LMFDB - Embedded newform 409.2.o.a.10.13

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			10.13
Character	$\chi$	$=$	409.10
Dual form			409.2.o.a.41.13

$q$-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 $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{53}{204}\right)$

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	0.473179	−	0.880966i	$-0.343106\pi$
$2$	−0.728280	−	1.02881i	−0.514972	−	0.727479i	−0.988151	+	0.153487i	$0.950950\pi$
$3$	−0.204754	−	0.381301i	−0.118215	−	0.220144i	0.815002	−	0.579459i	$-0.196736\pi$
$3$	−0.204754	−	0.381301i	−0.118215	−	0.220144i	−0.933216	+	0.359315i	$0.883010\pi$
$4$	0.136650	−	0.387785i	0.0683251	−	0.193892i
$5$	1.32548	+	1.20833i	0.592771	+	0.540382i	0.913526	−	0.406780i	$-0.133348\pi$
$5$	1.32548	+	1.20833i	0.592771	+	0.540382i	−0.320755	+	0.947162i	$0.603937\pi$
$6$	−0.243168	+	0.488347i	−0.0992728	+	0.199367i
$7$	1.05514	−	0.282723i	0.398804	−	0.106859i	−0.0538423	−	0.998549i	$-0.517147\pi$
$7$	1.05514	−	0.282723i	0.398804	−	0.106859i	0.452646	+	0.891690i	$0.350480\pi$
$8$	−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	0.779821	−	0.626003i	$-0.215310\pi$
$11$	3.39914	+	1.13928i	1.02488	+	0.343505i	0.245059	+	0.969508i	$0.421193\pi$
$12$	−0.175842	+	0.0272958i	−0.0507613	+	0.00787961i
$13$	0.507747	+	1.51491i	0.140824	+	0.420160i	0.995006	−	0.0998126i	$-0.0318243\pi$
$13$	0.507747	+	1.51491i	0.140824	+	0.420160i	−0.854183	+	0.519973i	$0.825942\pi$
$14$	−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	−0.351362	−	0.936240i	$-0.614281\pi$
$17$	2.45429	−	2.53107i	0.595254	−	0.613876i	0.946616	+	0.322364i	$0.104478\pi$
$18$	−3.54369	+	0.109180i	−0.835256	+	0.0257339i
$19$	−3.29642	−	3.96972i	−0.756250	−	0.910717i	0.241975	−	0.970283i	$-0.422205\pi$
$19$	−3.29642	−	3.96972i	−0.756250	−	0.910717i	−0.998224	+	0.0595657i	$0.981028\pi$
$20$	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	0.909133	−	0.416507i	$-0.136746\pi$
$23$	2.49776	+	2.42199i	0.520820	+	0.505021i	−0.388313	+	0.921528i	$0.626942\pi$
$24$	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	0.597295	−	0.802022i	$-0.296242\pi$
$29$	2.51910	+	1.02079i	0.467786	+	0.189557i	−0.129509	+	0.991578i	$0.541340\pi$
$30$	−0.912397	+	0.353465i	−0.166580	+	0.0645335i
$31$	1.65012	+	1.65012i	0.296371	+	0.296371i	0.839591	−	0.543220i	$-0.182795\pi$
$31$	1.65012	+	1.65012i	0.296371	+	0.296371i	−0.543220	+	0.839591i	$0.682795\pi$
$32$	−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	−0.995815	−	0.0913966i	$-0.970867\pi$
$37$	−8.42337	−	6.15967i	−1.38479	−	1.01264i	−0.388980	−	0.921246i	$-0.627172\pi$
$38$	−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	−0.895312	−	0.445441i	$-0.853047\pi$
$41$	−0.868841	−	7.01658i	−0.135690	−	1.09581i	0.759621	−	0.650366i	$-0.225384\pi$
$42$	−0.118508	+	0.584021i	−0.0182862	+	0.0901164i
$43$	−5.83662	+	7.02877i	−0.890076	+	1.07188i	0.106908	+	0.994269i	$0.465905\pi$
$43$	−5.83662	+	7.02877i	−0.890076	+	1.07188i	−0.996984	+	0.0776084i	$0.975272\pi$
$44$	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	−0.370826	−	0.928702i	$-0.620925\pi$
$47$	1.30323	−	12.0425i	0.190095	−	1.75657i	0.560921	−	0.827870i	$-0.310447\pi$
$48$	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	−0.907992	−	0.418987i	$-0.862385\pi$
$53$	−0.663532	+	1.14927i	−0.0911431	+	0.157864i	0.816849	+	0.576851i	$0.195719\pi$
$54$	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	−0.987679	−	0.156491i	$-0.949982\pi$
$59$	−3.72508	+	5.43795i	−0.484965	+	0.707961i	0.502715	+	0.864452i	$0.332335\pi$
$60$	−0.266057	−	0.176296i	−0.0343478	−	0.0227597i
$61$	13.7776	+	3.24046i	1.76404	+	0.414899i	0.978887	−	0.204403i	$-0.0655252\pi$
$61$	13.7776	+	3.24046i	1.76404	+	0.414899i	0.785154	+	0.619301i	$0.212584\pi$
$62$	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	0.985993	−	0.166789i	$-0.0533398\pi$
$67$	5.72403	+	6.47653i	0.699301	+	0.791234i	−0.286692	+	0.958023i	$0.592555\pi$
$68$	−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	0.653610	−	0.756832i	$-0.273254\pi$
