LMFDB - Embedded newform 26.6.e.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,6,Mod(17,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("26.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	26.e (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:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2164x^{10} + 1693662x^{8} + 565924828x^{6} + 68470588153x^{4} + 28868949144x^{2} + 2602224144 $ x^12 + 2164x^10 + 1693662x^8 + 565924828x^6 + 68470588153x^4 + 28868949144*x^2 + 2602224144
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.4
Root			$18.8114i$ of defining polynomial
Character	$\chi$	$=$	26.17
Dual form			26.6.e.a.23.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.46410 + 2.00000i) q^{2} +(-9.40569 + 16.2911i) q^{3} +(8.00000 + 13.8564i) q^{4} -10.8158i q^{5} +(-65.1645 + 37.6228i) q^{6} +(-167.247 + 96.5603i) q^{7} +64.0000i q^{8} +(-55.4339 - 96.0144i) q^{9} +O(q^{10})$	\(q+(3.46410 + 2.00000i) q^{2} +(-9.40569 + 16.2911i) q^{3} +(8.00000 + 13.8564i) q^{4} -10.8158i q^{5} +(-65.1645 + 37.6228i) q^{6} +(-167.247 + 96.5603i) q^{7} +64.0000i q^{8} +(-55.4339 - 96.0144i) q^{9} +(21.6316 - 37.4670i) q^{10} +(587.730 + 339.326i) q^{11} -300.982 q^{12} +(238.160 - 560.868i) q^{13} -772.482 q^{14} +(176.201 + 101.730i) q^{15} +(-128.000 + 221.703i) q^{16} +(316.169 + 547.620i) q^{17} -443.471i q^{18} +(662.519 - 382.506i) q^{19} +(149.868 - 86.5263i) q^{20} -3632.86i q^{21} +(1357.30 + 2350.92i) q^{22} +(155.838 - 269.918i) q^{23} +(-1042.63 - 601.964i) q^{24} +3008.02 q^{25} +(1946.75 - 1466.58i) q^{26} -2485.59 q^{27} +(-2675.96 - 1544.96i) q^{28} +(212.404 - 367.894i) q^{29} +(406.920 + 704.806i) q^{30} +5902.48i q^{31} +(-886.810 + 512.000i) q^{32} +(-11056.0 + 6383.19i) q^{33} +2529.35i q^{34} +(1044.38 + 1808.91i) q^{35} +(886.943 - 1536.23i) q^{36} +(-6833.52 - 3945.33i) q^{37} +3060.05 q^{38} +(6897.12 + 9155.24i) q^{39} +692.211 q^{40} +(-3958.15 - 2285.24i) q^{41} +(7265.73 - 12584.6i) q^{42} +(4709.97 + 8157.90i) q^{43} +10858.4i q^{44} +(-1038.47 + 599.562i) q^{45} +(1079.67 - 623.350i) q^{46} -26277.1i q^{47} +(-2407.86 - 4170.53i) q^{48} +(10244.3 - 17743.6i) q^{49} +(10420.1 + 6016.04i) q^{50} -11895.1 q^{51} +(9676.89 - 1186.91i) q^{52} -18260.7 q^{53} +(-8610.33 - 4971.18i) q^{54} +(3670.08 - 6356.76i) q^{55} +(-6179.86 - 10703.8i) q^{56} +14390.9i q^{57} +(1471.58 - 849.616i) q^{58} +(36290.1 - 20952.1i) q^{59} +3255.36i q^{60} +(14996.5 + 25974.7i) q^{61} +(-11805.0 + 20446.8i) q^{62} +(18542.3 + 10705.4i) q^{63} -4096.00 q^{64} +(-6066.23 - 2575.88i) q^{65} -51065.5 q^{66} +(42205.3 + 24367.3i) q^{67} +(-5058.70 + 8761.92i) q^{68} +(2931.52 + 5077.54i) q^{69} +8355.01i q^{70} +(-55683.6 + 32148.9i) q^{71} +(6144.92 - 3547.77i) q^{72} -74592.6i q^{73} +(-15781.3 - 27334.1i) q^{74} +(-28292.5 + 49004.0i) q^{75} +(10600.3 + 6120.09i) q^{76} -131062. q^{77} +(5581.84 + 45508.9i) q^{78} +91288.3 q^{79} +(2397.89 + 1384.42i) q^{80} +(36849.1 - 63824.5i) q^{81} +(-9140.96 - 15832.6i) q^{82} -32739.2i q^{83} +(50338.4 - 29062.9i) q^{84} +(5922.94 - 3419.61i) q^{85} +37679.7i q^{86} +(3995.61 + 6920.60i) q^{87} +(-21716.9 + 37614.7i) q^{88} +(64096.5 + 37006.2i) q^{89} -4796.49 q^{90} +(14326.0 + 116800. i) q^{91} +4986.80 q^{92} +(-96158.0 - 55516.9i) q^{93} +(52554.1 - 91026.4i) q^{94} +(-4137.10 - 7165.67i) q^{95} -19262.8i q^{96} +(102131. - 58965.4i) q^{97} +(70974.4 - 40977.1i) q^{98} -75240.7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9}+O(q^{10}) $ 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9	\( 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9} - 368 q^{10} + 504 q^{11} + 3202 q^{13} - 2272 q^{14} + 2112 q^{15} - 1536 q^{16} - 1910 q^{17} - 6888 q^{19} + 1440 q^{20} + 2160 q^{22} + 5920 q^{23} - 4672 q^{25} - 2320 q^{26} - 2736 q^{27} + 5760 q^{28} + 7922 q^{29} - 11696 q^{30} - 18780 q^{33} + 16864 q^{35} + 11296 q^{36} - 882 q^{37} + 26496 q^{38} + 48304 q^{39} - 11776 q^{40} + 44346 q^{41} + 23648 q^{42} - 41920 q^{43} - 158850 q^{45} - 33408 q^{46} + 4682 q^{49} + 11040 q^{50} + 133264 q^{51} + 43520 q^{52} - 187812 q^{53} + 1296 q^{54} + 17472 q^{55} - 18176 q^{56} - 73488 q^{58} + 74832 q^{59} + 27934 q^{61} - 4336 q^{62} + 156528 q^{63} - 49152 q^{64} + 69646 q^{65} + 6336 q^{66} + 85104 q^{67} + 30560 q^{68} - 77348 q^{69} - 106320 q^{71} - 78336 q^{72} + 96208 q^{74} + 192080 q^{75} - 110208 q^{76} - 151944 q^{77} + 9392 q^{78} + 30464 q^{79} + 23040 q^{80} - 72310 q^{81} - 87040 q^{82} + 53952 q^{84} - 148986 q^{85} - 121936 q^{87} - 34560 q^{88} + 93108 q^{89} + 282016 q^{90} - 56776 q^{91} + 189440 q^{92} + 107616 q^{93} + 158256 q^{94} + 232560 q^{95} + 147156 q^{97} + 46752 q^{98}+O(q^{100}) \) 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9 - 368 * q^10 + 504 * q^11 + 3202 * q^13 - 2272 * q^14 + 2112 * q^15 - 1536 * q^16 - 1910 * q^17 - 6888 * q^19 + 1440 * q^20 + 2160 * q^22 + 5920 * q^23 - 4672 * q^25 - 2320 * q^26 - 2736 * q^27 + 5760 * q^28 + 7922 * q^29 - 11696 * q^30 - 18780 * q^33 + 16864 * q^35 + 11296 * q^36 - 882 * q^37 + 26496 * q^38 + 48304 * q^39 - 11776 * q^40 + 44346 * q^41 + 23648 * q^42 - 41920 * q^43 - 158850 * q^45 - 33408 * q^46 + 4682 * q^49 + 11040 * q^50 + 133264 * q^51 + 43520 * q^52 - 187812 * q^53 + 1296 * q^54 + 17472 * q^55 - 18176 * q^56 - 73488 * q^58 + 74832 * q^59 + 27934 * q^61 - 4336 * q^62 + 156528 * q^63 - 49152 * q^64 + 69646 * q^65 + 6336 * q^66 + 85104 * q^67 + 30560 * q^68 - 77348 * q^69 - 106320 * q^71 - 78336 * q^72 + 96208 * q^74 + 192080 * q^75 - 110208 * q^76 - 151944 * q^77 + 9392 * q^78 + 30464 * q^79 + 23040 * q^80 - 72310 * q^81 - 87040 * q^82 + 53952 * q^84 - 148986 * q^85 - 121936 * q^87 - 34560 * q^88 + 93108 * q^89 + 282016 * q^90 - 56776 * q^91 + 189440 * q^92 + 107616 * q^93 + 158256 * q^94 + 232560 * q^95 + 147156 * q^97 + 46752 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	3.46410	+	2.00000i	0.612372	+	0.353553i
$2$	3.46410	+	2.00000i	0.612372	+	0.353553i
$3$	−9.40569	+	16.2911i	−0.603375	+	1.04508i	0.388931	+	0.921267i	$0.372844\pi$
$3$	−9.40569	+	16.2911i	−0.603375	+	1.04508i	−0.992306	+	0.123809i	$0.960489\pi$
$4$	8.00000	+	13.8564i	0.250000	+	0.433013i
$5$		−	10.8158i		−	0.193479i	−0.995310	−	0.0967394i	$-0.969159\pi$
$5$		−	10.8158i		−	0.193479i	0.995310	−	0.0967394i	$-0.0308413\pi$
$6$	−65.1645	+	37.6228i	−0.738981	+	0.426651i
$7$	−167.247	+	96.5603i	−1.29007	+	0.744824i	−0.978667	−	0.205454i	$-0.934133\pi$
$7$	−167.247	+	96.5603i	−1.29007	+	0.744824i	−0.311405	+	0.950277i	$0.600800\pi$
$8$			64.0000i			0.353553i
$9$	−55.4339	−	96.0144i	−0.228123	−	0.395121i
$10$	21.6316	−	37.4670i	0.0684051	−	0.118481i
$11$	587.730	+	339.326i	1.46452	+	0.845542i	0.999215	−	0.0396070i	$-0.0126106\pi$
$11$	587.730	+	339.326i	1.46452	+	0.845542i	0.465307	+	0.885149i	$0.345944\pi$
$12$	−300.982			−0.603375
$13$	238.160	−	560.868i	0.390850	−	0.920455i
$13$	238.160	−	560.868i	0.390850	−	0.920455i
$14$	−772.482			−1.05334
$15$	176.201	+	101.730i	0.202200	+	0.116740i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	316.169	+	547.620i	0.265336	+	0.459576i	0.967652	−	0.252290i	$-0.0811837\pi$
$17$	316.169	+	547.620i	0.265336	+	0.459576i	−0.702315	+	0.711866i	$0.747850\pi$
$18$		−	443.471i		−	0.322615i
$19$	662.519	−	382.506i	0.421031	−	0.243083i	−0.274487	−	0.961591i	$-0.588508\pi$
$19$	662.519	−	382.506i	0.421031	−	0.243083i	0.695519	+	0.718508i	$0.255175\pi$
$20$	149.868	−	86.5263i	0.0837788	−	0.0483697i
$21$		−	3632.86i		−	1.79763i
$22$	1357.30	+	2350.92i	0.597889	+	1.03557i
$23$	155.838	−	269.918i	0.0614260	−	0.106393i	−0.833677	−	0.552252i	$-0.813769\pi$
$23$	155.838	−	269.918i	0.0614260	−	0.106393i	0.895103	+	0.445859i	$0.147102\pi$
$24$	−1042.63	−	601.964i	−0.369490	−	0.213325i
$25$	3008.02			0.962566
$26$	1946.75	−	1466.58i	0.564775	−	0.425475i
$27$	−2485.59			−0.656175
$28$	−2675.96	−	1544.96i	−0.645036	−	0.372412i
$29$	212.404	−	367.894i	0.0468994	−	0.0812322i	−0.841623	−	0.540066i	$-0.818399\pi$
$29$	212.404	−	367.894i	0.0468994	−	0.0812322i	0.888522	+	0.458834i	$0.151733\pi$
$30$	406.920	+	704.806i	0.0825478	+	0.142977i
$31$			5902.48i			1.10314i	0.834129	+	0.551569i	$0.185971\pi$
$31$			5902.48i			1.10314i	−0.834129	+	0.551569i	$0.814029\pi$
$32$	−886.810	+	512.000i	−0.153093	+	0.0883883i
$33$	−11056.0	+	6383.19i	−1.76731	+	1.02036i
$34$			2529.35i			0.375242i
$35$	1044.38	+	1808.91i	0.144108	+	0.249602i
$36$	886.943	−	1536.23i	0.114062	−	0.197560i
$37$	−6833.52	−	3945.33i	−0.820616	−	0.473783i	0.0300128	−	0.999550i	$-0.490445\pi$
$37$	−6833.52	−	3945.33i	−0.820616	−	0.473783i	−0.850629	+	0.525767i	$0.823779\pi$
$38$	3060.05			0.343771
$39$	6897.12	+	9155.24i	0.726116	+	0.963847i
$40$	692.211			0.0684051
$41$	−3958.15	−	2285.24i	−0.367733	−	0.212311i	0.304735	−	0.952437i	$-0.401432\pi$
$41$	−3958.15	−	2285.24i	−0.367733	−	0.212311i	−0.672468	+	0.740126i	$0.734766\pi$
$42$	7265.73	−	12584.6i	0.635559	−	1.10082i
$43$	4709.97	+	8157.90i	0.388460	+	0.672833i	0.992243	−	0.124316i	$-0.0396737\pi$
$43$	4709.97	+	8157.90i	0.388460	+	0.672833i	−0.603782	+	0.797149i	$0.706340\pi$
$44$			10858.4i			0.845542i
$45$	−1038.47	+	599.562i	−0.0764475	+	0.0441370i
$46$	1079.67	−	623.350i	0.0752312	−	0.0434348i
$47$		−	26277.1i		−	1.73513i	−0.497323	−	0.867565i	$-0.665684\pi$
$47$		−	26277.1i		−	1.73513i	0.497323	−	0.867565i	$-0.334316\pi$
