LMFDB - Embedded newform 19.5.d.a.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,5,Mod(8,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("19.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	19.d (of order $6$, degree $2$, 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:	$1.96402929859$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 $ x^10 + 109x^8 + 4107x^6 + 61507x^4 + 300520x^2 + 108300
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			8.4
Root			$-2.91518i$ of defining polynomial
Character	$\chi$	$=$	19.8
Dual form			19.5.d.a.12.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52462 + 1.45759i) q^{2} +(8.18489 + 4.72555i) q^{3} +(-3.75086 - 6.49668i) q^{4} +(-7.00036 + 12.1250i) q^{5} +(13.7758 + 23.8604i) q^{6} +19.8223 q^{7} -68.5118i q^{8} +(4.16163 + 7.20815i) q^{9} +O(q^{10})$	\(q+(2.52462 + 1.45759i) q^{2} +(8.18489 + 4.72555i) q^{3} +(-3.75086 - 6.49668i) q^{4} +(-7.00036 + 12.1250i) q^{5} +(13.7758 + 23.8604i) q^{6} +19.8223 q^{7} -68.5118i q^{8} +(4.16163 + 7.20815i) q^{9} +(-35.3465 + 20.4073i) q^{10} -177.809 q^{11} -70.8995i q^{12} +(83.2716 - 48.0769i) q^{13} +(50.0437 + 28.8927i) q^{14} +(-114.594 + 66.1610i) q^{15} +(39.8484 - 69.0195i) q^{16} +(26.8637 - 46.5293i) q^{17} +24.2638i q^{18} +(161.512 + 322.854i) q^{19} +105.029 q^{20} +(162.243 + 93.6710i) q^{21} +(-448.901 - 259.173i) q^{22} +(372.053 + 644.415i) q^{23} +(323.756 - 560.761i) q^{24} +(214.490 + 371.508i) q^{25} +280.306 q^{26} -686.875i q^{27} +(-74.3505 - 128.779i) q^{28} +(-738.578 + 426.418i) q^{29} -385.743 q^{30} -317.572i q^{31} +(-748.123 + 431.929i) q^{32} +(-1455.35 - 840.247i) q^{33} +(135.641 - 78.3125i) q^{34} +(-138.763 + 240.344i) q^{35} +(31.2194 - 54.0735i) q^{36} -1697.87i q^{37} +(-62.8314 + 1050.50i) q^{38} +908.759 q^{39} +(830.703 + 479.607i) q^{40} +(1748.55 + 1009.53i) q^{41} +(273.068 + 472.968i) q^{42} +(938.059 - 1624.77i) q^{43} +(666.938 + 1155.17i) q^{44} -116.532 q^{45} +2169.20i q^{46} +(-665.166 - 1152.10i) q^{47} +(652.310 - 376.611i) q^{48} -2008.08 q^{49} +1250.55i q^{50} +(439.753 - 253.891i) q^{51} +(-624.680 - 360.659i) q^{52} +(-2043.31 + 1179.71i) q^{53} +(1001.18 - 1734.10i) q^{54} +(1244.73 - 2155.93i) q^{55} -1358.06i q^{56} +(-203.701 + 3405.76i) q^{57} -2486.17 q^{58} +(2574.85 + 1486.59i) q^{59} +(859.654 + 496.321i) q^{60} +(-2099.98 - 3637.27i) q^{61} +(462.890 - 801.750i) q^{62} +(82.4929 + 142.882i) q^{63} -3793.45 q^{64} +1346.22i q^{65} +(-2449.47 - 4242.61i) q^{66} +(7668.40 - 4427.35i) q^{67} -403.047 q^{68} +7032.62i q^{69} +(-700.647 + 404.519i) q^{70} +(-6430.03 - 3712.38i) q^{71} +(493.843 - 285.121i) q^{72} +(-4260.31 + 7379.07i) q^{73} +(2474.79 - 4286.47i) q^{74} +4054.33i q^{75} +(1491.67 - 2260.27i) q^{76} -3524.58 q^{77} +(2294.27 + 1324.60i) q^{78} +(3800.18 + 2194.04i) q^{79} +(557.906 + 966.322i) q^{80} +(3582.95 - 6205.86i) q^{81} +(2942.95 + 5097.34i) q^{82} +10166.0 q^{83} -1405.39i q^{84} +(376.111 + 651.443i) q^{85} +(4736.49 - 2734.61i) q^{86} -8060.24 q^{87} +12182.0i q^{88} +(-3232.45 + 1866.26i) q^{89} +(-294.198 - 169.855i) q^{90} +(1650.63 - 952.993i) q^{91} +(2791.04 - 4834.22i) q^{92} +(1500.70 - 2599.29i) q^{93} -3878.16i q^{94} +(-5045.24 - 301.760i) q^{95} -8164.40 q^{96} +(845.233 + 487.996i) q^{97} +(-5069.64 - 2926.96i) q^{98} +(-739.977 - 1281.68i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9 + 144 * q^10 + 50 * q^11 - 624 * q^13 - 474 * q^14 + 504 * q^15 + 285 * q^16 - 292 * q^17 + 305 * q^19 - 652 * q^20 + 1158 * q^21 + 1629 * q^22 + 98 * q^23 + 505 * q^24 - 681 * q^25 + 1524 * q^26 - 1472 * q^28 + 2598 * q^29 - 6656 * q^30 - 2745 * q^32 - 3441 * q^33 + 486 * q^34 + 694 * q^35 + 3402 * q^36 - 342 * q^38 - 5552 * q^39 + 8784 * q^40 - 1407 * q^41 + 292 * q^42 + 5424 * q^43 + 4151 * q^44 + 9572 * q^45 - 2416 * q^47 + 11481 * q^48 - 17826 * q^49 - 3342 * q^51 - 19962 * q^52 + 1122 * q^53 - 1039 * q^54 + 11424 * q^55 - 7906 * q^57 - 20236 * q^58 + 15387 * q^59 + 8886 * q^60 + 860 * q^61 + 21636 * q^62 + 5318 * q^63 + 19710 * q^64 - 13921 * q^66 + 14763 * q^67 - 48844 * q^68 - 20334 * q^70 - 27264 * q^71 + 354 * q^72 + 1561 * q^73 + 17094 * q^74 + 1955 * q^76 - 18392 * q^77 + 40266 * q^78 + 24750 * q^79 - 2002 * q^80 + 14311 * q^81 + 14479 * q^82 + 6002 * q^83 - 14944 * q^85 + 59946 * q^86 - 31996 * q^87 - 22566 * q^89 - 60630 * q^90 + 8724 * q^91 + 9572 * q^92 + 12476 * q^93 - 7312 * q^95 - 41850 * q^96 + 46287 * q^97 + 25515 * q^98 - 2048 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.52462	+	1.45759i	0.631155	+	0.364398i	0.781199	−	0.624282i	$-0.214608\pi$
$2$	2.52462	+	1.45759i	0.631155	+	0.364398i	−0.150044	+	0.988679i	$0.547942\pi$
$3$	8.18489	+	4.72555i	0.909432	+	0.525061i	0.880248	−	0.474513i	$-0.157376\pi$
$3$	8.18489	+	4.72555i	0.909432	+	0.525061i	0.0291839	+	0.999574i	$0.490709\pi$
$4$	−3.75086	−	6.49668i	−0.234429	−	0.406042i
$5$	−7.00036	+	12.1250i	−0.280014	+	0.484999i	−0.971388	−	0.237498i	$-0.923673\pi$
$5$	−7.00036	+	12.1250i	−0.280014	+	0.484999i	0.691374	+	0.722497i	$0.257006\pi$
$6$	13.7758	+	23.8604i	0.382662	+	0.662790i
$7$	19.8223			0.404536			0.202268	−	0.979330i	$-0.435169\pi$
$7$	19.8223			0.404536			0.202268	+	0.979330i	$0.435169\pi$
$8$		−	68.5118i		−	1.07050i
$9$	4.16163	+	7.20815i	0.0513781	+	0.0889896i
$10$	−35.3465	+	20.4073i	−0.353465	+	0.204073i
$11$	−177.809			−1.46950			−0.734749	−	0.678339i	$-0.762700\pi$
$11$	−177.809			−1.46950			−0.734749	+	0.678339i	$0.762700\pi$
$12$		−	70.8995i		−	0.492357i
$13$	83.2716	−	48.0769i	0.492732	−	0.284479i	−0.232975	−	0.972483i	$-0.574846\pi$
$13$	83.2716	−	48.0769i	0.492732	−	0.284479i	0.725707	+	0.688004i	$0.241513\pi$
$14$	50.0437	+	28.8927i	0.255325	+	0.147412i
$15$	−114.594	+	66.1610i	−0.509308	+	0.294049i
$16$	39.8484	−	69.0195i	0.155658	−	0.269607i
$17$	26.8637	−	46.5293i	0.0929539	−	0.161001i	−0.815799	−	0.578336i	$-0.803702\pi$
$17$	26.8637	−	46.5293i	0.0929539	−	0.161001i	0.908753	+	0.417335i	$0.137036\pi$
$18$			24.2638i			0.0748883i
$19$	161.512	+	322.854i	0.447403	+	0.894333i
$19$	161.512	+	322.854i	0.447403	+	0.894333i
$20$	105.029			0.262573
$21$	162.243	+	93.6710i	0.367898	+	0.212406i
$22$	−448.901	−	259.173i	−0.927482	−	0.535482i
$23$	372.053	+	644.415i	0.703314	+	1.21818i	0.967297	+	0.253648i	$0.0816305\pi$
$23$	372.053	+	644.415i	0.703314	+	1.21818i	−0.263983	+	0.964527i	$0.585036\pi$
$24$	323.756	−	560.761i	0.562076	−	0.973544i
$25$	214.490	+	371.508i	0.343184	+	0.594412i
$26$	280.306			0.414654
$27$		−	686.875i		−	0.942215i
$28$	−74.3505	−	128.779i	−0.0948348	−	0.164259i
$29$	−738.578	+	426.418i	−0.878213	+	0.507037i	−0.870069	−	0.492930i	$-0.835926\pi$
$29$	−738.578	+	426.418i	−0.878213	+	0.507037i	−0.00814454	+	0.999967i	$0.502593\pi$
$30$	−385.743			−0.428603
$31$		−	317.572i		−	0.330460i	−0.986255	−	0.165230i	$-0.947163\pi$
$31$		−	317.572i		−	0.330460i	0.986255	−	0.165230i	$-0.0528367\pi$
$32$	−748.123	+	431.929i	−0.730589	+	0.421805i
$33$	−1455.35	−	840.247i	−1.33641	−	0.771577i
$34$	135.641	−	78.3125i	0.117337	−	0.0677444i
$35$	−138.763	+	240.344i	−0.113276	+	0.196199i
$36$	31.2194	−	54.0735i	0.0240890	−	0.0417234i
$37$		−	1697.87i		−	1.24022i	−0.784514	−	0.620111i	$-0.787087\pi$
$37$		−	1697.87i		−	1.24022i	0.784514	−	0.620111i	$-0.212913\pi$
$38$	−62.8314	+	1050.50i	−0.0435121	+	0.727495i
$39$	908.759			0.597475
$40$	830.703	+	479.607i	0.519190	+	0.299754i
$41$	1748.55	+	1009.53i	1.04018	+	0.600551i	0.919885	−	0.392187i	$-0.128281\pi$
$41$	1748.55	+	1009.53i	1.04018	+	0.600551i	0.120299	+	0.992738i	$0.461615\pi$
$42$	273.068	+	472.968i	0.154801	+	0.268122i
$43$	938.059	−	1624.77i	0.507333	−	0.878727i	−0.492631	−	0.870238i	$-0.663965\pi$
$43$	938.059	−	1624.77i	0.507333	−	0.878727i	0.999964	−	0.00848857i	$-0.00270203\pi$
$44$	666.938	+	1155.17i	0.344493	+	0.596679i
$45$	−116.532			−0.0575464
$46$			2169.20i			1.02514i
$47$	−665.166	−	1152.10i	−0.301116	−	0.521549i	0.675273	−	0.737568i	$-0.264026\pi$
$47$	−665.166	−	1152.10i	−0.301116	−	0.521549i	−0.976389	+	0.216019i	$0.930693\pi$
$48$	652.310	−	376.611i	0.283121	−	0.163460i
$49$	−2008.08			−0.836351
$50$			1250.55i			0.500222i
$51$	439.753	−	253.891i	0.169071	−	0.0976129i
$52$	−624.680	−	360.659i	−0.231021	−	0.133380i
$53$	−2043.31	+	1179.71i	−0.727417	+	0.419974i	−0.817476	−	0.575962i	$-0.804628\pi$
$53$	−2043.31	+	1179.71i	−0.727417	+	0.419974i	0.0900597	+	0.995936i	$0.471294\pi$
$54$	1001.18	−	1734.10i	0.343341	−	0.594684i
$55$	1244.73	−	2155.93i	0.411481	−	0.712705i
$56$		−	1358.06i		−	0.433054i
$57$	−203.701	+	3405.76i	−0.0626966	+	1.04825i
$58$	−2486.17			−0.739052
$59$	2574.85	+	1486.59i	0.739686	+	0.427058i	0.821955	−	0.569552i	$-0.192883\pi$
$59$	2574.85	+	1486.59i	0.739686	+	0.427058i	−0.0822690	+	0.996610i	$0.526217\pi$
$60$	859.654	+	496.321i	0.238793	+	0.137867i
$61$	−2099.98	−	3637.27i	−0.564358	−	0.977497i	−0.997109	−	0.0759838i	$-0.975790\pi$
