LMFDB - Embedded newform 432.2.k.c.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, degree $2$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			325.1
Character	$\chi$	$=$	432.325
Dual form			432.2.k.c.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40946 - 0.115854i) q^{2} +(1.97316 + 0.326583i) q^{4} +(-1.78448 - 1.78448i) q^{5} -4.77575i q^{7} +(-2.74325 - 0.688904i) q^{8} +O(q^{10})$	\(q+(-1.40946 - 0.115854i) q^{2} +(1.97316 + 0.326583i) q^{4} +(-1.78448 - 1.78448i) q^{5} -4.77575i q^{7} +(-2.74325 - 0.688904i) q^{8} +(2.30841 + 2.72189i) q^{10} +(1.61691 + 1.61691i) q^{11} +(-1.94631 + 1.94631i) q^{13} +(-0.553289 + 6.73122i) q^{14} +(3.78669 + 1.28880i) q^{16} -4.57210 q^{17} +(-5.73692 + 5.73692i) q^{19} +(-2.93827 - 4.10383i) q^{20} +(-2.09164 - 2.46629i) q^{22} +0.0549093i q^{23} +1.36871i q^{25} +(2.96874 - 2.51776i) q^{26} +(1.55968 - 9.42329i) q^{28} +(4.88433 - 4.88433i) q^{29} -2.02436 q^{31} +(-5.18787 - 2.25521i) q^{32} +(6.44420 + 0.529697i) q^{34} +(-8.52221 + 8.52221i) q^{35} +(-2.82621 - 2.82621i) q^{37} +(8.75061 - 7.42132i) q^{38} +(3.66593 + 6.12460i) q^{40} -4.33200i q^{41} +(-1.74816 - 1.74816i) q^{43} +(2.66236 + 3.71847i) q^{44} +(0.00636145 - 0.0773924i) q^{46} -11.7093 q^{47} -15.8078 q^{49} +(0.158571 - 1.92915i) q^{50} +(-4.47601 + 3.20474i) q^{52} +(2.91666 + 2.91666i) q^{53} -5.77067i q^{55} +(-3.29003 + 13.1011i) q^{56} +(-7.45014 + 6.31840i) q^{58} +(5.09043 + 5.09043i) q^{59} +(4.33392 - 4.33392i) q^{61} +(2.85326 + 0.234530i) q^{62} +(7.05082 + 3.77967i) q^{64} +6.94629 q^{65} +(-2.89585 + 2.89585i) q^{67} +(-9.02148 - 1.49317i) q^{68} +(12.9990 - 11.0244i) q^{70} +6.50776i q^{71} -9.76411i q^{73} +(3.65600 + 4.31086i) q^{74} +(-13.1934 + 9.44626i) q^{76} +(7.72195 - 7.72195i) q^{77} -2.55495 q^{79} +(-4.45742 - 9.05709i) q^{80} +(-0.501880 + 6.10578i) q^{82} +(8.59304 - 8.59304i) q^{83} +(8.15881 + 8.15881i) q^{85} +(2.26143 + 2.66650i) q^{86} +(-3.32169 - 5.54948i) q^{88} -10.1186i q^{89} +(9.29509 + 9.29509i) q^{91} +(-0.0179324 + 0.108345i) q^{92} +(16.5037 + 1.35656i) q^{94} +20.4748 q^{95} -6.93376 q^{97} +(22.2804 + 1.83139i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{4}+O(q^{10}) $ 24 * q + 16 * q^4	$ 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) $ 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−1.40946	−	0.115854i	−0.996639	−	0.0819211i
$2$	−1.40946	−	0.115854i	−0.996639	−	0.0819211i
$3$		0			0
$3$		0			0
$4$	1.97316	+	0.326583i	0.986578	+	0.163292i
$5$	−1.78448	−	1.78448i	−0.798042	−	0.798042i	0.184744	−	0.982787i	$-0.440854\pi$
$5$	−1.78448	−	1.78448i	−0.798042	−	0.798042i	−0.982787	+	0.184744i	$0.940854\pi$
$6$		0			0
$7$		−	4.77575i		−	1.80506i	−0.430624	−	0.902531i	$-0.641707\pi$
$7$		−	4.77575i		−	1.80506i	0.430624	−	0.902531i	$-0.358293\pi$
$8$	−2.74325	−	0.688904i	−0.969885	−	0.243564i
$9$		0			0
$10$	2.30841	+	2.72189i	0.729983	+	0.860736i
$11$	1.61691	+	1.61691i	0.487516	+	0.487516i	0.907522	−	0.420005i	$-0.137972\pi$
$11$	1.61691	+	1.61691i	0.487516	+	0.487516i	−0.420005	+	0.907522i	$0.637972\pi$
$12$		0			0
$13$	−1.94631	+	1.94631i	−0.539810	+	0.539810i	−0.923473	−	0.383663i	$-0.874662\pi$
$13$	−1.94631	+	1.94631i	−0.539810	+	0.539810i	0.383663	+	0.923473i	$0.374662\pi$
$14$	−0.553289	+	6.73122i	−0.147873	+	1.79900i
$15$		0			0
$16$	3.78669	+	1.28880i	0.946672	+	0.322200i
$17$	−4.57210			−1.10890			−0.554449	−	0.832218i	$-0.687071\pi$
$17$	−4.57210			−1.10890			−0.554449	+	0.832218i	$0.687071\pi$
$18$		0			0
$19$	−5.73692	+	5.73692i	−1.31614	+	1.31614i	−0.399334	+	0.916805i	$0.630759\pi$
$19$	−5.73692	+	5.73692i	−1.31614	+	1.31614i	−0.916805	+	0.399334i	$0.869241\pi$
$20$	−2.93827	−	4.10383i	−0.657017	−	0.917644i
$21$		0			0
$22$	−2.09164	−	2.46629i	−0.445940	−	0.525816i
$23$			0.0549093i			0.0114494i	0.999984	+	0.00572469i	$0.00182223\pi$
$23$			0.0549093i			0.0114494i	−0.999984	+	0.00572469i	$0.998178\pi$
$24$		0			0
$25$			1.36871i			0.273743i
$26$	2.96874	−	2.51776i	0.582217	−	0.493773i
$27$		0			0
$28$	1.55968	−	9.42329i	0.294751	−	1.78083i
$29$	4.88433	−	4.88433i	0.906997	−	0.906997i	−0.0890316	−	0.996029i	$-0.528377\pi$
$29$	4.88433	−	4.88433i	0.906997	−	0.906997i	0.996029	+	0.0890316i	$0.0283772\pi$
$30$		0			0
$31$	−2.02436			−0.363586			−0.181793	−	0.983337i	$-0.558190\pi$
$31$	−2.02436			−0.363586			−0.181793	+	0.983337i	$0.558190\pi$
$32$	−5.18787	−	2.25521i	−0.917095	−	0.398669i
$33$		0			0
$34$	6.44420	+	0.529697i	1.10517	+	0.0908422i
$35$	−8.52221	+	8.52221i	−1.44052	+	1.44052i
$36$		0			0
$37$	−2.82621	−	2.82621i	−0.464626	−	0.464626i	0.435542	−	0.900168i	$-0.356557\pi$
$37$	−2.82621	−	2.82621i	−0.464626	−	0.464626i	−0.900168	+	0.435542i	$0.856557\pi$
$38$	8.75061	−	7.42132i	1.41954	−	1.20390i
$39$		0			0
$40$	3.66593	+	6.12460i	0.579634	+	0.968384i
$41$		−	4.33200i		−	0.676545i	−0.941048	−	0.338272i	$-0.890157\pi$
$41$		−	4.33200i		−	0.676545i	0.941048	−	0.338272i	$-0.109843\pi$
$42$		0			0
$43$	−1.74816	−	1.74816i	−0.266592	−	0.266592i	0.561133	−	0.827725i	$-0.310366\pi$
$43$	−1.74816	−	1.74816i	−0.266592	−	0.266592i	−0.827725	+	0.561133i	$0.810366\pi$
$44$	2.66236	+	3.71847i	0.401366	+	0.560580i
$45$		0			0
$46$	0.00636145	−	0.0773924i	0.000937945	−	0.0114109i
$47$	−11.7093			−1.70797			−0.853986	−	0.520296i	$-0.825822\pi$
$47$	−11.7093			−1.70797			−0.853986	+	0.520296i	$0.825822\pi$
$48$		0			0
$49$	−15.8078			−2.25825
$50$	0.158571	−	1.92915i	0.0224253	−	0.272823i
$51$		0			0
$52$	−4.47601	+	3.20474i	−0.620711	+	0.444418i
$53$	2.91666	+	2.91666i	0.400634	+	0.400634i	0.878457	−	0.477822i	$-0.158574\pi$
$53$	2.91666	+	2.91666i	0.400634	+	0.400634i	−0.477822	+	0.878457i	$0.658574\pi$
$54$		0			0
$55$		−	5.77067i		−	0.778117i
$56$	−3.29003	+	13.1011i	−0.439649	+	1.75070i
$57$		0			0
$58$	−7.45014	+	6.31840i	−0.978251	+	0.829646i
$59$	5.09043	+	5.09043i	0.662718	+	0.662718i	0.956020	−	0.293302i	$-0.0947542\pi$
$59$	5.09043	+	5.09043i	0.662718	+	0.662718i	−0.293302	+	0.956020i	$0.594754\pi$
$60$		0			0
$61$	4.33392	−	4.33392i	0.554901	−	0.554901i	−0.372950	−	0.927851i	$-0.621654\pi$
$61$	4.33392	−	4.33392i	0.554901	−	0.554901i	0.927851	+	0.372950i	$0.121654\pi$
$62$	2.85326	+	0.234530i	0.362364	+	0.0297854i
$63$		0			0
$64$	7.05082	+	3.77967i	0.881353	+	0.472459i
$65$	6.94629			0.861582
$66$		0			0
$67$	−2.89585	+	2.89585i	−0.353784	+	0.353784i	−0.861515	−	0.507731i	$-0.830484\pi$
$67$	−2.89585	+	2.89585i	−0.353784	+	0.353784i	0.507731	+	0.861515i	$0.330484\pi$
$68$	−9.02148	−	1.49317i	−1.09401	−	0.181074i
$69$		0			0
$70$	12.9990	−	11.0244i	1.55368	−	1.31767i
$71$			6.50776i			0.772329i	0.922430	+	0.386164i	$0.126200\pi$
$71$			6.50776i			0.772329i	−0.922430	+	0.386164i	$0.873800\pi$
$72$		0			0
$73$		−	9.76411i		−	1.14280i	−0.820671	−	0.571401i	$-0.806400\pi$
$73$		−	9.76411i		−	1.14280i	0.820671	−	0.571401i	$-0.193600\pi$
$74$	3.65600	+	4.31086i	0.425002	+	0.501127i
$75$		0			0
$76$	−13.1934	+	9.44626i	−1.51339	+	1.08356i
$77$	7.72195	−	7.72195i	0.879998	−	0.879998i
$78$		0			0
$79$	−2.55495			−0.287454			−0.143727	−	0.989617i	$-0.545909\pi$
