LMFDB - Embedded newform 135.2.q.a.113.7

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			113.7
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.639298 - 0.0559313i) q^{2} +(1.67717 + 0.432570i) q^{3} +(-1.56404 - 0.275783i) q^{4} +(-1.26232 + 1.84568i) q^{5} +(-1.04801 - 0.370347i) q^{6} +(3.52875 + 2.47086i) q^{7} +(2.22421 + 0.595975i) q^{8} +(2.62577 + 1.45098i) q^{9} +O(q^{10})$	\(q+(-0.639298 - 0.0559313i) q^{2} +(1.67717 + 0.432570i) q^{3} +(-1.56404 - 0.275783i) q^{4} +(-1.26232 + 1.84568i) q^{5} +(-1.04801 - 0.370347i) q^{6} +(3.52875 + 2.47086i) q^{7} +(2.22421 + 0.595975i) q^{8} +(2.62577 + 1.45098i) q^{9} +(0.910229 - 1.10934i) q^{10} +(-0.157893 + 0.433806i) q^{11} +(-2.50386 - 1.13909i) q^{12} +(-0.462462 - 5.28596i) q^{13} +(-2.11772 - 1.77698i) q^{14} +(-2.91551 + 2.54948i) q^{15} +(1.59619 + 0.580964i) q^{16} +(-4.93057 + 1.32114i) q^{17} +(-1.59749 - 1.07447i) q^{18} +(1.03667 - 0.598524i) q^{19} +(2.48333 - 2.53860i) q^{20} +(4.84948 + 5.67047i) q^{21} +(0.125204 - 0.268500i) q^{22} +(-1.57814 - 2.25381i) q^{23} +(3.47256 + 1.96168i) q^{24} +(-1.81310 - 4.65968i) q^{25} +3.40517i q^{26} +(3.77619 + 3.56937i) q^{27} +(-4.83770 - 4.83770i) q^{28} +(-0.00462297 + 0.00387914i) q^{29} +(2.00647 - 1.46681i) q^{30} +(-0.387533 + 2.19781i) q^{31} +(-5.16180 - 2.40699i) q^{32} +(-0.452464 + 0.659265i) q^{33} +(3.22599 - 0.568830i) q^{34} +(-9.01483 + 3.39395i) q^{35} +(-3.70665 - 2.99354i) q^{36} +(-1.94341 - 7.25290i) q^{37} +(-0.696220 + 0.324653i) q^{38} +(1.51093 - 9.06548i) q^{39} +(-3.90764 + 3.35288i) q^{40} +(3.02828 - 3.60897i) q^{41} +(-2.78310 - 3.89636i) q^{42} +(0.806157 + 1.72881i) q^{43} +(0.366587 - 0.634947i) q^{44} +(-5.99261 + 3.01473i) q^{45} +(0.882840 + 1.52912i) q^{46} +(6.47343 - 9.24502i) q^{47} +(2.42576 + 1.66484i) q^{48} +(3.95281 + 10.8602i) q^{49} +(0.898490 + 3.08033i) q^{50} +(-8.84086 + 0.0829548i) q^{51} +(-0.734468 + 8.39501i) q^{52} +(3.94023 - 3.94023i) q^{53} +(-2.21447 - 2.49310i) q^{54} +(-0.601359 - 0.839022i) q^{55} +(6.37611 + 7.59875i) q^{56} +(1.99758 - 0.555389i) q^{57} +(0.00317242 - 0.00222135i) q^{58} +(-0.388624 + 0.141448i) q^{59} +(5.26308 - 3.18344i) q^{60} +(0.399307 + 2.26458i) q^{61} +(0.370675 - 1.38338i) q^{62} +(5.68050 + 11.6081i) q^{63} +(0.223194 + 0.128861i) q^{64} +(10.3400 + 5.81901i) q^{65} +(0.326133 - 0.396160i) q^{66} +(-5.84619 + 0.511475i) q^{67} +(8.07597 - 0.706556i) q^{68} +(-1.67186 - 4.46267i) q^{69} +(5.95299 - 1.66553i) q^{70} +(0.648656 + 0.374502i) q^{71} +(4.97550 + 4.79218i) q^{72} +(-2.97508 + 11.1032i) q^{73} +(0.836752 + 4.74546i) q^{74} +(-1.02523 - 8.59935i) q^{75} +(-1.78647 + 0.650220i) q^{76} +(-1.62904 + 1.14066i) q^{77} +(-1.47297 + 5.71103i) q^{78} +(-1.01095 - 1.20481i) q^{79} +(-3.08717 + 2.21269i) q^{80} +(4.78929 + 7.61989i) q^{81} +(-2.13783 + 2.13783i) q^{82} +(0.930629 - 10.6371i) q^{83} +(-6.02097 - 10.2063i) q^{84} +(3.78554 - 10.7680i) q^{85} +(-0.418680 - 1.15031i) q^{86} +(-0.00943149 + 0.00450619i) q^{87} +(-0.609724 + 0.870776i) q^{88} +(6.36010 + 11.0160i) q^{89} +(3.99968 - 1.59214i) q^{90} +(11.4289 - 19.7955i) q^{91} +(1.84671 + 3.96028i) q^{92} +(-1.60066 + 3.51845i) q^{93} +(-4.65554 + 5.54825i) q^{94} +(-0.203927 + 2.66890i) q^{95} +(-7.61600 - 6.26976i) q^{96} +(-7.76434 + 3.62057i) q^{97} +(-1.91959 - 7.16401i) q^{98} +(-1.04404 + 0.909974i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.639298	−	0.0559313i	−0.452052	−	0.0395494i	−0.141143	−	0.989989i	$-0.545078\pi$
$2$	−0.639298	−	0.0559313i	−0.452052	−	0.0395494i	−0.310909	+	0.950440i	$0.600633\pi$
$3$	1.67717	+	0.432570i	0.968312	+	0.249745i
$3$	1.67717	+	0.432570i	0.968312	+	0.249745i
$4$	−1.56404	−	0.275783i	−0.782021	−	0.137891i
$5$	−1.26232	+	1.84568i	−0.564526	+	0.825415i
$5$	−1.26232	+	1.84568i	−0.564526	+	0.825415i
$6$	−1.04801	−	0.370347i	−0.427850	−	0.151194i
$7$	3.52875	+	2.47086i	1.33374	+	0.933897i	0.999962	−	0.00875387i	$-0.00278648\pi$
$7$	3.52875	+	2.47086i	1.33374	+	0.933897i	0.333781	+	0.942651i	$0.391675\pi$
$8$	2.22421	+	0.595975i	0.786377	+	0.210709i
$9$	2.62577	+	1.45098i	0.875255	+	0.483661i
$10$	0.910229	−	1.10934i	0.287840	−	0.350804i
$11$	−0.157893	+	0.433806i	−0.0476064	+	0.130798i	−0.961217	−	0.275792i	$-0.911060\pi$
$11$	−0.157893	+	0.433806i	−0.0476064	+	0.130798i	0.913611	+	0.406590i	$0.133282\pi$
$12$	−2.50386	−	1.13909i	−0.722803	−	0.328828i
$13$	−0.462462	−	5.28596i	−0.128264	−	1.46606i	−0.738720	−	0.674012i	$-0.764570\pi$
$13$	−0.462462	−	5.28596i	−0.128264	−	1.46606i	0.610457	−	0.792050i	$-0.290986\pi$
$14$	−2.11772	−	1.77698i	−0.565986	−	0.474918i
$15$	−2.91551	+	2.54948i	−0.752780	+	0.658272i
$16$	1.59619	+	0.580964i	0.399047	+	0.145241i
$17$	−4.93057	+	1.32114i	−1.19584	+	0.320424i	−0.801191	−	0.598409i	$-0.795800\pi$
$17$	−4.93057	+	1.32114i	−1.19584	+	0.320424i	−0.394647	+	0.918833i	$0.629133\pi$
$18$	−1.59749	−	1.07447i	−0.376532	−	0.253256i
$19$	1.03667	−	0.598524i	0.237829	−	0.137311i	−0.376349	−	0.926478i	$-0.622821\pi$
$19$	1.03667	−	0.598524i	0.237829	−	0.137311i	0.614179	+	0.789167i	$0.289487\pi$
$20$	2.48333	−	2.53860i	0.555289	−	0.567649i
$21$	4.84948	+	5.67047i	1.05824	+	1.23740i
$22$	0.125204	−	0.268500i	0.0266935	−	0.0572444i
$23$	−1.57814	−	2.25381i	−0.329064	−	0.469952i	0.620195	−	0.784448i	$-0.287054\pi$
$23$	−1.57814	−	2.25381i	−0.329064	−	0.469952i	−0.949259	+	0.314496i	$0.898165\pi$
$24$	3.47256	+	1.96168i	0.708834	+	0.400425i
$25$	−1.81310	−	4.65968i	−0.362621	−	0.931937i
$26$			3.40517i			0.667808i
$27$	3.77619	+	3.56937i	0.726728	+	0.686925i
$28$	−4.83770	−	4.83770i	−0.914239	−	0.914239i
$29$	−0.00462297	+	0.00387914i	−0.000858465	+	0.000720337i	−0.643217	−	0.765684i	$-0.722401\pi$
$29$	−0.00462297	+	0.00387914i	−0.000858465	+	0.000720337i	0.642358	+	0.766404i	$0.277956\pi$
$30$	2.00647	−	1.46681i	0.366330	−	0.267801i
$31$	−0.387533	+	2.19781i	−0.0696030	+	0.394738i	0.930026	+	0.367494i	$0.119784\pi$
$31$	−0.387533	+	2.19781i	−0.0696030	+	0.394738i	−0.999629	+	0.0272441i	$0.991327\pi$
$32$	−5.16180	−	2.40699i	−0.912486	−	0.425499i
$33$	−0.452464	+	0.659265i	−0.0787638	+	0.114763i
$34$	3.22599	−	0.568830i	0.553253	−	0.0975535i
$35$	−9.01483	+	3.39395i	−1.52379	+	0.573683i
$36$	−3.70665	−	2.99354i	−0.617775	−	0.498924i
$37$	−1.94341	−	7.25290i	−0.319494	−	1.19237i	−0.919732	−	0.392547i	$-0.871594\pi$
$37$	−1.94341	−	7.25290i	−0.319494	−	1.19237i	0.600238	−	0.799822i	$-0.295073\pi$
$38$	−0.696220	+	0.324653i	−0.112942	+	0.0526656i
$39$	1.51093	−	9.06548i	0.241942	−	1.45164i
$40$	−3.90764	+	3.35288i	−0.617853	+	0.530137i
$41$	3.02828	−	3.60897i	0.472939	−	0.563626i	−0.475855	−	0.879524i	$-0.657861\pi$
$41$	3.02828	−	3.60897i	0.472939	−	0.563626i	0.948793	+	0.315898i	$0.102306\pi$
$42$	−2.78310	−	3.89636i	−0.429442	−	0.601221i
$43$	0.806157	+	1.72881i	0.122938	+	0.263641i	0.958139	−	0.286304i	$-0.0924266\pi$
$43$	0.806157	+	1.72881i	0.122938	+	0.263641i	−0.835201	+	0.549945i	$0.814649\pi$
$44$	0.366587	−	0.634947i	0.0552651	−	0.0957219i
$45$	−5.99261	+	3.01473i	−0.893326	+	0.449410i
$46$	0.882840	+	1.52912i	0.130168	+	0.225457i
$47$	6.47343	−	9.24502i	0.944247	−	1.34853i	0.00695690	−	0.999976i	$-0.497786\pi$
$47$	6.47343	−	9.24502i	0.944247	−	1.34853i	0.937290	−	0.348549i	$-0.113326\pi$
$48$	2.42576	+	1.66484i	0.350128	+	0.240298i
$49$	3.95281	+	10.8602i	0.564687	+	1.55146i
$50$	0.898490	+	3.08033i	0.127066	+	0.435625i
$51$	−8.84086	+	0.0829548i	−1.23797	+	0.0116160i
$52$	−0.734468	+	8.39501i	−0.101852	+	1.16418i
$53$	3.94023	−	3.94023i	0.541233	−	0.541233i	−0.382657	−	0.923890i	$-0.624991\pi$
$53$	3.94023	−	3.94023i	0.541233	−	0.541233i	0.923890	+	0.382657i	$0.124991\pi$
$54$	−2.21447	−	2.49310i	−0.301351	−	0.339267i
$55$	−0.601359	−	0.839022i	−0.0810872	−	0.113134i
$56$	6.37611	+	7.59875i	0.852044	+	1.01543i
$57$	1.99758	−	0.555389i	0.264586	−	0.0735631i
$58$	0.00317242	−	0.00222135i	0.000416559	−	0.000291678i
$59$	−0.388624	+	0.141448i	−0.0505945	+	0.0184149i	−0.367193	−	0.930145i	$-0.619681\pi$
$59$	−0.388624	+	0.141448i	−0.0505945	+	0.0184149i	0.316599	+	0.948559i	$0.397459\pi$
$60$	5.26308	−	3.18344i	0.679460	−	0.410981i
$61$	0.399307	+	2.26458i	0.0511260	+	0.289950i	0.999641	−	0.0267812i	$-0.00852575\pi$
$61$	0.399307	+	2.26458i	0.0511260	+	0.289950i	−0.948515	+	0.316731i	$0.897415\pi$
$62$	0.370675	−	1.38338i	0.0470758	−	0.175689i
$63$	5.68050	+	11.6081i	0.715676	+	1.46248i
$64$	0.223194	+	0.128861i	0.0278993	+	0.0161077i
$65$	10.3400	+	5.81901i	1.28252	+	0.721759i
$66$	0.326133	−	0.396160i	0.0401441	−	0.0487639i
$67$	−5.84619	+	0.511475i	−0.714226	+	0.0624866i	−0.438476	−	0.898743i	$-0.644482\pi$
$67$	−5.84619	+	0.511475i	−0.714226	+	0.0624866i	−0.275750	+	0.961230i	$0.588926\pi$
$68$	8.07597	−	0.706556i	0.979355	−	0.0856824i
$69$	−1.67186	−	4.46267i	−0.201269	−	0.537242i
$70$	5.95299	−	1.66553i	0.711518	−	0.199069i
$71$	0.648656	+	0.374502i	0.0769813	+	0.0444452i	0.537997	−	0.842947i	$-0.319181\pi$
$71$	0.648656	+	0.374502i	0.0769813	+	0.0444452i	−0.461015	+	0.887392i	$0.652515\pi$
$72$	4.97550	+	4.79218i	0.586368	+	0.564764i
$73$	−2.97508	+	11.1032i	−0.348207	+	1.29953i	0.540614	+	0.841271i	$0.318192\pi$
$73$	−2.97508	+	11.1032i	−0.348207	+	1.29953i	−0.888821	+	0.458255i	$0.848475\pi$
$74$	0.836752	+	4.74546i	0.0972705	+	0.551648i
$75$	−1.02523	−	8.59935i	−0.118384	−	0.992968i
$76$	−1.78647	+	0.650220i	−0.204922	+	0.0745854i
$77$	−1.62904	+	1.14066i	−0.185646	+	0.129991i
$78$	−1.47297	+	5.71103i	−0.166782	+	0.646647i