$61$	−2099.98	−	3637.27i	−0.564358	−	0.977497i	0.432751	−	0.901514i	$-0.357543\pi$
$62$	462.890	−	801.750i	0.120419	−	0.208572i
$63$	82.4929	+	142.882i	0.0207843	+	0.0359995i
$64$	−3793.45			−0.926136
$65$			1346.22i			0.318632i
$66$	−2449.47	−	4242.61i	−0.562322	−	0.973969i
$67$	7668.40	−	4427.35i	1.70826	−	0.986266i	0.771551	−	0.636168i	$-0.219481\pi$
$67$	7668.40	−	4427.35i	1.70826	−	0.986266i	0.936713	−	0.350099i	$-0.113852\pi$
$68$	−403.047			−0.0871642
$69$			7032.62i			1.47713i
$70$	−700.647	+	404.519i	−0.142989	+	0.0825549i
$71$	−6430.03	−	3712.38i	−1.27555	−	0.736437i	−0.299520	−	0.954090i	$-0.596827\pi$
$71$	−6430.03	−	3712.38i	−1.27555	−	0.736437i	−0.976026	+	0.217653i	$0.930160\pi$
$72$	493.843	−	285.121i	0.0952630	−	0.0550001i
$73$	−4260.31	+	7379.07i	−0.799457	+	1.38470i	0.120512	+	0.992712i	$0.461546\pi$
$73$	−4260.31	+	7379.07i	−0.799457	+	1.38470i	−0.919970	+	0.391989i	$0.871787\pi$
$74$	2474.79	−	4286.47i	0.451934	−	0.782773i
$75$			4054.33i			0.720770i
$76$	1491.67	−	2260.27i	0.258253	−	0.391322i
$77$	−3524.58			−0.594465
$78$	2294.27	+	1324.60i	0.377099	+	0.217718i
$79$	3800.18	+	2194.04i	0.608906	+	0.351552i	0.772537	−	0.634970i	$-0.218987\pi$
$79$	3800.18	+	2194.04i	0.608906	+	0.351552i	−0.163631	+	0.986522i	$0.552321\pi$
$80$	557.906	+	966.322i	0.0871728	+	0.150988i
$81$	3582.95	−	6205.86i	0.546099	−	0.945871i
$82$	2942.95	+	5097.34i	0.437678	+	0.758081i
$83$	10166.0			1.47568			0.737840	−	0.674976i	$-0.235846\pi$
$83$	10166.0			1.47568			0.737840	+	0.674976i	$0.235846\pi$
$84$		−	1405.39i		−	0.199176i
$85$	376.111	+	651.443i	0.0520568	+	0.0901651i
$86$	4736.49	−	2734.61i	0.640412	−	0.369742i
$87$	−8060.24			−1.06490
$88$			12182.0i			1.57309i
$89$	−3232.45	+	1866.26i	−0.408087	+	0.235609i	−0.689967	−	0.723841i	$-0.742375\pi$
$89$	−3232.45	+	1866.26i	−0.408087	+	0.235609i	0.281881	+	0.959449i	$0.409042\pi$
$90$	−294.198	−	169.855i	−0.0363207	−	0.0209698i
$91$	1650.63	−	952.993i	0.199328	−	0.115082i
$92$	2791.04	−	4834.22i	0.329754	−	0.571150i
$93$	1500.70	−	2599.29i	0.173512	−	0.300531i
$94$		−	3878.16i		−	0.438905i
$95$	−5045.24	−	301.760i	−0.559029	−	0.0334360i
$96$	−8164.40			−0.885894
$97$	845.233	+	487.996i	0.0898324	+	0.0518648i	0.544243	−	0.838927i	$-0.316817\pi$
$97$	845.233	+	487.996i	0.0898324	+	0.0518648i	−0.454411	+	0.890792i	$0.650150\pi$
$98$	−5069.64	−	2926.96i	−0.527867	−	0.304764i
$99$	−739.977	−	1281.68i	−0.0755001	−	0.130770i
$100$	1609.04	−	2786.94i	0.160904	−	0.278694i
$101$	−4591.76	−	7953.16i	−0.450128	−	0.779645i	0.548265	−	0.836305i	$-0.315288\pi$
$101$	−4591.76	−	7953.16i	−0.450128	−	0.779645i	−0.998394	+	0.0566592i	$0.981955\pi$
$102$	1480.28			0.142280
$103$			12570.5i			1.18489i	0.805611	+	0.592445i	$0.201837\pi$
$103$			12570.5i			1.18489i	−0.805611	+	0.592445i	$0.798163\pi$
$104$	−3293.83	−	5705.09i	−0.304533	−	0.527467i
$105$	−2271.52	+	1311.46i	−0.206033	+	0.118953i
$106$	−6878.12			−0.612150
$107$			5292.95i			0.462307i	0.972917	+	0.231153i	$0.0742499\pi$
$107$			5292.95i			0.462307i	−0.972917	+	0.231153i	$0.925750\pi$
$108$	−4462.40	+	2576.37i	−0.382579	+	0.220882i
$109$	470.631	+	271.719i	0.0396121	+	0.0228700i	0.519675	−	0.854364i	$-0.326053\pi$
$109$	470.631	+	271.719i	0.0396121	+	0.0228700i	−0.480063	+	0.877234i	$0.659386\pi$
$110$	6284.94	−	3628.61i	0.519416	−	0.299885i
$111$	8023.35	−	13896.8i	0.651193	−	1.12790i
$112$	789.885	−	1368.12i	0.0629692	−	0.109066i
$113$		−	6154.75i		−	0.482007i	−0.970524	−	0.241003i	$-0.922523\pi$
$113$		−	6154.75i		−	0.482007i	0.970524	−	0.241003i	$-0.0774765\pi$
$114$	−5478.47	+	8301.34i	−0.421551	+	0.638761i
$115$	−10418.0			−0.787752
$116$	5540.60	+	3198.87i	0.411757	+	0.237728i
$117$	693.092	+	400.157i	0.0506313	+	0.0292320i
$118$	4333.68	+	7506.15i	0.311238	+	0.539080i
$119$	532.499	−	922.315i	0.0376032	−	0.0651306i
$120$	4532.81	+	7851.06i	0.314779	+	0.545212i
$121$	16975.2			1.15943
$122$		−	12243.6i		−	0.822604i
$123$	9541.12	+	16525.7i	0.630651	+	1.09232i
$124$	−2063.16	+	1191.17i	−0.134181	+	0.0774693i
$125$	−14756.5			−0.944414
$126$			480.964i			0.0302950i
$127$	798.363	−	460.935i	0.0494986	−	0.0285780i	−0.475046	−	0.879961i	$-0.657569\pi$
$127$	798.363	−	460.935i	0.0494986	−	0.0285780i	0.524545	+	0.851383i	$0.324235\pi$
$128$	2392.93	+	1381.56i	0.146053	+	0.0843238i
$129$	15355.8	−	8865.69i	0.922771	−	0.532762i
$130$	−1962.24	+	3398.70i	−0.116109	+	0.201107i
$131$	1380.77	−	2391.57i	0.0804599	−	0.139361i	−0.822988	−	0.568059i	$-0.807694\pi$
$131$	1380.77	−	2391.57i	0.0804599	−	0.139361i	0.903448	+	0.428699i	$0.141028\pi$
$132$			12606.6i			0.723519i
$133$	3201.54	+	6399.70i	0.180990	+	0.361790i
$134$	25813.1			1.43757
$135$	8328.34	+	4808.37i	0.456973	+	0.263834i
$136$	−3187.80	−	1840.48i	−0.172351	−	0.0995068i
$137$	1927.00	+	3337.67i	0.102669	+	0.177829i	0.912784	−	0.408443i	$-0.133928\pi$
$137$	1927.00	+	3337.67i	0.102669	+	0.177829i	−0.810114	+	0.586272i	$0.800595\pi$
$138$	−10250.7	+	17754.7i	−0.538263	+	0.932299i
$139$	−18557.2	−	32142.1i	−0.960469	−	1.66358i	−0.721324	−	0.692598i	$-0.756466\pi$
$139$	−18557.2	−	32142.1i	−0.960469	−	1.66358i	−0.239145	−	0.970984i	$-0.576867\pi$
$140$	2081.92			0.106220
$141$		−	12573.1i		−	0.632418i
$142$	−10822.3	−	18744.7i	−0.536712	−	0.929612i
$143$	−14806.5	+	8548.53i	−0.724069	+	0.418041i
$144$	663.337			0.0319896
$145$		−	11940.3i		−	0.567910i
$146$	−21511.3	+	12419.6i	−1.00916	+	0.582641i
$147$	−16435.9	−	9489.27i	−0.760604	−	0.439135i
$148$	−11030.5	+	6368.45i	−0.503583	+	0.290744i
$149$	−6237.55	+	10803.8i	−0.280958	+	0.486634i	−0.971621	−	0.236543i	$-0.923986\pi$
$149$	−6237.55	+	10803.8i	−0.280958	+	0.486634i	0.690663	+	0.723177i	$0.257319\pi$
$150$	−5909.56	+	10235.7i	−0.262647	+	0.454918i
$151$			477.784i			0.0209545i	0.999945	+	0.0104772i	$0.00333507\pi$
$151$			477.784i			0.0209545i	−0.999945	+	0.0104772i	$0.996665\pi$
$152$	22119.3	−	11065.5i	0.957380	−	0.478943i
$153$	447.187			0.0191032
$154$	−8898.24	−	5137.40i	−0.375200	−	0.216622i
$155$	3850.56	+	2223.12i	0.160273	+	0.0925336i
$156$	−3408.63	−	5903.91i	−0.140065	−	0.242600i
$157$	8199.07	−	14201.2i	0.332633	−	0.576137i	−0.650394	−	0.759597i	$-0.725396\pi$
$157$	8199.07	−	14201.2i	0.332633	−	0.576137i	0.983027	+	0.183459i	$0.0587296\pi$
$158$	6396.01	+	11078.2i	0.256209	+	0.443768i
$159$	−22299.1			−0.882048
$160$		−	12094.6i		−	0.472446i
$161$	7374.93	+	12773.8i	0.284516	+	0.492796i
$162$	18091.2	−	10445.0i	0.689346	−	0.397994i
$163$	31690.4			1.19276			0.596379	−	0.802703i	$-0.296606\pi$
$163$	31690.4			1.19276			0.596379	+	0.802703i	$0.296606\pi$
$164$		−	15146.3i		−	0.563145i
$165$	20375.9	−	11764.1i	0.748428	−	0.432105i
$166$	25665.2	+	14817.8i	0.931383	+	0.537734i
$167$	−23949.0	+	13827.0i	−0.858727	+	0.495786i	−0.863586	−	0.504202i	$-0.831787\pi$
$167$	−23949.0	+	13827.0i	−0.858727	+	0.495786i	0.00485911	+	0.999988i	$0.498453\pi$
$168$	6417.57	−	11115.6i	0.227380	−	0.393833i
$169$	−9657.72	+	16727.7i	−0.338144	+	0.585682i
$170$			2192.86i			0.0758776i
$171$	−1655.03	+	2507.81i	−0.0565995	+	0.0857633i
$172$	−14074.1			−0.475734
$173$	−5352.32	−	3090.16i	−0.178834	−	0.103250i	0.407911	−	0.913022i	$-0.366257\pi$
$173$	−5352.32	−	3090.16i	−0.178834	−	0.103250i	−0.586745	+	0.809772i	$0.699591\pi$
$174$	−20349.0	−	11748.5i	−0.672118	−	0.388048i
$175$	4251.68	+	7364.12i	0.138830	+	0.240461i
$176$	−7085.42	+	12272.3i	−0.228739	+	0.396188i
$177$	14049.9	+	24335.1i	0.448463	+	0.776761i
$178$	−10881.0			−0.343421
$179$			37842.6i			1.18107i	0.807012	+	0.590535i	$0.201083\pi$
$179$			37842.6i			1.18107i	−0.807012	+	0.590535i	$0.798917\pi$
$180$	437.093	+	757.068i	0.0134905	+	0.0233663i
$181$	−25195.1	+	14546.4i	−0.769059	+	0.444016i	−0.832539	−	0.553967i	$-0.813114\pi$
$181$	−25195.1	+	14546.4i	−0.769059	+	0.444016i	0.0634798	+	0.997983i	$0.479780\pi$
$182$	5556.29			0.167742
$183$		−	39694.2i		−	1.18529i
$184$	44150.0	−	25490.0i	1.30405	−	0.752895i
$185$	20586.6	+	11885.7i	0.601507	+	0.347280i
$186$	7577.42	−	4374.82i	0.219026	−	0.126455i
$187$	−4776.61	+	8273.34i	−0.136596	+	0.236591i
$188$	−4989.89	+	8642.74i	−0.141181	+	0.244532i
$189$		−	13615.4i		−	0.381160i
$190$	−12297.5	−	8115.73i	−0.340650	−	0.224812i
$191$	30917.5			0.847497			0.423748	−	0.905780i	$-0.360714\pi$
$191$	30917.5			0.847497			0.423748	+	0.905780i	$0.360714\pi$
$192$	−31049.0	−	17926.1i	−0.842258	−	0.486278i
$193$	29762.5	+	17183.4i	0.799016	+	0.461312i	0.843127	−	0.537715i	$-0.180712\pi$
$193$	29762.5	+	17183.4i	0.799016	+	0.461312i	−0.0441110	+	0.999027i	$0.514046\pi$
$194$	1422.60	+	2464.01i	0.0377988	+	0.0654694i
$195$	−6361.64	+	11018.7i	−0.167301	+	0.289775i
$196$	7532.02	+	13045.8i	0.196065	+	0.339594i
$197$	−40466.2			−1.04270			−0.521351	−	0.853342i	$-0.674572\pi$
$197$	−40466.2			−1.04270			−0.521351	+	0.853342i	$0.674572\pi$
$198$		−	4314.33i		−	0.110048i
$199$	3668.05	+	6353.25i	0.0926253	+	0.160432i	0.908615	−	0.417635i	$-0.137141\pi$
