LMFDB - Embedded newform 186.2.p.a.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [186,2,Mod(11,186)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(186, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 23]))

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

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

chi := DirichletCharacter("186.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.p (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(1.70450 - 0.307717i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.72504 - 0.995952i) q^{5} +(1.71616 + 0.234063i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(0.587785 + 0.809017i) q^{8} +(2.81062 - 1.04900i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(1.70450 - 0.307717i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.72504 - 0.995952i) q^{5} +(1.71616 + 0.234063i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(0.587785 + 0.809017i) q^{8} +(2.81062 - 1.04900i) q^{9} +(-1.33284 - 1.48027i) q^{10} +(0.977216 - 0.435084i) q^{11} +(1.55984 + 0.752930i) q^{12} +(-0.651734 + 3.06617i) q^{13} +(-0.260340 + 0.584733i) q^{14} +(-3.24679 - 1.16677i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.85104 - 3.05028i) q^{17} +(2.99722 - 0.129133i) q^{18} +(-3.06145 + 0.650731i) q^{19} +(-0.810180 - 1.81969i) q^{20} +(0.0818410 + 1.10561i) q^{21} +(1.06384 - 0.111814i) q^{22} +(0.0675204 - 0.0490565i) q^{23} +(1.25083 + 1.19810i) q^{24} +(-0.516161 - 0.894017i) q^{25} +(-1.56733 + 2.71470i) q^{26} +(4.46790 - 2.65290i) q^{27} +(-0.428291 + 0.475665i) q^{28} +(-1.21723 + 3.74626i) q^{29} +(-2.72733 - 2.11298i) q^{30} +(-1.13947 + 5.44992i) q^{31} +1.00000i q^{32} +(1.53178 - 1.04231i) q^{33} +(-5.57314 - 5.01808i) q^{34} +(0.749401 - 1.03146i) q^{35} +(2.89043 + 0.803379i) q^{36} +(7.15748 - 4.13237i) q^{37} +(-3.11270 - 0.327158i) q^{38} +(-0.167368 + 5.42682i) q^{39} +(-0.208211 - 1.98099i) q^{40} +(-0.135011 + 0.121564i) q^{41} +(-0.263817 + 1.07679i) q^{42} +(-1.99552 - 9.38821i) q^{43} +(1.04632 + 0.222402i) q^{44} +(-5.89319 - 0.989669i) q^{45} +(0.0793750 - 0.0257905i) q^{46} +(-0.690546 + 0.224372i) q^{47} +(0.819375 + 1.52598i) q^{48} +(6.44630 + 1.37020i) q^{49} +(-0.214632 - 1.00976i) q^{50} +(-12.6162 - 3.09101i) q^{51} +(-2.32951 + 2.09750i) q^{52} +(1.22033 + 11.6107i) q^{53} +(5.06902 - 1.14240i) q^{54} +(-2.11906 - 0.222722i) q^{55} +(-0.554317 + 0.320035i) q^{56} +(-5.01799 + 2.05123i) q^{57} +(-2.31532 + 3.18676i) q^{58} +(-3.05617 - 2.75179i) q^{59} +(-1.94090 - 2.85236i) q^{60} -2.42000i q^{61} +(-2.76782 + 4.83106i) q^{62} +(0.479712 + 1.85932i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(4.17802 - 4.64016i) q^{65} +(1.77890 - 0.517946i) q^{66} +(5.65968 - 9.80285i) q^{67} +(-3.74970 - 6.49467i) q^{68} +(0.0999929 - 0.104394i) q^{69} +(1.03146 - 0.749401i) q^{70} +(0.823066 - 0.0865077i) q^{71} +(2.50070 + 1.65725i) q^{72} +(4.58275 + 10.2930i) q^{73} +(8.08414 - 1.71834i) q^{74} +(-1.15490 - 1.36502i) q^{75} +(-2.85926 - 1.27302i) q^{76} +(0.211578 + 0.651170i) q^{77} +(-1.83616 + 5.10949i) q^{78} +(1.28631 - 2.88911i) q^{79} +(0.414140 - 1.94838i) q^{80} +(6.79918 - 5.89671i) q^{81} +(-0.165968 + 0.0738938i) q^{82} +(-5.34426 - 5.93540i) q^{83} +(-0.583650 + 0.942562i) q^{84} +(8.78038 + 12.0852i) q^{85} +(1.00326 - 9.54537i) q^{86} +(-0.921984 + 6.76005i) q^{87} +(0.926384 + 0.534848i) q^{88} +(13.6894 + 9.94595i) q^{89} +(-5.29893 - 2.76233i) q^{90} +(-1.90821 - 0.620014i) q^{91} +0.0834598 q^{92} +(-0.265196 + 9.64000i) q^{93} -0.726083 q^{94} +(5.92922 + 1.92652i) q^{95} +(0.307717 + 1.70450i) q^{96} +(2.30702 + 1.67615i) q^{97} +(5.70738 + 3.29516i) q^{98} +(2.29018 - 2.24796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	$ 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) $ 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	1.70450	−	0.307717i	0.984092	−	0.177660i
$3$	1.70450	−	0.307717i	0.984092	−	0.177660i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.72504	−	0.995952i	−0.771461	−	0.445403i	0.0619347	−	0.998080i	$-0.480273\pi$
$5$	−1.72504	−	0.995952i	−0.771461	−	0.445403i	−0.833395	+	0.552677i	$0.813606\pi$
$6$	1.71616	+	0.234063i	0.700621	+	0.0955557i
$7$	−0.0669056	+	0.636564i	−0.0252879	+	0.240599i	0.974575	+	0.224060i	$0.0719312\pi$
$7$	−0.0669056	+	0.636564i	−0.0252879	+	0.240599i	−0.999863	+	0.0165383i	$0.994735\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	2.81062	−	1.04900i	0.936874	−	0.349668i
$10$	−1.33284	−	1.48027i	−0.421482	−	0.468103i
$11$	0.977216	−	0.435084i	0.294642	−	0.131183i	−0.254092	−	0.967180i	$-0.581777\pi$
$11$	0.977216	−	0.435084i	0.294642	−	0.131183i	0.548734	+	0.835997i	$0.315110\pi$
$12$	1.55984	+	0.752930i	0.450287	+	0.217352i
$13$	−0.651734	+	3.06617i	−0.180758	+	0.850401i	0.790516	+	0.612441i	$0.209812\pi$
$13$	−0.651734	+	3.06617i	−0.180758	+	0.850401i	−0.971275	+	0.237961i	$0.923521\pi$
$14$	−0.260340	+	0.584733i	−0.0695788	+	0.156277i
$15$	−3.24679	−	1.16677i	−0.838319	−	0.301260i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−6.85104	−	3.05028i	−1.66162	−	0.739802i	−0.661672	−	0.749794i	$-0.730153\pi$
$17$	−6.85104	−	3.05028i	−1.66162	−	0.739802i	−0.999950	+	0.00999184i	$0.996819\pi$
$18$	2.99722	−	0.129133i	0.706451	−	0.0304369i
$19$	−3.06145	+	0.650731i	−0.702345	+	0.149288i	−0.545223	−	0.838291i	$-0.683555\pi$
$19$	−3.06145	+	0.650731i	−0.702345	+	0.149288i	−0.157122	+	0.987579i	$0.550222\pi$
$20$	−0.810180	−	1.81969i	−0.181162	−	0.406896i
$21$	0.0818410	+	1.10561i	0.0178592	+	0.241264i
$22$	1.06384	−	0.111814i	0.226811	−	0.0238387i
$23$	0.0675204	−	0.0490565i	0.0140790	−	0.0102290i	−0.580724	−	0.814101i	$-0.697230\pi$
$23$	0.0675204	−	0.0490565i	0.0140790	−	0.0102290i	0.594802	+	0.803872i	$0.297230\pi$
$24$	1.25083	+	1.19810i	0.255324	+	0.244560i
$25$	−0.516161	−	0.894017i	−0.103232	−	0.178803i
$26$	−1.56733	+	2.71470i	−0.307379	+	0.532396i
$27$	4.46790	−	2.65290i	0.859848	−	0.510551i
$28$	−0.428291	+	0.475665i	−0.0809393	+	0.0898922i
$29$	−1.21723	+	3.74626i	−0.226035	+	0.695663i	0.772150	+	0.635440i	$0.219181\pi$
$29$	−1.21723	+	3.74626i	−0.226035	+	0.695663i	−0.998185	+	0.0602230i	$0.980819\pi$
$30$	−2.72733	−	2.11298i	−0.497940	−	0.385776i
$31$	−1.13947	+	5.44992i	−0.204655	+	0.978834i
$31$	−1.13947	+	5.44992i	−0.204655	+	0.978834i
$32$			1.00000i			0.176777i
$33$	1.53178	−	1.04231i	0.266648	−	0.181442i
$34$	−5.57314	−	5.01808i	−0.955786	−	0.860593i
$35$	0.749401	−	1.03146i	0.126672	−	0.174349i
$36$	2.89043	+	0.803379i	0.481738	+	0.133897i
$37$	7.15748	−	4.13237i	1.17668	−	0.679358i	0.221438	−	0.975175i	$-0.428925\pi$
$37$	7.15748	−	4.13237i	1.17668	−	0.679358i	0.955245	+	0.295817i	$0.0955918\pi$
$38$	−3.11270	−	0.327158i	−0.504946	−	0.0530720i
$39$	−0.167368	+	5.42682i	−0.0268003	+	0.868987i
$40$	−0.208211	−	1.98099i	−0.0329210	−	0.313222i
$41$	−0.135011	+	0.121564i	−0.0210851	+	0.0189851i	−0.679606	−	0.733577i	$-0.737849\pi$
$41$	−0.135011	+	0.121564i	−0.0210851	+	0.0189851i	0.658521	+	0.752563i	$0.271182\pi$
$42$	−0.263817	+	1.07679i	−0.0407078	+	0.166152i
$43$	−1.99552	−	9.38821i	−0.304315	−	1.43169i	−0.818746	−	0.574156i	$-0.805330\pi$
$43$	−1.99552	−	9.38821i	−0.304315	−	1.43169i	0.514431	−	0.857532i	$-0.328003\pi$
$44$	1.04632	+	0.222402i	0.157739	+	0.0335284i
$45$	−5.89319	−	0.989669i	−0.878505	−	0.147531i
$46$	0.0793750	−	0.0257905i	0.0117032	−	0.00380260i
$47$	−0.690546	+	0.224372i	−0.100726	+	0.0327280i	−0.358947	−	0.933358i	$-0.616864\pi$
$47$	−0.690546	+	0.224372i	−0.100726	+	0.0327280i	0.258220	+	0.966086i	$0.416864\pi$
$48$	0.819375	+	1.52598i	0.118267	+	0.220257i
$49$	6.44630	+	1.37020i	0.920899	+	0.195743i
$50$	−0.214632	−	1.00976i	−0.0303535	−	0.142802i
$51$	−12.6162	−	3.09101i	−1.76662	−	0.432829i
$52$	−2.32951	+	2.09750i	−0.323045	+	0.290871i
$53$	1.22033	+	11.6107i	0.167625	+	1.59485i	0.678109	+	0.734962i	$0.262800\pi$
$53$	1.22033	+	11.6107i	0.167625	+	1.59485i	−0.510483	+	0.859888i	$0.670533\pi$
$54$	5.06902	−	1.14240i	0.689806	−	0.155461i
$55$	−2.11906	−	0.222722i	−0.285734	−	0.0300318i
$56$	−0.554317	+	0.320035i	−0.0740737	+	0.0427665i
$57$	−5.01799	+	2.05123i	−0.664649	+	0.271692i
$58$	−2.31532	+	3.18676i	−0.304016	+	0.418442i
$59$	−3.05617	−	2.75179i	−0.397879	−	0.358252i	0.445769	−	0.895148i	$-0.352930\pi$
$59$	−3.05617	−	2.75179i	−0.397879	−	0.358252i	−0.843649	+	0.536896i	$0.819597\pi$
$60$	−1.94090	−	2.85236i	−0.250569	−	0.368238i
$61$		−	2.42000i		−	0.309849i	−0.987926	−	0.154925i	$-0.950487\pi$
$61$		−	2.42000i		−	0.309849i	0.987926	−	0.154925i	$-0.0495135\pi$
$62$	−2.76782	+	4.83106i	−0.351513	+	0.613546i
$63$	0.479712	+	1.85932i	0.0604380	+	0.234253i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	4.17802	−	4.64016i	0.518219	−	0.575541i
$66$	1.77890	−	0.517946i	0.218967	−	0.0637547i
$67$	5.65968	−	9.80285i	0.691440	−	1.19761i	−0.279926	−	0.960022i	$-0.590310\pi$
$67$	5.65968	−	9.80285i	0.691440	−	1.19761i	0.971366	−	0.237588i	$-0.0763567\pi$
$68$	−3.74970	−	6.49467i	−0.454718	−	0.787595i
$69$	0.0999929	−	0.104394i	0.0120377	−	0.0125675i
$70$	1.03146	−	0.749401i	0.123283	−	0.0895706i
$71$	0.823066	−	0.0865077i	0.0976799	−	0.0102666i	−0.0555624	−	0.998455i	$-0.517695\pi$
$71$	0.823066	−	0.0865077i	0.0976799	−	0.0102666i	0.153242	+	0.988189i	$0.451029\pi$
$72$	2.50070	+	1.65725i	0.294711	+	0.195309i
$73$	4.58275	+	10.2930i	0.536370	+	1.20471i	0.955015	+	0.296557i	$0.0958386\pi$
$73$	4.58275	+	10.2930i	0.536370	+	1.20471i	−0.418645	+	0.908150i	$0.637495\pi$
$74$	8.08414	−	1.71834i	0.939762	−	0.199753i
