LMFDB - Embedded newform 765.2.bh.b.604.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(19,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 4, 7]))

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

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

chi := DirichletCharacter("765.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.bh (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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			604.1
Character	$\chi$	$=$	765.604
Dual form			765.2.bh.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.48843 - 1.48843i) q^{2} +2.43082i q^{4} +(2.22841 + 0.184902i) q^{5} +(-2.47912 + 1.02689i) q^{7} +(0.641241 - 0.641241i) q^{8} +(-3.04161 - 3.59203i) q^{10} +(0.901470 - 0.373401i) q^{11} -2.65240 q^{13} +(5.21843 + 2.16155i) q^{14} +2.95276 q^{16} +(-3.25539 + 2.53030i) q^{17} +(-0.478059 + 0.478059i) q^{19} +(-0.449464 + 5.41686i) q^{20} +(-1.89755 - 0.785991i) q^{22} +(-1.54397 - 3.72748i) q^{23} +(4.93162 + 0.824076i) q^{25} +(3.94790 + 3.94790i) q^{26} +(-2.49617 - 6.02630i) q^{28} +(-3.83958 + 9.26957i) q^{29} +(-9.10497 - 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} +(8.61157 + 1.07924i) q^{34} +(-5.71438 + 1.82993i) q^{35} +(-2.61646 + 6.31669i) q^{37} +1.42311 q^{38} +(1.54751 - 1.31038i) q^{40} +(-2.80190 - 6.76439i) q^{41} +(-6.29628 + 6.29628i) q^{43} +(0.907670 + 2.19131i) q^{44} +(-3.24999 + 7.84616i) q^{46} -0.874497 q^{47} +(0.141809 - 0.141809i) q^{49} +(-6.11377 - 8.56693i) q^{50} -6.44750i q^{52} +(2.00842 + 2.00842i) q^{53} +(2.07789 - 0.665407i) q^{55} +(-0.931234 + 2.24820i) q^{56} +(19.5120 - 8.08213i) q^{58} +(7.59005 + 7.59005i) q^{59} +(0.793008 + 1.91449i) q^{61} +(7.93862 + 19.1655i) q^{62} +10.9954i q^{64} +(-5.91063 - 0.490434i) q^{65} -5.73990i q^{67} +(-6.15070 - 7.91327i) q^{68} +(11.2291 + 5.78171i) q^{70} +(-1.03955 - 0.430595i) q^{71} +(2.77027 + 1.14748i) q^{73} +(13.2963 - 5.50752i) q^{74} +(-1.16208 - 1.16208i) q^{76} +(-1.85141 + 1.85141i) q^{77} +(-0.377872 + 0.156520i) q^{79} +(6.57996 + 0.545972i) q^{80} +(-5.89786 + 14.2387i) q^{82} +(4.64846 + 4.64846i) q^{83} +(-7.72221 + 5.03662i) q^{85} +18.7431 q^{86} +(0.338619 - 0.817499i) q^{88} +5.62649i q^{89} +(6.57562 - 2.72371i) q^{91} +(9.06082 - 3.75312i) q^{92} +(1.30162 + 1.30162i) q^{94} +(-1.15371 + 0.976918i) q^{95} +(14.2405 + 5.89862i) q^{97} -0.422145 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50}+ \cdots + 88 q^{95}+O(q^{100}) $ 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.48843	−	1.48843i	−1.05248	−	1.05248i	−0.998545	−	0.0539308i	$-0.982825\pi$
$2$	−1.48843	−	1.48843i	−1.05248	−	1.05248i	−0.0539308	−	0.998545i	$-0.517175\pi$
$3$		0			0
$3$		0			0
$4$			2.43082i			1.21541i
$5$	2.22841	+	0.184902i	0.996575	+	0.0826908i
$5$	2.22841	+	0.184902i	0.996575	+	0.0826908i
$6$		0			0
$7$	−2.47912	+	1.02689i	−0.937021	+	0.388127i	−0.798338	−	0.602210i	$-0.794287\pi$
$7$	−2.47912	+	1.02689i	−0.937021	+	0.388127i	−0.138683	+	0.990337i	$0.544287\pi$
$8$	0.641241	−	0.641241i	0.226713	−	0.226713i
$9$		0			0
$10$	−3.04161	−	3.59203i	−0.961841	−	1.13590i
$11$	0.901470	−	0.373401i	0.271803	−	0.112585i	−0.242619	−	0.970122i	$-0.578006\pi$
$11$	0.901470	−	0.373401i	0.271803	−	0.112585i	0.514422	+	0.857537i	$0.328006\pi$
$12$		0			0
$13$	−2.65240			−0.735643			−0.367821	−	0.929896i	$-0.619896\pi$
$13$	−2.65240			−0.735643			−0.367821	+	0.929896i	$0.619896\pi$
$14$	5.21843	+	2.16155i	1.39468	+	0.577697i
$15$		0			0
$16$	2.95276			0.738190
$17$	−3.25539	+	2.53030i	−0.789548	+	0.613688i
$17$	−3.25539	+	2.53030i	−0.789548	+	0.613688i
$18$		0			0
$19$	−0.478059	+	0.478059i	−0.109674	+	0.109674i	−0.759814	−	0.650140i	$-0.774710\pi$
$19$	−0.478059	+	0.478059i	−0.109674	+	0.109674i	0.650140	+	0.759814i	$0.274710\pi$
$20$	−0.449464	+	5.41686i	−0.100503	+	1.21125i
$21$		0			0
$22$	−1.89755	−	0.785991i	−0.404559	−	0.167574i
$23$	−1.54397	−	3.72748i	−0.321940	−	0.777233i	−0.999141	−	0.0414347i	$-0.986807\pi$
$23$	−1.54397	−	3.72748i	−0.321940	−	0.777233i	0.677201	−	0.735798i	$-0.263193\pi$
$24$		0			0
$25$	4.93162	+	0.824076i	0.986324	+	0.164815i
$26$	3.94790	+	3.94790i	0.774246	+	0.774246i
$27$		0			0
$28$	−2.49617	−	6.02630i	−0.471733	−	1.13886i
$29$	−3.83958	+	9.26957i	−0.712992	+	1.72132i	−0.0206072	+	0.999788i	$0.506560\pi$
$29$	−3.83958	+	9.26957i	−0.712992	+	1.72132i	−0.692385	+	0.721528i	$0.743440\pi$
$30$		0			0
$31$	−9.10497	−	3.77140i	−1.63530	−	0.677364i	−0.639490	−	0.768800i	$-0.720854\pi$
$31$	−9.10497	−	3.77140i	−1.63530	−	0.677364i	−0.995811	+	0.0914357i	$0.970854\pi$
$32$	−5.67744	−	5.67744i	−1.00364	−	1.00364i
$33$		0			0
$34$	8.61157	+	1.07924i	1.47687	+	0.185089i
$35$	−5.71438	+	1.82993i	−0.965906	+	0.309314i
$36$		0			0
$37$	−2.61646	+	6.31669i	−0.430143	+	1.03846i	0.549098	+	0.835758i	$0.314971\pi$
$37$	−2.61646	+	6.31669i	−0.430143	+	1.03846i	−0.979241	+	0.202699i	$0.935029\pi$
$38$	1.42311			0.230859
$39$		0			0
$40$	1.54751	−	1.31038i	0.244684	−	0.207189i
$41$	−2.80190	−	6.76439i	−0.437583	−	1.05642i	−0.976781	−	0.214240i	$-0.931272\pi$
$41$	−2.80190	−	6.76439i	−0.437583	−	1.05642i	0.539198	−	0.842179i	$-0.318728\pi$
$42$		0			0
$43$	−6.29628	+	6.29628i	−0.960173	+	0.960173i	−0.999237	−	0.0390633i	$-0.987563\pi$
$43$	−6.29628	+	6.29628i	−0.960173	+	0.960173i	0.0390633	+	0.999237i	$0.487563\pi$
$44$	0.907670	+	2.19131i	0.136836	+	0.330352i
$45$		0			0
$46$	−3.24999	+	7.84616i	−0.479184	+	1.15685i
$47$	−0.874497			−0.127558			−0.0637792	−	0.997964i	$-0.520315\pi$
$47$	−0.874497			−0.127558			−0.0637792	+	0.997964i	$0.520315\pi$
$48$		0			0
$49$	0.141809	−	0.141809i	0.0202585	−	0.0202585i
$50$	−6.11377	−	8.56693i	−0.864618	−	1.21155i
$51$		0			0
$52$		−	6.44750i		−	0.894107i
$53$	2.00842	+	2.00842i	0.275878	+	0.275878i	0.831461	−	0.555583i	$-0.187505\pi$
$53$	2.00842	+	2.00842i	0.275878	+	0.275878i	−0.555583	+	0.831461i	$0.687505\pi$
$54$		0			0
$55$	2.07789	−	0.665407i	0.280182	−	0.0897234i
$56$	−0.931234	+	2.24820i	−0.124441	+	0.300428i
$57$		0			0
$58$	19.5120	−	8.08213i	2.56205	−	1.06124i
$59$	7.59005	+	7.59005i	0.988140	+	0.988140i	0.999930	−	0.0117908i	$-0.00375321\pi$
$59$	7.59005	+	7.59005i	0.988140	+	0.988140i	−0.0117908	+	0.999930i	$0.503753\pi$
$60$		0			0
$61$	0.793008	+	1.91449i	0.101534	+	0.245125i	0.966481	−	0.256738i	$-0.0826479\pi$
$61$	0.793008	+	1.91449i	0.101534	+	0.245125i	−0.864947	+	0.501864i	$0.832648\pi$
$62$	7.93862	+	19.1655i	1.00821	+	2.43402i
$63$		0			0
$64$			10.9954i			1.37442i
$65$	−5.91063	−	0.490434i	−0.733123	−	0.0608309i
$66$		0			0
$67$		−	5.73990i		−	0.701240i	−0.936518	−	0.350620i	$-0.885971\pi$
$67$		−	5.73990i		−	0.701240i	0.936518	−	0.350620i	$-0.114029\pi$
$68$	−6.15070	−	7.91327i	−0.745882	−	0.959624i
$69$		0			0
$70$	11.2291	+	5.78171i	1.34214	+	0.691047i
$71$	−1.03955	−	0.430595i	−0.123372	−	0.0511022i	0.320144	−	0.947369i	$-0.396269\pi$
$71$	−1.03955	−	0.430595i	−0.123372	−	0.0511022i	−0.443515	+	0.896267i	$0.646269\pi$
$72$		0			0
$73$	2.77027	+	1.14748i	0.324236	+	0.134303i	0.538864	−	0.842393i	$-0.318854\pi$
$73$	2.77027	+	1.14748i	0.324236	+	0.134303i	−0.214628	+	0.976696i	$0.568854\pi$
$74$	13.2963	−	5.50752i	1.54567	−	0.640236i
$75$		0			0
$76$	−1.16208	−	1.16208i	−0.133299	−	0.133299i
$77$	−1.85141	+	1.85141i	−0.210988	+	0.210988i
$78$		0			0
$79$	−0.377872	+	0.156520i	−0.0425139	+	0.0176099i	−0.403839	−	0.914830i	$-0.632324\pi$
