412607 + 14.7013i) q^{90} +3.10487 q^{91} +(8.13378 - 12.1308i) q^{92} +0.169615i q^{93} +(-5.19647 - 11.3787i) q^{94} +(-1.70380 + 9.87477i) q^{95} +(1.14628 - 1.32288i) q^{96} +(2.24367 - 3.49121i) q^{97} +(-10.8180 + 9.37383i) q^{98} +(1.20487 + 8.38008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	2.04322	−	0.933106i	1.44477	−	0.659805i	0.469931	−	0.882703i	$-0.344279\pi$
$2$	2.04322	−	0.933106i	1.44477	−	0.659805i	0.974842	+	0.222898i	$0.0715516\pi$
$3$	−0.0755218	−	0.257204i	−0.0436026	−	0.148497i	0.934815	−	0.355136i	$-0.115565\pi$
$3$	−0.0755218	−	0.257204i	−0.0436026	−	0.148497i	−0.978417	+	0.206639i	$0.933747\pi$
$4$	1.99433	−	2.30158i	0.997164	−	1.15079i
$5$	−1.91428	+	1.15566i	−0.856090	+	0.516827i
$5$	−1.91428	+	1.15566i	−0.856090	+	0.516827i
$6$	−0.394306	−	0.455053i	−0.160975	−	0.185775i
$7$	−0.783997	+	0.112722i	−0.296323	+	0.0426048i	−0.288873	−	0.957367i	$-0.593281\pi$
$7$	−0.783997	+	0.112722i	−0.296323	+	0.0426048i	−0.00744997	+	0.999972i	$0.502371\pi$
$8$	0.661572	−	2.25311i	0.233901	−	0.796594i
$9$	2.46331	−	1.58307i	0.821103	−	0.527691i
$10$	−2.83293	+	4.14748i	−0.895850	+	1.31155i
$11$	−1.20111	+	2.63005i	−0.362147	+	0.792991i	0.637597	+	0.770370i	$0.279928\pi$
$11$	−1.20111	+	2.63005i	−0.362147	+	0.792991i	−0.999744	+	0.0226213i	$0.992799\pi$
$12$	−0.742589	−	0.339129i	−0.214367	−	0.0978982i
$13$	−3.88010	−	0.557874i	−1.07615	−	0.154726i	−0.418622	−	0.908160i	$-0.637487\pi$
$13$	−3.88010	−	0.557874i	−1.07615	−	0.154726i	−0.657524	+	0.753434i	$0.728396\pi$
$14$	−1.49669	+	0.961867i	−0.400008	+	0.257070i
$15$	0.441810	+	0.405081i	0.114075	+	0.104592i
$16$	0.116164	+	0.807941i	0.0290411	+	0.201985i
$17$	−2.16592	+	1.87678i	−0.525312	+	0.455186i	−0.876695	−	0.481046i	$-0.840257\pi$
$17$	−2.16592	+	1.87678i	−0.525312	+	0.455186i	0.351383	+	0.936232i	$0.385712\pi$
$18$	3.55590	−	5.53309i	0.838134	−	1.30416i
$19$	2.93468	−	3.38680i	0.673262	−	0.776986i	−0.311621	−	0.950207i	$-0.600872\pi$
$19$	2.93468	−	3.38680i	0.673262	−	0.776986i	0.984883	+	0.173220i	$0.0554173\pi$
$20$	−1.15785	+	6.71061i	−0.258904	+	1.50054i
$21$	0.0882013	+	0.193134i	0.0192471	+	0.0421453i
$22$			6.49453i			1.38464i
$23$	4.75940	−	0.590036i	0.992403	−	0.123031i
$23$	4.75940	−	0.590036i	0.992403	−	0.123031i
$24$	−0.629471			−0.128490
$25$	2.32890	−	4.42450i	0.465781	−	0.884900i
$26$	−8.44844	+	2.48069i	−1.65688	+	0.486503i
$27$	−1.20097	−	1.04065i	−0.231127	−	0.200272i
$28$	−1.30411	+	2.02923i	−0.246453	+	0.383489i
$29$	−3.85993	−	4.45460i	−0.716771	−	0.827198i	0.274144	−	0.961689i	$-0.411606\pi$
$29$	−3.85993	−	4.45460i	−0.716771	−	0.827198i	−0.990915	+	0.134491i	$0.957060\pi$
$30$	1.28070	+	0.415414i	0.233822	+	0.0758439i
$31$	−0.607115	−	0.178265i	−0.109041	−	0.0320174i	0.226757	−	0.973951i	$-0.427188\pi$
$31$	−0.607115	−	0.178265i	−0.109041	−	0.0320174i	−0.335798	+	0.941934i	$0.609006\pi$
$32$	3.53034	+	5.49332i	0.624082	+	0.971090i
$33$	0.767170	+	0.110302i	0.133547	+	0.0192012i
$34$	−2.67421	+	5.85570i	−0.458623	+	1.00424i
$35$	1.37052	−	1.12181i	0.231660	−	0.189621i
$36$	1.26908	−	8.82666i	0.211514	−	1.47111i
$37$	−3.20008	−	4.97942i	−0.526090	−	0.818612i	0.471922	−	0.881640i	$-0.343560\pi$
$37$	−3.20008	−	4.97942i	−0.526090	−	0.818612i	−0.998012	+	0.0630284i	$0.979924\pi$
$38$	2.83595	−	9.65834i	0.460051	−	1.56679i
$39$	0.149545	+	1.04011i	0.0239464	+	0.166551i
$40$	1.33739	+	5.07762i	0.211461	+	0.802843i
$41$	7.81204	+	5.02049i	1.22004	+	0.784069i	0.982310	−	0.187263i	$-0.0599617\pi$
$41$	7.81204	+	5.02049i	1.22004	+	0.784069i	0.237726	+	0.971332i	$0.423598\pi$
$42$	0.360429	+	0.312313i	0.0556154	+	0.0481910i
$43$	0.636806	+	2.16876i	0.0971120	+	0.330733i	0.993691	−	0.112150i	$-0.0357738\pi$
$43$	0.636806	+	2.16876i	0.0971120	+	0.330733i	−0.896579	+	0.442883i	$0.853956\pi$
$44$	3.65787	+	8.00963i	0.551445	+	1.20750i
$45$	−2.88596	+	5.87719i	−0.430214	+	0.876119i
$46$	9.17391	−	5.64659i	1.35262	−	0.832545i
$47$		−	5.56900i		−	0.812322i	−0.913801	−	0.406161i	$-0.866867\pi$
$47$		−	5.56900i		−	0.812322i	0.913801	−	0.406161i	$-0.133133\pi$
$48$	0.199033	−	0.0908952i	0.0287279	−	0.0131196i
$49$	−6.11451	+	1.79538i	−0.873501	+	0.256483i
$50$	0.629925	−	11.2133i	0.0890848	−	1.58580i
$51$	0.646289	+	0.415345i	0.0904985	+	0.0581599i
$52$	−9.02218	+	7.81776i	−1.25115	+	1.08413i
$53$	2.42492	−	0.348651i	0.333088	−	0.0478909i	0.0262583	−	0.999655i	$-0.491641\pi$
$53$	2.42492	−	0.348651i	0.333088	−	0.0478909i	0.306830	+	0.951764i	$0.400732\pi$
$54$	−3.42487	−	1.00563i	−0.466066	−	0.136849i
$55$	−0.740200	−	6.42272i	−0.0998085	−	0.866039i
$56$	−0.264696	+	1.84100i	−0.0353715	+	0.246014i
$57$	−1.09273	−	0.499034i	−0.144736	−	0.0660986i
$58$	−12.0433	−	5.49998i	−1.58136	−	0.722183i
$59$	−0.362875	+	2.52385i	−0.0472423	+	0.328577i	0.952471	+	0.304629i	$0.0985326\pi$
$59$	−0.362875	+	2.52385i	−0.0472423	+	0.328577i	−0.999713	+	0.0239478i	$0.992376\pi$
$60$	1.81344	−	0.208994i	0.234114	−	0.0269810i
$61$	−12.6025	−	3.70044i	−1.61359	−	0.473793i	−0.654305	−	0.756231i	$-0.727039\pi$
$61$	−12.6025	−	3.70044i	−1.61359	−	0.473793i	−0.959286	+	0.282438i	$0.908857\pi$
$62$	−1.40681	+	0.202269i	−0.178665	+	0.0256881i
$63$	−1.75278	+	1.51879i	−0.220830	+	0.191350i
$64$	10.9658	+	7.04726i	1.37072	+	0.880907i
$65$	8.07229	−	3.41615i	1.00124	−	0.423721i
$66$	1.67042	−	0.490479i	0.205614	−	0.0603738i
$67$	10.4047	−	4.75166i	1.27114	−	0.580508i	0.338377	−	0.941011i	$-0.390122\pi$
$67$	10.4047	−	4.75166i	1.27114	−	0.580508i	0.932758	+	0.360503i	$0.117395\pi$
$68$			8.72794i			1.05842i
$69$	−0.511198	−	1.17957i	−0.0615410	−	0.142004i
$70$	1.75349	−	3.57095i	0.209583	−	0.426810i
$71$	6.24137	+	13.6667i	0.740714	+	1.62194i	0.782377	+	0.622806i	$0.214007\pi$
$71$	6.24137	+	13.6667i	0.740714	+	1.62194i	−0.0416627	+	0.999132i	$0.513265\pi$
$72$	−1.93718	−	6.59742i	−0.228299	−	0.777514i
$73$	−0.336090	−	0.291224i	−0.0393364	−	0.0340852i	0.634971	−	0.772536i	$-0.281012\pi$
$73$	−0.336090	−	0.291224i	−0.0393364	−	0.0340852i	−0.674307	+	0.738451i	$0.735558\pi$
$74$	−11.1848	−	7.18803i	−1.30021	−	0.835591i
$75$	−1.31388	−	0.264856i	−0.151714	−	0.0305829i
$76$	−1.94227	−	13.5088i	−0.222794	−	1.54956i
$77$	0.645199	−	2.19734i	0.0735272	−	0.250411i
$78$	1.27608	+	1.98562i	0.144488	+	0.224828i
$79$	−1.28969	+	8.96996i	−0.145101	+	1.00920i	0.778993	+	0.627033i	$0.215731\pi$
$79$	−1.28969	+	8.96996i	−0.145101	+	1.00920i	−0.924094	+	0.382166i	$0.875178\pi$
$80$	−1.15608	−	1.41238i	−0.129253	−	0.157908i
$81$	3.47222	−	7.60311i	0.385803	−	0.844790i
$82$	20.6463	+	2.96850i	2.28001	+	0.327815i
$83$	−0.0445868	−	0.0693784i	−0.00489404	−	0.00761527i	0.838798	−	0.544443i	$-0.183259\pi$
$83$	−0.0445868	−	0.0693784i	−0.00489404	−	0.00761527i	−0.843692	+	0.536828i	$0.819623\pi$
$84$	0.620415	+	0.182170i	0.0676928	+	0.0198764i
$85$	1.97725	−	6.09574i	0.214463	−	0.661175i
$86$	3.32482	+	3.83704i	0.358524	+	0.413759i
$87$	−0.854230	+	1.32921i	−0.0915831	+	0.142506i
$88$	5.13118	+	4.44619i	0.546986	+	0.473966i
$89$	4.36696	−	1.28225i	0.462897	−	0.135919i	−0.0419648	−	0.999119i	$-0.513362\pi$
$89$	4.36696	−	1.28225i	0.462897	−	0.135919i	0.504862	+	0.863200i	$0.331544\pi$
$90$	−0.412607	+	14.7013i	−0.0434926	+	1.54965i
$91$	3.10487			0.325479
$92$	8.13378	−	12.1308i	0.848005	−	1.26473i
$93$			0.169615i			0.0175883i
$94$	−5.19647	−	11.3787i	−0.535975	−	1.17362i
$95$	−1.70380	+	9.87477i	−0.174806	+	1.01313i
$96$	1.14628	−	1.32288i	0.116992	−	0.135016i
$97$	2.24367	−	3.49121i	0.227810	−	0.354479i	−0.708466	−	0.705745i	$-0.750612\pi$
$97$	2.24367	−	3.49121i	0.227810	−	0.354479i	0.936276	+	0.351266i	$0.114249\pi$
$98$	−10.8180	+	9.37383i	−1.09278	+	0.946900i
$99$	1.20487	+	8.38008i	0.121094	+	0.842230i
$100$	−5.53873	−	14.1841i	−0.553873	−	1.41841i
$101$	−9.59720	+	6.16775i	−0.954957	+	0.613714i	−0.922598	−	0.385762i	$-0.873938\pi$
$101$	−9.59720	+	6.16775i	−0.954957	+	0.613714i	−0.0323593	+	0.999476i	$0.510302\pi$
$102$	1.70807	+	0.245583i	0.169124	+	0.0243164i
$103$	14.9312	+	6.81885i	1.47122	+	0.671881i	0.979971	−	0.199140i	$-0.0638150\pi$
$103$	14.9312	+	6.81885i	1.47122	+	0.671881i	0.491244	+	0.871022i	$0.336542\pi$
$104$	−3.82392	+	8.37321i	−0.374966	+	0.821061i
$105$	−0.392039	−	0.267781i	−0.0382591	−	0.0261327i
$106$	4.62931	−	2.97508i	0.449638	−	0.288965i
$107$	−3.82668	+	13.0325i	−0.369939	+	1.25990i	0.538765	+	0.842456i	$0.318891\pi$
$107$	−3.82668	+	13.0325i	−0.369939	+	1.25990i	−0.908704	+	0.417441i	$0.862927\pi$
$108$	−4.79025	+	0.688734i	−0.460942	+	0.0662735i
$109$	−6.55796	−	7.56829i	−0.628139	−	0.724911i	0.349093	−	0.937088i	$-0.386490\pi$
$109$	−6.55796	−	7.56829i	−0.628139	−	0.724911i	−0.977231	+	0.212178i	$0.931944\pi$
$110$	−7.50547	−	12.4323i	−0.715618	−	1.18538i
$111$	−1.03905	+	1.19913i	−0.0986223	+	0.113816i
$112$	−0.182145	−	0.620329i	−0.0172111	−	0.0586156i
$113$	−16.7132	+	7.63266i	−1.57225	+	0.718021i	−0.995123	−	0.0986369i	$-0.968552\pi$
$113$	−16.7132	+	7.63266i	−1.57225	+	0.718021i	−0.577122	+	0.816658i	$0.695824\pi$