$48$	−2407.86	−	4170.53i	−0.150844	−	0.261269i
$49$	10244.3	−	17743.6i	0.609524	−	1.05573i
$50$	10420.1	+	6016.04i	0.589449	+	0.340318i
$51$	−11895.1			−0.640389
$52$	9676.89	−	1186.91i	0.496281	−	0.0608707i
$53$	−18260.7			−0.892950			−0.446475	−	0.894796i	$-0.647321\pi$
$53$	−18260.7			−0.892950			−0.446475	+	0.894796i	$0.647321\pi$
$54$	−8610.33	−	4971.18i	−0.401823	−	0.231993i
$55$	3670.08	−	6356.76i	0.163594	−	0.283354i
$56$	−6179.86	−	10703.8i	−0.263335	−	0.456109i
$57$			14390.9i			0.586680i
$58$	1471.58	−	849.616i	0.0574398	−	0.0331629i
$59$	36290.1	−	20952.1i	1.35724	−	0.783605i	0.367992	−	0.929829i	$-0.380045\pi$
$59$	36290.1	−	20952.1i	1.35724	−	0.783605i	0.989251	+	0.146224i	$0.0467121\pi$
$60$			3255.36i			0.116740i
$61$	14996.5	+	25974.7i	0.516019	+	0.893771i	0.999827	+	0.0185970i	$0.00591996\pi$
$61$	14996.5	+	25974.7i	0.516019	+	0.893771i	−0.483808	+	0.875174i	$0.660747\pi$
$62$	−11805.0	+	20446.8i	−0.390018	+	0.675532i
$63$	18542.3	+	10705.4i	0.588591	+	0.339823i
$64$	−4096.00			−0.125000
$65$	−6066.23	−	2575.88i	−0.178088	−	0.0756211i
$66$	−51065.5			−1.44300
$67$	42205.3	+	24367.3i	1.14863	+	0.663162i	0.948553	−	0.316618i	$-0.102547\pi$
$67$	42205.3	+	24367.3i	1.14863	+	0.663162i	0.200077	+	0.979780i	$0.435881\pi$
$68$	−5058.70	+	8761.92i	−0.132668	+	0.229788i
$69$	2931.52	+	5077.54i	0.0741259	+	0.128390i
$70$			8355.01i			0.203799i
$71$	−55683.6	+	32148.9i	−1.31094	+	0.756869i	−0.982251	−	0.187570i	$-0.939939\pi$
$71$	−55683.6	+	32148.9i	−1.31094	+	0.756869i	−0.328685	+	0.944440i	$0.606605\pi$
$72$	6144.92	−	3547.77i	0.139696	−	0.0806537i
$73$		−	74592.6i		−	1.63828i	−0.573592	−	0.819141i	$-0.694450\pi$
$73$		−	74592.6i		−	1.63828i	0.573592	−	0.819141i	$-0.305550\pi$
$74$	−15781.3	−	27334.1i	−0.335015	−	0.580263i
$75$	−28292.5	+	49004.0i	−0.580788	+	1.00595i
$76$	10600.3	+	6120.09i	0.210516	+	0.121541i
$77$	−131062.			−2.51912
$78$	5581.84	+	45508.9i	0.103882	+	0.846954i
$79$	91288.3			1.64569			0.822843	−	0.568268i	$-0.192386\pi$
$79$	91288.3			1.64569			0.822843	+	0.568268i	$0.192386\pi$
$80$	2397.89	+	1384.42i	0.0418894	+	0.0241848i
$81$	36849.1	−	63824.5i	0.624043	−	1.08087i
$82$	−9140.96	−	15832.6i	−0.150126	−	0.260027i
$83$		−	32739.2i		−	0.521642i	−0.965387	−	0.260821i	$-0.916007\pi$
$83$		−	32739.2i		−	0.521642i	0.965387	−	0.260821i	$-0.0839932\pi$
$84$	50338.4	−	29062.9i	0.778398	−	0.449408i
$85$	5922.94	−	3419.61i	0.0889181	−	0.0513369i
$86$			37679.7i			0.549366i
$87$	3995.61	+	6920.60i	0.0565959	+	0.0980270i
$88$	−21716.9	+	37614.7i	−0.298944	+	0.517787i
$89$	64096.5	+	37006.2i	0.857748	+	0.495221i	0.863257	−	0.504764i	$-0.168420\pi$
$89$	64096.5	+	37006.2i	0.857748	+	0.495221i	−0.00550968	+	0.999985i	$0.501754\pi$
$90$	−4796.49			−0.0624191
$91$	14326.0	+	116800.i	0.181352	+	1.47857i
$92$	4986.80			0.0614260
$93$	−96158.0	−	55516.9i	−1.15286	−	0.665606i
$94$	52554.1	−	91026.4i	0.613461	−	1.06255i
$95$	−4137.10	−	7165.67i	−0.0470313	−	0.0814606i
$96$		−	19262.8i		−	0.213325i
$97$	102131.	−	58965.4i	1.10212	−	0.636309i	0.165343	−	0.986236i	$-0.447127\pi$
$97$	102131.	−	58965.4i	1.10212	−	0.636309i	0.936777	+	0.349927i	$0.113794\pi$
$98$	70974.4	−	40977.1i	0.746512	−	0.430999i
$99$		−	75240.7i		−	0.771551i
$100$	24064.1	+	41680.3i	0.240641	+	0.416803i
$101$	−15232.2	+	26383.0i	−0.148580	+	0.257348i	−0.930703	−	0.365776i	$-0.880804\pi$
$101$	−15232.2	+	26383.0i	−0.148580	+	0.257348i	0.782123	+	0.623124i	$0.214137\pi$
$102$	−41205.9	−	23790.3i	−0.392157	−	0.226412i
$103$	−114942.			−1.06754			−0.533770	−	0.845629i	$-0.679225\pi$
$103$	−114942.			−1.06754			−0.533770	+	0.845629i	$0.679225\pi$
$104$	35895.6	+	15242.2i	0.325430	+	0.138186i
$105$	−39292.3			−0.347804
$106$	−63256.8	−	36521.3i	−0.546818	−	0.315705i
$107$	−49933.2	+	86486.9i	−0.421629	+	0.730282i	−0.996099	−	0.0882433i	$-0.971875\pi$
$107$	−49933.2	+	86486.9i	−0.421629	+	0.730282i	0.574470	+	0.818525i	$0.305208\pi$
$108$	−19884.7	−	34441.3i	−0.164044	−	0.284132i
$109$			55466.9i			0.447165i	0.974685	+	0.223583i	$0.0717752\pi$
$109$			55466.9i			0.447165i	−0.974685	+	0.223583i	$0.928225\pi$
$110$	25427.1	−	14680.3i	0.200361	−	0.115679i
$111$	128548.	−	74217.2i	0.990279	−	0.571738i
$112$		−	49438.9i		−	0.372412i
$113$	−7989.18	−	13837.7i	−0.0588581	−	0.101945i	0.835095	−	0.550106i	$-0.185413\pi$
$113$	−7989.18	−	13837.7i	−0.0588581	−	0.101945i	−0.893953	+	0.448161i	$0.852079\pi$
$114$	−28781.8	+	49851.6i	−0.207423	+	0.359267i
$115$	−2919.38	−	1685.51i	−0.0205848	−	0.0118846i
$116$	6796.93			0.0468994
$117$	−67053.5	+	8224.37i	−0.452853	+	0.0555441i
$118$	167617.			1.10818
$119$	−105757.	−	61058.7i	−0.684606	−	0.395257i
$120$	−6510.72	+	11276.9i	−0.0412739	+	0.0714885i
$121$	149759.	+	259390.i	0.929884	+	1.61061i
$122$			119972.i			0.729761i
$123$	74458.3	−	42988.5i	0.443762	−	0.256206i
$124$	−81787.1	+	47219.8i	−0.477673	+	0.275785i
$125$		−	66333.4i		−	0.379715i
$126$	42821.7	+	74169.4i	0.240291	+	0.416196i
$127$	−30848.8	+	53431.8i	−0.169719	+	0.293961i	−0.938321	−	0.345766i	$-0.887619\pi$
$127$	−30848.8	+	53431.8i	−0.169719	+	0.293961i	0.768602	+	0.639727i	$0.220953\pi$
$128$	−14189.0	−	8192.00i	−0.0765466	−	0.0441942i
$129$	−177202.			−0.937549
$130$	−15862.3	−	21055.6i	−0.0823203	−	0.109272i
$131$	−325806.			−1.65875			−0.829374	−	0.558694i	$-0.811303\pi$
$131$	−325806.			−1.65875			−0.829374	+	0.558694i	$0.811303\pi$
$132$	−176896.	−	102131.i	−0.883656	−	0.510179i
$133$	−73869.7	+	127946.i	−0.362107	+	0.627188i
$134$	97469.0	+	168821.i	0.468926	+	0.812204i
$135$			26883.6i			0.126956i
$136$	−35047.7	+	20234.8i	−0.162485	+	0.0938105i
$137$	66673.6	−	38494.0i	0.303496	−	0.175223i	−0.340517	−	0.940239i	$-0.610602\pi$
$137$	66673.6	−	38494.0i	0.303496	−	0.175223i	0.644012	+	0.765015i	$0.277269\pi$
$138$			23452.1i			0.104830i
$139$	−131830.	−	228336.i	−0.578731	−	1.00239i	−0.995625	−	0.0934369i	$-0.970215\pi$
$139$	−131830.	−	228336.i	−0.578731	−	1.00239i	0.416894	−	0.908955i	$-0.363119\pi$
$140$	−16710.0	+	28942.6i	−0.0720538	+	0.124801i
$141$	428083.	+	247154.i	1.81334	+	1.04693i
$142$	−257192.			−1.07037
$143$	330291.	−	248825.i	1.35069	−	1.01755i
$144$	28382.2			0.114062
$145$	−3979.07	−	2297.32i	−0.0157167	−	0.00907404i
$146$	149185.	−	258396.i	0.579220	−	1.00324i
$147$	192709.	+	333782.i	0.735544	+	1.27400i
$148$		−	126251.i		−	0.473783i
$149$	317278.	−	183180.i	1.17078	−	0.675948i	0.216913	−	0.976191i	$-0.430401\pi$
$149$	317278.	−	183180.i	1.17078	−	0.675948i	0.953863	+	0.300243i	$0.0970677\pi$
$150$	−196016.	+	113170.i	−0.711318	+	0.410679i
$151$		−	431142.i		−	1.53879i	−0.638776	−	0.769393i	$-0.720559\pi$
$151$		−	431142.i		−	1.53879i	0.638776	−	0.769393i	$-0.279441\pi$
$152$	24480.4	+	42401.2i	0.0859427	+	0.148857i
$153$	35052.9	−	60713.4i	0.121059	−	0.209680i
$154$	−454011.	−	262123.i	−1.54264	−	0.890643i
$155$	63840.0			0.213434
$156$	−71681.8	+	168811.i	−0.235829	+	0.555379i
$157$	37726.5			0.122151			0.0610755	−	0.998133i	$-0.480547\pi$
$157$	37726.5			0.122151			0.0610755	+	0.998133i	$0.480547\pi$
$158$	316232.	+	182577.i	1.00777	+	0.581838i
$159$	171754.	−	297487.i	0.538784	−	0.933201i
$160$	5537.68	+	9591.55i	0.0171013	+	0.0296203i
$161$			60190.9i			0.183006i
$162$	255298.	−	147396.i	0.764293	−	0.441265i
$163$	−103308.	+	59644.9i	−0.304555	+	0.175835i	−0.644487	−	0.764615i	$-0.722929\pi$
$163$	−103308.	+	59644.9i	−0.304555	+	0.175835i	0.339933	+	0.940450i	$0.389596\pi$
$164$		−	73127.7i		−	0.212311i
$165$	69039.2	+	119579.i	0.197418	+	0.341937i
$166$	65478.4	−	113412.i	0.184428	−	0.319439i
$167$	−231138.	−	133448.i	−0.641329	−	0.370271i	0.143798	−	0.989607i	$-0.454069\pi$
$167$	−231138.	−	133448.i	−0.641329	−	0.370271i	−0.785126	+	0.619336i	$0.787402\pi$
$168$	232503.			0.635559
$169$	−257853.	−	267152.i	−0.694473	−	0.719519i
$170$	27356.9			0.0726013
$171$	−73452.1	−	42407.6i	−0.192094	−	0.110906i
$172$	−75359.5	+	130526.i	−0.194230	+	0.336417i
$173$	−60650.8	−	105050.i	−0.154071	−	0.266859i	0.778649	−	0.627459i	$-0.215905\pi$
$173$	−60650.8	−	105050.i	−0.154071	−	0.266859i	−0.932720	+	0.360600i	$0.882572\pi$
$174$			31964.9i			0.0800387i
$175$	−503083.	+	290455.i	−1.24178	+	0.716942i
$176$	−150459.	+	86867.4i	−0.366131	+	0.211386i
$177$			788275.i			1.89123i
$178$	148025.	+	256386.i	0.350174	+	0.606519i
$179$	−85576.2	+	148222.i	−0.199627	+	0.345765i	−0.948408	−	0.317053i	$-0.897307\pi$
$179$	−85576.2	+	148222.i	−0.199627	+	0.345765i	0.748780	+	0.662818i	$0.230640\pi$
$180$	−16615.5	−	9592.99i	−0.0382237	−	0.0220685i
$181$	113142.			0.256702			0.128351	−	0.991729i	$-0.459032\pi$
$181$	113142.			0.256702			0.128351	+	0.991729i	$0.459032\pi$
$182$	−183974.	+	433261.i	−0.411697	+	0.969551i
$183$	−564210.			−1.24541
$184$	17274.8	+	9973.60i	0.0376156	+	0.0217174i
$185$	−42671.9	+	73909.9i	−0.0916669	+	0.158772i
$186$	−222067.	−	384632.i	−0.470655	−	0.815198i
$187$			429137.i			0.897412i
$188$	364106.	−	210217.i	0.751334	−	0.433783i
$189$	415708.	−	240009.i	0.846513	−	0.488735i
$190$		−	33096.8i		−	0.0665123i
$191$	80435.7	+	139319.i	0.159538	+	0.276329i	0.934702	−	0.355432i	$-0.115666\pi$
$191$	80435.7	+	139319.i	0.159538	+	0.276329i	−0.775164	+	0.631760i	$0.782333\pi$
$192$	38525.7	−	66728.5i	0.0754219	−	0.130635i
$193$	138145.	+	79757.8i	0.266956	+	0.154127i	0.627504	−	0.778614i	$-0.284077\pi$
$193$	138145.	+	79757.8i	0.266956	+	0.154127i	−0.360547	+	0.932741i	$0.617410\pi$
