LMFDB - Embedded newform 1008.2.cz.g.367.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1008,2,Mod(367,1008)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1008, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1008.367"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-3,0,-3,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			367.11
Character	$\chi$	$=$	1008.367
Dual form			1008.2.cz.g.607.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64174 - 0.551995i) q^{3} +(2.87107 + 1.65762i) q^{5} +(-2.01336 + 1.71651i) q^{7} +(2.39060 - 1.81246i) q^{9} +(-4.94470 + 2.85482i) q^{11} +(-0.000820272 + 0.000473584i) q^{13} +(5.62854 + 1.13655i) q^{15} +(0.287517 + 0.165998i) q^{17} +(3.59975 + 6.23494i) q^{19} +(-2.35790 + 3.92941i) q^{21} +(5.37780 + 3.10487i) q^{23} +(2.99538 + 5.18815i) q^{25} +(2.92427 - 4.29519i) q^{27} +(5.06516 - 8.77311i) q^{29} +3.88013 q^{31} +(-6.54205 + 7.41631i) q^{33} +(-8.62580 + 1.59084i) q^{35} +(0.341973 + 0.592315i) q^{37} +(-0.00108526 + 0.00123029i) q^{39} +(-5.71168 + 3.29764i) q^{41} +(-6.16324 - 3.55835i) q^{43} +(9.86796 - 1.24101i) q^{45} -2.93515 q^{47} +(1.10722 - 6.91188i) q^{49} +(0.563657 + 0.113817i) q^{51} +(-0.211667 + 0.366617i) q^{53} -18.9288 q^{55} +(9.35150 + 8.24910i) q^{57} +0.323059 q^{59} -0.966271i q^{61} +(-1.70204 + 7.75262i) q^{63} -0.00314008 q^{65} -8.48735i q^{67} +(10.5428 + 2.12887i) q^{69} -3.04412i q^{71} +(-0.293235 - 0.169300i) q^{73} +(7.78145 + 6.86414i) q^{75} +(5.05512 - 14.2354i) q^{77} -11.5034i q^{79} +(2.42997 - 8.66575i) q^{81} +(-2.46263 + 4.26540i) q^{83} +(0.550322 + 0.953185i) q^{85} +(3.47295 - 17.1991i) q^{87} +(-8.40915 + 4.85502i) q^{89} +(0.000838591 - 0.00236150i) q^{91} +(6.37016 - 2.14181i) q^{93} +23.8680i q^{95} +(15.1955 + 8.77311i) q^{97} +(-6.64656 + 15.7868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37}+ \cdots + 30 q^{99}+O(q^{100}) $ 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.64174	−	0.551995i	0.947858	−	0.318694i
$3$	1.64174	−	0.551995i	0.947858	−	0.318694i
$4$		0			0
$5$	2.87107	+	1.65762i	1.28398	+	0.741308i	0.977574	−	0.210592i	$-0.0675391\pi$
$5$	2.87107	+	1.65762i	1.28398	+	0.741308i	0.306409	+	0.951900i	$0.400872\pi$
$6$		0			0
$7$	−2.01336	+	1.71651i	−0.760978	+	0.648778i
$7$	−2.01336	+	1.71651i	−0.760978	+	0.648778i
$8$		0			0
$9$	2.39060	−	1.81246i	0.796868	−	0.604154i
$10$		0			0
$11$	−4.94470	+	2.85482i	−1.49088	+	0.860761i	−0.999946	−	0.0104342i	$-0.996679\pi$
$11$	−4.94470	+	2.85482i	−1.49088	+	0.860761i	−0.490936	+	0.871195i	$0.663345\pi$
$12$		0			0
$13$	−0.000820272	0	0.000473584i	−0.000227503	0	0.000131349i	−0.500114	−	0.865960i	$-0.666708\pi$
$13$	−0.000820272	0	0.000473584i	−0.000227503	0	0.000131349i	0.499886	+	0.866091i	$0.333375\pi$
$14$		0			0
$15$	5.62854	+	1.13655i	1.45328	+	0.293456i
$16$		0			0
$17$	0.287517	+	0.165998i	0.0697331	+	0.0402604i	0.534461	−	0.845193i	$-0.320515\pi$
$17$	0.287517	+	0.165998i	0.0697331	+	0.0402604i	−0.464728	+	0.885453i	$0.653848\pi$
$18$		0			0
$19$	3.59975	+	6.23494i	0.825839	+	1.43039i	0.901277	+	0.433244i	$0.142631\pi$
$19$	3.59975	+	6.23494i	0.825839	+	1.43039i	−0.0754382	+	0.997150i	$0.524036\pi$
$20$		0			0
$21$	−2.35790	+	3.92941i	−0.514536	+	0.857469i
$22$		0			0
$23$	5.37780	+	3.10487i	1.12135	+	0.647411i	0.941745	−	0.336328i	$-0.109185\pi$
$23$	5.37780	+	3.10487i	1.12135	+	0.647411i	0.179604	+	0.983739i	$0.442518\pi$
$24$		0			0
$25$	2.99538	+	5.18815i	0.599076	+	1.03763i
$26$		0			0
$27$	2.92427	−	4.29519i	0.562777	−	0.826609i
$28$		0			0
$29$	5.06516	−	8.77311i	0.940576	−	1.62913i	0.176201	−	0.984354i	$-0.443619\pi$
$29$	5.06516	−	8.77311i	0.940576	−	1.62913i	0.764375	−	0.644772i	$-0.223047\pi$
$30$		0			0
$31$	3.88013			0.696892			0.348446	−	0.937329i	$-0.386709\pi$
$31$	3.88013			0.696892			0.348446	+	0.937329i	$0.386709\pi$
$32$		0			0
$33$	−6.54205	+	7.41631i	−1.13882	+	1.29101i
$34$		0			0
$35$	−8.62580	+	1.59084i	−1.45803	+	0.268901i
$36$		0			0
$37$	0.341973	+	0.592315i	0.0562200	+	0.0973759i	0.892766	−	0.450521i	$-0.148762\pi$
$37$	0.341973	+	0.592315i	0.0562200	+	0.0973759i	−0.836546	+	0.547897i	$0.815429\pi$
$38$		0			0
$39$	−0.00108526	+	0.00123029i	−0.000173780	+	0.000197004i
$40$		0			0
$41$	−5.71168	+	3.29764i	−0.892015	+	0.515005i	−0.874601	−	0.484843i	$-0.838877\pi$
$41$	−5.71168	+	3.29764i	−0.892015	+	0.515005i	−0.0174141	+	0.999848i	$0.505543\pi$
$42$		0			0
$43$	−6.16324	−	3.55835i	−0.939885	−	0.542643i	−0.0499605	−	0.998751i	$-0.515910\pi$
$43$	−6.16324	−	3.55835i	−0.939885	−	0.542643i	−0.889924	+	0.456109i	$0.849243\pi$
$44$		0			0
$45$	9.86796	−	1.24101i	1.47103	−	0.184999i
$46$		0			0
$47$	−2.93515			−0.428135			−0.214067	−	0.976819i	$-0.568671\pi$
$47$	−2.93515			−0.428135			−0.214067	+	0.976819i	$0.568671\pi$
$48$		0			0
$49$	1.10722	−	6.91188i	0.158174	−	0.987411i
$50$		0			0
$51$	0.563657	+	0.113817i	0.0789278	+	0.0159376i
$52$		0			0
$53$	−0.211667	+	0.366617i	−0.0290746	+	0.0503587i	−0.880197	−	0.474609i	$-0.842589\pi$
$53$	−0.211667	+	0.366617i	−0.0290746	+	0.0503587i	0.851122	+	0.524968i	$0.175923\pi$
$54$		0			0
$55$	−18.9288			−2.55236
$56$		0			0
$57$	9.35150	+	8.24910i	1.23864	+	1.09262i
$58$		0			0
$59$	0.323059			0.0420587			0.0210294	−	0.999779i	$-0.493306\pi$
$59$	0.323059			0.0420587			0.0210294	+	0.999779i	$0.493306\pi$
$60$		0			0
$61$		−	0.966271i		−	0.123718i	−0.998085	−	0.0618592i	$-0.980297\pi$
$61$		−	0.966271i		−	0.123718i	0.998085	−	0.0618592i	$-0.0197030\pi$
$62$		0			0
$63$	−1.70204	+	7.75262i	−0.214437	+	0.976738i
$64$		0			0
$65$	−0.00314008			−0.000389479
$66$		0			0
$67$		−	8.48735i		−	1.03689i	−0.855110	−	0.518447i	$-0.826510\pi$
$67$		−	8.48735i		−	1.03689i	0.855110	−	0.518447i	$-0.173490\pi$
$68$		0			0
$69$	10.5428	+	2.12887i	1.26920	+	0.256286i
$70$		0			0
$71$		−	3.04412i		−	0.361271i	−0.983550	−	0.180635i	$-0.942185\pi$
$71$		−	3.04412i		−	0.361271i	0.983550	−	0.180635i	$-0.0578154\pi$
$72$		0			0
$73$	−0.293235	−	0.169300i	−0.0343206	−	0.0198150i	0.482742	−	0.875763i	$-0.339641\pi$
$73$	−0.293235	−	0.169300i	−0.0343206	−	0.0198150i	−0.517062	+	0.855948i	$0.672974\pi$
$74$		0			0
$75$	7.78145	+	6.86414i	0.898525	+	0.792603i
$76$		0			0
$77$	5.05512	−	14.2354i	0.576085	−	1.62227i
$78$		0			0
$79$		−	11.5034i		−	1.29423i	−0.762392	−	0.647116i	$-0.775975\pi$
$79$		−	11.5034i		−	1.29423i	0.762392	−	0.647116i	$-0.224025\pi$
$80$		0			0
$81$	2.42997	−	8.66575i	0.269997	−	0.962861i
$82$		0			0
$83$	−2.46263	+	4.26540i	−0.270309	+	0.468188i	−0.968941	−	0.247293i	$-0.920459\pi$
$83$	−2.46263	+	4.26540i	−0.270309	+	0.468188i	0.698632	+	0.715481i	$0.253792\pi$
$84$		0			0
$85$	0.550322	+	0.953185i	0.0596908	+	0.103387i
