LMFDB - Embedded newform 387.3.j.f.37.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,3,Mod(37,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("387.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	387.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5449862307$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	387.37
Dual form			387.3.j.f.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.03676i q^{2} -5.22190 q^{4} +(0.820197 + 0.473541i) q^{5} +(6.81469 - 3.93447i) q^{7} -3.71061i q^{8} +O(q^{10})$	\(q+3.03676i q^{2} -5.22190 q^{4} +(0.820197 + 0.473541i) q^{5} +(6.81469 - 3.93447i) q^{7} -3.71061i q^{8} +(-1.43803 + 2.49074i) q^{10} +10.9867 q^{11} +(0.754855 + 1.30745i) q^{13} +(11.9480 + 20.6946i) q^{14} -9.61937 q^{16} +(15.7459 + 27.2727i) q^{17} +(6.05169 + 3.49394i) q^{19} +(-4.28299 - 2.47278i) q^{20} +33.3641i q^{22} +(-4.44080 + 7.69168i) q^{23} +(-12.0515 - 20.8738i) q^{25} +(-3.97040 + 2.29231i) q^{26} +(-35.5856 + 20.5454i) q^{28} +(12.2192 - 7.05476i) q^{29} +(-16.0057 + 27.7228i) q^{31} -44.0541i q^{32} +(-82.8207 + 47.8166i) q^{34} +7.45253 q^{35} +(36.3101 + 20.9636i) q^{37} +(-10.6103 + 18.3775i) q^{38} +(1.75713 - 3.04343i) q^{40} +9.97514 q^{41} +(-42.6128 - 5.75721i) q^{43} -57.3717 q^{44} +(-23.3578 - 13.4856i) q^{46} -11.9805 q^{47} +(6.46004 - 11.1891i) q^{49} +(63.3888 - 36.5975i) q^{50} +(-3.94178 - 6.82736i) q^{52} +(-18.9483 + 32.8194i) q^{53} +(9.01130 + 5.20268i) q^{55} +(-14.5993 - 25.2867i) q^{56} +(21.4236 + 37.1068i) q^{58} -37.1319 q^{59} +(9.39711 - 5.42542i) q^{61} +(-84.1873 - 48.6055i) q^{62} +95.3043 q^{64} +1.42982i q^{65} +(30.1733 - 52.2616i) q^{67} +(-82.2236 - 142.416i) q^{68} +22.6315i q^{70} +(65.2968 - 37.6991i) q^{71} +(91.3994 - 52.7695i) q^{73} +(-63.6615 + 110.265i) q^{74} +(-31.6013 - 18.2450i) q^{76} +(74.8713 - 43.2270i) q^{77} +(-54.4700 - 94.3448i) q^{79} +(-7.88978 - 4.55517i) q^{80} +30.2921i q^{82} +(-71.5581 + 123.942i) q^{83} +29.8254i q^{85} +(17.4833 - 129.405i) q^{86} -40.7675i q^{88} +(60.2970 + 34.8125i) q^{89} +(10.2882 + 5.93991i) q^{91} +(23.1894 - 40.1652i) q^{92} -36.3818i q^{94} +(3.30905 + 5.73144i) q^{95} -10.5101 q^{97} +(33.9786 + 19.6176i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) $ 28 * q - 84 * q^4 - 30 * q^7	$ 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) $ 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$			3.03676i			1.51838i	0.650870	+	0.759189i	$0.274404\pi$
$2$			3.03676i			1.51838i	−0.650870	+	0.759189i	$0.725596\pi$
$3$		0			0
$3$		0			0
$4$	−5.22190			−1.30547
$5$	0.820197	+	0.473541i	0.164039	+	0.0947082i	0.579772	−	0.814779i	$-0.303142\pi$
$5$	0.820197	+	0.473541i	0.164039	+	0.0947082i	−0.415733	+	0.909487i	$0.636475\pi$
$6$		0			0
$7$	6.81469	−	3.93447i	0.973528	−	0.562067i	0.0732179	−	0.997316i	$-0.476673\pi$
$7$	6.81469	−	3.93447i	0.973528	−	0.562067i	0.900310	+	0.435249i	$0.143340\pi$
$8$		−	3.71061i		−	0.463826i
$9$		0			0
$10$	−1.43803	+	2.49074i	−0.143803	+	0.249074i
$11$	10.9867			0.998795			0.499398	−	0.866373i	$-0.333555\pi$
$11$	10.9867			0.998795			0.499398	+	0.866373i	$0.333555\pi$
$12$		0			0
$13$	0.754855	+	1.30745i	0.0580658	+	0.100573i	0.893597	−	0.448870i	$-0.148173\pi$
$13$	0.754855	+	1.30745i	0.0580658	+	0.100573i	−0.835531	+	0.549443i	$0.814840\pi$
$14$	11.9480	+	20.6946i	0.853430	+	1.47818i
$15$		0			0
$16$	−9.61937			−0.601211
$17$	15.7459	+	27.2727i	0.926231	+	1.60428i	0.789569	+	0.613662i	$0.210304\pi$
$17$	15.7459	+	27.2727i	0.926231	+	1.60428i	0.136662	+	0.990618i	$0.456363\pi$
$18$		0			0
$19$	6.05169	+	3.49394i	0.318510	+	0.183892i	0.650728	−	0.759311i	$-0.274464\pi$
$19$	6.05169	+	3.49394i	0.318510	+	0.183892i	−0.332218	+	0.943202i	$0.607797\pi$
$20$	−4.28299	−	2.47278i	−0.214149	−	0.123639i
$21$		0			0
$22$			33.3641i			1.51655i
$23$	−4.44080	+	7.69168i	−0.193078	+	0.334421i	−0.946269	−	0.323381i	$-0.895180\pi$
$23$	−4.44080	+	7.69168i	−0.193078	+	0.334421i	0.753191	+	0.657802i	$0.228514\pi$
$24$		0			0
$25$	−12.0515	−	20.8738i	−0.482061	−	0.834954i
$26$	−3.97040	+	2.29231i	−0.152708	+	0.0881659i
$27$		0			0
$28$	−35.5856	+	20.5454i	−1.27092	+	0.733764i
$29$	12.2192	−	7.05476i	0.421352	−	0.243268i	−0.274304	−	0.961643i	$-0.588447\pi$
$29$	12.2192	−	7.05476i	0.421352	−	0.243268i	0.695656	+	0.718376i	$0.255114\pi$
$30$		0			0
$31$	−16.0057	+	27.7228i	−0.516314	+	0.894282i	0.483506	+	0.875341i	$0.339363\pi$
$31$	−16.0057	+	27.7228i	−0.516314	+	0.894282i	−0.999821	+	0.0189415i	$0.993970\pi$
$32$		−	44.0541i		−	1.37669i
$33$		0			0
$34$	−82.8207	+	47.8166i	−2.43590	+	1.40637i
$35$	7.45253			0.212929
$36$		0			0
$37$	36.3101	+	20.9636i	0.981354	+	0.566585i	0.902679	−	0.430316i	$-0.141598\pi$
$37$	36.3101	+	20.9636i	0.981354	+	0.566585i	0.0786751	+	0.996900i	$0.474931\pi$
$38$	−10.6103	+	18.3775i	−0.279217	+	0.483619i
$39$		0			0
$40$	1.75713	−	3.04343i	0.0439282	−	0.0760858i
$41$	9.97514			0.243296			0.121648	−	0.992573i	$-0.461182\pi$
$41$	9.97514			0.243296			0.121648	+	0.992573i	$0.461182\pi$
$42$		0			0
$43$	−42.6128	−	5.75721i	−0.990996	−	0.133889i
$43$	−42.6128	−	5.75721i	−0.990996	−	0.133889i
$44$	−57.3717			−1.30390
$45$		0			0
$46$	−23.3578	−	13.4856i	−0.507778	−	0.293166i
$47$	−11.9805			−0.254904			−0.127452	−	0.991845i	$-0.540680\pi$
$47$	−11.9805			−0.254904			−0.127452	+	0.991845i	$0.540680\pi$
$48$		0			0
$49$	6.46004	−	11.1891i	0.131838	−	0.228349i
$50$	63.3888	−	36.5975i	1.26778	−	0.731951i
$51$		0			0
$52$	−3.94178	−	6.82736i	−0.0758034	−	0.131295i
$53$	−18.9483	+	32.8194i	−0.357514	+	0.619233i	−0.987545	−	0.157337i	$-0.949709\pi$
$53$	−18.9483	+	32.8194i	−0.357514	+	0.619233i	0.630031	+	0.776570i	$0.283042\pi$
$54$		0			0
$55$	9.01130	+	5.20268i	0.163842	+	0.0945941i
$56$	−14.5993	−	25.2867i	−0.260701	−	0.451548i
$57$		0			0
$58$	21.4236	+	37.1068i	0.369372	+	0.639772i
$59$	−37.1319			−0.629354			−0.314677	−	0.949199i	$-0.601896\pi$
$59$	−37.1319			−0.629354			−0.314677	+	0.949199i	$0.601896\pi$
$60$		0			0
$61$	9.39711	−	5.42542i	0.154051	−	0.0889413i	−0.420993	−	0.907064i	$-0.638318\pi$
$61$	9.39711	−	5.42542i	0.154051	−	0.0889413i	0.575044	+	0.818123i	$0.304985\pi$
$62$	−84.1873	−	48.6055i	−1.35786	−	0.783960i
$63$		0			0
$64$	95.3043			1.48913
$65$			1.42982i			0.0219972i
$66$		0			0
$67$	30.1733	−	52.2616i	0.450347	−	0.780024i	−0.548060	−	0.836439i	$-0.684633\pi$
$67$	30.1733	−	52.2616i	0.450347	−	0.780024i	0.998407	+	0.0564145i	$0.0179668\pi$
$68$	−82.2236	−	142.416i	−1.20917	−	2.09435i
$69$		0			0
$70$			22.6315i			0.323307i
$71$	65.2968	−	37.6991i	0.919674	−	0.530974i	0.0361428	−	0.999347i	$-0.488493\pi$
$71$	65.2968	−	37.6991i	0.919674	−	0.530974i	0.883531	+	0.468373i	$0.155160\pi$
$72$		0			0
$73$	91.3994	−	52.7695i	1.25205	−	0.722869i	0.280531	−	0.959845i	$-0.409489\pi$
$73$	91.3994	−	52.7695i	1.25205	−	0.722869i	0.971516	+	0.236976i	$0.0761561\pi$
$74$	−63.6615	+	110.265i	−0.860290	+	1.49007i
$75$		0			0
$76$	−31.6013	−	18.2450i	−0.415806	−	0.240066i
