LMFDB - Embedded newform 409.2.o.a.41.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(2,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(204)) chi = DirichletCharacter(H, H._module([41])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.o (of order $204$, degree $64$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$0$
Dimension:	$2176$
Relative dimension:	$34$ over $\Q(\zeta_{204})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{204}]$

Embedding invariants

Embedding label			41.13
Character	$\chi$	$=$	409.41
Dual form			409.2.o.a.10.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.728280 + 1.02881i) q^{2} +(-0.204754 + 0.381301i) q^{3} +(0.136650 + 0.387785i) q^{4} +(1.32548 - 1.20833i) q^{5} +(-0.243168 - 0.488347i) q^{6} +(1.05514 + 0.282723i) q^{7} +(-2.92323 - 0.831729i) q^{8} +(1.55363 + 2.34466i) q^{9} +(0.277826 + 2.24367i) q^{10} +(3.39914 - 1.13928i) q^{11} +(-0.175842 - 0.0272958i) q^{12} +(0.507747 - 1.51491i) q^{13} +(-1.05930 + 0.879633i) q^{14} +(0.189341 + 0.752815i) q^{15} +(2.34397 - 1.88618i) q^{16} +(2.45429 + 2.53107i) q^{17} +(-3.54369 - 0.109180i) q^{18} +(-3.29642 + 3.96972i) q^{19} +(0.649699 + 0.348881i) q^{20} +(-0.323846 + 0.344435i) q^{21} +(-1.30343 + 4.32679i) q^{22} +(2.49776 - 2.42199i) q^{23} +(0.915681 - 0.944327i) q^{24} +(-0.164519 + 1.77544i) q^{25} +(1.18877 + 1.62565i) q^{26} +(-2.50499 + 0.232121i) q^{27} +(0.0345488 + 0.447800i) q^{28} +(2.51910 - 1.02079i) q^{29} +(-0.912397 - 0.353465i) q^{30} +(1.65012 - 1.65012i) q^{31} +(-0.140736 - 2.28179i) q^{32} +(-0.261581 + 1.52937i) q^{33} +(-4.39141 + 0.681673i) q^{34} +(1.74018 - 0.900210i) q^{35} +(-0.696921 + 0.922872i) q^{36} +(-8.42337 + 6.15967i) q^{37} +(-1.68338 - 6.28246i) q^{38} +(0.473673 + 0.503788i) q^{39} +(-4.87967 + 2.42979i) q^{40} +(-0.868841 + 7.01658i) q^{41} +(-0.118508 - 0.584021i) q^{42} +(-5.83662 - 7.02877i) q^{43} +(0.906288 + 1.16245i) q^{44} +(4.89242 + 1.23049i) q^{45} +(0.672702 + 4.33362i) q^{46} +(1.30323 + 12.0425i) q^{47} +(0.239266 + 1.27996i) q^{48} +(-5.02880 - 2.90338i) q^{49} +(-1.70678 - 1.46228i) q^{50} +(-1.46763 + 0.417576i) q^{51} +(0.656843 - 0.0101162i) q^{52} +(-0.663532 - 1.14927i) q^{53} +(1.58552 - 2.74621i) q^{54} +(3.12886 - 5.61737i) q^{55} +(-2.84925 - 1.70405i) q^{56} +(-0.838703 - 2.06974i) q^{57} +(-0.784409 + 3.33510i) q^{58} +(-3.72508 - 5.43795i) q^{59} +(-0.266057 + 0.176296i) q^{60} +(13.7776 - 3.24046i) q^{61} +(0.495913 + 2.89942i) q^{62} +(0.976400 + 2.91318i) q^{63} +(7.56602 + 4.68468i) q^{64} +(-1.15751 - 2.62150i) q^{65} +(-1.38292 - 1.38292i) q^{66} +(5.72403 - 6.47653i) q^{67} +(-0.646133 + 1.29761i) q^{68} +(0.412080 + 1.44831i) q^{69} +(-0.341191 + 2.44592i) q^{70} +(6.31798 - 2.00989i) q^{71} +(-2.59148 - 8.14617i) q^{72} +(0.0531733 - 0.689199i) q^{73} +(-0.202557 - 13.1520i) q^{74} +(-0.643292 - 0.426261i) q^{75} +(-1.98985 - 0.735837i) q^{76} +(3.90866 - 0.241078i) q^{77} +(-0.863269 + 0.120421i) q^{78} +(-3.97834 - 0.183930i) q^{79} +(0.827739 - 5.33238i) q^{80} +(-2.86464 + 6.76797i) q^{81} +(-6.58598 - 6.00391i) q^{82} +(4.63084 - 16.2757i) q^{83} +(-0.177820 - 0.0785153i) q^{84} +(6.31148 + 0.389279i) q^{85} +(11.4820 - 0.885860i) q^{86} +(-0.126567 + 1.16955i) q^{87} +(-10.8840 + 0.503199i) q^{88} +(10.2709 - 1.91997i) q^{89} +(-4.82900 + 4.13723i) q^{90} +(0.964041 - 1.45488i) q^{91} +(1.28053 + 0.637630i) q^{92} +(0.291324 + 0.967063i) q^{93} +(-13.3385 - 7.42950i) q^{94} +(0.427419 + 9.24493i) q^{95} +(0.898866 + 0.413544i) q^{96} +(-8.24837 - 15.9447i) q^{97} +(6.64940 - 3.05921i) q^{98} +(7.95223 + 6.19982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2176 q - 62 q^{2} - 56 q^{3} - 196 q^{4} - 68 q^{5} - 76 q^{6} - 64 q^{7} - 68 q^{8} - 126 q^{9} - 50 q^{10} - 54 q^{11} - 32 q^{12} - 68 q^{13} - 56 q^{14} - 44 q^{15} + 48 q^{16} - 64 q^{17} - 26 q^{18}+ \cdots - 14 q^{99}+O(q^{100}) $ 2176 * q - 62 * q^2 - 56 * q^3 - 196 * q^4 - 68 * q^5 - 76 * q^6 - 64 * q^7 - 68 * q^8 - 126 * q^9 - 50 * q^10 - 54 * q^11 - 32 * q^12 - 68 * q^13 - 56 * q^14 - 44 * q^15 + 48 * q^16 - 64 * q^17 - 26 * q^18 - 70 * q^19 - 62 * q^20 - 36 * q^21 - 64 * q^22 - 62 * q^23 - 24 * q^24 - 232 * q^25 - 56 * q^26 - 68 * q^27 - 90 * q^28 - 90 * q^29 - 44 * q^30 - 70 * q^31 + 118 * q^32 - 94 * q^33 - 62 * q^34 - 72 * q^35 - 296 * q^36 - 76 * q^37 - 236 * q^38 + 162 * q^39 - 68 * q^40 + 336 * q^41 + 42 * q^42 - 60 * q^43 - 66 * q^44 - 68 * q^45 - 206 * q^46 - 94 * q^47 - 68 * q^48 - 162 * q^49 - 44 * q^50 - 68 * q^51 - 122 * q^52 - 218 * q^53 + 152 * q^54 + 190 * q^55 - 138 * q^56 - 166 * q^57 - 74 * q^59 + 16 * q^60 - 28 * q^61 - 60 * q^62 - 68 * q^63 + 504 * q^64 - 24 * q^65 + 34 * q^66 - 40 * q^67 + 44 * q^68 + 92 * q^69 - 224 * q^70 - 154 * q^71 - 26 * q^72 - 120 * q^73 - 80 * q^74 + 112 * q^75 - 50 * q^76 + 74 * q^77 + 300 * q^78 - 82 * q^79 - 100 * q^80 + 408 * q^81 - 56 * q^82 - 84 * q^83 + 876 * q^84 - 180 * q^85 + 196 * q^86 - 156 * q^87 - 380 * q^88 - 128 * q^89 + 58 * q^90 - 126 * q^91 + 272 * q^92 + 56 * q^93 - 80 * q^94 - 90 * q^95 - 264 * q^96 - 68 * q^97 - 62 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{151}{204}\right)$

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 $

$2$	−0.728280	+	1.02881i	−0.514972	+	0.727479i	−0.988151	−	0.153487i	$-0.950950\pi$
$2$	−0.728280	+	1.02881i	−0.514972	+	0.727479i	0.473179	+	0.880966i	$0.343106\pi$
$3$	−0.204754	+	0.381301i	−0.118215	+	0.220144i	−0.933216	−	0.359315i	$-0.883010\pi$
$3$	−0.204754	+	0.381301i	−0.118215	+	0.220144i	0.815002	+	0.579459i	$0.196736\pi$
$4$	0.136650	+	0.387785i	0.0683251	+	0.193892i
$5$	1.32548	−	1.20833i	0.592771	−	0.540382i	−0.320755	−	0.947162i	$-0.603937\pi$
$5$	1.32548	−	1.20833i	0.592771	−	0.540382i	0.913526	+	0.406780i	$0.133348\pi$
$6$	−0.243168	−	0.488347i	−0.0992728	−	0.199367i
$7$	1.05514	+	0.282723i	0.398804	+	0.106859i	0.452646	−	0.891690i	$-0.350480\pi$
$7$	1.05514	+	0.282723i	0.398804	+	0.106859i	−0.0538423	+	0.998549i	$0.517147\pi$
$8$	−2.92323	−	0.831729i	−1.03352	−	0.294061i
$9$	1.55363	+	2.34466i	0.517876	+	0.781554i
$10$	0.277826	+	2.24367i	0.0878563	+	0.709510i
$11$	3.39914	−	1.13928i	1.02488	−	0.343505i	0.245059	−	0.969508i	$-0.421193\pi$
$11$	3.39914	−	1.13928i	1.02488	−	0.343505i	0.779821	+	0.626003i	$0.215310\pi$
$12$	−0.175842	−	0.0272958i	−0.0507613	−	0.00787961i
$13$	0.507747	−	1.51491i	0.140824	−	0.420160i	−0.854183	−	0.519973i	$-0.825942\pi$
$13$	0.507747	−	1.51491i	0.140824	−	0.420160i	0.995006	+	0.0998126i	$0.0318243\pi$
$14$	−1.05930	+	0.879633i	−0.283110	+	0.235092i
$15$	0.189341	+	0.752815i	0.0488875	+	0.194376i
$16$	2.34397	−	1.88618i	0.585992	−	0.471546i
$17$	2.45429	+	2.53107i	0.595254	+	0.613876i	0.946616	−	0.322364i	$-0.104478\pi$
$17$	2.45429	+	2.53107i	0.595254	+	0.613876i	−0.351362	+	0.936240i	$0.614281\pi$
$18$	−3.54369	−	0.109180i	−0.835256	−	0.0257339i
$19$	−3.29642	+	3.96972i	−0.756250	+	0.910717i	−0.998224	−	0.0595657i	$-0.981028\pi$
$19$	−3.29642	+	3.96972i	−0.756250	+	0.910717i	0.241975	+	0.970283i	$0.422205\pi$
$20$	0.649699	+	0.348881i	0.145277	+	0.0780121i
$21$	−0.323846	+	0.344435i	−0.0706689	+	0.0751619i
$22$	−1.30343	+	4.32679i	−0.277891	+	0.922474i
$23$	2.49776	−	2.42199i	0.520820	−	0.505021i	−0.388313	−	0.921528i	$-0.626942\pi$
$23$	2.49776	−	2.42199i	0.520820	−	0.505021i	0.909133	+	0.416507i	$0.136746\pi$
$24$	0.915681	−	0.944327i	0.186913	−	0.192760i
$25$	−0.164519	+	1.77544i	−0.0329038	+	0.355089i
$26$	1.18877	+	1.62565i	0.233138	+	0.318817i
$27$	−2.50499	+	0.232121i	−0.482085	+	0.0446718i
$28$	0.0345488	+	0.447800i	0.00652911	+	0.0846262i
$29$	2.51910	−	1.02079i	0.467786	−	0.189557i	−0.129509	−	0.991578i	$-0.541340\pi$
$29$	2.51910	−	1.02079i	0.467786	−	0.189557i	0.597295	+	0.802022i	$0.296242\pi$
$30$	−0.912397	−	0.353465i	−0.166580	−	0.0645335i
$31$	1.65012	−	1.65012i	0.296371	−	0.296371i	−0.543220	−	0.839591i	$-0.682795\pi$
$31$	1.65012	−	1.65012i	0.296371	−	0.296371i	0.839591	+	0.543220i	$0.182795\pi$
$32$	−0.140736	−	2.28179i	−0.0248789	−	0.403368i
$33$	−0.261581	+	1.52937i	−0.0455354	+	0.266229i
$34$	−4.39141	+	0.681673i	−0.753120	+	0.116906i
$35$	1.74018	−	0.900210i	0.294144	−	0.152163i
$36$	−0.696921	+	0.922872i	−0.116153	+	0.153812i
$37$	−8.42337	+	6.15967i	−1.38479	+	1.01264i	−0.388980	+	0.921246i	$0.627172\pi$
$37$	−8.42337	+	6.15967i	−1.38479	+	1.01264i	−0.995815	+	0.0913966i	$0.970867\pi$
$38$	−1.68338	−	6.28246i	−0.273080	−	1.01915i
$39$	0.473673	+	0.503788i	0.0758483	+	0.0806706i
$40$	−4.87967	+	2.42979i	−0.771543	+	0.384183i
$41$	−0.868841	+	7.01658i	−0.135690	+	1.09581i	0.759621	+	0.650366i	$0.225384\pi$
$41$	−0.868841	+	7.01658i	−0.135690	+	1.09581i	−0.895312	+	0.445441i	$0.853047\pi$
$42$	−0.118508	−	0.584021i	−0.0182862	−	0.0901164i
$43$	−5.83662	−	7.02877i	−0.890076	−	1.07188i	−0.996984	−	0.0776084i	$-0.975272\pi$
$43$	−5.83662	−	7.02877i	−0.890076	−	1.07188i	0.106908	−	0.994269i	$-0.465905\pi$
$44$	0.906288	+	1.16245i	0.136628	+	0.175247i
$45$	4.89242	+	1.23049i	0.729320	+	0.183431i
$46$	0.672702	+	4.33362i	0.0991844	+	0.638957i
$47$	1.30323	+	12.0425i	0.190095	+	1.75657i	0.560921	+	0.827870i	$0.310447\pi$
$47$	1.30323	+	12.0425i	0.190095	+	1.75657i	−0.370826	+	0.928702i	$0.620925\pi$
$48$	0.239266	+	1.27996i	0.0345351	+	0.184746i
$49$	−5.02880	−	2.90338i	−0.718400	−	0.414768i
$50$	−1.70678	−	1.46228i	−0.241375	−	0.206798i
$51$	−1.46763	+	0.417576i	−0.205509	+	0.0584723i
$52$	0.656843	−	0.0101162i	0.0910877	−	0.00140286i
$53$	−0.663532	−	1.14927i	−0.0911431	−	0.157864i	0.816849	−	0.576851i	$-0.195719\pi$
$53$	−0.663532	−	1.14927i	−0.0911431	−	0.157864i	−0.907992	+	0.418987i	$0.862385\pi$
$54$	1.58552	−	2.74621i	0.215762	−	0.373712i
$55$	3.12886	−	5.61737i	0.421895	−	0.757447i
$56$	−2.84925	−	1.70405i	−0.380747	−	0.227713i
$57$	−0.838703	−	2.06974i	−0.111089	−	0.274144i