$86$		0			0
$87$	3.47295	−	17.1991i	0.372339	−	1.84394i
$88$		0			0
$89$	−8.40915	+	4.85502i	−0.891368	+	0.514631i	−0.874390	−	0.485224i	$-0.838738\pi$
$89$	−8.40915	+	4.85502i	−0.891368	+	0.514631i	−0.0169782	+	0.999856i	$0.505405\pi$
$90$		0			0
$91$	0.000838591	−	0.00236150i	8.79082e−5	−	0.000247552i
$92$		0			0
$93$	6.37016	−	2.14181i	0.660554	−	0.222096i
$94$		0			0
$95$			23.8680i			2.44880i
$96$		0			0
$97$	15.1955	+	8.77311i	1.54287	+	0.890774i	0.998656	+	0.0518254i	$0.0165039\pi$
$97$	15.1955	+	8.77311i	1.54287	+	0.890774i	0.544210	+	0.838949i	$0.316829\pi$
$98$		0			0
$99$	−6.64656	+	15.7868i	−0.668004	+	1.58663i
$100$		0			0
$101$	−9.07215	+	5.23781i	−0.902712	+	0.521181i	−0.878079	−	0.478515i	$-0.841175\pi$
$101$	−9.07215	+	5.23781i	−0.902712	+	0.521181i	−0.0246332	+	0.999697i	$0.507842\pi$
$102$		0			0
$103$	7.69735	−	13.3322i	0.758442	−	1.31366i	−0.185202	−	0.982700i	$-0.559294\pi$
$103$	7.69735	−	13.3322i	0.758442	−	1.31366i	0.943645	−	0.330960i	$-0.107373\pi$
$104$		0			0
$105$	−13.2832	+	7.37314i	−1.29630	+	0.719545i
$106$		0			0
$107$	0.530413	−	0.306234i	0.0512769	−	0.0296047i	−0.474142	−	0.880448i	$-0.657242\pi$
$107$	0.530413	−	0.306234i	0.0512769	−	0.0296047i	0.525419	+	0.850843i	$0.323908\pi$
$108$		0			0
$109$	7.50285	−	12.9953i	0.718643	−	1.24473i	−0.242894	−	0.970053i	$-0.578097\pi$
$109$	7.50285	−	12.9953i	0.718643	−	1.24473i	0.961537	−	0.274674i	$-0.0885698\pi$
$110$		0			0
$111$	0.888384	+	0.783658i	0.0843217	+	0.0743815i
$112$		0			0
$113$	5.28753	+	9.15828i	0.497409	+	0.861538i	0.999996	−	0.00298888i	$-0.000951391\pi$
$113$	5.28753	+	9.15828i	0.497409	+	0.861538i	−0.502586	+	0.864527i	$0.667618\pi$
$114$		0			0
$115$	10.2934	+	17.8286i	0.959862	+	1.66253i
$116$		0			0
$117$	−0.00110259	+	0.00261886i	−0.000101935	+	0.000242114i
$118$		0			0
$119$	−0.863811	+	0.159311i	−0.0791854	+	0.0146040i
$120$		0			0
$121$	10.8000	−	18.7062i	0.981819	−	1.70056i
$122$		0			0
$123$	−7.55680	+	8.56668i	−0.681374	+	0.772432i
$124$		0			0
$125$			3.28458i			0.293782i
$126$		0			0
$127$		−	13.0147i		−	1.15486i	−0.816439	−	0.577432i	$-0.804055\pi$
$127$		−	13.0147i		−	1.15486i	0.816439	−	0.577432i	$-0.195945\pi$
$128$		0			0
$129$	−12.0826	−	2.43980i	−1.06381	−	0.214812i
$130$		0			0
$131$	−2.06878	+	3.58324i	−0.180750	+	0.313069i	−0.942136	−	0.335230i	$-0.891186\pi$
$131$	−2.06878	+	3.58324i	−0.180750	+	0.313069i	0.761386	+	0.648299i	$0.224519\pi$
$132$		0			0
$133$	−17.9499	−	6.37419i	−1.55645	−	0.552712i
$134$		0			0
$135$	15.5156	−	7.48447i	1.33537	−	0.644161i
$136$		0			0
$137$	−5.03745	−	8.72512i	−0.430378	−	0.745437i	0.566527	−	0.824043i	$-0.308287\pi$
$137$	−5.03745	−	8.72512i	−0.430378	−	0.745437i	−0.996906	+	0.0786057i	$0.974953\pi$
$138$		0			0
$139$	−9.47318	−	16.4080i	−0.803505	−	1.39171i	−0.917296	−	0.398207i	$-0.869633\pi$
$139$	−9.47318	−	16.4080i	−0.803505	−	1.39171i	0.113791	−	0.993505i	$-0.463701\pi$
$140$		0			0
$141$	−4.81874	+	1.62018i	−0.405811	+	0.136444i
$142$		0			0
$143$	0.00270400	−	0.00468346i	0.000226120	−	0.000391651i
$144$		0			0
$145$	29.0849	−	16.7922i	2.41537	−	1.39451i
$146$		0			0
$147$	−1.99756	−	11.9587i	−0.164756	−	0.986334i
$148$		0			0
$149$	−9.92295	+	17.1870i	−0.812920	+	1.40802i	0.0978927	+	0.995197i	$0.468790\pi$
$149$	−9.92295	+	17.1870i	−0.812920	+	1.40802i	−0.910812	+	0.412821i	$0.864544\pi$
$150$		0			0
$151$	1.45901	−	0.842359i	0.118732	−	0.0685502i	−0.439458	−	0.898263i	$-0.644829\pi$
$151$	1.45901	−	0.842359i	0.118732	−	0.0685502i	0.558190	+	0.829713i	$0.311496\pi$
$152$		0			0
$153$	0.988204	−	0.124278i	0.0798915	−	0.0100473i
$154$		0			0
$155$	11.1401	+	6.43176i	0.894798	+	0.516612i
$156$		0			0
$157$			15.8888i			1.26807i	0.773306	+	0.634033i	$0.218602\pi$
$157$			15.8888i			1.26807i	−0.773306	+	0.634033i	$0.781398\pi$
$158$		0			0
$159$	−0.145130	+	0.718728i	−0.0115096	+	0.0569988i
$160$		0			0
$161$	−16.1570	+	2.97980i	−1.27335	+	0.234841i
$162$		0			0
$163$	−9.64782	+	5.57017i	−0.755676	+	0.436290i	−0.827741	−	0.561110i	$-0.810374\pi$
$163$	−9.64782	+	5.57017i	−0.755676	+	0.436290i	0.0720652	+	0.997400i	$0.477041\pi$
$164$		0			0
$165$	−31.0761	+	10.4486i	−2.41927	+	0.813422i
$166$		0			0
$167$	−4.63866	−	8.03440i	−0.358950	−	0.621720i	0.628835	−	0.777538i	$-0.283532\pi$
$167$	−4.63866	−	8.03440i	−0.358950	−	0.621720i	−0.987786	+	0.155818i	$0.950199\pi$
$168$		0			0
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$		0			0
$171$	19.9062	+	8.38088i	1.52226	+	0.640902i
$172$		0			0
$173$		−	6.16863i		−	0.468992i	−0.972117	−	0.234496i	$-0.924656\pi$
$173$		−	6.16863i		−	0.468992i	0.972117	−	0.234496i	$-0.0753440\pi$
$174$		0			0
$175$	−14.9362	−	5.30401i	−1.12907	−	0.400946i
$176$		0			0
$177$	0.530378	−	0.178327i	0.0398657	−	0.0134039i
$178$		0			0
$179$	14.2231	+	8.21169i	1.06308	+	0.613771i	0.926283	−	0.376828i	$-0.122985\pi$
$179$	14.2231	+	8.21169i	1.06308	+	0.613771i	0.136799	+	0.990599i	$0.456319\pi$
$180$		0			0
$181$			10.7788i			0.801185i	0.916256	+	0.400592i	$0.131196\pi$
$181$			10.7788i			0.801185i	−0.916256	+	0.400592i	$0.868804\pi$
$182$		0			0
$183$	−0.533376	−	1.58636i	−0.0394283	−	0.117267i
$184$		0			0
$185$			2.26744i			0.166705i
$186$		0			0
$187$	−1.89558			−0.138618
$188$		0			0
$189$	1.48510	+	13.6673i	0.108025	+	0.994148i
$190$		0			0
$191$		−	2.14657i		−	0.155320i	−0.996980	−	0.0776602i	$-0.975255\pi$
$191$		−	2.14657i		−	0.155320i	0.996980	−	0.0776602i	$-0.0247449\pi$
$192$		0			0
$193$	−12.0308			−0.865996			−0.432998	−	0.901395i	$-0.642544\pi$
$193$	−12.0308			−0.865996			−0.432998	+	0.901395i	$0.642544\pi$
$194$		0			0
$195$	−0.00515519	+	0.00173331i	−0.000369171	+	0.000124125i
$196$		0			0
$197$	3.69745			0.263433			0.131716	−	0.991287i	$-0.457951\pi$
$197$	3.69745			0.263433			0.131716	+	0.991287i	$0.457951\pi$
$198$		0			0
$199$	10.2592	−	17.7695i	0.727256	−	1.25964i	−0.230782	−	0.973005i	$-0.574128\pi$
$199$	10.2592	−	17.7695i	0.727256	−	1.25964i	0.958039	−	0.286640i	$-0.0925382\pi$
$200$		0			0
$201$	−4.68497	−	13.9340i	−0.330452	−	0.982829i
$202$		0			0
$203$	4.86112	+	26.3578i	0.341184	+	1.84995i
$204$		0			0
$205$	−21.8649			−1.52711
$206$		0			0
$207$	18.4836	−	2.32453i	1.28470	−	0.161566i
$208$		0			0
$209$	−35.5993	−	20.5533i	−2.46246	−	1.42170i
$210$		0			0
$211$	4.03406	−	2.32907i	0.277716	−	0.160340i	−0.354673	−	0.934990i	$-0.615408\pi$
$211$	4.03406	−	2.32907i	0.277716	−	0.160340i	0.632389	+	0.774651i	$0.282074\pi$
$212$		0			0
$213$	−1.68034	−	4.99765i	−0.115135	−	0.342433i
$214$		0			0
$215$	−11.7967	−	20.4325i	−0.804531	−	1.39349i
$216$		0			0
$217$	−7.81209	+	6.66027i	−0.530319	+	0.452128i
$218$		0			0
$219$	−0.574868	−	0.116081i	−0.0388460	−	0.00784403i
