LMFDB - Embedded newform 33.6.f.a.2.8

Newspace parameters

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.f (of order $10$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			2.8
Character	$\chi$	$=$	33.2
Dual form			33.6.f.a.17.8

$q$-expansion

$f(q)$	$=$	$q+(-1.01916 + 3.13665i) q^{2} +(-8.08821 + 13.3259i) q^{3} +(17.0887 + 12.4156i) q^{4} +(-40.8503 + 13.2731i) q^{5} +(-33.5556 - 38.9511i) q^{6} +(39.2343 - 54.0014i) q^{7} +(-141.742 + 102.981i) q^{8} +(-112.162 - 215.566i) q^{9} +O(q^{10})$	\(q+(-1.01916 + 3.13665i) q^{2} +(-8.08821 + 13.3259i) q^{3} +(17.0887 + 12.4156i) q^{4} +(-40.8503 + 13.2731i) q^{5} +(-33.5556 - 38.9511i) q^{6} +(39.2343 - 54.0014i) q^{7} +(-141.742 + 102.981i) q^{8} +(-112.162 - 215.566i) q^{9} -141.660i q^{10} +(-397.241 + 57.0130i) q^{11} +(-303.667 + 127.302i) q^{12} +(-146.801 - 47.6985i) q^{13} +(129.397 + 178.100i) q^{14} +(153.530 - 651.725i) q^{15} +(30.3142 + 93.2975i) q^{16} +(19.0002 + 58.4765i) q^{17} +(790.466 - 132.115i) q^{18} +(1187.03 + 1633.81i) q^{19} +(-862.872 - 280.364i) q^{20} +(402.284 + 959.609i) q^{21} +(226.022 - 1304.11i) q^{22} +1286.90i q^{23} +(-225.887 - 2721.78i) q^{24} +(-1035.60 + 752.410i) q^{25} +(299.227 - 411.851i) q^{26} +(3779.81 + 248.886i) q^{27} +(1340.92 - 435.693i) q^{28} +(5642.83 + 4099.76i) q^{29} +(1887.76 + 1145.78i) q^{30} +(-840.834 + 2587.82i) q^{31} -5930.01 q^{32} +(2453.22 - 5754.75i) q^{33} -202.785 q^{34} +(-885.970 + 2726.73i) q^{35} +(759.701 - 5076.30i) q^{36} +(-9428.42 - 6850.15i) q^{37} +(-6334.47 + 2058.19i) q^{38} +(1822.99 - 1570.47i) q^{39} +(4423.32 - 6088.17i) q^{40} +(-10856.1 + 7887.45i) q^{41} +(-3419.95 + 283.830i) q^{42} +3417.72i q^{43} +(-7496.17 - 3957.73i) q^{44} +(7443.06 + 7317.22i) q^{45} +(-4036.56 - 1311.56i) q^{46} +(-5114.80 - 7039.92i) q^{47} +(-1488.47 - 350.645i) q^{48} +(3816.83 + 11747.0i) q^{49} +(-1304.60 - 4015.15i) q^{50} +(-932.933 - 219.775i) q^{51} +(-1916.42 - 2637.73i) q^{52} +(27613.0 + 8972.01i) q^{53} +(-4632.90 + 11602.3i) q^{54} +(15470.7 - 7601.61i) q^{55} +11694.7i q^{56} +(-31373.1 + 2603.73i) q^{57} +(-18610.4 + 13521.3i) q^{58} +(24093.0 - 33161.1i) q^{59} +(10715.2 - 9230.93i) q^{60} +(16570.6 - 5384.11i) q^{61} +(-7260.14 - 5274.80i) q^{62} +(-16041.5 - 2400.71i) q^{63} +(5073.57 - 15614.8i) q^{64} +6629.97 q^{65} +(15550.4 + 13559.9i) q^{66} +36858.5 q^{67} +(-401.336 + 1235.19i) q^{68} +(-17149.2 - 10408.8i) q^{69} +(-7649.86 - 5557.95i) q^{70} +(49329.1 - 16028.0i) q^{71} +(38097.3 + 19004.2i) q^{72} +(-42702.5 + 58774.9i) q^{73} +(31095.6 - 22592.3i) q^{74} +(-1650.39 - 19886.0i) q^{75} +42657.5i q^{76} +(-12506.7 + 23688.4i) q^{77} +(3068.09 + 7318.62i) q^{78} +(-9746.11 - 3166.70i) q^{79} +(-2476.69 - 3408.87i) q^{80} +(-33888.6 + 48356.5i) q^{81} +(-13676.0 - 42090.5i) q^{82} +(-14452.1 - 44479.1i) q^{83} +(-5039.66 + 21393.0i) q^{84} +(-1552.33 - 2136.60i) q^{85} +(-10720.2 - 3483.20i) q^{86} +(-100274. + 42036.4i) q^{87} +(50434.4 - 48989.6i) q^{88} +36845.4i q^{89} +(-30537.2 + 15888.9i) q^{90} +(-8335.42 + 6056.04i) q^{91} +(-15977.7 + 21991.5i) q^{92} +(-27684.3 - 32135.8i) q^{93} +(27294.5 - 8868.53i) q^{94} +(-70176.4 - 50986.2i) q^{95} +(47963.2 - 79023.0i) q^{96} +(38798.6 - 119410. i) q^{97} -40736.1 q^{98} +(56845.3 + 79237.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72q + 18q^{3} - 262q^{4} + 15q^{6} - 10q^{7} + 292q^{9} + O(q^{10}) $	$ 72q + 18q^{3} - 262q^{4} + 15q^{6} - 10q^{7} + 292q^{9} + 1854q^{12} - 10q^{13} - 762q^{15} - 10122q^{16} + 4815q^{18} + 4460q^{19} + 4628q^{22} - 805q^{24} + 13708q^{25} + 6108q^{27} - 28130q^{28} - 15470q^{30} + 4340q^{31} - 508q^{33} + 18732q^{34} - 56461q^{36} + 978q^{37} + 23360q^{39} + 69750q^{40} + 60788q^{42} - 31356q^{45} - 52090q^{46} + 4238q^{48} - 58448q^{49} - 178950q^{51} - 14190q^{52} + 86600q^{55} + 266190q^{57} + 137102q^{58} + 284090q^{60} - 77890q^{61} - 120330q^{63} - 379114q^{64} - 323304q^{66} + 42668q^{67} - 271816q^{69} + 87176q^{70} + 343960q^{72} + 116440q^{73} + 326202q^{75} + 155512q^{78} - 350590q^{79} - 208088q^{81} - 606424q^{82} - 220680q^{84} + 665610q^{85} + 1152974q^{88} + 293440q^{90} + 621014q^{91} + 478456q^{93} - 521270q^{94} - 1246430q^{96} - 1030446q^{97} - 590000q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

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 $

$2$	−1.01916	+	3.13665i	−0.180164	+	0.554486i	−0.999832	−	0.0183525i	$-0.994158\pi$
$2$	−1.01916	+	3.13665i	−0.180164	+	0.554486i	0.819668	+	0.572839i	$0.194158\pi$
$3$	−8.08821	+	13.3259i	−0.518859	+	0.854860i
$3$	−8.08821	+	13.3259i	−0.518859	+	0.854860i
$4$	17.0887	+	12.4156i	0.534021	+	0.387989i
$5$	−40.8503	+	13.2731i	−0.730753	+	0.237436i	−0.650679	−	0.759353i	$-0.725516\pi$
$5$	−40.8503	+	13.2731i	−0.730753	+	0.237436i	−0.0800739	+	0.996789i	$0.525516\pi$
$6$	−33.5556	−	38.9511i	−0.380529	−	0.441715i
$7$	39.2343	−	54.0014i	0.302636	−	0.416543i	−0.630431	−	0.776245i	$-0.717122\pi$
$7$	39.2343	−	54.0014i	0.302636	−	0.416543i	0.933067	+	0.359702i	$0.117122\pi$
$8$	−141.742	+	102.981i	−0.783020	+	0.568897i
$9$	−112.162	−	215.566i	−0.461570	−	0.887104i
$10$		−	141.660i		−	0.447970i
$11$	−397.241	+	57.0130i	−0.989857	+	0.142067i
$11$	−397.241	+	57.0130i	−0.989857	+	0.142067i
$12$	−303.667	+	127.302i	−0.608758	+	0.255201i
$13$	−146.801	−	47.6985i	−0.240919	−	0.0782792i	0.186069	−	0.982537i	$-0.440425\pi$
$13$	−146.801	−	47.6985i	−0.240919	−	0.0782792i	−0.426988	+	0.904257i	$0.640425\pi$
$14$	129.397	+	178.100i	0.176443	+	0.242853i
$15$	153.530	−	651.725i	0.176183	−	0.747887i
$16$	30.3142	+	93.2975i	0.0296037	+	0.0911109i
$17$	19.0002	+	58.4765i	0.0159454	+	0.0490749i	0.958713	−	0.284377i	$-0.0917866\pi$
$17$	19.0002	+	58.4765i	0.0159454	+	0.0490749i	−0.942767	+	0.333452i	$0.891787\pi$
$18$	790.466	−	132.115i	0.575045	−	0.0961107i
$19$	1187.03	+	1633.81i	0.754361	+	1.03829i	0.997662	+	0.0683377i	$0.0217695\pi$
$19$	1187.03	+	1633.81i	0.754361	+	1.03829i	−0.243302	+	0.969951i	$0.578230\pi$
$20$	−862.872	−	280.364i	−0.482360	−	0.156728i
$21$	402.284	+	959.609i	0.199060	+	0.474839i
$22$	226.022	−	1304.11i	0.0995621	−	0.574457i
$23$			1286.90i			0.507255i	0.967302	+	0.253628i	$0.0816238\pi$
$23$			1286.90i			0.507255i	−0.967302	+	0.253628i	$0.918376\pi$
$24$	−225.887	−	2721.78i	−0.0800503	−	0.964550i
$25$	−1035.60	+	752.410i	−0.331393	+	0.240771i
$26$	299.227	−	411.851i	0.0868095	−	0.119483i
$27$	3779.81	+	248.886i	0.997839	+	0.0657040i
$28$	1340.92	−	435.693i	0.323228	−	0.105023i
$29$	5642.83	+	4099.76i	1.24595	+	0.905239i	0.997980	−	0.0635274i	$-0.0202350\pi$
$29$	5642.83	+	4099.76i	1.24595	+	0.905239i	0.247975	+	0.968767i	$0.420235\pi$
$30$	1887.76	+	1145.78i	0.382951	+	0.232433i
$31$	−840.834	+	2587.82i	−0.157147	+	0.483649i	−0.998372	−	0.0570363i	$-0.981835\pi$
$31$	−840.834	+	2587.82i	−0.157147	+	0.483649i	0.841225	+	0.540685i	$0.181835\pi$
$32$	−5930.01			−1.02372
$33$	2453.22	−	5754.75i	0.392149	−	0.919902i
$34$	−202.785			−0.0300841
$35$	−885.970	+	2726.73i	−0.122250	+	0.376247i
$36$	759.701	−	5076.30i	0.0976981	−	0.652816i
$37$	−9428.42	−	6850.15i	−1.13223	−	0.822613i	−0.146212	−	0.989253i	$-0.546708\pi$
$37$	−9428.42	−	6850.15i	−1.13223	−	0.822613i	−0.986018	+	0.166640i	$0.946708\pi$
$38$	−6334.47	+	2058.19i	−0.711625	+	0.231221i
$39$	1822.99	−	1570.47i	0.191921	−	0.165336i
$40$	4423.32	−	6088.17i	0.437117	−	0.601640i
$41$	−10856.1	+	7887.45i	−1.00859	+	0.732786i	−0.963913	−	0.266216i	$-0.914227\pi$
$41$	−10856.1	+	7887.45i	−1.00859	+	0.732786i	−0.0446794	+	0.999001i	$0.514227\pi$