$58$	−0.784409	+	3.33510i	−0.102998	+	0.437920i
$59$	−3.72508	−	5.43795i	−0.484965	−	0.707961i	0.502715	−	0.864452i	$-0.332335\pi$
$59$	−3.72508	−	5.43795i	−0.484965	−	0.707961i	−0.987679	+	0.156491i	$0.949982\pi$
$60$	−0.266057	+	0.176296i	−0.0343478	+	0.0227597i
$61$	13.7776	−	3.24046i	1.76404	−	0.414899i	0.785154	−	0.619301i	$-0.212584\pi$
$61$	13.7776	−	3.24046i	1.76404	−	0.414899i	0.978887	+	0.204403i	$0.0655252\pi$
$62$	0.495913	+	2.89942i	0.0629810	+	0.368226i
$63$	0.976400	+	2.91318i	0.123015	+	0.367026i
$64$	7.56602	+	4.68468i	0.945752	+	0.585585i
$65$	−1.15751	−	2.62150i	−0.143571	−	0.325157i
$66$	−1.38292	−	1.38292i	−0.170226	−	0.170226i
$67$	5.72403	−	6.47653i	0.699301	−	0.791234i	−0.286692	−	0.958023i	$-0.592555\pi$
$67$	5.72403	−	6.47653i	0.699301	−	0.791234i	0.985993	+	0.166789i	$0.0533398\pi$
$68$	−0.646133	+	1.29761i	−0.0783551	+	0.157358i
$69$	0.412080	+	1.44831i	0.0496086	+	0.174356i
$70$	−0.341191	+	2.44592i	−0.0407801	+	0.292343i
$71$	6.31798	−	2.00989i	0.749806	−	0.238530i	0.0961964	−	0.995362i	$-0.469332\pi$
$71$	6.31798	−	2.00989i	0.749806	−	0.238530i	0.653610	+	0.756832i	$0.273254\pi$
$72$	−2.59148	−	8.14617i	−0.305409	−	0.960036i
$73$	0.0531733	−	0.689199i	0.00622347	−	0.0806647i	−0.993109	−	0.117193i	$-0.962610\pi$
$73$	0.0531733	−	0.689199i	0.00622347	−	0.0806647i	0.999333	+	0.0365285i	$0.0116300\pi$
$74$	−0.202557	−	13.1520i	−0.0235467	−	1.52889i
$75$	−0.643292	−	0.426261i	−0.0742810	−	0.0492203i
$76$	−1.98985	−	0.735837i	−0.228252	−	0.0844063i
$77$	3.90866	−	0.241078i	0.445433	−	0.0274733i
$78$	−0.863269	+	0.120421i	−0.0977459	+	0.0136350i
$79$	−3.97834	−	0.183930i	−0.447598	−	0.0206937i	−0.178789	−	0.983887i	$-0.557218\pi$
$79$	−3.97834	−	0.183930i	−0.447598	−	0.0206937i	−0.268808	+	0.963194i	$0.586630\pi$
$80$	0.827739	−	5.33238i	0.0925440	−	0.596178i
$81$	−2.86464	+	6.76797i	−0.318293	+	0.751997i
$82$	−6.58598	−	6.00391i	−0.727299	−	0.663021i
$83$	4.63084	−	16.2757i	0.508301	−	1.78649i	−0.102527	−	0.994730i	$-0.532693\pi$
$83$	4.63084	−	16.2757i	0.508301	−	1.78649i	0.610828	−	0.791763i	$-0.290836\pi$
$84$	−0.177820	−	0.0785153i	−0.0194018	−	0.00856672i
$85$	6.31148	+	0.389279i	0.684576	+	0.0422232i
$86$	11.4820	−	0.885860i	1.23813	−	0.0955248i
$87$	−0.126567	+	1.16955i	−0.0135695	+	0.125389i
$88$	−10.8840	+	0.503199i	−1.16024	+	0.0536412i
$89$	10.2709	−	1.91997i	1.08872	−	0.203516i	0.391358	−	0.920239i	$-0.372006\pi$
$89$	10.2709	−	1.91997i	1.08872	−	0.203516i	0.697359	+	0.716722i	$0.254359\pi$
$90$	−4.82900	+	4.13723i	−0.509021	+	0.436103i
$91$	0.964041	−	1.45488i	0.101059	−	0.152513i
$92$	1.28053	+	0.637630i	0.133505	+	0.0664775i
$93$	0.291324	+	0.967063i	0.0302088	+	0.100280i
$94$	−13.3385	−	7.42950i	−1.37576	−	0.766295i
$95$	0.427419	+	9.24493i	0.0438523	+	0.948510i
$96$	0.898866	+	0.413544i	0.0917401	+	0.0422071i
$97$	−8.24837	−	15.9447i	−0.837495	−	1.61894i	−0.784318	−	0.620359i	$-0.786987\pi$
$97$	−8.24837	−	15.9447i	−0.837495	−	1.61894i	−0.0531766	−	0.998585i	$-0.516935\pi$
$98$	6.64940	−	3.05921i	0.671691	−	0.309027i
$99$	7.95223	+	6.19982i	0.799229	+	0.623106i
$100$	−0.710972	+	0.178817i	−0.0710972	+	0.0178817i
$101$	−2.26268	−	5.34580i	−0.225145	−	0.531927i	0.769091	−	0.639140i	$-0.220709\pi$
$101$	−2.26268	−	5.34580i	−0.225145	−	0.531927i	−0.994236	+	0.107213i	$0.965807\pi$
$102$	0.639236	−	1.81402i	0.0632938	−	0.179615i
$103$	−4.60684	−	5.05346i	−0.453925	−	0.497932i	0.468846	−	0.883280i	$-0.344670\pi$
$103$	−4.60684	−	5.05346i	−0.453925	−	0.497932i	−0.922771	+	0.385348i	$0.874082\pi$
$104$	−2.74425	+	4.00612i	−0.269096	+	0.392832i
$105$	−0.0130579	+	0.847853i	−0.00127432	+	0.0827420i
$106$	1.66562	+	0.154342i	0.161779	+	0.0149910i
$107$	−4.16995	−	6.97235i	−0.403124	−	0.674042i	0.587718	−	0.809066i	$-0.300026\pi$
$107$	−4.16995	−	6.97235i	−0.403124	−	0.674042i	−0.990842	+	0.135023i	$0.956889\pi$
$108$	−0.432320	−	0.939677i	−0.0416000	−	0.0904205i
$109$	−2.11529	+	8.41037i	−0.202608	+	0.805567i	0.780893	+	0.624665i	$0.214765\pi$
$109$	−2.11529	+	8.41037i	−0.202608	+	0.805567i	−0.983501	+	0.180902i	$0.942098\pi$
$110$	3.50053	+	7.31002i	0.333762	+	0.696983i
$111$	−0.623964	−	4.47305i	−0.0592241	−	0.424563i
$112$	3.00647	−	1.32749i	0.284085	−	0.125436i
$113$	4.72620	−	1.74772i	0.444604	−	0.164412i	−0.114655	−	0.993405i	$-0.536576\pi$
$113$	4.72620	−	1.74772i	0.444604	−	0.164412i	0.559258	+	0.828993i	$0.311086\pi$
$114$	2.74018	+	0.644485i	0.256642	+	0.0603616i
$115$	0.384156	−	6.22842i	0.0358227	−	0.580803i
$116$	0.740084	+	0.837379i	0.0687151	+	0.0777486i
$117$	4.34080	−	1.16311i	0.401307	−	0.107530i
$118$	8.30752	+	0.127946i	0.764770	+	0.0117784i
$119$	1.87402	+	3.36451i	0.171791	+	0.308424i
$120$	0.0726532	−	2.35813i	0.00663230	−	0.215267i
$121$	1.47803	−	1.11616i	0.134366	−	0.101469i
$122$	−6.70013	+	16.5345i	−0.606601	+	1.49696i
$123$	−2.49753	−	1.76796i	−0.225195	−	0.159412i
$124$	0.865383	+	0.414403i	0.0777137	+	0.0372145i
$125$	7.33164	+	9.70866i	0.655762	+	0.868369i
$126$	−3.70820	−	1.11708i	−0.330353	−	0.0995175i
$127$	2.64487	−	1.69453i	0.234694	−	0.150365i	−0.416851	−	0.908975i	$-0.636866\pi$
$127$	2.64487	−	1.69453i	0.234694	−	0.150365i	0.651545	+	0.758610i	$0.274121\pi$
$128$	−6.11920	+	2.59004i	−0.540866	+	0.228929i
$129$	3.87514	−	0.786336i	0.341187	−	0.0692330i
$130$	3.54002	+	0.718333i	0.310480	+	0.0630019i
$131$	−7.81408	−	3.30742i	−0.682719	−	0.288970i	0.0206583	−	0.999787i	$-0.493424\pi$
$131$	−7.81408	−	3.30742i	−0.682719	−	0.288970i	−0.703378	+	0.710816i	$0.748326\pi$
$132$	−0.628810	+	0.107551i	−0.0547309	+	0.00936111i
$133$	−4.60050	+	3.25662i	−0.398914	+	0.282385i
$134$	2.49443	+	10.6057i	0.215486	+	0.916190i
$135$	−3.03982	+	3.33453i	−0.261626	+	0.286990i
$136$	−5.06928	−	9.44021i	−0.434688	−	0.809491i
$137$	3.14539	+	0.389484i	0.268729	+	0.0332758i	0.256121	−	0.966645i	$-0.417555\pi$
$137$	3.14539	+	0.389484i	0.268729	+	0.0332758i	0.0126076	+	0.999921i	$0.495987\pi$
$138$	−1.79015	−	0.630824i	−0.152388	−	0.0536993i
$139$	−1.30633	−	5.96490i	−0.110802	−	0.505936i	−0.998926	−	0.0463327i	$-0.985247\pi$
$139$	−1.30633	−	5.96490i	−0.110802	−	0.505936i	0.888124	−	0.459603i	$-0.152008\pi$
$140$	0.586884	+	0.551801i	0.0496007	+	0.0466357i
$141$	−4.85863	−	1.96882i	−0.409171	−	0.165805i
$142$	−2.53346	+	7.96377i	−0.212603	+	0.668304i
$143$		−	5.72786i		−	0.478988i
$144$	8.06412	+	2.56538i	0.672010	+	0.213782i
$145$	2.10555	−	4.39695i	0.174857	−	0.365147i
$146$	0.670330	+	0.556635i	0.0554769	+	0.0460675i
$147$	2.13673	−	1.32301i	0.176234	−	0.109120i
$148$	−3.53968	−	2.42474i	−0.290960	−	0.199312i
$149$	8.57580	−	8.06316i	0.702557	−	0.660559i	−0.248834	−	0.968546i	$-0.580047\pi$
$149$	8.57580	−	8.06316i	0.702557	−	0.660559i	0.951391	+	0.307987i	$0.0996552\pi$
$150$	0.907038	−	0.351388i	0.0740594	−	0.0286907i
$151$	4.41537	−	9.99987i	0.359318	−	0.813778i	−0.639663	−	0.768655i	$-0.720926\pi$
$151$	4.41537	−	9.99987i	0.359318	−	0.813778i	0.998981	−	0.0451227i	$-0.0143679\pi$
$152$	12.9379	−	8.86267i	1.04940	−	0.718857i
$153$	−2.12145	+	9.68684i	−0.171509	+	0.783134i
$154$	−2.59857	+	4.19684i	−0.209399	+	0.338191i
$155$	0.193304	−	4.18109i	0.0155265	−	0.335834i
$156$	−0.130634	+	0.252526i	−0.0104591	+	0.0202182i
$157$	−16.0937	+	12.5472i	−1.28442	+	1.00138i	−0.285340	+	0.958426i	$0.592107\pi$
$157$	−16.0937	+	12.5472i	−1.28442	+	1.00138i	−0.999077	+	0.0429488i	$0.986325\pi$
$158$	3.08657	−	3.95900i	0.245554	−	0.314961i
$159$	0.574078	−	0.0176872i	0.0455274	−	0.00140268i
$160$	−2.94371	−	2.85441i	−0.232720	−	0.225661i
$161$	3.32023	−	1.84936i	0.261671	−	0.145750i
$162$	−4.87670	−	7.87615i	−0.383150	−	0.618809i
$163$	−15.0124	+	5.29017i	−1.17586	+	0.414358i	−0.847809	−	0.530301i	$-0.822079\pi$
$163$	−15.0124	+	5.29017i	−1.17586	+	0.414358i	−0.328054	+	0.944659i	$0.606393\pi$
$164$	−2.83965	+	0.621894i	−0.221740	+	0.0485617i
$165$	1.50126	+	2.34321i	0.116873	+	0.182419i
$166$	13.3721	+	16.6175i	1.03788	+	1.28977i
$167$	−0.474863	−	15.4128i	−0.0367460	−	1.19268i	−0.820515	−	0.571626i	$-0.806313\pi$
$167$	−0.474863	−	15.4128i	−0.0367460	−	1.19268i	0.783769	−	0.621053i	$-0.213295\pi$
$168$	1.23315	−	0.737509i	0.0951396	−	0.0569001i
$169$	8.33708	+	6.29587i	0.641314	+	0.484298i
$170$	−4.99702	+	6.20981i	−0.383254	+	0.476271i
$171$	−14.4291	−	1.56150i	−1.10342	−	0.119411i
$172$	1.92808	−	3.22383i	0.147014	−	0.245815i
$173$	−3.17394	+	4.34038i	−0.241310	+	0.329993i	−0.910815	−	0.412815i	$-0.864546\pi$
$173$	−3.17394	+	4.34038i	−0.241310	+	0.329993i	0.669505	+	0.742808i	$0.266506\pi$
$174$	−1.11107	−	0.981971i	−0.0842297	−	0.0744431i
$175$	−0.675548	+	1.82682i	−0.0510667	+	0.138095i
$176$	5.81860	−	9.08184i	0.438593	−	0.684570i
$177$	2.83622	−	0.306934i	0.213183	−	0.0230705i
$178$	−5.50483	+	11.9651i	−0.412604	+	0.896823i
$179$	5.88732	+	4.73751i	0.440039	+	0.354098i	0.821424	−	0.570319i	$-0.193180\pi$
$179$	5.88732	+	4.73751i	0.440039	+	0.354098i	−0.381385	+	0.924416i	$0.624553\pi$
$180$	0.191383	+	2.06536i	0.0142649	+	0.153943i
$181$	−18.2228	+	16.1055i	−1.35449	+	1.19711i	−0.393898	+	0.919154i	$0.628874\pi$
$181$	−18.2228	+	16.1055i	−1.35449	+	1.19711i	−0.960593	+	0.277959i	$0.910342\pi$
$182$	0.794708	+	2.05138i	0.0589077	+	0.152058i
$183$	−1.58543	+	5.91690i	−0.117198	+	0.437390i
$184$	−9.31597	+	5.00257i	−0.686783	+	0.368794i
$185$	−3.72206	+	18.3427i	−0.273651	+	1.34858i
$186$	−1.20709	−	0.404575i	−0.0885081	−	0.0296649i
$187$	11.2261	+	5.80736i	0.820933	+	0.424676i
$188$	−4.49180	+	2.15097i	−0.327598	+	0.156876i
$189$	−2.70873	−	0.463298i	−0.197031	−	0.0336999i
$190$	−9.82256	−	6.29316i	−0.712604	−	0.456554i
$191$	6.48588	+	7.57035i	0.469302	+	0.547771i	0.942946	−	0.332945i	$-0.108042\pi$
$191$	6.48588	+	7.57035i	0.469302	+	0.547771i	−0.473645	+	0.880716i	$0.657062\pi$
$192$	−3.33544	+	1.92572i	−0.240715	+	0.138977i