$79$	−0.377872	+	0.156520i	−0.0425139	+	0.0176099i	0.361325	+	0.932440i	$0.382324\pi$
$80$	6.57996	+	0.545972i	0.735662	+	0.0610415i
$81$		0			0
$82$	−5.89786	+	14.2387i	−0.651310	+	1.57240i
$83$	4.64846	+	4.64846i	0.510235	+	0.510235i	0.914598	−	0.404363i	$-0.132507\pi$
$83$	4.64846	+	4.64846i	0.510235	+	0.510235i	−0.404363	+	0.914598i	$0.632507\pi$
$84$		0			0
$85$	−7.72221	+	5.03662i	−0.837591	+	0.546298i
$86$	18.7431			2.02112
$87$		0			0
$88$	0.338619	−	0.817499i	0.0360969	−	0.0871457i
$89$			5.62649i			0.596407i	0.954502	+	0.298204i	$0.0963874\pi$
$89$			5.62649i			0.596407i	−0.954502	+	0.298204i	$0.903613\pi$
$90$		0			0
$91$	6.57562	−	2.72371i	0.689312	−	0.285523i
$92$	9.06082	−	3.75312i	0.944656	−	0.391289i
$93$		0			0
$94$	1.30162	+	1.30162i	0.134252	+	0.134252i
$95$	−1.15371	+	0.976918i	−0.118368	+	0.100230i
$96$		0			0
$97$	14.2405	+	5.89862i	1.44591	+	0.598915i	0.961222	−	0.275774i	$-0.0889342\pi$
$97$	14.2405	+	5.89862i	1.44591	+	0.598915i	0.484685	+	0.874689i	$0.338934\pi$
$98$	−0.422145			−0.0426430
$99$		0			0
$100$	−2.00318	+	11.9879i	−0.200318	+	1.19879i
$101$	−14.6242			−1.45516			−0.727582	−	0.686021i	$-0.759356\pi$
$101$	−14.6242			−1.45516			−0.727582	+	0.686021i	$0.759356\pi$
$102$		0			0
$103$		−	1.63280i		−	0.160884i	−0.996759	−	0.0804421i	$-0.974367\pi$
$103$		−	1.63280i		−	0.160884i	0.996759	−	0.0804421i	$-0.0256332\pi$
$104$	−1.70083	+	1.70083i	−0.166780	+	0.166780i
$105$		0			0
$106$		−	5.97877i		−	0.580710i
$107$	5.14591	+	2.13151i	0.497474	+	0.206060i	0.617290	−	0.786736i	$-0.288231\pi$
$107$	5.14591	+	2.13151i	0.497474	+	0.206060i	−0.119816	+	0.992796i	$0.538231\pi$
$108$		0			0
$109$	−1.00965	−	2.43750i	−0.0967066	−	0.233470i	0.868122	−	0.496351i	$-0.165327\pi$
$109$	−1.00965	−	2.43750i	−0.0967066	−	0.233470i	−0.964828	+	0.262881i	$0.915327\pi$
$110$	−4.08319	−	2.10237i	−0.389317	−	0.200453i
$111$		0			0
$112$	−7.32025	+	3.03215i	−0.691699	+	0.286511i
$113$	−2.22293	−	5.36662i	−0.209115	−	0.504849i	0.784169	−	0.620547i	$-0.213090\pi$
$113$	−2.22293	−	5.36662i	−0.209115	−	0.504849i	−0.993284	+	0.115698i	$0.963090\pi$
$114$		0			0
$115$	−2.75138	−	8.59183i	−0.256568	−	0.801193i
$116$	−22.5326	−	9.33332i	−2.09210	−	0.866577i
$117$		0			0
$118$		−	22.5944i		−	2.07999i
$119$	5.47219	−	9.61585i	0.501634	−	0.881483i
$120$		0			0
$121$	−7.10496	+	7.10496i	−0.645905	+	0.645905i
$122$	1.66924	−	4.02991i	0.151126	−	0.364851i
$123$		0			0
$124$	9.16759	−	22.1325i	0.823274	−	1.98756i
$125$	10.8373	+	2.74825i	0.969318	+	0.245811i
$126$		0			0
$127$	7.53018	−	7.53018i	0.668195	−	0.668195i	−0.289103	−	0.957298i	$-0.593357\pi$
$127$	7.53018	−	7.53018i	0.668195	−	0.668195i	0.957298	+	0.289103i	$0.0933569\pi$
$128$	5.01091	−	5.01091i	0.442906	−	0.442906i
$129$		0			0
$130$	8.06755	+	9.52750i	0.707571	+	0.835617i
$131$	0.619360	−	1.49527i	0.0541137	−	0.130642i	−0.894511	−	0.447047i	$-0.852476\pi$
$131$	0.619360	−	1.49527i	0.0541137	−	0.130642i	0.948624	+	0.316405i	$0.102476\pi$
$132$		0			0
$133$	0.694256	−	1.67608i	0.0601996	−	0.145335i
$134$	−8.54341	+	8.54341i	−0.738038	+	0.738038i
$135$		0			0
$136$	−0.464958	+	3.71002i	−0.0398698	+	0.318132i
$137$		−	4.70326i		−	0.401826i	−0.979609	−	0.200913i	$-0.935609\pi$
$137$		−	4.70326i		−	0.401826i	0.979609	−	0.200913i	$-0.0643909\pi$
$138$		0			0
$139$	0.761078	+	0.315249i	0.0645538	+	0.0267391i	0.414727	−	0.909946i	$-0.363877\pi$
$139$	0.761078	+	0.315249i	0.0645538	+	0.0267391i	−0.350173	+	0.936685i	$0.613877\pi$
$140$	−4.44822	−	13.8906i	−0.375944	−	1.17397i
$141$		0			0
$142$	0.906381	+	2.18820i	0.0760618	+	0.183629i
$143$	−2.39106	+	0.990408i	−0.199950	+	0.0828221i
$144$		0			0
$145$	−10.2701	+	19.9465i	−0.852888	+	1.65646i
$146$	−2.41540	−	5.83129i	−0.199900	−	0.482601i
$147$		0			0
$148$	−15.3547	−	6.36014i	−1.26215	−	0.522800i
$149$			9.60320i			0.786725i	0.919383	+	0.393362i	$0.128688\pi$
$149$			9.60320i			0.786725i	−0.919383	+	0.393362i	$0.871312\pi$
$150$		0			0
$151$	−1.00179	+	1.00179i	−0.0815244	+	0.0815244i	−0.746693	−	0.665169i	$-0.768360\pi$
$151$	−1.00179	+	1.00179i	−0.0815244	+	0.0815244i	0.665169	+	0.746693i	$0.268360\pi$
$152$			0.613103i			0.0497292i
$153$		0			0
$154$	5.51138			0.444120
$155$	−19.5923	−	10.0878i	−1.57369	−	0.810268i
$156$		0			0
$157$	−4.81882			−0.384584			−0.192292	−	0.981338i	$-0.561592\pi$
$157$	−4.81882			−0.384584			−0.192292	+	0.981338i	$0.561592\pi$
$158$	0.795403	+	0.329467i	0.0632788	+	0.0262109i
$159$		0			0
$160$	−11.6019	−	13.7014i	−0.917210	−	1.08319i
$161$	7.65539	+	7.65539i	0.603330	+	0.603330i
$162$		0			0
$163$	−1.49578	+	0.619572i	−0.117158	+	0.0485286i	−0.440493	−	0.897756i	$-0.645196\pi$
$163$	−1.49578	+	0.619572i	−0.117158	+	0.0485286i	0.323334	+	0.946285i	$0.395196\pi$
$164$	16.4430	−	6.81091i	1.28398	−	0.531843i
$165$		0			0
$166$		−	13.8378i		−	1.07402i
$167$	8.47025	−	20.4490i	0.655447	−	1.58239i	−0.149313	−	0.988790i	$-0.547706\pi$
$167$	8.47025	−	20.4490i	0.655447	−	1.58239i	0.804760	−	0.593600i	$-0.202294\pi$
$168$		0			0
$169$	−5.96479			−0.458830
$170$	18.9906	+	3.99729i	1.45651	+	0.306579i
$171$		0			0
$172$	−15.3051	−	15.3051i	−1.16700	−	1.16700i
$173$	−3.97100	+	9.58685i	−0.301910	+	0.728875i	0.698008	+	0.716089i	$0.254070\pi$
$173$	−3.97100	+	9.58685i	−0.301910	+	0.728875i	−0.999918	+	0.0127852i	$0.995930\pi$
$174$		0			0
$175$	−13.0723	+	3.02123i	−0.988175	+	0.228384i
$176$	2.66182	−	1.10256i	0.200642	−	0.0831088i
$177$		0			0
$178$	8.37461	−	8.37461i	0.627704	−	0.627704i
$179$	−13.2428	−	13.2428i	−0.989813	−	0.989813i	0.0101361	−	0.999949i	$-0.496774\pi$
$179$	−13.2428	−	13.2428i	−0.989813	−	0.989813i	−0.999949	+	0.0101361i	$0.996774\pi$
$180$		0			0
$181$	−2.26809	+	0.939472i	−0.168585	+	0.0698304i	−0.465380	−	0.885111i	$-0.654082\pi$
$181$	−2.26809	+	0.939472i	−0.168585	+	0.0698304i	0.296795	+	0.954941i	$0.404082\pi$
$182$	−13.8414	−	5.73328i	−1.02599	−	0.424979i
$183$		0			0
$184$	−3.38027	−	1.40015i	−0.249197	−	0.103221i
$185$	−6.99851	+	13.5924i	−0.514541	+	0.999332i
$186$		0			0
$187$	−1.98982	+	3.49656i	−0.145510	+	0.255694i
$188$		−	2.12574i		−	0.155036i
$189$		0			0
$190$	3.17128	+	0.263137i	0.230069	+	0.0190899i
$191$		−	10.9126i		−	0.789607i	−0.918766	−	0.394803i	$-0.870813\pi$
$191$		−	10.9126i		−	0.789607i	0.918766	−	0.394803i	$-0.129187\pi$
$192$		0			0
$193$	−7.03202	−	16.9768i	−0.506176	−	1.22202i	−0.946069	−	0.323966i	$-0.894984\pi$
$193$	−7.03202	−	16.9768i	−0.506176	−	1.22202i	0.439893	−	0.898050i	$-0.355016\pi$
$194$	−12.4163	−	29.9756i	−0.891439	−	2.15213i
$195$		0			0
$196$	0.344712	+	0.344712i	0.0246223	+	0.0246223i
$197$	−18.0071	+	7.45879i	−1.28295	+	0.531417i	−0.916878	−	0.399168i	$-0.869299\pi$
$197$	−18.0071	+	7.45879i	−1.28295	+	0.531417i	−0.366076	+	0.930585i	$0.619299\pi$
$198$		0			0
$199$	−8.92336	+	21.5429i	−0.632560	+	1.52713i	0.203834	+	0.979005i	$0.434660\pi$
$199$	−8.92336	+	21.5429i	−0.632560	+	1.52713i	−0.836394	+	0.548129i	$0.815340\pi$
$200$	3.69079	−	2.63393i	0.260978	−	0.186247i
$201$		0			0
$202$	21.7670	+	21.7670i	1.53152	+	1.53152i
$203$		−	26.9232i		−	1.88964i
$204$		0			0
$205$	−4.99303	−	15.5919i	−0.348729	−	1.08899i
$206$	−2.43029	+	2.43029i	−0.169327	+	0.169327i
$207$		0			0
$208$	−7.83189			−0.543044
$209$	−0.252448	+	0.609464i	−0.0174622	+	0.0421575i
$210$		0			0
$211$	−8.77140	−	21.1760i	−0.603848	−	1.45782i	−0.869590	−	0.493774i	$-0.835617\pi$
