LMFDB - Embedded newform 540.2.q.a.251.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,2,Mod(71,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("540.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.q (of order $6$, degree $2$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.22
Character	$\chi$	$=$	540.251
Dual form			540.2.q.a.71.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34552 - 0.435401i) q^{2} +(1.62085 - 1.17168i) q^{4} +(0.866025 - 0.500000i) q^{5} +(3.61144 + 2.08506i) q^{7} +(1.67074 - 2.28224i) q^{8} +(0.947554 - 1.04983i) q^{10} +(-3.22095 + 5.57886i) q^{11} +(-0.887336 - 1.53691i) q^{13} +(5.76710 + 1.23307i) q^{14} +(1.25432 - 3.79825i) q^{16} -0.950682i q^{17} -2.19286i q^{19} +(0.817857 - 1.82513i) q^{20} +(-1.90482 + 8.90887i) q^{22} +(-1.01006 - 1.74948i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.86310 - 1.68160i) q^{26} +(8.29663 - 0.851880i) q^{28} +(-5.65260 - 3.26353i) q^{29} +(-2.46164 + 1.42123i) q^{31} +(0.0339479 - 5.65675i) q^{32} +(-0.413928 - 1.27916i) q^{34} +4.17013 q^{35} -5.83599 q^{37} +(-0.954776 - 2.95054i) q^{38} +(0.305778 - 2.81185i) q^{40} +(6.16222 - 3.55776i) q^{41} +(4.59844 + 2.65491i) q^{43} +(1.31596 + 12.8164i) q^{44} +(-2.12079 - 1.91418i) q^{46} +(0.201996 - 0.349867i) q^{47} +(5.19498 + 8.99797i) q^{49} +(0.295692 - 1.38296i) q^{50} +(-3.23901 - 1.45143i) q^{52} -4.87844i q^{53} +6.44191i q^{55} +(10.7924 - 4.75859i) q^{56} +(-9.02663 - 1.93000i) q^{58} +(-1.34391 - 2.32773i) q^{59} +(-2.04652 + 3.54468i) q^{61} +(-2.69338 + 2.98409i) q^{62} +(-2.41728 - 7.62606i) q^{64} +(-1.53691 - 0.887336i) q^{65} +(-9.43616 + 5.44797i) q^{67} +(-1.11390 - 1.54091i) q^{68} +(5.61099 - 1.81568i) q^{70} -2.23126 q^{71} -1.74662 q^{73} +(-7.85244 + 2.54100i) q^{74} +(-2.56934 - 3.55431i) q^{76} +(-23.2645 + 13.4318i) q^{77} +(-0.214428 - 0.123800i) q^{79} +(-0.812853 - 3.91654i) q^{80} +(6.74234 - 7.47008i) q^{82} +(-5.83641 + 10.1090i) q^{83} +(-0.475341 - 0.823315i) q^{85} +(7.34325 + 1.57007i) q^{86} +(7.35095 + 16.6718i) q^{88} -6.13881i q^{89} -7.40061i q^{91} +(-3.68701 - 1.65218i) q^{92} +(0.119457 - 0.558703i) q^{94} +(-1.09643 - 1.89908i) q^{95} +(-9.08503 + 15.7357i) q^{97} +(10.9077 + 9.84505i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 30 q^{14} + 24 q^{25} + 12 q^{29} - 6 q^{34} - 60 q^{38} - 6 q^{40} + 60 q^{41} - 12 q^{46} + 24 q^{49} - 18 q^{52} + 42 q^{56} - 18 q^{58} - 48 q^{64} - 48 q^{68} - 24 q^{73} - 84 q^{74} + 6 q^{76}+ \cdots - 12 q^{97}+O(q^{100}) $ 48 * q + 30 * q^14 + 24 * q^25 + 12 * q^29 - 6 * q^34 - 60 * q^38 - 6 * q^40 + 60 * q^41 - 12 * q^46 + 24 * q^49 - 18 * q^52 + 42 * q^56 - 18 * q^58 - 48 * q^64 - 48 * q^68 - 24 * q^73 - 84 * q^74 + 6 * q^76 - 48 * q^77 - 36 * q^82 + 54 * q^86 - 60 * q^92 + 18 * q^94 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.34552	−	0.435401i	0.951427	−	0.307875i
$2$	1.34552	−	0.435401i	0.951427	−	0.307875i
$3$		0			0
$3$		0			0
$4$	1.62085	−	1.17168i	0.810426	−	0.585842i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$		0			0
$7$	3.61144	+	2.08506i	1.36499	+	0.788080i	0.990284	−	0.139062i	$-0.0444087\pi$
$7$	3.61144	+	2.08506i	1.36499	+	0.788080i	0.374711	+	0.927142i	$0.377742\pi$
$8$	1.67074	−	2.28224i	0.590694	−	0.806895i
$9$		0			0
$10$	0.947554	−	1.04983i	0.299643	−	0.331985i
$11$	−3.22095	+	5.57886i	−0.971154	+	1.68209i	−0.279071	+	0.960271i	$0.590026\pi$
$11$	−3.22095	+	5.57886i	−0.971154	+	1.68209i	−0.692083	+	0.721818i	$0.743307\pi$
$12$		0			0
$13$	−0.887336	−	1.53691i	−0.246103	−	0.426262i	0.716338	−	0.697753i	$-0.245817\pi$
$13$	−0.887336	−	1.53691i	−0.246103	−	0.426262i	−0.962441	+	0.271491i	$0.912483\pi$
$14$	5.76710	+	1.23307i	1.54132	+	0.329552i
$15$		0			0
$16$	1.25432	−	3.79825i	0.313579	−	0.949562i
$17$		−	0.950682i		−	0.230574i	−0.993332	−	0.115287i	$-0.963221\pi$
$17$		−	0.950682i		−	0.230574i	0.993332	−	0.115287i	$-0.0367788\pi$
$18$		0			0
$19$		−	2.19286i		−	0.503078i	−0.967847	−	0.251539i	$-0.919063\pi$
$19$		−	2.19286i		−	0.503078i	0.967847	−	0.251539i	$-0.0809366\pi$
$20$	0.817857	−	1.82513i	0.182878	−	0.408112i
$21$		0			0
$22$	−1.90482	+	8.90887i	−0.406109	+	1.89938i
$23$	−1.01006	−	1.74948i	−0.210613	−	0.364793i	0.741293	−	0.671181i	$-0.234213\pi$
$23$	−1.01006	−	1.74948i	−0.210613	−	0.364793i	−0.951907	+	0.306388i	$0.900879\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.86310	−	1.68160i	−0.365384	−	0.329788i
$27$		0			0
$28$	8.29663	−	0.851880i	1.56792	−	0.160990i
$29$	−5.65260	−	3.26353i	−1.04966	−	0.606022i	−0.127107	−	0.991889i	$-0.540569\pi$
$29$	−5.65260	−	3.26353i	−1.04966	−	0.606022i	−0.922555	+	0.385867i	$0.873902\pi$
$30$		0			0
$31$	−2.46164	+	1.42123i	−0.442124	+	0.255260i	−0.704498	−	0.709706i	$-0.748828\pi$
$31$	−2.46164	+	1.42123i	−0.442124	+	0.255260i	0.262374	+	0.964966i	$0.415494\pi$
$32$	0.0339479	−	5.65675i	0.00600120	−	0.999982i
$33$		0			0
$34$	−0.413928	−	1.27916i	−0.0709881	−	0.219374i
$35$	4.17013			0.704880
$36$		0			0
$37$	−5.83599			−0.959431			−0.479715	−	0.877424i	$-0.659260\pi$
$37$	−5.83599			−0.959431			−0.479715	+	0.877424i	$0.659260\pi$
$38$	−0.954776	−	2.95054i	−0.154885	−	0.478642i
$39$		0			0
$40$	0.305778	−	2.81185i	0.0483477	−	0.444593i
$41$	6.16222	−	3.55776i	0.962378	−	0.555629i	0.0654736	−	0.997854i	$-0.479144\pi$
$41$	6.16222	−	3.55776i	0.962378	−	0.555629i	0.896904	+	0.442225i	$0.145811\pi$
$42$		0			0
$43$	4.59844	+	2.65491i	0.701256	+	0.404870i	0.807815	−	0.589436i	$-0.200650\pi$
$43$	4.59844	+	2.65491i	0.701256	+	0.404870i	−0.106559	+	0.994306i	$0.533983\pi$
$44$	1.31596	+	12.8164i	0.198389	+	1.93215i
$45$		0			0
$46$	−2.12079	−	1.91418i	−0.312694	−	0.282231i
$47$	0.201996	−	0.349867i	0.0294641	−	0.0510334i	−0.850917	−	0.525300i	$-0.823953\pi$
$47$	0.201996	−	0.349867i	0.0294641	−	0.0510334i	0.880381	+	0.474266i	$0.157287\pi$
$48$		0			0
$49$	5.19498	+	8.99797i	0.742140	+	1.28542i
$50$	0.295692	−	1.38296i	0.0418171	−	0.195579i
$51$		0			0
$52$	−3.23901	−	1.45143i	−0.449170	−	0.201277i
$53$		−	4.87844i		−	0.670106i	−0.942199	−	0.335053i	$-0.891246\pi$
$53$		−	4.87844i		−	0.670106i	0.942199	−	0.335053i	$-0.108754\pi$
$54$		0			0
$55$			6.44191i			0.868627i
$56$	10.7924	−	4.75859i	1.44219	−	0.635893i
$57$		0			0
$58$	−9.02663	−	1.93000i	−1.18526	−	0.253421i
$59$	−1.34391	−	2.32773i	−0.174963	−	0.303045i	0.765186	−	0.643810i	$-0.222647\pi$
$59$	−1.34391	−	2.32773i	−0.174963	−	0.303045i	−0.940148	+	0.340765i	$0.889314\pi$
$60$		0			0
$61$	−2.04652	+	3.54468i	−0.262030	+	0.453849i	−0.966781	−	0.255605i	$-0.917725\pi$
$61$	−2.04652	+	3.54468i	−0.262030	+	0.453849i	0.704751	+	0.709454i	$0.251059\pi$
$62$	−2.69338	+	2.98409i	−0.342060	+	0.378980i
$63$		0			0
$64$	−2.41728	−	7.62606i	−0.302160	−	0.953257i
$65$	−1.53691	−	0.887336i	−0.190630	−	0.110060i
$66$		0			0
$67$	−9.43616	+	5.44797i	−1.15281	+	0.665575i	−0.949571	−	0.313553i	$-0.898480\pi$
$67$	−9.43616	+	5.44797i	−1.15281	+	0.665575i	−0.203240	+	0.979129i	$0.565147\pi$
$68$	−1.11390	−	1.54091i	−0.135080	−	0.186863i
$69$		0			0
$70$	5.61099	−	1.81568i	0.670642	−	0.217015i
$71$	−2.23126			−0.264802			−0.132401	−	0.991196i	$-0.542269\pi$
$71$	−2.23126			−0.264802			−0.132401	+	0.991196i	$0.542269\pi$
$72$		0			0
$73$	−1.74662			−0.204426			−0.102213	−	0.994763i	$-0.532592\pi$
$73$	−1.74662			−0.204426			−0.102213	+	0.994763i	$0.532592\pi$
$74$	−7.85244	+	2.54100i	−0.912828	+	0.295385i
$75$		0			0
$76$	−2.56934	−	3.55431i	−0.294724	−	0.407707i
$77$	−23.2645	+	13.4318i	−2.65124	+	1.53069i