$77$	74.8713	−	43.2270i	0.972355	−	0.561389i
$78$		0			0
$79$	−54.4700	−	94.3448i	−0.689494	−	1.19424i	−0.972002	−	0.234974i	$-0.924500\pi$
$79$	−54.4700	−	94.3448i	−0.689494	−	1.19424i	0.282508	−	0.959265i	$-0.408834\pi$
$80$	−7.88978	−	4.55517i	−0.0986223	−	0.0569396i
$81$		0			0
$82$			30.2921i			0.369416i
$83$	−71.5581	+	123.942i	−0.862146	+	1.49328i	0.00770832	+	0.999970i	$0.497546\pi$
$83$	−71.5581	+	123.942i	−0.862146	+	1.49328i	−0.869854	+	0.493310i	$0.835787\pi$
$84$		0			0
$85$			29.8254i			0.350887i
$86$	17.4833	−	129.405i	0.203294	−	1.50471i
$87$		0			0
$88$		−	40.7675i		−	0.463268i
$89$	60.2970	+	34.8125i	0.677495	+	0.391152i	0.798910	−	0.601450i	$-0.205410\pi$
$89$	60.2970	+	34.8125i	0.677495	+	0.391152i	−0.121416	+	0.992602i	$0.538743\pi$
$90$		0			0
$91$	10.2882	+	5.93991i	0.113057	+	0.0652737i
$92$	23.1894	−	40.1652i	0.252059	−	0.436578i
$93$		0			0
$94$		−	36.3818i		−	0.387040i
$95$	3.30905	+	5.73144i	0.0348321	+	0.0603310i
$96$		0			0
$97$	−10.5101			−0.108351			−0.0541757	−	0.998531i	$-0.517253\pi$
$97$	−10.5101			−0.108351			−0.0541757	+	0.998531i	$0.517253\pi$
$98$	33.9786	+	19.6176i	0.346721	+	0.200179i
$99$		0			0
$100$	62.9318	+	109.001i	0.629318	+	1.09001i
$101$	−27.5378	−	47.6968i	−0.272651	−	0.472245i	0.696889	−	0.717179i	$-0.254567\pi$
$101$	−27.5378	−	47.6968i	−0.272651	−	0.472245i	−0.969540	+	0.244934i	$0.921234\pi$
$102$		0			0
$103$	9.14952	+	15.8474i	0.0888303	+	0.153859i	0.907017	−	0.421094i	$-0.138354\pi$
$103$	9.14952	+	15.8474i	0.0888303	+	0.153859i	−0.818187	+	0.574953i	$0.805020\pi$
$104$	4.85143	−	2.80097i	0.0466484	−	0.0269324i
$105$		0			0
$106$	−99.6644	−	57.5413i	−0.940230	−	0.542842i
$107$	29.7076			0.277642			0.138821	−	0.990318i	$-0.455669\pi$
$107$	29.7076			0.277642			0.138821	+	0.990318i	$0.455669\pi$
$108$		0			0
$109$	−37.3196	+	64.6394i	−0.342382	+	0.593022i	−0.984874	−	0.173269i	$-0.944567\pi$
$109$	−37.3196	+	64.6394i	−0.342382	+	0.593022i	0.642493	+	0.766292i	$0.277900\pi$
$110$	−15.7993	+	27.3651i	−0.143630	+	0.248774i
$111$		0			0
$112$	−65.5531	+	37.8471i	−0.585295	+	0.337920i
$113$			145.422i			1.28692i	0.765481	+	0.643458i	$0.222501\pi$
$113$			145.422i			1.28692i	−0.765481	+	0.643458i	$0.777499\pi$
$114$		0			0
$115$	−7.28466	+	4.20580i	−0.0633449	+	0.0365722i
$116$	−63.8074	+	36.8392i	−0.550064	+	0.317580i
$117$		0			0
$118$		−	112.761i		−	0.955598i
$119$	214.607	+	123.904i	1.80342	+	1.04121i
$120$		0			0
$121$	−0.291328			−0.00240767
$122$	16.4757	+	28.5367i	0.135047	+	0.233908i
$123$		0			0
$124$	83.5803	−	144.765i	0.674035	−	1.16746i
$125$		−	46.5046i		−	0.372037i
$126$		0			0
$127$	180.179			1.41873			0.709367	−	0.704839i	$-0.248981\pi$
$127$	180.179			1.41873			0.709367	+	0.704839i	$0.248981\pi$
$128$			113.199i			0.884371i
$129$		0			0
$130$	−4.34202			−0.0334001
$131$		−	12.8285i		−	0.0979272i	−0.998801	−	0.0489636i	$-0.984408\pi$
$131$		−	12.8285i		−	0.0979272i	0.998801	−	0.0489636i	$-0.0155918\pi$
$132$		0			0
$133$	54.9872			0.413437
$134$	158.706	+	91.6289i	1.18437	+	0.683798i
$135$		0			0
$136$	101.199	−	58.4270i	0.744107	−	0.429610i
$137$		−	39.1425i		−	0.285712i	−0.989743	−	0.142856i	$-0.954371\pi$
$137$		−	39.1425i		−	0.285712i	0.989743	−	0.142856i	$-0.0456286\pi$
$138$		0			0
$139$	106.778	−	184.945i	0.768186	−	1.33054i	−0.170359	−	0.985382i	$-0.554493\pi$
$139$	106.778	−	184.945i	0.768186	−	1.33054i	0.938545	−	0.345156i	$-0.112174\pi$
$140$	−38.9163			−0.277974
$141$		0			0
$142$	114.483	+	198.291i	0.806220	+	1.39641i
$143$	8.29341	+	14.3646i	0.0579959	+	0.100452i
$144$		0			0
$145$	13.3629			0.0921578
$146$	160.248	+	277.558i	1.09759	+	1.90108i
$147$		0			0
$148$	−189.608	−	109.470i	−1.28113	−	0.739662i
$149$	−150.783	−	87.0547i	−1.01197	−	0.584260i	−0.100200	−	0.994967i	$-0.531948\pi$
$149$	−150.783	−	87.0547i	−1.01197	−	0.584260i	−0.911767	+	0.410707i	$0.865282\pi$
$150$		0			0
$151$		−	10.3941i		−	0.0688351i	−0.999408	−	0.0344176i	$-0.989042\pi$
$151$		−	10.3941i		−	0.0688351i	0.999408	−	0.0344176i	$-0.0109576\pi$
$152$	12.9647	−	22.4554i	0.0852938	−	0.147733i
$153$		0			0
$154$	131.270	+	227.366i	0.852402	+	1.47640i
$155$	−26.2557	+	15.1588i	−0.169392	+	0.0977984i
$156$		0			0
$157$	153.792	−	88.7916i	0.979564	−	0.565552i	0.0774256	−	0.996998i	$-0.475330\pi$
$157$	153.792	−	88.7916i	0.979564	−	0.565552i	0.902139	+	0.431447i	$0.141997\pi$
$158$	286.502	−	165.412i	1.81331	−	1.04691i
$159$		0			0
$160$	20.8614	−	36.1331i	0.130384	−	0.225832i
$161$			69.8886i			0.434091i
$162$		0			0
$163$	199.114	−	114.959i	1.22156	−	0.705268i	0.256309	−	0.966595i	$-0.417494\pi$
$163$	199.114	−	114.959i	1.22156	−	0.705268i	0.965250	+	0.261327i	$0.0841602\pi$
$164$	−52.0892			−0.317617
$165$		0			0
$166$	−376.383	−	217.305i	−2.26736	−	1.30906i
$167$	67.3541	−	116.661i	0.403318	−	0.698567i	−0.590806	−	0.806814i	$-0.701190\pi$
$167$	67.3541	−	116.661i	0.403318	−	0.698567i	0.994124	+	0.108246i	$0.0345236\pi$
$168$		0			0
$169$	83.3604	−	144.384i	0.493257	−	0.854346i
$170$	−90.5725			−0.532779
$171$		0			0
$172$	222.520	+	30.0636i	1.29372	+	0.174788i
$173$	−75.7171			−0.437671			−0.218836	−	0.975762i	$-0.570226\pi$
$173$	−75.7171			−0.437671			−0.218836	+	0.975762i	$0.570226\pi$
$174$		0			0
$175$	−164.255	−	94.8326i	−0.938599	−	0.541900i
$176$	−105.686			−0.600486
$177$		0			0
$178$	−105.717	+	183.108i	−0.593917	+	1.02869i
$179$	−21.0506	+	12.1536i	−0.117601	+	0.0678972i	−0.557647	−	0.830078i	$-0.688296\pi$
$179$	−21.0506	+	12.1536i	−0.117601	+	0.0678972i	0.440045	+	0.897975i	$0.354962\pi$
$180$		0			0
$181$	−123.872	−	214.552i	−0.684374	−	1.18537i	−0.973633	−	0.228119i	$-0.926742\pi$
$181$	−123.872	−	214.552i	−0.684374	−	1.18537i	0.289260	−	0.957251i	$-0.406591\pi$
$182$	−18.0381	+	31.2428i	−0.0991102	+	0.171664i
$183$		0			0
$184$	28.5408	+	16.4781i	0.155113	+	0.0895547i
$185$	19.8543	+	34.3886i	0.107320	+	0.185885i
$186$		0			0
$187$	172.997	+	299.639i	0.925115	+	1.60235i
$188$	62.5608			0.332770
$189$		0			0
$190$	−17.4050	+	10.0488i	−0.0916053	+	0.0528883i
$191$	−276.681	−	159.742i	−1.44859	−	0.836345i	−0.450194	−	0.892931i	$-0.648645\pi$
$191$	−276.681	−	159.742i	−1.44859	−	0.836345i	−0.998398	+	0.0565861i	$0.981978\pi$
$192$		0			0
$193$	−195.998			−1.01553			−0.507766	−	0.861495i	$-0.669529\pi$
$193$	−195.998			−1.01553			−0.507766	+	0.861495i	$0.669529\pi$
$194$		−	31.9166i		−	0.164518i
$195$		0			0
$196$	−33.7337	+	58.4284i	−0.172111	+	0.298104i
$197$	−23.7998	−	41.2225i	−0.120811	−	0.209251i	0.799277	−	0.600963i	$-0.205216\pi$
$197$	−23.7998	−	41.2225i	−0.120811	−	0.209251i	−0.920088	+	0.391712i	$0.871883\pi$
$198$		0			0
$199$			27.5977i			0.138682i	0.997593	+	0.0693409i	$0.0220896\pi$
$199$			27.5977i			0.138682i	−0.997593	+	0.0693409i	$0.977910\pi$
$200$	−77.4547	+	44.7185i	−0.387273	+	0.223592i
$201$		0			0
$202$	144.844	−	83.6255i	0.717047	−	0.413988i
$203$	55.5134	−	96.1521i	0.273465	−	0.473655i
$204$		0			0
$205$	8.18158	+	4.72364i	0.0399102	+	0.0230421i
$206$	−48.1248	+	27.7849i	−0.233616	+	0.134878i