$211$	−8.77140	−	21.1760i	−0.603848	−	1.45782i	0.265742	−	0.964044i	$-0.414383\pi$
$212$	−4.88211	+	4.88211i	−0.335305	+	0.335305i
$213$		0			0
$214$	−4.48671	−	10.8319i	−0.306706	−	0.740453i
$215$	−15.1949	+	12.8665i	−1.03628	+	0.877488i
$216$		0			0
$217$	26.4451			1.79521
$218$	−2.12526	+	5.13082i	−0.143940	+	0.347503i
$219$		0			0
$220$	1.61748	+	5.05097i	0.109051	+	0.340536i
$221$	8.63459	−	6.71137i	0.580826	−	0.451455i
$222$		0			0
$223$	−9.23194	−	9.23194i	−0.618217	−	0.618217i	0.326857	−	0.945074i	$-0.394010\pi$
$223$	−9.23194	−	9.23194i	−0.618217	−	0.618217i	−0.945074	+	0.326857i	$0.894010\pi$
$224$	19.9052	+	8.24499i	1.32997	+	0.550892i
$225$		0			0
$226$	−4.67915	+	11.2965i	−0.311253	+	0.751430i
$227$	4.09453	+	9.88506i	0.271763	+	0.656095i	0.999559	−	0.0296996i	$-0.00945506\pi$
$227$	4.09453	+	9.88506i	0.271763	+	0.656095i	−0.727796	+	0.685794i	$0.759455\pi$
$228$		0			0
$229$	13.3171	+	13.3171i	0.880020	+	0.880020i	0.993536	−	0.113516i	$-0.0362113\pi$
$229$	13.3171	+	13.3171i	0.880020	+	0.880020i	−0.113516	+	0.993536i	$0.536211\pi$
$230$	−8.69307	+	16.8835i	−0.573204	+	1.11327i
$231$		0			0
$232$	3.48193	+	8.40612i	0.228600	+	0.551889i
$233$	2.07494	+	0.859469i	0.135934	+	0.0563057i	0.449613	−	0.893223i	$-0.351562\pi$
$233$	2.07494	+	0.859469i	0.135934	+	0.0563057i	−0.313679	+	0.949529i	$0.601562\pi$
$234$		0			0
$235$	−1.94874	−	0.161696i	−0.127122	−	0.0105479i
$236$	−18.4500	+	18.4500i	−1.20099	+	1.20099i
$237$		0			0
$238$	−22.4574	+	6.16753i	−1.45570	+	0.399782i
$239$	−16.7293			−1.08213			−0.541063	−	0.840982i	$-0.681978\pi$
$239$	−16.7293			−1.08213			−0.541063	+	0.840982i	$0.681978\pi$
$240$		0			0
$241$	10.8767	+	4.50526i	0.700627	+	0.290209i	0.704420	−	0.709784i	$-0.251207\pi$
$241$	10.8767	+	4.50526i	0.700627	+	0.290209i	−0.00379273	+	0.999993i	$0.501207\pi$
$242$	21.1504			1.35960
$243$		0			0
$244$	−4.65378	+	1.92766i	−0.297928	+	0.123406i
$245$	0.342230	−	0.289788i	0.0218643	−	0.0185139i
$246$		0			0
$247$	1.26800	−	1.26800i	0.0806812	−	0.0806812i
$248$	−8.25686	+	3.42010i	−0.524311	+	0.217177i
$249$		0			0
$250$	−12.0400	−	20.2211i	−0.761473	−	1.27889i
$251$		−	17.7019i		−	1.11733i	−0.829392	−	0.558666i	$-0.811313\pi$
$251$		−	17.7019i		−	1.11733i	0.829392	−	0.558666i	$-0.188687\pi$
$252$		0			0
$253$	−2.78369	−	2.78369i	−0.175009	−	0.175009i
$254$	−22.4162			−1.40652
$255$		0			0
$256$	7.07403			0.442127
$257$	5.44763	+	5.44763i	0.339814	+	0.339814i	0.856297	−	0.516483i	$-0.172759\pi$
$257$	5.44763	+	5.44763i	0.339814	+	0.339814i	−0.516483	+	0.856297i	$0.672759\pi$
$258$		0			0
$259$		−	18.3467i		−	1.14001i
$260$	1.19216	−	14.3677i	0.0739344	−	0.891045i
$261$		0			0
$262$	−3.14746	+	1.30372i	−0.194451	+	0.0805442i
$263$	4.45259	−	4.45259i	0.274558	−	0.274558i	−0.556374	−	0.830932i	$-0.687808\pi$
$263$	4.45259	−	4.45259i	0.274558	−	0.274558i	0.830932	+	0.556374i	$0.187808\pi$
$264$		0			0
$265$	4.10423	+	4.84695i	0.252121	+	0.297746i
$266$	−3.52807	+	1.46137i	−0.216320	+	0.0896026i
$267$		0			0
$268$	13.9527			0.852294
$269$	8.55428	+	3.54330i	0.521563	+	0.216039i	0.627904	−	0.778291i	$-0.283913\pi$
$269$	8.55428	+	3.54330i	0.521563	+	0.216039i	−0.106340	+	0.994330i	$0.533913\pi$
$270$		0			0
$271$	16.7791			1.01926			0.509628	−	0.860395i	$-0.329783\pi$
$271$	16.7791			1.01926			0.509628	+	0.860395i	$0.329783\pi$
$272$	−9.61239	+	7.47137i	−0.582837	+	0.453018i
$273$		0			0
$274$	−7.00044	+	7.00044i	−0.422912	+	0.422912i
$275$	4.75342	−	1.09859i	0.286642	−	0.0662476i
$276$		0			0
$277$	11.0923	+	4.59456i	0.666469	+	0.276061i	0.690158	−	0.723659i	$-0.257541\pi$
$277$	11.0923	+	4.59456i	0.666469	+	0.276061i	−0.0236887	+	0.999719i	$0.507541\pi$
$278$	−0.663584	−	1.60203i	−0.0397991	−	0.0960835i
$279$		0			0
$280$	−2.49087	+	4.83772i	−0.148858	+	0.289109i
$281$	19.9411	+	19.9411i	1.18959	+	1.18959i	0.977182	+	0.212403i	$0.0681291\pi$
$281$	19.9411	+	19.9411i	1.18959	+	1.18959i	0.212403	+	0.977182i	$0.431871\pi$
$282$		0			0
$283$	6.53556	+	15.7782i	0.388499	+	0.937919i	0.990258	+	0.139242i	$0.0444665\pi$
$283$	6.53556	+	15.7782i	0.388499	+	0.937919i	−0.601760	+	0.798677i	$0.705534\pi$
$284$	1.04670	−	2.52695i	0.0621101	−	0.149947i
$285$		0			0
$286$	5.03306	+	2.08476i	0.297611	+	0.123274i
$287$	13.8925	+	13.8925i	0.820049	+	0.820049i
$288$		0			0
$289$	4.19515	−	16.4742i	0.246774	−	0.969073i
$290$	44.9751	−	14.4025i	2.64103	−	0.845743i
$291$		0			0
$292$	−2.78933	+	6.73403i	−0.163233	+	0.394079i
$293$	−6.82563			−0.398758			−0.199379	−	0.979922i	$-0.563892\pi$
$293$	−6.82563			−0.398758			−0.199379	+	0.979922i	$0.563892\pi$
$294$		0			0
$295$	15.5103	+	18.3171i	0.903046	+	1.06647i
$296$	2.37274	+	5.72830i	0.137913	+	0.332951i
$297$		0			0
$298$	14.2936	−	14.2936i	0.828009	−	0.828009i
$299$	4.09523	+	9.88676i	0.236833	+	0.571766i
$300$		0			0
$301$	9.14369	−	22.0748i	0.527033	−	1.27237i
$302$	2.98218			0.171605
$303$		0			0
$304$	−1.41159	+	1.41159i	−0.0809605	+	0.0809605i
$305$	1.41315	+	4.41290i	0.0809169	+	0.252682i
$306$		0			0
$307$			0.746287i			0.0425929i	0.999773	+	0.0212964i	$0.00677938\pi$
$307$			0.746287i			0.0425929i	−0.999773	+	0.0212964i	$0.993221\pi$
$308$	−4.50045	−	4.50045i	−0.256437	−	0.256437i
$309$		0			0
$310$	14.1467	+	44.1765i	0.803481	+	2.50906i
$311$	6.96494	−	16.8149i	0.394946	−	0.953483i	−0.593900	−	0.804539i	$-0.702413\pi$
$311$	6.96494	−	16.8149i	0.394946	−	0.953483i	0.988846	−	0.148944i	$-0.0475874\pi$
$312$		0			0
$313$	9.16854	−	3.79773i	0.518236	−	0.214661i	−0.108206	−	0.994129i	$-0.534510\pi$
$313$	9.16854	−	3.79773i	0.518236	−	0.214661i	0.626442	+	0.779468i	$0.284510\pi$
$314$	7.17245	+	7.17245i	0.404765	+	0.404765i
$315$		0			0
$316$	−0.380471	−	0.918539i	−0.0214032	−	0.0516718i
$317$	−9.30367	−	22.4610i	−0.522546	−	1.26154i	−0.936317	−	0.351157i	$-0.885788\pi$
$317$	−9.30367	−	22.4610i	−0.522546	−	1.26154i	0.413770	−	0.910381i	$-0.364212\pi$
$318$		0			0
$319$			9.78994i			0.548131i
$320$	−2.03307	+	24.5022i	−0.113652	+	1.36971i
$321$		0			0
$322$		−	22.7890i		−	1.26998i
$323$	0.346636	−	2.76591i	0.0192874	−	0.153899i
$324$		0			0
$325$	−13.0806	−	2.18578i	−0.725582	−	0.121245i
$326$	3.14854	+	1.30417i	0.174381	+	0.0722312i
$327$		0			0
$328$	−6.13429	−	2.54091i	−0.338710	−	0.140298i
$329$	2.16799	−	0.898009i	0.119525	−	0.0495088i
$330$		0			0
$331$	−0.346315	−	0.346315i	−0.0190352	−	0.0190352i	0.697525	−	0.716560i	$-0.254285\pi$
$331$	−0.346315	−	0.346315i	−0.0190352	−	0.0190352i	−0.716560	+	0.697525i	$0.754285\pi$
$332$	−11.2996	+	11.2996i	−0.620144	+	0.620144i
$333$		0			0
$334$	−43.0441	+	17.8295i	−2.35527	+	0.975584i
$335$	1.06132	−	12.7908i	0.0579861	−	0.698839i
$336$		0			0
$337$	2.30186	−	5.55719i	0.125390	−	0.302719i	−0.848701	−	0.528872i	$-0.822615\pi$
$337$	2.30186	−	5.55719i	0.125390	−	0.302719i	0.974092	+	0.226153i	$0.0726150\pi$
$338$	8.87814	+	8.87814i	0.482907	+	0.482907i
$339$		0			0
$340$	−12.2431	−	18.7713i	−0.663976	−	1.01802i
$341$	−9.61610			−0.520741
$342$		0			0
$343$	6.98227	−	16.8567i	0.377007	−	0.910175i
$344$			8.07486i			0.435367i
$345$		0			0
$346$	20.1798	−	8.35877i	1.08488	−	0.449370i
$347$	7.29831	−	3.02306i	0.391794	−	0.162286i	−0.178085	−	0.984015i	$-0.556990\pi$
$347$	7.29831	−	3.02306i	0.391794	−	0.162286i	0.569879	+	0.821729i	$0.306990\pi$
$348$		0			0
$349$	−13.5417	−	13.5417i	−0.724868	−	0.724868i	0.244725	−	0.969593i	$-0.421302\pi$
$349$	−13.5417	−	13.5417i	−0.724868	−	0.724868i	−0.969593	+	0.244725i	$0.921302\pi$