$79$	−1.01095	−	1.20481i	−0.113741	−	0.135551i	0.706170	−	0.708043i	$-0.250422\pi$
$79$	−1.01095	−	1.20481i	−0.113741	−	0.135551i	−0.819911	+	0.572491i	$0.805977\pi$
$80$	−3.08717	+	2.21269i	−0.345156	+	0.247387i
$81$	4.78929	+	7.61989i	0.532143	+	0.846654i
$82$	−2.13783	+	2.13783i	−0.236084	+	0.236084i
$83$	0.930629	−	10.6371i	0.102150	−	1.16758i	−0.756139	−	0.654411i	$-0.772917\pi$
$83$	0.930629	−	10.6371i	0.102150	−	1.16758i	0.858289	−	0.513167i	$-0.171528\pi$
$84$	−6.02097	−	10.2063i	−0.656942	−	1.11359i
$85$	3.78554	−	10.7680i	0.410599	−	1.16795i
$86$	−0.418680	−	1.15031i	−0.0451474	−	0.124041i
$87$	−0.00943149	+	0.00450619i	−0.00101116	+	0.000483114i
$88$	−0.609724	+	0.870776i	−0.0649968	+	0.0928250i
$89$	6.36010	+	11.0160i	0.674169	+	1.16770i	0.976711	+	0.214559i	$0.0688315\pi$
$89$	6.36010	+	11.0160i	0.674169	+	1.16770i	−0.302542	+	0.953136i	$0.597835\pi$
$90$	3.99968	−	1.59214i	0.421603	−	0.167826i
$91$	11.4289	−	19.7955i	1.19808	−	2.07513i
$92$	1.84671	+	3.96028i	0.192533	+	0.412888i
$93$	−1.60066	+	3.51845i	−0.165981	+	0.364847i
$94$	−4.65554	+	5.54825i	−0.480182	+	0.572259i
$95$	−0.203927	+	2.66890i	−0.0209224	+	0.273824i
$96$	−7.61600	−	6.26976i	−0.777305	−	0.639904i
$97$	−7.76434	+	3.62057i	−0.788349	+	0.367613i	−0.774729	−	0.632294i	$-0.782114\pi$
$97$	−7.76434	+	3.62057i	−0.788349	+	0.367613i	−0.0136208	+	0.999907i	$0.504336\pi$
$98$	−1.91959	−	7.16401i	−0.193908	−	0.723675i
$99$	−1.04404	+	0.909974i	−0.104929	+	0.0914558i
$100$	1.55071	+	7.78797i	0.155071	+	0.778797i
$101$	−15.4590	+	2.72585i	−1.53823	+	0.271232i	−0.877569	−	0.479450i	$-0.840836\pi$
$101$	−15.4590	+	2.72585i	−1.53823	+	0.271232i	−0.660663	+	0.750682i	$0.729725\pi$
$102$	5.65658	+	0.441448i	0.560085	+	0.0437099i
$103$	−12.6867	−	5.91592i	−1.25006	−	0.582912i	−0.318992	−	0.947758i	$-0.603344\pi$
$103$	−12.6867	−	5.91592i	−1.25006	−	0.582912i	−0.931068	+	0.364845i	$0.881122\pi$
$104$	2.12169	−	12.0327i	0.208049	−	1.17990i
$105$	−16.5875	+	1.79267i	−1.61877	+	0.174946i
$106$	−2.73936	+	2.29860i	−0.266071	+	0.223260i
$107$	2.86472	+	2.86472i	0.276943	+	0.276943i	0.831887	−	0.554945i	$-0.187261\pi$
$107$	2.86472	+	2.86472i	0.276943	+	0.276943i	−0.554945	+	0.831887i	$0.687261\pi$
$108$	−4.92175	−	6.62405i	−0.473596	−	0.637400i
$109$			6.64284i			0.636269i	0.948046	+	0.318134i	$0.103056\pi$
$109$			6.64284i			0.636269i	−0.948046	+	0.318134i	$0.896944\pi$
$110$	0.337520	+	0.570019i	0.0321812	+	0.0543492i
$111$	−0.122027	−	13.0050i	−0.0115823	−	1.23438i
$112$	4.19706	+	5.99403i	0.396585	+	0.566382i
$113$	−2.96857	+	6.36611i	−0.279259	+	0.598874i	−0.995043	−	0.0994488i	$-0.968292\pi$
$113$	−2.96857	+	6.36611i	−0.279259	+	0.598874i	0.715783	+	0.698322i	$0.246070\pi$
$114$	−1.30811	+	0.243332i	−0.122516	+	0.0227901i
$115$	6.15193	−	0.0677124i	0.573671	−	0.00631422i
$116$	0.00830033	−	0.00479220i	0.000770666	−	0.000444944i
$117$	6.45553	−	14.5507i	0.596814	−	1.34521i
$118$	0.256358	−	0.0686908i	0.0235996	−	0.00632350i
$119$	−20.6631	−	7.52076i	−1.89418	−	0.689427i
$120$	−8.00412	+	3.93300i	−0.730673	+	0.359032i
$121$	8.26323	+	6.93367i	0.751203	+	0.630334i
$122$	−0.128615	−	1.47008i	−0.0116443	−	0.133094i
$123$	6.64007	−	4.74289i	0.598715	−	0.427652i
$124$	1.21224	−	3.33059i	0.108862	−	0.299096i
$125$	10.8890	+	2.53559i	0.973944	+	0.226790i
$126$	−2.98227	−	7.73872i	−0.265682	−	0.689420i
$127$	8.09882	+	2.17007i	0.718654	+	0.192563i	0.599571	−	0.800322i	$-0.295338\pi$
$127$	8.09882	+	2.17007i	0.718654	+	0.192563i	0.119083	+	0.992884i	$0.462005\pi$
$128$	9.19534	+	6.43865i	0.812761	+	0.569102i
$129$	0.604227	+	3.24822i	0.0531992	+	0.285990i
$130$	−6.28487	−	4.29841i	−0.551219	−	0.376995i
$131$	−11.2646	−	1.98625i	−0.984193	−	0.173540i	−0.341682	−	0.939816i	$-0.610996\pi$
$131$	−11.2646	−	1.98625i	−0.984193	−	0.173540i	−0.642512	+	0.766276i	$0.722108\pi$
$132$	0.889487	−	0.906337i	0.0774199	−	0.0788865i
$133$	5.13704	+	0.449432i	0.445437	+	0.0389707i
$134$	3.76606			0.325338
$135$	−11.3547	+	2.46397i	−0.977256	+	0.212065i
$136$	−11.7540			−1.00790
$137$	10.2700	+	0.898508i	0.877424	+	0.0767647i	0.516961	−	0.856009i	$-0.327063\pi$
$137$	10.2700	+	0.898508i	0.877424	+	0.0767647i	0.360463	+	0.932773i	$0.382619\pi$
$138$	0.819214	+	2.94648i	0.0697362	+	0.250821i
$139$	−1.70385	−	0.300434i	−0.144518	−	0.0254825i	0.100921	−	0.994894i	$-0.467821\pi$
$139$	−1.70385	−	0.300434i	−0.144518	−	0.0254825i	−0.245439	+	0.969412i	$0.578932\pi$
$140$	15.0356	−	2.82215i	1.27074	−	0.238515i
$141$	14.8561	−	12.7052i	1.25111	−	1.06997i
$142$	−0.393738	−	0.275698i	−0.0330417	−	0.0231361i
$143$	2.36610	+	0.633995i	0.197863	+	0.0530173i
$144$	3.34824	+	3.84152i	0.279020	+	0.320126i
$145$	−0.00132399	−	0.0134293i	−0.000109952	−	0.00111524i
$146$	2.52298	−	6.93182i	0.208803	−	0.573681i
$147$	1.93169	+	19.9243i	0.159323	+	1.64333i
$148$	1.03935	+	11.8798i	0.0854339	+	0.976513i
$149$	−3.51771	−	2.95171i	−0.288182	−	0.241813i	0.487223	−	0.873277i	$-0.338010\pi$
$149$	−3.51771	−	2.95171i	−0.288182	−	0.241813i	−0.775405	+	0.631464i	$0.782454\pi$
$150$	0.174455	+	5.55489i	0.0142442	+	0.453555i
$151$	−4.16351	−	1.51539i	−0.338821	−	0.123321i	0.167005	−	0.985956i	$-0.446590\pi$
$151$	−4.16351	−	1.51539i	−0.338821	−	0.123321i	−0.505827	+	0.862635i	$0.668813\pi$
$152$	2.66249	−	0.713411i	0.215956	−	0.0578653i
$153$	−14.8635	−	3.68517i	−1.20164	−	0.297928i
$154$	1.10524	−	0.638110i	0.0890627	−	0.0514204i
$155$	−3.56727	−	3.48960i	−0.286530	−	0.280291i
$156$	−4.86326	+	13.7621i	−0.389372	+	1.10185i
$157$	0.351788	−	0.754412i	0.0280757	−	0.0602086i	−0.891770	−	0.452489i	$-0.850536\pi$
$157$	0.351788	−	0.754412i	0.0280757	−	0.0602086i	0.919846	+	0.392281i	$0.128314\pi$
$158$	0.578913	+	0.826774i	0.0460559	+	0.0657746i
$159$	8.31285	−	4.90400i	0.659252	−	0.388912i
$160$	10.9584	−	6.48867i	0.866336	−	0.512974i
$161$		−	11.8525i		−	0.934107i
$162$	−2.63559	−	5.13925i	−0.207072	−	0.403777i
$163$	−10.1572	−	10.1572i	−0.795571	−	0.795571i	0.186823	−	0.982394i	$-0.440181\pi$
$163$	−10.1572	−	10.1572i	−0.795571	−	0.795571i	−0.982394	+	0.186823i	$0.940181\pi$
$164$	−5.73166	+	4.80943i	−0.447567	+	0.375554i
$165$	−0.645642	−	1.66731i	−0.0502632	−	0.129800i
$166$	−1.18990	+	6.74824i	−0.0923540	+	0.523765i
$167$	−20.3353	−	9.48250i	−1.57359	−	0.733778i	−0.577038	−	0.816718i	$-0.695791\pi$
$167$	−20.3353	−	9.48250i	−1.57359	−	0.733778i	−0.996555	+	0.0829395i	$0.973569\pi$
$168$	7.40680	+	15.5025i	0.571447	+	1.19604i
$169$	−14.9250	+	2.63168i	−1.14808	+	0.202437i
$170$	−3.02235	+	6.67221i	−0.231804	+	0.511735i
$171$	3.59051	−	0.0673863i	0.274573	−	0.00515316i
$172$	−0.784088	−	2.92626i	−0.0597861	−	0.223125i
$173$	2.09324	−	0.976093i	0.159146	−	0.0742110i	−0.341413	−	0.939913i	$-0.610906\pi$
$173$	2.09324	−	0.976093i	0.159146	−	0.0742110i	0.500559	+	0.865702i	$0.333128\pi$
$174$	0.00628157	−	0.00235328i	0.000476204	−	0.000178402i
$175$	5.11543	−	20.9228i	0.386690	−	1.58161i
$176$	−0.504052	+	0.600706i	−0.0379943	+	0.0452799i
$177$	−0.712973	+	0.0691237i	−0.0535903	+	0.00519565i
$178$	−3.44986	−	7.39824i	−0.258578	−	0.554522i
$179$	−10.3891	+	17.9945i	−0.776520	+	1.34497i	0.157416	+	0.987532i	$0.449684\pi$
$179$	−10.3891	+	17.9945i	−0.776520	+	1.34497i	−0.933936	+	0.357440i	$0.883650\pi$
$180$	10.2041	−	3.06251i	0.760570	−	0.228266i
$181$	1.61486	+	2.79701i	0.120031	+	0.207900i	0.919780	−	0.392435i	$-0.128367\pi$
$181$	1.61486	+	2.79701i	0.120031	+	0.207900i	−0.799748	+	0.600335i	$0.795034\pi$
$182$	−8.41369	+	12.0160i	−0.623664	+	0.890685i
$183$	−0.309888	+	3.97081i	−0.0229076	+	0.293531i
$184$	−2.16689	−	5.95348i	−0.159745	−	0.438896i
$185$	15.8398	+	5.56855i	1.16456	+	0.409408i
$186$	1.22009	−	2.15981i	0.0894615	−	0.158365i
$187$	0.205381	−	2.34751i	0.0150189	−	0.171667i
$188$	−12.6743	+	12.6743i	−0.924372	+	0.924372i
$189$	4.50583	+	21.9258i	0.327751	+	1.59487i
$190$	0.279645	−	1.69482i	0.0202876	−	0.122955i
$191$	0.296698	+	0.353591i	0.0214683	+	0.0255850i	0.776672	−	0.629905i	$-0.216906\pi$
$191$	0.296698	+	0.353591i	0.0214683	+	0.0255850i	−0.755203	+	0.655490i	$0.772462\pi$
$192$	0.318592	+	0.312669i	0.0229924	+	0.0225649i
$193$	−1.86360	+	1.30491i	−0.134145	+	0.0939292i	−0.638723	−	0.769437i	$-0.720537\pi$
$193$	−1.86360	+	1.30491i	−0.134145	+	0.0939292i	0.504578	+	0.863366i	$0.331648\pi$
$194$	5.16623	−	1.88035i	0.370914	−	0.135001i
$195$	14.8247	+	14.2322i	1.06162	+	1.01919i
$196$	−3.18729	−	18.0760i	−0.227663	−	1.29114i
$197$	6.91110	−	25.7926i	0.492396	−	1.83765i	−0.0517571	−	0.998660i	$-0.516482\pi$
$197$	6.91110	−	25.7926i	0.492396	−	1.83765i	0.544153	−	0.838986i	$-0.316851\pi$
$198$	0.718345	−	0.523350i	0.0510506	−	0.0371929i
$199$	20.6539	+	11.9246i	1.46412	+	0.845309i	0.999198	−	0.0400428i	$-0.0127494\pi$
$199$	20.6539	+	11.9246i	1.46412	+	0.845309i	0.464921	+	0.885352i	$0.346083\pi$
$200$	−1.25566	−	11.4447i	−0.0887889	−	0.809261i
$201$	−10.0263	−	1.67106i	−0.707199	−	0.117867i
$202$	10.0354	−	0.877983i	0.706088	−	0.0617747i
$203$	−0.0258981	+	0.00226579i	−0.00181769	+	0.000159027i
$204$	13.8504	+	2.30841i	0.969720	+	0.161621i
$205$	2.83836	+	10.1449i	0.198240	+	0.708552i
$206$	7.77970	+	4.49161i	0.542038	+	0.312946i
$207$	−0.873570	−	8.20783i	−0.0607173	−	0.570484i
$208$	2.33278	−	8.70605i	0.161749	−	0.603656i
$209$	0.0959604	+	0.544219i	0.00663772	+	0.0376444i
$210$	10.7046	−	0.218287i	0.738688	−	0.0150633i
$211$	20.3867	−	7.42015i	1.40348	−	0.510825i	0.474270	−	0.880379i	$-0.342712\pi$
