LMFDB - Embedded newform 171.4.y.a.53.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(53,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.y (of order $18$, degree $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.15
Character	$\chi$	$=$	171.53
Dual form			171.4.y.a.71.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.13604 + 1.14142i) q^{2} +(2.40352 + 2.01679i) q^{4} +(0.417489 + 0.497545i) q^{5} +(11.8643 - 20.5495i) q^{7} +(-8.11369 - 14.0533i) q^{8} +O(q^{10})$	\(q+(3.13604 + 1.14142i) q^{2} +(2.40352 + 2.01679i) q^{4} +(0.417489 + 0.497545i) q^{5} +(11.8643 - 20.5495i) q^{7} +(-8.11369 - 14.0533i) q^{8} +(0.741353 + 2.03685i) q^{10} +(38.3912 - 22.1652i) q^{11} +(90.6542 + 15.9848i) q^{13} +(60.6625 - 50.9019i) q^{14} +(-13.7627 - 78.0521i) q^{16} +(-31.8539 + 87.5179i) q^{17} +(-65.5942 + 50.5608i) q^{19} +2.03785i q^{20} +(145.696 - 25.6902i) q^{22} +(-35.0078 + 41.7207i) q^{23} +(21.6328 - 122.686i) q^{25} +(266.049 + 153.604i) q^{26} +(69.9602 - 25.4634i) q^{28} +(116.177 - 42.2851i) q^{29} +(-216.979 - 125.273i) q^{31} +(23.3874 - 132.637i) q^{32} +(-199.790 + 238.101i) q^{34} +(15.1775 - 2.67621i) q^{35} -307.282i q^{37} +(-263.417 + 83.6897i) q^{38} +(3.60477 - 9.90403i) q^{40} +(37.2798 + 211.424i) q^{41} +(-120.808 + 101.370i) q^{43} +(136.977 + 24.1527i) q^{44} +(-157.407 + 90.8789i) q^{46} +(189.763 + 521.370i) q^{47} +(-110.022 - 190.564i) q^{49} +(207.877 - 360.054i) q^{50} +(185.651 + 221.251i) q^{52} +(143.128 + 120.098i) q^{53} +(27.0561 + 9.84762i) q^{55} -385.052 q^{56} +412.602 q^{58} +(-667.917 - 243.102i) q^{59} +(-1.84636 - 1.54928i) q^{61} +(-537.465 - 640.525i) q^{62} +(-92.2863 + 159.845i) q^{64} +(29.8940 + 51.7780i) q^{65} +(253.079 + 695.329i) q^{67} +(-253.067 + 146.108i) q^{68} +(50.6519 + 8.93131i) q^{70} +(-171.607 + 143.996i) q^{71} +(4.49838 + 25.5116i) q^{73} +(350.739 - 963.648i) q^{74} +(-259.628 - 10.7661i) q^{76} -1051.90i q^{77} +(436.541 - 76.9740i) q^{79} +(33.0886 - 39.4335i) q^{80} +(-124.414 + 705.586i) q^{82} +(-245.815 - 141.921i) q^{83} +(-56.8428 + 20.6891i) q^{85} +(-494.565 + 180.007i) q^{86} +(-622.989 - 359.683i) q^{88} +(-280.955 + 1593.38i) q^{89} +(1404.03 - 1673.25i) q^{91} +(-168.284 + 29.6731i) q^{92} +1851.64i q^{94} +(-52.5412 - 11.5275i) q^{95} +(-208.736 + 573.498i) q^{97} +(-127.519 - 723.198i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 36 q^{4}+O(q^{10}) $ 120 * q - 36 * q^4	$ 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) $ 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	3.13604	+	1.14142i	1.10876	+	0.403554i	0.830537	−	0.556963i	$-0.188034\pi$
$2$	3.13604	+	1.14142i	1.10876	+	0.403554i	0.278219	+	0.960518i	$0.410256\pi$
$3$		0			0
$3$		0			0
$4$	2.40352	+	2.01679i	0.300440	+	0.252099i
$5$	0.417489	+	0.497545i	0.0373414	+	0.0445017i	0.784392	−	0.620266i	$-0.212975\pi$
$5$	0.417489	+	0.497545i	0.0373414	+	0.0445017i	−0.747051	+	0.664767i	$0.768531\pi$
$6$		0			0
$7$	11.8643	−	20.5495i	0.640611	−	1.10957i	−0.344686	−	0.938718i	$-0.612015\pi$
$7$	11.8643	−	20.5495i	0.640611	−	1.10957i	0.985297	−	0.170852i	$-0.0546521\pi$
$8$	−8.11369	−	14.0533i	−0.358578	−	0.621075i
$9$		0			0
$10$	0.741353	+	2.03685i	0.0234436	+	0.0644109i
$11$	38.3912	−	22.1652i	1.05231	−	0.607551i	0.129014	−	0.991643i	$-0.458819\pi$
$11$	38.3912	−	22.1652i	1.05231	−	0.607551i	0.923295	+	0.384092i	$0.125485\pi$
$12$		0			0
$13$	90.6542	+	15.9848i	1.93407	+	0.341029i	0.999876	−	0.0157304i	$-0.00500736\pi$
$13$	90.6542	+	15.9848i	1.93407	+	0.341029i	0.934196	+	0.356760i	$0.116118\pi$
$14$	60.6625	−	50.9019i	1.15805	−	0.971722i
$15$		0			0
$16$	−13.7627	−	78.0521i	−0.215042	−	1.21956i
$17$	−31.8539	+	87.5179i	−0.454454	+	1.24860i	0.475106	+	0.879929i	$0.342410\pi$
$17$	−31.8539	+	87.5179i	−0.454454	+	1.24860i	−0.929559	+	0.368672i	$0.879812\pi$
$18$		0			0
$19$	−65.5942	+	50.5608i	−0.792019	+	0.610497i
$19$	−65.5942	+	50.5608i	−0.792019	+	0.610497i
$20$			2.03785i			0.0227839i
$21$		0			0
$22$	145.696	−	25.6902i	1.41193	−	0.248962i
$23$	−35.0078	+	41.7207i	−0.317376	+	0.378234i	−0.901021	−	0.433775i	$-0.857181\pi$
$23$	−35.0078	+	41.7207i	−0.317376	+	0.378234i	0.583646	+	0.812009i	$0.301626\pi$
$24$		0			0
$25$	21.6328	−	122.686i	0.173062	−	0.981484i
$26$	266.049	+	153.604i	2.00679	+	1.15862i
$27$		0			0
$28$	69.9602	−	25.4634i	0.472187	−	0.171862i
$29$	116.177	−	42.2851i	0.743918	−	0.270764i	0.0578737	−	0.998324i	$-0.481568\pi$
$29$	116.177	−	42.2851i	0.743918	−	0.270764i	0.686044	+	0.727560i	$0.259346\pi$
$30$		0			0
$31$	−216.979	−	125.273i	−1.25712	−	0.725796i	−0.284602	−	0.958646i	$-0.591862\pi$
$31$	−216.979	−	125.273i	−1.25712	−	0.725796i	−0.972513	+	0.232850i	$0.925195\pi$
$32$	23.3874	−	132.637i	0.129199	−	0.732721i
$33$		0			0
$34$	−199.790	+	238.101i	−1.00776	+	1.20100i
$35$	15.1775	−	2.67621i	0.0732991	−	0.0129246i
$36$		0			0
$37$		−	307.282i		−	1.36532i	−0.730736	−	0.682660i	$-0.760823\pi$
$37$		−	307.282i		−	1.36532i	0.730736	−	0.682660i	$-0.239177\pi$
$38$	−263.417	+	83.6897i	−1.12452	+	0.357270i
$39$		0			0
$40$	3.60477	−	9.90403i	0.0142491	−	0.0391491i
$41$	37.2798	+	211.424i	0.142003	+	0.805339i	0.969725	+	0.244200i	$0.0785254\pi$
$41$	37.2798	+	211.424i	0.142003	+	0.805339i	−0.827722	+	0.561139i	$0.810363\pi$
$42$		0			0
$43$	−120.808	+	101.370i	−0.428444	+	0.359507i	−0.831364	−	0.555728i	$-0.812440\pi$
$43$	−120.808	+	101.370i	−0.428444	+	0.359507i	0.402921	+	0.915235i	$0.367995\pi$
$44$	136.977	+	24.1527i	0.469319	+	0.0827536i
$45$		0			0
$46$	−157.407	+	90.8789i	−0.504530	+	0.291291i
$47$	189.763	+	521.370i	0.588932	+	1.61808i	0.772460	+	0.635063i	$0.219026\pi$
$47$	189.763	+	521.370i	0.588932	+	1.61808i	−0.183528	+	0.983014i	$0.558752\pi$
$48$		0			0
$49$	−110.022	−	190.564i	−0.320764	−	0.555580i
$50$	207.877	−	360.054i	0.587966	−	1.01839i
$51$		0			0
$52$	185.651	+	221.251i	0.495100	+	0.590037i
$53$	143.128	+	120.098i	0.370945	+	0.311260i	0.809135	−	0.587622i	$-0.199936\pi$
$53$	143.128	+	120.098i	0.370945	+	0.311260i	−0.438190	+	0.898882i	$0.644380\pi$
$54$		0			0
$55$	27.0561	+	9.84762i	0.0663317	+	0.0241428i
$56$	−385.052			−0.918835
$57$		0			0
$58$	412.602			0.934092
$59$	−667.917	−	243.102i	−1.47382	−	0.536427i	−0.524686	−	0.851296i	$-0.675817\pi$
$59$	−667.917	−	243.102i	−1.47382	−	0.536427i	−0.949135	+	0.314869i	$0.898039\pi$
$60$		0			0
$61$	−1.84636	−	1.54928i	−0.00387544	−	0.00325188i	0.640848	−	0.767668i	$-0.278583\pi$
$61$	−1.84636	−	1.54928i	−0.00387544	−	0.00325188i	−0.644723	+	0.764416i	$0.723027\pi$
$62$	−537.465	−	640.525i	−1.10094	−	1.31205i
$63$		0			0
$64$	−92.2863	+	159.845i	−0.180247	+	0.312196i
$65$	29.8940	+	51.7780i	0.0570446	+	0.0988041i
$66$		0			0
$67$	253.079	+	695.329i	0.461471	+	1.26788i	0.924380	+	0.381474i	$0.124583\pi$
$67$	253.079	+	695.329i	0.461471	+	1.26788i	−0.462909	+	0.886406i	$0.653194\pi$
$68$	−253.067	+	146.108i	−0.451308	+	0.260563i
$69$		0			0
$70$	50.6519	+	8.93131i	0.0864867	+	0.0152499i
$71$	−171.607	+	143.996i	−0.286846	+	0.240692i	−0.774844	−	0.632152i	$-0.782172\pi$
$71$	−171.607	+	143.996i	−0.286846	+	0.240692i	0.487998	+	0.872845i	$0.337727\pi$
$72$		0			0
$73$	4.49838	+	25.5116i	0.00721226	+	0.0409028i	0.988202	−	0.153159i	$-0.0489448\pi$
$73$	4.49838	+	25.5116i	0.00721226	+	0.0409028i	−0.980989	+	0.194062i	$0.937834\pi$
$74$	350.739	−	963.648i	0.550981	−	1.51381i
$75$		0			0
$76$	−259.628	−	10.7661i	−0.391860	−	0.0162495i
$77$		−	1051.90i		−	1.55681i
$78$		0			0
