LMFDB - Embedded newform 19.5.d.a.12.4

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			12.4
Root			$2.91518i$ of defining polynomial
Character	$\chi$	$=$	19.12
Dual form			19.5.d.a.8.4

$q$-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 $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	−0.150044	−	0.988679i	$-0.547942\pi$
$2$	2.52462	−	1.45759i	0.631155	−	0.364398i	0.781199	+	0.624282i	$0.214608\pi$
$3$	8.18489	−	4.72555i	0.909432	−	0.525061i	0.0291839	−	0.999574i	$-0.490709\pi$
$3$	8.18489	−	4.72555i	0.909432	−	0.525061i	0.880248	+	0.474513i	$0.157376\pi$
$4$	−3.75086	+	6.49668i	−0.234429	+	0.406042i
$5$	−7.00036	−	12.1250i	−0.280014	−	0.484999i	0.691374	−	0.722497i	$-0.257006\pi$
$5$	−7.00036	−	12.1250i	−0.280014	−	0.484999i	−0.971388	+	0.237498i	$0.923673\pi$
$6$	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	0.725707	−	0.688004i	$-0.241513\pi$
$13$	83.2716	+	48.0769i	0.492732	+	0.284479i	−0.232975	+	0.972483i	$0.574846\pi$
$14$	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	0.908753	−	0.417335i	$-0.137036\pi$
$17$	26.8637	+	46.5293i	0.0929539	+	0.161001i	−0.815799	+	0.578336i	$0.803702\pi$
$18$		−	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	−0.263983	−	0.964527i	$-0.585036\pi$
$23$	372.053	−	644.415i	0.703314	−	1.21818i	0.967297	−	0.253648i	$-0.0816305\pi$
$24$	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	−0.00814454	−	0.999967i	$-0.502593\pi$
$29$	−738.578	−	426.418i	−0.878213	−	0.507037i	−0.870069	+	0.492930i	$0.835926\pi$
$30$	−385.743			−0.428603
$31$			317.572i			0.330460i	0.986255	+	0.165230i	$0.0528367\pi$
$31$			317.572i			0.330460i	−0.986255	+	0.165230i	$0.947163\pi$
$32$	−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	$0.212913\pi$
$37$			1697.87i			1.24022i	−0.784514	+	0.620111i	$0.787087\pi$
$38$	−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	0.120299	−	0.992738i	$-0.461615\pi$
$41$	1748.55	−	1009.53i	1.04018	−	0.600551i	0.919885	+	0.392187i	$0.128281\pi$
$42$	273.068	−	472.968i	0.154801	−	0.268122i
$43$	938.059	+	1624.77i	0.507333	+	0.878727i	0.999964	+	0.00848857i	$0.00270203\pi$
$43$	938.059	+	1624.77i	0.507333	+	0.878727i	−0.492631	+	0.870238i	$0.663965\pi$
$44$	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	−0.976389	−	0.216019i	$-0.930693\pi$
$47$	−665.166	+	1152.10i	−0.301116	+	0.521549i	0.675273	+	0.737568i	$0.264026\pi$
$48$	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	0.0900597	−	0.995936i	$-0.471294\pi$
$53$	−2043.31	−	1179.71i	−0.727417	−	0.419974i	−0.817476	+	0.575962i	$0.804628\pi$
$54$	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	−0.0822690	−	0.996610i	$-0.526217\pi$
$59$	2574.85	−	1486.59i	0.739686	−	0.427058i	0.821955	+	0.569552i	$0.192883\pi$
$60$	859.654	−	496.321i	0.238793	−	0.137867i
$61$	−2099.98	+	3637.27i	−0.564358	+	0.977497i	0.432751	+	0.901514i	$0.357543\pi$
$61$	−2099.98	+	3637.27i	−0.564358	+	0.977497i	−0.997109	+	0.0759838i	$0.975790\pi$
$62$	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	0.936713	+	0.350099i	$0.113852\pi$
$67$	7668.40	+	4427.35i	1.70826	+	0.986266i	0.771551	+	0.636168i	$0.219481\pi$
$68$	−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	−0.976026	−	0.217653i	$-0.930160\pi$
