LMFDB - Embedded newform 119.5.h.a.101.40

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(33,119)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("119.33"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.40
Character	$\chi$	$=$	119.101
Dual form			119.5.h.a.33.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.16216 + 5.47702i) q^{2} +(3.04558 - 5.27510i) q^{3} +(-11.9985 + 20.7820i) q^{4} +(-13.4734 - 23.3365i) q^{5} +38.5225 q^{6} +(41.9102 + 25.3877i) q^{7} -50.5753 q^{8} +(21.9488 + 38.0165i) q^{9} +(85.2097 - 147.588i) q^{10} +(123.338 + 71.2093i) q^{11} +(73.0847 + 126.586i) q^{12} +211.513i q^{13} +(-6.52207 + 309.823i) q^{14} -164.137 q^{15} +(32.0486 + 55.5098i) q^{16} +(-287.115 - 32.9519i) q^{17} +(-138.811 + 240.428i) q^{18} +(518.456 - 299.330i) q^{19} +646.639 q^{20} +(261.564 - 143.760i) q^{21} +900.700i q^{22} +(-214.486 + 123.834i) q^{23} +(-154.031 + 266.790i) q^{24} +(-50.5624 + 87.5766i) q^{25} +(-1158.46 + 668.837i) q^{26} +760.773 q^{27} +(-1030.47 + 566.364i) q^{28} -875.656i q^{29} +(-519.027 - 898.980i) q^{30} +(621.230 - 1076.00i) q^{31} +(-607.288 + 1051.85i) q^{32} +(751.273 - 433.747i) q^{33} +(-727.426 - 1676.73i) q^{34} +(27.7893 - 1320.10i) q^{35} -1053.41 q^{36} +(-437.792 + 252.759i) q^{37} +(3278.88 + 1893.06i) q^{38} +(1115.75 + 644.180i) q^{39} +(681.419 + 1180.25i) q^{40} -2117.57 q^{41} +(1614.48 + 977.996i) q^{42} -2587.32 q^{43} +(-2959.74 + 1708.81i) q^{44} +(591.449 - 1024.42i) q^{45} +(-1356.48 - 783.163i) q^{46} +(934.757 - 539.682i) q^{47} +390.426 q^{48} +(1111.93 + 2128.01i) q^{49} -639.545 q^{50} +(-1048.26 + 1414.21i) q^{51} +(-4395.65 - 2537.83i) q^{52} +(-2700.28 + 4677.02i) q^{53} +(2405.68 + 4166.76i) q^{54} -3837.71i q^{55} +(-2119.62 - 1283.99i) q^{56} -3646.54i q^{57} +(4795.98 - 2768.96i) q^{58} +(1790.24 + 1033.59i) q^{59} +(1969.39 - 3411.09i) q^{60} +(-1918.06 - 3322.18i) q^{61} +7857.70 q^{62} +(-45.2704 + 2150.51i) q^{63} -6655.81 q^{64} +(4935.97 - 2849.79i) q^{65} +(4751.28 + 2743.16i) q^{66} +(1392.61 - 2412.08i) q^{67} +(4129.75 - 5571.45i) q^{68} +1508.58i q^{69} +(7318.06 - 4022.15i) q^{70} -8089.92i q^{71} +(-1110.07 - 1922.70i) q^{72} +(-2651.56 + 4592.64i) q^{73} +(-2768.73 - 1598.53i) q^{74} +(307.984 + 533.444i) q^{75} +14366.0i q^{76} +(3361.29 + 6115.66i) q^{77} +8147.99i q^{78} +(6871.41 - 3967.21i) q^{79} +(863.603 - 1495.81i) q^{80} +(539.139 - 933.816i) q^{81} +(-6696.09 - 11598.0i) q^{82} -2253.96i q^{83} +(-150.740 + 7160.72i) q^{84} +(3099.42 + 7144.25i) q^{85} +(-8181.52 - 14170.8i) q^{86} +(-4619.18 - 2666.88i) q^{87} +(-6237.86 - 3601.43i) q^{88} +(5237.92 - 3024.11i) q^{89} +7481.02 q^{90} +(-5369.82 + 8864.54i) q^{91} -5943.26i q^{92} +(-3784.01 - 6554.10i) q^{93} +(5911.70 + 3413.12i) q^{94} +(-13970.7 - 8065.97i) q^{95} +(3699.09 + 6407.01i) q^{96} -13550.6 q^{97} +(-8139.02 + 12819.2i) q^{98} +6251.85i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) $ 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.16216	+	5.47702i	0.790539	+	1.36925i	0.925633	+	0.378422i	$0.123533\pi$
$2$	3.16216	+	5.47702i	0.790539	+	1.36925i	−0.135094	+	0.990833i	$0.543134\pi$
$3$	3.04558	−	5.27510i	0.338398	−	0.586123i	−0.645733	−	0.763563i	$-0.723448\pi$
$3$	3.04558	−	5.27510i	0.338398	−	0.586123i	0.984132	+	0.177440i	$0.0567816\pi$
$4$	−11.9985	+	20.7820i	−0.749905	+	1.29887i
$5$	−13.4734	−	23.3365i	−0.538934	−	0.933461i	−0.998962	−	0.0455566i	$-0.985494\pi$
$5$	−13.4734	−	23.3365i	−0.538934	−	0.933461i	0.460028	−	0.887905i	$-0.347839\pi$
$6$	38.5225			1.07007
$7$	41.9102	+	25.3877i	0.855310	+	0.518116i
$7$	41.9102	+	25.3877i	0.855310	+	0.518116i
$8$	−50.5753			−0.790239
$9$	21.9488	+	38.0165i	0.270973	+	0.469340i
$10$	85.2097	−	147.588i	0.852097	−	1.47588i
$11$	123.338	+	71.2093i	1.01932	+	0.588506i	0.913908	−	0.405922i	$-0.133050\pi$
$11$	123.338	+	71.2093i	1.01932	+	0.588506i	0.105415	+	0.994428i	$0.466383\pi$
$12$	73.0847	+	126.586i	0.507533	+	0.879073i
$13$			211.513i			1.25155i	0.780002	+	0.625777i	$0.215218\pi$
$13$			211.513i			1.25155i	−0.780002	+	0.625777i	$0.784782\pi$
$14$	−6.52207	+	309.823i	−0.0332759	+	1.58073i
$15$	−164.137			−0.729497
$16$	32.0486	+	55.5098i	0.125190	+	0.216835i
$17$	−287.115	−	32.9519i	−0.993478	−	0.114020i
$17$	−287.115	−	32.9519i	−0.993478	−	0.114020i
$18$	−138.811	+	240.428i	−0.428430	+	0.742063i
$19$	518.456	−	299.330i	1.43617	−	0.829170i	0.438585	−	0.898690i	$-0.355480\pi$
$19$	518.456	−	299.330i	1.43617	−	0.829170i	0.997581	+	0.0695196i	$0.0221466\pi$
$20$	646.639			1.61660
$21$	261.564	−	143.760i	0.593115	−	0.325987i
$22$			900.700i			1.86095i
$23$	−214.486	+	123.834i	−0.405456	+	0.234090i	−0.688835	−	0.724918i	$-0.741878\pi$
$23$	−214.486	+	123.834i	−0.405456	+	0.234090i	0.283380	+	0.959008i	$0.408544\pi$
$24$	−154.031	+	266.790i	−0.267416	+	0.463177i
$25$	−50.5624	+	87.5766i	−0.0808998	+	0.140123i
$26$	−1158.46	+	668.837i	−1.71370	+	0.989403i
$27$	760.773			1.04358
$28$	−1030.47	+	566.364i	−1.31437	+	0.722403i
$29$		−	875.656i		−	1.04121i	−0.853798	−	0.520604i	$-0.825707\pi$
$29$		−	875.656i		−	1.04121i	0.853798	−	0.520604i	$-0.174293\pi$
$30$	−519.027	−	898.980i	−0.576696	−	0.998867i
$31$	621.230	−	1076.00i	0.646441	−	1.11967i	−0.337526	−	0.941316i	$-0.609590\pi$
$31$	621.230	−	1076.00i	0.646441	−	1.11967i	0.983967	−	0.178352i	$-0.0570766\pi$
$32$	−607.288	+	1051.85i	−0.593055	+	1.02720i
$33$	751.273	−	433.747i	0.689874	−	0.398299i
$34$	−727.426	−	1676.73i	−0.629261	−	1.45046i
$35$	27.7893	−	1320.10i	0.0226852	−	1.07763i
$36$	−1053.41			−0.812818
$37$	−437.792	+	252.759i	−0.319790	+	0.184631i	−0.651299	−	0.758821i	$-0.725776\pi$
$37$	−437.792	+	252.759i	−0.319790	+	0.184631i	0.331509	+	0.943452i	$0.392442\pi$
$38$	3278.88	+	1893.06i	2.27069	+	1.31098i
$39$	1115.75	+	644.180i	0.733565	+	0.423524i
$40$	681.419	+	1180.25i	0.425887	+	0.737658i
$41$	−2117.57			−1.25971			−0.629854	−	0.776714i	$-0.716885\pi$
$41$	−2117.57			−1.25971			−0.629854	+	0.776714i	$0.716885\pi$
$42$	1614.48	+	977.996i	0.915240	+	0.554419i
$43$	−2587.32			−1.39931			−0.699655	−	0.714481i	$-0.746663\pi$
$43$	−2587.32			−1.39931			−0.699655	+	0.714481i	$0.746663\pi$
$44$	−2959.74	+	1708.81i	−1.52879	+	0.882648i
$45$	591.449	−	1024.42i	0.292074	−	0.505886i
$46$	−1356.48	−	783.163i	−0.641057	−	0.370115i
$47$	934.757	−	539.682i	0.423158	−	0.244311i	−0.273269	−	0.961938i	$-0.588105\pi$
$47$	934.757	−	539.682i	0.423158	−	0.244311i	0.696428	+	0.717627i	$0.254772\pi$
$48$	390.426			0.169456
$49$	1111.93	+	2128.01i	0.463112	+	0.886300i
$50$	−639.545			−0.255818
$51$	−1048.26	+	1414.21i	−0.403021	+	0.543716i
$52$	−4395.65	−	2537.83i	−1.62561	−	0.938547i
$53$	−2700.28	+	4677.02i	−0.961296	+	1.66501i	−0.242042	+	0.970266i	$0.577817\pi$
$53$	−2700.28	+	4677.02i	−0.961296	+	1.66501i	−0.719254	+	0.694747i	$0.755516\pi$
$54$	2405.68	+	4166.76i	0.824994	+	1.42893i
$55$		−	3837.71i		−	1.26866i
$56$	−2119.62	−	1283.99i	−0.675900	−	0.409436i
$57$		−	3646.54i		−	1.12236i
$58$	4795.98	−	2768.96i	1.42568	−	0.823116i
$59$	1790.24	+	1033.59i	0.514288	+	0.296924i	0.734594	−	0.678507i	$-0.237372\pi$
$59$	1790.24	+	1033.59i	0.514288	+	0.296924i	−0.220307	+	0.975431i	$0.570706\pi$
$60$	1969.39	−	3411.09i	0.547054	−	0.947525i
$61$	−1918.06	−	3322.18i	−0.515469	−	0.892819i	−0.999839	−	0.0179552i	$-0.994284\pi$
$61$	−1918.06	−	3322.18i	−0.515469	−	0.892819i	0.484370	−	0.874863i	$-0.339049\pi$
$62$	7857.70			2.04415
$63$	−45.2704	+	2150.51i	−0.0114060	+	0.541827i
$64$	−6655.81			−1.62495
$65$	4935.97	−	2849.79i	1.16828	−	0.674505i
$66$	4751.28	+	2743.16i	1.09074	+	0.629742i
$67$	1392.61	−	2412.08i	0.310228	−	0.537330i	−0.668184	−	0.743996i	$-0.732928\pi$
$67$	1392.61	−	2412.08i	0.310228	−	0.537330i	0.978412	+	0.206666i	$0.0662613\pi$
$68$	4129.75	−	5571.45i	0.893112	−	1.20490i
$69$			1508.58i			0.316862i
$70$	7318.06	−	4022.15i	1.49348	−	0.820847i
$71$		−	8089.92i		−	1.60482i	−0.596770	−	0.802412i	$-0.703549\pi$
$71$		−	8089.92i		−	1.60482i	0.596770	−	0.802412i	$-0.296451\pi$
$72$	−1110.07	−	1922.70i	−0.214134	−	0.370891i
$73$	−2651.56	+	4592.64i	−0.497572	+	0.861819i	−0.999996	−	0.00280171i	$-0.999108\pi$
$73$	−2651.56	+	4592.64i	−0.497572	+	0.861819i	0.502424	+	0.864621i	$0.332442\pi$
$74$	−2768.73	−	1598.53i	−0.505612	−	0.291915i
$75$	307.984	+	533.444i	0.0547527	+	0.0948344i
$76$			14366.0i			2.48720i
$77$	3361.29	+	6115.66i	0.566923	+	1.03148i
$78$			8147.99i			1.33925i
