LMFDB - Embedded newform 76.5.j.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(13,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.13");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.j (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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	76.13
Dual form			76.5.j.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.65644 + 12.7935i) q^{3} +(6.59099 + 37.3793i) q^{5} +(5.00284 - 8.66518i) q^{7} +(-79.9406 - 67.0781i) q^{9} +O(q^{10})$	\(q+(-4.65644 + 12.7935i) q^{3} +(6.59099 + 37.3793i) q^{5} +(5.00284 - 8.66518i) q^{7} +(-79.9406 - 67.0781i) q^{9} +(-7.63671 - 13.2272i) q^{11} +(-22.1718 - 60.9166i) q^{13} +(-508.902 - 89.7331i) q^{15} +(-348.579 + 292.493i) q^{17} +(281.167 - 226.421i) q^{19} +(87.5622 + 104.353i) q^{21} +(49.2696 - 279.422i) q^{23} +(-766.467 + 278.971i) q^{25} +(275.368 - 158.984i) q^{27} +(-472.367 + 562.945i) q^{29} +(1430.40 + 825.841i) q^{31} +(204.781 - 36.1084i) q^{33} +(356.872 + 129.891i) q^{35} -1474.16i q^{37} +882.576 q^{39} +(-842.731 + 2315.38i) q^{41} +(-329.577 - 1869.12i) q^{43} +(1980.45 - 3430.24i) q^{45} +(985.584 + 827.003i) q^{47} +(1150.44 + 1992.63i) q^{49} +(-2118.86 - 5821.51i) q^{51} +(3118.81 + 549.931i) q^{53} +(444.089 - 372.635i) q^{55} +(1587.47 + 4651.41i) q^{57} +(938.249 + 1118.16i) q^{59} +(-920.289 + 5219.22i) q^{61} +(-981.174 + 357.118i) q^{63} +(2130.89 - 1230.27i) q^{65} +(-4064.52 + 4843.91i) q^{67} +(3345.35 + 1931.44i) q^{69} +(-9089.14 + 1602.66i) q^{71} +(-3636.99 - 1323.76i) q^{73} -11104.8i q^{75} -152.821 q^{77} +(-1439.36 + 3954.62i) q^{79} +(-716.087 - 4061.13i) q^{81} +(6219.89 - 10773.2i) q^{83} +(-13230.7 - 11101.8i) q^{85} +(-5002.47 - 8664.53i) q^{87} +(4134.29 + 11358.9i) q^{89} +(-638.775 - 112.633i) q^{91} +(-17225.9 + 14454.3i) q^{93} +(10316.6 + 9017.49i) q^{95} +(-1907.80 - 2273.62i) q^{97} +(-276.771 + 1569.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	$ 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) $ 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.65644	+	12.7935i	−0.517382	+	1.42150i	0.356012	+	0.934481i	$0.384136\pi$
$3$	−4.65644	+	12.7935i	−0.517382	+	1.42150i	−0.873394	+	0.487014i	$0.838086\pi$
$4$		0			0
$5$	6.59099	+	37.3793i	0.263640	+	1.49517i	0.772881	+	0.634551i	$0.218815\pi$
$5$	6.59099	+	37.3793i	0.263640	+	1.49517i	−0.509242	+	0.860623i	$0.670074\pi$
$6$		0			0
$7$	5.00284	−	8.66518i	0.102099	−	0.176840i	−0.810450	−	0.585807i	$-0.800778\pi$
$7$	5.00284	−	8.66518i	0.102099	−	0.176840i	0.912549	+	0.408967i	$0.134111\pi$
$8$		0			0
$9$	−79.9406	−	67.0781i	−0.986921	−	0.828125i
$10$		0			0
$11$	−7.63671	−	13.2272i	−0.0631133	−	0.109315i	0.832742	−	0.553661i	$-0.186770\pi$
$11$	−7.63671	−	13.2272i	−0.0631133	−	0.109315i	−0.895856	+	0.444345i	$0.853436\pi$
$12$		0			0
$13$	−22.1718	−	60.9166i	−0.131194	−	0.360453i	0.856650	−	0.515897i	$-0.172541\pi$
$13$	−22.1718	−	60.9166i	−0.131194	−	0.360453i	−0.987845	+	0.155444i	$0.950319\pi$
$14$		0			0
$15$	−508.902	−	89.7331i	−2.26179	−	0.398814i
$16$		0			0
$17$	−348.579	+	292.493i	−1.20616	+	1.01209i	−0.206724	+	0.978399i	$0.566280\pi$
$17$	−348.579	+	292.493i	−1.20616	+	1.01209i	−0.999432	+	0.0336857i	$0.989275\pi$
$18$		0			0
$19$	281.167	−	226.421i	0.778855	−	0.627204i
$19$	281.167	−	226.421i	0.778855	−	0.627204i
$20$		0			0
$21$	87.5622	+	104.353i	0.198554	+	0.236627i
$22$		0			0
$23$	49.2696	−	279.422i	0.0931372	−	0.528207i	−0.902165	−	0.431391i	$-0.858023\pi$
$23$	49.2696	−	279.422i	0.0931372	−	0.528207i	0.995302	−	0.0968164i	$-0.0308660\pi$
$24$		0			0
$25$	−766.467	+	278.971i	−1.22635	+	0.446354i
$26$		0			0
$27$	275.368	−	158.984i	0.377734	−	0.218085i
$28$		0			0
$29$	−472.367	+	562.945i	−0.561673	+	0.669376i	−0.969900	−	0.243505i	$-0.921703\pi$
$29$	−472.367	+	562.945i	−0.561673	+	0.669376i	0.408227	+	0.912881i	$0.366147\pi$
$30$		0			0
$31$	1430.40	+	825.841i	1.48845	+	0.859356i	0.999913	−	0.0131887i	$-0.00419821\pi$
$31$	1430.40	+	825.841i	1.48845	+	0.859356i	0.488535	+	0.872544i	$0.337532\pi$
$32$		0			0
$33$	204.781	−	36.1084i	0.188045	−	0.0331574i
$34$		0			0
$35$	356.872	+	129.891i	0.291324	+	0.106033i
$36$		0			0
$37$		−	1474.16i		−	1.07681i	−0.842685	−	0.538407i	$-0.819026\pi$
$37$		−	1474.16i		−	1.07681i	0.842685	−	0.538407i	$-0.180974\pi$
$38$		0			0
$39$	882.576			0.580260
$40$		0			0
$41$	−842.731	+	2315.38i	−0.501327	+	1.37739i	0.388652	+	0.921385i	$0.372941\pi$
$41$	−842.731	+	2315.38i	−0.501327	+	1.37739i	−0.889979	+	0.456001i	$0.849281\pi$
$42$		0			0
$43$	−329.577	−	1869.12i	−0.178246	−	1.01088i	−0.934330	−	0.356409i	$-0.884001\pi$
$43$	−329.577	−	1869.12i	−0.178246	−	1.01088i	0.756084	−	0.654474i	$-0.227110\pi$
$44$		0			0
$45$	1980.45	−	3430.24i	0.978000	−	1.69395i
$46$		0			0
$47$	985.584	+	827.003i	0.446167	+	0.374379i	0.838011	−	0.545653i	$-0.183718\pi$
$47$	985.584	+	827.003i	0.446167	+	0.374379i	−0.391844	+	0.920032i	$0.628163\pi$
$48$		0			0
$49$	1150.44	+	1992.63i	0.479152	+	0.829915i
$50$		0			0
$51$	−2118.86	−	5821.51i	−0.814631	−	2.23818i
$52$		0			0
$53$	3118.81	+	549.931i	1.11029	+	0.195775i	0.698575	−	0.715537i	$-0.253818\pi$
$53$	3118.81	+	549.931i	1.11029	+	0.195775i	0.411718	+	0.911311i	$0.364929\pi$
$54$		0			0
$55$	444.089	−	372.635i	0.146806	−	0.123185i
$56$		0			0
$57$	1587.47	+	4651.41i	0.488603	+	1.43164i
$58$		0			0
$59$	938.249	+	1118.16i	0.269534	+	0.321218i	0.883786	−	0.467892i	$-0.154986\pi$
$59$	938.249	+	1118.16i	0.269534	+	0.321218i	−0.614251	+	0.789110i	$0.710542\pi$
$60$		0			0
$61$	−920.289	+	5219.22i	−0.247323	+	1.40264i	0.567712	+	0.823227i	$0.307829\pi$
$61$	−920.289	+	5219.22i	−0.247323	+	1.40264i	−0.815035	+	0.579411i	$0.803283\pi$
$62$		0			0
$63$	−981.174	+	357.118i	−0.247209	+	0.0899769i
$64$		0			0
$65$	2130.89	−	1230.27i	0.504352	−	0.291188i
$66$		0			0
$67$	−4064.52	+	4843.91i	−0.905441	+	1.07906i	0.0910906	+	0.995843i	$0.470965\pi$
$67$	−4064.52	+	4843.91i	−0.905441	+	1.07906i	−0.996531	+	0.0832195i	$0.973480\pi$
$68$		0			0
$69$	3345.35	+	1931.44i	0.702657	+	0.405679i
$70$		0			0
$71$	−9089.14	+	1602.66i	−1.80304	+	0.317925i	−0.971411	−	0.237402i	$-0.923704\pi$
$71$	−9089.14	+	1602.66i	−1.80304	+	0.317925i	−0.831632	+	0.555328i	$0.812593\pi$
$72$		0			0
$73$	−3636.99	−	1323.76i	−0.682491	−	0.248406i	−0.0225741	−	0.999745i	$-0.507186\pi$
$73$	−3636.99	−	1323.76i	−0.682491	−	0.248406i	−0.659917	+	0.751339i	$0.729408\pi$
$74$		0			0
$75$		−	11104.8i		−	1.97418i
$76$		0			0
$77$	−152.821			−0.0257752
$78$		0			0
$79$	−1439.36	+	3954.62i	−0.230630	+	0.633652i	−0.999987	−	0.00516827i	$-0.998355\pi$
$79$	−1439.36	+	3954.62i	−0.230630	+	0.633652i	0.769356	+	0.638820i	$0.220577\pi$
$80$		0			0
$81$	−716.087	−	4061.13i	−0.109143	−	0.618980i
$82$		0			0
$83$	6219.89	−	10773.2i	0.902873	−	1.56382i	0.0791251	−	0.996865i	$-0.474787\pi$
