LMFDB - Embedded newform 1386.2.bk.d.703.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.13
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.d.901.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23351 + 0.712169i) q^{5} +(0.484566 + 2.60100i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23351 + 0.712169i) q^{5} +(0.484566 + 2.60100i) q^{7} -1.00000i q^{8} +(-0.712169 + 1.23351i) q^{10} +(-3.13191 - 1.09140i) q^{11} +2.39347 q^{13} +(1.72015 + 2.01025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.529896 + 0.917806i) q^{17} +(2.37329 + 4.11067i) q^{19} +1.42434i q^{20} +(-3.25801 + 0.620776i) q^{22} +(1.72015 + 2.97938i) q^{23} +(-1.48563 + 2.57319i) q^{25} +(2.07281 - 1.19674i) q^{26} +(2.49481 + 0.880853i) q^{28} +4.13565i q^{29} +(0.122361 + 0.0706450i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.05979i q^{34} +(-2.45007 - 2.86327i) q^{35} +(1.19019 + 2.06146i) q^{37} +(4.11067 + 2.37329i) q^{38} +(0.712169 + 1.23351i) q^{40} +9.17779 q^{41} +5.73823i q^{43} +(-2.51113 + 2.16661i) q^{44} +(2.97938 + 1.72015i) q^{46} +(-3.08763 + 1.78265i) q^{47} +(-6.53039 + 2.52071i) q^{49} +2.97126i q^{50} +(1.19674 - 2.07281i) q^{52} +(-1.98826 + 3.44377i) q^{53} +(4.64051 - 0.884194i) q^{55} +(2.60100 - 0.484566i) q^{56} +(2.06783 + 3.58158i) q^{58} +(-4.71536 - 2.72242i) q^{59} +(5.58028 + 9.66532i) q^{61} +0.141290 q^{62} -1.00000 q^{64} +(-2.95237 + 1.70455i) q^{65} +(-0.567825 + 0.983502i) q^{67} +(0.529896 + 0.917806i) q^{68} +(-3.55346 - 1.25463i) q^{70} -10.9563 q^{71} +(0.969133 - 1.67859i) q^{73} +(2.06146 + 1.19019i) q^{74} +4.74659 q^{76} +(1.32111 - 8.67495i) q^{77} +(3.82226 - 2.20678i) q^{79} +(1.23351 + 0.712169i) q^{80} +(7.94820 - 4.58889i) q^{82} +3.73539 q^{83} -1.50950i q^{85} +(2.86912 + 4.96945i) q^{86} +(-1.09140 + 3.13191i) q^{88} +(-1.67859 + 0.969133i) q^{89} +(1.15980 + 6.22541i) q^{91} +3.44029 q^{92} +(-1.78265 + 3.08763i) q^{94} +(-5.85498 - 3.38037i) q^{95} -18.9915i q^{97} +(-4.39513 + 5.44820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.23351	+	0.712169i	−0.551643	+	0.318491i	−0.749785	−	0.661682i	$-0.769843\pi$
$5$	−1.23351	+	0.712169i	−0.551643	+	0.318491i	0.198141	+	0.980173i	$0.436510\pi$
$6$		0			0
$7$	0.484566	+	2.60100i	0.183149	+	0.983085i
$7$	0.484566	+	2.60100i	0.183149	+	0.983085i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.712169	+	1.23351i	−0.225207	+	0.390071i
$11$	−3.13191	−	1.09140i	−0.944306	−	0.329069i
$11$	−3.13191	−	1.09140i	−0.944306	−	0.329069i
$12$		0			0
$13$	2.39347			0.663829			0.331915	−	0.943309i	$-0.392305\pi$
$13$	2.39347			0.663829			0.331915	+	0.943309i	$0.392305\pi$
$14$	1.72015	+	2.01025i	0.459728	+	0.537261i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.529896	+	0.917806i	−0.128519	+	0.222601i	−0.923103	−	0.384553i	$-0.874356\pi$
$17$	−0.529896	+	0.917806i	−0.128519	+	0.222601i	0.794584	+	0.607154i	$0.207689\pi$
$18$		0			0
$19$	2.37329	+	4.11067i	0.544471	+	0.943052i	0.998640	+	0.0521360i	$0.0166029\pi$
$19$	2.37329	+	4.11067i	0.544471	+	0.943052i	−0.454169	+	0.890916i	$0.650064\pi$
$20$			1.42434i			0.318491i
$21$		0			0
$22$	−3.25801	+	0.620776i	−0.694610	+	0.132350i
$23$	1.72015	+	2.97938i	0.358675	+	0.621244i	0.987740	−	0.156109i	$-0.0498952\pi$
$23$	1.72015	+	2.97938i	0.358675	+	0.621244i	−0.629064	+	0.777353i	$0.716562\pi$
$24$		0			0
$25$	−1.48563	+	2.57319i	−0.297126	+	0.514638i
$26$	2.07281	−	1.19674i	0.406511	−	0.234699i
$27$		0			0
$28$	2.49481	+	0.880853i	0.471476	+	0.166466i
$29$			4.13565i			0.767971i	0.923339	+	0.383986i	$0.125449\pi$
$29$			4.13565i			0.767971i	−0.923339	+	0.383986i	$0.874551\pi$
$30$		0			0
$31$	0.122361	+	0.0706450i	0.0219766	+	0.0126882i	0.510948	−	0.859612i	$-0.329294\pi$
$31$	0.122361	+	0.0706450i	0.0219766	+	0.0126882i	−0.488971	+	0.872300i	$0.662628\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			1.05979i			0.181753i
$35$	−2.45007	−	2.86327i	−0.414137	−	0.483981i
$36$		0			0
$37$	1.19019	+	2.06146i	0.195665	+	0.338902i	0.947118	−	0.320884i	$-0.103980\pi$
$37$	1.19019	+	2.06146i	0.195665	+	0.338902i	−0.751453	+	0.659787i	$0.770647\pi$
$38$	4.11067	+	2.37329i	0.666838	+	0.384999i
$39$		0			0
$40$	0.712169	+	1.23351i	0.112604	+	0.195035i
$41$	9.17779			1.43333			0.716665	−	0.697418i	$-0.245668\pi$
$41$	9.17779			1.43333			0.716665	+	0.697418i	$0.245668\pi$
$42$		0			0
$43$			5.73823i			0.875072i	0.899201	+	0.437536i	$0.144149\pi$
$43$			5.73823i			0.875072i	−0.899201	+	0.437536i	$0.855851\pi$
$44$	−2.51113	+	2.16661i	−0.378567	+	0.326629i
$45$		0			0
$46$	2.97938	+	1.72015i	0.439286	+	0.253622i
$47$	−3.08763	+	1.78265i	−0.450378	+	0.260026i	−0.707990	−	0.706223i	$-0.750398\pi$
$47$	−3.08763	+	1.78265i	−0.450378	+	0.260026i	0.257612	+	0.966248i	$0.417064\pi$
$48$		0			0
$49$	−6.53039	+	2.52071i	−0.932913	+	0.360102i
$50$			2.97126i			0.420200i
$51$		0			0
$52$	1.19674	−	2.07281i	0.165957	−	0.287446i
$53$	−1.98826	+	3.44377i	−0.273109	+	0.473038i	−0.969656	−	0.244472i	$-0.921385\pi$
$53$	−1.98826	+	3.44377i	−0.273109	+	0.473038i	0.696547	+	0.717511i	$0.254719\pi$
$54$		0			0
$55$	4.64051	−	0.884194i	0.625726	−	0.119225i
$56$	2.60100	−	0.484566i	0.347573	−	0.0647529i
$57$		0			0
$58$	2.06783	+	3.58158i	0.271519	+	0.470284i
$59$	−4.71536	−	2.72242i	−0.613888	−	0.354428i	0.160598	−	0.987020i	$-0.448658\pi$
$59$	−4.71536	−	2.72242i	−0.613888	−	0.354428i	−0.774486	+	0.632592i	$0.781991\pi$
$60$		0			0
$61$	5.58028	+	9.66532i	0.714481	+	1.23752i	0.963159	+	0.268932i	$0.0866706\pi$
$61$	5.58028	+	9.66532i	0.714481	+	1.23752i	−0.248678	+	0.968586i	$0.579996\pi$
$62$	0.141290			0.0179438
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.95237	+	1.70455i	−0.366197	+	0.211424i
$66$		0			0
$67$	−0.567825	+	0.983502i	−0.0693709	+	0.120154i	−0.898625	−	0.438719i	$-0.855433\pi$
$67$	−0.567825	+	0.983502i	−0.0693709	+	0.120154i	0.829254	+	0.558872i	$0.188766\pi$
$68$	0.529896	+	0.917806i	0.0642593	+	0.111300i
$69$		0			0
$70$	−3.55346	−	1.25463i	−0.424719	−	0.149957i
$71$	−10.9563			−1.30027			−0.650137	−	0.759817i	$-0.725289\pi$
$71$	−10.9563			−1.30027			−0.650137	+	0.759817i	$0.725289\pi$
$72$		0			0
$73$	0.969133	−	1.67859i	0.113428	−	0.196464i	−0.803722	−	0.595005i	$-0.797150\pi$
$73$	0.969133	−	1.67859i	0.113428	−	0.196464i	0.917150	+	0.398541i	$0.130483\pi$
$74$	2.06146	+	1.19019i	0.239640	+	0.138356i
$75$		0			0
$76$	4.74659			0.544471
$77$	1.32111	−	8.67495i	0.150554	−	0.988602i
$78$		0			0
$79$	3.82226	−	2.20678i	0.430037	−	0.248282i	−0.269325	−	0.963049i	$-0.586801\pi$
$79$	3.82226	−	2.20678i	0.430037	−	0.248282i	0.699363	+	0.714767i	$0.253467\pi$
$80$	1.23351	+	0.712169i	0.137911	+	0.0796229i
$81$		0			0
$82$	7.94820	−	4.58889i	0.877732	−	0.506759i
$83$	3.73539			0.410013			0.205006	−	0.978761i	$-0.434279\pi$
$83$	3.73539			0.410013			0.205006	+	0.978761i	$0.434279\pi$
$84$		0			0
$85$		−	1.50950i		−	0.163728i
$86$	2.86912	+	4.96945i	0.309385	+	0.535870i
$87$		0			0
$88$	−1.09140	+	3.13191i	−0.116343	+	0.333863i
$89$	−1.67859	+	0.969133i	−0.177930	+	0.102728i	−0.586320	−	0.810080i	$-0.699424\pi$
