LMFDB - Embedded newform 608.2.s.c.559.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [608,2,Mod(335,608)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("608.335"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 608 = 2^{5} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	608.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.85490444289$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.10
Character	$\chi$	$=$	608.559
Dual form			608.2.s.c.335.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05104 + 0.606818i) q^{3} +(2.45005 + 1.41453i) q^{5} +0.450769i q^{7} +(-0.763544 - 1.32250i) q^{9} +2.15933 q^{11} +(1.86406 + 3.22864i) q^{13} +(1.71673 + 2.97346i) q^{15} +(-0.716566 + 1.24113i) q^{17} +(0.0305680 - 4.35879i) q^{19} +(-0.273535 + 0.473776i) q^{21} +(-1.12985 + 0.652319i) q^{23} +(1.50182 + 2.60122i) q^{25} -5.49424i q^{27} +(4.22992 + 7.32644i) q^{29} -0.497284 q^{31} +(2.26955 + 1.31032i) q^{33} +(-0.637628 + 1.10440i) q^{35} -6.72997 q^{37} +4.52457i q^{39} +(-7.30919 - 4.21996i) q^{41} +(-2.90174 + 5.02595i) q^{43} -4.32024i q^{45} +(-0.567335 + 0.327551i) q^{47} +6.79681 q^{49} +(-1.50628 + 0.869651i) q^{51} +(-3.86444 - 6.69340i) q^{53} +(5.29047 + 3.05445i) q^{55} +(2.67712 - 4.56271i) q^{57} +(12.1090 + 6.99113i) q^{59} +(2.13281 - 1.23138i) q^{61} +(0.596141 - 0.344182i) q^{63} +10.5471i q^{65} +(-2.16651 + 1.25083i) q^{67} -1.58336 q^{69} +(8.35311 - 14.4680i) q^{71} +(8.25523 - 14.2985i) q^{73} +3.64532i q^{75} +0.973361i q^{77} +(-4.05535 + 7.02407i) q^{79} +(1.04337 - 1.80717i) q^{81} -11.8333 q^{83} +(-3.51124 + 2.02722i) q^{85} +10.2672i q^{87} +(-6.95256 + 4.01406i) q^{89} +(-1.45537 + 0.840259i) q^{91} +(-0.522665 - 0.301761i) q^{93} +(6.24056 - 10.6360i) q^{95} +(-5.47310 - 3.15990i) q^{97} +(-1.64875 - 2.85571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) $ 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/608\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.05104	+	0.606818i	0.606818	+	0.350346i	0.771719	−	0.635964i	$-0.219397\pi$
$3$	1.05104	+	0.606818i	0.606818	+	0.350346i	−0.164901	+	0.986310i	$0.552731\pi$
$4$		0			0
$5$	2.45005	+	1.41453i	1.09569	+	0.632599i	0.935087	−	0.354419i	$-0.115321\pi$
$5$	2.45005	+	1.41453i	1.09569	+	0.632599i	0.160607	+	0.987018i	$0.448655\pi$
$6$		0			0
$7$			0.450769i			0.170375i	0.996365	+	0.0851873i	$0.0271489\pi$
$7$			0.450769i			0.170375i	−0.996365	+	0.0851873i	$0.972851\pi$
$8$		0			0
$9$	−0.763544	−	1.32250i	−0.254515	−	0.440832i
$10$		0			0
$11$	2.15933			0.651064			0.325532	−	0.945531i	$-0.394457\pi$
$11$	2.15933			0.651064			0.325532	+	0.945531i	$0.394457\pi$
$12$		0			0
$13$	1.86406	+	3.22864i	0.516996	+	0.895464i	0.999805	+	0.0197382i	$0.00628328\pi$
$13$	1.86406	+	3.22864i	0.516996	+	0.895464i	−0.482809	+	0.875726i	$0.660383\pi$
$14$		0			0
$15$	1.71673	+	2.97346i	0.443258	+	0.767745i
$16$		0			0
$17$	−0.716566	+	1.24113i	−0.173793	+	0.301018i	−0.939743	−	0.341882i	$-0.888936\pi$
$17$	−0.716566	+	1.24113i	−0.173793	+	0.301018i	0.765950	+	0.642900i	$0.222269\pi$
$18$		0			0
$19$	0.0305680	−	4.35879i	0.00701278	−	0.999975i
$19$	0.0305680	−	4.35879i	0.00701278	−	0.999975i
$20$		0			0
$21$	−0.273535	+	0.473776i	−0.0596901	+	0.103386i
$22$		0			0
$23$	−1.12985	+	0.652319i	−0.235590	+	0.136018i	−0.613148	−	0.789968i	$-0.710097\pi$
$23$	−1.12985	+	0.652319i	−0.235590	+	0.136018i	0.377558	+	0.925986i	$0.376764\pi$
$24$		0			0
$25$	1.50182	+	2.60122i	0.300363	+	0.520245i
$26$		0			0
$27$		−	5.49424i		−	1.05737i
$28$		0			0
$29$	4.22992	+	7.32644i	0.785477	+	1.36049i	0.928714	+	0.370797i	$0.120915\pi$
$29$	4.22992	+	7.32644i	0.785477	+	1.36049i	−0.143237	+	0.989688i	$0.545751\pi$
$30$		0			0
$31$	−0.497284			−0.0893149			−0.0446575	−	0.999002i	$-0.514220\pi$
$31$	−0.497284			−0.0893149			−0.0446575	+	0.999002i	$0.514220\pi$
$32$		0			0
$33$	2.26955	+	1.31032i	0.395077	+	0.228098i
$34$		0			0
$35$	−0.637628	+	1.10440i	−0.107779	+	0.186678i
$36$		0			0
$37$	−6.72997			−1.10640			−0.553200	−	0.833049i	$-0.686593\pi$
$37$	−6.72997			−1.10640			−0.553200	+	0.833049i	$0.686593\pi$
$38$		0			0
$39$			4.52457i			0.724511i
$40$		0			0
$41$	−7.30919	−	4.21996i	−1.14150	−	0.659047i	−0.194701	−	0.980863i	$-0.562374\pi$
$41$	−7.30919	−	4.21996i	−1.14150	−	0.659047i	−0.946802	+	0.321815i	$0.895707\pi$
$42$		0			0
$43$	−2.90174	+	5.02595i	−0.442511	+	0.766451i	−0.997875	−	0.0651562i	$-0.979245\pi$
$43$	−2.90174	+	5.02595i	−0.442511	+	0.766451i	0.555364	+	0.831607i	$0.312579\pi$
$44$		0			0
$45$		−	4.32024i		−	0.644023i
$46$		0			0
$47$	−0.567335	+	0.327551i	−0.0827543	+	0.0477782i	−0.540806	−	0.841147i	$-0.681881\pi$
$47$	−0.567335	+	0.327551i	−0.0827543	+	0.0477782i	0.458052	+	0.888925i	$0.348547\pi$
$48$		0			0
$49$	6.79681			0.970972
$50$		0			0
$51$	−1.50628	+	0.869651i	−0.210921	+	0.121775i
$52$		0			0
$53$	−3.86444	−	6.69340i	−0.530821	−	0.919409i	−0.999353	−	0.0359626i	$-0.988550\pi$
$53$	−3.86444	−	6.69340i	−0.530821	−	0.919409i	0.468532	−	0.883446i	$-0.344783\pi$
$54$		0			0
$55$	5.29047	+	3.05445i	0.713367	+	0.411862i
$56$		0			0
$57$	2.67712	−	4.56271i	0.354593	−	0.604346i
$58$		0			0
$59$	12.1090	+	6.99113i	1.57646	+	0.910168i	0.995348	+	0.0963425i	$0.0307144\pi$
$59$	12.1090	+	6.99113i	1.57646	+	0.910168i	0.581109	+	0.813826i	$0.302619\pi$
$60$		0			0
$61$	2.13281	−	1.23138i	0.273078	−	0.157662i	−0.357208	−	0.934025i	$-0.616271\pi$
$61$	2.13281	−	1.23138i	0.273078	−	0.157662i	0.630286	+	0.776363i	$0.282938\pi$
$62$		0			0
$63$	0.596141	−	0.344182i	0.0751067	−	0.0433629i
$64$		0			0
$65$			10.5471i			1.30821i
$66$		0			0
$67$	−2.16651	+	1.25083i	−0.264681	+	0.152814i	−0.626468	−	0.779447i	$-0.715500\pi$
$67$	−2.16651	+	1.25083i	−0.264681	+	0.152814i	0.361787	+	0.932261i	$0.382167\pi$
$68$		0			0
$69$	−1.58336			−0.190614
$70$		0			0
$71$	8.35311	−	14.4680i	0.991332	−	1.71704i	0.381888	−	0.924209i	$-0.375274\pi$
$71$	8.35311	−	14.4680i	0.991332	−	1.71704i	0.609444	−	0.792829i	$-0.291393\pi$
$72$		0			0
$73$	8.25523	−	14.2985i	0.966202	−	1.67351i	0.259851	−	0.965649i	$-0.416327\pi$
$73$	8.25523	−	14.2985i	0.966202	−	1.67351i	0.706351	−	0.707862i	$-0.250340\pi$
$74$		0			0
$75$			3.64532i			0.420925i
$76$		0			0
$77$			0.973361i			0.110925i
$78$		0			0
$79$	−4.05535	+	7.02407i	−0.456262	+	0.790269i	−0.998760	−	0.0497881i	$-0.984145\pi$
$79$	−4.05535	+	7.02407i	−0.456262	+	0.790269i	0.542498	+	0.840057i	$0.317479\pi$