$71$	6.31798	+	2.00989i	0.749806	+	0.238530i	0.0961964	+	0.995362i	$0.469332\pi$
$72$	−2.59148	+	8.14617i	−0.305409	+	0.960036i
$73$	0.0531733	+	0.689199i	0.00622347	+	0.0806647i	0.999333	−	0.0365285i	$-0.0116300\pi$
$73$	0.0531733	+	0.689199i	0.00622347	+	0.0806647i	−0.993109	+	0.117193i	$0.962610\pi$
$74$	−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	−0.268808	−	0.963194i	$-0.586630\pi$
$79$	−3.97834	+	0.183930i	−0.447598	+	0.0206937i	−0.178789	+	0.983887i	$0.557218\pi$
$80$	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	0.610828	+	0.791763i	$0.290836\pi$
$83$	4.63084	+	16.2757i	0.508301	+	1.78649i	−0.102527	+	0.994730i	$0.532693\pi$
$84$	−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	0.697359	−	0.716722i	$-0.254359\pi$
$89$	10.2709	+	1.91997i	1.08872	+	0.203516i	0.391358	+	0.920239i	$0.372006\pi$
$90$	−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	−0.0531766	+	0.998585i	$0.516935\pi$
$97$	−8.24837	+	15.9447i	−0.837495	+	1.61894i	−0.784318	+	0.620359i	$0.786987\pi$
$98$	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	−0.994236	−	0.107213i	$-0.965807\pi$
$101$	−2.26268	+	5.34580i	−0.225145	+	0.531927i	0.769091	+	0.639140i	$0.220709\pi$
$102$	0.639236	+	1.81402i	0.0632938	+	0.179615i
$103$	−4.60684	+	5.05346i	−0.453925	+	0.497932i	−0.922771	−	0.385348i	$-0.874082\pi$
$103$	−4.60684	+	5.05346i	−0.453925	+	0.497932i	0.468846	+	0.883280i	$0.344670\pi$
$104$	−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	−0.990842	−	0.135023i	$-0.956889\pi$
$107$	−4.16995	+	6.97235i	−0.403124	+	0.674042i	0.587718	+	0.809066i	$0.300026\pi$
$108$	−0.432320	+	0.939677i	−0.0416000	+	0.0904205i
$109$	−2.11529	−	8.41037i	−0.202608	−	0.805567i	−0.983501	−	0.180902i	$-0.942098\pi$
$109$	−2.11529	−	8.41037i	−0.202608	−	0.805567i	0.780893	−	0.624665i	$-0.214765\pi$
$110$	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	0.559258	−	0.828993i	$-0.311086\pi$
$113$	4.72620	+	1.74772i	0.444604	+	0.164412i	−0.114655	+	0.993405i	$0.536576\pi$
$114$	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	0.651545	−	0.758610i	$-0.274121\pi$
$127$	2.64487	+	1.69453i	0.234694	+	0.150365i	−0.416851	+	0.908975i	$0.636866\pi$
$128$	−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	−0.703378	−	0.710816i	$-0.748326\pi$
$131$	−7.81408	+	3.30742i	−0.682719	+	0.288970i	0.0206583	+	0.999787i	$0.493424\pi$
$132$	−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	0.0126076	−	0.999921i	$-0.495987\pi$
$137$	3.14539	−	0.389484i	0.268729	−	0.0332758i	0.256121	+	0.966645i	$0.417555\pi$
$138$	−1.79015	+	0.630824i	−0.152388	+	0.0536993i
$139$	−1.30633	+	5.96490i	−0.110802	+	0.505936i	0.888124	+	0.459603i	$0.152008\pi$
$139$	−1.30633	+	5.96490i	−0.110802	+	0.505936i	−0.998926	+	0.0463327i	$0.985247\pi$
$140$	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	0.951391	−	0.307987i	$-0.0996552\pi$
$149$	8.57580	+	8.06316i	0.702557	+	0.660559i	−0.248834	+	0.968546i	$0.580047\pi$
$150$	0.907038	+	0.351388i	0.0740594	+	0.0286907i
$151$	4.41537	+	9.99987i	0.359318	+	0.813778i	0.998981	+	0.0451227i	$0.0143679\pi$
$151$	4.41537	+	9.99987i	0.359318	+	0.813778i	−0.639663	+	0.768655i	$0.720926\pi$
$152$	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	−0.999077	−	0.0429488i	$-0.986325\pi$
$157$	−16.0937	−	12.5472i	−1.28442	−	1.00138i	−0.285340	−	0.958426i	$-0.592107\pi$
$158$	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	−0.328054	−	0.944659i	$-0.606393\pi$
$163$	−15.0124	−	5.29017i	−1.17586	−	0.414358i	−0.847809	+	0.530301i	$0.822079\pi$
$164$	−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	0.783769	+	0.621053i	$0.213295\pi$
$167$	−0.474863	+	15.4128i	−0.0367460	+	1.19268i	−0.820515	+	0.571626i	$0.806313\pi$
$168$	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	0.669505	−	0.742808i	$-0.266506\pi$
$173$	−3.17394	−	4.34038i	−0.241310	−	0.329993i	−0.910815	+	0.412815i	$0.864546\pi$
$174$	−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	−0.381385	−	0.924416i	$-0.624553\pi$