$78$		0			0
$79$	−0.214428	−	0.123800i	−0.0241250	−	0.0139286i	0.487889	−	0.872906i	$-0.337767\pi$
$79$	−0.214428	−	0.123800i	−0.0241250	−	0.0139286i	−0.512014	+	0.858977i	$0.671100\pi$
$80$	−0.812853	−	3.91654i	−0.0908797	−	0.437882i
$81$		0			0
$82$	6.74234	−	7.47008i	0.744567	−	0.824932i
$83$	−5.83641	+	10.1090i	−0.640629	+	1.10960i	0.344664	+	0.938726i	$0.387993\pi$
$83$	−5.83641	+	10.1090i	−0.640629	+	1.10960i	−0.985293	+	0.170876i	$0.945340\pi$
$84$		0			0
$85$	−0.475341	−	0.823315i	−0.0515580	−	0.0893010i
$86$	7.34325	+	1.57007i	0.791843	+	0.169305i
$87$		0			0
$88$	7.35095	+	16.6718i	0.783614	+	1.77722i
$89$		−	6.13881i		−	0.650713i	−0.945591	−	0.325356i	$-0.894516\pi$
$89$		−	6.13881i		−	0.650713i	0.945591	−	0.325356i	$-0.105484\pi$
$90$		0			0
$91$		−	7.40061i		−	0.775794i
$92$	−3.68701	−	1.65218i	−0.384397	−	0.172251i
$93$		0			0
$94$	0.119457	−	0.558703i	0.0123211	−	0.0576258i
$95$	−1.09643	−	1.89908i	−0.112492	−	0.194841i
$96$		0			0
$97$	−9.08503	+	15.7357i	−0.922446	+	1.59772i	−0.126827	+	0.991925i	$0.540479\pi$
$97$	−9.08503	+	15.7357i	−0.922446	+	1.59772i	−0.795619	+	0.605798i	$0.792854\pi$
$98$	10.9077	+	9.84505i	1.10184	+	0.994500i
$99$		0			0
$100$	−0.204282	−	1.98954i	−0.0204282	−	0.198954i
$101$	8.86799	+	5.11994i	0.882398	+	0.509453i	0.871448	−	0.490487i	$-0.163181\pi$
$101$	8.86799	+	5.11994i	0.882398	+	0.509453i	0.0109497	+	0.999940i	$0.496515\pi$
$102$		0			0
$103$	8.36568	−	4.82993i	0.824295	−	0.475907i	−0.0276004	−	0.999619i	$-0.508787\pi$
$103$	8.36568	−	4.82993i	0.824295	−	0.475907i	0.851895	+	0.523712i	$0.175453\pi$
$104$	−4.99011	−	0.542655i	−0.489321	−	0.0532117i
$105$		0			0
$106$	−2.12408	−	6.56405i	−0.206309	−	0.637557i
$107$	3.23356			0.312600			0.156300	−	0.987710i	$-0.450043\pi$
$107$	3.23356			0.312600			0.156300	+	0.987710i	$0.450043\pi$
$108$		0			0
$109$	2.88351			0.276190			0.138095	−	0.990419i	$-0.455902\pi$
$109$	2.88351			0.276190			0.138095	+	0.990419i	$0.455902\pi$
$110$	2.80482	+	8.66772i	0.267429	+	0.826435i
$111$		0			0
$112$	12.4495	−	11.1018i	1.17636	−	1.04902i
$113$	−2.67448	+	1.54411i	−0.251594	+	0.145258i	−0.620494	−	0.784211i	$-0.713068\pi$
$113$	−2.67448	+	1.54411i	−0.251594	+	0.145258i	0.368900	+	0.929469i	$0.379735\pi$
$114$		0			0
$115$	−1.74948	−	1.01006i	−0.163140	−	0.0941890i
$116$	−12.9858	+	1.33336i	−1.20571	+	0.123799i
$117$		0			0
$118$	−2.82176	−	2.54686i	−0.259764	−	0.234458i
$119$	1.98223	−	3.43333i	0.181711	−	0.314732i
$120$		0			0
$121$	−15.2491	−	26.4122i	−1.38628	−	2.40111i
$122$	−1.21028	+	5.66049i	−0.109573	+	0.512477i
$123$		0			0
$124$	−2.32472	+	5.18786i	−0.208766	+	0.465884i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			2.16321i			0.191954i	0.995384	+	0.0959771i	$0.0305976\pi$
$127$			2.16321i			0.191954i	−0.995384	+	0.0959771i	$0.969402\pi$
$128$	−6.57290	−	9.20853i	−0.580967	−	0.813927i
$129$		0			0
$130$	−2.45429	−	0.524756i	−0.215256	−	0.0460241i
$131$	−0.957206	−	1.65793i	−0.0836315	−	0.144854i	0.821176	−	0.570675i	$-0.193319\pi$
$131$	−0.957206	−	1.65793i	−0.0836315	−	0.144854i	−0.904807	+	0.425821i	$0.859985\pi$
$132$		0			0
$133$	4.57226	−	7.91939i	0.396465	−	0.686698i
$134$	−10.3245	+	11.4389i	−0.891901	+	0.988168i
$135$		0			0
$136$	−2.16969	−	1.58834i	−0.186049	−	0.136199i
$137$	10.0986	+	5.83040i	0.862778	+	0.498125i	0.864941	−	0.501873i	$-0.167355\pi$
$137$	10.0986	+	5.83040i	0.862778	+	0.498125i	−0.00216386	+	0.999998i	$0.500689\pi$
$138$		0			0
$139$	−6.63468	+	3.83054i	−0.562747	+	0.324902i	−0.754247	−	0.656591i	$-0.771998\pi$
$139$	−6.63468	+	3.83054i	−0.562747	+	0.324902i	0.191501	+	0.981493i	$0.438665\pi$
$140$	6.75916	−	4.88607i	0.571253	−	0.412948i
$141$		0			0
$142$	−3.00221	+	0.971495i	−0.251940	+	0.0815261i
$143$	11.4323			0.956014
$144$		0			0
$145$	−6.52706			−0.542043
$146$	−2.35011	+	0.760479i	−0.194496	+	0.0629377i
$147$		0			0
$148$	−9.45927	+	6.83793i	−0.777547	+	0.562074i
$149$	3.02622	−	1.74719i	0.247918	−	0.143135i	−0.370893	−	0.928676i	$-0.620948\pi$
$149$	3.02622	−	1.74719i	0.247918	−	0.143135i	0.618810	+	0.785540i	$0.287615\pi$
$150$		0			0
$151$	6.15927	+	3.55606i	0.501234	+	0.289388i	0.729223	−	0.684276i	$-0.239882\pi$
$151$	6.15927	+	3.55606i	0.501234	+	0.289388i	−0.227989	+	0.973664i	$0.573215\pi$
$152$	−5.00465	−	3.66370i	−0.405931	−	0.297165i
$153$		0			0
$154$	−25.4547	+	28.2022i	−2.05120	+	2.27259i
$155$	−1.42123	+	2.46164i	−0.114156	+	0.197724i
$156$		0			0
$157$	1.57938	+	2.73556i	0.126048	+	0.218321i	0.922142	−	0.386851i	$-0.126437\pi$
$157$	1.57938	+	2.73556i	0.126048	+	0.218321i	−0.796094	+	0.605173i	$0.793104\pi$
$158$	−0.342420	−	0.0732132i	−0.0272414	−	0.00582453i
$159$		0			0
$160$	−2.79898	−	4.91587i	−0.221279	−	0.388633i
$161$		−	8.42420i		−	0.663920i
$162$		0			0
$163$		−	14.1062i		−	1.10488i	−0.833551	−	0.552442i	$-0.813696\pi$
$163$		−	14.1062i		−	1.10488i	0.833551	−	0.552442i	$-0.186304\pi$
$164$	5.81948	−	12.9868i	0.454425	−	1.01410i
$165$		0			0
$166$	−3.45155	+	16.1430i	−0.267893	+	1.25294i
$167$	9.16640	+	15.8767i	0.709317	+	1.22857i	0.965111	+	0.261842i	$0.0843299\pi$
$167$	9.16640	+	15.8767i	0.709317	+	1.22857i	−0.255794	+	0.966731i	$0.582337\pi$
$168$		0			0
$169$	4.92527	−	8.53082i	0.378867	−	0.656217i
$170$	−0.998053	−	0.900823i	−0.0765472	−	0.0690899i
$171$		0			0
$172$	10.5641	−	1.08470i	0.805506	−	0.0827076i
$173$	6.82580	+	3.94088i	0.518956	+	0.299620i	0.736508	−	0.676429i	$-0.236474\pi$
$173$	6.82580	+	3.94088i	0.518956	+	0.299620i	−0.217551	+	0.976049i	$0.569807\pi$
$174$		0			0
$175$	3.61144	−	2.08506i	0.272999	−	0.157616i
$176$	17.1498	+	19.2316i	1.29271	+	1.44964i
$177$		0			0
$178$	−2.67285	−	8.25990i	−0.200338	−	0.619105i
$179$	−9.84108			−0.735557			−0.367778	−	0.929914i	$-0.619881\pi$
$179$	−9.84108			−0.735557			−0.367778	+	0.929914i	$0.619881\pi$
$180$		0			0
$181$	18.3215			1.36183			0.680913	−	0.732364i	$-0.261583\pi$
$181$	18.3215			1.36183			0.680913	+	0.732364i	$0.261583\pi$
$182$	−3.22223	−	9.95767i	−0.238848	−	0.738111i
$183$		0			0
$184$	−5.68030	−	0.617711i	−0.418757	−	0.0455383i
$185$	−5.05411	+	2.91799i	−0.371586	+	0.214535i
$186$		0			0
$187$	5.30372	+	3.06210i	0.387846	+	0.223923i
$188$	−0.0825282	−	0.803758i	−0.00601898	−	0.0586201i
$189$		0			0
$190$	−2.30213	−	2.07786i	−0.167014	−	0.150744i
$191$	9.54024	−	16.5242i	0.690307	−	1.19565i	−0.281430	−	0.959582i	$-0.590809\pi$
$191$	9.54024	−	16.5242i	0.690307	−	1.19565i	0.971737	−	0.236066i	$-0.0758580\pi$
$192$		0			0
$193$	6.50154	+	11.2610i	0.467991	+	0.810585i	0.999331	−	0.0365742i	$-0.0116445\pi$
$193$	6.50154	+	11.2610i	0.467991	+	0.810585i	−0.531340	+	0.847159i	$0.678311\pi$
$194$	−5.37274	+	25.1284i	−0.385740	+	1.80411i
$195$		0			0
$196$	18.9631	+	8.49750i	1.35450	+	0.606964i
$197$			15.8462i			1.12899i	0.825436	+	0.564496i	$0.190929\pi$
$197$			15.8462i			1.12899i	−0.825436	+	0.564496i	$0.809071\pi$
$198$		0			0
$199$		−	1.24563i		−	0.0883001i	−0.999025	−	0.0441500i	$-0.985942\pi$
$199$		−	1.24563i		−	0.0883001i	0.999025	−	0.0441500i	$-0.0140580\pi$
$200$	−1.14111	−	2.58802i	−0.0806889	−	0.183001i
$201$		0			0
$202$	14.1613	+	3.02784i	0.996385	+	0.213038i
$203$	−13.6093	−	23.5721i	−0.955188	−	1.65443i
$204$		0			0
$205$	3.55776	−	6.16222i	0.248485	−	0.430388i
$206$	9.15324	−	10.1412i	0.637736	−	0.706571i
$207$		0			0
$208$	−6.95057	+	1.44255i	−0.481935	+	0.100023i
$209$	12.2337	+	7.06312i	0.846221	+	0.488566i
$210$		0			0
$211$	14.1374	−	8.16221i	0.973256	−	0.561910i	0.0730289	−	0.997330i	$-0.476733\pi$
