LMFDB - Embedded newform 864.2.v.b.109.10

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			109.10
Character	$\chi$	$=$	864.109
Dual form			864.2.v.b.325.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877362 + 1.10916i) q^{2} +(-0.460473 - 1.94627i) q^{4} +(3.16129 - 1.30945i) q^{5} +(3.16733 - 3.16733i) q^{7} +(2.56273 + 1.19684i) q^{8} +O(q^{10})$	\(q+(-0.877362 + 1.10916i) q^{2} +(-0.460473 - 1.94627i) q^{4} +(3.16129 - 1.30945i) q^{5} +(3.16733 - 3.16733i) q^{7} +(2.56273 + 1.19684i) q^{8} +(-1.32120 + 4.65523i) q^{10} +(1.03307 + 2.49405i) q^{11} +(2.98219 + 1.23526i) q^{13} +(0.734183 + 6.29197i) q^{14} +(-3.57593 + 1.79241i) q^{16} -2.14766i q^{17} +(-6.92299 - 2.86759i) q^{19} +(-4.00422 - 5.54975i) q^{20} +(-3.67267 - 1.04234i) q^{22} +(5.16599 + 5.16599i) q^{23} +(4.74354 - 4.74354i) q^{25} +(-3.98656 + 2.22395i) q^{26} +(-7.62295 - 4.70601i) q^{28} +(0.875489 - 2.11362i) q^{29} -4.47936 q^{31} +(1.14931 - 5.53887i) q^{32} +(2.38210 + 1.88427i) q^{34} +(5.86539 - 14.1603i) q^{35} +(-2.25327 + 0.933333i) q^{37} +(9.25458 - 5.16278i) q^{38} +(9.66871 + 0.427809i) q^{40} +(-1.06719 - 1.06719i) q^{41} +(-1.57823 - 3.81019i) q^{43} +(4.37839 - 3.15907i) q^{44} +(-10.2623 + 1.19747i) q^{46} +5.62964i q^{47} -13.0640i q^{49} +(1.09955 + 9.42315i) q^{50} +(1.03094 - 6.37295i) q^{52} +(1.31226 + 3.16807i) q^{53} +(6.53164 + 6.53164i) q^{55} +(11.9078 - 4.32620i) q^{56} +(1.57622 + 2.82546i) q^{58} +(-10.5601 + 4.37413i) q^{59} +(-1.34023 + 3.23561i) q^{61} +(3.93002 - 4.96833i) q^{62} +(5.13513 + 6.13436i) q^{64} +11.0451 q^{65} +(-2.09986 + 5.06951i) q^{67} +(-4.17992 + 0.988940i) q^{68} +(10.5600 + 18.9294i) q^{70} +(-4.98493 + 4.98493i) q^{71} +(8.05547 + 8.05547i) q^{73} +(0.941713 - 3.31810i) q^{74} +(-2.39326 + 14.7944i) q^{76} +(11.1715 + 4.62740i) q^{77} -14.7761i q^{79} +(-8.95747 + 10.3488i) q^{80} +(2.11999 - 0.247373i) q^{82} +(-4.09240 - 1.69513i) q^{83} +(-2.81225 - 6.78937i) q^{85} +(5.61078 + 1.59240i) q^{86} +(-0.337513 + 7.62798i) q^{88} +(-10.3239 + 10.3239i) q^{89} +(13.3581 - 5.53310i) q^{91} +(7.67560 - 12.4332i) q^{92} +(-6.24417 - 4.93923i) q^{94} -25.6405 q^{95} +14.7875 q^{97} +(14.4901 + 11.4618i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) $ 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * 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 $

$2$	−0.877362	+	1.10916i	−0.620388	+	0.784295i
$2$	−0.877362	+	1.10916i	−0.620388	+	0.784295i
$3$		0			0
$3$		0			0
$4$	−0.460473	−	1.94627i	−0.230237	−	0.973135i
$5$	3.16129	−	1.30945i	1.41377	−	0.585603i	0.460483	−	0.887669i	$-0.347676\pi$
$5$	3.16129	−	1.30945i	1.41377	−	0.585603i	0.953287	+	0.302066i	$0.0976763\pi$
$6$		0			0
$7$	3.16733	−	3.16733i	1.19714	−	1.19714i	0.222120	−	0.975019i	$-0.428702\pi$
$7$	3.16733	−	3.16733i	1.19714	−	1.19714i	0.975019	−	0.222120i	$-0.0712975\pi$
$8$	2.56273	+	1.19684i	0.906061	+	0.423148i
$9$		0			0
$10$	−1.32120	+	4.65523i	−0.417801	+	1.47211i
$11$	1.03307	+	2.49405i	0.311482	+	0.751983i	0.999651	+	0.0264327i	$0.00841477\pi$
$11$	1.03307	+	2.49405i	0.311482	+	0.751983i	−0.688169	+	0.725550i	$0.741585\pi$
$12$		0			0
$13$	2.98219	+	1.23526i	0.827111	+	0.342600i	0.755758	−	0.654851i	$-0.227268\pi$
$13$	2.98219	+	1.23526i	0.827111	+	0.342600i	0.0713524	+	0.997451i	$0.477268\pi$
$14$	0.734183	+	6.29197i	0.196219	+	1.68160i
$15$		0			0
$16$	−3.57593	+	1.79241i	−0.893982	+	0.448102i
$17$		−	2.14766i		−	0.520884i	−0.965489	−	0.260442i	$-0.916132\pi$
$17$		−	2.14766i		−	0.520884i	0.965489	−	0.260442i	$-0.0838683\pi$
$18$		0			0
$19$	−6.92299	−	2.86759i	−1.58824	−	0.657871i	−0.598550	−	0.801085i	$-0.704256\pi$
$19$	−6.92299	−	2.86759i	−1.58824	−	0.657871i	−0.989692	+	0.143214i	$0.954256\pi$
$20$	−4.00422	−	5.54975i	−0.895372	−	1.24096i
$21$		0			0
$22$	−3.67267	−	1.04234i	−0.783016	−	0.222228i
$23$	5.16599	+	5.16599i	1.07718	+	1.07718i	0.996761	+	0.0804218i	$0.0256267\pi$
$23$	5.16599	+	5.16599i	1.07718	+	1.07718i	0.0804218	+	0.996761i	$0.474373\pi$
$24$		0			0
$25$	4.74354	−	4.74354i	0.948708	−	0.948708i
$26$	−3.98656	+	2.22395i	−0.781830	+	0.436153i
$27$		0			0
$28$	−7.62295	−	4.70601i	−1.44060	−	0.889352i
$29$	0.875489	−	2.11362i	0.162574	−	0.392489i	−0.821509	−	0.570195i	$-0.806868\pi$
$29$	0.875489	−	2.11362i	0.162574	−	0.392489i	0.984084	+	0.177706i	$0.0568676\pi$
$30$		0			0
$31$	−4.47936			−0.804517			−0.402259	−	0.915526i	$-0.631775\pi$
$31$	−4.47936			−0.804517			−0.402259	+	0.915526i	$0.631775\pi$
$32$	1.14931	−	5.53887i	0.203172	−	0.979143i
$33$		0			0
$34$	2.38210	+	1.88427i	0.408527	+	0.323150i
$35$	5.86539	−	14.1603i	0.991431	−	2.39353i
$36$		0			0
$37$	−2.25327	+	0.933333i	−0.370435	+	0.153439i	−0.560132	−	0.828404i	$-0.689249\pi$
$37$	−2.25327	+	0.933333i	−0.370435	+	0.153439i	0.189697	+	0.981843i	$0.439249\pi$
$38$	9.25458	−	5.16278i	1.50129	−	0.837514i
$39$		0			0
$40$	9.66871	+	0.427809i	1.52876	+	0.0676426i
$41$	−1.06719	−	1.06719i	−0.166667	−	0.166667i	0.618846	−	0.785513i	$-0.287601\pi$
$41$	−1.06719	−	1.06719i	−0.166667	−	0.166667i	−0.785513	+	0.618846i	$0.787601\pi$
$42$		0			0
$43$	−1.57823	−	3.81019i	−0.240678	−	0.581048i	0.756673	−	0.653794i	$-0.226824\pi$
$43$	−1.57823	−	3.81019i	−0.240678	−	0.581048i	−0.997350	+	0.0727462i	$0.976824\pi$
$44$	4.37839	−	3.15907i	0.660066	−	0.476248i
$45$		0			0
$46$	−10.2623	+	1.19747i	−1.51310	+	0.176557i
$47$			5.62964i			0.821167i	0.911823	+	0.410584i	$0.134675\pi$
$47$			5.62964i			0.821167i	−0.911823	+	0.410584i	$0.865325\pi$
$48$		0			0
$49$		−	13.0640i		−	1.86628i
$50$	1.09955	+	9.42315i	0.155499	+	1.33263i
$51$		0			0
$52$	1.03094	−	6.37295i	0.142965	−	0.883769i
$53$	1.31226	+	3.16807i	0.180252	+	0.435168i	0.988019	−	0.154335i	$-0.0493236\pi$
$53$	1.31226	+	3.16807i	0.180252	+	0.435168i	−0.807766	+	0.589503i	$0.799324\pi$
$54$		0			0
$55$	6.53164	+	6.53164i	0.880727	+	0.880727i
$56$	11.9078	−	4.32620i	1.59125	−	0.578113i
$57$		0			0
$58$	1.57622	+	2.82546i	0.206968	+	0.371002i
$59$	−10.5601	+	4.37413i	−1.37481	+	0.569464i	−0.943088	−	0.332544i	$-0.892093\pi$
$59$	−10.5601	+	4.37413i	−1.37481	+	0.569464i	−0.431719	+	0.902008i	$0.642093\pi$
$60$		0			0
$61$	−1.34023	+	3.23561i	−0.171600	+	0.414278i	−0.986159	−	0.165802i	$-0.946979\pi$
$61$	−1.34023	+	3.23561i	−0.171600	+	0.414278i	0.814560	+	0.580080i	$0.196979\pi$
$62$	3.93002	−	4.96833i	0.499113	−	0.630979i
$63$		0			0
$64$	5.13513	+	6.13436i	0.641891	+	0.766796i
$65$	11.0451			1.36997
$66$		0			0
$67$	−2.09986	+	5.06951i	−0.256539	+	0.619340i	−0.998705	−	0.0508765i	$-0.983799\pi$
$67$	−2.09986	+	5.06951i	−0.256539	+	0.619340i	0.742166	+	0.670216i	$0.233799\pi$
$68$	−4.17992	+	0.988940i	−0.506890	+	0.119927i
$69$		0			0
$70$	10.5600	+	18.9294i	1.26216	+	2.26249i
$71$	−4.98493	+	4.98493i	−0.591603	+	0.591603i	−0.938064	−	0.346462i	$-0.887383\pi$
$71$	−4.98493	+	4.98493i	−0.591603	+	0.591603i	0.346462	+	0.938064i	$0.387383\pi$
$72$		0			0
$73$	8.05547	+	8.05547i	0.942821	+	0.942821i	0.998451	−	0.0556300i	$-0.0177167\pi$
$73$	8.05547	+	8.05547i	0.942821	+	0.942821i	−0.0556300	+	0.998451i	$0.517717\pi$
$74$	0.941713	−	3.31810i	0.109472	−	0.385722i
$75$		0			0
$76$	−2.39326	+	14.7944i	−0.274526	+	1.69704i
$77$	11.1715	+	4.62740i	1.27312	+	0.527342i
$78$		0			0
$79$		−	14.7761i		−	1.66244i	−0.555945	−	0.831219i	$-0.687643\pi$
$79$		−	14.7761i		−	1.66244i	0.555945	−	0.831219i	$-0.312357\pi$
$80$	−8.95747	+	10.3488i	−1.00148	+	1.15703i
