LMFDB - Embedded newform 216.2.v.b.11.7

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			11.7
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21873 + 0.717416i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(0.970628 - 1.74868i) q^{4} +(1.70638 + 0.621073i) q^{5} +(2.36970 - 0.620081i) q^{6} +(-3.32069 - 0.585528i) q^{7} +(0.0715925 + 2.82752i) q^{8} +(2.55410 + 1.57371i) q^{9} +O(q^{10})$	\(q+(-1.21873 + 0.717416i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(0.970628 - 1.74868i) q^{4} +(1.70638 + 0.621073i) q^{5} +(2.36970 - 0.620081i) q^{6} +(-3.32069 - 0.585528i) q^{7} +(0.0715925 + 2.82752i) q^{8} +(2.55410 + 1.57371i) q^{9} +(-2.52520 + 0.467264i) q^{10} +(-0.942090 - 2.58837i) q^{11} +(-2.44318 + 2.45578i) q^{12} +(-3.98305 - 4.74681i) q^{13} +(4.46711 - 1.66872i) q^{14} +(-2.55034 - 1.84070i) q^{15} +(-2.11576 - 3.39464i) q^{16} +(2.90072 - 1.67473i) q^{17} +(-4.24178 - 0.0855811i) q^{18} +(2.87704 - 4.98318i) q^{19} +(2.74232 - 2.38109i) q^{20} +(5.25729 + 2.54370i) q^{21} +(3.00510 + 2.47867i) q^{22} +(0.396921 + 2.25105i) q^{23} +(1.21578 - 4.74572i) 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} +(4.42874 + 0.413662i) q^{30} +(1.38814 - 0.244766i) q^{31} +(5.01392 + 2.61928i) q^{32} +(0.347781 + 4.75822i) q^{33} +(-2.33373 + 4.12208i) q^{34} +(-5.30272 - 3.06153i) q^{35} +(5.23100 - 2.93882i) q^{36} +(-4.33391 + 2.50218i) q^{37} +(0.0686647 + 8.13721i) q^{38} +(4.39622 + 9.79102i) q^{39} +(-1.63393 + 4.86930i) q^{40} +(1.54991 + 1.84711i) q^{41} +(-8.23214 + 0.671572i) q^{42} +(3.42707 - 1.24735i) q^{43} +(-5.44065 - 0.864933i) q^{44} +(3.38089 + 4.27164i) q^{45} +(-2.09868 - 2.45867i) q^{46} +(-0.530155 + 3.00666i) q^{47} +(1.92295 + 6.65600i) q^{48} +(4.10632 + 1.49458i) q^{49} +(2.37460 + 0.398076i) q^{50} +(-5.62467 + 1.42121i) q^{51} +(-12.1667 + 2.35769i) q^{52} +0.184564 q^{53} +(7.02829 + 2.14548i) q^{54} -5.00186i q^{55} +(1.41786 - 9.43125i) q^{56} +(-7.14737 + 6.94575i) q^{57} +(12.8626 + 2.15628i) q^{58} +(-4.44089 + 12.2012i) q^{59} +(-5.69423 + 2.67310i) q^{60} +(13.9331 + 2.45678i) q^{61} +(-1.51617 + 1.29418i) q^{62} +(-7.55994 - 6.72131i) q^{63} +(-7.98975 + 0.404858i) q^{64} +(-3.84849 - 10.5736i) q^{65} +(-3.83748 - 5.54950i) q^{66} +(4.70680 - 3.94947i) q^{67} +(-0.113048 - 6.69798i) q^{68} +(0.401441 - 3.93867i) q^{69} +(8.65900 - 0.0730677i) q^{70} +(-1.83700 - 3.18178i) q^{71} +(-4.26684 + 7.33444i) q^{72} +(0.136500 - 0.236424i) q^{73} +(3.48678 - 6.15871i) q^{74} +(1.65667 + 2.43951i) q^{75} +(-5.92145 - 9.86784i) q^{76} +(1.61283 + 9.14681i) q^{77} +(-12.3821 - 8.77873i) 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} +(9.55100 - 6.72434i) q^{84} +(5.98987 - 1.05618i) q^{85} +(-3.28182 + 3.97883i) q^{86} +(8.97377 + 13.2142i) q^{87} +(7.25123 - 2.84909i) q^{88} +(5.59452 + 3.23000i) q^{89} +(-7.18495 - 2.78049i) q^{90} +(10.4471 + 18.0949i) q^{91} +(4.32163 + 1.49084i) q^{92} +(-2.42883 - 0.247553i) q^{93} +(-1.51091 - 4.04466i) q^{94} +(8.00425 - 6.71636i) q^{95} +(-7.11868 - 6.73234i) q^{96} +(-14.5548 + 5.29750i) q^{97} +(-6.07674 + 1.12444i) 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 $

$2$	−1.21873	+	0.717416i	−0.861776	+	0.507290i
$2$	−1.21873	+	0.717416i	−0.861776	+	0.507290i
$3$	−1.66645	−	0.472175i	−0.962125	−	0.272610i
$3$	−1.66645	−	0.472175i	−0.962125	−	0.272610i
$4$	0.970628	−	1.74868i	0.485314	−	0.874340i
$5$	1.70638	+	0.621073i	0.763118	+	0.277752i	0.694115	−	0.719864i	$-0.255796\pi$
$5$	1.70638	+	0.621073i	0.763118	+	0.277752i	0.0690029	+	0.997616i	$0.478018\pi$
$6$	2.36970	−	0.620081i	0.967428	−	0.253147i
$7$	−3.32069	−	0.585528i	−1.25510	−	0.221309i	−0.493727	−	0.869617i	$-0.664366\pi$
$7$	−3.32069	−	0.585528i	−1.25510	−	0.221309i	−0.761378	+	0.648308i	$0.775477\pi$
$8$	0.0715925	+	2.82752i	0.0253118	+	0.999680i
$9$	2.55410	+	1.57371i	0.851367	+	0.524570i
$10$	−2.52520	+	0.467264i	−0.798537	+	0.147762i
$11$	−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	$-0.247419\pi$
$12$	−2.44318	+	2.45578i	−0.705287	+	0.708922i
$13$	−3.98305	−	4.74681i	−1.10470	−	1.31653i	−0.944155	−	0.329501i	$-0.893120\pi$
$13$	−3.98305	−	4.74681i	−1.10470	−	1.31653i	−0.160544	−	0.987029i	$-0.551325\pi$
$14$	4.46711	−	1.66872i	1.19389	−	0.445983i
$15$	−2.55034	−	1.84070i	−0.658496	−	0.475266i
$16$	−2.11576	−	3.39464i	−0.528940	−	0.848659i
$17$	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	$0.200193\pi$
$18$	−4.24178	−	0.0855811i	−0.999797	−	0.0201717i
$19$	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	$-0.0627933\pi$
$20$	2.74232	−	2.38109i	0.613202	−	0.532427i
$21$	5.25729	+	2.54370i	1.14724	+	0.555081i
$22$	3.00510	+	2.47867i	0.640689	+	0.528454i
$23$	0.396921	+	2.25105i	0.0827637	+	0.469376i	0.997817	+	0.0660428i	$0.0210374\pi$
$23$	0.396921	+	2.25105i	0.0827637	+	0.469376i	−0.915053	+	0.403333i	$0.867852\pi$
$24$	1.21578	−	4.74572i	0.248170	−	0.968717i
$25$	−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	$-0.950562\pi$
$29$	−7.06459	−	5.92789i	−1.31186	−	1.10078i	−0.323897	−	0.946092i	$-0.604993\pi$
$30$	4.42874	+	0.413662i	0.808573	+	0.0755241i
$31$	1.38814	−	0.244766i	0.249317	−	0.0439613i	−0.0475930	−	0.998867i	$-0.515155\pi$
$31$	1.38814	−	0.244766i	0.249317	−	0.0439613i	0.296910	+	0.954906i	$0.404044\pi$
$32$	5.01392	+	2.61928i	0.886344	+	0.463028i
$33$	0.347781	+	4.75822i	0.0605409	+	0.828299i
$34$	−2.33373	+	4.12208i	−0.400232	+	0.706931i
$35$	−5.30272	−	3.06153i	−0.896323	−	0.517493i
$36$	5.23100	−	2.93882i	0.871833	−	0.489803i
$37$	−4.33391	+	2.50218i	−0.712490	+	0.411356i	−0.811982	−	0.583682i	$-0.801611\pi$
$37$	−4.33391	+	2.50218i	−0.712490	+	0.411356i	0.0994922	+	0.995038i	$0.468278\pi$
$38$	0.0686647	+	8.13721i	0.0111389	+	1.32003i
$39$	4.39622	+	9.79102i	0.703959	+	1.56782i
$40$	−1.63393	+	4.86930i	−0.258347	+	0.769904i
$41$	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	$0.717485\pi$
$42$	−8.23214	+	0.671572i	−1.27025	+	0.103626i
$43$	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	$0.299190\pi$
$44$	−5.44065	−	0.864933i	−0.820209	−	0.130394i
$45$	3.38089	+	4.27164i	0.503993	+	0.636778i
$46$	−2.09868	−	2.45867i	−0.309433	−	0.362512i
$47$	−0.530155	+	3.00666i	−0.0773310	+	0.438566i	0.921419	+	0.388572i	$0.127031\pi$
$47$	−0.530155	+	3.00666i	−0.0773310	+	0.438566i	−0.998750	+	0.0499942i	$0.984080\pi$
$48$	1.92295	+	6.65600i	0.277553	+	0.960710i
$49$	4.10632	+	1.49458i	0.586617	+	0.213511i
$50$	2.37460	+	0.398076i	0.335819	+	0.0562964i
$51$	−5.62467	+	1.42121i	−0.787612	+	0.199009i
$52$	−12.1667	+	2.35769i	−1.68722	+	0.326952i
$53$	0.184564			0.0253518			0.0126759	−	0.999920i	$-0.495965\pi$
$53$	0.184564			0.0253518			0.0126759	+	0.999920i	$0.495965\pi$
$54$	7.02829	+	2.14548i	0.956430	+	0.291962i
$55$		−	5.00186i		−	0.674450i
$56$	1.41786	−	9.43125i	0.189469	−	1.26030i
$57$	−7.14737	+	6.94575i	−0.946693	+	0.919987i
$58$	12.8626	+	2.15628i	1.68894	+	0.283133i
$59$	−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	$0.790589\pi$
$60$	−5.69423	+	2.67310i	−0.735121	+	0.345096i
$61$	13.9331	+	2.45678i	1.78395	+	0.314559i	0.965576	−	0.260122i	$-0.0837629\pi$
$61$	13.9331	+	2.45678i	1.78395	+	0.314559i	0.818377	+	0.574681i	$0.194874\pi$
$62$	−1.51617	+	1.29418i	−0.192554	+	0.164361i
$63$	−7.55994	−	6.72131i	−0.952463	−	0.846805i
$64$	−7.98975	+	0.404858i	−0.998719	+	0.0506073i
$65$	−3.84849	−	10.5736i	−0.477347	−	1.31150i
$66$	−3.83748	−	5.54950i	−0.472361	−	0.683096i
$67$	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	$0.155310\pi$
$68$	−0.113048	−	6.69798i	−0.0137091	−	0.812249i
$69$	0.401441	−	3.93867i	0.0483278	−	0.474160i
$70$	8.65900	−	0.0730677i	1.03495	−	0.00873326i
$71$	−1.83700	−	3.18178i	−0.218012	−	0.377608i	0.736188	−	0.676777i	$-0.236624\pi$
$71$	−1.83700	−	3.18178i	−0.218012	−	0.377608i	−0.954200	+	0.299169i	$0.903291\pi$
$72$	−4.26684	+	7.33444i	−0.502852	+	0.864372i
$73$	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	$0.161581\pi$
