LMFDB - Embedded newform 243.2.g.a.100.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(10,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, not 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			100.8
Character	$\chi$	$=$	243.100
Dual form			243.2.g.a.226.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45464 + 1.95391i) q^{2} +(-1.12821 + 3.76849i) q^{4} +(2.46571 - 1.62172i) q^{5} +(-1.57141 + 1.66559i) q^{7} +(-4.42639 + 1.61107i) q^{8} +O(q^{10})$	\(q+(1.45464 + 1.95391i) q^{2} +(-1.12821 + 3.76849i) q^{4} +(2.46571 - 1.62172i) q^{5} +(-1.57141 + 1.66559i) q^{7} +(-4.42639 + 1.61107i) q^{8} +(6.75541 + 2.45877i) q^{10} +(-2.11643 + 1.06291i) q^{11} +(0.243103 + 0.563577i) q^{13} +(-5.54025 - 0.647562i) q^{14} +(-3.01348 - 1.98200i) q^{16} +(5.54151 - 4.64988i) q^{17} +(-3.45309 - 2.89749i) q^{19} +(3.32960 + 11.1216i) q^{20} +(-5.15546 - 2.58917i) q^{22} +(-5.13927 - 5.44731i) q^{23} +(1.46933 - 3.40630i) q^{25} +(-0.747554 + 1.29480i) q^{26} +(-4.50389 - 7.80096i) q^{28} +(-2.15715 + 0.252135i) q^{29} +(3.02111 - 0.716016i) q^{31} +(0.0369153 + 0.633812i) q^{32} +(17.1464 + 4.06376i) q^{34} +(-1.17350 + 6.65525i) q^{35} +(0.740274 + 4.19830i) q^{37} +(0.638454 - 10.9618i) q^{38} +(-8.30146 + 11.1508i) q^{40} +(3.84487 - 5.16456i) q^{41} +(0.236494 - 4.06045i) q^{43} +(-1.61778 - 9.17491i) q^{44} +(3.16781 - 17.9655i) q^{46} +(0.841921 + 0.199539i) q^{47} +(0.102130 + 1.75351i) q^{49} +(8.79296 - 2.08397i) q^{50} +(-2.39810 + 0.280298i) q^{52} +(1.55323 + 2.69028i) q^{53} +(-3.49475 + 6.05308i) q^{55} +(4.27226 - 9.90421i) q^{56} +(-3.63052 - 3.84812i) q^{58} +(-0.548384 - 0.275409i) q^{59} +(1.56794 + 5.23730i) q^{61} +(5.79364 + 4.86144i) q^{62} +(-6.71074 + 5.63098i) q^{64} +(1.51339 + 0.995369i) q^{65} +(-0.280399 - 0.0327739i) q^{67} +(11.2710 + 26.1292i) q^{68} +(-14.7108 + 7.38804i) q^{70} +(-7.71930 - 2.80960i) q^{71} +(-14.3245 + 5.21369i) q^{73} +(-7.12630 + 7.55343i) q^{74} +(14.8149 - 9.74394i) q^{76} +(1.55539 - 5.19537i) q^{77} +(4.45162 + 5.97957i) q^{79} -10.6446 q^{80} +15.6840 q^{82} +(3.27078 + 4.39342i) q^{83} +(6.12294 - 20.4520i) q^{85} +(8.27778 - 5.44438i) q^{86} +(7.65569 - 8.11456i) q^{88} +(-8.64084 + 3.14501i) q^{89} +(-1.32070 - 0.480697i) q^{91} +(26.3263 - 13.2216i) q^{92} +(0.834806 + 1.93530i) q^{94} +(-13.2132 - 1.54440i) q^{95} +(1.43000 + 0.940523i) q^{97} +(-3.27764 + 2.75027i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.45464	+	1.95391i	1.02858	+	1.38163i	0.921942	+	0.387328i	$0.126602\pi$
$2$	1.45464	+	1.95391i	1.02858	+	1.38163i	0.106641	+	0.994298i	$0.465991\pi$
$3$		0			0
$3$		0			0
$4$	−1.12821	+	3.76849i	−0.564105	+	1.88424i
$5$	2.46571	−	1.62172i	1.10270	−	0.725256i	0.138480	−	0.990365i	$-0.455778\pi$
$5$	2.46571	−	1.62172i	1.10270	−	0.725256i	0.964218	+	0.265110i	$0.0854081\pi$
$6$		0			0
$7$	−1.57141	+	1.66559i	−0.593936	+	0.629535i	−0.952707	−	0.303890i	$-0.901714\pi$
$7$	−1.57141	+	1.66559i	−0.593936	+	0.629535i	0.358771	+	0.933426i	$0.383196\pi$
$8$	−4.42639	+	1.61107i	−1.56496	+	0.569600i
$9$		0			0
$10$	6.75541	+	2.45877i	2.13625	+	0.777531i
$11$	−2.11643	+	1.06291i	−0.638127	+	0.320479i	−0.738282	−	0.674493i	$-0.764362\pi$
$11$	−2.11643	+	1.06291i	−0.638127	+	0.320479i	0.100155	+	0.994972i	$0.468066\pi$
$12$		0			0
$13$	0.243103	+	0.563577i	0.0674247	+	0.156308i	0.948596	−	0.316488i	$-0.102504\pi$
$13$	0.243103	+	0.563577i	0.0674247	+	0.156308i	−0.881172	+	0.472796i	$0.843245\pi$
$14$	−5.54025	−	0.647562i	−1.48069	−	0.173068i
$15$		0			0
$16$	−3.01348	−	1.98200i	−0.753371	−	0.495500i
$17$	5.54151	−	4.64988i	1.34401	−	1.12776i	0.363439	−	0.931618i	$-0.381602\pi$
$17$	5.54151	−	4.64988i	1.34401	−	1.12776i	0.980575	−	0.196144i	$-0.0628421\pi$
$18$		0			0
$19$	−3.45309	−	2.89749i	−0.792193	−	0.664729i	0.154094	−	0.988056i	$-0.450754\pi$
$19$	−3.45309	−	2.89749i	−0.792193	−	0.664729i	−0.946287	+	0.323327i	$0.895199\pi$
$20$	3.32960	+	11.1216i	0.744520	+	2.48687i
$21$		0			0
$22$	−5.15546	−	2.58917i	−1.09915	−	0.552013i
$23$	−5.13927	−	5.44731i	−1.07161	−	1.13584i	−0.990270	−	0.139156i	$-0.955561\pi$
$23$	−5.13927	−	5.44731i	−1.07161	−	1.13584i	−0.0813417	−	0.996686i	$-0.525921\pi$
$24$		0			0
$25$	1.46933	−	3.40630i	0.293867	−	0.681260i
$26$	−0.747554	+	1.29480i	−0.146607	+	0.253931i
$27$		0			0
$28$	−4.50389	−	7.80096i	−0.851155	−	1.47424i
$29$	−2.15715	+	0.252135i	−0.400573	+	0.0468203i	−0.313995	−	0.949425i	$-0.601667\pi$
$29$	−2.15715	+	0.252135i	−0.400573	+	0.0468203i	−0.0865783	+	0.996245i	$0.527593\pi$
$30$		0			0
$31$	3.02111	−	0.716016i	0.542607	−	0.128600i	0.0498330	−	0.998758i	$-0.484131\pi$
$31$	3.02111	−	0.716016i	0.542607	−	0.128600i	0.492774	+	0.870157i	$0.335983\pi$
$32$	0.0369153	+	0.633812i	0.00652577	+	0.112043i
$33$		0			0
$34$	17.1464	+	4.06376i	2.94057	+	0.696929i
$35$	−1.17350	+	6.65525i	−0.198358	+	1.12494i
$36$		0			0
$37$	0.740274	+	4.19830i	0.121700	+	0.690197i	0.983213	+	0.182461i	$0.0584063\pi$
$37$	0.740274	+	4.19830i	0.121700	+	0.690197i	−0.861513	+	0.507736i	$0.830483\pi$
$38$	0.638454	−	10.9618i	0.103571	−	1.77824i
$39$		0			0
$40$	−8.30146	+	11.1508i	−1.31258	+	1.76310i
$41$	3.84487	−	5.16456i	0.600468	−	0.806568i	−0.393137	−	0.919480i	$-0.628610\pi$
$41$	3.84487	−	5.16456i	0.600468	−	0.806568i	0.993605	+	0.112912i	$0.0360177\pi$
$42$		0			0
$43$	0.236494	−	4.06045i	0.0360650	−	0.619213i	−0.931053	−	0.364884i	$-0.881109\pi$
$43$	0.236494	−	4.06045i	0.0360650	−	0.619213i	0.967118	−	0.254328i	$-0.0818544\pi$
$44$	−1.61778	−	9.17491i	−0.243890	−	1.38317i
$45$		0			0
$46$	3.16781	−	17.9655i	0.467068	−	2.64887i
$47$	0.841921	+	0.199539i	0.122807	+	0.0291058i	0.291560	−	0.956553i	$-0.405826\pi$
$47$	0.841921	+	0.199539i	0.122807	+	0.0291058i	−0.168753	+	0.985658i	$0.553974\pi$
$48$		0			0
$49$	0.102130	+	1.75351i	0.0145900	+	0.250501i
$50$	8.79296	−	2.08397i	1.24351	−	0.294718i
$51$		0			0
$52$	−2.39810	+	0.280298i	−0.332557	+	0.0388703i
$53$	1.55323	+	2.69028i	0.213353	+	0.369538i	0.952762	−	0.303718i	$-0.0982282\pi$
$53$	1.55323	+	2.69028i	0.213353	+	0.369538i	−0.739409	+	0.673257i	$0.764895\pi$
$54$		0			0
$55$	−3.49475	+	6.05308i	−0.471231	+	0.816197i
$56$	4.27226	−	9.90421i	0.570905	−	1.32351i
$57$		0			0
$58$	−3.63052	−	3.84812i	−0.476710	−	0.505283i
$59$	−0.548384	−	0.275409i	−0.0713935	−	0.0358552i	0.412744	−	0.910847i	$-0.364570\pi$
$59$	−0.548384	−	0.275409i	−0.0713935	−	0.0358552i	−0.484138	+	0.874992i	$0.660867\pi$
$60$		0			0
$61$	1.56794	+	5.23730i	0.200755	+	0.670567i	0.997778	+	0.0666193i	$0.0212213\pi$
$61$	1.56794	+	5.23730i	0.200755	+	0.670567i	−0.797024	+	0.603948i	$0.793594\pi$
$62$	5.79364	+	4.86144i	0.735793	+	0.617404i
$63$		0			0
$64$	−6.71074	+	5.63098i	−0.838842	+	0.703872i
$65$	1.51339	+	0.995369i	0.187712	+	0.123460i
$66$		0			0
$67$	−0.280399	−	0.0327739i	−0.0342561	−	0.00400397i	0.0989476	−	0.995093i	$-0.468452\pi$
$67$	−0.280399	−	0.0327739i	−0.0342561	−	0.00400397i	−0.133204	+	0.991089i	$0.542526\pi$
$68$	11.2710	+	26.1292i	1.36681	+	3.16863i
$69$		0			0
$70$	−14.7108	+	7.38804i	−1.75828	+	0.883040i
$71$	−7.71930	−	2.80960i	−0.916113	−	0.333438i	−0.159422	−	0.987211i	$-0.550963\pi$
$71$	−7.71930	−	2.80960i	−0.916113	−	0.333438i	−0.756691	+	0.653773i	$0.773185\pi$
$72$		0			0
$73$	−14.3245	+	5.21369i	−1.67656	+	0.610216i	−0.992831	−	0.119525i	$-0.961863\pi$
$73$	−14.3245	+	5.21369i	−1.67656	+	0.610216i	−0.683724	+	0.729741i	$0.739641\pi$
$74$	−7.12630	+	7.55343i	−0.828415	+	0.878069i
$75$		0			0
$76$	14.8149	−	9.74394i	1.69939	−	1.11771i
$77$	1.55539	−	5.19537i	0.177253	−	0.592067i
$78$		0			0
$79$	4.45162	+	5.97957i	0.500847	+	0.672754i	0.978608	−	0.205736i	$-0.0659588\pi$
$79$	4.45162	+	5.97957i	0.500847	+	0.672754i	−0.477761	+	0.878490i	$0.658551\pi$