$89$	−1.67859	+	0.969133i	−0.177930	+	0.102728i	0.408390	+	0.912808i	$0.366090\pi$
$90$		0			0
$91$	1.15980	+	6.22541i	0.121580	+	0.652601i
$92$	3.44029			0.358675
$93$		0			0
$94$	−1.78265	+	3.08763i	−0.183866	+	0.318465i
$95$	−5.85498	−	3.38037i	−0.600708	−	0.346819i
$96$		0			0
$97$		−	18.9915i		−	1.92829i	−0.265368	−	0.964147i	$-0.585493\pi$
$97$		−	18.9915i		−	1.92829i	0.265368	−	0.964147i	$-0.414507\pi$
$98$	−4.39513	+	5.44820i	−0.443975	+	0.550351i
$99$		0			0
$100$	1.48563	+	2.57319i	0.148563	+	0.257319i
$101$	2.97996	−	5.16145i	0.296518	−	0.513583i	−0.678819	−	0.734305i	$-0.737508\pi$
$101$	2.97996	−	5.16145i	0.296518	−	0.513583i	0.975337	+	0.220722i	$0.0708414\pi$
$102$		0			0
$103$	9.65167	−	5.57240i	0.951008	−	0.549064i	0.0576138	−	0.998339i	$-0.481651\pi$
$103$	9.65167	−	5.57240i	0.951008	−	0.549064i	0.893394	+	0.449274i	$0.148317\pi$
$104$		−	2.39347i		−	0.234699i
$105$		0			0
$106$			3.97653i			0.386234i
$107$	3.72394	−	2.15002i	0.360007	−	0.207850i	−0.309077	−	0.951037i	$-0.600020\pi$
$107$	3.72394	−	2.15002i	0.360007	−	0.207850i	0.669084	+	0.743187i	$0.266687\pi$
$108$		0			0
$109$	9.85329	+	5.68880i	0.943774	+	0.544888i	0.891141	−	0.453726i	$-0.149905\pi$
$109$	9.85329	+	5.68880i	0.943774	+	0.544888i	0.0526326	+	0.998614i	$0.483239\pi$
$110$	3.57670	−	3.08599i	0.341025	−	0.294237i
$111$		0			0
$112$	2.01025	−	1.72015i	0.189951	−	0.162539i
$113$	−8.29122			−0.779973			−0.389986	−	0.920821i	$-0.627520\pi$
$113$	−8.29122			−0.779973			−0.389986	+	0.920821i	$0.627520\pi$
$114$		0			0
$115$	−4.24364	−	2.45007i	−0.395722	−	0.228470i
$116$	3.58158	+	2.06783i	0.332541	+	0.191993i
$117$		0			0
$118$	−5.44483			−0.501238
$119$	−2.64398	−	0.933520i	−0.242374	−	0.0855757i
$120$		0			0
$121$	8.61770	+	6.83632i	0.783427	+	0.621483i
$122$	9.66532	+	5.58028i	0.875057	+	0.505215i
$123$		0			0
$124$	0.122361	−	0.0706450i	0.0109883	−	0.00634411i
$125$		−	11.3538i		−	1.01551i
$126$		0			0
$127$			9.86776i			0.875622i	0.899067	+	0.437811i	$0.144246\pi$
$127$			9.86776i			0.875622i	−0.899067	+	0.437811i	$0.855754\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.70455	+	2.95237i	−0.149499	+	0.258940i
$131$	−4.97078	−	8.60965i	−0.434299	−	0.752228i	0.562939	−	0.826498i	$-0.309671\pi$
$131$	−4.97078	−	8.60965i	−0.434299	−	0.752228i	−0.997238	+	0.0742702i	$0.976337\pi$
$132$		0			0
$133$	−9.54182	+	8.16483i	−0.827381	+	0.707980i
$134$			1.13565i			0.0981053i
$135$		0			0
$136$	0.917806	+	0.529896i	0.0787013	+	0.0454382i
$137$	7.68510	−	13.3110i	0.656583	−	1.13723i	−0.324912	−	0.945744i	$-0.605335\pi$
$137$	7.68510	−	13.3110i	0.656583	−	1.13723i	0.981495	−	0.191490i	$-0.0613320\pi$
$138$		0			0
$139$	−2.38399			−0.202208			−0.101104	−	0.994876i	$-0.532237\pi$
$139$	−2.38399			−0.202208			−0.101104	+	0.994876i	$0.532237\pi$
$140$	−3.70470	+	0.690186i	−0.313104	+	0.0583314i
$141$		0			0
$142$	−9.48844	+	5.47815i	−0.796252	+	0.459716i
$143$	−7.49613	−	2.61223i	−0.626858	−	0.218446i
$144$		0			0
$145$	−2.94528	−	5.10138i	−0.244592	−	0.423646i
$146$		−	1.93827i		−	0.160412i
$147$		0			0
$148$	2.38037			0.195665
$149$	10.6719	−	6.16145i	0.874280	−	0.504766i	0.00551161	−	0.999985i	$-0.498246\pi$
$149$	10.6719	−	6.16145i	0.874280	−	0.504766i	0.868768	+	0.495219i	$0.164912\pi$
$150$		0			0
$151$	1.22136	+	0.705152i	0.0993928	+	0.0573844i	0.548872	−	0.835906i	$-0.315057\pi$
$151$	1.22136	+	0.705152i	0.0993928	+	0.0573844i	−0.449480	+	0.893291i	$0.648391\pi$
$152$	4.11067	−	2.37329i	0.333419	−	0.192500i
$153$		0			0
$154$	−3.19336	−	8.17328i	−0.257328	−	0.658621i
$155$	−0.201245			−0.0161644
$156$		0			0
$157$	−6.57056	−	3.79351i	−0.524388	−	0.302755i	0.214340	−	0.976759i	$-0.431240\pi$
$157$	−6.57056	−	3.79351i	−0.524388	−	0.302755i	−0.738728	+	0.674004i	$0.764573\pi$
$158$	2.20678	−	3.82226i	0.175562	−	0.304082i
$159$		0			0
$160$	1.42434			0.112604
$161$	−6.91584	+	5.91781i	−0.545045	+	0.466388i
$162$		0			0
$163$	3.65275	+	6.32675i	0.286106	+	0.495549i	0.972877	−	0.231324i	$-0.0743059\pi$
$163$	3.65275	+	6.32675i	0.286106	+	0.495549i	−0.686771	+	0.726874i	$0.740973\pi$
$164$	4.58889	−	7.94820i	0.358332	−	0.620650i
$165$		0			0
$166$	3.23495	−	1.86770i	0.251080	−	0.144961i
$167$	11.1448			0.862410			0.431205	−	0.902254i	$-0.358089\pi$
$167$	11.1448			0.862410			0.431205	+	0.902254i	$0.358089\pi$
$168$		0			0
$169$	−7.27130			−0.559331
$170$	−0.754750	−	1.30727i	−0.0578867	−	0.100263i
$171$		0			0
$172$	4.96945	+	2.86912i	0.378917	+	0.218768i
$173$	−0.813549	−	1.40911i	−0.0618530	−	0.107133i	0.833441	−	0.552609i	$-0.186368\pi$
$173$	−0.813549	−	1.40911i	−0.0618530	−	0.107133i	−0.895294	+	0.445476i	$0.853034\pi$
$174$		0			0
$175$	−7.41275	−	2.61725i	−0.560351	−	0.197845i
$176$	0.620776	+	3.25801i	0.0467927	+	0.245582i
$177$		0			0
$178$	−0.969133	+	1.67859i	−0.0726396	+	0.125815i
$179$	−8.77643	+	15.2012i	−0.655981	+	1.13619i	0.325665	+	0.945485i	$0.394412\pi$
$179$	−8.77643	+	15.2012i	−0.655981	+	1.13619i	−0.981647	+	0.190708i	$0.938922\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	4.11712	+	4.81147i	0.305181	+	0.356650i
$183$		0			0
$184$	2.97938	−	1.72015i	0.219643	−	0.126811i
$185$	−2.93622	−	1.69523i	−0.215875	−	0.124636i
$186$		0			0
$187$	2.66128	−	2.29616i	0.194612	−	0.167912i
$188$			3.56529i			0.260026i
$189$		0			0
$190$	−6.76074			−0.490476
$191$	−11.5035	−	19.9247i	−0.832366	−	1.44170i	−0.896157	−	0.443738i	$-0.853652\pi$
$191$	−11.5035	−	19.9247i	−0.832366	−	1.44170i	0.0637902	−	0.997963i	$-0.479681\pi$
$192$		0			0
$193$	−14.2144	−	8.20668i	−1.02317	−	0.590730i	−0.108152	−	0.994134i	$-0.534493\pi$
$193$	−14.2144	−	8.20668i	−1.02317	−	0.590730i	−0.915022	+	0.403405i	$0.867827\pi$
$194$	−9.49575	−	16.4471i	−0.681755	−	1.18083i
$195$		0			0
$196$	−1.08219	+	6.91584i	−0.0772995	+	0.493989i
$197$			8.65167i			0.616406i	0.951321	+	0.308203i	$0.0997276\pi$
$197$			8.65167i			0.616406i	−0.951321	+	0.308203i	$0.900272\pi$
$198$		0			0
$199$	−11.0608	−	6.38595i	−0.784078	−	0.452688i	0.0537956	−	0.998552i	$-0.482868\pi$
$199$	−11.0608	−	6.38595i	−0.784078	−	0.452688i	−0.837874	+	0.545864i	$0.816201\pi$
$200$	2.57319	+	1.48563i	0.181952	+	0.105050i
$201$		0			0
$202$		−	5.95993i		−	0.419339i
$203$	−10.7568	+	2.00400i	−0.754981	+	0.140653i
$204$		0			0
$205$	−11.3209	+	6.53613i	−0.790687	+	0.456503i
$206$	5.57240	−	9.65167i	0.388247	−	0.672464i
$207$		0			0
$208$	−1.19674	−	2.07281i	−0.0829786	−	0.143723i
$209$	−2.94657	−	15.4644i	−0.203818	−	1.06970i
$210$		0			0
$211$		−	22.2186i		−	1.52959i	−0.644272	−	0.764797i	$-0.722839\pi$
$211$		−	22.2186i		−	1.52959i	0.644272	−	0.764797i	$-0.277161\pi$
$212$	1.98826	+	3.44377i	0.136554	+	0.236519i
$213$		0			0
$214$	2.15002	−	3.72394i	0.146972	−	0.254563i
$215$	−4.08659	−	7.07818i	−0.278703	−	0.482728i
$216$		0			0
$217$	−0.124456	+	0.352492i	−0.00844860	+	0.0239287i
$218$	11.3776			0.770588
$219$		0			0
$220$	1.55452	−	4.46089i	0.104806	−	0.300753i
$221$	−1.26829	+	2.19674i	−0.0853144	+	0.147769i
$222$		0			0
$223$		−	5.98498i		−	0.400784i	−0.979716	−	0.200392i	$-0.935778\pi$
$223$		−	5.98498i		−	0.400784i	0.979716	−	0.200392i	$-0.0642215\pi$