$71$	−6430.03	+	3712.38i	−1.27555	+	0.736437i	−0.299520	+	0.954090i	$0.596827\pi$
$72$	493.843	+	285.121i	0.0952630	+	0.0550001i
$73$	−4260.31	−	7379.07i	−0.799457	−	1.38470i	−0.919970	−	0.391989i	$-0.871787\pi$
$73$	−4260.31	−	7379.07i	−0.799457	−	1.38470i	0.120512	−	0.992712i	$-0.461546\pi$
$74$	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	−0.163631	−	0.986522i	$-0.552321\pi$
$79$	3800.18	−	2194.04i	0.608906	−	0.351552i	0.772537	+	0.634970i	$0.218987\pi$
$80$	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	0.281881	−	0.959449i	$-0.409042\pi$
$89$	−3232.45	−	1866.26i	−0.408087	−	0.235609i	−0.689967	+	0.723841i	$0.742375\pi$
$90$	−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	−0.454411	−	0.890792i	$-0.650150\pi$
$97$	845.233	−	487.996i	0.0898324	−	0.0518648i	0.544243	+	0.838927i	$0.316817\pi$
$98$	−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	−0.998394	−	0.0566592i	$-0.981955\pi$
$101$	−4591.76	+	7953.16i	−0.450128	+	0.779645i	0.548265	+	0.836305i	$0.315288\pi$
$102$	1480.28			0.142280
$103$		−	12570.5i		−	1.18489i	−0.805611	−	0.592445i	$-0.798163\pi$
$103$		−	12570.5i		−	1.18489i	0.805611	−	0.592445i	$-0.201837\pi$
$104$	−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	$-0.925750\pi$
$107$		−	5292.95i		−	0.462307i	0.972917	−	0.231153i	$-0.0742499\pi$
$108$	−4462.40	−	2576.37i	−0.382579	−	0.220882i
$109$	470.631	−	271.719i	0.0396121	−	0.0228700i	−0.480063	−	0.877234i	$-0.659386\pi$
$109$	470.631	−	271.719i	0.0396121	−	0.0228700i	0.519675	+	0.854364i	$0.326053\pi$
$110$	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	$0.0774765\pi$
$113$			6154.75i			0.482007i	−0.970524	+	0.241003i	$0.922523\pi$
$114$	−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	0.524545	−	0.851383i	$-0.324235\pi$
$127$	798.363	+	460.935i	0.0494986	+	0.0285780i	−0.475046	+	0.879961i	$0.657569\pi$
$128$	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	0.903448	−	0.428699i	$-0.141028\pi$
$131$	1380.77	+	2391.57i	0.0804599	+	0.139361i	−0.822988	+	0.568059i	$0.807694\pi$
$132$		−	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	−0.810114	−	0.586272i	$-0.800595\pi$
$137$	1927.00	−	3337.67i	0.102669	−	0.177829i	0.912784	+	0.408443i	$0.133928\pi$
$138$	−10250.7	−	17754.7i	−0.538263	−	0.932299i
$139$	−18557.2	+	32142.1i	−0.960469	+	1.66358i	−0.239145	+	0.970984i	$0.576867\pi$
$139$	−18557.2	+	32142.1i	−0.960469	+	1.66358i	−0.721324	+	0.692598i	$0.756466\pi$
$140$	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	0.690663	−	0.723177i	$-0.257319\pi$
$149$	−6237.55	−	10803.8i	−0.280958	−	0.486634i	−0.971621	+	0.236543i	$0.923986\pi$
$150$	−5909.56	−	10235.7i	−0.262647	−	0.454918i
$151$		−	477.784i		−	0.0209545i	−0.999945	−	0.0104772i	$-0.996665\pi$
$151$		−	477.784i		−	0.0209545i	0.999945	−	0.0104772i	$-0.00333507\pi$
$152$	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	0.983027	−	0.183459i	$-0.0587296\pi$
$157$	8199.07	+	14201.2i	0.332633	+	0.576137i	−0.650394	+	0.759597i	$0.725396\pi$
$158$	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	0.00485911	−	0.999988i	$-0.498453\pi$
$167$	−23949.0	−	13827.0i	−0.858727	−	0.495786i	−0.863586	+	0.504202i	$0.831787\pi$
$168$	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	−0.586745	−	0.809772i	$-0.699591\pi$
