LMFDB - Embedded newform 50.6.d.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,6,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.01919099065$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	50.31
Dual form			50.6.d.b.21.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 - 3.80423i) q^{2} +(17.4616 - 12.6866i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(53.8689 - 14.9378i) q^{5} +(-69.8465 - 50.7465i) q^{6} +157.525 q^{7} +(51.7771 + 37.6183i) q^{8} +(68.8673 - 211.952i) q^{9} +O(q^{10})$	\(q+(-1.23607 - 3.80423i) q^{2} +(17.4616 - 12.6866i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(53.8689 - 14.9378i) q^{5} +(-69.8465 - 50.7465i) q^{6} +157.525 q^{7} +(51.7771 + 37.6183i) q^{8} +(68.8673 - 211.952i) q^{9} +(-123.412 - 186.465i) q^{10} +(-28.9573 - 89.1214i) q^{11} +(-106.716 + 328.438i) q^{12} +(-194.950 + 599.996i) q^{13} +(-194.712 - 599.262i) q^{14} +(751.129 - 944.253i) q^{15} +(79.1084 - 243.470i) q^{16} +(-905.297 - 657.737i) q^{17} -891.436 q^{18} +(-1501.65 - 1091.01i) q^{19} +(-556.810 + 699.973i) q^{20} +(2750.65 - 1998.47i) q^{21} +(-303.245 + 220.320i) q^{22} +(-144.446 - 444.560i) q^{23} +1381.36 q^{24} +(2678.72 - 1609.37i) q^{25} +2523.49 q^{26} +(134.335 + 413.440i) q^{27} +(-2039.05 + 1481.46i) q^{28} +(-4995.92 + 3629.75i) q^{29} +(-4520.60 - 1690.30i) q^{30} +(5630.27 + 4090.63i) q^{31} -1024.00 q^{32} +(-1636.29 - 1188.84i) q^{33} +(-1383.17 + 4256.96i) q^{34} +(8485.73 - 2353.09i) q^{35} +(1101.88 + 3391.23i) q^{36} +(-5049.57 + 15541.0i) q^{37} +(-2294.32 + 7061.18i) q^{38} +(4207.77 + 12950.2i) q^{39} +(3351.11 + 1253.02i) q^{40} +(2640.18 - 8125.65i) q^{41} +(-11002.6 - 7993.86i) q^{42} +3858.84 q^{43} +(1212.98 + 881.281i) q^{44} +(543.710 - 12446.3i) q^{45} +(-1512.66 + 1099.01i) q^{46} +(12130.1 - 8813.01i) q^{47} +(-1707.46 - 5255.01i) q^{48} +8007.27 q^{49} +(-9433.49 - 8201.18i) q^{50} -24152.4 q^{51} +(-3119.21 - 9599.93i) q^{52} +(14555.8 - 10575.4i) q^{53} +(1406.77 - 1022.08i) q^{54} +(-2891.18 - 4368.32i) q^{55} +(8156.21 + 5925.83i) q^{56} -40062.5 q^{57} +(19983.7 + 14519.0i) q^{58} +(-10162.9 + 31278.1i) q^{59} +(-842.528 + 19286.7i) q^{60} +(4836.13 + 14884.1i) q^{61} +(8602.29 - 26475.1i) q^{62} +(10848.3 - 33387.8i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-1539.14 + 35233.3i) q^{65} +(-2500.03 + 7694.30i) q^{66} +(-31331.7 - 22763.8i) q^{67} +17904.1 q^{68} +(-8162.24 - 5930.21i) q^{69} +(-19440.6 - 29373.1i) q^{70} +(23131.6 - 16806.1i) q^{71} +(11539.0 - 8383.57i) q^{72} +(-25875.1 - 79635.3i) q^{73} +65363.0 q^{74} +(26357.4 - 62086.2i) q^{75} +29698.3 q^{76} +(-4561.51 - 14038.9i) q^{77} +(44064.3 - 32014.6i) q^{78} +(-71627.4 + 52040.4i) q^{79} +(624.564 - 14297.2i) q^{80} +(51403.0 + 37346.5i) q^{81} -34175.2 q^{82} +(53476.1 + 38852.7i) q^{83} +(-16810.5 + 51737.4i) q^{84} +(-58592.5 - 21908.4i) q^{85} +(-4769.79 - 14679.9i) q^{86} +(-41187.7 + 126763. i) q^{87} +(1853.27 - 5703.77i) q^{88} +(-3395.16 - 10449.2i) q^{89} +(-48020.7 + 13316.1i) q^{90} +(-30709.7 + 94514.6i) q^{91} +(6050.65 + 4396.05i) q^{92} +150210. q^{93} +(-48520.3 - 35252.0i) q^{94} +(-97189.7 - 36340.3i) q^{95} +(-17880.7 + 12991.1i) q^{96} +(-39565.7 + 28746.1i) q^{97} +(-9897.53 - 30461.5i) q^{98} -20883.