$74$	3.48678	−	6.15871i	0.405330	−	0.715936i
$75$	1.65667	+	2.43951i	0.191296	+	0.281691i
$76$	−5.92145	−	9.86784i	−0.679237	−	1.13192i
$77$	1.61283	+	9.14681i	0.183799	+	1.04238i
$78$	−12.3821	−	8.77873i	−1.40199	−	0.993996i
$79$	−0.710677	+	0.846952i	−0.0799574	+	0.0952895i	−0.804540	−	0.593898i	$-0.797588\pi$
$79$	−0.710677	+	0.846952i	−0.0799574	+	0.0952895i	0.724583	+	0.689188i	$0.242033\pi$
$80$	−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	$0.156386\pi$
$84$	9.55100	−	6.72434i	1.04210	−	0.733685i
$85$	5.98987	−	1.05618i	0.649693	−	0.114558i
$86$	−3.28182	+	3.97883i	−0.353888	+	0.429048i
$87$	8.97377	+	13.2142i	0.962089	+	1.41672i
$88$	7.25123	−	2.84909i	0.772983	−	0.303714i
$89$	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	$0.555434\pi$
$90$	−7.18495	−	2.78049i	−0.757360	−	0.293089i
$91$	10.4471	+	18.0949i	1.09515	+	1.89686i
$92$	4.32163	+	1.49084i	0.450561	+	0.155431i
$93$	−2.42883	−	0.247553i	−0.251858	−	0.0256701i
$94$	−1.51091	−	4.04466i	−0.155838	−	0.417175i
$95$	8.00425	−	6.71636i	0.821219	−	0.689084i
$96$	−7.11868	−	6.73234i	−0.726547	−	0.687117i
$97$	−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	$0.676909\pi$
$98$	−6.07674	+	1.12444i	−0.613844	+	0.113586i
$99$	1.66715	−	8.09354i	0.167555	−	0.813431i
$100$	−3.17959	+	1.21843i	−0.317959	+	0.121843i
$101$	−1.50674	+	8.54518i	−0.149927	+	0.850277i	0.813352	+	0.581772i	$0.197641\pi$
$101$	−1.50674	+	8.54518i	−0.149927	+	0.850277i	−0.963278	+	0.268504i	$0.913471\pi$
$102$	5.83538	−	5.76731i	0.577789	−	0.571048i
$103$	3.88002	−	10.6603i	0.382309	−	1.05039i	−0.588072	−	0.808809i	$-0.700113\pi$
$103$	3.88002	−	10.6603i	0.382309	−	1.05039i	0.970381	−	0.241578i	$-0.0776649\pi$
$104$	13.1366	−	11.6020i	1.28815	−	1.13767i
$105$	7.39114	+	7.60569i	0.721301	+	0.742239i
$106$	−0.224934	+	0.132409i	−0.0218475	+	0.0128607i
$107$			1.12727i			0.108978i	0.998514	+	0.0544888i	$0.0173529\pi$
$107$			1.12727i			0.108978i	−0.998514	+	0.0544888i	$0.982647\pi$
$108$	−10.1048	+	2.42744i	−0.972337	+	0.233581i
$109$		−	10.2698i		−	0.983665i	−0.870690	−	0.491832i	$-0.836327\pi$
$109$		−	10.2698i		−	0.983665i	0.870690	−	0.491832i	$-0.163673\pi$
$110$	3.58841	+	6.09594i	0.342142	+	0.581225i
$111$	8.40370	−	2.12340i	0.797644	−	0.201544i
$112$	5.03814	+	12.5114i	0.476060	+	1.18221i
$113$	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	$-0.155965\pi$
$114$	3.72776	−	13.5927i	0.349137	−	1.27307i
$115$	−0.720766	+	4.08767i	−0.0672118	+	0.381177i
$116$	−17.2231	+	6.59992i	−1.59912	+	0.612787i
$117$	−2.70301	−	18.3920i	−0.249893	−	1.70034i
$118$	−3.34110	−	18.0560i	−0.307573	−	1.66219i
$119$	−10.6130	+	3.86282i	−0.972893	+	0.354104i
$120$	5.02202	−	7.34293i	0.458446	−	0.670315i
$121$	2.61436	−	2.19371i	0.237669	−	0.199428i
$122$	−18.7433	+	7.00167i	−1.69694	+	0.633902i
$123$	−1.71069	−	3.80994i	−0.154247	−	0.343531i
$124$	0.919348	−	2.66498i	0.0825599	−	0.239323i
$125$	−6.08554	−	10.5405i	−0.544307	−	0.942768i
$126$	14.0355	+	2.76787i	1.25038	+	0.246581i
$127$	−2.22917	−	1.28701i	−0.197806	−	0.114204i	0.397825	−	0.917461i	$-0.369765\pi$
$127$	−2.22917	−	1.28701i	−0.197806	−	0.114204i	−0.595632	+	0.803258i	$0.703098\pi$
$128$	9.44693	−	6.22539i	0.834999	−	0.550252i
$129$	−6.30001	+	0.460472i	−0.554685	+	0.0405423i
$130$	12.2760	+	10.1255i	1.07668	+	0.888065i
$131$	−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	$0.725735\pi$
$132$	8.65817	+	4.01030i	0.753597	+	0.349052i
$133$	−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	$0.261145\pi$
$138$	2.33642	+	5.08820i	0.198889	+	0.433136i
$139$	−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	$0.989926\pi$
$140$	−10.5006	+	6.30115i	−0.887463	+	0.532545i
$141$	2.30314	−	4.76011i	0.193960	−	0.400874i
$142$	4.52148	+	2.55985i	0.379434	+	0.214818i
$143$	−8.53412	+	14.7815i	−0.713659	+	1.23609i
$144$	−0.0616969	−	11.9998i	−0.00514141	−	0.999987i
$145$	−8.37324	−	14.5029i	−0.695360	−	1.20440i
$146$	0.00325775	+	0.386065i	0.000269614	+	0.0319510i
$147$	−6.13726	−	4.42953i	−0.506193	−	0.365342i
$148$	0.168902	+	10.0073i	0.0138837	+	0.822596i
$149$	8.18651	−	6.86930i	0.670665	−	0.562755i	−0.242597	−	0.970127i	$-0.577999\pi$
$149$	8.18651	−	6.86930i	0.670665	−	0.562755i	0.913262	+	0.407372i	$0.133555\pi$
$150$	−3.76919	−	1.78460i	−0.307753	−	0.145712i
$151$	1.16307	+	3.19552i	0.0946497	+	0.260048i	0.977978	−	0.208706i	$-0.0669253\pi$
$151$	1.16307	+	3.19552i	0.0946497	+	0.260048i	−0.883329	+	0.468754i	$0.844703\pi$
$152$	14.2960	+	7.77813i	1.15956	+	0.630890i
$153$	10.0443	+	0.287457i	0.812032	+	0.0232395i
$154$	−8.52768	−	9.99046i	−0.687180	−	0.805054i
$155$	2.52071	+	0.444469i	0.202468	+	0.0357006i
$156$	21.3884	+	1.81585i	1.71245	+	0.145385i
$157$	−4.73154	+	12.9998i	−0.377618	+	1.03750i	0.594723	+	0.803931i	$0.297262\pi$
$157$	−4.73154	+	12.9998i	−0.377618	+	1.03750i	−0.972341	+	0.233567i	$0.924960\pi$
$158$	0.258510	−	1.54206i	0.0205659	−	0.122680i
$159$	−0.307566	−	0.0871463i	−0.0243916	−	0.00691115i
$160$	6.92890	+	7.58350i	0.547778	+	0.599528i
$161$		−	7.70745i		−	0.607432i
$162$	−10.6993	−	6.89391i	−0.840613	−	0.541637i
$163$	15.6961			1.22941			0.614706	−	0.788757i	$-0.289275\pi$
$163$	15.6961			1.22941			0.614706	+	0.788757i	$0.289275\pi$
$164$	4.73439	−	0.917437i	0.369694	−	0.0716398i
$165$	−2.36175	+	8.33534i	−0.183862	+	0.648905i
$166$	−0.874895	+	5.21892i	−0.0679050	+	0.405066i
$167$	14.4977	+	5.27671i	1.12186	+	0.408324i	0.835331	−	0.549747i	$-0.185276\pi$
$167$	14.4977	+	5.27671i	1.12186	+	0.408324i	0.286531	+	0.958071i	$0.407498\pi$
$168$	−6.81598	+	15.0472i	−0.525864	+	1.16092i
$169$	−4.41013	+	25.0111i	−0.339241	+	1.92393i
$170$	−6.54235	+	5.58443i	−0.501775	+	0.428306i
$171$	15.1903	−	8.19992i	1.16163	−	0.627064i
$172$	1.14519	−	7.20357i	0.0873203	−	0.549267i
$173$	−1.50008	+	0.545984i	−0.114049	+	0.0415104i	−0.398414	−	0.917206i	$-0.630439\pi$
$173$	−1.50008	+	0.545984i	−0.114049	+	0.0415104i	0.284365	+	0.958716i	$0.408217\pi$
$174$	−20.4168	−	9.66673i	−1.54779	−	0.732833i
$175$	3.69010	+	4.39769i	0.278946	+	0.332434i
$176$	−6.79334	+	8.67443i	−0.512067	+	0.653860i
$177$	13.1616	−	18.2359i	0.989289	−	1.37069i
$178$	−9.13549	+	0.0770885i	−0.684734	+	0.00577802i
$179$	−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	$0.357011\pi$
$180$	10.7513	−	1.76592i	0.801355	−	0.131624i
$181$	−0.664023	−	0.383374i	−0.0493565	−	0.0284960i	0.475119	−	0.879922i	$-0.342405\pi$
$181$	−0.664023	−	0.383374i	−0.0493565	−	0.0284960i	−0.524475	+	0.851426i	$0.675738\pi$
$182$	−25.7138	−	14.5580i	−1.90603	−	1.07911i
$183$	−22.0588	−	10.6730i	−1.63063	−	0.788969i
$184$	−6.33647	+	1.28346i	−0.467131	+	0.0946179i
$185$	−8.94935	+	1.57801i	−0.657969	+	0.116018i
$186$	3.13770	−	1.44078i	0.230067	−	0.105643i
$187$	−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	0.638986	−	0.769219i	$-0.279354\pi$
$191$	−0.104873	−	0.0879985i	−0.00758831	−	0.00636735i	−0.646574	+	0.762851i	$0.723799\pi$
$192$	13.5057	+	3.09788i	0.974688	+	0.223570i
$193$	−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	$-0.265112\pi$
$194$	13.9379	−	16.8981i	1.00068	−	1.21321i
$195$	1.42071	+	19.4376i	0.101739	+	1.39196i
$196$	6.59924	−	5.72995i	0.471374	−	0.409282i
$197$	−2.84664	+	4.93053i	−0.202815	+	0.351286i	−0.949434	−	0.313966i	$-0.898342\pi$
$197$	−2.84664	+	4.93053i	−0.202815	+	0.351286i	0.746619	+	0.665251i	$0.231676\pi$
$198$	3.77462	+	11.0599i	0.268251	+	0.785994i
$199$	12.2625	−	7.07975i	0.869265	−	0.501870i	0.00216093	−	0.999998i	$-0.499312\pi$
$199$	12.2625	−	7.07975i	0.869265	−	0.501870i	0.867104	+	0.498127i	$0.165979\pi$
$200$	3.00096	−	3.76603i	0.212200	−	0.266298i
$201$	−9.70848	+	4.35916i	−0.684783	+	0.307472i
$202$	−4.29412	−	11.4953i	−0.302133	−	0.808804i
$203$	19.9884	+	23.8212i	1.40291	+	1.67192i
$204$	−2.97423	+	11.2152i	−0.208238	+	0.785222i
$205$	1.49755	+	4.11448i	0.104593	+	0.287368i
$206$	2.91913	+	15.7756i	0.203385	+	1.09914i
$207$	−2.52872	+	6.37405i	−0.175758	+	0.443027i
