LMFDB - Embedded newform 729.2.c.d.244.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(244,729)] 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("729.244"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,3,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.5
Root			$1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.d.487.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.06251 + 1.84033i) q^{2} +(-1.25787 + 2.17870i) q^{4} +(1.03547 - 1.79349i) q^{5} +(-2.42434 - 4.19907i) q^{7} -1.09598 q^{8} +4.40081 q^{10} +(-2.07474 - 3.59356i) q^{11} +(0.608008 - 1.05310i) q^{13} +(5.15178 - 8.92315i) q^{14} +(1.35126 + 2.34044i) q^{16} +2.36364 q^{17} -1.83801 q^{19} +(2.60498 + 4.51196i) q^{20} +(4.40889 - 7.63642i) q^{22} +(2.15178 - 3.72700i) q^{23} +(0.355603 + 0.615922i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(-1.49091 - 2.58233i) q^{29} +(-0.736793 + 1.27616i) q^{31} +(-3.96743 + 6.87180i) q^{32} +(2.51140 + 4.34987i) q^{34} -10.0413 q^{35} +8.97108 q^{37} +(-1.95291 - 3.38254i) q^{38} +(-1.13485 + 1.96562i) q^{40} +(-1.13026 + 1.95767i) q^{41} +(2.74243 + 4.75003i) q^{43} +10.4391 q^{44} +9.14521 q^{46} +(-3.59157 - 6.22077i) q^{47} +(-8.25481 + 14.2978i) q^{49} +(-0.755667 + 1.30885i) q^{50} +(1.52959 + 2.64933i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(2.65702 + 4.60209i) q^{56} +(3.16823 - 5.48753i) q^{58} +(-0.131128 + 0.227121i) q^{59} +(2.22780 + 3.85867i) q^{61} -3.13141 q^{62} -11.4568 q^{64} +(-1.25915 - 2.18091i) q^{65} +(-2.06555 + 3.57764i) q^{67} +(-2.97316 + 5.14966i) q^{68} +(-10.6690 - 18.4793i) q^{70} +3.08551 q^{71} +12.7601 q^{73} +(9.53190 + 16.5097i) q^{74} +(2.31198 - 4.00447i) q^{76} +(-10.0598 + 17.4240i) q^{77} +(-2.27620 - 3.94250i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(4.22653 + 7.32056i) q^{83} +(2.44748 - 4.23915i) q^{85} +(-5.82774 + 10.0939i) q^{86} +(2.27387 + 3.93846i) q^{88} +16.9632 q^{89} -5.89606 q^{91} +(5.41335 + 9.37619i) q^{92} +(7.63218 - 13.2193i) q^{94} +(-1.90320 + 3.29644i) q^{95} +(2.55489 + 4.42519i) q^{97} -35.0834 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots - 36 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.06251	+	1.84033i	0.751311	+	1.30131i	0.947187	+	0.320680i	$0.103912\pi$
$2$	1.06251	+	1.84033i	0.751311	+	1.30131i	−0.195876	+	0.980629i	$0.562755\pi$
$3$		0			0
$3$		0			0
$4$	−1.25787	+	2.17870i	−0.628937	+	1.08935i
$5$	1.03547	−	1.79349i	0.463076	−	0.802072i	−0.536036	−	0.844195i	$-0.680079\pi$
$5$	1.03547	−	1.79349i	0.463076	−	0.802072i	0.999112	+	0.0421233i	$0.0134122\pi$
$6$		0			0
$7$	−2.42434	−	4.19907i	−0.916313	−	1.58710i	−0.804967	−	0.593319i	$-0.797817\pi$
$7$	−2.42434	−	4.19907i	−0.916313	−	1.58710i	−0.111346	−	0.993782i	$-0.535516\pi$
$8$	−1.09598			−0.387487
$9$		0			0
$10$	4.40081			1.39166
$11$	−2.07474	−	3.59356i	−0.625559	−	1.08350i	−0.988432	−	0.151662i	$-0.951538\pi$
$11$	−2.07474	−	3.59356i	−0.625559	−	1.08350i	0.362874	−	0.931838i	$-0.381796\pi$
$12$		0			0
$13$	0.608008	−	1.05310i	0.168631	−	0.292077i	−0.769308	−	0.638878i	$-0.779399\pi$
$13$	0.608008	−	1.05310i	0.168631	−	0.292077i	0.937939	+	0.346801i	$0.112732\pi$
$14$	5.15178	−	8.92315i	1.37687	−	2.38481i
$15$		0			0
$16$	1.35126	+	2.34044i	0.337814	+	0.585111i
$17$	2.36364			0.573266			0.286633	−	0.958040i	$-0.407464\pi$
$17$	2.36364			0.573266			0.286633	+	0.958040i	$0.407464\pi$
$18$		0			0
$19$	−1.83801			−0.421668			−0.210834	−	0.977522i	$-0.567618\pi$
$19$	−1.83801			−0.421668			−0.210834	+	0.977522i	$0.567618\pi$
$20$	2.60498	+	4.51196i	0.582491	+	1.00890i
$21$		0			0
$22$	4.40889	−	7.63642i	0.939979	−	1.62809i
$23$	2.15178	−	3.72700i	0.448678	−	0.777133i	−0.549622	−	0.835413i	$-0.685228\pi$
$23$	2.15178	−	3.72700i	0.448678	−	0.777133i	0.998300	+	0.0582801i	$0.0185617\pi$
$24$		0			0
$25$	0.355603	+	0.615922i	0.0711206	+	0.123184i
$26$	2.58407			0.506777
$27$		0			0
$28$	12.1980			2.30521
$29$	−1.49091	−	2.58233i	−0.276855	−	0.479527i	0.693746	−	0.720219i	$-0.255959\pi$
$29$	−1.49091	−	2.58233i	−0.276855	−	0.479527i	−0.970601	+	0.240692i	$0.922626\pi$
$30$		0			0
$31$	−0.736793	+	1.27616i	−0.132332	+	0.229206i	−0.924575	−	0.381000i	$-0.875580\pi$
$31$	−0.736793	+	1.27616i	−0.132332	+	0.229206i	0.792243	+	0.610206i	$0.208913\pi$
$32$	−3.96743	+	6.87180i	−0.701350	+	1.21477i
$33$		0			0
$34$	2.51140	+	4.34987i	0.430701	+	0.745997i
$35$	−10.0413			−1.69729
$36$		0			0
$37$	8.97108			1.47484			0.737418	−	0.675436i	$-0.236045\pi$
$37$	8.97108			1.47484			0.737418	+	0.675436i	$0.236045\pi$
$38$	−1.95291	−	3.38254i	−0.316804	−	0.548720i
$39$		0			0
$40$	−1.13485	+	1.96562i	−0.179436	+	0.310792i
$41$	−1.13026	+	1.95767i	−0.176517	+	0.305737i	−0.940685	−	0.339280i	$-0.889816\pi$
$41$	−1.13026	+	1.95767i	−0.176517	+	0.305737i	0.764168	+	0.645017i	$0.223150\pi$
$42$		0			0
$43$	2.74243	+	4.75003i	0.418216	+	0.724372i	0.995760	−	0.0919876i	$-0.0293220\pi$
$43$	2.74243	+	4.75003i	0.418216	+	0.724372i	−0.577544	+	0.816360i	$0.695989\pi$
$44$	10.4391			1.57375
$45$		0			0
$46$	9.14521			1.34839
$47$	−3.59157	−	6.22077i	−0.523884	−	0.907393i	−0.999613	−	0.0278017i	$-0.991149\pi$
$47$	−3.59157	−	6.22077i	−0.523884	−	0.907393i	0.475730	−	0.879591i	$-0.342184\pi$
$48$		0			0
$49$	−8.25481	+	14.2978i	−1.17926	+	2.04254i
$50$	−0.755667	+	1.30885i	−0.106867	+	0.185100i
$51$		0			0
$52$	1.52959	+	2.64933i	0.212116	+	0.367396i
$53$	−6.32803			−0.869222			−0.434611	−	0.900618i	$-0.643114\pi$
$53$	−6.32803			−0.869222			−0.434611	+	0.900618i	$0.643114\pi$
$54$		0			0
$55$	−8.59334			−1.15873
$56$	2.65702	+	4.60209i	0.355059	+	0.614980i
$57$		0			0
$58$	3.16823	−	5.48753i	0.416009	−	0.720548i
$59$	−0.131128	+	0.227121i	−0.0170715	+	0.0295686i	−0.874435	−	0.485143i	$-0.838768\pi$
$59$	−0.131128	+	0.227121i	−0.0170715	+	0.0295686i	0.857363	+	0.514711i	$0.172101\pi$
$60$		0			0
$61$	2.22780	+	3.85867i	0.285241	+	0.494052i	0.972668	−	0.232202i	$-0.0745931\pi$
$61$	2.22780	+	3.85867i	0.285241	+	0.494052i	−0.687427	+	0.726254i	$0.741260\pi$
$62$	−3.13141			−0.397690
$63$		0			0
$64$	−11.4568			−1.43210
$65$	−1.25915	−	2.18091i	−0.156178	−	0.270508i
$66$		0			0
$67$	−2.06555	+	3.57764i	−0.252347	+	0.437078i	−0.964172	−	0.265279i	$-0.914536\pi$
$67$	−2.06555	+	3.57764i	−0.252347	+	0.437078i	0.711824	+	0.702358i	$0.247869\pi$
$68$	−2.97316	+	5.14966i	−0.360548	+	0.624488i
$69$		0			0
$70$	−10.6690	−	18.4793i	−1.27519	−	2.20870i
$71$	3.08551			0.366183			0.183091	−	0.983096i	$-0.441390\pi$
$71$	3.08551			0.366183			0.183091	+	0.983096i	$0.441390\pi$
$72$		0			0
$73$	12.7601			1.49345			0.746726	−	0.665132i	$-0.231625\pi$
$73$	12.7601			1.49345			0.746726	+	0.665132i	$0.231625\pi$
$74$	9.53190	+	16.5097i	1.10806	+	1.91922i
$75$		0			0
$76$	2.31198	−	4.00447i	0.265202	−	0.459344i
$77$	−10.0598	+	17.4240i	−1.14642	+	1.98565i
$78$		0			0
$79$	−2.27620	−	3.94250i	−0.256093	−	0.443566i	0.709099	−	0.705109i	$-0.249102\pi$
$79$	−2.27620	−	3.94250i	−0.256093	−	0.443566i	−0.965192	+	0.261543i	$0.915769\pi$
$80$	5.59674			0.625734
$81$		0			0
$82$	−4.80368			−0.530478