$75$	−1.15490	−	1.36502i	−0.133356	−	0.157619i
$76$	−2.85926	−	1.27302i	−0.327979	−	0.146026i
$77$	0.211578	+	0.651170i	0.0241115	+	0.0742077i
$78$	−1.83616	+	5.10949i	−0.207904	+	0.578536i
$79$	1.28631	−	2.88911i	0.144721	−	0.325050i	−0.826611	−	0.562773i	$-0.809734\pi$
$79$	1.28631	−	2.88911i	0.144721	−	0.325050i	0.971333	+	0.237723i	$0.0764012\pi$
$80$	0.414140	−	1.94838i	0.0463023	−	0.217835i
$81$	6.79918	−	5.89671i	0.755464	−	0.655190i
$82$	−0.165968	+	0.0738938i	−0.0183281	+	0.00816021i
$83$	−5.34426	−	5.93540i	−0.586609	−	0.651495i	0.374642	−	0.927169i	$-0.377765\pi$
$83$	−5.34426	−	5.93540i	−0.586609	−	0.651495i	−0.961251	+	0.275674i	$0.911099\pi$
$84$	−0.583650	+	0.942562i	−0.0636814	+	0.102842i
$85$	8.78038	+	12.0852i	0.952366	+	1.31082i
$86$	1.00326	−	9.54537i	0.108184	−	1.02930i
$87$	−0.921984	+	6.76005i	−0.0988471	+	0.724753i
$88$	0.926384	+	0.534848i	0.0987528	+	0.0570150i
$89$	13.6894	+	9.94595i	1.45108	+	1.05427i	0.985579	+	0.169219i	$0.0541245\pi$
$89$	13.6894	+	9.94595i	1.45108	+	1.05427i	0.465497	+	0.885049i	$0.345876\pi$
$90$	−5.29893	−	2.76233i	−0.558556	−	0.291175i
$91$	−1.90821	−	0.620014i	−0.200034	−	0.0649951i
$92$	0.0834598			0.00870129
$93$	−0.265196	+	9.64000i	−0.0274996	+	0.999622i
$94$	−0.726083			−0.0748897
$95$	5.92922	+	1.92652i	0.608325	+	0.197657i
$96$	0.307717	+	1.70450i	0.0314062	+	0.173965i
$97$	2.30702	+	1.67615i	0.234242	+	0.170187i	0.698714	−	0.715401i	$-0.253756\pi$
$97$	2.30702	+	1.67615i	0.234242	+	0.170187i	−0.464472	+	0.885588i	$0.653756\pi$
$98$	5.70738	+	3.29516i	0.576532	+	0.332861i
$99$	2.29018	−	2.24796i	0.230171	−	0.225929i
$100$	0.107907	−	1.02667i	0.0107907	−	0.102667i
$101$	−2.32653	−	3.20219i	−0.231498	−	0.318630i	0.677426	−	0.735591i	$-0.263095\pi$
$101$	−2.32653	−	3.20219i	−0.231498	−	0.318630i	−0.908925	+	0.416961i	$0.863095\pi$
$102$	−11.0435	−	6.83835i	−1.09347	−	0.677098i
$103$	7.65563	+	8.50243i	0.754331	+	0.837770i	0.991006	−	0.133819i	$-0.0427241\pi$
$103$	7.65563	+	8.50243i	0.754331	+	0.837770i	−0.236674	+	0.971589i	$0.576057\pi$
$104$	−2.86366	+	1.27498i	−0.280805	+	0.125022i
$105$	0.959954	−	1.98873i	0.0936820	−	0.194080i
$106$	−2.42729	+	11.4195i	−0.235759	+	1.10916i
$107$	4.66771	−	10.4839i	0.451245	−	1.01351i	−0.534485	−	0.845178i	$-0.679494\pi$
$107$	4.66771	−	10.4839i	0.451245	−	1.01351i	0.985730	−	0.168335i	$-0.0538390\pi$
$108$	5.17394	+	0.479924i	0.497863	+	0.0461807i
$109$	−0.906042	−	2.78851i	−0.0867831	−	0.267091i	0.898242	−	0.439501i	$-0.144845\pi$
$109$	−0.906042	−	2.78851i	−0.0867831	−	0.267091i	−0.985025	+	0.172410i	$0.944845\pi$
$110$	−1.94652	−	0.866646i	−0.185593	−	0.0826315i
$111$	10.9283	−	9.24609i	1.03727	−	0.877600i
$112$	−0.626083	+	0.133078i	−0.0591593	+	0.0125747i
$113$	0.372023	+	0.835577i	0.0349970	+	0.0786044i	0.930198	−	0.367058i	$-0.119635\pi$
$113$	0.372023	+	0.835577i	0.0349970	+	0.0786044i	−0.895201	+	0.445662i	$0.852968\pi$
$114$	−5.40626	+	0.400190i	−0.506342	+	0.0374812i
$115$	−0.165333	+	0.0173772i	−0.0154174	+	0.00162043i
$116$	−3.18676	+	2.31532i	−0.295883	+	0.214972i
$117$	1.38465	+	9.30150i	0.128010	+	0.859924i
$118$	−2.05624	−	3.56151i	−0.189292	−	0.327864i
$119$	2.40007	−	4.15705i	0.220014	−	0.381076i
$120$	−0.964478	−	3.31252i	−0.0880444	−	0.302391i
$121$	−6.59478	+	7.32425i	−0.599526	+	0.665841i
$122$	0.747821	−	2.30156i	0.0677045	−	0.208373i
$123$	−0.192718	+	0.248751i	−0.0173768	+	0.0224291i
$124$	−4.12523	+	3.73931i	−0.370457	+	0.335800i
$125$			12.0158i			1.07473i
$126$	−0.118329	+	1.91656i	−0.0105416	+	0.170741i
$127$	−11.0145	−	9.91754i	−0.977383	−	0.880039i	0.0154102	−	0.999881i	$-0.495095\pi$
$127$	−11.0145	−	9.91754i	−0.977383	−	0.880039i	−0.992793	+	0.119842i	$0.961761\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−6.29027	−	15.3881i	−0.553828	−	1.35485i
$130$	5.40742	−	3.12198i	0.474262	−	0.273815i
$131$	16.9742	+	1.78406i	1.48304	+	0.155874i	0.811177	−	0.584800i	$-0.198827\pi$
$131$	16.9742	+	1.78406i	1.48304	+	0.155874i	0.671864	+	0.740674i	$0.265494\pi$
$132$	1.85189	+	0.0571138i	0.161186	+	0.00497112i
$133$	−0.209404	−	1.99235i	−0.0181576	−	0.172758i
$134$	8.41193	−	7.57413i	0.726680	−	0.654305i
$135$	−10.3495	+	0.126544i	−0.890740	+	0.0108912i
$136$	−1.55921	−	7.33552i	−0.133701	−	0.629016i
$137$	0.237618	+	0.0505074i	0.0203011	+	0.00431514i	0.218051	−	0.975937i	$-0.430030\pi$
$137$	0.237618	+	0.0505074i	0.0203011	+	0.00431514i	−0.197750	+	0.980252i	$0.563363\pi$
$138$	0.127358	−	0.0683849i	0.0108415	−	0.00582131i
$139$	−21.5436	+	6.99993i	−1.82730	+	0.593726i	−0.827838	+	0.560968i	$0.810429\pi$
$139$	−21.5436	+	6.99993i	−1.82730	+	0.593726i	−0.999463	+	0.0327586i	$0.989571\pi$
$140$	1.21256	−	0.393984i	0.102480	−	0.0332977i
$141$	−1.10799	+	0.594934i	−0.0933096	+	0.0501025i
$142$	0.809514	+	0.172068i	0.0679329	+	0.0144396i
$143$	0.697157	+	3.27986i	0.0582992	+	0.274276i
$144$	1.86619	+	2.34890i	0.155516	+	0.195742i
$145$	5.83087	−	5.25014i	0.484227	−	0.436000i
$146$	1.17773	+	11.2054i	0.0974700	+	0.927365i
$147$	11.4093	+	0.351873i	0.941025	+	0.0290220i
$148$	8.21947	+	0.863901i	0.675636	+	0.0710122i
$149$	6.20496	−	3.58243i	0.508330	−	0.293484i	−0.223817	−	0.974631i	$-0.571852\pi$
$149$	6.20496	−	3.58243i	0.508330	−	0.293484i	0.732147	+	0.681147i	$0.238518\pi$
$150$	−0.676560	−	1.65509i	−0.0552409	−	0.135138i
$151$	5.08368	−	6.99708i	0.413704	−	0.569415i	−0.550413	−	0.834893i	$-0.685530\pi$
$151$	5.08368	−	6.99708i	0.413704	−	0.569415i	0.964117	+	0.265478i	$0.0855297\pi$
$152$	−2.32593	−	2.09427i	−0.188658	−	0.169868i
$153$	−22.4554	−	1.38641i	−1.81541	−	0.112085i
$154$			0.684680i			0.0551731i
$155$	7.39349	−	8.26646i	0.593859	−	0.663978i
$156$	−3.32521	+	4.29201i	−0.266230	+	0.343636i
$157$	4.35758	−	13.4113i	0.347773	−	1.07034i	−0.612310	−	0.790618i	$-0.709759\pi$
$157$	4.35758	−	13.4113i	0.347773	−	1.07034i	0.960082	−	0.279717i	$-0.0902406\pi$
$158$	2.11614	−	2.35021i	0.168351	−	0.186973i
$159$	5.65285	+	19.4149i	0.448300	+	1.53970i
$160$	0.995952	−	1.72504i	0.0787369	−	0.136376i
$161$	0.0267101	+	0.0462632i	0.00210505	+	0.00364605i
$162$	8.28859	−	3.50704i	0.651213	−	0.275539i
$163$	−9.39390	+	6.82507i	−0.735787	+	0.534581i	−0.891389	−	0.453239i	$-0.850268\pi$
$163$	−9.39390	+	6.82507i	−0.735787	+	0.534581i	0.155602	+	0.987820i	$0.450268\pi$
$164$	−0.180680	+	0.0189902i	−0.0141087	+	0.00148289i
$165$	−3.68046	+	0.272440i	−0.286524	+	0.0212095i
$166$	−3.24855	−	7.29637i	−0.252137	−	0.566308i
$167$	−21.9324	+	4.66187i	−1.69718	+	0.360746i	−0.951995	−	0.306113i	$-0.900971\pi$
$167$	−21.9324	+	4.66187i	−1.69718	+	0.360746i	−0.745183	+	0.666860i	$0.767638\pi$
$168$	−0.846352	+	0.716072i	−0.0652974	+	0.0552461i
$169$	2.89948	+	1.29093i	0.223037	+	0.0993023i
$170$	4.61612	+	14.2070i	0.354040	+	1.08962i
$171$	−7.92196	+	5.04043i	−0.605807	+	0.385452i
$172$	3.90384	−	8.76816i	0.297665	−	0.668566i
$173$	2.88585	−	13.5768i	0.219407	−	1.03223i	−0.721199	−	0.692728i	$-0.756409\pi$
$173$	2.88585	−	13.5768i	0.219407	−	1.03223i	0.940606	−	0.339500i	$-0.110258\pi$
$174$	−2.96583	+	6.14428i	−0.224839	+	0.465797i
$175$	0.603633	−	0.268755i	0.0456303	−	0.0203159i
$176$	0.715766	+	0.794939i	0.0539529	+	0.0599208i
$177$	−6.05600	−	3.74998i	−0.455197	−	0.281866i
$178$	9.94595	+	13.6894i	0.745480	+	1.02607i
$179$	−1.42045	+	13.5147i	−0.106170	+	1.01014i	0.803642	+	0.595114i	$0.202893\pi$
$179$	−1.42045	+	13.5147i	−0.106170	+	1.01014i	−0.909811	+	0.415022i	$0.863774\pi$
$180$	−4.18598	−	4.26459i	−0.312004	−	0.317864i
$181$	−21.7876	−	12.5791i	−1.61946	−	0.934994i	−0.987060	−	0.160350i	$-0.948738\pi$
$181$	−21.7876	−	12.5791i	−1.61946	−	0.934994i	−0.632397	−	0.774644i	$-0.717929\pi$
$182$	−1.62322	−	1.17934i	−0.120321	−	0.0874182i
$183$	−0.744674	−	4.12488i	−0.0550479	−	0.304920i
$184$	0.0793750	+	0.0257905i	0.00585160	+	0.00190130i
$185$	−16.4626			−1.21035
$186$	−3.23114	+	9.08624i	−0.236919	+	0.666235i
$187$	−8.02207			−0.586632
$188$	−0.690546	−	0.224372i	−0.0503632	−	0.0163640i
$189$	1.38981	+	3.02160i	0.101094	+	0.219789i
$190$	5.04369	+	3.66446i	0.365908	+	0.265848i
$191$	−18.1731	−	10.4922i	−1.31496	−	0.759192i	−0.332046	−	0.943263i	$-0.607739\pi$
$191$	−18.1731	−	10.4922i	−1.31496	−	0.759192i	−0.982913	+	0.184071i	$0.941072\pi$
$192$	−0.234063	+	1.71616i	−0.0168920	+	0.123853i
$193$	−1.71215	+	16.2900i	−0.123243	+	1.17258i	0.741707	+	0.670724i	$0.234016\pi$
$193$	−1.71215	+	16.2900i	−0.123243	+	1.17258i	−0.864950	+	0.501858i	$0.832650\pi$
$194$	1.67615	+	2.30702i	0.120340	+	0.165634i
$195$	5.69357	−	9.19478i	0.407725	−	0.658452i
$196$	4.40978	+	4.89755i	0.314984	+	0.349825i
$197$	−15.4230	+	6.86678i	−1.09885	+	0.489238i	−0.874379	−	0.485244i	$-0.838731\pi$
$197$	−15.4230	+	6.86678i	−1.09885	+	0.489238i	−0.224467	+	0.974482i	$0.572064\pi$
$198$	2.87275	−	1.43023i	0.204157	−	0.101642i
$199$	−1.01666	+	4.78302i	−0.0720692	+	0.339059i	−0.999379	−	0.0352356i	$-0.988782\pi$
$199$	−1.01666	+	4.78302i	−0.0720692	+	0.339059i	0.927310	+	0.374295i	$0.122115\pi$
$200$	0.419883	−	0.943073i	0.0296902	−	0.0666853i
$201$	6.63041	−	18.4505i	0.467673	−	1.30140i
$202$	−1.22313	−	3.76440i	−0.0860591	−	0.264863i
$203$	−2.30329	−	1.02549i	−0.161659	−	0.0719754i
$204$	−8.38987	−	9.91630i	−0.587408	−	0.694280i
$205$	0.353971	−	0.0752388i	0.0247224	−	0.00525491i
$206$	4.65354	+	10.4520i	0.324227	+	0.728226i
$207$	0.138314	−	0.208708i	0.00961348	−	0.0145062i
$208$	−3.11749	+	0.327662i	−0.216159	+	0.0227193i
$209$	−2.70857	+	1.96789i	−0.187356	+	0.136122i
$210$	1.52752	−	1.59475i	0.105409	−	0.110048i
$211$	−5.53328	−	9.58393i	−0.380927	−	0.659785i	0.610268	−	0.792195i	$-0.291062\pi$
