LMFDB - Embedded newform 135.2.q.a.122.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.16
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05499 + 1.43892i) q^{2} +(0.551185 - 1.64201i) q^{3} +(1.46845 + 4.03452i) q^{4} +(-1.82626 + 1.29027i) q^{5} +(3.49539 - 2.58120i) q^{6} +(-1.14217 - 2.44940i) q^{7} +(-1.48912 + 5.55747i) q^{8} +(-2.39239 - 1.81010i) q^{9} +O(q^{10})$	\(q+(2.05499 + 1.43892i) q^{2} +(0.551185 - 1.64201i) q^{3} +(1.46845 + 4.03452i) q^{4} +(-1.82626 + 1.29027i) q^{5} +(3.49539 - 2.58120i) q^{6} +(-1.14217 - 2.44940i) q^{7} +(-1.48912 + 5.55747i) q^{8} +(-2.39239 - 1.81010i) q^{9} +(-5.60952 + 0.0236494i) q^{10} +(-2.09979 - 2.50243i) q^{11} +(7.43411 - 0.187436i) q^{12} +(1.80484 + 2.57758i) q^{13} +(1.17733 - 6.67697i) q^{14} +(1.11203 + 3.70991i) q^{15} +(-4.47891 + 3.75825i) q^{16} +(1.57770 + 5.88806i) q^{17} +(-2.31175 - 7.16218i) q^{18} +(2.91796 - 1.68469i) q^{19} +(-7.88737 - 5.47338i) q^{20} +(-4.65148 + 0.525389i) q^{21} +(-0.714248 - 8.16389i) q^{22} +(-4.50352 - 2.10003i) q^{23} +(8.30464 + 5.50834i) q^{24} +(1.67042 - 4.71272i) q^{25} +7.89390i q^{26} +(-4.29085 + 2.93063i) q^{27} +(8.20493 - 8.20493i) q^{28} +(0.541940 + 3.07349i) q^{29} +(-3.05305 + 9.22392i) q^{30} +(0.346096 - 0.125969i) q^{31} +(-3.14866 + 0.275472i) q^{32} +(-5.26639 + 2.06857i) q^{33} +(-5.23028 + 14.3701i) q^{34} +(5.24628 + 2.99952i) q^{35} +(3.78979 - 12.3102i) q^{36} +(-4.28145 + 1.14721i) q^{37} +(8.42050 + 0.736698i) q^{38} +(5.22721 - 1.54284i) q^{39} +(-4.45110 - 12.0707i) q^{40} +(7.54663 + 1.33068i) q^{41} +(-10.3147 - 5.61343i) q^{42} +(0.386956 - 4.42293i) q^{43} +(7.01269 - 12.1463i) q^{44} +(6.70463 + 0.218885i) q^{45} +(-6.23291 - 10.7957i) q^{46} +(-6.23750 + 2.90859i) q^{47} +(3.70238 + 9.42590i) q^{48} +(-0.195477 + 0.232960i) q^{49} +(10.2139 - 7.28096i) q^{50} +(10.5379 + 0.654808i) q^{51} +(-7.74898 + 11.0667i) q^{52} +(3.48010 + 3.48010i) q^{53} +(-13.0346 - 0.151776i) q^{54} +(7.06356 + 1.86079i) q^{55} +(15.3133 - 2.70014i) q^{56} +(-1.15794 - 5.71990i) q^{57} +(-3.30882 + 7.09579i) q^{58} +(5.87095 + 4.92631i) q^{59} +(-13.3347 + 9.93429i) q^{60} +(-6.73344 - 2.45077i) q^{61} +(0.892481 + 0.239140i) q^{62} +(-1.70113 + 7.92737i) q^{63} +(3.26012 + 1.88223i) q^{64} +(-6.62186 - 2.37859i) q^{65} +(-13.7989 - 3.32701i) q^{66} +(-0.315748 + 0.221089i) q^{67} +(-21.4388 + 15.0116i) q^{68} +(-5.93054 + 6.23732i) q^{69} +(6.46497 + 13.7129i) q^{70} +(-8.46099 - 4.88495i) q^{71} +(13.6221 - 10.6002i) q^{72} +(-0.0248963 - 0.00667095i) q^{73} +(-10.4491 - 3.80315i) q^{74} +(-6.81761 - 5.34043i) q^{75} +(11.0818 + 9.29871i) q^{76} +(-3.73113 + 8.00143i) q^{77} +(12.9619 + 4.35099i) q^{78} +(10.9549 - 1.93165i) q^{79} +(3.33049 - 12.6425i) q^{80} +(2.44707 + 8.66094i) q^{81} +(13.5935 + 13.5935i) q^{82} +(-0.627725 + 0.896484i) q^{83} +(-8.95014 - 17.9950i) q^{84} +(-10.4785 - 8.71746i) q^{85} +(7.15941 - 8.53226i) q^{86} +(5.34541 + 0.804192i) q^{87} +(17.0340 - 7.94310i) q^{88} +(-3.93198 - 6.81039i) q^{89} +(13.4630 + 10.0972i) q^{90} +(4.25207 - 7.36481i) q^{91} +(1.85943 - 21.2533i) q^{92} +(-0.0160789 - 0.637725i) q^{93} +(-17.0032 - 2.99812i) q^{94} +(-3.15525 + 6.84162i) q^{95} +(-1.28317 + 5.32197i) q^{96} +(-5.10752 - 0.446850i) q^{97} +(-0.736913 + 0.197455i) q^{98} +(0.493864 + 9.78763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.05499	+	1.43892i	1.45309	+	1.01747i	0.991462	+	0.130396i	$0.0416250\pi$
$2$	2.05499	+	1.43892i	1.45309	+	1.01747i	0.461633	+	0.887071i	$0.347264\pi$
$3$	0.551185	−	1.64201i	0.318227	−	0.948015i
$3$	0.551185	−	1.64201i	0.318227	−	0.948015i
$4$	1.46845	+	4.03452i	0.734223	+	2.01726i
$5$	−1.82626	+	1.29027i	−0.816727	+	0.577025i
$5$	−1.82626	+	1.29027i	−0.816727	+	0.577025i
$6$	3.49539	−	2.58120i	1.42699	−	1.05377i
$7$	−1.14217	−	2.44940i	−0.431701	−	0.925785i	−0.995032	−	0.0995542i	$-0.968258\pi$
$7$	−1.14217	−	2.44940i	−0.431701	−	0.925785i	0.563331	−	0.826231i	$-0.309519\pi$
$8$	−1.48912	+	5.55747i	−0.526483	+	1.96486i
$9$	−2.39239	−	1.81010i	−0.797464	−	0.603367i
$10$	−5.60952	+	0.0236494i	−1.77389	+	0.00747861i
$11$	−2.09979	−	2.50243i	−0.633111	−	0.754512i	0.350155	−	0.936692i	$-0.386129\pi$
$11$	−2.09979	−	2.50243i	−0.633111	−	0.754512i	−0.983265	+	0.182180i	$0.941685\pi$
$12$	7.43411	−	0.187436i	2.14604	−	0.0541081i
$13$	1.80484	+	2.57758i	0.500572	+	0.714891i	0.987336	−	0.158642i	$-0.0507117\pi$
$13$	1.80484	+	2.57758i	0.500572	+	0.714891i	−0.486764	+	0.873534i	$0.661823\pi$
$14$	1.17733	−	6.67697i	0.314655	−	1.78450i
$15$	1.11203	+	3.70991i	0.287124	+	0.957893i
$16$	−4.47891	+	3.75825i	−1.11973	+	0.939563i
$17$	1.57770	+	5.88806i	0.382649	+	1.42807i	0.841840	+	0.539728i	$0.181473\pi$
$17$	1.57770	+	5.88806i	0.382649	+	1.42807i	−0.459191	+	0.888338i	$0.651861\pi$
$18$	−2.31175	−	7.16218i	−0.544884	−	1.68814i
$19$	2.91796	−	1.68469i	0.669427	−	0.386494i	−0.126433	−	0.991975i	$-0.540353\pi$
$19$	2.91796	−	1.68469i	0.669427	−	0.386494i	0.795859	+	0.605481i	$0.207019\pi$
$20$	−7.88737	−	5.47338i	−1.76367	−	1.22389i
$21$	−4.65148	+	0.525389i	−1.01504	+	0.114649i
$22$	−0.714248	−	8.16389i	−0.152278	−	1.74055i
$23$	−4.50352	−	2.10003i	−0.939049	−	0.437886i	−0.108041	−	0.994146i	$-0.534458\pi$
$23$	−4.50352	−	2.10003i	−0.939049	−	0.437886i	−0.831008	+	0.556261i	$0.812236\pi$
$24$	8.30464	+	5.50834i	1.69518	+	1.12438i
$25$	1.67042	−	4.71272i	0.334085	−	0.942543i
$26$			7.89390i			1.54812i
$27$	−4.29085	+	2.93063i	−0.825775	+	0.564000i
$28$	8.20493	−	8.20493i	1.55059	−	1.55059i
$29$	0.541940	+	3.07349i	0.100636	+	0.570733i	0.992874	+	0.119169i	$0.0380229\pi$
$29$	0.541940	+	3.07349i	0.100636	+	0.570733i	−0.892238	+	0.451565i	$0.850866\pi$
$30$	−3.05305	+	9.22392i	−0.557408	+	1.68405i
$31$	0.346096	−	0.125969i	0.0621607	−	0.0226246i	−0.310753	−	0.950491i	$-0.600581\pi$
$31$	0.346096	−	0.125969i	0.0621607	−	0.0226246i	0.372913	+	0.927866i	$0.378359\pi$
$32$	−3.14866	+	0.275472i	−0.556610	+	0.0486971i
$33$	−5.26639	+	2.06857i	−0.916761	+	0.360092i
$34$	−5.23028	+	14.3701i	−0.896985	+	2.46445i
$35$	5.24628	+	2.99952i	0.886783	+	0.507011i
$36$	3.78979	−	12.3102i	0.631632	−	2.05170i
$37$	−4.28145	+	1.14721i	−0.703866	+	0.188600i	−0.592962	−	0.805231i	$-0.702041\pi$
$37$	−4.28145	+	1.14721i	−0.703866	+	0.188600i	−0.110904	+	0.993831i	$0.535375\pi$
$38$	8.42050	+	0.736698i	1.36599	+	0.119508i
$39$	5.22721	−	1.54284i	0.837023	−	0.247052i
$40$	−4.45110	−	12.0707i	−0.703781	−	1.90855i
$41$	7.54663	+	1.33068i	1.17859	+	0.207817i	0.728422	−	0.685129i	$-0.240254\pi$
$41$	7.54663	+	1.33068i	1.17859	+	0.207817i	0.450164	+	0.892946i	$0.351365\pi$
$42$	−10.3147	−	5.61343i	−1.59160	−	0.866171i
$43$	0.386956	−	4.42293i	0.0590102	−	0.674490i	−0.907869	−	0.419255i	$-0.862291\pi$
$43$	0.386956	−	4.42293i	0.0590102	−	0.674490i	0.966879	−	0.255236i	$-0.0821530\pi$
$44$	7.01269	−	12.1463i	1.05720	−	1.83113i
$45$	6.70463	+	0.218885i	0.999468	+	0.0326295i
$46$	−6.23291	−	10.7957i	−0.918992	−	1.59174i
$47$	−6.23750	+	2.90859i	−0.909832	+	0.424262i	−0.820439	−	0.571735i	$-0.806271\pi$
$47$	−6.23750	+	2.90859i	−0.909832	+	0.424262i	−0.0893938	+	0.995996i	$0.528493\pi$
$48$	3.70238	+	9.42590i	0.534392	+	1.36051i
$49$	−0.195477	+	0.232960i	−0.0279253	+	0.0332800i
$50$	10.2139	−	7.28096i	1.44446	−	1.02968i
$51$	10.5379	+	0.654808i	1.47560	+	0.0916915i
$52$	−7.74898	+	11.0667i	−1.07459	+	1.53467i
$53$	3.48010	+	3.48010i	0.478029	+	0.478029i	0.904501	−	0.426472i	$-0.140244\pi$
$53$	3.48010	+	3.48010i	0.478029	+	0.478029i	−0.426472	+	0.904501i	$0.640244\pi$
$54$	−13.0346	−	0.151776i	−1.77378	−	0.0206542i
$55$	7.06356	+	1.86079i	0.952450	+	0.250909i
$56$	15.3133	−	2.70014i	2.04632	−	0.360822i
$57$	−1.15794	−	5.71990i	−0.153372	−	0.757619i
$58$	−3.30882	+	7.09579i	−0.434470	+	0.931723i
$59$	5.87095	+	4.92631i	0.764332	+	0.641351i	0.939251	−	0.343232i	$-0.111522\pi$
$59$	5.87095	+	4.92631i	0.764332	+	0.641351i	−0.174918	+	0.984583i	$0.555966\pi$
$60$	−13.3347	+	9.93429i	−1.72151	+	1.28251i
$61$	−6.73344	−	2.45077i	−0.862128	−	0.313789i	−0.127153	−	0.991883i	$-0.540584\pi$
$61$	−6.73344	−	2.45077i	−0.862128	−	0.313789i	−0.734975	+	0.678094i	$0.762806\pi$
$62$	0.892481	+	0.239140i	0.113345	+	0.0303708i
$63$	−1.70113	+	7.92737i	−0.214323	+	0.998754i
$64$	3.26012	+	1.88223i	0.407515	+	0.235279i
$65$	−6.62186	−	2.37859i	−0.821341	−	0.295028i
$66$	−13.7989	−	3.32701i	−1.69852	−	0.409526i
$67$	−0.315748	+	0.221089i	−0.0385747	+	0.0270103i	−0.592705	−	0.805420i	$-0.701940\pi$
$67$	−0.315748	+	0.221089i	−0.0385747	+	0.0270103i	0.554130	+	0.832430i	$0.313051\pi$
$68$	−21.4388	+	15.0116i	−2.59983	+	1.82042i
$69$	−5.93054	+	6.23732i	−0.713953	+	0.750885i
$70$	6.46497	+	13.7129i	0.772711	+	1.63901i
$71$	−8.46099	−	4.88495i	−1.00413	−	0.579737i	−0.0946655	−	0.995509i	$-0.530178\pi$
$71$	−8.46099	−	4.88495i	−1.00413	−	0.579737i	−0.909469	+	0.415772i	$0.863511\pi$
$72$	13.6221	−	10.6002i	1.60538	−	1.24924i
$73$	−0.0248963	−	0.00667095i	−0.00291389	−	0.000780776i	0.257362	−	0.966315i	$-0.417147\pi$
$73$	−0.0248963	−	0.00667095i	−0.00291389	−	0.000780776i	−0.260276	+	0.965534i	$0.583813\pi$
$74$	−10.4491	−	3.80315i	−1.21468	−	0.442107i
$75$	−6.81761	−	5.34043i	−0.787230	−	0.616659i
$76$	11.0818	+	9.29871i	1.27117	+	1.06664i
$77$	−3.73113	+	8.00143i	−0.425202	+	0.911848i
$78$	12.9619	+	4.35099i	1.46764	+	0.492653i