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9 - 220 * q^10 - 389 * q^11 + 192 * q^12 + 1047 * q^13 + 164 * q^14 - 640 * q^15 - 1792 * q^16 + 909 * q^17 - 11576 * q^18 + 260 * q^19 - 1040 * q^20 - 1849 * q^21 + 556 * q^22 + 817 * q^23 + 2432 * q^24 + 16055 * q^25 - 4528 * q^26 + 1675 * q^27 + 2544 * q^28 - 2445 * q^29 - 5440 * q^30 + 16731 * q^31 - 28672 * q^32 + 29629 * q^33 - 7576 * q^34 - 825 * q^35 - 7136 * q^36 + 39819 * q^37 + 3100 * q^38 + 26008 * q^39 + 10231 * q^41 + 7396 * q^42 - 86148 * q^43 - 2224 * q^44 - 7870 * q^45 - 11708 * q^46 + 10019 * q^47 + 3072 * q^48 + 147076 * q^49 + 16520 * q^50 - 108074 * q^51 + 16752 * q^52 + 74512 * q^53 + 4260 * q^54 + 2735 * q^55 - 10176 * q^56 - 176840 * q^57 + 9780 * q^58 - 13430 * q^59 + 5760 * q^60 - 29774 * q^61 + 63956 * q^62 - 206818 * q^63 - 28672 * q^64 + 51235 * q^65 + 23264 * q^66 - 85061 * q^67 - 89696 * q^68 - 185227 * q^69 - 25260 * q^70 + 148501 * q^71 + 64064 * q^72 + 189082 * q^73 + 305304 * q^74 + 93630 * q^75 + 16480 * q^76 + 127243 * q^77 + 32028 * q^78 + 46930 * q^79 + 39680 * q^80 - 179812 * q^81 - 338864 * q^82 + 66807 * q^83 - 34464 * q^84 - 877380 * q^85 + 121332 * q^86 - 226000 * q^87 + 24896 * q^88 - 347190 * q^89 + 628660 * q^90 + 197001 * q^91 + 46832 * q^92 - 64906 * q^93 - 40076 * q^94 + 85970 * q^95 - 7168 * q^96 + 502364 * q^97 + 185056 * q^98 + 1151018 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$2$	−1.23607	−	3.80423i	−0.218508	−	0.672499i
$3$	17.4616	−	12.6866i	1.12016	−	0.813847i	0.135931	−	0.990718i	$-0.456598\pi$
$3$	17.4616	−	12.6866i	1.12016	−	0.813847i	0.984234	+	0.176871i	$0.0565976\pi$
$4$	−12.9443	+	9.40456i	−0.404508	+	0.293893i
$5$	53.8689	−	14.9378i	0.963637	−	0.267216i
$5$	53.8689	−	14.9378i	0.963637	−	0.267216i
$6$	−69.8465	−	50.7465i	−0.792076	−	0.575477i
$7$	157.525			1.21508			0.607541	−	0.794288i	$-0.292156\pi$
$7$	157.525			1.21508			0.607541	+	0.794288i	$0.292156\pi$
$8$	51.7771	+	37.6183i	0.286031	+	0.207813i
$9$	68.8673	−	211.952i	0.283404	−	0.872229i
$10$	−123.412	−	186.465i	−0.390265	−	0.589655i
$11$	−28.9573	−	89.1214i	−0.0721567	−	0.222075i	0.908474	−	0.417941i	$-0.137248\pi$
$11$	−28.9573	−	89.1214i	−0.0721567	−	0.222075i	−0.980631	+	0.195866i	$0.937248\pi$
$12$	−106.716	+	328.438i	−0.213932	+	0.658416i
$13$	−194.950	+	599.996i	−0.319938	+	0.984668i	0.653736	+	0.756723i	$0.273201\pi$
$13$	−194.950	+	599.996i	−0.319938	+	0.984668i	−0.973674	+	0.227945i	$0.926799\pi$
$14$	−194.712	−	599.262i	−0.265505	−	0.817141i
$15$	751.129	−	944.253i	0.861959	−	1.08358i
$16$	79.1084	−	243.470i	0.0772542	−	0.237764i
$17$	−905.297	−	657.737i	−0.759747	−	0.551988i	0.139086	−	0.990280i	$-0.455584\pi$
$17$	−905.297	−	657.737i	−0.759747	−	0.551988i	−0.898833	+	0.438292i	$0.855584\pi$
$18$	−891.436			−0.648499
$19$	−1501.65	−	1091.01i	−0.954300	−	0.693339i	−0.00247996	−	0.999997i	$-0.500789\pi$
$19$	−1501.65	−	1091.01i	−0.954300	−	0.693339i	−0.951820	+	0.306657i	$0.900789\pi$
$20$	−556.810	+	699.973i	−0.311266	+	0.391297i
$21$	2750.65	−	1998.47i	1.36109	−	0.988891i
$22$	−303.245	+	220.320i	−0.133579	+	0.0970505i
$23$	−144.446	−	444.560i	−0.0569360	−	0.175231i	0.918544	−	0.395318i	$-0.129366\pi$
$23$	−144.446	−	444.560i	−0.0569360	−	0.175231i	−0.975480	+	0.220087i	$0.929366\pi$
$24$	1381.36			0.489530
$25$	2678.72	−	1609.37i	0.857191	−	0.514998i
$26$	2523.49			0.732097
$27$	134.335	+	413.440i	0.0354633	+	0.109145i
$28$	−2039.05	+	1481.46i	−0.491511	+	0.357104i
$29$	−4995.92	+	3629.75i	−1.10311	+	0.801459i	−0.981565	−	0.191127i	$-0.938786\pi$
$29$	−4995.92	+	3629.75i	−1.10311	+	0.801459i	−0.121548	+	0.992586i	$0.538786\pi$
$30$	−4520.60	−	1690.30i	−0.917050	−	0.342895i