$114$	−2.69834			−0.252723
$115$	−8.42892	+	6.62973i	−0.786001	+	0.618226i
$116$	−17.9506			−1.66667
$117$	−10.4410	+	4.76827i	−0.965275	+	0.440826i
$118$	1.61359	+	5.49537i	0.148543	+	0.505890i
$119$	1.48652	−	1.71553i	0.136269	−	0.157263i
$120$	1.20498	−	0.727454i	0.109999	−	0.0664072i
$121$	1.72894	+	1.99530i	0.157176	+	0.181391i
$122$	−29.2026	+	4.19871i	−2.64388	+	0.380133i
$123$	0.701310	−	2.38844i	0.0632350	−	0.215359i
$124$	−1.62108	+	1.04180i	−0.145577	+	0.0935567i
$125$	0.655055	+	11.1611i	0.0585899	+	0.998282i
$126$	−2.16412	+	4.73875i	−0.192795	+	0.422162i
$127$	−17.6165	−	8.04517i	−1.56321	−	0.713894i	−0.569099	−	0.822269i	$-0.692708\pi$
$127$	−17.6165	−	8.04517i	−1.56321	−	0.713894i	−0.994110	+	0.108376i	$0.965435\pi$
$128$	16.0543	+	2.30827i	1.41902	+	0.204024i
$129$	0.509721	−	0.327578i	0.0448784	−	0.0288416i
$130$	13.3058	−	14.5122i	1.16700	−	1.27281i
$131$	2.42667	+	16.8779i	0.212020	+	1.47463i	0.766399	+	0.642365i	$0.222046\pi$
$131$	2.42667	+	16.8779i	0.212020	+	1.47463i	−0.554380	+	0.832264i	$0.687044\pi$
$132$	1.78386	−	1.54572i	0.155265	−	0.134538i
$133$	−1.91901	+	2.98605i	−0.166400	+	0.258923i
$134$	16.8252	−	19.4174i	1.45348	−	1.67740i
$135$	3.50162	+	0.604172i	0.301371	+	0.0519988i
$136$	2.79568	+	6.12167i	0.239727	+	0.524929i
$137$		−	9.02755i		−	0.771275i	−0.922650	−	0.385638i	$-0.873981\pi$
$137$		−	9.02755i		−	0.771275i	0.922650	−	0.385638i	$-0.126019\pi$
$138$	−2.14516	−	1.93312i	−0.182608	−	0.164558i
$139$	13.0825			1.10965			0.554823	−	0.831968i	$-0.312786\pi$
$139$	13.0825			1.10965			0.554823	+	0.831968i	$0.312786\pi$
$140$	0.151322	−	5.39161i	0.0127890	−	0.455675i
$141$	−1.43237	+	0.420581i	−0.120627	+	0.0354193i
$142$	25.5049	+	22.1001i	2.14033	+	1.85460i
$143$	6.12765	−	9.53481i	0.512420	−	0.797341i
$144$	1.56518	+	1.80631i	0.130432	+	0.150526i
$145$	12.5370	+	4.06656i	1.04114	+	0.337710i
$146$	−0.958448	−	0.281426i	−0.0793218	−	0.0232910i
$147$	0.923558	+	1.43708i	0.0761737	+	0.118529i
$148$	−17.8425	−	2.56537i	−1.46665	−	0.210872i
$149$	2.35760	−	5.16242i	0.193142	−	0.422922i	−0.788141	−	0.615495i	$-0.788956\pi$
$149$	2.35760	−	5.16242i	0.193142	−	0.422922i	0.981283	+	0.192573i	$0.0616833\pi$
$150$	−2.93168	+	0.684832i	−0.239371	+	0.0559163i
$151$	2.39114	−	16.6307i	0.194588	−	1.35339i	−0.625085	−	0.780557i	$-0.714936\pi$
$151$	2.39114	−	16.6307i	0.194588	−	1.35339i	0.819673	−	0.572832i	$-0.194155\pi$
$152$	−5.68933	−	8.85277i	−0.461466	−	0.718055i
$153$	−2.36425	+	8.05190i	−0.191138	+	0.650957i
$154$	−0.732075	−	5.09169i	−0.0589923	−	0.410300i
$155$	1.36820	−	0.360370i	0.109896	−	0.0289456i
$156$	2.69213	+	1.73013i	0.215543	+	0.138521i
$157$	0.663593	+	0.575007i	0.0529605	+	0.0458905i	0.680939	−	0.732340i	$-0.261572\pi$
$157$	0.663593	+	0.575007i	0.0529605	+	0.0458905i	−0.627978	+	0.778231i	$0.716117\pi$
$158$	5.73481	+	19.5310i	0.456237	+	1.55380i
$159$	−0.272809	−	0.597368i	−0.0216351	−	0.0473743i
$160$	−13.1064	−	6.43585i	−1.03616	−	0.508799i
$161$	−3.66484	+	0.999074i	−0.288830	+	0.0787380i
$162$		−	18.7748i		−	1.47508i
$163$	3.68921	−	1.68481i	0.288961	−	0.131964i	−0.265661	−	0.964067i	$-0.585590\pi$
$163$	3.68921	−	1.68481i	0.288961	−	0.131964i	0.554622	+	0.832102i	$0.312863\pi$
$164$	27.1348	−	7.96750i	2.11887	−	0.622157i
$165$	−1.59605	+	0.675438i	−0.124252	+	0.0525828i
$166$	−0.155838	−	0.100151i	−0.0120954	−	0.00777322i
$167$	−1.17735	+	1.02018i	−0.0911058	+	0.0789436i	−0.699223	−	0.714904i	$-0.746471\pi$
$167$	−1.17735	+	1.02018i	−0.0911058	+	0.0789436i	0.608117	+	0.793847i	$0.291925\pi$
$168$	0.493503	−	0.0709551i	0.0380746	−	0.00547430i
$169$	2.27054	+	0.666692i	0.174657	+	0.0512840i
$170$	−1.64802	−	14.2999i	−0.126398	−	1.09675i
$171$	1.86747	−	12.9886i	0.142809	−	0.993261i
$172$	6.26157	+	2.85956i	0.477440	+	0.218040i
$173$	4.10820	+	1.87615i	0.312341	+	0.142641i	0.565417	−	0.824805i	$-0.308715\pi$
$173$	4.10820	+	1.87615i	0.312341	+	0.142641i	−0.253077	+	0.967446i	$0.581442\pi$
$174$	−0.505086	+	3.51295i	−0.0382904	+	0.266316i
$175$	−1.32711	+	3.73131i	−0.100320	+	0.282061i
$176$	−2.26446	−	0.664904i	−0.170690	−	0.0501190i
$177$	0.676549	−	0.0972730i	0.0508525	−	0.00731149i
$178$	7.72616	−	6.69476i	0.579100	−	0.501793i
$179$	−14.6988	−	9.44633i	−1.09864	−	0.706052i	−0.139849	−	0.990173i	$-0.544662\pi$
$179$	−14.6988	−	9.44633i	−1.09864	−	0.706052i	−0.958788	+	0.284121i	$0.908298\pi$
$180$	7.77124	+	18.3633i	0.579234	+	1.36872i
$181$	1.71690	−	0.504127i	0.127616	−	0.0374715i	−0.217301	−	0.976105i	$-0.569725\pi$
$181$	1.71690	−	0.504127i	0.127616	−	0.0374715i	0.344917	+	0.938633i	$0.387907\pi$
$182$	6.34392	−	2.89717i	0.470243	−	0.214753i
$183$			3.52089i			0.260271i
$184$	1.81927	−	11.1138i	0.134118	−	0.819319i
$185$	11.8804	+	5.83378i	0.873461	+	0.428908i
$186$	0.158269	+	0.346561i	0.0116048	+	0.0254111i
$187$	−2.33453	−	7.95069i	−0.170718	−	0.581412i
$188$	−12.8175	−	11.1064i	−0.934811	−	0.810018i
$189$	1.05886	+	0.680488i	0.0770207	+	0.0494982i
$190$	5.73297	+	21.7661i	0.415914	+	1.57908i
$191$	−1.77790	−	12.3655i	−0.128644	−	0.894740i	−0.947275	−	0.320420i	$-0.896176\pi$
$191$	−1.77790	−	12.3655i	−0.128644	−	0.894740i	0.818631	−	0.574319i	$-0.194733\pi$
$192$	0.984428	−	3.35265i	0.0710450	−	0.241957i
$193$	−9.16080	−	14.2545i	−0.659409	−	1.02606i	−0.996418	−	0.0845591i	$-0.973052\pi$
$193$	−9.16080	−	14.2545i	−0.659409	−	1.02606i	0.337010	−	0.941501i	$-0.390585\pi$
$194$	1.32663	−	9.22689i	0.0952462	−	0.662452i
$195$	−1.48828	−	1.81823i	−0.106578	−	0.130206i
$196$	−8.06212	+	17.6536i	−0.575866	+	1.26097i
$197$	22.8780	+	3.28936i	1.62999	+	0.234357i	0.895758	−	0.444541i	$-0.146633\pi$
$197$	22.8780	+	3.28936i	1.62999	+	0.234357i	0.734232	+	0.678898i	$0.237542\pi$
$198$	10.2813	+	15.9980i	0.730662	+	1.13693i
$199$	−6.39048	−	1.87641i	−0.453009	−	0.133015i	0.0472654	−	0.998882i	$-0.484949\pi$
$199$	−6.39048	−	1.87641i	−0.453009	−	0.133015i	−0.500274	+	0.865867i	$0.666768\pi$
$200$	−8.42814	−	8.17440i	−0.595960	−	0.578017i
$201$	−2.00793	−	2.31727i	−0.141628	−	0.163448i
$202$	−13.8540	+	21.5573i	−0.974764	+	1.51676i
$203$	3.52830	+	3.05729i	0.247638	+	0.214580i
$204$	2.24486	−	0.659150i	0.157172	−	0.0461497i
$205$	−20.7564	−	0.582550i	−1.44969	−	0.0406871i
$206$	36.8704			2.56888
$207$	10.7898	−	8.98792i	0.749943	−	0.624703i
$208$		−	3.19970i		−	0.221859i
$209$	5.38262	+	11.7863i	0.372323	+	0.815274i
$210$	−1.05089	−	0.181321i	−0.0725182	−	0.0125123i
$211$	−6.26888	+	7.23467i	−0.431568	+	0.498056i	−0.929326	−	0.369260i	$-0.879611\pi$
$211$	−6.26888	+	7.23467i	−0.431568	+	0.498056i	0.497758	+	0.867316i	$0.334157\pi$
$212$	4.03364	−	6.27646i	0.277031	−	0.431069i
$213$	3.04376	−	2.63744i	0.208555	−	0.180714i
$214$	4.34194	+	30.1989i	0.296809	+	2.06435i
$215$	−3.72537	−	3.41568i	−0.254068	−	0.232947i
$216$	−3.13922	+	2.01745i	−0.213597	+	0.137270i
$217$	0.496071	+	0.0713242i	0.0336755	+	0.00484180i
$218$	−20.4613	−	9.34438i	−1.38582	−	0.632882i
$219$	−0.0495217	+	0.108437i	−0.00334637	+	0.00732753i
$220$	−16.2586	−	11.1054i	−1.09615	−	0.748724i
$221$	9.45099	−	6.07378i	0.635742	−	0.408567i
$222$	−1.00409	+	3.41962i	−0.0673902	+	0.229510i
$223$	2.76264	−	0.397208i	0.185000	−	0.0265990i	−0.0491921	−	0.998789i	$-0.515665\pi$
$223$	2.76264	−	0.397208i	0.185000	−	0.0265990i	0.234192	+	0.972190i	$0.424756\pi$
$224$	−3.38699	−	3.90880i	−0.226303	−	0.261167i
$225$	−1.26750	−	14.5857i	−0.0845000	−	0.972383i
$226$	−27.0266	+	31.1904i	−1.79778	+	2.07475i
$227$	−6.95544	−	23.6881i	−0.461649	−	1.57223i	−0.780959	−	0.624582i	$-0.785269\pi$
$227$	−6.95544	−	23.6881i	−0.461649	−	1.57223i	0.319310	−	0.947650i	$-0.396549\pi$
$228$	−3.32783	+	1.51977i	−0.220391	+	0.100649i
$229$	1.98905			0.131440			0.0657200	−	0.997838i	$-0.479066\pi$
$229$	1.98905			0.131440			0.0657200	+	0.997838i	$0.479066\pi$
$230$	−11.0359	+	21.4111i	−0.727683	+	1.41180i
$231$	−0.613892			−0.0403911
$232$	−12.5903	+	5.74980i	−0.826595	+	0.377493i
$233$	−1.31976	−	4.49469i	−0.0864603	−	0.294457i	0.904900	−	0.425625i	$-0.139946\pi$
$233$	−1.31976	−	4.49469i	−0.0864603	−	0.294457i	−0.991360	+	0.131168i	$0.958127\pi$
$234$	−16.8840	+	19.4852i	−1.10374	+	1.27379i
$235$	6.43587	+	10.6606i	0.419830	+	0.695421i
$236$	5.08514	+	5.86857i	0.331015	+	0.382011i
$237$	2.40451	−	0.345716i	0.156189	−	0.0224567i
$238$	1.43651	−	4.89229i	0.0931148	−	0.317120i
$239$	2.03622	−	1.30860i	0.131712	−	0.0846461i	−0.473126	−	0.880995i	$-0.656874\pi$
$239$	2.03622	−	1.30860i	0.131712	−	0.0846461i	0.604838	+	0.796349i	$0.293238\pi$
$240$	−0.275959	+	0.404012i	−0.0178131	+	0.0260789i
$241$	9.16531	−	20.0692i	0.590389	−	1.29277i	−0.344817	−	0.938670i	$-0.612059\pi$
$241$	9.16531	−	20.0692i	0.590389	−	1.29277i	0.935207	−	0.354103i	$-0.115214\pi$
$242$	5.39441	+	2.46355i	0.346766	+	0.158363i
$243$	−6.93659	−	0.997330i	−0.444982	−	0.0639788i
$244$	−33.6504	+	21.6258i	−2.15425	+	1.38445i
$245$	9.63000	−	10.5031i	0.615238	−	0.671021i
$246$	−0.795741	−	5.53450i	−0.0507346	−	0.352867i
