LMFDB - Embedded newform 672.2.bk.a.625.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(529,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("672.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bk (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			625.3
Character	$\chi$	$=$	672.625
Dual form			672.2.bk.a.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(-1.23074 - 0.710569i) q^{5} +(-1.39545 + 2.24783i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(-1.23074 - 0.710569i) q^{5} +(-1.39545 + 2.24783i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.832525 - 0.480658i) q^{11} -3.57192i q^{13} +1.42114 q^{15} +(2.43064 + 4.21000i) q^{17} +(-6.28094 - 3.62630i) q^{19} +(0.0845812 - 2.64440i) q^{21} +(2.72132 - 4.71346i) q^{23} +(-1.49018 - 2.58107i) q^{25} +1.00000i q^{27} -6.78641i q^{29} +(-3.67285 - 6.36156i) q^{31} +(-0.480658 + 0.832525i) q^{33} +(3.31467 - 1.77493i) q^{35} +(2.21085 + 1.27644i) q^{37} +(1.78596 + 3.09338i) q^{39} +2.20216 q^{41} -4.45897i q^{43} +(-1.23074 + 0.710569i) q^{45} +(-0.211793 + 0.366836i) q^{47} +(-3.10544 - 6.27345i) q^{49} +(-4.21000 - 2.43064i) q^{51} +(-8.41117 + 4.85619i) q^{53} -1.36616 q^{55} +7.25260 q^{57} +(-6.43952 + 3.71786i) q^{59} +(1.67889 + 0.969306i) q^{61} +(1.24895 + 2.33241i) q^{63} +(-2.53810 + 4.39612i) q^{65} +(9.13752 - 5.27555i) q^{67} +5.44264i q^{69} +8.12089 q^{71} +(-4.99925 - 8.65896i) q^{73} +(2.58107 + 1.49018i) q^{75} +(-0.0813093 + 2.54211i) q^{77} +(-0.139607 + 0.241807i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.69361i q^{83} -6.90856i q^{85} +(3.39320 + 5.87720i) q^{87} +(-1.07402 + 1.86026i) q^{89} +(8.02906 + 4.98444i) q^{91} +(6.36156 + 3.67285i) q^{93} +(5.15348 + 8.92608i) q^{95} -9.44983 q^{97} -0.961317i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^9	$ 32 q + 16 q^{9} + 8 q^{23} + 16 q^{25} + 24 q^{31} + 24 q^{47} + 8 q^{49} + 64 q^{55} - 16 q^{57} + 80 q^{71} + 8 q^{73} - 8 q^{79} - 16 q^{81} - 24 q^{87} - 24 q^{95} - 48 q^{97}+O(q^{100}) $ 32 * q + 16 * q^9 + 8 * q^23 + 16 * q^25 + 24 * q^31 + 24 * q^47 + 8 * q^49 + 64 * q^55 - 16 * q^57 + 80 * q^71 + 8 * q^73 - 8 * q^79 - 16 * q^81 - 24 * q^87 - 24 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$	−1.23074	−	0.710569i	−0.550405	−	0.317776i	0.198881	−	0.980024i	$-0.436269\pi$
$5$	−1.23074	−	0.710569i	−0.550405	−	0.317776i	−0.749285	+	0.662248i	$0.769603\pi$
$6$		0			0
$7$	−1.39545	+	2.24783i	−0.527430	+	0.849598i
$7$	−1.39545	+	2.24783i	−0.527430	+	0.849598i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	0.832525	−	0.480658i	0.251016	−	0.144924i	−0.369214	−	0.929345i	$-0.620373\pi$
$11$	0.832525	−	0.480658i	0.251016	−	0.144924i	0.620229	+	0.784421i	$0.287040\pi$
$12$		0			0
$13$		−	3.57192i		−	0.990673i	−0.868701	−	0.495337i	$-0.835045\pi$
$13$		−	3.57192i		−	0.990673i	0.868701	−	0.495337i	$-0.164955\pi$
$14$		0			0
$15$	1.42114			0.366936
$16$		0			0
$17$	2.43064	+	4.21000i	0.589518	+	1.02107i	0.994296	+	0.106659i	$0.0340154\pi$
$17$	2.43064	+	4.21000i	0.589518	+	1.02107i	−0.404778	+	0.914415i	$0.632651\pi$
$18$		0			0
$19$	−6.28094	−	3.62630i	−1.44095	−	0.831931i	−0.443033	−	0.896505i	$-0.646098\pi$
$19$	−6.28094	−	3.62630i	−1.44095	−	0.831931i	−0.997913	+	0.0645747i	$0.979431\pi$
$20$		0			0
$21$	0.0845812	−	2.64440i	0.0184571	−	0.577055i
$22$		0			0
$23$	2.72132	−	4.71346i	0.567434	−	0.982824i	−0.429385	−	0.903122i	$-0.641270\pi$
$23$	2.72132	−	4.71346i	0.567434	−	0.982824i	0.996819	−	0.0797027i	$-0.0253971\pi$
$24$		0			0
$25$	−1.49018	−	2.58107i	−0.298037	−	0.516214i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	6.78641i		−	1.26020i	−0.776512	−	0.630102i	$-0.783013\pi$
$29$		−	6.78641i		−	1.26020i	0.776512	−	0.630102i	$-0.216987\pi$
$30$		0			0
$31$	−3.67285	−	6.36156i	−0.659663	−	1.14257i	−0.980703	−	0.195504i	$-0.937366\pi$
$31$	−3.67285	−	6.36156i	−0.659663	−	1.14257i	0.321040	−	0.947066i	$-0.395968\pi$
$32$		0			0
$33$	−0.480658	+	0.832525i	−0.0836719	+	0.144924i
$34$		0			0
$35$	3.31467	−	1.77493i	0.560282	−	0.300018i
$36$		0			0
$37$	2.21085	+	1.27644i	0.363462	+	0.209845i	0.670598	−	0.741821i	$-0.266037\pi$
$37$	2.21085	+	1.27644i	0.363462	+	0.209845i	−0.307136	+	0.951666i	$0.599371\pi$
$38$		0			0
$39$	1.78596	+	3.09338i	0.285983	+	0.495337i
$40$		0			0
$41$	2.20216			0.343920			0.171960	−	0.985104i	$-0.444990\pi$
$41$	2.20216			0.343920			0.171960	+	0.985104i	$0.444990\pi$
$42$		0			0
$43$		−	4.45897i		−	0.679986i	−0.940428	−	0.339993i	$-0.889575\pi$
$43$		−	4.45897i		−	0.679986i	0.940428	−	0.339993i	$-0.110425\pi$
$44$		0			0
$45$	−1.23074	+	0.710569i	−0.183468	+	0.105925i
$46$		0			0
$47$	−0.211793	+	0.366836i	−0.0308932	+	0.0535086i	−0.881059	−	0.473007i	$-0.843169\pi$
$47$	−0.211793	+	0.366836i	−0.0308932	+	0.0535086i	0.850165	+	0.526516i	$0.176502\pi$
$48$		0			0
$49$	−3.10544	−	6.27345i	−0.443635	−	0.896208i
$50$		0			0
$51$	−4.21000	−	2.43064i	−0.589518	−	0.340358i
$52$		0			0
$53$	−8.41117	+	4.85619i	−1.15536	+	0.667049i	−0.950188	−	0.311676i	$-0.899110\pi$
$53$	−8.41117	+	4.85619i	−1.15536	+	0.667049i	−0.205175	+	0.978725i	$0.565776\pi$
$54$		0			0
$55$	−1.36616			−0.184214
$56$		0			0
$57$	7.25260			0.960631
$58$		0			0
$59$	−6.43952	+	3.71786i	−0.838354	+	0.484024i	−0.856704	−	0.515808i	$-0.827492\pi$
$59$	−6.43952	+	3.71786i	−0.838354	+	0.484024i	0.0183503	+	0.999832i	$0.494159\pi$
$60$		0			0
$61$	1.67889	+	0.969306i	0.214960	+	0.124107i	0.603614	−	0.797277i	$-0.293727\pi$
$61$	1.67889	+	0.969306i	0.214960	+	0.124107i	−0.388655	+	0.921384i	$0.627060\pi$
$62$		0			0
$63$	1.24895	+	2.33241i	0.157353	+	0.293856i
$64$		0			0
$65$	−2.53810	+	4.39612i	−0.314812	+	0.545271i
$66$		0			0
$67$	9.13752	−	5.27555i	1.11633	−	0.644511i	0.175866	−	0.984414i	$-0.443728\pi$
$67$	9.13752	−	5.27555i	1.11633	−	0.644511i	0.940460	+	0.339903i	$0.110394\pi$
$68$		0			0
$69$			5.44264i			0.655216i
$70$		0			0
$71$	8.12089			0.963772			0.481886	−	0.876234i	$-0.339952\pi$
$71$	8.12089			0.963772			0.481886	+	0.876234i	$0.339952\pi$
$72$		0			0
$73$	−4.99925	−	8.65896i	−0.585118	−	1.01345i	−0.994861	−	0.101253i	$-0.967715\pi$
$73$	−4.99925	−	8.65896i	−0.585118	−	1.01345i	0.409743	−	0.912201i	$-0.365619\pi$
$74$		0			0
$75$	2.58107	+	1.49018i	0.298037	+	0.172071i
$76$		0			0
$77$	−0.0813093	+	2.54211i	−0.00926606	+	0.289700i
$78$		0			0
$79$	−0.139607	+	0.241807i	−0.0157071	+	0.0272054i	−0.873772	−	0.486336i	$-0.838333\pi$
$79$	−0.139607	+	0.241807i	−0.0157071	+	0.0272054i	0.858065	+	0.513541i	$0.171667\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	6.69361i		−	0.734719i	−0.930079	−	0.367359i	$-0.880262\pi$
