LMFDB - Embedded newform 216.2.v.b.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.494886 + 1.32480i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(-1.51018 - 1.31125i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(1.45024 - 1.97403i) q^{6} +(3.32069 + 0.585528i) q^{7} +(2.48450 - 1.35176i) q^{8} +(2.55410 + 1.57371i) q^{9} +O(q^{10})$	\(q+(-0.494886 + 1.32480i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(-1.51018 - 1.31125i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(1.45024 - 1.97403i) q^{6} +(3.32069 + 0.585528i) q^{7} +(2.48450 - 1.35176i) q^{8} +(2.55410 + 1.57371i) q^{9} +(1.66726 - 1.95325i) q^{10} +(-0.942090 - 2.58837i) q^{11} +(1.89749 + 2.89819i) q^{12} +(3.98305 + 4.74681i) q^{13} +(-2.41907 + 4.10948i) q^{14} +(2.55034 + 1.84070i) q^{15} +(0.561263 + 3.96043i) q^{16} +(2.90072 - 1.67473i) q^{17} +(-3.34884 + 2.60486i) q^{18} +(2.87704 - 4.98318i) q^{19} +(1.76256 + 3.17542i) q^{20} +(-5.25729 - 2.54370i) q^{21} +(3.89529 + 0.0328699i) q^{22} +(-0.396921 - 2.25105i) q^{23} +(-4.77856 + 1.07952i) q^{24} +(-1.30421 - 1.09436i) q^{25} +(-8.25972 + 2.92760i) q^{26} +(-3.51321 - 3.82849i) q^{27} +(-4.24706 - 5.23850i) q^{28} +(7.06459 + 5.92789i) q^{29} +(-3.70068 + 2.46776i) q^{30} +(-1.38814 + 0.244766i) q^{31} +(-5.52452 - 1.21640i) q^{32} +(0.347781 + 4.75822i) q^{33} +(0.783155 + 4.67167i) q^{34} +(-5.30272 - 3.06153i) q^{35} +(-1.79362 - 5.72564i) q^{36} +(4.33391 - 2.50218i) q^{37} +(5.17790 + 6.27760i) q^{38} +(-4.39622 - 9.79102i) q^{39} +(-5.07905 + 0.763564i) q^{40} +(1.54991 + 1.84711i) q^{41} +(5.97165 - 5.70601i) q^{42} +(3.42707 - 1.24735i) q^{43} +(-1.97127 + 5.14421i) q^{44} +(-3.38089 - 4.27164i) q^{45} +(3.17861 + 0.588173i) q^{46} +(0.530155 - 3.00666i) q^{47} +(0.934698 - 6.86486i) q^{48} +(4.10632 + 1.49458i) q^{49} +(2.09524 - 1.18623i) q^{50} +(-5.62467 + 1.42121i) q^{51} +(0.209139 - 12.3913i) q^{52} -0.184564 q^{53} +(6.81061 - 2.75963i) q^{54} +5.00186i q^{55} +(9.04176 - 3.03403i) q^{56} +(-7.14737 + 6.94575i) q^{57} +(-11.3494 + 6.42551i) q^{58} +(-4.44089 + 12.2012i) q^{59} +(-1.43786 - 6.12391i) q^{60} +(-13.9331 - 2.45678i) q^{61} +(0.362704 - 1.96013i) q^{62} +(7.55994 + 6.72131i) q^{63} +(4.34549 - 6.71690i) q^{64} +(-3.84849 - 10.5736i) q^{65} +(-6.47579 - 1.89404i) q^{66} +(4.70680 - 3.94947i) q^{67} +(-6.57659 - 1.27442i) q^{68} +(-0.401441 + 3.93867i) q^{69} +(6.68014 - 5.50992i) q^{70} +(1.83700 + 3.18178i) q^{71} +(8.47295 + 0.457353i) q^{72} +(0.136500 - 0.236424i) q^{73} +(1.17010 + 6.97985i) q^{74} +(1.65667 + 2.43951i) q^{75} +(-10.8790 + 3.75297i) q^{76} +(-1.61283 - 9.14681i) q^{77} +(15.1467 - 0.978667i) q^{78} +(0.710677 - 0.846952i) q^{79} +(1.50198 - 7.10659i) q^{80} +(4.04687 + 8.03883i) q^{81} +(-3.21407 + 1.13921i) q^{82} +(2.40520 - 2.86641i) q^{83} +(4.60402 + 10.7350i) q^{84} +(-5.98987 + 1.05618i) q^{85} +(-0.0435206 + 5.15748i) q^{86} +(-8.97377 - 13.2142i) q^{87} +(-5.83948 - 5.15733i) q^{88} +(5.59452 + 3.23000i) q^{89} +(7.33220 - 2.36502i) q^{90} +(10.4471 + 18.0949i) q^{91} +(-2.35226 + 3.91994i) q^{92} +(2.42883 + 0.247553i) q^{93} +(3.72084 + 2.19030i) q^{94} +(-8.00425 + 6.71636i) q^{95} +(8.63198 + 4.63561i) q^{96} +(-14.5548 + 5.29750i) q^{97} +(-4.01217 + 4.70039i) q^{98} +(1.66715 - 8.09354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−0.494886	+	1.32480i	−0.349937	+	0.936773i
$2$	−0.494886	+	1.32480i	−0.349937	+	0.936773i
$3$	−1.66645	−	0.472175i	−0.962125	−	0.272610i
$3$	−1.66645	−	0.472175i	−0.962125	−	0.272610i
$4$	−1.51018	−	1.31125i	−0.755088	−	0.655623i
$5$	−1.70638	−	0.621073i	−0.763118	−	0.277752i	−0.0690029	−	0.997616i	$-0.521982\pi$
$5$	−1.70638	−	0.621073i	−0.763118	−	0.277752i	−0.694115	+	0.719864i	$0.744204\pi$
$6$	1.45024	−	1.97403i	0.592057	−	0.805896i
$7$	3.32069	+	0.585528i	1.25510	+	0.221309i	0.761378	−	0.648308i	$-0.224523\pi$
$7$	3.32069	+	0.585528i	1.25510	+	0.221309i	0.493727	+	0.869617i	$0.335634\pi$
$8$	2.48450	−	1.35176i	0.878404	−	0.477919i
$9$	2.55410	+	1.57371i	0.851367	+	0.524570i
$10$	1.66726	−	1.95325i	0.527234	−	0.617672i
$11$	−0.942090	−	2.58837i	−0.284051	−	0.780423i	−0.996869	−	0.0790741i	$-0.974804\pi$
$11$	−0.942090	−	2.58837i	−0.284051	−	0.780423i	0.712818	−	0.701349i	$-0.247419\pi$
$12$	1.89749	+	2.89819i	0.547759	+	0.836636i
$13$	3.98305	+	4.74681i	1.10470	+	1.31653i	0.944155	+	0.329501i	$0.106880\pi$
$13$	3.98305	+	4.74681i	1.10470	+	1.31653i	0.160544	+	0.987029i	$0.448675\pi$
$14$	−2.41907	+	4.10948i	−0.646524	+	1.09830i
$15$	2.55034	+	1.84070i	0.658496	+	0.475266i
$16$	0.561263	+	3.96043i	0.140316	+	0.990107i
$17$	2.90072	−	1.67473i	0.703529	−	0.406182i	−0.105132	−	0.994458i	$-0.533526\pi$
$17$	2.90072	−	1.67473i	0.703529	−	0.406182i	0.808660	+	0.588276i	$0.200193\pi$
$18$	−3.34884	+	2.60486i	−0.789328	+	0.613972i
$19$	2.87704	−	4.98318i	0.660038	−	1.14322i	−0.320567	−	0.947226i	$-0.603873\pi$
$19$	2.87704	−	4.98318i	0.660038	−	1.14322i	0.980605	−	0.195994i	$-0.0627933\pi$
$20$	1.76256	+	3.17542i	0.394120	+	0.710045i
$21$	−5.25729	−	2.54370i	−1.14724	−	0.555081i
$22$	3.89529	+	0.0328699i	0.830479	+	0.00700788i
$23$	−0.396921	−	2.25105i	−0.0827637	−	0.469376i	−0.997817	−	0.0660428i	$-0.978963\pi$
$23$	−0.396921	−	2.25105i	−0.0827637	−	0.469376i	0.915053	−	0.403333i	$-0.132148\pi$
$24$	−4.77856	+	1.07952i	−0.975420	+	0.220356i
$25$	−1.30421	−	1.09436i	−0.260842	−	0.218872i
$26$	−8.25972	+	2.92760i	−1.61986	+	0.574150i
$27$	−3.51321	−	3.82849i	−0.676118	−	0.736793i
$28$	−4.24706	−	5.23850i	−0.802619	−	0.989983i
$29$	7.06459	+	5.92789i	1.31186	+	1.10078i	0.987963	+	0.154690i	$0.0494377\pi$
$29$	7.06459	+	5.92789i	1.31186	+	1.10078i	0.323897	+	0.946092i	$0.395007\pi$
$30$	−3.70068	+	2.46776i	−0.675649	+	0.450548i
$31$	−1.38814	+	0.244766i	−0.249317	+	0.0439613i	−0.296910	−	0.954906i	$-0.595956\pi$
$31$	−1.38814	+	0.244766i	−0.249317	+	0.0439613i	0.0475930	+	0.998867i	$0.484845\pi$
$32$	−5.52452	−	1.21640i	−0.976607	−	0.215031i
$33$	0.347781	+	4.75822i	0.0605409	+	0.828299i
$34$	0.783155	+	4.67167i	0.134310	+	0.801185i
$35$	−5.30272	−	3.06153i	−0.896323	−	0.517493i
$36$	−1.79362	−	5.72564i	−0.298937	−	0.954273i
$37$	4.33391	−	2.50218i	0.712490	−	0.411356i	−0.0994922	−	0.995038i	$-0.531722\pi$
$37$	4.33391	−	2.50218i	0.712490	−	0.411356i	0.811982	+	0.583682i	$0.198389\pi$
$38$	5.17790	+	6.27760i	0.839966	+	1.01836i
$39$	−4.39622	−	9.79102i	−0.703959	−	1.56782i
$40$	−5.07905	+	0.763564i	−0.803069	+	0.120730i
$41$	1.54991	+	1.84711i	0.242055	+	0.288470i	0.873371	−	0.487056i	$-0.161929\pi$
$41$	1.54991	+	1.84711i	0.242055	+	0.288470i	−0.631316	+	0.775526i	$0.717485\pi$
$42$	5.97165	−	5.70601i	0.921445	−	0.880456i
$43$	3.42707	−	1.24735i	0.522624	−	0.190220i	−0.0672179	−	0.997738i	$-0.521412\pi$
$43$	3.42707	−	1.24735i	0.522624	−	0.190220i	0.589842	+	0.807519i	$0.299190\pi$
$44$	−1.97127	+	5.14421i	−0.297180	+	0.775519i
$45$	−3.38089	−	4.27164i	−0.503993	−	0.636778i
$46$	3.17861	+	0.588173i	0.468661	+	0.0867213i
$47$	0.530155	−	3.00666i	0.0773310	−	0.438566i	−0.921419	−	0.388572i	$-0.872969\pi$
$47$	0.530155	−	3.00666i	0.0773310	−	0.438566i	0.998750	−	0.0499942i	$-0.0159203\pi$
$48$	0.934698	−	6.86486i	0.134912	−	0.990858i
$49$	4.10632	+	1.49458i	0.586617	+	0.213511i
$50$	2.09524	−	1.18623i	0.296312	−	0.167758i
$51$	−5.62467	+	1.42121i	−0.787612	+	0.199009i
$52$	0.209139	−	12.3913i	0.0290024	−	1.71836i
$53$	−0.184564			−0.0253518			−0.0126759	−	0.999920i	$-0.504035\pi$
$53$	−0.184564			−0.0253518			−0.0126759	+	0.999920i	$0.504035\pi$
$54$	6.81061	−	2.75963i	0.926807	−	0.375538i
$55$			5.00186i			0.674450i
$56$	9.04176	−	3.03403i	1.20826	−	0.405440i
$57$	−7.14737	+	6.94575i	−0.946693	+	0.919987i
$58$	−11.3494	+	6.42551i	−1.49025	+	0.843711i
$59$	−4.44089	+	12.2012i	−0.578154	+	1.58847i	0.213134	+	0.977023i	$0.431633\pi$
$59$	−4.44089	+	12.2012i	−0.578154	+	1.58847i	−0.791288	+	0.611443i	$0.790589\pi$
$60$	−1.43786	−	6.12391i	−0.185627	−	0.790593i
$61$	−13.9331	−	2.45678i	−1.78395	−	0.314559i	−0.818377	−	0.574681i	$-0.805126\pi$
$61$	−13.9331	−	2.45678i	−1.78395	−	0.314559i	−0.965576	+	0.260122i	$0.916237\pi$
$62$	0.362704	−	1.96013i	0.0460635	−	0.248937i
$63$	7.55994	+	6.72131i	0.952463	+	0.846805i
$64$	4.34549	−	6.71690i	0.543187	−	0.839612i
$65$	−3.84849	−	10.5736i	−0.477347	−	1.31150i
$66$	−6.47579	−	1.89404i	−0.797114	−	0.233140i
$67$	4.70680	−	3.94947i	0.575027	−	0.482505i	−0.308283	−	0.951295i	$-0.599754\pi$
$67$	4.70680	−	3.94947i	0.575027	−	0.482505i	0.883310	+	0.468790i	$0.155310\pi$
$68$	−6.57659	−	1.27442i	−0.797529	−	0.154546i
$69$	−0.401441	+	3.93867i	−0.0483278	+	0.474160i
$70$	6.68014	−	5.50992i	0.798430	−	0.658562i
$71$	1.83700	+	3.18178i	0.218012	+	0.377608i	0.954200	−	0.299169i	$-0.0967095\pi$
$71$	1.83700	+	3.18178i	0.218012	+	0.377608i	−0.736188	+	0.676777i	$0.763376\pi$
$72$	8.47295	+	0.457353i	0.998546	+	0.0538995i
$73$	0.136500	−	0.236424i	0.0159761	−	0.0276713i	−0.857927	−	0.513772i	$-0.828248\pi$
$73$	0.136500	−	0.236424i	0.0159761	−	0.0276713i	0.873903	+	0.486101i	$0.161581\pi$
$74$	1.17010	+	6.97985i	0.136021	+	0.811391i
$75$	1.65667	+	2.43951i	0.191296	+	0.281691i
$76$	−10.8790	+	3.75297i	−1.24791	+	0.430495i
$77$	−1.61283	−	9.14681i	−0.183799	−	1.04238i
$78$	15.1467	−	0.978667i	1.71503	−	0.110812i
$79$	0.710677	−	0.846952i	0.0799574	−	0.0952895i	−0.724583	−	0.689188i	$-0.757967\pi$