$199$	3668.05	+	6353.25i	0.0926253	+	0.160432i	−0.815990	+	0.578066i	$0.803807\pi$
$200$	25452.6	−	14695.1i	0.636316	−	0.367377i
$201$	83686.6			2.07140
$202$		−	26771.6i		−	0.656103i
$203$	−14640.3	+	8452.57i	−0.355269	+	0.205115i
$204$	−3298.90	−	1904.62i	−0.0792700	−	0.0457665i
$205$	−24480.9	+	14134.1i	−0.582533	+	0.336325i
$206$	−18322.6	+	31735.7i	−0.431771	+	0.747849i
$207$	−3096.69	+	5363.63i	−0.0722699	+	0.125175i
$208$		−	7663.15i		−	0.177125i
$209$	−28718.4	−	57406.5i	−0.657458	−	1.31422i
$210$	−7646.30			−0.173385
$211$	−46962.1	−	27113.6i	−1.05483	−	0.609007i	−0.130833	−	0.991404i	$-0.541765\pi$
$211$	−46962.1	−	27113.6i	−1.05483	−	0.609007i	−0.923998	+	0.382398i	$0.875098\pi$
$212$	15328.4	+	8849.83i	0.341055	+	0.196908i
$213$	−35086.1	−	60770.8i	−0.773349	−	1.33948i
$214$	−7714.96	+	13362.7i	−0.168464	+	0.291787i
$215$	13133.5	+	22747.9i	0.284121	+	0.492112i
$216$	−47059.0			−1.00864
$217$		−	6295.00i		−	0.133683i
$218$	792.110	+	1371.97i	0.0166676	+	0.0288691i
$219$	−69740.3	+	40264.6i	−1.45410	+	0.839528i
$220$	−18675.2			−0.385851
$221$		−	5166.09i		−	0.105774i
$222$	40511.8	−	23389.5i	0.822008	−	0.474586i
$223$	5412.68	+	3125.01i	0.108844	+	0.0628409i	0.553434	−	0.832893i	$-0.313317\pi$
$223$	5412.68	+	3125.01i	0.108844	+	0.0628409i	−0.444590	+	0.895734i	$0.646651\pi$
$224$	−14829.5	+	8561.80i	−0.295549	+	0.170635i
$225$	−1785.26	+	3092.15i	−0.0352643	+	0.0610796i
$226$	8971.10	−	15538.4i	0.175642	−	0.304221i
$227$			9794.98i			0.190087i	0.995473	+	0.0950434i	$0.0302990\pi$
$227$			9794.98i			0.190087i	−0.995473	+	0.0950434i	$0.969701\pi$
$228$	22890.2	−	11451.1i	0.440331	−	0.220282i
$229$	96224.9			1.83492			0.917458	−	0.397832i	$-0.130237\pi$
$229$	96224.9			1.83492			0.917458	+	0.397832i	$0.130237\pi$
$230$	−26301.5	−	15185.2i	−0.497194	−	0.287055i
$231$	−28848.3	−	16655.6i	−0.540626	−	0.312130i
$232$	29214.6	+	50601.3i	0.542781	+	0.940124i
$233$	−8410.60	+	14567.6i	−0.154923	+	0.268334i	−0.933031	−	0.359796i	$-0.882846\pi$
$233$	−8410.60	+	14567.6i	−0.154923	+	0.268334i	0.778108	+	0.628130i	$0.216180\pi$
$234$	1166.53	+	2020.49i	0.0213041	+	0.0368998i
$235$	18625.6			0.337268
$236$		−	22303.9i		−	0.400458i
$237$	20736.1	+	35915.9i	0.369173	+	0.639426i
$238$	2688.72	−	1552.33i	0.0474669	−	0.0274050i
$239$	72495.2			1.26915			0.634576	−	0.772860i	$-0.281175\pi$
$239$	72495.2			1.26915			0.634576	+	0.772860i	$0.281175\pi$
$240$			10545.7i			0.183084i
$241$	−9603.35	+	5544.50i	−0.165344	+	0.0954615i	−0.580389	−	0.814340i	$-0.697099\pi$
$241$	−9603.35	+	5544.50i	−0.165344	+	0.0954615i	0.415045	+	0.909801i	$0.363766\pi$
$242$	42855.9	+	24742.9i	0.731779	+	0.422493i
$243$	10469.2	−	6044.41i	0.177297	−	0.102363i
$244$	−15753.4	+	27285.8i	−0.264604	+	0.458307i
$245$	14057.3	−	24347.9i	0.234190	−	0.405629i
$246$			55628.2i			0.919232i
$247$	28971.2	+	19119.6i	0.474868	+	0.313389i
$248$	−21757.4			−0.353757
$249$	83207.2	+	48039.7i	1.34203	+	0.774822i
$250$	−37254.5	−	21508.9i	−0.596072	−	0.344142i
$251$	−29276.9	−	50709.1i	−0.464705	−	0.804893i	0.534483	−	0.845179i	$-0.320506\pi$
$251$	−29276.9	−	50709.1i	−0.464705	−	0.804893i	−0.999188	+	0.0402861i	$0.987173\pi$
$252$	618.838	−	1071.86i	0.00974487	−	0.0168786i
$253$	−66154.5	−	114583.i	−1.03352	−	1.79011i
$254$	2687.42			0.0416551
$255$			7109.32i			0.109332i
$256$	34375.1	+	59539.4i	0.524523	+	0.908500i
$257$	−36320.5	+	20969.6i	−0.549902	+	0.317486i	−0.749083	−	0.662477i	$-0.769505\pi$
$257$	−36320.5	+	20969.6i	−0.549902	+	0.317486i	0.199180	+	0.979963i	$0.436172\pi$
$258$	51690.2			0.776549
$259$		−	33655.5i		−	0.501715i
$260$	8745.97	−	5049.49i	0.129378	−	0.0746965i
$261$	−6147.37	−	3549.19i	−0.0902420	−	0.0521012i
$262$	6971.85	−	4025.20i	0.101565	−	0.0586388i
$263$	23379.5	−	40494.5i	0.338006	−	0.585443i	−0.646052	−	0.763294i	$-0.723581\pi$
$263$	23379.5	−	40494.5i	0.338006	−	0.585443i	0.984058	+	0.177850i	$0.0569143\pi$
$264$	−57566.8	+	99708.6i	−0.825970	+	1.43062i
$265$		−	33033.5i		−	0.470395i
$266$	−1245.46	+	20823.3i	−0.0176022	+	0.294298i
$267$	−35276.4			−0.494836
$268$	−57526.1	−	33212.7i	−0.800932	−	0.462418i
$269$	−31807.3	−	18364.0i	−0.439565	−	0.253783i	0.263848	−	0.964564i	$-0.415008\pi$
$269$	−31807.3	−	18364.0i	−0.439565	−	0.253783i	−0.703413	+	0.710781i	$0.748341\pi$
$270$	14017.3	+	24278.6i	0.192281	+	0.333040i
$271$	−39163.1	+	67832.5i	−0.533259	+	0.923632i	0.465986	+	0.884792i	$0.345700\pi$
$271$	−39163.1	+	67832.5i	−0.533259	+	0.923632i	−0.999245	+	0.0388401i	$0.987634\pi$
$272$	−2140.95	−	3708.23i	−0.0289380	−	0.0501221i
$273$	18013.7			0.241700
$274$			11235.1i			0.149650i
$275$	−38138.3	−	66057.5i	−0.504309	−	0.873488i
$276$	45688.7	−	26378.4i	0.599778	−	0.346282i
$277$	−106120.			−1.38305			−0.691524	−	0.722354i	$-0.743060\pi$
$277$	−106120.			−1.38305			−0.691524	+	0.722354i	$0.743060\pi$
$278$		−	108195.i		−	1.39997i
$279$	2289.11	−	1321.62i	0.0294075	−	0.0169784i
$280$	16466.4	+	9506.89i	0.210031	+	0.121261i
$281$	22141.4	−	12783.4i	0.280410	−	0.161895i	−0.353199	−	0.935548i	$-0.614906\pi$
$281$	22141.4	−	12783.4i	0.280410	−	0.161895i	0.633609	+	0.773654i	$0.281573\pi$
$282$	18326.4	−	31742.3i	0.230452	−	0.399154i
$283$	5959.93	−	10322.9i	0.0744164	−	0.128893i	−0.826416	−	0.563060i	$-0.809624\pi$
$283$	5959.93	−	10322.9i	0.0744164	−	0.128893i	0.900832	+	0.434167i	$0.142957\pi$
$284$			55698.4i			0.690568i
$285$	−39868.8	−	26311.4i	−0.490844	−	0.323932i
$286$	−49841.0			−0.609333
$287$	34660.2	+	20011.1i	0.420792	+	0.242944i
$288$	−6226.82	−	3595.06i	−0.0750726	−	0.0433432i
$289$	40317.2	+	69831.4i	0.482719	+	0.836094i
$290$	17404.1	−	30144.8i	0.206945	−	0.358439i
$291$	4612.09	+	7988.38i	0.0544643	+	0.0943350i
$292$	63919.2			0.749663
$293$		−	78303.7i		−	0.912110i	−0.889952	−	0.456055i	$-0.849262\pi$
$293$		−	78303.7i		−	0.912110i	0.889952	−	0.456055i	$-0.150738\pi$
$294$	−27663.0	−	47913.6i	−0.320040	−	0.554325i
$295$	−36049.7	+	20813.3i	−0.414245	+	0.239165i
$296$	−116324.			−1.32765
$297$			122133.i			1.38458i
$298$	−31494.9	+	18183.6i	−0.354657	+	0.204761i
$299$	61962.9	+	35774.3i	0.693090	+	0.400156i
$300$	26339.7	−	15207.2i	0.292663	−	0.168969i
$301$	18594.5	−	32206.5i	0.205234	−	0.355477i
$302$	−696.413	+	1206.22i	−0.00763577	+	0.0132255i
$303$		−	86794.4i		−	0.945380i
$304$	28719.2	+	1717.72i	0.310760	+	0.0185868i
$305$	58802.4			0.632114
$306$	1128.98	+	651.815i	0.0120571	+	0.00696116i
$307$	54731.0	+	31599.0i	0.580707	+	0.335271i	0.761414	−	0.648266i	$-0.224505\pi$
$307$	54731.0	+	31599.0i	0.580707	+	0.335271i	−0.180708	+	0.983537i	$0.557839\pi$
$308$	13220.2	+	22898.1i	0.139360	+	0.241378i
$309$	−59402.5	+	102888.i	−0.622139	+	1.07758i
$310$	6480.80	+	11225.1i	0.0674380	+	0.116806i
$311$	93030.4			0.961842			0.480921	−	0.876764i	$-0.340302\pi$
$311$	93030.4			0.961842			0.480921	+	0.876764i	$0.340302\pi$
$312$		−	62260.7i		−	0.639595i
$313$	63547.0	+	110067.i	0.648644	+	1.12348i	0.983447	+	0.181196i	$0.0579968\pi$
$313$	63547.0	+	110067.i	0.648644	+	1.12348i	−0.334803	+	0.942288i	$0.608670\pi$
$314$	41399.1	−	23901.8i	0.419886	−	0.242421i
$315$	−2309.92			−0.0232796
$316$		−	32918.1i		−	0.329655i
$317$	−162973.	+	94092.3i	−1.62180	+	0.936344i	−0.635356	+	0.772220i	$0.719146\pi$
$317$	−162973.	+	94092.3i	−1.62180	+	0.936344i	−0.986440	+	0.164124i	$0.947520\pi$
$318$	−56296.7	−	32502.9i	−0.556709	−	0.321416i
$319$	131326.	−	75821.1i	1.29053	−	0.745090i
$320$	26555.5	−	45995.5i	0.259331	−	0.449175i
$321$	−25012.1	+	43322.2i	−0.242739	+	0.420437i
$322$			42998.5i			0.414707i
$323$	19361.0	+	1158.00i	0.185576	+	0.0110995i
$324$	−53756.6			−0.512085
$325$	35721.9	+	20624.0i	0.338195	+	0.195257i
$326$	80006.2	+	46191.6i	0.752815	+	0.434638i
$327$	2568.04	+	4447.98i	0.0240163	+	0.0415975i
$328$	69164.4	−	119796.i	0.642887	−	1.11351i
$329$	−13185.1	−	22837.3i	−0.121812	−	0.210985i
$330$	68588.7			0.629832
$331$			126301.i			1.15279i	0.817171	+	0.576396i	$0.195541\pi$
$331$			126301.i			1.15279i	−0.817171	+	0.576396i	$0.804459\pi$
$332$	−38131.1	−	66044.9i	−0.345941	−	0.599188i
$333$	12238.5	−	7065.89i	0.110367	−	0.0637204i
$334$	−80616.3			−0.722653
$335$			123972.i			1.10467i
$336$	12930.3	−	7465.28i	0.114532	−	0.0661253i
$337$	−86740.5	−	50079.7i	−0.763769	−	0.440962i	0.0668782	−	0.997761i	$-0.478696\pi$
$337$	−86740.5	−	50079.7i	−0.763769	−	0.440962i	−0.830647	+	0.556799i	$0.812029\pi$
$338$	−48764.2	+	28154.0i	−0.426842	+	0.246438i
$339$	29084.6	−	50375.9i	0.253083	−	0.438353i
$340$	2821.47	−	4886.94i	0.0244072	−	0.0422745i
$341$			56467.3i			0.485611i
$342$	−7833.67	+	3918.91i	−0.0669751	+	0.0335052i
$343$	−87397.9			−0.742870
$344$	−111316.	−	64268.1i	−0.940674	−	0.543098i
$345$	−85270.3	−	49230.8i	−0.716407	−	0.413618i
$346$	−9008.39	−	15603.0i	−0.0752480	−	0.130333i
$347$	52875.4	−	91582.9i	0.439132	−	0.760598i	−0.558491	−	0.829511i	$-0.688620\pi$