$173$	−5352.32	+	3090.16i	−0.178834	+	0.103250i	0.407911	+	0.913022i	$0.366257\pi$
$174$	−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	$-0.798917\pi$
$179$		−	37842.6i		−	1.18107i	0.807012	−	0.590535i	$-0.201083\pi$
$180$	437.093	−	757.068i	0.0134905	−	0.0233663i
$181$	−25195.1	−	14546.4i	−0.769059	−	0.444016i	0.0634798	−	0.997983i	$-0.479780\pi$
$181$	−25195.1	−	14546.4i	−0.769059	−	0.444016i	−0.832539	+	0.553967i	$0.813114\pi$
$182$	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	−0.0441110	−	0.999027i	$-0.514046\pi$
$193$	29762.5	−	17183.4i	0.799016	−	0.461312i	0.843127	+	0.537715i	$0.180712\pi$
$194$	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	−0.815990	−	0.578066i	$-0.803807\pi$
$199$	3668.05	−	6353.25i	0.0926253	−	0.160432i	0.908615	+	0.417635i	$0.137141\pi$
$200$	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	−0.923998	−	0.382398i	$-0.875098\pi$
$211$	−46962.1	+	27113.6i	−1.05483	+	0.609007i	−0.130833	+	0.991404i	$0.541765\pi$
$212$	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	−0.444590	−	0.895734i	$-0.646651\pi$
$223$	5412.68	−	3125.01i	0.108844	−	0.0628409i	0.553434	+	0.832893i	$0.313317\pi$
$224$	−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	$-0.969701\pi$
$227$		−	9794.98i		−	0.190087i	0.995473	−	0.0950434i	$-0.0302990\pi$
$228$	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	0.778108	−	0.628130i	$-0.216180\pi$
$233$	−8410.60	−	14567.6i	−0.154923	−	0.268334i	−0.933031	+	0.359796i	$0.882846\pi$
$234$	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	0.415045	−	0.909801i	$-0.363766\pi$
$241$	−9603.35	−	5544.50i	−0.165344	−	0.0954615i	−0.580389	+	0.814340i	$0.697099\pi$
$242$	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	−0.999188	−	0.0402861i	$-0.987173\pi$
$251$	−29276.9	+	50709.1i	−0.464705	+	0.804893i	0.534483	+	0.845179i	$0.320506\pi$
$252$	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	0.199180	−	0.979963i	$-0.436172\pi$
$257$	−36320.5	−	20969.6i	−0.549902	−	0.317486i	−0.749083	+	0.662477i	$0.769505\pi$
$258$	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	0.984058	−	0.177850i	$-0.0569143\pi$
$263$	23379.5	+	40494.5i	0.338006	+	0.585443i	−0.646052	+	0.763294i	$0.723581\pi$
$264$	−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	−0.703413	−	0.710781i	$-0.748341\pi$
$269$	−31807.3	+	18364.0i	−0.439565	+	0.253783i	0.263848	+	0.964564i	$0.415008\pi$
$270$	14017.3	−	24278.6i	0.192281	−	0.333040i
$271$	−39163.1	−	67832.5i	−0.533259	−	0.923632i	−0.999245	−	0.0388401i	$-0.987634\pi$
$271$	−39163.1	−	67832.5i	−0.533259	−	0.923632i	0.465986	−	0.884792i	$-0.345700\pi$
$272$	−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	0.633609	−	0.773654i	$-0.281573\pi$
$281$	22141.4	+	12783.4i	0.280410	+	0.161895i	−0.353199	+	0.935548i	$0.614906\pi$
$282$	18326.4	+	31742.3i	0.230452	+	0.399154i
$283$	5959.93	+	10322.9i	0.0744164	+	0.128893i	0.900832	−	0.434167i	$-0.142957\pi$
$283$	5959.93	+	10322.9i	0.0744164	+	0.128893i	−0.826416	+	0.563060i	$0.809624\pi$
$284$		−	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	$0.150738\pi$
$293$			78303.7i			0.912110i	−0.889952	+	0.456055i	$0.849262\pi$
$294$	−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	−0.180708	−	0.983537i	$-0.557839\pi$