$247$	−13.2763	+	11.5040i	−0.844749	+	0.731979i
$248$	−0.803301	+	1.24996i	−0.0510097	+	0.0793726i
$249$	−0.0144771	+	0.0167075i	−0.000917450	+	0.00105879i
$250$	11.7529	+	22.1934i	0.743321	+	1.40363i
$251$	−11.1328	−	24.3775i	−0.702698	−	1.53869i	−0.836669	−	0.547709i	$-0.815500\pi$
$251$	−11.1328	−	24.3775i	−0.702698	−	1.53869i	0.133971	−	0.990985i	$-0.457227\pi$
$252$			7.06313i			0.444935i
$253$	−4.16471	+	13.2262i	−0.261833	+	0.831522i
$254$	−43.5013			−2.72951
$255$	−1.71717	−	0.0481943i	−0.107533	−	0.00301805i
$256$	9.94235	−	2.91934i	0.621397	−	0.182459i
$257$	1.46876	+	1.27269i	0.0916190	+	0.0793883i	0.699466	−	0.714666i	$-0.253421\pi$
$257$	1.46876	+	1.27269i	0.0916190	+	0.0793883i	−0.607847	+	0.794054i	$0.707967\pi$
$258$	0.735806	−	1.14494i	0.0458093	−	0.0712806i
$259$	3.07014	+	3.54313i	0.190769	+	0.220160i
$260$	8.23627	−	25.3919i	0.510792	−	1.57474i
$261$	−16.5602	−	4.86250i	−1.02505	−	0.300981i
$262$	20.7071	+	32.2209i	1.27929	+	1.99061i
$263$	0.419498	+	0.0603146i	0.0258673	+	0.00371916i	0.155236	−	0.987877i	$-0.450386\pi$
$263$	0.419498	+	0.0603146i	0.0258673	+	0.00371916i	−0.129369	+	0.991597i	$0.541295\pi$
$264$	0.756061	−	1.65554i	0.0465324	−	0.101892i
$265$	−4.23904	+	3.46980i	−0.260402	+	0.213148i
$266$	−1.13467	+	7.89178i	−0.0695709	+	0.483876i
$267$	−0.659602	−	1.02636i	−0.0403670	−	0.0628122i
$268$	9.81404	−	33.4236i	0.599488	−	2.04167i
$269$	1.68631	+	11.7286i	0.102816	+	0.715103i	0.974394	+	0.224846i	$0.0721880\pi$
$269$	1.68631	+	11.7286i	0.102816	+	0.715103i	−0.871578	+	0.490257i	$0.836903\pi$
$270$	7.71833	−	2.03293i	0.469722	−	0.123720i
$271$	0.609951	+	0.391992i	0.0370519	+	0.0238118i	0.559036	−	0.829144i	$-0.311171\pi$
$271$	0.609951	+	0.391992i	0.0370519	+	0.0238118i	−0.521984	+	0.852955i	$0.674808\pi$
$272$	−1.76793	−	1.53192i	−0.107197	−	0.0928863i
$273$	−0.234486	−	0.798584i	−0.0141917	−	0.0483325i
$274$	−8.42366	−	18.4452i	−0.508892	−	1.11432i
$275$	8.83942	+	11.4394i	0.533037	+	0.689824i
$276$	−3.73438	−	1.17590i	−0.224783	−	0.0707806i
$277$			10.7833i			0.647905i	0.946073	+	0.323952i	$0.105012\pi$
$277$			10.7833i			0.647905i	−0.946073	+	0.323952i	$0.894988\pi$
$278$	26.7305	−	12.2074i	1.60319	−	0.732151i
$279$	−1.77772	+	0.521986i	−0.106429	+	0.0312505i
$280$	−1.62087	−	3.83009i	−0.0968656	−	0.228891i
$281$	10.9427	+	7.03247i	0.652789	+	0.419522i	0.824684	−	0.565593i	$-0.191353\pi$
$281$	10.9427	+	7.03247i	0.652789	+	0.419522i	−0.171896	+	0.985115i	$0.554989\pi$
$282$	−2.53419	+	2.19589i	−0.150909	+	0.130763i
$283$	27.3313	−	3.92965i	1.62468	−	0.233593i	0.731024	−	0.682351i	$-0.239043\pi$
$283$	27.3313	−	3.92965i	1.62468	−	0.233593i	0.893653	+	0.448758i	$0.148134\pi$
$284$	43.9022	+	12.8909i	2.60512	+	0.764932i
$285$	2.66850	−	0.307537i	0.158068	−	0.0182169i
$286$	3.62313	−	25.1994i	0.214240	−	1.49007i
$287$	−6.69053	−	3.05546i	−0.394930	−	0.180358i
$288$	17.3926	+	7.94296i	1.02487	+	0.468043i
$289$	−1.25045	+	8.69706i	−0.0735558	+	0.511592i
$290$	29.4103	−	3.38945i	1.72703	−	0.199035i
$291$	−1.06740	−	0.313417i	−0.0625721	−	0.0183728i
$292$	−1.34055	+	0.192742i	−0.0784497	+	0.0112794i
$293$	−13.2886	+	11.5147i	−0.776330	+	0.672694i	−0.950049	−	0.312102i	$-0.898967\pi$
$293$	−13.2886	+	11.5147i	−0.776330	+	0.672694i	0.173719	+	0.984795i	$0.444422\pi$
$294$	3.22798	+	2.07450i	0.188260	+	0.120987i
$295$	−2.22207	−	5.25070i	−0.129374	−	0.305708i
$296$	−13.3363	+	3.91588i	−0.775155	+	0.227606i
$297$	4.17945	−	1.90869i	0.242516	−	0.110753i
$298$		−	12.7478i		−	0.738462i
$299$	−18.7961	−	0.365745i	−1.08701	−	0.0211516i
$300$	−3.22990	+	2.49579i	−0.186478	+	0.144094i
$301$	−0.743720	−	1.62852i	−0.0428673	−	0.0938664i
$302$	−10.6326	−	36.2113i	−0.611838	−	2.08373i
$303$	2.31117	+	2.00264i	0.132773	+	0.115048i
$304$	3.07724	+	1.97763i	0.176492	+	0.113425i
$305$	28.4012	−	7.48059i	1.62625	−	0.428337i
$306$	2.68260	+	18.6579i	0.153354	+	1.06660i
$307$	−6.76680	+	23.0456i	−0.386201	+	1.31528i	0.505566	+	0.862788i	$0.331284\pi$
$307$	−6.76680	+	23.0456i	−0.386201	+	1.31528i	−0.891768	+	0.452493i	$0.850535\pi$
$308$	−3.77062	−	5.86720i	−0.214851	−	0.334315i
$309$	0.626203	−	4.35533i	0.0356234	−	0.247766i
$310$	2.45927	−	2.01299i	0.139677	−	0.114330i
$311$	3.57535	−	7.82892i	0.202739	−	0.443937i	−0.780764	−	0.624826i	$-0.785170\pi$
$311$	3.57535	−	7.82892i	0.202739	−	0.443937i	0.983504	+	0.180889i	$0.0578973\pi$
$312$	2.44241	+	0.351166i	0.138274	+	0.0198808i
$313$	−16.4583	−	25.6096i	−0.930278	−	1.44754i	−0.893933	−	0.448201i	$-0.852065\pi$
$313$	−16.4583	−	25.6096i	−0.930278	−	1.44754i	−0.0363450	−	0.999339i	$-0.511572\pi$
$314$	1.89241	+	0.555661i	0.106795	+	0.0313577i
$315$	1.60010	−	4.93301i	0.0901553	−	0.277943i
$316$	18.0730	+	20.8573i	1.01668	+	1.17332i
$317$	−3.54566	+	5.51716i	−0.199144	+	0.309875i	−0.926435	−	0.376455i	$-0.877143\pi$
$317$	−3.54566	+	5.51716i	−0.199144	+	0.309875i	0.727291	+	0.686330i	$0.240779\pi$
$318$	−1.11481	−	0.965992i	−0.0625157	−	0.0541702i
$319$	16.3520	−	4.80139i	0.915537	−	0.268826i
$320$	−29.1357	−	0.817725i	−1.62874	−	0.0457122i
$321$	3.64100			0.203221
$322$	−6.55582	+	5.46101i	−0.365342	+	0.304330i
$323$			12.8433i			0.714620i
$324$	−10.5744	−	23.1547i	−0.587466	−	1.28637i
$325$	−11.5047	+	15.8683i	−0.638165	+	0.880213i
$326$	5.96575	−	6.88485i	0.330413	−	0.381316i
$327$	−1.45132	+	2.25830i	−0.0802584	+	0.124884i
$328$	16.4799	−	14.2800i	0.909953	−	0.788478i
$329$	0.627747	+	4.36608i	0.0346088	+	0.240710i
$330$	−2.63081	+	2.86935i	−0.144822	+	0.157952i
$331$	8.70657	−	5.59537i	0.478556	−	0.307549i	−0.279032	−	0.960282i	$-0.590014\pi$
$331$	8.70657	−	5.59537i	0.478556	−	0.307549i	0.757589	+	0.652732i	$0.226377\pi$
$332$	−0.248600	−	0.0357433i	−0.0136437	−	0.00196167i
$333$	−15.7656	−	7.19990i	−0.863949	−	0.394552i
$334$	−1.45364	+	3.18303i	−0.0795397	+	0.174168i
$335$	−14.4261	+	21.1203i	−0.788184	+	1.15392i
$336$	−0.145795	+	0.0936968i	−0.00795377	+	0.00511158i
$337$	−3.54128	+	12.0605i	−0.192906	+	0.656977i	0.805058	+	0.593196i	$0.202134\pi$
$337$	−3.54128	+	12.0605i	−0.192906	+	0.656977i	−0.997964	+	0.0637812i	$0.979684\pi$
$338$	5.26131	−	0.756462i	0.286177	−	0.0411461i
$339$	3.22536	+	3.72227i	0.175178	+	0.202166i
$340$	−10.0865	−	16.7077i	−0.547019	−	0.906101i
$341$	1.19806	−	1.38263i	0.0648784	−	0.0748737i
$342$	−8.30405	−	28.2810i	−0.449032	−	1.52926i
$343$	9.63475	−	4.40004i	0.520227	−	0.237580i
$344$	5.30775			0.286175
$345$	2.34176	+	1.66726i	0.126076	+	0.0897622i
$346$	10.1446			0.545377
$347$	−12.4931	+	5.70542i	−0.670666	+	0.306283i	−0.721490	−	0.692425i	$-0.756542\pi$
$347$	−12.4931	+	5.70542i	−0.670666	+	0.306283i	0.0508241	+	0.998708i	$0.483815\pi$
$348$	1.35566	+	4.61695i	0.0726710	+	0.247495i
$349$	−13.3245	+	15.3773i	−0.713245	+	0.823128i	−0.990478	−	0.137674i	$-0.956037\pi$
$349$	−13.3245	+	15.3773i	−0.713245	+	0.823128i	0.277233	+	0.960803i	$0.410583\pi$
$350$	0.770126	+	8.86222i	0.0411650	+	0.473706i
$351$	4.07933	+	4.70780i	0.217739	+	0.251284i
$352$	−18.6880	+	2.68693i	−0.996076	+	0.143214i
$353$	9.22791	−	31.4274i	0.491152	−	1.67271i	−0.224675	−	0.974434i	$-0.572132\pi$
$353$	9.22791	−	31.4274i	0.491152	−	1.67271i	0.715827	−	0.698277i	$-0.246050\pi$
$354$	1.29157	−	0.830041i	0.0686462	−	0.0441162i
$355$	−27.7417	−	18.9489i	−1.47238	−	1.00570i
$356$	5.75794	−	12.6081i	0.305170	−	0.668229i
$357$	−0.553507	−	0.252778i	−0.0292947	−	0.0133784i
$358$	−38.8472	−	5.58538i	−2.05314	−	0.295197i
$359$	−8.51582	+	5.47279i	−0.449448	+	0.288843i	−0.745718	−	0.666262i	$-0.767893\pi$
$359$	−8.51582	+	5.47279i	−0.449448	+	0.288843i	0.296270	+	0.955104i	$0.404257\pi$
$360$	11.3327	+	10.3906i	0.597284	+	0.547631i
$361$	−0.154099	−	1.07178i	−0.00811046	−	0.0564095i
$362$	3.03760	−	2.63209i	0.159652	−	0.138340i
$363$	0.382626	−	0.595377i	0.0200826	−	0.0312492i
$364$	6.19213	−	7.14610i	0.324556	−	0.374557i
$365$	0.979925	+	0.169077i	0.0512916	+	0.00884989i
$366$	3.28536	+	7.19393i	0.171729	+	0.376033i
$367$			13.3955i			0.699242i	0.936891	+	0.349621i	$0.113690\pi$
$367$			13.3955i			0.699242i	−0.936891	+	0.349621i	$0.886310\pi$
$368$	1.02959	+	3.77677i	0.0536709	+	0.196878i
$369$	27.1913			1.41552
$370$	29.7177	+	0.834059i	1.54495	+	0.0433607i
$371$	−1.86183	+	0.546682i	−0.0966613	+	0.0283823i
$372$	0.390382	+	0.338268i	0.0202404	+	0.0175384i
$373$	−10.3509	+	16.1063i	−0.535948	+	0.833952i	−0.998617	−	0.0525794i	$-0.983256\pi$
$373$	−10.3509	+	16.1063i	−0.535948	+	0.833952i	0.462668	+	0.886531i	$0.346892\pi$
$374$	−12.1888	−	14.0666i	−0.630268	−	0.727368i
$375$	2.82121	−	1.01139i	0.145687	−	0.0522281i
$376$	−12.5476	−	3.68430i	−0.647091	−	0.190003i
$377$	12.4918	+	19.4376i	0.643361	+	1.00109i
$378$	2.79845	+	0.402356i	0.143937	+	0.0206950i
$379$	6.49348	−	14.2187i	0.333548	−	0.730368i	−0.666335	−	0.745652i	$-0.732138\pi$
$379$	6.49348	−	14.2187i	0.333548	−	0.730368i	0.999883	+	0.0152844i	$0.00486536\pi$
$380$	19.3296	+	23.6149i	0.991588	+	1.21142i
$381$	−0.738820	+	5.13861i	−0.0378509	+	0.263259i