$220$		0			0
$221$	−0.000314456	0		−2.11526e−5	0
$222$		0			0
$223$	5.32491	−	9.22302i	0.356582	−	0.617619i	−0.630805	−	0.775941i	$-0.717275\pi$
$223$	5.32491	−	9.22302i	0.356582	−	0.617619i	0.987387	+	0.158322i	$0.0506085\pi$
$224$		0			0
$225$	16.5641	+	6.97380i	1.10427	+	0.464920i
$226$		0			0
$227$	3.96132	+	6.86121i	0.262922	+	0.455394i	0.967017	−	0.254711i	$-0.0819805\pi$
$227$	3.96132	+	6.86121i	0.262922	+	0.455394i	−0.704095	+	0.710106i	$0.748647\pi$
$228$		0			0
$229$	5.79610	+	3.34638i	0.383017	+	0.221135i	0.679130	−	0.734018i	$-0.262357\pi$
$229$	5.79610	+	3.34638i	0.383017	+	0.221135i	−0.296113	+	0.955153i	$0.595690\pi$
$230$		0			0
$231$	0.441333	−	26.1612i	0.0290376	−	1.72128i
$232$		0			0
$233$	−2.43240	−	4.21304i	−0.159352	−	0.276006i	0.775283	−	0.631614i	$-0.217607\pi$
$233$	−2.43240	−	4.21304i	−0.159352	−	0.276006i	−0.934635	+	0.355608i	$0.884274\pi$
$234$		0			0
$235$	−8.42702	−	4.86534i	−0.549718	−	0.317380i
$236$		0			0
$237$	−6.34981	−	18.8855i	−0.412464	−	1.22675i
$238$		0			0
$239$	4.72441	−	2.72764i	0.305597	−	0.176436i	−0.339358	−	0.940657i	$-0.610210\pi$
$239$	4.72441	−	2.72764i	0.305597	−	0.176436i	0.644954	+	0.764221i	$0.276876\pi$
$240$		0			0
$241$	3.65789	−	2.11188i	0.235625	−	0.136038i	−0.377539	−	0.925994i	$-0.623230\pi$
$241$	3.65789	−	2.11188i	0.235625	−	0.136038i	0.613164	+	0.789955i	$0.289896\pi$
$242$		0			0
$243$	−0.794073	−	15.5682i	−0.0509398	−	0.998702i
$244$		0			0
$245$	14.6361	−	18.0092i	0.935069	−	1.15056i
$246$		0			0
$247$	−0.00590554	−	0.00340957i	−0.000375761	−	0.000216946i
$248$		0			0
$249$	−1.68851	+	8.36202i	−0.107005	+	0.529922i
$250$		0			0
$251$	−12.2954			−0.776081			−0.388041	−	0.921642i	$-0.626848\pi$
$251$	−12.2954			−0.776081			−0.388041	+	0.921642i	$0.626848\pi$
$252$		0			0
$253$	−35.4554			−2.22906
$254$		0			0
$255$	1.42964	+	1.26110i	0.0895273	+	0.0789734i
$256$		0			0
$257$	7.16881	+	4.13891i	0.447178	+	0.258178i	0.706638	−	0.707576i	$-0.250211\pi$
$257$	7.16881	+	4.13891i	0.447178	+	0.258178i	−0.259460	+	0.965754i	$0.583544\pi$
$258$		0			0
$259$	−1.70523	−	0.605542i	−0.105958	−	0.0376266i
$260$		0			0
$261$	−3.79213	−	30.1534i	−0.234727	−	1.86645i
$262$		0			0
$263$	−13.3297	+	7.69589i	−0.821942	+	0.474549i	−0.851086	−	0.525027i	$-0.824055\pi$
$263$	−13.3297	+	7.69589i	−0.821942	+	0.474549i	0.0291434	+	0.999575i	$0.490722\pi$
$264$		0			0
$265$	−1.21542	+	0.701723i	−0.0746627	+	0.0431065i
$266$		0			0
$267$	−11.1257	+	12.6125i	−0.680880	+	0.771871i
$268$		0			0
$269$	13.8152	+	7.97621i	0.842328	+	0.486318i	0.858055	−	0.513558i	$-0.171673\pi$
$269$	13.8152	+	7.97621i	0.842328	+	0.486318i	−0.0157272	+	0.999876i	$0.505006\pi$
$270$		0			0
$271$	0.703800	+	1.21902i	0.0427528	+	0.0740501i	0.886610	−	0.462518i	$-0.153054\pi$
$271$	0.703800	+	1.21902i	0.0427528	+	0.0740501i	−0.843857	+	0.536568i	$0.819721\pi$
$272$		0			0
$273$	7.32125e−5	−	0.00433985i	4.43102e−6	−	0.000262660i
$274$		0			0
$275$	−29.6225	−	17.1025i	−1.78630	−	1.03132i
$276$		0			0
$277$	3.18950	+	5.52437i	0.191638	+	0.331927i	0.945793	−	0.324769i	$-0.105287\pi$
$277$	3.18950	+	5.52437i	0.191638	+	0.331927i	−0.754155	+	0.656696i	$0.771953\pi$
$278$		0			0
$279$	9.27585	−	7.03258i	0.555331	−	0.421030i
$280$		0			0
$281$	12.8423	−	22.2436i	0.766110	−	1.32694i	−0.173547	−	0.984826i	$-0.555523\pi$
$281$	12.8423	−	22.2436i	0.766110	−	1.32694i	0.939658	−	0.342116i	$-0.111144\pi$
$282$		0			0
$283$	−21.1502			−1.25725			−0.628625	−	0.777709i	$-0.716382\pi$
$283$	−21.1502			−1.25725			−0.628625	+	0.777709i	$0.716382\pi$
$284$		0			0
$285$	13.1750	+	39.1850i	0.780420	+	2.32112i
$286$		0			0
$287$	5.83924	−	16.4435i	0.344679	−	0.970627i
$288$		0			0
$289$	−8.44489	−	14.6270i	−0.496758	−	0.860410i
$290$		0			0
$291$	29.7897	+	6.01532i	1.74630	+	0.352624i
$292$		0			0
$293$	20.0856	−	11.5964i	1.17341	−	0.677469i	0.218930	−	0.975741i	$-0.429743\pi$
$293$	20.0856	−	11.5964i	1.17341	−	0.677469i	0.954481	+	0.298272i	$0.0964102\pi$
$294$		0			0
$295$	0.927526	+	0.535508i	0.0540027	+	0.0311785i
$296$		0			0
$297$	−2.19766	+	29.5867i	−0.127521	+	1.71679i
$298$		0			0
$299$	−0.00588168			−0.000340146
$300$		0			0
$301$	18.5167	−	3.41501i	1.06729	−	0.196838i
$302$		0			0
$303$	−12.0028	+	13.6069i	−0.689545	+	0.781695i
$304$		0			0
$305$	1.60171	−	2.77424i	0.0917134	−	0.158852i
$306$		0			0
$307$	4.55181			0.259786			0.129893	−	0.991528i	$-0.458537\pi$
$307$	4.55181			0.259786			0.129893	+	0.991528i	$0.458537\pi$
$308$		0			0
$309$	5.27772	−	26.1369i	0.300239	−	1.48687i
$310$		0			0
$311$	10.3728			0.588185			0.294093	−	0.955777i	$-0.404983\pi$
$311$	10.3728			0.588185			0.294093	+	0.955777i	$0.404983\pi$
$312$		0			0
$313$		−	31.6617i		−	1.78963i	−0.446442	−	0.894813i	$-0.647309\pi$
$313$		−	31.6617i		−	1.78963i	0.446442	−	0.894813i	$-0.352691\pi$
$314$		0			0
$315$	−17.7375	+	19.4370i	−0.999397	+	1.09515i
$316$		0			0
$317$	−17.5940			−0.988178			−0.494089	−	0.869411i	$-0.664498\pi$
$317$	−17.5940			−0.988178			−0.494089	+	0.869411i	$0.664498\pi$
$318$		0			0
$319$			57.8405i			3.23845i
$320$		0			0
$321$	0.701759	−	0.795541i	0.0391684	−	0.0444027i
$322$		0			0
$323$			2.39020i			0.132994i
$324$		0			0
$325$	−0.00491405	−	0.00283713i	−0.000272582	−	0.000157376i
$326$		0			0
$327$	5.14437	−	25.4764i	0.284484	−	1.40885i
$328$		0			0
$329$	5.90950	−	5.03819i	0.325801	−	0.277765i
$330$		0			0
$331$		−	15.1591i		−	0.833217i	−0.909086	−	0.416609i	$-0.863219\pi$
$331$		−	15.1591i		−	0.833217i	0.909086	−	0.416609i	$-0.136781\pi$
$332$		0			0
$333$	1.89107	+	0.796177i	0.103630	+	0.0436302i
$334$		0			0
$335$	14.0688	−	24.3678i	0.768659	−	1.33136i
$336$		0			0
$337$	7.63938	+	13.2318i	0.416143	+	0.720781i	0.995548	−	0.0942588i	$-0.0300481\pi$
$337$	7.63938	+	13.2318i	0.416143	+	0.720781i	−0.579404	+	0.815040i	$0.696715\pi$
$338$		0			0
$339$	13.7361	+	12.1168i	0.746041	+	0.658094i
$340$		0			0
$341$	−19.1861	+	11.0771i	−1.03898	+	0.599858i
$342$		0			0
$343$	9.63506	+	15.8166i	0.520244	+	0.854018i
$344$		0			0
$345$	26.7403	+	23.5881i	1.43965	+	1.26994i
$346$		0			0
$347$			16.4299i			0.882005i	0.897506	+	0.441003i	$0.145377\pi$
$347$			16.4299i			0.882005i	−0.897506	+	0.441003i	$0.854623\pi$
$348$		0			0
$349$	6.04060	+	3.48754i	0.323346	+	0.186684i	0.652883	−	0.757459i	$-0.273559\pi$
$349$	6.04060	+	3.48754i	0.323346	+	0.186684i	−0.329537	+	0.944143i	$0.606893\pi$
$350$		0			0
$351$	−0.000364569		0.00490811i	−1.94592e−5		0.000261976i
$352$		0			0
$353$	−16.9815	+	9.80426i	−0.903833	+	0.521828i	−0.878442	−	0.477849i	$-0.841416\pi$
$353$	−16.9815	+	9.80426i	−0.903833	+	0.521828i	−0.0253912	+	0.999678i	$0.508083\pi$
$354$		0			0
$355$	5.04598	−	8.73990i	0.267813	−	0.463866i
$356$		0			0