$208$	−7.68652	+	23.5641i	−0.532965	+	1.63388i
$209$	−15.6087	−	2.75224i	−1.07968	−	0.190377i
$210$	−14.4643	−	3.96680i	−0.998130	−	0.273735i
$211$	−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	$0.729565\pi$
$212$	0.179143	−	0.322743i	0.0123036	−	0.0221661i
$213$	1.55891	+	6.16966i	0.106815	+	0.422738i
$214$	−0.808724	−	1.37385i	−0.0552832	−	0.0939142i
$215$	6.62260			0.451658
$216$	10.5736	−	10.2078i	0.719443	−	0.694551i
$217$	−4.75290			−0.322648
$218$	7.36769	+	12.5161i	0.499003	+	0.847698i
$219$	−0.339103	+	0.329537i	−0.0229145	+	0.0222680i
$220$	−8.74665	−	4.85495i	−0.589699	−	0.327320i
$221$	−19.5034	−	7.09864i	−1.31194	−	0.477507i
$222$	−8.71853	+	8.61681i	−0.585149	+	0.578322i
$223$	24.8065	+	4.37405i	1.66116	+	0.292908i	0.923882	−	0.382677i	$-0.124998\pi$
$223$	24.8065	+	4.37405i	1.66116	+	0.292908i	0.737282	+	0.675585i	$0.236109\pi$
$224$	−15.1160	−	11.6336i	−1.00998	−	0.777304i
$225$	−1.60888	−	4.84756i	−0.107258	−	0.323171i
$226$	4.07021	+	21.9963i	0.270746	+	1.46317i
$227$	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	$0.846977\pi$
$228$	5.20845	+	19.2402i	0.344938	+	1.27421i
$229$	−5.68658	−	6.77700i	−0.375780	−	0.447837i	0.544698	−	0.838632i	$-0.316644\pi$
$229$	−5.68658	−	6.77700i	−0.375780	−	0.447837i	−0.920477	+	0.390796i	$0.872200\pi$
$230$	−2.05414	−	5.49887i	−0.135446	−	0.362585i
$231$	1.63120	−	16.0042i	0.107325	−	1.05300i
$232$	16.2555	−	20.3997i	1.06722	−	1.33930i
$233$	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	$0.0937058\pi$
$234$	16.4890	+	20.4758i	1.07792	+	1.33854i
$235$	−2.77200	+	4.80124i	−0.180825	+	0.313199i
$236$	17.0256	+	19.6086i	1.10827	+	1.27641i
$237$	1.58422	−	1.07584i	0.102906	−	0.0698832i
$238$	10.1632	−	12.3217i	0.658782	−	0.798697i
$239$	1.64140	+	9.30885i	0.106173	+	0.602139i	0.990745	+	0.135735i	$0.0433396\pi$
$239$	1.64140	+	9.30885i	0.106173	+	0.602139i	−0.884572	+	0.466404i	$0.845549\pi$
$240$	−0.852575	+	12.5520i	−0.0550335	+	0.810226i
$241$	−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
$246$	4.81818	+	3.41603i	0.307196	+	0.217798i
$247$	−35.1136	+	6.19148i	−2.23423	+	0.393954i
$248$	0.791461	+	3.90746i	0.0502578	+	0.248124i
$249$	−5.36159	+	3.64104i	−0.339777	+	0.230742i
$250$	14.9786	+	8.48017i	0.947327	+	0.536333i
$251$	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	$0.586220\pi$
$252$	−19.0913	+	6.69602i	−1.20264	+	0.421810i
$253$	5.45261	−	3.14807i	0.342803	−	0.197917i
$254$	3.64008	−	0.0307163i	0.228399	−	0.00192731i
$255$	−10.4805	−	1.06820i	−0.656316	−	0.0668935i
$256$	−7.04711	+	14.3645i	−0.440444	+	0.897780i
$257$	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	$0.693443\pi$
$258$	7.34769	−	5.08092i	0.457447	−	0.316324i
$259$	15.8567	−	5.77136i	0.985286	−	0.358615i
$260$	−22.2254	−	3.53330i	−1.37836	−	0.219126i
$261$	−8.71489	−	26.2580i	−0.539438	−	1.62533i
$262$	19.0355	−	16.2484i	1.17602	−	1.00383i
$263$	5.30413	−	30.0812i	0.327067	−	1.85489i	−0.167667	−	0.985844i	$-0.553623\pi$
$263$	5.30413	−	30.0812i	0.327067	−	1.85489i	0.494734	−	0.869045i	$-0.335266\pi$
$264$	−13.4291	+	1.32401i	−0.826502	+	0.0814872i
$265$	0.314936	+	0.114627i	0.0193464	+	0.00704151i
$266$	4.53655	−	27.0614i	0.278154	−	1.65924i
$267$	−7.79785	−	8.02421i	−0.477221	−	0.491074i
$268$	−2.33781	−	12.0642i	−0.142805	−	0.736936i
$269$	19.5851			1.19412			0.597061	−	0.802196i	$-0.296335\pi$
$269$	19.5851			1.19412			0.597061	+	0.802196i	$0.296335\pi$
$270$	10.6605	+	8.02609i	0.648775	+	0.488452i
$271$		−	4.73913i		−	0.287882i	−0.989586	−	0.143941i	$-0.954022\pi$
$271$		−	4.73913i		−	0.287882i	0.989586	−	0.143941i	$-0.0459775\pi$
$272$	−11.8223	−	6.30356i	−0.716835	−	0.382210i
$273$	−8.86559	−	35.0871i	−0.536570	−	2.12357i
$274$	0.667622	−	3.98249i	0.0403325	−	0.240591i
$275$	−1.60393	+	4.40677i	−0.0967207	+	0.265738i
$276$	−6.49783	−	4.52498i	−0.391123	−	0.272372i
$277$	7.26043	+	1.28021i	0.436237	+	0.0769203i	0.387454	−	0.921889i	$-0.373355\pi$
$277$	7.26043	+	1.28021i	0.436237	+	0.0769203i	0.0487830	+	0.998809i	$0.484466\pi$
$278$	3.08289	+	3.61171i	0.184899	+	0.216616i
$279$	3.93064	+	1.55937i	0.235321	+	0.0933569i
$280$	8.27690	−	15.2127i	0.494639	−	0.909135i
$281$	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	$0.851517\pi$
$282$	0.608061	+	7.45363i	0.0362095	+	0.443857i
$283$	−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	$0.448744\pi$
$284$	−7.34696	+	0.124001i	−0.435962	+	0.00735812i
$285$	−16.5100	+	7.41307i	−0.977966	+	0.439112i
$286$	−0.203679	−	24.1373i	−0.0120438	−	1.42727i
$287$	−4.06524	−	7.04120i	−0.239963	−	0.415629i
$288$	8.68407	+	14.5804i	0.511714	+	0.859156i
$289$	−2.89054	+	5.00656i	−0.170032	+	0.294504i
$290$	20.6094	+	11.6681i	1.21022	+	0.685172i
$291$	26.7561	−	1.95562i	1.56847	−	0.114640i
$292$	−0.280940	−	0.468174i	−0.0164408	−	0.0273978i
$293$	−2.84667	−	16.1443i	−0.166305	−	0.943160i	−0.947709	−	0.319135i	$-0.896608\pi$
$293$	−2.84667	−	16.1443i	−0.166305	−	0.943160i	0.781405	−	0.624025i	$-0.214504\pi$
$294$	10.6575	+	0.995456i	0.621559	+	0.0580562i
$295$	−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
$300$	5.87394	−	0.529122i	0.339132	−	0.0305489i
$301$	−12.1106	+	2.13543i	−0.698045	+	0.123084i
$302$	−3.71000	−	3.06008i	−0.213486	−	0.176088i
$303$	6.54573	−	13.5286i	0.376042	−	0.777201i
$304$	−23.0032	+	0.776714i	−1.31932	+	0.0445476i
$305$	22.2494	+	12.8457i	1.27400	+	0.735542i
$306$	−12.4475	+	6.85560i	−0.711579	+	0.391908i
$307$	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	$0.638773\pi$
$308$	17.5603	+	6.05783i	1.00059	+	0.345177i
$309$	−11.4994	+	15.9327i	−0.654175	+	0.906381i
$310$	−3.39095	+	1.26671i	−0.192593	+	0.0719442i
$311$	6.22295	−	5.22168i	0.352871	−	0.296094i	−0.449070	−	0.893496i	$-0.648245\pi$
$311$	6.22295	−	5.22168i	0.352871	−	0.296094i	0.801942	+	0.597402i	$0.203800\pi$
$312$	−27.3696	+	13.1314i	−1.54950	+	0.743418i
$313$	−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	$0.398570\pi$
$314$	−3.55978	−	19.2378i	−0.200890	−	1.08565i
$315$	−8.72573	−	16.1644i	−0.491639	−	0.910761i
$316$	0.791244	+	2.06482i	0.0445109	+	0.116155i
$317$	−3.11019	+	17.6387i	−0.174685	+	0.990690i	0.763821	+	0.645428i	$0.223321\pi$
$317$	−3.11019	+	17.6387i	−0.174685	+	0.990690i	−0.938506	+	0.345262i	$0.887790\pi$
$318$	0.437361	−	0.114444i	0.0245260	−	0.00641773i
$319$	−8.68811	+	23.8704i	−0.486441	+	1.33648i
$320$	−13.8850	−	4.27137i	−0.776196	−	0.238777i
$321$	0.532270	−	1.87854i	0.0297084	−	0.104850i
$322$	5.52945	+	9.39334i	0.308144	+	0.523470i
$323$		−	19.2731i		−	1.07238i
$324$	17.9854	+	0.726032i	0.999186	+	0.0403351i
$325$			10.5497i			0.585194i
$326$	−19.1293	+	11.2606i	−1.05948	+	0.623668i
$327$	−4.84912	+	17.1140i	−0.268157	+	0.946408i
$328$	−5.11178	+	4.51464i	−0.282251	+	0.249279i
$329$	3.52096	−	9.67376i	0.194117	−	0.533332i
$330$	−3.10156	−	11.8529i	−0.170735	−	0.652482i
$331$	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	$-0.0694650\pi$
$332$	−2.67787	−	6.98814i	−0.146967	−	0.383524i
$333$	−15.0070	−	0.429484i	−0.822376	−	0.0235356i
$334$	−21.4544	+	3.96994i	−1.17393	+	0.217225i
$335$	10.4845	−	3.81605i	0.572830	−	0.208493i
$336$	−2.48824	−	23.2285i	−0.135745	−	1.26722i
$337$	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	$0.101284\pi$
$338$	−12.5686	−	33.6458i	−0.683641	−	1.83009i
$339$	−16.0338	+	22.2153i	−0.870836	+	1.20657i
$340$	3.96703	−	11.4995i	0.215142	−	0.623649i
$341$	−1.94130	−	3.36242i	−0.105127	−	0.182085i
$342$	−12.6302	+	20.8913i	−0.682965	+	1.12967i
$343$	7.68048	+	4.43433i	0.414707	+	0.239431i
$344$	3.77227	+	9.60083i	0.203387	+	0.517642i
$345$	3.13121	−	6.47156i	0.168579	−	0.348417i
$346$	1.43650	−	1.74159i	0.0772268	−	0.0936285i
$347$	−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	$0.481179\pi$
$348$	31.8177	−	2.86612i	1.70561	−	0.153640i
$349$	6.39346	−	7.61943i	0.342234	−	0.407859i	−0.567284	−	0.823522i	$-0.692006\pi$
$349$	6.39346	−	7.61943i	0.342234	−	0.407859i	0.909519	+	0.415663i	$0.136450\pi$