$81$		0			0
$82$	2.11999	−	0.247373i	0.234114	−	0.0273177i
$83$	−4.09240	−	1.69513i	−0.449200	−	0.186065i	0.146603	−	0.989195i	$-0.453166\pi$
$83$	−4.09240	−	1.69513i	−0.449200	−	0.186065i	−0.595803	+	0.803131i	$0.703166\pi$
$84$		0			0
$85$	−2.81225	−	6.78937i	−0.305031	−	0.736410i
$86$	5.61078	+	1.59240i	0.605027	+	0.171713i
$87$		0			0
$88$	−0.337513	+	7.62798i	−0.0359790	+	0.813145i
$89$	−10.3239	+	10.3239i	−1.09433	+	1.09433i	−0.0992728	+	0.995060i	$0.531652\pi$
$89$	−10.3239	+	10.3239i	−1.09433	+	1.09433i	−0.995060	+	0.0992728i	$0.968348\pi$
$90$		0			0
$91$	13.3581	−	5.53310i	1.40031	−	0.580026i
$92$	7.67560	−	12.4332i	0.800237	−	1.29625i
$93$		0			0
$94$	−6.24417	−	4.93923i	−0.644037	−	0.509442i
$95$	−25.6405			−2.63066
$96$		0			0
$97$	14.7875			1.50145			0.750724	−	0.660616i	$-0.229705\pi$
$97$	14.7875			1.50145			0.750724	+	0.660616i	$0.229705\pi$
$98$	14.4901	+	11.4618i	1.46372	+	1.15782i
$99$		0			0
$100$	−11.4165	−	7.04793i	−1.14165	−	0.704793i
$101$	17.9029	−	7.41564i	1.78141	−	0.737884i	0.789075	−	0.614297i	$-0.210560\pi$
$101$	17.9029	−	7.41564i	1.78141	−	0.737884i	0.992334	−	0.123586i	$-0.0394395\pi$
$102$		0			0
$103$	1.80091	−	1.80091i	0.177449	−	0.177449i	−0.612794	−	0.790243i	$-0.709954\pi$
$103$	1.80091	−	1.80091i	0.177449	−	0.177449i	0.790243	+	0.612794i	$0.209954\pi$
$104$	6.16412	+	6.73486i	0.604442	+	0.660407i
$105$		0			0
$106$	−4.66522	−	1.32404i	−0.453126	−	0.128602i
$107$	−3.42310	−	8.26409i	−0.330923	−	0.798919i	−0.998519	−	0.0543959i	$-0.982677\pi$
$107$	−3.42310	−	8.26409i	−0.330923	−	0.798919i	0.667596	−	0.744524i	$-0.267323\pi$
$108$		0			0
$109$	4.67481	+	1.93637i	0.447766	+	0.185471i	0.595160	−	0.803607i	$-0.297089\pi$
$109$	4.67481	+	1.93637i	0.447766	+	0.185471i	−0.147394	+	0.989078i	$0.547089\pi$
$110$	−12.9753	+	1.51403i	−1.23714	+	0.144357i
$111$		0			0
$112$	−5.64900	+	17.0033i	−0.533780	+	1.60666i
$113$		−	4.34592i		−	0.408830i	−0.978884	−	0.204415i	$-0.934471\pi$
$113$		−	4.34592i		−	0.408830i	0.978884	−	0.204415i	$-0.0655292\pi$
$114$		0			0
$115$	23.0957	+	9.56657i	2.15369	+	0.892087i
$116$	−4.51681	−	0.730673i	−0.419375	−	0.0678413i
$117$		0			0
$118$	4.41341	−	15.5505i	0.406287	−	1.43154i
$119$	−6.80235	−	6.80235i	−0.623571	−	0.623571i
$120$		0			0
$121$	2.62514	−	2.62514i	0.238649	−	0.238649i
$122$	−2.41294	−	4.32534i	−0.218458	−	0.391598i
$123$		0			0
$124$	2.06263	+	8.71805i	0.185229	+	0.782904i
$125$	2.23703	−	5.40067i	0.200086	−	0.483051i
$126$		0			0
$127$	−0.358622			−0.0318226			−0.0159113	−	0.999873i	$-0.505065\pi$
$127$	−0.358622			−0.0318226			−0.0159113	+	0.999873i	$0.505065\pi$
$128$	−11.3094	+	0.313627i	−0.999616	+	0.0277210i
$129$		0			0
$130$	−9.69052	+	12.2507i	−0.849915	+	1.07446i
$131$	−6.94216	+	16.7599i	−0.606539	+	1.46431i	0.260201	+	0.965555i	$0.416211\pi$
$131$	−6.94216	+	16.7599i	−0.606539	+	1.46431i	−0.866740	+	0.498760i	$0.833789\pi$
$132$		0			0
$133$	−31.0100	+	12.8448i	−2.68891	+	1.11378i
$134$	−3.78056	−	6.77688i	−0.326591	−	0.585433i
$135$		0			0
$136$	2.57041	−	5.50386i	0.220411	−	0.471952i
$137$	−10.4005	−	10.4005i	−0.888572	−	0.888572i	0.105813	−	0.994386i	$-0.466255\pi$
$137$	−10.4005	−	10.4005i	−0.888572	−	0.888572i	−0.994386	+	0.105813i	$0.966255\pi$
$138$		0			0
$139$	4.47855	+	10.8122i	0.379866	+	0.917076i	0.991990	+	0.126315i	$0.0403151\pi$
$139$	4.47855	+	10.8122i	0.379866	+	0.917076i	−0.612125	+	0.790761i	$0.709685\pi$
$140$	−30.2606	−	4.89519i	−2.55749	−	0.413719i
$141$		0			0
$142$	−1.15550	−	9.90268i	−0.0969674	−	0.831014i
$143$			8.71383i			0.728687i
$144$		0			0
$145$		−	7.82815i		−	0.650093i
$146$	−16.0024	+	1.86725i	−1.32437	+	0.154534i
$147$		0			0
$148$	2.85409	+	3.95569i	0.234604	+	0.325155i
$149$	5.19971	+	12.5532i	0.425977	+	1.02840i	0.980551	+	0.196265i	$0.0628813\pi$
$149$	5.19971	+	12.5532i	0.425977	+	1.02840i	−0.554574	+	0.832134i	$0.687119\pi$
$150$		0			0
$151$	−2.94031	−	2.94031i	−0.239279	−	0.239279i	0.577273	−	0.816552i	$-0.304117\pi$
$151$	−2.94031	−	2.94031i	−0.239279	−	0.239279i	−0.816552	+	0.577273i	$0.804117\pi$
$152$	−14.3097	−	15.6346i	−1.16067	−	1.26813i
$153$		0			0
$154$	−14.9340	+	8.33112i	−1.20342	+	0.671341i
$155$	−14.1605	+	5.86549i	−1.13740	+	0.471127i
$156$		0			0
$157$	7.05322	−	17.0280i	0.562908	−	1.35898i	−0.344522	−	0.938778i	$-0.611959\pi$
$157$	7.05322	−	17.0280i	0.562908	−	1.35898i	0.907430	−	0.420203i	$-0.138041\pi$
$158$	16.3890	+	12.9640i	1.30384	+	1.03136i
$159$		0			0
$160$	−3.61955	−	19.0149i	−0.286151	−	1.50326i
$161$	32.7248			2.57907
$162$		0			0
$163$	−5.94501	+	14.3525i	−0.465649	+	1.12418i	0.500394	+	0.865798i	$0.333188\pi$
$163$	−5.94501	+	14.3525i	−0.465649	+	1.12418i	−0.966044	+	0.258379i	$0.916812\pi$
$164$	−1.58562	+	2.56845i	−0.123816	+	0.200562i
$165$		0			0
$166$	5.47069	−	3.05189i	0.424608	−	0.236873i
$167$	16.8895	−	16.8895i	1.30695	−	1.30695i	0.383339	−	0.923608i	$-0.374774\pi$
$167$	16.8895	−	16.8895i	1.30695	−	1.30695i	0.923608	−	0.383339i	$-0.125226\pi$
$168$		0			0
$169$	−1.82481	−	1.82481i	−0.140370	−	0.140370i
$170$	9.99785	+	2.83750i	0.766800	+	0.217626i
$171$		0			0
$172$	−6.68891	+	4.82615i	−0.510025	+	0.367990i
$173$	0.583010	+	0.241490i	0.0443254	+	0.0183602i	0.404736	−	0.914434i	$-0.367363\pi$
$173$	0.583010	+	0.241490i	0.0443254	+	0.0183602i	−0.360411	+	0.932794i	$0.617363\pi$
$174$		0			0
$175$		−	30.0487i		−	2.27147i
$176$	−8.16453	−	7.06685i	−0.615424	−	0.532684i
$177$		0			0
$178$	−2.39307	−	20.5087i	−0.179368	−	1.53719i
$179$	3.75968	+	1.55731i	0.281012	+	0.116399i	0.518738	−	0.854933i	$-0.326402\pi$
$179$	3.75968	+	1.55731i	0.281012	+	0.116399i	−0.237726	+	0.971332i	$0.576402\pi$
$180$		0			0
$181$	−0.877623	−	2.11877i	−0.0652332	−	0.157487i	0.887901	−	0.460034i	$-0.152163\pi$
$181$	−0.877623	−	2.11877i	−0.0652332	−	0.157487i	−0.953134	+	0.302548i	$0.902163\pi$
$182$	−5.58277	+	19.6708i	−0.413823	+	1.45809i
$183$		0			0
$184$	7.05613	+	19.4219i	0.520185	+	1.43180i
$185$	−5.90106	+	5.90106i	−0.433855	+	0.433855i
$186$		0			0
$187$	5.35636	−	2.21868i	0.391696	−	0.162246i
$188$	10.9568	−	2.59230i	0.799106	−	0.189063i
$189$		0			0
$190$	22.4960	−	28.4394i	1.63203	−	2.06321i
$191$	2.22748			0.161175			0.0805874	−	0.996748i	$-0.474320\pi$
$191$	2.22748			0.161175			0.0805874	+	0.996748i	$0.474320\pi$
$192$		0			0
$193$	−13.4213			−0.966083			−0.483041	−	0.875598i	$-0.660468\pi$
$193$	−13.4213			−0.966083			−0.483041	+	0.875598i	$0.660468\pi$
$194$	−12.9740	+	16.4018i	−0.931480	+	1.17758i
$195$		0			0
$196$	−25.4260	+	6.01561i	−1.81615	+	0.429687i
$197$	−14.0663	+	5.82644i	−1.00218	+	0.415117i	−0.822596	−	0.568626i	$-0.807475\pi$
$197$	−14.0663	+	5.82644i	−1.00218	+	0.415117i	−0.179584	+	0.983743i	$0.557475\pi$
$198$		0			0
$199$	12.5336	−	12.5336i	0.888483	−	0.888483i	−0.105894	−	0.994377i	$-0.533770\pi$
$199$	12.5336	−	12.5336i	0.888483	−	0.888483i	0.994377	+	0.105894i	$0.0337704\pi$
$200$	17.8337	−	6.47912i	1.26103	−	0.458143i
$201$		0			0
$202$	−7.48222	+	26.3634i	−0.526447	+	1.85492i
$203$	−3.92156	−	9.46749i	−0.275240	−	0.664488i
$204$		0			0
$205$	−4.77111	−	1.97626i	−0.333229	−	0.138028i
$206$	0.417449	+	3.57755i	0.0290851	+	0.249260i
$207$		0			0
$208$	−12.8782	+	0.928091i	−0.892942	+	0.0643515i
$209$		−	20.2287i		−	1.39925i
$210$		0			0
$211$	−9.88934	−	4.09630i	−0.680811	−	0.282001i	0.0153552	−	0.999882i	$-0.495112\pi$
$211$	−9.88934	−	4.09630i	−0.680811	−	0.282001i	−0.696166	+	0.717881i	$0.745112\pi$