$179$	5.88732	−	4.73751i	0.440039	−	0.354098i	0.821424	+	0.570319i	$0.193180\pi$
$180$	0.191383	−	2.06536i	0.0142649	−	0.153943i
$181$	−18.2228	−	16.1055i	−1.35449	−	1.19711i	−0.960593	−	0.277959i	$-0.910342\pi$
$181$	−18.2228	−	16.1055i	−1.35449	−	1.19711i	−0.393898	−	0.919154i	$-0.628874\pi$
$182$	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	−0.473645	−	0.880716i	$-0.657062\pi$
$191$	6.48588	−	7.57035i	0.469302	−	0.547771i	0.942946	+	0.332945i	$0.108042\pi$
$192$	−3.33544	−	1.92572i	−0.240715	−	0.138977i
$193$	1.98872	−	0.371757i	0.143151	−	0.0267596i	−0.111686	−	0.993744i	$-0.535625\pi$
$193$	1.98872	−	0.371757i	0.143151	−	0.0267596i	0.254837	+	0.966984i	$0.417978\pi$
$194$	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	0.644986	−	0.764194i	$-0.276863\pi$
$197$	−2.93485	−	3.42557i	−0.209099	−	0.244062i	−0.854086	+	0.520132i	$0.825883\pi$
$198$	−12.1699	−	3.66613i	−0.864877	−	0.260540i
$199$	−2.65134	+	1.93881i	−0.187948	+	0.137439i	−0.680235	−	0.732994i	$-0.738122\pi$
$199$	−2.65134	+	1.93881i	−0.187948	+	0.137439i	0.492286	+	0.870433i	$0.336161\pi$
$200$	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	−0.499141	−	0.866521i	$-0.666351\pi$
$211$	−20.2470	−	6.09933i	−1.39386	−	0.419895i	−0.894721	+	0.446626i	$0.852625\pi$
$212$	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	−0.173558	−	0.984824i	$-0.555526\pi$
$223$	4.20263	−	1.40858i	0.281429	−	0.0943255i	0.454987	+	0.890498i	$0.349644\pi$
$224$	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	0.0677892	+	0.997700i	$0.478405\pi$
$227$	−9.86034	+	25.4525i	−0.654454	+	1.68934i	−0.722243	+	0.691640i	$0.756889\pi$
$228$	0.688006	+	0.608067i	0.0455643	+	0.0402702i
$229$	−1.19648	+	12.9121i	−0.0790658	+	0.853256i	0.860175	+	0.509998i	$0.170354\pi$
$229$	−1.19648	+	12.9121i	−0.0790658	+	0.853256i	−0.939241	+	0.343258i	$0.888470\pi$
$230$	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	0.975688	+	0.219166i	$0.0703335\pi$
$233$	11.7076	+	18.2737i	0.766993	+	1.19715i	−0.208694	+	0.977981i	$0.566921\pi$
$234$	−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	0.360380	−	0.932805i	$-0.382647\pi$
$239$	−9.70751	−	12.0636i	−0.627927	−	0.780327i	−0.988307	+	0.152479i	$0.951274\pi$
$240$	1.86376	−	1.40744i	0.120305	−	0.0908501i
$241$	−10.5983	−	6.33850i	−0.682694	−	0.408299i	0.129584	−	0.991568i	$-0.458636\pi$
$241$	−10.5983	−	6.33850i	−0.682694	−	0.408299i	−0.812278	+	0.583270i	$0.801773\pi$
$242$	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	0.440389	−	0.897807i	$-0.354841\pi$
$251$	−8.51907	−	10.9270i	−0.537719	−	0.689707i	−0.978108	+	0.208100i	$0.933272\pi$
$252$	−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	0.668100	−	0.744072i	$-0.267108\pi$
$257$	3.45663	+	2.36785i	0.215619	+	0.147702i	−0.452481	+	0.891774i	$0.649461\pi$
$258$	−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	−0.976752	−	0.214372i	$-0.931230\pi$
$263$	−15.3336	+	12.7328i	−0.945509	+	0.785140i	0.0312437	+	0.999512i	$0.490053\pi$
$264$	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	−0.874061	−	0.485817i	$-0.838522\pi$
$269$	−7.26531	+	6.83100i	−0.442974	+	0.416494i	0.431087	+	0.902310i	$0.358130\pi$
$270$	−1.21675	+	5.55587i	−0.0740493	+	0.338119i
$271$	−0.650999	+	0.229403i	−0.0395454	+	0.0139352i	−0.352054	−	0.935980i	$-0.614517\pi$
$271$	−0.650999	+	0.229403i	−0.0395454	+	0.0139352i	0.312509	+	0.949915i	$0.398831\pi$
$272$	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	0.994930	−	0.100572i	$-0.0320674\pi$
$277$	31.6202	+	5.40829i	1.89988	+	0.324953i	0.904947	+	0.425525i	$0.139911\pi$
$278$	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	0.277785	−	0.960643i	$-0.410400\pi$
$281$	−3.66267	−	1.55028i	−0.218497	−	0.0924817i	−0.496282	+	0.868162i	$0.665302\pi$
$282$	5.56399	+	3.56476i	0.331331	+	0.212278i
$283$	−6.27625	+	1.89069i	−0.373084	+	0.112390i	−0.469457	−	0.882955i	$-0.655550\pi$
$283$	−6.27625	+	1.89069i	−0.373084	+	0.112390i	0.0963728	+	0.995345i	$0.469276\pi$
$284$	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	−0.987674	−	0.156524i	$-0.949971\pi$