$211$	20.3867	−	7.42015i	1.40348	−	0.510825i	0.929209	+	0.369555i	$0.120490\pi$
$212$	−7.24934	+	5.07605i	−0.497887	+	0.348624i
$213$	0.925905	+	0.908691i	0.0634420	+	0.0622625i
$214$	−1.67118	−	1.99163i	−0.114239	−	0.136145i
$215$	−4.20846	−	0.694397i	−0.287015	−	0.0473575i
$216$	6.27178	+	10.1895i	0.426741	+	0.693310i
$217$	−6.79799	+	6.79799i	−0.461477	+	0.461477i
$218$	0.371543	−	4.24675i	0.0251640	−	0.287626i
$219$	−9.79260	+	17.3349i	−0.661722	+	1.17138i
$220$	0.709163	+	1.47811i	0.0478118	+	0.0996542i
$221$	9.26370	+	25.4518i	0.623144	+	1.71207i
$222$	−0.649373	+	8.32087i	−0.0435831	+	0.558460i
$223$	−6.30605	+	9.00598i	−0.422285	+	0.603085i	−0.972774	−	0.231757i	$-0.925552\pi$
$223$	−6.30605	+	9.00598i	−0.422285	+	0.603085i	0.550489	+	0.834842i	$0.314441\pi$
$224$	−12.2674	−	21.2477i	−0.819649	−	1.41967i
$225$	2.00034	−	14.8660i	0.133356	−	0.991068i
$226$	2.25386	−	3.90381i	0.149925	−	0.259677i
$227$	4.18215	+	8.96865i	0.277579	+	0.595270i	0.994831	−	0.101544i	$-0.0323781\pi$
$227$	4.18215	+	8.96865i	0.277579	+	0.595270i	−0.717252	+	0.696814i	$0.754600\pi$
$228$	−3.27746	+	0.317755i	−0.217055	+	0.0210438i
$229$	6.25137	−	7.45009i	0.413102	−	0.492316i	−0.518866	−	0.854855i	$-0.673646\pi$
$229$	6.25137	−	7.45009i	0.413102	−	0.492316i	0.931968	+	0.362540i	$0.118090\pi$
$230$	−3.93670	−	0.300797i	−0.259579	−	0.0198340i
$231$	−3.22558	+	1.20841i	−0.212228	+	0.0795075i
$232$	−0.0125943	+	0.00587283i	−0.000826858	+	0.000385570i
$233$	−2.61861	−	9.77279i	−0.171551	−	0.640236i	−0.997113	−	0.0759259i	$-0.975809\pi$
$233$	−2.61861	−	9.77279i	−0.171551	−	0.640236i	0.825563	−	0.564311i	$-0.190858\pi$
$234$	−4.94084	+	8.94117i	−0.322993	+	0.584503i
$235$	8.89186	+	23.6181i	0.580041	+	1.54067i
$236$	0.646833	−	0.114054i	0.0421053	−	0.00742429i
$237$	−1.17437	−	2.45797i	−0.0762836	−	0.159662i
$238$	12.7892	+	5.96371i	0.829002	+	0.386570i
$239$	−0.554723	+	3.14599i	−0.0358821	+	0.203497i	−0.997478	−	0.0709702i	$-0.977390\pi$
$239$	−0.554723	+	3.14599i	−0.0358821	+	0.203497i	0.961596	+	0.274468i	$0.0885016\pi$
$240$	−6.13484	+	2.37563i	−0.396002	+	0.153347i
$241$	−15.5334	+	13.0341i	−1.00060	+	0.839600i	−0.987067	−	0.160309i	$-0.948751\pi$
$241$	−15.5334	+	13.0341i	−1.00060	+	0.839600i	−0.0135291	+	0.999908i	$0.504307\pi$
$242$	−4.89485	−	4.89485i	−0.314653	−	0.314653i
$243$	4.73629	+	14.8515i	0.303833	+	0.952725i
$244$		−	3.65203i		−	0.233797i
$245$	−25.0343	−	6.41346i	−1.59938	−	0.409741i
$246$	−4.51025	+	2.66073i	−0.287563	+	0.169642i
$247$	−3.64320	−	5.20303i	−0.231811	−	0.331061i
$248$	−2.17179	+	4.65743i	−0.137909	+	0.295747i
$249$	6.16213	−	17.4377i	0.390509	−	1.10507i
$250$	−6.81951	−	2.23003i	−0.431303	−	0.141040i
$251$	12.3046	−	7.10409i	0.776662	−	0.448406i	−0.0585840	−	0.998282i	$-0.518659\pi$
$251$	12.3046	−	7.10409i	0.776662	−	0.448406i	0.835246	+	0.549876i	$0.185325\pi$
$252$	−5.68324	−	19.7221i	−0.358010	−	1.24237i
$253$	1.22689	−	0.328745i	0.0771341	−	0.0206680i
$254$	−5.05618	−	1.84030i	−0.317253	−	0.115471i
$255$	11.0069	−	16.4222i	0.689278	−	1.02840i
$256$	−5.91329	−	4.96184i	−0.369581	−	0.310115i
$257$	2.46595	+	28.1859i	0.153822	+	1.75819i	0.545522	+	0.838096i	$0.316331\pi$
$257$	2.46595	+	28.1859i	0.153822	+	1.75819i	−0.391701	+	0.920093i	$0.628113\pi$
$258$	−0.204604	−	2.11037i	−0.0127381	−	0.131386i
$259$	11.0631	−	30.3956i	0.687426	−	1.88869i
$260$	−14.5674	−	11.9528i	−0.903432	−	0.741279i
$261$	−0.0177674	+	0.00347784i	−0.00109978	+	0.000215273i
$262$	7.09034	+	1.89985i	0.438043	+	0.117373i
$263$	−4.29988	−	3.01081i	−0.265142	−	0.185655i	0.433444	−	0.901181i	$-0.357298\pi$
$263$	−4.29988	−	3.01081i	−0.265142	−	0.185655i	−0.698586	+	0.715526i	$0.746187\pi$
$264$	−1.39928	+	1.19669i	−0.0861197	+	0.0736510i
$265$	2.29860	+	12.2463i	0.141202	+	0.752282i
$266$	−3.25896	−	0.574642i	−0.199819	−	0.0352336i
$267$	5.90173	+	21.2269i	0.361180	+	1.29906i
$268$	9.28474	+	0.812310i	0.567156	+	0.0496197i
$269$	11.2342			0.684961			0.342480	−	0.939525i	$-0.388733\pi$
$269$	11.2342			0.684961			0.342480	+	0.939525i	$0.388733\pi$
$270$	7.39683	−	0.940131i	0.450157	−	0.0572145i
$271$	−15.3871			−0.934699			−0.467349	−	0.884073i	$-0.654791\pi$
$271$	−15.3871			−0.934699			−0.467349	+	0.884073i	$0.654791\pi$
$272$	−8.63764	−	0.755696i	−0.523734	−	0.0458208i
$273$	27.7312	−	28.2565i	1.67837	−	1.71016i
$274$	−6.51532	−	1.14883i	−0.393605	−	0.0694032i
$275$	2.30768	−	0.0508059i	0.139158	−	0.00306371i
$276$	1.38414	+	7.44087i	0.0833152	+	0.447888i
$277$	−13.4512	−	9.41860i	−0.808202	−	0.565909i	0.0948247	−	0.995494i	$-0.469771\pi$
$277$	−13.4512	−	9.41860i	−0.808202	−	0.565909i	−0.903026	+	0.429585i	$0.858660\pi$
$278$	1.07246	+	0.287365i	0.0643219	+	0.0172350i
$279$	−4.20656	+	5.20863i	−0.251840	+	0.311832i
$280$	−22.0736	+	2.17624i	−1.31915	+	0.130055i
$281$	−3.30030	+	9.06751i	−0.196880	+	0.540922i	−0.998369	−	0.0570865i	$-0.981819\pi$
$281$	−3.30030	+	9.06751i	−0.196880	+	0.540922i	0.801490	+	0.598009i	$0.204041\pi$
$282$	−10.2081	+	7.29149i	−0.607884	+	0.434202i
$283$	−1.35265	−	15.4609i	−0.0804068	−	0.919054i	−0.924080	−	0.382198i	$-0.875167\pi$
$283$	−1.35265	−	15.4609i	−0.0804068	−	0.919054i	0.843674	−	0.536856i	$-0.180388\pi$
$284$	−0.911245	−	0.764625i	−0.0540724	−	0.0453721i
$285$	−1.49651	+	4.38798i	−0.0886454	+	0.259921i
$286$	−1.47718	−	0.537651i	−0.0873477	−	0.0317920i
$287$	19.6033	−	5.25269i	1.15715	−	0.310057i
$288$	−10.0612	−	13.8099i	−0.592861	−	0.813755i
$289$	7.84266	−	4.52796i	0.461333	−	0.266351i
$290$	9.53107e−5		0.00865934i	5.59684e−6		0.000508494i
$291$	−14.5882	+	2.71367i	−0.855177	+	0.159078i
$292$	7.71521	−	16.5453i	0.451499	−	0.968242i
$293$	5.53310	+	7.90208i	0.323247	+	0.461645i	0.947582	−	0.319512i	$-0.103519\pi$
$293$	5.53310	+	7.90208i	0.323247	+	0.461645i	−0.624335	+	0.781157i	$0.714630\pi$
$294$	−0.120532	−	12.8456i	−0.00702954	−	0.749170i
$295$	0.229500	−	0.895829i	0.0133620	−	0.0521572i
$296$		−	17.2902i		−	1.00497i
$297$	−2.14465	+	1.07456i	−0.124445	+	0.0623522i
$298$	2.08377	+	2.08377i	0.120709	+	0.120709i
$299$	−11.1837	+	9.38426i	−0.646772	+	0.542706i
$300$	−0.768050	+	13.7325i	−0.0443434	+	0.792846i
$301$	−1.42692	+	8.09244i	−0.0822460	+	0.466440i
$302$	2.57696	+	1.20166i	0.148288	+	0.0691476i
$303$	−27.1065	−	2.11543i	−1.55723	−	0.121528i
$304$	2.00245	−	0.353085i	0.114848	−	0.0202508i
$305$	−4.68376	−	2.12163i	−0.268191	−	0.121484i
$306$	9.29607	+	3.18725i	0.531421	+	0.182203i
$307$	−1.13471	−	4.23478i	−0.0647610	−	0.241692i	0.925956	−	0.377631i	$-0.123261\pi$
$307$	−1.13471	−	4.23478i	−0.0647610	−	0.241692i	−0.990717	+	0.135940i	$0.956595\pi$
$308$	2.86246	−	1.33479i	0.163104	−	0.0760566i
$309$	−18.7187	−	15.4099i	−1.06487	−	0.876637i
$310$	2.08537	+	2.43042i	0.118441	+	0.138038i
$311$	−5.33012	+	6.35219i	−0.302243	+	0.360199i	−0.895694	−	0.444671i	$-0.853321\pi$
$311$	−5.33012	+	6.35219i	−0.302243	+	0.360199i	0.593451	+	0.804870i	$0.297765\pi$
$312$	8.76341	−	19.2630i	0.496131	−	1.09055i
$313$	4.37462	+	9.38140i	0.247268	+	0.530268i	0.990293	−	0.138996i	$-0.0443874\pi$
$313$	4.37462	+	9.38140i	0.247268	+	0.530268i	−0.743025	+	0.669264i	$0.766610\pi$
$314$	−0.267093	+	0.462618i	−0.0150729	+	0.0261070i
$315$	−28.5954	−	4.16866i	−1.61117	−	0.234877i
$316$	1.24891	+	2.16317i	0.0702566	+	0.121688i
$317$	−0.779004	+	1.11253i	−0.0437532	+	0.0624861i	−0.840433	−	0.541916i	$-0.817699\pi$
$317$	−0.779004	+	1.11253i	−0.0437532	+	0.0624861i	0.796679	+	0.604402i	$0.206588\pi$
$318$	−5.58867	+	2.67016i	−0.313397	+	0.149735i
$319$	−0.000952860	−	0.00261796i	−5.33499e−5	−	0.000146578i
$320$	−0.519580	+	0.249282i	−0.0290454	+	0.0139353i
$321$	3.56541	+	6.04379i	0.199002	+	0.337332i
$322$	−0.662925	+	7.57727i	−0.0369434	+	0.422265i
$323$	−4.32066	+	4.32066i	−0.240408	+	0.240408i
$324$	−5.38922	−	13.2386i	−0.299401	−	0.735480i
$325$	−23.7924	+	11.7389i	−1.31977	+	0.651158i
$326$	5.92535	+	7.06156i	0.328175	+	0.391104i
$327$	−2.87350	+	11.1411i	−0.158905	+	0.616106i
$328$	8.88639	−	6.22232i	0.490669	−	0.343570i
$329$	45.6863	−	16.6284i	2.51877	−	0.916756i
$330$	0.319503	+	1.10202i	0.0175880	+	0.0606641i
$331$	1.24032	+	7.03423i	0.0681744	+	0.386636i	0.999734	+	0.0230485i	$0.00733722\pi$
$331$	1.24032	+	7.03423i	0.0681744	+	0.386636i	−0.931560	+	0.363588i	$0.881552\pi$
$332$	−4.38908	+	16.3803i	−0.240882	+	0.898985i
$333$	5.42091	−	21.8643i	0.297064	−	1.19815i
$334$	12.4699	+	7.19952i	0.682324	+	0.393940i
$335$	6.43573	−	11.4359i	0.351622	−	0.624808i
$336$	4.44633	+	11.8685i	0.242567	+	0.647480i
$337$	28.6457	−	2.50617i	1.56043	−	0.136520i	0.726023	−	0.687671i	$-0.241367\pi$
$337$	28.6457	−	2.50617i	1.56043	−	0.136520i	0.834406	+	0.551151i	$0.185811\pi$
$338$	9.68871	−	0.847653i	0.526997	−	0.0461062i
$339$	−7.73257	+	9.39291i	−0.419976	+	0.510153i
$340$	−8.89037	+	15.7976i	−0.482148	+	0.856744i
$341$	−0.892235	−	0.515132i	−0.0483172	−	0.0278960i
$342$	−2.29918	−	0.157742i	−0.124325	−	0.00852972i
$343$	−5.08105	+	18.9628i	−0.274351	+	1.02389i
$344$	0.762735	+	4.32568i	0.0411239	+	0.233225i
$345$	10.3471	+	2.54758i	0.557069	+	0.137157i
$346$	−1.39280	+	0.506936i	−0.0748772	+	0.0272531i
$347$	24.1565	−	16.9146i	1.29679	−	0.908021i	0.297874	−	0.954605i	$-0.403723\pi$
$347$	24.1565	−	16.9146i	1.29679	−	0.908021i	0.998914	+	0.0465844i	$0.0148337\pi$
$348$	0.0159940	−	0.00444683i	0.000857367	−	0.000238375i
$349$	−13.2402	−	15.7790i	−0.708730	−	0.844632i	0.284754	−	0.958601i	$-0.408088\pi$
$349$	−13.2402	−	15.7790i	−0.708730	−	0.844632i	−0.993484	+	0.113969i	$0.963644\pi$