$83$	4.22653	+	7.32056i	0.463922	+	0.803536i	0.999152	−	0.0411700i	$-0.0131085\pi$
$83$	4.22653	+	7.32056i	0.463922	+	0.803536i	−0.535230	+	0.844706i	$0.679775\pi$
$84$		0			0
$85$	2.44748	−	4.23915i	0.265466	−	0.459801i
$86$	−5.82774	+	10.0939i	−0.628421	+	1.08846i
$87$		0			0
$88$	2.27387	+	3.93846i	0.242396	+	0.419842i
$89$	16.9632			1.79809			0.899046	−	0.437854i	$-0.144261\pi$
$89$	16.9632			1.79809			0.899046	+	0.437854i	$0.144261\pi$
$90$		0			0
$91$	−5.89606			−0.618075
$92$	5.41335	+	9.37619i	0.564380	+	0.977535i
$93$		0			0
$94$	7.63218	−	13.2193i	0.787199	−	1.36347i
$95$	−1.90320	+	3.29644i	−0.195264	+	0.338208i
$96$		0			0
$97$	2.55489	+	4.42519i	0.259409	+	0.449310i	0.966084	−	0.258229i	$-0.0831388\pi$
$97$	2.55489	+	4.42519i	0.259409	+	0.449310i	−0.706674	+	0.707539i	$0.749805\pi$
$98$	−35.0834			−3.54396
$99$		0			0
$100$	−1.78921			−0.178921
$101$	−9.28994	−	16.0906i	−0.924384	−	1.60108i	−0.792550	−	0.609808i	$-0.791247\pi$
$101$	−9.28994	−	16.0906i	−0.924384	−	1.60108i	−0.131834	−	0.991272i	$-0.542087\pi$
$102$		0			0
$103$	−4.50288	+	7.79923i	−0.443682	+	0.768481i	−0.997959	−	0.0638518i	$-0.979662\pi$
$103$	−4.50288	+	7.79923i	−0.443682	+	0.768481i	0.554277	+	0.832332i	$0.312995\pi$
$104$	−0.666363	+	1.15417i	−0.0653422	+	0.113176i
$105$		0			0
$106$	−6.72362	−	11.6457i	−0.653056	−	1.13113i
$107$	7.42680			0.717976			0.358988	−	0.933342i	$-0.383122\pi$
$107$	7.42680			0.717976			0.358988	+	0.933342i	$0.383122\pi$
$108$		0			0
$109$	−5.62396			−0.538678			−0.269339	−	0.963045i	$-0.586805\pi$
$109$	−5.62396			−0.538678			−0.269339	+	0.963045i	$0.586805\pi$
$110$	−9.13055	−	15.8146i	−0.870564	−	1.50786i
$111$		0			0
$112$	6.55179	−	11.3480i	0.619086	−	1.07229i
$113$	1.20133	−	2.08077i	0.113012	−	0.195743i	−0.803971	−	0.594668i	$-0.797283\pi$
$113$	1.20133	−	2.08077i	0.113012	−	0.195743i	0.916983	+	0.398926i	$0.130617\pi$
$114$		0			0
$115$	−4.45622	−	7.71839i	−0.415544	−	0.719744i
$116$	7.50150			0.696497
$117$		0			0
$118$	−0.557303			−0.0513039
$119$	−5.73025	−	9.92509i	−0.525292	−	0.909832i
$120$		0			0
$121$	−3.10913	+	5.38517i	−0.282648	+	0.489561i
$122$	−4.73415	+	8.19978i	−0.428609	+	0.742373i
$123$		0			0
$124$	−1.85359	−	3.21050i	−0.166457	−	0.288312i
$125$	11.8276			1.05789
$126$		0			0
$127$	−9.23469			−0.819447			−0.409723	−	0.912210i	$-0.634375\pi$
$127$	−9.23469			−0.819447			−0.409723	+	0.912210i	$0.634375\pi$
$128$	−4.23815	−	7.34069i	−0.374603	−	0.648831i
$129$		0			0
$130$	2.67572	−	4.63449i	0.234677	−	0.406472i
$131$	7.66950	−	13.2840i	0.670088	−	1.16063i	−0.307791	−	0.951454i	$-0.599590\pi$
$131$	7.66950	−	13.2840i	0.670088	−	1.16063i	0.977879	−	0.209172i	$-0.0670768\pi$
$132$		0			0
$133$	4.45595	+	7.71792i	0.386380	+	0.669229i
$134$	−8.77871			−0.758365
$135$		0			0
$136$	−2.59049			−0.222133
$137$	1.82198	+	3.15577i	0.155663	+	0.269616i	0.933300	−	0.359097i	$-0.116915\pi$
$137$	1.82198	+	3.15577i	0.155663	+	0.269616i	−0.777637	+	0.628713i	$0.783582\pi$
$138$		0			0
$139$	−6.63777	+	11.4970i	−0.563008	+	0.975159i	0.434224	+	0.900805i	$0.357023\pi$
$139$	−6.63777	+	11.4970i	−0.563008	+	0.975159i	−0.997232	+	0.0743538i	$0.976311\pi$
$140$	12.6307	−	21.8770i	1.06749	−	1.84895i
$141$		0			0
$142$	3.27840	+	5.67835i	0.275117	+	0.476517i
$143$	−5.04584			−0.421954
$144$		0			0
$145$	−6.17517			−0.512820
$146$	13.5577	+	23.4827i	1.12205	+	1.94344i
$147$		0			0
$148$	−11.2845	+	19.5453i	−0.927579	+	1.60661i
$149$	−4.45549	+	7.71714i	−0.365008	+	0.632213i	−0.988777	−	0.149396i	$-0.952267\pi$
$149$	−4.45549	+	7.71714i	−0.365008	+	0.632213i	0.623769	+	0.781608i	$0.285600\pi$
$150$		0			0
$151$	0.356202	+	0.616960i	0.0289873	+	0.0502075i	0.880155	−	0.474686i	$-0.157438\pi$
$151$	0.356202	+	0.616960i	0.0289873	+	0.0502075i	−0.851168	+	0.524894i	$0.824105\pi$
$152$	2.01441			0.163391
$153$		0			0
$154$	−42.7545			−3.44526
$155$	1.52585	+	2.64286i	0.122560	+	0.212279i
$156$		0			0
$157$	6.90903	−	11.9668i	0.551400	−	0.955054i	−0.446773	−	0.894647i	$-0.647427\pi$
$157$	6.90903	−	11.9668i	0.551400	−	0.955054i	0.998174	−	0.0604064i	$-0.0192397\pi$
$158$	4.83700	−	8.37793i	0.384811	−	0.666512i
$159$		0			0
$160$	8.21632	+	14.2311i	0.649557	+	1.12507i
$161$	−20.8666			−1.64452
$162$		0			0
$163$	−1.19321			−0.0934597			−0.0467298	−	0.998908i	$-0.514880\pi$
$163$	−1.19321			−0.0934597			−0.0467298	+	0.998908i	$0.514880\pi$
$164$	−2.84345	−	4.92501i	−0.222036	−	0.384578i
$165$		0			0
$166$	−8.98150	+	15.5564i	−0.697099	+	1.20741i
$167$	11.9682	−	20.7295i	0.926124	−	1.60409i	0.136381	−	0.990657i	$-0.456453\pi$
$167$	11.9682	−	20.7295i	0.926124	−	1.60409i	0.789743	−	0.613437i	$-0.210214\pi$
$168$		0			0
$169$	5.76065	+	9.97774i	0.443127	+	0.767519i
$170$	10.4019			0.797791
$171$		0			0
$172$	−13.7985			−1.05213
$173$	4.57000	+	7.91547i	0.347451	+	0.601802i	0.985796	−	0.167948i	$-0.0537140\pi$
$173$	4.57000	+	7.91547i	0.347451	+	0.601802i	−0.638345	+	0.769750i	$0.720381\pi$
$174$		0			0
$175$	1.72420	−	2.98641i	0.130337	−	0.225751i
$176$	5.60702	−	9.71164i	0.422645	−	0.732043i
$177$		0			0
$178$	18.0236	+	31.2178i	1.35093	+	2.33987i
$179$	10.6008			0.792337			0.396169	−	0.918178i	$-0.370340\pi$
$179$	10.6008			0.792337			0.396169	+	0.918178i	$0.370340\pi$
$180$		0			0
$181$	−1.46292			−0.108738			−0.0543690	−	0.998521i	$-0.517315\pi$
$181$	−1.46292			−0.108738			−0.0543690	+	0.998521i	$0.517315\pi$
$182$	−6.26465	−	10.8507i	−0.464367	−	0.804307i
$183$		0			0
$184$	−2.35831	+	4.08471i	−0.173857	+	0.301129i
$185$	9.28929	−	16.0895i	0.682962	−	1.18292i
$186$		0			0
$187$	−4.90395	−	8.49388i	−0.358612	−	0.621134i
$188$	18.0709			1.31796
$189$		0			0
$190$	−8.08871			−0.586817
$191$	−6.21114	−	10.7580i	−0.449422	−	0.778422i	0.548926	−	0.835871i	$-0.315037\pi$
$191$	−6.21114	−	10.7580i	−0.449422	−	0.778422i	−0.998348	+	0.0574488i	$0.981703\pi$
$192$		0			0
$193$	−10.3867	+	17.9902i	−0.747647	+	1.29496i	0.201300	+	0.979530i	$0.435483\pi$
$193$	−10.3867	+	17.9902i	−0.747647	+	1.29496i	−0.948948	+	0.315434i	$0.897850\pi$
$194$	−5.42921	+	9.40366i	−0.389794	+	0.675143i
$195$		0			0
$196$	−20.7670	−	35.9695i	−1.48336	−	2.56925i
$197$	−14.1887			−1.01090			−0.505450	−	0.862856i	$-0.668674\pi$
$197$	−14.1887			−1.01090			−0.505450	+	0.862856i	$0.668674\pi$
$198$		0			0
$199$	20.3286			1.44106			0.720529	−	0.693424i	$-0.243899\pi$
$199$	20.3286			1.44106			0.720529	+	0.693424i	$0.243899\pi$
$200$	−0.389733	−	0.675037i	−0.0275583	−	0.0477323i
$201$		0			0
$202$	19.7414	−	34.1931i	1.38900	−	2.40582i
$203$	−7.22893	+	12.5209i	−0.507372	+	0.878794i
$204$		0			0
$205$	2.34071	+	4.05422i	0.163482	+	0.283159i
$206$	−19.1375			−1.33337
$207$		0			0
$208$	3.28629			0.227864
$209$	3.81339	+	6.60499i	0.263778	+	0.456877i
$210$		0			0
$211$	4.93166	−	8.54189i	0.339509	−	0.588048i	−0.644831	−	0.764325i	$-0.723072\pi$
$211$	4.93166	−	8.54189i	0.339509	−	0.588048i	0.984341	+	0.176278i	$0.0564056\pi$
$212$	7.95986	−	13.7869i	0.546685	−	0.946887i
$213$		0			0
$214$	7.89109	+	13.6678i	0.539424	+	0.934309i
$215$	11.3588			0.774665
$216$		0			0
$217$	7.14494			0.485030
$218$	−5.97554	−	10.3499i	−0.404715	−	0.700986i