$79$	436.541	−	76.9740i	0.621705	−	0.109623i	0.146082	−	0.989272i	$-0.453334\pi$
$79$	436.541	−	76.9740i	0.621705	−	0.109623i	0.475623	+	0.879649i	$0.342223\pi$
$80$	33.0886	−	39.4335i	0.0462428	−	0.0551100i
$81$		0			0
$82$	−124.414	+	705.586i	−0.167551	+	0.950230i
$83$	−245.815	−	141.921i	−0.325080	−	0.187685i	0.328574	−	0.944478i	$-0.393432\pi$
$83$	−245.815	−	141.921i	−0.325080	−	0.187685i	−0.653655	+	0.756793i	$0.726765\pi$
$84$		0			0
$85$	−56.8428	+	20.6891i	−0.0725348	+	0.0264005i
$86$	−494.565	+	180.007i	−0.620120	+	0.225705i
$87$		0			0
$88$	−622.989	−	359.683i	−0.754669	−	0.435708i
$89$	−280.955	+	1593.38i	−0.334620	+	1.89773i	0.0963274	+	0.995350i	$0.469290\pi$
$89$	−280.955	+	1593.38i	−0.334620	+	1.89773i	−0.430948	+	0.902377i	$0.641821\pi$
$90$		0			0
$91$	1404.03	−	1673.25i	1.61738	−	1.92752i
$92$	−168.284	+	29.6731i	−0.190705	+	0.0336264i
$93$		0			0
$94$			1851.64i			2.03172i
$95$	−52.5412	−	11.5275i	−0.0567433	−	0.0124494i
$96$		0			0
$97$	−208.736	+	573.498i	−0.218494	+	0.600308i	−0.999713	−	0.0239489i	$-0.992376\pi$
$97$	−208.736	+	573.498i	−0.218494	+	0.600308i	0.781219	+	0.624257i	$0.214598\pi$
$98$	−127.519	−	723.198i	−0.131443	−	0.745449i
$99$		0			0
$100$	299.426	−	251.249i	0.299426	−	0.251249i
$101$	1033.44	+	182.223i	1.01813	+	0.179524i	0.657713	−	0.753268i	$-0.271524\pi$
$101$	1033.44	+	182.223i	1.01813	+	0.179524i	0.360415	+	0.932792i	$0.382635\pi$
$102$		0			0
$103$	−474.718	+	274.079i	−0.454130	+	0.262192i	−0.709573	−	0.704632i	$-0.751112\pi$
$103$	−474.718	+	274.079i	−0.454130	+	0.262192i	0.255443	+	0.966824i	$0.417779\pi$
$104$	−510.900	−	1403.69i	−0.481711	−	1.32349i
$105$		0			0
$106$	311.770	+	540.002i	0.285677	+	0.494808i
$107$	−629.877	+	1090.98i	−0.569089	+	0.985691i	0.427567	+	0.903984i	$0.359371\pi$
$107$	−629.877	+	1090.98i	−0.569089	+	0.985691i	−0.996656	+	0.0817077i	$0.973963\pi$
$108$		0			0
$109$	−157.577	−	187.793i	−0.138469	−	0.165021i	0.692353	−	0.721559i	$-0.256574\pi$
$109$	−157.577	−	187.793i	−0.138469	−	0.165021i	−0.830823	+	0.556537i	$0.812130\pi$
$110$	73.6087	+	61.7650i	0.0638028	+	0.0535369i
$111$		0			0
$112$	−1767.22	−	643.215i	−1.49095	−	0.542662i
$113$	56.0092			0.0466274			0.0233137	−	0.999728i	$-0.492578\pi$
$113$	56.0092			0.0466274			0.0233137	+	0.999728i	$0.492578\pi$
$114$		0			0
$115$	−35.3733			−0.0286833
$116$	364.516	+	132.673i	0.291762	+	0.106193i
$117$		0			0
$118$	−1817.13	−	1524.75i	−1.41763	−	1.18953i
$119$	1420.53	+	1692.92i	1.09428	+	1.30412i
$120$		0			0
$121$	317.092	−	549.219i	0.238236	−	0.412636i
$122$	−4.02187	−	6.96608i	−0.00298461	−	0.00516950i
$123$		0			0
$124$	−268.864	−	738.698i	−0.194715	−	0.534976i
$125$	140.383	−	81.0503i	0.100450	−	0.0579949i
$126$		0			0
$127$	−432.119	−	76.1943i	−0.301924	−	0.0532374i	0.0206338	−	0.999787i	$-0.493432\pi$
$127$	−432.119	−	76.1943i	−0.301924	−	0.0532374i	−0.322558	+	0.946550i	$0.604543\pi$
$128$	−1297.25	+	1088.52i	−0.895794	+	0.751660i
$129$		0			0
$130$	34.6481	+	196.499i	0.0233757	+	0.132570i
$131$	724.082	−	1989.40i	0.482926	−	1.32683i	−0.424047	−	0.905640i	$-0.639391\pi$
$131$	724.082	−	1989.40i	0.482926	−	1.32683i	0.906973	−	0.421188i	$-0.138387\pi$
$132$		0			0
$133$	260.772	+	1947.80i	0.170014	+	1.26989i
$134$			2469.45i			1.59200i
$135$		0			0
$136$	1488.37	−	262.440i	0.938431	−	0.165471i
$137$	−1065.61	+	1269.95i	−0.664536	+	0.791963i	−0.988029	−	0.154267i	$-0.950698\pi$
$137$	−1065.61	+	1269.95i	−0.664536	+	0.791963i	0.323493	+	0.946230i	$0.395143\pi$
$138$		0			0
$139$	−297.353	+	1686.38i	−0.181447	+	1.02904i	0.748988	+	0.662584i	$0.230540\pi$
$139$	−297.353	+	1686.38i	−0.181447	+	1.02904i	−0.930435	+	0.366456i	$0.880571\pi$
$140$	41.8769	+	24.1776i	0.0252803	+	0.0145956i
$141$		0			0
$142$	−702.527	+	255.699i	−0.415174	+	0.151111i
$143$	3834.63	−	1395.69i	2.24243	−	0.816179i
$144$		0			0
$145$	69.5416	+	40.1499i	0.0398284	+	0.0229949i
$146$	−15.0124	+	85.1397i	−0.00850985	+	0.0482617i
$147$		0			0
$148$	619.725	−	738.559i	0.344196	−	0.410197i
$149$	1134.92	−	200.118i	0.624003	−	0.110029i	0.147299	−	0.989092i	$-0.452942\pi$
$149$	1134.92	−	200.118i	0.624003	−	0.110029i	0.476705	+	0.879063i	$0.341831\pi$
$150$		0			0
$151$		−	2672.16i		−	1.44011i	−0.693915	−	0.720057i	$-0.744115\pi$
$151$		−	2672.16i		−	1.44011i	0.693915	−	0.720057i	$-0.255885\pi$
$152$	1242.76	+	511.582i	0.663164	+	0.272992i
$153$		0			0
$154$	1200.66	−	3298.78i	0.628259	−	1.72613i
$155$	−28.2576	−	160.257i	−0.0146433	−	0.0830460i
$156$		0			0
$157$	1816.99	−	1524.64i	0.923640	−	0.775026i	−0.0510243	−	0.998697i	$-0.516249\pi$
$157$	1816.99	−	1524.64i	0.923640	−	0.775026i	0.974665	+	0.223671i	$0.0718041\pi$
$158$	1456.87	+	256.885i	0.733559	+	0.129346i
$159$		0			0
$160$	75.7567	−	43.7381i	0.0374318	−	0.0216113i
$161$	441.999	+	1214.38i	0.216363	+	0.594451i
$162$		0			0
$163$	−481.206	−	833.473i	−0.231233	−	0.400507i	0.726938	−	0.686703i	$-0.240943\pi$
$163$	−481.206	−	833.473i	−0.231233	−	0.400507i	−0.958171	+	0.286196i	$0.907609\pi$
$164$	−336.796	+	583.348i	−0.160362	+	0.277755i
$165$		0			0
$166$	−608.892	−	725.649i	−0.284694	−	0.339285i
$167$	−468.946	−	393.493i	−0.217294	−	0.182332i	0.527643	−	0.849466i	$-0.323076\pi$
$167$	−468.946	−	393.493i	−0.217294	−	0.182332i	−0.744937	+	0.667135i	$0.767520\pi$
$168$		0			0
$169$	5898.16	+	2146.75i	2.68464	+	0.977130i
$170$	−201.876			−0.0910775
$171$		0			0
$172$	−494.808			−0.219353
$173$	−1269.87	−	462.196i	−0.558073	−	0.203122i	0.0475570	−	0.998869i	$-0.484856\pi$
$173$	−1269.87	−	462.196i	−0.558073	−	0.203122i	−0.605630	+	0.795747i	$0.707079\pi$
$174$		0			0
$175$	−2264.47	−	1900.12i	−0.978160	−	0.820774i
$176$	−2258.41	−	2691.47i	−0.967238	−	1.15271i
$177$		0			0
$178$	−2699.81	+	4676.20i	−1.13685	+	1.96908i
$179$	−923.274	−	1599.16i	−0.385524	−	0.667747i	0.606318	−	0.795222i	$-0.292646\pi$
$179$	−923.274	−	1599.16i	−0.385524	−	0.667747i	−0.991842	+	0.127476i	$0.959313\pi$
$180$		0			0
$181$	−539.217	−	1481.49i	−0.221435	−	0.608386i	0.778377	−	0.627797i	$-0.216043\pi$
$181$	−539.217	−	1481.49i	−0.221435	−	0.608386i	−0.999812	+	0.0194107i	$0.993821\pi$
$182$	6312.97	−	3644.79i	2.57114	−	1.48445i
$183$		0			0
$184$	870.357	+	153.467i	0.348715	+	0.0614879i
$185$	152.887	−	128.287i	0.0607591	−	0.0509830i
$186$		0			0
$187$	716.940	+	4065.97i	0.280363	+	1.59002i
$188$	−595.396	+	1635.84i	−0.230977	+	0.634605i
$189$		0			0
$190$	−151.613	−	96.1223i	−0.0578904	−	0.0367023i
$191$		−	2045.89i		−	0.775056i	−0.921858	−	0.387528i	$-0.873329\pi$
$191$		−	2045.89i		−	0.775056i	0.921858	−	0.387528i	$-0.126671\pi$
$192$		0			0
$193$	3789.04	−	668.110i	1.41317	−	0.249179i	0.585625	−	0.810582i	$-0.300849\pi$
$193$	3789.04	−	668.110i	1.41317	−	0.249179i	0.827543	+	0.561403i	$0.189738\pi$
$194$	−1309.21	+	1560.25i	−0.484514	+	0.577422i
$195$		0			0
$196$	119.888	−	679.917i	0.0436909	−	0.247783i
$197$	1734.02	+	1001.14i	0.627126	+	0.362072i	0.779638	−	0.626230i	$-0.215403\pi$
$197$	1734.02	+	1001.14i	0.627126	+	0.362072i	−0.152512	+	0.988302i	$0.548736\pi$
$198$		0			0
$199$	280.155	−	101.968i	0.0997975	−	0.0363233i	−0.291639	−	0.956529i	$-0.594201\pi$
$199$	280.155	−	101.968i	0.0997975	−	0.0363233i	0.391436	+	0.920205i	$0.371978\pi$
$200$	−1899.66	+	691.420i	−0.671631	+	0.244454i
$201$		0			0
$202$	3032.91	+	1751.05i	1.05641	+	0.609918i
$203$	509.422	−	2889.08i	0.176130	−	0.998884i
$204$		0			0
$205$	−89.6290	+	106.816i	−0.0305364	+	0.0363918i
$206$	−1801.57	+	317.666i	−0.609328	+	0.107441i
$207$		0			0
$208$		−	7295.75i		−	2.43206i