$307$	54731.0	−	31599.0i	0.580707	−	0.335271i	0.761414	+	0.648266i	$0.224505\pi$
$308$	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	−0.334803	−	0.942288i	$-0.608670\pi$
$313$	63547.0	−	110067.i	0.648644	−	1.12348i	0.983447	−	0.181196i	$-0.0579968\pi$
$314$	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	−0.986440	−	0.164124i	$-0.947520\pi$
$317$	−162973.	−	94092.3i	−1.62180	−	0.936344i	−0.635356	−	0.772220i	$-0.719146\pi$
$318$	−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	$-0.804459\pi$
$331$		−	126301.i		−	1.15279i	0.817171	−	0.576396i	$-0.195541\pi$
$332$	−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	−0.830647	−	0.556799i	$-0.812029\pi$
$337$	−86740.5	+	50079.7i	−0.763769	+	0.440962i	0.0668782	+	0.997761i	$0.478696\pi$
$338$	−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	0.997623	−	0.0689122i	$-0.0219528\pi$
$347$	52875.4	+	91582.9i	0.439132	+	0.760598i	−0.558491	+	0.829511i	$0.688620\pi$
$348$	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	0.852244	+	0.523145i	$0.175241\pi$
$359$	113309.	+	196258.i	0.879179	+	1.52278i	0.0269346	+	0.999637i	$0.491425\pi$
$360$		−	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	−0.992930	−	0.118704i	$-0.962126\pi$
$367$	−53022.3	+	91837.3i	−0.393664	+	0.681847i	0.599265	+	0.800550i	$0.295459\pi$
$368$	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	$-0.845189\pi$
$373$		−	130059.i		−	0.934810i	0.884043	−	0.467405i	$-0.154811\pi$
$374$	−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	$0.0733886\pi$
$379$			65649.6i			0.457040i	−0.973539	+	0.228520i	$0.926611\pi$
$380$	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	−0.738934	−	0.673778i	$-0.764670\pi$
$383$	−76995.9	+	44453.6i	−0.524892	+	0.303047i	0.214042	+	0.976824i	$0.431337\pi$
$384$	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	0.413285	+	0.910602i	$0.364381\pi$
$389$	−88063.1	+	152530.i	−0.581962	+	1.00799i	−0.995247	+	0.0973858i	$0.968952\pi$
$390$	−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	0.969606	+	0.244671i	$0.0786799\pi$
$397$	109805.	+	190188.i	0.696694	+	1.20671i	−0.272912	+	0.962039i	$0.587987\pi$
$398$		−	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	0.235017	−	0.971991i	$-0.424485\pi$
$401$	192044.	−	110877.i	1.19429	−	0.689526i	0.959278	+	0.282465i	$0.0911521\pi$
$402$	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	0.999983	−	0.00574553i	$-0.00182887\pi$
$409$	250085.	+	144387.i	1.49500	+	0.863138i	0.495016	+	0.868884i	$0.335162\pi$
$410$	−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	0.181012	−	0.983481i	$-0.442063\pi$
$421$	199084.	−	114941.i	1.12324	−	0.648501i	0.942225	+	0.334980i	$0.108729\pi$
$422$	−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	0.245072	−	0.969505i	$-0.421189\pi$
$431$	−87680.8	−	50622.5i	−0.472008	−	0.272514i	−0.717080	+	0.696991i	$0.754522\pi$
$432$	−47407.7	+	27370.9i	−0.254028	+	0.146663i
$433$	−184631.	−	106597.i	−0.984756	−	0.568549i	−0.0810530	−	0.996710i	$-0.525828\pi$
$433$	−184631.	−	106597.i	−0.984756	−	0.568549i	−0.903703	+	0.428161i	$0.859162\pi$
$434$	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	−0.517453	+	0.855711i	$0.673120\pi$
