LMFDB - Embedded newform 186.2.p.a.17.3

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			17.3
Character	$\chi$	$=$	186.17
Dual form			186.2.p.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.127863 + 1.72732i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.72504 + 0.995952i) q^{5} +(0.655377 - 1.60327i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.96730 - 0.441720i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.127863 + 1.72732i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.72504 + 0.995952i) q^{5} +(0.655377 - 1.60327i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.96730 - 0.441720i) q^{9} +(-1.33284 - 1.48027i) q^{10} +(-0.977216 + 0.435084i) q^{11} +(-1.11874 + 1.32228i) q^{12} +(-0.651734 + 3.06617i) q^{13} +(0.260340 - 0.584733i) q^{14} +(-1.94090 + 2.85236i) q^{15} +(0.309017 + 0.951057i) q^{16} +(6.85104 + 3.05028i) q^{17} +(2.68557 + 1.33705i) q^{18} +(-3.06145 + 0.650731i) q^{19} +(0.810180 + 1.81969i) q^{20} +(-1.09100 - 0.196960i) q^{21} +(1.06384 - 0.111814i) q^{22} +(-0.0675204 + 0.0490565i) q^{23} +(1.47259 - 0.911853i) q^{24} +(-0.516161 - 0.894017i) q^{25} +(1.56733 - 2.71470i) q^{26} +(1.14240 - 5.06902i) 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} +(-0.626583 - 1.74360i) q^{33} +(-5.57314 - 5.01808i) q^{34} +(-0.749401 + 1.03146i) q^{35} +(-2.14096 - 2.10150i) q^{36} +(7.15748 - 4.13237i) q^{37} +(3.11270 + 0.327158i) q^{38} +(-5.21293 - 1.51780i) q^{39} +(-0.208211 - 1.98099i) q^{40} +(0.135011 - 0.121564i) q^{41} +(0.976737 + 0.524457i) q^{42} +(-1.99552 - 9.38821i) q^{43} +(-1.04632 - 0.222402i) q^{44} +(-4.67878 - 3.71727i) q^{45} +(0.0793750 - 0.0257905i) q^{46} +(0.690546 - 0.224372i) q^{47} +(-1.68230 + 0.412168i) q^{48} +(6.44630 + 1.37020i) q^{49} +(0.214632 + 1.00976i) q^{50} +(-6.14482 + 11.4440i) q^{51} +(-2.32951 + 2.09750i) q^{52} +(-1.22033 - 11.6107i) q^{53} +(-2.65290 + 4.46790i) q^{54} +(-2.11906 - 0.222722i) q^{55} +(0.554317 - 0.320035i) q^{56} +(-0.732580 - 5.37132i) q^{57} +(-2.31532 + 3.18676i) q^{58} +(3.05617 + 2.75179i) q^{59} +(-3.24679 + 1.16677i) 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} +(0.0571138 + 1.85189i) q^{66} +(5.65968 - 9.80285i) q^{67} +(3.74970 + 6.49467i) q^{68} +(-0.0761031 - 0.122902i) q^{69} +(1.03146 - 0.749401i) q^{70} +(-0.823066 + 0.0865077i) q^{71} +(1.38678 + 2.66023i) q^{72} +(4.58275 + 10.2930i) q^{73} +(-8.08414 + 1.71834i) q^{74} +(1.61025 - 0.777266i) q^{75} +(-2.85926 - 1.27302i) q^{76} +(-0.211578 - 0.651170i) q^{77} +(4.48877 + 3.05440i) q^{78} +(1.28631 - 2.88911i) q^{79} +(-0.414140 + 1.94838i) q^{80} +(8.60977 + 2.62143i) q^{81} +(-0.165968 + 0.0738938i) q^{82} +(5.34426 + 5.93540i) q^{83} +(-0.766865 - 0.800617i) q^{84} +(8.78038 + 12.0852i) q^{85} +(-1.00326 + 9.54537i) q^{86} +(6.31537 + 2.58156i) q^{87} +(0.926384 + 0.534848i) q^{88} +(-13.6894 - 9.94595i) q^{89} +(3.30108 + 4.98116i) q^{90} +(-1.90821 - 0.620014i) q^{91} -0.0834598 q^{92} +(-9.26808 - 2.66508i) q^{93} -0.726083 q^{94} +(-5.92922 - 1.92652i) q^{95} +(1.72732 + 0.127863i) q^{96} +(2.30702 + 1.67615i) q^{97} +(-5.70738 - 3.29516i) q^{98} +(3.09188 - 0.859371i) 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
$3$	−0.127863	+	1.72732i	−0.0738215	+	0.997271i
$3$	−0.127863	+	1.72732i	−0.0738215	+	0.997271i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	1.72504	+	0.995952i	0.771461	+	0.445403i	0.833395	−	0.552677i	$-0.186394\pi$
$5$	1.72504	+	0.995952i	0.771461	+	0.445403i	−0.0619347	+	0.998080i	$0.519727\pi$
$6$	0.655377	−	1.60327i	0.267557	−	0.654533i
$7$	−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
$9$	−2.96730	−	0.441720i	−0.989101	−	0.147240i
$10$	−1.33284	−	1.48027i	−0.421482	−	0.468103i
$11$	−0.977216	+	0.435084i	−0.294642	+	0.131183i	−0.548734	−	0.835997i	$-0.684890\pi$
$11$	−0.977216	+	0.435084i	−0.294642	+	0.131183i	0.254092	+	0.967180i	$0.418223\pi$
$12$	−1.11874	+	1.32228i	−0.322952	+	0.381709i
$13$	−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
$15$	−1.94090	+	2.85236i	−0.501138	+	0.736476i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	6.85104	+	3.05028i	1.66162	+	0.739802i	0.999950	−	0.00999184i	$-0.00318055\pi$
$17$	6.85104	+	3.05028i	1.66162	+	0.739802i	0.661672	+	0.749794i	$0.269847\pi$
$18$	2.68557	+	1.33705i	0.632996	+	0.315145i
$19$	−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
$21$	−1.09100	−	0.196960i	−0.238075	−	0.0429803i
$22$	1.06384	−	0.111814i	0.226811	−	0.0238387i
$23$	−0.0675204	+	0.0490565i	−0.0140790	+	0.0102290i	−0.594802	−	0.803872i	$-0.702770\pi$
$23$	−0.0675204	+	0.0490565i	−0.0140790	+	0.0102290i	0.580724	+	0.814101i	$0.302770\pi$
$24$	1.47259	−	0.911853i	0.300591	−	0.186131i
$25$	−0.516161	−	0.894017i	−0.103232	−	0.178803i
$26$	1.56733	−	2.71470i	0.307379	−	0.532396i
$27$	1.14240	−	5.06902i	0.219855	−	0.975533i
$28$	−0.428291	+	0.475665i	−0.0809393	+	0.0898922i
$29$	1.21723	−	3.74626i	0.226035	−	0.695663i	−0.772150	−	0.635440i	$-0.780819\pi$
$29$	1.21723	−	3.74626i	0.226035	−	0.695663i	0.998185	−	0.0602230i	$-0.0191812\pi$
$30$	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
$33$	−0.626583	−	1.74360i	−0.109074	−	0.303522i
$34$	−5.57314	−	5.01808i	−0.955786	−	0.860593i
$35$	−0.749401	+	1.03146i	−0.126672	+	0.174349i
$36$	−2.14096	−	2.10150i	−0.356827	−	0.350249i
$37$	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
$39$	−5.21293	−	1.51780i	−0.834737	−	0.243043i
$40$	−0.208211	−	1.98099i	−0.0329210	−	0.313222i
$41$	0.135011	−	0.121564i	0.0210851	−	0.0189851i	−0.658521	−	0.752563i	$-0.728818\pi$
$41$	0.135011	−	0.121564i	0.0210851	−	0.0189851i	0.679606	+	0.733577i	$0.262151\pi$
$42$	0.976737	+	0.524457i	0.150714	+	0.0809255i
$43$	−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
$45$	−4.67878	−	3.71727i	−0.697471	−	0.554138i
$46$	0.0793750	−	0.0257905i	0.0117032	−	0.00380260i
$47$	0.690546	−	0.224372i	0.100726	−	0.0327280i	−0.258220	−	0.966086i	$-0.583136\pi$
$47$	0.690546	−	0.224372i	0.100726	−	0.0327280i	0.358947	+	0.933358i	$0.383136\pi$
$48$	−1.68230	+	0.412168i	−0.242818	+	0.0594914i
$49$	6.44630	+	1.37020i	0.920899	+	0.195743i
$50$	0.214632	+	1.00976i	0.0303535	+	0.142802i
$51$	−6.14482	+	11.4440i	−0.860447	+	1.60247i
$52$	−2.32951	+	2.09750i	−0.323045	+	0.290871i
$53$	−1.22033	−	11.6107i	−0.167625	−	1.59485i	−0.678109	−	0.734962i	$-0.737200\pi$
$53$	−1.22033	−	11.6107i	−0.167625	−	1.59485i	0.510483	−	0.859888i	$-0.329467\pi$
$54$	−2.65290	+	4.46790i	−0.361014	+	0.608004i
$55$	−2.11906	−	0.222722i	−0.285734	−	0.0300318i
$56$	0.554317	−	0.320035i	0.0740737	−	0.0427665i
$57$	−0.732580	−	5.37132i	−0.0970325	−	0.711449i
$58$	−2.31532	+	3.18676i	−0.304016	+	0.418442i
$59$	3.05617	+	2.75179i	0.397879	+	0.358252i	0.843649	−	0.536896i	$-0.180403\pi$
$59$	3.05617	+	2.75179i	0.397879	+	0.358252i	−0.445769	+	0.895148i	$0.647070\pi$
$60$	−3.24679	+	1.16677i	−0.419159	+	0.150630i
$61$		−	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
$66$	0.0571138	+	1.85189i	0.00703022	+	0.227951i
$67$	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
$69$	−0.0761031	−	0.122902i	−0.00916174	−	0.0147957i
$70$	1.03146	−	0.749401i	0.123283	−	0.0895706i
$71$	−0.823066	+	0.0865077i	−0.0976799	+	0.0102666i	−0.153242	−	0.988189i	$-0.548971\pi$
$71$	−0.823066	+	0.0865077i	−0.0976799	+	0.0102666i	0.0555624	+	0.998455i	$0.482305\pi$