$79$	−2.55495			−0.287454			−0.143727	+	0.989617i	$0.545909\pi$
$80$	−4.45742	−	9.05709i	−0.498355	−	1.01261i
$81$		0			0
$82$	−0.501880	+	6.10578i	−0.0554233	+	0.674271i
$83$	8.59304	−	8.59304i	0.943208	−	0.943208i	−0.0552635	−	0.998472i	$-0.517600\pi$
$83$	8.59304	−	8.59304i	0.943208	−	0.943208i	0.998472	+	0.0552635i	$0.0175999\pi$
$84$		0			0
$85$	8.15881	+	8.15881i	0.884948	+	0.884948i
$86$	2.26143	+	2.66650i	0.243857	+	0.287536i
$87$		0			0
$88$	−3.32169	−	5.54948i	−0.354093	−	0.591576i
$89$		−	10.1186i		−	1.07257i	−0.844038	−	0.536284i	$-0.819828\pi$
$89$		−	10.1186i		−	1.07257i	0.844038	−	0.536284i	$-0.180172\pi$
$90$		0			0
$91$	9.29509	+	9.29509i	0.974390	+	0.974390i
$92$	−0.0179324	+	0.108345i	−0.00186959	+	0.0112957i
$93$		0			0
$94$	16.5037	+	1.35656i	1.70223	+	0.139919i
$95$	20.4748			2.10067
$96$		0			0
$97$	−6.93376			−0.704016			−0.352008	−	0.935997i	$-0.614501\pi$
$97$	−6.93376			−0.704016			−0.352008	+	0.935997i	$0.614501\pi$
$98$	22.2804	+	1.83139i	2.25066	+	0.184998i
$99$		0			0
$100$	−0.446999	+	2.70069i	−0.0446999	+	0.270069i
$101$	−5.13965	−	5.13965i	−0.511415	−	0.511415i	0.403545	−	0.914960i	$-0.367778\pi$
$101$	−5.13965	−	5.13965i	−0.511415	−	0.511415i	−0.914960	+	0.403545i	$0.867778\pi$
$102$		0			0
$103$			4.74494i			0.467533i	0.972293	+	0.233766i	$0.0751051\pi$
$103$			4.74494i			0.467533i	−0.972293	+	0.233766i	$0.924895\pi$
$104$	6.68004	−	3.99839i	0.655032	−	0.392075i
$105$		0			0
$106$	−3.77301	−	4.44883i	−0.366467	−	0.432108i
$107$	−1.13958	−	1.13958i	−0.110167	−	0.110167i	0.649874	−	0.760042i	$-0.274821\pi$
$107$	−1.13958	−	1.13958i	−0.110167	−	0.110167i	−0.760042	+	0.649874i	$0.774821\pi$
$108$		0			0
$109$	2.54746	−	2.54746i	0.244003	−	0.244003i	−0.574501	−	0.818504i	$-0.694804\pi$
$109$	2.54746	−	2.54746i	0.244003	−	0.244003i	0.818504	+	0.574501i	$0.194804\pi$
$110$	−0.668555	+	8.13353i	−0.0637443	+	0.775502i
$111$		0			0
$112$	6.15498	−	18.0843i	0.581591	−	1.70880i
$113$	9.39661			0.883958			0.441979	−	0.897025i	$-0.354276\pi$
$113$	9.39661			0.883958			0.441979	+	0.897025i	$0.354276\pi$
$114$		0			0
$115$	0.0979843	−	0.0979843i	0.00913708	−	0.00913708i
$116$	11.2327	−	8.04240i	1.04293	−	0.746718i
$117$		0			0
$118$	−6.58501	−	7.76450i	−0.606199	−	0.714781i
$119$			21.8352i			2.00163i
$120$		0			0
$121$		−	5.77121i		−	0.524655i
$122$	−6.61059	+	5.60638i	−0.598494	+	0.507578i
$123$		0			0
$124$	−3.99438	−	0.661122i	−0.358706	−	0.0593705i
$125$	−6.47995	+	6.47995i	−0.579584	+	0.579584i
$126$		0			0
$127$	17.0522			1.51314			0.756571	−	0.653912i	$-0.226873\pi$
$127$	17.0522			1.51314			0.756571	+	0.653912i	$0.226873\pi$
$128$	−9.49996	−	6.14416i	−0.839686	−	0.543072i
$129$		0			0
$130$	−9.79053	−	0.804756i	−0.858686	−	0.0705818i
$131$	−9.34322	+	9.34322i	−0.816321	+	0.816321i	−0.985573	−	0.169252i	$-0.945865\pi$
$131$	−9.34322	+	9.34322i	−0.816321	+	0.816321i	0.169252	+	0.985573i	$0.445865\pi$
$132$		0			0
$133$	27.3981	+	27.3981i	2.37571	+	2.37571i
$134$	4.41708	−	3.74609i	0.381577	−	0.323612i
$135$		0			0
$136$	12.5424	+	3.14974i	1.07550	+	0.270088i
$137$		−	7.73456i		−	0.660808i	−0.943840	−	0.330404i	$-0.892815\pi$
$137$		−	7.73456i		−	0.660808i	0.943840	−	0.330404i	$-0.107185\pi$
$138$		0			0
$139$	0.907485	+	0.907485i	0.0769718	+	0.0769718i	0.744545	−	0.667573i	$-0.232667\pi$
$139$	0.907485	+	0.907485i	0.0769718	+	0.0769718i	−0.667573	+	0.744545i	$0.732667\pi$
$140$	−19.5989	+	14.0324i	−1.65641	+	1.18596i
$141$		0			0
$142$	0.753950	−	9.17243i	0.0632701	−	0.769733i
$143$	−6.29402			−0.526332
$144$		0			0
$145$	−17.4319			−1.44764
$146$	−1.13121	+	13.7621i	−0.0936197	+	1.13896i
$147$		0			0
$148$	−4.65356	−	6.49955i	−0.382520	−	0.534260i
$149$	−8.00910	−	8.00910i	−0.656131	−	0.656131i	0.298332	−	0.954462i	$-0.403570\pi$
$149$	−8.00910	−	8.00910i	−0.656131	−	0.656131i	−0.954462	+	0.298332i	$0.903570\pi$
$150$		0			0
$151$		−	17.7384i		−	1.44353i	−0.692138	−	0.721765i	$-0.743331\pi$
$151$		−	17.7384i		−	1.44353i	0.692138	−	0.721765i	$-0.256669\pi$
$152$	19.6900	−	11.7856i	1.59707	−	0.955939i
$153$		0			0
$154$	−11.7784	+	9.98916i	−0.949130	+	0.804950i
$155$	3.61242	+	3.61242i	0.290157	+	0.290157i
$156$		0			0
$157$	17.1765	−	17.1765i	1.37083	−	1.37083i	0.511620	−	0.859212i	$-0.329046\pi$
$157$	17.1765	−	17.1765i	1.37083	−	1.37083i	0.859212	−	0.511620i	$-0.170954\pi$
$158$	3.60110	+	0.296001i	0.286488	+	0.0235486i
$159$		0			0
$160$	5.23326	+	13.2820i	0.413726	+	1.05004i
$161$	0.262233			0.0206668
$162$		0			0
$163$	−3.94500	+	3.94500i	−0.308996	+	0.308996i	−0.844520	−	0.535524i	$-0.820114\pi$
$163$	−3.94500	+	3.94500i	−0.308996	+	0.308996i	0.535524	+	0.844520i	$0.320114\pi$
$164$	1.41476	−	8.54771i	0.110474	−	0.667464i
$165$		0			0
$166$	−13.1071	+	11.1160i	−1.01731	+	0.862769i
$167$		−	12.2975i		−	0.951613i	−0.879550	−	0.475806i	$-0.842156\pi$
$167$		−	12.2975i		−	0.951613i	0.879550	−	0.475806i	$-0.157844\pi$
$168$		0			0
$169$			5.42374i			0.417211i
$170$	−10.5543	−	12.4448i	−0.809477	−	0.954469i
$171$		0			0
$172$	−2.87848	−	4.02032i	−0.219482	−	0.306546i
$173$	−10.8664	+	10.8664i	−0.826158	+	0.826158i	−0.986983	−	0.160825i	$-0.948584\pi$
$173$	−10.8664	+	10.8664i	−0.826158	+	0.826158i	0.160825	+	0.986983i	$0.448584\pi$
$174$		0			0
$175$	6.53663			0.494123
$176$	4.03886	+	8.20660i	0.304440	+	0.618596i
$177$		0			0
$178$	−1.17228	+	14.2617i	−0.0878659	+	1.06896i
$179$	1.13958	−	1.13958i	0.0851762	−	0.0851762i	−0.663235	−	0.748411i	$-0.730817\pi$
$179$	1.13958	−	1.13958i	0.0851762	−	0.0851762i	0.748411	+	0.663235i	$0.230817\pi$
$180$		0			0
$181$	−3.01618	−	3.01618i	−0.224191	−	0.224191i	0.586070	−	0.810260i	$-0.300674\pi$
$181$	−3.01618	−	3.01618i	−0.224191	−	0.224191i	−0.810260	+	0.586070i	$0.800674\pi$
$182$	−12.0242	−	14.1779i	−0.891292	−	1.05094i
$183$		0			0
$184$	0.0378272	−	0.150630i	0.00278866	−	0.0111046i
$185$			10.0866i			0.741583i
$186$		0			0
$187$	−7.39268	−	7.39268i	−0.540606	−	0.540606i
$188$	−23.1042	−	3.82405i	−1.68505	−	0.278897i
$189$		0			0
$190$	−28.8584	−	2.37209i	−2.09361	−	0.172089i
$191$	1.41532			0.102409			0.0512047	−	0.998688i	$-0.483694\pi$
$191$	1.41532			0.102409			0.0512047	+	0.998688i	$0.483694\pi$
$192$		0			0
$193$	10.1540			0.730898			0.365449	−	0.930831i	$-0.380915\pi$
$193$	10.1540			0.730898			0.365449	+	0.930831i	$0.380915\pi$
$194$	9.77285	+	0.803303i	0.701650	+	0.0576738i
$195$		0			0
$196$	−31.1912	−	5.16255i	−2.22794	−	0.368753i
$197$	−3.79645	−	3.79645i	−0.270486	−	0.270486i	0.558810	−	0.829296i	$-0.311258\pi$
$197$	−3.79645	−	3.79645i	−0.270486	−	0.270486i	−0.829296	+	0.558810i	$0.811258\pi$
$198$		0			0
$199$		−	10.0596i		−	0.713106i	−0.934275	−	0.356553i	$-0.883952\pi$
$199$		−	10.0596i		−	0.713106i	0.934275	−	0.356553i	$-0.116048\pi$
$200$	0.942912	−	3.75472i	0.0666740	−	0.265499i
$201$		0			0
$202$	6.64869	+	7.83959i	0.467800	+	0.551591i
$203$	−23.3263	−	23.3263i	−1.63719	−	1.63719i
$204$		0			0
$205$	−7.73036	+	7.73036i	−0.539911	+	0.539911i
$206$	0.549720	−	6.68780i	0.0383008	−	0.465961i
$207$		0			0
$208$	−9.87848	+	4.86167i	−0.684949	+	0.337096i
$209$	−18.5522			−1.28328
$210$		0			0