$80$		0			0
$81$	1.04337	−	1.80717i	0.115930	−	0.200796i
$82$		0			0
$83$	−11.8333			−1.29887			−0.649435	−	0.760417i	$-0.724994\pi$
$83$	−11.8333			−1.29887			−0.649435	+	0.760417i	$0.724994\pi$
$84$		0			0
$85$	−3.51124	+	2.02722i	−0.380848	+	0.219882i
$86$		0			0
$87$			10.2672i			1.10076i
$88$		0			0
$89$	−6.95256	+	4.01406i	−0.736970	+	0.425490i	−0.820967	−	0.570976i	$-0.806565\pi$
$89$	−6.95256	+	4.01406i	−0.736970	+	0.425490i	0.0839965	+	0.996466i	$0.473232\pi$
$90$		0			0
$91$	−1.45537	+	0.840259i	−0.152564	+	0.0880831i
$92$		0			0
$93$	−0.522665	−	0.301761i	−0.0541979	−	0.0312912i
$94$		0			0
$95$	6.24056	−	10.6360i	0.640267	−	1.09123i
$96$		0			0
$97$	−5.47310	−	3.15990i	−0.555709	−	0.320839i	0.195712	−	0.980661i	$-0.437298\pi$
$97$	−5.47310	−	3.15990i	−0.555709	−	0.320839i	−0.751422	+	0.659822i	$0.770632\pi$
$98$		0			0
$99$	−1.64875	−	2.85571i	−0.165705	−	0.287010i
$100$		0			0
$101$	4.61075	−	2.66202i	0.458787	−	0.264881i	−0.252747	−	0.967532i	$-0.581334\pi$
$101$	4.61075	−	2.66202i	0.458787	−	0.264881i	0.711534	+	0.702652i	$0.248001\pi$
$102$		0			0
$103$	−17.9095			−1.76468			−0.882340	−	0.470613i	$-0.844033\pi$
$103$	−17.9095			−1.76468			−0.882340	+	0.470613i	$0.844033\pi$
$104$		0			0
$105$	−1.34034	+	0.773848i	−0.130804	+	0.0755199i
$106$		0			0
$107$			0.909747i			0.0879485i	0.999033	+	0.0439743i	$0.0140020\pi$
$107$			0.909747i			0.0879485i	−0.999033	+	0.0439743i	$0.985998\pi$
$108$		0			0
$109$	0.935166	−	1.61976i	0.0895727	−	0.155144i	−0.817758	−	0.575562i	$-0.804783\pi$
$109$	0.935166	−	1.61976i	0.0895727	−	0.155144i	0.907331	+	0.420418i	$0.138117\pi$
$110$		0			0
$111$	−7.07346	−	4.08386i	−0.671383	−	0.387623i
$112$		0			0
$113$			2.34200i			0.220317i	0.993914	+	0.110159i	$0.0351359\pi$
$113$			2.34200i			0.220317i	−0.993914	+	0.110159i	$0.964864\pi$
$114$		0			0
$115$	−3.69091			−0.344179
$116$		0			0
$117$	2.84658	−	4.93042i	0.263166	−	0.455818i
$118$		0			0
$119$	−0.559462	−	0.323006i	−0.0512858	−	0.0296099i
$120$		0			0
$121$	−6.33727			−0.576116
$122$		0			0
$123$	−5.12150	−	8.87069i	−0.461790	−	0.799843i
$124$		0			0
$125$		−	5.64786i		−	0.505160i
$126$		0			0
$127$	−1.06604	−	1.84643i	−0.0945955	−	0.163844i	0.814844	−	0.579680i	$-0.196822\pi$
$127$	−1.06604	−	1.84643i	−0.0945955	−	0.163844i	−0.909440	+	0.415836i	$0.863489\pi$
$128$		0			0
$129$	−6.09968	+	3.52165i	−0.537047	+	0.310064i
$130$		0			0
$131$	8.72441	−	15.1111i	0.762255	−	1.32026i	−0.179430	−	0.983771i	$-0.557425\pi$
$131$	8.72441	−	15.1111i	0.762255	−	1.32026i	0.941686	−	0.336494i	$-0.109241\pi$
$132$		0			0
$133$	1.96481	+	0.0137791i	0.170370	+	0.00119480i
$134$		0			0
$135$	7.77179	−	13.4611i	0.668889	−	1.15855i
$136$		0			0
$137$	−4.28881	−	7.42843i	−0.366417	−	0.634654i	0.622585	−	0.782552i	$-0.286082\pi$
$137$	−4.28881	−	7.42843i	−0.366417	−	0.634654i	−0.989003	+	0.147898i	$0.952749\pi$
$138$		0			0
$139$	2.38145	+	4.12479i	0.201992	+	0.349860i	0.949170	−	0.314763i	$-0.101925\pi$
$139$	2.38145	+	4.12479i	0.201992	+	0.349860i	−0.747178	+	0.664624i	$0.768592\pi$
$140$		0			0
$141$	−0.795055			−0.0669557
$142$		0			0
$143$	4.02512	+	6.97172i	0.336598	+	0.583004i
$144$		0			0
$145$			23.9335i			1.98757i
$146$		0			0
$147$	7.14371	+	4.12442i	0.589203	+	0.340177i
$148$		0			0
$149$	−9.33207	−	5.38787i	−0.764513	−	0.441392i	0.0664008	−	0.997793i	$-0.478848\pi$
$149$	−9.33207	−	5.38787i	−0.764513	−	0.441392i	−0.830914	+	0.556401i	$0.812182\pi$
$150$		0			0
$151$	−5.40642			−0.439968			−0.219984	−	0.975503i	$-0.570601\pi$
$151$	−5.40642			−0.439968			−0.219984	+	0.975503i	$0.570601\pi$
$152$		0			0
$153$	2.18852			0.176931
$154$		0			0
$155$	−1.21837	−	0.703426i	−0.0978618	−	0.0565005i
$156$		0			0
$157$	−13.3288	−	7.69539i	−1.06375	−	0.614159i	−0.137286	−	0.990531i	$-0.543838\pi$
$157$	−13.3288	−	7.69539i	−1.06375	−	0.614159i	−0.926468	+	0.376373i	$0.877171\pi$
$158$		0			0
$159$		−	9.38003i		−	0.743885i
$160$		0			0
$161$	−0.294045	−	0.509301i	−0.0231740	−	0.0401386i
$162$		0			0
$163$	−0.534048			−0.0418298			−0.0209149	−	0.999781i	$-0.506658\pi$
$163$	−0.534048			−0.0418298			−0.0209149	+	0.999781i	$0.506658\pi$
$164$		0			0
$165$	3.70699	+	6.42070i	0.288589	+	0.499851i
$166$		0			0
$167$	−6.81811	−	11.8093i	−0.527601	−	0.913832i	−0.999482	−	0.0321697i	$-0.989758\pi$
$167$	−6.81811	−	11.8093i	−0.527601	−	0.913832i	0.471881	−	0.881662i	$-0.343575\pi$
$168$		0			0
$169$	−0.449417	+	0.778413i	−0.0345705	+	0.0598779i
$170$		0			0
$171$	−5.78783	+	3.28770i	−0.442606	+	0.251417i
$172$		0			0
$173$	−0.822987	+	1.42546i	−0.0625706	+	0.108375i	−0.895614	−	0.444833i	$-0.853263\pi$
$173$	−0.822987	+	1.42546i	−0.0625706	+	0.108375i	0.833043	+	0.553208i	$0.186597\pi$
$174$		0			0
$175$	−1.17255	+	0.676972i	−0.0886365	+	0.0511743i
$176$		0			0
$177$	8.48469	+	14.6959i	0.637748	+	1.10461i
$178$		0			0
$179$		−	7.67159i		−	0.573402i	−0.958020	−	0.286701i	$-0.907441\pi$
$179$		−	7.67159i		−	0.573402i	0.958020	−	0.286701i	$-0.0925586\pi$
$180$		0			0
$181$	11.7649	+	20.3774i	0.874479	+	1.51464i	0.857316	+	0.514790i	$0.172130\pi$
$181$	11.7649	+	20.3774i	0.874479	+	1.51464i	0.0171632	+	0.999853i	$0.494537\pi$
$182$		0			0
$183$	2.98889			0.220945
$184$		0			0
$185$	−16.4887	−	9.51977i	−1.21228	−	0.699908i
$186$		0			0
$187$	−1.54731	+	2.68001i	−0.113150	+	0.195982i
$188$		0			0
$189$	2.47663			0.180148
$190$		0			0
$191$		−	23.8645i		−	1.72678i	−0.504540	−	0.863388i	$-0.668338\pi$
$191$		−	23.8645i		−	1.72678i	0.504540	−	0.863388i	$-0.331662\pi$
$192$		0			0
$193$	16.5463	+	9.55301i	1.19103	+	0.687641i	0.958540	−	0.284958i	$-0.0919798\pi$
$193$	16.5463	+	9.55301i	1.19103	+	0.687641i	0.232489	+	0.972599i	$0.425313\pi$
$194$		0			0
$195$	−6.40016	+	11.0854i	−0.458325	+	0.793843i
$196$		0			0
$197$		−	11.2480i		−	0.801385i	−0.916213	−	0.400693i	$-0.868770\pi$
$197$		−	11.2480i		−	0.801385i	0.916213	−	0.400693i	$-0.131230\pi$
$198$		0			0
$199$	−9.91953	+	5.72704i	−0.703177	+	0.405979i	−0.808530	−	0.588456i	$-0.799736\pi$
$199$	−9.91953	+	5.72704i	−0.703177	+	0.405979i	0.105353	+	0.994435i	$0.466403\pi$
$200$		0			0
$201$	−3.03611			−0.214151
$202$		0			0
$203$	−3.30253	+	1.90672i	−0.231792	+	0.133825i
$204$		0			0
$205$	−11.9386	−	20.6782i	−0.833825	−	1.44423i
$206$		0			0
$207$	1.72538	+	0.996149i	0.119922	+	0.0692371i
$208$		0			0
$209$	0.0660065	−	9.41209i	0.00456577	−	0.651048i
$210$		0			0