$80$	−10.6446			−1.19010
$81$		0			0
$82$	15.6840			1.73201
$83$	3.27078	+	4.39342i	0.359015	+	0.482241i	0.944532	−	0.328419i	$-0.106516\pi$
$83$	3.27078	+	4.39342i	0.359015	+	0.482241i	−0.585517	+	0.810660i	$0.699109\pi$
$84$		0			0
$85$	6.12294	−	20.4520i	0.664126	−	2.21833i
$86$	8.27778	−	5.44438i	0.892616	−	0.587083i
$87$		0			0
$88$	7.65569	−	8.11456i	0.816100	−	0.865015i
$89$	−8.64084	+	3.14501i	−0.915927	+	0.333370i	−0.756617	−	0.653858i	$-0.773149\pi$
$89$	−8.64084	+	3.14501i	−0.915927	+	0.333370i	−0.159310	+	0.987229i	$0.550927\pi$
$90$		0			0
$91$	−1.32070	−	0.480697i	−0.138447	−	0.0503907i
$92$	26.3263	−	13.2216i	2.74471	−	1.37844i
$93$		0			0
$94$	0.834806	+	1.93530i	0.0861037	+	0.199611i
$95$	−13.2132	−	1.54440i	−1.35565	−	0.158453i
$96$		0			0
$97$	1.43000	+	0.940523i	0.145194	+	0.0954957i	0.620028	−	0.784580i	$-0.287121\pi$
$97$	1.43000	+	0.940523i	0.145194	+	0.0954957i	−0.474834	+	0.880076i	$0.657492\pi$
$98$	−3.27764	+	2.75027i	−0.331092	+	0.277819i
$99$		0			0
$100$	11.1789	+	9.38019i	1.11789	+	0.938019i
$101$	−2.43084	−	8.11958i	−0.241878	−	0.807928i	−0.989591	−	0.143907i	$-0.954033\pi$
$101$	−2.43084	−	8.11958i	−0.241878	−	0.807928i	0.747713	−	0.664022i	$-0.231152\pi$
$102$		0			0
$103$	−1.62114	−	0.814165i	−0.159735	−	0.0802221i	0.367135	−	0.930167i	$-0.380339\pi$
$103$	−1.62114	−	0.814165i	−0.159735	−	0.0802221i	−0.526871	+	0.849945i	$0.676635\pi$
$104$	−1.98403	−	2.10295i	−0.194550	−	0.206211i
$105$		0			0
$106$	−2.99719	+	6.94826i	−0.291113	+	0.674875i
$107$	−2.26668	+	3.92601i	−0.219129	+	0.379542i	−0.954542	−	0.298077i	$-0.903655\pi$
$107$	−2.26668	+	3.92601i	−0.219129	+	0.379542i	0.735413	+	0.677619i	$0.236988\pi$
$108$		0			0
$109$	−6.62630	−	11.4771i	−0.634684	−	1.09931i	−0.986582	−	0.163267i	$-0.947797\pi$
$109$	−6.62630	−	11.4771i	−0.634684	−	1.09931i	0.351898	−	0.936039i	$-0.385537\pi$
$110$	−16.9108	+	1.97659i	−1.61238	+	0.188460i
$111$		0			0
$112$	8.03661	−	1.90471i	0.759388	−	0.179978i
$113$	−0.249581	−	4.28515i	−0.0234786	−	0.403113i	−0.989489	−	0.144609i	$-0.953808\pi$
$113$	−0.249581	−	4.28515i	−0.0234786	−	0.403113i	0.966010	−	0.258504i	$-0.0832295\pi$
$114$		0			0
$115$	−21.5060	−	5.09701i	−2.00544	−	0.475298i
$116$	1.48355	−	8.41365i	0.137745	−	0.781188i
$117$		0			0
$118$	−0.259574	−	1.47211i	−0.0238957	−	0.135519i
$119$	−0.963157	+	16.5368i	−0.0882924	+	1.51592i
$120$		0			0
$121$	−3.21926	+	4.32422i	−0.292660	+	0.393111i
$122$	−7.95244	+	10.6820i	−0.719980	+	0.967101i
$123$		0			0
$124$	−0.710151	+	12.1928i	−0.0637734	+	1.09495i
$125$	0.661249	+	3.75013i	0.0591439	+	0.335422i
$126$		0			0
$127$	−1.02230	+	5.79777i	−0.0907147	+	0.514469i	0.905262	+	0.424854i	$0.139675\pi$
$127$	−1.02230	+	5.79777i	−0.0907147	+	0.514469i	−0.995977	+	0.0896144i	$0.971437\pi$
$128$	−19.5286	−	4.62836i	−1.72610	−	0.409093i
$129$		0			0
$130$	0.256558	+	4.40492i	0.0225016	+	0.386337i
$131$	12.7074	−	3.01172i	1.11025	−	0.263135i	0.365723	−	0.930724i	$-0.380822\pi$
$131$	12.7074	−	3.01172i	1.11025	−	0.263135i	0.744530	+	0.667589i	$0.232674\pi$
$132$		0			0
$133$	10.2522	−	1.19832i	0.888982	−	0.103907i
$134$	−0.343840	−	0.595549i	−0.0297033	−	0.0514476i
$135$		0			0
$136$	−17.0376	+	29.5099i	−1.46096	+	2.53046i
$137$	−1.79314	+	4.15695i	−0.153198	+	0.355153i	−0.977480	−	0.211026i	$-0.932320\pi$
$137$	−1.79314	+	4.15695i	−0.153198	+	0.355153i	0.824283	+	0.566179i	$0.191579\pi$
$138$		0			0
$139$	3.28896	+	3.48609i	0.278966	+	0.295686i	0.851673	−	0.524074i	$-0.175588\pi$
$139$	3.28896	+	3.48609i	0.278966	+	0.295686i	−0.572707	+	0.819760i	$0.694107\pi$
$140$	−23.7563	−	11.9308i	−2.00777	−	1.00834i
$141$		0			0
$142$	−5.73906	−	19.1698i	−0.481611	−	1.60869i
$143$	−1.11354	−	0.934372i	−0.0931189	−	0.0781361i
$144$		0			0
$145$	−4.91001	+	4.11999i	−0.407754	+	0.342146i
$146$	−31.0240	−	20.4048i	−2.56757	−	1.68871i
$147$		0			0
$148$	−16.6564	−	1.94686i	−1.36915	−	0.160031i
$149$	3.88776	+	9.01284i	0.318498	+	0.738360i	0.999979	+	0.00652473i	$0.00207690\pi$
$149$	3.88776	+	9.01284i	0.318498	+	0.738360i	−0.681481	+	0.731836i	$0.738664\pi$
$150$		0			0
$151$	11.9329	−	5.99293i	0.971087	−	0.487698i	0.108770	−	0.994067i	$-0.465309\pi$
$151$	11.9329	−	5.99293i	0.971087	−	0.487698i	0.862317	+	0.506369i	$0.169013\pi$
$152$	19.9528	+	7.26221i	1.61838	+	0.589043i
$153$		0			0
$154$	12.4138	−	4.51826i	1.00033	−	0.364092i
$155$	6.28799	−	6.66488i	0.505064	−	0.535336i
$156$		0			0
$157$	2.50572	−	1.64804i	0.199978	−	0.131528i	−0.445571	−	0.895247i	$-0.646999\pi$
$157$	2.50572	−	1.64804i	0.199978	−	0.131528i	0.645549	+	0.763719i	$0.276629\pi$
$158$	−5.20808	+	17.3962i	−0.414332	+	1.38397i
$159$		0			0
$160$	1.11889	+	1.50293i	0.0884559	+	0.118817i
$161$	17.1489			1.35152
$162$		0			0
$163$	17.7302			1.38874			0.694370	−	0.719618i	$-0.255683\pi$
$163$	17.7302			1.38874			0.694370	+	0.719618i	$0.255683\pi$
$164$	15.1247	+	20.3160i	1.18104	+	1.58642i
$165$		0			0
$166$	−3.82657	+	12.7816i	−0.297000	+	0.992048i
$167$	−18.3735	+	12.0845i	−1.42179	+	0.935123i	−0.422196	+	0.906505i	$0.638740\pi$
$167$	−18.3735	+	12.0845i	−1.42179	+	0.935123i	−0.999590	+	0.0286186i	$0.990889\pi$
$168$		0			0
$169$	8.66262	−	9.18184i	0.666356	−	0.706296i
$170$	48.8682	−	17.7866i	3.74802	−	1.36417i
$171$		0			0
$172$	15.0349	+	5.47227i	1.14640	+	0.417256i
$173$	−9.67356	+	4.85824i	−0.735467	+	0.369366i	−0.776773	−	0.629781i	$-0.783145\pi$
$173$	−9.67356	+	4.85824i	−0.735467	+	0.369366i	0.0413055	+	0.999147i	$0.486848\pi$
$174$		0			0
$175$	3.36459	+	7.79999i	0.254339	+	0.589624i
$176$	8.48450	+	0.991696i	0.639543	+	0.0747519i
$177$		0			0
$178$	−18.7143	−	12.3086i	−1.40270	−	0.922570i
$179$	6.84973	−	5.74761i	0.511973	−	0.429596i	−0.349850	−	0.936806i	$-0.613767\pi$
$179$	6.84973	−	5.74761i	0.511973	−	0.429596i	0.861823	+	0.507210i	$0.169323\pi$
$180$		0			0
$181$	3.31310	+	2.78002i	0.246261	+	0.206637i	0.757560	−	0.652765i	$-0.226391\pi$
$181$	3.31310	+	2.78002i	0.246261	+	0.206637i	−0.511299	+	0.859403i	$0.670836\pi$
$182$	−0.981902	−	3.27978i	−0.0727834	−	0.243113i
$183$		0			0
$184$	31.5244	+	15.8322i	2.32401	+	1.16716i
$185$	8.63378	+	9.15127i	0.634768	+	0.672815i
$186$		0			0
$187$	−6.78580	+	15.7313i	−0.496227	+	1.15038i
$188$	−1.70182	+	2.94765i	−0.124118	+	0.214979i
$189$		0			0
$190$	−16.2028	−	28.0640i	−1.17547	−	2.03598i
$191$	21.0691	−	2.46263i	1.52451	−	0.178189i	0.687824	−	0.725877i	$-0.258566\pi$
$191$	21.0691	−	2.46263i	1.52451	−	0.178189i	0.836683	+	0.547688i	$0.184492\pi$
$192$		0			0
$193$	−17.6655	+	4.18680i	−1.27159	+	0.301373i	−0.810373	−	0.585914i	$-0.800736\pi$
$193$	−17.6655	+	4.18680i	−1.27159	+	0.301373i	−0.461218	+	0.887287i	$0.652587\pi$
$194$	0.242421	+	4.16221i	0.0174048	+	0.298829i
$195$		0			0
$196$	−6.72329	−	1.59345i	−0.480235	−	0.113818i
$197$	−1.23957	+	7.02994i	−0.0883155	+	0.500862i	0.908276	+	0.418371i	$0.137399\pi$
$197$	−1.23957	+	7.02994i	−0.0883155	+	0.500862i	−0.996592	+	0.0824914i	$0.973712\pi$
$198$		0			0
$199$	−0.634860	−	3.60047i	−0.0450040	−	0.255231i	0.954002	−	0.299799i	$-0.0969197\pi$
$199$	−0.634860	−	3.60047i	−0.0450040	−	0.255231i	−0.999006	+	0.0445688i	$0.985809\pi$
$200$	−1.01604	+	17.4448i	−0.0718451	+	1.23353i
$201$		0			0
$202$	12.3290	−	16.5607i	0.867463	−	1.16521i
$203$	2.96981	−	3.98914i	0.208440	−	0.279983i
$204$		0			0
$205$	1.10485	−	18.9696i	0.0771663	−	1.32489i
$206$	−0.767353	−	4.35187i	−0.0534640	−	0.303209i
$207$		0			0
$208$	0.384421	−	2.18016i	0.0266548	−	0.151167i
$209$	10.3880	+	2.46199i	0.718551	+	0.170300i
$210$		0			0
$211$	1.03801	+	17.8219i	0.0714594	+	1.22691i	0.823316	+	0.567584i	$0.192122\pi$
$211$	1.03801	+	17.8219i	0.0714594	+	1.22691i	−0.751856	+	0.659327i	$0.770841\pi$
$212$	−11.8907	+	2.81814i	−0.816654	+	0.193550i
$213$		0			0