$439$	−292406.	+	168820.i	−1.51725	+	0.875983i	−0.999795	+	0.0202720i	$0.993547\pi$
$440$	−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	−0.473835	−	0.880614i	$-0.657131\pi$
$443$	103171.	−	178698.i	0.525717	−	0.910568i	0.999551	−	0.0299541i	$-0.00953610\pi$
$444$	−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	$0.179025\pi$
$449$			215003.i			1.06648i	−0.845965	+	0.533239i	$0.820975\pi$
$450$	−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	0.863449	+	0.504436i	$0.168300\pi$
$461$	184591.	+	319721.i	0.868579	+	1.50442i	0.00512983	+	0.999987i	$0.498367\pi$
$462$	−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	−0.471318	−	0.881963i	$-0.656222\pi$
$479$	121178.	−	209886.i	0.528144	−	0.914772i	0.999462	−	0.0328084i	$-0.0104451\pi$
$480$	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	$-0.982916\pi$
$487$		−	25446.0i		−	0.107290i	0.998560	−	0.0536452i	$-0.0170840\pi$
$488$	−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	0.990654	−	0.136402i	$-0.0435540\pi$
$491$	90935.5	+	157505.i	0.377199	+	0.653328i	−0.613455	+	0.789730i	$0.710221\pi$
$492$	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	0.570617	−	0.821216i	$-0.306704\pi$
$499$	−106046.	−	183677.i	−0.425885	−	0.737655i	−0.996503	+	0.0835609i	$0.973371\pi$
$500$	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	−0.812186	−	0.583399i	$-0.801723\pi$
$503$	25084.6	−	43447.7i	0.0991449	−	0.171724i	0.911331	+	0.411674i	$0.135056\pi$
$504$	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	0.800242	−	0.599678i	$-0.204705\pi$
$509$	176441.	+	101868.i	0.681026	+	0.393191i	−0.119215	+	0.992868i	$0.538038\pi$
$510$	−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	$0.179101\pi$
$521$			289594.i			1.06688i	−0.845839	+	0.533439i	$0.820899\pi$
$522$	−10346.5	+	17920.7i	−0.0379711	+	0.0657679i
$523$	−169469.	−	97843.1i	−0.619566	−	0.357706i	0.157134	−	0.987577i	$-0.449774\pi$
$523$	−169469.	−	97843.1i	−0.619566	−	0.357706i	−0.776700	+	0.629871i	$0.783108\pi$
$524$	−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	−0.556252	−	0.831014i	$-0.687761\pi$
$541$	129234.	−	223840.i	0.441553	−	0.764793i	0.997805	+	0.0662210i	$0.0210942\pi$
$542$	−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	0.622127	−	0.782916i	$-0.286269\pi$
$547$	76348.0	+	44079.5i	0.255166	+	0.147320i	−0.366961	+	0.930236i	$0.619602\pi$
$548$	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	0.239729	+	0.970840i	$0.422942\pi$
$557$	−223661.	+	387392.i	−0.720908	+	1.24865i	−0.960636	+	0.277809i	$0.910392\pi$
$558$	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	$0.181353\pi$
$563$			341953.i			1.07882i	−0.842043	+	0.539410i	$0.818647\pi$
$564$	−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	$0.0289216\pi$
$569$			58752.9i			0.181470i	−0.995875	+	0.0907349i	$0.971078\pi$
$570$	−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	0.828445	−	0.560071i	$-0.189226\pi$
$587$	−24400.0	−	42262.1i	−0.0708132	−	0.122652i	−0.899258	+	0.437419i	$0.855893\pi$
$588$		−	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	−0.0131462	+	0.999914i	$0.504185\pi$
$593$	−306822.	+	531431.i	−0.872524	+	1.51126i	−0.859377	+	0.511342i	$0.829149\pi$
$594$	−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	0.891630	−	0.452765i	$-0.149562\pi$