$72$	1.38678	+	2.66023i	0.163433	+	0.313512i
$73$	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
$75$	1.61025	−	0.777266i	0.185936	−	0.0897510i
$76$	−2.85926	−	1.27302i	−0.327979	−	0.146026i
$77$	−0.211578	−	0.651170i	−0.0241115	−	0.0742077i
$78$	4.48877	+	3.05440i	0.508253	+	0.345843i
$79$	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
$81$	8.60977	+	2.62143i	0.956641	+	0.291271i
$82$	−0.165968	+	0.0738938i	−0.0183281	+	0.00816021i
$83$	5.34426	+	5.93540i	0.586609	+	0.651495i	0.961251	−	0.275674i	$-0.0889012\pi$
$83$	5.34426	+	5.93540i	0.586609	+	0.651495i	−0.374642	+	0.927169i	$0.622235\pi$
$84$	−0.766865	−	0.800617i	−0.0836719	−	0.0873544i
$85$	8.78038	+	12.0852i	0.952366	+	1.31082i
$86$	−1.00326	+	9.54537i	−0.108184	+	1.02930i
$87$	6.31537	+	2.58156i	0.677078	+	0.276773i
$88$	0.926384	+	0.534848i	0.0987528	+	0.0570150i
$89$	−13.6894	−	9.94595i	−1.45108	−	1.05427i	−0.985579	−	0.169219i	$-0.945876\pi$
$89$	−13.6894	−	9.94595i	−1.45108	−	1.05427i	−0.465497	−	0.885049i	$-0.654124\pi$
$90$	3.30108	+	4.98116i	0.347965	+	0.525060i
$91$	−1.90821	−	0.620014i	−0.200034	−	0.0649951i
$92$	−0.0834598			−0.00870129
$93$	−9.26808	−	2.66508i	−0.961055	−	0.276356i
$94$	−0.726083			−0.0748897
$95$	−5.92922	−	1.92652i	−0.608325	−	0.197657i
$96$	1.72732	+	0.127863i	0.176294	+	0.0130499i
$97$	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
$99$	3.09188	−	0.859371i	0.310746	−	0.0863700i
$100$	0.107907	−	1.02667i	0.0107907	−	0.102667i
$101$	2.32653	+	3.20219i	0.231498	+	0.318630i	0.908925	−	0.416961i	$-0.136905\pi$
$101$	2.32653	+	3.20219i	0.231498	+	0.318630i	−0.677426	+	0.735591i	$0.736905\pi$
$102$	9.38045	−	8.98500i	0.928803	−	0.889648i
$103$	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
$105$	−1.68585	−	1.42635i	−0.164522	−	0.139197i
$106$	−2.42729	+	11.4195i	−0.235759	+	1.10916i
$107$	−4.66771	+	10.4839i	−0.451245	+	1.01351i	0.534485	+	0.845178i	$0.320506\pi$
$107$	−4.66771	+	10.4839i	−0.451245	+	1.01351i	−0.985730	+	0.168335i	$0.946161\pi$
$108$	3.90371	−	3.42943i	0.375635	−	0.329997i
$109$	−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
$111$	6.22278	+	12.8917i	0.590640	+	1.22362i
$112$	−0.626083	+	0.133078i	−0.0591593	+	0.0125747i
$113$	−0.372023	−	0.835577i	−0.0349970	−	0.0786044i	0.895201	−	0.445662i	$-0.147032\pi$
$113$	−0.372023	−	0.835577i	−0.0349970	−	0.0786044i	−0.930198	+	0.367058i	$0.880365\pi$
$114$	−0.963105	+	5.33481i	−0.0902031	+	0.499651i
$115$	−0.165333	+	0.0173772i	−0.0154174	+	0.00162043i
$116$	3.18676	−	2.31532i	0.295883	−	0.214972i
$117$	3.28828	−	8.81036i	0.304001	−	0.814518i
$118$	−2.05624	−	3.56151i	−0.189292	−	0.327864i
$119$	−2.40007	+	4.15705i	−0.220014	+	0.381076i
$120$	3.44844	−	0.106353i	0.314798	−	0.00970864i
$121$	−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
$126$	−1.03080	+	1.62008i	−0.0918306	+	0.144328i
$127$	−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
$129$	16.4716	−	2.24652i	1.45025	−	0.197795i
$130$	5.40742	−	3.12198i	0.474262	−	0.273815i
$131$	−16.9742	−	1.78406i	−1.48304	−	0.155874i	−0.671864	−	0.740674i	$-0.734506\pi$
$131$	−16.9742	−	1.78406i	−1.48304	−	0.155874i	−0.811177	+	0.584800i	$0.801173\pi$
$132$	0.517946	−	1.77890i	0.0450814	−	0.154833i
$133$	−0.209404	−	1.99235i	−0.0181576	−	0.172758i
$134$	−8.41193	+	7.57413i	−0.726680	+	0.654305i
$135$	7.01918	−	7.60647i	0.604115	−	0.654661i
$136$	−1.55921	−	7.33552i	−0.133701	−	0.629016i
$137$	−0.237618	−	0.0505074i	−0.0203011	−	0.00431514i	0.197750	−	0.980252i	$-0.436637\pi$
$137$	−0.237618	−	0.0505074i	−0.0203011	−	0.00431514i	−0.218051	+	0.975937i	$0.569970\pi$
$138$	0.0343995	+	0.140404i	0.00292828	+	0.0119520i
$139$	−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
$141$	0.299268	+	1.22149i	0.0252029	+	0.102868i
$142$	0.809514	+	0.172068i	0.0679329	+	0.0144396i
$143$	−0.697157	−	3.27986i	−0.0582992	−	0.274276i
$144$	−0.496846	−	2.95857i	−0.0414038	−	0.246548i
$145$	5.83087	−	5.25014i	0.484227	−	0.436000i
$146$	−1.17773	−	11.2054i	−0.0974700	−	0.927365i
$147$	−3.19102	+	10.9596i	−0.263191	+	0.903937i
$148$	8.21947	+	0.863901i	0.675636	+	0.0710122i
$149$	−6.20496	+	3.58243i	−0.508330	+	0.293484i	−0.732147	−	0.681147i	$-0.761482\pi$
$149$	−6.20496	+	3.58243i	−0.508330	+	0.293484i	0.223817	+	0.974631i	$0.428148\pi$
$150$	−1.77163	+	0.241628i	−0.144653	+	0.0197288i
$151$	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
$153$	−18.9817	−	12.0773i	−1.53458	−	0.976396i
$154$			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
$159$	20.2114	−	0.623338i	1.60287	−	0.0494339i
$160$	0.995952	−	1.72504i	0.0787369	−	0.136376i
$161$	−0.0267101	−	0.0462632i	−0.00210505	−	0.00364605i
$162$	−7.37831	−	5.15370i	−0.579695	−	0.404913i
$163$	−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
$165$	0.655661	−	3.63182i	0.0510432	−	0.282737i
$166$	−3.24855	−	7.29637i	−0.252137	−	0.566308i
$167$	21.9324	−	4.66187i	1.69718	−	0.360746i	0.745183	−	0.666860i	$-0.232362\pi$
$167$	21.9324	−	4.66187i	1.69718	−	0.360746i	0.951995	+	0.306113i	$0.0990287\pi$
$168$	0.481928	+	0.998406i	0.0371816	+	0.0770287i
$169$	2.89948	+	1.29093i	0.223037	+	0.0993023i
$170$	−4.61612	−	14.2070i	−0.354040	−	1.08962i
$171$	9.37169	−	0.578612i	0.716671	−	0.0442476i
$172$	3.90384	−	8.76816i	0.297665	−	0.668566i
$173$	−2.88585	+	13.5768i	−0.219407	+	1.03223i	0.721199	+	0.692728i	$0.243591\pi$
$173$	−2.88585	+	13.5768i	−0.219407	+	1.03223i	−0.940606	+	0.339500i	$0.889742\pi$
$174$	−5.20852	−	4.40677i	−0.394857	−	0.334076i
$175$	0.603633	−	0.268755i	0.0456303	−	0.0203159i
$176$	−0.715766	−	0.794939i	−0.0539529	−	0.0599208i
$177$	−5.14400	+	4.92714i	−0.386647	+	0.370347i
$178$	9.94595	+	13.6894i	0.745480	+	1.02607i
$179$	1.42045	−	13.5147i	0.106170	−	1.01014i	−0.803642	−	0.595114i	$-0.797107\pi$
$179$	1.42045	−	13.5147i	0.106170	−	1.01014i	0.909811	−	0.415022i	$-0.136226\pi$
$180$	−1.60025	−	5.75746i	−0.119276	−	0.429135i
$181$	−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
$183$	4.18013	+	0.309427i	0.309004	+	0.0228735i
$184$	0.0793750	+	0.0257905i	0.00585160	+	0.00190130i
$185$	16.4626			1.21035
$186$	7.99092	+	5.39864i	0.585922	+	0.395847i
$187$	−8.02207			−0.586632
$188$	0.690546	+	0.224372i	0.0503632	+	0.0163640i
$189$	3.15032	+	1.06636i	0.229152	+	0.0775660i
$190$	5.04369	+	3.66446i	0.365908	+	0.265848i
$191$	18.1731	+	10.4922i	1.31496	+	0.759192i	0.982913	−	0.184071i	$-0.0589277\pi$
$191$	18.1731	+	10.4922i	1.31496	+	0.759192i	0.332046	+	0.943263i	$0.392261\pi$
$192$	−1.60327	−	0.655377i	−0.115706	−	0.0472978i
$193$	−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
$195$	−7.48085	−	7.81010i	−0.535715	−	0.559293i
$196$	4.40978	+	4.89755i	0.314984	+	0.349825i
$197$	15.4230	−	6.86678i	1.09885	−	0.489238i	0.224467	−	0.974482i	$-0.427936\pi$
$197$	15.4230	−	6.86678i	1.09885	−	0.489238i	0.874379	+	0.485244i	$0.161269\pi$
$198$	−3.20611	−	0.138133i	−0.227848	−	0.00981667i
$199$	−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
$201$	16.2091	+	11.0295i	1.14330	+	0.777963i
$202$	−1.22313	−	3.76440i	−0.0860591	−	0.264863i
$203$	2.30329	+	1.02549i	0.161659	+	0.0719754i
$204$	−11.6979	+	5.64652i	−0.819013	+	0.395336i
$205$	0.353971	−	0.0752388i	0.0247224	−	0.00525491i
$206$	−4.65354	−	10.4520i	−0.324227	−	0.728226i
$207$	0.222023	−	0.115740i	0.0154316	−	0.00804450i
$208$	−3.11749	+	0.327662i	−0.216159	+	0.0227193i