$347$	52875.4	−	91582.9i	0.439132	−	0.760598i	0.997623	+	0.0689122i	$0.0219528\pi$
$348$	30232.8	+	52364.7i	0.249643	+	0.432395i
$349$	−157850.			−1.29597			−0.647985	−	0.761653i	$-0.724388\pi$
$349$	−157850.			−1.29597			−0.647985	+	0.761653i	$0.724388\pi$
$350$			24788.8i			0.202358i
$351$	−33022.8	−	57197.2i	−0.268040	−	0.464259i
$352$	133023.	−	76801.0i	1.07360	−	0.619843i
$353$	41636.7			0.334139			0.167069	−	0.985945i	$-0.446570\pi$
$353$	41636.7			0.334139			0.167069	+	0.985945i	$0.446570\pi$
$354$			81916.0i			0.653676i
$355$	90025.0	−	51975.9i	0.714342	−	0.412426i
$356$	24248.9	+	14000.1i	0.191334	+	0.110467i
$357$	8716.89	−	5032.70i	0.0683951	−	0.0394879i
$358$	−55159.1	+	95538.3i	−0.430379	+	0.745438i
$359$	113309.	−	196258.i	0.879179	−	1.52278i	0.0269346	−	0.999637i	$-0.491425\pi$
$359$	113309.	−	196258.i	0.879179	−	1.52278i	0.852244	−	0.523145i	$-0.175241\pi$
$360$			7983.78i			0.0616033i
$361$	−78148.5	+	104290.i	−0.599661	+	0.800254i
$362$	−84810.9			−0.647194
$363$	138940.	+	80217.0i	1.05442	+	0.608770i
$364$	−12382.6	−	7149.08i	−0.0934562	−	0.0539570i
$365$	−59647.4	−	103312.i	−0.447719	−	0.775472i
$366$	57857.9	−	100213.i	0.431917	−	0.748102i
$367$	−53022.3	−	91837.3i	−0.393664	−	0.681847i	0.599265	−	0.800550i	$-0.295459\pi$
$367$	−53022.3	−	91837.3i	−0.393664	−	0.681847i	−0.992930	+	0.118704i	$0.962126\pi$
$368$	59302.9			0.437905
$369$			16805.1i			0.123421i
$370$	34648.9	+	60013.6i	0.253096	+	0.438375i
$371$	−40503.1	+	23384.5i	−0.294266	+	0.169895i
$372$	−22515.7			−0.162705
$373$			130059.i			0.934810i	0.884043	+	0.467405i	$0.154811\pi$
$373$			130059.i			0.934810i	−0.884043	+	0.467405i	$0.845189\pi$
$374$	−24118.3	+	13924.7i	−0.172426	+	0.0995503i
$375$	−120780.	−	69732.4i	−0.858881	−	0.495875i
$376$	−78932.5	+	45571.7i	−0.558316	+	0.322344i
$377$	−41001.7	+	71017.1i	−0.288482	+	0.499666i
$378$	19845.7	−	34373.8i	0.138894	−	0.240571i
$379$		−	65649.6i		−	0.457040i	−0.973539	−	0.228520i	$-0.926611\pi$
$379$		−	65649.6i		−	0.457040i	0.973539	−	0.228520i	$-0.0733886\pi$
$380$	16963.5	+	33909.2i	0.117476	+	0.234828i
$381$	8712.68			0.0600208
$382$	78055.1	+	45065.1i	0.534902	+	0.308826i
$383$	−76995.9	−	44453.6i	−0.524892	−	0.303047i	0.214042	−	0.976824i	$-0.431337\pi$
$383$	−76995.9	−	44453.6i	−0.524892	−	0.303047i	−0.738934	+	0.673778i	$0.764670\pi$
$384$	13057.3	+	22615.9i	0.0885503	+	0.153374i
$385$	24673.3	−	42735.5i	0.166459	−	0.288315i
$386$	50092.8	+	86763.2i	0.336202	+	0.582319i
$387$	15615.4			0.104263
$388$		−	7321.61i		−	0.0486343i
$389$	−88063.1	−	152530.i	−0.581962	−	1.00799i	−0.995247	−	0.0973858i	$-0.968952\pi$
$389$	−88063.1	−	152530.i	−0.581962	−	1.00799i	0.413285	−	0.910602i	$-0.364381\pi$
$390$	−32121.5	+	18545.3i	−0.211186	+	0.121929i
$391$	39978.9			0.261503
$392$			137577.i			0.895311i
$393$	22602.9	−	13049.8i	0.146346	−	0.0844927i
$394$	−102162.	−	58983.2i	−0.658107	−	0.379958i
$395$	−53205.2	+	30718.1i	−0.341005	+	0.196879i
$396$	−5551.10	+	9614.78i	−0.0353988	+	0.0613125i
$397$	109805.	−	190188.i	0.696694	−	1.20671i	−0.272912	−	0.962039i	$-0.587987\pi$
$397$	109805.	−	190188.i	0.696694	−	1.20671i	0.969606	−	0.244671i	$-0.0786799\pi$
$398$			21386.1i			0.135010i
$399$	−4037.82	+	67509.8i	−0.0253630	+	0.424054i
$400$	34188.3			0.213677
$401$	192044.	+	110877.i	1.19429	+	0.689526i	0.959278	−	0.282465i	$-0.0911521\pi$
$401$	192044.	+	110877.i	1.19429	+	0.689526i	0.235017	+	0.971991i	$0.424485\pi$
$402$	211277.	+	121981.i	1.30738	+	0.754814i
$403$	−15267.9	−	26444.8i	−0.0940089	−	0.162828i
$404$	−34446.1	+	59662.4i	−0.211046	+	0.365542i
$405$	50163.9	+	86886.4i	0.305831	+	0.529715i
$406$	−49281.5			−0.298973
$407$			301896.i			1.82251i
$408$	−17394.5	−	30128.2i	−0.104494	−	0.180989i
$409$	250085.	−	144387.i	1.49500	−	0.863138i	0.495016	−	0.868884i	$-0.335162\pi$
$409$	250085.	−	144387.i	1.49500	−	0.863138i	0.999983	+	0.00574553i	$0.00182887\pi$
$410$	−82406.8			−0.490225
$411$			36424.6i			0.215631i
$412$	81666.4	−	47150.1i	0.481115	−	0.277772i
$413$	51039.3	+	29467.5i	0.299230	+	0.172760i
$414$	−15636.0	+	9027.43i	−0.0912271	+	0.0526700i
$415$	−71165.3	+	123262.i	−0.413211	+	0.715703i
$416$	−41531.6	+	71934.8i	−0.239989	+	0.415674i
$417$		−	350772.i		−	2.01722i
$418$	11172.0	−	186789.i	0.0639409	−	1.06905i
$419$	180068.			1.02567			0.512835	−	0.858487i	$-0.328595\pi$
$419$	180068.			1.02567			0.512835	+	0.858487i	$0.328595\pi$
$420$	17040.3	+	9838.21i	0.0966002	+	0.0557722i
$421$	199084.	+	114941.i	1.12324	+	0.648501i	0.942225	−	0.334980i	$-0.108729\pi$
$421$	199084.	+	114941.i	1.12324	+	0.648501i	0.181012	+	0.983481i	$0.442063\pi$
$422$	−79041.0	−	136903.i	−0.443841	−	0.768756i
$423$	5536.35	−	9589.24i	0.0309416	−	0.0535924i
$424$	80823.8	+	139991.i	0.449581	+	0.778697i
$425$	23048.0			0.127601
$426$		−	204564.i		−	1.12723i
$427$	−41626.3	−	72098.9i	−0.228303	−	0.395433i
$428$	34386.6	−	19853.1i	0.187716	−	0.108378i
$429$	−161586.			−0.877989
$430$			76573.1i			0.414132i
$431$	−87680.8	+	50622.5i	−0.472008	+	0.272514i	−0.717080	−	0.696991i	$-0.754522\pi$
$431$	−87680.8	+	50622.5i	−0.472008	+	0.272514i	0.245072	+	0.969505i	$0.421189\pi$
$432$	−47407.7	−	27370.9i	−0.254028	−	0.146663i
$433$	−184631.	+	106597.i	−0.984756	+	0.568549i	−0.903703	−	0.428161i	$-0.859162\pi$
$433$	−184631.	+	106597.i	−0.984756	+	0.568549i	−0.0810530	+	0.996710i	$0.525828\pi$
$434$	9175.53	−	15892.5i	0.0487138	−	0.0843747i
$435$	56424.5	−	97730.1i	0.298187	−	0.516476i
$436$		−	4076.72i		−	0.0214456i
$437$	−147961.	+	224200.i	−0.774789	+	1.17401i
$438$	−234757.			−1.22369
$439$	−292406.	−	168820.i	−1.51725	−	0.875983i	−0.999795	−	0.0202720i	$-0.993547\pi$
$439$	−292406.	−	168820.i	−1.51725	−	0.875983i	−0.517453	−	0.855711i	$-0.673120\pi$
$440$	−147707.	−	85278.6i	−0.762948	−	0.440489i
$441$	−8356.88	−	14474.5i	−0.0429702	−	0.0744265i
$442$	7530.05	−	13042.4i	0.0385437	−	0.0667596i
$443$	103171.	+	178698.i	0.525717	+	0.910568i	0.999551	+	0.0299541i	$0.00953610\pi$
$443$	103171.	+	178698.i	0.525717	+	0.910568i	−0.473835	+	0.880614i	$0.657131\pi$
$444$	−120378.			−0.610633
$445$		−	52257.9i		−	0.263895i
$446$	9109.98	+	15779.0i	0.0457981	+	0.0793247i
$447$	−102107.	+	58951.7i	−0.511025	+	0.295040i
$448$	−75194.8			−0.374655
$449$		−	215003.i		−	1.06648i	−0.845965	−	0.533239i	$-0.820975\pi$
$449$		−	215003.i		−	1.06648i	0.845965	−	0.533239i	$-0.179025\pi$
$450$	−9014.19	+	5204.35i	−0.0445145	+	0.0257005i
$451$	−310908.	−	179503.i	−1.52855	−	0.882508i
$452$	−39985.4	+	23085.6i	−0.195715	+	0.112996i
$453$	−2257.79	+	3910.61i	−0.0110024	+	0.0190567i
$454$	−14277.1	+	24728.6i	−0.0692672	+	0.119974i
$455$			26685.2i			0.128898i
$456$	233335.	+	13955.9i	1.12215	+	0.0671165i
$457$	70263.0			0.336430			0.168215	−	0.985750i	$-0.446200\pi$
$457$	70263.0			0.336430			0.168215	+	0.985750i	$0.446200\pi$
$458$	242931.	+	140257.i	1.15812	+	0.668640i
$459$	−31959.8	−	18452.0i	−0.151698	−	0.0875826i
$460$	39076.5	+	67682.5i	0.184672	+	0.319860i
$461$	184591.	−	319721.i	0.868579	−	1.50442i	0.00512983	−	0.999987i	$-0.498367\pi$
$461$	184591.	−	319721.i	0.868579	−	1.50442i	0.863449	−	0.504436i	$-0.168300\pi$
$462$	−48554.1	−	84098.1i	−0.227479	−	0.394006i
$463$	113555.			0.529719			0.264860	−	0.964287i	$-0.414674\pi$
$463$	113555.			0.529719			0.264860	+	0.964287i	$0.414674\pi$
$464$			67968.3i			0.315697i
$465$	21010.9	+	36392.0i	0.0971715	+	0.168306i
$466$	−42467.2	+	24518.4i	−0.195561	+	0.112907i
$467$	97414.0			0.446671			0.223335	−	0.974742i	$-0.428305\pi$
$467$	97414.0			0.446671			0.223335	+	0.974742i	$0.428305\pi$
$468$		−	6003.72i		−	0.0274113i
$469$	152005.	−	87760.1i	0.691054	−	0.398980i
$470$	47022.6	+	27148.5i	0.212868	+	0.122900i
$471$	134217.	−	77490.2i	0.605015	−	0.349305i
$472$	101849.	−	176407.i	0.457164	−	0.791831i
$473$	−166796.	+	288899.i	−0.745526	+	1.29129i
$474$			120899.i			0.538102i
$475$	−85299.9	+	129252.i	−0.378061	+	0.572862i
$476$	−7989.31			−0.0352610
$477$	−17007.0	−	9819.01i	−0.0747466	−	0.0431550i
$478$	183023.	+	105668.i	0.801032	+	0.462476i
$479$	121178.	+	209886.i	0.528144	+	0.914772i	0.999462	+	0.0328084i	$0.0104451\pi$
$479$	121178.	+	209886.i	0.528144	+	0.914772i	−0.471318	+	0.881963i	$0.656222\pi$
$480$	57153.7	−	98993.2i	0.248063	−	0.429658i
$481$	−81628.1	−	141384.i	−0.352817	−	0.611097i
$482$	−32326.4			−0.139144
$483$			139402.i			0.597552i
$484$	−63671.5	−	110282.i	−0.271803	−	0.470776i
$485$	−11833.9	+	6832.28i	−0.0503087	+	0.0290457i
$486$	35241.1			0.149203
$487$			25446.0i			0.107290i	0.998560	+	0.0536452i	$0.0170840\pi$
$487$			25446.0i			0.107290i	−0.998560	+	0.0536452i	$0.982916\pi$
$488$	−249196.	+	143873.i	−1.04641	+	0.604144i
$489$	259382.	+	149754.i	1.08473	+	0.626270i
$490$	70978.5	−	40979.5i	0.295621	−	0.170677i
$491$	90935.5	−	157505.i	0.377199	−	0.653328i	−0.613455	−	0.789730i	$-0.710221\pi$
$491$	90935.5	−	157505.i	0.377199	−	0.653328i	0.990654	+	0.136402i	$0.0435540\pi$