$224$	0.880853	−	2.49481i	0.0588544	−	0.166692i
$225$		0			0
$226$	−7.18041	+	4.14561i	−0.477634	+	0.275762i
$227$	−2.52071	+	4.36600i	−0.167306	+	0.289782i	−0.937472	−	0.348062i	$-0.886840\pi$
$227$	−2.52071	+	4.36600i	−0.167306	+	0.289782i	0.770166	+	0.637843i	$0.220173\pi$
$228$		0			0
$229$	18.3837	−	10.6138i	1.21483	−	0.701381i	0.251021	−	0.967982i	$-0.419234\pi$
$229$	18.3837	−	10.6138i	1.21483	−	0.701381i	0.963807	+	0.266601i	$0.0859004\pi$
$230$	−4.90014			−0.323105
$231$		0			0
$232$	4.13565			0.271519
$233$	−12.7287	+	7.34890i	−0.833883	+	0.481443i	−0.855180	−	0.518331i	$-0.826554\pi$
$233$	−12.7287	+	7.34890i	−0.833883	+	0.481443i	0.0212973	+	0.999773i	$0.493220\pi$
$234$		0			0
$235$	2.53909	−	4.39783i	0.165632	−	0.286883i
$236$	−4.71536	+	2.72242i	−0.306944	+	0.177214i
$237$		0			0
$238$	−2.75652	+	0.513539i	−0.178678	+	0.0332878i
$239$			21.0320i			1.36045i	0.733003	+	0.680225i	$0.238118\pi$
$239$			21.0320i			1.36045i	−0.733003	+	0.680225i	$0.761882\pi$
$240$		0			0
$241$	−9.15656	+	15.8596i	−0.589826	+	1.02161i	0.404429	+	0.914569i	$0.367470\pi$
$241$	−9.15656	+	15.8596i	−0.589826	+	1.02161i	−0.994255	+	0.107039i	$0.965863\pi$
$242$	10.8813	+	1.61157i	0.699477	+	0.103596i
$243$		0			0
$244$	11.1606			0.714481
$245$	6.26014	−	7.76007i	0.399946	−	0.495773i
$246$		0			0
$247$	5.68041	+	9.83876i	0.361436	+	0.626025i
$248$	0.0706450	−	0.122361i	0.00448596	−	0.00776991i
$249$		0			0
$250$	−5.67688	−	9.83265i	−0.359038	−	0.621871i
$251$			30.7321i			1.93979i	0.243522	+	0.969895i	$0.421697\pi$
$251$			30.7321i			1.93979i	−0.243522	+	0.969895i	$0.578303\pi$
$252$		0			0
$253$	−2.13565	−	11.2085i	−0.134267	−	0.704673i
$254$	4.93388	+	8.54573i	0.309579	+	0.536207i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.7582	−	6.21128i	0.671081	−	0.387449i	−0.125405	−	0.992106i	$-0.540023\pi$
$257$	10.7582	−	6.21128i	0.671081	−	0.387449i	0.796486	+	0.604657i	$0.206690\pi$
$258$		0			0
$259$	−4.78514	+	4.09459i	−0.297334	+	0.254425i
$260$			3.40911i			0.211424i
$261$		0			0
$262$	−8.60965	−	4.97078i	−0.531906	−	0.307096i
$263$	1.49710	+	0.864349i	0.0923150	+	0.0532981i	0.545447	−	0.838145i	$-0.316360\pi$
$263$	1.49710	+	0.864349i	0.0923150	+	0.0532981i	−0.453132	+	0.891444i	$0.649693\pi$
$264$		0			0
$265$		−	5.66391i		−	0.347931i
$266$	−4.18105	+	11.8419i	−0.256356	+	0.726071i
$267$		0			0
$268$	0.567825	+	0.983502i	0.0346854	+	0.0600770i
$269$	0.418337	+	0.241527i	0.0255065	+	0.0147262i	0.512699	−	0.858568i	$-0.328646\pi$
$269$	0.418337	+	0.241527i	0.0255065	+	0.0147262i	−0.487193	+	0.873295i	$0.661979\pi$
$270$		0			0
$271$	−6.53549	−	11.3198i	−0.397002	−	0.687628i	0.596352	−	0.802723i	$-0.296616\pi$
$271$	−6.53549	−	11.3198i	−0.397002	−	0.687628i	−0.993355	+	0.115095i	$0.963283\pi$
$272$	1.05979			0.0642593
$273$		0			0
$274$		−	15.3702i		−	0.928548i
$275$	7.46124	−	6.43758i	0.449929	−	0.388201i
$276$		0			0
$277$	−18.7031	−	10.7982i	−1.12376	−	0.648802i	−0.181400	−	0.983409i	$-0.558063\pi$
$277$	−18.7031	−	10.7982i	−1.12376	−	0.648802i	−0.942358	+	0.334608i	$0.891396\pi$
$278$	−2.06460	+	1.19200i	−0.123826	+	0.0714912i
$279$		0			0
$280$	−2.86327	+	2.45007i	−0.171113	+	0.146420i
$281$		−	1.07487i		−	0.0641213i	−0.999486	−	0.0320607i	$-0.989793\pi$
$281$		−	1.07487i		−	0.0641213i	0.999486	−	0.0320607i	$-0.0102070\pi$
$282$		0			0
$283$	14.4644	−	25.0531i	0.859821	−	1.48925i	−0.0122775	−	0.999925i	$-0.503908\pi$
$283$	14.4644	−	25.0531i	0.859821	−	1.48925i	0.872099	−	0.489330i	$-0.162759\pi$
$284$	−5.47815	+	9.48844i	−0.325069	+	0.563035i
$285$		0			0
$286$	−7.79795	+	1.48581i	−0.461103	+	0.0878577i
$287$	4.44725	+	23.8714i	0.262513	+	1.40909i
$288$		0			0
$289$	7.93842	+	13.7497i	0.466966	+	0.808809i
$290$	−5.10138	−	2.94528i	−0.299563	−	0.172953i
$291$		0			0
$292$	−0.969133	−	1.67859i	−0.0567142	−	0.0982319i
$293$	23.8916			1.39576			0.697882	−	0.716213i	$-0.254126\pi$
$293$	23.8916			1.39576			0.697882	+	0.716213i	$0.254126\pi$
$294$		0			0
$295$	7.75528			0.451530
$296$	2.06146	−	1.19019i	0.119820	−	0.0691782i
$297$		0			0
$298$	6.16145	−	10.6719i	0.356923	−	0.618209i
$299$	4.11712	+	7.13106i	0.238099	+	0.412400i
$300$		0			0
$301$	−14.9251	+	2.78055i	−0.860270	+	0.160268i
$302$	1.41030			0.0811539
$303$		0			0
$304$	2.37329	−	4.11067i	0.136118	−	0.235763i
$305$	−13.7667	−	7.94820i	−0.788278	−	0.455112i
$306$		0			0
$307$	−18.5620			−1.05939			−0.529695	−	0.848188i	$-0.677694\pi$
$307$	−18.5620			−1.05939			−0.529695	+	0.848188i	$0.677694\pi$
$308$	−6.85217	−	5.48159i	−0.390439	−	0.312342i
$309$		0			0
$310$	−0.174283	+	0.100622i	−0.00989860	+	0.00571496i
$311$	−5.13370	−	2.96394i	−0.291105	−	0.168070i	0.347335	−	0.937741i	$-0.387087\pi$
$311$	−5.13370	−	2.96394i	−0.291105	−	0.168070i	−0.638440	+	0.769671i	$0.720420\pi$
$312$		0			0
$313$	19.5264	−	11.2736i	1.10370	−	0.637219i	0.166507	−	0.986040i	$-0.446751\pi$
$313$	19.5264	−	11.2736i	1.10370	−	0.637219i	0.937189	+	0.348821i	$0.113418\pi$
$314$	−7.58703			−0.428161
$315$		0			0
$316$		−	4.41356i		−	0.248282i
$317$	9.12767	+	15.8096i	0.512661	+	0.887955i	0.999892	+	0.0146817i	$0.00467350\pi$
$317$	9.12767	+	15.8096i	0.512661	+	0.887955i	−0.487231	+	0.873273i	$0.661993\pi$
$318$		0			0
$319$	4.51364	−	12.9525i	0.252715	−	0.725200i
$320$	1.23351	−	0.712169i	0.0689554	−	0.0398114i
$321$		0			0
$322$	−3.03039	+	8.58289i	−0.168877	+	0.478306i
$323$	−5.03040			−0.279899
$324$		0			0
$325$	−3.55581	+	6.15885i	−0.197241	+	0.341632i
$326$	6.32675	+	3.65275i	0.350406	+	0.202307i
$327$		0			0
$328$		−	9.17779i		−	0.506759i
$329$	−6.13282	−	7.16712i	−0.338113	−	0.395136i
$330$		0			0
$331$	13.6240	+	23.5975i	0.748844	+	1.29704i	0.948377	+	0.317144i	$0.102724\pi$
$331$	13.6240	+	23.5975i	0.748844	+	1.29704i	−0.199534	+	0.979891i	$0.563943\pi$
$332$	1.86770	−	3.23495i	0.102503	−	0.177541i
$333$		0			0
$334$	9.65167	−	5.57240i	0.528116	−	0.304908i
$335$		−	1.61755i		−	0.0883762i
$336$		0			0
$337$		−	20.1352i		−	1.09683i	−0.836206	−	0.548416i	$-0.815231\pi$
$337$		−	20.1352i		−	1.09683i	0.836206	−	0.548416i	$-0.184769\pi$
$338$	−6.29713	+	3.63565i	−0.342519	+	0.197753i
$339$		0			0
$340$	−1.30727	−	0.754750i	−0.0708964	−	0.0409321i
$341$	−0.306121	−	0.354798i	−0.0165774	−	0.0192134i
$342$		0			0
$343$	−9.72078	−	15.7641i	−0.524873	−	0.851181i
$344$	5.73823			0.309385
$345$		0			0
$346$	−1.40911	−	0.813549i	−0.0757541	−	0.0437367i
$347$	−21.1648	−	12.2195i	−1.13619	−	0.655977i	−0.190702	−	0.981648i	$-0.561077\pi$
$347$	−21.1648	−	12.2195i	−1.13619	−	0.655977i	−0.945483	+	0.325671i	$0.894410\pi$
$348$		0			0
$349$	3.06974			0.164319			0.0821596	−	0.996619i	$-0.473818\pi$
$349$	3.06974			0.164319			0.0821596	+	0.996619i	$0.473818\pi$
$350$	−7.72825	+	1.43977i	−0.413092	+	0.0769592i
$351$		0			0
$352$	2.16661	+	2.51113i	0.115481	+	0.133844i
$353$	29.1124	+	16.8081i	1.54950	+	0.894604i	0.998180	+	0.0603093i	$0.0192087\pi$
$353$	29.1124	+	16.8081i	1.54950	+	0.894604i	0.551319	+	0.834294i	$0.314125\pi$
$354$		0			0
$355$	13.5147	−	7.80274i	0.717288	−	0.414126i
$356$			1.93827i			0.102728i
$357$		0			0
$358$			17.5529i			0.927698i