$42$	−3419.95	+	283.830i	−0.299155	+	0.0248276i
$43$			3417.72i			0.281881i	0.990018	+	0.140940i	$0.0450126\pi$
$43$			3417.72i			0.281881i	−0.990018	+	0.140940i	$0.954987\pi$
$44$	−7496.17	−	3957.73i	−0.583725	−	0.308187i
$45$	7443.06	+	7317.22i	0.547924	+	0.538660i
$46$	−4036.56	−	1311.56i	−0.281266	−	0.0913889i
$47$	−5114.80	−	7039.92i	−0.337741	−	0.464861i	0.606039	−	0.795435i	$-0.292758\pi$
$47$	−5114.80	−	7039.92i	−0.337741	−	0.464861i	−0.943780	+	0.330574i	$0.892758\pi$
$48$	−1488.47	−	350.645i	−0.0932472	−	0.0219667i
$49$	3816.83	+	11747.0i	0.227098	+	0.698935i
$50$	−1304.60	−	4015.15i	−0.0737993	−	0.227131i
$51$	−932.933	−	219.775i	−0.0502256	−	0.0118319i
$52$	−1916.42	−	2637.73i	−0.0982841	−	0.135277i
$53$	27613.0	+	8972.01i	1.35028	+	0.438733i	0.892787	−	0.450480i	$-0.148747\pi$
$53$	27613.0	+	8972.01i	1.35028	+	0.438733i	0.457494	+	0.889213i	$0.348747\pi$
$54$	−4632.90	+	11602.3i	−0.216206	+	0.541451i
$55$	15470.7	−	7601.61i	0.689609	−	0.338843i
$56$			11694.7i			0.498330i
$57$	−31373.1	+	2603.73i	−1.27900	+	0.106147i
$58$	−18610.4	+	13521.3i	−0.726418	+	0.527774i
$59$	24093.0	−	33161.1i	0.901074	−	1.24022i	−0.0690507	−	0.997613i	$-0.521997\pi$
$59$	24093.0	−	33161.1i	0.901074	−	1.24022i	0.970124	−	0.242608i	$-0.0780030\pi$
$60$	10715.2	−	9230.93i	0.384257	−	0.331030i
$61$	16570.6	−	5384.11i	0.570181	−	0.185263i	−0.00971591	−	0.999953i	$-0.503093\pi$
$61$	16570.6	−	5384.11i	0.570181	−	0.185263i	0.579897	+	0.814690i	$0.303093\pi$
$62$	−7260.14	−	5274.80i	−0.239864	−	0.174272i
$63$	−16041.5	−	2400.71i	−0.509205	−	0.0762058i
$64$	5073.57	−	15614.8i	0.154833	−	0.476527i
$65$	6629.97			0.194638
$66$	15550.4	+	13559.9i	0.439422	+	0.383174i
$67$	36858.5			1.00311			0.501557	−	0.865125i	$-0.332761\pi$
$67$	36858.5			1.00311			0.501557	+	0.865125i	$0.332761\pi$
$68$	−401.336	+	1235.19i	−0.0105253	+	0.0323937i
$69$	−17149.2	−	10408.8i	−0.433632	−	0.263194i
$70$	−7649.86	−	5557.95i	−0.186599	−	0.135572i
$71$	49329.1	−	16028.0i	1.16133	−	0.377340i	0.335932	−	0.941886i	$-0.390949\pi$
$71$	49329.1	−	16028.0i	1.16133	−	0.377340i	0.825402	+	0.564546i	$0.190949\pi$
$72$	38097.3	+	19004.2i	0.866089	+	0.432034i
$73$	−42702.5	+	58774.9i	−0.937878	+	1.29088i	0.0188288	+	0.999823i	$0.494006\pi$
$73$	−42702.5	+	58774.9i	−0.937878	+	1.29088i	−0.956706	+	0.291055i	$0.905994\pi$
$74$	31095.6	−	22592.3i	0.660114	−	0.479601i
$75$	−1650.39	−	19886.0i	−0.0338792	−	0.408221i
$76$			42657.5i			0.847151i
$77$	−12506.7	+	23688.4i	−0.240390	+	0.455312i
$78$	3068.09	+	7318.62i	0.0570993	+	0.136205i
$79$	−9746.11	−	3166.70i	−0.175697	−	0.0570873i	0.219848	−	0.975534i	$-0.429444\pi$
$79$	−9746.11	−	3166.70i	−0.175697	−	0.0570873i	−0.395544	+	0.918447i	$0.629444\pi$
$80$	−2476.69	−	3408.87i	−0.0432660	−	0.0595505i
$81$	−33888.6	+	48356.5i	−0.573906	+	0.818921i
$82$	−13676.0	−	42090.5i	−0.224608	−	0.691272i
$83$	−14452.1	−	44479.1i	−0.230270	−	0.708697i	−0.997714	−	0.0675810i	$-0.978472\pi$
$83$	−14452.1	−	44479.1i	−0.230270	−	0.708697i	0.767444	−	0.641116i	$-0.221528\pi$
$84$	−5039.66	+	21393.0i	−0.0779298	+	0.330807i
$85$	−1552.33	−	2136.60i	−0.0233043	−	0.0320756i
$86$	−10720.2	−	3483.20i	−0.156299	−	0.0507847i
$87$	−100274.	+	42036.4i	−1.42033	+	0.595425i
$88$	50434.4	−	48989.6i	0.694256	−	0.674368i
$89$			36845.4i			0.493070i	0.969134	+	0.246535i	$0.0792920\pi$
$89$			36845.4i			0.493070i	−0.969134	+	0.246535i	$0.920708\pi$
$90$	−30537.2	+	15888.9i	−0.397396	+	0.206770i
$91$	−8335.42	+	6056.04i	−0.105517	+	0.0766629i
$92$	−15977.7	+	21991.5i	−0.196809	+	0.270885i
$93$	−27684.3	−	32135.8i	−0.331915	−	0.385284i
$94$	27294.5	−	8868.53i	0.318608	−	0.103522i
$95$	−70176.4	−	50986.2i	−0.797778	−	0.579620i
$96$	47963.2	−	79023.0i	0.531166	−	0.875136i
$97$	38798.6	−	119410.i	0.418685	−	1.28858i	−0.490228	−	0.871594i	$-0.663087\pi$
$97$	38798.6	−	119410.i	0.418685	−	1.28858i	0.908913	−	0.416985i	$-0.136913\pi$
$98$	−40736.1			−0.428464
$99$	56845.3	+	79237.1i	0.582917	+	0.812532i
$100$	−27038.7			−0.270387
$101$	31493.0	−	96925.6i	0.307193	−	0.945442i	−0.671657	−	0.740862i	$-0.734417\pi$
$101$	31493.0	−	96925.6i	0.307193	−	0.945442i	0.978850	−	0.204580i	$-0.0655829\pi$
$102$	1640.16	−	2702.30i	0.0156094	−	0.0257177i
$103$	−142938.	−	103851.i	−1.32756	−	0.964532i	−0.999805	−	0.0197704i	$-0.993706\pi$
$103$	−142938.	−	103851.i	−1.32756	−	0.964532i	−0.327759	−	0.944761i	$-0.606294\pi$
$104$	25719.9	−	8356.90i	0.233177	−	0.0757638i
$105$	−29170.4	−	33860.8i	−0.258208	−	0.299726i
$106$	−56284.1	+	77468.4i	−0.486543	+	0.669669i
$107$	−78863.7	+	57297.9i	−0.665914	+	0.483815i	−0.868655	−	0.495418i	$-0.835015\pi$
$107$	−78863.7	+	57297.9i	−0.665914	+	0.483815i	0.202741	+	0.979232i	$0.435015\pi$
$108$	61501.8	+	51181.9i	0.507374	+	0.422238i
$109$			219803.i			1.77201i	0.463673	+	0.886006i	$0.346531\pi$
$109$			219803.i			1.77201i	−0.463673	+	0.886006i	$0.653469\pi$
$110$	8076.49	+	56273.4i	0.0636416	+	0.443426i
$111$	167544.	−	70237.1i	1.29069	−	0.541077i
$112$	6227.55	+	2023.45i	0.0469107	+	0.0152422i
$113$	84104.7	+	115760.i	0.619618	+	0.852831i	0.997325	−	0.0730939i	$-0.0232873\pi$
$113$	84104.7	+	115760.i	0.619618	+	0.852831i	−0.377707	+	0.925925i	$0.623287\pi$
$114$	23807.2	−	101060.i	0.171572	−	0.728311i
$115$	−17081.2	−	52570.4i	−0.120441	−	0.370678i
$116$	45527.4	+	140119.i	0.314143	+	0.966833i
$117$	6183.24	+	36995.3i	0.0417591	+	0.249851i
$118$	79460.2	+	109368.i	0.525345	+	0.723076i
$119$	3903.27	+	1268.25i	0.0252675	+	0.00820989i
$120$	45353.9	+	108187.i	0.287516	+	0.685841i
$121$	154550.	−	45295.8i	0.959634	−	0.281251i
$122$			57463.3i			0.349535i
$123$	−17300.9	−	208464.i	−0.103111	−	1.24242i
$124$	−46498.2	+	33782.9i	−0.271570	+	0.197307i
$125$	111214.	−	153074.i	0.636629	−	0.876244i
$126$	23879.0	−	47869.7i	0.133995	−	0.268617i
$127$	−26429.8	+	8587.55i	−0.145407	+	0.0472455i	−0.380816	−	0.924651i	$-0.624357\pi$
$127$	−26429.8	+	8587.55i	−0.145407	+	0.0472455i	0.235409	+	0.971896i	$0.424357\pi$
$128$	−109712.	−	79710.4i	−0.591873	−	0.430021i
$129$	−45544.4	−	27643.3i	−0.240969	−	0.146257i
$130$	−6757.00	+	20795.9i	−0.0350667	+	0.107924i
$131$	21872.3			0.111357			0.0556784	−	0.998449i	$-0.482268\pi$
$131$	21872.3			0.111357			0.0556784	+	0.998449i	$0.482268\pi$
$132$	113371.	−	67882.7i	0.566327	−	0.339097i
$133$	134801.			0.660788
$134$	−37564.6	+	115612.i	−0.180725	+	0.556213i
$135$	−157710.	+	40002.6i	−0.744774	+	0.188910i
$136$	−8715.11	−	6331.90i	−0.0404041	−	0.0293553i
$137$	−150568.	+	48922.5i	−0.685379	+	0.222693i	−0.630949	−	0.775824i	$-0.717334\pi$
$137$	−150568.	+	48922.5i	−0.685379	+	0.222693i	−0.0544304	+	0.998518i	$0.517334\pi$
$138$	50126.4	−	43182.9i	0.224062	−	0.193025i
$139$	133849.	−	184228.i	0.587596	−	0.808757i	−0.406906	−	0.913470i	$-0.633392\pi$
$139$	133849.	−	184228.i	0.587596	−	0.808757i	0.994502	+	0.104713i	$0.0333924\pi$
$140$	−48994.2	+	35596.4i	−0.211264	+	0.153492i
$141$	135183.	−	11219.2i	0.572631	−	0.0475240i
$142$			171063.i			0.711927i
$143$	61034.8	+	10578.3i	0.249596	+	0.0432587i
$144$	16711.7	−	16999.1i	0.0671606	−	0.0683156i
$145$	−284928.	−	92578.7i	−1.12542	−	0.365672i
$146$	−140836.	−	193844.i	−0.546803	−	0.752609i
$147$	−187411.	−	44149.3i	−0.715323	−	0.168512i
$148$	−76070.1	−	234120.i	−0.285470	−	0.878585i
$149$	142334.	+	438058.i	0.525221	+	1.61646i	0.763878	+	0.645361i	$0.223293\pi$
$149$	142334.	+	438058.i	0.525221	+	1.61646i	−0.238657	+	0.971104i	$0.576707\pi$
$150$	64057.5	+	15090.3i	0.232457	+	0.0547609i
$151$	175340.	+	241335.i	0.625805	+	0.861346i	0.997759	−	0.0669045i	$-0.0213123\pi$