$209$	−1397.55	+	3395.00i	−0.462540	+	1.12362i
$210$		0			0
$211$	203.278	−	558.502i	0.0663234	−	0.182222i	−0.902103	−	0.431520i	$-0.857978\pi$
$211$	203.278	−	558.502i	0.0663234	−	0.182222i	0.968427	+	0.249298i	$0.0801997\pi$
$212$	101.797	+	577.318i	0.0329784	+	0.187030i
$213$		0			0
$214$	−3220.59	+	2702.39i	−1.02876	+	0.863233i
$215$	−100.872	−	17.7865i	−0.0319974	−	0.00564200i
$216$		0			0
$217$	−5148.60	+	2972.54i	−1.61064	+	0.929905i
$218$	−279.816	−	768.789i	−0.0869337	−	0.238848i
$219$		0			0
$220$	45.1693	+	78.2356i	0.0138423	+	0.0239756i
$221$	−4286.65	+	7424.69i	−1.30476	+	2.25990i
$222$		0			0
$223$	1351.53	+	1610.69i	0.405852	+	0.483676i	0.929795	−	0.368077i	$-0.119984\pi$
$223$	1351.53	+	1610.69i	0.405852	+	0.483676i	−0.523943	+	0.851754i	$0.675539\pi$
$224$	−2448.15	−	2054.24i	−0.730240	−	0.612744i
$225$		0			0
$226$	175.647	+	63.9302i	0.0516985	+	0.0188167i
$227$	508.586			0.148705			0.0743526	−	0.997232i	$-0.476311\pi$
$227$	508.586			0.148705			0.0743526	+	0.997232i	$0.476311\pi$
$228$		0			0
$229$	591.325			0.170637			0.0853185	−	0.996354i	$-0.472809\pi$
$229$	591.325			0.170637			0.0853185	+	0.996354i	$0.472809\pi$
$230$	−110.932	−	40.3760i	−0.0318028	−	0.0115753i
$231$		0			0
$232$	−1536.87	−	1289.59i	−0.434917	−	0.364939i
$233$	−4012.45	−	4781.85i	−1.12817	−	1.34450i	−0.931375	−	0.364061i	$-0.881390\pi$
$233$	−4012.45	−	4781.85i	−1.12817	−	1.34450i	−0.196798	−	0.980444i	$-0.563054\pi$
$234$		0			0
$235$	−180.181	+	312.082i	−0.0500157	+	0.0866298i
$236$	−1115.07	−	1931.35i	−0.307562	−	0.532714i
$237$		0			0
$238$	2522.49	+	6930.49i	0.687012	+	1.88755i
$239$	2114.13	−	1220.59i	0.572183	−	0.330350i	−0.185838	−	0.982580i	$-0.559500\pi$
$239$	2114.13	−	1220.59i	0.572183	−	0.330350i	0.758021	+	0.652230i	$0.226167\pi$
$240$		0			0
$241$	−3975.65	−	701.015i	−1.06263	−	0.187371i	−0.385108	−	0.922872i	$-0.625836\pi$
$241$	−3975.65	−	701.015i	−1.06263	−	0.187371i	−0.677524	+	0.735501i	$0.736947\pi$
$242$	1621.30	−	1360.43i	0.430666	−	0.361372i
$243$		0			0
$244$	−1.31319	−	7.44746i	−0.000344542	−	0.00195399i
$245$	48.8810	−	134.299i	0.0127465	−	0.0350207i
$246$		0			0
$247$	−6754.60	+	3535.04i	−1.74002	+	0.910644i
$248$			4065.70i			1.04102i
$249$		0			0
$250$	532.760	−	93.9399i	0.134779	−	0.0237651i
$251$	−433.228	+	516.301i	−0.108945	+	0.129835i	−0.817761	−	0.575558i	$-0.804785\pi$
$251$	−433.228	+	516.301i	−0.108945	+	0.129835i	0.708816	+	0.705393i	$0.249229\pi$
$252$		0			0
$253$	−419.247	+	2377.67i	−0.104181	+	0.590840i
$254$	−1268.17	−	732.179i	−0.313276	−	0.180870i
$255$		0			0
$256$	−3923.15	+	1427.91i	−0.957800	+	0.348611i
$257$	1973.05	−	718.132i	0.478893	−	0.174303i	−0.0912835	−	0.995825i	$-0.529097\pi$
$257$	1973.05	−	718.132i	0.478893	−	0.174303i	0.570177	+	0.821522i	$0.306875\pi$
$258$		0			0
$259$	−6314.50	−	3645.68i	−1.51492	−	0.874639i
$260$	−32.5746	+	184.740i	−0.00776996	+	0.0440656i
$261$		0			0
$262$	4541.49	−	5412.34i	1.07089	−	1.27624i
$263$	−4670.11	+	823.466i	−1.09495	+	0.193069i	−0.691817	−	0.722073i	$-0.743189\pi$
$263$	−4670.11	+	823.466i	−1.09495	+	0.193069i	−0.403131	+	0.915142i	$0.632078\pi$
$264$		0			0
$265$			121.352i			0.0281306i
$266$	−1405.47	+	6406.02i	−0.323966	+	1.47661i
$267$		0			0
$268$	−794.055	+	2181.65i	−0.180987	+	0.497259i
$269$	−715.612	−	4058.43i	−0.162199	−	0.919878i	−0.951905	−	0.306392i	$-0.900878\pi$
$269$	−715.612	−	4058.43i	−0.162199	−	0.919878i	0.789706	−	0.613485i	$-0.210233\pi$
$270$		0			0
$271$	1145.12	−	960.869i	0.256683	−	0.215382i	−0.505361	−	0.862908i	$-0.668641\pi$
$271$	1145.12	−	960.869i	0.256683	−	0.215382i	0.762044	+	0.647526i	$0.224196\pi$
$272$	7269.36	+	1281.78i	1.62048	+	0.285734i
$273$		0			0
$274$	−4791.35	+	2766.29i	−1.05641	+	0.609918i
$275$	−1888.84	−	5189.54i	−0.414187	−	1.13797i
$276$		0			0
$277$	−636.840	−	1103.04i	−0.138137	−	0.239261i	0.788654	−	0.614837i	$-0.210778\pi$
$277$	−636.840	−	1103.04i	−0.138137	−	0.239261i	−0.926792	+	0.375576i	$0.877445\pi$
$278$	−2857.38	+	4949.13i	−0.616454	+	1.06773i
$279$		0			0
$280$	−160.755	−	191.581i	−0.0343106	−	0.0408898i
$281$	−4513.62	−	3787.38i	−0.958221	−	0.804043i	0.0224418	−	0.999748i	$-0.492856\pi$
$281$	−4513.62	−	3787.38i	−0.958221	−	0.804043i	−0.980663	+	0.195705i	$0.937300\pi$
$282$		0			0
$283$	−1804.14	−	656.654i	−0.378958	−	0.137930i	0.145516	−	0.989356i	$-0.453516\pi$
$283$	−1804.14	−	656.654i	−0.378958	−	0.137930i	−0.524474	+	0.851426i	$0.675738\pi$
$284$	−702.871			−0.146858
$285$		0			0
$286$	13618.6			2.81569
$287$	4786.96	+	1742.31i	0.984549	+	0.358346i
$288$		0			0
$289$	−2881.14	−	2417.56i	−0.586432	−	0.492075i
$290$	172.257	+	205.288i	0.0348803	+	0.0415687i
$291$		0			0
$292$	−40.6396	+	70.3899i	−0.00814470	+	0.0141070i
$293$	1324.77	+	2294.56i	0.264142	+	0.457508i	0.967339	−	0.253488i	$-0.0815778\pi$
$293$	1324.77	+	2294.56i	0.264142	+	0.457508i	−0.703196	+	0.710996i	$0.748244\pi$
$294$		0			0
$295$	−157.894	−	433.811i	−0.0311626	−	0.0856185i
$296$	−4318.33	+	2493.19i	−0.847966	+	0.489573i
$297$		0			0
$298$	3787.58	+	667.852i	0.736270	+	0.129824i
$299$	−3840.50	+	3222.57i	−0.742816	+	0.623297i
$300$		0			0
$301$	649.806	+	3685.23i	0.124433	+	0.705692i
$302$	3050.07	−	8379.99i	0.581165	−	1.59674i
$303$		0			0
$304$	4849.13	+	4423.92i	0.914858	+	0.834635i
$305$		−	1.56545i		−	0.000293894i
$306$		0			0
$307$	771.811	−	136.091i	0.143484	−	0.0253001i	−0.101445	−	0.994841i	$-0.532347\pi$
$307$	771.811	−	136.091i	0.143484	−	0.0253001i	0.244929	+	0.969541i	$0.421235\pi$
$308$	2121.46	−	2528.26i	0.392472	−	0.467730i
$309$		0			0
$310$	94.3041	−	534.825i	0.0172778	−	0.0979872i
$311$	−2502.13	−	1444.60i	−0.456214	−	0.263395i	0.254237	−	0.967142i	$-0.418176\pi$
$311$	−2502.13	−	1444.60i	−0.456214	−	0.263395i	−0.710451	+	0.703747i	$0.751509\pi$
$312$		0			0
$313$	3345.74	−	1217.75i	0.604193	−	0.219908i	−0.0217672	−	0.999763i	$-0.506929\pi$
$313$	3345.74	−	1217.75i	0.604193	−	0.219908i	0.625961	+	0.779855i	$0.284707\pi$
$314$	7438.40	−	2707.36i	1.33686	−	0.486576i
$315$		0			0
$316$	1204.48	+	695.405i	0.214421	+	0.123796i
$317$	−883.690	+	5011.66i	−0.156571	+	0.887958i	0.800765	+	0.598979i	$0.204427\pi$
$317$	−883.690	+	5011.66i	−0.156571	+	0.887958i	−0.957336	+	0.288979i	$0.906684\pi$
$318$		0			0
$319$	3522.94	−	4198.48i	0.618328	−	0.736895i
$320$	−118.058	+	20.8169i	−0.0206239	+	0.00363656i
$321$		0			0
$322$			4312.85i			0.746416i
$323$	−2335.54	−	7351.23i	−0.402331	−	1.26636i
$324$		0			0
$325$	3922.20	−	10776.2i	0.669429	−	1.83924i
$326$	−557.733	−	3163.06i	−0.0947546	−	0.537380i
$327$		0			0
$328$	2668.73	−	2239.33i	0.449256	−	0.376971i
$329$	12965.3	+	2286.13i	2.17265	+	0.383096i
$330$		0			0
$331$	−5276.43	+	3046.35i	−0.876189	+	0.505868i	−0.869400	−	0.494109i	$-0.835494\pi$
$331$	−5276.43	+	3046.35i	−0.876189	+	0.505868i	−0.00678929	+	0.999977i	$0.502161\pi$
$332$	−304.595	−	836.868i	−0.0503519	−	0.138341i
$333$		0			0
$334$	−1021.49	−	1769.27i	−0.167346	−	0.289852i
$335$	−240.299	+	416.211i	−0.0391909	+	0.0678807i
$336$		0			0
$337$	−324.599	−	386.843i	−0.0524690	−	0.0625301i	0.739172	−	0.673517i	$-0.235217\pi$
$337$	−324.599	−	386.843i	−0.0524690	−	0.0625301i	−0.791641	+	0.610987i	$0.790773\pi$
$338$	16046.5	+	13464.6i	2.58229	+	2.16680i
$339$		0			0
$340$	−178.348	−	64.9135i	−0.0284479	−	0.0103542i
$341$	−11106.8			−1.76383
$342$		0			0
$343$	2917.56			0.459281
$344$	2404.79	+	875.270i	0.376911	+	0.137184i
$345$		0			0
$346$	−3454.80	−	2898.92i	−0.536796	−	0.450425i