$31$	5630.27	+	4090.63i	1.05226	+	0.764515i	0.972642	−	0.232310i	$-0.0746284\pi$
$31$	5630.27	+	4090.63i	1.05226	+	0.764515i	0.0796229	+	0.996825i	$0.474628\pi$
$32$	−1024.00			−0.176777
$33$	−1636.29	−	1188.84i	−0.261563	−	0.190036i
$34$	−1383.17	+	4256.96i	−0.205201	+	0.631542i
$35$	8485.73	−	2353.09i	1.17090	−	0.324689i
$36$	1101.88	+	3391.23i	0.141702	+	0.436114i
$37$	−5049.57	+	15541.0i	−0.606387	+	1.86627i	−0.119429	+	0.992843i	$0.538107\pi$
$37$	−5049.57	+	15541.0i	−0.606387	+	1.86627i	−0.486958	+	0.873425i	$0.661893\pi$
$38$	−2294.32	+	7061.18i	−0.257748	+	0.793265i
$39$	4207.77	+	12950.2i	0.442986	+	1.36337i
$40$	3351.11	+	1253.02i	0.331161	+	0.123825i
$41$	2640.18	−	8125.65i	0.245287	−	0.754915i	−0.750302	−	0.661095i	$-0.770092\pi$
$41$	2640.18	−	8125.65i	0.245287	−	0.754915i	0.995589	−	0.0938204i	$-0.0299079\pi$
$42$	−11002.6	−	7993.86i	−0.962437	−	0.699252i
$43$	3858.84			0.318262			0.159131	−	0.987257i	$-0.449131\pi$
$43$	3858.84			0.318262			0.159131	+	0.987257i	$0.449131\pi$
$44$	1212.98	+	881.281i	0.0944543	+	0.0686251i
$45$	543.710	−	12446.3i	0.0400255	−	0.916242i
$46$	−1512.66	+	1099.01i	−0.105402	+	0.0765788i
$47$	12130.1	−	8813.01i	0.800974	−	0.581942i	−0.110226	−	0.993907i	$-0.535157\pi$
$47$	12130.1	−	8813.01i	0.800974	−	0.581942i	0.911200	+	0.411965i	$0.135157\pi$
$48$	−1707.46	−	5255.01i	−0.106966	−	0.329208i
$49$	8007.27			0.476425
$50$	−9433.49	−	8201.18i	−0.533639	−	0.463929i
$51$	−24152.4			−1.30028
$52$	−3119.21	−	9599.93i	−0.159969	−	0.492334i
$53$	14555.8	−	10575.4i	0.711781	−	0.517139i	−0.171967	−	0.985103i	$-0.555012\pi$
$53$	14555.8	−	10575.4i	0.711781	−	0.517139i	0.883748	+	0.467964i	$0.155012\pi$
$54$	1406.77	−	1022.08i	0.0656506	−	0.0476980i
$55$	−2891.18	−	4368.32i	−0.128875	−	0.194719i
$56$	8156.21	+	5925.83i	0.347551	+	0.252510i
$57$	−40062.5			−1.63325
$58$	19983.7	+	14519.0i	0.780019	+	0.566717i
$59$	−10162.9	+	31278.1i	−0.380090	+	1.16980i	0.559890	+	0.828567i	$0.310843\pi$
$59$	−10162.9	+	31278.1i	−0.380090	+	1.16980i	−0.939980	+	0.341229i	$0.889157\pi$
$60$	−842.528	+	19286.7i	−0.0302139	+	0.691640i
$61$	4836.13	+	14884.1i	0.166408	+	0.512150i	0.999137	−	0.0415299i	$-0.0132232\pi$
$61$	4836.13	+	14884.1i	0.166408	+	0.512150i	−0.832730	+	0.553680i	$0.813223\pi$
$62$	8602.29	−	26475.1i	0.284207	−	0.874699i
$63$	10848.3	−	33387.8i	0.344360	−	1.05983i
$64$	1265.73	+	3895.53i	0.0386271	+	0.118882i
$65$	−1539.14	+	35233.3i	−0.0451851	+	1.03435i
$66$	−2500.03	+	7694.30i	−0.0706457	+	0.217425i
$67$	−31331.7	−	22763.8i	−0.852700	−	0.619523i	0.0731891	−	0.997318i	$-0.476682\pi$
$67$	−31331.7	−	22763.8i	−0.852700	−	0.619523i	−0.925889	+	0.377795i	$0.876682\pi$
$68$	17904.1			0.469549
$69$	−8162.24	−	5930.21i	−0.206389	−	0.149950i
$70$	−19440.6	−	29373.1i	−0.474204	−	0.716480i
$71$	23131.6	−	16806.1i	0.544577	−	0.395659i	−0.281205	−	0.959648i	$-0.590734\pi$
$71$	23131.6	−	16806.1i	0.544577	−	0.395659i	0.825782	+	0.563989i	$0.190734\pi$
$72$	11539.0	−	8383.57i	0.262323	−	0.190589i
$73$	−25875.1	−	79635.3i	−0.568296	−	1.74904i	−0.657949	−	0.753063i	$-0.728576\pi$
$73$	−25875.1	−	79635.3i	−0.568296	−	1.74904i	0.0896526	−	0.995973i	$-0.471424\pi$
$74$	65363.0			1.38756
$75$	26357.4	−	62086.2i	0.541066	−	1.27451i
$76$	29698.3			0.589790
$77$	−4561.51	−	14038.9i	−0.0876763	−	0.269840i
$78$	44064.3	−	32014.6i	0.820069	−	0.595815i
$79$	−71627.4	+	52040.4i	−1.29125	+	0.938151i	−0.999830	−	0.0184433i	$-0.994129\pi$
$79$	−71627.4	+	52040.4i	−1.29125	+	0.938151i	−0.291424	+	0.956594i	$0.594129\pi$