$599$	339188.	+	195830.i	0.945338	+	0.545791i	0.0537086	+	0.998557i	$0.482896\pi$
$600$	277770.			0.771582
$601$		−	100418.i		−	0.278011i	−0.990292	−	0.139006i	$-0.955609\pi$
$601$		−	100418.i		−	0.278011i	0.990292	−	0.139006i	$-0.0443906\pi$
$602$	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	$-0.895283\pi$
$607$		−	238074.i		−	0.646152i	0.946373	−	0.323076i	$-0.104717\pi$
$608$	−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	0.843714	−	0.536794i	$-0.180365\pi$
$613$	−16165.6	−	27999.6i	−0.0430201	−	0.0745129i	−0.886734	+	0.462281i	$0.847031\pi$
$614$	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	−0.921420	−	0.388567i	$-0.872970\pi$
$617$	−47281.9	+	81894.6i	−0.124201	+	0.215122i	0.797219	+	0.603690i	$0.206303\pi$
$618$	−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	−0.912576	−	0.408907i	$-0.865910\pi$
$631$	−40677.8	+	70456.0i	−0.102164	+	0.176954i	0.810412	+	0.585861i	$0.199243\pi$
$632$	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	−0.218688	−	0.975795i	$-0.570178\pi$
$641$	212439.	−	122651.i	0.517032	−	0.298509i	0.735719	+	0.677286i	$0.236844\pi$
$642$	−126292.	−	72914.8i	−0.306412	−	0.176907i
$643$	−44740.9	−	77493.5i	−0.108214	−	0.187432i	0.806833	−	0.590780i	$-0.201180\pi$
$643$	−44740.9	−	77493.5i	−0.108214	−	0.187432i	−0.915047	+	0.403348i	$0.867846\pi$
$644$	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	−0.992522	−	0.122066i	$-0.961048\pi$
$659$	−692459.	−	399791.i	−1.59450	−	0.920582i	−0.601974	−	0.798516i	$-0.705619\pi$
$660$	−152855.	+	88250.6i	−0.350906	+	0.202595i
$661$	363517.	+	209877.i	0.831997	+	0.480354i	0.854536	−	0.519392i	$-0.173842\pi$
$661$	363517.	+	209877.i	0.831997	+	0.480354i	−0.0225389	+	0.999746i	$0.507175\pi$
$662$	−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	$0.0674490\pi$
$673$			190516.i			0.420630i	−0.977634	+	0.210315i	$0.932551\pi$
$674$	−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	$0.109645\pi$
$677$			309546.i			0.675379i	−0.941258	+	0.337690i	$0.890355\pi$
$678$	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	$-0.731781\pi$
$683$		−	696373.i		−	1.49280i	0.665500	−	0.746398i	$-0.268219\pi$
$684$	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	−0.980988	−	0.194070i	$-0.937831\pi$
$701$	−323619.	−	560524.i	−0.658564	−	1.14067i	0.322424	−	0.946595i	$-0.395502\pi$
$702$			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	−0.388297	−	0.921534i	$-0.626937\pi$
$709$	303581.	−	525817.i	0.603923	−	1.04603i	0.992221	−	0.124492i	$-0.0397300\pi$
$710$	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	0.845961	−	0.533245i	$-0.179028\pi$
$719$	−20070.2	−	34762.5i	−0.0388233	−	0.0672440i	−0.884784	+	0.466001i	$0.845694\pi$
$720$	−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	0.996942	−	0.0781484i	$-0.0249008\pi$
$727$	227686.	+	394364.i	0.430792	+	0.746154i	−0.566149	+	0.824303i	$0.691567\pi$
$728$	−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	0.898925	−	0.438102i	$-0.144349\pi$
$739$	38258.8	+	66266.2i	0.0700555	+	0.121340i	−0.828870	+	0.559441i	$0.811016\pi$
$740$			178326.i			0.325650i
$741$	146776.	−	293397.i	0.267312	−	0.534341i
$742$	−136340.			−0.247637