$211$	−6.59568	+	6.59568i	−0.454066	+	0.454066i	−0.896701	−	0.442636i	$-0.854043\pi$
$211$	−6.59568	+	6.59568i	−0.454066	+	0.454066i	0.442636	+	0.896701i	$0.354043\pi$
$212$	4.80250	+	6.70756i	0.329837	+	0.460677i
$213$		0			0
$214$	1.47417	+	1.73822i	0.100772	+	0.118822i
$215$			6.23911i			0.425504i
$216$		0			0
$217$			9.66783i			0.656295i
$218$	−3.88568	+	3.29541i	−0.263172	+	0.223194i
$219$		0			0
$220$	1.88460	−	11.3864i	0.127060	−	0.767673i
$221$	8.89874	−	8.89874i	0.598594	−	0.598594i
$222$		0			0
$223$	−1.93893			−0.129841			−0.0649203	−	0.997890i	$-0.520679\pi$
$223$	−1.93893			−0.129841			−0.0649203	+	0.997890i	$0.520679\pi$
$224$	−10.7703	+	24.7760i	−0.719623	+	1.65541i
$225$		0			0
$226$	−13.2441	−	1.08863i	−0.880987	−	0.0724149i
$227$	0.135956	−	0.135956i	0.00902370	−	0.00902370i	−0.702581	−	0.711604i	$-0.747969\pi$
$227$	0.135956	−	0.135956i	0.00902370	−	0.00902370i	0.711604	+	0.702581i	$0.247969\pi$
$228$		0			0
$229$	3.45402	+	3.45402i	0.228248	+	0.228248i	0.811960	−	0.583713i	$-0.198400\pi$
$229$	3.45402	+	3.45402i	0.228248	+	0.228248i	−0.583713	+	0.811960i	$0.698400\pi$
$230$	−0.149457	+	0.126753i	−0.00985489	+	0.00835785i
$231$		0			0
$232$	−16.7638	+	10.0341i	−1.10059	+	0.658771i
$233$			14.7128i			0.963869i	0.876207	+	0.481934i	$0.160066\pi$
$233$			14.7128i			0.963869i	−0.876207	+	0.481934i	$0.839934\pi$
$234$		0			0
$235$	20.8949	+	20.8949i	1.36303	+	1.36303i
$236$	8.38176	+	11.7067i	0.545606	+	0.762039i
$237$		0			0
$238$	2.52970	−	30.7759i	0.163976	−	1.99490i
$239$	−6.99700			−0.452598			−0.226299	−	0.974058i	$-0.572663\pi$
$239$	−6.99700			−0.452598			−0.226299	+	0.974058i	$0.572663\pi$
$240$		0			0
$241$	18.7002			1.20459			0.602294	−	0.798274i	$-0.294253\pi$
$241$	18.7002			1.20459			0.602294	+	0.798274i	$0.294253\pi$
$242$	−0.668617	+	8.13429i	−0.0429804	+	0.522892i
$243$		0			0
$244$	9.96688	−	7.13611i	0.638064	−	0.456843i
$245$	28.2086	+	28.2086i	1.80218	+	1.80218i
$246$		0			0
$247$		−	22.3317i		−	1.42093i
$248$	5.55332	+	1.39459i	0.352636	+	0.0885565i
$249$		0			0
$250$	9.88395	−	8.38250i	0.625116	−	0.530156i
$251$	4.57136	+	4.57136i	0.288542	+	0.288542i	0.836503	−	0.547962i	$-0.184596\pi$
$251$	4.57136	+	4.57136i	0.288542	+	0.288542i	−0.547962	+	0.836503i	$0.684596\pi$
$252$		0			0
$253$	−0.0887833	+	0.0887833i	−0.00558176	+	0.00558176i
$254$	−24.0345	−	1.97557i	−1.50806	−	0.123958i
$255$		0			0
$256$	12.6780	+	9.76055i	0.792375	+	0.610035i
$257$	26.2965			1.64033			0.820167	−	0.572124i	$-0.193881\pi$
$257$	26.2965			1.64033			0.820167	+	0.572124i	$0.193881\pi$
$258$		0			0
$259$	−13.4973	+	13.4973i	−0.838680	+	0.838680i
$260$	13.7061	+	2.26854i	0.850018	+	0.140689i
$261$		0			0
$262$	14.2513	−	12.0864i	0.880451	−	0.746703i
$263$		−	29.5593i		−	1.82271i	−0.411624	−	0.911354i	$-0.635038\pi$
$263$		−	29.5593i		−	1.82271i	0.411624	−	0.911354i	$-0.364962\pi$
$264$		0			0
$265$		−	10.4094i		−	0.639446i
$266$	−35.4423	−	41.7907i	−2.17311	−	2.56235i
$267$		0			0
$268$	−6.65969	+	4.76822i	−0.406805	+	0.291266i
$269$	−6.82293	+	6.82293i	−0.416001	+	0.416001i	−0.883823	−	0.467822i	$-0.845039\pi$
$269$	−6.82293	+	6.82293i	−0.416001	+	0.416001i	0.467822	+	0.883823i	$0.345039\pi$
$270$		0			0
$271$	3.28197			0.199366			0.0996828	−	0.995019i	$-0.468217\pi$
$271$	3.28197			0.199366			0.0996828	+	0.995019i	$0.468217\pi$
$272$	−17.3131	−	5.89252i	−1.04976	−	0.357287i
$273$		0			0
$274$	−0.896079	+	10.9015i	−0.0541341	+	0.658587i
$275$	−2.21309	+	2.21309i	−0.133454	+	0.133454i
$276$		0			0
$277$	−11.9478	−	11.9478i	−0.717873	−	0.717873i	0.250296	−	0.968169i	$-0.419472\pi$
$277$	−11.9478	−	11.9478i	−0.717873	−	0.717873i	−0.968169	+	0.250296i	$0.919472\pi$
$278$	−1.17393	−	1.38420i	−0.0704075	−	0.0830188i
$279$		0			0
$280$	29.2495	−	17.5076i	1.74799	−	1.04628i
$281$		−	31.5153i		−	1.88005i	−0.341112	−	0.940023i	$-0.610804\pi$
$281$		−	31.5153i		−	1.88005i	0.341112	−	0.940023i	$-0.389196\pi$
$282$		0			0
$283$	19.3322	+	19.3322i	1.14918	+	1.14918i	0.986714	+	0.162464i	$0.0519441\pi$
$283$	19.3322	+	19.3322i	1.14918	+	1.14918i	0.162464	+	0.986714i	$0.448056\pi$
$284$	−2.12532	+	12.8408i	−0.126115	+	0.761963i
$285$		0			0
$286$	8.87117	+	0.729187i	0.524563	+	0.0431177i
$287$	−20.6885			−1.22121
$288$		0			0
$289$	3.90414			0.229656
$290$	24.5696	+	2.01956i	1.44278	+	0.118593i
$291$		0			0
$292$	3.18879	−	19.2661i	0.186610	−	1.12746i
$293$	−12.8368	−	12.8368i	−0.749936	−	0.749936i	0.224531	−	0.974467i	$-0.427915\pi$
$293$	−12.8368	−	12.8368i	−0.749936	−	0.749936i	−0.974467	+	0.224531i	$0.927915\pi$
$294$		0			0
$295$		−	18.1675i		−	1.05775i
$296$	5.80601	+	9.69999i	0.337468	+	0.563800i
$297$		0			0
$298$	10.3606	+	12.2164i	0.600174	+	0.707676i
$299$	−0.106871	−	0.106871i	−0.00618048	−	0.00618048i
$300$		0			0
$301$	−8.34878	+	8.34878i	−0.481216	+	0.481216i
$302$	−2.05506	+	25.0016i	−0.118256	+	1.43868i
$303$		0			0
$304$	−29.1177	+	14.3302i	−1.67001	+	0.821892i
$305$	−15.4675			−0.885669
$306$		0			0
$307$	−7.63784	+	7.63784i	−0.435915	+	0.435915i	−0.890634	−	0.454720i	$-0.849739\pi$
$307$	−7.63784	+	7.63784i	−0.435915	+	0.435915i	0.454720	+	0.890634i	$0.349739\pi$
$308$	17.7585	−	12.7147i	1.01188	−	0.724490i
$309$		0			0
$310$	−4.67305	−	5.51008i	−0.265412	−	0.312952i
$311$		−	2.90605i		−	0.164787i	−0.996600	−	0.0823936i	$-0.973744\pi$
$311$		−	2.90605i		−	0.164787i	0.996600	−	0.0823936i	$-0.0262565\pi$
$312$		0			0
$313$			17.3826i			0.982525i	0.871012	+	0.491262i	$0.163464\pi$
$313$			17.3826i			0.982525i	−0.871012	+	0.491262i	$0.836536\pi$
$314$	−26.1995	+	22.2196i	−1.47852	+	1.25392i
$315$		0			0
$316$	−5.04131	−	0.834402i	−0.283596	−	0.0469388i
$317$	−1.16003	+	1.16003i	−0.0651540	+	0.0651540i	−0.738933	−	0.673779i	$-0.764670\pi$
$317$	−1.16003	+	1.16003i	−0.0651540	+	0.0651540i	0.673779	+	0.738933i	$0.264670\pi$
$318$		0			0
$319$	15.7950			0.884352
$320$	−5.83730	−	19.3268i	−0.326315	−	1.08040i
$321$		0			0
$322$	−0.369607	−	0.0303807i	−0.0205974	−	0.00169305i
$323$	26.2298	−	26.2298i	1.45947	−	1.45947i
$324$		0			0
$325$	−2.66394	−	2.66394i	−0.147769	−	0.147769i
$326$	6.01736	−	5.10327i	0.333271	−	0.282644i
$327$		0			0
$328$	−2.98433	+	11.8838i	−0.164782	+	0.656171i
$329$			55.9205i			3.08300i
$330$		0			0
$331$	−7.34342	−	7.34342i	−0.403631	−	0.403631i	0.475880	−	0.879510i	$-0.342130\pi$
$331$	−7.34342	−	7.34342i	−0.403631	−	0.403631i	−0.879510	+	0.475880i	$0.842130\pi$
$332$	19.7617	−	14.1491i	1.08457	−	0.776530i
$333$		0			0
$334$	−1.42472	+	17.3329i	−0.0779572	+	0.948414i
$335$	10.3351			0.564669
$336$		0			0
$337$	−10.1328			−0.551970			−0.275985	−	0.961162i	$-0.589004\pi$
$337$	−10.1328			−0.551970			−0.275985	+	0.961162i	$0.589004\pi$
$338$	0.628362	−	7.64455i	0.0341784	−	0.415809i
$339$		0			0
$340$	13.4341	+	18.7631i	0.728565	+	1.01757i
$341$	−3.27321	−	3.27321i	−0.177254	−	0.177254i
$342$		0			0
$343$			42.0636i			2.27122i
$344$	3.59133	+	5.99996i	0.193631	+	0.323496i
$345$		0			0
$346$	16.5747	−	14.0569i	0.891061	−	0.755701i
$347$	16.9815	+	16.9815i	0.911617	+	0.911617i	0.996399	−	0.0847826i	$-0.0270196\pi$
$347$	16.9815	+	16.9815i	0.911617	+	0.911617i	−0.0847826	+	0.996399i	$0.527020\pi$