$80$	624.564	−	14297.2i	0.0109107	−	0.249762i
$81$	51403.0	+	37346.5i	0.870514	+	0.632465i
$82$	−34175.2			−0.561277
$83$	53476.1	+	38852.7i	0.852049	+	0.619050i	0.925710	−	0.378233i	$-0.123468\pi$
$83$	53476.1	+	38852.7i	0.852049	+	0.619050i	−0.0736612	+	0.997283i	$0.523468\pi$
$84$	−16810.5	+	51737.4i	−0.259945	+	0.800030i
$85$	−58592.5	−	21908.4i	−0.879620	−	0.328900i
$86$	−4769.79	−	14679.9i	−0.0695429	−	0.214031i
$87$	−41187.7	+	126763.i	−0.583403	+	1.79553i
$88$	1853.27	−	5703.77i	0.0255112	−	0.0785155i
$89$	−3395.16	−	10449.2i	−0.0454344	−	0.139833i	0.925766	−	0.378097i	$-0.123421\pi$
$89$	−3395.16	−	10449.2i	−0.0454344	−	0.139833i	−0.971200	+	0.238264i	$0.923421\pi$
$90$	−48020.7	+	13316.1i	−0.624917	+	0.173289i
$91$	−30709.7	+	94514.6i	−0.388751	+	1.19645i
$92$	6050.65	+	4396.05i	0.0745302	+	0.0541494i
$93$	150210.			1.80091
$94$	−48520.3	−	35252.0i	−0.566374	−	0.411495i
$95$	−97189.7	−	36340.3i	−1.10487	−	0.413123i
$96$	−17880.7	+	12991.1i	−0.198019	+	0.143869i
$97$	−39565.7	+	28746.1i	−0.426962	+	0.310206i	−0.780433	−	0.625239i	$-0.785001\pi$
$97$	−39565.7	+	28746.1i	−0.426962	+	0.310206i	0.353471	+	0.935445i	$0.385001\pi$
$98$	−9897.53	−	30461.5i	−0.104103	−	0.320395i
$99$	−20883.6			−0.214150
$100$	−19538.7	+	46024.3i	−0.195387	+	0.460243i
$101$	120723.			1.17757			0.588784	−	0.808291i	$-0.299607\pi$
$101$	120723.			1.17757			0.588784	+	0.808291i	$0.299607\pi$
$102$	29854.0	+	91881.3i	0.284121	+	0.874433i
$103$	−157978.	+	114778.i	−1.46725	+	1.06602i	−0.485852	+	0.874041i	$0.661490\pi$
$103$	−157978.	+	114778.i	−1.46725	+	1.06602i	−0.981399	+	0.191979i	$0.938510\pi$
$104$	−32664.8	+	23732.3i	−0.296139	+	0.215158i
$105$	118322.	−	148744.i	1.04735	−	1.31664i
$106$	−58223.2	−	42301.6i	−0.503305	−	0.365672i
$107$	−19431.8			−0.164079			−0.0820395	−	0.996629i	$-0.526143\pi$
$107$	−19431.8			−0.164079			−0.0820395	+	0.996629i	$0.526143\pi$
$108$	−5627.08	−	4088.32i	−0.0464220	−	0.0337276i
$109$	69255.9	−	213148.i	0.558330	−	1.71836i	−0.128655	−	0.991689i	$-0.541066\pi$
$109$	69255.9	−	213148.i	0.558330	−	1.71836i	0.686984	−	0.726672i	$-0.258934\pi$
$110$	−13044.4	+	16398.2i	−0.102788	+	0.129216i
$111$	108989.	+	335433.i	0.839604	+	2.58403i
$112$	12461.6	−	38352.8i	0.0938703	−	0.288903i
$113$	−47133.9	+	145063.i	−0.347246	+	1.06871i	0.613124	+	0.789987i	$0.289913\pi$
$113$	−47133.9	+	145063.i	−0.347246	+	1.06871i	−0.960370	+	0.278727i	$0.910087\pi$
$114$	49520.0	+	152407.i	0.356877	+	1.09835i
$115$	−14421.9	−	21790.3i	−0.101690	−	0.153645i
$116$	30532.3	−	93968.8i	0.210676	−	0.648394i
$117$	113744.	+	82640.1i	0.768184	+	0.558118i
$118$	131551.			0.869739
$119$	−142607.	−	103610.i	−0.923155	−	0.670711i
$120$	74412.5	−	20634.5i	0.471729	−	0.130810i
$121$	123189.	−	89502.0i	0.764906	−	0.555737i
$122$	50644.6	−	36795.4i	0.308059	−	0.223818i
$123$	−56985.1	−	175382.i	−0.339624	−	1.04526i
$124$	−111350.			−0.650335
$125$	120259.	−	126709.i	0.688405	−	0.725326i
$126$	−140424.			−0.787979
$127$	−7270.17	−	22375.3i	−0.0399977	−	0.123100i	0.929064	−	0.369919i	$-0.120615\pi$
$127$	−7270.17	−	22375.3i	−0.0399977	−	0.123100i	−0.969062	+	0.246819i	$0.920615\pi$
$128$	13254.9	−	9630.27i	0.0715077	−	0.0519534i
$129$	67381.6	−	48955.6i	0.356506	−	0.259017i
$130$	135938.	−	37695.5i	0.705475	−	0.195628i
$131$	−138547.	−	100660.i	−0.705375	−	0.512485i	0.176304	−	0.984336i	$-0.443586\pi$
$131$	−138547.	−	100660.i	−0.705375	−	0.512485i	−0.881678	+	0.471851i	$0.843586\pi$
$132$	32361.1			0.161655
