LMFDB - Embedded newform 26.5.f.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,5,Mod(7,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("26.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	26.f (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.68761904018$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.120336834816.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 46x^{5} + 445x^{4} + 68x^{3} + 32x^{2} + 1136x + 20164 $ x^8 - 2x^7 + 2x^6 + 46x^5 + 445x^4 + 68x^3 + 32x^2 + 1136*x + 20164
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.2
Root			$-2.40965 - 2.40965i$ of defining polynomial
Character	$\chi$	$=$	26.7
Dual form			26.5.f.a.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73205 + 0.732051i) q^{2} +(0.661634 - 1.14598i) q^{3} +(6.92820 - 4.00000i) q^{4} +(18.3715 + 18.3715i) q^{5} +(-0.968699 + 3.61523i) q^{6} +(57.6222 + 15.4398i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(39.6245 + 68.6316i) q^{9} +O(q^{10})$	\(q+(-2.73205 + 0.732051i) q^{2} +(0.661634 - 1.14598i) q^{3} +(6.92820 - 4.00000i) q^{4} +(18.3715 + 18.3715i) q^{5} +(-0.968699 + 3.61523i) q^{6} +(57.6222 + 15.4398i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(39.6245 + 68.6316i) q^{9} +(-63.6409 - 36.7431i) q^{10} +(-15.9184 - 59.4083i) q^{11} -10.5861i q^{12} +(-46.0115 - 162.616i) q^{13} -168.730 q^{14} +(33.2087 - 8.89824i) q^{15} +(32.0000 - 55.4256i) q^{16} +(-276.620 + 159.706i) q^{17} +(-158.498 - 158.498i) q^{18} +(21.4833 - 80.1767i) q^{19} +(200.768 + 53.7956i) q^{20} +(55.8186 - 55.8186i) q^{21} +(86.9798 + 150.653i) q^{22} +(378.392 + 218.465i) q^{23} +(7.74959 + 28.9219i) q^{24} +50.0265i q^{25} +(244.749 + 410.592i) q^{26} +212.052 q^{27} +(460.978 - 123.519i) q^{28} +(-194.488 + 336.864i) q^{29} +(-84.2139 + 48.6209i) q^{30} +(-771.990 - 771.990i) q^{31} +(-46.8513 + 174.851i) q^{32} +(-78.6130 - 21.0643i) q^{33} +(638.826 - 638.826i) q^{34} +(774.955 + 1342.26i) q^{35} +(549.053 + 316.996i) q^{36} +(-508.713 - 1898.54i) q^{37} +234.774i q^{38} +(-216.798 - 54.8637i) q^{39} -587.889 q^{40} +(-2774.10 + 743.319i) q^{41} +(-111.637 + 193.361i) q^{42} +(850.135 - 490.826i) q^{43} +(-347.919 - 347.919i) q^{44} +(-532.906 + 1988.83i) q^{45} +(-1193.71 - 319.854i) q^{46} +(3074.22 - 3074.22i) q^{47} +(-42.3445 - 73.3429i) q^{48} +(1002.61 + 578.854i) q^{49} +(-36.6219 - 136.675i) q^{50} +422.669i q^{51} +(-969.241 - 942.590i) q^{52} -3410.30 q^{53} +(-579.337 + 155.233i) q^{54} +(798.976 - 1383.87i) q^{55} +(-1168.99 + 674.918i) q^{56} +(-77.6671 - 77.6671i) q^{57} +(284.751 - 1062.70i) q^{58} +(1939.23 + 519.616i) q^{59} +(194.484 - 194.484i) q^{60} +(2461.73 + 4263.85i) q^{61} +(2674.25 + 1543.98i) q^{62} +(1223.59 + 4566.50i) q^{63} -512.000i q^{64} +(2142.20 - 3832.81i) q^{65} +230.195 q^{66} +(3346.23 - 896.620i) q^{67} +(-1277.65 + 2212.96i) q^{68} +(500.713 - 289.087i) q^{69} +(-3099.82 - 3099.82i) q^{70} +(-1162.52 + 4338.59i) q^{71} +(-1732.10 - 464.114i) q^{72} +(2887.41 - 2887.41i) q^{73} +(2779.66 + 4814.52i) q^{74} +(57.3295 + 33.0992i) q^{75} +(-171.866 - 641.413i) q^{76} -3669.02i q^{77} +(632.466 - 8.81658i) q^{78} -11252.5 q^{79} +(1606.14 - 430.365i) q^{80} +(-3069.28 + 5316.15i) q^{81} +(7034.85 - 4061.57i) q^{82} +(-5383.22 - 5383.22i) q^{83} +(163.448 - 609.997i) q^{84} +(-8015.98 - 2147.88i) q^{85} +(-1963.30 + 1963.30i) q^{86} +(257.360 + 445.760i) q^{87} +(1205.23 + 695.838i) q^{88} +(-382.485 - 1427.45i) q^{89} -5823.70i q^{90} +(-140.525 - 10080.7i) q^{91} +3495.43 q^{92} +(-1395.46 + 373.913i) q^{93} +(-6148.45 + 10649.4i) q^{94} +(1867.65 - 1078.29i) q^{95} +(169.378 + 169.378i) q^{96} +(-553.976 + 2067.47i) q^{97} +(-3162.92 - 847.502i) q^{98} +(3446.53 - 3446.53i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9} + 132 q^{10} + 192 q^{11} - 78 q^{13} - 344 q^{14} + 132 q^{15} + 256 q^{16} - 870 q^{17} - 360 q^{18} - 218 q^{19} - 144 q^{20} + 1914 q^{21} + 948 q^{22} + 264 q^{23} - 288 q^{24} - 520 q^{26} - 2268 q^{27} - 736 q^{28} - 252 q^{29} + 1728 q^{30} - 3376 q^{31} + 512 q^{32} + 1698 q^{33} + 1080 q^{34} + 6474 q^{35} + 2016 q^{36} + 2552 q^{37} - 5928 q^{39} - 960 q^{40} - 8472 q^{41} - 3828 q^{42} + 7290 q^{43} - 3792 q^{44} - 6282 q^{45} - 540 q^{46} + 4848 q^{47} + 9678 q^{49} + 2524 q^{50} - 832 q^{52} - 6840 q^{53} + 2268 q^{54} + 294 q^{55} + 4320 q^{56} - 4434 q^{57} - 7008 q^{58} - 4632 q^{59} + 9024 q^{60} + 8670 q^{61} + 3936 q^{62} + 8100 q^{63} - 2808 q^{65} - 984 q^{66} - 12446 q^{67} - 2160 q^{68} + 19206 q^{69} - 25896 q^{70} - 4554 q^{71} - 5472 q^{72} + 19294 q^{73} + 10112 q^{74} - 25992 q^{75} + 1744 q^{76} - 8580 q^{78} - 11328 q^{79} - 1152 q^{80} + 6048 q^{81} + 42672 q^{82} + 10344 q^{83} - 8592 q^{84} - 23178 q^{85} + 13536 q^{86} + 18372 q^{87} + 1440 q^{88} - 2538 q^{89} + 1456 q^{91} + 96 q^{92} - 162 q^{93} - 9696 q^{94} + 26568 q^{95} - 64282 q^{97} - 31676 q^{98} + 9504 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9 + 132 * q^10 + 192 * q^11 - 78 * q^13 - 344 * q^14 + 132 * q^15 + 256 * q^16 - 870 * q^17 - 360 * q^18 - 218 * q^19 - 144 * q^20 + 1914 * q^21 + 948 * q^22 + 264 * q^23 - 288 * q^24 - 520 * q^26 - 2268 * q^27 - 736 * q^28 - 252 * q^29 + 1728 * q^30 - 3376 * q^31 + 512 * q^32 + 1698 * q^33 + 1080 * q^34 + 6474 * q^35 + 2016 * q^36 + 2552 * q^37 - 5928 * q^39 - 960 * q^40 - 8472 * q^41 - 3828 * q^42 + 7290 * q^43 - 3792 * q^44 - 6282 * q^45 - 540 * q^46 + 4848 * q^47 + 9678 * q^49 + 2524 * q^50 - 832 * q^52 - 6840 * q^53 + 2268 * q^54 + 294 * q^55 + 4320 * q^56 - 4434 * q^57 - 7008 * q^58 - 4632 * q^59 + 9024 * q^60 + 8670 * q^61 + 3936 * q^62 + 8100 * q^63 - 2808 * q^65 - 984 * q^66 - 12446 * q^67 - 2160 * q^68 + 19206 * q^69 - 25896 * q^70 - 4554 * q^71 - 5472 * q^72 + 19294 * q^73 + 10112 * q^74 - 25992 * q^75 + 1744 * q^76 - 8580 * q^78 - 11328 * q^79 - 1152 * q^80 + 6048 * q^81 + 42672 * q^82 + 10344 * q^83 - 8592 * q^84 - 23178 * q^85 + 13536 * q^86 + 18372 * q^87 + 1440 * q^88 - 2538 * q^89 + 1456 * q^91 + 96 * q^92 - 162 * q^93 - 9696 * q^94 + 26568 * q^95 - 64282 * q^97 - 31676 * q^98 + 9504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−2.73205	+	0.732051i	−0.683013	+	0.183013i
$2$	−2.73205	+	0.732051i	−0.683013	+	0.183013i
$3$	0.661634	−	1.14598i	0.0735148	−	0.127331i	−0.826925	−	0.562313i	$-0.809912\pi$
$3$	0.661634	−	1.14598i	0.0735148	−	0.127331i	0.900439	+	0.434981i	$0.143245\pi$
$4$	6.92820	−	4.00000i	0.433013	−	0.250000i
$5$	18.3715	+	18.3715i	0.734861	+	0.734861i	0.971579	−	0.236717i	$-0.0760715\pi$
$5$	18.3715	+	18.3715i	0.734861	+	0.734861i	−0.236717	+	0.971579i	$0.576072\pi$
$6$	−0.968699	+	3.61523i	−0.0269083	+	0.100423i
$7$	57.6222	+	15.4398i	1.17596	+	0.315099i	0.793324	−	0.608799i	$-0.208349\pi$
$7$	57.6222	+	15.4398i	1.17596	+	0.315099i	0.382639	+	0.923898i	$0.375015\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$	39.6245	+	68.6316i	0.489191	+	0.847304i
$10$	−63.6409	−	36.7431i	−0.636409	−	0.367431i
$11$	−15.9184	−	59.4083i	−0.131557	−	0.490978i	0.868431	−	0.495810i	$-0.165129\pi$
$11$	−15.9184	−	59.4083i	−0.131557	−	0.490978i	−0.999988	+	0.00483191i	$0.998462\pi$
$12$		−	10.5861i		−	0.0735148i
$13$	−46.0115	−	162.616i	−0.272258	−	0.962224i
$13$	−46.0115	−	162.616i	−0.272258	−	0.962224i
$14$	−168.730			−0.860865
$15$	33.2087	−	8.89824i	0.147594	−	0.0395477i
$16$	32.0000	−	55.4256i	0.125000	−	0.216506i
$17$	−276.620	+	159.706i	−0.957162	+	0.552618i	−0.895298	−	0.445467i	$-0.853038\pi$
$17$	−276.620	+	159.706i	−0.957162	+	0.552618i	−0.0618634	+	0.998085i	$0.519704\pi$
$18$	−158.498	−	158.498i	−0.489191	−	0.489191i
$19$	21.4833	−	80.1767i	0.0595105	−	0.222096i	−0.929766	−	0.368151i	$-0.879991\pi$
$19$	21.4833	−	80.1767i	0.0595105	−	0.222096i	0.989276	+	0.146055i	$0.0466576\pi$
$20$	200.768	+	53.7956i	0.501920	+	0.134489i
$21$	55.8186	−	55.8186i	0.126573	−	0.126573i
$22$	86.9798	+	150.653i	0.179710	+	0.311267i
$23$	378.392	+	218.465i	0.715297	+	0.412977i	0.813019	−	0.582237i	$-0.197822\pi$
$23$	378.392	+	218.465i	0.715297	+	0.412977i	−0.0977226	+	0.995214i	$0.531156\pi$
$24$	7.74959	+	28.9219i	0.0134541	+	0.0502116i
$25$			50.0265i			0.0800423i
$26$	244.749	+	410.592i	0.362055	+	0.607385i
$27$	212.052			0.290881
$28$	460.978	−	123.519i	0.587982	−	0.157549i
$29$	−194.488	+	336.864i	−0.231258	+	0.400551i	−0.958179	−	0.286171i	$-0.907618\pi$
$29$	−194.488	+	336.864i	−0.231258	+	0.400551i	0.726920	+	0.686722i	$0.240951\pi$
$30$	−84.2139	+	48.6209i	−0.0935709	+	0.0540232i
$31$	−771.990	−	771.990i	−0.803319	−	0.803319i	0.180293	−	0.983613i	$-0.442295\pi$
$31$	−771.990	−	771.990i	−0.803319	−	0.803319i	−0.983613	+	0.180293i	$0.942295\pi$
$32$	−46.8513	+	174.851i	−0.0457532	+	0.170753i
$33$	−78.6130	−	21.0643i	−0.0721883	−	0.0193428i
$34$	638.826	−	638.826i	0.552618	−	0.552618i
$35$	774.955	+	1342.26i	0.632617	+	1.09572i
$36$	549.053	+	316.996i	0.423652	+	0.244596i
$37$	−508.713	−	1898.54i	−0.371595	−	1.38681i	−0.858257	−	0.513221i	$-0.828452\pi$
$37$	−508.713	−	1898.54i	−0.371595	−	1.38681i	0.486662	−	0.873590i	$-0.338214\pi$
$38$			234.774i			0.162586i
$39$	−216.798	−	54.8637i	−0.142536	−	0.0360708i
$40$	−587.889			−0.367431
$41$	−2774.10	+	743.319i	−1.65027	+	0.442189i	−0.959688	−	0.281066i	$-0.909312\pi$
$41$	−2774.10	+	743.319i	−1.65027	+	0.442189i	−0.690582	+	0.723254i	$0.742645\pi$
$42$	−111.637	+	193.361i	−0.0632864	+	0.109615i
$43$	850.135	−	490.826i	0.459781	−	0.265455i	−0.252171	−	0.967683i	$-0.581145\pi$
$43$	850.135	−	490.826i	0.459781	−	0.265455i	0.711952	+	0.702228i	$0.247811\pi$
$44$	−347.919	−	347.919i	−0.179710	−	0.179710i
$45$	−532.906	+	1988.83i	−0.263163	+	0.982139i