$492$	71574.8	−	123971.i	0.295685	−	0.512142i
$493$			45820.6i			0.188524i
$494$	45272.9	+	90497.9i	0.185517	+	0.370838i
$495$	20720.4			0.0845644
$496$	−21918.7	−	12654.8i	−0.0890945	−	0.0514387i
$497$	−127458.	−	73587.7i	−0.516004	−	0.297915i
$498$	140045.	+	242564.i	0.564687	+	0.978066i
$499$	−106046.	+	183677.i	−0.425885	+	0.737655i	−0.996503	−	0.0835609i	$-0.973371\pi$
$499$	−106046.	+	183677.i	−0.425885	+	0.737655i	0.570617	+	0.821216i	$0.306704\pi$
$500$	55349.4	+	95868.0i	0.221398	+	0.383472i
$501$	−261360.			−1.04127
$502$		−	170695.i		−	0.677350i
$503$	25084.6	+	43447.7i	0.0991449	+	0.171724i	0.911331	−	0.411674i	$-0.135056\pi$
$503$	25084.6	+	43447.7i	0.0991449	+	0.171724i	−0.812186	+	0.583399i	$0.801723\pi$
$504$	9789.09	−	5651.73i	0.0385373	−	0.0222495i
$505$	128576.			0.504169
$506$		−	385705.i		−	1.50645i
$507$	−158095.	+	91276.1i	−0.615038	+	0.355092i
$508$	−5989.09	−	3457.80i	−0.0232078	−	0.0133990i
$509$	176441.	−	101868.i	0.681026	−	0.393191i	−0.119215	−	0.992868i	$-0.538038\pi$
$509$	176441.	−	101868.i	0.681026	−	0.393191i	0.800242	+	0.599678i	$0.204705\pi$
$510$	−10362.5	+	17948.3i	−0.0398404	+	0.0690055i
$511$	−84448.9	+	146270.i	−0.323409	+	0.560161i
$512$			156209.i			0.595892i
$513$	221760.	−	110939.i	0.842654	−	0.421550i
$514$	−122261.			−0.462765
$515$	−152417.	−	87997.9i	−0.574670	−	0.331786i
$516$	−115195.	−	66507.9i	−0.432648	−	0.249789i
$517$	118273.	+	204854.i	0.442490	+	0.766416i
$518$	49056.0	−	84967.4i	0.182824	−	0.316660i
$519$	−29205.4	−	50585.3i	−0.108425	−	0.187797i
$520$	92232.0			0.341095
$521$		−	289594.i		−	1.06688i	−0.845839	−	0.533439i	$-0.820899\pi$
$521$		−	289594.i		−	1.06688i	0.845839	−	0.533439i	$-0.179101\pi$
$522$	−10346.5	−	17920.7i	−0.0379711	−	0.0657679i
$523$	−169469.	+	97843.1i	−0.619566	+	0.357706i	−0.776700	−	0.629871i	$-0.783108\pi$
$523$	−169469.	+	97843.1i	−0.619566	+	0.357706i	0.157134	+	0.987577i	$0.449774\pi$
$524$	−20716.3			−0.0754484
$525$			80366.0i			0.291577i
$526$	118049.	−	68155.6i	0.426668	−	0.246337i
$527$	−14776.4	−	8531.16i	−0.0532044	−	0.0307176i
$528$	−115987.	+	66965.0i	−0.416045	+	0.240204i
$529$	−136926.	+	237164.i	−0.489301	+	0.847494i
$530$	48149.3	−	83397.0i	0.171411	−	0.296892i
$531$			24746.5i			0.0877658i
$532$	29568.2	−	44803.7i	0.104473	−	0.158304i
$533$	194139.			0.683375
$534$	−89059.5	−	51418.5i	−0.312318	−	0.180317i
$535$	−64176.9	−	37052.5i	−0.224218	−	0.129452i
$536$	−303326.	−	525375.i	−1.05579	−	1.82869i
$537$	−178827.	+	309738.i	−0.620133	+	1.07410i
$538$	−53534.3	−	92724.1i	−0.184956	−	0.320353i
$539$	357055.			1.22902
$540$		−	72142.0i		−	0.247401i
$541$	129234.	+	223840.i	0.441553	+	0.764793i	0.997805	−	0.0662210i	$-0.0210942\pi$
$541$	129234.	+	223840.i	0.441553	+	0.764793i	−0.556252	+	0.831014i	$0.687761\pi$
$542$	−197744.	+	114168.i	−0.673139	+	0.388637i
$543$	−274959.			−0.932543
$544$			46412.8i			0.156834i
$545$	−6589.17	+	3804.26i	−0.0221839	+	0.0128079i
$546$	45477.7	+	26256.5i	0.152550	+	0.0880749i
$547$	76348.0	−	44079.5i	0.255166	−	0.147320i	−0.366961	−	0.930236i	$-0.619602\pi$
$547$	76348.0	−	44079.5i	0.255166	−	0.147320i	0.622127	+	0.782916i	$0.286269\pi$
$548$	14455.8	−	25038.2i	0.0481373	−	0.0833762i
$549$	17478.7	−	30273.9i	0.0579914	−	0.100444i
$550$		−	222360.i		−	0.735076i
$551$	−256960.	−	169581.i	−0.846375	−	0.558565i
$552$	481817.			1.58126
$553$	75328.2	+	43490.7i	0.246324	+	0.142215i
$554$	−267912.	−	154679.i	−0.872918	−	0.503979i
$555$	112333.	+	194566.i	0.364686	+	0.631655i
$556$	−139211.	+	241121.i	−0.450323	+	0.779982i
$557$	−223661.	−	387392.i	−0.720908	−	1.24865i	−0.960636	−	0.277809i	$-0.910392\pi$
$557$	−223661.	−	387392.i	−0.720908	−	1.24865i	0.239729	−	0.970840i	$-0.422942\pi$
$558$	7705.52			0.0247476
$559$		−	180396.i		−	0.577302i
$560$	11059.0	+	19154.7i	0.0352645	+	0.0610800i
$561$	−78192.1	+	45144.2i	−0.248449	+	0.143442i
$562$	74531.6			0.235976
$563$		−	341953.i		−	1.07882i	−0.842043	−	0.539410i	$-0.818647\pi$
$563$		−	341953.i		−	1.07882i	0.842043	−	0.539410i	$-0.181353\pi$
$564$	−81683.4	+	47159.9i	−0.256788	+	0.148257i
$565$	74626.1	+	43085.4i	0.233773	+	0.134969i
$566$	30093.1	−	17374.3i	0.0939366	−	0.0542343i
$567$	71022.2	−	123014.i	0.220916	−	0.382639i
$568$	−254342.	+	440533.i	−0.788353	+	1.36547i
$569$		−	58752.9i		−	0.181470i	−0.995875	−	0.0907349i	$-0.971078\pi$
$569$		−	58752.9i		−	0.181470i	0.995875	−	0.0907349i	$-0.0289216\pi$
$570$	−62302.3	−	124539.i	−0.191758	−	0.383314i
$571$	−184183.			−0.564907			−0.282453	−	0.959281i	$-0.591148\pi$
$571$	−184183.			−0.564907			−0.282453	+	0.959281i	$0.591148\pi$
$572$	111074.	+	64128.6i	0.339485	+	0.196002i
$573$	253057.	+	146102.i	0.770741	+	0.444988i
$574$	58335.9	+	101041.i	0.177057	+	0.306671i
$575$	−159603.	+	276441.i	−0.482732	+	0.836117i
$576$	−15786.9	−	27343.8i	−0.0475831	−	0.0824164i
$577$	148555.			0.446207			0.223103	−	0.974795i	$-0.428381\pi$
$577$	148555.			0.446207			0.223103	+	0.974795i	$0.428381\pi$
$578$			235064.i			0.703607i
$579$	162402.	+	281289.i	0.484434	+	0.839064i
$580$	−77572.3	+	44786.4i	−0.230595	+	0.133134i
$581$	201512.			0.596965
$582$			26890.2i			0.0793867i
$583$	363320.	−	209763.i	1.06894	−	0.617152i
$584$	505553.	+	291881.i	1.48232	+	0.855816i
$585$	−9703.77	+	5602.48i	−0.0283550	+	0.0163707i
$586$	114135.	−	197687.i	0.332371	−	0.575683i
$587$	−24400.0	+	42262.1i	−0.0708132	+	0.122652i	−0.899258	−	0.437419i	$-0.855893\pi$
$587$	−24400.0	+	42262.1i	−0.0708132	+	0.122652i	0.828445	+	0.560071i	$0.189226\pi$
$588$			142372.i			0.411783i
$589$	102530.	−	51291.9i	0.295541	−	0.147849i
$590$	−121349.			−0.348604
$591$	−331212.	−	191225.i	−0.948267	−	0.547482i
$592$	−117186.	−	67657.2i	−0.334373	−	0.193050i
$593$	−306822.	−	531431.i	−0.872524	−	1.51126i	−0.859377	−	0.511342i	$-0.829149\pi$
$593$	−306822.	−	531431.i	−0.872524	−	1.51126i	−0.0131462	−	0.999914i	$-0.504185\pi$
$594$	−178020.	+	308339.i	−0.504539	+	0.873888i
$595$	7455.36	+	12913.1i	0.0210589	+	0.0364750i
$596$	93584.7			0.263459
$597$			69334.3i			0.194536i
$598$	104289.	+	180633.i	0.291632	+	0.505121i
$599$	339188.	−	195830.i	0.945338	−	0.545791i	0.0537086	−	0.998557i	$-0.482896\pi$
$599$	339188.	−	195830.i	0.945338	−	0.545791i	0.891630	+	0.452765i	$0.149562\pi$
$600$	277770.			0.771582
$601$			100418.i			0.278011i	0.990292	+	0.139006i	$0.0443906\pi$
$601$			100418.i			0.278011i	−0.990292	+	0.139006i	$0.955609\pi$
$602$	93887.9	−	54206.2i	0.259070	−	0.149574i
$603$	63826.0	+	36850.0i	0.175535	+	0.101345i
$604$	3104.00	−	1792.10i	0.00850841	−	0.00491233i
$605$	−118832.	+	205823.i	−0.324656	+	0.562321i
$606$	126511.	−	219123.i	0.344494	−	0.596681i
$607$			238074.i			0.646152i	0.946373	+	0.323076i	$0.104717\pi$
$607$			238074.i			0.646152i	−0.946373	+	0.323076i	$0.895283\pi$
$608$	−260281.	−	171773.i	−0.704102	−	0.464672i
$609$	−159772.			−0.430791
$610$	148454.	+	85709.8i	0.398962	+	0.230341i
$611$	−110779.	−	63958.3i	−0.296739	−	0.171322i
$612$	−1677.33	−	2905.23i	−0.00447834	−	0.00775671i
$613$	−16165.6	+	27999.6i	−0.0430201	+	0.0745129i	−0.886734	−	0.462281i	$-0.847031\pi$
$613$	−16165.6	+	27999.6i	−0.0430201	+	0.0745129i	0.843714	+	0.536794i	$0.180365\pi$
$614$	92116.7	+	159551.i	0.244344	+	0.423216i
$615$	−267165.			−0.706365
$616$			241475.i			0.636373i
$617$	−47281.9	−	81894.6i	−0.124201	−	0.215122i	0.797219	−	0.603690i	$-0.206303\pi$
$617$	−47281.9	−	81894.6i	−0.124201	−	0.215122i	−0.921420	+	0.388567i	$0.872970\pi$
$618$	−299938.	+	173169.i	−0.785333	+	0.453412i
$619$	351256.			0.916731			0.458366	−	0.888764i	$-0.348435\pi$
$619$	351256.			0.916731			0.458366	+	0.888764i	$0.348435\pi$
$620$		−	33354.4i		−	0.0867701i
$621$	442632.	−	255554.i	1.14778	−	0.662673i
$622$	234866.	+	135600.i	0.607072	+	0.350493i
$623$	−64074.5	+	36993.4i	−0.165086	+	0.0953122i
$624$	36212.6	−	62722.1i	0.0930016	−	0.161084i
$625$	−30755.7	+	53270.5i	−0.0787347	+	0.136372i
$626$			370502.i			0.945457i
$627$	36220.0	−	605576.i	0.0921326	−	1.54040i
$628$	−123014.			−0.311915
$629$	−79000.4	−	45610.9i	−0.199677	−	0.115284i
$630$	−5831.67	−	3366.92i	−0.0146930	−	0.00848303i
$631$	−40677.8	−	70456.0i	−0.102164	−	0.176954i	0.810412	−	0.585861i	$-0.199243\pi$
$631$	−40677.8	−	70456.0i	−0.102164	−	0.176954i	−0.912576	+	0.408907i	$0.865910\pi$
$632$	150317.	−	260357.i	0.376335	−	0.651832i
$633$	−256253.	−	443844.i	−0.639531	−	1.10770i
$634$	−548592.			−1.36481
$635$			12906.8i			0.0320090i
$636$	83640.6	+	144870.i	0.206777	+	0.358149i
$637$	−167216.	+	96542.2i	−0.412096	+	0.237924i
$638$	442065.			1.08604
$639$		−	61798.2i		−	0.151347i
$640$	−33502.8	+	19342.8i	−0.0817939	+	0.0472237i
$641$	212439.	+	122651.i	0.517032	+	0.298509i	0.735719	−	0.677286i	$-0.236844\pi$
$641$	212439.	+	122651.i	0.517032	+	0.298509i	−0.218688	+	0.975795i	$0.570178\pi$
$642$	−126292.	+	72914.8i	−0.306412	+	0.176907i
$643$	−44740.9	+	77493.5i	−0.108214	+	0.187432i	−0.915047	−	0.403348i	$-0.867846\pi$