$79$	0.710677	−	0.846952i	0.0799574	−	0.0952895i	0.804540	+	0.593898i	$0.202412\pi$
$80$	1.50198	−	7.10659i	0.167927	−	0.794541i
$81$	4.04687	+	8.03883i	0.449653	+	0.893204i
$82$	−3.21407	+	1.13921i	−0.354935	+	0.125804i
$83$	2.40520	−	2.86641i	0.264005	−	0.314629i	−0.617715	−	0.786402i	$-0.711941\pi$
$83$	2.40520	−	2.86641i	0.264005	−	0.314629i	0.881720	+	0.471773i	$0.156386\pi$
$84$	4.60402	+	10.7350i	0.502340	+	1.17129i
$85$	−5.98987	+	1.05618i	−0.649693	+	0.114558i
$86$	−0.0435206	+	5.15748i	−0.00469295	+	0.556145i
$87$	−8.97377	−	13.2142i	−0.962089	−	1.41672i
$88$	−5.83948	−	5.15733i	−0.622491	−	0.549773i
$89$	5.59452	+	3.23000i	0.593018	+	0.342379i	0.766290	−	0.642495i	$-0.222101\pi$
$89$	5.59452	+	3.23000i	0.593018	+	0.342379i	−0.173272	+	0.984874i	$0.555434\pi$
$90$	7.33220	−	2.36502i	0.772882	−	0.249295i
$91$	10.4471	+	18.0949i	1.09515	+	1.89686i
$92$	−2.35226	+	3.91994i	−0.245240	+	0.408682i
$93$	2.42883	+	0.247553i	0.251858	+	0.0256701i
$94$	3.72084	+	2.19030i	0.383776	+	0.225912i
$95$	−8.00425	+	6.71636i	−0.821219	+	0.689084i
$96$	8.63198	+	4.63561i	0.880998	+	0.473120i
$97$	−14.5548	+	5.29750i	−1.47781	+	0.537879i	−0.950209	−	0.311612i	$-0.899131\pi$
$97$	−14.5548	+	5.29750i	−1.47781	+	0.537879i	−0.527602	+	0.849492i	$0.676909\pi$
$98$	−4.01217	+	4.70039i	−0.405290	+	0.474811i
$99$	1.66715	−	8.09354i	0.167555	−	0.813431i
$100$	0.534608	+	3.36282i	0.0534608	+	0.336282i
$101$	1.50674	−	8.54518i	0.149927	−	0.850277i	−0.813352	−	0.581772i	$-0.802359\pi$
$101$	1.50674	−	8.54518i	0.149927	−	0.850277i	0.963278	−	0.268504i	$-0.0865294\pi$
$102$	0.900757	−	8.15489i	0.0891883	−	0.807454i
$103$	−3.88002	+	10.6603i	−0.382309	+	1.05039i	0.588072	+	0.808809i	$0.299887\pi$
$103$	−3.88002	+	10.6603i	−0.382309	+	1.05039i	−0.970381	+	0.241578i	$0.922335\pi$
$104$	16.3124	+	6.40934i	1.59957	+	0.628487i
$105$	7.39114	+	7.60569i	0.721301	+	0.742239i
$106$	0.0913380	−	0.244510i	0.00887153	−	0.0237489i
$107$			1.12727i			0.108978i	0.998514	+	0.0544888i	$0.0173529\pi$
$107$			1.12727i			0.108978i	−0.998514	+	0.0544888i	$0.982647\pi$
$108$	0.285476	+	10.3884i	0.0274699	+	0.999623i
$109$			10.2698i			0.983665i	0.870690	+	0.491832i	$0.163673\pi$
$109$			10.2698i			0.983665i	−0.870690	+	0.491832i	$0.836327\pi$
$110$	−6.62645	−	2.47535i	−0.631807	−	0.236015i
$111$	−8.40370	+	2.12340i	−0.797644	+	0.201544i
$112$	−0.455158	+	13.4800i	−0.0430084	+	1.27374i
$113$	5.40999	−	14.8638i	0.508929	−	1.39827i	−0.373414	−	0.927665i	$-0.621813\pi$
$113$	5.40999	−	14.8638i	0.508929	−	1.39827i	0.882343	−	0.470607i	$-0.155965\pi$
$114$	−5.66457	−	12.9062i	−0.530536	−	1.20877i
$115$	−0.720766	+	4.08767i	−0.0672118	+	0.381177i
$116$	−2.89584	−	18.2156i	−0.268872	−	1.69127i
$117$	2.70301	+	18.3920i	0.249893	+	1.70034i
$118$	−13.9664	−	11.9215i	−1.28571	−	1.09746i
$119$	10.6130	−	3.86282i	0.972893	−	0.354104i
$120$	8.82451	+	1.12576i	0.805564	+	0.102767i
$121$	2.61436	−	2.19371i	0.237669	−	0.199428i
$122$	10.1500	−	17.2427i	0.918942	−	1.56108i
$123$	−1.71069	−	3.80994i	−0.154247	−	0.343531i
$124$	2.41728	+	1.45055i	0.217078	+	0.130263i
$125$	6.08554	+	10.5405i	0.544307	+	0.942768i
$126$	−12.6457	+	6.68911i	−1.12657	+	0.595913i
$127$	2.22917	+	1.28701i	0.197806	+	0.114204i	0.595632	−	0.803258i	$-0.296902\pi$
$127$	2.22917	+	1.28701i	0.197806	+	0.114204i	−0.397825	+	0.917461i	$0.630235\pi$
$128$	6.74800	+	9.08099i	0.596445	+	0.802654i
$129$	−6.30001	+	0.460472i	−0.554685	+	0.0405423i
$130$	15.9125	+	0.134275i	1.39562	+	0.0117767i
$131$	−17.4280	+	3.07303i	−1.52269	+	0.268492i	−0.871491	−	0.490411i	$-0.836846\pi$
$131$	−17.4280	+	3.07303i	−1.52269	+	0.268492i	−0.651203	+	0.758904i	$0.725735\pi$
$132$	5.71399	−	7.64177i	0.497339	−	0.665131i
$133$	12.4716	−	14.8630i	1.08142	−	1.28879i
$134$	2.90292	+	8.19009i	0.250774	+	0.707516i
$135$	3.61712	+	8.71483i	0.311312	+	0.750053i
$136$	4.94301	−	8.08196i	0.423860	−	0.693022i
$137$	−1.83538	+	2.18732i	−0.156807	+	0.186875i	−0.838728	−	0.544550i	$-0.816700\pi$
$137$	−1.83538	+	2.18732i	−0.156807	+	0.186875i	0.681921	+	0.731426i	$0.261145\pi$
$138$	−5.01928	−	2.48102i	−0.427269	−	0.211199i
$139$	−0.583063	−	3.30671i	−0.0494548	−	0.280472i	0.950044	−	0.312115i	$-0.101037\pi$
$139$	−0.583063	−	3.30671i	−0.0494548	−	0.280472i	−0.999499	+	0.0316426i	$0.989926\pi$
$140$	3.99362	+	11.5766i	0.337523	+	0.978403i
$141$	−2.30314	+	4.76011i	−0.193960	+	0.400874i
$142$	−5.12432	+	0.859037i	−0.430023	+	0.0720888i
$143$	8.53412	−	14.7815i	0.713659	−	1.23609i
$144$	−4.79904	+	10.9986i	−0.399920	+	0.916550i
$145$	−8.37324	−	14.5029i	−0.695360	−	1.20440i
$146$	0.245662	+	0.297837i	0.0203312	+	0.0246492i
$147$	−6.13726	−	4.42953i	−0.506193	−	0.365342i
$148$	−9.82594	−	1.90409i	−0.807688	−	0.156515i
$149$	−8.18651	+	6.86930i	−0.670665	+	0.562755i	−0.913262	−	0.407372i	$-0.866445\pi$
$149$	−8.18651	+	6.86930i	−0.670665	+	0.562755i	0.242597	+	0.970127i	$0.422001\pi$
$150$	−4.05172	+	0.987470i	−0.330822	+	0.0806266i
$151$	−1.16307	−	3.19552i	−0.0946497	−	0.260048i	0.883329	−	0.468754i	$-0.155297\pi$
$151$	−1.16307	−	3.19552i	−0.0946497	−	0.260048i	−0.977978	+	0.208706i	$0.933075\pi$
$152$	0.411949	−	16.2698i	0.0334135	−	1.31965i
$153$	10.0443	+	0.287457i	0.812032	+	0.0232395i
$154$	12.9158	+	2.38995i	1.04079	+	0.192588i
$155$	2.52071	+	0.444469i	0.202468	+	0.0357006i
$156$	−6.19937	+	20.5507i	−0.496347	+	1.64537i
$157$	4.73154	−	12.9998i	0.377618	−	1.03750i	−0.594723	−	0.803931i	$-0.702738\pi$
$157$	4.73154	−	12.9998i	0.377618	−	1.03750i	0.972341	−	0.233567i	$-0.0750397\pi$
$158$	0.770335	+	1.36065i	0.0612846	+	0.108247i
$159$	0.307566	+	0.0871463i	0.0243916	+	0.00691115i
$160$	8.67148	+	5.50678i	0.685541	+	0.435349i
$161$		−	7.70745i		−	0.607432i
$162$	−12.6526	+	1.38298i	−0.994079	+	0.108657i
$163$	15.6961			1.22941			0.614706	−	0.788757i	$-0.289275\pi$
$163$	15.6961			1.22941			0.614706	+	0.788757i	$0.289275\pi$
$164$	0.0813815	−	4.82177i	0.00635482	−	0.376517i
$165$	2.36175	−	8.33534i	0.183862	−	0.648905i
$166$	2.60711	+	4.60495i	0.202351	+	0.357413i
$167$	−14.4977	−	5.27671i	−1.12186	−	0.408324i	−0.286531	−	0.958071i	$-0.592502\pi$
$167$	−14.4977	−	5.27671i	−1.12186	−	0.408324i	−0.835331	+	0.549747i	$0.814724\pi$
$168$	−16.5002	+	0.786772i	−1.27302	+	0.0607008i
$169$	−4.41013	+	25.0111i	−0.339241	+	1.92393i
$170$	1.56508	−	8.45806i	0.120036	−	0.648703i
$171$	15.1903	−	8.19992i	1.16163	−	0.627064i
$172$	−6.81107	−	2.61002i	−0.519340	−	0.199012i
$173$	1.50008	−	0.545984i	0.114049	−	0.0415104i	−0.284365	−	0.958716i	$-0.591783\pi$
$173$	1.50008	−	0.545984i	0.114049	−	0.0415104i	0.398414	+	0.917206i	$0.369561\pi$
$174$	21.9472	−	5.34888i	1.66381	−	0.405498i
$175$	−3.69010	−	4.39769i	−0.278946	−	0.332434i
$176$	9.72229	−	5.18384i	0.732846	−	0.390746i
$177$	13.1616	−	18.2359i	0.989289	−	1.37069i
$178$	−7.04774	+	5.81312i	−0.528250	+	0.435712i
$179$	−1.72215	+	0.994286i	−0.128720	+	0.0743164i	−0.562977	−	0.826472i	$-0.690344\pi$
$179$	−1.72215	+	0.994286i	−0.128720	+	0.0743164i	0.434257	+	0.900789i	$0.357011\pi$
$180$	−0.495432	+	10.8841i	−0.0369273	+	0.811253i
$181$	0.664023	+	0.383374i	0.0493565	+	0.0284960i	0.524475	−	0.851426i	$-0.324262\pi$
$181$	0.664023	+	0.383374i	0.0493565	+	0.0284960i	−0.475119	+	0.879922i	$0.657595\pi$
$182$	−29.1422	+	4.88537i	−2.16016	+	0.362128i
$183$	22.0588	+	10.6730i	1.63063	+	0.788969i
$184$	−4.02903	−	5.05619i	−0.297024	−	0.372747i
$185$	−8.94935	+	1.57801i	−0.657969	+	0.116018i
$186$	−1.52995	+	3.09520i	−0.112182	+	0.226951i
$187$	−7.06757	−	5.93040i	−0.516832	−	0.433674i
$188$	−4.74310	+	3.84542i	−0.345926	+	0.280456i
$189$	−9.42462	−	14.7703i	−0.685540	−	1.07438i
$190$	−4.93663	−	13.9278i	−0.358141	−	1.01043i
$191$	0.104873	+	0.0879985i	0.00758831	+	0.00636735i	0.646574	−	0.762851i	$-0.276201\pi$
$191$	0.104873	+	0.0879985i	0.00758831	+	0.00636735i	−0.638986	+	0.769219i	$0.720646\pi$
$192$	−10.4131	+	9.14153i	−0.751500	+	0.659733i
$193$	−2.95183	−	16.7407i	−0.212478	−	1.20502i	−0.885230	−	0.465153i	$-0.845999\pi$
$193$	−2.95183	−	16.7407i	−0.212478	−	1.20502i	0.672753	−	0.739867i	$-0.265112\pi$
$194$	0.184832	−	21.9038i	0.0132701	−	1.57260i
$195$	1.42071	+	19.4376i	0.101739	+	1.39196i
$196$	−4.24150	−	7.64147i	−0.302964	−	0.545819i
$197$	2.84664	−	4.93053i	0.202815	−	0.351286i	−0.746619	−	0.665251i	$-0.768324\pi$
$197$	2.84664	−	4.93053i	0.202815	−	0.351286i	0.949434	+	0.313966i	$0.101658\pi$
$198$	9.89725	+	6.21402i	0.703367	+	0.441611i
$199$	−12.2625	+	7.07975i	−0.869265	+	0.501870i	−0.867104	−	0.498127i	$-0.834021\pi$
$199$	−12.2625	+	7.07975i	−0.869265	+	0.501870i	−0.00216093	+	0.999998i	$0.500688\pi$
$200$	−4.71963	−	0.955966i	−0.333728	−	0.0675970i
$201$	−9.70848	+	4.35916i	−0.684783	+	0.307472i
$202$	10.5750	+	6.22502i	0.744051	+	0.437991i
$203$	19.9884	+	23.8212i	1.40291	+	1.67192i
$204$	10.3578	+	5.22906i	0.725191	+	0.366107i
$205$	−1.49755	−	4.11448i	−0.104593	−	0.287368i
$206$	−12.2025	−	10.4158i	−0.850190	−	0.725706i
$207$	2.52872	−	6.37405i	0.175758	−	0.443027i
$208$	−16.5639	+	18.4388i	−1.14850	+	1.27850i
$209$	−15.6087	−	2.75224i	−1.07968	−	0.190377i
$210$	−13.7338	+	6.02781i	−0.947720	+	0.415958i
$211$	−9.92628	−	3.61287i	−0.683354	−	0.248720i	−0.0230668	−	0.999734i	$-0.507343\pi$
$211$	−9.92628	−	3.61287i	−0.683354	−	0.248720i	−0.660287	+	0.751014i	$0.729565\pi$