$133$	−236548.	−	171862.i	−1.15955	−	0.842464i
$134$	−47870.5	+	147330.i	−0.230306	+	0.708810i
$135$	13412.4	+	20264.9i	0.0633389	+	0.0956995i
$136$	−22130.7	−	68111.4i	−0.102600	−	0.315771i
$137$	31832.8	−	97971.4i	0.144902	−	0.445962i	−0.852097	−	0.523385i	$-0.824669\pi$
$137$	31832.8	−	97971.4i	0.144902	−	0.445962i	0.996998	+	0.0774227i	$0.0246691\pi$
$138$	−12470.8	+	38381.1i	−0.0557438	+	0.171562i
$139$	62894.9	+	193571.i	0.276108	+	0.849772i	0.988924	+	0.148421i	$0.0474192\pi$
$139$	62894.9	+	193571.i	0.276108	+	0.849772i	−0.712817	+	0.701350i	$0.752581\pi$
$140$	−87711.8	+	110264.i	−0.378214	+	0.475458i
$141$	100003.	−	307779.i	0.423611	−	1.30374i
$142$	−92526.3	−	67224.3i	−0.385074	−	0.279773i
$143$	59117.7			0.241756
$144$	−46156.0	−	33534.3i	−0.185491	−	0.134767i
$145$	−214904.	+	270159.i	−0.848838	+	1.06708i
$146$	−270967.	+	196869.i	−1.05205	+	0.764357i
$147$	139820.	−	101585.i	0.533674	−	0.387737i
$148$	−80793.1	−	248656.i	−0.303194	−	0.933134i
$149$	276441.			1.02009			0.510043	−	0.860149i	$-0.329629\pi$
$149$	276441.			1.02009			0.510043	+	0.860149i	$0.329629\pi$
$150$	−268769.	−	23526.9i	−0.975330	−	0.0853763i
$151$	266883.			0.952528			0.476264	−	0.879302i	$-0.341991\pi$
$151$	266883.			0.952528			0.476264	+	0.879302i	$0.341991\pi$
$152$	−36709.1	−	112979.i	−0.128874	−	0.396633i
$153$	−201754.	+	146583.i	−0.696776	+	0.506237i
$154$	−47768.8	+	34706.0i	−0.162309	+	0.117924i
$155$	364402.	+	136254.i	1.21829	+	0.455533i
$156$	−176257.	−	128058.i	−0.579876	−	0.421305i
$157$	−280945.			−0.909646			−0.454823	−	0.890582i	$-0.650297\pi$
$157$	−280945.			−0.909646			−0.454823	+	0.890582i	$0.650297\pi$
$158$	286510.	+	208161.i	0.913054	+	0.663373i
$159$	120002.	−	369328.i	0.376439	−	1.15856i
$160$	−55161.8	+	15296.3i	−0.170349	+	0.0472375i
$161$	−22754.0	−	70029.6i	−0.0691819	−	0.212920i
$162$	78536.8	−	241711.i	0.235118	−	0.723618i
$163$	−98028.8	+	301701.i	−0.288991	+	0.889423i	0.696183	+	0.717865i	$0.254880\pi$
$163$	−98028.8	+	301701.i	−0.288991	+	0.889423i	−0.985174	+	0.171559i	$0.945120\pi$
$164$	42242.9	+	130010.i	0.122643	+	0.377458i
$165$	−105904.	−	39598.7i	−0.302832	−	0.113232i
$166$	81704.2	−	251460.i	0.230131	−	0.708269i
$167$	−315580.	−	229282.i	−0.875624	−	0.636178i	0.0564660	−	0.998405i	$-0.482017\pi$
$167$	−315580.	−	229282.i	−0.875624	−	0.636178i	−0.932090	+	0.362226i	$0.882017\pi$
$168$	217600.			0.594819
$169$	−21606.9	−	15698.3i	−0.0581937	−	0.0422802i
$170$	−10920.2	+	249980.i	−0.0289807	+	0.663410i
$171$	−334657.	+	243142.i	−0.875203	+	0.635873i
$172$	−49949.8	+	36290.7i	−0.128740	+	0.0935350i
$173$	−14041.8	−	43216.2i	−0.0356703	−	0.109782i	0.931636	−	0.363393i	$-0.118382\pi$
$173$	−14041.8	−	43216.2i	−0.0356703	−	0.109782i	−0.967306	+	0.253611i	$0.918382\pi$
$174$	533144.			1.33497
$175$	421967.	−	253517.i	1.04156	−	0.625765i
$176$	−23989.2			−0.0583760
$177$	219353.	+	675099.i	0.526272	+	1.61970i
$178$	−35554.5	+	25831.9i	−0.0841095	+	0.0611091i
$179$	273256.	−	198532.i	0.637436	−	0.463124i	−0.221532	−	0.975153i	$-0.571106\pi$
$179$	273256.	−	198532.i	0.637436	−	0.463124i	0.858968	+	0.512029i	$0.171106\pi$
$180$	110014.	+	166222.i	0.253086	+	0.382391i
$181$	−339352.	−	246553.i	−0.769934	−	0.559390i	0.132007	−	0.991249i	$-0.457858\pi$
$181$	−339352.	−	246553.i	−0.769934	−	0.559390i	−0.901941	+	0.431859i	$0.857858\pi$
$182$	397514.			0.889558
$183$	273275.	+	198546.i	0.603216	+	0.438262i
$184$	9244.57	−	28451.9i	0.0201299	−	0.0619535i
$185$	−39866.6	+	912605.i	−0.0856406	+	1.96044i