$214$	−10.9683	+	1.28201i	−0.749777	+	0.0876364i
$215$	−6.00179	−	10.3954i	−0.409319	−	0.708961i
$216$		0			0
$217$	−3.55480	+	6.15709i	−0.241315	+	0.417970i
$218$	12.7864	−	29.6422i	0.866004	−	2.00762i
$219$		0			0
$220$	−18.8681	−	19.9990i	−1.27209	−	1.34834i
$221$	3.96772	+	1.99267i	0.266898	+	0.134041i
$222$		0			0
$223$	4.04573	+	13.5137i	0.270922	+	0.904942i	0.979862	+	0.199674i	$0.0639883\pi$
$223$	4.04573	+	13.5137i	0.270922	+	0.904942i	−0.708940	+	0.705268i	$0.750827\pi$
$224$	−1.11368	−	0.934490i	−0.0744110	−	0.0624383i
$225$		0			0
$226$	8.00976	−	6.72099i	0.532801	−	0.447073i
$227$	−4.80660	−	3.16135i	−0.319026	−	0.209826i	0.379888	−	0.925032i	$-0.375962\pi$
$227$	−4.80660	−	3.16135i	−0.319026	−	0.209826i	−0.698914	+	0.715206i	$0.746333\pi$
$228$		0			0
$229$	24.4091	+	2.85301i	1.61300	+	0.188532i	0.874258	−	0.485461i	$-0.161348\pi$
$229$	24.4091	+	2.85301i	1.61300	+	0.188532i	0.738738	+	0.673993i	$0.235422\pi$
$230$	−21.3242	−	49.4351i	−1.40608	−	3.25965i
$231$		0			0
$232$	9.14217	−	4.59137i	0.600213	−	0.301438i
$233$	−11.9802	−	4.36045i	−0.784852	−	0.285663i	−0.0816576	−	0.996660i	$-0.526021\pi$
$233$	−11.9802	−	4.36045i	−0.784852	−	0.285663i	−0.703194	+	0.710998i	$0.748244\pi$
$234$		0			0
$235$	2.39953	−	0.873357i	0.156528	−	0.0569715i
$236$	1.65657	−	1.75586i	0.107833	−	0.114297i
$237$		0			0
$238$	−33.7125	+	22.1730i	−2.18525	+	1.43726i
$239$	6.98430	−	23.3292i	0.451777	−	1.50904i	−0.364403	−	0.931241i	$-0.618727\pi$
$239$	6.98430	−	23.3292i	0.451777	−	1.50904i	0.816180	−	0.577798i	$-0.196088\pi$
$240$		0			0
$241$	−17.3603	−	23.3190i	−1.11828	−	1.50211i	−0.840776	−	0.541384i	$-0.817901\pi$
$241$	−17.3603	−	23.3190i	−1.11828	−	1.50211i	−0.277503	−	0.960725i	$-0.589507\pi$
$242$	−13.1320			−0.844157
$243$		0			0
$244$	−21.5057			−1.37676
$245$	3.09552	+	4.15801i	0.197766	+	0.265646i
$246$		0			0
$247$	0.793498	−	2.65047i	0.0504891	−	0.168645i
$248$	−12.2190	+	8.03658i	−0.775909	+	0.510324i
$249$		0			0
$250$	−6.36555	+	6.74709i	−0.402593	+	0.426724i
$251$	−22.4049	+	8.15471i	−1.41418	+	0.514721i	−0.932355	−	0.361545i	$-0.882249\pi$
$251$	−22.4049	+	8.15471i	−1.41418	+	0.514721i	−0.481828	+	0.876266i	$0.660027\pi$
$252$		0			0
$253$	16.6669	+	6.06625i	1.04784	+	0.381382i
$254$	−12.8154	+	6.43614i	−0.804111	+	0.403839i
$255$		0			0
$256$	−12.4240	−	28.8021i	−0.776502	−	1.80013i
$257$	12.0552	+	1.40905i	0.751985	+	0.0878944i	0.483446	−	0.875374i	$-0.339385\pi$
$257$	12.0552	+	1.40905i	0.751985	+	0.0878944i	0.268539	+	0.963269i	$0.413459\pi$
$258$		0			0
$259$	−8.15594	−	5.36425i	−0.506786	−	0.333318i
$260$	−5.45845	+	4.58018i	−0.338519	+	0.284051i
$261$		0			0
$262$	24.3693	+	20.4483i	1.50554	+	1.26330i
$263$	2.29491	+	7.66554i	0.141510	+	0.472677i	0.999134	−	0.0415999i	$-0.0132455\pi$
$263$	2.29491	+	7.66554i	0.141510	+	0.472677i	−0.857624	+	0.514277i	$0.828060\pi$
$264$		0			0
$265$	8.19270	+	4.11453i	0.503274	+	0.252754i
$266$	17.2547	+	18.2889i	1.05795	+	1.12136i
$267$		0			0
$268$	0.439856	−	1.01970i	0.0268685	−	0.0622882i
$269$	11.2578	−	19.4990i	0.686397	−	1.18887i	−0.286598	−	0.958051i	$-0.592524\pi$
$269$	11.2578	−	19.4990i	0.686397	−	1.18887i	0.972995	−	0.230824i	$-0.0741422\pi$
$270$		0			0
$271$	15.1514	+	26.2430i	0.920381	+	1.59415i	0.798826	+	0.601562i	$0.205455\pi$
$271$	15.1514	+	26.2430i	0.920381	+	1.59415i	0.121555	+	0.992585i	$0.461212\pi$
$272$	−25.9153	+	3.02907i	−1.57135	+	0.183664i
$273$		0			0
$274$	−10.7307	+	2.54322i	−0.648265	+	0.153642i
$275$	0.510850	+	8.77095i	0.0308054	+	0.528908i
$276$		0			0
$277$	−4.30449	−	1.02018i	−0.258632	−	0.0612968i	0.0992544	−	0.995062i	$-0.468354\pi$
$277$	−4.30449	−	1.02018i	−0.258632	−	0.0612968i	−0.357886	+	0.933765i	$0.616502\pi$
$278$	−2.02729	+	11.4973i	−0.121589	+	0.689564i
$279$		0			0
$280$	−5.52773	−	31.3493i	−0.330345	−	1.87348i
$281$	0.329570	−	5.65850i	0.0196605	−	0.337558i	−0.974107	−	0.226087i	$-0.927407\pi$
$281$	0.329570	−	5.65850i	0.0196605	−	0.337558i	0.993768	−	0.111471i	$-0.0355562\pi$
$282$		0			0
$283$	17.2121	−	23.1199i	1.02315	−	1.37433i	0.0978106	−	0.995205i	$-0.468816\pi$
$283$	17.2121	−	23.1199i	1.02315	−	1.37433i	0.925344	−	0.379130i	$-0.123777\pi$
$284$	19.2969	−	25.9203i	1.14506	−	1.53808i
$285$		0			0
$286$	0.205886	−	3.53493i	0.0121743	−	0.209025i
$287$	2.56020	+	14.5196i	0.151124	+	0.857065i
$288$		0			0
$289$	6.13495	−	34.7930i	0.360879	−	2.04665i
$290$	−15.1924	−	3.60066i	−0.892127	−	0.211438i
$291$		0			0
$292$	−3.48667	−	59.8638i	−0.204042	−	3.50326i
$293$	−2.10652	+	0.499253i	−0.123064	+	0.0291667i	−0.291686	−	0.956514i	$-0.594216\pi$
$293$	−2.10652	+	0.499253i	−0.123064	+	0.0291667i	0.168622	+	0.985681i	$0.446068\pi$
$294$		0			0
$295$	−1.79879	+	0.210249i	−0.104730	+	0.0122411i
$296$	−10.0405	−	17.3907i	−0.583593	−	1.01081i
$297$		0			0
$298$	−11.9550	+	20.7067i	−0.692537	+	1.19951i
$299$	1.82060	−	4.22063i	0.105288	−	0.244085i
$300$		0			0
$301$	6.39143	+	6.77452i	0.368396	+	0.390477i
$302$	29.0677	+	14.5984i	1.67266	+	0.840041i
$303$		0			0
$304$	4.66301	+	15.5755i	0.267442	+	0.893318i
$305$	12.3595	+	10.3709i	0.707704	+	0.593835i
$306$		0			0
$307$	3.63465	−	3.04984i	0.207441	−	0.174063i	−0.533148	−	0.846022i	$-0.678991\pi$
$307$	3.63465	−	3.04984i	0.207441	−	0.174063i	0.740589	+	0.671959i	$0.234547\pi$
$308$	17.8239	+	11.7229i	1.01561	+	0.667976i
$309$		0			0
$310$	22.1693	+	2.59122i	1.25913	+	0.147172i
$311$	−9.34927	−	21.6740i	−0.530149	−	1.22902i	−0.947348	−	0.320207i	$-0.896247\pi$
$311$	−9.34927	−	21.6740i	−0.530149	−	1.22902i	0.417199	−	0.908815i	$-0.363012\pi$
$312$		0			0
$313$	21.1167	−	10.6052i	1.19359	−	0.599442i	0.262745	−	0.964865i	$-0.415372\pi$
$313$	21.1167	−	10.6052i	1.19359	−	0.599442i	0.930841	+	0.365424i	$0.119076\pi$
$314$	6.86503	+	2.49867i	0.387416	+	0.141008i
$315$		0			0
$316$	−27.5563	+	10.0297i	−1.55016	+	0.564213i
$317$	23.3831	−	24.7847i	1.31333	−	1.39205i	0.445418	−	0.895323i	$-0.353055\pi$
$317$	23.3831	−	24.7847i	1.31333	−	1.39205i	0.867909	−	0.496723i	$-0.165464\pi$
$318$		0			0
$319$	4.29745	−	2.82648i	0.240611	−	0.158253i
$320$	−7.41484	+	24.7673i	−0.414502	+	1.38453i
$321$		0			0
$322$	24.9454	+	33.5075i	1.39015	+	1.86730i
$323$	−32.6083			−1.81437
$324$		0			0
$325$	2.27691			0.126300
$326$	25.7910	+	34.6434i	1.42843	+	1.91872i
$327$		0			0
$328$	−8.69840	+	29.0547i	−0.480289	+	1.60428i
$329$	−1.65535	+	1.08874i	−0.0912625	+	0.0600243i
$330$		0			0
$331$	−17.7922	+	18.8586i	−0.977947	+	1.03656i	0.0213759	+	0.999772i	$0.493195\pi$
$331$	−17.7922	+	18.8586i	−0.977947	+	1.03656i	−0.999323	+	0.0367918i	$0.988286\pi$
$332$	−20.2467	+	7.36919i	−1.11118	+	0.404437i
$333$		0			0
$334$	−50.3388	−	18.3218i	−2.75441	−	1.00252i
$335$	−0.744531	+	0.373917i	−0.0406781	+	0.0204293i
$336$		0			0
$337$	8.77373	+	20.3398i	0.477936	+	1.10798i	0.971236	+	0.238120i	$0.0765313\pi$
$337$	8.77373	+	20.3398i	0.477936	+	1.10798i	−0.493300	+	0.869859i	$0.664209\pi$
$338$	30.5415	+	3.56979i	1.66124	+	0.194171i
$339$		0			0
$340$	70.1652	+	46.1484i	3.80524	+	2.50275i
$341$	−5.63289	+	4.72656i	−0.305038	+	0.255957i
$342$		0			0
$343$	−15.3601	−	12.8887i	−0.829369	−	0.695923i
$344$	5.49486	+	18.3541i	0.296263	+	0.989588i
$345$		0			0
$346$	−23.5641	−	11.8343i	−1.26681	−	0.636218i
$347$	1.23071	+	1.30447i	0.0660678	+	0.0700277i	0.759564	−	0.650432i	$-0.225412\pi$
$347$	1.23071	+	1.30447i	0.0660678	+	0.0700277i	−0.693497	+	0.720460i	$0.743931\pi$
$348$		0			0
$349$	0.0696613	−	0.161493i	0.00372889	−	0.00864453i	−0.916341	−	0.400398i	$-0.868872\pi$
$349$	0.0696613	−	0.161493i	0.00372889	−	0.00864453i	0.920070	+	0.391753i	$0.128131\pi$
$350$	−10.3463	+	17.9203i	−0.553031	+	0.957878i
$351$		0			0
$352$	−0.751813	−	1.30218i	−0.0400718	−	0.0694064i