$350$	−4.44052	+	13.0898i	−0.237356	+	0.699678i
$351$	17.1212	−	21.6115i	0.913862	−	1.15354i
$352$	1.85918	−	1.85918i	0.0990944	−	0.0990944i
$353$	0.152839	−	1.74696i	0.00813482	−	0.0929814i	−0.991042	−	0.133552i	$-0.957362\pi$
$353$	0.152839	−	1.74696i	0.00813482	−	0.0929814i	0.999177	+	0.0405701i	$0.0129174\pi$
$354$	0.459668	−	0.00431311i	0.0244311	−	0.000229239i
$355$	−1.51002	+	0.724474i	−0.0801437	+	0.0384511i
$356$	−6.90944	−	18.9835i	−0.366199	−	1.00612i
$357$	−31.4022	−	21.5518i	−1.66198	−	1.14064i
$358$	7.64820	−	10.9228i	0.404220	−	0.577286i
$359$	9.41628	+	16.3095i	0.496972	+	0.860781i	0.999994	−	0.00349274i	$-0.00111178\pi$
$359$	9.41628	+	16.3095i	0.496972	+	0.860781i	−0.503022	+	0.864274i	$0.667778\pi$
$360$	−15.1255	+	3.13394i	−0.797185	+	0.165173i
$361$	−8.78354	+	15.2135i	−0.462291	+	0.800712i
$362$	−0.875933	−	1.87844i	−0.0460380	−	0.0987288i
$363$	10.8595	+	15.2033i	0.569976	+	0.797969i
$364$	−23.3346	+	27.8091i	−1.22307	+	1.45759i
$365$	−16.7374	−	19.5068i	−0.876076	−	1.02103i
$366$	0.420203	−	2.52120i	0.0219644	−	0.131785i
$367$	−24.3645	+	11.3614i	−1.27182	+	0.593058i	−0.937034	−	0.349237i	$-0.886441\pi$
$367$	−24.3645	+	11.3614i	−1.27182	+	0.593058i	−0.334783	+	0.942295i	$0.608663\pi$
$368$	−1.20961	−	4.51434i	−0.0630555	−	0.235326i
$369$	13.1881	−	5.08231i	0.686546	−	0.264575i
$370$	−9.81486	−	4.44590i	−0.510251	−	0.231131i
$371$	23.6399	−	4.16835i	1.22732	−	0.216410i
$372$	3.47384	−	5.06158i	0.180110	−	0.262431i
$373$	2.86161	+	1.33439i	0.148169	+	0.0690922i	0.495288	−	0.868729i	$-0.335062\pi$
$373$	2.86161	+	1.33439i	0.148169	+	0.0690922i	−0.347120	+	0.937821i	$0.612840\pi$
$374$	−0.262599	+	1.48927i	−0.0135786	+	0.0770083i
$375$	17.1659	+	8.96287i	0.886441	+	0.462841i
$376$	19.9081	−	16.7049i	1.02668	−	0.861487i
$377$	0.0226429	+	0.0226429i	0.00116617	+	0.00116617i
$378$	−1.65423	−	14.2692i	−0.0850842	−	0.733926i
$379$			7.29800i			0.374873i	0.982277	+	0.187436i	$0.0600179\pi$
$379$			7.29800i			0.374873i	−0.982277	+	0.187436i	$0.939982\pi$
$380$	1.05499	−	4.11804i	0.0541197	−	0.211251i
$381$	12.6443	+	7.14288i	0.647789	+	0.365941i
$382$	−0.169902	−	0.242645i	−0.00869293	−	0.0124148i
$383$	−7.76938	+	16.6615i	−0.396997	+	0.851362i	0.601620	+	0.798783i	$0.294522\pi$
$383$	−7.76938	+	16.6615i	−0.396997	+	0.851362i	−0.998617	+	0.0525799i	$0.983256\pi$
$384$	12.6369	+	14.7763i	0.644876	+	0.754051i
$385$	−0.0489420	−	4.44657i	−0.00249432	−	0.226618i
$386$	1.26438	−	0.729990i	0.0643552	−	0.0371555i
$387$	−0.391696	+	5.70917i	−0.0199110	+	0.290213i
$388$	13.1423	−	3.52146i	0.667197	−	0.178775i
$389$	19.7491	+	7.18808i	1.00132	+	0.364450i	0.790093	−	0.612987i	$-0.210032\pi$
$389$	19.7491	+	7.18808i	1.00132	+	0.364450i	0.211226	+	0.977437i	$0.432254\pi$
$390$	−8.68139	−	9.92779i	−0.439599	−	0.502713i
$391$	10.7587	+	9.02763i	0.544091	+	0.456547i
$392$	2.31943	+	26.5112i	0.117149	+	1.33902i
$393$	−18.0334	−	8.20401i	−0.909665	−	0.413838i
$394$	−5.86086	+	16.1026i	−0.295266	+	0.811237i
$395$	3.49984	−	0.345050i	0.176096	−	0.0173614i
$396$	1.88387	−	1.13531i	0.0946681	−	0.0570515i
$397$	−32.7796	−	8.78326i	−1.64516	−	0.440819i	−0.686907	−	0.726745i	$-0.741032\pi$
$397$	−32.7796	−	8.78326i	−1.64516	−	0.440819i	−0.958252	+	0.285926i	$0.907699\pi$
$398$	−12.5371	−	8.77854i	−0.628426	−	0.440029i
$399$	8.42125	+	2.97590i	0.421590	+	0.148981i
$400$	−0.186940	−	8.49107i	−0.00934699	−	0.424554i
$401$	−26.7887	−	4.72357i	−1.33776	−	0.235884i	−0.541433	−	0.840744i	$-0.682118\pi$
$401$	−26.7887	−	4.72357i	−1.33776	−	0.235884i	−0.796332	+	0.604860i	$0.793229\pi$
$402$	6.31631	+	1.62909i	0.315029	+	0.0812515i
$403$	11.7968	+	1.03208i	0.587638	+	0.0514117i
$404$	24.9303			1.24033
$405$	−20.1095	−	0.779209i	−0.999250	−	0.0387192i
$406$	0.0166833			0.000827980
$407$	3.45320	+	0.302116i	0.171169	+	0.0149753i
$408$	−19.7134	−	5.08443i	−0.975957	−	0.251717i
$409$	−13.3695	−	2.35741i	−0.661081	−	0.116566i	−0.166965	−	0.985963i	$-0.553397\pi$
$409$	−13.3695	−	2.35741i	−0.661081	−	0.116566i	−0.494115	+	0.869396i	$0.664508\pi$
$410$	−1.24714	−	6.64438i	−0.0615917	−	0.328143i
$411$	16.8358	+	5.94944i	0.830449	+	0.293464i
$412$	18.2111	+	12.7515i	0.897195	+	0.628222i
$413$	−1.72085	−	0.461102i	−0.0846777	−	0.0226893i
$414$	0.0993966	+	5.29610i	0.00488508	+	0.260289i
$415$	18.4580	+	15.1451i	0.906070	+	0.743444i
$416$	−10.3361	+	28.3982i	−0.506769	+	1.39234i
$417$	−2.72767	−	1.24091i	−0.133575	−	0.0607677i
$418$	−0.0309084	−	0.353285i	−0.00151178	−	0.0172797i
$419$	−9.78730	−	8.21252i	−0.478141	−	0.401208i	0.371613	−	0.928388i	$-0.378805\pi$
$419$	−9.78730	−	8.21252i	−0.478141	−	0.401208i	−0.849754	+	0.527180i	$0.823249\pi$
$420$	26.4379	+	1.77074i	1.29004	+	0.0864033i
$421$	16.9246	+	6.16004i	0.824853	+	0.300222i	0.719745	−	0.694239i	$-0.244259\pi$
$421$	16.9246	+	6.16004i	0.824853	+	0.300222i	0.105108	+	0.994461i	$0.466481\pi$
$422$	−13.4482	+	3.60343i	−0.654648	+	0.175412i
$423$	30.4121	−	14.8824i	1.47869	−	0.723608i
$424$	11.1122	−	6.41562i	0.539656	−	0.311570i
$425$	15.0957	+	20.5795i	0.732251	+	0.998254i
$426$	−0.541105	−	0.632711i	−0.0262166	−	0.0306549i
$427$	−4.18641	+	8.97778i	−0.202595	+	0.434465i
$428$	−3.69050	−	5.27058i	−0.178387	−	0.254763i
$429$	3.69410	+	2.08682i	0.178353	+	0.100753i
$430$	2.65162	+	0.679311i	0.127873	+	0.0327593i
$431$		−	4.80209i		−	0.231309i	−0.993290	−	0.115654i	$-0.963104\pi$
$431$		−	4.80209i		−	0.231309i	0.993290	−	0.115654i	$-0.0368965\pi$
$432$	3.95383	+	7.89121i	0.190229	+	0.379666i
$433$	23.6615	+	23.6615i	1.13710	+	1.13710i	0.988968	+	0.148130i	$0.0473253\pi$
$433$	23.6615	+	23.6615i	1.13710	+	1.13710i	0.148130	+	0.988968i	$0.452675\pi$
$434$	4.72616	−	3.96572i	0.226863	−	0.190360i
$435$	0.00358854	−	0.0230958i	0.000172057	−	0.00110736i
$436$	1.83198	−	10.3897i	0.0877360	−	0.497576i
$437$	−2.98497	−	1.39192i	−0.142791	−	0.0665844i
$438$	7.22994	−	10.5344i	0.345460	−	0.503355i
$439$	0.531654	−	0.0937450i	0.0253745	−	0.00447420i	−0.160947	−	0.986963i	$-0.551455\pi$
$439$	0.531654	−	0.0937450i	0.0253745	−	0.00447420i	0.186321	+	0.982489i	$0.440344\pi$
$440$	−0.837512	−	2.22455i	−0.0399268	−	0.106051i
$441$	−5.37890	+	34.2519i	−0.256138	+	1.63104i
$442$	−4.49871	−	16.7894i	−0.213982	−	0.798591i
$443$	4.71408	−	2.19821i	0.223973	−	0.104440i	−0.307393	−	0.951583i	$-0.599457\pi$
$443$	4.71408	−	2.19821i	0.223973	−	0.104440i	0.531366	+	0.847142i	$0.321679\pi$
$444$	−3.39569	+	20.3740i	−0.161152	+	0.966906i
$445$	−28.3606	−	2.16699i	−1.34442	−	0.102725i
$446$	4.53516	−	5.40479i	0.214746	−	0.255924i
$447$	−4.62295	−	6.47215i	−0.218658	−	0.306122i
$448$	0.469199	+	1.00620i	0.0221676	+	0.0475385i
$449$	6.99817	−	12.1212i	0.330264	−	0.572034i	−0.652300	−	0.757961i	$-0.726196\pi$
$449$	6.99817	−	12.1212i	0.330264	−	0.572034i	0.982564	+	0.185927i	$0.0595289\pi$
$450$	−2.11029	+	9.39193i	−0.0994801	+	0.442740i
$451$	1.08745	+	1.88352i	0.0512060	+	0.0886914i
$452$	6.39863	−	9.13819i	0.300966	−	0.429824i
$453$	−6.32738	−	4.34257i	−0.297286	−	0.204032i
$454$	−2.17201	−	5.96755i	−0.101937	−	0.280071i
$455$	22.1093	+	46.0825i	1.03650	+	2.16038i
$456$	4.77403	−	0.0447952i	0.223564	−	0.00209773i
$457$	0.334574	−	3.82420i	0.0156507	−	0.178888i	−0.984346	−	0.176248i	$-0.943604\pi$
$457$	0.334574	−	3.82420i	0.0156507	−	0.178888i	0.999997	−	0.00264047i	$-0.000840488\pi$
$458$	−4.41318	+	4.41318i	−0.206214	+	0.206214i
$459$	−23.3344	−	12.6101i	−1.08916	−	0.588591i
$460$	−9.64056	−	1.59069i	−0.449493	−	0.0741664i
$461$	−14.3235	−	17.0701i	−0.667111	−	0.795032i	0.321276	−	0.946985i	$-0.395888\pi$
$461$	−14.3235	−	17.0701i	−0.667111	−	0.795032i	−0.988388	+	0.151953i	$0.951444\pi$
$462$	2.12970	−	0.592122i	0.0990824	−	0.0275480i
$463$	−0.977400	+	0.684383i	−0.0454236	+	0.0318060i	−0.596068	−	0.802934i	$-0.703271\pi$
$463$	−0.977400	+	0.684383i	−0.0454236	+	0.0318060i	0.550644	+	0.834740i	$0.314382\pi$
$464$	−0.00963277	+	0.00350604i	−0.000447190	+	0.000162764i
$465$	−4.47341	−	7.39573i	−0.207449	−	0.342969i
$466$	1.12747	+	6.39418i	0.0522289	+	0.296205i
$467$	0.233069	−	0.869824i	0.0107851	−	0.0402506i	−0.960324	−	0.278888i	$-0.910034\pi$
$467$	0.233069	−	0.869824i	0.0107851	−	0.0402506i	0.971109	+	0.238638i	$0.0767008\pi$
$468$	−14.1096	+	20.9776i	−0.652215	+	0.969691i
$469$	−21.8935	−	12.6402i	−1.01095	−	0.583672i
$470$	−4.36355	−	15.5963i	−0.201276	−	0.719404i
$471$	0.916343	−	1.11310i	0.0422229	−	0.0512890i
$472$	−0.948680	+	0.0829988i	−0.0436665	+	0.00382033i
$473$	−0.877255	+	0.0767499i	−0.0403362	+	0.00352896i
$474$	0.613295	+	1.63706i	0.0281696	+	0.0751925i
$475$	−4.66853	−	3.74539i	−0.214207	−	0.171850i
$476$	30.2439	+	17.4613i	1.38623	+	0.800338i
$477$	16.0634	−	4.62891i	0.735490	−	0.211943i
$478$	0.530593	−	1.98020i	0.0242687	−	0.0905722i
$479$	−5.10504	−	28.9521i	−0.233255	−	1.32286i	−0.846257	−	0.532775i	$-0.821149\pi$
$479$	−5.10504	−	28.9521i	−0.233255	−	1.32286i	0.613001	−	0.790082i	$-0.289962\pi$
$480$	21.1858	−	6.14230i	0.966996	−	0.280356i
$481$	−37.4398	+	13.6270i	−1.70711	+	0.621336i
$482$	10.6595	−	7.46386i	0.485527	−	0.339969i
$483$	5.12704	−	19.8786i	0.233288	−	0.904507i
$484$	−11.0119	−	13.1234i	−0.500539	−	0.596519i
$485$	3.11864	−	18.9008i	0.141610	−	0.858243i
$486$	−2.19724	−	9.75944i	−0.0996686	−	0.442697i
$487$	22.6006	−	22.6006i	1.02413	−	1.02413i	0.0244298	−	0.999702i	$-0.492223\pi$
$487$	22.6006	−	22.6006i	1.02413	−	1.02413i	0.999702	−	0.0244298i	$-0.00777702\pi$
$488$	−0.461492	+	5.27488i	−0.0208908	+	0.238783i