$209$	2.70857	−	1.96789i	0.187356	−	0.136122i
$210$	1.16257	+	1.87749i	0.0802253	+	0.129559i
$211$	−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
$213$	−0.0441876	−	1.43276i	−0.00302769	−	0.0981713i
$214$	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
$219$	−18.3654	+	6.59981i	−1.24102	+	0.445974i
$220$	−1.58344	−	1.42574i	−0.106756	−	0.0961231i
$221$	−13.8177	+	19.0185i	−0.929481	+	1.27932i
$222$	−1.93447	−	14.1836i	−0.129833	−	0.951944i
$223$	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
$225$	1.13670	+	2.88082i	0.0757800	+	0.192054i
$226$	0.0956072	+	0.909642i	0.00635970	+	0.0605085i
$227$	−13.0983	+	11.7937i	−0.869362	+	0.782777i	−0.977406	−	0.211369i	$-0.932208\pi$
$227$	−13.0983	+	11.7937i	−0.869362	+	0.782777i	0.108044	+	0.994146i	$0.465541\pi$
$228$	2.56451	−	4.77609i	0.169839	−	0.316304i
$229$	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
$231$	1.15183	−	0.282203i	0.0757851	−	0.0185676i
$232$	−3.74626	+	1.21723i	−0.245954	+	0.0799153i
$233$	−23.7568	+	7.71904i	−1.55636	+	0.505691i	−0.955832	−	0.293914i	$-0.905042\pi$
$233$	−23.7568	+	7.71904i	−1.55636	+	0.505691i	−0.600526	+	0.799606i	$0.705042\pi$
$234$	−5.84989	+	7.36301i	−0.382419	+	0.481335i
$235$	1.41468	+	0.300700i	0.0922837	+	0.0196155i
$236$	0.855033	+	4.02261i	0.0556579	+	0.261850i
$237$	4.82595	+	2.59129i	0.313479	+	0.168322i
$238$	3.56720	−	3.21192i	0.231227	−	0.208198i
$239$	−0.0667465	−	0.635051i	−0.00431747	−	0.0410780i	0.992151	−	0.125045i	$-0.0399076\pi$
$239$	−0.0667465	−	0.635051i	−0.00431747	−	0.0410780i	−0.996469	+	0.0839672i	$0.973241\pi$
$240$	−3.31252	−	0.964478i	−0.213823	−	0.0622568i
$241$	−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
$243$	−5.62894	+	14.5367i	−0.361096	+	0.932528i
$244$	1.42244	−	1.95782i	0.0910624	−	0.125337i
$245$	9.75546	+	8.78385i	0.623253	+	0.561180i
$246$	−0.106418	−	0.296129i	−0.00678494	−	0.0188805i
$247$		−	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	−0.224954	−	0.974369i	$-0.572223\pi$
$251$	12.1609	−	13.5061i	0.767592	−	0.852497i	0.992546	+	0.121872i	$0.0388899\pi$
$252$	1.48098	−	1.22226i	0.0932929	−	0.0769949i
$253$	0.0446383	−	0.0773158i	0.00280639	−	0.00486080i
$254$	7.41077	+	12.8358i	0.464993	+	0.805391i
$255$	−21.9977	+	13.6213i	−1.37755	+	0.853001i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	2.19661	−	0.230873i	0.137021	−	0.0144015i	−0.0357696	−	0.999360i	$-0.511388\pi$
$257$	2.19661	−	0.230873i	0.137021	−	0.0144015i	0.172791	+	0.984959i	$0.444722\pi$
$258$	−16.3597	−	2.95345i	−1.01851	−	0.183874i
$259$	2.15164	+	4.83267i	0.133697	+	0.300288i
$260$	−6.10751	+	1.29819i	−0.378771	+	0.0805103i
$261$	−5.26670	+	10.5786i	−0.326000	+	0.654799i
$262$	15.5921	+	6.94205i	0.963284	+	0.428882i
$263$	−2.55692	−	7.86938i	−0.157666	−	0.485247i	0.840755	−	0.541416i	$-0.182111\pi$
$263$	−2.55692	−	7.86938i	−0.157666	−	0.485247i	−0.998421	+	0.0561690i	$0.982111\pi$
$264$	−1.04231	+	1.53178i	−0.0641495	+	0.0942744i
$265$	9.45855	−	21.2443i	0.581034	−	1.30502i
$266$	−0.416514	+	1.95954i	−0.0255381	+	0.120147i
$267$	18.9302	−	22.3744i	1.15851	−	1.36929i
$268$	10.3408	−	4.60400i	0.631662	−	0.281234i
$269$	6.60884	+	7.33986i	0.402948	+	0.447519i	0.910132	−	0.414319i	$-0.135980\pi$
$269$	6.60884	+	7.33986i	0.402948	+	0.447519i	−0.507184	+	0.861838i	$0.669314\pi$
$270$	−9.02617	+	5.06514i	−0.549315	+	0.308255i
$271$	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
$273$	1.31495	−	3.21681i	0.0795846	−	0.194690i
$274$	0.210381	+	0.121463i	0.0127096	+	0.00733788i
$275$	0.893373	+	0.649074i	0.0538724	+	0.0391406i
$276$	0.0106714	−	0.144162i	0.000642342	−	0.00867755i
$277$	−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
$279$	5.78850	−	15.6682i	0.346548	−	0.938032i
$280$	1.27496			0.0761933
$281$	−17.3635	−	5.64176i	−1.03582	−	0.336559i	−0.258733	−	0.965949i	$-0.583305\pi$
$281$	−17.3635	−	5.64176i	−1.03582	−	0.336559i	−0.777090	+	0.629390i	$0.783305\pi$
$282$	0.0928388	−	1.25418i	0.00552847	−	0.0746854i
$283$	−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
$285$	4.08585	−	9.99535i	0.242025	−	0.592074i
$286$	−0.350498	+	3.33477i	−0.0207254	+	0.197189i
$287$	0.0683504	+	0.0940763i	0.00403460	+	0.00555315i
$288$	−0.441720	+	2.96730i	−0.0260286	+	0.174850i
$289$	26.2574	+	29.1617i	1.54455	+	1.71540i
$290$	−7.16787	+	3.19134i	−0.420912	+	0.187402i
$291$	−3.19023	+	3.77065i	−0.187015	+	0.221040i
$292$	−2.34257	+	11.0209i	−0.137088	+	0.644950i
$293$	−4.71107	+	10.5812i	−0.275223	+	0.618162i	−0.997283	−	0.0736692i	$-0.976529\pi$
$293$	−4.71107	+	10.5812i	−0.275223	+	0.618162i	0.722059	+	0.691831i	$0.243196\pi$
$294$	6.42156	−	9.43717i	0.374513	−	0.550387i
$295$	2.53136	+	7.79073i	0.147382	+	0.453594i
$296$	−7.55022	−	3.36157i	−0.438848	−	0.195388i
$297$	1.08908	+	5.45056i	0.0631947	+	0.316274i
$298$	7.00830	−	1.48966i	0.405980	−	0.0862937i
$299$	−0.106410	−	0.239001i	−0.00615384	−	0.0138218i
$300$	1.75959	+	0.317663i	0.101590	+	0.0183403i
$301$	6.10970	−	0.642156i	0.352157	−	0.0370132i
$302$	−6.99708	+	5.08368i	−0.402637	+	0.292533i
$303$	−5.82871	+	3.60923i	−0.334850	+	0.207345i
$304$	−1.56492	−	2.71052i	−0.0897545	−	0.155459i
$305$	2.41020	−	4.17459i	0.138008	−	0.239037i
$306$	14.3206	+	17.3519i	0.818655	+	0.991943i
$307$	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	$-0.846571\pi$
$311$		−	16.3500i		−	0.927125i	0.886064	−	0.463563i	$-0.153429\pi$
$312$	1.83616	+	5.10949i	0.103952	+	0.289268i
$313$	−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
$315$	2.67932	−	2.72964i	0.150962	−	0.153798i
$316$	2.73882	−	1.58126i	0.154071	−	0.0889528i
$317$	21.3632	+	2.24537i	1.19988	+	0.126112i	0.683306	−	0.730132i	$-0.260541\pi$
$317$	21.3632	+	2.24537i	1.19988	+	0.126112i	0.516572	+	0.856244i	$0.327208\pi$
$318$	−19.4149	−	5.65285i	−1.08873	−	0.316996i
$319$	0.440439	+	4.19050i	0.0246599	+	0.234623i
$320$	−1.48027	+	1.33284i	−0.0827498	+	0.0745082i
$321$	−17.5122	−	9.40315i	−0.977436	−	0.524833i
$322$	0.0111067	+	0.0522528i	0.000618951	+	0.00291193i
$323$	−22.9590	−	4.88009i	−1.27748	−	0.271536i
$324$	5.42461	+	7.18148i	0.301367	+	0.398971i
$325$	3.07760	−	0.999974i	0.170715	−	0.0554686i
$326$	11.0432	−	3.58815i	0.611626	−	0.198729i
$327$	4.93251	−	1.20848i	0.272769	−	0.0668293i
$328$	−0.177705	−	0.0377723i	−0.00981211	−	0.00208563i
$329$	0.0966257	+	0.454588i	0.00532715	+	0.0250623i
$330$	−1.74587	+	3.25146i	−0.0961068	+	0.178987i
$331$	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
$333$	−23.0638	+	9.10040i	−1.26389	+	0.498699i
$334$	−22.2995	−	2.34377i	−1.22018	−	0.128246i
$335$	19.5263	−	11.2735i	1.06684	−	0.615939i
$336$	−0.149817	−	1.09846i	−0.00817316	−	0.0599262i
$337$	−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
$339$	1.49088	−	0.535765i	0.0809735	−	0.0290988i
$340$			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
$345$	−0.00887619	−	0.287806i	−0.000477878	−	0.0154950i
$346$	6.94007	−	12.0206i	0.373101	−	0.646229i
$347$	10.4963	+	18.1802i	0.563472	+	0.975963i	0.997190	+	0.0749138i	$0.0238681\pi$
$347$	10.4963	+	18.1802i	0.563472	+	0.975963i	−0.433718	+	0.901049i	$0.642799\pi$
$348$	3.59183	+	5.80061i	0.192543	+	0.310945i
$349$	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
$351$	14.7979	+	6.80644i	0.789854	+	0.363301i
$352$	0.435084	+	0.977216i	0.0231901	+	0.0520858i
$353$	22.2687	−	4.73335i	1.18524	−	0.251931i	0.427213	−	0.904151i	$-0.359496\pi$