$359$	19.7114	−	11.3804i	1.04033	−	0.600633i	0.120401	−	0.992725i	$-0.461582\pi$
$359$	19.7114	−	11.3804i	1.04033	−	0.600633i	0.919926	+	0.392092i	$0.128249\pi$
$360$		0			0
$361$	−1.76505	+	3.05716i	−0.0928976	+	0.160903i
$362$	3.46410	+	6.00000i	0.182069	+	0.315353i
$363$		0			0
$364$	5.97126	+	2.10829i	0.312979	+	0.110505i
$365$			2.76074i			0.144504i
$366$		0			0
$367$	−11.0969	−	6.40682i	−0.579255	−	0.334433i	0.181582	−	0.983376i	$-0.441878\pi$
$367$	−11.0969	−	6.40682i	−0.579255	−	0.334433i	−0.760837	+	0.648943i	$0.775212\pi$
$368$	1.72015	−	2.97938i	0.0896688	−	0.155311i
$369$		0			0
$370$	−3.39045			−0.176261
$371$	−9.92069	−	3.50273i	−0.515057	−	0.181853i
$372$		0			0
$373$	12.3658	−	7.13940i	0.640277	−	0.369664i	−0.144444	−	0.989513i	$-0.546139\pi$
$373$	12.3658	−	7.13940i	0.640277	−	0.369664i	0.784721	+	0.619849i	$0.212806\pi$
$374$	1.15665	−	3.31917i	0.0598092	−	0.171630i
$375$		0			0
$376$	1.78265	+	3.08763i	0.0919329	+	0.159233i
$377$			9.89856i			0.509802i
$378$		0			0
$379$	−27.2480			−1.39964			−0.699819	−	0.714321i	$-0.746736\pi$
$379$	−27.2480			−1.39964			−0.699819	+	0.714321i	$0.746736\pi$
$380$	−5.85498	+	3.38037i	−0.300354	+	0.173409i
$381$		0			0
$382$	−19.9247	−	11.5035i	−1.01944	−	0.588572i
$383$	−10.7500	+	6.20654i	−0.549301	+	0.317139i	−0.748840	−	0.662751i	$-0.769389\pi$
$383$	−10.7500	+	6.20654i	−0.549301	+	0.317139i	0.199539	+	0.979890i	$0.436056\pi$
$384$		0			0
$385$	4.54842	+	11.6415i	0.231809	+	0.593306i
$386$	−16.4134			−0.835418
$387$		0			0
$388$	−16.4471	−	9.49575i	−0.834976	−	0.482074i
$389$	15.7575	−	27.2927i	0.798936	−	1.38380i	−0.121374	−	0.992607i	$-0.538730\pi$
$389$	15.7575	−	27.2927i	0.798936	−	1.38380i	0.920310	−	0.391190i	$-0.127937\pi$
$390$		0			0
$391$	−3.64599			−0.184386
$392$	2.52071	+	6.53039i	0.127315	+	0.329835i
$393$		0			0
$394$	4.32584	+	7.49257i	0.217932	+	0.377470i
$395$	−3.14320	+	5.44418i	−0.158152	+	0.273926i
$396$		0			0
$397$	14.1419	−	8.16483i	0.709761	−	0.409781i	−0.101211	−	0.994865i	$-0.532272\pi$
$397$	14.1419	−	8.16483i	0.709761	−	0.409781i	0.810973	+	0.585084i	$0.198938\pi$
$398$	−12.7719			−0.640197
$399$		0			0
$400$	2.97126			0.148563
$401$	−9.17852	−	15.8977i	−0.458354	−	0.793892i	0.540521	−	0.841331i	$-0.318227\pi$
$401$	−9.17852	−	15.8977i	−0.458354	−	0.793892i	−0.998874	+	0.0474391i	$0.984894\pi$
$402$		0			0
$403$	0.292867	+	0.169087i	0.0145887	+	0.00842281i
$404$	−2.97996	−	5.16145i	−0.148259	−	0.256792i
$405$		0			0
$406$	−8.31368	+	7.11392i	−0.412601	+	0.353058i
$407$	−1.47768	−	7.75528i	−0.0732458	−	0.384415i
$408$		0			0
$409$	16.7702	−	29.0468i	0.829233	−	1.43627i	−0.0694082	−	0.997588i	$-0.522111\pi$
$409$	16.7702	−	29.0468i	0.829233	−	1.43627i	0.898641	−	0.438685i	$-0.144556\pi$
$410$	−6.53613	+	11.3209i	−0.322797	+	0.559100i
$411$		0			0
$412$		−	11.1448i		−	0.549064i
$413$	4.79610	−	13.5838i	0.236000	−	0.668417i
$414$		0			0
$415$	−4.60765	+	2.66023i	−0.226181	+	0.130586i
$416$	−2.07281	−	1.19674i	−0.101628	−	0.0586748i
$417$		0			0
$418$	−10.2840	−	11.9193i	−0.503008	−	0.582993i
$419$			35.5948i			1.73892i	0.494005	+	0.869459i	$0.335533\pi$
$419$			35.5948i			1.73892i	−0.494005	+	0.869459i	$0.664467\pi$
$420$		0			0
$421$	−1.56215			−0.0761348			−0.0380674	−	0.999275i	$-0.512120\pi$
$421$	−1.56215			−0.0761348			−0.0380674	+	0.999275i	$0.512120\pi$
$422$	−11.1093	−	19.2419i	−0.540793	−	0.936681i
$423$		0			0
$424$	3.44377	+	1.98826i	0.167244	+	0.0965586i
$425$	−1.57446	−	2.72704i	−0.0763725	−	0.132281i
$426$		0			0
$427$	−22.4355	+	19.1978i	−1.08573	+	0.929046i
$428$		−	4.30004i		−	0.207850i
$429$		0			0
$430$	−7.07818	−	4.08659i	−0.341340	−	0.197073i
$431$	−9.26930	−	5.35164i	−0.446487	−	0.257779i	0.259859	−	0.965647i	$-0.416324\pi$
$431$	−9.26930	−	5.35164i	−0.446487	−	0.257779i	−0.706345	+	0.707867i	$0.749657\pi$
$432$		0			0
$433$		−	10.1461i		−	0.487589i	−0.969827	−	0.243794i	$-0.921608\pi$
$433$		−	10.1461i		−	0.487589i	0.969827	−	0.243794i	$-0.0783922\pi$
$434$	0.0684644	+	0.367495i	0.00328639	+	0.0176403i
$435$		0			0
$436$	9.85329	−	5.68880i	0.471887	−	0.272444i
$437$	−8.16483	+	14.1419i	−0.390577	+	0.676499i
$438$		0			0
$439$	10.4282	+	18.0622i	0.497711	+	0.862061i	0.999997	−	0.00264068i	$-0.000840554\pi$
$439$	10.4282	+	18.0622i	0.497711	+	0.862061i	−0.502285	+	0.864702i	$0.667507\pi$
$440$	−0.884194	−	4.64051i	−0.0421523	−	0.221227i
$441$		0			0
$442$			2.53658i			0.120653i
$443$	11.0758	+	19.1838i	0.526227	+	0.911452i	0.999533	+	0.0305538i	$0.00972709\pi$
$443$	11.0758	+	19.1838i	0.526227	+	0.911452i	−0.473306	+	0.880898i	$0.656940\pi$
$444$		0			0
$445$	1.38037	−	2.39087i	0.0654359	−	0.113338i
$446$	−2.99249	−	5.18314i	−0.141698	−	0.245429i
$447$		0			0
$448$	−0.484566	−	2.60100i	−0.0228936	−	0.122886i
$449$	36.1782			1.70735			0.853677	−	0.520802i	$-0.174367\pi$
$449$	36.1782			1.70735			0.853677	+	0.520802i	$0.174367\pi$
$450$		0			0
$451$	−28.7440	−	10.0166i	−1.35350	−	0.471664i
$452$	−4.14561	+	7.18041i	−0.194993	+	0.337738i
$453$		0			0
$454$			5.04143i			0.236606i
$455$	−5.86417	−	6.85315i	−0.274916	−	0.321281i
$456$		0			0
$457$	−28.5981	+	16.5111i	−1.33776	+	0.772358i	−0.986475	−	0.163909i	$-0.947590\pi$
$457$	−28.5981	+	16.5111i	−1.33776	+	0.772358i	−0.351288	+	0.936267i	$0.614256\pi$
$458$	10.6138	−	18.3837i	0.495951	−	0.859013i
$459$		0			0
$460$	−4.24364	+	2.45007i	−0.197861	+	0.114235i
$461$	36.8048			1.71417			0.857086	−	0.515174i	$-0.172273\pi$
$461$	36.8048			1.71417			0.857086	+	0.515174i	$0.172273\pi$
$462$		0			0
$463$	−21.0895			−0.980113			−0.490057	−	0.871691i	$-0.663024\pi$
$463$	−21.0895			−0.980113			−0.490057	+	0.871691i	$0.663024\pi$
$464$	3.58158	−	2.06783i	0.166271	−	0.0959964i
$465$		0			0
$466$	−7.34890	+	12.7287i	−0.340431	+	0.589644i
$467$	−4.00895	+	2.31457i	−0.185512	+	0.107106i	−0.589880	−	0.807491i	$-0.700825\pi$
$467$	−4.00895	+	2.31457i	−0.185512	+	0.107106i	0.404368	+	0.914597i	$0.367492\pi$
$468$		0			0
$469$	−2.83324	−	1.00034i	−0.130827	−	0.0461914i
$470$		−	5.07818i		−	0.234239i
$471$		0			0
$472$	−2.72242	+	4.71536i	−0.125309	+	0.217042i
$473$	6.26269	−	17.9716i	0.287959	−	0.826336i
$474$		0			0
$475$	−14.1034			−0.647107
$476$	−2.13044	+	1.82300i	−0.0976487	+	0.0835569i
$477$		0			0
$478$	10.5160	+	18.2143i	0.480992	+	0.833102i
$479$	−15.2924	+	26.4873i	−0.698729	+	1.21023i	0.270178	+	0.962810i	$0.412918\pi$
$479$	−15.2924	+	26.4873i	−0.698729	+	1.21023i	−0.968907	+	0.247425i	$0.920416\pi$
$480$		0			0
$481$	2.84867	+	4.93405i	0.129888	+	0.224973i
$482$			18.3131i			0.834140i
$483$		0			0
$484$	10.2293	−	4.04499i	0.464967	−	0.183863i
$485$	13.5251	+	23.4262i	0.614145	+	1.06373i
$486$		0			0
$487$	15.5293	−	26.8976i	0.703700	−	1.21884i	−0.263458	−	0.964671i	$-0.584863\pi$
$487$	15.5293	−	26.8976i	0.703700	−	1.21884i	0.967159	−	0.254174i	$-0.0818036\pi$
$488$	9.66532	−	5.58028i	0.437529	−	0.252607i
$489$		0			0
$490$	1.54141	−	9.85049i	0.0696337	−	0.445000i
$491$			32.7320i			1.47717i	0.674158	+	0.738587i	$0.264507\pi$
$491$			32.7320i			1.47717i	−0.674158	+	0.738587i	$0.735493\pi$
$492$		0			0