$357$	−1.33021	+	0.738366i	−0.0704023	+	0.0390785i
$358$		0			0
$359$	−25.2983	+	14.6060i	−1.33519	+	0.770873i	−0.986090	−	0.166212i	$-0.946846\pi$
$359$	−25.2983	+	14.6060i	−1.33519	+	0.770873i	−0.349101	+	0.937085i	$0.613513\pi$
$360$		0			0
$361$	−16.4164	+	28.4340i	−0.864019	+	1.49652i
$362$		0			0
$363$	7.40508	−	36.6722i	0.388666	−	1.92479i
$364$		0			0
$365$	−0.561267	−	0.972143i	−0.0293781	−	0.0508843i
$366$		0			0
$367$	2.86934	+	4.96984i	0.149778	+	0.259423i	0.931145	−	0.364648i	$-0.118811\pi$
$367$	2.86934	+	4.96984i	0.149778	+	0.259423i	−0.781367	+	0.624072i	$0.785477\pi$
$368$		0			0
$369$	−7.67753	+	18.2356i	−0.399676	+	0.949305i
$370$		0			0
$371$	−0.203140	−	1.10146i	−0.0105465	−	0.0571849i
$372$		0			0
$373$	−10.9310	+	18.9330i	−0.565986	+	0.980316i	0.430972	+	0.902365i	$0.358171\pi$
$373$	−10.9310	+	18.9330i	−0.565986	+	0.980316i	−0.996957	+	0.0779503i	$0.975162\pi$
$374$		0			0
$375$	1.81307	+	5.39242i	0.0936267	+	0.278464i
$376$		0			0
$377$			0.00959512i			0.000494174i
$378$		0			0
$379$			24.1783i			1.24196i	0.783827	+	0.620979i	$0.213265\pi$
$379$			24.1783i			1.24196i	−0.783827	+	0.620979i	$0.786735\pi$
$380$		0			0
$381$	−7.18402	−	21.3666i	−0.368048	−	1.09465i
$382$		0			0
$383$	−4.28089	+	7.41471i	−0.218743	+	0.378874i	−0.954424	−	0.298454i	$-0.903529\pi$
$383$	−4.28089	+	7.41471i	−0.218743	+	0.378874i	0.735681	+	0.677328i	$0.236862\pi$
$384$		0			0
$385$	38.1104	−	32.4914i	1.94229	−	1.65591i
$386$		0			0
$387$	−21.1832	+	2.66403i	−1.07680	+	0.135420i
$388$		0			0
$389$	6.18694	+	10.7161i	0.313690	+	0.543328i	0.979158	−	0.203099i	$-0.0651013\pi$
$389$	6.18694	+	10.7161i	0.313690	+	0.543328i	−0.665468	+	0.746426i	$0.731768\pi$
$390$		0			0
$391$	1.03081	+	1.78541i	0.0521301	+	0.0902919i
$392$		0			0
$393$	−1.41847	+	7.02469i	−0.0715523	+	0.354349i
$394$		0			0
$395$	19.0682	−	33.0271i	0.959425	−	1.66177i
$396$		0			0
$397$	13.0722	−	7.54724i	0.656075	−	0.378785i	−0.134705	−	0.990886i	$-0.543009\pi$
$397$	13.0722	−	7.54724i	0.656075	−	0.378785i	0.790780	+	0.612101i	$0.209675\pi$
$398$		0			0
$399$	−32.9875	−	0.556493i	−1.65144	−	0.0278595i
$400$		0			0
$401$	9.35460	−	16.2026i	0.467147	−	0.809122i	−0.532149	−	0.846651i	$-0.678615\pi$
$401$	9.35460	−	16.2026i	0.467147	−	0.809122i	0.999296	+	0.0375291i	$0.0119487\pi$
$402$		0			0
$403$	−0.00318276	+	0.00183757i	−0.000158545	+	9.15358e-5i
$404$		0			0
$405$	21.3411	−	20.8521i	1.06045	−	1.03615i
$406$		0			0
$407$	−3.38191	−	1.95254i	−0.167635	−	0.0967840i
$408$		0			0
$409$		−	9.51790i		−	0.470630i	−0.971919	−	0.235315i	$-0.924388\pi$
$409$		−	9.51790i		−	0.470630i	0.971919	−	0.235315i	$-0.0756122\pi$
$410$		0			0
$411$	−13.0864	−	11.5437i	−0.645504	−	0.569409i
$412$		0			0
$413$	−0.650433	+	0.554533i	−0.0320057	+	0.0272868i
$414$		0			0
$415$	−14.1408	+	8.16418i	−0.694144	+	0.400764i
$416$		0			0
$417$	−24.6096	−	21.7085i	−1.20514	−	1.06307i
$418$		0			0
$419$	−7.82197	−	13.5480i	−0.382128	−	0.661865i	0.609238	−	0.792987i	$-0.291475\pi$
$419$	−7.82197	−	13.5480i	−0.382128	−	0.661865i	−0.991366	+	0.131122i	$0.958142\pi$
$420$		0			0
$421$	5.10584	−	8.84357i	0.248843	−	0.431009i	−0.714362	−	0.699776i	$-0.753283\pi$
$421$	5.10584	−	8.84357i	0.248843	−	0.431009i	0.963205	+	0.268767i	$0.0866163\pi$
$422$		0			0
$423$	−7.01677	+	5.31984i	−0.341167	+	0.258659i
$424$		0			0
$425$			1.98891i			0.0964761i
$426$		0			0
$427$	1.65861	+	1.94545i	0.0802657	+	0.0941469i
$428$		0			0
$429$	0.00185401	−	0.00918161i	8.95124e−5	−	0.000443292i
$430$		0			0
$431$	−21.0606	−	12.1594i	−1.01445	−	0.585696i	−0.101962	−	0.994788i	$-0.532512\pi$
$431$	−21.0606	−	12.1594i	−1.01445	−	0.585696i	−0.912493	+	0.409093i	$0.865845\pi$
$432$		0			0
$433$		−	0.993040i		−	0.0477225i	−0.999715	−	0.0238612i	$-0.992404\pi$
$433$		−	0.993040i		−	0.0477225i	0.999715	−	0.0238612i	$-0.00759599\pi$
$434$		0			0
$435$	38.4806	−	43.6230i	1.84500	−	2.09156i
$436$		0			0
$437$			44.7070i			2.13863i
$438$		0			0
$439$	25.3902			1.21181			0.605905	−	0.795537i	$-0.292811\pi$
$439$	25.3902			1.21181			0.605905	+	0.795537i	$0.292811\pi$
$440$		0			0
$441$	−9.88059	−	18.5303i	−0.470504	−	0.882398i
$442$		0			0
$443$			16.1602i			0.767794i	0.923376	+	0.383897i	$0.125418\pi$
$443$			16.1602i			0.767794i	−0.923376	+	0.383897i	$0.874582\pi$
$444$		0			0
$445$	−32.1910			−1.52600
$446$		0			0
$447$	−6.80371	+	33.6940i	−0.321805	+	1.59367i
$448$		0			0
$449$	−40.3839			−1.90583			−0.952917	−	0.303230i	$-0.901935\pi$
$449$	−40.3839			−1.90583			−0.952917	+	0.303230i	$0.901935\pi$
$450$		0			0
$451$	18.8284	−	32.6117i	0.886593	−	1.53562i
$452$		0			0
$453$	1.93033	−	2.18830i	0.0906948	−	0.102815i
$454$		0			0
$455$	0.00632211	−	0.00538997i	0.000296385	−	0.000252686i
$456$		0			0
$457$	−4.82307			−0.225614			−0.112807	−	0.993617i	$-0.535984\pi$
$457$	−4.82307			−0.225614			−0.112807	+	0.993617i	$0.535984\pi$
$458$		0			0
$459$	1.55377	−	0.749515i	0.0725238	−	0.0349844i
$460$		0			0
$461$	27.6395	+	15.9576i	1.28730	+	0.743222i	0.978172	−	0.207799i	$-0.0666300\pi$
$461$	27.6395	+	15.9576i	1.28730	+	0.743222i	0.309126	+	0.951021i	$0.399963\pi$
$462$		0			0
$463$	35.4306	−	20.4559i	1.64660	−	0.950665i	0.668191	−	0.743990i	$-0.267069\pi$
$463$	35.4306	−	20.4559i	1.64660	−	0.950665i	0.978410	−	0.206675i	$-0.0662643\pi$
$464$		0			0
$465$	21.8395	+	4.40997i	1.01278	+	0.204507i
$466$		0			0
$467$	−15.0280	−	26.0293i	−0.695415	−	1.20449i	−0.970041	−	0.242943i	$-0.921887\pi$
$467$	−15.0280	−	26.0293i	−0.695415	−	1.20449i	0.274626	−	0.961551i	$-0.411446\pi$
$468$		0			0
$469$	14.5686	+	17.0881i	0.672715	+	0.789054i
$470$		0			0
$471$	8.77054	+	26.0853i	0.404125	+	1.20195i
$472$		0			0
$473$	40.6338			1.86834
$474$		0			0
$475$	−21.5652	+	37.3520i	−0.989479	+	1.71383i
$476$		0			0
$477$	0.158469	+	1.26007i	0.00725577	+	0.0576948i
$478$		0			0
$479$	5.96224	+	10.3269i	0.272422	+	0.471848i	0.969481	−	0.245165i	$-0.0788421\pi$
$479$	5.96224	+	10.3269i	0.272422	+	0.471848i	−0.697060	+	0.717013i	$0.745509\pi$
$480$		0			0
$481$	−0.000561022	0	0.000323906i	−2.55804e−5	0	1.47688e-5i
$482$		0			0
$483$	−24.8807	+	13.8106i	−1.13211	+	0.628405i
$484$		0			0
$485$	29.0849	+	50.3765i	1.32068	+	2.28748i
$486$		0			0
$487$	−16.7169	−	9.65151i	−0.757515	−	0.437352i	0.0708876	−	0.997484i	$-0.477417\pi$
$487$	−16.7169	−	9.65151i	−0.757515	−	0.437352i	−0.828403	+	0.560133i	$0.810750\pi$
$488$		0			0
$489$	−12.7645	+	14.4703i	−0.577230	+	0.654370i
$490$		0			0
$491$	−14.7903	+	8.53918i	−0.667477	+	0.385368i	−0.795120	−	0.606452i	$-0.792592\pi$
$491$	−14.7903	+	8.53918i	−0.667477	+	0.385368i	0.127643	+	0.991820i	$0.459259\pi$
$492$		0			0
$493$	2.91264	−	1.68161i	0.131179	−	0.0757360i
$494$		0			0