$347$	−3825.15	−	4558.64i	−0.591772	−	0.705246i	0.384174	−	0.923261i	$-0.374486\pi$
$347$	−3825.15	−	4558.64i	−0.591772	−	0.705246i	−0.975946	+	0.218015i	$0.930042\pi$
$348$		0			0
$349$	−4620.49	+	8002.92i	−0.708679	+	1.22747i	0.256669	+	0.966499i	$0.417375\pi$
$349$	−4620.49	+	8002.92i	−0.708679	+	1.22747i	−0.965347	+	0.260968i	$0.915958\pi$
$350$	−4932.63	−	8543.57i	−0.753315	−	1.30478i
$351$		0			0
$352$	−2042.05	−	5610.48i	−0.309209	−	0.849544i
$353$	4834.65	−	2791.29i	0.728959	−	0.420865i	−0.0890820	−	0.996024i	$-0.528393\pi$
$353$	4834.65	−	2791.29i	0.728959	−	0.420865i	0.818041	+	0.575159i	$0.195060\pi$
$354$		0			0
$355$	−143.288	−	25.2656i	−0.0214224	−	0.00377735i
$356$	−3888.80	+	3263.09i	−0.578949	+	0.485796i
$357$		0			0
$358$	−1070.10	−	6068.87i	−0.157980	−	0.895948i
$359$	815.024	−	2239.26i	0.119820	−	0.329202i	−0.865254	−	0.501333i	$-0.832843\pi$
$359$	815.024	−	2239.26i	0.119820	−	0.329202i	0.985074	+	0.172131i	$0.0550653\pi$
$360$		0			0
$361$	1746.21	−	6633.00i	0.254587	−	0.967050i
$362$		−	5261.47i		−	0.763913i
$363$		0			0
$364$	6749.22	−	1190.07i	0.971854	−	0.171364i
$365$	−10.8151	+	12.8889i	−0.00155093	+	0.00184832i
$366$		0			0
$367$	−709.932	+	4026.22i	−0.100976	+	0.572662i	0.891776	+	0.452478i	$0.149460\pi$
$367$	−709.932	+	4026.22i	−0.100976	+	0.572662i	−0.992752	+	0.120185i	$0.961651\pi$
$368$	3738.19	+	2158.25i	0.529530	+	0.305724i
$369$		0			0
$370$	625.888	−	227.804i	0.0879415	−	0.0320081i
$371$	4166.07	−	1516.33i	0.582996	−	0.212193i
$372$		0			0
$373$	9781.77	+	5647.51i	1.35786	+	0.783959i	0.989335	−	0.145660i	$-0.0465305\pi$
$373$	9781.77	+	5647.51i	1.35786	+	0.783959i	0.368522	+	0.929619i	$0.379864\pi$
$374$	−2392.65	+	13569.4i	−0.330804	+	1.87608i
$375$		0			0
$376$	5787.30	−	6897.04i	0.793769	−	0.945977i
$377$	11207.9	−	1976.25i	1.53113	−	0.269979i
$378$		0			0
$379$			9070.19i			1.22930i	0.788800	+	0.614649i	$0.210702\pi$
$379$			9070.19i			1.22930i	−0.788800	+	0.614649i	$0.789298\pi$
$380$	−103.035	−	133.671i	−0.0139095	−	0.0180452i
$381$		0			0
$382$	2335.23	−	6416.00i	0.312777	−	0.859348i
$383$	788.078	+	4469.41i	0.105141	+	0.596282i	0.991164	+	0.132642i	$0.0423460\pi$
$383$	788.078	+	4469.41i	0.105141	+	0.596282i	−0.886023	+	0.463641i	$0.846543\pi$
$384$		0			0
$385$	523.365	−	439.156i	0.0692809	−	0.0581336i
$386$	12645.2	+	2229.69i	1.66742	+	0.294010i
$387$		0			0
$388$	−1658.33	+	957.437i	−0.216982	+	0.125275i
$389$	4989.51	+	13708.6i	0.650330	+	1.78677i	0.616520	+	0.787339i	$0.288542\pi$
$389$	4989.51	+	13708.6i	0.650330	+	1.78677i	0.0338100	+	0.999428i	$0.489236\pi$
$390$		0			0
$391$	−2536.17	−	4392.78i	−0.328030	−	0.568165i
$392$	−1785.37	+	3092.35i	−0.230038	+	0.398437i
$393$		0			0
$394$	4295.23	+	5118.86i	0.549215	+	0.654529i
$395$	220.549	+	185.063i	0.0280938	+	0.0235735i
$396$		0			0
$397$	−7419.36	−	2700.42i	−0.937952	−	0.341386i	−0.172595	−	0.984993i	$-0.555215\pi$
$397$	−7419.36	−	2700.42i	−0.937952	−	0.341386i	−0.765357	+	0.643606i	$0.777437\pi$
$398$	994.967			0.125310
$399$		0			0
$400$	−9873.59			−1.23420
$401$	−5893.28	−	2144.98i	−0.733907	−	0.267120i	−0.0520890	−	0.998642i	$-0.516588\pi$
$401$	−5893.28	−	2144.98i	−0.733907	−	0.267120i	−0.681817	+	0.731522i	$0.738810\pi$
$402$		0			0
$403$	−17667.6	−	14824.9i	−2.18383	−	1.83245i
$404$	2116.39	+	2522.21i	0.260629	+	0.310606i
$405$		0			0
$406$	4895.23	−	8478.78i	0.598389	−	1.03644i
$407$	−6810.97	−	11796.9i	−0.829501	−	1.43674i
$408$		0			0
$409$	2854.80	+	7843.49i	0.345136	+	0.948253i	0.983879	+	0.178833i	$0.0572323\pi$
$409$	2854.80	+	7843.49i	0.345136	+	0.948253i	−0.638744	+	0.769420i	$0.720545\pi$
$410$	−403.002	+	232.673i	−0.0485435	+	0.0280266i
$411$		0			0
$412$	−1693.76	−	298.655i	−0.202537	−	0.0357128i
$413$	−12920.0	+	10841.2i	−1.53935	+	1.29167i
$414$		0			0
$415$	−32.0129	−	181.554i	−0.00378663	−	0.0214751i
$416$	4240.34	−	11650.2i	0.499759	−	1.37308i
$417$		0			0
$418$	−8257.92	+	9051.65i	−0.966287	+	1.05916i
$419$			9947.32i			1.15981i	0.814686	+	0.579903i	$0.196909\pi$
$419$			9947.32i			1.15981i	−0.814686	+	0.579903i	$0.803091\pi$
$420$		0			0
$421$	2245.66	−	395.970i	0.259968	−	0.0458394i	−0.0421448	−	0.999112i	$-0.513419\pi$
$421$	2245.66	−	395.970i	0.259968	−	0.0458394i	0.302113	+	0.953272i	$0.402308\pi$
$422$	1274.98	−	1519.46i	0.147073	−	0.175275i
$423$		0			0
$424$	526.487	−	2985.86i	0.0603030	−	0.341995i
$425$	10048.1	+	5801.27i	1.14683	+	0.662125i
$426$		0			0
$427$	−53.7427	+	19.5607i	−0.00609085	+	0.00221689i
$428$	−3714.21	+	1351.86i	−0.419469	+	0.152674i
$429$		0			0
$430$	−296.037	−	170.917i	−0.0332004	−	0.0191683i
$431$	2203.08	−	12494.3i	0.246215	−	1.39635i	−0.571440	−	0.820644i	$-0.693615\pi$
$431$	2203.08	−	12494.3i	0.246215	−	1.39635i	0.817654	−	0.575709i	$-0.195274\pi$
$432$		0			0
$433$	−6721.46	+	8010.33i	−0.745988	+	0.889034i	−0.996876	−	0.0789822i	$-0.974833\pi$
$433$	−6721.46	+	8010.33i	−0.745988	+	0.889034i	0.250888	+	0.968016i	$0.419277\pi$
$434$	−19539.1	+	3445.27i	−2.16108	+	0.381056i
$435$		0			0
$436$		−	769.166i		−	0.0844871i
$437$	186.880	−	4506.66i	0.0204569	−	0.493325i
$438$		0			0
$439$	−171.824	+	472.084i	−0.0186805	+	0.0513242i	−0.948682	−	0.316230i	$-0.897583\pi$
$439$	−171.824	+	472.084i	−0.0186805	+	0.0513242i	0.930002	+	0.367555i	$0.119805\pi$
$440$	−81.1331	−	460.129i	−0.00879061	−	0.0498540i
$441$		0			0
$442$	−21917.8	+	18391.2i	−2.35865	+	1.97914i
$443$	−5725.46	−	1009.55i	−0.614051	−	0.108274i	−0.142032	−	0.989862i	$-0.545364\pi$
$443$	−5725.46	−	1009.55i	−0.614051	−	0.108274i	−0.472019	+	0.881588i	$0.656475\pi$
$444$		0			0
$445$	−910.072	+	525.430i	−0.0969473	+	0.0559726i
$446$	2399.97	+	6593.85i	0.254802	+	0.700062i
$447$		0			0
$448$	2189.82	+	3792.88i	0.230936	+	0.399993i
$449$	−4756.91	+	8239.21i	−0.499983	+	0.865997i	−1.00000		1.91611e-5i	$-0.999994\pi$
$449$	−4756.91	+	8239.21i	−0.499983	+	0.865997i	0.500017	+	0.866016i	$0.333327\pi$
$450$		0			0
$451$	6117.47	+	7290.52i	0.638715	+	0.761191i
$452$	134.619	+	112.959i	0.0140088	+	0.0117547i
$453$		0			0
$454$	1594.95	+	580.513i	0.164878	+	0.0600106i
$455$	1418.68			0.146173
$456$		0			0
$457$	3290.66			0.336828			0.168414	−	0.985716i	$-0.446135\pi$
$457$	3290.66			0.336828			0.168414	+	0.985716i	$0.446135\pi$
$458$	1854.42	+	674.953i	0.189195	+	0.0688613i
$459$		0			0
$460$	−85.0206	−	71.3407i	−0.00861762	−	0.00723104i
$461$	−7903.62	−	9419.17i	−0.798500	−	0.951615i	0.201110	−	0.979569i	$-0.435545\pi$
$461$	−7903.62	−	9419.17i	−0.798500	−	0.951615i	−0.999609	+	0.0279539i	$0.991101\pi$
$462$		0			0
$463$	1688.63	−	2924.79i	0.169497	−	0.293578i	−0.768746	−	0.639554i	$-0.779119\pi$
$463$	1688.63	−	2924.79i	0.169497	−	0.293578i	0.938243	+	0.345976i	$0.112452\pi$
$464$	−4899.36	−	8485.94i	−0.490188	−	0.849030i
$465$		0			0
$466$	−7125.07	−	19576.0i	−0.708289	−	1.94601i
$467$	14507.9	−	8376.17i	1.43758	−	0.829984i	0.439894	−	0.898050i	$-0.355016\pi$
$467$	14507.9	−	8376.17i	1.43758	−	0.829984i	0.997681	+	0.0680650i	$0.0216825\pi$
$468$		0			0
$469$	17291.3	+	3048.92i	1.70243	+	0.300184i
$470$	−921.272	+	773.039i	−0.0904151	+	0.0758673i
$471$		0			0
$472$	2002.88	+	11358.9i	0.195318	+	1.10770i
$473$	−2391.09	+	6569.46i	−0.232436	+	0.638613i
$474$		0			0
$475$	4784.09	+	9141.24i	0.462125	+	0.883008i
$476$			6933.89i			0.667677i
$477$		0			0
$478$	8023.21	−	1414.71i	0.767726	−	0.135371i
$479$	5269.24	−	6279.63i	0.502625	−	0.599006i	−0.453756	−	0.891126i	$-0.649916\pi$
$479$	5269.24	−	6279.63i	0.502625	−	0.599006i	0.956382	+	0.292120i	$0.0943607\pi$
$480$		0			0