$293$	−12.1697	+	13.7696i	−0.710963	+	0.804429i	0.276711	+	0.960953i	$0.410755\pi$
$294$	−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	0.995601	+	0.0936922i	$0.0298670\pi$
$307$	4.88296	+	13.8568i	0.278686	+	0.790852i	−0.716916	+	0.697160i	$0.754447\pi$
$308$	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	0.375480	−	0.926831i	$-0.377478\pi$
$311$	−1.48251	−	0.682065i	−0.0840657	−	0.0386764i	−0.459546	+	0.888154i	$0.651988\pi$
$312$	−0.965637	+	1.86665i	−0.0546684	+	0.105678i
$313$	7.75946	−	3.56992i	0.438590	−	0.201784i	−0.186305	−	0.982492i	$-0.559651\pi$
$313$	7.75946	−	3.56992i	0.438590	−	0.201784i	0.624896	+	0.780708i	$0.285142\pi$
$314$	−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	−0.468974	−	0.883212i	$-0.655376\pi$
$317$	−0.832817	+	0.414694i	−0.0467757	+	0.0232915i	0.422198	+	0.906503i	$0.361259\pi$
$318$	−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	0.809311	−	0.587380i	$-0.199841\pi$
$331$	25.9617	+	3.62150i	1.42698	+	0.199056i	0.617672	+	0.786436i	$0.288076\pi$
$332$	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	−0.859552	−	0.511049i	$-0.829257\pi$
$337$	2.52017	−	7.92201i	0.137283	−	0.431539i	0.996834	+	0.0795097i	$0.0253355\pi$
$338$	−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	−0.646008	−	0.763330i	$-0.723563\pi$
$347$	4.04177	−	23.6307i	0.216974	−	1.26856i	0.862982	−	0.505235i	$-0.168594\pi$
$348$	−0.470828	−	0.110738i	−0.0252390	−	0.00593617i
$349$	3.40732	+	2.25777i	0.182389	+	0.120856i	0.640244	−	0.768171i	$-0.278833\pi$
$349$	3.40732	+	2.25777i	0.182389	+	0.120856i	−0.457855	+	0.889027i	$0.651382\pi$
$350$	−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	−0.372417	−	0.928066i	$-0.621471\pi$
$353$	5.05467	−	3.02304i	0.269033	−	0.160900i	0.641449	+	0.767165i	$0.278333\pi$
$354$	−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	−0.908384	−	0.418136i	$-0.862684\pi$
$359$	−12.0227	+	10.3004i	−0.634536	+	0.543637i	0.273849	+	0.961773i	$0.411703\pi$
$360$	−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	−0.574092	−	0.818791i	$-0.694645\pi$
$367$	5.24421	−	25.8440i	0.273746	−	1.34905i	0.847838	−	0.530256i	$-0.177904\pi$
$368$	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	0.514767	−	0.857330i	$-0.327879\pi$
$373$	−8.70462	−	11.5268i	−0.450708	−	0.596834i	−0.965475	+	0.260496i	$0.916114\pi$
$374$	−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	−0.684473	−	0.729039i	$-0.739968\pi$
$379$	−13.6111	+	5.27296i	−0.699154	+	0.270854i	−0.0146814	+	0.999892i	$0.504673\pi$
$380$	−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	−0.875048	−	0.484037i	$-0.839170\pi$
$383$	−2.90651	+	3.97467i	−0.148516	+	0.203096i	0.726532	+	0.687133i	$0.241131\pi$
$384$	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	0.608611	−	0.793469i	$-0.291727\pi$
$389$	31.6797	−	17.0116i	1.60622	−	0.862524i	0.997613	−	0.0690547i	$-0.0219983\pi$
$390$	−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	−0.403447	−	0.915003i	$-0.632188\pi$
$397$	−10.1721	+	1.57900i	−0.510523	+	0.0792478i	−0.107076	+	0.994251i	$0.534149\pi$
$398$	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	−0.000198026	−	1.00000i	$-0.500063\pi$
$401$	10.5345	−	2.99731i	0.526066	−	0.149679i	0.526264	+	0.850321i	$0.323592\pi$
$402$	−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	0.857641	+	0.514249i	$0.171929\pi$
$419$	−2.03731	+	16.4529i	−0.0995291	+	0.803776i	−0.957170	+	0.289527i	$0.906502\pi$
$420$	−0.330569	−	0.110796i	−0.0161301	−	0.00540627i
$421$	33.0891	−	5.13637i	1.61266	−	0.250332i	0.717661	−	0.696393i	$-0.245213\pi$
$421$	33.0891	−	5.13637i	1.61266	−	0.250332i	0.895002	+	0.446061i	$0.147174\pi$
$422$	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	−0.996665	−	0.0816033i	$-0.973996\pi$
$431$	−4.37876	−	14.5355i	−0.210917	−	0.700151i	0.785747	−	0.618547i	$-0.212279\pi$
$432$	−5.43379	−	5.26896i	−0.261433	−	0.253503i
$433$	−19.2678	−	19.8706i	−0.925951	−	0.954919i	0.0731495	−	0.997321i	$-0.476695\pi$
$433$	−19.2678	−	19.8706i	−0.925951	−	0.954919i	−0.999101	+	0.0424022i	$0.986499\pi$