$211$	13.8288	+	7.98406i	0.952013	+	0.549645i	0.893706	−	0.448653i	$-0.148096\pi$
$211$	13.8288	+	7.98406i	0.952013	+	0.549645i	0.0583076	+	0.998299i	$0.481430\pi$
$212$		0			0
$213$	17.5589	−	10.1376i	1.20312	−	0.694619i
$214$		0			0
$215$	−14.2188	+	8.20921i	−0.969712	+	0.559864i
$216$		0			0
$217$		−	0.224160i		−	0.0152170i
$218$		0			0
$219$	17.3531	−	10.0188i	1.17262	−	0.677011i
$220$		0			0
$221$	−5.34288			−0.359401
$222$		0			0
$223$	−8.06323	+	13.9659i	−0.539954	+	0.935227i	0.458952	+	0.888461i	$0.348225\pi$
$223$	−8.06323	+	13.9659i	−0.539954	+	0.935227i	−0.998906	+	0.0467660i	$0.985108\pi$
$224$		0			0
$225$	2.29341	−	3.97230i	0.152894	−	0.264820i
$226$		0			0
$227$			13.0282i			0.864715i	0.901702	+	0.432357i	$0.142318\pi$
$227$			13.0282i			0.864715i	−0.901702	+	0.432357i	$0.857682\pi$
$228$		0			0
$229$			12.7253i			0.840914i	0.907312	+	0.420457i	$0.138130\pi$
$229$			12.7253i			0.840914i	−0.907312	+	0.420457i	$0.861870\pi$
$230$		0			0
$231$	−0.590653	+	1.02304i	−0.0388621	+	0.0673111i
$232$		0			0
$233$	5.77758	−	10.0071i	0.378502	−	0.655585i	−0.612343	−	0.790593i	$-0.709773\pi$
$233$	5.77758	−	10.0071i	0.378502	−	0.655585i	0.990845	+	0.135008i	$0.0431060\pi$
$234$		0			0
$235$	−1.85333			−0.120898
$236$		0			0
$237$	−8.52466	+	4.92171i	−0.553736	+	0.319700i
$238$		0			0
$239$			18.8301i			1.21802i	0.793163	+	0.609010i	$0.208433\pi$
$239$			18.8301i			1.21802i	−0.793163	+	0.609010i	$0.791567\pi$
$240$		0			0
$241$	−8.47571	+	4.89346i	−0.545969	+	0.315215i	−0.747494	−	0.664268i	$-0.768743\pi$
$241$	−8.47571	+	4.89346i	−0.545969	+	0.315215i	0.201526	+	0.979483i	$0.435410\pi$
$242$		0			0
$243$	−12.0812	+	6.97509i	−0.775009	+	0.447452i
$244$		0			0
$245$	16.6525	+	9.61432i	1.06389	+	0.614236i
$246$		0			0
$247$	14.1300	−	8.02634i	0.899068	−	0.510704i
$248$		0			0
$249$	−12.4372	−	7.18063i	−0.788177	−	0.455054i
$250$		0			0
$251$	−8.19032	−	14.1861i	−0.516969	−	0.895416i	−0.999806	−	0.0197059i	$-0.993727\pi$
$251$	−8.19032	−	14.1861i	−0.516969	−	0.895416i	0.482837	−	0.875710i	$-0.339606\pi$
$252$		0			0
$253$	−2.43972	+	1.40858i	−0.153384	+	0.0885564i
$254$		0			0
$255$	−4.92060			−0.308140
$256$		0			0
$257$	7.56834	−	4.36958i	0.472100	−	0.272567i	−0.245019	−	0.969518i	$-0.578794\pi$
$257$	7.56834	−	4.36958i	0.472100	−	0.272567i	0.717118	+	0.696951i	$0.245461\pi$
$258$		0			0
$259$		−	3.03366i		−	0.188502i
$260$		0			0
$261$	6.45946	−	11.1881i	0.399831	−	0.692527i
$262$		0			0
$263$	24.1288	+	13.9308i	1.48785	+	0.859008i	0.999904	−	0.0138683i	$-0.00441455\pi$
$263$	24.1288	+	13.9308i	1.48785	+	0.859008i	0.487942	+	0.872876i	$0.337748\pi$
$264$		0			0
$265$		−	21.8655i		−	1.34319i
$266$		0			0
$267$	−9.74322			−0.596276
$268$		0			0
$269$	−11.8357	+	20.5001i	−0.721638	+	1.24991i	0.238704	+	0.971092i	$0.423277\pi$
$269$	−11.8357	+	20.5001i	−0.721638	+	1.24991i	−0.960343	+	0.278822i	$0.910056\pi$
$270$		0			0
$271$	15.9524	+	9.21013i	0.969041	+	0.559476i	0.898944	−	0.438064i	$-0.144336\pi$
$271$	15.9524	+	9.21013i	0.969041	+	0.559476i	0.0700969	+	0.997540i	$0.477669\pi$
$272$		0			0
$273$	−2.03954			−0.123438
$274$		0			0
$275$	3.24293	+	5.61691i	0.195556	+	0.338713i
$276$		0			0
$277$			26.0321i			1.56412i	0.623203	+	0.782060i	$0.285831\pi$
$277$			26.0321i			1.56412i	−0.623203	+	0.782060i	$0.714169\pi$
$278$		0			0
$279$	0.379699	+	0.657657i	0.0227320	+	0.0393729i
$280$		0			0
$281$	18.1670	−	10.4887i	1.08375	−	0.625706i	0.151848	−	0.988404i	$-0.451478\pi$
$281$	18.1670	−	10.4887i	1.08375	−	0.625706i	0.931907	+	0.362698i	$0.118144\pi$
$282$		0			0
$283$	5.72882	−	9.92260i	0.340543	−	0.589837i	−0.643991	−	0.765033i	$-0.722723\pi$
$283$	5.72882	−	9.92260i	0.340543	−	0.589837i	0.984534	+	0.175196i	$0.0560558\pi$
$284$		0			0
$285$	13.0132	−	7.39198i	0.770835	−	0.437863i
$286$		0			0
$287$	1.90223	−	3.29475i	0.112285	−	0.194483i
$288$		0			0
$289$	7.47307	+	12.9437i	0.439592	+	0.761396i
$290$		0			0
$291$	−3.83496	−	6.64235i	−0.224810	−	0.389382i
$292$		0			0
$293$	−10.4003			−0.607590			−0.303795	−	0.952737i	$-0.598254\pi$
$293$	−10.4003			−0.607590			−0.303795	+	0.952737i	$0.598254\pi$
$294$		0			0
$295$	19.7784	+	34.2572i	1.15154	+	1.99453i
$296$		0			0
$297$		−	11.8639i		−	0.688413i
$298$		0			0
$299$	−4.21221	−	2.43192i	−0.243598	−	0.140642i
$300$		0			0
$301$	−2.26554	−	1.30801i	−0.130584	−	0.0753926i
$302$		0			0
$303$	6.46144			0.371200
$304$		0			0
$305$	6.96731			0.398947
$306$		0			0
$307$	2.39992	+	1.38560i	0.136971	+	0.0790801i	0.566920	−	0.823773i	$-0.308135\pi$
$307$	2.39992	+	1.38560i	0.136971	+	0.0790801i	−0.429949	+	0.902853i	$0.641468\pi$
$308$		0			0
$309$	−18.8236	−	10.8678i	−1.07084	−	0.618249i
$310$		0			0
$311$		−	13.8001i		−	0.782530i	−0.920278	−	0.391265i	$-0.872038\pi$
$311$		−	13.8001i		−	0.782530i	0.920278	−	0.391265i	$-0.127962\pi$
$312$		0			0
$313$	5.89194	+	10.2051i	0.333032	+	0.576829i	0.983105	−	0.183043i	$-0.0585949\pi$
$313$	5.89194	+	10.2051i	0.333032	+	0.576829i	−0.650073	+	0.759872i	$0.725262\pi$
$314$		0			0
$315$	1.94743			0.109725
$316$		0			0
$317$	8.86581	+	15.3560i	0.497953	+	0.862480i	0.999997	−	0.00236177i	$-0.000751775\pi$
$317$	8.86581	+	15.3560i	0.497953	+	0.862480i	−0.502044	+	0.864842i	$0.667418\pi$
$318$		0			0
$319$	9.13381	+	15.8202i	0.511395	+	0.885763i
$320$		0			0
$321$	−0.552051	+	0.956180i	−0.0308125	+	0.0533687i
$322$		0			0
$323$	5.38792	+	3.16130i	0.299792	+	0.175900i
$324$		0			0
$325$	−5.59894	+	9.69766i	−0.310574	+	0.537929i
$326$		0			0
$327$	1.96579	−	1.13495i	0.108709	−	0.0627630i
$328$		0			0
$329$	−0.147650	−	0.255737i	−0.00814020	−	0.0140992i
$330$		0			0
$331$			27.3712i			1.50445i	0.658904	+	0.752227i	$0.271020\pi$
$331$			27.3712i			1.50445i	−0.658904	+	0.752227i	$0.728980\pi$
$332$		0			0
$333$	5.13863	+	8.90036i	0.281595	+	0.487737i
$334$		0			0
$335$	−7.07739			−0.386679
$336$		0			0
$337$	10.7104	+	6.18363i	0.583430	+	0.336844i	0.762495	−	0.646994i	$-0.223974\pi$
$337$	10.7104	+	6.18363i	0.583430	+	0.336844i	−0.179065	+	0.983837i	$0.557307\pi$
$338$		0			0
$339$	−1.42117	+	2.46154i	−0.0771873	+	0.133692i
$340$		0			0
$341$	−1.07380			−0.0581497
$342$		0			0
$343$			6.21917i			0.335804i
$344$		0			0
$345$	−3.87929	−	2.23971i	−0.208854	−	0.120582i
$346$		0			0
$347$	5.69195	−	9.85874i	0.305560	−	0.529245i	−0.671826	−	0.740709i	$-0.734490\pi$
$347$	5.69195	−	9.85874i	0.305560	−	0.529245i	0.977386	+	0.211464i	$0.0678231\pi$
$348$		0			0