$83$	6219.89	−	10773.2i	0.902873	−	1.56382i	0.823748	−	0.566957i	$-0.191879\pi$
$84$		0			0
$85$	−13230.7	−	11101.8i	−1.83123	−	1.53659i
$86$		0			0
$87$	−5002.47	−	8664.53i	−0.660915	−	1.14474i
$88$		0			0
$89$	4134.29	+	11358.9i	0.521940	+	1.43402i	0.868358	+	0.495938i	$0.165176\pi$
$89$	4134.29	+	11358.9i	0.521940	+	1.43402i	−0.346418	+	0.938080i	$0.612602\pi$
$90$		0			0
$91$	−638.775	−	112.633i	−0.0771374	−	0.0136014i
$92$		0			0
$93$	−17225.9	+	14454.3i	−1.99167	+	1.67121i
$94$		0			0
$95$	10316.6	+	9017.49i	1.14312	+	0.999168i
$96$		0			0
$97$	−1907.80	−	2273.62i	−0.202763	−	0.241643i	0.655075	−	0.755564i	$-0.272637\pi$
$97$	−1907.80	−	2273.62i	−0.202763	−	0.241643i	−0.857838	+	0.513920i	$0.828193\pi$
$98$		0			0
$99$	−276.771	+	1569.64i	−0.0282390	+	0.160151i
$100$		0			0
$101$	830.282	−	302.198i	0.0813923	−	0.0296244i	−0.301003	−	0.953623i	$-0.597321\pi$
$101$	830.282	−	302.198i	0.0813923	−	0.0296244i	0.382395	+	0.923999i	$0.375099\pi$
$102$		0			0
$103$	−1371.68	+	791.938i	−0.129294	+	0.0746477i	−0.563252	−	0.826285i	$-0.690450\pi$
$103$	−1371.68	+	791.938i	−0.129294	+	0.0746477i	0.433958	+	0.900933i	$0.357117\pi$
$104$		0			0
$105$	−3323.51	+	3960.80i	−0.301452	+	0.359256i
$106$		0			0
$107$	10273.8	+	5931.59i	0.897355	+	0.518088i	0.876341	−	0.481691i	$-0.159977\pi$
$107$	10273.8	+	5931.59i	0.897355	+	0.518088i	0.0210141	+	0.999779i	$0.493311\pi$
$108$		0			0
$109$	6748.93	−	1190.02i	0.568044	−	0.100161i	0.117752	−	0.993043i	$-0.462431\pi$
$109$	6748.93	−	1190.02i	0.568044	−	0.100161i	0.450292	+	0.892882i	$0.351320\pi$
$110$		0			0
$111$	18859.6	+	6864.33i	1.53069	+	0.557124i
$112$		0			0
$113$		−	353.475i		−	0.0276823i	−0.999904	−	0.0138412i	$-0.995594\pi$
$113$		−	353.475i		−	0.0276823i	0.999904	−	0.0138412i	$-0.00440592\pi$
$114$		0			0
$115$	10769.3			0.814317
$116$		0			0
$117$	−2313.74	+	6356.96i	−0.169022	+	0.464384i
$118$		0			0
$119$	790.614	+	4483.79i	0.0558304	+	0.316630i
$120$		0			0
$121$	7203.86	−	12477.5i	0.492033	−	0.852227i
$122$		0			0
$123$	−25697.7	−	21562.9i	−1.69857	−	1.42527i
$124$		0			0
$125$	−3618.28	−	6267.05i	−0.231570	−	0.401091i
$126$		0			0
$127$	761.552	+	2092.35i	0.0472163	+	0.129726i	0.961060	−	0.276341i	$-0.0891221\pi$
$127$	761.552	+	2092.35i	0.0472163	+	0.129726i	−0.913843	+	0.406067i	$0.866900\pi$
$128$		0			0
$129$	25447.2	+	4487.03i	1.52919	+	0.269637i
$130$		0			0
$131$	20343.3	−	17070.1i	1.18544	−	0.994700i	0.185510	−	0.982642i	$-0.440606\pi$
$131$	20343.3	−	17070.1i	1.18544	−	0.994700i	0.999927	−	0.0120581i	$-0.00383830\pi$
$132$		0			0
$133$	−555.343	−	3569.11i	−0.0313948	−	0.201770i
$134$		0			0
$135$	7757.67	+	9245.23i	0.425661	+	0.507283i
$136$		0			0
$137$	612.283	−	3472.43i	0.0326221	−	0.185009i	−0.964143	−	0.265385i	$-0.914501\pi$
$137$	612.283	−	3472.43i	0.0326221	−	0.185009i	0.996765	+	0.0803760i	$0.0256121\pi$
$138$		0			0
$139$	13225.7	−	4813.75i	0.684522	−	0.249146i	0.0237343	−	0.999718i	$-0.492444\pi$
$139$	13225.7	−	4813.75i	0.684522	−	0.249146i	0.660788	+	0.750573i	$0.270222\pi$
$140$		0			0
$141$	−15169.5	+	8758.14i	−0.763017	+	0.440528i
$142$		0			0
$143$	−636.434	+	758.472i	−0.0311230	+	0.0370909i
$144$		0			0
$145$	−24155.9	−	13946.4i	−1.14891	−	0.663325i
$146$		0			0
$147$	−30849.6	+	5439.61i	−1.42763	+	0.251729i
$148$		0			0
$149$	33951.2	+	12357.2i	1.52927	+	0.556607i	0.963442	−	0.267918i	$-0.0863357\pi$
$149$	33951.2	+	12357.2i	1.52927	+	0.556607i	0.565825	+	0.824526i	$0.308558\pi$
$150$		0			0
$151$		−	22405.3i		−	0.982644i	−0.870978	−	0.491322i	$-0.836514\pi$
$151$		−	22405.3i		−	0.982644i	0.870978	−	0.491322i	$-0.163486\pi$
$152$		0			0
$153$	47485.5			2.02851
$154$		0			0
$155$	−21441.7	+	58910.5i	−0.892473	+	2.45205i
$156$		0			0
$157$	−8341.26	−	47305.7i	−0.338402	−	1.91917i	−0.390654	−	0.920538i	$-0.627751\pi$
$157$	−8341.26	−	47305.7i	−0.338402	−	1.91917i	0.0522519	−	0.998634i	$-0.483360\pi$
$158$		0			0
$159$	−21558.1	+	37339.7i	−0.852738	+	1.47699i
$160$		0			0
$161$	−2174.75	−	1824.83i	−0.0838992	−	0.0703998i
$162$		0			0
$163$	5852.63	+	10137.0i	0.220280	+	0.381537i	0.954893	−	0.296950i	$-0.0959695\pi$
$163$	5852.63	+	10137.0i	0.220280	+	0.381537i	−0.734613	+	0.678487i	$0.762636\pi$
$164$		0			0
$165$	2699.42	+	7416.59i	0.0991522	+	0.272418i
$166$		0			0
$167$	11805.3	+	2081.60i	0.423297	+	0.0746387i	0.381239	−	0.924476i	$-0.375497\pi$
$167$	11805.3	+	2081.60i	0.423297	+	0.0746387i	0.0420580	+	0.999115i	$0.486609\pi$
$168$		0			0
$169$	18659.8	−	15657.4i	0.653330	−	0.548209i
$170$		0			0
$171$	−37664.5	−	759.921i	−1.28807	−	0.0259882i
$172$		0			0
$173$	−12729.2	−	15170.1i	−0.425315	−	0.506870i	0.510250	−	0.860026i	$-0.329553\pi$
$173$	−12729.2	−	15170.1i	−0.425315	−	0.506870i	−0.935564	+	0.353156i	$0.885108\pi$
$174$		0			0
$175$	−1417.18	+	8037.22i	−0.0462752	+	0.262440i
$176$		0			0
$177$	−18674.1	+	6796.80i	−0.596063	+	0.216949i
$178$		0			0
$179$	12656.1	−	7306.98i	0.394996	−	0.228051i	−0.289327	−	0.957230i	$-0.593431\pi$
$179$	12656.1	−	7306.98i	0.394996	−	0.228051i	0.684322	+	0.729179i	$0.260098\pi$
$180$		0			0
$181$	−19336.0	+	23043.8i	−0.590215	+	0.703391i	−0.975647	−	0.219345i	$-0.929608\pi$
$181$	−19336.0	+	23043.8i	−0.590215	+	0.703391i	0.385432	+	0.922736i	$0.374052\pi$
$182$		0			0
$183$	−62486.6	−	36076.6i	−1.86588	−	1.07727i
$184$		0			0
$185$	55103.1	−	9716.16i	1.61002	−	0.283891i
$186$		0			0
$187$	6530.84	+	2377.03i	0.186761	+	0.0679754i
$188$		0			0
$189$		−	3181.49i		−	0.0890649i
$190$		0			0
$191$	−26426.2			−0.724383			−0.362191	−	0.932104i	$-0.617971\pi$
$191$	−26426.2			−0.724383			−0.362191	+	0.932104i	$0.617971\pi$
$192$		0			0
$193$	−11007.9	+	30243.9i	−0.295521	+	0.811938i	0.699713	+	0.714424i	$0.253311\pi$
$193$	−11007.9	+	30243.9i	−0.295521	+	0.811938i	−0.995234	+	0.0975137i	$0.968911\pi$
$194$		0			0
$195$	5817.05	+	32990.1i	0.152980	+	0.867590i
$196$		0			0
$197$	−22446.5	+	38878.6i	−0.578385	+	1.00179i	0.417280	+	0.908778i	$0.362984\pi$
$197$	−22446.5	+	38878.6i	−0.578385	+	1.00179i	−0.995665	+	0.0930142i	$0.970350\pi$
$198$		0			0
$199$	−4917.74	−	4126.47i	−0.124182	−	0.104201i	0.578582	−	0.815625i	$-0.303606\pi$
$199$	−4917.74	−	4126.47i	−0.124182	−	0.104201i	−0.702764	+	0.711423i	$0.748051\pi$
$200$		0			0
$201$	−43044.2	−	74554.7i	−1.06542	−	1.84537i
$202$		0			0
$203$	2514.84	+	6909.47i	0.0610265	+	0.167669i
$204$		0			0
$205$	−92102.0	−	16240.1i	−2.19160	−	0.386438i
$206$		0			0
$207$	−22681.7	+	19032.2i	−0.529341	+	0.444170i
$208$		0			0
$209$	−5142.09	−	1989.93i	−0.117719	−	0.0455559i
$210$		0			0
$211$	32561.2	+	38804.9i	0.731367	+	0.871609i	0.995682	−	0.0928271i	$-0.0295904\pi$
$211$	32561.2	+	38804.9i	0.731367	+	0.871609i	−0.264315	+	0.964436i	$0.585146\pi$
$212$		0			0
$213$	21819.5	−	123744.i	0.480933	−	2.72751i
$214$		0			0
$215$	67694.4	−	24638.7i	1.46445	−	0.533018i