$434$	−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	−0.165713	−	0.986174i	$-0.552992\pi$
$439$	7.88238	−	3.05365i	0.376206	−	0.145743i	0.541918	+	0.840431i	$0.317698\pi$
$440$	−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	−0.218989	−	0.975727i	$-0.570276\pi$
$443$	−15.2272	−	2.36371i	−0.723468	−	0.112303i	−0.504479	+	0.863424i	$0.668315\pi$
$444$	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	0.818017	−	0.575194i	$-0.195074\pi$
$449$	18.0529	+	8.98926i	0.851967	+	0.424229i	0.0339504	+	0.999424i	$0.489191\pi$
$450$	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	−0.699014	−	0.715108i	$-0.746377\pi$
$457$	4.51332	−	24.1441i	0.211124	−	1.12941i	0.910138	−	0.414306i	$-0.135976\pi$
$458$	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	−0.735073	−	0.677988i	$-0.762852\pi$
$461$	−32.0062	−	0.492933i	−1.49068	−	0.0229582i	−0.755603	+	0.655030i	$0.772656\pi$
$462$	−1.06819	+	1.85016i	−0.0496966	+	0.0860771i
$463$	−13.3378	−	23.1018i	−0.619862	−	1.07363i	−0.989511	−	0.144461i	$-0.953855\pi$
$463$	−13.3378	−	23.1018i	−0.619862	−	1.07363i	0.369649	−	0.929172i	$-0.379478\pi$
$464$	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	0.973425	+	0.229004i	$0.0735470\pi$
$467$	4.41121	+	18.7553i	0.204127	+	0.867893i	−0.769299	+	0.638889i	$0.779394\pi$
$468$	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	0.967713	+	0.252054i	$0.0811059\pi$
$479$	2.31816	+	16.6184i	0.105920	+	0.759312i	−0.861794	+	0.507259i	$0.830659\pi$
$480$	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	0.404993	−	0.914320i	$-0.367274\pi$
$487$	12.0119	+	1.67558i	0.544309	+	0.0759279i	0.139317	+	0.990248i	$0.455509\pi$
$488$	−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	0.316780	−	0.948499i	$-0.397398\pi$
$491$	28.5947	−	26.0675i	1.29046	−	1.17641i	0.973682	−	0.227912i	$-0.0731899\pi$
$492$	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	0.864106	−	0.503310i	$-0.167884\pi$
$499$	11.1535	+	9.55574i	0.499300	+	0.427774i	−0.364806	+	0.931083i	$0.618865\pi$
$500$	−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	−0.572112	−	0.820175i	$-0.693876\pi$
$503$	−3.94644	+	2.19815i	−0.175963	+	0.0980108i	0.396149	+	0.918186i	$0.370346\pi$
$504$	−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	0.653610	−	0.756831i	$-0.273254\pi$
$509$	19.6596	+	4.94459i	0.871397	+	0.219165i	0.217786	+	0.975996i	$0.430116\pi$
$510$	−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	−0.544677	−	0.838646i	$-0.683348\pi$
$521$	−34.9546	−	15.4340i	−1.53139	−	0.676175i	−0.986713	+	0.162471i	$0.948053\pi$
$522$	−9.03837	−	3.34234i	−0.395599	−	0.146290i
$523$	22.0935	−	5.19634i	0.966080	−	0.227220i	0.284266	−	0.958745i	$-0.408250\pi$
$523$	22.0935	−	5.19634i	0.966080	−	0.227220i	0.681814	+	0.731525i	$0.261191\pi$
$524$	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	0.851699	−	0.524031i	$-0.175572\pi$
$541$	34.4430	+	5.89108i	1.48082	+	0.253277i	0.629120	+	0.777309i	$0.283416\pi$
$542$	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	−0.629127	−	0.777303i	$-0.716587\pi$
$547$	−14.7802	+	5.20836i	−0.631958	+	0.222693i	−0.00283095	+	0.999996i	$0.500901\pi$
$548$	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	−0.852588	−	0.522583i	$-0.824968\pi$
$557$	−15.8901	+	10.8850i	−0.673285	+	0.461211i	0.179304	+	0.983794i	$0.442616\pi$
$558$	−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	−0.983285	−	0.182072i	$-0.941719\pi$
$563$	−16.7987	−	27.1309i	−0.707982	−	1.14343i	0.275303	−	0.961357i	$-0.411222\pi$
$564$	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	−0.457603	−	0.889157i	$-0.651292\pi$
$569$	9.94796	−	9.64619i	0.417040	−	0.404389i	0.874643	+	0.484767i	$0.161096\pi$
$570$	4.41080	+	2.45680i	0.184748	+	0.102904i
$571$	−8.52304	+	13.7652i	−0.356678	+	0.576055i	−0.978282	−	0.207277i	$-0.933540\pi$
$571$	−8.52304	+	13.7652i	−0.356678	+	0.576055i	0.621604	+	0.783331i	$0.286481\pi$
$572$	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	0.307415	−	0.951576i	$-0.400536\pi$