$83$		−	6.69361i		−	0.734719i	0.930079	−	0.367359i	$-0.119738\pi$
$84$		0			0
$85$		−	6.90856i		−	0.749339i
$86$		0			0
$87$	3.39320	+	5.87720i	0.363790	+	0.630102i
$88$		0			0
$89$	−1.07402	+	1.86026i	−0.113846	+	0.197187i	−0.917318	−	0.398155i	$-0.869650\pi$
$89$	−1.07402	+	1.86026i	−0.113846	+	0.197187i	0.803472	+	0.595343i	$0.202984\pi$
$90$		0			0
$91$	8.02906	+	4.98444i	0.841674	+	0.522511i
$92$		0			0
$93$	6.36156	+	3.67285i	0.659663	+	0.380857i
$94$		0			0
$95$	5.15348	+	8.92608i	0.528735	+	0.915797i
$96$		0			0
$97$	−9.44983			−0.959485			−0.479742	−	0.877409i	$-0.659270\pi$
$97$	−9.44983			−0.959485			−0.479742	+	0.877409i	$0.659270\pi$
$98$		0			0
$99$		−	0.961317i		−	0.0966160i
$100$		0			0
$101$	−3.08218	+	1.77950i	−0.306689	+	0.177067i	−0.645444	−	0.763808i	$-0.723328\pi$
$101$	−3.08218	+	1.77950i	−0.306689	+	0.177067i	0.338755	+	0.940875i	$0.389994\pi$
$102$		0			0
$103$	0.618710	−	1.07164i	0.0609633	−	0.105591i	−0.833933	−	0.551866i	$-0.813916\pi$
$103$	0.618710	−	1.07164i	0.0609633	−	0.105591i	0.894896	+	0.446274i	$0.147249\pi$
$104$		0			0
$105$	−1.98313	+	3.19447i	−0.193533	+	0.311749i
$106$		0			0
$107$	14.4424	+	8.33834i	1.39620	+	0.806098i	0.993992	−	0.109450i	$-0.0349090\pi$
$107$	14.4424	+	8.33834i	1.39620	+	0.806098i	0.402210	+	0.915548i	$0.368242\pi$
$108$		0			0
$109$	−8.84714	+	5.10790i	−0.847403	+	0.489248i	−0.859774	−	0.510675i	$-0.829395\pi$
$109$	−8.84714	+	5.10790i	−0.847403	+	0.489248i	0.0123709	+	0.999923i	$0.496062\pi$
$110$		0			0
$111$	−2.55287			−0.242308
$112$		0			0
$113$	12.4039			1.16686			0.583432	−	0.812162i	$-0.301709\pi$
$113$	12.4039			1.16686			0.583432	+	0.812162i	$0.301709\pi$
$114$		0			0
$115$	−6.69848	+	3.86737i	−0.624636	+	0.360634i
$116$		0			0
$117$	−3.09338	−	1.78596i	−0.285983	−	0.165112i
$118$		0			0
$119$	−12.8552	−	0.411173i	−1.17843	−	0.0376922i
$120$		0			0
$121$	−5.03793	+	8.72596i	−0.457994	+	0.793269i
$122$		0			0
$123$	−1.90713	+	1.10108i	−0.171960	+	0.0992812i
$124$		0			0
$125$			11.3412i			1.01439i
$126$		0			0
$127$	−17.3710			−1.54142			−0.770712	−	0.637184i	$-0.780099\pi$
$127$	−17.3710			−1.54142			−0.770712	+	0.637184i	$0.780099\pi$
$128$		0			0
$129$	2.22948	+	3.86158i	0.196295	+	0.339993i
$130$		0			0
$131$	−12.8469	−	7.41718i	−1.12244	−	0.648042i	−0.180418	−	0.983590i	$-0.557745\pi$
$131$	−12.8469	−	7.41718i	−1.12244	−	0.648042i	−0.942023	+	0.335548i	$0.891079\pi$
$132$		0			0
$133$	16.9160	−	9.05814i	1.46681	−	0.785440i
$134$		0			0
$135$	0.710569	−	1.23074i	0.0611561	−	0.105925i
$136$		0			0
$137$	−6.93006	−	12.0032i	−0.592075	−	1.02550i	−0.993953	−	0.109810i	$-0.964976\pi$
$137$	−6.93006	−	12.0032i	−0.592075	−	1.02550i	0.401878	−	0.915693i	$-0.368358\pi$
$138$		0			0
$139$			20.8746i			1.77056i	0.465055	+	0.885282i	$0.346035\pi$
$139$			20.8746i			1.77056i	−0.465055	+	0.885282i	$0.653965\pi$
$140$		0			0
$141$		−	0.423586i		−	0.0356724i
$142$		0			0
$143$	−1.71687	−	2.97371i	−0.143572	−	0.248675i
$144$		0			0
$145$	−4.82221	+	8.35232i	−0.400463	+	0.693622i
$146$		0			0
$147$	5.82612	+	3.88025i	0.480530	+	0.320037i
$148$		0			0
$149$	17.9443	+	10.3601i	1.47005	+	0.848736i	0.999435	−	0.0336002i	$-0.0106973\pi$
$149$	17.9443	+	10.3601i	1.47005	+	0.848736i	0.470619	+	0.882337i	$0.344031\pi$
$150$		0			0
$151$	−1.23596	−	2.14074i	−0.100581	−	0.174211i	0.811343	−	0.584570i	$-0.198737\pi$
$151$	−1.23596	−	2.14074i	−0.100581	−	0.174211i	−0.911924	+	0.410359i	$0.865403\pi$
$152$		0			0
$153$	4.86129			0.393012
$154$		0			0
$155$			10.4392i			0.838501i
$156$		0			0
$157$	−2.59394	+	1.49761i	−0.207019	+	0.119522i	−0.599925	−	0.800056i	$-0.704803\pi$
$157$	−2.59394	+	1.49761i	−0.207019	+	0.119522i	0.392906	+	0.919578i	$0.371470\pi$
$158$		0			0
$159$	4.85619	−	8.41117i	0.385121	−	0.667049i
$160$		0			0
$161$	6.79758	+	12.6944i	0.535724	+	1.00046i
$162$		0			0
$163$	1.95349	+	1.12785i	0.153009	+	0.0883400i	0.574550	−	0.818470i	$-0.305177\pi$
$163$	1.95349	+	1.12785i	0.153009	+	0.0883400i	−0.421541	+	0.906810i	$0.638510\pi$
$164$		0			0
$165$	1.18313	−	0.683082i	0.0921068	−	0.0531779i
$166$		0			0
$167$	2.45671			0.190106			0.0950529	−	0.995472i	$-0.469698\pi$
$167$	2.45671			0.190106			0.0950529	+	0.995472i	$0.469698\pi$
$168$		0			0
$169$	0.241366			0.0185666
$170$		0			0
$171$	−6.28094	+	3.62630i	−0.480315	+	0.277310i
$172$		0			0
$173$	7.62911	+	4.40467i	0.580031	+	0.334881i	0.761146	−	0.648581i	$-0.224637\pi$
$173$	7.62911	+	4.40467i	0.580031	+	0.334881i	−0.181115	+	0.983462i	$0.557971\pi$
$174$		0			0
$175$	7.88128	+	0.252083i	0.595768	+	0.0190557i
$176$		0			0
$177$	3.71786	−	6.43952i	0.279451	−	0.484024i
$178$		0			0
$179$	−12.0819	+	6.97551i	−0.903046	+	0.521374i	−0.878187	−	0.478317i	$-0.841247\pi$
$179$	−12.0819	+	6.97551i	−0.903046	+	0.521374i	−0.0248589	+	0.999691i	$0.507914\pi$
$180$		0			0
$181$			15.7546i			1.17103i	0.810661	+	0.585515i	$0.199108\pi$
$181$			15.7546i			1.17103i	−0.810661	+	0.585515i	$0.800892\pi$
$182$		0			0
$183$	−1.93861			−0.143306
$184$		0			0
$185$	−1.81399	−	3.14193i	−0.133367	−	0.230999i
$186$		0			0
$187$	4.04714	+	2.33662i	0.295956	+	0.170870i
$188$		0			0
$189$	−2.24783	−	1.39545i	−0.163505	−	0.101504i
$190$		0			0
$191$	−6.21677	+	10.7678i	−0.449830	+	0.779128i	−0.998375	−	0.0569933i	$-0.981849\pi$
$191$	−6.21677	+	10.7678i	−0.449830	+	0.779128i	0.548545	+	0.836121i	$0.315182\pi$
$192$		0			0
$193$	2.92875	+	5.07274i	0.210816	+	0.365144i	0.951970	−	0.306191i	$-0.0990546\pi$
$193$	2.92875	+	5.07274i	0.210816	+	0.365144i	−0.741154	+	0.671335i	$0.765721\pi$
$194$		0			0
$195$		−	5.07620i		−	0.363514i
$196$		0			0
$197$		−	27.5019i		−	1.95943i	−0.200404	−	0.979713i	$-0.564226\pi$
$197$		−	27.5019i		−	1.95943i	0.200404	−	0.979713i	$-0.435774\pi$
$198$		0			0
$199$	−11.9106	−	20.6297i	−0.844318	−	1.46240i	−0.886212	−	0.463280i	$-0.846672\pi$
$199$	−11.9106	−	20.6297i	−0.844318	−	1.46240i	0.0418939	−	0.999122i	$-0.486661\pi$
$200$		0			0
$201$	−5.27555	+	9.13752i	−0.372109	+	0.644511i
$202$		0			0
$203$	15.2547	+	9.47008i	1.07067	+	0.664670i
$204$		0			0
$205$	−2.71029	−	1.56479i	−0.189295	−	0.109290i
$206$		0			0
$207$	−2.72132	−	4.71346i	−0.189145	−	0.327608i
$208$		0			0
$209$	−6.97205			−0.482267
$210$		0			0
$211$		−	26.3273i		−	1.81245i	−0.422800	−	0.906223i	$-0.638953\pi$
$211$		−	26.3273i		−	1.81245i	0.422800	−	0.906223i	$-0.361047\pi$
$212$		0			0
$213$	−7.03289	+	4.06044i	−0.481886	+	0.278217i
$214$		0			0
$215$	−3.16840	+	5.48784i	−0.216083	+	0.374267i
$216$		0			0
$217$	19.4249	+	0.621308i	1.31865	+	0.0421771i