$79$	10.9549	−	1.93165i	1.23253	−	0.217327i	0.480816	−	0.876822i	$-0.340341\pi$
$79$	10.9549	−	1.93165i	1.23253	−	0.217327i	0.751710	+	0.659494i	$0.229230\pi$
$80$	3.33049	−	12.6425i	0.372360	−	1.41348i
$81$	2.44707	+	8.66094i	0.271897	+	0.962326i
$82$	13.5935	+	13.5935i	1.50115	+	1.50115i
$83$	−0.627725	+	0.896484i	−0.0689018	+	0.0984019i	−0.852124	−	0.523340i	$-0.824686\pi$
$83$	−0.627725	+	0.896484i	−0.0689018	+	0.0984019i	0.783222	+	0.621742i	$0.213575\pi$
$84$	−8.95014	−	17.9950i	−0.976540	−	1.96342i
$85$	−10.4785	−	8.71746i	−1.13655	−	0.945541i
$86$	7.15941	−	8.53226i	0.772019	−	0.920057i
$87$	5.34541	+	0.804192i	0.573089	+	0.0862184i
$88$	17.0340	−	7.94310i	1.81583	−	0.846737i
$89$	−3.93198	−	6.81039i	−0.416789	−	0.721900i	0.578825	−	0.815452i	$-0.303511\pi$
$89$	−3.93198	−	6.81039i	−0.416789	−	0.721900i	−0.995614	+	0.0935515i	$0.970178\pi$
$90$	13.4630	+	10.0972i	1.41912	+	1.06434i
$91$	4.25207	−	7.36481i	0.445738	−	0.772042i
$92$	1.85943	−	21.2533i	0.193858	−	2.21581i
$93$	−0.0160789	−	0.637725i	−0.00166731	−	0.0661290i
$94$	−17.0032	−	2.99812i	−1.75375	−	0.309233i
$95$	−3.15525	+	6.84162i	−0.323722	+	0.701936i
$96$	−1.28317	+	5.32197i	−0.130963	+	0.543171i
$97$	−5.10752	−	0.446850i	−0.518590	−	0.0453707i	−0.175143	−	0.984543i	$-0.556039\pi$
$97$	−5.10752	−	0.446850i	−0.518590	−	0.0453707i	−0.343447	+	0.939172i	$0.611594\pi$
$98$	−0.736913	+	0.197455i	−0.0744394	+	0.0199460i
$99$	0.493864	+	9.78763i	0.0496352	+	0.983694i
$100$	21.4665	−	0.181006i	2.14665	−	0.0181006i
$101$	0.406707	−	1.11742i	0.0404688	−	0.111187i	−0.917812	−	0.397015i	$-0.870046\pi$
$101$	0.406707	−	1.11742i	0.0404688	−	0.111187i	0.958281	+	0.285827i	$0.0922684\pi$
$102$	20.7129	+	16.5087i	2.05089	+	1.63461i
$103$	0.187413	−	0.0163965i	0.0184664	−	0.00161560i	−0.0779188	−	0.996960i	$-0.524827\pi$
$103$	0.187413	−	0.0163965i	0.0184664	−	0.00161560i	0.0963852	+	0.995344i	$0.469272\pi$
$104$	−17.0124	+	6.19202i	−1.66821	+	0.607177i
$105$	7.81691	−	6.96115i	0.762852	−	0.679338i
$106$	2.14398	+	12.1591i	0.208242	+	1.18100i
$107$	−1.76707	+	1.76707i	−0.170829	+	0.170829i	−0.787344	−	0.616515i	$-0.788544\pi$
$107$	−1.76707	+	1.76707i	−0.170829	+	0.170829i	0.616515	+	0.787344i	$0.288544\pi$
$108$	−18.1246	−	13.0081i	−1.74404	−	1.25170i
$109$		−	7.80745i		−	0.747818i	−0.927465	−	0.373909i	$-0.878017\pi$
$109$		−	7.80745i		−	0.747818i	0.927465	−	0.373909i	$-0.121983\pi$
$110$	11.8380	+	13.9878i	1.12871	+	1.33368i
$111$	−0.476138	+	7.66250i	−0.0451930	+	0.727293i
$112$	14.3211	+	6.67806i	1.35322	+	0.631017i
$113$	−1.69916	−	19.4214i	−0.159843	−	1.82701i	−0.477298	−	0.878741i	$-0.658384\pi$
$113$	−1.69916	−	19.4214i	−0.159843	−	1.82701i	0.317455	−	0.948273i	$-0.397172\pi$
$114$	5.85091	−	13.4205i	0.547988	−	1.25694i
$115$	10.9342	−	1.97556i	1.01962	−	0.184222i
$116$	−11.6043	+	6.69973i	−1.07743	+	0.622054i
$117$	0.347794	−	9.43351i	0.0321536	−	0.872129i
$118$	4.97617	+	18.5713i	0.458093	+	1.70963i
$119$	12.6202	−	10.5896i	1.15689	−	0.970748i
$120$	−22.2736	+	0.655558i	−2.03329	+	0.0598440i
$121$	0.0570802	−	0.323718i	0.00518911	−	0.0294289i
$122$	−10.3107	−	14.7252i	−0.933484	−	1.33315i
$123$	6.34457	−	11.6582i	0.572071	−	1.05118i
$124$	1.01645	+	1.21135i	0.0912796	+	0.108783i
$125$	3.03004	+	10.7619i	0.271015	+	0.962575i
$126$	−14.9026	+	13.8428i	−1.32763	+	1.23322i
$127$	−5.52679	+	20.6263i	−0.490423	+	1.83028i	0.0638628	+	0.997959i	$0.479658\pi$
$127$	−5.52679	+	20.6263i	−0.490423	+	1.83028i	−0.554286	+	0.832326i	$0.687009\pi$
$128$	6.66265	+	14.2881i	0.588901	+	1.26290i
$129$	−7.04921	−	3.07324i	−0.620648	−	0.270583i
$130$	−10.1852	−	14.4163i	−0.893304	−	1.26439i
$131$	−5.67190	−	15.5834i	−0.495556	−	1.36153i	−0.895529	−	0.445003i	$-0.853203\pi$
$131$	−5.67190	−	15.5834i	−0.495556	−	1.36153i	0.399973	−	0.916527i	$-0.369020\pi$
$132$	−16.0791	−	18.2098i	−1.39951	−	1.58496i
$133$	−7.45929	−	5.22305i	−0.646802	−	0.452896i
$134$	−0.966985			−0.0835348
$135$	4.05490	−	10.8884i	0.348990	−	0.937126i
$136$	−35.0721			−3.00741
$137$	−16.4221	−	11.4989i	−1.40304	−	0.982418i	−0.997667	−	0.0682654i	$-0.978254\pi$
$137$	−16.4221	−	11.4989i	−1.40304	−	0.982418i	−0.405371	−	0.914152i	$-0.632858\pi$
$138$	−21.1622	+	4.28407i	−1.80144	+	0.364684i
$139$	6.07923	+	16.7026i	0.515634	+	1.41669i	0.875286	+	0.483606i	$0.160673\pi$
$139$	6.07923	+	16.7026i	0.515634	+	1.41669i	−0.359652	+	0.933087i	$0.617105\pi$
$140$	−4.39776	+	25.5708i	−0.371678	+	2.16113i
$141$	1.33792	+	11.8452i	0.112674	+	0.997546i
$142$	−10.3582	−	22.2132i	−0.869238	−	1.86409i
$143$	2.66043	−	9.92886i	0.222476	−	0.830293i
$144$	17.5181	−	0.883929i	1.45984	−	0.0736607i
$145$	−4.95535	−	4.91374i	−0.411519	−	0.408064i
$146$	−0.0415627	−	0.0495324i	−0.00343975	−	0.00409933i
$147$	0.274779	+	0.449379i	0.0226634	+	0.0370642i
$148$	−10.9155	−	15.5890i	−0.897250	−	1.28141i
$149$	−0.147586	+	0.837002i	−0.0120907	+	0.0685699i	−0.990256	−	0.139258i	$-0.955528\pi$
$149$	−0.147586	+	0.837002i	−0.0120907	+	0.0685699i	0.978165	+	0.207828i	$0.0666394\pi$
$150$	−6.32567	−	20.7845i	−0.516488	−	1.69705i
$151$	11.3395	−	9.51495i	0.922794	−	0.774316i	−0.0517160	−	0.998662i	$-0.516469\pi$
$151$	11.3395	−	9.51495i	0.922794	−	0.774316i	0.974510	+	0.224346i	$0.0720246\pi$
$152$	5.01740	+	18.7252i	0.406965	+	1.51881i
$153$	6.88351	−	16.9424i	0.556499	−	1.36971i
$154$	−19.1808	+	11.0740i	−1.54563	+	0.892372i
$155$	−0.469527	+	0.676607i	−0.0377133	+	0.0543464i
$156$	13.9005	+	18.8237i	1.11293	+	1.50710i
$157$	0.891290	+	10.1875i	0.0711327	+	0.813051i	0.945039	+	0.326957i	$0.106023\pi$
$157$	0.891290	+	10.1875i	0.0711327	+	0.813051i	−0.873907	+	0.486094i	$0.838421\pi$
$158$	25.2917	+	11.7937i	2.01210	+	0.938257i
$159$	7.63254	−	3.79618i	0.605300	−	0.301057i
$160$	5.39483	−	4.56570i	0.426499	−	0.360950i
$161$			13.4295i			1.05839i
$162$	−7.43367	+	21.3192i	−0.584045	+	1.67500i
$163$	−9.20802	+	9.20802i	−0.721228	+	0.721228i	−0.968855	−	0.247628i	$-0.920349\pi$
$163$	−9.20802	+	9.20802i	−0.721228	+	0.721228i	0.247628	+	0.968855i	$0.420349\pi$
$164$	5.71318	+	32.4011i	0.446125	+	2.53010i
$165$	6.94877	−	10.5728i	0.540961	−	0.823091i
$166$	−2.57993	+	0.939019i	−0.200242	+	0.0728820i
$167$	4.80307	−	0.420214i	0.371672	−	0.0325171i	0.100210	−	0.994966i	$-0.468048\pi$
$167$	4.80307	−	0.420214i	0.371672	−	0.0325171i	0.271462	+	0.962449i	$0.412493\pi$
$168$	4.00678	−	26.6328i	0.309130	−	2.05477i
$169$	1.05980	−	2.91178i	0.0815232	−	0.223983i
$170$	−8.98940	−	32.9919i	−0.689455	−	2.53036i
$171$	−10.0304	−	1.25138i	−0.767041	−	0.0956953i
$172$	18.4126	−	4.93365i	1.40395	−	0.376187i
$173$	6.42280	+	0.561923i	0.488317	+	0.0427222i	0.328656	−	0.944450i	$-0.393404\pi$
$173$	6.42280	+	0.561923i	0.488317	+	0.0427222i	0.159661	+	0.987172i	$0.448960\pi$
$174$	9.82759	+	9.34421i	0.745027	+	0.708383i
$175$	−13.4512	+	1.29120i	−1.01682	+	0.0976058i
$176$	18.8095	+	3.31663i	1.41782	+	0.250000i
$177$	11.3250	−	6.92485i	0.851241	−	0.520503i
$178$	1.71942	−	19.6531i	0.128876	−	1.47306i
$179$	1.30891	−	2.26710i	0.0978327	−	0.169451i	−0.812955	−	0.582327i	$-0.802142\pi$
$179$	1.30891	−	2.26710i	0.0978327	−	0.169451i	0.910787	+	0.412876i	$0.135476\pi$
$180$	8.96229	+	27.3714i	0.668010	+	2.04014i
$181$	8.91293	+	15.4376i	0.662493	+	1.14747i	0.979959	+	0.199202i	$0.0638348\pi$
$181$	8.91293	+	15.4376i	0.662493	+	1.14747i	−0.317466	+	0.948270i	$0.602832\pi$
$182$	19.3353	−	9.01620i	1.43323	−	0.668325i
$183$	−7.73556	+	9.70554i	−0.571829	+	0.717454i
$184$	18.3771	−	21.9010i	1.35478	−	1.61456i
$185$	6.33881	−	7.61931i	0.466039	−	0.560183i
$186$	0.884591	−	1.33365i	0.0648614	−	0.0977881i
$187$	11.4216	−	16.3118i	0.835233	−	1.19284i
$188$	−20.8942	−	20.8942i	−1.52387	−	1.52387i
$189$	12.0792	+	7.16272i	0.878630	+	0.521011i
$190$	−16.3285	+	9.51929i	−1.18460	+	0.690602i
$191$	−8.64200	+	1.52382i	−0.625313	+	0.110260i	−0.477321	−	0.878729i	$-0.658392\pi$
$191$	−8.64200	+	1.52382i	−0.625313	+	0.110260i	−0.147992	+	0.988989i	$0.547281\pi$
$192$	4.88757	−	4.31569i	0.352730	−	0.311458i
$193$	0.517574	−	1.10994i	0.0372558	−	0.0798952i	−0.886799	−	0.462155i	$-0.847076\pi$
$193$	0.517574	−	1.10994i	0.0372558	−	0.0798952i	0.924055	+	0.382260i	$0.124854\pi$
$194$	−9.85290	−	8.26756i	−0.707397	−	0.593576i
$195$	−7.55554	+	9.56211i	−0.541063	+	0.684757i
$196$	−1.22693	−	0.446566i	−0.0876379	−	0.0318976i
$197$	13.5645	+	3.63461i	0.966434	+	0.258955i	0.707321	−	0.706892i	$-0.249903\pi$
$197$	13.5645	+	3.63461i	0.966434	+	0.258955i	0.259112	+	0.965847i	$0.416570\pi$
$198$	−13.0687	+	20.8241i	−0.928752	+	1.47990i
$199$	−11.1726	−	6.45050i	−0.792004	−	0.457264i	0.0486637	−	0.998815i	$-0.484504\pi$
$199$	−11.1726	−	6.45050i	−0.792004	−	0.457264i	−0.840668	+	0.541552i	$0.817837\pi$
$200$	23.7033	+	16.3011i	1.67608	+	1.15266i
$201$	0.188995	+	0.640321i	0.0133307	+	0.0451648i
$202$	2.44365	−	1.71106i	0.171934	−	0.120390i
$203$	6.90922	−	4.83789i	0.484932	−	0.339553i
$204$	12.8324	+	43.4768i	0.898451	+	3.04398i
$205$	−15.4990	+	7.30702i	−1.08250	+	0.510344i
$206$	0.408725	+	0.235978i	0.0284772	+	0.0164413i
$207$	6.97292	+	13.1759i	0.484652	+	0.915789i
$208$	−17.7709	−	4.76170i	−1.23219	−	0.330164i
$209$	−10.3429	−	3.76452i	−0.715435	−	0.260397i
$210$	26.0801	−	3.05718i	1.79970	−	0.210966i
$211$	−0.0983096	−	0.0824916i	−0.00676791	−	0.00567895i	0.639397	−	0.768876i	$-0.279184\pi$