$207$		0			0
$208$	−7.26123	−	12.5768i	−0.0349098	−	0.0604655i
$209$	66.4884	+	38.3871i	0.318126	+	0.183670i
$210$		0			0
$211$			111.355i			0.527749i	0.964557	+	0.263874i	$0.0850004\pi$
$211$			111.355i			0.527749i	−0.964557	+	0.263874i	$0.915000\pi$
$212$	98.9459	−	171.379i	0.466726	−	0.808393i
$213$		0			0
$214$			90.2149i			0.421565i
$215$	−32.2247	−	24.9010i	−0.149882	−	0.115819i
$216$		0			0
$217$			251.896i			1.16081i
$218$	−196.294	−	113.331i	−0.900433	−	0.519865i
$219$		0			0
$220$	−47.0561	−	27.1679i	−0.213891	−	0.123490i
$221$	−23.7718	+	41.1740i	−0.107565	+	0.186308i
$222$		0			0
$223$		−	344.375i		−	1.54428i	−0.635452	−	0.772140i	$-0.719186\pi$
$223$		−	344.375i		−	1.54428i	0.635452	−	0.772140i	$-0.280814\pi$
$224$	−173.329	−	300.215i	−0.773792	−	1.34025i
$225$		0			0
$226$	−441.610			−1.95403
$227$	−64.2079	−	37.0705i	−0.282854	−	0.163306i	0.351861	−	0.936052i	$-0.385549\pi$
$227$	−64.2079	−	37.0705i	−0.282854	−	0.163306i	−0.634715	+	0.772746i	$0.718882\pi$
$228$		0			0
$229$	80.0779	+	138.699i	0.349685	+	0.605673i	0.986193	−	0.165597i	$-0.0529552\pi$
$229$	80.0779	+	138.699i	0.349685	+	0.605673i	−0.636508	+	0.771270i	$0.719622\pi$
$230$	−12.7720	−	22.1217i	−0.0555304	−	0.0961815i
$231$		0			0
$232$	−26.1775	−	45.3407i	−0.112834	−	0.195434i
$233$	−315.564	+	182.191i	−1.35435	+	0.781934i	−0.988855	−	0.148879i	$-0.952433\pi$
$233$	−315.564	+	182.191i	−1.35435	+	0.781934i	−0.365495	+	0.930813i	$0.619100\pi$
$234$		0			0
$235$	−9.82635	−	5.67325i	−0.0418143	−	0.0241415i
$236$	193.899			0.821606
$237$		0			0
$238$	−376.265	+	651.711i	−1.58095	+	2.73828i
$239$	200.174	−	346.712i	0.837549	−	1.45068i	−0.0543890	−	0.998520i	$-0.517321\pi$
$239$	200.174	−	346.712i	0.837549	−	1.45068i	0.891938	−	0.452158i	$-0.149346\pi$
$240$		0			0
$241$	−295.056	+	170.350i	−1.22430	+	0.706848i	−0.965831	−	0.259172i	$-0.916550\pi$
$241$	−295.056	+	170.350i	−1.22430	+	0.706848i	−0.258466	+	0.966020i	$0.583217\pi$
$242$		−	0.884693i		−	0.00365576i
$243$		0			0
$244$	−49.0707	+	28.3310i	−0.201110	+	0.116111i
$245$	10.5970	−	6.11819i	0.0432531	−	0.0249722i
$246$		0			0
$247$			10.5497i			0.0427113i
$248$	102.868	+	59.3910i	0.414792	+	0.239480i
$249$		0			0
$250$	141.223			0.564893
$251$	−1.90726	−	3.30347i	−0.00759864	−	0.0131612i	0.862201	−	0.506566i	$-0.169085\pi$
$251$	−1.90726	−	3.30347i	−0.00759864	−	0.0131612i	−0.869800	+	0.493405i	$0.835752\pi$
$252$		0			0
$253$	−48.7899	+	84.5066i	−0.192846	+	0.334018i
$254$			547.161i			2.15418i
$255$		0			0
$256$	37.4578			0.146319
$257$		−	450.213i		−	1.75180i	−0.482490	−	0.875902i	$-0.660267\pi$
$257$		−	450.213i		−	1.75180i	0.482490	−	0.875902i	$-0.339733\pi$
$258$		0			0
$259$	329.923			1.27383
$260$		−	7.46638i		−	0.0287168i
$261$		0			0
$262$	38.9569			0.148691
$263$	−332.861	−	192.177i	−1.26563	−	0.730712i	−0.291473	−	0.956579i	$-0.594145\pi$
$263$	−332.861	−	192.177i	−1.26563	−	0.730712i	−0.974158	+	0.225867i	$0.927479\pi$
$264$		0			0
$265$	−31.0826	+	17.9456i	−0.117293	+	0.0677191i
$266$			166.983i			0.627755i
$267$		0			0
$268$	−157.562	+	272.905i	−0.587917	+	1.01830i
$269$	−444.120			−1.65100			−0.825502	−	0.564400i	$-0.809108\pi$
$269$	−444.120			−1.65100			−0.825502	+	0.564400i	$0.809108\pi$
$270$		0			0
$271$	14.0250	+	24.2920i	0.0517527	+	0.0896383i	0.890741	−	0.454511i	$-0.150186\pi$
$271$	14.0250	+	24.2920i	0.0517527	+	0.0896383i	−0.838989	+	0.544149i	$0.816853\pi$
$272$	−151.466	−	262.347i	−0.556860	−	0.964510i
$273$		0			0
$274$	118.866			0.433819
$275$	−132.407	−	229.336i	−0.481480	−	0.833948i
$276$		0			0
$277$	−261.223	−	150.817i	−0.943042	−	0.544466i	−0.0521297	−	0.998640i	$-0.516601\pi$
$277$	−261.223	−	150.817i	−0.943042	−	0.544466i	−0.890913	+	0.454174i	$0.849934\pi$
$278$	561.632	+	324.259i	2.02026	+	1.16640i
$279$		0			0
$280$		−	27.6534i		−	0.0987622i
$281$	58.0433	−	100.534i	0.206560	−	0.357772i	−0.744069	−	0.668103i	$-0.767107\pi$
$281$	58.0433	−	100.534i	0.206560	−	0.357772i	0.950629	+	0.310331i	$0.100440\pi$
$282$		0			0
$283$	−206.613	−	357.865i	−0.730083	−	1.26454i	−0.956847	−	0.290591i	$-0.906148\pi$
$283$	−206.613	−	357.865i	−0.730083	−	1.26454i	0.226765	−	0.973950i	$-0.427185\pi$
$284$	−340.973	+	196.861i	−1.20061	+	0.693173i
$285$		0			0
$286$	−43.6218	+	25.1851i	−0.152524	+	0.0880597i
$287$	67.9775	−	39.2468i	0.236855	−	0.136749i
$288$		0			0
$289$	−351.369	+	608.588i	−1.21581	+	2.10584i
$290$			40.5798i			0.139930i
$291$		0			0
$292$	−477.278	+	275.557i	−1.63451	+	0.943688i
$293$	533.250			1.81996			0.909982	−	0.414647i	$-0.136095\pi$
$293$	533.250			1.81996			0.909982	+	0.414647i	$0.136095\pi$
$294$		0			0
$295$	−30.4555	−	17.5835i	−0.103239	−	0.0596050i
$296$	77.7879	−	134.733i	0.262797	−	0.455178i
$297$		0			0
$298$	264.364	−	457.892i	0.887128	−	1.53655i
$299$	−13.4086			−0.0448449
$300$		0			0
$301$	−313.045	+	128.425i	−1.04002	+	0.426662i
$302$	31.5644			0.104518
$303$		0			0
$304$	−58.2134	−	33.6095i	−0.191491	−	0.110558i
$305$	10.2766			0.0336939
$306$		0			0
$307$	179.967	−	311.712i	0.586212	−	1.01535i	−0.408511	−	0.912753i	$-0.633952\pi$
$307$	179.967	−	311.712i	0.586212	−	1.01535i	0.994723	−	0.102596i	$-0.0327148\pi$
$308$	−390.971	+	225.727i	−1.26938	+	0.732880i
$309$		0			0
$310$	−46.0335	−	79.7323i	−0.148495	−	0.257201i
$311$	−175.154	+	303.376i	−0.563197	+	0.975485i	0.434018	+	0.900904i	$0.357095\pi$
$311$	−175.154	+	303.376i	−0.563197	+	0.975485i	−0.997215	+	0.0745811i	$0.976238\pi$
$312$		0			0
$313$	155.617	+	89.8457i	0.497180	+	0.287047i	0.727548	−	0.686057i	$-0.240660\pi$
$313$	155.617	+	89.8457i	0.497180	+	0.287047i	−0.230368	+	0.973104i	$0.573993\pi$
$314$	269.639	+	467.028i	0.858722	+	1.48735i
$315$		0			0
$316$	284.437	+	492.659i	0.900117	+	1.55905i
$317$	455.210			1.43599			0.717996	−	0.696047i	$-0.245059\pi$
$317$	455.210			1.43599			0.717996	+	0.696047i	$0.245059\pi$
$318$		0			0
$319$	134.249	−	77.5089i	0.420844	−	0.242975i
$320$	78.1683	+	45.1305i	0.244276	+	0.141033i
$321$		0			0
$322$	−212.235			−0.659115
$323$			220.061i			0.681305i
$324$		0			0
$325$	18.1943	−	31.5135i	0.0559825	−	0.0969645i
$326$	349.102	+	604.662i	1.07086	+	1.85479i
$327$		0			0
$328$		−	37.0138i		−	0.112847i
$329$	−81.6432	+	47.1367i	−0.248156	+	0.143273i
$330$		0			0
$331$	499.114	−	288.164i	1.50790	−	0.870585i	0.507939	−	0.861393i	$-0.330407\pi$
$331$	499.114	−	288.164i	1.50790	−	0.870585i	0.999958	−	0.00919173i	$-0.00292586\pi$
$332$	373.669	−	647.214i	1.12551	−	1.94944i
$333$		0			0
$334$	354.270	+	204.538i	1.06069	+	0.612389i
$335$	49.4961	−	28.5766i	0.147749	−	0.0853032i
$336$		0			0
$337$	−53.6179	−	92.8689i	−0.159104	−	0.275575i	0.775442	−	0.631419i	$-0.217527\pi$
$337$	−53.6179	−	92.8689i	−0.159104	−	0.275575i	−0.934546	+	0.355843i	$0.884194\pi$
$338$	438.461	+	253.145i	1.29722	+	0.748951i
$339$		0			0
$340$		−	155.745i		−	0.458074i
$341$	−175.851	+	304.583i	−0.515692	+	0.893205i
$342$		0			0
$343$			283.910i			0.827727i
$344$	−21.3628	+	158.120i	−0.0621011	+	0.459650i