$151$	175340.	+	241335.i	0.625805	+	0.861346i	−0.371955	+	0.928251i	$0.621312\pi$
$152$	−336504.	−	109337.i	−1.18136	−	0.383847i
$153$	10474.5	−	10654.6i	0.0361746	−	0.0367967i
$154$	−61556.0	−	63371.4i	−0.209155	−	0.215323i
$155$		−	116874.i		−	0.390740i
$156$	50650.7	−	4203.63i	0.166638	−	0.0138297i
$157$	−79739.6	+	57934.2i	−0.258181	+	0.187580i	−0.709345	−	0.704861i	$-0.751009\pi$
$157$	−79739.6	+	57934.2i	−0.258181	+	0.187580i	0.451163	+	0.892441i	$0.351009\pi$
$158$	19865.7	−	27342.7i	0.0633083	−	0.0871363i
$159$	−342900.	+	295402.i	−1.07566	+	0.926660i
$160$	242243.	−	78709.5i	0.748086	−	0.243068i
$161$	69494.6	+	50490.8i	0.211294	+	0.153514i
$162$	−117139.	−	155579.i	−0.350684	−	0.465763i
$163$	−6395.96	+	19684.7i	−0.0188554	+	0.0580311i	−0.960042	−	0.279858i	$-0.909713\pi$
$163$	−6395.96	+	19684.7i	−0.0188554	+	0.0580311i	0.941186	+	0.337889i	$0.109713\pi$
$164$	−283445.			−0.822922
$165$	−23831.6	+	267645.i	−0.0681465	+	0.765331i
$166$	154244.			0.434449
$167$	25087.5	−	77211.4i	0.0696091	−	0.214235i	−0.910200	−	0.414168i	$-0.864073\pi$
$167$	25087.5	−	77211.4i	0.0696091	−	0.214235i	0.979810	+	0.199933i	$0.0640726\pi$
$168$	−155842.	−	94588.8i	−0.426002	−	0.258563i
$169$	−281107.	−	204236.i	−0.757103	−	0.550067i
$170$	8283.82	−	2691.58i	0.0219841	−	0.00714306i
$171$	219055.	−	439135.i	0.572879	−	1.14844i
$172$	−42433.2	+	58404.3i	−0.109367	+	0.150530i
$173$	59358.4	−	43126.4i	0.150788	−	0.109554i	−0.509833	−	0.860273i	$-0.670293\pi$
$173$	59358.4	−	43126.4i	0.150788	−	0.109554i	0.660621	+	0.750719i	$0.270293\pi$
$174$	−29658.6	−	357365.i	−0.0742638	−	0.894826i
$175$			85444.3i			0.210905i
$176$	−17361.2	−	35333.3i	−0.0422473	−	0.0859810i
$177$	247034.	+	589276.i	0.592685	+	1.41379i
$178$	−115571.	−	37551.3i	−0.273401	−	0.0888332i
$179$	39792.2	+	54769.3i	0.0928252	+	0.127763i	0.852904	−	0.522069i	$-0.174839\pi$
$179$	39792.2	+	54769.3i	0.0928252	+	0.127763i	−0.760078	+	0.649831i	$0.774839\pi$
$180$	36344.1	+	217452.i	0.0836088	+	0.500244i
$181$	93801.1	+	288690.i	0.212819	+	0.654991i	0.999301	+	0.0373775i	$0.0119004\pi$
$181$	93801.1	+	288690.i	0.212819	+	0.654991i	−0.786482	+	0.617614i	$0.788100\pi$
$182$	−10500.5	−	32317.3i	−0.0234981	−	0.0723198i
$183$	−62278.0	+	264366.i	−0.137470	+	0.583550i
$184$	−132527.	−	182408.i	−0.288576	−	0.397191i
$185$	476077.	+	154687.i	1.02270	+	0.332295i
$186$	129013.	−	54084.5i	0.273434	−	0.114628i
$187$	−10881.6	−	22146.0i	−0.0227556	−	0.0463118i
$188$		−	183806.i		−	0.379285i
$189$	161738.	−	194350.i	0.329351	−	0.395758i
$190$	231447.	−	168156.i	0.465122	−	0.337931i
$191$	382164.	−	526004.i	0.757995	−	1.04329i	−0.239383	−	0.970925i	$-0.576945\pi$
$191$	382164.	−	526004.i	0.757995	−	1.04329i	0.997378	−	0.0723656i	$-0.0230548\pi$
$192$	167046.	+	193906.i	0.327027	+	0.379611i
$193$	−549012.	+	178385.i	−1.06094	+	0.344719i	−0.786951	−	0.617015i	$-0.788342\pi$
$193$	−549012.	+	178385.i	−1.06094	+	0.344719i	−0.273984	+	0.961734i	$0.588342\pi$
$194$	335005.	+	243395.i	0.639068	+	0.464310i
$195$	−53624.7	+	88350.7i	−0.100990	+	0.166389i
$196$	−80622.0	+	248129.i	−0.149904	+	0.461357i
$197$	414287.			0.760565			0.380282	−	0.924870i	$-0.375827\pi$
$197$	414287.			0.760565			0.380282	+	0.924870i	$0.375827\pi$
$198$	−306473.	+	97548.5i	−0.555558	+	0.176831i
$199$	−375806.			−0.672715			−0.336357	−	0.941734i	$-0.609195\pi$
$199$	−375806.			−0.672715			−0.336357	+	0.941734i	$0.609195\pi$
$200$	69304.0	−	213296.i	0.122513	−	0.377057i
$201$	−298119.	+	491174.i	−0.520475	+	0.857522i
$202$	271925.	+	197565.i	0.468890	+	0.340668i
$203$	442785.	−	143870.i	0.754142	−	0.245036i
$204$	−13213.9	−	15338.6i	−0.0222309	−	0.0258054i
$205$	338786.	−	466299.i	0.563043	−	0.774962i
$206$	471420.	−	342507.i	0.773998	−	0.562343i
$207$	277413.	−	144341.i	0.449988	−	0.234134i
$208$		−	15142.1i		−	0.0242677i
$209$	−564687.	−	581341.i	−0.894215	−	0.920588i
$210$	135939.	−	56987.7i	0.212713	−	0.0891730i
$211$	494441.	+	160654.i	0.764555	+	0.248419i	0.665232	−	0.746637i	$-0.268333\pi$
$211$	494441.	+	160654.i	0.764555	+	0.248419i	0.0993223	+	0.995055i	$0.468333\pi$
$212$	360476.	+	496153.i	0.550855	+	0.758186i
$213$	−185396.	+	786995.i	−0.279996	+	1.18856i
$214$	−99348.6	−	305763.i	−0.148295	−	0.456406i
$215$	−45363.7	−	139615.i	−0.0669287	−	0.205985i
$216$	−561387.	+	353973.i	−0.818707	+	0.516220i
$217$	106756.	+	146938.i	0.153902	+	0.211828i
$218$	−689444.	−	224014.i	−0.982557	−	0.319252i
$219$	−437845.	−	1.04444e6i	−0.616893	−	1.47154i
$220$	358752.	+	62177.2i	0.499733	+	0.0866113i
$221$		−	9490.69i		−	0.0130713i
$222$	49555.5	+	597109.i	0.0674853	+	0.813151i
$223$	877899.	−	637831.i	1.18218	−	0.858902i	0.189761	−	0.981830i	$-0.439229\pi$
$223$	877899.	−	637831.i	1.18218	−	0.858902i	0.992416	+	0.122928i	$0.0392285\pi$
$224$	−232660.	+	320229.i	−0.309814	+	0.426423i
$225$	278349.	+	138850.i	0.366550	+	0.182847i
$226$	−448815.	+	145829.i	−0.584516	+	0.189921i
$227$	−794078.	−	576932.i	−1.02282	−	0.743121i	−0.0559600	−	0.998433i	$-0.517822\pi$
$227$	−794078.	−	576932.i	−1.02282	−	0.743121i	−0.966859	+	0.255312i	$0.917822\pi$
$228$	−568451.	−	345023.i	−0.724195	−	0.439552i
$229$	−341701.	+	1.05165e6i	−0.430584	+	1.32520i	0.466961	+	0.884278i	$0.345349\pi$
$229$	−341701.	+	1.05165e6i	−0.430584	+	1.32520i	−0.897545	+	0.440924i	$0.854651\pi$
$230$	182303.			0.227235
$231$	−214514.	−	358261.i	−0.264500	−	0.441742i
$232$	−1.22202e6			−1.49060
$233$	−347998.	+	1.07103e6i	−0.419939	+	1.29244i	0.487818	+	0.872945i	$0.337793\pi$
$233$	−347998.	+	1.07103e6i	−0.419939	+	1.29244i	−0.907757	+	0.419495i	$0.862207\pi$
$234$	−122343.	−	18309.4i	−0.146063	−	0.0218592i
$235$	302383.	+	219694.i	0.357180	+	0.259507i
$236$	823433.	−	267550.i	0.962384	−	0.312698i
$237$	121028.	−	104263.i	0.139963	−	0.120576i
$238$	−7956.11	+	10950.6i	−0.00910455	+	0.0125313i
$239$	−935104.	+	679393.i	−1.05892	+	0.769354i	−0.973889	−	0.227024i	$-0.927100\pi$
$239$	−935104.	+	679393.i	−1.05892	+	0.769354i	−0.0850353	+	0.996378i	$0.527100\pi$
$240$	65458.4	−	5432.55i	0.0733563	−	0.00608802i
$241$		−	678157.i		−	0.752121i	−0.926595	−	0.376060i	$-0.877279\pi$
$241$		−	678157.i		−	0.752121i	0.926595	−	0.376060i	$-0.122721\pi$
$242$	−15434.0	+	530933.i	−0.0169410	+	0.582775i
$243$	−370298.	−	842715.i	−0.402287	−	0.915514i
$244$	350016.	+	113727.i	0.376369	+	0.122290i
$245$	−311838.	−	429208.i	−0.331905	−	0.456827i
$246$	671510.	+	158191.i	0.707481	+	0.166665i
$247$	−96327.3	−	296465.i	−0.100463	−	0.309194i
$248$	−147316.	−	453393.i	−0.152097	−	0.468107i
$249$	709617.	+	167168.i	0.725314	+	0.170866i
$250$	366793.	+	504847.i	0.371168	+	0.510869i
$251$	336658.	+	109387.i	0.337291	+	0.109592i	0.472765	−	0.881188i	$-0.343256\pi$
$251$	336658.	+	109387.i	0.337291	+	0.109592i	−0.135474	+	0.990781i	$0.543256\pi$
$252$	−244321.	−	240190.i	−0.242359	−	0.238261i
$253$	−73370.2	−	511211.i	−0.0720640	−	0.502110i
$254$		−	91653.0i		−	0.0891379i
$255$	41027.7	−	3404.99i	0.0395118	−	0.00327918i
$256$	786886.	−	571706.i	0.750433	−	0.545222i
$257$	−849721.	+	1.16954e6i	−0.802498	+	1.10454i	0.189940	+	0.981796i	$0.439171\pi$
$257$	−849721.	+	1.16954e6i	−0.802498	+	1.10454i	−0.992438	+	0.122748i	$0.960829\pi$
$258$	133124.	−	114684.i	0.124511	−	0.107264i
$259$	−739835.	+	240387.i	−0.685307	+	0.222670i
$260$	113297.	+	82315.4i	0.103941	+	0.0755175i
$261$	250860.	−	1.67624e6i	0.227945	−	1.52312i
$262$	−22291.4	+	68605.9i	−0.0200625	+	0.0617459i
$263$	−63759.2			−0.0568399			−0.0284199	−	0.999596i	$-0.509048\pi$
$263$	−63759.2			−0.0568399			−0.0284199	+	0.999596i	$0.509048\pi$
$264$	244908.	+	1.06832e6i	0.216269	+	0.943394i