$349$			2.93676i			0.157201i	0.996906	+	0.0786007i	$0.0250452\pi$
$349$			2.93676i			0.157201i	−0.996906	+	0.0786007i	$0.974955\pi$
$350$		0			0
$351$	17.7389	−	10.2416i	0.946833	−	0.546655i
$352$		0			0
$353$	19.1919			1.02148			0.510740	−	0.859735i	$-0.329371\pi$
$353$	19.1919			1.02148			0.510740	+	0.859735i	$0.329371\pi$
$354$		0			0
$355$	40.9310	−	23.6315i	2.17239	−	1.25423i
$356$		0			0
$357$	−0.392011	−	0.678984i	−0.0207474	−	0.0359356i
$358$		0			0
$359$	−3.85728	−	2.22700i	−0.203579	−	0.117537i	0.394745	−	0.918791i	$-0.370833\pi$
$359$	−3.85728	−	2.22700i	−0.203579	−	0.117537i	−0.598324	+	0.801254i	$0.704166\pi$
$360$		0			0
$361$	−18.9981	−	0.266479i	−0.999902	−	0.0140252i
$362$		0			0
$363$	−6.66072	−	3.84557i	−0.349597	−	0.201840i
$364$		0			0
$365$	40.4514	−	23.3546i	2.11732	−	1.22244i
$366$		0			0
$367$	−16.5629	+	9.56259i	−0.864576	+	0.499163i	−0.865542	−	0.500837i	$-0.833026\pi$
$367$	−16.5629	+	9.56259i	−0.864576	+	0.499163i	0.000966198		1.00000i	$0.499692\pi$
$368$		0			0
$369$			12.8885i			0.670949i
$370$		0			0
$371$	3.01718	−	1.74197i	0.156644	−	0.0904384i
$372$		0			0
$373$	−20.6810			−1.07082			−0.535411	−	0.844592i	$-0.679843\pi$
$373$	−20.6810			−1.07082			−0.535411	+	0.844592i	$0.679843\pi$
$374$		0			0
$375$	3.42722	−	5.93612i	0.176981	−	0.306540i
$376$		0			0
$377$	−15.7696	+	27.3138i	−0.812177	+	1.40673i
$378$		0			0
$379$		−	2.56021i		−	0.131509i	−0.997836	−	0.0657546i	$-0.979055\pi$
$379$		−	2.56021i		−	0.131509i	0.997836	−	0.0657546i	$-0.0209454\pi$
$380$		0			0
$381$		−	2.58756i		−	0.132565i
$382$		0			0
$383$	−9.13650	+	15.8249i	−0.466853	+	0.808613i	−0.999283	−	0.0378608i	$-0.987946\pi$
$383$	−9.13650	+	15.8249i	−0.466853	+	0.808613i	0.532430	+	0.846474i	$0.321279\pi$
$384$		0			0
$385$	−1.37685	+	2.38478i	−0.0701709	+	0.121540i
$386$		0			0
$387$	8.86241			0.450502
$388$		0			0
$389$	12.4317	−	7.17743i	0.630311	−	0.363910i	−0.150562	−	0.988601i	$-0.548108\pi$
$389$	12.4317	−	7.17743i	0.630311	−	0.363910i	0.780872	+	0.624690i	$0.214775\pi$
$390$		0			0
$391$		−	1.86972i		−	0.0945558i
$392$		0			0
$393$	18.3394	−	10.5883i	0.925100	−	0.534107i
$394$		0			0
$395$	−19.8716	+	11.4729i	−0.999847	+	0.577262i
$396$		0			0
$397$	22.8960	+	13.2190i	1.14912	+	0.663444i	0.948673	−	0.316260i	$-0.102427\pi$
$397$	22.8960	+	13.2190i	1.14912	+	0.663444i	0.200447	+	0.979705i	$0.435761\pi$
$398$		0			0
$399$	2.05673	+	1.20676i	0.102965	+	0.0604137i
$400$		0			0
$401$	−6.10144	−	3.52267i	−0.304691	−	0.175914i	0.339857	−	0.940477i	$-0.389621\pi$
$401$	−6.10144	−	3.52267i	−0.304691	−	0.175914i	−0.644549	+	0.764563i	$0.722955\pi$
$402$		0			0
$403$	−0.926966	−	1.60555i	−0.0461755	−	0.0799783i
$404$		0			0
$405$	5.11260	−	2.95176i	0.254047	−	0.146674i
$406$		0			0
$407$	−14.5323			−0.720337
$408$		0			0
$409$	17.6696	−	10.2015i	0.873705	−	0.504434i	0.00512749	−	0.999987i	$-0.498368\pi$
$409$	17.6696	−	10.2015i	0.873705	−	0.504434i	0.868578	+	0.495553i	$0.165035\pi$
$410$		0			0
$411$		−	10.4101i		−	0.513492i
$412$		0			0
$413$	−3.15139	+	5.45836i	−0.155070	+	0.268588i
$414$		0			0
$415$	−28.9920	−	16.7386i	−1.42316	−	0.821664i
$416$		0			0
$417$			5.78043i			0.283069i
$418$		0			0
$419$	7.69306			0.375831			0.187915	−	0.982185i	$-0.439827\pi$
$419$	7.69306			0.375831			0.187915	+	0.982185i	$0.439827\pi$
$420$		0			0
$421$	−3.05025	+	5.28319i	−0.148660	+	0.257487i	−0.930732	−	0.365701i	$-0.880829\pi$
$421$	−3.05025	+	5.28319i	−0.148660	+	0.257487i	0.782072	+	0.623188i	$0.214163\pi$
$422$		0			0
$423$	0.866371	+	0.500199i	0.0421244	+	0.0243205i
$424$		0			0
$425$	−4.30461			−0.208804
$426$		0			0
$427$	0.555067	+	0.961404i	0.0268616	+	0.0465256i
$428$		0			0
$429$			9.77007i			0.471703i
$430$		0			0
$431$	4.72335	+	8.18108i	0.227516	+	0.394069i	0.957071	−	0.289853i	$-0.0936063\pi$
$431$	4.72335	+	8.18108i	0.227516	+	0.394069i	−0.729555	+	0.683922i	$0.760273\pi$
$432$		0			0
$433$	−14.9419	+	8.62669i	−0.718061	+	0.414572i	−0.814038	−	0.580811i	$-0.802736\pi$
$433$	−14.9419	+	8.62669i	−0.718061	+	0.414572i	0.0959778	+	0.995383i	$0.469402\pi$
$434$		0			0
$435$	−14.5233	+	25.1550i	−0.696337	+	1.20609i
$436$		0			0
$437$	2.80879	+	4.94472i	0.134362	+	0.236538i
$438$		0			0
$439$	4.84656	−	8.39450i	0.231314	−	0.400647i	−0.726881	−	0.686763i	$-0.759031\pi$
$439$	4.84656	−	8.39450i	0.231314	−	0.400647i	0.958195	+	0.286116i	$0.0923642\pi$
$440$		0			0
$441$	−5.18966	−	8.98876i	−0.247127	−	0.428036i
$442$		0			0
$443$	−8.03408	−	13.9154i	−0.381711	−	0.661142i	0.609596	−	0.792712i	$-0.291332\pi$
$443$	−8.03408	−	13.9154i	−0.381711	−	0.661142i	−0.991307	+	0.131570i	$0.957998\pi$
$444$		0			0
$445$	−22.7121			−1.07666
$446$		0			0
$447$	−6.53892	−	11.3257i	−0.309280	−	0.535689i
$448$		0			0
$449$		−	12.4409i		−	0.587123i	−0.955940	−	0.293562i	$-0.905159\pi$
$449$		−	12.4409i		−	0.587123i	0.955940	−	0.293562i	$-0.0948406\pi$
$450$		0			0
$451$	−15.7830	−	9.11231i	−0.743192	−	0.429082i
$452$		0			0
$453$	−5.68236	−	3.28071i	−0.266981	−	0.154141i
$454$		0			0
$455$	−4.75430			−0.222885
$456$		0			0
$457$	−23.5694			−1.10253			−0.551265	−	0.834330i	$-0.685855\pi$
$457$	−23.5694			−1.10253			−0.551265	+	0.834330i	$0.685855\pi$
$458$		0			0
$459$	6.81906	+	3.93698i	0.318286	+	0.183763i
$460$		0			0
$461$	−0.956655	−	0.552325i	−0.0445559	−	0.0257243i	0.477557	−	0.878601i	$-0.341523\pi$
$461$	−0.956655	−	0.552325i	−0.0445559	−	0.0257243i	−0.522112	+	0.852877i	$0.674856\pi$
$462$		0			0
$463$		−	26.1205i		−	1.21392i	−0.794731	−	0.606962i	$-0.792388\pi$
$463$		−	26.1205i		−	1.21392i	0.794731	−	0.606962i	$-0.207612\pi$
$464$		0			0
$465$	−0.853703	−	1.47866i	−0.0395895	−	0.0685711i
$466$		0			0
$467$	18.4324			0.852950			0.426475	−	0.904499i	$-0.359755\pi$
$467$	18.4324			0.852950			0.426475	+	0.904499i	$0.359755\pi$
$468$		0			0
$469$	−0.563837	−	0.976594i	−0.0260356	−	0.0450949i
$470$		0			0
$471$	−9.33940	−	16.1763i	−0.430337	−	0.745365i
$472$		0			0
$473$	−6.26582	+	10.8527i	−0.288103	+	0.499008i
$474$		0			0
$475$	11.3841	−	6.46659i	0.522338	−	0.296708i
$476$		0			0
$477$	−5.90133	+	10.2214i	−0.270204	+	0.468006i
$478$		0			0
$479$	26.2671	−	15.1653i	1.20018	−	0.692922i	0.239581	−	0.970876i	$-0.422990\pi$
$479$	26.2671	−	15.1653i	1.20018	−	0.692922i	0.960594	+	0.277955i	$0.0896565\pi$
$480$		0			0
$481$	−12.5450	−	21.7287i	−0.572005	−	0.990741i
$482$		0			0
$483$		−	0.713727i		−	0.0324757i
$484$		0			0