$193$	1.98872	+	0.371757i	0.143151	+	0.0267596i	0.254837	−	0.966984i	$-0.417978\pi$
$193$	1.98872	+	0.371757i	0.143151	+	0.0267596i	−0.111686	+	0.993744i	$0.535625\pi$
$194$	22.4112	+	3.12624i	1.60903	+	0.224451i
$195$	1.23658	+	0.0954054i	0.0885536	+	0.00683212i
$196$	0.438700	−	2.34684i	0.0313357	−	0.167631i
$197$	−2.93485	+	3.42557i	−0.209099	+	0.244062i	−0.854086	−	0.520132i	$-0.825883\pi$
$197$	−2.93485	+	3.42557i	−0.209099	+	0.244062i	0.644986	+	0.764194i	$0.276863\pi$
$198$	−12.1699	+	3.66613i	−0.864877	+	0.260540i
$199$	−2.65134	−	1.93881i	−0.187948	−	0.137439i	0.492286	−	0.870433i	$-0.336161\pi$
$199$	−2.65134	−	1.93881i	−0.187948	−	0.137439i	−0.680235	+	0.732994i	$0.738122\pi$
$200$	1.95762	−	5.05319i	0.138424	−	0.357314i
$201$	1.29749	+	3.50867i	0.0915177	+	0.247482i
$202$	7.14768	+	1.56537i	0.502909	+	0.110139i
$203$	2.94660	−	0.364868i	0.206810	−	0.0256087i
$204$	−0.362481	−	0.512061i	−0.0253787	−	0.0358515i
$205$	7.32673	+	10.3502i	0.511721	+	0.722886i
$206$	8.55412	−	1.05923i	0.595994	−	0.0738000i
$207$	9.55936	+	2.09353i	0.664421	+	0.145510i
$208$	−1.66726	−	4.50861i	−0.115604	−	0.312616i
$209$	−6.68237	+	17.2492i	−0.462229	+	1.19315i
$210$	−0.862770	−	0.630908i	−0.0595368	−	0.0435368i
$211$	−20.2470	+	6.09933i	−1.39386	+	0.419895i	−0.894721	−	0.446626i	$-0.852625\pi$
$211$	−20.2470	+	6.09933i	−1.39386	+	0.419895i	−0.499141	+	0.866521i	$0.666351\pi$
$212$	0.354998	−	0.414356i	0.0243814	−	0.0284581i
$213$	−0.527258	+	2.82058i	−0.0361271	+	0.193263i
$214$	10.2101	+	0.787734i	0.697949	+	0.0538484i
$215$	−16.2294	−	2.26390i	−1.10683	−	0.154397i
$216$	7.51571	+	1.40493i	0.511379	+	0.0955933i
$217$	2.20763	−	1.27458i	0.149864	−	0.0865239i
$218$	−7.11215	−	8.30134i	−0.481696	−	0.562238i
$219$	0.251905	+	0.161391i	0.0170221	+	0.0109058i
$220$	2.60589	+	0.445709i	0.175689	+	0.0300497i
$221$	5.08051	−	2.43289i	0.341752	−	0.163654i
$222$	5.05634	+	2.61569i	0.339360	+	0.175554i
$223$	4.20263	+	1.40858i	0.281429	+	0.0943255i	0.454987	−	0.890498i	$-0.349644\pi$
$223$	4.20263	+	1.40858i	0.281429	+	0.0943255i	−0.173558	+	0.984824i	$0.555526\pi$
$224$	0.496619	−	2.44739i	0.0331818	−	0.163523i
$225$	−4.41842	+	2.37264i	−0.294561	+	0.158176i
$226$	−1.64392	+	6.13520i	−0.109352	+	0.408107i
$227$	−9.86034	−	25.4525i	−0.654454	−	1.68934i	−0.722243	−	0.691640i	$-0.756889\pi$
$227$	−9.86034	−	25.4525i	−0.654454	−	1.68934i	0.0677892	−	0.997700i	$-0.478405\pi$
$228$	0.688006	−	0.608067i	0.0455643	−	0.0402702i
$229$	−1.19648	−	12.9121i	−0.0790658	−	0.853256i	−0.939241	−	0.343258i	$-0.888470\pi$
$229$	−1.19648	−	12.9121i	−0.0790658	−	0.853256i	0.860175	−	0.509998i	$-0.170354\pi$
$230$	6.12809	+	4.93126i	0.404074	+	0.325157i
$231$	−0.708390	+	1.53973i	−0.0466086	+	0.101307i
$232$	−8.21293	+	0.888797i	−0.539205	+	0.0583524i
$233$	11.7076	−	18.2737i	0.766993	−	1.19715i	−0.208694	−	0.977981i	$-0.566921\pi$
$233$	11.7076	−	18.2737i	0.766993	−	1.19715i	0.975688	−	0.219166i	$-0.0703335\pi$
$234$	−1.96469	+	5.31293i	−0.128436	+	0.347317i
$235$	16.2787	+	14.3872i	1.06190	+	0.938521i
$236$	1.59972	−	2.18763i	0.104133	−	0.142402i
$237$	0.884713	−	1.47928i	0.0574683	−	0.0960896i
$238$	−4.82625	−	0.522294i	−0.312840	−	0.0338553i
$239$	−9.70751	+	12.0636i	−0.627927	+	0.780327i	−0.988307	−	0.152479i	$-0.951274\pi$
$239$	−9.70751	+	12.0636i	−0.627927	+	0.780327i	0.360380	+	0.932805i	$0.382647\pi$
$240$	1.86376	+	1.40744i	0.120305	+	0.0908501i
$241$	−10.5983	+	6.33850i	−0.682694	+	0.408299i	−0.812278	−	0.583270i	$-0.801773\pi$
$241$	−10.5983	+	6.33850i	−0.682694	+	0.408299i	0.129584	+	0.991568i	$0.458636\pi$
$242$	0.0718940	+	2.33349i	0.00462152	+	0.150002i
$243$	−6.72558	−	8.35790i	−0.431446	−	0.536160i
$244$	3.13931	+	4.89993i	0.200974	+	0.313686i
$245$	−10.1738	+	2.22810i	−0.649980	+	0.142348i
$246$	3.63780	−	1.28191i	0.231938	−	0.0817317i
$247$	4.34003	+	7.00939i	0.276149	+	0.445997i
$248$	−6.19614	+	3.45123i	−0.393455	+	0.219153i
$249$	5.25776	+	5.09826i	0.333197	+	0.323089i
$250$	−15.3279	+	0.472246i	−0.969419	+	0.0298675i
$251$	−8.51907	+	10.9270i	−0.537719	+	0.689707i	−0.978108	−	0.208100i	$-0.933272\pi$
$251$	−8.51907	+	10.9270i	−0.537719	+	0.689707i	0.440389	+	0.897807i	$0.354841\pi$
$252$	−0.996263	+	0.776720i	−0.0627586	+	0.0489287i
$253$	5.73093	−	11.0784i	0.360301	−	0.696490i
$254$	−0.182858	+	3.95516i	−0.0114735	+	0.248169i
$255$	−1.44073	+	2.32686i	−0.0902222	+	0.145714i
$256$	−2.01571	+	9.20402i	−0.125982	+	0.575251i
$257$	3.45663	−	2.36785i	0.215619	−	0.147702i	−0.452481	−	0.891774i	$-0.649461\pi$
$257$	3.45663	−	2.36785i	0.215619	−	0.147702i	0.668100	+	0.744072i	$0.267108\pi$
$258$	−2.01320	+	4.55946i	−0.125336	+	0.283860i
$259$	−10.6293	+	4.11780i	−0.660471	+	0.255868i
$260$	0.858406	−	0.807092i	0.0532361	−	0.0500537i
$261$	6.30717	+	4.32051i	0.390404	+	0.267433i
$262$	9.09354	−	5.63048i	0.561801	−	0.347852i
$263$	−15.3336	−	12.7328i	−0.945509	−	0.785140i	0.0312437	−	0.999512i	$-0.490053\pi$
$263$	−15.3336	−	12.7328i	−0.945509	−	0.785140i	−0.976752	+	0.214372i	$0.931230\pi$
$264$	2.03668	−	4.25312i	0.125349	−	0.261761i
$265$	−2.26819	−	0.721565i	−0.139334	−	0.0443254i
$266$		−	7.10477i		−	0.435621i
$267$	−1.37093	+	4.30943i	−0.0838995	+	0.263733i
$268$	3.29369	+	1.33467i	0.201194	+	0.0815281i
$269$	−7.26531	−	6.83100i	−0.442974	−	0.416494i	0.431087	−	0.902310i	$-0.358130\pi$
$269$	−7.26531	−	6.83100i	−0.442974	−	0.416494i	−0.874061	+	0.485817i	$0.838522\pi$
$270$	−1.21675	−	5.55587i	−0.0740493	−	0.338119i
$271$	−0.650999	−	0.229403i	−0.0395454	−	0.0139352i	0.312509	−	0.949915i	$-0.398831\pi$
$271$	−0.650999	−	0.229403i	−0.0395454	−	0.0139352i	−0.352054	+	0.935980i	$0.614517\pi$
$272$	10.5269	+	1.30351i	0.638285	+	0.0790368i
$273$	0.357357	+	0.665483i	0.0216282	+	0.0402768i
$274$	−2.69143	+	2.95236i	−0.162595	+	0.178358i
$275$	1.46350	+	6.22242i	0.0882524	+	0.375226i
$276$	−0.505323	+	0.357711i	−0.0304169	+	0.0215316i
$277$	31.6202	−	5.40829i	1.89988	−	0.324953i	0.904947	−	0.425525i	$-0.139911\pi$
$277$	31.6202	−	5.40829i	1.89988	−	0.324953i	0.994930	+	0.100572i	$0.0320674\pi$
$278$	7.08812	+	3.00015i	0.425117	+	0.179937i
$279$	6.43266	+	1.30530i	0.385113	+	0.0781464i
$280$	−5.83567	+	1.18416i	−0.348748	+	0.0707671i
$281$	−3.66267	+	1.55028i	−0.218497	+	0.0924817i	−0.496282	−	0.868162i	$-0.665302\pi$
$281$	−3.66267	+	1.55028i	−0.218497	+	0.0924817i	0.277785	+	0.960643i	$0.410400\pi$
$282$	5.56399	−	3.56476i	0.331331	−	0.212278i
$283$	−6.27625	−	1.89069i	−0.373084	−	0.112390i	0.0963728	−	0.995345i	$-0.469276\pi$
$283$	−6.27625	−	1.89069i	−0.373084	−	0.112390i	−0.469457	+	0.882955i	$0.655550\pi$
$284$	1.64276	+	2.17536i	0.0974798	+	0.129084i
$285$	−3.61261	−	1.72996i	−0.213993	−	0.102474i
$286$	5.89288	+	4.17149i	0.348453	+	0.246665i
$287$	−2.90049	+	7.15780i	−0.171211	+	0.422512i
$288$	5.13138	−	3.87504i	0.302370	−	0.228339i
$289$	0.140737	−	4.56794i	0.00827864	−	0.268703i
$290$	2.99019	+	5.36842i	0.175590	+	0.315245i
$291$	7.76863	+	0.119646i	0.455405	+	0.00701378i
$292$	0.274527	−	0.0735593i	0.0160655	−	0.00430473i
$293$	−12.1697	−	13.7696i	−0.710963	−	0.804429i	0.276711	−	0.960953i	$-0.410755\pi$
$293$	−12.1697	−	13.7696i	−0.710963	−	0.804429i	−0.987674	+	0.156524i	$0.949971\pi$
$294$	−0.195013	+	3.16181i	−0.0113734	+	0.184400i
$295$	−11.5084	−	2.70674i	−0.670042	−	0.157592i
$296$	29.7466	−	11.0001i	1.72899	−	0.639370i
$297$	−8.25036	+	3.64289i	−0.478735	+	0.211382i
$298$	2.04988	+	14.6951i	0.118746	+	0.851264i
$299$	−2.40087	−	5.01365i	−0.138846	−	0.289947i
$300$	0.0773915	−	0.307708i	0.00446820	−	0.0177655i
$301$	−4.17123	−	9.06645i	−0.240426	−	0.522581i
$302$	7.07234	+	11.8253i	0.406968	+	0.680469i
$303$	2.50165	+	0.231812i	0.143716	+	0.0133173i
$304$	−0.239066	+	15.5226i	−0.0137114	+	0.890280i
$305$	14.3463	−	20.9430i	0.821468	−	1.19920i
$306$	−8.42091	−	9.23730i	−0.481391	−	0.528061i
$307$	4.88296	−	13.8568i	0.278686	−	0.790852i	−0.716916	−	0.697160i	$-0.754447\pi$
$307$	4.88296	−	13.8568i	0.278686	−	0.790852i	0.995601	−	0.0936922i	$-0.0298670\pi$
$308$	0.627605	+	1.48277i	0.0357611	+	0.0844889i
$309$	2.87015	−	0.721873i	0.163277	−	0.0410659i
$310$	4.16077	+	3.24388i	0.236316	+	0.184240i
$311$	−1.48251	+	0.682065i	−0.0840657	+	0.0386764i	−0.459546	−	0.888154i	$-0.651988\pi$
$311$	−1.48251	+	0.682065i	−0.0840657	+	0.0386764i	0.375480	+	0.926831i	$0.377478\pi$
$312$	−0.965637	−	1.86665i	−0.0546684	−	0.105678i
$313$	7.75946	+	3.56992i	0.438590	+	0.201784i	0.624896	−	0.780708i	$-0.285142\pi$
$313$	7.75946	+	3.56992i	0.438590	+	0.201784i	−0.186305	+	0.982492i	$0.559651\pi$
$314$	−1.18796	−	25.6952i	−0.0670406	−	1.45007i
$315$	4.81428	+	2.68154i	0.271254	+	0.151087i
$316$	−0.472315	−	1.56787i	−0.0265698	−	0.0881997i
$317$	−0.832817	−	0.414694i	−0.0467757	−	0.0232915i	0.422198	−	0.906503i	$-0.361259\pi$
$317$	−0.832817	−	0.414694i	−0.0467757	−	0.0232915i	−0.468974	+	0.883212i	$0.655376\pi$
$318$	−0.399893	+	0.603499i	−0.0224249	+	0.0338425i
$319$	7.39982	−	6.33978i	0.414311	−	0.354960i
$320$	15.6892	−	2.93282i	0.877054	−	0.163950i
$321$	3.51237	−	0.162387i	0.196042	−	0.00906355i
$322$	−0.515420	+	4.76274i	−0.0287232	+	0.265417i
$323$	−18.1380	+	1.39939i	−1.00923	+	0.0778642i
$324$	−3.01597	−	0.186019i	−0.167554	−	0.0103344i
$325$	2.60610	+	1.15071i	0.144561	+	0.0638298i
$326$	5.49066	−	19.2977i	0.304099	−	1.06880i
$327$	−2.77376	−	2.52862i	−0.153389	−	0.139833i
$328$	8.37572	−	19.7884i	0.462472	−	1.09263i
$329$	−2.02959	+	13.0749i	−0.111895	+	0.720841i
$330$	−3.50406	−	0.162003i	−0.192892	−	0.00891795i
$331$	25.9617	−	3.62150i	1.42698	−	0.199056i	0.617672	−	0.786436i	$-0.288076\pi$
$331$	25.9617	−	3.62150i	1.42698	−	0.199056i	0.809311	+	0.587380i	$0.199841\pi$
$332$	6.94429	−	0.428309i	0.381117	−	0.0235065i
$333$	−27.5291	−	10.1801i	−1.50859	−	0.557867i
$334$	16.2027	+	10.7363i	0.886572	+	0.587464i
$335$	−0.238734	−	15.5010i	−0.0130434	−	0.846910i