$212$	5.56166	−	4.01282i	0.381976	−	0.275601i
$213$		0			0
$214$	12.1695	+	3.45383i	0.831889	+	0.236099i
$215$	−9.97847	−	9.97847i	−0.680526	−	0.680526i
$216$		0			0
$217$	−14.1876	+	14.1876i	−0.963119	+	0.963119i
$218$	−6.24924	+	3.48622i	−0.423252	+	0.236116i
$219$		0			0
$220$	9.70469	−	15.7200i	0.654290	−	1.05984i
$221$	2.65293	−	6.40473i	0.178455	−	0.430829i
$222$		0			0
$223$	−23.0450			−1.54321			−0.771603	−	0.636105i	$-0.780545\pi$
$223$	−23.0450			−1.54321			−0.771603	+	0.636105i	$0.780545\pi$
$224$	−13.9032	−	21.1837i	−0.928945	−	1.41540i
$225$		0			0
$226$	4.82033	+	3.81295i	0.320643	+	0.253633i
$227$	−1.86974	+	4.51396i	−0.124099	+	0.299602i	−0.973704	−	0.227819i	$-0.926841\pi$
$227$	−1.86974	+	4.51396i	−0.124099	+	0.299602i	0.849604	+	0.527420i	$0.176841\pi$
$228$		0			0
$229$	0.0247816	−	0.0102649i	0.00163761	−	0.000678321i	−0.381864	−	0.924218i	$-0.624718\pi$
$229$	0.0247816	−	0.0102649i	0.00163761	−	0.000678321i	0.383502	+	0.923540i	$0.374718\pi$
$230$	−30.8742	+	17.2235i	−2.03578	+	1.13569i
$231$		0			0
$232$	4.77331	−	4.36880i	0.313383	−	0.286826i
$233$	14.4840	+	14.4840i	0.948880	+	0.948880i	0.998755	−	0.0498757i	$-0.0158825\pi$
$233$	14.4840	+	14.4840i	0.948880	+	0.948880i	−0.0498757	+	0.998755i	$0.515883\pi$
$234$		0			0
$235$	7.37171	+	17.7969i	0.480878	+	1.16094i
$236$	13.3759	+	18.5386i	0.870696	+	1.20676i
$237$		0			0
$238$	13.5130	−	1.57678i	0.875919	−	0.102207i
$239$			3.63220i			0.234947i	0.993076	+	0.117474i	$0.0374796\pi$
$239$			3.63220i			0.234947i	−0.993076	+	0.117474i	$0.962520\pi$
$240$		0			0
$241$			0.903699i			0.0582124i	0.999576	+	0.0291062i	$0.00926609\pi$
$241$			0.903699i			0.0582124i	−0.999576	+	0.0291062i	$0.990734\pi$
$242$	0.608503	+	5.21489i	0.0391161	+	0.335226i
$243$		0			0
$244$	6.91452	+	1.11855i	0.442657	+	0.0716075i
$245$	−17.1066	−	41.2990i	−1.09290	−	2.63850i
$246$		0			0
$247$	−17.1034	−	17.1034i	−1.08826	−	1.08826i
$248$	−11.4794	−	5.36110i	−0.728941	−	0.340430i
$249$		0			0
$250$	4.02753	+	7.21957i	0.254723	+	0.456606i
$251$	−11.4132	+	4.72750i	−0.720394	+	0.298397i	−0.712598	−	0.701573i	$-0.752482\pi$
$251$	−11.4132	+	4.72750i	−0.720394	+	0.298397i	−0.00779601	+	0.999970i	$0.502482\pi$
$252$		0			0
$253$	−7.54739	+	18.2210i	−0.474501	+	1.14555i
$254$	0.314641	−	0.397769i	0.0197423	−	0.0249583i
$255$		0			0
$256$	9.57454	−	12.8191i	0.598409	−	0.801191i
$257$	−18.0043			−1.12308			−0.561538	−	0.827451i	$-0.689790\pi$
$257$	−18.0043			−1.12308			−0.561538	+	0.827451i	$0.689790\pi$
$258$		0			0
$259$	−4.18066	+	10.0930i	−0.259774	+	0.627149i
$260$	−5.08596	−	21.4967i	−0.315418	−	1.33317i
$261$		0			0
$262$	−12.4986	−	22.4044i	−0.772165	−	1.38415i
$263$	−5.23706	+	5.23706i	−0.322931	+	0.322931i	−0.849890	−	0.526959i	$-0.823332\pi$
$263$	−5.23706	+	5.23706i	−0.322931	+	0.322931i	0.526959	+	0.849890i	$0.323332\pi$
$264$		0			0
$265$	8.29684	+	8.29684i	0.509671	+	0.509671i
$266$	12.9601	−	45.6646i	0.794634	−	2.79988i
$267$		0			0
$268$	10.8336	+	1.75252i	0.661765	+	0.107052i
$269$	−8.98052	−	3.71985i	−0.547552	−	0.226803i	0.0917191	−	0.995785i	$-0.470764\pi$
$269$	−8.98052	−	3.71985i	−0.547552	−	0.226803i	−0.639271	+	0.768981i	$0.720764\pi$
$270$		0			0
$271$			29.7258i			1.80571i	0.429943	+	0.902856i	$0.358534\pi$
$271$			29.7258i			1.80571i	−0.429943	+	0.902856i	$0.641466\pi$
$272$	3.84949	+	7.67988i	0.233409	+	0.465661i
$273$		0			0
$274$	20.6608	−	2.41082i	1.24816	−	0.145643i
$275$	16.7310	+	6.93021i	1.00892	+	0.417907i
$276$		0			0
$277$	−2.51213	−	6.06483i	−0.150940	−	0.364400i	0.830266	−	0.557368i	$-0.188189\pi$
$277$	−2.51213	−	6.06483i	−0.150940	−	0.364400i	−0.981205	+	0.192968i	$0.938189\pi$
$278$	−15.9217	−	4.51876i	−0.954922	−	0.271017i
$279$		0			0
$280$	31.9790	−	29.2690i	1.91111	−	1.74916i
$281$	11.9451	−	11.9451i	0.712585	−	0.712585i	−0.254490	−	0.967075i	$-0.581908\pi$
$281$	11.9451	−	11.9451i	0.712585	−	0.712585i	0.967075	+	0.254490i	$0.0819077\pi$
$282$		0			0
$283$	0.0177223	−	0.00734080i	0.00105348	−	0.000436365i	−0.382157	−	0.924098i	$-0.624819\pi$
$283$	0.0177223	−	0.00734080i	0.00105348	−	0.000436365i	0.383210	+	0.923661i	$0.374819\pi$
$284$	11.9974	+	7.40659i	0.711917	+	0.439500i
$285$		0			0
$286$	−9.66503	−	7.64518i	−0.571505	−	0.452069i
$287$	−6.76028			−0.399047
$288$		0			0
$289$	12.3876			0.728680
$290$	8.68268	+	6.86812i	0.509864	+	0.403310i
$291$		0			0
$292$	11.9688	−	19.3874i	0.700420	−	1.13456i
$293$	−27.4669	+	11.3772i	−1.60463	+	0.664660i	−0.992061	−	0.125756i	$-0.959864\pi$
$293$	−27.4669	+	11.3772i	−1.60463	+	0.664660i	−0.612570	+	0.790416i	$0.709864\pi$
$294$		0			0
$295$	−27.6558	+	27.6558i	−1.61018	+	1.61018i
$296$	−6.89156	−	0.304929i	−0.400564	−	0.0177236i
$297$		0			0
$298$	−18.4856	−	5.24640i	−1.07084	−	0.303916i
$299$	9.02460	+	21.7873i	0.521906	+	1.25999i
$300$		0			0
$301$	−17.0669	−	7.06934i	−0.983720	−	0.407470i
$302$	5.84099	−	0.681560i	0.336111	−	0.0392194i
$303$		0			0
$304$	29.8960	−	2.15451i	1.71465	−	0.123570i
$305$			11.9837i			0.686183i
$306$		0			0
$307$	17.6501	+	7.31091i	1.00734	+	0.417256i	0.824485	−	0.565884i	$-0.191465\pi$
$307$	17.6501	+	7.31091i	1.00734	+	0.417256i	0.182859	+	0.983139i	$0.441465\pi$
$308$	3.86198	−	23.8736i	0.220057	−	1.36033i
$309$		0			0
$310$	5.91815	−	20.8525i	0.336128	−	1.18434i
$311$	−6.33988	−	6.33988i	−0.359502	−	0.359502i	0.504127	−	0.863629i	$-0.331814\pi$
$311$	−6.33988	−	6.33988i	−0.359502	−	0.359502i	−0.863629	+	0.504127i	$0.831814\pi$
$312$		0			0
$313$	12.7171	−	12.7171i	0.718813	−	0.718813i	−0.249549	−	0.968362i	$-0.580282\pi$
$313$	12.7171	−	12.7171i	0.718813	−	0.718813i	0.968362	+	0.249549i	$0.0802824\pi$
$314$	12.6985	+	22.7629i	0.716620	+	1.28458i
$315$		0			0
$316$	−28.7582	+	6.80399i	−1.61778	+	0.382754i
$317$	−10.6058	+	25.6046i	−0.595679	+	1.43810i	0.282267	+	0.959336i	$0.408914\pi$
$317$	−10.6058	+	25.6046i	−0.595679	+	1.43810i	−0.877946	+	0.478760i	$0.841086\pi$
$318$		0			0
$319$	6.17590			0.345784
$320$	24.2662	+	12.6683i	1.35652	+	0.708179i
$321$		0			0
$322$	−28.7115	+	36.2970i	−1.60003	+	2.02275i
$323$	−6.15862	+	14.8682i	−0.342675	+	0.827290i
$324$		0			0
$325$	20.0057	−	8.28662i	1.10971	−	0.459659i
$326$	−10.7033	−	19.1863i	−0.592803	−	1.06263i
$327$		0			0
$328$	−1.45765	−	4.01217i	−0.0804854	−	0.221535i
$329$	17.8309	+	17.8309i	0.983051	+	0.983051i
$330$		0			0
$331$	−4.11606	−	9.93704i	−0.226239	−	0.546189i	0.769475	−	0.638677i	$-0.220518\pi$
$331$	−4.11606	−	9.93704i	−0.226239	−	0.546189i	−0.995714	+	0.0924879i	$0.970518\pi$
$332$	−1.41474	+	8.74548i	−0.0776437	+	0.479971i
$333$		0			0
$334$	3.91496	+	33.5513i	0.214217	+	1.83585i
$335$			18.7758i			1.02583i
$336$		0			0
$337$			2.78551i			0.151736i	0.997118	+	0.0758681i	$0.0241728\pi$
$337$			2.78551i			0.151736i	−0.997118	+	0.0758681i	$0.975827\pi$
$338$	3.62502	−	0.422988i	0.197175	−	0.0230075i
$339$		0			0
$340$	−11.9190	+	8.59971i	−0.646397	+	0.466385i
$341$	−4.62749	−	11.1717i	−0.250592	−	0.604983i
$342$		0			0
$343$	−19.2067	−	19.2067i	−1.03706	−	1.03706i
$344$	0.515623	−	11.6534i	0.0278006	−	0.628307i
$345$		0			0
$346$	−0.779362	+	0.434777i	−0.0418987	+	0.0233737i
$347$	1.49458	−	0.619077i	0.0802335	−	0.0332338i	−0.342206	−	0.939625i	$-0.611174\pi$
$347$	1.49458	−	0.619077i	0.0802335	−	0.0332338i	0.422439	+	0.906391i	$0.361174\pi$
$348$		0			0
$349$	−1.23167	+	2.97350i	−0.0659296	+	0.159168i	−0.953410	−	0.301677i	$-0.902454\pi$