$353$	−30.2081	+	3.53082i	−1.60781	+	0.187927i	−0.872087	−	0.489351i	$-0.837234\pi$
$353$	−30.2081	+	3.53082i	−1.60781	+	0.187927i	−0.735727	+	0.677278i	$0.763159\pi$
$354$		0			0
$355$	−23.5899	+	5.59091i	−1.25202	+	0.296735i
$356$	−2.10323	−	36.1111i	−0.111471	−	1.91388i
$357$		0			0
$358$	21.1942	+	5.02311i	1.12015	+	0.265480i
$359$	1.11991	−	6.35130i	0.0591064	−	0.335209i	−0.940887	−	0.338719i	$-0.890006\pi$
$359$	1.11991	−	6.35130i	0.0591064	−	0.335209i	0.999994	+	0.00351034i	$0.00111738\pi$
$360$		0			0
$361$	0.229085	+	1.29920i	0.0120571	+	0.0683792i
$362$	−0.612570	+	10.5174i	−0.0321960	+	0.552783i
$363$		0			0
$364$	3.30153	−	4.43472i	0.173047	−	0.232443i
$365$	−26.8649	+	36.0858i	−1.40617	+	1.88882i
$366$		0			0
$367$	−1.07014	+	18.3735i	−0.0558607	+	0.959091i	0.847658	+	0.530543i	$0.178012\pi$
$367$	−1.07014	+	18.3735i	−0.0558607	+	0.959091i	−0.903519	+	0.428548i	$0.859025\pi$
$368$	4.69054	+	26.6014i	0.244512	+	1.38669i
$369$		0			0
$370$	−5.32180	+	30.1814i	−0.276667	+	1.56906i
$371$	−6.92167	−	1.64047i	−0.359355	−	0.0851688i
$372$		0			0
$373$	1.87718	+	32.2299i	0.0971967	+	1.66880i	0.596680	+	0.802479i	$0.296486\pi$
$373$	1.87718	+	32.2299i	0.0971967	+	1.66880i	−0.499483	+	0.866324i	$0.666477\pi$
$374$	−40.6084	+	9.62437i	−2.09981	+	0.497664i
$375$		0			0
$376$	−4.04814	+	0.473160i	−0.208767	+	0.0244013i
$377$	−0.666508	−	1.15442i	−0.0343269	−	0.0594559i
$378$		0			0
$379$	11.0163	−	19.0808i	0.565870	−	0.980116i	−0.431098	−	0.902305i	$-0.641874\pi$
$379$	11.0163	−	19.0808i	0.565870	−	0.980116i	0.996968	−	0.0778111i	$-0.0247931\pi$
$380$	20.7274	−	48.0514i	1.06329	−	2.46499i
$381$		0			0
$382$	35.4596	+	37.5850i	1.81427	+	1.92302i
$383$	12.7129	+	6.38463i	0.649596	+	0.326240i	0.742904	−	0.669398i	$-0.233448\pi$
$383$	12.7129	+	6.38463i	0.649596	+	0.326240i	−0.0933078	+	0.995637i	$0.529744\pi$
$384$		0			0
$385$	−4.59030	−	15.3327i	−0.233943	−	0.781425i
$386$	−33.8775	−	28.4266i	−1.72432	−	1.44688i
$387$		0			0
$388$	−5.15768	+	4.32781i	−0.261842	+	0.219711i
$389$	10.2482	+	6.74032i	0.519603	+	0.341748i	0.782068	−	0.623194i	$-0.214165\pi$
$389$	10.2482	+	6.74032i	0.519603	+	0.341748i	−0.262465	+	0.964941i	$0.584535\pi$
$390$		0			0
$391$	−53.8087	−	6.28933i	−2.72122	−	0.318065i
$392$	−3.27710	−	7.59716i	−0.165518	−	0.383715i
$393$		0			0
$394$	−15.5390	+	7.80399i	−0.782844	+	0.393159i
$395$	20.6736	+	7.52457i	1.04020	+	0.378602i
$396$		0			0
$397$	−9.12859	+	3.32254i	−0.458151	+	0.166753i	−0.560777	−	0.827967i	$-0.689498\pi$
$397$	−9.12859	+	3.32254i	−0.458151	+	0.166753i	0.102626	+	0.994720i	$0.467275\pi$
$398$	6.11152	−	6.47783i	0.306343	−	0.324704i
$399$		0			0
$400$	−11.1791	+	7.35260i	−0.558955	+	0.367630i
$401$	0.335348	−	1.12014i	0.0167465	−	0.0559372i	−0.949208	−	0.314650i	$-0.898113\pi$
$401$	0.335348	−	1.12014i	0.0167465	−	0.0559372i	0.965954	+	0.258712i	$0.0832982\pi$
$402$		0			0
$403$	1.13797	+	1.52856i	0.0566864	+	0.0761430i
$404$	33.3410			1.65878
$405$		0			0
$406$	12.1144			0.601229
$407$	−6.02915	−	8.09856i	−0.298854	−	0.401431i
$408$		0			0
$409$	7.87588	−	26.3073i	0.389437	−	1.30081i	−0.508643	−	0.860978i	$-0.669853\pi$
$409$	7.87588	−	26.3073i	0.389437	−	1.30081i	0.898080	−	0.439833i	$-0.144962\pi$
$410$	38.6721	−	25.4351i	1.90988	−	1.25615i
$411$		0			0
$412$	4.89715	−	5.19068i	0.241265	−	0.255726i
$413$	1.32045	−	0.480606i	0.0649753	−	0.0236491i
$414$		0			0
$415$	15.1897	+	5.52860i	0.745633	+	0.271388i
$416$	−0.348227	+	0.174886i	−0.0170732	+	0.00857451i
$417$		0			0
$418$	10.3002	+	23.8785i	0.503798	+	1.16794i
$419$	24.4312	+	2.85560i	1.19354	+	0.139505i	0.689573	−	0.724216i	$-0.257798\pi$
$419$	24.4312	+	2.85560i	1.19354	+	0.139505i	0.503970	+	0.863721i	$0.331872\pi$
$420$		0			0
$421$	10.2783	+	6.76018i	0.500936	+	0.329471i	0.774703	−	0.632325i	$-0.217899\pi$
$421$	10.2783	+	6.76018i	0.500936	+	0.329471i	−0.273767	+	0.961796i	$0.588270\pi$
$422$	−33.3126	+	27.9526i	−1.62163	+	1.36071i
$423$		0			0
$424$	−11.2094	−	9.40584i	−0.544379	−	0.456788i
$425$	−7.69655	−	25.7083i	−0.373338	−	1.24703i
$426$		0			0
$427$	−11.1871	−	5.61837i	−0.541381	−	0.271892i
$428$	−12.2378	−	12.9713i	−0.591538	−	0.626993i
$429$		0			0
$430$	11.5813	−	26.8485i	0.558501	−	1.29475i
$431$	−3.97831	+	6.89064i	−0.191628	+	0.331910i	−0.945790	−	0.324779i	$-0.894710\pi$
$431$	−3.97831	+	6.89064i	−0.191628	+	0.331910i	0.754162	+	0.656689i	$0.228044\pi$
$432$		0			0
$433$	−5.95735	−	10.3184i	−0.286292	−	0.495872i	0.686630	−	0.727007i	$-0.259089\pi$
$433$	−5.95735	−	10.3184i	−0.286292	−	0.495872i	−0.972922	+	0.231135i	$0.925756\pi$
$434$	−17.2014	+	2.01055i	−0.825692	+	0.0965095i
$435$		0			0
$436$	50.7271	−	12.0225i	2.42939	−	0.575775i
$437$	1.96286	+	33.7010i	0.0938963	+	1.61214i
$438$		0			0
$439$	6.71977	+	1.59261i	0.320717	+	0.0760114i	0.387821	−	0.921735i	$-0.373228\pi$
$439$	6.71977	+	1.59261i	0.320717	+	0.0760114i	−0.0671041	+	0.997746i	$0.521376\pi$
$440$	5.71714	−	32.4235i	0.272554	−	1.54573i
$441$		0			0
$442$	1.87809	+	10.6512i	0.0893318	+	0.506626i
$443$	0.421264	−	7.23283i	0.0200149	−	0.343642i	−0.973403	−	0.229098i	$-0.926422\pi$
$443$	0.421264	−	7.23283i	0.0200149	−	0.343642i	0.993418	−	0.114544i	$-0.0365407\pi$
$444$		0			0
$445$	−16.2055	+	21.7677i	−0.768212	+	1.03189i
$446$	−20.5195	+	27.5625i	−0.971626	+	1.30512i
$447$		0			0
$448$	1.16638	−	20.0259i	0.0551061	−	0.946135i
$449$	−5.97095	−	33.8630i	−0.281787	−	1.59809i	−0.716542	−	0.697543i	$-0.754276\pi$
$449$	−5.97095	−	33.8630i	−0.281787	−	1.59809i	0.434756	−	0.900548i	$-0.356835\pi$
$450$		0			0
$451$	−2.64793	+	15.0172i	−0.124686	+	0.707130i
$452$	16.4301	+	3.89400i	0.772807	+	0.183159i
$453$		0			0
$454$	−0.814843	−	13.9903i	−0.0382425	−	0.656598i
$455$	−4.03602	+	0.956555i	−0.189212	+	0.0448440i
$456$		0			0
$457$	−16.5411	+	1.93338i	−0.773760	+	0.0904396i	−0.493804	−	0.869573i	$-0.664394\pi$
$457$	−16.5411	+	1.93338i	−0.773760	+	0.0904396i	−0.279956	+	0.960013i	$0.590320\pi$
$458$	29.9317	+	51.8433i	1.39862	+	2.42248i
$459$		0			0
$460$	43.4712	−	75.2944i	2.02686	−	3.51062i
$461$	−5.45935	+	12.6562i	−0.254267	+	0.589458i	−0.996763	−	0.0803927i	$-0.974383\pi$
$461$	−5.45935	+	12.6562i	−0.254267	+	0.589458i	0.742496	+	0.669851i	$0.233642\pi$
$462$		0			0
$463$	−8.40156	−	8.90513i	−0.390454	−	0.413857i	0.502092	−	0.864814i	$-0.332564\pi$
$463$	−8.40156	−	8.90513i	−0.390454	−	0.413857i	−0.892545	+	0.450958i	$0.851082\pi$
$464$	7.00027	+	3.51567i	0.324979	+	0.163211i
$465$		0			0
$466$	−8.90694	−	29.7512i	−0.412606	−	1.37820i
$467$	11.7925	+	9.89507i	0.545691	+	0.457889i	0.873479	−	0.486862i	$-0.161859\pi$
$467$	11.7925	+	9.89507i	0.545691	+	0.457889i	−0.327788	+	0.944751i	$0.606303\pi$
$468$		0			0
$469$	0.495208	−	0.415529i	0.0228666	−	0.0191873i
$470$	5.19690	+	3.41806i	0.239715	+	0.157663i
$471$		0			0
$472$	2.87106	+	0.335579i	0.132151	+	0.0154463i
$473$	3.81537	+	8.84501i	0.175431	+	0.406694i
$474$		0			0
$475$	−14.9434	+	7.50488i	−0.685652	+	0.344347i
$476$	−61.2319	−	22.2866i	−2.80656	−	1.02150i
$477$		0			0
$478$	55.7428	−	20.2887i	2.54962	−	0.927985i
$479$	−10.3968	+	11.0200i	−0.475043	+	0.503516i	−0.919937	−	0.392067i	$-0.871760\pi$
$479$	−10.3968	+	11.0200i	−0.475043	+	0.503516i	0.444894	+	0.895583i	$0.353242\pi$
$480$		0			0
$481$	−2.18610	+	1.43782i	−0.0996777	+	0.0655591i
$482$	20.3103	−	67.8413i	0.925111	−	3.09008i
$483$		0			0
$484$	−12.6637	−	17.0104i	−0.575625	−	0.773198i
$485$	5.05122			0.229364
$486$		0			0
$487$	−9.74343			−0.441517			−0.220758	−	0.975329i	$-0.570853\pi$
$487$	−9.74343			−0.441517			−0.220758	+	0.975329i	$0.570853\pi$
$488$	−15.3780	−	20.6562i	−0.696129	−	0.935063i
$489$		0			0
$490$	−3.62154	+	12.0968i	−0.163604	+	0.546477i
$491$	−15.9865	+	10.5145i	−0.721461	+	0.474512i	−0.856381	−	0.516344i	$-0.827293\pi$