$46$	−1193.71	−	319.854i	−0.564137	−	0.151160i
$47$	3074.22	−	3074.22i	1.39168	−	1.39168i	0.570118	−	0.821563i	$-0.306898\pi$
$47$	3074.22	−	3074.22i	1.39168	−	1.39168i	0.821563	−	0.570118i	$-0.193102\pi$
$48$	−42.3445	−	73.3429i	−0.0183787	−	0.0318329i
$49$	1002.61	+	578.854i	0.417578	+	0.241089i
$50$	−36.6219	−	136.675i	−0.0146488	−	0.0546699i
$51$			422.669i			0.162502i
$52$	−969.241	−	942.590i	−0.358447	−	0.348591i
$53$	−3410.30			−1.21406			−0.607031	−	0.794678i	$-0.707640\pi$
$53$	−3410.30			−1.21406			−0.607031	+	0.794678i	$0.707640\pi$
$54$	−579.337	+	155.233i	−0.198675	+	0.0532349i
$55$	798.976	−	1383.87i	0.264124	−	0.457477i
$56$	−1168.99	+	674.918i	−0.372766	+	0.215216i
$57$	−77.6671	−	77.6671i	−0.0239049	−	0.0239049i
$58$	284.751	−	1062.70i	0.0846464	−	0.315905i
$59$	1939.23	+	519.616i	0.557090	+	0.149272i	0.526369	−	0.850256i	$-0.323553\pi$
$59$	1939.23	+	519.616i	0.557090	+	0.149272i	0.0307211	+	0.999528i	$0.490220\pi$
$60$	194.484	−	194.484i	0.0540232	−	0.0540232i
$61$	2461.73	+	4263.85i	0.661579	+	1.14589i	0.980201	+	0.198006i	$0.0634465\pi$
$61$	2461.73	+	4263.85i	0.661579	+	1.14589i	−0.318622	+	0.947882i	$0.603220\pi$
$62$	2674.25	+	1543.98i	0.695695	+	0.401660i
$63$	1223.59	+	4566.50i	0.308287	+	1.15054i
$64$		−	512.000i		−	0.125000i
$65$	2142.20	−	3832.81i	0.507030	−	0.907173i
$66$	230.195			0.0528455
$67$	3346.23	−	896.620i	0.745429	−	0.199737i	0.133939	−	0.990990i	$-0.457237\pi$
$67$	3346.23	−	896.620i	0.745429	−	0.199737i	0.611490	+	0.791252i	$0.290571\pi$
$68$	−1277.65	+	2212.96i	−0.276309	+	0.478581i
$69$	500.713	−	289.087i	0.105170	−	0.0607198i
$70$	−3099.82	−	3099.82i	−0.632617	−	0.632617i
$71$	−1162.52	+	4338.59i	−0.230613	+	0.860660i	0.749464	+	0.662045i	$0.230311\pi$
$71$	−1162.52	+	4338.59i	−0.230613	+	0.860660i	−0.980078	+	0.198615i	$0.936356\pi$
$72$	−1732.10	−	464.114i	−0.334124	−	0.0895282i
$73$	2887.41	−	2887.41i	0.541830	−	0.541830i	−0.382235	−	0.924065i	$-0.624846\pi$
$73$	2887.41	−	2887.41i	0.541830	−	0.541830i	0.924065	+	0.382235i	$0.124846\pi$
$74$	2779.66	+	4814.52i	0.507608	+	0.879203i
$75$	57.3295	+	33.0992i	0.0101919	+	0.00588430i
$76$	−171.866	−	641.413i	−0.0297552	−	0.111048i
$77$		−	3669.02i		−	0.618825i
$78$	632.466	−	8.81658i	0.103956	−	0.00144914i
$79$	−11252.5			−1.80299			−0.901497	−	0.432785i	$-0.857531\pi$
$79$	−11252.5			−1.80299			−0.901497	+	0.432785i	$0.857531\pi$
$80$	1606.14	−	430.365i	0.250960	−	0.0672445i
$81$	−3069.28	+	5316.15i	−0.467807	+	0.810266i
$82$	7034.85	−	4061.57i	1.04623	−	0.604041i
$83$	−5383.22	−	5383.22i	−0.781423	−	0.781423i	0.198648	−	0.980071i	$-0.436345\pi$
$83$	−5383.22	−	5383.22i	−0.781423	−	0.781423i	−0.980071	+	0.198648i	$0.936345\pi$
$84$	163.448	−	609.997i	0.0231644	−	0.0864508i
$85$	−8015.98	−	2147.88i	−1.10948	−	0.297284i
$86$	−1963.30	+	1963.30i	−0.265455	+	0.265455i
$87$	257.360	+	445.760i	0.0340018	+	0.0588929i
$88$	1205.23	+	695.838i	0.155634	+	0.0898552i
$89$	−382.485	−	1427.45i	−0.0482875	−	0.180211i	0.937570	−	0.347796i	$-0.113070\pi$
$89$	−382.485	−	1427.45i	−0.0482875	−	0.180211i	−0.985858	+	0.167585i	$0.946403\pi$
$90$		−	5823.70i		−	0.718975i
$91$	−140.525	−	10080.7i	−0.0169696	−	1.21733i
$92$	3495.43			0.412977
$93$	−1395.46	+	373.913i	−0.161344	+	0.0432319i
$94$	−6148.45	+	10649.4i	−0.695840	+	1.20523i
$95$	1867.65	−	1078.29i	0.206942	−	0.119478i
$96$	169.378	+	169.378i	0.0183787	+	0.0183787i
$97$	−553.976	+	2067.47i	−0.0588773	+	0.219733i	−0.989096	−	0.147273i	$-0.952950\pi$
$97$	−553.976	+	2067.47i	−0.0588773	+	0.219733i	0.930219	+	0.367006i	$0.119617\pi$
$98$	−3162.92	−	847.502i	−0.329334	−	0.0882447i
$99$	3446.53	−	3446.53i	0.351651	−	0.351651i
$100$	200.106	+	346.594i	0.0200106	+	0.0346594i
$101$	610.425	+	352.429i	0.0598397	+	0.0345485i	0.529621	−	0.848234i	$-0.322334\pi$
$101$	610.425	+	352.429i	0.0598397	+	0.0345485i	−0.469782	+	0.882783i	$0.655667\pi$
$102$	−309.415	−	1154.75i	−0.0297400	−	0.110991i
$103$			20728.4i			1.95385i	0.213578	+	0.976926i	$0.431488\pi$
$103$			20728.4i			1.95385i	−0.213578	+	0.976926i	$0.568512\pi$
$104$	3338.04	+	1865.67i	0.308621	+	0.172492i
$105$	2050.95			0.186027
$106$	9317.11	−	2496.51i	0.829219	−	0.222189i
$107$	6665.01	−	11544.1i	0.582147	−	1.00831i	−0.413077	−	0.910696i	$-0.635546\pi$
$107$	6665.01	−	11544.1i	0.582147	−	1.00831i	0.995224	−	0.0976129i	$-0.0311207\pi$
$108$	1469.14	−	848.209i	0.125955	−	0.0727202i
$109$	12969.1	+	12969.1i	1.09159	+	1.09159i	0.995360	+	0.0962261i	$0.0306772\pi$
$109$	12969.1	+	12969.1i	1.09159	+	1.09159i	0.0962261	+	0.995360i	$0.469323\pi$
$110$	−1169.78	+	4365.69i	−0.0966762	+	0.360801i
$111$	−2512.28	−	673.164i	−0.203902	−	0.0546355i
$112$	2699.67	−	2699.67i	0.215216	−	0.215216i
$113$	1912.38	+	3312.34i	0.149768	+	0.259405i	0.931141	−	0.364658i	$-0.118814\pi$
$113$	1912.38	+	3312.34i	0.149768	+	0.259405i	−0.781374	+	0.624063i	$0.785481\pi$
$114$	269.047	+	155.334i	0.0207023	+	0.0119525i
$115$	2938.11	+	10965.2i	0.222163	+	0.829124i
$116$			3111.81i			0.231258i
$117$	9337.41	−	9601.42i	0.682110	−	0.701397i
$118$	−5678.46			−0.407818
$119$	−18405.3	+	4931.68i	−1.29972	+	0.348258i
$120$	−388.967	+	673.711i	−0.0270116	+	0.0467855i
$121$	9403.53	−	5429.13i	0.642274	−	0.370817i
$122$	−9846.94	−	9846.94i	−0.661579	−	0.661579i
$123$	−983.610	+	3670.88i	−0.0650148	+	0.242639i
$124$	−8436.46	−	2260.54i	−0.548677	−	0.147018i
$125$	10563.1	−	10563.1i	0.676041	−	0.676041i
$126$	−6685.82	−	11580.2i	−0.421128	−	0.729414i
$127$	−5328.66	−	3076.50i	−0.330377	−	0.190744i	0.325631	−	0.945497i	$-0.394423\pi$
$127$	−5328.66	−	3076.50i	−0.330377	−	0.190744i	−0.656009	+	0.754753i	$0.727757\pi$
$128$	374.810	+	1398.81i	0.0228766	+	0.0853766i
$129$		−	1298.99i		−	0.0780594i
$130$	−3046.79	+	12039.6i	−0.180284	+	0.712404i
$131$	−8267.18			−0.481742			−0.240871	−	0.970557i	$-0.577433\pi$
$131$	−8267.18			−0.481742			−0.240871	+	0.970557i	$0.577433\pi$
$132$	−628.904	+	168.514i	−0.0360941	+	0.00967140i
$133$	2475.83	−	4288.26i	0.139964	−	0.242425i
$134$	−8485.70	+	4899.22i	−0.472583	+	0.272846i
$135$	3895.72	+	3895.72i	0.213757	+	0.213757i
$136$	1870.61	−	6981.22i	0.101136	−	0.377445i
$137$	11295.3	+	3026.57i	0.601807	+	0.161254i	0.546844	−	0.837235i	$-0.315829\pi$
$137$	11295.3	+	3026.57i	0.601807	+	0.161254i	0.0549632	+	0.998488i	$0.482496\pi$
$138$	−1156.35	+	1156.35i	−0.0607198	+	0.0607198i
$139$	−3002.25	−	5200.04i	−0.155388	−	0.269139i	0.777812	−	0.628496i	$-0.216329\pi$
$139$	−3002.25	−	5200.04i	−0.155388	−	0.269139i	−0.933200	+	0.359357i	$0.882996\pi$
$140$	10738.1	+	6199.64i	0.547862	+	0.316308i
$141$	−1489.00	−	5557.02i	−0.0748955	−	0.279514i
$142$		−	12704.3i		−	0.630047i
$143$	−8928.31	+	5322.05i	−0.436613	+	0.260260i
$144$	5071.93			0.244596
$145$	−9761.75	+	2615.65i	−0.464292	+	0.124407i
$146$	−5774.82	+	10002.3i	−0.270915	+	0.469238i
$147$	1326.71	−	765.979i	0.0613964	−	0.0354472i
$148$	−11118.6	−	11118.6i	−0.507608	−	0.507608i
$149$	464.284	−	1732.73i	0.0209127	−	0.0780474i	−0.954681	−	0.297631i	$-0.903803\pi$
$149$	464.284	−	1732.73i	0.0209127	−	0.0780474i	0.975594	+	0.219584i	$0.0704700\pi$
$150$	−180.857	−	48.4606i	−0.00803810	−	0.00215380i
$151$	−23646.7	+	23646.7i	−1.03709	+	1.03709i	−0.0378064	+	0.999285i	$0.512037\pi$
$151$	−23646.7	+	23646.7i	−1.03709	+	1.03709i	−0.999285	+	0.0378064i	$0.987963\pi$
$152$	939.094	+	1626.56i	0.0406464	+	0.0704016i
$153$	−21921.8	−	12656.6i	−0.936470	−	0.540671i
$154$	2685.91	+	10023.9i	0.113253	+	0.422666i
$155$		−	28365.3i		−	1.18066i
$156$	−1721.47	+	487.084i	−0.0707378	+	0.0200150i
$157$	17674.2			0.717034			0.358517	−	0.933523i	$-0.383283\pi$
$157$	17674.2			0.717034			0.358517	+	0.933523i	$0.383283\pi$
$158$	30742.4	−	8237.39i	1.23147	−	0.329971i
$159$	−2256.37	+	3908.14i	−0.0892515	+	0.154588i
$160$	−4073.01	+	2351.56i	−0.159102	+	0.0918577i
$161$	18430.7	+	18430.7i	0.711034	+	0.711034i
$162$	4493.74	−	16770.9i	0.171229	−	0.639036i
$163$	40736.9	+	10915.4i	1.53325	+	0.410833i	0.924078	−	0.382205i	$-0.124835\pi$
$163$	40736.9	+	10915.4i	1.53325	+	0.410833i	0.609173	+	0.793038i	$0.291502\pi$
$164$	−16246.3	+	16246.3i	−0.604041	+	0.604041i
$165$	−1057.26	−	1831.23i	−0.0388341	−	0.0672627i
$166$	18648.0	+	10766.4i	0.676732	+	0.390711i
$167$	−10986.9	−	41003.7i	−0.393951	−	1.47025i	−0.823559	−	0.567230i	$-0.808015\pi$
$167$	−10986.9	−	41003.7i	−0.393951	−	1.47025i	0.429608	−	0.903015i	$-0.358652\pi$
$168$			1786.19i			0.0632864i
$169$	−24326.9	+	14964.4i	−0.851752	+	0.523946i
$170$	23472.4			0.812195
$171$	6353.92	−	1702.53i	0.217295	−	0.0582240i
$172$	3926.61	−	6801.08i	0.132727	−	0.229890i
$173$	−37886.8	+	21873.9i	−1.26589	+	0.730861i	−0.974207	−	0.225655i	$-0.927548\pi$
$173$	−37886.8	+	21873.9i	−1.26589	+	0.730861i	−0.291681	+	0.956516i	$0.594215\pi$
$174$	−1029.44	−	1029.44i	−0.0340018	−	0.0340018i
$175$	−772.400	+	2882.64i	−0.0252212	+	0.0941269i
$176$	−3802.13	−	1018.78i	−0.122744	−	0.0328893i
$177$	1878.53	−	1878.53i	0.0599614	−	0.0599614i
$178$	2089.94	+	3619.88i	0.0659619	+	0.114249i
$179$	7994.42	+	4615.58i	0.249506	+	0.144052i	0.619538	−	0.784967i	$-0.287320\pi$
$179$	7994.42	+	4615.58i	0.249506	+	0.144052i	−0.370032	+	0.929019i	$0.620653\pi$
$180$	4263.24	+	15910.6i	0.131582	+	0.491069i
$181$			17915.6i			0.546857i	0.961892	+	0.273428i	$0.0881577\pi$
$181$			17915.6i			0.546857i	−0.961892	+	0.273428i	$0.911842\pi$
$182$	7763.51	+	27438.1i	0.234377	+	0.828345i
$183$	6515.06			0.194543
$184$	−9549.70	+	2558.84i	−0.282068	+	0.0755800i
$185$	25533.3	−	44225.0i	0.746043	−	1.29218i
$186$	3538.75	−	2043.10i	0.102288	−	0.0590559i
$187$	13891.2	+	13891.2i	0.397244	+	0.397244i
$188$	9001.95	−	33595.7i	0.254695	−	0.950536i