$219$		0			0
$220$	10.8093	−	18.7223i	0.728766	−	1.26226i
$221$	1.43711	−	2.48915i	0.0966705	−	0.167438i
$222$		0			0
$223$	−7.53569	−	13.0522i	−0.504627	−	0.874040i	−0.999986	−	0.00535136i	$-0.998297\pi$
$223$	−7.53569	−	13.0522i	−0.504627	−	0.874040i	0.495358	−	0.868689i	$-0.335037\pi$
$224$	38.4736			2.57062
$225$		0			0
$226$	5.10574			0.339629
$227$	11.3463	+	19.6523i	0.753079	+	1.30437i	0.946324	+	0.323221i	$0.104766\pi$
$227$	11.3463	+	19.6523i	0.753079	+	1.30437i	−0.193245	+	0.981151i	$0.561901\pi$
$228$		0			0
$229$	−4.35835	+	7.54888i	−0.288008	+	0.498844i	−0.973334	−	0.229392i	$-0.926326\pi$
$229$	−4.35835	+	7.54888i	−0.288008	+	0.498844i	0.685326	+	0.728236i	$0.259660\pi$
$230$	9.46959	−	16.4018i	0.624406	−	1.08150i
$231$		0			0
$232$	1.63400	+	2.83018i	0.107278	+	0.185810i
$233$	−23.5890			−1.54536			−0.772682	−	0.634793i	$-0.781085\pi$
$233$	−23.5890			−1.54536			−0.772682	+	0.634793i	$0.781085\pi$
$234$		0			0
$235$	−14.8758			−0.970393
$236$	−0.329886	−	0.571379i	−0.0214737	−	0.0371936i
$237$		0			0
$238$	12.1770	−	21.0911i	0.789315	−	1.36713i
$239$	−4.97726	+	8.62086i	−0.321952	+	0.557637i	−0.980891	−	0.194559i	$-0.937672\pi$
$239$	−4.97726	+	8.62086i	−0.321952	+	0.557637i	0.658939	+	0.752197i	$0.271006\pi$
$240$		0			0
$241$	−2.85672	−	4.94799i	−0.184018	−	0.318728i	0.759227	−	0.650826i	$-0.225577\pi$
$241$	−2.85672	−	4.94799i	−0.184018	−	0.318728i	−0.943245	+	0.332097i	$0.892244\pi$
$242$	−13.2140			−0.849427
$243$		0			0
$244$	−11.2092			−0.717594
$245$	17.0952	+	29.6098i	1.09217	+	1.89170i
$246$		0			0
$247$	−1.11752	+	1.93560i	−0.0711062	+	0.123160i
$248$	0.807509	−	1.39865i	0.0512769	−	0.0888141i
$249$		0			0
$250$	12.5670	+	21.7666i	0.794804	+	1.37664i
$251$	−7.28966			−0.460120			−0.230060	−	0.973176i	$-0.573892\pi$
$251$	−7.28966			−0.460120			−0.230060	+	0.973176i	$0.573892\pi$
$252$		0			0
$253$	−17.8576			−1.12270
$254$	−9.81199	−	16.9949i	−0.615659	−	1.06635i
$255$		0			0
$256$	−2.45062	+	4.24459i	−0.153163	+	0.265287i
$257$	11.6215	−	20.1291i	0.724932	−	1.25562i	−0.234071	−	0.972220i	$-0.575205\pi$
$257$	11.6215	−	20.1291i	0.724932	−	1.25562i	0.959002	−	0.283399i	$-0.0914620\pi$
$258$		0			0
$259$	−21.7489	−	37.6702i	−1.35141	−	2.34071i
$260$	6.33539			0.392904
$261$		0			0
$262$	32.5958			2.01378
$263$	13.6998	+	23.7288i	0.844766	+	1.46318i	0.885824	+	0.464021i	$0.153594\pi$
$263$	13.6998	+	23.7288i	0.844766	+	1.46318i	−0.0410581	+	0.999157i	$0.513073\pi$
$264$		0			0
$265$	−6.55249	+	11.3492i	−0.402516	+	0.697178i
$266$	−9.46901	+	16.4008i	−0.580582	+	1.00560i
$267$		0			0
$268$	−5.19641	−	9.00044i	−0.317421	−	0.549789i
$269$	9.41973			0.574331			0.287166	−	0.957881i	$-0.407287\pi$
$269$	9.41973			0.574331			0.287166	+	0.957881i	$0.407287\pi$
$270$		0			0
$271$	26.2797			1.59638			0.798189	−	0.602408i	$-0.205792\pi$
$271$	26.2797			1.59638			0.798189	+	0.602408i	$0.205792\pi$
$272$	3.19388	+	5.53196i	0.193657	+	0.335424i
$273$		0			0
$274$	−3.87177	+	6.70610i	−0.233902	+	0.405131i
$275$	1.47557	−	2.55576i	0.0889803	−	0.154118i
$276$		0			0
$277$	−0.187406	−	0.324597i	−0.0112601	−	0.0195031i	0.860340	−	0.509720i	$-0.170251\pi$
$277$	−0.187406	−	0.324597i	−0.0112601	−	0.0195031i	−0.871601	+	0.490217i	$0.836918\pi$
$278$	−28.2109			−1.69198
$279$		0			0
$280$	11.0051			0.657678
$281$	−6.99079	−	12.1084i	−0.417036	−	0.722327i	0.578604	−	0.815609i	$-0.303598\pi$
$281$	−6.99079	−	12.1084i	−0.417036	−	0.722327i	−0.995640	+	0.0932815i	$0.970264\pi$
$282$		0			0
$283$	−7.78094	+	13.4770i	−0.462529	+	0.801124i	−0.999086	−	0.0427401i	$-0.986391\pi$
$283$	−7.78094	+	13.4770i	−0.462529	+	0.801124i	0.536557	+	0.843864i	$0.319725\pi$
$284$	−3.88118	+	6.72240i	−0.230306	+	0.398901i
$285$		0			0
$286$	−5.36128	−	9.28601i	−0.317019	−	0.549093i
$287$	10.9605			0.646980
$288$		0			0
$289$	−11.4132			−0.671366
$290$	−6.56121	−	11.3643i	−0.385287	−	0.667337i
$291$		0			0
$292$	−16.0505	+	27.8004i	−0.939287	+	1.62689i
$293$	−12.3121	+	21.3252i	−0.719281	+	1.24583i	0.242004	+	0.970275i	$0.422195\pi$
$293$	−12.3121	+	21.3252i	−0.719281	+	1.24583i	−0.961285	+	0.275556i	$0.911138\pi$
$294$		0			0
$295$	0.271559	+	0.470354i	0.0158108	+	0.0273851i
$296$	−9.83210			−0.571479
$297$		0			0
$298$	−18.9361			−1.09694
$299$	−2.61660	−	4.53209i	−0.151322	−	0.262097i
$300$		0			0
$301$	13.2971	−	23.0313i	0.766434	−	1.32750i
$302$	−0.756939	+	1.31106i	−0.0435570	+	0.0754429i
$303$		0			0
$304$	−2.48362	−	4.30175i	−0.142445	−	0.246722i
$305$	9.22729			0.528353
$306$		0			0
$307$	−20.3912			−1.16379			−0.581893	−	0.813265i	$-0.697688\pi$
$307$	−20.3912			−1.16379			−0.581893	+	0.813265i	$0.697688\pi$
$308$	−25.3078	−	43.8344i	−1.44205	−	2.49770i
$309$		0			0
$310$	−3.24249	+	5.61615i	−0.184161	+	0.318976i
$311$	−11.0895	+	19.2076i	−0.628828	+	1.08916i	0.358959	+	0.933353i	$0.383132\pi$
$311$	−11.0895	+	19.2076i	−0.628828	+	1.08916i	−0.987787	+	0.155809i	$0.950201\pi$
$312$		0			0
$313$	5.58602	+	9.67527i	0.315740	+	0.546879i	0.979595	−	0.200984i	$-0.0644138\pi$
$313$	5.58602	+	9.67527i	0.315740	+	0.546879i	−0.663854	+	0.747862i	$0.731080\pi$
$314$	29.3638			1.65709
$315$		0			0
$316$	11.4527			0.644265
$317$	−12.6083	−	21.8383i	−0.708154	−	1.22656i	−0.965541	−	0.260251i	$-0.916195\pi$
$317$	−12.6083	−	21.8383i	−0.708154	−	1.22656i	0.257387	−	0.966309i	$-0.417139\pi$
$318$		0			0
$319$	−6.18651	+	10.7154i	−0.346378	+	0.599945i
$320$	−11.8632	+	20.5476i	−0.663172	+	1.14865i
$321$		0			0
$322$	−22.1711	−	38.4014i	−1.23554	−	2.14003i
$323$	−4.34438			−0.241728
$324$		0			0
$325$	0.864837			0.0479725
$326$	−1.26781	−	2.19591i	−0.0702173	−	0.121620i
$327$		0			0
$328$	1.23874	−	2.14556i	0.0683981	−	0.118469i
$329$	−17.4143	+	30.1625i	−0.960083	+	1.66291i
$330$		0			0
$331$	13.0828	+	22.6602i	0.719098	+	1.24551i	0.961357	+	0.275303i	$0.0887782\pi$
$331$	13.0828	+	22.6602i	0.719098	+	1.24551i	−0.242259	+	0.970212i	$0.577888\pi$
$332$	−21.2658			−1.16711
$333$		0			0
$334$	50.8654			2.78323
$335$	4.27763	+	7.40908i	0.233712	+	0.404801i
$336$		0			0
$337$	−5.47302	+	9.47956i	−0.298135	+	0.516384i	−0.975709	−	0.219070i	$-0.929698\pi$
$337$	−5.47302	+	9.47956i	−0.298135	+	0.516384i	0.677575	+	0.735454i	$0.263031\pi$
$338$	−12.2416	+	21.2030i	−0.665853	+	1.15329i
$339$		0			0
$340$	6.15723	+	10.6646i	0.333923	+	0.578371i
$341$	6.11463			0.331126
$342$		0			0
$343$	46.1091			2.48966
$344$	−3.00564	−	5.20592i	−0.162053	−	0.280684i
$345$		0			0
$346$	−9.71138	+	16.8206i	−0.522087	+	0.904282i
$347$	−1.75669	+	3.04268i	−0.0943040	+	0.163339i	−0.909318	−	0.416102i	$-0.863396\pi$
$347$	−1.75669	+	3.04268i	−0.0943040	+	0.163339i	0.815014	+	0.579441i	$0.196729\pi$
$348$		0			0
$349$	14.5984	+	25.2852i	0.781436	+	1.35349i	0.931105	+	0.364750i	$0.118846\pi$
$349$	14.5984	+	25.2852i	0.781436	+	1.35349i	−0.149670	+	0.988736i	$0.547821\pi$
$350$	7.32796			0.391696
$351$		0			0
$352$	32.9256			1.75494
$353$	12.5384	+	21.7172i	0.667352	+	1.15589i	0.978642	+	0.205573i	$0.0659056\pi$
$353$	12.5384	+	21.7172i	0.667352	+	1.15589i	−0.311290	+	0.950315i	$0.600761\pi$
$354$		0			0