$79$	6871.41	−	3967.21i	1.10101	−	0.635669i	0.164524	−	0.986373i	$-0.447391\pi$
$79$	6871.41	−	3967.21i	1.10101	−	0.635669i	0.936486	+	0.350704i	$0.114058\pi$
$80$	863.603	−	1495.81i	0.134938	−	0.233720i
$81$	539.139	−	933.816i	0.0821733	−	0.142328i
$82$	−6696.09	−	11598.0i	−0.995849	−	1.72486i
$83$		−	2253.96i		−	0.327182i	−0.986528	−	0.163591i	$-0.947692\pi$
$83$		−	2253.96i		−	0.327182i	0.986528	−	0.163591i	$-0.0523077\pi$
$84$	−150.740	+	7160.72i	−0.0213634	+	1.01484i
$85$	3099.42	+	7144.25i	0.428986	+	0.988823i
$86$	−8181.52	−	14170.8i	−1.10621	−	1.91601i
$87$	−4619.18	−	2666.88i	−0.610276	−	0.352343i
$88$	−6237.86	−	3601.43i	−0.805509	−	0.465061i
$89$	5237.92	−	3024.11i	0.661270	−	0.381784i	−0.131491	−	0.991317i	$-0.541976\pi$
$89$	5237.92	−	3024.11i	0.661270	−	0.381784i	0.792761	+	0.609533i	$0.208643\pi$
$90$	7481.02			0.923583
$91$	−5369.82	+	8864.54i	−0.648450	+	1.07047i
$92$		−	5943.26i		−	0.702181i
$93$	−3784.01	−	6554.10i	−0.437509	−	0.757787i
$94$	5911.70	+	3413.12i	0.669047	+	0.386274i
$95$	−13970.7	−	8065.97i	−1.54800	−	0.893736i
$96$	3699.09	+	6407.01i	0.401377	+	0.695205i
$97$	−13550.6			−1.44017			−0.720085	−	0.693885i	$-0.755897\pi$
$97$	−13550.6			−1.44017			−0.720085	+	0.693885i	$0.755897\pi$
$98$	−8139.02	+	12819.2i	−0.847462	+	1.33477i
$99$			6251.85i			0.637878i
$100$	−1213.34	−	2101.57i	−0.121334	−	0.210157i
$101$	−8161.35	−	4711.96i	−0.800054	−	0.461912i	0.0434358	−	0.999056i	$-0.486170\pi$
$101$	−8161.35	−	4711.96i	−0.800054	−	0.461912i	−0.843490	+	0.537145i	$0.819503\pi$
$102$	−11060.4	−	1269.39i	−1.06309	−	0.122009i
$103$	13134.0	−	7582.93i	1.23801	−	0.714764i	0.269320	−	0.963051i	$-0.413201\pi$
$103$	13134.0	−	7582.93i	1.23801	−	0.714764i	0.968687	+	0.248287i	$0.0798676\pi$
$104$		−	10697.3i		−	0.989028i
$105$	−6879.01	−	4167.05i	−0.623946	−	0.377964i
$106$	−34154.8			−3.03977
$107$	−10196.8	+	5887.14i	−0.890631	+	0.514206i	−0.874149	−	0.485658i	$-0.838580\pi$
$107$	−10196.8	+	5887.14i	−0.890631	+	0.514206i	−0.0164819	+	0.999864i	$0.505247\pi$
$108$	−9128.12	+	15810.4i	−0.782589	+	1.35548i
$109$	7786.24	+	4495.39i	0.655352	+	0.378368i	0.790504	−	0.612457i	$-0.209819\pi$
$109$	7786.24	+	4495.39i	0.655352	+	0.378368i	−0.135151	+	0.990825i	$0.543152\pi$
$110$	21019.2	−	12135.4i	1.73712	−	1.00293i
$111$			3079.20i			0.249915i
$112$	−66.1014	+	3140.06i	−0.00526957	+	0.250324i
$113$		−	1424.45i		−	0.111556i	−0.998443	−	0.0557778i	$-0.982236\pi$
$113$		−	1424.45i		−	0.111556i	0.998443	−	0.0557778i	$-0.0177638\pi$
$114$	19972.2	−	11530.9i	1.53679	−	0.887269i
$115$	5779.69	+	3336.91i	0.437028	+	0.252318i
$116$	18197.9	+	10506.5i	1.35240	+	0.780807i
$117$	−8040.98	+	4642.46i	−0.587404	+	0.339138i
$118$			13073.5i			0.938921i
$119$	−11196.5	−	8670.21i	−0.790657	−	0.612260i
$120$	8301.27			0.576477
$121$	2821.02	+	4886.14i	0.192679	+	0.333730i
$122$	12130.4	−	21010.5i	0.814997	−	1.41162i
$123$	−6449.23	+	11170.4i	−0.426283	+	0.738343i
$124$	14907.6	+	25820.8i	0.969538	+	1.67929i
$125$	−14116.7			−0.903469
$126$	−11921.5	+	6552.31i	−0.750916	+	0.412718i
$127$	17714.5			1.09830			0.549152	−	0.835722i	$-0.314951\pi$
$127$	17714.5			1.09830			0.549152	+	0.835722i	$0.314951\pi$
$128$	−11330.1	−	19624.3i	−0.691534	−	1.19777i
$129$	−7879.91	+	13648.4i	−0.473524	+	0.820167i
$130$	31216.7	+	18022.9i	1.84714	+	1.06645i
$131$	3796.42	+	6575.59i	0.221224	+	0.383171i	0.955180	−	0.296026i	$-0.0956616\pi$
$131$	3796.42	+	6575.59i	0.221224	+	0.383171i	−0.733956	+	0.679197i	$0.762328\pi$
$132$			20817.2i			1.19475i
$133$	29327.9	+	617.381i	1.65797	+	0.0349020i
$134$	17614.6			0.980989
$135$	−10250.2	−	17753.8i	−0.562423	−	0.974145i
$136$	14520.9	+	1666.55i	0.785086	+	0.0901033i
$137$	9968.74	−	17266.4i	0.531128	−	0.919940i	−0.468212	−	0.883616i	$-0.655102\pi$
$137$	9968.74	−	17266.4i	0.531128	−	0.919940i	0.999340	−	0.0363243i	$-0.0115649\pi$
$138$	−8262.53	+	4770.37i	−0.433865	+	0.250492i
$139$	4871.23			0.252121			0.126060	−	0.992023i	$-0.459767\pi$
$139$	4871.23			0.252121			0.126060	+	0.992023i	$0.459767\pi$
$140$	27100.8	+	16416.7i	1.38269	+	0.837585i
$141$		−	6574.58i		−	0.330697i
$142$	44308.6	−	25581.6i	2.19741	−	1.26868i
$143$	−15061.7	+	26087.6i	−0.736548	+	1.27574i
$144$	−1406.86	+	2436.75i	−0.0678462	+	0.117513i
$145$	−20434.8	+	11798.0i	−0.971927	+	0.561142i
$146$	−33538.6			−1.57340
$147$	14611.9	+	615.464i	0.676197	+	0.0284818i
$148$		−	12130.9i		−	0.553822i
$149$	−13215.6	−	22890.1i	−0.595271	−	1.03104i	−0.993509	−	0.113758i	$-0.963711\pi$
$149$	−13215.6	−	22890.1i	−0.595271	−	1.03104i	0.398237	−	0.917282i	$-0.369622\pi$
$150$	−1947.79	+	3373.67i	−0.0865683	+	0.149941i
$151$	1244.26	−	2155.13i	0.0545706	−	0.0945190i	−0.837450	−	0.546514i	$-0.815954\pi$
$151$	1244.26	−	2155.13i	0.0545706	−	0.0945190i	0.892020	+	0.451995i	$0.149288\pi$
$152$	−26221.1	+	15138.7i	−1.13491	+	0.655243i
$153$	−5049.13	−	11638.4i	−0.215692	−	0.497175i
$154$	−22866.7	+	37748.5i	−0.964188	+	1.59169i
$155$	−33480.2			−1.39356
$156$	−26774.7	+	15458.4i	−1.10021	+	0.635205i
$157$	−896.016	−	517.315i	−0.0363510	−	0.0209873i	0.481714	−	0.876328i	$-0.340014\pi$
$157$	−896.016	−	517.315i	−0.0363510	−	0.0209873i	−0.518065	+	0.855341i	$0.673348\pi$
$158$	43456.9	+	25089.9i	1.74078	+	1.00504i
$159$	16447.9	+	28488.5i	0.650601	+	1.12687i
$160$	32728.8			1.27847
$161$	−12133.0	−	255.412i	−0.468076	−	0.00985346i
$162$	6819.37			0.259845
$163$	−21240.6	+	12263.2i	−0.799449	+	0.461562i	−0.843278	−	0.537477i	$-0.819377\pi$
$163$	−21240.6	+	12263.2i	−0.799449	+	0.461562i	0.0438296	+	0.999039i	$0.486044\pi$
$164$	25407.6	−	44007.3i	0.944661	−	1.63620i
$165$	−20244.3	−	11688.1i	−0.743593	−	0.429314i
$166$	12345.0	−	7127.37i	0.447995	−	0.258650i
$167$	−30719.3			−1.10149			−0.550743	−	0.834675i	$-0.685656\pi$
$167$	−30719.3			−1.10149			−0.550743	+	0.834675i	$0.685656\pi$
$168$	−13228.7	+	7270.73i	−0.468703	+	0.257608i
$169$	−16176.6			−0.566389
$170$	−29328.3	+	39566.8i	−1.01482	+	1.36909i
$171$	22759.0	+	13139.9i	0.778325	+	0.449366i
$172$	31043.9	−	53769.7i	1.04935	−	1.81753i
$173$	−20756.2	−	35950.9i	−0.693516	−	1.20121i	−0.970678	−	0.240382i	$-0.922727\pi$
$173$	−20756.2	−	35950.9i	−0.693516	−	1.20121i	0.277162	−	0.960823i	$-0.410606\pi$
$174$		−	33732.4i		−	1.11416i
$175$	−4342.45	+	2386.69i	−0.141794	+	0.0779328i
$176$			9128.62i			0.294700i
$177$	10904.6	−	6295.79i	0.348068	−	0.200957i
$178$	33126.2	+	19125.4i	1.04552	+	0.603631i
$179$	2584.69	−	4476.82i	0.0806682	−	0.139722i	−0.822869	−	0.568231i	$-0.807628\pi$
$179$	2584.69	−	4476.82i	0.0806682	−	0.139722i	0.903537	+	0.428510i	$0.140961\pi$
$180$	14193.0	+	24583.0i	0.438055	+	0.758734i
$181$	21722.2			0.663050			0.331525	−	0.943447i	$-0.392437\pi$
$181$	21722.2			0.663050			0.331525	+	0.943447i	$0.392437\pi$
$182$	−65531.5	−	1379.50i	−1.97837	−	0.0416466i
$183$	−23366.4			−0.697735
$184$	10847.7	−	6262.92i	0.320407	−	0.184987i
$185$	11797.0	+	6811.03i	0.344691	+	0.199007i
$186$	23931.3	−	41450.2i	0.691736	−	1.19812i
$187$	−33065.8	−	24509.5i	−0.945574	−	0.700892i
$188$			25901.5i			0.732839i
$189$	31884.1	+	19314.3i	0.892588	+	0.540697i
$190$		−	102023.i		−	2.82613i
$191$	26949.4	+	46677.8i	0.738725	+	1.27951i	0.953070	+	0.302751i	$0.0979050\pi$
$191$	26949.4	+	46677.8i	0.738725	+	1.27951i	−0.214345	+	0.976758i	$0.568762\pi$
$192$	−20270.8	+	35110.1i	−0.549881	+	0.952422i
$193$	8173.93	+	4719.22i	0.219440	+	0.126694i	0.605691	−	0.795700i	$-0.292897\pi$
$193$	8173.93	+	4719.22i	0.219440	+	0.126694i	−0.386251	+	0.922394i	$0.626230\pi$
$194$	−42849.0	−	74216.7i	−1.13851	−	1.97196i
$195$		−	34717.0i		−	0.913005i
$196$	−57565.7	−	2424.70i	−1.49848	−	0.0631170i
$197$		−	15579.1i		−	0.401431i	−0.979650	−	0.200716i	$-0.935673\pi$
$197$		−	15579.1i		−	0.401431i	0.979650	−	0.200716i	$-0.0643267\pi$
$198$	−34241.5	+	19769.3i	−0.873418	+	0.504268i
$199$	−13382.5	+	23179.1i	−0.337932	+	0.585316i	−0.984044	−	0.177927i	$-0.943061\pi$
$199$	−13382.5	+	23179.1i	−0.337932	+	0.585316i	0.646111	+	0.763243i	$0.276394\pi$
$200$	2557.21	−	4429.22i	0.0639302	−	0.110730i
$201$	−8482.64	−	14692.4i	−0.209961	−	0.363663i
$202$		−	59599.8i		−	1.46064i
$203$	22230.9	−	36698.9i	0.539466	−	0.890556i
$204$	−16812.5	−	38753.2i	−0.403991	−	0.931209i
$205$	28530.8	+	49416.7i	0.678899	+	1.17589i
$206$	83063.7	+	47956.8i	1.95739	+	1.13010i
$207$	−9415.44	−	5436.01i	−0.219735	−	0.126864i
$208$	−11741.0	+	6778.68i	−0.271381	+	0.156682i
$209$	85260.4			1.95189
$210$	1070.51	−	50853.3i	0.0242747	−	1.15314i
