LMFDB - Embedded newform 405.3.h.k.269.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(134,405)] 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("405.134"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,-48,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.11
Character	$\chi$	$=$	405.269
Dual form			405.3.h.k.134.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0484988 + 0.0840023i) q^{2} +(1.99530 + 3.45595i) q^{4} +(-0.121738 + 4.99852i) q^{5} +(-8.81825 - 5.09122i) q^{7} -0.775068 q^{8} +(-0.413983 - 0.252648i) q^{10} +(1.54895 + 0.894287i) q^{11} +(-11.8975 + 6.86902i) q^{13} +(0.855349 - 0.493836i) q^{14} +(-7.94359 + 13.7587i) q^{16} +13.0802 q^{17} -16.5731 q^{19} +(-17.5175 + 9.55280i) q^{20} +(-0.150244 + 0.0867437i) q^{22} +(-20.8350 - 36.0872i) q^{23} +(-24.9704 - 1.21702i) q^{25} -1.33256i q^{26} -40.6340i q^{28} +(38.2663 + 22.0931i) q^{29} +(-3.23261 - 5.59904i) q^{31} +(-2.32064 - 4.01947i) q^{32} +(-0.634376 + 1.09877i) q^{34} +(26.5221 - 43.4584i) q^{35} -20.6967i q^{37} +(0.803775 - 1.39218i) q^{38} +(0.0943554 - 3.87419i) q^{40} +(-49.3054 + 28.4665i) q^{41} +(-29.7314 - 17.1654i) q^{43} +7.13747i q^{44} +4.04188 q^{46} +(-30.0635 + 52.0715i) q^{47} +(27.3411 + 47.3561i) q^{49} +(1.31326 - 2.03854i) q^{50} +(-47.4780 - 27.4114i) q^{52} +25.5290 q^{53} +(-4.65868 + 7.63359i) q^{55} +(6.83474 + 3.94604i) q^{56} +(-3.71174 + 2.14297i) q^{58} +(35.1292 - 20.2819i) q^{59} +(-34.6084 + 59.9435i) q^{61} +0.627110 q^{62} -63.0986 q^{64} +(-32.8865 - 60.3060i) q^{65} +(-52.0413 + 30.0461i) q^{67} +(26.0989 + 45.2047i) q^{68} +(2.36432 + 4.33560i) q^{70} +91.1989i q^{71} +74.8762i q^{73} +(1.73857 + 1.00376i) q^{74} +(-33.0682 - 57.2759i) q^{76} +(-9.10603 - 15.7721i) q^{77} +(30.8261 - 53.3923i) q^{79} +(-67.8061 - 41.3812i) q^{80} -5.52236i q^{82} +(-29.2645 + 50.6877i) q^{83} +(-1.59237 + 65.3818i) q^{85} +(2.88387 - 1.66500i) q^{86} +(-1.20054 - 0.693133i) q^{88} -66.7514i q^{89} +139.887 q^{91} +(83.1439 - 144.009i) q^{92} +(-2.91608 - 5.05081i) q^{94} +(2.01758 - 82.8409i) q^{95} +(136.899 + 79.0389i) q^{97} -5.30403 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) $ 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.0484988	+	0.0840023i	−0.0242494	+	0.0420012i	−0.877895	−	0.478852i	$-0.841053\pi$
$2$	−0.0484988	+	0.0840023i	−0.0242494	+	0.0420012i	0.853646	+	0.520854i	$0.174386\pi$
$3$		0			0
$3$		0			0
$4$	1.99530	+	3.45595i	0.498824	+	0.863988i
$5$	−0.121738	+	4.99852i	−0.0243476	+	0.999704i
$5$	−0.121738	+	4.99852i	−0.0243476	+	0.999704i
$6$		0			0
$7$	−8.81825	−	5.09122i	−1.25975	−	0.727317i	−0.286725	−	0.958013i	$-0.592566\pi$
$7$	−8.81825	−	5.09122i	−1.25975	−	0.727317i	−0.973026	+	0.230696i	$0.925900\pi$
$8$	−0.775068			−0.0968835
$9$		0			0
$10$	−0.413983	−	0.252648i	−0.0413983	−	0.0252648i
$11$	1.54895	+	0.894287i	0.140814	+	0.0812988i	0.568752	−	0.822509i	$-0.307427\pi$
$11$	1.54895	+	0.894287i	0.140814	+	0.0812988i	−0.427938	+	0.903808i	$0.640760\pi$
$12$		0			0
$13$	−11.8975	+	6.86902i	−0.915191	+	0.528386i	−0.882098	−	0.471066i	$-0.843869\pi$
$13$	−11.8975	+	6.86902i	−0.915191	+	0.528386i	−0.0330935	+	0.999452i	$0.510536\pi$
$14$	0.855349	−	0.493836i	0.0610964	−	0.0352740i
$15$		0			0
$16$	−7.94359	+	13.7587i	−0.496475	+	0.859919i
$17$	13.0802			0.769426			0.384713	−	0.923036i	$-0.374300\pi$
$17$	13.0802			0.769426			0.384713	+	0.923036i	$0.374300\pi$
$18$		0			0
$19$	−16.5731			−0.872268			−0.436134	−	0.899882i	$-0.643653\pi$
$19$	−16.5731			−0.872268			−0.436134	+	0.899882i	$0.643653\pi$
$20$	−17.5175	+	9.55280i	−0.875877	+	0.477640i
$21$		0			0
$22$	−0.150244	+	0.0867437i	−0.00682929	+	0.00394289i
$23$	−20.8350	−	36.0872i	−0.905869	−	1.56901i	−0.819747	−	0.572726i	$-0.805886\pi$
$23$	−20.8350	−	36.0872i	−0.905869	−	1.56901i	−0.0861214	−	0.996285i	$-0.527447\pi$
$24$		0			0
$25$	−24.9704	−	1.21702i	−0.998814	−	0.0486809i
$26$		−	1.33256i		−	0.0512521i
$27$		0			0
$28$		−	40.6340i		−	1.45121i
$29$	38.2663	+	22.0931i	1.31953	+	0.761830i	0.983653	−	0.180077i	$-0.0576347\pi$
$29$	38.2663	+	22.0931i	1.31953	+	0.761830i	0.335875	+	0.941907i	$0.390968\pi$
$30$		0			0
$31$	−3.23261	−	5.59904i	−0.104278	−	0.180614i	0.809165	−	0.587581i	$-0.199920\pi$
$31$	−3.23261	−	5.59904i	−0.104278	−	0.180614i	−0.913443	+	0.406967i	$0.866586\pi$
$32$	−2.32064	−	4.01947i	−0.0725201	−	0.125609i
$33$		0			0
$34$	−0.634376	+	1.09877i	−0.0186581	+	0.0323168i
$35$	26.5221	−	43.4584i	0.757774	−	1.24167i
$36$		0			0
$37$		−	20.6967i		−	0.559370i	−0.960092	−	0.279685i	$-0.909770\pi$
$37$		−	20.6967i		−	0.559370i	0.960092	−	0.279685i	$-0.0902300\pi$
$38$	0.803775	−	1.39218i	0.0211520	−	0.0366363i
$39$		0			0
$40$	0.0943554	−	3.87419i	0.00235888	−	0.0968547i
$41$	−49.3054	+	28.4665i	−1.20257	+	0.694305i	−0.961126	−	0.276109i	$-0.910955\pi$
$41$	−49.3054	+	28.4665i	−1.20257	+	0.694305i	−0.241445	+	0.970414i	$0.577622\pi$
$42$		0			0
$43$	−29.7314	−	17.1654i	−0.691427	−	0.399196i	0.112719	−	0.993627i	$-0.464044\pi$
$43$	−29.7314	−	17.1654i	−0.691427	−	0.399196i	−0.804146	+	0.594431i	$0.797377\pi$
$44$			7.13747i			0.162215i
$45$		0			0
$46$	4.04188			0.0878670
$47$	−30.0635	+	52.0715i	−0.639649	+	1.10790i	0.345861	+	0.938286i	$0.387587\pi$
$47$	−30.0635	+	52.0715i	−0.639649	+	1.10790i	−0.985510	+	0.169618i	$0.945747\pi$
$48$		0			0
$49$	27.3411	+	47.3561i	0.557981	+	0.966451i
$50$	1.31326	−	2.03854i	0.0262653	−	0.0407709i
$51$		0			0
$52$	−47.4780	−	27.4114i	−0.913039	−	0.527143i
$53$	25.5290			0.481680			0.240840	−	0.970565i	$-0.422577\pi$
$53$	25.5290			0.481680			0.240840	+	0.970565i	$0.422577\pi$
$54$		0			0
$55$	−4.65868	+	7.63359i	−0.0847032	+	0.138793i
$56$	6.83474	+	3.94604i	0.122049	+	0.0704650i
$57$		0			0
$58$	−3.71174	+	2.14297i	−0.0639955	+	0.0369478i
$59$	35.1292	−	20.2819i	0.595411	−	0.343761i	−0.171823	−	0.985128i	$-0.554966\pi$
$59$	35.1292	−	20.2819i	0.595411	−	0.343761i	0.767234	+	0.641367i	$0.221632\pi$
$60$		0			0
$61$	−34.6084	+	59.9435i	−0.567351	+	0.982681i	0.429476	+	0.903079i	$0.358698\pi$
$61$	−34.6084	+	59.9435i	−0.567351	+	0.982681i	−0.996827	+	0.0796026i	$0.974635\pi$
$62$	0.627110			0.0101147
$63$		0			0
$64$	−63.0986			−0.985915
$65$	−32.8865	−	60.3060i	−0.505947	−	0.927785i
$66$		0			0
$67$	−52.0413	+	30.0461i	−0.776736	+	0.448449i	−0.835272	−	0.549836i	$-0.814690\pi$
$67$	−52.0413	+	30.0461i	−0.776736	+	0.448449i	0.0585360	+	0.998285i	$0.481357\pi$
$68$	26.0989	+	45.2047i	0.383808	+	0.664775i
$69$		0			0
$70$	2.36432	+	4.33560i	0.0337760	+	0.0619371i
$71$			91.1989i			1.28449i	0.766499	+	0.642246i	$0.221997\pi$
$71$			91.1989i			1.28449i	−0.766499	+	0.642246i	$0.778003\pi$
$72$		0			0
$73$			74.8762i			1.02570i	0.858478	+	0.512850i	$0.171410\pi$
$73$			74.8762i			1.02570i	−0.858478	+	0.512850i	$0.828590\pi$
$74$	1.73857	+	1.00376i	0.0234942	+	0.0135644i
$75$		0			0
$76$	−33.0682	−	57.2759i	−0.435108	−	0.753630i
$77$	−9.10603	−	15.7721i	−0.118260	−	0.204833i
$78$		0			0
$79$	30.8261	−	53.3923i	0.390203	−	0.675852i	−0.602273	−	0.798290i	$-0.705738\pi$
$79$	30.8261	−	53.3923i	0.390203	−	0.675852i	0.992476	+	0.122438i	$0.0390713\pi$
$80$	−67.8061	−	41.3812i	−0.847576	−	0.517264i
$81$		0			0
$82$		−	5.52236i		−	0.0673459i