$485$	−8.93957	−	15.4838i	−0.405925	−	0.703083i
$486$		0			0
$487$	−41.6132			−1.88568			−0.942838	−	0.333253i	$-0.891854\pi$
$487$	−41.6132			−1.88568			−0.942838	+	0.333253i	$0.891854\pi$
$488$		0			0
$489$	−0.561305	−	0.324070i	−0.0253831	−	0.0146549i
$490$		0			0
$491$	−15.3752	+	26.6306i	−0.693873	+	1.20182i	0.276686	+	0.960960i	$0.410764\pi$
$491$	−15.3752	+	26.6306i	−0.693873	+	1.20182i	−0.970559	+	0.240863i	$0.922570\pi$
$492$		0			0
$493$	−12.1241			−0.546041
$494$		0			0
$495$		−	9.32884i		−	0.419300i
$496$		0			0
$497$	6.52173	+	3.76532i	0.292540	+	0.168898i
$498$		0			0
$499$	−12.0566	+	20.8826i	−0.539728	+	0.934835i	0.459191	+	0.888338i	$0.348139\pi$
$499$	−12.0566	+	20.8826i	−0.539728	+	0.934835i	−0.998918	+	0.0464978i	$0.985194\pi$
$500$		0			0
$501$		−	16.5494i		−	0.739373i
$502$		0			0
$503$	−10.6337	+	6.13939i	−0.474135	+	0.273742i	−0.717969	−	0.696075i	$-0.754928\pi$
$503$	−10.6337	+	6.13939i	−0.474135	+	0.273742i	0.243834	+	0.969817i	$0.421595\pi$
$504$		0			0
$505$	15.0621			0.670253
$506$		0			0
$507$	−0.944710	+	0.545429i	−0.0419560	+	0.0242233i
$508$		0			0
$509$	2.27630	+	3.94266i	0.100895	+	0.174755i	0.912054	−	0.410071i	$-0.134496\pi$
$509$	2.27630	+	3.94266i	0.100895	+	0.174755i	−0.811159	+	0.584826i	$0.801163\pi$
$510$		0			0
$511$	6.44531	+	3.72120i	0.285124	+	0.164616i
$512$		0			0
$513$	−23.9482	−	0.167948i	−1.05734	−	0.00741507i
$514$		0			0
$515$	−43.8792	−	25.3337i	−1.93355	−	1.11633i
$516$		0			0
$517$	−1.22507	+	0.707292i	−0.0538784	+	0.0311067i
$518$		0			0
$519$	−1.72998	+	0.998807i	−0.0759379	+	0.0438428i
$520$		0			0
$521$			14.0347i			0.614871i	0.951569	+	0.307436i	$0.0994709\pi$
$521$			14.0347i			0.614871i	−0.951569	+	0.307436i	$0.900529\pi$
$522$		0			0
$523$	5.94814	−	3.43416i	0.260094	−	0.150165i	−0.364283	−	0.931288i	$-0.618686\pi$
$523$	5.94814	−	3.43416i	0.260094	−	0.150165i	0.624378	+	0.781123i	$0.285353\pi$
$524$		0			0
$525$	−1.64320			−0.0717149
$526$		0			0
$527$	0.356337	−	0.617194i	0.0155223	−	0.0268854i
$528$		0			0
$529$	−10.6490	+	18.4445i	−0.462998	+	0.801936i
$530$		0			0
$531$		−	21.3522i		−	0.926605i
$532$		0			0
$533$		−	31.4650i		−	1.36290i
$534$		0			0
$535$	−1.28687	+	2.22892i	−0.0556362	+	0.0963647i
$536$		0			0
$537$	4.65526	−	8.06314i	0.200889	−	0.347950i
$538$		0			0
$539$	14.6766			0.632165
$540$		0			0
$541$	34.4443	−	19.8865i	1.48088	−	0.854985i	0.481113	−	0.876659i	$-0.340233\pi$
$541$	34.4443	−	19.8865i	1.48088	−	0.854985i	0.999765	+	0.0216733i	$0.00689936\pi$
$542$		0			0
$543$			28.5566i			1.22548i
$544$		0			0
$545$	4.58240	−	2.64565i	0.196289	−	0.113327i
$546$		0			0
$547$	9.78439	−	5.64902i	0.418350	−	0.241535i	−0.276021	−	0.961152i	$-0.589016\pi$
$547$	9.78439	−	5.64902i	0.418350	−	0.241535i	0.694371	+	0.719617i	$0.255683\pi$
$548$		0			0
$549$	−3.25699	−	1.88042i	−0.139005	−	0.0802545i
$550$		0			0
$551$	32.0637	−	18.2134i	1.36596	−	0.775916i
$552$		0			0
$553$	−3.16623	−	1.82802i	−0.134642	−	0.0777355i
$554$		0			0
$555$	−11.5535	−	20.0113i	−0.490420	−	0.849433i
$556$		0			0
$557$	−20.8369	+	12.0302i	−0.882888	+	0.509735i	−0.871609	−	0.490201i	$-0.836923\pi$
$557$	−20.8369	+	12.0302i	−0.882888	+	0.509735i	−0.0112782	+	0.999936i	$0.503590\pi$
$558$		0			0
$559$	−21.6360			−0.915106
$560$		0			0
$561$	−3.25256	+	1.87787i	−0.137323	+	0.0792836i
$562$		0			0
$563$			30.2137i			1.27336i	0.771130	+	0.636678i	$0.219692\pi$
$563$			30.2137i			1.27336i	−0.771130	+	0.636678i	$0.780308\pi$
$564$		0			0
$565$	−3.31284	+	5.73801i	−0.139372	+	0.241400i
$566$		0			0
$567$	0.814614	+	0.470318i	0.0342106	+	0.0197515i
$568$		0			0
$569$			31.3114i			1.31264i	0.754482	+	0.656320i	$0.227888\pi$
$569$			31.3114i			1.31264i	−0.754482	+	0.656320i	$0.772112\pi$
$570$		0			0
$571$	36.8938			1.54396			0.771978	−	0.635649i	$-0.219267\pi$
$571$	36.8938			1.54396			0.771978	+	0.635649i	$0.219267\pi$
$572$		0			0
$573$	14.4814	−	25.0826i	0.604970	−	1.04784i
$574$		0			0
$575$	−3.39366	−	1.95933i	−0.141525	−	0.0817096i
$576$		0			0
$577$	−1.16074			−0.0483220			−0.0241610	−	0.999708i	$-0.507691\pi$
$577$	−1.16074			−0.0483220			−0.0241610	+	0.999708i	$0.507691\pi$
$578$		0			0
$579$	11.5939	+	20.0812i	0.481825	+	0.834545i
$580$		0			0
$581$		−	5.33407i		−	0.221294i
$582$		0			0
$583$	−8.34461	−	14.4533i	−0.345598	−	0.598594i
$584$		0			0
$585$	13.9485	−	8.05317i	0.576700	−	0.332958i
$586$		0			0
$587$	0.751317	−	1.30132i	0.0310102	−	0.0537112i	−0.850104	−	0.526615i	$-0.823461\pi$
$587$	0.751317	−	1.30132i	0.0310102	−	0.0537112i	0.881114	+	0.472904i	$0.156794\pi$
$588$		0			0
$589$	−0.0152010	+	2.16756i	−0.000626346	+	0.0893127i
$590$		0			0
$591$	6.82547	−	11.8221i	0.280763	−	0.486295i
$592$		0			0
$593$	9.24084	+	16.0056i	0.379476	+	0.657271i	0.990986	−	0.133965i	$-0.0427710\pi$
$593$	9.24084	+	16.0056i	0.379476	+	0.657271i	−0.611510	+	0.791237i	$0.709438\pi$
$594$		0			0
$595$	−0.913806	−	1.58276i	−0.0374624	−	0.0648868i
$596$		0			0
$597$	−13.9011			−0.568934
$598$		0			0
$599$	16.6212	+	28.7888i	0.679124	+	1.17628i	0.975245	+	0.221127i	$0.0709734\pi$
$599$	16.6212	+	28.7888i	0.679124	+	1.17628i	−0.296121	+	0.955150i	$0.595693\pi$
$600$		0			0
$601$		−	11.1345i		−	0.454186i	−0.973873	−	0.227093i	$-0.927078\pi$
$601$		−	11.1345i		−	0.454186i	0.973873	−	0.227093i	$-0.0729221\pi$
$602$		0			0
$603$	3.30845	+	1.91013i	0.134730	+	0.0777867i
$604$		0			0
$605$	−15.5266	−	8.96429i	−0.631247	−	0.364450i
$606$		0			0
$607$	11.2378			0.456127			0.228064	−	0.973646i	$-0.426761\pi$
$607$	11.2378			0.456127			0.228064	+	0.973646i	$0.426761\pi$
$608$		0			0
$609$	−4.62812			−0.187541
$610$		0			0
$611$	−2.11509	−	1.22115i	−0.0855674	−	0.0494024i
$612$		0			0
$613$	20.5664	+	11.8740i	0.830669	+	0.479587i	0.854082	−	0.520139i	$-0.174120\pi$
$613$	20.5664	+	11.8740i	0.830669	+	0.479587i	−0.0234126	+	0.999726i	$0.507453\pi$
$614$		0			0
$615$		−	28.9781i		−	1.16851i
$616$		0			0
$617$	−2.53920	−	4.39802i	−0.102224	−	0.177058i	0.810376	−	0.585910i	$-0.199263\pi$
$617$	−2.53920	−	4.39802i	−0.102224	−	0.177058i	−0.912601	+	0.408852i	$0.865929\pi$
$618$		0			0
$619$	−45.0160			−1.80935			−0.904674	−	0.426105i	$-0.859885\pi$
$619$	−45.0160			−1.80935			−0.904674	+	0.426105i	$0.859885\pi$
$620$		0			0
$621$	3.58400	+	6.20766i	0.143821	+	0.249105i
$622$		0			0
$623$	−1.80941	−	3.13400i	−0.0724927	−	0.125561i
$624$		0			0
$625$	15.4982	−	26.8436i	0.619927	−	1.07375i