$382$	−15.1710	−	23.6065i	−0.776216	−	1.20782i
$383$	−4.59981	+	15.6655i	−0.235039	+	0.800471i	0.754512	+	0.656287i	$0.227874\pi$
$383$	−4.59981	+	15.6655i	−0.235039	+	0.800471i	−0.989551	+	0.144184i	$0.953944\pi$
$384$	−0.618759	−	4.30356i	−0.0315759	−	0.219615i
$385$	1.30429	+	4.95195i	0.0664730	+	0.252375i
$386$	−32.0184	−	20.5770i	−1.62970	−	1.04734i
$387$	5.00196	+	4.33422i	0.254264	+	0.220321i
$388$	−3.56069	−	12.1266i	−0.180767	−	0.615634i
$389$	−6.17050	−	13.5115i	−0.312857	−	0.685061i	0.686248	−	0.727368i	$-0.259257\pi$
$389$	−6.17050	−	13.5115i	−0.312857	−	0.685061i	−0.999105	+	0.0423069i	$0.986529\pi$
$390$	−4.73748	−	2.32632i	−0.239892	−	0.117798i
$391$	−9.20110	+	10.2103i	−0.465320	+	0.516357i
$392$			14.9644i			0.755817i
$393$	4.15779	−	1.89880i	0.209733	−	0.0957818i
$394$	49.8141	−	14.6267i	2.50960	−	0.736884i
$395$	−7.89740	−	18.6614i	−0.397361	−	0.938957i
$396$	21.6903	+	13.9395i	1.08998	+	0.700487i
$397$	25.5734	−	22.1595i	1.28349	−	1.11215i	0.295881	−	0.955225i	$-0.404387\pi$
$397$	25.5734	−	22.1595i	1.28349	−	1.11215i	0.987610	−	0.156927i	$-0.0501587\pi$
$398$	−14.8080	+	2.12907i	−0.742259	+	0.106721i
$399$	0.912950	+	0.268066i	0.0457047	+	0.0134201i
$400$	3.84527	+	1.36765i	0.192264	+	0.0683824i
$401$	−4.25808	+	29.6156i	−0.212638	+	1.47893i	0.551661	+	0.834069i	$0.313994\pi$
$401$	−4.25808	+	29.6156i	−0.212638	+	1.47893i	−0.764299	+	0.644862i	$0.776915\pi$
$402$	−6.26489	−	2.86108i	−0.312464	−	0.142698i
$403$	2.25622	+	1.03038i	0.112390	+	0.0513269i
$404$	−4.94442	+	34.3892i	−0.245994	+	1.71093i
$405$	2.13981	+	18.5672i	0.106328	+	0.922610i
$406$	10.0619	+	2.95443i	0.499362	+	0.146626i
$407$	16.9398	−	2.43557i	0.839674	−	0.120727i
$408$	1.36338	−	1.18138i	0.0674975	−	0.0584869i
$409$	10.6120	+	6.81994i	0.524731	+	0.337224i	0.776041	−	0.630682i	$-0.217225\pi$
$409$	10.6120	+	6.81994i	0.524731	+	0.337224i	−0.251310	+	0.967907i	$0.580861\pi$
$410$	−42.9534	+	18.1776i	−2.12131	+	0.897729i
$411$	−2.32192	+	0.681777i	−0.114532	+	0.0336296i
$412$	45.4718	−	20.7663i	2.24024	−	1.02308i
$413$		−	2.01959i		−	0.0993777i
$414$	13.6592	−	28.4323i	0.671314	−	1.39737i
$415$	0.165529	+	0.0812823i	0.00812551	+	0.00398999i
$416$	−10.6335	−	23.2841i	−0.521350	−	1.14160i
$417$	−0.988017	−	3.36488i	−0.0483834	−	0.164779i
$418$	21.9957	+	19.0594i	1.07585	+	0.932225i
$419$	−17.0313	−	10.9454i	−0.832034	−	0.534716i	0.0538897	−	0.998547i	$-0.482838\pi$
$419$	−17.0313	−	10.9454i	−0.832034	−	0.534716i	−0.885924	+	0.463831i	$0.846474\pi$
$420$	−1.39817	+	0.368264i	−0.0682238	+	0.0179695i
$421$	0.588468	+	4.09288i	0.0286802	+	0.199475i	0.999124	−	0.0418531i	$-0.0133261\pi$
$421$	0.588468	+	4.09288i	0.0286802	+	0.199475i	−0.970444	+	0.241328i	$0.922417\pi$
$422$	−6.05797	+	20.6315i	−0.294897	+	1.00433i
$423$	−8.81614	−	13.7182i	−0.428655	−	0.667001i
$424$	0.818712	−	5.69426i	0.0397602	−	0.276538i
$425$	3.25960	+	13.9539i	0.158114	+	0.676866i
$426$	3.75806	−	8.22901i	0.182079	−	0.398697i
$427$	10.2975	+	1.48055i	0.498330	+	0.0716490i
$428$	22.3636	+	34.7984i	1.08098	+	1.68205i
$429$	−2.91516	−	0.855968i	−0.140745	−	0.0413265i
$430$	−10.7989	−	3.50280i	−0.520771	−	0.168920i
$431$	−10.1470	−	11.7103i	−0.488765	−	0.564065i	0.456770	−	0.889585i	$-0.349006\pi$
$431$	−10.1470	−	11.7103i	−0.488765	−	0.564065i	−0.945535	+	0.325520i	$0.894461\pi$
$432$	0.701271	−	1.09120i	0.0337399	−	0.0525004i
$433$	13.5801	+	11.7672i	0.652616	+	0.565495i	0.916982	−	0.398928i	$-0.130618\pi$
$433$	13.5801	+	11.7672i	0.652616	+	0.565495i	−0.264367	+	0.964422i	$0.585163\pi$
$434$	1.08013	−	0.317156i	0.0518481	−	0.0152240i
$435$	0.0991202	−	3.53167i	0.00475245	−	0.169331i
$436$	−30.4977			−1.46058
$437$	11.9690	−	17.8507i	0.572554	−	0.853915i
$438$			0.267770i			0.0127946i
$439$	−0.378300	−	0.828362i	−0.0180553	−	0.0395356i	0.900390	−	0.435085i	$-0.143282\pi$
$439$	−0.378300	−	0.828362i	−0.0180553	−	0.0395356i	−0.918445	+	0.395549i	$0.870554\pi$
$440$	−14.9608	−	2.58134i	−0.713227	−	0.123061i
$441$	−12.2197	+	14.1023i	−0.581891	+	0.671538i
$442$	13.6429	−	21.2288i	0.648928	−	1.00975i
$443$	−0.415788	+	0.360282i	−0.0197547	+	0.0171175i	−0.664682	−	0.747126i	$-0.731433\pi$
$443$	−0.415788	+	0.360282i	−0.0197547	+	0.0171175i	0.644927	+	0.764244i	$0.276888\pi$
$444$	0.687678	+	4.78291i	0.0326358	+	0.226987i
$445$	−6.87771	+	7.50131i	−0.326035	+	0.355596i
$446$	5.27403	−	3.38942i	0.249733	−	0.160493i
$447$	−1.50584	−	0.216508i	−0.0712240	−	0.0102405i
$448$	−9.39149	−	4.28895i	−0.443706	−	0.202634i
$449$	2.09483	−	4.58703i	0.0988609	−	0.216475i	−0.853739	−	0.520701i	$-0.825671\pi$
$449$	2.09483	−	4.58703i	0.0988609	−	0.216475i	0.952600	+	0.304226i	$0.0983978\pi$
$450$	−16.1998	−	28.6191i	−0.763667	−	1.34912i
$451$	−22.5873	+	14.5159i	−1.06359	+	0.683529i
$452$	−15.7644	+	53.6887i	−0.741497	+	2.52531i
$453$	−4.45807	+	0.640973i	−0.209458	+	0.0301155i
$454$	−36.3149	−	41.9097i	−1.70434	−	1.96692i
$455$	−5.94358	+	3.58817i	−0.278639	+	0.168216i
$456$	−1.84730	+	2.13190i	−0.0865076	+	0.0998351i
$457$	1.12144	+	3.81927i	0.0524588	+	0.178658i	0.981555	−	0.191180i	$-0.0612314\pi$
$457$	1.12144	+	3.81927i	0.0524588	+	0.178658i	−0.929096	+	0.369838i	$0.879413\pi$
$458$	4.06406	−	1.85599i	0.189901	−	0.0867249i
$459$	4.55427			0.212575
$460$	−1.55118	+	32.6217i	−0.0723242	+	1.52099i
$461$	6.72233			0.313090			0.156545	−	0.987671i	$-0.449964\pi$
$461$	6.72233			0.313090			0.156545	+	0.987671i	$0.449964\pi$
$462$	−1.25431	+	0.572826i	−0.0583560	+	0.0266503i
$463$	2.92591	+	9.96473i	0.135978	+	0.463100i	0.999124	−	0.0418556i	$-0.0133270\pi$
$463$	2.92591	+	9.96473i	0.135978	+	0.463100i	−0.863145	+	0.504956i	$0.831509\pi$
$464$	3.15067	−	3.63606i	0.146266	−	0.168800i
$465$	−0.196017	−	0.324690i	−0.00909009	−	0.0150572i
$466$	−6.89058	−	7.95215i	−0.319200	−	0.368376i
$467$	0.845513	−	0.121566i	0.0391257	−	0.00562542i	−0.122724	−	0.992441i	$-0.539163\pi$
$467$	0.845513	−	0.121566i	0.0391257	−	0.00562542i	0.161850	+	0.986815i	$0.448254\pi$
$468$	−9.84833	+	33.5403i	−0.455239	+	1.55040i
$469$	−7.62163	+	4.89812i	−0.351934	+	0.226174i
$470$	23.0974	+	15.7766i	1.06540	+	0.727719i
$471$	0.0977781	−	0.214104i	0.00450538	−	0.00986540i
$472$	5.44644	+	2.48731i	0.250693	+	0.114488i
$473$	−6.46883	−	0.930078i	−0.297437	−	0.0427650i
$474$	4.59034	−	2.95003i	0.210841	−	0.135499i
$475$	−8.15033	−	20.8720i	−0.373963	−	0.957675i
$476$	−0.983828	−	6.84267i	−0.0450937	−	0.313633i
$477$	5.42139	−	4.69766i	0.248228	−	0.215091i
$478$	2.93937	−	4.57375i	0.134444	−	0.209199i
$479$	11.1602	−	12.8795i	0.509922	−	0.588481i	−0.441157	−	0.897430i	$-0.645432\pi$
$479$	11.1602	−	12.8795i	0.509922	−	0.588481i	0.951079	+	0.308949i	$0.0999772\pi$
$480$	−0.665502	+	3.85707i	−0.0303759	+	0.176051i
$481$	9.63874	+	21.1059i	0.439489	+	0.962346i
$482$		−	49.5580i		−	2.25730i
$483$	0.533741	+	0.867159i	0.0242861	+	0.0394571i
$484$	8.04039			0.365472
$485$	−0.260343	+	9.27606i	−0.0118216	+	0.421204i
$486$	−15.1036	+	4.43481i	−0.685112	+	0.201167i
$487$	15.4338	+	13.3734i	0.699371	+	0.606008i	0.930229	−	0.366979i	$-0.119608\pi$
$487$	15.4338	+	13.3734i	0.699371	+	0.606008i	−0.230858	+	0.972987i	$0.574153\pi$
$488$	−16.6750	+	25.9468i	−0.754841	+	1.17456i
$489$	−0.711954	−	0.821639i	−0.0321957	−	0.0371558i
$490$	9.87564	−	30.4460i	0.446136	−	1.37541i
$491$	17.0396	+	5.00327i	0.768985	+	0.225794i	0.642616	−	0.766189i	$-0.277849\pi$
$491$	17.0396	+	5.00327i	0.768985	+	0.225794i	0.126370	+	0.991983i	$0.459667\pi$
$492$	−4.09854	−	6.37745i	−0.184776	−	0.287518i
$493$	16.7206	+	2.40406i	0.753058	+	0.108273i
$494$	−16.3919	+	35.8932i	−0.737506	+	1.61491i
$495$	−11.9910	−	14.6494i	−0.538954	−	0.658440i
$496$	0.0735026	−	0.511222i	0.00330036	−	0.0229545i
$497$	−6.43374	−	10.0111i	−0.288593	−	0.449059i
$498$	−0.0139900	+	0.0476457i	−0.000626909	+	0.00213505i
$499$	0.842957	+	5.86290i	0.0377359	+	0.262459i	0.999952	−	0.00982891i	$-0.00312869\pi$
$499$	0.842957	+	5.86290i	0.0377359	+	0.262459i	−0.962216	+	0.272288i	$0.912220\pi$
$500$	26.9946	+	20.7513i	1.20723	+	0.928026i
$501$	0.351308	+	0.225772i	0.0156953	+	0.0100868i
$502$	−45.4936	−	39.4204i	−2.03048	−	1.75942i
$503$	−1.55438	−	5.29373i	−0.0693064	−	0.236036i	0.917554	−	0.397611i	$-0.130161\pi$
$503$	−1.55438	−	5.29373i	−0.0693064	−	0.236036i	−0.986860	+	0.161575i	$0.948343\pi$
$504$	2.26241	+	4.95400i	0.100776	+	0.220669i
$505$	11.2439	−	22.8979i	0.500346	−	1.01894i
$506$	3.83201	+	30.9100i	0.170354	+	1.37412i
$507$		−	0.634342i		−	0.0281721i
$508$	−53.6496	+	24.5009i	−2.38031	+	1.08705i
$509$	−1.32916	+	0.390276i	−0.0589139	+	0.0172987i	−0.311057	−	0.950391i	$-0.600683\pi$
$509$	−1.32916	+	0.390276i	−0.0589139	+	0.0172987i	0.252143	+	0.967690i	$0.418865\pi$
$510$	−3.55353	+	1.50383i	−0.157353	+	0.0665908i
$511$	0.296321	+	0.190434i	0.0131085	+	0.00842430i
$512$	−6.92533	+	6.00083i	−0.306059	+	0.265202i
$513$	−7.04893	+	1.01348i	−0.311218	+	0.0447464i
$514$	4.18856	+	1.22987i	0.184749	+	0.0542473i