$265$	−1.24709e6			−1.09089
$266$	−137383.	+	422822.i	−0.119050	+	0.366398i
$267$	−491000.	−	298014.i	−0.421506	−	0.255834i
$268$	629862.	+	457622.i	0.535684	+	0.389197i
$269$	−831747.	+	270251.i	−0.700827	+	0.227712i	−0.637691	−	0.770293i	$-0.720110\pi$
$269$	−831747.	+	270251.i	−0.700827	+	0.227712i	−0.0631360	+	0.998005i	$0.520110\pi$
$270$	35257.4	−	535450.i	0.0294334	−	0.447002i
$271$	569134.	−	783345.i	0.470751	−	0.647933i	−0.505944	−	0.862566i	$-0.668856\pi$
$271$	569134.	−	783345.i	0.470751	−	0.647933i	0.976695	+	0.214633i	$0.0688557\pi$
$272$	−4879.74	+	3545.34i	−0.00399921	+	0.00290560i
$273$	−13283.8	−	160060.i	−0.0107873	−	0.129980i
$274$		−	522138.i		−	0.420155i
$275$	368487.	−	357931.i	0.293826	−	0.285409i
$276$	−163826.	−	390790.i	−0.129452	−	0.308795i
$277$	−40100.0	−	13029.3i	−0.0314011	−	0.0102028i	0.293274	−	0.956028i	$-0.405255\pi$
$277$	−40100.0	−	13029.3i	−0.0314011	−	0.0102028i	−0.324675	+	0.945825i	$0.605255\pi$
$278$	441444.	+	607595.i	0.342581	+	0.471523i
$279$	652156.	−	108999.i	0.501581	−	0.0838323i
$280$	−155224.	−	477730.i	−0.118322	−	0.364156i
$281$	−444465.	−	1.36792e6i	−0.335793	−	1.03347i	−0.966330	−	0.257306i	$-0.917165\pi$
$281$	−444465.	−	1.36792e6i	−0.335793	−	1.03347i	0.630537	−	0.776160i	$-0.282835\pi$
$282$	−102582.	+	435456.i	−0.0768158	+	0.326078i
$283$	1.35713e6	+	1.86793e6i	1.00729	+	1.38642i	0.920744	+	0.390168i	$0.127583\pi$
$283$	1.35713e6	+	1.86793e6i	1.00729	+	1.38642i	0.0865467	+	0.996248i	$0.472417\pi$
$284$	1.04197e6	+	338555.i	0.766581	+	0.249077i
$285$	1.24704e6	−	522780.i	0.909428	−	0.381248i
$286$	−95384.4	+	180664.i	−0.0689545	+	0.130604i
$287$			895705.i			0.641890i
$288$	665120.	+	1.27831e6i	0.472518	+	0.908145i
$289$	1.14563e6	−	832349.i	0.806863	−	0.586220i
$290$	580774.	−	799367.i	0.405520	−	0.558150i
$291$	1.27744e6	+	1.48284e6i	0.884316	+	1.02651i
$292$	−1.45946e6	+	474206.i	−1.00169	+	0.325470i
$293$	334947.	+	243353.i	0.227933	+	0.165603i	0.695890	−	0.718148i	$-0.255010\pi$
$293$	334947.	+	243353.i	0.227933	+	0.165603i	−0.467958	+	0.883751i	$0.655010\pi$
$294$	329483.	−	542848.i	0.222313	−	0.366277i
$295$	−544056.	+	1.67443e6i	−0.363989	+	1.12024i
$296$	2.04184e6			1.35454
$297$	−1.51569e6	+	116630.i	−0.997053	+	0.0767222i
$298$	−1.51910e6			−0.990933
$299$	61383.4	−	188919.i	0.0397075	−	0.122207i
$300$	218695.	−	360317.i	0.140293	−	0.231143i
$301$	184562.	+	134092.i	0.117416	+	0.0853074i
$302$	−935682.	+	304022.i	−0.590352	+	0.191817i
$303$	1.03690e6	+	1.20363e6i	0.648831	+	0.753158i
$304$	−116447.	+	160275.i	−0.0722675	+	0.0994676i
$305$	−605450.	+	439885.i	−0.372674	+	0.270763i
$306$	22744.6	+	43713.5i	0.0138859	+	0.0266877i
$307$		−	962836.i		−	0.583051i	−0.956563	−	0.291525i	$-0.905837\pi$
$307$		−	962836.i		−	0.583051i	0.956563	−	0.291525i	$-0.0941628\pi$
$308$	−507830.	+	249525.i	−0.305029	+	0.149878i
$309$	2.54002e6	−	1.06482e6i	1.51336	−	0.634425i
$310$	366592.	+	119113.i	0.216660	+	0.0703971i
$311$	56693.8	+	78032.3i	0.0332380	+	0.0457481i	0.825313	−	0.564676i	$-0.190999\pi$
$311$	56693.8	+	78032.3i	0.0332380	+	0.0457481i	−0.792075	+	0.610424i	$0.790999\pi$
$312$	−96664.4	+	410334.i	−0.0562186	+	0.238644i
$313$	319446.	+	983153.i	0.184305	+	0.567232i	0.999936	−	0.0113409i	$-0.00361001\pi$
$313$	319446.	+	983153.i	0.184305	+	0.567232i	−0.815631	+	0.578572i	$0.803610\pi$
$314$	−100452.	−	309159.i	−0.0574956	−	0.176953i
$315$	687163.	−	114850.i	0.390197	−	0.0652159i
$316$	−127231.	−	175119.i	−0.0716764	−	0.0986541i
$317$	−2.27509e6	−	739222.i	−1.27160	−	0.413168i	−0.405986	−	0.913879i	$-0.633072\pi$
$317$	−2.27509e6	−	739222.i	−1.27160	−	0.413168i	−0.865614	+	0.500712i	$0.833072\pi$
$318$	−577102.	−	1.37662e6i	−0.320026	−	0.763389i
$319$	−2.47531e6	−	1.30688e6i	−1.36192	−	0.719049i
$320$			705214.i			0.384987i
$321$	−125681.	−	1.51437e6i	−0.0680782	−	0.820294i
$322$	−229198.	+	166522.i	−0.123189	+	0.0895018i
$323$	−72985.8	+	100456.i	−0.0389253	+	0.0535761i
$324$	−1.17949e6	+	405600.i	−0.624210	+	0.214652i
$325$	187916.	−	61057.7i	0.0986861	−	0.0320651i
$326$	−55225.6	−	40123.8i	−0.0287804	−	0.0209102i
$327$	−2.92908e6	−	1.77781e6i	−1.51482	−	0.919425i
$328$	726508.	−	2.23596e6i	0.372869	−	1.14757i
$329$	−580841.			−0.295847
$330$	−815220.	−	347524.i	−0.412088	−	0.175671i
$331$	−875794.			−0.439372			−0.219686	−	0.975571i	$-0.570503\pi$
$331$	−875794.			−0.439372			−0.219686	+	0.975571i	$0.570503\pi$
$332$	305269.	−	939520.i	0.151998	−	0.467801i
$333$	−419154.	+	2.80077e6i	−0.207139	+	1.38410i
$334$	216617.	+	157381.i	0.106249	+	0.0771946i
$335$	−1.50568e6	+	489225.i	−0.733029	+	0.238175i
$336$	−77334.2	+	66621.9i	−0.0373700	+	0.0321935i
$337$	2.21164e6	−	3.04407e6i	1.06082	−	1.46009i	0.181779	−	0.983339i	$-0.441815\pi$
$337$	2.21164e6	−	3.04407e6i	1.06082	−	1.46009i	0.879039	−	0.476750i	$-0.158185\pi$
$338$	927110.	−	673585.i	0.441407	−	0.320701i
$339$	−2.22287e6	+	184481.i	−1.05055	+	0.0871873i
$340$		−	55784.7i		−	0.0261709i
$341$	186474.	−	1.07593e6i	0.0868427	−	0.501069i
$342$	1.15416e6	+	1.13465e6i	0.533582	+	0.524560i
$343$	1.85105e6	+	601444.i	0.849540	+	0.276032i
$344$	−351962.	−	484434.i	−0.160361	−	0.220718i
$345$	838707.	+	197578.i	0.379370	+	0.0893699i
$346$	74776.7	+	230139.i	0.0335796	+	0.103347i
$347$	1.11736e6	+	3.43888e6i	0.498161	+	1.53318i	0.811972	+	0.583696i	$0.198394\pi$
$347$	1.11736e6	+	3.43888e6i	0.498161	+	1.53318i	−0.313811	+	0.949485i	$0.601606\pi$
$348$	−2.23545e6	−	526616.i	−0.989503	−	0.233102i
$349$	1.57095e6	+	2.16222e6i	0.690396	+	0.950248i	1.00000		0.000617535i	$-0.000196567\pi$
$349$	1.57095e6	+	2.16222e6i	0.690396	+	0.950248i	−0.309604	+	0.950866i	$0.600197\pi$
$350$	−268009.	−	87081.3i	−0.116944	−	0.0379975i
$351$	−543008.	−	216828.i	−0.235255	−	0.0939394i
$352$	2.35565e6	−	338088.i	1.01334	−	0.145436i
$353$		−	2.70403e6i		−	1.15498i	−0.816397	−	0.577491i	$-0.804032\pi$
$353$		−	2.70403e6i		−	1.15498i	0.816397	−	0.577491i	$-0.195968\pi$
$354$	−2.10012e6	+	174294.i	−0.890708	+	0.0739220i
$355$	−1.80237e6	+	1.30950e6i	−0.759054	+	0.551485i
$356$	−457460.	+	629639.i	−0.191306	+	0.263310i
$357$	−48471.1	+	41756.9i	−0.0201286	+	0.0173404i
$358$	−212347.	+	68995.6i	−0.0875665	+	0.0284521i
$359$	3.19453e6	+	2.32096e6i	1.30819	+	0.950456i	1.00000		0.000868475i	$-0.000276444\pi$
$359$	3.19453e6	+	2.32096e6i	1.30819	+	0.950456i	0.308191	+	0.951325i	$0.400276\pi$
$360$	−1.80853e6	−	270658.i	−0.735478	−	0.110069i
$361$	−495135.	+	1.52387e6i	−0.199966	+	0.615431i
$362$	−1.00112e6			−0.401526
$363$	−646424.	+	2.42589e6i	−0.257484	+	0.966282i
$364$	−217631.			−0.0860928
$365$	964287.	−	2.96777e6i	0.378856	−	1.16600i
$366$	−765753.	−	464776.i	−0.298804	−	0.181360i
$367$	−3.22194e6	−	2.34088e6i	−1.24868	−	0.907222i	−0.250540	−	0.968106i	$-0.580608\pi$
$367$	−3.22194e6	−	2.34088e6i	−1.24868	−	0.907222i	−0.998145	+	0.0608840i	$0.980608\pi$
$368$	−120065.	+	39011.5i	−0.0462165	+	0.0150166i
$369$	2.91791e6	+	1.45555e6i	1.11559	+	0.556494i
$370$	−970396.	+	1.33563e6i	−0.368506	+	0.507205i
$371$	1.56788e6	−	1.13913e6i	0.591395	−	0.429673i
$372$	−74101.9	−	892876.i	−0.0277634	−	0.334529i
$373$			2.11449e6i			0.786925i	0.919341	+	0.393462i	$0.128723\pi$
$373$			2.11449e6i			0.786925i	−0.919341	+	0.393462i	$0.871277\pi$
$374$	80554.4	−	11561.4i	0.0297790	−	0.00427395i
$375$	1.14032e6	+	2.72013e6i	0.418745	+	0.998876i
$376$	1.44996e6	+	471121.i	0.528916	+	0.171855i
$377$	−632821.	−	871003.i	−0.229312	−	0.315621i
$378$	444771.	+	705390.i	0.160106	+	0.253922i
$379$	−303951.	−	935464.i	−0.108694	−	0.334525i	0.881886	−	0.471463i	$-0.156274\pi$