$349$	−1.23167	+	2.97350i	−0.0659296	+	0.159168i	0.887481	+	0.460845i	$0.152454\pi$
$350$	33.3289	+	26.3636i	1.78150	+	1.40919i
$351$		0			0
$352$	15.0015	−	2.85559i	0.799583	−	0.152203i
$353$	17.8308			0.949036			0.474518	−	0.880246i	$-0.342622\pi$
$353$	17.8308			0.949036			0.474518	+	0.880246i	$0.342622\pi$
$354$		0			0
$355$	−9.23129	+	22.2863i	−0.489946	+	1.18283i
$356$	24.8470	+	15.3392i	1.31689	+	0.812978i
$357$		0			0
$358$	−5.02591	+	2.80377i	−0.265628	+	0.148184i
$359$	3.39018	−	3.39018i	0.178927	−	0.178927i	−0.611961	−	0.790888i	$-0.709619\pi$
$359$	3.39018	−	3.39018i	0.178927	−	0.178927i	0.790888	+	0.611961i	$0.209619\pi$
$360$		0			0
$361$	26.2696	+	26.2696i	1.38261	+	1.38261i
$362$	3.12005	+	0.885502i	0.163986	+	0.0465410i
$363$		0			0
$364$	−16.9199	−	23.4506i	−0.886845	−	1.22914i
$365$	36.0139	+	14.9174i	1.88505	+	0.780814i
$366$		0			0
$367$		−	16.6458i		−	0.868905i	−0.900695	−	0.434452i	$-0.856942\pi$
$367$		−	16.6458i		−	0.868905i	0.900695	−	0.434452i	$-0.143058\pi$
$368$	−27.7328	−	9.21364i	−1.44567	−	0.480294i
$369$		0			0
$370$	−1.36786	−	11.7226i	−0.0711116	−	0.609429i
$371$	14.1907	+	5.87797i	0.736744	+	0.305169i
$372$		0			0
$373$	10.3822	+	25.0650i	0.537572	+	1.29781i	0.926413	+	0.376509i	$0.122876\pi$
$373$	10.3822	+	25.0650i	0.537572	+	1.29781i	−0.388841	+	0.921305i	$0.627124\pi$
$374$	−2.23860	+	7.88765i	−0.115755	+	0.407861i
$375$		0			0
$376$	−6.73780	+	14.4272i	−0.347475	+	0.744027i
$377$	5.22175	−	5.22175i	0.268934	−	0.268934i
$378$		0			0
$379$	−12.4831	+	5.17068i	−0.641215	+	0.265600i	−0.679509	−	0.733667i	$-0.737807\pi$
$379$	−12.4831	+	5.17068i	−0.641215	+	0.265600i	0.0382950	+	0.999266i	$0.487807\pi$
$380$	11.8068	+	49.9033i	0.605674	+	2.55999i
$381$		0			0
$382$	−1.95431	+	2.47063i	−0.0999910	+	0.126409i
$383$	8.27723			0.422947			0.211473	−	0.977384i	$-0.432174\pi$
$383$	8.27723			0.422947			0.211473	+	0.977384i	$0.432174\pi$
$384$		0			0
$385$	41.3758			2.10870
$386$	11.7753	−	14.8863i	0.599347	−	0.757694i
$387$		0			0
$388$	−6.80926	−	28.7805i	−0.345688	−	1.46111i
$389$	4.37154	−	1.81075i	0.221646	−	0.0918087i	−0.269097	−	0.963113i	$-0.586725\pi$
$389$	4.37154	−	1.81075i	0.221646	−	0.0918087i	0.490743	+	0.871304i	$0.336725\pi$
$390$		0			0
$391$	11.0948	−	11.0948i	0.561087	−	0.561087i
$392$	15.6355	−	33.4794i	0.789714	−	1.69097i
$393$		0			0
$394$	5.87875	−	20.7136i	0.296167	−	1.04354i
$395$	−19.3485	−	46.7114i	−0.973528	−	2.35031i
$396$		0			0
$397$	−28.1806	−	11.6728i	−1.41434	−	0.585841i	−0.460912	−	0.887446i	$-0.652478\pi$
$397$	−28.1806	−	11.6728i	−1.41434	−	0.585841i	−0.953433	+	0.301605i	$0.902478\pi$
$398$	2.90527	+	24.8983i	0.145628	+	1.24804i
$399$		0			0
$400$	−8.46020	+	25.4649i	−0.423010	+	1.27325i
$401$		−	12.3267i		−	0.615564i	−0.951457	−	0.307782i	$-0.900413\pi$
$401$		−	12.3267i		−	0.615564i	0.951457	−	0.307782i	$-0.0995867\pi$
$402$		0			0
$403$	−13.3583	−	5.53319i	−0.665425	−	0.275628i
$404$	−22.6766	−	31.4292i	−1.12821	−	1.56366i
$405$		0			0
$406$	13.9416	+	3.95677i	0.691910	+	0.196371i
$407$	−4.65555	−	4.65555i	−0.230767	−	0.230767i
$408$		0			0
$409$	−6.40427	+	6.40427i	−0.316671	+	0.316671i	−0.847487	−	0.530816i	$-0.821886\pi$
$409$	−6.40427	+	6.40427i	−0.316671	+	0.316671i	0.530816	+	0.847487i	$0.321886\pi$
$410$	6.37798	−	3.55803i	0.314986	−	0.175719i
$411$		0			0
$412$	−4.33433	−	2.67579i	−0.213537	−	0.131827i
$413$	−19.5930	+	47.3017i	−0.964108	+	2.32756i
$414$		0			0
$415$	−15.1569			−0.744025
$416$	10.2694	−	15.0983i	0.503501	−	0.740253i
$417$		0			0
$418$	22.4368	+	17.7479i	1.09742	+	0.868076i
$419$	−0.382197	+	0.922704i	−0.0186715	+	0.0450771i	−0.932940	−	0.360031i	$-0.882766\pi$
$419$	−0.382197	+	0.922704i	−0.0186715	+	0.0450771i	0.914269	+	0.405108i	$0.132766\pi$
$420$		0			0
$421$	−19.5113	+	8.08183i	−0.950920	+	0.393884i	−0.803577	−	0.595201i	$-0.797072\pi$
$421$	−19.5113	+	8.08183i	−0.950920	+	0.393884i	−0.147344	+	0.989085i	$0.547072\pi$
$422$	13.2200	−	7.37493i	0.643539	−	0.359006i
$423$		0			0
$424$	−0.428727	+	9.68946i	−0.0208208	+	0.470562i
$425$	−10.1875	−	10.1875i	−0.494167	−	0.494167i
$426$		0			0
$427$	6.00329	+	14.4932i	0.290520	+	0.701377i
$428$	−14.5079	+	10.4677i	−0.701266	+	0.505973i
$429$		0			0
$430$	19.8225	−	2.31300i	0.955924	−	0.111543i
$431$		−	7.17292i		−	0.345508i	−0.984965	−	0.172754i	$-0.944733\pi$
$431$		−	7.17292i		−	0.345508i	0.984965	−	0.172754i	$-0.0552665\pi$
$432$		0			0
$433$		−	0.476736i		−	0.0229105i	−0.999934	−	0.0114552i	$-0.996354\pi$
$433$		−	0.476736i		−	0.0229105i	0.999934	−	0.0114552i	$-0.00364639\pi$
$434$	−3.28867	−	28.1840i	−0.157861	−	1.35288i
$435$		0			0
$436$	1.61607	−	9.99008i	0.0773958	−	0.478438i
$437$	−20.9501	−	50.5780i	−1.00218	−	2.41947i
$438$		0			0
$439$	19.6261	+	19.6261i	0.936703	+	0.936703i	0.998113	−	0.0614094i	$-0.0195595\pi$
$439$	19.6261	+	19.6261i	0.936703	+	0.936703i	−0.0614094	+	0.998113i	$0.519560\pi$
$440$	8.92146	+	24.5562i	0.425314	+	1.17067i
$441$		0			0
$442$	4.77630	+	8.56178i	0.227185	+	0.407243i
$443$	−19.6174	+	8.12579i	−0.932050	+	0.386068i	−0.796456	−	0.604697i	$-0.793294\pi$
$443$	−19.6174	+	8.12579i	−0.932050	+	0.386068i	−0.135594	+	0.990764i	$0.543294\pi$
$444$		0			0
$445$	−19.1182	+	46.1555i	−0.906291	+	2.18798i
$446$	20.2188	−	25.5606i	0.957387	−	1.21033i
$447$		0			0
$448$	35.6942	+	3.16491i	1.68639	+	0.149528i
$449$	7.14672			0.337275			0.168637	−	0.985678i	$-0.446063\pi$
$449$	7.14672			0.337275			0.168637	+	0.985678i	$0.446063\pi$
$450$		0			0
$451$	1.55914	−	3.76409i	0.0734170	−	0.177244i
$452$	−8.45834	+	2.00118i	−0.397847	+	0.0941276i
$453$		0			0
$454$	−3.36626	−	6.03422i	−0.157986	−	0.283200i
$455$	34.9834	−	34.9834i	1.64005	−	1.64005i
$456$		0			0
$457$	−18.8753	−	18.8753i	−0.882948	−	0.882948i	0.110885	−	0.993833i	$-0.464631\pi$
$457$	−18.8753	−	18.8753i	−0.882948	−	0.882948i	−0.993833	+	0.110885i	$0.964631\pi$
$458$	−0.0103570	+	0.0364927i	−0.000483951	+	0.00170519i
$459$		0			0
$460$	7.98415	−	49.3557i	0.372263	−	2.30122i
$461$	35.8179	+	14.8363i	1.66821	+	0.690994i	0.998659	−	0.0517742i	$-0.0164876\pi$
$461$	35.8179	+	14.8363i	1.66821	+	0.690994i	0.669549	+	0.742768i	$0.266488\pi$
$462$		0			0
$463$			2.19902i			0.102197i	0.998694	+	0.0510986i	$0.0162723\pi$
$463$			2.19902i			0.102197i	−0.998694	+	0.0510986i	$0.983728\pi$
$464$	0.657781	+	9.12738i	0.0305367	+	0.423728i
$465$		0			0
$466$	−28.7728	+	3.35738i	−1.33288	+	0.155527i
$467$	33.5771	+	13.9081i	1.55376	+	0.643591i	0.983992	−	0.178212i	$-0.0570312\pi$
$467$	33.5771	+	13.9081i	1.55376	+	0.643591i	0.569773	+	0.821802i	$0.307031\pi$
$468$		0			0
$469$	9.40587	+	22.7078i	0.434323	+	1.04855i
$470$	−26.2073	−	7.43790i	−1.20885	−	0.343085i
$471$		0			0
$472$	−32.2978	−	1.42907i	−1.48663	−	0.0657784i
$473$	7.87236	−	7.87236i	0.361971	−	0.361971i
$474$		0			0
$475$	−46.4420	+	19.2369i	−2.13091	+	0.882650i
$476$	−10.1069	+	16.3715i	−0.463249	+	0.750387i
$477$		0			0
$478$	−4.02869	−	3.18675i	−0.184268	−	0.145759i
$479$	14.4612			0.660748			0.330374	−	0.943850i	$-0.392825\pi$
$479$	14.4612			0.660748			0.330374	+	0.943850i	$0.392825\pi$
$480$		0			0
$481$	−7.87258			−0.358959
$482$	−1.00235	−	0.792871i	−0.0456556	−	0.0361143i
$483$		0			0
$484$	−6.31803	−	3.90042i	−0.287183	−	0.177292i
$485$	46.7476	−	19.3635i	2.12270	−	0.879251i
$486$		0			0
$487$	2.84778	−	2.84778i	0.129045	−	0.129045i	−0.639634	−	0.768679i	$-0.720914\pi$