$350$	−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	$0.381982\pi$
$354$	−2.95783	+	31.6670i	−0.157207	+	1.68308i
$355$	−1.15851	−	6.57025i	−0.0614874	−	0.348712i
$356$	11.0784	−	6.64789i	0.587156	−	0.352338i
$357$	19.5100	−	1.42600i	1.03258	−	0.0754717i
$358$	1.38553	−	2.44727i	0.0732276	−	0.129342i
$359$	16.4564	−	28.5033i	0.868536	−	1.50435i	0.00504305	−	0.999987i	$-0.498395\pi$
$359$	16.4564	−	28.5033i	0.868536	−	1.50435i	0.863493	−	0.504361i	$-0.168272\pi$
$360$	−11.8361	+	9.86535i	−0.623817	+	0.519950i
$361$	−7.05472	−	12.2191i	−0.371301	−	0.643113i
$362$	1.08431	−	0.00914977i	0.0569899	−	0.000480901i
$363$	−5.39251	+	2.42127i	−0.283033	+	0.127084i
$364$	41.7824	−	0.705200i	2.18999	−	0.0369625i
$365$	0.379757	−	0.318654i	0.0198774	−	0.0166791i
$366$	34.5408	−	2.81781i	1.80548	−	0.147289i
$367$	−12.7028	−	34.9007i	−0.663082	−	1.82180i	−0.562366	−	0.826888i	$-0.690109\pi$
$367$	−12.7028	−	34.9007i	−0.663082	−	1.82180i	−0.100716	−	0.994915i	$-0.532113\pi$
$368$	6.80170	−	6.11008i	0.354563	−	0.318510i
$369$	1.05181	+	7.15681i	0.0547551	+	0.372569i
$370$	9.77479	−	8.34358i	0.508167	−	0.433762i
$371$	−0.612880	−	0.108067i	−0.0318191	−	0.00561057i
$372$	−2.79038	+	4.00697i	−0.144675	+	0.207752i
$373$	8.37871	−	23.0203i	0.433833	−	1.19195i	−0.509608	−	0.860407i	$-0.670209\pi$
$373$	8.37871	−	23.0203i	0.433833	−	1.19195i	0.943441	−	0.331540i	$-0.107568\pi$
$374$	12.8681	+	2.15719i	0.665391	+	0.111546i
$375$	5.16430	+	20.4386i	0.266683	+	1.05544i
$376$	−8.53934	−	1.28377i	−0.440383	−	0.0662053i
$377$			57.1454i			2.94314i
$378$	−22.0826	−	11.2397i	−1.13581	−	0.578110i
$379$	−32.5154			−1.67021			−0.835103	−	0.550094i	$-0.814592\pi$
$379$	−32.5154			−1.67021			−0.835103	+	0.550094i	$0.814592\pi$
$380$	−3.97562	−	20.5160i	−0.203945	−	1.05245i
$381$	3.10710	+	3.19729i	0.159181	+	0.163802i
$382$	0.190943	+	0.0320096i	0.00976951	+	0.00163775i
$383$	−21.7889	−	7.93050i	−1.11336	−	0.405230i	−0.281135	−	0.959668i	$-0.590711\pi$
$383$	−21.7889	−	7.93050i	−1.11336	−	0.405230i	−0.832225	+	0.554439i	$0.812933\pi$
$384$	−18.6823	+	5.91369i	−0.953377	+	0.301782i
$385$	−2.92873	+	16.6096i	−0.149262	+	0.846506i
$386$	15.6075	+	18.2847i	0.794402	+	0.930669i
$387$	10.7161	+	2.20735i	0.544729	+	0.112206i
$388$	−4.86363	+	30.5935i	−0.246914	+	1.55315i
$389$	9.45367	−	3.44085i	0.479320	−	0.174458i	−0.0910496	−	0.995846i	$-0.529022\pi$
$389$	9.45367	−	3.44085i	0.479320	−	0.174458i	0.570370	+	0.821388i	$0.306800\pi$
$390$	−15.6763	−	22.6700i	−0.793801	−	1.14794i
$391$	4.92126	+	5.86493i	0.248879	+	0.296602i
$392$	−3.93197	+	11.7177i	−0.198594	+	0.591833i
$393$	30.4939	+	3.10803i	1.53822	+	0.156779i
$394$	−0.0679392	−	8.05124i	−0.00342273	−	0.405615i
$395$	−1.73871	+	1.00384i	−0.0874838	+	0.0505088i
$396$	−12.5348	−	10.7711i	−0.629899	−	0.541270i
$397$	12.5559	+	7.24913i	0.630161	+	0.363823i	0.780814	−	0.624763i	$-0.214805\pi$
$397$	12.5559	+	7.24913i	0.630161	+	0.363823i	−0.150654	+	0.988587i	$0.548138\pi$
$398$	−9.86559	+	17.4256i	−0.494517	+	0.873469i
$399$	27.8012	−	18.8797i	1.39180	−	0.945168i
$400$	−0.955564	+	6.74273i	−0.0477782	+	0.337136i
$401$	−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	$0.474197\pi$
$402$	8.70473	−	12.2777i	0.434152	−	0.612355i
$403$	−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
$408$	−4.42118	−	15.8021i	−0.218881	−	0.782322i
$409$	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	$0.722184\pi$
$410$	−4.77691	−	3.94010i	−0.235915	−	0.194588i
$411$	4.09136	−	2.77844i	0.201812	−	0.137050i
$412$	−14.8753	−	17.1321i	−0.732855	−	0.844036i
$413$	21.8910	−	37.9163i	1.07719	−	1.86574i
$414$	−1.49100	−	9.58242i	−0.0732787	−	0.470950i
$415$	5.88444	−	3.39738i	0.288856	−	0.166771i
$416$	−7.53745	−	34.2329i	−0.369554	−	1.67840i
$417$	−0.589703	+	5.78578i	−0.0288779	+	0.283331i
$418$	20.9974	−	7.84371i	1.02702	−	0.383649i
$419$	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	$0.673007\pi$
$420$	20.4740	−	5.54243i	0.999027	−	0.270443i
$421$	−1.63940	−	4.50421i	−0.0798994	−	0.219522i	0.893311	−	0.449440i	$-0.148376\pi$
$421$	−1.63940	−	4.50421i	−0.0798994	−	0.219522i	−0.973210	+	0.229918i	$0.926154\pi$
$422$	14.6894	−	2.71814i	0.715071	−	0.132317i
$423$	−6.08567	+	6.84500i	−0.295896	+	0.332815i
$424$	0.0132134	+	0.521858i	0.000641698	+	0.0253437i
$425$	−5.61592	−	0.990237i	−0.272412	−	0.0480336i
$426$	−6.32611	−	6.40079i	−0.306501	−	0.310119i
$427$	−44.8291	−	16.3165i	−2.16943	−	0.789609i
$428$	1.97124	+	1.09416i	0.0952834	+	0.0528884i
$429$	21.2011	−	20.6031i	1.02360	−	0.994726i
$430$	−8.07119	+	4.75116i	−0.389227	+	0.229121i
$431$	−18.8441			−0.907686			−0.453843	−	0.891082i	$-0.649947\pi$
$431$	−18.8441			−0.907686			−0.453843	+	0.891082i	$0.649947\pi$
$432$	−5.56321	+	20.0263i	−0.267660	+	0.963513i
$433$	32.5586			1.56466			0.782332	−	0.622861i	$-0.214030\pi$
$433$	32.5586			1.56466			0.782332	+	0.622861i	$0.214030\pi$
$434$	5.79252	−	3.40980i	0.278050	−	0.163676i
$435$	7.10568	+	28.1219i	0.340691	+	1.34834i
$436$	−17.9585	−	9.96812i	−0.860057	−	0.477387i
$437$	12.3593	+	4.49843i	0.591227	+	0.215189i
$438$	0.176861	−	0.644896i	0.00845076	−	0.0308143i
$439$	−2.24864	−	0.396495i	−0.107322	−	0.0189237i	0.119729	−	0.992807i	$-0.461797\pi$
$439$	−2.24864	−	0.396495i	−0.107322	−	0.0189237i	−0.227051	+	0.973883i	$0.572908\pi$
$440$	14.1429	−	0.358095i	0.674234	−	0.0170715i
$441$	8.13592	+	10.2795i	0.387425	+	0.489498i
$442$	28.8621	−	5.34066i	1.37283	−	0.254029i
$443$	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	$0.836723\pi$
$444$	4.44373	−	16.7564i	0.210890	−	0.795224i
$445$	7.54033	+	8.98621i	0.357446	+	0.425987i
$446$	−33.3705	+	12.4658i	−1.58014	+	0.590271i
$447$	−16.8859	+	7.58187i	−0.798676	+	0.358610i
$448$	26.7686	+	3.33381i	1.26470	+	0.157508i
$449$	−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	$0.408214\pi$
$450$	5.43851	+	4.75366i	0.256374	+	0.224090i
$451$	3.32085	−	5.75188i	0.156373	−	0.270846i
$452$	−20.7410	−	23.8876i	−0.975574	−	1.12358i
$453$	−0.429360	−	5.87435i	−0.0201731	−	0.276001i
$454$	−4.31609	−	3.56001i	−0.202564	−	0.167079i
$455$	6.58850	+	37.3652i	0.308874	+	1.75171i
$456$	−20.1509	−	19.7121i	−0.943654	−	0.923103i
$457$	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	0.996394	−	0.0848500i	$-0.0270411\pi$
$461$	23.3143	+	19.5630i	1.08585	+	0.911140i	0.0894610	+	0.995990i	$0.471486\pi$
$462$	9.49369	+	20.6751i	0.441686	+	0.961895i
$463$	21.1468	−	3.72876i	0.982776	−	0.173290i	0.340901	−	0.940099i	$-0.389268\pi$
$463$	21.1468	−	3.72876i	0.982776	−	0.173290i	0.641875	+	0.766809i	$0.278157\pi$
$464$	−5.17606	+	36.5237i	−0.240292	+	1.69557i
$465$	−3.99077	−	1.93090i	−0.185067	−	0.0895434i
$466$	−14.5427	+	25.6868i	−0.673677	+	1.18992i
$467$	−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	$0.977232\pi$
$468$	−34.7854	−	13.1251i	−1.60795	−	0.606709i
$469$	−17.9424	+	10.3590i	−0.828501	+	0.478336i
$470$	−0.0661577	−	7.84012i	−0.00305163	−	0.361638i
$471$	14.0231	−	19.4294i	0.646148	−	0.895259i
$472$	−34.8172	−	11.6832i	−1.60259	−	0.537762i
$473$	−6.45723	−	7.69542i	−0.296904	−	0.353836i
$474$	−1.15892	+	2.44770i	−0.0532307	+	0.112427i
$475$	−9.20567	+	3.35059i	−0.422385	+	0.153736i
$476$	−3.54646	+	22.3081i	−0.162552	+	1.02249i
$477$	0.471395	+	0.290450i	0.0215837	+	0.0132988i
$478$	−8.67875	−	10.1674i	−0.396957	−	0.465048i
$479$	−4.55057	+	25.8076i	−0.207921	+	1.17918i	0.684856	+	0.728679i	$0.259865\pi$
$479$	−4.55057	+	25.8076i	−0.207921	+	1.17918i	−0.892777	+	0.450500i	$0.851246\pi$
$480$	−7.96592	−	15.9092i	−0.363593	−	0.726151i
$481$	29.1396	+	10.6059i	1.32865	+	0.483589i
$482$	27.9757	+	4.68982i	1.27426	+	0.213615i
$483$	−3.63926	+	12.8441i	−0.165592	+	0.584425i
$484$	−1.29852	−	6.70095i	−0.0590237	−	0.304589i
$485$	−28.1261			−1.27714
$486$	14.5746	+	16.5403i	0.661118	+	0.750282i
$487$			23.1000i			1.04676i	0.852099	+	0.523380i	$0.175329\pi$
$487$			23.1000i			1.04676i	−0.852099	+	0.523380i	$0.824671\pi$
$488$	−5.94910	+	39.5721i	−0.269303	+	1.79134i