$194$	471723.			0.899877
$195$	99021.2	−	74597.8i	0.186484	−	0.140488i
$196$	327817.			0.609524
$197$	−133432.	−	77036.8i	−0.244959	−	0.141427i	0.372495	−	0.928034i	$-0.378502\pi$
$197$	−133432.	−	77036.8i	−0.244959	−	0.141427i	−0.617454	+	0.786607i	$0.711836\pi$
$198$	150481.	−	260641.i	0.272784	−	0.472477i
$199$	−246646.	−	427204.i	−0.441512	−	0.764720i	0.556290	−	0.830988i	$-0.312224\pi$
$199$	−246646.	−	427204.i	−0.441512	−	0.764720i	−0.997802	+	0.0662676i	$0.978891\pi$
$200$			192513.i			0.340318i
$201$	−793940.	+	458382.i	−1.38611	+	0.800271i
$202$	−105532.	+	60928.9i	−0.181972	+	0.105062i
$203$			82039.1i			0.139727i
$204$	−95161.1	−	164824.i	−0.160097	−	0.277297i
$205$	−24716.7	+	42810.5i	−0.0410776	+	0.0711486i
$206$	−398170.	−	229883.i	−0.653733	−	0.377433i
$207$	−34554.7			−0.0560508
$208$	93861.4	+	124592.i	0.150428	+	0.199678i
$209$	519176.			0.822147
$210$	−136112.	−	78584.6i	−0.212985	−	0.122967i
$211$	−364528.	+	631382.i	−0.563670	+	0.976306i	0.433502	+	0.901153i	$0.357278\pi$
$211$	−364528.	+	631382.i	−0.563670	+	0.976306i	−0.997172	+	0.0751529i	$0.976056\pi$
$212$	−146085.	−	253027.i	−0.223237	−	0.386659i
$213$		−	1.20953e6i		−	1.82670i
$214$	−345947.	+	199733.i	−0.516387	+	0.298136i
$215$	88234.2	−	50942.0i	0.130179	−	0.0751588i
$216$		−	159078.i		−	0.231993i
$217$	−569945.	−	987174.i	−0.821644	−	1.42313i
$218$	−110934.	+	192143.i	−0.158097	+	0.273832i
$219$	1.21520e6	+	701595.i	1.71213	+	0.988499i
$220$	117443.			0.163594
$221$	382441.	−	46907.9i	0.526725	−	0.0646048i
$222$	593737.			0.808559
$223$	1.07435e6	+	620274.i	1.44671	+	0.835260i	0.998284	−	0.0585588i	$-0.0186505\pi$
$223$	1.07435e6	+	620274.i	1.44671	+	0.835260i	0.448429	+	0.893819i	$0.351984\pi$
$224$	98877.7	−	171261.i	0.131667	−	0.228055i
$225$	−166746.	−	288813.i	−0.219584	−	0.380330i
$226$		−	63913.4i		−	0.0832379i
$227$	−1.03900e6	+	599868.i	−1.33829	+	0.772665i	−0.986554	−	0.163433i	$-0.947743\pi$
$227$	−1.03900e6	+	599868.i	−1.33829	+	0.772665i	−0.351740	+	0.936098i	$0.614410\pi$
$228$	−199406.	+	115127.i	−0.254040	+	0.146670i
$229$		−	69321.7i		−	0.0873536i	−0.999046	−	0.0436768i	$-0.986093\pi$
$229$		−	69321.7i		−	0.0873536i	0.999046	−	0.0436768i	$-0.0139072\pi$
$230$	−6742.02	−	11677.5i	−0.00840370	−	0.0145556i
$231$	1.23272e6	−	2.13514e6i	1.51997	−	2.63267i
$232$	23545.2	+	13593.9i	0.0287199	+	0.0165815i
$233$	275286.			0.332197			0.166098	−	0.986109i	$-0.446883\pi$
$233$	275286.			0.332197			0.166098	+	0.986109i	$0.446883\pi$
$234$	−248729.	−	105617.i	−0.296952	−	0.126094i
$235$	−284207.			−0.335711
$236$	580641.	+	335233.i	0.678622	+	0.391802i
$237$	−858629.	+	1.48719e6i	−0.992967	+	1.71987i
$238$	−244235.	−	423027.i	−0.279489	−	0.484089i
$239$		−	695882.i		−	0.788026i	−0.919105	−	0.394013i	$-0.871086\pi$
$239$		−	695882.i		−	0.788026i	0.919105	−	0.394013i	$-0.128914\pi$
$240$	−45107.6	+	26042.9i	−0.0505500	+	0.0291851i
$241$	499499.	−	288386.i	0.553977	−	0.319839i	−0.196748	−	0.980454i	$-0.563038\pi$
$241$	499499.	−	288386.i	0.553977	−	0.319839i	0.750724	+	0.660615i	$0.229705\pi$
$242$			1.19807e6i			1.31505i
$243$	391183.	+	677550.i	0.424976	+	0.736081i
$244$	−239944.	+	415596.i	−0.258010	+	0.446886i
$245$	−191911.	−	110800.i	−0.204261	−	0.117930i
$246$	343908.			0.362330
$247$	−56749.9	−	462683.i	−0.0591865	−	0.482549i
$248$	−377759.			−0.390018
$249$	533358.	+	307934.i	0.545156	+	0.314746i
$250$	132667.	−	229786.i	0.134249	−	0.232527i
$251$	−903159.	−	1.56432e6i	−0.904857	−	1.56726i	−0.821109	−	0.570772i	$-0.806644\pi$
$251$	−903159.	−	1.56432e6i	−0.904857	−	1.56726i	−0.0837484	−	0.996487i	$-0.526689\pi$
$252$			342574.i			0.339823i
$253$	183181.	−	105759.i	0.179920	−	0.103877i
$254$	−213727.	+	123395.i	−0.207862	+	0.120009i
$255$			128655.i			0.123902i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−605140.	+	1.04813e6i	−0.571509	+	0.989883i	0.424902	+	0.905239i	$0.360309\pi$
$257$	−605140.	+	1.04813e6i	−0.571509	+	0.989883i	−0.996411	+	0.0846438i	$0.973025\pi$
$258$	−613846.	−	354404.i	−0.574129	−	0.331474i
$259$	1.52385e6			1.41154
$260$	−12837.3	−	104663.i	−0.0117772	−	0.0960198i
$261$	−47097.5			−0.0427954
$262$	−1.12862e6	−	651611.i	−1.01577	−	0.586456i
$263$	−449631.	+	778784.i	−0.400836	+	0.694269i	−0.993827	−	0.110940i	$-0.964614\pi$
$263$	−449631.	+	778784.i	−0.400836	+	0.694269i	0.592991	+	0.805209i	$0.297947\pi$
$264$	−408524.	−	707584.i	−0.360751	−	0.624839i
$265$			197504.i			0.172767i
$266$	−511784.	+	295479.i	−0.443489	+	0.256049i
$267$	−1.20574e6	+	696137.i	−1.03509	+	0.597608i
$268$			779752.i			0.663162i
$269$	−38241.0	−	66235.4i	−0.0322217	−	0.0558097i	0.849465	−	0.527645i	$-0.176925\pi$
$269$	−38241.0	−	66235.4i	−0.0322217	−	0.0558097i	−0.881687	+	0.471836i	$0.843592\pi$
$270$	−53767.2	+	93127.5i	−0.0448857	+	0.0777443i
$271$	−94473.9	−	54544.5i	−0.0781427	−	0.0451157i	0.460420	−	0.887701i	$-0.347699\pi$
$271$	−94473.9	−	54544.5i	−0.0781427	−	0.0451157i	−0.538562	+	0.842586i	$0.681032\pi$
$272$	−161878.			−0.132668
$273$	−2.03756e6	−	865201.i	−1.65464	−	0.702604i
$274$	307952.			0.247803
$275$	1.76790e6	+	1.02070e6i	1.40970	+	0.813890i
$276$	−46904.3	+	81240.6i	−0.0370629	+	0.0641949i
$277$	1.04001e6	+	1.80134e6i	0.814397	+	1.41058i	0.909760	+	0.415134i	$0.136265\pi$
$277$	1.04001e6	+	1.80134e6i	0.814397	+	1.41058i	−0.0953635	+	0.995443i	$0.530401\pi$
$278$		−	1.05464e6i		−	0.818450i
$279$	566723.	−	327197.i	0.435873	−	0.251651i
$280$	−115770.	+	66840.1i	−0.0882475	+	0.0509497i
$281$		−	1.01098e6i		−	0.763794i	−0.924205	−	0.381897i	$-0.875271\pi$
$281$		−	1.01098e6i		−	0.763794i	0.924205	−	0.381897i	$-0.124729\pi$
$282$	988616.	+	1.71233e6i	0.740295	+	1.28223i
$283$	93310.9	−	161619.i	0.0692574	−	0.119957i	−0.829317	−	0.558778i	$-0.811270\pi$
$283$	93310.9	−	161619.i	0.0692574	−	0.119957i	0.898575	+	0.438821i	$0.144604\pi$
$284$	−890938.	−	514383.i	−0.655468	−	0.378435i
$285$	155649.			0.113510
$286$	1.64181e6	−	201374.i	1.18688	−	0.145576i
$287$	882654.			0.632537
$288$	98318.7	+	56764.3i	0.0698482	+	0.0403269i
$289$	510003.	−	883352.i	0.359193	−	0.622141i
$290$	−9189.27	−	15916.3i	−0.00641632	−	0.0111134i
$291$			2.21844e6i			1.53573i
$292$	1.03359e6	−	596741.i	0.709397	−	0.409571i
$293$	−1.73949e6	+	1.00429e6i	−1.18373	+	0.683427i	−0.956874	−	0.290502i	$-0.906178\pi$
$293$	−1.73949e6	+	1.00429e6i	−1.18373	+	0.683427i	−0.226855	+	0.973929i	$0.572844\pi$
$294$			1.54167e6i			1.04022i
$295$	−226613.	−	392506.i	−0.151611	−	0.262598i
$296$	252501.	−	437345.i	0.167508	−	0.290132i
$297$	−1.46085e6	−	843424.i	−0.960983	−	0.554824i
$298$	1.46544e6			0.955935
$299$	−114274.	−	151688.i	−0.0739216	−	0.0981235i
$300$	−905359.			−0.580788
$301$	−1.57546e6	−	909592.i	−1.00228	−	0.578669i
$302$	862284.	−	1.49352e6i	0.544043	−	0.942310i
$303$	−286539.	−	496300.i	−0.179299	−	0.310555i
$304$			195843.i			0.121541i
$305$	280937.	−	162199.i	0.172926	−	0.0998387i
$306$	242854.	−	140212.i	0.148266	−	0.0856014i
$307$			1.19470e6i			0.723458i	0.932283	+	0.361729i	$0.117813\pi$
$307$			1.19470e6i			0.723458i	−0.932283	+	0.361729i	$0.882187\pi$
$308$	−1.04849e6	−	1.81604e6i	−0.629780	−	1.09081i
$309$	1.08111e6	−	1.87253e6i	0.644128	−	1.11566i
$310$	221148.	+	127680.i	0.130701	+	0.0754603i
$311$	−174722.			−0.102435			−0.0512173	−	0.998688i	$-0.516310\pi$
$311$	−174722.			−0.102435			−0.0512173	+	0.998688i	$0.516310\pi$
$312$	−585935.	+	441416.i	−0.340771	+	0.256721i
$313$	5740.58			0.00331204			0.00165602	−	0.999999i	$-0.499473\pi$
$313$	5740.58			0.00331204			0.00165602	+	0.999999i	$0.499473\pi$
$314$	130688.	+	75452.9i	0.0748019	+	0.0431869i
$315$	115788.	−	200550.i	0.0657485	−	0.113880i
$316$	730306.	+	1.26493e6i	0.411422	+	0.712603i
$317$		−	3.31208e6i		−	1.85120i	−0.378507	−	0.925599i	$-0.623562\pi$
$317$		−	3.31208e6i		−	1.85120i	0.378507	−	0.925599i	$-0.376438\pi$
$318$	1.18995e6	−	687016.i	0.659872	−	0.380978i
$319$	249672.	−	144148.i	0.137371	−	0.0793109i
$320$			44301.5i			0.0241848i
$321$	−939312.	−	1.62694e6i	−0.508800	−	0.881268i
$322$	−120382.	+	208507.i	−0.0647025	+	0.112068i
$323$	418936.	+	241873.i	0.223430	+	0.128997i
$324$	1.17917e6			0.624043
$325$	716389.	−	1.68710e6i	0.376219	−	0.885998i
$326$	−477160.			−0.248668
$327$	−903619.	−	521705.i	−0.467322	−	0.269808i
$328$	146255.	−	253322.i	0.0750632	−	0.130013i
$329$	2.53732e6	+	4.39477e6i	1.29237	+	2.23844i
$330$			552314.i			0.279191i
$331$	−1.98590e6	+	1.14656e6i	−0.996296	+	0.575212i	−0.907150	−	0.420807i	$-0.861747\pi$
$331$	−1.98590e6	+	1.14656e6i	−0.996296	+	0.575212i	−0.0891455	+	0.996019i	$0.528414\pi$
$332$	453647.	−	261913.i	0.225878	−	0.130410i
$333$			874821.i			0.432323i
$334$	−533791.	−	924553.i	−0.261821	−	0.453488i
$335$	263551.	−	456484.i	0.128308	−	0.222236i
$336$	805415.	+	465007.i	0.389199	+	0.224704i
$337$	2.05867e6			0.987444			0.493722	−	0.869620i	$-0.335636\pi$
$337$	2.05867e6			0.987444			0.493722	+	0.869620i	$0.335636\pi$
$338$	−358924.	−	1.44115e6i	−0.170888	−	0.686147i
$339$	300575.			0.142054
$340$	94767.1	+	54713.8i	0.0444591	+	0.0256685i
$341$	−2.00286e6	+	3.46906e6i	−0.932751	+	1.61557i
$342$	−169630.	−	293808.i	−0.0784220	−	0.135831i
$343$			710984.i			0.326305i
$344$	−522106.	+	301438.i	−0.237882	+	0.137341i
$345$	54917.6	−	31706.7i	0.0248407	−	0.0143418i
$346$		−	485206.i		−	0.217889i
$347$	1.13558e6	+	1.96688e6i	0.506284	+	0.876909i	0.999974	+	0.00727103i	$0.00231446\pi$