$353$	22.2687	−	4.73335i	1.18524	−	0.251931i	0.758030	+	0.652220i	$0.226162\pi$
$354$	6.41480	−	3.09641i	0.340943	−	0.164572i
$355$	−1.50598	−	0.670504i	−0.0799290	−	0.0355867i
$356$	−5.22889	−	16.0929i	−0.277131	−	0.852921i
$357$	−6.87369	−	4.67723i	−0.363794	−	0.247545i
$358$	−5.52720	+	12.4143i	−0.292122	+	0.656116i
$359$	4.91547	−	23.1255i	0.259429	−	1.22052i	−0.634719	−	0.772743i	$-0.718884\pi$
$359$	4.91547	−	23.1255i	0.259429	−	1.22052i	0.894147	−	0.447773i	$-0.147783\pi$
$360$	−0.257220	+	5.97017i	−0.0135567	+	0.314656i
$361$	−8.40834	+	3.74363i	−0.442544	+	0.197033i
$362$	16.8341	+	18.6961i	0.884779	+	0.982647i
$363$	−11.8081	−	12.3278i	−0.619766	−	0.647043i
$364$	−1.17934	−	1.62322i	−0.0618140	−	0.0850797i
$365$	−2.34593	+	22.3201i	−0.122792	+	1.16829i
$366$	−3.87992	−	1.58601i	−0.202807	−	0.0829022i
$367$	−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
$369$	−0.454315	+	0.301081i	−0.0236507	+	0.0156736i
$370$	−15.6568	−	5.08721i	−0.813960	−	0.264472i
$371$	7.47258			0.387957
$372$	−5.93154	−	7.60374i	−0.307536	−	0.394235i
$373$	−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
$375$	20.7552	+	1.53637i	1.07179	+	0.0793378i
$376$	−0.587413	−	0.426781i	−0.0302935	−	0.0220095i
$377$	10.6933	+	6.17380i	0.550735	+	0.317967i
$378$	−2.66661	−	1.98767i	−0.137156	−	0.102235i
$379$	−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
$381$	18.5392	−	17.7576i	0.949790	−	0.909750i
$382$	−14.0414	−	15.5945i	−0.718418	−	0.797884i
$383$	−3.31247	+	1.47481i	−0.169259	+	0.0753592i	−0.489617	−	0.871937i	$-0.662864\pi$
$383$	−3.31247	+	1.47481i	−0.169259	+	0.0753592i	0.320358	+	0.947297i	$0.396197\pi$
$384$	1.32228	+	1.11874i	0.0674773	+	0.0570904i
$385$	0.283553	−	1.33401i	0.0144512	−	0.0679877i
$386$	6.66225	−	14.9636i	0.339099	−	0.761630i
$387$	1.77437	+	28.7391i	0.0901961	+	1.46089i
$388$	0.881202	+	2.71206i	0.0447363	+	0.137684i
$389$	−3.73499	−	1.66292i	−0.189372	−	0.0843136i	0.309860	−	0.950782i	$-0.399718\pi$
$389$	−3.73499	−	1.66292i	−0.189372	−	0.0843136i	−0.499232	+	0.866468i	$0.666384\pi$
$390$	4.70126	+	9.73955i	0.238058	+	0.493182i
$391$	−0.612221	+	0.130132i	−0.0309614	+	0.00658104i
$392$	−2.68052	−	6.02055i	−0.135387	−	0.304084i
$393$	5.25201	−	29.0918i	0.264929	−	1.46749i
$394$	−16.7901	+	1.76471i	−0.845874	+	0.0889050i
$395$	5.09635	−	3.70271i	0.256425	−	0.186304i
$396$	3.00651	+	1.12212i	0.151083	+	0.0563884i
$397$	−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
$399$	3.46820	−	0.106962i	0.173627	−	0.00535482i
$400$	0.690758	−	0.767164i	0.0345379	−	0.0383582i
$401$	7.01809	−	21.5995i	0.350467	−	1.07863i	−0.608125	−	0.793842i	$-0.708078\pi$
$401$	7.01809	−	21.5995i	0.350467	−	1.07863i	0.958592	−	0.284785i	$-0.0919221\pi$
$402$	−12.0074	−	15.4986i	−0.598875	−	0.772999i
$403$	−15.9677	−	7.04571i	−0.795409	−	0.350972i
$404$			3.95813i			0.196924i
$405$	12.2414	+	13.0970i	0.608278	+	0.650795i
$406$	−1.87367	−	1.68706i	−0.0929886	−	0.0837273i
$407$	−5.19647	+	7.15233i	−0.257579	+	0.354528i
$408$	12.8702	−	1.75533i	0.637169	−	0.0869017i
$409$	−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
$411$	0.117625	−	0.403986i	0.00580202	−	0.0199272i
$412$	1.19593	+	11.3785i	0.0589191	+	0.560577i
$413$	−1.95616	+	1.76134i	−0.0962564	+	0.0866697i
$414$	−0.246922	+	0.0414667i	−0.0121355	+	0.00203798i
$415$	3.30768	+	15.5614i	0.162368	+	0.763880i
$416$	3.06617	+	0.651734i	0.150331	+	0.0319539i
$417$	−9.33654	−	38.1078i	−0.457212	−	1.86614i
$418$	−3.18412	+	1.03458i	−0.155740	+	0.0506031i
$419$	−1.91732	+	0.622976i	−0.0936674	+	0.0304344i	−0.355476	−	0.934685i	$-0.615681\pi$
$419$	−1.91732	+	0.622976i	−0.0936674	+	0.0304344i	0.261808	+	0.965120i	$0.415681\pi$
$420$	−0.525497	−	2.14486i	−0.0256416	−	0.104658i
$421$	−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
$423$	−2.14817	+	0.360751i	−0.104447	+	0.0175403i
$424$	−8.67594	+	7.81185i	−0.421341	+	0.379377i
$425$	−0.809238	−	7.69938i	−0.0392538	−	0.373475i
$426$	−0.400723	+	1.37629i	−0.0194151	+	0.0666816i
$427$	1.54048	+	0.161911i	0.0745493	+	0.00783544i
$428$	−9.93852	+	5.73801i	−0.480396	+	0.277357i
$429$	5.75453	−	0.784844i	0.277831	−	0.0378926i
$430$	−11.2374	+	15.4669i	−0.541915	+	0.745882i
$431$	−23.5949	−	21.2449i	−1.13653	−	1.02333i	−0.999463	−	0.0327708i	$-0.989567\pi$
$431$	−23.5949	−	21.2449i	−1.13653	−	1.02333i	−0.137064	−	0.990562i	$-0.543766\pi$
$432$	5.17394	−	0.479924i	0.248931	−	0.0230904i
$433$		−	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
$438$	19.5059	−	0.601580i	0.932030	−	0.0287446i
$439$	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
$441$	−18.5229	−	6.91326i	−0.882041	−	0.329203i
$442$	19.0185	−	13.8177i	0.904616	−	0.657242i
$443$	−24.1723	+	2.54061i	−1.14846	+	0.120708i	−0.659574	−	0.751640i	$-0.729263\pi$
$443$	−24.1723	+	2.54061i	−1.14846	+	0.120708i	−0.488885	+	0.872348i	$0.662596\pi$
$444$	−2.54320	+	14.0872i	−0.120695	+	0.668551i
$445$	−13.7091	−	30.7911i	−0.649874	−	1.45964i
$446$	−14.1569	+	3.00914i	−0.670348	+	0.142487i
$447$	−5.39464	−	11.1760i	−0.255158	−	0.528608i
$448$	−0.584733	−	0.260340i	−0.0276260	−	0.0122999i
$449$	−0.271312	−	0.835013i	−0.0128040	−	0.0394067i	0.944450	−	0.328654i	$-0.106595\pi$
$449$	−0.271312	−	0.835013i	−0.0128040	−	0.0394067i	−0.957254	+	0.289247i	$0.906595\pi$
$450$	−0.190845	−	3.09108i	−0.00899650	−	0.145715i
$451$	−0.0790439	+	0.177536i	−0.00372203	+	0.00835982i
$452$	0.190167	−	0.894665i	0.00894470	−	0.0420815i
$453$	11.4362	+	9.67583i	0.537321	+	0.454610i
$454$	16.1016	−	7.16891i	0.755688	−	0.336454i
$455$	−2.67423	−	2.97003i	−0.125370	−	0.139237i
$456$	−3.91489	+	3.74985i	−0.183332	+	0.175603i
$457$	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
$459$	23.2886	−	31.2434i	1.08702	−	1.45832i
$460$	−0.143971	−	0.0831220i	−0.00671270	−	0.00387558i
$461$	−22.4822	−	16.3343i	−1.04710	−	0.760764i	−0.0754429	−	0.997150i	$-0.524037\pi$
$461$	−22.4822	−	16.3343i	−1.04710	−	0.760764i	−0.971659	+	0.236386i	$0.924037\pi$
$462$	−1.18267	−	0.0875449i	−0.0550226	−	0.00407296i
$463$	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
$465$	−13.3335	−	13.8279i	−0.618327	−	0.641255i
$466$	24.9793			1.15715
$467$	−9.65389	−	3.13674i	−0.446729	−	0.145151i	0.0770092	−	0.997030i	$-0.475463\pi$
$467$	−9.65389	−	3.13674i	−0.446729	−	0.145151i	−0.523738	+	0.851879i	$0.675463\pi$
$468$	7.83887	−	5.19493i	0.362352	−	0.240136i
$469$	5.86148	+	4.25861i	0.270658	+	0.196645i
$470$	−1.25252	−	0.723143i	−0.0577745	−	0.0333561i
$471$	22.6084	+	9.24176i	1.04174	+	0.425838i
$472$	0.429871	−	4.08995i	0.0197864	−	0.188255i
$473$	6.03472	+	8.30608i	0.277477	+	0.381914i
$474$	−3.78900	−	3.95576i	−0.174035	−	0.181694i
$475$	2.16197	+	2.40111i	0.0991978	+	0.110170i
$476$	−4.38515	+	1.95239i	−0.200993	+	0.0894878i
$477$	−1.50758	+	34.9914i	−0.0690273	+	1.60215i
$478$	−0.132762	+	0.624595i	−0.00607238	+	0.0285683i
$479$	−8.56881	+	19.2459i	−0.391519	+	0.879366i	0.605018	+	0.796212i	$0.293166\pi$
$479$	−8.56881	+	19.2459i	−0.391519	+	0.879366i	−0.996537	+	0.0831540i	$0.973501\pi$
$480$	2.85236	+	1.94090i	0.130192	+	0.0885895i
$481$	8.00577	+	24.6392i	0.365032	+	1.12345i
$482$	15.4323	+	6.87090i	0.702922	+	0.312961i
$483$	0.0833268	−	0.0402216i	0.00379150	−	0.00183015i
$484$	−9.64038	+	2.04913i	−0.438199	+	0.0931421i
$485$	2.31033	+	5.18910i	0.104907	+	0.235625i
$486$	9.84552	−	12.0858i	0.446602	−	0.548222i
