LMFDB - Embedded newform 92.5.g.a.3.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [92,5,Mod(3,92)] 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("92.3"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(92, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 16])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	92.g (of order $22$, degree $10$, 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:	$9.51003660371$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			3.11
Character	$\chi$	$=$	92.3
Dual form			92.5.g.a.31.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.96738 + 2.68229i) q^{2} +(-4.62172 - 2.11067i) q^{3} +(1.61066 - 15.9187i) q^{4} +(-13.3793 + 15.4406i) q^{5} +(19.3758 - 6.13364i) q^{6} +(-22.6762 - 35.2848i) q^{7} +(37.9192 + 51.5571i) q^{8} +(-36.1383 - 41.7058i) q^{9} +(-1.71453 - 81.7053i) q^{10} +(61.5092 + 8.84369i) q^{11} +(-41.0432 + 70.1724i) q^{12} +(89.6447 + 57.6112i) q^{13} +(161.933 + 43.8793i) q^{14} +(94.4256 - 43.1227i) q^{15} +(-250.812 - 51.2793i) q^{16} +(309.477 + 90.8707i) q^{17} +(219.103 + 26.8236i) q^{18} +(37.3966 + 127.361i) q^{19} +(224.245 + 237.852i) q^{20} +(30.3284 + 210.939i) q^{21} +(-206.242 + 138.743i) q^{22} +(-158.804 + 504.601i) q^{23} +(-66.4318 - 318.318i) q^{24} +(29.5420 + 205.469i) q^{25} +(-420.539 + 69.4989i) q^{26} +(194.941 + 663.909i) q^{27} +(-598.213 + 304.144i) q^{28} +(976.281 + 286.662i) q^{29} +(-164.529 + 381.238i) q^{30} +(131.598 - 60.0987i) q^{31} +(881.798 - 520.584i) q^{32} +(-265.613 - 170.699i) q^{33} +(-1162.08 + 560.459i) q^{34} +(848.210 + 121.954i) q^{35} +(-722.110 + 508.102i) q^{36} +(-277.549 - 320.309i) q^{37} +(-452.589 - 277.620i) q^{38} +(-292.715 - 455.473i) q^{39} +(-1303.41 - 104.306i) q^{40} +(1897.53 - 2189.87i) q^{41} +(-655.794 - 544.585i) q^{42} +(1314.19 + 600.170i) q^{43} +(239.851 - 964.904i) q^{44} +1127.47 q^{45} +(-882.252 - 1923.30i) q^{46} -1217.24i q^{47} +(1050.95 + 766.379i) q^{48} +(266.602 - 583.777i) q^{49} +(-638.789 - 530.464i) q^{50} +(-1238.52 - 1073.18i) q^{51} +(1061.48 - 1334.24i) q^{52} +(934.341 - 600.465i) q^{53} +(-2359.26 - 1447.18i) q^{54} +(-959.504 + 831.415i) q^{55} +(959.322 - 2507.09i) q^{56} +(95.9806 - 667.560i) q^{57} +(-3665.90 + 1768.03i) q^{58} +(-3008.92 + 4681.97i) q^{59} +(-534.371 - 1572.59i) q^{60} +(-594.843 - 1302.52i) q^{61} +(-229.298 + 531.319i) q^{62} +(-652.104 + 2220.86i) q^{63} +(-1220.27 + 3910.01i) q^{64} +(-2088.94 + 613.367i) q^{65} +(1246.04 - 205.922i) q^{66} +(3828.44 - 550.447i) q^{67} +(1945.01 - 4780.12i) q^{68} +(1799.00 - 1996.94i) q^{69} +(-2844.08 + 1913.26i) q^{70} +(-1265.61 + 181.968i) q^{71} +(779.898 - 3444.64i) q^{72} +(952.131 - 279.571i) q^{73} +(1682.76 + 206.011i) q^{74} +(297.142 - 1011.97i) q^{75} +(2087.66 - 390.171i) q^{76} +(-1082.75 - 2370.88i) q^{77} +(2090.31 + 566.416i) q^{78} +(-3864.40 + 6013.13i) q^{79} +(4147.47 - 3186.59i) q^{80} +(-135.814 + 944.604i) q^{81} +(243.165 + 11587.9i) q^{82} +(8324.67 - 7213.36i) q^{83} +(3406.72 - 143.039i) q^{84} +(-5543.70 + 3562.72i) q^{85} +(-5509.53 + 1744.10i) q^{86} +(-3907.05 - 3385.48i) q^{87} +(1876.42 + 3506.58i) q^{88} +(-3980.50 + 8716.07i) q^{89} +(-3345.63 + 3024.20i) q^{90} -4469.50i q^{91} +(7776.82 + 3340.71i) q^{92} -735.057 q^{93} +(3264.99 + 3612.02i) q^{94} +(-2466.87 - 1126.58i) q^{95} +(-5174.21 + 544.809i) q^{96} +(-5474.83 + 6318.29i) q^{97} +(774.749 + 2447.39i) q^{98} +(-1854.01 - 2884.89i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) $ 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$

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 $

$2$	−2.96738	+	2.68229i	−0.741844	+	0.670572i
$2$	−2.96738	+	2.68229i	−0.741844	+	0.670572i
$3$	−4.62172	−	2.11067i	−0.513525	−	0.234519i	0.141760	−	0.989901i	$-0.454724\pi$
$3$	−4.62172	−	2.11067i	−0.513525	−	0.234519i	−0.655285	+	0.755382i	$0.727451\pi$
$4$	1.61066	−	15.9187i	0.100666	−	0.994920i
$5$	−13.3793	+	15.4406i	−0.535174	+	0.617623i	−0.957364	−	0.288884i	$-0.906716\pi$
$5$	−13.3793	+	15.4406i	−0.535174	+	0.617623i	0.422191	+	0.906507i	$0.361261\pi$
$6$	19.3758	−	6.13364i	0.538217	−	0.170379i
$7$	−22.6762	−	35.2848i	−0.462779	−	0.720098i	0.528921	−	0.848671i	$-0.322597\pi$
$7$	−22.6762	−	35.2848i	−0.462779	−	0.720098i	−0.991700	+	0.128573i	$0.958960\pi$
$8$	37.9192	+	51.5571i	0.592487	+	0.805580i
$9$	−36.1383	−	41.7058i	−0.446152	−	0.514887i
$10$	−1.71453	−	81.7053i	−0.0171453	−	0.817053i
$11$	61.5092	+	8.84369i	0.508341	+	0.0730884i	0.391713	−	0.920087i	$-0.371883\pi$
$11$	61.5092	+	8.84369i	0.508341	+	0.0730884i	0.116628	+	0.993176i	$0.462792\pi$
$12$	−41.0432	+	70.1724i	−0.285022	+	0.487308i
$13$	89.6447	+	57.6112i	0.530442	+	0.340894i	0.778290	−	0.627904i	$-0.216087\pi$
$13$	89.6447	+	57.6112i	0.530442	+	0.340894i	−0.247848	+	0.968799i	$0.579723\pi$
$14$	161.933	+	43.8793i	0.826188	+	0.223874i
$15$	94.4256	−	43.1227i	0.419669	−	0.191657i
$16$	−250.812	−	51.2793i	−0.979733	−	0.200310i
$17$	309.477	+	90.8707i	1.07086	+	0.314431i	0.769215	−	0.638990i	$-0.220648\pi$
$17$	309.477	+	90.8707i	1.07086	+	0.314431i	0.301640	+	0.953422i	$0.402466\pi$
$18$	219.103	+	26.8236i	0.676244	+	0.0827889i
$19$	37.3966	+	127.361i	0.103592	+	0.352801i	0.994934	−	0.100530i	$-0.0320538\pi$
$19$	37.3966	+	127.361i	0.103592	+	0.352801i	−0.891342	+	0.453331i	$0.850236\pi$
$20$	224.245	+	237.852i	0.560612	+	0.594629i
$21$	30.3284	+	210.939i	0.0687719	+	0.478319i
$22$	−206.242	+	138.743i	−0.426121	+	0.286659i
$23$	−158.804	+	504.601i	−0.300197	+	0.953877i
$23$	−158.804	+	504.601i	−0.300197	+	0.953877i
$24$	−66.4318	−	318.318i	−0.115333	−	0.552635i
$25$	29.5420	+	205.469i	0.0472672	+	0.328750i
$26$	−420.539	+	69.4989i	−0.622100	+	0.102809i
$27$	194.941	+	663.909i	0.267409	+	0.910712i
$28$	−598.213	+	304.144i	−0.763027	+	0.387939i
$29$	976.281	+	286.662i	1.16086	+	0.340858i	0.804766	−	0.593593i	$-0.202291\pi$
$29$	976.281	+	286.662i	1.16086	+	0.340858i	0.356092	+	0.934451i	$0.384109\pi$
$30$	−164.529	+	381.238i	−0.182810	+	0.423598i
$31$	131.598	−	60.0987i	0.136938	−	0.0625377i	−0.345767	−	0.938320i	$-0.612381\pi$
$31$	131.598	−	60.0987i	0.136938	−	0.0625377i	0.482706	+	0.875783i	$0.339654\pi$
$32$	881.798	−	520.584i	0.861131	−	0.508383i
$33$	−265.613	−	170.699i	−0.243905	−	0.156748i
$34$	−1162.08	+	560.459i	−1.00526	+	0.484826i
$35$	848.210	+	121.954i	0.692417	+	0.0995545i
$36$	−722.110	+	508.102i	−0.557184	+	0.392054i
$37$	−277.549	−	320.309i	−0.202739	−	0.233973i	0.645271	−	0.763954i	$-0.276745\pi$
$37$	−277.549	−	320.309i	−0.202739	−	0.233973i	−0.848010	+	0.529981i	$0.822199\pi$
$38$	−452.589	−	277.620i	−0.313427	−	0.192258i
$39$	−292.715	−	455.473i	−0.192449	−	0.299457i
$40$	−1303.41	−	104.306i	−0.814628	−	0.0651914i
$41$	1897.53	−	2189.87i	1.12881	−	1.30272i	0.181146	−	0.983456i	$-0.442019\pi$
$41$	1897.53	−	2189.87i	1.12881	−	1.30272i	0.947666	−	0.319263i	$-0.103435\pi$
$42$	−655.794	−	544.585i	−0.371765	−	0.308722i
$43$	1314.19	+	600.170i	0.710757	+	0.324592i	0.737778	−	0.675043i	$-0.235875\pi$
$43$	1314.19	+	600.170i	0.710757	+	0.324592i	−0.0270215	+	0.999635i	$0.508602\pi$
$44$	239.851	−	964.904i	0.123890	−	0.498401i
$45$	1127.47			0.556775
$46$	−882.252	−	1923.30i	−0.416943	−	0.908932i
$47$		−	1217.24i		−	0.551037i	−0.961296	−	0.275519i	$-0.911150\pi$
$47$		−	1217.24i		−	0.551037i	0.961296	−	0.275519i	$-0.0888496\pi$
$48$	1050.95	+	766.379i	0.456141	+	0.332630i
$49$	266.602	−	583.777i	0.111038	−	0.243139i
$50$	−638.789	−	530.464i	−0.255516	−	0.212186i
$51$	−1238.52	−	1073.18i	−0.476171	−	0.412604i
$52$	1061.48	−	1334.24i	0.392560	−	0.493431i
$53$	934.341	−	600.465i	0.332624	−	0.213765i	−0.363658	−	0.931532i	$-0.618472\pi$
$53$	934.341	−	600.465i	0.332624	−	0.213765i	0.696283	+	0.717768i	$0.254836\pi$
$54$	−2359.26	−	1447.18i	−0.809074	−	0.496289i
$55$	−959.504	+	831.415i	−0.317192	+	0.274848i
$56$	959.322	−	2507.09i	0.305906	−	0.799454i
$57$	95.9806	−	667.560i	0.0295416	−	0.205466i
$58$	−3665.90	+	1768.03i	−1.08975	+	0.525575i
$59$	−3008.92	+	4681.97i	−0.864383	+	1.34501i	0.0732256	+	0.997315i	$0.476671\pi$
$59$	−3008.92	+	4681.97i	−0.864383	+	1.34501i	−0.937609	+	0.347691i	$0.886966\pi$
$60$	−534.371	−	1572.59i	−0.148436	−	0.436831i
$61$	−594.843	−	1302.52i	−0.159861	−	0.350047i	0.812704	−	0.582676i	$-0.197994\pi$
$61$	−594.843	−	1302.52i	−0.159861	−	0.350047i	−0.972565	+	0.232629i	$0.925267\pi$
$62$	−229.298	+	531.319i	−0.0596510	+	0.138220i
$63$	−652.104	+	2220.86i	−0.164299	+	0.559552i
$64$	−1220.27	+	3910.01i	−0.297918	+	0.954591i
$65$	−2088.94	+	613.367i	−0.494423	+	0.145176i
$66$	1246.04	−	205.922i	0.286051	−	0.0472731i
$67$	3828.44	−	550.447i	0.852849	−	0.122621i	0.297994	−	0.954568i	$-0.403683\pi$
$67$	3828.44	−	550.447i	0.852849	−	0.122621i	0.554856	+	0.831947i	$0.312773\pi$
$68$	1945.01	−	4780.12i	0.420633	−	1.03376i
$69$	1799.00	−	1996.94i	0.377861	−	0.419438i
$70$	−2844.08	+	1913.26i	−0.580424	+	0.390461i
$71$	−1265.61	+	181.968i	−0.251064	+	0.0360975i	−0.266698	−	0.963780i	$-0.585933\pi$
$71$	−1265.61	+	181.968i	−0.251064	+	0.0360975i	0.0156338	+	0.999878i	$0.495023\pi$
$72$	779.898	−	3444.64i	0.150443	−	0.664475i
$73$	952.131	−	279.571i	0.178670	−	0.0524621i	−0.191174	−	0.981556i	$-0.561229\pi$
$73$	952.131	−	279.571i	0.178670	−	0.0524621i	0.369844	+	0.929094i	$0.379411\pi$
$74$	1682.76	+	206.011i	0.307296	+	0.0376206i