$743$	496683.	−	286760.i	0.899709	−	0.519447i	0.0226030	−	0.999745i	$-0.492805\pi$
$743$	496683.	−	286760.i	0.899709	−	0.519447i	0.877106	+	0.480297i	$0.159471\pi$
$744$	−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	−0.996170	−	0.0874337i	$-0.972133\pi$
$751$	−885468.	−	511225.i	−1.56998	−	0.906426i	−0.573805	−	0.818992i	$-0.694533\pi$
$752$	−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	0.985518	+	0.169571i	$0.0542382\pi$
$757$	366529.	+	634847.i	0.639612	+	1.10784i	−0.345906	+	0.938269i	$0.612429\pi$
$758$	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	−0.925581	−	0.378550i	$-0.876423\pi$
$769$	−79807.9	+	138231.i	−0.134956	+	0.233751i	0.790624	+	0.612301i	$0.209756\pi$
$770$	124582.	+	71927.2i	0.210123	+	0.121314i
$771$	−396372.			−0.666799
$772$			257810.i			0.432579i
$773$	−154342.	−	89109.5i	−0.258301	−	0.149130i	0.365258	−	0.930906i	$-0.380981\pi$
$773$	−154342.	−	89109.5i	−0.258301	−	0.149130i	−0.623559	+	0.781776i	$0.714314\pi$
$774$	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	$0.117046\pi$
$787$			445302.i			0.718961i	−0.933153	+	0.359481i	$0.882954\pi$
$788$	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	$-0.707948\pi$
$797$		−	1.00882e6i		−	1.58818i	0.607802	−	0.794089i	$-0.292052\pi$
$798$	−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	0.513232	−	0.858250i	$-0.328448\pi$
$811$	17483.1	+	10093.9i	0.0265814	+	0.0153468i	−0.486650	+	0.873597i	$0.661781\pi$
$812$	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	−0.970971	−	0.239199i	$-0.923115\pi$
$821$	−187608.	+	324946.i	−0.278333	+	0.482087i	0.692638	+	0.721286i	$0.256449\pi$
$822$	−53092.1	−	91958.3i	−0.0785754	−	0.136097i
$823$	237091.	−	410654.i	0.350039	−	0.606285i	−0.636217	−	0.771510i	$-0.719502\pi$
$823$	237091.	−	410654.i	0.350039	−	0.606285i	0.986256	+	0.165225i	$0.0528352\pi$
$824$	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	0.607481	−	0.794334i	$-0.292180\pi$
$827$	152726.	+	88176.7i	0.223307	+	0.128927i	−0.384173	+	0.923261i	$0.625513\pi$
$828$	46461.0			0.0677686
$829$		−	1.17657e6i		−	1.71202i	−0.516958	−	0.856011i	$-0.672936\pi$
$829$		−	1.17657e6i		−	1.71202i	0.516958	−	0.856011i	$-0.327064\pi$
$830$	−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	−0.562945	−	0.826494i	$-0.690332\pi$
$839$	−90561.0	+	52285.4i	−0.128652	+	0.0742774i	0.434293	+	0.900772i	$0.356998\pi$
$840$	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	0.978574	+	0.205894i	$0.0660104\pi$
$853$	485750.	+	841343.i	0.667597	+	1.15631i	−0.310977	+	0.950417i	$0.600656\pi$
$854$			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	−0.894408	−	0.447252i	$-0.852403\pi$
$857$	−700870.	+	404647.i	−0.954280	+	0.550954i	−0.0598720	+	0.998206i	$0.519069\pi$
$858$	−407943.	+	235526.i	−0.554147	+	0.319937i
$859$	345904.	−	599124.i	0.468781	−	0.811952i	−0.530582	−	0.847633i	$-0.678027\pi$
$859$	345904.	−	599124.i	0.468781	−	0.811952i	0.999363	+	0.0356812i	$0.0113601\pi$
$860$	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	$0.0514687\pi$
$863$			239801.i			0.321980i	−0.986956	+	0.160990i	$0.948531\pi$
$864$	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	−0.413113	−	0.910680i	$-0.635559\pi$
$877$	129985.	−	75046.6i	0.169002	−	0.0975735i	0.582115	+	0.813106i	$0.302225\pi$