$216$		0			0
$217$	14312.1	−	8263.10i	0.303937	−	0.175478i
$218$		0			0
$219$	33870.9	−	40365.7i	0.706217	−	0.841637i
$220$		0			0
$221$	25546.3	+	14749.2i	0.523050	+	0.301983i
$222$		0			0
$223$	2412.23	−	425.340i	0.0485074	−	0.00855317i	−0.149342	−	0.988786i	$-0.547715\pi$
$223$	2412.23	−	425.340i	0.0485074	−	0.00855317i	0.197849	+	0.980232i	$0.436604\pi$
$224$		0			0
$225$	79984.7	+	29112.0i	1.57994	+	0.575053i
$226$		0			0
$227$			35918.6i			0.697056i	0.937298	+	0.348528i	$0.113318\pi$
$227$			35918.6i			0.697056i	−0.937298	+	0.348528i	$0.886682\pi$
$228$		0			0
$229$	−33051.1			−0.630253			−0.315126	−	0.949050i	$-0.602047\pi$
$229$	−33051.1			−0.630253			−0.315126	+	0.949050i	$0.602047\pi$
$230$		0			0
$231$	711.601	−	1955.11i	0.0133356	−	0.0366393i
$232$		0			0
$233$	−3363.41	−	19074.9i	−0.0619539	−	0.351358i	−0.999988	−	0.00481606i	$-0.998467\pi$
$233$	−3363.41	−	19074.9i	−0.0619539	−	0.351358i	0.938035	−	0.346542i	$-0.112644\pi$
$234$		0			0
$235$	−24416.9	+	42291.2i	−0.442134	+	0.765799i
$236$		0			0
$237$	−43891.0	−	36828.9i	−0.781409	−	0.655680i
$238$		0			0
$239$	28728.8	+	49759.7i	0.502946	+	0.871127i	0.999994	+	0.00340461i	$0.00108372\pi$
$239$	28728.8	+	49759.7i	0.502946	+	0.871127i	−0.497049	+	0.867723i	$0.665583\pi$
$240$		0			0
$241$	19044.5	+	52324.4i	0.327896	+	0.900887i	0.988644	+	0.150279i	$0.0480171\pi$
$241$	19044.5	+	52324.4i	0.327896	+	0.900887i	−0.660748	+	0.750608i	$0.729761\pi$
$242$		0			0
$243$	80654.5	+	14221.6i	1.36589	+	0.240843i
$244$		0			0
$245$	−66900.5	+	56136.2i	−1.11454	+	0.935213i
$246$		0			0
$247$	−20026.8	−	12107.5i	−0.328259	−	0.198455i
$248$		0			0
$249$	108864.	+	129739.i	1.75584	+	2.09252i
$250$		0			0
$251$	−2649.04	+	15023.4i	−0.0420476	+	0.238464i	−0.998587	−	0.0531390i	$-0.983077\pi$
$251$	−2649.04	+	15023.4i	−0.0420476	+	0.238464i	0.956540	+	0.291603i	$0.0941885\pi$
$252$		0			0
$253$	−4072.21	+	1482.16i	−0.0636194	+	0.0231556i
$254$		0			0
$255$	203639.	−	117571.i	3.13170	−	1.80809i
$256$		0			0
$257$	−6421.48	+	7652.82i	−0.0972230	+	0.115866i	−0.812462	−	0.583014i	$-0.801873\pi$
$257$	−6421.48	+	7652.82i	−0.0972230	+	0.115866i	0.715239	+	0.698880i	$0.246318\pi$
$258$		0			0
$259$	−12773.8	−	7374.98i	−0.190424	−	0.109941i
$260$		0			0
$261$	75522.6	−	13316.7i	1.10865	−	0.195486i
$262$		0			0
$263$	−33819.4	−	12309.2i	−0.488938	−	0.177959i	0.0857740	−	0.996315i	$-0.472664\pi$
$263$	−33819.4	−	12309.2i	−0.488938	−	0.177959i	−0.574712	+	0.818356i	$0.694886\pi$
$264$		0			0
$265$			120204.i			1.71169i
$266$		0			0
$267$	−164570.			−2.30849
$268$		0			0
$269$	43070.1	−	118334.i	0.595211	−	1.63533i	−0.165478	−	0.986214i	$-0.552917\pi$
$269$	43070.1	−	118334.i	0.595211	−	1.63533i	0.760689	−	0.649116i	$-0.224861\pi$
$270$		0			0
$271$	−12760.4	−	72368.0i	−0.173751	−	0.985389i	−0.939576	−	0.342340i	$-0.888780\pi$
$271$	−12760.4	−	72368.0i	−0.173751	−	0.985389i	0.765825	−	0.643049i	$-0.222331\pi$
$272$		0			0
$273$	4415.39	−	7647.67i	0.0592439	−	0.102613i
$274$		0			0
$275$	9543.28	+	8007.76i	0.126192	+	0.105888i
$276$		0			0
$277$	−3268.44	−	5661.10i	−0.0425971	−	0.0737804i	0.843941	−	0.536436i	$-0.180230\pi$
$277$	−3268.44	−	5661.10i	−0.0425971	−	0.0737804i	−0.886538	+	0.462656i	$0.846897\pi$
$278$		0			0
$279$	−58951.1	−	161967.i	−0.757327	−	2.08074i
$280$		0			0
$281$	23883.9	+	4211.38i	0.302477	+	0.0533349i	0.322827	−	0.946458i	$-0.395367\pi$
$281$	23883.9	+	4211.38i	0.302477	+	0.0533349i	−0.0203497	+	0.999793i	$0.506478\pi$
$282$		0			0
$283$	50567.4	−	42431.1i	0.631390	−	0.529799i	−0.269970	−	0.962869i	$-0.587014\pi$
$283$	50567.4	−	42431.1i	0.631390	−	0.529799i	0.901361	+	0.433069i	$0.142569\pi$
$284$		0			0
$285$	−163404.	+	89996.0i	−2.01174	+	1.10798i
$286$		0			0
$287$	15847.2	+	18885.9i	0.192392	+	0.229284i
$288$		0			0
$289$	21452.2	−	121661.i	0.256848	−	1.45666i
$290$		0			0
$291$	37971.1	−	13820.3i	0.448401	−	0.163205i
$292$		0			0
$293$	94398.8	−	54501.2i	1.09959	−	0.634849i	0.163478	−	0.986547i	$-0.447729\pi$
$293$	94398.8	−	54501.2i	1.09959	−	0.634849i	0.936114	+	0.351698i	$0.114396\pi$
$294$		0			0
$295$	−35612.2	+	42440.9i	−0.409218	+	0.487686i
$296$		0			0
$297$	−4205.82	−	2428.23i	−0.0476801	−	0.0275281i
$298$		0			0
$299$	−18113.8	+	3193.95i	−0.202613	+	0.0357262i
$300$		0			0
$301$	−17845.1	−	6495.09i	−0.196964	−	0.0716889i
$302$		0			0
$303$			12029.4i			0.131026i
$304$		0			0
$305$	−201157.			−2.16239
$306$		0			0
$307$	−33364.0	+	91666.9i	−0.353999	+	0.972603i	0.627073	+	0.778960i	$0.284253\pi$
$307$	−33364.0	+	91666.9i	−0.353999	+	0.972603i	−0.981072	+	0.193643i	$0.937970\pi$
$308$		0			0
$309$	−3744.50	−	21236.1i	−0.0392172	−	0.222412i
$310$		0			0
$311$	−28528.3	+	49412.5i	−0.294955	+	0.510876i	−0.974974	−	0.222317i	$-0.928638\pi$
$311$	−28528.3	+	49412.5i	−0.294955	+	0.510876i	0.680020	+	0.733194i	$0.261971\pi$
$312$		0			0
$313$	126121.	+	105828.i	1.28735	+	1.08022i	0.992185	+	0.124772i	$0.0398201\pi$
$313$	126121.	+	105828.i	1.28735	+	1.08022i	0.295168	+	0.955445i	$0.404624\pi$
$314$		0			0
$315$	−19815.8	−	34321.9i	−0.199705	−	0.345900i
$316$		0			0
$317$	−1581.86	−	4346.13i	−0.0157416	−	0.0432498i	0.931573	−	0.363554i	$-0.118437\pi$
$317$	−1581.86	−	4346.13i	−0.0157416	−	0.0432498i	−0.947315	+	0.320305i	$0.896215\pi$
$318$		0			0
$319$	11053.5	+	1949.03i	0.108622	+	0.0191530i
$320$		0			0
$321$	−123725.	+	103818.i	−1.20074	+	1.00754i
$322$		0			0
$323$	−31782.4	+	161165.i	−0.304636	+	1.54477i
$324$		0			0
$325$	33987.9	+	40505.2i	0.321779	+	0.383482i
$326$		0			0
$327$	−16201.5	+	91883.4i	−0.151517	+	0.859293i
$328$		0			0
$329$	12096.8	−	4402.89i	0.111758	−	0.0406767i
$330$		0			0
$331$	153760.	−	88773.4i	1.40342	−	0.810264i	0.408677	−	0.912679i	$-0.365990\pi$
$331$	153760.	−	88773.4i	1.40342	−	0.810264i	0.994742	+	0.102415i	$0.0326570\pi$
$332$		0			0
$333$	−98883.8	+	117845.i	−0.891737	+	1.06273i
$334$		0			0
$335$	−207851.	−	120003.i	−1.85210	−	1.06931i
$336$		0			0
$337$	81386.6	−	14350.7i	0.716627	−	0.126361i	0.196567	−	0.980490i	$-0.437021\pi$
$337$	81386.6	−	14350.7i	0.716627	−	0.126361i	0.520060	+	0.854130i	$0.325910\pi$
$338$		0			0
$339$	4522.17	+	1645.94i	0.0393503	+	0.0143223i
$340$		0			0
$341$		−	25226.8i		−	0.216947i
$342$		0			0
$343$	47045.6			0.399881
$344$		0			0
$345$	−50146.8	+	137777.i	−0.421313	+	1.15755i
$346$		0			0
$347$	−27172.5	−	154103.i	−0.225668	−	1.27983i	−0.861404	−	0.507921i	$-0.830414\pi$
$347$	−27172.5	−	154103.i	−0.225668	−	1.27983i	0.635735	−	0.771907i	$-0.280697\pi$
$348$		0			0
$349$	−53851.5	+	93273.5i	−0.442127	+	0.765786i	−0.997847	−	0.0655833i	$-0.979109\pi$
$349$	−53851.5	+	93273.5i	−0.442127	+	0.765786i	0.555720	+	0.831369i	$0.312443\pi$
$350$		0			0
$351$	−15790.2	−	13249.5i	−0.128166	−	0.107544i
$352$		0			0
$353$	−38337.3	−	66402.2i	−0.307661	−	0.532884i	0.670189	−	0.742190i	$-0.266213\pi$
