LMFDB - Embedded newform 864.2.v.a.109.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.7
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17722 + 0.783679i) q^{2} +(0.771696 - 1.84512i) q^{4} +(-3.84162 + 1.59125i) q^{5} +(-2.86540 + 2.86540i) q^{7} +(0.537529 + 2.77688i) q^{8} +O(q^{10})$	\(q+(-1.17722 + 0.783679i) q^{2} +(0.771696 - 1.84512i) q^{4} +(-3.84162 + 1.59125i) q^{5} +(-2.86540 + 2.86540i) q^{7} +(0.537529 + 2.77688i) q^{8} +(3.27540 - 4.88384i) q^{10} +(1.44931 + 3.49895i) q^{11} +(0.694364 + 0.287615i) q^{13} +(1.12766 - 5.61876i) q^{14} +(-2.80897 - 2.84775i) q^{16} +6.47207i q^{17} +(0.222052 + 0.0919770i) q^{19} +(-0.0285041 + 8.31622i) q^{20} +(-4.44821 - 2.98324i) q^{22} +(-5.63006 - 5.63006i) q^{23} +(8.69041 - 8.69041i) q^{25} +(-1.04282 + 0.205572i) q^{26} +(3.07581 + 7.49824i) q^{28} +(0.607498 - 1.46663i) q^{29} +2.58386 q^{31} +(5.53850 + 1.15110i) q^{32} +(-5.07202 - 7.61905i) q^{34} +(6.44820 - 15.5673i) q^{35} +(-5.21659 + 2.16078i) q^{37} +(-0.333485 + 0.0657403i) q^{38} +(-6.48369 - 9.81236i) q^{40} +(-4.92361 - 4.92361i) q^{41} +(0.733289 + 1.77032i) q^{43} +(7.57442 + 0.0259616i) q^{44} +(11.0400 + 2.21566i) q^{46} -3.13117i q^{47} -9.42105i q^{49} +(-3.42004 + 17.0410i) q^{50} +(1.06652 - 1.05924i) q^{52} +(-2.43120 - 5.86943i) q^{53} +(-11.1354 - 11.1354i) q^{55} +(-9.49711 - 6.41664i) q^{56} +(0.434207 + 2.20263i) q^{58} +(-0.500271 + 0.207219i) q^{59} +(-0.858724 + 2.07314i) q^{61} +(-3.04177 + 2.02492i) q^{62} +(-7.42212 + 2.98531i) q^{64} -3.12515 q^{65} +(-5.48254 + 13.2360i) q^{67} +(11.9418 + 4.99447i) q^{68} +(4.60884 + 23.3795i) q^{70} +(-4.53047 + 4.53047i) q^{71} +(-0.809706 - 0.809706i) q^{73} +(4.44772 - 6.63185i) q^{74} +(0.341066 - 0.338736i) q^{76} +(-14.1788 - 5.87303i) q^{77} -3.87921i q^{79} +(15.3225 + 6.47019i) q^{80} +(9.65471 + 1.93765i) q^{82} +(4.86848 + 2.01659i) q^{83} +(-10.2987 - 24.8632i) q^{85} +(-2.25060 - 1.50939i) q^{86} +(-8.93711 + 5.90535i) q^{88} +(11.2465 - 11.2465i) q^{89} +(-2.81376 + 1.16550i) q^{91} +(-14.7328 + 6.04347i) q^{92} +(2.45383 + 3.68607i) q^{94} -0.999397 q^{95} +8.17436 q^{97} +(7.38308 + 11.0907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.17722	+	0.783679i	−0.832421	+	0.554144i
$2$	−1.17722	+	0.783679i	−0.832421	+	0.554144i
$3$		0			0
$3$		0			0
$4$	0.771696	−	1.84512i	0.385848	−	0.922562i
$5$	−3.84162	+	1.59125i	−1.71802	+	0.711628i	−0.718147	+	0.695892i	$0.755009\pi$
$5$	−3.84162	+	1.59125i	−1.71802	+	0.711628i	−0.999876	+	0.0157367i	$0.994991\pi$
$6$		0			0
$7$	−2.86540	+	2.86540i	−1.08302	+	1.08302i	−0.0867936	+	0.996226i	$0.527662\pi$
$7$	−2.86540	+	2.86540i	−1.08302	+	1.08302i	−0.996226	+	0.0867936i	$0.972338\pi$
$8$	0.537529	+	2.77688i	0.190045	+	0.981775i
$9$		0			0
$10$	3.27540	−	4.88384i	1.03577	−	1.54441i
$11$	1.44931	+	3.49895i	0.436984	+	1.05497i	0.976985	+	0.213308i	$0.0684238\pi$
$11$	1.44931	+	3.49895i	0.436984	+	1.05497i	−0.540001	+	0.841664i	$0.681576\pi$
$12$		0			0
$13$	0.694364	+	0.287615i	0.192582	+	0.0797701i	0.476890	−	0.878963i	$-0.341764\pi$
$13$	0.694364	+	0.287615i	0.192582	+	0.0797701i	−0.284308	+	0.958733i	$0.591764\pi$
$14$	1.12766	−	5.61876i	0.301378	−	1.50168i
$15$		0			0
$16$	−2.80897	−	2.84775i	−0.702243	−	0.711937i
$17$			6.47207i			1.56971i	0.619681	+	0.784854i	$0.287262\pi$
$17$			6.47207i			1.56971i	−0.619681	+	0.784854i	$0.712738\pi$
$18$		0			0
$19$	0.222052	+	0.0919770i	0.0509422	+	0.0211010i	0.408009	−	0.912978i	$-0.366223\pi$
$19$	0.222052	+	0.0919770i	0.0509422	+	0.0211010i	−0.357067	+	0.934079i	$0.616223\pi$
$20$	−0.0285041	+	8.31622i	−0.00637371	+	1.85956i
$21$		0			0
$22$	−4.44821	−	2.98324i	−0.948362	−	0.636029i
$23$	−5.63006	−	5.63006i	−1.17395	−	1.17395i	−0.981260	−	0.192688i	$-0.938280\pi$
$23$	−5.63006	−	5.63006i	−1.17395	−	1.17395i	−0.192688	−	0.981260i	$-0.561720\pi$
$24$		0			0
$25$	8.69041	−	8.69041i	1.73808	−	1.73808i
$26$	−1.04282	+	0.205572i	−0.204513	+	0.0403160i
$27$		0			0
$28$	3.07581	+	7.49824i	0.581273	+	1.41703i
$29$	0.607498	−	1.46663i	0.112809	−	0.272346i	−0.857384	−	0.514677i	$-0.827912\pi$
$29$	0.607498	−	1.46663i	0.112809	−	0.272346i	0.970194	+	0.242331i	$0.0779119\pi$
$30$		0			0
$31$	2.58386			0.464075			0.232038	−	0.972707i	$-0.425461\pi$
$31$	2.58386			0.464075			0.232038	+	0.972707i	$0.425461\pi$
$32$	5.53850	+	1.15110i	0.979078	+	0.203487i
$33$		0			0
$34$	−5.07202	−	7.61905i	−0.869845	−	1.30666i
$35$	6.44820	−	15.5673i	1.08995	−	2.63136i
$36$		0			0
$37$	−5.21659	+	2.16078i	−0.857602	+	0.355230i	−0.767769	−	0.640727i	$-0.778633\pi$
$37$	−5.21659	+	2.16078i	−0.857602	+	0.355230i	−0.0898327	+	0.995957i	$0.528633\pi$
$38$	−0.333485	+	0.0657403i	−0.0540983	+	0.0106645i
$39$		0			0
$40$	−6.48369	−	9.81236i	−1.02516	−	1.55147i
$41$	−4.92361	−	4.92361i	−0.768939	−	0.768939i	0.208981	−	0.977920i	$-0.432985\pi$
$41$	−4.92361	−	4.92361i	−0.768939	−	0.768939i	−0.977920	+	0.208981i	$0.932985\pi$
$42$		0			0
$43$	0.733289	+	1.77032i	0.111825	+	0.269971i	0.969878	−	0.243591i	$-0.0783256\pi$
$43$	0.733289	+	1.77032i	0.111825	+	0.269971i	−0.858052	+	0.513562i	$0.828326\pi$
$44$	7.57442	+	0.0259616i	1.14189	+	0.00391385i
$45$		0			0
$46$	11.0400	+	2.21566i	1.62775	+	0.326682i
$47$		−	3.13117i		−	0.456728i	−0.973576	−	0.228364i	$-0.926662\pi$
$47$		−	3.13117i		−	0.456728i	0.973576	−	0.228364i	$-0.0733376\pi$
$48$		0			0
$49$		−	9.42105i		−	1.34586i
$50$	−3.42004	+	17.0410i	−0.483666	+	2.40996i
$51$		0			0
$52$	1.06652	−	1.05924i	0.147900	−	0.146890i
$53$	−2.43120	−	5.86943i	−0.333950	−	0.806228i	−0.998271	−	0.0587798i	$-0.981279\pi$
$53$	−2.43120	−	5.86943i	−0.333950	−	0.806228i	0.664321	−	0.747448i	$-0.268721\pi$
$54$		0			0
$55$	−11.1354	−	11.1354i	−1.50150	−	1.50150i
$56$	−9.49711	−	6.41664i	−1.26911	−	0.857459i
$57$		0			0
$58$	0.434207	+	2.20263i	0.0570142	+	0.289219i
$59$	−0.500271	+	0.207219i	−0.0651297	+	0.0269776i	−0.415010	−	0.909817i	$-0.636222\pi$
$59$	−0.500271	+	0.207219i	−0.0651297	+	0.0269776i	0.349881	+	0.936794i	$0.386222\pi$
$60$		0			0
$61$	−0.858724	+	2.07314i	−0.109948	+	0.265439i	−0.969271	−	0.245995i	$-0.920885\pi$
$61$	−0.858724	+	2.07314i	−0.109948	+	0.265439i	0.859323	+	0.511434i	$0.170885\pi$
$62$	−3.04177	+	2.02492i	−0.386306	+	0.257165i
$63$		0			0
$64$	−7.42212	+	2.98531i	−0.927766	+	0.373164i
$65$	−3.12515			−0.387627
$66$		0			0
$67$	−5.48254	+	13.2360i	−0.669799	+	1.61704i	0.112148	+	0.993692i	$0.464227\pi$
$67$	−5.48254	+	13.2360i	−0.669799	+	1.61704i	−0.781947	+	0.623345i	$0.785773\pi$
$68$	11.9418	+	4.99447i	1.44815	+	0.605668i
$69$		0			0
$70$	4.60884	+	23.3795i	0.550861	+	2.79439i
$71$	−4.53047	+	4.53047i	−0.537667	+	0.537667i	−0.922843	−	0.385176i	$-0.874141\pi$
$71$	−4.53047	+	4.53047i	−0.537667	+	0.537667i	0.385176	+	0.922843i	$0.374141\pi$
$72$		0			0
$73$	−0.809706	−	0.809706i	−0.0947690	−	0.0947690i	0.658133	−	0.752902i	$-0.271347\pi$
$73$	−0.809706	−	0.809706i	−0.0947690	−	0.0947690i	−0.752902	+	0.658133i	$0.771347\pi$
$74$	4.44772	−	6.63185i	0.517036	−	0.770936i
$75$		0			0
$76$	0.341066	−	0.338736i	0.0391229	−	0.0388556i
$77$	−14.1788	−	5.87303i	−1.61582	−	0.669294i
$78$		0			0
$79$		−	3.87921i		−	0.436445i	−0.975899	−	0.218223i	$-0.929974\pi$
$79$		−	3.87921i		−	0.436445i	0.975899	−	0.218223i	$-0.0700259\pi$
$80$	15.3225	+	6.47019i	1.71310	+	0.723389i
$81$		0			0
$82$	9.65471	+	1.93765i	1.06618	+	0.213977i