$189$	12218.9	+	3274.05i	0.342065	+	0.0916561i
$190$	−4313.15	+	4313.15i	−0.119478	+	0.119478i
$191$	−7271.83	−	12595.2i	−0.199332	−	0.345253i	0.748980	−	0.662593i	$-0.230544\pi$
$191$	−7271.83	−	12595.2i	−0.199332	−	0.345253i	−0.948312	+	0.317340i	$0.897211\pi$
$192$	−586.743	−	338.756i	−0.0159164	−	0.00918935i
$193$	5610.60	+	20939.1i	0.150624	+	0.562138i	0.999440	+	0.0334494i	$0.0106492\pi$
$193$	5610.60	+	20939.1i	0.150624	+	0.562138i	−0.848816	+	0.528688i	$0.822684\pi$
$194$		−	6053.96i		−	0.160856i
$195$	−2974.98	−	4990.84i	−0.0782374	−	0.131252i
$196$	9261.67			0.241089
$197$	−14367.6	+	3849.79i	−0.370213	+	0.0991983i	−0.439129	−	0.898424i	$-0.644713\pi$
$197$	−14367.6	+	3849.79i	−0.370213	+	0.0991983i	0.0689155	+	0.997622i	$0.478046\pi$
$198$	−6893.06	+	11939.1i	−0.175825	+	0.304538i
$199$	−22664.8	+	13085.5i	−0.572330	+	0.330435i	−0.758079	−	0.652162i	$-0.773862\pi$
$199$	−22664.8	+	13085.5i	−0.572330	+	0.330435i	0.185750	+	0.982597i	$0.440529\pi$
$200$	−800.423	−	800.423i	−0.0200106	−	0.0200106i
$201$	1186.47	−	4427.96i	0.0293673	−	0.109600i
$202$	−1925.71	−	515.992i	−0.0471941	−	0.0126456i
$203$	−16408.0	+	16408.0i	−0.398164	+	0.398164i
$204$	1690.67	+	2928.33i	0.0406256	+	0.0703656i
$205$	−64620.5	−	37308.6i	−1.53767	−	0.887772i
$206$	−15174.3	−	56631.1i	−0.357580	−	1.33451i
$207$			34626.2i			0.808098i
$208$	−10485.5	−	2653.49i	−0.242360	−	0.0613325i
$209$	−5105.14			−0.116873
$210$	−5603.29	+	1501.40i	−0.127059	+	0.0340453i
$211$	41576.9	−	72013.4i	0.933872	−	1.61751i	0.157240	−	0.987560i	$-0.449740\pi$
$211$	41576.9	−	72013.4i	0.933872	−	1.61751i	0.776632	−	0.629954i	$-0.216926\pi$
$212$	−23627.2	+	13641.2i	−0.525704	+	0.303515i
$213$	4202.78	+	4202.78i	0.0926356	+	0.0926356i
$214$	−9758.25	+	36418.3i	−0.213081	+	0.795228i
$215$	24635.5	+	6601.06i	0.532948	+	0.142803i
$216$	−3392.83	+	3392.83i	−0.0727202	+	0.0727202i
$217$	−32564.4	−	56403.2i	−0.691550	−	1.19780i
$218$	−44926.4	−	25938.3i	−0.945341	−	0.545793i
$219$	−1398.52	−	5219.33i	−0.0291594	−	0.108824i
$220$		−	12783.6i		−	0.264124i
$221$	38698.5	+	37634.4i	0.792337	+	0.770550i
$222$	7356.47			0.149267
$223$	2880.06	−	771.710i	0.0579151	−	0.0155183i	−0.229745	−	0.973251i	$-0.573789\pi$
$223$	2880.06	−	771.710i	0.0579151	−	0.0155183i	0.287660	+	0.957733i	$0.407123\pi$
$224$	−5399.35	+	9351.94i	−0.107608	+	0.186383i
$225$	−3433.40	+	1982.27i	−0.0678202	+	0.0391560i
$226$	−7649.52	−	7649.52i	−0.149768	−	0.149768i
$227$	2399.20	−	8953.95i	0.0465603	−	0.173765i	−0.938730	−	0.344653i	$-0.887997\pi$
$227$	2399.20	−	8953.95i	0.0465603	−	0.173765i	0.985291	+	0.170887i	$0.0546634\pi$
$228$	−848.761	−	227.425i	−0.0163274	−	0.00437490i
$229$	−1910.72	+	1910.72i	−0.0364356	+	0.0364356i	−0.725090	−	0.688654i	$-0.758202\pi$
$229$	−1910.72	+	1910.72i	−0.0364356	+	0.0364356i	0.688654	+	0.725090i	$0.258202\pi$
$230$	−16054.1	−	27806.6i	−0.303481	−	0.525644i
$231$	−4204.63	−	2427.54i	−0.0787959	−	0.0454928i
$232$	−2278.00	−	8501.63i	−0.0423232	−	0.157952i
$233$			64094.4i			1.18061i	0.807179	+	0.590307i	$0.200993\pi$
$233$			64094.4i			1.18061i	−0.807179	+	0.590307i	$0.799007\pi$
$234$	−18481.6	+	33067.0i	−0.337526	+	0.603898i
$235$	112956.			2.04538
$236$	15513.9	−	4156.92i	0.278545	−	0.0746360i
$237$	−7445.02	+	12895.2i	−0.132547	+	0.229578i
$238$	46673.9	−	26947.2i	0.823987	−	0.475729i
$239$	50392.1	+	50392.1i	0.882199	+	0.882199i	0.993758	−	0.111559i	$-0.0355843\pi$
$239$	50392.1	+	50392.1i	0.882199	+	0.882199i	−0.111559	+	0.993758i	$0.535584\pi$
$240$	569.487	−	2125.36i	0.00988693	−	0.0368985i
$241$	−36349.1	−	9739.70i	−0.625834	−	0.167692i	−0.0680555	−	0.997682i	$-0.521679\pi$
$241$	−36349.1	−	9739.70i	−0.625834	−	0.167692i	−0.557779	+	0.829990i	$0.688346\pi$
$242$	−21716.5	+	21716.5i	−0.370817	+	0.370817i
$243$	12649.6	+	21909.7i	0.214222	+	0.371043i
$244$	34110.8	+	19693.9i	0.572944	+	0.330789i
$245$	7784.95	+	29053.8i	0.129695	+	0.484029i
$246$		−	10749.1i		−	0.177624i
$247$	−14026.5	+	195.529i	−0.229908	+	0.00320493i
$248$	24703.7			0.401660
$249$	−9730.80	+	2607.36i	−0.156946	+	0.0420535i
$250$	−21126.3	+	36591.8i	−0.338021	+	0.585469i
$251$	7574.87	−	4373.35i	0.120234	−	0.0694172i	−0.438677	−	0.898645i	$-0.644553\pi$
$251$	7574.87	−	4373.35i	0.120234	−	0.0694172i	0.558911	+	0.829228i	$0.311219\pi$
$252$	26743.3	+	26743.3i	0.421128	+	0.421128i
$253$	6955.22	−	25957.2i	0.108660	−	0.405525i
$254$	16810.3	+	4504.31i	0.260560	+	0.0698170i
$255$	−7765.07	+	7765.07i	−0.119417	+	0.119417i
$256$	−2048.00	−	3547.24i	−0.0312500	−	0.0541266i
$257$	84073.4	+	48539.8i	1.27289	+	0.734906i	0.975532	−	0.219859i	$-0.0705596\pi$
$257$	84073.4	+	48539.8i	1.27289	+	0.734906i	0.297363	+	0.954765i	$0.403893\pi$
$258$	950.924	+	3548.90i	0.0142859	+	0.0533156i
$259$		−	117253.i		−	1.74793i
$260$	−489.619	−	35123.3i	−0.00724288	−	0.519575i
$261$	−30826.0			−0.452518
$262$	22586.4	−	6051.99i	0.329036	−	0.0881649i
$263$	−40236.2	+	69691.2i	−0.581709	+	1.00755i	0.413568	+	0.910473i	$0.364282\pi$
$263$	−40236.2	+	69691.2i	−0.581709	+	1.00755i	−0.995277	+	0.0970764i	$0.969051\pi$
$264$	1594.84	−	920.780i	0.0228828	−	0.0132114i
$265$	−62652.4	−	62652.4i	−0.892167	−	0.892167i
$266$	−3624.86	+	13528.2i	−0.0512305	+	0.191195i
$267$	−1888.90	−	506.130i	−0.0264964	−	0.00709969i
$268$	19596.9	−	19596.9i	0.272846	−	0.272846i
$269$	−29904.1	−	51795.3i	−0.413262	−	0.715791i	0.581982	−	0.813202i	$-0.302277\pi$
$269$	−29904.1	−	51795.3i	−0.413262	−	0.715791i	−0.995244	+	0.0974106i	$0.968944\pi$
$270$	−13495.2	−	7791.45i	−0.185119	−	0.106879i
$271$	14660.8	+	54715.0i	0.199628	+	0.745020i	0.991020	+	0.133712i	$0.0426897\pi$
$271$	14660.8	+	54715.0i	0.199628	+	0.745020i	−0.791393	+	0.611308i	$0.790644\pi$
$272$			20442.4i			0.276309i
$273$	−11645.3	−	6508.69i	−0.156252	−	0.0873310i
$274$	−33075.0			−0.440553
$275$	2971.99	−	796.342i	0.0392990	−	0.0105301i
$276$	2312.70	−	4005.71i	0.0303599	−	0.0525849i
$277$	19495.3	−	11255.6i	0.254081	−	0.146693i	−0.367551	−	0.930003i	$-0.619804\pi$
$277$	19495.3	−	11255.6i	0.254081	−	0.146693i	0.621631	+	0.783310i	$0.286470\pi$
$278$	12009.0	+	12009.0i	0.155388	+	0.155388i
$279$	22393.2	−	83572.6i	0.287679	−	1.07363i
$280$	−33875.5	−	9076.91i	−0.432085	−	0.115777i
$281$	−51880.2	+	51880.2i	−0.657035	+	0.657035i	−0.954678	−	0.297642i	$-0.903800\pi$
$281$	−51880.2	+	51880.2i	−0.657035	+	0.657035i	0.297642	+	0.954678i	$0.403800\pi$
$282$	8136.04	+	14092.0i	0.102309	+	0.177205i
$283$	−85119.2	−	49143.6i	−1.06281	−	0.613612i	−0.136600	−	0.990626i	$-0.543618\pi$
$283$	−85119.2	−	49143.6i	−1.06281	−	0.613612i	−0.926208	+	0.377014i	$0.876951\pi$
$284$	9300.17	+	34708.7i	0.115307	+	0.430330i
$285$		−	2853.73i		−	0.0351336i
$286$	20496.6	−	21076.1i	0.250582	−	0.257667i
$287$	−171327.			−2.07999
$288$	−13856.8	+	3712.91i	−0.167062	+	0.0447641i
$289$	9251.82	−	16024.6i	0.110772	−	0.191863i
$290$	24754.8	−	14292.2i	0.294350	−	0.169943i
$291$	2002.75	+	2002.75i	0.0236506	+	0.0236506i
$292$	8454.92	−	31554.2i	0.0991617	−	0.370077i
$293$	−57128.2	−	15307.4i	−0.665449	−	0.178307i	−0.0897452	−	0.995965i	$-0.528605\pi$
$293$	−57128.2	−	15307.4i	−0.665449	−	0.178307i	−0.575704	+	0.817658i	$0.695272\pi$
$294$	−3063.92	+	3063.92i	−0.0354472	+	0.0354472i
$295$	26080.5	+	45172.8i	0.299690	+	0.519078i
$296$	38516.1	+	22237.3i	0.439602	+	0.253804i
$297$	−3375.53	−	12597.7i	−0.0382674	−	0.142816i
$298$			5073.79i			0.0571347i
$299$	18115.4	−	71584.4i	0.202631	−	0.800712i
$300$	529.587			0.00588430
$301$	56564.9	−	15156.5i	0.624330	−	0.167289i
$302$	47293.4	−	81914.6i	0.518546	−	0.898148i
$303$	807.755	−	466.358i	0.00879822	−	0.00507965i
$304$	−3756.38	−	3756.38i	−0.0406464	−	0.0406464i
$305$	−33107.6	+	123559.i	−0.355900	+	1.32824i
$306$	69156.8	+	18530.5i	0.738571	+	0.197899i
$307$	25027.7	−	25027.7i	0.265548	−	0.265548i	−0.561755	−	0.827304i	$-0.689874\pi$
$307$	25027.7	−	25027.7i	0.265548	−	0.265548i	0.827304	+	0.561755i	$0.189874\pi$
$308$	−14676.1	−	25419.7i	−0.154706	−	0.267959i
$309$	23754.4	+	13714.6i	0.248787	+	0.143637i
$310$	20764.8	+	77495.4i	0.216075	+	0.806404i
$311$		−	55730.1i		−	0.576195i	−0.957601	−	0.288097i	$-0.906977\pi$
$311$		−	55730.1i		−	0.576195i	0.957601	−	0.288097i	$-0.0930227\pi$
$312$	4346.58	−	2590.95i	0.0446518	−	0.0266164i
$313$	50667.8			0.517182			0.258591	−	0.965987i	$-0.416742\pi$
$313$	50667.8			0.517182			0.258591	+	0.965987i	$0.416742\pi$
$314$	−48286.7	+	12938.4i	−0.489743	+	0.131226i
$315$	−61414.4	+	106373.i	−0.618941	+	1.07204i
$316$	−77959.5	+	45010.0i	−0.780719	+	0.450749i
$317$	33100.3	+	33100.3i	0.329392	+	0.329392i	0.852355	−	0.522963i	$-0.175173\pi$
$317$	33100.3	+	33100.3i	0.329392	+	0.329392i	−0.522963	+	0.852355i	$0.675173\pi$
$318$	3303.55	−	12329.0i	0.0326683	−	0.121920i
$319$	23108.4	+	6191.89i	0.227085	+	0.0608473i
$320$	9406.23	−	9406.23i	0.0918577	−	0.0918577i
$321$	−8819.58	−	15276.0i	−0.0855930	−	0.148251i
$322$	−63845.9	−	36861.4i	−0.615774	−	0.355517i
$323$	6862.04	+	25609.5i	0.0657731	+	0.245468i
$324$			49108.5i			0.467807i
$325$	8135.10	−	2301.79i	0.0770187	−	0.0217921i
$326$	−119286.			−1.12242
$327$	23443.2	−	6281.59i	0.219241	−	0.0587454i
$328$	32492.6	−	56278.8i	0.302020	−	0.523115i
$329$	224609.	−	129678.i	2.07508	−	1.19805i
$330$	4229.03	+	4229.03i	0.0388341	+	0.0388341i
$331$	−33871.6	+	126410.i	−0.309157	+	1.15379i	0.620150	+	0.784483i	$0.287072\pi$
$331$	−33871.6	+	126410.i	−0.309157	+	1.15379i	−0.929307	+	0.369307i	$0.879595\pi$
$332$	−58828.9	−	15763.2i	−0.533722	−	0.143010i
$333$	110143.	−	110143.i	0.993270	−	0.993270i
$334$	60033.6	+	103981.i	0.538147	+	0.932098i
$335$	77947.7	+	45003.1i	0.694566	+	0.401008i