$212$	0.278724	+	0.242009i	0.0191428	+	0.0166212i
$213$	−1.55891	−	6.16966i	−0.106815	−	0.422738i
$214$	−1.49341	−	0.557871i	−0.102087	−	0.0381353i
$215$	−6.62260			−0.451658
$216$	−13.9038	−	4.76287i	−0.946032	−	0.324072i
$217$	−4.75290			−0.322648
$218$	−13.6054	−	5.08236i	−0.921471	−	0.344221i
$219$	−0.339103	+	0.329537i	−0.0229145	+	0.0222680i
$220$	6.55867	−	7.55369i	0.442186	−	0.509269i
$221$	19.5034	+	7.09864i	1.31194	+	0.477507i
$222$	1.34580	−	12.1840i	0.0903244	−	0.817739i
$223$	−24.8065	−	4.37405i	−1.66116	−	0.292908i	−0.737282	−	0.675585i	$-0.763891\pi$
$223$	−24.8065	−	4.37405i	−1.66116	−	0.292908i	−0.923882	+	0.382677i	$0.875002\pi$
$224$	−17.6330	−	7.27405i	−1.17816	−	0.486018i
$225$	−1.60888	−	4.84756i	−0.107258	−	0.323171i
$226$	17.0142	+	14.5230i	1.13177	+	0.966058i
$227$	1.35308	+	3.71757i	0.0898074	+	0.246744i	0.976462	−	0.215688i	$-0.0691993\pi$
$227$	1.35308	+	3.71757i	0.0898074	+	0.246744i	−0.886655	+	0.462432i	$0.846977\pi$
$228$	19.9014	−	1.11733i	1.31800	−	0.0739971i
$229$	5.68658	+	6.77700i	0.375780	+	0.447837i	0.920477	−	0.390796i	$-0.127800\pi$
$229$	5.68658	+	6.77700i	0.375780	+	0.447837i	−0.544698	+	0.838632i	$0.683356\pi$
$230$	−5.05863	−	2.97780i	−0.333556	−	0.196350i
$231$	−1.63120	+	16.0042i	−0.107325	+	1.05300i
$232$	25.5651	+	5.17823i	1.67843	+	0.339968i
$233$	18.0759	−	10.4361i	1.18419	−	0.683694i	0.227211	−	0.973845i	$-0.427039\pi$
$233$	18.0759	−	10.4361i	1.18419	−	0.683694i	0.956981	+	0.290152i	$0.0937058\pi$
$234$	−25.7034	−	5.52101i	−1.68028	−	0.360920i
$235$	−2.77200	+	4.80124i	−0.180825	+	0.313199i
$236$	22.7054	−	12.6029i	1.47799	−	0.820380i
$237$	−1.58422	+	1.07584i	−0.102906	+	0.0698832i
$238$	−0.134775	+	15.9717i	−0.00873618	+	1.03529i
$239$	−1.64140	−	9.30885i	−0.106173	−	0.602139i	−0.990745	−	0.135735i	$-0.956660\pi$
$239$	−1.64140	−	9.30885i	−0.106173	−	0.602139i	0.884572	−	0.466404i	$-0.154451\pi$
$240$	−5.85853	+	11.1336i	−0.378167	+	0.718669i
$241$	−15.3652	−	12.8929i	−0.989759	−	0.830506i	−0.00422600	−	0.999991i	$-0.501345\pi$
$241$	−15.3652	−	12.8929i	−0.989759	−	0.830506i	−0.985533	+	0.169485i	$0.945790\pi$
$242$	1.61241	+	4.54913i	0.103650	+	0.292429i
$243$	−2.94817	−	15.3071i	−0.189125	−	0.981953i
$244$	17.8200	+	21.9799i	1.14081	+	1.40712i
$245$	−6.07871	−	5.10064i	−0.388354	−	0.325868i
$246$	5.89399	−	0.380825i	0.375787	−	0.0242805i
$247$	35.1136	−	6.19148i	2.23423	−	0.393954i
$248$	−3.11796	+	2.48455i	−0.197991	+	0.157769i
$249$	−5.36159	+	3.64104i	−0.339777	+	0.230742i
$250$	−16.9756	+	2.84578i	−1.07363	+	0.179983i
$251$	6.86153	+	3.96150i	0.433096	+	0.250048i	0.700665	−	0.713491i	$-0.252887\pi$
$251$	6.86153	+	3.96150i	0.433096	+	0.250048i	−0.267569	+	0.963539i	$0.586220\pi$
$252$	−2.60355	−	20.0633i	−0.164008	−	1.26387i
$253$	−5.45261	+	3.14807i	−0.342803	+	0.197917i
$254$	−2.80821	+	2.31627i	−0.176203	+	0.145336i
$255$	10.4805	+	1.06820i	0.656316	+	0.0668935i
$256$	−15.3700	+	4.44568i	−0.960623	+	0.277855i
$257$	5.39668	+	6.43152i	0.336636	+	0.401187i	0.907633	−	0.419765i	$-0.137888\pi$
$257$	5.39668	+	6.43152i	0.336636	+	0.401187i	−0.570997	+	0.820952i	$0.693443\pi$
$258$	2.50776	−	8.57412i	0.156126	−	0.533801i
$259$	15.8567	−	5.77136i	0.985286	−	0.358615i
$260$	−8.05276	+	21.0144i	−0.499411	+	1.30326i
$261$	8.71489	+	26.2580i	0.539438	+	1.62533i
$262$	4.55374	−	24.6094i	0.281331	−	1.52037i
$263$	−5.30413	+	30.0812i	−0.327067	+	1.85489i	0.167667	+	0.985844i	$0.446377\pi$
$263$	−5.30413	+	30.0812i	−0.327067	+	1.85489i	−0.494734	+	0.869045i	$0.664734\pi$
$264$	7.29603	+	11.3517i	0.449040	+	0.698648i
$265$	0.314936	+	0.114627i	0.0193464	+	0.00704151i
$266$	13.5185	+	23.8778i	0.828872	+	1.46404i
$267$	−7.79785	−	8.02421i	−0.477221	−	0.491074i
$268$	−12.2868	−	0.207376i	−0.750538	−	0.0126675i
$269$	−19.5851			−1.19412			−0.597061	−	0.802196i	$-0.703665\pi$
$269$	−19.5851			−1.19412			−0.597061	+	0.802196i	$0.703665\pi$
$270$	−13.3354	+	0.479102i	−0.811569	+	0.0291572i
$271$			4.73913i			0.287882i	0.989586	+	0.143941i	$0.0459775\pi$
$271$			4.73913i			0.287882i	−0.989586	+	0.143941i	$0.954022\pi$
$272$	8.26073	+	10.5481i	0.500880	+	0.639575i
$273$	−8.86559	−	35.0871i	−0.536570	−	2.12357i
$274$	−1.98945	−	3.51398i	−0.120187	−	0.212287i
$275$	−1.60393	+	4.40677i	−0.0967207	+	0.265738i
$276$	5.77082	−	5.42170i	0.347362	−	0.326348i
$277$	−7.26043	−	1.28021i	−0.436237	−	0.0769203i	−0.0487830	−	0.998809i	$-0.515534\pi$
$277$	−7.26043	−	1.28021i	−0.436237	−	0.0769203i	−0.387454	+	0.921889i	$0.626645\pi$
$278$	4.66928	+	0.864006i	0.280045	+	0.0518196i
$279$	−3.93064	−	1.55937i	−0.235321	−	0.0933569i
$280$	−17.3131	−	0.438365i	−1.03465	−	0.0261973i
$281$	1.34319	+	3.69038i	0.0801279	+	0.220150i	0.973287	−	0.229591i	$-0.0737387\pi$
$281$	1.34319	+	3.69038i	0.0801279	+	0.220150i	−0.893159	+	0.449740i	$0.851517\pi$
$282$	−5.16639	−	5.40691i	−0.307654	−	0.321977i
$283$	−13.1871	+	11.0653i	−0.783894	+	0.657765i	−0.944226	−	0.329298i	$-0.893188\pi$
$283$	−13.1871	+	11.0653i	−0.783894	+	0.657765i	0.160332	+	0.987063i	$0.448744\pi$
$284$	1.39790	−	7.21381i	0.0829503	−	0.428061i
$285$	16.5100	−	7.41307i	0.977966	−	0.439112i
$286$	15.3591	+	18.6212i	0.908204	+	1.10109i
$287$	4.06524	+	7.04120i	0.239963	+	0.415629i
$288$	−12.1959	−	11.8008i	−0.718653	−	0.695369i
$289$	−2.89054	+	5.00656i	−0.170032	+	0.294504i
$290$	23.3572	−	3.91558i	1.37158	−	0.229931i
$291$	26.7561	−	1.95562i	1.56847	−	0.114640i
$292$	−0.516149	+	0.178057i	−0.0302053	+	0.0104200i
$293$	2.84667	+	16.1443i	0.166305	+	0.943160i	0.947709	+	0.319135i	$0.103392\pi$
$293$	2.84667	+	16.1443i	0.166305	+	0.943160i	−0.781405	+	0.624025i	$0.785496\pi$
$294$	8.90548	−	5.93852i	0.519378	−	0.346341i
$295$	15.1557	−	18.0619i	0.882400	−	1.05160i
$296$	7.38525	−	12.0751i	0.429259	−	0.701850i
$297$	−6.59979	+	12.7003i	−0.382958	+	0.736945i
$298$	−5.04904	−	14.2450i	−0.292483	−	0.825190i
$299$	9.10435	−	10.8501i	0.526518	−	0.627480i
$300$	0.696943	−	5.85640i	0.0402380	−	0.338119i
$301$	12.1106	−	2.13543i	0.698045	−	0.123084i
$302$	4.80901	+	0.0405801i	0.276727	+	0.00233512i
$303$	−6.54573	+	13.5286i	−0.376042	+	0.777201i
$304$	21.3503	+	8.59743i	1.22452	+	0.493097i
$305$	22.2494	+	12.8457i	1.27400	+	0.735542i
$306$	−5.35160	+	13.1644i	−0.305930	+	0.752558i
$307$	10.0551	+	17.4159i	0.573874	+	0.993979i	0.996163	+	0.0875176i	$0.0278934\pi$
$307$	10.0551	+	17.4159i	0.573874	+	0.993979i	−0.422289	+	0.906461i	$0.638773\pi$
$308$	−9.55807	+	15.9281i	−0.544621	+	0.907588i
$309$	11.4994	−	15.9327i	0.654175	−	0.906381i
$310$	−1.83630	+	3.11947i	−0.104295	+	0.177174i
$311$	−6.22295	+	5.22168i	−0.352871	+	0.296094i	−0.801942	−	0.597402i	$-0.796200\pi$
$311$	−6.22295	+	5.22168i	−0.352871	+	0.296094i	0.449070	+	0.893496i	$0.351755\pi$
$312$	−24.1575	−	18.3832i	−1.36765	−	1.04074i
$313$	−1.01105	+	0.367994i	−0.0571482	+	0.0208002i	−0.370436	−	0.928858i	$-0.620792\pi$
$313$	−1.01105	+	0.367994i	−0.0571482	+	0.0208002i	0.313288	+	0.949658i	$0.398570\pi$
$314$	14.8805	+	12.7018i	0.839757	+	0.716802i
$315$	−8.72573	−	16.1644i	−0.491639	−	0.910761i
$316$	−2.18381	+	0.347173i	−0.122849	+	0.0195300i
$317$	3.11019	−	17.6387i	0.174685	−	0.990690i	−0.763821	−	0.645428i	$-0.776679\pi$
$317$	3.11019	−	17.6387i	0.174685	−	0.990690i	0.938506	−	0.345262i	$-0.112210\pi$
$318$	−0.267661	+	0.364335i	−0.0150097	+	0.0204309i
$319$	8.68811	−	23.8704i	0.486441	−	1.33648i
$320$	−11.5868	+	8.76273i	−0.647719	+	0.489852i
$321$	0.532270	−	1.87854i	0.0297084	−	0.104850i
$322$	10.2108	+	3.81431i	0.569026	+	0.212563i
$323$		−	19.2731i		−	1.07238i
$324$	4.42940	−	17.4465i	0.246078	−	0.969250i
$325$		−	10.5497i		−	0.585194i
$326$	−7.76776	+	20.7941i	−0.430217	+	1.15168i
$327$	4.84912	−	17.1140i	0.268157	−	0.946408i
$328$	6.34760	+	2.49404i	0.350487	+	0.137710i
$329$	3.52096	−	9.67376i	0.194117	−	0.533332i
$330$	9.87384	+	7.25388i	0.543537	+	0.399313i
$331$	2.41836	−	13.7152i	0.132925	−	0.753857i	−0.843357	−	0.537354i	$-0.819424\pi$
$331$	2.41836	−	13.7152i	0.132925	−	0.753857i	0.976282	−	0.216503i	$-0.0694650\pi$
$332$	−7.39084	+	1.17497i	−0.405625	+	0.0644846i
$333$	15.0070	+	0.429484i	0.822376	+	0.0235356i
$334$	14.1653	−	16.5951i	0.775089	−	0.908043i
$335$	−10.4845	+	3.81605i	−0.572830	+	0.208493i
$336$	7.12341	−	22.2488i	0.388614	−	1.21377i
$337$	14.8078	−	12.4253i	0.806635	−	0.676847i	−0.143167	−	0.989699i	$-0.545729\pi$
$337$	14.8078	−	12.4253i	0.806635	−	0.676847i	0.949802	+	0.312852i	$0.101284\pi$
$338$	−30.9521	−	18.2202i	−1.68357	−	0.991046i
$339$	−16.0338	+	22.2153i	−0.870836	+	1.20657i
$340$	10.4307	+	6.25919i	0.565683	+	0.339452i
$341$	1.94130	+	3.36242i	0.105127	+	0.182085i
$342$	3.34575	+	24.1821i	0.180918	+	1.30762i
$343$	−7.68048	−	4.43433i	−0.414707	−	0.239431i
$344$	6.82845	−	7.73163i	0.368165	−	0.416862i
$345$	3.13121	−	6.47156i	0.168579	−	0.348417i
$346$	−0.0190496	+	2.25750i	−0.00102411	+	0.121364i
$347$	−4.22476	+	0.744938i	−0.226797	+	0.0399904i	−0.285892	−	0.958262i	$-0.592290\pi$
$347$	−4.22476	+	0.744938i	−0.226797	+	0.0399904i	0.0590948	+	0.998252i	$0.481179\pi$
$348$	−3.77517	+	31.7227i	−0.202370	+	1.70051i
$349$	−6.39346	+	7.61943i	−0.342234	+	0.407859i	−0.909519	−	0.415663i	$-0.863550\pi$
$349$	−6.39346	+	7.61943i	−0.342234	+	0.407859i	0.567284	+	0.823522i	$0.307994\pi$
$350$	7.65223	−	2.71228i	0.409029	−	0.144978i