$487$	−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
$489$	−10.5880	−	17.0990i	−0.478805	−	0.773243i
$490$	−6.56363	−	11.3685i	−0.296515	−	0.513578i
$491$	2.70340	−	4.68243i	0.122003	−	0.211315i	−0.798555	−	0.601922i	$-0.794402\pi$
$491$	2.70340	−	4.68243i	0.122003	−	0.211315i	0.920557	+	0.390607i	$0.127735\pi$
$492$	0.00970009	+	0.314521i	0.000437314	+	0.0141797i
$493$	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
$498$	13.0186	−	4.67837i	0.583376	−	0.209643i
$499$	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
$501$	5.24824	+	38.4804i	0.234474	+	1.71918i
$502$	−15.7394	+	9.08712i	−0.702482	+	0.405578i
$503$	30.2586	+	3.18030i	1.34916	+	0.141803i	0.751387	−	0.659861i	$-0.229385\pi$
$503$	30.2586	+	3.18030i	1.34916	+	0.141803i	0.597775	+	0.801664i	$0.296052\pi$
$504$	−1.78619	+	0.704788i	−0.0795633	+	0.0313937i
$505$	0.824124	+	7.84102i	0.0366731	+	0.348921i
$506$	−0.0663455	+	0.0597377i	−0.00294942	+	0.00265567i
$507$	−2.60059	+	4.84327i	−0.115496	+	0.215097i
$508$	−3.08157	−	14.4976i	−0.136723	−	0.643229i
$509$	−18.6818	−	3.97095i	−0.828058	−	0.176009i	−0.225661	−	0.974206i	$-0.572454\pi$
$509$	−18.6818	−	3.97095i	−0.828058	−	0.176009i	−0.602397	+	0.798197i	$0.705788\pi$
$510$	25.1303	−	6.15700i	1.11279	−	0.272637i
$511$	−6.85878	+	2.22855i	−0.303414	+	0.0985853i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−0.198836	+	16.2619i	−0.00877884	+	0.717982i
$514$	−2.16045	−	0.459217i	−0.0952933	−	0.0202552i
$515$	4.73824	+	22.2917i	0.208792	+	0.982288i
$516$	14.6463	+	7.86431i	0.644768	+	0.346207i
$517$	−0.577191	+	0.519705i	−0.0253848	+	0.0228566i
$518$	−0.552957	−	5.26104i	−0.0242956	−	0.231157i
$519$	−23.0826	−	6.72076i	−1.01321	−	0.295009i
$520$	6.20975	+	0.652671i	0.272315	+	0.0286215i
$521$	−34.6844	+	20.0251i	−1.51955	+	0.877314i	−0.519818	+	0.854277i	$0.674000\pi$
$521$	−34.6844	+	20.0251i	−1.51955	+	0.877314i	−0.999735	+	0.0230373i	$0.992666\pi$
$522$	8.27790	−	8.43335i	0.362314	−	0.369118i
$523$	−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
$525$	0.387045	+	1.07703i	0.0168920	+	0.0470056i
$526$			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
$531$	−7.85305	−	9.51535i	−0.340794	−	0.412931i
$532$	1.00166	−	1.73493i	0.0434275	−	0.0752186i
$533$	0.284745	+	0.493193i	0.0123337	+	0.0213626i
$534$	−24.9178	+	15.4295i	−1.07830	+	0.667700i
$535$	−18.4934	+	13.4362i	−0.799540	+	0.580899i
$536$	−11.2574	+	1.18320i	−0.486244	+	0.0511063i
$537$	23.1627	+	4.18161i	0.999542	+	0.180450i
$538$	−4.01724	−	9.02286i	−0.173195	−	0.389003i
$539$	−6.89557	+	1.46570i	−0.297013	+	0.0631322i
$540$	10.1496	−	2.02799i	0.436770	−	0.0872710i
$541$	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
$543$	24.5139	−	36.0258i	1.05199	−	1.54602i
$544$	3.05028	−	6.85104i	0.130780	−	0.293736i
$545$	1.21426	−	5.71266i	0.0520134	−	0.244704i
$546$	−2.24464	+	2.65303i	−0.0960619	+	0.113539i
$547$	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
$549$	−1.06896	+	7.18087i	−0.0456222	+	0.306472i
$550$	−0.649074	−	0.893373i	−0.0276766	−	0.0380936i
$551$	−1.28869	+	12.2611i	−0.0549001	+	0.522339i
$552$	−0.0546977	+	0.133809i	−0.00232809	+	0.00569528i
$553$	1.75304	+	1.01212i	0.0745468	+	0.0430396i
$554$	7.57518	+	5.50369i	0.321839	+	0.233829i
$555$	−2.10495	+	28.4362i	−0.0893500	+	1.20705i
$556$	−21.5436	−	6.99993i	−0.913651	−	0.296863i
$557$	−21.0884			−0.893544			−0.446772	−	0.894648i	$-0.647427\pi$
$557$	−21.0884			−0.893544			−0.446772	+	0.894648i	$0.647427\pi$
$558$	−10.3469	+	13.1126i	−0.438021	+	0.555102i
$559$	30.0863			1.27252
$560$	−1.21256	−	0.393984i	−0.0512399	−	0.0166488i
$561$	1.02572	−	13.8567i	0.0433060	−	0.585032i
$562$	14.7703	+	10.7313i	0.623048	+	0.452671i
$563$	12.8332	+	7.40925i	0.540855	+	0.312263i	0.745425	−	0.666589i	$-0.232246\pi$
$563$	12.8332	+	7.40925i	0.540855	+	0.312263i	−0.204570	+	0.978852i	$0.565580\pi$
$564$	−0.475858	+	1.16411i	−0.0200372	+	0.0490178i
$565$	0.190440	−	1.81192i	0.00801189	−	0.0762280i
$566$	9.60688	+	13.2227i	0.403807	+	0.555793i
$567$	−2.24475	+	5.30528i	−0.0942707	+	0.222801i
$568$	0.553772	+	0.615026i	0.0232358	+	0.0258059i
$569$	9.29957	−	4.14043i	0.389858	−	0.173576i	−0.202440	−	0.979295i	$-0.564887\pi$
$569$	9.29957	−	4.14043i	0.389858	−	0.173576i	0.592299	+	0.805719i	$0.298221\pi$
$570$	−6.97461	+	8.24355i	−0.292134	+	0.345284i
$571$	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
$573$	−20.4472	+	30.0493i	−0.854193	+	1.25533i
$574$	−0.0359339	−	0.110593i	−0.00149985	−	0.00461608i
$575$	0.0787087	+	0.0350434i	0.00328238	+	0.00146141i
$576$	1.33705	−	2.68557i	0.0557103	−	0.111899i
$577$	−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
$579$	−27.9192	−	5.04032i	−1.16028	−	0.209469i
$580$	7.80322	−	0.820152i	0.324011	−	0.0340549i
$581$	−4.13582	+	3.00485i	−0.171583	+	0.124662i
$582$	4.19929	−	2.60027i	0.174066	−	0.107785i
$583$	6.24415	+	10.8152i	0.258606	+	0.447919i
$584$	5.63356	−	9.75761i	0.233118	−	0.403773i
$585$	14.4471	−	11.9232i	0.597314	−	0.492965i
$586$	7.75027	−	8.60755i	0.320161	−	0.355574i
$587$	−6.82206	+	20.9962i	−0.281577	+	0.866604i	0.705827	+	0.708384i	$0.250575\pi$
$587$	−6.82206	+	20.9962i	−0.281577	+	0.866604i	−0.987404	+	0.158220i	$0.949425\pi$
$588$	−9.02351	+	6.99091i	−0.372123	+	0.288300i
$589$	−0.0579951	−	17.4261i	−0.00238965	−	0.718032i
$590$		−	8.19166i		−	0.337245i
$591$	9.88913	+	27.5186i	0.406784	+	1.13196i
$592$	6.14190	+	5.53019i	0.252431	+	0.227290i
$593$	−11.9102	+	16.3930i	−0.489094	+	0.673181i	−0.980221	−	0.197908i	$-0.936585\pi$
$593$	−11.9102	+	16.3930i	−0.489094	+	0.673181i	0.491126	+	0.871088i	$0.336585\pi$
$594$	0.648542	−	5.52034i	0.0266100	−	0.226502i
$595$	−8.28043	+	4.78071i	−0.339465	+	0.195990i
$596$	−7.12562	−	0.748932i	−0.291877	−	0.0306775i
$597$	−8.13183	−	2.36767i	−0.332814	−	0.0969024i
$598$	0.0273466	+	0.260185i	0.00111829	+	0.0106398i
$599$	18.5246	−	16.6796i	0.756894	−	0.681511i	−0.197419	−	0.980319i	$-0.563256\pi$
$599$	18.5246	−	16.6796i	0.756894	−	0.681511i	0.954313	+	0.298808i	$0.0965892\pi$
$600$	−1.57531	−	0.845858i	−0.0643116	−	0.0345320i
$601$	−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
$603$	−21.1241	+	26.5880i	−0.860240	+	1.08275i
$604$	8.22557	−	2.67265i	0.334694	−	0.108749i
$605$	−18.6709	+	6.06653i	−0.759078	+	0.246640i
$606$	6.65874	−	1.63142i	0.270493	−	0.0662717i
$607$	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
$609$	−2.06586	+	3.84741i	−0.0837130	+	0.155905i
$610$	−3.58226	+	3.22548i	−0.145041	+	0.130596i
$611$	0.237910	+	2.26356i	0.00962479	+	0.0915738i
$612$	−8.25767	−	20.9280i	−0.333796	−	0.845963i
$613$	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
$615$	0.0847023	+	0.621043i	0.00341553	+	0.0250429i
$616$	−0.402445	+	0.553918i	−0.0162150	+	0.0223180i
$617$	10.0155	+	9.01797i	0.403207	+	0.363050i	0.845641	−	0.533751i	$-0.179218\pi$
$617$	10.0155	+	9.01797i	0.403207	+	0.363050i	−0.442434	+	0.896801i	$0.645885\pi$
$618$	18.6490	−	6.70175i	0.750174	−	0.269584i
$619$		−	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
$624$	−0.167368	−	5.42682i	−0.00670007	−	0.217247i
$625$	9.38635	−	16.2576i	0.375454	−	0.650306i
$626$	2.78787	+	4.82874i	0.111426	+	0.192995i
$627$	3.05287	+	4.93021i	0.121920	+	0.196893i
$628$	11.4083	−	8.28862i	0.455241	−	0.330752i
$629$	61.6411	−	6.47874i	2.45779	−	0.258324i
$630$	−3.39169	+	1.76808i	−0.135128	+	0.0704421i