$211$	−0.0983096	−	0.0824916i	−0.00676791	−	0.00567895i	−0.646165	+	0.763197i	$0.723628\pi$
$212$	−8.93021	+	19.1509i	−0.613329	+	1.31529i
$213$	−12.6847	+	11.2005i	−0.869142	+	0.767446i
$214$	−6.17397	+	1.08864i	−0.422044	+	0.0744177i
$215$	5.00008	+	8.57668i	0.341002	+	0.584924i
$216$	−9.89729	−	28.2103i	−0.673425	−	1.91947i
$217$	−0.703849	−	0.703849i	−0.0477804	−	0.0477804i
$218$	11.2343	−	16.0442i	0.760881	−	1.08665i
$219$	−0.0246762	+	0.0372031i	−0.00166747	+	0.00251395i
$220$	2.86504	+	31.2306i	0.193161	+	2.10556i
$221$	−12.3294	+	14.6937i	−0.829368	+	0.988402i
$222$	−12.0042	+	15.0612i	−0.805667	+	1.01084i
$223$	−7.59226	+	3.54033i	−0.508415	+	0.237078i	−0.659861	−	0.751388i	$-0.729385\pi$
$223$	−7.59226	+	3.54033i	−0.508415	+	0.237078i	0.151446	+	0.988466i	$0.451607\pi$
$224$	4.27106	+	7.39769i	0.285372	+	0.494279i
$225$	−12.5268	+	8.25102i	−0.835120	+	0.550068i
$226$	24.4541	−	42.3557i	1.62666	−	2.81746i
$227$	0.314610	−	3.59601i	0.0208814	−	0.238675i	−0.978580	−	0.205866i	$-0.933999\pi$
$227$	0.314610	−	3.59601i	0.0208814	−	0.238675i	0.999462	−	0.0328096i	$-0.0104455\pi$
$228$	21.3767	−	13.0711i	1.41571	−	0.865653i
$229$	−1.22130	−	0.215349i	−0.0807059	−	0.0142306i	0.133149	−	0.991096i	$-0.457491\pi$
$229$	−1.22130	−	0.215349i	−0.0807059	−	0.0142306i	−0.213855	+	0.976865i	$0.568602\pi$
$230$	25.3122	+	11.6736i	1.66904	+	0.769736i
$231$	11.0819	+	10.5368i	0.729135	+	0.693272i
$232$	−17.8879	−	1.56498i	−1.17440	−	0.102746i
$233$	−20.0624	+	5.37571i	−1.31433	+	0.352175i	−0.846852	−	0.531828i	$-0.821505\pi$
$233$	−20.0624	+	5.37571i	−1.31433	+	0.352175i	−0.467481	+	0.884003i	$0.654839\pi$
$234$	14.2888	−	18.8853i	0.934085	−	1.23457i
$235$	7.63841	−	13.3599i	0.498275	−	0.871502i
$236$	−11.2541	+	30.9205i	−0.732582	+	2.01275i
$237$	2.86640	−	19.0528i	0.186193	−	1.23761i
$238$	41.1719	−	3.60207i	2.66878	−	0.233488i
$239$	−11.3730	+	4.13943i	−0.735658	+	0.267758i	−0.682558	−	0.730831i	$-0.739133\pi$
$239$	−11.3730	+	4.13943i	−0.735658	+	0.267758i	−0.0531004	+	0.998589i	$0.516910\pi$
$240$	−18.9234	−	12.4371i	−1.22150	−	0.802808i
$241$	−1.19187	−	6.75943i	−0.0767751	−	0.435413i	−0.998830	−	0.0483548i	$-0.984602\pi$
$241$	−1.19187	−	6.75943i	−0.0767751	−	0.435413i	0.922055	−	0.387059i	$-0.126509\pi$
$242$	0.583102	−	0.583102i	0.0374832	−	0.0374832i
$243$	15.5701	+	0.755664i	0.998824	+	0.0484759i
$244$		−	30.7650i		−	1.96953i
$245$	0.0564100	−	0.677662i	0.00360390	−	0.0432943i
$246$	29.8132	−	14.8281i	1.90082	−	0.945407i
$247$	9.60887	+	4.48069i	0.611397	+	0.285099i
$248$	0.184689	+	2.11100i	0.0117277	+	0.134049i
$249$	1.12604	+	1.52486i	0.0713601	+	0.0966340i
$250$	−9.25882	+	26.4756i	−0.585579	+	1.67446i
$251$	8.53784	−	4.92932i	0.538904	−	0.311136i	−0.205731	−	0.978609i	$-0.565957\pi$
$251$	8.53784	−	4.92932i	0.538904	−	0.311136i	0.744634	+	0.667472i	$0.232624\pi$
$252$	−34.4811	+	4.77765i	−2.17211	+	0.300964i
$253$	4.20128	+	15.6794i	0.264132	+	0.985754i
$254$	−41.0369	+	34.4341i	−2.57489	+	2.16059i
$255$	−20.0897	+	12.4008i	−1.25807	+	0.776569i
$256$	−5.56035	+	31.5343i	−0.347522	+	1.97090i
$257$	6.45152	+	9.21372i	0.402435	+	0.574736i	0.968309	−	0.249755i	$-0.0803502\pi$
$257$	6.45152	+	9.21372i	0.402435	+	0.574736i	−0.565874	+	0.824491i	$0.691461\pi$
$258$	−10.0639	−	16.4587i	−0.626550	−	1.02467i
$259$	7.70013	+	9.17666i	0.478463	+	0.570210i
$260$	−0.127359	−	30.2089i	−0.00789847	−	1.87347i
$261$	4.26680	−	8.33396i	0.264108	−	0.515859i
$262$	10.7676	−	40.1851i	0.665222	−	2.48264i
$263$	3.48321	+	7.46977i	0.214784	+	0.460606i	0.983950	−	0.178443i	$-0.0571059\pi$
$263$	3.48321	+	7.46977i	0.214784	+	0.460606i	−0.769166	+	0.639049i	$0.779328\pi$
$264$	−3.65375	−	32.3482i	−0.224873	−	1.99089i
$265$	−10.8458	−	1.86530i	−0.666254	−	0.114584i
$266$	−7.81320	−	21.4666i	−0.479058	−	1.31620i
$267$	−13.3500	+	2.70257i	−0.817005	+	0.165395i
$268$	−1.35565	−	0.949234i	−0.0828093	−	0.0579837i
$269$	21.3745			1.30322			0.651612	−	0.758553i	$-0.274093\pi$
$269$	21.3745			1.30322			0.651612	+	0.758553i	$0.274093\pi$
$270$	24.0003	−	16.5409i	1.46061	−	1.00665i
$271$	−16.0063			−0.972313			−0.486157	−	0.873872i	$-0.661602\pi$
$271$	−16.0063			−0.972313			−0.486157	+	0.873872i	$0.661602\pi$
$272$	−29.1952	−	20.4427i	−1.77022	−	1.23952i
$273$	−9.74941	−	11.0413i	−0.590061	−	0.668251i
$274$	−17.2013	−	47.2602i	−1.03917	−	2.85509i
$275$	−15.3008	+	5.71559i	−0.922672	+	0.344663i
$276$	−33.8733	−	14.7677i	−2.03893	−	0.888911i
$277$	6.07443	+	13.0267i	0.364977	+	0.782696i	0.999948	+	0.0101600i	$0.00323409\pi$
$277$	6.07443	+	13.0267i	0.364977	+	0.782696i	−0.634971	+	0.772536i	$0.718988\pi$
$278$	−11.5408	+	43.0710i	−0.692174	+	2.58323i
$279$	−1.05601	−	0.325103i	−0.0632219	−	0.0194634i
$280$	−24.4821	+	24.6894i	−1.46308	+	1.47547i
$281$	−6.85563	−	8.17022i	−0.408973	−	0.487395i	0.521761	−	0.853091i	$-0.325275\pi$
$281$	−6.85563	−	8.17022i	−0.408973	−	0.487395i	−0.930734	+	0.365697i	$0.880831\pi$
$282$	−14.2948	+	26.2669i	−0.851245	+	1.56417i
$283$	14.1133	+	20.1559i	0.838951	+	1.19815i	0.978154	+	0.207882i	$0.0666570\pi$
$283$	14.1133	+	20.1559i	0.838951	+	1.19815i	−0.139203	+	0.990264i	$0.544454\pi$
$284$	7.28395	−	41.3093i	0.432223	−	2.45126i
$285$	9.49488	+	8.95195i	0.562428	+	0.530268i
$286$	19.7539	−	16.5755i	1.16808	−	0.980132i
$287$	−5.36021	−	20.0046i	−0.316403	−	1.18083i
$288$	8.03146	+	5.04036i	0.473258	+	0.297006i
$289$	−17.4577	+	10.0792i	−1.02692	+	0.592895i
$290$	−3.11271	−	17.2280i	−0.182784	−	1.01166i
$291$	−3.54892	+	8.14030i	−0.208041	+	0.477193i
$292$	−0.00964481	−	0.110241i	−0.000564420	−	0.00645135i
$293$	21.7565	+	10.1452i	1.27103	+	0.592691i	0.936821	−	0.349809i	$-0.113753\pi$
$293$	21.7565	+	10.1452i	1.27103	+	0.592691i	0.334208	+	0.942499i	$0.391531\pi$
$294$	−0.0819517	+	1.31885i	−0.00477952	+	0.0769170i
$295$	−17.0781	−	1.42162i	−0.994326	−	0.0827697i
$296$		−	25.5023i		−	1.48229i
$297$	16.3436	+	4.58386i	0.948351	+	0.265983i
$298$	−1.50766	+	1.50766i	−0.0873366	+	0.0873366i
$299$	−2.71515	−	15.3984i	−0.157021	−	0.890512i
$300$	11.5348	−	35.3479i	0.665961	−	2.04081i
$301$	−11.2755	+	4.10394i	−0.649908	+	0.236547i
$302$	36.9937	−	3.23653i	2.12875	−	0.186241i
$303$	−1.61064	−	1.28372i	−0.0925289	−	0.0737478i
$304$	−6.73782	+	18.5120i	−0.386440	+	1.06174i
$305$	15.4591	−	4.21219i	0.885187	−	0.241190i
$306$	38.5241	−	24.9115i	2.20228	−	1.42410i
$307$	−3.92820	+	1.05256i	−0.224194	+	0.0600726i	−0.369167	−	0.929363i	$-0.620357\pi$
$307$	−3.92820	+	1.05256i	−0.224194	+	0.0600726i	0.144973	+	0.989436i	$0.453690\pi$
$308$	−37.7609	−	3.30365i	−2.15163	−	0.188243i
$309$	0.0763761	−	0.316772i	0.00434488	−	0.0180205i
$310$	−1.93845	+	0.714808i	−0.110097	+	0.0405984i
$311$	−9.98381	−	1.76041i	−0.566130	−	0.0998239i	−0.116744	−	0.993162i	$-0.537246\pi$
$311$	−9.98381	−	1.76041i	−0.566130	−	0.0998239i	−0.449385	+	0.893338i	$0.648357\pi$
$312$	0.790363	+	31.3475i	0.0447455	+	1.77470i
$313$	−2.56936	+	29.3680i	−0.145229	+	1.65998i	0.478316	+	0.878188i	$0.341247\pi$
$313$	−2.56936	+	29.3680i	−0.145229	+	1.65998i	−0.623545	+	0.781787i	$0.714308\pi$
$314$	−12.8274	+	22.2177i	−0.723890	+	1.25381i
$315$	−7.12171	−	16.6723i	−0.401263	−	0.939379i
$316$	23.8800	+	41.3614i	1.34335	+	2.32676i
$317$	2.83348	−	1.32127i	0.159144	−	0.0742101i	−0.341414	−	0.939913i	$-0.610906\pi$
$317$	2.83348	−	1.32127i	0.159144	−	0.0742101i	0.500558	+	0.865703i	$0.333128\pi$
$318$	21.1472	+	3.18149i	1.18587	+	0.178409i
$319$	6.55325	−	7.80986i	0.366912	−	0.437268i
$320$	−8.38239	+	0.768988i	−0.468590	+	0.0429877i
$321$	1.92756	+	3.87553i	0.107586	+	0.216311i
$322$	−19.3239	+	27.5975i	−1.07688	+	1.53795i
$323$	14.5232	+	14.5232i	0.808094	+	0.808094i
$324$	−31.3494	+	22.5909i	−1.74163	+	1.25505i
$325$	15.1622	−	4.20005i	0.841049	−	0.232977i
$326$	−32.1719	+	5.67278i	−1.78184	+	0.314186i
$327$	−12.8199	−	4.30335i	−0.708943	−	0.237976i
$328$	−18.6330	+	39.9586i	−1.02884	+	2.20635i
$329$	14.2486	+	11.9560i	0.785551	+	0.659155i
$330$	29.4930	−	11.7282i	1.62354	−	0.645619i
$331$	27.5786	+	10.0378i	1.51586	+	0.551727i	0.960109	−	0.279624i	$-0.0902099\pi$
$331$	27.5786	+	10.0378i	1.51586	+	0.551727i	0.555747	+	0.831351i	$0.312432\pi$
$332$	−4.53867	−	1.21613i	−0.249092	−	0.0667439i
$333$	12.3195	+	5.00528i	0.675103	+	0.274288i
$334$	10.4749	+	6.04768i	0.573160	+	0.330914i
$335$	0.291372	−	0.811164i	0.0159194	−	0.0443186i
$336$	18.8590	−	19.8346i	1.02884	−	1.08207i
$337$	13.1165	−	9.18427i	0.714501	−	0.500299i	−0.158904	−	0.987294i	$-0.550796\pi$
$337$	13.1165	−	9.18427i	0.714501	−	0.500299i	0.873405	+	0.486995i	$0.161907\pi$
$338$	6.36769	−	4.45870i	0.346356	−	0.242521i
$339$	−32.8267	−	7.91477i	−1.78290	−	0.429871i
$340$	19.7837	−	55.0767i	1.07292	−	2.98695i
$341$	−1.04196	−	0.601574i	−0.0564252	−	0.0325771i
$342$	−18.8116	−	17.0044i	−1.01722	−	0.919494i
$343$	−17.4798	−	4.68369i	−0.943819	−	0.252896i
$344$	24.0041	+	8.73676i	1.29421	+	0.471055i
$345$	2.78287	−	19.0429i	0.149825	−	1.02524i
$346$	12.3902	+	10.3966i	0.666102	+	0.558926i
$347$	0.872755	−	1.87163i	0.0468520	−	0.100474i	−0.881488	−	0.472206i	$-0.843458\pi$
$347$	0.872755	−	1.87163i	0.0468520	−	0.100474i	0.928340	+	0.371731i	$0.121236\pi$
$348$	4.60492	+	22.7471i	0.246850	+	1.21937i
$349$	0.561803	−	0.0990609i	0.0300726	−	0.00530261i	−0.158592	−	0.987344i	$-0.550695\pi$
$349$	0.561803	−	0.0990609i	0.0300726	−	0.00530261i	0.188664	+	0.982042i	$0.439584\pi$