$515$	−36.4627	+	4.20222i	−1.60674	+	0.185172i
$516$	0.262605	−	1.82646i	0.0115605	−	0.0804054i
$517$	14.6468	+	6.68896i	0.644165	+	0.294180i
$518$	9.57908	+	4.37462i	0.420881	+	0.192210i
$519$	0.172295	−	1.19833i	0.00756289	−	0.0526011i
$520$	−2.35655	−	20.4478i	−0.103341	−	0.896695i
$521$	21.0426	+	6.17866i	0.921892	+	0.270692i	0.708039	−	0.706174i	$-0.249580\pi$
$521$	21.0426	+	6.17866i	0.921892	+	0.270692i	0.213854	+	0.976866i	$0.431398\pi$
$522$	−38.3732	+	5.51724i	−1.67955	+	0.241483i
$523$	10.7879	−	9.34773i	0.471720	−	0.408748i	−0.386293	−	0.922376i	$-0.626244\pi$
$523$	10.7879	−	9.34773i	0.471720	−	0.408748i	0.858013	+	0.513629i	$0.171699\pi$
$524$	43.6853	+	28.0749i	1.90840	+	1.22646i
$525$	1.05993	+	0.0595433i	0.0462593	+	0.00259868i
$526$	0.913404	−	0.268200i	0.0398263	−	0.0116941i
$527$	1.64953	−	0.753314i	0.0718545	−	0.0328149i
$528$			0.632641i			0.0275322i
$529$	22.3037	−	5.61643i	0.969727	−	0.244193i
$530$	−5.42360	+	11.0450i	−0.235586	+	0.479765i
$531$	3.10157	+	6.79148i	0.134597	+	0.294725i
$532$	3.04547	+	10.3719i	0.132038	+	0.449679i
$533$	−27.5107	−	23.8381i	−1.19162	−	1.03254i
$534$	−2.30541	−	1.48160i	−0.0997649	−	0.0641150i
$535$	−7.73578	−	29.3701i	−0.334447	−	1.26978i
$536$	−3.82256	−	26.5865i	−0.165109	−	1.14836i
$537$	−1.31955	+	4.49398i	−0.0569429	+	0.193930i
$538$	14.3895	+	22.3905i	0.620375	+	0.965323i
$539$	2.62222	−	18.2379i	0.112947	−	0.785563i
$540$	8.37392	−	6.85433i	0.360356	−	0.294963i
$541$	6.00206	−	13.1427i	0.258049	−	0.565048i	−0.735620	−	0.677394i	$-0.763109\pi$
$541$	6.00206	−	13.1427i	0.258049	−	0.565048i	0.993669	+	0.112346i	$0.0358365\pi$
$542$	1.61203	+	0.231775i	0.0692427	+	0.00995559i
$543$	−0.259327	−	0.403521i	−0.0111288	−	0.0173167i
$544$	−17.9562	−	5.27241i	−0.769864	−	0.226053i
$545$	21.3001	+	6.90902i	0.912396	+	0.295950i
$546$	−1.22427	−	1.41288i	−0.0523939	−	0.0604657i
$547$	−11.2770	+	17.5474i	−0.482171	+	0.750273i	−0.994066	−	0.108775i	$-0.965307\pi$
$547$	−11.2770	+	17.5474i	−0.482171	+	0.750273i	0.511895	+	0.859048i	$0.328944\pi$
$548$	−20.7776	−	18.0039i	−0.887575	−	0.769088i
$549$	−36.9021	+	10.8354i	−1.57494	+	0.462444i
$550$	28.7351	+	15.1251i	1.22527	+	0.644938i
$551$	−26.4145			−1.12530
$552$	−2.99590	+	0.371411i	−0.127514	+	0.0158083i
$553$		−	7.17779i		−	0.305231i
$554$	10.0619	+	22.0326i	0.427491	+	0.936075i
$555$	0.603245	−	3.49625i	0.0256063	−	0.148408i
$556$	26.0909	−	30.1105i	1.10650	−	1.27697i
$557$	−13.4735	+	20.9651i	−0.570890	+	0.888322i	−0.999888	−	0.0149836i	$-0.995230\pi$
$557$	−13.4735	+	20.9651i	−0.570890	+	0.888322i	0.428998	+	0.903305i	$0.358867\pi$
$558$	−3.14520	+	2.72533i	−0.133147	+	0.115372i
$559$	−1.26097	−	8.77027i	−0.0533335	−	0.370943i
$560$	1.06557	+	0.976983i	0.0450283	+	0.0412851i
$561$	−1.86864	+	1.20090i	−0.0788941	+	0.0507021i
$562$	28.9204	+	4.15813i	1.21993	+	0.175400i
$563$	35.9176	+	16.4030i	1.51375	+	0.691306i	0.987295	−	0.158898i	$-0.0507942\pi$
$563$	35.9176	+	16.4030i	1.51375	+	0.691306i	0.526453	+	0.850204i	$0.323521\pi$
$564$	−1.88861	+	4.13548i	−0.0795249	+	0.174135i
$565$	23.1729	−	33.9258i	0.974892	−	1.42727i
$566$	52.1770	−	33.5321i	2.19316	−	1.40946i
$567$	−1.86518	+	6.35221i	−0.0783301	+	0.266768i
$568$	34.9216	−	5.02097i	1.46528	−	0.210675i
$569$	−2.75568	−	3.18022i	−0.115524	−	0.133322i	0.695042	−	0.718969i	$-0.255386\pi$
$569$	−2.75568	−	3.18022i	−0.115524	−	0.133322i	−0.810566	+	0.585647i	$0.800840\pi$
$570$	5.16536	−	3.11836i	0.216353	−	0.130614i
$571$	16.5956	−	19.1523i	0.694504	−	0.801500i	−0.293495	−	0.955961i	$-0.594818\pi$
$571$	16.5956	−	19.1523i	0.694504	−	0.801500i	0.987999	+	0.154460i	$0.0493639\pi$
$572$	−9.72455	−	33.1188i	−0.406604	−	1.38477i
$573$	−3.04620	+	1.39115i	−0.127257	+	0.0581162i
$574$	−16.5213			−0.689585
$575$	8.47356	−	22.4321i	0.353372	−	0.935483i
$576$	38.1684			1.59035
$577$	−18.8257	+	8.59742i	−0.783725	+	0.357915i	−0.766754	−	0.641941i	$-0.778130\pi$
$577$	−18.8257	+	8.59742i	−0.783725	+	0.357915i	−0.0169709	+	0.999856i	$0.505402\pi$
$578$	5.56034	+	18.9368i	0.231280	+	0.787666i
$579$	−2.97447	+	3.43272i	−0.123615	+	0.142659i
$580$	34.3623	−	20.7447i	1.42682	−	0.861378i
$581$	0.0427764	+	0.0493666i	0.00177466	+	0.00204807i
$582$	−2.47338	+	0.355618i	−0.102525	+	0.0147408i
$583$	−1.99561	+	6.79644i	−0.0826499	+	0.281480i
$584$	−0.878507	+	0.564582i	−0.0363529	+	0.0233626i
$585$	14.4765	−	21.1941i	0.598532	−	0.876267i
$586$	−16.4072	+	35.9266i	−0.677773	+	1.48412i
$587$	2.82810	+	1.29155i	0.116728	+	0.0533079i	0.472923	−	0.881104i	$-0.343199\pi$
$587$	2.82810	+	1.29155i	0.116728	+	0.0533079i	−0.356195	+	0.934412i	$0.615926\pi$
$588$	5.14943	+	0.740377i	0.212359	+	0.0305326i
$589$	−2.38544	+	1.53303i	−0.0982903	+	0.0631674i
$590$	−9.43963	−	8.65490i	−0.388623	−	0.356317i
$591$	−0.881753	−	6.13273i	−0.0362705	−	0.252267i
$592$	3.65135	−	3.16391i	0.150069	−	0.130036i
$593$	−1.68830	+	2.62705i	−0.0693303	+	0.107880i	−0.874188	−	0.485588i	$-0.838605\pi$
$593$	−1.68830	+	2.62705i	−0.0693303	+	0.107880i	0.804857	+	0.593468i	$0.202242\pi$
$594$	6.75851	−	7.79974i	0.277305	−	0.320027i
$595$	−0.863034	+	5.00192i	−0.0353809	+	0.205059i
$596$	−7.17988	−	15.7217i	−0.294099	−	0.643988i
$597$			1.78537i			0.0730701i
$598$	−38.7458	+	16.7915i	−1.58443	+	0.686654i
$599$	−36.0959			−1.47484			−0.737419	−	0.675436i	$-0.763956\pi$
$599$	−36.0959			−1.47484			−0.737419	+	0.675436i	$0.763956\pi$
$600$	−1.46598	+	2.78510i	−0.0598483	+	0.113701i
$601$	6.09345	−	1.78920i	0.248557	−	0.0729830i	−0.155081	−	0.987902i	$-0.549564\pi$
$601$	6.09345	−	1.78920i	0.248557	−	0.0729830i	0.403638	+	0.914919i	$0.367746\pi$
$602$	−3.03916	−	2.63345i	−0.123867	−	0.107331i
$603$	18.1077	−	28.1762i	0.737404	−	1.14742i
$604$	−33.5082	−	38.6705i	−1.36343	−	1.57348i
$605$	−5.61554	−	1.82149i	−0.228304	−	0.0740541i
$606$	6.59089	+	1.93526i	0.267736	+	0.0786145i
$607$	−18.7571	−	29.1867i	−0.761329	−	1.18465i	−0.978040	−	0.208415i	$-0.933169\pi$
$607$	−18.7571	−	29.1867i	−0.761329	−	1.18465i	0.216711	−	0.976236i	$-0.430467\pi$
$608$	28.9652	+	4.16457i	1.17469	+	0.168896i
$609$	0.519883	−	1.13839i	0.0210667	−	0.0461297i
$610$	51.0496	−	41.7858i	2.06694	−	1.69186i
$611$	−3.10680	+	21.6083i	−0.125688	+	0.874178i
$612$	13.8170	+	21.4996i	0.558518	+	0.869071i
$613$	−10.0334	+	34.1705i	−0.405244	+	1.38014i	0.464036	+	0.885816i	$0.346401\pi$
$613$	−10.0334	+	34.1705i	−0.405244	+	1.38014i	−0.869281	+	0.494319i	$0.835417\pi$
$614$	7.67794	+	53.4013i	0.309857	+	2.15510i
$615$	1.41773	+	5.38261i	0.0571682	+	0.217048i
$616$	−4.52401	−	2.90741i	−0.182278	−	0.117143i
$617$	−3.13422	−	2.71581i	−0.126179	−	0.109335i	0.589486	−	0.807779i	$-0.299330\pi$
$617$	−3.13422	−	2.71581i	−0.126179	−	0.109335i	−0.715664	+	0.698444i	$0.753876\pi$
$618$	−2.78452	−	9.48321i	−0.112010	−	0.381470i
$619$	9.94282	+	21.7717i	0.399636	+	0.875080i	0.997307	+	0.0733388i	$0.0233654\pi$
$619$	9.94282	+	21.7717i	0.399636	+	0.875080i	−0.597671	+	0.801741i	$0.703907\pi$
$620$	1.89922	−	3.86771i	0.0762745	−	0.155331i
$621$	−6.32991	−	4.24423i	−0.254011	−	0.170315i
$622$		−	19.3323i		−	0.775157i
$623$	−3.27914	+	1.49753i	−0.131376	+	0.0599975i
$624$	−0.822975	+	0.241647i	−0.0329453	+	0.00967363i
$625$	−14.1524	−	20.6085i	−0.566097	−	0.824339i
$626$	−57.5243	−	36.9686i	−2.29913	−	1.47756i
$627$	2.62497	−	2.27455i	0.104831	−	0.0908368i
$628$	2.64684	−	0.380559i	0.105621	−	0.0151859i
$629$	16.2764	+	4.77918i	0.648982	+	0.190558i
$630$	−1.33367	−	11.5723i	−0.0531347	−	0.461050i
$631$	−5.30611	+	36.9048i	−0.211233	+	1.46916i	0.557815	+	0.829965i	$0.311640\pi$
$631$	−5.30611	+	36.9048i	−0.211233	+	1.46916i	−0.769048	+	0.639191i	$0.779269\pi$
$632$	19.3571	+	8.84007i	0.769983	+	0.351639i
$633$	2.33422	+	1.06600i	0.0927770	+	0.0423699i
$634$	−2.09647	+	14.5812i	−0.0832613	+	0.579095i
$635$	43.0203	−	4.95796i	1.70721	−	0.196751i
$636$	−1.91896	−	0.563457i	−0.0760916	−	0.0223425i
$637$	24.7265	−	3.55513i	0.979699	−	0.140859i
$638$	28.9305	−	25.0684i	1.14537	−	0.992469i
$639$	37.0098	+	23.7847i	1.46408	+	0.940910i
$640$	−33.4000	+	14.1347i	−1.32025	+	0.558723i
$641$	9.11829	−	2.67737i	0.360151	−	0.105750i	−0.0966510	−	0.995318i	$-0.530813\pi$
$641$	9.11829	−	2.67737i	0.360151	−	0.105750i	0.456802	+	0.889569i	$0.348995\pi$
$642$	7.43935	−	3.39744i	0.293608	−	0.134086i
$643$			3.92083i			0.154622i	0.997007	+	0.0773112i	$0.0246335\pi$
$643$			3.92083i			0.154622i	−0.997007	+	0.0773112i	$0.975367\pi$
$644$	−5.00945	+	10.4274i	−0.197400	+	0.410897i
$645$	−0.597178	+	1.21614i	−0.0235139	+	0.0478854i
$646$	11.9842	+	26.2416i	0.471510	+	1.03246i
$647$	10.1613	+	34.6061i	0.399480	+	1.36051i	0.876411	+	0.481564i	$0.159931\pi$
$647$	10.1613	+	34.6061i	0.399480	+	1.36051i	−0.476930	+	0.878941i	$0.658251\pi$
$648$	−14.8335	−	12.8533i	−0.582715	−	0.504926i
$649$	−6.20201	−	3.98579i	−0.243450	−	0.156456i
$650$	−8.69980	+	43.1574i	−0.341234	+	1.69277i
$651$	−0.0191193	−	0.132978i	−0.000749345	−	0.00521181i
$652$	3.47978	−	11.8511i	0.136279	−	0.464123i