$487$	2.84778	−	2.84778i	0.129045	−	0.129045i	0.768679	+	0.639634i	$0.220914\pi$
$488$	−7.30718	+	6.68794i	−0.330780	+	0.302749i
$489$		0			0
$490$	60.8159	+	17.2602i	2.74738	+	0.779736i
$491$	−5.61819	−	13.5635i	−0.253546	−	0.612113i	0.744940	−	0.667132i	$-0.232478\pi$
$491$	−5.61819	−	13.5635i	−0.253546	−	0.612113i	−0.998485	+	0.0550187i	$0.982478\pi$
$492$		0			0
$493$	−4.53933	−	1.88025i	−0.204441	−	0.0846823i
$494$	33.9763	−	3.96455i	1.52867	−	0.178374i
$495$		0			0
$496$	16.0179	−	8.02885i	0.719224	−	0.360506i
$497$			31.5779i			1.41646i
$498$		0			0
$499$	24.3884	+	10.1020i	1.09177	+	0.452227i	0.854625	−	0.519246i	$-0.173787\pi$
$499$	24.3884	+	10.1020i	1.09177	+	0.452227i	0.237148	+	0.971474i	$0.423787\pi$
$500$	−11.5413	−	1.86700i	−0.516141	−	0.0834949i
$501$		0			0
$502$	4.76994	−	16.8068i	0.212893	−	0.750123i
$503$	−21.4060	−	21.4060i	−0.954446	−	0.954446i	0.0445606	−	0.999007i	$-0.485811\pi$
$503$	−21.4060	−	21.4060i	−0.954446	−	0.954446i	−0.999007	+	0.0445606i	$0.985811\pi$
$504$		0			0
$505$	46.8859	−	46.8859i	2.08640	−	2.08640i
$506$	−13.5882	−	24.3577i	−0.604071	−	1.08283i
$507$		0			0
$508$	0.165136	+	0.697975i	0.00732672	+	0.0309676i
$509$	−3.58323	+	8.65068i	−0.158824	+	0.383434i	−0.983181	−	0.182636i	$-0.941537\pi$
$509$	−3.58323	+	8.65068i	−0.158824	+	0.383434i	0.824357	+	0.566070i	$0.191537\pi$
$510$		0			0
$511$	51.0287			2.25738
$512$	5.81806	+	21.8666i	0.257124	+	0.966378i
$513$		0			0
$514$	15.7963	−	19.9696i	0.696744	−	0.880823i
$515$	3.33500	−	8.05140i	0.146958	−	0.354787i
$516$		0			0
$517$	−14.0406	+	5.81580i	−0.617504	+	0.255778i
$518$	−7.52682	−	13.4923i	−0.330709	−	0.592815i
$519$		0			0
$520$	28.3055	+	13.2192i	1.24128	+	0.579701i
$521$	−16.2581	−	16.2581i	−0.712280	−	0.712280i	0.254732	−	0.967012i	$-0.418013\pi$
$521$	−16.2581	−	16.2581i	−0.712280	−	0.712280i	−0.967012	+	0.254732i	$0.918013\pi$
$522$		0			0
$523$	12.6633	+	30.5720i	0.553729	+	1.33682i	0.914659	+	0.404227i	$0.132459\pi$
$523$	12.6633	+	30.5720i	0.553729	+	1.33682i	−0.360930	+	0.932593i	$0.617541\pi$
$524$	35.8159	+	5.79385i	1.56462	+	0.253105i
$525$		0			0
$526$	−1.21394	−	10.4035i	−0.0529305	−	0.453616i
$527$			9.62015i			0.419060i
$528$		0			0
$529$			30.3748i			1.32065i
$530$	−16.4819	+	1.92320i	−0.715926	+	0.0835383i
$531$		0			0
$532$	39.2787	+	54.4392i	1.70295	+	2.36024i
$533$	−1.86430	−	4.50082i	−0.0807517	−	0.194952i
$534$		0			0
$535$	−21.6428	−	21.6428i	−0.935699	−	0.935699i
$536$	−11.4488	+	10.4786i	−0.494512	+	0.452605i
$537$		0			0
$538$	12.0051	−	6.69718i	0.517576	−	0.288736i
$539$	32.5822	−	13.4960i	1.40341	−	0.581313i
$540$		0			0
$541$	−14.9868	+	36.1815i	−0.644335	+	1.55556i	0.176441	+	0.984311i	$0.443542\pi$
$541$	−14.9868	+	36.1815i	−0.644335	+	1.55556i	−0.820776	+	0.571251i	$0.806458\pi$
$542$	−32.9706	−	26.0802i	−1.41621	−	1.12024i
$543$		0			0
$544$	−11.8956	−	2.46833i	−0.510020	−	0.105829i
$545$	17.3140			0.741649
$546$		0			0
$547$	8.97063	−	21.6570i	0.383556	−	0.925987i	−0.607716	−	0.794155i	$-0.707914\pi$
$547$	8.97063	−	21.6570i	0.383556	−	0.925987i	0.991272	−	0.131832i	$-0.0420861\pi$
$548$	−15.4530	+	25.0313i	−0.660119	+	1.06928i
$549$		0			0
$550$	−22.3659	+	12.4771i	−0.953683	+	0.532024i
$551$	−12.1220	+	12.1220i	−0.516414	+	0.516414i
$552$		0			0
$553$	−46.8007	−	46.8007i	−1.99017	−	1.99017i
$554$	8.93092	+	2.53469i	0.379438	+	0.107689i
$555$		0			0
$556$	18.9811	−	13.6952i	0.804980	−	0.580805i
$557$	5.59184	+	2.31621i	0.236934	+	0.0981412i	0.497991	−	0.867182i	$-0.334071\pi$
$557$	5.59184	+	2.31621i	0.236934	+	0.0981412i	−0.261057	+	0.965323i	$0.584071\pi$
$558$		0			0
$559$		−	13.3122i		−	0.563047i
$560$	4.40684	+	61.1494i	0.186223	+	2.58403i
$561$		0			0
$562$	2.76886	+	23.7292i	0.116797	+	1.00096i
$563$	9.24452	+	3.82921i	0.389610	+	0.161382i	0.568885	−	0.822417i	$-0.307375\pi$
$563$	9.24452	+	3.82921i	0.389610	+	0.161382i	−0.179275	+	0.983799i	$0.557375\pi$
$564$		0			0
$565$	−5.69076	−	13.7387i	−0.239412	−	0.577992i
$566$	−0.00740671	+	0.0260974i	−0.000311327	+	0.00109695i
$567$		0			0
$568$	−18.7412	+	6.80883i	−0.786363	+	0.285692i
$569$	−25.4326	+	25.4326i	−1.06619	+	1.06619i	−0.0685420	+	0.997648i	$0.521835\pi$
$569$	−25.4326	+	25.4326i	−1.06619	+	1.06619i	−0.997648	+	0.0685420i	$0.978165\pi$
$570$		0			0
$571$	−12.6828	+	5.25338i	−0.530758	+	0.219847i	−0.631935	−	0.775021i	$-0.717739\pi$
$571$	−12.6828	+	5.25338i	−0.530758	+	0.219847i	0.101177	+	0.994868i	$0.467739\pi$
$572$	16.9595	−	4.01248i	0.709111	−	0.167770i
$573$		0			0
$574$	5.93121	−	7.49823i	0.247564	−	0.312970i
$575$	49.0101			2.04386
$576$		0			0
$577$	−11.7655			−0.489805			−0.244902	−	0.969548i	$-0.578756\pi$
$577$	−11.7655			−0.489805			−0.244902	+	0.969548i	$0.578756\pi$
$578$	−10.8684	+	13.7398i	−0.452064	+	0.571500i
$579$		0			0
$580$	−15.2357	+	3.60465i	−0.632628	+	0.149675i
$581$	−18.3310	+	7.59297i	−0.760500	+	0.315009i
$582$		0			0
$583$	−6.54566	+	6.54566i	−0.271094	+	0.271094i
$584$	11.0028	+	30.2851i	0.455300	+	1.25321i
$585$		0			0
$586$	11.4793	−	40.4470i	0.474205	−	1.67085i
$587$	0.0776482	+	0.187459i	0.00320488	+	0.00773727i	0.925474	−	0.378811i	$-0.123667\pi$
$587$	0.0776482	+	0.187459i	0.00320488	+	0.00773727i	−0.922269	+	0.386549i	$0.873667\pi$
$588$		0			0
$589$	31.0106	+	12.8450i	1.27777	+	0.529269i
$590$	−6.41057	−	54.9388i	−0.263919	−	2.26179i
$591$		0			0
$592$	6.38460	−	7.37631i	0.262406	−	0.303164i
$593$		−	18.6303i		−	0.765054i	−0.923944	−	0.382527i	$-0.875054\pi$
$593$		−	18.6303i		−	0.765054i	0.923944	−	0.382527i	$-0.124946\pi$
$594$		0			0
$595$	−30.4115	−	12.5969i	−1.24675	−	0.516421i
$596$	22.0376	−	15.9005i	0.902696	−	0.651308i
$597$		0			0
$598$	−32.0835	−	9.10562i	−1.31199	−	0.372357i
$599$	−10.0240	−	10.0240i	−0.409569	−	0.409569i	0.472019	−	0.881588i	$-0.343525\pi$
$599$	−10.0240	−	10.0240i	−0.409569	−	0.409569i	−0.881588	+	0.472019i	$0.843525\pi$
$600$		0			0
$601$	13.3956	−	13.3956i	0.546418	−	0.546418i	−0.378985	−	0.925403i	$-0.623727\pi$
$601$	13.3956	−	13.3956i	0.546418	−	0.546418i	0.925403	+	0.378985i	$0.123727\pi$
$602$	22.8149	−	12.7276i	0.929865	−	0.518737i
$603$		0			0
$604$	−4.36870	+	7.07657i	−0.177760	+	0.287941i
$605$	4.86133	−	11.7363i	0.197641	−	0.477148i
$606$		0			0
$607$	−14.0623			−0.570770			−0.285385	−	0.958413i	$-0.592122\pi$
$607$	−14.0623			−0.570770			−0.285385	+	0.958413i	$0.592122\pi$
$608$	−23.8399	+	35.0498i	−0.966836	+	1.42146i
$609$		0			0
$610$	−13.2918	−	10.5140i	−0.538169	−	0.425700i
$611$	−6.95409	+	16.7886i	−0.281332	+	0.679196i
$612$		0			0
$613$	−20.9598	+	8.68185i	−0.846560	+	0.350657i	−0.763437	−	0.645883i	$-0.776489\pi$
$613$	−20.9598	+	8.68185i	−0.846560	+	0.350657i	−0.0831231	+	0.996539i	$0.526489\pi$
$614$	−23.5945	+	13.1625i	−0.952196	+	0.531194i
$615$		0			0
$616$	23.0913	+	25.2294i	0.930376	+	1.01652i
$617$	−16.7319	−	16.7319i	−0.673600	−	0.673600i	0.284944	−	0.958544i	$-0.408025\pi$
$617$	−16.7319	−	16.7319i	−0.673600	−	0.673600i	−0.958544	+	0.284944i	$0.908025\pi$
$618$		0			0
$619$	−6.80263	−	16.4230i	−0.273421	−	0.660096i	0.726204	−	0.687479i	$-0.241283\pi$
$619$	−6.80263	−	16.4230i	−0.273421	−	0.660096i	−0.999625	+	0.0273830i	$0.991283\pi$
$620$	17.9364	+	24.8593i	0.720342	+	0.998375i
$621$		0			0
$622$	12.5943	−	1.46958i	0.504986	−	0.0589246i
$623$			65.3986i			2.62014i
$624$		0			0
$625$			13.5396i			0.541582i
$626$	2.94781	+	25.2628i	0.117818	+	1.00970i
$627$		0			0