$495$	−45.2512	+	34.3077i	−2.03389	+	1.54202i
$496$		0			0
$497$	5.22525	+	6.12891i	0.234385	+	0.274919i
$498$		0			0
$499$	24.2856	+	14.0213i	1.08717	+	0.627680i	0.932822	−	0.360336i	$-0.117338\pi$
$499$	24.2856	+	14.0213i	1.08717	+	0.627680i	0.154351	+	0.988016i	$0.450671\pi$
$500$		0			0
$501$	−12.0504	−	10.6299i	−0.538372	−	0.474907i
$502$		0			0
$503$	29.0641			1.29590			0.647952	−	0.761681i	$-0.275626\pi$
$503$	29.0641			1.29590			0.647952	+	0.761681i	$0.275626\pi$
$504$		0			0
$505$	−34.7291			−1.54542
$506$		0			0
$507$	−4.45675	+	22.0712i	−0.197931	+	0.980216i
$508$		0			0
$509$	−20.1178	−	11.6150i	−0.891707	−	0.514827i	−0.0172064	−	0.999852i	$-0.505477\pi$
$509$	−20.1178	−	11.6150i	−0.891707	−	0.514827i	−0.874500	+	0.485025i	$0.838811\pi$
$510$		0			0
$511$	0.880992	−	0.162480i	0.0389728	−	0.00718768i
$512$		0			0
$513$	37.3069	+	2.77111i	1.64714	+	0.122348i
$514$		0			0
$515$	44.1993	−	25.5185i	1.94766	−	1.12448i
$516$		0			0
$517$	14.5134	−	8.37932i	0.638299	−	0.368522i
$518$		0			0
$519$	−3.40505	−	10.1273i	−0.149465	−	0.444538i
$520$		0			0
$521$	−8.35723	−	4.82505i	−0.366137	−	0.211389i	0.305633	−	0.952150i	$-0.401132\pi$
$521$	−8.35723	−	4.82505i	−0.366137	−	0.211389i	−0.671769	+	0.740760i	$0.734465\pi$
$522$		0			0
$523$	16.5493	+	28.6642i	0.723650	+	1.25340i	0.959527	+	0.281616i	$0.0908704\pi$
$523$	16.5493	+	28.6642i	0.723650	+	1.25340i	−0.235877	+	0.971783i	$0.575796\pi$
$524$		0			0
$525$	−27.4492	−	0.463062i	−1.19798	−	0.0202097i
$526$		0			0
$527$	1.11560	+	0.644094i	0.0485964	+	0.0280572i
$528$		0			0
$529$	7.78048	+	13.4762i	0.338282	+	0.585921i
$530$		0			0
$531$	0.772306	−	0.585532i	0.0335152	−	0.0254099i
$532$		0			0
$533$	0.00312342	−	0.00540993i	0.000135290	−	0.000234330i
$534$		0			0
$535$	2.03047			0.0877850
$536$		0			0
$537$	27.8834	+	5.63039i	1.20326	+	0.242969i
$538$		0			0
$539$	14.2573	+	37.3380i	0.614107	+	1.60826i
$540$		0			0
$541$	−5.01990	−	8.69473i	−0.215823	−	0.373816i	0.737704	−	0.675124i	$-0.235910\pi$
$541$	−5.01990	−	8.69473i	−0.215823	−	0.373816i	−0.953527	+	0.301309i	$0.902577\pi$
$542$		0			0
$543$	5.94986	+	17.6960i	0.255333	+	0.759409i
$544$		0			0
$545$	43.0825	−	24.8737i	1.84545	−	1.06547i
$546$		0			0
$547$	−29.4450	−	17.0001i	−1.25898	−	0.726871i	−0.286101	−	0.958199i	$-0.592359\pi$
$547$	−29.4450	−	17.0001i	−1.25898	−	0.726871i	−0.972876	+	0.231329i	$0.925693\pi$
$548$		0			0
$549$	−1.75133	−	2.30997i	−0.0747449	−	0.0985872i
$550$		0			0
$551$	72.9331			3.10706
$552$		0			0
$553$	19.7456	+	23.1604i	0.839669	+	0.984881i
$554$		0			0
$555$	1.25161	+	3.72254i	0.0531281	+	0.158013i
$556$		0			0
$557$	−8.11569	+	14.0568i	−0.343873	+	0.595605i	−0.985148	−	0.171705i	$-0.945072\pi$
$557$	−8.11569	+	14.0568i	−0.343873	+	0.595605i	0.641275	+	0.767311i	$0.278406\pi$
$558$		0			0
$559$	0.00674071			0.000285102
$560$		0			0
$561$	−3.11204	+	1.04635i	−0.131391	+	0.0441769i
$562$		0			0
$563$	21.0656			0.887808			0.443904	−	0.896074i	$-0.353593\pi$
$563$	21.0656			0.887808			0.443904	+	0.896074i	$0.353593\pi$
$564$		0			0
$565$			35.0588i			1.47493i
$566$		0			0
$567$	9.98241	+	21.6183i	0.419222	+	0.907884i
$568$		0			0
$569$	11.5642			0.484796			0.242398	−	0.970177i	$-0.422066\pi$
$569$	11.5642			0.484796			0.242398	+	0.970177i	$0.422066\pi$
$570$		0			0
$571$			28.1907i			1.17974i	0.807497	+	0.589871i	$0.200822\pi$
$571$			28.1907i			1.17974i	−0.807497	+	0.589871i	$0.799178\pi$
$572$		0			0
$573$	−1.18490	−	3.52410i	−0.0494997	−	0.147222i
$574$		0			0
$575$			37.2011i			1.55139i
$576$		0			0
$577$	18.5712	+	10.7221i	0.773129	+	0.446366i	0.833990	−	0.551780i	$-0.186051\pi$
$577$	18.5712	+	10.7221i	0.773129	+	0.446366i	−0.0608607	+	0.998146i	$0.519385\pi$
$578$		0			0
$579$	−19.7514	+	6.64094i	−0.820841	+	0.275988i
$580$		0			0
$581$	−2.36343	−	12.8149i	−0.0980515	−	0.531651i
$582$		0			0
$583$		−	2.41708i		−	0.100105i
$584$		0			0
$585$	−0.00750669	+	0.00569128i	−0.000310364	+	0.000235305i
$586$		0			0
$587$	−9.04636	+	15.6688i	−0.373383	+	0.646719i	−0.990084	−	0.140479i	$-0.955136\pi$
$587$	−9.04636	+	15.6688i	−0.373383	+	0.646719i	0.616700	+	0.787198i	$0.288469\pi$
$588$		0			0
$589$	13.9675	+	24.1924i	0.575520	+	0.996830i
$590$		0			0
$591$	6.07025	−	2.04097i	0.249697	−	0.0839545i
$592$		0			0
$593$	−15.3219	+	8.84608i	−0.629193	+	0.363265i	−0.780440	−	0.625231i	$-0.785005\pi$
$593$	−15.3219	+	8.84608i	−0.629193	+	0.363265i	0.151246	+	0.988496i	$0.451671\pi$
$594$		0			0
$595$	−2.74414	−	0.974472i	−0.112499	−	0.0399495i
$596$		0			0
$597$	7.03428	−	34.8359i	0.287894	−	1.42574i
$598$		0			0
$599$			9.35286i			0.382148i	0.981576	+	0.191074i	$0.0611970\pi$
$599$			9.35286i			0.382148i	−0.981576	+	0.191074i	$0.938803\pi$
$600$		0			0
$601$	2.53177	+	1.46172i	0.103273	+	0.0596246i	0.550747	−	0.834672i	$-0.314343\pi$
$601$	2.53177	+	1.46172i	0.103273	+	0.0596246i	−0.447474	+	0.894297i	$0.647676\pi$
$602$		0			0
$603$	−15.3830	−	20.2899i	−0.626444	−	0.826268i
$604$		0			0
$605$	62.0153	−	35.8045i	2.52128	−	1.45566i
$606$		0			0
$607$	−9.51622	+	16.4826i	−0.386252	+	0.669007i	−0.991942	−	0.126693i	$-0.959564\pi$
$607$	−9.51622	+	16.4826i	−0.386252	+	0.669007i	0.605690	+	0.795700i	$0.292897\pi$
$608$		0			0
$609$	22.5300	+	40.5892i	0.912963	+	1.64476i
$610$		0			0
$611$	0.00240762	−	0.00139004i	9.74018e−5	−	5.62350e-5i
$612$		0			0
$613$	−17.9515	+	31.0928i	−0.725052	+	1.25583i	0.233900	+	0.972261i	$0.424851\pi$
$613$	−17.9515	+	31.0928i	−0.725052	+	1.25583i	−0.958952	+	0.283567i	$0.908482\pi$
$614$		0			0
$615$	−35.8964	+	12.0693i	−1.44748	+	0.486681i
$616$		0			0
$617$	16.3406	+	28.3028i	0.657849	+	1.13943i	0.981171	+	0.193139i	$0.0618669\pi$
$617$	16.3406	+	28.3028i	0.657849	+	1.13943i	−0.323322	+	0.946289i	$0.604800\pi$
$618$		0			0
$619$	10.8879	+	18.8583i	0.437620	+	0.757981i	0.997505	−	0.0705896i	$-0.0224881\pi$
$619$	10.8879	+	18.8583i	0.437620	+	0.757981i	−0.559885	+	0.828570i	$0.689155\pi$
$620$		0			0
$621$	29.0622	−	14.0191i	1.16622	−	0.562569i
$622$		0			0
$623$	8.59694	−	24.2092i	0.344429	−	0.969923i
$624$		0			0
$625$	9.53231	−	16.5105i	0.381293	−	0.660418i
$626$		0			0
$627$	−69.7900	−	14.0924i	−2.78714	−	0.562798i
$628$		0			0
$629$			0.227067i			0.00905377i
$630$		0			0
$631$		−	15.5776i		−	0.620134i	−0.950715	−	0.310067i	$-0.899648\pi$
$631$		−	15.5776i		−	0.620134i	0.950715	−	0.310067i	$-0.100352\pi$
$632$		0			0
$633$	5.33724	−	6.05050i	0.212136	−	0.240486i
$634$		0			0
$635$	21.5733	−	37.3660i	0.856110	−	1.48283i
$636$		0			0
$637$	0.00236514	+	0.00619398i	9.37102e−5	+	0.000245415i
$638$		0			0
$639$	−5.51735	−	7.27729i	−0.218263	−	0.287885i
$640$		0			0
$641$	−12.9884	−	22.4966i	−0.513012	−	0.888563i	−0.999886	−	0.0150911i	$-0.995196\pi$