$878$	−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	0.490722	+	0.871316i	$0.336733\pi$
$883$	−397034.	+	687684.i	−0.509221	+	0.881997i	−0.999943	+	0.0106809i	$0.996600\pi$
$884$	−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	−0.298475	−	0.954418i	$-0.596478\pi$
$887$	−1.00255e6	−	578822.i	−1.27426	−	0.735695i	−0.975787	+	0.218722i	$0.929811\pi$
$888$	−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	0.236993	−	0.971511i	$-0.423838\pi$
$907$	984582.	−	568449.i	1.19684	−	0.690998i	0.959850	+	0.280513i	$0.0905047\pi$
$908$	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	$-0.911504\pi$
$911$		−	455546.i		−	0.548903i	0.961601	−	0.274452i	$-0.0884963\pi$
$912$	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	0.594947	+	0.803765i	$0.297173\pi$
$929$	857478.	+	1.48520e6i	0.993554	+	1.72089i	0.398607	+	0.917122i	$0.369494\pi$
$930$		−	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	−0.831249	−	0.555901i	$-0.812373\pi$
$937$	57770.1	−	100061.i	0.0657997	−	0.113969i	0.897048	+	0.441932i	$0.145707\pi$
$938$	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	0.983470	−	0.181073i	$-0.0579571\pi$
$941$	1.16741e6	+	674004.i	1.31839	+	0.761173i	0.334921	+	0.942246i	$0.391290\pi$
$942$	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	0.590978	−	0.806687i	$-0.298742\pi$
$947$	−361524.	−	626178.i	−0.403123	−	0.698229i	−0.994101	+	0.108459i	$0.965408\pi$
$948$	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	−0.282944	−	0.959136i	$-0.591311\pi$
$953$	368933.	−	213004.i	0.406221	−	0.234532i	0.689165	+	0.724605i	$0.257978\pi$
$954$	−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	0.770217	−	0.637782i	$-0.220148\pi$
$967$	−156372.	−	270844.i	−0.167226	−	0.289645i	−0.937444	+	0.348137i	$0.886814\pi$
$968$			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	−0.461018	−	0.887391i	$-0.652515\pi$
$971$	72576.9	−	41902.3i	0.0769769	−	0.0444426i	0.537994	+	0.842948i	$0.319182\pi$
$972$	−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	$0.0740054\pi$
$977$			439858.i			0.460812i	−0.973095	+	0.230406i	$0.925995\pi$
$978$	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	−0.0784772	−	0.996916i	$-0.525006\pi$
$983$	720503.	−	415982.i	0.745639	−	0.430495i	0.824116	+	0.566421i	$0.191672\pi$
$984$	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	−0.340154	−	0.940370i	$-0.610479\pi$
$991$	298704.	−	172457.i	0.304154	−	0.175603i	0.644307	+	0.764767i	$0.277146\pi$
$992$	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	0.205090	+	0.978743i	$0.434251\pi$
$997$	−740608.	+	1.28277e6i	−0.745071	+	1.29050i	−0.950161	+	0.311758i	$0.899082\pi$
$998$	−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.12.4	yes	10
3.2	odd	2		171.5.p.a.145.2		10
4.3	odd	2		304.5.r.a.145.2		10
19.8	odd	6	inner	19.5.d.a.8.4	✓	10
57.8	even	6		171.5.p.a.46.2		10
76.27	even	6		304.5.r.a.65.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.d.a.8.4	✓	10	19.8	odd	6	inner
19.5.d.a.12.4	yes	10	1.1	even	1	trivial
171.5.p.a.46.2		10	57.8	even	6
171.5.p.a.145.2		10	3.2	odd	2
304.5.r.a.65.2		10	76.27	even	6
304.5.r.a.145.2		10	4.3	odd	2

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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