$347$	1.13558e6	+	1.96688e6i	0.506284	+	0.876909i	−0.493690	+	0.869638i	$0.664352\pi$
$348$	−63929.8	+	110730.i	−0.0282980	+	0.0490135i
$349$	−1.47303e6	−	850457.i	−0.647365	−	0.373756i	0.140081	−	0.990140i	$-0.455264\pi$
$349$	−1.47303e6	−	850457.i	−0.647365	−	0.373756i	−0.787446	+	0.616384i	$0.788597\pi$
$350$	−2.32364e6			−1.01391
$351$	−591967.	+	1.39409e6i	−0.256466	+	0.603979i
$352$	−694940.			−0.298944
$353$	859695.	+	496345.i	0.367204	+	0.212005i	0.672236	−	0.740337i	$-0.265334\pi$
$353$	859695.	+	496345.i	0.367204	+	0.212005i	−0.305032	+	0.952342i	$0.598667\pi$
$354$	−1.57655e6	+	2.73066e6i	−0.668651	+	1.15814i
$355$	347716.	+	602262.i	0.146438	+	0.253638i
$356$			1.18420e6i			0.495221i
$357$	1.98943e6	−	1.14860e6i	0.826148	−	0.476977i
$358$	−592889.	+	342305.i	−0.244493	+	0.141158i
$359$		−	3.00075e6i		−	1.22884i	−0.788980	−	0.614419i	$-0.789391\pi$
$359$		−	3.00075e6i		−	1.22884i	0.788980	−	0.614419i	$-0.210609\pi$
$360$	−38371.9	−	66462.2i	−0.0156048	−	0.0270283i
$361$	−945428.	+	1.63753e6i	−0.381822	+	0.661335i
$362$	391937.	+	226285.i	0.157197	+	0.0907579i
$363$	−5.63433e6			−2.24428
$364$	−1.50383e6	+	1.13291e6i	−0.594900	+	0.448169i
$365$	−806778.			−0.316973
$366$	−1.95448e6	−	1.12842e6i	−0.762656	−	0.440320i
$367$	747764.	−	1.29517e6i	0.289801	−	0.501950i	−0.683961	−	0.729518i	$-0.739744\pi$
$367$	747764.	−	1.29517e6i	0.289801	−	0.501950i	0.973762	+	0.227569i	$0.0730776\pi$
$368$	39894.4	+	69099.1i	0.0153565	+	0.0265982i
$369$			506719.i			0.193732i
$370$	−295640.	+	170688.i	−0.112269	+	0.0648183i
$371$	3.05405e6	−	1.76326e6i	1.15197	−	0.665090i
$372$		−	1.77654e6i		−	0.665606i
$373$	1.37851e6	+	2.38764e6i	0.513023	+	0.888582i	0.999886	+	0.0151036i	$0.00480779\pi$
$373$	1.37851e6	+	2.38764e6i	0.513023	+	0.888582i	−0.486863	+	0.873478i	$0.661859\pi$
$374$	−858274.	+	1.48657e6i	−0.317283	+	0.549550i
$375$	1.08065e6	+	623912.i	0.396831	+	0.229110i
$376$	1.68173e6			0.613461
$377$	−155754.	−	206748.i	−0.0564399	−	0.0749184i
$378$	1.92007e6			0.691175
$379$	−1.90981e6	−	1.10263e6i	−0.682954	−	0.394304i	0.118013	−	0.993012i	$-0.462347\pi$
$379$	−1.90981e6	−	1.10263e6i	−0.682954	−	0.394304i	−0.800967	+	0.598708i	$0.795681\pi$
$380$	66193.6	−	114651.i	0.0235157	−	0.0407303i
$381$	−580309.	−	1.00512e6i	−0.204808	−	0.354738i
$382$			643485.i			0.225621i
$383$	1.88731e6	−	1.08964e6i	0.657424	−	0.379564i	−0.133871	−	0.990999i	$-0.542741\pi$
$383$	1.88731e6	−	1.08964e6i	0.657424	−	0.379564i	0.791295	+	0.611435i	$0.209407\pi$
$384$	266914.	−	154103.i	0.0923726	−	0.0533313i
$385$			1.41754e6i			0.487396i
$386$	319031.	+	552578.i	0.108984	+	0.188767i
$387$	522184.	−	904449.i	0.177234	−	0.306978i
$388$	1.63410e6	+	943447.i	0.551060	+	0.318154i
$389$	−1.07952e6			−0.361705			−0.180853	−	0.983510i	$-0.557886\pi$
$389$	−1.07952e6			−0.361705			−0.180853	+	0.983510i	$0.557886\pi$
$390$	492215.	−	60372.0i	0.163868	−	0.0200990i
$391$	197084.			0.0651942
$392$	1.13559e6	+	655634.i	0.373256	+	0.215499i
$393$	3.06443e6	−	5.30774e6i	1.00085	−	1.73352i
$394$	−308147.	−	533727.i	−0.100004	−	0.173212i
$395$		−	987355.i		−	0.318405i
$396$	1.04257e6	−	601925.i	0.334091	−	0.192888i
$397$	2.05190e6	−	1.18467e6i	0.653402	−	0.377242i	−0.136356	−	0.990660i	$-0.543539\pi$
$397$	2.05190e6	−	1.18467e6i	0.653402	−	0.377242i	0.789758	+	0.613418i	$0.210206\pi$
$398$		−	1.97317e6i		−	0.624392i
$399$	−1.38959e6	−	2.40684e6i	−0.436973	−	0.756860i
$400$	−385026.	+	666885.i	−0.120321	+	0.208402i
$401$	3.02661e6	+	1.74741e6i	0.939930	+	0.542669i	0.889938	−	0.456081i	$-0.150747\pi$
$401$	3.02661e6	+	1.74741e6i	0.939930	+	0.542669i	0.0499917	+	0.998750i	$0.484081\pi$
$402$	−3.66705e6			−1.13175
$403$	3.31051e6	+	1.40573e6i	1.01539	+	0.431161i
$404$	−487431.			−0.148580
$405$	−690313.	−	398552.i	−0.209126	−	0.120739i
$406$	−164078.	+	284192.i	−0.0494010	+	0.0855651i
$407$	−2.67751e6	−	4.63758e6i	−0.801207	−	1.38773i
$408$		−	761288.i		−	0.226412i
$409$	1.42983e6	−	825512.i	0.422645	−	0.244014i	−0.273563	−	0.961854i	$-0.588202\pi$
$409$	1.42983e6	−	825512.i	0.422645	−	0.244014i	0.696208	+	0.717840i	$0.254869\pi$
$410$	−171242.	+	98866.7i	−0.0503096	+	0.0290463i
$411$			1.44825e6i			0.422902i
$412$	−919534.	−	1.59268e6i	−0.266885	−	0.462259i
$413$	−4.04628e6	+	7.00836e6i	−1.16729	+	2.02181i
$414$	−119701.	−	69109.5i	−0.0343240	−	0.0198169i
$415$	−354100.			−0.100927
$416$	75962.1	+	619321.i	0.0215211	+	0.175462i
$417$	4.95980e6			1.39677
$418$	1.79848e6	+	1.03835e6i	0.503460	+	0.290673i
$419$	1.23722e6	−	2.14293e6i	0.344280	−	0.596310i	−0.640943	−	0.767589i	$-0.721456\pi$
$419$	1.23722e6	−	2.14293e6i	0.344280	−	0.596310i	0.985223	+	0.171278i	$0.0547898\pi$
$420$	−314338.	−	544450.i	−0.0869509	−	0.150603i
$421$		−	1.87886e6i		−	0.516642i	−0.966059	−	0.258321i	$-0.916831\pi$
$421$		−	1.87886e6i		−	0.516642i	0.966059	−	0.258321i	$-0.0831693\pi$
$422$	−2.52553e6	+	1.45811e6i	−0.690352	+	0.398575i
$423$	−2.52298e6	+	1.45664e6i	−0.685586	+	0.395823i
$424$		−	1.16868e6i		−	0.315705i
$425$	951041.	+	1.64725e6i	0.255404	+	0.442372i
$426$	2.41906e6	−	4.18994e6i	0.645838	−	1.11862i
$427$	−5.01625e6	−	2.89614e6i	−1.33140	−	0.768686i
$428$	−1.59786e6			−0.421629
$429$	947032.	+	7.72118e6i	0.248440	+	2.02554i
$430$	407536.			0.106291
$431$	1.13124e6	+	653124.i	0.293335	+	0.169357i	0.639445	−	0.768837i	$-0.279164\pi$
$431$	1.13124e6	+	653124.i	0.293335	+	0.169357i	−0.346110	+	0.938194i	$0.612498\pi$
$432$	318155.	−	551061.i	0.0820219	−	0.142066i
$433$	−1.88398e6	−	3.26316e6i	−0.482900	−	0.836408i	0.516907	−	0.856042i	$-0.327083\pi$
$433$	−1.88398e6	−	3.26316e6i	−0.482900	−	0.836408i	−0.999807	+	0.0196338i	$0.993750\pi$
$434$		−	4.55956e6i		−	1.16198i
$435$	74851.8	−	43215.7i	0.0189661	−	0.0109501i
$436$	−768572.	+	443735.i	−0.193628	+	0.111791i
$437$		−	238435.i		−	0.0597264i
$438$	2.80638e6	+	4.86079e6i	0.698974	+	1.21066i
$439$	−2.20155e6	+	3.81320e6i	−0.545215	+	0.944341i	0.453378	+	0.891318i	$0.350219\pi$
$439$	−2.20155e6	+	3.81320e6i	−0.545215	+	0.944341i	−0.998593	+	0.0530223i	$0.983115\pi$
$440$	406833.	+	234885.i	0.100181	+	0.0578394i
$441$	−2.27152e6			−0.556186
$442$	1.41863e6	+	602389.i	0.345393	+	0.146663i
$443$	−2.66694e6			−0.645661			−0.322830	−	0.946457i	$-0.604634\pi$
$443$	−2.66694e6			−0.645661			−0.322830	+	0.946457i	$0.604634\pi$
$444$	2.05677e6	+	1.18747e6i	0.495139	+	0.285869i
$445$	400251.	−	693255.i	0.0958147	−	0.165956i
$446$	2.48110e6	+	4.29739e6i	0.590618	+	1.02298i
$447$			6.89175e6i			1.63140i
$448$	685045.	−	395511.i	0.161259	−	0.0931029i
$449$	236311.	−	136434.i	0.0553183	−	0.0319380i	−0.472086	−	0.881553i	$-0.656499\pi$
$449$	236311.	−	136434.i	0.0553183	−	0.0319380i	0.527404	+	0.849615i	$0.323165\pi$
$450$		−	1.33397e6i		−	0.310538i
$451$	−1.55088e6	−	2.68621e6i	−0.359036	−	0.621868i
$452$	127827.	−	221403.i	0.0294290	−	0.0509726i
$453$	7.02379e6	+	4.05519e6i	1.60815	+	0.928465i
$454$	−4.79894e6			−1.09271
$455$	1.26329e6	−	154947.i	0.286071	−	0.0350877i
$456$	−921019.			−0.207423
$457$	−5.91669e6	−	3.41600e6i	−1.32522	−	0.765116i	−0.340664	−	0.940185i	$-0.610652\pi$
$457$	−5.91669e6	−	3.41600e6i	−1.32522	−	0.765116i	−0.984556	+	0.175069i	$0.943985\pi$
$458$	138643.	−	240138.i	0.0308842	−	0.0534929i
$459$	−785865.	−	1.36116e6i	−0.174107	−	0.301562i
$460$		−	53936.2i		−	0.0118846i
$461$	360877.	−	208352.i	0.0790873	−	0.0456611i	−0.459935	−	0.887953i	$-0.652127\pi$
$461$	360877.	−	208352.i	0.0790873	−	0.0456611i	0.539022	+	0.842292i	$0.318794\pi$
$462$	8.54057e6	−	4.93090e6i	1.86158	−	1.07478i
$463$		−	5.71411e6i		−	1.23878i	−0.785082	−	0.619392i	$-0.787379\pi$
$463$		−	5.71411e6i		−	1.23878i	0.785082	−	0.619392i	$-0.212621\pi$
$464$	54375.4	+	94181.0i	0.0117249	+	0.0203080i
$465$	−600459.	+	1.04003e6i	−0.128781	+	0.223055i
$466$	953620.	+	550573.i	0.203428	+	0.117449i
$467$	1.43077e6			0.303582			0.151791	−	0.988413i	$-0.451496\pi$
$467$	1.43077e6			0.303582			0.151791	+	0.988413i	$0.451496\pi$
$468$	−650388.	−	863326.i	−0.137264	−	0.182205i
$469$	−9.41164e6			−1.97575
$470$	−984523.	−	568415.i	−0.205580	−	0.118692i
$471$	−354843.	+	614607.i	−0.0737029	+	0.127657i
$472$	1.34093e6	+	2.32256e6i	0.277046	+	0.479858i
$473$			6.39286e6i			1.31384i
$474$	−5.94876e6	+	3.43452e6i	−1.21613	+	0.702133i
$475$	1.99287e6	−	1.15058e6i	0.405271	−	0.233983i
$476$		−	1.95388e6i		−	0.395257i
$477$	1.01226e6	+	1.75329e6i	0.203702	+	0.352823i
$478$	1.39176e6	−	2.41061e6i	0.278609	−	0.482566i
$479$	−2.86040e6	−	1.65145e6i	−0.569624	−	0.328873i	0.187375	−	0.982288i	$-0.440002\pi$
$479$	−2.86040e6	−	1.65145e6i	−0.569624	−	0.328873i	−0.756999	+	0.653416i	$0.773335\pi$
$480$	−208343.			−0.0412739
$481$	−3.84028e6	+	2.89308e6i	−0.756833	+	0.570162i
$482$	2.30709e6			0.452320
$483$	−980577.	−	566136.i	−0.191255	−	0.110421i
$484$	−2.39614e6	+	4.15024e6i	−0.464942	+	0.805303i
$485$	−637758.	−	1.10463e6i	−0.123112	−	0.213237i
$486$			3.12947e6i			0.601007i
$487$	−1.27928e6	+	738594.i	−0.244424	+	0.141118i	−0.617208	−	0.786800i	$-0.711736\pi$
$487$	−1.27928e6	+	738594.i	−0.244424	+	0.141118i	0.372784	+	0.927918i	$0.378403\pi$
$488$	−1.66238e6	+	959777.i	−0.315996	+	0.182440i
$489$		−	2.24401e6i		−	0.424377i
$490$	−443200.	−	767645.i	−0.0833891	−	0.144434i
$491$	−981996.	+	1.70087e6i	−0.183826	+	0.318395i	−0.943180	−	0.332282i	$-0.892182\pi$
$491$	−981996.	+	1.70087e6i	−0.183826	+	0.318395i	0.759355	+	0.650677i	$0.225515\pi$