$491$	−15.9865	+	10.5145i	−0.721461	+	0.474512i	0.134920	+	0.990856i	$0.456922\pi$
$492$		0			0
$493$	−10.7815	+	11.4277i	−0.485574	+	0.514678i
$494$	6.33304	−	2.30504i	0.284937	−	0.103709i
$495$		0			0
$496$	−10.5232	−	3.83013i	−0.472506	−	0.171978i
$497$	16.8098	−	8.44220i	0.754023	−	0.378685i
$498$		0			0
$499$	−10.3471	−	23.9872i	−0.463198	−	1.07381i	−0.976483	−	0.215596i	$-0.930831\pi$
$499$	−10.3471	−	23.9872i	−0.463198	−	1.07381i	0.513284	−	0.858219i	$-0.328429\pi$
$500$	−14.8783	−	1.73903i	−0.665379	−	0.0777717i
$501$		0			0
$502$	−48.5245	−	31.9151i	−2.16576	−	1.42444i
$503$	−0.849443	+	0.712768i	−0.0378748	+	0.0317807i	−0.661529	−	0.749920i	$-0.730092\pi$
$503$	−0.849443	+	0.712768i	−0.0378748	+	0.0317807i	0.623654	+	0.781701i	$0.285648\pi$
$504$		0			0
$505$	−19.1614	−	16.0784i	−0.852673	−	0.715477i
$506$	12.3913	+	41.3898i	0.550861	+	1.84000i
$507$		0			0
$508$	−20.6954	−	10.3936i	−0.918211	−	0.461143i
$509$	−11.6487	−	12.3469i	−0.516321	−	0.547268i	0.415781	−	0.909465i	$-0.363508\pi$
$509$	−11.6487	−	12.3469i	−0.516321	−	0.547268i	−0.932102	+	0.362197i	$0.882027\pi$
$510$		0			0
$511$	13.8257	−	32.0516i	0.611614	−	1.41788i
$512$	18.1349	−	31.4106i	0.801458	−	1.38817i
$513$		0			0
$514$	14.7828	+	25.6045i	0.652041	+	1.12937i
$515$	−5.31760	+	0.621538i	−0.234321	+	0.0273882i
$516$		0			0
$517$	−1.99396	+	0.472576i	−0.0876941	+	0.0207839i
$518$	−1.38264	−	23.7390i	−0.0607498	−	1.04303i
$519$		0			0
$520$	−8.30244	−	1.96771i	−0.364086	−	0.0862900i
$521$	5.42618	−	30.7734i	0.237725	−	1.34821i	−0.599072	−	0.800695i	$-0.704464\pi$
$521$	5.42618	−	30.7734i	0.237725	−	1.34821i	0.836798	−	0.547512i	$-0.184425\pi$
$522$		0			0
$523$	−2.23807	−	12.6927i	−0.0978638	−	0.555013i	−0.993832	−	0.110895i	$-0.964628\pi$
$523$	−2.23807	−	12.6927i	−0.0978638	−	0.555013i	0.895968	−	0.444118i	$-0.146483\pi$
$524$	−2.98705	+	51.2856i	−0.130490	+	2.24042i
$525$		0			0
$526$	−11.6395	+	15.6346i	−0.507508	+	0.681702i
$527$	13.4121	−	18.0156i	0.584241	−	0.784772i
$528$		0			0
$529$	−1.92374	+	33.0293i	−0.0836408	+	1.43606i
$530$	3.87796	+	21.9930i	0.168448	+	0.955314i
$531$		0			0
$532$	−7.05085	+	39.9874i	−0.305693	+	1.73367i
$533$	3.84532	+	0.911358i	0.166559	+	0.0394753i
$534$		0			0
$535$	0.777918	+	13.3563i	0.0336323	+	0.577445i
$536$	1.29395	−	0.306672i	0.0558903	−	0.0132462i
$537$		0			0
$538$	54.4753	−	6.36725i	2.34860	−	0.274512i
$539$	−2.07997	−	3.60261i	−0.0895907	−	0.155176i
$540$		0			0
$541$	−3.97103	+	6.87802i	−0.170728	+	0.295709i	−0.938675	−	0.344804i	$-0.887945\pi$
$541$	−3.97103	+	6.87802i	−0.170728	+	0.295709i	0.767947	+	0.640514i	$0.221279\pi$
$542$	−29.2368	+	67.7785i	−1.25583	+	2.91133i
$543$		0			0
$544$	3.15172	+	3.34063i	0.135129	+	0.143228i
$545$	−34.9511	−	17.5531i	−1.49714	−	0.751893i
$546$		0			0
$547$	3.10681	+	10.3775i	0.132838	+	0.443709i	0.998365	−	0.0571522i	$-0.0182020\pi$
$547$	3.10681	+	10.3775i	0.132838	+	0.443709i	−0.865528	+	0.500861i	$0.833017\pi$
$548$	−13.6424	−	11.4473i	−0.582774	−	0.489005i
$549$		0			0
$550$	−16.3946	+	13.7567i	−0.699067	+	0.586587i
$551$	8.17939	+	5.37967i	0.348454	+	0.229182i
$552$		0			0
$553$	−16.9548	−	1.98174i	−0.720993	−	0.0842720i
$554$	−4.26811	−	9.89459i	−0.181335	−	0.420381i
$555$		0			0
$556$	−16.8479	+	8.46134i	−0.714511	+	0.358841i
$557$	−1.66135	−	0.604682i	−0.0703937	−	0.0256212i	0.306583	−	0.951844i	$-0.400814\pi$
$557$	−1.66135	−	0.604682i	−0.0703937	−	0.0256212i	−0.376977	+	0.926223i	$0.623036\pi$
$558$		0			0
$559$	2.34587	−	0.853825i	0.0992196	−	0.0361130i
$560$	16.7270	−	17.7296i	0.706845	−	0.749212i
$561$		0			0
$562$	11.5356	−	7.58710i	0.486601	−	0.320042i
$563$	−2.19425	+	7.32932i	−0.0924768	+	0.308894i	−0.991696	−	0.128604i	$-0.958950\pi$
$563$	−2.19425	+	7.32932i	−0.0924768	+	0.308894i	0.899219	+	0.437498i	$0.144135\pi$
$564$		0			0
$565$	−7.56471	−	10.1612i	−0.318250	−	0.427484i
$566$	70.2116			2.95121
$567$		0			0
$568$	38.6951			1.62361
$569$	−11.8825	−	15.9609i	−0.498139	−	0.669116i	0.479952	−	0.877295i	$-0.340654\pi$
$569$	−11.8825	−	15.9609i	−0.498139	−	0.669116i	−0.978091	+	0.208178i	$0.933247\pi$
$570$		0			0
$571$	13.2127	−	44.1334i	0.552933	−	1.84692i	0.0215917	−	0.999767i	$-0.493127\pi$
$571$	13.2127	−	44.1334i	0.552933	−	1.84692i	0.531341	−	0.847158i	$-0.321688\pi$
$572$	4.77747	−	3.14219i	0.199756	−	0.131382i
$573$		0			0
$574$	−24.6459	+	26.1231i	−1.02870	+	1.09036i
$575$	−26.1065	+	9.50198i	−1.08872	+	0.396260i
$576$		0			0
$577$	−24.3829	−	8.87465i	−1.01507	−	0.369457i	−0.219695	−	0.975569i	$-0.570506\pi$
$577$	−24.3829	−	8.87465i	−1.01507	−	0.369457i	−0.795379	+	0.606112i	$0.792728\pi$
$578$	76.9067	−	38.6240i	3.19890	−	1.60655i
$579$		0			0
$580$	−9.98659	−	23.1515i	−0.414671	−	0.961314i
$581$	−12.4574	−	1.45606i	−0.516819	−	0.0604075i
$582$		0			0
$583$	−6.14683	−	4.04283i	−0.254576	−	0.167437i
$584$	55.0061	−	46.1556i	2.27617	−	1.90993i
$585$		0			0
$586$	−4.03971	−	3.38972i	−0.166879	−	0.140028i
$587$	6.02715	+	20.1321i	0.248767	+	0.830939i	0.987592	+	0.157042i	$0.0501958\pi$
$587$	6.02715	+	20.1321i	0.248767	+	0.830939i	−0.738825	+	0.673897i	$0.764619\pi$
$588$		0			0
$589$	−12.5068	−	6.28115i	−0.515334	−	0.258810i
$590$	−3.02739	−	3.20885i	−0.124636	−	0.132106i
$591$		0			0
$592$	6.09023	−	14.1187i	0.250307	−	0.580277i
$593$	12.9024	−	22.3476i	0.529837	−	0.917705i	−0.469557	−	0.882902i	$-0.655586\pi$
$593$	12.9024	−	22.3476i	0.529837	−	0.917705i	0.999394	−	0.0348027i	$-0.0110803\pi$
$594$		0			0
$595$	24.4432	+	42.3368i	1.00207	+	1.73564i
$596$	−38.3510	+	4.48258i	−1.57092	+	0.183614i
$597$		0			0
$598$	10.8951	−	2.58218i	0.445532	−	0.105593i
$599$	−1.59636	−	27.4085i	−0.0652255	−	1.11988i	−0.859104	−	0.511802i	$-0.828978\pi$
$599$	−1.59636	−	27.4085i	−0.0652255	−	1.11988i	0.793878	−	0.608077i	$-0.208059\pi$
$600$		0			0
$601$	0.371180	+	0.0879713i	0.0151407	+	0.00358842i	0.238179	−	0.971221i	$-0.423449\pi$
$601$	0.371180	+	0.0879713i	0.0151407	+	0.00358842i	−0.223039	+	0.974810i	$0.571598\pi$
$602$	−3.93963	+	22.3428i	−0.160567	+	0.910623i
$603$		0			0
$604$	9.12145	+	51.7303i	0.371146	+	2.10488i
$605$	−0.925079	+	15.8830i	−0.0376098	+	0.645736i
$606$		0			0
$607$	3.67880	−	4.94148i	0.149318	−	0.200569i	−0.721171	−	0.692757i	$-0.756396\pi$
$607$	3.67880	−	4.94148i	0.149318	−	0.200569i	0.870488	+	0.492189i	$0.163803\pi$
$608$	1.70899	−	2.29557i	0.0693087	−	0.0930977i
$609$		0			0
$610$	−2.28520	+	39.2353i	−0.0925249	+	1.58859i
$611$	0.0922182	+	0.522996i	0.00373075	+	0.0211581i
$612$		0			0
$613$	−4.86771	+	27.6062i	−0.196605	+	1.11500i	0.713509	+	0.700646i	$0.247105\pi$
$613$	−4.86771	+	27.6062i	−0.196605	+	1.11500i	−0.910114	+	0.414357i	$0.864006\pi$
$614$	11.2462	+	2.66540i	0.453860	+	0.107567i
$615$		0			0
$616$	1.48535	+	25.5025i	0.0598466	+	1.02753i
$617$	14.5202	−	3.44136i	0.584563	−	0.138544i	0.0723152	−	0.997382i	$-0.476961\pi$
$617$	14.5202	−	3.44136i	0.584563	−	0.138544i	0.512247	+	0.858838i	$0.328813\pi$
$618$		0			0
$619$	4.14630	−	0.484633i	0.166654	−	0.0194790i	−0.0323567	−	0.999476i	$-0.510301\pi$
$619$	4.14630	−	0.484633i	0.166654	−	0.0194790i	0.199011	+	0.979997i	$0.436227\pi$
$620$	18.0223	+	31.2156i	0.723794	+	1.25365i
$621$		0			0
$622$	28.7494	−	49.7955i	1.15275	−	1.99662i
$623$	8.33996	−	19.3342i	0.334134	−	0.774609i
$624$		0			0
$625$	20.4408	+	21.6660i	0.817633	+	0.866641i
$626$	51.4388	+	25.8335i	2.05591	+	1.03251i
$627$		0			0
$628$	3.38362	+	11.3021i	0.135021	+	0.451003i
$629$	23.6239	+	19.8228i	0.941945	+	0.790386i
$630$		0			0
$631$	24.5789	−	20.6241i	0.978470	−	0.821034i	−0.00538805	−	0.999985i	$-0.501715\pi$
$631$	24.5789	−	20.6241i	0.978470	−	0.821034i	0.983858	+	0.178952i	$0.0572706\pi$
$632$	−29.3381	−	19.2960i	−1.16701	−	0.767553i
$633$		0			0