$83$	−29.2645	+	50.6877i	−0.352585	+	0.610695i	−0.986702	−	0.162543i	$-0.948031\pi$
$83$	−29.2645	+	50.6877i	−0.352585	+	0.610695i	0.634117	+	0.773237i	$0.281364\pi$
$84$		0			0
$85$	−1.59237	+	65.3818i	−0.0187337	+	0.769198i
$86$	2.88387	−	1.66500i	0.0335334	−	0.0193605i
$87$		0			0
$88$	−1.20054	−	0.693133i	−0.0136425	−	0.00787651i
$89$		−	66.7514i		−	0.750016i	−0.927022	−	0.375008i	$-0.877640\pi$
$89$		−	66.7514i		−	0.750016i	0.927022	−	0.375008i	$-0.122360\pi$
$90$		0			0
$91$	139.887			1.53722
$92$	83.1439	−	144.009i	0.903738	−	1.56532i
$93$		0			0
$94$	−2.91608	−	5.05081i	−0.0310222	−	0.0537320i
$95$	2.01758	−	82.8409i	0.0212377	−	0.872010i
$96$		0			0
$97$	136.899	+	79.0389i	1.41133	+	0.814834i	0.995514	−	0.0946130i	$-0.0301614\pi$
$97$	136.899	+	79.0389i	1.41133	+	0.814834i	0.415820	+	0.909447i	$0.363495\pi$
$98$	−5.30403			−0.0541228
$99$		0			0
$100$	−45.6173	−	88.7247i	−0.456173	−	0.887247i
$101$	82.9054	+	47.8654i	0.820845	+	0.473915i	0.850708	−	0.525639i	$-0.176174\pi$
$101$	82.9054	+	47.8654i	0.820845	+	0.473915i	−0.0298626	+	0.999554i	$0.509507\pi$
$102$		0			0
$103$	82.7872	−	47.7972i	0.803759	−	0.464051i	−0.0410247	−	0.999158i	$-0.513062\pi$
$103$	82.7872	−	47.7972i	0.803759	−	0.464051i	0.844784	+	0.535107i	$0.179729\pi$
$104$	9.22136	−	5.32395i	0.0886669	−	0.0511919i
$105$		0			0
$106$	−1.23813	+	2.14450i	−0.0116804	+	0.0202311i
$107$	−60.3812			−0.564310			−0.282155	−	0.959369i	$-0.591049\pi$
$107$	−60.3812			−0.564310			−0.282155	+	0.959369i	$0.591049\pi$
$108$		0			0
$109$	80.8515			0.741757			0.370878	−	0.928681i	$-0.379057\pi$
$109$	80.8515			0.741757			0.370878	+	0.928681i	$0.379057\pi$
$110$	−0.415299	−	0.761560i	−0.00377545	−	0.00692327i
$111$		0			0
$112$	140.097	−	80.8852i	1.25087	−	0.722189i
$113$	61.8236	+	107.082i	0.547112	+	0.947625i	0.998471	+	0.0552829i	$0.0176061\pi$
$113$	61.8236	+	107.082i	0.547112	+	0.947625i	−0.451359	+	0.892342i	$0.649061\pi$
$114$		0			0
$115$	182.919	−	99.7508i	1.59060	−	0.867398i
$116$			176.329i			1.52008i
$117$		0			0
$118$			3.93458i			0.0333439i
$119$	−115.345	−	66.5944i	−0.969285	−	0.559617i
$120$		0			0
$121$	−58.9005	−	102.019i	−0.486781	−	0.843129i
$122$	−3.35693	−	5.81438i	−0.0275158	−	0.0476588i
$123$		0			0
$124$	12.9000	−	22.3435i	0.104032	−	0.180189i
$125$	9.12315	−	124.667i	0.0729852	−	0.997333i
$126$		0			0
$127$			151.814i			1.19539i	0.801724	+	0.597694i	$0.203916\pi$
$127$			151.814i			1.19539i	−0.801724	+	0.597694i	$0.796084\pi$
$128$	12.3428	−	21.3783i	0.0964280	−	0.167018i
$129$		0			0
$130$	6.66080	+	0.162223i	0.0512369	+	0.00124787i
$131$	−135.726	+	78.3614i	−1.03608	+	0.598178i	−0.918719	−	0.394911i	$-0.870775\pi$
$131$	−135.726	+	78.3614i	−1.03608	+	0.598178i	−0.117356	+	0.993090i	$0.537442\pi$
$132$		0			0
$133$	146.146	+	84.3773i	1.09884	+	0.634416i
$134$		−	5.82879i		−	0.0434985i
$135$		0			0
$136$	−10.1381			−0.0745446
$137$	−37.7777	+	65.4329i	−0.275750	+	0.477613i	−0.970324	−	0.241808i	$-0.922259\pi$
$137$	−37.7777	+	65.4329i	−0.275750	+	0.477613i	0.694574	+	0.719421i	$0.255593\pi$
$138$		0			0
$139$	−47.7956	−	82.7844i	−0.343853	−	0.595571i	0.641291	−	0.767297i	$-0.278399\pi$
$139$	−47.7956	−	82.7844i	−0.343853	−	0.595571i	−0.985145	+	0.171726i	$0.945066\pi$
$140$	203.110	+	4.94671i	1.45078	+	0.0353336i
$141$		0			0
$142$	−7.66092	−	4.42303i	−0.0539501	−	0.0311481i
$143$	−24.5715			−0.171829
$144$		0			0
$145$	−115.091	+	188.585i	−0.793731	+	1.30059i
$146$	−6.28977	−	3.63140i	−0.0430806	−	0.0248726i
$147$		0			0
$148$	71.5268	−	41.2960i	0.483289	−	0.279027i
$149$	41.8031	−	24.1350i	0.280557	−	0.161980i	−0.353118	−	0.935579i	$-0.614879\pi$
$149$	41.8031	−	24.1350i	0.280557	−	0.161980i	0.633676	+	0.773599i	$0.281545\pi$
$150$		0			0
$151$	11.4151	−	19.7716i	0.0755968	−	0.130938i	−0.825749	−	0.564038i	$-0.809247\pi$
$151$	11.4151	−	19.7716i	0.0755968	−	0.130938i	0.901346	+	0.433100i	$0.142580\pi$
$152$	12.8453			0.0845084
$153$		0			0
$154$	1.76652			0.0114709
$155$	28.3804	−	15.4766i	0.183100	−	0.0998493i
$156$		0			0
$157$	−101.514	+	58.6091i	−0.646585	+	0.373306i	−0.787147	−	0.616766i	$-0.788443\pi$
$157$	−101.514	+	58.6091i	−0.646585	+	0.373306i	0.140561	+	0.990072i	$0.455109\pi$
$158$	2.99005	+	5.17892i	0.0189244	+	0.0327780i
$159$		0			0
$160$	20.3739	−	11.1105i	0.127337	−	0.0694404i
$161$			424.302i			2.63542i
$162$		0			0
$163$			91.1992i			0.559504i	0.960072	+	0.279752i	$0.0902523\pi$
$163$			91.1992i			0.559504i	−0.960072	+	0.279752i	$0.909748\pi$
$164$	−196.758	−	113.598i	−1.19974	−	0.692672i
$165$		0			0
$166$	−2.83859	−	4.91658i	−0.0170999	−	0.0296179i
$167$	82.1001	+	142.201i	0.491617	+	0.851506i	0.999953	−	0.00965281i	$-0.00307263\pi$
$167$	82.1001	+	142.201i	0.491617	+	0.851506i	−0.508336	+	0.861159i	$0.669739\pi$
$168$		0			0
$169$	9.86679	−	17.0898i	0.0583834	−	0.101123i
$170$	−5.41500	−	3.30470i	−0.0318529	−	0.0194394i
$171$		0			0
$172$		−	137.000i		−	0.796513i
$173$	112.723	−	195.241i	0.651576	−	1.12856i	−0.331164	−	0.943573i	$-0.607441\pi$
$173$	112.723	−	195.241i	0.651576	−	1.12856i	0.982740	−	0.184990i	$-0.0592252\pi$
$174$		0			0
$175$	213.999	+	137.862i	1.22285	+	0.787781i
$176$	−24.6085	+	14.2077i	−0.139821	+	0.0807256i
$177$		0			0
$178$	5.60728	+	3.23736i	0.0315016	+	0.0181874i
$179$		−	349.517i		−	1.95261i	−0.216395	−	0.976306i	$-0.569430\pi$
$179$		−	349.517i		−	1.95261i	0.216395	−	0.976306i	$-0.430570\pi$
$180$		0			0
$181$	254.586			1.40655			0.703275	−	0.710918i	$-0.251720\pi$
$181$	254.586			1.40655			0.703275	+	0.710918i	$0.251720\pi$
$182$	−6.78434	+	11.7508i	−0.0372766	+	0.0645649i
$183$		0			0
$184$	16.1485	+	27.9701i	0.0877637	+	0.152011i
$185$	103.453	+	2.51958i	0.559204	+	0.0136193i
$186$		0			0
$187$	20.2607	+	11.6975i	0.108346	+	0.0625534i
$188$	−239.942			−1.27629
$189$		0			0
$190$	6.86098	+	4.18716i	0.0361104	+	0.0220377i
$191$	232.380	+	134.165i	1.21665	+	0.702433i	0.964200	−	0.265177i	$-0.0854305\pi$
$191$	232.380	+	134.165i	1.21665	+	0.702433i	0.252450	+	0.967610i	$0.418764\pi$
$192$		0			0
$193$	−265.924	+	153.531i	−1.37784	+	0.795499i	−0.991900	−	0.127023i	$-0.959458\pi$
$193$	−265.924	+	153.531i	−1.37784	+	0.795499i	−0.385944	+	0.922522i	$0.626124\pi$
$194$	−13.2789	+	7.66658i	−0.0684480	+	0.0395185i
$195$		0			0
$196$	−109.107	+	188.979i	−0.556668	+	0.964178i
$197$	−62.4666			−0.317089			−0.158545	−	0.987352i	$-0.550680\pi$
$197$	−62.4666			−0.317089			−0.158545	+	0.987352i	$0.550680\pi$
$198$		0			0
$199$	74.6147			0.374948			0.187474	−	0.982270i	$-0.439970\pi$
$199$	74.6147			0.374948			0.187474	+	0.982270i	$0.439970\pi$
$200$	19.3537	+	0.943274i	0.0967686	+	0.00471637i
$201$		0			0
$202$	−8.04162	+	4.64283i	−0.0398100	+	0.0229843i
$203$	−224.961	−	389.644i	−1.10818	−	1.91943i
$204$		0			0
$205$	−136.288	−	249.920i	−0.664820	−	1.21912i
$206$			9.27243i			0.0450118i
$207$		0			0
$208$		−	218.259i		−	1.04932i
$209$	−25.6709	−	14.8211i	−0.122827	−	0.0709144i
$210$		0			0
$211$	−81.7692	−	141.628i	−0.387532	−	0.671225i	0.604585	−	0.796541i	$-0.293339\pi$
$211$	−81.7692	−	141.628i	−0.387532	−	0.671225i	−0.992117	+	0.125316i	$0.960006\pi$
$212$	50.9380	+	88.2271i	0.240273	+	0.416166i
$213$		0			0
$214$	2.92841	−	5.07216i	0.0136842	−	0.0237017i