$75$	297.142	−	1011.97i	0.0528253	−	0.179907i
$76$	2087.66	−	390.171i	0.361437	−	0.0675503i
$77$	−1082.75	−	2370.88i	−0.182619	−	0.399879i
$78$	2090.31	+	566.416i	0.343574	+	0.0930992i
$79$	−3864.40	+	6013.13i	−0.619196	+	0.963487i	0.380062	+	0.924961i	$0.375903\pi$
$79$	−3864.40	+	6013.13i	−0.619196	+	0.963487i	−0.999258	+	0.0385264i	$0.987734\pi$
$80$	4147.47	−	3186.59i	0.648043	−	0.497905i
$81$	−135.814	+	944.604i	−0.0207001	+	0.143973i
$82$	243.165	+	11587.9i	0.0361638	+	1.72337i
$83$	8324.67	−	7213.36i	1.20840	−	1.04708i	0.210822	−	0.977524i	$-0.432386\pi$
$83$	8324.67	−	7213.36i	1.20840	−	1.04708i	0.997578	−	0.0695600i	$-0.0221595\pi$
$84$	3406.72	−	143.039i	0.482812	−	0.0202720i
$85$	−5543.70	+	3562.72i	−0.767293	+	0.493110i
$86$	−5509.53	+	1744.10i	−0.744933	+	0.235817i
$87$	−3907.05	−	3385.48i	−0.516191	−	0.447282i
$88$	1876.42	+	3506.58i	0.242307	+	0.452813i
$89$	−3980.50	+	8716.07i	−0.502524	+	1.10038i	0.473116	+	0.881000i	$0.343129\pi$
$89$	−3980.50	+	8716.07i	−0.502524	+	1.10038i	−0.975641	+	0.219375i	$0.929598\pi$
$90$	−3345.63	+	3024.20i	−0.413040	+	0.373358i
$91$		−	4469.50i		−	0.539729i
$92$	7776.82	+	3340.71i	0.918812	+	0.394696i
$93$	−735.057			−0.0849876
$94$	3264.99	+	3612.02i	0.369510	+	0.408784i
$95$	−2466.87	−	1126.58i	−0.273338	−	0.124829i
$96$	−5174.21	+	544.809i	−0.561438	+	0.0591155i
$97$	−5474.83	+	6318.29i	−0.581872	+	0.671516i	−0.968006	−	0.250927i	$-0.919265\pi$
$97$	−5474.83	+	6318.29i	−0.581872	+	0.671516i	0.386134	+	0.922443i	$0.373810\pi$
$98$	774.749	+	2447.39i	0.0806694	+	0.254830i
$99$	−1854.01	−	2884.89i	−0.189165	−	0.294346i
$100$	3318.39	−	139.330i	0.331839	−	0.0139330i
$101$	3410.06	+	3935.42i	0.334287	+	0.385787i	0.897862	−	0.440277i	$-0.145120\pi$
$101$	3410.06	+	3935.42i	0.334287	+	0.385787i	−0.563575	+	0.826065i	$0.690574\pi$
$102$	6553.74	−	137.526i	0.629925	−	0.0132186i
$103$	6484.14	+	932.278i	0.611192	+	0.0878761i	0.440958	−	0.897528i	$-0.354639\pi$
$103$	6484.14	+	932.278i	0.611192	+	0.0878761i	0.170234	+	0.985404i	$0.445548\pi$
$104$	428.988	+	6806.39i	0.0396623	+	0.629289i
$105$	−3662.79	−	2353.93i	−0.332226	−	0.213509i
$106$	−1161.92	+	4287.98i	−0.103411	+	0.381629i
$107$	12438.1	−	5680.28i	1.08639	−	0.496138i	0.209981	−	0.977705i	$-0.432660\pi$
$107$	12438.1	−	5680.28i	1.08639	−	0.496138i	0.876409	+	0.481568i	$0.159932\pi$
$108$	10882.6	−	2033.88i	0.933005	−	0.174373i
$109$	5777.75	+	1696.50i	0.486301	+	0.142791i	0.515687	−	0.856777i	$-0.327537\pi$
$109$	5777.75	+	1696.50i	0.486301	+	0.142791i	−0.0293854	+	0.999568i	$0.509355\pi$
$110$	617.116	−	5040.79i	0.0510014	−	0.416594i
$111$	606.690	+	2066.20i	0.0492403	+	0.167697i
$112$	3878.07	+	10012.7i	0.309157	+	0.798203i
$113$	3255.80	+	22644.6i	0.254977	+	1.77340i	0.567383	+	0.823454i	$0.307956\pi$
$113$	3255.80	+	22644.6i	0.254977	+	1.77340i	−0.312406	+	0.949949i	$0.601135\pi$
$114$	1505.78	+	2238.35i	0.115865	+	0.172234i
$115$	−5666.63	−	9203.26i	−0.428479	−	0.695899i
$116$	6135.75	−	15079.4i	0.455986	−	1.12065i
$117$	−836.887	−	5820.68i	−0.0611357	−	0.425208i
$118$	−3629.79	−	21964.0i	−0.260686	−	1.57742i
$119$	−3811.40	−	12980.4i	−0.269148	−	0.916633i
$120$	5803.82	+	3233.13i	0.403043	+	0.224523i
$121$	−10342.8	−	3036.91i	−0.706425	−	0.207425i
$122$	5258.87	+	2269.54i	0.353324	+	0.152482i
$123$	−13392.0	+	6115.91i	−0.885186	+	0.404251i
$124$	−744.735	−	2191.67i	−0.0484349	−	0.142538i
$125$	−14310.0	−	9196.48i	−0.915840	−	0.588574i
$126$	−4021.95	−	8339.27i	−0.253336	−	0.525275i
$127$	9815.57	+	1411.27i	0.608566	+	0.0874986i	0.439707	−	0.898141i	$-0.355082\pi$
$127$	9815.57	+	1411.27i	0.608566	+	0.0874986i	0.168860	+	0.985640i	$0.445991\pi$
$128$	−6866.75	−	14875.6i	−0.419113	−	0.907934i
$129$	−4807.06	−	5547.64i	−0.288868	−	0.333372i
$130$	4553.44	−	7423.22i	0.269434	−	0.439244i
$131$	−3487.19	−	5426.17i	−0.203204	−	0.316192i	0.724662	−	0.689104i	$-0.241996\pi$
$131$	−3487.19	−	5426.17i	−0.203204	−	0.316192i	−0.927867	+	0.372912i	$0.878359\pi$
$132$	−3145.12	+	3953.28i	−0.180505	+	0.226887i
$133$	3645.90	−	4207.60i	0.206111	−	0.237865i
$134$	−9883.97	+	11902.4i	−0.550455	+	0.662863i
$135$	−12859.3	−	5872.66i	−0.705587	−	0.322231i
$136$	7050.08	+	19401.5i	0.381168	+	1.04896i
$137$	20054.1			1.06847			0.534234	−	0.845336i	$-0.320600\pi$
$137$	20054.1			1.06847			0.534234	+	0.845336i	$0.320600\pi$
$138$	18.0721	+	10751.1i	0.000948966	+	0.564541i
$139$			14351.3i			0.742780i	0.928477	+	0.371390i	$0.121119\pi$
$139$			14351.3i			0.742780i	−0.928477	+	0.371390i	$0.878881\pi$
$140$	3307.53	−	13306.0i	0.168752	−	0.678877i
$141$	−2569.20	+	5625.75i	−0.129229	+	0.282971i
$142$	3267.46	−	3934.71i	0.162044	−	0.195135i
$143$	5004.48	+	4336.41i	0.244730	+	0.212060i
$144$	6925.26	+	12313.5i	0.333973	+	0.593820i
$145$	−17488.2	+	11239.0i	−0.831782	+	0.534554i
$146$	−2075.44	+	3383.48i	−0.0973654	+	0.158730i
$147$	−2464.32	+	2135.35i	−0.114041	+	0.0988175i
$148$	−5545.95	+	3902.32i	−0.253193	+	0.178156i
$149$	2617.39	−	18204.4i	0.117895	−	0.819979i	−0.841971	−	0.539522i	$-0.818605\pi$
$149$	2617.39	−	18204.4i	0.117895	−	0.819979i	0.959867	−	0.280457i	$-0.0904861\pi$
$150$	1832.67	+	3799.93i	0.0814521	+	0.168886i
$151$	−4793.71	+	7459.15i	−0.210241	+	0.327141i	−0.930319	−	0.366752i	$-0.880470\pi$
$151$	−4793.71	+	7459.15i	−0.210241	+	0.327141i	0.720078	+	0.693893i	$0.244106\pi$
$152$	−5148.33	+	6757.49i	−0.222833	+	0.292481i
$153$	−7394.14	−	16190.9i	−0.315868	−	0.691653i
$154$	9572.31	+	4131.07i	0.403622	+	0.174189i
$155$	−832.733	+	2836.03i	−0.0346611	+	0.118045i
$156$	−7722.02	+	3926.04i	−0.317309	+	0.161326i
$157$	−28067.0	+	8241.22i	−1.13867	+	0.334343i	−0.796109	−	0.605153i	$-0.793112\pi$
$157$	−28067.0	+	8241.22i	−1.13867	+	0.334343i	−0.342559	+	0.939496i	$0.611294\pi$
$158$	−4661.80	−	28208.7i	−0.186741	−	1.12997i
$159$	−5585.65	+	803.095i	−0.220943	+	0.0317668i
$160$	−3759.76	+	20580.5i	−0.146866	+	0.803928i
$161$	21405.8	−	5839.03i	0.825810	−	0.225263i
$162$	−2130.69	−	3167.29i	−0.0811877	−	0.120686i
$163$	9182.78	−	1320.28i	0.345620	−	0.0496927i	0.0326809	−	0.999466i	$-0.489595\pi$
$163$	9182.78	−	1320.28i	0.345620	−	0.0496927i	0.312939	+	0.949773i	$0.398686\pi$
$164$	−31803.7	−	33733.5i	−1.18247	−	1.25422i
$165$	6189.41	−	1817.37i	0.227343	−	0.0667539i
$166$	−5354.11	+	43733.9i	−0.194299	+	1.58709i
$167$	−12055.2	+	41056.1i	−0.432255	+	1.47213i	0.399371	+	0.916789i	$0.369229\pi$
$167$	−12055.2	+	41056.1i	−0.432255	+	1.47213i	−0.831626	+	0.555336i	$0.812590\pi$
$168$	−9725.36	+	9562.26i	−0.344578	+	0.338799i
$169$	−7147.54	−	15650.9i	−0.250255	−	0.547982i
$170$	6894.00	−	25441.7i	0.238547	−	0.880336i
$171$	3960.25	−	6162.27i	0.135435	−	0.210741i
$172$	11670.7	−	19953.5i	0.394492	−	0.674471i
$173$	6690.18	−	46531.2i	0.223535	−	1.55472i	−0.500979	−	0.865460i	$-0.667027\pi$
$173$	6690.18	−	46531.2i	0.223535	−	1.55472i	0.724514	−	0.689260i	$-0.242064\pi$
$174$	20674.5	−	433.842i	0.682869	−	0.0143296i
$175$	6580.04	−	5701.63i	0.214858	−	0.186176i
$176$	−14973.7	−	5372.25i	−0.483398	−	0.173433i
$177$	23788.5	−	15287.9i	0.759312	−	0.487980i
$178$	−11567.4	−	36540.7i	−0.365086	−	1.15329i
$179$	345.845	+	299.677i	0.0107938	+	0.00935291i	0.660241	−	0.751054i	$-0.270454\pi$
$179$	345.845	+	299.677i	0.0107938	+	0.00935291i	−0.649447	+	0.760407i	$0.725000\pi$
$180$	1815.97	−	17947.9i	0.0560484	−	0.553947i
$181$	−5988.21	+	13112.4i	−0.182785	+	0.400243i	−0.978738	−	0.205116i	$-0.934243\pi$
$181$	−5988.21	+	13112.4i	−0.182785	+	0.400243i	0.795953	+	0.605359i	$0.206970\pi$
$182$	11988.5	+	13262.7i	0.361927	+	0.400395i
$183$			7275.43i			0.217248i
$184$	−32037.5	+	10946.5i	−0.946287	+	0.323327i
$185$	8659.18			0.253008
$186$	2181.19	−	1971.64i	0.0630475	−	0.0569903i
$187$	18232.1	+	8326.31i	0.521378	+	0.238105i
$188$	−19376.9	−	1960.56i	−0.548238	−	0.0554709i
$189$	19005.4	−	21933.4i	0.532051	−	0.614019i
$190$	10342.0	−	3273.86i	0.286481	−	0.0906888i
$191$	2160.09	+	3361.17i	0.0592115	+	0.0921349i	0.869597	−	0.493762i	$-0.164379\pi$
$191$	2160.09	+	3361.17i	0.0592115	+	0.0921349i	−0.810385	+	0.585897i	$0.800742\pi$
$192$	13892.5	−	15495.4i	0.376858	−	0.420339i
$193$	31014.7	+	35792.9i	0.832632	+	0.960908i	0.999686	−	0.0250395i	$-0.00797116\pi$
$193$	31014.7	+	35792.9i	0.832632	+	0.960908i	−0.167055	+	0.985948i	$0.553426\pi$
$194$	−701.588	−	33433.8i	−0.0186414	−	0.888347i
$195$	10949.1	+	1574.24i	0.287945	+	0.0414002i
$196$	−8863.58	−	5184.23i	−0.230726	−	0.134950i
$197$	58797.5	+	37786.8i	1.51505	+	0.973662i	0.992658	+	0.120955i	$0.0385956\pi$
$197$	58797.5	+	37786.8i	1.51505	+	0.973662i	0.522389	+	0.852707i	$0.325041\pi$
$198$	13239.6	+	3587.58i	0.337712	+	0.0915105i
$199$	1464.38	−	668.760i	0.0369783	−	0.0168874i	−0.396840	−	0.917888i	$-0.629893\pi$
$199$	1464.38	−	668.760i	0.0369783	−	0.0168874i	0.433818	+	0.901000i	$0.357166\pi$
$200$	−9473.18	+	9314.31i	−0.236830	+	0.232858i
$201$	−18855.8	−	5536.57i	−0.466716	−	0.137040i
$202$	−20674.9	−	2531.11i	−0.506687	−	0.0620309i
$203$	−12023.5	−	40948.3i	−0.291769	−	0.993674i
$204$	−19078.5	+	17987.1i	−0.458443	+	0.432217i
$205$	8425.13	+	58598.0i	0.200479	+	1.39436i
$206$	−21741.5	+	14625.9i	−0.512337	+	0.344658i
$207$	26783.7	−	11612.4i	0.625073	−	0.271006i
$208$	−19529.7	−	19046.5i	−0.451407	−	0.440238i
$209$	1173.89	+	8164.61i	0.0268742	+	0.186914i
$210$	17182.8	−	2839.65i	0.389633	−	0.0643912i
$211$	−12669.9	−	43149.6i	−0.284582	−	0.969196i	−0.970416	−	0.241439i	$-0.922381\pi$