$489$	−26.1567	−	7.41129i	−1.18285	−	0.335150i
$490$	−11.0676	−	1.85537i	−0.499984	−	0.0838169i
$491$	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	$-0.155289\pi$
$492$	−8.32281	−	0.706597i	−0.375221	−	0.0318558i
$493$	−30.4200	−	5.36387i	−1.37005	−	0.241577i
$494$	38.3523	−	32.7368i	1.72555	−	1.47290i
$495$	7.87148	−	12.7753i	0.353796	−	0.574205i
$496$	−3.76786	−	4.19435i	−0.169182	−	0.188332i
$497$	4.23710	+	11.6413i	0.190060	+	0.522185i
$498$	3.92221	−	8.28395i	0.175758	−	0.371213i
$499$	−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	$0.343192\pi$
$500$	−24.3387	+	0.410786i	−1.08846	+	0.0183709i
$501$	−21.6681	−	15.6388i	−0.968058	−	0.698690i
$502$	−11.2044	+	0.0945469i	−0.500078	+	0.00421984i
$503$	7.67973	+	13.3017i	0.342422	+	0.593093i	0.984882	−	0.173227i	$-0.0554193\pi$
$503$	7.67973	+	13.3017i	0.342422	+	0.593093i	−0.642460	+	0.766319i	$0.722086\pi$
$504$	18.4634	−	21.8571i	0.822425	−	0.973592i
$505$	−7.87826	+	13.6455i	−0.350578	+	0.607219i
$506$	−4.38681	+	7.74845i	−0.195018	+	0.344461i
$507$	19.1589	−	39.5973i	0.850875	−	1.75858i
$508$	−4.41426	+	2.64889i	−0.195851	+	0.117525i
$509$	6.62546	+	37.5748i	0.293668	+	1.66548i	0.672566	+	0.740037i	$0.265192\pi$
$509$	6.62546	+	37.5748i	0.293668	+	1.66548i	−0.378898	+	0.925439i	$0.623697\pi$
$510$	13.5393	−	6.21704i	0.599531	−	0.275295i
$511$	−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
$516$	−5.30975	+	11.4637i	−0.233749	+	0.504659i
$517$	8.28179	−	1.46030i	0.364233	−	0.0642241i
$518$	−15.1846	+	18.4096i	−0.667174	+	0.808871i
$519$	2.75761	−	0.201555i	0.121045	−	0.00884729i
$520$	29.6217	−	11.6387i	1.29900	−	0.510390i
$521$	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	$0.639210\pi$
$522$	29.4591	+	25.7494i	1.28939	+	1.12702i
$523$	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	$0.654541\pi$
$524$	−11.5424	+	33.4588i	−0.504232	+	1.46166i
$525$	−4.07289	−	9.07090i	−0.177755	−	0.395887i
$526$	15.1164	+	40.4663i	0.659108	+	1.76442i
$527$	3.61668	−	3.03476i	0.157545	−	0.132196i
$528$	15.4166	−	11.2478i	0.670921	−	0.489500i
$529$	16.7033	−	6.07949i	0.726229	−	0.264326i
$530$	−0.466059	+	0.0862400i	−0.0202443	+	0.00374602i
$531$	−30.5437	+	24.1745i	−1.32548	+	1.04909i
$532$	13.8854	+	36.2352i	0.602009	+	1.57100i
$533$	2.59452	−	14.7143i	0.112381	−	0.637345i
$534$	15.2602	+	4.18508i	0.660374	+	0.181106i
$535$	−0.700118	+	1.92356i	−0.0302688	+	0.0831627i
$536$	11.5042	+	13.0258i	0.496905	+	0.562630i
$537$	3.33936	−	0.843769i	0.144104	−	0.0364113i
$538$	−23.8690	+	14.0506i	−1.02907	+	0.605766i
$539$		−	12.0367i		−	0.518457i
$540$	−18.7503	−	2.13368i	−0.806885	−	0.0918190i
$541$			8.40412i			0.361321i	0.983546	+	0.180661i	$0.0578236\pi$
$541$			8.40412i			0.361321i	−0.983546	+	0.180661i	$0.942176\pi$
$542$	3.39993	+	5.77574i	0.146039	+	0.248089i
$543$	0.925541	+	0.952408i	0.0397188	+	0.0408718i
$544$	18.9306	−	0.799170i	0.811642	−	0.0342641i
$545$	6.37827	−	17.5241i	0.273215	−	0.750652i
$546$	35.9768	+	36.4015i	1.53967	+	1.55784i
$547$	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	$-0.182767\pi$
$548$	2.04345	+	5.33257i	0.0872919	+	0.227796i
$549$	31.7203	+	28.2016i	1.35379	+	1.20361i
$550$	−1.20672	−	6.52137i	−0.0514546	−	0.278072i
$551$	−49.8648	+	18.1493i	−2.12431	+	0.773187i
$552$	11.1654	+	0.853102i	0.475232	+	0.0363104i
$553$	2.85585	−	2.39635i	0.121443	−	0.101903i
$554$	−9.76698	+	3.64851i	−0.414959	+	0.155010i
$555$	15.6587	+	1.59598i	0.664676	+	0.0677456i
$556$	−6.34832	−	2.19000i	−0.269229	−	0.0928767i
$557$	8.29813	+	14.3728i	0.351603	+	0.608994i	0.986530	−	0.163578i	$-0.0523034\pi$
$557$	8.29813	+	14.3728i	0.351603	+	0.608994i	−0.634928	+	0.772572i	$0.718970\pi$
$558$	−5.90912	+	0.919445i	−0.250153	+	0.0389232i
$559$	−19.5712	−	11.2994i	−0.827772	−	0.477914i
$560$	0.826519	+	24.4783i	0.0349268	+	1.03440i
$561$	8.97756	+	13.2198i	0.379033	+	0.558142i
$562$	−4.28453	−	3.53397i	−0.180732	−	0.149072i
$563$	−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	$0.669827\pi$
$564$	−6.08842	−	8.64776i	−0.256369	−	0.364136i
$565$	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	$0.332055\pi$
$570$	14.8030	−	20.8791i	0.620030	−	0.874529i
$571$	−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	$0.969683\pi$
$572$	17.5647	+	29.2708i	0.734417	+	1.22387i
$573$	0.133214	+	0.196163i	0.00556510	+	0.00819483i
$574$	10.0059	+	5.66489i	0.417639	+	0.236448i
$575$	1.94579	−	3.37022i	0.0811452	−	0.140548i
$576$	−21.0438	−	11.5395i	−0.876823	−	0.480812i
$577$	−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	$-0.337512\pi$
$578$	−0.0689868	−	8.17539i	−0.00286947	−	0.340051i
$579$	−2.98545	+	29.2913i	−0.124071	+	1.21730i
$580$	−33.4882	+	0.565211i	−1.39052	+	0.0234691i
$581$	−9.66529	+	8.11014i	−0.400984	+	0.336465i
$582$	−31.2056	+	21.5786i	−1.29351	+	0.894463i
$583$	−0.173876	−	0.477719i	−0.00720119	−	0.0197851i
$584$	0.678266	+	0.369029i	0.0280669	+	0.0152705i
$585$	6.81041	−	33.0626i	0.281576	−	1.36697i
$586$	15.0515	+	17.6334i	0.621772	+	0.728427i
$587$	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	$0.338836\pi$
$588$	−13.7028	+	6.43268i	−0.565095	+	0.265279i
$589$	2.77401	−	7.62154i	0.114301	−	0.314040i
$590$	5.51291	−	32.8856i	0.226963	−	1.35388i
$591$	7.07186	−	6.87236i	0.290897	−	0.282691i
$592$	17.6635	+	9.41802i	0.725966	+	0.387078i
$593$		−	38.8450i		−	1.59517i	−0.603206	−	0.797586i	$-0.706110\pi$
$593$		−	38.8450i		−	1.59517i	0.603206	−	0.797586i	$-0.293890\pi$
$594$	−1.06800	−	20.2131i	−0.0438204	−	0.829352i
$595$	−20.5090			−0.840785
$596$	−4.06614	−	20.9831i	−0.166556	−	0.859502i
$597$	−23.7777	+	6.00800i	−0.973156	+	0.245891i
$598$	−3.31172	+	19.7551i	−0.135426	+	0.807844i
$599$	−42.6481	−	15.5226i	−1.74255	−	0.634238i	−0.743163	−	0.669110i	$-0.766675\pi$
$599$	−42.6481	−	15.5226i	−1.74255	−	0.634238i	−0.999392	+	0.0348721i	$0.988898\pi$
$600$	−6.77917	+	4.85892i	−0.276758	+	0.198364i
$601$	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	$-0.0302537\pi$
$602$	13.2276	−	11.2909i	0.539119	−	0.460182i
$603$	18.2370	−	2.68022i	0.742667	−	0.109147i
$604$	6.71686	+	1.06782i	0.273305	+	0.0434489i
$605$	5.82355	−	2.11960i	0.236761	−	0.0861739i
$606$	1.72816	+	21.1838i	0.0702018	+	0.860535i
$607$	0.568907	+	0.677997i	0.0230912	+	0.0275190i	0.777466	−	0.628924i	$-0.216505\pi$
$607$	0.568907	+	0.677997i	0.0230912	+	0.0275190i	−0.754375	+	0.656443i	$0.772060\pi$
$608$	27.4776	−	17.4495i	1.11436	−	0.707670i
$609$	−22.0618	−	49.1349i	−0.893990	−	1.99104i
$610$	−36.3318	+	0.306581i	−1.47103	+	0.0124131i
$611$	16.3837	−	9.45912i	0.662812	−	0.382675i
$612$	10.2519	−	17.2852i	0.414410	−	0.698714i
$613$	1.26069	+	0.727860i	0.0509188	+	0.0293980i	0.525243	−	0.850952i	$-0.323974\pi$
$613$	1.26069	+	0.727860i	0.0509188	+	0.0293980i	−0.474324	+	0.880350i	$0.657308\pi$
$614$	−24.7489	−	14.0117i	−0.998786	−	0.565466i
$615$	−0.552834	−	7.56368i	−0.0222924	−	0.304997i
$616$	−25.7473	+	5.21515i	−1.03739	+	0.210124i
$617$	−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	$0.521687\pi$
$618$	2.58427	−	27.6676i	0.103954	−	1.11295i
$619$	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
$624$	23.9356	−	35.6390i	0.958190	−	1.42670i
$625$	−2.35967	−	13.3823i	−0.0943867	−	0.535293i
$626$	0.968203	−	1.17383i	0.0386972	−	0.0469158i
$627$	24.7116	+	11.9565i	0.986888	+	0.477498i
$628$	18.1399	+	20.8919i	0.723862	+	0.833679i
$629$	−8.38098	+	14.5163i	−0.334171	+	0.578802i
$630$	22.2310	+	13.4401i	0.885702	+	0.535468i
$631$	22.9218	−	13.2339i	0.912502	−	0.526834i	0.0312670	−	0.999511i	$-0.490046\pi$
$631$	22.9218	−	13.2339i	0.912502	−	0.526834i	0.881235	+	0.472678i	$0.156712\pi$
$632$	−2.44565	−	1.94882i	−0.0972828	−	0.0775198i
$633$	14.8357	+	10.7076i	0.589667	+	0.425589i
$634$	−8.86382	−	23.7282i	−0.352027	−	0.942369i
$635$	−3.00448	−	3.58061i	−0.119229	−	0.142092i
$636$	−0.450923	+	0.453248i	−0.0178803	+	0.0179724i
$637$	−9.26118	−	25.4449i	−0.366941	−	1.00816i
$638$	−6.53649	−	35.3246i	−0.258782	−	1.39852i