$336$	−1307.59	−	4879.97i	−0.0115822	−	0.0432254i
$337$			79520.5i			0.700195i	0.936713	+	0.350098i	$0.113852\pi$
$337$			79520.5i			0.700195i	−0.936713	+	0.350098i	$0.886148\pi$
$338$	55507.6	−	58692.1i	0.485868	−	0.513743i
$339$	5061.18			0.0440405
$340$	−64127.9	+	17183.0i	−0.554739	+	0.148642i
$341$	−33573.8	+	58151.5i	−0.288730	+	0.500094i
$342$	−16112.9	+	9302.78i	−0.137759	+	0.0795354i
$343$	−52445.0	−	52445.0i	−0.445775	−	0.445775i
$344$	−5748.95	+	21455.4i	−0.0485816	+	0.181309i
$345$	14509.8	+	3887.90i	0.121906	+	0.0326646i
$346$	87495.8	−	87495.8i	0.730861	−	0.730861i
$347$	62641.8	+	108499.i	0.520242	+	0.901086i	0.999723	+	0.0235336i	$0.00749167\pi$
$347$	62641.8	+	108499.i	0.520242	+	0.901086i	−0.479481	+	0.877552i	$0.659175\pi$
$348$	3566.08	+	2058.88i	0.0294465	+	0.0170009i
$349$	−39283.9	−	146610.i	−0.322526	−	1.20368i	−0.916776	−	0.399402i	$-0.869218\pi$
$349$	−39283.9	−	146610.i	−0.322526	−	1.20368i	0.594250	−	0.804280i	$-0.297449\pi$
$350$		−	8440.94i		−	0.0689057i
$351$	−9756.85	−	34483.1i	−0.0791945	−	0.279893i
$352$	11133.4			0.0898552
$353$	−22392.9	+	6000.17i	−0.179706	+	0.0481520i	−0.347550	−	0.937662i	$-0.612986\pi$
$353$	−22392.9	+	6000.17i	−0.179706	+	0.0481520i	0.167844	+	0.985814i	$0.446320\pi$
$354$	−3757.06	+	6507.42i	−0.0299807	+	0.0519281i
$355$	−101064.	+	58349.2i	−0.801934	+	0.462997i
$356$	−8359.75	−	8359.75i	−0.0659619	−	0.0659619i
$357$	−6525.93	+	24355.1i	−0.0512043	+	0.191097i
$358$	−25220.0	−	6757.68i	−0.196779	−	0.0527268i
$359$	10930.4	−	10930.4i	0.0848097	−	0.0848097i	−0.663429	−	0.748239i	$-0.730900\pi$
$359$	10930.4	−	10930.4i	0.0848097	−	0.0848097i	0.748239	+	0.663429i	$0.230900\pi$
$360$	−23294.8	−	40347.8i	−0.179744	−	0.311325i
$361$	106895.	+	61715.6i	0.820240	+	0.473566i
$362$	−13115.1	−	48946.3i	−0.100082	−	0.373510i
$363$		−	14368.4i		−	0.109042i
$364$	−41296.4	−	69279.0i	−0.311680	−	0.522877i
$365$	106092.			0.796339
$366$	−17799.5	+	4769.36i	−0.132876	+	0.0356039i
$367$	−66757.4	+	115627.i	−0.495641	+	0.858475i	−0.999987	−	0.00502612i	$-0.998400\pi$
$367$	−66757.4	+	115627.i	−0.495641	+	0.858475i	0.504346	+	0.863501i	$0.331733\pi$
$368$	24217.1	−	13981.7i	0.178824	−	0.103244i
$369$	−160938.	−	160938.i	−1.18197	−	1.18197i
$370$	−37383.4	+	139517.i	−0.273071	+	1.01911i
$371$	−196509.	−	52654.4i	−1.42769	−	0.382549i
$372$	−8172.39	+	8172.39i	−0.0590559	+	0.0590559i
$373$	127719.	+	221215.i	0.917986	+	1.59000i	0.802469	+	0.596694i	$0.203519\pi$
$373$	127719.	+	221215.i	0.917986	+	1.59000i	0.115517	+	0.993305i	$0.463147\pi$
$374$	−48120.7	−	27782.5i	−0.344024	−	0.198622i
$375$	−5116.25	−	19094.1i	−0.0363822	−	0.135780i
$376$			98375.1i			0.695840i
$377$	63728.1	+	16127.3i	0.448382	+	0.113469i
$378$	−35779.5			−0.250409
$379$	121494.	−	32554.3i	0.845819	−	0.226637i	0.190216	−	0.981742i	$-0.439081\pi$
$379$	121494.	−	32554.3i	0.845819	−	0.226637i	0.655603	+	0.755106i	$0.272414\pi$
$380$	8626.30	−	14941.2i	0.0597389	−	0.103471i
$381$	−7051.24	+	4071.03i	−0.0485753	+	0.0280450i
$382$	29087.3	+	29087.3i	0.199332	+	0.199332i
$383$	60929.3	−	227391.i	0.415364	−	1.55016i	−0.368743	−	0.929531i	$-0.620212\pi$
$383$	60929.3	−	227391.i	0.415364	−	1.55016i	0.784106	−	0.620626i	$-0.213122\pi$
$384$	1851.00	+	495.974i	0.0125529	+	0.00336354i
$385$	67405.4	−	67405.4i	0.454751	−	0.454751i
$386$	−30656.9	−	53099.3i	−0.205757	−	0.356381i
$387$	67372.3	+	38897.4i	0.449842	+	0.259716i
$388$	4431.81	+	16539.7i	0.0294386	+	0.109866i
$389$			50206.9i			0.331791i	0.986143	+	0.165895i	$0.0530514\pi$
$389$			50206.9i			0.331791i	−0.986143	+	0.165895i	$0.946949\pi$
$390$	11781.3	+	11457.4i	0.0774579	+	0.0753280i
$391$	−139561.			−0.912873
$392$	−25303.4	+	6780.01i	−0.164667	+	0.0441223i
$393$	−5469.84	+	9474.04i	−0.0354152	+	0.0613409i
$394$	36434.8	−	21035.6i	0.234706	−	0.135507i
$395$	−206725.	−	206725.i	−1.32495	−	1.32495i
$396$	10092.1	−	37664.4i	0.0643566	−	0.240182i
$397$	−275911.	−	73930.2i	−1.75061	−	0.469074i	−0.765851	−	0.643018i	$-0.777682\pi$
$397$	−275911.	−	73930.2i	−1.75061	−	0.469074i	−0.984756	+	0.173944i	$0.944349\pi$
$398$	52342.2	−	52342.2i	0.330435	−	0.330435i
$399$	−3276.18	−	5674.51i	−0.0205789	−	0.0356437i
$400$	2772.75	+	1600.85i	0.0173297	+	0.0100053i
$401$	−31922.7	−	119137.i	−0.198523	−	0.740897i	−0.991327	−	0.131420i	$-0.958046\pi$
$401$	−31922.7	−	119137.i	−0.198523	−	0.740897i	0.792804	−	0.609477i	$-0.208620\pi$
$402$			12966.0i			0.0802329i
$403$	−90017.4	+	161058.i	−0.554264	+	0.991683i
$404$	5638.87			0.0345485
$405$	−154053.	+	41278.5i	−0.939206	+	0.251660i
$406$	32815.9	−	56838.8i	0.199082	−	0.344821i
$407$	−104691.	+	60443.6i	−0.632007	+	0.364890i
$408$	−6762.70	−	6762.70i	−0.0406256	−	0.0406256i
$409$	1348.10	−	5031.19i	0.00805892	−	0.0300763i	−0.961779	−	0.273826i	$-0.911711\pi$
$409$	1348.10	−	5031.19i	0.00805892	−	0.0300763i	0.969838	+	0.243750i	$0.0783775\pi$
$410$	203858.	+	54623.6i	1.21272	+	0.324947i
$411$	10941.8	−	10941.8i	0.0647744	−	0.0647744i
$412$	82913.7	+	143611.i	0.488463	+	0.846043i
$413$	103720.	+	59882.8i	0.608083	+	0.351077i
$414$	−25348.1	−	94600.5i	−0.147892	−	0.551941i
$415$		−	197796.i		−	1.14847i
$416$	30589.3	−	426.415i	0.176760	−	0.00246403i
$417$	−7945.55			−0.0456932
$418$	13947.5	−	3737.22i	0.0798259	−	0.0213893i
$419$	11158.9	−	19327.9i	0.0635616	−	0.110092i	−0.832493	−	0.554035i	$-0.813087\pi$
$419$	11158.9	−	19327.9i	0.0635616	−	0.110092i	0.896055	+	0.443943i	$0.146421\pi$
$420$	14209.4	−	8203.78i	0.0805520	−	0.0465067i
$421$	25272.1	+	25272.1i	0.142586	+	0.142586i	0.774797	−	0.632211i	$-0.217852\pi$
$421$	25272.1	+	25272.1i	0.142586	+	0.142586i	−0.632211	+	0.774797i	$0.717852\pi$
$422$	−60872.9	+	227181.i	−0.341821	+	1.27569i
$423$	332803.	+	89174.4i	1.85997	+	0.498379i
$424$	54564.8	−	54564.8i	0.303515	−	0.303515i
$425$	−7989.55	−	13838.3i	−0.0442328	−	0.0766135i
$426$	−14558.9	−	8405.57i	−0.0802248	−	0.0463178i
$427$	76017.5	+	283701.i	0.416925	+	1.55598i
$428$		−	106640.i		−	0.582147i
$429$	191.716	+	13752.9i	0.00104170	+	0.0747276i
$430$	−72137.8			−0.390145
$431$	197570.	−	52938.7i	1.06357	−	0.284983i	0.315721	−	0.948852i	$-0.397754\pi$
$431$	197570.	−	52938.7i	1.06357	−	0.284983i	0.747849	+	0.663869i	$0.231087\pi$
$432$	6785.67	−	11753.1i	0.0363601	−	0.0629776i
$433$	−4934.60	+	2848.99i	−0.0263194	+	0.0151955i	−0.513102	−	0.858328i	$-0.671504\pi$
$433$	−4934.60	+	2848.99i	−0.0263194	+	0.0151955i	0.486783	+	0.873523i	$0.338170\pi$
$434$	130258.	+	130258.i	0.691550	+	0.691550i
$435$	−3461.21	+	12917.4i	−0.0182915	+	0.0682648i
$436$	141729.	+	37976.2i	0.745567	+	0.199774i
$437$	25644.9	−	25644.9i	0.134288	−	0.134288i
$438$	7641.63	+	13235.7i	0.0398325	+	0.0689919i
$439$	79785.1	+	46063.9i	0.413993	+	0.239019i	0.692504	−	0.721414i	$-0.256508\pi$
$439$	79785.1	+	46063.9i	0.413993	+	0.239019i	−0.278511	+	0.960433i	$0.589841\pi$
$440$	9358.26	+	34925.5i	0.0483381	+	0.180400i
$441$			91747.2i			0.471754i
$442$	−133277.	−	74489.9i	−0.682196	−	0.381288i
$443$	−319278.			−1.62690			−0.813450	−	0.581634i	$-0.802414\pi$
$443$	−319278.			−1.62690			−0.813450	+	0.581634i	$0.802414\pi$
$444$	−20098.3	+	5385.31i	−0.101951	+	0.0273177i
$445$	19197.7	−	33251.4i	0.0969458	−	0.167915i
$446$	−7303.54	+	4216.70i	−0.0367167	+	0.0211984i
$447$	−1678.49	−	1678.49i	−0.00840049	−	0.00840049i
$448$	7905.19	−	29502.6i	0.0393873	−	0.146995i
$449$	26729.6	+	7162.17i	0.132587	+	0.0355265i	0.324502	−	0.945885i	$-0.394803\pi$
$449$	26729.6	+	7162.17i	0.132587	+	0.0355265i	−0.191915	+	0.981411i	$0.561470\pi$
$450$	7929.09	−	7929.09i	0.0391560	−	0.0391560i
$451$	88318.6	+	152972.i	0.434209	+	0.752073i
$452$	26498.7	+	15299.0i	0.129702	+	0.0748838i
$453$	11453.3	+	42744.2i	0.0558127	+	0.208296i
$454$			26219.0i			0.127205i
$455$	182616.	−	187780.i	0.882098	−	0.907038i
$456$	2485.35			0.0119525
$457$	−38999.4	+	10449.8i	−0.186735	+	0.0500354i	−0.350974	−	0.936385i	$-0.614150\pi$
$457$	−38999.4	+	10449.8i	−0.186735	+	0.0500354i	0.164240	+	0.986420i	$0.447483\pi$
$458$	3821.44	−	6618.92i	0.0182178	−	0.0315541i
$459$	−58657.8	+	33866.1i	−0.278420	+	0.160746i
$460$	64216.5	+	64216.5i	0.303481	+	0.303481i
$461$	−4500.84	+	16797.4i	−0.0211783	+	0.0790386i	−0.975706	−	0.219083i	$-0.929693\pi$
$461$	−4500.84	+	16797.4i	−0.0211783	+	0.0790386i	0.954528	+	0.298122i	$0.0963601\pi$
$462$	13264.3	+	3554.17i	0.0621444	+	0.0166515i
$463$	−54673.1	+	54673.1i	−0.255042	+	0.255042i	−0.823034	−	0.567992i	$-0.807720\pi$
$463$	−54673.1	+	54673.1i	−0.255042	+	0.255042i	0.567992	+	0.823034i	$0.307720\pi$
$464$	12447.2	+	21559.3i	0.0578146	+	0.100138i
$465$	−32506.1	−	18767.4i	−0.150335	−	0.0867958i
$466$	−46920.3	−	175109.i	−0.216067	−	0.806375i
$467$		−	118350.i		−	0.542667i	−0.962485	−	0.271333i	$-0.912535\pi$
$467$		−	118350.i		−	0.542667i	0.962485	−	0.271333i	$-0.0874646\pi$
$468$	26285.8	−	103870.i	0.120013	−	0.474241i
$469$	206661.			0.939534
$470$	−308603.	+	82689.8i	−1.39702	+	0.374331i
$471$	11693.8	−	20254.3i	0.0527126	−	0.0913009i
$472$	−39341.6	+	22713.9i	−0.176591	+	0.101955i
$473$	−42691.9	−	42691.9i	−0.190820	−	0.190820i
$474$	10900.3	−	40680.4i	0.0485155	−	0.181062i
$475$	4010.96	+	1074.73i	0.0177771	+	0.00476336i
$476$	−107789.	+	107789.i	−0.475729	+	0.475729i
$477$	−135131.	−	234054.i	−0.593908	−	1.02868i
$478$	−174563.	−	100784.i	−0.764007	−	0.441100i
$479$	−46063.3	−	171911.i	−0.200763	−	0.749258i	−0.990699	−	0.136069i	$-0.956553\pi$
$479$	−46063.3	−	171911.i	−0.200763	−	0.749258i	0.789936	−	0.613189i	$-0.210114\pi$
$480$			6223.47i			0.0270116i
$481$	−285327.	+	170080.i	−1.23325	+	0.735128i
$482$	106437.			0.458142
$483$	33315.7	−	8926.91i	0.142809	−	0.0382655i