$215$	89.4211	−	146.523i	0.415912	−	0.681503i
$216$		0			0
$217$			65.8317i			0.303372i
$218$	−3.92120	+	6.79171i	−0.0179871	+	0.0311546i
$219$		0			0
$220$	−35.6768	−	0.868903i	−0.162167	−	0.00394956i
$221$	−155.622	+	89.8484i	−0.704172	+	0.406554i
$222$		0			0
$223$	15.5644	+	8.98609i	0.0697954	+	0.0402964i	0.534492	−	0.845174i	$-0.320503\pi$
$223$	15.5644	+	8.98609i	0.0697954	+	0.0402964i	−0.464696	+	0.885470i	$0.653836\pi$
$224$			47.2597i			0.210981i
$225$		0			0
$226$	−11.9935			−0.0530685
$227$	−16.0367	+	27.7764i	−0.0706464	+	0.122363i	−0.899185	−	0.437569i	$-0.855840\pi$
$227$	−16.0367	+	27.7764i	−0.0706464	+	0.122363i	0.828538	+	0.559932i	$0.189173\pi$
$228$		0			0
$229$	80.3274	+	139.131i	0.350775	+	0.607559i	0.986385	−	0.164450i	$-0.0525850\pi$
$229$	80.3274	+	139.131i	0.350775	+	0.607559i	−0.635611	+	0.772010i	$0.719252\pi$
$230$	−0.492052	+	20.2034i	−0.00213936	+	0.0878410i
$231$		0			0
$232$	−29.6590	−	17.1236i	−0.127840	−	0.0738087i
$233$	345.174			1.48143			0.740717	−	0.671817i	$-0.234486\pi$
$233$	345.174			1.48143			0.740717	+	0.671817i	$0.234486\pi$
$234$		0			0
$235$	−256.620	−	156.612i	−1.09200	−	0.666434i
$236$	140.186	+	80.9367i	0.594010	+	0.342952i
$237$		0			0
$238$	11.1882	−	6.45949i	0.0470091	−	0.0271407i
$239$	93.8860	−	54.2051i	0.392828	−	0.226800i	−0.290557	−	0.956858i	$-0.593840\pi$
$239$	93.8860	−	54.2051i	0.392828	−	0.226800i	0.683385	+	0.730058i	$0.260507\pi$
$240$		0			0
$241$	−109.271	+	189.263i	−0.453406	+	0.785323i	−0.998595	−	0.0529906i	$-0.983125\pi$
$241$	−109.271	+	189.263i	−0.453406	+	0.785323i	0.545189	+	0.838313i	$0.316458\pi$
$242$	11.4264			0.0472166
$243$		0			0
$244$	−276.216			−1.13203
$245$	−240.039	+	130.900i	−0.979750	+	0.534285i
$246$		0			0
$247$	197.178	−	113.841i	0.798292	−	0.460894i
$248$	2.50549	+	4.33964i	0.0101028	+	0.0174985i
$249$		0			0
$250$	10.0298	+	6.81254i	0.0401193	+	0.0272502i
$251$			178.976i			0.713053i	0.934285	+	0.356527i	$0.116039\pi$
$251$			178.976i			0.713053i	−0.934285	+	0.356527i	$0.883961\pi$
$252$		0			0
$253$		−	74.5298i		−	0.294584i
$254$	−12.7528	−	7.36281i	−0.0502077	−	0.0289874i
$255$		0			0
$256$	−125.000	−	216.506i	−0.488281	−	0.845727i
$257$	−213.437	−	369.683i	−0.830493	−	1.43846i	−0.897647	−	0.440714i	$-0.854725\pi$
$257$	−213.437	−	369.683i	−0.830493	−	1.43846i	0.0671541	−	0.997743i	$-0.478608\pi$
$258$		0			0
$259$	−105.371	+	182.509i	−0.406840	+	0.704667i
$260$	142.796	−	233.983i	0.549217	−	0.899933i
$261$		0			0
$262$		−	15.2017i		−	0.0580218i
$263$	−194.336	+	336.599i	−0.738919	+	1.27984i	0.214064	+	0.976820i	$0.431330\pi$
$263$	−194.336	+	336.599i	−0.738919	+	1.27984i	−0.952983	+	0.303025i	$0.902003\pi$
$264$		0			0
$265$	−3.10786	+	127.607i	−0.0117278	+	0.481537i
$266$	−14.1758	+	8.18439i	−0.0532924	+	0.0307684i
$267$		0			0
$268$	−207.676	−	119.902i	−0.774909	−	0.447394i
$269$		−	57.7020i		−	0.214506i	−0.994232	−	0.107253i	$-0.965795\pi$
$269$		−	57.7020i		−	0.214506i	0.994232	−	0.107253i	$-0.0342054\pi$
$270$		0			0
$271$	−102.825			−0.379428			−0.189714	−	0.981839i	$-0.560756\pi$
$271$	−102.825			−0.379428			−0.189714	+	0.981839i	$0.560756\pi$
$272$	−103.904	+	179.967i	−0.382000	+	0.661644i
$273$		0			0
$274$	−3.66435	−	6.34683i	−0.0133735	−	0.0231636i
$275$	−37.5895	−	24.2158i	−0.136689	−	0.0880574i
$276$		0			0
$277$	−438.281	−	253.042i	−1.58224	−	0.913508i	−0.994531	−	0.104438i	$-0.966696\pi$
$277$	−438.281	−	253.042i	−1.58224	−	0.913508i	−0.587712	−	0.809070i	$-0.699971\pi$
$278$	9.27211			0.0333529
$279$		0			0
$280$	−20.5564	+	33.6832i	−0.0734157	+	0.120297i
$281$	−75.2955	−	43.4719i	−0.267956	−	0.154704i	0.360003	−	0.932951i	$-0.382776\pi$
$281$	−75.2955	−	43.4719i	−0.267956	−	0.154704i	−0.627958	+	0.778247i	$0.716109\pi$
$282$		0			0
$283$	79.8056	−	46.0758i	0.281998	−	0.162812i	−0.352329	−	0.935876i	$-0.614610\pi$
$283$	79.8056	−	46.0758i	0.281998	−	0.162812i	0.634328	+	0.773064i	$0.281277\pi$
$284$	−315.179	+	181.969i	−1.10979	+	0.640735i
$285$		0			0
$286$	1.19169	−	2.06406i	0.00416674	−	0.00721701i
$287$	579.717			2.01992
$288$		0			0
$289$	−117.907			−0.407984
$290$	−10.2598	−	18.8141i	−0.0353787	−	0.0648761i
$291$		0			0
$292$	−258.769	+	149.400i	−0.886194	+	0.511644i
$293$	197.351	+	341.822i	0.673554	+	1.16663i	0.976889	+	0.213745i	$0.0685662\pi$
$293$	197.351	+	341.822i	0.673554	+	1.16663i	−0.303336	+	0.952884i	$0.598100\pi$
$294$		0			0
$295$	97.1028	+	178.063i	0.329162	+	0.603604i
$296$			16.0413i			0.0541937i
$297$		0			0
$298$			4.68207i			0.0157117i
$299$	495.768	+	286.232i	1.65809	+	0.957296i
$300$		0			0
$301$	174.786	+	302.738i	0.580684	+	1.00577i
$302$	1.10724	+	1.91779i	0.00366635	+	0.00635031i
$303$		0			0
$304$	131.650	−	228.024i	0.433059	−	0.750080i
$305$	−295.416	−	180.288i	−0.968576	−	0.591109i
$306$		0			0
$307$		−	296.956i		−	0.967283i	−0.875266	−	0.483642i	$-0.839314\pi$
$307$		−	296.956i		−	0.967283i	0.875266	−	0.483642i	$-0.160686\pi$
$308$	36.3384	−	62.9400i	0.117982	−	0.204351i
$309$		0			0
$310$	−0.0763433	+	3.13462i	−0.000246269	+	0.0101117i
$311$	−467.099	+	269.679i	−1.50192	+	0.867137i	−0.501927	+	0.864910i	$0.667375\pi$
$311$	−467.099	+	269.679i	−1.50192	+	0.867137i	−0.999998	+	0.00222672i	$0.999291\pi$
$312$		0			0
$313$	−380.914	−	219.921i	−1.21698	−	0.702623i	−0.252708	−	0.967542i	$-0.581321\pi$
$313$	−380.914	−	219.921i	−1.21698	−	0.702623i	−0.964271	+	0.264919i	$0.914655\pi$
$314$		−	11.3699i		−	0.0362098i
$315$		0			0
$316$	246.029			0.778571
$317$	122.438	−	212.069i	0.386240	−	0.668987i	−0.605701	−	0.795693i	$-0.707107\pi$
$317$	122.438	−	212.069i	0.386240	−	0.668987i	0.991940	+	0.126706i	$0.0404404\pi$
$318$		0			0
$319$	39.5151	+	68.4421i	0.123872	+	0.214552i
$320$	7.68151	−	315.399i	0.0240047	−	0.985623i
$321$		0			0
$322$	−35.6423	−	20.5781i	−0.110691	−	0.0639072i
$323$	−216.780			−0.671146
$324$		0			0
$325$	305.444	−	157.042i	0.939828	−	0.483207i
$326$	−7.66095	−	4.42305i	−0.0234998	−	0.0135676i
$327$		0			0
$328$	38.2151	−	22.0635i	0.116509	−	0.0672667i
$329$	530.215	−	306.120i	1.61160	−	0.930455i
$330$		0			0
$331$	−180.657	+	312.906i	−0.545790	+	0.945336i	0.452767	+	0.891629i	$0.350437\pi$
$331$	−180.657	+	312.906i	−0.545790	+	0.945336i	−0.998557	+	0.0537071i	$0.982896\pi$
$332$	−233.566			−0.703511
$333$		0			0
$334$	−15.9270			−0.0476857
$335$	−143.850	−	263.787i	−0.429404	−	0.787425i
$336$		0			0
$337$	−218.562	+	126.187i	−0.648552	+	0.374442i	−0.787901	−	0.615801i	$-0.788832\pi$
$337$	−218.562	+	126.187i	−0.648552	+	0.374442i	0.139349	+	0.990243i	$0.455499\pi$
$338$	0.957055	+	1.65767i	0.00283152	+	0.00490434i
$339$		0			0
$340$	−229.134	+	124.953i	−0.673923	+	0.367509i
$341$		−	11.5635i		−	0.0339106i
$342$		0			0
$343$		−	57.8579i		−	0.168682i
$344$	23.0438	+	13.3044i	0.0669879	+	0.0386755i
$345$		0			0
$346$	10.9338	+	18.9379i	0.0316006	+	0.0547339i
$347$	−53.9964	−	93.5244i	−0.155609	−	0.269523i	0.777672	−	0.628671i	$-0.216401\pi$
$347$	−53.9964	−	93.5244i	−0.155609	−	0.269523i	−0.933281	+	0.359148i	$0.883067\pi$
$348$		0			0
$349$	0.857841	−	1.48582i	0.00245800	−	0.00425738i	−0.864794	−	0.502127i	$-0.832551\pi$
$349$	0.857841	−	1.48582i	0.00245800	−	0.00425738i	0.867252	+	0.497870i	$0.165884\pi$
$350$	−21.9594	+	11.2903i	−0.0627411	+	0.0322580i