$634$	82.4410	+	9.63597i	3.27415	+	0.382693i
$635$	6.88166	+	15.9535i	0.273090	+	0.633095i
$636$		0			0
$637$	−0.963408	+	0.483841i	−0.0381716	+	0.0191705i
$638$	11.7739	+	4.28536i	0.466134	+	0.169659i
$639$		0			0
$640$	−55.6576	+	20.2577i	−2.20006	+	0.800757i
$641$	−27.0420	+	28.6629i	−1.06810	+	1.13212i	−0.0772655	+	0.997011i	$0.524619\pi$
$641$	−27.0420	+	28.6629i	−1.06810	+	1.13212i	−0.990831	+	0.135106i	$0.956863\pi$
$642$		0			0
$643$	23.8482	−	15.6852i	0.940483	−	0.618565i	0.0160342	−	0.999871i	$-0.494896\pi$
$643$	23.8482	−	15.6852i	0.940483	−	0.618565i	0.924449	+	0.381306i	$0.124526\pi$
$644$	−19.3476	+	64.6253i	−0.762401	+	2.54660i
$645$		0			0
$646$	−47.4332	−	63.7138i	−1.86623	−	2.50679i
$647$	−3.61582			−0.142153			−0.0710764	−	0.997471i	$-0.522643\pi$
$647$	−3.61582			−0.142153			−0.0710764	+	0.997471i	$0.522643\pi$
$648$		0			0
$649$	1.45335			0.0570489
$650$	3.31207	+	4.44889i	0.129910	+	0.174500i
$651$		0			0
$652$	−20.0035	+	66.8162i	−0.783396	+	2.61672i
$653$	9.91451	−	6.52088i	0.387985	−	0.255182i	−0.340499	−	0.940245i	$-0.610596\pi$
$653$	9.91451	−	6.52088i	0.387985	−	0.255182i	0.728483	+	0.685063i	$0.240226\pi$
$654$		0			0
$655$	26.4486	−	28.0339i	1.03343	−	1.09538i
$656$	−21.8226	+	7.94277i	−0.852029	+	0.310113i
$657$		0			0
$658$	−4.53524	−	1.65069i	−0.176802	−	0.0643507i
$659$	2.35237	−	1.18141i	0.0916354	−	0.0460210i	−0.402391	−	0.915468i	$-0.631821\pi$
$659$	2.35237	−	1.18141i	0.0916354	−	0.0460210i	0.494027	+	0.869447i	$0.335525\pi$
$660$		0			0
$661$	10.2372	+	23.7324i	0.398179	+	0.923083i	0.992878	+	0.119135i	$0.0380120\pi$
$661$	10.2372	+	23.7324i	0.398179	+	0.923083i	−0.594699	+	0.803948i	$0.702729\pi$
$662$	−62.7293	−	7.33200i	−2.43804	−	0.284966i
$663$		0			0
$664$	−21.5559	−	14.1775i	−0.836529	−	0.550194i
$665$	23.3357	−	19.5810i	0.904919	−	0.759317i
$666$		0			0
$667$	12.4596	+	10.4549i	0.482439	+	0.404815i
$668$	−24.8109	−	82.8742i	−0.959962	−	3.20650i
$669$		0			0
$670$	−1.81362	−	0.910836i	−0.0700664	−	0.0351887i
$671$	−8.88521	−	9.41777i	−0.343010	−	0.363569i
$672$		0			0
$673$	0.476679	−	1.10507i	0.0183746	−	0.0425972i	−0.908782	−	0.417272i	$-0.862986\pi$
$673$	0.476679	−	1.10507i	0.0183746	−	0.0425972i	0.927156	+	0.374675i	$0.122246\pi$
$674$	−26.9796	+	46.7301i	−1.03922	+	1.79998i
$675$		0			0
$676$	24.8284	+	43.0040i	0.954938	+	1.65400i
$677$	−38.9380	+	4.55120i	−1.49651	+	0.174917i	−0.824600	−	0.565716i	$-0.808600\pi$
$677$	−38.9380	+	4.55120i	−1.49651	+	0.174917i	−0.671910	+	0.740633i	$0.734526\pi$
$678$		0			0
$679$	−3.81363	+	0.903848i	−0.146354	+	0.0346865i
$680$	5.84723	+	100.393i	0.224231	+	3.84990i
$681$		0			0
$682$	−17.4291	−	4.13077i	−0.667394	−	0.158175i
$683$	−1.15437	+	6.54674i	−0.0441706	+	0.250504i	−0.998896	−	0.0469860i	$-0.985038\pi$
$683$	−1.15437	+	6.54674i	−0.0441706	+	0.250504i	0.954725	+	0.297490i	$0.0961495\pi$
$684$		0			0
$685$	2.32008	+	13.1578i	0.0886455	+	0.502734i
$686$	2.83999	−	48.7607i	0.108431	−	1.86169i
$687$		0			0
$688$	−8.76047	+	11.7674i	−0.333990	+	0.448626i
$689$	−1.13858	+	1.52938i	−0.0433765	+	0.0582648i
$690$		0			0
$691$	0.661006	−	11.3490i	0.0251458	−	0.431738i	−0.962117	−	0.272638i	$-0.912104\pi$
$691$	0.661006	−	11.3490i	0.0251458	−	0.431738i	0.987263	−	0.159100i	$-0.0508591\pi$
$692$	−7.39441	−	41.9358i	−0.281093	−	1.59416i
$693$		0			0
$694$	−0.758598	+	4.30222i	−0.0287960	+	0.163310i
$695$	13.7631	+	3.26191i	0.522063	+	0.123731i
$696$		0			0
$697$	−2.70818	−	46.4977i	−0.102580	−	1.76122i
$698$	0.416876	−	0.0988013i	0.0157790	−	0.00373969i
$699$		0			0
$700$	−33.1901	+	3.87937i	−1.25447	+	0.146626i
$701$	14.2748	+	24.7247i	0.539152	+	0.933838i	0.998950	+	0.0458147i	$0.0145884\pi$
$701$	14.2748	+	24.7247i	0.539152	+	0.933838i	−0.459798	+	0.888023i	$0.652078\pi$
$702$		0			0
$703$	9.60829	−	16.6421i	0.362384	−	0.627667i
$704$	8.21756	−	19.0504i	0.309711	−	0.717991i
$705$		0			0
$706$	−50.8407	−	53.8879i	−1.91341	−	2.02810i
$707$	17.3438	+	8.71036i	0.652279	+	0.327587i
$708$		0			0
$709$	12.5196	+	41.8183i	0.470183	+	1.57052i	0.783827	+	0.620979i	$0.213265\pi$
$709$	12.5196	+	41.8183i	0.470183	+	1.57052i	−0.313645	+	0.949540i	$0.601550\pi$
$710$	−45.2389	−	37.9599i	−1.69779	−	1.42461i
$711$		0			0
$712$	33.1808	−	27.8420i	1.24350	−	1.04342i
$713$	−19.4267	−	12.7771i	−0.727534	−	0.478507i
$714$		0			0
$715$	−4.26096	−	0.498034i	−0.159351	−	0.0186254i
$716$	13.9318	+	32.2976i	0.520657	+	1.20702i
$717$		0			0
$718$	14.0390	−	7.05063i	0.523929	−	0.263127i
$719$	28.1797	+	10.2566i	1.05093	+	0.382506i	0.809012	−	0.587792i	$-0.200002\pi$
$719$	28.1797	+	10.2566i	1.05093	+	0.382506i	0.241914	+	0.970298i	$0.422225\pi$
$720$		0			0
$721$	3.90353	−	1.42077i	0.145375	−	0.0529122i
$722$	−2.20530	+	2.33748i	−0.0820728	+	0.0869920i
$723$		0			0
$724$	−14.2143	+	9.34891i	−0.528272	+	0.347450i
$725$	−2.31073	+	7.71837i	−0.0858183	+	0.286653i
$726$		0			0
$727$	23.9355	+	32.1509i	0.887717	+	1.19241i	0.980460	+	0.196721i	$0.0630293\pi$
$727$	23.9355	+	32.1509i	0.887717	+	1.19241i	−0.0927425	+	0.995690i	$0.529563\pi$
$728$	6.62038			0.245368
$729$		0			0
$730$	−109.587			−4.05600
$731$	−17.5701	−	23.6007i	−0.649853	−	0.872903i
$732$		0			0
$733$	−7.87673	+	26.3101i	−0.290934	+	0.971787i	0.680155	+	0.733068i	$0.261912\pi$
$733$	−7.87673	+	26.3101i	−0.290934	+	0.971787i	−0.971089	+	0.238718i	$0.923273\pi$
$734$	−37.4570	+	24.6358i	−1.38256	+	0.909325i
$735$		0			0
$736$	3.26285	−	3.45842i	0.120270	−	0.127479i
$737$	0.628278	−	0.228675i	0.0231429	−	0.00842334i
$738$		0			0
$739$	−29.1919	−	10.6250i	−1.07384	−	0.390846i	−0.256229	−	0.966616i	$-0.582480\pi$
$739$	−29.1919	−	10.6250i	−1.07384	−	0.390846i	−0.817612	+	0.575770i	$0.804702\pi$
$740$	−44.2272	+	22.2117i	−1.62582	+	0.816519i
$741$		0			0
$742$	−6.86318	−	15.9106i	−0.251955	−	0.584098i
$743$	−6.43298	−	0.751908i	−0.236003	−	0.0275848i	−0.00273096	−	0.999996i	$-0.500869\pi$
$743$	−6.43298	−	0.751908i	−0.236003	−	0.0275848i	−0.233272	+	0.972411i	$0.574943\pi$
$744$		0			0
$745$	24.2024	+	15.9182i	0.886707	+	0.583196i
$746$	−60.2439	+	50.5507i	−2.20569	+	1.85079i
$747$		0			0
$748$	−51.6272	−	43.3204i	−1.88768	−	1.58395i
$749$	−2.97726	−	9.94474i	−0.108787	−	0.363373i
$750$		0			0
$751$	−6.62351	−	3.32645i	−0.241695	−	0.121384i	0.323829	−	0.946116i	$-0.395030\pi$
$751$	−6.62351	−	3.32645i	−0.241695	−	0.121384i	−0.565524	+	0.824732i	$0.691326\pi$
$752$	−2.14163	−	2.26999i	−0.0780972	−	0.0827782i
$753$		0			0
$754$	1.28612	−	2.98157i	0.0468378	−	0.108582i
$755$	19.7042	−	34.1287i	0.717109	−	1.24207i
$756$		0			0
$757$	−22.2841	−	38.5972i	−0.809930	−	1.40284i	−0.912912	−	0.408157i	$-0.866172\pi$
$757$	−22.2841	−	38.5972i	−0.809930	−	1.40284i	0.102981	−	0.994683i	$-0.467162\pi$
$758$	53.3070	−	6.23070i	1.93620	−	0.226309i
$759$		0			0
$760$	60.9750	−	14.4513i	2.21179	−	0.524205i
$761$	−1.16403	−	19.9857i	−0.0421961	−	0.724480i	−0.951368	−	0.308058i	$-0.900321\pi$
$761$	−1.16403	−	19.9857i	−0.0421961	−	0.724480i	0.909171	−	0.416422i	$-0.136716\pi$
$762$		0			0
$763$	29.5288	+	6.99845i	1.06901	+	0.253361i
$764$	−14.4900	+	82.1770i	−0.524231	+	2.97306i
$765$		0			0
$766$	6.01753	+	34.1271i	0.217422	+	1.23306i
$767$	0.0219000	−	0.376009i	0.000790765	−	0.0135769i
$768$		0			0
$769$	−2.97889	+	4.00134i	−0.107421	+	0.144292i	−0.852583	−	0.522592i	$-0.824965\pi$
$769$	−2.97889	+	4.00134i	−0.107421	+	0.144292i	0.745161	+	0.666884i	$0.232372\pi$
$770$	23.2815	−	31.2725i	0.839007	−	1.12698i
$771$		0			0
$772$	4.15251	−	71.2958i	0.149452	−	2.56599i
$773$	4.06522	+	23.0550i	0.146216	+	0.829232i	0.966383	+	0.257108i	$0.0827695\pi$
$773$	4.06522	+	23.0550i	0.146216	+	0.829232i	−0.820167	+	0.572124i	$0.806119\pi$
$774$		0			0
$775$	2.00005	−	11.3429i	0.0718440	−	0.407448i