$484$	43433.0	−	75228.2i	0.185408	−	0.321137i
$485$	−48159.9	+	27805.2i	−0.204740	+	0.118207i
$486$	−50598.4	−	50598.4i	−0.214222	−	0.214222i
$487$	13035.1	−	48647.6i	0.0549611	−	0.205118i	−0.932985	−	0.359915i	$-0.882806\pi$
$487$	13035.1	−	48647.6i	0.0549611	−	0.205118i	0.987946	+	0.154797i	$0.0494724\pi$
$488$	−107609.	−	28833.8i	−0.451867	−	0.121077i
$489$	39461.8	−	39461.8i	0.165029	−	0.165029i
$490$	−42537.8	−	73677.6i	−0.177167	−	0.306862i
$491$	64633.3	+	37316.0i	0.268098	+	0.154786i	0.628023	−	0.778195i	$-0.283864\pi$
$491$	64633.3	+	37316.0i	0.268098	+	0.154786i	−0.359925	+	0.932981i	$0.617198\pi$
$492$	7868.88	+	29367.0i	0.0325074	+	0.121319i
$493$		−	124244.i		−	0.511190i
$494$	38177.9	−	10802.3i	0.156444	−	0.0442652i
$495$	126636.			0.516829
$496$	−67491.7	+	18084.3i	−0.274339	+	0.0735088i
$497$	−133974.	+	232050.i	−0.542385	+	0.939439i
$498$	24676.3	−	14246.9i	0.0994997	−	0.0574462i
$499$	179976.	+	179976.i	0.722792	+	0.722792i	0.969173	−	0.246381i	$-0.0792413\pi$
$499$	179976.	+	179976.i	0.722792	+	0.722792i	−0.246381	+	0.969173i	$0.579241\pi$
$500$	30931.0	−	115436.i	0.123724	−	0.461745i
$501$	−54258.8	−	14538.6i	−0.216170	−	0.0579225i
$502$	−17493.4	+	17493.4i	−0.0694172	+	0.0694172i
$503$	−149757.	−	259387.i	−0.591905	−	1.02521i	−0.993976	−	0.109601i	$-0.965043\pi$
$503$	−149757.	−	259387.i	−0.591905	−	1.02521i	0.402071	−	0.915609i	$-0.368291\pi$
$504$	−92641.5	−	53486.6i	−0.364707	−	0.210564i
$505$	4739.78	+	17689.1i	0.0185856	+	0.0693623i
$506$			76008.0i			0.296865i
$507$	1053.49	+	37779.1i	0.00409840	+	0.146973i
$508$	−49224.0			−0.190744
$509$	−2833.40	+	759.208i	−0.0109364	+	0.00293039i	−0.264283	−	0.964445i	$-0.585135\pi$
$509$	−2833.40	+	759.208i	−0.0109364	+	0.00293039i	0.253347	+	0.967376i	$0.418469\pi$
$510$	15530.1	−	26899.0i	0.0597084	−	0.103418i
$511$	210960.	−	121798.i	0.807902	−	0.466442i
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	4555.58	−	17001.6i	0.0173105	−	0.0646035i
$514$	−265226.	−	71067.2i	−1.00390	−	0.268994i
$515$	−380813.	+	380813.i	−1.43581	+	1.43581i
$516$	−5195.95	−	8999.65i	−0.0195149	−	0.0338007i
$517$	−231571.	−	133698.i	−0.866370	−	0.500199i
$518$	85835.0	+	320341.i	0.319893	+	1.19386i
$519$			57890.1i			0.214917i
$520$	27049.7	+	95600.1i	0.100036	+	0.353551i
$521$	311482.			1.14751			0.573757	−	0.819025i	$-0.305485\pi$
$521$	311482.			1.14751			0.573757	+	0.819025i	$0.305485\pi$
$522$	84218.2	−	22566.2i	0.309076	−	0.0828166i
$523$	176887.	−	306378.i	0.646685	−	1.12009i	−0.337224	−	0.941424i	$-0.609488\pi$
$523$	176887.	−	306378.i	0.646685	−	1.12009i	0.983910	−	0.178668i	$-0.0571786\pi$
$524$	−57276.7	+	33068.7i	−0.208600	+	0.120436i
$525$	2792.41	+	2792.41i	0.0101312	+	0.0101312i
$526$	58909.9	−	219855.i	0.212920	−	0.794629i
$527$	336839.	+	90255.9i	1.21284	+	0.324978i
$528$	−3683.12	+	3683.12i	−0.0132114	+	0.0132114i
$529$	−44466.9	−	77018.9i	−0.158901	−	0.275224i
$530$	217034.	+	125305.i	0.772639	+	0.446083i
$531$	41179.0	+	153682.i	0.146045	+	0.545047i
$532$		−	39613.3i		−	0.139964i
$533$	248516.	+	416912.i	0.874783	+	1.46754i
$534$	5531.09			0.0193967
$535$	334530.	−	89637.0i	1.16876	−	0.313170i
$536$	−39193.8	+	67885.6i	−0.136423	+	0.236291i
$537$	10578.7	−	6107.64i	0.0366848	−	0.0211800i
$538$	119616.	+	119616.i	0.413262	+	0.413262i
$539$	18428.9	−	68777.5i	0.0634339	−	0.236739i
$540$	42573.3	+	11407.5i	0.145999	+	0.0391203i
$541$	163897.	−	163897.i	0.559986	−	0.559986i	−0.369317	−	0.929303i	$-0.620408\pi$
$541$	163897.	−	163897.i	0.559986	−	0.559986i	0.929303	+	0.369317i	$0.120408\pi$
$542$	−80108.4	−	138752.i	−0.272696	−	0.472324i
$543$	20530.9	+	11853.5i	0.0696321	+	0.0402021i
$544$	−14964.9	−	55849.8i	−0.0505680	−	0.188722i
$545$			476526.i			1.60433i
$546$	36580.2	+	9257.13i	0.122705	+	0.0310521i
$547$	194880.			0.651316			0.325658	−	0.945488i	$-0.394414\pi$
$547$	194880.			0.651316			0.325658	+	0.945488i	$0.394414\pi$
$548$	90362.5	−	24212.6i	0.300903	−	0.0806268i
$549$	−195090.	+	337906.i	−0.647277	+	1.12112i
$550$	−7536.66	+	4351.29i	−0.0249146	+	0.0143844i
$551$	22830.4	+	22830.4i	0.0751986	+	0.0751986i
$552$	−3386.02	+	12636.8i	−0.0111125	+	0.0414724i
$553$	−648393.	−	173736.i	−2.12026	−	0.568121i
$554$	−45022.6	+	45022.6i	−0.146693	+	0.146693i
$555$	−33787.4	−	58521.5i	−0.109690	−	0.189989i
$556$	−41600.3	−	24018.0i	−0.134570	−	0.0776939i
$557$	−76006.1	−	283658.i	−0.244984	−	0.914293i	−0.973391	−	0.229149i	$-0.926406\pi$
$557$	−76006.1	−	283658.i	−0.244984	−	0.914293i	0.728407	−	0.685144i	$-0.240261\pi$
$558$			244718.i			0.785954i
$559$	−118932.	−	115662.i	−0.380606	−	0.370140i
$560$	99194.3			0.316308
$561$	25110.0	−	6728.21i	0.0797850	−	0.0213783i
$562$	103760.	−	179718.i	0.328518	−	0.569009i
$563$	127586.	−	73662.0i	0.402520	−	0.232395i	−0.285051	−	0.958512i	$-0.592010\pi$
$563$	127586.	−	73662.0i	0.402520	−	0.232395i	0.687571	+	0.726117i	$0.258677\pi$
$564$	−32544.1	−	32544.1i	−0.102309	−	0.102309i
$565$	−25719.4	+	95986.2i	−0.0805683	+	0.300685i
$566$	268526.	+	71951.2i	0.838210	+	0.224598i
$567$	−258939.	+	258939.i	−0.805438	+	0.805438i
$568$	−50817.1	−	88017.7i	−0.157512	−	0.272818i
$569$	−428143.	−	247188.i	−1.32240	−	0.763490i	−0.338292	−	0.941041i	$-0.609849\pi$
$569$	−428143.	−	247188.i	−1.32240	−	0.763490i	−0.984112	+	0.177551i	$0.943182\pi$
$570$	2089.07	+	7796.52i	0.00642989	+	0.0239967i
$571$		−	356539.i		−	1.09354i	−0.837283	−	0.546770i	$-0.815857\pi$
$571$		−	356539.i		−	1.09354i	0.837283	−	0.546770i	$-0.184143\pi$
$572$	−40568.9	+	72585.5i	−0.123994	+	0.221849i
$573$	−19245.1			−0.0586154
$574$	468073.	−	125420.i	1.42066	−	0.380665i
$575$	−10929.0	+	18929.6i	−0.0330556	+	0.0572540i
$576$	35139.4	−	20287.7i	0.105913	−	0.0611489i
$577$	212452.	+	212452.i	0.638129	+	0.638129i	0.950094	−	0.311965i	$-0.100987\pi$
$577$	212452.	+	212452.i	0.638129	+	0.638129i	−0.311965	+	0.950094i	$0.600987\pi$
$578$	−13545.6	+	50552.9i	−0.0405455	+	0.151318i
$579$	27708.0	+	7424.33i	0.0826509	+	0.0221462i
$580$	−57168.8	+	57168.8i	−0.169943	+	0.169943i
$581$	−227077.	−	393309.i	−0.672700	−	1.16515i
$582$	−6937.74	−	4005.51i	−0.0204820	−	0.0118253i
$583$	54286.5	+	202600.i	0.159718	+	0.596077i
$584$			92397.1i			0.270915i
$585$	347935.	−	4850.22i	1.01669	−	0.0141726i
$586$	167283.			0.487143
$587$	−128771.	+	34504.1i	−0.373716	+	0.100137i	−0.440788	−	0.897611i	$-0.645301\pi$
$587$	−128771.	+	34504.1i	−0.373716	+	0.100137i	0.0670721	+	0.997748i	$0.478634\pi$
$588$	6127.83	−	10613.7i	0.0177236	−	0.0306982i
$589$	−78480.5	+	45310.7i	−0.226220	+	0.130608i
$590$	−104322.	−	104322.i	−0.299690	−	0.299690i
$591$	−5094.30	+	19012.2i	−0.0145851	+	0.0544323i
$592$	−121507.	−	32557.7i	−0.346703	−	0.0928987i
$593$	−96795.0	+	96795.0i	−0.275260	+	0.275260i	−0.831214	−	0.555953i	$-0.812353\pi$
$593$	−96795.0	+	96795.0i	−0.275260	+	0.275260i	0.555953	+	0.831214i	$0.312353\pi$
$594$	18444.3	+	31946.4i	0.0522743	+	0.0905417i
$595$	−428736.	−	247531.i	−1.21103	−	0.699190i
$596$	−3714.27	−	13861.8i	−0.0104564	−	0.0390237i
$597$			34631.3i			0.0971674i
$598$	2911.15	+	208834.i	0.00814070	+	0.583980i
$599$	49396.8			0.137672			0.0688360	−	0.997628i	$-0.478071\pi$
$599$	49396.8			0.137672			0.0688360	+	0.997628i	$0.478071\pi$
$600$	−1446.86	+	387.685i	−0.00401905	+	0.00107690i
$601$	265122.	−	459204.i	0.734001	−	1.27133i	−0.221160	−	0.975238i	$-0.570984\pi$
$601$	265122.	−	459204.i	0.734001	−	1.27133i	0.955160	−	0.296089i	$-0.0956825\pi$
$602$	−143443.	+	82816.8i	−0.395809	+	0.228521i
$603$	194129.	+	194129.i	0.533895	+	0.533895i
$604$	−69242.4	+	258416.i	−0.189801	+	0.708347i
$605$	272499.	+	73015.8i	0.744481	+	0.199483i
$606$	−1865.43	+	1865.43i	−0.00507965	+	0.00507965i
$607$	15771.8	+	27317.5i	0.0428059	+	0.0741420i	0.886635	−	0.462471i	$-0.153037\pi$
$607$	15771.8	+	27317.5i	0.0428059	+	0.0741420i	−0.843829	+	0.536613i	$0.819704\pi$
$608$	13012.5	+	7512.76i	0.0352008	+	0.0203232i
$609$	7947.19	+	29659.3i	0.0214279	+	0.0799699i
$610$		−	361807.i		−	0.972337i
$611$	−641367.	−	358468.i	−1.71800	−	0.960213i
$612$	−202505.			−0.540671
$613$	−497808.	+	133387.i	−1.32477	+	0.354972i	−0.850764	−	0.525549i	$-0.823860\pi$
$613$	−497808.	+	133387.i	−1.32477	+	0.354972i	−0.474008	+	0.880520i	$0.657193\pi$
$614$	−50055.3	+	86698.4i	−0.132774	+	0.229972i
$615$	−85510.1	+	49369.3i	−0.226083	+	0.130529i
$616$	58704.3	+	58704.3i	0.154706	+	0.154706i
$617$	128998.	−	481427.i	0.338854	−	1.26462i	−0.560776	−	0.827967i	$-0.689497\pi$
$617$	128998.	−	481427.i	0.338854	−	1.26462i	0.899630	−	0.436652i	$-0.143836\pi$
$618$	−74938.0	−	20079.6i	−0.196212	−	0.0525748i
$619$	−447819.	+	447819.i	−1.16875	+	1.16875i	−0.186245	+	0.982503i	$0.559632\pi$
$619$	−447819.	+	447819.i	−1.16875	+	1.16875i	−0.982503	+	0.186245i	$0.940368\pi$
$620$	−113461.	−	196520.i	−0.295164	−	0.511239i
$621$	80238.8	+	46325.9i	0.208066	+	0.120127i
$622$	40797.3	+	152258.i	0.105451	+	0.393548i
$623$		−	88158.6i		−	0.227137i
$624$	−9978.39	+	10260.5i	−0.0256266	+	0.0263512i
$625$	419389.			1.07364
$626$	−138427.	+	37091.4i	−0.353242	+	0.0946509i
$627$	−3377.73	+	5850.40i	−0.00859192	+	0.0148816i
$628$	122450.	−	70696.7i	0.310485	−	0.179258i
$629$	443930.	+	443930.i	1.12205	+	1.12205i
$630$	89916.9	−	335575.i	0.226548	−	0.845489i
$631$	270359.	+	72442.6i	0.679021	+	0.181943i	0.581815	−	0.813321i	$-0.302343\pi$
$631$	270359.	+	72442.6i	0.679021	+	0.181943i	0.0972057	+	0.995264i	$0.469010\pi$
$632$	180040.	−	180040.i	0.450749	−	0.450749i
$633$	−55017.4	−	95292.9i	−0.137307	−	0.237823i
$634$	−114663.	−	66200.6i	−0.285262	−	0.164696i
$635$	−41375.6	−	154416.i	−0.102612	−	0.382952i
$636$			36101.9i			0.0892515i
$637$	47999.5	−	189674.i	0.118293	−	0.467442i