$83$	4.86848	+	2.01659i	0.534385	+	0.221350i	0.633523	−	0.773724i	$-0.281608\pi$
$83$	4.86848	+	2.01659i	0.534385	+	0.221350i	−0.0991375	+	0.995074i	$0.531608\pi$
$84$		0			0
$85$	−10.2987	−	24.8632i	−1.11705	−	2.69679i
$86$	−2.25060	−	1.50939i	−0.242689	−	0.162762i
$87$		0			0
$88$	−8.93711	+	5.90535i	−0.952699	+	0.629513i
$89$	11.2465	−	11.2465i	1.19212	−	1.19212i	0.215652	−	0.976470i	$-0.430812\pi$
$89$	11.2465	−	11.2465i	1.19212	−	1.19212i	0.976470	−	0.215652i	$-0.0691877\pi$
$90$		0			0
$91$	−2.81376	+	1.16550i	−0.294963	+	0.122178i
$92$	−14.7328	+	6.04347i	−1.53601	+	0.630075i
$93$		0			0
$94$	2.45383	+	3.68607i	0.253093	+	0.380190i
$95$	−0.999397			−0.102536
$96$		0			0
$97$	8.17436			0.829980			0.414990	−	0.909826i	$-0.363785\pi$
$97$	8.17436			0.829980			0.414990	+	0.909826i	$0.363785\pi$
$98$	7.38308	+	11.0907i	0.745803	+	1.12033i
$99$		0			0
$100$	−9.32854	−	22.7412i	−0.932854	−	2.27412i
$101$	16.1227	−	6.67825i	1.60427	−	0.664511i	0.612259	−	0.790657i	$-0.290261\pi$
$101$	16.1227	−	6.67825i	1.60427	−	0.664511i	0.992012	+	0.126146i	$0.0402608\pi$
$102$		0			0
$103$	4.54543	−	4.54543i	0.447875	−	0.447875i	−0.446773	−	0.894647i	$-0.647427\pi$
$103$	4.54543	−	4.54543i	0.447875	−	0.447875i	0.894647	+	0.446773i	$0.147427\pi$
$104$	−0.425431	+	2.08277i	−0.0417170	+	0.204232i
$105$		0			0
$106$	7.46180	+	5.00433i	0.724754	+	0.486064i
$107$	5.55019	+	13.3993i	0.536557	+	1.29536i	0.927112	+	0.374784i	$0.122283\pi$
$107$	5.55019	+	13.3993i	0.536557	+	1.29536i	−0.390555	+	0.920579i	$0.627717\pi$
$108$		0			0
$109$	8.42407	+	3.48936i	0.806880	+	0.334221i	0.747708	−	0.664027i	$-0.231154\pi$
$109$	8.42407	+	3.48936i	0.806880	+	0.334221i	0.0591714	+	0.998248i	$0.481154\pi$
$110$	21.8354	+	4.38224i	2.08192	+	0.417831i
$111$		0			0
$112$	16.2088	+	0.111113i	1.53159	+	0.0104992i
$113$		−	8.49618i		−	0.799253i	−0.916678	−	0.399627i	$-0.869140\pi$
$113$		−	8.49618i		−	0.799253i	0.916678	−	0.399627i	$-0.130860\pi$
$114$		0			0
$115$	30.5873	+	12.6697i	2.85228	+	1.18145i
$116$	−2.23731	−	2.25270i	−0.207729	−	0.209158i
$117$		0			0
$118$	0.426536	−	0.635994i	0.0392658	−	0.0585480i
$119$	−18.5451	−	18.5451i	−1.70002	−	1.70002i
$120$		0			0
$121$	−2.36396	+	2.36396i	−0.214905	+	0.214905i
$122$	−0.613771	−	3.11351i	−0.0555682	−	0.281884i
$123$		0			0
$124$	1.99395	−	4.76755i	0.179062	−	0.428138i
$125$	−11.6004	+	28.0057i	−1.03757	+	2.50491i
$126$		0			0
$127$	−3.52454			−0.312753			−0.156376	−	0.987698i	$-0.549981\pi$
$127$	−3.52454			−0.312753			−0.156376	+	0.987698i	$0.549981\pi$
$128$	6.39795	−	9.33093i	0.565505	−	0.824745i
$129$		0			0
$130$	3.67899	−	2.44911i	0.322669	−	0.214801i
$131$	−2.48683	+	6.00375i	−0.217276	+	0.524550i	−0.994508	−	0.104664i	$-0.966623\pi$
$131$	−2.48683	+	6.00375i	−0.217276	+	0.524550i	0.777232	+	0.629214i	$0.216623\pi$
$132$		0			0
$133$	−0.899819	+	0.372717i	−0.0780242	+	0.0323187i
$134$	−3.91863	−	19.8783i	−0.338518	−	1.71722i
$135$		0			0
$136$	−17.9722	+	3.47893i	−1.54110	+	0.298315i
$137$	−11.6777	−	11.6777i	−0.997692	−	0.997692i	0.00230518	−	0.999997i	$-0.499266\pi$
$137$	−11.6777	−	11.6777i	−0.997692	−	0.997692i	−0.999997	+	0.00230518i	$0.999266\pi$
$138$		0			0
$139$	−2.56150	−	6.18400i	−0.217263	−	0.524520i	0.777243	−	0.629201i	$-0.216618\pi$
$139$	−2.56150	−	6.18400i	−0.217263	−	0.524520i	−0.994506	+	0.104681i	$0.966618\pi$
$140$	−23.7476	−	23.9110i	−2.00704	−	2.02085i
$141$		0			0
$142$	1.78293	−	8.88379i	0.149620	−	0.745511i
$143$			2.84639i			0.238027i
$144$		0			0
$145$			6.60090i			0.548175i
$146$	1.58775	+	0.318653i	0.131403	+	0.0263719i
$147$		0			0
$148$	−0.0387061	+	11.2927i	−0.00318162	+	0.928256i
$149$	0.00231794	+	0.00559600i	0.000189893	+	0.000458442i	0.923974	−	0.382454i	$-0.124921\pi$
$149$	0.00231794	+	0.00559600i	0.000189893	+	0.000458442i	−0.923785	+	0.382913i	$0.874921\pi$
$150$		0			0
$151$	4.76738	+	4.76738i	0.387964	+	0.387964i	0.873961	−	0.485997i	$-0.161543\pi$
$151$	4.76738	+	4.76738i	0.387964	+	0.387964i	−0.485997	+	0.873961i	$0.661543\pi$
$152$	−0.136050	+	0.666052i	−0.0110351	+	0.0540240i
$153$		0			0
$154$	21.2941	−	4.19773i	1.71593	−	0.338263i
$155$	−9.92620	+	4.11157i	−0.797292	+	0.330249i
$156$		0			0
$157$	−4.04197	+	9.75818i	−0.322585	+	0.778788i	0.676518	+	0.736426i	$0.263488\pi$
$157$	−4.04197	+	9.75818i	−0.322585	+	0.778788i	−0.999102	+	0.0423617i	$0.986512\pi$
$158$	3.04005	+	4.56668i	0.241854	+	0.363306i
$159$		0			0
$160$	−23.1085	+	4.39106i	−1.82689	+	0.347144i
$161$	32.2647			2.54282
$162$		0			0
$163$	−4.91500	+	11.8659i	−0.384973	+	0.929406i	0.606015	+	0.795453i	$0.292767\pi$
$163$	−4.91500	+	11.8659i	−0.384973	+	0.929406i	−0.990988	+	0.133953i	$0.957233\pi$
$164$	−12.8842	+	5.28515i	−1.00609	+	0.412701i
$165$		0			0
$166$	−7.31163	+	1.44135i	−0.567493	+	0.111871i
$167$	3.05415	−	3.05415i	0.236337	−	0.236337i	−0.578994	−	0.815332i	$-0.696555\pi$
$167$	3.05415	−	3.05415i	0.236337	−	0.236337i	0.815332	+	0.578994i	$0.196555\pi$
$168$		0			0
$169$	−8.79297	−	8.79297i	−0.676382	−	0.676382i
$170$	31.6086	+	21.1986i	2.42427	+	1.62586i
$171$		0			0
$172$	3.83233	+	0.0131354i	0.292212	+	0.00100157i
$173$	2.00425	+	0.830189i	0.152381	+	0.0631181i	0.457570	−	0.889173i	$-0.348720\pi$
$173$	2.00425	+	0.830189i	0.152381	+	0.0631181i	−0.305190	+	0.952292i	$0.598720\pi$
$174$		0			0
$175$			49.8030i			3.76475i
$176$	5.89305	−	13.9557i	0.444205	−	1.05195i
$177$		0			0
$178$	−4.42595	+	22.0532i	−0.331739	+	1.65296i
$179$	−11.9037	−	4.93068i	−0.889725	−	0.368536i	−0.109464	−	0.993991i	$-0.534914\pi$
$179$	−11.9037	−	4.93068i	−0.889725	−	0.368536i	−0.780261	+	0.625455i	$0.784914\pi$
$180$		0			0
$181$	2.14955	+	5.18948i	0.159775	+	0.385731i	0.983412	−	0.181386i	$-0.0580585\pi$
$181$	2.14955	+	5.18948i	0.159775	+	0.385731i	−0.823637	+	0.567118i	$0.808058\pi$
$182$	2.39904	−	3.57714i	0.177829	−	0.265155i
$183$		0			0
$184$	12.6077	−	18.6603i	0.929450	−	1.37566i
$185$	16.6018	−	16.6018i	1.22059	−	1.22059i
$186$		0			0
$187$	−22.6454	+	9.38004i	−1.65600	+	0.685937i
$188$	−5.77739	−	2.41631i	−0.421360	−	0.176227i
$189$		0			0
$190$	1.17651	−	0.783206i	0.0853530	−	0.0568197i
$191$	−7.01800			−0.507805			−0.253902	−	0.967230i	$-0.581714\pi$
$191$	−7.01800			−0.507805			−0.253902	+	0.967230i	$0.581714\pi$
$192$		0			0
$193$	5.26222			0.378783			0.189391	−	0.981902i	$-0.439348\pi$
$193$	5.26222			0.378783			0.189391	+	0.981902i	$0.439348\pi$
$194$	−9.62302	+	6.40607i	−0.690893	+	0.459929i
$195$		0			0
$196$	−17.3830	−	7.27018i	−1.24164	−	0.519299i
$197$	0.956250	−	0.396092i	0.0681300	−	0.0282204i	−0.348358	−	0.937361i	$-0.613261\pi$
$197$	0.956250	−	0.396092i	0.0681300	−	0.0282204i	0.416488	+	0.909141i	$0.363261\pi$
$198$		0			0
$199$	−14.4006	+	14.4006i	−1.02083	+	1.02083i	−0.0210514	+	0.999778i	$0.506701\pi$
$199$	−14.4006	+	14.4006i	−1.02083	+	1.02083i	−0.999778	+	0.0210514i	$0.993299\pi$
$200$	28.8036	+	19.4609i	2.03672	+	1.37609i
$201$		0			0
$202$	−13.7464	+	20.4968i	−0.967193	+	1.44215i
$203$	2.46176	+	5.94320i	0.172781	+	0.417131i
$204$		0			0
$205$	26.7493	+	11.0799i	1.86825	+	0.773856i
$206$	−1.78882	+	8.91313i	−0.124633	+	0.621007i
$207$		0			0
$208$	−1.13139	−	2.78528i	−0.0784480	−	0.193124i
$209$			0.910252i			0.0629634i
$210$		0			0
$211$	−21.8522	−	9.05149i	−1.50437	−	0.623130i	−0.529982	−	0.848009i	$-0.677801\pi$