$481$	4911.83	−	27856.4i	0.465614	−	2.64063i
$482$	−11667.6	−	6736.31i	−1.10259	−	0.636578i
$483$		0			0
$484$	1869.80	−	680.551i	0.175601	−	0.0639135i
$485$	−372.486	+	135.574i	−0.0348737	+	0.0126930i
$486$		0			0
$487$	−7957.08	−	4594.02i	−0.740389	−	0.427464i	0.0818214	−	0.996647i	$-0.473926\pi$
$487$	−7957.08	−	4594.02i	−0.740389	−	0.427464i	−0.822211	+	0.569183i	$0.807260\pi$
$488$	−6.79174	+	38.5178i	−0.000630015	+	0.00357299i
$489$		0			0
$490$	306.585	−	365.374i	0.0282655	−	0.0336855i
$491$	6759.07	−	1191.81i	0.621248	−	0.109543i	0.145840	−	0.989308i	$-0.453412\pi$
$491$	6759.07	−	1191.81i	0.621248	−	0.109543i	0.475408	+	0.879765i	$0.342300\pi$
$492$		0			0
$493$			11514.6i			1.05191i
$494$	−25217.6	+	3376.15i	−2.29675	+	0.307490i
$495$		0			0
$496$	−6791.60	+	18659.8i	−0.614822	+	1.68921i
$497$	923.046	+	5234.85i	0.0833084	+	0.472465i
$498$		0			0
$499$	1098.86	−	922.057i	0.0985810	−	0.0827193i	−0.592165	−	0.805817i	$-0.701727\pi$
$499$	1098.86	−	922.057i	0.0985810	−	0.0827193i	0.690746	+	0.723097i	$0.257282\pi$
$500$	500.876	+	88.3180i	0.0447997	+	0.00789940i
$501$		0			0
$502$	−1947.94	+	1124.64i	−0.173189	+	0.0999906i
$503$	−4447.39	−	12219.1i	−0.394233	−	1.08315i	−0.965049	−	0.262068i	$-0.915595\pi$
$503$	−4447.39	−	12219.1i	−0.394233	−	1.08315i	0.570816	−	0.821078i	$-0.306627\pi$
$504$		0			0
$505$	340.786	+	590.258i	0.0300292	+	0.0520122i
$506$	−4028.70	+	6977.91i	−0.353948	+	0.613055i
$507$		0			0
$508$	−884.940	−	1054.63i	−0.0772891	−	0.0921095i
$509$	198.099	+	166.225i	0.0172507	+	0.0144750i	0.651372	−	0.758758i	$-0.274194\pi$
$509$	198.099	+	166.225i	0.0172507	+	0.0144750i	−0.634122	+	0.773233i	$0.718638\pi$
$510$		0			0
$511$	577.621	+	210.237i	0.0500047	+	0.0182002i
$512$	−385.493			−0.0332745
$513$		0			0
$514$	7007.25			0.601317
$515$	−334.556	−	121.769i	−0.0286259	−	0.0104190i
$516$		0			0
$517$	18841.5	+	15809.9i	1.60280	+	1.34491i
$518$	−15641.2	−	18640.5i	−1.32671	−	1.58111i
$519$		0			0
$520$	485.101	−	840.220i	0.0409098	−	0.0708579i
$521$	−5415.23	−	9379.46i	−0.455366	−	0.788717i	0.543343	−	0.839511i	$-0.317158\pi$
$521$	−5415.23	−	9379.46i	−0.455366	−	0.788717i	−0.998709	+	0.0507938i	$0.983825\pi$
$522$		0			0
$523$	3218.95	+	8844.00i	0.269130	+	0.739429i	0.998471	+	0.0552784i	$0.0176046\pi$
$523$	3218.95	+	8844.00i	0.269130	+	0.739429i	−0.729341	+	0.684151i	$0.760173\pi$
$524$	5752.55	−	3321.24i	0.479583	−	0.276887i
$525$		0			0
$526$	−15585.6	−	2748.16i	−1.29194	−	0.227805i
$527$	17875.3	−	14999.1i	1.47753	−	1.23979i
$528$		0			0
$529$	1597.71	+	9061.05i	0.131315	+	0.744723i
$530$	−138.514	+	380.565i	−0.0113522	+	0.0311900i
$531$		0			0
$532$	−3301.54	+	5207.50i	−0.269060	+	0.424387i
$533$			19762.4i			1.60601i
$534$		0			0
$535$	−805.778	+	142.080i	−0.0651156	+	0.0114816i
$536$	7718.28	−	9198.28i	0.621975	−	0.741241i
$537$		0			0
$538$	2388.21	−	13544.2i	0.191381	−	1.08538i
$539$	−8447.78	−	4877.33i	−0.675086	−	0.389761i
$540$		0			0
$541$	−2903.68	+	1056.85i	−0.230756	+	0.0839882i	−0.454810	−	0.890588i	$-0.650293\pi$
$541$	−2903.68	+	1056.85i	−0.230756	+	0.0839882i	0.224054	+	0.974577i	$0.428071\pi$
$542$	4687.90	−	1706.25i	0.371517	−	0.135221i
$543$		0			0
$544$	10863.1	+	6271.82i	0.856162	+	0.494305i
$545$	27.6487	−	156.803i	0.00217310	−	0.0123242i
$546$		0			0
$547$	3240.93	−	3862.39i	0.253331	−	0.301908i	−0.624358	−	0.781138i	$-0.714639\pi$
$547$	3240.93	−	3862.39i	0.253331	−	0.301908i	0.877690	+	0.479230i	$0.159084\pi$
$548$	−5122.45	+	903.225i	−0.399307	+	0.0704085i
$549$		0			0
$550$		−	18430.6i		−	1.42888i
$551$	−5482.60	+	8647.69i	−0.423896	+	0.668610i
$552$		0			0
$553$	3597.47	−	9883.96i	0.276636	−	0.760052i
$554$	−738.119	−	4186.08i	−0.0566059	−	0.321028i
$555$		0			0
$556$	−4115.77	+	3453.54i	−0.313934	+	0.263422i
$557$	8222.47	+	1449.84i	0.625488	+	0.110290i	0.477404	−	0.878684i	$-0.341578\pi$
$557$	8222.47	+	1449.84i	0.625488	+	0.110290i	0.148085	+	0.988975i	$0.452689\pi$
$558$		0			0
$559$	−12572.1	+	7258.53i	−0.951243	+	0.549201i
$560$	−417.767	−	1147.81i	−0.0315248	−	0.0866137i
$561$		0			0
$562$	−9831.88	−	17029.3i	−0.737959	−	1.27818i
$563$	3656.56	−	6333.35i	0.273722	−	0.474101i	−0.696090	−	0.717955i	$-0.745078\pi$
$563$	3656.56	−	6333.35i	0.273722	−	0.474101i	0.969812	+	0.243854i	$0.0784118\pi$
$564$		0			0
$565$	23.3832	+	27.8671i	0.00174113	+	0.00207500i
$566$	−4908.34	−	4118.58i	−0.364510	−	0.305860i
$567$		0			0
$568$	3415.98	+	1243.32i	0.252344	+	0.0918458i
$569$	−1729.34			−0.127412			−0.0637061	−	0.997969i	$-0.520292\pi$
$569$	−1729.34			−0.127412			−0.0637061	+	0.997969i	$0.520292\pi$
$570$		0			0
$571$	−6132.55			−0.449456			−0.224728	−	0.974422i	$-0.572149\pi$
$571$	−6132.55			−0.449456			−0.224728	+	0.974422i	$0.572149\pi$
$572$	12031.4	+	4379.09i	0.879476	+	0.320103i
$573$		0			0
$574$	13023.4	+	10927.9i	0.947012	+	0.794638i
$575$	4361.21	+	5197.49i	0.316305	+	0.376957i
$576$		0			0
$577$	−912.698	+	1580.84i	−0.0658512	+	0.114058i	−0.897071	−	0.441886i	$-0.854310\pi$
$577$	−912.698	+	1580.84i	−0.0658512	+	0.114058i	0.831220	+	0.555944i	$0.187643\pi$
$578$	−6275.90	−	10870.2i	−0.451631	−	0.782248i
$579$		0			0
$580$	86.1708	+	236.752i	0.00616905	+	0.0169493i
$581$	−5832.83	+	3367.58i	−0.416500	+	0.240466i
$582$		0			0
$583$	8156.85	+	1438.27i	0.579455	+	0.102174i
$584$	322.024	−	270.210i	0.0228175	−	0.0191462i
$585$		0			0
$586$	1535.45	+	8707.96i	0.108240	+	0.613861i
$587$	−758.606	+	2084.25i	−0.0533407	+	0.146552i	−0.963502	−	0.267702i	$-0.913736\pi$
$587$	−758.606	+	2084.25i	−0.0533407	+	0.146552i	0.910161	+	0.414255i	$0.135958\pi$
$588$		0			0
$589$	20566.5	−	2753.45i	1.43875	−	0.192621i
$590$		−	1540.67i		−	0.107506i
$591$		0			0
$592$	−23984.0	+	4229.03i	−1.66510	+	0.293601i
$593$	−8346.12	+	9946.52i	−0.577967	+	0.688794i	−0.973246	−	0.229767i	$-0.926204\pi$
$593$	−8346.12	+	9946.52i	−0.577967	+	0.688794i	0.395279	+	0.918561i	$0.370648\pi$
$594$		0			0
$595$	−249.248	+	1413.55i	−0.0171734	+	0.0973950i
$596$	3131.41	+	1807.92i	0.215214	+	0.124254i
$597$		0			0
$598$	−15722.3	+	5722.44i	−1.07514	+	0.391318i
$599$	−13762.7	+	5009.21i	−0.938778	+	0.341687i	−0.765683	−	0.643218i	$-0.777599\pi$
$599$	−13762.7	+	5009.21i	−0.938778	+	0.341687i	−0.173095	+	0.984905i	$0.555377\pi$
$600$		0			0
$601$	19762.5	+	11409.9i	1.34132	+	0.774409i	0.987000	−	0.160718i	$-0.0513809\pi$
$601$	19762.5	+	11409.9i	1.34132	+	0.774409i	0.354315	+	0.935126i	$0.384714\pi$
$602$	−2168.60	+	12298.7i	−0.146820	+	0.832656i
$603$		0			0
$604$	5389.20	−	6422.60i	0.363052	−	0.432668i
$605$	405.643	−	71.5259i	0.0272591	−	0.00480651i
$606$		0			0
$607$		−	18360.5i		−	1.22773i	−0.789413	−	0.613863i	$-0.789615\pi$
$607$		−	18360.5i		−	1.22773i	0.789413	−	0.613863i	$-0.210385\pi$
$608$	5172.14	+	9882.69i	0.344997	+	0.659204i
$609$		0			0
$610$	1.78685	−	4.90932i	0.000118602	−	0.000325857i
$611$	8868.84	+	50297.7i	0.587226	+	3.33032i
$612$		0			0
$613$	5146.62	−	4318.53i	0.339103	−	0.284541i	−0.457294	−	0.889316i	$-0.651181\pi$
$613$	5146.62	−	4318.53i	0.339103	−	0.284541i	0.796397	+	0.604775i	$0.206737\pi$
$614$	2575.76	+	454.177i	0.169299	+	0.0298519i
$615$		0			0
$616$	−14782.6	+	8534.76i	−0.966898	+	0.558239i
$617$	−8520.17	−	23409.0i	−0.555931	−	1.52741i	−0.825486	−	0.564422i	$-0.809099\pi$
$617$	−8520.17	−	23409.0i	−0.555931	−	1.52741i	0.269555	−	0.962985i	$-0.413123\pi$
$618$		0			0
$619$	−11964.9	−	20723.8i	−0.776912	−	1.34565i	−0.933714	−	0.358021i	$-0.883452\pi$
$619$	−11964.9	−	20723.8i	−0.776912	−	1.34565i	0.156802	−	0.987630i	$-0.449882\pi$