$350$	23.9541	+	14.9603i	1.28040	+	0.799662i
$351$		0			0
$352$	−7.23801	−	2.99808i	−0.385787	−	0.159798i
$353$	13.7165			0.730055			0.365027	−	0.930997i	$-0.381060\pi$
$353$	13.7165			0.730055			0.365027	+	0.930997i	$0.381060\pi$
$354$		0			0
$355$	−2.23692	−	1.15176i	−0.118723	−	0.0611289i
$356$	−13.6770			−0.724879
$357$		0			0
$358$			39.4218i			2.08351i
$359$	−17.6460	+	17.6460i	−0.931322	+	0.931322i	−0.997789	−	0.0664662i	$-0.978828\pi$
$359$	−17.6460	+	17.6460i	−0.931322	+	0.931322i	0.0664662	+	0.997789i	$0.478828\pi$
$360$		0			0
$361$			18.5429i			0.975943i
$362$	4.77421	+	1.97754i	0.250927	+	0.103937i
$363$		0			0
$364$	6.62085	+	15.9841i	0.347027	+	0.837797i
$365$	5.96113	+	3.06929i	0.312020	+	0.160654i
$366$		0			0
$367$	−7.87910	+	3.26363i	−0.411286	+	0.170360i	−0.578726	−	0.815522i	$-0.696450\pi$
$367$	−7.87910	+	3.26363i	−0.411286	+	0.170360i	0.167440	+	0.985882i	$0.446450\pi$
$368$	−4.55898	−	11.0063i	−0.237653	−	0.573745i
$369$		0			0
$370$	30.6480	−	9.81449i	1.59331	−	0.510231i
$371$	−7.04155	−	2.91670i	−0.365579	−	0.151428i
$372$		0			0
$373$		−	11.5593i		−	0.598519i	−0.954172	−	0.299260i	$-0.903260\pi$
$373$		−	11.5593i		−	0.598519i	0.954172	−	0.299260i	$-0.0967397\pi$
$374$	8.16606	−	2.24266i	0.422257	−	0.115965i
$375$		0			0
$376$	−0.560763	+	0.560763i	−0.0289192	+	0.0289192i
$377$	10.1841	−	24.5866i	0.524508	−	1.26627i
$378$		0			0
$379$	4.70807	−	11.3663i	0.241837	−	0.583847i	−0.755628	−	0.655001i	$-0.772668\pi$
$379$	4.70807	−	11.3663i	0.241837	−	0.583847i	0.997465	+	0.0711543i	$0.0226683\pi$
$380$	−2.37471	−	2.80445i	−0.121820	−	0.143865i
$381$		0			0
$382$	−16.2426	+	16.2426i	−0.831042	+	0.831042i
$383$	−4.00295	+	4.00295i	−0.204541	+	0.204541i	−0.801942	−	0.597401i	$-0.796200\pi$
$383$	−4.00295	+	4.00295i	−0.204541	+	0.204541i	0.597401	+	0.801942i	$0.296200\pi$
$384$		0			0
$385$	−4.46804	+	3.78338i	−0.227712	+	0.192819i
$386$	−14.8020	+	35.7353i	−0.753404	+	1.81888i
$387$		0			0
$388$	−14.3385	+	34.6162i	−0.727926	+	1.75737i
$389$	−1.15168	+	1.15168i	−0.0583927	+	0.0583927i	−0.735700	−	0.677307i	$-0.763147\pi$
$389$	−1.15168	+	1.15168i	−0.0583927	+	0.0583927i	0.677307	+	0.735700i	$0.263147\pi$
$390$		0			0
$391$	14.4579	+	8.22769i	0.731166	+	0.416092i
$392$		−	0.181868i		−	0.00918570i
$393$		0			0
$394$	37.9041	+	15.7004i	1.90958	+	0.790975i
$395$	−0.870995	+	0.278921i	−0.0438245	+	0.0140340i
$396$		0			0
$397$	−4.91819	−	11.8736i	−0.246837	−	0.595917i	0.751095	−	0.660194i	$-0.229526\pi$
$397$	−4.91819	−	11.8736i	−0.246837	−	0.595917i	−0.997932	+	0.0642772i	$0.979526\pi$
$398$	45.3467	−	18.7832i	2.27303	−	0.941518i
$399$		0			0
$400$	14.5619	+	2.43330i	0.728095	+	0.121665i
$401$	11.0222	+	26.6099i	0.550422	+	1.32884i	0.917163	+	0.398512i	$0.130473\pi$
$401$	11.0222	+	26.6099i	0.550422	+	1.32884i	−0.366741	+	0.930323i	$0.619527\pi$
$402$		0			0
$403$	24.1500	+	10.0033i	1.20300	+	0.498298i
$404$		−	35.5488i		−	1.76862i
$405$		0			0
$406$	−40.0732	+	40.0732i	−1.98880	+	1.98880i
$407$			6.67129i			0.330684i
$408$		0			0
$409$	−13.6197			−0.673451			−0.336725	−	0.941603i	$-0.609319\pi$
$409$	−13.6197			−0.673451			−0.336725	+	0.941603i	$0.609319\pi$
$410$	−15.7756	+	30.6391i	−0.779103	+	1.51316i
$411$		0			0
$412$	3.96903			0.195540
$413$	−26.6108	−	11.0225i	−1.30943	−	0.542384i
$414$		0			0
$415$	9.49917	+	11.2182i	0.466296	+	0.550679i
$416$	15.0588	+	15.0588i	0.738320	+	0.738320i
$417$		0			0
$418$	1.28289	−	0.531391i	0.0627483	−	0.0259912i
$419$	−13.1802	+	5.45940i	−0.643893	+	0.266709i	−0.680643	−	0.732615i	$-0.738299\pi$
$419$	−13.1802	+	5.45940i	−0.643893	+	0.266709i	0.0367500	+	0.999324i	$0.488299\pi$
$420$		0			0
$421$			28.9349i			1.41020i	0.709107	+	0.705101i	$0.249098\pi$
$421$			28.9349i			1.41020i	−0.709107	+	0.705101i	$0.750902\pi$
$422$	−18.4634	+	44.5745i	−0.898783	+	2.16985i
$423$		0			0
$424$	2.57576			0.125090
$425$	−18.1395	+	9.79580i	−0.879896	+	0.475166i
$426$		0			0
$427$	−3.93193	−	3.93193i	−0.190279	−	0.190279i
$428$	−5.18130	+	12.5088i	−0.250448	+	0.604634i
$429$		0			0
$430$	41.7673	+	3.46564i	2.01420	+	0.167128i
$431$	18.9908	−	7.86623i	0.914753	−	0.378903i	0.124879	−	0.992172i	$-0.460146\pi$
$431$	18.9908	−	7.86623i	0.914753	−	0.378903i	0.789874	+	0.613269i	$0.210146\pi$
$432$		0			0
$433$	−17.0995	+	17.0995i	−0.821748	+	0.821748i	−0.986359	−	0.164611i	$-0.947363\pi$
$433$	−17.0995	+	17.0995i	−0.821748	+	0.821748i	0.164611	+	0.986359i	$0.447363\pi$
$434$	−39.3616	−	39.3616i	−1.88942	−	1.88942i
$435$		0			0
$436$	5.92512	−	2.45427i	0.283762	−	0.117538i
$437$	2.52007	+	1.04385i	0.120551	+	0.0499339i
$438$		0			0
$439$	−20.3668	−	8.43621i	−0.972055	−	0.402638i	−0.160578	−	0.987023i	$-0.551336\pi$
$439$	−20.3668	−	8.43621i	−0.972055	−	0.402638i	−0.811477	+	0.584385i	$0.801336\pi$
$440$	0.905740	−	1.75911i	0.0431795	−	0.0838624i
$441$		0			0
$442$	−22.8413	−	2.86258i	−1.08645	−	0.136159i
$443$			32.3324i			1.53616i	0.640356	+	0.768079i	$0.278787\pi$
$443$			32.3324i			1.53616i	−0.640356	+	0.768079i	$0.721213\pi$
$444$		0			0
$445$	−1.04035	+	12.5381i	−0.0493174	+	0.594365i
$446$			27.4821i			1.30132i
$447$		0			0
$448$	−11.2910	−	27.2589i	−0.533450	−	1.28786i
$449$	−12.0051	−	28.9829i	−0.566556	−	1.36779i	−0.904441	−	0.426599i	$-0.859712\pi$
$449$	−12.0051	−	28.9829i	−0.566556	−	1.36779i	0.337885	−	0.941187i	$-0.390288\pi$
$450$		0			0
$451$	−5.05166	−	5.05166i	−0.237873	−	0.237873i
$452$	13.0453	−	5.40353i	0.613598	−	0.254161i
$453$		0			0
$454$	8.61878	−	20.8076i	0.404499	−	0.976548i
$455$	15.1568	−	4.85370i	0.710562	−	0.227545i
$456$		0			0
$457$	−9.01432	−	9.01432i	−0.421672	−	0.421672i	0.464107	−	0.885779i	$-0.346375\pi$
$457$	−9.01432	−	9.01432i	−0.421672	−	0.421672i	−0.885779	+	0.464107i	$0.846375\pi$
$458$		−	39.6431i		−	1.85240i
$459$		0			0
$460$	20.8852	−	6.68811i	0.973777	−	0.311835i
$461$	12.3023	−	12.3023i	0.572974	−	0.572974i	−0.359984	−	0.932958i	$-0.617218\pi$
$461$	12.3023	−	12.3023i	0.572974	−	0.572974i	0.932958	+	0.359984i	$0.117218\pi$
$462$		0			0
$463$	29.5747			1.37445			0.687227	−	0.726443i	$-0.258828\pi$
$463$	29.5747			1.37445			0.687227	+	0.726443i	$0.258828\pi$
$464$	−11.3374	+	27.3708i	−0.526324	+	1.27066i
$465$		0			0
$466$	−1.80914	−	4.36765i	−0.0838068	−	0.202327i
$467$	−23.2530	+	23.2530i	−1.07602	+	1.07602i	−0.0791599	+	0.996862i	$0.525224\pi$
$467$	−23.2530	+	23.2530i	−1.07602	+	1.07602i	−0.996862	+	0.0791599i	$0.974776\pi$
$468$		0			0
$469$	5.89422	+	14.2299i	0.272170	+	0.657076i
$470$	2.65988	+	3.14122i	0.122691	+	0.144894i
$471$		0			0
$472$	9.73409			0.448048
$473$	−3.32487	+	8.02694i	−0.152878	+	0.369079i
$474$		0			0
$475$	−2.75157	+	1.96365i	−0.126251	+	0.0900985i
$476$	23.3744	+	13.3019i	1.07136	+	0.609691i
$477$		0			0
$478$	24.9003	+	24.9003i	1.13891	+	1.13891i
$479$	−0.548605	−	0.227240i	−0.0250664	−	0.0103828i	0.370115	−	0.928986i	$-0.379318\pi$
$479$	−0.548605	−	0.227240i	−0.0250664	−	0.0103828i	−0.395181	+	0.918603i	$0.629318\pi$
$480$		0			0
$481$	6.93989	−	16.7544i	0.316432	−	0.763934i
$482$	−9.48335	−	22.8948i	−0.431955	−	1.04283i
$483$		0			0
$484$	−17.2709	−	17.2709i	−0.785039	−	0.785039i
$485$	30.6431	+	15.7777i	1.39143	+	0.716427i
$486$		0			0
$487$	0.862103	+	2.08130i	0.0390656	+	0.0943127i	0.942208	−	0.335028i	$-0.108746\pi$
$487$	0.862103	+	2.08130i	0.0390656	+	0.0943127i	−0.903142	+	0.429341i	$0.858746\pi$
$488$	1.73616	+	0.719141i	0.0785922	+	0.0325540i