$492$	1.19133e6	+	687816.i	0.221881	+	0.128103i
$493$	268622.			0.0497765
$494$	728779.	−	1.71628e6i	0.134363	−	0.316425i
$495$	−813787.			−0.149279
$496$	−1.30859e6	−	755517.i	−0.238837	−	0.137892i
$497$	6.20862e6	−	1.07537e7i	1.12747	−	1.95283i
$498$	1.23174e6	+	2.13343e6i	0.222559	+	0.385483i
$499$			6.30938e6i			1.13432i	0.823608	+	0.567160i	$0.191958\pi$
$499$			6.30938e6i			1.13432i	−0.823608	+	0.567160i	$0.808042\pi$
$500$	919143.	−	530668.i	0.164421	−	0.0949287i
$501$	4.34803e6	−	2.51034e6i	0.773923	−	0.446825i
$502$		−	7.22527e6i		−	1.27966i
$503$	−457703.	−	792766.i	−0.0806611	−	0.139709i	0.822873	−	0.568225i	$-0.192370\pi$
$503$	−457703.	−	792766.i	−0.0806611	−	0.139709i	−0.903534	+	0.428516i	$0.859036\pi$
$504$	−685147.	+	1.18671e6i	−0.120146	+	0.208098i
$505$	285353.	+	164749.i	0.0497913	+	0.0287470i
$506$	846075.			0.146904
$507$	6.77750e6	−	1.68796e6i	1.17098	−	0.291638i
$508$	−987163.			−0.169719
$509$	2.96866e6	+	1.71396e6i	0.507885	+	0.293228i	0.731964	−	0.681343i	$-0.238604\pi$
$509$	2.96866e6	+	1.71396e6i	0.507885	+	0.293228i	−0.224079	+	0.974571i	$0.571937\pi$
$510$	−257311.	+	445675.i	−0.0438058	+	0.0758740i
$511$	7.20269e6	+	1.24754e7i	1.22023	+	2.11350i
$512$		−	262144.i		−	0.0441942i
$513$	−1.64675e6	+	950751.i	−0.276270	+	0.159505i
$514$	−4.19254e6	+	2.42056e6i	−0.699953	+	0.404118i
$515$			1.24319e6i			0.206546i
$516$	−1.41762e6	−	2.45538e6i	−0.234387	−	0.405971i
$517$	8.91649e6	−	1.54438e7i	1.46713	−	2.54114i
$518$	5.27877e6	+	3.04770e6i	0.864387	+	0.499054i
$519$	2.28185e6			0.371851
$520$	164857.	−	388239.i	0.0267361	−	0.0629638i
$521$	554843.			0.0895521			0.0447761	−	0.998997i	$-0.485743\pi$
$521$	554843.			0.0895521			0.0447761	+	0.998997i	$0.485743\pi$
$522$	−163151.	−	94195.1i	−0.0262067	−	0.0151305i
$523$	−109474.	+	189614.i	−0.0175007	+	0.0303121i	−0.874643	−	0.484767i	$-0.838904\pi$
$523$	−109474.	+	189614.i	−0.0175007	+	0.0303121i	0.857142	+	0.515079i	$0.172238\pi$
$524$	−2.60644e6	−	4.51449e6i	−0.414687	−	0.718259i
$525$		−	1.09277e7i		−	1.73034i
$526$	−3.11514e6	+	1.79853e6i	−0.490922	+	0.283434i
$527$	−3.23232e6	+	1.86618e6i	−0.506976	+	0.292703i
$528$		−	3.26819e6i		−	0.510179i
$529$	3.16960e6	+	5.48991e6i	0.492454	+	0.852955i
$530$	−395007.	+	684172.i	−0.0610823	+	0.105798i
$531$	−4.02340e6	−	2.32291e6i	−0.619237	−	0.357517i
$532$	−2.36383e6			−0.362107
$533$	−2.22439e6	+	1.67575e6i	−0.339151	+	0.255500i
$534$	−5.56909e6			−0.845145
$535$	935424.	+	540067.i	0.141294	+	0.0815762i
$536$	−1.55950e6	+	2.70114e6i	−0.234463	+	0.406102i
$537$	−1.60981e6	−	2.78827e6i	−0.240901	−	0.417252i
$538$		−	305928.i		−	0.0455684i
$539$	1.20417e7	−	6.95230e6i	1.78532	−	1.03076i
$540$	−372510.	+	215069.i	−0.0549735	+	0.0317390i
$541$		−	351603.i		−	0.0516488i	−0.999666	−	0.0258244i	$-0.991779\pi$
$541$		−	351603.i		−	0.0516488i	0.999666	−	0.0258244i	$-0.00822107\pi$
$542$	−218178.	−	377896.i	−0.0319016	−	0.0552552i
$543$	−1.06418e6	+	1.84322e6i	−0.154888	+	0.268273i
$544$	−560763.	−	323757.i	−0.0812423	−	0.0469052i
$545$	599919.			0.0865169
$546$	−5.32790e6	−	7.07226e6i	−0.764847	−	1.01526i
$547$	6.07461e6			0.868061			0.434030	−	0.900898i	$-0.357091\pi$
$547$	6.07461e6			0.868061			0.434030	+	0.900898i	$0.357091\pi$
$548$	1.06678e6	+	615904.i	0.151748	+	0.0876117i
$549$	1.66263e6	−	2.87976e6i	0.235432	−	0.407780i
$550$	4.08280e6	+	7.07161e6i	0.575507	+	0.996808i
$551$		−	324983.i		−	0.0456017i
$552$	−324962.	+	187617.i	−0.0453926	+	0.0262075i
$553$	−1.52677e7	+	8.81482e6i	−2.12306	+	1.22575i
$554$			8.32004e6i			1.15173i
$555$	−802717.	−	1.39035e6i	−0.110619	−	0.191598i
$556$	2.10928e6	−	3.65338e6i	0.289366	−	0.501196i
$557$	−7.45893e6	−	4.30642e6i	−1.01868	−	0.588136i	−0.104960	−	0.994476i	$-0.533472\pi$
$557$	−7.45893e6	−	4.30642e6i	−1.01868	−	0.588136i	−0.913722	+	0.406340i	$0.866805\pi$
$558$	2.61758e6			0.355889
$559$	5.69723e6	−	698787.i	0.771142	−	0.0945835i
$560$	−534720.			−0.0720538
$561$	−6.99112e6	−	4.03633e6i	−0.937864	−	0.541476i
$562$	2.02196e6	−	3.50213e6i	0.270042	−	0.467727i
$563$	−2.86457e6	−	4.96158e6i	−0.380880	−	0.659703i	0.610308	−	0.792164i	$-0.291046\pi$
$563$	−2.86457e6	−	4.96158e6i	−0.380880	−	0.659703i	−0.991188	+	0.132461i	$0.957712\pi$
$564$			7.90892e6i			1.04693i
$565$	−149665.	+	86409.3i	−0.0197242	+	0.0113878i
$566$	646477.	−	373244.i	0.0848227	−	0.0489724i
$567$			1.42326e7i			1.85921i
$568$	−2.05753e6	−	3.56375e6i	−0.267594	−	0.463486i
$569$	−5.97471e6	+	1.03485e7i	−0.773635	+	1.33998i	0.161923	+	0.986803i	$0.448230\pi$
$569$	−5.97471e6	+	1.03485e7i	−0.773635	+	1.33998i	−0.935558	+	0.353172i	$0.885103\pi$
$570$	539184.	+	311298.i	0.0695105	+	0.0401319i
$571$	−802594.			−0.103016			−0.0515081	−	0.998673i	$-0.516403\pi$
$571$	−802594.			−0.103016			−0.0515081	+	0.998673i	$0.516403\pi$
$572$	6.09015e6	+	2.58604e6i	0.778283	+	0.330480i
$573$	−3.02621e6			−0.385046
$574$	3.05760e6	+	1.76531e6i	0.387348	+	0.223635i
$575$	468762.	−	811920.i	0.0591266	−	0.102410i
$576$	227057.	+	393275.i	0.0285154	+	0.0493901i
$577$			3.08080e6i			0.385233i	0.981274	+	0.192617i	$0.0616974\pi$
$577$			3.08080e6i			0.385233i	−0.981274	+	0.192617i	$0.938303\pi$
$578$	3.53341e6	−	2.04001e6i	0.439920	−	0.253988i
$579$	−2.59869e6	+	1.50035e6i	−0.322150	+	0.185993i
$580$		−	73514.1i		−	0.00907404i
$581$	3.16130e6	+	5.47554e6i	0.388531	+	0.672956i
$582$	−4.43688e6	+	7.68491e6i	−0.542963	+	0.940440i
$583$	−1.07323e7	−	6.19632e6i	−1.30774	−	0.755027i
$584$	4.77393e6			0.579220
$585$	88953.0	+	725237.i	0.0107466	+	0.0876174i
$586$	−8.03435e6			−0.966511
$587$	3.58219e6	+	2.06818e6i	0.429095	+	0.247738i	0.698961	−	0.715160i	$-0.253646\pi$
$587$	3.58219e6	+	2.06818e6i	0.429095	+	0.247738i	−0.269866	+	0.962898i	$0.586979\pi$
$588$	−3.08334e6	+	5.34051e6i	−0.367772	+	0.637000i
$589$	2.25773e6	+	3.91051e6i	0.268154	+	0.464456i
$590$		−	1.81291e6i		−	0.214410i
$591$	2.51003e6	−	1.44917e6i	0.295604	−	0.170667i
$592$	1.74938e6	−	1.01001e6i	0.205154	−	0.118446i
$593$		−	226602.i		−	0.0264623i	−0.999912	−	0.0132312i	$-0.995788\pi$
$593$		−	226602.i		−	0.0264623i	0.999912	−	0.0132312i	$-0.00421173\pi$
$594$	−3.37370e6	−	5.84342e6i	−0.392320	−	0.679518i
$595$	−660398.	+	1.14384e6i	−0.0764739	+	0.132457i
$596$	5.07644e6	+	2.93089e6i	0.585388	+	0.337974i
$597$	9.27952e6			1.06559
$598$	−92482.4	−	754011.i	−0.0105756	−	0.0862234i
$599$	1.13975e7			1.29791			0.648953	−	0.760828i	$-0.275207\pi$
$599$	1.13975e7			1.29791			0.648953	+	0.760828i	$0.275207\pi$
$600$	−3.13626e6	−	1.81072e6i	−0.355659	−	0.205340i
$601$	−3.06371e6	+	5.30651e6i	−0.345989	+	0.599270i	−0.985533	−	0.169484i	$-0.945790\pi$
$601$	−3.06371e6	+	5.30651e6i	−0.345989	+	0.599270i	0.639544	+	0.768754i	$0.279123\pi$
$602$	−3.63837e6	−	6.30184e6i	−0.409181	−	0.708722i
$603$		−	5.40309e6i		−	0.605130i
$604$	5.97408e6	−	3.44914e6i	0.666314	−	0.384696i
$605$	2.80550e6	−	1.61976e6i	0.311618	−	0.179913i
$606$		−	2.29231e6i		−	0.253567i
$607$	6.98496e6	+	1.20983e7i	0.769471	+	1.33276i	0.937850	+	0.347041i	$0.112813\pi$
$607$	6.98496e6	+	1.20983e7i	0.769471	+	1.33276i	−0.168379	+	0.985722i	$0.553853\pi$
$608$	−391686.	+	678420.i	−0.0429713	+	0.0744285i
$609$	−1.33651e6	−	771635.i	−0.146026	−	0.0843079i
$610$	1.29759e6			0.141193
$611$	−1.47380e7	−	6.25814e6i	−1.59711	−	0.678175i
$612$	1.12169e6			0.121059
$613$	1.22837e6	+	709200.i	0.132032	+	0.0762286i	0.564561	−	0.825391i	$-0.309045\pi$
$613$	1.22837e6	+	709200.i	0.132032	+	0.0762286i	−0.432529	+	0.901620i	$0.642379\pi$
$614$	−2.38940e6	+	4.13857e6i	−0.255781	+	0.443026i
$615$	−464955.	−	805325.i	−0.0495704	−	0.0858585i
$616$		−	8.38795e6i		−	0.890643i
$617$	−1.32531e7	+	7.65167e6i	−1.40154	+	0.809177i	−0.994550	−	0.104258i	$-0.966753\pi$
$617$	−1.32531e7	+	7.65167e6i	−1.40154	+	0.809177i	−0.406985	+	0.913435i	$0.633420\pi$
$618$	7.49012e6	−	4.32442e6i	0.788892	−	0.455467i
$619$		−	6.89318e6i		−	0.723092i	−0.932354	−	0.361546i	$-0.882249\pi$
$619$		−	6.89318e6i		−	0.723092i	0.932354	−	0.361546i	$-0.117751\pi$
$620$	510720.	+	884593.i	0.0533585	+	0.0924196i
$621$	−387348.	+	670906.i	−0.0403062	+	0.0698124i
$622$	−605255.	−	349444.i	−0.0627282	−	0.0362161i
$623$	−1.42933e7			−1.47541
$624$	−2.91257e6	+	357238.i	−0.299444	+	0.0367279i
$625$	8.68261e6			0.889099
$626$	19886.0	+	11481.2i	0.00202820	+	0.00117098i
$627$	−4.88321e6	+	8.45797e6i	−0.496063	+	0.859206i
$628$	301812.	+	522753.i	0.0305377	+	0.0528929i
$629$		−	4.98956e6i		−	0.502847i
$630$	802201.	−	463151.i	0.0805252	−	0.0464912i
$631$	4.02910e6	−	2.32620e6i	0.402842	−	0.232581i	−0.284868	−	0.958567i	$-0.591950\pi$
$631$	4.02910e6	−	2.32620e6i	0.402842	−	0.232581i	0.687709	+	0.725986i	$0.258616\pi$
$632$			5.84245e6i			0.581838i
$633$	−6.85728e6	−	1.18772e7i	−0.680209	−	1.17816i
$634$	6.62416e6	−	1.14734e7i	0.654497	−	1.13362i
$635$	577907.	+	333655.i	0.0568753	+	0.0328370i
$636$	5.49613e6			0.538784
$637$	−7.51205e6	−	9.97150e6i	−0.733516	−	0.973670i
$638$	1.15319e6			0.112163
$639$	6.17352e6	+	3.56428e6i	0.598110	+	0.345319i
$640$	−88603.0	+	153465.i	−0.00855063	+	0.0148101i
$641$	−7.99531e6	−	1.38483e7i	−0.768582	−	1.33122i	−0.938332	−	0.345735i	$-0.887630\pi$
$641$	−7.99531e6	−	1.38483e7i	−0.768582	−	1.33122i	0.169750	−	0.985487i	$-0.445704\pi$
$642$		−	7.51450e6i		−	0.719552i
$643$	1.28915e7	−	7.44292e6i	1.22964	−	0.709931i	0.262683	−	0.964882i	$-0.415393\pi$
$643$	1.28915e7	−	7.44292e6i	1.22964	−	0.709931i	0.966954	+	0.254951i	$0.0820594\pi$