$628$	−36.3889	−	5.88654i	−1.45207	−	0.234899i
$629$	2.00448	+	4.83925i	0.0799239	+	0.192953i
$630$		0			0
$631$	−7.92748	−	7.92748i	−0.315588	−	0.315588i	0.531482	−	0.847070i	$-0.321635\pi$
$631$	−7.92748	−	7.92748i	−0.315588	−	0.315588i	−0.847070	+	0.531482i	$0.821635\pi$
$632$	17.6847	−	37.8670i	0.703458	−	1.50627i
$633$		0			0
$634$	−19.0945	−	34.2280i	−0.758339	−	1.35937i
$635$	−1.13371	+	0.469597i	−0.0449898	+	0.0186354i
$636$		0			0
$637$	16.1375	−	38.9593i	0.639390	−	1.54362i
$638$	−5.41850	+	6.85006i	−0.214520	+	0.271197i
$639$		0			0
$640$	−35.3414	+	15.8005i	−1.39699	+	0.624569i
$641$	−20.6275			−0.814738			−0.407369	−	0.913264i	$-0.633554\pi$
$641$	−20.6275			−0.814738			−0.407369	+	0.913264i	$0.633554\pi$
$642$		0			0
$643$	12.9627	−	31.2947i	0.511199	−	1.23414i	−0.431988	−	0.901879i	$-0.642188\pi$
$643$	12.9627	−	31.2947i	0.511199	−	1.23414i	0.943187	−	0.332263i	$-0.107812\pi$
$644$	−15.0689	−	63.6913i	−0.593797	−	2.50979i
$645$		0			0
$646$	−11.0879	−	19.8757i	−0.436248	−	0.781999i
$647$	27.2096	−	27.2096i	1.06972	−	1.06972i	0.0723408	−	0.997380i	$-0.476953\pi$
$647$	27.2096	−	27.2096i	1.06972	−	1.06972i	0.997380	−	0.0723408i	$-0.0230469\pi$
$648$		0			0
$649$	−21.8186	−	21.8186i	−0.856454	−	0.856454i
$650$	−8.36101	+	29.4598i	−0.327946	+	1.15551i
$651$		0			0
$652$	30.6714	+	4.96164i	1.20118	+	0.194313i
$653$	0.333778	+	0.138255i	0.0130617	+	0.00541035i	0.389205	−	0.921151i	$-0.372750\pi$
$653$	0.333778	+	0.138255i	0.0130617	+	0.00541035i	−0.376143	+	0.926562i	$0.622750\pi$
$654$		0			0
$655$			62.0731i			2.42540i
$656$	5.72903	+	1.90335i	0.223681	+	0.0743133i
$657$		0			0
$658$	−35.4215	+	4.13319i	−1.38088	+	0.161128i
$659$	28.4298	+	11.7760i	1.10747	+	0.458729i	0.860065	−	0.510184i	$-0.170423\pi$
$659$	28.4298	+	11.7760i	1.10747	+	0.458729i	0.247404	+	0.968912i	$0.420423\pi$
$660$		0			0
$661$	−8.13018	−	19.6280i	−0.316227	−	0.763441i	−0.999448	−	0.0332283i	$-0.989421\pi$
$661$	−8.13018	−	19.6280i	−0.316227	−	0.763441i	0.683220	−	0.730212i	$-0.260579\pi$
$662$	14.6330	+	4.15301i	0.568729	+	0.161411i
$663$		0			0
$664$	−8.45891	−	9.24212i	−0.328269	−	0.358664i
$665$	−81.2120	+	81.2120i	−3.14927	+	3.14927i
$666$		0			0
$667$	15.4417	−	6.39615i	0.597904	−	0.247660i
$668$	−40.6486	−	25.0943i	−1.57274	−	0.970928i
$669$		0			0
$670$	−20.8254	−	16.4732i	−0.804556	−	0.636415i
$671$	−9.45432			−0.364980
$672$		0			0
$673$	−10.2866			−0.396519			−0.198259	−	0.980150i	$-0.563529\pi$
$673$	−10.2866			−0.396519			−0.198259	+	0.980150i	$0.563529\pi$
$674$	−3.08957	−	2.44390i	−0.119006	−	0.0941354i
$675$		0			0
$676$	−2.71129	+	4.39184i	−0.104280	+	0.168917i
$677$	−15.8496	+	6.56511i	−0.609148	+	0.252317i	−0.665864	−	0.746073i	$-0.731937\pi$
$677$	−15.8496	+	6.56511i	−0.609148	+	0.252317i	0.0567160	+	0.998390i	$0.481937\pi$
$678$		0			0
$679$	46.8370	−	46.8370i	1.79744	−	1.79744i
$680$	0.918789	−	20.7651i	0.0352339	−	0.796305i
$681$		0			0
$682$	16.4512	+	4.66903i	0.629950	+	0.178786i
$683$	−6.96297	−	16.8101i	−0.266431	−	0.643220i	0.732880	−	0.680358i	$-0.238176\pi$
$683$	−6.96297	−	16.8101i	−0.266431	−	0.643220i	−0.999310	+	0.0371380i	$0.988176\pi$
$684$		0			0
$685$	−46.4977	−	19.2600i	−1.77659	−	0.735887i
$686$	38.1544	−	4.45208i	1.45674	−	0.169981i
$687$		0			0
$688$	12.4731	+	10.7961i	0.475531	+	0.411598i
$689$			11.0688i			0.421687i
$690$		0			0
$691$	19.5571	+	8.10080i	0.743985	+	0.308169i	0.722285	−	0.691596i	$-0.243092\pi$
$691$	19.5571	+	8.10080i	0.743985	+	0.308169i	0.0217005	+	0.999765i	$0.493092\pi$
$692$	0.201545	−	1.24589i	0.00766160	−	0.0473618i
$693$		0			0
$694$	−0.624635	+	2.20089i	−0.0237108	+	0.0835446i
$695$	28.3159	+	28.3159i	1.07408	+	1.07408i
$696$		0			0
$697$	−2.29196	+	2.29196i	−0.0868140	+	0.0868140i
$698$	−2.21748	−	3.97495i	−0.0839327	−	0.150454i
$699$		0			0
$700$	−58.4829	+	13.8366i	−2.21045	+	0.522976i
$701$	−6.37917	+	15.4007i	−0.240938	+	0.581676i	−0.997376	−	0.0723890i	$-0.976938\pi$
$701$	−6.37917	+	15.4007i	−0.240938	+	0.581676i	0.756438	+	0.654065i	$0.226938\pi$
$702$		0			0
$703$	18.2757			0.689283
$704$	−9.99445	+	19.1445i	−0.376680	+	0.721534i
$705$		0			0
$706$	−15.6440	+	19.7772i	−0.588771	+	0.744324i
$707$	33.2167	−	80.1923i	1.24924	−	3.01594i
$708$		0			0
$709$	1.58634	−	0.657082i	0.0595761	−	0.0246772i	−0.352696	−	0.935738i	$-0.614735\pi$
$709$	1.58634	−	0.657082i	0.0595761	−	0.0246772i	0.412273	+	0.911061i	$0.364735\pi$
$710$	−16.6199	−	29.7921i	−0.623734	−	1.11808i
$711$		0			0
$712$	−38.8135	+	14.1013i	−1.45460	+	0.528467i
$713$	−23.1403	−	23.1403i	−0.866612	−	0.866612i
$714$		0			0
$715$	11.4103	+	27.5469i	0.426721	+	1.03020i
$716$	1.29972	−	8.03446i	0.0485726	−	0.300262i
$717$		0			0
$718$	0.785838	+	6.73466i	0.0293272	+	0.251335i
$719$			6.90348i			0.257456i	0.991680	+	0.128728i	$0.0410895\pi$
$719$			6.90348i			0.257456i	−0.991680	+	0.128728i	$0.958911\pi$
$720$		0			0
$721$		−	11.4082i		−	0.424863i
$722$	−52.1852	+	6.08926i	−1.94213	+	0.226619i
$723$		0			0
$724$	−3.71957	+	2.68373i	−0.138237	+	0.0997399i
$725$	−5.87311	−	14.1789i	−0.218122	−	0.526593i
$726$		0			0
$727$	11.8637	+	11.8637i	0.439999	+	0.439999i	0.892012	−	0.452013i	$-0.149294\pi$
$727$	11.8637	+	11.8637i	0.439999	+	0.439999i	−0.452013	+	0.892012i	$0.649294\pi$
$728$	40.8553	+	1.80772i	1.51420	+	0.0669985i
$729$		0			0
$730$	−48.1430	+	26.8572i	−1.78185	+	0.994028i
$731$	−8.18298	+	3.38950i	−0.302659	+	0.125365i
$732$		0			0
$733$	7.88542	−	19.0371i	0.291255	−	0.703151i	−0.708743	−	0.705467i	$-0.750737\pi$
$733$	7.88542	−	19.0371i	0.291255	−	0.703151i	0.999997	+	0.00231621i	$0.000737274\pi$
$734$	18.4629	+	14.6044i	0.681477	+	0.539058i
$735$		0			0
$736$	34.5511	−	22.6764i	1.27357	−	0.835863i
$737$	−14.8129			−0.545640
$738$		0			0
$739$	4.41786	−	10.6657i	0.162514	−	0.392342i	−0.821556	−	0.570128i	$-0.806893\pi$
$739$	4.41786	−	10.6657i	0.162514	−	0.392342i	0.984069	+	0.177786i	$0.0568935\pi$
$740$	14.2023	+	8.76778i	0.522088	+	0.322310i
$741$		0			0
$742$	−18.9700	+	10.5826i	−0.696410	+	0.388501i
$743$	−15.1798	+	15.1798i	−0.556893	+	0.556893i	−0.928422	−	0.371529i	$-0.878834\pi$
$743$	−15.1798	+	15.1798i	−0.556893	+	0.556893i	0.371529	+	0.928422i	$0.378834\pi$
$744$		0			0
$745$	32.8755	+	32.8755i	1.20447	+	1.20447i
$746$	−36.9100	−	10.4755i	−1.35137	−	0.383534i
$747$		0			0
$748$	−6.78461	−	9.40328i	−0.248070	−	0.343818i
$749$	−37.0172	−	15.3330i	−1.35258	−	0.560256i
$750$		0			0
$751$		−	17.2078i		−	0.627923i	−0.949436	−	0.313961i	$-0.898344\pi$
$751$		−	17.2078i		−	0.627923i	0.949436	−	0.313961i	$-0.101656\pi$
$752$	−10.0906	−	20.1312i	−0.367967	−	0.734109i
$753$		0			0
$754$	1.21039	+	10.3731i	0.0440800	+	0.377767i
$755$	−13.1453	−	5.44498i	−0.478408	−	0.198163i
$756$		0			0
$757$	−5.16011	−	12.4576i	−0.187548	−	0.452780i	0.801939	−	0.597406i	$-0.203802\pi$
$757$	−5.16011	−	12.4576i	−0.187548	−	0.452780i	−0.989486	+	0.144626i	$0.953802\pi$
$758$	5.21710	−	18.3823i	0.189494	−	0.667676i
$759$		0			0
$760$	−65.7096	−	30.6877i	−2.38354	−	1.11316i
$761$	−0.423855	+	0.423855i	−0.0153647	+	0.0153647i	−0.714747	−	0.699383i	$-0.753458\pi$
$761$	−0.423855	+	0.423855i	−0.0153647	+	0.0153647i	0.699383	+	0.714747i	$0.253458\pi$
$762$		0			0
$763$	20.9398	−	8.67355i	0.758072	−	0.314004i
$764$	−1.02570	−	4.33528i	−0.0371083	−	0.156845i
$765$		0			0
$766$	−7.26213	+	9.18078i	−0.262391	+	0.331715i
$767$	−36.8954			−1.33222
$768$		0			0