$336$	−0.109416	+	1.41818i	−0.00596912	+	0.0773679i
$337$	2.52017	+	7.92201i	0.137283	+	0.431539i	0.996834	−	0.0795097i	$-0.0253355\pi$
$337$	2.52017	+	7.92201i	0.137283	+	0.431539i	−0.859552	+	0.511049i	$0.829257\pi$
$338$	−12.5490	+	3.99212i	−0.682575	+	0.217143i
$339$	−0.301301	+	2.15996i	−0.0163644	+	0.117313i
$340$	0.711508	+	2.50069i	0.0385869	+	0.135619i
$341$	3.72906	−	7.48896i	0.201940	−	0.405550i
$342$	12.1149	−	13.7076i	0.655098	−	0.741220i
$343$	−9.89210	−	9.89210i	−0.534123	−	0.534123i
$344$	11.2157	+	25.4012i	0.604711	+	1.36954i
$345$	2.29624	+	1.42177i	0.123626	+	0.0765457i
$346$	−2.15391	−	6.42640i	−0.115795	−	0.345485i
$347$	4.04177	+	23.6307i	0.216974	+	1.26856i	0.862982	+	0.505235i	$0.168594\pi$
$347$	4.04177	+	23.6307i	0.216974	+	1.26856i	−0.646008	+	0.763330i	$0.723563\pi$
$348$	−0.470828	+	0.110738i	−0.0252390	+	0.00593617i
$349$	3.40732	−	2.25777i	0.182389	−	0.120856i	−0.457855	−	0.889027i	$-0.651382\pi$
$349$	3.40732	−	2.25777i	0.182389	−	0.120856i	0.640244	+	0.768171i	$0.278833\pi$
$350$	−1.38746	−	2.02545i	−0.0741631	−	0.108265i
$351$	−0.920257	+	3.91269i	−0.0491197	+	0.208844i
$352$	−3.07798	−	7.59581i	−0.164057	−	0.404858i
$353$	5.05467	+	3.02304i	0.269033	+	0.160900i	0.641449	−	0.767165i	$-0.278333\pi$
$353$	5.05467	+	3.02304i	0.269033	+	0.160900i	−0.372417	+	0.928066i	$0.621471\pi$
$354$	−1.74979	+	3.14147i	−0.0930000	+	0.166967i
$355$	5.94571	−	10.2983i	0.315565	−	0.546575i
$356$	2.14806	+	3.72055i	0.113847	+	0.197189i
$357$	−1.66660	+	0.0256676i	−0.0882059	+	0.00135848i
$358$	−9.16161	+	2.60670i	−0.484206	+	0.137769i
$359$	−12.0227	−	10.3004i	−0.634536	−	0.543637i	0.273849	−	0.961773i	$-0.411703\pi$
$359$	−12.0227	−	10.3004i	−0.634536	−	0.543637i	−0.908384	+	0.418136i	$0.862684\pi$
$360$	−13.2782	−	7.66619i	−0.699824	−	0.404043i
$361$	−1.40110	−	7.49523i	−0.0737421	−	0.394486i
$362$	−3.29821	−	30.4771i	−0.173350	−	1.60184i
$363$	0.122958	+	0.792111i	0.00645364	+	0.0415751i
$364$	0.695918	+	0.175030i	0.0364760	+	0.00917409i
$365$	−0.762301	−	0.977768i	−0.0399006	−	0.0511787i
$366$	−4.93273	−	5.94027i	−0.257838	−	0.310503i
$367$	5.24421	+	25.8440i	0.273746	+	1.34905i	0.847838	+	0.530256i	$0.177904\pi$
$367$	5.24421	+	25.8440i	0.273746	+	1.34905i	−0.574092	+	0.818791i	$0.694645\pi$
$368$	1.28635	−	10.3883i	0.0670558	−	0.541529i
$369$	−17.8014	+	8.86403i	−0.926702	+	0.461443i
$370$	−16.1605	−	17.1879i	−0.840143	−	0.893558i
$371$	−0.375191	−	1.40023i	−0.0194789	−	0.0726964i
$372$	−0.335203	+	0.245120i	−0.0173795	+	0.0127089i
$373$	−8.70462	+	11.5268i	−0.450708	+	0.596834i	−0.965475	−	0.260496i	$-0.916114\pi$
$373$	−8.70462	+	11.5268i	−0.450708	+	0.596834i	0.514767	+	0.857330i	$0.327879\pi$
$374$	−14.1504	+	7.32014i	−0.731700	+	0.378515i
$375$	−5.20310	+	0.807671i	−0.268687	+	0.0417079i
$376$	6.20644	−	36.2867i	0.320073	−	1.87135i
$377$	−0.267344	−	4.33452i	−0.0137689	−	0.223239i
$378$	2.44936	−	2.44936i	0.125981	−	0.125981i
$379$	−13.6111	−	5.27296i	−0.699154	−	0.270854i	−0.0146814	−	0.999892i	$-0.504673\pi$
$379$	−13.6111	−	5.27296i	−0.699154	−	0.270854i	−0.684473	+	0.729039i	$0.739968\pi$
$380$	−3.52664	+	1.42907i	−0.180913	+	0.0733096i
$381$	0.104576	+	1.35545i	0.00535761	+	0.0694419i
$382$	−12.5120	+	1.15941i	−0.640169	+	0.0593204i
$383$	−2.90651	−	3.97467i	−0.148516	−	0.203096i	0.726532	−	0.687133i	$-0.241131\pi$
$383$	−2.90651	−	3.97467i	−0.148516	−	0.203096i	−0.875048	+	0.484037i	$0.839170\pi$
$384$	0.265349	−	2.86358i	0.0135411	−	0.146131i
$385$	4.88953	−	5.04249i	0.249193	−	0.256989i
$386$	−1.83081	+	1.77528i	−0.0931860	+	0.0903592i
$387$	7.41215	−	24.6050i	0.376781	−	1.25074i
$388$	5.05599	−	5.37744i	0.256679	−	0.272998i
$389$	31.6797	+	17.0116i	1.60622	+	0.862524i	0.997613	+	0.0690547i	$0.0219983\pi$
$389$	31.6797	+	17.0116i	1.60622	+	0.862524i	0.608611	+	0.793469i	$0.291727\pi$
$390$	−0.998734	+	1.20273i	−0.0505728	+	0.0609026i
$391$	12.2605	+	0.377742i	0.620040	+	0.0191032i
$392$	12.2855	+	12.6698i	0.620511	+	0.639923i
$393$	2.86108	−	2.30231i	0.144323	−	0.116136i
$394$	−1.38687	−	5.51417i	−0.0698695	−	0.277800i
$395$	−5.49544	+	4.56335i	−0.276505	+	0.229607i
$396$	−1.31753	+	3.93096i	−0.0662081	+	0.197538i
$397$	−10.1721	−	1.57900i	−0.510523	−	0.0792478i	−0.107076	−	0.994251i	$-0.534149\pi$
$397$	−10.1721	−	1.57900i	−0.510523	−	0.0792478i	−0.403447	+	0.915003i	$0.632188\pi$
$398$	3.92559	−	1.31572i	0.196772	−	0.0659513i
$399$	−0.299782	−	2.42098i	−0.0150079	−	0.121200i
$400$	2.96319	+	4.47190i	0.148159	+	0.223595i
$401$	10.5345	+	2.99731i	0.526066	+	0.149679i	0.526264	−	0.850321i	$-0.323592\pi$
$401$	10.5345	+	2.99731i	0.526066	+	0.149679i	−0.000198026		1.00000i	$0.500063\pi$
$402$	−4.55469	−	1.22043i	−0.227167	−	0.0608693i
$403$	−1.66194	−	3.33763i	−0.0827873	−	0.166259i
$404$	1.76383	−	1.60794i	0.0877536	−	0.0799980i
$405$	4.38094	+	12.4322i	0.217691	+	0.617762i
$406$	−1.77057	+	3.29721i	−0.0878718	+	0.163638i
$407$	−21.6147	+	30.5342i	−1.07140	+	1.51352i
$408$	4.63751			0.229591
$409$	−4.89150	−	19.6233i	−0.241869	−	0.970309i
$409$	−4.89150	−	19.6233i	−0.241869	−	0.970309i
$410$	−15.9843			−0.789406
$411$	−0.792541	+	1.11959i	−0.0390932	+	0.0552253i
$412$	1.33013	−	2.47702i	0.0655308	−	0.122034i
$413$	−2.39303	−	6.79094i	−0.117754	−	0.334160i
$414$	−9.11573	+	8.31009i	−0.448014	+	0.408419i
$415$	−13.5284	−	27.1687i	−0.664083	−	1.33366i
$416$	−3.52817	−	0.945371i	−0.172983	−	0.0463506i
$417$	2.54189	+	0.723231i	0.124477	+	0.0354168i
$418$	−12.8795	−	19.4371i	−0.629957	−	0.950701i
$419$	−2.03731	−	16.4529i	−0.0995291	−	0.803776i	−0.957170	−	0.289527i	$-0.906502\pi$
$419$	−2.03731	−	16.4529i	−0.0995291	−	0.803776i	0.857641	−	0.514249i	$-0.171929\pi$
$420$	−0.330569	+	0.110796i	−0.0161301	+	0.00540627i
$421$	33.0891	+	5.13637i	1.61266	+	0.250332i	0.895002	−	0.446061i	$-0.147174\pi$
$421$	33.0891	+	5.13637i	1.61266	+	0.250332i	0.717661	+	0.696393i	$0.245213\pi$
$422$	8.47044	−	25.2723i	0.412334	−	1.23024i
$423$	−26.2107	+	21.7651i	−1.27441	+	1.05826i
$424$	0.983771	+	3.91146i	0.0477761	+	0.189957i
$425$	−4.89756	+	3.94105i	−0.237567	+	0.191169i
$426$	−2.51785	−	2.59662i	−0.121990	−	0.125807i
$427$	15.4534	+	0.476114i	0.747841	+	0.0230407i
$428$	2.13395	−	2.56982i	0.103148	−	0.124217i
$429$	2.18404	+	1.17280i	0.105446	+	0.0566234i
$430$	14.1486	−	15.0482i	0.682308	−	0.725688i
$431$	−4.37876	+	14.5355i	−0.210917	+	0.700151i	0.785747	+	0.618547i	$0.212279\pi$
$431$	−4.37876	+	14.5355i	−0.210917	+	0.700151i	−0.996665	+	0.0816033i	$0.973996\pi$
$432$	−5.43379	+	5.26896i	−0.261433	+	0.253503i
$433$	−19.2678	+	19.8706i	−0.925951	+	0.954919i	−0.999101	−	0.0424022i	$-0.986499\pi$
$433$	−19.2678	+	19.8706i	−0.925951	+	0.954919i	0.0731495	+	0.997321i	$0.476695\pi$
$434$	−0.296476	+	3.19948i	−0.0142313	+	0.153580i
$435$	1.24544	+	1.70314i	0.0597141	+	0.0816594i
$436$	−3.55047	+	0.329000i	−0.170037	+	0.0157562i
$437$	1.38098	+	17.8993i	0.0660610	+	0.856241i
$438$	−0.349498	+	0.141624i	−0.0166997	+	0.00676705i
$439$	7.88238	+	3.05365i	0.376206	+	0.145743i	0.541918	−	0.840431i	$-0.317698\pi$
$439$	7.88238	+	3.05365i	0.376206	+	0.145743i	−0.165713	+	0.986174i	$0.552992\pi$
$440$	−13.8185	+	13.8185i	−0.658771	+	0.658771i
$441$	−1.00545	−	16.3016i	−0.0478785	−	0.776267i
$442$	−1.19705	+	6.99870i	−0.0569379	+	0.332894i
$443$	−15.2272	+	2.36371i	−0.723468	+	0.112303i	−0.504479	−	0.863424i	$-0.668315\pi$
$443$	−15.2272	+	2.36371i	−0.723468	+	0.112303i	−0.218989	+	0.975727i	$0.570276\pi$
$444$	1.64932	−	0.853207i	0.0782732	−	0.0404914i
$445$	11.2939	−	14.9556i	0.535383	−	0.708961i
$446$	−4.50986	+	3.29787i	−0.213548	+	0.156159i
$447$	1.31856	+	4.92092i	0.0623656	+	0.232751i
$448$	6.65871	+	7.08205i	0.314594	+	0.334596i
$449$	18.0529	−	8.98926i	0.851967	−	0.424229i	0.0339504	−	0.999424i	$-0.489191\pi$
$449$	18.0529	−	8.98926i	0.851967	−	0.424229i	0.818017	+	0.575194i	$0.195074\pi$
$450$	0.776848	−	6.27366i	0.0366210	−	0.295743i
$451$	5.04052	+	24.8402i	0.237349	+	1.16968i
$452$	1.32358	+	1.59392i	0.0622558	+	0.0749718i
$453$	2.90889	+	3.73110i	0.136672	+	0.175302i
$454$	33.3668	+	8.39210i	1.56598	+	0.393861i
$455$	−0.480168	−	3.09329i	−0.0225106	−	0.145016i
$456$	0.730252	+	6.74790i	0.0341972	+	0.315999i
$457$	4.51332	+	24.1441i	0.211124	+	1.12941i	0.910138	+	0.414306i	$0.135976\pi$
$457$	4.51332	+	24.1441i	0.211124	+	1.12941i	−0.699014	+	0.715108i	$0.746377\pi$
$458$	14.1555	+	8.17268i	0.661443	+	0.381884i
$459$	−6.73549	−	5.77062i	−0.314386	−	0.269349i
$460$	2.46778	−	0.702145i	0.115061	−	0.0327377i
$461$	−32.0062	+	0.492933i	−1.49068	+	0.0229582i	−0.755603	−	0.655030i	$-0.772656\pi$
$461$	−32.0062	+	0.492933i	−1.49068	+	0.0229582i	−0.735073	+	0.677988i	$0.762852\pi$
$462$	−1.06819	−	1.85016i	−0.0496966	−	0.0860771i
$463$	−13.3378	+	23.1018i	−0.619862	+	1.07363i	0.369649	+	0.929172i	$0.379478\pi$
$463$	−13.3378	+	23.1018i	−0.619862	+	1.07363i	−0.989511	+	0.144461i	$0.953855\pi$
$464$	3.97929	−	7.14420i	0.184734	−	0.331661i
$465$	1.55467	+	0.929803i	0.0720963	+	0.0431186i
$466$	10.2737	+	25.3533i	0.475919	+	1.17447i
$467$	4.41121	−	18.7553i	0.204127	−	0.867893i	−0.769299	−	0.638889i	$-0.779394\pi$
$467$	4.41121	−	18.7553i	0.204127	−	0.867893i	0.973425	−	0.229004i	$-0.0735470\pi$
$468$	1.04421	+	1.52436i	0.0482686	+	0.0704635i
$469$	7.87068	−	5.21530i	0.363434	−	0.240820i
$470$	−26.6572	+	6.26971i	−1.22960	+	0.289200i
$471$	−1.48900	−	8.70563i	−0.0686095	−	0.401134i
$472$	6.36636	+	18.9946i	0.293035	+	0.874298i
$473$	−27.8472	−	17.2423i	−1.28042	−	0.792800i
$474$	0.877581	+	1.98753i	0.0403086	+	0.0912904i
$475$	−6.50570	−	6.50570i	−0.298502	−	0.298502i
$476$	−1.04862	+	1.18648i	−0.0480635	+	0.0543821i
$477$	1.66377	−	3.34130i	0.0761787	−	0.152988i
$478$	−5.34133	−	18.7728i	−0.244307	−	0.858649i
$479$	2.31816	−	16.6184i	0.105920	−	0.759312i	−0.861794	−	0.507259i	$-0.830659\pi$