$351$	4.17982	−	31.9256i	0.223102	−	1.70406i
$352$	2.05611	+	15.4455i	0.109591	+	0.823247i
$353$	−11.6202	+	13.8484i	−0.618481	+	0.737077i	−0.980808	−	0.194974i	$-0.937538\pi$
$353$	−11.6202	+	13.8484i	−0.618481	+	0.737077i	0.362327	+	0.932051i	$0.381982\pi$
$354$	17.6453	+	26.4612i	0.937838	+	1.40639i
$355$	−1.15851	−	6.57025i	−0.0614874	−	0.348712i
$356$	−4.21338	−	12.2137i	−0.223309	−	0.647323i
$357$	−19.5100	+	1.42600i	−1.03258	+	0.0754717i
$358$	−0.464958	−	2.77356i	−0.0245738	−	0.146587i
$359$	−16.4564	+	28.5033i	−0.868536	+	1.50435i	−0.00504305	+	0.999987i	$0.501605\pi$
$359$	−16.4564	+	28.5033i	−0.868536	+	1.50435i	−0.863493	+	0.504361i	$0.831728\pi$
$360$	−14.1740	−	6.04273i	−0.747038	−	0.318480i
$361$	−7.05472	−	12.2191i	−0.371301	−	0.643113i
$362$	−0.836509	+	0.689970i	−0.0439659	+	0.0362640i
$363$	−5.39251	+	2.42127i	−0.283033	+	0.127084i
$364$	7.94993	−	41.0252i	0.416690	−	2.15031i
$365$	−0.379757	+	0.318654i	−0.0198774	+	0.0166791i
$366$	−25.0561	+	23.9415i	−1.30970	+	1.25144i
$367$	12.7028	+	34.9007i	0.663082	+	1.82180i	0.562366	+	0.826888i	$0.309891\pi$
$367$	12.7028	+	34.9007i	0.663082	+	1.82180i	0.100716	+	0.994915i	$0.467887\pi$
$368$	8.69234	−	2.83541i	0.453119	−	0.147806i
$369$	1.05181	+	7.15681i	0.0547551	+	0.372569i
$370$	2.33836	−	12.6370i	0.121566	−	0.656967i
$371$	−0.612880	−	0.108067i	−0.0318191	−	0.00561057i
$372$	−3.34336	−	3.55865i	−0.173345	−	0.184507i
$373$	−8.37871	+	23.0203i	−0.433833	+	1.19195i	0.509608	+	0.860407i	$0.329791\pi$
$373$	−8.37871	+	23.0203i	−0.433833	+	1.19195i	−0.943441	+	0.331540i	$0.892432\pi$
$374$	11.3542	−	6.42823i	0.587112	−	0.332396i
$375$	−5.16430	−	20.4386i	−0.266683	−	1.05544i
$376$	−2.74711	−	8.18668i	−0.141671	−	0.422196i
$377$			57.1454i			2.94314i
$378$	24.2318	−	5.17608i	1.24635	−	0.266229i
$379$	−32.5154			−1.67021			−0.835103	−	0.550094i	$-0.814592\pi$
$379$	−32.5154			−1.67021			−0.835103	+	0.550094i	$0.814592\pi$
$380$	20.8946	+	0.352658i	1.07187	+	0.0180910i
$381$	−3.10710	−	3.19729i	−0.159181	−	0.163802i
$382$	−0.168480	+	0.0953857i	−0.00862019	+	0.00488035i
$383$	21.7889	+	7.93050i	1.11336	+	0.405230i	0.832225	−	0.554439i	$-0.187067\pi$
$383$	21.7889	+	7.93050i	1.11336	+	0.405230i	0.281135	+	0.959668i	$0.409289\pi$
$384$	−6.95739	−	18.3192i	−0.355043	−	0.934850i
$385$	−2.92873	+	16.6096i	−0.149262	+	0.846506i
$386$	23.6388	+	4.37414i	1.20318	+	0.222638i
$387$	10.7161	+	2.20735i	0.544729	+	0.112206i
$388$	28.9266	+	11.0847i	1.46852	+	0.562742i
$389$	−9.45367	+	3.44085i	−0.479320	+	0.174458i	−0.570370	−	0.821388i	$-0.693200\pi$
$389$	−9.45367	+	3.44085i	−0.479320	+	0.174458i	0.0910496	+	0.995846i	$0.470978\pi$
$390$	−26.4540	−	7.73725i	−1.33955	−	0.391791i
$391$	−4.92126	−	5.86493i	−0.248879	−	0.296602i
$392$	12.2225	−	1.83747i	0.617327	−	0.0928065i
$393$	30.4939	+	3.10803i	1.53822	+	0.156779i
$394$	5.12319	+	6.21127i	0.258103	+	0.312919i
$395$	−1.73871	+	1.00384i	−0.0874838	+	0.0505088i
$396$	−13.1303	+	10.0366i	−0.659823	+	0.504359i
$397$	−12.5559	−	7.24913i	−0.630161	−	0.363823i	0.150654	−	0.988587i	$-0.451862\pi$
$397$	−12.5559	−	7.24913i	−0.630161	−	0.363823i	−0.780814	+	0.624763i	$0.785195\pi$
$398$	−3.31070	−	19.7490i	−0.165951	−	0.989927i
$399$	−27.8012	+	18.8797i	−1.39180	+	0.945168i
$400$	3.60214	−	5.77945i	0.180107	−	0.288973i
$401$	−3.68121	+	0.649097i	−0.183831	+	0.0324143i	−0.264806	−	0.964302i	$-0.585308\pi$
$401$	−3.68121	+	0.649097i	−0.183831	+	0.0324143i	0.0809748	+	0.996716i	$0.474197\pi$
$402$	−0.970417	−	15.0191i	−0.0484000	−	0.749082i
$403$	−6.69088	−	5.61431i	−0.333296	−	0.279669i
$404$	−13.4803	+	10.9290i	−0.670669	+	0.543738i
$405$	−1.91282	−	16.2307i	−0.0950487	−	0.806511i
$406$	−41.4503	+	14.6918i	−2.05714	+	0.729140i
$407$	−10.5595	−	8.86048i	−0.523415	−	0.439198i
$408$	−12.0534	+	11.1342i	−0.596731	+	0.551225i
$409$	4.51536	+	25.6079i	0.223270	+	1.26623i	0.865965	+	0.500105i	$0.166705\pi$
$409$	4.51536	+	25.6079i	0.223270	+	1.26623i	−0.642695	+	0.766122i	$0.722184\pi$
$410$	6.19197	+	0.0522500i	0.305800	+	0.00258045i
$411$	4.09136	−	2.77844i	0.201812	−	0.137050i
$412$	19.8377	−	11.0112i	0.977335	−	0.542483i
$413$	−21.8910	+	37.9163i	−1.07719	+	1.86574i
$414$	7.19289	+	6.50447i	0.353511	+	0.319677i
$415$	−5.88444	+	3.39738i	−0.288856	+	0.166771i
$416$	−16.2304	−	31.0689i	−0.795762	−	1.52328i
$417$	−0.589703	+	5.78578i	−0.0288779	+	0.283331i
$418$	11.3707	−	19.3164i	0.556160	−	0.944795i
$419$	8.50595	+	10.1370i	0.415543	+	0.495225i	0.932694	−	0.360670i	$-0.117452\pi$
$419$	8.50595	+	10.1370i	0.415543	+	0.495225i	−0.517151	+	0.855894i	$0.673007\pi$
$420$	−1.18898	−	21.1775i	−0.0580163	−	1.03336i
$421$	1.63940	+	4.50421i	0.0798994	+	0.219522i	0.973210	−	0.229918i	$-0.0738458\pi$
$421$	1.63940	+	4.50421i	0.0798994	+	0.219522i	−0.893311	+	0.449440i	$0.851624\pi$
$422$	9.69870	−	11.3624i	0.472125	−	0.553111i
$423$	6.08567	−	6.84500i	0.295896	−	0.332815i
$424$	−0.458549	+	0.249486i	−0.0222691	+	0.0121161i
$425$	−5.61592	−	0.990237i	−0.272412	−	0.0480336i
$426$	8.94503	+	0.988034i	0.433388	+	0.0478704i
$427$	−44.8291	−	16.3165i	−2.16943	−	0.789609i
$428$	1.47813	−	1.70238i	0.0714483	−	0.0822877i
$429$	−21.2011	+	20.6031i	−1.02360	+	0.994726i
$430$	3.27743	−	8.77360i	0.158052	−	0.423101i
$431$	18.8441			0.907686			0.453843	−	0.891082i	$-0.350053\pi$
$431$	18.8441			0.907686			0.453843	+	0.891082i	$0.350053\pi$
$432$	13.1906	−	16.0626i	0.634634	−	0.772813i
$433$	32.5586			1.56466			0.782332	−	0.622861i	$-0.214030\pi$
$433$	32.5586			1.56466			0.782332	+	0.622861i	$0.214030\pi$
$434$	2.35214	−	6.29662i	0.112906	−	0.302248i
$435$	7.10568	+	28.1219i	0.340691	+	1.34834i
$436$	13.4662	−	15.5091i	0.644914	−	0.742754i
$437$	−12.3593	−	4.49843i	−0.591227	−	0.215189i
$438$	−0.268752	−	0.612326i	−0.0128415	−	0.0292581i
$439$	2.24864	+	0.396495i	0.107322	+	0.0189237i	0.227051	−	0.973883i	$-0.427092\pi$
$439$	2.24864	+	0.396495i	0.107322	+	0.0189237i	−0.119729	+	0.992807i	$0.538203\pi$
$440$	6.76131	+	12.4271i	0.322333	+	0.592440i
$441$	8.13592	+	10.2795i	0.387425	+	0.489498i
$442$	−19.0562	+	22.3250i	−0.906411	+	1.06189i
$443$	2.34896	+	6.45372i	0.111603	+	0.306626i	0.982903	−	0.184125i	$-0.0589450\pi$
$443$	2.34896	+	6.45372i	0.111603	+	0.306626i	−0.871300	+	0.490750i	$0.836723\pi$
$444$	15.4754	+	7.81263i	0.734429	+	0.370771i
$445$	−7.54033	−	8.98621i	−0.357446	−	0.425987i
$446$	18.0711	−	30.6989i	0.855691	−	1.45363i
$447$	16.8859	−	7.58187i	0.798676	−	0.358610i
$448$	18.3630	−	19.7603i	0.867569	−	0.933589i
$449$	−8.55447	+	4.93893i	−0.403710	+	0.233082i	−0.688084	−	0.725631i	$-0.741548\pi$
$449$	−8.55447	+	4.93893i	−0.403710	+	0.233082i	0.284373	+	0.958714i	$0.408214\pi$
$450$	7.21825	+	0.267554i	0.340271	+	0.0126126i
$451$	3.32085	−	5.75188i	0.156373	−	0.270846i
$452$	−27.6602	+	15.3532i	−1.30103	+	0.722152i
$453$	0.429360	+	5.87435i	0.0201731	+	0.276001i
$454$	−5.59465	−	0.0472096i	−0.262570	−	0.00221566i
$455$	−6.58850	−	37.3652i	−0.308874	−	1.75171i
$456$	−8.36867	+	26.9182i	−0.391899	+	1.26056i
$457$	21.3478	+	17.9129i	0.998607	+	0.837931i	0.986791	−	0.162000i	$-0.0517944\pi$
$457$	21.3478	+	17.9129i	0.998607	+	0.837931i	0.0118159	+	0.999930i	$0.496239\pi$
$458$	−11.7924	+	4.17972i	−0.551021	+	0.195306i
$459$	−16.6026	−	5.22169i	−0.774941	−	0.243728i
$460$	6.44843	−	5.22800i	0.300659	−	0.243757i
$461$	−23.3143	−	19.5630i	−1.08585	−	0.911140i	−0.0894610	−	0.995990i	$-0.528514\pi$
$461$	−23.3143	−	19.5630i	−1.08585	−	0.911140i	−0.996394	+	0.0848500i	$0.972959\pi$
$462$	−20.3951	−	10.0813i	−0.948866	−	0.469023i
$463$	−21.1468	+	3.72876i	−0.982776	+	0.173290i	−0.641875	−	0.766809i	$-0.721843\pi$
$463$	−21.1468	+	3.72876i	−0.982776	+	0.173290i	−0.340901	+	0.940099i	$0.610732\pi$
$464$	−19.5119	+	31.3059i	−0.905817	+	1.45334i
$465$	−3.99077	−	1.93090i	−0.185067	−	0.0895434i
$466$	4.88025	+	29.1116i	0.226073	+	1.34857i
$467$	−30.9949	−	17.8949i	−1.43427	−	0.828078i	−0.436830	−	0.899544i	$-0.643899\pi$
$467$	−30.9949	−	17.8949i	−1.43427	−	0.828078i	−0.997443	+	0.0714659i	$0.977232\pi$
$468$	20.0345	−	31.3195i	0.926093	−	1.44774i
$469$	17.9424	−	10.3590i	0.828501	−	0.478336i
$470$	−4.98885	−	6.04840i	−0.230119	−	0.278992i
$471$	−14.0231	+	19.4294i	−0.646148	+	0.895259i
$472$	5.45975	+	36.3170i	0.251305	+	1.67163i
$473$	−6.45723	−	7.69542i	−0.296904	−	0.353836i
$474$	−0.641261	−	2.63118i	−0.0294541	−	0.120854i
$475$	−9.20567	+	3.35059i	−0.422385	+	0.153736i
$476$	−21.0926	−	8.08274i	−0.966779	−	0.370472i
$477$	−0.471395	−	0.290450i	−0.0215837	−	0.0132988i
$478$	13.1446	+	2.43229i	0.601222	+	0.111250i
$479$	4.55057	−	25.8076i	0.207921	−	1.17918i	−0.684856	−	0.728679i	$-0.740135\pi$
$479$	4.55057	−	25.8076i	0.207921	−	1.17918i	0.892777	−	0.450500i	$-0.148754\pi$
$480$	−11.8504	−	13.2712i	−0.540895	−	0.605745i
$481$	29.1396	+	10.6059i	1.32865	+	0.483589i
$482$	24.6845	−	13.9752i	1.12435	−	0.636555i
$483$	−3.63926	+	12.8441i	−0.165592	+	0.584425i
$484$	−6.82463	−	0.115186i	−0.310211	−	0.00523571i
$485$	28.1261			1.27714
$486$	21.7379	+	3.66955i	0.986049	+	0.166454i
$487$		−	23.1000i		−	1.04676i	−0.852099	−	0.523380i	$-0.824671\pi$
$487$		−	23.1000i		−	1.04676i	0.852099	−	0.523380i	$-0.175329\pi$
$488$	−37.9378	+	12.7303i	−1.71736	+	0.576275i
$489$	−26.1567	−	7.41129i	−1.18285	−	0.335150i
$490$	9.76558	−	5.52882i	0.441164	−	0.249767i