$218$		0			0
$219$	8.65896	+	4.99925i	0.585118	+	0.337818i
$220$		0			0
$221$	15.0378	−	8.68207i	1.01155	−	0.584019i
$222$		0			0
$223$	15.5052			1.03831			0.519153	−	0.854681i	$-0.326247\pi$
$223$	15.5052			1.03831			0.519153	+	0.854681i	$0.326247\pi$
$224$		0			0
$225$	−2.98037			−0.198691
$226$		0			0
$227$	−1.11618	+	0.644429i	−0.0740837	+	0.0427722i	−0.536584	−	0.843847i	$-0.680286\pi$
$227$	−1.11618	+	0.644429i	−0.0740837	+	0.0427722i	0.462501	+	0.886619i	$0.346952\pi$
$228$		0			0
$229$	−2.71834	−	1.56943i	−0.179633	−	0.103711i	0.407487	−	0.913211i	$-0.366405\pi$
$229$	−2.71834	−	1.56943i	−0.179633	−	0.103711i	−0.587120	+	0.809500i	$0.699738\pi$
$230$		0			0
$231$	−1.20064	−	2.24218i	−0.0789961	−	0.147525i
$232$		0			0
$233$	2.33320	−	4.04121i	0.152853	−	0.264749i	−0.779422	−	0.626499i	$-0.784487\pi$
$233$	2.33320	−	4.04121i	0.152853	−	0.264749i	0.932275	+	0.361750i	$0.117821\pi$
$234$		0			0
$235$	0.521325	−	0.300987i	0.0340075	−	0.0196342i
$236$		0			0
$237$		−	0.279215i		−	0.0181370i
$238$		0			0
$239$	18.2659			1.18152			0.590762	−	0.806846i	$-0.298827\pi$
$239$	18.2659			1.18152			0.590762	+	0.806846i	$0.298827\pi$
$240$		0			0
$241$	−11.6727	−	20.2178i	−0.751908	−	1.30234i	−0.946897	−	0.321537i	$-0.895801\pi$
$241$	−11.6727	−	20.2178i	−0.751908	−	1.30234i	0.194989	−	0.980805i	$-0.437533\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−0.635722	+	9.92763i	−0.0406148	+	0.634253i
$246$		0			0
$247$	−12.9529	+	22.4350i	−0.824171	+	1.42751i
$248$		0			0
$249$	3.34680	+	5.79683i	0.212095	+	0.367359i
$250$		0			0
$251$			0.893668i			0.0564078i	0.999602	+	0.0282039i	$0.00897877\pi$
$251$			0.893668i			0.0564078i	−0.999602	+	0.0282039i	$0.991021\pi$
$252$		0			0
$253$		−	5.23210i		−	0.328939i
$254$		0			0
$255$	3.45428	+	5.98299i	0.216315	+	0.374669i
$256$		0			0
$257$	14.9284	−	25.8568i	0.931209	−	1.61290i	0.149952	−	0.988693i	$-0.452088\pi$
$257$	14.9284	−	25.8568i	0.931209	−	1.61290i	0.781258	−	0.624209i	$-0.214579\pi$
$258$		0			0
$259$	−5.95434	+	3.18841i	−0.369985	+	0.198118i
$260$		0			0
$261$	−5.87720	−	3.39320i	−0.363790	−	0.210034i
$262$		0			0
$263$	0.498465	+	0.863366i	0.0307367	+	0.0532375i	0.880985	−	0.473145i	$-0.156881\pi$
$263$	0.498465	+	0.863366i	0.0307367	+	0.0532375i	−0.850248	+	0.526382i	$0.823548\pi$
$264$		0			0
$265$	13.8026			0.847890
$266$		0			0
$267$		−	2.14805i		−	0.131458i
$268$		0			0
$269$	−14.3936	+	8.31015i	−0.877593	+	0.506679i	−0.869864	−	0.493291i	$-0.835794\pi$
$269$	−14.3936	+	8.31015i	−0.877593	+	0.506679i	−0.00772927	+	0.999970i	$0.502460\pi$
$270$		0			0
$271$	3.96742	−	6.87177i	0.241004	−	0.417430i	−0.719997	−	0.693977i	$-0.755857\pi$
$271$	3.96742	−	6.87177i	0.241004	−	0.417430i	0.961000	+	0.276547i	$0.0891901\pi$
$272$		0			0
$273$	−9.44559	−	0.302118i	−0.571673	−	0.0182850i
$274$		0			0
$275$	−2.48123	−	1.43254i	−0.149624	−	0.0863853i
$276$		0			0
$277$	−12.3878	+	7.15213i	−0.744313	+	0.429730i	−0.823636	−	0.567119i	$-0.808058\pi$
$277$	−12.3878	+	7.15213i	−0.744313	+	0.429730i	0.0793221	+	0.996849i	$0.474724\pi$
$278$		0			0
$279$	−7.34569			−0.439775
$280$		0			0
$281$	−30.9343			−1.84539			−0.922694	−	0.385534i	$-0.874017\pi$
$281$	−30.9343			−1.84539			−0.922694	+	0.385534i	$0.874017\pi$
$282$		0			0
$283$	0.109033	−	0.0629502i	0.00648134	−	0.00374200i	−0.496756	−	0.867890i	$-0.665476\pi$
$283$	0.109033	−	0.0629502i	0.00648134	−	0.00374200i	0.503237	+	0.864148i	$0.332142\pi$
$284$		0			0
$285$	−8.92608	−	5.15348i	−0.528735	−	0.305266i
$286$		0			0
$287$	−3.07301	+	4.95008i	−0.181394	+	0.292194i
$288$		0			0
$289$	−3.31605	+	5.74357i	−0.195062	+	0.337857i
$290$		0			0
$291$	8.18379	−	4.72492i	0.479742	−	0.276979i
$292$		0			0
$293$		−	11.5096i		−	0.672397i	−0.941791	−	0.336198i	$-0.890859\pi$
$293$		−	11.5096i		−	0.672397i	0.941791	−	0.336198i	$-0.109141\pi$
$294$		0			0
$295$	10.5672			0.615245
$296$		0			0
$297$	0.480658	+	0.832525i	0.0278906	+	0.0483080i
$298$		0			0
$299$	−16.8361	−	9.72034i	−0.973658	−	0.562142i
$300$		0			0
$301$	10.0230	+	6.22226i	0.577715	+	0.358645i
$302$		0			0
$303$	1.77950	−	3.08218i	0.102230	−	0.177067i
$304$		0			0
$305$	−1.37752	−	2.38593i	−0.0788765	−	0.136618i
$306$		0			0
$307$		−	18.0146i		−	1.02815i	−0.857745	−	0.514075i	$-0.828135\pi$
$307$		−	18.0146i		−	1.02815i	0.857745	−	0.514075i	$-0.171865\pi$
$308$		0			0
$309$			1.23742i			0.0703943i
$310$		0			0
$311$	1.55812	+	2.69875i	0.0883532	+	0.153032i	0.906815	−	0.421529i	$-0.138506\pi$
$311$	1.55812	+	2.69875i	0.0883532	+	0.153032i	−0.818462	+	0.574561i	$0.805173\pi$
$312$		0			0
$313$	0.726624	−	1.25855i	0.0410712	−	0.0711375i	−0.844759	−	0.535147i	$-0.820256\pi$
$313$	0.726624	−	1.25855i	0.0410712	−	0.0711375i	0.885830	+	0.464009i	$0.153590\pi$
$314$		0			0
$315$	0.120202	−	3.75806i	0.00677259	−	0.211743i
$316$		0			0
$317$	−15.5731	−	8.99111i	−0.874671	−	0.504991i	−0.00577305	−	0.999983i	$-0.501838\pi$
$317$	−15.5731	−	8.99111i	−0.874671	−	0.504991i	−0.868897	+	0.494992i	$0.835171\pi$
$318$		0			0
$319$	−3.26194	−	5.64985i	−0.182634	−	0.316331i
$320$		0			0
$321$	−16.6767			−0.930801
$322$		0			0
$323$		−	35.2570i		−	1.96175i
$324$		0			0
$325$	−9.21939	+	5.32282i	−0.511400	+	0.295257i
$326$		0			0
$327$	5.10790	−	8.84714i	0.282468	−	0.489248i
$328$		0			0
$329$	−0.529038	−	0.987975i	−0.0291668	−	0.0544688i
$330$		0			0
$331$	7.56479	+	4.36753i	0.415798	+	0.240061i	0.693278	−	0.720670i	$-0.256166\pi$
$331$	7.56479	+	4.36753i	0.415798	+	0.240061i	−0.277480	+	0.960731i	$0.589499\pi$
$332$		0			0
$333$	2.21085	−	1.27644i	0.121154	−	0.0699483i
$334$		0			0
$335$	−14.9946			−0.819241
$336$		0			0
$337$	7.28406			0.396788			0.198394	−	0.980122i	$-0.436427\pi$
$337$	7.28406			0.396788			0.198394	+	0.980122i	$0.436427\pi$
$338$		0			0
$339$	−10.7421	+	6.20197i	−0.583432	+	0.336845i
$340$		0			0
$341$	−6.11547	−	3.53077i	−0.331171	−	0.191202i
$342$		0			0
$343$	18.4351	+	1.77378i	0.995403	+	0.0957754i
$344$		0			0
$345$	3.86737	−	6.69848i	0.208212	−	0.360634i
$346$		0			0
$347$	0.264838	−	0.152905i	0.0142173	−	0.00820835i	−0.492875	−	0.870100i	$-0.664054\pi$
$347$	0.264838	−	0.152905i	0.0142173	−	0.00820835i	0.507092	+	0.861892i	$0.330721\pi$
$348$		0			0
$349$		−	6.94160i		−	0.371575i	−0.982590	−	0.185788i	$-0.940516\pi$
$349$		−	6.94160i		−	0.371575i	0.982590	−	0.185788i	$-0.0594837\pi$
$350$		0			0
$351$	3.57192			0.190655
$352$		0			0
$353$	17.9762	+	31.1356i	0.956775	+	1.65718i	0.730253	+	0.683176i	$0.239402\pi$
$353$	17.9762	+	31.1356i	0.956775	+	1.65718i	0.226521	+	0.974006i	$0.427265\pi$
$354$		0			0