$345$		0			0
$346$		−	229.935i		−	0.664551i
$347$	−168.657	−	97.3742i	−0.486043	−	0.280617i	0.236888	−	0.971537i	$-0.423872\pi$
$347$	−168.657	−	97.3742i	−0.486043	−	0.280617i	−0.722932	+	0.690920i	$0.757206\pi$
$348$		0			0
$349$	171.372	+	98.9417i	0.491037	+	0.283501i	0.725005	−	0.688744i	$-0.241838\pi$
$349$	171.372	+	98.9417i	0.491037	+	0.283501i	−0.233967	+	0.972244i	$0.575171\pi$
$350$	287.984	−	498.802i	0.822810	−	1.42515i
$351$		0			0
$352$		−	484.012i		−	1.37503i
$353$	−132.488	−	229.476i	−0.375319	−	0.650072i	0.615055	−	0.788484i	$-0.289134\pi$
$353$	−132.488	−	229.476i	−0.375319	−	0.650072i	−0.990375	+	0.138412i	$0.955800\pi$
$354$		0			0
$355$	71.4084			0.201150
$356$	−314.865	−	181.787i	−0.884452	−	0.510639i
$357$		0			0
$358$	−36.9075	−	63.9257i	−0.103094	−	0.178563i
$359$	244.538	+	423.553i	0.681166	+	1.17981i	0.974625	+	0.223842i	$0.0718600\pi$
$359$	244.538	+	423.553i	0.681166	+	1.17981i	−0.293460	+	0.955971i	$0.594807\pi$
$360$		0			0
$361$	−156.085	−	270.347i	−0.432368	−	0.748883i
$362$	651.542	−	376.168i	1.79984	−	1.03914i
$363$		0			0
$364$	−53.7240	−	31.0176i	−0.147594	−	0.0852131i
$365$	99.9541			0.273847
$366$		0			0
$367$	−151.707	+	262.765i	−0.413371	+	0.715980i	−0.995256	−	0.0972911i	$-0.968982\pi$
$367$	−151.707	+	262.765i	−0.413371	+	0.715980i	0.581885	+	0.813271i	$0.302316\pi$
$368$	42.7177	−	73.9892i	0.116081	−	0.201058i
$369$		0			0
$370$	−104.430	+	60.2927i	−0.282243	+	0.162953i
$371$			298.205i			0.803787i
$372$		0			0
$373$	−201.104	+	116.108i	−0.539154	+	0.311281i	−0.744736	−	0.667359i	$-0.767425\pi$
$373$	−201.104	+	116.108i	−0.539154	+	0.311281i	0.205582	+	0.978640i	$0.434091\pi$
$374$	−909.931	+	525.349i	−2.43297	+	1.40468i
$375$		0			0
$376$			44.4548i			0.118231i
$377$	18.4475	+	10.6506i	0.0489323	+	0.0282511i
$378$		0			0
$379$	651.595			1.71925			0.859624	−	0.510926i	$-0.170698\pi$
$379$	651.595			1.71925			0.859624	+	0.510926i	$0.170698\pi$
$380$	−17.2795	−	29.9290i	−0.0454724	−	0.0787606i
$381$		0			0
$382$	485.097	−	840.213i	1.26989	−	2.19951i
$383$			148.879i			0.388718i	0.980930	+	0.194359i	$0.0622627\pi$
$383$			148.879i			0.388718i	−0.980930	+	0.194359i	$0.937737\pi$
$384$		0			0
$385$	81.8790			0.212673
$386$		−	595.198i		−	1.54196i
$387$		0			0
$388$	54.8826			0.141450
$389$			145.528i			0.374108i	0.982350	+	0.187054i	$0.0598939\pi$
$389$			145.528i			0.374108i	−0.982350	+	0.187054i	$0.940106\pi$
$390$		0			0
$391$	−279.698			−0.715340
$392$	−41.5184	−	23.9707i	−0.105914	−	0.0611497i
$393$		0			0
$394$	125.183	−	72.2743i	0.317723	−	0.183437i
$395$		−	103.175i		−	0.261203i
$396$		0			0
$397$	51.5897	−	89.3559i	0.129949	−	0.225078i	−0.793708	−	0.608299i	$-0.791852\pi$
$397$	51.5897	−	89.3559i	0.129949	−	0.225078i	0.923657	+	0.383221i	$0.125185\pi$
$398$	−83.8075			−0.210572
$399$		0			0
$400$	115.928	+	200.793i	0.289820	+	0.501983i
$401$	65.7024	+	113.800i	0.163846	+	0.283790i	0.936245	−	0.351348i	$-0.114277\pi$
$401$	65.7024	+	113.800i	0.163846	+	0.283790i	−0.772399	+	0.635138i	$0.780943\pi$
$402$		0			0
$403$	−48.3281			−0.119921
$404$	143.799	+	249.068i	0.355939	+	0.616504i
$405$		0			0
$406$	291.991	+	168.581i	0.719188	+	0.415224i
$407$	398.930	+	230.322i	0.980172	+	0.565902i
$408$		0			0
$409$			618.645i			1.51258i	0.654237	+	0.756290i	$0.272990\pi$
$409$			618.645i			1.51258i	−0.654237	+	0.756290i	$0.727010\pi$
$410$	−14.3445	+	24.8455i	−0.0349867	+	0.0605987i
$411$		0			0
$412$	−47.7779	−	82.7537i	−0.115966	−	0.200858i
$413$	−253.042	+	146.094i	−0.612693	+	0.353739i
$414$		0			0
$415$	−117.383	+	67.7714i	−0.282852	+	0.163305i
$416$	57.5985	−	33.2545i	0.138458	−	0.0799387i
$417$		0			0
$418$	−116.572	+	201.909i	−0.278881	+	0.483036i
$419$			751.232i			1.79292i	0.443127	+	0.896459i	$0.353869\pi$
$419$			751.232i			1.79292i	−0.443127	+	0.896459i	$0.646131\pi$
$420$		0			0
$421$	−628.309	+	362.755i	−1.49242	+	0.861650i	−0.999962	−	0.00868591i	$-0.997235\pi$
$421$	−628.309	+	362.755i	−1.49242	+	0.861650i	−0.492459	+	0.870336i	$0.663902\pi$
$422$	−338.158			−0.801323
$423$		0			0
$424$	121.780	+	70.3096i	0.287217	+	0.165825i
$425$	379.525	−	657.356i	0.892999	−	1.54672i
$426$		0			0
$427$	42.6923	−	73.9452i	0.0999819	−	0.173174i
$428$	−155.130			−0.362454
$429$		0			0
$430$	75.6183	−	97.8585i	0.175856	−	0.227578i
$431$	−210.326			−0.487996			−0.243998	−	0.969776i	$-0.578459\pi$
$431$	−210.326			−0.487996			−0.243998	+	0.969776i	$0.578459\pi$
$432$		0			0
$433$	−649.809	−	375.168i	−1.50071	−	0.866438i	−1.00000		0.000825596i	$-0.999737\pi$
$433$	−649.809	−	375.168i	−1.50071	−	0.866438i	−0.500715	−	0.865612i	$-0.666929\pi$
$434$	−764.947			−1.76255
$435$		0			0
$436$	194.879	−	337.541i	0.446971	−	0.774176i
$437$	−53.7486	+	31.0318i	−0.122995	+	0.0710109i
$438$		0			0
$439$	−77.4428	−	134.135i	−0.176407	−	0.305546i	0.764240	−	0.644932i	$-0.223114\pi$
$439$	−77.4428	−	134.135i	−0.176407	−	0.305546i	−0.940647	+	0.339385i	$0.889781\pi$
$440$	19.3051	−	33.4374i	0.0438752	−	0.0759942i
$441$		0			0
$442$	−125.035	−	72.1892i	−0.282885	−	0.163324i
$443$	−186.121	−	322.371i	−0.420138	−	0.727700i	0.575815	−	0.817580i	$-0.304685\pi$
$443$	−186.121	−	322.371i	−0.420138	−	0.727700i	−0.995953	+	0.0898803i	$0.971352\pi$
$444$		0			0
$445$	32.9703	+	57.1063i	0.0740906	+	0.128329i
$446$	1045.78			2.34480
$447$		0			0
$448$	649.469	−	374.971i	1.44971	−	0.836990i
$449$	−37.2771	−	21.5220i	−0.0830225	−	0.0479331i	0.457914	−	0.888996i	$-0.348597\pi$
$449$	−37.2771	−	21.5220i	−0.0830225	−	0.0479331i	−0.540937	+	0.841063i	$0.681930\pi$
$450$		0			0
$451$	109.594			0.243003
$452$		−	759.376i		−	1.68004i
$453$		0			0
$454$	112.574	−	194.984i	0.247960	−	0.429480i
$455$	5.62558	+	9.74379i	0.0123639	+	0.0214149i
$456$		0			0
$457$			478.744i			1.04758i	0.851847	+	0.523790i	$0.175483\pi$
$457$			478.744i			1.04758i	−0.851847	+	0.523790i	$0.824517\pi$
$458$	−421.195	+	243.177i	−0.919641	+	0.530955i
$459$		0			0
$460$	38.0397	−	21.9623i	0.0826951	−	0.0477440i
$461$	352.762	−	611.002i	0.765210	−	1.32538i	−0.174925	−	0.984582i	$-0.555968\pi$
$461$	352.762	−	611.002i	0.765210	−	1.32538i	0.940135	−	0.340801i	$-0.110698\pi$
$462$		0			0
$463$	21.8750	+	12.6296i	0.0472463	+	0.0272777i	0.523437	−	0.852064i	$-0.324650\pi$
$463$	21.8750	+	12.6296i	0.0472463	+	0.0272777i	−0.476191	+	0.879342i	$0.657983\pi$
$464$	−117.541	+	67.8623i	−0.253321	+	0.146255i
$465$		0			0
$466$	−553.269	−	958.290i	−1.18727	−	2.05642i
$467$	291.386	+	168.232i	0.623952	+	0.360239i	0.778406	−	0.627761i	$-0.216028\pi$
$467$	291.386	+	168.232i	0.623952	+	0.360239i	−0.154454	+	0.988000i	$0.549362\pi$
$468$		0			0
$469$		−	474.863i		−	1.01250i
$470$	17.2283	−	29.8402i	0.0366559	−	0.0634899i
$471$		0			0
$472$			137.782i			0.291911i
$473$	−468.177	−	63.2531i	−0.989803	−	0.133727i
$474$		0			0
$475$		−	168.429i		−	0.354588i
$476$	−1120.66	−	647.012i	−2.35432	−	1.35927i
$477$		0			0
$478$	1052.88	+	607.881i	2.20268	+	1.27172i
$479$	328.259	−	568.561i	0.685300	−	1.18697i	−0.288042	−	0.957618i	$-0.593004\pi$