$211$	−12669.9	−	43149.6i	−0.284582	−	0.969196i	0.685834	−	0.727758i	$-0.259437\pi$
$212$	−8053.73	−	15840.7i	−0.179195	−	0.352453i
$213$	6233.39	+	1830.29i	0.137393	+	0.0403423i
$214$	−21672.3	+	50218.0i	−0.473236	+	1.09656i
$215$	−26850.0	+	12262.0i	−0.580854	+	0.265267i
$216$	−26837.2	+	35225.5i	−0.575215	+	0.755004i
$217$	−5104.71	−	3280.60i	−0.108406	−	0.0696680i
$218$	−21695.3	+	10463.4i	−0.456512	+	0.220171i
$219$	−4990.57	−	717.535i	−0.104055	−	0.0149608i
$220$	11689.6	+	16613.2i	0.241521	+	0.343248i
$221$	22507.8	+	25975.4i	0.460839	+	0.531836i
$222$	−7342.41	−	4503.87i	−0.148982	−	0.0913860i
$223$	17385.8	+	27052.8i	0.349610	+	0.544004i	0.970872	−	0.239599i	$-0.0770160\pi$
$223$	17385.8	+	27052.8i	0.349610	+	0.544004i	−0.621262	+	0.783603i	$0.713380\pi$
$224$	−38364.5	−	19309.2i	−0.764599	−	0.384830i
$225$	7501.66	−	8657.37i	0.148181	−	0.171010i
$226$	−70400.5	−	58462.0i	−1.37835	−	1.14461i
$227$	83172.8	+	37983.7i	1.61410	+	0.737133i	0.998695	−	0.0510804i	$-0.0162665\pi$
$227$	83172.8	+	37983.7i	1.61410	+	0.737133i	0.615402	+	0.788213i	$0.288994\pi$
$228$	−10472.1	−	2603.10i	−0.201449	−	0.0500751i
$229$	−16857.9			−0.321464			−0.160732	−	0.986998i	$-0.551386\pi$
$229$	−16857.9			−0.321464			−0.160732	+	0.986998i	$0.551386\pi$
$230$	41500.8	+	12110.0i	0.784515	+	0.228923i
$231$			13242.9i			0.248175i
$232$	22240.3	+	61204.2i	0.413204	+	1.13712i
$233$	18808.5	−	41184.9i	0.346452	−	0.758624i	−0.653546	−	0.756886i	$-0.726720\pi$
$233$	18808.5	−	41184.9i	0.346452	−	0.758624i	0.999998	−	0.00173775i	$-0.000553144\pi$
$234$	18096.1	+	15027.4i	0.330486	+	0.274443i
$235$	18794.9	+	16285.9i	0.340333	+	0.294901i
$236$	69684.6	+	55439.2i	1.25116	+	0.995389i
$237$	30551.9	−	19634.5i	0.543929	−	0.349562i
$238$	46127.2	+	28294.6i	0.814334	+	0.499516i
$239$	−78808.3	+	68287.8i	−1.37967	+	1.19549i	−0.422365	+	0.906426i	$0.638800\pi$
$239$	−78808.3	+	68287.8i	−1.37967	+	1.19549i	−0.957309	+	0.289068i	$0.906655\pi$
$240$	−25894.3	+	5973.60i	−0.449554	+	0.103708i
$241$	4236.69	−	29466.8i	0.0729445	−	0.507340i	−0.920292	−	0.391232i	$-0.872049\pi$
$241$	4236.69	−	29466.8i	0.0729445	−	0.507340i	0.993237	−	0.116108i	$-0.0370420\pi$
$242$	38836.7	−	18730.6i	0.663151	−	0.319832i
$243$	32922.7	−	51228.7i	0.557549	−	0.867563i
$244$	−21692.6	+	7371.22i	−0.364361	+	0.123811i
$245$	5446.90	+	11927.0i	0.0907438	+	0.198701i
$246$	23334.4	−	54069.4i	0.385591	−	0.893472i
$247$	−3985.02	+	13571.7i	−0.0653185	+	0.222454i
$248$	8088.60	+	4505.91i	0.131513	+	0.0732621i
$249$	−53699.4	+	15767.6i	−0.866105	+	0.254311i
$250$	67130.8	−	11094.1i	1.07409	−	0.177506i
$251$	−13233.6	+	1902.70i	−0.210053	+	0.0302011i	−0.246538	−	0.969133i	$-0.579293\pi$
$251$	−13233.6	+	1902.70i	−0.210053	+	0.0302011i	0.0364848	+	0.999334i	$0.488384\pi$
$252$	34303.0	+	13957.7i	0.540170	+	0.219793i
$253$	−14230.5	+	29633.2i	−0.222320	+	0.462954i
$254$	−32911.9	+	22140.4i	−0.510136	+	0.343177i
$255$	33141.2	−	4764.98i	0.509668	−	0.0732792i
$256$	60276.9	+	25722.9i	0.919752	+	0.392500i
$257$	−43070.8	+	12646.7i	−0.652104	+	0.191475i	−0.591019	−	0.806658i	$-0.701274\pi$
$257$	−43070.8	+	12646.7i	−0.652104	+	0.191475i	−0.0610849	+	0.998133i	$0.519456\pi$
$258$	29144.7	+	3568.03i	0.437845	+	0.0536030i
$259$	−5008.29	+	17056.7i	−0.0746603	+	0.254270i
$260$	6399.46	+	34241.1i	0.0946665	+	0.506526i
$261$	−23325.7	−	51076.1i	−0.342415	−	0.749785i
$262$	24902.4	+	6747.86i	0.362776	+	0.0983022i
$263$	−43614.9	+	67866.1i	−0.630556	+	0.981164i	0.368123	+	0.929777i	$0.380000\pi$
$263$	−43614.9	+	67866.1i	−0.630556	+	0.981164i	−0.998679	+	0.0513867i	$0.983636\pi$
$264$	−1271.07	−	20167.0i	−0.0182373	−	0.289356i
$265$	−3229.35	+	22460.6i	−0.0459857	+	0.319838i
$266$	467.215	+	22264.9i	0.00660319	+	0.314671i
$267$	36793.5	−	31881.8i	0.516118	−	0.447219i
$268$	−2596.09	−	61830.5i	−0.0361452	−	0.860861i
$269$	−53680.4	+	34498.3i	−0.741842	+	0.476753i	−0.856173	−	0.516690i	$-0.827164\pi$
$269$	−53680.4	+	34498.3i	−0.741842	+	0.476753i	0.114331	+	0.993443i	$0.463528\pi$
$270$	53910.6	−	17066.0i	0.739515	−	0.234102i
$271$	9698.94	+	8404.18i	0.132064	+	0.114434i	0.718389	−	0.695642i	$-0.244880\pi$
$271$	9698.94	+	8404.18i	0.132064	+	0.114434i	−0.586324	+	0.810077i	$0.699425\pi$
$272$	−72960.7	−	38661.2i	−0.986168	−	0.522561i
$273$	−9433.64	+	20656.8i	−0.126577	+	0.277164i
$274$	−59508.1	+	53790.8i	−0.792638	+	0.716485i
$275$			12899.5i			0.170572i
$276$	−28891.2	−	31854.1i	−0.379269	−	0.418165i
$277$	−109581.			−1.42815			−0.714075	−	0.700069i	$-0.753152\pi$
$277$	−109581.			−1.42815			−0.714075	+	0.700069i	$0.753152\pi$
$278$	−38494.2	−	42585.6i	−0.498087	−	0.551027i
$279$	−7262.19	−	3316.53i	−0.0932952	−	0.0426065i
$280$	25875.8	+	48355.7i	0.330049	+	0.616782i
$281$	90699.1	−	104672.i	1.14866	−	1.32562i	0.211231	−	0.977436i	$-0.432253\pi$
$281$	90699.1	−	104672.i	1.14866	−	1.32562i	0.937426	−	0.348185i	$-0.113202\pi$
$282$	−7466.12	−	23585.1i	−0.0938851	−	0.296578i
$283$	−74014.6	−	115169.i	−0.924154	−	1.43801i	−0.898813	−	0.438333i	$-0.855569\pi$
$283$	−74014.6	−	115169.i	−0.924154	−	1.43801i	−0.0253416	−	0.999679i	$-0.508067\pi$
$284$	858.221	+	20440.0i	0.0106405	+	0.253422i
$285$	9023.36	+	10413.5i	0.111091	+	0.128206i
$286$	−26481.7	+	555.702i	−0.323753	+	0.00679375i
$287$	−120298.	−	17296.2i	−1.46048	−	0.209985i
$288$	−53578.1	−	17963.1i	−0.645955	−	0.216569i
$289$	17256.3	+	11089.9i	0.206610	+	0.132780i
$290$	21747.9	−	80258.8i	0.258596	−	0.954326i
$291$	38639.0	−	17645.8i	0.456289	−	0.208380i
$292$	−2916.85	−	15607.0i	−0.0342096	−	0.183043i
$293$	37592.6	+	11038.2i	0.437892	+	0.128577i	0.493246	−	0.869890i	$-0.335810\pi$
$293$	37592.6	+	11038.2i	0.437892	+	0.128577i	−0.0553535	+	0.998467i	$0.517629\pi$
$294$	1584.96	−	12946.4i	0.0183368	−	0.149780i
$295$	−32035.0	−	109101.i	−0.368112	−	1.25368i
$296$	5989.77	−	26455.5i	0.0683639	−	0.301948i
$297$	6119.28	+	42560.5i	0.0693725	+	0.482496i
$298$	41062.6	+	61039.8i	0.462395	+	0.687354i
$299$	−43306.6	+	36085.9i	−0.484409	+	0.403641i
$300$	−15630.7	−	6360.08i	−0.173675	−	0.0706675i
$301$	−8623.89	−	59980.5i	−0.0951854	−	0.662029i
$302$	−5782.86	−	34992.2i	−0.0634058	−	0.383670i
$303$	−7453.98	−	25385.9i	−0.0811901	−	0.276508i
$304$	−2848.51	−	33861.3i	−0.0308227	−	0.366401i
$305$	28070.3	+	8242.20i	0.301750	+	0.0886019i
$306$	65369.9	+	28211.3i	0.698128	+	0.301287i
$307$	158813.	−	72527.7i	1.68504	−	0.769532i	0.685917	−	0.727680i	$-0.259401\pi$
$307$	158813.	−	72527.7i	1.68504	−	0.769532i	0.999124	−	0.0418528i	$-0.0133260\pi$
$308$	−39485.4	+	13417.2i	−0.416231	+	0.141437i
$309$	−28000.2	−	17994.6i	−0.293254	−	0.188463i
$310$	−5136.01	−	10649.2i	−0.0534444	−	0.110814i
$311$	−89323.5	−	12842.8i	−0.923517	−	0.132782i	−0.335878	−	0.941905i	$-0.609033\pi$
$311$	−89323.5	−	12842.8i	−0.923517	−	0.132782i	−0.587638	+	0.809124i	$0.699942\pi$
$312$	12383.4	−	32362.7i	0.127213	−	0.332457i
$313$	−64251.8	−	74150.5i	−0.655838	−	0.756877i	0.326254	−	0.945282i	$-0.394214\pi$
$313$	−64251.8	−	74150.5i	−0.655838	−	0.756877i	−0.982091	+	0.188405i	$0.939668\pi$
$314$	61180.1	−	99738.7i	0.620513	−	1.01159i
$315$	−25566.7	−	39782.5i	−0.257664	−	0.400933i
$316$	89497.0	+	71201.4i	0.896261	+	0.713041i
$317$	−34142.2	+	39402.2i	−0.339761	+	0.392105i	−0.899758	−	0.436390i	$-0.856257\pi$
$317$	−34142.2	+	39402.2i	−0.339761	+	0.392105i	0.559997	+	0.828495i	$0.310802\pi$
$318$	14420.6	−	17365.4i	0.142603	−	0.171724i
$319$	57515.1	+	26266.3i	0.565198	+	0.258117i
$320$	−44046.3	−	71155.0i	−0.430140	−	0.694873i
$321$	−69474.6			−0.674242
$322$	−47857.2	+	74743.2i	−0.461568	+	0.720875i
$323$			42813.6i			0.410371i
$324$	14818.1	+	3683.42i	0.141157	+	0.0350882i
$325$	−9189.02	+	20121.2i	−0.0869967	+	0.190496i
$326$	−23707.4	+	28548.6i	−0.223074	+	0.268627i
$327$	−23122.4	−	20035.7i	−0.216241	−	0.187374i
$328$	184856.	+	14793.3i	1.71825	+	0.137505i
$329$	−42950.1	+	27602.4i	−0.396801	+	0.255009i
$330$	−13491.6	+	21994.6i	−0.123890	+	0.201971i
$331$	8252.27	−	7150.63i	0.0753212	−	0.0652662i	−0.616387	−	0.787444i	$-0.711404\pi$
$331$	8252.27	−	7150.63i	0.0753212	−	0.0652662i	0.691708	+	0.722178i	$0.256859\pi$
$332$	−101419.	−	144136.i	−0.920120	−	1.30767i
$333$	−3328.59	+	23150.9i	−0.0300173	+	0.208775i
$334$	−74352.1	−	154164.i	−0.666500	−	1.38195i
$335$	−42722.8	+	66478.0i	−0.380689	+	0.592363i
$336$	3210.07	−	54461.1i	0.0284339	−	0.482400i
$337$	−62262.0	−	136335.i	−0.548230	−	1.20046i	−0.957603	−	0.288090i	$-0.906980\pi$
$337$	−62262.0	−	136335.i	−0.548230	−	1.20046i	0.409373	−	0.912367i	$-0.365748\pi$
$338$	63189.7	+	27270.5i	0.553112	+	0.238704i
$339$	32747.9	−	111529.i	0.284960	−	0.970484i
$340$	47784.9	+	93986.9i	0.413364	+	0.813035i
$341$	8625.97	−	2532.81i	0.0741821	−	0.0217818i
$342$	4777.43	+	28908.3i	0.0408453	+	0.247156i
$343$	−126324.	+	18162.7i	−1.07374	+	0.154380i
$344$	18889.9	+	90513.8i	0.159630	+	0.764888i
$345$	6764.56	+	54495.3i	0.0568331	+	0.457848i
$346$	104958.	+	156021.i	0.876724	+	1.30326i
$347$	215674.	−	31009.3i	1.79118	−	0.257533i	0.834987	−	0.550270i	$-0.185475\pi$
$347$	215674.	−	31009.3i	1.79118	−	0.257533i	0.956193	+	0.292737i	$0.0945660\pi$
$348$	−60185.5	+	56742.4i	−0.496973	+	0.468543i
$349$	−99795.1	+	29302.5i	−0.819329	+	0.240577i	−0.664427	−	0.747353i	$-0.731324\pi$
$349$	−99795.1	+	29302.5i	−0.819329	+	0.240577i	−0.154902	+	0.987930i	$0.549506\pi$