$211$		−	12280.5i		−	0.275837i	−0.990444	−	0.137918i	$-0.955959\pi$
$211$		−	12280.5i		−	0.275837i	0.990444	−	0.137918i	$-0.0440412\pi$
$212$	−64798.5	−	112234.i	−1.44176	−	2.49720i
$213$	−42675.2	−	24638.5i	−0.940624	−	0.543070i
$214$	−64488.0	−	37232.1i	−1.40816	−	0.813000i
$215$	34859.9	+	60379.1i	0.754135	+	1.30620i
$216$	−38476.3			−0.824681
$217$	53353.0	−	29323.9i	1.13303	−	0.622733i
$218$			56860.5i			1.19646i
$219$	16151.1	+	27974.5i	0.336755	+	0.583276i
$220$	79755.2	+	46046.7i	1.64783	+	0.951378i
$221$	6969.74	−	60728.5i	0.142703	−	1.24339i
$222$	−16864.8	+	9736.91i	−0.342197	+	0.197567i
$223$		−	37003.1i		−	0.744095i	−0.928214	−	0.372047i	$-0.878656\pi$
$223$		−	37003.1i		−	0.744095i	0.928214	−	0.372047i	$-0.121344\pi$
$224$	−52155.7	+	28665.8i	−1.03945	+	0.571304i
$225$	−4439.15			−0.0876868
$226$	7801.75	−	4504.34i	0.152748	−	0.0881891i
$227$	10304.9	−	17848.6i	0.199982	−	0.346379i	−0.748540	−	0.663089i	$-0.769245\pi$
$227$	10304.9	−	17848.6i	0.199982	−	0.346379i	0.948522	+	0.316710i	$0.102578\pi$
$228$	75782.4	+	43753.0i	1.45780	+	0.841663i
$229$	−43798.7	+	25287.2i	−0.835200	+	0.482203i	−0.855630	−	0.517588i	$-0.826830\pi$
$229$	−43798.7	+	25287.2i	−0.835200	+	0.482203i	0.0204298	+	0.999791i	$0.493497\pi$
$230$			42207.3i			0.797870i
$231$	42497.8	+	894.621i	0.796421	+	0.0167654i
$232$			44286.6i			0.822803i
$233$	−12405.5	+	7162.34i	−0.228509	+	0.131930i	−0.609884	−	0.792491i	$-0.708784\pi$
$233$	−12405.5	+	7162.34i	−0.228509	+	0.131930i	0.381375	+	0.924420i	$0.375451\pi$
$234$	−50853.7	−	29360.4i	−0.928733	−	0.536204i
$235$	−25188.6	−	14542.7i	−0.456109	−	0.263335i
$236$	−42960.2	+	24803.1i	−0.771334	+	0.445330i
$237$		−	48329.9i		−	0.860436i
$238$	12081.8	−	88739.9i	0.213294	−	1.56663i
$239$	−12636.3			−0.221220			−0.110610	−	0.993864i	$-0.535281\pi$
$239$	−12636.3			−0.221220			−0.110610	+	0.993864i	$0.535281\pi$
$240$	−5260.35	−	9111.20i	−0.0913256	−	0.158180i
$241$	−20130.8	+	34867.6i	−0.346599	+	0.600327i	−0.985643	−	0.168843i	$-0.945997\pi$
$241$	−20130.8	+	34867.6i	−0.346599	+	0.600327i	0.639044	+	0.769170i	$0.279330\pi$
$242$	−17841.0	+	30901.5i	−0.304641	+	0.527654i
$243$	27527.3	+	47678.7i	0.466177	+	0.807443i
$244$	92055.2			1.54621
$245$	34678.8	−	54620.0i	0.577740	−	0.909954i
$246$	−81573.9			−1.34797
$247$	63312.2	+	109660.i	1.03775	+	1.79744i
$248$	−31418.9	+	54419.1i	−0.510843	+	0.884806i
$249$	−11889.9	−	6864.61i	−0.191769	−	0.110718i
$250$	−44639.3	−	77317.5i	−0.714228	−	1.23708i
$251$			10745.9i			0.170567i	0.996357	+	0.0852833i	$0.0271795\pi$
$251$			10745.9i			0.170567i	−0.996357	+	0.0852833i	$0.972820\pi$
$252$	−44148.7	−	26743.7i	−0.695211	−	0.421134i
$253$	−35272.4			−0.551054
$254$	56016.2	+	97022.9i	0.868253	+	1.50386i
$255$	47126.2	+	5408.61i	0.724740	+	0.0831774i
$256$	18408.7	−	31884.8i	0.280894	−	0.486523i
$257$	−15377.9	+	8878.41i	−0.232825	+	0.134422i	−0.611875	−	0.790955i	$-0.709584\pi$
$257$	−15377.9	+	8878.41i	−0.232825	+	0.134422i	0.379050	+	0.925376i	$0.376251\pi$
$258$	−99670.0			−1.49736
$259$	−24764.9	−	521.326i	−0.369179	−	0.00777159i
$260$			136772.i			2.02326i
$261$	33289.4	−	19219.6i	0.488680	−	0.282140i
$262$	−24009.8	+	41586.1i	−0.349772	+	0.605823i
$263$	−1001.96	+	1735.45i	−0.0144857	+	0.0250900i	−0.873177	−	0.487403i	$-0.837944\pi$
$263$	−1001.96	+	1735.45i	−0.0144857	+	0.0250900i	0.858692	+	0.512493i	$0.171278\pi$
$264$	−37995.8	+	21936.9i	−0.545165	+	0.314751i
$265$	145527.			2.07230
$266$	89358.0	+	162582.i	1.26290	+	2.29778i
$267$		−	36840.8i		−	0.516780i
$268$	33418.5	+	57882.5i	0.465283	+	0.805894i
$269$	39843.1	−	69010.2i	0.550615	−	0.953694i	−0.447615	−	0.894226i	$-0.647726\pi$
$269$	39843.1	−	69010.2i	0.550615	−	0.953694i	0.998230	−	0.0594673i	$-0.0189402\pi$
$270$	64825.2	−	112281.i	0.889235	−	1.54020i
$271$	−35291.5	+	20375.5i	−0.480542	+	0.277441i	−0.720642	−	0.693307i	$-0.756153\pi$
$271$	−35291.5	+	20375.5i	−0.480542	+	0.277441i	0.240101	+	0.970748i	$0.422820\pi$
$272$	−7372.49	−	16993.8i	−0.0996497	−	0.229695i
$273$	30407.2	+	55324.0i	0.407991	+	0.742316i
$274$	126091.			1.67951
$275$	−12472.5	+	7201.02i	−0.164926	+	0.0952201i
$276$	−31351.3	−	18100.7i	−0.411564	−	0.237617i
$277$	101874.	+	58817.0i	1.32771	+	0.766555i	0.984945	−	0.172865i	$-0.0553025\pi$
$277$	101874.	+	58817.0i	1.32771	+	0.766555i	0.342767	+	0.939420i	$0.388636\pi$
$278$	15403.6	+	26679.8i	0.199311	+	0.345218i
$279$	54541.1			0.700673
$280$	−1405.45	+	66764.3i	−0.0179267	+	0.851585i
$281$	51874.3			0.656961			0.328480	−	0.944511i	$-0.393464\pi$
$281$	51874.3			0.656961			0.328480	+	0.944511i	$0.393464\pi$
$282$	36009.1	−	20789.9i	0.452808	−	0.261429i
$283$	8344.08	−	14452.4i	0.104185	−	0.180454i	−0.809220	−	0.587506i	$-0.800110\pi$
$283$	8344.08	−	14452.4i	0.104185	−	0.180454i	0.913405	+	0.407052i	$0.133443\pi$
$284$	168125.	+	97066.8i	2.08446	+	1.20347i
$285$	−85097.7	+	49131.2i	−1.04768	+	0.604877i
$286$	−190509.			−2.32908
$287$	−88747.8	−	53760.2i	−1.07744	−	0.652675i
$288$	−53317.1			−0.642808
$289$	81349.4	+	18922.0i	0.973999	+	0.226553i
$290$	−129236.	−	74614.4i	−1.53669	−	0.887210i
$291$	−41269.4	+	71480.7i	−0.487351	+	0.844117i
$292$	−63629.4	−	110209.i	−0.746263	−	1.29257i
$293$			2492.78i			0.0290367i	0.999895	+	0.0145184i	$0.00462150\pi$
$293$			2492.78i			0.0290367i	−0.999895	+	0.0145184i	$0.995378\pi$
$294$	42834.3	+	81976.0i	0.495561	+	0.948401i
$295$		−	55703.8i		−	0.640090i
$296$	22141.5	−	12783.4i	0.252710	−	0.145902i
$297$	93832.2	+	54174.1i	1.06375	+	0.614156i
$298$	83579.7	−	144764.i	0.941171	−	1.63016i
$299$	−26192.4	−	45366.5i	−0.292976	−	0.507450i
$300$	−14781.4			−0.164237
$301$	−108435.	−	65686.1i	−1.19684	−	0.725004i
$302$	15738.2			0.172561
$303$	−49712.2	+	28701.3i	−0.541474	+	0.312620i
$304$	33231.5	+	19186.2i	0.359586	+	0.207607i
$305$	−51685.4	+	89521.7i	−0.555608	+	0.962341i
$306$	47777.4	−	64456.6i	0.510247	−	0.688374i
$307$		−	95340.3i		−	1.01158i	−0.862657	−	0.505789i	$-0.831201\pi$
$307$		−	95340.3i		−	1.01158i	0.862657	−	0.505789i	$-0.168799\pi$
$308$	−167426.	−	3524.48i	−1.76490	−	0.0371530i
$309$		−	92377.7i		−	0.967499i
$310$	−105870.	−	183372.i	−1.10166	−	1.90813i
$311$	−58735.7	+	101733.i	−0.607269	+	1.05182i	0.384420	+	0.923158i	$0.374402\pi$
$311$	−58735.7	+	101733.i	−0.607269	+	1.05182i	−0.991688	+	0.128662i	$0.958932\pi$
$312$	−56429.5	−	32579.6i	−0.579692	−	0.334685i
$313$	−17310.7	−	29983.0i	−0.176696	−	0.306046i	0.764051	−	0.645156i	$-0.223207\pi$
$313$	−17310.7	−	29983.0i	−0.176696	−	0.306046i	−0.940747	+	0.339110i	$0.889874\pi$
$314$		−	6543.32i		−	0.0663650i
$315$	50795.4	−	27918.1i	0.511921	−	0.281362i
$316$			190402.i			1.90677i
$317$	−81486.3	+	47046.1i	−0.810898	+	0.468172i	−0.847268	−	0.531166i	$-0.821754\pi$
$317$	−81486.3	+	47046.1i	−0.810898	+	0.468172i	0.0363699	+	0.999338i	$0.488421\pi$
$318$	−104021.	+	180170.i	−1.02865	+	1.78168i
$319$	62354.8	−	108002.i	0.612757	−	1.06133i
$320$	89676.0	+	155323.i	0.875742	+	1.51683i
$321$			71719.1i			0.696025i
$322$	−36967.6	−	67260.3i	−0.356541	−	0.648705i
$323$	−158720.	+	68858.3i	−1.52134	+	0.660011i
$324$	12937.7	+	22408.8i	0.123244	+	0.213466i
$325$	−18523.6	−	10694.6i	−0.175371	−	0.101251i
$326$	−134332.	−	77556.6i	−1.26399	−	0.729766i
$327$	47427.3	−	27382.2i	0.443540	−	0.256078i
$328$	107097.			0.995471
$329$	52877.1	+	1113.12i	0.488513	+	0.0102837i
$330$		−	147838.i		−	1.35756i
$331$	59987.0	+	103901.i	0.547522	+	0.948335i	0.998444	+	0.0557718i	$0.0177619\pi$
$331$	59987.0	+	103901.i	0.547522	+	0.948335i	−0.450922	+	0.892563i	$0.648905\pi$
$332$	46841.7	+	27044.1i	0.424968	+	0.245355i
$333$	−19218.1	−	11095.5i	−0.173309	−	0.100060i
$334$	−97139.4	−	168250.i	−0.870768	−	1.50821i
$335$	−75052.7			−0.668769
$336$	16362.9	+	9912.02i	0.144937	+	0.0877978i
$337$			114197.i			1.00553i	0.864423	+	0.502766i	$0.167684\pi$
$337$			114197.i			1.00553i	−0.864423	+	0.502766i	$0.832316\pi$
$338$	−51153.1	−	88599.7i	−0.447753	−	0.775531i
$339$	−7514.14	−	4338.29i	−0.0653852	−	0.0377502i
$340$	−185660.	−	21308.0i	−1.60605	−	0.184325i
$341$	153242.	−	88474.6i	1.31786	−	0.760869i
$342$			166202.i			1.42097i
$343$	−7423.85	+	117415.i	−0.0631017	+	0.998007i
$344$	130855.			1.10579
$345$	35205.1	−	20325.7i	0.295779	−	0.170768i
$346$	131269.	−	227365.i	1.09650	−	1.89920i
$347$	111384.	+	64307.6i	0.925047	+	0.534076i	0.885242	−	0.465131i	$-0.153993\pi$
$347$	111384.	+	64307.6i	0.925047	+	0.534076i	0.0398054	+	0.999207i	$0.487326\pi$