$211$	−5.53328	−	9.58393i	−0.380927	−	0.659785i	−0.991195	+	0.132410i	$0.957728\pi$
$212$	−5.83732	+	10.1105i	−0.400909	+	0.694394i
$213$	1.37629	−	0.400723i	0.0943020	−	0.0274571i
$214$	7.67895	−	8.52834i	0.524922	−	0.582985i
$215$	−5.90784	+	18.1825i	−0.402911	+	1.24003i
$216$	4.77241	+	2.05527i	0.324721	+	0.139843i
$217$	−3.39298	−	1.08998i	−0.230331	−	0.0739924i
$218$		−	2.93201i		−	0.198581i
$219$	10.9786	+	16.1342i	0.741866	+	1.09025i
$220$	−1.58344	−	1.42574i	−0.106756	−	0.0961231i
$221$	13.8177	−	19.0185i	0.929481	−	1.27932i
$222$	13.2506	−	5.41653i	0.889324	−	0.363533i
$223$	12.5341	−	7.23658i	0.839347	−	0.484597i	−0.0176955	−	0.999843i	$-0.505633\pi$
$223$	12.5341	−	7.23658i	0.839347	−	0.484597i	0.857042	+	0.515246i	$0.172300\pi$
$224$	−0.636564	−	0.0669056i	−0.0425322	−	0.00447032i
$225$	−2.38856	−	1.97129i	−0.159237	−	0.131419i
$226$	0.0956072	+	0.909642i	0.00635970	+	0.0605085i
$227$	13.0983	−	11.7937i	0.869362	−	0.782777i	−0.108044	−	0.994146i	$-0.534459\pi$
$227$	13.0983	−	11.7937i	0.869362	−	0.782777i	0.977406	+	0.211369i	$0.0677922\pi$
$228$	−5.26532	−	1.29002i	−0.348705	−	0.0854338i
$229$	6.12824	+	28.8311i	0.404965	+	1.90521i	0.424550	+	0.905404i	$0.360432\pi$
$229$	6.12824	+	28.8311i	0.404965	+	1.90521i	−0.0195847	+	0.999808i	$0.506234\pi$
$230$	−0.162611	−	0.0345641i	−0.0107223	−	0.00227909i
$231$	0.561010	+	1.04481i	0.0369117	+	0.0687435i
$232$	−3.74626	+	1.21723i	−0.245954	+	0.0799153i
$233$	23.7568	−	7.71904i	1.55636	−	0.505691i	0.600526	−	0.799606i	$-0.294958\pi$
$233$	23.7568	−	7.71904i	1.55636	−	0.505691i	0.955832	+	0.293914i	$0.0949581\pi$
$234$	−1.55745	+	9.27413i	−0.101813	+	0.606269i
$235$	1.41468	+	0.300700i	0.0922837	+	0.0196155i
$236$	−0.855033	−	4.02261i	−0.0556579	−	0.261850i
$237$	1.30349	−	5.32029i	0.0846708	−	0.345590i
$238$	3.56720	−	3.21192i	0.231227	−	0.208198i
$239$	0.0667465	+	0.635051i	0.00431747	+	0.0410780i	0.996469	−	0.0839672i	$-0.0267591\pi$
$239$	0.0667465	+	0.635051i	0.00431747	+	0.0410780i	−0.992151	+	0.125045i	$0.960092\pi$
$240$	0.106353	−	3.44844i	0.00686504	−	0.222596i
$241$	−16.8002	−	1.76577i	−1.08220	−	0.113743i	−0.453395	−	0.891309i	$-0.649787\pi$
$241$	−16.8002	−	1.76577i	−1.08220	−	0.113743i	−0.628801	+	0.777566i	$0.716454\pi$
$242$	−8.53533	+	4.92788i	−0.548672	+	0.316776i
$243$	9.77467	−	12.1431i	0.627045	−	0.778983i
$244$	1.42244	−	1.95782i	0.0910624	−	0.125337i
$245$	−9.75546	−	8.78385i	−0.623253	−	0.561180i
$246$	−0.260154	+	0.177023i	−0.0165868	+	0.0112866i
$247$		−	9.81102i		−	0.624260i
$248$	−5.07884	+	2.28153i	−0.322507	+	0.144877i
$249$	−10.9357	−	8.47236i	−0.693022	−	0.536914i
$250$	−3.71309	+	11.4277i	−0.234836	+	0.722752i
$251$	−12.1609	+	13.5061i	−0.767592	+	0.852497i	−0.992546	−	0.121872i	$-0.961110\pi$
$251$	−12.1609	+	13.5061i	−0.767592	+	0.852497i	0.224954	+	0.974369i	$0.427777\pi$
$252$	−0.704788	+	1.78619i	−0.0443975	+	0.112520i
$253$	0.0446383	−	0.0773158i	0.00280639	−	0.00486080i
$254$	−7.41077	−	12.8358i	−0.464993	−	0.805391i
$255$	18.6849	+	17.8972i	1.17010	+	1.12077i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.19661	+	0.230873i	−0.137021	+	0.0144015i	−0.172791	−	0.984959i	$-0.555278\pi$
$257$	−2.19661	+	0.230873i	−0.137021	+	0.0144015i	0.0357696	+	0.999360i	$0.488612\pi$
$258$	−1.22722	−	16.5788i	−0.0764032	−	1.03215i
$259$	2.15164	+	4.83267i	0.133697	+	0.300288i
$260$	6.10751	−	1.29819i	0.378771	−	0.0805103i
$261$	0.508661	+	11.8062i	0.0314853	+	0.730785i
$262$	15.5921	+	6.94205i	0.963284	+	0.428882i
$263$	2.55692	+	7.86938i	0.157666	+	0.485247i	0.998421	−	0.0561690i	$-0.0178886\pi$
$263$	2.55692	+	7.86938i	0.157666	+	0.485247i	−0.840755	+	0.541416i	$0.817889\pi$
$264$	1.74360	+	0.626583i	0.107311	+	0.0385635i
$265$	9.45855	−	21.2443i	0.581034	−	1.30502i
$266$	0.416514	−	1.95954i	0.0255381	−	0.120147i
$267$	26.3941	+	12.7404i	1.61529	+	0.779698i
$268$	10.3408	−	4.60400i	0.631662	−	0.281234i
$269$	−6.60884	−	7.33986i	−0.402948	−	0.447519i	0.507184	−	0.861838i	$-0.330686\pi$
$269$	−6.60884	−	7.33986i	−0.402948	−	0.447519i	−0.910132	+	0.414319i	$0.864020\pi$
$270$	−9.88202	−	3.07781i	−0.601401	−	0.187309i
$271$	4.52044	+	6.22186i	0.274597	+	0.377951i	0.923935	−	0.382549i	$-0.124954\pi$
$271$	4.52044	+	6.22186i	0.274597	+	0.377951i	−0.649338	+	0.760500i	$0.724954\pi$
$272$	0.783901	−	7.45832i	0.0475310	−	0.452227i
$273$	−3.44332	−	0.469625i	−0.208399	−	0.0284230i
$274$	0.210381	+	0.121463i	0.0127096	+	0.00733788i
$275$	−0.893373	−	0.649074i	−0.0538724	−	0.0391406i
$276$	0.142257	−	0.0256820i	0.00856287	−	0.00154587i
$277$	−8.90516	−	2.89346i	−0.535059	−	0.173851i	0.0290095	−	0.999579i	$-0.490765\pi$
$277$	−8.90516	−	2.89346i	−0.535059	−	0.173851i	−0.564069	+	0.825728i	$0.690765\pi$
$278$	−22.6522			−1.35859
$279$	2.51436	+	16.5130i	0.150531	+	0.988605i
$280$	1.27496			0.0761933
$281$	17.3635	+	5.64176i	1.03582	+	0.336559i	0.777090	−	0.629390i	$-0.216695\pi$
$281$	17.3635	+	5.64176i	1.03582	+	0.336559i	0.258733	+	0.965949i	$0.416695\pi$
$282$	−1.23761	+	0.223428i	−0.0736984	+	0.0133049i
$283$	−13.2227	−	9.60688i	−0.786010	−	0.571070i	0.120767	−	0.992681i	$-0.461465\pi$
$283$	−13.2227	−	9.60688i	−0.786010	−	0.571070i	−0.906777	+	0.421611i	$0.861465\pi$
$284$	0.716722	+	0.413800i	0.0425296	+	0.0245545i
$285$	10.6992	+	1.45923i	0.633763	+	0.0864372i
$286$	−0.350498	+	3.33477i	−0.0207254	+	0.197189i
$287$	−0.0683504	−	0.0940763i	−0.00403460	−	0.00555315i
$288$	1.04900	+	2.81062i	0.0618132	+	0.165617i
$289$	26.2574	+	29.1617i	1.54455	+	1.71540i
$290$	7.16787	−	3.19134i	0.420912	−	0.187402i
$291$	4.44808	+	2.14708i	0.260751	+	0.125864i
$292$	−2.34257	+	11.0209i	−0.137088	+	0.644950i
$293$	4.71107	−	10.5812i	0.275223	−	0.618162i	−0.722059	−	0.691831i	$-0.756804\pi$
$293$	4.71107	−	10.5812i	0.275223	−	0.618162i	0.997283	+	0.0736692i	$0.0234709\pi$
$294$	10.7422	+	3.86033i	0.626497	+	0.225139i
$295$	2.53136	+	7.79073i	0.147382	+	0.453594i
$296$	7.55022	+	3.36157i	0.438848	+	0.195388i
$297$	3.21187	−	4.53637i	0.186371	−	0.263227i
$298$	7.00830	−	1.48966i	0.405980	−	0.0862937i
$299$	0.106410	+	0.239001i	0.00615384	+	0.0138218i
$300$	−0.131995	−	1.78315i	−0.00762075	−	0.102950i
$301$	6.10970	−	0.642156i	0.352157	−	0.0370132i
$302$	6.99708	−	5.08368i	0.402637	−	0.292533i
$303$	−4.95093	−	4.74222i	−0.284424	−	0.272433i
$304$	−1.56492	−	2.71052i	−0.0897545	−	0.155459i
$305$	−2.41020	+	4.17459i	−0.138008	+	0.239037i
$306$	−20.9280	−	8.25767i	−1.19637	−	0.472059i
$307$	17.0531	−	18.9394i	0.973274	−	1.08093i	−0.0234236	−	0.999726i	$-0.507457\pi$
$307$	17.0531	−	18.9394i	0.973274	−	1.08093i	0.996697	−	0.0812045i	$-0.0258767\pi$
$308$	−0.211578	+	0.651170i	−0.0120558	+	0.0371038i
$309$	15.6653	+	12.1366i	0.891170	+	0.690428i
$310$	9.58610	−	5.57716i	0.544454	−	0.316761i
$311$			16.3500i			0.927125i	0.886064	+	0.463563i	$0.153429\pi$
$311$			16.3500i			0.927125i	−0.886064	+	0.463563i	$0.846571\pi$
$312$	−4.48877	+	3.05440i	−0.254126	+	0.172921i
$313$	−4.14358	−	3.73090i	−0.234209	−	0.210883i	0.543666	−	0.839302i	$-0.317036\pi$
$313$	−4.14358	−	3.73090i	−0.234209	−	0.210883i	−0.777875	+	0.628419i	$0.783702\pi$
$314$	8.28862	−	11.4083i	0.467754	−	0.643808i
$315$	1.02427	−	3.68518i	0.0577113	−	0.207636i
$316$	2.73882	−	1.58126i	0.154071	−	0.0889528i
$317$	−21.3632	−	2.24537i	−1.19988	−	0.126112i	−0.516572	−	0.856244i	$-0.672792\pi$
$317$	−21.3632	−	2.24537i	−1.19988	−	0.126112i	−0.683306	+	0.730132i	$0.739459\pi$
$318$	−0.623338	+	20.2114i	−0.0349551	+	1.13340i
$319$	0.440439	+	4.19050i	0.0246599	+	0.234623i
$320$	1.48027	−	1.33284i	0.0827498	−	0.0745082i
$321$	4.73005	−	19.3060i	0.264005	−	1.07756i
$322$	0.0111067	+	0.0522528i	0.000618951	+	0.00291193i
$323$	22.9590	+	4.88009i	1.27748	+	0.271536i
$324$	8.96665	−	0.774079i	0.498147	−	0.0430044i
$325$	3.07760	−	0.999974i	0.170715	−	0.0554686i
$326$	−11.0432	+	3.58815i	−0.611626	+	0.198729i
$327$	−2.40242	−	4.47420i	−0.132854	−	0.247424i
$328$	−0.177705	−	0.0377723i	−0.00981211	−	0.00208563i
$329$	−0.0966257	−	0.454588i	−0.00532715	−	0.0250623i
$330$	−3.58452	−	0.878219i	−0.197321	−	0.0483444i
$331$	18.1573	−	16.3489i	0.998013	−	0.898615i	0.00316559	−	0.999995i	$-0.498992\pi$
$331$	18.1573	−	16.3489i	0.998013	−	0.898615i	0.994848	+	0.101380i	$0.0323257\pi$
$332$	−0.834855	−	7.94312i	−0.0458186	−	0.435935i
$333$	15.7821	−	19.1228i	0.864853	−	1.04792i
$334$	−22.2995	−	2.34377i	−1.22018	−	0.128246i
$335$	−19.5263	+	11.2735i	−1.06684	+	0.615939i
$336$	−1.02621	+	0.419487i	−0.0559842	+	0.0228849i
$337$	−7.18315	+	9.88676i	−0.391291	+	0.538566i	−0.958532	−	0.284986i	$-0.908011\pi$
$337$	−7.18315	+	9.88676i	−0.391291	+	0.538566i	0.567240	+	0.823552i	$0.308011\pi$
$338$	2.35865	+	2.12373i	0.128293	+	0.115516i
$339$	0.891233	+	1.30976i	0.0484051	+	0.0711364i
$340$			14.9381i			0.810131i
$341$	1.25766	+	5.82151i	0.0681063	+	0.315252i
$342$	−9.09181	+	2.34572i	−0.491629	+	0.126842i
$343$	−2.68806	+	8.27301i	−0.145142	+	0.446700i
$344$	6.42228	−	7.13266i	0.346266	−	0.384567i
$345$	−0.276463	+	0.0804952i	−0.0148843	+	0.00433372i
$346$	6.94007	−	12.0206i	0.373101	−	0.646229i
$347$	−10.4963	−	18.1802i	−0.563472	−	0.975963i	−0.997190	−	0.0749138i	$-0.976132\pi$
$347$	−10.4963	−	18.1802i	−0.563472	−	0.975963i	0.433718	−	0.901049i	$-0.357201\pi$
$348$	−4.71936	+	4.92707i	−0.252984	+	0.264118i
$349$	10.4202	−	7.57072i	0.557780	−	0.405251i	−0.272866	−	0.962052i	$-0.587971\pi$
$349$	10.4202	−	7.57072i	0.557780	−	0.405251i	0.830646	+	0.556801i	$0.187971\pi$
$350$	0.657139	−	0.0690680i	0.0351255	−	0.00369184i
$351$	5.22235	+	15.4283i	0.278748	+	0.823502i