$620$	255.287	−	442.171i	0.0165364	−	0.0286419i
$621$		0			0
$622$	−6197.86	−	7386.32i	−0.399536	−	0.476149i
$623$	29409.8	+	24677.8i	1.89130	+	1.58699i
$624$		0			0
$625$	−14534.2	−	5290.02i	−0.930190	−	0.338561i
$626$	11882.3			0.758648
$627$		0			0
$628$	7442.05			0.472882
$629$	26892.7	+	9788.14i	1.70474	+	0.620475i
$630$		0			0
$631$	2578.39	+	2163.53i	0.162669	+	0.136496i	0.720489	−	0.693467i	$-0.243917\pi$
$631$	2578.39	+	2163.53i	0.162669	+	0.136496i	−0.557820	+	0.829962i	$0.688362\pi$
$632$	−4623.70	−	5510.31i	−0.291014	−	0.346817i
$633$		0			0
$634$	−8491.71	+	14708.1i	−0.531938	+	0.921344i
$635$	−142.495	−	246.809i	−0.00890511	−	0.0154241i
$636$		0			0
$637$	−6927.85	−	19034.1i	−0.430913	−	1.18392i
$638$	15840.3	−	9145.41i	0.982953	−	0.567508i
$639$		0			0
$640$	−1083.17	−	190.993i	−0.0669004	−	0.0117963i
$641$	−13228.9	+	11100.4i	−0.815148	+	0.683991i	−0.951831	−	0.306624i	$-0.900801\pi$
$641$	−13228.9	+	11100.4i	−0.815148	+	0.683991i	0.136682	+	0.990615i	$0.456356\pi$
$642$		0			0
$643$	−4738.13	−	26871.3i	−0.290597	−	1.64806i	−0.684579	−	0.728939i	$-0.740014\pi$
$643$	−4738.13	−	26871.3i	−0.290597	−	1.64806i	0.393982	−	0.919118i	$-0.371097\pi$
$644$	−1386.80	+	3810.21i	−0.0848567	+	0.233142i
$645$		0			0
$646$	1066.53	−	25719.6i	0.0649565	−	1.56644i
$647$		−	4344.89i		−	0.264011i	−0.991249	−	0.132006i	$-0.957858\pi$
$647$		−	4344.89i		−	0.264011i	0.991249	−	0.132006i	$-0.0421417\pi$
$648$		0			0
$649$	−31030.6	+	5471.53i	−1.87682	+	0.330934i
$650$	24600.3	−	29317.5i	1.48447	−	1.76912i
$651$		0			0
$652$	524.355	−	2973.77i	0.0314959	−	0.178622i
$653$	−6067.34	−	3502.98i	−0.363604	−	0.209927i	0.307057	−	0.951691i	$-0.400656\pi$
$653$	−6067.34	−	3502.98i	−0.363604	−	0.209927i	−0.670661	+	0.741764i	$0.733989\pi$
$654$		0			0
$655$	1292.11	−	470.290i	0.0770793	−	0.0280546i
$656$	15989.0	−	5819.53i	0.951626	−	0.346364i
$657$		0			0
$658$	38050.3	+	21968.3i	2.25434	+	1.30154i
$659$	469.063	−	2660.19i	0.0277270	−	0.157248i	−0.967801	−	0.251718i	$-0.919005\pi$
$659$	469.063	−	2660.19i	0.0277270	−	0.157248i	0.995528	+	0.0944700i	$0.0301156\pi$
$660$		0			0
$661$	−10160.4	+	12108.7i	−0.597874	+	0.712518i	−0.977099	−	0.212786i	$-0.931746\pi$
$661$	−10160.4	+	12108.7i	−0.597874	+	0.712518i	0.379225	+	0.925304i	$0.376191\pi$
$662$	−20024.2	+	3530.81i	−1.17563	+	0.207295i
$663$		0			0
$664$			4606.02i			0.269199i
$665$	−860.247	+	942.931i	−0.0501638	+	0.0549854i
$666$		0			0
$667$	−2302.96	+	6327.32i	−0.133689	+	0.367309i
$668$	−333.529	−	1891.54i	−0.0193183	−	0.109560i
$669$		0			0
$670$	−1228.66	+	1030.97i	−0.0708467	+	0.0594474i
$671$	−105.224	−	18.5539i	−0.00605385	−	0.00106746i
$672$		0			0
$673$	12595.3	−	7271.90i	0.721416	−	0.416510i	−0.0938574	−	0.995586i	$-0.529920\pi$
$673$	12595.3	−	7271.90i	0.721416	−	0.416510i	0.815274	+	0.579076i	$0.196586\pi$
$674$	−576.404	−	1583.66i	−0.0329410	−	0.0905048i
$675$		0			0
$676$	9846.80	+	17055.2i	0.560241	+	0.970366i
$677$	−10866.7	+	18821.7i	−0.616899	+	1.06850i	0.373149	+	0.927772i	$0.378278\pi$
$677$	−10866.7	+	18821.7i	−0.616899	+	1.06850i	−0.990048	+	0.140729i	$0.955055\pi$
$678$		0			0
$679$	9308.62	+	11093.6i	0.526115	+	0.626999i
$680$	751.954	+	630.965i	0.0424061	+	0.0355829i
$681$		0			0
$682$	−34831.3	−	12677.6i	−1.95566	−	0.711802i
$683$	26369.4			1.47730			0.738651	−	0.674088i	$-0.235463\pi$
$683$	26369.4			1.47730			0.738651	+	0.674088i	$0.235463\pi$
$684$		0			0
$685$	−1076.74			−0.0600584
$686$	9149.57	+	3330.17i	0.509231	+	0.185345i
$687$		0			0
$688$	9574.80	+	8034.21i	0.530575	+	0.445206i
$689$	11055.4	+	13175.3i	0.611286	+	0.728502i
$690$		0			0
$691$	12254.5	−	21225.3i	0.674647	−	1.16852i	−0.301924	−	0.953332i	$-0.597629\pi$
$691$	12254.5	−	21225.3i	0.674647	−	1.16852i	0.976572	−	0.215192i	$-0.0690377\pi$
$692$	−2120.01	−	3671.97i	−0.116461	−	0.201716i
$693$		0			0
$694$	−6792.48	−	18662.2i	−0.371526	−	1.02076i
$695$	−963.189	+	556.097i	−0.0525695	+	0.0303510i
$696$		0			0
$697$	−19690.9	−	3472.04i	−1.07008	−	0.188684i
$698$	−23624.7	+	19823.5i	−1.28110	+	1.07497i
$699$		0			0
$700$	−1610.56	−	9133.95i	−0.0869622	−	0.493187i
$701$	7916.65	−	21750.8i	0.426544	−	1.17192i	−0.521352	−	0.853342i	$-0.674572\pi$
$701$	7916.65	−	21750.8i	0.426544	−	1.17192i	0.947896	−	0.318579i	$-0.103206\pi$
$702$		0			0
$703$	15536.4	+	20155.9i	0.833524	+	1.08136i
$704$			8182.17i			0.438036i
$705$		0			0
$706$	18347.7	−	3235.19i	0.978080	−	0.172462i
$707$	16005.6	−	19074.7i	0.851418	−	1.01468i
$708$		0			0
$709$	3260.57	−	18491.6i	0.172713	−	0.979503i	−0.768038	−	0.640404i	$-0.778767\pi$
$709$	3260.57	−	18491.6i	0.172713	−	0.979503i	0.940751	−	0.339099i	$-0.110122\pi$
$710$	−420.519	−	242.787i	−0.0222279	−	0.0128333i
$711$		0			0
$712$	24671.8	−	8979.81i	1.29862	−	0.472658i
$713$	12822.4	−	4666.99i	0.673498	−	0.245133i
$714$		0			0
$715$	2295.34	+	1325.21i	0.120057	+	0.0693149i
$716$	1006.06	−	5705.67i	0.0525116	−	0.297808i
$717$		0			0
$718$	5111.89	−	6092.11i	0.265702	−	0.316651i
$719$	−35663.3	+	6288.40i	−1.84981	+	0.326172i	−0.984544	−	0.175136i	$-0.943964\pi$
$719$	−35663.3	+	6288.40i	−1.84981	+	0.326172i	−0.865269	+	0.501308i	$0.832852\pi$
$720$		0			0
$721$			13007.0i			0.671852i
$722$	13047.2	−	18808.2i	0.672532	−	0.969483i
$723$		0			0
$724$	1691.83	−	4648.27i	0.0868459	−	0.238607i
$725$	−2674.53	−	15168.0i	−0.137007	−	0.777003i
$726$		0			0
$727$	5506.75	−	4620.71i	0.280927	−	0.235726i	−0.491426	−	0.870919i	$-0.663524\pi$
$727$	5506.75	−	4620.71i	0.280927	−	0.235726i	0.772353	+	0.635193i	$0.219080\pi$
$728$	−34906.6	−	6154.97i	−1.77709	−	0.313350i
$729$		0			0
$730$	−48.6283	+	28.0756i	−0.00246550	+	0.00142346i
$731$	−5023.49	−	13801.9i	−0.254173	−	0.698334i
$732$		0			0
$733$	−14800.1	−	25634.5i	−0.745775	−	1.29172i	−0.949832	−	0.312761i	$-0.898746\pi$
$733$	−14800.1	−	25634.5i	−0.745775	−	1.29172i	0.204057	−	0.978959i	$-0.434587\pi$
$734$	−6822.00	+	11816.0i	−0.343058	+	0.594194i
$735$		0			0
$736$	4714.96	+	5619.07i	0.236135	+	0.281415i
$737$	25128.1	+	21085.0i	1.25591	+	1.05383i
$738$		0			0
$739$	−7319.55	−	2664.10i	−0.364349	−	0.132612i	0.153357	−	0.988171i	$-0.450992\pi$
$739$	−7319.55	−	2664.10i	−0.364349	−	0.132612i	−0.517706	+	0.855559i	$0.673214\pi$
$740$	626.195			0.0311073
$741$		0			0
$742$	14795.7			0.732032
$743$	−20762.4	−	7556.88i	−1.02516	−	0.373129i	−0.225926	−	0.974144i	$-0.572541\pi$
$743$	−20762.4	−	7556.88i	−1.02516	−	0.373129i	−0.799238	+	0.601015i	$0.794763\pi$
$744$		0			0
$745$	573.386	+	481.128i	0.0281976	+	0.0236606i
$746$	24229.8	+	28875.9i	1.18916	+	1.41719i
$747$		0			0
$748$	−6477.05	+	11218.6i	−0.316610	+	0.548384i
$749$	14946.1	+	25887.4i	0.729129	+	1.26289i
$750$		0			0
$751$	2732.26	+	7506.82i	0.132758	+	0.364751i	0.988204	−	0.153142i	$-0.0489391\pi$
$751$	2732.26	+	7506.82i	0.132758	+	0.364751i	−0.855446	+	0.517892i	$0.826717\pi$
$752$	38082.4	−	21986.9i	1.84671	−	1.06620i
$753$		0			0
$754$	37404.1	+	6595.35i	1.80660	+	0.318552i
$755$	1329.52	−	1115.60i	0.0640876	−	0.0537759i
$756$		0			0
$757$	4721.53	+	26777.1i	0.226694	+	1.28564i	0.859421	+	0.511269i	$0.170824\pi$
$757$	4721.53	+	26777.1i	0.226694	+	1.28564i	−0.632727	+	0.774375i	$0.718065\pi$
$758$	−10352.9	+	28444.4i	−0.496089	+	1.36299i
$759$		0			0
$760$	264.303	+	831.908i	0.0126149	+	0.0397059i
$761$		−	10543.8i		−	0.502250i	−0.967955	−	0.251125i	$-0.919199\pi$
$761$		−	10543.8i		−	0.502250i	0.967955	−	0.251125i	$-0.0808005\pi$
$762$		0			0