$348$	110846.	−	63997.1i	0.915298	−	0.528447i
$349$		−	32893.9i		−	0.270062i	−0.990841	−	0.135031i	$-0.956887\pi$
$349$		−	32893.9i		−	0.270062i	0.990841	−	0.135031i	$-0.0431134\pi$
$350$	−26803.5	−	16236.6i	−0.218804	−	0.132543i
$351$			160913.i			1.30610i
$352$	−149803.	+	86489.0i	−1.20903	+	0.698033i
$353$	104960.	+	60598.4i	0.842311	+	0.486308i	0.858049	−	0.513568i	$-0.171676\pi$
$353$	104960.	+	60598.4i	0.842311	+	0.486308i	−0.0157382	+	0.999876i	$0.505010\pi$
$354$	68964.3	+	39816.5i	0.550323	+	0.317729i
$355$	−188791.	+	108998.i	−1.49804	+	0.864895i
$356$			145139.i			1.14521i
$357$	−79836.1	+	32656.8i	−0.626416	+	0.256234i
$358$	32692.8			0.255086
$359$	−83010.5	−	143778.i	−0.644087	−	1.11559i	−0.984512	−	0.175319i	$-0.943904\pi$
$359$	−83010.5	−	143778.i	−0.644087	−	1.11559i	0.340425	−	0.940272i	$-0.389429\pi$
$360$	−29912.7	+	51810.4i	−0.230808	+	0.399771i
$361$	114037.	−	197518.i	0.875047	−	1.51563i
$362$	68688.9	+	118973.i	0.524167	+	0.907884i
$363$	34366.6			0.260809
$364$	−119793.	−	217957.i	−0.904126	−	1.64500i
$365$	142902.			1.07263
$366$	−73888.4	−	127978.i	−0.551587	−	0.955377i
$367$	43843.0	−	75938.3i	0.325513	−	0.563805i	−0.656103	−	0.754671i	$-0.727796\pi$
$367$	43843.0	−	75938.3i	0.325513	−	0.563805i	0.981616	+	0.190867i	$0.0611298\pi$
$368$	−13747.9	−	7937.38i	−0.101518	−	0.0586113i
$369$	−46478.2	−	80502.6i	−0.341347	−	0.591231i
$370$			86150.2i			0.629293i
$371$	−231908.	+	127461.i	−1.68488	+	0.926040i
$372$	181610.			1.31236
$373$	8277.72	+	14337.4i	0.0594968	+	0.103051i	0.894240	−	0.447589i	$-0.147717\pi$
$373$	8277.72	+	14337.4i	0.0594968	+	0.103051i	−0.834743	+	0.550640i	$0.814384\pi$
$374$	29679.7	−	258605.i	0.212186	−	1.84881i
$375$	−42993.6	+	74467.1i	−0.305732	+	0.529544i
$376$	−47275.6	+	27294.6i	−0.334396	+	0.193064i
$377$	185212.			1.30313
$378$	−4961.81	+	235705.i	−0.0347262	+	1.64962i
$379$		−	192800.i		−	1.34224i	−0.741349	−	0.671119i	$-0.765814\pi$
$379$		−	192800.i		−	1.34224i	0.741349	−	0.671119i	$-0.234186\pi$
$380$	335254.	−	193559.i	2.32170	−	1.34043i
$381$	53951.1	−	93446.1i	0.371664	−	0.643741i
$382$	−170437.	+	295205.i	−1.16798	+	2.02300i
$383$	7960.30	−	4595.88i	0.0542665	−	0.0313308i	−0.472621	−	0.881266i	$-0.656692\pi$
$383$	7960.30	−	4595.88i	0.0542665	−	0.0313308i	0.526888	+	0.849935i	$0.323359\pi$
$384$	−138027.			−0.936056
$385$	97430.5	−	160839.i	0.657315	−	1.08510i
$386$			59691.6i			0.400626i
$387$	−56788.8	−	98361.0i	−0.379176	−	0.656751i
$388$	162586.	−	281608.i	1.07999	−	1.87060i
$389$	−104606.	+	181183.i	−0.691286	+	1.19734i	0.280131	+	0.959962i	$0.409622\pi$
$389$	−104606.	+	181183.i	−0.691286	+	1.19734i	−0.971417	+	0.237381i	$0.923711\pi$
$390$	190146.	−	109781.i	1.25014	−	0.721767i
$391$	65662.8	−	28486.8i	0.429502	−	0.186333i
$392$	−56236.3	−	107625.i	−0.365969	−	0.700389i
$393$	46249.2			0.299447
$394$	85327.3	−	49263.7i	0.549662	−	0.317347i
$395$	−185162.	−	106903.i	−1.18674	−	0.685167i
$396$	−129926.	−	75012.7i	−0.828523	−	0.478348i
$397$	28682.2	+	49679.1i	0.181983	+	0.315205i	0.942556	−	0.334049i	$-0.108415\pi$
$397$	28682.2	+	49679.1i	0.181983	+	0.315205i	−0.760572	+	0.649253i	$0.775082\pi$
$398$	−169270.			−1.06860
$399$	92577.3	−	152827.i	0.581512	−	0.959965i
$400$	−6481.81			−0.0405113
$401$	−193801.	+	111891.i	−1.20522	+	0.695835i	−0.961712	−	0.274064i	$-0.911632\pi$
$401$	−193801.	+	111891.i	−1.20522	+	0.695835i	−0.243510	+	0.969898i	$0.578299\pi$
$402$	53646.9	−	92919.1i	0.331965	−	0.574980i
$403$	227588.	+	131398.i	1.40133	+	0.809056i
$404$	195848.	−	113073.i	1.19993	−	0.692780i
$405$	−29056.0			−0.177144
$406$	271298.	+	5711.09i	1.64587	+	0.0346471i
$407$	−71995.2			−0.434625
$408$	53016.0	−	71523.9i	0.318483	−	0.429666i
$409$	115785.	+	66848.6i	0.692159	+	0.399618i	0.804420	−	0.594060i	$-0.202476\pi$
$409$	115785.	+	66848.6i	0.692159	+	0.399618i	−0.112261	+	0.993679i	$0.535809\pi$
$410$	−180437.	+	312527.i	−1.07339	+	1.85917i
$411$	−60721.2	−	105172.i	−0.359465	−	0.622612i
$412$			363934.i			2.14402i
$413$	48788.6	+	88768.0i	0.286034	+	0.520423i
$414$		−	68758.1i		−	0.401165i
$415$	−52599.5	+	30368.3i	−0.305412	+	0.176329i
$416$	−222480.	−	128449.i	−1.28560	−	0.742240i
$417$	14835.7	−	25696.2i	0.0853172	−	0.147774i
$418$	269607.	+	466973.i	1.54304	+	2.67263i
$419$	−140630.			−0.801034			−0.400517	−	0.916289i	$-0.631169\pi$
$419$	−140630.			−0.801034			−0.400517	+	0.916289i	$0.631169\pi$
$420$	169137.	−	92961.1i	0.958828	−	0.526990i
$421$	−251702.			−1.42011			−0.710055	−	0.704147i	$-0.751330\pi$
$421$	−251702.			−1.42011			−0.710055	+	0.704147i	$0.751330\pi$
$422$	67260.7	−	38833.0i	0.377691	−	0.218060i
$423$	41033.7	+	23690.8i	0.229329	+	0.132403i
$424$	136568.	−	236542.i	0.759654	−	1.31576i
$425$	17403.0	−	23478.5i	0.0963490	−	0.129985i
$426$		−	311644.i		−	1.71727i
$427$	3956.07	−	187928.i	0.0216974	−	1.03071i
$428$		−	282547.i		−	1.54242i
$429$	91743.1	+	158904.i	0.498493	+	0.863415i
$430$	−220465.	+	381857.i	−1.19235	+	2.06521i
$431$	−182752.	−	105512.i	−0.983799	−	0.567997i	−0.0803843	−	0.996764i	$-0.525615\pi$
$431$	−182752.	−	105512.i	−0.983799	−	0.567997i	−0.903415	+	0.428767i	$0.858948\pi$
$432$	24381.7	+	42230.3i	0.130646	+	0.226286i
$433$		−	63778.1i		−	0.340170i	−0.985429	−	0.170085i	$-0.945596\pi$
$433$		−	63778.1i		−	0.340170i	0.985429	−	0.170085i	$-0.0544042\pi$
$434$	329318.	+	199489.i	1.74838	+	1.05911i
$435$			143727.i			0.759558i
$436$	−186846.	+	107876.i	−0.982904	+	0.567480i
$437$	−74134.3	+	128404.i	−0.388201	+	0.672384i
$438$	−102145.	+	176920.i	−0.532436	+	0.922206i
$439$	133474.	+	231184.i	0.692578	+	1.19958i	0.970990	+	0.239118i	$0.0768584\pi$
$439$	133474.	+	231184.i	0.692578	+	1.19958i	−0.278413	+	0.960462i	$0.589808\pi$
$440$			194093.i			1.00255i
$441$	−56493.8	+	88979.1i	−0.290485	+	0.457521i
$442$	354651.	−	153860.i	1.81533	−	0.787555i
$443$	−49865.1	−	86368.8i	−0.254091	−	0.440098i	0.710557	−	0.703639i	$-0.248443\pi$
$443$	−49865.1	−	86368.8i	−0.254091	−	0.440098i	−0.964648	+	0.263541i	$0.915110\pi$
$444$	−63991.8	−	36945.7i	−0.324607	−	0.187412i
$445$	−141145.	−	81489.9i	−0.712762	−	0.411513i
$446$	202667.	−	117010.i	1.01886	−	0.588236i
$447$	−160997.			−0.805755
$448$	−278946.	−	168975.i	−1.38984	−	0.841914i
$449$		−	52102.3i		−	0.258443i	−0.991616	−	0.129221i	$-0.958752\pi$
$449$		−	52102.3i		−	0.258443i	0.991616	−	0.129221i	$-0.0412478\pi$
$450$	−14037.3	−	24313.3i	−0.0693199	−	0.120066i
$451$	−261177.	−	150791.i	−1.28405	−	0.741346i
$452$	29603.0	+	17091.3i	0.144897	+	0.0836561i
$453$	−7579.02	−	13127.2i	−0.0369332	−	0.0639701i
$454$	130343.			0.632375
$455$	279217.	+	5877.79i	1.34871	+	0.0283917i
$456$			184425.i			0.886932i
$457$	6827.60	+	11825.8i	0.0326916	+	0.0566235i	0.881908	−	0.471421i	$-0.156259\pi$
$457$	6827.60	+	11825.8i	0.0326916	+	0.0566235i	−0.849217	+	0.528044i	$0.822925\pi$
$458$	−276997.	−	159924.i	−1.32052	−	0.762401i
$459$	−218429.	−	25068.9i	−1.03678	−	0.118990i
$460$	−138695.	+	80075.6i	−0.655459	+	0.378429i
$461$		−	317894.i		−	1.49582i	−0.663797	−	0.747912i	$-0.731056\pi$
$461$		−	317894.i		−	1.49582i	0.663797	−	0.747912i	$-0.268944\pi$
$462$	129485.	+	235590.i	0.606646	+	1.10376i
$463$	21383.5			0.0997508			0.0498754	−	0.998755i	$-0.484118\pi$
$463$	21383.5			0.0997508			0.0498754	+	0.998755i	$0.484118\pi$
$464$	48607.4	−	28063.5i	0.225770	−	0.130349i
$465$	−101967.	+	176611.i	−0.471577	+	0.816795i
$466$	−78456.5	−	45296.9i	−0.361291	−	0.208592i
$467$	−125455.	+	72431.4i	−0.575246	+	0.332119i	−0.759242	−	0.650808i	$-0.774430\pi$
$467$	−125455.	+	72431.4i	−0.575246	+	0.332119i	0.183996	+	0.982927i	$0.441097\pi$
$468$		−	222810.i		−	1.01729i
$469$	119602.	−	65735.4i	0.543741	−	0.298850i
$470$		−	183945.i		−	0.832705i
$471$	−5457.78	+	3151.05i	−0.0246022	+	0.0142041i
$472$	−90541.7	−	52274.3i	−0.406410	−	0.234641i
$473$	−319115.	−	184241.i	−1.42635	−	0.823502i
$474$	264703.	−	152827.i	1.17816	−	0.680209i
$475$			60539.5i			0.268319i
$476$	314525.	−	128656.i	1.38817	−	0.567827i
$477$	−237072.			−1.04194
$478$	−39958.1	−	69209.4i	−0.174884	−	0.302907i
$479$	164289.	−	284557.i	0.716040	−	1.24022i	−0.246518	−	0.969138i	$-0.579286\pi$
$479$	164289.	−	284557.i	0.716040	−	1.24022i	0.962557	−	0.271079i	$-0.0873804\pi$
$480$	99678.3	−	172648.i	0.432632	−	0.749340i
$481$	−53461.8	−	92598.6i	−0.231075	−	0.400234i
$482$	−254627.			−1.09600
$483$	−38299.4	+	63225.0i	−0.164171	+	0.271016i
$484$	−135392.			−0.577965
$485$	182572.	+	316223.i	0.776157	+	1.34434i