$352$	0.435084	+	0.977216i	0.0231901	+	0.0520858i
$353$	−22.2687	+	4.73335i	−1.18524	+	0.251931i	−0.758030	−	0.652220i	$-0.773838\pi$
$353$	−22.2687	+	4.73335i	−1.18524	+	0.251931i	−0.427213	+	0.904151i	$0.640504\pi$
$354$	−4.60079	−	5.43785i	−0.244529	−	0.289018i
$355$	−1.50598	−	0.670504i	−0.0799290	−	0.0355867i
$356$	5.22889	+	16.0929i	0.277131	+	0.852921i
$357$	2.81172	−	7.82421i	0.148812	−	0.414101i
$358$	−5.52720	+	12.4143i	−0.292122	+	0.656116i
$359$	−4.91547	+	23.1255i	−0.259429	+	1.22052i	0.634719	+	0.772743i	$0.281116\pi$
$359$	−4.91547	+	23.1255i	−0.259429	+	1.22052i	−0.894147	+	0.447773i	$0.852217\pi$
$360$	−2.66327	−	5.34940i	−0.140367	−	0.281938i
$361$	−8.40834	+	3.74363i	−0.442544	+	0.197033i
$362$	−16.8341	−	18.6961i	−0.884779	−	0.982647i
$363$	−8.98700	+	14.5135i	−0.471695	+	0.761761i
$364$	−1.17934	−	1.62322i	−0.0618140	−	0.0850797i
$365$	2.34593	−	22.3201i	0.122792	−	1.16829i
$366$	0.566432	−	4.15311i	0.0296078	−	0.217087i
$367$	−11.1363	−	6.42952i	−0.581308	−	0.335618i	0.180345	−	0.983603i	$-0.442278\pi$
$367$	−11.1363	−	6.42952i	−0.581308	−	0.335618i	−0.761653	+	0.647985i	$0.775612\pi$
$368$	0.0675204	+	0.0490565i	0.00351975	+	0.00255724i
$369$	−0.251943	+	0.483298i	−0.0131156	+	0.0251595i
$370$	−15.6568	−	5.08721i	−0.813960	−	0.264472i
$371$	−7.47258			−0.387957
$372$	−5.88080	+	7.64305i	−0.304905	+	0.396274i
$373$	−23.1735			−1.19988			−0.599939	−	0.800045i	$-0.704809\pi$
$373$	−23.1735			−1.19988			−0.599939	+	0.800045i	$0.704809\pi$
$374$	−7.62945	−	2.47896i	−0.394509	−	0.128184i
$375$	3.69746	+	20.4809i	0.190936	+	1.05763i
$376$	−0.587413	−	0.426781i	−0.0302935	−	0.0220095i
$377$	−10.6933	−	6.17380i	−0.550735	−	0.317967i
$378$	0.388066	+	3.30318i	0.0199600	+	0.169898i
$379$	−1.14473	+	10.8914i	−0.0588010	+	0.559455i	0.924972	+	0.380036i	$0.124088\pi$
$379$	−1.14473	+	10.8914i	−0.0588010	+	0.559455i	−0.983773	+	0.179419i	$0.942578\pi$
$380$	3.66446	+	5.04369i	0.187983	+	0.258736i
$381$	−21.8261	−	13.5151i	−1.11818	−	0.692398i
$382$	−14.0414	−	15.5945i	−0.718418	−	0.797884i
$383$	3.31247	−	1.47481i	0.169259	−	0.0753592i	−0.320358	−	0.947297i	$-0.603803\pi$
$383$	3.31247	−	1.47481i	0.169259	−	0.0753592i	0.489617	+	0.871937i	$0.337136\pi$
$384$	−0.752930	+	1.55984i	−0.0384228	+	0.0796002i
$385$	0.283553	−	1.33401i	0.0144512	−	0.0679877i
$386$	−6.66225	+	14.9636i	−0.339099	+	0.761630i
$387$	−15.4569	−	24.2934i	−0.785720	−	1.23490i
$388$	0.881202	+	2.71206i	0.0447363	+	0.137684i
$389$	3.73499	+	1.66292i	0.189372	+	0.0843136i	0.499232	−	0.866468i	$-0.333616\pi$
$389$	3.73499	+	1.66292i	0.189372	+	0.0843136i	−0.309860	+	0.950782i	$0.600282\pi$
$390$	8.25625	−	6.98535i	0.418071	−	0.353717i
$391$	−0.612221	+	0.130132i	−0.0309614	+	0.00658104i
$392$	2.68052	+	6.02055i	0.135387	+	0.304084i
$393$	29.4814	−	2.18232i	1.48714	−	0.110083i
$394$	−16.7901	+	1.76471i	−0.845874	+	0.0889050i
$395$	−5.09635	+	3.70271i	−0.256425	+	0.186304i
$396$	3.17411	−	0.472506i	0.159505	−	0.0237443i
$397$	−6.98168	−	12.0926i	−0.350400	−	0.606911i	0.635919	−	0.771756i	$-0.280621\pi$
$397$	−6.98168	−	12.0926i	−0.350400	−	0.606911i	−0.986320	+	0.164845i	$0.947288\pi$
$398$	−2.44494	+	4.23475i	−0.122554	+	0.212269i
$399$	−0.970007	−	3.33151i	−0.0485611	−	0.166784i
$400$	0.690758	−	0.767164i	0.0345379	−	0.0383582i
$401$	−7.01809	+	21.5995i	−0.350467	+	1.07863i	0.608125	+	0.793842i	$0.291922\pi$
$401$	−7.01809	+	21.5995i	−0.350467	+	1.07863i	−0.958592	+	0.284785i	$0.908078\pi$
$402$	12.0074	−	15.4986i	0.598875	−	0.772999i
$403$	−15.9677	−	7.04571i	−0.795409	−	0.350972i
$404$		−	3.95813i		−	0.196924i
$405$	−17.6017	+	3.40040i	−0.874635	+	0.168967i
$406$	−1.87367	−	1.68706i	−0.0929886	−	0.0837273i
$407$	5.19647	−	7.15233i	0.257579	−	0.354528i
$408$	−4.91494	−	12.0236i	−0.243326	−	0.595256i
$409$	−17.1209	+	9.88474i	−0.846573	+	0.488769i	−0.859493	−	0.511147i	$-0.829221\pi$
$409$	−17.1209	+	9.88474i	−0.846573	+	0.488769i	0.0129201	+	0.999917i	$0.495887\pi$
$410$	0.359896	+	0.0378266i	0.0177740	+	0.00186812i
$411$	0.420562	+	0.0129705i	0.0207448	+	0.000639787i
$412$	1.19593	+	11.3785i	0.0589191	+	0.560577i
$413$	1.95616	−	1.76134i	0.0962564	−	0.0866697i
$414$	0.196039	−	0.155752i	0.00963478	−	0.00765480i
$415$	3.30768	+	15.5614i	0.162368	+	0.763880i
$416$	−3.06617	−	0.651734i	−0.150331	−	0.0319539i
$417$	−34.5669	+	18.5607i	−1.69275	+	0.908920i
$418$	−3.18412	+	1.03458i	−0.155740	+	0.0506031i
$419$	1.91732	−	0.622976i	0.0936674	−	0.0304344i	−0.261808	−	0.965120i	$-0.584319\pi$
$419$	1.91732	−	0.622976i	0.0936674	−	0.0304344i	0.355476	+	0.934685i	$0.384319\pi$
$420$	1.94556	−	1.04467i	0.0949338	−	0.0509746i
$421$	−7.64033	−	1.62400i	−0.372367	−	0.0791491i	0.0179270	−	0.999839i	$-0.494293\pi$
$421$	−7.64033	−	1.62400i	−0.372367	−	0.0791491i	−0.390294	+	0.920690i	$0.627627\pi$
$422$	−2.30087	−	10.8247i	−0.112005	−	0.526940i
$423$	−1.70550	+	1.35501i	−0.0829240	+	0.0658828i
$424$	−8.67594	+	7.81185i	−0.421341	+	0.379377i
$425$	0.809238	+	7.69938i	0.0392538	+	0.373475i
$426$	1.43276	+	0.0441876i	0.0694176	+	0.00214090i
$427$	1.54048	+	0.161911i	0.0745493	+	0.00783544i
$428$	9.93852	−	5.73801i	0.480396	−	0.277357i
$429$	2.19757	+	5.37599i	0.106100	+	0.259555i
$430$	−11.2374	+	15.4669i	−0.541915	+	0.745882i
$431$	23.5949	+	21.2449i	1.13653	+	1.02333i	0.999463	+	0.0327708i	$0.0104331\pi$
$431$	23.5949	+	21.2449i	1.13653	+	1.02333i	0.137064	+	0.990562i	$0.456234\pi$
$432$	3.90371	+	3.42943i	0.187818	+	0.164999i
$433$		−	14.5844i		−	0.700881i	−0.936585	−	0.350441i	$-0.886032\pi$
$433$		−	14.5844i		−	0.700881i	0.936585	−	0.350441i	$-0.113968\pi$
$434$	−2.89010	−	2.08512i	−0.138729	−	0.100089i
$435$	8.32314	−	10.7431i	0.399064	−	0.515092i
$436$	0.906042	−	2.78851i	0.0433915	−	0.133545i
$437$	−0.174788	+	0.194122i	−0.00836124	+	0.00928609i
$438$	5.45553	+	18.7372i	0.260675	+	0.895296i
$439$	12.9947	−	22.5074i	0.620201	−	1.07422i	−0.369246	−	0.929331i	$-0.620384\pi$
$439$	12.9947	−	22.5074i	0.620201	−	1.07422i	0.989448	−	0.144889i	$-0.0462825\pi$
$440$	−1.06537	−	1.84527i	−0.0507893	−	0.0879696i
$441$	19.5554	−	2.91107i	0.931212	−	0.138623i
$442$	19.0185	−	13.8177i	0.904616	−	0.657242i
$443$	24.1723	−	2.54061i	1.14846	−	0.120708i	0.488885	−	0.872348i	$-0.337404\pi$
$443$	24.1723	−	2.54061i	1.14846	−	0.120708i	0.659574	+	0.751640i	$0.270737\pi$
$444$	14.2759	−	1.05675i	0.677504	−	0.0501512i
$445$	−13.7091	−	30.7911i	−0.649874	−	1.45964i
$446$	14.1569	−	3.00914i	0.670348	−	0.142487i
$447$	9.47396	−	8.01562i	0.448103	−	0.379126i
$448$	−0.584733	−	0.260340i	−0.0276260	−	0.0122999i
$449$	0.271312	+	0.835013i	0.0128040	+	0.0394067i	0.957254	−	0.289247i	$-0.0934050\pi$
$449$	0.271312	+	0.835013i	0.0128040	+	0.0394067i	−0.944450	+	0.328654i	$0.893405\pi$
$450$	−1.66249	−	2.61291i	−0.0783707	−	0.123174i
$451$	−0.0790439	+	0.177536i	−0.00372203	+	0.00835982i
$452$	−0.190167	+	0.894665i	−0.00894470	+	0.0420815i
$453$	6.51200	−	13.4908i	0.305960	−	0.633855i
$454$	16.1016	−	7.16891i	0.755688	−	0.336454i
$455$	2.67423	+	2.97003i	0.125370	+	0.139237i
$456$	−4.60898	−	2.85396i	−0.215835	−	0.133649i
$457$	7.43679	+	10.2359i	0.347878	+	0.478813i	0.946722	−	0.322053i	$-0.104373\pi$
$457$	7.43679	+	10.2359i	0.347878	+	0.478813i	−0.598844	+	0.800866i	$0.704373\pi$
$458$	−3.08100	+	29.3137i	−0.143966	+	1.36974i
$459$	−38.7019	+	4.54678i	−1.80645	+	0.212226i
$460$	−0.143971	−	0.0831220i	−0.00671270	−	0.00387558i
$461$	22.4822	+	16.3343i	1.04710	+	0.760764i	0.971659	−	0.236386i	$-0.0759629\pi$
$461$	22.4822	+	16.3343i	1.04710	+	0.760764i	0.0754429	+	0.997150i	$0.475963\pi$
$462$	0.210688	+	1.16704i	0.00980207	+	0.0542954i
$463$	30.3313	+	9.85524i	1.40962	+	0.458012i	0.912287	−	0.409551i	$-0.134314\pi$
$463$	30.3313	+	9.85524i	1.40962	+	0.458012i	0.497328	+	0.867562i	$0.334314\pi$
$464$	−3.93905			−0.182866
$465$	10.0585	−	16.3653i	0.466449	−	0.758921i
$466$	24.9793			1.15715
$467$	9.65389	+	3.13674i	0.446729	+	0.145151i	0.523738	−	0.851879i	$-0.324537\pi$
$467$	9.65389	+	3.13674i	0.446729	+	0.145151i	−0.0770092	+	0.997030i	$0.524537\pi$
$468$	−4.34708	+	8.33895i	−0.200944	+	0.385468i
$469$	5.86148	+	4.25861i	0.270658	+	0.196645i
$470$	1.25252	+	0.723143i	0.0577745	+	0.0333561i
$471$	3.30062	−	24.2004i	0.152084	−	1.11509i
$472$	0.429871	−	4.08995i	0.0197864	−	0.188255i
$473$	−6.03472	−	8.30608i	−0.277477	−	0.381914i
$474$	2.88375	−	4.65710i	0.132455	−	0.213908i
$475$	2.16197	+	2.40111i	0.0991978	+	0.110170i
$476$	4.38515	−	1.95239i	0.200993	−	0.0894878i
$477$	15.6095	+	31.3531i	0.714712	+	1.43556i
$478$	−0.132762	+	0.624595i	−0.00607238	+	0.0285683i
$479$	8.56881	−	19.2459i	0.391519	−	0.879366i	−0.605018	−	0.796212i	$-0.706834\pi$
$479$	8.56881	−	19.2459i	0.391519	−	0.879366i	0.996537	−	0.0831540i	$-0.0264993\pi$
$480$	1.16677	−	3.24679i	0.0532557	−	0.148195i
$481$	8.00577	+	24.6392i	0.365032	+	1.12345i
$482$	−15.4323	−	6.87090i	−0.702922	−	0.312961i
$483$	0.0597632	+	0.0706364i	0.00271932	+	0.00321407i
$484$	−9.64038	+	2.04913i	−0.438199	+	0.0931421i
$485$	−2.31033	−	5.18910i	−0.104907	−	0.235625i
$486$	13.0487	−	8.52828i	0.591901	−	0.386850i
$487$	−24.6316	+	2.58889i	−1.11617	+	0.117314i	−0.644602	−	0.764518i	$-0.722977\pi$
$487$	−24.6316	+	2.58889i	−1.11617	+	0.117314i	−0.471564	+	0.881832i	$0.656310\pi$
$488$	1.95782	−	1.42244i	0.0886264	−	0.0643908i
$489$	−13.9117	+	14.5240i	−0.629108	+	0.656797i
$490$	−6.56363	−	11.3685i	−0.296515	−	0.513578i
$491$	−2.70340	+	4.68243i	−0.122003	+	0.211315i	−0.920557	−	0.390607i	$-0.872265\pi$
$491$	−2.70340	+	4.68243i	−0.122003	+	0.211315i	0.798555	+	0.601922i	$0.205598\pi$