$355$	−9.99472	−	5.77045i	−0.530464	−	0.306264i
$356$		0			0
$357$	11.3385	−	6.07150i	0.600097	−	0.321338i
$358$		0			0
$359$	5.85386	−	10.1392i	0.308955	−	0.535126i	−0.669179	−	0.743101i	$-0.733354\pi$
$359$	5.85386	−	10.1392i	0.308955	−	0.535126i	0.978134	+	0.207975i	$0.0666874\pi$
$360$		0			0
$361$	16.8001	+	29.0987i	0.884217	+	1.53151i
$362$		0			0
$363$		−	10.0759i		−	0.528846i
$364$		0			0
$365$			14.2093i			0.743747i
$366$		0			0
$367$	14.9631	+	25.9169i	0.781068	+	1.35285i	0.931320	+	0.364202i	$0.118658\pi$
$367$	14.9631	+	25.9169i	0.781068	+	1.35285i	−0.150252	+	0.988648i	$0.548008\pi$
$368$		0			0
$369$	1.10108	−	1.90713i	0.0573200	−	0.0992812i
$370$		0			0
$371$	0.821485	−	25.6834i	0.0426494	−	1.33342i
$372$		0			0
$373$	−0.0152179	−	0.00878607i	−0.000787954	−	0.000454926i	0.499606	−	0.866253i	$-0.333478\pi$
$373$	−0.0152179	−	0.00878607i	−0.000787954	−	0.000454926i	−0.500394	+	0.865798i	$0.666811\pi$
$374$		0			0
$375$	−5.67060	−	9.82177i	−0.292829	−	0.507194i
$376$		0			0
$377$	−24.2405			−1.24845
$378$		0			0
$379$		−	3.37530i		−	0.173377i	−0.996235	−	0.0866887i	$-0.972371\pi$
$379$		−	3.37530i		−	0.173377i	0.996235	−	0.0866887i	$-0.0276286\pi$
$380$		0			0
$381$	15.0437	−	8.68548i	0.770712	−	0.444971i
$382$		0			0
$383$	5.19747	−	9.00228i	0.265578	−	0.459995i	−0.702137	−	0.712042i	$-0.747770\pi$
$383$	5.19747	−	9.00228i	0.265578	−	0.459995i	0.967715	+	0.252047i	$0.0811038\pi$
$384$		0			0
$385$	1.90641	−	3.07090i	0.0971598	−	0.156508i
$386$		0			0
$387$	−3.86158	−	2.22948i	−0.196295	−	0.113331i
$388$		0			0
$389$	11.8164	−	6.82217i	0.599113	−	0.345898i	−0.169580	−	0.985516i	$-0.554241\pi$
$389$	11.8164	−	6.82217i	0.599113	−	0.345898i	0.768692	+	0.639619i	$0.220908\pi$
$390$		0			0
$391$	26.4582			1.33805
$392$		0			0
$393$	14.8344			0.748294
$394$		0			0
$395$	0.343641	−	0.198402i	0.0172905	−	0.00998266i
$396$		0			0
$397$	−18.0104	−	10.3983i	−0.903917	−	0.521876i	−0.0254477	−	0.999676i	$-0.508101\pi$
$397$	−18.0104	−	10.3983i	−0.903917	−	0.521876i	−0.878469	+	0.477800i	$0.841434\pi$
$398$		0			0
$399$	−10.1206	+	16.3026i	−0.506666	+	0.816150i
$400$		0			0
$401$	9.16853	−	15.8804i	0.457855	−	0.793028i	−0.540993	−	0.841027i	$-0.681951\pi$
$401$	9.16853	−	15.8804i	0.457855	−	0.793028i	0.998847	+	0.0479997i	$0.0152846\pi$
$402$		0			0
$403$	−22.7230	+	13.1191i	−1.13191	+	0.653510i
$404$		0			0
$405$			1.42114i			0.0706169i
$406$		0			0
$407$	2.45412			0.121646
$408$		0			0
$409$	0.0404092	+	0.0699908i	0.00199811	+	0.00346082i	0.867023	−	0.498269i	$-0.166031\pi$
$409$	0.0404092	+	0.0699908i	0.00199811	+	0.00346082i	−0.865025	+	0.501729i	$0.832697\pi$
$410$		0			0
$411$	12.0032	+	6.93006i	0.592075	+	0.341835i
$412$		0			0
$413$	0.628922	−	19.6630i	0.0309472	−	0.967553i
$414$		0			0
$415$	−4.75627	+	8.23810i	−0.233476	+	0.404392i
$416$		0			0
$417$	−10.4373	−	18.0780i	−0.511118	−	0.885282i
$418$		0			0
$419$			22.5177i			1.10006i	0.835144	+	0.550031i	$0.185384\pi$
$419$			22.5177i			1.10006i	−0.835144	+	0.550031i	$0.814616\pi$
$420$		0			0
$421$		−	24.4058i		−	1.18947i	−0.803923	−	0.594733i	$-0.797258\pi$
$421$		−	24.4058i		−	1.18947i	0.803923	−	0.594733i	$-0.202742\pi$
$422$		0			0
$423$	0.211793	+	0.366836i	0.0102977	+	0.0178362i
$424$		0			0
$425$	7.24421	−	12.5473i	0.351396	−	0.608635i
$426$		0			0
$427$	−4.52163	+	2.42123i	−0.218817	+	0.117172i
$428$		0			0
$429$	2.97371	+	1.71687i	0.143572	+	0.0828915i
$430$		0			0
$431$	−16.8626	−	29.2068i	−0.812241	−	1.40684i	−0.911292	−	0.411760i	$-0.864914\pi$
$431$	−16.8626	−	29.2068i	−0.812241	−	1.40684i	0.0990516	−	0.995082i	$-0.468419\pi$
$432$		0			0
$433$	24.9475			1.19890			0.599449	−	0.800413i	$-0.295386\pi$
$433$	24.9475			1.19890			0.599449	+	0.800413i	$0.295386\pi$
$434$		0			0
$435$		−	9.64442i		−	0.462415i
$436$		0			0
$437$	−34.1849	+	19.7366i	−1.63528	+	0.944131i
$438$		0			0
$439$	−1.69821	+	2.94139i	−0.0810513	+	0.140385i	−0.903702	−	0.428162i	$-0.859161\pi$
$439$	−1.69821	+	2.94139i	−0.0810513	+	0.140385i	0.822650	+	0.568547i	$0.192494\pi$
$440$		0			0
$441$	−6.98569	−	0.447333i	−0.332652	−	0.0213016i
$442$		0			0
$443$	3.89785	+	2.25043i	0.185193	+	0.106921i	0.589730	−	0.807600i	$-0.299234\pi$
$443$	3.89785	+	2.25043i	0.185193	+	0.106921i	−0.404537	+	0.914521i	$0.632567\pi$
$444$		0			0
$445$	2.64369	−	1.52634i	0.125323	−	0.0723552i
$446$		0			0
$447$	−20.7203			−0.980036
$448$		0			0
$449$	1.45841			0.0688264			0.0344132	−	0.999408i	$-0.489044\pi$
$449$	1.45841			0.0688264			0.0344132	+	0.999408i	$0.489044\pi$
$450$		0			0
$451$	1.83336	−	1.05849i	0.0863294	−	0.0498423i
$452$		0			0
$453$	2.14074	+	1.23596i	0.100581	+	0.0580703i
$454$		0			0
$455$	−6.33992	−	11.8398i	−0.297220	−	0.555056i
$456$		0			0
$457$	−13.8539	+	23.9957i	−0.648058	+	1.12247i	0.335528	+	0.942030i	$0.391085\pi$
$457$	−13.8539	+	23.9957i	−0.648058	+	1.12247i	−0.983586	+	0.180439i	$0.942248\pi$
$458$		0			0
$459$	−4.21000	+	2.43064i	−0.196506	+	0.113453i
$460$		0			0
$461$		−	16.9591i		−	0.789865i	−0.918710	−	0.394933i	$-0.870768\pi$
$461$		−	16.9591i		−	0.789865i	0.918710	−	0.394933i	$-0.129232\pi$
$462$		0			0
$463$	−8.12386			−0.377548			−0.188774	−	0.982021i	$-0.560451\pi$
$463$	−8.12386			−0.377548			−0.188774	+	0.982021i	$0.560451\pi$
$464$		0			0
$465$	−5.21962	−	9.04065i	−0.242054	−	0.419250i
$466$		0			0
$467$	19.8375	+	11.4532i	0.917972	+	0.529991i	0.882988	−	0.469396i	$-0.155528\pi$
$467$	19.8375	+	11.4532i	0.917972	+	0.529991i	0.0349845	+	0.999388i	$0.488862\pi$
$468$		0			0
$469$	−0.892425	+	27.9013i	−0.0412084	+	1.28836i
$470$		0			0
$471$	1.49761	−	2.59394i	0.0690062	−	0.119522i
$472$		0			0
$473$	−2.14324	−	3.71220i	−0.0985463	−	0.170687i
$474$		0			0
$475$			21.6154i			0.991783i
$476$		0			0
$477$			9.71238i			0.444700i
$478$		0			0
$479$	−2.85974	−	4.95322i	−0.130665	−	0.226318i	0.793268	−	0.608872i	$-0.208378\pi$
$479$	−2.85974	−	4.95322i	−0.130665	−	0.226318i	−0.923933	+	0.382554i	$0.875045\pi$
$480$		0			0
$481$	4.55933	−	7.89700i	0.207888	−	0.360072i
$482$		0			0
$483$	−12.2341	−	7.59492i	−0.556671	−	0.345581i
$484$		0			0
$485$	11.6303	+	6.71476i	0.528105	+	0.304901i
$486$		0			0
$487$	11.3841	+	19.7178i	0.515862	+	0.893499i	0.999830	+	0.0184136i	$0.00586157\pi$
$487$	11.3841	+	19.7178i	0.515862	+	0.893499i	−0.483969	+	0.875085i	$0.660805\pi$
$488$		0			0
$489$	−2.25570			−0.102006
$490$		0			0
$491$			8.65619i			0.390649i	0.980739	+	0.195324i	$0.0625759\pi$
$491$			8.65619i			0.390649i	−0.980739	+	0.195324i	$0.937424\pi$
$492$		0			0
$493$	28.5708	−	16.4953i	1.28676	−	0.742912i
$494$		0			0