$211$	−21.8522	−	9.05149i	−1.50437	−	0.623130i	−0.974387	+	0.224879i	$0.927801\pi$
$212$	−12.7060	−	0.0435501i	−0.872649	−	0.00299103i
$213$		0			0
$214$	−17.0346	−	11.4244i	−1.16446	−	0.780957i
$215$	−5.63403	−	5.63403i	−0.384237	−	0.384237i
$216$		0			0
$217$	−7.40380	+	7.40380i	−0.502603	+	0.502603i
$218$	−12.6515	+	2.49401i	−0.856870	+	0.168916i
$219$		0			0
$220$	−29.1393	+	11.9531i	−1.96457	+	0.805875i
$221$	−1.86146	+	4.49397i	−0.125216	+	0.302297i
$222$		0			0
$223$	2.53509			0.169762			0.0848812	−	0.996391i	$-0.472949\pi$
$223$	2.53509			0.169762			0.0848812	+	0.996391i	$0.472949\pi$
$224$	−19.1684	+	12.5717i	−1.28074	+	0.839980i
$225$		0			0
$226$	6.65827	+	10.0019i	0.442902	+	0.665315i
$227$	−3.78205	+	9.13066i	−0.251023	+	0.606024i	−0.998287	−	0.0585037i	$-0.981367\pi$
$227$	−3.78205	+	9.13066i	−0.251023	+	0.606024i	0.747264	+	0.664527i	$0.231367\pi$
$228$		0			0
$229$	15.2552	−	6.31892i	1.00809	−	0.417566i	0.183334	−	0.983051i	$-0.441311\pi$
$229$	15.2552	−	6.31892i	1.00809	−	0.417566i	0.824759	+	0.565485i	$0.191311\pi$
$230$	−45.9370	+	9.05563i	−3.02900	+	0.597110i
$231$		0			0
$232$	4.39920	+	0.898592i	0.288822	+	0.0589954i
$233$	−14.9506	−	14.9506i	−0.979444	−	0.979444i	0.0203487	−	0.999793i	$-0.493522\pi$
$233$	−14.9506	−	14.9506i	−0.979444	−	0.979444i	−0.999793	+	0.0203487i	$0.993522\pi$
$234$		0			0
$235$	4.98247	+	12.0287i	0.325020	+	0.784669i
$236$	−0.00371192	+	1.08297i	−0.000241625	+	0.0704955i
$237$		0			0
$238$	36.3650	+	7.29826i	2.35719	+	0.473076i
$239$			15.0929i			0.976279i	0.872766	+	0.488140i	$0.162324\pi$
$239$			15.0929i			0.976279i	−0.872766	+	0.488140i	$0.837676\pi$
$240$		0			0
$241$		−	19.5256i		−	1.25775i	−0.777505	−	0.628877i	$-0.783515\pi$
$241$		−	19.5256i		−	1.25775i	0.777505	−	0.628877i	$-0.216485\pi$
$242$	0.930316	−	4.63548i	0.0598030	−	0.297980i
$243$		0			0
$244$	3.16254	+	3.18429i	0.202461	+	0.203853i
$245$	14.9912	+	36.1921i	0.957755	+	2.31223i
$246$		0			0
$247$	0.127731	+	0.127731i	0.00812733	+	0.00812733i
$248$	1.38890	+	7.17507i	0.0881953	+	0.455618i
$249$		0			0
$250$	−8.29132	−	42.0599i	−0.524389	−	2.66010i
$251$	0.360801	−	0.149449i	0.0227736	−	0.00943313i	−0.371268	−	0.928526i	$-0.621077\pi$
$251$	0.360801	−	0.149449i	0.0227736	−	0.00943313i	0.394041	+	0.919093i	$0.371077\pi$
$252$		0			0
$253$	11.5396	−	27.8590i	0.725486	−	1.75148i
$254$	4.14917	−	2.76211i	0.260342	−	0.173310i
$255$		0			0
$256$	−0.219354	+	15.9985i	−0.0137096	+	0.999906i
$257$	−13.9022			−0.867197			−0.433599	−	0.901106i	$-0.642756\pi$
$257$	−13.9022			−0.867197			−0.433599	+	0.901106i	$0.642756\pi$
$258$		0			0
$259$	8.75611	−	21.1391i	0.544078	−	1.31352i
$260$	−2.41166	+	5.76629i	−0.149565	+	0.357610i
$261$		0			0
$262$	−1.77746	−	9.01661i	−0.109812	−	0.557048i
$263$	−4.20051	+	4.20051i	−0.259015	+	0.259015i	−0.824653	−	0.565639i	$-0.808630\pi$
$263$	−4.20051	+	4.20051i	−0.259015	+	0.259015i	0.565639	+	0.824653i	$0.308630\pi$
$264$		0			0
$265$	18.6794	+	18.6794i	1.14747	+	1.14747i
$266$	0.767195	−	1.14394i	0.0470397	−	0.0701394i
$267$		0			0
$268$	20.1913	+	20.3301i	1.23338	+	1.24186i
$269$	−9.48655	−	3.92946i	−0.578405	−	0.239583i	0.0742485	−	0.997240i	$-0.476344\pi$
$269$	−9.48655	−	3.92946i	−0.578405	−	0.239583i	−0.652653	+	0.757657i	$0.726344\pi$
$270$		0			0
$271$		−	1.66720i		−	0.101275i	−0.998717	−	0.0506376i	$-0.983875\pi$
$271$		−	1.66720i		−	0.101275i	0.998717	−	0.0506376i	$-0.0161253\pi$
$272$	18.4308	−	18.1799i	1.11753	−	1.10232i
$273$		0			0
$274$	22.8988	+	4.59566i	1.38337	+	0.277634i
$275$	43.0024	+	17.8122i	2.59314	+	1.07411i
$276$		0			0
$277$	−6.36754	−	15.3726i	−0.382588	−	0.923650i	−0.991464	−	0.130384i	$-0.958379\pi$
$277$	−6.36754	−	15.3726i	−0.382588	−	0.923650i	0.608875	−	0.793266i	$-0.291621\pi$
$278$	7.86171	+	5.27254i	0.471514	+	0.316226i
$279$		0			0
$280$	46.6947	+	9.53799i	2.79054	+	0.570004i
$281$	−13.0676	+	13.0676i	−0.779548	+	0.779548i	−0.979754	−	0.200206i	$-0.935839\pi$
$281$	−13.0676	+	13.0676i	−0.779548	+	0.779548i	0.200206	+	0.979754i	$0.435839\pi$
$282$		0			0
$283$	−5.64866	+	2.33975i	−0.335778	+	0.139084i	−0.544201	−	0.838955i	$-0.683167\pi$
$283$	−5.64866	+	2.33975i	−0.335778	+	0.139084i	0.208423	+	0.978039i	$0.433167\pi$
$284$	4.86314	+	11.8554i	0.288574	+	0.703490i
$285$		0			0
$286$	−2.23065	−	3.35083i	−0.131901	−	0.198138i
$287$	28.2163			1.66555
$288$		0			0
$289$	−24.8877			−1.46398
$290$	−5.17299	−	7.77072i	−0.303768	−	0.456312i
$291$		0			0
$292$	−2.11886	+	0.869163i	−0.123997	+	0.0508639i
$293$	−19.6601	+	8.14349i	−1.14856	+	0.475748i	−0.874049	−	0.485837i	$-0.838515\pi$
$293$	−19.6601	+	8.14349i	−1.14856	+	0.475748i	−0.274507	+	0.961585i	$0.588515\pi$
$294$		0			0
$295$	1.59211	−	1.59211i	0.0926963	−	0.0926963i
$296$	−8.80430	−	13.3244i	−0.511740	−	0.774462i
$297$		0			0
$298$	−0.00711419	−	0.00477121i	−0.000412114	−	0.000276388i
$299$	−2.29002	−	5.52860i	−0.132435	−	0.319727i
$300$		0			0
$301$	−7.17383	−	2.97150i	−0.413493	−	0.171274i
$302$	−9.34835	−	1.87616i	−0.537937	−	0.107961i
$303$		0			0
$304$	−0.361811	−	0.890709i	−0.0207513	−	0.0510857i
$305$		−	9.33067i		−	0.534272i
$306$		0			0
$307$	0.386184	+	0.159963i	0.0220407	+	0.00912956i	0.393677	−	0.919249i	$-0.371203\pi$
$307$	0.386184	+	0.159963i	0.0220407	+	0.00912956i	−0.371636	+	0.928379i	$0.621203\pi$
$308$	−21.7782	+	21.6294i	−1.24093	+	1.23245i
$309$		0			0
$310$	8.46318	−	12.6192i	0.480676	−	0.716721i
$311$	19.5250	+	19.5250i	1.10716	+	1.10716i	0.993522	+	0.113640i	$0.0362510\pi$
$311$	19.5250	+	19.5250i	1.10716	+	1.10716i	0.113640	+	0.993522i	$0.463749\pi$
$312$		0			0
$313$	−19.7547	+	19.7547i	−1.11660	+	1.11660i	−0.124364	+	0.992237i	$0.539689\pi$
$313$	−19.7547	+	19.7547i	−1.11660	+	1.11660i	−0.992237	+	0.124364i	$0.960311\pi$
$314$	−2.88899	−	14.6551i	−0.163035	−	0.827037i
$315$		0			0
$316$	−7.15762	−	2.99357i	−0.402648	−	0.168401i
$317$	−8.46612	+	20.4390i	−0.475505	+	1.14797i	0.486191	+	0.873852i	$0.338386\pi$
$317$	−8.46612	+	20.4390i	−0.475505	+	1.14797i	−0.961696	+	0.274118i	$0.911614\pi$
$318$		0			0
$319$	6.01211			0.336614
$320$	23.7626	−	23.2789i	1.32837	−	1.30133i
$321$		0			0
$322$	−37.9827	+	25.2852i	−2.11669	+	1.40909i
$323$	−0.595281	+	1.43714i	−0.0331223	+	0.0799644i
$324$		0			0
$325$	8.53380	−	3.53481i	0.473370	−	0.196076i
$326$	−3.51298	−	17.8205i	−0.194566	−	0.986987i
$327$		0			0
$328$	11.0257	−	16.3189i	0.608792	−	0.901059i
$329$	8.97205	+	8.97205i	0.494645	+	0.494645i
$330$		0			0
$331$	−10.5951	−	25.5788i	−0.582358	−	1.40594i	−0.890669	−	0.454652i	$-0.849764\pi$
$331$	−10.5951	−	25.5788i	−0.582358	−	1.40594i	0.308311	−	0.951286i	$-0.400236\pi$
$332$	7.47785	−	7.42676i	0.410400	−	0.407596i
$333$		0			0
$334$	−1.20194	+	5.98888i	−0.0657670	+	0.327697i
$335$		−	59.5718i		−	3.25475i
$336$		0			0
$337$		−	18.7365i		−	1.02064i	−0.859985	−	0.510320i	$-0.829527\pi$
$337$		−	18.7365i		−	1.02064i	0.859985	−	0.510320i	$-0.170473\pi$
$338$	17.2421	+	3.46040i	0.937848	+	0.188221i
$339$		0			0
$340$	−53.8232	−	0.184480i	−2.91897	−	0.0100049i
$341$	3.74482	+	9.04080i	0.202793	+	0.489587i
$342$		0			0
$343$	6.93728	+	6.93728i	0.374578	+	0.374578i
$344$	−4.52179	+	2.98785i	−0.243799	+	0.161094i
$345$		0			0
$346$	−3.01005	+	0.593375i	−0.161821	+	0.0319001i
$347$	15.1570	−	6.27824i	0.813671	−	0.337034i	0.0632533	−	0.997998i	$-0.479852\pi$