$489$	−12.6416	−	21.4289i	−0.571671	−	0.969050i
$490$	15.6456	+	5.50031i	0.706798	+	0.248479i
$491$	−4.34237	−	11.9306i	−0.195968	−	0.538419i	0.802320	−	0.596894i	$-0.203599\pi$
$491$	−4.34237	−	11.9306i	−0.195968	−	0.538419i	−0.998289	+	0.0584746i	$0.981376\pi$
$492$	−11.6934	+	5.58687i	−0.527177	+	0.251875i
$493$	0.0176690	−	0.0252339i	0.000795772	−	0.00113648i
$494$	2.03808	+	3.53005i	0.0916974	+	0.158824i
$495$	−0.361620	−	3.07564i	−0.0162536	−	0.138240i
$496$	−1.89542	+	3.28297i	−0.0851071	+	0.147410i
$497$	1.36361	+	2.92426i	0.0611661	+	0.131171i
$498$	−4.91475	+	10.8032i	−0.220235	+	0.484103i
$499$	−7.76871	+	9.25839i	−0.347775	+	0.414463i	−0.911369	−	0.411589i	$-0.864974\pi$
$499$	−7.76871	+	9.25839i	−0.347775	+	0.414463i	0.563594	+	0.826052i	$0.309418\pi$
$500$	−16.3316	−	6.96878i	−0.730372	−	0.311653i
$501$	−30.0038	−	24.7002i	−1.34047	−	1.10352i
$502$	−8.26367	+	3.85341i	−0.368825	+	0.171986i
$503$	5.65132	+	21.0910i	0.251980	+	0.940402i	0.969746	+	0.244117i	$0.0784982\pi$
$503$	5.65132	+	21.0910i	0.251980	+	0.940402i	−0.717766	+	0.696285i	$0.754835\pi$
$504$	5.71650	+	29.2042i	0.254633	+	1.30086i
$505$	14.4832	−	31.9734i	0.644493	−	1.42280i
$506$	−0.802737	+	0.141544i	−0.0356860	+	0.00629241i
$507$	−26.1701	−	2.04235i	−1.16225	−	0.0907041i
$508$	−12.0684	−	5.62760i	−0.535450	−	0.249684i
$509$	−0.934268	+	5.29850i	−0.0414107	+	0.234852i	−0.998487	−	0.0549834i	$-0.982489\pi$
$509$	−0.934268	+	5.29850i	−0.0414107	+	0.234852i	0.957077	+	0.289835i	$0.0936005\pi$
$510$	−7.95518	+	9.88302i	−0.352261	+	0.437627i
$511$	−37.9326	+	31.8293i	−1.67804	+	1.40804i
$512$	−12.3723	−	12.3723i	−0.546785	−	0.546785i
$513$	6.05103	+	1.44013i	0.267160	+	0.0635834i
$514$		−	18.1571i		−	0.800876i
$515$	26.9336	−	15.9479i	1.18684	−	0.702749i
$516$	−0.0492331	−	5.24699i	−0.00216736	−	0.230986i
$517$	2.98844	+	4.26794i	0.131432	+	0.187704i
$518$	−8.77266	+	18.8130i	−0.385449	+	0.826597i
$519$	3.93293	−	0.731596i	0.172637	−	0.0321135i
$520$	19.5303	+	19.1051i	0.856461	+	0.837813i
$521$	−2.74885	+	1.58705i	−0.120429	+	0.0695300i	−0.559005	−	0.829165i	$-0.688817\pi$
$521$	−2.74885	+	1.58705i	−0.120429	+	0.0695300i	0.438575	+	0.898694i	$0.355483\pi$
$522$	0.0115532	−	0.00122962i	0.000505669	−	5.38190e-5i
$523$	−11.6055	+	3.10969i	−0.507473	+	0.135977i	−0.503466	−	0.864015i	$-0.667942\pi$
$523$	−11.6055	+	3.10969i	−0.507473	+	0.135977i	−0.00400710	+	0.999992i	$0.501276\pi$
$524$	17.0706	+	6.21317i	0.745731	+	0.271424i
$525$	17.6300	−	32.8782i	0.769436	−	1.43492i
$526$	2.58051	+	2.16530i	0.112515	+	0.0944116i
$527$	−0.992860	−	11.3484i	−0.0432496	−	0.494346i
$528$	−1.10523	+	0.789445i	−0.0480988	+	0.0343562i
$529$	5.27731	−	14.4993i	0.229448	−	0.630404i
$530$	−0.784539	−	7.95757i	−0.0340782	−	0.345655i
$531$	−1.22567	−	0.192479i	−0.0531897	−	0.00835288i
$532$	−7.91060	−	2.11964i	−0.342968	−	0.0918980i
$533$	−20.4773	−	14.3384i	−0.886972	−	0.621064i
$534$	−2.58572	−	13.9004i	−0.111895	−	0.601528i
$535$	−8.90355	+	1.67118i	−0.384934	+	0.0722513i
$536$	−13.3080	−	2.34655i	−0.574817	−	0.101356i
$537$	−25.2082	+	25.6857i	−1.08781	+	1.10842i
$538$	−7.18199	−	0.628343i	−0.309638	−	0.0270898i
$539$	−5.33536			−0.229810
$540$	18.4387	−	0.722333i	0.793477	−	0.0310843i
$541$	33.7781			1.45223			0.726116	−	0.687572i	$-0.241324\pi$
$541$	33.7781			1.45223			0.726116	+	0.687572i	$0.241324\pi$
$542$	9.83692	+	0.860619i	0.422532	+	0.0369668i
$543$	1.49847	+	5.38959i	0.0643057	+	0.231289i
$544$	28.6306	+	5.04834i	1.22753	+	0.216446i
$545$	−12.2606	−	8.38538i	−0.525186	−	0.359190i
$546$	−19.3089	+	16.5133i	−0.826345	+	0.706704i
$547$	11.7446	+	8.22365i	0.502162	+	0.351618i	0.797049	−	0.603914i	$-0.206393\pi$
$547$	11.7446	+	8.22365i	0.502162	+	0.351618i	−0.294887	+	0.955532i	$0.595282\pi$
$548$	−15.8149	−	4.23759i	−0.675579	−	0.181021i
$549$	−2.23739	+	6.52565i	−0.0954894	+	0.278508i
$550$	−1.47813	−	0.0965912i	−0.0630278	−	0.00411866i
$551$	−0.00247076	+	0.00678836i	−0.000105258	+	0.000289194i
$552$	−1.05893	−	10.9223i	−0.0450711	−	0.464884i
$553$	−0.590495	−	6.74939i	−0.0251104	−	0.287013i
$554$	8.07250	+	6.77363i	0.342968	+	0.287784i
$555$	24.1571	+	16.1912i	1.02541	+	0.687278i
$556$	2.58203	+	0.939783i	0.109503	+	0.0398557i
$557$	−9.77642	+	2.61958i	−0.414240	+	0.110995i	−0.459919	−	0.887961i	$-0.652122\pi$
$557$	−9.77642	+	2.61958i	−0.414240	+	0.110995i	0.0456789	+	0.998956i	$0.485455\pi$
$558$	2.98057	−	3.09459i	0.126177	−	0.131004i
$559$	8.76560	−	5.06082i	0.370745	−	0.214050i
$560$	−16.3611	+	0.180082i	−0.691383	+	0.00760984i
$561$	1.35992	−	3.84832i	0.0574159	−	0.162476i
$562$	2.61703	−	5.61224i	0.110393	−	0.236738i
$563$	−16.1451	−	23.0577i	−0.680437	−	0.971765i	−0.999710	−	0.0241016i	$-0.992327\pi$
$563$	−16.1451	−	23.0577i	−0.680437	−	0.971765i	0.319273	−	0.947663i	$-0.396561\pi$
$564$	−26.7395	+	15.7744i	−1.12594	+	0.664223i
$565$	−8.00256	−	13.5151i	−0.336670	−	0.568585i
$566$			9.95976i			0.418640i
$567$	−1.92745	+	38.7224i	−0.0809453	+	1.62619i
$568$	1.21955	+	1.21955i	0.0511713	+	0.0511713i
$569$	−7.66040	+	6.42784i	−0.321141	+	0.269469i	−0.789078	−	0.614292i	$-0.789442\pi$
$569$	−7.66040	+	6.42784i	−0.321141	+	0.269469i	0.467938	+	0.883761i	$0.344997\pi$
$570$	1.20214	−	2.72152i	0.0503520	−	0.113992i
$571$	4.25288	−	24.1193i	0.177978	−	1.00936i	−0.756673	−	0.653794i	$-0.773176\pi$
$571$	4.25288	−	24.1193i	0.177978	−	1.00936i	0.934651	−	0.355568i	$-0.115712\pi$
$572$	−3.52584	−	1.64413i	−0.147423	−	0.0687444i
$573$	0.344659	+	0.721374i	0.0143983	+	0.0301358i
$574$	−12.8261	+	2.26159i	−0.535353	+	0.0943971i
$575$	−7.64073	+	11.4400i	−0.318640	+	0.477081i
$576$	0.399080	+	0.662211i	0.0166283	+	0.0275921i
$577$	−4.13963	−	15.4493i	−0.172335	−	0.643163i	−0.996990	−	0.0775272i	$-0.975298\pi$
$577$	−4.13963	−	15.4493i	−0.172335	−	0.643163i	0.824655	−	0.565636i	$-0.191369\pi$
$578$	−5.26705	+	2.45606i	−0.219080	+	0.102159i
$579$	−3.69003	+	1.38240i	−0.153352	+	0.0574508i
$580$	−0.00163278	+	0.0213691i	−6.77973e−5	+	0.000887302i
$581$	29.5668	−	35.2364i	1.22664	−	1.46185i
$582$	9.47800	−	0.918905i	0.392876	−	0.0380898i
$583$	1.08716	+	2.33143i	0.0450258	+	0.0965581i
$584$	−13.2344	+	22.9227i	−0.547643	+	0.948546i
$585$	18.7071	+	30.2825i	0.773443	+	1.25203i
$586$	−3.09532	−	5.36125i	−0.127867	−	0.221471i
$587$	−11.3970	+	16.2765i	−0.470403	+	0.671805i	−0.982316	−	0.187233i	$-0.940048\pi$
$587$	−11.3970	+	16.2765i	−0.470403	+	0.671805i	0.511913	+	0.859037i	$0.328937\pi$
$588$	2.47354	−	31.6952i	0.102007	−	1.30709i
$589$	0.913697	+	2.51036i	0.0376482	+	0.103438i
$590$	−0.196823	+	0.559865i	−0.00810309	+	0.0230493i
$591$	22.7482	−	40.2689i	0.935735	−	1.65644i
$592$	1.11163	−	12.7060i	0.0456878	−	0.522214i
$593$	−24.0438	+	24.0438i	−0.987362	+	0.987362i	−0.999921	−	0.0125593i	$-0.996002\pi$
$593$	−24.0438	+	24.0438i	−0.987362	+	0.987362i	0.0125593	+	0.999921i	$0.496002\pi$
$594$	1.43117	−	0.567010i	0.0587216	−	0.0232647i
$595$	39.9644	−	28.6440i	1.63838	−	1.17429i
$596$	4.68781	+	5.58672i	0.192020	+	0.228841i
$597$	29.4819	+	28.9337i	1.20661	+	1.18418i
$598$	7.67460	−	5.37382i	0.313838	−	0.219752i
$599$	−32.8027	+	11.9392i	−1.34028	+	0.487823i	−0.909901	−	0.414825i	$-0.863843\pi$
$599$	−32.8027	+	11.9392i	−1.34028	+	0.487823i	−0.430381	+	0.902647i	$0.641621\pi$
$600$	2.84467	−	19.7378i	0.116133	−	0.805791i
$601$	−4.52626	−	25.6697i	−0.184630	−	1.04709i	−0.926430	−	0.376467i	$-0.877139\pi$
$601$	−4.52626	−	25.6697i	−0.184630	−	1.04709i	0.741800	−	0.670621i	$-0.233972\pi$
$602$	1.36484	−	5.09367i	0.0556269	−	0.207602i
$603$	−16.0929	−	7.13971i	−0.655352	−	0.290752i
$604$	6.09398	+	3.51836i	0.247961	+	0.143160i
$605$	−23.2282	+	6.49881i	−0.944361	+	0.264214i
$606$	17.2108	+	2.86849i	0.699141	+	0.116524i
$607$	−3.56643	+	0.312022i	−0.144757	+	0.0126646i	−0.159304	−	0.987230i	$-0.550925\pi$
$607$	−3.56643	+	0.312022i	−0.144757	+	0.0126646i	0.0145470	+	0.999894i	$0.495369\pi$
$608$	−6.79175	+	0.594201i	−0.275442	+	0.0240980i
$609$	−0.0444155	−	0.00740266i	−0.00179981	−	0.000299971i
$610$	2.87565	+	1.61832i	0.116432	+	0.0655239i
$611$	−51.8625	−	29.9428i	−2.09813	−	1.21136i
$612$	22.2308	+	9.86285i	0.898627	+	0.398682i
$613$	4.71891	−	17.6112i	0.190595	−	0.711310i	−0.802768	−	0.596291i	$-0.796640\pi$
$613$	4.71891	−	17.6112i	0.190595	−	0.711310i	0.993363	−	0.115019i	$-0.0366928\pi$
$614$	0.488558	+	2.77075i	0.0197166	+	0.111818i
$615$	0.371999	+	18.2425i	0.0150005	+	0.735609i
$616$	−4.30313	+	1.56621i	−0.173378	+	0.0631044i
$617$	2.52278	−	1.76647i	0.101563	−	0.0711153i	−0.521692	−	0.853134i	$-0.674699\pi$
$617$	2.52278	−	1.76647i	0.101563	−	0.0711153i	0.623255	+	0.782019i	$0.285810\pi$
$618$	11.1049	+	10.8984i	0.446705	+	0.438400i
$619$	22.9284	+	27.3250i	0.921572	+	1.09829i	0.994889	+	0.100978i	$0.0321970\pi$
$619$	22.9284	+	27.3250i	0.921572	+	1.09829i	−0.0733171	+	0.997309i	$0.523359\pi$
$620$	4.61699	+	6.44168i	0.185423	+	0.258704i
$621$	2.08534	−	14.1438i	0.0836820	−	0.567570i
$622$	3.76282	−	3.76282i	0.150875	−	0.150875i
$623$	−4.77580	+	54.5877i	−0.191339	+	2.18701i
$624$	7.67844	−	13.5924i	0.307383	−	0.544131i
$625$	−18.4253	+	16.8970i	−0.737013	+	0.675879i
$626$	−2.27197	−	6.24218i	−0.0908062	−	0.249488i
$627$	−0.0744714	+	0.954254i	−0.00297410	+	0.0381092i
$628$	−0.758266	+	1.08292i	−0.0302581	+	0.0432130i
$629$	19.1642	+	33.1934i	0.764127	+	1.32351i
$630$	18.0478	+	4.26439i	0.719042	+	0.169897i
$631$	0.459598	−	0.796047i	0.0182963	−	0.0316901i	−0.856732	−	0.515761i	$-0.827509\pi$