$493$	−3.79573	−	2.19146i	−0.170951	−	0.0986986i
$494$	9.83876	+	5.68041i	0.442667	+	0.255574i
$495$		0			0
$496$		−	0.141290i		−	0.00634411i
$497$	−5.30906	−	28.4973i	−0.238144	−	1.27828i
$498$		0			0
$499$	19.0033	+	32.9147i	0.850705	+	1.47346i	0.880573	+	0.473910i	$0.157158\pi$
$499$	19.0033	+	32.9147i	0.850705	+	1.47346i	−0.0298682	+	0.999554i	$0.509509\pi$
$500$	−9.83265	−	5.67688i	−0.439730	−	0.253878i
$501$		0			0
$502$	15.3660	+	26.6147i	0.685820	+	1.18787i
$503$	11.9467			0.532678			0.266339	−	0.963879i	$-0.414186\pi$
$503$	11.9467			0.532678			0.266339	+	0.963879i	$0.414186\pi$
$504$		0			0
$505$			8.48895i			0.377753i
$506$	−7.45378	−	8.63903i	−0.331361	−	0.384052i
$507$		0			0
$508$	8.54573	+	4.93388i	0.379156	+	0.218906i
$509$	26.5048	−	15.3026i	1.17481	−	0.678275i	0.219999	−	0.975500i	$-0.429395\pi$
$509$	26.5048	−	15.3026i	1.17481	−	0.678275i	0.954807	+	0.297226i	$0.0960614\pi$
$510$		0			0
$511$	4.83561	+	1.70733i	0.213915	+	0.0755277i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	6.21128	−	10.7582i	0.273968	−	0.474526i
$515$	−7.93697	+	13.7472i	−0.349745	+	0.605776i
$516$		0			0
$517$	11.6158	−	2.21325i	0.510861	−	0.0973385i
$518$	−2.09676	+	5.93859i	−0.0921262	+	0.260926i
$519$		0			0
$520$	1.70455	+	2.95237i	0.0747496	+	0.129470i
$521$	−18.8615	−	10.8897i	−0.826335	−	0.477085i	0.0262609	−	0.999655i	$-0.491640\pi$
$521$	−18.8615	−	10.8897i	−0.826335	−	0.477085i	−0.852596	+	0.522570i	$0.824973\pi$
$522$		0			0
$523$	6.66648	+	11.5467i	0.291505	+	0.504901i	0.974166	−	0.225834i	$-0.0725107\pi$
$523$	6.66648	+	11.5467i	0.291505	+	0.504901i	−0.682661	+	0.730735i	$0.739177\pi$
$524$	−9.94156			−0.434299
$525$		0			0
$526$	1.72870			0.0753749
$527$	−0.129677	+	0.0748690i	−0.00564881	+	0.00326134i
$528$		0			0
$529$	5.58219	−	9.66864i	0.242704	−	0.420376i
$530$	−2.83196	−	4.90509i	−0.123012	−	0.213064i
$531$		0			0
$532$	2.30004	+	12.3459i	0.0997193	+	0.535262i
$533$	21.9668			0.951486
$534$		0			0
$535$	−3.06235	+	5.30415i	−0.132397	+	0.229318i
$536$	0.983502	+	0.567825i	0.0424808	+	0.0245263i
$537$		0			0
$538$	0.483054			0.0208259
$539$	23.2037	−	0.767388i	0.999454	−	0.0330538i
$540$		0			0
$541$	2.35710	−	1.36087i	0.101340	−	0.0585085i	−0.448474	−	0.893796i	$-0.648032\pi$
$541$	2.35710	−	1.36087i	0.101340	−	0.0585085i	0.549813	+	0.835288i	$0.314699\pi$
$542$	−11.3198	−	6.53549i	−0.486227	−	0.280723i
$543$		0			0
$544$	0.917806	−	0.529896i	0.0393506	−	0.0227191i
$545$	−16.2055			−0.694169
$546$		0			0
$547$			40.1418i			1.71634i	0.513365	+	0.858170i	$0.328399\pi$
$547$			40.1418i			1.71634i	−0.513365	+	0.858170i	$0.671601\pi$
$548$	−7.68510	−	13.3110i	−0.328291	−	0.568617i
$549$		0			0
$550$	3.24283	−	9.30572i	0.138275	−	0.396797i
$551$	−17.0003	+	9.81512i	−0.724236	+	0.418138i
$552$		0			0
$553$	7.59197	+	8.87235i	0.322843	+	0.377291i
$554$	−21.5964			−0.917544
$555$		0			0
$556$	−1.19200	+	2.06460i	−0.0505519	+	0.0875585i
$557$	−9.06246	−	5.23221i	−0.383989	−	0.221696i	0.295564	−	0.955323i	$-0.404493\pi$
$557$	−9.06246	−	5.23221i	−0.383989	−	0.221696i	−0.679552	+	0.733627i	$0.737826\pi$
$558$		0			0
$559$			13.7343i			0.580898i
$560$	−1.25463	+	3.55346i	−0.0530178	+	0.150161i
$561$		0			0
$562$	−0.537434	−	0.930864i	−0.0226703	−	0.0392661i
$563$	−5.24207	+	9.07954i	−0.220927	+	0.382657i	−0.955090	−	0.296317i	$-0.904242\pi$
$563$	−5.24207	+	9.07954i	−0.220927	+	0.382657i	0.734163	+	0.678974i	$0.237575\pi$
$564$		0			0
$565$	10.2273	−	5.90475i	0.430267	−	0.248415i
$566$		−	28.9289i		−	1.21597i
$567$		0			0
$568$			10.9563i			0.459716i
$569$	−7.77730	+	4.49022i	−0.326041	+	0.188240i	−0.654082	−	0.756424i	$-0.726945\pi$
$569$	−7.77730	+	4.49022i	−0.326041	+	0.188240i	0.328041	+	0.944664i	$0.393612\pi$
$570$		0			0
$571$	20.8399	+	12.0319i	0.872121	+	0.503519i	0.868052	−	0.496473i	$-0.165372\pi$
$571$	20.8399	+	12.0319i	0.872121	+	0.503519i	0.00406827	+	0.999992i	$0.498705\pi$
$572$	−6.01032	+	5.18572i	−0.251304	+	0.216826i
$573$		0			0
$574$	15.7871	+	18.4496i	0.658942	+	0.770073i
$575$	−10.2220			−0.426288
$576$		0			0
$577$	−11.6693	−	6.73730i	−0.485801	−	0.280478i	0.237030	−	0.971502i	$-0.423826\pi$
$577$	−11.6693	−	6.73730i	−0.485801	−	0.280478i	−0.722831	+	0.691025i	$0.757159\pi$
$578$	13.7497	+	7.93842i	0.571914	+	0.330195i
$579$		0			0
$580$	−5.89056			−0.244592
$581$	1.81005	+	9.71575i	0.0750934	+	0.403077i
$582$		0			0
$583$	9.98558	−	8.61559i	0.413561	−	0.356821i
$584$	−1.67859	−	0.969133i	−0.0694604	−	0.0401030i
$585$		0			0
$586$	20.6908	−	11.9458i	0.854727	−	0.493477i
$587$		−	5.46623i		−	0.225616i	−0.993617	−	0.112808i	$-0.964016\pi$
$587$		−	5.46623i		−	0.225616i	0.993617	−	0.112808i	$-0.0359844\pi$
$588$		0			0
$589$			0.670645i			0.0276335i
$590$	6.71627	−	3.87764i	0.276504	−	0.159640i
$591$		0			0
$592$	1.19019	−	2.06146i	0.0489163	−	0.0847256i
$593$	17.1992	+	29.7899i	0.706286	+	1.22332i	0.966226	+	0.257698i	$0.0829639\pi$
$593$	17.1992	+	29.7899i	0.706286	+	1.22332i	−0.259940	+	0.965625i	$0.583703\pi$
$594$		0			0
$595$	3.92621	−	0.731453i	0.160959	−	0.0299867i
$596$		−	12.3229i		−	0.504766i
$597$		0			0
$598$	7.13106	+	4.11712i	0.291611	+	0.168361i
$599$	13.6689	−	23.6753i	0.558497	−	0.967345i	−0.439125	−	0.898426i	$-0.644712\pi$
$599$	13.6689	−	23.6753i	0.558497	−	0.967345i	0.997622	−	0.0689193i	$-0.0219551\pi$
$600$		0			0
$601$	20.3071			0.828343			0.414172	−	0.910199i	$-0.364071\pi$
$601$	20.3071			0.828343			0.414172	+	0.910199i	$0.364071\pi$
$602$	−11.5353	+	9.87060i	−0.470142	+	0.402295i
$603$		0			0
$604$	1.22136	−	0.705152i	0.0496964	−	0.0286922i
$605$	−15.4987	−	2.29542i	−0.630110	−	0.0933223i
$606$		0			0
$607$	−6.37513	−	11.0420i	−0.258758	−	0.448183i	0.707151	−	0.707062i	$-0.249980\pi$
$607$	−6.37513	−	11.0420i	−0.258758	−	0.448183i	−0.965910	+	0.258880i	$0.916647\pi$
$608$		−	4.74659i		−	0.192500i
$609$		0			0
$610$	−15.8964			−0.643626
$611$	−7.39016	+	4.26671i	−0.298974	+	0.172613i
$612$		0			0
$613$	13.6426	+	7.87655i	0.551019	+	0.318131i	0.749533	−	0.661967i	$-0.230278\pi$
$613$	13.6426	+	7.87655i	0.551019	+	0.318131i	−0.198514	+	0.980098i	$0.563612\pi$
$614$	−16.0752	+	9.28101i	−0.648742	+	0.374551i
$615$		0			0
$616$	−8.67495	−	1.32111i	−0.349524	−	0.0532289i
$617$	21.5108			0.865992			0.432996	−	0.901396i	$-0.357456\pi$
$617$	21.5108			0.865992			0.432996	+	0.901396i	$0.357456\pi$
$618$		0			0
$619$	−29.3551	−	16.9482i	−1.17988	−	0.681206i	−0.223896	−	0.974613i	$-0.571877\pi$
$619$	−29.3551	−	16.9482i	−1.17988	−	0.681206i	−0.955988	+	0.293407i	$0.905211\pi$
$620$	−0.100622	+	0.174283i	−0.00404109	+	0.00699937i
$621$		0			0
$622$	−5.92789			−0.237687
$623$	−3.33410	−	3.89639i	−0.133578	−	0.156106i
$624$		0			0
$625$	0.657638	+	1.13906i	0.0263055	+	0.0455625i
$626$	11.2736	−	19.5264i	0.450582	−	0.780431i
$627$		0			0
$628$	−6.57056	+	3.79351i	−0.262194	+	0.151378i
$629$	−2.52270			−0.100587
$630$		0			0
$631$	0.994535			0.0395918			0.0197959	−	0.999804i	$-0.493698\pi$
$631$	0.994535			0.0395918			0.0197959	+	0.999804i	$0.493698\pi$
$632$	−2.20678	−	3.82226i	−0.0877810	−	0.152041i
$633$		0			0
$634$	15.8096	+	9.12767i	0.627879	+	0.362506i