$486$	−174091.	+	301535.i	−0.737063	+	1.27663i
$487$	171184.	+	98833.4i	0.721782	+	0.416721i	0.815408	−	0.578886i	$-0.196512\pi$
$487$	171184.	+	98833.4i	0.721782	+	0.416721i	−0.0936260	+	0.995607i	$0.529846\pi$
$488$	97006.5	+	168020.i	0.407344	+	0.705540i
$489$			149395.i			0.624767i
$490$	408815.	+	17219.5i	1.70268	+	0.0717181i
$491$	240544.			0.997771			0.498885	−	0.866668i	$-0.333743\pi$
$491$	240544.			0.997771			0.498885	+	0.866668i	$0.333743\pi$
$492$	−154762.	−	268056.i	−0.639343	−	1.10737i
$493$	−28854.5	+	251414.i	−0.118719	+	1.03442i
$494$	−400406.	+	693524.i	−1.64077	+	2.84189i
$495$	145896.	−	84233.3i	0.595435	−	0.343774i
$496$	79638.1			0.323711
$497$	205384.	−	339050.i	0.831485	−	1.37262i
$498$		−	86827.9i		−	0.350107i
$499$	−302462.	+	174626.i	−1.21470	+	0.701308i	−0.963780	−	0.266700i	$-0.914067\pi$
$499$	−302462.	+	174626.i	−1.21470	+	0.701308i	−0.250921	+	0.968008i	$0.580733\pi$
$500$	169379.	−	293373.i	0.677516	−	1.17349i
$501$	−93558.3	+	162048.i	−0.372741	+	0.645606i
$502$	−58855.3	+	33980.1i	−0.233549	+	0.134840i
$503$	−61620.6			−0.243551			−0.121775	−	0.992558i	$-0.538859\pi$
$503$	−61620.6			−0.243551			−0.121775	+	0.992558i	$0.538859\pi$
$504$	2289.56	−	108763.i	0.00901346	−	0.428173i
$505$			253944.i			0.995760i
$506$	−111537.	−	193188.i	−0.435630	−	0.754533i
$507$	−49267.3	+	85333.5i	−0.191665	+	0.331974i
$508$	−212548.	+	368143.i	−0.823624	+	1.42656i
$509$	221275.	−	127753.i	0.854075	−	0.493101i	−0.00794842	−	0.999968i	$-0.502530\pi$
$509$	221275.	−	127753.i	0.854075	−	0.493101i	0.862024	+	0.506868i	$0.169197\pi$
$510$	119397.	+	275214.i	0.459044	+	1.05811i
$511$	−227724.	+	125161.i	−0.872101	+	0.479323i
$512$	−129719.			−0.494837
$513$	394427.	−	227722.i	1.49876	−	0.865309i
$514$	−97254.5	−	56149.9i	−0.368115	−	0.212531i
$515$	−353918.	−	204335.i	−1.33441	−	0.770421i
$516$	−189094.	−	327520.i	−0.710195	−	1.23009i
$517$	153721.			0.575113
$518$	−75455.3	−	137286.i	−0.281210	−	0.511644i
$519$	−252859.			−0.938738
$520$	−249638.	+	144129.i	−0.923219	+	0.533021i
$521$	37099.2	−	64257.7i	0.136675	−	0.236728i	−0.789561	−	0.613672i	$-0.789692\pi$
$521$	37099.2	−	64257.7i	0.136675	−	0.236728i	0.926236	+	0.376944i	$0.123025\pi$
$522$	210533.	+	121551.i	0.772642	+	0.446085i
$523$	−344390.	+	198834.i	−1.25906	+	0.726920i	−0.972892	−	0.231258i	$-0.925716\pi$
$523$	−344390.	+	198834.i	−1.25906	+	0.726920i	−0.286171	+	0.958179i	$0.592382\pi$
$524$	−182205.			−0.663587
$525$	−635.229	+	30175.7i	−0.00230468	+	0.109481i
$526$	−12673.5			−0.0458061
$527$	−213821.	+	288466.i	−0.769890	+	1.03866i
$528$	48154.4	+	27802.0i	0.172730	+	0.0997259i
$529$	−109251.	+	189228.i	−0.390404	+	0.676199i
$530$	460180.	+	797055.i	1.63823	+	2.83751i
$531$			90744.7i			0.321834i
$532$	−364721.	+	602084.i	−1.28866	+	2.12732i
$533$		−	447893.i		−	1.57659i
$534$	201777.	−	116496.i	0.707604	−	0.408535i
$535$	274771.	+	158639.i	0.959982	+	0.554246i
$536$	−70431.8	+	121992.i	−0.245154	+	0.424620i
$537$	−15743.8	−	27269.0i	−0.0545960	−	0.0945630i
$538$	503960.			1.74113
$539$	−14390.3	+	341644.i	−0.0495326	+	1.17597i
$540$	491945.			1.68706
$541$	476053.	−	274849.i	1.62652	−	0.939074i	0.641404	−	0.767203i	$-0.278352\pi$
$541$	476053.	−	274849.i	1.62652	−	0.939074i	0.985120	−	0.171870i	$-0.0549810\pi$
$542$	−223194.	−	128861.i	−0.759774	−	0.438656i
$543$	66156.7	−	114587.i	0.224375	−	0.388628i
$544$	209022.	−	281992.i	0.706309	−	0.952881i
$545$		−	242272.i		−	0.815661i
$546$	−206859.	+	341484.i	−0.693886	+	1.14547i
$547$			207107.i			0.692182i	0.938201	+	0.346091i	$0.112491\pi$
$547$			207107.i			0.692182i	−0.938201	+	0.346091i	$0.887509\pi$
$548$	239219.	+	414340.i	0.796591	+	1.37974i
$549$	84198.4	−	145836.i	0.279357	−	0.483860i
$550$	−78880.2	−	45541.5i	−0.260761	−	0.150550i
$551$	−262110.	−	453989.i	−0.863339	−	1.49535i
$552$		−	76297.0i		−	0.250397i
$553$	388700.	+	8182.52i	1.27106	+	0.0267570i
$554$			743955.i			2.42397i
$555$	71857.8	−	41487.1i	0.233286	−	0.134687i
$556$	−58447.3	+	101234.i	−0.189067	+	0.327473i
$557$	256443.	−	444172.i	0.826570	−	1.43166i	−0.0741426	−	0.997248i	$-0.523622\pi$
$557$	256443.	−	444172.i	0.826570	−	1.43166i	0.900713	−	0.434414i	$-0.143045\pi$
$558$	172468.	+	298723.i	0.553910	+	0.959400i
$559$		−	547252.i		−	1.75131i
$560$	74168.8	−	40764.6i	0.236508	−	0.129989i
$561$	−229995.	+	99779.7i	−0.730789	+	0.317042i
$562$	164035.	+	284116.i	0.519353	+	0.899546i
$563$	318676.	+	183988.i	1.00539	+	0.580459i	0.909837	−	0.414965i	$-0.136206\pi$
$563$	318676.	+	183988.i	1.00539	+	0.580459i	0.0955481	+	0.995425i	$0.469540\pi$
$564$	136633.	+	78885.0i	0.429534	+	0.247991i
$565$	−33241.8	+	19192.2i	−0.104133	+	0.0601211i
$566$	105541.			0.329450
$567$	46302.9	−	25449.0i	0.144026	−	0.0791596i
$568$			409150.i			1.26820i
$569$	41567.8	+	71997.6i	0.128390	+	0.222379i	0.923053	−	0.384672i	$-0.125686\pi$
$569$	41567.8	+	71997.6i	0.128390	+	0.222379i	−0.794663	+	0.607051i	$0.792352\pi$
$570$	−538184.	−	310721.i	−1.65646	−	0.956359i
$571$	475756.	+	274678.i	1.45919	+	0.842465i	0.998972	−	0.0453403i	$-0.0144372\pi$
$571$	475756.	+	274678.i	1.45919	+	0.842465i	0.460220	+	0.887805i	$0.347771\pi$
$572$	−361434.	−	626022.i	−1.10468	−	1.91337i
$573$	328307.			0.999932
$574$	13810.9	−	656071.i	0.0419179	−	1.99126i
$575$		−	25045.3i		−	0.0757513i
$576$	−146087.	−	253031.i	−0.440319	−	0.762655i
$577$	−152398.	−	87986.8i	−0.457748	−	0.264281i	0.253349	−	0.967375i	$-0.418468\pi$
$577$	−152398.	−	87986.8i	−0.457748	−	0.264281i	−0.711097	+	0.703094i	$0.751801\pi$
$578$	153604.	+	505386.i	0.459775	+	1.51275i
$579$	49788.7	−	28745.5i	0.148516	−	0.0857459i
$580$		−	566233.i		−	1.68321i
$581$	57222.7	−	94463.8i	0.169518	−	0.279842i
$582$	−522001.			−1.54108
$583$	−666095.	+	384570.i	−1.95974	+	1.13146i
$584$	134103.	−	232274.i	0.393201	−	0.681044i
$585$	216678.	+	125099.i	0.633144	+	0.365546i
$586$	−13653.0	+	7882.55i	−0.0397587	+	0.0229547i
$587$			102820.i			0.298402i	0.988807	+	0.149201i	$0.0476702\pi$
$587$			102820.i			0.298402i	−0.988807	+	0.149201i	$0.952330\pi$
$588$	−188112.	+	296280.i	−0.544078	+	0.856935i
$589$		−	743812.i		−	2.14404i
$590$	305091.	−	176144.i	0.876446	−	0.506016i
$591$	−82181.6	−	47447.6i	−0.235288	−	0.135844i
$592$	−28061.2	−	16201.1i	−0.0800687	−	0.0462277i
$593$	−185910.	+	107335.i	−0.528682	+	0.305235i	−0.740480	−	0.672079i	$-0.765402\pi$
$593$	−185910.	+	107335.i	−0.528682	+	0.305235i	0.211798	+	0.977314i	$0.432068\pi$
$594$			685228.i			1.94206i
$595$	−51478.3	+	378104.i	−0.145409	+	1.06801i
$596$	634269.			1.78559
$597$	81514.8	+	141188.i	0.228711	+	0.396140i
$598$	165649.	−	286912.i	0.463219	−	0.802318i
$599$	−204824.	+	354766.i	−0.570858	+	0.988754i	0.425620	+	0.904902i	$0.360056\pi$
$599$	−204824.	+	354766.i	−0.570858	+	0.988754i	−0.996478	+	0.0838527i	$0.973277\pi$
$600$	−15576.4	−	26979.1i	−0.0432677	−	0.0749419i
$601$	−441187.			−1.22145			−0.610723	−	0.791845i	$-0.709121\pi$
$601$	−441187.			−1.22145			−0.610723	+	0.791845i	$0.709121\pi$
$602$	16874.7	−	801612.i	0.0465633	−	2.21193i
$603$	122265.			0.336254
$604$	29858.6	+	51716.5i	0.0818455	+	0.141761i
$605$	76017.1	−	131665.i	0.207683	−	0.359717i
$606$	−314395.	−	181516.i	−0.856113	−	0.494277i
$607$	72277.1	+	125188.i	0.196166	+	0.339769i	0.947282	−	0.320401i	$-0.103818\pi$
$607$	72277.1	+	125188.i	0.196166	+	0.339769i	−0.751116	+	0.660170i	$0.770484\pi$
$608$			727119.i			1.96697i
$609$	−125885.	−	229040.i	−0.339421	−	0.617556i
$610$	−653750.			−1.75692
$611$	114150.	+	197713.i	0.305768	+	0.529606i
$612$	302451.	+	34711.9i	0.807517	+	0.0926777i
$613$	175481.	−	303942.i	0.466991	−	0.808852i	−0.532298	−	0.846557i	$-0.678671\pi$
$613$	175481.	−	303942.i	0.466991	−	0.808852i	0.999289	+	0.0377048i	$0.0120046\pi$
$614$	522180.	−	301481.i	1.38511	−	0.799693i
$615$	347571.			0.918953
$616$	−169998.	−	309302.i	−0.448005	−	0.815118i
$617$			237587.i			0.624098i	0.950066	+	0.312049i	$0.101015\pi$
$617$			237587.i			0.624098i	−0.950066	+	0.312049i	$0.898985\pi$
$618$	505954.	−	292113.i	1.32475	−	0.764846i
$619$	−32636.1	+	56527.4i	−0.0851760	+	0.147529i	−0.905466	−	0.424418i	$-0.860479\pi$
$619$	−32636.1	+	56527.4i	−0.0851760	+	0.147529i	0.820290	+	0.571948i	$0.193812\pi$
$620$	401711.	−	695784.i	1.04503	−	1.81005i
$621$	−163175.	+	94209.2i	−0.423127	+	0.244292i
$622$	−742926.			−1.92028
$623$	296298.	+	6237.35i	0.763400	+	0.0160703i
$624$			82580.2i			0.212083i
$625$	221801.	+	384170.i	0.567810	+	0.983476i