$379$	−303951.	−	935464.i	−0.108694	−	0.334525i	−0.990580	+	0.136938i	$0.956274\pi$
$380$	−566196.	−	1.74257e6i	−0.201144	−	0.619058i
$381$	99332.4	−	421660.i	0.0350573	−	0.148816i
$382$	1.26040e6	+	1.73480e6i	0.441927	+	0.608261i
$383$	3.88935e6	+	1.26373e6i	1.35482	+	0.440206i	0.894309	−	0.447450i	$-0.147668\pi$
$383$	3.88935e6	+	1.26373e6i	1.35482	+	0.440206i	0.460507	+	0.887656i	$0.347668\pi$
$384$	1.94959e6	−	817300.i	0.674707	−	0.282848i
$385$	196484.	−	1.13368e6i	0.0675579	−	0.389798i
$386$		−	1.90386e6i		−	0.650380i
$387$	736745.	−	383337.i	0.250058	−	0.130108i
$388$	2.14557e6	−	1.55885e6i	0.723541	−	0.525683i
$389$	141113.	−	194226.i	0.0472817	−	0.0650777i	−0.784721	−	0.619849i	$-0.787194\pi$
$389$	141113.	−	194226.i	0.0472817	−	0.0650777i	0.832003	+	0.554771i	$0.187194\pi$
$390$	−222473.	−	258245.i	−0.0740655	−	0.0859747i
$391$	−75253.7	+	24451.4i	−0.0248935	+	0.00808839i
$392$	−1.75073e6	−	1.27198e6i	−0.575444	−	0.418084i
$393$	−176908.	+	291470.i	−0.0577785	+	0.0951945i
$394$	−422225.	+	1.29947e6i	−0.137026	+	0.421723i
$395$	440164.			0.141945
$396$	−12369.4	+	2.05983e6i	−0.00396380	+	0.660074i
$397$	−176136.			−0.0560882			−0.0280441	−	0.999607i	$-0.508928\pi$
$397$	−176136.			−0.0560882			−0.0280441	+	0.999607i	$0.508928\pi$
$398$	383006.	−	1.17877e6i	0.121199	−	0.373011i
$399$	−1.09030e6	+	1.79634e6i	−0.342856	+	0.564881i
$400$	−101591.	−	73810.5i	−0.0317473	−	0.0230658i
$401$	779035.	−	253124.i	0.241934	−	0.0786090i	−0.185540	−	0.982637i	$-0.559404\pi$
$401$	779035.	−	253124.i	0.241934	−	0.0786090i	0.427474	+	0.904028i	$0.359404\pi$
$402$	−1.23681e6	−	1.43568e6i	−0.381714	−	0.443090i
$403$	246871.	−	339788.i	0.0757193	−	0.104219i
$404$	1.74157e6	−	1.26532e6i	0.530868	−	0.385698i
$405$	742519.	−	2.42518e6i	0.224942	−	0.734695i
$406$			1.53549e6i			0.462308i
$407$	4.13590e6	+	2.18362e6i	1.23761	+	0.653417i
$408$	154868.	−	64923.4i	0.0460587	−	0.0193086i
$409$	−3.37829e6	−	1.09767e6i	−0.998594	−	0.324463i	−0.236290	−	0.971683i	$-0.575932\pi$
$409$	−3.37829e6	−	1.09767e6i	−0.998594	−	0.324463i	−0.762303	+	0.647220i	$0.775932\pi$
$410$	1.11734e6	+	1.53789e6i	0.328266	+	0.451819i
$411$	565887.	−	2.40216e6i	0.165244	−	0.701450i
$412$	−1.15325e6	−	3.54934e6i	−0.334719	−	1.03016i
$413$	−845476.	−	2.60211e6i	−0.243908	−	0.750672i
$414$	170020.	+	1.01725e6i	0.0487526	+	0.291694i
$415$	1.18075e6	+	1.62516e6i	0.336540	+	0.463208i
$416$	870532.	+	282853.i	0.246633	+	0.0801359i
$417$	1.37241e6	+	3.27374e6i	0.386494	+	0.921943i
$418$	2.39897e6	−	1.17875e6i	0.671558	−	0.329974i
$419$		−	88856.3i		−	0.0247259i	−0.999924	−	0.0123630i	$-0.996065\pi$
$419$		−	88856.3i		−	0.0247259i	0.999924	−	0.0123630i	$-0.00393536\pi$
$420$	−78079.7	−	940805.i	−0.0215981	−	0.260241i
$421$	1.20189e6	−	873226.i	0.330491	−	0.240116i	−0.410148	−	0.912019i	$-0.634523\pi$
$421$	1.20189e6	−	873226.i	0.330491	−	0.240116i	0.740639	+	0.671903i	$0.234523\pi$
$422$	−1.00783e6	+	1.38716e6i	−0.275490	+	0.379179i
$423$	−943884.	+	1.89219e6i	−0.256488	+	0.514177i
$424$	−4.83787e6	+	1.57192e6i	−1.30689	+	0.424634i
$425$	−63675.0	−	46262.6i	−0.0171000	−	0.0124239i
$426$	−2.27958e6	−	1.38359e6i	−0.608598	−	0.369390i
$427$	359386.	−	1.10608e6i	0.0953874	−	0.293572i
$428$	−2.05907e6			−0.543326
$429$	−634628.	+	727787.i	−0.166485	+	0.190924i
$430$	484156.			0.126274
$431$	−2.21277e6	+	6.81020e6i	−0.573777	+	1.76590i	0.0665310	+	0.997784i	$0.478807\pi$
$431$	−2.21277e6	+	6.81020e6i	−0.573777	+	1.76590i	−0.640308	+	0.768119i	$0.721193\pi$
$432$	91361.5	+	360192.i	0.0235534	+	0.0928591i
$433$	−1.16756e6	−	848284.i	−0.299268	−	0.217431i	0.428010	−	0.903774i	$-0.359215\pi$
$433$	−1.16756e6	−	848284.i	−0.299268	−	0.217431i	−0.727278	+	0.686343i	$0.759215\pi$
$434$	−569693.	+	185105.i	−0.145183	+	0.0471729i
$435$	3.53826e6	−	3.04814e6i	0.896533	−	0.772345i
$436$	−2.72899e6	+	3.75614e6i	−0.687521	+	0.946292i
$437$	−2.10256e6	+	1.52760e6i	−0.526677	+	0.382653i
$438$	3.72226e6	−	308919.i	0.927089	−	0.0769413i
$439$			3.23825e6i			0.801954i	0.916088	+	0.400977i	$0.131329\pi$
$439$			3.23825e6i			0.801954i	−0.916088	+	0.400977i	$0.868671\pi$
$440$	−1.41002e6	+	2.67066e6i	−0.347211	+	0.657638i
$441$	2.10415e6	−	2.14034e6i	0.515206	−	0.524067i
$442$	29769.0	+	9672.52i	0.00724783	+	0.00235496i
$443$	−2.88825e6	−	3.97534e6i	−0.699239	−	0.962420i	−0.999962	−	0.00870834i	$-0.997228\pi$
$443$	−2.88825e6	−	3.97534e6i	−0.699239	−	0.962420i	0.300723	−	0.953711i	$-0.402772\pi$
$444$	3.73514e6	+	879905.i	0.899186	+	0.211826i
$445$	−489052.	−	1.50515e6i	−0.117073	−	0.360312i
$446$	1.10593e6	+	3.40371e6i	0.263264	+	0.810244i
$447$	−6.98877e6	−	1.64638e6i	−1.65437	−	0.389727i
$448$	−644165.	−	886617.i	−0.151636	−	0.208709i
$449$	−5.72820e6	−	1.86121e6i	−1.34092	−	0.435691i	−0.451291	−	0.892377i	$-0.649036\pi$
$449$	−5.72820e6	−	1.86121e6i	−1.34092	−	0.435691i	−0.889628	+	0.456686i	$0.849036\pi$
$450$	−719204.	+	731573.i	−0.167425	+	0.170305i
$451$	3.86282e6	−	3.75216e6i	0.894258	−	0.868641i
$452$			3.02240e6i			0.695835i
$453$	−4.63420e6	+	384604.i	−1.06103	+	0.0880578i
$454$	2.61892e6	−	1.90276e6i	0.596325	−	0.433256i
$455$	260122.	−	358028.i	0.0589046	−	0.0810752i
$456$	4.17874e6	−	3.59990e6i	0.941094	−	0.810734i
$457$	2.75445e6	−	894976.i	0.616943	−	0.200457i	0.0161604	−	0.999869i	$-0.494856\pi$
$457$	2.75445e6	−	894976.i	0.616943	−	0.200457i	0.600783	+	0.799412i	$0.294856\pi$
$458$	−2.95040e6	−	2.14359e6i	−0.657231	−	0.477506i
$459$	57263.1	+	225759.i	0.0126865	+	0.0500165i
$460$	360801.	−	1.11043e6i	0.0795012	−	0.244679i
$461$	−7.38752e6			−1.61900			−0.809500	−	0.587120i	$-0.800261\pi$
$461$	−7.38752e6			−1.61900			−0.809500	+	0.587120i	$0.800261\pi$
$462$	1.34236e6	−	307730.i	0.292593	−	0.0670757i
$463$	−539443.			−0.116948			−0.0584740	−	0.998289i	$-0.518623\pi$
$463$	−539443.			−0.116948			−0.0584740	+	0.998289i	$0.518623\pi$
$464$	−211439.	+	650743.i	−0.0455922	+	0.140318i
$465$	1.55745e6	+	945301.i	0.334028	+	0.202739i
$466$	−3.00477e6	−	2.18309e6i	−0.640983	−	0.465701i
$467$	3.51676e6	−	1.14267e6i	0.746193	−	0.242453i	0.0888504	−	0.996045i	$-0.471681\pi$
$467$	3.51676e6	−	1.14267e6i	0.746193	−	0.242453i	0.657342	+	0.753592i	$0.271681\pi$
$468$	−353657.	+	708969.i	−0.0746392	+	0.149628i
$469$	1.44612e6	−	1.99041e6i	0.303579	−	0.417840i
$470$	−997278.	+	724565.i	−0.208244	+	0.151298i
$471$	−127077.	−	1.53119e6i	−0.0263946	−	0.318036i
$472$			7.18144e6i			1.48374i
$473$	−194855.	−	1.35766e6i	−0.0400459	−	0.279022i
$474$	203690.	+	485883.i	0.0416413	+	0.0993312i
$475$	−2.45859e6	−	798845.i	−0.499980	−	0.162453i
$476$	50955.6	+	70134.3i	0.0103080	+	0.0141877i
$477$	−1.16306e6	−	6.95875e6i	−0.234048	−	1.40034i
$478$	−1.17800e6	−	3.62550e6i	−0.235816	−	0.725769i
$479$	490503.	+	1.50961e6i	0.0976794	+	0.300626i	0.987943	−	0.154820i	$-0.0494797\pi$
$479$	490503.	+	1.50961e6i	0.0976794	+	0.300626i	−0.890263	+	0.455446i	$0.849480\pi$
$480$	−910435.	+	3.86474e6i	−0.180362	+	0.765626i
$481$	1.05736e6	+	1.45533e6i	0.208382	+	0.286813i
$482$	2.12714e6	+	691149.i	0.417041	+	0.135505i
$483$	−1.23492e6	+	517701.i	−0.240864	+	0.100974i
$484$	3.20343e6	+	1.14479e6i	0.621587	+	0.222133i
$485$			5.39291e6i			1.04104i
$486$	3.02069e6	−	302635.i	0.580117	−	0.0581203i
$487$	−4.17014e6	+	3.02978e6i	−0.796761	+	0.578880i	−0.909962	−	0.414692i	$-0.863889\pi$
$487$	−4.17014e6	+	3.02978e6i	−0.796761	+	0.578880i	0.113201	+	0.993572i	$0.463889\pi$
$488$	−1.79428e6	+	2.46961e6i	−0.341068	+	0.469439i
$489$	−210586.	−	244447.i	−0.0398251	−	0.0462287i
$490$	1.66409e6	−	540694.i	0.313102	−	0.101733i