$347$	15.1570	−	6.27824i	0.813671	−	0.337034i	0.750418	+	0.660964i	$0.229852\pi$
$348$		0			0
$349$	13.6390	−	32.9274i	0.730077	−	1.76256i	0.0877332	−	0.996144i	$-0.472038\pi$
$349$	13.6390	−	32.9274i	0.730077	−	1.76256i	0.642343	−	0.766417i	$-0.277962\pi$
$350$	−39.0295	−	58.6291i	−2.08622	−	3.13386i
$351$		0			0
$352$	3.99938	+	21.0472i	0.213168	+	1.12182i
$353$	15.3455			0.816760			0.408380	−	0.912812i	$-0.366094\pi$
$353$	15.3455			0.816760			0.408380	+	0.912812i	$0.366094\pi$
$354$		0			0
$355$	10.1952	−	24.6134i	0.541106	−	1.30634i
$356$	−12.0723	−	29.4300i	−0.639830	−	1.55979i
$357$		0			0
$358$	17.8774	−	3.52419i	0.944848	−	0.186259i
$359$	−14.3419	+	14.3419i	−0.756938	+	0.756938i	−0.975764	−	0.218826i	$-0.929777\pi$
$359$	−14.3419	+	14.3419i	−0.756938	+	0.756938i	0.218826	+	0.975764i	$0.429777\pi$
$360$		0			0
$361$	−13.3942	−	13.3942i	−0.704957	−	0.704957i
$362$	−6.59739	−	4.42461i	−0.346751	−	0.232552i
$363$		0			0
$364$	−0.0208776	+	6.09116i	−0.00109428	+	0.319263i
$365$	4.39903	+	1.82214i	0.230256	+	0.0953750i
$366$		0			0
$367$			10.0067i			0.522346i	0.965292	+	0.261173i	$0.0841094\pi$
$367$			10.0067i			0.522346i	−0.965292	+	0.261173i	$0.915891\pi$
$368$	−0.218320	+	31.8477i	−0.0113807	+	1.66017i
$369$		0			0
$370$	−6.53350	+	32.5544i	−0.339660	+	1.69242i
$371$	23.7846	+	9.85191i	1.23484	+	0.511486i
$372$		0			0
$373$	7.00402	+	16.9092i	0.362654	+	0.875525i	0.994910	+	0.100765i	$0.0321291\pi$
$373$	7.00402	+	16.9092i	0.362654	+	0.875525i	−0.632256	+	0.774760i	$0.717871\pi$
$374$	19.3077	−	28.7891i	0.998378	−	1.48865i
$375$		0			0
$376$	8.69488	−	1.68309i	0.448404	−	0.0867989i
$377$	0.843649	−	0.843649i	0.0434501	−	0.0434501i
$378$		0			0
$379$	−30.1378	+	12.4835i	−1.54808	+	0.641234i	−0.982967	−	0.183782i	$-0.941166\pi$
$379$	−30.1378	+	12.4835i	−1.54808	+	0.641234i	−0.565109	+	0.825016i	$0.691166\pi$
$380$	−0.771230	+	1.84401i	−0.0395633	+	0.0945958i
$381$		0			0
$382$	8.26173	−	5.49986i	0.422707	−	0.281397i
$383$	−20.3553			−1.04011			−0.520054	−	0.854133i	$-0.674088\pi$
$383$	−20.3553			−1.04011			−0.520054	+	0.854133i	$0.674088\pi$
$384$		0			0
$385$	63.8148			3.25230
$386$	−6.19479	+	4.12389i	−0.315307	+	0.209900i
$387$		0			0
$388$	6.30812	−	15.0827i	0.320246	−	0.765709i
$389$	−18.2140	+	7.54450i	−0.923489	+	0.382521i	−0.793205	−	0.608955i	$-0.791589\pi$
$389$	−18.2140	+	7.54450i	−0.923489	+	0.382521i	−0.130284	+	0.991477i	$0.541589\pi$
$390$		0			0
$391$	36.4381	−	36.4381i	1.84275	−	1.84275i
$392$	26.1611	−	5.06409i	1.32134	−	0.255775i
$393$		0			0
$394$	−0.815308	+	1.21568i	−0.0410746	+	0.0612450i
$395$	6.17279	+	14.9024i	0.310587	+	0.749823i
$396$		0			0
$397$	−7.36714	−	3.05157i	−0.369746	−	0.153154i	0.190070	−	0.981770i	$-0.439128\pi$
$397$	−7.36714	−	3.05157i	−0.369746	−	0.153154i	−0.559816	+	0.828617i	$0.689128\pi$
$398$	5.66723	−	28.2381i	0.284072	−	1.41545i
$399$		0			0
$400$	−49.1592	−	0.336993i	−2.45796	−	0.0168497i
$401$		−	19.1977i		−	0.958689i	−0.877627	−	0.479345i	$-0.840874\pi$
$401$		−	19.1977i		−	0.958689i	0.877627	−	0.479345i	$-0.159126\pi$
$402$		0			0
$403$	1.79414	+	0.743157i	0.0893725	+	0.0370193i
$404$	0.119628	−	34.9020i	0.00595170	−	1.73644i
$405$		0			0
$406$	−7.55559	−	5.06724i	−0.374978	−	0.251483i
$407$	−15.1209	−	15.1209i	−0.749516	−	0.749516i
$408$		0			0
$409$	−11.2817	+	11.2817i	−0.557844	+	0.557844i	−0.928693	−	0.370849i	$-0.879067\pi$
$409$	−11.2817	+	11.2817i	−0.557844	+	0.557844i	0.370849	+	0.928693i	$0.379067\pi$
$410$	−40.1730	+	7.91935i	−1.98400	+	0.391109i
$411$		0			0
$412$	−4.87920	−	11.8946i	−0.240381	−	0.586004i
$413$	0.839711	−	2.02724i	0.0413195	−	0.0997540i
$414$		0			0
$415$	−21.9117			−1.07560
$416$	3.51466	+	2.39224i	0.172320	+	0.117289i
$417$		0			0
$418$	−0.713345	−	1.07157i	−0.0348908	−	0.0524121i
$419$	2.73201	−	6.59565i	0.133467	−	0.322219i	−0.842990	−	0.537929i	$-0.819207\pi$
$419$	2.73201	−	6.59565i	0.133467	−	0.322219i	0.976457	+	0.215711i	$0.0692068\pi$
$420$		0			0
$421$	−31.1085	+	12.8856i	−1.51613	+	0.628004i	−0.976813	−	0.214096i	$-0.931319\pi$
$421$	−31.1085	+	12.8856i	−1.51613	+	0.628004i	−0.539322	+	0.842100i	$0.681319\pi$
$422$	32.8183	−	6.46953i	1.59757	−	0.314932i
$423$		0			0
$424$	14.9919	−	9.90613i	0.728069	−	0.481084i
$425$	56.2449	+	56.2449i	2.72828	+	2.72828i
$426$		0			0
$427$	−3.47980	−	8.40098i	−0.168399	−	0.406552i
$428$	29.0065	+	0.0994207i	1.40208	+	0.00480568i
$429$		0			0
$430$	11.0478	+	2.21722i	0.532770	+	0.106924i
$431$			5.39288i			0.259766i	0.991529	+	0.129883i	$0.0414601\pi$
$431$			5.39288i			0.259766i	−0.991529	+	0.129883i	$0.958540\pi$
$432$		0			0
$433$		−	27.7550i		−	1.33382i	−0.745139	−	0.666910i	$-0.767617\pi$
$433$		−	27.7550i		−	1.33382i	0.745139	−	0.666910i	$-0.232383\pi$
$434$	2.91370	−	14.5181i	0.139862	−	0.696891i
$435$		0			0
$436$	12.9391	−	12.8507i	0.619672	−	0.615439i
$437$	−0.732330	−	1.76800i	−0.0350321	−	0.0845750i
$438$		0			0
$439$	15.2464	+	15.2464i	0.727672	+	0.727672i	0.970156	−	0.242484i	$-0.0779621\pi$
$439$	15.2464	+	15.2464i	0.727672	+	0.727672i	−0.242484	+	0.970156i	$0.577962\pi$
$440$	24.9361	−	36.9073i	1.18878	−	1.75948i
$441$		0			0
$442$	−1.33048	−	6.74918i	−0.0632843	−	0.321026i
$443$	24.7637	−	10.2575i	1.17656	−	0.487346i	0.293203	−	0.956050i	$-0.405279\pi$
$443$	24.7637	−	10.2575i	1.17656	−	0.487346i	0.883355	+	0.468704i	$0.155279\pi$
$444$		0			0
$445$	−25.3087	+	61.1005i	−1.19975	+	2.89644i
$446$	−2.98436	+	1.98670i	−0.141314	+	0.0940729i
$447$		0			0
$448$	12.7133	−	29.8215i	0.600645	−	1.40893i
$449$	2.13005			0.100523			0.0502616	−	0.998736i	$-0.483994\pi$
$449$	2.13005			0.100523			0.0502616	+	0.998736i	$0.483994\pi$
$450$		0			0
$451$	10.0916	−	24.3633i	0.475196	−	1.14722i
$452$	−15.6765	−	6.55646i	−0.737361	−	0.308390i
$453$		0			0
$454$	−2.70321	−	13.7127i	−0.126868	−	0.643569i
$455$	8.95480	−	8.95480i	0.419808	−	0.419808i
$456$		0			0
$457$	−10.0712	−	10.0712i	−0.471109	−	0.471109i	0.431165	−	0.902273i	$-0.358103\pi$
$457$	−10.0712	−	10.0712i	−0.471109	−	0.471109i	−0.902273	+	0.431165i	$0.858103\pi$
$458$	−13.0067	+	19.3939i	−0.607765	+	0.906219i
$459$		0			0
$460$	46.9813	−	46.6603i	2.19051	−	2.17555i
$461$	13.7031	+	5.67601i	0.638217	+	0.264358i	0.678240	−	0.734841i	$-0.262743\pi$
$461$	13.7031	+	5.67601i	0.638217	+	0.264358i	−0.0400229	+	0.999199i	$0.512743\pi$
$462$		0			0
$463$			26.0596i			1.21109i	0.795809	+	0.605547i	$0.207046\pi$
$463$			26.0596i			1.21109i	−0.795809	+	0.605547i	$0.792954\pi$
$464$	−5.88303	+	2.38972i	−0.273113	+	0.110940i
$465$		0			0
$466$	29.3166	+	5.88367i	1.35806	+	0.272556i
$467$	2.26841	+	0.939606i	0.104970	+	0.0434798i	0.434550	−	0.900648i	$-0.356907\pi$
$467$	2.26841	+	0.939606i	0.104970	+	0.0434798i	−0.329581	+	0.944127i	$0.606907\pi$
$468$		0			0
$469$	−22.2168	−	53.6362i	−1.02588	−	2.47669i
$470$	−15.2921	−	10.2558i	−0.705373	−	0.473066i
$471$		0			0
$472$	−0.844332	−	1.27781i	−0.0388635	−	0.0588158i
$473$	−5.13148	+	5.13148i	−0.235946	+	0.235946i
$474$		0			0
$475$	2.72904	−	1.13041i	0.125217	−	0.0518665i
$476$	−48.5291	+	19.9068i	−2.22433	+	0.912428i
$477$		0			0
$478$	−11.8280	−	17.7677i	−0.541000	−	0.812675i
$479$	−6.51774			−0.297803			−0.148901	−	0.988852i	$-0.547574\pi$
$479$	−6.51774			−0.297803			−0.148901	+	0.988852i	$0.547574\pi$
$480$		0			0
$481$	−4.24368			−0.193495
$482$	15.3018	+	22.9859i	0.696978	+	1.04698i
$483$		0			0