$626$	109478.	−	189622.i	0.279370	−	0.483882i
$627$	259668.	−	449758.i	0.660515	−	1.14405i
$628$	21501.7	−	12414.0i	0.0545196	−	0.0314769i
$629$	134026.	−	58145.0i	0.338756	−	0.146964i
$630$	313531.	+	189926.i	0.789950	+	0.478523i
$631$	78196.3			0.196394			0.0981968	−	0.995167i	$-0.468693\pi$
$631$	78196.3			0.196394			0.0981968	+	0.995167i	$0.468693\pi$
$632$	−347524.	+	200643.i	−0.870062	+	0.502331i
$633$	−64781.1	−	37401.4i	−0.161674	−	0.0933427i
$634$	−515345.	−	297535.i	−1.28209	−	0.740217i
$635$	−238674.	−	413396.i	−0.591914	−	1.02522i
$636$	−789397.			−1.95156
$637$	−450100.	+	235188.i	−1.10925	+	0.579610i
$638$	788703.			1.93764
$639$	307551.	−	177564.i	0.753208	−	0.434865i
$640$	−305309.	+	528810.i	−0.745383	+	1.29104i
$641$	−464097.	−	267946.i	−1.12952	−	0.652126i	−0.185703	−	0.982606i	$-0.559456\pi$
$641$	−464097.	−	267946.i	−1.12952	−	0.652126i	−0.943813	+	0.330480i	$0.892789\pi$
$642$	−392807.	+	226787.i	−0.953035	+	0.550235i
$643$	−222605.			−0.538409			−0.269205	−	0.963083i	$-0.586761\pi$
$643$	−222605.			−0.538409			−0.269205	+	0.963083i	$0.586761\pi$
$644$	150886.	−	249083.i	0.363811	−	0.600583i
$645$	424675.			1.02079
$646$	−879036.	−	651572.i	−2.10640	−	1.56134i
$647$	−32270.8	−	18631.6i	−0.0770905	−	0.0445082i	0.460959	−	0.887421i	$-0.347505\pi$
$647$	−32270.8	−	18631.6i	−0.0770905	−	0.0445082i	−0.538050	+	0.842913i	$0.680839\pi$
$648$	−27267.1	+	47228.1i	−0.0649366	+	0.112473i
$649$	147203.	+	254963.i	0.349483	+	0.605323i
$650$		−	135272.i		−	0.320170i
$651$	7804.67	−	370751.i	0.0184159	−	0.874823i
$652$		−	588561.i		−	1.38451i
$653$	62900.6	−	36315.7i	0.147512	−	0.0851664i	−0.424427	−	0.905462i	$-0.639524\pi$
$653$	62900.6	−	36315.7i	0.147512	−	0.0851664i	0.571940	+	0.820296i	$0.306191\pi$
$654$	299945.	+	173173.i	0.701272	+	0.404879i
$655$	102301.	−	177191.i	0.238450	−	0.413007i
$656$	−67865.1	−	117546.i	−0.157703	−	0.273149i
$657$	−232795.			−0.539315
$658$	161109.	+	293129.i	0.372108	+	0.677028i
$659$	447818.			1.03117			0.515586	−	0.856838i	$-0.327574\pi$
$659$	447818.			1.03117			0.515586	+	0.856838i	$0.327574\pi$
$660$	485802.	−	280478.i	1.11525	−	0.643889i
$661$	102879.	+	59397.4i	0.235464	+	0.135945i	0.613090	−	0.790013i	$-0.289926\pi$
$661$	102879.	+	59397.4i	0.235464	+	0.135945i	−0.377626	+	0.925958i	$0.623259\pi$
$662$	−379377.	+	657100.i	−0.865675	+	1.49939i
$663$	−299122.	−	221720.i	−0.680490	−	0.504403i
$664$			113995.i			0.258552i
$665$	−380737.	−	692729.i	−0.860959	−	1.56646i
$666$		−	140344.i		−	0.316405i
$667$	108436.	+	187816.i	0.243736	+	0.422164i
$668$	368585.	−	638409.i	0.826010	−	1.43069i
$669$	−195195.	−	112696.i	−0.436131	−	0.251800i
$670$	−237328.	−	411065.i	−0.528689	−	0.915716i
$671$		−	546335.i		−	1.21343i
$672$	−7629.52	+	362431.i	−0.0168950	+	0.802576i
$673$			228997.i			0.505592i	0.967520	+	0.252796i	$0.0813502\pi$
$673$			228997.i			0.505592i	−0.967520	+	0.252796i	$0.918650\pi$
$674$	−625460.	+	361109.i	−1.37683	+	0.794912i
$675$	−38466.5	+	66625.9i	−0.0844257	+	0.146230i
$676$	194095.	−	336183.i	0.424738	−	0.735668i
$677$	−178612.	−	309365.i	−0.389702	−	0.674984i	0.602707	−	0.797963i	$-0.294089\pi$
$677$	−178612.	−	309365.i	−0.389702	−	0.674984i	−0.992409	+	0.122978i	$0.960755\pi$
$678$		−	54873.4i		−	0.119372i
$679$	−567907.	−	344017.i	−1.23179	−	0.746175i
$680$	−156754.	−	361323.i	−0.339002	−	0.781407i
$681$	−62768.7	−	108719.i	−0.135347	−	0.234428i
$682$	969154.	+	559541.i	2.08365	+	1.20299i
$683$	569226.	+	328643.i	1.22023	+	0.704502i	0.964968	−	0.262368i	$-0.0845035\pi$
$683$	569226.	+	328643.i	1.22023	+	0.704502i	0.255266	+	0.966871i	$0.417837\pi$
$684$	−546147.	+	315318.i	−1.16734	+	0.673964i
$685$	−537249.			−1.14497
$686$	−666557.	+	330623.i	−1.41641	+	0.702562i
$687$			308057.i			0.652706i
$688$	−82920.0	−	143622.i	−0.175179	−	0.303419i
$689$	−989250.	−	571144.i	−2.08386	−	1.20311i
$690$	222648.	+	128546.i	0.467649	+	0.269998i
$691$	−15717.2	−	27223.1i	−0.0329170	−	0.0570139i	0.849098	−	0.528236i	$-0.177146\pi$
$691$	−15717.2	−	27223.1i	−0.0329170	−	0.0570139i	−0.882015	+	0.471222i	$0.843813\pi$
$692$	996174.			2.08028
$693$	−158720.	+	262016.i	−0.330495	+	0.545584i
$694$			813403.i			1.68883i
$695$	−65631.7	−	113678.i	−0.135877	−	0.235345i
$696$	233616.	+	134878.i	0.482264	+	0.278435i
$697$	607986.	+	69777.8i	1.25149	+	0.143632i
$698$	180160.	−	104016.i	0.369784	−	0.213495i
$699$			87254.0i			0.178579i
$700$	2502.57	−	118881.i	0.00510728	−	0.242615i
$701$	−123802.			−0.251937			−0.125968	−	0.992034i	$-0.540204\pi$
$701$	−123802.			−0.251937			−0.125968	+	0.992034i	$0.540204\pi$
$702$	−881324.	+	508833.i	−1.78839	+	1.03253i
$703$	−151317.	+	262089.i	−0.306180	+	0.530320i
$704$	−820914.	−	473955.i	−1.65635	−	0.956295i
$705$	−153428.	+	88581.7i	−0.308693	+	0.178224i
$706$			766487.i			1.53778i
$707$	−222418.	−	404677.i	−0.444971	−	0.809599i
$708$			302159.i			0.602795i
$709$	−642055.	+	370690.i	−1.27726	+	0.737427i	−0.976344	−	0.216224i	$-0.930626\pi$
$709$	−642055.	+	370690.i	−1.27726	+	0.737427i	−0.300917	+	0.953650i	$0.597293\pi$
$710$	−1.19397e6	−	689340.i	−2.36852	−	1.36747i
$711$	301639.	+	174151.i	0.596689	+	0.344499i
$712$	−264909.	+	152946.i	−0.522561	+	0.301701i
$713$			307716.i			0.605301i
$714$	−431316.	−	333998.i	−0.846057	−	0.655160i
$715$	811724.			1.58780
$716$	62024.7	+	107430.i	0.120987	+	0.209556i
$717$	−38485.0	+	66658.0i	−0.0748606	+	0.129662i
$718$	524985.	−	909300.i	1.01835	−	1.76384i
$719$	285317.	+	494183.i	0.551911	+	0.955938i	0.998137	+	0.0610177i	$0.0194346\pi$
$719$	285317.	+	494183.i	0.551911	+	0.955938i	−0.446225	+	0.894921i	$0.647232\pi$
$720$	75820.4			0.146259
$721$	742962.	+	15640.1i	1.42921	+	0.0300863i
$722$	1.44241e6			2.76704
$723$	122620.	+	212384.i	0.234577	+	0.406299i
$724$	−260633.	+	451430.i	−0.497224	+	0.861218i
$725$	76687.0	+	44275.2i	0.145897	+	0.0842335i
$726$	108672.	+	188226.i	0.206180	+	0.357114i
$727$		−	192841.i		−	0.364864i	−0.983218	−	0.182432i	$-0.941603\pi$
$727$		−	192841.i		−	0.364864i	0.983218	−	0.182432i	$-0.0583970\pi$
$728$	271580.	−	448327.i	0.512431	−	0.845926i
$729$	422687.			0.795361
$730$	451877.	+	782674.i	0.847959	+	1.46871i
$731$	742860.	+	85257.1i	1.39018	+	0.159550i
$732$	280362.	−	485601.i	0.523235	−	0.906270i
$733$	−136832.	+	78999.9i	−0.254671	+	0.147034i	−0.621901	−	0.783096i	$-0.713639\pi$
$733$	−136832.	+	78999.9i	−0.254671	+	0.147034i	0.367230	+	0.930130i	$0.380306\pi$
$734$	554554.			1.02932
$735$	−182509.	−	349284.i	−0.337839	−	0.646553i
$736$		−	300811.i		−	0.555312i
$737$	343524.	−	198334.i	0.632445	−	0.365142i
$738$	293943.	−	509124.i	0.539697	−	0.934783i
$739$	−438930.	+	760248.i	−0.803722	+	1.39209i	0.113428	+	0.993546i	$0.463817\pi$
$739$	−438930.	+	760248.i	−0.803722	+	1.39209i	−0.917150	+	0.398541i	$0.869517\pi$
$740$	−283093.	+	163444.i	−0.516971	+	0.298473i
$741$	771290.			1.40469
$742$	−1.43144e6	−	867112.i	−2.59995	−	1.57495i
$743$		−	92883.9i		−	0.168253i	−0.996455	−	0.0841265i	$-0.973190\pi$
$743$		−	92883.9i		−	0.168253i	0.996455	−	0.0841265i	$-0.0268100\pi$
$744$	191378.	+	331476.i	0.345737	+	0.598833i
$745$	−356117.	+	616813.i	−0.641624	+	1.11133i
$746$	−52350.9	+	90674.5i	−0.0940691	+	0.162932i
$747$	85687.6	−	49471.7i	0.153560	−	0.0886576i
$748$	906095.	−	393095.i	1.61946	−	0.702578i
$749$	−576812.	−	12142.5i	−1.02818	−	0.0216443i
$750$	−543810.			−0.966774
$751$	532425.	−	307396.i	0.944015	−	0.545027i	0.0527984	−	0.998605i	$-0.483186\pi$
$751$	532425.	−	307396.i	0.944015	−	0.545027i	0.891217	+	0.453578i	$0.149853\pi$
$752$	59915.2	+	34592.1i	0.105950	+	0.0611704i
$753$	56685.6	+	32727.4i	0.0999730	+	0.0577194i
$754$	585671.	+	1.01441e6i	1.03017	+	1.78431i
$755$	−67057.6			−0.117640
$756$	−783950.	+	430874.i	−1.37165	+	0.753888i
$757$	122338.			0.213487			0.106743	−	0.994287i	$-0.465958\pi$
$757$	122338.			0.213487			0.106743	+	0.994287i	$0.465958\pi$
$758$	1.05597e6	−	609666.i	1.83787	−	1.06109i
$759$	−107425.	+	186066.i	−0.186475	+	0.322985i
$760$	706571.	+	407939.i	1.22329	+	0.706266i
$761$	−351437.	+	202902.i	−0.606845	+	0.350362i	−0.771730	−	0.635951i	$-0.780608\pi$
$761$	−351437.	+	202902.i	−0.606845	+	0.350362i	0.164884	+	0.986313i	$0.447275\pi$
$762$	682408.			1.17526
$763$	212196.	+	386077.i	0.364491	+	0.663170i
$764$	−1.29341e6			−2.21589
$765$	−203571.	+	274637.i	−0.347850	+	0.469285i
$766$	50343.4	+	29065.8i	0.0857996	+	0.0495364i
$767$	−218618.	+	378658.i	−0.371617	+	0.643659i