$350$	−4232.03	+	34568.5i	−0.0345472	+	0.282191i
$351$	−20773.1	+	70746.7i	−0.168612	+	0.574238i
$352$	58842.6	−	24222.4i	0.474905	−	0.195493i
$353$	49175.8	+	107680.i	0.394641	+	0.864143i	0.997786	+	0.0665113i	$0.0211868\pi$
$353$	49175.8	+	107680.i	0.394641	+	0.864143i	−0.603145	+	0.797632i	$0.706086\pi$
$354$	−29582.8	+	109173.i	−0.236066	+	0.871179i
$355$	14123.4	−	21976.4i	0.112068	−	0.174381i
$356$	132338.	+	77403.1i	1.04420	+	0.610742i
$357$	−9782.19	+	68036.7i	−0.0767538	+	0.533834i
$358$	−1830.07	+	38.4029i	−0.0142791	+	0.000299639i
$359$	25453.4	−	22055.5i	0.197495	−	0.171131i	−0.550499	−	0.834836i	$-0.685562\pi$
$359$	25453.4	−	22055.5i	0.197495	−	0.171131i	0.747994	+	0.663705i	$0.231017\pi$
$360$	42752.7	+	58129.1i	0.329882	+	0.448527i
$361$	94810.6	−	60931.1i	0.727516	−	0.467546i
$362$	−17401.8	−	54971.4i	−0.132794	−	0.419488i
$363$	41391.5	+	35865.9i	0.314122	+	0.272188i
$364$	−71148.7	−	7198.84i	−0.536988	−	0.0543325i
$365$	−8422.14	+	18441.9i	−0.0632174	+	0.138427i
$366$	−19514.8	−	21588.9i	−0.145681	−	0.161164i
$367$			60199.7i			0.446953i	0.974709	+	0.223477i	$0.0717406\pi$
$367$			60199.7i			0.446953i	−0.974709	+	0.223477i	$0.928259\pi$
$368$	65705.6	−	118416.i	0.485184	−	0.874412i
$369$	−159904.			−1.17438
$370$	−25695.1	+	23226.4i	−0.187692	+	0.169660i
$371$	−42374.6	−	19351.8i	−0.307863	−	0.140596i
$372$	−1183.93	+	11701.2i	−0.00855538	+	0.0845558i
$373$	92894.4	−	107206.i	0.667685	−	0.770550i	−0.316327	−	0.948650i	$-0.602450\pi$
$373$	92894.4	−	107206.i	0.667685	−	0.770550i	0.984012	+	0.178100i	$0.0569952\pi$
$374$	−76435.0	+	24196.4i	−0.546448	+	0.172984i
$375$	46726.1	+	72707.3i	0.332275	+	0.517029i
$376$	62757.5	−	46156.8i	0.443905	−	0.326482i
$377$	71003.5	+	81942.4i	0.499571	+	0.576536i
$378$	2435.50	+	116063.i	0.0170453	+	0.812285i
$379$	83921.4	+	12066.1i	0.584244	+	0.0840016i	0.428098	−	0.903732i	$-0.359184\pi$
$379$	83921.4	+	12066.1i	0.584244	+	0.0840016i	0.156146	+	0.987734i	$0.450093\pi$
$380$	−21907.0	+	37454.9i	−0.151711	+	0.259383i
$381$	−42386.1	−	27239.9i	−0.291994	−	0.187653i
$382$	−15425.5	−	4179.87i	−0.105709	−	0.0286442i
$383$	−47249.4	+	21578.1i	−0.322106	+	0.147101i	−0.569905	−	0.821711i	$-0.693020\pi$
$383$	−47249.4	+	21578.1i	−0.322106	+	0.147101i	0.247799	+	0.968811i	$0.420293\pi$
$384$	338.763	+	83244.3i	0.00229738	+	0.564537i
$385$	51094.2	+	15002.6i	0.344707	+	0.101215i
$386$	−188039.	−	23020.6i	−1.26204	−	0.154505i
$387$	−22462.0	−	76498.5i	−0.149978	−	0.510777i
$388$	91761.1	+	97329.0i	0.609530	+	0.646515i
$389$	12329.1	+	85750.8i	0.0814765	+	0.566681i	0.989139	+	0.146981i	$0.0469556\pi$
$389$	12329.1	+	85750.8i	0.0814765	+	0.566681i	−0.907663	+	0.419700i	$0.862135\pi$
$390$	−36712.7	+	24697.3i	−0.241372	+	0.162375i
$391$	−94999.8	+	141732.i	−0.621397	+	0.927073i
$392$	40207.2	−	8391.11i	0.261656	−	0.0546068i
$393$	4663.97	+	32438.6i	0.0301974	+	0.210028i
$394$	−275829.	+	45583.9i	−1.77684	+	0.293643i
$395$	−41143.0	−	140120.i	−0.263695	−	0.898063i
$396$	−48909.9	+	24866.8i	−0.311894	+	0.158573i
$397$	29622.0	+	8697.81i	0.187946	+	0.0551860i	0.374351	−	0.927287i	$-0.377865\pi$
$397$	29622.0	+	8697.81i	0.187946	+	0.0551860i	−0.186405	+	0.982473i	$0.559684\pi$
$398$	−2551.56	+	5912.35i	−0.0161079	+	0.0373245i
$399$	−25731.2	+	11751.0i	−0.161627	+	0.0738127i
$400$	3126.84	−	53048.9i	0.0195427	−	0.331555i
$401$	166855.	+	107231.i	1.03765	+	0.666856i	0.944404	−	0.328788i	$-0.106640\pi$
$401$	166855.	+	107231.i	1.03765	+	0.666856i	0.0932436	+	0.995643i	$0.470276\pi$
$402$	70803.0	−	34147.6i	0.438126	−	0.211304i
$403$	15259.4	+	2193.97i	0.0939567	+	0.0135089i
$404$	68139.3	−	47945.2i	0.417479	−	0.293753i
$405$	−12768.1	−	14735.2i	−0.0778427	−	0.0898352i
$406$	145513.	+	89258.6i	0.882777	+	0.541499i
$407$	−14239.1	−	22156.5i	−0.0859597	−	0.133756i
$408$	8366.61	−	104549.i	0.0502608	−	0.628056i
$409$	−79740.9	+	92025.9i	−0.476688	+	0.550127i	−0.942260	−	0.334883i	$-0.891303\pi$
$409$	−79740.9	+	92025.9i	−0.476688	+	0.550127i	0.465572	+	0.885010i	$0.345849\pi$
$410$	−182177.	−	151284.i	−1.08374	−	0.899964i
$411$	−92684.5	−	42327.6i	−0.548685	−	0.250576i
$412$	25284.4	−	101718.i	0.148956	−	0.599241i
$413$	233433.			1.36856
$414$	−48329.8	+	106300.i	−0.281977	+	0.620201i
$415$			225048.i			1.30671i
$416$	109040.	+	4133.85i	0.630085	+	0.0238873i
$417$	30290.8	−	66327.5i	0.174196	−	0.381436i
$418$	−25383.2	−	21078.8i	−0.145276	−	0.120640i
$419$	138935.	+	120388.i	0.791376	+	0.685731i	0.953618	−	0.301020i	$-0.0973270\pi$
$419$	138935.	+	120388.i	0.791376	+	0.685731i	−0.162242	+	0.986751i	$0.551872\pi$
$420$	−43371.1	+	54515.5i	−0.245868	+	0.309045i
$421$	84437.3	−	54264.5i	0.476398	−	0.306162i	−0.280317	−	0.959908i	$-0.590440\pi$
$421$	84437.3	−	54264.5i	0.476398	−	0.306162i	0.756715	+	0.653745i	$0.226803\pi$
$422$	153336.	+	94056.9i	0.861031	+	0.528160i
$423$	−50766.1	+	43989.1i	−0.283722	+	0.245846i
$424$	66387.7	+	25402.8i	0.369280	+	0.141303i
$425$	−9528.54	+	66272.4i	−0.0527532	+	0.366906i
$426$	−23406.2	+	11288.6i	−0.128977	+	0.0622043i
$427$	−32470.6	+	50525.2i	−0.178088	+	0.277110i
$428$	−70389.3	−	207147.i	−0.384255	−	1.13082i
$429$	−13976.6	−	30604.5i	−0.0759429	−	0.166292i
$430$	46783.8	−	108405.i	0.253022	−	0.586291i
$431$	86502.6	−	294601.i	0.465666	−	1.58591i	−0.307395	−	0.951582i	$-0.599457\pi$
$431$	86502.6	−	294601.i	0.465666	−	1.58591i	0.773061	−	0.634331i	$-0.218725\pi$
$432$	−14848.7	−	176512.i	−0.0795649	−	0.945819i
$433$	66341.6	−	19479.7i	0.353843	−	0.103898i	−0.0999804	−	0.994989i	$-0.531878\pi$
$433$	66341.6	−	19479.7i	0.353843	−	0.103898i	0.453823	+	0.891092i	$0.350060\pi$
$434$	23947.1	−	3957.53i	0.127137	−	0.0210109i
$435$	104548.	−	15031.7i	0.552504	−	0.0794381i
$436$	36312.1	−	89241.9i	0.191020	−	0.469457i
$437$	−70205.3	−	1355.16i	−0.367627	−	0.00709621i
$438$	16733.5	−	11256.9i	0.0872247	−	0.0586776i
$439$	195120.	−	28054.0i	1.01245	−	0.145568i	0.383929	−	0.923362i	$-0.374571\pi$
$439$	195120.	−	28054.0i	1.01245	−	0.145568i	0.628519	+	0.777794i	$0.283662\pi$
$440$	−79249.0	−	17942.7i	−0.409344	−	0.0926793i
$441$	−33981.5	+	9977.86i	−0.174729	+	0.0513050i
$442$	−136463.	−	16706.4i	−0.698505	−	0.0855142i
$443$	−49685.6	+	169214.i	−0.253176	+	0.862240i	0.730595	+	0.682811i	$0.239243\pi$
$443$	−49685.6	+	169214.i	−0.253176	+	0.862240i	−0.983771	+	0.179428i	$0.942575\pi$
$444$	33868.4	−	6329.79i	0.171802	−	0.0321087i
$445$	−81324.8	−	178076.i	−0.410679	−	0.899262i
$446$	−124153.	−	33642.2i	−0.624150	−	0.169127i
$447$	−50520.3	+	78611.1i	−0.252843	+	0.393431i
$448$	165635.	−	45606.9i	0.825270	−	0.227234i
$449$	−8629.11	+	60016.8i	−0.0428029	+	0.297701i	0.957164	+	0.289547i	$0.0935046\pi$
$449$	−8629.11	+	60016.8i	−0.0428029	+	0.297701i	−0.999967	+	0.00815402i	$0.997404\pi$
$450$	961.322	+	45811.3i	0.00474727	+	0.226229i
$451$	136082.	−	117916.i	0.669035	−	0.579722i
$452$	365717.	−	15355.4i	1.79006	−	0.0751598i
$453$	37899.0	−	24356.2i	0.184685	−	0.118690i
$454$	−348688.	+	110381.i	−1.69171	+	0.535530i
$455$	69011.6	+	59798.9i	0.333349	+	0.288849i
$456$	38057.0	−	20364.8i	0.183023	−	0.0979380i
$457$	129915.	−	284473.i	0.622051	−	1.36210i	−0.291967	−	0.956428i	$-0.594310\pi$
$457$	129915.	−	284473.i	0.622051	−	1.36210i	0.914018	−	0.405673i	$-0.132963\pi$
$458$	50023.8	−	45217.8i	0.238476	−	0.215565i
$459$			223179.i			1.05932i
$460$	−155631.	+	75382.2i	−0.735497	+	0.356249i
$461$	249972.			1.17622			0.588111	−	0.808780i	$-0.299872\pi$
$461$	249972.			1.17622			0.588111	+	0.808780i	$0.299872\pi$
$462$	−35521.2	−	39296.6i	−0.166419	−	0.184108i
$463$	−341568.	−	155989.i	−1.59336	−	0.727665i	−0.596194	−	0.802841i	$-0.703321\pi$
$463$	−341568.	−	155989.i	−1.59336	−	0.727665i	−0.997170	+	0.0751759i	$0.976048\pi$
$464$	−230163.	−	121961.i	−1.06905	−	0.566481i
$465$	9834.58	−	11349.7i	0.0454831	−	0.0524903i
$466$	54657.9	+	172661.i	0.251699	+	0.795102i
$467$	27324.2	+	42517.3i	0.125289	+	0.194954i	0.898232	−	0.439522i	$-0.144852\pi$
$467$	27324.2	+	42517.3i	0.125289	+	0.194954i	−0.772942	+	0.634476i	$0.781216\pi$
$468$	−94005.7	+	3947.04i	−0.429203	+	0.0180210i
$469$	−106237.	−	122604.i	−0.482980	−	0.557389i
$470$	−99455.0	+	2087.00i	−0.450227	+	0.00944773i
$471$	147113.	+	21151.6i	0.663144	+	0.0953457i
$472$	−355485.	+	22405.2i	−1.59565	+	0.100569i
$473$	75527.1	+	48538.3i	0.337583	+	0.216951i
$474$	−37993.6	+	140212.i	−0.169104	+	0.624064i
$475$	−25064.0	+	11446.3i	−0.111087	+	0.0507317i
$476$	−212771.	+	39765.6i	−0.939071	+	0.175507i
$477$	−58808.4	−	17267.7i	−0.258466	−	0.0758923i
$478$	50686.5	−	414022.i	0.221838	−	1.81204i
$479$	57643.3	+	196315.i	0.251234	+	0.855624i	0.984456	+	0.175634i	$0.0561975\pi$
$479$	57643.3	+	196315.i	0.251234	+	0.855624i	−0.733222	+	0.679990i	$0.761984\pi$
$480$	60815.4	−	87182.0i	0.263956	−	0.378394i
$481$	−6427.46	−	44704.0i	−0.0277811	−	0.193222i
$482$	66466.7	+	98803.3i	0.286095	+	0.425282i
$483$	−111256.	−	18194.3i	−0.476903	−	0.0779902i
$484$	−65002.4	+	159752.i	−0.277484	+	0.681955i
$485$	−24308.5	−	169069.i	−0.103341	−	0.718755i
$486$	39716.1	+	240323.i	0.168149	+	1.01747i
$487$	−93521.8	−	318506.i	−0.394326	−	1.34295i	−0.882545	−	0.470228i	$-0.844172\pi$
$487$	−93521.8	−	318506.i	−0.394326	−	1.34295i	0.488219	−	0.872721i	$-0.337647\pi$
$488$	44598.5	−	80059.0i	0.187275	−	0.336179i
$489$	−45227.0	−	13279.8i	−0.189138	−	0.0555360i
$490$	−48154.8	−	20781.9i	−0.200561	−	0.0865551i