$350$	−29.5000	−	16.7018i	−1.57684	−	0.892748i
$351$	−15.2982	−	5.77069i	−0.816559	−	0.308017i
$352$	7.30088	+	7.30088i	0.389138	+	0.389138i
$353$	4.33346	−	6.18882i	0.230647	−	0.329398i	−0.687101	−	0.726562i	$-0.741117\pi$
$353$	4.33346	−	6.18882i	0.230647	−	0.329398i	0.917747	+	0.397165i	$0.130006\pi$
$354$	33.2370	+	2.06530i	1.76653	+	0.109770i
$355$	21.7548	−	1.99575i	1.15463	−	0.105924i
$356$	21.7028	−	25.8644i	1.15024	−	1.37081i
$357$	−10.4322	−	26.5593i	−0.552129	−	1.40567i
$358$	5.95197	−	2.77545i	0.314571	−	0.146687i
$359$	7.12655	+	12.3435i	0.376125	+	0.651467i	0.990495	−	0.137551i	$-0.0439231\pi$
$359$	7.12655	+	12.3435i	0.376125	+	0.651467i	−0.614370	+	0.789018i	$0.710590\pi$
$360$	−11.2004	+	36.9348i	−0.590315	+	1.94664i
$361$	−3.82366	+	6.62277i	−0.201245	+	0.348567i
$362$	−3.89754	+	44.5491i	−0.204850	+	2.34145i
$363$	−0.500086	−	0.272154i	−0.0262477	−	0.0142844i
$364$	35.9574	+	6.34026i	1.88468	+	0.332320i
$365$	0.0540744	−	0.0199400i	0.00283038	−	0.00104371i
$366$	−29.8619	+	8.81393i	−1.56091	+	0.460712i
$367$	−17.9778	−	1.57285i	−0.938434	−	0.0821024i	−0.392335	−	0.919823i	$-0.628332\pi$
$367$	−17.9778	−	1.57285i	−0.938434	−	0.0821024i	−0.546100	+	0.837720i	$0.683888\pi$
$368$	28.0633	−	7.51954i	1.46290	−	0.391983i
$369$	−15.6458	−	16.8437i	−0.814490	−	0.876846i
$370$	23.9897	−	6.53655i	1.24717	−	0.339819i
$371$	4.54928	−	12.4990i	0.236187	−	0.648918i
$372$	2.54930	−	1.00134i	0.132175	−	0.0519168i
$373$	−5.43209	+	0.475246i	−0.281263	+	0.0246073i	−0.226914	−	0.973915i	$-0.572864\pi$
$373$	−5.43209	+	0.475246i	−0.281263	+	0.0246073i	−0.0543485	+	0.998522i	$0.517308\pi$
$374$	46.9426	−	17.0857i	2.42735	−	0.883481i
$375$	19.3413	+	0.956452i	0.998780	+	0.0493910i
$376$	−6.87604	−	38.9959i	−0.354604	−	2.01106i
$377$	−6.94405	+	6.94405i	−0.357637	+	0.357637i
$378$	14.5160	+	32.1002i	0.746621	+	1.65106i
$379$		−	4.04015i		−	0.207529i	−0.994602	−	0.103764i	$-0.966911\pi$
$379$		−	4.04015i		−	0.207529i	0.994602	−	0.103764i	$-0.0330888\pi$
$380$	−32.2360	−	2.68339i	−1.65367	−	0.137655i
$381$	30.8222	+	20.4439i	1.57907	+	1.04737i
$382$	−19.9518	−	9.30369i	−1.02082	−	0.476018i
$383$	−2.67534	−	30.5793i	−0.136704	−	1.56253i	−0.686436	−	0.727190i	$-0.740826\pi$
$383$	−2.67534	−	30.5793i	−0.136704	−	1.56253i	0.549732	−	0.835341i	$-0.314730\pi$
$384$	27.1336	−	3.06476i	1.38465	−	0.156398i
$385$	−3.50998	−	19.4268i	−0.178885	−	0.990082i
$386$	2.66072	−	1.53617i	0.135427	−	0.0781888i
$387$	−8.93170	+	9.88094i	−0.454024	+	0.502277i
$388$	−5.69729	−	21.2626i	−0.289236	−	1.07944i
$389$	−23.0823	+	19.3684i	−1.17032	+	0.982014i	−0.999994	−	0.00337359i	$-0.998926\pi$
$389$	−23.0823	+	19.3684i	−1.17032	+	0.982014i	−0.170325	+	0.985388i	$0.554482\pi$
$390$	−29.2856	+	8.77822i	−1.48293	+	0.444502i
$391$	5.25988	−	29.8302i	0.266003	−	1.50858i
$392$	−1.00358	−	1.43326i	−0.0506885	−	0.0723907i
$393$	−28.7144	+	0.723975i	−1.44845	+	0.0365197i
$394$	22.6451	+	26.9873i	1.14084	+	1.35960i
$395$	−17.5142	+	17.6625i	−0.881233	+	0.888695i
$396$	−38.7632	+	16.3651i	−1.94792	+	0.822378i
$397$	7.37720	−	27.5321i	0.370251	−	1.38180i	−0.489910	−	0.871773i	$-0.662970\pi$
$397$	7.37720	−	27.5321i	0.370251	−	1.38180i	0.860161	−	0.510023i	$-0.170363\pi$
$398$	−13.6778	−	29.3321i	−0.685605	−	1.47029i
$399$	−12.6877	+	9.36936i	−0.635182	+	0.469055i
$400$	10.2299	+	27.3857i	0.511494	+	1.36928i
$401$	9.65646	+	26.5309i	0.482221	+	1.32489i	0.907585	+	0.419868i	$0.137924\pi$
$401$	9.65646	+	26.5309i	0.482221	+	1.32489i	−0.425364	+	0.905022i	$0.639854\pi$
$402$	−0.532987	+	1.58780i	−0.0265830	+	0.0791922i
$403$	0.949342	+	0.664736i	0.0472901	+	0.0331129i
$404$	5.10547			0.254007
$405$	−15.6439	−	12.6597i	−0.777351	−	0.629067i
$406$	21.1597			1.05014
$407$	11.8610	+	8.30514i	0.587926	+	0.411670i
$408$	−19.3312	+	57.5888i	−0.957038	+	2.85107i
$409$	6.83310	+	18.7738i	0.337875	+	0.928304i	0.985996	+	0.166767i	$0.0533328\pi$
$409$	6.83310	+	18.7738i	0.337875	+	0.928304i	−0.648121	+	0.761537i	$0.724445\pi$
$410$	−42.3644	−	7.28597i	−2.09223	−	0.359828i
$411$	−27.9329	+	20.6273i	−1.37783	+	1.01747i
$412$	0.341359	+	0.732046i	0.0168175	+	0.0360653i
$413$	5.36086	−	20.0070i	0.263790	−	0.984479i
$414$	−4.62978	+	37.1098i	−0.227541	+	1.82385i
$415$	−0.0103170	−	2.44714i	−0.000506443	−	0.120126i
$416$	−6.39288	−	7.61873i	−0.313437	−	0.373539i
$417$	30.7765	−	0.775968i	1.50713	−	0.0379993i
$418$	−15.8377	−	22.6186i	−0.774649	−	1.10631i
$419$	1.26780	−	7.19003i	0.0619359	−	0.351256i	−0.938053	−	0.346492i	$-0.887373\pi$
$419$	1.26780	−	7.19003i	0.0619359	−	0.351256i	0.999989	−	0.00476336i	$-0.00151623\pi$
$420$	39.5636	+	21.3154i	1.93051	+	1.04009i
$421$	−22.3147	+	18.7243i	−1.08755	+	0.912566i	−0.996526	−	0.0832827i	$-0.973460\pi$
$421$	−22.3147	+	18.7243i	−1.08755	+	0.912566i	−0.0910275	+	0.995848i	$0.529015\pi$
$422$	−0.0833264	−	0.310978i	−0.00405627	−	0.0151382i
$423$	20.1874	+	4.33201i	0.981544	+	0.210629i
$424$	−24.5229	+	14.1583i	−1.19094	+	0.687587i
$425$	30.3842	+	2.40030i	1.47385	+	0.116432i
$426$	−42.1835	+	4.76466i	−2.04380	+	0.230848i
$427$	1.68784	+	19.2921i	0.0816802	+	0.933609i
$428$	−9.72412	−	4.53443i	−0.470033	−	0.219180i
$429$	−14.8369	−	9.84109i	−0.716332	−	0.475132i
$430$	−2.06604	+	24.8196i	−0.0996331	+	1.19691i
$431$		−	14.3391i		−	0.690690i	−0.938476	−	0.345345i	$-0.887762\pi$
$431$		−	14.3391i		−	0.690690i	0.938476	−	0.345345i	$-0.112238\pi$
$432$	8.20429	−	29.2521i	0.394729	−	1.40739i
$433$	16.2907	−	16.2907i	0.782881	−	0.782881i	−0.197435	−	0.980316i	$-0.563261\pi$
$433$	16.2907	−	16.2907i	0.782881	−	0.782881i	0.980316	+	0.197435i	$0.0632612\pi$
$434$	−0.433620	−	2.45918i	−0.0208144	−	0.118044i
$435$	−10.7997	+	5.42835i	−0.517807	+	0.260269i
$436$	31.4993	−	11.4648i	1.50854	−	0.549065i
$437$	−16.6790	+	1.45922i	−0.797865	+	0.0698041i
$438$	−0.104241	+	0.0409448i	−0.00498085	+	0.00195642i
$439$	6.36027	−	17.4747i	0.303559	−	0.834021i	−0.690316	−	0.723508i	$-0.742528\pi$
$439$	6.36027	−	17.4747i	0.303559	−	0.834021i	0.993875	−	0.110513i	$-0.0352494\pi$
$440$	−20.8598	+	36.4846i	−0.994451	+	1.73933i
$441$	0.889339	−	0.203499i	0.0423495	−	0.00969044i
$442$	−46.4798	+	12.4542i	−2.21082	+	0.592387i
$443$	27.1205	+	2.37273i	1.28853	+	0.112732i	0.710741	−	0.703453i	$-0.248360\pi$
$443$	27.1205	+	2.37273i	1.28853	+	0.112732i	0.577790	+	0.816185i	$0.303915\pi$
$444$	−31.6137	+	9.33098i	−1.50032	+	0.442829i
$445$	15.9680	+	7.36422i	0.756957	+	0.349097i
$446$	−20.6962	−	3.64930i	−0.979994	−	0.172799i
$447$	1.29302	+	0.703680i	0.0611577	+	0.0332829i
$448$	0.886712	−	10.1352i	0.0418932	−	0.478841i
$449$	15.3860	−	26.6493i	0.726109	−	1.25766i	−0.232407	−	0.972619i	$-0.574660\pi$
$449$	15.3860	−	26.6493i	0.726109	−	1.25766i	0.958516	−	0.285039i	$-0.0920064\pi$
$450$	−37.6149	−	1.06928i	−1.77318	−	0.0504064i
$451$	−12.5164	−	21.6791i	−0.589375	−	1.02083i
$452$	75.8611	−	35.3746i	3.56820	−	1.66388i
$453$	−9.37350	−	23.8640i	−0.440405	−	1.12123i
$454$	5.82087	−	6.93705i	0.273187	−	0.325572i
$455$	1.73719	+	18.9363i	0.0814407	+	0.887749i
$456$	33.5125	+	2.08242i	1.56936	+	0.0975182i
$457$	13.4321	−	19.1830i	0.628327	−	0.897344i	−0.371185	−	0.928559i	$-0.621049\pi$
$457$	13.4321	−	19.1830i	0.628327	−	0.897344i	0.999513	+	0.0312144i	$0.00993748\pi$
$458$	−2.19989	−	2.19989i	−0.102794	−	0.102794i
$459$	−24.0254	−	20.6412i	−1.12141	−	0.963446i
$460$	24.0267	+	41.2132i	1.12025	+	1.92157i
$461$	31.1056	−	5.48476i	1.44873	−	0.255451i	0.606724	−	0.794913i	$-0.292483\pi$
$461$	31.1056	−	5.48476i	1.44873	−	0.255451i	0.842010	+	0.539462i	$0.181372\pi$
$462$	7.61152	+	37.5989i	0.354120	+	1.74926i
$463$	12.3947	−	26.5805i	0.576030	−	1.23530i	−0.375236	−	0.926929i	$-0.622438\pi$
$463$	12.3947	−	26.5805i	0.576030	−	1.23530i	0.951266	−	0.308371i	$-0.0997839\pi$
$464$	−13.9783	−	11.7292i	−0.648924	−	0.544512i
$465$	0.852200	+	1.14390i	0.0395198	+	0.0530473i
$466$	−48.9632	−	17.8212i	−2.26818	−	0.825549i
$467$	−20.0112	−	5.36199i	−0.926008	−	0.248123i	−0.235857	−	0.971788i	$-0.575790\pi$
$467$	−20.0112	−	5.36199i	−0.926008	−	0.248123i	−0.690152	+	0.723665i	$0.742456\pi$
$468$	38.5704	−	12.4494i	1.78292	−	0.575475i
$469$	0.902173	+	0.520870i	0.0416585	+	0.0240515i
$470$	34.9206	−	16.4633i	1.61077	−	0.759396i
$471$	17.2192	+	4.15168i	0.793420	+	0.191299i
$472$	−36.1204	+	25.2917i	−1.66257	+	1.16415i
$473$	−11.8806	+	8.31889i	−0.546271	+	0.382503i
$474$	33.3058	−	35.0287i	1.52979	−	1.60892i
$475$	−3.06521	−	16.5657i	−0.140642	−	0.760085i
$476$	61.2561	+	35.3662i	2.80767	+	1.62101i
$477$	−2.02643	−	14.6251i	−0.0927839	−	0.669638i
$478$	−29.3277	−	7.85832i	−1.34142	−	0.359431i
$479$	7.18880	+	2.61651i	0.328465	+	0.119551i	0.500988	−	0.865454i	$-0.332970\pi$
$479$	7.18880	+	2.61651i	0.328465	+	0.119551i	−0.172524	+	0.985005i	$0.555192\pi$
$480$	−4.52337	−	11.3749i	−0.206463	−	0.519191i
$481$	−10.6843	−	8.96523i	−0.487164	−	0.408779i
$482$	7.27698	−	15.6055i	0.331458	−	0.710813i
$483$	22.0514	+	7.40214i	1.00337	+	0.336809i
$484$	1.38986	−	0.245071i	0.0631757	−	0.0111396i
$485$	9.90419	−	5.77400i	0.449726	−	0.262184i
$486$	30.9091	+	23.9570i	1.40206	+	1.08671i
$487$	8.90898	+	8.90898i	0.403704	+	0.403704i	0.879536	−	0.475832i	$-0.157853\pi$
$487$	8.90898	+	8.90898i	0.403704	+	0.403704i	−0.475832	+	0.879536i	$0.657853\pi$
$488$	23.6470	−	33.7714i	1.07045	−	1.52876i