$348$		0			0
$349$	4.45040	−	4.45040i	0.238224	−	0.238224i	−0.577890	−	0.816115i	$-0.696124\pi$
$349$	4.45040	−	4.45040i	0.238224	−	0.238224i	0.816115	+	0.577890i	$0.196124\pi$
$350$	−9.21312	−	0.757295i	−0.492462	−	0.0404791i
$351$		0			0
$352$	−4.74184	−	12.0348i	−0.252741	−	0.641457i
$353$	−33.4741			−1.78164			−0.890822	−	0.454352i	$-0.849871\pi$
$353$	−33.4741			−1.78164			−0.890822	+	0.454352i	$0.849871\pi$
$354$		0			0
$355$	11.6129	−	11.6129i	0.616351	−	0.616351i
$356$	3.30456	−	19.9655i	0.175141	−	1.05817i
$357$		0			0
$358$	−1.73822	+	1.47417i	−0.0918676	+	0.0779121i
$359$		−	11.5563i		−	0.609917i	−0.952366	−	0.304958i	$-0.901357\pi$
$359$		−	11.5563i		−	0.609917i	0.952366	−	0.304958i	$-0.0986425\pi$
$360$		0			0
$361$		−	46.8245i		−	2.46445i
$362$	3.90174	+	4.60062i	0.205071	+	0.241803i
$363$		0			0
$364$	15.3050	+	21.3763i	0.802202	+	1.12042i
$365$	−17.4238	+	17.4238i	−0.912005	+	0.912005i
$366$		0			0
$367$	0.429107			0.0223992			0.0111996	−	0.999937i	$-0.496435\pi$
$367$	0.429107			0.0223992			0.0111996	+	0.999937i	$0.496435\pi$
$368$	−0.0707670	+	0.207924i	−0.00368898	+	0.0108388i
$369$		0			0
$370$	1.16857	−	14.2167i	0.0607513	−	0.739090i
$371$	13.9292	−	13.9292i	0.723170	−	0.723170i
$372$		0			0
$373$	−12.7715	−	12.7715i	−0.661282	−	0.661282i	0.294400	−	0.955682i	$-0.404880\pi$
$373$	−12.7715	−	12.7715i	−0.661282	−	0.661282i	−0.955682	+	0.294400i	$0.904880\pi$
$374$	9.56321	+	11.2762i	0.494502	+	0.583076i
$375$		0			0
$376$	32.1214	+	8.06656i	1.65654	+	0.416001i
$377$			19.0129i			0.979212i
$378$		0			0
$379$	−19.2342	−	19.2342i	−0.987994	−	0.987994i	0.0119348	−	0.999929i	$-0.496201\pi$
$379$	−19.2342	−	19.2342i	−0.987994	−	0.987994i	−0.999929	+	0.0119348i	$0.996201\pi$
$380$	40.4000	+	6.68672i	2.07247	+	0.343022i
$381$		0			0
$382$	−1.99484	−	0.163971i	−0.102065	−	0.00838949i
$383$	29.8114			1.52329			0.761645	−	0.647994i	$-0.224392\pi$
$383$	29.8114			1.52329			0.761645	+	0.647994i	$0.224392\pi$
$384$		0			0
$385$	−27.5593			−1.40455
$386$	−14.3116	−	1.17638i	−0.728441	−	0.0598760i
$387$		0			0
$388$	−13.6814	−	2.26445i	−0.694567	−	0.114960i
$389$	21.0399	+	21.0399i	1.06676	+	1.06676i	0.997606	+	0.0691588i	$0.0220315\pi$
$389$	21.0399	+	21.0399i	1.06676	+	1.06676i	0.0691588	+	0.997606i	$0.477968\pi$
$390$		0			0
$391$		−	0.251051i		−	0.0126962i
$392$	43.3646	+	10.8900i	2.19024	+	0.550029i
$393$		0			0
$394$	4.91111	+	5.79078i	0.247418	+	0.291735i
$395$	4.55924	+	4.55924i	0.229400	+	0.229400i
$396$		0			0
$397$	21.3140	−	21.3140i	1.06972	−	1.06972i	0.0723394	−	0.997380i	$-0.476954\pi$
$397$	21.3140	−	21.3140i	1.06972	−	1.06972i	0.997380	−	0.0723394i	$-0.0230465\pi$
$398$	−1.16544	+	14.1786i	−0.0584184	+	0.710709i
$399$		0			0
$400$	−1.76400	+	5.18289i	−0.0881998	+	0.259145i
$401$	−24.4482			−1.22088			−0.610442	−	0.792061i	$-0.709008\pi$
$401$	−24.4482			−1.22088			−0.610442	+	0.792061i	$0.709008\pi$
$402$		0			0
$403$	3.94004	−	3.94004i	0.196267	−	0.196267i
$404$	−8.46281	−	11.8199i	−0.421041	−	0.588060i
$405$		0			0
$406$	30.1751	+	35.5800i	1.49756	+	1.76580i
$407$		−	9.13945i		−	0.453026i
$408$		0			0
$409$			8.78525i			0.434402i	0.976127	+	0.217201i	$0.0696928\pi$
$409$			8.78525i			0.434402i	−0.976127	+	0.217201i	$0.930307\pi$
$410$	11.7912	−	10.0000i	0.582327	−	0.493867i
$411$		0			0
$412$	−1.54962	+	9.36250i	−0.0763441	+	0.461257i
$413$	24.3106	−	24.3106i	1.19625	−	1.19625i
$414$		0			0
$415$	−30.6681			−1.50544
$416$	14.4866	−	5.70787i	0.710262	−	0.279851i
$417$		0			0
$418$	26.1485	+	2.14934i	1.27897	+	0.105128i
$419$	−16.8995	+	16.8995i	−0.825594	+	0.825594i	−0.986904	−	0.161310i	$-0.948428\pi$
$419$	−16.8995	+	16.8995i	−0.825594	+	0.825594i	0.161310	+	0.986904i	$0.448428\pi$
$420$		0			0
$421$	14.8905	+	14.8905i	0.725718	+	0.725718i	0.969764	−	0.244046i	$-0.0784748\pi$
$421$	14.8905	+	14.8905i	0.725718	+	0.725718i	−0.244046	+	0.969764i	$0.578475\pi$
$422$	10.0605	−	8.53222i	0.489737	−	0.415342i
$423$		0			0
$424$	−5.99183	−	10.0104i	−0.290989	−	0.486149i
$425$		−	6.25790i		−	0.303553i
$426$		0			0
$427$	−20.6977	−	20.6977i	−1.00163	−	1.00163i
$428$	−1.87640	−	2.62073i	−0.0906992	−	0.126678i
$429$		0			0
$430$	0.722826	−	8.79377i	0.0348577	−	0.424073i
$431$	21.7025			1.04537			0.522685	−	0.852526i	$-0.324930\pi$
$431$	21.7025			1.04537			0.522685	+	0.852526i	$0.324930\pi$
$432$		0			0
$433$	−36.8767			−1.77218			−0.886091	−	0.463512i	$-0.846589\pi$
$433$	−36.8767			−1.77218			−0.886091	+	0.463512i	$0.846589\pi$
$434$	1.12006	−	13.6264i	0.0537645	−	0.654089i
$435$		0			0
$436$	5.85850	−	4.19458i	0.280571	−	0.200884i
$437$	−0.315010	−	0.315010i	−0.0150690	−	0.0150690i
$438$		0			0
$439$			14.6269i			0.698103i	0.937103	+	0.349052i	$0.113496\pi$
$439$			14.6269i			0.698103i	−0.937103	+	0.349052i	$0.886504\pi$
$440$	−3.97544	+	15.8304i	−0.189522	+	0.754684i
$441$		0			0
$442$	−13.5734	+	11.5115i	−0.645620	+	0.547545i
$443$	0.0290852	+	0.0290852i	0.00138188	+	0.00138188i	0.707797	−	0.706416i	$-0.249689\pi$
$443$	0.0290852	+	0.0290852i	0.00138188	+	0.00138188i	−0.706416	+	0.707797i	$0.749689\pi$
$444$		0			0
$445$	−18.0564	+	18.0564i	−0.855954	+	0.855954i
$446$	2.73285	+	0.224633i	0.129404	+	0.0106367i
$447$		0			0
$448$	18.0507	−	33.6729i	0.852817	−	1.59090i
$449$	36.5678			1.72574			0.862870	−	0.505426i	$-0.168665\pi$
$449$	36.5678			1.72574			0.862870	+	0.505426i	$0.168665\pi$
$450$		0			0
$451$	7.00445	−	7.00445i	0.329827	−	0.329827i
$452$	18.5410	+	3.06877i	0.872094	+	0.144343i
$453$		0			0
$454$	−0.207375	+	0.175873i	−0.00973260	+	0.00825414i
$455$		−	33.1737i		−	1.55521i
$456$		0			0
$457$			17.6231i			0.824376i	0.911099	+	0.412188i	$0.135235\pi$
$457$			17.6231i			0.824376i	−0.911099	+	0.412188i	$0.864765\pi$
$458$	−4.46814	−	5.26846i	−0.208782	−	0.246179i
$459$		0			0
$460$	0.225338	−	0.161338i	0.0105064	−	0.00752243i
$461$	−10.6861	+	10.6861i	−0.497703	+	0.497703i	−0.910722	−	0.413019i	$-0.864474\pi$
$461$	−10.6861	+	10.6861i	−0.497703	+	0.497703i	0.413019	+	0.910722i	$0.364474\pi$
$462$		0			0
$463$	−15.5271			−0.721607			−0.360804	−	0.932642i	$-0.617498\pi$
$463$	−15.5271			−0.721607			−0.360804	+	0.932642i	$0.617498\pi$
$464$	24.7903	−	12.2005i	1.15086	−	0.566394i
$465$		0			0
$466$	1.70454	−	20.7371i	0.0789612	−	0.960629i
$467$	1.69985	−	1.69985i	0.0786598	−	0.0786598i	−0.666682	−	0.745342i	$-0.732286\pi$
$467$	1.69985	−	1.69985i	0.0786598	−	0.0786598i	0.745342	+	0.666682i	$0.232286\pi$
$468$		0			0
$469$	13.8298	+	13.8298i	0.638602	+	0.638602i
$470$	−27.0298	−	31.8713i	−1.24679	−	1.47011i
$471$		0			0
$472$	−10.4575	−	17.4711i	−0.481345	−	0.804174i
$473$		−	5.65324i		−	0.259936i
$474$		0			0
$475$	−7.85220	−	7.85220i	−0.360284	−	0.360284i
$476$	−7.13101	+	43.0843i	−0.326849	+	1.97476i
$477$		0			0
$478$	9.86199	+	0.810630i	0.451077	+	0.0370774i
$479$	−32.1292			−1.46802			−0.734009	−	0.679139i	$-0.762353\pi$
$479$	−32.1292			−1.46802			−0.734009	+	0.679139i	$0.762353\pi$
$480$		0			0
$481$	11.0014			0.501620
$482$	−26.3572	−	2.16650i	−1.20054	−	0.0986812i
$483$		0			0
$484$	1.88478	−	11.3875i	0.0856718	−	0.517613i