$776$	−7.84496	−	1.85929i	−0.281618	−	0.0667446i
$777$		0			0
$778$	1.73733	+	29.8287i	0.0622862	+	1.06941i
$779$	−28.2409	+	6.69322i	−1.01184	+	0.239809i
$780$		0			0
$781$	19.3237	−	2.25861i	0.691456	−	0.0808196i
$782$	−65.9832	−	114.286i	−2.35955	−	4.08687i
$783$		0			0
$784$	3.16768	−	5.48659i	0.113132	−	0.195950i
$785$	3.50571	−	8.12715i	0.125124	−	0.290070i
$786$		0			0
$787$	34.2546	+	36.3078i	1.22105	+	1.29423i	0.942657	+	0.333764i	$0.108319\pi$
$787$	34.2546	+	36.3078i	1.22105	+	1.29423i	0.278388	+	0.960469i	$0.410200\pi$
$788$	−25.0937	−	12.6025i	−0.893927	−	0.448947i
$789$		0			0
$790$	15.3702	+	51.3399i	0.546846	+	1.82659i
$791$	7.52951	+	6.31801i	0.267719	+	0.224642i
$792$		0			0
$793$	−2.57045	+	2.15686i	−0.0912792	+	0.0765923i
$794$	−19.7707	−	13.0034i	−0.701636	−	0.461474i
$795$		0			0
$796$	14.2846	+	1.66963i	0.506303	+	0.0591784i
$797$	15.9248	+	36.9179i	0.564087	+	1.30770i	0.926715	+	0.375766i	$0.122620\pi$
$797$	15.9248	+	36.9179i	0.564087	+	1.30770i	−0.362628	+	0.931934i	$0.618120\pi$
$798$		0			0
$799$	5.59335	−	2.80909i	0.197879	−	0.0993783i
$800$	2.21319	+	0.805537i	0.0782482	+	0.0284800i
$801$		0			0
$802$	2.67647	−	0.974155i	0.0945094	−	0.0343986i
$803$	24.7751	−	26.2600i	0.874293	−	0.926696i
$804$		0			0
$805$	42.2841	−	27.8107i	1.49032	−	0.980199i
$806$	−1.33134	+	4.44699i	−0.0468945	+	0.156639i
$807$		0			0
$808$	23.8411	+	32.0241i	0.838726	+	1.12660i
$809$	−44.4490			−1.56274			−0.781371	−	0.624066i	$-0.785479\pi$
$809$	−44.4490			−1.56274			−0.781371	+	0.624066i	$0.785479\pi$
$810$		0			0
$811$	−38.6494			−1.35716			−0.678582	−	0.734524i	$-0.737405\pi$
$811$	−38.6494			−1.35716			−0.678582	+	0.734524i	$0.737405\pi$
$812$	11.6825	+	15.6923i	0.409974	+	0.550691i
$813$		0			0
$814$	7.05367	−	23.5609i	0.247231	−	0.825809i
$815$	43.7176	−	28.7535i	1.53136	−	1.00719i
$816$		0			0
$817$	−12.5817	+	13.3359i	−0.440179	+	0.466562i
$818$	62.8587	−	22.8787i	2.19780	−	0.799934i
$819$		0			0
$820$	70.2401	+	25.5653i	2.45289	+	0.892780i
$821$	−38.6944	+	19.4330i	−1.35044	+	0.678218i	−0.969204	−	0.246259i	$-0.920799\pi$
$821$	−38.6944	+	19.4330i	−1.35044	+	0.678218i	−0.381238	+	0.924477i	$0.624502\pi$
$822$		0			0
$823$	−11.9237	−	27.6422i	−0.415633	−	0.963545i	−0.989492	−	0.144591i	$-0.953813\pi$
$823$	−11.9237	−	27.6422i	−0.415633	−	0.963545i	0.573859	−	0.818954i	$-0.305446\pi$
$824$	8.48745	+	0.992041i	0.295674	+	0.0345594i
$825$		0			0
$826$	2.85984	+	1.88095i	0.0995066	+	0.0654465i
$827$	12.5660	−	10.5441i	0.436963	−	0.366655i	−0.397609	−	0.917555i	$-0.630160\pi$
$827$	12.5660	−	10.5441i	0.436963	−	0.366655i	0.834571	+	0.550900i	$0.185715\pi$
$828$		0			0
$829$	22.2396	+	18.6612i	0.772413	+	0.648132i	0.941326	−	0.337500i	$-0.109581\pi$
$829$	22.2396	+	18.6612i	0.772413	+	0.648132i	−0.168913	+	0.985631i	$0.554026\pi$
$830$	11.2931	+	37.7214i	0.391988	+	1.30933i
$831$		0			0
$832$	−4.80489	−	2.41311i	−0.166580	−	0.0836594i
$833$	8.71956	+	9.24219i	0.302115	+	0.320223i
$834$		0			0
$835$	−25.7061	+	59.5935i	−0.889597	+	2.06232i
$836$	−20.9978	+	36.3693i	−0.726224	+	1.25786i
$837$		0			0
$838$	29.9589	+	51.8904i	1.03491	+	1.79252i
$839$	35.2631	−	4.12166i	1.21742	−	0.142296i	0.516972	−	0.856002i	$-0.327059\pi$
$839$	35.2631	−	4.12166i	1.21742	−	0.142296i	0.700445	+	0.713707i	$0.252985\pi$
$840$		0			0
$841$	−23.6286	+	5.60007i	−0.814778	+	0.193106i
$842$	1.74244	+	29.9166i	0.0600486	+	1.03099i
$843$		0			0
$844$	−68.3327	−	16.1951i	−2.35211	−	0.557460i
$845$	6.46910	−	36.6881i	0.222544	−	1.26211i
$846$		0			0
$847$	−2.14362	−	12.1571i	−0.0736557	−	0.417722i
$848$	0.651488	−	11.1856i	0.0223722	−	0.384116i
$849$		0			0
$850$	39.0361	−	52.4346i	1.33893	−	1.79849i
$851$	19.0650	−	25.6087i	0.653540	−	0.877856i
$852$		0			0
$853$	0.0559581	−	0.960764i	0.00191597	−	0.0328959i	−0.997215	−	0.0745849i	$-0.976237\pi$
$853$	0.0559581	−	0.960764i	0.00191597	−	0.0328959i	0.999131	+	0.0416890i	$0.0132739\pi$
$854$	−5.29532	−	30.0313i	−0.181202	−	1.02765i
$855$		0			0
$856$	3.70813	−	21.0298i	0.126741	−	0.718785i
$857$	−0.552270	−	0.130890i	−0.0188652	−	0.00447113i	0.221172	−	0.975235i	$-0.429012\pi$
$857$	−0.552270	−	0.130890i	−0.0188652	−	0.00447113i	−0.240038	+	0.970764i	$0.577160\pi$
$858$		0			0
$859$	−1.16923	−	20.0749i	−0.0398936	−	0.684947i	−0.957673	−	0.287857i	$-0.907057\pi$
$859$	−1.16923	−	20.0749i	−0.0398936	−	0.684947i	0.917780	−	0.397090i	$-0.129980\pi$
$860$	45.9462	−	10.8895i	1.56675	−	0.371327i
$861$		0			0
$862$	−19.2507	+	2.25008i	−0.655682	+	0.0766382i
$863$	18.8153	+	32.5891i	0.640481	+	1.10935i	0.985326	+	0.170686i	$0.0545982\pi$
$863$	18.8153	+	32.5891i	0.640481	+	1.10935i	−0.344845	+	0.938660i	$0.612068\pi$
$864$		0			0
$865$	−15.9735	+	27.6668i	−0.543114	+	0.940700i
$866$	11.4956	−	26.6497i	0.390635	−	0.905594i
$867$		0			0
$868$	−19.1923	−	20.3427i	−0.651431	−	0.690476i
$869$	−15.7773	−	7.92365i	−0.535207	−	0.268791i
$870$		0			0
$871$	−0.0496952	−	0.165993i	−0.00168386	−	0.00562447i
$872$	47.8210	+	40.1266i	1.61942	+	1.35886i
$873$		0			0
$874$	−62.9936	+	52.8579i	−2.13079	+	1.78795i
$875$	−7.28528	−	4.79160i	−0.246287	−	0.161986i
$876$		0			0
$877$	−27.2207	−	3.18164i	−0.919178	−	0.107437i	−0.356672	−	0.934230i	$-0.616089\pi$
$877$	−27.2207	−	3.18164i	−0.919178	−	0.107437i	−0.562506	+	0.826793i	$0.690163\pi$
$878$	6.66298	+	15.4465i	0.224865	+	0.521295i
$879$		0			0
$880$	22.5285	−	11.3143i	0.759437	−	0.381404i
$881$	31.5862	+	11.4964i	1.06417	+	0.387324i	0.813992	−	0.580877i	$-0.197290\pi$
$881$	31.5862	+	11.4964i	1.06417	+	0.387324i	0.250174	+	0.968201i	$0.419512\pi$
$882$		0			0
$883$	40.4061	−	14.7066i	1.35977	−	0.494917i	0.443789	−	0.896131i	$-0.353634\pi$
$883$	40.4061	−	14.7066i	1.35977	−	0.494917i	0.915984	+	0.401214i	$0.131412\pi$
$884$	−11.9858	+	12.7042i	−0.403125	+	0.427287i
$885$		0			0
$886$	14.7451	−	9.69802i	0.495372	−	0.325811i
$887$	−8.89124	+	29.6988i	−0.298539	+	0.997189i	0.668745	+	0.743492i	$0.266832\pi$
$887$	−8.89124	+	29.6988i	−0.298539	+	0.997189i	−0.967284	+	0.253697i	$0.918353\pi$
$888$		0			0
$889$	−8.05027	−	10.8134i	−0.269997	−	0.362669i
$890$	−66.1052			−2.21585
$891$		0			0
$892$	−55.4905			−1.85796
$893$	−2.32907	−	3.12848i	−0.0779393	−	0.104691i
$894$		0			0
$895$	7.56841	−	25.2803i	0.252984	−	0.845026i
$896$	38.3963	−	25.2536i	1.28273	−	0.843665i
$897$		0			0
$898$	57.4798	−	60.9250i	1.91812	−	2.03309i
$899$	−6.33645	+	2.30628i	−0.211333	+	0.0769188i
$900$		0			0
$901$	21.1167	+	7.68587i	0.703501	+	0.256053i
$902$	−33.1940	+	16.6707i	−1.10524	+	0.555072i
$903$		0			0
$904$	8.00843	+	18.5656i	0.266356	+	0.617483i
$905$	12.6775	+	1.48179i	0.421416	+	0.0492565i
$906$		0			0
$907$	3.26950	+	2.15039i	0.108562	+	0.0714024i	0.602629	−	0.798021i	$-0.294120\pi$
$907$	3.26950	+	2.15039i	0.108562	+	0.0714024i	−0.494067	+	0.869424i	$0.664490\pi$
$908$	17.3364	−	14.5469i	0.575328	−	0.482757i
$909$		0			0
$910$	−7.73997	−	6.49461i	−0.256577	−	0.215294i
$911$	11.1761	+	37.3309i	0.370282	+	1.23683i	0.916789	+	0.399373i	$0.130772\pi$
$911$	11.1761	+	37.3309i	0.370282	+	1.23683i	−0.546507	+	0.837455i	$0.684043\pi$
$912$		0			0
$913$	−11.5922	−	5.82181i	−0.383645	−	0.192674i
$914$	−27.8389	−	29.5075i	−0.920830	−	0.976022i
$915$		0			0
$916$	−38.2901	+	88.7664i	−1.26514	+	2.93292i
$917$	−14.9522	+	25.8980i	−0.493766	+	0.855228i
$918$		0			0
$919$	10.6253	+	18.4036i	0.350497	+	0.607078i	0.986337	−	0.164743i	$-0.0526794\pi$
$919$	10.6253	+	18.4036i	0.350497	+	0.607078i	−0.635840	+	0.771821i	$0.719346\pi$
$920$	103.405	−	12.0863i	3.40917	−	0.398475i
$921$		0			0
$922$	−32.6705	+	7.74305i	−1.07595	+	0.255004i
$923$	−0.293164	−	5.03344i	−0.00964963	−	0.165678i
$924$		0			0
$925$	15.3884	+	3.64712i	0.505967	+	0.119916i
$926$	5.17866	−	29.3696i	0.170181	−	0.965146i