$489$	10.0443	+	20.1950i	0.454221	+	0.913248i
$490$	1.09102	−	1.31142i	0.0492873	−	0.0592438i
$491$	2.30460	−	2.74652i	0.104005	−	0.123949i	−0.711531	−	0.702655i	$-0.751998\pi$
$491$	2.30460	−	2.74652i	0.104005	−	0.123949i	0.815536	+	0.578706i	$0.196442\pi$
$492$	56.3519	+	8.47787i	2.54054	+	0.382212i
$493$	−17.2419	+	8.04003i	−0.776536	+	0.362105i
$494$	13.2987	+	23.0341i	0.598339	+	1.03635i
$495$	−13.5306	−	17.2375i	−0.608154	−	0.774768i
$496$	−1.07671	+	1.86492i	−0.0483458	+	0.0837373i
$497$	−2.30128	+	26.3038i	−0.103227	+	1.17989i
$498$	0.119859	+	4.75385i	0.00537099	+	0.213025i
$499$	−0.621729	−	0.109628i	−0.0278324	−	0.00490760i	0.159715	−	0.987163i	$-0.448943\pi$
$499$	−0.621729	−	0.109628i	−0.0278324	−	0.00490760i	−0.187547	+	0.982256i	$0.560054\pi$
$500$	−38.9697	+	28.0280i	−1.74278	+	1.25345i
$501$	1.95738	−	8.11829i	0.0874493	−	0.362699i
$502$	24.6380	+	2.15555i	1.09965	+	0.0962068i
$503$	−36.5596	+	9.79612i	−1.63011	+	0.436788i	−0.953950	−	0.299964i	$-0.903025\pi$
$503$	−36.5596	+	9.79612i	−1.63011	+	0.436788i	−0.676163	+	0.736752i	$0.736359\pi$
$504$	−41.5229	−	21.2588i	−1.84958	−	0.946941i
$505$	0.699016	+	2.56545i	0.0311058	+	0.114161i
$506$	−13.9278	+	38.2662i	−0.619164	+	1.70114i
$507$	−4.19702	−	3.34513i	−0.186396	−	0.148563i
$508$	−91.3329	+	7.99059i	−4.05224	+	0.354525i
$509$	−27.9791	+	10.1836i	−1.24015	+	0.451378i	−0.877063	−	0.480376i	$-0.840500\pi$
$509$	−27.9791	+	10.1836i	−1.24015	+	0.451378i	−0.363089	+	0.931754i	$0.618278\pi$
$510$	−59.1278	−	3.42394i	−2.61822	−	0.151615i
$511$	0.0120961	+	0.0686004i	0.000535100	+	0.00303470i
$512$	−34.5064	+	34.5064i	−1.52498	+	1.52498i
$513$	−7.58336	+	15.7802i	−0.334813	+	0.696713i
$514$			28.2173i			1.24461i
$515$	−0.321109	+	0.271757i	−0.0141497	+	0.0119751i
$516$	2.04766	−	32.9531i	0.0901431	−	1.45068i
$517$	20.3760	+	9.50148i	0.896135	+	0.417875i
$518$	2.61921	+	29.9377i	0.115082	+	1.31539i
$519$	4.46283	−	10.2366i	0.195897	−	0.449336i
$520$	23.0797	−	33.2588i	1.01211	−	1.45849i
$521$	27.1230	−	15.6595i	1.18828	−	0.686054i	0.230365	−	0.973104i	$-0.426008\pi$
$521$	27.1230	−	15.6595i	1.18828	−	0.686054i	0.957915	+	0.287050i	$0.0926747\pi$
$522$	20.7601	−	10.9866i	0.908645	−	0.480871i
$523$	8.52925	+	31.8316i	0.372958	+	1.39190i	0.856305	+	0.516470i	$0.172754\pi$
$523$	8.52925	+	31.8316i	0.372958	+	1.39190i	−0.483347	+	0.875429i	$0.660579\pi$
$524$	54.5428	−	45.7668i	2.38271	−	1.99933i
$525$	−5.29394	+	22.7987i	−0.231046	+	0.995018i
$526$	−3.59043	+	20.3623i	−0.156550	+	0.887840i
$527$	1.28775	+	1.83910i	0.0560952	+	0.0801122i
$528$	15.8135	−	29.0574i	0.688193	−	1.26456i
$529$	1.08748	+	1.29601i	0.0472817	+	0.0563482i
$530$	−19.6040	−	19.4394i	−0.851543	−	0.844394i
$531$	−5.12848	−	22.4127i	−0.222557	−	0.972627i
$532$	10.1189	−	37.7644i	0.438712	−	1.63730i
$533$	10.1905	+	21.8537i	0.441401	+	0.946588i
$534$	−31.3228	−	13.6558i	−1.35547	−	0.590943i
$535$	0.947130	−	5.50711i	0.0409480	−	0.238093i
$536$	−0.758509	−	2.08399i	−0.0327626	−	0.0900144i
$537$	−3.00115	−	3.39884i	−0.129509	−	0.146671i
$538$	43.9242	+	30.7561i	1.89371	+	1.32599i
$539$	0.993428			0.0427900
$540$	49.8840	+	0.370530i	2.14666	+	0.0159451i
$541$	−19.8436			−0.853142			−0.426571	−	0.904454i	$-0.640279\pi$
$541$	−19.8436			−0.853142			−0.426571	+	0.904454i	$0.640279\pi$
$542$	−32.8927	−	23.0317i	−1.41286	−	0.989297i
$543$	30.2614	−	6.12612i	1.29864	−	0.262897i
$544$	−6.58965	−	18.1049i	−0.282529	−	0.776241i
$545$	10.0737	+	14.2584i	0.431510	+	0.610763i
$546$	−4.14736	−	36.7183i	−0.177491	−	1.57140i
$547$	7.36373	+	15.7916i	0.314851	+	0.675199i	0.998508	−	0.0546038i	$-0.0173896\pi$
$547$	7.36373	+	15.7916i	0.314851	+	0.675199i	−0.683658	+	0.729803i	$0.739612\pi$
$548$	22.2776	−	83.1410i	0.951650	−	3.55161i
$549$	11.6729	+	18.0514i	0.498186	+	0.770415i
$550$	−39.6672	−	10.2711i	−1.69141	−	0.437961i
$551$	6.75924	+	8.05534i	0.287953	+	0.343169i
$552$	−25.8325	−	42.2469i	−1.09950	−	1.79815i
$553$	−17.2438	−	24.6267i	−0.733281	−	1.04723i
$554$	−6.26140	+	35.5102i	−0.266022	+	1.50868i
$555$	−9.01713	−	14.6080i	−0.382756	−	0.620077i
$556$	−58.4598	+	49.0536i	−2.47925	+	2.08034i
$557$	−2.61924	−	9.77513i	−0.110981	−	0.414185i	0.887974	−	0.459893i	$-0.152112\pi$
$557$	−2.61924	−	9.77513i	−0.110981	−	0.414185i	−0.998955	+	0.0457078i	$0.985446\pi$
$558$	−1.70230	−	2.18760i	−0.0720640	−	0.0926083i
$559$	12.0988	−	6.98526i	0.511726	−	0.295445i
$560$	−34.7705	+	6.28225i	−1.46932	+	0.265473i
$561$	−20.4887	−	27.7453i	−0.865033	−	1.17141i
$562$	−2.33196	−	26.6544i	−0.0983676	−	1.12435i
$563$	−33.8599	−	15.7891i	−1.42702	−	0.665432i	−0.452923	−	0.891550i	$-0.649619\pi$
$563$	−33.8599	−	15.7891i	−1.42702	−	0.665432i	−0.974100	+	0.226118i	$0.927397\pi$
$564$	−45.8251	+	22.7919i	−1.92958	+	0.959713i
$565$	28.1619	+	33.2761i	1.18478	+	1.39994i
$566$			61.7281i			2.59462i
$567$	18.4191	−	15.8861i	0.773530	−	0.667155i
$568$	39.7474	−	39.7474i	1.66776	−	1.66776i
$569$	0.949414	+	5.38439i	0.0398015	+	0.225725i	0.998220	−	0.0596413i	$-0.0189957\pi$
$569$	0.949414	+	5.38439i	0.0398015	+	0.225725i	−0.958418	+	0.285367i	$0.907885\pi$
$570$	6.63073	+	32.0585i	0.277731	+	1.34278i
$571$	−27.1899	+	9.89631i	−1.13786	+	0.414148i	−0.841141	−	0.540817i	$-0.818115\pi$
$571$	−27.1899	+	9.89631i	−1.13786	+	0.414148i	−0.296721	+	0.954964i	$0.595893\pi$
$572$	43.9649	−	3.84643i	1.83826	−	0.160827i
$573$	−2.26121	+	15.0302i	−0.0944636	+	0.627894i
$574$	17.7698	−	48.8220i	0.741695	−	2.03779i
$575$	−17.4196	+	17.7159i	−0.726448	+	0.738803i
$576$	−4.39245	−	10.4042i	−0.183019	−	0.433507i
$577$	−13.3085	+	3.56601i	−0.554041	+	0.148455i	−0.524967	−	0.851122i	$-0.675922\pi$
$577$	−13.3085	+	3.56601i	−0.554041	+	0.148455i	−0.0290738	+	0.999577i	$0.509256\pi$
$578$	−50.3785	−	4.40755i	−2.09547	−	0.183330i
$579$	−1.53725	−	1.46164i	−0.0638861	−	0.0607438i
$580$	12.5479	−	27.2080i	0.521024	−	1.12975i
$581$	2.91282	+	0.513608i	0.120844	+	0.0213081i
$582$	−19.0062	+	11.6216i	−0.787832	+	0.481731i
$583$	1.40124	−	16.0162i	0.0580333	−	0.663324i
$584$	0.0741472	−	0.128427i	0.00306823	−	0.00531433i
$585$	11.5366	+	17.6768i	0.476979	+	0.730844i
$586$	30.1112	+	52.1541i	1.24388	+	2.15447i
$587$	−19.2878	+	8.99405i	−0.796093	+	0.371224i	−0.777723	−	0.628607i	$-0.783625\pi$
$587$	−19.2878	+	8.99405i	−0.796093	+	0.371224i	−0.0183698	+	0.999831i	$0.505848\pi$
$588$	−1.40953	+	1.76849i	−0.0581281	+	0.0729313i
$589$	0.797678	−	0.950636i	0.0328678	−	0.0391703i
$590$	−33.0497	−	27.4954i	−1.36063	−	1.13197i
$591$	13.4446	−	20.2698i	0.553038	−	0.833787i
$592$	14.8647	−	21.2290i	0.610936	−	0.872507i
$593$	−9.84862	−	9.84862i	−0.404434	−	0.404434i	0.475358	−	0.879792i	$-0.342319\pi$
$593$	−9.84862	−	9.84862i	−0.404434	−	0.404434i	−0.879792	+	0.475358i	$0.842319\pi$
$594$	26.9901	+	32.9368i	1.10742	+	1.35141i
$595$	−9.38431	+	35.6228i	−0.384719	+	1.46039i
$596$	−3.59362	+	0.633653i	−0.147201	+	0.0259554i
$597$	−16.7499	+	14.7901i	−0.685529	+	0.605318i
$598$	16.5774	−	35.5503i	0.677900	−	1.45376i
$599$	7.79546	+	6.54117i	0.318514	+	0.267265i	0.788000	−	0.615675i	$-0.211116\pi$
$599$	7.79546	+	6.54117i	0.318514	+	0.267265i	−0.469486	+	0.882940i	$0.655561\pi$
$600$	39.8315	−	29.9361i	1.62611	−	1.22214i
$601$	29.1191	+	10.5985i	1.18779	+	0.432321i	0.858948	−	0.512063i	$-0.171119\pi$
$601$	29.1191	+	10.5985i	1.18779	+	0.432321i	0.328845	+	0.944384i	$0.393341\pi$
$602$	−29.0762	−	7.79094i	−1.18506	−	0.317535i
$603$	1.15558	+	0.0426040i	0.0470591	+	0.00173497i
$604$	55.0397	+	31.7772i	2.23953	+	1.29299i
$605$	0.313439	+	0.664840i	0.0127431	+	0.0270296i
$606$	−1.46268	−	4.95560i	−0.0594172	−	0.201308i
$607$	−24.8874	+	17.4264i	−1.01015	+	0.707315i	−0.956646	−	0.291253i	$-0.905928\pi$
$607$	−24.8874	+	17.4264i	−1.01015	+	0.707315i	−0.0535038	+	0.998568i	$0.517039\pi$
$608$	−8.72359	+	6.10833i	−0.353788	+	0.247725i
$609$	−4.13560	−	14.0116i	−0.167583	−	0.567778i
$610$	37.8293	+	13.5884i	1.53166	+	0.550178i
$611$	−18.7548	−	10.8281i	−0.758738	−	0.438058i
$612$	78.4623	+	2.89274i	3.17165	+	0.116932i
$613$	3.57095	+	0.956834i	0.144229	+	0.0386462i	0.330211	−	0.943907i	$-0.392880\pi$
$613$	3.57095	+	0.956834i	0.144229	+	0.0386462i	−0.185982	+	0.982553i	$0.559547\pi$
$614$	−9.58694	−	3.48936i	−0.386897	−	0.140819i
$615$	3.45537	+	29.4770i	0.139334	+	1.18863i
$616$	−38.9116	−	32.6507i	−1.56779	−	1.31553i
$617$	6.83850	−	14.6652i	0.275308	−	0.590399i	−0.719231	−	0.694771i	$-0.755506\pi$
$617$	6.83850	−	14.6652i	0.275308	−	0.590399i	0.994538	+	0.104372i	$0.0332833\pi$
$618$	0.612760	−	0.541063i	0.0246488	−	0.0217648i
$619$	−20.5670	+	3.62651i	−0.826656	+	0.145762i	−0.570942	−	0.820991i	$-0.693422\pi$
$619$	−20.5670	+	3.62651i	−0.826656	+	0.145762i	−0.255714	+	0.966752i	$0.582311\pi$
$620$	−3.41926	−	0.900756i	−0.137321	−	0.0361752i
$621$	25.4783	−	4.18725i	1.02241	−	0.168029i
$622$	−17.9835	−	17.9835i	−0.721072	−	0.721072i
$623$	−12.1904	+	17.4096i	−0.488396	+	0.697502i
$624$	−17.6138	+	26.5554i	−0.705116	+	1.06307i
$625$	−19.4194	−	15.7445i	−0.776775	−	0.629778i
$626$	−47.5380	+	56.6536i	−1.90000	+	2.26433i
$627$	−11.8822	+	14.9082i	−0.474531	+	0.595378i
$628$	−39.7929	+	18.5557i	−1.58791	+	0.740454i
$629$	−13.5097	−	23.3995i	−0.538667	−	0.932999i
$630$	9.35505	−	44.5089i	0.372714	−	1.77328i
$631$	7.86152	−	13.6165i	0.312962	−	0.542066i	−0.666040	−	0.745916i	$-0.732012\pi$