$491$	312167.	+	226803.i	0.0584364	+	0.0424565i	0.616620	−	0.787261i	$-0.288502\pi$
$491$	312167.	+	226803.i	0.0584364	+	0.0424565i	−0.558184	+	0.829717i	$0.688502\pi$
$492$	2.29256e6	−	3.77717e6i	0.426981	−	0.703483i
$493$	−132525.	+	407870.i	−0.0245573	+	0.0755795i
$494$	1.02808e6			0.189544
$495$	−3.37387e6	−	2.48235e6i	−0.618892	−	0.455355i
$496$	−266927.			−0.0487178
$497$	1.06986e6	−	3.29269e6i	0.194283	−	0.597942i
$498$	−1.24756e6	+	2.05545e6i	−0.225418	+	0.371393i
$499$	−730334.	−	530618.i	−0.131302	−	0.0953962i	0.520196	−	0.854047i	$-0.325859\pi$
$499$	−730334.	−	530618.i	−0.131302	−	0.0953962i	−0.651498	+	0.758651i	$0.725859\pi$
$500$	3.80101e6	−	1.23502e6i	0.679946	−	0.220928i
$501$	826001.	+	958817.i	0.147023	+	0.170664i
$502$	−686216.	+	944495.i	−0.121535	+	0.167279i
$503$	2.99564e6	−	2.17646e6i	0.527922	−	0.383558i	−0.291658	−	0.956523i	$-0.594207\pi$
$503$	2.99564e6	−	2.17646e6i	0.527922	−	0.383558i	0.819580	+	0.572965i	$0.194207\pi$
$504$	2.52097e6	−	1.31169e6i	0.442071	−	0.230014i
$505$			4.37745e6i			0.763823i
$506$	1.67827e6	+	290869.i	0.291396	+	0.0505034i
$507$	4.99529e6	−	2.09411e6i	0.863060	−	0.361809i
$508$	−558269.	−	181393.i	−0.0959808	−	0.0311861i
$509$	−617505.	−	849923.i	−0.105644	−	0.145407i	0.752921	−	0.658110i	$-0.228644\pi$
$509$	−617505.	−	849923.i	−0.105644	−	0.145407i	−0.858566	+	0.512704i	$0.828644\pi$
$510$	−31133.5	+	132160.i	−0.00530033	+	0.0224995i
$511$	1.49853e6	+	4.61199e6i	0.253870	+	0.781332i
$512$	−349720.	−	1.07633e6i	−0.0589583	−	0.181455i
$513$	4.08013e6	+	6.47093e6i	0.684511	+	1.08561i
$514$	−2.80244e6	−	3.85723e6i	−0.467873	−	0.643972i
$515$	7.21749e6	+	2.34511e6i	1.19914	+	0.389623i
$516$	−435084.	−	1.03785e6i	−0.0719364	−	0.171597i
$517$	2.43318e6	+	2.50493e6i	0.400357	+	0.412164i
$518$		−	2.56559e6i		−	0.420111i
$519$	94596.5	+	1.13982e6i	0.0154155	+	0.185746i
$520$	−939744.	+	682764.i	−0.152406	+	0.110729i
$521$	−909723.	+	1.25213e6i	−0.146830	+	0.202094i	−0.876097	−	0.482135i	$-0.839861\pi$
$521$	−909723.	+	1.25213e6i	−0.146830	+	0.202094i	0.729267	+	0.684229i	$0.239861\pi$
$522$	5.00211e6	+	2.49521e6i	0.803483	+	0.400804i
$523$	4.09185e6	−	1.32952e6i	0.654131	−	0.212540i	0.0368965	−	0.999319i	$-0.488253\pi$
$523$	4.09185e6	−	1.32952e6i	0.654131	−	0.212540i	0.617235	+	0.786779i	$0.288253\pi$
$524$	373769.	+	271559.i	0.0594669	+	0.0432052i
$525$	−1.13863e6	−	691091.i	−0.180295	−	0.109430i
$526$	64980.7	−	199990.i	0.0102405	−	0.0315169i
$527$	−167303.			−0.0262408
$528$	611271.	+	54428.7i	0.0954221	+	0.00849656i
$529$	4.78022e6			0.742692
$530$	1.27098e6	−	3.91167e6i	0.196539	−	0.604885i
$531$	−9.85072e6	−	1.47422e6i	−1.51611	−	0.226896i
$532$	2.30356e6	+	1.67364e6i	0.352875	+	0.256379i
$533$	1.96991e6	−	640063.i	0.300351	−	0.0975899i
$534$	1.43517e6	−	1.23637e6i	0.217796	−	0.187627i
$535$	2.46109e6	−	3.38740e6i	0.371743	−	0.511661i
$536$	−5.22438e6	+	3.79574e6i	−0.785458	+	0.570669i
$537$	−1.05170e6	+	87283.2i	−0.157383	+	0.0130616i
$538$		−	2.88433e6i		−	0.429624i
$539$	−2.18593e6	−	4.44878e6i	−0.324090	−	0.659582i
$540$	−3.19171e6	−	1.27448e6i	−0.471020	−	0.188082i
$541$	−7.84180e6	−	2.54795e6i	−1.15192	−	0.374282i	−0.330054	−	0.943962i	$-0.607067\pi$
$541$	−7.84180e6	−	2.54795e6i	−1.15192	−	0.374282i	−0.821866	+	0.569680i	$0.807067\pi$
$542$	1.87704e6	+	2.58353e6i	0.274458	+	0.377759i
$543$	−4.60575e6	−	1.08500e6i	−0.670349	−	0.157917i
$544$	−112671.	−	346767.i	−0.0163236	−	0.0502389i
$545$	−2.91746e6	−	8.97901e6i	−0.420740	−	1.29490i
$546$	515590.	+	121460.i	0.0740155	+	0.0174362i
$547$	4.47609e6	+	6.16081e6i	0.639633	+	0.880379i	0.998596	−	0.0529727i	$-0.0168696\pi$
$547$	4.47609e6	+	6.16081e6i	0.639633	+	0.880379i	−0.358963	+	0.933352i	$0.616870\pi$
$548$	−3.18041e6	−	1.03338e6i	−0.452409	−	0.146997i
$549$	−3.01921e6	−	2.96817e6i	−0.427526	−	0.420298i
$550$	747157.	+	1.52060e6i	0.105319	+	0.214343i
$551$			1.40859e7i			1.97654i
$552$	3.50267e6	−	290695.i	0.489273	−	0.0406059i
$553$	−553388.	+	402060.i	−0.0769515	+	0.0559085i
$554$	81736.6	−	112501.i	0.0113147	−	0.0155733i
$555$	−5.91196e6	+	5.09303e6i	−0.814702	+	0.701850i
$556$	4.57461e6	−	1.48638e6i	0.627577	−	0.203912i
$557$	6.77355e6	+	4.92127e6i	0.925077	+	0.672108i	0.944783	−	0.327698i	$-0.106273\pi$
$557$	6.77355e6	+	4.92127e6i	0.925077	+	0.672108i	−0.0197051	+	0.999806i	$0.506273\pi$
$558$	−322760.	+	2.15667e6i	−0.0438828	+	0.293223i
$559$	163020.	−	501725.i	0.0220654	−	0.0679104i
$560$	−281255.			−0.0378992
$561$	383129.	+	34114.5i	0.0513971	+	0.00457649i
$562$	4.74368e6			0.633540
$563$	1.99413e6	−	6.13729e6i	0.265144	−	0.816030i	−0.726516	−	0.687149i	$-0.758862\pi$
$563$	1.99413e6	−	6.13729e6i	0.265144	−	0.816030i	0.991660	−	0.128880i	$-0.0411382\pi$
$564$	2.44939e6	+	1.48666e6i	0.324236	+	0.196796i
$565$	−4.97220e6	−	3.61251e6i	−0.655281	−	0.476089i
$566$	−7.24216e6	+	2.35312e6i	−0.950226	+	0.308747i
$567$	1.28172e6	+	3.72726e6i	0.167431	+	0.486892i
$568$	−5.34141e6	+	7.35181e6i	−0.694680	+	0.956145i
$569$	1.85632e6	−	1.34870e6i	0.240365	−	0.174636i	−0.461081	−	0.887358i	$-0.652538\pi$
$569$	1.85632e6	−	1.34870e6i	0.240365	−	0.174636i	0.701446	+	0.712723i	$0.252538\pi$
$570$	368845.	+	4.44432e6i	0.0475507	+	0.572952i
$571$		−	6.81659e6i		−	0.874938i	−0.899234	−	0.437469i	$-0.855875\pi$
$571$		−	6.81659e6i		−	0.874938i	0.899234	−	0.437469i	$-0.144125\pi$
$572$	911668.	+	938555.i	0.116506	+	0.119942i
$573$	3.91847e6	+	9.34713e6i	0.498575	+	1.18930i
$574$	−2.80951e6	−	912866.i	−0.355919	−	0.115645i
$575$	−968279.	−	1.33272e6i	−0.122132	−	0.168101i
$576$	−3.93509e6	+	657696.i	−0.494195	+	0.0825978i
$577$	57163.4	+	175931.i	0.00714791	+	0.0219990i	0.954567	−	0.297997i	$-0.0963185\pi$
$577$	57163.4	+	175931.i	0.00714791	+	0.0219990i	−0.947419	+	0.319996i	$0.896318\pi$
$578$	1.44321e6	+	4.44173e6i	0.179684	+	0.553010i
$579$	2.06338e6	−	8.75892e6i	0.255790	−	1.08581i
$580$	−3.71962e6	−	5.11961e6i	−0.459122	−	0.631927i
$581$	−2.96895e6	−	964670.i	−0.364890	−	0.118560i
$582$	−5.95307e6	+	2.49562e6i	−0.728506	+	0.305402i
$583$	−1.14805e7	−	1.98975e6i	−1.39891	−	0.242453i
$584$		−	1.27284e7i		−	1.54434i
$585$	−743629.	−	1.42920e6i	−0.0898393	−	0.172664i
$586$	−1.10468e6	+	802594.i	−0.132890	+	0.0965499i
$587$	9.41513e6	−	1.29588e7i	1.12780	−	1.55228i	0.335612	−	0.942000i	$-0.391057\pi$
$587$	9.41513e6	−	1.29588e7i	1.12780	−	1.55228i	0.792185	−	0.610280i	$-0.208943\pi$
$588$	−2.65446e6	−	3.08128e6i	−0.316616	−	0.367526i
$589$	−5.22611e6	+	1.69807e6i	−0.620713	+	0.201682i
$590$	−4.69762e6	−	3.41302e6i	−0.555582	−	0.403654i
$591$	−3.35084e6	+	5.52077e6i	−0.394626	+	0.650176i
$592$	353287.	−	1.08731e6i	0.0414308	−	0.127511i
$593$	1.03545e7			1.20918			0.604591	−	0.796536i	$-0.293336\pi$
$593$	1.03545e7			1.20918			0.604591	+	0.796536i	$0.293336\pi$
$594$	1.17890e6	−	4.87304e6i	0.137091	−	0.566674i
$595$	−176284.			−0.0204136
$596$	−3.00648e6	+	9.25300e6i	−0.346691	+	1.06701i
$597$	3.03960e6	−	5.00797e6i	0.349044	−	0.575077i
$598$	530012.	+	385076.i	0.0606084	+	0.0440346i
$599$	−2.36085e6	+	767086.i	−0.268844	+	0.0873528i	−0.440337	−	0.897833i	$-0.645141\pi$
$599$	−2.36085e6	+	767086.i	−0.268844	+	0.0873528i	0.171493	+	0.985185i	$0.445141\pi$
$600$	2.28182e6	+	2.64872e6i	0.258764	+	0.300371i
$601$	5.18786e6	−	7.14047e6i	0.585871	−	0.806382i	−0.408453	−	0.912779i	$-0.633932\pi$
$601$	5.18786e6	−	7.14047e6i	0.585871	−	0.806382i	0.994324	+	0.106398i	$0.0339316\pi$
$602$	−608697.	+	442244.i	−0.0684558	+	0.0497360i
$603$	−4.13411e6	−	7.94544e6i	−0.463008	−	0.889866i
$604$			6.30105e6i			0.702782i