$768$	−112130.	−	194215.i	−0.190108	−	0.329277i
$769$			1.11657e6i			1.88814i	0.329744	+	0.944070i	$0.393038\pi$
$769$			1.11657e6i			1.88814i	−0.329744	+	0.944070i	$0.606962\pi$
$770$	1.18901e6	+	25029.8i	2.00541	+	0.0422159i
$771$			108160.i			0.181952i
$772$	−196149.	+	113247.i	−0.329119	+	0.190017i
$773$	230661.	+	133172.i	0.386025	+	0.222872i	0.680436	−	0.732807i	$-0.261790\pi$
$773$	230661.	+	133172.i	0.386025	+	0.222872i	−0.294411	+	0.955679i	$0.595124\pi$
$774$	359150.	−	622066.i	0.599507	−	1.03838i
$775$	62821.7	+	108810.i	0.104594	+	0.181162i
$776$	685324.			1.13808
$777$	−78173.7	+	129050.i	−0.129485	+	0.213755i
$778$	−1.32312e6			−2.18596
$779$	−1.09787e6	+	633853.i	−1.80915	+	1.04451i
$780$	721489.	+	416552.i	1.18588	+	0.684667i
$781$	576077.	−	997795.i	0.944449	−	1.63583i
$782$	363659.	+	269556.i	0.594676	+	0.440794i
$783$		−	666175.i		−	1.08659i
$784$	−82489.3	+	129923.i	−0.134204	+	0.211375i
$785$			27879.9i			0.0452430i
$786$	146247.	+	253308.i	0.236724	+	0.410019i
$787$	296084.	−	512833.i	0.478042	−	0.827993i	−0.521641	−	0.853165i	$-0.674680\pi$
$787$	296084.	−	512833.i	0.478042	−	0.827993i	0.999683	+	0.0251721i	$0.00801339\pi$
$788$	323766.	+	186926.i	0.521409	+	0.301035i
$789$	6103.12	+	10570.9i	0.00980388	+	0.0169808i
$790$		−	1.35218e6i		−	2.16661i
$791$	36163.6	−	59699.1i	0.0577987	−	0.0954146i
$792$		−	316189.i		−	0.504077i
$793$	702683.	−	405694.i	1.11741	−	0.645138i
$794$	−181395.	+	314186.i	−0.287730	+	0.498363i
$795$	443215.	−	767672.i	0.701262	−	1.21462i
$796$	−321138.	−	556228.i	−0.506834	−	0.877863i
$797$			1.10246e6i			1.73559i	0.496924	+	0.867794i	$0.334463\pi$
$797$			1.10246e6i			1.73559i	−0.496924	+	0.867794i	$0.665537\pi$
$798$	1.12978e6	+	23783.0i	1.77414	+	0.0373475i
$799$	−286166.	+	124149.i	−0.448255	+	0.194469i
$800$	−61411.8	−	106368.i	−0.0959560	−	0.166201i
$801$	229933.	+	132752.i	0.358373	+	0.206907i
$802$	−1.22566e6	−	707634.i	−1.90555	−	1.10017i
$803$	−654076.	+	377631.i	−1.01437	+	0.585648i
$804$	407115.			0.629803
$805$	157512.	+	286583.i	0.243064	+	0.442241i
$806$			1.66200e6i			2.55836i
$807$	−242691.	−	420353.i	−0.372654	−	0.645456i
$808$	412763.	+	238309.i	0.632234	+	0.365021i
$809$	974396.	+	562568.i	1.48881	+	0.859563i	0.999918	−	0.0127828i	$-0.00406902\pi$
$809$	974396.	+	562568.i	1.48881	+	0.859563i	0.488889	+	0.872346i	$0.337402\pi$
$810$	−91879.8	−	159140.i	−0.140039	−	0.242555i
$811$	−637321.			−0.968983			−0.484492	−	0.874796i	$-0.660995\pi$
$811$	−637321.			−0.968983			−0.484492	+	0.874796i	$0.660995\pi$
$812$	495940.	+	902333.i	0.752171	+	1.36853i
$813$			248221.i			0.375542i
$814$	−227660.	−	394319.i	−0.343588	−	0.595112i
$815$	572363.	+	330454.i	0.861700	+	0.497503i
$816$	−112097.	−	12865.3i	−0.168351	−	0.0193214i
$817$	−1.34141e6	+	774465.i	−2.00964	+	1.16027i
$818$			845543.i			1.26366i
$819$	−454860.	−	9575.26i	−0.678126	−	0.0142752i
$820$	−1.36930e6			−2.03644
$821$	−422850.	+	244133.i	−0.627336	+	0.362193i	−0.779720	−	0.626129i	$-0.784638\pi$
$821$	−422850.	+	244133.i	−0.627336	+	0.362193i	0.152384	+	0.988321i	$0.451305\pi$
$822$	384020.	−	665142.i	0.568343	−	0.984399i
$823$	839873.	+	484901.i	1.23998	+	0.715902i	0.969090	−	0.246709i	$-0.0793493\pi$
$823$	839873.	+	484901.i	1.23998	+	0.715902i	0.270888	+	0.962611i	$0.412683\pi$
$824$	−664257.	+	383509.i	−0.978322	+	0.564834i
$825$			87725.2i			0.128889i
$826$	−331907.	+	547915.i	−0.486470	+	0.803069i
$827$			244109.i			0.356921i	0.983947	+	0.178460i	$0.0571116\pi$
$827$			244109.i			0.356921i	−0.983947	+	0.178460i	$0.942888\pi$
$828$	225942.	−	130448.i	0.329561	−	0.190272i
$829$	−132314.	−	76391.8i	−0.192530	−	0.111157i	0.400636	−	0.916237i	$-0.368789\pi$
$829$	−132314.	−	76391.8i	−0.192530	−	0.111157i	−0.593166	+	0.805080i	$0.702122\pi$
$830$	−332656.	−	192059.i	−0.482880	−	0.278791i
$831$	620532.	−	358264.i	0.898591	−	0.518802i
$832$		−	1.40779e6i		−	2.03372i
$833$	−249131.	−	647623.i	−0.359035	−	0.933324i
$834$	187652.			0.269786
$835$	413892.	+	716883.i	0.593628	+	1.02819i
$836$	−1.02300e6	+	1.77188e6i	−1.46373	+	2.53526i
$837$	472614.	−	818592.i	0.674615	−	1.16847i
$838$	−444695.	−	770235.i	−0.633249	−	1.09682i
$839$	−658686.			−0.935738			−0.467869	−	0.883798i	$-0.654978\pi$
$839$	−658686.			−0.935738			−0.467869	+	0.883798i	$0.654978\pi$
$840$	347908.	+	210750.i	0.493067	+	0.298682i
$841$	−59492.1			−0.0841138
$842$	−795920.	−	1.37857e6i	−1.12265	−	1.94449i
$843$	157987.	−	273642.i	0.222314	−	0.385060i
$844$	255214.	+	147348.i	0.358277	+	0.206851i
$845$	217954.	+	377507.i	0.305246	+	0.528702i
$846$			299656.i			0.418680i
$847$	−5818.46	+	276398.i	−0.00811038	+	0.385273i
$848$	−346161.			−0.481378
$849$	−50825.2	−	88031.8i	−0.0705121	−	0.122131i
$850$	183623.	+	21074.2i	0.254150	+	0.0291684i
$851$	62600.2	−	108427.i	0.0864403	−	0.149719i
$852$	1.02407e6	−	591250.i	1.41076	−	0.814501i
$853$	−349144.			−0.479850			−0.239925	−	0.970791i	$-0.577123\pi$
$853$	−349144.			−0.479850			−0.239925	+	0.970791i	$0.577123\pi$
$854$	1.04180e6	−	572591.i	1.42846	−	0.785107i
$855$		−	708155.i		−	0.968715i
$856$	515708.	−	297744.i	0.703811	−	0.406346i
$857$	198860.	−	344436.i	0.270761	−	0.468972i	−0.698296	−	0.715809i	$-0.746058\pi$
$857$	198860.	−	344436.i	0.270761	−	0.468972i	0.969057	+	0.246837i	$0.0793913\pi$
$858$	−580212.	+	1.00496e6i	−0.788156	+	1.36513i
$859$	−974453.	+	562600.i	−1.32061	+	0.762454i	−0.983826	−	0.179128i	$-0.942672\pi$
$859$	−974453.	+	562600.i	−1.32061	+	0.762454i	−0.336784	+	0.941582i	$0.609339\pi$
$860$	−1.67306e6			−2.26212
$861$	−553879.	+	304423.i	−0.747152	+	0.410649i
$862$		−	1.33458e6i		−	1.79610i
$863$	98079.7	+	169879.i	0.131691	+	0.228096i	0.924329	−	0.381597i	$-0.124626\pi$
$863$	98079.7	+	169879.i	0.131691	+	0.228096i	−0.792637	+	0.609693i	$0.791293\pi$
$864$	−462008.	+	800221.i	−0.618902	+	1.07197i
$865$	−559312.	+	968757.i	−0.747519	+	1.29474i
$866$	349314.	−	201676.i	0.465779	−	0.268918i
$867$	347572.	−	371498.i	0.462387	−	0.494218i
$868$	−30747.6	+	1.46062e6i	−0.0408104	+	1.93865i
$869$	1.13001e6			1.49638
$870$	−787197.	+	454489.i	−1.04003	+	0.600461i
$871$	510185.	+	294555.i	0.672498	+	0.388267i
$872$	−393792.	−	227356.i	−0.517885	−	0.299001i
$873$	−297419.	−	515145.i	−0.390248	−	0.675930i
$874$	−937698.			−1.22755
$875$	−591634.	−	358390.i	−0.772747	−	0.468102i
$876$	−775154.			−1.01014
$877$	477140.	−	275477.i	0.620363	−	0.358167i	−0.156647	−	0.987655i	$-0.550069\pi$
$877$	477140.	−	275477.i	0.620363	−	0.358167i	0.777011	+	0.629488i	$0.216735\pi$
$878$	−844133.	+	1.46208e6i	−1.09502	+	1.89663i
$879$	13149.7	+	7591.96i	0.0170191	+	0.00982598i
$880$	213030.	−	122993.i	0.275091	−	0.158824i
$881$	−1.37686e6			−1.77394			−0.886969	−	0.461830i	$-0.847193\pi$
$881$	−1.37686e6			−1.77394			−0.886969	+	0.461830i	$0.847193\pi$
$882$	−665982.	−	28051.6i	−0.856102	−	0.0360595i
$883$	−1.44935e6			−1.85888			−0.929441	−	0.368972i	$-0.879710\pi$
$883$	−1.44935e6			−1.85888			−0.929441	+	0.368972i	$0.879710\pi$
$884$	1.17843e6	+	873495.i	1.50800	+	1.11778i
$885$	−293844.	−	169651.i	−0.375171	−	0.216605i
$886$	315362.	−	546224.i	0.401738	−	0.695830i
$887$	−87596.5	−	151722.i	−0.111337	−	0.192841i	0.804973	−	0.593312i	$-0.202180\pi$
$887$	−87596.5	−	151722.i	−0.111337	−	0.192841i	−0.916310	+	0.400471i	$0.868847\pi$
$888$		−	155731.i		−	0.197492i
$889$	742421.	+	449731.i	0.939391	+	0.569049i
$890$		−	1.03074e6i		−	1.30127i
$891$	132993.	−	76783.4i	0.167522	−	0.0967190i
$892$	768998.	+	443981.i	0.966485	+	0.558001i
$893$	323087.	−	559602.i	0.405150	−	0.701741i
$894$	−509098.	−	881784.i	−0.636981	−	1.10328i
$895$	−139298.			−0.173899
$896$	23368.8	−	1.11010e6i	0.0291085	−	1.38276i
$897$	−319084.			−0.396571
$898$	285365.	−	164756.i	0.353874	−	0.204309i
$899$	−942207.	−	543983.i	−1.16581	−	0.673079i
$900$	53263.0	−	92254.2i	0.0657568	−	0.113894i
$901$	929408.	−	1.25387e6i	1.14487	−	1.54455i
$902$		−	1.90729e6i		−	2.34425i
$903$	−676750.	+	371955.i	−0.829951	+	0.456157i
$904$			72042.2i			0.0881556i
$905$	−292670.	−	506920.i	−0.357340	−	0.618931i
$906$	47932.1	−	83020.8i	0.0583943	−	0.101142i
$907$	267771.	+	154598.i	0.325498	+	0.187927i	0.653841	−	0.756632i	$-0.273157\pi$
$907$	267771.	+	154598.i	0.325498	+	0.187927i	−0.328342	+	0.944559i	$0.606490\pi$
$908$	247286.	+	428312.i	0.299935	+	0.519503i
$909$		−	413688.i		−	0.500663i
$910$	850736.	+	1.54786e6i	1.02733	+	1.86917i
$911$		−	869279.i		−	1.04742i	−0.851895	−	0.523712i	$-0.824547\pi$