$641$	−12.9884	−	22.4966i	−0.513012	−	0.888563i	0.486874	−	0.873472i	$-0.338137\pi$
$642$		0			0
$643$	−0.284908	−	0.493476i	−0.0112357	−	0.0194608i	0.860353	−	0.509699i	$-0.170243\pi$
$643$	−0.284908	−	0.493476i	−0.0112357	−	0.0194608i	−0.871589	+	0.490238i	$0.836910\pi$
$644$		0			0
$645$	−30.6458	−	27.0331i	−1.20668	−	1.06443i
$646$		0			0
$647$	−18.2339	+	31.5820i	−0.716847	+	1.24162i	0.245395	+	0.969423i	$0.421082\pi$
$647$	−18.2339	+	31.5820i	−0.716847	+	1.24162i	−0.962243	+	0.272193i	$0.912251\pi$
$648$		0			0
$649$	−1.59743	+	0.922276i	−0.0627046	+	0.0362025i
$650$		0			0
$651$	−9.14897	+	15.2466i	−0.358576	+	0.597563i
$652$		0			0
$653$	−13.9896	+	24.2307i	−0.547456	+	0.948221i	0.450992	+	0.892528i	$0.351070\pi$
$653$	−13.9896	+	24.2307i	−0.547456	+	0.948221i	−0.998448	+	0.0556930i	$0.982263\pi$
$654$		0			0
$655$	−11.8793	+	6.85849i	−0.464161	+	0.267983i
$656$		0			0
$657$	−1.00786	+	0.126750i	−0.0393203	+	0.00494497i
$658$		0			0
$659$	−31.2032	−	18.0152i	−1.21551	−	0.701773i	−0.251553	−	0.967844i	$-0.580941\pi$
$659$	−31.2032	−	18.0152i	−1.21551	−	0.701773i	−0.963953	+	0.266071i	$0.914274\pi$
$660$		0			0
$661$		−	13.3239i		−	0.518239i	−0.965845	−	0.259120i	$-0.916568\pi$
$661$		−	13.3239i		−	0.518239i	0.965845	−	0.259120i	$-0.0834324\pi$
$662$		0			0
$663$	−0.000516254	0	0.000173578i	−2.00497e−5	0	6.74122e-6i
$664$		0			0
$665$	−40.9695	−	48.0548i	−1.58873	−	1.86348i
$666$		0			0
$667$	54.4788	−	31.4533i	2.10943	−	1.21788i
$668$		0			0
$669$	3.65105	−	18.0811i	0.141158	−	0.699056i
$670$		0			0
$671$	2.75853	+	4.77792i	0.106492	+	0.184449i
$672$		0			0
$673$	8.09477	−	14.0206i	0.312031	−	0.540453i	−0.666771	−	0.745262i	$-0.732324\pi$
$673$	8.09477	−	14.0206i	0.312031	−	0.540453i	0.978802	+	0.204810i	$0.0656575\pi$
$674$		0			0
$675$	31.0434	+	2.30586i	1.19486	+	0.0887527i
$676$		0			0
$677$		−	10.3418i		−	0.397467i	−0.980054	−	0.198733i	$-0.936317\pi$
$677$		−	10.3418i		−	0.397467i	0.980054	−	0.198733i	$-0.0636828\pi$
$678$		0			0
$679$	−45.6530	+	8.41971i	−1.75200	+	0.323119i
$680$		0			0
$681$	10.2908	+	9.07767i	0.394344	+	0.347857i
$682$		0			0
$683$	6.56278	+	3.78902i	0.251118	+	0.144983i	0.620276	−	0.784384i	$-0.287021\pi$
$683$	6.56278	+	3.78902i	0.251118	+	0.144983i	−0.369158	+	0.929367i	$0.620354\pi$
$684$		0			0
$685$		−	33.4006i		−	1.27617i
$686$		0			0
$687$	11.3629	+	2.29446i	0.433520	+	0.0875392i
$688$		0			0
$689$		0	0.000400968i		0	1.52757e-5i
$690$		0			0
$691$	4.79448			0.182391			0.0911954	−	0.995833i	$-0.470931\pi$
$691$	4.79448			0.182391			0.0911954	+	0.995833i	$0.470931\pi$
$692$		0			0
$693$	−13.7163	−	43.1934i	−0.521038	−	1.64078i
$694$		0			0
$695$		−	62.8116i		−	2.38258i
$696$		0			0
$697$	−2.18961			−0.0829373
$698$		0			0
$699$	−6.31894	−	5.57404i	−0.239004	−	0.210829i
$700$		0			0
$701$	15.7368			0.594370			0.297185	−	0.954820i	$-0.403952\pi$
$701$	15.7368			0.594370			0.297185	+	0.954820i	$0.403952\pi$
$702$		0			0
$703$	−2.46203	+	4.26437i	−0.0928573	+	0.160834i
$704$		0			0
$705$	−16.5206	−	3.33594i	−0.622202	−	0.125639i
$706$		0			0
$707$	9.27475	−	26.1180i	0.348813	−	0.982267i
$708$		0			0
$709$	−9.77428			−0.367081			−0.183540	−	0.983012i	$-0.558756\pi$
$709$	−9.77428			−0.367081			−0.183540	+	0.983012i	$0.558756\pi$
$710$		0			0
$711$	−20.8494	−	27.5000i	−0.781915	−	1.03133i
$712$		0			0
$713$	20.8666	+	12.0473i	0.781459	+	0.451175i
$714$		0			0
$715$	0.0155268	−	0.00896438i	0.000580668	−	0.000335249i
$716$		0			0
$717$	6.25060	−	7.08592i	0.233433	−	0.264628i
$718$		0			0
$719$	−7.31528	−	12.6704i	−0.272814	−	0.472528i	0.696767	−	0.717297i	$-0.254621\pi$
$719$	−7.31528	−	12.6704i	−0.272814	−	0.472528i	−0.969581	+	0.244770i	$0.921288\pi$
$720$		0			0
$721$	7.38728	+	40.0550i	0.275117	+	1.49173i
$722$		0			0
$723$	4.83954	−	5.48629i	0.179985	−	0.204037i
$724$		0			0
$725$	60.6882			2.25390
$726$		0			0
$727$	13.0584	−	22.6179i	0.484311	−	0.838851i	−0.515527	−	0.856874i	$-0.672404\pi$
$727$	13.0584	−	22.6179i	0.484311	−	0.838851i	0.999838	+	0.0180224i	$0.00573701\pi$
$728$		0			0
$729$	−9.89723	−	25.1206i	−0.366564	−	0.930393i
$730$		0			0
$731$	−1.18136	−	2.04617i	−0.0436940	−	0.0756803i
$732$		0			0
$733$	−18.9737	−	10.9545i	−0.700810	−	0.404613i	0.106839	−	0.994276i	$-0.465927\pi$
$733$	−18.9737	−	10.9545i	−0.700810	−	0.404613i	−0.807649	+	0.589664i	$0.799260\pi$
$734$		0			0
$735$	14.0877	−	37.6454i	0.519634	−	1.38857i
$736$		0			0
$737$	24.2299	+	41.9674i	0.892519	+	1.54589i
$738$		0			0
$739$	−27.5091	−	15.8824i	−1.01194	−	0.584242i	−0.100179	−	0.994969i	$-0.531942\pi$
$739$	−27.5091	−	15.8824i	−1.01194	−	0.584242i	−0.911758	+	0.410727i	$0.865275\pi$
$740$		0			0
$741$	−0.0115774	−	0.00233779i	−0.000425307	−	8.58807e-5i
$742$		0			0
$743$	17.6322	−	10.1799i	0.646862	−	0.373466i	−0.140391	−	0.990096i	$-0.544836\pi$
$743$	17.6322	−	10.1799i	0.646862	−	0.373466i	0.787253	+	0.616630i	$0.211503\pi$
$744$		0			0
$745$	−56.9790	+	32.8969i	−2.08755	+	1.20525i
$746$		0			0
$747$	1.84370	+	14.6603i	0.0674574	+	0.536392i
$748$		0			0
$749$	−0.542258	+	1.52701i	−0.0198137	+	0.0557959i
$750$		0			0
$751$	2.79726	+	1.61500i	0.102073	+	0.0589320i	0.550168	−	0.835054i	$-0.314564\pi$
$751$	2.79726	+	1.61500i	0.102073	+	0.0589320i	−0.448094	+	0.893986i	$0.647897\pi$
$752$		0			0
$753$	−20.1859	+	6.78702i	−0.735615	+	0.247333i
$754$		0			0
$755$	5.58523			0.203267
$756$		0			0
$757$	39.1407			1.42259			0.711297	−	0.702892i	$-0.248108\pi$
$757$	39.1407			1.42259			0.711297	+	0.702892i	$0.248108\pi$
$758$		0			0
$759$	−58.2085	+	19.5712i	−2.11284	+	0.710390i
$760$		0			0
$761$	−42.6464	−	24.6219i	−1.54593	−	0.892544i	−0.998446	−	0.0557291i	$-0.982252\pi$
$761$	−42.6464	−	24.6219i	−1.54593	−	0.892544i	−0.547486	−	0.836815i	$-0.684415\pi$
$762$		0			0
$763$	7.20062	+	39.0429i	0.260680	+	1.41345i
$764$		0			0
$765$	3.04321	+	1.28125i	0.110028	+	0.0463237i
$766$		0			0
$767$	−0.000264996	0	0.000152996i	−9.56846e−6	0	5.52435e-6i
$768$		0			0
$769$	−25.9493	+	14.9818i	−0.935757	+	0.540259i	−0.888628	−	0.458630i	$-0.848341\pi$
$769$	−25.9493	+	14.9818i	−0.935757	+	0.540259i	−0.0471290	+	0.998889i	$0.515007\pi$
$770$		0			0
$771$	14.0540	+	2.83786i	0.506141	+	0.102203i
$772$		0			0
$773$	9.98091	+	5.76248i	0.358988	+	0.207262i	0.668637	−	0.743589i	$-0.266878\pi$
$773$	9.98091	+	5.76248i	0.358988	+	0.207262i	−0.309649	+	0.950851i	$0.600211\pi$
$774$		0			0
$775$	11.6225	+	20.1307i	0.417491	+	0.723116i
$776$		0			0
$777$	−3.13379	−	0.0528664i	−0.112424	−	0.00189657i
$778$		0			0
$779$	−41.1212	−	23.7414i	−1.47332	−	0.850622i
$780$		0			0
$781$	8.69042	+	15.0523i	0.310968	+	0.538612i
$782$		0			0
$783$	−22.8702	−	47.4108i	−0.817315	−	1.69432i