$355$	3.19495	−	5.53382i	0.169571	−	0.293705i
$356$	−21.3375	+	36.9577i	−1.13089	+	1.95875i
$357$		0			0
$358$	11.2635	+	19.5089i	0.595292	+	1.03108i
$359$	4.20724			0.222050			0.111025	−	0.993818i	$-0.464587\pi$
$359$	4.20724			0.222050			0.111025	+	0.993818i	$0.464587\pi$
$360$		0			0
$361$	−15.6217			−0.822196
$362$	−1.55437	−	2.69225i	−0.0816961	−	0.141502i
$363$		0			0
$364$	7.41650	−	12.8458i	0.388730	−	0.673300i
$365$	13.2127	−	22.8850i	0.691582	−	1.19786i
$366$		0			0
$367$	−8.74832	−	15.1525i	−0.456658	−	0.790956i	0.542123	−	0.840299i	$-0.317620\pi$
$367$	−8.74832	−	15.1525i	−0.456658	−	0.790956i	−0.998782	+	0.0493433i	$0.984287\pi$
$368$	11.6304			0.606279
$369$		0			0
$370$	39.4800			2.05247
$371$	15.3413	+	26.5719i	0.796479	+	1.37954i
$372$		0			0
$373$	14.8273	−	25.6816i	0.767728	−	1.32974i	−0.171065	−	0.985260i	$-0.554721\pi$
$373$	14.8273	−	25.6816i	0.767728	−	1.32974i	0.938792	−	0.344483i	$-0.111946\pi$
$374$	10.4210	−	18.0497i	0.538858	−	0.933330i
$375$		0			0
$376$	3.93627	+	6.81783i	0.202998	+	0.351603i
$377$	−3.62594			−0.186745
$378$		0			0
$379$	20.9523			1.07625			0.538124	−	0.842865i	$-0.319133\pi$
$379$	20.9523			1.07625			0.538124	+	0.842865i	$0.319133\pi$
$380$	−4.78797	−	8.29301i	−0.245618	−	0.425422i
$381$		0			0
$382$	13.1988	−	22.8611i	0.675312	−	1.16967i
$383$	−4.94839	+	8.57086i	−0.252851	+	0.437950i	−0.964310	−	0.264777i	$-0.914702\pi$
$383$	−4.94839	+	8.57086i	−0.252851	+	0.437950i	0.711459	+	0.702728i	$0.248035\pi$
$384$		0			0
$385$	20.8332	+	36.0841i	1.06176	+	1.83902i
$386$	−44.1439			−2.24686
$387$		0			0
$388$	−12.8549			−0.652608
$389$	10.5574	+	18.2859i	0.535281	+	0.927133i	0.999150	+	0.0412294i	$0.0131274\pi$
$389$	10.5574	+	18.2859i	0.535281	+	0.927133i	−0.463869	+	0.885904i	$0.653539\pi$
$390$		0			0
$391$	5.08604	−	8.80928i	0.257212	−	0.445504i
$392$	9.04709	−	15.6700i	0.456947	−	0.791455i
$393$		0			0
$394$	−15.0757	−	26.1118i	−0.759501	−	1.31549i
$395$	−9.42776			−0.474362
$396$		0			0
$397$	−9.77909			−0.490799			−0.245399	−	0.969422i	$-0.578919\pi$
$397$	−9.77909			−0.490799			−0.245399	+	0.969422i	$0.578919\pi$
$398$	21.5995	+	37.4114i	1.08268	+	1.87526i
$399$		0			0
$400$	−0.961021	+	1.66454i	−0.0480510	+	0.0832268i
$401$	9.56967	−	16.5752i	0.477886	−	0.827724i	−0.521792	−	0.853073i	$-0.674736\pi$
$401$	9.56967	−	16.5752i	0.477886	−	0.827724i	0.999679	+	0.0253491i	$0.00806972\pi$
$402$		0			0
$403$	0.895952	+	1.55183i	0.0446305	+	0.0773024i
$404$	46.7423			2.32552
$405$		0			0
$406$	−30.7234			−1.52478
$407$	−18.6127	−	32.2381i	−0.922597	−	1.59799i
$408$		0			0
$409$	−7.49778	+	12.9865i	−0.370741	+	0.642143i	−0.989680	−	0.143297i	$-0.954230\pi$
$409$	−7.49778	+	12.9865i	−0.370741	+	0.642143i	0.618938	+	0.785439i	$0.287563\pi$
$410$	−4.97407	+	8.61534i	−0.245652	+	0.425481i
$411$		0			0
$412$	−11.3281	−	19.6209i	−0.558096	−	0.966651i
$413$	1.27160			0.0625712
$414$		0			0
$415$	17.5058			0.859325
$416$	4.82446	+	8.35621i	0.236539	+	0.409697i
$417$		0			0
$418$	−8.10357	+	14.0358i	−0.396359	+	0.686513i
$419$	−2.90590	+	5.03317i	−0.141963	+	0.245886i	−0.928236	−	0.371993i	$-0.878675\pi$
$419$	−2.90590	+	5.03317i	−0.141963	+	0.245886i	0.786273	+	0.617879i	$0.212008\pi$
$420$		0			0
$421$	6.65676	+	11.5298i	0.324431	+	0.561930i	0.981397	−	0.191990i	$-0.0614940\pi$
$421$	6.65676	+	11.5298i	0.324431	+	0.561930i	−0.656966	+	0.753920i	$0.728161\pi$
$422$	20.9598			1.02031
$423$		0			0
$424$	6.93538			0.336812
$425$	0.840517	+	1.45582i	0.0407711	+	0.0706175i
$426$		0			0
$427$	10.8019	−	18.7094i	0.522740	−	0.905412i
$428$	−9.34198	+	16.1808i	−0.451562	+	0.782128i
$429$		0			0
$430$	12.0689	+	20.9040i	0.582014	+	1.00808i
$431$	−36.4166			−1.75413			−0.877064	−	0.480374i	$-0.840501\pi$
$431$	−36.4166			−1.75413			−0.877064	+	0.480374i	$0.840501\pi$
$432$		0			0
$433$	−10.8761			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$433$	−10.8761			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$434$	7.59160	+	13.1490i	0.364408	+	0.631174i
$435$		0			0
$436$	7.07423	−	12.2529i	0.338794	−	0.586809i
$437$	−3.95499	+	6.85025i	−0.189193	+	0.327692i
$438$		0			0
$439$	−4.72663	−	8.18677i	−0.225590	−	0.390733i	0.730906	−	0.682478i	$-0.239098\pi$
$439$	−4.72663	−	8.18677i	−0.225590	−	0.390733i	−0.956496	+	0.291745i	$0.905764\pi$
$440$	9.41811			0.448991
$441$		0			0
$442$	6.10780			0.290518
$443$	−8.26196	−	14.3101i	−0.392537	−	0.679895i	0.600246	−	0.799815i	$-0.295069\pi$
$443$	−8.26196	−	14.3101i	−0.392537	−	0.679895i	−0.992783	+	0.119921i	$0.961736\pi$
$444$		0			0
$445$	17.5649	−	30.4232i	0.832654	−	1.44220i
$446$	16.0136	−	27.7363i	0.758264	−	1.31335i
$447$		0			0
$448$	27.7751	+	48.1080i	1.31225	+	2.27289i
$449$	−4.74362			−0.223865			−0.111933	−	0.993716i	$-0.535704\pi$
$449$	−4.74362			−0.223865			−0.111933	+	0.993716i	$0.535704\pi$
$450$		0			0
$451$	9.38002			0.441688
$452$	3.02225	+	5.23470i	0.142155	+	0.246219i
$453$		0			0
$454$	−24.1112	+	41.7618i	−1.13159	+	1.95998i
$455$	−6.10519	+	10.5745i	−0.286216	+	0.495741i
$456$		0			0
$457$	11.2043	+	19.4064i	0.524114	+	0.907792i	0.999606	+	0.0280718i	$0.00893670\pi$
$457$	11.2043	+	19.4064i	0.524114	+	0.907792i	−0.475492	+	0.879720i	$0.657730\pi$
$458$	−18.5232			−0.865534
$459$		0			0
$460$	22.4214			1.04540
$461$	7.46113	+	12.9231i	0.347499	+	0.601887i	0.985805	−	0.167897i	$-0.0536975\pi$
$461$	7.46113	+	12.9231i	0.347499	+	0.601887i	−0.638305	+	0.769783i	$0.720364\pi$
$462$		0			0
$463$	7.42359	−	12.8580i	0.345003	−	0.597563i	−0.640351	−	0.768082i	$-0.721211\pi$
$463$	7.42359	−	12.8580i	0.345003	−	0.597563i	0.985354	+	0.170519i	$0.0545444\pi$
$464$	4.02920	−	6.97878i	0.187051	−	0.323982i
$465$		0			0
$466$	−25.0636	−	43.4114i	−1.16105	−	2.01100i
$467$	−15.3514			−0.710379			−0.355190	−	0.934794i	$-0.615584\pi$
$467$	−15.3514			−0.710379			−0.355190	+	0.934794i	$0.615584\pi$
$468$		0			0
$469$	20.0304			0.924917
$470$	−15.8058	−	27.3764i	−0.729067	−	1.26278i
$471$		0			0
$472$	0.143714	−	0.248920i	0.00661496	−	0.0114574i
$473$	11.3797	−	19.7102i	0.523238	−	0.906275i
$474$		0			0
$475$	−0.653601	−	1.13207i	−0.0299893	−	0.0519429i
$476$	28.8317			1.32150
$477$		0			0
$478$	−21.1536			−0.967545
$479$	−5.22430	−	9.04876i	−0.238705	−	0.413448i	0.721638	−	0.692270i	$-0.243389\pi$
$479$	−5.22430	−	9.04876i	−0.238705	−	0.413448i	−0.960343	+	0.278822i	$0.910056\pi$
$480$		0			0
$481$	5.45449	−	9.44745i	0.248703	−	0.430766i
$482$	6.07062	−	10.5146i	0.276509	−	0.478928i
$483$		0			0
$484$	−7.82178	−	13.5477i	−0.355536	−	0.615806i
$485$	10.5820			0.480505
$486$		0			0
$487$	−16.1649			−0.732500			−0.366250	−	0.930516i	$-0.619359\pi$
$487$	−16.1649			−0.732500			−0.366250	+	0.930516i	$0.619359\pi$
$488$	−2.44162	−	4.22901i	−0.110527	−	0.191438i
$489$		0			0
$490$	−36.3278	+	62.9217i	−1.64112	+	2.84251i
$491$	5.38867	−	9.33345i	0.243187	−	0.421213i	−0.718433	−	0.695596i	$-0.755140\pi$
$491$	5.38867	−	9.33345i	0.243187	−	0.421213i	0.961620	+	0.274383i	$0.0884737\pi$
$492$		0			0
$493$	−3.52397	−	6.10370i	−0.158712	−	0.274897i
$494$	−4.74953			−0.213692
$495$		0			0