$491$	11.2556	−	30.9245i	0.507957	−	1.39560i	−0.375383	−	0.926870i	$-0.622489\pi$
$491$	11.2556	−	30.9245i	0.507957	−	1.39560i	0.883341	−	0.468732i	$-0.155289\pi$
$492$	−2.41234	+	7.99681i	−0.108757	+	0.360524i
$493$	30.4200	+	5.36387i	1.37005	+	0.241577i
$494$	−9.17478	+	49.5825i	−0.412793	+	2.23082i
$495$	−7.87148	+	12.7753i	−0.353796	+	0.574205i
$496$	−1.74849	−	5.36024i	−0.0785094	−	0.240682i
$497$	4.23710	+	11.6413i	0.190060	+	0.522185i
$498$	−2.17027	−	8.90492i	−0.0972521	−	0.399039i
$499$	−6.98386	+	5.86015i	−0.312640	+	0.262336i	−0.785582	−	0.618757i	$-0.787636\pi$
$499$	−6.98386	+	5.86015i	−0.312640	+	0.262336i	0.472942	+	0.881094i	$0.343192\pi$
$500$	4.63092	−	23.8976i	0.207101	−	1.06873i
$501$	21.6681	+	15.6388i	0.968058	+	0.698690i
$502$	−8.64386	+	7.12964i	−0.385794	+	0.318211i
$503$	−7.67973	−	13.3017i	−0.342422	−	0.593093i	0.642460	−	0.766319i	$-0.277914\pi$
$503$	−7.67973	−	13.3017i	−0.342422	−	0.593093i	−0.984882	+	0.173227i	$0.944581\pi$
$504$	27.8683	+	6.47987i	1.24135	+	0.288637i
$505$	−7.87826	+	13.6455i	−0.350578	+	0.607219i
$506$	−1.47213	−	8.78154i	−0.0654442	−	0.390387i
$507$	19.1589	−	39.5973i	0.850875	−	1.75858i
$508$	−1.67885	−	4.86660i	−0.0744867	−	0.215920i
$509$	−6.62546	−	37.5748i	−0.293668	−	1.66548i	−0.672566	−	0.740037i	$-0.734808\pi$
$509$	−6.62546	−	37.5748i	−0.293668	−	1.66548i	0.378898	−	0.925439i	$-0.376303\pi$
$510$	−6.60181	+	13.3559i	−0.292333	+	0.591410i
$511$	0.591706	−	0.705168i	0.0261755	−	0.0311948i
$512$	1.71675	−	22.5622i	0.0758704	−	0.997118i
$513$	−29.1857	+	6.49226i	−1.28858	+	0.286640i
$514$	−11.1912	+	3.96665i	−0.493623	+	0.174961i
$515$	13.2416	−	15.7807i	0.583494	−	0.695381i
$516$	10.1179	+	7.56548i	0.445417	+	0.333052i
$517$	−8.28179	+	1.46030i	−0.364233	+	0.0642241i
$518$	−0.201365	+	23.8631i	−0.00884747	+	1.04848i
$519$	−2.75761	+	0.201555i	−0.121045	+	0.00884729i
$520$	−23.8546	−	21.0680i	−1.04609	−	0.923893i
$521$	3.40601	+	1.96646i	0.149220	+	0.0861521i	0.572751	−	0.819729i	$-0.305876\pi$
$521$	3.40601	+	1.96646i	0.149220	+	0.0861521i	−0.423531	+	0.905882i	$0.639210\pi$
$522$	−39.0995	−	1.44927i	−1.71134	−	0.0634329i
$523$	12.1806	+	21.0974i	0.532619	+	0.922523i	0.999275	+	0.0380841i	$0.0121255\pi$
$523$	12.1806	+	21.0974i	0.532619	+	0.922523i	−0.466656	+	0.884439i	$0.654541\pi$
$524$	30.3489	+	18.2116i	1.32580	+	0.795579i
$525$	4.07289	+	9.07090i	0.177755	+	0.395887i
$526$	−37.2266	−	21.9137i	−1.62316	−	0.955482i
$527$	−3.61668	+	3.03476i	−0.157545	+	0.132196i
$528$	−18.6494	+	4.04797i	−0.811610	+	0.176165i
$529$	16.7033	−	6.07949i	0.726229	−	0.264326i
$530$	−0.307716	+	0.360499i	−0.0133663	+	0.0156591i
$531$	−30.5437	+	24.1745i	−1.32548	+	1.04909i
$532$	−38.3234	+	6.09249i	−1.66153	+	0.264143i
$533$	−2.59452	+	14.7143i	−0.112381	+	0.637345i
$534$	14.4895	−	6.35951i	0.627022	−	0.275203i
$535$	0.700118	−	1.92356i	0.0302688	−	0.0831627i
$536$	6.35531	−	16.1749i	0.274508	−	0.698651i
$537$	3.33936	−	0.843769i	0.144104	−	0.0364113i
$538$	9.69237	−	25.9462i	0.417868	−	1.11862i
$539$		−	12.0367i		−	0.518457i
$540$	5.96481	−	17.9039i	0.256685	−	0.770460i
$541$		−	8.40412i		−	0.361321i	−0.983546	−	0.180661i	$-0.942176\pi$
$541$		−	8.40412i		−	0.361321i	0.983546	−	0.180661i	$-0.0578236\pi$
$542$	−6.27839	−	2.34533i	−0.269680	−	0.100740i
$543$	−0.925541	−	0.952408i	−0.0397188	−	0.0408718i
$544$	−18.0623	+	5.72367i	−0.774413	+	0.245400i
$545$	6.37827	−	17.5241i	0.273215	−	0.750652i
$546$	50.8707	+	5.61898i	2.17707	+	0.240470i
$547$	5.52901	−	31.3566i	0.236403	−	1.34071i	−0.603235	−	0.797564i	$-0.706122\pi$
$547$	5.52901	−	31.3566i	0.236403	−	1.34071i	0.839638	−	0.543146i	$-0.182767\pi$
$548$	5.63986	−	0.896602i	0.240923	−	0.0383010i
$549$	−31.7203	−	28.2016i	−1.35379	−	1.20361i
$550$	−5.04431	−	4.30573i	−0.215090	−	0.183597i
$551$	49.8648	−	18.1493i	2.12431	−	0.773187i
$552$	4.32676	+	10.3283i	0.184159	+	0.439601i
$553$	2.85585	−	2.39635i	0.121443	−	0.101903i
$554$	5.28910	−	8.98504i	0.224712	−	0.381738i
$555$	15.6587	+	1.59598i	0.664676	+	0.0677456i
$556$	−3.45539	+	5.75826i	−0.146541	+	0.244205i
$557$	−8.29813	−	14.3728i	−0.351603	−	0.608994i	0.634928	−	0.772572i	$-0.281030\pi$
$557$	−8.29813	−	14.3728i	−0.351603	−	0.608994i	−0.986530	+	0.163578i	$0.947697\pi$
$558$	4.01106	−	4.43559i	0.169802	−	0.187773i
$559$	19.5712	+	11.2994i	0.827772	+	0.477914i
$560$	9.14873	−	22.7194i	0.386605	−	0.960068i
$561$	8.97756	+	13.2198i	0.379033	+	0.558142i
$562$	−5.55373	−	0.0468644i	−0.234270	−	0.00197685i
$563$	−30.3941	+	5.35931i	−1.28096	+	0.225868i	−0.772388	−	0.635151i	$-0.780938\pi$
$563$	−30.3941	+	5.35931i	−1.28096	+	0.225868i	−0.508573	+	0.861019i	$0.669827\pi$
$564$	9.71983	−	4.16862i	0.409279	−	0.175531i
$565$	−18.4630	+	22.0034i	−0.776746	+	0.925690i
$566$	−8.13318	−	22.9464i	−0.341863	−	0.964508i
$567$	8.73147	+	29.0641i	0.366687	+	1.22058i
$568$	8.86503	+	5.42195i	0.371969	+	0.227500i
$569$	−10.3725	+	12.3615i	−0.434838	+	0.518220i	−0.938312	−	0.345791i	$-0.887611\pi$
$569$	−10.3725	+	12.3615i	−0.434838	+	0.518220i	0.503473	+	0.864011i	$0.332055\pi$
$570$	1.65026	+	25.5410i	0.0691220	+	1.06979i
$571$	−0.657320	−	3.72785i	−0.0275080	−	0.156006i	0.967960	−	0.251105i	$-0.0807941\pi$
$571$	−0.657320	−	3.72785i	−0.0275080	−	0.156006i	−0.995468	+	0.0950998i	$0.969683\pi$
$572$	−32.2703	+	11.1324i	−1.34929	+	0.465468i
$573$	−0.133214	−	0.196163i	−0.00556510	−	0.00819483i
$574$	−11.3400	+	1.90103i	−0.473322	+	0.0793473i
$575$	−1.94579	+	3.37022i	−0.0811452	+	0.140548i
$576$	21.6693	−	10.3171i	0.902887	−	0.429879i
$577$	−12.2824	−	21.2738i	−0.511325	−	0.885641i	−0.999914	−	0.0131265i	$-0.995822\pi$
$577$	−12.2824	−	21.2738i	−0.511325	−	0.885641i	0.488589	−	0.872514i	$-0.337512\pi$
$578$	−5.20219	−	6.30706i	−0.216383	−	0.262339i
$579$	−2.98545	+	29.2913i	−0.124071	+	1.21730i
$580$	−6.37179	+	32.8813i	−0.264574	+	1.36532i
$581$	9.66529	−	8.11014i	0.400984	−	0.336465i
$582$	−10.6504	+	36.4142i	−0.441474	+	1.50942i
$583$	0.173876	+	0.477719i	0.00720119	+	0.0197851i
$584$	0.0195447	−	0.771910i	0.000808764	−	0.0319419i
$585$	6.81041	−	33.0626i	0.281576	−	1.36697i
$586$	−22.7967	−	4.21832i	−0.941723	−	0.174257i
$587$	30.0373	+	5.29639i	1.23977	+	0.218605i	0.754819	−	0.655934i	$-0.227725\pi$
$587$	30.0373	+	5.29639i	1.23977	+	0.218605i	0.484955	+	0.874539i	$0.338836\pi$
$588$	3.46013	+	14.7368i	0.142694	+	0.607737i
$589$	−2.77401	+	7.62154i	−0.114301	+	0.314040i
$590$	16.4280	+	29.0168i	0.676329	+	1.19460i
$591$	−7.07186	+	6.87236i	−0.290897	+	0.282691i
$592$	12.3422	+	15.7597i	0.507260	+	0.647722i
$593$		−	38.8450i		−	1.59517i	−0.603206	−	0.797586i	$-0.706110\pi$
$593$		−	38.8450i		−	1.59517i	0.603206	−	0.797586i	$-0.293890\pi$
$594$	−13.5592	−	15.0286i	−0.556339	−	0.616630i
$595$	−20.5090			−0.840785
$596$	21.3704	+	0.360688i	0.875366	+	0.0147744i
$597$	23.7777	−	6.00800i	0.973156	−	0.245891i
$598$	9.86863	+	17.4310i	0.403558	+	0.712807i
$599$	42.6481	+	15.5226i	1.74255	+	0.634238i	0.999392	−	0.0348721i	$-0.0111024\pi$
$599$	42.6481	+	15.5226i	1.74255	+	0.634238i	0.743163	+	0.669110i	$0.233325\pi$
$600$	7.41363	+	3.82156i	0.302660	+	0.156014i
$601$	2.26751	−	12.8597i	0.0924935	−	0.524557i	−0.902993	−	0.429655i	$-0.858635\pi$
$601$	2.26751	−	12.8597i	0.0924935	−	0.524557i	0.995487	−	0.0949017i	$-0.0302537\pi$
$602$	−3.16437	+	17.1009i	−0.128970	+	0.696981i
$603$	18.2370	−	2.68022i	0.742667	−	0.109147i
$604$	−2.43367	+	6.35088i	−0.0990246	+	0.258414i
$605$	−5.82355	+	2.11960i	−0.236761	+	0.0861739i
$606$	−14.6833	−	15.3669i	−0.596469	−	0.624238i
$607$	−0.568907	−	0.677997i	−0.0230912	−	0.0275190i	0.754375	−	0.656443i	$-0.227940\pi$
$607$	−0.568907	−	0.677997i	−0.0230912	−	0.0275190i	−0.777466	+	0.628924i	$0.783495\pi$
$608$	−21.9558	+	24.0301i	−0.890426	+	0.974548i
$609$	−22.0618	−	49.1349i	−0.893990	−	1.99104i
$610$	−28.0289	+	23.1188i	−1.13486	+	0.936052i
$611$	16.3837	−	9.45912i	0.662812	−	0.382675i
$612$	−14.7917	−	13.6046i	−0.597919	−	0.549935i
$613$	−1.26069	−	0.727860i	−0.0509188	−	0.0293980i	0.474324	−	0.880350i	$-0.342692\pi$
$613$	−1.26069	−	0.727860i	−0.0509188	−	0.0293980i	−0.525243	+	0.850952i	$0.676026\pi$
$614$	−28.0487	+	4.70206i	−1.13195	+	0.189760i
$615$	0.552834	+	7.56368i	0.0222924	+	0.304997i
$616$	−16.3714	−	20.5451i	−0.659621	−	0.827786i
$617$	−11.7561	+	2.07291i	−0.473281	+	0.0834522i	−0.405201	−	0.914228i	$-0.632798\pi$
$617$	−11.7561	+	2.07291i	−0.473281	+	0.0834522i	−0.0680800	+	0.997680i	$0.521687\pi$
$618$	15.4168	+	23.1192i	0.620153	+	0.929990i
$619$	1.39092	+	1.16712i	0.0559059	+	0.0469106i	0.670312	−	0.742079i	$-0.266160\pi$
$619$	1.39092	+	1.16712i	0.0559059	+	0.0469106i	−0.614407	+	0.788990i	$0.710605\pi$
$620$	−3.22391	−	3.97650i	−0.129475	−	0.159700i
$621$	−7.22365	+	9.42802i	−0.289875	+	0.378333i
$622$	−3.83801	−	10.8283i	−0.153890	−	0.434175i
$623$	16.6864	+	14.0016i	0.668528	+	0.560961i
$624$	36.3092	−	22.9063i	1.45353	−	0.916984i
$625$	−2.35967	−	13.3823i	−0.0943867	−	0.535293i
$626$	0.0128394	−	1.52156i	0.000513167	−	0.0608137i
$627$	24.7116	+	11.9565i	0.986888	+	0.477498i
$628$	−24.1914	+	13.4278i	−0.965343	+	0.535827i
$629$	8.38098	−	14.5163i	0.334171	−	0.578802i
$630$	25.7328	−	3.56030i	1.02522	−	0.141846i
$631$	−22.9218	+	13.2339i	−0.912502	+	0.526834i	−0.881235	−	0.472678i	$-0.843288\pi$
$631$	−22.9218	+	13.2339i	−0.912502	+	0.526834i	−0.0312670	+	0.999511i	$0.509954\pi$