$784$		0			0
$785$	−26.3375	+	45.6180i	−0.940027	+	1.62818i
$786$		0			0
$787$	−7.61311			−0.271378			−0.135689	−	0.990751i	$-0.543325\pi$
$787$	−7.61311			−0.271378			−0.135689	+	0.990751i	$0.543325\pi$
$788$		0			0
$789$	−17.6357	+	19.9925i	−0.627848	+	0.711753i
$790$		0			0
$791$	−26.3659	−	9.36280i	−0.937465	−	0.332903i
$792$		0			0
$793$	0.000457611	0	0.000792605i	1.62502e−5	0	2.81462e-5i
$794$		0			0
$795$	−1.60805	+	1.82295i	−0.0570318	+	0.0646534i
$796$		0			0
$797$	11.9451	−	6.89649i	0.423116	−	0.244286i	−0.273293	−	0.961931i	$-0.588113\pi$
$797$	11.9451	−	6.89649i	0.423116	−	0.244286i	0.696410	+	0.717644i	$0.254780\pi$
$798$		0			0
$799$	−0.843904	−	0.487228i	−0.0298552	−	0.0172369i
$800$		0			0
$801$	−11.3034	+	26.8477i	−0.399386	+	0.948616i
$802$		0			0
$803$	1.93328			0.0682240
$804$		0			0
$805$	−51.3272	−	18.2268i	−1.80905	−	0.642410i
$806$		0			0
$807$	27.0838	+	5.46892i	0.953393	+	0.192515i
$808$		0			0
$809$	8.55901	−	14.8246i	0.300919	−	0.521207i	−0.675426	−	0.737428i	$-0.736040\pi$
$809$	8.55901	−	14.8246i	0.300919	−	0.521207i	0.976344	+	0.216222i	$0.0693734\pi$
$810$		0			0
$811$	38.2446			1.34295			0.671475	−	0.741027i	$-0.265661\pi$
$811$	38.2446			1.34295			0.671475	+	0.741027i	$0.265661\pi$
$812$		0			0
$813$	1.82835	+	1.61281i	0.0641229	+	0.0565638i
$814$		0			0
$815$	−36.9328			−1.29370
$816$		0			0
$817$		−	51.2366i		−	1.79254i
$818$		0			0
$819$	−0.00227538	−	0.00716532i	−7.95083e−5	−	0.000250376i
$820$		0			0
$821$	−10.6974			−0.373342			−0.186671	−	0.982422i	$-0.559770\pi$
$821$	−10.6974			−0.373342			−0.186671	+	0.982422i	$0.559770\pi$
$822$		0			0
$823$		−	5.80426i		−	0.202324i	−0.994870	−	0.101162i	$-0.967744\pi$
$823$		−	5.80426i		−	0.202324i	0.994870	−	0.101162i	$-0.0322560\pi$
$824$		0			0
$825$	−58.0728	−	11.7264i	−2.02184	−	0.408262i
$826$		0			0
$827$		−	3.81051i		−	0.132504i	−0.997803	−	0.0662522i	$-0.978896\pi$
$827$		−	3.81051i		−	0.132504i	0.997803	−	0.0662522i	$-0.0211042\pi$
$828$		0			0
$829$	8.85003	+	5.10957i	0.307374	+	0.177463i	0.645751	−	0.763548i	$-0.276544\pi$
$829$	8.85003	+	5.10957i	0.307374	+	0.177463i	−0.338377	+	0.941011i	$0.609878\pi$
$830$		0			0
$831$	8.28574	+	7.30898i	0.287429	+	0.253546i
$832$		0			0
$833$	1.46570	−	1.80349i	0.0507835	−	0.0624871i
$834$		0			0
$835$		−	30.7565i		−	1.06437i
$836$		0			0
$837$	11.3466	−	16.6659i	0.392195	−	0.576057i
$838$		0			0
$839$	−4.61871	+	7.99984i	−0.159456	+	0.276185i	−0.934673	−	0.355510i	$-0.884307\pi$
$839$	−4.61871	+	7.99984i	−0.159456	+	0.276185i	0.775217	+	0.631695i	$0.217641\pi$
$840$		0			0
$841$	−36.8116	−	63.7596i	−1.26937	−	2.19861i
$842$		0			0
$843$	8.80541	−	43.6071i	0.303275	−	1.50191i
$844$		0			0
$845$	−37.3240	+	21.5490i	−1.28398	+	0.741308i
$846$		0			0
$847$	10.3650	+	56.2005i	0.356144	+	1.93107i
$848$		0			0
$849$	−34.7231	+	11.6748i	−1.19169	+	0.400678i
$850$		0			0
$851$			4.24713i			0.145590i
$852$		0			0
$853$	−21.3274	−	12.3134i	−0.730238	−	0.421603i	0.0882715	−	0.996096i	$-0.471866\pi$
$853$	−21.3274	−	12.3134i	−0.730238	−	0.421603i	−0.818509	+	0.574494i	$0.805199\pi$
$854$		0			0
$855$	43.2598	+	57.0589i	1.47945	+	1.95137i
$856$		0			0
$857$	−33.4015	+	19.2843i	−1.14097	+	0.658741i	−0.946671	−	0.322201i	$-0.895577\pi$
$857$	−33.4015	+	19.2843i	−1.14097	+	0.658741i	−0.194301	+	0.980942i	$0.562244\pi$
$858$		0			0
$859$	−18.5281	+	32.0915i	−0.632169	+	1.09495i	0.354938	+	0.934890i	$0.384502\pi$
$859$	−18.5281	+	32.0915i	−0.632169	+	1.09495i	−0.987107	+	0.160059i	$0.948832\pi$
$860$		0			0
$861$	0.509790	−	30.2191i	0.0173736	−	1.02986i
$862$		0			0
$863$	4.66058	−	2.69079i	0.158648	−	0.0915955i	−0.418574	−	0.908183i	$-0.637470\pi$
$863$	4.66058	−	2.69079i	0.158648	−	0.0915955i	0.577222	+	0.816587i	$0.304137\pi$
$864$		0			0
$865$	10.2252	−	17.7106i	0.347668	−	0.602178i
$866$		0			0
$867$	−21.9383	−	19.3521i	−0.745064	−	0.657233i
$868$		0			0
$869$	32.8401	+	56.8807i	1.11402	+	1.92955i
$870$		0			0
$871$	0.00401948	+	0.00696194i	0.000136195	+	0.000235896i
$872$		0			0
$873$	52.2273	−	6.56817i	1.76763	−	0.222299i
$874$		0			0
$875$	−5.63801	−	6.61304i	−0.190599	−	0.223562i
$876$		0			0
$877$	−20.5147	+	35.5326i	−0.692734	+	1.19985i	0.278205	+	0.960522i	$0.410261\pi$
$877$	−20.5147	+	35.5326i	−0.692734	+	1.19985i	−0.970939	+	0.239328i	$0.923073\pi$
$878$		0			0
$879$	26.5741	−	30.1254i	0.896321	−	1.01610i
$880$		0			0
$881$		−	21.9199i		−	0.738500i	−0.929330	−	0.369250i	$-0.879615\pi$
$881$		−	21.9199i		−	0.738500i	0.929330	−	0.369250i	$-0.120385\pi$
$882$		0			0
$883$			42.0376i			1.41468i	0.706875	+	0.707339i	$0.250105\pi$
$883$			42.0376i			1.41468i	−0.706875	+	0.707339i	$0.749895\pi$
$884$		0			0
$885$	1.81835	+	0.367173i	0.0611232	+	0.0123424i
$886$		0			0
$887$	−6.22411	+	10.7805i	−0.208985	+	0.361973i	−0.951395	−	0.307973i	$-0.900349\pi$
$887$	−6.22411	+	10.7805i	−0.208985	+	0.361973i	0.742410	+	0.669946i	$0.233683\pi$
$888$		0			0
$889$	22.3397	+	26.2031i	0.749250	+	0.878825i
$890$		0			0
$891$	12.7237	+	49.7866i	0.426260	+	1.66792i
$892$		0			0
$893$	−10.5658	−	18.3005i	−0.353570	−	0.612402i
$894$		0			0
$895$	27.2237	+	47.1528i	0.909987	+	1.57614i
$896$		0			0
$897$	−0.00965617	+	0.00324666i	−0.000322410	+	0.000108403i
$898$		0			0
$899$	19.6535	−	34.0408i	0.655480	−	1.13532i
$900$		0			0
$901$	−0.121715	+	0.0702724i	−0.00405493	+	0.00234111i
$902$		0			0
$903$	28.5145	−	15.8277i	0.948904	−	0.526712i
$904$		0			0
$905$	−17.8672	+	30.9468i	−0.593925	+	1.02871i
$906$		0			0
$907$	21.7847	−	12.5774i	0.723351	−	0.417627i	−0.0926340	−	0.995700i	$-0.529529\pi$
$907$	21.7847	−	12.5774i	0.723351	−	0.417627i	0.815985	+	0.578073i	$0.196195\pi$
$908$		0			0
$909$	−12.1946	+	28.9644i	−0.404469	+	0.960690i
$910$		0			0
$911$	−28.9750	−	16.7287i	−0.959985	−	0.554247i	−0.0638164	−	0.997962i	$-0.520327\pi$
$911$	−28.9750	−	16.7287i	−0.959985	−	0.554247i	−0.896168	+	0.443714i	$0.853661\pi$
$912$		0			0
$913$		−	28.1215i		−	0.930685i
$914$		0			0
$915$	1.09822	−	5.43870i	0.0363059	−	0.179798i
$916$		0			0
$917$	−1.98545	−	10.7654i	−0.0655652	−	0.355505i
$918$		0			0
$919$	23.3339	−	13.4718i	0.769715	−	0.444395i	−0.0630579	−	0.998010i	$-0.520085\pi$
$919$	23.3339	−	13.4718i	0.769715	−	0.444395i	0.832773	+	0.553615i	$0.186752\pi$
$920$		0			0
$921$	7.47288	−	2.51258i	0.246240	−	0.0827922i
$922$		0			0
$923$	0.00144165	+	0.00249701i	4.74524e−5	+	8.21900e-5i
$924$		0			0
$925$	−2.04868	+	3.54841i	−0.0673601	+	0.116671i
$926$		0			0
$927$	−5.76278	−	45.8232i	−0.189275	−	1.50503i
$928$		0			0
$929$		−	20.2980i		−	0.665955i	−0.942935	−	0.332977i	$-0.891947\pi$
$929$		−	20.2980i		−	0.665955i	0.942935	−	0.332977i	$-0.108053\pi$
$930$		0			0