$479$	328.259	−	568.561i	0.685300	−	1.18697i	0.973342	−	0.229357i	$-0.0736624\pi$
$480$		0			0
$481$			63.2981i			0.131597i
$482$	−517.313	−	896.012i	−1.07326	−	1.85895i
$483$		0			0
$484$	1.52129			0.00314315
$485$	−8.62034	−	4.97696i	−0.0177739	−	0.0102618i
$486$		0			0
$487$	67.9720	+	117.731i	0.139573	+	0.241747i	0.927335	−	0.374232i	$-0.122094\pi$
$487$	67.9720	+	117.731i	0.139573	+	0.241747i	−0.787762	+	0.615980i	$0.788760\pi$
$488$	−20.1316	−	34.8690i	−0.0412533	−	0.0714529i
$489$		0			0
$490$	18.5795	+	32.1806i	0.0379173	+	0.0656746i
$491$	−117.771	+	67.9950i	−0.239859	+	0.138483i	−0.615112	−	0.788440i	$-0.710889\pi$
$491$	−117.771	+	67.9950i	−0.239859	+	0.138483i	0.375253	+	0.926922i	$0.377556\pi$
$492$		0			0
$493$	384.805	+	222.167i	0.780538	+	0.450644i
$494$	−32.0368			−0.0648519
$495$		0			0
$496$	153.965	−	266.675i	0.310414	−	0.537652i
$497$	296.652	−	513.816i	0.596885	−	1.03384i
$498$		0			0
$499$	−201.614	+	116.402i	−0.404037	+	0.233271i	−0.688224	−	0.725498i	$-0.741609\pi$
$499$	−201.614	+	116.402i	−0.404037	+	0.233271i	0.284188	+	0.958769i	$0.408276\pi$
$500$			242.842i			0.485685i
$501$		0			0
$502$	10.0318	−	5.79188i	0.0199837	−	0.0115376i
$503$	10.8313	−	6.25347i	0.0215335	−	0.0124323i	−0.489195	−	0.872175i	$-0.662709\pi$
$503$	10.8313	−	6.25347i	0.0215335	−	0.0124323i	0.510728	+	0.859742i	$0.329376\pi$
$504$		0			0
$505$		−	52.1610i		−	0.103289i
$506$	−256.626	−	148.163i	−0.507166	−	0.292813i
$507$		0			0
$508$	−940.878			−1.85212
$509$	252.810	+	437.880i	0.496680	+	0.860275i	0.999993	−	0.00382918i	$-0.00121887\pi$
$509$	252.810	+	437.880i	0.496680	+	0.860275i	−0.503313	+	0.864104i	$0.667886\pi$
$510$		0			0
$511$	415.239	−	719.216i	0.812601	−	1.40747i
$512$			566.548i			1.10654i
$513$		0			0
$514$	1367.19			2.65990
$515$			17.3307i			0.0336518i
$516$		0			0
$517$	−131.626			−0.254597
$518$			1001.90i			1.93416i
$519$		0			0
$520$	5.30551			0.0102029
$521$	−64.9091	−	37.4753i	−0.124586	−	0.0719296i	0.436412	−	0.899747i	$-0.356249\pi$
$521$	−64.9091	−	37.4753i	−0.124586	−	0.0719296i	−0.560998	+	0.827817i	$0.689582\pi$
$522$		0			0
$523$	−105.070	+	60.6623i	−0.200899	+	0.115989i	−0.597075	−	0.802186i	$-0.703670\pi$
$523$	−105.070	+	60.6623i	−0.200899	+	0.115989i	0.396176	+	0.918175i	$0.370337\pi$
$524$			66.9889i			0.127841i
$525$		0			0
$526$	583.596	−	1010.82i	1.10950	−	1.92171i
$527$	−1008.10			−1.91290
$528$		0			0
$529$	225.059	+	389.813i	0.425442	+	0.736887i
$530$	−54.4963	−	94.3904i	−0.102823	−	0.178095i
$531$		0			0
$532$	−287.137			−0.539732
$533$	7.52979	+	13.0420i	0.0141272	+	0.0244690i
$534$		0			0
$535$	24.3661	+	14.0678i	0.0455442	+	0.0262949i
$536$	−193.923	−	111.961i	−0.361796	−	0.208883i
$537$		0			0
$538$		−	1348.68i		−	2.50685i
$539$	70.9748	−	122.932i	0.131679	−	0.228074i
$540$		0			0
$541$	404.742	+	701.034i	0.748137	+	1.29581i	0.948715	+	0.316133i	$0.102385\pi$
$541$	404.742	+	701.034i	0.748137	+	1.29581i	−0.200578	+	0.979678i	$0.564282\pi$
$542$	−73.7689	+	42.5905i	−0.136105	+	0.0785802i
$543$		0			0
$544$	1201.48	−	693.673i	2.20860	−	1.27513i
$545$	−61.2189	+	35.3447i	−0.112328	+	0.0648527i
$546$		0			0
$547$	−172.970	+	299.593i	−0.316216	+	0.547702i	−0.979695	−	0.200492i	$-0.935746\pi$
$547$	−172.970	+	299.593i	−0.316216	+	0.547702i	0.663479	+	0.748195i	$0.269079\pi$
$548$			204.398i			0.372990i
$549$		0			0
$550$	696.437	−	402.088i	1.26625	−	0.731069i
$551$	98.5957			0.178940
$552$		0			0
$553$	−742.393	−	428.621i	−1.34248	−	0.775083i
$554$	457.995	−	793.270i	0.826705	−	1.43190i
$555$		0			0
$556$	−557.583	+	965.763i	−1.00285	+	1.73698i
$557$	−489.320			−0.878491			−0.439246	−	0.898367i	$-0.644754\pi$
$557$	−489.320			−0.878491			−0.439246	+	0.898367i	$0.644754\pi$
$558$		0			0
$559$	−24.6393	−	60.0599i	−0.0440774	−	0.107442i
$560$	−71.6886			−0.128015
$561$		0			0
$562$	305.297	+	176.264i	0.543234	+	0.313636i
$563$	1040.45			1.84804			0.924020	−	0.382344i	$-0.124883\pi$
$563$	1040.45			1.84804			0.924020	+	0.382344i	$0.124883\pi$
$564$		0			0
$565$	−68.8631	+	119.274i	−0.121882	+	0.211105i
$566$	1086.75	−	627.435i	1.92005	−	1.10854i
$567$		0			0
$568$	−139.887	−	242.291i	−0.246280	−	0.426569i
$569$	−250.718	+	434.257i	−0.440629	+	0.763193i	−0.997736	−	0.0672483i	$-0.978578\pi$
$569$	−250.718	+	434.257i	−0.440629	+	0.763193i	0.557107	+	0.830441i	$0.311911\pi$
$570$		0			0
$571$	−579.549	−	334.603i	−1.01497	−	0.585994i	−0.102328	−	0.994751i	$-0.532629\pi$
$571$	−579.549	−	334.603i	−1.01497	−	0.585994i	−0.912643	+	0.408757i	$0.865962\pi$
$572$	−43.3073	−	75.0105i	−0.0757121	−	0.131137i
$573$		0			0
$574$	119.183	+	206.431i	0.207636	+	0.359636i
$575$	214.073			0.372301
$576$		0			0
$577$	73.7567	−	42.5835i	0.127828	−	0.0738015i	−0.434722	−	0.900564i	$-0.643154\pi$
$577$	73.7567	−	42.5835i	0.127828	−	0.0738015i	0.562550	+	0.826763i	$0.309820\pi$
$578$	−1848.14	−	1067.02i	−3.19747	−	1.84606i
$579$		0			0
$580$	−69.7796			−0.120310
$581$			1126.17i			1.93833i
$582$		0			0
$583$	−208.180	+	360.578i	−0.357084	+	0.618487i
$584$	−195.807	−	339.148i	−0.335286	−	0.580732i
$585$		0			0
$586$			1619.35i			2.76340i
$587$	244.586	−	141.212i	0.416671	−	0.240565i	−0.276981	−	0.960875i	$-0.589334\pi$
$587$	244.586	−	141.212i	0.416671	−	0.240565i	0.693652	+	0.720310i	$0.256001\pi$
$588$		0			0
$589$	−193.723	+	111.846i	−0.328902	+	0.189892i
$590$	53.3968	−	92.4859i	0.0905030	−	0.156756i
$591$		0			0
$592$	−349.280	−	201.657i	−0.590000	−	0.340637i
$593$	975.936	−	563.457i	1.64576	−	0.950180i	0.667029	−	0.745032i	$-0.267566\pi$
$593$	975.936	−	563.457i	1.64576	−	0.950180i	0.978731	−	0.205148i	$-0.0657676\pi$
$594$		0			0
$595$	117.347	+	203.251i	0.197222	+	0.341598i
$596$	787.374	+	454.591i	1.32110	+	0.762736i
$597$		0			0
$598$		−	40.7188i		−	0.0680916i
$599$	−417.943	+	723.899i	−0.697735	+	1.20851i	0.271515	+	0.962434i	$0.412475\pi$
$599$	−417.943	+	723.899i	−0.697735	+	1.20851i	−0.969250	+	0.246078i	$0.920858\pi$
$600$		0			0
$601$			458.410i			0.762745i	0.924421	+	0.381373i	$0.124549\pi$
$601$			458.410i			0.762745i	−0.924421	+	0.381373i	$0.875451\pi$
$602$	−389.996	−	950.642i	−0.647834	−	1.57914i
$603$		0			0
$604$			54.2770i			0.0898625i
$605$	−0.238947	−	0.137956i	−0.000394953	−	0.000228026i
$606$		0			0
$607$	−67.7886	−	39.1378i	−0.111678	−	0.0644774i	0.443121	−	0.896462i	$-0.353871\pi$
$607$	−67.7886	−	39.1378i	−0.111678	−	0.0644774i	−0.554799	+	0.831985i	$0.687205\pi$
$608$	153.923	−	266.602i	0.253162	−	0.438490i
$609$		0			0
$610$			31.2077i			0.0511601i
$611$	−9.04352	−	15.6638i	−0.0148012	−	0.0256364i
$612$		0			0
$613$	−325.111			−0.530360			−0.265180	−	0.964199i	$-0.585431\pi$
$613$	−325.111			−0.530360			−0.265180	+	0.964199i	$0.585431\pi$
$614$	946.595	+	546.517i	1.54168	+	0.890092i
$615$		0			0
$616$	−160.398	−	277.818i	−0.260387	−	0.451004i
$617$	376.634	+	652.349i	0.610428	+	1.05729i	0.991168	+	0.132610i	$0.0423358\pi$
$617$	376.634	+	652.349i	0.610428	+	1.05729i	−0.380740	+	0.924682i	$0.624331\pi$