$492$	−0.302124	+	0.0879669i	−0.0136208	+	0.00396585i
$493$	19.7665	−	21.9529i	0.890236	−	0.988708i
$494$	3.03177	−	9.33083i	0.136406	−	0.419814i
$495$	−6.18950	+	1.59691i	−0.278198	+	0.0717759i
$496$	−5.53530	+	0.600415i	−0.248542	+	0.0269594i
$497$			0.529722i			0.0237613i
$498$	−7.78236	−	11.4370i	−0.348736	−	0.512504i
$499$	15.9222	+	14.3365i	0.712778	+	0.641788i	0.943554	−	0.331219i	$-0.107460\pi$
$499$	15.9222	+	14.3365i	0.712778	+	0.641788i	−0.230776	+	0.973007i	$0.574127\pi$
$500$	−7.06271	+	9.72099i	−0.315854	+	0.434736i
$501$	−35.9491	+	14.6951i	−1.60609	+	0.656529i
$502$	−15.7394	+	9.08712i	−0.702482	+	0.405578i
$503$	−30.2586	−	3.18030i	−1.34916	−	0.141803i	−0.597775	−	0.801664i	$-0.703948\pi$
$503$	−30.2586	−	3.18030i	−1.34916	−	0.141803i	−0.751387	+	0.659861i	$0.770615\pi$
$504$	−1.22226	+	1.48098i	−0.0544436	+	0.0659680i
$505$	0.824124	+	7.84102i	0.0366731	+	0.348921i
$506$	0.0663455	−	0.0597377i	0.00294942	−	0.00265567i
$507$	5.33939	+	1.30817i	0.237131	+	0.0580978i
$508$	−3.08157	−	14.4976i	−0.136723	−	0.643229i
$509$	18.6818	+	3.97095i	0.828058	+	0.176009i	0.602397	−	0.798197i	$-0.294212\pi$
$509$	18.6818	+	3.97095i	0.828058	+	0.176009i	0.225661	+	0.974206i	$0.427546\pi$
$510$	12.2399	+	22.7953i	0.541991	+	1.00939i
$511$	−6.85878	+	2.22855i	−0.303414	+	0.0985853i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−11.9519	+	11.0291i	−0.527690	+	0.486948i
$514$	−2.16045	−	0.459217i	−0.0952933	−	0.0202552i
$515$	−4.73824	−	22.2917i	−0.208792	−	0.982288i
$516$	3.95597	−	16.1466i	0.174152	−	0.710813i
$517$	−0.577191	+	0.519705i	−0.0253848	+	0.0228566i
$518$	0.552957	+	5.26104i	0.0242956	+	0.231157i
$519$	0.741096	−	24.0297i	0.0325305	−	1.05479i
$520$	6.20975	+	0.652671i	0.272315	+	0.0286215i
$521$	34.6844	−	20.0251i	1.51955	−	0.877314i	0.519818	−	0.854277i	$-0.326000\pi$
$521$	34.6844	−	20.0251i	1.51955	−	0.877314i	0.999735	−	0.0230373i	$-0.00733365\pi$
$522$	−3.16455	+	11.3855i	−0.138509	+	0.498332i
$523$	−12.4870	+	17.1869i	−0.546019	+	0.751531i	−0.989465	−	0.144770i	$-0.953756\pi$
$523$	−12.4870	+	17.1869i	−0.546019	+	0.751531i	0.443446	+	0.896301i	$0.353756\pi$
$524$	12.6838	+	11.4205i	0.554093	+	0.498907i
$525$	0.946190	−	0.643839i	0.0412951	−	0.0280995i
$526$			8.27435i			0.360779i
$527$	24.4304	−	33.8619i	1.06420	−	1.47505i
$528$	1.46464	+	1.13472i	0.0637401	+	0.0493822i
$529$	−7.10524	+	21.8677i	−0.308923	+	0.950768i
$530$	15.5605	−	17.2816i	0.675903	−	0.750666i
$531$	−11.4764	−	4.52829i	−0.498032	−	0.196511i
$532$	1.00166	−	1.73493i	0.0434275	−	0.0752186i
$533$	−0.284745	−	0.493193i	−0.0123337	−	0.0213626i
$534$	21.1653	+	20.2730i	0.915912	+	0.877300i
$535$	−18.4934	+	13.4362i	−0.799540	+	0.580899i
$536$	11.2574	−	1.18320i	0.486244	−	0.0511063i
$537$	1.73754	+	23.4729i	0.0749805	+	1.01293i
$538$	−4.01724	−	9.02286i	−0.173195	−	0.389003i
$539$	6.89557	−	1.46570i	0.297013	−	0.0631322i
$540$	−8.44727	−	5.98088i	−0.363513	−	0.257376i
$541$	29.2366	+	13.0170i	1.25698	+	0.559644i	0.923676	−	0.383175i	$-0.125169\pi$
$541$	29.2366	+	13.0170i	1.25698	+	0.559644i	0.333305	+	0.942819i	$0.391836\pi$
$542$	2.37654	+	7.31423i	0.102081	+	0.314173i
$543$	−41.0076	−	14.7366i	−1.75981	−	0.632407i
$544$	3.05028	−	6.85104i	0.130780	−	0.293736i
$545$	−1.21426	+	5.71266i	−0.0520134	+	0.244704i
$546$	−3.12967	−	1.51068i	−0.133937	−	0.0646513i
$547$	15.5239	−	6.91171i	0.663756	−	0.295523i	−0.0470695	−	0.998892i	$-0.514988\pi$
$547$	15.5239	−	6.91171i	0.663756	−	0.295523i	0.710826	+	0.703368i	$0.248322\pi$
$548$	0.162550	+	0.180530i	0.00694379	+	0.00771186i
$549$	−2.53859	−	6.80170i	−0.108344	−	0.290290i
$550$	−0.649074	−	0.893373i	−0.0276766	−	0.0380936i
$551$	1.28869	−	12.2611i	0.0549001	−	0.522339i
$552$	0.143231	+	0.0195348i	0.00609630	+	0.000831457i
$553$	1.75304	+	1.01212i	0.0745468	+	0.0430396i
$554$	−7.57518	−	5.50369i	−0.321839	−	0.233829i
$555$	−28.0604	+	5.06581i	−1.19110	+	0.215032i
$556$	−21.5436	−	6.99993i	−0.913651	−	0.296863i
$557$	21.0884			0.893544			0.446772	−	0.894648i	$-0.352573\pi$
$557$	21.0884			0.893544			0.446772	+	0.894648i	$0.352573\pi$
$558$	−2.71148	+	16.4817i	−0.114786	+	0.697728i
$559$	30.0863			1.27252
$560$	1.21256	+	0.393984i	0.0512399	+	0.0166488i
$561$	−13.6736	+	2.46853i	−0.577300	+	0.104221i
$562$	14.7703	+	10.7313i	0.623048	+	0.452671i
$563$	−12.8332	−	7.40925i	−0.540855	−	0.312263i	0.204570	−	0.978852i	$-0.434420\pi$
$563$	−12.8332	−	7.40925i	−0.540855	−	0.312263i	−0.745425	+	0.666589i	$0.767754\pi$
$564$	−1.24608	−	0.169949i	−0.0524693	−	0.00715614i
$565$	0.190440	−	1.81192i	0.00801189	−	0.0762280i
$566$	−9.60688	−	13.2227i	−0.403807	−	0.555793i
$567$	3.29873	+	4.72263i	0.138534	+	0.198332i
$568$	0.553772	+	0.615026i	0.0232358	+	0.0258059i
$569$	−9.29957	+	4.14043i	−0.389858	+	0.173576i	−0.592299	−	0.805719i	$-0.701779\pi$
$569$	−9.29957	+	4.14043i	−0.389858	+	0.173576i	0.202440	+	0.979295i	$0.435113\pi$
$570$	9.72458	+	4.69403i	0.407318	+	0.196611i
$571$	1.20565	−	5.67215i	0.0504550	−	0.237372i	−0.945693	−	0.325061i	$-0.894615\pi$
$571$	1.20565	−	5.67215i	0.0504550	−	0.237372i	0.996148	+	0.0876895i	$0.0279483\pi$
$572$	−1.36384	+	3.06324i	−0.0570252	+	0.128081i
$573$	−34.2046	−	12.2918i	−1.42892	−	0.513499i
$574$	−0.0359339	−	0.110593i	−0.00149985	−	0.00461608i
$575$	−0.0787087	−	0.0350434i	−0.00328238	−	0.00146141i
$576$	0.129133	+	2.99722i	0.00538054	+	0.124884i
$577$	−6.46293	+	1.37374i	−0.269055	+	0.0571895i	−0.340464	−	0.940258i	$-0.610584\pi$
$577$	−6.46293	+	1.37374i	−0.269055	+	0.0571895i	0.0714083	+	0.997447i	$0.477251\pi$
$578$	15.9608	+	35.8484i	0.663880	+	1.49110i
$579$	2.09436	+	28.2932i	0.0870385	+	1.17582i
$580$	7.80322	−	0.820152i	0.324011	−	0.0340549i
$581$	4.13582	−	3.00485i	0.171583	−	0.124662i
$582$	3.56689	+	3.41653i	0.147853	+	0.141620i
$583$	6.24415	+	10.8152i	0.258606	+	0.447919i
$584$	−5.63356	+	9.75761i	−0.233118	+	0.403773i
$585$	6.87528	−	17.4245i	0.284258	−	0.720414i
$586$	7.75027	−	8.60755i	0.320161	−	0.355574i
$587$	6.82206	−	20.9962i	0.281577	−	0.866604i	−0.705827	−	0.708384i	$-0.749425\pi$
$587$	6.82206	−	20.9962i	0.281577	−	0.866604i	0.987404	−	0.158220i	$-0.0505755\pi$
$588$	9.02351	+	6.99091i	0.372123	+	0.288300i
$589$	−0.0579951	−	17.4261i	−0.00238965	−	0.718032i
$590$			8.19166i			0.337245i
$591$	−24.1755	+	16.4503i	−0.994447	+	0.676676i
$592$	6.14190	+	5.53019i	0.252431	+	0.227290i
$593$	11.9102	−	16.3930i	0.489094	−	0.673181i	−0.491126	−	0.871088i	$-0.663415\pi$
$593$	11.9102	−	16.3930i	0.489094	−	0.673181i	0.980221	+	0.197908i	$0.0634146\pi$
$594$	4.45648	−	3.32182i	0.182852	−	0.136296i
$595$	−8.28043	+	4.78071i	−0.339465	+	0.195990i
$596$	7.12562	+	0.748932i	0.291877	+	0.0306775i
$597$	−0.261083	+	8.46548i	−0.0106854	+	0.346469i
$598$	0.0273466	+	0.260185i	0.00111829	+	0.0106398i
$599$	−18.5246	+	16.6796i	−0.756894	+	0.681511i	−0.954313	−	0.298808i	$-0.903411\pi$
$599$	−18.5246	+	16.6796i	−0.756894	+	0.681511i	0.197419	+	0.980319i	$0.436744\pi$
$600$	0.425490	−	1.73667i	0.0173706	−	0.0708992i
$601$	−2.93501	−	13.8081i	−0.119722	−	0.563246i	−0.996590	−	0.0825150i	$-0.973705\pi$
$601$	−2.93501	−	13.8081i	−0.119722	−	0.563246i	0.876868	−	0.480731i	$-0.159629\pi$
$602$	6.00911	+	1.27728i	0.244913	+	0.0520579i
$603$	5.62398	−	33.4891i	0.229026	−	1.36378i
$604$	8.22557	−	2.67265i	0.334694	−	0.108749i
$605$	18.6709	−	6.06653i	0.759078	−	0.246640i
$606$	−3.24319	−	6.04004i	−0.131746	−	0.245360i
$607$	14.6676	+	3.11770i	0.595340	+	0.126543i	0.495720	−	0.868482i	$-0.334904\pi$
$607$	14.6676	+	3.11770i	0.595340	+	0.126543i	0.0996197	+	0.995026i	$0.468237\pi$
$608$	−0.650731	−	3.06145i	−0.0263906	−	0.124158i
$609$	−4.24152	−	1.03919i	−0.171875	−	0.0421100i
$610$	−3.58226	+	3.22548i	−0.145041	+	0.130596i
$611$	−0.237910	−	2.26356i	−0.00962479	−	0.0915738i
$612$	−17.3519	−	14.3206i	−0.701410	−	0.578876i
$613$	34.9682	+	3.67530i	1.41235	+	0.148444i	0.779778	−	0.626056i	$-0.215332\pi$
$613$	34.9682	+	3.67530i	1.41235	+	0.148444i	0.632574	+	0.774500i	$0.281999\pi$
$614$	22.0711	−	12.7428i	0.890717	−	0.514256i
$615$	0.580190	−	0.237167i	0.0233955	−	0.00956350i
$616$	−0.402445	+	0.553918i	−0.0162150	+	0.0223180i
$617$	−10.0155	−	9.01797i	−0.403207	−	0.363050i	0.442434	−	0.896801i	$-0.354115\pi$
$617$	−10.0155	−	9.01797i	−0.403207	−	0.363050i	−0.845641	+	0.533751i	$0.820782\pi$
$618$	11.1482	+	16.3835i	0.448446	+	0.659039i
$619$		−	27.0877i		−	1.08875i	−0.838843	−	0.544373i	$-0.816768\pi$
$619$		−	27.0877i		−	1.08875i	0.838843	−	0.544373i	$-0.183232\pi$
$620$	10.8404	−	2.34192i	0.435359	−	0.0940539i
$621$	0.171533	−	0.398304i	0.00688336	−	0.0159834i
$622$	−5.05244	+	15.5498i	−0.202584	+	0.623490i
$623$	−7.24713	+	8.04875i	−0.290350	+	0.322466i
$624$	−5.21293	+	1.51780i	−0.208684	+	0.0607608i
$625$	9.38635	−	16.2576i	0.375454	−	0.650306i
$626$	−2.78787	−	4.82874i	−0.111426	−	0.192995i
$627$	−4.01120	+	4.18774i	−0.160192	+	0.167242i
$628$	11.4083	−	8.28862i	0.455241	−	0.330752i
$629$	−61.6411	+	6.47874i	−2.45779	+	0.258324i
$630$	2.11292	−	3.18829i	0.0841809	−	0.127025i
$631$	11.2085	+	25.1747i	0.446204	+	1.00219i	0.986953	+	0.161006i	$0.0514739\pi$
$631$	11.2085	+	25.1747i	0.446204	+	1.00219i	−0.540750	+	0.841183i	$0.681859\pi$
$632$	3.09341	−	0.657525i	0.123049	−	0.0261549i
$633$	−12.3806	−	14.6331i	−0.492085	−	0.581613i
$634$	−19.6238	−	8.73707i	−0.779360	−	0.346993i
$635$	9.12313	+	28.0781i	0.362040	+	1.11425i
$636$	−6.83851	+	19.0296i	−0.271165	+	0.754573i
$637$	−8.40254	+	18.8724i	−0.332921	+	0.747752i
$638$	−0.876053	+	4.12151i	−0.0346833	+	0.163172i
$639$	2.22258	−	1.10654i	0.0879238	−	0.0437740i