$479$	2.31816	−	16.6184i	0.105920	−	0.759312i	0.967713	−	0.252054i	$-0.0811059\pi$
$480$	1.69112	−	0.537985i	0.0771888	−	0.0245555i
$481$	5.05440	+	15.8882i	0.230461	+	0.724440i
$482$	1.19739	−	15.5198i	0.0545396	−	0.706908i
$483$	0.0253299	+	1.64467i	0.00115255	+	0.0748351i
$484$	0.634802	+	0.420635i	0.0288546	+	0.0191198i
$485$	−30.1995	−	11.1676i	−1.37129	−	0.507096i
$486$	13.4968	−	0.832454i	0.612227	−	0.0377609i
$487$	12.0119	−	1.67558i	0.544309	−	0.0759279i	0.139317	−	0.990248i	$-0.455509\pi$
$487$	12.0119	−	1.67558i	0.544309	−	0.0759279i	0.404993	+	0.914320i	$0.367274\pi$
$488$	−42.9702	−	1.98663i	−1.94517	−	0.0899306i
$489$	1.05671	−	6.80743i	0.0477860	−	0.307842i
$490$	5.11708	−	12.0896i	0.231166	−	0.546152i
$491$	28.5947	+	26.0675i	1.29046	+	1.17641i	0.973682	+	0.227912i	$0.0731899\pi$
$491$	28.5947	+	26.0675i	1.29046	+	1.17641i	0.316780	+	0.948499i	$0.397398\pi$
$492$	0.344302	−	1.21010i	0.0155223	−	0.0545553i
$493$	8.76632	+	3.87071i	0.394815	+	0.174328i
$494$	−10.3721	−	0.639728i	−0.466662	−	0.0287827i
$495$	18.0319	−	1.39121i	0.810475	−	0.0625300i
$496$	0.755401	−	6.98028i	0.0339185	−	0.313424i
$497$	7.23456	−	0.334474i	0.324514	−	0.0150032i
$498$	−9.07427	+	1.69627i	−0.406628	+	0.0760119i
$499$	11.1535	−	9.55574i	0.499300	−	0.427774i	−0.364806	−	0.931083i	$-0.618865\pi$
$499$	11.1535	−	9.55574i	0.499300	−	0.427774i	0.864106	+	0.503310i	$0.167884\pi$
$500$	−2.76300	+	4.16979i	−0.123565	+	0.186479i
$501$	5.97414	+	2.97477i	0.266905	+	0.132903i
$502$	−5.03756	−	16.7224i	−0.224837	−	0.746359i
$503$	−3.94644	−	2.19815i	−0.175963	−	0.0980108i	0.396149	−	0.918186i	$-0.370346\pi$
$503$	−3.94644	−	2.19815i	−0.175963	−	0.0980108i	−0.572112	+	0.820175i	$0.693876\pi$
$504$	−0.431259	−	9.32799i	−0.0192098	−	0.415502i
$505$	−9.45863	−	4.35166i	−0.420903	−	0.193646i
$506$	7.22380	+	13.9642i	0.321137	+	0.620784i
$507$	−4.10767	+	1.88983i	−0.182428	+	0.0839302i
$508$	1.01853	+	0.794084i	0.0451902	+	0.0352318i
$509$	19.6596	−	4.94459i	0.871397	−	0.219165i	0.217786	−	0.975996i	$-0.430116\pi$
$509$	19.6596	−	4.94459i	0.871397	−	0.219165i	0.653610	+	0.756831i	$0.273254\pi$
$510$	−1.34465	−	3.17685i	−0.0595419	−	0.140673i
$511$	0.250957	−	0.712165i	0.0111017	−	0.0315043i
$512$	−16.9543	−	18.5980i	−0.749281	−	0.821922i
$513$	7.33603	−	10.7093i	0.323893	−	0.472826i
$514$	−0.0813287	+	5.28068i	−0.00358725	+	0.232921i
$515$	−12.2125	−	1.13165i	−0.538147	−	0.0498667i
$516$	0.834468	+	1.39527i	0.0367354	+	0.0614233i
$517$	18.1495	+	39.4493i	0.798216	+	1.73498i
$518$	3.50465	−	13.9344i	0.153985	−	0.612243i
$519$	−1.00511	−	2.09894i	−0.0441195	−	0.0921331i
$520$	1.20327	+	8.62598i	0.0527670	+	0.378274i
$521$	−34.9546	+	15.4340i	−1.53139	+	0.676175i	−0.986713	−	0.162471i	$-0.948053\pi$
$521$	−34.9546	+	15.4340i	−1.53139	+	0.676175i	−0.544677	+	0.838646i	$0.683348\pi$
$522$	−9.03837	+	3.34234i	−0.395599	+	0.146290i
$523$	22.0935	+	5.19634i	0.966080	+	0.227220i	0.681814	−	0.731525i	$-0.261191\pi$
$523$	22.0935	+	5.19634i	0.966080	+	0.227220i	0.284266	+	0.958745i	$0.408250\pi$
$524$	0.214771	−	3.48214i	0.00938232	−	0.152118i
$525$	−0.558247	−	0.631636i	−0.0243639	−	0.0275669i
$526$	24.2668	−	6.50227i	1.05808	−	0.283512i
$527$	8.22647	+	0.126697i	0.358351	+	0.00551902i
$528$	2.27153	+	4.07818i	0.0988557	+	0.177480i
$529$	−0.335516	+	10.8899i	−0.0145876	+	0.473476i
$530$	2.39423	−	1.80804i	0.103999	−	0.0785363i
$531$	6.96276	−	17.1826i	0.302158	−	0.745662i
$532$	−1.89153	−	1.33898i	−0.0820081	−	0.0580523i
$533$	10.1883	+	4.87886i	0.441306	+	0.211327i
$534$	−3.43517	−	4.54890i	−0.148654	−	0.196850i
$535$	−13.9521	−	4.20300i	−0.603200	−	0.181712i
$536$	−22.1193	+	14.1715i	−0.955410	+	0.612116i
$537$	−3.01186	+	1.27481i	−0.129972	+	0.0550122i
$538$	12.3190	−	2.49974i	0.531109	−	0.107771i
$539$	−20.4014	−	4.13980i	−0.878749	−	0.178314i
$540$	−1.70847	−	0.723134i	−0.0735209	−	0.0311187i
$541$	34.4430	−	5.89108i	1.48082	−	0.253277i	0.629120	−	0.777309i	$-0.283416\pi$
$541$	34.4430	−	5.89108i	1.48082	−	0.253277i	0.851699	+	0.524031i	$0.175572\pi$
$542$	0.710122	−	0.502685i	0.0305023	−	0.0215922i
$543$	−2.40985	−	10.2460i	−0.103416	−	0.439699i
$544$	5.42998	−	5.95641i	0.232809	−	0.255379i
$545$	7.35874	+	13.7037i	0.315214	+	0.587003i
$546$	−0.944911	−	0.117005i	−0.0404385	−	0.00500737i
$547$	−14.7802	−	5.20836i	−0.631958	−	0.222693i	−0.00283095	−	0.999996i	$-0.500901\pi$
$547$	−14.7802	−	5.20836i	−0.631958	−	0.222693i	−0.629127	+	0.777303i	$0.716587\pi$
$548$	0.278782	+	1.27296i	0.0119090	+	0.0543780i
$549$	29.0031	+	27.2693i	1.23782	+	1.16383i
$550$	−7.46753	−	3.02600i	−0.318417	−	0.129029i
$551$	−4.25174	+	13.3651i	−0.181130	+	0.569372i
$552$		−	4.57648i		−	0.194788i
$553$	−4.14568	−	1.31884i	−0.176292	−	0.0560826i
$554$	−17.4643	+	36.4700i	−0.741986	+	1.54946i
$555$	−6.23198	−	5.17497i	−0.264533	−	0.219665i
$556$	2.13459	−	1.32168i	0.0905266	−	0.0560517i
$557$	−15.8901	−	10.8850i	−0.673285	−	0.461211i	0.179304	−	0.983794i	$-0.442616\pi$
$557$	−15.8901	−	10.8850i	−0.673285	−	0.461211i	−0.852588	+	0.522583i	$0.824968\pi$
$558$	−6.02769	+	5.66737i	−0.255172	+	0.239919i
$559$	−13.6115	+	5.27311i	−0.575704	+	0.223029i
$560$	2.38096	−	5.39236i	0.100614	−	0.227869i
$561$	−4.51294	+	3.09143i	−0.190536	+	0.130520i
$562$	1.07251	−	4.89723i	0.0452411	−	0.206577i
$563$	−16.7987	+	27.1309i	−0.707982	+	1.14343i	0.275303	+	0.961357i	$0.411222\pi$
$563$	−16.7987	+	27.1309i	−0.707982	+	1.14343i	−0.983285	+	0.182072i	$0.941719\pi$
$564$	0.0995459	−	2.15314i	0.00419164	−	0.0906637i
$565$	4.15264	−	8.02738i	0.174703	−	0.337714i
$566$	6.51603	−	5.08012i	0.273889	−	0.213533i
$567$	−4.93604	+	6.33123i	−0.207294	+	0.265887i
$568$	−20.1406	+	0.620524i	−0.845079	+	0.0260366i
$569$	9.94796	+	9.64619i	0.417040	+	0.404389i	0.874643	−	0.484767i	$-0.161096\pi$
$569$	9.94796	+	9.64619i	0.417040	+	0.404389i	−0.457603	+	0.889157i	$0.651292\pi$
$570$	4.41080	−	2.45680i	0.184748	−	0.102904i
$571$	−8.52304	−	13.7652i	−0.356678	−	0.576055i	0.621604	−	0.783331i	$-0.286481\pi$
$571$	−8.52304	−	13.7652i	−0.356678	−	0.576055i	−0.978282	+	0.207277i	$0.933540\pi$
$572$	2.22118	−	0.782713i	0.0928721	−	0.0327269i
$573$	−4.21459	+	0.923009i	−0.176067	+	0.0385593i
$574$	−5.25165	−	8.19694i	−0.219200	−	0.342134i
$575$	3.88919	+	4.83311i	0.162190	+	0.201554i
$576$	0.770796	+	25.0180i	0.0321165	+	1.04242i
$577$	−9.25999	+	5.53812i	−0.385499	+	0.230555i	−0.692914	−	0.721021i	$-0.743673\pi$
$577$	−9.25999	+	5.53812i	−0.385499	+	0.230555i	0.307415	+	0.951576i	$0.400536\pi$
$578$	4.59705	+	3.47153i	0.191212	+	0.144397i
$579$	−0.548950	+	0.682183i	−0.0228136	+	0.0283505i
$580$	1.99279	+	0.215659i	0.0827463	+	0.00895474i
$581$	9.48768	−	15.8638i	0.393615	−	0.658143i
$582$	−5.78083	+	7.90531i	−0.239623	+	0.327686i
$583$	−3.56478	−	3.15059i	−0.147638	−	0.130484i
$584$	−0.728665	+	1.97046i	−0.0301524	+	0.0815382i
$585$	4.34820	−	6.78680i	0.179776	−	0.280600i
$586$	23.0293	−	2.49221i	0.951331	−	0.102952i
$587$	15.2648	−	33.1791i	0.630047	−	1.36945i	−0.282020	−	0.959409i	$-0.591004\pi$
$587$	15.2648	−	33.1791i	0.630047	−	1.36945i	0.912067	−	0.410041i	$-0.134486\pi$
$588$	0.805025	+	0.647802i	0.0331987	+	0.0267149i
$589$	1.11104	+	11.9900i	0.0457796	+	0.494041i
$590$	11.1660	−	9.86865i	0.459698	−	0.406286i
$591$	−0.705249	−	1.82046i	−0.0290101	−	0.0748836i
$592$	−8.12586	+	30.3261i	−0.333971	+	1.24640i
$593$	−9.97732	+	5.35771i	−0.409719	+	0.220015i	−0.664986	−	0.746856i	$-0.731562\pi$
$593$	−9.97732	+	5.35771i	−0.409719	+	0.220015i	0.255266	+	0.966871i	$0.417837\pi$
$594$	2.26073	−	11.1411i	0.0927588	−	0.457125i
$595$	6.54941	+	2.19514i	0.268500	+	0.0899920i
$596$	4.29865	+	2.22373i	0.176080	+	0.0910877i
$597$	1.28214	−	0.613976i	0.0524746	−	0.0251284i
$598$	6.90660	+	1.18130i	0.282432	+	0.0483068i
$599$	21.7071	+	13.9074i	0.886927	+	0.568241i	0.902043	−	0.431645i	$-0.142067\pi$
$599$	21.7071	+	13.9074i	0.886927	+	0.568241i	−0.0151162	+	0.999886i	$0.504812\pi$
$600$	1.52595	+	1.78110i	0.0622968	+	0.0727132i
$601$	1.81134	−	1.04578i	0.0738861	−	0.0426581i	−0.462602	−	0.886566i	$-0.653084\pi$
$601$	1.81134	−	1.04578i	0.0738861	−	0.0426581i	0.536488	+	0.843908i	$0.319751\pi$
$602$	12.3655	+	2.31151i	0.503979	+	0.0942100i
$603$	24.0783	+	3.35878i	0.980544	+	0.136780i
$604$	4.48116	+	0.345732i	0.182336	+	0.0140676i
$605$	0.610407	−	3.26539i	0.0248166	−	0.132757i
$606$	−2.06039	+	2.40490i	−0.0836977	+	0.0976924i
$607$	14.9708	−	4.50989i	0.607646	−	0.183051i	0.0302873	−	0.999541i	$-0.490358\pi$
$607$	14.9708	−	4.50989i	0.607646	−	0.183051i	0.577359	+	0.816490i	$0.304083\pi$
$608$	9.52202	+	6.96306i	0.386169	+	0.282389i
$609$	−0.464203	+	1.19825i	−0.0188105	+	0.0485554i
$610$	11.0983	+	30.0120i	0.449357	+	1.21515i
$611$	18.9049	+	4.14025i	0.764812	+	0.167496i
$612$	−4.04631	+	0.501041i	−0.163562	+	0.0202534i
$613$	6.18033	+	8.73069i	0.249621	+	0.352629i	0.921736	−	0.387817i	$-0.126771\pi$
$613$	6.18033	+	8.73069i	0.249621	+	0.352629i	−0.672115	+	0.740447i	$0.734614\pi$
$614$	10.6999	+	15.1153i	0.431813	+	0.610004i
$615$	−5.44670	+	0.674447i	−0.219632	+	0.0271963i
$616$	−11.6264	−	2.54622i	−0.468441	−	0.102590i
$617$	3.33431	+	9.01666i	0.134234	+	0.362997i	0.987313	−	0.158785i	$-0.0507576\pi$
$617$	3.33431	+	9.01666i	0.134234	+	0.362997i	−0.853079	+	0.521782i	$0.825267\pi$
$618$	−1.34761	+	3.47857i	−0.0542086	+	0.139929i
$619$	4.86484	+	3.55746i	0.195535	+	0.142986i	0.683696	−	0.729767i	$-0.260371\pi$
$619$	4.86484	+	3.55746i	0.195535	+	0.142986i	−0.488161	+	0.872753i	$0.662332\pi$
$620$	1.64778	−	0.496387i	0.0661764	−	0.0199354i
$621$	−5.69467	+	6.64685i	−0.228519	+	0.266729i
$622$	0.377970	−	2.02196i	0.0151552	−	0.0810733i
$623$	11.3800	+	0.877997i	0.455932	+	0.0351762i
$624$	2.06051	+	0.287429i	0.0824865	+	0.0115064i
$625$	12.6857	+	2.37137i	0.507429	+	0.0948550i
$626$	−9.32382	+	5.38311i	−0.372655	+	0.215152i
$627$	−5.20888	−	6.07983i	−0.208023	−	0.242805i