$618$		0			0
$619$	−304.390	−	527.219i	−0.491745	−	0.851727i	0.508210	−	0.861233i	$-0.330307\pi$
$619$	−304.390	−	527.219i	−0.491745	−	0.851727i	−0.999955	+	0.00950602i	$0.996974\pi$
$620$	137.105	−	79.1575i	0.221137	−	0.127673i
$621$		0			0
$622$	−921.279	−	531.901i	−1.48116	−	0.855146i
$623$	547.875			0.879413
$624$		0			0
$625$	−279.266	+	483.703i	−0.446826	+	0.773925i
$626$	−272.840	+	472.572i	−0.435846	+	0.754907i
$627$		0			0
$628$	−803.084	+	463.661i	−1.27880	+	0.738313i
$629$			1320.37i			2.09915i
$630$		0			0
$631$	83.3654	−	48.1311i	0.132116	−	0.0762774i	−0.432485	−	0.901641i	$-0.642363\pi$
$631$	83.3654	−	48.1311i	0.132116	−	0.0762774i	0.564602	+	0.825364i	$0.309030\pi$
$632$	−350.077	+	202.117i	−0.553919	+	0.319805i
$633$		0			0
$634$			1382.36i			2.18038i
$635$	147.783	+	85.3223i	0.232728	+	0.134366i
$636$		0			0
$637$	19.5056			0.0306210
$638$	235.376	+	407.683i	0.368927	+	0.639001i
$639$		0			0
$640$	−53.6046	+	92.8459i	−0.0837572	+	0.145072i
$641$			751.100i			1.17176i	0.810397	+	0.585881i	$0.199251\pi$
$641$			751.100i			1.17176i	−0.810397	+	0.585881i	$0.800749\pi$
$642$		0			0
$643$	−160.364			−0.249400			−0.124700	−	0.992194i	$-0.539797\pi$
$643$	−160.364			−0.249400			−0.124700	+	0.992194i	$0.539797\pi$
$644$		−	364.951i		−	0.566695i
$645$		0			0
$646$	−668.273			−1.03448
$647$			519.911i			0.803571i	0.915734	+	0.401786i	$0.131610\pi$
$647$			519.911i			0.803571i	−0.915734	+	0.401786i	$0.868390\pi$
$648$		0			0
$649$	−407.959			−0.628596
$650$	95.6988	+	55.2517i	0.147229	+	0.0850026i
$651$		0			0
$652$	−1039.75	+	600.302i	−1.59471	+	0.920709i
$653$			663.088i			1.01545i	0.861520	+	0.507724i	$0.169513\pi$
$653$			663.088i			1.01545i	−0.861520	+	0.507724i	$0.830487\pi$
$654$		0			0
$655$	6.07480	−	10.5219i	0.00927451	−	0.0160639i
$656$	−95.9545			−0.146272
$657$		0			0
$658$	−143.143	−	247.931i	−0.217542	−	0.376794i
$659$	−115.264	−	199.644i	−0.174908	−	0.302950i	0.765221	−	0.643767i	$-0.222629\pi$
$659$	−115.264	−	199.644i	−0.174908	−	0.302950i	−0.940129	+	0.340818i	$0.889296\pi$
$660$		0			0
$661$	389.085			0.588631			0.294315	−	0.955708i	$-0.404908\pi$
$661$	389.085			0.588631			0.294315	+	0.955708i	$0.404908\pi$
$662$	875.083	+	1515.69i	1.32188	+	2.28956i
$663$		0			0
$664$	459.901	+	265.524i	0.692622	+	0.399886i
$665$	45.1003	+	26.0387i	0.0678201	+	0.0391559i
$666$		0			0
$667$			125.315i			0.187879i
$668$	−351.716	+	609.190i	−0.526521	+	0.911962i
$669$		0			0
$670$	86.7801	+	150.308i	0.129523	+	0.224340i
$671$	103.244	−	59.6078i	0.153865	−	0.0888342i
$672$		0			0
$673$	−823.355	+	475.364i	−1.22341	+	0.706336i	−0.965643	−	0.259871i	$-0.916320\pi$
$673$	−823.355	+	475.364i	−1.22341	+	0.706336i	−0.257766	+	0.966207i	$0.582986\pi$
$674$	282.020	−	162.825i	0.418428	−	0.241579i
$675$		0			0
$676$	−435.299	+	753.961i	−0.643934	+	1.11533i
$677$		−	1060.20i		−	1.56602i	−0.622008	−	0.783011i	$-0.713683\pi$
$677$		−	1060.20i		−	1.56602i	0.622008	−	0.783011i	$-0.286317\pi$
$678$		0			0
$679$	−71.6230	+	41.3516i	−0.105483	+	0.0609007i
$680$	110.670			0.162751
$681$		0			0
$682$	−924.945	−	534.017i	−1.35622	−	0.783016i
$683$	316.096	−	547.494i	0.462805	−	0.801602i	−0.536294	−	0.844031i	$-0.680176\pi$
$683$	316.096	−	547.494i	0.462805	−	0.801602i	0.999099	+	0.0424288i	$0.0135096\pi$
$684$		0			0
$685$	18.5356	−	32.1046i	0.0270593	−	0.0468680i
$686$	−862.167			−1.25680
$687$		0			0
$688$	409.909	+	55.3808i	0.595798	+	0.0804953i
$689$	−57.2128			−0.0830374
$690$		0			0
$691$	515.257	+	297.484i	0.745669	+	0.430512i	0.824127	−	0.566405i	$-0.191666\pi$
$691$	515.257	+	297.484i	0.745669	+	0.430512i	−0.0784581	+	0.996917i	$0.525000\pi$
$692$	395.387			0.571369
$693$		0			0
$694$	295.702	−	512.171i	0.426083	−	0.737998i
$695$	175.158	−	101.127i	0.252026	−	0.145507i
$696$		0			0
$697$	157.068	+	272.049i	0.225348	+	0.390315i
$698$	−300.462	+	520.415i	−0.430461	+	0.745581i
$699$		0			0
$700$	857.722	+	495.206i	1.22532	+	0.707437i
$701$	38.2998	+	66.3371i	0.0546359	+	0.0946322i	0.892050	−	0.451937i	$-0.149267\pi$
$701$	38.2998	+	66.3371i	0.0546359	+	0.0946322i	−0.837414	+	0.546569i	$0.815934\pi$
$702$		0			0
$703$	146.491	+	253.731i	0.208380	+	0.360926i
$704$	1047.08			1.48734
$705$		0			0
$706$	696.862	−	402.333i	0.987056	−	0.569877i
$707$	−375.323	−	216.693i	−0.530867	−	0.306496i
$708$		0			0
$709$	−97.2271			−0.137133			−0.0685664	−	0.997647i	$-0.521842\pi$
$709$	−97.2271			−0.137133			−0.0685664	+	0.997647i	$0.521842\pi$
$710$			216.850i			0.305423i
$711$		0			0
$712$	129.176	−	223.739i	0.181426	−	0.314240i
$713$	−142.156	−	246.222i	−0.199378	−	0.345333i
$714$		0			0
$715$			15.7091i			0.0219707i
$716$	109.924	−	63.4648i	0.153526	−	0.0886380i
$717$		0			0
$718$	−1286.23	+	742.604i	−1.79140	+	1.03427i
$719$	117.654	−	203.783i	0.163636	−	0.283426i	−0.772534	−	0.634973i	$-0.781011\pi$
$719$	117.654	−	203.783i	0.163636	−	0.283426i	0.936170	+	0.351547i	$0.114344\pi$
$720$		0			0
$721$	124.702	+	71.9969i	0.172957	+	0.0998570i
$722$	820.977	−	473.992i	1.13709	−	0.656498i
$723$		0			0
$724$	646.845	+	1120.37i	0.893432	+	1.54747i
$725$	−294.520	−	170.041i	−0.406234	−	0.234539i
$726$		0			0
$727$		−	725.103i		−	0.997391i	−0.866777	−	0.498696i	$-0.833813\pi$
$727$		−	725.103i		−	0.997391i	0.866777	−	0.498696i	$-0.166187\pi$
$728$	22.0407	−	38.1756i	0.0302757	−	0.0524390i
$729$		0			0
$730$			303.536i			0.415803i
$731$	−513.964	−	1252.82i	−0.703097	−	1.71385i
$732$		0			0
$733$		−	777.184i		−	1.06028i	−0.847911	−	0.530139i	$-0.822140\pi$
$733$		−	777.184i		−	1.06028i	0.847911	−	0.530139i	$-0.177860\pi$
$734$	−797.953	−	460.698i	−1.08713	−	0.627654i
$735$		0			0
$736$	338.851	+	195.635i	0.460395	+	0.265809i
$737$	331.506	−	574.186i	0.449805	−	0.779085i
$738$		0			0
$739$		−	240.672i		−	0.325673i	−0.986653	−	0.162836i	$-0.947936\pi$
$739$		−	240.672i		−	0.325673i	0.986653	−	0.162836i	$-0.0520643\pi$
$740$	−103.677	−	179.574i	−0.140104	−	0.242668i
$741$		0			0
$742$	−905.577			−1.22045
$743$	−987.688	−	570.242i	−1.32932	−	0.767486i	−0.344129	−	0.938922i	$-0.611826\pi$
$743$	−987.688	−	570.242i	−1.32932	−	0.767486i	−0.985195	+	0.171436i	$0.945159\pi$
$744$		0			0
$745$	−82.4480	−	142.804i	−0.110668	−	0.191683i
$746$	−352.591	−	610.705i	−0.472642	−	0.818640i
$747$		0			0
$748$	−903.371	−	1564.68i	−1.20771	−	2.09182i
$749$	202.449	−	116.884i	0.270292	−	0.156053i
$750$		0			0
$751$	705.389	+	407.256i	0.939266	+	0.542286i	0.889730	−	0.456487i	$-0.150892\pi$
$751$	705.389	+	407.256i	0.939266	+	0.542286i	0.0495360	+	0.998772i	$0.484226\pi$
$752$	115.245			0.153251
$753$		0			0
$754$	−32.3434	+	56.0205i	−0.0428958	+	0.0742977i
$755$	4.92204	−	8.52522i	0.00651925	−	0.0112917i
$756$		0			0
$757$	66.5413	−	38.4176i	0.0879013	−	0.0507498i	−0.455405	−	0.890284i	$-0.650506\pi$
$757$	66.5413	−	38.4176i	0.0879013	−	0.0507498i	0.543306	+	0.839535i	$0.317172\pi$
$758$			1978.74i			2.61047i
$759$		0			0
$760$	21.2672	−	12.2786i	0.0279831	−	0.0161560i