$605$	−5.71221e6	+	3.90170e6i	−0.634476	+	0.433377i
$606$	−4.83213e6	+	2.02571e6i	−0.534511	+	0.224076i
$607$	−1.02006e6	−	331438.i	−0.112371	−	0.0365116i	0.252292	−	0.967651i	$-0.418816\pi$
$607$	−1.02006e6	−	331438.i	−0.112371	−	0.0365116i	−0.364663	+	0.931140i	$0.618816\pi$
$608$	−7.03913e6	−	9.68853e6i	−0.772253	−	1.06292i
$609$	−1.66414e6	+	7.06418e6i	−0.181822	+	0.771825i
$610$	−762715.	−	2.34740e6i	−0.0829923	−	0.255424i
$611$	415064.	+	1.27744e6i	0.0449792	+	0.138432i
$612$	311279.	−	52025.9i	0.0335947	−	0.00561489i
$613$	862160.	+	1.18666e6i	0.0926694	+	0.127549i	0.852834	−	0.522182i	$-0.174882\pi$
$613$	862160.	+	1.18666e6i	0.0926694	+	0.127549i	−0.760165	+	0.649730i	$0.774882\pi$
$614$	3.02008e6	+	981283.i	0.323294	+	0.105045i
$615$	3.47370e6	+	8.28618e6i	0.370344	+	0.883418i
$616$	−666747.	−	4.64560e6i	−0.0707961	−	0.493276i
$617$		−	4.28685e6i		−	0.453342i	−0.973971	−	0.226671i	$-0.927216\pi$
$617$		−	4.28685e6i		−	0.453342i	0.973971	−	0.226671i	$-0.0727842\pi$
$618$	751279.	+	9.05238e6i	0.0791280	+	0.953436i
$619$	5.60756e6	−	4.07413e6i	0.588230	−	0.427374i	−0.253452	−	0.967348i	$-0.581566\pi$
$619$	5.60756e6	−	4.07413e6i	0.588230	−	0.427374i	0.841682	+	0.539974i	$0.181566\pi$
$620$	1.45106e6	−	1.99722e6i	0.151603	−	0.208663i
$621$	−320293.	+	4.86425e6i	−0.0333287	+	0.506159i
$622$	−302540.	+	98301.1i	−0.0313550	+	0.0101878i
$623$	1.98970e6	+	1.44560e6i	0.205385	+	0.149221i
$624$	201783.	+	122473.i	0.0207455	+	0.0125915i
$625$	−1.27525e6	+	3.92481e6i	−0.130586	+	0.401901i
$626$	−3.40937e6			−0.347727
$627$	1.23142e7	−	2.82298e6i	1.25095	−	0.286773i
$628$	−2.08193e6			−0.210653
$629$	221431.	−	681496.i	0.0223158	−	0.0686810i
$630$	−340085.	+	2.27244e6i	−0.0341379	+	0.228108i
$631$	8.02071e6	+	5.82739e6i	0.801936	+	0.582640i	0.911481	−	0.411341i	$-0.134940\pi$
$631$	8.02071e6	+	5.82739e6i	0.801936	+	0.582640i	−0.109546	+	0.993982i	$0.534940\pi$
$632$	1.70754e6	−	554814.i	0.170051	−	0.0552528i
$633$	−6.14001e6	+	5.28949e6i	−0.609059	+	0.524692i
$634$	4.63736e6	−	6.38277e6i	0.458192	−	0.630647i
$635$	965681.	−	701609.i	0.0950385	−	0.0690495i
$636$	−9.52732e6	+	790695.i	−0.933959	+	0.0775115i
$637$		−	1.90653e6i		−	0.186163i
$638$	6.62195e6	−	6.43225e6i	0.644071	−	0.625620i
$639$	−8.98792e6	−	8.83596e6i	−0.870777	−	0.856055i
$640$	5.53977e6	+	1.79998e6i	0.534616	+	0.173707i
$641$	1.02647e7	+	1.41282e7i	0.986737	+	1.35813i	0.933120	+	0.359565i	$0.117075\pi$
$641$	1.02647e7	+	1.41282e7i	0.986737	+	1.35813i	0.0536166	+	0.998562i	$0.482925\pi$
$642$	4.87814e6	+	1.14917e6i	0.467107	+	0.110039i
$643$	3.74542e6	+	1.15272e7i	0.357250	+	1.09950i	0.954693	+	0.297592i	$0.0961834\pi$
$643$	3.74542e6	+	1.15272e7i	0.357250	+	1.09950i	−0.597443	+	0.801911i	$0.703817\pi$
$644$	560694.	+	1.72564e6i	0.0532735	+	0.163959i
$645$	2.22741e6	+	524723.i	0.210815	+	0.0496627i
$646$	−240712.	−	331312.i	−0.0226943	−	0.0312360i
$647$	−255495.	−	83015.3i	−0.0239950	−	0.00779646i	0.296995	−	0.954879i	$-0.404016\pi$
$647$	−255495.	−	83015.3i	−0.0239950	−	0.00779646i	−0.320990	+	0.947083i	$0.604016\pi$
$648$	−176396.	−	1.03440e7i	−0.0165026	−	0.967725i
$649$	−7.68010e6	+	1.45466e7i	−0.715740	+	1.35565i
$650$			651655.i			0.0604971i
$651$	−2.82155e6	+	234167.i	−0.260937	+	0.0216558i
$652$	−353697.	+	256976.i	−0.0325846	+	0.0236741i
$653$	2.78584e6	−	3.83438e6i	0.255666	−	0.351895i	−0.661819	−	0.749663i	$-0.730215\pi$
$653$	2.78584e6	−	3.83438e6i	0.255666	−	0.351895i	0.917486	+	0.397769i	$0.130215\pi$
$654$	8.56157e6	−	7.37562e6i	0.782724	−	0.674301i
$655$	−893493.	+	290313.i	−0.0813744	+	0.0264401i
$656$	−1.06497e6	−	773750.i	−0.0966228	−	0.0702006i
$657$	1.74595e7	+	2.61292e6i	1.57804	+	0.236164i
$658$	591969.	−	1.82189e6i	0.0533009	−	0.164043i
$659$	1.07295e7			0.962425			0.481212	−	0.876604i	$-0.340197\pi$
$659$	1.07295e7			0.962425			0.481212	+	0.876604i	$0.340197\pi$
$660$	−3.73024e6	+	4.27781e6i	−0.333332	+	0.382263i
$661$	−1.60341e6			−0.142738			−0.0713690	−	0.997450i	$-0.522737\pi$
$661$	−1.60341e6			−0.142738			−0.0713690	+	0.997450i	$0.522737\pi$
$662$	892574.	−	2.74706e6i	0.0791588	−	0.243626i
$663$	126472.	+	76762.8i	0.0111741	+	0.00678214i
$664$	6.62898e6	+	4.81624e6i	0.583481	+	0.423924i
$665$	−5.50665e6	+	1.78922e6i	−0.482873	+	0.156895i
$666$	−8.35785e6	−	4.16917e6i	−0.730145	−	0.364220i
$667$	−5.27599e6	+	7.26178e6i	−0.459187	+	0.632017i
$668$	1.38734e6	−	1.00796e6i	0.120293	−	0.0873983i
$669$	1.39907e6	+	1.68578e7i	0.120857	+	1.45624i
$670$		−	5.22139e6i		−	0.449365i
$671$	−6.27555e6	+	3.08353e6i	−0.538078	+	0.264388i
$672$	−2.38555e6	−	5.69049e6i	−0.203782	−	0.486101i
$673$	1.19036e7	+	3.86771e6i	1.01307	+	0.329167i	0.768077	−	0.640358i	$-0.221214\pi$
$673$	1.19036e7	+	3.86771e6i	1.01307	+	0.329167i	0.244995	+	0.969524i	$0.421214\pi$
$674$	7.29415e6	+	1.00395e7i	0.618479	+	0.851264i
$675$	−4.10165e6	+	2.58622e6i	−0.346496	+	0.218477i
$676$	−2.26802e6	−	6.98025e6i	−0.190889	−	0.587495i
$677$	2.61432e6	+	8.04604e6i	0.219223	+	0.674699i	0.998827	+	0.0484262i	$0.0154206\pi$
$677$	2.61432e6	+	8.04604e6i	0.219223	+	0.674699i	−0.779604	+	0.626273i	$0.784579\pi$
$678$	1.68681e6	−	7.16038e6i	0.140926	−	0.598221i
$679$	−4.92606e6	−	6.78015e6i	−0.410039	−	0.564371i
$680$	440059.	+	142984.i	0.0364955	+	0.0118581i
$681$	1.41108e7	−	5.91550e6i	1.16596	−	0.488791i
$682$	3.18476e6	+	1.68145e6i	0.262190	+	0.138427i
$683$		−	1.53241e7i		−	1.25697i	−0.777823	−	0.628484i	$-0.783676\pi$
$683$		−	1.53241e7i		−	1.25697i	0.777823	−	0.628484i	$-0.216324\pi$
$684$	9.19550e6	−	4.78453e6i	0.751511	−	0.391020i
$685$	5.50140e6	−	3.99700e6i	0.447968	−	0.325468i
$686$	−3.77304e6	+	5.19314e6i	−0.306112	+	0.421327i
$687$	−1.12505e7	−	1.30595e7i	−0.909449	−	1.05568i
$688$	−318865.	+	103606.i	−0.0256824	+	0.00834472i
$689$	−3.62566e6	−	2.63420e6i	−0.290964	−	0.211398i
$690$	−1.47451e6	+	2.42936e6i	−0.117903	+	0.194254i
$691$	586069.	−	1.80374e6i	0.0466932	−	0.143707i	−0.924992	−	0.379987i	$-0.875928\pi$
$691$	586069.	−	1.80374e6i	0.0466932	−	0.143707i	0.971685	+	0.236280i	$0.0759284\pi$
$692$	1.54980e6			0.123030
$693$	6.50920e6	+	39088.3i	0.514866	+	0.00309181i
$694$	−1.19253e7			−0.939879
$695$	−3.02252e6	+	9.30235e6i	−0.237360	+	0.730518i
$696$	9.88399e6	−	1.62846e7i	0.773409	−	1.27425i
$697$	−667499.	−	484967.i	−0.0520438	−	0.0378120i
$698$	−8.38318e6	+	2.72386e6i	−0.651284	+	0.211615i
$699$	−1.14578e7	−	1.33001e7i	−0.886966	−	1.02958i
$700$	−1.06085e6	+	1.46013e6i	−0.0818290	+	0.112628i
$701$	−1.05589e7	+	7.67151e6i	−0.811568	+	0.589639i	−0.914285	−	0.405072i	$-0.867246\pi$
$701$	−1.05589e7	+	7.67151e6i	−0.811568	+	0.589639i	0.102717	+	0.994711i	$0.467246\pi$
$702$	1.23353e6	−	1.48224e6i	0.0944725	−	0.113521i
$703$		−	2.35356e7i		−	1.79613i
$704$	−1.12518e6	+	6.49212e6i	−0.0855640	+	0.493691i
$705$	−5.37336e6	+	2.25260e6i	−0.407168	+	0.170692i
$706$	8.48159e6	+	2.75584e6i	0.640421	+	0.208085i
$707$	−3.99851e6	−	5.50347e6i	−0.300850	−	0.414084i
$708$	−3.09475e6	+	1.31370e7i	−0.232029	+	0.984949i
$709$	1.69994e6	+	5.23188e6i	0.127004	+	0.390879i	0.994261	−	0.106982i	$-0.0341188\pi$
$709$	1.69994e6	+	5.23188e6i	0.127004	+	0.390879i	−0.867257	+	0.497861i	$0.834119\pi$
$710$	−2.27053e6	−	6.98798e6i	−0.169037	−	0.520243i
$711$	410505.	+	2.45611e6i	0.0304540	+	0.182211i
$712$	−3.79439e6	−	5.22253e6i	−0.280506	−	0.386083i
$713$	−3.33028e6	−	1.08207e6i	−0.245333	−	0.0797136i
$714$	−81577.0	−	194594.i	−0.00598856	−	0.0142851i
$715$	−2.63370e6	+	377995.i	−0.192664	+	0.0276516i
$716$			1.42998e6i			0.104243i
$717$	−1.49023e6	−	1.79562e7i	−0.108257	−	1.30442i
$718$	−1.05358e7	+	7.65469e6i	−0.762703	+	0.554136i