$351$		0			0
$352$		−	8.30129i		−	0.0235832i
$353$	−74.5906	+	129.195i	−0.211305	+	0.365991i	−0.952123	−	0.305715i	$-0.901105\pi$
$353$	−74.5906	+	129.195i	−0.211305	+	0.365991i	0.740818	+	0.671705i	$0.234438\pi$
$354$		0			0
$355$	−455.859	−	11.1024i	−1.28411	−	0.0312743i
$356$	230.690	−	133.189i	0.648005	−	0.374126i
$357$		0			0
$358$	29.3603	+	16.9512i	0.0820120	+	0.0473496i
$359$			108.011i			0.300865i	0.988620	+	0.150433i	$0.0480666\pi$
$359$			108.011i			0.300865i	−0.988620	+	0.150433i	$0.951933\pi$
$360$		0			0
$361$	−86.3325			−0.239148
$362$	−12.3471	+	21.3858i	−0.0341080	+	0.0590768i
$363$		0			0
$364$	279.115	+	483.442i	0.766801	+	1.32814i
$365$	−374.270	−	9.11529i	−1.02540	−	0.0249734i
$366$		0			0
$367$	415.166	+	239.696i	1.13124	+	0.653123i	0.944247	−	0.329237i	$-0.106792\pi$
$367$	415.166	+	239.696i	1.13124	+	0.653123i	0.186996	+	0.982361i	$0.440125\pi$
$368$	662.018			1.79896
$369$		0			0
$370$	−5.22898	+	8.56808i	−0.0141324	+	0.0231570i
$371$	−225.121	−	129.974i	−0.606796	−	0.350334i
$372$		0			0
$373$	−91.0064	+	52.5426i	−0.243985	+	0.140865i	−0.617007	−	0.786958i	$-0.711655\pi$
$373$	−91.0064	+	52.5426i	−0.243985	+	0.140865i	0.373022	+	0.927823i	$0.378322\pi$
$374$	−1.96523	+	1.13463i	−0.00525464	+	0.00303376i
$375$		0			0
$376$	23.3012	−	40.3589i	0.0619714	−	0.107338i
$377$	−607.030			−1.61016
$378$		0			0
$379$	−175.029			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$379$	−175.029			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$380$	290.320	−	158.319i	0.764000	−	0.416630i
$381$		0			0
$382$	−22.5403	+	13.0136i	−0.0590060	+	0.0340671i
$383$	155.870	+	269.975i	0.406972	+	0.704896i	0.994549	−	0.104272i	$-0.0332513\pi$
$383$	155.870	+	269.975i	0.406972	+	0.704896i	−0.587577	+	0.809168i	$0.699918\pi$
$384$		0			0
$385$	79.9457	−	43.5966i	0.207651	−	0.113238i
$386$		−	29.7843i		−	0.0771614i
$387$		0			0
$388$			630.824i			1.62583i
$389$	10.1966	+	5.88701i	0.0262123	+	0.0151337i	0.513049	−	0.858359i	$-0.328516\pi$
$389$	10.1966	+	5.88701i	0.0262123	+	0.0151337i	−0.486837	+	0.873493i	$0.661849\pi$
$390$		0			0
$391$	−272.526	−	472.030i	−0.696999	−	1.20724i
$392$	−21.1912	−	36.7042i	−0.0540591	−	0.0936332i
$393$		0			0
$394$	3.02955	−	5.24734i	0.00768922	−	0.0133181i
$395$	263.130	+	160.585i	0.666151	+	0.406543i
$396$		0			0
$397$			261.770i			0.659369i	0.944091	+	0.329685i	$0.106942\pi$
$397$			261.770i			0.659369i	−0.944091	+	0.329685i	$0.893058\pi$
$398$	−3.61872	+	6.26781i	−0.00909227	+	0.0157483i
$399$		0			0
$400$	215.099	−	333.892i	0.537748	−	0.834731i
$401$	286.137	−	165.201i	0.713559	−	0.411973i	−0.0988186	−	0.995105i	$-0.531506\pi$
$401$	286.137	−	165.201i	0.713559	−	0.411973i	0.812377	+	0.583132i	$0.198173\pi$
$402$		0			0
$403$	76.9198	+	44.4097i	0.190868	+	0.110198i
$404$			382.023i			0.945601i
$405$		0			0
$406$	43.6414			0.107491
$407$	18.5088	−	32.0582i	0.0454761	−	0.0787670i
$408$		0			0
$409$	−255.501	−	442.540i	−0.624696	−	1.08201i	−0.988599	−	0.150569i	$-0.951889\pi$
$409$	−255.501	−	442.540i	−0.624696	−	1.08201i	0.363903	−	0.931437i	$-0.381444\pi$
$410$	27.6036	+	0.672283i	0.0673259	+	0.00163971i
$411$		0			0
$412$	330.370	+	190.739i	0.801869	+	0.462959i
$413$	−413.038			−1.00009
$414$		0			0
$415$	−249.801	−	152.450i	−0.601929	−	0.367349i
$416$	55.2197	+	31.8811i	0.132740	+	0.0766372i
$417$		0			0
$418$	2.49002	−	1.43761i	0.00595698	−	0.00343926i
$419$	52.9387	−	30.5642i	0.126345	−	0.0729455i	−0.435495	−	0.900191i	$-0.643427\pi$
$419$	52.9387	−	30.5642i	0.126345	−	0.0729455i	0.561841	+	0.827245i	$0.310093\pi$
$420$		0			0
$421$	309.246	−	535.629i	0.734551	−	1.27228i	−0.220370	−	0.975416i	$-0.570726\pi$
$421$	309.246	−	535.629i	0.734551	−	1.27228i	0.954920	−	0.296862i	$-0.0959403\pi$
$422$	15.8628			0.0375896
$423$		0			0
$424$	−19.7867			−0.0466668
$425$	−326.618	−	15.9189i	−0.768514	−	0.0374563i
$426$		0			0
$427$	610.372	−	352.398i	1.42944	−	0.825289i
$428$	−120.478	−	208.674i	−0.281491	−	0.487557i
$429$		0			0
$430$	7.97147	+	14.6178i	0.0185383	+	0.0339948i
$431$		−	344.839i		−	0.800089i	−0.916496	−	0.400045i	$-0.868995\pi$
$431$		−	344.839i		−	0.800089i	0.916496	−	0.400045i	$-0.131005\pi$
$432$		0			0
$433$		−	164.525i		−	0.379966i	−0.981787	−	0.189983i	$-0.939157\pi$
$433$		−	164.525i		−	0.379966i	0.981787	−	0.189983i	$-0.0608433\pi$
$434$	−5.53002	−	3.19276i	−0.0127420	−	0.00735658i
$435$		0			0
$436$	161.323	+	279.419i	0.370006	+	0.640869i
$437$	345.300	+	598.077i	0.790160	+	1.36860i
$438$		0			0
$439$	163.542	−	283.263i	0.372533	−	0.645246i	−0.617422	−	0.786632i	$-0.711823\pi$
$439$	163.542	−	283.263i	0.372533	−	0.645246i	0.989954	+	0.141387i	$0.0451561\pi$
$440$	3.61079	−	5.91655i	0.00820634	−	0.0134467i
$441$		0			0
$442$		−	17.4301i		−	0.0394347i
$443$	178.631	−	309.398i	0.403230	−	0.698415i	−0.590884	−	0.806757i	$-0.701221\pi$
$443$	178.631	−	309.398i	0.403230	−	0.698415i	0.994114	+	0.108342i	$0.0345541\pi$
$444$		0			0
$445$	333.658	+	8.12620i	0.749794	+	0.0182611i
$446$	−1.50971	+	0.871629i	−0.00338499	+	0.00195432i
$447$		0			0
$448$	556.419	+	321.249i	1.24201	+	0.717073i
$449$			154.756i			0.344668i	0.985039	+	0.172334i	$0.0551309\pi$
$449$			154.756i			0.344668i	−0.985039	+	0.172334i	$0.944869\pi$
$450$		0			0
$451$	−101.829			−0.225785
$452$	−246.713	+	427.319i	−0.545825	+	0.945396i
$453$		0			0
$454$	−1.55552	−	2.69425i	−0.00342626	−	0.00593446i
$455$	−17.0296	+	699.226i	−0.0374276	+	1.53676i
$456$		0			0
$457$	−134.021	−	77.3772i	−0.293263	−	0.169316i	0.346149	−	0.938179i	$-0.387489\pi$
$457$	−134.021	−	77.3772i	−0.293263	−	0.169316i	−0.639413	+	0.768864i	$0.720822\pi$
$458$	−15.5831			−0.0340243
$459$		0			0
$460$	709.712	+	433.128i	1.54285	+	0.941582i
$461$	−226.337	−	130.676i	−0.490970	−	0.283462i	0.234007	−	0.972235i	$-0.424816\pi$
$461$	−226.337	−	130.676i	−0.490970	−	0.283462i	−0.724977	+	0.688773i	$0.758149\pi$
$462$		0			0
$463$	689.113	−	397.860i	1.48837	−	0.859308i	0.488454	−	0.872590i	$-0.337561\pi$
$463$	689.113	−	397.860i	1.48837	−	0.859308i	0.999912	+	0.0132816i	$0.00422778\pi$
$464$	−607.944	+	350.997i	−1.31022	+	0.756458i
$465$		0			0
$466$	−16.7405	+	28.9954i	−0.0359239	+	0.0622220i
$467$	427.874			0.916218			0.458109	−	0.888896i	$-0.348527\pi$
$467$	427.874			0.916218			0.458109	+	0.888896i	$0.348527\pi$
$468$		0			0
$469$	611.885			1.30466
$470$	25.6015	−	13.9612i	0.0544714	−	0.0297047i
$471$		0			0
$472$	−27.2275	+	15.7198i	−0.0576855	+	0.0333047i
$473$	−30.7016	−	53.1768i	−0.0649083	−	0.112424i
$474$		0			0
$475$	413.836	+	20.1698i	0.871234	+	0.0424628i
$476$		−	531.502i		−	1.11660i
$477$		0			0
$478$			10.5155i			0.0219990i
$479$	188.554	+	108.862i	0.393641	+	0.227269i	0.683736	−	0.729729i	$-0.260354\pi$
$479$	188.554	+	108.862i	0.393641	+	0.227269i	−0.290096	+	0.956998i	$0.593687\pi$
$480$		0			0
$481$	142.166	+	246.239i	0.295563	+	0.511931i
$482$	−10.5990	−	18.3580i	−0.0219896	−	0.0380872i
$483$		0			0
$484$	235.048	−	407.115i	0.485636	−	0.841146i
$485$	−411.743	+	674.672i	−0.848955	+	1.39108i
$486$		0			0
$487$		−	106.417i		−	0.218515i	−0.994013	−	0.109257i	$-0.965153\pi$
$487$		−	106.417i		−	0.218515i	0.994013	−	0.109257i	$-0.0348473\pi$
$488$	26.8239	−	46.4603i	0.0549670	−	0.0952056i