$761$	−776.632	+	448.389i	−1.02054	+	0.589210i	−0.914261	−	0.405127i	$-0.867227\pi$
$761$	−776.632	+	448.389i	−1.02054	+	0.589210i	−0.106280	+	0.994336i	$0.533894\pi$
$762$		0			0
$763$			587.331i			0.769765i
$764$	1444.80	+	834.156i	1.89110	+	1.09183i
$765$		0			0
$766$	−452.109			−0.590221
$767$	−28.0292	−	48.5480i	−0.0365439	−	0.0632960i
$768$		0			0
$769$	−141.129	+	244.443i	−0.183523	+	0.317872i	−0.943078	−	0.332572i	$-0.892084\pi$
$769$	−141.129	+	244.443i	−0.183523	+	0.317872i	0.759555	+	0.650443i	$0.225417\pi$
$770$			248.647i			0.322918i
$771$		0			0
$772$	1023.48			1.32575
$773$			69.3145i			0.0896695i	0.998994	+	0.0448347i	$0.0142761\pi$
$773$			69.3145i			0.0896695i	−0.998994	+	0.0448347i	$0.985724\pi$
$774$		0			0
$775$	771.574			0.995579
$776$			38.9988i			0.0502562i
$777$		0			0
$778$	−441.933			−0.568038
$779$	60.3664	+	34.8526i	0.0774922	+	0.0447401i
$780$		0			0
$781$	717.400	−	414.191i	0.918566	−	0.530334i
$782$		−	849.375i		−	1.08616i
$783$		0			0
$784$	−62.1415	+	107.632i	−0.0792621	+	0.137286i
$785$	168.186			0.214250
$786$		0			0
$787$	−525.688	−	910.518i	−0.667964	−	1.15695i	−0.978473	−	0.206377i	$-0.933833\pi$
$787$	−525.688	−	910.518i	−0.667964	−	1.15695i	0.310509	−	0.950571i	$-0.399501\pi$
$788$	124.280	+	215.260i	0.157716	+	0.273172i
$789$		0			0
$790$	313.318			0.396605
$791$	572.156	+	991.003i	0.723333	+	1.25285i
$792$		0			0
$793$	14.1869	+	8.19082i	0.0178902	+	0.0103289i
$794$	271.352	+	156.665i	0.341753	+	0.197311i
$795$		0			0
$796$		−	144.112i		−	0.181046i
$797$	714.442	−	1237.45i	0.896414	−	1.55263i	0.0643689	−	0.997926i	$-0.479497\pi$
$797$	714.442	−	1237.45i	0.896414	−	1.55263i	0.832045	−	0.554708i	$-0.187170\pi$
$798$		0			0
$799$	−188.644	−	326.740i	−0.236100	−	0.408937i
$800$	−919.579	+	530.919i	−1.14947	+	0.663649i
$801$		0			0
$802$	−345.583	+	199.522i	−0.430901	+	0.248781i
$803$	1004.18	−	579.765i	1.25054	−	0.721999i
$804$		0			0
$805$	−33.0951	+	57.3225i	−0.0411120	+	0.0712080i
$806$		−	146.761i		−	0.182085i
$807$		0			0
$808$	−176.984	+	102.182i	−0.219040	+	0.126463i
$809$	−1428.72			−1.76604			−0.883018	−	0.469339i	$-0.844492\pi$
$809$	−1428.72			−1.76604			−0.883018	+	0.469339i	$0.844492\pi$
$810$		0			0
$811$	576.649	+	332.928i	0.711034	+	0.410516i	0.811444	−	0.584430i	$-0.198682\pi$
$811$	576.649	+	332.928i	0.711034	+	0.410516i	−0.100409	+	0.994946i	$0.532015\pi$
$812$	−289.885	+	502.096i	−0.357002	+	0.618345i
$813$		0			0
$814$	−699.433	+	1211.45i	−0.859254	+	1.48827i
$815$	217.751			0.267179
$816$		0			0
$817$	−237.764	−	183.728i	−0.291021	−	0.224881i
$818$	−1878.67			−2.29667
$819$		0			0
$820$	−42.7234	−	24.6664i	−0.0521017	−	0.0300809i
$821$	−1331.56			−1.62187			−0.810936	−	0.585135i	$-0.801042\pi$
$821$	−1331.56			−1.62187			−0.810936	+	0.585135i	$0.801042\pi$
$822$		0			0
$823$	734.877	−	1272.84i	0.892925	−	1.54659i	0.0565732	−	0.998398i	$-0.481983\pi$
$823$	734.877	−	1272.84i	0.892925	−	1.54659i	0.836352	−	0.548193i	$-0.184684\pi$
$824$	58.8036	−	33.9503i	0.0713636	−	0.0412018i
$825$		0			0
$826$	−443.652	−	768.429i	−0.537109	−	0.930301i
$827$	−363.025	+	628.777i	−0.438966	+	0.760311i	−0.997610	−	0.0690965i	$-0.977988\pi$
$827$	−363.025	+	628.777i	−0.438966	+	0.760311i	0.558644	+	0.829407i	$0.311322\pi$
$828$		0			0
$829$	402.971	+	232.656i	0.486093	+	0.280646i	0.722952	−	0.690898i	$-0.242785\pi$
$829$	402.971	+	232.656i	0.486093	+	0.280646i	−0.236859	+	0.971544i	$0.576118\pi$
$830$	−205.805	−	356.465i	−0.247958	−	0.429476i
$831$		0			0
$832$	71.9410	+	124.605i	0.0864675	+	0.149766i
$833$	406.877			0.488448
$834$		0			0
$835$	110.487	−	63.7899i	0.132320	−	0.0763950i
$836$	−347.195	−	200.453i	−0.415306	−	0.239777i
$837$		0			0
$838$	−2281.31			−2.72233
$839$		−	929.733i		−	1.10814i	−0.832469	−	0.554072i	$-0.813073\pi$
$839$		−	929.733i		−	1.10814i	0.832469	−	0.554072i	$-0.186927\pi$
$840$		0			0
$841$	−320.961	+	555.920i	−0.381642	+	0.661023i
$842$	−1101.60	−	1908.02i	−1.30831	−	2.26606i
$843$		0			0
$844$		−	581.484i		−	0.688963i
$845$	136.744	−	78.9491i	0.161827	−	0.0934309i
$846$		0			0
$847$	−1.98531	+	1.14622i	−0.00234393	+	0.00135327i
$848$	182.270	−	315.701i	0.214941	−	0.372289i
$849$		0			0
$850$	1996.23	+	1152.52i	2.34851	+	1.35591i
$851$	−322.491	+	186.190i	−0.378956	+	0.218790i
$852$		0			0
$853$	760.871	+	1317.87i	0.891994	+	1.54498i	0.837482	+	0.546466i	$0.184027\pi$
$853$	760.871	+	1317.87i	0.891994	+	1.54498i	0.0545122	+	0.998513i	$0.482640\pi$
$854$	224.554	+	129.646i	0.262943	+	0.151810i
$855$		0			0
$856$		−	110.233i		−	0.128777i
$857$	−90.8719	+	157.395i	−0.106035	+	0.183658i	−0.914161	−	0.405352i	$-0.867149\pi$
$857$	−90.8719	+	157.395i	−0.106035	+	0.183658i	0.808126	+	0.589010i	$0.200482\pi$
$858$		0			0
$859$		−	688.831i		−	0.801899i	−0.916100	−	0.400949i	$-0.868680\pi$
$859$		−	688.831i		−	0.801899i	0.916100	−	0.400949i	$-0.131320\pi$
$860$	168.274	+	130.030i	0.195667	+	0.151198i
$861$		0			0
$862$		−	638.709i		−	0.740962i
$863$	−1111.63	−	641.803i	−1.28811	−	0.743688i	−0.309789	−	0.950805i	$-0.600258\pi$
$863$	−1111.63	−	641.803i	−1.28811	−	0.743688i	−0.978316	+	0.207117i	$0.933592\pi$
$864$		0			0
$865$	−62.1030	−	35.8552i	−0.0717954	−	0.0414511i
$866$	1139.29	−	1973.31i	1.31558	−	2.27865i
$867$		0			0
$868$		−	1315.38i		−	1.51541i
$869$	−598.449	−	1036.54i	−0.688663	−	1.19280i
$870$		0			0
$871$	91.1058			0.104599
$872$	239.852	+	138.478i	0.275059	+	0.158806i
$873$		0			0
$874$	−94.2360	−	163.221i	−0.107821	−	0.186752i
$875$	−182.971	−	316.915i	−0.209109	−	0.362188i
$876$		0			0
$877$	−449.636	−	778.792i	−0.512698	−	0.888019i	−0.999892	−	0.0147248i	$-0.995313\pi$
$877$	−449.636	−	778.792i	−0.512698	−	0.888019i	0.487194	−	0.873294i	$-0.338021\pi$
$878$	407.335	−	235.175i	0.463935	−	0.267853i
$879$		0			0
$880$	−86.6831	−	50.0465i	−0.0985035	−	0.0568710i
$881$	−271.479			−0.308149			−0.154074	−	0.988059i	$-0.549240\pi$
$881$	−271.479			−0.308149			−0.154074	+	0.988059i	$0.549240\pi$
$882$		0			0
$883$	−188.847	+	327.092i	−0.213869	+	0.370432i	−0.952922	−	0.303215i	$-0.901940\pi$
$883$	−188.847	+	327.092i	−0.213869	+	0.370432i	0.739053	+	0.673647i	$0.235273\pi$
$884$	124.134	−	215.006i	0.140423	−	0.243220i
$885$		0			0
$886$	978.963	−	565.204i	1.10492	−	0.637928i
$887$			549.517i			0.619523i	0.950814	+	0.309762i	$0.100249\pi$
$887$			549.517i			0.619523i	−0.950814	+	0.309762i	$0.899751\pi$
$888$		0			0
$889$	1227.87	−	708.909i	1.38118	−	0.797423i
$890$	−173.418	+	100.123i	−0.194852	+	0.112498i
$891$		0			0
$892$			1798.29i			2.01602i
$893$	−72.5020	−	41.8591i	−0.0811893	−	0.0468747i
$894$		0			0
$895$	−23.0209			−0.0257217
$896$	445.379	+	771.420i	0.497075	+	0.860959i
$897$		0			0
$898$	65.3570	−	113.202i	0.0727806	−	0.126060i
$899$			451.667i			0.502410i
$900$		0			0
$901$	−1193.43			−1.32456
$902$			332.811i			0.368971i
$903$		0			0
$904$	539.603			0.596906
$905$		−	234.633i		−	0.259263i
$906$		0			0
$907$	854.651			0.942284			0.471142	−	0.882057i	$-0.343842\pi$