$631$	0.459598	−	0.796047i	0.0182963	−	0.0316901i	0.875029	+	0.484071i	$0.160842\pi$
$632$	−1.53054	−	3.28225i	−0.0608815	−	0.130561i
$633$	37.4016	−	3.62614i	1.48658	−	0.144126i
$634$	0.560241	−	0.667669i	0.0222500	−	0.0265165i
$635$	−14.2286	+	12.2085i	−0.564643	+	0.484481i
$636$	−14.3541	+	5.37751i	−0.569177	+	0.213232i
$637$	55.5788	−	25.9168i	2.20211	−	1.02686i
$638$	0.000462735		0.00172695i	1.83199e−5		6.83707e-5i
$639$	1.15982	+	1.92454i	0.0458819	+	0.0761338i
$640$	−23.4912	+	8.84408i	−0.928570	+	0.349593i
$641$	28.1175	−	4.95787i	1.11057	−	0.195824i	0.411875	−	0.911240i	$-0.364874\pi$
$641$	28.1175	−	4.95787i	1.11057	−	0.195824i	0.698699	+	0.715416i	$0.253763\pi$
$642$	−1.94132	−	4.06320i	−0.0766178	−	0.160362i
$643$	34.3252	+	16.0061i	1.35365	+	0.631220i	0.957891	−	0.287133i	$-0.0927020\pi$
$643$	34.3252	+	16.0061i	1.35365	+	0.631220i	0.395764	+	0.918352i	$0.370480\pi$
$644$	−3.26871	+	18.5378i	−0.128805	+	0.730492i
$645$	−6.75791	−	2.98508i	−0.266093	−	0.117537i
$646$	3.00385	−	2.52053i	0.118185	−	0.0991688i
$647$	30.2410	+	30.2410i	1.18890	+	1.18890i	0.977373	+	0.211525i	$0.0678429\pi$
$647$	30.2410	+	30.2410i	1.18890	+	1.18890i	0.211525	+	0.977373i	$0.432157\pi$
$648$	6.11112	+	19.8025i	0.240067	+	0.777917i
$649$		−	0.190921i		−	0.00749431i
$650$	15.8670	−	6.17392i	0.622355	−	0.242161i
$651$	−14.3420	+	8.46074i	−0.562105	+	0.331602i
$652$	13.0851	+	18.6874i	0.512451	+	0.731856i
$653$	15.4696	−	33.1747i	0.605374	−	1.29823i	−0.329804	−	0.944049i	$-0.606983\pi$
$653$	15.4696	−	33.1747i	0.605374	−	1.29823i	0.935178	−	0.354178i	$-0.115239\pi$
$654$	2.46016	−	6.96178i	0.0961998	−	0.272227i
$655$	17.8855	−	18.2836i	0.698845	−	0.714400i
$656$	6.93039	−	4.00126i	0.270586	−	0.156223i
$657$	−23.9224	+	24.8375i	−0.933300	+	0.969002i
$658$	−30.1372	+	8.07523i	−1.17487	+	0.314805i
$659$	−29.4659	−	10.7247i	−1.14783	−	0.417776i	−0.303095	−	0.952960i	$-0.598020\pi$
$659$	−29.4659	−	10.7247i	−1.14783	−	0.417776i	−0.844735	+	0.535184i	$0.820242\pi$
$660$	0.549997	+	2.78580i	0.0214086	+	0.108437i
$661$	3.28171	+	2.75368i	0.127644	+	0.107106i	0.704375	−	0.709828i	$-0.251227\pi$
$661$	3.28171	+	2.75368i	0.127644	+	0.107106i	−0.576731	+	0.816934i	$0.695672\pi$
$662$	−0.399503	−	4.56634i	−0.0155271	−	0.177476i
$663$	4.52706	+	46.6941i	0.175816	+	1.81345i
$664$	8.40938	−	23.1046i	0.326347	−	0.896632i
$665$	−7.31409	+	8.91402i	−0.283628	+	0.345671i
$666$	−4.68847	+	13.6746i	−0.181674	+	0.529879i
$667$	0.0160385	+	0.00429751i	0.000621014	+	0.000166400i
$668$	29.1901	+	20.4392i	1.12940	+	0.790815i
$669$	−14.4720	+	12.3767i	−0.559520	+	0.478511i
$670$	−4.75397	+	6.95096i	−0.183662	+	0.268539i
$671$	−1.04544	−	0.184339i	−0.0403587	−	0.00711633i
$672$	−11.3833	−	40.9425i	−0.439120	−	1.57939i
$673$	28.3733	+	2.48234i	1.09371	+	0.0956872i	0.619705	−	0.784835i	$-0.287252\pi$
$673$	28.3733	+	2.48234i	1.09371	+	0.0956872i	0.474005	+	0.880522i	$0.342808\pi$
$674$	−18.4533			−0.710793
$675$	9.78551	−	24.0675i	0.376644	−	0.926358i
$676$	24.0691			0.925735
$677$	42.4749	+	3.71607i	1.63244	+	0.142820i	0.866189	−	0.499717i	$-0.166563\pi$
$677$	42.4749	+	3.71607i	1.63244	+	0.142820i	0.766255	+	0.642537i	$0.222118\pi$
$678$	5.46877	−	5.57237i	0.210027	−	0.214006i
$679$	−36.3444	−	6.40849i	−1.39477	−	0.245935i
$680$	14.8373	−	21.6941i	0.568983	−	0.831933i
$681$	3.13458	+	16.8510i	0.120118	+	0.645731i
$682$	0.541592	+	0.379227i	0.0207386	+	0.0145213i
$683$	−16.5292	−	4.42899i	−0.632473	−	0.169471i	−0.0716812	−	0.997428i	$-0.522836\pi$
$683$	−16.5292	−	4.42899i	−0.632473	−	0.169471i	−0.560792	+	0.827957i	$0.689503\pi$
$684$	−5.63430	−	0.884807i	−0.215433	−	0.0338314i
$685$	−14.6224	+	17.8210i	−0.558692	+	0.680904i
$686$	4.30892	−	11.8386i	0.164515	−	0.452002i
$687$	13.7073	−	9.79087i	0.522965	−	0.373545i
$688$	0.282400	+	3.22785i	0.0107664	+	0.123061i
$689$	−22.6501	−	19.0057i	−0.862901	−	0.724060i
$690$	−6.47239	−	2.20739i	−0.246400	−	0.0840338i
$691$	−28.7479	−	10.4634i	−1.09362	−	0.398045i	−0.268660	−	0.963235i	$-0.586581\pi$
$691$	−28.7479	−	10.4634i	−1.09362	−	0.398045i	−0.824961	+	0.565190i	$0.808803\pi$
$692$	−3.54310	+	0.949372i	−0.134689	+	0.0360897i
$693$	−5.93256	+	0.631410i	−0.225359	+	0.0239853i
$694$	−16.3892	+	9.46233i	−0.622127	+	0.359185i
$695$	2.70530	−	2.76552i	0.102618	−	0.104902i
$696$	−0.0236632	+	0.00440177i	−0.000896951	+	0.000166849i
$697$	−10.1632	+	21.7951i	−0.384959	+	0.825547i
$698$	7.58187	+	10.8280i	0.286978	+	0.409847i
$699$	−0.164423	−	17.5233i	−0.00621905	−	0.662792i
$700$	−13.7709	+	31.3134i	−0.520491	+	1.18353i
$701$			33.1045i			1.25034i	0.780488	+	0.625171i	$0.214971\pi$
$701$			33.1045i			1.25034i	−0.780488	+	0.625171i	$0.785029\pi$
$702$	−12.1543	+	12.8586i	−0.458734	+	0.485315i
$703$	−6.35572	−	6.35572i	−0.239710	−	0.239710i
$704$	−0.0911416	+	0.0764768i	−0.00343503	+	0.00288233i
$705$	4.69663	+	43.4578i	0.176885	+	1.63671i
$706$	−0.195420	+	1.10828i	−0.00735472	+	0.0417107i
$707$	−61.2863	−	28.5783i	−2.30491	−	1.07480i
$708$	1.13418	+	0.0885133i	0.0426252	+	0.00332653i
$709$	36.6991	−	6.47105i	1.37827	−	0.243025i	0.565083	−	0.825034i	$-0.308844\pi$
$709$	36.6991	−	6.47105i	1.37827	−	0.243025i	0.813182	+	0.582009i	$0.197733\pi$
$710$	1.00587	−	0.378697i	0.0377498	−	0.0142122i
$711$	−0.906370	−	4.63042i	−0.0339915	−	0.173654i
$712$	7.58092	+	28.2924i	0.284107	+	1.06030i
$713$	5.56503	−	2.59502i	0.208412	−	0.0971841i
$714$	18.8699	+	15.5344i	0.706189	+	0.581359i
$715$	−4.15693	+	3.56677i	−0.155460	+	0.133390i
$716$	21.2116	−	25.2790i	0.792716	−	0.944722i
$717$	−2.29123	+	5.03639i	−0.0855674	+	0.188087i
$718$	−5.10759	−	10.9533i	−0.190614	−	0.408772i
$719$	21.5770	−	37.3725i	0.804687	−	1.39376i	−0.111816	−	0.993729i	$-0.535667\pi$
$719$	21.5770	−	37.3725i	0.804687	−	1.39376i	0.916502	−	0.400029i	$-0.131000\pi$
$720$	−11.3168	+	1.33058i	−0.421751	+	0.0495877i
$721$	−30.1509	−	52.2229i	−1.12288	−	1.94488i
$722$	6.46621	−	9.23470i	0.240647	−	0.343680i
$723$	−31.6903	+	15.1410i	−1.17857	+	0.563101i
$724$	−1.75433	−	4.82000i	−0.0651993	−	0.179134i
$725$	0.0264575	+	0.0145083i	0.000982606	+	0.000538826i
$726$	−6.09211	−	10.3268i	−0.226099	−	0.383265i
$727$	0.590839	−	6.75332i	0.0219130	−	0.250467i	−0.977335	−	0.211698i	$-0.932101\pi$
$727$	0.590839	−	6.75332i	0.0219130	−	0.250467i	0.999248	−	0.0387690i	$-0.0123436\pi$
$728$	37.2180	−	37.2180i	1.37939	−	1.37939i
$729$	1.51922	+	26.9572i	0.0562673	+	0.998416i
$730$	9.60915	+	13.4068i	0.355651	+	0.496207i
$731$	−6.25882	−	7.45897i	−0.231491	−	0.275880i
$732$	1.57976	−	6.12505i	0.0583896	−	0.226388i
$733$	−20.8024	+	14.5660i	−0.768353	+	0.538006i	−0.890760	−	0.454474i	$-0.849827\pi$
$733$	−20.8024	+	14.5660i	−0.768353	+	0.538006i	0.122408	+	0.992480i	$0.460938\pi$
$734$	16.2116	−	5.90055i	0.598382	−	0.217793i
$735$	−39.2124	−	21.5855i	−1.44637	−	0.796194i
$736$	2.72113	+	15.4323i	0.100302	+	0.568841i
$737$	0.701189	−	2.61687i	0.0258286	−	0.0963937i
$738$	−8.71539	+	2.51148i	−0.320818	+	0.0924489i
$739$	−31.3022	−	18.0723i	−1.15147	−	0.664801i	−0.202224	−	0.979339i	$-0.564817\pi$
$739$	−31.3022	−	18.0723i	−1.15147	−	0.664801i	−0.949245	+	0.314538i	$0.898150\pi$
$740$	−23.2384	−	13.0778i	−0.854259	−	0.480749i
$741$	−3.85957	−	10.3023i	−0.141785	−	0.378463i
$742$	−15.3461	+	1.34261i	−0.563371	+	0.0492886i
$743$	35.7603	−	3.12862i	1.31192	−	0.114778i	0.590365	−	0.807136i	$-0.298984\pi$
$743$	35.7603	−	3.12862i	1.31192	−	0.114778i	0.721554	+	0.692358i	$0.243428\pi$
$744$	−5.65712	+	6.87182i	−0.207400	+	0.251933i
$745$	9.88838	−	2.76658i	0.362282	−	0.101360i
$746$	−1.75479	−	1.01313i	−0.0642473	−	0.0370932i
$747$	17.8779	−	26.5803i	0.654119	−	0.972522i
$748$	−0.968627	+	3.61497i	−0.0354165	+	0.132176i
$749$	3.03056	+	17.1872i	0.110734	+	0.628006i
$750$	−10.4728	−	6.69005i	−0.382412	−	0.244286i
$751$	20.6234	−	7.50630i	0.752558	−	0.273909i	0.0628763	−	0.998021i	$-0.479973\pi$
$751$	20.6234	−	7.50630i	0.752558	−	0.273909i	0.689682	+	0.724113i	$0.257750\pi$
$752$	15.7038	−	10.9959i	0.572660	−	0.400981i
$753$	23.7099	−	6.59210i	0.864038	−	0.240230i
$754$	−0.0132091	−	0.0157420i	−0.000481047	−	0.000573290i
$755$	8.05261	−	5.77161i	0.293065	−	0.210051i
$756$	−1.00054	−	35.5356i	−0.0363892	−	1.29242i
$757$	−19.9998	+	19.9998i	−0.726906	+	0.726906i	−0.970002	−	0.243096i	$-0.921837\pi$
$757$	−19.9998	+	19.9998i	−0.726906	+	0.726906i	0.243096	+	0.970002i	$0.421837\pi$
$758$	0.408186	−	4.66559i	0.0148260	−	0.169462i
$759$	2.19991	−	0.0206420i	0.0798516	−	0.000749256i
$760$	−2.04417	+	5.81466i	−0.0741500	+	0.210920i
$761$	17.7365	+	48.7306i	0.642947	+	1.76648i	0.642264	+	0.766484i	$0.277995\pi$
$761$	17.7365	+	48.7306i	0.642947	+	1.76648i	0.000683402		1.00000i	$0.499782\pi$
$762$	−7.68399	−	5.27364i	−0.278362	−	0.191044i
$763$	−16.4135	+	23.4409i	−0.594209	+	0.848619i
$764$	−0.366534	−	0.634856i	−0.0132607	−	0.0229683i
$765$	25.5641	−	22.7814i	0.924272	−	0.823664i
$766$	5.89884	−	10.2171i	0.213134	−	0.369159i
$767$	0.927410	+	1.98884i	0.0334868	+	0.0718127i
$768$	−7.77122	−	10.8797i	−0.280420	−	0.392589i
$769$	28.9226	−	34.4686i	1.04298	−	1.24297i	0.0736257	−	0.997286i	$-0.476543\pi$
$769$	28.9226	−	34.4686i	1.04298	−	1.24297i	0.969350	−	0.245684i	$-0.0790126\pi$
$770$	−0.217414	+	2.84542i	−0.00783506	+	0.102542i
$771$	−8.05659	+	48.3391i	−0.290151	+	1.74089i
$772$	3.27462	−	1.52698i	0.117856	−	0.0549572i
$773$	6.21709	+	23.2025i	0.223613	+	0.834536i	0.982955	+	0.183844i	$0.0588542\pi$
$773$	6.21709	+	23.2025i	0.223613	+	0.834536i	−0.759342	+	0.650691i	$0.774479\pi$