$626$		0			0
$627$	5.78080	−	9.85242i	0.230863	−	0.393468i
$628$		0			0
$629$	4.82247	−	8.35276i	0.192284	−	0.333046i
$630$		0			0
$631$	20.6719	−	11.9349i	0.822936	−	0.475122i	−0.0284918	−	0.999594i	$-0.509070\pi$
$631$	20.6719	−	11.9349i	0.822936	−	0.475122i	0.851428	+	0.524472i	$0.175737\pi$
$632$		0			0
$633$	9.68974	+	16.7831i	0.385132	+	0.667069i
$634$		0			0
$635$		−	6.03179i		−	0.239364i
$636$		0			0
$637$	12.6696	+	21.9445i	0.501989	+	0.869471i
$638$		0			0
$639$	−25.5119			−1.00923
$640$		0			0
$641$	−0.303877	−	0.175444i	−0.0120024	−	0.00692960i	0.493987	−	0.869469i	$-0.335539\pi$
$641$	−0.303877	−	0.175444i	−0.0120024	−	0.00692960i	−0.505989	+	0.862540i	$0.668872\pi$
$642$		0			0
$643$	−7.67194	+	13.2882i	−0.302552	+	0.524035i	−0.976713	−	0.214549i	$-0.931172\pi$
$643$	−7.67194	+	13.2882i	−0.302552	+	0.524035i	0.674161	+	0.738584i	$0.264505\pi$
$644$		0			0
$645$	−19.9260			−0.784585
$646$		0			0
$647$			12.4035i			0.487632i	0.969821	+	0.243816i	$0.0783994\pi$
$647$			12.4035i			0.487632i	−0.969821	+	0.243816i	$0.921601\pi$
$648$		0			0
$649$	26.1474	+	15.0962i	1.02637	+	0.592578i
$650$		0			0
$651$	0.136024	−	0.235601i	0.00533122	−	0.00923394i
$652$		0			0
$653$		−	38.6270i		−	1.51159i	−0.654808	−	0.755795i	$-0.727250\pi$
$653$		−	38.6270i		−	1.51159i	0.654808	−	0.755795i	$-0.272750\pi$
$654$		0			0
$655$	42.7504	−	24.6820i	1.67040	−	0.964404i
$656$		0			0
$657$	−25.2129			−0.983650
$658$		0			0
$659$	−0.427803	+	0.246992i	−0.0166648	+	0.00962144i	−0.508309	−	0.861175i	$-0.669729\pi$
$659$	−0.427803	+	0.246992i	−0.0166648	+	0.00962144i	0.491644	+	0.870796i	$0.336396\pi$
$660$		0			0
$661$	−12.5398	−	21.7195i	−0.487740	−	0.844791i	0.512160	−	0.858890i	$-0.328845\pi$
$661$	−12.5398	−	21.7195i	−0.487740	−	0.844791i	−0.999901	+	0.0140991i	$0.995512\pi$
$662$		0			0
$663$	−5.61558	−	3.24216i	−0.218091	−	0.125915i
$664$		0			0
$665$	4.79438	+	2.81305i	0.185918	+	0.109085i
$666$		0			0
$667$	−9.55835	−	5.51852i	−0.370101	−	0.213678i
$668$		0			0
$669$	−16.9495	+	9.78582i	−0.655307	+	0.378342i
$670$		0			0
$671$	4.60545	−	2.65896i	0.177791	−	0.102648i
$672$		0			0
$673$		−	12.2784i		−	0.473296i	−0.971595	−	0.236648i	$-0.923951\pi$
$673$		−	12.2784i		−	0.473296i	0.971595	−	0.236648i	$-0.0760489\pi$
$674$		0			0
$675$	14.2917	−	8.25134i	0.550089	−	0.317594i
$676$		0			0
$677$	−6.28293			−0.241473			−0.120736	−	0.992685i	$-0.538526\pi$
$677$	−6.28293			−0.241473			−0.120736	+	0.992685i	$0.538526\pi$
$678$		0			0
$679$	1.42438	−	2.46710i	0.0546628	−	0.0946788i
$680$		0			0
$681$	−7.90577	+	13.6932i	−0.302950	+	0.524724i
$682$		0			0
$683$			28.9958i			1.10949i	0.832020	+	0.554746i	$0.187185\pi$
$683$			28.9958i			1.10949i	−0.832020	+	0.554746i	$0.812815\pi$
$684$		0			0
$685$		−	24.2667i		−	0.927181i
$686$		0			0
$687$	−7.72197	+	13.3748i	−0.294611	+	0.510282i
$688$		0			0
$689$	14.4071	−	24.9538i	0.548865	−	0.950662i
$690$		0			0
$691$	−29.0538			−1.10526			−0.552629	−	0.833427i	$-0.686375\pi$
$691$	−29.0538			−1.10526			−0.552629	+	0.833427i	$0.686375\pi$
$692$		0			0
$693$	1.28727	−	0.743204i	0.0488992	−	0.0282320i
$694$		0			0
$695$			13.4746i			0.511120i
$696$		0			0
$697$	10.4750	−	6.04776i	0.396770	−	0.229075i
$698$		0			0
$699$	12.1449	−	7.01188i	0.459363	−	0.265214i
$700$		0			0
$701$	−21.1436	−	12.2073i	−0.798584	−	0.461063i	0.0443920	−	0.999014i	$-0.485865\pi$
$701$	−21.1436	−	12.2073i	−0.798584	−	0.461063i	−0.842976	+	0.537952i	$0.819198\pi$
$702$		0			0
$703$	−0.205722	+	29.3345i	−0.00775894	+	1.10637i
$704$		0			0
$705$	−1.94792	−	1.12463i	−0.0733630	−	0.0423561i
$706$		0			0
$707$	1.19995	+	2.07838i	0.0451289	+	0.0781656i
$708$		0			0
$709$	−3.14824	+	1.81764i	−0.118235	+	0.0682627i	−0.557951	−	0.829874i	$-0.688412\pi$
$709$	−3.14824	+	1.81764i	−0.118235	+	0.0682627i	0.439716	+	0.898137i	$0.355079\pi$
$710$		0			0
$711$	12.3857			0.464502
$712$		0			0
$713$	0.561857	−	0.324388i	0.0210417	−	0.0121484i
$714$		0			0
$715$			22.7747i			0.851726i
$716$		0			0
$717$	−11.4265	+	19.7912i	−0.426729	+	0.739116i
$718$		0			0
$719$	−34.9775	−	20.1943i	−1.30444	−	0.753120i	−0.323279	−	0.946304i	$-0.604785\pi$
$719$	−34.9775	−	20.1943i	−1.30444	−	0.753120i	−0.981163	+	0.193184i	$0.938119\pi$
$720$		0			0
$721$		−	8.07306i		−	0.300657i
$722$		0			0
$723$	−11.8777			−0.441738
$724$		0			0
$725$	−12.7051	+	22.0059i	−0.471857	+	0.817280i
$726$		0			0
$727$	4.07642	+	2.35352i	0.151186	+	0.0872873i	0.573685	−	0.819076i	$-0.305514\pi$
$727$	4.07642	+	2.35352i	0.151186	+	0.0872873i	−0.422499	+	0.906364i	$0.638847\pi$
$728$		0			0
$729$	−23.1906			−0.858912
$730$		0			0
$731$	−4.15857	−	7.20286i	−0.153810	−	0.266407i
$732$		0			0
$733$			23.9315i			0.883930i	0.897032	+	0.441965i	$0.145718\pi$
$733$			23.9315i			0.883930i	−0.897032	+	0.441965i	$0.854282\pi$
$734$		0			0
$735$	11.6683	+	20.2101i	0.430391	+	0.745459i
$736$		0			0
$737$	−4.67821	+	2.70097i	−0.172324	+	0.0994915i
$738$		0			0
$739$	−1.44053	+	2.49507i	−0.0529906	+	0.0917825i	−0.891304	−	0.453406i	$-0.850209\pi$
$739$	−1.44053	+	2.49507i	−0.0529906	+	0.0917825i	0.838313	+	0.545189i	$0.183542\pi$
$740$		0			0
$741$	19.7217	+	0.138307i	0.724494	+	0.00508084i
$742$		0			0
$743$	−17.8747	+	30.9598i	−0.655758	+	1.13581i	0.325945	+	0.945389i	$0.394318\pi$
$743$	−17.8747	+	30.9598i	−0.655758	+	1.13581i	−0.981703	+	0.190418i	$0.939016\pi$
$744$		0			0
$745$	−15.2427	−	26.4011i	−0.558448	−	0.967261i
$746$		0			0
$747$	9.03522	+	15.6495i	0.330581	+	0.572584i
$748$		0			0
$749$	−0.410086			−0.0149842
$750$		0			0
$751$	−24.3250	−	42.1322i	−0.887632	−	1.53742i	−0.842667	−	0.538436i	$-0.819015\pi$
$751$	−24.3250	−	42.1322i	−0.887632	−	1.53742i	−0.0449656	−	0.998989i	$-0.514318\pi$
$752$		0			0
$753$		−	19.8801i		−	0.724473i
$754$		0			0
$755$	−13.2460	−	7.64757i	−0.482071	−	0.278324i
$756$		0			0
$757$	−29.4372	−	16.9956i	−1.06991	−	0.617716i	−0.141757	−	0.989902i	$-0.545275\pi$
$757$	−29.4372	−	16.9956i	−1.06991	−	0.617716i	−0.928158	+	0.372186i	$0.878608\pi$
$758$		0			0
$759$	−3.41899			−0.124102
$760$		0			0
$761$	−34.2969			−1.24326			−0.621631	−	0.783310i	$-0.713530\pi$
$761$	−34.2969			−1.24326			−0.621631	+	0.783310i	$0.713530\pi$
$762$		0			0
$763$	0.730135	+	0.421544i	0.0264327	+	0.0152609i
$764$		0			0
$765$	5.36198	+	3.09574i	0.193863	+	0.111927i
$766$		0			0
$767$			52.1275i			1.88221i
$768$		0			0
$769$	−5.78344	−	10.0172i	−0.208556	−	0.361230i	0.742704	−	0.669620i	$-0.233543\pi$