$635$	−7.02751	−	12.1720i	−0.278878	−	0.483031i
$636$		0			0
$637$	−15.6303	+	6.03325i	−0.619295	+	0.239046i
$638$	−2.56731	−	13.4740i	−0.101641	−	0.533441i
$639$		0			0
$640$	0.712169	−	1.23351i	0.0281509	−	0.0487589i
$641$	7.95305	−	13.7751i	0.314127	−	0.544083i	−0.665125	−	0.746732i	$-0.731622\pi$
$641$	7.95305	−	13.7751i	0.314127	−	0.544083i	0.979251	+	0.202649i	$0.0649550\pi$
$642$		0			0
$643$		−	14.3990i		−	0.567841i	−0.958848	−	0.283920i	$-0.908365\pi$
$643$		−	14.3990i		−	0.567841i	0.958848	−	0.283920i	$-0.0916351\pi$
$644$	1.66705	+	8.94820i	0.0656910	+	0.352608i
$645$		0			0
$646$	−4.35645	+	2.51520i	−0.171402	+	0.0989591i
$647$	21.9409	+	12.6676i	0.862585	+	0.498014i	0.864877	−	0.501984i	$-0.167396\pi$
$647$	21.9409	+	12.6676i	0.862585	+	0.498014i	−0.00229205	+	0.999997i	$0.500730\pi$
$648$		0			0
$649$	11.7968	+	13.6727i	0.463067	+	0.536700i
$650$			7.11163i			0.278941i
$651$		0			0
$652$	7.30550			0.286106
$653$	−23.0579	−	39.9375i	−0.902326	−	1.56287i	−0.824467	−	0.565911i	$-0.808525\pi$
$653$	−23.0579	−	39.9375i	−0.902326	−	1.56287i	−0.0778597	−	0.996964i	$-0.524809\pi$
$654$		0			0
$655$	12.2630	+	7.08007i	0.479157	+	0.276641i
$656$	−4.58889	−	7.94820i	−0.179166	−	0.310325i
$657$		0			0
$658$	−8.89474	−	3.14050i	−0.346753	−	0.122429i
$659$		−	5.72654i		−	0.223074i	−0.993760	−	0.111537i	$-0.964423\pi$
$659$		−	5.72654i		−	0.223074i	0.993760	−	0.111537i	$-0.0355774\pi$
$660$		0			0
$661$	−6.83855	−	3.94824i	−0.265989	−	0.153569i	0.361075	−	0.932537i	$-0.382410\pi$
$661$	−6.83855	−	3.94824i	−0.265989	−	0.153569i	−0.627063	+	0.778968i	$0.715743\pi$
$662$	23.5975	+	13.6240i	0.917142	+	0.529512i
$663$		0			0
$664$		−	3.73539i		−	0.144961i
$665$	5.95522	−	16.8668i	0.230933	−	0.654066i
$666$		0			0
$667$	−12.3217	+	7.11392i	−0.477097	+	0.275452i
$668$	5.57240	−	9.65167i	0.215602	−	0.373434i
$669$		0			0
$670$	−0.808775	−	1.40084i	−0.0312457	−	0.0541191i
$671$	−6.92820	−	36.3612i	−0.267460	−	1.40371i
$672$		0			0
$673$			11.3080i			0.435893i	0.975961	+	0.217947i	$0.0699358\pi$
$673$			11.3080i			0.435893i	−0.975961	+	0.217947i	$0.930064\pi$
$674$	−10.0676	−	17.4376i	−0.387789	−	0.671670i
$675$		0			0
$676$	−3.63565	+	6.29713i	−0.139833	+	0.242197i
$677$	22.4183	+	38.8297i	0.861607	+	1.49235i	0.870377	+	0.492386i	$0.163875\pi$
$677$	22.4183	+	38.8297i	0.861607	+	1.49235i	−0.00876985	+	0.999962i	$0.502792\pi$
$678$		0			0
$679$	49.3969	−	9.20264i	1.89568	−	0.353165i
$680$	−1.50950			−0.0578867
$681$		0			0
$682$	−0.442507	−	0.154204i	−0.0169445	−	0.00590476i
$683$	−21.9999	+	38.1050i	−0.841804	+	1.45805i	0.0465632	+	0.998915i	$0.485173\pi$
$683$	−21.9999	+	38.1050i	−0.841804	+	1.45805i	−0.888368	+	0.459133i	$0.848160\pi$
$684$		0			0
$685$			21.8924i			0.836464i
$686$	−16.3005	−	8.79171i	−0.622355	−	0.335669i
$687$		0			0
$688$	4.96945	−	2.86912i	0.189459	−	0.109384i
$689$	−4.75885	+	8.24256i	−0.181298	+	0.314017i
$690$		0			0
$691$	0.380577	−	0.219726i	0.0144778	−	0.00835878i	−0.492744	−	0.870175i	$-0.664006\pi$
$691$	0.380577	−	0.219726i	0.0144778	−	0.00835878i	0.507221	+	0.861816i	$0.330673\pi$
$692$	−1.62710			−0.0618530
$693$		0			0
$694$	−24.4390			−0.927692
$695$	2.94069	−	1.69781i	0.111547	−	0.0644014i
$696$		0			0
$697$	−4.86327	+	8.42343i	−0.184210	+	0.319060i
$698$	2.65847	−	1.53487i	0.100625	−	0.0580956i
$699$		0			0
$700$	−5.97298	+	5.11101i	−0.225757	+	0.193178i
$701$		−	5.98591i		−	0.226085i	−0.993590	−	0.113042i	$-0.963940\pi$
$701$		−	5.98591i		−	0.226085i	0.993590	−	0.113042i	$-0.0360596\pi$
$702$		0			0
$703$	−5.64932	+	9.78492i	−0.213068	+	0.369045i
$704$	3.13191	+	1.09140i	0.118038	+	0.0411336i
$705$		0			0
$706$	33.6162			1.26516
$707$	14.8689	+	5.24982i	0.559203	+	0.197440i
$708$		0			0
$709$	7.51308	+	13.0130i	0.282160	+	0.488715i	0.971916	−	0.235326i	$-0.0756158\pi$
$709$	7.51308	+	13.0130i	0.282160	+	0.488715i	−0.689757	+	0.724041i	$0.742282\pi$
$710$	7.80274	−	13.5147i	0.292832	−	0.507199i
$711$		0			0
$712$	0.969133	+	1.67859i	0.0363198	+	0.0629077i
$713$			0.486079i			0.0182038i
$714$		0			0
$715$	11.1069	−	2.11629i	0.415375	−	0.0791448i
$716$	8.77643	+	15.2012i	0.327991	+	0.568097i
$717$		0			0
$718$	11.3804	−	19.7114i	0.424712	−	0.735622i
$719$	19.6269	−	11.3316i	0.731961	−	0.422598i	−0.0871782	−	0.996193i	$-0.527785\pi$
$719$	19.6269	−	11.3316i	0.731961	−	0.422598i	0.819139	+	0.573595i	$0.194452\pi$
$720$		0			0
$721$	19.1707	+	22.4038i	0.713953	+	0.834361i
$722$			3.53011i			0.131377i
$723$		0			0
$724$	6.00000	+	3.46410i	0.222988	+	0.128742i
$725$	−10.6418	−	6.14405i	−0.395227	−	0.228184i
$726$		0			0
$727$		−	4.35788i		−	0.161625i	−0.996729	−	0.0808124i	$-0.974249\pi$
$727$		−	4.35788i		−	0.161625i	0.996729	−	0.0808124i	$-0.0257515\pi$
$728$	6.22541	−	1.15980i	0.230729	−	0.0429849i
$729$		0			0
$730$	1.38037	+	2.39087i	0.0510899	+	0.0884902i
$731$	−5.26658	−	3.04066i	−0.194792	−	0.112463i
$732$		0			0
$733$	−8.95832	−	15.5163i	−0.330883	−	0.573106i	0.651802	−	0.758389i	$-0.274013\pi$
$733$	−8.95832	−	15.5163i	−0.330883	−	0.573106i	−0.982685	+	0.185283i	$0.940680\pi$
$734$	−12.8136			−0.472960
$735$		0			0
$736$		−	3.44029i		−	0.126811i
$737$	2.85177	−	2.46052i	0.105046	−	0.0906343i
$738$		0			0
$739$	3.10706	+	1.79386i	0.114295	+	0.0659883i	0.556058	−	0.831144i	$-0.312313\pi$
$739$	3.10706	+	1.79386i	0.114295	+	0.0659883i	−0.441763	+	0.897132i	$0.645647\pi$
$740$	−2.93622	+	1.69523i	−0.107938	+	0.0623178i
$741$		0			0
$742$	−10.3429	+	1.92689i	−0.379701	+	0.0707384i
$743$		−	39.1927i		−	1.43784i	−0.695092	−	0.718921i	$-0.744636\pi$
$743$		−	39.1927i		−	1.43784i	0.695092	−	0.718921i	$-0.255364\pi$
$744$		0			0
$745$	−8.77598	+	15.2004i	−0.321527	+	0.556901i
$746$	7.13940	−	12.3658i	0.261392	−	0.452744i
$747$		0			0
$748$	−0.657893	−	3.45281i	−0.0240550	−	0.126247i
$749$	7.39669	+	8.64414i	0.270269	+	0.315850i
$750$		0			0
$751$	−3.04203	−	5.26894i	−0.111005	−	0.192267i	0.805171	−	0.593043i	$-0.202074\pi$
$751$	−3.04203	−	5.26894i	−0.111005	−	0.192267i	−0.916176	+	0.400777i	$0.868740\pi$
$752$	3.08763	+	1.78265i	0.112594	+	0.0650064i
$753$		0			0
$754$	4.94928	+	8.57240i	0.180242	+	0.312188i
$755$	−2.00875			−0.0731058
$756$		0			0
$757$	−0.922974			−0.0335461			−0.0167730	−	0.999859i	$-0.505339\pi$
$757$	−0.922974			−0.0335461			−0.0167730	+	0.999859i	$0.505339\pi$
$758$	−23.5975	+	13.6240i	−0.857099	+	0.494847i
$759$		0			0
$760$	−3.38037	+	5.85498i	−0.122619	+	0.212382i
$761$	17.7810	+	30.7976i	0.644561	+	1.11641i	0.984403	+	0.175929i	$0.0562930\pi$
$761$	17.7810	+	30.7976i	0.644561	+	1.11641i	−0.339842	+	0.940482i	$0.610374\pi$
$762$		0			0
$763$	−10.0220	+	28.3850i	−0.362820	+	1.02761i
$764$	−23.0071			−0.832366
$765$		0			0
$766$	−6.20654	+	10.7500i	−0.224251	+	0.388415i
$767$	−11.2861	−	6.51602i	−0.407517	−	0.235280i
$768$		0			0
$769$	50.1085			1.80696			0.903478	−	0.428633i	$-0.141005\pi$
$769$	50.1085			1.80696			0.903478	+	0.428633i	$0.141005\pi$
$770$	9.75980	+	7.80763i	0.351719	+	0.281367i
$771$		0			0
$772$	−14.2144	+	8.20668i	−0.511587	+	0.295365i
$773$	30.2054	+	17.4391i	1.08641	+	0.627240i	0.932619	−	0.360863i	$-0.117518\pi$