$353$	−38337.3	−	66402.2i	−0.307661	−	0.532884i	−0.977850	+	0.209306i	$0.932880\pi$
$354$		0			0
$355$	−119813.	−	329183.i	−0.950707	−	2.61205i
$356$		0			0
$357$	−61044.7	−	10763.8i	−0.478973	−	0.0844559i
$358$		0			0
$359$	−34087.3	+	28602.6i	−0.264486	+	0.221931i	−0.765380	−	0.643578i	$-0.777449\pi$
$359$	−34087.3	+	28602.6i	−0.264486	+	0.221931i	0.500894	+	0.865509i	$0.333005\pi$
$360$		0			0
$361$	27788.3	−	127324.i	0.213230	−	0.977002i
$362$		0			0
$363$	126085.	+	150263.i	0.956868	+	1.14035i
$364$		0			0
$365$	25509.8	−	144673.i	0.191479	−	1.08593i
$366$		0			0
$367$	−105525.	+	38408.0i	−0.783473	+	0.285161i	−0.702620	−	0.711565i	$-0.747987\pi$
$367$	−105525.	+	38408.0i	−0.783473	+	0.285161i	−0.0808531	+	0.996726i	$0.525764\pi$
$368$		0			0
$369$	222680.	−	128564.i	1.63542	−	0.944209i
$370$		0			0
$371$	20368.2	−	24273.8i	0.147980	−	0.176356i
$372$		0			0
$373$	135345.	+	78141.6i	0.972804	+	0.561649i	0.900090	−	0.435704i	$-0.143501\pi$
$373$	135345.	+	78141.6i	0.972804	+	0.561649i	0.0727141	+	0.997353i	$0.476834\pi$
$374$		0			0
$375$	97025.6	−	17108.2i	0.689960	−	0.121659i
$376$		0			0
$377$	44765.9	+	16293.5i	0.314967	+	0.114639i
$378$		0			0
$379$		−	180715.i		−	1.25810i	−0.777364	−	0.629051i	$-0.783443\pi$
$379$		−	180715.i		−	1.25810i	0.777364	−	0.629051i	$-0.216557\pi$
$380$		0			0
$381$	−30314.5			−0.208834
$382$		0			0
$383$	11888.3	−	32662.7i	0.0810439	−	0.222666i	−0.892552	−	0.450944i	$-0.851087\pi$
$383$	11888.3	−	32662.7i	0.0810439	−	0.222666i	0.973596	+	0.228278i	$0.0733095\pi$
$384$		0			0
$385$	−1007.24	−	5712.35i	−0.00679535	−	0.0385383i
$386$		0			0
$387$	−99030.7	+	171526.i	−0.661223	+	1.14527i
$388$		0			0
$389$	−179821.	−	150888.i	−1.18834	−	0.997137i	−0.999887	−	0.0150555i	$-0.995208\pi$
$389$	−179821.	−	150888.i	−1.18834	−	0.997137i	−0.188455	−	0.982082i	$-0.560348\pi$
$390$		0			0
$391$	64554.4	+	111812.i	0.422253	+	0.731363i
$392$		0			0
$393$	123658.	+	339747.i	0.800638	+	2.19973i
$394$		0			0
$395$	−157308.	−	27737.6i	−1.00822	−	0.177777i
$396$		0			0
$397$	−164819.	+	138300.i	−1.04575	+	0.877487i	−0.992640	−	0.121102i	$-0.961357\pi$
$397$	−164819.	+	138300.i	−1.04575	+	0.877487i	−0.0531080	+	0.998589i	$0.516913\pi$
$398$		0			0
$399$	48247.1	+	9514.56i	0.303058	+	0.0597644i
$400$		0			0
$401$	118155.	+	140811.i	0.734789	+	0.875688i	0.995978	−	0.0895999i	$-0.0285588\pi$
$401$	118155.	+	140811.i	0.734789	+	0.875688i	−0.261188	+	0.965288i	$0.584114\pi$
$402$		0			0
$403$	18592.9	−	105445.i	0.114482	−	0.649258i
$404$		0			0
$405$	147083.	−	53533.7i	0.896709	−	0.326375i
$406$		0			0
$407$	−19498.9	+	11257.7i	−0.117712	+	0.0679612i
$408$		0			0
$409$	161880.	−	192921.i	0.967714	−	1.15328i	−0.0204371	−	0.999791i	$-0.506506\pi$
$409$	161880.	−	192921.i	0.967714	−	1.15328i	0.988151	−	0.153485i	$-0.0490498\pi$
$410$		0			0
$411$	41573.4	+	24002.4i	0.246111	+	0.142092i
$412$		0			0
$413$	14383.0	−	2536.11i	0.0843235	−	0.0148685i
$414$		0			0
$415$	443689.	+	161490.i	2.57622	+	0.937667i
$416$		0			0
$417$			191617.i			1.10195i
$418$		0			0
$419$	155593.			0.886261			0.443130	−	0.896457i	$-0.353868\pi$
$419$	155593.			0.886261			0.443130	+	0.896457i	$0.353868\pi$
$420$		0			0
$421$	−113197.	+	311006.i	−0.638661	+	1.75471i	0.0172286	+	0.999852i	$0.494516\pi$
$421$	−113197.	+	311006.i	−0.638661	+	1.75471i	−0.655890	+	0.754856i	$0.727707\pi$
$422$		0			0
$423$	−23314.4	−	132222.i	−0.130299	−	0.738965i
$424$		0			0
$425$	185577.	−	321429.i	1.02742	−	1.77954i
$426$		0			0
$427$	40621.4	+	34085.4i	0.222792	+	0.186944i
$428$		0			0
$429$	−6739.97	−	11674.0i	−0.0366221	−	0.0634314i
$430$		0			0
$431$	11427.4	+	31396.5i	0.0615166	+	0.169016i	0.966643	−	0.256127i	$-0.0824464\pi$
$431$	11427.4	+	31396.5i	0.0615166	+	0.169016i	−0.905127	+	0.425142i	$0.860224\pi$
$432$		0			0
$433$	−87468.3	−	15423.0i	−0.466525	−	0.0822609i	−0.0645556	−	0.997914i	$-0.520563\pi$
$433$	−87468.3	−	15423.0i	−0.466525	−	0.0822609i	−0.401969	+	0.915653i	$0.631674\pi$
$434$		0			0
$435$	290903.	−	244097.i	1.53734	−	1.28998i
$436$		0			0
$437$	−49413.9	−	89719.7i	−0.258754	−	0.469813i
$438$		0			0
$439$	−11796.9	−	14059.0i	−0.0612124	−	0.0729501i	0.734569	−	0.678534i	$-0.237384\pi$
$439$	−11796.9	−	14059.0i	−0.0612124	−	0.0729501i	−0.795782	+	0.605583i	$0.792940\pi$
$440$		0			0
$441$	41694.5	−	236461.i	0.214389	−	1.21586i
$442$		0			0
$443$	−5871.78	+	2137.15i	−0.0299201	+	0.0108900i	−0.356937	−	0.934129i	$-0.616179\pi$
$443$	−5871.78	+	2137.15i	−0.0299201	+	0.0108900i	0.327017	+	0.945019i	$0.393957\pi$
$444$		0			0
$445$	−397338.	+	229403.i	−2.00650	+	1.15846i
$446$		0			0
$447$	−316184.	+	376813.i	−1.58243	+	1.88587i
$448$		0			0
$449$	−86468.3	−	49922.5i	−0.428908	−	0.247630i	0.269973	−	0.962868i	$-0.412985\pi$
$449$	−86468.3	−	49922.5i	−0.428908	−	0.247630i	−0.698881	+	0.715238i	$0.746319\pi$
$450$		0			0
$451$	37061.7	−	6534.97i	0.182210	−	0.0321285i
$452$		0			0
$453$	286641.	+	104329.i	1.39682	+	0.508402i
$454$		0			0
$455$		−	24619.4i		−	0.118920i
$456$		0			0
$457$	304377.			1.45740			0.728700	−	0.684833i	$-0.240125\pi$
$457$	304377.			1.45740			0.728700	+	0.684833i	$0.240125\pi$
$458$		0			0
$459$	−49486.0	+	135962.i	−0.234886	+	0.645344i
$460$		0			0
$461$	8793.03	+	49867.7i	0.0413749	+	0.234648i	0.998482	−	0.0550872i	$-0.0175437\pi$
$461$	8793.03	+	49867.7i	0.0413749	+	0.234648i	−0.957107	+	0.289736i	$0.906433\pi$
$462$		0			0
$463$	−38991.0	+	67534.3i	−0.181887	+	0.315038i	−0.942523	−	0.334141i	$-0.891554\pi$
$463$	−38991.0	+	67534.3i	−0.181887	+	0.315038i	0.760636	+	0.649179i	$0.224887\pi$
$464$		0			0
$465$	−653827.	−	548626.i	−3.02383	−	2.53729i
$466$		0			0
$467$	−187480.	−	324725.i	−0.859649	−	1.48896i	−0.872264	−	0.489035i	$-0.837349\pi$
$467$	−187480.	−	324725.i	−0.859649	−	1.48896i	0.0126152	−	0.999920i	$-0.495984\pi$
$468$		0			0
$469$	21639.2	+	59453.1i	0.0983773	+	0.270289i
$470$		0			0
$471$	644044.	+	113562.i	2.90318	+	0.511908i
$472$		0			0
$473$	−22206.3	+	18633.3i	−0.0992554	+	0.0832852i
$474$		0			0
$475$	−152340.	+	251981.i	−0.675191	+	1.11681i
$476$		0			0
$477$	−212431.	−	253166.i	−0.933646	−	1.11268i
$478$		0			0
$479$	−45381.3	+	257370.i	−0.197791	+	1.12173i	0.710597	+	0.703599i	$0.248425\pi$
$479$	−45381.3	+	257370.i	−0.197791	+	1.12173i	−0.908388	+	0.418128i	$0.862686\pi$
$480$		0			0
$481$	−89800.7	+	32684.8i	−0.388141	+	0.141272i
$482$		0			0
$483$	33472.5	−	19325.4i	0.143481	−	0.0828387i
$484$		0			0
$485$	72412.3	−	86297.6i	0.307843	−	0.366873i
$486$		0			0
$487$	−276196.	−	159462.i	−1.16455	−	0.672355i	−0.212162	−	0.977235i	$-0.568050\pi$
$487$	−276196.	−	159462.i	−1.16455	−	0.672355i	−0.952391	+	0.304880i	$0.901384\pi$
$488$		0			0
$489$	−156940.	+	27672.8i	−0.656322	+	0.115727i
$490$		0			0
$491$	−370318.	−	134785.i	−1.53607	−	0.559085i	−0.570973	−	0.820969i	$-0.693434\pi$