$485$	12.3731	+	12.3731i	0.561835	+	0.561835i
$486$		0			0
$487$			18.4662i			0.836784i	0.908267	+	0.418392i	$0.137406\pi$
$487$			18.4662i			0.836784i	−0.908267	+	0.418392i	$0.862594\pi$
$488$	−14.8747	+	8.90336i	−0.673344	+	0.403036i
$489$		0			0
$490$	−36.4908	−	43.0269i	−1.64849	−	1.94376i
$491$	−3.75000	−	3.75000i	−0.169235	−	0.169235i	0.617408	−	0.786643i	$-0.288183\pi$
$491$	−3.75000	−	3.75000i	−0.169235	−	0.169235i	−0.786643	+	0.617408i	$0.788183\pi$
$492$		0			0
$493$	−22.3317	+	22.3317i	−1.00577	+	1.00577i
$494$	−2.58721	+	31.4756i	−0.116404	+	1.41615i
$495$		0			0
$496$	−7.66562	−	2.60899i	−0.344197	−	0.117147i
$497$	31.0794			1.39410
$498$		0			0
$499$	−0.749066	+	0.749066i	−0.0335328	+	0.0335328i	−0.723674	−	0.690142i	$-0.757548\pi$
$499$	−0.749066	+	0.749066i	−0.0335328	+	0.0335328i	0.690142	+	0.723674i	$0.257548\pi$
$500$	−14.9022	+	10.6697i	−0.666446	+	0.477163i
$501$		0			0
$502$	−5.91354	−	6.97276i	−0.263934	−	0.311209i
$503$		−	25.7573i		−	1.14846i	−0.818694	−	0.574231i	$-0.805301\pi$
$503$		−	25.7573i		−	1.14846i	0.818694	−	0.574231i	$-0.194699\pi$
$504$		0			0
$505$			18.3432i			0.816261i
$506$	0.135422	−	0.114851i	0.00602026	−	0.00510573i
$507$		0			0
$508$	33.6467	+	5.56897i	1.49283	+	0.247083i
$509$	5.70060	−	5.70060i	0.252675	−	0.252675i	−0.569392	−	0.822066i	$-0.692821\pi$
$509$	5.70060	−	5.70060i	0.252675	−	0.252675i	0.822066	+	0.569392i	$0.192821\pi$
$510$		0			0
$511$	−46.6309			−2.06283
$512$	−16.7383	−	15.2259i	−0.739737	−	0.672896i
$513$		0			0
$514$	−37.0639	−	3.04656i	−1.63482	−	0.134378i
$515$	8.46723	−	8.46723i	0.373111	−	0.373111i
$516$		0			0
$517$	−18.9328	−	18.9328i	−0.832664	−	0.832664i
$518$	20.5876	−	17.4602i	0.904566	−	0.767155i
$519$		0			0
$520$	−19.0554	−	4.78533i	−0.835635	−	0.209851i
$521$			2.37173i			0.103907i	0.998649	+	0.0519537i	$0.0165448\pi$
$521$			2.37173i			0.103907i	−0.998649	+	0.0519537i	$0.983455\pi$
$522$		0			0
$523$	−18.0719	−	18.0719i	−0.790230	−	0.790230i	0.191301	−	0.981531i	$-0.438729\pi$
$523$	−18.0719	−	18.0719i	−0.790230	−	0.790230i	−0.981531	+	0.191301i	$0.938729\pi$
$524$	−21.4870	+	15.3843i	−0.938663	+	0.672066i
$525$		0			0
$526$	−3.42457	+	41.6627i	−0.149318	+	1.81658i
$527$	9.25559			0.403180
$528$		0			0
$529$	22.9970			0.999869
$530$	−1.20597	+	14.6717i	−0.0523842	+	0.637297i
$531$		0			0
$532$	45.1129	+	63.0084i	1.95589	+	2.73176i
$533$	8.43142	+	8.43142i	0.365205	+	0.365205i
$534$		0			0
$535$			4.06711i			0.175836i
$536$	9.93899	−	5.94907i	0.429299	−	0.256961i
$537$		0			0
$538$	10.4071	−	8.82619i	0.448683	−	0.380524i
$539$	−25.5597	−	25.5597i	−1.10093	−	1.10093i
$540$		0			0
$541$	−19.8404	+	19.8404i	−0.853006	+	0.853006i	−0.990502	−	0.137496i	$-0.956095\pi$
$541$	−19.8404	+	19.8404i	−0.853006	+	0.853006i	0.137496	+	0.990502i	$0.456095\pi$
$542$	−4.62581	−	0.380229i	−0.198695	−	0.0163323i
$543$		0			0
$544$	23.7195	+	10.3111i	1.01696	+	0.442084i
$545$	−9.09178			−0.389449
$546$		0			0
$547$	20.6820	−	20.6820i	0.884300	−	0.884300i	−0.109668	−	0.993968i	$-0.534979\pi$
$547$	20.6820	−	20.6820i	0.884300	−	0.884300i	0.993968	+	0.109668i	$0.0349788\pi$
$548$	2.52598	−	15.2615i	0.107904	−	0.651938i
$549$		0			0
$550$	3.37565	−	2.86286i	0.143938	−	0.122073i
$551$			56.0420i			2.38747i
$552$		0			0
$553$			12.2018i			0.518872i
$554$	15.4557	+	18.2241i	0.656651	+	0.774269i
$555$		0			0
$556$	1.49424	+	2.08698i	0.0633699	+	0.0885076i
$557$	−6.06679	+	6.06679i	−0.257058	+	0.257058i	−0.823857	−	0.566798i	$-0.808182\pi$
$557$	−6.06679	+	6.06679i	−0.257058	+	0.257058i	0.566798	+	0.823857i	$0.308182\pi$
$558$		0			0
$559$	6.80494			0.287818
$560$	−43.2543	+	21.2875i	−1.82783	+	0.899562i
$561$		0			0
$562$	−3.65117	+	44.4196i	−0.154015	+	1.87373i
$563$	−19.2415	+	19.2415i	−0.810933	+	0.810933i	−0.984774	−	0.173841i	$-0.944382\pi$
$563$	−19.2415	+	19.2415i	−0.810933	+	0.810933i	0.173841	+	0.984774i	$0.444382\pi$
$564$		0			0
$565$	−16.7680	−	16.7680i	−0.705436	−	0.705436i
$566$	−25.0082	−	29.4876i	−1.05117	−	1.23946i
$567$		0			0
$568$	4.48322	−	17.8524i	0.188112	−	0.749070i
$569$			17.7984i			0.746147i	0.927802	+	0.373073i	$0.121696\pi$
$569$			17.7984i			0.746147i	−0.927802	+	0.373073i	$0.878304\pi$
$570$		0			0
$571$	−2.48654	−	2.48654i	−0.104058	−	0.104058i	0.653161	−	0.757219i	$-0.273443\pi$
$571$	−2.48654	−	2.48654i	−0.104058	−	0.104058i	−0.757219	+	0.653161i	$0.773443\pi$
$572$	−12.4191	−	2.05552i	−0.519268	−	0.0859456i
$573$		0			0
$574$	29.1597	+	2.39685i	1.21710	+	0.100043i
$575$	−0.0751551			−0.00313418
$576$		0			0
$577$	26.8106			1.11614			0.558070	−	0.829794i	$-0.311542\pi$
$577$	26.8106			1.11614			0.558070	+	0.829794i	$0.311542\pi$
$578$	−5.50274	−	0.452311i	−0.228884	−	0.0188136i
$579$		0			0
$580$	−34.3959	−	5.69298i	−1.42821	−	0.236388i
$581$	−41.0382	−	41.0382i	−1.70255	−	1.70255i
$582$		0			0
$583$			9.43196i			0.390632i
$584$	−6.72653	+	26.7854i	−0.278346	+	1.10839i
$585$		0			0
$586$	16.6058	+	19.5802i	0.685979	+	0.808851i
$587$	−9.36505	−	9.36505i	−0.386537	−	0.386537i	0.486913	−	0.873450i	$-0.338123\pi$
$587$	−9.36505	−	9.36505i	−0.386537	−	0.386537i	−0.873450	+	0.486913i	$0.838123\pi$
$588$		0			0
$589$	11.6136	−	11.6136i	0.478530	−	0.478530i
$590$	−2.10478	+	25.6064i	−0.0866523	+	1.05420i
$591$		0			0
$592$	−7.05956	−	14.3444i	−0.290146	−	0.589551i
$593$	−0.951289			−0.0390648			−0.0195324	−	0.999809i	$-0.506218\pi$
$593$	−0.951289			−0.0390648			−0.0195324	+	0.999809i	$0.506218\pi$
$594$		0			0
$595$	38.9644	−	38.9644i	1.59739	−	1.59739i
$596$	−13.1876	−	18.4188i	−0.540183	−	0.754465i
$597$		0			0
$598$	0.138248	+	0.163011i	0.00565339	+	0.00666602i
$599$			8.25825i			0.337423i	0.985665	+	0.168711i	$0.0539606\pi$
$599$			8.25825i			0.337423i	−0.985665	+	0.168711i	$0.946039\pi$
$600$		0			0
$601$		−	38.9645i		−	1.58940i	−0.607005	−	0.794698i	$-0.707629\pi$
$601$		−	38.9645i		−	1.58940i	0.607005	−	0.794698i	$-0.292371\pi$
$602$	12.7345	−	10.8000i	0.519020	−	0.440176i
$603$		0			0
$604$	5.79306	−	35.0006i	0.235716	−	1.42416i
$605$	−10.2986	+	10.2986i	−0.418697	+	0.418697i
$606$		0			0
$607$	−0.766686			−0.0311188			−0.0155594	−	0.999879i	$-0.504953\pi$
$607$	−0.766686			−0.0311188			−0.0155594	+	0.999879i	$0.504953\pi$
$608$	42.7004	−	16.8244i	1.73173	−	0.682321i
$609$		0			0
$610$	21.8009	+	1.79198i	0.882692	+	0.0725550i
$611$	22.7899	−	22.7899i	0.921980	−	0.921980i
$612$		0			0
$613$	−17.1693	−	17.1693i	−0.693461	−	0.693461i	0.269531	−	0.962992i	$-0.413131\pi$
$613$	−17.1693	−	17.1693i	−0.693461	−	0.693461i	−0.962992	+	0.269531i	$0.913131\pi$
$614$	11.6501	−	9.88036i	0.470160	−	0.398739i
$615$		0			0
$616$	−26.5029	+	15.8635i	−1.06783	+	0.639160i
$617$			19.3721i			0.779890i	0.920838	+	0.389945i	$0.127506\pi$
$617$			19.3721i			0.779890i	−0.920838	+	0.389945i	$0.872494\pi$
$618$		0			0
$619$	21.2390	+	21.2390i	0.853667	+	0.853667i	0.990583	−	0.136916i	$-0.0437190\pi$
$619$	21.2390	+	21.2390i	0.853667	+	0.853667i	−0.136916	+	0.990583i	$0.543719\pi$
$620$	5.94812	+	8.30763i	0.238882	+	0.333643i
$621$		0			0
$622$	−0.336678	+	4.09597i	−0.0134996	+	0.164233i
$623$	−48.3238			−1.93605
$624$		0			0