$643$	−44740.9	+	77493.5i	−0.108214	+	0.187432i	0.806833	+	0.590780i	$0.201180\pi$
$644$	55324.6	−	95825.1i	0.133397	−	0.231051i
$645$			248252.i			0.596724i
$646$	47191.3	+	31143.9i	0.113083	+	0.0746290i
$647$	75843.0			0.181179			0.0905893	−	0.995888i	$-0.471125\pi$
$647$	75843.0			0.181179			0.0905893	+	0.995888i	$0.471125\pi$
$648$	−425174.	−	245475.i	−1.01255	−	0.584597i
$649$	−457832.	−	264329.i	−1.08697	−	0.627561i
$650$	60122.8	+	104136.i	0.142303	+	0.246475i
$651$	29747.3	−	51523.9i	0.0701917	−	0.121576i
$652$	−118866.	−	205882.i	−0.279616	−	0.484310i
$653$	42943.0			0.100709			0.0503543	−	0.998731i	$-0.483965\pi$
$653$	42943.0			0.100709			0.0503543	+	0.998731i	$0.483965\pi$
$654$			14972.6i			0.0350060i
$655$	19331.8	+	33483.6i	0.0450598	+	0.0780459i
$656$	139354.	−	80456.0i	0.323826	−	0.186961i
$657$	−70919.3			−0.164299
$658$		−	76873.9i		−	0.177553i
$659$	−692459.	+	399791.i	−1.59450	+	0.920582i	−0.601974	+	0.798516i	$0.705619\pi$
$659$	−692459.	+	399791.i	−1.59450	+	0.920582i	−0.992522	+	0.122066i	$0.961048\pi$
$660$	−152855.	−	88250.6i	−0.350906	−	0.202595i
$661$	363517.	−	209877.i	0.831997	−	0.480354i	−0.0225389	−	0.999746i	$-0.507175\pi$
$661$	363517.	−	209877.i	0.831997	−	0.480354i	0.854536	+	0.519392i	$0.173842\pi$
$662$	−184095.	+	318862.i	−0.420075	+	0.727591i
$663$	24412.6	−	42283.9i	0.0555376	−	0.0961940i
$664$		−	696488.i		−	1.57971i
$665$	−100008.	−	5981.56i	−0.226147	−	0.0135261i
$666$	41196.7			0.0928782
$667$	−549580.	−	317300.i	−1.23532	−	0.713212i
$668$	179659.	+	103726.i	0.402620	+	0.232453i
$669$	29534.8	+	51155.8i	0.0659906	+	0.114299i
$670$	−180701.	+	312983.i	−0.402541	+	0.697221i
$671$	373396.	+	646740.i	0.829324	+	1.43643i
$672$	−161837.			−0.358376
$673$		−	190516.i		−	0.420630i	−0.977634	−	0.210315i	$-0.932551\pi$
$673$		−	190516.i		−	0.420630i	0.977634	−	0.210315i	$-0.0674490\pi$
$674$	−145991.	−	252864.i	−0.321371	−	0.556632i
$675$	255179.	−	147328.i	0.560064	−	0.323353i
$676$	144899.			0.317082
$677$		−	309546.i		−	0.675379i	−0.941258	−	0.337690i	$-0.890355\pi$
$677$		−	309546.i		−	0.675379i	0.941258	−	0.337690i	$-0.109645\pi$
$678$	146855.	−	84786.8i	0.319469	−	0.184446i
$679$	16754.4	+	9673.17i	0.0363404	+	0.0209812i
$680$	44631.5	−	25768.0i	0.0965214	−	0.0557267i
$681$	−46286.7	+	80170.9i	−0.0998072	+	0.172871i
$682$	−82306.3	+	142559.i	−0.176956	+	0.306496i
$683$			696373.i			1.49280i	0.665500	+	0.746398i	$0.268219\pi$
$683$			696373.i			1.49280i	−0.665500	+	0.746398i	$0.731781\pi$
$684$	22500.2	+	1345.75i	0.0480921	+	0.00287643i
$685$	−53958.8			−0.114996
$686$	−220647.	−	127390.i	−0.468866	−	0.270700i
$687$	787590.	+	454715.i	1.66873	+	0.963443i
$688$	−74760.3	−	129489.i	−0.157941	−	0.273562i
$689$	−113433.	+	196472.i	−0.238947	+	0.413869i
$690$	−143517.	−	248578.i	−0.301443	−	0.522114i
$691$	−138751.			−0.290590			−0.145295	−	0.989388i	$-0.546413\pi$
$691$	−138751.			−0.290590			−0.145295	+	0.989388i	$0.546413\pi$
$692$			46363.0i			0.0968188i
$693$	−14668.0	−	25405.7i	−0.0305425	−	0.0529012i
$694$	266981.	−	154141.i	0.554321	−	0.320037i
$695$	519629.			1.07578
$696$			552221.i			1.13997i
$697$	93944.9	−	54239.1i	0.193378	−	0.111647i
$698$	−398513.	−	230081.i	−0.817959	−	0.472249i
$699$	−137680.	+	79489.4i	−0.281784	+	0.162688i
$700$	31894.9	−	55243.5i	0.0650916	−	0.112742i
$701$	−323619.	+	560524.i	−0.658564	+	1.14067i	0.322424	+	0.946595i	$0.395502\pi$
$701$	−323619.	+	560524.i	−0.658564	+	1.14067i	−0.980988	+	0.194070i	$0.937831\pi$
$702$		−	192535.i		−	0.390693i
$703$	548163.	−	274226.i	1.10917	−	0.554879i
$704$	674511.			1.36096
$705$	152448.	+	88016.2i	0.306722	+	0.177086i
$706$	105117.	+	60689.2i	0.210893	+	0.121759i
$707$	−91019.0	−	157650.i	−0.182093	−	0.315394i
$708$	105398.	−	182555.i	0.210265	−	0.364190i
$709$	303581.	+	525817.i	0.603923	+	1.04603i	0.992221	+	0.124492i	$0.0397300\pi$
$709$	303581.	+	525817.i	0.603923	+	1.04603i	−0.388297	+	0.921534i	$0.626937\pi$
$710$	303039.			0.601148
$711$			36523.1i			0.0722484i
$712$	127861.	+	221461.i	0.252218	+	0.436855i
$713$	204648.	−	118154.i	0.402559	−	0.232417i
$714$	29342.5			0.0575573
$715$		−	239371.i		−	0.468230i
$716$	245851.	−	141942.i	0.479564	−	0.276876i
$717$	593366.	+	342580.i	1.15421	+	0.666382i
$718$	572127.	−	330318.i	1.10980	−	0.640741i
$719$	−20070.2	+	34762.5i	−0.0388233	+	0.0672440i	−0.884784	−	0.466001i	$-0.845694\pi$
$719$	−20070.2	+	34762.5i	−0.0388233	+	0.0672440i	0.845961	+	0.533245i	$0.179028\pi$
$720$	−4643.60	+	8042.95i	−0.00895756	+	0.0155149i
$721$			249175.i			0.479330i
$722$	−349307.	+	149384.i	−0.670090	+	0.286569i
$723$	−104803.			−0.200492
$724$	189007.	+	109123.i	0.360579	+	0.208180i
$725$	−316835.	−	182925.i	−0.602778	−	0.348014i
$726$	233847.	+	405035.i	0.443669	+	0.768457i
$727$	227686.	−	394364.i	0.430792	−	0.746154i	−0.566149	−	0.824303i	$-0.691567\pi$
$727$	227686.	−	394364.i	0.430792	−	0.746154i	0.996942	+	0.0781484i	$0.0249008\pi$
$728$	−65291.2	−	113088.i	−0.123195	−	0.213379i
$729$	−466186.			−0.877211
$730$		−	347766.i		−	0.652591i
$731$	−50399.4	−	87294.4i	−0.0943172	−	0.163362i
$732$	−257880.	+	148887.i	−0.481278	+	0.277866i
$733$	−727011.			−1.35311			−0.676555	−	0.736392i	$-0.736528\pi$
$733$	−727011.			−1.35311			−0.676555	+	0.736392i	$0.736528\pi$
$734$		−	309139.i		−	0.573802i
$735$	230114.	−	132857.i	0.425960	−	0.245928i
$736$	−556683.	−	321401.i	−1.02767	−	0.593323i
$737$	−1.36351e6	+	787224.i	−2.51029	+	1.44932i
$738$	−24494.9	+	42426.5i	−0.0449742	+	0.0778976i
$739$	38258.8	−	66266.2i	0.0700555	−	0.121340i	−0.828870	−	0.559441i	$-0.811016\pi$
$739$	38258.8	−	66266.2i	0.0700555	−	0.121340i	0.898925	+	0.438102i	$0.144349\pi$
$740$		−	178326.i		−	0.325650i
$741$	146776.	+	293397.i	0.267312	+	0.534341i
$742$	−136340.			−0.247637
$743$	496683.	+	286760.i	0.899709	+	0.519447i	0.877106	−	0.480297i	$-0.159471\pi$
$743$	496683.	+	286760.i	0.899709	+	0.519447i	0.0226030	+	0.999745i	$0.492805\pi$
$744$	−178082.	−	102816.i	−0.321718	−	0.185744i
$745$	−87330.2	−	151260.i	−0.157345	−	0.272529i
$746$	−189573.	+	328350.i	−0.340643	+	0.590010i
$747$	42306.9	+	73277.8i	0.0758177	+	0.131320i
$748$	71665.6			0.128088
$749$			104918.i			0.187020i
$750$	−203283.	−	352096.i	−0.361391	−	0.625948i
$751$	−885468.	+	511225.i	−1.56998	+	0.906426i	−0.573805	+	0.818992i	$0.694533\pi$
$751$	−885468.	+	511225.i	−1.56998	+	0.906426i	−0.996170	+	0.0874337i	$0.972133\pi$
$752$	−106023.			−0.187485
$753$		−	553398.i		−	0.975995i
$754$	−207028.	+	119527.i	−0.364154	+	0.210245i
$755$	−5793.11	−	3344.65i	−0.0101629	−	0.00586756i
$756$	−88454.9	+	51069.5i	−0.154767	+	0.0893548i
$757$	366529.	−	634847.i	0.639612	−	1.10784i	−0.345906	−	0.938269i	$-0.612429\pi$
$757$	366529.	−	634847.i	0.639612	−	1.10784i	0.985518	−	0.169571i	$-0.0542382\pi$
$758$	95690.3	−	165740.i	0.166544	−	0.288463i
$759$		−	1.25047e6i		−	2.17064i
$760$	−20674.1	+	345658.i	−0.0357931	+	0.598439i
$761$	−250969.			−0.433362			−0.216681	−	0.976242i	$-0.569523\pi$
$761$	−250969.			−0.433362			−0.216681	+	0.976242i	$0.569523\pi$
$762$	21996.2	+	12699.5i	0.0378825	+	0.0218714i
$763$	9328.97	+	5386.08i	0.0160245	+	0.00925175i
$764$	−115967.	−	200861.i	−0.198677	−	0.344120i
$765$	−3130.47	+	5422.13i	−0.00534917	+	0.00926503i
$766$	−129590.	−	224457.i	−0.220859	−	0.382539i
$767$	285882.			0.485956
$768$			649765.i			1.10163i
$769$	−79807.9	−	138231.i	−0.134956	−	0.233751i	0.790624	−	0.612301i	$-0.209756\pi$
$769$	−79807.9	−	138231.i	−0.134956	−	0.233751i	−0.925581	+	0.378550i	$0.876423\pi$
$770$	124582.	−	71927.2i	0.210123	−	0.121314i
$771$	−396372.			−0.666799
$772$		−	257810.i		−	0.432579i
$773$	−154342.	+	89109.5i	−0.258301	+	0.149130i	−0.623559	−	0.781776i	$-0.714314\pi$
$773$	−154342.	+	89109.5i	−0.258301	+	0.149130i	0.365258	+	0.930906i	$0.380981\pi$
$774$	39423.0	+	22760.9i	0.0658064	+	0.0379933i
$775$	117981.	−	68116.1i	0.196430	−	0.113409i
$776$	33433.4	−	57908.4i	0.0555210	−	0.0961653i
$777$	159041.	−	275467.i	0.263431	−	0.456276i
$778$		−	513440.i		−	0.848262i
$779$	−43517.0	+	727577.i	−0.0717106	+	1.19896i
$780$	95446.4			0.156881
$781$	1.14332e6	+	660096.i	1.87441	+	1.08219i
$782$	100931.	+	58272.8i	0.165049	+	0.0952911i
$783$	292896.	+	507310.i	0.477738	+	0.827466i
$784$	−80018.7	+	138596.i	−0.130185	+	0.225486i
$785$	114793.	+	198827.i	0.186284	+	0.322653i
$786$	76085.1			0.123156
$787$		−	445302.i		−	0.718961i	−0.933153	−	0.359481i	$-0.882954\pi$
$787$		−	445302.i		−	0.718961i	0.933153	−	0.359481i	$-0.117046\pi$
$788$	151783.	+	262896.i	0.244439	+	0.423381i
$789$	382718.	−	220962.i	0.614787	−	0.354947i
$790$	−179097.			−0.286969
$791$		−	122001.i		−	0.194989i
$792$	−87810.0	+	50697.1i	−0.139989	+	0.0808226i
$793$	−349737.	−	201921.i	−0.556155	−	0.321096i
$794$	554434.	−	320102.i	0.879445	−	0.507748i
$795$	156101.	−	270375.i	0.246986	−	0.427792i
$796$	27516.7	−	47660.3i	0.0434280	−	0.0752195i