$491$	−58723.8	+	26818.3i	−0.243586	+	0.111242i	−0.533467	−	0.845821i	$-0.679111\pi$
$491$	−58723.8	+	26818.3i	−0.243586	+	0.111242i	0.289882	+	0.957062i	$0.406384\pi$
$492$	75787.6	+	223034.i	0.313089	+	0.921384i
$493$	276087.	+	177431.i	1.13593	+	0.730020i
$494$	−24578.2	−	50961.4i	−0.100716	−	0.208827i
$495$	69349.7	+	9970.99i	0.283031	+	0.0406938i
$496$	−36088.1	+	8325.21i	−0.146690	+	0.0338401i
$497$	35120.0	+	40530.6i	0.142181	+	0.164085i
$498$	117053.	−	190825.i	0.471981	−	0.769445i
$499$	−216567.	−	336985.i	−0.869744	−	1.35335i	−0.934692	−	0.355460i	$-0.884324\pi$
$499$	−216567.	−	336985.i	−0.869744	−	1.35335i	0.0649473	−	0.997889i	$-0.479312\pi$
$500$	−169445.	+	212984.i	−0.677779	+	0.851938i
$501$	142372.	−	164306.i	0.567215	−	0.654601i
$502$	34165.4	−	41142.3i	0.135575	−	0.163260i
$503$	311360.	+	142193.i	1.23063	+	0.562009i	0.921265	−	0.388934i	$-0.127157\pi$
$503$	311360.	+	142193.i	1.23063	+	0.562009i	0.309364	+	0.950944i	$0.399884\pi$
$504$	−139229.	+	50592.7i	−0.548109	+	0.199171i
$505$	−106389.			−0.417173
$506$	−37257.6	−	126103.i	−0.145517	−	0.492521i
$507$			87420.4i			0.340092i
$508$	38275.1	−	153978.i	0.148316	−	0.596667i
$509$	−146628.	+	321071.i	−0.565954	+	1.23927i	0.382969	+	0.923761i	$0.374902\pi$
$509$	−146628.	+	321071.i	−0.565954	+	1.23927i	−0.948924	+	0.315506i	$0.897826\pi$
$510$	−85561.3	+	103034.i	−0.328955	+	0.396131i
$511$	−31455.3	−	27256.2i	−0.120462	−	0.104381i
$512$	−247860.	+	85350.4i	−0.945512	+	0.325586i
$513$	−77266.1	+	49655.9i	−0.293599	+	0.188684i
$514$	93885.2	−	153056.i	0.355362	−	0.579327i
$515$	−101148.	+	87645.6i	−0.381368	+	0.330457i
$516$	−96053.9	+	67586.9i	−0.360758	+	0.253842i
$517$	10764.9	−	74871.6i	0.0402744	−	0.280115i
$518$	−30889.4	−	64047.2i	−0.115120	−	0.238694i
$519$	−129132.	+	200934.i	−0.479402	+	0.745964i
$520$	−110834.	−	84441.2i	−0.409890	−	0.312283i
$521$	−186947.	−	409357.i	−0.688721	−	1.50809i	−0.853131	−	0.521697i	$-0.825299\pi$
$521$	−186947.	−	409357.i	−0.688721	−	1.50809i	0.164409	−	0.986392i	$-0.447428\pi$
$522$	206217.	+	88995.9i	0.756804	+	0.326610i
$523$	−10473.6	+	35669.9i	−0.0382907	+	0.130406i	−0.976420	−	0.215878i	$-0.930739\pi$
$523$	−10473.6	+	35669.9i	−0.0382907	+	0.130406i	0.938130	+	0.346284i	$0.112557\pi$
$524$	−91994.4	+	46771.9i	−0.335042	+	0.170342i
$525$	−42445.4	+	12463.1i	−0.153997	+	0.0452176i
$526$	−52614.6	−	318372.i	−0.190167	−	1.15070i
$527$	46187.7	−	6640.79i	0.166305	−	0.0239111i
$528$	57865.4	+	56433.7i	0.207563	+	0.202428i
$529$	−229403.	−	160266.i	−0.819763	−	0.572703i
$530$	−50663.1	−	75311.1i	−0.180360	−	0.268106i
$531$	304003.	−	43709.0i	1.07817	−	0.155018i
$532$	−61107.3	−	64815.1i	−0.215908	−	0.229009i
$533$	296265.	−	86991.2i	1.04286	−	0.306211i
$534$	−23664.2	+	193296.i	−0.0829868	+	0.677861i
$535$	−78706.4	+	268050.i	−0.274981	+	0.936499i
$536$	173551.	+	176511.i	0.604083	+	0.614387i
$537$	−965.882	−	2114.99i	−0.00334947	−	0.00733431i
$538$	66755.7	−	246356.i	0.230634	−	0.851135i
$539$	21561.2	−	33549.9i	0.0742157	−	0.115482i
$540$	−114197.	+	195245.i	−0.391623	+	0.669565i
$541$	−58672.3	+	408075.i	−0.200465	+	1.39427i	0.602443	+	0.798162i	$0.294194\pi$
$541$	−58672.3	+	408075.i	−0.200465	+	1.39427i	−0.802908	+	0.596103i	$0.796715\pi$
$542$	−51322.9	+	1076.98i	−0.174708	+	0.00366614i
$543$	55351.7	−	47962.6i	0.187729	−	0.162668i
$544$	320202.	−	80979.1i	1.08200	−	0.273637i
$545$	−103497.	+	66513.7i	−0.348447	+	0.223933i
$546$	−27414.3	−	86600.2i	−0.0919585	−	0.290492i
$547$	27595.0	+	23911.2i	0.0922266	+	0.0799148i	0.699754	−	0.714384i	$-0.253293\pi$
$547$	27595.0	+	23911.2i	0.0922266	+	0.0799148i	−0.607527	+	0.794299i	$0.707838\pi$
$548$	32300.3	−	319236.i	0.107559	−	1.06304i
$549$	−32826.3	+	71879.5i	−0.108912	+	0.238484i
$550$	−34600.2	−	38277.7i	−0.114381	−	0.126538i
$551$			135060.i			0.444862i
$552$	171173.	+	17028.7i	0.561768	+	0.0558860i
$553$	299802.			0.980357
$554$	325167.	−	293926.i	1.05946	−	0.957677i
$555$	−40020.4	−	18276.7i	−0.129926	−	0.0593351i
$556$	228454.	+	23115.0i	0.739007	+	0.0747729i
$557$	−122800.	+	141718.i	−0.395810	+	0.456789i	−0.918317	−	0.395846i	$-0.870451\pi$
$557$	−122800.	+	141718.i	−0.395810	+	0.456789i	0.522507	+	0.852635i	$0.324997\pi$
$558$	30445.6	−	9637.89i	0.0977812	−	0.0309538i
$559$	83233.6	+	129514.i	0.266364	+	0.414470i
$560$	−206487.	−	74083.2i	−0.658441	−	0.236235i
$561$	−66689.5	−	76963.8i	−0.211900	−	0.244546i
$562$	11622.9	+	553884.i	0.0367995	+	1.75366i
$563$	−497321.	−	71503.9i	−1.56899	−	0.225586i	−0.697712	−	0.716379i	$-0.745798\pi$
$563$	−497321.	−	71503.9i	−1.56899	−	0.225586i	−0.871277	+	0.490792i	$0.836707\pi$
$564$	85416.7	+	49959.5i	0.268525	+	0.157058i
$565$	−393206.	−	252698.i	−1.23175	−	0.791599i
$566$	528546.	+	143221.i	1.64987	+	0.447069i
$567$	36409.9	−	16627.9i	0.113254	−	0.0517214i
$568$	−57372.7	−	58351.3i	−0.177832	−	0.180865i
$569$	331109.	+	97222.3i	1.02270	+	0.300290i	0.749737	−	0.661736i	$-0.230180\pi$
$569$	331109.	+	97222.3i	1.02270	+	0.300290i	0.272958	+	0.962026i	$0.411998\pi$
$570$	−54707.7	−	6697.57i	−0.168383	−	0.0206142i
$571$	−149371.	−	508711.i	−0.458136	−	1.56027i	−0.787654	−	0.616118i	$-0.788704\pi$
$571$	−149371.	−	508711.i	−0.458136	−	1.56027i	0.329518	−	0.944149i	$-0.393114\pi$
$572$	77090.6	−	72680.5i	0.235619	−	0.222139i
$573$	−2889.03	−	20093.7i	−0.00879920	−	0.0611998i
$574$	403363.	−	271349.i	1.22426	−	0.823579i
$575$	−108371.	−	17722.5i	−0.327777	−	0.0536030i
$576$	207169.	−	90408.5i	0.624423	−	0.272499i
$577$	39291.4	+	273278.i	0.118017	+	0.820829i	0.959734	+	0.280910i	$0.0906362\pi$
$577$	39291.4	+	273278.i	0.118017	+	0.820829i	−0.841717	+	0.539919i	$0.818455\pi$
$578$	−80952.3	+	13378.3i	−0.242311	+	0.0400447i
$579$	−67794.4	−	230887.i	−0.202226	−	0.688718i
$580$	150743.	+	296492.i	0.448106	+	0.881369i
$581$	−443294.	−	130163.i	−1.31323	−	0.385598i
$582$	−67325.3	+	156003.i	−0.198761	+	0.460560i
$583$	62780.9	−	28671.1i	0.184710	−	0.0843543i
$584$	50517.9	+	38488.0i	0.148122	+	0.112850i
$585$	101072.	+	64954.8i	0.295337	+	0.189801i
$586$	−141159.	+	68079.7i	−0.411068	+	0.198254i
$587$	291073.	+	41850.0i	0.844746	+	0.121456i	0.551080	−	0.834452i	$-0.314216\pi$
$587$	291073.	+	41850.0i	0.844746	+	0.121456i	0.293665	+	0.955908i	$0.405125\pi$
$588$	30022.8	+	42668.2i	0.0868354	+	0.123410i
$589$	12575.6	+	14513.0i	0.0362490	+	0.0418336i
$590$	387700.	+	237817.i	1.11376	+	0.683186i
$591$	−191990.	−	298742.i	−0.549672	−	0.855307i
$592$	53187.4	+	94569.8i	0.151763	+	0.269842i
$593$	−214244.	+	247251.i	−0.609255	+	0.703118i	−0.973630	−	0.228134i	$-0.926737\pi$
$593$	−214244.	+	247251.i	−0.609255	+	0.703118i	0.364374	+	0.931253i	$0.381283\pi$
$594$	−132318.	−	109879.i	−0.375012	−	0.311418i
$595$	251420.	+	114819.i	0.710175	+	0.324326i
$596$	−285575.	−	70986.6i	−0.803946	−	0.199841i
$597$	−8179.49			−0.0229497
$598$	31714.3	−	223241.i	0.0886856	−	0.624270i
$599$		−	225230.i		−	0.627729i	−0.949468	−	0.313865i	$-0.898376\pi$
$599$		−	225230.i		−	0.627729i	0.949468	−	0.313865i	$-0.101624\pi$
$600$	63441.9	−	23053.4i	0.176227	−	0.0640373i
$601$	−45704.2	+	100078.i	−0.126534	+	0.277071i	−0.962288	−	0.272034i	$-0.912304\pi$
$601$	−45704.2	+	100078.i	−0.126534	+	0.277071i	0.835754	+	0.549105i	$0.185031\pi$
$602$	186475.	+	154853.i	0.514551	+	0.427294i
$603$	−161310.	−	139776.i	−0.443637	−	0.384413i
$604$	111019.	+	88323.8i	0.304315	+	0.242105i
$605$	185271.	−	119066.i	0.506170	−	0.325296i
$606$	90211.1	+	55335.9i	0.245649	+	0.150682i
$607$	−487654.	+	422554.i	−1.32353	+	1.14685i	−0.345493	+	0.938421i	$0.612288\pi$
$607$	−487654.	+	422554.i	−1.32353	+	1.14685i	−0.978038	+	0.208425i	$0.933166\pi$
$608$	99278.4	+	92838.8i	0.268564	+	0.251144i
$609$	−30859.1	+	214629.i	−0.0832047	+	0.578702i
$610$	−105403.	+	50835.0i	−0.283266	+	0.136617i
$611$	70126.7	−	109119.i	0.187846	−	0.292293i
$612$	−269648.	+	91627.3i	−0.719937	+	0.244637i
$613$	114419.	+	250543.i	0.304494	+	0.666748i	0.998587	−	0.0531367i	$-0.0169219\pi$
$613$	114419.	+	250543.i	0.304494	+	0.666748i	−0.694094	+	0.719885i	$0.744195\pi$
$614$	−276719.	+	641200.i	−0.734011	+	1.70081i
$615$	84742.6	−	288607.i	0.224053	−	0.763056i
$616$	81179.1	−	145725.i	0.213935	−	0.384037i
$617$	−644687.	+	189297.i	−1.69347	+	0.497249i	−0.979248	−	0.202666i	$-0.935039\pi$
$617$	−644687.	+	189297.i	−1.69347	+	0.497249i	−0.714226	+	0.699915i	$0.753221\pi$
$618$	131354.	−	21707.7i	0.343926	−	0.0568377i
$619$	523452.	−	75261.1i	1.36614	−	0.196422i	0.580075	−	0.814563i	$-0.303023\pi$
$619$	523452.	−	75261.1i	1.36614	−	0.196422i	0.786067	+	0.618141i	$0.212114\pi$
$620$	43804.7	+	17823.9i	0.113956	+	0.0463682i
$621$	−365967.	−	7064.16i	−0.948983	−	0.0183180i
$622$	299504.	−	201482.i	0.774145	−	0.520781i
$623$	397807.	−	57196.1i	1.02494	−	0.147364i
$624$	50059.9	+	129248.i	0.128565	+	0.331937i
$625$	208974.	−	61360.3i	0.534973	−	0.157082i
$626$	389552.	+	47690.7i	0.994070	+	0.121699i
$627$	11807.4	−	40212.3i	0.0300344	−	0.102288i
$628$	85983.3	+	460065.i	0.218019	+	1.16654i
$629$	−56788.5	−	124349.i	−0.143535	−	0.314299i
$630$	182574.	+	49472.6i	0.460001	+	0.124648i
$631$	298932.	−	465148.i	0.750782	−	1.16824i	−0.230011	−	0.973188i	$-0.573876\pi$
$631$	298932.	−	465148.i	0.750782	−	1.16824i	0.980793	−	0.195052i	$-0.0624875\pi$
$632$	−456554.	+	28775.3i	−1.14303	+	0.0720421i
$633$	−32518.0	+	226167.i	−0.0811551	+	0.564446i
$634$	−4375.26	−	208501.i	−0.0108849	−	0.518715i