$639$	0.315310	−	11.0175i	0.0124735	−	0.435845i
$640$	19.9865	−	4.75567i	0.790036	−	0.187984i
$641$	−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	$0.755371\pi$
$642$	0.699001	+	2.67130i	0.0275874	+	0.105428i
$643$	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	$0.294717\pi$
$644$	−13.4779	−	7.48107i	−0.531102	−	0.294795i
$645$	−11.0362	−	3.12702i	−0.434551	−	0.123126i
$646$	13.8268	+	23.4888i	0.544009	+	0.924154i
$647$	−1.31046			−0.0515196			−0.0257598	−	0.999668i	$-0.508201\pi$
$647$	−1.31046			−0.0515196			−0.0257598	+	0.999668i	$0.508201\pi$
$648$	−22.4402	+	12.0181i	−0.881536	+	0.472117i
$649$	35.7651			1.40390
$650$	−7.56855	−	12.8573i	−0.296863	−	0.504306i
$651$	7.92046	+	2.24420i	0.310427	+	0.0879570i
$652$	15.2351	−	27.4474i	0.596651	−	1.07492i
$653$	−45.3419	−	16.5031i	−1.77436	−	0.645816i	−0.999913	−	0.0131827i	$-0.995804\pi$
$653$	−45.3419	−	16.5031i	−1.77436	−	0.645816i	−0.774452	−	0.632633i	$-0.781974\pi$
$654$	−6.36809	−	24.3363i	−0.249012	−	0.951625i
$655$	−31.6475	−	5.58030i	−1.23657	−	0.218040i
$656$	2.99103	−	9.16942i	0.116780	−	0.358006i
$657$	0.720697	−	0.389041i	0.0281171	−	0.0151779i
$658$	2.64900	+	14.3157i	0.103269	+	0.558086i
$659$	−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	$-0.309024\pi$
$660$	12.2835	+	12.2205i	0.478133	+	0.475681i
$661$	1.72700	+	2.05816i	0.0671726	+	0.0800532i	0.798584	−	0.601883i	$-0.205583\pi$
$661$	1.72700	+	2.05816i	0.0671726	+	0.0800532i	−0.731412	+	0.681936i	$0.761138\pi$
$662$	6.89218	+	18.4502i	0.267872	+	0.717087i
$663$	29.1496	+	21.0385i	1.13207	+	0.817069i
$664$	8.27702	+	6.59554i	0.321210	+	0.255957i
$665$	−30.5123	+	17.6163i	−1.18322	+	0.683130i
$666$	18.5976	−	10.2428i	0.720643	−	0.396901i
$667$	10.5399	−	18.2556i	0.408106	−	0.706861i
$668$	23.2991	−	20.2300i	0.901470	−	0.782723i
$669$	−39.2734	−	19.0021i	−1.51840	−	0.734664i
$670$	−10.0401	+	12.1725i	−0.387885	+	0.470265i
$671$	−6.76718	−	38.3786i	−0.261244	−	1.48159i
$672$	19.6970	+	26.5242i	0.759827	+	1.02319i
$673$	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	−0.109186	−	0.994021i	$-0.534824\pi$
$677$	−28.8050	−	24.1702i	−1.10707	−	0.928938i	−0.997880	+	0.0650833i	$0.979269\pi$
$678$	3.60330	−	38.5775i	0.138384	−	1.48156i
$679$	51.4337	−	9.06915i	1.97385	−	0.348042i
$680$	3.41519	+	16.8609i	0.130967	+	0.646585i
$681$	−0.499503	−	6.83403i	−0.0191410	−	0.261881i
$682$	4.77818	+	2.70518i	0.182966	+	0.103587i
$683$	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	$0.642887\pi$
$684$	0.405131	−	34.5221i	0.0154906	−	1.31999i
$685$	−4.49034	+	2.59250i	−0.171567	+	0.0990544i
$686$	−12.5417	+	0.105832i	−0.478845	+	0.00404067i
$687$	6.27646	+	13.9786i	0.239462	+	0.533316i
$688$	−11.4852	−	8.99457i	−0.437868	−	0.342915i
$689$	−0.735126	−	0.876089i	−0.0280061	−	0.0333764i
$690$	0.826684	+	10.1335i	0.0314713	+	0.385776i
$691$	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	$0.242816\pi$
$692$	−0.501268	+	3.15311i	−0.0190554	+	0.119863i
$693$	−10.2751	+	25.9000i	−0.390318	+	0.983860i
$694$	4.61442	−	3.93879i	0.175161	−	0.149514i
$695$	1.05878	−	6.00465i	0.0401619	−	0.227769i
$696$	−36.7211	+	26.3196i	−1.39191	+	0.997640i
$697$	7.58927	+	2.76227i	0.287464	+	0.104628i
$698$	−2.32563	+	13.8728i	−0.0880265	+	0.525095i
$699$	−35.0502	+	8.85629i	−1.32572	+	0.334975i
$700$	11.2719	−	2.18428i	0.426037	−	0.0825581i
$701$	−15.2353			−0.575429			−0.287715	−	0.957716i	$-0.592895\pi$
$701$	−15.2353			−0.575429			−0.287715	+	0.957716i	$0.592895\pi$
$702$	−17.8099	−	41.9075i	−0.672190	−	1.58170i
$703$			28.7955i			1.08604i
$704$	8.57499	+	20.2990i	0.323182	+	0.765048i
$705$	6.88642	−	6.69216i	0.259358	−	0.252041i
$706$	4.22687	−	25.2141i	0.159080	−	0.948944i
$707$	10.0069	−	27.4937i	0.376347	−	1.03401i
$708$	−19.1136	−	40.7157i	−0.718334	−	1.53019i
$709$	37.6664	+	6.64161i	1.41459	+	0.249431i	0.828126	−	0.560542i	$-0.189407\pi$
$709$	37.6664	+	6.64161i	1.41459	+	0.249431i	0.586467	+	0.809973i	$0.300518\pi$
$710$	6.12552	+	7.17625i	0.229887	+	0.269320i
$711$	−3.14800	+	1.04480i	−0.118059	+	0.0391831i
$712$	−8.73236	+	16.0499i	−0.327259	+	0.601494i
$713$	1.10196	+	3.02761i	0.0412687	+	0.113385i
$714$	−22.7544	+	15.7347i	−0.851564	+	0.588855i
$715$	−23.7429	+	19.9227i	−0.887934	+	0.745065i
$716$	0.0671163	+	3.97658i	0.00250825	+	0.148612i
$717$	1.66009	−	16.2877i	0.0619973	−	0.608277i
$718$	0.392756	+	46.5441i	0.0146575	+	1.73701i
$719$	11.2648	+	19.5112i	0.420106	+	0.727645i	0.995949	−	0.0899151i	$-0.0286596\pi$
$719$	11.2648	+	19.5112i	0.420106	+	0.727645i	−0.575843	+	0.817560i	$0.695326\pi$
$720$	7.34749	−	20.5146i	0.273825	−	0.764536i
$721$	−19.1262	+	33.1276i	−0.712298	+	1.23374i
$722$	17.3640	+	9.83072i	0.646223	+	0.365861i
$723$	19.5176	+	28.7404i	0.725867	+	1.06887i
$724$	−1.31492	+	0.789050i	−0.0488686	+	0.0293248i
$725$	2.72644	+	15.4624i	0.101258	+	0.574260i
$726$	4.83498	−	6.81955i	0.179443	−	0.253097i
$727$	15.4990	−	18.4710i	0.574827	−	0.685052i	−0.397787	−	0.917478i	$-0.630222\pi$
$727$	15.4990	−	18.4710i	0.574827	−	0.685052i	0.972614	+	0.232425i	$0.0746662\pi$
$728$	−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
$732$	−40.0745	+	28.2143i	−1.48120	+	1.04283i
$733$	−13.4649	+	2.37423i	−0.497339	+	0.0876942i	−0.416691	−	0.909048i	$-0.636810\pi$
$733$	−13.4649	+	2.37423i	−0.497339	+	0.0876942i	−0.0806481	+	0.996743i	$0.525699\pi$
$734$	40.5197	+	33.4215i	1.49561	+	1.23361i
$735$	−7.72146	−	11.3702i	−0.284810	−	0.419395i
$736$	−3.90600	+	12.3262i	−0.143977	+	0.454350i
$737$	−14.6569	−	8.46218i	−0.539895	−	0.311708i
$738$	−6.41629	−	7.96767i	−0.236187	−	0.293294i
$739$	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	$0.787239\pi$
$740$	−5.92705	+	17.1812i	−0.217883	+	0.631594i
$741$	61.4385	+	6.26199i	2.25700	+	0.230040i
$742$	0.824467	−	0.307984i	0.0302671	−	0.0113065i
$743$	2.44427	−	2.05099i	0.0896717	−	0.0752435i	−0.596850	−	0.802353i	$-0.703581\pi$
$743$	2.44427	−	2.05099i	0.0896717	−	0.0752435i	0.686522	+	0.727109i	$0.259137\pi$
$744$	0.526076	−	6.88530i	0.0192869	−	0.252427i
$745$	18.2357	−	6.63724i	0.668103	−	0.243170i
$746$	6.30372	+	34.0667i	0.230796	+	1.24727i
$747$	10.6540	−	3.53600i	0.389810	−	0.129376i
$748$	−17.2303	+	6.60271i	−0.630004	+	0.241419i
$749$	0.660050	−	3.74333i	0.0241177	−	0.136778i
$750$	−20.9569	−	21.2043i	−0.765237	−	0.774270i
$751$	−7.59333	+	20.8625i	−0.277085	+	0.761284i	0.720605	+	0.693346i	$0.243864\pi$
$751$	−7.59333	+	20.8625i	−0.277085	+	0.761284i	−0.997690	+	0.0679380i	$0.978358\pi$
$752$	11.3282	−	4.56168i	0.413096	−	0.166348i
$753$	−9.56386	−	9.84148i	−0.348526	−	0.358644i
$754$	−40.9970	−	69.6450i	−1.49302	−	2.53632i
$755$			6.17514i			0.224736i
$756$	34.9764	−	2.14414i	1.27208	−	0.0779817i
$757$		−	39.4292i		−	1.43308i	−0.697546	−	0.716540i	$-0.745725\pi$
$757$		−	39.4292i		−	1.43308i	0.697546	−	0.716540i	$-0.254275\pi$
$758$	39.6277	−	23.3271i	1.43934	−	0.847278i
$759$	−10.5729	+	2.67151i	−0.383773	+	0.0969696i
$760$	19.5637	+	22.1513i	0.709650	+	0.803514i
$761$	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	$-0.0798775\pi$
$762$	−6.08051	−	1.66757i	−0.220274	−	0.0604096i
$763$	−6.01323	+	34.1027i	−0.217694	+	1.23460i
$764$	−0.255673	+	0.0979746i	−0.00924994	+	0.00354460i
$765$	16.9609	+	6.72874i	0.613221	+	0.243278i
$766$	32.2443	−	5.96651i	1.16503	−	0.215579i
$767$	75.6053	−	27.5181i	2.72995	−	0.993620i
$768$	18.5262	−	20.6102i	0.668506	−	0.743706i
$769$	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	$0.242488\pi$
$770$	−8.34668	−	22.3439i	−0.300794	−	0.805217i
$771$	−5.95650	−	13.2660i	−0.214518	−	0.477762i
$772$	−32.1392	−	11.0872i	−1.15672	−	0.399036i
$773$	18.0562	+	31.2743i	0.649437	+	1.12486i	0.983258	+	0.182221i	$0.0583287\pi$
$773$	18.0562	+	31.2743i	0.649437	+	1.12486i	−0.333820	+	0.942637i	$0.608338\pi$
$774$	−14.6436	+	4.99770i	−0.526355	+	0.179639i
$775$	−2.07829	−	1.19990i	−0.0746542	−	0.0431016i
$776$	−16.0208	−	40.7746i	−0.575113	−	1.46372i
$777$	−29.1494	+	2.13055i	−1.04573	+	0.0764331i