$773$	30.2054	+	17.4391i	1.08641	+	0.627240i	0.153793	+	0.988103i	$0.450851\pi$
$774$		0			0
$775$	−0.363566	+	0.209905i	−0.0130597	+	0.00754000i
$776$	−18.9915			−0.681755
$777$		0			0
$778$		−	31.5149i		−	1.12987i
$779$	21.7816	+	37.7268i	0.780407	+	1.35170i
$780$		0			0
$781$	34.3142	+	11.9577i	1.22786	+	0.427880i
$782$	−3.15752	+	1.82300i	−0.112913	+	0.0651902i
$783$		0			0
$784$	5.44820	+	4.39513i	0.194578	+	0.156969i
$785$	10.8065			0.385700
$786$		0			0
$787$	5.96056	−	10.3240i	0.212471	−	0.368011i	−0.740016	−	0.672589i	$-0.765182\pi$
$787$	5.96056	−	10.3240i	0.212471	−	0.368011i	0.952487	+	0.304578i	$0.0985155\pi$
$788$	7.49257	+	4.32584i	0.266912	+	0.154102i
$789$		0			0
$790$			6.28640i			0.223660i
$791$	−4.01765	−	21.5655i	−0.142851	−	0.766780i
$792$		0			0
$793$	13.3562	+	23.1337i	0.474294	+	0.821501i
$794$	8.16483	−	14.1419i	0.289759	−	0.501877i
$795$		0			0
$796$	−11.0608	+	6.38595i	−0.392039	+	0.226344i
$797$		−	10.4434i		−	0.369923i	−0.982746	−	0.184961i	$-0.940784\pi$
$797$		−	10.4434i		−	0.369923i	0.982746	−	0.184961i	$-0.0592160\pi$
$798$		0			0
$799$		−	3.77847i		−	0.133673i
$800$	2.57319	−	1.48563i	0.0909760	−	0.0525250i
$801$		0			0
$802$	−15.8977	−	9.17852i	−0.561366	−	0.324105i
$803$	−4.86724	+	4.19947i	−0.171761	+	0.148196i
$804$		0			0
$805$	4.31630	−	12.2249i	0.152130	−	0.430872i
$806$	0.338173			0.0119116
$807$		0			0
$808$	−5.16145	−	2.97996i	−0.181579	−	0.104835i
$809$	26.8647	+	15.5104i	0.944513	+	0.545315i	0.891372	−	0.453272i	$-0.149743\pi$
$809$	26.8647	+	15.5104i	0.944513	+	0.545315i	0.0531410	+	0.998587i	$0.483077\pi$
$810$		0			0
$811$	26.1419			0.917968			0.458984	−	0.888445i	$-0.348214\pi$
$811$	26.1419			0.917968			0.458984	+	0.888445i	$0.348214\pi$
$812$	−3.64290	+	10.3177i	−0.127841	+	0.362080i
$813$		0			0
$814$	−5.15735	−	5.97743i	−0.180765	−	0.209509i
$815$	−9.01143	−	5.20275i	−0.315657	−	0.182244i
$816$		0			0
$817$	−23.5880	+	13.6185i	−0.825238	+	0.476451i
$818$		−	33.5404i		−	1.17271i
$819$		0			0
$820$			13.0723i			0.456503i
$821$	−8.69274	+	5.01876i	−0.303379	+	0.175156i	−0.643960	−	0.765059i	$-0.722710\pi$
$821$	−8.69274	+	5.01876i	−0.303379	+	0.175156i	0.340581	+	0.940215i	$0.389376\pi$
$822$		0			0
$823$	−27.0320	+	46.8209i	−0.942278	+	1.63207i	−0.181166	+	0.983453i	$0.557987\pi$
$823$	−27.0320	+	46.8209i	−0.942278	+	1.63207i	−0.761112	+	0.648621i	$0.775346\pi$
$824$	−5.57240	−	9.65167i	−0.194124	−	0.336232i
$825$		0			0
$826$	−2.63838	−	14.1620i	−0.0918011	−	0.492759i
$827$		−	27.7091i		−	0.963541i	−0.876297	−	0.481771i	$-0.839994\pi$
$827$		−	27.7091i		−	0.963541i	0.876297	−	0.481771i	$-0.160006\pi$
$828$		0			0
$829$	−1.30844	−	0.755429i	−0.0454440	−	0.0262371i	0.477106	−	0.878846i	$-0.341686\pi$
$829$	−1.30844	−	0.755429i	−0.0454440	−	0.0262371i	−0.522550	+	0.852609i	$0.675019\pi$
$830$	−2.66023	+	4.60765i	−0.0923379	+	0.159934i
$831$		0			0
$832$	−2.39347			−0.0829786
$833$	1.14690	−	7.32935i	0.0397377	−	0.253947i
$834$		0			0
$835$	−13.7472	+	7.93697i	−0.475743	+	0.274670i
$836$	−14.8659	−	5.18042i	−0.514147	−	0.179168i
$837$		0			0
$838$	17.7974	+	30.8260i	0.614800	+	1.06487i
$839$		−	9.67749i		−	0.334104i	−0.985948	−	0.167052i	$-0.946575\pi$
$839$		−	9.67749i		−	0.334104i	0.985948	−	0.167052i	$-0.0534248\pi$
$840$		0			0
$841$	11.8964			0.410220
$842$	−1.35287	+	0.781077i	−0.0466228	+	0.0269177i
$843$		0			0
$844$	−19.2419	−	11.1093i	−0.662333	−	0.382398i
$845$	8.96924	−	5.17839i	0.308551	−	0.178142i
$846$		0			0
$847$	−13.6054	+	25.7273i	−0.467487	+	0.884000i
$848$	3.97653			0.136554
$849$		0			0
$850$	−2.72704	−	1.57446i	−0.0935369	−	0.0540035i
$851$	−4.09459	+	7.09203i	−0.140361	+	0.243112i
$852$		0			0
$853$	2.71419			0.0929320			0.0464660	−	0.998920i	$-0.485204\pi$
$853$	2.71419			0.0929320			0.0464660	+	0.998920i	$0.485204\pi$
$854$	−9.83080	+	27.8435i	−0.336403	+	0.952785i
$855$		0			0
$856$	−2.15002	−	3.72394i	−0.0734861	−	0.127282i
$857$	8.74704	−	15.1503i	0.298793	−	0.517525i	−0.677067	−	0.735921i	$-0.736749\pi$
$857$	8.74704	−	15.1503i	0.298793	−	0.517525i	0.975860	+	0.218397i	$0.0700826\pi$
$858$		0			0
$859$	40.8720	−	23.5975i	1.39454	−	0.805136i	0.400723	−	0.916199i	$-0.368759\pi$
$859$	40.8720	−	23.5975i	1.39454	−	0.805136i	0.993813	+	0.111063i	$0.0354257\pi$
$860$	−8.17318			−0.278703
$861$		0			0
$862$	−10.7033			−0.364555
$863$	−3.72585	−	6.45336i	−0.126829	−	0.219675i	0.795617	−	0.605800i	$-0.207147\pi$
$863$	−3.72585	−	6.45336i	−0.126829	−	0.219675i	−0.922447	+	0.386125i	$0.873813\pi$
$864$		0			0
$865$	2.00705	+	1.15877i	0.0682416	+	0.0393993i
$866$	−5.07303	−	8.78675i	−0.172389	−	0.298586i
$867$		0			0
$868$	0.243039	+	0.284028i	0.00824929	+	0.00964053i
$869$	−14.3794	+	2.73983i	−0.487789	+	0.0929424i
$870$		0			0
$871$	−1.35907	+	2.35398i	−0.0460504	+	0.0797617i
$872$	5.68880	−	9.85329i	0.192647	−	0.333674i
$873$		0			0
$874$			16.3297i			0.552359i
$875$	29.5311	−	5.50165i	0.998335	−	0.185990i
$876$		0			0
$877$	−20.6239	+	11.9072i	−0.696420	+	0.402078i	−0.806013	−	0.591898i	$-0.798379\pi$
$877$	−20.6239	+	11.9072i	−0.696420	+	0.402078i	0.109593	+	0.993977i	$0.465045\pi$
$878$	18.0622	+	10.4282i	0.609569	+	0.351935i
$879$		0			0
$880$	−3.08599	−	3.57670i	−0.104029	−	0.120571i
$881$			42.1622i			1.42048i	0.703960	+	0.710240i	$0.251414\pi$
$881$			42.1622i			1.42048i	−0.703960	+	0.710240i	$0.748586\pi$
$882$		0			0
$883$	−2.28264			−0.0768170			−0.0384085	−	0.999262i	$-0.512229\pi$
$883$	−2.28264			−0.0768170			−0.0384085	+	0.999262i	$0.512229\pi$
$884$	1.26829	+	2.19674i	0.0426572	+	0.0738844i
$885$		0			0
$886$	19.1838	+	11.0758i	0.644494	+	0.372099i
$887$	−23.7065	−	41.0608i	−0.795985	−	1.37869i	−0.922212	−	0.386685i	$-0.873620\pi$
$887$	−23.7065	−	41.0608i	−0.795985	−	1.37869i	0.126227	−	0.992001i	$-0.459713\pi$
$888$		0			0
$889$	−25.6660	+	4.78159i	−0.860811	+	0.160369i
$890$		−	2.76074i		−	0.0925403i
$891$		0			0
$892$	−5.18314	−	2.99249i	−0.173544	−	0.100196i
$893$	−14.6557	−	8.46149i	−0.490435	−	0.283153i
$894$		0			0
$895$		−	25.0012i		−	0.835698i
$896$	−1.72015	−	2.01025i	−0.0574661	−	0.0671577i
$897$		0			0
$898$	31.3312	−	18.0891i	1.04554	−	0.603641i
$899$	−0.292163	+	0.506041i	−0.00974418	+	0.0168774i
$900$		0			0
$901$	−2.10714	−	3.64968i	−0.0701991	−	0.121588i
$902$	−29.9013	+	5.69735i	−0.995606	+	0.189701i
$903$		0			0
$904$			8.29122i			0.275762i
$905$	−4.93405	−	8.54602i	−0.164013	−	0.284079i
$906$		0			0
$907$	−3.05727	+	5.29534i	−0.101515	+	0.175829i	−0.912309	−	0.409503i	$-0.865702\pi$
$907$	−3.05727	+	5.29534i	−0.101515	+	0.175829i	0.810794	+	0.585332i	$0.199036\pi$
$908$	2.52071	+	4.36600i	0.0836528	+	0.144891i
$909$		0			0
$910$	−8.50509	−	3.00292i	−0.281941	−	0.0995459i
$911$	−45.2069			−1.49777			−0.748886	−	0.662699i	$-0.769411\pi$
$911$	−45.2069			−1.49777			−0.748886	+	0.662699i	$0.769411\pi$
$912$		0			0
$913$	−11.6989	−	4.07680i	−0.387177	−	0.134922i
$914$	−16.5111	+	28.5981i	−0.546140	+	0.945942i
$915$		0			0
$916$		−	21.2276i		−	0.701381i
$917$	19.9850	−	17.1009i	0.659963	−	0.564723i
$918$		0			0