$211$	14.1374	−	8.16221i	0.973256	−	0.561910i	0.900227	+	0.435420i	$0.143400\pi$
$212$	−5.71599	−	7.90723i	−0.392576	−	0.543071i
$213$		0			0
$214$	4.35083	−	1.40790i	0.297416	−	0.0962420i
$215$	5.30982			0.362127
$216$		0			0
$217$	−11.8534			−0.804662
$218$	3.87982	−	1.25548i	0.262774	−	0.0850320i
$219$		0			0
$220$	7.54787	+	10.4414i	0.508878	+	0.703957i
$221$	−1.46111	+	0.843574i	−0.0982851	+	0.0567449i
$222$		0			0
$223$	−15.5241	−	8.96287i	−1.03957	−	0.600198i	−0.119861	−	0.992791i	$-0.538245\pi$
$223$	−15.5241	−	8.96287i	−1.03957	−	0.600198i	−0.919713	+	0.392592i	$0.871578\pi$
$224$	11.9173	−	20.3582i	0.796257	−	1.36024i
$225$		0			0
$226$	−2.92626	+	3.24211i	−0.194652	+	0.215662i
$227$	−5.21522	+	9.03303i	−0.346146	+	0.599543i	−0.985561	−	0.169319i	$-0.945843\pi$
$227$	−5.21522	+	9.03303i	−0.346146	+	0.599543i	0.639415	+	0.768862i	$0.279177\pi$
$228$		0			0
$229$	9.39388	+	16.2707i	0.620765	+	1.07520i	0.989344	+	0.145600i	$0.0465112\pi$
$229$	9.39388	+	16.2707i	0.620765	+	1.07520i	−0.368578	+	0.929597i	$0.620155\pi$
$230$	−2.79375	−	0.597335i	−0.184214	−	0.0393871i
$231$		0			0
$232$	−16.8922	+	7.44812i	−1.10903	+	0.488993i
$233$			7.28693i			0.477382i	0.971096	+	0.238691i	$0.0767184\pi$
$233$			7.28693i			0.477382i	−0.971096	+	0.238691i	$0.923282\pi$
$234$		0			0
$235$		−	0.403992i		−	0.0263535i
$236$	−4.90565	−	2.19826i	−0.319330	−	0.143095i
$237$		0			0
$238$	1.17226	−	5.48268i	0.0759862	−	0.355389i
$239$	−14.8408	−	25.7051i	−0.959973	−	1.66272i	−0.722553	−	0.691316i	$-0.757031\pi$
$239$	−14.8408	−	25.7051i	−0.959973	−	1.66272i	−0.237421	−	0.971407i	$-0.576302\pi$
$240$		0			0
$241$	6.37517	−	11.0421i	0.410661	−	0.711285i	−0.584301	−	0.811537i	$-0.698631\pi$
$241$	6.37517	−	11.0421i	0.410661	−	0.711285i	0.994962	+	0.100251i	$0.0319647\pi$
$242$	−32.0179	−	28.8987i	−2.05819	−	1.85768i
$243$		0			0
$244$	0.836133	+	8.14327i	0.0535279	+	0.521319i
$245$	8.99797	+	5.19498i	0.574859	+	0.331895i
$246$		0			0
$247$	−3.37024	+	1.94581i	−0.214443	+	0.123809i
$248$	−0.869161	+	7.99257i	−0.0551918	+	0.507528i
$249$		0			0
$250$	−0.435401	−	1.34552i	−0.0275372	−	0.0850982i
$251$	−2.89830			−0.182939			−0.0914694	−	0.995808i	$-0.529156\pi$
$251$	−2.89830			−0.182939			−0.0914694	+	0.995808i	$0.529156\pi$
$252$		0			0
$253$	13.0135			0.818151
$254$	0.941867	+	2.91065i	0.0590980	+	0.182630i
$255$		0			0
$256$	−12.8534	−	9.52842i	−0.803336	−	0.595526i
$257$	8.63093	−	4.98307i	0.538382	−	0.310835i	−0.206041	−	0.978543i	$-0.566058\pi$
$257$	8.63093	−	4.98307i	0.538382	−	0.310835i	0.744423	+	0.667708i	$0.232725\pi$
$258$		0			0
$259$	−21.0763	−	12.1684i	−1.30962	−	0.756108i
$260$	−3.53078	+	0.362533i	−0.218970	+	0.0224833i
$261$		0			0
$262$	−2.00981	−	1.81401i	−0.124166	−	0.112070i
$263$	−0.610808	+	1.05795i	−0.0376640	+	0.0652360i	−0.884243	−	0.467027i	$-0.845325\pi$
$263$	−0.610808	+	1.05795i	−0.0376640	+	0.0652360i	0.846579	+	0.532263i	$0.178658\pi$
$264$		0			0
$265$	−2.43922	−	4.22486i	−0.149840	−	0.259531i
$266$	2.70396	−	12.6465i	0.165790	−	0.775405i
$267$		0			0
$268$	−8.91132	+	19.8865i	−0.544345	+	1.21476i
$269$		−	19.0910i		−	1.16400i	−0.813190	−	0.581998i	$-0.802271\pi$
$269$		−	19.0910i		−	1.16400i	0.813190	−	0.581998i	$-0.197729\pi$
$270$		0			0
$271$			12.0019i			0.729061i	0.931191	+	0.364531i	$0.118771\pi$
$271$			12.0019i			0.729061i	−0.931191	+	0.364531i	$0.881229\pi$
$272$	−3.61092	−	1.19246i	−0.218944	−	0.0723033i
$273$		0			0
$274$	16.1264	+	3.44800i	0.974230	+	0.208301i
$275$	3.22095	+	5.57886i	0.194231	+	0.336418i
$276$		0			0
$277$	12.0141	−	20.8091i	0.721860	−	1.25030i	−0.238394	−	0.971169i	$-0.576621\pi$
$277$	12.0141	−	20.8091i	0.721860	−	1.25030i	0.960254	−	0.279129i	$-0.0900458\pi$
$278$	−7.25928	+	8.04282i	−0.435383	+	0.482376i
$279$		0			0
$280$	6.96718	−	9.51725i	0.416369	−	0.568764i
$281$	−1.34110	−	0.774283i	−0.0800031	−	0.0461898i	0.459465	−	0.888196i	$-0.348041\pi$
$281$	−1.34110	−	0.774283i	−0.0800031	−	0.0461898i	−0.539468	+	0.842006i	$0.681375\pi$
$282$		0			0
$283$	−21.2674	+	12.2787i	−1.26422	+	0.729895i	−0.973887	−	0.227032i	$-0.927098\pi$
$283$	−21.2674	+	12.2787i	−1.26422	+	0.729895i	−0.290328	+	0.956927i	$0.593765\pi$
$284$	−3.61655	+	2.61433i	−0.214603	+	0.155132i
$285$		0			0
$286$	15.3824	−	4.97763i	0.909578	−	0.294333i
$287$	29.6726			1.75152
$288$		0			0
$289$	16.0962			0.946836
$290$	−8.78229	+	2.84189i	−0.515714	+	0.166882i
$291$		0			0
$292$	−2.83101	+	2.04648i	−0.165672	+	0.119761i
$293$	23.5288	−	13.5844i	1.37457	−	0.793607i	0.383068	−	0.923720i	$-0.374867\pi$
$293$	23.5288	−	13.5844i	1.37457	−	0.793607i	0.991499	+	0.130113i	$0.0415341\pi$
$294$		0			0
$295$	−2.32773	−	1.34391i	−0.135526	−	0.0782458i
$296$	−9.75040	+	13.3192i	−0.566730	+	0.774160i
$297$		0			0
$298$	3.31111	−	3.66850i	0.191808	−	0.212511i
$299$	−1.79253	+	3.10476i	−0.103665	+	0.179553i
$300$		0			0
$301$	11.0713	+	19.1761i	0.638140	+	1.10529i
$302$	9.83574	+	2.10299i	0.565983	+	0.121014i
$303$		0			0
$304$	−8.32904	−	2.75055i	−0.477703	−	0.157755i
$305$			4.09304i			0.234367i
$306$		0			0
$307$			3.96646i			0.226378i	0.993573	+	0.113189i	$0.0361065\pi$
$307$			3.96646i			0.226378i	−0.993573	+	0.113189i	$0.963893\pi$
$308$	−21.9706	+	49.0296i	−1.25189	+	2.79372i
$309$		0			0
$310$	−0.840491	+	3.93099i	−0.0477367	+	0.223265i
$311$	9.69205	+	16.7871i	0.549586	+	0.951911i	0.998303	+	0.0582368i	$0.0185478\pi$
$311$	9.69205	+	16.7871i	0.549586	+	0.951911i	−0.448717	+	0.893674i	$0.648119\pi$
$312$		0			0
$313$	−10.9851	+	19.0268i	−0.620915	+	1.07546i	0.368400	+	0.929667i	$0.379906\pi$
$313$	−10.9851	+	19.0268i	−0.620915	+	1.07546i	−0.989316	+	0.145789i	$0.953428\pi$
$314$	3.31615	+	2.99309i	0.187141	+	0.168910i
$315$		0			0
$316$	−0.492610	+	0.0505801i	−0.0277115	+	0.00284535i
$317$	−23.0559	−	13.3113i	−1.29495	−	0.747640i	−0.315423	−	0.948951i	$-0.602146\pi$
$317$	−23.0559	−	13.3113i	−1.29495	−	0.747640i	−0.979527	+	0.201311i	$0.935480\pi$
$318$		0			0
$319$	36.4135	−	21.0234i	2.03877	−	1.17708i
$320$	−5.90645	−	5.39572i	−0.330181	−	0.301630i
$321$		0			0
$322$	−3.66791	−	11.3349i	−0.204404	−	0.631671i
$323$	−2.08472			−0.115997
$324$		0			0
$325$	−1.77467			−0.0984411
$326$	−6.14187	−	18.9802i	−0.340167	−	1.05122i
$327$		0			0
$328$	2.17577	−	20.0078i	0.120137	−	1.10474i
$329$	1.45899	−	0.842349i	0.0804368	−	0.0464402i
$330$		0			0
$331$	−28.7664	−	16.6083i	−1.58115	−	0.912876i	−0.994692	−	0.102894i	$-0.967190\pi$
$331$	−28.7664	−	16.6083i	−1.58115	−	0.912876i	−0.586455	−	0.809982i	$-0.699477\pi$
$332$	2.38454	+	23.2235i	0.130869	+	1.27456i
$333$		0			0
$334$	19.2463	+	17.3713i	1.05311	+	0.950516i
$335$	−5.44797	+	9.43616i	−0.297654	+	0.515553i
$336$		0			0
$337$	−0.808583	−	1.40051i	−0.0440463	−	0.0762905i	0.843162	−	0.537660i	$-0.180692\pi$
$337$	−0.808583	−	1.40051i	−0.0440463	−	0.0762905i	−0.887208	+	0.461370i	$0.847358\pi$
$338$	2.91272	−	13.6229i	0.158431	−	0.740986i
$339$		0			0
$340$	−1.73512	−	0.777522i	−0.0941001	−	0.0421670i
$341$		−	18.3109i		−	0.991588i
$342$		0			0
$343$			14.1366i			0.763302i
$344$	13.7419	−	6.05911i	0.740916	−	0.326685i
$345$		0			0
$346$	10.9001	+	2.33057i	0.585994	+	0.125292i
$347$	−2.59298	−	4.49117i	−0.139198	−	0.241099i	0.787995	−	0.615682i	$-0.211119\pi$
$347$	−2.59298	−	4.49117i	−0.139198	−	0.241099i	−0.927193	+	0.374583i	$0.877786\pi$
$348$		0			0
$349$	9.16716	−	15.8780i	0.490707	−	0.849929i	−0.509236	−	0.860627i	$-0.670072\pi$
$349$	9.16716	−	15.8780i	0.490707	−	0.849929i	0.999943	+	0.0106977i	$0.00340525\pi$
$350$	3.95142	−	4.37792i	0.211212	−	0.234010i