$719$	−1.49201e7	+	2.05358e7i	−1.07634	+	1.48146i	−0.212855	+	0.977084i	$0.568276\pi$
$719$	−1.49201e7	+	2.05358e7i	−1.07634	+	1.48146i	−0.863486	+	0.504373i	$0.831724\pi$
$720$	−457048.	+	916235.i	−0.0328572	+	0.0658682i
$721$	−1.12162e7	+	3.64435e6i	−0.803538	+	0.261085i
$722$	−4.27522e6	−	3.10613e6i	−0.305222	−	0.221757i
$723$	9.03708e6	+	5.48508e6i	0.642958	+	0.390245i
$724$	−1.98134e6	+	6.09793e6i	−0.140479	+	0.432350i
$725$	−8.92843e6			−0.630856
$726$	−6.95035e6	−	4.49997e6i	−0.489401	−	0.316860i
$727$	581464.			0.0408025			0.0204012	−	0.999792i	$-0.493506\pi$
$727$	581464.			0.0408025			0.0204012	+	0.999792i	$0.493506\pi$
$728$	557818.	−	1.71679e6i	0.0390089	−	0.120057i
$729$	1.42250e7	+	1.88149e6i	0.991366	+	0.131124i
$730$	8.32609e6	+	6.04926e6i	0.578274	+	0.420141i
$731$	−199857.	+	64937.4i	−0.0138333	+	0.00449470i
$732$	−4.34653e6	+	3.74445e6i	−0.299823	+	0.258291i
$733$	−505342.	+	695544.i	−0.0347397	+	0.0478151i	−0.826034	−	0.563621i	$-0.809408\pi$
$733$	−505342.	+	695544.i	−0.0347397	+	0.0478151i	0.791294	+	0.611436i	$0.209408\pi$
$734$	1.06262e7	−	7.72037e6i	0.728010	−	0.528930i
$735$	8.24180e6	−	684007.i	0.562735	−	0.0467027i
$736$		−	7.63136e6i		−	0.519287i
$737$	−1.46417e7	+	2.10141e6i	−0.992940	+	0.142509i
$738$	−7.53936e6	+	7.66902e6i	−0.509558	+	0.518321i
$739$	2.47301e7	+	8.03530e6i	1.66577	+	0.541241i	0.982069	−	0.188521i	$-0.0603695\pi$
$739$	2.47301e7	+	8.03530e6i	1.66577	+	0.541241i	0.683700	+	0.729763i	$0.260369\pi$
$740$	6.21498e6	+	8.55419e6i	0.417216	+	0.574248i
$741$	4.72979e6	+	1.11422e6i	0.316444	+	0.0745462i
$742$	1.97513e6	+	6.07884e6i	0.131700	+	0.405332i
$743$	−2.14598e6	−	6.60464e6i	−0.142611	−	0.438912i	0.854085	−	0.520134i	$-0.174118\pi$
$743$	−2.14598e6	−	6.60464e6i	−0.142611	−	0.438912i	−0.996696	+	0.0812217i	$0.974118\pi$
$744$	7.23341e6	+	1.70401e6i	0.479083	+	0.112860i
$745$	−1.16288e7	−	1.60056e7i	−0.767614	−	1.05653i
$746$	−6.63241e6	−	2.15500e6i	−0.436339	−	0.141775i
$747$	−7.96721e6	+	8.10423e6i	−0.522402	+	0.531386i
$748$	89005.6	−	513548.i	0.00581652	−	0.0335604i
$749$			6.50679e6i			0.423801i
$750$	−9.69426e6	+	804550.i	−0.629306	+	0.0522276i
$751$	−1.22373e7	+	8.89089e6i	−0.791743	+	0.575235i	−0.908480	−	0.417928i	$-0.862756\pi$
$751$	−1.22373e7	+	8.89089e6i	−0.791743	+	0.575235i	0.116737	+	0.993163i	$0.462756\pi$
$752$	501756.	−	690608.i	0.0323555	−	0.0445335i
$753$	−4.18064e6	+	3.60154e6i	−0.268693	+	0.231473i
$754$	3.37698e6	−	1.09725e6i	0.216322	−	0.0702871i
$755$	−1.03660e7	−	7.53131e6i	−0.661823	−	0.480843i
$756$	5.17687e6	−	1.31310e6i	0.329430	−	0.0835588i
$757$	3.88222e6	−	1.19482e7i	0.246230	−	0.757817i	−0.749202	−	0.662341i	$-0.769563\pi$
$757$	3.88222e6	−	1.19482e7i	0.246230	−	0.757817i	0.995432	−	0.0954755i	$-0.0304372\pi$
$758$	3.24399e6			0.205072
$759$	7.40580e6	+	3.15706e6i	0.466625	+	0.198920i
$760$	1.51976e7			0.954420
$761$	−1.67326e6	+	5.14975e6i	−0.104737	+	0.322348i	−0.989669	−	0.143373i	$-0.954205\pi$
$761$	−1.67326e6	+	5.14975e6i	−0.104737	+	0.322348i	0.884932	+	0.465721i	$0.154205\pi$
$762$	1.22136e6	+	741309.i	0.0762004	+	0.0462500i
$763$	1.18697e7	+	8.62381e6i	0.738119	+	0.536275i
$764$	1.30613e7	−	4.24389e6i	0.809570	−	0.263045i
$765$	−286466.	+	574273.i	−0.0176978	+	0.0354785i
$766$	−7.92773e6	+	1.09116e7i	−0.488177	+	0.671918i
$767$	−5.11861e6	+	3.71889e6i	−0.314169	+	0.228257i
$768$	1.25402e6	+	1.51101e7i	0.0767189	+	0.924408i

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01916 + 3.13665i) q^{2} +(-8.08821 + 13.3259i) q^{3} +(17.0887 + 12.4156i) q^{4} +(-40.8503 + 13.2731i) q^{5} +(-33.5556 - 38.9511i) q^{6} +(39.2343 - 54.0014i) q^{7} +(-141.742 + 102.981i) q^{8} +(-112.162 - 215.566i) q^{9} +O(q^{10})\)	\(q+(-1.01916 + 3.13665i) q^{2} +(-8.08821 + 13.3259i) q^{3} +(17.0887 + 12.4156i) q^{4} +(-40.8503 + 13.2731i) q^{5} +(-33.5556 - 38.9511i) q^{6} +(39.2343 - 54.0014i) q^{7} +(-141.742 + 102.981i) q^{8} +(-112.162 - 215.566i) q^{9} -141.660i q^{10} +(-397.241 + 57.0130i) q^{11} +(-303.667 + 127.302i) q^{12} +(-146.801 - 47.6985i) q^{13} +(129.397 + 178.100i) q^{14} +(153.530 - 651.725i) q^{15} +(30.3142 + 93.2975i) q^{16} +(19.0002 + 58.4765i) q^{17} +(790.466 - 132.115i) q^{18} +(1187.03 + 1633.81i) q^{19} +(-862.872 - 280.364i) q^{20} +(402.284 + 959.609i) q^{21} +(226.022 - 1304.11i) q^{22} +1286.90i q^{23} +(-225.887 - 2721.78i) q^{24} +(-1035.60 + 752.410i) q^{25} +(299.227 - 411.851i) q^{26} +(3779.81 + 248.886i) q^{27} +(1340.92 - 435.693i) q^{28} +(5642.83 + 4099.76i) q^{29} +(1887.76 + 1145.78i) q^{30} +(-840.834 + 2587.82i) q^{31} -5930.01 q^{32} +(2453.22 - 5754.75i) q^{33} -202.785 q^{34} +(-885.970 + 2726.73i) q^{35} +(759.701 - 5076.30i) q^{36} +(-9428.42 - 6850.15i) q^{37} +(-6334.47 + 2058.19i) q^{38} +(1822.99 - 1570.47i) q^{39} +(4423.32 - 6088.17i) q^{40} +(-10856.1 + 7887.45i) q^{41} +(-3419.95 + 283.830i) q^{42} +3417.72i q^{43} +(-7496.17 - 3957.73i) q^{44} +(7443.06 + 7317.22i) q^{45} +(-4036.56 - 1311.56i) q^{46} +(-5114.80 - 7039.92i) q^{47} +(-1488.47 - 350.645i) q^{48} +(3816.83 + 11747.0i) q^{49} +(-1304.60 - 4015.15i) q^{50} +(-932.933 - 219.775i) q^{51} +(-1916.42 - 2637.73i) q^{52} +(27613.0 + 8972.01i) q^{53} +(-4632.90 + 11602.3i) q^{54} +(15470.7 - 7601.61i) q^{55} +11694.7i q^{56} +(-31373.1 + 2603.73i) q^{57} +(-18610.4 + 13521.3i) q^{58} +(24093.0 - 33161.1i) q^{59} +(10715.2 - 9230.93i) q^{60} +(16570.6 - 5384.11i) q^{61} +(-7260.14 - 5274.80i) q^{62} +(-16041.5 - 2400.71i) q^{63} +(5073.57 - 15614.8i) q^{64} +6629.97 q^{65} +(15550.4 + 13559.9i) q^{66} +36858.5 q^{67} +(-401.336 + 1235.19i) q^{68} +(-17149.2 - 10408.8i) q^{69} +(-7649.86 - 5557.95i) q^{70} +(49329.1 - 16028.0i) q^{71} +(38097.3 + 19004.2i) q^{72} +(-42702.5 + 58774.9i) q^{73} +(31095.6 - 22592.3i) q^{74} +(-1650.39 - 19886.0i) q^{75} +42657.5i q^{76} +(-12506.7 + 23688.4i) q^{77} +(3068.09 + 7318.62i) q^{78} +(-9746.11 - 3166.70i) q^{79} +(-2476.69 - 3408.87i) q^{80} +(-33888.6 + 48356.5i) q^{81} +(-13676.0 - 42090.5i) q^{82} +(-14452.1 - 44479.1i) q^{83} +(-5039.66 + 21393.0i) q^{84} +(-1552.33 - 2136.60i) q^{85} +(-10720.2 - 3483.20i) q^{86} +(-100274. + 42036.4i) q^{87} +(50434.4 - 48989.6i) q^{88} +36845.4i q^{89} +(-30537.2 + 15888.9i) q^{90} +(-8335.42 + 6056.04i) q^{91} +(-15977.7 + 21991.5i) q^{92} +(-27684.3 - 32135.8i) q^{93} +(27294.5 - 8868.53i) q^{94} +(-70176.4 - 50986.2i) q^{95} +(47963.2 - 79023.0i) q^{96} +(38798.6 - 119410. i) q^{97} -40736.1 q^{98} +(56845.3 + 79237.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72q + 18q^{3} - 262q^{4} + 15q^{6} - 10q^{7} + 292q^{9} + O(q^{10}) \)	\( 72q + 18q^{3} - 262q^{4} + 15q^{6} - 10q^{7} + 292q^{9} + 1854q^{12} - 10q^{13} - 762q^{15} - 10122q^{16} + 4815q^{18} + 4460q^{19} + 4628q^{22} - 805q^{24} + 13708q^{25} + 6108q^{27} - 28130q^{28} - 15470q^{30} + 4340q^{31} - 508q^{33} + 18732q^{34} - 56461q^{36} + 978q^{37} + 23360q^{39} + 69750q^{40} + 60788q^{42} - 31356q^{45} - 52090q^{46} + 4238q^{48} - 58448q^{49} - 178950q^{51} - 14190q^{52} + 86600q^{55} + 266190q^{57} + 137102q^{58} + 284090q^{60} - 77890q^{61} - 120330q^{63} - 379114q^{64} - 323304q^{66} + 42668q^{67} - 271816q^{69} + 87176q^{70} + 343960q^{72} + 116440q^{73} + 326202q^{75} + 155512q^{78} - 350590q^{79} - 208088q^{81} - 606424q^{82} - 220680q^{84} + 665610q^{85} + 1152974q^{88} + 293440q^{90} + 621014q^{91} + 478456q^{93} - 521270q^{94} - 1246430q^{96} - 1030446q^{97} - 590000q^{99} + O(q^{100}) \)

Introduction

L-functions

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