$489$		0			0
$490$	−0.940711	−	0.0780555i	−0.0424970	−	0.00352619i
$491$	5.16155	−	5.16155i	0.232937	−	0.232937i	−0.580980	−	0.813918i	$-0.697331\pi$
$491$	5.16155	−	5.16155i	0.232937	−	0.232937i	0.813918	+	0.580980i	$0.197331\pi$
$492$		0			0
$493$	−10.9555	−	39.8914i	−0.493409	−	1.79662i
$494$	−3.77466			−0.169830
$495$		0			0
$496$	−26.8848	−	11.1360i	−1.20716	−	0.500023i
$497$	3.01934			0.135436
$498$		0			0
$499$	−7.02196	+	2.90859i	−0.314346	+	0.130206i	−0.534278	−	0.845309i	$-0.679416\pi$
$499$	−7.02196	+	2.90859i	−0.314346	+	0.130206i	0.219932	+	0.975515i	$0.429416\pi$
$500$	−6.68049	+	26.3435i	−0.298761	+	1.17812i
$501$		0			0
$502$	−26.3479	+	26.3479i	−1.17597	+	1.17597i
$503$	−14.3260	+	5.93402i	−0.638764	+	0.264585i	−0.678472	−	0.734627i	$-0.737357\pi$
$503$	−14.3260	+	5.93402i	−0.638764	+	0.264585i	0.0397075	+	0.999211i	$0.487357\pi$
$504$		0			0
$505$	−32.5887	−	2.70405i	−1.45018	−	0.120329i
$506$			8.28662i			0.368385i
$507$		0			0
$508$	18.3045	+	18.3045i	0.812131	+	0.812131i
$509$	29.3375			1.30036			0.650182	−	0.759779i	$-0.274693\pi$
$509$	29.3375			1.30036			0.650182	+	0.759779i	$0.274693\pi$
$510$		0			0
$511$	−8.04618			−0.355942
$512$	−20.5510	−	20.5510i	−0.908233	−	0.908233i
$513$		0			0
$514$		−	16.2168i		−	0.715292i
$515$	0.301908	−	3.63854i	0.0133036	−	0.160333i
$516$		0			0
$517$	−0.788333	+	0.326538i	−0.0346708	+	0.0143611i
$518$	−27.3076	+	27.3076i	−1.19983	+	1.19983i
$519$		0			0
$520$	−4.10462	+	3.47565i	−0.180000	+	0.152417i
$521$	14.0288	−	5.81093i	0.614614	−	0.254581i	−0.0535860	−	0.998563i	$-0.517065\pi$
$521$	14.0288	−	5.81093i	0.614614	−	0.254581i	0.668200	+	0.743982i	$0.267065\pi$
$522$		0			0
$523$	−35.8569			−1.56791			−0.783957	−	0.620815i	$-0.786802\pi$
$523$	−35.8569			−1.56791			−0.783957	+	0.620815i	$0.786802\pi$
$524$	3.63472	+	1.50555i	0.158784	+	0.0657703i
$525$		0			0
$526$	−13.2547			−0.577932
$527$	39.1830	−	10.7609i	1.70684	−	0.468753i
$528$		0			0
$529$	4.75321	−	4.75321i	0.206661	−	0.206661i
$530$	1.10549	−	13.3232i	0.0480194	−	0.578721i
$531$		0			0
$532$	4.07425	+	1.68761i	0.176641	+	0.0731671i
$533$	7.43175	+	17.9418i	0.321905	+	0.777148i
$534$		0			0
$535$	11.0731	+	5.70136i	0.478731	+	0.246491i
$536$	−3.68066	−	3.68066i	−0.158980	−	0.158980i
$537$		0			0
$538$	−7.45847	−	18.0063i	−0.321557	−	0.776308i
$539$	0.0748850	−	0.180788i	0.00322553	−	0.00778711i
$540$		0			0
$541$	24.6831	+	10.2241i	1.06121	+	0.439568i	0.843881	−	0.536531i	$-0.180266\pi$
$541$	24.6831	+	10.2241i	1.06121	+	0.439568i	0.217329	+	0.976098i	$0.430266\pi$
$542$	−24.9744	−	24.9744i	−1.07274	−	1.07274i
$543$		0			0
$544$	32.8479	+	4.11666i	1.40834	+	0.176500i
$545$	−1.79921	−	5.61844i	−0.0770695	−	0.240667i
$546$		0			0
$547$	5.16946	−	12.4802i	0.221030	−	0.533614i	−0.774000	−	0.633185i	$-0.781747\pi$
$547$	5.16946	−	12.4802i	0.221030	−	0.533614i	0.995030	+	0.0995712i	$0.0317471\pi$
$548$	11.4328			0.488383
$549$		0			0
$550$	−8.71028	−	5.43994i	−0.371408	−	0.231960i
$551$	−2.59586	−	6.26695i	−0.110587	−	0.266981i
$552$		0			0
$553$	0.776064	−	0.776064i	0.0330016	−	0.0330016i
$554$	−9.67133	−	23.3487i	−0.410895	−	0.991989i
$555$		0			0
$556$	−0.766313	+	1.85004i	−0.0324989	+	0.0784593i
$557$	16.9198			0.716915			0.358458	−	0.933546i	$-0.383303\pi$
$557$	16.9198			0.716915			0.358458	+	0.933546i	$0.383303\pi$
$558$		0			0
$559$	16.7002	−	16.7002i	0.706345	−	0.706345i
$560$	−16.8732	+	5.40334i	−0.713022	+	0.228333i
$561$		0			0
$562$		−	59.3616i		−	2.50402i
$563$	26.6224	+	26.6224i	1.12200	+	1.12200i	0.991441	+	0.130558i	$0.0416768\pi$
$563$	26.6224	+	26.6224i	1.12200	+	1.12200i	0.130558	+	0.991441i	$0.458323\pi$
$564$		0			0
$565$	−3.96129	−	12.3701i	−0.166653	−	0.520412i
$566$	13.7570	−	33.2124i	0.578251	−	1.39602i
$567$		0			0
$568$	−0.942715	+	0.390485i	−0.0395555	+	0.0163844i
$569$	21.0557	+	21.0557i	0.882701	+	0.882701i	0.993808	−	0.111108i	$-0.0354398\pi$
$569$	21.0557	+	21.0557i	0.882701	+	0.882701i	−0.111108	+	0.993808i	$0.535440\pi$
$570$		0			0
$571$	−3.82363	−	9.23107i	−0.160014	−	0.386308i	0.823456	−	0.567381i	$-0.192043\pi$
$571$	−3.82363	−	9.23107i	−0.160014	−	0.386308i	−0.983470	+	0.181072i	$0.942043\pi$
$572$	−2.40750	−	5.81222i	−0.100663	−	0.243021i
$573$		0			0
$574$		−	41.3559i		−	1.72616i
$575$	−4.54256	−	19.6549i	−0.189438	−	0.819665i
$576$		0			0
$577$			17.5104i			0.728968i	0.931210	+	0.364484i	$0.118755\pi$
$577$			17.5104i			0.728968i	−0.931210	+	0.364484i	$0.881245\pi$
$578$	−30.7648	+	18.2765i	−1.27965	+	0.760203i
$579$		0			0
$580$	−48.4862	−	24.9648i	−2.01328	−	1.03661i
$581$	−16.2976	−	6.75067i	−0.676137	−	0.280065i
$582$		0			0
$583$	2.56048	+	1.06058i	0.106044	+	0.0439249i
$584$	2.51222	−	1.04060i	0.103957	−	0.0430602i
$585$		0			0
$586$	10.1594	+	10.1594i	0.419683	+	0.419683i
$587$	−11.3396	+	11.3396i	−0.468036	+	0.468036i	−0.901278	−	0.433242i	$-0.857370\pi$
$587$	−11.3396	+	11.3396i	−0.468036	+	0.468036i	0.433242	+	0.901278i	$0.357370\pi$
$588$		0			0
$589$	6.15567	−	2.54976i	0.253640	−	0.105061i
$590$	4.17776	−	50.3496i	0.171996	−	2.07286i
$591$		0			0
$592$	−7.72577	+	18.6517i	−0.317527	+	0.766579i
$593$	−27.1563	−	27.1563i	−1.11517	−	1.11517i	−0.992439	−	0.122735i	$-0.960833\pi$
$593$	−27.1563	−	27.1563i	−1.11517	−	1.11517i	−0.122735	−	0.992439i	$-0.539167\pi$
$594$		0			0
$595$	13.9723	−	20.4162i	0.572807	−	0.836984i
$596$	−23.3436			−0.956193
$597$		0			0
$598$	8.62025	−	20.8111i	0.352508	−	0.851031i
$599$		−	23.5261i		−	0.961251i	−0.876926	−	0.480625i	$-0.840410\pi$
$599$		−	23.5261i		−	0.961251i	0.876926	−	0.480625i	$-0.159590\pi$
$600$		0			0
$601$	23.1362	−	9.58331i	0.943744	−	0.390911i	0.142868	−	0.989742i	$-0.454368\pi$
$601$	23.1362	−	9.58331i	0.943744	−	0.390911i	0.800876	+	0.598830i	$0.204368\pi$
$602$	−46.4664	+	19.2470i	−1.89383	+	0.784450i
$603$		0			0
$604$	−2.43517	−	2.43517i	−0.0990855	−	0.0990855i
$605$	−17.1465	+	14.5190i	−0.697103	+	0.590283i
$606$		0			0
$607$	−29.8946	−	12.3827i	−1.21338	−	0.502600i	−0.318083	−	0.948063i	$-0.603039\pi$
$607$	−29.8946	−	12.3827i	−1.21338	−	0.502600i	−0.895300	+	0.445463i	$0.853039\pi$
$608$	5.42831			0.220147
$609$		0			0
$610$	4.46490	−	8.67164i	0.180778	−	0.351105i
$611$	2.31951			0.0938375
$612$		0			0
$613$			25.0386i			1.01130i	0.862739	+	0.505650i	$0.168747\pi$
$613$			25.0386i			1.01130i	−0.862739	+	0.505650i	$0.831253\pi$
$614$	1.11079	−	1.11079i	0.0448280	−	0.0448280i
$615$		0			0
$616$			2.37441i			0.0956675i
$617$	9.00101	+	3.72834i	0.362367	+	0.150097i	0.556436	−	0.830891i	$-0.312169\pi$
$617$	9.00101	+	3.72834i	0.362367	+	0.150097i	−0.194069	+	0.980988i	$0.562169\pi$
$618$		0			0
$619$	−2.82897	−	6.82973i	−0.113706	−	0.274510i	0.856774	−	0.515692i	$-0.172465\pi$
$619$	−2.82897	−	6.82973i	−0.113706	−	0.274510i	−0.970480	+	0.241182i	$0.922465\pi$
$620$	24.5215	−	47.6252i	0.984808	−	1.91268i
$621$		0			0
$622$	−35.3944	+	14.6609i	−1.41919	+	0.587847i
$623$	−5.77777	−	13.9488i	−0.231481	−	0.558846i
$624$		0			0
$625$	23.6418	+	8.12807i	0.945672	+	0.325123i
$626$	−19.2993	−	7.99404i	−0.771356	−	0.319506i
$627$		0			0
$628$		−	11.7137i		−	0.467426i
$629$	−7.46553	−	27.1837i	−0.297670	−	1.08389i
$630$		0			0
$631$	−6.09529	+	6.09529i	−0.242650	+	0.242650i	−0.817945	−	0.575296i	$-0.804887\pi$
$631$	−6.09529	+	6.09529i	−0.242650	+	0.242650i	0.575296	+	0.817945i	$0.304887\pi$
$632$	−0.141940	+	0.342674i	−0.00564608	+	0.0136308i
$633$		0			0