$491$	−370318.	−	134785.i	−1.53607	−	0.559085i	−0.965099	+	0.261884i	$0.915656\pi$
$492$		0			0
$493$		−	334395.i		−	1.37583i
$494$		0			0
$495$	−60496.5			−0.246899
$496$		0			0
$497$	−31584.2	+	86776.9i	−0.127867	+	0.351310i
$498$		0			0
$499$	−13867.0	−	78643.7i	−0.0556906	−	0.315837i	0.944219	−	0.329320i	$-0.106819\pi$
$499$	−13867.0	−	78643.7i	−0.0556906	−	0.315837i	−0.999909	+	0.0134826i	$0.995708\pi$
$500$		0			0
$501$	−81601.7	+	141338.i	−0.325105	+	0.563098i
$502$		0			0
$503$	86261.9	+	72382.4i	0.340944	+	0.286086i	0.797142	−	0.603793i	$-0.206344\pi$
$503$	86261.9	+	72382.4i	0.340944	+	0.286086i	−0.456197	+	0.889879i	$0.650789\pi$
$504$		0			0
$505$	16768.3	+	29043.6i	0.0657518	+	0.113885i
$506$		0			0
$507$	113424.	+	311631.i	0.441255	+	1.21234i
$508$		0			0
$509$	161578.	+	28490.6i	0.623658	+	0.109968i	0.476542	−	0.879151i	$-0.341890\pi$
$509$	161578.	+	28490.6i	0.623658	+	0.109968i	0.147116	+	0.989119i	$0.453001\pi$
$510$		0			0
$511$	−29665.9	+	24892.6i	−0.113610	+	0.0953299i
$512$		0			0
$513$	41427.1	−	107050.i	0.157416	−	0.406773i
$514$		0			0
$515$	−38642.8	−	46052.7i	−0.145698	−	0.173636i
$516$		0			0
$517$	3412.29	−	19352.1i	0.0127663	−	0.0724012i
$518$		0			0
$519$	253351.	−	92212.3i	0.940564	−	0.342337i
$520$		0			0
$521$	−165547.	+	95578.7i	−0.609883	+	0.352116i	−0.772919	−	0.634504i	$-0.781204\pi$
$521$	−165547.	+	95578.7i	−0.609883	+	0.352116i	0.163037	+	0.986620i	$0.447871\pi$
$522$		0			0
$523$	53445.8	−	63694.2i	0.195393	−	0.232861i	−0.659448	−	0.751750i	$-0.729210\pi$
$523$	53445.8	−	63694.2i	0.195393	−	0.232861i	0.854841	+	0.518889i	$0.173654\pi$
$524$		0			0
$525$	−96224.8	−	55555.4i	−0.349115	−	0.201562i
$526$		0			0
$527$	−740159.	+	130510.i	−2.66504	+	0.469919i
$528$		0			0
$529$	187316.	+	68177.3i	0.669364	+	0.243629i
$530$		0			0
$531$		−	152323.i		−	0.540225i
$532$		0			0
$533$	159730.			0.562254
$534$		0			0
$535$	−154004.	+	423124.i	−0.538054	+	1.47829i
$536$		0			0
$537$	34549.4	+	195939.i	0.119810	+	0.679474i
$538$		0			0
$539$	17571.2	−	30434.2i	0.0604817	−	0.104757i
$540$		0			0
$541$	−47919.3	−	40209.1i	−0.163725	−	0.137382i	0.557244	−	0.830349i	$-0.311859\pi$
$541$	−47919.3	−	40209.1i	−0.163725	−	0.137382i	−0.720969	+	0.692967i	$0.756303\pi$
$542$		0			0
$543$	−204773.	−	354677.i	−0.694500	−	1.20291i
$544$		0			0
$545$	88964.2	+	244427.i	0.299518	+	0.822918i
$546$		0			0
$547$	36797.9	+	6488.47i	0.122984	+	0.0216854i	0.234801	−	0.972043i	$-0.424556\pi$
$547$	36797.9	+	6488.47i	0.122984	+	0.0216854i	−0.111817	+	0.993729i	$0.535667\pi$
$548$		0			0
$549$	423664.	−	355496.i	1.40565	−	1.17948i
$550$		0			0
$551$	−5351.39	+	265235.i	−0.0176264	+	0.873630i
$552$		0			0
$553$	27066.6	+	32256.7i	0.0885081	+	0.105480i
$554$		0			0
$555$	−132281.	+	750202.i	−0.429448	+	2.43552i
$556$		0			0
$557$	449858.	−	163735.i	1.44999	−	0.527753i	0.507402	−	0.861709i	$-0.330606\pi$
$557$	449858.	−	163735.i	1.44999	−	0.527753i	0.942589	+	0.333956i	$0.108384\pi$
$558$		0			0
$559$	−106553.	+	61518.6i	−0.340991	+	0.196871i
$560$		0			0
$561$	−60820.9	+	72483.6i	−0.193254	+	0.230311i
$562$		0			0
$563$	158180.	+	91325.4i	0.499040	+	0.288121i	0.728317	−	0.685240i	$-0.240303\pi$
$563$	158180.	+	91325.4i	0.499040	+	0.288121i	−0.229277	+	0.973361i	$0.573636\pi$
$564$		0			0
$565$	13212.7	−	2329.75i	0.0413899	−	0.00729815i
$566$		0			0
$567$	−38772.9	−	14112.2i	−0.120604	−	0.0438963i
$568$		0			0
$569$		−	307756.i		−	0.950565i	−0.879833	−	0.475283i	$-0.842346\pi$
$569$		−	307756.i		−	0.950565i	0.879833	−	0.475283i	$-0.157654\pi$
$570$		0			0
$571$	474577.			1.45557			0.727787	−	0.685803i	$-0.240549\pi$
$571$	474577.			1.45557			0.727787	+	0.685803i	$0.240549\pi$
$572$		0			0
$573$	123052.	−	338083.i	0.374783	−	1.02971i
$574$		0			0
$575$	40187.1	+	227912.i	0.121549	+	0.689338i
$576$		0			0
$577$	−15494.2	+	26836.7i	−0.0465390	+	0.0806078i	−0.888357	−	0.459154i	$-0.848152\pi$
$577$	−15494.2	+	26836.7i	−0.0465390	+	0.0806078i	0.841818	+	0.539762i	$0.181486\pi$
$578$		0			0
$579$	−335666.	−	281657.i	−1.00127	−	0.840164i
$580$		0			0
$581$	−62234.2	−	107793.i	−0.184364	−	0.319329i
$582$		0			0
$583$	−16543.4	−	45452.7i	−0.0486730	−	0.133728i
$584$		0			0
$585$	−252869.	−	44587.6i	−0.738896	−	0.130287i
$586$		0			0
$587$	−355861.	+	298603.i	−1.03277	+	0.866598i	−0.991178	−	0.132536i	$-0.957688\pi$
$587$	−355861.	+	298603.i	−1.03277	+	0.866598i	−0.0415934	+	0.999135i	$0.513243\pi$
$588$		0			0
$589$	589168.	−	91673.0i	1.69828	−	0.264247i
$590$		0			0
$591$	−392870.	−	468205.i	−1.12480	−	1.34048i
$592$		0			0
$593$	−483.474	+	2741.92i	−0.00137488	+	0.00779731i	−0.985487	−	0.169748i	$-0.945705\pi$
$593$	−483.474	+	2741.92i	−0.00137488	+	0.00779731i	0.984113	+	0.177545i	$0.0568157\pi$
$594$		0			0
$595$	−162390.	+	59105.3i	−0.458697	+	0.166952i
$596$		0			0
$597$	75691.0	−	43700.2i	0.212371	−	0.122613i
$598$		0			0
$599$	−18966.7	+	22603.6i	−0.0528613	+	0.0629976i	−0.791827	−	0.610745i	$-0.790870\pi$
$599$	−18966.7	+	22603.6i	−0.0528613	+	0.0629976i	0.738966	+	0.673743i	$0.235314\pi$
$600$		0			0
$601$	−20074.7	−	11590.2i	−0.0555777	−	0.0320878i	0.471954	−	0.881623i	$-0.343549\pi$
$601$	−20074.7	−	11590.2i	−0.0555777	−	0.0320878i	−0.527531	+	0.849536i	$0.676882\pi$
$602$		0			0
$603$	649841.	−	114585.i	1.78720	−	0.315131i
$604$		0			0
$605$	513880.	+	187037.i	1.40395	+	0.510995i
$606$		0			0
$607$		−	199091.i		−	0.540350i	−0.962811	−	0.270175i	$-0.912918\pi$
$607$		−	199091.i		−	0.540350i	0.962811	−	0.270175i	$-0.0870815\pi$
$608$		0			0
$609$	−100106.			−0.269915
$610$		0			0
$611$	28526.0	−	78374.6i	0.0764115	−	0.209939i
$612$		0			0
$613$	−73960.7	−	419452.i	−0.196825	−	1.11625i	−0.909796	−	0.415056i	$-0.863762\pi$
$613$	−73960.7	−	419452.i	−0.196825	−	1.11625i	0.712971	−	0.701194i	$-0.247349\pi$
$614$		0			0
$615$	636634.	−	1.10268e6i	1.68322	−	2.91541i
$616$		0			0
$617$	−5407.03	−	4537.04i	−0.0142033	−	0.0119180i	0.635658	−	0.771971i	$-0.280729\pi$
$617$	−5407.03	−	4537.04i	−0.0142033	−	0.0119180i	−0.649862	+	0.760053i	$0.725173\pi$
$618$		0			0
$619$	267202.	+	462808.i	0.697362	+	1.20787i	0.969378	+	0.245574i	$0.0789765\pi$
$619$	267202.	+	462808.i	0.697362	+	1.20787i	−0.272015	+	0.962293i	$0.587690\pi$
$620$		0			0
$621$	−30856.3	−	84777.0i	−0.0800130	−	0.219834i
$622$		0			0
$623$	119110.	+	21002.3i	0.306882	+	0.0541115i
$624$		0			0
$625$	−180108.	+	151129.i	−0.461077	+	0.386889i
$626$		0			0
$627$	49401.9	−	56519.2i	0.125663	−	0.143767i
$628$		0			0
$629$	431180.	+	513861.i	1.08983	+	1.29881i
$630$		0			0
$631$	130960.	−	742708.i	0.328911	−	1.86535i	−0.151720	−	0.988424i	$-0.548481\pi$
$631$	130960.	−	742708.i	0.328911	−	1.86535i	0.480631	−	0.876923i	$-0.340408\pi$
$632$		0			0
$633$	−648068.	+	235878.i	−1.61738	+	0.588680i
$634$		0			0