$778$	−9.05299	+	10.9757i	−0.324565	+	0.393498i
$779$	13.6636	−	2.40927i	0.489550	−	0.0863209i
$780$	35.3691	+	16.3823i	1.26642	+	0.586581i
$781$	−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
$786$	−39.3938	+	18.0890i	−1.40513	+	0.645212i
$787$	−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	$0.956889\pi$
$788$	5.85889	+	9.76358i	0.208714	+	0.347813i
$789$	−23.0427	+	47.6244i	−0.820341	+	1.69547i
$790$	1.39885	−	2.47079i	0.0497688	−	0.0879068i
$791$	−26.6681	+	46.1905i	−0.948209	+	1.64235i
$792$	23.0040	+	4.13447i	0.817412	+	0.146912i
$793$	−43.8344	−	75.9234i	−1.55661	−	2.69612i
$794$	−20.5029	+	0.173011i	−0.727621	+	0.00613992i
$795$	−0.470701	−	0.339726i	−0.0166940	−	0.0120488i
$796$	−0.477898	−	28.3150i	−0.0169386	−	1.00360i
$797$	33.5503	−	28.1520i	1.18841	−	0.997197i	0.188527	−	0.982068i	$-0.439629\pi$
$797$	33.5503	−	28.1520i	1.18841	−	0.997197i	0.999886	−	0.0151286i	$-0.00481575\pi$
$798$	−20.3376	+	42.9544i	−0.719944	+	1.52057i
$799$	3.49751	+	9.60934i	0.123733	+	0.339954i
$800$	−3.67276	−	8.90313i	−0.129852	−	0.314773i
$801$	9.20589	+	17.0539i	0.325274	+	0.602570i
$802$	4.02075	−	3.43204i	0.141977	−	0.121189i
$803$	−0.740548	−	0.130579i	−0.0261334	−	0.00460802i
$804$	−1.80055	+	21.2081i	−0.0635004	+	0.747954i
$805$	4.78689	−	13.1519i	0.168716	−	0.463542i
$806$	12.1822	+	2.04221i	0.429100	+	0.0719340i
$807$	−32.6375	−	9.24758i	−1.14889	−	0.325530i
$808$	−24.2695	−	3.64858i	−0.853799	−	0.128357i
$809$		−	2.63212i		−	0.0925405i	−0.998929	−	0.0462703i	$-0.985266\pi$
$809$		−	2.63212i		−	0.0925405i	0.998929	−	0.0462703i	$-0.0147335\pi$
$810$	−13.9754	−	18.4087i	−0.491046	−	0.646815i
$811$	−41.8492			−1.46952			−0.734762	−	0.678324i	$-0.762706\pi$
$811$	−41.8492			−1.46952			−0.734762	+	0.678324i	$0.762706\pi$
$812$	61.0570	−	11.8317i	2.14268	−	0.415212i
$813$	−2.23770	+	7.89752i	−0.0784795	+	0.276978i
$814$	−19.2259	−	3.22301i	−0.673867	−	0.112967i
$815$	26.7835	+	9.74840i	0.938186	+	0.341472i
$816$	16.7249	+	16.0868i	0.585490	+	0.563150i
$817$	3.64405	−	20.6664i	0.127489	−	0.723026i
$818$	−23.8745	−	27.9698i	−0.834753	−	0.977941i
$819$	−1.79318	+	62.6569i	−0.0626587	+	2.18941i
$820$	8.64848	+	1.37490i	0.302018	+	0.0480136i
$821$	−37.0662	+	13.4910i	−1.29362	+	0.470839i	−0.894913	−	0.446240i	$-0.852763\pi$
$821$	−37.0662	+	13.4910i	−1.29362	+	0.470839i	−0.398706	+	0.917079i	$0.630541\pi$
$822$	−2.99299	+	6.32139i	−0.104393	+	0.220484i
$823$	−24.6788	−	29.4111i	−0.860249	−	1.02521i	−0.999390	−	0.0349324i	$-0.988878\pi$
$823$	−24.6788	−	29.4111i	−0.860249	−	1.02521i	0.139140	−	0.990273i	$-0.455566\pi$
$824$	30.4199	+	10.2076i	1.05973	+	0.355600i
$825$	4.75363	−	6.58631i	0.165500	−	0.229306i
$826$	0.522460	+	61.9149i	0.0181787	+	2.15429i
$827$	−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	$0.492112\pi$
$828$	8.69171	+	10.6088i	0.302058	+	0.368680i
$829$	−10.9778	−	6.33802i	−0.381274	−	0.220129i	0.297098	−	0.954847i	$-0.403981\pi$
$829$	−10.9778	−	6.33802i	−0.381274	−	0.220129i	−0.678372	+	0.734718i	$0.737314\pi$
$830$	−4.73423	+	8.36210i	−0.164328	+	0.290253i
$831$	−11.4947	−	5.56160i	−0.398745	−	0.192930i
$832$	33.7454	+	36.3133i	1.16991	+	1.25894i
$833$	14.4143	−	2.54163i	0.499426	−	0.0880623i
$834$	−3.43212	−	7.47439i	−0.118845	−	0.258817i
$835$	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	0.521140	−	0.853471i	$-0.325507\pi$
$839$	−6.62933	−	5.56267i	−0.228870	−	0.192045i	−0.750010	+	0.661426i	$0.769951\pi$
$840$	−20.9761	+	21.4431i	−0.723744	+	0.739857i
$841$	9.73268	+	55.1968i	0.335610	+	1.90334i
$842$	5.22939	+	4.31331i	0.180217	+	0.148646i
$843$	−0.495850	−	6.78405i	−0.0170780	−	0.233655i
$844$	−15.9525	+	13.8511i	−0.549107	+	0.476776i
$845$	−23.0591	+	39.9395i	−0.793256	+	1.37396i
$846$	2.50611	−	12.7082i	0.0861619	−	0.436917i
$847$	−9.96596	+	5.75385i	−0.342434	+	0.197705i
$848$	−0.390493	−	0.626527i	−0.0134096	−	0.0215150i
$849$	27.2005	−	12.2132i	0.933517	−	0.419155i
$850$	7.55472	−	2.82211i	0.259125	−	0.0967976i
$851$	−7.35275	−	8.76267i	−0.252049	−	0.300380i
$852$	12.3019	+	3.26241i	0.421455	+	0.111768i
$853$	8.97988	+	24.6720i	0.307465	+	0.844754i	0.993149	+	0.116854i	$0.0372811\pi$
$853$	8.97988	+	24.6720i	0.307465	+	0.844754i	−0.685684	+	0.727900i	$0.740497\pi$
$854$	66.3405	−	12.2757i	2.27012	−	0.420065i
$855$	31.0133	−	4.55791i	1.06063	−	0.155877i
$856$	−3.18739	+	0.0807042i	−0.108943	+	0.00275841i
$857$	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	$0.353402\pi$
$858$	−11.0576	+	40.3197i	−0.377500	+	1.37649i
$859$	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	$0.553522\pi$
$860$	6.42808	−	11.5808i	0.219196	−	0.394902i
$861$	3.44983	+	13.6533i	0.117570	+	0.465303i
$862$	22.9659	−	13.5190i	0.782222	−	0.460460i
$863$	−4.89855			−0.166748			−0.0833742	−	0.996518i	$-0.526570\pi$
$863$	−4.89855			−0.166748			−0.0833742	+	0.996518i	$0.526570\pi$
$864$	−7.58708	−	28.3978i	−0.258118	−	0.966113i
$865$	−2.89881			−0.0985624
$866$	−39.6803	+	23.3580i	−1.34839	+	0.793738i
$867$	7.18091	−	6.97834i	0.243876	−	0.236997i
$868$	−4.61330	+	8.31129i	−0.156585	+	0.282104i
$869$	2.86175	+	1.04159i	0.0970781	+	0.0353335i
$870$	−28.8351	−	29.1754i	−0.977600	−	0.989140i
$871$	−37.4948	−	6.61135i	−1.27046	−	0.224017i
$872$	29.0380	−	0.735238i	0.983350	−	0.0248983i
$873$	−45.5111	−	9.37462i	−1.54032	−	0.317283i
$874$	−18.2900	+	3.38439i	−0.618668	+	0.114479i
$875$	14.0365	+	38.5649i	0.474520	+	1.30373i
$876$	0.247112	+	0.912840i	0.00834913	+	0.0308420i
$877$	−2.27420	−	2.71029i	−0.0767944	−	0.0915200i	0.726279	−	0.687400i	$-0.241248\pi$
$877$	−2.27420	−	2.71029i	−0.0767944	−	0.0915200i	−0.803074	+	0.595880i	$0.796803\pi$
$878$	3.02494	−	1.12999i	0.102087	−	0.0381352i
$879$	−2.87909	+	28.2478i	−0.0971093	+	0.952774i
$880$	−16.9795	+	10.5827i	−0.572379	+	0.356744i
$881$	−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	$0.362444\pi$
$882$	−17.2902	−	6.69109i	−0.582190	−	0.225301i
$883$	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	$0.0250507\pi$
$884$	−31.3438	+	27.2150i	−1.05421	+	0.915339i
$885$	33.7846	−	22.9430i	1.13566	−	0.771222i
$886$	−7.49277	−	6.18019i	−0.251724	−	0.207628i
$887$	−1.48892	−	8.44410i	−0.0499931	−	0.283525i	0.949554	−	0.313602i	$-0.101536\pi$
$887$	−1.48892	−	8.44410i	−0.0499931	−	0.283525i	−0.999548	+	0.0300771i	$0.990425\pi$
$888$	6.60559	+	23.6096i	0.221669	+	0.792287i
$889$	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
$894$	15.1401	−	21.3545i	0.506360	−	0.714202i
$895$	−3.55618	+	0.627050i	−0.118870	+	0.0209600i
$896$	−35.0155	+	15.1412i	−1.16979	+	0.505831i
$897$	−20.2951	+	13.7824i	−0.677634	+	0.460180i
$898$	6.88237	−	12.1564i	0.229668	−	0.405663i
$899$	−11.2576	−	6.49956i	−0.375461	−	0.216772i
$900$	−10.0385	−	1.89177i	−0.334615	−	0.0630590i
$901$	0.535368	−	0.309095i	0.0178357	−	0.0102974i
$902$	0.0792568	+	9.39245i	0.00263896	+	0.312734i
$903$	21.1900	+	2.15975i	0.705160	+	0.0718719i
$904$	42.4151	+	14.2327i	1.41071	+	0.473373i
$905$	−0.894975	−	1.06659i	−0.0297500	−	0.0354546i
$906$	4.73763	+	6.85124i	0.157397	+	0.227617i
$907$	−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	$0.395178\pi$
$908$	7.81418	+	1.24227i	0.259323	+	0.0412261i
$909$	−17.2960	+	19.4541i	−0.573672	+	0.645251i
$910$	−34.8361	−	40.8116i	−1.15480	−	1.35289i
$911$	−0.397752	+	2.25577i	−0.0131781	+	0.0747368i	−0.990688	−	0.136155i	$-0.956526\pi$
$911$	−0.397752	+	2.25577i	−0.0131781	+	0.0747368i	0.977509	+	0.210892i	$0.0676367\pi$
$912$	38.7004	+	9.56718i	1.28150	+	0.316801i
$913$	−9.68523	−	3.52514i	−0.320534	−	0.116665i
$914$	−38.8683	−	6.51585i	−1.28565	−	0.215525i
$915$	−31.0121	−	31.9123i	−1.02523	−	1.05499i
$916$	−17.3704	+	3.36605i	−0.573933	+	0.111218i
$917$	59.6725			1.97056
$918$	23.9802	−	5.54708i	0.791466	−	0.183081i
$919$		−	17.5458i		−	0.578782i	−0.957211	−	0.289391i	$-0.906547\pi$
$919$		−	17.5458i		−	0.578782i	0.957211	−	0.289391i	$-0.0934528\pi$
$920$	−11.6096	−	1.74534i	−0.382756	−	0.0575420i