$495$	−0.683082	+	1.18313i	−0.0307023	+	0.0531779i
$496$		0			0
$497$	−11.3323	+	18.2543i	−0.508322	+	0.818819i
$498$		0			0
$499$	−3.20914	−	1.85280i	−0.143661	−	0.0829426i	0.426447	−	0.904513i	$-0.359765\pi$
$499$	−3.20914	−	1.85280i	−0.143661	−	0.0829426i	−0.570108	+	0.821570i	$0.693098\pi$
$500$		0			0
$501$	−2.12757	+	1.22835i	−0.0950529	+	0.0548788i
$502$		0			0
$503$	−10.6986			−0.477028			−0.238514	−	0.971139i	$-0.576660\pi$
$503$	−10.6986			−0.477028			−0.238514	+	0.971139i	$0.576660\pi$
$504$		0			0
$505$	5.05783			0.225070
$506$		0			0
$507$	−0.209029	+	0.120683i	−0.00928330	+	0.00535971i
$508$		0			0
$509$	8.03974	+	4.64175i	0.356355	+	0.205742i	0.667481	−	0.744627i	$-0.267373\pi$
$509$	8.03974	+	4.64175i	0.356355	+	0.205742i	−0.311125	+	0.950369i	$0.600706\pi$
$510$		0			0
$511$	26.4400	+	0.845685i	1.16964	+	0.0374109i
$512$		0			0
$513$	3.62630	−	6.28094i	0.160105	−	0.277310i
$514$		0			0
$515$	−1.52294	+	0.879272i	−0.0671089	+	0.0387454i
$516$		0			0
$517$			0.407200i			0.0179087i
$518$		0			0
$519$	−8.80934			−0.386687
$520$		0			0
$521$	−6.29844	−	10.9092i	−0.275940	−	0.477942i	0.694432	−	0.719558i	$-0.255656\pi$
$521$	−6.29844	−	10.9092i	−0.275940	−	0.477942i	−0.970372	+	0.241617i	$0.922322\pi$
$522$		0			0
$523$	20.1037	+	11.6069i	0.879074	+	0.507534i	0.870353	−	0.492428i	$-0.163891\pi$
$523$	20.1037	+	11.6069i	0.879074	+	0.507534i	0.00872093	+	0.999962i	$0.497224\pi$
$524$		0			0
$525$	−6.95143	+	3.72233i	−0.303385	+	0.162456i
$526$		0			0
$527$	17.8548	−	30.9254i	0.777766	−	1.34713i
$528$		0			0
$529$	−3.31114	−	5.73506i	−0.143963	−	0.249350i
$530$		0			0
$531$			7.43572i			0.322683i
$532$		0			0
$533$		−	7.86596i		−	0.340712i
$534$		0			0
$535$	−11.8499	−	20.5247i	−0.512317	−	0.887359i
$536$		0			0
$537$	6.97551	−	12.0819i	0.301015	−	0.521374i
$538$		0			0
$539$	−5.60075	−	3.73015i	−0.241241	−	0.160669i
$540$		0			0
$541$	0.0793579	+	0.0458173i	0.00341186	+	0.00196984i	0.501705	−	0.865039i	$-0.332706\pi$
$541$	0.0793579	+	0.0458173i	0.00341186	+	0.00196984i	−0.498293	+	0.867009i	$0.666040\pi$
$542$		0			0
$543$	−7.87730	−	13.6439i	−0.338047	−	0.585515i
$544$		0			0
$545$	14.5181			0.621886
$546$		0			0
$547$			17.7752i			0.760015i	0.924983	+	0.380007i	$0.124079\pi$
$547$			17.7752i			0.760015i	−0.924983	+	0.380007i	$0.875921\pi$
$548$		0			0
$549$	1.67889	−	0.969306i	0.0716532	−	0.0413690i
$550$		0			0
$551$	−24.6096	+	42.6250i	−1.04840	+	1.81589i
$552$		0			0
$553$	−0.348725	−	0.651243i	−0.0148293	−	0.0276937i
$554$		0			0
$555$	3.14193	+	1.81399i	0.133367	+	0.0769997i
$556$		0			0
$557$	4.26326	−	2.46139i	0.180640	−	0.104293i	−0.406953	−	0.913449i	$-0.633409\pi$
$557$	4.26326	−	2.46139i	0.180640	−	0.104293i	0.587593	+	0.809156i	$0.300075\pi$
$558$		0			0
$559$	−15.9271			−0.673644
$560$		0			0
$561$	−4.67324			−0.197304
$562$		0			0
$563$	14.6661	−	8.46747i	0.618102	−	0.356862i	−0.158028	−	0.987435i	$-0.550513\pi$
$563$	14.6661	−	8.46747i	0.618102	−	0.356862i	0.776130	+	0.630573i	$0.217180\pi$
$564$		0			0
$565$	−15.2660	−	8.81385i	−0.642247	−	0.370802i
$566$		0			0
$567$	2.64440	+	0.0845812i	0.111054	+	0.00355208i
$568$		0			0
$569$	−10.2382	+	17.7331i	−0.429208	+	0.743411i	−0.996803	−	0.0798973i	$-0.974541\pi$
$569$	−10.2382	+	17.7331i	−0.429208	+	0.743411i	0.567595	+	0.823308i	$0.307874\pi$
$570$		0			0
$571$	−4.92200	+	2.84172i	−0.205979	+	0.118922i	−0.599441	−	0.800419i	$-0.704611\pi$
$571$	−4.92200	+	2.84172i	−0.205979	+	0.118922i	0.393462	+	0.919341i	$0.371277\pi$
$572$		0			0
$573$		−	12.4335i		−	0.519419i
$574$		0			0
$575$	−16.2210			−0.676464
$576$		0			0
$577$	−9.12362	−	15.8026i	−0.379821	−	0.657870i	0.611215	−	0.791465i	$-0.290681\pi$
$577$	−9.12362	−	15.8026i	−0.379821	−	0.657870i	−0.991036	+	0.133595i	$0.957348\pi$
$578$		0			0
$579$	−5.07274	−	2.92875i	−0.210816	−	0.121715i
$580$		0			0
$581$	15.0461	+	9.34059i	0.624216	+	0.387513i
$582$		0			0
$583$	−4.66834	+	8.08580i	−0.193343	+	0.334880i
$584$		0			0
$585$	2.53810	+	4.39612i	0.104937	+	0.181757i
$586$		0			0
$587$			3.25244i			0.134243i	0.997745	+	0.0671213i	$0.0213815\pi$
$587$			3.25244i			0.134243i	−0.997745	+	0.0671213i	$0.978619\pi$
$588$		0			0
$589$			53.2754i			2.19517i
$590$		0			0
$591$	13.7509	+	23.8173i	0.565638	+	0.979713i
$592$		0			0
$593$	−10.6829	+	18.5034i	−0.438696	+	0.759843i	−0.997589	−	0.0693963i	$-0.977893\pi$
$593$	−10.6829	+	18.5034i	−0.438696	+	0.759843i	0.558894	+	0.829239i	$0.311226\pi$
$594$		0			0
$595$	15.5292	+	9.64054i	0.636637	+	0.395224i
$596$		0			0
$597$	20.6297	+	11.9106i	0.844318	+	0.487467i
$598$		0			0
$599$	0.572755	+	0.992041i	0.0234021	+	0.0405337i	0.877489	−	0.479596i	$-0.159217\pi$
$599$	0.572755	+	0.992041i	0.0234021	+	0.0405337i	−0.854087	+	0.520130i	$0.825884\pi$
$600$		0			0
$601$	38.8738			1.58570			0.792848	−	0.609419i	$-0.208597\pi$
$601$	38.8738			1.58570			0.792848	+	0.609419i	$0.208597\pi$
$602$		0			0
$603$		−	10.5511i		−	0.429674i
$604$		0			0
$605$	12.4008	−	7.15960i	0.504164	−	0.291079i
$606$		0			0
$607$	−2.80705	+	4.86195i	−0.113935	+	0.197341i	−0.917353	−	0.398074i	$-0.869679\pi$
$607$	−2.80705	+	4.86195i	−0.113935	+	0.197341i	0.803419	+	0.595414i	$0.203012\pi$
$608$		0			0
$609$	−17.9460	−	0.574002i	−0.727207	−	0.0232598i
$610$		0			0
$611$	1.31031	+	0.756508i	0.0530095	+	0.0306051i
$612$		0			0
$613$	34.5018	−	19.9196i	1.39351	−	0.804545i	0.399810	−	0.916598i	$-0.369076\pi$
$613$	34.5018	−	19.9196i	1.39351	−	0.804545i	0.993702	+	0.112053i	$0.0357426\pi$
$614$		0			0
$615$	3.12958			0.126197
$616$		0			0
$617$	8.53231			0.343498			0.171749	−	0.985141i	$-0.445058\pi$
$617$	8.53231			0.343498			0.171749	+	0.985141i	$0.445058\pi$
$618$		0			0
$619$	−6.85011	+	3.95491i	−0.275329	+	0.158961i	−0.631307	−	0.775533i	$-0.717481\pi$
$619$	−6.85011	+	3.95491i	−0.275329	+	0.158961i	0.355978	+	0.934494i	$0.384148\pi$
$620$		0			0
$621$	4.71346	+	2.72132i	0.189145	+	0.109203i
$622$		0			0
$623$	−2.68280	−	5.01012i	−0.107484	−	0.200726i
$624$		0			0
$625$	0.607795	−	1.05273i	0.0243118	−	0.0421093i
$626$		0			0
$627$	6.03797	−	3.48602i	0.241133	−	0.139218i
$628$		0			0
$629$			12.4103i			0.494829i
$630$		0			0
$631$	−0.418675			−0.0166672			−0.00833360	−	0.999965i	$-0.502653\pi$
$631$	−0.418675			−0.0166672			−0.00833360	+	0.999965i	$0.502653\pi$
$632$		0			0
$633$	13.1637	+	22.8001i	0.523208	+	0.906223i
$634$		0			0
$635$	21.3792	+	12.3433i	0.848407	+	0.489828i
$636$		0			0
$637$	−22.4083	+	11.0924i	−0.887849	+	0.439497i
$638$		0			0
$639$	4.06044	−	7.03289i	0.160629	−	0.278217i
$640$		0			0