$628$	−7.06482	−	4.52632i	−0.281917	−	0.180620i
$629$	−36.2640	−	6.20255i	−1.44594	−	0.247312i
$630$	−6.26494	+	3.00007i	−0.249601	+	0.119526i
$631$	−40.2191	−	20.8057i	−1.60110	−	0.828262i	−0.999567	−	0.0294109i	$-0.990637\pi$
$631$	−40.2191	−	20.8057i	−1.60110	−	0.828262i	−0.601529	−	0.798851i	$-0.705442\pi$
$632$	11.4766	+	3.84657i	0.456514	+	0.153008i
$633$	1.81998	−	8.96906i	0.0723377	−	0.356488i
$634$	1.03317	−	0.554798i	0.0410322	−	0.0220338i
$635$	1.45816	−	5.44193i	0.0578654	−	0.215957i
$636$	0.0853067	+	0.220202i	0.00338263	+	0.00873157i
$637$	−6.95171	+	6.14400i	−0.275437	+	0.243434i
$638$	1.13329	+	12.2302i	0.0448674	+	0.484196i
$639$	14.5283	+	11.6909i	0.574731	+	0.462484i
$640$	−4.98123	+	10.8271i	−0.196901	+	0.427977i
$641$	−26.4747	+	2.86508i	−1.04569	+	0.113164i	−0.614356	−	0.789029i	$-0.710584\pi$
$641$	−26.4747	+	2.86508i	−1.04569	+	0.113164i	−0.431333	+	0.902193i	$0.641957\pi$
$642$	−2.39093	+	3.73183i	−0.0943623	+	0.147284i
$643$	−8.51797	+	23.0343i	−0.335916	+	0.908385i	0.652659	+	0.757652i	$0.273654\pi$
$643$	−8.51797	+	23.0343i	−0.335916	+	0.908385i	−0.988575	+	0.150733i	$0.951837\pi$
$644$	1.17086	+	1.03482i	0.0461385	+	0.0407777i
$645$	4.18626	−	5.72472i	0.164834	−	0.225411i
$646$	11.7699	−	19.6797i	0.463079	−	0.774289i
$647$	8.87691	+	0.960653i	0.348987	+	0.0377672i	0.280415	−	0.959879i	$-0.409528\pi$
$647$	8.87691	+	0.960653i	0.348987	+	0.0377672i	0.0685727	+	0.997646i	$0.478155\pi$
$648$	14.0031	−	17.4017i	0.550094	−	0.683604i
$649$	−18.8574	−	14.2405i	−0.740219	−	0.558987i
$650$	−3.08183	+	1.84315i	−0.120879	+	0.0722943i
$651$	0.0339752	+	1.10275i	0.00133159	+	0.0432200i
$652$	−4.10290	−	5.09869i	−0.160682	−	0.199680i
$653$	16.9466	+	26.4508i	0.663172	+	1.03510i	0.995757	+	0.0920251i	$0.0293340\pi$
$653$	16.9466	+	26.4508i	0.663172	+	1.03510i	−0.332585	+	0.943073i	$0.607921\pi$
$654$	4.62155	−	1.01213i	0.180717	−	0.0395776i
$655$	−14.3538	+	5.05809i	−0.560850	+	0.197636i
$656$	11.1980	+	18.0854i	0.437210	+	0.706118i
$657$	1.69855	−	0.946086i	0.0662668	−	0.0369103i
$658$	−11.9734	−	11.6102i	−0.466774	−	0.452614i
$659$	18.3972	−	0.566811i	0.716652	−	0.0220798i	0.329578	−	0.944128i	$-0.393094\pi$
$659$	18.3972	−	0.566811i	0.716652	−	0.0220798i	0.387074	+	0.922049i	$0.373486\pi$
$660$	−0.703516	+	0.902367i	−0.0273843	+	0.0351246i
$661$	20.3960	−	15.9014i	0.793314	−	0.618494i	−0.134765	−	0.990878i	$-0.543028\pi$
$661$	20.3960	−	15.9014i	0.793314	−	0.618494i	0.928079	+	0.372383i	$0.121459\pi$
$662$	−15.1815	+	29.3471i	−0.590047	+	1.14061i
$663$	−0.112593	+	2.43534i	−0.00437274	+	0.0945809i
$664$	−27.0740	+	43.7260i	−1.05068	+	1.69690i
$665$	−2.16277	+	9.87550i	−0.0838685	+	0.382955i
$666$	30.5223	−	20.9083i	1.18272	−	0.810179i
$667$	3.81977	−	8.65095i	0.147902	−	0.334966i
$668$	5.91196	−	2.29031i	0.228741	−	0.0886146i
$669$	−1.39760	+	1.31405i	−0.0540343	+	0.0508043i
$670$	16.1215	+	11.0435i	0.622826	+	0.426646i
$671$	43.1402	−	26.7113i	1.66541	−	1.03118i
$672$	0.831507	+	0.690475i	0.0320761	+	0.0266356i
$673$	−17.5013	+	36.5473i	−0.674626	+	1.40879i	0.225969	+	0.974135i	$0.427445\pi$
$673$	−17.5013	+	36.5473i	−0.674626	+	1.40879i	−0.900595	+	0.434660i	$0.856869\pi$
$674$	−9.98564	−	3.17666i	−0.384632	−	0.122360i
$675$		−	4.48566i		−	0.172653i
$676$	−1.30218	+	4.09332i	−0.0500839	+	0.157436i
$677$	−5.13197	−	2.07958i	−0.197238	−	0.0799248i	0.274807	−	0.961499i	$-0.411386\pi$
$677$	−5.13197	−	2.07958i	−0.197238	−	0.0799248i	−0.472045	+	0.881574i	$0.656484\pi$
$678$	−2.00275	−	1.88303i	−0.0769153	−	0.0723175i
$679$	−4.19520	−	19.1559i	−0.160997	−	0.735135i
$680$	−18.1261	−	6.38739i	−0.695104	−	0.244945i
$681$	11.7240	+	1.45174i	0.449264	+	0.0556309i
$682$	4.98892	+	9.29055i	0.191036	+	0.355754i
$683$	−12.8412	+	14.0861i	−0.491355	+	0.538991i	−0.933796	−	0.357807i	$-0.883525\pi$
$683$	−12.8412	+	14.0861i	−0.491355	+	0.538991i	0.442441	+	0.896798i	$0.354113\pi$
$684$	−1.36621	−	5.80875i	−0.0522382	−	0.222103i
$685$	4.63976	−	3.28442i	0.177276	−	0.125491i
$686$	17.3813	−	2.97288i	0.663622	−	0.113505i
$687$	5.16838	+	2.18759i	0.197186	+	0.0834617i
$688$	−26.9384	−	5.46628i	−1.02702	−	0.208400i
$689$	−2.07795	+	0.421653i	−0.0791635	+	0.0160637i
$690$	−3.13504	+	1.32695i	−0.119349	+	0.0505161i
$691$	18.6501	−	11.9489i	0.709485	−	0.454556i	−0.134507	−	0.990913i	$-0.542945\pi$
$691$	18.6501	−	11.9489i	0.709485	−	0.454556i	0.843991	+	0.536357i	$0.180200\pi$
$692$	−2.11685	−	0.637693i	−0.0804707	−	0.0242415i
$693$	6.63785	+	8.78993i	0.252151	+	0.333902i
$694$	−27.2551	−	13.0516i	−1.03459	−	0.495431i
$695$	−8.93908	−	6.32784i	−0.339079	−	0.240029i
$696$	1.34273	−	3.31358i	0.0508961	−	0.125601i
$697$	−19.8919	+	15.0217i	−0.753459	+	0.568986i
$698$	−0.158663	+	5.14977i	−0.00600547	+	0.194922i
$699$	4.57056	+	8.20573i	0.172875	+	0.310369i
$700$	−0.800727	−	0.0123321i	−0.0302647	−	0.000466111i
$701$	−30.7923	+	8.25077i	−1.16301	+	0.311627i	−0.788167	−	0.615462i	$-0.788970\pi$
$701$	−30.7923	+	8.25077i	−1.16301	+	0.311627i	−0.374841	+	0.927089i	$0.622303\pi$
$702$	−3.35521	−	3.79630i	−0.126634	−	0.143282i
$703$	3.31477	−	53.7433i	0.125019	−	2.02697i
$704$	31.0551	+	7.30410i	1.17043	+	0.275284i
$705$	−8.81899	+	3.26121i	−0.332142	+	0.122824i
$706$	−6.79135	+	2.99867i	−0.255596	+	0.112857i
$707$	−0.876058	−	6.28026i	−0.0329476	−	0.236193i
$708$	0.506594	+	1.05790i	0.0190390	+	0.0397583i
$709$	4.88243	−	19.4124i	0.183363	−	0.729050i	−0.806999	−	0.590552i	$-0.798910\pi$
$709$	4.88243	−	19.4124i	0.183363	−	0.729050i	0.990363	−	0.138497i	$-0.0442273\pi$
$710$	6.26483	+	13.6170i	0.235115	+	0.511038i
$711$	−5.74961	−	9.61361i	−0.215627	−	0.360538i
$712$	−31.6211	−	2.93013i	−1.18505	−	0.109811i
$713$	0.125030	−	8.11821i	0.00468241	−	0.304029i
$714$	1.18735	−	1.73331i	0.0444353	−	0.0648675i
$715$	−6.92115	−	7.59214i	−0.258836	−	0.283930i
$716$	−1.03263	+	2.93039i	−0.0385912	+	0.109514i
$717$	−2.61219	−	6.17154i	−0.0975540	−	0.230480i
$718$	19.3531	−	4.86751i	0.722252	−	0.181654i
$719$	−19.8437	−	15.4708i	−0.740046	−	0.576964i	0.172952	−	0.984930i	$-0.444670\pi$
$719$	−19.8437	−	15.4708i	−0.740046	−	0.576964i	−0.912997	+	0.407966i	$0.866238\pi$
$720$	13.7886	−	6.34378i	0.513872	−	0.236419i
$721$	−3.43211	−	6.63454i	−0.127818	−	0.247083i
$722$	8.73156	+	4.01716i	0.324955	+	0.149503i
$723$	−0.246835	−	5.33896i	−0.00917989	−	0.198558i
$724$	−8.73562	−	4.86571i	−0.324657	−	0.180833i
$725$	1.39792	+	4.64047i	0.0519175	+	0.172343i
$726$	−0.904481	−	0.450378i	−0.0335684	−	0.0167151i
$727$	−19.1016	+	28.8272i	−0.708439	+	1.06914i	0.285411	+	0.958405i	$0.407870\pi$
$727$	−19.1016	+	28.8272i	−0.708439	+	1.06914i	−0.993850	+	0.110736i	$0.964679\pi$
$728$	−4.02818	+	3.45113i	−0.149294	+	0.127907i
$729$	−17.1084	+	3.19812i	−0.633645	+	0.118449i
$730$	1.56111	−	0.0721743i	0.0577791	−	0.00267129i
$731$	3.46557	−	32.0236i	0.128179	−	1.18443i
$732$	−2.51113	+	0.193740i	−0.0928142	+	0.00716083i
$733$	46.8107	+	2.88719i	1.72899	+	0.106641i	0.895265	−	0.445534i	$-0.146986\pi$
$733$	46.8107	+	2.88719i	1.72899	+	0.106641i	0.833728	+	0.552175i	$0.186202\pi$
$734$	−30.4079	−	13.4264i	−1.12237	−	0.495577i
$735$	1.23355	−	4.33548i	0.0455002	−	0.159917i
$736$	−5.87802	−	5.35852i	−0.216667	−	0.197518i
$737$	12.0782	−	28.5359i	0.444907	−	1.05113i
$738$	3.84497	−	24.7697i	0.141535	−	0.911786i
$739$	53.4455	+	2.47094i	1.96603	+	0.0908949i	0.991225	−	0.132182i	$-0.0421983\pi$
$739$	53.4455	+	2.47094i	1.96603	+	0.0908949i	0.974801	+	0.223077i	$0.0716101\pi$
$740$	−7.62165	+	1.06317i	−0.280177	+	0.0390831i
$741$	−3.56132	+	0.219655i	−0.130828	+	0.00806922i
$742$	1.71382	+	0.633760i	0.0629162	+	0.0232661i
$743$	26.4868	+	17.5508i	0.971707	+	0.643876i	0.934700	−	0.355439i	$-0.115669\pi$
$743$	26.4868	+	17.5508i	0.971707	+	0.643876i	0.0370071	+	0.999315i	$0.488218\pi$
$744$	−0.0472700	−	3.06924i	−0.00173300	−	0.112524i
$745$	1.62405	−	21.0499i	0.0595006	−	0.771209i
$746$	−5.51947	−	17.3501i	−0.202082	−	0.635233i
$747$	45.3557	−	14.4287i	1.65948	−	0.527918i
$748$	−0.717960	+	5.14688i	−0.0262512	+	0.188189i
$749$	−2.42862	−	8.53571i	−0.0887398	−	0.311888i
$750$	2.95837	−	5.94122i	0.108025	−	0.216943i
$751$	−22.9669	+	25.9863i	−0.838075	+	0.948252i	−0.999252	−	0.0386735i	$-0.987687\pi$
$751$	−22.9669	+	25.9863i	−0.838075	+	0.948252i	0.161177	+	0.986926i	$0.448471\pi$
$752$	25.7690	+	25.7690i	0.939699	+	0.939699i
$753$	−2.42216	−	5.48568i	−0.0882686	−	0.199909i
$754$	4.65410	+	2.88170i	0.169492	+	0.104945i
$755$	−6.23068	−	18.5898i	−0.226758	−	0.676553i
$756$	−0.190488	−	1.11371i	−0.00692799	−	0.0405054i
$757$	−21.7905	+	5.12509i	−0.791991	+	0.186275i	−0.605146	−	0.796115i	$-0.706885\pi$
$757$	−21.7905	+	5.12509i	−0.791991	+	0.186275i	−0.186845	+	0.982389i	$0.559826\pi$
$758$	15.3375	−	10.1630i	0.557085	−	0.369138i
$759$	3.05075	+	4.45355i	0.110735	+	0.161653i
$760$	6.43984	−	27.3805i	0.233598	−	0.993196i
$761$	1.76166	+	4.34741i	0.0638602	+	0.157594i	0.955373	−	0.295402i	$-0.0954535\pi$
$761$	1.76166	+	4.34741i	0.0638602	+	0.157594i	−0.891513	+	0.452995i	$0.850355\pi$
$762$	−1.47066	−	0.879559i	−0.0532765	−	0.0318631i
$763$	−4.60972	+	8.27604i	−0.166883	+	0.299613i
$764$	−2.04937	+	3.54962i	−0.0741437	+	0.128421i
$765$	8.89297	+	15.4031i	0.321526	+	0.556899i
$766$	6.20594	−	0.0955788i	0.224230	−	0.00345340i
$767$	−10.1294	+	2.88206i	−0.365752	+	0.104065i
$768$	−3.09677	−	2.65315i	−0.111745	−	0.0957374i
$769$	−10.7246	−	6.19186i	−0.386740	−	0.223284i	0.294007	−	0.955803i	$-0.405011\pi$
$769$	−10.7246	−	6.19186i	−0.386740	−	0.223284i	−0.680746	+	0.732519i	$0.738344\pi$
$770$	1.62682	+	8.70274i	0.0586267	+	0.313625i
$771$	0.195102	+	1.80284i	0.00702644	+	0.0649278i
$772$	0.127598	+	0.821998i	0.00459234	+	0.0295843i
$773$	−18.4109	−	4.63053i	−0.662195	−	0.166549i	−0.101839	−	0.994801i	$-0.532473\pi$