$653$	−7.75233	−	12.0629i	−0.303372	−	0.472056i	0.655778	−	0.754954i	$-0.272341\pi$
$653$	−7.75233	−	12.0629i	−0.303372	−	0.472056i	−0.959150	+	0.282897i	$0.908704\pi$
$654$	−0.858132	+	5.96844i	−0.0335556	+	0.233384i
$655$	−24.1504	−	29.5045i	−0.943635	−	1.15284i
$656$	−3.14878	+	6.89487i	−0.122939	+	0.269200i
$657$	−1.28892	−	0.185319i	−0.0502857	−	0.00722999i
$658$	5.35664	+	8.33509i	0.208824	+	0.324936i
$659$	−11.1277	−	3.26739i	−0.433473	−	0.127279i	0.0577140	−	0.998333i	$-0.481619\pi$
$659$	−11.1277	−	3.26739i	−0.433473	−	0.127279i	−0.491188	+	0.871054i	$0.663437\pi$
$660$	−1.62847	+	5.02047i	−0.0633880	+	0.195421i
$661$	9.07291	+	10.4707i	0.352895	+	0.407263i	0.904247	−	0.427010i	$-0.140433\pi$
$661$	9.07291	+	10.4707i	0.352895	+	0.407263i	−0.551352	+	0.834273i	$0.685888\pi$
$662$	12.5683	−	19.5567i	0.488482	−	0.760093i
$663$	−2.27596	−	1.97213i	−0.0883908	−	0.0765910i
$664$	−0.185815	+	0.0545601i	−0.00721100	+	0.00211734i
$665$	0.222672	−	7.93384i	0.00863485	−	0.307661i
$666$	−38.9308			−1.50854
$667$	−20.9993	−	18.9237i	−0.813097	−	0.732729i
$668$			4.74432i			0.183563i
$669$	−0.310803	−	0.680563i	−0.0120163	−	0.0263121i
$670$	−9.76829	+	56.6144i	−0.377382	+	2.18721i
$671$	24.8694	−	28.7008i	0.960071	−	1.10798i
$672$	−0.749565	+	1.16635i	−0.0289151	+	0.0449928i
$673$	−20.1810	+	17.4870i	−0.777921	+	0.674073i	−0.950431	−	0.310935i	$-0.899358\pi$
$673$	−20.1810	+	17.4870i	−0.777921	+	0.674073i	0.172510	+	0.985008i	$0.444812\pi$
$674$	4.01812	+	27.9466i	0.154772	+	1.07646i
$675$	−7.40128	+	2.89013i	−0.284876	+	0.111241i
$676$	6.06265	−	3.89623i	0.233179	−	0.149855i
$677$	13.9301	+	2.00284i	0.535376	+	0.0769755i	0.404700	−	0.914450i	$-0.367376\pi$
$677$	13.9301	+	2.00284i	0.535376	+	0.0769755i	0.130676	+	0.991425i	$0.458285\pi$
$678$	10.0634	+	4.59579i	0.386482	+	0.176500i
$679$	−1.36549	+	2.99001i	−0.0524028	+	0.114746i
$680$	−12.4263	−	8.48772i	−0.476525	−	0.325489i
$681$	−5.56737	+	3.57793i	−0.213342	+	0.137107i
$682$	1.15775	−	3.94293i	0.0443325	−	0.150983i
$683$	−39.7423	+	5.71408i	−1.52070	+	0.218643i	−0.851465	−	0.524411i	$-0.824285\pi$
$683$	−39.7423	+	5.71408i	−1.52070	+	0.218643i	−0.669231	+	0.743054i	$0.733376\pi$
$684$	−26.1698	−	30.2016i	−1.00063	−	1.15479i
$685$	10.4328	+	17.2812i	0.398616	+	0.660281i
$686$	15.5802	−	17.9805i	0.594854	−	0.686498i
$687$	−0.150217	−	0.511591i	−0.00573112	−	0.0195184i
$688$	−1.67826	+	0.766435i	−0.0639830	+	0.0292201i
$689$	−9.60343			−0.365862
$690$	6.34045	+	1.22146i	0.241377	+	0.0465003i
$691$	1.22724			0.0466864			0.0233432	−	0.999728i	$-0.492569\pi$
$691$	1.22724			0.0466864			0.0233432	+	0.999728i	$0.492569\pi$
$692$	12.5112	−	5.71367i	0.475604	−	0.217201i
$693$	−1.88923	−	6.43414i	−0.0717661	−	0.244413i
$694$	−20.2024	+	23.3148i	−0.766873	+	0.885018i
$695$	−25.0436	+	15.1190i	−0.949957	+	0.573495i
$696$	2.42971	+	2.80404i	0.0920981	+	0.106287i
$697$	−26.3426	+	3.78749i	−0.997797	+	0.143462i
$698$	−12.8762	+	43.8524i	−0.487372	+	1.65984i
$699$	−1.05638	+	0.678894i	−0.0399560	+	0.0256781i
$700$	5.94120	+	10.4959i	0.224556	+	0.396708i
$701$	−3.73967	+	8.18874i	−0.141245	+	0.309284i	−0.967013	−	0.254726i	$-0.918015\pi$
$701$	−3.73967	+	8.18874i	−0.141245	+	0.309284i	0.825768	+	0.564010i	$0.190742\pi$
$702$	12.7278	+	5.81261i	0.480381	+	0.219383i
$703$	−26.2555	−	3.77498i	−0.990247	−	0.142376i
$704$	−31.7057	+	20.3760i	−1.19495	+	0.767950i
$705$	2.25590	−	2.46044i	0.0849621	−	0.0926655i
$706$	−10.4705	−	72.8236i	−0.394061	−	2.74075i
$707$	6.82894	−	5.91731i	0.256829	−	0.222543i
$708$	1.12538	−	1.75112i	0.0422943	−	0.0658112i
$709$	−0.426606	+	0.492329i	−0.0160215	+	0.0184898i	−0.763704	−	0.645567i	$-0.776621\pi$
$709$	−0.426606	+	0.492329i	−0.0160215	+	0.0184898i	0.747682	+	0.664057i	$0.231167\pi$
$710$	−74.3637	−	12.8308i	−2.79082	−	0.481530i
$711$	11.0232	+	24.1375i	0.413402	+	0.905225i
$712$		−	10.6875i		−	0.400532i
$713$	−2.99469	−	0.490215i	−0.112152	−	0.0183587i
$714$	−1.36680			−0.0511513
$715$	−0.711019	+	25.3337i	−0.0265906	+	0.947428i
$716$	−51.0556	+	14.9913i	−1.90804	+	0.560250i
$717$	−0.490355	−	0.424895i	−0.0183126	−	0.0158680i
$718$	−12.2930	+	19.1283i	−0.458770	+	0.713860i
$719$	−30.5143	−	35.2154i	−1.13799	−	1.31331i	−0.943108	−	0.332486i	$-0.892113\pi$
$719$	−30.5143	−	35.2154i	−1.13799	−	1.31331i	−0.194883	−	0.980826i	$-0.562433\pi$
$720$	−5.08367	−	1.64897i	−0.189457	−	0.0614534i
$721$	−12.4746	−	3.66289i	−0.464580	−	0.136413i
$722$	−1.31494	−	2.04609i	−0.0489371	−	0.0761476i
$723$	−5.85406	−	0.841687i	−0.217715	−	0.0313027i
$724$	2.26377	−	4.95697i	0.0841325	−	0.184224i
$725$	−28.6988	+	6.70394i	−1.06585	+	0.248978i
$726$	0.226237	−	1.57352i	0.00839645	−	0.0583986i
$727$	8.68216	+	13.5097i	0.322003	+	0.501047i	0.964087	−	0.265588i	$-0.0855660\pi$
$727$	8.68216	+	13.5097i	0.322003	+	0.501047i	−0.642083	+	0.766635i	$0.721930\pi$
$728$	2.05410	−	6.99561i	0.0761299	−	0.259275i
$729$	−3.30125	−	22.9607i	−0.122268	−	0.850395i
$730$	2.15997	−	0.568913i	0.0799440	−	0.0210564i
$731$	−5.44956	−	3.50222i	−0.201559	−	0.129534i
$732$	8.10359	+	7.02180i	0.299517	+	0.259533i
$733$	0.629446	+	2.14369i	0.0232491	+	0.0791792i	0.970300	−	0.241903i	$-0.0777716\pi$
$733$	0.629446	+	2.14369i	0.0232491	+	0.0791792i	−0.947051	+	0.321082i	$0.895953\pi$
$734$	12.4995	+	27.3700i	0.461364	+	1.01025i
$735$	−3.42872	−	1.68366i	−0.126470	−	0.0621026i
$736$	20.0435	+	24.0618i	0.738815	+	0.886931i
$737$			33.0721i			1.21823i
$738$	55.5577	−	25.3723i	2.04511	−	0.933969i
$739$	−3.36678	+	0.988577i	−0.123849	+	0.0363654i	−0.343070	−	0.939310i	$-0.611467\pi$
$739$	−3.36678	+	0.988577i	−0.123849	+	0.0363654i	0.219221	+	0.975675i	$0.429649\pi$
$740$	37.1202	−	15.7091i	1.36457	−	0.577477i
$741$	3.96151	+	2.54591i	0.145530	+	0.0935262i
$742$	−3.29401	+	2.85427i	−0.120927	+	0.104784i
$743$	28.1809	−	4.05180i	1.03386	−	0.148646i	0.395563	−	0.918439i	$-0.370550\pi$
$743$	28.1809	−	4.05180i	1.03386	−	0.148646i	0.638294	+	0.769793i	$0.279640\pi$
$744$	0.382162	+	0.112213i	0.0140107	+	0.00411392i
$745$	1.45291	+	12.6069i	0.0532304	+	0.461880i
$746$	−6.12023	+	42.5671i	−0.224077	+	1.55849i
$747$	−0.219662	−	0.100316i	−0.00803702	−	0.00367039i
$748$	−22.9550	−	10.4832i	−0.839316	−	0.383303i
$749$	1.53106	−	10.6488i	0.0559438	−	0.389098i
$750$	4.82062	−	4.69899i	0.176024	−	0.171583i
$751$	47.6325	+	13.9862i	1.73813	+	0.510362i	0.988465	−	0.151451i	$-0.0483946\pi$
$751$	47.6325	+	13.9862i	1.73813	+	0.510362i	0.749669	+	0.661813i	$0.230213\pi$
$752$	4.49943	−	0.646920i	0.164077	−	0.0235907i
$753$	−5.42921	+	4.70444i	−0.197851	+	0.171439i
$754$	43.6609	+	28.0591i	1.59003	+	1.02185i
$755$	14.6421	+	34.5991i	0.532882	+	1.25919i
$756$	3.67791	−	1.07993i	0.133764	−	0.0392767i
$757$	1.34022	−	0.612059i	0.0487112	−	0.0222457i	−0.390910	−	0.920429i	$-0.627840\pi$
$757$	1.34022	−	0.612059i	0.0487112	−	0.0222457i	0.439622	+	0.898183i	$0.355113\pi$
$758$		−	35.1111i		−	1.27529i
$759$	3.71635	+	0.0723148i	0.134895	+	0.00262486i
$760$	21.1217	+	10.3717i	0.766166	+	0.376222i
$761$	−13.1300	−	28.7508i	−0.475964	−	1.04221i	−0.983554	−	0.180616i	$-0.942191\pi$
$761$	−13.1300	−	28.7508i	−0.475964	−	1.04221i	0.507590	−	0.861599i	$-0.330536\pi$
$762$	3.28530	+	11.1887i	0.119014	+	0.405323i
$763$	5.99453	+	5.19429i	0.217017	+	0.188046i
$764$	−32.0060	−	20.5690i	−1.15794	−	0.744160i
$765$	−4.77942	−	18.1458i	−0.172800	−	0.656064i
$766$	5.21918	+	36.3002i	0.188576	+	1.31158i
$767$	2.81598	−	9.59035i	0.101679	−	0.346288i
$768$	−1.50173	−	2.33674i	−0.0541890	−	0.0843197i
$769$	1.33281	−	9.26992i	0.0480625	−	0.334282i	−0.951576	−	0.307412i	$-0.900537\pi$
$769$	1.33281	−	9.26992i	0.0480625	−	0.334282i	0.999639	−	0.0268698i	$-0.00855394\pi$
$770$	7.28565	+	8.90087i	0.262557	+	0.320765i
$771$	0.216417	−	0.473888i	0.00779408	−	0.0170666i
$772$	−51.0774	−	7.34382i	−1.83832	−	0.264310i
$773$	−20.0422	−	31.1863i	−0.720868	−	1.12169i	−0.987458	−	0.157883i	$-0.949533\pi$
$773$	−20.0422	−	31.1863i	−0.720868	−	1.12169i	0.266590	−	0.963810i	$-0.414103\pi$
$774$	14.2644	+	4.18840i	0.512723	+	0.150549i
$775$	−2.20265	+	2.27102i	−0.0791214	+	0.0815775i
$776$	−6.38174	−	7.36492i	−0.229091	−	0.264385i
$777$	0.679444	−	1.05724i	0.0243749	−	0.0379281i
$778$	−25.2153	−	21.8492i	−0.904014	−	0.783333i
$779$	39.9293	−	11.7243i	1.43061	−	0.420066i
$780$	−7.15291	−	0.200754i	−0.256115	−	0.00718816i
$781$	−43.4407			−1.55443
$782$	−9.27254	+	29.4475i	−0.331585	+	1.05304i
$783$			9.36666i			0.334737i
$784$	−2.16085	−	4.73160i	−0.0771732	−	0.168986i
$785$	−1.93481	−	0.333834i	−0.0690564	−	0.0119150i
$786$	6.72349	−	7.75932i	0.239819	−	0.276766i
$787$	14.6745	−	22.8340i	0.523090	−	0.813944i	−0.474716	−	0.880139i	$-0.657449\pi$
$787$	14.6745	−	22.8340i	0.523090	−	0.813944i	0.997807	+	0.0661944i	$0.0210858\pi$
$788$	53.1969	−	46.0954i	1.89506	−	1.64208i
$789$	−0.0161681	−	0.112451i	−0.000575599	−	0.00400338i
$790$	−33.5492	−	30.7602i	−1.19363	−	1.09440i
$791$	12.2427	−	7.86792i	0.435301	−	0.279751i