$644$	−834029.	+	481527.i	−0.0792440	+	0.0457516i
$645$			1.91658e6i			0.181396i
$646$	967490.	+	1.67574e6i	0.0912148	+	0.157989i
$647$	3.74967e6	−	6.49461e6i	0.352153	−	0.609948i	−0.634473	−	0.772945i	$-0.718783\pi$
$647$	3.74967e6	−	6.49461e6i	0.352153	−	0.609948i	0.986627	+	0.162997i	$0.0521162\pi$
$648$	4.08477e6	+	2.35834e6i	0.382147	+	0.220632i
$649$	2.84383e7			2.65028
$650$	5.85585e6	−	4.41151e6i	0.543634	−	0.409547i
$651$	2.14429e7			1.98304
$652$	−1.65293e6	−	954319.i	−0.152277	−	0.0879174i
$653$	−3.13924e6	+	5.43732e6i	−0.288098	+	0.499001i	−0.973356	−	0.229300i	$-0.926356\pi$
$653$	−3.13924e6	+	5.43732e6i	−0.288098	+	0.499001i	0.685257	+	0.728301i	$0.259690\pi$
$654$	−2.08682e6	−	3.61448e6i	−0.190783	−	0.330446i
$655$			3.52384e6i			0.320932i
$656$	1.01329e6	−	585021.i	0.0919333	−	0.0530777i
$657$	−7.16196e6	+	4.13496e6i	−0.647320	+	0.373730i
$658$			2.02986e7i			1.82768i
$659$	−1.02396e7	−	1.77356e7i	−0.918484	−	1.59086i	−0.801719	−	0.597701i	$-0.796081\pi$
$659$	−1.02396e7	−	1.77356e7i	−0.918484	−	1.59086i	−0.116765	−	0.993160i	$-0.537252\pi$
$660$	−1.10463e6	+	1.91327e6i	−0.0987088	+	0.170969i
$661$	7.94477e6	+	4.58691e6i	0.707257	+	0.408335i	0.810045	−	0.586368i	$-0.199443\pi$
$661$	7.94477e6	+	4.58691e6i	0.707257	+	0.408335i	−0.102787	+	0.994703i	$0.532776\pi$
$662$	−9.17250e6			−0.813472
$663$	−2.83294e6	+	6.67160e6i	−0.250296	+	0.589449i
$664$	2.09531e6			0.184428
$665$	1.38384e6	+	798959.i	0.121348	+	0.0700601i
$666$	−1.74964e6	+	3.03047e6i	−0.152849	+	0.264743i
$667$	−66201.0	−	114664.i	−0.00576169	−	0.00997954i
$668$		−	4.27033e6i		−	0.370271i
$669$	−2.02099e7	+	1.16682e7i	−1.74582	+	1.00795i
$670$	1.82594e6	−	1.05420e6i	0.157144	−	0.0907273i
$671$			2.03548e7i			1.74526i
$672$	1.86003e6	+	3.22166e6i	0.158890	+	0.275205i
$673$	7.38539e6	−	1.27919e7i	0.628544	−	1.08867i	−0.359300	−	0.933222i	$-0.616984\pi$
$673$	7.38539e6	−	1.27919e7i	0.628544	−	1.08867i	0.987844	−	0.155449i	$-0.0496823\pi$
$674$	7.13145e6	+	4.11734e6i	0.604683	+	0.349114i
$675$	−7.47669e6			−0.631612
$676$	1.63895e6	−	5.71013e6i	0.137943	−	0.480595i
$677$	−9.33977e6			−0.783185			−0.391593	−	0.920139i	$-0.628076\pi$
$677$	−9.33977e6			−0.783185			−0.391593	+	0.920139i	$0.628076\pi$
$678$	1.04122e6	+	601150.i	0.0869900	+	0.0502237i
$679$	−1.13874e7	+	1.97236e7i	−0.947876	+	1.64177i
$680$	218855.	+	379068.i	0.0181503	+	0.0314373i
$681$		−	2.25687e7i		−	1.86483i
$682$	−1.38762e7	+	8.01146e6i	−1.14238	+	0.659554i
$683$	1.05650e7	−	6.09970e6i	0.866598	−	0.500330i	0.000381557	−	1.00000i	$-0.499879\pi$
$683$	1.05650e7	−	6.09970e6i	0.866598	−	0.500330i	0.866216	+	0.499670i	$0.166545\pi$
$684$		−	1.35704e6i		−	0.110906i
$685$	−416343.	−	721128.i	−0.0339020	−	0.0587200i
$686$	−1.42197e6	+	2.46292e6i	−0.115366	+	0.199820i
$687$	1.12933e6	+	652019.i	0.0912912	+	0.0527070i
$688$	−2.41150e6			−0.194230
$689$	−4.34895e6	+	1.02418e7i	−0.349009	+	0.821919i
$690$	253653.			0.0202823
$691$	6.09145e6	+	3.51690e6i	0.485317	+	0.280198i	0.722630	−	0.691235i	$-0.242933\pi$
$691$	6.09145e6	+	3.51690e6i	0.485317	+	0.280198i	−0.237313	+	0.971433i	$0.576267\pi$
$692$	970412.	−	1.68080e6i	0.0770355	−	0.133429i
$693$	7.26526e6	+	1.25838e7i	0.574669	+	0.995357i
$694$			9.08464e6i			0.715993i
$695$	−2.46964e6	+	1.42584e6i	−0.193942	+	0.111972i
$696$	−442918.	+	255719.i	−0.0346578	+	0.0200097i
$697$		−	2.89008e6i		−	0.225335i
$698$	−3.40183e6	−	5.89214e6i	−0.264286	−	0.457756i
$699$	−2.58926e6	+	4.48473e6i	−0.200439	+	0.347171i
$700$	−8.04933e6	−	4.64728e6i	−0.620890	−	0.358471i
$701$	340984.			0.0262083			0.0131041	−	0.999914i	$-0.495829\pi$
$701$	340984.			0.0262083			0.0131041	+	0.999914i	$0.495829\pi$
$702$	−4.83881e6	+	3.64532e6i	−0.370592	+	0.279186i
$703$	−6.03645e6			−0.460674
$704$	−2.40734e6	−	1.38988e6i	−0.183065	−	0.105693i
$705$	2.67316e6	−	4.63006e6i	0.202560	−	0.350844i
$706$	1.98538e6	+	3.43878e6i	0.149910	+	0.259653i
$707$		−	5.88331e6i		−	0.442663i
$708$	−1.09227e7	+	6.30620e6i	−0.818927	+	0.472808i
$709$	−5.21505e6	+	3.01091e6i	−0.389622	+	0.224948i	−0.681996	−	0.731356i	$-0.738888\pi$
$709$	−5.21505e6	+	3.01091e6i	−0.389622	+	0.224948i	0.292374	+	0.956304i	$0.405555\pi$
$710$			2.78173e6i			0.207095i
$711$	−5.06047e6	−	8.76498e6i	−0.375419	−	0.650245i
$712$	−2.36839e6	+	4.10218e6i	−0.175087	+	0.303260i
$713$	1.59319e6	+	919827.i	0.117366	+	0.0677614i
$714$	9.18878e6			0.674547
$715$	−2.69124e6	−	3.57235e6i	−0.196874	−	0.261330i
$716$	−2.73844e6			−0.199627
$717$	1.13367e7	+	6.54525e6i	0.823548	+	0.475475i
$718$	6.00151e6	−	1.03949e7i	0.434459	−	0.752506i
$719$	−7.95673e6	−	1.37815e7i	−0.574000	−	0.994198i	−0.996149	−	0.0876714i	$-0.972057\pi$
$719$	−7.95673e6	−	1.37815e7i	−0.574000	−	0.994198i	0.422149	−	0.906526i	$-0.361276\pi$
$720$		−	306976.i		−	0.0220685i
$721$	1.92237e7	−	1.10988e7i	1.37720	−	0.795130i
$722$	−6.55012e6	+	3.78171e6i	−0.467634	+	0.269989i
$723$			1.08499e7i			0.771931i
$724$	905140.	+	1.56775e6i	0.0641755	+	0.111155i
$725$	638915.	−	1.10663e6i	0.0451438	−	0.0781913i
$726$	−1.95179e7	−	1.12687e7i	−1.37433	−	0.793471i
$727$	−1.87981e6			−0.131910			−0.0659551	−	0.997823i	$-0.521009\pi$
$727$	−1.87981e6			−0.131910			−0.0659551	+	0.997823i	$0.521009\pi$
$728$	−7.47523e6	+	916865.i	−0.522752	+	0.0641176i
$729$	3.19127e6			0.222405
$730$	−2.79476e6	−	1.61356e6i	−0.194105	−	0.112067i
$731$	−2.97829e6	+	5.15855e6i	−0.206145	+	0.357054i
$732$	−4.51368e6	−	7.81792e6i	−0.311353	−	0.539279i
$733$			1.09255e7i			0.751072i	0.926808	+	0.375536i	$0.122541\pi$
$733$			1.09255e7i			0.751072i	−0.926808	+	0.375536i	$0.877459\pi$
$734$	5.18066e6	−	2.99106e6i	0.354932	−	0.204920i
$735$	3.61011e6	−	2.08430e6i	0.246492	−	0.142312i
$736$			319155.i			0.0217174i
$737$	1.65369e7	+	2.86427e7i	1.12146	+	1.94243i
$738$	−1.01344e6	+	1.75533e6i	−0.0684946	+	0.118636i
$739$	−8.35535e6	−	4.82396e6i	−0.562799	−	0.324932i	0.191469	−	0.981499i	$-0.438675\pi$
$739$	−8.35535e6	−	4.82396e6i	−0.562799	−	0.324932i	−0.754268	+	0.656566i	$0.772008\pi$
$740$	−1.36550e6			−0.0916669
$741$	8.07140e6	+	3.42734e6i	0.540012	+	0.229304i
$742$	1.41060e7			0.940579
$743$	9.88748e6	+	5.70854e6i	0.657073	+	0.379361i	0.791161	−	0.611608i	$-0.209477\pi$
$743$	9.88748e6	+	5.70854e6i	0.657073	+	0.379361i	−0.134088	+	0.990969i	$0.542810\pi$
$744$	3.55308e6	−	6.15411e6i	0.235327	−	0.407599i
$745$	−1.98124e6	−	3.43161e6i	−0.130782	−	0.226520i
$746$			1.10281e7i			0.725524i
$747$	−3.14343e6	+	1.81486e6i	−0.206112	+	0.118999i
$748$	−5.94629e6	+	3.43309e6i	−0.388591	+	0.224353i
$749$		−	1.92863e7i		−	1.25616i
$750$	2.49565e6	+	4.32259e6i	0.162006	+	0.280602i
$751$	3.62906e6	−	6.28572e6i	0.234798	−	0.406682i	−0.724416	−	0.689363i	$-0.757890\pi$
$751$	3.62906e6	−	6.28572e6i	0.234798	−	0.406682i	0.959214	+	0.282681i	$0.0912238\pi$
$752$	5.82569e6	+	3.36346e6i	0.375667	+	0.216891i
$753$	3.39793e7			2.18387
$754$	−126052.	−	1.02771e6i	−0.00807460	−	0.0658325i
$755$	−4.66314e6			−0.297722
$756$	6.65133e6	+	3.84014e6i	0.423257	+	0.244367i
$757$	1.19170e7	−	2.06408e7i	0.755835	−	1.30914i	−0.189124	−	0.981953i	$-0.560565\pi$
$757$	1.19170e7	−	2.06408e7i	0.755835	−	1.30914i	0.944958	−	0.327191i	$-0.106102\pi$
$758$	−4.41051e6	−	7.63923e6i	−0.278815	−	0.482921i
$759$			3.97896e6i			0.250706i
$760$	458603.	−	264774.i	0.0288007	−	0.0166281i
$761$	1.47926e6	−	854053.i	0.0925942	−	0.0534593i	−0.452988	−	0.891517i	$-0.649642\pi$
$761$	1.47926e6	−	854053.i	0.0925942	−	0.0534593i	0.545582	+	0.838057i	$0.316309\pi$
$762$		−	4.64247e6i		−	0.289642i
$763$	−5.35590e6	−	9.27670e6i	−0.333059	−	0.576875i
$764$	−1.28697e6	+	2.22910e6i	−0.0797692	+	0.138164i
$765$	−656664.	−	379125.i	−0.0405686	−	0.0234223i
$766$	8.71709e6			0.536784
$767$	−3.10852e6	−	2.53439e7i	−0.190794	−	1.55555i
$768$	1.23282e6			0.0754219
$769$	−8.28415e6	−	4.78285e6i	−0.505163	−	0.291656i	0.225680	−	0.974202i	$-0.427540\pi$
$769$	−8.28415e6	−	4.78285e6i	−0.505163	−	0.291656i	−0.730843	+	0.682545i	$0.760873\pi$
$770$	−2.83507e6	+	4.91049e6i	−0.172321	+	0.298468i
$771$	−1.13835e7	−	1.97168e7i	−0.689669	−	1.19454i
$772$			2.55225e6i			0.154127i
$773$	−2.02094e7	+	1.16679e7i	−1.21648	+	0.702334i	−0.964163	−	0.265311i	$-0.914526\pi$
$773$	−2.02094e7	+	1.16679e7i	−1.21648	+	0.702334i	−0.252316	+	0.967645i	$0.581192\pi$
$774$	3.61780e6	−	2.08874e6i	0.217066	−	0.125323i
$775$			1.77548e7i			1.06184i
$776$	3.77379e6	+	6.53639e6i	0.224969	+	0.389658i
$777$	−1.43329e7	+	2.48252e7i	−0.851687	+	1.47517i
$778$	−3.73955e6	−	2.15903e6i	−0.221498	−	0.127882i
$779$	−3.49647e6			−0.206436
$780$	1.82583e6	+	775295.i	0.107454	+	0.0456279i
$781$	−4.36359e7			−2.55986
$782$	682718.	+	394167.i	0.0399231	+	0.0230496i
$783$	−527949.	+	914434.i	−0.0307742	+	0.0533025i
$784$	2.62253e6	+	4.54236e6i	0.152381	+	0.263932i
$785$		−	408042.i		−	0.0236336i
$786$	2.12310e7	−	1.22577e7i	1.22578	−	0.707706i
$787$	−1.59295e7	+	9.19692e6i	−0.916782	+	0.529305i	−0.882607	−	0.470111i	$-0.844214\pi$
$787$	−1.59295e7	+	9.19692e6i	−0.916782	+	0.529305i	−0.0341753	+	0.999416i	$0.510880\pi$
$788$		−	2.46518e6i		−	0.141427i
$789$	−8.45818e6	−	1.46500e7i	−0.483710	−	0.837810i
$790$	1.97471e6	−	3.42030e6i	0.112573	−	0.194983i
$791$	2.67234e6	+	1.54288e6i	0.151862	+	0.0876778i
$792$	4.81540e6			0.272784
$793$	1.81400e7	−	2.22493e6i	1.02436	−	0.125642i
$794$	9.47733e6			0.533500
$795$	−3.21756e6	−	1.85766e6i	−0.180554	−	0.104243i