$577$	−9.25999	−	5.53812i	−0.385499	−	0.230555i	−0.692914	+	0.721021i	$0.743673\pi$
$578$	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	0.912067	+	0.410041i	$0.134486\pi$
$587$	15.2648	+	33.1791i	0.630047	+	1.36945i	−0.282020	+	0.959409i	$0.591004\pi$
$588$	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	0.255266	−	0.966871i	$-0.417837\pi$
$593$	−9.97732	−	5.35771i	−0.409719	−	0.220015i	−0.664986	+	0.746856i	$0.731562\pi$
$594$	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	−0.0151162	−	0.999886i	$-0.504812\pi$
$599$	21.7071	−	13.9074i	0.886927	−	0.568241i	0.902043	+	0.431645i	$0.142067\pi$
$600$	1.52595	−	1.78110i	0.0622968	−	0.0727132i
$601$	1.81134	+	1.04578i	0.0738861	+	0.0426581i	0.536488	−	0.843908i	$-0.319751\pi$
$601$	1.81134	+	1.04578i	0.0738861	+	0.0426581i	−0.462602	+	0.886566i	$0.653084\pi$
$602$	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	0.577359	−	0.816490i	$-0.304083\pi$
$607$	14.9708	+	4.50989i	0.607646	+	0.183051i	0.0302873	+	0.999541i	$0.490358\pi$
$608$	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	−0.672115	−	0.740447i	$-0.734614\pi$
$613$	6.18033	−	8.73069i	0.249621	−	0.352629i	0.921736	+	0.387817i	$0.126771\pi$
$614$	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	−0.853079	−	0.521782i	$-0.825267\pi$
$617$	3.33431	−	9.01666i	0.134234	−	0.362997i	0.987313	+	0.158785i	$0.0507576\pi$
$618$	−1.34761	−	3.47857i	−0.0542086	−	0.139929i
$619$	4.86484	−	3.55746i	0.195535	−	0.142986i	−0.488161	−	0.872753i	$-0.662332\pi$
$619$	4.86484	−	3.55746i	0.195535	−	0.142986i	0.683696	+	0.729767i	$0.260371\pi$
$620$	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	−0.601529	+	0.798851i	$0.705442\pi$
$631$	−40.2191	+	20.8057i	−1.60110	+	0.828262i	−0.999567	+	0.0294109i	$0.990637\pi$
$632$	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	−0.431333	−	0.902193i	$-0.641957\pi$
$641$	−26.4747	−	2.86508i	−1.04569	−	0.113164i	−0.614356	+	0.789029i	$0.710584\pi$
$642$	−2.39093	−	3.73183i	−0.0943623	−	0.147284i
$643$	−8.51797	−	23.0343i	−0.335916	−	0.908385i	−0.988575	−	0.150733i	$-0.951837\pi$
$643$	−8.51797	−	23.0343i	−0.335916	−	0.908385i	0.652659	−	0.757652i	$-0.273654\pi$
$644$	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	0.0685727	−	0.997646i	$-0.478155\pi$
$647$	8.87691	−	0.960653i	0.348987	−	0.0377672i	0.280415	+	0.959879i	$0.409528\pi$
$648$	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	−0.332585	−	0.943073i	$-0.607921\pi$
$653$	16.9466	−	26.4508i	0.663172	−	1.03510i	0.995757	−	0.0920251i	$-0.0293340\pi$
$654$	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	0.387074	−	0.922049i	$-0.373486\pi$
$659$	18.3972	+	0.566811i	0.716652	+	0.0220798i	0.329578	+	0.944128i	$0.393094\pi$
$660$	−0.703516	−	0.902367i	−0.0273843	−	0.0351246i
$661$	20.3960	+	15.9014i	0.793314	+	0.618494i	0.928079	−	0.372383i	$-0.121459\pi$
$661$	20.3960	+	15.9014i	0.793314	+	0.618494i	−0.134765	+	0.990878i	$0.543028\pi$
$662$	−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	−0.900595	−	0.434660i	$-0.856869\pi$
$673$	−17.5013	−	36.5473i	−0.674626	−	1.40879i	0.225969	−	0.974135i	$-0.427445\pi$
$674$	−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	−0.472045	−	0.881574i	$-0.656484\pi$
$677$	−5.13197	+	2.07958i	−0.197238	+	0.0799248i	0.274807	+	0.961499i	$0.411386\pi$
$678$	−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	0.442441	−	0.896798i	$-0.354113\pi$
$683$	−12.8412	−	14.0861i	−0.491355	−	0.538991i	−0.933796	+	0.357807i	$0.883525\pi$
$684$	−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	0.843991	−	0.536357i	$-0.180200\pi$
$691$	18.6501	+	11.9489i	0.709485	+	0.454556i	−0.134507	+	0.990913i	$0.542945\pi$
$692$	−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	−0.374841	−	0.927089i	$-0.622303\pi$
$701$	−30.7923	−	8.25077i	−1.16301	−	0.311627i	−0.788167	+	0.615462i	$0.788970\pi$
$702$	−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	0.990363	+	0.138497i	$0.0442273\pi$
$709$	4.88243	+	19.4124i	0.183363	+	0.729050i	−0.806999	+	0.590552i	$0.798910\pi$