$631$	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
$633$	17.2621	−	8.33235i	0.686105	−	0.331181i
$634$	−19.6238	−	8.73707i	−0.779360	−	0.346993i
$635$	−9.12313	−	28.0781i	−0.362040	−	1.11425i
$636$	16.7178	+	11.3757i	0.662904	+	0.451076i
$637$	−8.40254	+	18.8724i	−0.332921	+	0.747752i
$638$	0.876053	−	4.12151i	0.0346833	−	0.163172i
$639$	2.48050	+	0.106870i	0.0981269	+	0.00422772i
$640$	1.81969	−	0.810180i	0.0719297	−	0.0320252i
$641$	−9.06035	−	10.0625i	−0.357862	−	0.397446i	0.537151	−	0.843486i	$-0.319501\pi$
$641$	−9.06035	−	10.0625i	−0.357862	−	0.397446i	−0.895013	+	0.446040i	$0.852834\pi$
$642$	13.7494	+	14.3545i	0.542644	+	0.566527i
$643$	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
$645$	30.6516	+	12.5296i	1.20691	+	0.493353i
$646$	20.3273	+	11.7360i	0.799767	+	0.461746i
$647$	−1.08772	−	0.790274i	−0.0427627	−	0.0310689i	0.566199	−	0.824269i	$-0.308414\pi$
$647$	−1.08772	−	0.790274i	−0.0427627	−	0.0310689i	−0.608961	+	0.793200i	$0.708414\pi$
$648$	−2.93991	−	8.50629i	−0.115491	−	0.334159i
$649$	−4.18379	−	1.35940i	−0.164228	−	0.0533610i
$650$	−3.23598			−0.126926
$651$	2.31658	−	5.72142i	0.0907939	−	0.224240i
$652$	−11.6115			−0.454741
$653$	2.66488	+	0.865873i	0.104285	+	0.0338842i	0.360695	−	0.932684i	$-0.382540\pi$
$653$	2.66488	+	0.865873i	0.104285	+	0.0338842i	−0.256410	+	0.966568i	$0.582540\pi$
$654$	−5.06454	−	0.374895i	−0.198039	−	0.0146595i
$655$	−27.5043	−	19.9830i	−1.07468	−	0.780802i
$656$	0.157335	+	0.0908375i	0.00614290	+	0.00354661i
$657$	−9.05177	−	32.5668i	−0.353143	−	1.27055i
$658$	0.0485790	−	0.462198i	0.00189381	−	0.0180184i
$659$	9.40591	+	12.9461i	0.366402	+	0.504309i	0.951919	−	0.306351i	$-0.0991082\pi$
$659$	9.40591	+	12.9461i	0.366402	+	0.504309i	−0.585516	+	0.810661i	$0.699108\pi$
$660$	2.66517	−	2.55282i	0.103742	−	0.0993683i
$661$	−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
$663$	−31.0843	−	26.2994i	−1.20721	−	1.02139i
$664$	1.66056	−	7.81234i	0.0644424	−	0.303177i
$665$	1.62305	−	3.64543i	0.0629392	−	0.141364i
$666$	24.7471	−	1.52790i	0.958931	−	0.0592048i
$667$	0.101590	+	0.312662i	0.00393358	+	0.0121063i
$668$	20.4838	+	9.12000i	0.792544	+	0.352863i
$669$	10.8973	+	22.5758i	0.421313	+	0.872830i
$670$	−22.0544	+	4.68780i	−0.852034	+	0.181106i
$671$	1.05290	+	2.36486i	0.0406469	+	0.0912945i
$672$	−0.196960	+	1.09100i	−0.00759791	+	0.0420862i
$673$	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
$675$	−5.12145	+	1.59510i	−0.197125	+	0.0613955i
$676$	1.58694	+	2.74865i	0.0610360	+	0.105717i
$677$	21.2437	−	36.7951i	0.816461	−	1.41415i	−0.0918132	−	0.995776i	$-0.529266\pi$
$677$	21.2437	−	36.7951i	0.816461	−	1.41415i	0.908274	−	0.418376i	$-0.137400\pi$
$678$	−1.58347	+	0.0488356i	−0.0608129	+	0.00187552i
$679$	−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	$0.0485807\pi$
$683$			7.94632i			0.304058i	−0.988376	+	0.152029i	$0.951419\pi$
$684$	7.92196	+	5.04043i	0.302904	+	0.192726i
$685$	−0.359598	−	0.323784i	−0.0137395	−	0.0123711i
$686$	5.11300	−	7.03744i	0.195215	−	0.268691i
$687$	−50.5842	+	6.89904i	−1.92991	+	0.263215i
$688$	8.31206	−	4.79897i	0.316894	−	0.182959i
$689$	36.3956	+	3.82533i	1.38656	+	0.145734i
$690$	−0.0804952	+	0.276463i	−0.00306440	+	0.0105248i
$691$	−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
$693$	0.340181	+	2.02568i	0.0129224	+	0.0769490i
$694$	−4.36462	−	20.5339i	−0.165679	−	0.779457i
$695$	−44.1351	−	9.38120i	−1.67414	−	0.355849i
$696$	−1.62355	−	6.62664i	−0.0615405	−	0.251182i
$697$	1.29577	−	0.421021i	0.0490808	−	0.0159473i
$698$	−12.2497	+	3.98016i	−0.463657	+	0.150651i
$699$	−10.2957	−	42.0226i	−0.389419	−	1.58944i
$700$	0.646319	+	0.137379i	0.0244286	+	0.00519245i
$701$	−4.66103	−	21.9284i	−0.176045	−	0.828225i	−0.974185	−	0.225753i	$-0.927516\pi$
$701$	−4.66103	−	21.9284i	−0.176045	−	0.828225i	0.798140	−	0.602472i	$-0.205818\pi$
$702$	−11.9703	−	11.0461i	−0.451791	−	0.416909i
$703$	−19.2232	+	17.3086i	−0.725017	+	0.652808i
$704$	−0.111814	−	1.06384i	−0.00421413	−	0.0400948i
$705$	−0.700291	+	2.40517i	−0.0263745	+	0.0905838i
$706$	−22.6415	−	2.37971i	−0.852123	−	0.0895617i
$707$	−2.19406	+	1.26674i	−0.0825161	+	0.0476407i
$708$	−7.05768	+	0.962578i	−0.265244	+	0.0361759i
$709$	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
$711$	−5.09305	+	8.00466i	−0.191004	+	0.300198i
$712$			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
$717$	1.10547	−	0.0340937i	0.0412847	−	0.00127325i
$718$	−11.8211	+	20.4747i	−0.441158	+	0.764108i
$719$	16.2437	+	28.1349i	0.605787	+	1.04925i	0.991927	+	0.126814i	$0.0404750\pi$
$719$	16.2437	+	28.1349i	0.605787	+	1.04925i	−0.386140	+	0.922440i	$0.626192\pi$
$720$	2.08952	−	5.59848i	0.0778716	−	0.208643i
$721$	−5.92455	+	4.30443i	−0.220642	+	0.160306i
$722$	9.15365	−	0.962088i	0.340664	−	0.0358052i
$723$	5.19818	−	28.7936i	0.193322	−	1.07085i
$724$	−10.2327	−	22.9831i	−0.380296	−	0.854160i
$725$	−3.97751	+	0.845445i	−0.147721	+	0.0313990i
$726$	7.42069	+	15.3734i	0.275408	+	0.570560i
$727$	−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
$729$	−24.3898	−	11.5817i	−0.903327	−	0.428952i
$730$	9.12839	−	20.5027i	0.337857	−	0.758839i
$731$	14.9652	−	70.4059i	0.553509	−	2.60406i
$732$	3.19992	+	2.70735i	0.118272	+	0.100066i
$733$	−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
$735$	−16.4199	+	15.7277i	−0.605658	+	0.580126i
$736$	0.0490565	+	0.0675204i	0.00180825	+	0.00248884i
$737$	−1.26566	+	12.0419i	−0.0466211	+	0.443571i
$738$	0.525119	−	0.145954i	0.0193299	−	0.00537263i
$739$	−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
$741$	16.9468	+	1.25446i	0.622557	+	0.0460838i
$742$	−7.10685	−	2.30916i	−0.260901	−	0.0847718i
$743$	13.5099			0.495629			0.247814	−	0.968808i	$-0.420288\pi$
$743$	13.5099			0.495629			0.247814	+	0.968808i	$0.420288\pi$
$744$	3.29155	+	9.06453i	0.120674	+	0.332322i
$745$	−14.2717			−0.522875
$746$	22.0393	+	7.16101i	0.806917	+	0.262183i
$747$	−13.2362	−	19.9728i	−0.484289	−	0.730766i
$748$	−6.48999	−	4.71526i	−0.237298	−	0.172407i
$749$	−6.36135	−	3.67273i	−0.232439	−	0.134198i
$750$	−19.2646	−	7.87488i	−0.703444	−	0.287550i
$751$	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
$753$	21.7745	+	22.7328i	0.793506	+	0.828430i
$754$	−8.26216	−	9.17606i	−0.300890	−	0.334172i
$755$	15.7383	−	7.00714i	0.572775	−	0.255016i
$756$	1.92187	+	2.71441i	0.0698978	+	0.0987222i
$757$	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
$759$	0.127842	+	0.0869907i	0.00464037	+	0.00315756i
$760$	1.92652	+	5.92922i	0.0698822	+	0.215075i
$761$	−16.0222	−	7.13355i	−0.580805	−	0.258591i	0.0952365	−	0.995455i	$-0.469639\pi$
$761$	−16.0222	−	7.13355i	−0.580805	−	0.258591i	−0.676041	+	0.736864i	$0.736306\pi$
$762$	−23.1192	+	11.1596i	−0.837520	+	0.404269i
$763$	1.83568	−	0.390187i	0.0664562	−	0.0141257i
$764$	8.53516	+	19.1703i	0.308791	+	0.693556i
$765$	−20.7158	−	39.7388i	−0.748981	−	1.43676i
$766$	3.60609	−	0.379015i	0.130293	−	0.0136944i
$767$	−10.4292	+	7.57729i	−0.376578	+	0.273600i
$768$	−0.911853	−	1.47259i	−0.0329037	−	0.0531375i
$769$	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
$771$	0.117929	+	3.82379i	0.00424710	+	0.137710i
$772$	−10.9602	+	12.1725i	−0.394466	+	0.438099i
$773$	−7.83211	+	24.1048i	−0.281701	+	0.866988i	0.705667	+	0.708544i	$0.250648\pi$
$773$	−7.83211	+	24.1048i	−0.281701	+	0.866988i	−0.987368	+	0.158444i	$0.949352\pi$