$773$	−18.4109	−	4.63053i	−0.662195	−	0.166549i	−0.560356	+	0.828252i	$0.689336\pi$
$774$	19.9158	+	25.5450i	0.715857	+	0.918197i
$775$	2.65823	+	3.20118i	0.0954863	+	0.114990i
$776$	10.8501	+	53.4705i	0.389497	+	1.91948i
$777$	0.606267	−	4.89609i	0.0217497	−	0.175646i
$778$	−40.5734	+	20.2032i	−1.45463	+	0.724318i
$779$	−24.9898	−	26.5786i	−0.895354	−	0.952279i
$780$	0.131983	+	0.492566i	0.00472574	+	0.0176367i
$781$	19.1859	−	14.0298i	0.686525	−	0.502027i
$782$	−9.31769	+	12.3386i	−0.333200	+	0.441228i
$783$	−6.07338	+	3.14181i	−0.217045	+	0.112279i
$784$	−17.2637	+	2.67982i	−0.616559	+	0.0957077i
$785$	−6.17066	+	36.0775i	−0.220240	+	1.28766i
$786$	0.284966	+	4.62024i	0.0101644	+	0.164798i
$787$	−36.4661	+	36.4661i	−1.29988	+	1.29988i	−0.371405	+	0.928471i	$0.621124\pi$
$787$	−36.4661	+	36.4661i	−1.29988	+	1.29988i	−0.928471	+	0.371405i	$0.878876\pi$
$788$	−1.72943	−	0.669985i	−0.0616084	−	0.0238672i
$789$	7.99465	−	3.23960i	0.284617	−	0.115333i
$790$	−0.692609	−	8.97716i	−0.0246419	−	0.319393i
$791$	5.48090	−	0.507880i	0.194878	−	0.0180581i
$792$	−18.0896	−	24.7376i	−0.642785	−	0.879012i
$793$	2.08652	−	22.5172i	0.0740946	−	0.799608i
$794$	9.03263	−	9.31520i	0.320556	−	0.330584i
$795$	0.739555	−	0.717120i	0.0262293	−	0.0254336i
$796$	0.389537	−	1.29309i	0.0138068	−	0.0458323i
$797$	−12.8120	+	13.6266i	−0.453825	+	0.482679i	−0.914325	−	0.404981i	$-0.867278\pi$
$797$	−12.8120	+	13.6266i	−0.453825	+	0.482679i	0.460500	+	0.887660i	$0.347670\pi$
$798$	2.70905	+	1.45473i	0.0958994	+	0.0514969i
$799$	−27.2818	+	32.8543i	−0.965162	+	1.16230i
$800$	4.07435	+	0.125530i	0.144050	+	0.00443814i
$801$	20.4589	+	21.0989i	0.722879	+	0.745494i
$802$	−10.7557	+	8.65508i	−0.379797	+	0.305621i
$803$	−0.604446	−	2.40327i	−0.0213304	−	0.0848094i
$804$	−1.18331	+	0.982606i	−0.0417320	+	0.0346538i
$805$	2.16625	−	6.46322i	0.0763503	−	0.227798i
$806$	4.64415	+	0.720906i	0.163583	+	0.0253928i
$807$	4.09227	−	1.37159i	0.144055	−	0.0482822i
$808$	2.16807	+	17.5089i	0.0762726	+	0.615962i
$809$	−17.1896	−	25.9418i	−0.604356	−	0.912064i	0.395624	−	0.918412i	$-0.370528\pi$
$809$	−17.1896	−	25.9418i	−0.604356	−	0.912064i	−0.999980	+	0.00634834i	$0.997979\pi$
$810$	−15.9809	−	4.54697i	−0.561513	−	0.159764i
$811$	16.5431	+	4.43271i	0.580907	+	0.155653i	0.537294	−	0.843395i	$-0.319447\pi$
$811$	16.5431	+	4.43271i	0.580907	+	0.155653i	0.0436127	+	0.999049i	$0.486113\pi$
$812$	0.544143	+	1.09279i	0.0190957	+	0.0383493i
$813$	0.220766	−	0.201255i	0.00774261	−	0.00705832i
$814$	−15.6723	−	44.4748i	−0.549315	−	1.55884i
$815$	−13.5063	+	25.1520i	−0.473106	+	0.881035i
$816$	−2.65245	+	3.74700i	−0.0928542	+	0.131171i
$817$	47.1422			1.64930
$818$	23.7510	+	9.25881i	0.830435	+	0.323727i
$819$	4.90897			0.171533
$820$	−3.01244	+	4.25554i	−0.105199	+	0.148610i
$821$	7.92407	−	14.7565i	0.276552	−	0.515005i	−0.704265	−	0.709937i	$-0.748723\pi$
$821$	7.92407	−	14.7565i	0.276552	−	0.515005i	0.980817	+	0.194932i	$0.0624487\pi$
$822$	−0.574654	−	1.63075i	−0.0200434	−	0.0568789i
$823$	−24.8007	+	22.6089i	−0.864500	+	0.788095i	−0.978686	−	0.205364i	$-0.934162\pi$
$823$	−24.8007	+	22.6089i	−0.864500	+	0.788095i	0.114186	+	0.993459i	$0.463574\pi$
$824$	9.26371	+	18.6040i	0.322717	+	0.648102i
$825$	−2.67227	−	0.716033i	−0.0930365	−	0.0249291i
$826$	8.72939	+	2.48373i	0.303734	+	0.0864199i
$827$	−4.83938	−	7.30336i	−0.168282	−	0.253963i	0.739733	−	0.672900i	$-0.234952\pi$
$827$	−4.83938	−	7.30336i	−0.168282	−	0.253963i	−0.908015	+	0.418937i	$0.862403\pi$
$828$	0.494447	+	3.99306i	0.0171832	+	0.138768i
$829$	−6.57600	+	2.20405i	−0.228394	+	0.0765499i	−0.429675	−	0.902984i	$-0.641372\pi$
$829$	−6.57600	+	2.20405i	−0.228394	+	0.0765499i	0.201281	+	0.979534i	$0.435490\pi$
$830$	37.8039	+	5.86825i	1.31219	+	0.203690i
$831$	−4.41219	+	13.1642i	−0.153057	+	0.456660i
$832$	10.9385	−	9.08320i	0.379224	−	0.314903i
$833$	−4.99348	−	19.8540i	−0.173014	−	0.687900i
$834$	−2.59528	+	2.08841i	−0.0898672	+	0.0723158i
$835$	−19.2532	−	19.8555i	−0.666284	−	0.687128i
$836$	−7.60212	−	0.234219i	−0.262925	−	0.00810063i
$837$	−3.75051	+	4.51657i	−0.129637	+	0.156115i
$838$	18.4106	+	9.88630i	0.635985	+	0.341517i
$839$	1.35579	−	1.44199i	0.0468070	−	0.0497829i	−0.704718	−	0.709488i	$-0.748926\pi$
$839$	1.35579	−	1.44199i	0.0468070	−	0.0497829i	0.751525	+	0.659705i	$0.229319\pi$
$840$	0.743355	−	2.46760i	0.0256482	−	0.0851404i
$841$	−15.5156	+	15.0449i	−0.535020	+	0.518790i
$842$	−29.3825	+	30.3017i	−1.01259	+	1.04426i
$843$	0.158826	−	1.71400i	0.00547025	−	0.0590334i
$844$	−5.13198	−	7.01801i	−0.176650	−	0.241570i
$845$	18.6581	−	1.72893i	0.641858	−	0.0594769i
$846$	−3.30343	−	42.8170i	−0.113574	−	1.47208i
$847$	1.87509	−	0.759824i	0.0644287	−	0.0261079i
$848$	−3.72303	−	1.44231i	−0.127850	−	0.0495292i
$849$	2.00601	−	2.00601i	0.0688461	−	0.0688461i
$850$	−0.487801	−	7.90885i	−0.0167314	−	0.271271i
$851$	−6.12092	+	35.7868i	−0.209823	+	1.22675i
$852$	−1.16583	+	0.180970i	−0.0399406	+	0.00619993i
$853$	−9.71910	+	5.02778i	−0.332776	+	0.172148i	−0.617724	−	0.786395i	$-0.711945\pi$
$853$	−9.71910	+	5.02778i	−0.332776	+	0.172148i	0.284948	+	0.958543i	$0.408024\pi$
$854$	−11.7442	+	15.5519i	−0.401879	+	0.532174i
$855$	−21.0122	+	15.3653i	−0.718602	+	0.525484i
$856$	6.39059	+	23.8500i	0.218426	+	0.815177i
$857$	16.6567	+	17.7157i	0.568982	+	0.605157i	0.947233	−	0.320546i	$-0.103866\pi$
$857$	16.6567	+	17.7157i	0.568982	+	0.605157i	−0.378251	+	0.925703i	$0.623474\pi$
$858$	−2.79718	+	1.39283i	−0.0954942	+	0.0475505i
$859$	3.02695	−	24.4450i	0.103278	−	0.834052i	−0.848910	−	0.528538i	$-0.822740\pi$
$859$	3.02695	−	24.4450i	0.103278	−	0.834052i	0.952188	−	0.305514i	$-0.0988283\pi$
$860$	−1.33984	−	6.60287i	−0.0456881	−	0.225156i
$861$	−2.13539	−	2.57155i	−0.0727738	−	0.0876381i
$862$	−11.7653	−	15.0908i	−0.400728	−	0.513996i
$863$	4.13061	+	1.03889i	0.140607	+	0.0353642i	0.313576	−	0.949563i	$-0.398473\pi$
$863$	4.13061	+	1.03889i	0.140607	+	0.0353642i	−0.172968	+	0.984927i	$0.555336\pi$
$864$	0.882196	+	5.68320i	0.0300129	+	0.193346i
$865$	1.03763	+	9.58824i	0.0352806	+	0.326010i
$866$	−6.41071	−	34.2942i	−0.217845	−	1.16537i
$867$	1.71294	+	0.988968i	0.0581746	+	0.0335871i
$868$	0.795935	+	0.681915i	0.0270158	+	0.0231457i
$869$	−13.7325	+	3.90723i	−0.465842	+	0.132544i
$870$	−2.65924	+	0.0409554i	−0.0901566	+	0.00138852i
$871$	−6.90501	−	11.9598i	−0.233967	−	0.405243i
$872$	13.1786	−	22.8261i	0.446285	−	0.772988i
$873$	24.5701	−	44.1119i	0.831573	−	1.49296i
$874$	−19.4208	−	11.6150i	−0.656917	−	0.392882i
$875$	4.99102	+	12.3168i	0.168727	+	0.416383i
$876$	−0.0281623	+	0.119739i	−0.000951517	+	0.00404560i
$877$	−31.4550	−	45.9187i	−1.06216	−	1.55056i	−0.813143	−	0.582064i	$-0.802245\pi$
$877$	−31.4550	−	45.9187i	−1.06216	−	1.55056i	−0.249018	−	0.968499i	$-0.580108\pi$
$878$	−8.88221	+	5.88556i	−0.299760	+	0.198628i
$879$	7.74216	−	1.82094i	0.261137	−	0.0614188i
$880$	−3.26146	−	19.0686i	−0.109944	−	0.642801i
$881$	−11.5784	−	34.5452i	−0.390086	−	1.16386i	−0.943620	−	0.331032i	$-0.892603\pi$
$881$	−11.5784	−	34.5452i	−0.390086	−	1.16386i	0.553534	−	0.832827i	$-0.313279\pi$
$882$	17.5035	+	10.8377i	0.589374	+	0.364925i
$883$	−14.6226	−	33.1170i	−0.492089	−	1.11448i	−0.971533	−	0.236903i	$-0.923868\pi$
$883$	−14.6226	−	33.1170i	−0.492089	−	1.11448i	0.479444	−	0.877572i	$-0.340838\pi$
$884$	1.63769	+	1.63769i	0.0550815	+	0.0550815i
$885$	3.38846	−	3.83392i	0.113902	−	0.128876i
$886$	8.65789	−	17.3874i	0.290867	−	0.584141i
$887$	−3.36486	−	11.8263i	−0.112981	−	0.397087i	0.884620	−	0.466313i	$-0.154418\pi$
$887$	−3.36486	−	11.8263i	−0.112981	−	0.397087i	−0.997601	+	0.0692254i	$0.977947\pi$
$888$	−1.89638	+	13.5947i	−0.0636384	+	0.456209i
$889$	3.26978	−	1.04019i	0.109665	−	0.0348869i
$890$	7.16130	+	22.5111i	0.240047	+	0.754574i
$891$	−2.02671	+	26.2689i	−0.0678973	+	0.880042i
$892$	0.0280640	+	1.82220i	0.000939654	+	0.0610118i
$893$	−52.1012	−	34.5235i	−1.74350	−	1.15528i
$894$	−6.02297	−	2.22726i	−0.201438	−	0.0744908i
$895$	13.5280	−	0.834376i	0.452190	−	0.0278901i
$896$	−7.18885	+	1.00280i	−0.240163	+	0.0335012i
$897$	2.40329	+	0.111111i	0.0802437	+	0.00370989i
$898$	−3.89929	+	25.1197i	−0.130121	+	0.838254i
$899$	2.47240	−	5.84127i	0.0824590	−	0.194817i
$900$	−1.52385	−	1.38917i	−0.0507951	−	0.0463058i
$901$	1.28039	−	4.50009i	0.0426559	−	0.149920i
$902$	−29.2268	−	12.9049i	−0.973146	−	0.429686i
$903$	4.31112	+	0.265901i	0.143465	+	0.00884862i
$904$	−15.2694	+	1.17807i	−0.507852	+	0.0391820i
$905$	−4.69311	+	43.3666i	−0.156004	+	1.44156i
$906$	−5.95708	+	0.275412i	−0.197911	+	0.00914996i
$907$	47.7577	−	8.92746i	1.58577	−	0.296432i	0.684275	−	0.729224i	$-0.260119\pi$
$907$	47.7577	−	8.92746i	1.58577	−	0.296432i	0.901494	+	0.432792i	$0.142472\pi$
$908$	8.52267	−	7.30177i	0.282835	−	0.242318i
$909$	9.01872	−	13.6106i	0.299132	−	0.451436i
$910$	3.53211	+	1.75878i	0.117088	+	0.0583030i
$911$	12.3903	+	41.1301i	0.410508	+	1.36270i	0.877982	+	0.478694i	$0.158890\pi$
$911$	12.3903	+	41.1301i	0.410508	+	1.36270i	−0.467474	+	0.884007i	$0.654836\pi$
$912$	−5.86981	−	3.26946i	−0.194369	−	0.108263i
$913$	−2.80168	−	60.5993i	−0.0927220	−	2.00555i
$914$	−28.1267	−	12.9403i	−0.930348	−	0.428028i
$915$	5.04813	+	9.75843i	0.166886	+	0.322604i
$916$	4.84362	−	2.22842i	0.160038	−	0.0736291i
$917$	−7.30983	−	5.69899i	−0.241392	−	0.188197i
$918$	10.8422	−	2.72692i	0.357846	−	0.0900018i
$919$	−8.08862	−	19.1101i	−0.266819	−	0.630385i	0.731877	−	0.681437i	$-0.238645\pi$
$919$	−8.08862	−	19.1101i	−0.266819	−	0.630385i	−0.998696	+	0.0510518i	$0.983743\pi$
$920$	−6.30333	+	17.8876i	−0.207815	+	0.589736i
$921$	4.28382	+	4.69912i	0.141157	+	0.154841i
$922$	22.8023	−	33.2873i	0.750954	−	1.09626i
$923$	0.163124	−	10.5917i	0.00536931	−	0.348630i
$924$	−0.693887	−	0.0642981i	−0.0228272	−	0.00211525i
$925$	−9.55034	−	15.9686i	−0.314013	−	0.525045i
$926$	−14.0537	−	30.5467i	−0.461834	−	1.00383i