$641$	8.64934	+	14.9811i	0.341629	+	0.591718i	0.984735	−	0.174059i	$-0.0556882\pi$
$641$	8.64934	+	14.9811i	0.341629	+	0.591718i	−0.643107	+	0.765777i	$0.722355\pi$
$642$		0			0
$643$			3.36919i			0.132868i	0.997791	+	0.0664340i	$0.0211622\pi$
$643$			3.36919i			0.132868i	−0.997791	+	0.0664340i	$0.978838\pi$
$644$		0			0
$645$		−	6.33681i		−	0.249512i
$646$		0			0
$647$	7.44102	+	12.8882i	0.292537	+	0.506688i	0.974409	−	0.224783i	$-0.0721673\pi$
$647$	7.44102	+	12.8882i	0.292537	+	0.506688i	−0.681872	+	0.731471i	$0.738834\pi$
$648$		0			0
$649$	−3.57404	+	6.19042i	−0.140293	+	0.242995i
$650$		0			0
$651$	−17.1332	+	9.17441i	−0.671501	+	0.359573i
$652$		0			0
$653$	−6.62437	−	3.82458i	−0.259232	−	0.149668i	0.364752	−	0.931105i	$-0.381154\pi$
$653$	−6.62437	−	3.82458i	−0.259232	−	0.149668i	−0.623984	+	0.781437i	$0.714487\pi$
$654$		0			0
$655$	10.5408	+	18.2573i	0.411865	+	0.713370i
$656$		0			0
$657$	−9.99850			−0.390079
$658$		0			0
$659$			39.2806i			1.53015i	0.643939	+	0.765077i	$0.277299\pi$
$659$			39.2806i			1.53015i	−0.643939	+	0.765077i	$0.722701\pi$
$660$		0			0
$661$	−16.6484	+	9.61194i	−0.647547	+	0.373861i	−0.787516	−	0.616295i	$-0.788633\pi$
$661$	−16.6484	+	9.61194i	−0.647547	+	0.373861i	0.139969	+	0.990156i	$0.455300\pi$
$662$		0			0
$663$	−8.68207	+	15.0378i	−0.337184	+	0.584019i
$664$		0			0
$665$	−27.2557	−	0.871774i	−1.05693	−	0.0338060i
$666$		0			0
$667$	−31.9875	−	18.4680i	−1.23856	−	0.715083i
$668$		0			0
$669$	−13.4279	+	7.75261i	−0.519153	+	0.299733i
$670$		0			0
$671$	1.86362			0.0719443
$672$		0			0
$673$	−37.7330			−1.45450			−0.727250	−	0.686373i	$-0.759202\pi$
$673$	−37.7330			−1.45450			−0.727250	+	0.686373i	$0.759202\pi$
$674$		0			0
$675$	2.58107	−	1.49018i	0.0993455	−	0.0573572i
$676$		0			0
$677$	10.7109	+	6.18392i	0.411652	+	0.237667i	0.691499	−	0.722377i	$-0.256951\pi$
$677$	10.7109	+	6.18392i	0.411652	+	0.237667i	−0.279847	+	0.960044i	$0.590284\pi$
$678$		0			0
$679$	13.1868	−	21.2416i	0.506061	−	0.815177i
$680$		0			0
$681$	0.644429	−	1.11618i	0.0246946	−	0.0427722i
$682$		0			0
$683$	7.14537	−	4.12538i	0.273410	−	0.157853i	−0.357026	−	0.934094i	$-0.616209\pi$
$683$	7.14537	−	4.12538i	0.273410	−	0.157853i	0.630436	+	0.776241i	$0.282876\pi$
$684$		0			0
$685$			19.6971i			0.752589i
$686$		0			0
$687$	3.13887			0.119755
$688$		0			0
$689$	17.3459	+	30.0441i	0.660828	+	1.14459i
$690$		0			0
$691$	13.2717	+	7.66244i	0.504880	+	0.291493i	0.730727	−	0.682670i	$-0.239181\pi$
$691$	13.2717	+	7.66244i	0.504880	+	0.291493i	−0.225846	+	0.974163i	$0.572515\pi$
$692$		0			0
$693$	2.16087	+	1.34147i	0.0820848	+	0.0509582i
$694$		0			0
$695$	14.8329	−	25.6913i	0.562643	−	0.974526i
$696$		0			0
$697$	5.35267	+	9.27110i	0.202747	+	0.351168i
$698$		0			0
$699$			4.66639i			0.176499i
$700$		0			0
$701$			41.2674i			1.55865i	0.626622	+	0.779324i	$0.284437\pi$
$701$			41.2674i			1.55865i	−0.626622	+	0.779324i	$0.715563\pi$
$702$		0			0
$703$	−9.25749	−	16.0344i	−0.349153	−	0.604751i
$704$		0			0
$705$	−0.300987	+	0.521325i	−0.0113358	+	0.0196342i
$706$		0			0
$707$	0.301024	−	9.41141i	0.0113212	−	0.353952i
$708$		0			0
$709$	6.38237	+	3.68486i	0.239695	+	0.138388i	0.615037	−	0.788499i	$-0.289141\pi$
$709$	6.38237	+	3.68486i	0.239695	+	0.138388i	−0.375342	+	0.926887i	$0.622475\pi$
$710$		0			0
$711$	0.139607	+	0.241807i	0.00523569	+	0.00906848i
$712$		0			0
$713$	−39.9799			−1.49726
$714$		0			0
$715$			4.87983i			0.182495i
$716$		0			0
$717$	−15.8187	+	9.13296i	−0.590762	+	0.341077i
$718$		0			0
$719$	0.151601	−	0.262580i	0.00565375	−	0.00979259i	−0.863185	−	0.504888i	$-0.831534\pi$
$719$	0.151601	−	0.262580i	0.00565375	−	0.00979259i	0.868838	+	0.495096i	$0.164867\pi$
$720$		0			0
$721$	1.54547	+	2.88617i	0.0575565	+	0.107486i
$722$		0			0
$723$	20.2178	+	11.6727i	0.751908	+	0.434114i
$724$		0			0
$725$	−17.5162	+	10.1130i	−0.650536	+	0.375587i
$726$		0			0
$727$	−9.78796			−0.363015			−0.181508	−	0.983390i	$-0.558098\pi$
$727$	−9.78796			−0.363015			−0.181508	+	0.983390i	$0.558098\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	18.7722	−	10.8382i	0.694316	−	0.400864i
$732$		0			0
$733$	23.6363	+	13.6464i	0.873026	+	0.504042i	0.868353	−	0.495947i	$-0.165179\pi$
$733$	23.6363	+	13.6464i	0.873026	+	0.504042i	0.00467329	+	0.999989i	$0.498512\pi$
$734$		0			0
$735$	−4.41327	−	8.91544i	−0.162786	−	0.328851i
$736$		0			0
$737$	5.07148	−	8.78405i	0.186810	−	0.323565i
$738$		0			0
$739$	−1.81086	+	1.04550i	−0.0666134	+	0.0384593i	−0.532937	−	0.846155i	$-0.678912\pi$
$739$	−1.81086	+	1.04550i	−0.0666134	+	0.0384593i	0.466323	+	0.884614i	$0.345578\pi$
$740$		0			0
$741$		−	25.9057i		−	0.951671i
$742$		0			0
$743$	47.9593			1.75945			0.879727	−	0.475479i	$-0.157725\pi$
$743$	47.9593			1.75945			0.879727	+	0.475479i	$0.157725\pi$
$744$		0			0
$745$	−14.7232	−	25.5013i	−0.539416	−	0.934297i
$746$		0			0
$747$	−5.79683	−	3.34680i	−0.212095	−	0.122453i
$748$		0			0
$749$	−38.8968	+	20.8283i	−1.42126	+	0.761051i
$750$		0			0
$751$	−13.6435	+	23.6313i	−0.497859	+	0.862317i	−0.999997	−	0.00247029i	$-0.999214\pi$
$751$	−13.6435	+	23.6313i	−0.497859	+	0.862317i	0.502138	+	0.864788i	$0.332547\pi$
$752$		0			0
$753$	−0.446834	−	0.773939i	−0.0162835	−	0.0282039i
$754$		0			0
$755$			3.51293i			0.127849i
$756$		0			0
$757$			11.9222i			0.433320i	0.976247	+	0.216660i	$0.0695163\pi$
$757$			11.9222i			0.433320i	−0.976247	+	0.216660i	$0.930484\pi$
$758$		0			0
$759$	2.61605	+	4.53113i	0.0949565	+	0.164470i
$760$		0			0
$761$	12.9315	−	22.3980i	0.468767	−	0.811928i	−0.530596	−	0.847625i	$-0.678032\pi$
$761$	12.9315	−	22.3980i	0.468767	−	0.811928i	0.999363	+	0.0356967i	$0.0113650\pi$
$762$		0			0
$763$	0.864065	−	27.0147i	0.0312812	−	0.977996i
$764$		0			0
$765$	−5.98299	−	3.45428i	−0.216315	−	0.124890i
$766$		0			0
$767$	13.2799	+	23.0015i	0.479510	+	0.830535i
$768$		0			0
$769$	1.72326			0.0621423			0.0310712	−	0.999517i	$-0.490108\pi$
$769$	1.72326			0.0621423			0.0310712	+	0.999517i	$0.490108\pi$
$770$		0			0
$771$			29.8568i			1.07527i
$772$		0			0
$773$	22.4410	−	12.9563i	0.807145	−	0.466005i	−0.0388184	−	0.999246i	$-0.512359\pi$
$773$	22.4410	−	12.9563i	0.807145	−	0.466005i	0.845963	+	0.533241i	$0.179026\pi$
$774$		0			0
$775$	−10.9464	+	18.9598i	−0.393207	+	0.681055i
$776$		0			0
$777$	3.56241	−	5.73842i	0.127801	−	0.205865i
$778$		0			0
$779$	−13.8317	−	7.98571i	−0.495570	−	0.286118i
$780$		0			0
$781$	6.76084	−	3.90337i	0.241922	−	0.139674i
$782$		0			0
$783$	6.78641			0.242526
$784$		0			0
$785$	4.25662			0.151925
$786$		0			0
$787$	34.3131	−	19.8107i	1.22313	−	0.706174i	0.257546	−	0.966266i	$-0.417086\pi$