$632$	0.620802	−	3.06492i	0.0246942	−	0.121916i
$633$	14.8357	+	10.7076i	0.589667	+	0.425589i
$634$	21.8286	+	12.8495i	0.866923	+	0.510320i
$635$	−3.00448	−	3.58061i	−0.119229	−	0.142092i
$636$	−0.350208	−	0.534901i	−0.0138867	−	0.0212102i
$637$	9.26118	+	25.4449i	0.366941	+	1.00816i
$638$	27.3238	+	23.3231i	1.08176	+	0.923370i
$639$	−0.315310	+	11.0175i	−0.0124735	+	0.435845i
$640$	−5.87472	−	19.6867i	−0.232219	−	0.778183i
$641$	−29.2875	−	5.16418i	−1.15679	−	0.203973i	−0.437850	−	0.899048i	$-0.644260\pi$
$641$	−29.2875	−	5.16418i	−1.15679	−	0.203973i	−0.718937	+	0.695075i	$0.755371\pi$
$642$	2.22528	+	1.63481i	0.0878246	+	0.0645209i
$643$	39.9458	+	14.5391i	1.57531	+	0.573366i	0.974177	−	0.225784i	$-0.0724944\pi$
$643$	39.9458	+	14.5391i	1.57531	+	0.573366i	0.601132	+	0.799150i	$0.294717\pi$
$644$	−10.1064	+	11.6396i	−0.398247	+	0.458665i
$645$	11.0362	+	3.12702i	0.434551	+	0.123126i
$646$	25.5329	+	9.53798i	1.00458	+	0.375267i
$647$	1.31046			0.0515196			0.0257598	−	0.999668i	$-0.491799\pi$
$647$	1.31046			0.0515196			0.0257598	+	0.999668i	$0.491799\pi$
$648$	20.9210	+	14.5021i	0.821856	+	0.569696i
$649$	35.7651			1.40390
$650$	13.9763	+	5.22092i	0.548194	+	0.204781i
$651$	7.92046	+	2.24420i	0.310427	+	0.0879570i
$652$	−23.7038	−	20.5814i	−0.928314	−	0.806031i
$653$	45.3419	+	16.5031i	1.77436	+	0.645816i	0.999913	+	0.0131827i	$0.00419629\pi$
$653$	45.3419	+	16.5031i	1.77436	+	0.645816i	0.774452	+	0.632633i	$0.218026\pi$
$654$	20.2729	+	14.8936i	0.792732	+	0.582386i
$655$	31.6475	+	5.58030i	1.23657	+	0.218040i
$656$	−6.44544	+	7.17502i	−0.251652	+	0.280137i
$657$	0.720697	−	0.389041i	0.0281171	−	0.0151779i
$658$	11.0733	+	9.45197i	0.431682	+	0.368476i
$659$	−10.2281	−	28.1016i	−0.398432	−	1.09468i	−0.963048	−	0.269328i	$-0.913198\pi$
$659$	−10.2281	−	28.1016i	−0.398432	−	1.09468i	0.564617	−	0.825353i	$-0.309024\pi$
$660$	−14.4964	+	9.49099i	−0.564270	+	0.369436i
$661$	−1.72700	−	2.05816i	−0.0671726	−	0.0800532i	0.731412	−	0.681936i	$-0.238862\pi$
$661$	−1.72700	−	2.05816i	−0.0671726	−	0.0800532i	−0.798584	+	0.601883i	$0.794417\pi$
$662$	16.9731	+	9.99131i	0.659677	+	0.388323i
$663$	−29.1496	−	21.0385i	−1.13207	−	0.817069i
$664$	2.10103	−	10.3728i	0.0815358	−	0.402544i
$665$	−30.5123	+	17.6163i	−1.18322	+	0.683130i
$666$	−7.99571	+	19.6686i	−0.309827	+	0.762144i
$667$	10.5399	−	18.2556i	0.408106	−	0.706861i
$668$	14.9749	+	26.9788i	0.579398	+	1.04384i
$669$	39.2734	+	19.0021i	1.51840	+	0.734664i
$670$	0.133143	−	15.7784i	0.00514378	−	0.609571i
$671$	6.76718	+	38.3786i	0.261244	+	1.48159i
$672$	25.9499	+	20.4477i	1.00104	+	0.788787i
$673$	9.16634	+	7.69147i	0.353337	+	0.296485i	0.802128	−	0.597152i	$-0.203701\pi$
$673$	9.16634	+	7.69147i	0.353337	+	0.296485i	−0.448792	+	0.893636i	$0.648145\pi$
$674$	9.13276	+	25.7665i	0.351781	+	0.992488i
$675$	0.392214	+	8.83788i	0.0150963	+	0.340170i
$676$	39.4558	−	31.9884i	1.51753	−	1.23032i
$677$	28.8050	+	24.1702i	1.10707	+	0.928938i	0.997880	−	0.0650833i	$-0.0207313\pi$
$677$	28.8050	+	24.1702i	1.10707	+	0.928938i	0.109186	+	0.994021i	$0.465176\pi$
$678$	−21.4959	−	32.2356i	−0.825546	−	1.23800i
$679$	−51.4337	+	9.06915i	−1.97385	+	0.348042i
$680$	−13.4542	+	10.7209i	−0.515943	+	0.411129i
$681$	−0.499503	−	6.83403i	−0.0191410	−	0.261881i
$682$	−5.41525	+	0.907808i	−0.207361	+	0.0347618i
$683$	3.37848	+	1.95057i	0.129274	+	0.0746363i	0.563242	−	0.826292i	$-0.309554\pi$
$683$	3.37848	+	1.95057i	0.129274	+	0.0746363i	−0.433968	+	0.900928i	$0.642887\pi$
$684$	−33.6922	−	7.53495i	−1.28825	−	0.288106i
$685$	4.49034	−	2.59250i	0.171567	−	0.0990544i
$686$	9.67555	−	7.98060i	0.369414	−	0.304701i
$687$	−6.27646	−	13.9786i	−0.239462	−	0.533316i
$688$	6.86354	+	12.8726i	0.261670	+	0.490763i
$689$	−0.735126	−	0.876089i	−0.0280061	−	0.0333764i
$690$	7.02391	+	7.35091i	0.267396	+	0.279844i
$691$	21.8838	−	7.96504i	0.832497	−	0.303004i	0.109614	−	0.993974i	$-0.465039\pi$
$691$	21.8838	−	7.96504i	0.832497	−	0.303004i	0.722883	+	0.690970i	$0.242816\pi$
$692$	−2.98131	−	1.14244i	−0.113332	−	0.0434292i
$693$	10.2751	−	25.9000i	0.390318	−	0.983860i
$694$	1.10388	−	5.96560i	0.0419027	−	0.226451i
$695$	−1.05878	+	6.00465i	−0.0401619	+	0.227769i
$696$	−40.1578	−	20.7004i	−1.52218	−	0.784648i
$697$	7.58927	+	2.76227i	0.287464	+	0.104628i
$698$	−6.93017	−	12.2408i	−0.262311	−	0.463321i
$699$	−35.0502	+	8.85629i	−1.32572	+	0.334975i
$700$	−0.193757	+	11.4799i	−0.00732333	+	0.433900i
$701$	15.2353			0.575429			0.287715	−	0.957716i	$-0.407105\pi$
$701$	15.2353			0.575429			0.287715	+	0.957716i	$0.407105\pi$
$702$	40.2265	+	21.3370i	1.51825	+	0.805312i
$703$		−	28.7955i		−	1.08604i
$704$	−21.4797	−	4.91982i	−0.809545	−	0.185423i
$705$	6.88642	−	6.69216i	0.259358	−	0.252041i
$706$	−12.5957	−	22.2478i	−0.474045	−	0.837307i
$707$	10.0069	−	27.4937i	0.376347	−	1.03401i
$708$	−43.7881	+	10.2812i	−1.64566	+	0.386392i
$709$	−37.6664	−	6.64161i	−1.41459	−	0.249431i	−0.586467	−	0.809973i	$-0.699482\pi$
$709$	−37.6664	−	6.64161i	−1.41459	−	0.249431i	−0.828126	+	0.560542i	$0.810593\pi$
$710$	9.27758	+	1.71673i	0.348181	+	0.0644277i
$711$	3.14800	−	1.04480i	0.118059	−	0.0391831i
$712$	18.2658	+	0.462487i	0.684539	+	0.0173324i
$713$	1.10196	+	3.02761i	0.0412687	+	0.113385i
$714$	7.76605	−	26.5525i	0.290637	−	0.993701i
$715$	−23.7429	+	19.9227i	−0.887934	+	0.745065i
$716$	3.90451	+	0.756622i	0.145918	+	0.0282763i
$717$	−1.66009	+	16.2877i	−0.0619973	+	0.608277i
$718$	−29.6171	−	35.9073i	−1.10530	−	1.34005i
$719$	−11.2648	−	19.5112i	−0.420106	−	0.727645i	0.575843	−	0.817560i	$-0.304674\pi$
$719$	−11.2648	−	19.5112i	−0.420106	−	0.727645i	−0.995949	+	0.0899151i	$0.971340\pi$
$720$	15.0199	−	15.7873i	0.559760	−	0.588357i
$721$	−19.1262	+	33.1276i	−0.712298	+	1.23374i
$722$	19.6792	−	3.29900i	0.732383	−	0.122776i
$723$	19.5176	+	28.7404i	0.725867	+	1.06887i
$724$	−0.500094	−	1.44966i	−0.0185859	−	0.0538762i
$725$	−2.72644	−	15.4624i	−0.101258	−	0.574260i
$726$	−0.539012	−	8.34223i	−0.0200046	−	0.309609i
$727$	−15.4990	+	18.4710i	−0.574827	+	0.685052i	−0.972614	−	0.232425i	$-0.925334\pi$
$727$	−15.4990	+	18.4710i	−0.574827	+	0.685052i	0.397787	+	0.917478i	$0.369778\pi$
$728$	50.4158	+	30.8348i	1.86853	+	1.14282i
$729$	−2.31466	+	26.9006i	−0.0857282	+	0.996319i
$730$	−0.234216	−	0.660798i	−0.00866871	−	0.0244572i
$731$	7.85201	−	9.35766i	0.290417	−	0.346106i
$732$	−19.3178	−	45.0426i	−0.714005	−	1.66482i
$733$	13.4649	−	2.37423i	0.497339	−	0.0876942i	0.0806481	−	0.996743i	$-0.474301\pi$
$733$	13.4649	−	2.37423i	0.497339	−	0.0876942i	0.416691	+	0.909048i	$0.363190\pi$
$734$	−52.5228	−	0.443206i	−1.93865	−	0.0163590i
$735$	7.72146	+	11.3702i	0.284810	+	0.419395i
$736$	−0.545377	+	12.9188i	−0.0201029	+	0.476193i
$737$	−14.6569	−	8.46218i	−0.539895	−	0.311708i
$738$	−10.0019	−	2.14837i	−0.368173	−	0.0790826i
$739$	3.92286	+	6.79458i	0.144305	+	0.249943i	0.929113	−	0.369795i	$-0.120572\pi$
$739$	3.92286	+	6.79458i	0.144305	+	0.249943i	−0.784809	+	0.619738i	$0.787239\pi$
$740$	15.5842	+	9.35173i	0.572888	+	0.343776i
$741$	−61.4385	−	6.26199i	−2.25700	−	0.230040i
$742$	0.446473	−	0.758460i	0.0163905	−	0.0278440i
$743$	−2.44427	+	2.05099i	−0.0896717	+	0.0752435i	−0.686522	−	0.727109i	$-0.740863\pi$
$743$	−2.44427	+	2.05099i	−0.0896717	+	0.0752435i	0.596850	+	0.802353i	$0.296419\pi$
$744$	6.36907	−	2.66815i	0.233501	−	0.0978191i
$745$	18.2357	−	6.63724i	0.668103	−	0.243170i
$746$	−26.3508	−	22.4925i	−0.964770	−	0.823510i
$747$	10.6540	−	3.53600i	0.389810	−	0.129376i
$748$	2.89706	+	18.2233i	0.105927	+	0.666309i
$749$	−0.660050	+	3.74333i	−0.0241177	+	0.136778i
$750$	29.6327	+	3.27312i	1.08203	+	0.119517i
$751$	7.59333	−	20.8625i	0.277085	−	0.761284i	−0.720605	−	0.693346i	$-0.756136\pi$
$751$	7.59333	−	20.8625i	0.277085	−	0.761284i	0.997690	−	0.0679380i	$-0.0216420\pi$
$752$	12.2052	+	0.412114i	0.445078	+	0.0150282i
$753$	−9.56386	−	9.84148i	−0.348526	−	0.358644i
$754$	−75.7060	−	28.2804i	−2.75705	−	1.02991i
$755$			6.17514i			0.224736i
$756$	−5.13471	+	34.6638i	−0.186748	+	1.26071i
$757$			39.4292i			1.43308i	0.697546	+	0.716540i	$0.254275\pi$
$757$			39.4292i			1.43308i	−0.697546	+	0.716540i	$0.745725\pi$
$758$	16.0914	−	43.0763i	0.584467	−	1.56460i
$759$	10.5729	−	2.67151i	0.383773	−	0.0969696i
$760$	−10.8077	+	27.5066i	−0.392035	+	0.997771i
$761$	10.6550	−	29.2743i	0.386243	−	1.06119i	−0.582436	−	0.812877i	$-0.697900\pi$
$761$	10.6550	−	29.2743i	0.386243	−	1.06119i	0.968679	−	0.248317i	$-0.0798775\pi$
$762$	5.77342	−	2.53398i	0.209149	−	0.0917964i
$763$	−6.01323	+	34.1027i	−0.217694	+	1.23460i
$764$	−0.0429882	−	0.270407i	−0.00155526	−	0.00978298i
$765$	−16.9609	−	6.72874i	−0.613221	−	0.243278i
$766$	−21.2893	+	24.9411i	−0.769214	+	0.901160i
$767$	−75.6053	+	27.5181i	−2.72995	+	0.993620i
$768$	27.7124	−	0.151190i	0.999985	−	0.00545561i
$769$	4.70066	−	3.94432i	0.169510	−	0.142236i	−0.554086	−	0.832459i	$-0.686932\pi$
$769$	4.70066	−	3.94432i	0.169510	−	0.142236i	0.723596	+	0.690223i	$0.242488\pi$
$770$	−20.5550	−	12.0998i	−0.740752	−	0.436048i
$771$	−5.95650	−	13.2660i	−0.214518	−	0.477762i
$772$	−17.4934	+	29.1519i	−0.629600	+	1.04920i
$773$	−18.0562	−	31.2743i	−0.649437	−	1.12486i	−0.983258	−	0.182221i	$-0.941671\pi$
$773$	−18.0562	−	31.2743i	−0.649437	−	1.12486i	0.333820	−	0.942637i	$-0.391662\pi$
$774$	−8.22753	+	13.1042i	−0.295732	+	0.471022i