$631$	7.86152	−	13.6165i	0.312962	−	0.542066i	0.979002	+	0.203850i	$0.0653454\pi$
$632$	−5.57811	+	63.7581i	−0.221885	+	2.53616i
$633$	−0.189639	+	0.115957i	−0.00753746	+	0.00460889i
$634$	7.72396	+	1.36194i	0.306758	+	0.0540897i
$635$	−16.5200	−	44.7999i	−0.655578	−	1.77783i
$636$	26.5238	+	25.2192i	1.05174	+	1.00001i
$637$	−0.953277	−	0.0834010i	−0.0377702	−	0.00330447i
$638$	24.7046	−	6.61957i	0.978063	−	0.262071i
$639$	11.3997	+	27.0020i	0.450966	+	1.06818i
$640$	−30.6032	−	17.4971i	−1.20970	−	0.691635i
$641$	13.8355	−	38.0128i	0.546471	−	1.50142i	−0.291971	−	0.956427i	$-0.594311\pi$
$641$	13.8355	−	38.0128i	0.546471	−	1.50142i	0.838443	−	0.544990i	$-0.183467\pi$
$642$	−1.61544	+	10.7378i	−0.0637565	+	0.423785i
$643$	25.8204	−	2.25900i	1.01826	−	0.0890861i	0.434216	−	0.900809i	$-0.357026\pi$
$643$	25.8204	−	2.25900i	1.01826	−	0.0890861i	0.584043	+	0.811723i	$0.301470\pi$
$644$	−54.1816	+	19.7205i	−2.13506	+	0.777097i
$645$	16.8389	−	3.48284i	0.663033	−	0.137137i
$646$	8.94731	+	50.7427i	0.352027	+	1.99645i
$647$	23.1817	−	23.1817i	0.911366	−	0.911366i	−0.0850141	−	0.996380i	$-0.527094\pi$
$647$	23.1817	−	23.1817i	0.911366	−	0.911366i	0.996380	+	0.0850141i	$0.0270935\pi$
$648$	−51.7769	+	0.702344i	−2.03399	+	0.0275907i
$649$		−	25.0359i		−	0.982744i
$650$	37.2017	+	13.1862i	1.45917	+	0.517203i
$651$	−1.54368	+	0.767776i	−0.0605015	+	0.0300915i
$652$	−50.6714	−	23.6285i	−1.98445	−	0.925362i
$653$	2.87574	+	32.8699i	0.112537	+	1.28630i	0.817033	+	0.576591i	$0.195617\pi$
$653$	2.87574	+	32.8699i	0.112537	+	1.28630i	−0.704496	+	0.709708i	$0.748827\pi$
$654$	−20.1526	−	27.2901i	−0.788028	−	1.06713i
$655$	30.4651	+	21.1411i	1.19037	+	0.826049i
$656$	−38.8017	+	22.4022i	−1.51495	+	0.874658i
$657$	0.0474867	+	0.0610244i	0.00185263	+	0.00238079i
$658$	12.0770	+	45.0720i	0.470810	+	1.75709i
$659$	12.5302	−	10.5141i	0.488108	−	0.409571i	−0.365240	−	0.930914i	$-0.619013\pi$
$659$	12.5302	−	10.5141i	0.488108	−	0.409571i	0.853348	+	0.521342i	$0.174568\pi$
$660$	52.8600	+	12.5094i	2.05757	+	0.486927i
$661$	4.84704	−	27.4889i	0.188528	−	1.06920i	−0.732810	−	0.680433i	$-0.761792\pi$
$661$	4.84704	−	27.4889i	0.188528	−	1.06920i	0.921338	−	0.388762i	$-0.127097\pi$
$662$	42.2301	+	60.3108i	1.64132	+	2.34405i
$663$	17.3313	+	28.3440i	0.673093	+	1.10079i
$664$	−4.04743	−	4.82353i	−0.157071	−	0.187189i
$665$	20.3617	−	0.0858439i	0.789593	−	0.00332888i
$666$	18.1142	+	28.0125i	0.701909	+	1.08546i
$667$	4.01378	−	14.9796i	0.155414	−	0.580014i
$668$	8.74840	+	18.7610i	0.338486	+	0.725885i
$669$	1.62852	+	14.4179i	0.0629621	+	0.557429i
$670$	1.76596	−	1.24767i	0.0682251	−	0.0482017i
$671$	8.00592	+	21.9961i	0.309065	+	0.849149i
$672$	14.5012	−	2.93562i	0.559396	−	0.113244i
$673$	−29.0771	−	20.3600i	−1.12084	−	0.784821i	−0.142085	−	0.989854i	$-0.545381\pi$
$673$	−29.0771	−	20.3600i	−1.12084	−	0.784821i	−0.978755	+	0.205034i	$0.934270\pi$
$674$	40.1696			1.54728
$675$	6.64368	+	25.1170i	0.255715	+	0.966752i
$676$	13.3039			0.511688
$677$	−1.67557	−	1.17325i	−0.0643975	−	0.0450916i	0.540934	−	0.841065i	$-0.318071\pi$
$677$	−1.67557	−	1.17325i	−0.0643975	−	0.0450916i	−0.605332	+	0.795973i	$0.706960\pi$
$678$	−56.0698	−	63.4997i	−2.15335	−	2.43869i
$679$	4.73916	+	13.0207i	0.181872	+	0.499689i
$680$	64.0507	−	45.2524i	2.45623	−	1.73535i
$681$	−5.73127	−	2.49866i	−0.219623	−	0.0957487i
$682$	−1.27559	−	2.73552i	−0.0488450	−	0.104748i
$683$	2.32207	−	8.66609i	0.0888516	−	0.331599i	−0.907164	−	0.420777i	$-0.861757\pi$
$683$	2.32207	−	8.66609i	0.0888516	−	0.331599i	0.996016	+	0.0891783i	$0.0284241\pi$
$684$	−9.68033	−	42.3053i	−0.370137	−	1.61758i
$685$	44.8277	−	0.188991i	1.71278	−	0.00722098i
$686$	−29.1812	−	34.7769i	−1.11415	−	1.32779i
$687$	−1.02677	+	1.88669i	−0.0391736	+	0.0719819i
$688$	14.8893	+	21.2642i	0.567650	+	0.810689i
$689$	−2.68921	+	15.2513i	−0.102451	+	0.581027i
$690$	33.1199	−	35.1286i	1.26085	−	1.33732i
$691$	−22.2034	+	18.6309i	−0.844657	+	0.708752i	−0.958606	−	0.284735i	$-0.908094\pi$
$691$	−22.2034	+	18.6309i	−0.844657	+	0.708752i	0.113949	+	0.993487i	$0.463650\pi$
$692$	7.16445	+	26.7381i	0.272352	+	1.01643i
$693$	23.4097	−	12.3888i	0.889262	−	0.470613i
$694$	4.48662	−	2.59035i	0.170310	−	0.0983284i
$695$	−32.6530	−	22.6593i	−1.23860	−	0.859517i
$696$	−12.4292	+	28.5094i	−0.471129	+	1.08065i
$697$	4.07124	+	46.5345i	0.154209	+	1.76262i
$698$	1.29704	+	0.604818i	0.0490936	+	0.0228927i
$699$	−2.23113	+	35.9057i	−0.0843892	+	1.35808i
$700$	−24.9618	−	52.3732i	−0.943467	−	1.97952i
$701$		−	4.40189i		−	0.166257i	−0.996539	−	0.0831285i	$-0.973509\pi$
$701$		−	4.40189i		−	0.166257i	0.996539	−	0.0831285i	$-0.0264912\pi$
$702$	−23.1341	−	33.8715i	−0.873140	−	1.27840i
$703$	−10.5604	+	10.5604i	−0.398294	+	0.398294i
$704$	−2.13541	−	12.1105i	−0.0804813	−	0.456432i
$705$	−17.7269	−	19.9061i	−0.667632	−	0.749707i
$706$	17.8104	−	6.48245i	0.670303	−	0.243970i
$707$	−3.20153	+	0.280098i	−0.120406	+	0.0105342i
$708$	44.5686	+	35.5223i	1.67499	+	1.33501i
$709$	−8.05475	+	22.1303i	−0.302503	+	0.831119i	0.691561	+	0.722318i	$0.256923\pi$
$709$	−8.05475	+	22.1303i	−0.302503	+	0.831119i	−0.994064	+	0.108801i	$0.965299\pi$
$710$	47.5776	+	27.2021i	1.78555	+	1.02088i
$711$	−29.7049	−	15.2083i	−1.11402	−	0.570354i
$712$	43.7037	−	11.7104i	1.63787	−	0.438865i
$713$	−1.82319	−	0.159508i	−0.0682790	−	0.00597364i
$714$	16.7787	−	69.5901i	0.627926	−	2.60434i
$715$	7.95225	+	21.5653i	0.297397	+	0.806497i
$716$	11.0687	+	1.95172i	0.413658	+	0.0729391i
$717$	0.528367	+	20.9562i	0.0197322	+	0.782623i
$718$	−3.11637	+	35.6203i	−0.116302	+	1.32934i
$719$	−3.55440	+	6.15640i	−0.132557	+	0.229595i	−0.924661	−	0.380790i	$-0.875652\pi$
$719$	−3.55440	+	6.15640i	−0.132557	+	0.229595i	0.792105	+	0.610385i	$0.208985\pi$
$720$	−30.8521	+	24.2173i	−1.14979	+	0.902526i
$721$	−0.254220	−	0.440322i	−0.00946765	−	0.0163985i
$722$	−17.3872	+	8.10778i	−0.647084	+	0.301740i
$723$	−11.7560	−	1.76863i	−0.437210	−	0.0657762i
$724$	−49.1954	+	58.6288i	−1.82833	+	2.17892i
$725$	15.3898	+	2.58003i	0.571562	+	0.0958198i
$726$	−0.636062	−	1.27886i	−0.0236065	−	0.0474628i
$727$	11.1796	−	15.9661i	0.414627	−	0.592148i	−0.556460	−	0.830874i	$-0.687841\pi$
$727$	11.1796	−	15.9661i	0.414627	−	0.592148i	0.971087	+	0.238726i	$0.0767298\pi$
$728$	34.5978	+	34.5978i	1.28228	+	1.28228i
$729$	9.82282	−	25.1498i	0.363808	−	0.931474i
$730$	0.139814	+	0.0368320i	0.00517475	+	0.00136321i
$731$	26.6530	−	4.69964i	0.985796	−	0.173822i
$732$	−50.5165	−	16.9572i	−1.86714	−	0.626756i
$733$	15.4914	−	33.2213i	0.572186	−	1.22706i	−0.380972	−	0.924587i	$-0.624411\pi$
$733$	15.4914	−	33.2213i	0.572186	−	1.22706i	0.953159	−	0.302471i	$-0.0978116\pi$
$734$	−34.6809	−	29.1008i	−1.28010	−	1.07413i
$735$	−1.08164	−	0.466143i	−0.0398967	−	0.0171939i
$736$	14.7586	+	5.37168i	0.544008	+	0.198003i
$737$	1.21626	+	0.325897i	0.0448017	+	0.0120046i
$738$	−7.91536	−	57.1266i	−0.291368	−	2.10286i
$739$	−39.9362	−	23.0572i	−1.46908	−	0.848172i	−0.469678	−	0.882838i	$-0.655630\pi$
$739$	−39.9362	−	23.0572i	−1.46908	−	0.848172i	−0.999399	+	0.0346657i	$0.988963\pi$
$740$	40.0485	+	14.3855i	1.47221	+	0.528823i
$741$	12.6536	−	13.3082i	0.464841	−	0.488888i
$742$	27.3338	−	19.1393i	1.00345	−	0.702626i
$743$	5.71577	−	4.00223i	0.209691	−	0.146828i	−0.464013	−	0.885828i	$-0.653591\pi$
$743$	5.71577	−	4.00223i	0.209691	−	0.146828i	0.673705	+	0.739001i	$0.264702\pi$
$744$	3.56808	+	0.860291i	0.130812	+	0.0315398i
$745$	−0.810426	−	1.71901i	−0.0296917	−	0.0629795i
$746$	−11.8467	−	6.83970i	−0.433739	−	0.250419i
$747$	3.12449	−	1.00850i	0.114319	−	0.0368989i
$748$	82.5823	+	22.1279i	3.01951	+	0.809075i
$749$	6.34655	+	2.30996i	0.231898	+	0.0844040i
$750$	38.3698	+	29.7960i	1.40107	+	1.08800i
$751$	14.9900	+	12.5781i	0.546995	+	0.458983i	0.873922	−	0.486067i	$-0.161569\pi$
$751$	14.9900	+	12.5781i	0.546995	+	0.458983i	−0.326927	+	0.945050i	$0.606013\pi$
$752$	17.0060	−	36.4694i	0.620144	−	1.32990i
$753$	−3.38807	−	16.7362i	−0.123468	−	0.609900i
$754$	−24.2618	+	4.27802i	−0.883564	+	0.155796i
$755$	−8.43197	+	32.0077i	−0.306871	+	1.16488i
$756$	−11.1605	+	59.2517i	−0.405905	+	2.15496i
$757$	−13.8377	−	13.8377i	−0.502940	−	0.502940i	0.409411	−	0.912350i	$-0.365734\pi$
$757$	−13.8377	−	13.8377i	−0.502940	−	0.502940i	−0.912350	+	0.409411i	$0.865734\pi$
$758$	5.81344	−	8.30245i	0.211154	−	0.301559i
$759$	28.0614	+	1.74369i	1.01856	+	0.0632921i
$760$	−33.3235	−	27.7232i	−1.20877	−	1.00563i
$761$	−4.04597	+	4.82180i	−0.146666	+	0.174790i	−0.834376	−	0.551196i	$-0.814172\pi$
$761$	−4.04597	+	4.82180i	−0.146666	+	0.174790i	0.687710	+	0.725986i	$0.258616\pi$
$762$	33.9222	+	86.3626i	1.22887	+	3.12859i
$763$	−19.1236	+	8.91746i	−0.692319	+	0.322834i
$764$	−18.8382	−	32.6287i	−0.681542	−	1.18046i
$765$	9.28910	+	39.8226i	0.335848	+	1.43979i
$766$	38.5033	−	66.6897i	1.39118	−	2.40960i
$767$	−2.10183	+	24.0240i	−0.0758927	+	0.867457i
$768$	48.7149	+	26.5114i	1.75785	+	0.956647i
$769$	−43.7099	−	7.70724i	−1.57622	−	0.277930i	−0.683983	−	0.729498i	$-0.739754\pi$
$769$	−43.7099	−	7.70724i	−1.57622	−	0.277930i	−0.892237	+	0.451567i	$0.850865\pi$
$770$	20.7406	−	44.9724i	0.747439	−	1.62069i
$771$	18.6850	−	5.51499i	0.672924	−	0.198618i
$772$	5.23811	+	0.458275i	0.188524	+	0.0164937i
$773$	17.1792	−	4.60315i	0.617893	−	0.165564i	0.0637231	−	0.997968i	$-0.479703\pi$