$186$	−185670.	−	571433.i	−0.393513	−	1.21111i
$187$	−32403.5	+	99727.7i	−0.0677622	+	0.208551i
$188$	−74132.4	+	228156.i	−0.152972	+	0.470801i
$189$	21161.1	+	65127.3i	0.0430908	+	0.132620i
$190$	−18113.8	+	414651.i	−0.0364019	+	0.833294i
$191$	−49770.4	+	153178.i	−0.0987160	+	0.303817i	−0.988204	−	0.153141i	$-0.951061\pi$
$191$	−49770.4	+	153178.i	−0.0987160	+	0.303817i	0.889488	+	0.456958i	$0.151061\pi$
$192$	71522.9	+	51964.4i	0.140021	+	0.101731i
$193$	−723215.			−1.39757			−0.698786	−	0.715330i	$-0.746276\pi$
$193$	−723215.			−1.39757			−0.698786	+	0.715330i	$0.746276\pi$
$194$	158263.	+	114985.i	0.301908	+	0.219349i
$195$	420115.	+	634757.i	0.791192	+	1.19542i
$196$	−103648.	+	75304.9i	−0.192718	+	0.140018i
$197$	599767.	−	435756.i	1.10107	−	0.799977i	0.119840	−	0.992793i	$-0.461762\pi$
$197$	599767.	−	435756.i	1.10107	−	0.799977i	0.981235	+	0.192816i	$0.0617620\pi$
$198$	25813.6	+	79446.1i	0.0467935	+	0.144016i
$199$	−819946.			−1.46775			−0.733876	−	0.679284i	$-0.762291\pi$
$199$	−819946.			−1.46775			−0.733876	+	0.679284i	$0.762291\pi$
$200$	199238.	+	17440.5i	0.352207	+	0.0308307i
$201$	−835897.			−1.45936
$202$	−149222.	−	459257.i	−0.257308	−	0.791912i
$203$	−786984.	+	571777.i	−1.34037	+	0.973838i
$204$	312636.	−	227143.i	0.525973	−	0.382141i
$205$	20844.4	−	477158.i	0.0346421	−	0.793009i
$206$	631913.	+	459112.i	1.03750	+	0.753790i
$207$	−104173.			−0.168977
$208$	130659.	+	94929.4i	0.209402	+	0.152140i
$209$	−53748.9	+	165422.i	−0.0851145	+	0.261956i
$210$	−712110.	−	266266.i	−1.11429	−	0.416646i
$211$	64792.7	+	199411.i	0.100189	+	0.308350i	0.988571	−	0.150755i	$-0.0481703\pi$
$211$	64792.7	+	199411.i	0.100189	+	0.308350i	−0.888382	+	0.459105i	$0.848170\pi$
$212$	−88957.1	+	273782.i	−0.135938	+	0.418374i
$213$	190703.	−	586923.i	0.288011	−	0.886405i
$214$	24019.0	+	73922.8i	0.0358526	+	0.110343i
$215$	207871.	−	57642.6i	0.306689	−	0.0850447i
$216$	−8597.42	+	26460.1i	−0.0125382	+	0.0385885i
$217$	886911.	+	644378.i	1.27859	+	0.928949i
$218$	−896467.			−1.27760
$219$	−1.46212e6	−	1.06230e6i	−2.06003	−	1.49670i
$220$	78506.3	+	29354.4i	0.109357	+	0.0408899i
$221$	571127.	−	414948.i	0.786597	−	0.571496i
$222$	1.14135e6	−	829236.i	1.55430	−	1.12926i
$223$	87790.8	+	270192.i	0.118219	+	0.363841i	0.992605	−	0.121391i	$-0.0387354\pi$
$223$	87790.8	+	270192.i	0.118219	+	0.363841i	−0.874386	+	0.485231i	$0.838735\pi$
$224$	−161306.			−0.214798
$225$	−156632.	−	678593.i	−0.206264	−	0.893620i
$226$	610115.			0.794585
$227$	118603.	+	365022.i	0.152767	+	0.470170i	0.997928	−	0.0643431i	$-0.0204952\pi$
$227$	118603.	+	365022.i	0.152767	+	0.470170i	−0.845160	+	0.534513i	$0.820495\pi$
$228$	518580.	−	376771.i	0.660662	−	0.479999i
$229$	671977.	−	488220.i	0.846771	−	0.615215i	−0.0774829	−	0.996994i	$-0.524688\pi$
$229$	671977.	−	488220.i	0.846771	−	0.615215i	0.924254	+	0.381779i	$0.124688\pi$
$230$	−65068.6	+	81798.5i	−0.0811058	+	0.101959i
$231$	−257758.	−	187272.i	−0.317820	−	0.230910i
$232$	−395219.			−0.482078
$233$	−1.13856e6	−	827215.i	−1.37394	−	0.998225i	−0.997418	−	0.0718175i	$-0.977120\pi$
$233$	−1.13856e6	−	827215.i	−1.37394	−	0.998225i	−0.376522	−	0.926408i	$-0.622880\pi$
$234$	173786.	−	534858.i	0.207479	−	0.638556i
$235$	521786.	−	655944.i	0.616344	−	0.774813i
$236$	−162606.	−	500449.i	−0.190045	−	0.584898i
$237$	−590516.	+	1.81742e6i	−0.682905	+	2.10177i
$238$	−217885.	+	670580.i	−0.249336	+	0.767376i
$239$	−310026.	−	954162.i	−0.351078	−	1.08051i	−0.958249	−	0.285935i	$-0.907696\pi$