$634$	−19.5838	+	47.2794i	−0.777771	+	1.87770i
$635$	18.1727	−	15.3880i	0.721161	−	0.610653i
$636$		0			0
$637$	−0.376134	+	0.376134i	−0.0149030	+	0.0149030i
$638$	14.5716	−	14.5716i	0.576895	−	0.576895i
$639$		0			0
$640$	12.0929	−	10.2398i	0.478013	−	0.404765i
$641$	14.9873	−	36.1825i	0.591963	−	1.42912i	−0.289641	−	0.957135i	$-0.593536\pi$
$641$	14.9873	−	36.1825i	0.591963	−	1.42912i	0.881604	−	0.471989i	$-0.156464\pi$
$642$		0			0
$643$	−17.4803	+	42.2011i	−0.689355	+	1.66425i	0.0567210	+	0.998390i	$0.481935\pi$
$643$	−17.4803	+	42.2011i	−0.689355	+	1.66425i	−0.746076	+	0.665861i	$0.768065\pi$
$644$	−18.6089	+	18.6089i	−0.733292	+	0.733292i
$645$		0			0
$646$	−4.63279	+	3.60090i	−0.182275	+	0.141676i
$647$		−	9.17577i		−	0.360737i	−0.983599	−	0.180368i	$-0.942271\pi$
$647$		−	9.17577i		−	0.360737i	0.983599	−	0.180368i	$-0.0577290\pi$
$648$		0			0
$649$	9.67633	+	4.00807i	0.379829	+	0.157330i
$650$	16.2162	+	22.7229i	0.636050	+	0.891265i
$651$		0			0
$652$	−1.50607	−	3.63596i	−0.0589821	−	0.142395i
$653$	15.3604	−	6.36250i	0.601100	−	0.248984i	−0.0613178	−	0.998118i	$-0.519530\pi$
$653$	15.3604	−	6.36250i	0.601100	−	0.248984i	0.662418	+	0.749134i	$0.269530\pi$
$654$		0			0
$655$	1.65667	−	3.21755i	0.0647313	−	0.125720i
$656$	−8.27334	−	19.9736i	−0.323020	−	0.779838i
$657$		0			0
$658$	−4.56350	−	1.89027i	−0.177904	−	0.0736902i
$659$		−	5.95839i		−	0.232106i	−0.993243	−	0.116053i	$-0.962976\pi$
$659$		−	5.95839i		−	0.232106i	0.993243	−	0.116053i	$-0.0370242\pi$
$660$		0			0
$661$	30.3724	−	30.3724i	1.18135	−	1.18135i	0.201955	−	0.979395i	$-0.435270\pi$
$661$	30.3724	−	30.3724i	1.18135	−	1.18135i	0.979395	−	0.201955i	$-0.0647296\pi$
$662$			1.03093i			0.0400681i
$663$		0			0
$664$	5.96157			0.231354
$665$	1.85700	−	3.60663i	0.0720113	−	0.139859i
$666$		0			0
$667$	40.4803			1.56740
$668$	49.7078	+	20.5896i	1.92325	+	0.796637i
$669$		0			0
$670$	−20.6179	+	17.4585i	−0.796539	+	0.674482i
$671$	1.42975	+	1.42975i	0.0551947	+	0.0551947i
$672$		0			0
$673$	−16.0256	+	6.63803i	−0.617743	+	0.255877i	−0.669535	−	0.742781i	$-0.733507\pi$
$673$	−16.0256	+	6.63803i	−0.617743	+	0.255877i	0.0517924	+	0.998658i	$0.483507\pi$
$674$	−11.6976	+	4.84531i	−0.450575	+	0.186634i
$675$		0			0
$676$		−	14.4993i		−	0.557666i
$677$	−9.79369	+	23.6441i	−0.376402	+	0.908715i	0.616232	+	0.787565i	$0.288658\pi$
$677$	−9.79369	+	23.6441i	−0.376402	+	0.908715i	−0.992634	+	0.121150i	$0.961342\pi$
$678$		0			0
$679$	−41.3613			−1.58730
$680$	−1.72211	+	8.18148i	−0.0660398	+	0.313745i
$681$		0			0
$682$	14.3128	+	14.3128i	0.548067	+	0.548067i
$683$	2.34480	−	5.66085i	0.0897213	−	0.216606i	−0.872649	−	0.488348i	$-0.837600\pi$
$683$	2.34480	−	5.66085i	0.0897213	−	0.216606i	0.962370	+	0.271742i	$0.0875996\pi$
$684$		0			0
$685$	0.869643	−	10.4808i	0.0332273	−	0.400450i
$686$	−35.4825	+	14.6973i	−1.35473	+	0.561146i
$687$		0			0
$688$	−18.5914	+	18.5914i	−0.708790	+	0.708790i
$689$	−5.32713	−	5.32713i	−0.202948	−	0.202948i
$690$		0			0
$691$	−6.87633	+	2.84827i	−0.261588	+	0.108353i	−0.509623	−	0.860398i	$-0.670215\pi$
$691$	−6.87633	+	2.84827i	−0.261588	+	0.108353i	0.248035	+	0.968751i	$0.420215\pi$
$692$	−23.3039	−	9.65279i	−0.885881	−	0.366944i
$693$		0			0
$694$	−15.3626	−	6.36339i	−0.583156	−	0.241551i
$695$	1.63770	+	0.843229i	0.0621217	+	0.0319855i
$696$		0			0
$697$	26.2372	+	14.9311i	0.993806	+	0.565555i
$698$			40.3115i			1.52581i
$699$		0			0
$700$	−7.34406	−	31.7765i	−0.277579	−	1.20104i
$701$			25.3350i			0.956891i	0.878117	+	0.478445i	$0.158800\pi$
$701$			25.3350i			0.956891i	−0.878117	+	0.478445i	$0.841200\pi$
$702$		0			0
$703$	−1.76893	−	4.27058i	−0.0667165	−	0.161068i
$704$	4.10568	+	9.91200i	0.154739	+	0.373573i
$705$		0			0
$706$	−20.4160	−	20.4160i	−0.768365	−	0.768365i
$707$	36.2552	−	15.0174i	1.36352	−	0.564788i
$708$		0			0
$709$	6.10174	−	14.7309i	0.229156	−	0.553231i	−0.766919	−	0.641744i	$-0.778211\pi$
$709$	6.10174	−	14.7309i	0.229156	−	0.553231i	0.996075	+	0.0885126i	$0.0282113\pi$
$710$	1.61519	+	5.04379i	0.0606168	+	0.189290i
$711$		0			0
$712$	3.60794	+	3.60794i	0.135213	+	0.135213i
$713$			39.7615i			1.48908i
$714$		0			0
$715$	−5.51138	+	1.76492i	−0.206114	+	0.0660044i
$716$	32.1908	−	32.1908i	1.20303	−	1.20303i
$717$		0			0
$718$	52.5296			1.96039
$719$	−7.42813	+	17.9331i	−0.277022	+	0.668791i	−0.999750	−	0.0223415i	$-0.992888\pi$
$719$	−7.42813	+	17.9331i	−0.277022	+	0.668791i	0.722728	+	0.691132i	$0.242888\pi$
$720$		0			0
$721$	1.67670	+	4.04790i	0.0624434	+	0.150752i
$722$	27.5997	−	27.5997i	1.02716	−	1.02716i
$723$		0			0
$724$	−2.28369	−	5.51330i	−0.0848725	−	0.204900i
$725$	−26.5742	+	42.5499i	−0.986941	+	1.58026i
$726$		0			0
$727$	26.1442			0.969633			0.484817	−	0.874616i	$-0.338886\pi$
$727$	26.1442			0.969633			0.484817	+	0.874616i	$0.338886\pi$
$728$	2.47000	−	5.96311i	0.0915444	−	0.221008i
$729$		0			0
$730$	−4.30428	−	13.4411i	−0.159308	−	0.497478i
$731$	4.56537	−	36.4283i	0.168856	−	1.34735i
$732$		0			0
$733$	3.23474	+	3.23474i	0.119478	+	0.119478i	0.764318	−	0.644840i	$-0.223076\pi$
$733$	3.23474	+	3.23474i	0.119478	+	0.119478i	−0.644840	+	0.764318i	$0.723076\pi$
$734$	16.5851	+	6.86978i	0.612168	+	0.253568i
$735$		0			0
$736$	−12.3967	+	29.9284i	−0.456950	+	1.10317i
$737$	−2.14328	−	5.17435i	−0.0789489	−	0.190599i
$738$		0			0
$739$	28.5736	+	28.5736i	1.05110	+	1.05110i	0.998622	+	0.0524727i	$0.0167103\pi$
$739$	28.5736	+	28.5736i	1.05110	+	1.05110i	0.0524727	+	0.998622i	$0.483290\pi$
$740$	−33.0406	−	17.0121i	−1.21460	−	0.625378i
$741$		0			0
$742$	6.13952	+	14.8221i	0.225389	+	0.544137i
$743$	−21.6747	−	8.97795i	−0.795168	−	0.329369i	−0.0521484	−	0.998639i	$-0.516607\pi$
$743$	−21.6747	−	8.97795i	−0.795168	−	0.329369i	−0.743019	+	0.669270i	$0.766607\pi$
$744$		0			0
$745$	−1.77565	+	21.3999i	−0.0650549	+	0.784030i
$746$	−17.2052	+	17.2052i	−0.629927	+	0.629927i
$747$		0			0
$748$	−8.49949	−	4.83689i	−0.310772	−	0.176854i
$749$	−14.9462			−0.546121
$750$		0			0
$751$	−29.7279	−	12.3137i	−1.08479	−	0.449333i	−0.232600	−	0.972572i	$-0.574723\pi$
$751$	−29.7279	−	12.3137i	−1.08479	−	0.449333i	−0.852186	+	0.523239i	$0.824723\pi$
$752$	−2.58218			−0.0941624
$753$		0			0
$754$	−51.7536	+	21.4370i	−1.88475	+	0.780690i
$755$	−2.41763	+	2.04716i	−0.0879865	+	0.0745039i
$756$		0			0
$757$	−25.3721	+	25.3721i	−0.922165	+	0.922165i	−0.997182	−	0.0750172i	$-0.976099\pi$
$757$	−25.3721	+	25.3721i	−0.922165	+	0.922165i	0.0750172	+	0.997182i	$0.476099\pi$
$758$	−23.9255	+	9.91025i	−0.869012	+	0.359957i
$759$		0			0
$760$	−0.113364	+	1.36624i	−0.00411215	+	0.0495589i
$761$			26.9643i			0.977453i	0.872437	+	0.488727i	$0.162538\pi$
$761$			26.9643i			0.977453i	−0.872437	+	0.488727i	$0.837462\pi$
$762$		0			0
$763$	5.00607	+	5.00607i	0.181232	+	0.181232i
$764$	26.5265			0.959695
$765$		0			0
$766$	11.9162			0.430549
$767$	−20.1318	−	20.1318i	−0.726918	−	0.726918i
$768$		0			0
$769$			13.1666i			0.474800i	0.971412	+	0.237400i	$0.0762952\pi$
$769$			13.1666i			0.474800i	−0.971412	+	0.237400i	$0.923705\pi$
$770$	12.2816	+	1.01907i	0.442599	+	0.0367246i
$771$		0			0
$772$	41.2675	−	17.0936i	1.48525	−	0.615210i
$773$	22.4347	−	22.4347i	0.806920	−	0.806920i	−0.177247	−	0.984166i	$-0.556719\pi$
$773$	22.4347	−	22.4347i	0.806920	−	0.806920i	0.984166	+	0.177247i	$0.0567191\pi$
$774$		0			0
$775$	−41.7943	−	26.1023i	−1.50130	−	0.937623i
$776$	12.9141	−	5.34918i	0.463587	−	0.192024i