$496$	−3.98238			−0.178814
$497$	−7.48032	−	12.9563i	−0.335538	−	0.581169i
$498$		0			0
$499$	9.59359	−	16.6166i	0.429468	−	0.743861i	−0.567358	−	0.823471i	$-0.692034\pi$
$499$	9.59359	−	16.6166i	0.429468	−	0.743861i	0.996826	+	0.0796106i	$0.0253677\pi$
$500$	−14.8776	+	25.7687i	−0.665346	+	1.15241i
$501$		0			0
$502$	−7.74537	−	13.4154i	−0.345693	−	0.598758i
$503$	−12.0251			−0.536171			−0.268086	−	0.963395i	$-0.586391\pi$
$503$	−12.0251			−0.536171			−0.268086	+	0.963395i	$0.586391\pi$
$504$		0			0
$505$	−38.4778			−1.71224
$506$	−18.9740	−	32.8639i	−0.843496	−	1.46098i
$507$		0			0
$508$	11.6161	−	20.1196i	0.515380	−	0.892664i
$509$	7.47651	−	12.9497i	0.331391	−	0.573985i	−0.651394	−	0.758739i	$-0.725816\pi$
$509$	7.47651	−	12.9497i	0.331391	−	0.573985i	0.982785	+	0.184754i	$0.0591489\pi$
$510$		0			0
$511$	−30.9347	−	53.5804i	−1.36847	−	2.37026i
$512$	−27.3678			−1.20950
$513$		0			0
$514$	49.3922			2.17860
$515$	9.32521	+	16.1517i	0.410918	+	0.711730i
$516$		0			0
$517$	−14.9032	+	25.8130i	−0.655440	+	1.13526i
$518$	46.2171	−	80.0503i	2.03066	−	3.51721i
$519$		0			0
$520$	1.38000	+	2.39023i	0.0605169	+	0.104818i
$521$	37.4188			1.63935			0.819673	−	0.572832i	$-0.194155\pi$
$521$	37.4188			1.63935			0.819673	+	0.572832i	$0.194155\pi$
$522$		0			0
$523$	−8.44979			−0.369483			−0.184742	−	0.982787i	$-0.559145\pi$
$523$	−8.44979			−0.369483			−0.184742	+	0.982787i	$0.559145\pi$
$524$	19.2945	+	33.4191i	0.842885	+	1.45992i
$525$		0			0
$526$	−29.1125	+	50.4243i	−1.26936	+	2.19860i
$527$	−1.74151	+	3.01639i	−0.0758615	+	0.131396i
$528$		0			0
$529$	2.23965	+	3.87918i	0.0973760	+	0.168660i
$530$	−27.8484			−1.20966
$531$		0			0
$532$	−22.4201			−0.972033
$533$	1.37442	+	2.38056i	0.0595326	+	0.103113i
$534$		0			0
$535$	7.69023	−	13.3199i	0.332478	−	0.575868i
$536$	2.26380	−	3.92101i	0.0977812	−	0.169362i
$537$		0			0
$538$	10.0086	+	17.3354i	0.431501	+	0.747382i
$539$	68.5065			2.95078
$540$		0			0
$541$	12.6259			0.542828			0.271414	−	0.962463i	$-0.412509\pi$
$541$	12.6259			0.542828			0.271414	+	0.962463i	$0.412509\pi$
$542$	27.9225	+	48.3633i	1.19938	+	2.07738i
$543$		0			0
$544$	−9.37758	+	16.2424i	−0.402060	+	0.696389i
$545$	−5.82345	+	10.0865i	−0.249449	+	0.432058i
$546$		0			0
$547$	−15.6975	−	27.1889i	−0.671178	−	1.16251i	−0.977570	−	0.210609i	$-0.932455\pi$
$547$	−15.6975	−	27.1889i	−0.671178	−	1.16251i	0.306393	−	0.951905i	$-0.400878\pi$
$548$	−9.16731			−0.391608
$549$		0			0
$550$	6.27126			0.267407
$551$	2.74030	+	4.74634i	0.116741	+	0.202201i
$552$		0			0
$553$	−11.0366	+	19.1159i	−0.469322	+	0.812890i
$554$	0.398243	−	0.689777i	0.0169197	−	0.0293058i
$555$		0			0
$556$	−16.6989	−	28.9234i	−0.708193	−	1.22663i
$557$	−15.9303			−0.674988			−0.337494	−	0.941328i	$-0.609579\pi$
$557$	−15.9303			−0.674988			−0.337494	+	0.941328i	$0.609579\pi$
$558$		0			0
$559$	6.66967			0.282097
$560$	−13.5684	−	23.5011i	−0.573369	−	0.993103i
$561$		0			0
$562$	14.8556	−	25.7307i	0.626647	−	1.08538i
$563$	12.4304	−	21.5301i	0.523880	−	0.907387i	−0.475734	−	0.879589i	$-0.657817\pi$
$563$	12.4304	−	21.5301i	0.523880	−	0.907387i	0.999614	−	0.0277973i	$-0.00884931\pi$
$564$		0			0
$565$	−2.48789	−	4.30915i	−0.104666	−	0.181287i
$566$	−33.0695			−1.39001
$567$		0			0
$568$	−3.38165			−0.141891
$569$	−9.59500	−	16.6190i	−0.402243	−	0.696706i	0.591753	−	0.806119i	$-0.298436\pi$
$569$	−9.59500	−	16.6190i	−0.402243	−	0.696706i	−0.993996	+	0.109413i	$0.965103\pi$
$570$		0			0
$571$	10.1896	−	17.6489i	0.426422	−	0.738585i	−0.570130	−	0.821555i	$-0.693107\pi$
$571$	10.1896	−	17.6489i	0.426422	−	0.738585i	0.996552	+	0.0829696i	$0.0264404\pi$
$572$	6.34703	−	10.9934i	0.265383	−	0.459656i
$573$		0			0
$574$	11.6457	+	20.1710i	0.486084	+	0.841921i
$575$	3.06072			0.127641
$576$		0			0
$577$	23.2991			0.969953			0.484976	−	0.874527i	$-0.338828\pi$
$577$	23.2991			0.969953			0.484976	+	0.874527i	$0.338828\pi$
$578$	−12.1267	−	21.0041i	−0.504404	−	0.873654i
$579$		0			0
$580$	7.76758	−	13.4539i	0.322531	−	0.558641i
$581$	20.4931	−	35.4950i	0.850195	−	1.47258i
$582$		0			0
$583$	13.1290	+	22.7402i	0.543749	+	0.941802i
$584$	−13.9847			−0.578693
$585$		0			0
$586$	−52.3272			−2.16162
$587$	18.4546	+	31.9644i	0.761704	+	1.31931i	0.941971	+	0.335693i	$0.108970\pi$
$587$	18.4546	+	31.9644i	0.761704	+	1.31931i	−0.180267	+	0.983618i	$0.557696\pi$
$588$		0			0
$589$	1.35423	−	2.34560i	0.0558001	−	0.0966486i
$590$	−0.577071	+	0.999516i	−0.0237576	+	0.0411494i
$591$		0			0
$592$	12.1222	+	20.9963i	0.498220	+	0.862943i
$593$	4.36830			0.179385			0.0896923	−	0.995970i	$-0.471412\pi$
$593$	4.36830			0.179385			0.0896923	+	0.995970i	$0.471412\pi$
$594$		0			0
$595$	−23.7340			−0.973000
$596$	−11.2089	−	19.4144i	−0.459134	−	0.795244i
$597$		0			0
$598$	5.56036	−	9.63082i	0.227380	−	0.393833i
$599$	15.6028	−	27.0249i	0.637513	−	1.10421i	−0.348463	−	0.937322i	$-0.613296\pi$
$599$	15.6028	−	27.0249i	0.637513	−	1.10421i	0.985977	−	0.166883i	$-0.0533702\pi$
$600$		0			0
$601$	−21.9686	−	38.0507i	−0.896116	−	1.55212i	−0.832417	−	0.554149i	$-0.813044\pi$
$601$	−21.9686	−	38.0507i	−0.896116	−	1.55212i	−0.0636987	−	0.997969i	$-0.520290\pi$
$602$	56.5136			2.30332
$603$		0			0
$604$	−1.79223			−0.0729247
$605$	6.43882	+	11.1524i	0.261775	+	0.453408i
$606$		0			0
$607$	−8.67933	+	15.0330i	−0.352283	+	0.610172i	−0.986649	−	0.162861i	$-0.947928\pi$
$607$	−8.67933	+	15.0330i	−0.352283	+	0.610172i	0.634366	+	0.773033i	$0.281261\pi$
$608$	7.29217	−	12.6304i	0.295736	−	0.512231i
$609$		0			0
$610$	9.80413	+	16.9813i	0.396958	+	0.687551i
$611$	−8.73480			−0.353372
$612$		0			0
$613$	−1.19805			−0.0483887			−0.0241944	−	0.999707i	$-0.507702\pi$
$613$	−1.19805			−0.0483887			−0.0241944	+	0.999707i	$0.507702\pi$
$614$	−21.6659	−	37.5265i	−0.874365	−	1.51444i
$615$		0			0
$616$	11.0253	−	19.0963i	0.444221	−	0.769413i
$617$	−13.0069	+	22.5285i	−0.523636	+	0.906965i	0.475985	+	0.879453i	$0.342092\pi$
$617$	−13.0069	+	22.5285i	−0.523636	+	0.906965i	−0.999621	+	0.0275115i	$0.991242\pi$
$618$		0			0
$619$	−4.81567	−	8.34099i	−0.193558	−	0.335253i	0.752869	−	0.658171i	$-0.228670\pi$
$619$	−4.81567	−	8.34099i	−0.193558	−	0.335253i	−0.946427	+	0.322918i	$0.895336\pi$
$620$	−7.67733			−0.308329
$621$		0			0
$622$	−47.1311			−1.88978
$623$	−41.1244	−	71.2296i	−1.64762	−	2.85375i
$624$		0			0
$625$	10.4691	−	18.1330i	0.418763	−	0.725319i
$626$	−11.8705	+	20.5602i	−0.474439	+	0.821752i
$627$		0			0
$628$	17.3814	+	30.1054i	0.693592	+	1.20134i
$629$	21.2044			0.845474
$630$		0			0
$631$	−14.1673			−0.563992			−0.281996	−	0.959416i	$-0.590997\pi$
$631$	−14.1673			−0.563992			−0.281996	+	0.959416i	$0.590997\pi$
$632$	2.49467	+	4.32089i	0.0992325	+	0.171876i
$633$		0			0
$634$	26.7931	−	46.4069i	1.06409	−	1.84306i
$635$	−9.56225	+	16.5623i	−0.379466	+	0.657255i
$636$		0			0
$637$	10.0380	+	17.3863i	0.397719	+	0.688870i
$638$	−26.2930			−1.04095
$639$		0			0
$640$	−17.5539			−0.693879
$641$	−11.1005	−	19.2266i	−0.438442	−	0.759403i	0.559128	−	0.829081i	$-0.311136\pi$
$641$	−11.1005	−	19.2266i	−0.438442	−	0.759403i	−0.997570	+	0.0696782i	$0.977803\pi$