$351$		0			0
$352$	31.4489	+	18.4095i	1.67623	+	0.981231i
$353$	−9.26426	−	5.34873i	−0.493087	−	0.284684i	0.232767	−	0.972532i	$-0.425222\pi$
$353$	−9.26426	−	5.34873i	−0.493087	−	0.284684i	−0.725854	+	0.687849i	$0.758555\pi$
$354$		0			0
$355$	−1.93233	+	1.11563i	−0.102557	+	0.0592116i
$356$	−7.19274	−	9.95010i	−0.381215	−	0.527354i
$357$		0			0
$358$	−13.2414	+	4.28482i	−0.699828	+	0.226460i
$359$	15.1958			0.802005			0.401002	−	0.916077i	$-0.368662\pi$
$359$	15.1958			0.802005			0.401002	+	0.916077i	$0.368662\pi$
$360$		0			0
$361$	14.1913			0.746913
$362$	24.6520	−	7.97721i	1.29568	−	0.419273i
$363$		0			0
$364$	−8.67116	−	11.9953i	−0.454492	−	0.628724i
$365$	−1.51261	+	0.873308i	−0.0791739	+	0.0457110i
$366$		0			0
$367$	21.2680	+	12.2791i	1.11018	+	0.640964i	0.938877	−	0.344254i	$-0.111868\pi$
$367$	21.2680	+	12.2791i	1.11018	+	0.640964i	0.171306	+	0.985218i	$0.445201\pi$
$368$	−7.91192	+	1.64207i	−0.412437	+	0.0855987i
$369$		0			0
$370$	−5.52992	+	6.12679i	−0.287487	+	0.318517i
$371$	10.1719	−	17.6182i	0.528097	−	0.914691i
$372$		0			0
$373$	−9.30451	−	16.1159i	−0.481769	−	0.834449i	0.518012	−	0.855373i	$-0.326672\pi$
$373$	−9.30451	−	16.1159i	−0.481769	−	0.834449i	−0.999781	+	0.0209247i	$0.993339\pi$
$374$	8.46950	+	1.81088i	0.437948	+	0.0936382i
$375$		0			0
$376$	−0.461001	−	1.04554i	−0.0237743	−	0.0539196i
$377$			11.5834i			0.596575i
$378$		0			0
$379$		−	27.9052i		−	1.43339i	−0.697386	−	0.716696i	$-0.745653\pi$
$379$		−	27.9052i		−	1.43339i	0.697386	−	0.716696i	$-0.254347\pi$
$380$	−4.00227	−	1.79345i	−0.205312	−	0.0920020i
$381$		0			0
$382$	5.64194	−	26.3875i	0.288667	−	1.35010i
$383$	−3.70117	−	6.41061i	−0.189121	−	0.327567i	0.755837	−	0.654760i	$-0.227230\pi$
$383$	−3.70117	−	6.41061i	−0.189121	−	0.327567i	−0.944957	+	0.327194i	$0.893897\pi$
$384$		0			0
$385$	−13.4318	+	23.2645i	−0.684547	+	1.18567i
$386$	13.6510	+	12.3211i	0.694818	+	0.627129i
$387$		0			0
$388$	3.71181	+	36.1501i	0.188439	+	1.83524i
$389$	15.5362	+	8.96985i	0.787718	+	0.454789i	0.839159	−	0.543887i	$-0.183048\pi$
$389$	15.5362	+	8.96985i	0.787718	+	0.454789i	−0.0514403	+	0.998676i	$0.516381\pi$
$390$		0			0
$391$	−1.66320	+	0.960250i	−0.0841118	+	0.0485619i
$392$	29.2150	+	3.17702i	1.47558	+	0.160464i
$393$		0			0
$394$	6.89944	+	21.3213i	0.347589	+	1.07415i
$395$	−0.247600			−0.0124581
$396$		0			0
$397$	−27.9101			−1.40077			−0.700383	−	0.713768i	$-0.746987\pi$
$397$	−27.9101			−1.40077			−0.700383	+	0.713768i	$0.746987\pi$
$398$	−0.542347	−	1.67602i	−0.0271854	−	0.0840111i
$399$		0			0
$400$	−2.66222	−	2.98539i	−0.133111	−	0.149270i
$401$	−3.46154	+	1.99852i	−0.172861	+	0.0998015i	−0.583934	−	0.811801i	$-0.698487\pi$
$401$	−3.46154	+	1.99852i	−0.172861	+	0.0998015i	0.411073	+	0.911602i	$0.365154\pi$
$402$		0			0
$403$	4.36860	+	2.52221i	0.217616	+	0.125640i
$404$	20.3726	−	2.09182i	1.01358	−	0.104072i
$405$		0			0
$406$	−28.5749	−	25.7912i	−1.41815	−	1.27999i
$407$	18.7974	−	32.5581i	0.931755	−	1.61385i
$408$		0			0
$409$	−11.0645	−	19.1644i	−0.547107	−	0.947616i	−0.998471	−	0.0552767i	$-0.982396\pi$
$409$	−11.0645	−	19.1644i	−0.547107	−	0.947616i	0.451364	−	0.892340i	$-0.350937\pi$
$410$	2.10400	−	9.84045i	0.103909	−	0.485985i
$411$		0			0
$412$	7.90038	−	17.6305i	0.389224	−	0.868593i
$413$		−	11.2086i		−	0.551539i
$414$		0			0
$415$			11.6728i			0.572996i
$416$	−8.72405	+	4.96726i	−0.427732	+	0.243540i
$417$		0			0
$418$	19.5360	+	4.17701i	0.955535	+	0.204304i
$419$	15.8068	+	27.3783i	0.772215	+	1.33752i	0.936347	+	0.351077i	$0.114184\pi$
$419$	15.8068	+	27.3783i	0.772215	+	1.33752i	−0.164132	+	0.986438i	$0.552482\pi$
$420$		0			0
$421$	−15.0283	+	26.0298i	−0.732435	+	1.26861i	0.223405	+	0.974726i	$0.428283\pi$
$421$	−15.0283	+	26.0298i	−0.732435	+	1.26861i	−0.955840	+	0.293889i	$0.905050\pi$
$422$	15.4683	−	17.1379i	0.752984	−	0.834258i
$423$		0			0
$424$	−11.1338	−	8.15059i	−0.540705	−	0.395828i
$425$	−0.823315	−	0.475341i	−0.0399366	−	0.0230574i
$426$		0			0
$427$	−14.7817	+	8.53425i	−0.715339	+	0.413001i
$428$	5.24113	−	3.78871i	0.253339	−	0.183134i
$429$		0			0
$430$	7.14448	−	2.31191i	0.344537	−	0.111490i
$431$	−25.0832			−1.20822			−0.604108	−	0.796902i	$-0.706471\pi$
$431$	−25.0832			−1.20822			−0.604108	+	0.796902i	$0.706471\pi$
$432$		0			0
$433$	29.4297			1.41430			0.707151	−	0.707062i	$-0.249980\pi$
$433$	29.4297			1.41430			0.707151	+	0.707062i	$0.249980\pi$
$434$	−15.9490	+	5.16099i	−0.765577	+	0.247736i
$435$		0			0
$436$	4.67374	−	3.37856i	0.223831	−	0.161804i
$437$	−3.83638	+	2.21494i	−0.183519	+	0.105955i
$438$		0			0
$439$	24.8161	+	14.3276i	1.18441	+	0.683819i	0.957031	−	0.289987i	$-0.0936510\pi$
$439$	24.8161	+	14.3276i	1.18441	+	0.683819i	0.227379	+	0.973806i	$0.426984\pi$
$440$	14.7020	+	10.7627i	0.700891	+	0.513093i
$441$		0			0
$442$	−1.59866	+	1.77122i	−0.0760407	+	0.0842482i
$443$	−14.9290	+	25.8577i	−0.709297	+	1.22854i	0.255822	+	0.966724i	$0.417654\pi$
$443$	−14.9290	+	25.8577i	−0.709297	+	1.22854i	−0.965118	+	0.261814i	$0.915679\pi$
$444$		0			0
$445$	−3.06941	−	5.31637i	−0.145504	−	0.252020i
$446$	−24.7905	−	5.30049i	−1.17386	−	0.250986i
$447$		0			0
$448$	7.17096	−	32.5812i	0.338796	−	1.53932i
$449$			14.7017i			0.693815i	0.937899	+	0.346908i	$0.112768\pi$
$449$			14.7017i			0.693815i	−0.937899	+	0.346908i	$0.887232\pi$
$450$		0			0
$451$			45.8375i			2.15841i
$452$	−2.52573	+	5.63642i	−0.118800	+	0.265115i
$453$		0			0
$454$	−3.08420	+	14.4248i	−0.144748	+	0.676991i
$455$	−3.70030	−	6.40911i	−0.173473	−	0.300464i
$456$		0			0
$457$	4.41668	−	7.64991i	0.206604	−	0.357848i	−0.744039	−	0.668136i	$-0.767092\pi$
$457$	4.41668	−	7.64991i	0.206604	−	0.357848i	0.950642	+	0.310288i	$0.100426\pi$
$458$	19.7239	+	17.8024i	0.921639	+	0.831853i
$459$		0			0
$460$	−4.01913	+	0.412675i	−0.187393	+	0.0192411i
$461$	−0.791004	−	0.456686i	−0.0368407	−	0.0212700i	0.481467	−	0.876464i	$-0.340104\pi$
$461$	−0.791004	−	0.456686i	−0.0368407	−	0.0212700i	−0.518307	+	0.855194i	$0.673438\pi$
$462$		0			0
$463$	6.81678	−	3.93567i	0.316803	−	0.182906i	−0.333164	−	0.942869i	$-0.608116\pi$
$463$	6.81678	−	3.93567i	0.316803	−	0.182906i	0.649967	+	0.759963i	$0.274783\pi$
$464$	−19.4859	+	17.3765i	−0.904608	+	0.806682i
$465$		0			0
$466$	3.17274	+	9.80471i	0.146974	+	0.454194i
$467$	−28.6765			−1.32699			−0.663495	−	0.748181i	$-0.730928\pi$
$467$	−28.6765			−1.32699			−0.663495	+	0.748181i	$0.730928\pi$
$468$		0			0
$469$	−45.4375			−2.09811
$470$	−0.175899	−	0.543580i	−0.00811360	−	0.0250735i
$471$		0			0
$472$	−7.55777	−	0.821879i	−0.347875	−	0.0378300i
$473$	−29.6227	+	17.1027i	−1.36206	+	0.786383i
$474$		0			0
$475$	−1.89908	−	1.09643i	−0.0871356	−	0.0503078i
$476$	−0.809867	−	7.88746i	−0.0371202	−	0.361521i
$477$		0			0
$478$	−31.1607	−	28.1250i	−1.42526	−	1.28641i
$479$	−13.1909	+	22.8473i	−0.602706	+	1.04392i	0.389703	+	0.920941i	$0.372578\pi$
$479$	−13.1909	+	22.8473i	−0.602706	+	1.04392i	−0.992409	+	0.122977i	$0.960756\pi$
$480$		0			0
$481$	5.17848	+	8.96939i	0.236118	+	0.408969i
$482$	3.77017	−	17.6332i	0.171726	−	0.803168i
$483$		0			0
$484$	−55.6632	−	24.9431i	−2.53015	−	1.13378i
$485$			18.1701i			0.825060i
$486$		0			0
$487$			7.87222i			0.356724i	0.983965	+	0.178362i	$0.0570799\pi$
$487$			7.87222i			0.356724i	−0.983965	+	0.178362i	$0.942920\pi$
$488$	4.67062	+	10.5929i	0.211429	+	0.479517i
$489$		0			0
$490$	14.3689	+	3.07222i	0.649119	+	0.138789i
$491$	9.74699	+	16.8823i	0.439876	+	0.761887i	0.997679	−	0.0680859i	$-0.0216892\pi$