$625$	29.9702			1.19881
$626$	2.01385	−	24.5001i	0.0804895	−	0.979222i
$627$		0			0
$628$	39.5014	−	28.2823i	1.57628	−	1.12859i
$629$	12.9217	+	12.9217i	0.515223	+	0.515223i
$630$		0			0
$631$		−	10.6793i		−	0.425137i	−0.977146	−	0.212568i	$-0.931817\pi$
$631$		−	10.6793i		−	0.425137i	0.977146	−	0.212568i	$-0.0681828\pi$
$632$	7.00885	+	1.76011i	0.278797	+	0.0700135i
$633$		0			0
$634$	1.76942	−	1.50063i	0.0702725	−	0.0595975i
$635$	−30.4293	−	30.4293i	−1.20755	−	1.20755i
$636$		0			0
$637$	30.7668	−	30.7668i	1.21903	−	1.21903i
$638$	−22.2625	−	1.82992i	−0.881380	−	0.0724471i
$639$		0			0
$640$	5.98836	+	27.9166i	0.236711	+	1.10350i
$641$	14.7990			0.584526			0.292263	−	0.956338i	$-0.405592\pi$
$641$	14.7990			0.584526			0.292263	+	0.956338i	$0.405592\pi$
$642$		0			0
$643$	−33.5447	+	33.5447i	−1.32287	+	1.32287i	−0.411432	+	0.911441i	$0.634971\pi$
$643$	−33.5447	+	33.5447i	−1.32287	+	1.32287i	−0.911441	+	0.411432i	$0.865029\pi$
$644$	0.517426	+	0.0856408i	0.0203894	+	0.00337472i
$645$		0			0
$646$	−40.0087	+	33.9310i	−1.57412	+	1.33500i
$647$			37.2920i			1.46610i	0.680174	+	0.733051i	$0.261904\pi$
$647$			37.2920i			1.46610i	−0.680174	+	0.733051i	$0.738096\pi$
$648$		0			0
$649$			16.4615i			0.646171i
$650$	3.44609	+	4.06335i	0.135167	+	0.159378i
$651$		0			0
$652$	−9.07246	+	6.49572i	−0.355305	+	0.254392i
$653$	−22.8982	+	22.8982i	−0.896075	+	0.896075i	−0.995086	−	0.0990113i	$-0.968432\pi$
$653$	−22.8982	+	22.8982i	−0.896075	+	0.896075i	0.0990113	+	0.995086i	$0.468432\pi$
$654$		0			0
$655$	33.3455			1.30292
$656$	5.58308	−	16.4039i	0.217983	−	0.640466i
$657$		0			0
$658$	6.47861	−	78.8177i	0.252563	−	3.07263i
$659$	9.53009	−	9.53009i	0.371239	−	0.371239i	−0.496689	−	0.867929i	$-0.665451\pi$
$659$	9.53009	−	9.53009i	0.371239	−	0.371239i	0.867929	+	0.496689i	$0.165451\pi$
$660$		0			0
$661$	−5.40368	−	5.40368i	−0.210179	−	0.210179i	0.594165	−	0.804343i	$-0.297483\pi$
$661$	−5.40368	−	5.40368i	−0.210179	−	0.210179i	−0.804343	+	0.594165i	$0.797483\pi$
$662$	9.49949	+	11.2010i	0.369208	+	0.435340i
$663$		0			0
$664$	−29.4926	+	17.6531i	−1.14454	+	0.685071i
$665$		−	97.7825i		−	3.79184i
$666$		0			0
$667$	0.268195	+	0.268195i	0.0103845	+	0.0103845i
$668$	4.01617	−	24.2650i	0.155390	−	0.938840i
$669$		0			0
$670$	−14.5670	−	1.19737i	−0.562771	−	0.0462583i
$671$	14.0151			0.541047
$672$		0			0
$673$	36.0565			1.38988			0.694939	−	0.719069i	$-0.255432\pi$
$673$	36.0565			1.38988			0.694939	+	0.719069i	$0.255432\pi$
$674$	14.2818	+	1.17393i	0.550115	+	0.0452180i
$675$		0			0
$676$	−1.77130	+	10.7019i	−0.0681270	+	0.411611i
$677$	−20.3823	−	20.3823i	−0.783357	−	0.783357i	0.197038	−	0.980396i	$-0.436868\pi$
$677$	−20.3823	−	20.3823i	−0.783357	−	0.783357i	−0.980396	+	0.197038i	$0.936868\pi$
$678$		0			0
$679$			33.1139i			1.27079i
$680$	−16.7610	−	28.0023i	−0.642756	−	1.07384i
$681$		0			0
$682$	4.23424	+	4.99267i	0.162137	+	0.191179i
$683$	34.0116	+	34.0116i	1.30142	+	1.30142i	0.927436	+	0.373981i	$0.122007\pi$
$683$	34.0116	+	34.0116i	1.30142	+	1.30142i	0.373981	+	0.927436i	$0.377993\pi$
$684$		0			0
$685$	−13.8021	+	13.8021i	−0.527352	+	0.527352i
$686$	4.87324	−	59.2870i	0.186061	−	2.26359i
$687$		0			0
$688$	−4.36671	−	8.87277i	−0.166479	−	0.338271i
$689$	−11.3535			−0.432533
$690$		0			0
$691$	19.5942	−	19.5942i	0.745400	−	0.745400i	−0.228212	−	0.973612i	$-0.573288\pi$
$691$	19.5942	−	19.5942i	0.745400	−	0.745400i	0.973612	+	0.228212i	$0.0732878\pi$
$692$	−24.9899	+	17.8923i	−0.949973	+	0.680164i
$693$		0			0
$694$	−21.9674	−	25.9022i	−0.833872	−	0.983233i
$695$		−	3.23877i		−	0.122854i
$696$		0			0
$697$			19.8064i			0.750220i
$698$	−6.78825	+	5.75706i	−0.256939	+	0.217908i
$699$		0			0
$700$	12.8978	+	2.13475i	0.487491	+	0.0806861i
$701$	−2.97652	+	2.97652i	−0.112422	+	0.112422i	−0.761080	−	0.648658i	$-0.775330\pi$
$701$	−2.97652	+	2.97652i	−0.112422	+	0.112422i	0.648658	+	0.761080i	$0.275330\pi$
$702$		0			0
$703$	32.4275			1.22303
$704$	5.28916	+	17.5119i	0.199343	+	0.660005i
$705$		0			0
$706$	47.1804	+	3.87810i	1.77566	+	0.145954i
$707$	−24.5457	+	24.5457i	−0.923136	+	0.923136i
$708$		0			0
$709$	−28.1306	−	28.1306i	−1.05647	−	1.05647i	−0.998307	−	0.0581584i	$-0.981477\pi$
$709$	−28.1306	−	28.1306i	−1.05647	−	1.05647i	−0.0581584	−	0.998307i	$-0.518523\pi$
$710$	−17.7134	+	15.0226i	−0.664772	+	0.563787i
$711$		0			0
$712$	−6.97073	+	27.7578i	−0.261239	+	1.04027i
$713$		−	0.111156i		−	0.00416283i
$714$		0			0
$715$	11.2315	+	11.2315i	0.420035	+	0.420035i
$716$	2.62073	−	1.87640i	0.0979415	−	0.0701244i
$717$		0			0
$718$	−1.33884	+	16.2881i	−0.0499651	+	0.607866i
$719$	40.0816			1.49479			0.747396	−	0.664379i	$-0.231304\pi$
$719$	40.0816			1.49479			0.747396	+	0.664379i	$0.231304\pi$
$720$		0			0
$721$	22.6606			0.843926
$722$	−5.42480	+	65.9973i	−0.201890	+	2.45616i
$723$		0			0
$724$	−4.96635	−	6.93642i	−0.184573	−	0.257790i
$725$	6.68525	+	6.68525i	0.248284	+	0.248284i
$726$		0			0
$727$			26.2537i			0.973696i	0.873487	+	0.486848i	$0.161853\pi$
$727$			26.2537i			0.973696i	−0.873487	+	0.486848i	$0.838147\pi$
$728$	−19.0953	−	31.9022i	−0.707720	−	1.18237i
$729$		0			0
$730$	26.5768	−	22.5396i	0.983652	−	0.834227i
$731$	7.99278	+	7.99278i	0.295624	+	0.295624i
$732$		0			0
$733$	−21.3204	+	21.3204i	−0.787488	+	0.787488i	−0.981082	−	0.193594i	$-0.937986\pi$
$733$	−21.3204	+	21.3204i	−0.787488	+	0.787488i	0.193594	+	0.981082i	$0.437986\pi$
$734$	−0.604809	−	0.0497137i	−0.0223239	−	0.00183497i
$735$		0			0
$736$	0.123832	−	0.284862i	0.00456451	−	0.0105002i
$737$	−9.36464			−0.344951
$738$		0			0
$739$	7.69784	−	7.69784i	0.283170	−	0.283170i	−0.551202	−	0.834372i	$-0.685831\pi$
$739$	7.69784	−	7.69784i	0.283170	−	0.283170i	0.834372	+	0.551202i	$0.185831\pi$
$740$	−3.29412	+	19.9025i	−0.121094	+	0.731629i
$741$		0			0
$742$	−21.2465	+	18.0190i	−0.779982	+	0.661497i
$743$			44.2909i			1.62488i	0.583047	+	0.812438i	$0.301860\pi$
$743$			44.2909i			1.62488i	−0.583047	+	0.812438i	$0.698140\pi$
$744$		0			0
$745$			28.5841i			1.04724i
$746$	16.5213	+	19.4805i	0.604886	+	0.713232i
$747$		0			0
$748$	−12.1726	−	17.0012i	−0.445074	−	0.621627i
$749$	−5.44234	+	5.44234i	−0.198859	+	0.198859i
$750$		0			0
$751$	−26.5577			−0.969102			−0.484551	−	0.874763i	$-0.661017\pi$
$751$	−26.5577			−0.969102			−0.484551	+	0.874763i	$0.661017\pi$
$752$	−44.3393	−	15.0909i	−1.61689	−	0.550308i
$753$		0			0
$754$	2.20271	−	26.7979i	0.0802181	−	0.975920i
$755$	−31.6538	+	31.6538i	−1.15200	+	1.15200i
$756$		0			0
$757$	−0.900800	−	0.900800i	−0.0327401	−	0.0327401i	0.690547	−	0.723287i	$-0.257370\pi$
$757$	−0.900800	−	0.900800i	−0.0327401	−	0.0327401i	−0.723287	+	0.690547i	$0.757370\pi$
$758$	24.8815	+	29.3382i	0.903736	+	1.06561i
$759$		0			0
$760$	−56.1675	−	14.1052i	−2.03741	−	0.511648i
$761$			3.79604i			0.137606i	0.997630	+	0.0688031i	$0.0219180\pi$
$761$			3.79604i			0.137606i	−0.997630	+	0.0688031i	$0.978082\pi$
$762$		0			0
$763$	−12.1660	−	12.1660i	−0.440440	−	0.440440i
$764$	2.79266	+	0.462221i	0.101035	+	0.0167226i
$765$		0			0
$766$	−42.0180	−	3.45377i	−1.51817	−	0.124790i
$767$	−19.8151			−0.715483