$484$	2.53754	+	6.18606i	0.115343	+	0.281184i
$485$	−31.4027	+	13.0074i	−1.42593	+	0.590637i
$486$		0			0
$487$	29.5067	−	29.5067i	1.33708	−	1.33708i	0.438199	−	0.898878i	$-0.355617\pi$
$487$	29.5067	−	29.5067i	1.33708	−	1.33708i	0.898878	−	0.438199i	$-0.144383\pi$
$488$	−6.21846	−	1.27020i	−0.281497	−	0.0574992i
$489$		0			0
$490$	−46.0109	−	30.8577i	−2.07856	−	1.39401i
$491$	7.72387	+	18.6471i	0.348573	+	0.841531i	0.996789	+	0.0800738i	$0.0255156\pi$
$491$	7.72387	+	18.6471i	0.348573	+	0.841531i	−0.648215	+	0.761457i	$0.724484\pi$
$492$		0			0
$493$	9.49212	+	3.93177i	0.427504	+	0.177078i
$494$	−0.250468	−	0.0502675i	−0.0112691	−	0.00226164i
$495$		0			0
$496$	−7.25799	−	7.35819i	−0.325894	−	0.330392i
$497$		−	25.9632i		−	1.16461i
$498$		0			0
$499$	3.54310	+	1.46760i	0.158611	+	0.0656989i	0.460576	−	0.887620i	$-0.347643\pi$
$499$	3.54310	+	1.46760i	0.158611	+	0.0656989i	−0.301965	+	0.953319i	$0.597643\pi$
$500$	42.7221	+	43.0160i	1.91059	+	1.92373i
$501$		0			0
$502$	−0.307623	+	0.458687i	−0.0137299	+	0.0204722i
$503$	−11.3667	−	11.3667i	−0.506815	−	0.506815i	0.406732	−	0.913547i	$-0.366668\pi$
$503$	−11.3667	−	11.3667i	−0.506815	−	0.506815i	−0.913547	+	0.406732i	$0.866668\pi$
$504$		0			0
$505$	−51.3106	+	51.3106i	−2.28329	+	2.28329i
$506$	8.24787	+	41.8395i	0.366663	+	1.85999i
$507$		0			0
$508$	−2.71988	+	6.50323i	−0.120675	+	0.288534i
$509$	14.2510	−	34.4050i	0.631665	−	1.52497i	−0.205864	−	0.978581i	$-0.566001\pi$
$509$	14.2510	−	34.4050i	0.631665	−	1.52497i	0.837529	−	0.546393i	$-0.183999\pi$
$510$		0			0
$511$	4.64027			0.205273
$512$	−12.2795	−	19.0057i	−0.542680	−	0.839939i
$513$		0			0
$514$	16.3660	−	10.8949i	0.721873	−	0.480553i
$515$	−10.2289	+	24.6947i	−0.450738	+	1.08818i
$516$		0			0
$517$	10.9558	−	4.53804i	0.481835	−	0.199583i
$518$	6.25841	+	31.7474i	0.274979	+	1.39490i
$519$		0			0
$520$	−1.67986	−	8.67816i	−0.0736666	−	0.380562i
$521$	6.37098	+	6.37098i	0.279118	+	0.279118i	0.832757	−	0.553639i	$-0.186761\pi$
$521$	6.37098	+	6.37098i	0.279118	+	0.279118i	−0.553639	+	0.832757i	$0.686761\pi$
$522$		0			0
$523$	6.20259	+	14.9744i	0.271220	+	0.654783i	0.999536	−	0.0304582i	$-0.00969664\pi$
$523$	6.20259	+	14.9744i	0.271220	+	0.654783i	−0.728316	+	0.685242i	$0.759697\pi$
$524$	9.15859	+	9.22158i	0.400095	+	0.402847i
$525$		0			0
$526$	1.65308	−	8.23678i	0.0720775	−	0.359141i
$527$			16.7229i			0.728462i
$528$		0			0
$529$			40.3951i			1.75631i
$530$	−36.6285	−	7.35114i	−1.59104	−	0.319313i
$531$		0			0
$532$	−0.00667649	+	1.94790i	−0.000289463	+	0.0844523i
$533$	−2.00267	−	4.83488i	−0.0867455	−	0.209422i
$534$		0			0
$535$	−42.6434	−	42.6434i	−1.84363	−	1.84363i
$536$	−39.7019	−	8.10960i	−1.71486	−	0.350282i
$537$		0			0
$538$	14.2472	−	2.80857i	0.614240	−	0.121086i
$539$	32.9638	−	13.6540i	1.41985	−	0.588121i
$540$		0			0
$541$	−10.0473	+	24.2564i	−0.431968	+	1.04286i	0.546685	+	0.837339i	$0.315890\pi$
$541$	−10.0473	+	24.2564i	−0.431968	+	1.04286i	−0.978652	+	0.205523i	$0.934110\pi$
$542$	1.30655	+	1.96266i	0.0561211	+	0.0843036i
$543$		0			0
$544$	−7.44998	+	35.8455i	−0.319415	+	1.53687i
$545$	−37.9145			−1.62408
$546$		0			0
$547$	1.61145	−	3.89040i	0.0689008	−	0.166341i	−0.885678	−	0.464300i	$-0.846306\pi$
$547$	1.61145	−	3.89040i	0.0689008	−	0.166341i	0.954579	+	0.297959i	$0.0963059\pi$
$548$	−30.5584	+	12.5352i	−1.30539	+	0.535476i
$549$		0			0
$550$	−64.5823	+	12.7312i	−2.75380	+	0.542860i
$551$	0.269792	−	0.269792i	0.0114935	−	0.0114935i
$552$		0			0
$553$	11.1155	+	11.1155i	0.472679	+	0.472679i
$554$	19.5432	+	13.1068i	0.830310	+	0.556856i
$555$		0			0
$556$	−13.3869	−	0.0458841i	−0.567733	−	0.00194592i
$557$	35.0566	+	14.5209i	1.48539	+	0.615270i	0.970309	−	0.241869i	$-0.0777604\pi$
$557$	35.0566	+	14.5209i	1.48539	+	0.615270i	0.515085	+	0.857139i	$0.327760\pi$
$558$		0			0
$559$			1.44015i			0.0609118i
$560$	−62.4447	+	25.3654i	−2.63877	+	1.07188i
$561$		0			0
$562$	5.14265	−	25.6242i	0.216929	−	1.08089i
$563$	−21.4965	−	8.90414i	−0.905969	−	0.375265i	−0.119457	−	0.992839i	$-0.538115\pi$
$563$	−21.4965	−	8.90414i	−0.905969	−	0.375265i	−0.786512	+	0.617575i	$0.788115\pi$
$564$		0			0
$565$	13.5195	+	32.6391i	0.568771	+	1.37314i
$566$	4.81610	−	7.18114i	0.202436	−	0.301846i
$567$		0			0
$568$	−15.0158	−	10.1453i	−0.630050	−	0.425687i
$569$	16.1459	−	16.1459i	0.676872	−	0.676872i	−0.282419	−	0.959291i	$-0.591137\pi$
$569$	16.1459	−	16.1459i	0.676872	−	0.676872i	0.959291	+	0.282419i	$0.0911369\pi$
$570$		0			0
$571$	5.63198	−	2.33284i	0.235691	−	0.0976264i	−0.261712	−	0.965146i	$-0.584287\pi$
$571$	5.63198	−	2.33284i	0.235691	−	0.0976264i	0.497403	+	0.867520i	$0.334287\pi$
$572$	5.25194	+	2.19654i	0.219595	+	0.0918421i
$573$		0			0
$574$	−33.2167	+	22.1125i	−1.38644	+	0.922957i
$575$	−97.8549			−4.08083
$576$		0			0
$577$	28.5232			1.18744			0.593719	−	0.804672i	$-0.297659\pi$
$577$	28.5232			1.18744			0.593719	+	0.804672i	$0.297659\pi$
$578$	29.2983	−	19.5039i	1.21865	−	0.811257i
$579$		0			0
$580$	12.1795	+	5.09389i	0.505726	+	0.211512i
$581$	−19.7285	+	8.17181i	−0.818476	+	0.339024i
$582$		0			0
$583$	17.0133	−	17.0133i	0.704617	−	0.704617i
$584$	1.81322	−	2.68370i	0.0750314	−	0.111052i
$585$		0			0
$586$	16.7624	−	24.9939i	0.692449	−	1.03249i
$587$	−8.75656	−	21.1402i	−0.361422	−	0.872549i	−0.995093	−	0.0989466i	$-0.968453\pi$
$587$	−8.75656	−	21.1402i	−0.361422	−	0.872549i	0.633671	−	0.773603i	$-0.281547\pi$
$588$		0			0
$589$	0.573752	+	0.237656i	0.0236410	+	0.00979243i
$590$	−0.626562	+	3.12197i	−0.0257952	+	0.128529i
$591$		0			0
$592$	20.8066	+	8.78596i	0.855147	+	0.361101i
$593$			19.8413i			0.814784i	0.913253	+	0.407392i	$0.133562\pi$
$593$			19.8413i			0.814784i	−0.913253	+	0.407392i	$0.866438\pi$
$594$		0			0
$595$	100.753	+	41.7332i	4.13047	+	1.71089i
$596$	0.0121141		4.15213e-5i	0.000496211		1.70078e-6i
$597$		0			0
$598$	7.02850	+	4.71374i	0.287417	+	0.192759i
$599$	24.2292	+	24.2292i	0.989980	+	0.989980i	0.999950	−	0.00997077i	$-0.00317385\pi$
$599$	24.2292	+	24.2292i	0.989980	+	0.989980i	−0.00997077	+	0.999950i	$0.503174\pi$
$600$		0			0
$601$	−16.1726	+	16.1726i	−0.659693	+	0.659693i	−0.955307	−	0.295615i	$-0.904476\pi$
$601$	−16.1726	+	16.1726i	−0.659693	+	0.659693i	0.295615	+	0.955307i	$0.404476\pi$
$602$	10.7739	−	2.12387i	0.439111	−	0.0865625i
$603$		0			0
$604$	12.4754	−	5.11744i	0.507616	−	0.208226i
$605$	5.31977	−	12.8431i	0.216280	−	0.522145i
$606$		0			0
$607$	−28.3786			−1.15185			−0.575925	−	0.817503i	$-0.695358\pi$
$607$	−28.3786			−1.15185			−0.575925	+	0.817503i	$0.695358\pi$
$608$	1.12396	+	0.765018i	0.0455826	+	0.0310256i
$609$		0			0
$610$	7.31224	+	10.9843i	0.296064	+	0.444739i
$611$	0.900571	−	2.17417i	0.0364332	−	0.0879575i
$612$		0			0
$613$	4.78336	−	1.98133i	0.193198	−	0.0800253i	−0.283987	−	0.958828i	$-0.591657\pi$
$613$	4.78336	−	1.98133i	0.193198	−	0.0800253i	0.477185	+	0.878803i	$0.341657\pi$
$614$	−0.579983	+	0.114333i	−0.0234062	+	0.00461410i
$615$		0			0
$616$	8.68721	−	42.5296i	0.350018	−	1.71357i
$617$	−14.2389	−	14.2389i	−0.573235	−	0.573235i	0.359796	−	0.933031i	$-0.382846\pi$
$617$	−14.2389	−	14.2389i	−0.573235	−	0.573235i	−0.933031	+	0.359796i	$0.882846\pi$
$618$		0			0
$619$	4.40491	+	10.6344i	0.177048	+	0.427432i	0.987345	−	0.158588i	$-0.0506941\pi$
$619$	4.40491	+	10.6344i	0.177048	+	0.427432i	−0.810297	+	0.586020i	$0.800694\pi$