$787$	34.3131	−	19.8107i	1.22313	−	0.706174i	0.965584	+	0.260092i	$0.0837529\pi$
$788$		0			0
$789$	−0.863366	−	0.498465i	−0.0307367	−	0.0177458i
$790$		0			0
$791$	−17.3091	+	27.8819i	−0.615439	+	0.991366i
$792$		0			0
$793$	3.46229	−	5.99686i	0.122949	−	0.212955i
$794$		0			0
$795$	−11.9534	+	6.90132i	−0.423945	+	0.244765i
$796$		0			0
$797$		−	15.7107i		−	0.556502i	−0.960508	−	0.278251i	$-0.910245\pi$
$797$		−	15.7107i		−	0.556502i	0.960508	−	0.278251i	$-0.0897547\pi$
$798$		0			0
$799$	−2.05917			−0.0728483
$800$		0			0
$801$	1.07402	+	1.86026i	0.0379487	+	0.0657291i
$802$		0			0
$803$	−8.32400	−	4.80587i	−0.293748	−	0.169595i
$804$		0			0
$805$	0.654213	−	20.4537i	0.0230580	−	0.720899i
$806$		0			0
$807$	8.31015	−	14.3936i	0.292531	−	0.506679i
$808$		0			0
$809$	−16.4434	−	28.4809i	−0.578121	−	1.00133i	−0.995695	−	0.0926918i	$-0.970453\pi$
$809$	−16.4434	−	28.4809i	−0.578121	−	1.00133i	0.417574	−	0.908643i	$-0.362880\pi$
$810$		0			0
$811$		−	43.5139i		−	1.52798i	−0.645227	−	0.763991i	$-0.723237\pi$
$811$		−	43.5139i		−	1.52798i	0.645227	−	0.763991i	$-0.276763\pi$
$812$		0			0
$813$			7.93484i			0.278287i
$814$		0			0
$815$	−1.60283	−	2.77618i	−0.0561447	−	0.0972455i
$816$		0			0
$817$	−16.1696	+	28.0065i	−0.565701	+	0.979823i
$818$		0			0
$819$	8.33118	−	4.46115i	0.291115	−	0.155885i
$820$		0			0
$821$	−29.4342	−	16.9938i	−1.02726	−	0.593089i	−0.111062	−	0.993814i	$-0.535425\pi$
$821$	−29.4342	−	16.9938i	−1.02726	−	0.593089i	−0.916199	+	0.400725i	$0.868758\pi$
$822$		0			0
$823$	5.27792	+	9.14163i	0.183977	+	0.318657i	0.943231	−	0.332137i	$-0.107770\pi$
$823$	5.27792	+	9.14163i	0.183977	+	0.318657i	−0.759254	+	0.650794i	$0.774436\pi$
$824$		0			0
$825$	2.86508			0.0997491
$826$		0			0
$827$			7.79584i			0.271088i	0.990771	+	0.135544i	$0.0432782\pi$
$827$			7.79584i			0.271088i	−0.990771	+	0.135544i	$0.956722\pi$
$828$		0			0
$829$	46.7154	−	26.9712i	1.62249	−	0.936747i	0.636244	−	0.771488i	$-0.280487\pi$
$829$	46.7154	−	26.9712i	1.62249	−	0.936747i	0.986250	−	0.165260i	$-0.0528462\pi$
$830$		0			0
$831$	7.15213	−	12.3878i	0.248104	−	0.429730i
$832$		0			0
$833$	18.8630	−	28.3224i	0.653564	−	0.981314i
$834$		0			0
$835$	−3.02357	−	1.74566i	−0.104635	−	0.0604111i
$836$		0			0
$837$	6.36156	−	3.67285i	0.219888	−	0.126952i
$838$		0			0
$839$	−32.7564			−1.13088			−0.565439	−	0.824790i	$-0.691293\pi$
$839$	−32.7564			−1.13088			−0.565439	+	0.824790i	$0.691293\pi$
$840$		0			0
$841$	−17.0553			−0.588115
$842$		0			0
$843$	26.7899	−	15.4672i	0.922694	−	0.532717i
$844$		0			0
$845$	−0.297059	−	0.171507i	−0.0102191	−	0.00590002i
$846$		0			0
$847$	−12.5843	−	23.5010i	−0.432400	−	0.807505i
$848$		0			0
$849$	−0.0629502	+	0.109033i	−0.00216045	+	0.00374200i
$850$		0			0
$851$	12.0329	−	6.94718i	0.412481	−	0.238146i
$852$		0			0
$853$			29.5726i			1.01255i	0.862373	+	0.506274i	$0.168978\pi$
$853$			29.5726i			1.01255i	−0.862373	+	0.506274i	$0.831022\pi$
$854$		0			0
$855$	10.3070			0.352490
$856$		0			0
$857$	−13.3754	−	23.1669i	−0.456895	−	0.791366i	0.541900	−	0.840443i	$-0.317705\pi$
$857$	−13.3754	−	23.1669i	−0.456895	−	0.791366i	−0.998795	+	0.0490772i	$0.984372\pi$
$858$		0			0
$859$	1.51398	+	0.874100i	0.0516565	+	0.0298239i	0.525606	−	0.850728i	$-0.323839\pi$
$859$	1.51398	+	0.874100i	0.0516565	+	0.0298239i	−0.473949	+	0.880552i	$0.657172\pi$
$860$		0			0
$861$	0.186262	−	5.82340i	0.00634778	−	0.198461i
$862$		0			0
$863$	−24.1071	+	41.7548i	−0.820617	+	1.42135i	0.0846071	+	0.996414i	$0.473036\pi$
$863$	−24.1071	+	41.7548i	−0.820617	+	1.42135i	−0.905224	+	0.424935i	$0.860297\pi$
$864$		0			0
$865$	−6.25965	−	10.8420i	−0.212834	−	0.368640i
$866$		0			0
$867$		−	6.63210i		−	0.225238i
$868$		0			0
$869$			0.268414i			0.00910532i
$870$		0			0
$871$	−18.8439	−	32.6385i	−0.638500	−	1.10591i
$872$		0			0
$873$	−4.72492	+	8.18379i	−0.159914	+	0.276979i
$874$		0			0
$875$	−25.4931	−	15.8261i	−0.861823	−	0.535019i
$876$		0			0
$877$	−29.8088	−	17.2101i	−1.00657	−	0.581144i	−0.0963845	−	0.995344i	$-0.530728\pi$
$877$	−29.8088	−	17.2101i	−1.00657	−	0.581144i	−0.910186	+	0.414201i	$0.864061\pi$
$878$		0			0
$879$	5.75479	+	9.96759i	0.194104	+	0.336198i
$880$		0			0
$881$	53.0365			1.78685			0.893423	−	0.449216i	$-0.148297\pi$
$881$	53.0365			1.78685			0.893423	+	0.449216i	$0.148297\pi$
$882$		0			0
$883$			1.90861i			0.0642300i	0.999484	+	0.0321150i	$0.0102243\pi$
$883$			1.90861i			0.0642300i	−0.999484	+	0.0321150i	$0.989776\pi$
$884$		0			0
$885$	−9.15145	+	5.28359i	−0.307623	+	0.177606i
$886$		0			0
$887$	28.0441	−	48.5738i	0.941629	−	1.63095i	0.179265	−	0.983801i	$-0.442628\pi$
$887$	28.0441	−	48.5738i	0.941629	−	1.63095i	0.762364	−	0.647148i	$-0.224039\pi$
$888$		0			0
$889$	24.2403	−	39.0469i	0.812993	−	1.30959i
$890$		0			0
$891$	−0.832525	−	0.480658i	−0.0278906	−	0.0161027i
$892$		0			0
$893$	2.66052	−	1.53605i	0.0890308	−	0.0514020i
$894$		0			0
$895$	19.8263			0.662721
$896$		0			0
$897$	19.4407			0.649105
$898$		0			0
$899$	−43.1721	+	24.9254i	−1.43987	+	0.831310i
$900$		0			0
$901$	−40.8891	−	23.6073i	−1.36221	−	0.786474i
$902$		0			0
$903$	−11.7913	−	0.377145i	−0.392389	−	0.0125506i
$904$		0			0
$905$	11.1947	−	19.3899i	0.372126	−	0.644541i
$906$		0			0
$907$	0.681646	−	0.393549i	0.0226337	−	0.0130676i	−0.488640	−	0.872485i	$-0.662507\pi$
$907$	0.681646	−	0.393549i	0.0226337	−	0.0130676i	0.511274	+	0.859418i	$0.329174\pi$
$908$		0			0
$909$			3.55900i			0.118044i
$910$		0			0
$911$	−25.5097			−0.845175			−0.422587	−	0.906322i	$-0.638878\pi$
$911$	−25.5097			−0.845175			−0.422587	+	0.906322i	$0.638878\pi$
$912$		0			0
$913$	−3.21734	−	5.57259i	−0.106478	−	0.184426i
$914$		0			0
$915$	2.38593	+	1.37752i	0.0788765	+	0.0455393i
$916$		0			0
$917$	34.5998	−	18.5274i	1.14258	−	0.611828i
$918$		0			0
$919$	0.0790741	−	0.136960i	0.00260841	−	0.00451790i	−0.864718	−	0.502257i	$-0.832503\pi$
$919$	0.0790741	−	0.136960i	0.00260841	−	0.00451790i	0.867327	+	0.497739i	$0.165836\pi$
$920$		0			0
$921$	9.00732	+	15.6011i	0.296801	+	0.514075i
$922$		0			0
$923$		−	29.0072i		−	0.954783i
$924$		0			0
$925$		−	7.60850i		−	0.250166i
$926$		0			0
$927$	−0.618710	−	1.07164i	−0.0203211	−	0.0351972i
$928$		0			0
$929$	−10.9079	+	18.8931i	−0.357878	+	0.619862i	−0.987606	−	0.156953i	$-0.949833\pi$
$929$	−10.9079	+	18.8931i	−0.357878	+	0.619862i	0.629728	+	0.776815i	$0.283166\pi$
$930$		0			0
$931$	−3.24433	+	50.6644i	−0.106329	+	1.66046i
$932$		0			0
$933$	−2.69875	−	1.55812i	−0.0883532	−	0.0510107i
$934$		0			0
$935$	−3.32066	−	5.75155i	−0.108597	−	0.188096i
$936$		0			0