$489$		0			0
$490$	0.645704	−	26.5123i	0.00131776	−	0.0541067i
$491$	526.599	−	304.032i	1.07250	−	0.619210i	0.143639	−	0.989630i	$-0.454120\pi$
$491$	526.599	−	304.032i	1.07250	−	0.619210i	0.928864	+	0.370420i	$0.120786\pi$
$492$		0			0
$493$	500.532	+	288.983i	1.01528	+	0.586171i
$494$			22.0846i			0.0447056i
$495$		0			0
$496$	102.714			0.207085
$497$	464.314	−	804.215i	0.934233	−	1.61814i
$498$		0			0
$499$	−284.944	−	493.538i	−0.571030	−	0.989054i	−0.996460	−	0.0840624i	$-0.973211\pi$
$499$	−284.944	−	493.538i	−0.571030	−	0.989054i	0.425430	−	0.904991i	$-0.360123\pi$
$500$	449.045	−	217.218i	0.898091	−	0.434435i
$501$		0			0
$502$	−15.0344	−	8.68014i	−0.0299491	−	0.0172911i
$503$	−811.764			−1.61385			−0.806923	−	0.590657i	$-0.798869\pi$
$503$	−811.764			−1.61385			−0.806923	+	0.590657i	$0.798869\pi$
$504$		0			0
$505$	−249.349	+	408.577i	−0.493760	+	0.809063i
$506$	6.26068	+	3.61460i	0.0123729	+	0.00714349i
$507$		0			0
$508$	−524.663	+	302.914i	−1.03280	+	0.596288i
$509$	293.109	−	169.227i	0.575853	−	0.332469i	−0.183631	−	0.982995i	$-0.558785\pi$
$509$	293.109	−	169.227i	0.575853	−	0.332469i	0.759484	+	0.650527i	$0.225452\pi$
$510$		0			0
$511$	381.211	−	660.277i	0.746010	−	1.29213i
$512$	122.992			0.240218
$513$		0			0
$514$	41.4057			0.0805558
$515$	228.837	+	419.632i	0.444343	+	0.814820i
$516$		0			0
$517$	−93.1337	+	53.7708i	−0.180143	+	0.104005i
$518$	−10.2208	−	17.7029i	−0.0197312	−	0.0341755i
$519$		0			0
$520$	25.4893	+	46.7413i	0.0490179	+	0.0898870i
$521$		−	90.5848i		−	0.173867i	−0.996214	−	0.0869336i	$-0.972293\pi$
$521$		−	90.5848i		−	0.173867i	0.996214	−	0.0869336i	$-0.0277068\pi$
$522$		0			0
$523$		−	350.782i		−	0.670712i	−0.942091	−	0.335356i	$-0.891143\pi$
$523$		−	350.782i		−	0.670712i	0.942091	−	0.335356i	$-0.108857\pi$
$524$	−541.627	−	312.708i	−1.03364	−	0.596771i
$525$		0			0
$526$	−18.8501	−	32.6493i	−0.0358367	−	0.0620709i
$527$	−42.2833	−	73.2368i	−0.0802340	−	0.138969i
$528$		0			0
$529$	−603.692	+	1045.63i	−1.14120	+	1.97661i
$530$	−10.5686	−	6.44986i	−0.0199407	−	0.0121696i
$531$		0			0
$532$			673.431i			1.26585i
$533$	391.074	−	677.360i	0.733722	−	1.27084i
$534$		0			0
$535$	7.35069	−	301.816i	0.0137396	−	0.564143i
$536$	40.3356	−	23.2877i	0.0752529	−	0.0434473i
$537$		0			0
$538$	4.84711	+	2.79848i	0.00900949	+	0.00520163i
$539$			97.8031i			0.181453i
$540$		0			0
$541$	−845.632			−1.56309			−0.781545	−	0.623848i	$-0.785568\pi$
$541$	−845.632			−1.56309			−0.781545	+	0.623848i	$0.785568\pi$
$542$	4.98689	−	8.63754i	0.00920090	−	0.0159364i
$543$		0			0
$544$	−30.3546	−	52.5757i	−0.0557989	−	0.0966465i
$545$	−9.84272	+	404.138i	−0.0180600	+	0.741537i
$546$		0			0
$547$	85.5754	+	49.4070i	0.156445	+	0.0903235i	0.576179	−	0.817324i	$-0.304543\pi$
$547$	85.5754	+	49.4070i	0.156445	+	0.0903235i	−0.419734	+	0.907647i	$0.637877\pi$
$548$	−301.511			−0.550202
$549$		0			0
$550$	3.85723	−	1.98317i	0.00701314	−	0.00360576i
$551$	−634.191	−	366.150i	−1.15098	−	0.664520i
$552$		0			0
$553$	−543.664	+	313.885i	−0.983118	+	0.567603i
$554$	42.5122	−	24.5444i	0.0767368	−	0.0443040i
$555$		0			0
$556$	190.733	−	330.359i	0.343044	−	0.594170i
$557$	−569.696			−1.02279			−0.511397	−	0.859345i	$-0.670872\pi$
$557$	−569.696			−1.02279			−0.511397	+	0.859345i	$0.670872\pi$
$558$		0			0
$559$	471.638			0.843717
$560$	387.251	+	710.125i	0.691519	+	1.26808i
$561$		0			0
$562$	7.30348	−	4.21667i	0.0129955	−	0.00750297i
$563$	−315.194	−	545.931i	−0.559847	−	0.969683i	−0.997509	−	0.0705431i	$-0.977527\pi$
$563$	−315.194	−	545.931i	−0.559847	−	0.969683i	0.437662	−	0.899139i	$-0.355807\pi$
$564$		0			0
$565$	−542.776	+	295.991i	−0.960665	+	0.523877i
$566$			8.93847i			0.0157924i
$567$		0			0
$568$		−	70.6853i		−	0.124446i
$569$	−502.877	−	290.336i	−0.883790	−	0.510257i	−0.0118840	−	0.999929i	$-0.503783\pi$
$569$	−502.877	−	290.336i	−0.883790	−	0.510257i	−0.871906	+	0.489673i	$0.837116\pi$
$570$		0			0
$571$	416.566	+	721.514i	0.729538	+	1.26360i	0.957079	+	0.289828i	$0.0935982\pi$
$571$	416.566	+	721.514i	0.729538	+	1.26360i	−0.227541	+	0.973769i	$0.573068\pi$
$572$	−49.0274	−	84.9180i	−0.0857123	−	0.148458i
$573$		0			0
$574$	−28.1156	+	48.6976i	−0.0489818	+	0.0848390i
$575$	476.338	+	926.468i	0.828414	+	1.61125i
$576$		0			0
$577$			454.896i			0.788382i	0.919029	+	0.394191i	$0.128975\pi$
$577$			454.896i			0.788382i	−0.919029	+	0.394191i	$0.871025\pi$
$578$	5.71836	−	9.90449i	0.00989336	−	0.0171358i
$579$		0			0
$580$	−881.382	−	21.4660i	−1.51962	−	0.0370103i
$581$	516.124	−	297.984i	0.888338	−	0.512882i
$582$		0			0
$583$	39.5432	+	22.8303i	0.0678271	+	0.0391600i
$584$		−	58.0341i		−	0.0993734i
$585$		0			0
$586$	−38.2852			−0.0653330
$587$	−41.2876	+	71.5121i	−0.0703365	+	0.121826i	−0.899049	−	0.437848i	$-0.855741\pi$
$587$	−41.2876	+	71.5121i	−0.0703365	+	0.121826i	0.828712	+	0.559675i	$0.189074\pi$
$588$		0			0
$589$	53.5743	+	92.7935i	0.0909581	+	0.157544i
$590$	−19.6671	−	0.478989i	−0.0333341	−	0.000811846i
$591$		0			0
$592$	284.760	+	164.406i	0.481013	+	0.277713i
$593$	588.773			0.992872			0.496436	−	0.868073i	$-0.334642\pi$
$593$	588.773			0.992872			0.496436	+	0.868073i	$0.334642\pi$
$594$		0			0
$595$	346.915	−	568.446i	0.583051	−	0.955372i
$596$	166.819	+	96.3129i	0.279898	+	0.161599i
$597$		0			0
$598$	−48.0882	+	27.7638i	−0.0804151	+	0.0464277i
$599$	260.869	−	150.613i	0.435508	−	0.251441i	−0.266182	−	0.963923i	$-0.585762\pi$
$599$	260.869	−	150.613i	0.435508	−	0.251441i	0.701690	+	0.712482i	$0.252429\pi$
$600$		0			0
$601$	−3.33029	+	5.76822i	−0.00554124	+	0.00959771i	−0.868783	−	0.495193i	$-0.835097\pi$
$601$	−3.33029	+	5.76822i	−0.00554124	+	0.00959771i	0.863241	+	0.504791i	$0.168431\pi$
$602$	−33.9076			−0.0563249
$603$		0			0
$604$	91.1062			0.150838
$605$	517.113	−	281.996i	0.854731	−	0.466108i
$606$		0			0
$607$	350.322	−	202.258i	0.577137	−	0.333210i	−0.182858	−	0.983139i	$-0.558535\pi$
$607$	350.322	−	202.258i	0.577137	−	0.333210i	0.759995	+	0.649929i	$0.225202\pi$
$608$	38.4603	+	66.6151i	0.0632570	+	0.109564i
$609$		0			0
$610$	29.4719	−	16.0719i	0.0483146	−	0.0263473i
$611$		−	826.026i		−	1.35193i
$612$		0			0
$613$			27.7082i			0.0452010i	0.999745	+	0.0226005i	$0.00719458\pi$
$613$			27.7082i			0.0452010i	−0.999745	+	0.0226005i	$0.992805\pi$
$614$	24.9450	+	14.4020i	0.0406270	+	0.0234560i
$615$		0			0
$616$	7.05779	+	12.2245i	0.0114575	+	0.0198449i
$617$	229.443	+	397.407i	0.371869	+	0.644095i	0.989853	−	0.142095i	$-0.0453839\pi$
$617$	229.443	+	397.407i	0.371869	+	0.644095i	−0.617984	+	0.786190i	$0.712051\pi$
$618$		0			0
$619$	−30.4780	+	52.7895i	−0.0492375	+	0.0852819i	−0.889594	−	0.456753i	$-0.849012\pi$
$619$	−30.4780	+	52.7895i	−0.0492375	+	0.0852819i	0.840356	+	0.542035i	$0.182346\pi$
$620$	110.114	+	67.2010i	0.177603	+	0.108389i
$621$		0			0
$622$		−	52.3165i		−	0.0841101i
$623$	−339.846	+	588.631i	−0.545500	+	0.944833i
$624$		0			0
$625$	622.038	+	60.7789i	0.995260	+	0.0972463i
$626$	36.9478	−	21.3318i	0.0590220	−	0.0340764i
$627$		0			0
$628$	−405.100	−	233.885i	−0.645064	−	0.372428i
$629$		−	270.718i		−	0.430394i
$630$		0			0
$631$	−590.614			−0.935997			−0.467999	−	0.883729i	$-0.655025\pi$
$631$	−590.614			−0.935997			−0.467999	+	0.883729i	$0.655025\pi$