$620$	−0.0736506	+	21.4880i	−0.00295788	+	0.862977i
$621$		0			0
$622$	−38.2866	−	7.68391i	−1.53515	−	0.308097i
$623$			64.4512i			2.58218i
$624$		0			0
$625$		−	64.5958i		−	2.58383i
$626$	7.77429	−	38.7369i	0.310723	−	1.54824i
$627$		0			0
$628$	14.8859	+	14.9883i	0.594012	+	0.598098i
$629$	−13.9847	−	33.7621i	−0.557608	−	1.34618i
$630$		0			0
$631$	−29.4108	−	29.4108i	−1.17083	−	1.17083i	−0.982013	−	0.188815i	$-0.939535\pi$
$631$	−29.4108	−	29.4108i	−1.17083	−	1.17083i	−0.188815	−	0.982013i	$-0.560465\pi$
$632$	10.7721	−	2.08519i	0.428491	−	0.0829443i
$633$		0			0
$634$	−6.05114	−	30.6960i	−0.240321	−	1.21909i
$635$	13.5399	−	5.60843i	0.537316	−	0.222564i
$636$		0			0
$637$	2.70964	−	6.54164i	0.107360	−	0.259189i
$638$	−7.07758	+	4.71156i	−0.280204	+	0.186533i
$639$		0			0
$640$	−9.73065	+	46.0266i	−0.384638	+	1.81936i
$641$	35.1063			1.38662			0.693309	−	0.720641i	$-0.256152\pi$
$641$	35.1063			1.38662			0.693309	+	0.720641i	$0.256152\pi$
$642$		0			0
$643$	10.8918	−	26.2952i	0.429531	−	1.03698i	−0.549906	−	0.835227i	$-0.685336\pi$
$643$	10.8918	−	26.2952i	0.429531	−	1.03698i	0.979437	−	0.201753i	$-0.0646637\pi$
$644$	24.8986	−	59.5325i	0.981141	−	2.34591i
$645$		0			0
$646$	−0.425476	−	2.15833i	−0.0167401	−	0.0849186i
$647$	24.9325	−	24.9325i	0.980199	−	0.980199i	−0.0196090	−	0.999808i	$-0.506242\pi$
$647$	24.9325	−	24.9325i	0.980199	−	0.980199i	0.999808	+	0.0196090i	$0.00624214\pi$
$648$		0			0
$649$	−1.45010	−	1.45010i	−0.0569213	−	0.0569213i
$650$	−7.27600	+	10.8490i	−0.285388	+	0.425533i
$651$		0			0
$652$	18.1011	+	18.2256i	0.708894	+	0.713770i
$653$	21.3882	+	8.85929i	0.836986	+	0.346691i	0.759664	−	0.650315i	$-0.225363\pi$
$653$	21.3882	+	8.85929i	0.836986	+	0.346691i	0.0773216	+	0.997006i	$0.475363\pi$
$654$		0			0
$655$		−	27.0213i		−	1.05581i
$656$	−0.190926	+	27.8515i	−0.00745440	+	1.08742i
$657$		0			0
$658$	−17.5933	−	3.53088i	−0.685858	−	0.137648i
$659$	−12.9107	−	5.34777i	−0.502928	−	0.208320i	0.116772	−	0.993159i	$-0.462745\pi$
$659$	−12.9107	−	5.34777i	−0.502928	−	0.208320i	−0.619699	+	0.784839i	$0.712745\pi$
$660$		0			0
$661$	−3.34388	−	8.07284i	−0.130062	−	0.313997i	0.845411	−	0.534116i	$-0.179355\pi$
$661$	−3.34388	−	8.07284i	−0.130062	−	0.313997i	−0.975473	+	0.220119i	$0.929355\pi$
$662$	32.5183	+	21.8087i	1.26386	+	0.847620i
$663$		0			0
$664$	−2.98288	+	14.6032i	−0.115758	+	0.566713i
$665$	2.86367	−	2.86367i	0.111049	−	0.111049i
$666$		0			0
$667$	−11.6774	+	4.83696i	−0.452153	+	0.187288i
$668$	−3.27842	−	7.99217i	−0.126846	−	0.309226i
$669$		0			0
$670$	46.6851	+	70.1291i	1.80360	+	2.70932i
$671$	−8.49838			−0.328076
$672$		0			0
$673$	−18.6237			−0.717892			−0.358946	−	0.933358i	$-0.616864\pi$
$673$	−18.6237			−0.717892			−0.358946	+	0.933358i	$0.616864\pi$
$674$	14.6834	+	22.0569i	0.565582	+	0.849601i
$675$		0			0
$676$	−23.0096	+	9.43863i	−0.884985	+	0.363024i
$677$	20.6985	−	8.57358i	0.795507	−	0.329510i	0.0523514	−	0.998629i	$-0.483328\pi$
$677$	20.6985	−	8.57358i	0.795507	−	0.329510i	0.743155	+	0.669119i	$0.233328\pi$
$678$		0			0
$679$	−23.4228	+	23.4228i	−0.898885	+	0.898885i
$680$	63.5063	−	41.9629i	2.43535	−	1.60920i
$681$		0			0
$682$	−11.4936	−	7.70827i	−0.440111	−	0.295165i
$683$	6.04261	+	14.5881i	0.231214	+	0.558200i	0.996321	−	0.0857037i	$-0.0273138\pi$
$683$	6.04261	+	14.5881i	0.231214	+	0.558200i	−0.765107	+	0.643903i	$0.777314\pi$
$684$		0			0
$685$	63.4433	+	26.2791i	2.42404	+	1.00407i
$686$	−13.6033	−	2.73011i	−0.519377	−	0.104236i
$687$		0			0
$688$	2.98163	−	7.06099i	0.113673	−	0.269198i
$689$		−	4.77477i		−	0.181904i
$690$		0			0
$691$	−20.1195	−	8.33376i	−0.765381	−	0.317031i	−0.0343809	−	0.999409i	$-0.510946\pi$
$691$	−20.1195	−	8.33376i	−0.765381	−	0.317031i	−0.731000	+	0.682378i	$0.760946\pi$
$692$	3.07848	−	3.05745i	0.117026	−	0.116227i
$693$		0			0
$694$	−12.9230	+	19.2691i	−0.490551	+	0.731445i
$695$	19.6806	+	19.6806i	0.746527	+	0.746527i
$696$		0			0
$697$	31.8660	−	31.8660i	1.20701	−	1.20701i
$698$	9.74841	+	49.4513i	0.368983	+	1.87176i
$699$		0			0
$700$	91.8928	+	38.4328i	3.47322	+	1.45262i
$701$	7.48642	−	18.0738i	0.282758	−	0.682638i	−0.717140	−	0.696929i	$-0.754549\pi$
$701$	7.48642	−	18.0738i	0.282758	−	0.682638i	0.999898	+	0.0142909i	$0.00454909\pi$
$702$		0			0
$703$	−1.35710			−0.0511839
$704$	−21.2024	−	21.6430i	−0.799096	−	0.815701i
$705$		0			0
$706$	−18.0651	+	12.0260i	−0.679888	+	0.452603i
$707$	−27.0622	+	65.3339i	−1.01778	+	2.45714i
$708$		0			0
$709$	−17.2656	+	7.15166i	−0.648424	+	0.268586i	−0.682558	−	0.730831i	$-0.739133\pi$
$709$	−17.2656	+	7.15166i	−0.648424	+	0.268586i	0.0341341	+	0.999417i	$0.489133\pi$
$710$	7.28700	+	36.9652i	0.273476	+	1.38728i
$711$		0			0
$712$	37.2754	+	25.1848i	1.39695	+	0.943839i
$713$	−14.5473	−	14.5473i	−0.544800	−	0.544800i
$714$		0			0
$715$	−4.52931	−	10.9347i	−0.169387	−	0.408936i
$716$	−18.2838	+	18.1588i	−0.683296	+	0.678628i
$717$		0			0
$718$	5.64415	−	28.1231i	0.210638	−	1.04954i
$719$		−	46.1319i		−	1.72043i	−0.509932	−	0.860215i	$-0.670330\pi$
$719$		−	46.1319i		−	1.72043i	0.509932	−	0.860215i	$-0.329670\pi$
$720$		0			0
$721$			26.0490i			0.970114i
$722$	26.2646	+	5.27117i	0.977469	+	0.196173i
$723$		0			0
$724$	11.2340	+	0.0385050i	0.417510	+	0.00143103i
$725$	−7.46620	−	18.0250i	−0.277288	−	0.669432i
$726$		0			0
$727$	−22.0962	−	22.0962i	−0.819503	−	0.819503i	0.166533	−	0.986036i	$-0.446743\pi$
$727$	−22.0962	−	22.0962i	−0.819503	−	0.819503i	−0.986036	+	0.166533i	$0.946743\pi$
$728$	−4.74893	−	7.18700i	−0.176007	−	0.266368i
$729$		0			0
$730$	−6.60659	+	1.30237i	−0.244521	+	0.0482028i
$731$	−11.4576	+	4.74589i	−0.423775	+	0.175533i
$732$		0			0
$733$	−10.3493	+	24.9854i	−0.382260	+	0.922857i	0.609268	+	0.792964i	$0.291463\pi$
$733$	−10.3493	+	24.9854i	−0.382260	+	0.922857i	−0.991528	+	0.129893i	$0.958537\pi$
$734$	−7.84205	−	11.7801i	−0.289455	−	0.434812i
$735$		0			0
$736$	−24.7013	−	37.6628i	−0.910503	−	1.38827i
$737$	−54.2580			−1.99862
$738$		0			0
$739$	−11.4851	+	27.7275i	−0.422487	+	1.01997i	0.559125	+	0.829084i	$0.311137\pi$
$739$	−11.4851	+	27.7275i	−0.422487	+	1.01997i	−0.981611	+	0.190890i	$0.938863\pi$
$740$	−17.8208	−	43.4439i	−0.655107	−	1.59703i
$741$		0			0
$742$	−35.7205	+	7.04162i	−1.31134	+	0.258506i
$743$	3.41524	−	3.41524i	0.125293	−	0.125293i	−0.641680	−	0.766973i	$-0.721762\pi$
$743$	3.41524	−	3.41524i	0.125293	−	0.125293i	0.766973	+	0.641680i	$0.221762\pi$
$744$		0			0
$745$	−0.0178093	−	0.0178093i	−0.000652481	−	0.000652481i
$746$	−21.4966	−	14.4169i	−0.787048	−	0.527842i
$747$		0			0
$748$	−0.168025	+	49.0222i	−0.00614360	+	1.79243i
$749$	−54.2980	−	22.4910i	−1.98401	−	0.821802i
$750$		0			0
$751$		−	18.9125i		−	0.690127i	−0.938579	−	0.345063i	$-0.887857\pi$
$751$		−	18.9125i		−	0.690127i	0.938579	−	0.345063i	$-0.112143\pi$
$752$	−8.91678	+	8.79536i	−0.325162	+	0.320734i
$753$		0			0
$754$	−0.332011	+	1.65431i	−0.0120911	+	0.0602464i
$755$	−25.9005	−	10.7284i	−0.942617	−	0.390445i
$756$		0			0
$757$	3.48353	+	8.40999i	0.126611	+	0.305666i	0.974456	−	0.224578i	$-0.0721003\pi$
$757$	3.48353	+	8.40999i	0.126611	+	0.305666i	−0.847845	+	0.530244i	$0.822100\pi$
$758$	25.6958	−	38.3142i	0.933314	−	1.39163i
$759$		0			0
$760$	−0.537205	−	2.77521i	−0.0194865	−	0.100667i
$761$	4.39524	−	4.39524i	0.159327	−	0.159327i	−0.622941	−	0.782269i	$-0.714062\pi$