$777$		0			0
$778$	3.42839			0.122914
$779$	4.57325	+	1.89430i	0.163854	+	0.0678705i
$780$		0			0
$781$	−1.09791			−0.0392861
$782$	−9.27317	−	33.7658i	−0.331608	−	1.20746i
$783$		0			0
$784$	0.418728	−	0.418728i	0.0149546	−	0.0149546i
$785$	−10.7383	−	0.891011i	−0.383266	−	0.0318015i
$786$		0			0
$787$	10.3704	+	4.29554i	0.369663	+	0.153120i	0.559779	−	0.828642i	$-0.310886\pi$
$787$	10.3704	+	4.29554i	0.369663	+	0.153120i	−0.190115	+	0.981762i	$0.560886\pi$
$788$	−18.1310	−	43.7720i	−0.645889	−	1.55931i
$789$		0			0
$790$	1.71156	+	0.881258i	0.0608947	+	0.0313538i
$791$	11.0218	+	11.0218i	0.391891	+	0.391891i
$792$		0			0
$793$	−2.10337	−	5.07799i	−0.0746930	−	0.180325i
$794$	−10.3525	+	24.9932i	−0.367398	+	0.886977i
$795$		0			0
$796$	−52.3668	−	21.6911i	−1.85609	−	0.768819i
$797$	23.8591	+	23.8591i	0.845134	+	0.845134i	0.989521	−	0.144388i	$-0.0461212\pi$
$797$	23.8591	+	23.8591i	0.845134	+	0.845134i	−0.144388	+	0.989521i	$0.546121\pi$
$798$		0			0
$799$	2.84683	−	2.21274i	0.100714	−	0.0782811i
$800$	−23.3204	−	32.6776i	−0.824499	−	1.15533i
$801$		0			0
$802$	23.2012	−	56.0125i	0.819261	−	1.97787i
$803$	2.92579			0.103249
$804$		0			0
$805$	15.6439	+	18.4749i	0.551374	+	0.651153i
$806$	−21.0564	−	50.8346i	−0.741679	−	1.79057i
$807$		0			0
$808$	−9.37764	+	9.37764i	−0.329904	+	0.329904i
$809$	5.44317	+	13.1410i	0.191372	+	0.462012i	0.990219	−	0.139522i	$-0.0445566\pi$
$809$	5.44317	+	13.1410i	0.191372	+	0.462012i	−0.798847	+	0.601534i	$0.794557\pi$
$810$		0			0
$811$	−9.42238	+	22.7476i	−0.330865	+	0.798778i	0.667659	+	0.744467i	$0.267296\pi$
$811$	−9.42238	+	22.7476i	−0.330865	+	0.798778i	−0.998524	+	0.0543111i	$0.982704\pi$
$812$	65.4455			2.29669
$813$		0			0
$814$	9.92972	−	9.92972i	0.348037	−	0.348037i
$815$	−3.44777	+	1.10409i	−0.120770	+	0.0386745i
$816$		0			0
$817$		−	6.01999i		−	0.210613i
$818$	20.2719	+	20.2719i	0.708790	+	0.708790i
$819$		0			0
$820$	37.9011	−	12.1372i	1.32356	−	0.423848i
$821$	−9.55514	+	23.0681i	−0.333477	+	0.805084i	0.664835	+	0.746991i	$0.268502\pi$
$821$	−9.55514	+	23.0681i	−0.333477	+	0.805084i	−0.998311	+	0.0580931i	$0.981498\pi$
$822$		0			0
$823$	26.6778	−	11.0503i	0.929931	−	0.385190i	0.134279	−	0.990944i	$-0.457128\pi$
$823$	26.6778	−	11.0503i	0.929931	−	0.385190i	0.795652	+	0.605753i	$0.207128\pi$
$824$	−1.04702	−	1.04702i	−0.0364745	−	0.0364745i
$825$		0			0
$826$	23.2019	+	56.0144i	0.807298	+	1.94899i
$827$	6.20037	+	14.9690i	0.215608	+	0.520524i	0.994267	−	0.106923i	$-0.0340999\pi$
$827$	6.20037	+	14.9690i	0.215608	+	0.520524i	−0.778659	+	0.627447i	$0.784100\pi$
$828$		0			0
$829$			22.2311i			0.772117i	0.922474	+	0.386058i	$0.126164\pi$
$829$			22.2311i			0.772117i	−0.922474	+	0.386058i	$0.873836\pi$
$830$	2.55864	−	30.8362i	0.0888116	−	1.07034i
$831$		0			0
$832$		−	29.1641i		−	1.01108i
$833$	−0.102824	+	0.820464i	−0.00356266	+	0.0284274i
$834$		0			0
$835$	22.6562	−	44.0026i	0.784052	−	1.52277i
$836$	−1.48150	−	0.613656i	−0.0512386	−	0.0212237i
$837$		0			0
$838$	27.7436	+	11.4918i	0.958386	+	0.396977i
$839$	−43.2196	+	17.9021i	−1.49211	+	0.618051i	−0.971774	−	0.235914i	$-0.924192\pi$
$839$	−43.2196	+	17.9021i	−1.49211	+	0.618051i	−0.520332	+	0.853964i	$0.674192\pi$
$840$		0			0
$841$	−50.6764	−	50.6764i	−1.74746	−	1.74746i
$842$	43.0675	−	43.0675i	1.48420	−	1.48420i
$843$		0			0
$844$	51.4751	−	21.3217i	1.77185	−	0.733923i
$845$	−13.2920	−	1.10290i	−0.457258	−	0.0379410i
$846$		0			0
$847$	10.3181	−	24.9100i	0.354533	−	0.855919i
$848$	5.93039	+	5.93039i	0.203650	+	0.203650i
$849$		0			0
$850$	41.5796	+	12.4190i	1.42617	+	0.425969i
$851$	27.5851			0.945604
$852$		0			0
$853$	−14.6828	+	35.4475i	−0.502731	+	1.21370i	0.445259	+	0.895402i	$0.353111\pi$
$853$	−14.6828	+	35.4475i	−0.502731	+	1.21370i	−0.947990	+	0.318299i	$0.896889\pi$
$854$			11.7048i			0.400529i
$855$		0			0
$856$	4.66658	−	1.93296i	0.159500	−	0.0660672i
$857$	−5.10428	+	2.11426i	−0.174359	+	0.0722218i	−0.468155	−	0.883646i	$-0.655081\pi$
$857$	−5.10428	+	2.11426i	−0.174359	+	0.0722218i	0.293796	+	0.955868i	$0.405081\pi$
$858$		0			0
$859$	10.1314	+	10.1314i	0.345680	+	0.345680i	0.858498	−	0.512817i	$-0.171398\pi$
$859$	10.1314	+	10.1314i	0.345680	+	0.345680i	−0.512817	+	0.858498i	$0.671398\pi$
$860$	−31.2761	−	36.9360i	−1.06651	−	1.25951i
$861$		0			0
$862$	−39.9746	−	16.5580i	−1.36154	−	0.563969i
$863$	−9.68459			−0.329667			−0.164834	−	0.986321i	$-0.552709\pi$
$863$	−9.68459			−0.329667			−0.164834	+	0.986321i	$0.552709\pi$
$864$		0			0
$865$	−10.6217	+	20.6292i	−0.361147	+	0.701413i
$866$	50.9025			1.72974
$867$		0			0
$868$			64.2833i			2.18192i
$869$	−0.282196	+	0.282196i	−0.00957284	+	0.00957284i
$870$		0			0
$871$			15.2245i			0.515862i
$872$	−2.21045	−	0.915599i	−0.0748553	−	0.0310061i
$873$		0			0
$874$	−2.19724	−	5.30462i	−0.0743229	−	0.179431i
$875$	−29.6891	+	4.31543i	−1.00368	+	0.145888i
$876$		0			0
$877$	13.8214	−	5.72500i	0.466714	−	0.193319i	−0.136918	−	0.990582i	$-0.543720\pi$
$877$	13.8214	−	5.72500i	0.466714	−	0.193319i	0.603632	+	0.797263i	$0.293720\pi$
$878$	17.7578	+	42.8711i	0.599297	+	1.44683i
$879$		0			0
$880$	6.13550	−	1.96479i	0.206828	−	0.0662329i
$881$	−9.80896	−	4.06301i	−0.330472	−	0.136886i	0.211277	−	0.977426i	$-0.432238\pi$
$881$	−9.80896	−	4.06301i	−0.330472	−	0.136886i	−0.541749	+	0.840540i	$0.682238\pi$
$882$		0			0
$883$			52.5251i			1.76761i	0.467855	+	0.883805i	$0.345027\pi$
$883$			52.5251i			1.76761i	−0.467855	+	0.883805i	$0.654973\pi$
$884$	16.3141	+	20.9891i	0.548703	+	0.705941i
$885$		0			0
$886$	48.1243	−	48.1243i	1.61677	−	1.61677i
$887$	−6.57850	+	15.8819i	−0.220884	+	0.533262i	−0.995011	−	0.0997691i	$-0.968190\pi$
$887$	−6.57850	+	15.8819i	−0.220884	+	0.533262i	0.774126	+	0.633031i	$0.218190\pi$
$888$		0			0
$889$	−10.9356	+	26.4009i	−0.366768	+	0.885457i
$890$	20.2106	−	17.1136i	0.677459	−	0.573649i
$891$		0			0
$892$	22.4412	−	22.4412i	0.751386	−	0.751386i
$893$	0.418062	−	0.418062i	0.0139899	−	0.0139899i
$894$		0			0
$895$	−27.0617	−	31.9590i	−0.904574	−	1.06827i
$896$	−7.27703	+	17.5683i	−0.243108	+	0.586916i
$897$		0			0
$898$	−25.2701	+	61.0075i	−0.843276	+	2.03585i
$899$	69.9185	−	69.9185i	2.33191	−	2.33191i
$900$		0			0
$901$	−11.6201	−	1.45629i	−0.387122	−	0.0485160i
$902$			15.0380i			0.500712i
$903$		0			0
$904$	−4.86673	−	2.01586i	−0.161865	−	0.0670467i
$905$	−5.22794	+	1.67415i	−0.173782	+	0.0556508i
$906$		0			0
$907$	−4.28190	−	10.3374i	−0.142178	−	0.343248i	0.836710	−	0.547647i	$-0.184476\pi$
$907$	−4.28190	−	10.3374i	−0.142178	−	0.343248i	−0.978888	+	0.204398i	$0.934476\pi$
$908$	−24.0288	+	9.95305i	−0.797423	+	0.330304i
$909$		0			0
$910$	−29.7841	−	15.3354i	−0.987334	−	0.508363i
$911$	−1.24981	−	3.01730i	−0.0414080	−	0.0999677i	0.901822	−	0.432107i	$-0.142230\pi$
$911$	−1.24981	−	3.01730i	−0.0414080	−	0.0999677i	−0.943230	+	0.332139i	$0.892230\pi$
$912$		0			0
$913$	5.92619	+	2.45471i	0.196128	+	0.0812390i
$914$			26.8343i			0.887599i
$915$		0			0
$916$	−32.3715	+	32.3715i	−1.06958	+	1.06958i
$917$			4.34296i			0.143417i
$918$		0			0
$919$	32.6905			1.07836			0.539179	−	0.842191i	$-0.318735\pi$
$919$	32.6905			1.07836			0.539179	+	0.842191i	$0.318735\pi$
$920$	−7.27373	−	3.74514i	−0.239808	−	0.123473i
$921$		0			0
$922$	−36.6220			−1.20608
$923$	2.75729	+	1.14211i	0.0907574	+	0.0375930i
$924$		0			0
$925$	−18.1088	+	28.9954i	−0.595414	+	0.953362i
$926$	−44.0198	−	44.0198i	−1.44658	−	1.44658i