$773$	17.1792	−	4.60315i	0.617893	−	0.165564i	0.554170	+	0.832404i	$0.313036\pi$
$774$	−32.5724	+	7.45323i	−1.17079	+	0.267901i
$775$	−0.0155274	−	1.84147i	−0.000557760	−	0.0661477i
$776$	10.0891	−	27.7195i	0.362176	−	0.995071i
$777$	19.3124	−	7.58565i	0.692827	−	0.272134i
$778$	−75.3032	+	6.58818i	−2.69975	+	0.236198i
$779$	24.2626	−	8.83085i	0.869297	−	0.316398i
$780$	−49.6735	−	16.4415i	−1.77860	−	0.588702i
$781$	5.54203	+	31.4304i	0.198310	+	1.12467i
$782$	53.7322	−	53.7322i	1.92146	−	1.92146i
$783$	−11.3327	−	11.5997i	−0.404996	−	0.414539i
$784$		−	1.77806i		−	0.0635021i
$785$	−14.7723	−	17.4550i	−0.527246	−	0.622995i
$786$	−60.0494	−	39.8299i	−2.14189	−	1.42068i
$787$	−27.1112	−	12.6422i	−0.966410	−	0.450644i	−0.125663	−	0.992073i	$-0.540106\pi$
$787$	−27.1112	−	12.6422i	−0.966410	−	0.450644i	−0.840747	+	0.541429i	$0.817884\pi$
$788$	5.25489	+	60.0637i	0.187198	+	2.13968i
$789$	14.1853	−	1.60224i	0.505011	−	0.0570414i
$790$	−61.4062	+	11.0947i	−2.18473	+	0.394731i
$791$	−45.6301	+	26.3445i	−1.62242	+	0.936704i
$792$	−55.1299	−	11.8303i	−1.95895	−	0.420372i
$793$	−5.83572	−	21.7792i	−0.207232	−	0.773402i
$794$	54.7764	−	45.9629i	1.94394	−	1.63116i
$795$	−9.04089	+	16.7808i	−0.320647	+	0.595154i
$796$	9.61833	−	54.5483i	0.340913	−	1.93341i
$797$	−14.2699	−	20.3795i	−0.505466	−	0.721880i	0.482612	−	0.875834i	$-0.339688\pi$
$797$	−14.2699	−	20.3795i	−0.505466	−	0.721880i	−0.988078	+	0.153954i	$0.950799\pi$
$798$	−39.5549	+	0.997295i	−1.40023	+	0.0353038i
$799$	−26.9669	−	32.1379i	−0.954020	−	1.13696i
$800$	−3.96138	+	15.2989i	−0.140056	+	0.540898i
$801$	−2.92066	+	23.4104i	−0.103196	+	0.827166i
$802$	−18.3319	+	68.4155i	−0.647321	+	2.41584i
$803$	0.0355835	+	0.0763090i	0.00125571	+	0.00269289i
$804$	−2.30586	+	1.70278i	−0.0813215	+	0.0600525i
$805$	−17.3276	−	24.5257i	−0.610719	−	0.864418i
$806$	0.994384	+	2.73205i	0.0350257	+	0.0962323i
$807$	11.7813	−	35.0971i	0.414720	−	1.23548i
$808$	5.60438	+	3.92423i	0.197161	+	0.138054i
$809$	−27.7036			−0.974006			−0.487003	−	0.873400i	$-0.661910\pi$
$809$	−27.7036			−0.974006			−0.487003	+	0.873400i	$0.661910\pi$
$810$	−13.9317	−	48.5258i	−0.489510	−	1.70502i
$811$	−16.0245			−0.562695			−0.281347	−	0.959606i	$-0.590781\pi$
$811$	−16.0245			−0.562695			−0.281347	+	0.959606i	$0.590781\pi$
$812$	29.6644	+	20.7712i	1.04102	+	0.728927i
$813$	−8.82242	+	26.2825i	−0.309416	+	0.921767i
$814$	12.4237	+	34.1339i	0.435451	+	1.19639i
$815$	4.93540	−	28.6970i	0.172880	−	1.00521i
$816$	−49.6591	+	36.6711i	−1.73841	+	1.28375i
$817$	−6.32213	−	13.5578i	−0.221183	−	0.474329i
$818$	−12.9720	+	48.4121i	−0.453555	+	1.69269i
$819$	−23.5037	+	9.92282i	−0.821285	+	0.346731i
$820$	−52.2398	−	51.8011i	−1.82429	−	1.80897i
$821$	−36.5832	−	43.5982i	−1.27676	−	1.52159i	−0.727920	−	0.685663i	$-0.759513\pi$
$821$	−36.5832	−	43.5982i	−1.27676	−	1.52159i	−0.548844	−	0.835925i	$-0.684932\pi$
$822$	−87.0828	+	2.19561i	−3.03736	+	0.0765808i
$823$	30.0764	+	42.9536i	1.04840	+	1.49727i	0.856700	+	0.515815i	$0.172511\pi$
$823$	30.0764	+	42.9536i	1.04840	+	1.49727i	0.191699	+	0.981454i	$0.438600\pi$
$824$	−0.187958	+	1.06596i	−0.00654781	+	0.0371345i
$825$	0.951494	+	28.2744i	0.0331268	+	0.984388i
$826$	39.8049	−	33.4002i	1.38499	−	1.16214i
$827$	−5.56271	−	20.7603i	−0.193434	−	0.721907i	−0.992667	−	0.120885i	$-0.961427\pi$
$827$	−5.56271	−	20.7603i	−0.193434	−	0.721907i	0.799232	−	0.601023i	$-0.205240\pi$
$828$	−42.9191	+	47.4805i	−1.49154	+	1.65006i
$829$	−27.5695	+	15.9172i	−0.957527	+	0.552828i	−0.895411	−	0.445241i	$-0.853118\pi$
$829$	−27.5695	+	15.9172i	−0.957527	+	0.552828i	−0.0621158	+	0.998069i	$0.519785\pi$
$830$	3.50003	−	5.04369i	0.121488	−	0.175069i
$831$	24.7380	−	2.79418i	0.858152	−	0.0969290i
$832$	1.03240	+	11.8003i	0.0357919	+	0.409103i
$833$	−1.68009	−	0.783438i	−0.0582116	−	0.0271445i
$834$	64.3619	+	42.6903i	2.22867	+	1.47824i
$835$	−8.22944	+	6.96465i	−0.284792	+	0.241022i
$836$		−	47.2568i		−	1.63441i
$837$	−1.11588	+	1.55479i	−0.0385704	+	0.0537415i
$838$	12.9511	−	12.9511i	0.447390	−	0.447390i
$839$	5.41257	+	30.6962i	0.186863	+	1.05975i	0.923539	+	0.383505i	$0.125283\pi$
$839$	5.41257	+	30.6962i	0.186863	+	1.05975i	−0.736676	+	0.676246i	$0.763606\pi$
$840$	27.0460	+	53.8082i	0.933177	+	1.85656i
$841$	18.0984	−	6.58729i	0.624084	−	0.227148i
$842$	−72.7991	+	6.36910i	−2.50882	+	0.219494i
$843$	−17.1943	+	6.75371i	−0.592203	+	0.232610i
$844$	0.188452	−	0.517767i	0.00648677	−	0.0178223i
$845$	1.82150	+	6.68508i	0.0626617	+	0.229974i
$846$	35.2514	+	37.9502i	1.21197	+	1.30475i
$847$	−0.858109	+	0.229930i	−0.0294850	+	0.00790047i
$848$	−28.6662	−	2.50796i	−0.984400	−	0.0861239i
$849$	40.8753	−	12.0646i	1.40284	−	0.414056i
$850$	58.9853	+	48.6529i	2.02318	+	1.66878i
$851$	21.6908	+	3.82467i	0.743550	+	0.131108i
$852$	−63.8155	−	34.7294i	−2.18628	−	1.18981i
$853$	3.05541	−	34.9235i	0.104615	−	1.19576i	−0.744526	−	0.667593i	$-0.767325\pi$
$853$	3.05541	−	34.9235i	0.104615	−	1.19576i	0.849142	−	0.528165i	$-0.177120\pi$
$854$	−24.2912	+	42.0736i	−0.831228	+	1.43973i
$855$	19.9326	−	10.6565i	0.681681	−	0.364445i
$856$	−7.18905	−	12.4518i	−0.245717	−	0.425594i
$857$	−50.5751	+	23.5835i	−1.72761	+	0.805599i	−0.735904	+	0.677086i	$0.763242\pi$
$857$	−50.5751	+	23.5835i	−1.72761	+	0.805599i	−0.991708	+	0.128512i	$0.958980\pi$
$858$	−16.3291	−	41.5723i	−0.557467	−	1.41926i
$859$	18.4923	−	22.0383i	0.630949	−	0.751936i	−0.351962	−	0.936014i	$-0.614486\pi$
$859$	18.4923	−	22.0383i	0.630949	−	0.751936i	0.982912	+	0.184078i	$0.0589300\pi$
$860$	−27.2604	+	32.7673i	−0.929573	+	1.11736i
$861$	−35.8022	−	2.22470i	−1.22013	−	0.0758175i
$862$	20.6328	−	29.4666i	0.702754	−	1.00364i
$863$	−20.3595	−	20.3595i	−0.693044	−	0.693044i	0.269856	−	0.962901i	$-0.413024\pi$
$863$	−20.3595	−	20.3595i	−0.693044	−	0.693044i	−0.962901	+	0.269856i	$0.913024\pi$
$864$	12.7031	−	10.4096i	0.432169	−	0.354141i
$865$	−12.4547	+	7.26092i	−0.423473	+	0.246879i
$866$	56.9181	−	10.0362i	1.93416	−	0.341044i
$867$	6.92775	+	34.2213i	0.235279	+	1.16221i
$868$	1.80613	−	3.87326i	0.0613040	−	0.131467i
$869$	−27.8369	−	23.3579i	−0.944301	−	0.792363i
$870$	−30.0042	−	4.38471i	−1.01724	−	0.148656i
$871$	−1.13975	−	0.414834i	−0.0386189	−	0.0140561i
$872$	43.3897	+	11.6262i	1.46936	+	0.393714i
$873$	11.4103	+	10.3142i	0.386181	+	0.349082i
$874$	−36.3748	−	21.0010i	−1.23040	−	0.710370i
$875$	22.8994	−	19.7137i	0.774141	−	0.666446i
$876$	−0.186332	−	0.0449261i	−0.00629559	−	0.00151791i
$877$	34.6324	−	24.2499i	1.16945	−	0.818860i	0.183034	−	0.983107i	$-0.441408\pi$
$877$	34.6324	−	24.2499i	1.16945	−	0.818860i	0.986419	+	0.164247i	$0.0525193\pi$
$878$	38.2149	−	26.7583i	1.28969	−	0.903050i
$879$	28.6504	−	30.1325i	0.966355	−	1.01634i
$880$	−38.6304	+	18.2123i	−1.30223	+	0.613937i
$881$	17.8875	+	10.3273i	0.602644	+	0.347936i	0.770081	−	0.637946i	$-0.220216\pi$
$881$	17.8875	+	10.3273i	0.602644	+	0.347936i	−0.167437	+	0.985883i	$0.553549\pi$
$882$	2.12040	+	0.861496i	0.0713975	+	0.0290081i
$883$	18.3993	+	4.93007i	0.619185	+	0.165910i	0.554757	−	0.832012i	$-0.312811\pi$
$883$	18.3993	+	4.93007i	0.619185	+	0.165910i	0.0644275	+	0.997922i	$0.479478\pi$
$884$	−77.3870	−	28.1666i	−2.60281	−	0.947344i
$885$	−11.7475	+	27.2588i	−0.394888	+	0.916296i
$886$	52.3180	+	43.9000i	1.75766	+	1.47485i
$887$	15.4260	−	33.0811i	0.517954	−	1.11076i	−0.457228	−	0.889350i	$-0.651158\pi$
$887$	15.4260	−	33.0811i	0.517954	−	1.11076i	0.975182	−	0.221406i	$-0.0710646\pi$
$888$	−41.8751	−	14.0565i	−1.40524	−	0.471705i
$889$	56.8345	−	10.0215i	1.90617	−	0.336109i
$890$	22.2176	+	38.1100i	0.744735	+	1.27745i
$891$	16.5351	−	24.3098i	0.553946	−	0.814408i
$892$	−25.4323	−	25.4323i	−0.851538	−	0.851538i
$893$	−13.3007	+	18.9954i	−0.445092	+	0.635657i
$894$	1.64460	+	3.30660i	0.0550035	+	0.110589i
$895$	0.534758	+	5.82916i	0.0178750	+	0.194847i
$896$	27.3874	−	32.6390i	0.914947	−	1.09039i
$897$	−26.7808	−	4.02905i	−0.894186	−	0.134526i
$898$	69.9640	−	32.6248i	2.33473	−	1.08870i
$899$	0.574727	+	0.995457i	0.0191682	+	0.0332003i
$900$	−51.6838	−	38.4235i	−1.72279	−	1.28078i
$901$	−15.0005	+	25.9816i	−0.499739	+	0.865574i
$902$	5.47332	−	62.5603i	0.182242	−	2.08303i
$903$	0.523836	+	20.7765i	0.0174322	+	0.691398i
$904$	110.464	+	19.4778i	3.67399	+	0.647823i
$905$	−36.1960	−	16.6930i	−1.20319	−	0.554896i
$906$	15.0759	−	62.5279i	0.500865	−	2.07735i
$907$	36.0031	+	3.14986i	1.19546	+	0.104589i	0.667455	−	0.744650i	$-0.267384\pi$
$907$	36.0031	+	3.14986i	1.19546	+	0.104589i	0.528008	+	0.849240i	$0.322939\pi$
$908$	14.9702	−	4.01124i	0.496802	−	0.133118i
$909$	−2.99564	+	1.93712i	−0.0993591	+	0.0642502i
$910$	−23.6779	+	41.4136i	−0.784915	+	1.37285i
$911$	−1.01321	+	2.78377i	−0.0335691	+	0.0922304i	−0.955345	−	0.295493i	$-0.904516\pi$
$911$	−1.01321	+	2.78377i	−0.0335691	+	0.0922304i	0.921776	+	0.387723i	$0.126738\pi$
$912$	26.6831	+	21.2671i	0.883566	+	0.704224i
$913$	3.56148	−	0.311589i	0.117868	−	0.0103121i
$914$	55.2056	−	20.0932i	1.82604	−	0.664623i
$915$	1.60437	−	27.7057i	0.0530389	−	0.915923i
$916$	−0.924588	−	5.24360i	−0.0305492	−	0.173253i
$917$	−31.6917	+	31.6917i	−1.04655	+	1.04655i
$918$	−19.6710	−	76.9879i	−0.649240	−	2.54098i
$919$		−	31.4414i		−	1.03716i	−0.855030	−	0.518578i	$-0.826462\pi$
$919$		−	31.4414i		−	1.03716i	0.855030	−	0.518578i	$-0.173538\pi$
$920$	−5.30320	+	63.7082i	−0.174841	+	2.10040i