$761$	4.39524	−	4.39524i	0.159327	−	0.159327i	0.782269	+	0.622941i	$0.214062\pi$
$762$		0			0
$763$	−34.1368	+	14.1399i	−1.23583	+	0.511899i
$764$	−5.41576	+	12.9491i	−0.195935	+	0.468482i
$765$		0			0
$766$	23.9627	−	15.9520i	0.865807	−	0.576370i
$767$	−0.406969			−0.0146948
$768$		0			0
$769$	46.2066			1.66625			0.833126	−	0.553084i	$-0.186549\pi$
$769$	46.2066			1.66625			0.833126	+	0.553084i	$0.186549\pi$
$770$	−75.1241	+	50.0103i	−2.70728	+	1.80225i
$771$		0			0
$772$	4.06083	−	9.70946i	0.146153	−	0.349451i
$773$	−13.0080	+	5.38808i	−0.467864	+	0.193796i	−0.604145	−	0.796875i	$-0.706485\pi$
$773$	−13.0080	+	5.38808i	−0.467864	+	0.193796i	0.136281	+	0.990670i	$0.456485\pi$
$774$		0			0
$775$	22.4548	−	22.4548i	0.806600	−	0.806600i
$776$	4.39396	+	22.6992i	0.157734	+	0.814854i
$777$		0			0
$778$	15.5295	−	23.1555i	0.556759	−	0.830165i
$779$	−0.640439	−	1.54616i	−0.0229461	−	0.0553968i
$780$		0			0
$781$	−22.4179	−	9.28581i	−0.802176	−	0.332272i
$782$	−14.3399	+	71.4514i	−0.512794	+	2.55510i
$783$		0			0
$784$	−26.8288	+	26.4635i	−0.958171	+	0.945124i
$785$		−	43.9190i		−	1.56754i
$786$		0			0
$787$	−14.3685	−	5.95164i	−0.512183	−	0.212153i	0.111596	−	0.993754i	$-0.464404\pi$
$787$	−14.3685	−	5.95164i	−0.512183	−	0.212153i	−0.623779	+	0.781601i	$0.714404\pi$
$788$	0.00709520	−	2.07006i	0.000252756	−	0.0737429i
$789$		0			0
$790$	−18.9454	−	12.7060i	−0.674049	−	0.452058i
$791$	24.3450	+	24.3450i	0.865607	+	0.865607i
$792$		0			0
$793$	−1.19253	+	1.19253i	−0.0423481	+	0.0423481i
$794$	11.0642	−	2.18110i	0.392654	−	0.0774044i
$795$		0			0
$796$	15.4580	+	37.6837i	0.547894	+	1.33566i
$797$	−14.2369	+	34.3710i	−0.504299	+	1.21748i	0.442823	+	0.896609i	$0.353977\pi$
$797$	−14.2369	+	34.3710i	−0.504299	+	1.21748i	−0.947121	+	0.320875i	$0.896023\pi$
$798$		0			0
$799$	20.2651			0.716929
$800$	58.1353	−	38.1283i	2.05539	−	1.34804i
$801$		0			0
$802$	15.0449	+	22.6000i	0.531252	+	0.798033i
$803$	1.65960	−	4.00664i	0.0585661	−	0.141391i
$804$		0			0
$805$	−123.949	+	51.3413i	−4.36862	+	1.80954i
$806$	−2.69450	+	0.531170i	−0.0949095	+	0.0187097i
$807$		0			0
$808$	27.2111	+	41.1811i	0.957284	+	1.44875i
$809$	7.42564	+	7.42564i	0.261072	+	0.261072i	0.825489	−	0.564418i	$-0.190899\pi$
$809$	7.42564	+	7.42564i	0.261072	+	0.261072i	−0.564418	+	0.825489i	$0.690899\pi$
$810$		0			0
$811$	−1.21922	−	2.94346i	−0.0428126	−	0.103359i	0.901027	−	0.433764i	$-0.142815\pi$
$811$	−1.21922	−	2.94346i	−0.0428126	−	0.103359i	−0.943839	+	0.330405i	$0.892815\pi$
$812$	12.8657	+	0.0440975i	0.451497	+	0.00154752i
$813$		0			0
$814$	29.6506	+	5.95072i	1.03925	+	0.208572i
$815$		−	53.4051i		−	1.87070i
$816$		0			0
$817$			0.460548i			0.0161125i
$818$	4.43982	−	22.1223i	0.155235	−	0.773488i
$819$		0			0
$820$	41.0862	−	40.8055i	1.43479	−	1.42499i
$821$	14.8665	+	35.8908i	0.518843	+	1.25260i	0.938615	+	0.344967i	$0.112110\pi$
$821$	14.8665	+	35.8908i	0.518843	+	1.25260i	−0.419772	+	0.907630i	$0.637890\pi$
$822$		0			0
$823$	22.5809	+	22.5809i	0.787121	+	0.787121i	0.981021	−	0.193900i	$-0.0621138\pi$
$823$	22.5809	+	22.5809i	0.787121	+	0.787121i	−0.193900	+	0.981021i	$0.562114\pi$
$824$	15.0654	+	10.1788i	0.524829	+	0.354596i
$825$		0			0
$826$	0.600181	+	3.04457i	0.0208830	+	0.105934i
$827$	−50.1317	+	20.7652i	−1.74325	+	0.722078i	−0.744748	+	0.667346i	$0.767430\pi$
$827$	−50.1317	+	20.7652i	−1.74325	+	0.722078i	−0.998501	+	0.0547320i	$0.982570\pi$
$828$		0			0
$829$	−2.12358	+	5.12677i	−0.0737549	+	0.178060i	−0.956457	−	0.291872i	$-0.905722\pi$
$829$	−2.12358	+	5.12677i	−0.0737549	+	0.178060i	0.882702	+	0.469932i	$0.155722\pi$
$830$	25.7949	−	17.1718i	0.895355	−	0.596040i
$831$		0			0
$832$	−6.01228	−	0.0618237i	−0.208438	−	0.00214335i
$833$	60.9737			2.11261
$834$		0			0
$835$	−6.87296	+	16.5928i	−0.237849	+	0.574217i
$836$	1.67953	+	0.702437i	0.0580877	+	0.0242943i
$837$		0			0
$838$	1.95270	+	9.90555i	0.0674548	+	0.342182i
$839$	−37.8215	+	37.8215i	−1.30574	+	1.30574i	−0.381284	+	0.924458i	$0.624518\pi$
$839$	−37.8215	+	37.8215i	−1.30574	+	1.30574i	−0.924458	+	0.381284i	$0.875482\pi$
$840$		0			0
$841$	18.7241	+	18.7241i	0.645660	+	0.645660i
$842$	26.5234	−	39.5482i	0.914057	−	1.36292i
$843$		0			0
$844$	−33.5644	+	33.3351i	−1.15533	+	1.14744i
$845$	47.7710	+	19.7874i	1.64337	+	0.680707i
$846$		0			0
$847$		−	13.5474i		−	0.465493i
$848$	−9.88549	+	23.4105i	−0.339469	+	0.803919i
$849$		0			0
$850$	−110.291	−	22.1347i	−3.78293	−	0.759214i
$851$	41.5350	+	17.2044i	1.42380	+	0.589758i
$852$		0			0
$853$	−10.6997	−	25.8314i	−0.366351	−	0.884449i	−0.994342	−	0.106229i	$-0.966122\pi$
$853$	−10.6997	−	25.8314i	−0.366351	−	0.884449i	0.627991	−	0.778221i	$-0.283878\pi$
$854$	10.6802	+	7.16276i	0.365468	+	0.245105i
$855$		0			0
$856$	−34.2250	+	22.6147i	−1.16979	+	0.772956i
$857$	−15.9700	+	15.9700i	−0.545525	+	0.545525i	−0.925143	−	0.379618i	$-0.876055\pi$
$857$	−15.9700	+	15.9700i	−0.545525	+	0.545525i	0.379618	+	0.925143i	$0.376055\pi$
$858$		0			0
$859$	32.3474	−	13.3987i	1.10368	−	0.457159i	0.244923	−	0.969543i	$-0.421237\pi$
$859$	32.3474	−	13.3987i	1.10368	−	0.457159i	0.858757	+	0.512384i	$0.171237\pi$
$860$	−14.7432	+	6.04773i	−0.502740	+	0.206226i
$861$		0			0
$862$	−4.22628	−	6.34860i	−0.143948	−	0.216234i
$863$	−22.1603			−0.754347			−0.377173	−	0.926143i	$-0.623104\pi$
$863$	−22.1603			−0.754347			−0.377173	+	0.926143i	$0.623104\pi$
$864$		0			0
$865$	−9.02061			−0.306710
$866$	21.7510	+	32.6737i	0.739129	+	1.11030i
$867$		0			0
$868$	7.94746	+	19.3744i	0.269754	+	0.657610i
$869$	13.5732	−	5.62218i	0.460438	−	0.190719i
$870$		0			0
$871$	−7.61375	+	7.61375i	−0.257982	+	0.257982i
$872$	−5.16136	+	25.2683i	−0.174786	+	0.855692i
$873$		0			0
$874$	2.24766	+	1.50742i	0.0760282	+	0.0509891i
$875$	−47.0080	−	113.487i	−1.58916	−	3.83657i
$876$		0			0
$877$	−13.0797	−	5.41778i	−0.441669	−	0.182945i	0.150756	−	0.988571i	$-0.451829\pi$
$877$	−13.0797	−	5.41778i	−0.441669	−	0.182945i	−0.592425	+	0.805626i	$0.701829\pi$
$878$	−29.8967	−	6.00010i	−1.00896	−	0.202494i
$879$		0			0
$880$	−0.431804	+	62.9898i	−0.0145561	+	2.12339i
$881$			27.0472i			0.911242i	0.890174	+	0.455621i	$0.150583\pi$
$881$			27.0472i			0.911242i	−0.890174	+	0.455621i	$0.849417\pi$
$882$		0			0
$883$	−8.33972	−	3.45443i	−0.280654	−	0.116251i	0.237916	−	0.971286i	$-0.423536\pi$
$883$	−8.33972	−	3.45443i	−0.280654	−	0.116251i	−0.518570	+	0.855035i	$0.673536\pi$
$884$	6.85546	+	6.90261i	0.230574	+	0.232160i
$885$		0			0
$886$	−21.1138	+	31.4821i	−0.709331	+	1.05766i
$887$	−21.3235	−	21.3235i	−0.715972	−	0.715972i	0.251806	−	0.967778i	$-0.418976\pi$
$887$	−21.3235	−	21.3235i	−0.715972	−	0.715972i	−0.967778	+	0.251806i	$0.918976\pi$
$888$		0			0
$889$	10.0992	−	10.0992i	0.338717	−	0.338717i
$890$	−18.0893	−	91.7626i	−0.606354	−	3.07589i
$891$		0			0
$892$	1.95632	−	4.67756i	0.0655024	−	0.156616i
$893$	0.287995	−	0.695282i	0.00963739	−	0.0232667i
$894$		0			0
$895$	53.5754			1.79083
$896$	8.40414	+	45.0696i	0.280763	+	1.50567i
$897$		0			0
$898$	−2.50754	+	1.66927i	−0.0836776	+	0.0557044i
$899$	1.56969	−	3.78957i	0.0523521	−	0.126389i
$900$		0			0
$901$	37.9873	−	15.7349i	1.26554	−	0.524204i
$902$	7.21295	+	36.5896i	0.240165	+	1.21830i
$903$		0			0
$904$	23.5929	−	4.56694i	0.784687	−	0.151894i
$905$	−16.5155	−	16.5155i	−0.548995	−	0.548995i
$906$		0			0
$907$	−9.53648	−	23.0231i	−0.316654	−	0.764470i	−0.999427	−	0.0338397i	$-0.989226\pi$