$239$	−310026.	−	954162.i	−0.351078	−	1.08051i	0.607171	−	0.794571i	$-0.292304\pi$
$240$	−170477.	−	257576.i	−0.191046	−	0.288654i
$241$	97175.3	−	299075.i	0.107774	−	0.331694i	−0.882598	−	0.470129i	$-0.844207\pi$
$241$	97175.3	−	299075.i	0.107774	−	0.331694i	0.990371	+	0.138435i	$0.0442074\pi$
$242$	−492756.	−	358008.i	−0.540870	−	0.392965i
$243$	1.26574e6			1.37509
$244$	−202578.	−	147182.i	−0.217830	−	0.158263i
$245$	431343.	−	119611.i	0.459100	−	0.127308i
$246$	−596756.	+	433568.i	−0.628722	+	0.456793i
$247$	947351.	−	688291.i	0.988026	−	0.717843i
$248$	137637.	+	423602.i	0.142103	+	0.437350i
$249$	1.42669e6			1.45825
$250$	−630680.	−	300873.i	−0.638203	−	0.304462i
$251$	728890.			0.730260			0.365130	−	0.930957i	$-0.381025\pi$
$251$	728890.			0.730260			0.365130	+	0.930957i	$0.381025\pi$
$252$	173574.	+	534204.i	0.172180	+	0.529915i
$253$	−35437.1	+	25746.5i	−0.0348062	+	0.0252882i
$254$	−76134.2	+	55314.7i	−0.0740450	+	0.0537968i
$255$	−1.30107e6	+	360785.i	−1.25299	+	0.347454i
$256$	−53019.7	−	38521.1i	−0.0505636	−	0.0367366i
$257$	−411872.			−0.388982			−0.194491	−	0.980904i	$-0.562305\pi$
$257$	−411872.			−0.388982			−0.194491	+	0.980904i	$0.562305\pi$
$258$	−269526.	−	195822.i	−0.252088	−	0.183153i
$259$	−795436.	+	2.44810e6i	−0.736810	+	2.26767i
$260$	−311430.	−	470544.i	−0.285711	−	0.431685i
$261$	425275.	+	1.30886e6i	0.386428	+	1.18930i
$262$	−211681.	+	651488.i	−0.190515	+	0.586345i
$263$	600010.	−	1.84664e6i	0.534895	−	1.64624i	−0.208980	−	0.977920i	$-0.567014\pi$
$263$	600010.	−	1.84664e6i	0.534895	−	1.64624i	0.743875	−	0.668319i	$-0.232986\pi$
$264$	−40000.5	−	123109.i	−0.0353228	−	0.108713i
$265$	626131.	−	787117.i	0.547710	−	0.688533i
$266$	−361413.	+	1.11232e6i	−0.313185	+	0.963883i
$267$	−191850.	−	139387.i	−0.164696	−	0.119659i
$268$	619649.			0.526998
$269$	−109721.	−	79717.1i	−0.0924506	−	0.0671693i	0.540600	−	0.841280i	$-0.318197\pi$
$269$	−109721.	−	79717.1i	−0.0924506	−	0.0671693i	−0.633050	+	0.774111i	$0.718197\pi$
$270$	60513.6	−	76072.4i	0.0505177	−	0.0635064i
$271$	461883.	−	335578.i	0.382040	−	0.277569i	−0.380146	−	0.924927i	$-0.624126\pi$
$271$	461883.	−	335578.i	0.382040	−	0.277569i	0.762186	+	0.647358i	$0.224126\pi$
$272$	−231756.	+	168381.i	−0.189937	+	0.137997i
$273$	662830.	+	2.03998e6i	0.538264	+	1.65661i
$274$	−412053.			−0.331571
$275$	−220998.	−	192129.i	−0.176220	−	0.153201i
$276$	161425.			0.127555
$277$	−23396.2	−	72006.1i	−0.0183209	−	0.0563858i	0.941478	−	0.337074i	$-0.109437\pi$
$277$	−23396.2	−	72006.1i	−0.0183209	−	0.0563858i	−0.959799	+	0.280688i	$0.909437\pi$
$278$	658644.	−	478533.i	0.511139	−	0.371364i
$279$	1.25476e6	−	911634.i	0.965049	−	0.701149i
$280$	527885.	+	197382.i	0.402388	+	0.150457i
$281$	−1.07832e6	−	783444.i	−0.814669	−	0.591892i	0.100512	−	0.994936i	$-0.467952\pi$
$281$	−1.07832e6	−	783444.i	−0.814669	−	0.591892i	−0.915180	+	0.403044i	$0.867952\pi$
$282$	−1.29447e6			−0.969326
$283$	−300641.	−	218429.i	−0.223143	−	0.162123i	0.470598	−	0.882348i	$-0.344038\pi$
$283$	−300641.	−	218429.i	−0.223143	−	0.162123i	−0.693740	+	0.720225i	$0.744038\pi$
$284$	−141368.	+	435085.i	−0.104005	+	0.320094i
$285$	−2.15813e6	+	598447.i	−1.57386	+	0.436429i
$286$	−73073.5	−	224897.i	−0.0528257	−	0.162581i
$287$	415896.	−	1.28000e6i	0.298044	−	0.917284i
$288$	−70520.1	+	217038.i	−0.0500993	+	0.154190i
$289$	−51814.7	−	159469.i	−0.0364929	−	0.112314i
$290$	1.29338e6	+	483610.i	0.903091	+	0.337676i