$797$			1.00882e6i			1.58818i	0.607802	+	0.794089i	$0.292052\pi$
$797$			1.00882e6i			1.58818i	−0.607802	+	0.794089i	$0.707948\pi$
$798$	−108596.	+	164551.i	−0.170532	+	0.258402i
$799$	−71475.2			−0.111960
$800$	−320930.	−	185289.i	−0.501453	−	0.289514i
$801$	−26904.6	−	15533.3i	−0.0419335	−	0.0242103i
$802$	323225.	+	559842.i	0.502524	+	0.870396i
$803$	757523.	−	1.31207e6i	1.17480	−	2.03482i
$804$	−313897.	−	543685.i	−0.485595	−	0.841076i
$805$	−206509.			−0.318674
$806$		−	89017.4i		−	0.137027i
$807$	−173560.	−	300614.i	−0.266503	−	0.461596i
$808$	−544885.	+	314590.i	−0.834608	+	0.481861i
$809$	−720314.			−1.10059			−0.550294	−	0.834971i	$-0.685484\pi$
$809$	−720314.			−1.10059			−0.550294	+	0.834971i	$0.685484\pi$
$810$			292474.i			0.445776i
$811$	17483.1	−	10093.9i	0.0265814	−	0.0153468i	−0.486650	−	0.873597i	$-0.661781\pi$
$811$	17483.1	−	10093.9i	0.0265814	−	0.0153468i	0.513232	+	0.858250i	$0.328448\pi$
$812$	109827.	+	63408.7i	0.166570	+	0.0961694i
$813$	−641091.	+	370134.i	−0.969926	+	0.559987i
$814$	−440041.	+	762174.i	−0.664117	+	1.15028i
$815$	−221844.	+	384245.i	−0.333989	+	0.578486i
$816$		−	40468.7i		−	0.0607769i
$817$	676071.	+	40436.3i	1.01286	+	0.0605797i
$818$	841827.			1.25810
$819$	13738.6	+	7932.01i	0.0204822	+	0.0118254i
$820$	183649.	+	106030.i	0.273125	+	0.157689i
$821$	−187608.	−	324946.i	−0.278333	−	0.482087i	0.692638	−	0.721286i	$-0.256449\pi$
$821$	−187608.	−	324946.i	−0.278333	−	0.482087i	−0.970971	+	0.239199i	$0.923115\pi$
$822$	−53092.1	+	91958.3i	−0.0785754	+	0.136097i
$823$	237091.	+	410654.i	0.350039	+	0.606285i	0.986256	−	0.165225i	$-0.0528352\pi$
$823$	237091.	+	410654.i	0.350039	+	0.606285i	−0.636217	+	0.771510i	$0.719502\pi$
$824$	861227.			1.26842
$825$		−	720898.i		−	1.05917i
$826$	85903.3	+	148789.i	0.125907	+	0.218077i
$827$	152726.	−	88176.7i	0.223307	−	0.128927i	−0.384173	−	0.923261i	$-0.625513\pi$
$827$	152726.	−	88176.7i	0.223307	−	0.128927i	0.607481	+	0.794334i	$0.292180\pi$
$828$	46461.0			0.0677686
$829$			1.17657e6i			1.71202i	0.516958	+	0.856011i	$0.327064\pi$
$829$			1.17657e6i			1.71202i	−0.516958	+	0.856011i	$0.672936\pi$
$830$	−359331.	+	207460.i	−0.521601	+	0.301146i
$831$	−868579.	−	501474.i	−1.25779	−	0.726184i
$832$	−315887.	+	182377.i	−0.456336	+	0.263466i
$833$	−53944.4	+	93434.4i	−0.0777421	+	0.134653i
$834$	511283.	−	885567.i	0.735070	−	1.27318i
$835$		−	387175.i		−	0.555309i
$836$	−265233.	+	401898.i	−0.379502	+	0.575047i
$837$	−218132.			−0.311365
$838$	454603.	+	262465.i	0.647357	+	0.373752i
$839$	−90561.0	−	52285.4i	−0.128652	−	0.0742774i	0.434293	−	0.900772i	$-0.356998\pi$
$839$	−90561.0	−	52285.4i	−0.128652	−	0.0742774i	−0.562945	+	0.826494i	$0.690332\pi$
$840$	89850.5	+	155626.i	0.127339	+	0.220558i
$841$	10024.0	−	17362.1i	0.0141726	−	0.0245477i
$842$	335074.	+	580365.i	0.472625	+	0.818610i
$843$	241633.			0.340018
$844$			406797.i			0.571074i
$845$	−135215.	−	234199.i	−0.189370	−	0.327999i
$846$	27954.4	−	16139.5i	0.0390579	−	0.0225501i
$847$	336486.			0.469030
$848$			188038.i			0.261489i
$849$	97562.8	−	56327.9i	0.135353	−	0.0781463i
$850$	58187.4	+	33594.5i	0.0805362	+	0.0464976i
$851$	1.09413e6	−	631696.i	1.51081	−	0.872266i
$852$	−263206.	+	455886.i	−0.362590	+	0.628025i
$853$	485750.	−	841343.i	0.667597	−	1.15631i	−0.310977	−	0.950417i	$-0.600656\pi$
$853$	485750.	−	841343.i	0.667597	−	1.15631i	0.978574	−	0.205894i	$-0.0660104\pi$
$854$		−	242696.i		−	0.332773i
$855$	−18821.3	−	37622.7i	−0.0257464	−	0.0514657i
$856$	362629.			0.494898
$857$	−700870.	−	404647.i	−0.954280	−	0.550954i	−0.0598720	−	0.998206i	$-0.519069\pi$
$857$	−700870.	−	404647.i	−0.954280	−	0.550954i	−0.894408	+	0.447252i	$0.852403\pi$
$858$	−407943.	−	235526.i	−0.554147	−	0.319937i
$859$	345904.	+	599124.i	0.468781	+	0.811952i	0.999363	−	0.0356812i	$-0.0113601\pi$
$859$	345904.	+	599124.i	0.468781	+	0.811952i	−0.530582	+	0.847633i	$0.678027\pi$
$860$	98523.8	−	170648.i	0.133212	−	0.230730i
$861$	189127.	+	327577.i	0.255121	+	0.441883i
$862$	−295148.			−0.397214
$863$		−	239801.i		−	0.321980i	−0.986956	−	0.160990i	$-0.948531\pi$
$863$		−	239801.i		−	0.321980i	0.986956	−	0.160990i	$-0.0514687\pi$
$864$	296681.	+	513867.i	0.397432	+	0.688372i
$865$	74936.3	−	43264.5i	0.100152	−	0.0578228i
$866$	−621497.			−0.828712
$867$			762083.i			1.01383i
$868$	−40896.6	+	23611.6i	−0.0542810	+	0.0313391i
$869$	−675708.	−	390120.i	−0.894787	−	0.516605i
$870$	284901.	−	164488.i	0.376405	−	0.217318i
$871$	425707.	−	737346.i	0.561144	−	0.971929i
$872$	18615.9	−	32243.8i	0.0244823	−	0.0424046i
$873$			8123.43i			0.0106589i
$874$	−700336.	+	350353.i	−0.916820	+	0.458652i
$875$	−292507.			−0.382049
$876$	523172.	+	302054.i	0.681768	+	0.393619i
$877$	129985.	+	75046.6i	0.169002	+	0.0975735i	0.582115	−	0.813106i	$-0.302225\pi$
$877$	129985.	+	75046.6i	0.169002	+	0.0975735i	−0.413113	+	0.910680i	$0.635559\pi$
$878$	−492142.	−	852415.i	−0.638413	−	1.10576i
$879$	370028.	−	640907.i	0.478913	−	0.829502i
$880$	−99200.9	−	171821.i	−0.128100	−	0.221876i
$881$	472353.			0.608576			0.304288	−	0.952580i	$-0.401581\pi$
$881$	472353.			0.608576			0.304288	+	0.952580i	$0.401581\pi$
$882$		−	48723.6i		−	0.0626329i
$883$	−397034.	−	687684.i	−0.509221	−	0.881997i	−0.999943	−	0.0106809i	$-0.996600\pi$
$883$	−397034.	−	687684.i	−0.509221	−	0.881997i	0.490722	−	0.871316i	$-0.336733\pi$
$884$	−33562.4	+	19377.3i	−0.0429486	+	0.0247964i
$885$	−393417.			−0.502304
$886$			601527.i			0.766280i
$887$	−1.00255e6	+	578822.i	−1.27426	+	0.735695i	−0.975787	−	0.218722i	$-0.929811\pi$
$887$	−1.00255e6	+	578822.i	−1.27426	+	0.735695i	−0.298475	+	0.954418i	$0.596478\pi$
$888$	−952097.	−	549694.i	−1.20741	−	0.697100i
$889$	15825.3	−	9136.77i	0.0200240	−	0.0115608i
$890$	76170.6	−	131931.i	0.0961629	−	0.166559i
$891$	−637083.	+	1.10346e6i	−0.802492	+	1.38996i
$892$		−	46885.9i		−	0.0589268i
$893$	264528.	−	400830.i	0.331718	−	0.502641i
$894$	−343710.			−0.430048
$895$	−458841.	−	264912.i	−0.572817	−	0.330716i
$896$	47433.4	+	27385.7i	0.0590837	+	0.0341120i
$897$	338107.	+	585618.i	0.420212	+	0.727829i
$898$	313386.	−	542801.i	0.388622	−	0.673113i
$899$	135419.	+	234552.i	0.167556	+	0.290215i
$900$	26785.0			0.0330679
$901$			126765.i			0.156153i
$902$	−523284.	−	906355.i	−0.643168	−	1.11400i
$903$	304387.	−	175738.i	0.373294	−	0.215521i
$904$	−421673.			−0.515987
$905$		−	407321.i		−	0.497324i
$906$	−11400.1	+	6581.87i	−0.0138884	+	0.00801849i
$907$	984582.	+	568449.i	1.19684	+	0.690998i	0.959850	−	0.280513i	$-0.0905047\pi$
$907$	984582.	+	568449.i	1.19684	+	0.690998i	0.236993	+	0.971511i	$0.423838\pi$
$908$	63634.8	−	36739.6i	0.0771833	−	0.0445618i
$909$	38218.4	−	66196.2i	0.0462535	−	0.0801135i
$910$	−38896.0	+	67369.9i	−0.0469702	+	0.0813548i
$911$			455546.i			0.548903i	0.961601	+	0.274452i	$0.0884963\pi$
$911$			455546.i			0.548903i	−0.961601	+	0.274452i	$0.911504\pi$
$912$	226947.	+	149773.i	0.272856	+	0.180072i
$913$	−1.80760e6			−2.16851
$914$	177387.	+	102415.i	0.212339	+	0.122594i
$915$	481291.	+	277873.i	0.574865	+	0.331898i
$916$	−360926.	−	625142.i	−0.430157	−	0.745054i
$917$	27370.0	−	47406.3i	0.0325489	−	0.0563764i
$918$	−53790.9	−	93168.6i	−0.0638298	−	0.110556i
$919$	−1.09770e6			−1.29972			−0.649862	−	0.760052i	$-0.725173\pi$
$919$	−1.09770e6			−1.29972			−0.649862	+	0.760052i	$0.725173\pi$
$920$			713757.i			0.843285i
$921$	298645.	+	517268.i	0.352076	+	0.609813i
$922$	932046.	−	538117.i	1.09642	−	0.633016i
$923$	−713919.			−0.838003
$924$			249891.i			0.292689i
$925$	630770.	−	364175.i	0.737204	−	0.425625i
$926$	286684.	+	165517.i	0.334335	+	0.193028i
$927$	−90610.0	+	52313.7i	−0.105443	+	0.0608774i
$928$	368364.	−	638026.i	0.427742	−	0.740871i
$929$	857478.	−	1.48520e6i	0.993554	−	1.72089i	0.398607	−	0.917122i	$-0.369494\pi$
$929$	857478.	−	1.48520e6i	0.993554	−	1.72089i	0.594947	−	0.803765i	$-0.297173\pi$
$930$			122501.i			0.141636i
$931$	−324330.	−	648316.i	−0.374186	−	0.747976i
$932$	126188.			0.145273
$933$	761443.	+	439620.i	0.874731	+	0.505026i
$934$	245933.	+	141990.i	0.281919	+	0.162766i
$935$	−66876.0	−	115833.i	−0.0764975	−	0.132497i
$936$	27415.4	−	47484.9i	0.0312927	−	0.0542006i
$937$	57770.1	+	100061.i	0.0657997	+	0.113969i	0.897048	−	0.441932i	$-0.145707\pi$
$937$	57770.1	+	100061.i	0.0657997	+	0.113969i	−0.831249	+	0.555901i	$0.812373\pi$
$938$	511673.			0.581550
$939$			1.20118e6i			1.36231i
$940$	−69862.0	−	121004.i	−0.0790652	−	0.136945i
$941$	1.16741e6	−	674004.i	1.31839	−	0.761173i	0.334921	−	0.942246i	$-0.391290\pi$
$941$	1.16741e6	−	674004.i	1.31839	−	0.761173i	0.983470	+	0.181073i	$0.0579571\pi$
$942$	451796.			0.509144
$943$			1.50239e6i			1.68950i
$944$	205207.	−	118476.i	0.230276	−	0.132950i
$945$	165086.	+	95312.7i	0.184862	+	0.106730i
$946$	−842192.	+	486240.i	−0.941085	+	0.543336i
$947$	−361524.	+	626178.i	−0.403123	+	0.698229i	−0.994101	−	0.108459i	$-0.965408\pi$