$763$	−5728.60	+	1010.11i	−0.271808	+	0.0479270i
$764$	4126.15	−	4917.35i	0.195391	−	0.232858i
$765$		0			0
$766$	−2630.05	+	14915.8i	−0.124057	+	0.703562i
$767$	−56663.6	−	32714.7i	−2.66754	−	1.54010i
$768$		0			0
$769$	30280.1	−	11021.1i	1.41993	−	0.516814i	0.485905	−	0.874012i	$-0.338490\pi$
$769$	30280.1	−	11021.1i	1.41993	−	0.516814i	0.934029	+	0.357198i	$0.116268\pi$
$770$	2142.56	−	779.826i	0.100276	−	0.0364974i
$771$		0			0
$772$	10454.5	+	6035.90i	0.487390	+	0.281395i
$773$	1303.14	−	7390.48i	0.0606349	−	0.343877i	−0.939365	−	0.342920i	$-0.888584\pi$
$773$	1303.14	−	7390.48i	0.0606349	−	0.343877i	1.00000		0.000957567i	$-0.000304803\pi$
$774$		0			0
$775$	−20063.0	+	23910.2i	−0.929916	+	1.10823i
$776$	9753.17	−	1719.75i	0.451184	−	0.0795558i
$777$		0			0
$778$			48685.8i			2.24353i
$779$	−13135.1	−	11983.3i	−0.604126	−	0.551151i
$780$		0			0
$781$	−3396.53	+	9331.88i	−0.155617	+	0.427556i
$782$	−2939.51	−	16670.8i	−0.134420	−	0.762335i
$783$		0			0
$784$	−13359.7	+	11210.1i	−0.608588	+	0.510666i
$785$	1517.15	+	267.514i	0.0689800	+	0.0121630i
$786$		0			0
$787$	21769.8	−	12568.8i	0.986036	−	0.569288i	0.0819491	−	0.996637i	$-0.473886\pi$
$787$	21769.8	−	12568.8i	0.986036	−	0.569288i	0.904087	+	0.427348i	$0.140552\pi$
$788$	2148.67	+	5903.42i	0.0971360	+	0.266879i
$789$		0			0
$790$	480.416	+	832.104i	0.0216360	+	0.0374746i
$791$	664.508	−	1150.96i	0.0298700	−	0.0517364i
$792$		0			0
$793$	−142.615	−	169.962i	−0.00638640	−	0.00761102i
$794$	−20185.0	−	16937.3i	−0.902192	−	0.757029i
$795$		0			0
$796$	879.009	+	319.933i	0.0391403	+	0.0142459i
$797$	−19343.8			−0.859715			−0.429858	−	0.902897i	$-0.641436\pi$
$797$	−19343.8			−0.859715			−0.429858	+	0.902897i	$0.641436\pi$
$798$		0			0
$799$	−51673.9			−2.28798
$800$	−15766.7	−	5738.60i	−0.696795	−	0.253613i
$801$		0			0
$802$	−16033.2	−	13453.5i	−0.705926	−	0.592342i
$803$	738.167	+	879.713i	0.0324400	+	0.0386605i
$804$		0			0
$805$	−419.679	+	726.905i	−0.0183748	+	0.0318261i
$806$	−38484.7	−	66657.5i	−1.68185	−	2.91304i
$807$		0			0
$808$	−5824.16	−	16001.7i	−0.253581	−	0.696707i
$809$	−21248.2	+	12267.6i	−0.923419	+	0.533136i	−0.884724	−	0.466115i	$-0.845653\pi$
$809$	−21248.2	+	12267.6i	−0.923419	+	0.533136i	−0.0386947	+	0.999251i	$0.512320\pi$
$810$		0			0
$811$	28285.6	+	4987.51i	1.22471	+	0.215950i	0.748352	−	0.663301i	$-0.230845\pi$
$811$	28285.6	+	4987.51i	1.22471	+	0.215950i	0.476359	+	0.879251i	$0.341956\pi$
$812$	7051.08	−	5916.56i	0.304734	−	0.255703i
$813$		0			0
$814$	−7894.13	−	44769.8i	−0.339913	−	1.92774i
$815$	213.792	−	587.388i	0.00918871	−	0.0252458i
$816$		0			0
$817$	2798.97	−	12757.5i	0.119857	−	0.546300i
$818$			27856.0i			1.19066i
$819$		0			0
$820$	−430.850	+	75.9706i	−0.0183487	+	0.00323537i
$821$	−9984.71	+	11899.3i	−0.424444	+	0.505833i	−0.935311	−	0.353827i	$-0.884880\pi$
$821$	−9984.71	+	11899.3i	−0.424444	+	0.505833i	0.510867	+	0.859660i	$0.329325\pi$
$822$		0			0
$823$	5585.05	−	31674.4i	0.236552	−	1.34156i	−0.602767	−	0.797917i	$-0.705935\pi$
$823$	5585.05	−	31674.4i	0.236552	−	1.34156i	0.839320	−	0.543638i	$-0.182954\pi$
$824$	7703.43	+	4447.58i	0.325682	+	0.188032i
$825$		0			0
$826$	−52891.9	+	19251.1i	−2.22802	+	0.810934i
$827$	67.8044	−	24.6788i	0.00285102	−	0.00103769i	−0.340594	−	0.940210i	$-0.610628\pi$
$827$	67.8044	−	24.6788i	0.00285102	−	0.00103769i	0.343445	+	0.939173i	$0.388406\pi$
$828$		0			0
$829$	−7886.87	−	4553.49i	−0.330425	−	0.190771i	0.325605	−	0.945506i	$-0.394432\pi$
$829$	−7886.87	−	4553.49i	−0.330425	−	0.190771i	−0.656030	+	0.754735i	$0.727765\pi$
$830$	106.837	−	605.901i	0.00446790	−	0.0253387i
$831$		0			0
$832$	−10921.2	+	13015.4i	−0.455078	+	0.542341i
$833$	20182.4	−	3558.70i	0.839471	−	0.148021i
$834$		0			0
$835$		−	397.601i		−	0.0164785i
$836$	−10206.1	+	5341.38i	−0.422230	+	0.220975i
$837$		0			0
$838$	−11354.1	+	31195.2i	−0.468044	+	1.28594i
$839$	6261.98	+	35513.5i	0.257673	+	1.46134i	0.789117	+	0.614243i	$0.210538\pi$
$839$	6261.98	+	35513.5i	0.257673	+	1.46134i	−0.531444	+	0.847093i	$0.678350\pi$
$840$		0			0
$841$	−6973.88	+	5851.78i	−0.285944	+	0.239935i
$842$	7494.43	+	1321.47i	0.306740	+	0.0540866i
$843$		0			0
$844$	1614.97	−	932.402i	0.0658643	−	0.0380268i
$845$	1394.31	+	3830.85i	0.0567643	+	0.155959i
$846$		0			0
$847$	−7524.13	−	13032.2i	−0.305233	−	0.528679i
$848$	7404.11	−	12824.3i	0.299833	−	0.519326i
$849$		0			0
$850$	24889.5	+	29662.1i	1.00436	+	1.19694i
$851$	12820.0	+	10757.3i	0.516410	+	0.433319i
$852$		0			0
$853$	6387.31	+	2324.79i	0.256386	+	0.0933169i	0.467016	−	0.884249i	$-0.345329\pi$
$853$	6387.31	+	2324.79i	0.256386	+	0.0933169i	−0.210630	+	0.977566i	$0.567551\pi$
$854$	−190.866			−0.00764790
$855$		0			0
$856$	20442.5			0.816251
$857$	3798.60	+	1382.58i	0.151409	+	0.0551085i	0.416613	−	0.909084i	$-0.363217\pi$
$857$	3798.60	+	1382.58i	0.151409	+	0.0551085i	−0.265204	+	0.964192i	$0.585439\pi$
$858$		0			0
$859$	27548.3	+	23115.8i	1.09422	+	0.918160i	0.997023	−	0.0771052i	$-0.0245677\pi$
$859$	27548.3	+	23115.8i	1.09422	+	0.918160i	0.0971974	+	0.995265i	$0.469012\pi$
$860$	−206.577	−	246.189i	−0.00819095	−	0.00976160i
$861$		0			0
$862$	21170.2	−	36667.9i	0.836497	−	1.44885i
$863$	−4756.94	−	8239.26i	−0.187634	−	0.324991i	0.756827	−	0.653615i	$-0.226749\pi$
$863$	−4756.94	−	8239.26i	−0.187634	−	0.324991i	−0.944461	+	0.328624i	$0.893415\pi$
$864$		0			0
$865$	−300.195	−	824.780i	−0.0117999	−	0.0324201i
$866$	−30221.9	+	17448.6i	−1.18589	+	0.684675i
$867$		0			0
$868$	−18369.8	−	3239.09i	−0.718331	−	0.126661i
$869$	15053.2	−	12631.1i	0.587624	−	0.493075i
$870$		0			0
$871$	11828.0	+	67079.9i	0.460134	+	2.60955i
$872$	−1360.58	+	3738.18i	−0.0528386	+	0.145173i
$873$		0			0
$874$	5730.08	−	13919.8i	0.221765	−	0.538722i
$875$		−	3846.41i		−	0.148609i
$876$		0			0
$877$	−19644.5	+	3463.86i	−0.756384	+	0.133371i	−0.538525	−	0.842609i	$-0.681018\pi$
$877$	−19644.5	+	3463.86i	−0.756384	+	0.133371i	−0.217859	+	0.975980i	$0.569907\pi$
$878$	−1077.70	+	1284.35i	−0.0414242	+	0.0493675i
$879$		0			0
$880$	396.263	−	2247.32i	0.0151796	−	0.0860876i
$881$	20787.9	+	12001.9i	0.794963	+	0.458972i	0.841707	−	0.539935i	$-0.181551\pi$
$881$	20787.9	+	12001.9i	0.794963	+	0.458972i	−0.0467437	+	0.998907i	$0.514884\pi$
$882$		0			0
$883$	−47464.3	+	17275.6i	−1.80895	+	0.658403i	−0.811716	+	0.584052i	$0.801466\pi$
$883$	−47464.3	+	17275.6i	−1.80895	+	0.658403i	−0.997232	+	0.0743512i	$0.976311\pi$
$884$	−25277.1	+	9200.12i	−0.961721	+	0.350038i
$885$		0			0
$886$	−16802.9	−	9701.17i	−0.637139	−	0.367852i
$887$	−1675.98	+	9504.98i	−0.0634431	+	0.359804i	0.936515	+	0.350628i	$0.114032\pi$
$887$	−1675.98	+	9504.98i	−0.0634431	+	0.359804i	−0.999958	+	0.00917566i	$0.997079\pi$
$888$		0			0
$889$	−6692.54	+	7975.86i	−0.252487	+	0.300902i
$890$	−3453.76	+	608.991i	−0.130079	+	0.0229364i
$891$		0			0
$892$			6597.09i			0.247631i
$893$	−38808.3	−	24604.3i	−1.45428	−	0.922006i
$894$		0			0
$895$	410.195	−	1127.00i	0.0153199	−	0.0420911i
$896$	6977.67	+	39572.4i	0.260165	+	1.47547i
$897$		0			0
$898$	−24322.3	+	20408.8i	−0.903837	+	0.758409i
$899$	−30505.3	−	5378.90i	−1.13171	−	0.199551i
$900$		0			0
$901$	−15069.9	+	8700.63i	−0.557217	+	0.321709i
$902$	10863.0	+	29846.0i	0.400997	+	1.10173i
$903$		0			0
$904$	−454.441	−	787.114i	−0.0167196	−	0.0289591i
$905$	511.988	−	886.789i	0.0188056	−	0.0325722i
$906$		0			0
$907$	−19230.3	−	22917.7i	−0.704002	−	0.838997i	0.288971	−	0.957338i	$-0.406687\pi$
$907$	−19230.3	−	22917.7i	−0.704002	−	0.838997i	−0.992973	+	0.118341i	$0.962242\pi$