$640$	1.81969	−	0.810180i	0.0719297	−	0.0320252i
$641$	9.06035	+	10.0625i	0.357862	+	0.397446i	0.895013	−	0.446040i	$-0.147166\pi$
$641$	9.06035	+	10.0625i	0.357862	+	0.397446i	−0.537151	+	0.843486i	$0.680499\pi$
$642$	10.4644	−	16.8995i	0.412998	−	0.666969i
$643$	3.33937	+	4.59624i	0.131692	+	0.181258i	0.869771	−	0.493456i	$-0.164267\pi$
$643$	3.33937	+	4.59624i	0.131692	+	0.181258i	−0.738079	+	0.674715i	$0.764267\pi$
$644$	−0.00558393	+	0.0531275i	−0.000220038	+	0.00209352i
$645$	−4.47485	+	32.8099i	−0.176197	+	1.29189i
$646$	20.3273	+	11.7360i	0.799767	+	0.461746i
$647$	1.08772	+	0.790274i	0.0427627	+	0.0310689i	0.608961	−	0.793200i	$-0.291586\pi$
$647$	1.08772	+	0.790274i	0.0427627	+	0.0310689i	−0.566199	+	0.824269i	$0.691586\pi$
$648$	8.76699	+	2.03465i	0.344400	+	0.0799288i
$649$	−4.18379	−	1.35940i	−0.164228	−	0.0533610i
$650$	3.23598			0.126926
$651$	−6.11873	−	0.813784i	−0.239812	−	0.0318947i
$652$	−11.6115			−0.454741
$653$	−2.66488	−	0.865873i	−0.104285	−	0.0338842i	0.256410	−	0.966568i	$-0.417460\pi$
$653$	−2.66488	−	0.865873i	−0.104285	−	0.0338842i	−0.360695	+	0.932684i	$0.617460\pi$
$654$	−0.902230	−	4.99761i	−0.0352800	−	0.195422i
$655$	−27.5043	−	19.9830i	−1.07468	−	0.780802i
$656$	−0.157335	−	0.0908375i	−0.00614290	−	0.00354661i
$657$	23.6778	+	24.1225i	0.923759	+	0.941107i
$658$	0.0485790	−	0.462198i	0.00189381	−	0.0180184i
$659$	−9.40591	−	12.9461i	−0.366402	−	0.504309i	0.585516	−	0.810661i	$-0.300892\pi$
$659$	−9.40591	−	12.9461i	−0.366402	−	0.504309i	−0.951919	+	0.306351i	$0.900892\pi$
$660$	−3.13769	−	1.94291i	−0.122135	−	0.0756278i
$661$	−5.93560	−	6.59215i	−0.230868	−	0.256405i	0.616569	−	0.787301i	$-0.288522\pi$
$661$	−5.93560	−	6.59215i	−0.230868	−	0.256405i	−0.847437	+	0.530896i	$0.821855\pi$
$662$	22.3207	−	9.93780i	0.867517	−	0.386244i
$663$	17.7000	−	36.6689i	0.687410	−	1.42410i
$664$	1.66056	−	7.81234i	0.0644424	−	0.303177i
$665$	−1.62305	+	3.64543i	−0.0629392	+	0.141364i
$666$	20.9189	−	13.3099i	0.810591	−	0.515748i
$667$	0.101590	+	0.312662i	0.00393358	+	0.0121063i
$668$	−20.4838	−	9.12000i	−0.792544	−	0.352863i
$669$	19.1376	−	16.1917i	0.739901	−	0.626007i
$670$	−22.0544	+	4.68780i	−0.852034	+	0.181106i
$671$	−1.05290	−	2.36486i	−0.0406469	−	0.0912945i
$672$	−1.10561	+	0.0818410i	−0.0426498	+	0.00315708i
$673$	22.1724	−	2.33041i	0.854682	−	0.0898307i	0.332955	−	0.942943i	$-0.391954\pi$
$673$	22.1724	−	2.33041i	0.854682	−	0.0898307i	0.521728	+	0.853112i	$0.325288\pi$
$674$	−9.88676	+	7.18315i	−0.380824	+	0.276685i
$675$	−4.67789	−	2.62505i	−0.180052	−	0.101038i
$676$	1.58694	+	2.74865i	0.0610360	+	0.105717i
$677$	−21.2437	+	36.7951i	−0.816461	+	1.41415i	0.0918132	+	0.995776i	$0.470734\pi$
$677$	−21.2437	+	36.7951i	−0.816461	+	1.41415i	−0.908274	+	0.418376i	$0.862600\pi$
$678$	0.442874	+	1.52106i	0.0170085	+	0.0584160i
$679$	−1.22133	+	1.35642i	−0.0468702	+	0.0520546i
$680$	−4.61612	+	14.2070i	−0.177020	+	0.544812i
$681$	18.6968	−	24.1329i	0.716464	−	0.924776i
$682$	−0.602836	+	5.92523i	−0.0230838	+	0.226889i
$683$		−	7.94632i		−	0.304058i	−0.988376	−	0.152029i	$-0.951419\pi$
$683$		−	7.94632i		−	0.304058i	0.988376	−	0.152029i	$-0.0485807\pi$
$684$	−9.37169	−	0.578612i	−0.358335	−	0.0221238i
$685$	−0.359598	−	0.323784i	−0.0137395	−	0.0123711i
$686$	−5.11300	+	7.03744i	−0.195215	+	0.268691i
$687$	19.3174	+	47.2568i	0.737004	+	1.80296i
$688$	8.31206	−	4.79897i	0.316894	−	0.182959i
$689$	−36.3956	−	3.82533i	−1.38656	−	0.145734i
$690$	−0.287806	−	0.00887619i	−0.0109566	−	0.000337911i
$691$	−0.878693	−	8.36020i	−0.0334271	−	0.318037i	−0.998440	−	0.0558350i	$-0.982218\pi$
$691$	−0.878693	−	8.36020i	−0.0334271	−	0.318037i	0.965013	−	0.262202i	$-0.0844487\pi$
$692$	10.3150	−	9.28763i	0.392116	−	0.353063i
$693$	1.27774	+	1.60824i	0.0485375	+	0.0610922i
$694$	−4.36462	−	20.5339i	−0.165679	−	0.779457i
$695$	44.1351	+	9.38120i	1.67414	+	0.355849i
$696$	−6.01092	+	3.22756i	−0.227843	+	0.122340i
$697$	1.29577	−	0.421021i	0.0490808	−	0.0159473i
$698$	12.2497	−	3.98016i	0.463657	−	0.150651i
$699$	38.1181	−	20.4674i	1.44176	−	0.774149i
$700$	0.646319	+	0.137379i	0.0244286	+	0.00519245i
$701$	4.66103	+	21.9284i	0.176045	+	0.828225i	0.974185	+	0.225753i	$0.0724842\pi$
$701$	4.66103	+	21.9284i	0.176045	+	0.828225i	−0.798140	+	0.602472i	$0.794182\pi$
$702$	0.199143	+	16.2870i	0.00751616	+	0.614713i
$703$	−19.2232	+	17.3086i	−0.725017	+	0.652808i
$704$	0.111814	+	1.06384i	0.00421413	+	0.0400948i
$705$	2.50385	+	0.0772209i	0.0943005	+	0.00290831i
$706$	−22.6415	−	2.37971i	−0.852123	−	0.0895617i
$707$	2.19406	−	1.26674i	0.0825161	−	0.0476407i
$708$	−2.69523	−	6.59342i	−0.101293	−	0.247796i
$709$	7.46651	−	10.2768i	0.280411	−	0.385952i	−0.645459	−	0.763795i	$-0.723334\pi$
$709$	7.46651	−	10.2768i	0.280411	−	0.385952i	0.925870	+	0.377843i	$0.123334\pi$
$710$	−1.22507	−	1.10306i	−0.0459761	−	0.0413971i
$711$	0.584653	−	9.46953i	0.0219262	−	0.355135i
$712$			16.9211i			0.634143i
$713$	0.190416	+	0.423879i	0.00713114	+	0.0158744i
$714$	5.09192	−	6.57240i	0.190560	−	0.245966i
$715$	2.06396	−	6.35223i	0.0771879	−	0.237560i
$716$	−9.09291	+	10.0987i	−0.339818	+	0.377406i
$717$	0.309185	+	1.06190i	0.0115467	+	0.0396575i
$718$	−11.8211	+	20.4747i	−0.441158	+	0.764108i
$719$	−16.2437	−	28.1349i	−0.605787	−	1.04925i	−0.991927	−	0.126814i	$-0.959525\pi$
$719$	−16.2437	−	28.1349i	−0.605787	−	1.04925i	0.386140	−	0.922440i	$-0.373808\pi$
$720$	−0.879864	−	5.91058i	−0.0327906	−	0.220274i
$721$	−5.92455	+	4.30443i	−0.220642	+	0.160306i
$722$	−9.15365	+	0.962088i	−0.340664	+	0.0358052i
$723$	−29.1793	+	2.15995i	−1.08519	+	0.0803294i
$724$	−10.2327	−	22.9831i	−0.380296	−	0.854160i
$725$	3.97751	−	0.845445i	0.147721	−	0.0313990i
$726$	−13.0321	+	11.0260i	−0.483665	+	0.409214i
$727$	−20.5546	−	9.15149i	−0.762327	−	0.339410i	−0.0115220	−	0.999934i	$-0.503668\pi$
$727$	−20.5546	−	9.15149i	−0.762327	−	0.339410i	−0.750805	+	0.660524i	$0.770334\pi$
$728$	−0.620014	−	1.90821i	−0.0229792	−	0.0707228i
$729$	12.9242	−	23.7058i	0.478676	−	0.877992i
$730$	9.12839	−	20.5027i	0.337857	−	0.758839i
$731$	−14.9652	+	70.4059i	−0.553509	+	2.60406i
$732$	1.82209	−	3.77481i	0.0673464	−	0.139521i
$733$	−28.1088	+	12.5149i	−1.03822	+	0.462247i	−0.853800	−	0.520601i	$-0.825708\pi$
$733$	−28.1088	+	12.5149i	−1.03822	+	0.462247i	−0.184422	+	0.982847i	$0.559041\pi$
$734$	−8.60437	−	9.55613i	−0.317593	−	0.352723i
$735$	−19.3311	−	11.9701i	−0.713038	−	0.441525i
$736$	0.0490565	+	0.0675204i	0.00180825	+	0.00248884i
$737$	1.26566	−	12.0419i	0.0466211	−	0.443571i
$738$	−0.388959	+	0.381789i	−0.0143178	+	0.0140538i
$739$	−16.1915	−	9.34816i	−0.595614	−	0.343878i	0.171700	−	0.985149i	$-0.445074\pi$
$739$	−16.1915	−	9.34816i	−0.595614	−	0.343878i	−0.767314	+	0.641271i	$0.778407\pi$
$740$	−13.3185	−	9.67646i	−0.489598	−	0.355714i
$741$	−3.01901	−	16.7228i	−0.110906	−	0.614329i
$742$	−7.10685	−	2.30916i	−0.260901	−	0.0847718i
$743$	−13.5099			−0.495629			−0.247814	−	0.968808i	$-0.579712\pi$
$743$	−13.5099			−0.495629			−0.247814	+	0.968808i	$0.579712\pi$
$744$	−7.95481	+	5.45170i	−0.291637	+	0.199869i
$745$	−14.2717			−0.522875
$746$	−22.0393	−	7.16101i	−0.806917	−	0.262183i
$747$	−21.2469	−	11.0760i	−0.777385	−	0.405250i
$748$	−6.48999	−	4.71526i	−0.237298	−	0.172407i
$749$	6.36135	+	3.67273i	0.232439	+	0.134198i
$750$	−2.81245	+	20.6211i	−0.102696	+	0.752975i
$751$	2.15071	−	20.4626i	0.0784804	−	0.746691i	−0.882544	−	0.470229i	$-0.844171\pi$
$751$	2.15071	−	20.4626i	0.0784804	−	0.746691i	0.961025	−	0.276462i	$-0.0891620\pi$
$752$	−0.426781	−	0.587413i	−0.0155631	−	0.0214208i
$753$	−16.5722	+	26.7632i	−0.603926	+	0.975306i
$754$	−8.26216	−	9.17606i	−0.300890	−	0.334172i
$755$	−15.7383	+	7.00714i	−0.572775	+	0.255016i
$756$	−0.651668	+	3.26143i	−0.0237009	+	0.118617i
$757$	8.17778	−	38.4734i	0.297226	−	1.39834i	−0.535444	−	0.844571i	$-0.679856\pi$
$757$	8.17778	−	38.4734i	0.297226	−	1.39834i	0.832670	−	0.553770i	$-0.186811\pi$
$758$	−4.45434	+	10.0046i	−0.161789	+	0.363384i
$759$	0.0522945	−	0.145521i	0.00189817	−	0.00528206i
$760$	1.92652	+	5.92922i	0.0698822	+	0.215075i
$761$	16.0222	+	7.13355i	0.580805	+	0.258591i	0.676041	−	0.736864i	$-0.263694\pi$
$761$	16.0222	+	7.13355i	0.580805	+	0.258591i	−0.0952365	+	0.995455i	$0.530361\pi$
$762$	−16.5814	−	19.5982i	−0.600682	−	0.709968i
$763$	1.83568	−	0.390187i	0.0664562	−	0.0141257i
$764$	−8.53516	−	19.1703i	−0.308791	−	0.693556i
$765$	37.3557	+	24.7561i	1.35060	+	0.895060i
$766$	3.60609	−	0.379015i	0.130293	−	0.0136944i
$767$	10.4292	−	7.57729i	0.376578	−	0.273600i
$768$	−1.19810	+	1.25083i	−0.0432326	+	0.0451353i
$769$	5.42463	+	9.39574i	0.195617	+	0.338819i	0.947103	−	0.320931i	$-0.103996\pi$
$769$	5.42463	+	9.39574i	0.195617	+	0.338819i	−0.751485	+	0.659750i	$0.770662\pi$
$770$	0.681908	−	1.18110i	0.0245743	−	0.0425639i
$771$	−3.67308	+	1.06946i	−0.132283	+	0.0385156i
$772$	−10.9602	+	12.1725i	−0.394466	+	0.438099i
$773$	7.83211	−	24.1048i	0.281701	−	0.866988i	−0.705667	−	0.708544i	$-0.749352\pi$
$773$	7.83211	−	24.1048i	0.281701	−	0.866988i	0.987368	−	0.158444i	$-0.0506476\pi$
$774$	−7.19335	−	27.8808i	−0.258560	−	1.00216i
$775$	5.46047	−	1.79433i	0.196146	−	0.0644541i
$776$			2.85163i			0.102368i
$777$	5.15456	+	7.57518i	0.184919	+	0.271758i
$778$	3.03831	+	2.73571i	0.108929	+	0.0980800i
$779$	0.334223	−	0.460019i	0.0119748	−	0.0164819i
$780$	10.0108	−	4.09214i	0.358442	−	0.146522i
$781$	0.766674	−	0.442640i	0.0274338	−	0.0158389i
$782$	−0.622470	−	0.0654242i	−0.0222595	−	0.00233957i
$783$	4.49997	+	19.9671i	0.160816	+	0.713566i
$784$	0.688875	+	6.55421i	0.0246027	+	0.234079i