$638$	−67666.2			−0.166238
$639$	−343829.	+	92128.6i	−0.842055	+	0.225628i
$640$	−18812.5	+	32584.1i	−0.0459288	+	0.0795511i
$641$	−279670.	+	161467.i	−0.680658	+	0.392978i	−0.800103	−	0.599863i	$-0.795222\pi$
$641$	−279670.	+	161467.i	−0.680658	+	0.392978i	0.119445	+	0.992841i	$0.461889\pi$
$642$	35278.3	+	35278.3i	0.0855930	+	0.0855930i
$643$	−27065.0	+	101008.i	−0.0654615	+	0.244306i	−0.990902	−	0.134588i	$-0.957029\pi$
$643$	−27065.0	+	101008.i	−0.0654615	+	0.244306i	0.925440	+	0.378894i	$0.123695\pi$
$644$	201415.	+	53968.9i	0.485646	+	0.130128i
$645$	23864.4	−	23864.4i	0.0573629	−	0.0573629i
$646$	−37494.9	−	64943.0i	−0.0898477	−	0.155621i
$647$	186919.	+	107918.i	0.446523	+	0.257800i	0.706361	−	0.707852i	$-0.250336\pi$
$647$	186919.	+	107918.i	0.446523	+	0.257800i	−0.259837	+	0.965652i	$0.583669\pi$
$648$	−35949.9	−	134167.i	−0.0856146	−	0.319518i
$649$		−	123478.i		−	0.293157i
$650$	−20540.5	+	12243.9i	−0.0486165	+	0.0289797i
$651$	−86182.8			−0.203357
$652$	325895.	−	87323.4i	0.766625	−	0.205417i
$653$	372141.	−	644567.i	0.872732	−	1.51162i	0.0135725	−	0.999908i	$-0.495680\pi$
$653$	372141.	−	644567.i	0.872732	−	1.51162i	0.859159	−	0.511708i	$-0.170987\pi$
$654$	−59449.6	+	34323.2i	−0.138993	+	0.0802477i
$655$	−151881.	−	151881.i	−0.354014	−	0.354014i
$656$	−47572.4	+	177543.i	−0.110547	+	0.412568i
$657$	312580.	+	83755.5i	0.724153	+	0.194036i
$658$	−518712.	+	518712.i	−1.19805	+	1.19805i
$659$	301976.	+	523038.i	0.695347	+	1.20438i	0.970064	+	0.242851i	$0.0780825\pi$
$659$	301976.	+	523038.i	0.695347	+	1.20438i	−0.274717	+	0.961525i	$0.588584\pi$
$660$	−14649.8	−	8458.07i	−0.0336313	−	0.0194171i
$661$	125562.	+	468603.i	0.287379	+	1.07251i	0.947084	+	0.320987i	$0.104014\pi$
$661$	125562.	+	468603.i	0.287379	+	1.07251i	−0.659705	+	0.751524i	$0.729319\pi$
$662$		−	370155.i		−	0.844633i
$663$	68732.7	−	19447.6i	0.156364	−	0.0442425i
$664$	172263.			0.390711
$665$	124267.	−	33297.2i	0.281003	−	0.0752946i
$666$	−220285.	+	381545.i	−0.496635	+	0.860197i
$667$	−147186.	+	84977.6i	−0.330837	+	0.191009i
$668$	−240134.	−	240134.i	−0.538147	−	0.538147i
$669$	1021.18	−	3811.09i	0.00228165	−	0.00851524i
$670$	−245902.	−	65889.1i	−0.547787	−	0.146779i
$671$	214121.	−	214121.i	0.475570	−	0.475570i
$672$	7144.78	+	12375.1i	0.0158216	+	0.0274038i
$673$	319400.	+	184406.i	0.705188	+	0.407141i	0.809277	−	0.587427i	$-0.199859\pi$
$673$	319400.	+	184406.i	0.705188	+	0.407141i	−0.104089	+	0.994568i	$0.533193\pi$
$674$	−58213.0	−	217254.i	−0.128145	−	0.478242i
$675$			10608.2i			0.0232828i
$676$	−108684.	+	200984.i	−0.237833	+	0.439813i
$677$	−279249.			−0.609276			−0.304638	−	0.952468i	$-0.598535\pi$
$677$	−279249.			−0.609276			−0.304638	+	0.952468i	$0.598535\pi$
$678$	−13827.4	+	3705.04i	−0.0300802	+	0.00805998i
$679$	−63842.7	+	110579.i	−0.138475	+	0.239846i
$680$	162622.	−	93889.7i	0.351691	−	0.203049i
$681$	−8673.68	−	8673.68i	−0.0187029	−	0.0187029i
$682$	49155.4	−	183450.i	0.105682	−	0.394412i
$683$	481641.	+	129055.i	1.03248	+	0.276653i	0.734995	−	0.678073i	$-0.237185\pi$
$683$	481641.	+	129055.i	1.03248	+	0.276653i	0.297487	+	0.954726i	$0.403851\pi$
$684$	37211.1	−	37211.1i	0.0795354	−	0.0795354i
$685$	151910.	+	263115.i	0.323746	+	0.560744i
$686$	181675.	+	104890.i	0.386053	+	0.222888i
$687$	925.455	+	3453.85i	0.00196084	+	0.00731795i
$688$		−	62825.7i		−	0.132727i
$689$	156913.	+	554569.i	0.330537	+	1.16820i
$690$	−42487.8			−0.0892413
$691$	473771.	−	126946.i	0.992229	−	0.265867i	0.274043	−	0.961718i	$-0.411639\pi$
$691$	473771.	−	126946.i	0.992229	−	0.265867i	0.718187	+	0.695850i	$0.244972\pi$
$692$	−174992.	+	303094.i	−0.365431	+	0.632944i
$693$	251810.	−	145383.i	0.524333	−	0.302724i
$694$	−250567.	−	250567.i	−0.520242	−	0.520242i
$695$	40376.9	−	150689.i	0.0835917	−	0.311969i
$696$	−11249.9	−	3014.41i	−0.0232237	−	0.00622277i
$697$	648659.	−	648659.i	1.33521	−	1.33521i
$698$	214651.	+	371787.i	0.440578	+	0.763104i
$699$	73451.1	+	42407.0i	0.150329	+	0.0867927i
$700$	6179.20	+	23061.1i	0.0126106	+	0.0470634i
$701$			841179.i			1.71180i	0.517143	+	0.855899i	$0.326995\pi$
$701$			841179.i			1.71180i	−0.517143	+	0.855899i	$0.673005\pi$
$702$	51899.6	+	87067.0i	0.105315	+	0.176677i
$703$	−163148.			−0.330119
$704$	−30417.1	+	8150.22i	−0.0613722	+	0.0164446i
$705$	74735.7	−	129446.i	0.150366	−	0.260442i
$706$	56786.2	−	32785.5i	0.113929	−	0.0657768i
$707$	29732.6	+	29732.6i	0.0594832	+	0.0594832i
$708$	5500.72	−	20529.0i	0.0109737	−	0.0409544i
$709$	−501761.	−	134446.i	−0.998170	−	0.267459i	−0.277491	−	0.960728i	$-0.589503\pi$
$709$	−501761.	−	134446.i	−0.998170	−	0.267459i	−0.720679	+	0.693269i	$0.756170\pi$
$710$	233397.	−	233397.i	0.462997	−	0.462997i
$711$	−445874.	−	772276.i	−0.882009	−	1.52768i
$712$	28959.0	+	16719.5i	0.0571247	+	0.0329810i
$713$	−123462.	−	460767.i	−0.242859	−	0.906364i
$714$		−	71316.7i		−	0.139893i
$715$	−261801.	−	66252.4i	−0.512105	−	0.129595i
$716$	73849.3			0.144052
$717$	91089.6	−	24407.4i	0.177186	−	0.0474769i
$718$	−21860.7	+	37863.9i	−0.0424049	+	0.0734474i
$719$	−443568.	+	256094.i	−0.858030	+	0.495384i	−0.863352	−	0.504602i	$-0.831639\pi$
$719$	−443568.	+	256094.i	−0.858030	+	0.495384i	0.00532203	+	0.999986i	$0.498306\pi$
$720$	93179.2	+	93179.2i	0.179744	+	0.179744i
$721$	−320043.	+	1.19442e6i	−0.615656	+	2.29766i
$722$	−337220.	−	90357.9i	−0.646903	−	0.173337i
$723$	−35211.3	+	35211.3i	−0.0673605	+	0.0673605i
$724$	71662.3	+	124123.i	0.136714	+	0.236796i
$725$	−16852.1	−	9729.56i	−0.0320611	−	0.0185105i
$726$	10518.4	+	39255.1i	0.0199561	+	0.0744772i
$727$		−	291618.i		−	0.551755i	−0.961193	−	0.275877i	$-0.911032\pi$
$727$		−	291618.i		−	0.551755i	0.961193	−	0.275877i	$-0.0889684\pi$
$728$	163540.	+	159043.i	0.308575	+	0.300090i
$729$	−463746.			−0.872620
$730$	−289850.	+	77665.0i	−0.543910	+	0.145740i
$731$	−156776.	+	271544.i	−0.293390	+	0.508166i
$732$	45137.7	−	26060.3i	0.0842397	−	0.0486358i
$733$	−502473.	−	502473.i	−0.935201	−	0.935201i	0.0628232	−	0.998025i	$-0.479990\pi$
$733$	−502473.	−	502473.i	−0.935201	−	0.935201i	−0.998025	+	0.0628232i	$0.979990\pi$
$734$	97739.6	−	364769.i	0.181417	−	0.677058i
$735$	38446.0	+	10301.6i	0.0711666	+	0.0190690i
$736$	−55926.9	+	55926.9i	−0.103244	+	0.103244i
$737$	−106533.	−	184521.i	−0.196133	−	0.339712i
$738$	557504.	+	321875.i	1.02361	+	0.590983i
$739$	12485.2	+	46595.3i	0.0228615	+	0.0853205i	0.976414	−	0.215906i	$-0.0692706\pi$
$739$	12485.2	+	46595.3i	0.0228615	+	0.0853205i	−0.953553	+	0.301227i	$0.902604\pi$
$740$		−	408533.i		−	0.746043i
$741$	−9056.32	+	16203.5i	−0.0164936	+	0.0295102i
$742$	575418.			1.04514
$743$	−642723.	+	172217.i	−1.16425	+	0.311960i	−0.788662	−	0.614827i	$-0.789226\pi$
$743$	−642723.	+	172217.i	−1.16425	+	0.311960i	−0.375588	+	0.926787i	$0.622559\pi$
$744$	16344.8	−	28310.0i	0.0295280	−	0.0511439i
$745$	40362.5	−	23303.3i	0.0727220	−	0.0419861i
$746$	−510874.	−	510874.i	−0.917986	−	0.917986i
$747$	156152.	−	582767.i	0.279837	−	1.04437i
$748$	151806.	+	40676.4i	0.271323	+	0.0727008i
$749$	562292.	−	562292.i	1.00230	−	1.00230i
$750$	27955.7	+	48420.7i	0.0496991	+	0.0860813i
$751$	−364896.	−	210673.i	−0.646978	−	0.373533i	0.140319	−	0.990106i	$-0.455187\pi$
$751$	−364896.	−	210673.i	−0.646978	−	0.373533i	−0.787298	+	0.616573i	$0.788520\pi$
$752$	−72015.6	−	268766.i	−0.127348	−	0.475268i
$753$		−	11574.2i		−	0.0204128i
$754$	−185914.	+	2591.65i	−0.327017	+	0.00455862i
$755$	−868853.			−1.52424
$756$	97751.3	−	26192.4i	0.171033	−	0.0458281i
$757$	311246.	−	539093.i	0.543140	−	0.940746i	−0.455582	−	0.890194i	$-0.650569\pi$
$757$	311246.	−	539093.i	0.543140	−	0.940746i	0.998721	−	0.0505518i	$-0.0160980\pi$
$758$	−308097.	+	177880.i	−0.536228	+	0.309591i
$759$	−25144.7	−	25144.7i	−0.0436479	−	0.0436479i
$760$	−12629.8	+	47135.0i	−0.0218660	+	0.0816049i
$761$	−86684.9	−	23227.1i	−0.149684	−	0.0401076i	0.183199	−	0.983076i	$-0.441355\pi$
$761$	−86684.9	−	23227.1i	−0.149684	−	0.0401076i	−0.332883	+	0.942968i	$0.608021\pi$
$762$	16284.1	−	16284.1i	0.0280450	−	0.0280450i
$763$	547069.	+	947551.i	0.939708	+	1.62762i
$764$	−100761.	−	58174.6i	−0.172626	−	0.0996659i
$765$	−170217.	−	635258.i	−0.290857	−	1.08549i
$766$			665847.i			1.13479i
$767$	−4729.27	−	339258.i	−0.00803902	−	0.576686i
$768$	−5420.10			−0.00918935
$769$	−529026.	+	141752.i	−0.894590	+	0.239705i	−0.676692	−	0.736267i	$-0.736587\pi$
$769$	−529026.	+	141752.i	−0.894590	+	0.239705i	−0.217899	+	0.975971i	$0.569920\pi$
$770$	−134811.	+	233499.i	−0.227375	+	0.393826i
$771$	111252.	−	64231.1i	0.187153	−	0.108053i
$772$	122628.	+	122628.i	0.205757	+	0.205757i
$773$	−5527.01	+	20627.1i	−0.00924977	+	0.0345206i	−0.970396	−	0.241517i	$-0.922355\pi$
$773$	−5527.01	+	20627.1i	−0.00924977	+	0.0345206i	0.961147	+	0.276038i	$0.0890216\pi$
$774$	−212539.	−	56949.8i	−0.354779	−	0.0950627i
$775$	38619.9	−	38619.9i	0.0642996	−	0.0642996i
$776$	−24215.9	−	41943.1i	−0.0402139	−	0.0696526i
$777$	−134370.	−	77578.4i	−0.222566	−	0.128499i
$778$	−36754.0	−	137168.i	−0.0607220	−	0.226617i
$779$			238387.i			0.392833i
$780$	−40574.6	−	22677.6i	−0.0666907	−	0.0372742i
$781$	276254.			0.452904
$782$	381287.	−	102166.i	0.623504	−	0.167067i
$783$	−41241.7	+	71432.6i	−0.0672686	+	0.116513i
$784$	64166.7	−	37046.7i	0.104395	−	0.0602722i
$785$	324702.	+	324702.i	0.526920	+	0.526920i
$786$	8008.40	−	29887.8i	0.0129629	−	0.0483781i
$787$	80989.2	+	21701.0i	0.130761	+	0.0350373i	0.323606	−	0.946192i	$-0.395105\pi$
$787$	80989.2	+	21701.0i	0.130761	+	0.0350373i	−0.192845	+	0.981229i	$0.561771\pi$
$788$	−84142.5	+	84142.5i	−0.135507	+	0.135507i
$789$	53243.3	+	92220.1i	0.0855285	+	0.148140i