$907$	−9.53648	−	23.0231i	−0.316654	−	0.764470i	0.682774	−	0.730630i	$-0.260774\pi$
$908$	13.9286	+	14.0244i	0.462238	+	0.465417i
$909$		0			0
$910$	−3.52409	+	17.5595i	−0.116822	+	0.582090i
$911$		−	32.1146i		−	1.06400i	−0.846743	−	0.532002i	$-0.821440\pi$
$911$		−	32.1146i		−	1.06400i	0.846743	−	0.532002i	$-0.178560\pi$
$912$		0			0
$913$			19.9572i			0.660488i
$914$	19.7485	+	3.96342i	0.653223	+	0.131098i
$915$		0			0
$916$	0.113191	−	33.0240i	0.00373993	−	1.09115i
$917$	−10.0774	−	24.3289i	−0.332784	−	0.803412i
$918$		0			0
$919$	−32.5946	−	32.5946i	−1.07520	−	1.07520i	−0.996933	−	0.0782648i	$-0.975062\pi$
$919$	−32.5946	−	32.5946i	−1.07520	−	1.07520i	−0.0782648	−	0.996933i	$-0.524938\pi$
$920$	−18.7406	+	91.7477i	−0.617860	+	3.02483i
$921$		0			0
$922$	−20.5797	+	4.05691i	−0.677757	+	0.133607i
$923$	−4.44882	+	1.84276i	−0.146435	+	0.0606553i
$924$		0			0
$925$	−26.5562	+	64.1123i	−0.873162	+	2.10800i
$926$	−20.4224	−	30.6779i	−0.671121	−	1.00814i
$927$		0			0
$928$	5.05286	−	7.42363i	0.165868	−	0.243693i
$929$	−8.99533			−0.295127			−0.147564	−	0.989053i	$-0.547143\pi$
$929$	−8.99533			−0.295127			−0.147564	+	0.989053i	$0.547143\pi$
$930$		0			0
$931$	0.866520	−	2.09196i	0.0283990	−	0.0685613i
$932$	−39.1230	+	16.0484i	−1.28151	+	0.525682i
$933$		0			0
$934$	−3.40677	+	0.671581i	−0.111473	+	0.0219748i
$935$	72.0691	−	72.0691i	2.35691	−	2.35691i
$936$		0			0
$937$	42.2833	+	42.2833i	1.38133	+	1.38133i	0.842256	+	0.539078i	$0.181227\pi$
$937$	42.2833	+	42.2833i	1.38133	+	1.38133i	0.539078	+	0.842256i	$0.318773\pi$
$938$	68.1876	+	45.7307i	2.22641	+	1.49316i
$939$		0			0
$940$	26.0395	+	0.0892511i	0.849314	+	0.00291105i
$941$	−32.4653	−	13.4476i	−1.05834	−	0.438378i	−0.215477	−	0.976509i	$-0.569131\pi$
$941$	−32.4653	−	13.4476i	−1.05834	−	0.438378i	−0.842861	+	0.538131i	$0.819131\pi$
$942$		0			0
$943$			55.4404i			1.80539i
$944$	1.99535	+	0.842574i	0.0649432	+	0.0274234i
$945$		0			0
$946$	2.01945	−	10.0623i	0.0656580	−	0.327154i
$947$	−23.1555	−	9.59133i	−0.752454	−	0.311676i	−0.0267113	−	0.999643i	$-0.508503\pi$
$947$	−23.1555	−	9.59133i	−0.752454	−	0.311676i	−0.725742	+	0.687967i	$0.758503\pi$
$948$		0			0
$949$	−0.329347	−	0.795115i	−0.0106911	−	0.0258105i
$950$	−2.32681	+	3.46943i	−0.0754916	+	0.112563i
$951$		0			0
$952$	41.5289	−	61.4660i	1.34596	−	1.99212i
$953$	17.4727	−	17.4727i	0.565997	−	0.565997i	−0.365007	−	0.931005i	$-0.618934\pi$
$953$	17.4727	−	17.4727i	0.565997	−	0.565997i	0.931005	+	0.365007i	$0.118934\pi$
$954$		0			0
$955$	26.9605	−	11.1674i	0.872420	−	0.361368i
$956$	27.8483	+	11.6471i	0.900679	+	0.376695i
$957$		0			0
$958$	7.67281	−	5.10781i	0.247897	−	0.165026i
$959$	66.9225			2.16104
$960$		0			0
$961$	−24.3237			−0.784634
$962$	4.99575	−	3.32569i	0.161070	−	0.107224i
$963$		0			0
$964$	−36.0272	−	15.0678i	−1.16036	−	0.485302i
$965$	−20.2154	+	8.37351i	−0.650758	+	0.269553i
$966$		0			0
$967$	−4.29017	+	4.29017i	−0.137963	+	0.137963i	−0.772715	−	0.634753i	$-0.781102\pi$
$967$	−4.29017	+	4.29017i	−0.137963	+	0.137963i	0.634753	+	0.772715i	$0.281102\pi$
$968$	−7.83513	−	5.29373i	−0.251830	−	0.170147i
$969$		0			0
$970$	26.7743	−	39.9223i	0.859671	−	1.28183i
$971$	−5.94304	−	14.3478i	−0.190721	−	0.460442i	0.799375	−	0.600832i	$-0.205164\pi$
$971$	−5.94304	−	14.3478i	−0.190721	−	0.460442i	−0.990096	+	0.140391i	$0.955164\pi$
$972$		0			0
$973$	25.0594	+	10.3799i	0.803366	+	0.332765i
$974$	−11.6121	+	57.8597i	−0.372076	+	1.85394i
$975$		0			0
$976$	8.31593	−	3.37797i	0.266186	−	0.108126i
$977$		−	29.9611i		−	0.958539i	−0.877668	−	0.479270i	$-0.840902\pi$
$977$		−	29.9611i		−	0.958539i	0.877668	−	0.479270i	$-0.159098\pi$
$978$		0			0
$979$	55.6504	+	23.0512i	1.77859	+	0.736718i
$980$	78.3475	+	0.268538i	2.50272	+	0.00857815i
$981$		0			0
$982$	−23.7060	−	15.8987i	−0.756489	−	0.507347i
$983$	6.13319	+	6.13319i	0.195618	+	0.195618i	0.798119	−	0.602500i	$-0.205829\pi$
$983$	6.13319	+	6.13319i	0.195618	+	0.195618i	−0.602500	+	0.798119i	$0.705829\pi$
$984$		0			0
$985$	−3.04326	+	3.04326i	−0.0969664	+	0.0969664i
$986$	−14.2556	+	2.81022i	−0.453989	+	0.0894956i
$987$		0			0
$988$	0.334249	−	0.137110i	0.0106339	−	0.00436206i
$989$	5.83852	−	14.0954i	0.185654	−	0.448209i
$990$		0			0
$991$	−8.67514			−0.275575			−0.137787	−	0.990462i	$-0.543999\pi$
$991$	−8.67514			−0.275575			−0.137787	+	0.990462i	$0.543999\pi$
$992$	14.3107	+	2.97428i	0.454366	+	0.0944334i
$993$		0			0
$994$	20.3468	+	30.5644i	0.645362	+	0.969444i
$995$	32.4066	−	78.2364i	1.02736	−	2.48026i
$996$		0			0
$997$	−26.5390	+	10.9928i	−0.840499	+	0.348146i	−0.761050	−	0.648693i	$-0.775316\pi$
$997$	−26.5390	+	10.9928i	−0.840499	+	0.348146i	−0.0794486	+	0.996839i	$0.525316\pi$
$998$	−5.32114	+	1.04896i	−0.168438	+	0.0332044i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.7	✓	128
3.2	odd	2	inner	864.2.v.a.109.26	yes	128
32.5	even	8	inner	864.2.v.a.325.7	yes	128
96.5	odd	8	inner	864.2.v.a.325.26	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.7	✓	128	1.1	even	1	trivial
864.2.v.a.109.26	yes	128	3.2	odd	2	inner
864.2.v.a.325.7	yes	128	32.5	even	8	inner
864.2.v.a.325.26	yes	128	96.5	odd	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17722 + 0.783679i) q^{2} +(0.771696 - 1.84512i) q^{4} +(-3.84162 + 1.59125i) q^{5} +(-2.86540 + 2.86540i) q^{7} +(0.537529 + 2.77688i) q^{8} +O(q^{10})\)	\(q+(-1.17722 + 0.783679i) q^{2} +(0.771696 - 1.84512i) q^{4} +(-3.84162 + 1.59125i) q^{5} +(-2.86540 + 2.86540i) q^{7} +(0.537529 + 2.77688i) q^{8} +(3.27540 - 4.88384i) q^{10} +(1.44931 + 3.49895i) q^{11} +(0.694364 + 0.287615i) q^{13} +(1.12766 - 5.61876i) q^{14} +(-2.80897 - 2.84775i) q^{16} +6.47207i q^{17} +(0.222052 + 0.0919770i) q^{19} +(-0.0285041 + 8.31622i) q^{20} +(-4.44821 - 2.98324i) q^{22} +(-5.63006 - 5.63006i) q^{23} +(8.69041 - 8.69041i) q^{25} +(-1.04282 + 0.205572i) q^{26} +(3.07581 + 7.49824i) q^{28} +(0.607498 - 1.46663i) q^{29} +2.58386 q^{31} +(5.53850 + 1.15110i) q^{32} +(-5.07202 - 7.61905i) q^{34} +(6.44820 - 15.5673i) q^{35} +(-5.21659 + 2.16078i) q^{37} +(-0.333485 + 0.0657403i) q^{38} +(-6.48369 - 9.81236i) q^{40} +(-4.92361 - 4.92361i) q^{41} +(0.733289 + 1.77032i) q^{43} +(7.57442 + 0.0259616i) q^{44} +(11.0400 + 2.21566i) q^{46} -3.13117i q^{47} -9.42105i q^{49} +(-3.42004 + 17.0410i) q^{50} +(1.06652 - 1.05924i) q^{52} +(-2.43120 - 5.86943i) q^{53} +(-11.1354 - 11.1354i) q^{55} +(-9.49711 - 6.41664i) q^{56} +(0.434207 + 2.20263i) q^{58} +(-0.500271 + 0.207219i) q^{59} +(-0.858724 + 2.07314i) q^{61} +(-3.04177 + 2.02492i) q^{62} +(-7.42212 + 2.98531i) q^{64} -3.12515 q^{65} +(-5.48254 + 13.2360i) q^{67} +(11.9418 + 4.99447i) q^{68} +(4.60884 + 23.3795i) q^{70} +(-4.53047 + 4.53047i) q^{71} +(-0.809706 - 0.809706i) q^{73} +(4.44772 - 6.63185i) q^{74} +(0.341066 - 0.338736i) q^{76} +(-14.1788 - 5.87303i) q^{77} -3.87921i q^{79} +(15.3225 + 6.47019i) q^{80} +(9.65471 + 1.93765i) q^{82} +(4.86848 + 2.01659i) q^{83} +(-10.2987 - 24.8632i) q^{85} +(-2.25060 - 1.50939i) q^{86} +(-8.93711 + 5.90535i) q^{88} +(11.2465 - 11.2465i) q^{89} +(-2.81376 + 1.16550i) q^{91} +(-14.7328 + 6.04347i) q^{92} +(2.45383 + 3.68607i) q^{94} -0.999397 q^{95} +8.17436 q^{97} +(7.38308 + 11.0907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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