$491$	9.74699	+	16.8823i	0.439876	+	0.761887i	−0.557804	+	0.829973i	$0.688356\pi$
$492$		0			0
$493$	−3.10258	+	5.37382i	−0.139733	+	0.242025i
$494$	−3.68752	+	4.08553i	−0.165909	+	0.183817i
$495$		0			0
$496$	2.31050	+	11.1326i	0.103745	+	0.499868i
$497$	−8.05806	−	4.65233i	−0.361454	−	0.208685i
$498$		0			0
$499$	0.733058	−	0.423231i	0.0328162	−	0.0189464i	−0.483502	−	0.875343i	$-0.660635\pi$
$499$	0.733058	−	0.423231i	0.0328162	−	0.0189464i	0.516318	+	0.856397i	$0.327302\pi$
$500$	−1.17168	−	1.62085i	−0.0523993	−	0.0724867i
$501$		0			0
$502$	−3.89972	+	1.26192i	−0.174053	+	0.0563224i
$503$	18.5253			0.826002			0.413001	−	0.910731i	$-0.364481\pi$
$503$	18.5253			0.826002			0.413001	+	0.910731i	$0.364481\pi$
$504$		0			0
$505$	10.2399			0.455668
$506$	17.5099	−	5.66609i	0.778411	−	0.251888i
$507$		0			0
$508$	2.53460	+	3.50625i	0.112455	+	0.155565i
$509$	23.6460	−	13.6520i	1.04809	−	0.605115i	0.125976	−	0.992033i	$-0.459794\pi$
$509$	23.6460	−	13.6520i	1.04809	−	0.605115i	0.922114	+	0.386918i	$0.126460\pi$
$510$		0			0
$511$	−6.30779	−	3.64181i	−0.279040	−	0.161104i
$512$	−21.4432	−	7.22431i	−0.947663	−	0.319272i
$513$		0			0
$514$	9.44345	−	10.4627i	0.416533	−	0.461491i
$515$	4.82993	−	8.36568i	0.212832	−	0.368636i
$516$		0			0
$517$	1.30124	+	2.25381i	0.0572285	+	0.0991226i
$518$	−33.6567	−	7.19619i	−1.47879	−	0.316183i
$519$		0			0
$520$	−4.59289	+	2.02510i	−0.201412	+	0.0888066i
$521$			25.9868i			1.13850i	0.822163	+	0.569252i	$0.192767\pi$
$521$			25.9868i			1.13850i	−0.822163	+	0.569252i	$0.807233\pi$
$522$		0			0
$523$		−	30.1683i		−	1.31917i	−0.751631	−	0.659584i	$-0.770732\pi$
$523$		−	30.1683i		−	1.31917i	0.751631	−	0.659584i	$-0.229268\pi$
$524$	−3.49406	−	1.56571i	−0.152639	−	0.0683986i
$525$		0			0
$526$	−0.361222	+	1.68944i	−0.0157500	+	0.0736631i
$527$	1.35114	+	2.34024i	0.0588564	+	0.101942i
$528$		0			0
$529$	9.45954	−	16.3844i	0.411284	−	0.712365i
$530$	−5.12153	−	4.62259i	−0.222465	−	0.200793i
$531$		0			0
$532$	−1.86806	−	18.1934i	−0.0809906	−	0.788784i
$533$	−10.9359	−	6.31386i	−0.473687	−	0.273484i
$534$		0			0
$535$	2.80035	−	1.61678i	0.121070	−	0.0698996i
$536$	−3.33174	+	30.6377i	−0.143909	+	1.32335i
$537$		0			0
$538$	−8.31223	−	25.6873i	−0.358366	−	1.10746i
$539$	−66.9311			−2.88293
$540$		0			0
$541$	−34.2068			−1.47067			−0.735333	−	0.677706i	$-0.762974\pi$
$541$	−34.2068			−1.47067			−0.735333	+	0.677706i	$0.762974\pi$
$542$	5.22563	+	16.1488i	0.224460	+	0.693648i
$543$		0			0
$544$	−5.37777	−	0.0322736i	−0.230570	−	0.00138372i
$545$	2.49719	−	1.44175i	0.106968	−	0.0617579i
$546$		0			0
$547$	−13.8696	−	8.00761i	−0.593020	−	0.342380i	0.173270	−	0.984874i	$-0.444567\pi$
$547$	−13.8696	−	8.00761i	−0.593020	−	0.342380i	−0.766291	+	0.642494i	$0.777900\pi$
$548$	23.1996	−	2.38209i	0.991039	−	0.101758i
$549$		0			0
$550$	6.76290	+	6.10406i	0.288371	+	0.260278i
$551$	−7.15648	+	12.3954i	−0.304876	+	0.528061i
$552$		0			0
$553$	−0.516261	−	0.894191i	−0.0219537	−	0.0380249i
$554$	7.10496	−	33.2301i	0.301861	−	1.41181i
$555$		0			0
$556$	−6.26566	+	13.9825i	−0.265723	+	0.592989i
$557$			16.0344i			0.679401i	0.940534	+	0.339701i	$0.110326\pi$
$557$			16.0344i			0.679401i	−0.940534	+	0.339701i	$0.889674\pi$
$558$		0			0
$559$		−	9.42320i		−	0.398559i
$560$	5.23066	−	15.8392i	0.221036	−	0.669327i
$561$		0			0
$562$	−2.14160	−	0.457898i	−0.0903378	−	0.0193153i
$563$	−2.23682	−	3.87428i	−0.0942707	−	0.163282i	0.815033	−	0.579414i	$-0.196719\pi$
$563$	−2.23682	−	3.87428i	−0.0942707	−	0.163282i	−0.909304	+	0.416133i	$0.863385\pi$
$564$		0			0
$565$	−1.54411	+	2.67448i	−0.0649613	+	0.112516i
$566$	−23.2695	+	25.7812i	−0.978092	+	1.08366i
$567$		0			0
$568$	−3.72785	+	5.09229i	−0.156417	+	0.213668i
$569$	−35.5461	−	20.5225i	−1.49017	−	0.860349i	−0.490232	−	0.871592i	$-0.663088\pi$
$569$	−35.5461	−	20.5225i	−1.49017	−	0.860349i	−0.999937	+	0.0112430i	$0.996421\pi$
$570$		0			0
$571$	39.1877	−	22.6250i	1.63995	−	0.946828i	0.659107	−	0.752049i	$-0.270935\pi$
$571$	39.1877	−	22.6250i	1.63995	−	0.946828i	0.980847	−	0.194778i	$-0.0623988\pi$
$572$	18.5300	−	13.3950i	0.774779	−	0.560073i
$573$		0			0
$574$	39.9251	−	12.9195i	1.66644	−	0.539250i
$575$	−2.02013			−0.0842452
$576$		0			0
$577$	−27.1400			−1.12985			−0.564927	−	0.825141i	$-0.691096\pi$
$577$	−27.1400			−1.12985			−0.564927	+	0.825141i	$0.691096\pi$
$578$	21.6578	−	7.00831i	0.900845	−	0.291507i
$579$		0			0
$580$	−10.5794	+	7.64765i	−0.439285	+	0.317551i
$581$	−42.1556	+	24.3386i	−1.74891	+	1.00973i
$582$		0			0
$583$	27.2161	+	15.7132i	1.12718	+	0.650776i
$584$	−2.91814	+	3.98621i	−0.120753	+	0.164950i
$585$		0			0
$586$	25.7438	−	28.5225i	1.06347	−	1.17825i
$587$	−8.76914	+	15.1886i	−0.361941	+	0.626901i	−0.988280	−	0.152650i	$-0.951219\pi$
$587$	−8.76914	+	15.1886i	−0.361941	+	0.626901i	0.626339	+	0.779551i	$0.284553\pi$
$588$		0			0
$589$	3.11656	+	5.39805i	0.128416	+	0.222423i
$590$	−3.71715	−	0.794769i	−0.153033	−	0.0327201i
$591$		0			0
$592$	−7.32018	+	22.1665i	−0.300858	+	0.911039i
$593$		−	15.6793i		−	0.643872i	−0.946761	−	0.321936i	$-0.895666\pi$
$593$		−	15.6793i		−	0.643872i	0.946761	−	0.321936i	$-0.104334\pi$
$594$		0			0
$595$		−	3.96446i		−	0.162527i
$596$	2.85790	−	6.37771i	0.117064	−	0.261241i
$597$		0			0
$598$	−1.06007	+	4.95799i	−0.0433497	+	0.202747i
$599$	3.60975	+	6.25226i	0.147490	+	0.255461i	0.930299	−	0.366801i	$-0.119547\pi$
$599$	3.60975	+	6.25226i	0.147490	+	0.255461i	−0.782809	+	0.622262i	$0.786214\pi$
$600$		0			0
$601$	−22.9958	+	39.8299i	−0.938019	+	1.62470i	−0.168860	+	0.985640i	$0.554008\pi$
$601$	−22.9958	+	39.8299i	−0.938019	+	1.62470i	−0.769160	+	0.639057i	$0.779325\pi$
$602$	23.2460	+	20.9814i	0.947436	+	0.855136i
$603$		0			0
$604$	14.1498	−	1.45287i	0.575748	−	0.0591166i
$605$	−26.4122	−	15.2491i	−1.07381	−	0.619963i
$606$		0			0
$607$	1.86077	−	1.07432i	0.0755263	−	0.0436052i	−0.461761	−	0.887004i	$-0.652782\pi$
$607$	1.86077	−	1.07432i	0.0755263	−	0.0436052i	0.537288	+	0.843399i	$0.319449\pi$
$608$	−12.4045	−	0.0744431i	−0.503069	−	0.00301907i
$609$		0			0
$610$	1.78211	+	5.50727i	0.0721557	+	0.222983i
$611$	−0.716953			−0.0290048
$612$		0			0
$613$	−44.8432			−1.81120			−0.905601	−	0.424131i	$-0.860579\pi$
$613$	−44.8432			−1.81120			−0.905601	+	0.424131i	$0.860579\pi$
$614$	1.72700	+	5.33696i	0.0696962	+	0.215382i
$615$		0			0
$616$	−8.21428	+	75.5363i	−0.330963	+	3.04345i
$617$	29.8311	−	17.2230i	1.20095	−	0.693371i	0.240186	−	0.970727i	$-0.422792\pi$
$617$	29.8311	−	17.2230i	1.20095	−	0.693371i	0.960767	+	0.277356i	$0.0894582\pi$
$618$		0			0
$619$	11.0619	+	6.38657i	0.444614	+	0.256698i	0.705553	−	0.708657i	$-0.250699\pi$
$619$	11.0619	+	6.38657i	0.444614	+	0.256698i	−0.260939	+	0.965355i	$0.584032\pi$
$620$	0.580662	+	5.65518i	0.0233199	+	0.227118i
$621$		0			0
$622$	20.3500	+	18.3675i	0.815961	+	0.736469i
$623$	12.7998	−	22.1699i	0.512814	−	0.888219i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.49641	+	30.3838i	−0.259649	+	1.21438i
$627$		0			0
$628$	5.76514	+	2.58341i	0.230054	+	0.103089i
$629$			5.54817i			0.221220i
$630$		0			0
$631$			12.9765i			0.516586i	0.966067	+	0.258293i	$0.0831600\pi$
$631$			12.9765i			0.516586i	−0.966067	+	0.258293i	$0.916840\pi$
$632$	−0.640794	+	0.282540i	−0.0254894	+	0.0112388i
$633$		0			0
$634$	−36.8180	−	7.87211i	−1.46223	−	0.312641i
$635$	1.08161	+	1.87340i	0.0429223	+	0.0743436i
$636$		0			0
$637$	9.21938	−	15.9684i	0.365285	−	0.632693i
$638$	39.8415	−	44.1419i	1.57734	−	1.74759i
$639$		0			0