$775$	2.07829	+	1.19990i	0.0746542	+	0.0431016i
$776$	−29.0004	+	32.8362i	−1.04105	+	1.17875i
$777$	−29.1494	+	2.13055i	−1.04573	+	0.0764331i
$778$	0.120053	−	14.2270i	0.00430410	−	0.510064i
$779$	13.6636	−	2.40927i	0.489550	−	0.0863209i
$780$	23.3420	−	31.2171i	0.835777	−	1.11775i
$781$	6.50500	−	7.75236i	0.232767	−	0.277401i
$782$	10.2053	−	3.61720i	0.364941	−	0.129351i
$783$	−2.12453	−	47.8726i	−0.0759245	−	1.71083i
$784$	−3.61444	+	17.1016i	−0.129087	+	0.610772i
$785$	−16.1476	+	19.2440i	−0.576334	+	0.686848i
$786$	−19.2085	+	38.8602i	−0.685145	+	1.38610i
$787$	−0.380802	−	2.15964i	−0.0135741	−	0.0769828i	0.977268	−	0.212007i	$-0.0679999\pi$
$787$	−0.380802	−	2.15964i	−0.0135741	−	0.0769828i	−0.990842	+	0.135024i	$0.956889\pi$
$788$	−10.7641	+	3.71332i	−0.383454	+	0.132281i
$789$	23.0427	−	47.6244i	0.820341	−	1.69547i
$790$	−0.469426	−	2.80022i	−0.0167014	−	0.0996273i
$791$	26.6681	−	46.1905i	0.948209	−	1.64235i
$792$	−6.79848	−	22.3620i	−0.241573	−	0.794599i
$793$	−43.8344	−	75.9234i	−1.55661	−	2.69612i
$794$	15.8173	−	13.0465i	0.561337	−	0.463002i
$795$	−0.470701	−	0.339726i	−0.0166940	−	0.0120488i
$796$	27.8018	+	5.38748i	0.985409	+	0.190954i
$797$	−33.5503	+	28.1520i	−1.18841	+	0.997197i	−0.188527	+	0.982068i	$0.560371\pi$
$797$	−33.5503	+	28.1520i	−1.18841	+	0.997197i	−0.999886	+	0.0151286i	$0.995184\pi$
$798$	−11.2534	−	46.1742i	−0.398366	−	1.63455i
$799$	−3.49751	−	9.60934i	−0.123733	−	0.339954i
$800$	5.87396	+	7.63227i	0.207676	+	0.269842i
$801$	9.20589	+	17.0539i	0.325274	+	0.602570i
$802$	0.961857	−	5.19808i	0.0339644	−	0.183551i
$803$	−0.740548	−	0.130579i	−0.0261334	−	0.00460802i
$804$	20.3775	+	6.14711i	0.718657	+	0.216792i
$805$	−4.78689	+	13.1519i	−0.168716	+	0.463542i
$806$	10.7490	−	6.08561i	0.378619	−	0.214357i
$807$	32.6375	+	9.24758i	1.14889	+	0.325530i
$808$	−7.80751	−	23.2673i	−0.274667	−	0.818539i
$809$		−	2.63212i		−	0.0925405i	−0.998929	−	0.0462703i	$-0.985266\pi$
$809$		−	2.63212i		−	0.0925405i	0.998929	−	0.0462703i	$-0.0147335\pi$
$810$	22.4491	+	5.49826i	0.788779	+	0.193189i
$811$	−41.8492			−1.46952			−0.734762	−	0.678324i	$-0.762706\pi$
$811$	−41.8492			−1.46952			−0.734762	+	0.678324i	$0.762706\pi$
$812$	1.04953	−	62.1839i	0.0368315	−	2.18223i
$813$	2.23770	−	7.89752i	0.0784795	−	0.276978i
$814$	16.9641	−	9.60428i	0.594591	−	0.336630i
$815$	−26.7835	−	9.74840i	−0.938186	−	0.341472i
$816$	−8.78551	−	21.4784i	−0.307554	−	0.751895i
$817$	3.64405	−	20.6664i	0.127489	−	0.723026i
$818$	−36.1598	−	6.69103i	−1.26430	−	0.233947i
$819$	−1.79318	+	62.6569i	−0.0626587	+	2.18941i
$820$	−3.13354	+	8.17725i	−0.109428	+	0.285562i
$821$	37.0662	−	13.4910i	1.29362	−	0.470839i	0.398706	−	0.917079i	$-0.369459\pi$
$821$	37.0662	−	13.4910i	1.29362	−	0.470839i	0.894913	+	0.446240i	$0.147237\pi$
$822$	1.65611	+	6.79524i	0.0577634	+	0.237011i
$823$	24.6788	+	29.4111i	0.860249	+	1.02521i	0.999390	+	0.0349324i	$0.0111216\pi$
$823$	24.6788	+	29.4111i	0.860249	+	1.02521i	−0.139140	+	0.990273i	$0.544434\pi$
$824$	4.77020	+	31.7303i	0.166178	+	1.10538i
$825$	4.75363	−	6.58631i	0.165500	−	0.229306i
$826$	−39.3979	−	47.7654i	−1.37083	−	1.66197i
$827$	−23.8283	+	13.7573i	−0.828592	+	0.478388i	−0.853370	−	0.521305i	$-0.825445\pi$
$827$	−23.8283	+	13.7573i	−0.828592	+	0.478388i	0.0247780	+	0.999693i	$0.492112\pi$
$828$	−12.1768	+	6.31015i	−0.423172	+	0.219293i
$829$	10.9778	+	6.33802i	0.381274	+	0.220129i	0.678372	−	0.734718i	$-0.262686\pi$
$829$	10.9778	+	6.33802i	0.381274	+	0.220129i	−0.297098	+	0.954847i	$0.596019\pi$
$830$	−1.58872	−	9.47700i	−0.0551452	−	0.328952i
$831$	11.4947	+	5.56160i	0.398745	+	0.192930i
$832$	49.1922	−	6.12649i	1.70543	−	0.212398i
$833$	14.4143	−	2.54163i	0.499426	−	0.0880623i
$834$	−7.37315	−	3.64454i	−0.255311	−	0.126200i
$835$	21.4613	+	18.0082i	0.742700	+	0.623199i
$836$	19.9631	+	24.6233i	0.690438	+	0.851615i
$837$	5.81391	+	4.45455i	0.200958	+	0.153972i
$838$	−17.6389	+	6.25201i	−0.609327	+	0.215972i
$839$	6.62933	+	5.56267i	0.228870	+	0.192045i	0.750010	−	0.661426i	$-0.230049\pi$
$839$	6.62933	+	5.56267i	0.228870	+	0.192045i	−0.521140	+	0.853471i	$0.674493\pi$
$840$	28.6443	+	8.90530i	0.988324	+	0.307262i
$841$	9.73268	+	55.1968i	0.335610	+	1.90334i
$842$	−6.77848	−	0.0571992i	−0.233602	−	0.00197122i
$843$	−0.495850	−	6.78405i	−0.0170780	−	0.233655i
$844$	10.2531	+	18.4719i	0.352925	+	0.635828i
$845$	23.0591	−	39.9395i	0.793256	−	1.37396i
$846$	6.05652	+	11.4498i	0.208227	+	0.393651i
$847$	9.96596	−	5.75385i	0.342434	−	0.197705i
$848$	−0.103589	−	0.730951i	−0.00355725	−	0.0251010i
$849$	27.2005	−	12.2132i	0.933517	−	0.419155i
$850$	4.09110	−	6.94990i	0.140324	−	0.238379i
$851$	−7.35275	−	8.76267i	−0.252049	−	0.300380i
$852$	−5.73571	+	11.3614i	−0.196502	+	0.389235i
$853$	−8.97988	−	24.6720i	−0.307465	−	0.844754i	−0.993149	−	0.116854i	$-0.962719\pi$
$853$	−8.97988	−	24.6720i	−0.307465	−	0.844754i	0.685684	−	0.727900i	$-0.259503\pi$
$854$	43.8013	−	51.3147i	1.49885	−	1.75595i
$855$	−31.0133	+	4.55791i	−1.06063	+	0.155877i
$856$	1.52380	+	2.80071i	0.0520825	+	0.0957263i
$857$	34.2064	+	6.03150i	1.16847	+	0.206032i	0.724024	−	0.689775i	$-0.242291\pi$
$857$	34.2064	+	6.03150i	1.16847	+	0.206032i	0.444443	+	0.895807i	$0.353402\pi$
$858$	−16.8027	−	38.2834i	−0.573636	−	1.30697i
$859$	9.91134	+	3.60743i	0.338171	+	0.123084i	0.505523	−	0.862813i	$-0.331300\pi$
$859$	9.91134	+	3.60743i	0.338171	+	0.123084i	−0.167352	+	0.985897i	$0.553522\pi$
$860$	10.0013	+	8.68386i	0.341041	+	0.296117i
$861$	−3.44983	−	13.6533i	−0.117570	−	0.465303i
$862$	−9.32566	+	24.9646i	−0.317633	+	0.850296i
$863$	4.89855			0.166748			0.0833742	−	0.996518i	$-0.473430\pi$
$863$	4.89855			0.166748			0.0833742	+	0.996518i	$0.473430\pi$
$864$	14.7519	+	25.4241i	0.501869	+	0.864944i
$865$	−2.89881			−0.0985624
$866$	−16.1128	+	43.1335i	−0.547534	+	1.46574i
$867$	7.18091	−	6.97834i	0.243876	−	0.236997i
$868$	7.17771	+	6.23222i	0.243627	+	0.211535i
$869$	−2.86175	−	1.04159i	−0.0970781	−	0.0353335i
$870$	−40.7724	−	4.50356i	−1.38231	−	0.152685i
$871$	37.4948	+	6.61135i	1.27046	+	0.224017i
$872$	13.8823	+	25.5152i	0.470112	+	0.864055i
$873$	−45.5111	−	9.37462i	−1.54032	−	0.317283i
$874$	12.0760	−	14.1474i	0.408476	−	0.478543i
$875$	14.0365	+	38.5649i	0.474520	+	1.30373i
$876$	0.944209	−	0.0530112i	0.0319019	−	0.00179108i
$877$	2.27420	+	2.71029i	0.0767944	+	0.0915200i	0.803074	−	0.595880i	$-0.203197\pi$
$877$	2.27420	+	2.71029i	0.0767944	+	0.0915200i	−0.726279	+	0.687400i	$0.758752\pi$
$878$	−1.63810	+	2.78277i	−0.0552830	+	0.0939139i
$879$	2.87909	−	28.2478i	0.0971093	−	0.952774i
$880$	−19.8095	+	2.80736i	−0.667778	+	0.0946360i
$881$	−4.69517	+	2.71076i	−0.158184	+	0.0913277i	−0.577003	−	0.816742i	$-0.695778\pi$
$881$	−4.69517	+	2.71076i	−0.158184	+	0.0913277i	0.418818	+	0.908070i	$0.362444\pi$
$882$	−17.6445	+	5.69129i	−0.594123	+	0.191636i
$883$	12.7885	−	22.1503i	0.430367	−	0.745418i	−0.566537	−	0.824036i	$-0.691717\pi$
$883$	12.7885	−	22.1503i	0.430367	−	0.745418i	0.996905	+	0.0786177i	$0.0250507\pi$
$884$	−20.1454	−	36.2939i	−0.677564	−	1.22070i
$885$	−33.7846	+	22.9430i	−1.13566	+	0.771222i
$886$	−9.71234	−	0.0819562i	−0.326293	−	0.00275337i
$887$	1.48892	+	8.44410i	0.0499931	+	0.283525i	0.999548	−	0.0300771i	$-0.00957528\pi$
$887$	1.48892	+	8.44410i	0.0499931	+	0.283525i	−0.949554	+	0.313602i	$0.898464\pi$
$888$	−18.0087	+	16.6354i	−0.604332	+	0.558246i
$889$	6.64880	+	5.57900i	0.222993	+	0.187114i
$890$	15.6365	−	5.54226i	0.524137	−	0.185777i
$891$	16.9950	−	18.0481i	0.569353	−	0.604635i
$892$	31.7267	+	39.1330i	1.06229	+	1.31027i
$893$	−13.4574	−	11.2921i	−0.450336	−	0.377877i
$894$	1.68784	+	26.1226i	0.0564499	+	0.873669i
$895$	3.55618	−	0.627050i	0.118870	−	0.0209600i
$896$	17.0909	+	34.1063i	0.570966	+	1.13941i
$897$	−20.2951	+	13.7824i	−0.677634	+	0.460180i
$898$	−2.30959	−	13.7771i	−0.0770720	−	0.459749i
$899$	−11.2576	−	6.49956i	−0.375461	−	0.216772i
$900$	−3.92666	+	9.43031i	−0.130889	+	0.314344i
$901$	−0.535368	+	0.309095i	−0.0178357	+	0.0102974i
$902$	5.97664	+	7.24598i	0.199000	+	0.241265i
$903$	−21.1900	−	2.15975i	−0.705160	−	0.0718719i
$904$	−6.65119	−	44.2422i	−0.221215	−	1.47147i
$905$	−0.894975	−	1.06659i	−0.0297500	−	0.0354546i
$906$	−7.99480	−	2.33832i	−0.265610	−	0.0776854i
$907$	−1.11817	+	0.406982i	−0.0371283	+	0.0135136i	−0.360518	−	0.932752i	$-0.617400\pi$
$907$	−1.11817	+	0.406982i	−0.0371283	+	0.0135136i	0.323389	+	0.946266i	$0.395178\pi$
$908$	2.83126	−	7.38841i	0.0939585	−	0.245193i
$909$	17.2960	−	19.4541i	0.573672	−	0.645251i
$910$	52.7619	+	9.76310i	1.74904	+	0.323644i
$911$	0.397752	−	2.25577i	0.0131781	−	0.0747368i	−0.977509	−	0.210892i	$-0.932363\pi$
$911$	0.397752	−	2.25577i	0.0131781	−	0.0747368i	0.990688	+	0.136155i	$0.0434744\pi$
$912$	−31.5197	−	24.4083i	−1.04372	−	0.808238i
$913$	−9.68523	−	3.52514i	−0.320534	−	0.116665i
$914$	−34.2957	+	19.4166i	−1.13440	+	0.642245i
$915$	−31.0121	−	31.9123i	−1.02523	−	1.05499i
$916$	0.298587	−	17.6910i	0.00986558	−	0.584526i
$917$	−59.6725			−1.97056
$918$	15.1341	−	19.4109i	0.499498	−	0.640654i
$919$			17.5458i			0.578782i	0.957211	+	0.289391i	$0.0934528\pi$
$919$			17.5458i			0.578782i	−0.957211	+	0.289391i	$0.906547\pi$
$920$	3.73480	+	11.1301i	0.123133	+	0.366949i
$921$	−8.53292	−	33.7705i	−0.281169	−	1.11278i
$922$	37.4549	−	21.2053i	1.23351	−	0.698358i