$774$	0.569731	−	3.62795i	0.0204786	−	0.130404i
$775$	10.9437	−	2.17907i	0.393111	−	0.0782746i
$776$	−19.4273	+	3.42556i	−0.697399	+	0.122970i
$777$	31.7028	−	46.1928i	1.13733	−	1.65716i
$778$	−12.2235	−	5.69992i	−0.438234	−	0.204352i
$779$	0.979290	−	5.55383i	0.0350867	−	0.198987i
$780$	−19.2615	−	26.3482i	−0.689673	−	0.943417i
$781$	−0.264879	+	0.222260i	−0.00947813	+	0.00795309i
$782$	−6.37309	−	6.37309i	−0.227901	−	0.227901i
$783$	−0.0313033	−	0.00185275i	−0.00111869	−	6.62117e-5i
$784$			19.6314i			0.701122i
$785$	0.948338	+	1.60160i	0.0338476	+	0.0571635i
$786$	11.0699	+	6.25344i	0.394849	+	0.223053i
$787$	−18.8846	−	26.9699i	−0.673162	−	0.961375i	−0.999868	−	0.0162488i	$-0.994828\pi$
$787$	−18.8846	−	26.9699i	−0.673162	−	0.961375i	0.326706	−	0.945126i	$-0.394061\pi$
$788$	−17.9224	+	38.4347i	−0.638460	+	1.36918i
$789$	−5.90923	−	6.90963i	−0.210374	−	0.245989i
$790$	−2.25674	+	0.0248392i	−0.0802911	+	0.000883739i
$791$	−26.2051	+	15.1295i	−0.931746	+	0.537944i
$792$	−2.86447	+	1.40175i	−0.101785	+	0.0498092i
$793$	11.7858	−	3.15800i	0.418527	−	0.112144i
$794$	20.4646	+	7.44852i	0.726263	+	0.264338i
$795$	−1.44224	+	21.5333i	−0.0511511	+	0.763708i
$796$	−29.0150	−	24.3465i	−1.02841	−	0.862939i
$797$	4.05225	+	46.3175i	0.143538	+	1.64065i	0.636988	+	0.770874i	$0.280180\pi$
$797$	4.05225	+	46.3175i	0.143538	+	1.64065i	−0.493449	+	0.869774i	$0.664264\pi$
$798$	−5.21724	−	2.37350i	−0.184688	−	0.0840209i
$799$	−19.7037	+	54.1355i	−0.697068	+	1.91518i
$800$	−1.85692	+	28.4165i	−0.0656522	+	1.00467i
$801$	0.716067	+	38.1539i	0.0253010	+	1.34810i
$802$	16.8618	+	4.51810i	0.595410	+	0.159540i
$803$	−4.34687	−	3.04371i	−0.153398	−	0.107410i
$804$	15.2207	+	5.37868i	0.536792	+	0.189692i
$805$	21.8760	+	14.9616i	0.771026	+	0.527328i
$806$	−7.48391	−	1.31962i	−0.263610	−	0.0464815i
$807$	18.8416	+	4.85958i	0.663256	+	0.171065i
$808$	−36.0087	−	3.15035i	−1.26678	−	0.110829i
$809$	−14.6731			−0.515879			−0.257939	−	0.966161i	$-0.583043\pi$
$809$	−14.6731			−0.515879			−0.257939	+	0.966161i	$0.583043\pi$
$810$	12.8124	+	1.62290i	0.450181	+	0.0570228i
$811$	30.4369			1.06878			0.534392	−	0.845237i	$-0.320541\pi$
$811$	30.4369			1.06878			0.534392	+	0.845237i	$0.320541\pi$
$812$	0.0411306	+	0.00359846i	0.00144340	+	0.000126281i
$813$	−25.8067	−	6.65600i	−0.905080	−	0.233436i
$814$	−2.19073	−	0.386284i	−0.0767849	−	0.0135393i
$815$	31.5685	−	5.92535i	1.10580	−	0.207556i
$816$	−14.1599	−	5.00381i	−0.495694	−	0.175169i
$817$	1.87046	+	1.30971i	0.0654390	+	0.0458209i
$818$	8.41525	+	2.25486i	0.294232	+	0.0788393i
$819$	58.7327	−	35.3952i	2.05229	−	1.23681i
$820$	−1.64152	−	16.6499i	−0.0573242	−	0.581439i
$821$	5.06906	−	13.9271i	0.176911	−	0.486060i	−0.819266	−	0.573414i	$-0.805619\pi$
$821$	5.06906	−	13.9271i	0.176911	−	0.486060i	0.996177	+	0.0873536i	$0.0278410\pi$
$822$	−10.4303	−	4.74511i	−0.363799	−	0.165505i
$823$	−1.04135	−	11.9027i	−0.0362993	−	0.414903i	−0.992505	−	0.122206i	$-0.961003\pi$
$823$	−1.04135	−	11.9027i	−0.0362993	−	0.414903i	0.956205	−	0.292696i	$-0.0945525\pi$
$824$	−24.6922	−	20.7192i	−0.860193	−	0.721788i
$825$	3.89233	+	0.913023i	0.135514	+	0.0317874i
$826$	1.07435	+	0.391031i	0.0373813	+	0.0136057i
$827$	5.37558	−	1.44038i	0.186927	−	0.0500870i	−0.164141	−	0.986437i	$-0.552485\pi$
$827$	5.37558	−	1.44038i	0.186927	−	0.0500870i	0.351068	+	0.936350i	$0.385819\pi$
$828$	−0.897279	+	13.0783i	−0.0311826	+	0.454503i
$829$	−34.1754	+	19.7312i	−1.18696	+	0.685293i	−0.957615	−	0.288052i	$-0.906992\pi$
$829$	−34.1754	+	19.7312i	−1.18696	+	0.685293i	−0.229347	+	0.973345i	$0.573659\pi$
$830$	−10.9531	−	10.7146i	−0.380188	−	0.371910i
$831$	−18.4856	−	21.6151i	−0.641258	−	0.749820i
$832$	0.577937	−	1.23939i	0.0200364	−	0.0429681i
$833$	−33.8375	−	48.3250i	−1.17240	−	1.67436i
$834$	1.67439	+	0.945873i	0.0579793	+	0.0327529i
$835$	43.1713	−	25.5626i	1.49401	−	0.884630i
$836$		−	0.877645i		−	0.0303540i
$837$	−9.30819	+	6.91610i	−0.321738	+	0.239055i
$838$	5.79766	+	5.79766i	0.200277	+	0.200277i
$839$	34.4322	−	28.8921i	1.18873	−	0.997464i	0.188851	−	0.982006i	$-0.439524\pi$
$839$	34.4322	−	28.8921i	1.18873	−	0.997464i	0.999881	−	0.0154586i	$-0.00492084\pi$
$840$	−37.9624	−	5.89847i	−1.30983	−	0.203516i
$841$	−5.03579	+	28.5594i	−0.173648	+	0.984807i
$842$	−10.4753	−	4.88471i	−0.361003	−	0.168338i
$843$	−9.45749	+	13.7801i	−0.325733	+	0.474612i
$844$	−33.9320	+	5.98313i	−1.16799	+	0.205948i
$845$	13.9829	−	30.8689i	0.481025	−	1.06192i
$846$	−20.2748	+	7.81330i	−0.697061	+	0.268627i
$847$	12.0268	+	44.8845i	0.413244	+	1.54225i
$848$	8.57848	−	4.00021i	0.294586	−	0.137368i
$849$	4.41930	−	26.5156i	0.151670	−	0.910012i
$850$	−8.49962	−	14.0008i	−0.291535	−	0.480222i
$851$	−13.2797	+	15.8261i	−0.455222	+	0.542513i
$852$	−1.19755	−	1.67658i	−0.0410275	−	0.0574387i
$853$	−3.70943	−	7.95489i	−0.127008	−	0.272370i	0.832513	−	0.554005i	$-0.186901\pi$
$853$	−3.70943	−	7.95489i	−0.127008	−	0.272370i	−0.959522	+	0.281635i	$0.909123\pi$
$854$	3.17850	−	5.50532i	0.108766	−	0.188388i
$855$	−4.40800	+	6.71202i	−0.150750	+	0.229546i
$856$	4.66443	+	8.07903i	0.159427	+	0.276135i
$857$	−19.8301	+	28.3204i	−0.677385	+	0.967406i	0.322399	+	0.946604i	$0.395511\pi$
$857$	−19.8301	+	28.3204i	−0.677385	+	0.967406i	−0.999784	+	0.0208017i	$0.993378\pi$
$858$	−2.24491	−	1.54072i	−0.0766399	−	0.0525991i
$859$	6.70299	+	18.4163i	0.228703	+	0.628357i	0.999967	−	0.00815913i	$-0.00259716\pi$
$859$	6.70299	+	18.4163i	0.228703	+	0.628357i	−0.771264	+	0.636516i	$0.780375\pi$
$860$	6.39071	+	2.24669i	0.217922	+	0.0766114i
$861$	35.1502	−	0.329818i	1.19791	−	0.0112402i
$862$	−0.268587	+	3.06997i	−0.00914812	+	0.104563i
$863$	29.8911	−	29.8911i	1.01750	−	1.01750i	0.0176605	−	0.999844i	$-0.494378\pi$
$863$	29.8911	−	29.8911i	1.01750	−	1.01750i	0.999844	−	0.0176605i	$-0.00562181\pi$
$864$	−10.9005	−	27.5136i	−0.370843	−	0.936032i
$865$	−0.840774	+	5.09560i	−0.0285872	+	0.173255i
$866$	−13.8033	−	16.4501i	−0.469055	−	0.558998i
$867$	15.1121	−	4.20164i	0.513234	−	0.142695i
$868$	12.5071	−	8.75757i	0.424519	−	0.297251i
$869$	0.682275	−	0.248328i	0.0231446	−	0.00842394i
$870$	−0.00358592	+	0.0145644i	−0.000121574	+	0.000493779i
$871$	5.40728	+	30.6662i	0.183219	+	1.03908i
$872$	−3.95897	+	14.7751i	−0.134068	+	0.500347i
$873$	−25.6407	−	1.75916i	−0.867807	−	0.0595386i
$874$	1.83043	+	1.05680i	0.0619154	+	0.0357469i
$875$	32.1596	+	35.8527i	1.08719	+	1.21204i
$876$	20.0967	−	24.4119i	0.679005	−	0.824801i
$877$	−32.6921	+	2.86019i	−1.10393	+	0.0965817i	−0.624521	−	0.781008i	$-0.714706\pi$
$877$	−32.6921	+	2.86019i	−1.10393	+	0.0965817i	−0.479413	+	0.877590i	$0.659150\pi$
$878$	−0.345129	+	0.0301948i	−0.0116475	+	0.00101903i
$879$	5.86171	+	15.6465i	0.197711	+	0.527745i
$880$	−0.472439	−	1.68860i	−0.0159259	−	0.0569228i
$881$	−10.5631	−	6.09860i	−0.355879	−	0.205467i	0.311392	−	0.950281i	$-0.399205\pi$
$881$	−10.5631	−	6.09860i	−0.355879	−	0.205467i	−0.667272	+	0.744814i	$0.732538\pi$
$882$	5.35447	−	21.5963i	0.180294	−	0.727186i
$883$	9.21415	−	34.3877i	0.310081	−	1.15724i	−0.618402	−	0.785862i	$-0.712220\pi$
$883$	9.21415	−	34.3877i	0.310081	−	1.15724i	0.928483	−	0.371376i	$-0.121114\pi$
$884$	−7.46965	−	42.3625i	−0.251232	−	1.42480i
$885$	0.772418	−	1.40318i	0.0259646	−	0.0471673i
$886$	−3.13665	+	1.14165i	−0.105378	+	0.0383544i
$887$	8.21054	−	5.74909i	0.275683	−	0.193035i	−0.427556	−	0.903989i	$-0.640625\pi$
$887$	8.21054	−	5.74909i	0.275683	−	0.193035i	0.703239	+	0.710954i	$0.251736\pi$
$888$	7.47922	−	28.9985i	0.250986	−	0.973126i
$889$	23.2168	+	27.6687i	0.778666	+	0.927978i
$890$	18.0096	+	2.97159i	0.603684	+	0.0996080i
$891$	−4.06175	+	0.874500i	−0.136074	+	0.0292969i
$892$	12.3466	−	12.3466i	0.413396	−	0.413396i
$893$	1.17747	−	13.4586i	0.0394027	−	0.450374i
$894$	2.59345	+	4.39620i	0.0867378	+	0.147031i
$895$	−20.0978	−	41.8899i	−0.671795	−	1.40022i
$896$	16.5391	+	45.4408i	0.552532	+	1.51807i
$897$	−22.8163	+	10.9012i	−0.761815	+	0.363981i
$898$	−5.15187	+	7.35763i	−0.171920	+	0.245527i
$899$	−0.00673405	−	0.0116637i	−0.000224593	−	0.000389007i
$900$	−7.22842	+	22.6994i	−0.240947	+	0.756648i
$901$	−14.2220	+	24.6332i	−0.473803	+	0.820651i
$902$	−0.589856	−	1.26495i	−0.0196401	−	0.0421183i
$903$	−5.89372	+	12.9551i	−0.196131	+	0.431119i
$904$	−10.3968	+	12.3904i	−0.345791	+	0.412098i
$905$	−7.20086	−	0.550206i	−0.239365	−	0.0182895i
$906$	3.80219	+	3.13010i	0.126319	+	0.103990i
$907$	−16.0298	+	7.47482i	−0.532261	+	0.248197i	−0.670118	−	0.742255i	$-0.733756\pi$
$907$	−16.0298	+	7.47482i	−0.532261	+	0.248197i	0.137857	+	0.990452i	$0.455979\pi$
$908$	−4.06766	−	15.1807i	−0.134990	−	0.503790i
$909$	−44.5470	−	15.2734i	−1.47753	−	0.506587i
$910$	−11.5570	−	30.6970i	−0.383110	−	1.01760i
$911$	15.2588	−	2.69054i	0.505547	−	0.0891416i	0.0849428	−	0.996386i	$-0.472929\pi$
$911$	15.2588	−	2.69054i	0.505547	−	0.0891416i	0.420604	+	0.907244i	$0.361818\pi$
$912$	3.51117	+	0.274017i	0.116266	+	0.00907360i
$913$	4.46752	+	2.08324i	0.147853	+	0.0689451i
$914$	−0.427785	+	2.42609i	−0.0141499	+	0.0802478i
$915$	−6.93768	−	5.58438i	−0.229353	−	0.184614i
$916$	−11.8320	+	9.92824i	−0.390941	+	0.328038i
$917$	−34.8423	−	34.8423i	−1.15059	−	1.15059i
$918$	14.2123	+	9.36675i	0.469077	+	0.309149i
$919$		−	18.6392i		−	0.614851i	−0.951572	−	0.307426i	$-0.900532\pi$
$919$		−	18.6392i		−	0.614851i	0.951572	−	0.307426i	$-0.0994676\pi$
$920$	13.7235	+	3.51579i	0.452452	+	0.115912i
$921$	−0.0712484	−	7.59326i	−0.00234771	−	0.250206i