$911$		−	869279.i		−	1.04742i	0.851895	−	0.523712i	$-0.175453\pi$
$912$	202419.	−	116867.i	0.243367	−	0.140508i
$913$	160503.	−	277999.i	0.192549	−	0.333504i
$914$	−43179.9	+	74789.8i	−0.0516879	+	0.0895261i
$915$	314824.	+	545292.i	0.376033	+	0.651308i
$916$		−	1.21363e6i		−	1.44643i
$917$	−7830.26	+	371967.i	−0.00931189	+	0.442349i
$918$	−553406.	−	1.27561e6i	−0.656687	−	1.51368i
$919$	−458352.	−	793889.i	−0.542710	−	0.940002i	−0.998747	−	0.0500409i	$-0.984065\pi$
$919$	−458352.	−	793889.i	−0.542710	−	0.940002i	0.456037	−	0.889961i	$-0.349268\pi$
$920$	−292310.	−	168765.i	−0.345357	−	0.199392i
$921$	−502930.	−	290367.i	−0.592909	−	0.342316i
$922$	1.74111e6	−	1.00523e6i	2.04816	−	1.18251i
$923$	1.71112e6			2.00853
$924$	−528501.	+	872455.i	−0.619016	+	1.02188i
$925$		−	51120.4i		−	0.0597463i
$926$	67617.9	+	117118.i	0.0788569	+	0.136584i
$927$	576553.	+	332873.i	0.670934	+	0.387364i
$928$	921062.	+	531775.i	1.06953	+	0.617493i
$929$	752935.	+	1.30412e6i	0.872421	+	1.51108i	0.859485	+	0.511161i	$0.170785\pi$
$929$	752935.	+	1.30412e6i	0.872421	+	1.51108i	0.0129364	+	0.999916i	$0.495882\pi$
$930$	−1.28974e6			−1.49120
$931$	1.21346e6	+	770442.i	1.40000	+	0.888874i
$932$		−	343749.i		−	0.395739i
$933$	357769.	+	619673.i	0.410997	+	0.711868i
$934$	−793416.	−	458079.i	−0.909510	−	0.525106i
$935$	−126460.	+	1.10186e6i	−0.144653	+	1.26039i
$936$	406675.	−	234794.i	0.464190	−	0.268000i
$937$		−	1.44183e6i		−	1.64223i	−0.570764	−	0.821114i	$-0.693353\pi$
$937$		−	1.44183e6i		−	1.64223i	0.570764	−	0.821114i	$-0.306647\pi$
$938$	738234.	+	447195.i	0.839051	+	0.508266i
$939$	−210885.			−0.239174
$940$	604450.	−	348979.i	0.684077	−	0.394952i
$941$	−75589.5	+	130925.i	−0.0853655	+	0.147857i	−0.905547	−	0.424246i	$-0.860539\pi$
$941$	−75589.5	+	130925.i	−0.0853655	+	0.147857i	0.820181	+	0.572104i	$0.193872\pi$
$942$	−34516.7	−	19928.2i	−0.0388980	−	0.0224578i
$943$	454189.	−	262226.i	0.510756	−	0.294885i
$944$			132501.i			0.148687i
$945$	21141.3	−	1.00429e6i	0.0236739	−	1.12460i
$946$		−	2.33040e6i		−	2.60404i
$947$	−838130.	+	483894.i	−0.934569	+	0.539574i	−0.888254	−	0.459353i	$-0.848081\pi$
$947$	−838130.	+	483894.i	−0.934569	+	0.539574i	−0.0463152	+	0.998927i	$0.514748\pi$
$948$	1.00439e6	+	579885.i	1.11760	+	0.645246i
$949$	−971401.	−	560839.i	−1.07861	−	0.622738i
$950$	−331576.	+	191435.i	−0.367397	+	0.212117i
$951$			573132.i			0.633714i
$952$	566266.	+	438499.i	0.624808	+	0.483832i
$953$	1.24063e6			1.36602			0.683009	−	0.730410i	$-0.260671\pi$
$953$	1.24063e6			1.36602			0.683009	+	0.730410i	$0.260671\pi$
$954$	−749660.	−	1.29845e6i	−0.823697	−	1.42668i
$955$	726198.	−	1.25781e6i	0.796248	−	1.37914i
$956$	151617.	−	262608.i	0.165894	−	0.287337i
$957$	−379813.	−	657856.i	−0.414712	−	0.718302i
$958$	2.07803e6			2.26423
$959$	856145.	−	470554.i	0.930915	−	0.511649i
$960$	1.09246e6			1.18540
$961$	−310092.	−	537095.i	−0.335771	−	0.581573i
$962$	338109.	−	585622.i	0.365348	−	0.632802i
$963$	−447617.	−	258432.i	−0.482674	−	0.278672i
$964$	−483079.	−	836717.i	−0.519833	−	0.900377i
$965$		−	254335.i		−	0.273118i
$966$	−467393.	−	9839.08i	−0.500873	−	0.0105439i
$967$	980907.			1.04900			0.524499	−	0.851411i	$-0.324253\pi$
$967$	980907.			1.04900			0.524499	+	0.851411i	$0.324253\pi$
$968$	−142674.	−	247118.i	−0.152263	−	0.263727i
$969$	−120160.	+	1.04698e6i	−0.127972	+	1.11504i
$970$	−1.15464e6	+	1.99990e6i	−1.22717	+	2.12551i
$971$	647301.	−	373719.i	0.686543	−	0.396376i	−0.115773	−	0.993276i	$-0.536934\pi$
$971$	647301.	−	373719.i	0.686543	−	0.396376i	0.802316	+	0.596900i	$0.203601\pi$
$972$	−1.32114e6			−1.39836
$973$	204154.	+	123669.i	0.215642	+	0.130628i
$974$			1.25011e6i			1.31774i
$975$	−112830.	+	65142.5i	−0.118690	+	0.0685260i
$976$	122942.	−	212942.i	0.129063	−	0.223543i
$977$	−484096.	+	838479.i	−0.507157	+	0.878422i	0.492809	+	0.870138i	$0.335970\pi$
$977$	−484096.	+	838479.i	−0.507157	+	0.878422i	−0.999966	+	0.00828389i	$0.997363\pi$
$978$	−818238.	+	472410.i	−0.855465	+	0.493903i
$979$	861380.			0.898730
$980$	719018.	+	1.37605e6i	0.748665	+	1.43279i
$981$			394674.i			0.410111i
$982$	760637.	+	1.31746e6i	0.788777	+	1.36620i
$983$	569172.	−	985834.i	0.589028	−	1.02023i	−0.405332	−	0.914170i	$-0.632844\pi$
$983$	569172.	−	985834.i	0.589028	−	1.02023i	0.994360	−	0.106057i	$-0.0338227\pi$
$984$	326172.	−	564946.i	0.336865	−	0.583468i
$985$	−363563.	+	209903.i	−0.374721	+	0.216345i
$986$	−1.46824e6	+	636975.i	−1.51023	+	0.655192i
$987$	166913.	−	275542.i	0.171339	−	0.282848i
$988$	−3.03860e6			−3.11286
$989$	554945.	−	320397.i	0.567358	−	0.327564i
$990$	922695.	+	532718.i	0.941429	+	0.543534i
$991$	298263.	+	172202.i	0.303706	+	0.175344i	0.644106	−	0.764936i	$-0.277229\pi$
$991$	298263.	+	172202.i	0.303706	+	0.175344i	−0.340401	+	0.940280i	$0.610563\pi$
$992$	754530.	+	1.30688e6i	0.766749	+	1.32805i
$993$	730782.			0.741121
$994$	2.50644e6	+	52763.1i	2.53679	+	0.0534020i
$995$	721226.			0.728493
$996$	285320.	−	164730.i	0.287617	−	0.166056i
$997$	−500179.	+	866335.i	−0.503193	+	0.871556i	0.496800	+	0.867865i	$0.334508\pi$
$997$	−500179.	+	866335.i	−0.503193	+	0.871556i	−0.999993	+	0.00369120i	$0.998825\pi$
$998$	−1.91286e6	−	1.10439e6i	−1.92054	−	1.10882i
$999$	−333060.	+	192292.i	−0.333727	+	0.192677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.h.a.101.40	yes	92
7.5	odd	6	inner	119.5.h.a.33.39	✓	92
17.16	even	2	inner	119.5.h.a.101.39	yes	92
119.33	odd	6	inner	119.5.h.a.33.40	yes	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.h.a.33.39	✓	92	7.5	odd	6	inner
119.5.h.a.33.40	yes	92	119.33	odd	6	inner
119.5.h.a.101.39	yes	92	17.16	even	2	inner
119.5.h.a.101.40	yes	92	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.16216 + 5.47702i) q^{2} +(3.04558 - 5.27510i) q^{3} +(-11.9985 + 20.7820i) q^{4} +(-13.4734 - 23.3365i) q^{5} +38.5225 q^{6} +(41.9102 + 25.3877i) q^{7} -50.5753 q^{8} +(21.9488 + 38.0165i) q^{9} +(85.2097 - 147.588i) q^{10} +(123.338 + 71.2093i) q^{11} +(73.0847 + 126.586i) q^{12} +211.513i q^{13} +(-6.52207 + 309.823i) q^{14} -164.137 q^{15} +(32.0486 + 55.5098i) q^{16} +(-287.115 - 32.9519i) q^{17} +(-138.811 + 240.428i) q^{18} +(518.456 - 299.330i) q^{19} +646.639 q^{20} +(261.564 - 143.760i) q^{21} +900.700i q^{22} +(-214.486 + 123.834i) q^{23} +(-154.031 + 266.790i) q^{24} +(-50.5624 + 87.5766i) q^{25} +(-1158.46 + 668.837i) q^{26} +760.773 q^{27} +(-1030.47 + 566.364i) q^{28} -875.656i q^{29} +(-519.027 - 898.980i) q^{30} +(621.230 - 1076.00i) q^{31} +(-607.288 + 1051.85i) q^{32} +(751.273 - 433.747i) q^{33} +(-727.426 - 1676.73i) q^{34} +(27.7893 - 1320.10i) q^{35} -1053.41 q^{36} +(-437.792 + 252.759i) q^{37} +(3278.88 + 1893.06i) q^{38} +(1115.75 + 644.180i) q^{39} +(681.419 + 1180.25i) q^{40} -2117.57 q^{41} +(1614.48 + 977.996i) q^{42} -2587.32 q^{43} +(-2959.74 + 1708.81i) q^{44} +(591.449 - 1024.42i) q^{45} +(-1356.48 - 783.163i) q^{46} +(934.757 - 539.682i) q^{47} +390.426 q^{48} +(1111.93 + 2128.01i) q^{49} -639.545 q^{50} +(-1048.26 + 1414.21i) q^{51} +(-4395.65 - 2537.83i) q^{52} +(-2700.28 + 4677.02i) q^{53} +(2405.68 + 4166.76i) q^{54} -3837.71i q^{55} +(-2119.62 - 1283.99i) q^{56} -3646.54i q^{57} +(4795.98 - 2768.96i) q^{58} +(1790.24 + 1033.59i) q^{59} +(1969.39 - 3411.09i) q^{60} +(-1918.06 - 3322.18i) q^{61} +7857.70 q^{62} +(-45.2704 + 2150.51i) q^{63} -6655.81 q^{64} +(4935.97 - 2849.79i) q^{65} +(4751.28 + 2743.16i) q^{66} +(1392.61 - 2412.08i) q^{67} +(4129.75 - 5571.45i) q^{68} +1508.58i q^{69} +(7318.06 - 4022.15i) q^{70} -8089.92i q^{71} +(-1110.07 - 1922.70i) q^{72} +(-2651.56 + 4592.64i) q^{73} +(-2768.73 - 1598.53i) q^{74} +(307.984 + 533.444i) q^{75} +14366.0i q^{76} +(3361.29 + 6115.66i) q^{77} +8147.99i q^{78} +(6871.41 - 3967.21i) q^{79} +(863.603 - 1495.81i) q^{80} +(539.139 - 933.816i) q^{81} +(-6696.09 - 11598.0i) q^{82} -2253.96i q^{83} +(-150.740 + 7160.72i) q^{84} +(3099.42 + 7144.25i) q^{85} +(-8181.52 - 14170.8i) q^{86} +(-4619.18 - 2666.88i) q^{87} +(-6237.86 - 3601.43i) q^{88} +(5237.92 - 3024.11i) q^{89} +7481.02 q^{90} +(-5369.82 + 8864.54i) q^{91} -5943.26i q^{92} +(-3784.01 - 6554.10i) q^{93} +(5911.70 + 3413.12i) q^{94} +(-13970.7 - 8065.97i) q^{95} +(3699.09 + 6407.01i) q^{96} -13550.6 q^{97} +(-8139.02 + 12819.2i) q^{98} +6251.85i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) \) 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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