$640$	−10.2966	−	4.68837i	−0.407007	−	0.185324i
$641$	−26.4627	−	15.2782i	−1.04521	−	0.603453i	−0.123907	−	0.992294i	$-0.539542\pi$
$641$	−26.4627	−	15.2782i	−1.04521	−	0.603453i	−0.921305	+	0.388840i	$0.872876\pi$
$642$		0			0
$643$	−5.34706	+	3.08712i	−0.210867	+	0.121744i	−0.601714	−	0.798711i	$-0.705515\pi$
$643$	−5.34706	+	3.08712i	−0.210867	+	0.121744i	0.390847	+	0.920456i	$0.372182\pi$
$644$	−9.87049	−	13.6544i	−0.388952	−	0.538058i
$645$		0			0
$646$	−2.80503	+	0.907688i	−0.110362	+	0.0357125i
$647$	−9.68580			−0.380788			−0.190394	−	0.981708i	$-0.560977\pi$
$647$	−9.68580			−0.380788			−0.190394	+	0.981708i	$0.560977\pi$
$648$		0			0
$649$	17.3148			0.679663
$650$	−2.38786	+	0.772694i	−0.0936595	+	0.0303076i
$651$		0			0
$652$	−16.5280	−	22.8641i	−0.647287	−	0.895427i
$653$	14.1565	−	8.17325i	0.553986	−	0.319844i	−0.196742	−	0.980455i	$-0.563036\pi$
$653$	14.1565	−	8.17325i	0.553986	−	0.319844i	0.750728	+	0.660611i	$0.229703\pi$
$654$		0			0
$655$	−1.65793	−	0.957206i	−0.0647807	−	0.0374011i
$656$	−5.78387	−	27.8682i	−0.225822	−	1.08807i
$657$		0			0
$658$	1.59634	−	1.76864i	0.0622319	−	0.0689490i
$659$	11.5429	−	19.9929i	0.449648	−	0.778812i	−0.548715	−	0.836009i	$-0.684883\pi$
$659$	11.5429	−	19.9929i	0.449648	−	0.778812i	0.998363	+	0.0571968i	$0.0182163\pi$
$660$		0			0
$661$	−9.23504	−	15.9956i	−0.359202	−	0.622155i	0.628626	−	0.777708i	$-0.283618\pi$
$661$	−9.23504	−	15.9956i	−0.359202	−	0.622155i	−0.987828	+	0.155552i	$0.950284\pi$
$662$	−45.9371	−	9.82188i	−1.78540	−	0.381738i
$663$		0			0
$664$	13.3200	+	30.2095i	0.516917	+	1.17236i
$665$		−	9.14452i		−	0.354609i
$666$		0			0
$667$			13.1855i			0.510545i
$668$	33.4598	+	14.9936i	1.29460	+	0.580120i
$669$		0			0
$670$	−3.22184	+	15.0686i	−0.124470	+	0.582151i
$671$	−13.1835	−	22.8345i	−0.508943	−	0.881515i
$672$		0			0
$673$	15.1577	−	26.2539i	0.584286	−	1.01201i	−0.410678	−	0.911780i	$-0.634708\pi$
$673$	15.1577	−	26.2539i	0.584286	−	1.01201i	0.994964	−	0.100233i	$-0.0319587\pi$
$674$	−1.69775	−	1.53235i	−0.0653948	−	0.0590240i
$675$		0			0
$676$	−2.01228	−	19.5980i	−0.0773956	−	0.753771i
$677$	36.7101	+	21.1946i	1.41088	+	0.814573i	0.995471	−	0.0950610i	$-0.0303046\pi$
$677$	36.7101	+	21.1946i	1.41088	+	0.814573i	0.415410	+	0.909634i	$0.363638\pi$
$678$		0			0
$679$	−65.6200	+	37.8857i	−2.51827	+	1.45392i
$680$	−2.67317	−	0.290697i	−0.102512	−	0.0111477i
$681$		0			0
$682$	−7.97257	−	24.6376i	−0.305285	−	0.943423i
$683$	20.7847			0.795303			0.397652	−	0.917536i	$-0.369825\pi$
$683$	20.7847			0.795303			0.397652	+	0.917536i	$0.369825\pi$
$684$		0			0
$685$	11.6608			0.445536
$686$	6.15508	+	19.0210i	0.235002	+	0.726226i
$687$		0			0
$688$	15.8519	−	14.1359i	0.604349	−	0.538927i
$689$	−7.49773	+	4.32882i	−0.285641	+	0.164915i
$690$		0			0
$691$	−36.9591	−	21.3383i	−1.40599	−	0.811748i	−0.410991	−	0.911639i	$-0.634817\pi$
$691$	−36.9591	−	21.3383i	−1.40599	−	0.811748i	−0.994998	+	0.0998910i	$0.968151\pi$
$692$	15.6811	−	1.61010i	0.596105	−	0.0612068i
$693$		0			0
$694$	−5.44437	−	4.91398i	−0.206665	−	0.186532i
$695$	−3.83054	+	6.63468i	−0.145301	+	0.251668i
$696$		0			0
$697$	−3.38230	−	5.85831i	−0.128114	−	0.221899i
$698$	5.42131	−	25.3556i	0.205199	−	0.959722i
$699$		0			0
$700$	3.41057	−	7.61104i	0.128907	−	0.287670i
$701$			26.5424i			1.00249i	0.865305	+	0.501247i	$0.167125\pi$
$701$			26.5424i			1.00249i	−0.865305	+	0.501247i	$0.832875\pi$
$702$		0			0
$703$			12.7975i			0.482668i
$704$	50.3306	+	11.0775i	1.89691	+	0.417500i
$705$		0			0
$706$	−14.7941	−	3.16315i	−0.556783	−	0.119047i
$707$	21.3508	+	36.9806i	0.802979	+	1.39080i
$708$		0			0
$709$	−23.1270	+	40.0571i	−0.868553	+	1.50438i	−0.00507739	+	0.999987i	$0.501616\pi$
$709$	−23.1270	+	40.0571i	−0.868553	+	1.50438i	−0.863476	+	0.504391i	$0.831717\pi$
$710$	−2.11424	+	2.34244i	−0.0793461	+	0.0879104i
$711$		0			0
$712$	−14.0103	−	10.2563i	−0.525057	−	0.384372i
$713$	4.97283	+	2.87107i	0.186234	+	0.107522i
$714$		0			0
$715$	9.90064	−	5.71613i	0.370263	−	0.213771i
$716$	−15.9509	+	11.5306i	−0.596114	+	0.430920i
$717$		0			0
$718$	20.4463	−	6.61628i	0.763049	−	0.246917i
$719$	44.9992			1.67819			0.839094	−	0.543986i	$-0.183086\pi$
$719$	44.9992			1.67819			0.839094	+	0.543986i	$0.183086\pi$
$720$		0			0
$721$	40.2828			1.50021
$722$	19.0947	−	6.17893i	0.710633	−	0.229956i
$723$		0			0
$724$	29.6964	−	21.4670i	1.10366	−	0.797815i
$725$	−5.65260	+	3.26353i	−0.209932	+	0.121204i
$726$		0			0
$727$	30.8806	+	17.8289i	1.14530	+	0.661237i	0.947737	−	0.319054i	$-0.103365\pi$
$727$	30.8806	+	17.8289i	1.14530	+	0.661237i	0.197560	+	0.980291i	$0.436698\pi$
$728$	−16.8900	−	12.3645i	−0.625985	−	0.458257i
$729$		0			0
$730$	−1.65501	+	1.83365i	−0.0612548	+	0.0678664i
$731$	2.52398	−	4.37166i	0.0933526	−	0.161692i
$732$		0			0
$733$	23.5696	+	40.8238i	0.870563	+	1.50786i	0.861415	+	0.507902i	$0.169579\pi$
$733$	23.5696	+	40.8238i	0.870563	+	1.50786i	0.00914815	+	0.999958i	$0.497088\pi$
$734$	33.9629	+	7.26166i	1.25359	+	0.268033i
$735$		0			0
$736$	−9.93069	+	5.65430i	−0.366050	+	0.208420i
$737$		−	70.1906i		−	2.58551i
$738$		0			0
$739$			40.9282i			1.50557i	0.658268	+	0.752784i	$0.271289\pi$
$739$			40.9282i			1.50557i	−0.658268	+	0.752784i	$0.728711\pi$
$740$	−4.77300	+	10.6515i	−0.175459	+	0.391555i
$741$		0			0
$742$	6.01547	−	28.1345i	0.220835	−	1.03285i
$743$	16.9276	+	29.3195i	0.621014	+	1.07563i	0.989297	+	0.145915i	$0.0466125\pi$
$743$	16.9276	+	29.3195i	0.621014	+	1.07563i	−0.368283	+	0.929714i	$0.620054\pi$
$744$		0			0
$745$	1.74719	−	3.02622i	0.0640121	−	0.110872i
$746$	−19.5363	−	17.6331i	−0.715274	−	0.645592i
$747$		0			0
$748$	12.1843	−	1.25106i	0.445504	−	0.0457434i
$749$	11.6778	+	6.74219i	0.426698	+	0.246354i
$750$		0			0
$751$	−5.93626	+	3.42730i	−0.216617	+	0.125064i	−0.604383	−	0.796694i	$-0.706580\pi$
$751$	−5.93626	+	3.42730i	−0.216617	+	0.125064i	0.387766	+	0.921758i	$0.373247\pi$
$752$	−1.07552	−	1.20608i	−0.0392200	−	0.0439811i
$753$		0			0
$754$	5.04342	+	15.5857i	0.183671	+	0.567597i
$755$	7.11211			0.258836
$756$		0			0
$757$	40.8568			1.48497			0.742483	−	0.669865i	$-0.233648\pi$
$757$	40.8568			1.48497			0.742483	+	0.669865i	$0.233648\pi$
$758$	−12.1499	−	37.5470i	−0.441306	−	1.36377i
$759$		0			0
$760$	−6.16601	−	0.670529i	−0.223665	−	0.0243227i
$761$	24.1632	−	13.9506i	0.875916	−	0.505710i	0.00660605	−	0.999978i	$-0.497897\pi$
$761$	24.1632	−	13.9506i	0.875916	−	0.505710i	0.869310	+	0.494268i	$0.164564\pi$
$762$		0			0
$763$	10.4136	+	6.01230i	0.376998	+	0.217660i
$764$	−3.89779	−	37.9614i	−0.141017	−	1.37339i
$765$		0			0
$766$	−7.77118	−	7.01411i	−0.280784	−	0.253430i
$767$	−2.38501	+	4.13095i	−0.0861176	+	0.149160i
$768$		0			0
$769$	−3.06170	−	5.30302i	−0.110408	−	0.191232i	0.805527	−	0.592559i	$-0.201882\pi$
$769$	−3.06170	−	5.30302i	−0.110408	−	0.191232i	−0.915935	+	0.401327i	$0.868549\pi$
$770$	−7.94333	+	37.1511i	−0.286258	+	1.33883i
$771$		0			0
$772$	23.7324	+	10.6347i	0.854146	+	0.382750i
$773$			14.8193i			0.533012i	0.963833	+	0.266506i	$0.0858692\pi$
$773$			14.8193i			0.533012i	−0.963833	+	0.266506i	$0.914131\pi$
$774$		0			0
$775$			2.84246i			0.102104i
$776$	20.7341	+	47.0245i	0.744311	+	1.68808i
$777$		0			0
$778$	24.8098	+	5.30462i	0.889475	+	0.190180i
$779$	−7.80169	−	13.5129i	−0.279525	−	0.484151i
$780$		0			0
$781$	7.18680	−	12.4479i	0.257164	−	0.445421i
$782$	−1.81978	+	2.01620i	−0.0650751	+	0.0720991i
$783$		0			0
$784$	40.6927	−	8.44551i	1.45331	−	0.301625i
$785$	2.73556	+	1.57938i	0.0976363	+	0.0563703i
$786$		0			0