$921$	−8.53292	−	33.7705i	−0.281169	−	1.11278i
$922$	−42.4488	−	7.11607i	−1.39798	−	0.234355i
$923$	−7.78645	+	21.3931i	−0.256294	+	0.704162i
$924$	−26.4030	−	18.3866i	−0.868594	−	0.604874i
$925$	8.39062	+	1.47949i	0.275882	+	0.0486454i
$926$	−23.0973	+	19.7154i	−0.759024	+	0.647890i
$927$	26.6861	−	21.1214i	0.876487	−	0.693717i
$928$	−19.8944	−	48.2261i	−0.653067	−	1.58310i
$929$	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	$0.817704\pi$
$930$	6.24895	−	0.509785i	0.204911	−	0.0167165i
$931$	19.2618	−	16.1626i	0.631279	−	0.529706i
$932$	−0.704460	−	41.7386i	−0.0230754	−	1.36719i
$933$	−12.8358	+	5.76334i	−0.420225	+	0.188683i
$934$	50.6127	−	0.427088i	1.65610	−	0.0139747i
$935$	−8.37678	−	14.5090i	−0.273950	−	0.474495i
$936$	51.8103	−	8.95954i	1.69347	−	0.292852i
$937$	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	$0.0936507\pi$
$938$	14.4352	−	25.4970i	0.471328	−	0.832508i
$939$	1.85863	−	0.135848i	0.0606540	−	0.00443324i
$940$	5.70525	+	9.50756i	0.186085	+	0.310102i
$941$	−4.43143	−	25.1319i	−0.144460	−	0.819276i	−0.967799	−	0.251725i	$-0.919002\pi$
$941$	−4.43143	−	25.1319i	−0.144460	−	0.819276i	0.823338	−	0.567551i	$-0.192109\pi$
$942$	−3.15142	+	33.7396i	−0.102679	+	1.09930i
$943$	−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	$0.891420\pi$
$948$	−0.343611	−	3.81452i	−0.0111600	−	0.123890i
$949$	−1.66595	+	0.293751i	−0.0540789	+	0.00953557i
$950$	8.81550	−	10.6878i	0.286013	−	0.346757i
$951$	13.5115	−	27.9255i	0.438141	−	0.905546i
$952$	−11.6820	−	29.7320i	−0.378616	−	0.963619i
$953$	−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	$0.711745\pi$
$954$	−0.782878	−	0.0157952i	−0.0253466	−	0.000511387i
$955$	−0.124299	−	0.215293i	−0.00402223	−	0.00696671i
$956$	17.8714	+	6.16515i	0.578002	+	0.199395i
$957$	25.7493	−	35.6764i	0.832356	−	1.15326i
$958$	−12.9688	−	34.7172i	−0.419004	−	1.12166i
$959$	7.37547	−	6.18875i	0.238166	−	0.199845i
$960$	21.1218	+	13.6742i	0.681704	+	0.441332i
$961$	−27.2635	+	9.92309i	−0.879466	+	0.320100i
$962$	−43.1223	+	7.97937i	−1.39032	+	0.257265i
$963$	−1.77400	+	2.87917i	−0.0571664	+	0.0927800i
$964$	−37.4595	+	14.3546i	−1.20649	+	0.462329i
$965$	5.36022	−	30.3993i	0.172552	−	0.978588i
$966$	−4.77925	−	18.2644i	−0.153770	−	0.587647i
$967$	1.06732	−	2.93244i	0.0343227	−	0.0943009i	−0.921348	−	0.388740i	$-0.872911\pi$
$967$	1.06732	−	2.93244i	0.0343227	−	0.0943009i	0.955670	+	0.294439i	$0.0951327\pi$
$968$	6.38992	+	7.23510i	0.205380	+	0.232545i
$969$	−9.10027	+	32.1176i	−0.292343	+	1.03177i
$970$	34.2783	−	20.1781i	1.10061	−	0.647881i
$971$		−	0.0539562i		−	0.00173154i	−1.00000		0.000865769i	$-0.999724\pi$
$971$		−	0.0539562i		−	0.00173154i	1.00000		0.000865769i	$-0.000275583\pi$
$972$	−29.6289	−	9.70212i	−0.950346	−	0.311196i
$973$			11.3220i			0.362966i
$974$	−16.5723	−	28.1528i	−0.531011	−	0.902073i
$975$	4.98132	−	17.5806i	0.159530	−	0.563030i
$976$	−21.1393	−	52.4958i	−0.676651	−	1.68035i
$977$	−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	$0.985657\pi$
$978$	37.1951	−	9.73284i	1.18937	−	0.311222i
$979$	3.08989	−	17.5236i	0.0987533	−	0.560058i
$980$	14.8196	−	5.67888i	0.473393	−	0.181405i
$981$	16.1616	−	26.2300i	0.516001	−	0.837460i
$982$	8.46813	+	45.7636i	0.270229	+	1.46038i
$983$	48.9235	−	17.8067i	1.56042	−	0.567946i	0.589586	−	0.807705i	$-0.299291\pi$
$983$	48.9235	−	17.8067i	1.56042	−	0.567946i	0.970832	+	0.239759i	$0.0770685\pi$
$984$	10.6502	−	5.10976i	0.339516	−	0.162893i
$985$	−7.91968	+	6.64540i	−0.252342	+	0.211740i
$986$	40.9221	−	15.2867i	1.30322	−	0.486827i
$987$	−10.4352	+	14.4583i	−0.332156	+	0.460213i
$988$	−23.2554	+	67.4121i	−0.739852	+	2.14466i
$989$	4.16813	+	7.21941i	0.132539	+	0.229564i
$990$	−0.428065	+	21.2168i	−0.0136048	+	0.674313i
$991$	−10.0455	−	5.79977i	−0.319106	−	0.184236i	0.331888	−	0.943319i	$-0.392314\pi$
$991$	−10.0455	−	5.79977i	−0.319106	−	0.184236i	−0.650994	+	0.759083i	$0.725648\pi$
$992$	7.60112	+	2.40868i	0.241336	+	0.0764758i
$993$	−10.5061	+	21.7138i	−0.333400	+	0.689067i
$994$	−13.5156	−	11.1479i	−0.428688	−	0.353591i
$995$	25.3215	−	4.46487i	0.802747	−	0.141546i
$996$	1.16291	+	12.9098i	0.0368482	+	0.409063i
$997$	−25.3340	+	30.1918i	−0.802334	+	0.956185i	−0.999709	−	0.0241434i	$-0.992314\pi$
$997$	−25.3340	+	30.1918i	−0.802334	+	0.956185i	0.197374	+	0.980328i	$0.436759\pi$
$998$	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.11.7	✓	192
3.2	odd	2		648.2.v.b.35.26		192
4.3	odd	2		864.2.bh.b.335.30		192
8.3	odd	2	inner	216.2.v.b.11.12	yes	192
8.5	even	2		864.2.bh.b.335.29		192
24.11	even	2		648.2.v.b.35.21		192
27.5	odd	18	inner	216.2.v.b.59.12	yes	192
27.22	even	9		648.2.v.b.611.21		192
108.59	even	18		864.2.bh.b.815.29		192
216.5	odd	18		864.2.bh.b.815.30		192
216.59	even	18	inner	216.2.v.b.59.7	yes	192
216.211	odd	18		648.2.v.b.611.26		192

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

\(f(q)\)	\(=\)	\(q+(-1.21873 + 0.717416i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(0.970628 - 1.74868i) q^{4} +(1.70638 + 0.621073i) q^{5} +(2.36970 - 0.620081i) q^{6} +(-3.32069 - 0.585528i) q^{7} +(0.0715925 + 2.82752i) q^{8} +(2.55410 + 1.57371i) q^{9} +O(q^{10})\)	\(q+(-1.21873 + 0.717416i) q^{2} +(-1.66645 - 0.472175i) q^{3} +(0.970628 - 1.74868i) q^{4} +(1.70638 + 0.621073i) q^{5} +(2.36970 - 0.620081i) q^{6} +(-3.32069 - 0.585528i) q^{7} +(0.0715925 + 2.82752i) q^{8} +(2.55410 + 1.57371i) q^{9} +(-2.52520 + 0.467264i) q^{10} +(-0.942090 - 2.58837i) q^{11} +(-2.44318 + 2.45578i) q^{12} +(-3.98305 - 4.74681i) q^{13} +(4.46711 - 1.66872i) q^{14} +(-2.55034 - 1.84070i) q^{15} +(-2.11576 - 3.39464i) q^{16} +(2.90072 - 1.67473i) q^{17} +(-4.24178 - 0.0855811i) q^{18} +(2.87704 - 4.98318i) q^{19} +(2.74232 - 2.38109i) q^{20} +(5.25729 + 2.54370i) q^{21} +(3.00510 + 2.47867i) q^{22} +(0.396921 + 2.25105i) q^{23} +(1.21578 - 4.74572i) 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} +(4.42874 + 0.413662i) q^{30} +(1.38814 - 0.244766i) q^{31} +(5.01392 + 2.61928i) q^{32} +(0.347781 + 4.75822i) q^{33} +(-2.33373 + 4.12208i) q^{34} +(-5.30272 - 3.06153i) q^{35} +(5.23100 - 2.93882i) q^{36} +(-4.33391 + 2.50218i) q^{37} +(0.0686647 + 8.13721i) q^{38} +(4.39622 + 9.79102i) q^{39} +(-1.63393 + 4.86930i) q^{40} +(1.54991 + 1.84711i) q^{41} +(-8.23214 + 0.671572i) q^{42} +(3.42707 - 1.24735i) q^{43} +(-5.44065 - 0.864933i) q^{44} +(3.38089 + 4.27164i) q^{45} +(-2.09868 - 2.45867i) q^{46} +(-0.530155 + 3.00666i) q^{47} +(1.92295 + 6.65600i) q^{48} +(4.10632 + 1.49458i) q^{49} +(2.37460 + 0.398076i) q^{50} +(-5.62467 + 1.42121i) q^{51} +(-12.1667 + 2.35769i) q^{52} +0.184564 q^{53} +(7.02829 + 2.14548i) q^{54} -5.00186i q^{55} +(1.41786 - 9.43125i) q^{56} +(-7.14737 + 6.94575i) q^{57} +(12.8626 + 2.15628i) q^{58} +(-4.44089 + 12.2012i) q^{59} +(-5.69423 + 2.67310i) q^{60} +(13.9331 + 2.45678i) q^{61} +(-1.51617 + 1.29418i) q^{62} +(-7.55994 - 6.72131i) q^{63} +(-7.98975 + 0.404858i) q^{64} +(-3.84849 - 10.5736i) q^{65} +(-3.83748 - 5.54950i) q^{66} +(4.70680 - 3.94947i) q^{67} +(-0.113048 - 6.69798i) q^{68} +(0.401441 - 3.93867i) q^{69} +(8.65900 - 0.0730677i) q^{70} +(-1.83700 - 3.18178i) q^{71} +(-4.26684 + 7.33444i) q^{72} +(0.136500 - 0.236424i) q^{73} +(3.48678 - 6.15871i) q^{74} +(1.65667 + 2.43951i) q^{75} +(-5.92145 - 9.86784i) q^{76} +(1.61283 + 9.14681i) q^{77} +(-12.3821 - 8.77873i) 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} +(9.55100 - 6.72434i) q^{84} +(5.98987 - 1.05618i) q^{85} +(-3.28182 + 3.97883i) q^{86} +(8.97377 + 13.2142i) q^{87} +(7.25123 - 2.84909i) q^{88} +(5.59452 + 3.23000i) q^{89} +(-7.18495 - 2.78049i) q^{90} +(10.4471 + 18.0949i) q^{91} +(4.32163 + 1.49084i) q^{92} +(-2.42883 - 0.247553i) q^{93} +(-1.51091 - 4.04466i) q^{94} +(8.00425 - 6.71636i) q^{95} +(-7.11868 - 6.73234i) q^{96} +(-14.5548 + 5.29750i) q^{97} +(-6.07674 + 1.12444i) 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

Properties

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