$907$	854.651			0.942284			0.471142	+	0.882057i	$0.343842\pi$
$908$	335.287	+	193.578i	0.369259	+	0.213192i
$909$		0			0
$910$	−29.5895	+	17.0835i	−0.0325160	+	0.0187731i
$911$			1038.45i			1.13991i	0.821677	+	0.569953i	$0.193039\pi$
$911$			1038.45i			1.13991i	−0.821677	+	0.569953i	$0.806961\pi$
$912$		0			0
$913$	−786.191	+	1361.72i	−0.861107	+	1.49148i
$914$	−1453.83			−1.59062
$915$		0			0
$916$	−418.159	−	724.272i	−0.456505	−	0.790690i
$917$	−50.4731	−	87.4220i	−0.0550416	−	0.0953348i
$918$		0			0
$919$	−558.615			−0.607851			−0.303925	−	0.952696i	$-0.598297\pi$
$919$	−558.615			−0.607851			−0.303925	+	0.952696i	$0.598297\pi$
$920$	15.6061	+	27.0305i	0.0169631	+	0.0293810i
$921$		0			0
$922$	1855.46	+	1071.25i	2.01243	+	1.16188i
$923$	98.5794	+	56.9148i	0.106803	+	0.0616629i
$924$		0			0
$925$		−	1010.57i		−	1.09251i
$926$	−38.3529	+	66.4292i	−0.0414178	+	0.0717378i
$927$		0			0
$928$	−310.791	−	538.306i	−0.334904	−	0.580072i
$929$	−942.741	+	544.292i	−1.01479	+	0.585890i	−0.912591	−	0.408874i	$-0.865922\pi$
$929$	−942.741	+	544.292i	−1.01479	+	0.585890i	−0.102200	+	0.994764i	$0.532588\pi$
$930$		0			0
$931$	78.1882	−	45.1420i	0.0839831	−	0.0484877i
$932$	1647.84	−	951.381i	1.76807	−	1.02080i
$933$		0			0
$934$	−510.879	+	884.868i	−0.546979	+	0.947396i
$935$			327.684i			0.350464i
$936$		0			0
$937$	−1402.75	+	809.879i	−1.49707	+	0.864332i	−0.999994	−	0.00337768i	$-0.998925\pi$
$937$	−1402.75	+	809.879i	−1.49707	+	0.864332i	−0.497072	+	0.867709i	$0.665592\pi$
$938$	1442.04			1.53736
$939$		0			0
$940$	51.3122	+	29.6251i	0.0545874	+	0.0315161i
$941$	682.564	−	1182.23i	0.725360	−	1.25636i	−0.233466	−	0.972365i	$-0.575007\pi$
$941$	682.564	−	1182.23i	0.725360	−	1.25636i	0.958826	−	0.283995i	$-0.0916600\pi$
$942$		0			0
$943$	−44.2976	+	76.7256i	−0.0469751	+	0.0813633i
$944$	357.185			0.378374
$945$		0			0
$946$	192.084	−	1421.74i	0.203049	−	1.50290i
$947$	−1676.30			−1.77012			−0.885060	−	0.465477i	$-0.845883\pi$
$947$	−1676.30			−1.77012			−0.885060	+	0.465477i	$0.845883\pi$
$948$		0			0
$949$	137.987	+	79.6666i	0.145402	+	0.0839480i
$950$	511.479			0.538399
$951$		0			0
$952$	459.758	−	796.324i	0.482939	−	0.836475i
$953$	1084.99	−	626.421i	1.13850	−	0.657315i	0.192444	−	0.981308i	$-0.438359\pi$
$953$	1084.99	−	626.421i	1.13850	−	0.657315i	0.946059	+	0.323993i	$0.105025\pi$
$954$		0			0
$955$	−151.289	−	262.040i	−0.158417	−	0.274387i
$956$	−1045.29	+	1810.49i	−1.09340	+	1.89382i
$957$		0			0
$958$	1726.58	+	996.843i	1.80228	+	1.04055i
$959$	−154.005	−	266.745i	−0.160589	−	0.278149i
$960$		0			0
$961$	−31.8673	−	55.1957i	−0.0331605	−	0.0574357i
$962$	−192.221			−0.199814
$963$		0			0
$964$	1540.75	−	889.553i	1.59829	−	0.922773i
$965$	−160.757	−	92.8130i	−0.166587	−	0.0961793i
$966$		0			0
$967$	953.901			0.986454			0.493227	−	0.869901i	$-0.335817\pi$
$967$	953.901			0.986454			0.493227	+	0.869901i	$0.335817\pi$
$968$			1.08101i			0.00111674i
$969$		0			0
$970$	15.1138	−	26.1779i	0.0155813	−	0.0269875i
$971$	538.229	+	932.239i	0.554303	+	0.960081i	0.997957	+	0.0638834i	$0.0203486\pi$
$971$	538.229	+	932.239i	0.554303	+	0.960081i	−0.443654	+	0.896198i	$0.646318\pi$
$972$		0			0
$973$		−	1680.46i		−	1.72709i
$974$	−357.520	+	206.414i	−0.367064	+	0.211924i
$975$		0			0
$976$	−90.3942	+	52.1891i	−0.0926170	+	0.0534725i
$977$	−76.8969	+	133.189i	−0.0787072	+	0.136325i	−0.902692	−	0.430286i	$-0.858413\pi$
$977$	−76.8969	+	133.189i	−0.0787072	+	0.136325i	0.823985	+	0.566611i	$0.191746\pi$
$978$		0			0
$979$	662.468	+	382.476i	0.676679	+	0.390681i
$980$	−55.3365	+	31.9486i	−0.0564658	+	0.0326006i
$981$		0			0
$982$	−206.484	−	357.641i	−0.210269	−	0.364197i
$983$	−359.633	−	207.634i	−0.365853	−	0.211225i	0.305792	−	0.952098i	$-0.401079\pi$
$983$	−359.633	−	207.634i	−0.365853	−	0.211225i	−0.671645	+	0.740873i	$0.734412\pi$
$984$		0			0
$985$		−	45.0808i		−	0.0457673i
$986$	−674.669	+	1168.56i	−0.684248	+	1.18515i
$987$		0			0
$988$		−	55.0894i		−	0.0557585i
$989$	233.518	−	302.198i	0.236115	−	0.305559i
$990$		0			0
$991$		−	527.154i		−	0.531941i	−0.963981	−	0.265971i	$-0.914308\pi$
$991$		−	527.154i		−	0.531941i	0.963981	−	0.265971i	$-0.0856924\pi$
$992$	1221.30	+	705.119i	1.23115	+	0.710805i
$993$		0			0
$994$	1560.34	+	900.860i	1.56975	+	0.906298i
$995$	−13.0686	+	22.6355i	−0.0131343	+	0.0227493i
$996$		0			0
$997$			657.186i			0.659163i	0.944127	+	0.329582i	$0.106908\pi$
$997$			657.186i			0.659163i	−0.944127	+	0.329582i	$0.893092\pi$
$998$	−353.485	−	612.254i	−0.354193	−	0.613481i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.3.j.f.37.12	yes	28
3.2	odd	2	inner	387.3.j.f.37.3	✓	28
43.7	odd	6	inner	387.3.j.f.136.3	yes	28
129.50	even	6	inner	387.3.j.f.136.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.3.j.f.37.3	✓	28	3.2	odd	2	inner
387.3.j.f.37.12	yes	28	1.1	even	1	trivial
387.3.j.f.136.3	yes	28	43.7	odd	6	inner
387.3.j.f.136.12	yes	28	129.50	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+3.03676i q^{2} -5.22190 q^{4} +(0.820197 + 0.473541i) q^{5} +(6.81469 - 3.93447i) q^{7} -3.71061i q^{8} +O(q^{10})\)	\(q+3.03676i q^{2} -5.22190 q^{4} +(0.820197 + 0.473541i) q^{5} +(6.81469 - 3.93447i) q^{7} -3.71061i q^{8} +(-1.43803 + 2.49074i) q^{10} +10.9867 q^{11} +(0.754855 + 1.30745i) q^{13} +(11.9480 + 20.6946i) q^{14} -9.61937 q^{16} +(15.7459 + 27.2727i) q^{17} +(6.05169 + 3.49394i) q^{19} +(-4.28299 - 2.47278i) q^{20} +33.3641i q^{22} +(-4.44080 + 7.69168i) q^{23} +(-12.0515 - 20.8738i) q^{25} +(-3.97040 + 2.29231i) q^{26} +(-35.5856 + 20.5454i) q^{28} +(12.2192 - 7.05476i) q^{29} +(-16.0057 + 27.7228i) q^{31} -44.0541i q^{32} +(-82.8207 + 47.8166i) q^{34} +7.45253 q^{35} +(36.3101 + 20.9636i) q^{37} +(-10.6103 + 18.3775i) q^{38} +(1.75713 - 3.04343i) q^{40} +9.97514 q^{41} +(-42.6128 - 5.75721i) q^{43} -57.3717 q^{44} +(-23.3578 - 13.4856i) q^{46} -11.9805 q^{47} +(6.46004 - 11.1891i) q^{49} +(63.3888 - 36.5975i) q^{50} +(-3.94178 - 6.82736i) q^{52} +(-18.9483 + 32.8194i) q^{53} +(9.01130 + 5.20268i) q^{55} +(-14.5993 - 25.2867i) q^{56} +(21.4236 + 37.1068i) q^{58} -37.1319 q^{59} +(9.39711 - 5.42542i) q^{61} +(-84.1873 - 48.6055i) q^{62} +95.3043 q^{64} +1.42982i q^{65} +(30.1733 - 52.2616i) q^{67} +(-82.2236 - 142.416i) q^{68} +22.6315i q^{70} +(65.2968 - 37.6991i) q^{71} +(91.3994 - 52.7695i) q^{73} +(-63.6615 + 110.265i) q^{74} +(-31.6013 - 18.2450i) q^{76} +(74.8713 - 43.2270i) q^{77} +(-54.4700 - 94.3448i) q^{79} +(-7.88978 - 4.55517i) q^{80} +30.2921i q^{82} +(-71.5581 + 123.942i) q^{83} +29.8254i q^{85} +(17.4833 - 129.405i) q^{86} -40.7675i q^{88} +(60.2970 + 34.8125i) q^{89} +(10.2882 + 5.93991i) q^{91} +(23.1894 - 40.1652i) q^{92} -36.3818i q^{94} +(3.30905 + 5.73144i) q^{95} -10.5101 q^{97} +(33.9786 + 19.6176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) \) 28 * q - 84 * q^4 - 30 * q^7	\( 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) \) 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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