$927$	4.69133	−	18.6527i	0.154084	−	0.612634i
$928$	−2.68377	−	5.60441i	−0.0880991	−	0.183974i
$929$	−7.25460	−	52.0065i	−0.238016	−	1.70628i	−0.622064	−	0.782966i	$-0.713706\pi$
$929$	−7.25460	−	52.0065i	−0.238016	−	1.70628i	0.384048	−	0.923313i	$-0.374530\pi$
$930$	−2.08883	+	0.922308i	−0.0684954	+	0.0302437i
$931$	28.1026	−	10.3922i	0.921026	−	0.340590i
$932$	8.68610	+	2.04295i	0.284523	+	0.0669191i
$933$	0.0434792	−	0.704939i	0.00142344	−	0.0230787i
$934$	16.0831	+	18.1974i	0.526255	+	0.595438i
$935$	21.8971	−	5.86732i	0.716112	−	0.191882i
$936$	−13.6565	−	0.210327i	−0.446378	−	0.00687475i
$937$	9.09985	+	16.3374i	0.297279	+	0.533718i	0.980506	−	0.196488i	$-0.0629536\pi$
$937$	9.09985	+	16.3374i	0.297279	+	0.533718i	−0.683227	+	0.730206i	$0.739424\pi$
$938$	−0.366501	+	11.8956i	−0.0119667	+	0.388407i
$939$	−2.94999	+	2.22773i	−0.0962693	+	0.0726992i
$940$	−3.35468	+	8.27864i	−0.109418	+	0.270019i
$941$	−22.8780	−	16.1950i	−0.745801	−	0.527942i	0.141047	−	0.990003i	$-0.454953\pi$
$941$	−22.8780	−	16.1950i	−0.745801	−	0.527942i	−0.886848	+	0.462061i	$0.847110\pi$
$942$	10.0408	+	4.80823i	0.327149	+	0.156661i
$943$	14.8240	+	19.6301i	0.482735	+	0.639244i
$944$	−18.9885	−	5.72019i	−0.618022	−	0.186176i
$945$	−4.15017	+	2.65895i	−0.135005	+	0.0864956i
$946$	38.0196	−	16.0923i	1.23612	−	0.523206i
$947$	49.5521	−	10.0550i	1.61023	−	0.326744i	0.691726	−	0.722160i	$-0.256851\pi$
$947$	49.5521	−	10.0550i	1.61023	−	0.326744i	0.918502	+	0.395416i	$0.129400\pi$
$948$	0.694539	+	0.140934i	0.0225576	+	0.00457733i
$949$	−1.01708	−	0.430491i	−0.0330157	−	0.0139743i
$950$	11.4311	−	1.95516i	0.370874	−	0.0634338i
$951$	0.328646	−	0.232643i	0.0106571	−	0.00754398i
$952$	−2.67982	−	11.3939i	−0.0868535	−	0.369278i
$953$	20.8036	−	22.8204i	0.673894	−	0.739227i	−0.302990	−	0.952994i	$-0.597985\pi$
$953$	20.8036	−	22.8204i	0.673894	−	0.739227i	0.976885	+	0.213767i	$0.0685733\pi$
$954$	2.22587	+	4.14510i	0.0720653	+	0.134203i
$955$	17.7444	+	2.19723i	0.574194	+	0.0711007i
$956$	−6.00460	−	2.11594i	−0.194203	−	0.0684343i
$957$	0.902218	+	4.11965i	0.0291646	+	0.133169i
$958$	15.4089	+	14.4878i	0.497838	+	0.468079i
$959$	3.20869	+	1.30023i	0.103614	+	0.0419866i
$960$	−2.09414	+	6.58281i	−0.0675882	+	0.212459i
$961$			25.5542i			0.824328i
$962$	−20.0270	−	6.37104i	−0.645695	−	0.205411i
$963$	9.86924	−	20.6096i	0.318032	−	0.664134i
$964$	−3.90623	−	3.24369i	−0.125811	−	0.104472i
$965$	3.08521	−	1.91028i	0.0993164	−	0.0614941i
$966$	−1.71050	−	1.17172i	−0.0550344	−	0.0376995i
$967$	10.8750	−	10.2250i	0.349718	−	0.328812i	−0.490115	−	0.871658i	$-0.663045\pi$
$967$	10.8750	−	10.2250i	0.349718	−	0.328812i	0.839833	+	0.542846i	$0.182653\pi$
$968$	−5.24896	+	2.03346i	−0.168708	+	0.0653578i
$969$	3.18025	−	7.20257i	0.102164	−	0.231380i
$970$	33.4831	−	22.9364i	1.07508	−	0.736445i
$971$	1.04834	−	4.78687i	0.0336428	−	0.153618i	−0.957003	−	0.290080i	$-0.906318\pi$
$971$	1.04834	−	4.78687i	0.0336428	−	0.153618i	0.990645	+	0.136462i	$0.0435731\pi$
$972$	2.32202	−	3.75019i	0.0744787	−	0.120287i
$973$	0.308054	−	6.66310i	0.00987575	−	0.213609i
$974$	−7.02414	+	13.5782i	−0.225068	+	0.435074i
$975$	−0.972376	+	0.758097i	−0.0311410	+	0.0242785i
$976$	26.1821	−	33.5826i	0.838070	−	1.07495i
$977$	46.5277	−	1.43350i	1.48855	−	0.0458618i	0.723721	−	0.690093i	$-0.242430\pi$
$977$	46.5277	−	1.43350i	1.48855	−	0.0458618i	0.764831	+	0.644231i	$0.222822\pi$
$978$	6.23397	+	6.04486i	0.199340	+	0.193293i
$979$	32.7250	−	18.2277i	1.04589	−	0.582560i
$980$	−2.25427	−	3.64077i	−0.0720101	−	0.116300i
$981$	−23.0059	+	8.10695i	−0.734520	+	0.258835i
$982$	−47.6435	+	10.4341i	−1.52037	+	0.332965i
$983$	18.2184	+	28.4358i	0.581077	+	0.906962i	0.999999	−	0.00105952i	$-0.000337255\pi$
$983$	18.2184	+	28.4358i	0.581077	+	0.906962i	−0.418923	+	0.908022i	$0.637592\pi$
$984$	5.83037	+	7.24542i	0.185865	+	0.230976i
$985$	0.249151	+	8.08677i	0.00793861	+	0.257666i
$986$	−10.3666	+	6.19992i	−0.330139	+	0.197446i
$987$	−4.56989	−	3.45102i	−0.145461	−	0.109847i
$988$	−2.12507	+	2.64083i	−0.0676075	+	0.0840160i
$989$	−31.6021	−	3.41996i	−1.00489	−	0.108748i
$990$	−11.7010	+	19.5646i	−0.371882	+	0.621804i
$991$	−18.7999	+	25.7089i	−0.597197	+	0.816670i	−0.994902	−	0.100843i	$-0.967846\pi$
$991$	−18.7999	+	25.7089i	−0.597197	+	0.816670i	0.397705	+	0.917513i	$0.369807\pi$
$992$	−3.99748	−	3.53301i	−0.126920	−	0.112173i
$993$	−3.93488	+	10.6407i	−0.124870	+	0.337673i
$994$	−4.92468	+	7.68658i	−0.156201	+	0.243804i
$995$	−5.85701	+	0.633842i	−0.185680	+	0.0200941i
$996$	−1.25856	+	2.73556i	−0.0398789	+	0.0866795i
$997$	0.594747	+	0.478591i	0.0188358	+	0.0151571i	0.636296	−	0.771445i	$-0.280466\pi$
$997$	0.594747	+	0.478591i	0.0188358	+	0.0151571i	−0.617460	+	0.786602i	$0.711838\pi$
$998$	1.70817	+	18.4341i	0.0540712	+	0.583521i
$999$	19.6707	−	17.3851i	0.622352	−	0.550041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.o.a.41.13	yes	2176
409.10	even	204	inner	409.2.o.a.10.13	✓	2176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.o.a.10.13	✓	2176	409.10	even	204	inner
409.2.o.a.41.13	yes	2176	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.o (of order \(204\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.728280 + 1.02881i) q^{2} +(-0.204754 + 0.381301i) q^{3} +(0.136650 + 0.387785i) q^{4} +(1.32548 - 1.20833i) q^{5} +(-0.243168 - 0.488347i) q^{6} +(1.05514 + 0.282723i) q^{7} +(-2.92323 - 0.831729i) q^{8} +(1.55363 + 2.34466i) q^{9} +(0.277826 + 2.24367i) q^{10} +(3.39914 - 1.13928i) q^{11} +(-0.175842 - 0.0272958i) q^{12} +(0.507747 - 1.51491i) q^{13} +(-1.05930 + 0.879633i) q^{14} +(0.189341 + 0.752815i) q^{15} +(2.34397 - 1.88618i) q^{16} +(2.45429 + 2.53107i) q^{17} +(-3.54369 - 0.109180i) q^{18} +(-3.29642 + 3.96972i) q^{19} +(0.649699 + 0.348881i) q^{20} +(-0.323846 + 0.344435i) q^{21} +(-1.30343 + 4.32679i) q^{22} +(2.49776 - 2.42199i) q^{23} +(0.915681 - 0.944327i) q^{24} +(-0.164519 + 1.77544i) q^{25} +(1.18877 + 1.62565i) q^{26} +(-2.50499 + 0.232121i) q^{27} +(0.0345488 + 0.447800i) q^{28} +(2.51910 - 1.02079i) q^{29} +(-0.912397 - 0.353465i) q^{30} +(1.65012 - 1.65012i) q^{31} +(-0.140736 - 2.28179i) q^{32} +(-0.261581 + 1.52937i) q^{33} +(-4.39141 + 0.681673i) q^{34} +(1.74018 - 0.900210i) q^{35} +(-0.696921 + 0.922872i) q^{36} +(-8.42337 + 6.15967i) q^{37} +(-1.68338 - 6.28246i) q^{38} +(0.473673 + 0.503788i) q^{39} +(-4.87967 + 2.42979i) q^{40} +(-0.868841 + 7.01658i) q^{41} +(-0.118508 - 0.584021i) q^{42} +(-5.83662 - 7.02877i) q^{43} +(0.906288 + 1.16245i) q^{44} +(4.89242 + 1.23049i) q^{45} +(0.672702 + 4.33362i) q^{46} +(1.30323 + 12.0425i) q^{47} +(0.239266 + 1.27996i) q^{48} +(-5.02880 - 2.90338i) q^{49} +(-1.70678 - 1.46228i) q^{50} +(-1.46763 + 0.417576i) q^{51} +(0.656843 - 0.0101162i) q^{52} +(-0.663532 - 1.14927i) q^{53} +(1.58552 - 2.74621i) q^{54} +(3.12886 - 5.61737i) q^{55} +(-2.84925 - 1.70405i) q^{56} +(-0.838703 - 2.06974i) q^{57} +(-0.784409 + 3.33510i) q^{58} +(-3.72508 - 5.43795i) q^{59} +(-0.266057 + 0.176296i) q^{60} +(13.7776 - 3.24046i) q^{61} +(0.495913 + 2.89942i) q^{62} +(0.976400 + 2.91318i) q^{63} +(7.56602 + 4.68468i) q^{64} +(-1.15751 - 2.62150i) q^{65} +(-1.38292 - 1.38292i) q^{66} +(5.72403 - 6.47653i) q^{67} +(-0.646133 + 1.29761i) q^{68} +(0.412080 + 1.44831i) q^{69} +(-0.341191 + 2.44592i) q^{70} +(6.31798 - 2.00989i) q^{71} +(-2.59148 - 8.14617i) q^{72} +(0.0531733 - 0.689199i) q^{73} +(-0.202557 - 13.1520i) q^{74} +(-0.643292 - 0.426261i) q^{75} +(-1.98985 - 0.735837i) q^{76} +(3.90866 - 0.241078i) q^{77} +(-0.863269 + 0.120421i) q^{78} +(-3.97834 - 0.183930i) q^{79} +(0.827739 - 5.33238i) q^{80} +(-2.86464 + 6.76797i) q^{81} +(-6.58598 - 6.00391i) q^{82} +(4.63084 - 16.2757i) q^{83} +(-0.177820 - 0.0785153i) q^{84} +(6.31148 + 0.389279i) q^{85} +(11.4820 - 0.885860i) q^{86} +(-0.126567 + 1.16955i) q^{87} +(-10.8840 + 0.503199i) q^{88} +(10.2709 - 1.91997i) q^{89} +(-4.82900 + 4.13723i) q^{90} +(0.964041 - 1.45488i) q^{91} +(1.28053 + 0.637630i) q^{92} +(0.291324 + 0.967063i) q^{93} +(-13.3385 - 7.42950i) q^{94} +(0.427419 + 9.24493i) q^{95} +(0.898866 + 0.413544i) q^{96} +(-8.24837 - 15.9447i) q^{97} +(6.64940 - 3.05921i) q^{98} +(7.95223 + 6.19982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2176 q - 62 q^{2} - 56 q^{3} - 196 q^{4} - 68 q^{5} - 76 q^{6} - 64 q^{7} - 68 q^{8} - 126 q^{9} - 50 q^{10} - 54 q^{11} - 32 q^{12} - 68 q^{13} - 56 q^{14} - 44 q^{15} + 48 q^{16} - 64 q^{17} - 26 q^{18}+ \cdots - 14 q^{99}+O(q^{100}) \) 2176 * q - 62 * q^2 - 56 * q^3 - 196 * q^4 - 68 * q^5 - 76 * q^6 - 64 * q^7 - 68 * q^8 - 126 * q^9 - 50 * q^10 - 54 * q^11 - 32 * q^12 - 68 * q^13 - 56 * q^14 - 44 * q^15 + 48 * q^16 - 64 * q^17 - 26 * q^18 - 70 * q^19 - 62 * q^20 - 36 * q^21 - 64 * q^22 - 62 * q^23 - 24 * q^24 - 232 * q^25 - 56 * q^26 - 68 * q^27 - 90 * q^28 - 90 * q^29 - 44 * q^30 - 70 * q^31 + 118 * q^32 - 94 * q^33 - 62 * q^34 - 72 * q^35 - 296 * q^36 - 76 * q^37 - 236 * q^38 + 162 * q^39 - 68 * q^40 + 336 * q^41 + 42 * q^42 - 60 * q^43 - 66 * q^44 - 68 * q^45 - 206 * q^46 - 94 * q^47 - 68 * q^48 - 162 * q^49 - 44 * q^50 - 68 * q^51 - 122 * q^52 - 218 * q^53 + 152 * q^54 + 190 * q^55 - 138 * q^56 - 166 * q^57 - 74 * q^59 + 16 * q^60 - 28 * q^61 - 60 * q^62 - 68 * q^63 + 504 * q^64 - 24 * q^65 + 34 * q^66 - 40 * q^67 + 44 * q^68 + 92 * q^69 - 224 * q^70 - 154 * q^71 - 26 * q^72 - 120 * q^73 - 80 * q^74 + 112 * q^75 - 50 * q^76 + 74 * q^77 + 300 * q^78 - 82 * q^79 - 100 * q^80 + 408 * q^81 - 56 * q^82 - 84 * q^83 + 876 * q^84 - 180 * q^85 + 196 * q^86 - 156 * q^87 - 380 * q^88 - 128 * q^89 + 58 * q^90 - 126 * q^91 + 272 * q^92 + 56 * q^93 - 80 * q^94 - 90 * q^95 - 264 * q^96 - 68 * q^97 - 62 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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