$632$	−23.8923	+	41.3827i	−0.0378043	+	0.0654789i
$633$		0			0
$634$	11.8762	+	20.5702i	0.0187322	+	0.0324450i
$635$	−758.846	−	18.4816i	−1.19503	−	0.0291049i
$636$		0			0
$637$	−650.580	−	375.612i	−1.02132	−	0.589659i
$638$	−7.66573			−0.0120153
$639$		0			0
$640$	105.357	+	64.2982i	0.164621	+	0.100466i
$641$	241.560	+	139.465i	0.376848	+	0.217573i	0.676446	−	0.736492i	$-0.263519\pi$
$641$	241.560	+	139.465i	0.376848	+	0.217573i	−0.299598	+	0.954066i	$0.596852\pi$
$642$		0			0
$643$	640.916	−	370.033i	0.996759	−	0.575479i	0.0894713	−	0.995989i	$-0.471482\pi$
$643$	640.916	−	370.033i	0.996759	−	0.575479i	0.907288	+	0.420510i	$0.138149\pi$
$644$	−1466.37	+	846.608i	−2.27697	+	1.31461i
$645$		0			0
$646$	10.5136	−	18.2100i	0.0162749	−	0.0281889i
$647$	71.8283			0.111017			0.0555087	−	0.998458i	$-0.482322\pi$
$647$	71.8283			0.111017			0.0555087	+	0.998458i	$0.482322\pi$
$648$		0			0
$649$	72.5513			0.111789
$650$	−1.62175	+	33.2744i	−0.00249500	+	0.0511914i
$651$		0			0
$652$	−315.180	+	181.969i	−0.483405	+	0.279094i
$653$	244.236	+	423.029i	0.374021	+	0.647824i	0.990180	−	0.139798i	$-0.0446454\pi$
$653$	244.236	+	423.029i	0.374021	+	0.647824i	−0.616159	+	0.787622i	$0.711312\pi$
$654$		0			0
$655$	−375.168	−	687.968i	−0.572775	−	1.05033i
$656$		−	904.505i		−	1.37882i
$657$		0			0
$658$			59.3857i			0.0902518i
$659$	378.708	+	218.647i	0.574671	+	0.331786i	0.759013	−	0.651076i	$-0.225682\pi$
$659$	378.708	+	218.647i	0.574671	+	0.331786i	−0.184342	+	0.982862i	$0.559015\pi$
$660$		0			0
$661$	476.242	+	824.876i	0.720487	+	1.24792i	0.960805	+	0.277226i	$0.0894152\pi$
$661$	476.242	+	824.876i	0.720487	+	1.24792i	−0.240317	+	0.970694i	$0.577251\pi$
$662$	−17.5232	−	30.3511i	−0.0264701	−	0.0458476i
$663$		0			0
$664$	22.6820	−	39.2864i	0.0341596	−	0.0591662i
$665$	−439.553	+	720.240i	−0.660982	+	1.08307i
$666$		0			0
$667$		−	1841.23i		−	2.76047i
$668$	−327.628	+	567.468i	−0.490461	+	0.849503i
$669$		0			0
$670$	29.1353	+	0.709587i	0.0434856	+	0.00105908i
$671$	−107.214	+	61.8997i	−0.159782	+	0.0922500i
$672$		0			0
$673$	−741.142	−	427.899i	−1.10125	−	0.635808i	−0.164702	−	0.986343i	$-0.552666\pi$
$673$	−741.142	−	427.899i	−1.10125	−	0.635808i	−0.936549	+	0.350535i	$0.886000\pi$
$674$		−	24.4796i		−	0.0363199i
$675$		0			0
$676$	78.7487			0.116492
$677$	−519.485	+	899.774i	−0.767333	+	1.32906i	0.171671	+	0.985154i	$0.445083\pi$
$677$	−519.485	+	899.774i	−0.767333	+	1.32906i	−0.939004	+	0.343906i	$0.888250\pi$
$678$		0			0
$679$	−804.809	−	1393.97i	−1.18529	−	2.05298i
$680$	1.23419	−	50.6753i	0.00181499	−	0.0745225i
$681$		0			0
$682$	0.971363	+	0.560817i	0.00142429	+	0.000822312i
$683$	1308.84			1.91632			0.958158	−	0.286238i	$-0.0924049\pi$
$683$	1308.84			1.91632			0.958158	+	0.286238i	$0.0924049\pi$
$684$		0			0
$685$	−322.469	−	196.798i	−0.470757	−	0.287297i
$686$	4.86020	+	2.80604i	0.00708484	+	0.00409044i
$687$		0			0
$688$	472.348	−	272.710i	0.686552	−	0.396381i
$689$	−303.731	+	175.359i	−0.440829	+	0.254513i
$690$		0			0
$691$	159.467	−	276.204i	0.230776	−	0.399717i	−0.727260	−	0.686362i	$-0.759207\pi$
$691$	159.467	−	276.204i	0.230776	−	0.399717i	0.958037	+	0.286645i	$0.0925401\pi$
$692$	899.660			1.30009
$693$		0			0
$694$	10.4750			0.0150937
$695$	419.618	−	228.829i	0.603767	−	0.329251i
$696$		0			0
$697$	−644.927	+	372.349i	−0.925290	+	0.534216i
$698$	0.0832085	+	0.144121i	0.000119210	+	0.000206477i
$699$		0			0
$700$	−49.4524	+	1014.64i	−0.0706463	+	1.44949i
$701$		−	823.878i		−	1.17529i	−0.809119	−	0.587644i	$-0.800055\pi$
$701$		−	823.878i		−	1.17529i	0.809119	−	0.587644i	$-0.199945\pi$
$702$		0			0
$703$			343.008i			0.487921i
$704$	−97.7366	−	56.4282i	−0.138830	−	0.0801537i
$705$		0			0
$706$	−7.23510	−	12.5316i	−0.0102480	−	0.0177501i
$707$	−487.387	−	844.179i	−0.689374	−	1.19403i
$708$		0			0
$709$	−531.033	+	919.776i	−0.748989	+	1.29729i	0.199319	+	0.979935i	$0.436127\pi$
$709$	−531.033	+	919.776i	−0.748989	+	1.29729i	−0.948308	+	0.317352i	$0.897206\pi$
$710$	23.0412	−	37.7548i	0.0324524	−	0.0531757i
$711$		0			0
$712$			51.7369i			0.0726642i
$713$	−134.703	+	233.312i	−0.188924	+	0.327226i
$714$		0			0
$715$	2.99129	−	122.821i	0.00418362	−	0.171778i
$716$	1207.92	−	697.391i	1.68703	−	0.974009i
$717$		0			0
$718$	−9.07314	−	5.23838i	−0.0126367	−	0.00729579i
$719$			325.811i			0.453144i	0.973994	+	0.226572i	$0.0727519\pi$
$719$			325.811i			0.453144i	−0.973994	+	0.226572i	$0.927248\pi$
$720$		0			0
$721$	−973.385			−1.35005
$722$	4.18702	−	7.25213i	0.00579920	−	0.0100445i
$723$		0			0
$724$	507.974	+	879.836i	0.701621	+	1.21524i
$725$	−928.636	−	598.243i	−1.28088	−	0.825162i
$726$		0			0
$727$	39.2560	+	22.6645i	0.0539973	+	0.0311754i	0.526756	−	0.850017i	$-0.323408\pi$
$727$	39.2560	+	22.6645i	0.0539973	+	0.0311754i	−0.472758	+	0.881192i	$0.656742\pi$
$728$	−108.422			−0.148931
$729$		0			0
$730$	18.9173	−	30.9975i	0.0259142	−	0.0424623i
$731$	−388.893	−	224.528i	−0.532002	−	0.307151i
$732$		0			0
$733$	−535.405	+	309.116i	−0.730429	+	0.421714i	−0.818579	−	0.574394i	$-0.805238\pi$
$733$	−535.405	+	309.116i	−0.730429	+	0.421714i	0.0881499	+	0.996107i	$0.471905\pi$
$734$	−40.2701	+	23.2500i	−0.0548639	+	0.0316757i
$735$		0			0
$736$	−96.7011	+	167.491i	−0.131387	+	0.227570i
$737$	−107.479			−0.145834
$738$		0			0
$739$	−62.7472			−0.0849082			−0.0424541	−	0.999098i	$-0.513518\pi$
$739$	−62.7472			−0.0849082			−0.0424541	+	0.999098i	$0.513518\pi$
$740$	197.711	+	362.555i	0.267178	+	0.489940i
$741$		0			0
$742$	21.8362	−	12.6071i	0.0294289	−	0.0169908i
$743$	136.862	+	237.052i	0.184202	+	0.319047i	0.943307	−	0.331921i	$-0.107697\pi$
$743$	136.862	+	237.052i	0.184202	+	0.319047i	−0.759105	+	0.650968i	$0.774363\pi$
$744$		0			0
$745$	115.550	+	211.891i	0.155101	+	0.284418i
$746$		−	10.1930i		−	0.0136635i
$747$		0			0
$748$			93.3598i			0.124813i
$749$	532.456	+	307.414i	0.710890	+	0.410432i
$750$		0			0
$751$	−207.136	−	358.769i	−0.275813	−	0.477722i	0.694527	−	0.719467i	$-0.255614\pi$
$751$	−207.136	−	358.769i	−0.275813	−	0.477722i	−0.970340	+	0.241745i	$0.922280\pi$
$752$	−477.624	−	827.269i	−0.635138	−	1.10009i
$753$		0			0
$754$	29.4402	−	50.9920i	0.0390454	−	0.0676286i
$755$	97.4389	+	59.4656i	0.129058	+	0.0787624i
$756$		0			0
$757$		−	93.2727i		−	0.123214i	−0.998100	−	0.0616068i	$-0.980378\pi$
$757$		−	93.2727i		−	0.123214i	0.998100	−	0.0616068i	$-0.0196225\pi$
$758$	8.48868	−	14.7028i	0.0111988	−	0.0193969i
$759$		0			0
$760$	−1.56376	+	64.2073i	−0.00205758	+	0.0844833i
$761$	−222.719	+	128.587i	−0.292666	+	0.168971i	−0.639144	−	0.769087i	$-0.720711\pi$
$761$	−222.719	+	128.587i	−0.292666	+	0.168971i	0.346477	+	0.938058i	$0.387378\pi$
$762$		0			0
$763$	−712.969	−	411.633i	−0.934428	−	0.539492i
$764$			1070.79i			1.40156i
$765$		0			0
$766$	−30.2381			−0.0394753
$767$	−278.633	+	482.607i	−0.363277	+	0.629213i
$768$		0			0
$769$	204.932	+	354.952i	0.266491	+	0.461576i	0.967953	−	0.251131i	$-0.0808024\pi$
$769$	204.932	+	354.952i	0.266491	+	0.461576i	−0.701462	+	0.712707i	$0.747469\pi$
$770$	−0.215054	+	8.83001i	−0.000279290	+	0.0114675i
$771$		0			0
$772$	−1061.19	−	612.680i	−1.37460	−	0.793628i
$773$	−27.9346			−0.0361379			−0.0180690	−	0.999837i	$-0.505752\pi$