$792$	19.6783	+	2.82932i	0.699239	+	0.100535i
$793$	46.8348	+	21.3887i	1.66315	+	0.759536i
$794$	31.5748	−	69.1393i	1.12055	−	2.45366i
$795$	1.21258	+	0.828253i	0.0430059	+	0.0293751i
$796$	−17.0634	+	10.9660i	−0.604797	+	0.388679i
$797$	11.6366	−	39.6305i	0.412188	−	1.40378i	−0.448103	−	0.893982i	$-0.647900\pi$
$797$	11.6366	−	39.6305i	0.412188	−	1.40378i	0.860291	−	0.509803i	$-0.170282\pi$
$798$	2.11549	−	0.304161i	0.0748875	−	0.0107672i
$799$	10.4518	+	12.0620i	0.369758	+	0.426723i
$800$	32.5270	−	2.82660i	1.15000	−	0.0999352i
$801$	8.72727	−	10.0718i	0.308363	−	0.355870i
$802$	18.9343	+	64.4843i	0.668593	+	2.27702i
$803$	1.16962	−	0.534145i	0.0412748	−	0.0188496i
$804$	−9.33784			−0.329320
$805$	5.86093	−	6.14781i	0.206571	−	0.216682i
$806$	5.57140			0.196244
$807$	2.88928	−	1.31949i	0.101707	−	0.0464482i
$808$	7.54736	+	25.7040i	0.265515	+	0.904262i
$809$	21.0966	−	24.3468i	0.741719	−	0.855989i	−0.252020	−	0.967722i	$-0.581095\pi$
$809$	21.0966	−	24.3468i	0.741719	−	0.855989i	0.993738	+	0.111733i	$0.0356402\pi$
$810$	21.6972	+	35.9401i	0.762363	+	1.26281i
$811$	1.41262	+	1.63025i	0.0496038	+	0.0572459i	0.780009	−	0.625768i	$-0.215214\pi$
$811$	1.41262	+	1.63025i	0.0496038	+	0.0572459i	−0.730405	+	0.683014i	$0.760669\pi$
$812$	14.0732	−	2.02342i	0.493872	−	0.0710080i
$813$	0.0547571	−	0.186486i	0.00192042	−	0.00654033i
$814$	32.3390	−	20.7830i	1.13348	−	0.728445i
$815$	−5.11510	+	7.48865i	−0.179174	+	0.262316i
$816$	−0.260498	+	0.570412i	−0.00911927	+	0.0199684i
$817$	9.21400	+	4.20789i	0.322357	+	0.147215i
$818$	28.0464	+	4.03247i	0.980620	+	0.140992i
$819$	7.64826	−	4.91524i	0.267252	−	0.171752i
$820$	−42.7358	+	46.6106i	−1.49240	+	1.62771i
$821$	−1.41655	−	9.85232i	−0.0494379	−	0.343848i	−0.999495	−	0.0317725i	$-0.989885\pi$
$821$	−1.41655	−	9.85232i	−0.0494379	−	0.343848i	0.950057	−	0.312076i	$-0.101024\pi$
$822$	−4.10801	+	3.55962i	−0.143283	+	0.124156i
$823$	29.7884	−	46.3517i	1.03836	−	1.61572i	0.284507	−	0.958674i	$-0.408170\pi$
$823$	29.7884	−	46.3517i	1.03836	−	1.61572i	0.753852	−	0.657044i	$-0.228194\pi$
$824$	25.2417	−	29.1305i	0.879336	−	1.01481i
$825$	2.27470	−	3.13746i	0.0791948	−	0.109232i
$826$	−1.88449	−	4.12647i	−0.0655700	−	0.143578i
$827$			25.6991i			0.893646i	0.894622	+	0.446823i	$0.147445\pi$
$827$			25.6991i			0.893646i	−0.894622	+	0.446823i	$0.852555\pi$
$828$	0.832017	−	42.7584i	0.0289146	−	1.48596i
$829$	9.97789			0.346547			0.173273	−	0.984874i	$-0.444566\pi$
$829$	9.97789			0.346547			0.173273	+	0.984874i	$0.444566\pi$
$830$	0.414057	+	0.0116210i	0.0143721	+	0.000403370i
$831$	2.77350	−	0.814373i	0.0962117	−	0.0282503i
$832$	−38.6167	−	33.4616i	−1.33879	−	1.16007i
$833$	9.87399	−	15.3642i	0.342113	−	0.532339i
$834$	−5.15852	−	5.95325i	−0.178625	−	0.206144i
$835$	1.07479	−	3.31351i	0.0371946	−	0.114669i
$836$	37.8617	+	11.1172i	1.30948	+	0.384497i
$837$	0.543616	+	0.845883i	0.0187901	+	0.0292380i
$838$	−45.0118	−	6.47173i	−1.55491	−	0.223562i
$839$	−16.0250	+	35.0899i	−0.553245	+	1.21144i	0.402005	+	0.915638i	$0.368314\pi$
$839$	−16.0250	+	35.0899i	−0.553245	+	1.21144i	−0.955250	+	0.295800i	$0.904414\pi$
$840$	−0.862701	+	0.706149i	−0.0297660	+	0.0243645i
$841$	−0.817243	+	5.68405i	−0.0281808	+	0.196002i
$842$	5.02146	+	7.81355i	0.173051	+	0.269273i
$843$	0.982362	−	3.34562i	0.0338343	−	0.115229i
$844$	4.14896	+	28.8566i	0.142813	+	0.993286i
$845$	−5.11691	+	1.34774i	−0.176027	+	0.0463638i
$846$	−30.8138	−	19.8028i	−1.05940	−	0.680835i
$847$	−1.58039	−	1.36942i	−0.0543029	−	0.0470538i
$848$	0.563379	+	1.91869i	0.0193465	+	0.0658882i
$849$	−3.07483	−	6.73294i	−0.105528	−	0.231074i
$850$	19.6806	+	25.4694i	0.675038	+	0.873593i
$851$	−18.1685	−	21.8109i	−0.622808	−	0.747667i
$852$		−	12.2654i		−	0.420205i
$853$	−23.6283	+	10.7907i	−0.809018	+	0.369466i	−0.776589	−	0.630008i	$-0.783052\pi$
$853$	−23.6283	+	10.7907i	−0.809018	+	0.369466i	−0.0324292	+	0.999474i	$0.510324\pi$
$854$	22.4215	−	6.58354i	0.767247	−	0.225284i
$855$	11.4355	+	27.0219i	0.391086	+	0.924128i
$856$	26.8320	+	17.2439i	0.917097	+	0.589383i
$857$	−8.41868	+	7.29483i	−0.287577	+	0.249187i	−0.786687	−	0.617352i	$-0.788206\pi$
$857$	−8.41868	+	7.29483i	−0.287577	+	0.249187i	0.499111	+	0.866538i	$0.333660\pi$
$858$	−6.75501	+	0.971224i	−0.230612	+	0.0331571i
$859$	−10.7354	−	3.15220i	−0.366287	−	0.107552i	0.0934090	−	0.995628i	$-0.470224\pi$
$859$	−10.7354	−	3.15220i	−0.366287	−	0.107552i	−0.459696	+	0.888076i	$0.652042\pi$
$860$	−15.2911	+	1.76225i	−0.521421	+	0.0600922i
$861$	−0.280595	+	1.95158i	−0.00956267	+	0.0665098i
$862$	−31.6595	−	14.4584i	−1.07833	−	0.492456i
$863$	11.9195	+	5.44345i	0.405744	+	0.185297i	0.607824	−	0.794072i	$-0.292043\pi$
$863$	11.9195	+	5.44345i	0.405744	+	0.185297i	−0.202080	+	0.979369i	$0.564770\pi$
$864$	1.47677	−	10.2711i	0.0502406	−	0.349431i
$865$	−10.0324	+	1.15621i	−0.341112	+	0.0393122i
$866$	38.7270	+	11.3713i	1.31600	+	0.386412i
$867$	2.33135	−	0.335198i	0.0791769	−	0.0113839i
$868$	1.15349	−	0.999501i	0.0391518	−	0.0339253i
$869$	−22.0424	−	14.1658i	−0.747738	−	0.480542i
$870$	−3.09290	−	7.30846i	−0.104859	−	0.247780i
$871$	−43.0221	+	12.6324i	−1.45775	+	0.428033i
$872$	−21.3907	+	9.76882i	−0.724382	+	0.330814i
$873$		−	12.1518i		−	0.411277i
$874$	7.79862	−	47.6412i	0.263792	−	1.61149i
$875$	−1.77166	−	8.67645i	−0.0598931	−	0.293318i
$876$	0.150815	+	0.330238i	0.00509555	+	0.0111577i
$877$	−2.53109	−	8.62010i	−0.0854689	−	0.291080i	0.905656	−	0.424013i	$-0.139379\pi$
$877$	−2.53109	−	8.62010i	−0.0854689	−	0.291080i	−0.991125	+	0.132933i	$0.957561\pi$
$878$	−1.54590	−	1.33953i	−0.0521716	−	0.0452069i
$879$	3.96520	+	2.54828i	0.133743	+	0.0859512i
$880$	5.10320	−	1.34413i	0.172029	−	0.0453106i
$881$	−5.89294	−	40.9863i	−0.198538	−	1.38086i	−0.808530	−	0.588455i	$-0.799736\pi$
$881$	−5.89294	−	40.9863i	−0.198538	−	1.38086i	0.609992	−	0.792408i	$-0.291173\pi$
$882$	−11.8086	+	40.2163i	−0.397616	+	1.35415i
$883$	13.0863	+	20.3627i	0.440388	+	0.685258i	0.988512	−	0.151139i	$-0.0482942\pi$
$883$	13.0863	+	20.3627i	0.440388	+	0.685258i	−0.548124	+	0.836397i	$0.684658\pi$
$884$	4.86909	−	33.8653i	0.163765	−	1.13901i
$885$	−1.18269	+	0.968067i	−0.0397556	+	0.0325412i
$886$	−0.513363	+	1.12411i	−0.0172468	+	0.0377652i
$887$	−36.5094	−	5.24926i	−1.22587	−	0.176253i	−0.501187	−	0.865339i	$-0.667103\pi$
$887$	−36.5094	−	5.24926i	−1.22587	−	0.176253i	−0.724679	+	0.689086i	$0.758012\pi$
$888$	2.01436	+	3.13440i	0.0675974	+	0.105184i
$889$	14.7181	+	4.32163i	0.493630	+	0.144943i
$890$	−7.05315	+	21.7444i	−0.236422	+	0.728875i
$891$	15.8261	+	18.2643i	0.530194	+	0.611876i
$892$	4.59540	−	7.15059i	0.153865	−	0.239419i
$893$	−18.8611	−	16.3433i	−0.631163	−	0.546906i
$894$	−3.27879	+	0.962740i	−0.109659	+	0.0321988i
$895$	39.0542	+	1.09610i	1.30544	+	0.0366386i
$896$	−12.8467			−0.429180
$897$	1.32545	+	4.86205i	0.0442553	+	0.162339i
$898$		−	11.3270i		−	0.377986i
$899$	1.54932	+	3.39255i	0.0516728	+	0.113148i
$900$	−36.0980	−	26.1715i	−1.20327	−	0.872383i
$901$	−4.59784	+	5.30619i	−0.153176	+	0.176775i
$902$	−32.6057	+	50.7355i	−1.08565	+	1.68931i
$903$	−0.362694	+	0.314277i	−0.0120697	+	0.0104585i
$904$	6.14023	+	42.7062i	0.204221	+	1.42039i
$905$	−2.70402	+	2.94919i	−0.0898847	+	0.0980344i
$906$	−8.51070	+	5.46949i	−0.282749	+	0.181712i
$907$	−47.6921	−	6.85709i	−1.58359	−	0.227686i	−0.706394	−	0.707818i	$-0.749679\pi$
$907$	−47.6921	−	6.85709i	−1.58359	−	0.227686i	−0.877196	+	0.480133i	$0.840589\pi$
$908$	−68.3913	−	31.2333i	−2.26965	−	1.03651i
$909$	−13.8769	+	30.3862i	−0.460267	+	1.00785i
$910$	−8.79587	+	12.8774i	−0.291580	+	0.426882i
$911$	5.65352	−	3.63330i	0.187309	−	0.120376i	−0.443625	−	0.896212i	$-0.646308\pi$
$911$	5.65352	−	3.63330i	0.187309	−	0.120376i	0.630935	+	0.775836i	$0.282672\pi$
$912$	0.276253	−	0.940833i	0.00914767	−	0.0311541i
$913$	0.236023	−	0.0339349i	0.00781121	−	0.00112308i
$914$	5.85513	+	6.75718i	0.193671	+	0.223508i
$915$	−4.06895	−	6.73995i	−0.134515	−	0.222816i
$916$	3.96682	−	4.57795i	0.131067	−	0.151260i
$917$	−3.80501	−	12.9587i	−0.125653	−	0.427933i
$918$	9.30535	−	4.24961i	0.307122	−	0.140258i
$919$	45.5884			1.50382			0.751910	−	0.659265i	$-0.229133\pi$
$919$	45.5884			1.50382			0.751910	+	0.659265i	$0.229133\pi$
$920$	9.36117	+	23.3773i	0.308629	+	0.770727i
$921$	6.43845			0.212154
$922$	13.7352	−	6.27265i	0.452344	−	0.206579i
$923$	−16.5928	−	56.5100i	−0.546160	−	1.86005i
$924$	−1.22430	+	1.41292i	−0.0402766	+	0.0464816i
$925$	−29.4841	+	2.56217i	−0.969432	+	0.0842436i
$926$	15.2764	+	17.6299i	0.502014	+	0.579355i
$927$	47.5749	−	6.84024i	1.56257	−	0.224663i
$928$	10.8436	−	36.9301i	0.355960	−	1.21229i
$929$	−3.63014	+	2.33295i	−0.119101	+	0.0765416i	−0.598835	−	0.800872i	$-0.704370\pi$
$929$	−3.63014	+	2.33295i	−0.119101	+	0.0765416i	0.479734	+	0.877414i	$0.340733\pi$
$930$	−0.703477	−	0.480508i	−0.0230679	−	0.0157565i
$931$	−11.8635	+	25.9775i	−0.388811	+	0.851378i
$932$	−12.9769	−	5.92635i	−0.425073	−	0.194124i