$769$	−5.78344	−	10.0172i	−0.208556	−	0.361230i	−0.951260	+	0.308390i	$0.900210\pi$
$770$		0			0
$771$	10.6062			0.381971
$772$		0			0
$773$	11.6089	+	20.1073i	0.417545	+	0.723209i	0.995692	−	0.0927238i	$-0.0295574\pi$
$773$	11.6089	+	20.1073i	0.417545	+	0.723209i	−0.578147	+	0.815933i	$0.696224\pi$
$774$		0			0
$775$	−0.746830	−	1.29355i	−0.0268269	−	0.0464656i
$776$		0			0
$777$	1.84088	−	3.18850i	0.0660412	−	0.114387i
$778$		0			0
$779$	−18.6174	+	31.7302i	−0.667036	+	1.13685i
$780$		0			0
$781$	18.0372	−	31.2413i	0.645421	−	1.11790i
$782$		0			0
$783$	40.2532	−	23.2402i	1.43853	−	0.830536i
$784$		0			0
$785$	−21.7708	−	37.7081i	−0.777033	−	1.34586i
$786$		0			0
$787$			33.9207i			1.20914i	0.796552	+	0.604571i	$0.206655\pi$
$787$			33.9207i			1.20914i	−0.796552	+	0.604571i	$0.793345\pi$
$788$		0			0
$789$	16.9069	+	29.2836i	0.601901	+	1.04252i
$790$		0			0
$791$	−1.05570			−0.0375364
$792$		0			0
$793$	7.95135	+	4.59072i	0.282361	+	0.163021i
$794$		0			0
$795$	13.2684	−	22.9815i	0.470581	−	0.815070i
$796$		0			0
$797$	12.2630			0.434378			0.217189	−	0.976130i	$-0.430311\pi$
$797$	12.2630			0.434378			0.217189	+	0.976130i	$0.430311\pi$
$798$		0			0
$799$		−	0.938848i		−	0.0332141i
$800$		0			0
$801$	10.6172	+	6.12983i	0.375139	+	0.216587i
$802$		0			0
$803$	17.8258	−	30.8752i	0.629059	−	1.08956i
$804$		0			0
$805$		−	1.66375i		−	0.0586394i
$806$		0			0
$807$	−24.8797	+	14.3643i	−0.875806	+	0.505647i
$808$		0			0
$809$	35.6199			1.25233			0.626164	−	0.779691i	$-0.284624\pi$
$809$	35.6199			1.25233			0.626164	+	0.779691i	$0.284624\pi$
$810$		0			0
$811$	−16.4875	+	9.51908i	−0.578956	+	0.334260i	−0.760718	−	0.649082i	$-0.775153\pi$
$811$	−16.4875	+	9.51908i	−0.578956	+	0.334260i	0.181763	+	0.983342i	$0.441820\pi$
$812$		0			0
$813$	11.1777	+	19.3604i	0.392021	+	0.679000i
$814$		0			0
$815$	−1.30844	−	0.755429i	−0.0458327	−	0.0264615i
$816$		0			0
$817$	21.8184	+	12.8017i	0.763329	+	0.447875i
$818$		0			0
$819$	2.22248	+	1.28315i	0.0776597	+	0.0448369i
$820$		0			0
$821$	34.7173	−	20.0441i	1.21164	−	0.699543i	0.248526	−	0.968625i	$-0.420054\pi$
$821$	34.7173	−	20.0441i	1.21164	−	0.699543i	0.963117	+	0.269082i	$0.0867204\pi$
$822$		0			0
$823$	27.7423	−	16.0170i	0.967037	−	0.558319i	0.0687052	−	0.997637i	$-0.478113\pi$
$823$	27.7423	−	16.0170i	0.967037	−	0.558319i	0.898332	+	0.439318i	$0.144780\pi$
$824$		0			0
$825$			7.87146i			0.274049i
$826$		0			0
$827$	13.4637	−	7.77329i	0.468180	−	0.270304i	−0.247298	−	0.968940i	$-0.579543\pi$
$827$	13.4637	−	7.77329i	0.468180	−	0.270304i	0.715477	+	0.698636i	$0.246209\pi$
$828$		0			0
$829$	−5.94617			−0.206519			−0.103260	−	0.994654i	$-0.532927\pi$
$829$	−5.94617			−0.206519			−0.103260	+	0.994654i	$0.532927\pi$
$830$		0			0
$831$	−15.7968	+	27.3608i	−0.547984	+	0.949136i
$832$		0			0
$833$	−4.87036	+	8.43572i	−0.168748	+	0.292280i
$834$		0			0
$835$		−	38.5778i		−	1.33504i
$836$		0			0
$837$			2.73220i			0.0944386i
$838$		0			0
$839$	6.06590	−	10.5064i	0.209418	−	0.362723i	−0.742113	−	0.670274i	$-0.766176\pi$
$839$	6.06590	−	10.5064i	0.209418	−	0.362723i	0.951531	+	0.307552i	$0.0995097\pi$
$840$		0			0
$841$	−21.2845	+	36.8658i	−0.733947	+	1.27123i
$842$		0			0
$843$	25.4590			0.876855
$844$		0			0
$845$	−2.20218	+	1.27143i	−0.0757575	+	0.0437386i
$846$		0			0
$847$		−	2.85665i		−	0.0981555i
$848$		0			0
$849$	12.0424	−	6.95270i	0.413295	−	0.238616i
$850$		0			0
$851$	7.60385	−	4.39009i	0.260657	−	0.150490i
$852$		0			0
$853$	13.8144	+	7.97575i	0.472996	+	0.273085i	0.717493	−	0.696565i	$-0.245289\pi$
$853$	13.8144	+	7.97575i	0.472996	+	0.273085i	−0.244497	+	0.969650i	$0.578623\pi$
$854$		0			0
$855$	−18.8310	−	0.132061i	−0.644007	−	0.00451639i
$856$		0			0
$857$	46.8936	+	27.0741i	1.60186	+	0.924832i	0.991116	+	0.133001i	$0.0424614\pi$
$857$	46.8936	+	27.0741i	1.60186	+	0.924832i	0.610740	+	0.791831i	$0.290872\pi$
$858$		0			0
$859$	−10.3529	−	17.9317i	−0.353236	−	0.611823i	0.633578	−	0.773678i	$-0.281585\pi$
$859$	−10.3529	−	17.9317i	−0.353236	−	0.611823i	−0.986814	+	0.161856i	$0.948252\pi$
$860$		0			0
$861$	3.99863	−	2.30861i	0.136273	−	0.0786773i
$862$		0			0
$863$	−24.9184			−0.848231			−0.424115	−	0.905608i	$-0.639415\pi$
$863$	−24.9184			−0.848231			−0.424115	+	0.905608i	$0.639415\pi$
$864$		0			0
$865$	−4.03271	+	2.32829i	−0.137116	+	0.0791642i
$866$		0			0
$867$			18.1392i			0.616038i
$868$		0			0
$869$	−8.75685	+	15.1673i	−0.297056	+	0.514516i
$870$		0			0
$871$	−8.07699	−	4.66325i	−0.273678	−	0.158008i
$872$		0			0
$873$			9.65089i			0.326633i
$874$		0			0
$875$	2.54588			0.0860664
$876$		0			0
$877$	−19.0653	+	33.0221i	−0.643790	+	1.11508i	0.340790	+	0.940140i	$0.389306\pi$
$877$	−19.0653	+	33.0221i	−0.643790	+	1.11508i	−0.984580	+	0.174937i	$0.944028\pi$
$878$		0			0
$879$	−10.9311	−	6.31106i	−0.368696	−	0.212867i
$880$		0			0
$881$	16.6723			0.561702			0.280851	−	0.959751i	$-0.409383\pi$
$881$	16.6723			0.561702			0.280851	+	0.959751i	$0.409383\pi$
$882$		0			0
$883$	−16.1610	−	27.9917i	−0.543861	−	0.941994i	−0.998678	−	0.0514093i	$-0.983629\pi$
$883$	−16.1610	−	27.9917i	−0.543861	−	0.941994i	0.454817	−	0.890585i	$-0.349705\pi$
$884$		0			0
$885$			48.0076i			1.61376i
$886$		0			0
$887$	5.27663	+	9.13939i	0.177172	+	0.306871i	0.940911	−	0.338655i	$-0.109972\pi$
$887$	5.27663	+	9.13939i	0.177172	+	0.306871i	−0.763739	+	0.645525i	$0.776639\pi$
$888$		0			0
$889$	0.832314	−	0.480537i	0.0279149	−	0.0161167i
$890$		0			0
$891$	2.25298	−	3.90228i	0.0754777	−	0.130731i
$892$		0			0
$893$	1.41038	+	2.48291i	0.0471967	+	0.0830874i
$894$		0			0
$895$	10.8517	−	18.7958i	0.362733	−	0.628273i
$896$		0			0
$897$	−2.95147	−	5.11209i	−0.0985465	−	0.170688i
$898$		0			0
$899$	−2.10347	−	3.64332i	−0.0701548	−	0.121512i
$900$		0			0
$901$	11.0765			0.369012
$902$		0			0
$903$	−1.58745	−	2.74954i	−0.0528270	−	0.0914991i
$904$		0			0
$905$			66.5675i			2.21278i
$906$		0			0
$907$	32.3892	+	18.6999i	1.07546	+	0.620920i	0.929669	−	0.368395i	$-0.120093\pi$
$907$	32.3892	+	18.6999i	1.07546	+	0.620920i	0.145795	+	0.989315i	$0.453426\pi$
$908$		0			0
$909$	−7.04102	−	4.06513i	−0.233536	−	0.134832i
$910$		0			0
$911$	40.7900			1.35143			0.675717	−	0.737162i	$-0.263834\pi$
$911$	40.7900			1.35143			0.675717	+	0.737162i	$0.263834\pi$
$912$		0			0
$913$	−25.5520			−0.845647
$914$		0			0
$915$	7.32291	+	4.22789i	0.242088	+	0.139770i
$916$		0			0