$773$	−27.9346			−0.0361379			−0.0180690	+	0.999837i	$0.505752\pi$
$774$		0			0
$775$	73.9053	+	143.744i	0.0953616	+	0.185476i
$776$	−106.106	−	61.2605i	−0.136735	−	0.0789439i
$777$		0			0
$778$	−0.989045	+	0.571025i	−0.00127127	+	0.000733966i
$779$	817.144	−	471.778i	1.04897	−	0.605620i
$780$		0			0
$781$	−81.5580	+	141.263i	−0.104428	+	0.180874i
$782$	52.8688			0.0676072
$783$		0			0
$784$	−868.745			−1.10809
$785$	−280.600	−	514.554i	−0.357453	−	0.655483i
$786$		0			0
$787$	−879.225	+	507.621i	−1.11719	+	0.645008i	−0.940681	−	0.339292i	$-0.889812\pi$
$787$	−879.225	+	507.621i	−1.11719	+	0.645008i	−0.176505	+	0.984300i	$0.556479\pi$
$788$	−124.639	−	215.882i	−0.158172	−	0.273961i
$789$		0			0
$790$	−26.2510	+	14.3154i	−0.0332291	+	0.0181207i
$791$		−	1259.03i		−	1.59170i
$792$		0			0
$793$		−	950.903i		−	1.19912i
$794$	−21.9893	−	12.6955i	−0.0276943	−	0.0159893i
$795$		0			0
$796$	148.878	+	257.865i	0.187033	+	0.323951i
$797$	252.602	+	437.519i	0.316941	+	0.548958i	0.979848	−	0.199744i	$-0.0640110\pi$
$797$	252.602	+	437.519i	0.316941	+	0.548958i	−0.662907	+	0.748701i	$0.730678\pi$
$798$		0			0
$799$	−393.238	+	681.107i	−0.492162	+	0.852450i
$800$	53.0555	+	103.192i	0.0663194	+	0.128990i
$801$		0			0
$802$			32.0482i			0.0399604i
$803$	−66.9608	+	115.980i	−0.0833883	+	0.144433i
$804$		0			0
$805$	−2120.88	−	51.6538i	−2.63463	−	0.0641662i
$806$	−7.46104	+	4.30763i	−0.00925687	+	0.00534446i
$807$		0			0
$808$	−64.2573	−	37.0990i	−0.0795263	−	0.0459146i
$809$		−	326.016i		−	0.402986i	−0.979490	−	0.201493i	$-0.935421\pi$
$809$		−	326.016i		−	0.402986i	0.979490	−	0.201493i	$-0.0645794\pi$
$810$		0			0
$811$	−176.933			−0.218167			−0.109083	−	0.994033i	$-0.534792\pi$
$811$	−176.933			−0.218167			−0.109083	+	0.994033i	$0.534792\pi$
$812$	897.729	−	1554.91i	1.10558	−	1.91492i
$813$		0			0
$814$	1.79531	+	3.10956i	0.00220554	+	0.00382010i
$815$	−455.861	−	11.1024i	−0.559338	−	0.0136226i
$816$		0			0
$817$	492.741	+	284.484i	0.603110	+	0.348206i
$818$	49.5659			0.0605940
$819$		0			0
$820$	591.776	−	969.668i	0.721678	−	1.18252i
$821$	−196.287	−	113.326i	−0.239083	−	0.138035i	0.375672	−	0.926753i	$-0.377412\pi$
$821$	−196.287	−	113.326i	−0.239083	−	0.138035i	−0.614755	+	0.788718i	$0.710745\pi$
$822$		0			0
$823$	15.8312	−	9.14018i	0.0192360	−	0.0111059i	−0.490351	−	0.871525i	$-0.663131\pi$
$823$	15.8312	−	9.14018i	0.0192360	−	0.0111059i	0.509587	+	0.860419i	$0.329798\pi$
$824$	−64.1657	+	37.0461i	−0.0778710	+	0.0449588i
$825$		0			0
$826$	20.0318	−	34.6962i	0.0242516	−	0.0420050i
$827$	−1046.88			−1.26588			−0.632940	−	0.774201i	$-0.718152\pi$
$827$	−1046.88			−1.26588			−0.632940	+	0.774201i	$0.718152\pi$
$828$		0			0
$829$	1083.19			1.30662			0.653309	−	0.757091i	$-0.273380\pi$
$829$	1083.19			1.30662			0.653309	+	0.757091i	$0.273380\pi$
$830$	24.9212	−	13.5902i	0.0300255	−	0.0163737i
$831$		0			0
$832$	750.714	−	433.425i	0.902301	−	0.520944i
$833$	357.628	+	619.429i	0.429325	+	0.743613i
$834$		0			0
$835$	−720.791	+	393.067i	−0.863223	+	0.470739i
$836$		−	118.290i		−	0.141495i
$837$		0			0
$838$			5.92930i			0.00707553i
$839$	1112.94	+	642.555i	1.32651	+	0.765858i	0.984757	−	0.173933i	$-0.0556478\pi$
$839$	1112.94	+	642.555i	1.32651	+	0.765858i	0.341748	+	0.939792i	$0.388981\pi$
$840$		0			0
$841$	555.707	+	962.512i	0.660769	+	1.14449i
$842$	29.9961	+	51.9547i	0.0356248	+	0.0617040i
$843$		0			0
$844$	326.308	−	565.181i	0.386620	−	0.669646i
$845$	84.2224	+	51.3998i	0.0996715	+	0.0608282i
$846$		0			0
$847$			1199.50i			1.41618i
$848$	−202.792	+	351.246i	−0.239142	+	0.414206i
$849$		0			0
$850$	17.1778	−	26.6647i	0.0202092	−	0.0313702i
$851$	−746.886	+	431.215i	−0.877657	+	0.506716i
$852$		0			0
$853$	−167.854	−	96.9105i	−0.196781	−	0.113611i	0.398372	−	0.917224i	$-0.369575\pi$
$853$	−167.854	−	96.9105i	−0.196781	−	0.113611i	−0.595153	+	0.803612i	$0.702909\pi$
$854$			68.3635i			0.0800510i
$855$		0			0
$856$	46.7995			0.0546723
$857$	−15.0743	+	26.1094i	−0.0175896	+	0.0304661i	−0.874686	−	0.484690i	$-0.838933\pi$
$857$	−15.0743	+	26.1094i	−0.0175896	+	0.0304661i	0.857097	+	0.515156i	$0.172266\pi$
$858$		0			0
$859$	386.902	+	670.134i	0.450410	+	0.780133i	0.998411	−	0.0563445i	$-0.0179445\pi$
$859$	386.902	+	670.134i	0.450410	+	0.780133i	−0.548001	+	0.836477i	$0.684611\pi$
$860$	684.798	+	16.6782i	0.796277	+	0.0193932i
$861$		0			0
$862$	28.9672	+	16.7242i	0.0336047	+	0.0194017i
$863$	−421.375			−0.488267			−0.244134	−	0.969742i	$-0.578504\pi$
$863$	−421.375			−0.488267			−0.244134	+	0.969742i	$0.578504\pi$
$864$		0			0
$865$	962.195	+	587.215i	1.11236	+	0.678861i
$866$	13.8205	+	7.97927i	0.0159590	+	0.00921394i
$867$		0			0
$868$	−227.511	+	131.354i	−0.262110	+	0.151329i
$869$	95.4962	−	55.1347i	0.109892	−	0.0634462i
$870$		0			0
$871$	412.774	−	714.946i	0.473908	−	0.820833i
$872$	−62.6654			−0.0718640
$873$		0			0
$874$	−66.9865			−0.0766436
$875$	−715.156	+	1052.89i	−0.817321	+	1.20331i
$876$		0			0
$877$	773.514	−	446.589i	0.882000	−	0.509223i	0.0106829	−	0.999943i	$-0.496599\pi$
$877$	773.514	−	446.589i	0.882000	−	0.509223i	0.871317	+	0.490720i	$0.163266\pi$
$878$	15.8632	+	27.4758i	0.0180674	+	0.0312936i
$879$		0			0
$880$	−68.0217	−	124.736i	−0.0772974	−	0.141745i
$881$			718.024i			0.815011i	0.913203	+	0.407505i	$0.133601\pi$
$881$			718.024i			0.815011i	−0.913203	+	0.407505i	$0.866399\pi$
$882$		0			0
$883$			274.425i			0.310788i	0.987853	+	0.155394i	$0.0496646\pi$
$883$			274.425i			0.310788i	−0.987853	+	0.155394i	$0.950335\pi$
$884$	−621.024	−	358.548i	−0.702516	−	0.405598i
$885$		0			0
$886$	17.3268	+	30.0108i	0.0195562	+	0.0338723i
$887$	119.843	+	207.574i	0.135110	+	0.234018i	0.925640	−	0.378406i	$-0.123528\pi$
$887$	119.843	+	207.574i	0.135110	+	0.234018i	−0.790529	+	0.612424i	$0.790194\pi$
$888$		0			0
$889$	772.920	−	1338.74i	0.869426	−	1.50589i
$890$	−16.8646	+	27.6340i	−0.0189490	+	0.0310494i
$891$		0			0
$892$			71.7196i			0.0804032i
$893$	498.245	−	862.986i	0.557945	−	0.966389i
$894$		0			0
$895$	1747.07	+	42.5496i	1.95203	+	0.0475415i
$896$	−217.684	+	125.680i	−0.242950	+	0.140267i
$897$		0			0
$898$	−12.9999	−	7.50548i	−0.0144765	−	0.00835800i
$899$		−	285.673i		−	0.317767i
$900$		0			0
$901$	333.926			0.370617
$902$	4.93858	−	8.55387i	0.00547514	−	0.00948323i
$903$		0			0
$904$	−47.9175	−	82.9955i	−0.0530061	−	0.0918092i
$905$	−30.9928	+	1272.55i	−0.0342462	+	1.40613i
$906$		0			0
$907$	181.082	+	104.548i	0.199649	+	0.115268i	0.596492	−	0.802619i	$-0.296561\pi$
$907$	181.082	+	104.548i	0.199649	+	0.115268i	−0.396843	+	0.917887i	$0.629894\pi$
$908$	−127.992			−0.140960
$909$		0			0
$910$	−57.9107	−	35.3421i	−0.0636382	−	0.0388375i
$911$	−1365.31	−	788.262i	−1.49869	−	0.865271i	−0.498694	−	0.866778i	$-0.666187\pi$
$911$	−1365.31	−	788.262i	−1.49869	−	0.865271i	−0.999999	+	0.00150692i	$0.999520\pi$
$912$		0			0
$913$	−90.6587	+	52.3418i	−0.0992976	+	0.0573295i
$914$	12.9997	−	7.50540i	0.0142229	−	0.00821160i
$915$		0			0
$916$	−320.554	+	555.215i	−0.349950	+	0.606130i
$917$	1595.82			1.74026
$918$		0			0
$919$	−1192.75			−1.29788			−0.648939	−	0.760841i	$-0.724787\pi$
$919$	−1192.75			−1.29788			−0.648939	+	0.760841i	$0.724787\pi$
$920$	−141.775	+	77.3136i	−0.154103	+	0.0840366i