$769$	−0.327983			−0.0118274			−0.00591369	−	0.999983i	$-0.501882\pi$
$769$	−0.327983			−0.0118274			−0.00591369	+	0.999983i	$0.501882\pi$
$770$	−36.3015	+	45.8924i	−1.30822	+	1.65385i
$771$		0			0
$772$	6.18013	+	26.1214i	0.222428	+	0.940129i
$773$	−48.3516	+	20.0279i	−1.73908	+	0.720353i	−0.740238	+	0.672345i	$0.765287\pi$
$773$	−48.3516	+	20.0279i	−1.73908	+	0.720353i	−0.998847	+	0.0480077i	$0.984713\pi$
$774$		0			0
$775$	−21.2480	+	21.2480i	−0.763252	+	0.763252i
$776$	37.8964	+	17.6984i	1.36040	+	0.635335i
$777$		0			0
$778$	−1.82701	+	6.43742i	−0.0655014	+	0.230793i
$779$	4.32786	+	10.4484i	0.155062	+	0.374352i
$780$		0			0
$781$	−17.5824	−	7.28288i	−0.629148	−	0.260602i
$782$	2.57176	+	22.0400i	0.0919658	+	0.788150i
$783$		0			0
$784$	23.4160	+	46.7159i	0.836286	+	1.66842i
$785$		−	63.0662i		−	2.25093i
$786$		0			0
$787$	29.1153	+	12.0599i	1.03785	+	0.429890i	0.835539	−	0.549432i	$-0.185156\pi$
$787$	29.1153	+	12.0599i	1.03785	+	0.429890i	0.202308	+	0.979322i	$0.435156\pi$
$788$	17.8170	+	24.6938i	0.634703	+	0.879682i
$789$		0			0
$790$	68.7860	+	19.5222i	2.44730	+	0.694569i
$791$	−13.7650	−	13.7650i	−0.489426	−	0.489426i
$792$		0			0
$793$	−7.99367	+	7.99367i	−0.283864	+	0.283864i
$794$	37.6716	−	21.0156i	1.33691	−	0.745814i
$795$		0			0
$796$	−30.1651	−	18.6224i	−1.06918	−	0.660053i
$797$	−8.65082	+	20.8849i	−0.306428	+	0.739782i	0.693388	+	0.720565i	$0.256117\pi$
$797$	−8.65082	+	20.8849i	−0.306428	+	0.739782i	−0.999815	+	0.0192171i	$0.993883\pi$
$798$		0			0
$799$	12.0905			0.427733
$800$	−20.8220	−	31.7257i	−0.736170	−	1.12167i
$801$		0			0
$802$	13.6722	+	10.8149i	0.482783	+	0.381888i
$803$	−11.7689	+	28.4126i	−0.415314	+	1.00266i
$804$		0			0
$805$	103.452	−	42.8514i	3.64622	−	1.51031i
$806$	17.8573	−	9.96190i	0.628995	−	0.350893i
$807$		0			0
$808$	54.7557	+	2.42276i	1.92630	+	0.0852325i
$809$	−24.5223	−	24.5223i	−0.862157	−	0.862157i	0.129431	−	0.991588i	$-0.458685\pi$
$809$	−24.5223	−	24.5223i	−0.862157	−	0.862157i	−0.991588	+	0.129431i	$0.958685\pi$
$810$		0			0
$811$	−2.20295	−	5.31840i	−0.0773561	−	0.186754i	0.880471	−	0.474101i	$-0.157227\pi$
$811$	−2.20295	−	5.31840i	−0.0773561	−	0.186754i	−0.957827	+	0.287347i	$0.907227\pi$
$812$	−16.6205	+	11.9919i	−0.583266	+	0.420835i
$813$		0			0
$814$	9.24835	−	1.07915i	0.324155	−	0.0378242i
$815$			53.1571i			1.86201i
$816$		0			0
$817$			30.9036i			1.08118i
$818$	−1.48450	−	12.7222i	−0.0519044	−	0.444822i
$819$		0			0
$820$	−1.64936	+	10.1959i	−0.0575983	+	0.356056i
$821$	−4.73918	−	11.4414i	−0.165398	−	0.399307i	0.819349	−	0.573294i	$-0.194335\pi$
$821$	−4.73918	−	11.4414i	−0.165398	−	0.399307i	−0.984748	+	0.173987i	$0.944335\pi$
$822$		0			0
$823$	−14.1969	−	14.1969i	−0.494872	−	0.494872i	0.414965	−	0.909837i	$-0.363794\pi$
$823$	−14.1969	−	14.1969i	−0.494872	−	0.494872i	−0.909837	+	0.414965i	$0.863794\pi$
$824$	6.77066	−	2.45984i	0.235867	−	0.0856924i
$825$		0			0
$826$	−35.2750	−	63.2324i	−1.22737	−	2.20014i
$827$	12.3173	−	5.10201i	0.428316	−	0.177414i	−0.158102	−	0.987423i	$-0.550538\pi$
$827$	12.3173	−	5.10201i	0.428316	−	0.177414i	0.586418	+	0.810009i	$0.300538\pi$
$828$		0			0
$829$	6.72762	−	16.2419i	0.233660	−	0.564105i	−0.762943	−	0.646466i	$-0.776246\pi$
$829$	6.72762	−	16.2419i	0.233660	−	0.564105i	0.996603	+	0.0823612i	$0.0262461\pi$
$830$	13.2981	−	16.8115i	0.461584	−	0.583535i
$831$		0			0
$832$	7.73638	+	24.6371i	0.268211	+	0.854137i
$833$	−28.0570			−0.972117
$834$		0			0
$835$	31.2766	−	75.5083i	1.08237	−	2.61307i
$836$	−39.3704	+	9.31476i	−1.36165	+	0.322158i
$837$		0			0
$838$	−0.688102	−	1.23346i	−0.0237701	−	0.0426093i
$839$	20.2307	−	20.2307i	0.698441	−	0.698441i	−0.265633	−	0.964074i	$-0.585581\pi$
$839$	20.2307	−	20.2307i	0.698441	−	0.698441i	0.964074	+	0.265633i	$0.0855810\pi$
$840$		0			0
$841$	16.8052	+	16.8052i	0.579490	+	0.579490i
$842$	8.15439	−	28.7318i	0.281019	−	0.990163i
$843$		0			0
$844$	−3.41873	+	21.1336i	−0.117677	+	0.727447i
$845$	−8.15822	−	3.37925i	−0.280651	−	0.116250i
$846$		0			0
$847$		−	16.6294i		−	0.571392i
$848$	−10.3710	−	8.97669i	−0.356142	−	0.308261i
$849$		0			0
$850$	20.2377	−	2.36145i	0.694148	−	0.0809971i
$851$	−16.4619	−	6.81875i	−0.564308	−	0.233744i
$852$		0			0
$853$	−1.36035	−	3.28419i	−0.0465777	−	0.112448i	0.898878	−	0.438198i	$-0.144383\pi$
$853$	−1.36035	−	3.28419i	−0.0465777	−	0.112448i	−0.945456	+	0.325750i	$0.894383\pi$
$854$	−21.3424	−	6.05719i	−0.730321	−	0.207273i
$855$		0			0
$856$	1.11836	−	25.2755i	0.0382247	−	0.863899i
$857$	−4.90569	+	4.90569i	−0.167575	+	0.167575i	−0.785913	−	0.618338i	$-0.787806\pi$
$857$	−4.90569	+	4.90569i	−0.167575	+	0.167575i	0.618338	+	0.785913i	$0.287806\pi$
$858$		0			0
$859$	−16.1750	+	6.69989i	−0.551882	+	0.228597i	−0.641157	−	0.767410i	$-0.721545\pi$
$859$	−16.1750	+	6.69989i	−0.551882	+	0.228597i	0.0892744	+	0.996007i	$0.471545\pi$
$860$	−14.8260	+	24.0156i	−0.505562	+	0.818926i
$861$		0			0
$862$	7.95592	+	6.29325i	0.270980	+	0.214349i
$863$	33.0350			1.12453			0.562263	−	0.826958i	$-0.309931\pi$
$863$	33.0350			1.12453			0.562263	+	0.826958i	$0.309931\pi$
$864$		0			0
$865$	2.15928			0.0734177
$866$	0.528776	+	0.418270i	0.0179685	+	0.0142134i
$867$		0			0
$868$	34.1460	+	21.0799i	1.15899	+	0.715499i
$869$	36.8522	−	15.2647i	1.25013	−	0.517819i
$870$		0			0
$871$	−12.5244	+	12.5244i	−0.424372	+	0.424372i
$872$	9.66273	+	10.5574i	0.327221	+	0.357519i
$873$		0			0
$874$	74.4799	+	21.1382i	2.51932	+	0.715010i
$875$	−10.0203	−	24.1911i	−0.338748	−	0.817810i
$876$		0			0
$877$	9.15342	+	3.79147i	0.309089	+	0.128029i	0.531836	−	0.846847i	$-0.321502\pi$
$877$	9.15342	+	3.79147i	0.309089	+	0.128029i	−0.222747	+	0.974876i	$0.571502\pi$
$878$	−38.9877	+	4.54931i	−1.31577	+	0.153532i
$879$		0			0
$880$	−35.0641	−	11.6493i	−1.18201	−	0.392698i
$881$		−	9.57139i		−	0.322468i	−0.986916	−	0.161234i	$-0.948453\pi$
$881$		−	9.57139i		−	0.322468i	0.986916	−	0.161234i	$-0.0515474\pi$
$882$		0			0
$883$	11.2754	+	4.67041i	0.379446	+	0.157172i	0.564251	−	0.825604i	$-0.309165\pi$
$883$	11.2754	+	4.67041i	0.379446	+	0.157172i	−0.184805	+	0.982775i	$0.559165\pi$
$884$	−13.6869	−	2.21410i	−0.460341	−	0.0744683i
$885$		0			0
$886$	8.19874	−	28.8881i	0.275442	−	0.970514i
$887$	40.5935	+	40.5935i	1.36300	+	1.36300i	0.870072	+	0.492924i	$0.164072\pi$
$887$	40.5935	+	40.5935i	1.36300	+	1.36300i	0.492924	+	0.870072i	$0.335928\pi$
$888$		0			0
$889$	−1.13588	+	1.13588i	−0.0380960	+	0.0380960i
$890$	−34.4202	−	61.7002i	−1.15377	−	2.06820i
$891$		0			0
$892$	10.6116	+	44.8517i	0.355302	+	1.50175i
$893$	16.1435	−	38.9739i	0.540222	−	1.30421i
$894$		0			0
$895$	13.9247			0.465450
$896$	−34.8271	+	36.8139i	−1.16349	+	1.22986i
$897$		0			0
$898$	−6.27026	+	7.92686i	−0.209241	+	0.264523i
$899$	−3.92163	+	9.46766i	−0.130794	+	0.315764i
$900$		0			0
$901$	6.80394	−	2.81828i	0.226672	−	0.0938906i
$902$	2.80705	+	5.03181i	0.0934647	+	0.167541i
$903$		0			0
$904$	5.20139	−	11.1374i	0.172996	−	0.370425i
$905$	−5.54883	−	5.54883i	−0.184449	−	0.184449i
$906$		0			0
$907$	−12.5547	−	30.3096i	−0.416871	−	1.00641i	−0.983249	−	0.182269i	$-0.941656\pi$
$907$	−12.5547	−	30.3096i	−0.416871	−	1.00641i	0.566378	−	0.824146i	$-0.308344\pi$
$908$	9.64634	+	1.56047i	0.320125	+	0.0517859i
$909$		0			0
$910$	8.10910	+	69.4953i	0.268814	+	2.30375i
$911$		−	47.8856i		−	1.58652i	−0.608883	−	0.793260i	$-0.708382\pi$
$911$		−	47.8856i		−	1.58652i	0.608883	−	0.793260i	$-0.291618\pi$
$912$		0			0