$635$	−153117.	+	132676.i	−0.379730	+	0.329038i
$636$	3787.67	+	90210.0i	0.00936392	+	0.223018i
$637$	57531.5	−	36973.3i	0.141784	−	0.0911190i
$638$	−241123.	+	76330.2i	−0.592376	+	0.187523i
$639$	53326.2	+	46207.4i	0.130599	+	0.113165i
$640$	321560.	+	92998.9i	0.785059	+	0.227048i
$641$	−21608.7	+	47316.5i	−0.0525912	+	0.115159i	−0.934103	−	0.357003i	$-0.883799\pi$
$641$	−21608.7	+	47316.5i	−0.0525912	+	0.115159i	0.881512	+	0.472161i	$0.156526\pi$
$642$	206157.	−	186351.i	0.500183	−	0.452128i
$643$		−	142298.i		−	0.344172i	−0.985082	−	0.172086i	$-0.944949\pi$
$643$		−	142298.i		−	0.344172i	0.985082	−	0.172086i	$-0.0550508\pi$
$644$	−58472.4	−	350158.i	−0.140987	−	0.844292i
$645$	149974.			0.360493
$646$	−114838.	−	127044.i	−0.275183	−	0.304432i
$647$	−445900.	−	203636.i	−1.06519	−	0.486458i	−0.195834	−	0.980637i	$-0.562741\pi$
$647$	−445900.	−	203636.i	−1.06519	−	0.486458i	−0.869360	+	0.494179i	$0.835469\pi$
$648$	−53851.0	+	28816.5i	−0.128246	+	0.0686263i
$649$	−226482.	+	261374.i	−0.537706	+	0.620545i
$650$	−26703.4	−	84354.7i	−0.0632034	−	0.199656i
$651$	16668.3	+	25936.4i	0.0393305	+	0.0611994i
$652$	−6226.91	−	148305.i	−0.0146480	−	0.348867i
$653$	107826.	+	124438.i	0.252870	+	0.291827i	0.867965	−	0.496626i	$-0.165428\pi$
$653$	107826.	+	124438.i	0.252870	+	0.291827i	−0.615095	+	0.788453i	$0.710882\pi$
$654$	122354.	−	2567.53i	0.286065	−	0.00600289i
$655$	130440.	+	18754.4i	0.304037	+	0.0437140i
$656$	−588219.	+	451941.i	−1.36688	+	1.05020i
$657$	−46068.1	−	29606.2i	−0.106726	−	0.0685886i
$658$	53411.8	−	197111.i	0.123363	−	0.455260i
$659$	−383528.	+	175151.i	−0.883133	+	0.403314i	−0.804753	−	0.593610i	$-0.797702\pi$
$659$	−383528.	+	175151.i	−0.883133	+	0.403314i	−0.0783806	+	0.996924i	$0.524975\pi$
$660$	−18961.2	−	101455.i	−0.0435290	−	0.232908i
$661$	12878.5	+	3781.47i	0.0294756	+	0.00865482i	0.296437	−	0.955052i	$-0.404201\pi$
$661$	12878.5	+	3781.47i	0.0294756	+	0.00865482i	−0.266962	+	0.963707i	$0.586020\pi$
$662$	−5307.54	+	43353.6i	−0.0121109	+	0.0989257i
$663$	−49199.4	−	167558.i	−0.111926	−	0.381187i
$664$	687565.	+	155671.i	1.55947	+	0.353079i
$665$	16188.0	+	112590.i	0.0366057	+	0.254598i
$666$	−52220.1	−	77625.6i	−0.117731	−	0.175007i
$667$	−299688.	+	447109.i	−0.673624	+	1.00499i
$668$	634144.	+	258030.i	1.42113	+	0.578253i
$669$	−23252.7	−	161726.i	−0.0519542	−	0.361350i
$670$	−51538.4	−	311860.i	−0.114810	−	0.694720i
$671$	−25069.2	−	85377.9i	−0.0556795	−	0.189627i
$672$	136555.	+	170217.i	0.302391	+	0.376933i
$673$	47418.6	+	13923.4i	0.104693	+	0.0307407i	0.333660	−	0.942694i	$-0.391716\pi$
$673$	47418.6	+	13923.4i	0.104693	+	0.0307407i	−0.228966	+	0.973434i	$0.573535\pi$
$674$	550444.	+	237552.i	1.21169	+	0.522924i
$675$	−130654.	+	59667.6i	−0.286757	+	0.130958i
$676$	−260655.	+	88571.4i	−0.570391	+	0.193821i
$677$	14377.1	+	9239.61i	0.0313686	+	0.0201593i	0.556231	−	0.831028i	$-0.312247\pi$
$677$	14377.1	+	9239.61i	0.0313686	+	0.0201593i	−0.524863	+	0.851187i	$0.675883\pi$
$678$	201978.	+	418788.i	0.439383	+	0.911034i
$679$	347088.	+	49903.7i	0.752836	+	0.108241i
$680$	−393896.	−	150722.i	−0.851851	−	0.325955i
$681$	−304230.	−	351101.i	−0.656007	−	0.757072i
$682$	−18802.8	+	30653.2i	−0.0404253	+	0.0659032i
$683$	332688.	+	517673.i	0.713175	+	1.10972i	0.988914	+	0.148489i	$0.0474410\pi$
$683$	332688.	+	517673.i	0.713175	+	1.10972i	−0.275739	+	0.961232i	$0.588923\pi$
$684$	−91716.9	−	72967.5i	−0.196037	−	0.155961i
$685$	−268310.	+	309647.i	−0.571816	+	0.659911i
$686$	326135.	−	392734.i	0.693025	−	0.834546i
$687$	77912.6	+	35581.5i	0.165080	+	0.0753895i
$688$	−298838.	−	217920.i	−0.631333	−	0.460385i
$689$	118352.			0.249309
$690$	−166245.	−	143564.i	−0.349181	−	0.301541i
$691$			719251.i			1.50635i	0.657823	+	0.753173i	$0.271478\pi$
$691$			719251.i			1.50635i	−0.657823	+	0.753173i	$0.728522\pi$
$692$	−729942.	−	181445.i	−1.52432	−	0.378907i
$693$	−59751.0	+	130837.i	−0.124417	+	0.272435i
$694$	−556811.	+	670517.i	−1.15608	+	1.39216i
$695$	−221592.	−	192010.i	−0.458758	−	0.397516i
$696$	26393.4	−	329811.i	0.0544851	−	0.680843i
$697$	786238.	−	505285.i	1.61841	−	1.04009i
$698$	217532.	−	354631.i	0.446491	−	0.727890i
$699$	−173856.	+	150647.i	−0.355824	+	0.308323i
$700$	−80164.5	−	113929.i	−0.163601	−	0.232508i
$701$	84998.6	−	591179.i	0.172972	−	1.20305i	−0.699590	−	0.714544i	$-0.746634\pi$
$701$	84998.6	−	591179.i	0.172972	−	1.20305i	0.872562	−	0.488503i	$-0.162457\pi$
$702$	−128121.	−	265652.i	−0.259985	−	0.539062i
$703$	30415.5	−	47327.5i	0.0615439	−	0.0957641i
$704$	−109637.	+	229710.i	−0.221214	+	0.463483i
$705$	−52490.8	−	114939.i	−0.105610	−	0.231253i
$706$	−434752.	−	187624.i	−0.872232	−	0.376424i
$707$	61533.4	−	209563.i	0.123104	−	0.419254i
$708$	−205049.	−	403306.i	−0.409064	−	0.804578i
$709$	317440.	−	93208.9i	0.631495	−	0.185424i	0.0497065	−	0.998764i	$-0.484171\pi$
$709$	317440.	−	93208.9i	0.631495	−	0.185424i	0.581788	+	0.813340i	$0.302353\pi$
$710$	17037.7	+	103095.i	0.0337982	+	0.204514i
$711$	390435.	−	56136.1i	0.772343	−	0.111046i
$712$	−600313.	+	125283.i	−1.18418	+	0.247134i
$713$	9427.54	+	75948.3i	0.0185447	+	0.149396i
$714$	−153466.	−	228129.i	−0.301035	−	0.447491i
$715$	−133913.	+	19253.8i	−0.261946	+	0.0376621i
$716$	5327.51	−	5022.74i	0.0103920	−	0.00979748i
$717$	508363.	−	149269.i	0.988863	−	0.290356i
$718$	−16370.7	+	133720.i	−0.0317554	+	0.259387i
$719$	−140166.	+	477363.i	−0.271135	+	0.923402i	0.705538	+	0.708672i	$0.250705\pi$
$719$	−140166.	+	477363.i	−0.271135	+	0.923402i	−0.976673	+	0.214730i	$0.931113\pi$
$720$	−282782.	−	57815.8i	−0.545490	−	0.111527i
$721$	−114140.	−	249932.i	−0.219567	−	0.480786i
$722$	−117904.	+	435115.i	−0.226180	+	0.834699i
$723$	−81775.6	+	127245.i	−0.156440	+	0.243425i
$724$	199087.	+	116444.i	0.379810	+	0.222147i
$725$	−30058.9	+	209064.i	−0.0571869	+	0.397744i
$726$	−219027.	+	4596.14i	−0.415551	+	0.00872008i
$727$	630083.	−	545970.i	1.19215	−	1.03300i	0.193493	−	0.981102i	$-0.438018\pi$
$727$	630083.	−	545970.i	1.19215	−	1.03300i	0.998652	−	0.0518983i	$-0.0165272\pi$
$728$	230434.	−	169480.i	0.434795	−	0.319783i
$729$	−195258.	+	125485.i	−0.367412	+	0.236121i
$730$	−24474.9	−	77314.8i	−0.0459277	−	0.145083i
$731$	352174.	+	305160.i	0.659056	+	0.571075i
$732$	115816.	+	11718.2i	0.216145	+	0.0218696i
$733$	−102592.	+	224646.i	−0.190944	+	0.418110i	−0.980755	−	0.195240i	$-0.937451\pi$
$733$	−102592.	+	224646.i	−0.190944	+	0.418110i	0.789811	+	0.613350i	$0.210179\pi$
$734$	−161473.	−	178635.i	−0.299714	−	0.331570i
$735$		−	66620.1i		−	0.123319i
$736$	122654.	+	527627.i	0.226425	+	0.974029i
$737$	240352.			0.442500
$738$	474496.	−	428909.i	0.871204	−	0.787503i
$739$	177084.	+	80871.4i	0.324257	+	0.148083i	0.570892	−	0.821025i	$-0.306598\pi$
$739$	177084.	+	80871.4i	0.324257	+	0.148083i	−0.246635	+	0.969109i	$0.579325\pi$
$740$	13947.0	−	137843.i	0.0254693	−	0.251722i
$741$	47063.1	−	54313.7i	0.0857124	−	0.0989174i
$742$	177649.	−	56236.7i	0.322666	−	0.102144i
$743$	−495235.	−	770601.i	−0.897086	−	1.39589i	−0.918201	−	0.396116i	$-0.870358\pi$
$743$	−495235.	−	770601.i	−0.897086	−	1.39589i	0.0211149	−	0.999777i	$-0.493278\pi$
$744$	−27872.8	−	37897.4i	−0.0503540	−	0.0684643i
$745$	246067.	+	283976.i	0.443344	+	0.511646i
$746$	11904.2	+	567290.i	0.0213906	+	1.01936i
$747$	−601679.	−	86508.4i	−1.07826	−	0.155030i
$748$	161910.	−	276820.i	0.289381	−	0.494760i
$749$	−482476.	−	310068.i	−0.860026	−	0.552705i
$750$	−333676.	−	90417.0i	−0.593202	−	0.160741i
$751$	−622874.	+	284457.i	−1.10438	+	0.504355i	−0.882307	−	0.470674i	$-0.844011\pi$
$751$	−622874.	+	284457.i	−1.10438	+	0.504355i	−0.222077	+	0.975029i	$0.571284\pi$
$752$	−62419.3	+	305298.i	−0.110378	+	0.539869i
$753$	65177.9	+	19138.0i	0.114950	+	0.0337525i
$754$	−430487.	−	52702.2i	−0.757213	−	0.0927014i
$755$	−51037.0	−	173816.i	−0.0895347	−	0.304927i
$756$	−318540.	−	337869.i	−0.557341	−	0.591159i
$757$	−141765.	−	985994.i	−0.247387	−	1.72061i	−0.613204	−	0.789925i	$-0.710120\pi$
$757$	−141765.	−	985994.i	−0.247387	−	1.72061i	0.365818	−	0.930687i	$-0.380789\pi$
$758$	−281391.	+	189297.i	−0.489747	+	0.329462i
$759$	128315.	−	106921.i	0.222738	−	0.185600i
$760$	−35458.4	−	169904.i	−0.0613891	−	0.294155i
$761$	−7741.38	−	53842.5i	−0.0133675	−	0.0929727i	0.982046	−	0.188644i	$-0.0604093\pi$
$761$	−7741.38	−	53842.5i	−0.0133675	−	0.0929727i	−0.995413	+	0.0956714i	$0.969500\pi$
$762$	198841.	−	32860.7i	0.342449	−	0.0565936i
$763$	−71156.5	−	242337.i	−0.122227	−	0.416266i
$764$	56984.8	−	28972.2i	0.0976275	−	0.0496358i
$765$	348926.	+	102454.i	0.596225	+	0.175068i
$766$	82328.2	−	190767.i	0.140311	−	0.325121i
$767$	−539467.	+	246366.i	−0.917011	+	0.418785i
$768$	−224291.	−	246109.i	−0.380267	−	0.417258i
$769$	−593863.	−	381652.i	−1.00423	−	0.645380i	−0.0683369	−	0.997662i	$-0.521769\pi$
$769$	−593863.	−	381652.i	−1.00423	−	0.645380i	−0.935894	+	0.352282i	$0.885406\pi$
$770$	−191857.	+	92531.0i	−0.323591	+	0.156065i
$771$	225755.	+	32458.6i	0.379776	+	0.0546036i
$772$	619731.	−	436064.i	1.03984	−	0.731671i
$773$	705532.	+	814227.i	1.18075	+	1.36266i	0.917405	+	0.397955i	$0.130280\pi$
$773$	705532.	+	814227.i	1.18075	+	1.36266i	0.263344	+	0.964702i	$0.415175\pi$
$774$	271844.	+	166750.i	0.453773	+	0.278346i
$775$	16236.1	+	25263.8i	0.0270320	+	0.0420626i
$776$	−533354.	−	42682.1i	−0.885711	−	0.0708799i
$777$	59147.9	−	68260.4i	0.0979710	−	0.113065i