$921$		0			0
$922$	21.9541	−	12.6752i	0.0238114	−	0.0137475i
$923$	−626.447	−	1085.04i	−0.678707	−	1.17555i
$924$		0			0
$925$	−25.1883	+	516.804i	−0.0272306	+	0.558707i
$926$			77.1828i			0.0833508i
$927$		0			0
$928$		−	205.081i		−	0.220992i
$929$	1169.54	+	675.233i	1.25892	+	0.726838i	0.972865	−	0.231375i	$-0.0743223\pi$
$929$	1169.54	+	675.233i	1.25892	+	0.726838i	0.286056	+	0.958213i	$0.407656\pi$
$930$		0			0
$931$	−453.126	−	784.837i	−0.486709	−	0.843005i
$932$	688.724	+	1192.91i	0.738975	+	1.27994i
$933$		0			0
$934$	−20.7514	+	35.9424i	−0.0222177	+	0.0384822i
$935$	−60.9366	+	99.8492i	−0.0651729	+	0.106791i
$936$		0			0
$937$		−	559.923i		−	0.597570i	−0.954320	−	0.298785i	$-0.903419\pi$
$937$		−	559.923i		−	0.597570i	0.954320	−	0.298785i	$-0.0965813\pi$
$938$	−29.6757	+	51.3998i	−0.0316372	+	0.0547972i
$939$		0			0
$940$	29.2101	−	1199.36i	0.0310746	−	1.27591i
$941$	1015.67	−	586.395i	1.07935	−	0.623161i	0.148627	−	0.988893i	$-0.452515\pi$
$941$	1015.67	−	586.395i	1.07935	−	0.623161i	0.930720	+	0.365732i	$0.119181\pi$
$942$		0			0
$943$	2054.56	+	1186.20i	2.17874	+	1.25790i
$944$			644.444i			0.682674i
$945$		0			0
$946$	5.95596			0.00629594
$947$	−245.184	+	424.672i	−0.258906	+	0.448439i	−0.965949	−	0.258732i	$-0.916695\pi$
$947$	−245.184	+	424.672i	−0.258906	+	0.448439i	0.707043	+	0.707171i	$0.250029\pi$
$948$		0			0
$949$	−514.326	−	890.838i	−0.541966	−	0.938712i
$950$	−21.7649	+	33.7850i	−0.0229104	+	0.0355632i
$951$		0			0
$952$	89.4001	+	51.6152i	0.0939077	+	0.0542176i
$953$	−607.867			−0.637846			−0.318923	−	0.947781i	$-0.603321\pi$
$953$	−607.867			−0.637846			−0.318923	+	0.947781i	$0.603321\pi$
$954$		0			0
$955$	−698.914	+	1145.22i	−0.731847	+	1.19919i
$956$	374.661	+	216.310i	0.391904	+	0.226266i
$957$		0			0
$958$	−18.2893	+	10.5593i	−0.0190911	+	0.0110223i
$959$	666.267	−	384.669i	0.694752	−	0.401115i
$960$		0			0
$961$	459.600	−	796.051i	0.478252	−	0.828357i
$962$	−27.5795			−0.0286689
$963$		0			0
$964$	−872.111			−0.904680
$965$	−735.056	−	1347.92i	−0.761716	−	1.39680i
$966$		0			0
$967$	93.0243	−	53.7076i	0.0961989	−	0.0555405i	−0.451129	−	0.892459i	$-0.648978\pi$
$967$	93.0243	−	53.7076i	0.0961989	−	0.0555405i	0.547328	+	0.836918i	$0.315645\pi$
$968$	45.6519	+	79.0714i	0.0471610	+	0.0816853i
$969$		0			0
$970$	−36.7050	−	67.3082i	−0.0378402	−	0.0693899i
$971$		−	351.974i		−	0.362486i	−0.983438	−	0.181243i	$-0.941988\pi$
$971$		−	351.974i		−	0.362486i	0.983438	−	0.181243i	$-0.0580120\pi$
$972$		0			0
$973$			973.352i			1.00036i
$974$	8.93926	+	5.16108i	0.00917788	+	0.00529885i
$975$		0			0
$976$	−549.830	−	952.334i	−0.563351	−	0.975752i
$977$	−192.866	−	334.054i	−0.197407	−	0.341919i	0.750280	−	0.661120i	$-0.229919\pi$
$977$	−192.866	−	334.054i	−0.197407	−	0.341919i	−0.947687	+	0.319202i	$0.896585\pi$
$978$		0			0
$979$	59.6950	−	103.395i	0.0609754	−	0.105613i
$980$	−931.332	−	568.379i	−0.950339	−	0.579979i
$981$		0			0
$982$			58.9808i			0.0600619i
$983$	−24.5779	+	42.5702i	−0.0250030	+	0.0433064i	−0.878256	−	0.478190i	$-0.841293\pi$
$983$	−24.5779	+	42.5702i	−0.0250030	+	0.0433064i	0.853253	+	0.521497i	$0.174626\pi$
$984$		0			0
$985$	7.60457	−	312.240i	0.00772037	−	0.316995i
$986$	−48.5504	+	28.0306i	−0.0492398	+	0.0284286i
$987$		0			0
$988$	786.858	+	454.292i	0.796415	+	0.459810i
$989$			1430.56i			1.44647i
$990$		0			0
$991$	775.701			0.782746			0.391373	−	0.920232i	$-0.372000\pi$
$991$	775.701			0.782746			0.391373	+	0.920232i	$0.372000\pi$
$992$	−15.0035	+	25.9868i	−0.0151245	+	0.0261963i
$993$		0			0
$994$	45.0373	+	78.0068i	0.0453091	+	0.0784777i
$995$	−9.08347	+	372.963i	−0.00912911	+	0.374837i
$996$		0			0
$997$	628.638	+	362.945i	0.630530	+	0.364037i	0.780957	−	0.624584i	$-0.214732\pi$
$997$	628.638	+	362.945i	0.630530	+	0.364037i	−0.150427	+	0.988621i	$0.548065\pi$
$998$	55.2778			0.0553885
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.h.k.269.11		48
3.2	odd	2	inner	405.3.h.k.269.14		48
5.4	even	2	inner	405.3.h.k.269.13		48
9.2	odd	6		405.3.d.b.404.12	yes	24
9.4	even	3	inner	405.3.h.k.134.12		48
9.5	odd	6	inner	405.3.h.k.134.13		48
9.7	even	3		405.3.d.b.404.13	yes	24
15.14	odd	2	inner	405.3.h.k.269.12		48
45.4	even	6	inner	405.3.h.k.134.14		48
45.14	odd	6	inner	405.3.h.k.134.11		48
45.29	odd	6		405.3.d.b.404.14	yes	24
45.34	even	6		405.3.d.b.404.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.3.d.b.404.11	✓	24	45.34	even	6
405.3.d.b.404.12	yes	24	9.2	odd	6
405.3.d.b.404.13	yes	24	9.7	even	3
405.3.d.b.404.14	yes	24	45.29	odd	6
405.3.h.k.134.11		48	45.14	odd	6	inner
405.3.h.k.134.12		48	9.4	even	3	inner
405.3.h.k.134.13		48	9.5	odd	6	inner
405.3.h.k.134.14		48	45.4	even	6	inner
405.3.h.k.269.11		48	1.1	even	1	trivial
405.3.h.k.269.12		48	15.14	odd	2	inner
405.3.h.k.269.13		48	5.4	even	2	inner
405.3.h.k.269.14		48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0484988 + 0.0840023i) q^{2} +(1.99530 + 3.45595i) q^{4} +(-0.121738 + 4.99852i) q^{5} +(-8.81825 - 5.09122i) q^{7} -0.775068 q^{8} +(-0.413983 - 0.252648i) q^{10} +(1.54895 + 0.894287i) q^{11} +(-11.8975 + 6.86902i) q^{13} +(0.855349 - 0.493836i) q^{14} +(-7.94359 + 13.7587i) q^{16} +13.0802 q^{17} -16.5731 q^{19} +(-17.5175 + 9.55280i) q^{20} +(-0.150244 + 0.0867437i) q^{22} +(-20.8350 - 36.0872i) q^{23} +(-24.9704 - 1.21702i) q^{25} -1.33256i q^{26} -40.6340i q^{28} +(38.2663 + 22.0931i) q^{29} +(-3.23261 - 5.59904i) q^{31} +(-2.32064 - 4.01947i) q^{32} +(-0.634376 + 1.09877i) q^{34} +(26.5221 - 43.4584i) q^{35} -20.6967i q^{37} +(0.803775 - 1.39218i) q^{38} +(0.0943554 - 3.87419i) q^{40} +(-49.3054 + 28.4665i) q^{41} +(-29.7314 - 17.1654i) q^{43} +7.13747i q^{44} +4.04188 q^{46} +(-30.0635 + 52.0715i) q^{47} +(27.3411 + 47.3561i) q^{49} +(1.31326 - 2.03854i) q^{50} +(-47.4780 - 27.4114i) q^{52} +25.5290 q^{53} +(-4.65868 + 7.63359i) q^{55} +(6.83474 + 3.94604i) q^{56} +(-3.71174 + 2.14297i) q^{58} +(35.1292 - 20.2819i) q^{59} +(-34.6084 + 59.9435i) q^{61} +0.627110 q^{62} -63.0986 q^{64} +(-32.8865 - 60.3060i) q^{65} +(-52.0413 + 30.0461i) q^{67} +(26.0989 + 45.2047i) q^{68} +(2.36432 + 4.33560i) q^{70} +91.1989i q^{71} +74.8762i q^{73} +(1.73857 + 1.00376i) q^{74} +(-33.0682 - 57.2759i) q^{76} +(-9.10603 - 15.7721i) q^{77} +(30.8261 - 53.3923i) q^{79} +(-67.8061 - 41.3812i) q^{80} -5.52236i q^{82} +(-29.2645 + 50.6877i) q^{83} +(-1.59237 + 65.3818i) q^{85} +(2.88387 - 1.66500i) q^{86} +(-1.20054 - 0.693133i) q^{88} -66.7514i q^{89} +139.887 q^{91} +(83.1439 - 144.009i) q^{92} +(-2.91608 - 5.05081i) q^{94} +(2.01758 - 82.8409i) q^{95} +(136.899 + 79.0389i) q^{97} -5.30403 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 24 q^{10} - 96 q^{16} - 48 q^{25} - 144 q^{34} - 72 q^{40} - 336 q^{46} + 288 q^{49} - 264 q^{55} + 360 q^{61} - 144 q^{64} + 156 q^{70} - 48 q^{76} + 480 q^{79} + 456 q^{85} - 96 q^{91}+ \cdots - 384 q^{94}+O(q^{100}) \) 48 * q - 48 * q^4 + 24 * q^10 - 96 * q^16 - 48 * q^25 - 144 * q^34 - 72 * q^40 - 336 * q^46 + 288 * q^49 - 264 * q^55 + 360 * q^61 - 144 * q^64 + 156 * q^70 - 48 * q^76 + 480 * q^79 + 456 * q^85 - 96 * q^91 - 384 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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