$919$	21.5385	−	12.4352i	0.710489	−	0.410201i	−0.100753	−	0.994911i	$-0.532125\pi$
$919$	21.5385	−	12.4352i	0.710489	−	0.410201i	0.811242	+	0.584711i	$0.198792\pi$
$920$	−2.45007	+	4.24364i	−0.0807764	+	0.139909i
$921$		0			0
$922$	31.8739	−	18.4024i	1.04971	−	0.606051i
$923$	−26.2236			−0.863160
$924$		0			0
$925$	−7.07271			−0.232549
$926$	−18.2641	+	10.5448i	−0.600194	+	0.346522i
$927$		0			0
$928$	2.06783	−	3.58158i	0.0678797	−	0.117571i
$929$	16.0270	−	9.25316i	0.525827	−	0.303586i	−0.213488	−	0.976946i	$-0.568483\pi$
$929$	16.0270	−	9.25316i	0.525827	−	0.303586i	0.739316	+	0.673359i	$0.235149\pi$
$930$		0			0
$931$	−25.8604	−	20.8619i	−0.847539	−	0.683720i
$932$			14.6978i			0.481443i
$933$		0			0
$934$	−2.31457	+	4.00895i	−0.0757351	+	0.131177i
$935$	−1.64747	+	4.72762i	−0.0538779	+	0.154610i
$936$		0			0
$937$	−48.2698			−1.57691			−0.788453	−	0.615094i	$-0.789118\pi$
$937$	−48.2698			−1.57691			−0.788453	+	0.615094i	$0.789118\pi$
$938$	−2.95383	+	0.550298i	−0.0964458	+	0.0179679i
$939$		0			0
$940$	−2.53909	−	4.39783i	−0.0828159	−	0.143441i
$941$	−8.14181	+	14.1020i	−0.265415	+	0.459713i	−0.967672	−	0.252211i	$-0.918842\pi$
$941$	−8.14181	+	14.1020i	−0.265415	+	0.459713i	0.702257	+	0.711924i	$0.252176\pi$
$942$		0			0
$943$	15.7871	+	27.3441i	0.514100	+	0.890447i
$944$			5.44483i			0.177214i
$945$		0			0
$946$	−3.56215	−	18.6952i	−0.115816	−	0.607834i
$947$	25.9080	+	44.8740i	0.841897	+	1.45821i	0.888289	+	0.459285i	$0.151894\pi$
$947$	25.9080	+	44.8740i	0.841897	+	1.45821i	−0.0463918	+	0.998923i	$0.514772\pi$
$948$		0			0
$949$	2.31959	−	4.01765i	0.0752971	−	0.130418i
$950$	−12.2139	+	7.05168i	−0.396270	+	0.228787i
$951$		0			0
$952$	−0.933520	+	2.64398i	−0.0302556	+	0.0856920i
$953$			9.07156i			0.293857i	0.989147	+	0.146928i	$0.0469387\pi$
$953$			9.07156i			0.293857i	−0.989147	+	0.146928i	$0.953061\pi$
$954$		0			0
$955$	28.3795	+	16.3849i	0.918339	+	0.530203i
$956$	18.2143	+	10.5160i	0.589092	+	0.340112i
$957$		0			0
$958$			30.5849i			0.988153i
$959$	38.3458	+	13.5389i	1.23825	+	0.437193i
$960$		0			0
$961$	−15.4900	−	26.8295i	−0.499678	−	0.865468i
$962$	4.93405	+	2.84867i	0.159080	+	0.0918450i
$963$		0			0
$964$	9.15656	+	15.8596i	0.294913	+	0.510804i
$965$	23.3782			0.752570
$966$		0			0
$967$			6.46214i			0.207809i	0.994587	+	0.103904i	$0.0331336\pi$
$967$			6.46214i			0.207809i	−0.994587	+	0.103904i	$0.966866\pi$
$968$	6.83632	−	8.61770i	0.219728	−	0.276983i
$969$		0			0
$970$	23.4262	+	13.5251i	0.752171	+	0.434266i
$971$	−23.2226	+	13.4076i	−0.745250	+	0.430270i	−0.823975	−	0.566626i	$-0.808248\pi$
$971$	−23.2226	+	13.4076i	−0.745250	+	0.430270i	0.0787253	+	0.996896i	$0.474915\pi$
$972$		0			0
$973$	−1.15520	−	6.20076i	−0.0370341	−	0.198787i
$974$		−	31.0586i		−	0.995183i
$975$		0			0
$976$	5.58028	−	9.66532i	0.178620	−	0.309379i
$977$	−10.9940	+	19.0422i	−0.351730	+	0.609215i	−0.986553	−	0.163443i	$-0.947740\pi$
$977$	−10.9940	+	19.0422i	−0.351730	+	0.609215i	0.634822	+	0.772658i	$0.281073\pi$
$978$		0			0
$979$	6.31489	−	1.20323i	0.201825	−	0.0384553i
$980$	−3.59035	−	9.30148i	−0.114689	−	0.297125i
$981$		0			0
$982$	16.3660	+	28.3467i	0.522260	+	0.904581i
$983$	−28.9179	−	16.6957i	−0.922337	−	0.532512i	−0.0379571	−	0.999279i	$-0.512085\pi$
$983$	−28.9179	−	16.6957i	−0.922337	−	0.532512i	−0.884380	+	0.466768i	$0.845418\pi$
$984$		0			0
$985$	−6.16145	−	10.6719i	−0.196320	−	0.340036i
$986$	−4.38293			−0.139581
$987$		0			0
$988$	11.3608			0.361436
$989$	−17.0964	+	9.87060i	−0.543633	+	0.313867i
$990$		0			0
$991$	20.9097	−	36.2166i	0.664218	−	1.15046i	−0.315279	−	0.948999i	$-0.602098\pi$
$991$	20.9097	−	36.2166i	0.664218	−	1.15046i	0.979497	−	0.201460i	$-0.0645687\pi$
$992$	−0.0706450	−	0.122361i	−0.00224298	−	0.00388496i
$993$		0			0
$994$	−18.8465	−	22.0249i	−0.597773	−	0.698587i
$995$	18.1915			0.576709
$996$		0			0
$997$	−17.8703	+	30.9523i	−0.565959	+	0.980269i	0.431001	+	0.902351i	$0.358161\pi$
$997$	−17.8703	+	30.9523i	−0.565959	+	0.980269i	−0.996960	+	0.0779180i	$0.975173\pi$
$998$	32.9147	+	19.0033i	1.04190	+	0.601539i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.d.703.13	yes	32
3.2	odd	2	inner	1386.2.bk.d.703.4	yes	32
7.5	odd	6	inner	1386.2.bk.d.901.3	yes	32
11.10	odd	2	inner	1386.2.bk.d.703.3	✓	32
21.5	even	6	inner	1386.2.bk.d.901.14	yes	32
33.32	even	2	inner	1386.2.bk.d.703.14	yes	32
77.54	even	6	inner	1386.2.bk.d.901.13	yes	32
231.131	odd	6	inner	1386.2.bk.d.901.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bk.d.703.3	✓	32	11.10	odd	2	inner
1386.2.bk.d.703.4	yes	32	3.2	odd	2	inner
1386.2.bk.d.703.13	yes	32	1.1	even	1	trivial
1386.2.bk.d.703.14	yes	32	33.32	even	2	inner
1386.2.bk.d.901.3	yes	32	7.5	odd	6	inner
1386.2.bk.d.901.4	yes	32	231.131	odd	6	inner
1386.2.bk.d.901.13	yes	32	77.54	even	6	inner
1386.2.bk.d.901.14	yes	32	21.5	even	6	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23351 + 0.712169i) q^{5} +(0.484566 + 2.60100i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.23351 + 0.712169i) q^{5} +(0.484566 + 2.60100i) q^{7} -1.00000i q^{8} +(-0.712169 + 1.23351i) q^{10} +(-3.13191 - 1.09140i) q^{11} +2.39347 q^{13} +(1.72015 + 2.01025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.529896 + 0.917806i) q^{17} +(2.37329 + 4.11067i) q^{19} +1.42434i q^{20} +(-3.25801 + 0.620776i) q^{22} +(1.72015 + 2.97938i) q^{23} +(-1.48563 + 2.57319i) q^{25} +(2.07281 - 1.19674i) q^{26} +(2.49481 + 0.880853i) q^{28} +4.13565i q^{29} +(0.122361 + 0.0706450i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.05979i q^{34} +(-2.45007 - 2.86327i) q^{35} +(1.19019 + 2.06146i) q^{37} +(4.11067 + 2.37329i) q^{38} +(0.712169 + 1.23351i) q^{40} +9.17779 q^{41} +5.73823i q^{43} +(-2.51113 + 2.16661i) q^{44} +(2.97938 + 1.72015i) q^{46} +(-3.08763 + 1.78265i) q^{47} +(-6.53039 + 2.52071i) q^{49} +2.97126i q^{50} +(1.19674 - 2.07281i) q^{52} +(-1.98826 + 3.44377i) q^{53} +(4.64051 - 0.884194i) q^{55} +(2.60100 - 0.484566i) q^{56} +(2.06783 + 3.58158i) q^{58} +(-4.71536 - 2.72242i) q^{59} +(5.58028 + 9.66532i) q^{61} +0.141290 q^{62} -1.00000 q^{64} +(-2.95237 + 1.70455i) q^{65} +(-0.567825 + 0.983502i) q^{67} +(0.529896 + 0.917806i) q^{68} +(-3.55346 - 1.25463i) q^{70} -10.9563 q^{71} +(0.969133 - 1.67859i) q^{73} +(2.06146 + 1.19019i) q^{74} +4.74659 q^{76} +(1.32111 - 8.67495i) q^{77} +(3.82226 - 2.20678i) q^{79} +(1.23351 + 0.712169i) q^{80} +(7.94820 - 4.58889i) q^{82} +3.73539 q^{83} -1.50950i q^{85} +(2.86912 + 4.96945i) q^{86} +(-1.09140 + 3.13191i) q^{88} +(-1.67859 + 0.969133i) q^{89} +(1.15980 + 6.22541i) q^{91} +3.44029 q^{92} +(-1.78265 + 3.08763i) q^{94} +(-5.85498 - 3.38037i) q^{95} -18.9915i q^{97} +(-4.39513 + 5.44820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} + 20 q^{22} + 36 q^{25} + 12 q^{31} - 20 q^{37} - 44 q^{49} - 32 q^{64} + 48 q^{67} + 36 q^{70} + 72 q^{82} + 10 q^{88} + 144 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 + 36 * q^25 + 12 * q^31 - 20 * q^37 - 44 * q^49 - 32 * q^64 + 48 * q^67 + 36 * q^70 + 72 * q^82 + 10 * q^88 + 144 * q^91

Introduction

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