$931$	47.0809	−	17.9776i	1.54301	−	0.589191i
$932$		0			0
$933$	17.0294	−	5.72571i	0.557516	−	0.187451i
$934$		0			0
$935$	−5.44235	−	3.14214i	−0.177984	−	0.102759i
$936$		0			0
$937$			1.13526i			0.0370873i	0.999828	+	0.0185436i	$0.00590296\pi$
$937$			1.13526i			0.0370873i	−0.999828	+	0.0185436i	$0.994097\pi$
$938$		0			0
$939$	−17.4771	−	51.9802i	−0.570343	−	1.69631i
$940$		0			0
$941$		−	60.2781i		−	1.96501i	−0.186233	−	0.982506i	$-0.559628\pi$
$941$		−	60.2781i		−	1.96501i	0.186233	−	0.982506i	$-0.440372\pi$
$942$		0			0
$943$	−40.9550			−1.33368
$944$		0			0
$945$	−18.3913	+	41.7015i	−0.598268	+	1.35655i
$946$		0			0
$947$			15.2331i			0.495010i	0.968887	+	0.247505i	$0.0796107\pi$
$947$			15.2331i			0.495010i	−0.968887	+	0.247505i	$0.920389\pi$
$948$		0			0
$949$	0.000320711	0		1.04107e−5	0
$950$		0			0
$951$	−28.8847	+	9.71180i	−0.936652	+	0.314927i
$952$		0			0
$953$	36.5921			1.18533			0.592667	−	0.805448i	$-0.298075\pi$
$953$	36.5921			1.18533			0.592667	+	0.805448i	$0.298075\pi$
$954$		0			0
$955$	3.55819	−	6.16296i	0.115140	−	0.199429i
$956$		0			0
$957$	31.9276	+	94.9589i	1.03207	+	3.06959i
$958$		0			0
$959$	25.1189	+	8.91997i	0.811132	+	0.288041i
$960$		0			0
$961$	−15.9446			−0.514342
$962$		0			0
$963$	0.712969	−	1.69344i	0.0229751	−	0.0545702i
$964$		0			0
$965$	−34.5413	−	19.9424i	−1.11192	−	0.641970i
$966$		0			0
$967$	−24.8576	+	14.3515i	−0.799367	+	0.461515i	−0.843250	−	0.537522i	$-0.819360\pi$
$967$	−24.8576	+	14.3515i	−0.799367	+	0.461515i	0.0438830	+	0.999037i	$0.486027\pi$
$968$		0			0
$969$	1.31938	+	3.92409i	0.0423846	+	0.126060i
$970$		0			0
$971$	−5.70321	−	9.87825i	−0.183025	−	0.317008i	0.759884	−	0.650058i	$-0.225255\pi$
$971$	−5.70321	−	9.87825i	−0.183025	−	0.317008i	−0.942909	+	0.333050i	$0.891922\pi$
$972$		0			0
$973$	47.2374	+	16.7745i	1.51436	+	0.537765i
$974$		0			0
$975$	−0.00963366	−	0.00194529i	−0.000308524	−	6.22991e-5i
$976$		0			0
$977$	−43.1702			−1.38114			−0.690569	−	0.723267i	$-0.742640\pi$
$977$	−43.1702			−1.38114			−0.690569	+	0.723267i	$0.742640\pi$
$978$		0			0
$979$	27.7205	−	48.0132i	0.885950	−	1.53451i
$980$		0			0
$981$	−5.61717	−	44.6653i	−0.179342	−	1.42605i
$982$		0			0
$983$	8.26491	+	14.3152i	0.263610	+	0.456585i	0.967198	−	0.254022i	$-0.0817536\pi$
$983$	8.26491	+	14.3152i	0.263610	+	0.456585i	−0.703589	+	0.710607i	$0.748420\pi$
$984$		0			0
$985$	10.6157	+	6.12896i	0.338243	+	0.195285i
$986$		0			0
$987$	6.92079	−	11.5334i	0.220291	−	0.367112i
$988$		0			0
$989$	−22.0964	−	38.2721i	−0.702625	−	1.21698i
$990$		0			0
$991$	14.7154	+	8.49594i	0.467450	+	0.269883i	0.715172	−	0.698949i	$-0.246348\pi$
$991$	14.7154	+	8.49594i	0.467450	+	0.269883i	−0.247721	+	0.968831i	$0.579682\pi$
$992$		0			0
$993$	−8.36772	−	24.8872i	−0.265542	−	0.789771i
$994$		0			0
$995$	58.9099	−	34.0117i	1.86757	−	1.07824i
$996$		0			0
$997$	−52.7142	+	30.4345i	−1.66947	+	0.963872i	−0.701554	+	0.712616i	$0.747510\pi$
$997$	−52.7142	+	30.4345i	−1.66947	+	0.963872i	−0.967921	+	0.251256i	$0.919157\pi$
$998$		0			0
$999$	3.54412	+	0.263253i	0.112131	+	0.00832896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cz.g.367.11	yes	24
3.2	odd	2		3024.2.cz.h.2719.1		24
4.3	odd	2		1008.2.cz.h.367.2	yes	24
7.5	odd	6		1008.2.bf.g.943.8	yes	24
9.4	even	3		1008.2.bf.h.31.5	yes	24
9.5	odd	6		3024.2.bf.g.1711.12		24
12.11	even	2		3024.2.cz.g.2719.1		24
21.5	even	6		3024.2.bf.h.2287.1		24
28.19	even	6		1008.2.bf.h.943.5	yes	24
36.23	even	6		3024.2.bf.h.1711.12		24
36.31	odd	6		1008.2.bf.g.31.8	✓	24
63.5	even	6		3024.2.cz.g.1279.1		24
63.40	odd	6		1008.2.cz.h.607.2	yes	24
84.47	odd	6		3024.2.bf.g.2287.1		24
252.103	even	6	inner	1008.2.cz.g.607.11	yes	24
252.131	odd	6		3024.2.cz.h.1279.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.g.31.8	✓	24	36.31	odd	6
1008.2.bf.g.943.8	yes	24	7.5	odd	6
1008.2.bf.h.31.5	yes	24	9.4	even	3
1008.2.bf.h.943.5	yes	24	28.19	even	6
1008.2.cz.g.367.11	yes	24	1.1	even	1	trivial
1008.2.cz.g.607.11	yes	24	252.103	even	6	inner
1008.2.cz.h.367.2	yes	24	4.3	odd	2
1008.2.cz.h.607.2	yes	24	63.40	odd	6
3024.2.bf.g.1711.12		24	9.5	odd	6
3024.2.bf.g.2287.1		24	84.47	odd	6
3024.2.bf.h.1711.12		24	36.23	even	6
3024.2.bf.h.2287.1		24	21.5	even	6
3024.2.cz.g.1279.1		24	63.5	even	6
3024.2.cz.g.2719.1		24	12.11	even	2
3024.2.cz.h.1279.1		24	252.131	odd	6
3024.2.cz.h.2719.1		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64174 - 0.551995i) q^{3} +(2.87107 + 1.65762i) q^{5} +(-2.01336 + 1.71651i) q^{7} +(2.39060 - 1.81246i) q^{9} +(-4.94470 + 2.85482i) q^{11} +(-0.000820272 + 0.000473584i) q^{13} +(5.62854 + 1.13655i) q^{15} +(0.287517 + 0.165998i) q^{17} +(3.59975 + 6.23494i) q^{19} +(-2.35790 + 3.92941i) q^{21} +(5.37780 + 3.10487i) q^{23} +(2.99538 + 5.18815i) q^{25} +(2.92427 - 4.29519i) q^{27} +(5.06516 - 8.77311i) q^{29} +3.88013 q^{31} +(-6.54205 + 7.41631i) q^{33} +(-8.62580 + 1.59084i) q^{35} +(0.341973 + 0.592315i) q^{37} +(-0.00108526 + 0.00123029i) q^{39} +(-5.71168 + 3.29764i) q^{41} +(-6.16324 - 3.55835i) q^{43} +(9.86796 - 1.24101i) q^{45} -2.93515 q^{47} +(1.10722 - 6.91188i) q^{49} +(0.563657 + 0.113817i) q^{51} +(-0.211667 + 0.366617i) q^{53} -18.9288 q^{55} +(9.35150 + 8.24910i) q^{57} +0.323059 q^{59} -0.966271i q^{61} +(-1.70204 + 7.75262i) q^{63} -0.00314008 q^{65} -8.48735i q^{67} +(10.5428 + 2.12887i) q^{69} -3.04412i q^{71} +(-0.293235 - 0.169300i) q^{73} +(7.78145 + 6.86414i) q^{75} +(5.05512 - 14.2354i) q^{77} -11.5034i q^{79} +(2.42997 - 8.66575i) q^{81} +(-2.46263 + 4.26540i) q^{83} +(0.550322 + 0.953185i) q^{85} +(3.47295 - 17.1991i) q^{87} +(-8.40915 + 4.85502i) q^{89} +(0.000838591 - 0.00236150i) q^{91} +(6.37016 - 2.14181i) q^{93} +23.8680i q^{95} +(15.1955 + 8.77311i) q^{97} +(-6.64656 + 15.7868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{3} - 3 q^{5} + 4 q^{7} + 17 q^{9} - 9 q^{11} - 3 q^{13} - 6 q^{15} - 3 q^{17} - 4 q^{19} + 13 q^{21} - 6 q^{23} + 15 q^{25} + 9 q^{27} + 18 q^{29} + 34 q^{31} - 21 q^{33} - 42 q^{35} - 3 q^{37}+ \cdots + 30 q^{99}+O(q^{100}) \) 24 * q - 3 * q^3 - 3 * q^5 + 4 * q^7 + 17 * q^9 - 9 * q^11 - 3 * q^13 - 6 * q^15 - 3 * q^17 - 4 * q^19 + 13 * q^21 - 6 * q^23 + 15 * q^25 + 9 * q^27 + 18 * q^29 + 34 * q^31 - 21 * q^33 - 42 * q^35 - 3 * q^37 + 27 * q^39 + 36 * q^41 + 24 * q^43 + 21 * q^45 - 42 * q^47 + 30 * q^49 - 6 * q^51 - 12 * q^53 - 30 * q^55 - 13 * q^57 - 12 * q^59 - 3 * q^63 + 6 * q^69 + 48 * q^73 + 36 * q^75 - 48 * q^77 - 31 * q^81 - 48 * q^83 - 21 * q^85 + 15 * q^87 + 39 * q^89 + 9 * q^91 + 10 * q^93 + 3 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

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Database

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