$774$	7.19335	−	27.8808i	0.258560	−	1.00216i
$775$	5.46047	−	1.79433i	0.196146	−	0.0644541i
$776$		−	2.85163i		−	0.102368i
$777$	−8.62271	+	3.09867i	−0.309338	+	0.111164i
$778$	3.03831	+	2.73571i	0.108929	+	0.0980800i
$779$	−0.334223	+	0.460019i	−0.0119748	+	0.0164819i
$780$	−1.46148	−	10.7156i	−0.0523292	−	0.383681i
$781$	0.766674	−	0.442640i	0.0274338	−	0.0158389i
$782$	0.622470	+	0.0654242i	0.0222595	+	0.00233957i
$783$	−17.5993	−	10.4499i	−0.628947	−	0.373449i
$784$	0.688875	+	6.55421i	0.0246027	+	0.234079i
$785$	20.8740	−	18.7950i	0.745024	−	0.670822i
$786$	−13.9848	+	26.0450i	−0.498822	+	0.928995i
$787$	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
$789$	13.9199	−	3.41043i	0.495562	−	0.121414i
$790$	−5.99112	+	1.94663i	−0.213154	+	0.0692580i
$791$	0.556788	−	0.180911i	0.0197971	−	0.00643247i
$792$	−2.51261	−	1.99626i	−0.0892816	−	0.0709339i
$793$	7.42012	+	1.57720i	0.263496	+	0.0560078i
$794$	2.90314	+	13.6582i	0.103029	+	0.484712i
$795$	35.4863	+	19.0543i	1.25857	+	0.675788i
$796$	−3.63388	+	3.27196i	−0.128800	+	0.115972i
$797$	−5.10566	−	48.5771i	−0.180852	−	1.72069i	−0.589306	−	0.807910i	$-0.700599\pi$
$797$	−5.10566	−	48.5771i	−0.180852	−	1.72069i	0.408455	−	0.912779i	$-0.366068\pi$
$798$	−3.33151	−	0.970007i	−0.117934	−	0.0343379i
$799$	5.41536	+	0.569177i	0.191582	+	0.0201360i
$800$	−0.894017	+	0.516161i	−0.0316083	+	0.0182490i
$801$	36.2273	+	35.5595i	1.28003	+	1.25643i
$802$	−13.3492	+	18.3736i	−0.471377	+	0.648795i
$803$	−8.95667	−	8.06462i	−0.316074	−	0.284594i
$804$	6.63041	+	18.4505i	0.233836	+	0.650700i
$805$		−	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	−0.954798	−	0.297255i	$-0.903929\pi$
$809$	−15.9101	+	17.6699i	−0.559368	+	0.621241i	0.395430	+	0.918496i	$0.370596\pi$
$810$	−7.59503	−	16.2388i	−0.266862	−	0.570572i
$811$	−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
$813$	−11.3252	+	7.01273i	−0.397191	+	0.245947i
$814$	7.15233	−	5.19647i	0.250689	−	0.182136i
$815$	−23.0023	+	2.41764i	−0.805735	+	0.0846861i
$816$	−12.7827	−	2.30769i	−0.447484	−	0.0807853i
$817$	12.2184	+	27.4430i	0.427468	+	0.960108i
$818$	19.3375	−	4.11031i	0.676119	−	0.143714i
$819$	5.38835	+	2.68266i	0.188284	+	0.0937398i
$820$	0.330593	+	0.147189i	0.0115448	+	0.00514008i
$821$	−8.63540	−	26.5770i	−0.301378	−	0.927545i	−0.981004	−	0.193987i	$-0.937858\pi$
$821$	−8.63540	−	26.5770i	−0.301378	−	0.927545i	0.679626	−	0.733558i	$-0.262142\pi$
$822$	−0.236707	+	0.347866i	−0.00825610	+	0.0121332i
$823$	−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
$825$	−1.23539	+	1.46015i	−0.0430108	+	0.0508360i
$826$	2.40470	−	1.07064i	0.0836703	−	0.0372524i
$827$	36.4814	+	40.5167i	1.26858	+	1.40890i	0.870960	+	0.491354i	$0.163498\pi$
$827$	36.4814	+	40.5167i	1.26858	+	1.40890i	0.397622	+	0.917549i	$0.369835\pi$
$828$	0.247651	+	0.0368659i	0.00860645	+	0.00128118i
$829$	−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
$831$	6.13658	−	15.0121i	0.212876	−	0.520765i
$832$	−2.71470	−	1.56733i	−0.0941153	−	0.0543375i
$833$	39.9843	+	29.0503i	1.38538	+	1.00653i
$834$	−2.89637	+	39.1278i	−0.100293	+	1.35488i
$835$	42.4772	+	13.8017i	1.46998	+	0.477627i
$836$	3.34798			0.115792
$837$	26.3240	+	12.0020i	0.909890	+	0.414850i
$838$	2.01599			0.0696414
$839$	1.21504	+	0.394791i	0.0419479	+	0.0136297i	0.329916	−	0.944010i	$-0.392980\pi$
$839$	1.21504	+	0.394791i	0.0419479	+	0.0136297i	−0.287968	+	0.957640i	$0.592980\pi$
$840$	−0.163019	+	2.20227i	−0.00562470	+	0.0759854i
$841$	10.9087	+	7.92563i	0.376162	+	0.273298i
$842$	6.76455	+	3.90551i	0.233122	+	0.134593i
$843$	11.9653	−	29.2711i	0.412107	−	1.00815i
$844$	1.15677	−	11.0059i	0.0398177	−	0.378840i
$845$	3.71600	+	5.11464i	0.127834	+	0.175949i
$846$	2.15451	+	0.320725i	0.0740735	+	0.0110268i
$847$	−4.22113	−	4.68803i	−0.145040	−	0.161083i
$848$	10.6653	−	4.74850i	0.366248	−	0.163064i
$849$	18.2849	−	21.6116i	0.627536	−	0.741708i
$850$	−1.60961	+	7.57262i	−0.0552091	+	0.259739i
$851$	−0.280556	+	0.630140i	−0.00961735	+	0.0216009i
$852$	0.806408	−	1.18510i	0.0276271	−	0.0406009i
$853$	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
$855$	16.7428	+	8.33562i	0.572592	+	0.285072i
$856$	11.2252	−	2.38600i	0.383671	−	0.0815517i
$857$	2.03043	+	4.56042i	0.0693581	+	0.155781i	0.944898	−	0.327365i	$-0.106161\pi$
$857$	2.03043	+	4.56042i	0.0693581	+	0.155781i	−0.875540	+	0.483146i	$0.839494\pi$
$858$	−5.71541	−	1.03182i	−0.195121	−	0.0352256i
$859$	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
$861$	−0.171240	+	0.106035i	−0.00583584	+	0.00361365i
$862$	15.8750	+	27.4964i	0.540706	+	0.936530i
$863$	−27.4975	+	47.6270i	−0.936024	+	1.62124i	−0.163228	+	0.986588i	$0.552190\pi$
$863$	−27.4975	+	47.6270i	−0.936024	+	1.62124i	−0.772797	+	0.634653i	$0.781143\pi$
$864$	−5.06902	−	1.14240i	−0.172451	−	0.0388653i
$865$	−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
$870$	−4.59598	−	12.7893i	−0.155818	−	0.433597i
$871$	26.3686	+	23.7424i	0.893465	+	0.804480i
$872$	−1.72339	+	2.37205i	−0.0583615	+	0.0803277i
$873$	−6.10523	−	5.99269i	−0.206631	−	0.202822i
$874$	−0.226220	+	0.130608i	−0.00765200	+	0.00441789i
$875$	7.64882	+	0.803924i	0.258577	+	0.0271776i
$876$	−18.7372	−	5.45553i	−0.633070	−	0.184325i
$877$	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
$879$	−17.6749	−	9.49048i	−0.596158	−	0.320106i
$880$	−0.443004	−	2.08417i	−0.0149337	−	0.0702573i
$881$	12.2657	+	2.60715i	0.413241	+	0.0878372i	0.409841	−	0.912157i	$-0.365584\pi$
$881$	12.2657	+	2.60715i	0.413241	+	0.0878372i	0.00340052	+	0.999994i	$0.498918\pi$
$882$	15.4800	+	12.2988i	0.521238	+	0.414122i
$883$	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
$885$	−13.7808	+	3.37634i	−0.463236	+	0.113495i
$886$	23.7743	+	5.05338i	0.798713	+	0.169772i
$887$	−4.63228	−	21.7932i	−0.155537	−	0.731744i	−0.984913	−	0.173052i	$-0.944637\pi$
$887$	−4.63228	−	21.7932i	−0.155537	−	0.731744i	0.829376	−	0.558691i	$-0.188696\pi$
$888$	6.77192	−	12.6119i	0.227251	−	0.423226i
$889$	7.05008	−	6.34792i	0.236452	−	0.212902i
$890$	3.52314	+	33.5205i	0.118096	+	1.12361i
$891$	−9.55414	+	1.18427i	−0.320076	+	0.0396745i
$892$	14.3939	+	1.51286i	0.481942	+	0.0506542i
$893$	−1.96807	+	1.13626i	−0.0658588	+	0.0380236i
$894$	1.67703	+	12.2961i	0.0560882	+	0.411242i
$895$	15.9103	−	21.8987i	0.531823	−	0.731992i
$896$	0.475665	+	0.428291i	0.0158908	+	0.0143082i
$897$	0.426437	−	0.153245i	0.0142383	−	0.00511671i
$898$			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
$903$	0.328010	+	10.6356i	0.0109155	+	0.353929i
$904$	−0.457326	+	0.792112i	−0.0152104	+	0.0263453i
$905$	−25.0563	−	43.3987i	−0.832899	−	1.44262i
$906$	−7.88650	−	12.7363i	−0.262011	−	0.423134i
$907$	−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
$909$	−5.48904	−	10.5296i	−0.182060	−	0.349243i
$910$	1.62555	+	3.65105i	0.0538865	+	0.121031i
$911$	38.1409	−	8.10709i	1.26366	−	0.268600i	0.473116	−	0.881000i	$-0.343129\pi$
$911$	38.1409	−	8.10709i	1.26366	−	0.268600i	0.790548	+	0.612400i	$0.209796\pi$
$912$	4.88205	−	2.35655i	0.161661	−	0.0780333i
$913$	−7.80489	−	3.47496i	−0.258304	−	0.115004i
$914$	−3.90975	−	12.0330i	−0.129323	−	0.398015i
$915$	6.90270	+	4.69698i	0.228196	+	0.155277i
$916$	−11.9886	+	26.9269i	−0.396116	+	0.889691i
$917$	2.27134	−	10.6858i	0.0750061	−	0.352876i
$918$	−31.8035	+	22.5177i	−1.04967	+	0.743194i