$923$	−7.78645	+	21.3931i	−0.256294	+	0.704162i
$924$	23.4489	−	22.0303i	0.771411	−	0.724743i
$925$	−8.39062	−	1.47949i	−0.275882	−	0.0486454i
$926$	5.52542	−	29.8606i	0.181577	−	0.981279i
$927$	−26.6861	+	21.1214i	−0.876487	+	0.693717i
$928$	−31.8178	−	41.3421i	−1.04447	−	1.35712i
$929$	4.62384	+	12.7039i	0.151703	+	0.416801i	0.992144	−	0.125102i	$-0.0399260\pi$
$929$	4.62384	+	12.7039i	0.151703	+	0.416801i	−0.840441	+	0.541904i	$0.817704\pi$
$930$	4.53303	−	4.33138i	0.148644	−	0.142032i
$931$	19.2618	−	16.1626i	0.631279	−	0.529706i
$932$	−40.9821	−	7.94158i	−1.34241	−	0.260135i
$933$	12.8358	−	5.76334i	0.420225	−	0.188683i
$934$	39.0461	−	32.2060i	1.27763	−	1.05381i
$935$	8.37678	+	14.5090i	0.273950	+	0.474495i
$936$	31.5772	+	42.0412i	1.03213	+	1.37416i
$937$	6.96020	−	12.0554i	0.227380	−	0.393834i	−0.729651	−	0.683820i	$-0.760317\pi$
$937$	6.96020	−	12.0554i	0.227380	−	0.393834i	0.957031	+	0.289986i	$0.0936507\pi$
$938$	4.84419	+	28.8965i	0.158168	+	0.943505i
$939$	1.85863	−	0.135848i	0.0606540	−	0.00443324i
$940$	10.4818	−	3.61595i	0.341879	−	0.117939i
$941$	4.43143	+	25.1319i	0.144460	+	0.819276i	0.967799	+	0.251725i	$0.0809978\pi$
$941$	4.43143	+	25.1319i	0.144460	+	0.819276i	−0.823338	+	0.567551i	$0.807891\pi$
$942$	−18.8002	−	28.1930i	−0.612544	−	0.918579i
$943$	3.54274	−	4.22208i	0.115368	−	0.137490i
$944$	−50.8146	−	10.7397i	−1.65388	−	0.349548i
$945$	6.90857	+	31.0572i	0.224736	+	1.01029i
$946$	13.3905	−	4.74616i	0.435362	−	0.154311i
$947$	−34.1029	+	40.6422i	−1.10819	+	1.32069i	−0.165812	+	0.986157i	$0.553024\pi$
$947$	−34.1029	+	40.6422i	−1.10819	+	1.32069i	−0.942383	+	0.334537i	$0.891420\pi$
$948$	3.80313	+	0.452593i	0.123520	+	0.0146996i
$949$	1.66595	−	0.293751i	0.0540789	−	0.00953557i
$950$	0.116903	−	13.8538i	0.00379284	−	0.449477i
$951$	−13.5115	+	27.9255i	−0.438141	+	0.905546i
$952$	21.1464	−	23.9434i	0.685360	−	0.776011i
$953$	−7.54701	−	4.35727i	−0.244472	−	0.141146i	0.372759	−	0.927928i	$-0.378412\pi$
$953$	−7.54701	−	4.35727i	−0.244472	−	0.141146i	−0.617230	+	0.786783i	$0.711745\pi$
$954$	0.618074	−	0.480763i	0.0200109	−	0.0155653i
$955$	−0.124299	−	0.215293i	−0.00402223	−	0.00696671i
$956$	−9.72739	+	16.2103i	−0.314606	+	0.524278i
$957$	−25.7493	+	35.6764i	−0.832356	+	1.15326i
$958$	31.9378	+	18.8004i	1.03186	+	0.607413i
$959$	−7.37547	+	6.18875i	−0.238166	+	0.199845i
$960$	23.4463	−	9.13167i	0.756725	−	0.294723i
$961$	−27.2635	+	9.92309i	−0.879466	+	0.320100i
$962$	−28.4715	+	33.3553i	−0.917957	+	1.07542i
$963$	−1.77400	+	2.87917i	−0.0571664	+	0.0927800i
$964$	6.29833	+	39.6181i	0.202856	+	1.27601i
$965$	−5.36022	+	30.3993i	−0.172552	+	0.978588i
$966$	−15.2148	−	11.1776i	−0.489527	−	0.359635i
$967$	−1.06732	+	2.93244i	−0.0343227	+	0.0943009i	−0.955670	−	0.294439i	$-0.904867\pi$
$967$	−1.06732	+	2.93244i	−0.0343227	+	0.0943009i	0.921348	+	0.388740i	$0.127089\pi$
$968$	3.53001	−	8.98425i	0.113459	−	0.288765i
$969$	−9.10027	+	32.1176i	−0.292343	+	1.03177i
$970$	−13.9192	+	37.2614i	−0.446919	+	1.19639i
$971$		−	0.0539562i		−	0.00173154i	−1.00000		0.000865769i	$-0.999724\pi$
$971$		−	0.0539562i		−	0.00173154i	1.00000		0.000865769i	$-0.000275583\pi$
$972$	−15.6192	+	26.9822i	−0.500985	+	0.865456i
$973$		−	11.3220i		−	0.362966i
$974$	30.6028	+	11.4319i	0.980577	+	0.366300i
$975$	−4.98132	+	17.5806i	−0.159530	+	0.563030i
$976$	1.90977	−	56.5600i	0.0611304	−	1.81044i
$977$	−8.21037	+	22.5578i	−0.262673	+	0.721689i	0.736312	+	0.676642i	$0.236566\pi$
$977$	−8.21037	+	22.5578i	−0.262673	+	0.721689i	−0.998985	+	0.0450461i	$0.985657\pi$
$978$	22.7630	−	30.9846i	0.727882	−	0.990778i
$979$	3.08989	−	17.5236i	0.0987533	−	0.560058i
$980$	2.49172	+	15.6736i	0.0795950	+	0.500673i
$981$	−16.1616	+	26.2300i	−0.516001	+	0.837460i
$982$	35.3984	+	30.2154i	1.12961	+	0.964213i
$983$	−48.9235	+	17.8067i	−1.56042	+	0.567946i	−0.970832	−	0.239759i	$-0.922932\pi$
$983$	−48.9235	+	17.8067i	−1.56042	+	0.567946i	−0.589586	+	0.807705i	$0.700709\pi$
$984$	−9.40032	−	7.15337i	−0.299671	−	0.228041i
$985$	−7.91968	+	6.64540i	−0.252342	+	0.211740i
$986$	−22.1605	+	37.6459i	−0.705734	+	1.19889i
$987$	−10.4352	+	14.4583i	−0.332156	+	0.460213i
$988$	−61.1463	−	36.6924i	−1.94532	−	1.16734i
$989$	−4.16813	−	7.21941i	−0.132539	−	0.229564i
$990$	−13.0291	−	16.7504i	−0.414093	−	0.532363i
$991$	10.0455	+	5.79977i	0.319106	+	0.184236i	0.650994	−	0.759083i	$-0.274352\pi$
$991$	10.0455	+	5.79977i	0.319106	+	0.184236i	−0.331888	+	0.943319i	$0.607686\pi$
$992$	7.96653	+	0.336314i	0.252938	+	0.0106780i
$993$	−10.5061	+	21.7138i	−0.333400	+	0.689067i
$994$	−17.5193	−	0.147834i	−0.555678	−	0.00468901i
$995$	25.3215	−	4.46487i	0.802747	−	0.141546i
$996$	12.8712	+	1.53175i	0.407841	+	0.0485353i
$997$	25.3340	−	30.1918i	0.802334	−	0.956185i	−0.197374	−	0.980328i	$-0.563241\pi$
$997$	25.3340	−	30.1918i	0.802334	−	0.956185i	0.999709	+	0.0241434i	$0.00768584\pi$
$998$	−4.30730	−	12.1523i	−0.136345	−	0.384674i
$999$	−24.8055	−	7.80162i	−0.784812	−	0.246832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.12	yes	192
3.2	odd	2		648.2.v.b.35.21		192
4.3	odd	2		864.2.bh.b.335.29		192
8.3	odd	2	inner	216.2.v.b.11.7	✓	192
8.5	even	2		864.2.bh.b.335.30		192
24.11	even	2		648.2.v.b.35.26		192
27.5	odd	18	inner	216.2.v.b.59.7	yes	192
27.22	even	9		648.2.v.b.611.26		192
108.59	even	18		864.2.bh.b.815.30		192
216.5	odd	18		864.2.bh.b.815.29		192
216.59	even	18	inner	216.2.v.b.59.12	yes	192
216.211	odd	18		648.2.v.b.611.21		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.7	✓	192	8.3	odd	2	inner
216.2.v.b.11.12	yes	192	1.1	even	1	trivial
216.2.v.b.59.7	yes	192	27.5	odd	18	inner
216.2.v.b.59.12	yes	192	216.59	even	18	inner
648.2.v.b.35.21		192	3.2	odd	2
648.2.v.b.35.26		192	24.11	even	2
648.2.v.b.611.21		192	216.211	odd	18
648.2.v.b.611.26		192	27.22	even	9
864.2.bh.b.335.29		192	4.3	odd	2
864.2.bh.b.335.30		192	8.5	even	2
864.2.bh.b.815.29		192	216.5	odd	18
864.2.bh.b.815.30		192	108.59	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.494886 + 1.32480i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(-1.51018 - 1.31125i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(1.45024 - 1.97403i) q^{6} +(3.32069 + 0.585528i) q^{7} +(2.48450 - 1.35176i) q^{8} +(2.55410 + 1.57371i) q^{9} +O(q^{10})\)	\(q+(-0.494886 + 1.32480i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(-1.51018 - 1.31125i) q^{4} +(-1.70638 - 0.621073i) q^{5} +(1.45024 - 1.97403i) q^{6} +(3.32069 + 0.585528i) q^{7} +(2.48450 - 1.35176i) q^{8} +(2.55410 + 1.57371i) q^{9} +(1.66726 - 1.95325i) q^{10} +(-0.942090 - 2.58837i) q^{11} +(1.89749 + 2.89819i) q^{12} +(3.98305 + 4.74681i) q^{13} +(-2.41907 + 4.10948i) q^{14} +(2.55034 + 1.84070i) q^{15} +(0.561263 + 3.96043i) q^{16} +(2.90072 - 1.67473i) q^{17} +(-3.34884 + 2.60486i) q^{18} +(2.87704 - 4.98318i) q^{19} +(1.76256 + 3.17542i) q^{20} +(-5.25729 - 2.54370i) q^{21} +(3.89529 + 0.0328699i) q^{22} +(-0.396921 - 2.25105i) q^{23} +(-4.77856 + 1.07952i) q^{24} +(-1.30421 - 1.09436i) q^{25} +(-8.25972 + 2.92760i) q^{26} +(-3.51321 - 3.82849i) q^{27} +(-4.24706 - 5.23850i) q^{28} +(7.06459 + 5.92789i) q^{29} +(-3.70068 + 2.46776i) q^{30} +(-1.38814 + 0.244766i) q^{31} +(-5.52452 - 1.21640i) q^{32} +(0.347781 + 4.75822i) q^{33} +(0.783155 + 4.67167i) q^{34} +(-5.30272 - 3.06153i) q^{35} +(-1.79362 - 5.72564i) q^{36} +(4.33391 - 2.50218i) q^{37} +(5.17790 + 6.27760i) q^{38} +(-4.39622 - 9.79102i) q^{39} +(-5.07905 + 0.763564i) q^{40} +(1.54991 + 1.84711i) q^{41} +(5.97165 - 5.70601i) q^{42} +(3.42707 - 1.24735i) q^{43} +(-1.97127 + 5.14421i) q^{44} +(-3.38089 - 4.27164i) q^{45} +(3.17861 + 0.588173i) q^{46} +(0.530155 - 3.00666i) q^{47} +(0.934698 - 6.86486i) q^{48} +(4.10632 + 1.49458i) q^{49} +(2.09524 - 1.18623i) q^{50} +(-5.62467 + 1.42121i) q^{51} +(0.209139 - 12.3913i) q^{52} -0.184564 q^{53} +(6.81061 - 2.75963i) q^{54} +5.00186i q^{55} +(9.04176 - 3.03403i) q^{56} +(-7.14737 + 6.94575i) q^{57} +(-11.3494 + 6.42551i) q^{58} +(-4.44089 + 12.2012i) q^{59} +(-1.43786 - 6.12391i) q^{60} +(-13.9331 - 2.45678i) q^{61} +(0.362704 - 1.96013i) q^{62} +(7.55994 + 6.72131i) q^{63} +(4.34549 - 6.71690i) q^{64} +(-3.84849 - 10.5736i) q^{65} +(-6.47579 - 1.89404i) q^{66} +(4.70680 - 3.94947i) q^{67} +(-6.57659 - 1.27442i) q^{68} +(-0.401441 + 3.93867i) q^{69} +(6.68014 - 5.50992i) q^{70} +(1.83700 + 3.18178i) q^{71} +(8.47295 + 0.457353i) q^{72} +(0.136500 - 0.236424i) q^{73} +(1.17010 + 6.97985i) q^{74} +(1.65667 + 2.43951i) q^{75} +(-10.8790 + 3.75297i) q^{76} +(-1.61283 - 9.14681i) q^{77} +(15.1467 - 0.978667i) q^{78} +(0.710677 - 0.846952i) q^{79} +(1.50198 - 7.10659i) q^{80} +(4.04687 + 8.03883i) q^{81} +(-3.21407 + 1.13921i) q^{82} +(2.40520 - 2.86641i) q^{83} +(4.60402 + 10.7350i) q^{84} +(-5.98987 + 1.05618i) q^{85} +(-0.0435206 + 5.15748i) q^{86} +(-8.97377 - 13.2142i) q^{87} +(-5.83948 - 5.15733i) q^{88} +(5.59452 + 3.23000i) q^{89} +(7.33220 - 2.36502i) q^{90} +(10.4471 + 18.0949i) q^{91} +(-2.35226 + 3.91994i) q^{92} +(2.42883 + 0.247553i) q^{93} +(3.72084 + 2.19030i) q^{94} +(-8.00425 + 6.71636i) q^{95} +(8.63198 + 4.63561i) q^{96} +(-14.5548 + 5.29750i) q^{97} +(-4.01217 + 4.70039i) q^{98} +(1.66715 - 8.09354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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