$785$	−20.8740	+	18.7950i	−0.745024	+	0.670822i
$786$	28.7129	+	7.03476i	1.02415	+	0.250922i
$787$	0.982892	+	4.62414i	0.0350363	+	0.164833i	0.992187	−	0.124756i	$-0.0398148\pi$
$787$	0.982892	+	4.62414i	0.0350363	+	0.164833i	−0.957151	+	0.289589i	$0.906481\pi$
$788$	−16.5137	−	3.51009i	−0.588276	−	0.125042i
$789$	6.77979	+	12.6265i	0.241367	+	0.449516i
$790$	−5.99112	+	1.94663i	−0.213154	+	0.0692580i
$791$	−0.556788	+	0.180911i	−0.0197971	+	0.00643247i
$792$	3.16477	+	0.531474i	0.112455	+	0.0188851i
$793$	7.42012	+	1.57720i	0.263496	+	0.0560078i
$794$	−2.90314	−	13.6582i	−0.103029	−	0.484712i
$795$	9.58486	−	39.1213i	0.339940	−	1.38749i
$796$	−3.63388	+	3.27196i	−0.128800	+	0.115972i
$797$	5.10566	+	48.5771i	0.180852	+	1.72069i	0.589306	+	0.807910i	$0.299401\pi$
$797$	5.10566	+	48.5771i	0.180852	+	1.72069i	−0.408455	+	0.912779i	$0.633932\pi$
$798$	0.106962	−	3.46820i	0.00378643	−	0.122773i
$799$	5.41536	+	0.569177i	0.191582	+	0.0201360i
$800$	0.894017	−	0.516161i	0.0316083	−	0.0182490i
$801$	48.9091	+	13.5940i	1.72812	+	0.480321i
$802$	−13.3492	+	18.3736i	−0.471377	+	0.648795i
$803$	8.95667	+	8.06462i	0.316074	+	0.284594i
$804$	16.2091	−	11.0295i	0.571649	−	0.388981i
$805$		−	0.106408i		−	0.00375038i
$806$	−13.0090	−	11.6352i	−0.458221	−	0.409831i
$807$	−13.5233	−	10.4771i	−0.476044	−	0.368812i
$808$	1.22313	−	3.76440i	0.0430295	−	0.132431i
$809$	15.9101	−	17.6699i	0.559368	−	0.621241i	−0.395430	−	0.918496i	$-0.629404\pi$
$809$	15.9101	−	17.6699i	0.559368	−	0.621241i	0.954798	+	0.297255i	$0.0960711\pi$
$810$	−17.7910	−	2.20525i	−0.625111	−	0.0774846i
$811$	−22.4901	+	38.9540i	−0.789734	+	1.36786i	0.136396	+	0.990654i	$0.456448\pi$
$811$	−22.4901	+	38.9540i	−0.789734	+	1.36786i	−0.926130	+	0.377205i	$0.876885\pi$
$812$	−1.26063	−	2.18348i	−0.0442396	−	0.0766252i
$813$	9.61965	+	9.21412i	0.337376	+	0.323153i
$814$	7.15233	−	5.19647i	0.250689	−	0.182136i
$815$	23.0023	−	2.41764i	0.805735	−	0.0846861i
$816$	−0.958892	−	12.9539i	−0.0335679	−	0.453477i
$817$	12.2184	+	27.4430i	0.427468	+	0.960108i
$818$	−19.3375	+	4.11031i	−0.676119	+	0.143714i
$819$	−6.01364	+	0.259093i	−0.210134	+	0.00905344i
$820$	0.330593	+	0.147189i	0.0115448	+	0.00514008i
$821$	8.63540	+	26.5770i	0.301378	+	0.927545i	0.981004	+	0.193987i	$0.0621419\pi$
$821$	8.63540	+	26.5770i	0.301378	+	0.927545i	−0.679626	+	0.733558i	$0.737858\pi$
$822$	0.395970	+	0.142296i	0.0138110	+	0.00496316i
$823$	−0.204860	+	0.460123i	−0.00714097	+	0.0160389i	−0.917081	−	0.398702i	$-0.869461\pi$
$823$	−0.204860	+	0.460123i	−0.00714097	+	0.0160389i	0.909940	+	0.414740i	$0.136128\pi$
$824$	−2.37875	+	11.1911i	−0.0828677	+	0.389862i
$825$	−1.72248	−	0.831438i	−0.0599691	−	0.0289470i
$826$	2.40470	−	1.07064i	0.0836703	−	0.0372524i
$827$	−36.4814	−	40.5167i	−1.26858	−	1.40890i	−0.870960	−	0.491354i	$-0.836502\pi$
$827$	−36.4814	−	40.5167i	−1.26858	−	1.40890i	−0.397622	−	0.917549i	$-0.630165\pi$
$828$	0.234574	−	0.0875497i	0.00815201	−	0.00304256i
$829$	−26.4775	−	36.4431i	−0.919600	−	1.26572i	−0.963780	−	0.266698i	$-0.914068\pi$
$829$	−26.4775	−	36.4431i	−0.919600	−	1.26572i	0.0441801	−	0.999024i	$-0.485932\pi$
$830$	−1.66295	+	15.8219i	−0.0577219	+	0.549187i
$831$	−16.0692	−	2.19163i	−0.557434	−	0.0760268i
$832$	−2.71470	−	1.56733i	−0.0941153	−	0.0543375i
$833$	−39.9843	−	29.0503i	−1.38538	−	1.00653i
$834$	−38.6107	+	6.97047i	−1.33698	+	0.241368i
$835$	42.4772	+	13.8017i	1.46998	+	0.477627i
$836$	−3.34798			−0.115792
$837$	9.36704	+	27.3726i	0.323772	+	0.946135i
$838$	2.01599			0.0696414
$839$	−1.21504	−	0.394791i	−0.0419479	−	0.0136297i	0.287968	−	0.957640i	$-0.407020\pi$
$839$	−1.21504	−	0.394791i	−0.0419479	−	0.0136297i	−0.329916	+	0.944010i	$0.607020\pi$
$840$	2.17316	−	0.392326i	0.0749812	−	0.0135365i
$841$	10.9087	+	7.92563i	0.376162	+	0.273298i
$842$	−6.76455	−	3.90551i	−0.233122	−	0.134593i
$843$	31.3322	+	4.27331i	1.07914	+	0.147181i
$844$	1.15677	−	11.0059i	0.0398177	−	0.378840i
$845$	−3.71600	−	5.11464i	−0.127834	−	0.175949i
$846$	−2.04074	+	0.761664i	−0.0701622	+	0.0261866i
$847$	−4.22113	−	4.68803i	−0.145040	−	0.161083i
$848$	−10.6653	+	4.74850i	−0.366248	+	0.163064i
$849$	−25.4943	−	12.3060i	−0.874962	−	0.422342i
$850$	−1.60961	+	7.57262i	−0.0552091	+	0.259739i
$851$	0.280556	−	0.630140i	0.00961735	−	0.0216009i
$852$	1.34898	+	0.484773i	0.0462154	+	0.0166080i
$853$	3.83832	+	11.8131i	0.131421	+	0.404474i	0.995016	−	0.0997128i	$-0.0317924\pi$
$853$	3.83832	+	11.8131i	0.131421	+	0.404474i	−0.863595	+	0.504187i	$0.831792\pi$
$854$	1.41505	+	0.630023i	0.0484222	+	0.0215589i
$855$	18.6857	−	0.805059i	0.639038	−	0.0275324i
$856$	11.2252	−	2.38600i	0.383671	−	0.0815517i
$857$	−2.03043	−	4.56042i	−0.0693581	−	0.155781i	0.875540	−	0.483146i	$-0.160506\pi$
$857$	−2.03043	−	4.56042i	−0.0693581	−	0.155781i	−0.944898	+	0.327365i	$0.893839\pi$
$858$	0.428741	+	5.79196i	0.0146370	+	0.197734i
$859$	15.6080	−	1.64046i	0.532537	−	0.0559719i	0.165556	−	0.986200i	$-0.447058\pi$
$859$	15.6080	−	1.64046i	0.532537	−	0.0559719i	0.366981	+	0.930228i	$0.380391\pi$
$860$	−15.4669	+	11.2374i	−0.527418	+	0.383192i
$861$	−0.145452	−	0.139320i	−0.00495699	−	0.00474802i
$862$	15.8750	+	27.4964i	0.540706	+	0.936530i
$863$	27.4975	−	47.6270i	0.936024	−	1.62124i	0.163228	−	0.986588i	$-0.447810\pi$
$863$	27.4975	−	47.6270i	0.936024	−	1.62124i	0.772797	−	0.634653i	$-0.218857\pi$
$864$	2.65290	+	4.46790i	0.0902535	+	0.152001i
$865$	−18.5001	+	20.5464i	−0.629021	+	0.698599i
$866$	4.50683	−	13.8706i	0.153148	−	0.471342i
$867$	53.7291	+	41.6263i	1.82474	+	1.41370i
$868$	−2.10431	−	2.87616i	−0.0714249	−	0.0976231i
$869$		−	3.38293i		−	0.114758i
$870$	11.2356	−	7.64530i	0.380922	−	0.259200i
$871$	26.3686	+	23.7424i	0.893465	+	0.804480i
$872$	1.72339	−	2.37205i	0.0583615	−	0.0803277i
$873$	8.24244	+	2.29094i	0.278964	+	0.0775366i
$874$	−0.226220	+	0.130608i	−0.00765200	+	0.00441789i
$875$	−7.64882	−	0.803924i	−0.258577	−	0.0271776i
$876$	−0.601580	+	19.5059i	−0.0203255	+	0.659045i
$877$	0.345289	+	3.28521i	0.0116596	+	0.110934i	0.998804	−	0.0488990i	$-0.0155712\pi$
$877$	0.345289	+	3.28521i	0.0116596	+	0.110934i	−0.987144	+	0.159833i	$0.948905\pi$
$878$	19.3138	−	17.3903i	0.651810	−	0.586893i
$879$	4.77398	−	19.4853i	0.161022	−	0.657224i
$880$	−0.443004	−	2.08417i	−0.0149337	−	0.0702573i
$881$	−12.2657	−	2.60715i	−0.413241	−	0.0878372i	−0.00340052	−	0.999994i	$-0.501082\pi$
$881$	−12.2657	−	2.60715i	−0.413241	−	0.0878372i	−0.409841	+	0.912157i	$0.634416\pi$
$882$	19.4979	+	3.27437i	0.656529	+	0.110254i
$883$	4.37700	−	1.42217i	0.147298	−	0.0478599i	−0.234440	−	0.972131i	$-0.575326\pi$
$883$	4.37700	−	1.42217i	0.147298	−	0.0478599i	0.381738	+	0.924271i	$0.375326\pi$
$884$	22.3575	−	7.26441i	0.751966	−	0.244328i
$885$	6.71204	+	12.5003i	0.225623	+	0.420194i
$886$	23.7743	+	5.05338i	0.798713	+	0.169772i
$887$	4.63228	+	21.7932i	0.155537	+	0.731744i	0.984913	+	0.173052i	$0.0553630\pi$
$887$	4.63228	+	21.7932i	0.155537	+	0.731744i	−0.829376	+	0.558691i	$0.811304\pi$
$888$	13.9037	+	3.40647i	0.466579	+	0.114313i
$889$	7.05008	−	6.34792i	0.236452	−	0.212902i
$890$	−3.52314	−	33.5205i	−0.118096	−	1.12361i
$891$	4.07870	−	8.72057i	0.136642	−	0.292150i
$892$	14.3939	+	1.51286i	0.481942	+	0.0506542i
$893$	1.96807	−	1.13626i	0.0658588	−	0.0380236i
$894$	11.4872	−	4.69569i	0.384190	−	0.157047i
$895$	15.9103	−	21.8987i	0.531823	−	0.731992i
$896$	−0.475665	−	0.428291i	−0.0158908	−	0.0143082i
$897$	0.254920	+	0.374632i	0.00851153	+	0.0125086i
$898$			0.877984i			0.0292987i
$899$	−19.0298	−	10.9026i	−0.634679	−	0.363621i
$900$	−0.773692	−	2.99877i	−0.0257897	−	0.0999588i
$901$	27.0553	−	83.2676i	0.901342	−	2.77405i
$902$	−0.130037	+	0.144420i	−0.00432975	+	0.00480867i
$903$	10.2164	−	2.97461i	0.339980	−	0.0989888i
$904$	−0.457326	+	0.792112i	−0.0152104	+	0.0263453i
$905$	25.0563	+	43.3987i	0.832899	+	1.44262i
$906$	10.3622	−	10.8182i	0.344260	−	0.359412i
$907$	−9.04887	+	6.57439i	−0.300463	+	0.218299i	−0.727793	−	0.685796i	$-0.759454\pi$
$907$	−9.04887	+	6.57439i	−0.300463	+	0.218299i	0.427331	+	0.904095i	$0.359454\pi$
$908$	17.5289	−	1.84236i	0.581717	−	0.0611409i
$909$	−9.89811	−	6.55961i	−0.328300	−	0.217569i
$910$	1.62555	+	3.65105i	0.0538865	+	0.121031i
$911$	−38.1409	+	8.10709i	−1.26366	+	0.268600i	−0.790548	−	0.612400i	$-0.790204\pi$
$911$	−38.1409	+	8.10709i	−1.26366	+	0.268600i	−0.473116	+	0.881000i	$0.656871\pi$
$912$	−3.50148	−	4.13853i	−0.115946	−	0.137040i
$913$	−7.80489	−	3.47496i	−0.258304	−	0.115004i
$914$	3.90975	+	12.0330i	0.129323	+	0.398015i
$915$	−2.82359	+	7.85724i	−0.0933451	+	0.259752i
$916$	−11.9886	+	26.9269i	−0.396116	+	0.889691i
$917$	−2.27134	+	10.6858i	−0.0750061	+	0.352876i
$918$	−38.2127	−	7.63528i	−1.26121	−	0.252002i
$919$	−26.1298	+	11.6337i	−0.861942	+	0.383761i	−0.789603	−	0.613619i	$-0.789713\pi$
$919$	−26.1298	+	11.6337i	−0.861942	+	0.383761i	−0.0723396	+	0.997380i	$0.523047\pi$
$920$	−0.111239	−	0.123543i	−0.00366744	−	0.00407310i
$921$	23.2390	−	37.5297i	0.765753	−	1.23665i
$922$	16.3343	+	22.4822i	0.537942	+	0.740413i
$923$	−0.271173	+	2.58004i	−0.00892576	+	0.0849229i
$924$	−0.160258	+	1.17502i	−0.00527210	+	0.0386554i
$925$	−7.38882	−	4.26594i	−0.242943	−	0.140263i
$926$	25.8014	+	18.7458i	0.847885	+	0.616025i
$927$	30.4362	+	15.8663i	0.999655	+	0.521119i
$928$	−3.74626	−	1.21723i	−0.122977	−	0.0399576i
$929$	−8.33903			−0.273595			−0.136797	−	0.990599i	$-0.543681\pi$
$929$	−8.33903			−0.273595			−0.136797	+	0.990599i	$0.543681\pi$
$930$	14.6233	−	12.4561i	0.479517	−	0.408450i
$931$	−20.6266			−0.676011