$787$	−13.6200	+	7.86353i	−0.485502	+	0.280305i	−0.722707	−	0.691155i	$-0.757102\pi$
$787$	−13.6200	+	7.86353i	−0.485502	+	0.280305i	0.237205	+	0.971460i	$0.423769\pi$
$788$	18.5667	+	25.6843i	0.661411	+	0.914964i
$789$		0			0
$790$	−0.333151	+	0.107805i	−0.0118530	+	0.00383554i
$791$	−12.8783			−0.457900
$792$		0			0
$793$	7.26380			0.257945
$794$	−37.5535	+	12.1521i	−1.33273	+	0.431261i
$795$		0			0
$796$	−1.45948	−	2.01897i	−0.0517299	−	0.0715607i
$797$	37.5576	−	21.6839i	1.33036	−	0.768083i	0.345005	−	0.938601i	$-0.387877\pi$
$797$	37.5576	−	21.6839i	1.33036	−	0.768083i	0.985355	+	0.170517i	$0.0545439\pi$
$798$		0			0
$799$	−0.332613	−	0.192034i	−0.0117670	−	0.00679367i
$800$	−4.88192	−	2.85778i	−0.172602	−	0.101038i
$801$		0			0
$802$	−3.78742	+	4.19622i	−0.133738	+	0.148174i
$803$	5.62577	−	9.74412i	0.198529	−	0.343863i
$804$		0			0
$805$	−4.21210	−	7.29557i	−0.148457	−	0.257135i
$806$	6.97622	+	1.49160i	0.245727	+	0.0525392i
$807$		0			0
$808$	26.5010	−	11.6849i	0.932303	−	0.411072i
$809$			0.395982i			0.0139220i	0.999976	+	0.00696100i	$0.00221577\pi$
$809$			0.395982i			0.0139220i	−0.999976	+	0.00696100i	$0.997784\pi$
$810$		0			0
$811$		−	45.9241i		−	1.61261i	−0.591498	−	0.806307i	$-0.701463\pi$
$811$		−	45.9241i		−	1.61261i	0.591498	−	0.806307i	$-0.298537\pi$
$812$	−49.6777	−	22.2610i	−1.74334	−	0.781207i
$813$		0			0
$814$	11.1165	−	51.9921i	0.389633	−	1.82232i
$815$	−7.05311	−	12.2163i	−0.247060	−	0.427920i
$816$		0			0
$817$	5.82186	−	10.0838i	0.203681	−	0.352786i
$818$	−23.2318	−	20.9685i	−0.812279	−	0.733147i
$819$		0			0
$820$	−1.45357	−	14.1566i	−0.0507609	−	0.494370i
$821$	−29.4827	−	17.0219i	−1.02895	−	0.594067i	−0.112270	−	0.993678i	$-0.535812\pi$
$821$	−29.4827	−	17.0219i	−1.02895	−	0.594067i	−0.916685	+	0.399610i	$0.869145\pi$
$822$		0			0
$823$	9.10490	−	5.25672i	0.317377	−	0.183238i	−0.332846	−	0.942981i	$-0.608009\pi$
$823$	9.10490	−	5.25672i	0.317377	−	0.183238i	0.650223	+	0.759744i	$0.274676\pi$
$824$	2.95377	−	27.1621i	0.102899	−	0.946235i
$825$		0			0
$826$	−4.88024	−	15.0814i	−0.169805	−	0.524749i
$827$	−40.8826			−1.42163			−0.710813	−	0.703381i	$-0.751673\pi$
$827$	−40.8826			−1.42163			−0.710813	+	0.703381i	$0.751673\pi$
$828$		0			0
$829$	24.0184			0.834194			0.417097	−	0.908862i	$-0.363048\pi$
$829$	24.0184			0.834194			0.417097	+	0.908862i	$0.363048\pi$
$830$	5.08236	+	15.7060i	0.176411	+	0.545164i
$831$		0			0
$832$	−9.57563	+	10.4820i	−0.331975	+	0.363399i
$833$	8.55420	−	4.93877i	0.296386	−	0.171118i
$834$		0			0
$835$	15.8767	+	9.16640i	0.549435	+	0.317216i
$836$	28.1047	−	2.88573i	0.972021	−	0.0998050i
$837$		0			0
$838$	33.1890	+	29.9557i	1.14649	+	1.03480i
$839$	17.0952	−	29.6098i	0.590192	−	1.02224i	−0.404014	−	0.914753i	$-0.632385\pi$
$839$	17.0952	−	29.6098i	0.590192	−	1.02224i	0.994206	−	0.107490i	$-0.0342813\pi$
$840$		0			0
$841$	6.80125	+	11.7801i	0.234526	+	0.406211i
$842$	−8.88749	+	41.5670i	−0.306283	+	1.43249i
$843$		0			0
$844$	13.3510	−	29.7942i	0.459562	−	1.02556i
$845$		−	9.85054i		−	0.338869i
$846$		0			0
$847$		−	127.181i		−	4.37000i
$848$	−18.5295	−	6.11912i	−0.636307	−	0.210131i
$849$		0			0
$850$	−1.31475	−	0.281109i	−0.0450956	−	0.00964195i
$851$	5.89473	+	10.2100i	0.202069	+	0.349993i
$852$		0			0
$853$	12.3742	−	21.4327i	0.423683	−	0.733840i	−0.572614	−	0.819825i	$-0.694070\pi$
$853$	12.3742	−	21.4327i	0.423683	−	0.733840i	0.996296	+	0.0859851i	$0.0274038\pi$
$854$	−16.1733	+	17.9190i	−0.553440	+	0.613176i
$855$		0			0
$856$	5.40243	−	7.37979i	0.184651	−	0.252236i
$857$	9.24145	+	5.33556i	0.315682	+	0.182259i	0.649466	−	0.760390i	$-0.274992\pi$
$857$	9.24145	+	5.33556i	0.315682	+	0.182259i	−0.333784	+	0.942649i	$0.608326\pi$
$858$		0			0
$859$	−20.6204	+	11.9052i	−0.703560	+	0.406200i	−0.808672	−	0.588260i	$-0.799813\pi$
$859$	−20.6204	+	11.9052i	−0.703560	+	0.406200i	0.105112	+	0.994460i	$0.466480\pi$
$860$	8.60644	−	6.22143i	0.293477	−	0.212149i
$861$		0			0
$862$	−33.7500	+	10.9213i	−1.14953	+	0.371980i
$863$	−53.1072			−1.80779			−0.903896	−	0.427753i	$-0.859305\pi$
$863$	−53.1072			−1.80779			−0.903896	+	0.427753i	$0.859305\pi$
$864$		0			0
$865$	7.88176			0.267988
$866$	39.5983	−	12.8137i	1.34561	−	0.435429i
$867$		0			0
$868$	−19.2126	+	13.8884i	−0.652119	+	0.471404i
$869$	1.38132	−	0.797508i	0.0468582	−	0.0270536i
$870$		0			0
$871$	16.7461	+	9.66836i	0.567419	+	0.327600i
$872$	4.81758	−	6.58087i	0.163144	−	0.222856i
$873$		0			0
$874$	−4.19754	+	4.65061i	−0.141984	+	0.157309i
$875$	2.08506	−	3.61144i	0.0704880	−	0.122089i
$876$		0			0
$877$	20.7138	+	35.8774i	0.699456	+	1.21149i	0.968655	+	0.248409i	$0.0799077\pi$
$877$	20.7138	+	35.8774i	0.699456	+	1.21149i	−0.269199	+	0.963085i	$0.586759\pi$
$878$	39.6289	+	8.47311i	1.33741	+	0.285954i
$879$		0			0
$880$	24.4680	+	8.08020i	0.824815	+	0.272383i
$881$			18.8579i			0.635340i	0.948201	+	0.317670i	$0.102900\pi$
$881$			18.8579i			0.635340i	−0.948201	+	0.317670i	$0.897100\pi$
$882$		0			0
$883$			36.0305i			1.21252i	0.795266	+	0.606261i	$0.207331\pi$
$883$			36.0305i			1.21252i	−0.795266	+	0.606261i	$0.792669\pi$
$884$	−1.37985	+	3.07927i	−0.0464092	+	0.103567i
$885$		0			0
$886$	−8.82874	+	41.2922i	−0.296607	+	1.38724i
$887$	9.66809	+	16.7456i	0.324623	+	0.562263i	0.981436	−	0.191790i	$-0.0614293\pi$
$887$	9.66809	+	16.7456i	0.324623	+	0.562263i	−0.656813	+	0.754053i	$0.728096\pi$
$888$		0			0
$889$	−4.51044	+	7.81231i	−0.151275	+	0.262016i
$890$	−6.44470	−	5.81686i	−0.216027	−	0.194981i
$891$		0			0
$892$	−35.6640	+	3.66190i	−1.19412	+	0.122609i
$893$	−0.767212	−	0.442950i	−0.0256738	−	0.0148228i
$894$		0			0
$895$	−8.52262	+	4.92054i	−0.284880	+	0.164475i
$896$	−4.53722	−	46.9609i	−0.151578	−	1.56885i
$897$		0			0
$898$	6.40113	+	19.7814i	0.213609	+	0.660114i
$899$	18.5529			0.618774
$900$		0			0
$901$	−4.63785			−0.154509
$902$	19.9577	+	61.6753i	0.664520	+	2.05356i
$903$		0			0
$904$	−0.944311	+	8.68363i	−0.0314073	+	0.288813i
$905$	15.8669	−	9.16075i	0.527433	−	0.304514i
$906$		0			0
$907$	−14.8178	−	8.55508i	−0.492018	−	0.284067i	0.233393	−	0.972382i	$-0.425017\pi$
$907$	−14.8178	−	8.55508i	−0.492018	−	0.284067i	−0.725411	+	0.688316i	$0.758350\pi$
$908$	2.13075	+	20.7518i	0.0707114	+	0.688672i
$909$		0			0
$910$	−7.76937	−	7.01248i	−0.257552	−	0.232461i
$911$	5.66416	−	9.81062i	0.187662	−	0.325040i	−0.756808	−	0.653637i	$-0.773242\pi$
$911$	5.66416	−	9.81062i	0.187662	−	0.325040i	0.944470	+	0.328597i	$0.106576\pi$
$912$		0			0
$913$	−37.5976	−	65.1210i	−1.24430	−	2.15519i
$914$	2.61195	−	12.2161i	0.0863956	−	0.404074i
$915$		0			0
$916$	34.2902	+	15.3657i	1.13298	+	0.507697i
$917$		−	7.98334i		−	0.263633i
$918$		0			0
$919$		−	33.3567i		−	1.10034i	−0.835054	−	0.550169i	$-0.814563\pi$
$919$		−	33.3567i		−	1.10034i	0.835054	−	0.550169i	$-0.185437\pi$
$920$	−5.22814	+	2.30520i	−0.172367	+	0.0760001i
$921$		0			0
$922$	−1.26315	−	0.270077i	−0.0415997	−	0.00889450i
$923$	1.97988	+	3.42925i	0.0651685	+	0.112875i
$924$		0			0
$925$	−2.91799	+	5.05411i	−0.0959431	+	0.166178i
$926$	7.45853	−	8.26357i	0.245102	−	0.271558i
$927$		0			0
$928$	−18.6529	+	31.8646i	−0.612311	+	1.04601i
$929$	9.08679	+	5.24626i	0.298128	+	0.172124i	0.641602	−	0.767038i	$-0.278270\pi$
$929$	9.08679	+	5.24626i	0.298128	+	0.172124i	−0.343474	+	0.939162i	$0.611604\pi$
$930$		0			0
$931$	19.7313	−	11.3919i	0.646668	−	0.373354i
$932$	8.53797	+	11.8110i	0.279670	+	0.386883i
$933$		0			0
$934$	−38.5848	+	12.4858i	−1.26253	+	0.408547i
$935$	6.12420			0.200283
$936$		0			0