$768$		0			0
$769$	15.1181			0.545174			0.272587	−	0.962131i	$-0.412121\pi$
$769$	15.1181			0.545174			0.272587	+	0.962131i	$0.412121\pi$
$770$	38.8437	+	3.19285i	1.39983	+	0.115062i
$771$		0			0
$772$	20.0353	+	3.31611i	0.721088	+	0.119349i
$773$	−15.6773	−	15.6773i	−0.563875	−	0.563875i	0.366531	−	0.930406i	$-0.380545\pi$
$773$	−15.6773	−	15.6773i	−0.563875	−	0.563875i	−0.930406	+	0.366531i	$0.880545\pi$
$774$		0			0
$775$		−	2.77077i		−	0.0995290i
$776$	19.0210	+	4.77669i	0.682815	+	0.171473i
$777$		0			0
$778$	−27.2173	−	32.0924i	−0.975788	−	1.15057i
$779$	24.8523	+	24.8523i	0.890428	+	0.890428i
$780$		0			0
$781$	−10.5225	+	10.5225i	−0.376523	+	0.376523i
$782$	−0.0290852	+	0.353846i	−0.00104009	+	0.0126535i
$783$		0			0
$784$	−59.8590	−	20.3730i	−2.13782	−	0.727608i
$785$	−61.3020			−2.18796
$786$		0			0
$787$	3.20620	−	3.20620i	0.114289	−	0.114289i	−0.647650	−	0.761938i	$-0.724248\pi$
$787$	3.20620	−	3.20620i	0.114289	−	0.114289i	0.761938	+	0.647650i	$0.224248\pi$
$788$	−6.25113	−	8.73084i	−0.222687	−	0.311023i
$789$		0			0
$790$	−5.89786	−	6.95428i	−0.209837	−	0.247422i
$791$		−	44.8758i		−	1.59560i
$792$		0			0
$793$			16.8703i			0.599082i
$794$	−32.5106	+	27.5719i	−1.15376	+	0.978491i
$795$		0			0
$796$	3.28529	−	19.8491i	0.116444	−	0.703534i
$797$	23.8504	−	23.8504i	0.844825	−	0.844825i	−0.144657	−	0.989482i	$-0.546208\pi$
$797$	23.8504	−	23.8504i	0.844825	−	0.844825i	0.989482	+	0.144657i	$0.0462078\pi$
$798$		0			0
$799$	53.5360			1.89397
$800$	3.08674	−	7.10071i	0.109133	−	0.251048i
$801$		0			0
$802$	34.4587	+	2.83242i	1.21678	+	0.100016i
$803$	15.7877	−	15.7877i	0.557135	−	0.557135i
$804$		0			0
$805$	−0.467948	−	0.467948i	−0.0164930	−	0.0164930i
$806$	−6.00979	+	5.09686i	−0.211686	+	0.179529i
$807$		0			0
$808$	10.5586	+	17.6401i	0.371451	+	0.620576i
$809$			0.0416430i			0.00146409i	1.00000		0.000732045i	$0.000233017\pi$
$809$			0.0416430i			0.00146409i	−1.00000		0.000732045i	$0.999767\pi$
$810$		0			0
$811$	20.2999	+	20.2999i	0.712827	+	0.712827i	0.967126	−	0.254299i	$-0.0818446\pi$
$811$	20.2999	+	20.2999i	0.712827	+	0.712827i	−0.254299	+	0.967126i	$0.581845\pi$
$812$	−38.4085	−	53.6444i	−1.34787	−	1.88255i
$813$		0			0
$814$	−1.05884	+	12.8817i	−0.0371124	+	0.451503i
$815$	14.0795			0.493184
$816$		0			0
$817$	20.0581			0.701745
$818$	1.01781	−	12.3825i	0.0355867	−	0.432942i
$819$		0			0
$820$	−17.7778	+	12.7286i	−0.620828	+	0.444502i
$821$	−6.87984	−	6.87984i	−0.240108	−	0.240108i	0.576787	−	0.816895i	$-0.304306\pi$
$821$	−6.87984	−	6.87984i	−0.240108	−	0.240108i	−0.816895	+	0.576787i	$0.804306\pi$
$822$		0			0
$823$			16.9089i			0.589407i	0.955589	+	0.294704i	$0.0952209\pi$
$823$			16.9089i			0.589407i	−0.955589	+	0.294704i	$0.904779\pi$
$824$	3.26881	−	13.0165i	0.113874	−	0.453453i
$825$		0			0
$826$	−37.0813	+	31.4483i	−1.29022	+	1.09423i
$827$	−25.6816	−	25.6816i	−0.893038	−	0.893038i	0.101770	−	0.994808i	$-0.467550\pi$
$827$	−25.6816	−	25.6816i	−0.893038	−	0.893038i	−0.994808	+	0.101770i	$0.967550\pi$
$828$		0			0
$829$	−6.78542	+	6.78542i	−0.235667	+	0.235667i	−0.815053	−	0.579386i	$-0.803292\pi$
$829$	−6.78542	+	6.78542i	−0.235667	+	0.235667i	0.579386	+	0.815053i	$0.303292\pi$
$830$	43.2255	+	3.55303i	1.50038	+	0.123327i
$831$		0			0
$832$	−21.0795	+	6.36669i	−0.730801	+	0.220725i
$833$	72.2747			2.50417
$834$		0			0
$835$	−21.9447	+	21.9447i	−0.759427	+	0.759427i
$836$	−36.6063	−	6.05882i	−1.26606	−	0.209549i
$837$		0			0
$838$	25.7770	−	21.8613i	0.890452	−	0.755185i
$839$			27.1441i			0.937119i	0.883432	+	0.468559i	$0.155227\pi$
$839$			27.1441i			0.937119i	−0.883432	+	0.468559i	$0.844773\pi$
$840$		0			0
$841$		−	18.7133i		−	0.645288i
$842$	−19.2624	−	22.7127i	−0.663827	−	0.782730i
$843$		0			0
$844$	−15.1683	+	10.8603i	−0.522116	+	0.373826i
$845$	9.67854	−	9.67854i	0.332952	−	0.332952i
$846$		0			0
$847$	−27.5618			−0.947036
$848$	7.28550	+	14.8035i	0.250185	+	0.508354i
$849$		0			0
$850$	−0.725003	+	8.82027i	−0.0248674	+	0.302533i
$851$	0.155185	−	0.155185i	0.00531968	−	0.00531968i
$852$		0			0
$853$	−15.0466	−	15.0466i	−0.515186	−	0.515186i	0.400925	−	0.916111i	$-0.368689\pi$
$853$	−15.0466	−	15.0466i	−0.515186	−	0.515186i	−0.916111	+	0.400925i	$0.868689\pi$
$854$	26.7747	+	31.5705i	0.916210	+	1.08032i
$855$		0			0
$856$	2.34109	+	3.91121i	0.0800168	+	0.133682i
$857$		−	47.1788i		−	1.61160i	−0.592190	−	0.805798i	$-0.701736\pi$
$857$		−	47.1788i		−	1.61160i	0.592190	−	0.805798i	$-0.298264\pi$
$858$		0			0
$859$	−11.1674	−	11.1674i	−0.381027	−	0.381027i	0.490445	−	0.871472i	$-0.336834\pi$
$859$	−11.1674	−	11.1674i	−0.381027	−	0.381027i	−0.871472	+	0.490445i	$0.836834\pi$
$860$	−2.03759	+	12.3107i	−0.0694812	+	0.419793i
$861$		0			0
$862$	−30.5888	−	2.51432i	−1.04186	−	0.0856380i
$863$	−5.49973			−0.187213			−0.0936065	−	0.995609i	$-0.529840\pi$
$863$	−5.49973			−0.187213			−0.0936065	+	0.995609i	$0.529840\pi$
$864$		0			0
$865$	38.7817			1.31862
$866$	51.9763	+	4.27231i	1.76623	+	0.145179i
$867$		0			0
$868$	−3.15735	+	19.0761i	−0.107167	+	0.647486i
$869$	−4.13112	−	4.13112i	−0.140139	−	0.140139i
$870$		0			0
$871$		−	11.2724i		−	0.381952i
$872$	−8.74328	+	5.23337i	−0.296085	+	0.177224i
$873$		0			0
$874$	0.407499	+	0.480489i	0.0137839	+	0.0162528i
$875$	30.9466	+	30.9466i	1.04619	+	1.04619i
$876$		0			0
$877$	3.57280	−	3.57280i	0.120645	−	0.120645i	−0.644207	−	0.764852i	$-0.722812\pi$
$877$	3.57280	−	3.57280i	0.120645	−	0.120645i	0.764852	+	0.644207i	$0.222812\pi$
$878$	1.69458	−	20.6160i	0.0571894	−	0.695757i
$879$		0			0
$880$	7.43724	−	21.8517i	0.250709	−	0.736622i
$881$	−5.28112			−0.177925			−0.0889627	−	0.996035i	$-0.528355\pi$
$881$	−5.28112			−0.177925			−0.0889627	+	0.996035i	$0.528355\pi$
$882$		0			0
$883$	−20.7335	+	20.7335i	−0.697736	+	0.697736i	−0.963922	−	0.266185i	$-0.914237\pi$
$883$	−20.7335	+	20.7335i	−0.697736	+	0.697736i	0.266185	+	0.963922i	$0.414237\pi$
$884$	20.4648	−	14.6524i	0.688305	−	0.492814i
$885$		0			0
$886$	−0.0376248	−	0.0443641i	−0.00126403	−	0.00149044i
$887$			5.09406i			0.171042i	0.996336	+	0.0855208i	$0.0272554\pi$
$887$			5.09406i			0.171042i	−0.996336	+	0.0855208i	$0.972745\pi$
$888$		0			0
$889$		−	81.4372i		−	2.73132i
$890$	27.5416	−	23.3578i	0.923198	−	0.782956i
$891$		0			0
$892$	−3.82582	−	0.633223i	−0.128098	−	0.0212019i
$893$	67.1751	−	67.1751i	2.24793	−	2.24793i
$894$		0			0
$895$	−4.06711			−0.135948
$896$	−29.3429	+	45.3694i	−0.980279	+	1.51569i
$897$		0			0
$898$	−51.5408	−	4.23652i	−1.71994	−	0.141375i
$899$	−9.88764	+	9.88764i	−0.329771	+	0.329771i
$900$		0			0
$901$	−13.3353	−	13.3353i	−0.444263	−	0.444263i
$902$	−10.6840	+	9.06100i	−0.355738	+	0.301698i
$903$		0			0
$904$	−25.7772	−	6.47336i	−0.857338	−	0.215301i
$905$			10.7646i			0.357827i
$906$		0			0
$907$	10.3597	+	10.3597i	0.343987	+	0.343987i	0.857864	−	0.513877i	$-0.171791\pi$
$907$	10.3597	+	10.3597i	0.343987	+	0.343987i	−0.513877	+	0.857864i	$0.671791\pi$
$908$	0.312663	−	0.223861i	0.0103761	−	0.00742909i
$909$		0			0
$910$	−3.84331	+	46.7571i	−0.127404	+	1.54998i
$911$	20.8084			0.689413			0.344706	−	0.938711i	$-0.387978\pi$