$790$	716118.	+	413451.i	1.14744	+	0.662475i
$791$	59053.7	+	220391.i	0.0943830	+	0.352242i
$792$			110289.i			0.175825i
$793$	580101.	−	596503.i	0.922481	−	0.948564i
$794$	807925.			1.28153
$795$	−113252.	+	30345.7i	−0.179188	+	0.0480134i
$796$	−104684.	+	181319.i	−0.165217	+	0.286165i
$797$	289042.	−	166878.i	0.455034	−	0.262714i	−0.254920	−	0.966962i	$-0.582049\pi$
$797$	289042.	−	166878.i	0.455034	−	0.262714i	0.709954	+	0.704248i	$0.248716\pi$
$798$	13104.7	+	13104.7i	0.0205789	+	0.0205789i
$799$	−359417.	+	1.34136e6i	−0.562996	+	2.10113i
$800$	−8747.19	−	2343.80i	−0.0136675	−	0.00366219i
$801$	82812.7	−	82812.7i	0.129072	−	0.129072i
$802$	174429.	+	302119.i	0.271187	+	0.469710i
$803$	−217499.	−	125573.i	−0.337308	−	0.194745i
$804$	−9491.74	−	35423.7i	−0.0146836	−	0.0548001i
$805$			677201.i			1.04502i
$806$	128029.	−	505917.i	0.197079	−	0.778770i
$807$	−79142.1			−0.121524
$808$	−15405.7	+	4127.94i	−0.0235971	+	0.00632281i
$809$	−347860.	+	602512.i	−0.531506	+	0.920595i	0.467818	+	0.883825i	$0.345040\pi$
$809$	−347860.	+	602512.i	−0.531506	+	0.920595i	−0.999324	+	0.0367700i	$0.988293\pi$
$810$	390664.	−	225550.i	0.595433	−	0.343773i
$811$	−151540.	−	151540.i	−0.230402	−	0.230402i	0.582459	−	0.812860i	$-0.302091\pi$
$811$	−151540.	−	151540.i	−0.230402	−	0.230402i	−0.812860	+	0.582459i	$0.802091\pi$
$812$	−48045.8	+	179310.i	−0.0728692	+	0.271951i
$813$	72402.6	+	19400.2i	0.109540	+	0.0293512i
$814$	241774.	−	241774.i	0.364890	−	0.364890i
$815$	547867.	+	948933.i	0.824821	+	1.42863i
$816$	23426.7	+	13525.4i	0.0351828	+	0.0203128i
$817$	−21089.1	−	78705.5i	−0.0315947	−	0.117913i
$818$			14732.4i			0.0220174i
$819$	686287.	−	409087.i	1.02315	−	0.609885i
$820$	−596938.			−0.887772
$821$	−314936.	+	84386.8i	−0.467235	+	0.125195i	−0.484753	−	0.874651i	$-0.661090\pi$
$821$	−314936.	+	84386.8i	−0.467235	+	0.125195i	0.0175175	+	0.999847i	$0.494424\pi$
$822$	−21883.5	+	37903.4i	−0.0323872	+	0.0560963i
$823$	33756.9	−	19489.6i	0.0498383	−	0.0287741i	−0.474874	−	0.880054i	$-0.657506\pi$
$823$	33756.9	−	19489.6i	0.0498383	−	0.0287741i	0.524712	+	0.851280i	$0.324173\pi$
$824$	−331655.	−	331655.i	−0.488463	−	0.488463i
$825$	1053.77	−	3932.73i	0.00154824	−	0.00577812i
$826$	−327206.	−	87674.5i	−0.479580	−	0.128503i
$827$	862141.	−	862141.i	1.26057	−	1.26057i	0.309754	−	0.950817i	$-0.399753\pi$
$827$	862141.	−	862141.i	1.26057	−	1.26057i	0.950817	−	0.309754i	$-0.100247\pi$
$828$	138505.	+	239897.i	0.202025	+	0.349917i
$829$	345372.	+	199401.i	0.502549	+	0.290147i	0.729766	−	0.683697i	$-0.239629\pi$
$829$	345372.	+	199401.i	0.502549	+	0.290147i	−0.227216	+	0.973844i	$0.572962\pi$
$830$	144797.	+	540389.i	0.210185	+	0.784423i
$831$		−	29788.4i		−	0.0431366i
$832$	−83259.4	+	23557.9i	−0.120278	+	0.0340322i
$833$	−369787.			−0.532920
$834$	21707.6	−	5816.54i	0.0312090	−	0.00836244i
$835$	551454.	−	955147.i	0.790927	−	1.36993i
$836$	−35369.4	+	20420.6i	−0.0506076	+	0.0292183i
$837$	−163702.	−	163702.i	−0.233670	−	0.233670i
$838$	−16337.8	+	60973.6i	−0.0232652	+	0.0868268i
$839$	649448.	+	174019.i	0.922616	+	0.247214i	0.688703	−	0.725044i	$-0.258180\pi$
$839$	649448.	+	174019.i	0.922616	+	0.247214i	0.233913	+	0.972258i	$0.424847\pi$
$840$	−32815.1	+	32815.1i	−0.0465067	+	0.0465067i
$841$	277989.	+	481491.i	0.393039	+	0.680764i
$842$	−87545.0	−	50544.1i	−0.123483	−	0.0712929i
$843$	25128.1	+	93779.5i	0.0353594	+	0.131963i
$844$		−	665231.i		−	0.933872i
$845$	−721841.	−	172003.i	−1.01095	−	0.240892i
$846$	−974516.			−1.36160
$847$	625677.	−	167650.i	0.872134	−	0.233688i
$848$	−109130.	+	189018.i	−0.151758	+	0.262852i
$849$	−112635.	+	65030.1i	−0.156264	+	0.0902192i
$850$	31958.2	+	31958.2i	0.0442328	+	0.0442328i
$851$	222272.	−	829530.i	0.306920	−	1.14544i
$852$	45928.9	+	12306.6i	0.0632713	+	0.0169535i
$853$	−518767.	+	518767.i	−0.712975	+	0.712975i	−0.967156	−	0.254182i	$-0.918194\pi$
$853$	−518767.	+	518767.i	−0.712975	+	0.712975i	0.254182	+	0.967156i	$0.418194\pi$
$854$	−415367.	−	719437.i	−0.569530	−	0.986455i
$855$	148009.	+	85453.2i	0.202468	+	0.116895i
$856$	78066.0	+	291346.i	0.106540	+	0.397614i
$857$		−	299228.i		−	0.407418i	−0.979031	−	0.203709i	$-0.934700\pi$
$857$		−	299228.i		−	0.407418i	0.979031	−	0.203709i	$-0.0652997\pi$
$858$	−10591.6	−	37433.4i	−0.0143876	−	0.0508492i
$859$	−739565.			−1.00228			−0.501141	−	0.865366i	$-0.667086\pi$
$859$	−739565.			−1.00228			−0.501141	+	0.865366i	$0.667086\pi$
$860$	197084.	−	52808.5i	0.266474	−	0.0714014i
$861$	−113356.	+	196338.i	−0.152910	+	0.264848i
$862$	−501017.	+	289262.i	−0.674276	+	0.389294i
$863$	271930.	+	271930.i	0.365119	+	0.365119i	0.865694	−	0.500574i	$-0.166878\pi$
$863$	271930.	+	271930.i	0.365119	+	0.365119i	−0.500574	+	0.865694i	$0.666878\pi$
$864$	−9934.91	+	37077.6i	−0.0133087	+	0.0496688i
$865$	−1.09790e6	−	294180.i	−1.46733	−	0.393171i
$866$	11396.0	−	11396.0i	0.0151955	−	0.0151955i
$867$	−12242.6	−	21204.9i	−0.0162868	−	0.0282096i
$868$	−451225.	−	260515.i	−0.598900	−	0.345775i
$869$	179122.	+	668491.i	0.237197	+	0.885230i
$870$		−	37824.8i		−	0.0499733i
$871$	−299770.	−	502895.i	−0.395141	−	0.662890i
$872$	−415012.			−0.545793
$873$	−163845.	+	43902.0i	−0.214983	+	0.0576045i
$874$	−51289.7	+	88836.4i	−0.0671441	+	0.116297i
$875$	771765.	−	445579.i	1.00802	−	0.581980i
$876$	−30566.5	−	30566.5i	−0.0398325	−	0.0398325i
$877$	−183486.	+	684780.i	−0.238564	+	0.890332i	0.737946	+	0.674859i	$0.235796\pi$
$877$	−183486.	+	684780.i	−0.238564	+	0.890332i	−0.976510	+	0.215472i	$0.930871\pi$
$878$	−251698.	−	67442.3i	−0.326506	−	0.0874869i
$879$	−55340.0	+	55340.0i	−0.0716244	+	0.0716244i
$880$	−51134.5	−	88567.5i	−0.0660311	−	0.114369i
$881$	183045.	+	105681.i	0.235834	+	0.136159i	0.613261	−	0.789881i	$-0.289858\pi$
$881$	183045.	+	105681.i	0.235834	+	0.136159i	−0.377426	+	0.926040i	$0.623191\pi$
$882$	−67163.6	−	250658.i	−0.0863370	−	0.322214i
$883$		−	1.18538e6i		−	1.52033i	−0.649730	−	0.760165i	$-0.725118\pi$
$883$		−	1.18538e6i		−	1.52033i	0.649730	−	0.760165i	$-0.274882\pi$
$884$	418649.	+	105945.i	0.535729	+	0.135574i
$885$	69023.0			0.0881267
$886$	872283.	−	233727.i	1.11119	−	0.297744i
$887$	−612022.	+	1.06005e6i	−0.777892	+	1.34735i	0.155262	+	0.987873i	$0.450378\pi$
$887$	−612022.	+	1.06005e6i	−0.777892	+	1.34735i	−0.933154	+	0.359476i	$0.882955\pi$
$888$	50967.1	−	29425.9i	0.0646345	−	0.0373167i
$889$	−259548.	−	259548.i	−0.328409	−	0.328409i
$890$	−28107.4	+	104898.i	−0.0354846	+	0.132430i
$891$	364682.	+	97716.2i	0.459366	+	0.123087i
$892$	16866.8	−	16866.8i	0.0211984	−	0.0211984i
$893$	−180437.	−	312525.i	−0.226267	−	0.391906i
$894$	5814.47	+	3356.99i	0.00727504	+	0.00420025i
$895$	62074.4	+	231665.i	0.0774937	+	0.289211i
$896$			86389.5i			0.107608i
$897$	−70048.8	−	68122.6i	−0.0870594	−	0.0846655i
$898$	−78269.7			−0.0970601
$899$	410198.	−	109912.i	0.507545	−	0.135996i
$900$	−15858.2	+	27467.2i	−0.0195780	+	0.0339101i
$901$	943356.	−	544647.i	1.16205	−	0.670912i
$902$	−353275.	−	353275.i	−0.434209	−	0.434209i
$903$	20056.1	−	74850.5i	0.0245964	−	0.0917951i
$904$	−83595.6	−	22399.4i	−0.102293	−	0.0274094i
$905$	−329137.	+	329137.i	−0.401864	+	0.401864i
$906$	−62581.9	−	108395.i	−0.0762416	−	0.132054i
$907$	410985.	+	237282.i	0.499587	+	0.288437i	0.728543	−	0.685000i	$-0.240198\pi$
$907$	410985.	+	237282.i	0.499587	+	0.288437i	−0.228956	+	0.973437i	$0.573531\pi$
$908$	−19193.6	−	71631.6i	−0.0232801	−	0.0868826i
$909$			55859.3i			0.0676033i
$910$	−361453.	+	646708.i	−0.436484	+	0.780954i
$911$	−303437.			−0.365621			−0.182811	−	0.983148i	$-0.558520\pi$
$911$	−303437.			−0.365621			−0.182811	+	0.983148i	$0.558520\pi$
$912$	−6790.09	+	1819.40i	−0.00816368	+	0.00218745i
$913$	−234116.	+	405500.i	−0.280859	+	0.486463i
$914$	98898.4	−	57099.0i	0.118385	−	0.0683497i
$915$	119692.	+	119692.i	0.142962	+	0.142962i
$916$	−5594.97	+	20880.7i	−0.00666817	+	0.0248860i
$917$	−476373.	−	127644.i	−0.566511	−	0.151796i
$918$	135464.	−	135464.i	0.160746	−	0.160746i
$919$	−172152.	−	298175.i	−0.203836	−	0.353054i	0.745926	−	0.666029i	$-0.232007\pi$
$919$	−172152.	−	298175.i	−0.203836	−	0.353054i	−0.949761	+	0.312976i	$0.898674\pi$
$920$	−222452.	−	128433.i	−0.262822	−	0.151740i
$921$	−12122.1	−	45240.4i	−0.0142909	−	0.0533344i
$922$		−	49186.1i		−	0.0578602i
$923$	759013.	−	10580.6i	0.890934	−	0.0124196i
$924$	−38840.7			−0.0454928
$925$	94977.5	−	25449.1i	0.111004	−	0.0297433i
$926$	109346.	−	189393.i	0.127521	−	0.220873i
$927$	−1.42262e6	+	821353.i	−1.65551	+	0.955807i
$928$	−49789.0	−	49789.0i	−0.0578146	−	0.0578146i
$929$	221763.	−	827629.i	0.256955	−	0.958969i	−0.710038	−	0.704164i	$-0.751322\pi$
$929$	221763.	−	827629.i	0.256955	−	0.958969i	0.966993	−	0.254805i	$-0.0820112\pi$
$930$	102547.	+	27477.4i	0.118565	+	0.0317695i
$931$	67949.9	−	67949.9i	0.0783952	−	0.0783952i
$932$	256378.	+	444059.i	0.295154	+	0.511221i
$933$	−63865.8	−	36872.9i	−0.0733677	−	0.0423589i
$934$	86637.9	+	323337.i	0.0993149	+	0.370648i
$935$			510407.i			0.583839i
$936$	4224.12	+	303021.i	0.00482153	+	0.345877i
$937$	875504.			0.997193			0.498596	−	0.866834i	$-0.333849\pi$
$937$	875504.			0.997193			0.498596	+	0.866834i	$0.333849\pi$
$938$	−564608.	+	151286.i	−0.641714	+	0.171947i
$939$	33523.5	−	58064.4i	0.0380206	−	0.0658535i
$940$	782585.	−	451825.i	0.885678	−	0.511346i
$941$	−497941.	−	497941.i	−0.562339	−	0.562339i	0.367632	−	0.929971i	$-0.380169\pi$
$941$	−497941.	−	497941.i	−0.562339	−	0.562339i	−0.929971	+	0.367632i	$0.880169\pi$
$942$	−17120.9	+	63896.2i	−0.0192942	+	0.0720068i
$943$	−1.21209e6	−	324778.i	−1.36305	−	0.365227i
$944$	90855.4	−	90855.4i	0.101955	−	0.101955i
$945$	164331.	+	284630.i	0.184016	+	0.318725i