$937$	29.4458			0.961952			0.480976	−	0.876734i	$-0.340282\pi$
$937$	29.4458			0.961952			0.480976	+	0.876734i	$0.340282\pi$
$938$	−61.1370	+	19.7835i	−1.99619	+	0.645955i
$939$		0			0
$940$	−0.473351	−	0.654811i	−0.0154390	−	0.0213576i
$941$	31.2128	−	18.0207i	1.01751	−	0.587459i	0.104128	−	0.994564i	$-0.466795\pi$
$941$	31.2128	−	18.0207i	1.01751	−	0.587459i	0.913382	+	0.407105i	$0.133462\pi$
$942$		0			0
$943$	−12.4485	−	7.18714i	−0.405379	−	0.234045i
$944$	−10.5270	+	2.18481i	−0.342624	+	0.0711095i
$945$		0			0
$946$	−32.4115	+	35.9098i	−1.05379	+	1.16753i
$947$	6.08631	−	10.5418i	0.197778	−	0.342562i	−0.750029	−	0.661405i	$-0.769961\pi$
$947$	6.08631	−	10.5418i	0.197778	−	0.342562i	0.947808	+	0.318842i	$0.103294\pi$
$948$		0			0
$949$	1.54984	+	2.68439i	0.0503098	+	0.0871391i
$950$	−3.03263	−	0.648412i	−0.0983917	−	0.0210373i
$951$		0			0
$952$	−4.52390	−	10.2601i	−0.146621	−	0.332532i
$953$			25.0300i			0.810801i	0.914139	+	0.405400i	$0.132868\pi$
$953$			25.0300i			0.810801i	−0.914139	+	0.405400i	$0.867132\pi$
$954$		0			0
$955$		−	19.0805i		−	0.617430i
$956$	−54.1730	−	24.2753i	−1.75208	−	0.785121i
$957$		0			0
$958$	−7.80086	+	36.4848i	−0.252034	+	1.17877i
$959$	24.3135	+	42.1122i	0.785124	+	1.35988i
$960$		0			0
$961$	−11.4602	+	19.8497i	−0.369684	+	0.640312i
$962$	10.8730	+	9.81379i	0.350561	+	0.316409i
$963$		0			0
$964$	−2.60466	−	25.3673i	−0.0838905	−	0.817026i
$965$	11.2610	+	6.50154i	0.362505	+	0.209292i
$966$		0			0
$967$	2.38621	−	1.37768i	0.0767353	−	0.0443032i	−0.461141	−	0.887327i	$-0.652560\pi$
$967$	2.38621	−	1.37768i	0.0767353	−	0.0443032i	0.537877	+	0.843023i	$0.319227\pi$
$968$	−85.7563	−	9.32566i	−2.75631	−	0.299738i
$969$		0			0
$970$	7.91127	+	24.4482i	0.254016	+	0.784984i
$971$	33.6700			1.08052			0.540261	−	0.841497i	$-0.318325\pi$
$971$	33.6700			1.08052			0.540261	+	0.841497i	$0.318325\pi$
$972$		0			0
$973$	−31.9476			−1.02419
$974$	3.42758	+	10.5922i	0.109827	+	0.339397i
$975$		0			0
$976$	10.8966	+	12.2193i	0.348791	+	0.391132i
$977$	−48.5624	+	28.0375i	−1.55365	+	0.897000i	−0.555810	+	0.831309i	$0.687592\pi$
$977$	−48.5624	+	28.0375i	−1.55365	+	0.897000i	−0.997840	+	0.0656907i	$0.979075\pi$
$978$		0			0
$979$	34.2475	+	19.7728i	1.09456	+	0.631942i
$980$	20.6712	−	2.12248i	0.660318	−	0.0678001i
$981$		0			0
$982$	20.4654	+	18.4716i	0.653076	+	0.589453i
$983$	7.52662	−	13.0365i	0.240062	−	0.415799i	−0.720670	−	0.693278i	$-0.756166\pi$
$983$	7.52662	−	13.0365i	0.240062	−	0.415799i	0.960732	+	0.277479i	$0.0894989\pi$
$984$		0			0
$985$	7.92308	+	13.7232i	0.252450	+	0.437257i
$986$	−1.83481	+	8.58146i	−0.0584323	+	0.273289i
$987$		0			0
$988$	−3.18278	+	7.10271i	−0.101258	+	0.225967i
$989$		−	10.7265i		−	0.341084i
$990$		0			0
$991$			32.4096i			1.02953i	0.857333	+	0.514763i	$0.172120\pi$
$991$			32.4096i			1.02953i	−0.857333	+	0.514763i	$0.827880\pi$
$992$	7.95597	+	13.9731i	0.252602	+	0.443648i
$993$		0			0
$994$	−12.8679	−	2.75131i	−0.408146	−	0.0872662i
$995$	−0.622813	−	1.07874i	−0.0197445	−	0.0341985i
$996$		0			0
$997$	22.0749	−	38.2349i	0.699120	−	1.21091i	−0.269652	−	0.962958i	$-0.586909\pi$
$997$	22.0749	−	38.2349i	0.699120	−	1.21091i	0.968772	−	0.247954i	$-0.0797581\pi$
$998$	0.802069	−	0.888641i	0.0253891	−	0.0281294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.q.a.251.22		48
3.2	odd	2		180.2.q.a.11.3	✓	48
4.3	odd	2	inner	540.2.q.a.251.15		48
9.2	odd	6		1620.2.e.b.971.38		48
9.4	even	3		180.2.q.a.131.10	yes	48
9.5	odd	6	inner	540.2.q.a.71.15		48
9.7	even	3		1620.2.e.b.971.11		48
12.11	even	2		180.2.q.a.11.10	yes	48
15.2	even	4		900.2.o.c.299.10		48
15.8	even	4		900.2.o.b.299.15		48
15.14	odd	2		900.2.r.f.551.22		48
36.7	odd	6		1620.2.e.b.971.37		48
36.11	even	6		1620.2.e.b.971.12		48
36.23	even	6	inner	540.2.q.a.71.22		48
36.31	odd	6		180.2.q.a.131.3	yes	48
45.4	even	6		900.2.r.f.851.15		48
45.13	odd	12		900.2.o.c.599.23		48
45.22	odd	12		900.2.o.b.599.2		48
60.23	odd	4		900.2.o.b.299.2		48
60.47	odd	4		900.2.o.c.299.23		48
60.59	even	2		900.2.r.f.551.15		48
180.67	even	12		900.2.o.b.599.15		48
180.103	even	12		900.2.o.c.599.10		48
180.139	odd	6		900.2.r.f.851.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.3	✓	48	3.2	odd	2
180.2.q.a.11.10	yes	48	12.11	even	2
180.2.q.a.131.3	yes	48	36.31	odd	6
180.2.q.a.131.10	yes	48	9.4	even	3
540.2.q.a.71.15		48	9.5	odd	6	inner
540.2.q.a.71.22		48	36.23	even	6	inner
540.2.q.a.251.15		48	4.3	odd	2	inner
540.2.q.a.251.22		48	1.1	even	1	trivial
900.2.o.b.299.2		48	60.23	odd	4
900.2.o.b.299.15		48	15.8	even	4
900.2.o.b.599.2		48	45.22	odd	12
900.2.o.b.599.15		48	180.67	even	12
900.2.o.c.299.10		48	15.2	even	4
900.2.o.c.299.23		48	60.47	odd	4
900.2.o.c.599.10		48	180.103	even	12
900.2.o.c.599.23		48	45.13	odd	12
900.2.r.f.551.15		48	60.59	even	2
900.2.r.f.551.22		48	15.14	odd	2
900.2.r.f.851.15		48	45.4	even	6
900.2.r.f.851.22		48	180.139	odd	6
1620.2.e.b.971.11		48	9.7	even	3
1620.2.e.b.971.12		48	36.11	even	6
1620.2.e.b.971.37		48	36.7	odd	6
1620.2.e.b.971.38		48	9.2	odd	6

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.34552 - 0.435401i) q^{2} +(1.62085 - 1.17168i) q^{4} +(0.866025 - 0.500000i) q^{5} +(3.61144 + 2.08506i) q^{7} +(1.67074 - 2.28224i) q^{8} +(0.947554 - 1.04983i) q^{10} +(-3.22095 + 5.57886i) q^{11} +(-0.887336 - 1.53691i) q^{13} +(5.76710 + 1.23307i) q^{14} +(1.25432 - 3.79825i) q^{16} -0.950682i q^{17} -2.19286i q^{19} +(0.817857 - 1.82513i) q^{20} +(-1.90482 + 8.90887i) q^{22} +(-1.01006 - 1.74948i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.86310 - 1.68160i) q^{26} +(8.29663 - 0.851880i) q^{28} +(-5.65260 - 3.26353i) q^{29} +(-2.46164 + 1.42123i) q^{31} +(0.0339479 - 5.65675i) q^{32} +(-0.413928 - 1.27916i) q^{34} +4.17013 q^{35} -5.83599 q^{37} +(-0.954776 - 2.95054i) q^{38} +(0.305778 - 2.81185i) q^{40} +(6.16222 - 3.55776i) q^{41} +(4.59844 + 2.65491i) q^{43} +(1.31596 + 12.8164i) q^{44} +(-2.12079 - 1.91418i) q^{46} +(0.201996 - 0.349867i) q^{47} +(5.19498 + 8.99797i) q^{49} +(0.295692 - 1.38296i) q^{50} +(-3.23901 - 1.45143i) q^{52} -4.87844i q^{53} +6.44191i q^{55} +(10.7924 - 4.75859i) q^{56} +(-9.02663 - 1.93000i) q^{58} +(-1.34391 - 2.32773i) q^{59} +(-2.04652 + 3.54468i) q^{61} +(-2.69338 + 2.98409i) q^{62} +(-2.41728 - 7.62606i) q^{64} +(-1.53691 - 0.887336i) q^{65} +(-9.43616 + 5.44797i) q^{67} +(-1.11390 - 1.54091i) q^{68} +(5.61099 - 1.81568i) q^{70} -2.23126 q^{71} -1.74662 q^{73} +(-7.85244 + 2.54100i) q^{74} +(-2.56934 - 3.55431i) q^{76} +(-23.2645 + 13.4318i) q^{77} +(-0.214428 - 0.123800i) q^{79} +(-0.812853 - 3.91654i) q^{80} +(6.74234 - 7.47008i) q^{82} +(-5.83641 + 10.1090i) q^{83} +(-0.475341 - 0.823315i) q^{85} +(7.34325 + 1.57007i) q^{86} +(7.35095 + 16.6718i) q^{88} -6.13881i q^{89} -7.40061i q^{91} +(-3.68701 - 1.65218i) q^{92} +(0.119457 - 0.558703i) q^{94} +(-1.09643 - 1.89908i) q^{95} +(-9.08503 + 15.7357i) q^{97} +(10.9077 + 9.84505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 30 q^{14} + 24 q^{25} + 12 q^{29} - 6 q^{34} - 60 q^{38} - 6 q^{40} + 60 q^{41} - 12 q^{46} + 24 q^{49} - 18 q^{52} + 42 q^{56} - 18 q^{58} - 48 q^{64} - 48 q^{68} - 24 q^{73} - 84 q^{74} + 6 q^{76}+ \cdots - 12 q^{97}+O(q^{100}) \) 48 * q + 30 * q^14 + 24 * q^25 + 12 * q^29 - 6 * q^34 - 60 * q^38 - 6 * q^40 + 60 * q^41 - 12 * q^46 + 24 * q^49 - 18 * q^52 + 42 * q^56 - 18 * q^58 - 48 * q^64 - 48 * q^68 - 24 * q^73 - 84 * q^74 + 6 * q^76 - 48 * q^77 - 36 * q^82 + 54 * q^86 - 60 * q^92 + 18 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more