$908$	1222.40	+	1025.71i	0.0446770	+	0.0374885i
$909$		0			0
$910$	4449.05	+	1619.32i	0.162071	+	0.0589889i
$911$	22280.6			0.810306			0.405153	−	0.914249i	$-0.367218\pi$
$911$	22280.6			0.810306			0.405153	+	0.914249i	$0.367218\pi$
$912$		0			0
$913$	−12582.8			−0.456113
$914$	10319.6	+	3756.04i	0.373461	+	0.135929i
$915$		0			0
$916$	1421.26	+	1192.58i	0.0512662	+	0.0430175i
$917$	−32290.5	−	38482.3i	−1.16284	−	1.38582i
$918$		0			0
$919$	−1254.70	+	2173.20i	−0.0450366	+	0.0780057i	−0.887665	−	0.460490i	$-0.847674\pi$
$919$	−1254.70	+	2173.20i	−0.0450366	+	0.0780057i	0.842628	+	0.538496i	$0.181007\pi$
$920$	287.008	+	497.113i	0.0102852	+	0.0178145i
$921$		0			0
$922$	−14034.8	−	38560.2i	−0.501313	−	1.37735i
$923$	−17858.7	+	10310.7i	−0.636863	+	0.367693i
$924$		0			0
$925$	−37699.1	−	6647.36i	−1.34004	−	0.236285i
$926$	8634.03	−	7244.81i	0.306406	−	0.257105i
$927$		0			0
$928$	−2891.47	−	16398.3i	−0.102281	−	0.580067i
$929$	12528.0	−	34420.5i	0.442445	−	1.21561i	−0.495435	−	0.868645i	$-0.664991\pi$
$929$	12528.0	−	34420.5i	0.442445	−	1.21561i	0.937879	−	0.346961i	$-0.112787\pi$
$930$		0			0
$931$	16851.9	+	6937.10i	0.593232	+	0.244204i
$932$		−	19585.6i		−	0.688355i
$933$		0			0
$934$	55058.2	−	9708.25i	1.92886	−	0.340111i
$935$	−1723.69	+	2054.21i	−0.0602894	+	0.0718501i
$936$		0			0
$937$	5344.16	−	30308.2i	0.186325	−	1.05670i	−0.737917	−	0.674891i	$-0.764191\pi$
$937$	5344.16	−	30308.2i	0.186325	−	1.05670i	0.924242	−	0.381808i	$-0.124698\pi$
$938$	50746.0	+	29298.2i	1.76643	+	1.01985i
$939$		0			0
$940$	−1062.47	+	386.709i	−0.0368660	+	0.0134181i
$941$	−43012.2	+	15655.2i	−1.49007	+	0.542342i	−0.953469	−	0.301493i	$-0.902515\pi$
$941$	−43012.2	+	15655.2i	−1.49007	+	0.542342i	−0.536604	+	0.843834i	$0.680293\pi$
$942$		0			0
$943$	−10125.8	−	5846.16i	−0.349674	−	0.201885i
$944$	−9782.29	+	55478.1i	−0.337274	+	1.91277i
$945$		0			0
$946$	−14997.1	+	17872.8i	−0.515430	+	0.614266i
$947$	42340.7	−	7465.80i	1.45289	−	0.256184i	0.609201	−	0.793016i	$-0.291490\pi$
$947$	42340.7	−	7465.80i	1.45289	−	0.256184i	0.843689	+	0.536832i	$0.180379\pi$
$948$		0			0
$949$			2384.63i			0.0815685i
$950$	4569.07	+	34127.9i	0.156042	+	1.16553i
$951$		0			0
$952$	12265.4	−	33699.0i	0.417568	−	1.14726i
$953$	−9006.99	−	51081.2i	−0.306154	−	1.73629i	−0.618022	−	0.786161i	$-0.712066\pi$
$953$	−9006.99	−	51081.2i	−0.306154	−	1.73629i	0.311867	−	0.950126i	$-0.399046\pi$
$954$		0			0
$955$	1017.92	−	854.139i	0.0344913	−	0.0289417i
$956$	7543.05	+	1330.04i	0.255188	+	0.0449965i
$957$		0			0
$958$	23692.2	−	13678.7i	0.799021	−	0.461315i
$959$	13454.1	+	36964.8i	0.453030	+	1.24469i
$960$		0			0
$961$	16491.1	+	28563.4i	0.553559	+	0.958792i
$962$	47199.7	−	81752.2i	1.58189	−	2.73991i
$963$		0			0
$964$	−8141.76	−	9702.98i	−0.272021	−	0.324182i
$965$	1914.30	+	1606.29i	0.0638586	+	0.0535837i
$966$		0			0
$967$	−4570.26	−	1663.44i	−0.151985	−	0.0553180i	0.264907	−	0.964274i	$-0.414659\pi$
$967$	−4570.26	−	1663.44i	−0.151985	−	0.0553180i	−0.416892	+	0.908956i	$0.636881\pi$
$968$	−10291.1			−0.341704
$969$		0			0
$970$	−1322.88			−0.0437887
$971$	−3459.24	−	1259.06i	−0.114328	−	0.0416120i	0.284223	−	0.958758i	$-0.408264\pi$
$971$	−3459.24	−	1259.06i	−0.114328	−	0.0416120i	−0.398551	+	0.917146i	$0.630487\pi$
$972$		0			0
$973$	31126.3	+	26118.1i	1.02555	+	0.860542i
$974$	−19710.0	−	23489.4i	−0.648407	−	0.772741i
$975$		0			0
$976$	−95.5137	+	165.435i	−0.00313250	+	0.00542565i
$977$	1357.18	+	2350.71i	0.0444423	+	0.0769764i	0.887391	−	0.461018i	$-0.152516\pi$
$977$	1357.18	+	2350.71i	0.0444423	+	0.0769764i	−0.842949	+	0.537994i	$0.819182\pi$
$978$		0			0
$979$	24531.3	+	67399.2i	0.800841	+	2.20029i
$980$	388.341	−	224.209i	0.0126583	−	0.00730825i
$981$		0			0
$982$	22557.1	+	3977.42i	0.733019	+	0.129251i
$983$	10652.6	−	8938.61i	0.345642	−	0.290028i	−0.453395	−	0.891309i	$-0.649787\pi$
$983$	10652.6	−	8938.61i	0.345642	−	0.290028i	0.799037	+	0.601282i	$0.205343\pi$
$984$		0			0
$985$	225.825	+	1280.72i	0.00730496	+	0.0414285i
$986$	−13143.0	+	36110.1i	−0.424501	+	1.16631i
$987$		0			0
$988$	−23364.3	−	5126.09i	−0.752344	−	0.165063i
$989$		−	8588.95i		−	0.276150i
$990$		0			0
$991$	−12854.7	+	2266.63i	−0.412051	+	0.0726557i	−0.375831	−	0.926688i	$-0.622643\pi$
$991$	−12854.7	+	2266.63i	−0.412051	+	0.0726557i	−0.0362197	+	0.999344i	$0.511532\pi$
$992$	−21690.4	+	25849.6i	−0.694223	+	0.827343i
$993$		0			0
$994$	−3080.48	+	17470.3i	−0.0982967	+	0.557468i
$995$	167.696	+	96.8192i	0.00534303	+	0.00308480i
$996$		0			0
$997$	32009.4	−	11650.5i	1.01680	−	0.370084i	0.220758	−	0.975329i	$-0.429147\pi$
$997$	32009.4	−	11650.5i	1.01680	−	0.370084i	0.796040	+	0.605245i	$0.206925\pi$
$998$	4498.54	−	1637.33i	0.142684	−	0.0519328i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.y.a.53.15	yes	120
3.2	odd	2	inner	171.4.y.a.53.6	✓	120
19.14	odd	18	inner	171.4.y.a.71.6	yes	120
57.14	even	18	inner	171.4.y.a.71.15	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.y.a.53.6	✓	120	3.2	odd	2	inner
171.4.y.a.53.15	yes	120	1.1	even	1	trivial
171.4.y.a.71.6	yes	120	19.14	odd	18	inner
171.4.y.a.71.15	yes	120	57.14	even	18	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.y (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.13604 + 1.14142i) q^{2} +(2.40352 + 2.01679i) q^{4} +(0.417489 + 0.497545i) q^{5} +(11.8643 - 20.5495i) q^{7} +(-8.11369 - 14.0533i) q^{8} +O(q^{10})\)	\(q+(3.13604 + 1.14142i) q^{2} +(2.40352 + 2.01679i) q^{4} +(0.417489 + 0.497545i) q^{5} +(11.8643 - 20.5495i) q^{7} +(-8.11369 - 14.0533i) q^{8} +(0.741353 + 2.03685i) q^{10} +(38.3912 - 22.1652i) q^{11} +(90.6542 + 15.9848i) q^{13} +(60.6625 - 50.9019i) q^{14} +(-13.7627 - 78.0521i) q^{16} +(-31.8539 + 87.5179i) q^{17} +(-65.5942 + 50.5608i) q^{19} +2.03785i q^{20} +(145.696 - 25.6902i) q^{22} +(-35.0078 + 41.7207i) q^{23} +(21.6328 - 122.686i) q^{25} +(266.049 + 153.604i) q^{26} +(69.9602 - 25.4634i) q^{28} +(116.177 - 42.2851i) q^{29} +(-216.979 - 125.273i) q^{31} +(23.3874 - 132.637i) q^{32} +(-199.790 + 238.101i) q^{34} +(15.1775 - 2.67621i) q^{35} -307.282i q^{37} +(-263.417 + 83.6897i) q^{38} +(3.60477 - 9.90403i) q^{40} +(37.2798 + 211.424i) q^{41} +(-120.808 + 101.370i) q^{43} +(136.977 + 24.1527i) q^{44} +(-157.407 + 90.8789i) q^{46} +(189.763 + 521.370i) q^{47} +(-110.022 - 190.564i) q^{49} +(207.877 - 360.054i) q^{50} +(185.651 + 221.251i) q^{52} +(143.128 + 120.098i) q^{53} +(27.0561 + 9.84762i) q^{55} -385.052 q^{56} +412.602 q^{58} +(-667.917 - 243.102i) q^{59} +(-1.84636 - 1.54928i) q^{61} +(-537.465 - 640.525i) q^{62} +(-92.2863 + 159.845i) q^{64} +(29.8940 + 51.7780i) q^{65} +(253.079 + 695.329i) q^{67} +(-253.067 + 146.108i) q^{68} +(50.6519 + 8.93131i) q^{70} +(-171.607 + 143.996i) q^{71} +(4.49838 + 25.5116i) q^{73} +(350.739 - 963.648i) q^{74} +(-259.628 - 10.7661i) q^{76} -1051.90i q^{77} +(436.541 - 76.9740i) q^{79} +(33.0886 - 39.4335i) q^{80} +(-124.414 + 705.586i) q^{82} +(-245.815 - 141.921i) q^{83} +(-56.8428 + 20.6891i) q^{85} +(-494.565 + 180.007i) q^{86} +(-622.989 - 359.683i) q^{88} +(-280.955 + 1593.38i) q^{89} +(1404.03 - 1673.25i) q^{91} +(-168.284 + 29.6731i) q^{92} +1851.64i q^{94} +(-52.5412 - 11.5275i) q^{95} +(-208.736 + 573.498i) q^{97} +(-127.519 - 723.198i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 36 q^{4}+O(q^{10}) \) 120 * q - 36 * q^4	\( 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) \) 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more