$919$	−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
$921$	30.5341	+	31.8779i	1.00613	+	1.05041i
$922$	16.3343	+	22.4822i	0.537942	+	0.740413i
$923$	0.271173	−	2.58004i	0.00892576	−	0.0849229i
$924$	1.09773	+	0.448724i	0.0361126	+	0.0147619i
$925$	−7.38882	−	4.26594i	−0.242943	−	0.140263i
$926$	−25.8014	−	18.7458i	−0.847885	−	0.616025i
$927$	−18.9609	−	28.6109i	−0.622756	−	0.939707i
$928$	−3.74626	−	1.21723i	−0.122977	−	0.0399576i
$929$	8.33903			0.273595			0.136797	−	0.990599i	$-0.456319\pi$
$929$	8.33903			0.273595			0.136797	+	0.990599i	$0.456319\pi$
$930$	8.40786	+	17.2714i	0.275705	+	0.566352i
$931$	−20.6266			−0.676011
$932$	−23.7568	−	7.71904i	−0.778179	−	0.252846i
$933$	28.2418	+	2.09056i	0.924595	+	0.0684417i
$934$	8.21209	+	5.96643i	0.268708	+	0.195228i
$935$	−13.8384	−	7.98960i	−0.452564	−	0.261288i
$936$	−9.06053	+	2.51832i	−0.296153	+	0.0823140i
$937$	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
$939$	6.97429	−	6.68027i	0.227597	−	0.218003i
$940$	0.967755	+	1.07480i	0.0315647	+	0.0350561i
$941$	−8.05457	+	3.58613i	−0.262572	+	0.116904i	−0.533800	−	0.845611i	$-0.679237\pi$
$941$	−8.05457	+	3.58613i	−0.262572	+	0.116904i	0.271229	+	0.962515i	$0.412570\pi$
$942$	−18.6460	−	15.7758i	−0.607521	−	0.514004i
$943$	−0.00315247	+	0.0148312i	−0.000102659	+	0.000482971i
$944$	−1.67270	+	3.75694i	−0.0544416	+	0.122278i
$945$	4.37238	+	4.97707i	0.142234	+	0.161904i
$946$	−3.17264	−	9.76438i	−0.103151	−	0.317467i
$947$	3.91956	+	1.74510i	0.127369	+	0.0567082i	0.469431	−	0.882969i	$-0.344459\pi$
$947$	3.91956	+	1.74510i	0.127369	+	0.0567082i	−0.342063	+	0.939677i	$0.611126\pi$
$948$	2.38116	+	4.93302i	0.0773364	+	0.160217i
$949$	−34.5469	+	7.34316i	−1.12144	+	0.238369i
$950$	−1.31417	−	2.95167i	−0.0426373	−	0.0957649i
$951$	−6.61003	+	36.6141i	−0.214345	+	1.18729i
$952$	4.77385	−	0.501751i	0.154721	−	0.0162619i
$953$	29.3911	−	21.3539i	0.952070	−	0.691719i	0.000774154	−	1.00000i	$-0.499754\pi$
$953$	29.3911	−	21.3539i	0.952070	−	0.691719i	0.951295	+	0.308281i	$0.0997536\pi$
$954$	12.2467	−	32.8130i	0.396503	−	1.06236i
$955$	20.8995	+	36.1990i	0.676293	+	1.17137i
$956$	0.319274	−	0.552999i	0.0103261	−	0.0178853i
$957$	−7.29467	+	0.224974i	−0.235803	+	0.00727238i
$958$	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
$963$	18.4815	−	29.0470i	0.595556	−	0.936025i
$964$	−12.5538	−	11.3035i	−0.404329	−	0.364060i
$965$	−19.1776	+	26.3957i	−0.617349	+	0.849708i
$966$	−0.0916777	+	0.0125037i	−0.00294968	+	0.000402299i
$967$	−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
$969$	11.3651	−	39.0337i	0.365100	−	1.25394i
$970$	−0.593740	−	5.64906i	−0.0190638	−	0.181380i
$971$	−23.9294	+	21.5462i	−0.767932	+	0.691449i	−0.956862	−	0.290541i	$-0.906165\pi$
$971$	−23.9294	+	21.5462i	−0.767932	+	0.691449i	0.188930	+	0.981990i	$0.439498\pi$
$972$	−13.0984	+	8.45182i	−0.420130	+	0.271092i
$973$	−3.01452	−	14.1822i	−0.0966410	−	0.454660i
$974$	24.2261	+	5.14941i	0.776254	+	0.164998i
$975$	1.33377	+	5.44388i	0.0427148	+	0.174344i
$976$	2.30156	−	0.747821i	0.0736710	−	0.0239372i
$977$	−34.0853	+	11.0750i	−1.09048	+	0.354320i	−0.798434	−	0.602083i	$-0.794338\pi$
$977$	−34.0853	+	11.0750i	−1.09048	+	0.354320i	−0.292051	+	0.956403i	$0.594338\pi$
$978$	4.78589	+	19.5340i	0.153036	+	0.624628i
$979$	17.7048	+	3.76328i	0.565849	+	0.120275i
$980$	2.72931	+	12.8404i	0.0871846	+	0.410171i
$981$	1.45676	+	8.67457i	0.0465107	+	0.276958i
$982$	−4.01804	+	3.61786i	−0.128221	+	0.115450i
$983$	1.59535	+	15.1787i	0.0508836	+	0.484125i	0.990055	+	0.140678i	$0.0449281\pi$
$983$	1.59535	+	15.1787i	0.0508836	+	0.484125i	−0.939172	+	0.343448i	$0.888405\pi$
$984$	0.0879669	−	0.302124i	0.00280428	−	0.00963137i
$985$	33.4443	+	3.51514i	1.06562	+	0.112002i
$986$	−25.5828	+	14.7703i	−0.814723	+	0.470381i
$987$	−0.797576	+	0.108779i	−0.0253871	+	0.00346248i
$988$	5.76677	−	7.93728i	0.183465	−	0.252518i
$989$	0.595291	+	0.536002i	0.0189291	+	0.0170439i
$990$	−5.39309	−	3.43142i	−0.171404	−	0.109058i
$991$			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
$996$	−13.8271	+	0.426439i	−0.438128	+	0.0135122i
$997$	−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
$999$	−12.7703	−	41.0022i	−0.404036	−	1.29725i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.127863 + 1.72732i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.72504 + 0.995952i) q^{5} +(0.655377 - 1.60327i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.96730 - 0.441720i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.127863 + 1.72732i) q^{3} +(0.809017 + 0.587785i) q^{4} +(1.72504 + 0.995952i) q^{5} +(0.655377 - 1.60327i) q^{6} +(-0.0669056 + 0.636564i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-2.96730 - 0.441720i) q^{9} +(-1.33284 - 1.48027i) q^{10} +(-0.977216 + 0.435084i) q^{11} +(-1.11874 + 1.32228i) q^{12} +(-0.651734 + 3.06617i) q^{13} +(0.260340 - 0.584733i) q^{14} +(-1.94090 + 2.85236i) q^{15} +(0.309017 + 0.951057i) q^{16} +(6.85104 + 3.05028i) q^{17} +(2.68557 + 1.33705i) q^{18} +(-3.06145 + 0.650731i) q^{19} +(0.810180 + 1.81969i) q^{20} +(-1.09100 - 0.196960i) q^{21} +(1.06384 - 0.111814i) q^{22} +(-0.0675204 + 0.0490565i) q^{23} +(1.47259 - 0.911853i) q^{24} +(-0.516161 - 0.894017i) q^{25} +(1.56733 - 2.71470i) q^{26} +(1.14240 - 5.06902i) 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} +(-0.626583 - 1.74360i) q^{33} +(-5.57314 - 5.01808i) q^{34} +(-0.749401 + 1.03146i) q^{35} +(-2.14096 - 2.10150i) q^{36} +(7.15748 - 4.13237i) q^{37} +(3.11270 + 0.327158i) q^{38} +(-5.21293 - 1.51780i) q^{39} +(-0.208211 - 1.98099i) q^{40} +(0.135011 - 0.121564i) q^{41} +(0.976737 + 0.524457i) q^{42} +(-1.99552 - 9.38821i) q^{43} +(-1.04632 - 0.222402i) q^{44} +(-4.67878 - 3.71727i) q^{45} +(0.0793750 - 0.0257905i) q^{46} +(0.690546 - 0.224372i) q^{47} +(-1.68230 + 0.412168i) q^{48} +(6.44630 + 1.37020i) q^{49} +(0.214632 + 1.00976i) q^{50} +(-6.14482 + 11.4440i) q^{51} +(-2.32951 + 2.09750i) q^{52} +(-1.22033 - 11.6107i) q^{53} +(-2.65290 + 4.46790i) q^{54} +(-2.11906 - 0.222722i) q^{55} +(0.554317 - 0.320035i) q^{56} +(-0.732580 - 5.37132i) q^{57} +(-2.31532 + 3.18676i) q^{58} +(3.05617 + 2.75179i) q^{59} +(-3.24679 + 1.16677i) 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} +(0.0571138 + 1.85189i) q^{66} +(5.65968 - 9.80285i) q^{67} +(3.74970 + 6.49467i) q^{68} +(-0.0761031 - 0.122902i) q^{69} +(1.03146 - 0.749401i) q^{70} +(-0.823066 + 0.0865077i) q^{71} +(1.38678 + 2.66023i) q^{72} +(4.58275 + 10.2930i) q^{73} +(-8.08414 + 1.71834i) q^{74} +(1.61025 - 0.777266i) q^{75} +(-2.85926 - 1.27302i) q^{76} +(-0.211578 - 0.651170i) q^{77} +(4.48877 + 3.05440i) q^{78} +(1.28631 - 2.88911i) q^{79} +(-0.414140 + 1.94838i) q^{80} +(8.60977 + 2.62143i) q^{81} +(-0.165968 + 0.0738938i) q^{82} +(5.34426 + 5.93540i) q^{83} +(-0.766865 - 0.800617i) q^{84} +(8.78038 + 12.0852i) q^{85} +(-1.00326 + 9.54537i) q^{86} +(6.31537 + 2.58156i) q^{87} +(0.926384 + 0.534848i) q^{88} +(-13.6894 - 9.94595i) q^{89} +(3.30108 + 4.98116i) q^{90} +(-1.90821 - 0.620014i) q^{91} -0.0834598 q^{92} +(-9.26808 - 2.66508i) q^{93} -0.726083 q^{94} +(-5.92922 - 1.92652i) q^{95} +(1.72732 + 0.127863i) q^{96} +(2.30702 + 1.67615i) q^{97} +(-5.70738 - 3.29516i) q^{98} +(3.09188 - 0.859371i) 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

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