$796$	3.94634e6	−	6.83527e6i	0.220756	−	0.382360i
$797$	1.55260e7	+	2.68919e7i	0.865794	+	1.49960i	0.866257	+	0.499599i	$0.166519\pi$
$797$	1.55260e7	+	2.68919e7i	0.865794	+	1.49960i	−0.000462692		1.00000i	$0.500147\pi$
$798$		−	1.11167e7i		−	0.617973i
$799$	1.43898e7	−	8.30798e6i	0.797424	−	0.460393i
$800$	−2.66754e6	+	1.54011e6i	−0.147362	+	0.0850796i
$801$		−	8.20558e6i		−	0.451885i
$802$	6.98966e6	+	1.21064e7i	0.383725	+	0.664631i
$803$	2.53112e7	−	4.38403e7i	1.38524	−	2.39930i
$804$	−1.27030e7	−	7.33411e6i	−0.693055	−	0.400135i
$805$	651012.			0.0354078
$806$	8.65648e6	+	1.14906e7i	0.469358	+	0.623026i
$807$	1.43873e6			0.0777672
$808$	−1.68851e6	−	974863.i	−0.0909862	−	0.0525309i
$809$	1.75731e6	−	3.04376e6i	0.0944013	−	0.163508i	−0.814957	−	0.579521i	$-0.803240\pi$
$809$	1.75731e6	−	3.04376e6i	0.0944013	−	0.163508i	0.909359	+	0.416013i	$0.136573\pi$
$810$	−1.59421e6	−	2.76125e6i	−0.0853754	−	0.147874i
$811$			3.14290e7i			1.67795i	0.544170	+	0.838975i	$0.316845\pi$
$811$			3.14290e7i			1.67795i	−0.544170	+	0.838975i	$0.683155\pi$
$812$	−1.13677e6	+	656313.i	−0.0605037	+	0.0349318i
$813$	1.77718e6	−	1.02606e6i	0.0942987	−	0.0544434i
$814$		−	2.14201e7i		−	1.13308i
$815$	645107.	+	1.11736e6i	0.0340203	+	0.0589248i
$816$	1.52258e6	−	2.63718e6i	0.0800486	−	0.138648i
$817$	6.24089e6	+	3.60318e6i	0.327108	+	0.188856i
$818$	6.60409e6			0.345088
$819$	1.04204e7	−	7.85021e6i	0.542842	−	0.408951i
$820$	−790934.			−0.0410776
$821$	1.33282e7	+	7.69503e6i	0.690102	+	0.398431i	0.803650	−	0.595102i	$-0.202888\pi$
$821$	1.33282e7	+	7.69503e6i	0.690102	+	0.398431i	−0.113548	+	0.993532i	$0.536222\pi$
$822$	−2.89650e6	+	5.01689e6i	−0.149518	+	0.258973i
$823$	9.54478e6	+	1.65320e7i	0.491209	+	0.850799i	0.999949	−	0.0101213i	$-0.00322175\pi$
$823$	9.54478e6	+	1.65320e7i	0.491209	+	0.850799i	−0.508740	+	0.860920i	$0.669888\pi$
$824$		−	7.35627e6i		−	0.377433i
$825$	−3.32567e7	+	1.92007e7i	−1.70116	+	0.982162i
$826$	−2.80334e7	+	1.61851e7i	−1.42964	+	0.825402i
$827$		−	6.04481e6i		−	0.307340i	−0.988122	−	0.153670i	$-0.950891\pi$
$827$		−	6.04481e6i		−	0.307340i	0.988122	−	0.153670i	$-0.0491092\pi$
$828$	−276438.	−	478804.i	−0.0140127	−	0.0242707i
$829$	−2.26351e6	+	3.92051e6i	−0.114392	+	0.198133i	−0.917537	−	0.397651i	$-0.869825\pi$
$829$	−2.26351e6	+	3.92051e6i	−0.114392	+	0.198133i	0.803145	+	0.595784i	$0.203159\pi$
$830$	−1.22664e6	−	708200.i	−0.0618047	−	0.0356830i
$831$	−3.91279e7			−1.96555
$832$	−975502.	+	2.29732e6i	−0.0488562	+	0.115057i
$833$	1.29557e7			0.646915
$834$	1.71813e7	+	9.91961e6i	0.855343	+	0.493832i
$835$	−1.44334e6	+	2.49994e6i	−0.0716396	+	0.124083i
$836$	4.15341e6	+	7.19392e6i	0.205537	+	0.356000i
$837$		−	1.46711e7i		−	0.723852i
$838$	8.57171e6	−	4.94888e6i	0.421655	−	0.243443i
$839$	−8.59684e6	+	4.96339e6i	−0.421632	+	0.243430i	−0.695775	−	0.718259i	$-0.744939\pi$
$839$	−8.59684e6	+	4.96339e6i	−0.421632	+	0.243430i	0.274143	+	0.961689i	$0.411606\pi$
$840$		−	2.51471e6i		−	0.122967i
$841$	1.01653e7	+	1.76069e7i	0.495601	+	0.858406i
$842$	3.75773e6	−	6.50857e6i	0.182661	−	0.316378i
$843$	1.64700e7	+	9.50895e6i	0.798223	+	0.460854i
$844$	−1.16649e7			−0.563670
$845$	−2.88946e6	+	2.78888e6i	−0.139212	+	0.134366i
$846$	−1.16531e7			−0.559779
$847$	−5.00935e7	−	2.89215e7i	−2.39923	−	1.38520i
$848$	2.33737e6	−	4.04844e6i	0.111619	−	0.193329i
$849$	1.75531e6	+	3.04028e6i	0.0835764	+	0.144759i
$850$			7.60833e6i			0.361195i
$851$	−2.12984e6	+	1.22966e6i	−0.100814	+	0.0582052i
$852$	1.67598e7	−	9.67626e6i	0.790986	−	0.456676i
$853$		−	7.82388e6i		−	0.368171i	−0.982910	−	0.184085i	$-0.941068\pi$
$853$		−	7.82388e6i		−	0.368171i	0.982910	−	0.184085i	$-0.0589323\pi$
$854$	−1.15845e7	−	2.00650e7i	−0.543543	−	0.941445i
$855$	−458671.	+	794442.i	−0.0214579	+	0.0371661i
$856$	−5.53516e6	−	3.19573e6i	−0.258194	−	0.149068i
$857$	−1.78880e7			−0.831974			−0.415987	−	0.909371i	$-0.636564\pi$
$857$	−1.78880e7			−0.831974			−0.415987	+	0.909371i	$0.636564\pi$
$858$	−1.21617e7	+	2.86410e7i	−0.563998	+	1.32822i
$859$	−3.87910e7			−1.79369			−0.896846	−	0.442342i	$-0.854148\pi$
$859$	−3.87910e7			−1.79369			−0.896846	+	0.442342i	$0.854148\pi$
$860$	1.41175e6	+	815072.i	0.0650895	+	0.0375794i
$861$	−8.30196e6	+	1.43794e7i	−0.381657	+	0.661049i
$862$	2.61250e6	+	4.52498e6i	0.119753	+	0.207419i
$863$			2.54400e7i			1.16276i	0.813631	+	0.581381i	$0.197487\pi$
$863$			2.54400e7i			1.16276i	−0.813631	+	0.581381i	$0.802513\pi$
$864$	2.20424e6	−	1.27262e6i	0.100456	−	0.0579982i
$865$	−1.13620e6	+	655986.i	−0.0516315	+	0.0298095i
$866$		−	1.50719e7i		−	0.682924i
$867$	9.59386e6	+	1.66171e7i	0.433457	+	0.750769i
$868$	9.11912e6	−	1.57948e7i	0.410822	−	0.711564i
$869$	5.36528e7	+	3.09765e7i	2.41015	+	1.39150i
$870$	345725.			0.0154858
$871$	2.37184e7	−	1.78683e7i	1.05935	−	0.798065i
$872$	−3.54988e6			−0.158097
$873$	−1.13231e7	−	6.53737e6i	−0.502838	−	0.290314i
$874$	476870.	−	825963.i	0.0211165	−	0.0365748i
$875$	6.40518e6	+	1.10941e7i	0.282821	+	0.489860i
$876$			2.24510e7i			0.988499i
$877$	−2.22521e7	+	1.28472e7i	−0.976948	+	0.564041i	−0.901347	−	0.433097i	$-0.857421\pi$
$877$	−2.22521e7	+	1.28472e7i	−0.976948	+	0.564041i	−0.0756007	+	0.997138i	$0.524087\pi$
$878$	−1.52528e7	+	8.80622e6i	−0.667750	+	0.385525i
$879$		−	3.77843e7i		−	1.64945i
$880$	939540.	+	1.62733e6i	0.0408986	+	0.0708385i
$881$	−7.92801e6	+	1.37317e7i	−0.344132	+	0.596053i	−0.985196	−	0.171434i	$-0.945160\pi$
$881$	−7.92801e6	+	1.37317e7i	−0.344132	+	0.596053i	0.641064	+	0.767487i	$0.278493\pi$
$882$	−7.86878e6	−	4.54304e6i	−0.340593	−	0.196642i
$883$	1.02095e6			0.0440660			0.0220330	−	0.999757i	$-0.492986\pi$
$883$	1.02095e6			0.0440660			0.0220330	+	0.999757i	$0.492986\pi$
$884$	3.70950e6	+	4.92400e6i	0.159656	+	0.211927i
$885$	8.52582e6			0.365913
$886$	−9.23856e6	−	5.33389e6i	−0.395385	−	0.228276i
$887$	−6.16382e6	+	1.06761e7i	−0.263052	+	0.455619i	−0.967051	−	0.254582i	$-0.918062\pi$
$887$	−6.16382e6	+	1.06761e7i	−0.263052	+	0.455619i	0.704000	+	0.710200i	$0.251396\pi$
$888$	4.74990e6	+	8.22706e6i	0.202140	+	0.350116i
$889$		−	1.19151e7i		−	0.505642i
$890$	2.77302e6	−	1.60100e6i	0.117349	−	0.0677512i
$891$	4.33146e7	−	2.50077e7i	1.82785	−	1.05531i
$892$			1.98488e7i			0.835260i
$893$	−1.00511e7	−	1.74091e7i	−0.421780	−	0.730545i
$894$	−1.37835e7	+	2.38737e7i	−0.576787	+	0.999025i
$895$	1.60314e6	+	925574.i	0.0668982	+	0.0386237i
$896$	3.16409e6			0.131667
$897$	3.54600e6	−	434930.i	0.147149	−	0.0180484i
$898$	1.09147e6			0.0451672
$899$	2.17149e6	+	1.25371e6i	0.0896104	+	0.0517366i
$900$	2.66794e6	−	4.62101e6i	0.109792	−	0.190165i
$901$	−5.77345e6	−	9.99991e6i	−0.236932	−	0.410378i
$902$		−	1.24071e7i		−	0.507753i
$903$	2.96365e7	−	1.71107e7i	1.20951	−	0.698309i
$904$	885611.	−	511308.i	0.0360431	−	0.0208095i
$905$		−	1.22373e6i		−	0.0496664i
$906$	1.62208e7	+	2.80952e7i	0.656524	+	1.13713i
$907$	−1.06094e7	+	1.83760e7i	−0.428224	+	0.741706i	−0.996715	−	0.0809830i	$-0.974194\pi$
$907$	−1.06094e7	+	1.83760e7i	−0.428224	+	0.741706i	0.568491	+	0.822689i	$0.307527\pi$
$908$	−1.66240e7	−	9.59789e6i	−0.669147	−	0.386332i
$909$	3.37753e6			0.135578
$910$	4.68606e6	+	1.98983e6i	0.187588	+	0.0796547i
$911$	1.89806e7			0.757728			0.378864	−	0.925452i	$-0.376315\pi$
$911$	1.89806e7			0.757728			0.378864	+	0.925452i	$0.376315\pi$
$912$	−3.19050e6	−	1.84204e6i	−0.127020	−	0.0733350i
$913$	1.11093e7	−	1.92418e7i	0.441070	−	0.763956i
$914$	−1.36640e7	−	2.36667e7i	−0.541019	−	0.937072i
$915$			6.10238e6i			0.240961i
$916$	960550.	−	554574.i	0.0378252	−	0.0218384i
$917$	5.44901e7	−	3.14599e7i	2.13990	−	1.23547i
$918$		−	6.28692e6i		−	0.246224i
$919$	−1.51148e7	−	2.61796e7i	−0.590355	−	1.02252i	−0.994184	−	0.107690i	$-0.965655\pi$
$919$	−1.51148e7	−	2.61796e7i	−0.590355	−	1.02252i	0.403830	−	0.914834i	$-0.367679\pi$
$920$	107872.	−	186840.i	0.00420185	−	0.00727782i
$921$	−1.94630e7	−	1.12370e7i	−0.756069	−	0.436517i
$922$	1.66682e6			0.0645745
$923$	4.76973e6	+	3.88877e7i	0.184285	+	1.50248i
$924$	3.94472e7			1.51997
$925$	−2.05554e7	−	1.18676e7i	−0.789897	−	0.456047i
$926$	1.14282e7	−	1.97942e7i	0.437977	−	0.758598i
$927$	6.37167e6	+	1.10361e7i	0.243531	+	0.421808i
$928$			435003.i			0.0165815i
$929$	3.56438e7	−	2.05790e7i	1.35502	−	0.782319i	0.366070	−	0.930587i	$-0.380703\pi$
$929$	3.56438e7	−	2.05790e7i	1.35502	−	0.782319i	0.988947	+	0.148268i	$0.0473699\pi$
$930$	−4.16010e6	+	2.40184e6i	−0.157724	+	0.0910617i
$931$		−	1.56740e7i		−	0.592659i
$932$	2.20229e6	+	3.81448e6i	0.0830491	+	0.143845i
$933$	1.64338e6	−	2.84642e6i	0.0618065	−	0.107052i
$934$	4.95632e6	+	2.86153e6i	0.185905	+	0.107332i
$935$	4.64145e6			0.173630
$936$	−526360.	−	4.29142e6i	−0.0196378	−	0.160108i
$937$	−2.53118e7			−0.941834			−0.470917	−	0.882177i	$-0.656077\pi$
$937$	−2.53118e7			−0.941834			−0.470917	+	0.882177i	$0.656077\pi$
$938$	−3.26029e7	−	1.88233e7i	−1.20990	−	0.698535i
$939$	−53994.1	+	93520.6i	−0.00199840	+	0.00346133i
$940$	−2.27366e6	−	3.93809e6i	−0.0839277	−	0.145367i
$941$		−	2.97268e7i		−	1.09440i	−0.837004	−	0.547198i	$-0.815695\pi$
$941$		−	2.97268e7i		−	1.09440i	0.837004	−	0.547198i	$-0.184305\pi$
$942$	−2.45843e6	+	1.41937e6i	−0.0902672	+	0.0521158i
$943$	−1.23366e6	+	712252.i	−0.0451768	+	0.0260828i
$944$			1.07275e7i			0.391802i
$945$	−2.59589e6	−	4.49621e6i	−0.0945598	−	0.163782i
$946$	−1.27857e7	+	2.21455e7i	−0.464512	+	0.804559i