$642$		0			0
$643$	−10.7684	+	18.6514i	−0.424664	+	0.735540i	−0.996389	−	0.0849056i	$-0.972941\pi$
$643$	−10.7684	+	18.6514i	−0.424664	+	0.735540i	0.571725	+	0.820445i	$0.306274\pi$
$644$	26.2475	−	45.4621i	1.03430	−	1.79146i
$645$		0			0
$646$	−4.61597	−	7.99509i	−0.181613	−	0.314563i
$647$	13.4037			0.526952			0.263476	−	0.964666i	$-0.415131\pi$
$647$	13.4037			0.526952			0.263476	+	0.964666i	$0.415131\pi$
$648$		0			0
$649$	1.08823			0.0427168
$650$	0.918902	+	1.59159i	0.0360423	+	0.0624271i
$651$		0			0
$652$	1.50091	−	2.59966i	0.0587802	−	0.101810i
$653$	9.45543	−	16.3773i	0.370020	−	0.640893i	−0.619548	−	0.784958i	$-0.712684\pi$
$653$	9.45543	−	16.3773i	0.370020	−	0.640893i	0.989568	+	0.144066i	$0.0460176\pi$
$654$		0			0
$655$	−15.8831	−	27.5103i	−0.620603	−	1.07492i
$656$	−6.10909			−0.238520
$657$		0			0
$658$	−74.0119			−2.88528
$659$	0.0140907	+	0.0244058i	0.000548897	+	0.000950717i	0.866300	−	0.499525i	$-0.166492\pi$
$659$	0.0140907	+	0.0244058i	0.000548897	+	0.000950717i	−0.865751	+	0.500475i	$0.833159\pi$
$660$		0			0
$661$	22.5209	−	39.0073i	0.875960	−	1.51721i	0.0202238	−	0.999795i	$-0.493562\pi$
$661$	22.5209	−	39.0073i	0.875960	−	1.51721i	0.855736	−	0.517412i	$-0.173105\pi$
$662$	−27.8014	+	48.1535i	−1.08053	+	1.87154i
$663$		0			0
$664$	−4.63218	−	8.02317i	−0.179763	−	0.311359i
$665$	18.4560			0.715693
$666$		0			0
$667$	−12.8325			−0.496875
$668$	30.1089	+	52.1501i	1.16495	+	2.01775i
$669$		0			0
$670$	−9.09010	+	15.7445i	−0.351181	+	0.608263i
$671$	9.24424	−	16.0115i	0.356870	−	0.618117i
$672$		0			0
$673$	4.87984	+	8.45214i	0.188104	+	0.325806i	0.944618	−	0.328172i	$-0.106432\pi$
$673$	4.87984	+	8.45214i	0.188104	+	0.325806i	−0.756514	+	0.653978i	$0.773099\pi$
$674$	−23.2607			−0.895968
$675$		0			0
$676$	−28.9847			−1.11480
$677$	−20.4404	−	35.4038i	−0.785588	−	1.36068i	−0.928647	−	0.370964i	$-0.879027\pi$
$677$	−20.4404	−	35.4038i	−0.785588	−	1.36068i	0.143060	−	0.989714i	$-0.454306\pi$
$678$		0			0
$679$	12.3878	−	21.4563i	0.475400	−	0.823417i
$680$	−2.68238	+	4.64602i	−0.102865	+	0.178167i
$681$		0			0
$682$	6.49688	+	11.2529i	0.248779	+	0.430897i
$683$	−44.0251			−1.68457			−0.842287	−	0.539029i	$-0.818791\pi$
$683$	−44.0251			−1.68457			−0.842287	+	0.539029i	$0.818791\pi$
$684$		0			0
$685$	7.54644			0.288335
$686$	48.9916	+	84.8559i	1.87051	+	3.23981i
$687$		0			0
$688$	−7.41144	+	12.8370i	−0.282559	+	0.489406i
$689$	−3.84749	+	6.66405i	−0.146578	+	0.253880i
$690$		0			0
$691$	−10.7758	−	18.6642i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$691$	−10.7758	−	18.6642i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967781\pi$
$692$	−22.9939			−0.874098
$693$		0			0
$694$	−7.46603			−0.283407
$695$	13.7464	+	23.8095i	0.521432	+	0.903146i
$696$		0			0
$697$	−2.67153	+	4.62723i	−0.101191	+	0.175269i
$698$	−31.0221	+	53.7318i	−1.17420	+	2.03378i
$699$		0			0
$700$	4.33766	+	7.51304i	0.163948	+	0.283966i
$701$	−12.8521			−0.485419			−0.242709	−	0.970099i	$-0.578036\pi$
$701$	−12.8521			−0.485419			−0.242709	+	0.970099i	$0.578036\pi$
$702$		0			0
$703$	−16.4889			−0.621891
$704$	23.7699	+	41.1707i	0.895863	+	1.55168i
$705$		0			0
$706$	−26.6445	+	46.1496i	−1.00278	+	1.73686i
$707$	−45.0439	+	78.0183i	−1.69405	+	2.93418i
$708$		0			0
$709$	24.8559	+	43.0516i	0.933481	+	1.61684i	0.777320	+	0.629105i	$0.216578\pi$
$709$	24.8559	+	43.0516i	0.933481	+	1.61684i	0.156161	+	0.987732i	$0.450088\pi$
$710$	13.5787			0.509601
$711$		0			0
$712$	−18.5912			−0.696737
$713$	3.17084	+	5.49206i	0.118749	+	0.205679i
$714$		0			0
$715$	−5.22482	+	9.04965i	−0.195397	+	0.338438i
$716$	−13.3344	+	23.0959i	−0.498330	+	0.863133i
$717$		0			0
$718$	4.47026	+	7.74271i	0.166828	+	0.288955i
$719$	−5.63745			−0.210242			−0.105121	−	0.994459i	$-0.533523\pi$
$719$	−5.63745			−0.210242			−0.105121	+	0.994459i	$0.533523\pi$
$720$		0			0
$721$	43.6660			1.62621
$722$	−16.5983	−	28.7491i	−0.617725	−	1.06993i
$723$		0			0
$724$	1.84017	−	3.18727i	0.0683893	−	0.118454i
$725$	1.06034	−	1.83657i	0.0393802	−	0.0682085i
$726$		0			0
$727$	22.7071	+	39.3299i	0.842161	+	1.45867i	0.888064	+	0.459720i	$0.152050\pi$
$727$	22.7071	+	39.3299i	0.842161	+	1.45867i	−0.0459026	+	0.998946i	$0.514616\pi$
$728$	6.46195			0.239496
$729$		0			0
$730$	56.1546			2.07837
$731$	6.48211	+	11.2273i	0.239749	+	0.415258i
$732$		0			0
$733$	12.8334	−	22.2281i	0.474013	−	0.821015i	−0.525544	−	0.850766i	$-0.676138\pi$
$733$	12.8334	−	22.2281i	0.474013	−	0.821015i	0.999557	+	0.0297511i	$0.00947148\pi$
$734$	18.5904	−	32.1996i	0.686185	−	1.18851i
$735$		0			0
$736$	17.0741	+	29.5733i	0.629361	+	1.09008i
$737$	17.1420			0.631433
$738$		0			0
$739$	−14.4553			−0.531745			−0.265873	−	0.964008i	$-0.585660\pi$
$739$	−14.4553			−0.531745			−0.265873	+	0.964008i	$0.585660\pi$
$740$	23.3695	+	40.4772i	0.859080	+	1.48797i
$741$		0			0
$742$	−32.6006	+	56.4660i	−1.19681	+	2.07293i
$743$	−17.3969	+	30.1323i	−0.638229	+	1.10545i	0.347592	+	0.937646i	$0.386999\pi$
$743$	−17.3969	+	30.1323i	−0.638229	+	1.10545i	−0.985821	+	0.167799i	$0.946334\pi$
$744$		0			0
$745$	9.22706	+	15.9817i	0.338053	+	0.585525i
$746$	63.0168			2.30721
$747$		0			0
$748$	24.6742			0.902177
$749$	−18.0051	−	31.1857i	−0.657891	−	1.13950i
$750$		0			0
$751$	−9.05922	+	15.6910i	−0.330576	+	0.572574i	−0.982625	−	0.185603i	$-0.940576\pi$
$751$	−9.05922	+	15.6910i	−0.330576	+	0.572574i	0.652049	+	0.758177i	$0.273910\pi$
$752$	9.70624	−	16.8117i	0.353950	−	0.613060i
$753$		0			0
$754$	−3.85261	−	6.67292i	−0.140304	−	0.243013i
$755$	1.47535			0.0536933
$756$		0			0
$757$	−37.0045			−1.34495			−0.672475	−	0.740120i	$-0.734769\pi$
$757$	−37.0045			−1.34495			−0.672475	+	0.740120i	$0.734769\pi$
$758$	22.2621	+	38.5592i	0.808598	+	1.40053i
$759$		0			0
$760$	2.08587	−	3.61282i	0.0756623	−	0.131051i
$761$	6.22221	−	10.7772i	0.225555	−	0.390673i	−0.730931	−	0.682452i	$-0.760914\pi$
$761$	6.22221	−	10.7772i	0.225555	−	0.390673i	0.956486	+	0.291779i	$0.0942472\pi$
$762$		0			0
$763$	13.6344	+	23.6154i	0.493598	+	0.854936i
$764$	31.2513			1.13063
$765$		0			0
$766$	−21.0309			−0.759878
$767$	0.159454	+	0.276183i	0.00575755	+	0.00997238i
$768$		0			0
$769$	20.4428	−	35.4079i	0.737186	−	1.27684i	−0.216572	−	0.976267i	$-0.569488\pi$
$769$	20.4428	−	35.4079i	0.737186	−	1.27684i	0.953758	−	0.300576i	$-0.0971790\pi$
$770$	−44.2711	+	76.6797i	−1.59542	+	2.76335i
$771$		0			0
$772$	−26.1302	−	45.2588i	−0.940446	−	1.62890i
$773$	−36.4162			−1.30980			−0.654900	−	0.755716i	$-0.727289\pi$
$773$	−36.4162			−1.30980			−0.654900	+	0.755716i	$0.727289\pi$
$774$		0			0
$775$	−1.04802			−0.0376461
$776$	−2.80010	−	4.84991i	−0.100518	−	0.174102i
$777$		0			0
$778$	−22.4347	+	38.8581i	−0.804324	+	1.39313i
$779$	2.07743	−	3.59821i	0.0744316	−	0.128919i
$780$		0			0
$781$	−6.40165	−	11.0880i	−0.229069	−	0.396759i
$782$	21.6160			0.772985
$783$		0			0
$784$	−44.6174			−1.59348
$785$	−14.3082	−	24.7825i	−0.510681	−	0.884525i
$786$		0			0
$787$	−9.17358	+	15.8891i	−0.327003	+	0.566385i	−0.981916	−	0.189319i	$-0.939372\pi$
$787$	−9.17358	+	15.8891i	−0.327003	+	0.566385i	0.654913	+	0.755704i	$0.272705\pi$