$933$	−2.28364	−	0.328338i	−0.0747631	−	0.0107493i
$934$	1.61413	−	1.03734i	0.0528160	−	0.0339428i
$935$	13.6572	+	12.5219i	0.446639	+	0.409510i
$936$	3.83591	+	26.6794i	0.125381	+	0.872042i
$937$	−5.22217	+	4.52503i	−0.170601	+	0.147826i	−0.735976	−	0.677007i	$-0.763277\pi$
$937$	−5.22217	+	4.52503i	−0.170601	+	0.147826i	0.565376	+	0.824833i	$0.308731\pi$
$938$	−11.0022	+	17.1197i	−0.359234	+	0.558978i
$939$	−5.34393	+	6.16722i	−0.174392	+	0.201260i
$940$	37.3714	+	6.44809i	1.21892	+	0.210314i
$941$	5.62210	+	12.3107i	0.183275	+	0.401317i	0.978862	−	0.204523i	$-0.0655644\pi$
$941$	5.62210	+	12.3107i	0.183275	+	0.401317i	−0.795586	+	0.605840i	$0.792837\pi$
$942$		−	0.528699i		−	0.0172259i
$943$	40.1429	+	19.2851i	1.30723	+	0.628010i
$944$	−2.08128			−0.0677398
$945$	−2.81336	−	0.0789601i	−0.0915187	−	0.00256857i
$946$	−14.0851	+	4.13576i	−0.457946	+	0.134465i
$947$	−9.50152	−	8.23311i	−0.308758	−	0.267540i	0.486673	−	0.873584i	$-0.338210\pi$
$947$	−9.50152	−	8.23311i	−0.308758	−	0.267540i	−0.795431	+	0.606044i	$0.792756\pi$
$948$	3.99968	−	6.22362i	0.129904	−	0.202134i
$949$	1.14160	+	1.31747i	0.0370578	+	0.0427670i
$950$	−36.1287	−	35.0410i	−1.17217	−	1.13688i
$951$	1.68681	+	0.495292i	0.0546986	+	0.0160609i
$952$	−2.88185	−	4.48424i	−0.0934012	−	0.145335i
$953$	37.4326	+	5.38200i	1.21256	+	0.174340i	0.718775	−	0.695243i	$-0.244703\pi$
$953$	37.4326	+	5.38200i	1.21256	+	0.174340i	0.493787	+	0.869583i	$0.335612\pi$
$954$	6.69366	−	14.6571i	0.216715	−	0.474540i
$955$	17.6937	+	21.6164i	0.572556	+	0.699491i
$956$	1.04905	−	7.29628i	0.0339286	−	0.235978i
$957$	−2.46987	−	3.84319i	−0.0798395	−	0.124233i
$958$	10.7847	−	36.7293i	0.348438	−	1.18667i
$959$	1.01760	+	7.07757i	0.0328600	+	0.228547i
$960$	1.99006	+	7.55557i	0.0642289	+	0.243855i
$961$	−25.7420	−	16.5434i	−0.830389	−	0.533658i
$962$	39.3881	+	34.1300i	1.26992	+	1.10039i
$963$	11.2051	+	38.1610i	0.361078	+	1.22972i
$964$	−27.9122	−	61.1193i	−0.898993	−	1.96852i
$965$	34.0096	+	16.7002i	1.09481	+	0.537600i
$966$	1.89970	+	1.27376i	0.0611219	+	0.0409825i
$967$			2.40190i			0.0772397i	0.999254	+	0.0386199i	$0.0122961\pi$
$967$			2.40190i			0.0772397i	−0.999254	+	0.0386199i	$0.987704\pi$
$968$	5.63944	−	2.57545i	0.181258	−	0.0827779i
$969$	3.30334	−	0.969949i	0.106119	−	0.0311593i
$970$	8.12361	+	19.1959i	0.260833	+	0.616344i
$971$	14.7531	+	9.48124i	0.473449	+	0.304267i	0.755519	−	0.655126i	$-0.227385\pi$
$971$	14.7531	+	9.48124i	0.473449	+	0.304267i	−0.282070	+	0.959394i	$0.591021\pi$
$972$	−16.1293	+	13.9761i	−0.517346	+	0.448283i
$973$	−10.2567	+	1.47469i	−0.328814	+	0.0472763i
$974$	44.0134	+	12.9235i	1.41028	+	0.414095i
$975$	4.95023	+	1.76065i	0.158534	+	0.0563859i
$976$	1.52577	−	10.6120i	0.0488388	−	0.339681i
$977$	2.18388	+	0.997344i	0.0698685	+	0.0319079i	0.450043	−	0.893007i	$-0.351409\pi$
$977$	2.18388	+	0.997344i	0.0698685	+	0.0319079i	−0.380174	+	0.924915i	$0.624136\pi$
$978$	−2.22135	−	1.01446i	−0.0710310	−	0.0324388i
$979$	−1.87278	+	13.0255i	−0.0598543	+	0.416296i
$980$	−4.96841	−	43.1109i	−0.158710	−	1.37713i
$981$	−28.1354	−	8.26131i	−0.898296	−	0.263763i
$982$	39.4841	−	5.67696i	1.25999	−	0.181159i
$983$	−29.1902	+	25.2934i	−0.931023	+	0.806736i	−0.981396	−	0.191995i	$-0.938504\pi$
$983$	−29.1902	+	25.2934i	−0.931023	+	0.806736i	0.0503734	+	0.998730i	$0.483959\pi$
$984$	−4.91745	−	3.16025i	−0.156763	−	0.100745i
$985$	−47.5962	+	20.1424i	−1.51654	+	0.641792i
$986$	36.4070	−	10.6901i	1.15944	−	0.340441i
$987$	1.07556	−	0.491193i	0.0342356	−	0.0156349i
$988$			53.4990i			1.70203i
$989$	4.31046	+	9.94626i	0.137065	+	0.316273i
$990$	−38.1696	−	18.7430i	−1.21311	−	0.595691i
$991$	−4.87703	−	10.6792i	−0.154924	−	0.339236i	0.816216	−	0.577747i	$-0.196068\pi$
$991$	−4.87703	−	10.6792i	−0.154924	−	0.339236i	−0.971140	+	0.238511i	$0.923341\pi$
$992$	−1.16406	−	3.96441i	−0.0369588	−	0.125870i
$993$	−2.09669	−	1.81679i	−0.0665363	−	0.0576541i
$994$	−22.4869	−	14.4515i	−0.713243	−	0.458373i
$995$	14.4016	−	3.79324i	0.456562	−	0.120254i
$996$	0.00958144	+	0.0666404i	0.000303599	+	0.00211158i
$997$	10.8333	−	36.8948i	0.343094	−	1.16847i	−0.589568	−	0.807719i	$-0.700702\pi$
$997$	10.8333	−	36.8948i	0.343094	−	1.16847i	0.932662	−	0.360751i	$-0.117480\pi$
$998$	7.19305	+	11.1926i	0.227692	+	0.354296i
$999$	−1.33862	+	9.31029i	−0.0423520	+	0.294564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.4.10	yes	100
5.2	odd	4		575.2.k.g.326.10		100
5.3	odd	4		575.2.k.g.326.1		100
5.4	even	2	inner	115.2.j.a.4.1	✓	100
23.6	even	11	inner	115.2.j.a.29.1	yes	100
115.29	even	22	inner	115.2.j.a.29.10	yes	100
115.52	odd	44		575.2.k.g.351.10		100
115.98	odd	44		575.2.k.g.351.1		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.4.1	✓	100	5.4	even	2	inner
115.2.j.a.4.10	yes	100	1.1	even	1	trivial
115.2.j.a.29.1	yes	100	23.6	even	11	inner
115.2.j.a.29.10	yes	100	115.29	even	22	inner
575.2.k.g.326.1		100	5.3	odd	4
575.2.k.g.326.10		100	5.2	odd	4
575.2.k.g.351.1		100	115.98	odd	44
575.2.k.g.351.10		100	115.52	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04322 - 0.933106i) q^{2} +(-0.0755218 - 0.257204i) q^{3} +(1.99433 - 2.30158i) q^{4} +(-1.91428 + 1.15566i) q^{5} +(-0.394306 - 0.455053i) q^{6} +(-0.783997 + 0.112722i) q^{7} +(0.661572 - 2.25311i) q^{8} +(2.46331 - 1.58307i) q^{9} +O(q^{10})\)	\(q+(2.04322 - 0.933106i) q^{2} +(-0.0755218 - 0.257204i) q^{3} +(1.99433 - 2.30158i) q^{4} +(-1.91428 + 1.15566i) q^{5} +(-0.394306 - 0.455053i) q^{6} +(-0.783997 + 0.112722i) q^{7} +(0.661572 - 2.25311i) q^{8} +(2.46331 - 1.58307i) q^{9} +(-2.83293 + 4.14748i) q^{10} +(-1.20111 + 2.63005i) q^{11} +(-0.742589 - 0.339129i) q^{12} +(-3.88010 - 0.557874i) q^{13} +(-1.49669 + 0.961867i) q^{14} +(0.441810 + 0.405081i) q^{15} +(0.116164 + 0.807941i) q^{16} +(-2.16592 + 1.87678i) q^{17} +(3.55590 - 5.53309i) q^{18} +(2.93468 - 3.38680i) q^{19} +(-1.15785 + 6.71061i) q^{20} +(0.0882013 + 0.193134i) q^{21} +6.49453i q^{22} +(4.75940 - 0.590036i) q^{23} -0.629471 q^{24} +(2.32890 - 4.42450i) q^{25} +(-8.44844 + 2.48069i) q^{26} +(-1.20097 - 1.04065i) q^{27} +(-1.30411 + 2.02923i) q^{28} +(-3.85993 - 4.45460i) q^{29} +(1.28070 + 0.415414i) q^{30} +(-0.607115 - 0.178265i) q^{31} +(3.53034 + 5.49332i) q^{32} +(0.767170 + 0.110302i) q^{33} +(-2.67421 + 5.85570i) q^{34} +(1.37052 - 1.12181i) q^{35} +(1.26908 - 8.82666i) q^{36} +(-3.20008 - 4.97942i) q^{37} +(2.83595 - 9.65834i) q^{38} +(0.149545 + 1.04011i) q^{39} +(1.33739 + 5.07762i) q^{40} +(7.81204 + 5.02049i) q^{41} +(0.360429 + 0.312313i) q^{42} +(0.636806 + 2.16876i) q^{43} +(3.65787 + 8.00963i) q^{44} +(-2.88596 + 5.87719i) q^{45} +(9.17391 - 5.64659i) q^{46} -5.56900i q^{47} +(0.199033 - 0.0908952i) q^{48} +(-6.11451 + 1.79538i) q^{49} +(0.629925 - 11.2133i) q^{50} +(0.646289 + 0.415345i) q^{51} +(-9.02218 + 7.81776i) q^{52} +(2.42492 - 0.348651i) q^{53} +(-3.42487 - 1.00563i) q^{54} +(-0.740200 - 6.42272i) q^{55} +(-0.264696 + 1.84100i) q^{56} +(-1.09273 - 0.499034i) q^{57} +(-12.0433 - 5.49998i) q^{58} +(-0.362875 + 2.52385i) q^{59} +(1.81344 - 0.208994i) q^{60} +(-12.6025 - 3.70044i) q^{61} +(-1.40681 + 0.202269i) q^{62} +(-1.75278 + 1.51879i) q^{63} +(10.9658 + 7.04726i) q^{64} +(8.07229 - 3.41615i) q^{65} +(1.67042 - 0.490479i) q^{66} +(10.4047 - 4.75166i) q^{67} +8.72794i q^{68} +(-0.511198 - 1.17957i) q^{69} +(1.75349 - 3.57095i) q^{70} +(6.24137 + 13.6667i) q^{71} +(-1.93718 - 6.59742i) q^{72} +(-0.336090 - 0.291224i) q^{73} +(-11.1848 - 7.18803i) q^{74} +(-1.31388 - 0.264856i) q^{75} +(-1.94227 - 13.5088i) q^{76} +(0.645199 - 2.19734i) q^{77} +(1.27608 + 1.98562i) q^{78} +(-1.28969 + 8.96996i) q^{79} +(-1.15608 - 1.41238i) q^{80} +(3.47222 - 7.60311i) q^{81} +(20.6463 + 2.96850i) q^{82} +(-0.0445868 - 0.0693784i) q^{83} +(0.620415 + 0.182170i) q^{84} +(1.97725 - 6.09574i) q^{85} +(3.32482 + 3.83704i) q^{86} +(-0.854230 + 1.32921i) q^{87} +(5.13118 + 4.44619i) q^{88} +(4.36696 - 1.28225i) q^{89} +(-0.412607 + 14.7013i) q^{90} +3.10487 q^{91} +(8.13378 - 12.1308i) q^{92} +0.169615i q^{93} +(-5.19647 - 11.3787i) q^{94} +(-1.70380 + 9.87477i) q^{95} +(1.14628 - 1.32288i) q^{96} +(2.24367 - 3.49121i) q^{97} +(-10.8180 + 9.37383i) q^{98} +(1.20487 + 8.38008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9}+O(q^{10}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30} - 12 q^{31} + 8 q^{34} - 37 q^{35} - 10 q^{36} + 14 q^{39} - q^{40} + 8 q^{41} + 166 q^{44} - 42 q^{45} - 18 q^{46} + 32 q^{49} - 23 q^{50} - 22 q^{51} + 116 q^{54} + 27 q^{55} - 116 q^{56} + 50 q^{59} + 123 q^{60} - 38 q^{61} + 10 q^{64} + 76 q^{65} - 28 q^{66} + 80 q^{69} + 102 q^{70} - 110 q^{71} + 22 q^{74} + 6 q^{75} + 4 q^{76} + 42 q^{79} + 18 q^{80} + 204 q^{81} + 56 q^{84} - 121 q^{85} + 132 q^{86} - 66 q^{89} - 198 q^{90} + 76 q^{91} - 70 q^{94} - 74 q^{95} + 236 q^{96} - 60 q^{99}+O(q^{100}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

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