$947$	−2.10487e7	−	1.21525e7i	−0.762695	−	0.440342i	0.0675676	−	0.997715i	$-0.478476\pi$
$947$	−2.10487e7	−	1.21525e7i	−0.762695	−	0.440342i	−0.830262	+	0.557373i	$0.811810\pi$
$948$	−2.74761e7			−0.992967
$949$	−4.18366e7	−	1.77650e7i	−1.50796	−	0.640322i
$950$	9.20467e6			0.330902
$951$	5.39575e7	+	3.11524e7i	1.93464	+	1.11697i
$952$	3.90775e6	−	6.76843e6i	0.139745	−	0.242045i
$953$	−1.20785e7	−	2.09206e7i	−0.430806	−	0.746178i	0.566137	−	0.824311i	$-0.308437\pi$
$953$	−1.20785e7	−	2.09206e7i	−0.430806	−	0.746178i	−0.996943	+	0.0781333i	$0.975104\pi$
$954$			8.09808e6i			0.288079i
$955$	1.50684e6	−	869975.i	0.0534637	−	0.0308673i
$956$	9.64242e6	−	5.56705e6i	0.341225	−	0.197007i
$957$			5.42326e6i			0.191417i
$958$	−6.60581e6	−	1.14416e7i	−0.232548	−	0.402785i
$959$	−7.43399e6	+	1.28760e7i	−0.261021	+	0.452102i
$960$	−721721.	−	416686.i	−0.0252750	−	0.0145925i
$961$	−6.21009e6			−0.216915
$962$	−1.90893e7	+	2.34137e6i	−0.665046	+	0.0815705i
$963$	1.10720e7			0.384733
$964$	7.99198e6	+	4.61417e6i	0.276988	+	0.159919i
$965$	862643.	−	1.49414e6i	0.0298204	−	0.0516504i
$966$	−2.26455e6	−	3.92231e6i	−0.0780797	−	0.135238i
$967$			2.55383e7i			0.878266i	0.898422	+	0.439133i	$0.144714\pi$
$967$			2.55383e7i			0.878266i	−0.898422	+	0.439133i	$0.855286\pi$
$968$	−1.66009e7	+	9.58456e6i	−0.569435	+	0.328764i
$969$	−7.88075e6	+	4.54996e6i	−0.269624	+	0.155667i
$970$		−	5.10206e6i		−	0.174107i
$971$	1.71362e7	+	2.96808e7i	0.583265	+	1.01025i	0.995089	+	0.0989818i	$0.0315586\pi$
$971$	1.71362e7	+	2.96808e7i	0.583265	+	1.01025i	−0.411824	+	0.911263i	$0.635108\pi$
$972$	−6.25893e6	+	1.08408e7i	−0.212488	+	0.368040i
$973$	4.40964e7	+	2.54591e7i	1.49321	+	0.862106i
$974$	−5.90875e6			−0.199572
$975$	2.07467e7	+	2.75391e7i	0.698935	+	0.927766i
$976$	−7.67821e6			−0.258010
$977$	−1.68091e7	−	9.70472e6i	−0.563388	−	0.325272i	0.191116	−	0.981567i	$-0.438789\pi$
$977$	−1.68091e7	−	9.70472e6i	−0.563388	−	0.325272i	−0.754504	+	0.656295i	$0.772123\pi$
$978$	4.48801e6	−	7.77347e6i	0.150040	−	0.259877i
$979$	2.51143e7	+	4.34992e7i	0.837460	+	1.45052i
$980$		−	3.54560e6i		−	0.117930i
$981$	5.32562e6	−	3.07475e6i	0.176684	−	0.102009i
$982$	−6.80347e6	+	3.92799e6i	−0.225140	+	0.129984i
$983$			5.39371e6i			0.178034i	0.996030	+	0.0890172i	$0.0283726\pi$
$983$			5.39371e6i			0.178034i	−0.996030	+	0.0890172i	$0.971627\pi$
$984$	2.75126e6	+	4.76533e6i	0.0905826	+	0.156894i
$985$	−833214.	+	1.44317e6i	−0.0273631	+	0.0473944i
$986$	930533.	+	537244.i	0.0304817	+	0.0175986i
$987$	−9.54610e7			−3.11913
$988$	5.95713e6	−	4.48782e6i	0.194153	−	0.146266i
$989$	2.93596e6			0.0954463
$990$	−2.81904e6	−	1.62757e6i	−0.0914142	−	0.0527780i
$991$	1.49929e7	−	2.59685e7i	0.484956	−	0.839968i	−0.514895	−	0.857253i	$-0.672169\pi$
$991$	1.49929e7	−	2.59685e7i	0.484956	−	0.839968i	0.999851	+	0.0172851i	$0.00550228\pi$
$992$	−3.02207e6	−	5.23438e6i	−0.0975046	−	0.168883i
$993$		−	4.31368e7i		−	1.38827i
$994$	4.30146e7	−	2.48345e7i	1.38086	−	0.797240i
$995$	−4.62055e6	+	2.66768e6i	−0.147957	+	0.0854231i
$996$			9.85390e6i			0.314746i
$997$	2.04803e6	+	3.54729e6i	0.0652526	+	0.113021i	0.896806	−	0.442424i	$-0.145881\pi$
$997$	2.04803e6	+	3.54729e6i	0.0652526	+	0.113021i	−0.831553	+	0.555445i	$0.812548\pi$
$998$	−1.26188e7	+	2.18563e7i	−0.401043	+	0.694626i
$999$	1.69853e7	+	9.80647e6i	0.538468	+	0.310885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.e.a.17.4	✓	12
3.2	odd	2		234.6.l.c.199.2		12
4.3	odd	2		208.6.w.c.17.5		12
13.4	even	6		338.6.b.g.337.11		12
13.6	odd	12		338.6.a.m.1.5		6
13.7	odd	12		338.6.a.o.1.5		6
13.9	even	3		338.6.b.g.337.5		12
13.10	even	6	inner	26.6.e.a.23.4	yes	12
39.23	odd	6		234.6.l.c.127.2		12
52.23	odd	6		208.6.w.c.49.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.e.a.17.4	✓	12	1.1	even	1	trivial
26.6.e.a.23.4	yes	12	13.10	even	6	inner
208.6.w.c.17.5		12	4.3	odd	2
208.6.w.c.49.5		12	52.23	odd	6
234.6.l.c.127.2		12	39.23	odd	6
234.6.l.c.199.2		12	3.2	odd	2
338.6.a.m.1.5		6	13.6	odd	12
338.6.a.o.1.5		6	13.7	odd	12
338.6.b.g.337.5		12	13.9	even	3
338.6.b.g.337.11		12	13.4	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	26.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.46410 + 2.00000i) q^{2} +(-9.40569 + 16.2911i) q^{3} +(8.00000 + 13.8564i) q^{4} -10.8158i q^{5} +(-65.1645 + 37.6228i) q^{6} +(-167.247 + 96.5603i) q^{7} +64.0000i q^{8} +(-55.4339 - 96.0144i) q^{9} +O(q^{10})\)	\(q+(3.46410 + 2.00000i) q^{2} +(-9.40569 + 16.2911i) q^{3} +(8.00000 + 13.8564i) q^{4} -10.8158i q^{5} +(-65.1645 + 37.6228i) q^{6} +(-167.247 + 96.5603i) q^{7} +64.0000i q^{8} +(-55.4339 - 96.0144i) q^{9} +(21.6316 - 37.4670i) q^{10} +(587.730 + 339.326i) q^{11} -300.982 q^{12} +(238.160 - 560.868i) q^{13} -772.482 q^{14} +(176.201 + 101.730i) q^{15} +(-128.000 + 221.703i) q^{16} +(316.169 + 547.620i) q^{17} -443.471i q^{18} +(662.519 - 382.506i) q^{19} +(149.868 - 86.5263i) q^{20} -3632.86i q^{21} +(1357.30 + 2350.92i) q^{22} +(155.838 - 269.918i) q^{23} +(-1042.63 - 601.964i) q^{24} +3008.02 q^{25} +(1946.75 - 1466.58i) q^{26} -2485.59 q^{27} +(-2675.96 - 1544.96i) q^{28} +(212.404 - 367.894i) q^{29} +(406.920 + 704.806i) q^{30} +5902.48i q^{31} +(-886.810 + 512.000i) q^{32} +(-11056.0 + 6383.19i) q^{33} +2529.35i q^{34} +(1044.38 + 1808.91i) q^{35} +(886.943 - 1536.23i) q^{36} +(-6833.52 - 3945.33i) q^{37} +3060.05 q^{38} +(6897.12 + 9155.24i) q^{39} +692.211 q^{40} +(-3958.15 - 2285.24i) q^{41} +(7265.73 - 12584.6i) q^{42} +(4709.97 + 8157.90i) q^{43} +10858.4i q^{44} +(-1038.47 + 599.562i) q^{45} +(1079.67 - 623.350i) q^{46} -26277.1i q^{47} +(-2407.86 - 4170.53i) q^{48} +(10244.3 - 17743.6i) q^{49} +(10420.1 + 6016.04i) q^{50} -11895.1 q^{51} +(9676.89 - 1186.91i) q^{52} -18260.7 q^{53} +(-8610.33 - 4971.18i) q^{54} +(3670.08 - 6356.76i) q^{55} +(-6179.86 - 10703.8i) q^{56} +14390.9i q^{57} +(1471.58 - 849.616i) q^{58} +(36290.1 - 20952.1i) q^{59} +3255.36i q^{60} +(14996.5 + 25974.7i) q^{61} +(-11805.0 + 20446.8i) q^{62} +(18542.3 + 10705.4i) q^{63} -4096.00 q^{64} +(-6066.23 - 2575.88i) q^{65} -51065.5 q^{66} +(42205.3 + 24367.3i) q^{67} +(-5058.70 + 8761.92i) q^{68} +(2931.52 + 5077.54i) q^{69} +8355.01i q^{70} +(-55683.6 + 32148.9i) q^{71} +(6144.92 - 3547.77i) q^{72} -74592.6i q^{73} +(-15781.3 - 27334.1i) q^{74} +(-28292.5 + 49004.0i) q^{75} +(10600.3 + 6120.09i) q^{76} -131062. q^{77} +(5581.84 + 45508.9i) q^{78} +91288.3 q^{79} +(2397.89 + 1384.42i) q^{80} +(36849.1 - 63824.5i) q^{81} +(-9140.96 - 15832.6i) q^{82} -32739.2i q^{83} +(50338.4 - 29062.9i) q^{84} +(5922.94 - 3419.61i) q^{85} +37679.7i q^{86} +(3995.61 + 6920.60i) q^{87} +(-21716.9 + 37614.7i) q^{88} +(64096.5 + 37006.2i) q^{89} -4796.49 q^{90} +(14326.0 + 116800. i) q^{91} +4986.80 q^{92} +(-96158.0 - 55516.9i) q^{93} +(52554.1 - 91026.4i) q^{94} +(-4137.10 - 7165.67i) q^{95} -19262.8i q^{96} +(102131. - 58965.4i) q^{97} +(70974.4 - 40977.1i) q^{98} -75240.7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9}+O(q^{10}) \) 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9	\( 12 q + 96 q^{4} + 360 q^{7} - 706 q^{9} - 368 q^{10} + 504 q^{11} + 3202 q^{13} - 2272 q^{14} + 2112 q^{15} - 1536 q^{16} - 1910 q^{17} - 6888 q^{19} + 1440 q^{20} + 2160 q^{22} + 5920 q^{23} - 4672 q^{25} - 2320 q^{26} - 2736 q^{27} + 5760 q^{28} + 7922 q^{29} - 11696 q^{30} - 18780 q^{33} + 16864 q^{35} + 11296 q^{36} - 882 q^{37} + 26496 q^{38} + 48304 q^{39} - 11776 q^{40} + 44346 q^{41} + 23648 q^{42} - 41920 q^{43} - 158850 q^{45} - 33408 q^{46} + 4682 q^{49} + 11040 q^{50} + 133264 q^{51} + 43520 q^{52} - 187812 q^{53} + 1296 q^{54} + 17472 q^{55} - 18176 q^{56} - 73488 q^{58} + 74832 q^{59} + 27934 q^{61} - 4336 q^{62} + 156528 q^{63} - 49152 q^{64} + 69646 q^{65} + 6336 q^{66} + 85104 q^{67} + 30560 q^{68} - 77348 q^{69} - 106320 q^{71} - 78336 q^{72} + 96208 q^{74} + 192080 q^{75} - 110208 q^{76} - 151944 q^{77} + 9392 q^{78} + 30464 q^{79} + 23040 q^{80} - 72310 q^{81} - 87040 q^{82} + 53952 q^{84} - 148986 q^{85} - 121936 q^{87} - 34560 q^{88} + 93108 q^{89} + 282016 q^{90} - 56776 q^{91} + 189440 q^{92} + 107616 q^{93} + 158256 q^{94} + 232560 q^{95} + 147156 q^{97} + 46752 q^{98}+O(q^{100}) \) 12 * q + 96 * q^4 + 360 * q^7 - 706 * q^9 - 368 * q^10 + 504 * q^11 + 3202 * q^13 - 2272 * q^14 + 2112 * q^15 - 1536 * q^16 - 1910 * q^17 - 6888 * q^19 + 1440 * q^20 + 2160 * q^22 + 5920 * q^23 - 4672 * q^25 - 2320 * q^26 - 2736 * q^27 + 5760 * q^28 + 7922 * q^29 - 11696 * q^30 - 18780 * q^33 + 16864 * q^35 + 11296 * q^36 - 882 * q^37 + 26496 * q^38 + 48304 * q^39 - 11776 * q^40 + 44346 * q^41 + 23648 * q^42 - 41920 * q^43 - 158850 * q^45 - 33408 * q^46 + 4682 * q^49 + 11040 * q^50 + 133264 * q^51 + 43520 * q^52 - 187812 * q^53 + 1296 * q^54 + 17472 * q^55 - 18176 * q^56 - 73488 * q^58 + 74832 * q^59 + 27934 * q^61 - 4336 * q^62 + 156528 * q^63 - 49152 * q^64 + 69646 * q^65 + 6336 * q^66 + 85104 * q^67 + 30560 * q^68 - 77348 * q^69 - 106320 * q^71 - 78336 * q^72 + 96208 * q^74 + 192080 * q^75 - 110208 * q^76 - 151944 * q^77 + 9392 * q^78 + 30464 * q^79 + 23040 * q^80 - 72310 * q^81 - 87040 * q^82 + 53952 * q^84 - 148986 * q^85 - 121936 * q^87 - 34560 * q^88 + 93108 * q^89 + 282016 * q^90 - 56776 * q^91 + 189440 * q^92 + 107616 * q^93 + 158256 * q^94 + 232560 * q^95 + 147156 * q^97 + 46752 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more