$710$	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	−0.912997	−	0.407966i	$-0.866238\pi$
$719$	−19.8437	+	15.4708i	−0.740046	+	0.576964i	0.172952	+	0.984930i	$0.444670\pi$
$720$	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	−0.993850	−	0.110736i	$-0.964679\pi$
$727$	−19.1016	−	28.8272i	−0.708439	−	1.06914i	0.285411	−	0.958405i	$-0.407870\pi$
$728$	−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	0.833728	−	0.552175i	$-0.186202\pi$
$733$	46.8107	−	2.88719i	1.72899	−	0.106641i	0.895265	+	0.445534i	$0.146986\pi$
$734$	−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	0.974801	−	0.223077i	$-0.0716101\pi$
$739$	53.4455	−	2.47094i	1.96603	−	0.0908949i	0.991225	+	0.132182i	$0.0421983\pi$
$740$	−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	0.0370071	−	0.999315i	$-0.488218\pi$
$743$	26.4868	−	17.5508i	0.971707	−	0.643876i	0.934700	+	0.355439i	$0.115669\pi$
$744$	−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	0.161177	−	0.986926i	$-0.448471\pi$
$751$	−22.9669	−	25.9863i	−0.838075	−	0.948252i	−0.999252	+	0.0386735i	$0.987687\pi$
$752$	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	−0.186845	−	0.982389i	$-0.559826\pi$
$757$	−21.7905	−	5.12509i	−0.791991	−	0.186275i	−0.605146	+	0.796115i	$0.706885\pi$
$758$	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	−0.891513	−	0.452995i	$-0.850355\pi$
$761$	1.76166	−	4.34741i	0.0638602	−	0.157594i	0.955373	+	0.295402i	$0.0954535\pi$
$762$	−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	−0.680746	−	0.732519i	$-0.738344\pi$
$769$	−10.7246	+	6.19186i	−0.386740	+	0.223284i	0.294007	+	0.955803i	$0.405011\pi$
$770$	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	−0.560356	−	0.828252i	$-0.689336\pi$
$773$	−18.4109	+	4.63053i	−0.662195	+	0.166549i	−0.101839	+	0.994801i	$0.532473\pi$
$774$	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	−0.928471	−	0.371405i	$-0.878876\pi$
$787$	−36.4661	−	36.4661i	−1.29988	−	1.29988i	−0.371405	−	0.928471i	$-0.621124\pi$
$788$	−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	0.460500	−	0.887660i	$-0.347670\pi$
$797$	−12.8120	−	13.6266i	−0.453825	−	0.482679i	−0.914325	+	0.404981i	$0.867278\pi$
$798$	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	−0.999980	−	0.00634834i	$-0.997979\pi$
$809$	−17.1896	+	25.9418i	−0.604356	+	0.912064i	0.395624	+	0.918412i	$0.370528\pi$
$810$	−15.9809	+	4.54697i	−0.561513	+	0.159764i
$811$	16.5431	−	4.43271i	0.580907	−	0.155653i	0.0436127	−	0.999049i	$-0.486113\pi$
$811$	16.5431	−	4.43271i	0.580907	−	0.155653i	0.537294	+	0.843395i	$0.319447\pi$
$812$	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	0.980817	−	0.194932i	$-0.0624487\pi$
$821$	7.92407	+	14.7565i	0.276552	+	0.515005i	−0.704265	+	0.709937i	$0.748723\pi$
$822$	−0.574654	+	1.63075i	−0.0200434	+	0.0568789i
$823$	−24.8007	−	22.6089i	−0.864500	−	0.788095i	0.114186	−	0.993459i	$-0.463574\pi$
$823$	−24.8007	−	22.6089i	−0.864500	−	0.788095i	−0.978686	+	0.205364i	$0.934162\pi$
$824$	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	−0.908015	−	0.418937i	$-0.862403\pi$
$827$	−4.83938	+	7.30336i	−0.168282	+	0.253963i	0.739733	+	0.672900i	$0.234952\pi$
$828$	0.494447	−	3.99306i	0.0171832	−	0.138768i
$829$	−6.57600	−	2.20405i	−0.228394	−	0.0765499i	0.201281	−	0.979534i	$-0.435490\pi$
$829$	−6.57600	−	2.20405i	−0.228394	−	0.0765499i	−0.429675	+	0.902984i	$0.641372\pi$
$830$	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	0.751525	−	0.659705i	$-0.229319\pi$
$839$	1.35579	+	1.44199i	0.0468070	+	0.0497829i	−0.704718	+	0.709488i	$0.748926\pi$
$840$	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	0.284948	−	0.958543i	$-0.408024\pi$
$853$	−9.71910	−	5.02778i	−0.332776	−	0.172148i	−0.617724	+	0.786395i	$0.711945\pi$
$854$	−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	−0.378251	−	0.925703i	$-0.623474\pi$
$857$	16.6567	−	17.7157i	0.568982	−	0.605157i	0.947233	+	0.320546i	$0.103866\pi$
$858$	−2.79718	−	1.39283i	−0.0954942	−	0.0475505i