$947$	−361524.	+	626178.i	−0.403123	+	0.698229i	0.590978	+	0.806687i	$0.298742\pi$
$948$	155556.	−	269431.i	0.173089	−	0.299799i
$949$			819290.i			0.909715i
$950$	−403747.	+	201980.i	−0.447365	+	0.223801i
$951$	−1.77855e6			−1.96655
$952$	−63189.4	−	36482.4i	−0.0697221	−	0.0402541i
$953$	368933.	+	213004.i	0.406221	+	0.234532i	0.689165	−	0.724605i	$-0.257978\pi$
$953$	368933.	+	213004.i	0.406221	+	0.234532i	−0.282944	+	0.959136i	$0.591311\pi$
$954$	−28624.2	−	49578.6i	−0.0314512	−	0.0544750i
$955$	−216434.	+	374874.i	−0.237311	+	0.411035i
$956$	−271919.	−	470978.i	−0.297526	−	0.515329i
$957$	1.43319e6			1.56487
$958$			706511.i			0.769817i
$959$	38197.5	+	66160.1i	0.0415334	+	0.0719380i
$960$	434708.	−	250979.i	0.471688	−	0.272329i
$961$	822669.			0.890796
$962$		−	475922.i		−	0.514263i
$963$	−38152.4	+	22027.3i	−0.0411405	+	0.0237525i
$964$	72041.6	+	41593.2i	0.0775228	+	0.0447578i
$965$	−416697.	+	240580.i	−0.447472	+	0.258348i
$966$	−203192.	+	351938.i	−0.217747	+	0.377148i
$967$	−156372.	+	270844.i	−0.167226	+	0.289645i	−0.937444	−	0.348137i	$-0.886814\pi$
$967$	−156372.	+	270844.i	−0.167226	+	0.289645i	0.770217	+	0.637782i	$0.220148\pi$
$968$		−	1.16300e6i		−	1.24116i
$969$	152995.	+	100969.i	0.162941	+	0.107533i
$970$	−39834.7			−0.0423368
$971$	72576.9	+	41902.3i	0.0769769	+	0.0444426i	0.537994	−	0.842948i	$-0.319182\pi$
$971$	72576.9	+	41902.3i	0.0769769	+	0.0444426i	−0.461018	+	0.887391i	$0.652515\pi$
$972$	−78537.1	−	45343.4i	−0.0831271	−	0.0479934i
$973$	−367846.	−	637128.i	−0.388544	−	0.672978i
$974$	−37089.8	+	64241.4i	−0.0390964	+	0.0677169i
$975$	194920.	+	337611.i	0.205044	+	0.355146i
$976$	−334723.			−0.351387
$977$		−	439858.i		−	0.460812i	−0.973095	−	0.230406i	$-0.925995\pi$
$977$		−	439858.i		−	0.460812i	0.973095	−	0.230406i	$-0.0740054\pi$
$978$	436561.	+	756146.i	0.456423	+	0.790548i
$979$	574761.	−	331838.i	0.599683	−	0.346227i
$980$	−210907.			−0.219603
$981$			4523.17i			0.00470008i
$982$	459155.	−	265093.i	0.476142	−	0.274901i
$983$	720503.	+	415982.i	0.745639	+	0.430495i	0.824116	−	0.566421i	$-0.191672\pi$
$983$	720503.	+	415982.i	0.745639	+	0.430495i	−0.0784772	+	0.996916i	$0.525006\pi$
$984$	1.13221e6	−	653679.i	1.16932	−	0.675110i
$985$	283278.	−	490652.i	0.291971	−	0.505709i
$986$	−66787.7	+	115680.i	−0.0686978	+	0.118988i
$987$		−	249227.i		−	0.255836i
$988$	15546.7	−	259931.i	0.0159267	−	0.266284i
$989$	1.39603e6			1.42726
$990$	52311.2	+	30201.9i	0.0533733	+	0.0308151i
$991$	298704.	+	172457.i	0.304154	+	0.175603i	0.644307	−	0.764767i	$-0.277146\pi$
$991$	298704.	+	172457.i	0.304154	+	0.175603i	−0.340154	+	0.940370i	$0.610479\pi$
$992$	137169.	+	237583.i	0.139390	+	0.241430i
$993$	−596842.	+	1.03376e6i	−0.605286	+	1.04839i
$994$	−214522.	−	371562.i	−0.217119	−	0.376061i
$995$	−102711.			−0.103746
$996$		−	720761.i		−	0.726562i
$997$	−740608.	−	1.28277e6i	−0.745071	−	1.29050i	−0.950161	−	0.311758i	$-0.899082\pi$
$997$	−740608.	−	1.28277e6i	−0.745071	−	1.29050i	0.205090	−	0.978743i	$-0.434251\pi$
$998$	−535452.	+	309143.i	−0.537600	+	0.310383i
$999$	−1.16622e6			−1.16856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.5.d.a.8.4	✓	10
3.2	odd	2		171.5.p.a.46.2		10
4.3	odd	2		304.5.r.a.65.2		10
19.12	odd	6	inner	19.5.d.a.12.4	yes	10
57.50	even	6		171.5.p.a.145.2		10
76.31	even	6		304.5.r.a.145.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.4	✓	10	1.1	even	1	trivial
19.5.d.a.12.4	yes	10	19.12	odd	6	inner
171.5.p.a.46.2		10	3.2	odd	2
171.5.p.a.145.2		10	57.50	even	6
304.5.r.a.65.2		10	4.3	odd	2
304.5.r.a.145.2		10	76.31	even	6

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	19.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.52462 + 1.45759i) q^{2} +(8.18489 + 4.72555i) q^{3} +(-3.75086 - 6.49668i) q^{4} +(-7.00036 + 12.1250i) q^{5} +(13.7758 + 23.8604i) q^{6} +19.8223 q^{7} -68.5118i q^{8} +(4.16163 + 7.20815i) q^{9} +O(q^{10})\)	\(q+(2.52462 + 1.45759i) q^{2} +(8.18489 + 4.72555i) q^{3} +(-3.75086 - 6.49668i) q^{4} +(-7.00036 + 12.1250i) q^{5} +(13.7758 + 23.8604i) q^{6} +19.8223 q^{7} -68.5118i q^{8} +(4.16163 + 7.20815i) q^{9} +(-35.3465 + 20.4073i) q^{10} -177.809 q^{11} -70.8995i q^{12} +(83.2716 - 48.0769i) q^{13} +(50.0437 + 28.8927i) q^{14} +(-114.594 + 66.1610i) q^{15} +(39.8484 - 69.0195i) q^{16} +(26.8637 - 46.5293i) q^{17} +24.2638i q^{18} +(161.512 + 322.854i) q^{19} +105.029 q^{20} +(162.243 + 93.6710i) q^{21} +(-448.901 - 259.173i) q^{22} +(372.053 + 644.415i) q^{23} +(323.756 - 560.761i) q^{24} +(214.490 + 371.508i) q^{25} +280.306 q^{26} -686.875i q^{27} +(-74.3505 - 128.779i) q^{28} +(-738.578 + 426.418i) q^{29} -385.743 q^{30} -317.572i q^{31} +(-748.123 + 431.929i) q^{32} +(-1455.35 - 840.247i) q^{33} +(135.641 - 78.3125i) q^{34} +(-138.763 + 240.344i) q^{35} +(31.2194 - 54.0735i) q^{36} -1697.87i q^{37} +(-62.8314 + 1050.50i) q^{38} +908.759 q^{39} +(830.703 + 479.607i) q^{40} +(1748.55 + 1009.53i) q^{41} +(273.068 + 472.968i) q^{42} +(938.059 - 1624.77i) q^{43} +(666.938 + 1155.17i) q^{44} -116.532 q^{45} +2169.20i q^{46} +(-665.166 - 1152.10i) q^{47} +(652.310 - 376.611i) q^{48} -2008.08 q^{49} +1250.55i q^{50} +(439.753 - 253.891i) q^{51} +(-624.680 - 360.659i) q^{52} +(-2043.31 + 1179.71i) q^{53} +(1001.18 - 1734.10i) q^{54} +(1244.73 - 2155.93i) q^{55} -1358.06i q^{56} +(-203.701 + 3405.76i) q^{57} -2486.17 q^{58} +(2574.85 + 1486.59i) q^{59} +(859.654 + 496.321i) q^{60} +(-2099.98 - 3637.27i) q^{61} +(462.890 - 801.750i) q^{62} +(82.4929 + 142.882i) q^{63} -3793.45 q^{64} +1346.22i q^{65} +(-2449.47 - 4242.61i) q^{66} +(7668.40 - 4427.35i) q^{67} -403.047 q^{68} +7032.62i q^{69} +(-700.647 + 404.519i) q^{70} +(-6430.03 - 3712.38i) q^{71} +(493.843 - 285.121i) q^{72} +(-4260.31 + 7379.07i) q^{73} +(2474.79 - 4286.47i) q^{74} +4054.33i q^{75} +(1491.67 - 2260.27i) q^{76} -3524.58 q^{77} +(2294.27 + 1324.60i) q^{78} +(3800.18 + 2194.04i) q^{79} +(557.906 + 966.322i) q^{80} +(3582.95 - 6205.86i) q^{81} +(2942.95 + 5097.34i) q^{82} +10166.0 q^{83} -1405.39i q^{84} +(376.111 + 651.443i) q^{85} +(4736.49 - 2734.61i) q^{86} -8060.24 q^{87} +12182.0i q^{88} +(-3232.45 + 1866.26i) q^{89} +(-294.198 - 169.855i) q^{90} +(1650.63 - 952.993i) q^{91} +(2791.04 - 4834.22i) q^{92} +(1500.70 - 2599.29i) q^{93} -3878.16i q^{94} +(-5045.24 - 301.760i) q^{95} -8164.40 q^{96} +(845.233 + 487.996i) q^{97} +(-5069.64 - 2926.96i) q^{98} +(-739.977 - 1281.68i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9	\( 10 q - 3 q^{2} + 9 q^{3} + 29 q^{4} + 8 q^{5} - 35 q^{6} - 24 q^{7} - 58 q^{9} + 144 q^{10} + 50 q^{11} - 624 q^{13} - 474 q^{14} + 504 q^{15} + 285 q^{16} - 292 q^{17} + 305 q^{19} - 652 q^{20} + 1158 q^{21} + 1629 q^{22} + 98 q^{23} + 505 q^{24} - 681 q^{25} + 1524 q^{26} - 1472 q^{28} + 2598 q^{29} - 6656 q^{30} - 2745 q^{32} - 3441 q^{33} + 486 q^{34} + 694 q^{35} + 3402 q^{36} - 342 q^{38} - 5552 q^{39} + 8784 q^{40} - 1407 q^{41} + 292 q^{42} + 5424 q^{43} + 4151 q^{44} + 9572 q^{45} - 2416 q^{47} + 11481 q^{48} - 17826 q^{49} - 3342 q^{51} - 19962 q^{52} + 1122 q^{53} - 1039 q^{54} + 11424 q^{55} - 7906 q^{57} - 20236 q^{58} + 15387 q^{59} + 8886 q^{60} + 860 q^{61} + 21636 q^{62} + 5318 q^{63} + 19710 q^{64} - 13921 q^{66} + 14763 q^{67} - 48844 q^{68} - 20334 q^{70} - 27264 q^{71} + 354 q^{72} + 1561 q^{73} + 17094 q^{74} + 1955 q^{76} - 18392 q^{77} + 40266 q^{78} + 24750 q^{79} - 2002 q^{80} + 14311 q^{81} + 14479 q^{82} + 6002 q^{83} - 14944 q^{85} + 59946 q^{86} - 31996 q^{87} - 22566 q^{89} - 60630 q^{90} + 8724 q^{91} + 9572 q^{92} + 12476 q^{93} - 7312 q^{95} - 41850 q^{96} + 46287 q^{97} + 25515 q^{98} - 2048 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 9 * q^3 + 29 * q^4 + 8 * q^5 - 35 * q^6 - 24 * q^7 - 58 * q^9 + 144 * q^10 + 50 * q^11 - 624 * q^13 - 474 * q^14 + 504 * q^15 + 285 * q^16 - 292 * q^17 + 305 * q^19 - 652 * q^20 + 1158 * q^21 + 1629 * q^22 + 98 * q^23 + 505 * q^24 - 681 * q^25 + 1524 * q^26 - 1472 * q^28 + 2598 * q^29 - 6656 * q^30 - 2745 * q^32 - 3441 * q^33 + 486 * q^34 + 694 * q^35 + 3402 * q^36 - 342 * q^38 - 5552 * q^39 + 8784 * q^40 - 1407 * q^41 + 292 * q^42 + 5424 * q^43 + 4151 * q^44 + 9572 * q^45 - 2416 * q^47 + 11481 * q^48 - 17826 * q^49 - 3342 * q^51 - 19962 * q^52 + 1122 * q^53 - 1039 * q^54 + 11424 * q^55 - 7906 * q^57 - 20236 * q^58 + 15387 * q^59 + 8886 * q^60 + 860 * q^61 + 21636 * q^62 + 5318 * q^63 + 19710 * q^64 - 13921 * q^66 + 14763 * q^67 - 48844 * q^68 - 20334 * q^70 - 27264 * q^71 + 354 * q^72 + 1561 * q^73 + 17094 * q^74 + 1955 * q^76 - 18392 * q^77 + 40266 * q^78 + 24750 * q^79 - 2002 * q^80 + 14311 * q^81 + 14479 * q^82 + 6002 * q^83 - 14944 * q^85 + 59946 * q^86 - 31996 * q^87 - 22566 * q^89 - 60630 * q^90 + 8724 * q^91 + 9572 * q^92 + 12476 * q^93 - 7312 * q^95 - 41850 * q^96 + 46287 * q^97 + 25515 * q^98 - 2048 * q^99

Introduction

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