$927$		0			0
$928$	74.4264	−	30.8284i	2.44317	−	1.01199i
$929$	7.83598	−	3.24577i	0.257090	−	0.106490i	−0.250416	−	0.968138i	$-0.580567\pi$
$929$	7.83598	−	3.24577i	0.257090	−	0.106490i	0.507506	+	0.861648i	$0.330567\pi$
$930$		0			0
$931$			0.135586i			0.00444367i
$932$	−2.08921	+	5.04381i	−0.0684344	+	0.165215i
$933$		0			0
$934$	69.2208			2.26497
$935$	−5.08066	+	7.42384i	−0.166155	+	0.242786i
$936$		0			0
$937$	22.0610	+	22.0610i	0.720703	+	0.720703i	0.968748	−	0.248045i	$-0.0797882\pi$
$937$	22.0610	+	22.0610i	0.720703	+	0.720703i	−0.248045	+	0.968748i	$0.579788\pi$
$938$	12.4071	−	29.9533i	0.405105	−	0.978009i
$939$		0			0
$940$	0.393055	−	4.73703i	0.0128200	−	0.154505i
$941$	−19.9946	+	8.28202i	−0.651804	+	0.269986i	−0.683985	−	0.729496i	$-0.739755\pi$
$941$	−19.9946	+	8.28202i	−0.651804	+	0.269986i	0.0321810	+	0.999482i	$0.489755\pi$
$942$		0			0
$943$	−20.8880	+	20.8880i	−0.680208	+	0.680208i
$944$	22.4116	+	22.4116i	0.729435	+	0.729435i
$945$		0			0
$946$	16.8963	−	6.99868i	0.549347	−	0.227547i
$947$	−3.63370	−	1.50513i	−0.118079	−	0.0489101i	0.322862	−	0.946446i	$-0.395355\pi$
$947$	−3.63370	−	1.50513i	−0.118079	−	0.0489101i	−0.440941	+	0.897536i	$0.645355\pi$
$948$		0			0
$949$	−7.34786	−	3.04358i	−0.238522	−	0.0987989i
$950$	7.01825	+	1.17275i	0.227702	+	0.0380491i
$951$		0			0
$952$	−2.65708	−	9.67506i	−0.0861166	−	0.313571i
$953$		−	4.24356i		−	0.137462i	−0.997635	−	0.0687312i	$-0.978105\pi$
$953$		−	4.24356i		−	0.137462i	0.997635	−	0.0687312i	$-0.0218951\pi$
$954$		0			0
$955$	2.01776	−	24.3177i	0.0652932	−	0.786903i
$956$		−	40.6658i		−	1.31523i
$957$		0			0
$958$	0.478328	+	1.15479i	0.0154541	+	0.0373095i
$959$	4.82971	+	11.6600i	0.155959	+	0.376519i
$960$		0			0
$961$	46.7567	+	46.7567i	1.50828	+	1.50828i
$962$	−35.2671	+	14.6081i	−1.13706	+	0.470985i
$963$		0			0
$964$	−10.9515	+	26.4392i	−0.352723	+	0.851549i
$965$	−12.5312	−	39.1315i	−0.403393	−	1.25969i
$966$		0			0
$967$	25.3036	+	25.3036i	0.813708	+	0.813708i	0.985188	−	0.171480i	$-0.0548548\pi$
$967$	25.3036	+	25.3036i	0.813708	+	0.813708i	−0.171480	+	0.985188i	$0.554855\pi$
$968$			9.11197i			0.292870i
$969$		0			0
$970$	−22.1261	−	69.0938i	−0.710425	−	2.21847i
$971$	26.0013	−	26.0013i	0.834423	−	0.834423i	−0.153695	−	0.988118i	$-0.549117\pi$
$971$	26.0013	−	26.0013i	0.834423	−	0.834423i	0.988118	+	0.153695i	$0.0491174\pi$
$972$		0			0
$973$	−2.21053			−0.0708664
$974$	1.81468	−	4.38103i	0.0581462	−	0.140377i
$975$		0			0
$976$	2.34156	+	5.65303i	0.0749516	+	0.180949i
$977$	−18.3472	+	18.3472i	−0.586977	+	0.586977i	−0.936812	−	0.349834i	$-0.886238\pi$
$977$	−18.3472	+	18.3472i	−0.586977	+	0.586977i	0.349834	+	0.936812i	$0.386238\pi$
$978$		0			0
$979$	2.10094	+	5.07211i	0.0671463	+	0.162105i
$980$	0.704422	+	0.831898i	0.0225019	+	0.0265740i
$981$		0			0
$982$	−15.3652			−0.490322
$983$	−12.6630	+	30.5712i	−0.403888	+	0.975071i	0.582825	+	0.812598i	$0.301947\pi$
$983$	−12.6630	+	30.5712i	−0.403888	+	0.975071i	−0.986713	+	0.162474i	$0.948053\pi$
$984$		0			0
$985$	−41.5064	+	13.2917i	−1.32250	+	0.423509i
$986$	−43.0689	+	75.6817i	−1.37159	+	2.41020i
$987$		0			0
$988$	3.08229	+	3.08229i	0.0980606	+	0.0980606i
$989$	33.1905	+	13.7480i	1.05540	+	0.437160i
$990$		0			0
$991$	13.3710	−	32.2804i	0.424744	−	1.02542i	−0.556186	−	0.831058i	$-0.687736\pi$
$991$	13.3710	−	32.2804i	0.424744	−	1.02542i	0.980930	−	0.194364i	$-0.0622643\pi$
$992$	30.2810	+	73.1049i	0.961423	+	2.32108i
$993$		0			0
$994$	−4.49406	−	4.49406i	−0.142543	−	0.142543i
$995$	−23.8682	+	46.3564i	−0.756674	+	1.46960i
$996$		0			0
$997$	6.29396	+	15.1950i	0.199332	+	0.481229i	0.991662	−	0.128862i	$-0.0411325\pi$
$997$	6.29396	+	15.1950i	0.199332	+	0.481229i	−0.792331	+	0.610092i	$0.791133\pi$
$998$	14.7809	+	6.12244i	0.467881	+	0.193802i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.bh.b.604.1		24
3.2	odd	2		85.2.m.a.9.6	yes	24
5.4	even	2	inner	765.2.bh.b.604.6		24
15.2	even	4		425.2.m.e.26.1		24
15.8	even	4		425.2.m.e.26.6		24
15.14	odd	2		85.2.m.a.9.1	✓	24
17.2	even	8	inner	765.2.bh.b.19.6		24
51.2	odd	8		85.2.m.a.19.1	yes	24
51.11	even	16		1445.2.b.i.579.22		24
51.23	even	16		1445.2.b.i.579.21		24
85.19	even	8	inner	765.2.bh.b.19.1		24
255.2	even	8		425.2.m.e.376.1		24
255.23	odd	16		7225.2.a.by.1.22		24
255.53	even	8		425.2.m.e.376.6		24
255.62	odd	16		7225.2.a.by.1.4		24
255.74	even	16		1445.2.b.i.579.4		24
255.104	odd	8		85.2.m.a.19.6	yes	24
255.113	odd	16		7225.2.a.by.1.21		24
255.164	even	16		1445.2.b.i.579.3		24
255.227	odd	16		7225.2.a.by.1.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.1	✓	24	15.14	odd	2
85.2.m.a.9.6	yes	24	3.2	odd	2
85.2.m.a.19.1	yes	24	51.2	odd	8
85.2.m.a.19.6	yes	24	255.104	odd	8
425.2.m.e.26.1		24	15.2	even	4
425.2.m.e.26.6		24	15.8	even	4
425.2.m.e.376.1		24	255.2	even	8
425.2.m.e.376.6		24	255.53	even	8
765.2.bh.b.19.1		24	85.19	even	8	inner
765.2.bh.b.19.6		24	17.2	even	8	inner
765.2.bh.b.604.1		24	1.1	even	1	trivial
765.2.bh.b.604.6		24	5.4	even	2	inner
1445.2.b.i.579.3		24	255.164	even	16
1445.2.b.i.579.4		24	255.74	even	16
1445.2.b.i.579.21		24	51.23	even	16
1445.2.b.i.579.22		24	51.11	even	16
7225.2.a.by.1.3		24	255.227	odd	16
7225.2.a.by.1.4		24	255.62	odd	16
7225.2.a.by.1.21		24	255.113	odd	16
7225.2.a.by.1.22		24	255.23	odd	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.bh (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48843 - 1.48843i) q^{2} +2.43082i q^{4} +(2.22841 + 0.184902i) q^{5} +(-2.47912 + 1.02689i) q^{7} +(0.641241 - 0.641241i) q^{8} +(-3.04161 - 3.59203i) q^{10} +(0.901470 - 0.373401i) q^{11} -2.65240 q^{13} +(5.21843 + 2.16155i) q^{14} +2.95276 q^{16} +(-3.25539 + 2.53030i) q^{17} +(-0.478059 + 0.478059i) q^{19} +(-0.449464 + 5.41686i) q^{20} +(-1.89755 - 0.785991i) q^{22} +(-1.54397 - 3.72748i) q^{23} +(4.93162 + 0.824076i) q^{25} +(3.94790 + 3.94790i) q^{26} +(-2.49617 - 6.02630i) q^{28} +(-3.83958 + 9.26957i) q^{29} +(-9.10497 - 3.77140i) q^{31} +(-5.67744 - 5.67744i) q^{32} +(8.61157 + 1.07924i) q^{34} +(-5.71438 + 1.82993i) q^{35} +(-2.61646 + 6.31669i) q^{37} +1.42311 q^{38} +(1.54751 - 1.31038i) q^{40} +(-2.80190 - 6.76439i) q^{41} +(-6.29628 + 6.29628i) q^{43} +(0.907670 + 2.19131i) q^{44} +(-3.24999 + 7.84616i) q^{46} -0.874497 q^{47} +(0.141809 - 0.141809i) q^{49} +(-6.11377 - 8.56693i) q^{50} -6.44750i q^{52} +(2.00842 + 2.00842i) q^{53} +(2.07789 - 0.665407i) q^{55} +(-0.931234 + 2.24820i) q^{56} +(19.5120 - 8.08213i) q^{58} +(7.59005 + 7.59005i) q^{59} +(0.793008 + 1.91449i) q^{61} +(7.93862 + 19.1655i) q^{62} +10.9954i q^{64} +(-5.91063 - 0.490434i) q^{65} -5.73990i q^{67} +(-6.15070 - 7.91327i) q^{68} +(11.2291 + 5.78171i) q^{70} +(-1.03955 - 0.430595i) q^{71} +(2.77027 + 1.14748i) q^{73} +(13.2963 - 5.50752i) q^{74} +(-1.16208 - 1.16208i) q^{76} +(-1.85141 + 1.85141i) q^{77} +(-0.377872 + 0.156520i) q^{79} +(6.57996 + 0.545972i) q^{80} +(-5.89786 + 14.2387i) q^{82} +(4.64846 + 4.64846i) q^{83} +(-7.72221 + 5.03662i) q^{85} +18.7431 q^{86} +(0.338619 - 0.817499i) q^{88} +5.62649i q^{89} +(6.57562 - 2.72371i) q^{91} +(9.06082 - 3.75312i) q^{92} +(1.30162 + 1.30162i) q^{94} +(-1.15371 + 0.976918i) q^{95} +(14.2405 + 5.89862i) q^{97} -0.422145 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50}+ \cdots + 88 q^{95}+O(q^{100}) \) 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

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