$778$	−266593.	−	221385.i	−0.440443	−	0.365753i
$779$	349866.	+	159778.i	0.576536	+	0.263295i
$780$	42695.2	−	171760.i	0.0701763	−	0.282315i
$781$	−79456.1			−0.130264
$782$	−98265.3	−	675389.i	−0.160689	−	1.10444i
$783$			704044.i			1.14836i
$784$	−96802.5	+	132747.i	−0.157491	+	0.215969i
$785$	248269.	−	543633.i	0.402887	−	0.882199i
$786$	−100849.	−	83747.4i	−0.163241	−	0.135558i
$787$	−135655.	−	117545.i	−0.219021	−	0.189783i	0.538439	−	0.842665i	$-0.319014\pi$
$787$	−135655.	−	117545.i	−0.219021	−	0.189783i	−0.757460	+	0.652882i	$0.773560\pi$
$788$	696221.	−	875119.i	1.12123	−	1.40934i
$789$	344819.	−	221602.i	0.553908	−	0.355975i
$790$	497930.	+	305432.i	0.797836	+	0.489396i
$791$	725181.	−	628373.i	1.15903	−	1.00430i
$792$	78434.2	−	204980.i	0.125042	−	0.326784i
$793$	21715.4	−	151034.i	0.0345320	−	0.240175i
$794$	−111230.	+	53645.1i	−0.176433	+	0.0850921i
$795$	62332.1	−	96990.6i	0.0986228	−	0.153460i
$796$	−8287.18	−	24388.2i	−0.0130792	−	0.0384905i
$797$	−420687.	−	921177.i	−0.662282	−	1.45019i	−0.880381	−	0.474268i	$-0.842713\pi$
$797$	−420687.	−	921177.i	−0.662282	−	1.45019i	0.218099	−	0.975927i	$-0.430014\pi$
$798$	44834.5	−	103888.i	0.0704055	−	0.163140i
$799$	110612.	−	376708.i	0.173263	−	0.590081i
$800$	133014.	+	165803.i	0.207834	+	0.259067i
$801$	507359.	−	148974.i	0.790771	−	0.232191i
$802$	−782746.	+	129358.i	−1.21695	+	0.201114i
$803$	61037.3	−	8775.83i	0.0946594	−	0.0136100i
$804$	−118505.	+	291243.i	−0.183327	+	0.450550i
$805$	−196238.	+	408641.i	−0.302824	+	0.630594i
$806$	−51165.3	+	34419.8i	−0.0787599	+	0.0529832i
$807$	320911.	−	46140.0i	0.492762	−	0.0708485i
$808$	−73592.2	+	325040.i	−0.112722	+	0.497869i
$809$	641655.	−	188407.i	0.980403	−	0.287872i	0.248012	−	0.968757i	$-0.420223\pi$
$809$	641655.	−	188407.i	0.980403	−	0.287872i	0.732391	+	0.680884i	$0.238404\pi$
$810$	77412.0	+	9477.13i	0.117988	+	0.0144446i
$811$	−332374.	+	1.13196e6i	−0.505343	+	1.72104i	0.171749	+	0.985141i	$0.445058\pi$
$811$	−332374.	+	1.13196e6i	−0.505343	+	1.72104i	−0.677092	+	0.735898i	$0.736760\pi$
$812$	−671210.	+	125445.i	−1.01800	+	0.190257i
$813$	−27087.4	−	59313.1i	−0.0409813	−	0.0897365i
$814$	101683.	+	27553.3i	0.153462	+	0.0415839i
$815$	−102474.	+	159452.i	−0.154275	+	0.240057i
$816$	255603.	+	332677.i	0.383871	+	0.499623i
$817$	−27292.1	+	189821.i	−0.0408878	+	0.284381i
$818$	−10218.6	−	486963.i	−0.0152716	−	0.727763i
$819$	−186404.	+	161520.i	−0.277900	+	0.240801i
$820$	946376.	−	39735.7i	1.40746	−	0.0590954i
$821$	−284810.	+	183036.i	−0.422540	+	0.271550i	−0.734584	−	0.678517i	$-0.762623\pi$
$821$	−284810.	+	183036.i	−0.422540	+	0.271550i	0.312044	+	0.950068i	$0.398986\pi$
$822$	388565.	−	123005.i	0.575069	−	0.182044i
$823$	335845.	+	291012.i	0.495838	+	0.429646i	0.866541	−	0.499105i	$-0.166338\pi$
$823$	335845.	+	291012.i	0.495838	+	0.429646i	−0.370703	+	0.928751i	$0.620883\pi$
$824$	197807.	+	369655.i	0.291332	+	0.544430i
$825$	27226.6	−	59617.9i	0.0400023	−	0.0875929i
$826$	−692684.	+	626135.i	−1.01526	+	0.917715i
$827$			599978.i			0.877252i	0.898670	+	0.438626i	$0.144535\pi$
$827$			599978.i			0.877252i	−0.898670	+	0.438626i	$0.855465\pi$
$828$	−141714.	−	445066.i	−0.206706	−	0.649179i
$829$	−257424.			−0.374576			−0.187288	−	0.982305i	$-0.559970\pi$
$829$	−257424.			−0.374576			−0.187288	+	0.982305i	$0.559970\pi$
$830$	−603643.	−	667802.i	−0.876242	−	0.969374i
$831$	506451.	+	231288.i	0.733390	+	0.334928i
$832$	−334651.	+	280210.i	−0.483443	+	0.404797i
$833$	135555.	−	156439.i	0.195356	−	0.225453i
$834$	88025.4	+	278067.i	0.126554	+	0.399777i
$835$	−472640.	−	735442.i	−0.677887	−	1.05481i
$836$	131861.	−	5536.48i	0.188670	−	0.00792175i
$837$	65553.9	+	75653.3i	0.0935724	+	0.107988i
$838$	−735186.	+	15427.4i	−1.04691	+	0.0219688i
$839$	231814.	+	33329.8i	0.329317	+	0.0473487i	0.304991	−	0.952355i	$-0.401347\pi$
$839$	231814.	+	33329.8i	0.329317	+	0.0473487i	0.0243269	+	0.999704i	$0.492256\pi$
$840$	−17528.0	−	278102.i	−0.0248412	−	0.394135i
$841$	275947.	+	177340.i	0.390152	+	0.250735i
$842$	−105004.	+	387508.i	−0.148109	+	0.546584i
$843$	−640115.	+	292331.i	−0.900747	+	0.411358i
$844$	−707293.	+	132189.i	−0.992921	+	0.185571i
$845$	337289.	+	99036.9i	0.472377	+	0.138702i
$846$	32650.8	−	266701.i	0.0456198	−	0.372636i
$847$	127378.	+	433808.i	0.177552	+	0.604687i
$848$	−265135.	+	102691.i	−0.368702	+	0.142804i
$849$	98991.3	+	688500.i	0.137335	+	0.955187i
$850$	−149487.	−	222214.i	−0.206902	−	0.307562i
$851$	205704.	−	89185.2i	0.284043	−	0.123150i
$852$	39175.7	−	96279.6i	0.0539682	−	0.132634i
$853$	112976.	+	785769.i	0.155271	+	1.07993i	0.907203	+	0.420692i	$0.138213\pi$
$853$	112976.	+	785769.i	0.155271	+	1.07993i	−0.751932	+	0.659240i	$0.770878\pi$
$854$	−39170.7	−	237023.i	−0.0537088	−	0.324993i
$855$	42163.5	+	143596.i	0.0576773	+	0.196431i
$856$	764500.	+	425880.i	1.04335	+	0.581219i
$857$	−763977.	−	224324.i	−1.04020	−	0.305431i	−0.283351	−	0.959016i	$-0.591446\pi$
$857$	−763977.	−	224324.i	−1.04020	−	0.305431i	−0.756853	+	0.653585i	$0.773264\pi$
$858$	123564.	+	53325.8i	0.167848	+	0.0724374i
$859$	−378657.	+	172927.i	−0.513168	+	0.234356i	−0.655130	−	0.755516i	$-0.727386\pi$
$859$	−378657.	+	172927.i	−0.513168	+	0.234356i	0.141962	+	0.989872i	$0.454659\pi$
$860$	151949.	+	447167.i	0.205447	+	0.604607i
$861$	519478.	+	333848.i	0.700746	+	0.450342i
$862$	533518.	+	1.10622e6i	0.718017	+	1.48876i
$863$	−39818.8	−	5725.08i	−0.0534647	−	0.00768706i	0.115531	−	0.993304i	$-0.463143\pi$
$863$	−39818.8	−	5725.08i	−0.0534647	−	0.00768706i	−0.168995	+	0.985617i	$0.554052\pi$
$864$	517519.	+	483951.i	0.693264	+	0.648296i
$865$	628959.	+	725857.i	0.840601	+	0.970105i
$866$	−144611.	+	235751.i	−0.192825	+	0.314353i
$867$	−56346.6	−	87677.0i	−0.0749599	−	0.116640i
$868$	−60444.9	+	75976.5i	−0.0802269	+	0.100842i
$869$	−290875.	+	335687.i	−0.385182	+	0.444524i
$870$	−269913.	+	325031.i	−0.356603	+	0.429424i
$871$	374911.	+	171216.i	0.494188	+	0.225688i
$872$	131621.	+	362214.i	0.173098	+	0.476357i
$873$	461361.			0.605358
$874$	211961.	−	184290.i	0.277480	−	0.241256i
$875$			713467.i			0.931875i
$876$	−19460.4	+	78287.8i	−0.0253596	+	0.102020i
$877$	−552236.	+	1.20923e6i	−0.718001	+	1.57220i	0.0986829	+	0.995119i	$0.468537\pi$
$877$	−552236.	+	1.20923e6i	−0.718001	+	1.57220i	−0.816684	+	0.577085i	$0.804190\pi$
$878$	−503746.	+	606615.i	−0.653465	+	0.786908i
$879$	−150445.	−	130361.i	−0.194715	−	0.168721i
$880$	283289.	−	159326.i	0.365818	−	0.205741i
$881$	133601.	−	85860.0i	0.172130	−	0.110621i	−0.451739	−	0.892150i	$-0.649196\pi$
$881$	133601.	−	85860.0i	0.172130	−	0.110621i	0.623869	+	0.781529i	$0.285560\pi$
$882$	74072.3	−	120756.i	0.0952179	−	0.155229i
$883$	440820.	−	381972.i	0.565379	−	0.489903i	−0.324634	−	0.945840i	$-0.605241\pi$
$883$	440820.	−	381972.i	0.565379	−	0.489903i	0.890012	+	0.455936i	$0.150696\pi$
$884$	449748.	−	316458.i	0.575526	−	0.404960i
$885$	−82219.7	+	571850.i	−0.104976	+	0.730123i
$886$	−306444.	−	635392.i	−0.390376	−	0.809421i
$887$	292938.	−	455821.i	0.372331	−	0.579358i	−0.603641	−	0.797256i	$-0.706284\pi$
$887$	292938.	−	455821.i	0.372331	−	0.579358i	0.975971	+	0.217899i	$0.0699202\pi$
$888$	−83521.9	+	109628.i	−0.105919	+	0.139025i
$889$	−172783.	−	378343.i	−0.218624	−	0.478720i
$890$	718974.	+	310284.i	0.907680	+	0.391723i
$891$	−16707.6	+	56900.8i	−0.0210454	+	0.0716742i
$892$	458648.	−	233186.i	0.576434	−	0.293071i
$893$	155029.	−	45520.7i	0.194407	−	0.0570829i
$894$	−60944.9	−	368779.i	−0.0762539	−	0.461414i
$895$	−9254.36	+	1330.58i	−0.0115531	+	0.00166109i
$896$	−369171.	+	579614.i	−0.459845	+	0.721976i
$897$	276317.	−	75373.1i	0.343417	−	0.0936766i
$898$	−135377.	−	201238.i	−0.167877	−	0.249550i
$899$	145704.	−	20949.1i	0.180282	−	0.0259207i
$900$	−125732.	−	133361.i	−0.155224	−	0.164643i
$901$	343722.	−	100926.i	0.423407	−	0.124323i
$902$	−87523.0	+	714914.i	−0.107574	+	0.878700i
$903$	−86741.8	+	295416.i	−0.106378	+	0.362291i
$904$	−1.04403e6	+	1.02652e6i	−1.27755	+	1.25612i
$905$	−122344.	−	267896.i	−0.149378	−	0.327092i
$906$	−47130.3	+	173930.i	−0.0574174	+	0.211894i
$907$	47136.1	−	73345.2i	0.0572979	−	0.0891573i	−0.811423	−	0.584460i	$-0.801306\pi$
$907$	47136.1	−	73345.2i	0.0572979	−	0.0891573i	0.868721	+	0.495303i	$0.164943\pi$
$908$	738616.	−	1.26283e6i	0.895874	−	1.53169i
$909$	40896.1	−	284439.i	0.0494942	−	0.344240i
$910$	−365182.	+	7663.11i	−0.440987	+	0.00925385i
$911$	1.14670e6	−	993625.i	1.38170	−	1.19725i	0.425353	−	0.905028i	$-0.360150\pi$
$911$	1.14670e6	−	993625.i	1.38170	−	1.19725i	0.956350	−	0.292224i	$-0.0943954\pi$
$912$	−58305.1	+	162510.i	−0.0700998	+	0.195385i
$913$	575837.	−	370068.i	0.690809	−	0.443956i
$914$	377534.	+	1.19261e6i	0.451922	+	1.42760i
$915$	−112337.	−	97340.4i	−0.134178	−	0.116266i
$916$	−27152.4	+	268356.i	−0.0323606	+	0.319831i
$917$	−112385.	+	246090.i	−0.133651	+	0.292654i
$918$	−598631.	−	662257.i	−0.710352	−	0.785852i
$919$		−	1.19196e6i		−	1.41134i	−0.708542	−	0.705668i	$-0.750647\pi$
$919$		−	1.19196e6i		−	1.41134i	0.708542	−	0.705668i	$-0.249353\pi$
$920$	259620.	−	641135.i	0.306734	−	0.757485i
$921$	−887074.			−1.04578
$922$	−741761.	+	670496.i	−0.872573	+	0.788741i
$923$	−123939.	−	56601.0i	−0.145480	−	0.0664386i
$924$	210810.	+	21329.8i	0.246915	+	0.0249829i
$925$	57614.2	−	66490.3i	0.0673358	−	0.0777097i
$926$	1.43197e6	−	453306.i	1.66998	−	0.528651i