$927$		0			0
$928$	−0.239438	−	1.35792i	−0.00785994	−	0.0445759i
$929$	0.950318	−	16.3163i	0.0311789	−	0.535321i	−0.946168	−	0.323677i	$-0.895081\pi$
$929$	0.950318	−	16.3163i	0.0311789	−	0.535321i	0.977347	−	0.211645i	$-0.0678819\pi$
$930$		0			0
$931$	4.72810	−	6.35094i	0.154957	−	0.208144i
$932$	29.9485	−	40.2279i	0.980997	−	1.31771i
$933$		0			0
$934$	−2.18035	+	37.4352i	−0.0713434	+	1.22492i
$935$	8.77991	+	49.7934i	0.287134	+	1.62842i
$936$		0			0
$937$	−3.94626	+	22.3803i	−0.128919	+	0.731134i	0.849984	+	0.526808i	$0.176611\pi$
$937$	−3.94626	+	22.3803i	−0.128919	+	0.731134i	−0.978903	+	0.204326i	$0.934500\pi$
$938$	1.53225	+	0.363151i	0.0500299	+	0.0118573i
$939$		0			0
$940$	0.584060	+	10.0279i	0.0190499	+	0.327075i
$941$	12.7527	−	3.02245i	0.415727	−	0.0985292i	−0.0174287	−	0.999848i	$-0.505548\pi$
$941$	12.7527	−	3.02245i	0.415727	−	0.0985292i	0.433156	+	0.901319i	$0.357400\pi$
$942$		0			0
$943$	−47.8928	+	5.59786i	−1.55960	+	0.182291i
$944$	1.10669	+	1.91684i	0.0360196	+	0.0623877i
$945$		0			0
$946$	−11.7324	+	20.3212i	−0.381454	+	0.660698i
$947$	−8.56599	+	19.8582i	−0.278357	+	0.645305i	−0.998839	−	0.0481689i	$-0.984661\pi$
$947$	−8.56599	+	19.8582i	−0.278357	+	0.645305i	0.720482	+	0.693474i	$0.243921\pi$
$948$		0			0
$949$	−6.42064	−	6.80548i	−0.208423	−	0.220915i
$950$	−36.4012	−	18.2813i	−1.18101	−	0.593125i
$951$		0			0
$952$	−22.3786	−	74.7498i	−0.725295	−	2.42266i
$953$	−16.8450	−	14.1347i	−0.545665	−	0.457867i	0.327805	−	0.944745i	$-0.393691\pi$
$953$	−16.8450	−	14.1347i	−0.545665	−	0.457867i	−0.873470	+	0.486878i	$0.838135\pi$
$954$		0			0
$955$	47.9566	−	40.2403i	1.55184	−	1.30215i
$956$	80.0359	+	52.6404i	2.58855	+	1.70251i
$957$		0			0
$958$	−36.6557	−	4.28444i	−1.18429	−	0.138424i
$959$	−4.10605	−	9.51890i	−0.132591	−	0.307381i
$960$		0			0
$961$	−19.0882	+	9.58645i	−0.615748	+	0.309240i
$962$	−5.98936	−	2.17995i	−0.193105	−	0.0702844i
$963$		0			0
$964$	107.463	−	39.1135i	3.46116	−	1.25976i
$965$	−36.7682	+	38.9720i	−1.18361	+	1.25455i
$966$		0			0
$967$	−19.8618	+	13.0633i	−0.638713	+	0.420088i	−0.827137	−	0.562000i	$-0.810032\pi$
$967$	−19.8618	+	13.0633i	−0.638713	+	0.420088i	0.188425	+	0.982088i	$0.439662\pi$
$968$	7.28306	−	24.3271i	0.234086	−	0.781903i
$969$		0			0
$970$	7.34768	+	9.86965i	0.235920	+	0.316895i
$971$	16.4980			0.529445			0.264723	−	0.964325i	$-0.414720\pi$
$971$	16.4980			0.529445			0.264723	+	0.964325i	$0.414720\pi$
$972$		0			0
$973$	−10.9747			−0.351833
$974$	−14.1731	−	19.0378i	−0.454136	−	0.610011i
$975$		0			0
$976$	5.65534	−	18.8902i	0.181023	−	0.604659i
$977$	−5.13809	+	3.37937i	−0.164382	+	0.108116i	−0.629035	−	0.777377i	$-0.716550\pi$
$977$	−5.13809	+	3.37937i	−0.164382	+	0.108116i	0.464653	+	0.885493i	$0.346179\pi$
$978$		0			0
$979$	14.9448	−	15.8406i	0.477639	−	0.506268i
$980$	−19.1618	+	6.97433i	−0.612101	+	0.222787i
$981$		0			0
$982$	−43.7990	−	15.9415i	−1.39768	−	0.508714i
$983$	−10.4161	+	5.23114i	−0.332221	+	0.166847i	−0.607088	−	0.794635i	$-0.707662\pi$
$983$	−10.4161	+	5.23114i	−0.332221	+	0.166847i	0.274867	+	0.961482i	$0.411366\pi$
$984$		0			0
$985$	8.34419	+	19.3440i	0.265868	+	0.616351i
$986$	−38.0119	−	4.44295i	−1.21054	−	0.141492i
$987$		0			0
$988$	9.09302	+	5.98057i	0.289287	+	0.190267i
$989$	−23.3339	+	19.5795i	−0.741976	+	0.622592i
$990$		0			0
$991$	−20.9608	−	17.5882i	−0.665840	−	0.558706i	0.245991	−	0.969272i	$-0.420887\pi$
$991$	−20.9608	−	17.5882i	−0.665840	−	0.558706i	−0.911831	+	0.410566i	$0.865331\pi$
$992$	0.565345	+	1.88838i	0.0179497	+	0.0599562i
$993$		0			0
$994$	40.9475	+	20.5646i	1.29878	+	0.652269i
$995$	−7.40434	−	7.84814i	−0.234733	−	0.248803i
$996$		0			0
$997$	21.6349	−	50.1553i	0.685184	−	1.58843i	−0.118211	−	0.992988i	$-0.537716\pi$
$997$	21.6349	−	50.1553i	0.685184	−	1.58843i	0.803395	−	0.595446i	$-0.203025\pi$
$998$	31.8177	−	55.1099i	1.00717	−	1.74447i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.100.8		144
3.2	odd	2		81.2.g.a.7.1	✓	144
9.2	odd	6		729.2.g.c.55.1		144
9.4	even	3		729.2.g.a.298.1		144
9.5	odd	6		729.2.g.d.298.8		144
9.7	even	3		729.2.g.b.55.8		144
81.4	even	27		729.2.g.b.676.8		144
81.23	odd	54		81.2.g.a.58.1	yes	144
81.25	even	27		6561.2.a.d.1.65		72
81.31	even	27		729.2.g.a.433.1		144
81.50	odd	54		729.2.g.d.433.8		144
81.56	odd	54		6561.2.a.c.1.8		72
81.58	even	27	inner	243.2.g.a.226.8		144
81.77	odd	54		729.2.g.c.676.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.1	✓	144	3.2	odd	2
81.2.g.a.58.1	yes	144	81.23	odd	54
243.2.g.a.100.8		144	1.1	even	1	trivial
243.2.g.a.226.8		144	81.58	even	27	inner
729.2.g.a.298.1		144	9.4	even	3
729.2.g.a.433.1		144	81.31	even	27
729.2.g.b.55.8		144	9.7	even	3
729.2.g.b.676.8		144	81.4	even	27
729.2.g.c.55.1		144	9.2	odd	6
729.2.g.c.676.1		144	81.77	odd	54
729.2.g.d.298.8		144	9.5	odd	6
729.2.g.d.433.8		144	81.50	odd	54
6561.2.a.c.1.8		72	81.56	odd	54
6561.2.a.d.1.65		72	81.25	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45464 + 1.95391i) q^{2} +(-1.12821 + 3.76849i) q^{4} +(2.46571 - 1.62172i) q^{5} +(-1.57141 + 1.66559i) q^{7} +(-4.42639 + 1.61107i) q^{8} +O(q^{10})\)	\(q+(1.45464 + 1.95391i) q^{2} +(-1.12821 + 3.76849i) q^{4} +(2.46571 - 1.62172i) q^{5} +(-1.57141 + 1.66559i) q^{7} +(-4.42639 + 1.61107i) q^{8} +(6.75541 + 2.45877i) q^{10} +(-2.11643 + 1.06291i) q^{11} +(0.243103 + 0.563577i) q^{13} +(-5.54025 - 0.647562i) q^{14} +(-3.01348 - 1.98200i) q^{16} +(5.54151 - 4.64988i) q^{17} +(-3.45309 - 2.89749i) q^{19} +(3.32960 + 11.1216i) q^{20} +(-5.15546 - 2.58917i) q^{22} +(-5.13927 - 5.44731i) q^{23} +(1.46933 - 3.40630i) q^{25} +(-0.747554 + 1.29480i) q^{26} +(-4.50389 - 7.80096i) q^{28} +(-2.15715 + 0.252135i) q^{29} +(3.02111 - 0.716016i) q^{31} +(0.0369153 + 0.633812i) q^{32} +(17.1464 + 4.06376i) q^{34} +(-1.17350 + 6.65525i) q^{35} +(0.740274 + 4.19830i) q^{37} +(0.638454 - 10.9618i) q^{38} +(-8.30146 + 11.1508i) q^{40} +(3.84487 - 5.16456i) q^{41} +(0.236494 - 4.06045i) q^{43} +(-1.61778 - 9.17491i) q^{44} +(3.16781 - 17.9655i) q^{46} +(0.841921 + 0.199539i) q^{47} +(0.102130 + 1.75351i) q^{49} +(8.79296 - 2.08397i) q^{50} +(-2.39810 + 0.280298i) q^{52} +(1.55323 + 2.69028i) q^{53} +(-3.49475 + 6.05308i) q^{55} +(4.27226 - 9.90421i) q^{56} +(-3.63052 - 3.84812i) q^{58} +(-0.548384 - 0.275409i) q^{59} +(1.56794 + 5.23730i) q^{61} +(5.79364 + 4.86144i) q^{62} +(-6.71074 + 5.63098i) q^{64} +(1.51339 + 0.995369i) q^{65} +(-0.280399 - 0.0327739i) q^{67} +(11.2710 + 26.1292i) q^{68} +(-14.7108 + 7.38804i) q^{70} +(-7.71930 - 2.80960i) q^{71} +(-14.3245 + 5.21369i) q^{73} +(-7.12630 + 7.55343i) q^{74} +(14.8149 - 9.74394i) q^{76} +(1.55539 - 5.19537i) q^{77} +(4.45162 + 5.97957i) q^{79} -10.6446 q^{80} +15.6840 q^{82} +(3.27078 + 4.39342i) q^{83} +(6.12294 - 20.4520i) q^{85} +(8.27778 - 5.44438i) q^{86} +(7.65569 - 8.11456i) q^{88} +(-8.64084 + 3.14501i) q^{89} +(-1.32070 - 0.480697i) q^{91} +(26.3263 - 13.2216i) q^{92} +(0.834806 + 1.93530i) q^{94} +(-13.2132 - 1.54440i) q^{95} +(1.43000 + 0.940523i) q^{97} +(-3.27764 + 2.75027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26} - 9 q^{28} - 9 q^{29} - 18 q^{31} - 36 q^{32} - 18 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} - 18 q^{40} - 18 q^{43} - 54 q^{44} - 18 q^{46} - 36 q^{47} - 18 q^{49} - 99 q^{50} - 45 q^{53} - 9 q^{55} - 126 q^{56} - 18 q^{58} - 45 q^{59} - 18 q^{61} - 81 q^{62} - 18 q^{64} + 9 q^{67} + 99 q^{68} + 36 q^{70} + 90 q^{71} - 18 q^{73} + 162 q^{74} + 63 q^{76} + 162 q^{77} + 36 q^{79} + 288 q^{80} - 36 q^{82} + 90 q^{83} + 36 q^{85} + 162 q^{86} + 63 q^{88} + 81 q^{89} - 18 q^{91} + 144 q^{92} + 36 q^{94} - 18 q^{95} + 9 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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