$932$	23.7568	+	7.71904i	0.778179	+	0.252846i
$933$	5.03118	+	27.8686i	0.164713	+	0.912376i
$934$	8.21209	+	5.96643i	0.268708	+	0.195228i
$935$	13.8384	+	7.98960i	0.452564	+	0.261288i
$936$	−6.71120	+	6.58749i	−0.219362	+	0.215319i
$937$	1.29882	−	12.3574i	0.0424304	−	0.403699i	−0.952607	−	0.304202i	$-0.901610\pi$
$937$	1.29882	−	12.3574i	0.0424304	−	0.403699i	0.995038	−	0.0994964i	$-0.0317232\pi$
$938$	4.25861	+	5.86148i	0.139049	+	0.191384i
$939$	−8.21079	−	5.08426i	−0.267949	−	0.165919i
$940$	0.967755	+	1.07480i	0.0315647	+	0.0350561i
$941$	8.05457	−	3.58613i	0.262572	−	0.116904i	−0.271229	−	0.962515i	$-0.587430\pi$
$941$	8.05457	−	3.58613i	0.262572	−	0.116904i	0.533800	+	0.845611i	$0.320763\pi$
$942$	10.6174	−	21.9960i	0.345933	−	0.716667i
$943$	−0.00315247	+	0.0148312i	−0.000102659	+	0.000482971i
$944$	1.67270	−	3.75694i	0.0544416	−	0.122278i
$945$	0.611883	−	6.59656i	0.0199046	−	0.214586i
$946$	−3.17264	−	9.76438i	−0.103151	−	0.317467i
$947$	−3.91956	−	1.74510i	−0.127369	−	0.0567082i	0.342063	−	0.939677i	$-0.388874\pi$
$947$	−3.91956	−	1.74510i	−0.127369	−	0.0567082i	−0.469431	+	0.882969i	$0.655541\pi$
$948$	4.18173	−	3.53803i	0.135816	−	0.114910i
$949$	−34.5469	+	7.34316i	−1.12144	+	0.238369i
$950$	1.31417	+	2.95167i	0.0426373	+	0.0957649i
$951$	−37.1045	+	2.74660i	−1.20320	+	0.0890647i
$952$	4.77385	−	0.501751i	0.154721	−	0.0162619i
$953$	−29.3911	+	21.3539i	−0.952070	+	0.691719i	−0.951295	−	0.308281i	$-0.900246\pi$
$953$	−29.3911	+	21.3539i	−0.952070	+	0.691719i	−0.000774154		1.00000i	$0.500246\pi$
$954$	5.15692	+	34.6422i	0.166961	+	1.12158i
$955$	20.8995	+	36.1990i	0.676293	+	1.17137i
$956$	−0.319274	+	0.552999i	−0.0103261	+	0.0178853i
$957$	2.04021	+	7.00717i	0.0659508	+	0.226510i
$958$	14.0967	−	15.6560i	0.455444	−	0.505822i
$959$	−0.0480492	+	0.147880i	−0.00155159	+	0.00477530i
$960$	2.11298	−	2.72733i	0.0681962	−	0.0880243i
$961$	−28.4032	−	12.4201i	−0.916232	−	0.400647i
$962$			25.9072i			0.835282i
$963$	2.12156	−	34.3626i	0.0683664	−	1.10732i
$964$	−12.5538	−	11.3035i	−0.404329	−	0.364060i
$965$	19.1776	−	26.3957i	0.617349	−	0.849708i
$966$	0.0350103	+	0.0856470i	0.00112644	+	0.00275565i
$967$	−35.7828	+	20.6592i	−1.15070	+	0.664356i	−0.949057	−	0.315103i	$-0.897961\pi$
$967$	−35.7828	+	20.6592i	−1.15070	+	0.664356i	−0.201641	+	0.979459i	$0.564628\pi$
$968$	−9.80176	−	1.03021i	−0.315041	−	0.0331121i
$969$	40.6353	+	1.25323i	1.30539	+	0.0402595i
$970$	−0.593740	−	5.64906i	−0.0190638	−	0.181380i
$971$	23.9294	−	21.5462i	0.767932	−	0.691449i	−0.188930	−	0.981990i	$-0.560502\pi$
$971$	23.9294	−	21.5462i	0.767932	−	0.691449i	0.956862	+	0.290541i	$0.0938354\pi$
$972$	15.0454	−	4.07860i	0.482582	−	0.130821i
$973$	−3.01452	−	14.1822i	−0.0966410	−	0.454660i
$974$	−24.2261	−	5.14941i	−0.776254	−	0.164998i
$975$	4.93806	−	2.65148i	0.158144	−	0.0849154i
$976$	2.30156	−	0.747821i	0.0736710	−	0.0239372i
$977$	34.0853	−	11.0750i	1.09048	−	0.354320i	0.292051	−	0.956403i	$-0.405662\pi$
$977$	34.0853	−	11.0750i	1.09048	−	0.354320i	0.798434	+	0.602083i	$0.205662\pi$
$978$	−17.7190	+	9.51417i	−0.566590	+	0.304230i
$979$	17.7048	+	3.76328i	0.565849	+	0.120275i
$980$	−2.72931	−	12.8404i	−0.0871846	−	0.410171i
$981$	−5.47170	−	6.88700i	−0.174698	−	0.219885i
$982$	−4.01804	+	3.61786i	−0.128221	+	0.115450i
$983$	−1.59535	−	15.1787i	−0.0508836	−	0.484125i	−0.990055	−	0.140678i	$-0.955072\pi$
$983$	−1.59535	−	15.1787i	−0.0508836	−	0.484125i	0.939172	−	0.343448i	$-0.111595\pi$
$984$	−0.314521	−	0.00970009i	−0.0100266	−	0.000309227i
$985$	33.4443	+	3.51514i	1.06562	+	0.112002i
$986$	25.5828	−	14.7703i	0.814723	−	0.470381i
$987$	−0.304583	−	0.745111i	−0.00969497	−	0.0237171i
$988$	5.76677	−	7.93728i	0.183465	−	0.252518i
$989$	−0.595291	−	0.536002i	−0.0189291	−	0.0170439i
$990$	−6.38004	−	0.393907i	−0.202771	−	0.0125192i
$991$			12.7801i			0.405972i	0.979182	+	0.202986i	$0.0650646\pi$
$991$			12.7801i			0.405972i	−0.979182	+	0.202986i	$0.934935\pi$
$992$	−5.44992	−	1.13947i	−0.173035	−	0.0361783i
$993$	25.9182	−	33.4539i	0.822489	−	1.06163i
$994$	−0.163693	+	0.503795i	−0.00519203	+	0.0159794i
$995$	6.51744	−	7.23834i	0.206617	−	0.229471i
$996$	−3.86724	−	13.2821i	−0.122538	−	0.420860i
$997$	−24.0908	+	41.7265i	−0.762963	+	1.32149i	0.178354	+	0.983966i	$0.442923\pi$
$997$	−24.0908	+	41.7265i	−0.762963	+	1.32149i	−0.941317	+	0.337524i	$0.890410\pi$
$998$	10.7127	+	18.5550i	0.339106	+	0.587349i
$999$	21.0161	−	37.4511i	0.664921	−	1.18490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.p.a.17.10	yes	80
3.2	odd	2	inner	186.2.p.a.17.3	yes	80
31.11	odd	30	inner	186.2.p.a.11.3	✓	80
93.11	even	30	inner	186.2.p.a.11.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.p.a.11.3	✓	80	31.11	odd	30	inner
186.2.p.a.11.10	yes	80	93.11	even	30	inner
186.2.p.a.17.3	yes	80	3.2	odd	2	inner
186.2.p.a.17.10	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(1.70450 - 0.307717i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.72504 - 0.995952i) q^{5} +(1.71616 + 0.234063i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(0.587785 + 0.809017i) q^{8} +(2.81062 - 1.04900i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(1.70450 - 0.307717i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.72504 - 0.995952i) q^{5} +(1.71616 + 0.234063i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(0.587785 + 0.809017i) q^{8} +(2.81062 - 1.04900i) q^{9} +(-1.33284 - 1.48027i) q^{10} +(0.977216 - 0.435084i) q^{11} +(1.55984 + 0.752930i) q^{12} +(-0.651734 + 3.06617i) q^{13} +(-0.260340 + 0.584733i) q^{14} +(-3.24679 - 1.16677i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-6.85104 - 3.05028i) q^{17} +(2.99722 - 0.129133i) q^{18} +(-3.06145 + 0.650731i) q^{19} +(-0.810180 - 1.81969i) q^{20} +(0.0818410 + 1.10561i) q^{21} +(1.06384 - 0.111814i) q^{22} +(0.0675204 - 0.0490565i) q^{23} +(1.25083 + 1.19810i) q^{24} +(-0.516161 - 0.894017i) q^{25} +(-1.56733 + 2.71470i) q^{26} +(4.46790 - 2.65290i) q^{27} +(-0.428291 + 0.475665i) q^{28} +(-1.21723 + 3.74626i) q^{29} +(-2.72733 - 2.11298i) q^{30} +(-1.13947 + 5.44992i) q^{31} +1.00000i q^{32} +(1.53178 - 1.04231i) q^{33} +(-5.57314 - 5.01808i) q^{34} +(0.749401 - 1.03146i) q^{35} +(2.89043 + 0.803379i) q^{36} +(7.15748 - 4.13237i) q^{37} +(-3.11270 - 0.327158i) q^{38} +(-0.167368 + 5.42682i) q^{39} +(-0.208211 - 1.98099i) q^{40} +(-0.135011 + 0.121564i) q^{41} +(-0.263817 + 1.07679i) q^{42} +(-1.99552 - 9.38821i) q^{43} +(1.04632 + 0.222402i) q^{44} +(-5.89319 - 0.989669i) q^{45} +(0.0793750 - 0.0257905i) q^{46} +(-0.690546 + 0.224372i) q^{47} +(0.819375 + 1.52598i) q^{48} +(6.44630 + 1.37020i) q^{49} +(-0.214632 - 1.00976i) q^{50} +(-12.6162 - 3.09101i) q^{51} +(-2.32951 + 2.09750i) q^{52} +(1.22033 + 11.6107i) q^{53} +(5.06902 - 1.14240i) q^{54} +(-2.11906 - 0.222722i) q^{55} +(-0.554317 + 0.320035i) q^{56} +(-5.01799 + 2.05123i) q^{57} +(-2.31532 + 3.18676i) q^{58} +(-3.05617 - 2.75179i) q^{59} +(-1.94090 - 2.85236i) q^{60} -2.42000i q^{61} +(-2.76782 + 4.83106i) q^{62} +(0.479712 + 1.85932i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(4.17802 - 4.64016i) q^{65} +(1.77890 - 0.517946i) q^{66} +(5.65968 - 9.80285i) q^{67} +(-3.74970 - 6.49467i) q^{68} +(0.0999929 - 0.104394i) q^{69} +(1.03146 - 0.749401i) q^{70} +(0.823066 - 0.0865077i) q^{71} +(2.50070 + 1.65725i) q^{72} +(4.58275 + 10.2930i) q^{73} +(8.08414 - 1.71834i) q^{74} +(-1.15490 - 1.36502i) q^{75} +(-2.85926 - 1.27302i) q^{76} +(0.211578 + 0.651170i) q^{77} +(-1.83616 + 5.10949i) q^{78} +(1.28631 - 2.88911i) q^{79} +(0.414140 - 1.94838i) q^{80} +(6.79918 - 5.89671i) q^{81} +(-0.165968 + 0.0738938i) q^{82} +(-5.34426 - 5.93540i) q^{83} +(-0.583650 + 0.942562i) q^{84} +(8.78038 + 12.0852i) q^{85} +(1.00326 - 9.54537i) q^{86} +(-0.921984 + 6.76005i) q^{87} +(0.926384 + 0.534848i) q^{88} +(13.6894 + 9.94595i) q^{89} +(-5.29893 - 2.76233i) q^{90} +(-1.90821 - 0.620014i) q^{91} +0.0834598 q^{92} +(-0.265196 + 9.64000i) q^{93} -0.726083 q^{94} +(5.92922 + 1.92652i) q^{95} +(0.307717 + 1.70450i) q^{96} +(2.30702 + 1.67615i) q^{97} +(5.70738 + 3.29516i) q^{98} +(2.29018 - 2.24796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9	\( 80 q + 20 q^{4} + 8 q^{7} + 4 q^{9} - 4 q^{10} - 10 q^{15} - 20 q^{16} - 8 q^{18} - 4 q^{19} + 30 q^{21} - 2 q^{22} + 12 q^{25} - 38 q^{28} - 86 q^{31} - 28 q^{34} - 4 q^{36} - 144 q^{37} - 16 q^{39} - 6 q^{40} - 6 q^{42} + 40 q^{43} - 24 q^{45} - 20 q^{46} + 10 q^{48} - 14 q^{49} - 92 q^{51} - 92 q^{55} - 96 q^{57} + 20 q^{58} - 10 q^{60} + 88 q^{63} + 20 q^{64} + 12 q^{66} + 40 q^{67} - 60 q^{69} + 24 q^{70} + 8 q^{72} + 56 q^{73} - 30 q^{75} - 36 q^{76} + 32 q^{78} + 32 q^{79} + 128 q^{81} + 36 q^{82} + 10 q^{84} + 100 q^{85} + 34 q^{87} + 42 q^{88} + 34 q^{90} + 60 q^{91} + 172 q^{93} + 24 q^{94} - 4 q^{97} + 150 q^{99}+O(q^{100}) \) 80 * q + 20 * q^4 + 8 * q^7 + 4 * q^9 - 4 * q^10 - 10 * q^15 - 20 * q^16 - 8 * q^18 - 4 * q^19 + 30 * q^21 - 2 * q^22 + 12 * q^25 - 38 * q^28 - 86 * q^31 - 28 * q^34 - 4 * q^36 - 144 * q^37 - 16 * q^39 - 6 * q^40 - 6 * q^42 + 40 * q^43 - 24 * q^45 - 20 * q^46 + 10 * q^48 - 14 * q^49 - 92 * q^51 - 92 * q^55 - 96 * q^57 + 20 * q^58 - 10 * q^60 + 88 * q^63 + 20 * q^64 + 12 * q^66 + 40 * q^67 - 60 * q^69 + 24 * q^70 + 8 * q^72 + 56 * q^73 - 30 * q^75 - 36 * q^76 + 32 * q^78 + 32 * q^79 + 128 * q^81 + 36 * q^82 + 10 * q^84 + 100 * q^85 + 34 * q^87 + 42 * q^88 + 34 * q^90 + 60 * q^91 + 172 * q^93 + 24 * q^94 - 4 * q^97 + 150 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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