$788$	17.8475	−	30.9128i	0.635792	−	1.10122i
$789$		0			0
$790$	−10.0171	−	17.3502i	−0.356394	−	0.617292i
$791$	−11.6498			−0.414218
$792$		0			0
$793$	5.41808			0.192402
$794$	−10.3904	−	17.9967i	−0.368742	−	0.638681i
$795$		0			0
$796$	−25.5709	+	44.2900i	−0.906335	+	1.56982i
$797$	−1.73246	+	3.00071i	−0.0613670	+	0.106291i	−0.895077	−	0.445912i	$-0.852879\pi$
$797$	−1.73246	+	3.00071i	−0.0613670	+	0.106291i	0.833710	+	0.552203i	$0.186213\pi$
$798$		0			0
$799$	−8.48916	−	14.7037i	−0.300325	−	0.520178i
$800$	−5.64333			−0.199522
$801$		0			0
$802$	40.6716			1.43617
$803$	−26.4739	−	45.8541i	−0.934243	−	1.61816i
$804$		0			0
$805$	−21.6067	+	37.4240i	−0.761537	+	1.31902i
$806$	−1.90392	+	3.29769i	−0.0670628	+	0.116156i
$807$		0			0
$808$	10.1816	+	17.6350i	0.358186	+	0.620397i
$809$	−24.8406			−0.873348			−0.436674	−	0.899620i	$-0.643844\pi$
$809$	−24.8406			−0.873348			−0.436674	+	0.899620i	$0.643844\pi$
$810$		0			0
$811$	−40.3286			−1.41613			−0.708063	−	0.706149i	$-0.750431\pi$
$811$	−40.3286			−1.41613			−0.708063	+	0.706149i	$0.750431\pi$
$812$	−18.1862	−	31.4994i	−0.638209	−	1.10541i
$813$		0			0
$814$	39.5525	−	68.5070i	1.38632	−	2.40117i
$815$	−1.23554	+	2.14001i	−0.0432790	+	0.0749614i
$816$		0			0
$817$	−5.04060	−	8.73058i	−0.176348	−	0.305444i
$818$	−31.8660			−1.11417
$819$		0			0
$820$	−11.7772			−0.411279
$821$	−20.0908	−	34.7983i	−0.701174	−	1.21447i	−0.968055	−	0.250740i	$-0.919326\pi$
$821$	−20.0908	−	34.7983i	−0.701174	−	1.21447i	0.266880	−	0.963730i	$-0.414007\pi$
$822$		0			0
$823$	23.9777	−	41.5306i	0.835810	−	1.44766i	−0.0575599	−	0.998342i	$-0.518332\pi$
$823$	23.9777	−	41.5306i	0.835810	−	1.44766i	0.893370	−	0.449323i	$-0.148335\pi$
$824$	4.93506	−	8.54777i	0.171921	−	0.297776i
$825$		0			0
$826$	1.35109	+	2.34016i	0.0470104	+	0.0814245i
$827$	−5.00048			−0.173884			−0.0869419	−	0.996213i	$-0.527709\pi$
$827$	−5.00048			−0.173884			−0.0869419	+	0.996213i	$0.527709\pi$
$828$		0			0
$829$	29.7037			1.03165			0.515826	−	0.856693i	$-0.327485\pi$
$829$	29.7037			1.03165			0.515826	+	0.856693i	$0.327485\pi$
$830$	18.6001	+	32.2164i	0.645620	+	1.11825i
$831$		0			0
$832$	−6.96582	+	12.0652i	−0.241496	+	0.418284i
$833$	−19.5114	+	33.7947i	−0.676030	+	1.17092i
$834$		0			0
$835$	−24.7853	−	42.9295i	−0.857732	−	1.48564i
$836$	−19.1871			−0.663599
$837$		0			0
$838$	−12.3502			−0.426632
$839$	12.9523	+	22.4340i	0.447162	+	0.774507i	0.998200	−	0.0599731i	$-0.0191015\pi$
$839$	12.9523	+	22.4340i	0.447162	+	0.774507i	−0.551038	+	0.834480i	$0.685768\pi$
$840$		0			0
$841$	10.0544	−	17.4147i	0.346703	−	0.600507i
$842$	−14.1458	+	24.5012i	−0.487497	+	0.844369i
$843$		0			0
$844$	12.4068	+	21.4892i	0.427060	+	0.739690i
$845$	23.8599			0.820807
$846$		0			0
$847$	30.1503			1.03598
$848$	−8.55078	−	14.8104i	−0.293635	−	0.508591i
$849$		0			0
$850$	−1.78612	+	3.09365i	−0.0612635	+	0.106111i
$851$	19.3038	−	33.4352i	0.661727	−	1.14614i
$852$		0			0
$853$	2.49583	+	4.32290i	0.0854556	+	0.148013i	0.905585	−	0.424164i	$-0.139432\pi$
$853$	2.49583	+	4.32290i	0.0854556	+	0.148013i	−0.820130	+	0.572178i	$0.806099\pi$
$854$	45.9086			1.57096
$855$		0			0
$856$	−8.13961			−0.278206
$857$	7.34151	+	12.7159i	0.250781	+	0.434366i	0.963741	−	0.266839i	$-0.0859792\pi$
$857$	7.34151	+	12.7159i	0.250781	+	0.434366i	−0.712960	+	0.701205i	$0.752646\pi$
$858$		0			0
$859$	8.74243	−	15.1423i	0.298288	−	0.516650i	−0.677457	−	0.735563i	$-0.736918\pi$
$859$	8.74243	−	15.1423i	0.298288	−	0.516650i	0.975744	+	0.218913i	$0.0702511\pi$
$860$	−14.2880	+	24.7475i	−0.487215	+	0.843881i
$861$		0			0
$862$	−38.6932	−	67.0186i	−1.31790	−	2.28266i
$863$	6.33263			0.215565			0.107783	−	0.994174i	$-0.465625\pi$
$863$	6.33263			0.215565			0.107783	+	0.994174i	$0.465625\pi$
$864$		0			0
$865$	18.9284			0.643585
$866$	−11.5560	−	20.0157i	−0.392691	−	0.680160i
$867$		0			0
$868$	−8.98743	+	15.5667i	−0.305053	+	0.528368i
$869$	−9.44508	+	16.3594i	−0.320402	+	0.554953i
$870$		0			0
$871$	2.51174	+	4.35047i	0.0851072	+	0.147410i
$872$	6.16374			0.208730
$873$		0			0
$874$	−16.8090			−0.568571
$875$	−28.6740	−	49.6648i	−0.969358	−	1.67898i
$876$		0			0
$877$	−16.2655	+	28.1727i	−0.549247	+	0.951323i	0.449080	+	0.893492i	$0.351752\pi$
$877$	−16.2655	+	28.1727i	−0.549247	+	0.951323i	−0.998326	+	0.0578315i	$0.981581\pi$
$878$	10.0442	−	17.3971i	0.338976	−	0.587124i
$879$		0			0
$880$	−11.6118	−	20.1122i	−0.391434	−	0.677983i
$881$	−33.3599			−1.12393			−0.561963	−	0.827163i	$-0.689954\pi$
$881$	−33.3599			−1.12393			−0.561963	+	0.827163i	$0.689954\pi$
$882$		0			0
$883$	−54.8511			−1.84589			−0.922944	−	0.384934i	$-0.874224\pi$
$883$	−54.8511			−1.84589			−0.922944	+	0.384934i	$0.874224\pi$
$884$	3.61541	+	6.26207i	0.121599	+	0.210616i
$885$		0			0
$886$	17.5569	−	30.4094i	0.589835	−	1.02162i
$887$	−10.5239	+	18.2279i	−0.353357	+	0.612032i	−0.986835	−	0.161728i	$-0.948293\pi$
$887$	−10.5239	+	18.2279i	−0.353357	+	0.612032i	0.633478	+	0.773760i	$0.281627\pi$
$888$		0			0
$889$	22.3880	+	38.7772i	0.750870	+	1.30054i
$890$	74.6516			2.50233
$891$		0			0
$892$	37.9158			1.26951
$893$	6.60132	+	11.4338i	0.220905	+	0.382618i
$894$		0			0
$895$	10.9768	−	19.0123i	0.366913	−	0.635512i
$896$	−20.5494	+	35.5926i	−0.686507	+	1.18906i
$897$		0			0
$898$	−5.04016	−	8.72982i	−0.168192	−	0.291318i
$899$	4.39397			0.146547
$900$		0			0
$901$	−14.9572			−0.498296
$902$	9.96641	+	17.2623i	0.331845	+	0.574772i
$903$		0			0
$904$	−1.31664	+	2.28048i	−0.0437906	+	0.0758476i
$905$	−1.51481	+	2.62373i	−0.0503540	+	0.0872157i
$906$		0			0
$907$	−7.41902	−	12.8501i	−0.246344	−	0.426681i	0.716164	−	0.697932i	$-0.245896\pi$
$907$	−7.41902	−	12.8501i	−0.246344	−	0.426681i	−0.962509	+	0.271251i	$0.912563\pi$
$908$	−57.0887			−1.89456
$909$		0			0
$910$	−25.9474			−0.860149
$911$	−9.01477	−	15.6140i	−0.298673	−	0.517316i	0.677160	−	0.735836i	$-0.263211\pi$
$911$	−9.01477	−	15.6140i	−0.298673	−	0.517316i	−0.975833	+	0.218520i	$0.929877\pi$
$912$		0			0
$913$	17.5379	−	30.3766i	0.580421	−	1.00532i
$914$	−23.8094	+	41.2391i	−0.787545	+	1.36407i
$915$		0			0
$916$	−10.9645	−	18.9911i	−0.362278	−	0.627483i
$917$	−74.3738			−2.45604
$918$		0			0
$919$	13.4881			0.444932			0.222466	−	0.974940i	$-0.428589\pi$
$919$	13.4881			0.444932			0.222466	+	0.974940i	$0.428589\pi$
$920$	4.88391	+	8.45919i	0.161018	+	0.278891i
$921$		0			0
$922$	−15.8551	+	27.4619i	−0.522160	+	0.904408i
$923$	1.87601	−	3.24935i	0.0617497	−	0.106954i
$924$		0			0
$925$	3.19014	+	5.52549i	0.104891	+	0.181677i
$926$	31.5507			1.03682
$927$		0			0
$928$	23.6603			0.776689
$929$	18.8106	+	32.5809i	0.617155	+	1.06894i	0.990002	+	0.141051i	$0.0450481\pi$
$929$	18.8106	+	32.5809i	0.617155	+	1.06894i	−0.372847	+	0.927893i	$0.621619\pi$
$930$		0			0
$931$	15.1724	−	26.2794i	0.497255	−	0.861272i
$932$	29.6719	−	51.3933i	0.971936	−	1.68344i
$933$		0			0
$934$	−16.3111	−	28.2517i	−0.533716	−	0.924423i
$935$	−20.3116			−0.664259
$936$		0			0
$937$	4.14458			0.135398			0.0676988	−	0.997706i	$-0.478434\pi$
$937$	4.14458			0.135398			0.0676988	+	0.997706i	$0.478434\pi$