$859$	3.02695	+	24.4450i	0.103278	+	0.834052i	0.952188	+	0.305514i	$0.0988283\pi$
$859$	3.02695	+	24.4450i	0.103278	+	0.834052i	−0.848910	+	0.528538i	$0.822740\pi$
$860$	−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	−0.172968	−	0.984927i	$-0.555336\pi$
$863$	4.13061	−	1.03889i	0.140607	−	0.0353642i	0.313576	+	0.949563i	$0.398473\pi$
$864$	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	−0.249018	+	0.968499i	$0.580108\pi$
$877$	−31.4550	+	45.9187i	−1.06216	+	1.55056i	−0.813143	+	0.582064i	$0.802245\pi$
$878$	−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	0.553534	+	0.832827i	$0.313279\pi$
$881$	−11.5784	+	34.5452i	−0.390086	+	1.16386i	−0.943620	+	0.331032i	$0.892603\pi$
$882$	17.5035	−	10.8377i	0.589374	−	0.364925i
$883$	−14.6226	+	33.1170i	−0.492089	+	1.11448i	0.479444	+	0.877572i	$0.340838\pi$
$883$	−14.6226	+	33.1170i	−0.492089	+	1.11448i	−0.971533	+	0.236903i	$0.923868\pi$
$884$	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	−0.997601	−	0.0692254i	$-0.977947\pi$
$887$	−3.36486	+	11.8263i	−0.112981	+	0.397087i	0.884620	+	0.466313i	$0.154418\pi$
$888$	−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	0.901494	−	0.432792i	$-0.142472\pi$
$907$	47.7577	+	8.92746i	1.58577	+	0.296432i	0.684275	+	0.729224i	$0.260119\pi$
$908$	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	−0.467474	−	0.884007i	$-0.654836\pi$
$911$	12.3903	−	41.1301i	0.410508	−	1.36270i	0.877982	−	0.478694i	$-0.158890\pi$
$912$	−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	−0.998696	−	0.0510518i	$-0.983743\pi$
$919$	−8.08862	+	19.1101i	−0.266819	+	0.630385i	0.731877	+	0.681437i	$0.238645\pi$
$920$	−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	0.384048	+	0.923313i	$0.374530\pi$
$929$	−7.25460	+	52.0065i	−0.238016	+	1.70628i	−0.622064	+	0.782966i	$0.713706\pi$
$930$	−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	−0.683227	−	0.730206i	$-0.739424\pi$
$937$	9.09985	−	16.3374i	0.297279	−	0.533718i	0.980506	+	0.196488i	$0.0629536\pi$
$938$	−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	−0.886848	−	0.462061i	$-0.847110\pi$
$941$	−22.8780	+	16.1950i	−0.745801	+	0.527942i	0.141047	+	0.990003i	$0.454953\pi$
$942$	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	0.918502	−	0.395416i	$-0.129400\pi$
$947$	49.5521	+	10.0550i	1.61023	+	0.326744i	0.691726	+	0.722160i	$0.256851\pi$
$948$	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	0.976885	−	0.213767i	$-0.0685733\pi$
$953$	20.8036	+	22.8204i	0.673894	+	0.739227i	−0.302990	+	0.952994i	$0.597985\pi$
$954$	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	0.839833	−	0.542846i	$-0.182653\pi$
$967$	10.8750	+	10.2250i	0.349718	+	0.328812i	−0.490115	+	0.871658i	$0.663045\pi$
$968$	−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	0.990645	−	0.136462i	$-0.0435731\pi$
$971$	1.04834	+	4.78687i	0.0336428	+	0.153618i	−0.957003	+	0.290080i	$0.906318\pi$
$972$	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	0.764831	−	0.644231i	$-0.222822\pi$
$977$	46.5277	+	1.43350i	1.48855	+	0.0458618i	0.723721	+	0.690093i	$0.242430\pi$
$978$	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	−0.418923	−	0.908022i	$-0.637592\pi$
$983$	18.2184	−	28.4358i	0.581077	−	0.906962i	0.999999	+	0.00105952i	$0.000337255\pi$
$984$	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	0.397705	−	0.917513i	$-0.369807\pi$
$991$	−18.7999	−	25.7089i	−0.597197	−	0.816670i	−0.994902	+	0.100843i	$0.967846\pi$
$992$	−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	−0.617460	−	0.786602i	$-0.711838\pi$
$997$	0.594747	−	0.478591i	0.0188358	−	0.0151571i	0.636296	+	0.771445i	$0.280466\pi$
$998$	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.10.13	✓	2176
409.41	even	204	inner	409.2.o.a.41.13	yes	2176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.o.a.10.13	✓	2176	1.1	even	1	trivial
409.2.o.a.41.13	yes	2176	409.41	even	204	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 $\F_{q}$
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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