$921$	−0.436853	+	7.03029i	−0.0143948	+	0.231656i
$922$	71.8138	+	33.4873i	2.36506	+	1.10285i
$923$	−2.67938	−	30.6254i	−0.0881927	−	1.00805i
$924$	−26.2379	+	60.1829i	−0.863162	+	1.97987i
$925$	−1.74536	+	22.0936i	−0.0573869	+	0.726432i
$926$	63.7180	−	36.7876i	2.09390	−	1.20892i
$927$	−0.478045	−	0.300010i	−0.0157011	−	0.00985362i
$928$	−2.55305	−	9.52810i	−0.0838079	−	0.312775i
$929$	−35.9403	+	30.1575i	−1.17916	+	0.989435i	−0.179178	+	0.983817i	$0.557344\pi$
$929$	−35.9403	+	30.1575i	−1.17916	+	0.989435i	−0.999984	+	0.00561833i	$0.998212\pi$
$930$	0.105277	+	3.57695i	0.00345217	+	0.117293i
$931$	−0.177929	+	1.00909i	−0.00583140	+	0.0330715i
$932$	−51.1490	−	73.0484i	−1.67544	−	2.39278i
$933$	−8.39354	+	15.4232i	−0.274792	+	0.504933i
$934$	−33.4073	−	39.8133i	−1.09312	−	1.30273i
$935$	0.187721	+	44.5265i	0.00613914	+	1.45617i
$936$	51.9085	+	15.9805i	1.69668	+	0.522338i
$937$	−12.2770	+	45.8184i	−0.401072	+	1.49682i	0.410114	+	0.912034i	$0.365489\pi$
$937$	−12.2770	+	45.8184i	−0.401072	+	1.49682i	−0.811186	+	0.584788i	$0.801178\pi$
$938$	1.10446	+	2.36853i	0.0360620	+	0.0773353i
$939$	46.8063	+	20.4061i	1.52747	+	0.665927i
$940$	65.1173	+	11.1991i	2.12389	+	0.365274i
$941$	3.46508	+	9.52023i	0.112958	+	0.310351i	0.983271	−	0.182149i	$-0.0583054\pi$
$941$	3.46508	+	9.52023i	0.112958	+	0.310351i	−0.870313	+	0.492500i	$0.836083\pi$
$942$	29.4113	+	33.3087i	0.958274	+	1.08526i
$943$	−31.1920	−	21.8409i	−1.01575	−	0.711236i
$944$	−44.8097			−1.45843
$945$	−31.3015	+	2.50439i	−1.01824	+	0.0814680i
$946$	−36.3847			−1.18297
$947$	23.0787	+	16.1599i	0.749958	+	0.525126i	0.884930	−	0.465723i	$-0.154206\pi$
$947$	23.0787	+	16.1599i	0.749958	+	0.525126i	−0.134973	+	0.990849i	$0.543095\pi$
$948$	81.0780	−	16.4134i	2.63329	−	0.533083i
$949$	−0.0277390	−	0.0762122i	−0.000900445	−	0.00247395i
$950$	17.5376	−	38.4528i	0.568996	−	1.24757i
$951$	−0.607773	−	5.38087i	−0.0197084	−	0.174487i
$952$	40.0584	+	85.9056i	1.29830	+	2.78422i
$953$	0.0393504	−	0.146858i	0.00127468	−	0.00475719i	−0.965286	−	0.261197i	$-0.915883\pi$
$953$	0.0393504	−	0.146858i	0.00127468	−	0.00475719i	0.966560	+	0.256440i	$0.0825495\pi$
$954$	16.8800	−	32.9703i	0.546511	−	1.06745i
$955$	13.8164	−	13.9334i	0.447087	−	0.450873i
$956$	−33.4013	−	39.8061i	−1.08027	−	1.28742i
$957$	−9.21181	−	15.0652i	−0.297776	−	0.486988i
$958$	11.0079	+	15.7210i	0.355651	+	0.507922i
$959$	−9.40847	+	53.3581i	−0.303815	+	1.72302i
$960$	−3.35756	+	14.1878i	−0.108365	+	0.457910i
$961$	−23.6435	+	19.8392i	−0.762692	+	0.639975i
$962$	−9.05596	−	33.7973i	−0.291976	−	1.08967i
$963$	7.42609	−	1.02895i	0.239302	−	0.0331573i
$964$	25.5209	−	14.7345i	0.821972	−	0.474566i
$965$	0.486897	+	2.69484i	0.0156738	+	0.0867501i
$966$	34.6642	+	46.9414i	1.11530	+	1.51031i
$967$	−3.42592	−	39.1584i	−0.110170	−	1.25925i	−0.827080	−	0.562084i	$-0.810000\pi$
$967$	−3.42592	−	39.1584i	−0.110170	−	1.25925i	0.716910	−	0.697165i	$-0.245556\pi$
$968$	1.71405	+	0.799275i	0.0550917	+	0.0256897i
$969$	31.8522	−	15.8423i	1.02324	−	0.508928i
$970$	28.6613	+	2.38582i	0.920258	+	0.0766041i
$971$			16.2895i			0.522755i	0.965237	+	0.261378i	$0.0841768\pi$
$971$			16.2895i			0.522755i	−0.965237	+	0.261378i	$0.915823\pi$
$972$	19.8151	+	63.9277i	0.635571	+	2.05048i
$973$	33.9677	−	33.9677i	1.08895	−	1.08895i
$974$	5.48855	+	31.1271i	0.175864	+	0.997376i
$975$	1.46067	−	27.2115i	0.0467790	−	0.871467i
$976$	39.3691	−	14.3292i	1.26017	−	0.458665i
$977$	44.6375	−	3.90528i	1.42808	−	0.124941i	0.653266	−	0.757129i	$-0.273398\pi$
$977$	44.6375	−	3.90528i	1.42808	−	0.124941i	0.774815	+	0.632188i	$0.217843\pi$
$978$	−8.41791	+	55.9533i	−0.269175	+	1.78919i
$979$	−8.78621	+	24.1399i	−0.280809	+	0.771515i
$980$	2.81688	−	0.767523i	0.0899819	−	0.0245176i
$981$	−14.1323	+	18.6785i	−0.451209	+	0.596358i
$982$	8.68793	−	2.32792i	0.277243	−	0.0742871i
$983$	−1.65951	−	0.145188i	−0.0529300	−	0.00463078i	0.0606600	−	0.998158i	$-0.480679\pi$
$983$	−1.65951	−	0.145188i	−0.0529300	−	0.00463078i	−0.113590	+	0.993528i	$0.536235\pi$
$984$	55.3422	+	52.6202i	1.76425	+	1.67747i
$985$	−29.4620	+	10.8642i	−0.938736	+	0.346161i
$986$	−47.0008	−	8.28751i	−1.49681	−	0.263928i
$987$	27.4855	−	16.8064i	0.874872	−	0.534953i
$988$	−3.96733	+	45.3468i	−0.126218	+	1.44267i
$989$	−11.0309	+	19.1061i	−0.350763	+	0.607540i
$990$	−3.00181	−	54.8922i	−0.0954038	−	1.74459i
$991$	20.3962	+	35.3273i	0.647908	+	1.12221i	0.983622	+	0.180246i	$0.0576892\pi$
$991$	20.3962	+	35.3273i	0.647908	+	1.12221i	−0.335714	+	0.941964i	$0.608977\pi$
$992$	−1.05504	+	0.491973i	−0.0334975	+	0.0156201i
$993$	31.6830	−	39.7517i	1.00543	−	1.26148i
$994$	−42.5781	+	50.7425i	−1.35049	+	1.60946i
$995$	28.7269	−	2.63536i	0.910703	−	0.0835465i
$996$	−4.49854	+	6.78222i	−0.142542	+	0.214903i
$997$	−32.5879	+	46.5404i	−1.03207	+	1.47395i	−0.158432	+	0.987370i	$0.550644\pi$
$997$	−32.5879	+	46.5404i	−1.03207	+	1.47395i	−0.873637	+	0.486578i	$0.838245\pi$
$998$	−1.11990	−	1.11990i	−0.0354498	−	0.0354498i
$999$	15.0090	−	17.4699i	0.474864	−	0.552722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.16	yes	192
3.2	odd	2		405.2.r.a.152.1		192
5.2	odd	4		675.2.ba.b.68.1		192
5.3	odd	4	inner	135.2.q.a.68.16	yes	192
5.4	even	2		675.2.ba.b.257.1		192
15.8	even	4		405.2.r.a.233.1		192
27.2	odd	18	inner	135.2.q.a.2.16	✓	192
27.25	even	9		405.2.r.a.332.1		192
135.2	even	36		675.2.ba.b.218.1		192
135.29	odd	18		675.2.ba.b.407.1		192
135.83	even	36	inner	135.2.q.a.83.16	yes	192
135.133	odd	36		405.2.r.a.8.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.16	✓	192	27.2	odd	18	inner
135.2.q.a.68.16	yes	192	5.3	odd	4	inner
135.2.q.a.83.16	yes	192	135.83	even	36	inner
135.2.q.a.122.16	yes	192	1.1	even	1	trivial
405.2.r.a.8.1		192	135.133	odd	36
405.2.r.a.152.1		192	3.2	odd	2
405.2.r.a.233.1		192	15.8	even	4
405.2.r.a.332.1		192	27.25	even	9
675.2.ba.b.68.1		192	5.2	odd	4
675.2.ba.b.218.1		192	135.2	even	36
675.2.ba.b.257.1		192	5.4	even	2
675.2.ba.b.407.1		192	135.29	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05499 + 1.43892i) q^{2} +(0.551185 - 1.64201i) q^{3} +(1.46845 + 4.03452i) q^{4} +(-1.82626 + 1.29027i) q^{5} +(3.49539 - 2.58120i) q^{6} +(-1.14217 - 2.44940i) q^{7} +(-1.48912 + 5.55747i) q^{8} +(-2.39239 - 1.81010i) q^{9} +O(q^{10})\)	\(q+(2.05499 + 1.43892i) q^{2} +(0.551185 - 1.64201i) q^{3} +(1.46845 + 4.03452i) q^{4} +(-1.82626 + 1.29027i) q^{5} +(3.49539 - 2.58120i) q^{6} +(-1.14217 - 2.44940i) q^{7} +(-1.48912 + 5.55747i) q^{8} +(-2.39239 - 1.81010i) q^{9} +(-5.60952 + 0.0236494i) q^{10} +(-2.09979 - 2.50243i) q^{11} +(7.43411 - 0.187436i) q^{12} +(1.80484 + 2.57758i) q^{13} +(1.17733 - 6.67697i) q^{14} +(1.11203 + 3.70991i) q^{15} +(-4.47891 + 3.75825i) q^{16} +(1.57770 + 5.88806i) q^{17} +(-2.31175 - 7.16218i) q^{18} +(2.91796 - 1.68469i) q^{19} +(-7.88737 - 5.47338i) q^{20} +(-4.65148 + 0.525389i) q^{21} +(-0.714248 - 8.16389i) q^{22} +(-4.50352 - 2.10003i) q^{23} +(8.30464 + 5.50834i) q^{24} +(1.67042 - 4.71272i) q^{25} +7.89390i q^{26} +(-4.29085 + 2.93063i) q^{27} +(8.20493 - 8.20493i) q^{28} +(0.541940 + 3.07349i) q^{29} +(-3.05305 + 9.22392i) q^{30} +(0.346096 - 0.125969i) q^{31} +(-3.14866 + 0.275472i) q^{32} +(-5.26639 + 2.06857i) q^{33} +(-5.23028 + 14.3701i) q^{34} +(5.24628 + 2.99952i) q^{35} +(3.78979 - 12.3102i) q^{36} +(-4.28145 + 1.14721i) q^{37} +(8.42050 + 0.736698i) q^{38} +(5.22721 - 1.54284i) q^{39} +(-4.45110 - 12.0707i) q^{40} +(7.54663 + 1.33068i) q^{41} +(-10.3147 - 5.61343i) q^{42} +(0.386956 - 4.42293i) q^{43} +(7.01269 - 12.1463i) q^{44} +(6.70463 + 0.218885i) q^{45} +(-6.23291 - 10.7957i) q^{46} +(-6.23750 + 2.90859i) q^{47} +(3.70238 + 9.42590i) q^{48} +(-0.195477 + 0.232960i) q^{49} +(10.2139 - 7.28096i) q^{50} +(10.5379 + 0.654808i) q^{51} +(-7.74898 + 11.0667i) q^{52} +(3.48010 + 3.48010i) q^{53} +(-13.0346 - 0.151776i) q^{54} +(7.06356 + 1.86079i) q^{55} +(15.3133 - 2.70014i) q^{56} +(-1.15794 - 5.71990i) q^{57} +(-3.30882 + 7.09579i) q^{58} +(5.87095 + 4.92631i) q^{59} +(-13.3347 + 9.93429i) q^{60} +(-6.73344 - 2.45077i) q^{61} +(0.892481 + 0.239140i) q^{62} +(-1.70113 + 7.92737i) q^{63} +(3.26012 + 1.88223i) q^{64} +(-6.62186 - 2.37859i) q^{65} +(-13.7989 - 3.32701i) q^{66} +(-0.315748 + 0.221089i) q^{67} +(-21.4388 + 15.0116i) q^{68} +(-5.93054 + 6.23732i) q^{69} +(6.46497 + 13.7129i) q^{70} +(-8.46099 - 4.88495i) q^{71} +(13.6221 - 10.6002i) q^{72} +(-0.0248963 - 0.00667095i) q^{73} +(-10.4491 - 3.80315i) q^{74} +(-6.81761 - 5.34043i) q^{75} +(11.0818 + 9.29871i) q^{76} +(-3.73113 + 8.00143i) q^{77} +(12.9619 + 4.35099i) q^{78} +(10.9549 - 1.93165i) q^{79} +(3.33049 - 12.6425i) q^{80} +(2.44707 + 8.66094i) q^{81} +(13.5935 + 13.5935i) q^{82} +(-0.627725 + 0.896484i) q^{83} +(-8.95014 - 17.9950i) q^{84} +(-10.4785 - 8.71746i) q^{85} +(7.15941 - 8.53226i) q^{86} +(5.34541 + 0.804192i) q^{87} +(17.0340 - 7.94310i) q^{88} +(-3.93198 - 6.81039i) q^{89} +(13.4630 + 10.0972i) q^{90} +(4.25207 - 7.36481i) q^{91} +(1.85943 - 21.2533i) q^{92} +(-0.0160789 - 0.637725i) q^{93} +(-17.0032 - 2.99812i) q^{94} +(-3.15525 + 6.84162i) q^{95} +(-1.28317 + 5.32197i) q^{96} +(-5.10752 - 0.446850i) q^{97} +(-0.736913 + 0.197455i) q^{98} +(0.493864 + 9.78763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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