$937$	21.9184			0.716044			0.358022	−	0.933713i	$-0.383451\pi$
$937$	21.9184			0.716044			0.358022	+	0.933713i	$0.383451\pi$
$938$		0			0
$939$			1.45325i			0.0474250i
$940$		0			0
$941$	46.0309	−	26.5760i	1.50056	−	0.866351i	0.500565	−	0.865699i	$-0.333126\pi$
$941$	46.0309	−	26.5760i	1.50056	−	0.866351i	1.00000		0.000652139i	$-0.000207582\pi$
$942$		0			0
$943$	5.99279	−	10.3798i	0.195152	−	0.338013i
$944$		0			0
$945$	1.77493	+	3.31467i	0.0577385	+	0.107826i
$946$		0			0
$947$	−8.42390	−	4.86354i	−0.273740	−	0.158044i	0.356846	−	0.934163i	$-0.383852\pi$
$947$	−8.42390	−	4.86354i	−0.273740	−	0.158044i	−0.630586	+	0.776119i	$0.717185\pi$
$948$		0			0
$949$	−30.9291	+	17.8569i	−1.00400	+	0.579661i
$950$		0			0
$951$	17.9822			0.583114
$952$		0			0
$953$	5.09514			0.165048			0.0825239	−	0.996589i	$-0.473702\pi$
$953$	5.09514			0.165048			0.0825239	+	0.996589i	$0.473702\pi$
$954$		0			0
$955$	15.3025	−	8.83489i	0.495177	−	0.285890i
$956$		0			0
$957$	5.64985	+	3.26194i	0.182634	+	0.105444i
$958$		0			0
$959$	36.6517	+	1.17231i	1.18354	+	0.0378557i
$960$		0			0
$961$	−11.4796	+	19.8833i	−0.370310	+	0.641396i
$962$		0			0
$963$	14.4424	−	8.33834i	0.465401	−	0.268699i
$964$		0			0
$965$		−	8.32431i		−	0.267969i
$966$		0			0
$967$	−38.9910			−1.25387			−0.626933	−	0.779073i	$-0.715690\pi$
$967$	−38.9910			−1.25387			−0.626933	+	0.779073i	$0.715690\pi$
$968$		0			0
$969$	17.6285	+	30.5334i	0.566309	+	0.980875i
$970$		0			0
$971$	−34.4205	−	19.8727i	−1.10461	−	0.637746i	−0.167181	−	0.985926i	$-0.553466\pi$
$971$	−34.4205	−	19.8727i	−1.10461	−	0.637746i	−0.937427	+	0.348181i	$0.886800\pi$
$972$		0			0
$973$	−46.9226	−	29.1295i	−1.50427	−	0.933849i
$974$		0			0
$975$	5.32282	−	9.21939i	0.170467	−	0.295257i
$976$		0			0
$977$	21.7445	+	37.6625i	0.695667	+	1.20493i	0.969955	+	0.243284i	$0.0782246\pi$
$977$	21.7445	+	37.6625i	0.695667	+	1.20493i	−0.274288	+	0.961648i	$0.588442\pi$
$978$		0			0
$979$			2.06495i			0.0659962i
$980$		0			0
$981$			10.2158i			0.326165i
$982$		0			0
$983$	17.3291	+	30.0149i	0.552713	+	0.957327i	0.998078	+	0.0619779i	$0.0197408\pi$
$983$	17.3291	+	30.0149i	0.552713	+	0.957327i	−0.445364	+	0.895349i	$0.646926\pi$
$984$		0			0
$985$	−19.5420	+	33.8477i	−0.622659	+	1.07848i
$986$		0			0
$987$	0.952148	+	0.591093i	0.0303072	+	0.0188147i
$988$		0			0
$989$	−21.0172	−	12.1343i	−0.668307	−	0.385847i
$990$		0			0
$991$	−15.4425	−	26.7473i	−0.490548	−	0.849655i	0.509392	−	0.860534i	$-0.329870\pi$
$991$	−15.4425	−	26.7473i	−0.490548	−	0.849655i	−0.999941	+	0.0108797i	$0.996537\pi$
$992$		0			0
$993$	−8.73506			−0.277199
$994$		0			0
$995$			33.8531i			1.07322i
$996$		0			0
$997$	29.4376	−	16.9958i	0.932297	−	0.538262i	0.0447599	−	0.998998i	$-0.485748\pi$
$997$	29.4376	−	16.9958i	0.932297	−	0.538262i	0.887537	+	0.460736i	$0.152414\pi$
$998$		0			0
$999$	−1.27644	+	2.21085i	−0.0403847	+	0.0699483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bk.a.625.3		32
3.2	odd	2		2016.2.cr.e.1297.11		32
4.3	odd	2		168.2.bc.a.37.9	✓	32
7.2	even	3		4704.2.c.e.2353.6		16
7.4	even	3	inner	672.2.bk.a.529.14		32
7.5	odd	6		4704.2.c.f.2353.11		16
8.3	odd	2		168.2.bc.a.37.13	yes	32
8.5	even	2	inner	672.2.bk.a.625.14		32
12.11	even	2		504.2.cj.e.37.8		32
21.11	odd	6		2016.2.cr.e.1873.6		32
24.5	odd	2		2016.2.cr.e.1297.6		32
24.11	even	2		504.2.cj.e.37.4		32
28.11	odd	6		168.2.bc.a.109.13	yes	32
28.19	even	6		1176.2.c.f.589.4		16
28.23	odd	6		1176.2.c.e.589.4		16
56.5	odd	6		4704.2.c.f.2353.6		16
56.11	odd	6		168.2.bc.a.109.9	yes	32
56.19	even	6		1176.2.c.f.589.3		16
56.37	even	6		4704.2.c.e.2353.11		16
56.51	odd	6		1176.2.c.e.589.3		16
56.53	even	6	inner	672.2.bk.a.529.3		32
84.11	even	6		504.2.cj.e.109.4		32
168.11	even	6		504.2.cj.e.109.8		32
168.53	odd	6		2016.2.cr.e.1873.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.9	✓	32	4.3	odd	2
168.2.bc.a.37.13	yes	32	8.3	odd	2
168.2.bc.a.109.9	yes	32	56.11	odd	6
168.2.bc.a.109.13	yes	32	28.11	odd	6
504.2.cj.e.37.4		32	24.11	even	2
504.2.cj.e.37.8		32	12.11	even	2
504.2.cj.e.109.4		32	84.11	even	6
504.2.cj.e.109.8		32	168.11	even	6
672.2.bk.a.529.3		32	56.53	even	6	inner
672.2.bk.a.529.14		32	7.4	even	3	inner
672.2.bk.a.625.3		32	1.1	even	1	trivial
672.2.bk.a.625.14		32	8.5	even	2	inner
1176.2.c.e.589.3		16	56.51	odd	6
1176.2.c.e.589.4		16	28.23	odd	6
1176.2.c.f.589.3		16	56.19	even	6
1176.2.c.f.589.4		16	28.19	even	6
2016.2.cr.e.1297.6		32	24.5	odd	2
2016.2.cr.e.1297.11		32	3.2	odd	2
2016.2.cr.e.1873.6		32	21.11	odd	6
2016.2.cr.e.1873.11		32	168.53	odd	6
4704.2.c.e.2353.6		16	7.2	even	3
4704.2.c.e.2353.11		16	56.37	even	6
4704.2.c.f.2353.6		16	56.5	odd	6
4704.2.c.f.2353.11		16	7.5	odd	6

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-1.23074 - 0.710569i) q^{5} +(-1.39545 + 2.24783i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(-1.23074 - 0.710569i) q^{5} +(-1.39545 + 2.24783i) q^{7} +(0.500000 - 0.866025i) q^{9} +(0.832525 - 0.480658i) q^{11} -3.57192i q^{13} +1.42114 q^{15} +(2.43064 + 4.21000i) q^{17} +(-6.28094 - 3.62630i) q^{19} +(0.0845812 - 2.64440i) q^{21} +(2.72132 - 4.71346i) q^{23} +(-1.49018 - 2.58107i) q^{25} +1.00000i q^{27} -6.78641i q^{29} +(-3.67285 - 6.36156i) q^{31} +(-0.480658 + 0.832525i) q^{33} +(3.31467 - 1.77493i) q^{35} +(2.21085 + 1.27644i) q^{37} +(1.78596 + 3.09338i) q^{39} +2.20216 q^{41} -4.45897i q^{43} +(-1.23074 + 0.710569i) q^{45} +(-0.211793 + 0.366836i) q^{47} +(-3.10544 - 6.27345i) q^{49} +(-4.21000 - 2.43064i) q^{51} +(-8.41117 + 4.85619i) q^{53} -1.36616 q^{55} +7.25260 q^{57} +(-6.43952 + 3.71786i) q^{59} +(1.67889 + 0.969306i) q^{61} +(1.24895 + 2.33241i) q^{63} +(-2.53810 + 4.39612i) q^{65} +(9.13752 - 5.27555i) q^{67} +5.44264i q^{69} +8.12089 q^{71} +(-4.99925 - 8.65896i) q^{73} +(2.58107 + 1.49018i) q^{75} +(-0.0813093 + 2.54211i) q^{77} +(-0.139607 + 0.241807i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.69361i q^{83} -6.90856i q^{85} +(3.39320 + 5.87720i) q^{87} +(-1.07402 + 1.86026i) q^{89} +(8.02906 + 4.98444i) q^{91} +(6.36156 + 3.67285i) q^{93} +(5.15348 + 8.92608i) q^{95} -9.44983 q^{97} -0.961317i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^9	\( 32 q + 16 q^{9} + 8 q^{23} + 16 q^{25} + 24 q^{31} + 24 q^{47} + 8 q^{49} + 64 q^{55} - 16 q^{57} + 80 q^{71} + 8 q^{73} - 8 q^{79} - 16 q^{81} - 24 q^{87} - 24 q^{95} - 48 q^{97}+O(q^{100}) \) 32 * q + 16 * q^9 + 8 * q^23 + 16 * q^25 + 24 * q^31 + 24 * q^47 + 8 * q^49 + 64 * q^55 - 16 * q^57 + 80 * q^71 + 8 * q^73 - 8 * q^79 - 16 * q^81 - 24 * q^87 - 24 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more