$911$	20.8084			0.689413			0.344706	+	0.938711i	$0.387978\pi$
$912$		0			0
$913$	27.7883			0.919659
$914$	2.04171	−	24.8391i	0.0675338	−	0.821605i
$915$		0			0
$916$	5.68729	+	7.94334i	0.187913	+	0.262455i
$917$	44.6209	+	44.6209i	1.47351	+	1.47351i
$918$		0			0
$919$		−	28.7774i		−	0.949280i	−0.880180	−	0.474640i	$-0.842578\pi$
$919$		−	28.7774i		−	0.949280i	0.880180	−	0.474640i	$-0.157422\pi$
$920$	−0.336297	+	0.201293i	−0.0110874	+	0.00663645i
$921$		0			0
$922$	16.2997	−	13.8236i	0.536802	−	0.455257i
$923$	−12.6661	−	12.6661i	−0.416911	−	0.416911i
$924$		0			0
$925$	3.86828	−	3.86828i	0.127188	−	0.127188i
$926$	21.8849	+	1.79888i	0.719182	+	0.0591149i
$927$		0			0
$928$	−36.3545	+	14.3241i	−1.19339	+	0.470211i
$929$	57.3646			1.88207			0.941035	−	0.338309i	$-0.109855\pi$
$929$	57.3646			1.88207			0.941035	+	0.338309i	$0.109855\pi$
$930$		0			0
$931$	90.6878	−	90.6878i	2.97217	−	2.97217i
$932$	−4.80496	+	29.0307i	−0.157392	+	0.950931i
$933$		0			0
$934$	−2.59281	+	2.19894i	−0.0848393	+	0.0719515i
$935$			26.3841i			0.862853i
$936$		0			0
$937$			53.0719i			1.73378i	0.498495	+	0.866892i	$0.333886\pi$
$937$			53.0719i			1.73378i	−0.498495	+	0.866892i	$0.666114\pi$
$938$	−17.8904	−	21.0948i	−0.584141	−	0.688771i
$939$		0			0
$940$	34.4050	+	48.0528i	1.12217	+	1.56731i
$941$	21.3060	−	21.3060i	0.694555	−	0.694555i	−0.268675	−	0.963231i	$-0.586586\pi$
$941$	21.3060	−	21.3060i	0.694555	−	0.694555i	0.963231	+	0.268675i	$0.0865859\pi$
$942$		0			0
$943$	0.237867			0.00774601
$944$	12.7153	+	25.8364i	0.413849	+	0.840903i
$945$		0			0
$946$	−0.654950	+	7.96801i	−0.0212943	+	0.259062i
$947$	−4.14066	+	4.14066i	−0.134554	+	0.134554i	−0.771176	−	0.636622i	$-0.780331\pi$
$947$	−4.14066	+	4.14066i	−0.134554	+	0.134554i	0.636622	+	0.771176i	$0.280331\pi$
$948$		0			0
$949$	19.0040	+	19.0040i	0.616896	+	0.616896i
$950$	10.1577	+	11.9771i	0.329558	+	0.388588i
$951$		0			0
$952$	15.0424	−	59.8994i	0.487526	−	1.94135i
$953$			18.2687i			0.591783i	0.955222	+	0.295891i	$0.0956167\pi$
$953$			18.2687i			0.591783i	−0.955222	+	0.295891i	$0.904383\pi$
$954$		0			0
$955$	−2.52561	−	2.52561i	−0.0817269	−	0.0817269i
$956$	−13.8062	−	2.28510i	−0.446523	−	0.0739055i
$957$		0			0
$958$	45.2848	+	3.72229i	1.46308	+	0.120262i
$959$	−36.9383			−1.19280
$960$		0			0
$961$	−26.9020			−0.867805
$962$	−15.5060	−	1.27455i	−0.499933	−	0.0410932i
$963$		0			0
$964$	36.8985	+	6.10718i	1.18842	+	0.196699i
$965$	−18.1195	−	18.1195i	−0.583287	−	0.583287i
$966$		0			0
$967$			23.2449i			0.747505i	0.927528	+	0.373753i	$0.121929\pi$
$967$			23.2449i			0.747505i	−0.927528	+	0.373753i	$0.878071\pi$
$968$	−3.97581	+	15.8319i	−0.127787	+	0.508855i
$969$		0			0
$970$	−16.0060	−	18.8729i	−0.513920	−	0.605972i
$971$	30.9576	+	30.9576i	0.993477	+	0.993477i	0.999979	−	0.00650176i	$-0.00206959\pi$
$971$	30.9576	+	30.9576i	0.993477	+	0.993477i	−0.00650176	+	0.999979i	$0.502070\pi$
$972$		0			0
$973$	4.33392	−	4.33392i	0.138939	−	0.138939i
$974$	2.13938	−	26.0274i	0.0685503	−	0.833972i
$975$		0			0
$976$	21.9967	−	10.8256i	0.704098	−	0.346520i
$977$	6.57724			0.210425			0.105212	−	0.994450i	$-0.466448\pi$
$977$	6.57724			0.210425			0.105212	+	0.994450i	$0.466448\pi$
$978$		0			0
$979$	16.3608	−	16.3608i	0.522894	−	0.522894i
$980$	46.4475	+	64.8724i	1.48371	+	2.07227i
$981$		0			0
$982$	4.85102	+	5.71993i	0.154802	+	0.182530i
$983$		−	13.4270i		−	0.428256i	−0.976806	−	0.214128i	$-0.931309\pi$
$983$		−	13.4270i		−	0.428256i	0.976806	−	0.214128i	$-0.0686909\pi$
$984$		0			0
$985$			13.5494i			0.431718i
$986$	34.0628	−	28.8884i	1.08478	−	0.919993i
$987$		0			0
$988$	7.29315	−	44.0639i	0.232026	−	1.40186i
$989$	0.0959903	−	0.0959903i	0.00305231	−	0.00305231i
$990$		0			0
$991$	−32.8217			−1.04261			−0.521307	−	0.853369i	$-0.674556\pi$
$991$	−32.8217			−1.04261			−0.521307	+	0.853369i	$0.674556\pi$
$992$	10.5021	+	4.56536i	0.333443	+	0.144950i
$993$		0			0
$994$	−43.8052	−	3.60067i	−1.38942	−	0.114206i
$995$	−17.9511	+	17.9511i	−0.569089	+	0.569089i
$996$		0			0
$997$	−9.52294	−	9.52294i	−0.301595	−	0.301595i	0.540043	−	0.841638i	$-0.318408\pi$
$997$	−9.52294	−	9.52294i	−0.301595	−	0.301595i	−0.841638	+	0.540043i	$0.818408\pi$
$998$	1.14256	−	0.968996i	0.0361671	−	0.0306730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.c.325.1	yes	24
3.2	odd	2	inner	432.2.k.c.325.12	yes	24
4.3	odd	2		1728.2.k.c.433.4		24
12.11	even	2		1728.2.k.c.433.9		24
16.3	odd	4		1728.2.k.c.1297.4		24
16.13	even	4	inner	432.2.k.c.109.1	✓	24
48.29	odd	4	inner	432.2.k.c.109.12	yes	24
48.35	even	4		1728.2.k.c.1297.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.c.109.1	✓	24	16.13	even	4	inner
432.2.k.c.109.12	yes	24	48.29	odd	4	inner
432.2.k.c.325.1	yes	24	1.1	even	1	trivial
432.2.k.c.325.12	yes	24	3.2	odd	2	inner
1728.2.k.c.433.4		24	4.3	odd	2
1728.2.k.c.433.9		24	12.11	even	2
1728.2.k.c.1297.4		24	16.3	odd	4
1728.2.k.c.1297.9		24	48.35	even	4

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40946 - 0.115854i) q^{2} +(1.97316 + 0.326583i) q^{4} +(-1.78448 - 1.78448i) q^{5} -4.77575i q^{7} +(-2.74325 - 0.688904i) q^{8} +O(q^{10})\)	\(q+(-1.40946 - 0.115854i) q^{2} +(1.97316 + 0.326583i) q^{4} +(-1.78448 - 1.78448i) q^{5} -4.77575i q^{7} +(-2.74325 - 0.688904i) q^{8} +(2.30841 + 2.72189i) q^{10} +(1.61691 + 1.61691i) q^{11} +(-1.94631 + 1.94631i) q^{13} +(-0.553289 + 6.73122i) q^{14} +(3.78669 + 1.28880i) q^{16} -4.57210 q^{17} +(-5.73692 + 5.73692i) q^{19} +(-2.93827 - 4.10383i) q^{20} +(-2.09164 - 2.46629i) q^{22} +0.0549093i q^{23} +1.36871i q^{25} +(2.96874 - 2.51776i) q^{26} +(1.55968 - 9.42329i) q^{28} +(4.88433 - 4.88433i) q^{29} -2.02436 q^{31} +(-5.18787 - 2.25521i) q^{32} +(6.44420 + 0.529697i) q^{34} +(-8.52221 + 8.52221i) q^{35} +(-2.82621 - 2.82621i) q^{37} +(8.75061 - 7.42132i) q^{38} +(3.66593 + 6.12460i) q^{40} -4.33200i q^{41} +(-1.74816 - 1.74816i) q^{43} +(2.66236 + 3.71847i) q^{44} +(0.00636145 - 0.0773924i) q^{46} -11.7093 q^{47} -15.8078 q^{49} +(0.158571 - 1.92915i) q^{50} +(-4.47601 + 3.20474i) q^{52} +(2.91666 + 2.91666i) q^{53} -5.77067i q^{55} +(-3.29003 + 13.1011i) q^{56} +(-7.45014 + 6.31840i) q^{58} +(5.09043 + 5.09043i) q^{59} +(4.33392 - 4.33392i) q^{61} +(2.85326 + 0.234530i) q^{62} +(7.05082 + 3.77967i) q^{64} +6.94629 q^{65} +(-2.89585 + 2.89585i) q^{67} +(-9.02148 - 1.49317i) q^{68} +(12.9990 - 11.0244i) q^{70} +6.50776i q^{71} -9.76411i q^{73} +(3.65600 + 4.31086i) q^{74} +(-13.1934 + 9.44626i) q^{76} +(7.72195 - 7.72195i) q^{77} -2.55495 q^{79} +(-4.45742 - 9.05709i) q^{80} +(-0.501880 + 6.10578i) q^{82} +(8.59304 - 8.59304i) q^{83} +(8.15881 + 8.15881i) q^{85} +(2.26143 + 2.66650i) q^{86} +(-3.32169 - 5.54948i) q^{88} -10.1186i q^{89} +(9.29509 + 9.29509i) q^{91} +(-0.0179324 + 0.108345i) q^{92} +(16.5037 + 1.35656i) q^{94} +20.4748 q^{95} -6.93376 q^{97} +(22.2804 + 1.83139i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{4}+O(q^{10}) \) 24 * q + 16 * q^4	\( 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) \) 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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