$635$	−73191.2	+	42257.0i	−0.181515	+	0.104797i
$636$		0			0
$637$	95876.6	−	114261.i	0.236284	−	0.281592i
$638$		0			0
$639$	834095.	+	481565.i	2.04274	+	1.17938i
$640$		0			0
$641$	−45355.0	+	7997.30i	−0.110385	+	0.0194638i	−0.228568	−	0.973528i	$-0.573404\pi$
$641$	−45355.0	+	7997.30i	−0.110385	+	0.0194638i	0.118183	+	0.992992i	$0.462293\pi$
$642$		0			0
$643$	−610909.	−	222353.i	−1.47759	−	0.537800i	−0.527442	−	0.849591i	$-0.676849\pi$
$643$	−610909.	−	222353.i	−1.47759	−	0.537800i	−0.950151	+	0.311791i	$0.899071\pi$
$644$		0			0
$645$			980774.i			2.35749i
$646$		0			0
$647$	−156389.			−0.373592			−0.186796	−	0.982399i	$-0.559810\pi$
$647$	−156389.			−0.373592			−0.186796	+	0.982399i	$0.559810\pi$
$648$		0			0
$649$	7624.97	−	20949.4i	0.0181029	−	0.0497374i
$650$		0			0
$651$	39070.2	+	221578.i	0.0921900	+	0.522835i
$652$		0			0
$653$	−161708.	+	280086.i	−0.379232	+	0.656849i	−0.990951	−	0.134226i	$-0.957145\pi$
$653$	−161708.	+	280086.i	−0.379232	+	0.656849i	0.611719	+	0.791075i	$0.290478\pi$
$654$		0			0
$655$	772150.	+	647911.i	1.79978	+	1.51019i
$656$		0			0
$657$	201948.	+	349785.i	0.467853	+	0.810345i
$658$		0			0
$659$	23712.1	+	65148.5i	0.0546009	+	0.150015i	0.963995	−	0.265922i	$-0.0856762\pi$
$659$	23712.1	+	65148.5i	0.0546009	+	0.150015i	−0.909394	+	0.415936i	$0.863454\pi$
$660$		0			0
$661$	−730123.	−	128740.i	−1.67106	−	0.294653i	−0.743616	−	0.668607i	$-0.766891\pi$
$661$	−730123.	−	128740.i	−1.67106	−	0.294653i	−0.927447	+	0.373954i	$0.878002\pi$
$662$		0			0
$663$	−307647.	+	258147.i	−0.699884	+	0.587273i
$664$		0			0
$665$	129751.	−	44282.3i	0.293404	−	0.100135i
$666$		0			0
$667$	134026.	+	159726.i	0.301257	+	0.359024i
$668$		0			0
$669$	−5790.80	+	32841.3i	−0.0129386	+	0.0733783i
$670$		0			0
$671$	76063.4	−	27684.8i	0.168939	−	0.0614889i
$672$		0			0
$673$	−555858.	+	320925.i	−1.22725	+	0.708554i	−0.966454	−	0.256839i	$-0.917319\pi$
$673$	−555858.	+	320925.i	−1.22725	+	0.708554i	−0.260798	+	0.965393i	$0.583986\pi$
$674$		0			0
$675$	−166709.	+	198676.i	−0.365890	+	0.436051i
$676$		0			0
$677$	276698.	+	159752.i	0.603711	+	0.348552i	0.770500	−	0.637440i	$-0.220007\pi$
$677$	276698.	+	159752.i	0.603711	+	0.348552i	−0.166789	+	0.985993i	$0.553340\pi$
$678$		0			0
$679$	−29245.8	+	5156.82i	−0.0634342	+	0.0111852i
$680$		0			0
$681$	−459523.	−	167253.i	−0.990862	−	0.360644i
$682$		0			0
$683$		−	368384.i		−	0.789694i	−0.918747	−	0.394847i	$-0.870798\pi$
$683$		−	368384.i		−	0.789694i	0.918747	−	0.394847i	$-0.129202\pi$
$684$		0			0
$685$	133833.			0.285221
$686$		0			0
$687$	153900.	−	422838.i	0.326081	−	0.895902i
$688$		0			0
$689$	−35649.9	−	202180.i	−0.0750964	−	0.425893i
$690$		0			0
$691$	165830.	−	287226.i	0.347302	−	0.601544i	−0.638467	−	0.769649i	$-0.720431\pi$
$691$	165830.	−	287226.i	0.347302	−	0.601544i	0.985769	+	0.168105i	$0.0537647\pi$
$692$		0			0
$693$	12216.6	+	10250.9i	0.0254381	+	0.0213451i
$694$		0			0
$695$	267105.	+	462639.i	0.552983	+	0.957795i
$696$		0			0
$697$	−383474.	−	1.05359e6i	−0.789352	−	2.16873i
$698$		0			0
$699$	259695.	+	45791.3i	0.531508	+	0.0937191i
$700$		0			0
$701$	24515.3	−	20570.8i	0.0498885	−	0.0418615i	−0.617502	−	0.786569i	$-0.711855\pi$
$701$	24515.3	−	20570.8i	0.0498885	−	0.0418615i	0.667391	+	0.744707i	$0.267411\pi$
$702$		0			0
$703$	−333780.	−	414484.i	−0.675382	−	0.838682i
$704$		0			0
$705$	−427356.	−	509303.i	−0.859827	−	1.02470i
$706$		0			0
$707$	1535.17	−	8706.39i	0.00307127	−	0.0174180i
$708$		0			0
$709$	−867795.	+	315852.i	−1.72633	+	0.628334i	−0.998359	−	0.0572695i	$-0.981761\pi$
$709$	−867795.	+	315852.i	−1.72633	+	0.628334i	−0.727975	+	0.685604i	$0.759538\pi$
$710$		0			0
$711$	380332.	−	219585.i	0.752357	−	0.434373i
$712$		0			0
$713$	301233.	−	358996.i	0.592548	−	0.706171i
$714$		0			0
$715$	−32545.9	−	18790.4i	−0.0636626	−	0.0367556i
$716$		0			0
$717$	−770372.	+	135837.i	−1.49852	+	0.264229i
$718$		0			0
$719$	−656850.	−	239074.i	−1.27060	−	0.462460i	−0.383287	−	0.923629i	$-0.625208\pi$
$719$	−656850.	−	239074.i	−1.27060	−	0.462460i	−0.887312	+	0.461169i	$0.847430\pi$
$720$		0			0
$721$			15847.8i			0.0304858i
$722$		0			0
$723$	−758090.			−1.45025
$724$		0			0
$725$	205008.	−	563255.i	0.390027	−	1.07159i
$726$		0			0
$727$	−97044.7	−	550368.i	−0.183613	−	1.04132i	−0.927725	−	0.373265i	$-0.878238\pi$
$727$	−97044.7	−	550368.i	−0.183613	−	1.04132i	0.744112	−	0.668055i	$-0.232873\pi$
$728$		0			0
$729$	−390492.	+	676353.i	−0.734780	+	1.27268i
$730$		0			0
$731$	661588.	+	555138.i	1.23809	+	1.03888i
$732$		0			0
$733$	93102.8	+	161259.i	0.173283	+	0.300134i	0.939566	−	0.342369i	$-0.111229\pi$
$733$	93102.8	+	161259.i	0.173283	+	0.300134i	−0.766283	+	0.642503i	$0.777896\pi$
$734$		0			0
$735$	−406658.	−	1.11728e6i	−0.752757	−	2.06818i
$736$		0			0
$737$	95110.8	+	16770.6i	0.175103	+	0.0308755i
$738$		0			0
$739$	620269.	−	520467.i	1.13577	−	0.953025i	0.136479	−	0.990643i	$-0.456421\pi$
$739$	620269.	−	520467.i	1.13577	−	0.953025i	0.999292	+	0.0376175i	$0.0119769\pi$
$740$		0			0
$741$	248151.	−	199833.i	0.451938	−	0.363942i
$742$		0			0
$743$	−315238.	−	375686.i	−0.571032	−	0.680530i	0.400810	−	0.916161i	$-0.368729\pi$
$743$	−315238.	−	375686.i	−0.571032	−	0.680530i	−0.971842	+	0.235631i	$0.924284\pi$
$744$		0			0
$745$	−238133.	+	1.35052e6i	−0.429050	+	2.43326i
$746$		0			0
$747$	−1.21987e6	+	443995.i	−2.18610	+	0.795677i
$748$		0			0
$749$	102797.	−	59349.6i	0.183238	−	0.105792i
$750$		0			0
$751$	−374067.	+	445796.i	−0.663239	+	0.790418i	−0.987847	−	0.155431i	$-0.950323\pi$
$751$	−374067.	+	445796.i	−0.663239	+	0.790418i	0.324608	+	0.945849i	$0.394768\pi$
$752$		0			0
$753$	−179867.	−	103846.i	−0.317220	−	0.183147i
$754$		0			0
$755$	837494.	−	147673.i	1.46922	−	0.259064i
$756$		0			0
$757$	186518.	+	67886.8i	0.325483	+	0.118466i	0.499593	−	0.866260i	$-0.333483\pi$
$757$	186518.	+	67886.8i	0.325483	+	0.118466i	−0.174111	+	0.984726i	$0.555705\pi$
$758$		0			0
$759$		−	58999.3i		−	0.102415i
$760$		0			0
$761$	−325873.			−0.562703			−0.281352	−	0.959605i	$-0.590783\pi$
$761$	−325873.			−0.562703			−0.281352	+	0.959605i	$0.590783\pi$
$762$		0			0
$763$	23452.1	−	64434.1i	0.0402840	−	0.110679i
$764$		0			0
$765$	312976.	+	1.77498e6i	0.534797	+	3.03298i
$766$		0			0
$767$	47311.9	−	81946.6i	0.0804229	−	0.139296i
$768$		0			0
$769$	512619.	+	430138.i	0.866845	+	0.727370i	0.963431	−	0.267955i	$-0.0863478\pi$
$769$	512619.	+	430138.i	0.866845	+	0.727370i	−0.0965860	+	0.995325i	$0.530792\pi$
$770$		0			0
$771$	−68004.9	−	117788.i	−0.114401	−	0.198149i
$772$		0			0
$773$	156644.	+	430375.i	0.262152	+	0.720257i	0.999022	+	0.0442223i	$0.0140810\pi$
$773$	156644.	+	430375.i	0.262152	+	0.720257i	−0.736870	+	0.676035i	$0.763697\pi$
$774$		0			0
$775$	−1.32674e6	−	233940.i	−2.20893	−	0.389494i
$776$		0			0
$777$	153832.	−	129080.i	0.254803	−	0.213805i
$778$		0			0