$913$		−	11.9578i		−	0.395746i
$914$	37.4961	−	4.37526i	1.24026	−	0.144721i
$915$		0			0
$916$	−0.0313894	−	0.0435049i	−0.00103714	−	0.00143744i
$917$	31.0959	+	75.0721i	1.02688	+	2.47910i
$918$		0			0
$919$	−3.68211	−	3.68211i	−0.121462	−	0.121462i	0.643763	−	0.765225i	$-0.277372\pi$
$919$	−3.68211	−	3.68211i	−0.121462	−	0.121462i	−0.765225	+	0.643763i	$0.777372\pi$
$920$	47.7384	+	52.1585i	1.57389	+	1.71961i
$921$		0			0
$922$	−47.8811	+	26.7110i	−1.57688	+	0.879682i
$923$	−21.0237	+	8.70831i	−0.692004	+	0.286637i
$924$		0			0
$925$	−6.26115	+	15.1158i	−0.205865	+	0.497003i
$926$	−2.43907	−	1.92934i	−0.0801527	−	0.0634019i
$927$		0			0
$928$	−10.7008	−	7.27843i	−0.351272	−	0.238926i
$929$	46.7702			1.53448			0.767240	−	0.641360i	$-0.221629\pi$
$929$	46.7702			1.53448			0.767240	+	0.641360i	$0.221629\pi$
$930$		0			0
$931$	−37.4622	+	90.4418i	−1.22777	+	2.96411i
$932$	21.5203	−	34.8593i	0.704921	−	1.14185i
$933$		0			0
$934$	−44.8856	+	25.0400i	−1.46870	+	0.819334i
$935$	14.0277	−	14.0277i	0.458756	−	0.458756i
$936$		0			0
$937$	17.9931	+	17.9931i	0.587810	+	0.587810i	0.937038	−	0.349228i	$-0.113556\pi$
$937$	17.9931	+	17.9931i	0.587810	+	0.587810i	−0.349228	+	0.937038i	$0.613556\pi$
$938$	−33.4389	−	9.49032i	−1.09182	−	0.309870i
$939$		0			0
$940$	31.2431	−	22.5423i	1.01904	−	0.735250i
$941$	20.3927	+	8.44695i	0.664785	+	0.275363i	0.689450	−	0.724333i	$-0.257852\pi$
$941$	20.3927	+	8.44695i	0.664785	+	0.275363i	−0.0246657	+	0.999696i	$0.507852\pi$
$942$		0			0
$943$		−	11.0262i		−	0.359061i
$944$	29.9219	−	34.5696i	0.973875	−	1.12514i
$945$		0			0
$946$	1.82480	+	15.6386i	0.0593294	+	0.508455i
$947$	42.6259	+	17.6562i	1.38516	+	0.573750i	0.945855	−	0.324590i	$-0.105226\pi$
$947$	42.6259	+	17.6562i	1.38516	+	0.573750i	0.439300	+	0.898340i	$0.355226\pi$
$948$		0			0
$949$	14.0723	+	33.9736i	0.456807	+	1.10283i
$950$	19.4096	−	68.3894i	0.629731	−	2.21884i
$951$		0			0
$952$	−9.29121	−	25.5739i	−0.301130	−	0.828855i
$953$	−31.0970	+	31.0970i	−1.00733	+	1.00733i	−0.00735671	+	0.999973i	$0.502342\pi$
$953$	−31.0970	+	31.0970i	−1.00733	+	1.00733i	−0.999973	+	0.00735671i	$0.997658\pi$
$954$		0			0
$955$	7.04170	−	2.91677i	0.227864	−	0.0943844i
$956$	7.06924	−	1.67253i	0.228636	−	0.0540935i
$957$		0			0
$958$	−12.6877	+	16.0398i	−0.409920	+	0.518221i
$959$	−65.8835			−2.12749
$960$		0			0
$961$	−10.9353			−0.352752
$962$	6.90710	−	8.73195i	0.222694	−	0.281529i
$963$		0			0
$964$	1.75884	−	0.416129i	0.0566485	−	0.0134026i
$965$	−42.4284	+	17.5744i	−1.36582	+	0.565741i
$966$		0			0
$967$	−26.9633	+	26.9633i	−0.867081	+	0.867081i	−0.992148	−	0.125068i	$-0.960085\pi$
$967$	−26.9633	+	26.9633i	−0.867081	+	0.867081i	0.125068	+	0.992148i	$0.460085\pi$
$968$	9.86939	−	3.58563i	0.317214	−	0.115247i
$969$		0			0
$970$	−19.5374	+	68.8394i	−0.627307	+	2.21030i
$971$	−3.52462	−	8.50919i	−0.113111	−	0.273073i	0.857179	−	0.515018i	$-0.172215\pi$
$971$	−3.52462	−	8.50919i	−0.113111	−	0.273073i	−0.970290	+	0.241945i	$0.922215\pi$
$972$		0			0
$973$	48.4308	+	20.0607i	1.55262	+	0.643116i
$974$	0.660111	+	5.65717i	0.0211513	+	0.181268i
$975$		0			0
$976$	−1.00696	−	13.9726i	−0.0322320	−	0.447251i
$977$			40.7546i			1.30386i	0.758281	+	0.651928i	$0.226039\pi$
$977$			40.7546i			1.30386i	−0.758281	+	0.651928i	$0.773961\pi$
$978$		0			0
$979$	−36.4136	−	15.0830i	−1.16378	−	0.482055i
$980$	−72.5018	+	52.3111i	−2.31599	+	1.67102i
$981$		0			0
$982$	19.9733	+	5.66863i	0.637374	+	0.180893i
$983$	2.62407	+	2.62407i	0.0836947	+	0.0836947i	0.747715	−	0.664020i	$-0.231151\pi$
$983$	2.62407	+	2.62407i	0.0836947	+	0.0836947i	−0.664020	+	0.747715i	$0.731151\pi$
$984$		0			0
$985$	−36.8381	+	36.8381i	−1.17376	+	1.17376i
$986$	6.06814	−	3.38518i	0.193249	−	0.107806i
$987$		0			0
$988$	−25.4122	+	41.1635i	−0.808470	+	1.30959i
$989$	11.5302	−	27.8365i	0.366641	−	0.885149i
$990$		0			0
$991$	−30.4629			−0.967687			−0.483844	−	0.875154i	$-0.660760\pi$
$991$	−30.4629			−0.967687			−0.483844	+	0.875154i	$0.660760\pi$
$992$	−5.14819	+	24.8106i	−0.163455	+	0.787738i
$993$		0			0
$994$	−35.0249	−	27.7052i	−1.11092	−	0.878756i
$995$	23.2102	−	56.0344i	0.735813	−	1.77641i
$996$		0			0
$997$	27.8167	−	11.5221i	0.880965	−	0.364908i	0.104094	−	0.994567i	$-0.466806\pi$
$997$	27.8167	−	11.5221i	0.880965	−	0.364908i	0.776871	+	0.629660i	$0.216806\pi$
$998$	−32.6021	+	18.1875i	−1.03200	+	0.575715i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.b.109.10	✓	128
3.2	odd	2	inner	864.2.v.b.109.23	yes	128
32.5	even	8	inner	864.2.v.b.325.10	yes	128
96.5	odd	8	inner	864.2.v.b.325.23	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.b.109.10	✓	128	1.1	even	1	trivial
864.2.v.b.109.23	yes	128	3.2	odd	2	inner
864.2.v.b.325.10	yes	128	32.5	even	8	inner
864.2.v.b.325.23	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)

\(f(q)\)	\(=\)	\(q+(-0.877362 + 1.10916i) q^{2} +(-0.460473 - 1.94627i) q^{4} +(3.16129 - 1.30945i) q^{5} +(3.16733 - 3.16733i) q^{7} +(2.56273 + 1.19684i) q^{8} +O(q^{10})\)	\(q+(-0.877362 + 1.10916i) q^{2} +(-0.460473 - 1.94627i) q^{4} +(3.16129 - 1.30945i) q^{5} +(3.16733 - 3.16733i) q^{7} +(2.56273 + 1.19684i) q^{8} +(-1.32120 + 4.65523i) q^{10} +(1.03307 + 2.49405i) q^{11} +(2.98219 + 1.23526i) q^{13} +(0.734183 + 6.29197i) q^{14} +(-3.57593 + 1.79241i) q^{16} -2.14766i q^{17} +(-6.92299 - 2.86759i) q^{19} +(-4.00422 - 5.54975i) q^{20} +(-3.67267 - 1.04234i) q^{22} +(5.16599 + 5.16599i) q^{23} +(4.74354 - 4.74354i) q^{25} +(-3.98656 + 2.22395i) q^{26} +(-7.62295 - 4.70601i) q^{28} +(0.875489 - 2.11362i) q^{29} -4.47936 q^{31} +(1.14931 - 5.53887i) q^{32} +(2.38210 + 1.88427i) q^{34} +(5.86539 - 14.1603i) q^{35} +(-2.25327 + 0.933333i) q^{37} +(9.25458 - 5.16278i) q^{38} +(9.66871 + 0.427809i) q^{40} +(-1.06719 - 1.06719i) q^{41} +(-1.57823 - 3.81019i) q^{43} +(4.37839 - 3.15907i) q^{44} +(-10.2623 + 1.19747i) q^{46} +5.62964i q^{47} -13.0640i q^{49} +(1.09955 + 9.42315i) q^{50} +(1.03094 - 6.37295i) q^{52} +(1.31226 + 3.16807i) q^{53} +(6.53164 + 6.53164i) q^{55} +(11.9078 - 4.32620i) q^{56} +(1.57622 + 2.82546i) q^{58} +(-10.5601 + 4.37413i) q^{59} +(-1.34023 + 3.23561i) q^{61} +(3.93002 - 4.96833i) q^{62} +(5.13513 + 6.13436i) q^{64} +11.0451 q^{65} +(-2.09986 + 5.06951i) q^{67} +(-4.17992 + 0.988940i) q^{68} +(10.5600 + 18.9294i) q^{70} +(-4.98493 + 4.98493i) q^{71} +(8.05547 + 8.05547i) q^{73} +(0.941713 - 3.31810i) q^{74} +(-2.39326 + 14.7944i) q^{76} +(11.1715 + 4.62740i) q^{77} -14.7761i q^{79} +(-8.95747 + 10.3488i) q^{80} +(2.11999 - 0.247373i) q^{82} +(-4.09240 - 1.69513i) q^{83} +(-2.81225 - 6.78937i) q^{85} +(5.61078 + 1.59240i) q^{86} +(-0.337513 + 7.62798i) q^{88} +(-10.3239 + 10.3239i) q^{89} +(13.3581 - 5.53310i) q^{91} +(7.67560 - 12.4332i) q^{92} +(-6.24417 - 4.93923i) q^{94} -25.6405 q^{95} +14.7875 q^{97} +(14.4901 + 11.4618i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 16 q^{10} - 32 q^{16} - 16 q^{22} - 32 q^{40} - 32 q^{46} - 80 q^{52} + 32 q^{55} - 32 q^{58} + 64 q^{61} + 48 q^{64} + 64 q^{67} - 96 q^{70} + 32 q^{76} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 48 q^{94}+O(q^{100}) \) 128 * q + 16 * q^10 - 32 * q^16 - 16 * q^22 - 32 * q^40 - 32 * q^46 - 80 * q^52 + 32 * q^55 - 32 * q^58 + 64 * q^61 + 48 * q^64 + 64 * q^67 - 96 * q^70 + 32 * q^76 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 48 * q^94

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