$917$	6.81162	+	3.93269i	0.224940	+	0.129869i
$918$		0			0
$919$		−	10.9991i		−	0.362826i	−0.983407	−	0.181413i	$-0.941933\pi$
$919$		−	10.9991i		−	0.362826i	0.983407	−	0.181413i	$-0.0580670\pi$
$920$		0			0
$921$	1.68161	+	2.91263i	0.0554109	+	0.0959744i
$922$		0			0
$923$	62.2827			2.05006
$924$		0			0
$925$	−10.1072	−	17.5061i	−0.332322	−	0.575599i
$926$		0			0
$927$	13.6747	+	23.6853i	0.449137	+	0.777928i
$928$		0			0
$929$	15.0117	−	26.0011i	0.492519	−	0.853067i	−0.507444	−	0.861685i	$-0.669410\pi$
$929$	15.0117	−	26.0011i	0.492519	−	0.853067i	0.999963	+	0.00861738i	$0.00274303\pi$
$930$		0			0
$931$	0.207765	−	29.6259i	0.00680921	−	0.970949i
$932$		0			0
$933$	8.37412	−	14.5044i	0.274156	−	0.474853i
$934$		0			0
$935$	−7.58194	+	4.37744i	−0.247956	+	0.143158i
$936$		0			0
$937$	20.0689	+	34.7604i	0.655623	+	1.13557i	0.981737	+	0.190241i	$0.0609271\pi$
$937$	20.0689	+	34.7604i	0.655623	+	1.13557i	−0.326115	+	0.945330i	$0.605740\pi$
$938$		0			0
$939$			14.3013i			0.466706i
$940$		0			0
$941$	−0.433456	−	0.750768i	−0.0141303	−	0.0244743i	0.858874	−	0.512187i	$-0.171165\pi$
$941$	−0.433456	−	0.750768i	−0.0141303	−	0.0244743i	−0.873004	+	0.487713i	$0.837831\pi$
$942$		0			0
$943$	11.0110			0.358569
$944$		0			0
$945$	6.06786	+	3.50328i	0.197387	+	0.113962i
$946$		0			0
$947$	12.4598	−	21.5809i	0.404888	−	0.701286i	−0.589421	−	0.807826i	$-0.700644\pi$
$947$	12.4598	−	21.5809i	0.404888	−	0.701286i	0.994308	+	0.106540i	$0.0339772\pi$
$948$		0			0
$949$	61.5529			1.99809
$950$		0			0
$951$			21.5197i			0.697825i
$952$		0			0
$953$	−25.5317	−	14.7407i	−0.827053	−	0.477499i	0.0257895	−	0.999667i	$-0.491790\pi$
$953$	−25.5317	−	14.7407i	−0.827053	−	0.477499i	−0.852843	+	0.522168i	$0.825123\pi$
$954$		0			0
$955$	33.7572	−	58.4692i	1.09236	−	1.89202i
$956$		0			0
$957$			22.1702i			0.716662i
$958$		0			0
$959$	3.34851	−	1.93326i	0.108129	−	0.0624282i
$960$		0			0
$961$	−30.7527			−0.992023
$962$		0			0
$963$	1.20314	−	0.694632i	0.0387706	−	0.0223842i
$964$		0			0
$965$	27.0261	+	46.8106i	0.870002	+	1.50689i
$966$		0			0
$967$	50.5276	+	29.1722i	1.62486	+	0.938113i	0.985594	+	0.169127i	$0.0540948\pi$
$967$	50.5276	+	29.1722i	1.62486	+	0.938113i	0.639265	+	0.768986i	$0.279239\pi$
$968$		0			0
$969$	3.74458	+	6.59214i	0.120293	+	0.211770i
$970$		0			0
$971$	0.791582	+	0.457020i	0.0254031	+	0.0146665i	0.512648	−	0.858599i	$-0.328665\pi$
$971$	0.791582	+	0.457020i	0.0254031	+	0.0146665i	−0.487245	+	0.873265i	$0.661998\pi$
$972$		0			0
$973$	−1.85933	+	1.07348i	−0.0596073	+	0.0344143i
$974$		0			0
$975$	−11.7694	+	6.79508i	−0.376923	+	0.217617i
$976$		0			0
$977$		−	19.2494i		−	0.615841i	−0.951412	−	0.307921i	$-0.900367\pi$
$977$		−	19.2494i		−	0.615841i	0.951412	−	0.307921i	$-0.0996331\pi$
$978$		0			0
$979$	−15.0129	+	8.66771i	−0.479815	+	0.277021i
$980$		0			0
$981$	−2.85616			−0.0911903
$982$		0			0
$983$	10.4028	−	18.0182i	0.331799	−	0.574693i	−0.651066	−	0.759021i	$-0.725678\pi$
$983$	10.4028	−	18.0182i	0.331799	−	0.574693i	0.982865	+	0.184329i	$0.0590111\pi$
$984$		0			0
$985$	15.9107	−	27.5581i	0.506956	−	0.878073i
$986$		0			0
$987$		−	0.358386i		−	0.0114076i
$988$		0			0
$989$		−	7.57143i		−	0.240758i
$990$		0			0
$991$	2.09378	−	3.62654i	0.0665113	−	0.115201i	−0.830852	−	0.556493i	$-0.812147\pi$
$991$	2.09378	−	3.62654i	0.0665113	−	0.115201i	0.897363	+	0.441292i	$0.145480\pi$
$992$		0			0
$993$	−16.6093	+	28.7682i	−0.527080	+	0.912930i
$994$		0			0
$995$	−32.4044			−1.02729
$996$		0			0
$997$	−4.65708	+	2.68877i	−0.147491	+	0.0851542i	−0.571930	−	0.820303i	$-0.693805\pi$
$997$	−4.65708	+	2.68877i	−0.147491	+	0.0851542i	0.424438	+	0.905457i	$0.360472\pi$
$998$		0			0
$999$			36.9760i			1.16987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	608.2.s.c.559.10		28
4.3	odd	2		152.2.o.c.27.12	yes	28
8.3	odd	2	inner	608.2.s.c.559.9		28
8.5	even	2		152.2.o.c.27.8	✓	28
19.12	odd	6	inner	608.2.s.c.335.9		28
76.31	even	6		152.2.o.c.107.8	yes	28
152.69	odd	6		152.2.o.c.107.12	yes	28
152.107	even	6	inner	608.2.s.c.335.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.8	✓	28	8.5	even	2
152.2.o.c.27.12	yes	28	4.3	odd	2
152.2.o.c.107.8	yes	28	76.31	even	6
152.2.o.c.107.12	yes	28	152.69	odd	6
608.2.s.c.335.9		28	19.12	odd	6	inner
608.2.s.c.335.10		28	152.107	even	6	inner
608.2.s.c.559.9		28	8.3	odd	2	inner
608.2.s.c.559.10		28	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	608.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05104 + 0.606818i) q^{3} +(2.45005 + 1.41453i) q^{5} +0.450769i q^{7} +(-0.763544 - 1.32250i) q^{9} +2.15933 q^{11} +(1.86406 + 3.22864i) q^{13} +(1.71673 + 2.97346i) q^{15} +(-0.716566 + 1.24113i) q^{17} +(0.0305680 - 4.35879i) q^{19} +(-0.273535 + 0.473776i) q^{21} +(-1.12985 + 0.652319i) q^{23} +(1.50182 + 2.60122i) q^{25} -5.49424i q^{27} +(4.22992 + 7.32644i) q^{29} -0.497284 q^{31} +(2.26955 + 1.31032i) q^{33} +(-0.637628 + 1.10440i) q^{35} -6.72997 q^{37} +4.52457i q^{39} +(-7.30919 - 4.21996i) q^{41} +(-2.90174 + 5.02595i) q^{43} -4.32024i q^{45} +(-0.567335 + 0.327551i) q^{47} +6.79681 q^{49} +(-1.50628 + 0.869651i) q^{51} +(-3.86444 - 6.69340i) q^{53} +(5.29047 + 3.05445i) q^{55} +(2.67712 - 4.56271i) q^{57} +(12.1090 + 6.99113i) q^{59} +(2.13281 - 1.23138i) q^{61} +(0.596141 - 0.344182i) q^{63} +10.5471i q^{65} +(-2.16651 + 1.25083i) q^{67} -1.58336 q^{69} +(8.35311 - 14.4680i) q^{71} +(8.25523 - 14.2985i) q^{73} +3.64532i q^{75} +0.973361i q^{77} +(-4.05535 + 7.02407i) q^{79} +(1.04337 - 1.80717i) q^{81} -11.8333 q^{83} +(-3.51124 + 2.02722i) q^{85} +10.2672i q^{87} +(-6.95256 + 4.01406i) q^{89} +(-1.45537 + 0.840259i) q^{91} +(-0.522665 - 0.301761i) q^{93} +(6.24056 - 10.6360i) q^{95} +(-5.47310 - 3.15990i) q^{97} +(-1.64875 - 2.85571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} + 8 q^{9} + 16 q^{11} - 22 q^{17} - 4 q^{19} + 16 q^{25} + 36 q^{33} + 28 q^{35} + 6 q^{41} - 30 q^{43} - 68 q^{49} + 42 q^{51} - 26 q^{57} + 18 q^{59} - 78 q^{67} + 14 q^{73} + 6 q^{81}+ \cdots + 28 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 + 8 * q^9 + 16 * q^11 - 22 * q^17 - 4 * q^19 + 16 * q^25 + 36 * q^33 + 28 * q^35 + 6 * q^41 - 30 * q^43 - 68 * q^49 + 42 * q^51 - 26 * q^57 + 18 * q^59 - 78 * q^67 + 14 * q^73 + 6 * q^81 + 32 * q^83 - 18 * q^89 + 12 * q^91 + 30 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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