$779$	287303.	+	841821.i	0.473441	+	1.38722i
$780$		0			0
$781$	90609.7	+	107984.i	0.148550	+	0.177035i
$782$		0			0
$783$	−40575.7	+	230116.i	−0.0661824	+	0.375339i
$784$		0			0
$785$	1.71328e6	−	623582.i	2.78028	−	1.01194i
$786$		0			0
$787$	405172.	−	233926.i	0.654169	−	0.377685i	−0.135883	−	0.990725i	$-0.543387\pi$
$787$	405172.	−	233926.i	0.654169	−	0.377685i	0.790052	+	0.613040i	$0.210054\pi$
$788$		0			0
$789$	314955.	−	375349.i	0.505936	−	0.602950i
$790$		0			0
$791$	−3062.93	−	1768.38i	−0.00489535	−	0.00282633i
$792$		0			0
$793$	338341.	−	59658.7i	0.538033	−	0.0948697i
$794$		0			0
$795$	−1.53782e6	−	559721.i	−2.43317	−	0.885600i
$796$		0			0
$797$			649953.i			1.02321i	0.859221	+	0.511605i	$0.170949\pi$
$797$			649953.i			1.02321i	−0.859221	+	0.511605i	$0.829051\pi$
$798$		0			0
$799$	−585446.			−0.917051
$800$		0			0
$801$	431434.	−	1.18536e6i	0.672433	−	1.84750i
$802$		0			0
$803$	10265.1	+	58216.2i	0.0159196	+	0.0902845i
$804$		0			0
$805$	53877.3	−	93318.2i	0.0831408	−	0.144004i
$806$		0			0
$807$	1.31335e6	+	1.10203e6i	2.01666	+	1.69218i
$808$		0			0
$809$	263790.	+	456898.i	0.403052	+	0.698107i	0.994093	−	0.108535i	$-0.0346160\pi$
$809$	263790.	+	456898.i	0.403052	+	0.698107i	−0.591041	+	0.806642i	$0.701283\pi$
$810$		0			0
$811$	25742.5	+	70727.0i	0.0391390	+	0.107533i	0.957723	−	0.287693i	$-0.0928883\pi$
$811$	25742.5	+	70727.0i	0.0391390	+	0.107533i	−0.918584	+	0.395227i	$0.870666\pi$
$812$		0			0
$813$	985255.	+	173727.i	1.49062	+	0.262837i
$814$		0			0
$815$	−340342.	+	285581.i	−0.512389	+	0.429945i
$816$		0			0
$817$	−515874.	−	450912.i	−0.772858	−	0.675535i
$818$		0			0
$819$	43508.8	+	51851.8i	0.0648649	+	0.0773030i
$820$		0			0
$821$	−14296.0	+	81076.9i	−0.0212094	+	0.120285i	−0.993574	−	0.113182i	$-0.963896\pi$
$821$	−14296.0	+	81076.9i	−0.0212094	+	0.120285i	0.972365	+	0.233466i	$0.0750069\pi$
$822$		0			0
$823$	928191.	−	337834.i	1.37037	−	0.498774i	0.451125	−	0.892461i	$-0.351023\pi$
$823$	928191.	−	337834.i	1.37037	−	0.498774i	0.919244	+	0.393687i	$0.128801\pi$
$824$		0			0
$825$	−146885.	+	84803.9i	−0.215808	+	0.124597i
$826$		0			0
$827$	526428.	−	627373.i	0.769712	−	0.917306i	−0.228709	−	0.973495i	$-0.573450\pi$
$827$	526428.	−	627373.i	0.769712	−	0.917306i	0.998420	+	0.0561884i	$0.0178948\pi$
$828$		0			0
$829$	−584819.	−	337646.i	−0.850967	−	0.491306i	0.0100101	−	0.999950i	$-0.496814\pi$
$829$	−584819.	−	337646.i	−0.850967	−	0.491306i	−0.860977	+	0.508644i	$0.830147\pi$
$830$		0			0
$831$	87644.3	−	15454.1i	0.126918	−	0.0223790i
$832$		0			0
$833$	−983849.	−	358092.i	−1.41788	−	0.516065i
$834$		0			0
$835$			454996.i			0.652581i
$836$		0			0
$837$	525182.			0.749651
$838$		0			0
$839$	290197.	−	797310.i	0.412258	−	1.13267i	−0.543729	−	0.839261i	$-0.682988\pi$
$839$	290197.	−	797310.i	0.412258	−	1.13267i	0.955987	−	0.293409i	$-0.0947897\pi$
$840$		0			0
$841$	29041.5	+	164703.i	0.0410608	+	0.232867i
$842$		0			0
$843$	−165092.	+	285948.i	−0.232312	+	0.402375i
$844$		0			0
$845$	708249.	+	594292.i	0.991911	+	0.832312i
$846$		0			0
$847$	−72079.6	−	124845.i	−0.100472	−	0.174023i
$848$		0			0
$849$	307377.	+	844510.i	0.426437	+	1.17163i
$850$		0			0
$851$	−411912.	−	72631.2i	−0.568781	−	0.100291i
$852$		0			0
$853$	674237.	−	565752.i	0.926647	−	0.777549i	−0.0485653	−	0.998820i	$-0.515465\pi$
$853$	674237.	−	565752.i	0.926647	−	0.777549i	0.975212	+	0.221271i	$0.0710205\pi$
$854$		0			0
$855$	−219841.	−	1.41288e6i	−0.300730	−	1.93274i
$856$		0			0
$857$	−839806.	−	1.00084e6i	−1.14345	−	1.36271i	−0.921838	−	0.387577i	$-0.873312\pi$
$857$	−839806.	−	1.00084e6i	−1.14345	−	1.36271i	−0.221613	−	0.975135i	$-0.571132\pi$
$858$		0			0
$859$	207717.	−	1.17802e6i	0.281505	−	1.59649i	−0.436006	−	0.899944i	$-0.643607\pi$
$859$	207717.	−	1.17802e6i	0.281505	−	1.59649i	0.717510	−	0.696548i	$-0.245282\pi$
$860$		0			0
$861$	−315408.	+	114799.i	−0.425467	+	0.154857i
$862$		0			0
$863$	−140092.	+	80882.2i	−0.188101	+	0.108600i	−0.591093	−	0.806603i	$-0.701304\pi$
$863$	−140092.	+	80882.2i	−0.188101	+	0.108600i	0.402992	+	0.915203i	$0.367970\pi$
$864$		0			0
$865$	483151.	−	575797.i	0.645729	−	0.769550i
$866$		0			0
$867$	1.45658e6	+	840957.i	1.93774	+	1.11876i
$868$		0			0
$869$	63300.4	−	11161.6i	0.0838237	−	0.0147804i
$870$		0			0
$871$	385192.	+	140199.i	0.507740	+	0.184802i
$872$		0			0
$873$			309726.i			0.406396i
$874$		0			0
$875$	−72406.8			−0.0945721
$876$		0			0
$877$	195670.	−	537599.i	0.254405	−	0.698972i	−0.745083	−	0.666972i	$-0.767590\pi$
$877$	195670.	−	537599.i	0.254405	−	0.698972i	0.999488	−	0.0320000i	$-0.0101876\pi$
$878$		0			0
$879$	257696.	+	1.46147e6i	0.333527	+	1.89152i
$880$		0			0
$881$	−339561.	+	588138.i	−0.437488	+	0.757752i	−0.997495	−	0.0707360i	$-0.977465\pi$
$881$	−339561.	+	588138.i	−0.437488	+	0.757752i	0.560007	+	0.828488i	$0.310799\pi$
$882$		0			0
$883$	−267811.	−	224720.i	−0.343484	−	0.288217i	0.454683	−	0.890653i	$-0.349752\pi$
$883$	−267811.	−	224720.i	−0.343484	−	0.288217i	−0.798167	+	0.602436i	$0.794197\pi$
$884$		0			0
$885$	−377140.	−	653226.i	−0.481522	−	0.834021i
$886$		0			0
$887$	404343.	+	1.11092e6i	0.513929	+	1.41201i	0.877110	+	0.480289i	$0.159468\pi$
$887$	404343.	+	1.11092e6i	0.513929	+	1.41201i	−0.363182	+	0.931718i	$0.618310\pi$
$888$		0			0
$889$	21940.5	+	3868.70i	0.0277615	+	0.00489510i
$890$		0			0
$891$	−48248.7	+	40485.4i	−0.0607757	+	0.0509969i
$892$		0			0
$893$	464364.	+	9369.02i	0.582312	+	0.0117487i
$894$		0			0
$895$	356546.	+	424915.i	0.445112	+	0.530464i
$896$		0			0
$897$	43484.1	−	246611.i	0.0540438	−	0.306498i
$898$		0			0
$899$	−1.14058e6	+	415136.i	−1.41125	+	0.513654i
$900$		0			0
$901$	−1.24800e6	+	720535.i	−1.53733	+	0.887576i
$902$		0			0
$903$	166189.	−	198057.i	0.203811	−	0.242892i
$904$		0			0
$905$	−988805.	−	570887.i	−1.20730	−	0.697032i
$906$		0			0
$907$	−671641.	+	118428.i	−0.816436	+	0.143960i	−0.566245	−	0.824237i	$-0.691605\pi$
$907$	−671641.	+	118428.i	−0.816436	+	0.143960i	−0.250191	+	0.968196i	$0.580493\pi$
$908$		0			0
$909$	−86644.2	−	31535.9i	−0.104860	−	0.0381661i
$910$		0			0
$911$			1.56668e6i			1.88774i	0.330312	+	0.943872i	$0.392846\pi$
$911$			1.56668e6i			1.88774i	−0.330312	+	0.943872i	$0.607154\pi$
$912$		0			0
$913$	−189998.			−0.227933
$914$		0			0
$915$	936673.	−	2.57349e6i	1.11878	−	3.07383i
$916$		0			0
$917$	−46140.7	−	261677.i	−0.0548714	−	0.311191i
$918$		0			0
$919$	174963.	−	303045.i	0.207165	−	0.358820i	−0.743656	−	0.668563i	$-0.766910\pi$
$919$	174963.	−	303045.i	0.207165	−	0.358820i	0.950820	+	0.309743i	$0.100243\pi$
$920$		0			0
$921$	−1.01738e6	−	853683.i	−1.19940	−	1.00642i
$922$		0			0
$923$	299151.	+	518145.i	0.351146	+	0.608203i
$924$		0			0
$925$	411247.	+	1.12989e6i	0.480640	+	1.32055i
$926$		0			0
$927$	162774.	+	28701.5i	0.189420	+	0.0333999i
$928$		0			0