$946$	147889.	+	85383.8i	0.165255	+	0.0954099i
$947$	202999.	+	757602.i	0.226357	+	0.844776i	0.981856	+	0.189626i	$0.0607276\pi$
$947$	202999.	+	757602.i	0.226357	+	0.844776i	−0.755499	+	0.655149i	$0.772606\pi$
$948$			119120.i			0.132547i
$949$	−602393.	−	336685.i	−0.668879	−	0.373844i
$950$	−11744.9			−0.0130137
$951$	59832.6	−	16032.1i	0.0661572	−	0.0177268i
$952$	215578.	−	373391.i	0.237865	−	0.411994i
$953$	1.07035e6	−	617967.i	1.17853	−	0.680424i	0.222855	−	0.974852i	$-0.428462\pi$
$953$	1.07035e6	−	617967.i	1.17853	−	0.680424i	0.955674	+	0.294428i	$0.0951290\pi$
$954$	540525.	+	540525.i	0.593908	+	0.593908i
$955$	97798.0	−	364987.i	0.107232	−	0.400194i
$956$	550695.	+	147558.i	0.602553	+	0.161454i
$957$	22385.1	−	22385.1i	0.0244419	−	0.0244419i
$958$	251695.	+	435948.i	0.274248	+	0.475011i
$959$	604131.	+	348795.i	0.656892	+	0.379257i
$960$	−4555.90	−	17002.8i	−0.00494347	−	0.0184493i
$961$			268416.i			0.290644i
$962$	655020.	−	673541.i	0.707790	−	0.727803i
$963$	1.05639e6			1.13913
$964$	−290793.	+	77917.6i	−0.312917	+	0.0838459i
$965$	−281607.	+	487758.i	−0.302405	+	0.523781i
$966$	−84485.2	+	48777.5i	−0.0905370	+	0.0522716i
$967$	761124.	+	761124.i	0.813959	+	0.813959i	0.985225	−	0.171266i	$-0.0547856\pi$
$967$	761124.	+	761124.i	0.813959	+	0.813959i	−0.171266	+	0.985225i	$0.554786\pi$
$968$	−63590.4	+	237323.i	−0.0678642	+	0.253273i
$969$	33888.2	+	9080.31i	0.0360911	+	0.00967059i
$970$	111221.	−	111221.i	0.118207	−	0.118207i
$971$	−531866.	−	921219.i	−0.564110	−	0.977067i	−0.997132	−	0.0756836i	$-0.975886\pi$
$971$	−531866.	−	921219.i	−0.564110	−	0.977067i	0.433022	−	0.901383i	$-0.357447\pi$
$972$	175278.	+	101197.i	0.185522	+	0.107111i
$973$	−92708.3	−	345992.i	−0.0979249	−	0.365461i
$974$			142450.i			0.150157i
$975$	2744.64	−	10845.6i	0.00288719	−	0.0114089i
$976$	315102.			0.330789
$977$	−871138.	+	233421.i	−0.912636	+	0.244540i	−0.684435	−	0.729074i	$-0.739951\pi$
$977$	−871138.	+	233421.i	−0.912636	+	0.244540i	−0.228201	+	0.973614i	$0.573284\pi$
$978$	−78923.6	+	136700.i	−0.0825143	+	0.142919i
$979$	−78714.1	+	45445.6i	−0.0821272	+	0.0474162i
$980$	170151.	+	170151.i	0.177167	+	0.177167i
$981$	−376197.	+	1.40399e6i	−0.390911	+	1.45890i
$982$	−203899.	−	54634.5i	−0.211442	−	0.0566557i
$983$	−10817.2	+	10817.2i	−0.0111946	+	0.0111946i	−0.712682	−	0.701487i	$-0.752520\pi$
$983$	−10817.2	+	10817.2i	−0.0111946	+	0.0111946i	0.701487	+	0.712682i	$0.252520\pi$
$984$	−42996.3	−	74471.8i	−0.0444060	−	0.0769134i
$985$	−334681.	−	193228.i	−0.344952	−	0.199158i
$986$	90953.0	+	339441.i	0.0935542	+	0.349149i
$987$		−	343197.i		−	0.352298i
$988$	−96396.2	+	57460.6i	−0.0987520	+	0.0588649i
$989$	428912.			0.438506
$990$	−345976.	+	92704.0i	−0.353001	+	0.0945863i
$991$	465381.	−	806064.i	0.473873	−	0.820772i	−0.525680	−	0.850682i	$-0.676189\pi$
$991$	465381.	−	806064.i	0.473873	−	0.820772i	0.999553	+	0.0299109i	$0.00952236\pi$
$992$	171152.	−	98814.7i	0.173924	−	0.100415i
$993$	122454.	+	122454.i	0.124186	+	0.124186i
$994$	196152.	−	732048.i	0.198527	−	0.740912i
$995$	−656789.	−	175986.i	−0.663407	−	0.177759i
$996$	−56987.5	+	56987.5i	−0.0574462	+	0.0574462i
$997$	−261191.	−	452396.i	−0.262765	−	0.455123i	0.704210	−	0.709991i	$-0.251301\pi$
$997$	−261191.	−	452396.i	−0.262765	−	0.455123i	−0.966976	+	0.254868i	$0.917968\pi$
$998$	−623455.	−	359952.i	−0.625957	−	0.361396i
$999$	−107874.	−	402590.i	−0.108090	−	0.403397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.5.f.a.7.2	✓	8
3.2	odd	2		234.5.bb.c.163.1		8
13.2	odd	12	inner	26.5.f.a.15.2	yes	8
13.4	even	6		338.5.d.e.99.2		8
13.6	odd	12		338.5.d.h.239.2		8
13.7	odd	12		338.5.d.e.239.2		8
13.9	even	3		338.5.d.h.99.2		8
39.2	even	12		234.5.bb.c.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.5.f.a.7.2	✓	8	1.1	even	1	trivial
26.5.f.a.15.2	yes	8	13.2	odd	12	inner
234.5.bb.c.145.1		8	39.2	even	12
234.5.bb.c.163.1		8	3.2	odd	2
338.5.d.e.99.2		8	13.4	even	6
338.5.d.e.239.2		8	13.7	odd	12
338.5.d.h.99.2		8	13.9	even	3
338.5.d.h.239.2		8	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73205 + 0.732051i) q^{2} +(0.661634 - 1.14598i) q^{3} +(6.92820 - 4.00000i) q^{4} +(18.3715 + 18.3715i) q^{5} +(-0.968699 + 3.61523i) q^{6} +(57.6222 + 15.4398i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(39.6245 + 68.6316i) q^{9} +O(q^{10})\)	\(q+(-2.73205 + 0.732051i) q^{2} +(0.661634 - 1.14598i) q^{3} +(6.92820 - 4.00000i) q^{4} +(18.3715 + 18.3715i) q^{5} +(-0.968699 + 3.61523i) q^{6} +(57.6222 + 15.4398i) q^{7} +(-16.0000 + 16.0000i) q^{8} +(39.6245 + 68.6316i) q^{9} +(-63.6409 - 36.7431i) q^{10} +(-15.9184 - 59.4083i) q^{11} -10.5861i q^{12} +(-46.0115 - 162.616i) q^{13} -168.730 q^{14} +(33.2087 - 8.89824i) q^{15} +(32.0000 - 55.4256i) q^{16} +(-276.620 + 159.706i) q^{17} +(-158.498 - 158.498i) q^{18} +(21.4833 - 80.1767i) q^{19} +(200.768 + 53.7956i) q^{20} +(55.8186 - 55.8186i) q^{21} +(86.9798 + 150.653i) q^{22} +(378.392 + 218.465i) q^{23} +(7.74959 + 28.9219i) q^{24} +50.0265i q^{25} +(244.749 + 410.592i) q^{26} +212.052 q^{27} +(460.978 - 123.519i) q^{28} +(-194.488 + 336.864i) q^{29} +(-84.2139 + 48.6209i) q^{30} +(-771.990 - 771.990i) q^{31} +(-46.8513 + 174.851i) q^{32} +(-78.6130 - 21.0643i) q^{33} +(638.826 - 638.826i) q^{34} +(774.955 + 1342.26i) q^{35} +(549.053 + 316.996i) q^{36} +(-508.713 - 1898.54i) q^{37} +234.774i q^{38} +(-216.798 - 54.8637i) q^{39} -587.889 q^{40} +(-2774.10 + 743.319i) q^{41} +(-111.637 + 193.361i) q^{42} +(850.135 - 490.826i) q^{43} +(-347.919 - 347.919i) q^{44} +(-532.906 + 1988.83i) q^{45} +(-1193.71 - 319.854i) q^{46} +(3074.22 - 3074.22i) q^{47} +(-42.3445 - 73.3429i) q^{48} +(1002.61 + 578.854i) q^{49} +(-36.6219 - 136.675i) q^{50} +422.669i q^{51} +(-969.241 - 942.590i) q^{52} -3410.30 q^{53} +(-579.337 + 155.233i) q^{54} +(798.976 - 1383.87i) q^{55} +(-1168.99 + 674.918i) q^{56} +(-77.6671 - 77.6671i) q^{57} +(284.751 - 1062.70i) q^{58} +(1939.23 + 519.616i) q^{59} +(194.484 - 194.484i) q^{60} +(2461.73 + 4263.85i) q^{61} +(2674.25 + 1543.98i) q^{62} +(1223.59 + 4566.50i) q^{63} -512.000i q^{64} +(2142.20 - 3832.81i) q^{65} +230.195 q^{66} +(3346.23 - 896.620i) q^{67} +(-1277.65 + 2212.96i) q^{68} +(500.713 - 289.087i) q^{69} +(-3099.82 - 3099.82i) q^{70} +(-1162.52 + 4338.59i) q^{71} +(-1732.10 - 464.114i) q^{72} +(2887.41 - 2887.41i) q^{73} +(2779.66 + 4814.52i) q^{74} +(57.3295 + 33.0992i) q^{75} +(-171.866 - 641.413i) q^{76} -3669.02i q^{77} +(632.466 - 8.81658i) q^{78} -11252.5 q^{79} +(1606.14 - 430.365i) q^{80} +(-3069.28 + 5316.15i) q^{81} +(7034.85 - 4061.57i) q^{82} +(-5383.22 - 5383.22i) q^{83} +(163.448 - 609.997i) q^{84} +(-8015.98 - 2147.88i) q^{85} +(-1963.30 + 1963.30i) q^{86} +(257.360 + 445.760i) q^{87} +(1205.23 + 695.838i) q^{88} +(-382.485 - 1427.45i) q^{89} -5823.70i q^{90} +(-140.525 - 10080.7i) q^{91} +3495.43 q^{92} +(-1395.46 + 373.913i) q^{93} +(-6148.45 + 10649.4i) q^{94} +(1867.65 - 1078.29i) q^{95} +(169.378 + 169.378i) q^{96} +(-553.976 + 2067.47i) q^{97} +(-3162.92 - 847.502i) q^{98} +(3446.53 - 3446.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9	\( 8 q - 8 q^{2} + 30 q^{5} + 36 q^{6} - 92 q^{7} - 128 q^{8} + 90 q^{9} + 132 q^{10} + 192 q^{11} - 78 q^{13} - 344 q^{14} + 132 q^{15} + 256 q^{16} - 870 q^{17} - 360 q^{18} - 218 q^{19} - 144 q^{20} + 1914 q^{21} + 948 q^{22} + 264 q^{23} - 288 q^{24} - 520 q^{26} - 2268 q^{27} - 736 q^{28} - 252 q^{29} + 1728 q^{30} - 3376 q^{31} + 512 q^{32} + 1698 q^{33} + 1080 q^{34} + 6474 q^{35} + 2016 q^{36} + 2552 q^{37} - 5928 q^{39} - 960 q^{40} - 8472 q^{41} - 3828 q^{42} + 7290 q^{43} - 3792 q^{44} - 6282 q^{45} - 540 q^{46} + 4848 q^{47} + 9678 q^{49} + 2524 q^{50} - 832 q^{52} - 6840 q^{53} + 2268 q^{54} + 294 q^{55} + 4320 q^{56} - 4434 q^{57} - 7008 q^{58} - 4632 q^{59} + 9024 q^{60} + 8670 q^{61} + 3936 q^{62} + 8100 q^{63} - 2808 q^{65} - 984 q^{66} - 12446 q^{67} - 2160 q^{68} + 19206 q^{69} - 25896 q^{70} - 4554 q^{71} - 5472 q^{72} + 19294 q^{73} + 10112 q^{74} - 25992 q^{75} + 1744 q^{76} - 8580 q^{78} - 11328 q^{79} - 1152 q^{80} + 6048 q^{81} + 42672 q^{82} + 10344 q^{83} - 8592 q^{84} - 23178 q^{85} + 13536 q^{86} + 18372 q^{87} + 1440 q^{88} - 2538 q^{89} + 1456 q^{91} + 96 q^{92} - 162 q^{93} - 9696 q^{94} + 26568 q^{95} - 64282 q^{97} - 31676 q^{98} + 9504 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 30 * q^5 + 36 * q^6 - 92 * q^7 - 128 * q^8 + 90 * q^9 + 132 * q^10 + 192 * q^11 - 78 * q^13 - 344 * q^14 + 132 * q^15 + 256 * q^16 - 870 * q^17 - 360 * q^18 - 218 * q^19 - 144 * q^20 + 1914 * q^21 + 948 * q^22 + 264 * q^23 - 288 * q^24 - 520 * q^26 - 2268 * q^27 - 736 * q^28 - 252 * q^29 + 1728 * q^30 - 3376 * q^31 + 512 * q^32 + 1698 * q^33 + 1080 * q^34 + 6474 * q^35 + 2016 * q^36 + 2552 * q^37 - 5928 * q^39 - 960 * q^40 - 8472 * q^41 - 3828 * q^42 + 7290 * q^43 - 3792 * q^44 - 6282 * q^45 - 540 * q^46 + 4848 * q^47 + 9678 * q^49 + 2524 * q^50 - 832 * q^52 - 6840 * q^53 + 2268 * q^54 + 294 * q^55 + 4320 * q^56 - 4434 * q^57 - 7008 * q^58 - 4632 * q^59 + 9024 * q^60 + 8670 * q^61 + 3936 * q^62 + 8100 * q^63 - 2808 * q^65 - 984 * q^66 - 12446 * q^67 - 2160 * q^68 + 19206 * q^69 - 25896 * q^70 - 4554 * q^71 - 5472 * q^72 + 19294 * q^73 + 10112 * q^74 - 25992 * q^75 + 1744 * q^76 - 8580 * q^78 - 11328 * q^79 - 1152 * q^80 + 6048 * q^81 + 42672 * q^82 + 10344 * q^83 - 8592 * q^84 - 23178 * q^85 + 13536 * q^86 + 18372 * q^87 + 1440 * q^88 - 2538 * q^89 + 1456 * q^91 + 96 * q^92 - 162 * q^93 - 9696 * q^94 + 26568 * q^95 - 64282 * q^97 - 31676 * q^98 + 9504 * q^99

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