$938$	21.2826	+	36.8625i	0.694900	+	1.20360i
$939$		0			0
$940$	18.7119	−	32.4100i	0.610316	−	1.05710i
$941$	1.76516	−	3.05735i	0.0575427	−	0.0996668i	−0.835819	−	0.549005i	$-0.815007\pi$
$941$	1.76516	−	3.05735i	0.0575427	−	0.0996668i	0.893362	+	0.449338i	$0.148340\pi$
$942$		0			0
$943$	4.86416	+	8.42497i	0.158399	+	0.274355i
$944$	−0.708752			−0.0230679
$945$		0			0
$946$	48.3643			1.57246
$947$	7.12754	+	12.3453i	0.231614	+	0.401167i	0.958283	−	0.285820i	$-0.0922661\pi$
$947$	7.12754	+	12.3453i	0.231614	+	0.401167i	−0.726669	+	0.686987i	$0.758933\pi$
$948$		0			0
$949$	7.75822	−	13.4376i	0.251842	−	0.436204i
$950$	1.38892	−	2.40568i	0.0450625	−	0.0780506i
$951$		0			0
$952$	6.28023	+	10.8777i	0.203543	+	0.352547i
$953$	11.6426			0.377141			0.188570	−	0.982060i	$-0.439615\pi$
$953$	11.6426			0.377141			0.188570	+	0.982060i	$0.439615\pi$
$954$		0			0
$955$	−25.7258			−0.832467
$956$	−12.5215	−	21.6879i	−0.404975	−	0.701437i
$957$		0			0
$958$	11.1018	−	19.2289i	0.358683	−	0.621257i
$959$	8.83421	−	15.3013i	0.285271	−	0.494105i
$960$		0			0
$961$	14.4143	+	24.9663i	0.464976	+	0.805363i
$962$	23.1819			0.747414
$963$		0			0
$964$	14.3736			0.462942
$965$	21.5101	+	37.2566i	0.692436	+	1.19933i
$966$		0			0
$967$	−14.5341	+	25.1737i	−0.467384	+	0.809533i	−0.999306	−	0.0372608i	$-0.988137\pi$
$967$	−14.5341	+	25.1737i	−0.467384	+	0.809533i	0.531922	+	0.846794i	$0.321470\pi$
$968$	3.40754	−	5.90202i	0.109522	−	0.189698i
$969$		0			0
$970$	11.2436	+	19.4744i	0.361009	+	0.625286i
$971$	47.5792			1.52689			0.763444	−	0.645874i	$-0.223507\pi$
$971$	47.5792			1.52689			0.763444	+	0.645874i	$0.223507\pi$
$972$		0			0
$973$	64.3687			2.06357
$974$	−17.1754	−	29.7487i	−0.550336	−	0.953209i
$975$		0			0
$976$	−6.02066	+	10.4281i	−0.192717	+	0.333795i
$977$	−3.05815	+	5.29687i	−0.0978389	+	0.169462i	−0.910790	−	0.412870i	$-0.864526\pi$
$977$	−3.05815	+	5.29687i	−0.0978389	+	0.169462i	0.812951	+	0.582332i	$0.197860\pi$
$978$		0			0
$979$	−35.1942	−	60.9582i	−1.12481	−	1.94823i
$980$	−86.0145			−2.74763
$981$		0			0
$982$	22.9022			0.730837
$983$	−5.32591	−	9.22474i	−0.169870	−	0.294224i	0.768504	−	0.639845i	$-0.221001\pi$
$983$	−5.32591	−	9.22474i	−0.169870	−	0.294224i	−0.938374	+	0.345621i	$0.887668\pi$
$984$		0			0
$985$	−14.6919	+	25.4472i	−0.468124	+	0.810814i
$986$	7.48854	−	12.9705i	0.238484	−	0.413066i
$987$		0			0
$988$	−2.81140	−	4.86949i	−0.0894426	−	0.154919i
$989$	23.6045			0.750578
$990$		0			0
$991$	23.9856			0.761928			0.380964	−	0.924590i	$-0.375592\pi$
$991$	23.9856			0.761928			0.380964	+	0.924590i	$0.375592\pi$
$992$	−5.84636	−	10.1262i	−0.185622	−	0.321507i
$993$		0			0
$994$	15.8959	−	27.5325i	0.504187	−	0.873277i
$995$	21.0497	−	36.4591i	0.667320	−	1.15583i
$996$		0			0
$997$	−2.15709	−	3.73619i	−0.0683157	−	0.118326i	0.829844	−	0.557995i	$-0.188429\pi$
$997$	−2.15709	−	3.73619i	−0.0683157	−	0.118326i	−0.898160	+	0.439669i	$0.855096\pi$
$998$	40.7733			1.29066
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.d.244.5		12
3.2	odd	2		729.2.c.a.244.2		12
9.2	odd	6		729.2.c.a.487.2		12
9.4	even	3		729.2.a.b.1.2	✓	6
9.5	odd	6		729.2.a.e.1.5	yes	6
9.7	even	3	inner	729.2.c.d.487.5		12
27.2	odd	18		729.2.e.u.82.2		12
27.4	even	9		729.2.e.j.649.1		12
27.5	odd	18		729.2.e.l.163.1		12
27.7	even	9		729.2.e.s.568.2		12
27.11	odd	18		729.2.e.k.325.2		12
27.13	even	9		729.2.e.t.406.1		12
27.14	odd	18		729.2.e.k.406.2		12
27.16	even	9		729.2.e.t.325.1		12
27.20	odd	18		729.2.e.l.568.1		12
27.22	even	9		729.2.e.s.163.2		12
27.23	odd	18		729.2.e.u.649.2		12
27.25	even	9		729.2.e.j.82.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.2	✓	6	9.4	even	3
729.2.a.e.1.5	yes	6	9.5	odd	6
729.2.c.a.244.2		12	3.2	odd	2
729.2.c.a.487.2		12	9.2	odd	6
729.2.c.d.244.5		12	1.1	even	1	trivial
729.2.c.d.487.5		12	9.7	even	3	inner
729.2.e.j.82.1		12	27.25	even	9
729.2.e.j.649.1		12	27.4	even	9
729.2.e.k.325.2		12	27.11	odd	18
729.2.e.k.406.2		12	27.14	odd	18
729.2.e.l.163.1		12	27.5	odd	18
729.2.e.l.568.1		12	27.20	odd	18
729.2.e.s.163.2		12	27.22	even	9
729.2.e.s.568.2		12	27.7	even	9
729.2.e.t.325.1		12	27.16	even	9
729.2.e.t.406.1		12	27.13	even	9
729.2.e.u.82.2		12	27.2	odd	18
729.2.e.u.649.2		12	27.23	odd	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.06251 + 1.84033i) q^{2} +(-1.25787 + 2.17870i) q^{4} +(1.03547 - 1.79349i) q^{5} +(-2.42434 - 4.19907i) q^{7} -1.09598 q^{8} +4.40081 q^{10} +(-2.07474 - 3.59356i) q^{11} +(0.608008 - 1.05310i) q^{13} +(5.15178 - 8.92315i) q^{14} +(1.35126 + 2.34044i) q^{16} +2.36364 q^{17} -1.83801 q^{19} +(2.60498 + 4.51196i) q^{20} +(4.40889 - 7.63642i) q^{22} +(2.15178 - 3.72700i) q^{23} +(0.355603 + 0.615922i) q^{25} +2.58407 q^{26} +12.1980 q^{28} +(-1.49091 - 2.58233i) q^{29} +(-0.736793 + 1.27616i) q^{31} +(-3.96743 + 6.87180i) q^{32} +(2.51140 + 4.34987i) q^{34} -10.0413 q^{35} +8.97108 q^{37} +(-1.95291 - 3.38254i) q^{38} +(-1.13485 + 1.96562i) q^{40} +(-1.13026 + 1.95767i) q^{41} +(2.74243 + 4.75003i) q^{43} +10.4391 q^{44} +9.14521 q^{46} +(-3.59157 - 6.22077i) q^{47} +(-8.25481 + 14.2978i) q^{49} +(-0.755667 + 1.30885i) q^{50} +(1.52959 + 2.64933i) q^{52} -6.32803 q^{53} -8.59334 q^{55} +(2.65702 + 4.60209i) q^{56} +(3.16823 - 5.48753i) q^{58} +(-0.131128 + 0.227121i) q^{59} +(2.22780 + 3.85867i) q^{61} -3.13141 q^{62} -11.4568 q^{64} +(-1.25915 - 2.18091i) q^{65} +(-2.06555 + 3.57764i) q^{67} +(-2.97316 + 5.14966i) q^{68} +(-10.6690 - 18.4793i) q^{70} +3.08551 q^{71} +12.7601 q^{73} +(9.53190 + 16.5097i) q^{74} +(2.31198 - 4.00447i) q^{76} +(-10.0598 + 17.4240i) q^{77} +(-2.27620 - 3.94250i) q^{79} +5.59674 q^{80} -4.80368 q^{82} +(4.22653 + 7.32056i) q^{83} +(2.44748 - 4.23915i) q^{85} +(-5.82774 + 10.0939i) q^{86} +(2.27387 + 3.93846i) q^{88} +16.9632 q^{89} -5.89606 q^{91} +(5.41335 + 9.37619i) q^{92} +(7.63218 - 13.2193i) q^{94} +(-1.90320 + 3.29644i) q^{95} +(2.55489 + 4.42519i) q^{97} -35.0834 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 9 q^{4} - 3 q^{5} - 6 q^{7} - 12 q^{8} + 12 q^{10} - 6 q^{11} - 6 q^{13} + 24 q^{14} - 15 q^{16} + 18 q^{17} + 24 q^{19} - 21 q^{20} - 3 q^{22} - 12 q^{23} - 9 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots - 36 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 9 * q^4 - 3 * q^5 - 6 * q^7 - 12 * q^8 + 12 * q^10 - 6 * q^11 - 6 * q^13 + 24 * q^14 - 15 * q^16 + 18 * q^17 + 24 * q^19 - 21 * q^20 - 3 * q^22 - 12 * q^23 - 9 * q^25 - 48 * q^26 + 6 * q^28 + 21 * q^29 - 15 * q^31 - 60 * q^35 + 6 * q^37 + 15 * q^38 - 3 * q^40 - 12 * q^41 - 6 * q^43 + 66 * q^44 - 6 * q^46 - 15 * q^47 - 12 * q^49 - 24 * q^50 - 3 * q^52 + 18 * q^53 + 30 * q^55 + 12 * q^56 + 15 * q^58 + 6 * q^59 - 24 * q^61 + 60 * q^62 + 12 * q^64 - 15 * q^65 - 15 * q^67 + 36 * q^68 + 15 * q^70 + 24 * q^73 + 24 * q^74 - 9 * q^76 + 15 * q^77 - 24 * q^79 + 42 * q^80 - 42 * q^82 - 6 * q^83 + 18 * q^85 - 30 * q^86 + 21 * q^88 + 18 * q^89 + 36 * q^91 + 6 * q^92 + 6 * q^94 - 33 * q^95 + 21 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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