$929$	227850.	−	191189.i	0.264009	−	0.221530i	−0.501168	−	0.865350i	$-0.667096\pi$
$929$	227850.	−	191189.i	0.264009	−	0.221530i	0.765177	+	0.643820i	$0.222652\pi$
$930$		0			0
$931$	774638.	+	299776.i	0.893716	+	0.345857i
$932$		0			0
$933$	−499316.	−	595062.i	−0.573604	−	0.683595i
$934$		0			0
$935$	−45807.2	+	259786.i	−0.0523975	+	0.297161i
$936$		0			0
$937$	1.20985e6	−	440350.i	1.37801	−	0.501556i	0.456438	−	0.889755i	$-0.349125\pi$
$937$	1.20985e6	−	440350.i	1.37801	−	0.501556i	0.921575	+	0.388200i	$0.126903\pi$
$938$		0			0
$939$	−1.94118e6	+	1.12074e6i	−2.20158	+	1.27108i
$940$		0			0
$941$	869893.	−	1.03670e6i	0.982396	−	1.17077i	−0.00291337	−	0.999996i	$-0.500927\pi$
$941$	869893.	−	1.03670e6i	0.982396	−	1.17077i	0.985309	−	0.170778i	$-0.0546282\pi$
$942$		0			0
$943$	605448.	+	349555.i	0.680853	+	0.393091i
$944$		0			0
$945$	118922.	−	20969.1i	0.133168	−	0.0234810i
$946$		0			0
$947$	1.43236e6	+	521336.i	1.59717	+	0.581323i	0.978846	−	0.204598i	$-0.0655888\pi$
$947$	1.43236e6	+	521336.i	1.59717	+	0.581323i	0.618326	+	0.785921i	$0.287811\pi$
$948$		0			0
$949$			250903.i			0.278595i
$950$		0			0
$951$	62967.8			0.0696238
$952$		0			0
$953$	−526703.	+	1.44710e6i	−0.579936	+	1.59336i	0.208352	+	0.978054i	$0.433190\pi$
$953$	−526703.	+	1.44710e6i	−0.579936	+	1.59336i	−0.788288	+	0.615307i	$0.789032\pi$
$954$		0			0
$955$	−174175.	−	987794.i	−0.190976	−	1.08308i
$956$		0			0
$957$	−76404.7	+	132337.i	−0.0834250	+	0.144496i
$958$		0			0
$959$	−27026.1	−	22677.6i	−0.0293864	−	0.0246581i
$960$		0			0
$961$	902266.	+	1.56277e6i	0.976985	+	1.69219i
$962$		0			0
$963$	−423415.	−	1.16332e6i	−0.456577	−	1.25444i
$964$		0			0
$965$	−1.20305e6	−	212130.i	−1.29190	−	0.227797i
$966$		0			0
$967$	−871233.	+	731051.i	−0.931711	+	0.781798i	−0.976124	−	0.217215i	$-0.930303\pi$
$967$	−871233.	+	731051.i	−0.931711	+	0.781798i	0.0444127	+	0.999013i	$0.485858\pi$
$968$		0			0
$969$	−1.91386e6	−	1.15706e6i	−2.03828	−	1.23228i
$970$		0			0
$971$	75845.2	+	90388.8i	0.0804433	+	0.0958686i	0.804765	−	0.593594i	$-0.202291\pi$
$971$	75845.2	+	90388.8i	0.0804433	+	0.0958686i	−0.724322	+	0.689462i	$0.757847\pi$
$972$		0			0
$973$	24453.9	−	138685.i	0.0258299	−	0.146489i
$974$		0			0
$975$	−676465.	+	246213.i	−0.711600	+	0.259001i
$976$		0			0
$977$	−402008.	+	232099.i	−0.421158	+	0.243156i	−0.695573	−	0.718456i	$-0.744849\pi$
$977$	−402008.	+	232099.i	−0.421158	+	0.243156i	0.274414	+	0.961612i	$0.411516\pi$
$978$		0			0
$979$	118673.	−	141429.i	0.123819	−	0.147562i
$980$		0			0
$981$	−619338.	−	357575.i	−0.643561	−	0.371560i
$982$		0			0
$983$	−905562.	+	159675.i	−0.937154	+	0.165246i	−0.621310	−	0.783565i	$-0.713399\pi$
$983$	−905562.	+	159675.i	−0.937154	+	0.165246i	−0.315845	+	0.948811i	$0.602288\pi$
$984$		0			0
$985$	−1.60120e6	−	582789.i	−1.65034	−	0.600674i
$986$		0			0
$987$			175262.i			0.179910i
$988$		0			0
$989$	−538512.			−0.550557
$990$		0			0
$991$	−301131.	+	827349.i	−0.306625	+	0.842445i	0.686684	+	0.726956i	$0.259066\pi$
$991$	−301131.	+	827349.i	−0.306625	+	0.842445i	−0.993309	+	0.115489i	$0.963157\pi$
$992$		0			0
$993$	419745.	+	2.38049e6i	0.425683	+	2.41417i
$994$		0			0
$995$	121832.	−	211019.i	0.123060	−	0.213145i
$996$		0			0
$997$	1.09217e6	+	916438.i	1.09875	+	0.921961i	0.997340	−	0.0728834i	$-0.0232201\pi$
$997$	1.09217e6	+	916438.i	1.09875	+	0.921961i	0.101410	+	0.994845i	$0.467665\pi$
$998$		0			0
$999$	−234368.	−	405937.i	−0.234837	−	0.406750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.j.a.13.1	✓	42
19.3	odd	18	inner	76.5.j.a.41.1	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.j.a.13.1	✓	42	1.1	even	1	trivial
76.5.j.a.41.1	yes	42	19.3	odd	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.65644 + 12.7935i) q^{3} +(6.59099 + 37.3793i) q^{5} +(5.00284 - 8.66518i) q^{7} +(-79.9406 - 67.0781i) q^{9} +O(q^{10})\)	\(q+(-4.65644 + 12.7935i) q^{3} +(6.59099 + 37.3793i) q^{5} +(5.00284 - 8.66518i) q^{7} +(-79.9406 - 67.0781i) q^{9} +(-7.63671 - 13.2272i) q^{11} +(-22.1718 - 60.9166i) q^{13} +(-508.902 - 89.7331i) q^{15} +(-348.579 + 292.493i) q^{17} +(281.167 - 226.421i) q^{19} +(87.5622 + 104.353i) q^{21} +(49.2696 - 279.422i) q^{23} +(-766.467 + 278.971i) q^{25} +(275.368 - 158.984i) q^{27} +(-472.367 + 562.945i) q^{29} +(1430.40 + 825.841i) q^{31} +(204.781 - 36.1084i) q^{33} +(356.872 + 129.891i) q^{35} -1474.16i q^{37} +882.576 q^{39} +(-842.731 + 2315.38i) q^{41} +(-329.577 - 1869.12i) q^{43} +(1980.45 - 3430.24i) q^{45} +(985.584 + 827.003i) q^{47} +(1150.44 + 1992.63i) q^{49} +(-2118.86 - 5821.51i) q^{51} +(3118.81 + 549.931i) q^{53} +(444.089 - 372.635i) q^{55} +(1587.47 + 4651.41i) q^{57} +(938.249 + 1118.16i) q^{59} +(-920.289 + 5219.22i) q^{61} +(-981.174 + 357.118i) q^{63} +(2130.89 - 1230.27i) q^{65} +(-4064.52 + 4843.91i) q^{67} +(3345.35 + 1931.44i) q^{69} +(-9089.14 + 1602.66i) q^{71} +(-3636.99 - 1323.76i) q^{73} -11104.8i q^{75} -152.821 q^{77} +(-1439.36 + 3954.62i) q^{79} +(-716.087 - 4061.13i) q^{81} +(6219.89 - 10773.2i) q^{83} +(-13230.7 - 11101.8i) q^{85} +(-5002.47 - 8664.53i) q^{87} +(4134.29 + 11358.9i) q^{89} +(-638.775 - 112.633i) q^{91} +(-17225.9 + 14454.3i) q^{93} +(10316.6 + 9017.49i) q^{95} +(-1907.80 - 2273.62i) q^{97} +(-276.771 + 1569.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9}+O(q^{10}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9	\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} - 45 q^{11} + 33 q^{13} - 393 q^{15} + 909 q^{17} + 1242 q^{19} + 1107 q^{21} - 360 q^{23} - 810 q^{25} - 7056 q^{27} - 2889 q^{29} + 2808 q^{31} + 10875 q^{33} + 6741 q^{35} - 3480 q^{39} - 3060 q^{41} - 8079 q^{43} - 4320 q^{45} - 2655 q^{47} - 474 q^{49} - 12222 q^{51} - 6705 q^{53} + 4623 q^{55} - 8022 q^{57} + 24309 q^{59} + 7104 q^{61} + 12063 q^{63} + 25245 q^{65} + 15573 q^{67} - 10881 q^{69} - 25506 q^{71} + 3036 q^{73} + 12924 q^{77} - 16839 q^{79} - 2208 q^{81} - 6363 q^{83} - 37890 q^{85} - 21924 q^{87} - 22644 q^{89} + 17418 q^{91} + 8184 q^{93} - 82413 q^{95} + 13383 q^{97} + 23565 q^{99}+O(q^{100}) \) 42 * q + 12 * q^3 - 45 * q^7 - 84 * q^9 - 45 * q^11 + 33 * q^13 - 393 * q^15 + 909 * q^17 + 1242 * q^19 + 1107 * q^21 - 360 * q^23 - 810 * q^25 - 7056 * q^27 - 2889 * q^29 + 2808 * q^31 + 10875 * q^33 + 6741 * q^35 - 3480 * q^39 - 3060 * q^41 - 8079 * q^43 - 4320 * q^45 - 2655 * q^47 - 474 * q^49 - 12222 * q^51 - 6705 * q^53 + 4623 * q^55 - 8022 * q^57 + 24309 * q^59 + 7104 * q^61 + 12063 * q^63 + 25245 * q^65 + 15573 * q^67 - 10881 * q^69 - 25506 * q^71 + 3036 * q^73 + 12924 * q^77 - 16839 * q^79 - 2208 * q^81 - 6363 * q^83 - 37890 * q^85 - 21924 * q^87 - 22644 * q^89 + 17418 * q^91 + 8184 * q^93 - 82413 * q^95 + 13383 * q^97 + 23565 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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