$922$	8.20222	+	11.7140i	0.270126	+	0.385779i
$923$	1.67962	−	3.60196i	0.0552855	−	0.118560i
$924$	5.37821	−	1.00044i	0.176930	−	0.0329121i
$925$	−30.2726	+	22.2059i	−0.995357	+	0.730126i
$926$	0.663128	−	0.382857i	0.0217917	−	0.0125815i
$927$	−24.7285	−	33.9420i	−0.812189	−	1.11480i
$928$	0.0331999	−	0.00889589i	0.00108984	−	0.000292022i
$929$	−9.92982	−	3.61416i	−0.325787	−	0.118577i	0.173949	−	0.984755i	$-0.444347\pi$
$929$	−9.92982	−	3.61416i	−0.325787	−	0.118577i	−0.499736	+	0.866178i	$0.666569\pi$
$930$	2.44619	+	4.97828i	0.0802136	+	0.163244i
$931$	10.5979	+	8.89269i	0.347332	+	0.291446i
$932$	1.40045	+	16.0072i	0.0458733	+	0.524334i
$933$	−11.6873	+	8.34801i	−0.382623	+	0.273302i
$934$	−0.197650	+	0.543040i	−0.00646732	+	0.0177688i
$935$	4.07351	+	3.34237i	0.133218	+	0.109307i
$936$	23.0303	−	28.5165i	0.752769	−	0.932091i
$937$	−14.3508	−	3.84529i	−0.468820	−	0.125620i	0.0166719	−	0.999861i	$-0.494693\pi$
$937$	−14.3508	−	3.84529i	−0.468820	−	0.125620i	−0.485492	+	0.874241i	$0.661360\pi$
$938$	13.2895	+	9.30540i	0.433917	+	0.303832i
$939$	3.27884	+	17.6265i	0.107001	+	0.575219i
$940$	−7.39378	−	39.3919i	−0.241159	−	1.28482i
$941$	16.9600	+	2.99051i	0.552882	+	0.0974879i	0.443107	−	0.896469i	$-0.353876\pi$
$941$	16.9600	+	2.99051i	0.552882	+	0.0974879i	0.109774	+	0.993957i	$0.464987\pi$
$942$	−0.648073	+	0.660350i	−0.0211154	+	0.0215154i
$943$	−12.9130	−	1.12974i	−0.420504	−	0.0367894i
$944$	−0.702492			−0.0228642
$945$	−46.1560	−	19.3611i	−1.50145	−	0.629815i
$946$	0.565120			0.0183736
$947$	−59.3613	−	5.19344i	−1.92898	−	0.168764i	−0.942678	−	0.333704i	$-0.891701\pi$
$947$	−59.3613	−	5.19344i	−1.92898	−	0.168764i	−0.986304	+	0.164940i	$0.947257\pi$
$948$	1.15890	+	4.16824i	0.0376394	+	0.135378i
$949$	60.0667	+	10.5914i	1.94985	+	0.343811i
$950$	2.77510	+	2.65554i	0.0900360	+	0.0861569i
$951$	−1.78777	+	1.52893i	−0.0579723	+	0.0495789i
$952$	−41.4769	−	29.0424i	−1.34427	−	0.941271i
$953$	−7.58847	−	2.03332i	−0.245815	−	0.0658658i	0.133808	−	0.991007i	$-0.457279\pi$
$953$	−7.58847	−	2.03332i	−0.245815	−	0.0658658i	−0.379623	+	0.925141i	$0.623946\pi$
$954$	−10.5282	+	2.06081i	−0.340862	+	0.0667212i
$955$	−1.02715	+	0.101267i	−0.0332377	+	0.00327691i
$956$	1.73522	−	4.76748i	0.0561211	−	0.154191i
$957$	−0.000465651	−	0.00480293i	−1.50524e−5	−	0.000155257i
$958$	1.64431	+	18.7946i	0.0531253	+	0.607225i
$959$	34.0202	+	28.5463i	1.09857	+	0.921808i
$960$	−0.979253	+	0.193333i	−0.0316052	+	0.00623979i
$961$	24.4503	+	8.89918i	0.788719	+	0.287070i
$962$	24.6973	−	6.61763i	0.796274	−	0.213361i
$963$	3.36542	+	11.6787i	0.108449	+	0.376342i
$964$	27.8895	−	16.1020i	0.898261	−	0.518611i
$965$	−0.0559891	−	5.08682i	−0.00180235	−	0.163751i
$966$	−4.38954	+	12.4216i	−0.141231	+	0.399657i
$967$	−13.1660	+	28.2347i	−0.423392	+	0.907966i	0.572710	+	0.819758i	$0.305892\pi$
$967$	−13.1660	+	28.2347i	−0.423392	+	0.907966i	−0.996102	+	0.0882085i	$0.971886\pi$
$968$	14.2469	+	20.3466i	0.457911	+	0.653965i
$969$	−9.11545	+	5.37747i	−0.292830	+	0.172749i
$970$	−3.05089	+	11.9088i	−0.0979581	+	0.382370i
$971$			46.4614i			1.49102i	0.666496	+	0.745509i	$0.267793\pi$
$971$			46.4614i			1.49102i	−0.666496	+	0.745509i	$0.732207\pi$
$972$	−3.31197	−	24.5346i	−0.106231	−	0.786947i
$973$	−5.27012	−	5.27012i	−0.168952	−	0.168952i
$974$	−15.7126	+	13.1844i	−0.503464	+	0.422456i
$975$	−44.9817	+	9.39620i	−1.44057	+	0.300919i
$976$	−0.678273	+	3.84668i	−0.0217110	+	0.123129i
$977$	30.9924	+	14.4520i	0.991534	+	0.462360i	0.849549	−	0.527509i	$-0.176874\pi$
$977$	30.9924	+	14.4520i	0.991534	+	0.462360i	0.141985	+	0.989869i	$0.454652\pi$
$978$	6.88317	+	14.4065i	0.220100	+	0.460670i
$979$	−5.78303	+	1.01970i	−0.184826	+	0.0325899i
$980$	37.3860	+	16.9349i	1.19425	+	0.540967i
$981$	−9.63865	+	17.4425i	−0.307739	+	0.556897i
$982$	2.10878	+	7.87006i	0.0672937	+	0.251144i
$983$	32.2428	−	15.0350i	1.02838	−	0.479543i	0.166175	−	0.986096i	$-0.446858\pi$
$983$	32.2428	−	15.0350i	1.02838	−	0.479543i	0.862209	+	0.506553i	$0.169081\pi$
$984$	17.5955	−	6.59187i	0.560925	−	0.210141i
$985$	38.8810	+	45.3142i	1.23885	+	1.44383i
$986$	−0.0127071	+	0.0151438i	−0.000404677	+	0.000482275i
$987$	83.8164	−	8.12612i	2.66791	−	0.258657i
$988$	4.26321	+	9.14249i	0.135631	+	0.290861i
$989$	2.62418	−	4.54522i	0.0834442	−	0.144530i
$990$	0.0591586	+	1.98647i	0.00188018	+	0.0631343i
$991$	−2.77369	−	4.80418i	−0.0881092	−	0.152610i	0.818603	−	0.574360i	$-0.194749\pi$
$991$	−2.77369	−	4.80418i	−0.0881092	−	0.152610i	−0.906712	+	0.421751i	$0.861416\pi$
$992$	7.29047	−	10.4119i	0.231473	−	0.330577i
$993$	−0.962571	+	12.3341i	−0.0305463	+	0.391411i
$994$	−0.708192	−	1.94574i	−0.0224625	−	0.0617152i
$995$	−48.0808	+	23.0681i	−1.52426	+	0.731307i
$996$	−14.4468	+	25.5739i	−0.457766	+	0.810338i
$997$	2.65905	−	30.3931i	0.0842129	−	0.962558i	−0.830117	−	0.557589i	$-0.811727\pi$
$997$	2.65905	−	30.3931i	0.0842129	−	0.962558i	0.914330	−	0.404969i	$-0.132718\pi$
$998$	5.48435	−	5.48435i	0.173604	−	0.173604i
$999$	18.5496	−	34.3251i	0.586883	−	1.08600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.7	yes	192
3.2	odd	2		405.2.r.a.368.10		192
5.2	odd	4	inner	135.2.q.a.32.10	✓	192
5.3	odd	4		675.2.ba.b.32.7		192
5.4	even	2		675.2.ba.b.518.10		192
15.2	even	4		405.2.r.a.287.7		192
27.11	odd	18	inner	135.2.q.a.38.10	yes	192
27.16	even	9		405.2.r.a.278.7		192
135.38	even	36		675.2.ba.b.632.10		192
135.92	even	36	inner	135.2.q.a.92.7	yes	192
135.97	odd	36		405.2.r.a.197.10		192
135.119	odd	18		675.2.ba.b.443.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.10	✓	192	5.2	odd	4	inner
135.2.q.a.38.10	yes	192	27.11	odd	18	inner
135.2.q.a.92.7	yes	192	135.92	even	36	inner
135.2.q.a.113.7	yes	192	1.1	even	1	trivial
405.2.r.a.197.10		192	135.97	odd	36
405.2.r.a.278.7		192	27.16	even	9
405.2.r.a.287.7		192	15.2	even	4
405.2.r.a.368.10		192	3.2	odd	2
675.2.ba.b.32.7		192	5.3	odd	4
675.2.ba.b.443.7		192	135.119	odd	18
675.2.ba.b.518.10		192	5.4	even	2
675.2.ba.b.632.10		192	135.38	even	36

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)

\(f(q)\)	\(=\)	\(q+(-0.639298 - 0.0559313i) q^{2} +(1.67717 + 0.432570i) q^{3} +(-1.56404 - 0.275783i) q^{4} +(-1.26232 + 1.84568i) q^{5} +(-1.04801 - 0.370347i) q^{6} +(3.52875 + 2.47086i) q^{7} +(2.22421 + 0.595975i) q^{8} +(2.62577 + 1.45098i) q^{9} +O(q^{10})\)	\(q+(-0.639298 - 0.0559313i) q^{2} +(1.67717 + 0.432570i) q^{3} +(-1.56404 - 0.275783i) q^{4} +(-1.26232 + 1.84568i) q^{5} +(-1.04801 - 0.370347i) q^{6} +(3.52875 + 2.47086i) q^{7} +(2.22421 + 0.595975i) q^{8} +(2.62577 + 1.45098i) q^{9} +(0.910229 - 1.10934i) q^{10} +(-0.157893 + 0.433806i) q^{11} +(-2.50386 - 1.13909i) q^{12} +(-0.462462 - 5.28596i) q^{13} +(-2.11772 - 1.77698i) q^{14} +(-2.91551 + 2.54948i) q^{15} +(1.59619 + 0.580964i) q^{16} +(-4.93057 + 1.32114i) q^{17} +(-1.59749 - 1.07447i) q^{18} +(1.03667 - 0.598524i) q^{19} +(2.48333 - 2.53860i) q^{20} +(4.84948 + 5.67047i) q^{21} +(0.125204 - 0.268500i) q^{22} +(-1.57814 - 2.25381i) q^{23} +(3.47256 + 1.96168i) q^{24} +(-1.81310 - 4.65968i) q^{25} +3.40517i q^{26} +(3.77619 + 3.56937i) q^{27} +(-4.83770 - 4.83770i) q^{28} +(-0.00462297 + 0.00387914i) q^{29} +(2.00647 - 1.46681i) q^{30} +(-0.387533 + 2.19781i) q^{31} +(-5.16180 - 2.40699i) q^{32} +(-0.452464 + 0.659265i) q^{33} +(3.22599 - 0.568830i) q^{34} +(-9.01483 + 3.39395i) q^{35} +(-3.70665 - 2.99354i) q^{36} +(-1.94341 - 7.25290i) q^{37} +(-0.696220 + 0.324653i) q^{38} +(1.51093 - 9.06548i) q^{39} +(-3.90764 + 3.35288i) q^{40} +(3.02828 - 3.60897i) q^{41} +(-2.78310 - 3.89636i) q^{42} +(0.806157 + 1.72881i) q^{43} +(0.366587 - 0.634947i) q^{44} +(-5.99261 + 3.01473i) q^{45} +(0.882840 + 1.52912i) q^{46} +(6.47343 - 9.24502i) q^{47} +(2.42576 + 1.66484i) q^{48} +(3.95281 + 10.8602i) q^{49} +(0.898490 + 3.08033i) q^{50} +(-8.84086 + 0.0829548i) q^{51} +(-0.734468 + 8.39501i) q^{52} +(3.94023 - 3.94023i) q^{53} +(-2.21447 - 2.49310i) q^{54} +(-0.601359 - 0.839022i) q^{55} +(6.37611 + 7.59875i) q^{56} +(1.99758 - 0.555389i) q^{57} +(0.00317242 - 0.00222135i) q^{58} +(-0.388624 + 0.141448i) q^{59} +(5.26308 - 3.18344i) q^{60} +(0.399307 + 2.26458i) q^{61} +(0.370675 - 1.38338i) q^{62} +(5.68050 + 11.6081i) q^{63} +(0.223194 + 0.128861i) q^{64} +(10.3400 + 5.81901i) q^{65} +(0.326133 - 0.396160i) q^{66} +(-5.84619 + 0.511475i) q^{67} +(8.07597 - 0.706556i) q^{68} +(-1.67186 - 4.46267i) q^{69} +(5.95299 - 1.66553i) q^{70} +(0.648656 + 0.374502i) q^{71} +(4.97550 + 4.79218i) q^{72} +(-2.97508 + 11.1032i) q^{73} +(0.836752 + 4.74546i) q^{74} +(-1.02523 - 8.59935i) q^{75} +(-1.78647 + 0.650220i) q^{76} +(-1.62904 + 1.14066i) q^{77} +(-1.47297 + 5.71103i) q^{78} +(-1.01095 - 1.20481i) q^{79} +(-3.08717 + 2.21269i) q^{80} +(4.78929 + 7.61989i) q^{81} +(-2.13783 + 2.13783i) q^{82} +(0.930629 - 10.6371i) q^{83} +(-6.02097 - 10.2063i) q^{84} +(3.78554 - 10.7680i) q^{85} +(-0.418680 - 1.15031i) q^{86} +(-0.00943149 + 0.00450619i) q^{87} +(-0.609724 + 0.870776i) q^{88} +(6.36010 + 11.0160i) q^{89} +(3.99968 - 1.59214i) q^{90} +(11.4289 - 19.7955i) q^{91} +(1.84671 + 3.96028i) q^{92} +(-1.60066 + 3.51845i) q^{93} +(-4.65554 + 5.54825i) q^{94} +(-0.203927 + 2.66890i) q^{95} +(-7.61600 - 6.26976i) q^{96} +(-7.76434 + 3.62057i) q^{97} +(-1.91959 - 7.16401i) q^{98} +(-1.04404 + 0.909974i) 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

Representations

Groups

Database

Properties

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