$927$	−195444.	−	304117.i	−0.227438	−	0.353901i
$928$	1.01011e6	−	255458.i	1.17294	−	0.296636i
$929$	−973148.	−	1.12307e6i	−1.12758	−	1.30130i	−0.948256	−	0.317507i	$-0.897154\pi$
$929$	−973148.	−	1.12307e6i	−1.12758	−	1.30130i	−0.179324	−	0.983790i	$-0.557391\pi$
$930$	1260.28	+	60058.1i	0.00145714	+	0.0694393i
$931$	84320.5	+	12123.5i	0.0972823	+	0.0139871i
$932$	−625318.	−	365743.i	−0.719895	−	0.421060i
$933$	385722.	+	247888.i	0.443109	+	0.284769i
$934$	−195125.	−	52873.5i	−0.223676	−	0.0606100i
$935$	−372496.	+	170113.i	−0.426087	+	0.194587i
$936$	268363.	−	263863.i	0.306317	−	0.301180i
$937$	−427244.	−	125450.i	−0.486627	−	0.142887i	0.0292098	−	0.999573i	$-0.490701\pi$
$937$	−427244.	−	125450.i	−0.486627	−	0.142887i	−0.515837	+	0.856687i	$0.672519\pi$
$938$	644103.	+	78854.1i	0.732066	+	0.0896228i
$939$	140447.	+	478317.i	0.159287	+	0.542482i
$940$	289523.	−	272960.i	0.327663	−	0.308918i
$941$	10959.3	+	76223.4i	0.0123766	+	0.0860813i	0.995074	−	0.0991396i	$-0.0316090\pi$
$941$	10959.3	+	76223.4i	0.0123766	+	0.0860813i	−0.982697	+	0.185221i	$0.940700\pi$
$942$	−493273.	+	331834.i	−0.555886	+	0.373954i
$943$	803674.	+	1.30526e6i	0.903767	+	1.46782i
$944$	994760.	−	1.02000e6i	1.11628	−	1.14460i
$945$	84384.7	+	586908.i	0.0944931	+	0.657214i
$946$	−354311.	+	58553.9i	−0.395915	+	0.0654295i
$947$	−378353.	−	1.28855e6i	−0.421888	−	1.43682i	−0.846959	−	0.531659i	$-0.821569\pi$
$947$	−378353.	−	1.28855e6i	−0.421888	−	1.43682i	0.425070	−	0.905160i	$-0.360249\pi$
$948$	−263348.	−	517972.i	−0.293031	−	0.576355i
$949$	101460.	+	29791.3i	0.112658	+	0.0330794i
$950$	43671.9	−	101194.i	0.0483900	−	0.112127i
$951$	240961.	−	110043.i	0.266432	−	0.121675i
$952$	524709.	−	688713.i	0.578955	−	0.759913i
$953$	−538050.	−	345783.i	−0.592429	−	0.380731i	0.209803	−	0.977744i	$-0.432718\pi$
$953$	−538050.	−	345783.i	−0.592429	−	0.380731i	−0.802232	+	0.597013i	$0.796354\pi$
$954$	220824.	−	106501.i	0.242632	−	0.117019i
$955$	−80799.1	−	11617.2i	−0.0885931	−	0.0127378i
$956$	960121.	+	1.36452e6i	1.05053	+	1.49301i
$957$	−210380.	−	242791.i	−0.229710	−	0.265099i
$958$	−697623.	−	427925.i	−0.760134	−	0.466269i
$959$	−454750.	−	707605.i	−0.494465	−	0.769403i
$960$	53385.1	+	421826.i	0.0579265	+	0.457711i
$961$	−591072.	+	682133.i	−0.640020	+	0.738622i
$962$	138982.	+	115413.i	0.150178	+	0.124711i
$963$	−686392.	−	313465.i	−0.740150	−	0.338015i
$964$	−462251.	−	114904.i	−0.497420	−	0.123646i
$965$	−967619.			−1.03908
$966$	378941.	−	244432.i	0.406086	−	0.261941i
$967$		−	688402.i		−	0.736188i	−0.929789	−	0.368094i	$-0.880010\pi$
$967$		−	688402.i		−	0.736188i	0.929789	−	0.368094i	$-0.119990\pi$
$968$	−235615.	−	648400.i	−0.251450	−	0.691978i
$969$	90365.5	−	197873.i	0.0962398	−	0.210736i
$970$	525625.	+	436490.i	0.558640	+	0.463907i
$971$	−1.00191e6	−	868164.i	−1.06265	−	0.920796i	−0.0656275	−	0.997844i	$-0.520905\pi$
$971$	−1.00191e6	−	868164.i	−1.06265	−	0.920796i	−0.997027	+	0.0770485i	$0.975450\pi$
$972$	−762468.	−	606599.i	−0.807029	−	0.642051i
$973$	506381.	−	325431.i	0.534875	−	0.343743i
$974$	1.13184e6	+	694275.i	1.19307	+	0.731836i
$975$	84938.3	−	73599.4i	0.0893499	−	0.0774221i
$976$	82400.9	+	357191.i	0.0865033	+	0.374974i
$977$	61744.5	−	429442.i	0.0646858	−	0.449900i	−0.931578	−	0.363541i	$-0.881568\pi$
$977$	61744.5	−	429442.i	0.0646858	−	0.449900i	0.996264	−	0.0863590i	$-0.0275232\pi$
$978$	169826.	−	81905.5i	0.177552	−	0.0856318i
$979$	−321920.	+	500917.i	−0.335878	+	0.522637i
$980$	198636.	−	67497.2i	0.206827	−	0.0702803i
$981$	−138044.	−	302274.i	−0.143443	−	0.314097i
$982$	102321.	−	237094.i	0.106107	−	0.245866i
$983$	436366.	−	1.48613e6i	0.451589	−	1.53797i	−0.348041	−	0.937479i	$-0.613153\pi$
$983$	436366.	−	1.48613e6i	0.451589	−	1.53797i	0.799630	−	0.600493i	$-0.205029\pi$
$984$	−823131.	−	458541.i	−0.850117	−	0.473575i
$985$	−1.37012e6	+	402304.i	−1.41217	+	0.414650i
$986$	−1.29518e6	+	214042.i	−1.33222	+	0.220164i
$987$	256763.	−	36917.0i	0.263572	−	0.0378959i
$988$	209626.	+	85295.8i	0.214749	+	0.0873803i
$989$	−511546.	+	567832.i	−0.522988	+	0.580533i
$990$	−232532.	+	156428.i	−0.237253	+	0.159604i
$991$	−691114.	+	99367.1i	−0.703724	+	0.101180i	−0.484881	−	0.874580i	$-0.661137\pi$
$991$	−691114.	+	99367.1i	−0.703724	+	0.101180i	−0.218842	+	0.975760i	$0.570228\pi$
$992$	84756.3	−	121503.i	0.0861289	−	0.123470i
$993$	−53232.3	+	15630.4i	−0.0539855	+	0.0158516i
$994$	−212929.	−	26067.7i	−0.215507	−	0.0263834i
$995$	−9266.39	+	31558.4i	−0.00935975	+	0.0318764i
$996$	164508.	+	880221.i	0.165832	+	0.887306i
$997$	214934.	+	470640.i	0.216230	+	0.473477i	0.986400	−	0.164361i	$-0.0525563\pi$
$997$	214934.	+	470640.i	0.216230	+	0.473477i	−0.770171	+	0.637838i	$0.779829\pi$
$998$	1.54653e6	+	419067.i	1.55273	+	0.420748i
$999$	158550.	−	246709.i	0.158868	−	0.247203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.5.g.a.3.11	✓	460
4.3	odd	2	inner	92.5.g.a.3.40	yes	460
23.8	even	11	inner	92.5.g.a.31.40	yes	460
92.31	odd	22	inner	92.5.g.a.31.11	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.5.g.a.3.11	✓	460	1.1	even	1	trivial
92.5.g.a.3.40	yes	460	4.3	odd	2	inner
92.5.g.a.31.11	yes	460	92.31	odd	22	inner
92.5.g.a.31.40	yes	460	23.8	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	92.g (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.96738 + 2.68229i) q^{2} +(-4.62172 - 2.11067i) q^{3} +(1.61066 - 15.9187i) q^{4} +(-13.3793 + 15.4406i) q^{5} +(19.3758 - 6.13364i) q^{6} +(-22.6762 - 35.2848i) q^{7} +(37.9192 + 51.5571i) q^{8} +(-36.1383 - 41.7058i) q^{9} +(-1.71453 - 81.7053i) q^{10} +(61.5092 + 8.84369i) q^{11} +(-41.0432 + 70.1724i) q^{12} +(89.6447 + 57.6112i) q^{13} +(161.933 + 43.8793i) q^{14} +(94.4256 - 43.1227i) q^{15} +(-250.812 - 51.2793i) q^{16} +(309.477 + 90.8707i) q^{17} +(219.103 + 26.8236i) q^{18} +(37.3966 + 127.361i) q^{19} +(224.245 + 237.852i) q^{20} +(30.3284 + 210.939i) q^{21} +(-206.242 + 138.743i) q^{22} +(-158.804 + 504.601i) q^{23} +(-66.4318 - 318.318i) q^{24} +(29.5420 + 205.469i) q^{25} +(-420.539 + 69.4989i) q^{26} +(194.941 + 663.909i) q^{27} +(-598.213 + 304.144i) q^{28} +(976.281 + 286.662i) q^{29} +(-164.529 + 381.238i) q^{30} +(131.598 - 60.0987i) q^{31} +(881.798 - 520.584i) q^{32} +(-265.613 - 170.699i) q^{33} +(-1162.08 + 560.459i) q^{34} +(848.210 + 121.954i) q^{35} +(-722.110 + 508.102i) q^{36} +(-277.549 - 320.309i) q^{37} +(-452.589 - 277.620i) q^{38} +(-292.715 - 455.473i) q^{39} +(-1303.41 - 104.306i) q^{40} +(1897.53 - 2189.87i) q^{41} +(-655.794 - 544.585i) q^{42} +(1314.19 + 600.170i) q^{43} +(239.851 - 964.904i) q^{44} +1127.47 q^{45} +(-882.252 - 1923.30i) q^{46} -1217.24i q^{47} +(1050.95 + 766.379i) q^{48} +(266.602 - 583.777i) q^{49} +(-638.789 - 530.464i) q^{50} +(-1238.52 - 1073.18i) q^{51} +(1061.48 - 1334.24i) q^{52} +(934.341 - 600.465i) q^{53} +(-2359.26 - 1447.18i) q^{54} +(-959.504 + 831.415i) q^{55} +(959.322 - 2507.09i) q^{56} +(95.9806 - 667.560i) q^{57} +(-3665.90 + 1768.03i) q^{58} +(-3008.92 + 4681.97i) q^{59} +(-534.371 - 1572.59i) q^{60} +(-594.843 - 1302.52i) q^{61} +(-229.298 + 531.319i) q^{62} +(-652.104 + 2220.86i) q^{63} +(-1220.27 + 3910.01i) q^{64} +(-2088.94 + 613.367i) q^{65} +(1246.04 - 205.922i) q^{66} +(3828.44 - 550.447i) q^{67} +(1945.01 - 4780.12i) q^{68} +(1799.00 - 1996.94i) q^{69} +(-2844.08 + 1913.26i) q^{70} +(-1265.61 + 181.968i) q^{71} +(779.898 - 3444.64i) q^{72} +(952.131 - 279.571i) q^{73} +(1682.76 + 206.011i) q^{74} +(297.142 - 1011.97i) q^{75} +(2087.66 - 390.171i) q^{76} +(-1082.75 - 2370.88i) q^{77} +(2090.31 + 566.416i) q^{78} +(-3864.40 + 6013.13i) q^{79} +(4147.47 - 3186.59i) q^{80} +(-135.814 + 944.604i) q^{81} +(243.165 + 11587.9i) q^{82} +(8324.67 - 7213.36i) q^{83} +(3406.72 - 143.039i) q^{84} +(-5543.70 + 3562.72i) q^{85} +(-5509.53 + 1744.10i) q^{86} +(-3907.05 - 3385.48i) q^{87} +(1876.42 + 3506.58i) q^{88} +(-3980.50 + 8716.07i) q^{89} +(-3345.63 + 3024.20i) q^{90} -4469.50i q^{91} +(7776.82 + 3340.71i) q^{92} -735.057 q^{93} +(3264.99 + 3612.02i) q^{94} +(-2466.87 - 1126.58i) q^{95} +(-5174.21 + 544.809i) q^{96} +(-5474.83 + 6318.29i) q^{97} +(774.749 + 2447.39i) q^{98} +(-1854.01 - 2884.89i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) \) 460 * q - 3 * q^2 - 43 * q^4 - 18 * q^5 - 44 * q^6 + 144 * q^8 + 1116 * q^9 - 77 * q^10 - 156 * q^12 - 18 * q^13 + 253 * q^14 - 795 * q^16 - 18 * q^17 - 676 * q^18 + 113 * q^20 + 266 * q^21 - 818 * q^22 + 1006 * q^24 - 4768 * q^25 + 1100 * q^26 + 499 * q^28 + 654 * q^29 - 1401 * q^30 - 2163 * q^32 - 342 * q^33 - 5959 * q^34 - 3317 * q^36 - 3666 * q^37 + 4444 * q^38 + 23023 * q^40 - 1266 * q^41 + 23419 * q^42 + 7066 * q^44 + 5464 * q^45 - 8019 * q^46 - 14166 * q^48 + 14620 * q^49 - 25358 * q^50 - 36264 * q^52 - 9138 * q^53 - 6990 * q^54 - 7592 * q^56 - 3862 * q^57 + 31769 * q^58 + 34819 * q^60 + 7534 * q^61 - 9320 * q^62 + 4562 * q^64 + 9106 * q^65 + 6490 * q^66 - 4842 * q^68 - 22 * q^69 - 4258 * q^70 - 27815 * q^72 - 18 * q^73 - 202 * q^74 + 73926 * q^76 - 56086 * q^77 - 328 * q^78 - 47488 * q^80 + 9788 * q^81 - 42110 * q^82 - 111651 * q^84 + 117026 * q^85 - 55391 * q^86 - 44639 * q^88 + 44574 * q^89 - 4626 * q^90 + 18106 * q^92 - 85004 * q^93 + 55547 * q^94 + 150069 * q^96 - 34146 * q^97 + 52545 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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