$291$	−326190.	+	1.00391e6i	−0.225807	+	0.694963i
$292$	1.08387e6	+	787478.i	0.743909	+	0.540482i
$293$	−193867.			−0.131927			−0.0659636	−	0.997822i	$-0.521012\pi$
$293$	−193867.			−0.131927			−0.0659636	+	0.997822i	$0.521012\pi$
$294$	−559280.	−	406341.i	−0.377365	−	0.274171i
$295$	−80236.3	+	1.83673e6i	−0.0536804	+	1.22882i
$296$	−846077.	+	614711.i	−0.561281	+	0.407795i
$297$	32956.4	−	23944.2i	0.0216794	−	0.0157510i
$298$	−341700.	−	1.05164e6i	−0.222897	−	0.686006i
$299$	294894.			0.190760
$300$	242715.	+	1.05154e6i	0.155702	+	0.674563i
$301$	607865.			0.386715
$302$	−329885.	−	1.01528e6i	−0.208135	−	0.640574i
$303$	2.10802e6	−	1.53156e6i	1.31907	−	0.958360i
$304$	−384423.	+	279299.i	−0.238575	+	0.173335i
$305$	482853.	+	729548.i	0.297211	+	0.449060i
$306$	807015.	+	586331.i	0.492695	+	0.357964i
$307$	−924473.			−0.559820			−0.279910	−	0.960026i	$-0.590305\pi$
$307$	−924473.			−0.559820			−0.279910	+	0.960026i	$0.590305\pi$
$308$	191075.	+	138824.i	0.114770	+	0.0833851i
$309$	−1.30242e6	+	4.00842e6i	−0.775985	+	2.38824i
$310$	67915.5	−	1.55469e6i	0.0401388	−	0.918837i
$311$	113039.	+	347899.i	0.0662717	+	0.203963i	0.978709	−	0.205254i	$-0.0658019\pi$
$311$	113039.	+	347899.i	0.0662717	+	0.203963i	−0.912437	+	0.409217i	$0.865802\pi$
$312$	−269297.	+	828811.i	−0.156619	+	0.482024i
$313$	194982.	−	600092.i	0.112495	−	0.346224i	−0.878921	−	0.476967i	$-0.841736\pi$
$313$	194982.	−	600092.i	0.112495	−	0.346224i	0.991416	+	0.130743i	$0.0417362\pi$
$314$	347267.	+	1.06878e6i	0.198765	+	0.611735i
$315$	85648.2	−	1.96061e6i	0.0486342	−	1.11331i
$316$	437748.	−	1.34725e6i	0.246608	−	0.758980i
$317$	−2.37783e6	−	1.72760e6i	−1.32902	−	0.965593i	−0.999772	−	0.0213509i	$-0.993203\pi$
$317$	−2.37783e6	−	1.72760e6i	−1.32902	−	0.965593i	−0.329252	−	0.944242i	$-0.606797\pi$
$318$	−1.55334e6			−0.861386
$319$	468156.	+	340135.i	0.257581	+	0.187144i
$320$	126374.	+	190941.i	0.0689897	+	0.104237i
$321$	−339310.	+	246523.i	−0.183795	+	0.133535i
$322$	−238283.	+	173123.i	−0.128072	+	0.0930495i
$323$	641841.	+	1.97538e6i	0.342311	+	1.05352i
$324$	−1.01660e6			−0.538007
$325$	443396.	+	1.92097e6i	0.232854	+	1.00882i
$326$	1.26891e6			0.661283
$327$	−1.49480e6	−	4.60053e6i	−0.773063	−	2.37924i
$328$	442374.	−	321403.i	0.227041	−	0.164955i
$329$	1.91079e6	−	1.38827e6i	0.973249	−	0.707107i
$330$	−19737.9	+	451829.i	−0.00997735	+	0.228396i
$331$	1.08788e6	+	790393.i	0.545773	+	0.396527i	0.826225	−	0.563341i	$-0.190484\pi$
$331$	1.08788e6	+	790393.i	0.545773	+	0.396527i	−0.280451	+	0.959868i	$0.590484\pi$
$332$	−1.05760e6			−0.526595
$333$	2.94619e6	+	2.14053e6i	1.45596	+	1.05782i
$334$	−482163.	+	1.48394e6i	−0.236498	+	0.727866i
$335$	−2.02784e6	−	758234.i	−0.987239	−	0.369140i
$336$	−268968.	−	827798.i	−0.129973	−	0.400015i
$337$	−299086.	+	920493.i	−0.143457	+	0.441515i	−0.996809	−	0.0798193i	$-0.974566\pi$
$337$	−299086.	+	920493.i	−0.143457	+	0.441515i	0.853352	+	0.521335i	$0.174566\pi$
$338$	−33012.4	+	101602.i	−0.0157176	+	0.0483738i
$339$	1.01733e6	+	3.13101e6i	0.480797	+	1.47974i
$340$	964477.	−	267449.i	0.452475	−	0.125471i
$341$	201525.	−	620231.i	0.0938520	−	0.288847i
$342$	1.33863e6	+	972569.i	0.618862	+	0.449630i
$343$	−1.38618e6			−0.636187
$344$	199799.	+	145163.i	0.0910328	+	0.0661392i
$345$	−528275.	−	197528.i	−0.238953	−	0.0893473i
$346$	−147047.	+	106836.i	−0.0660339	+	0.0479765i
$347$	240155.	−	174483.i	0.107070	−	0.0777908i	−0.532962	−	0.846139i	$-0.678921\pi$
$347$	240155.	−	174483.i	0.107070	−	0.0777908i	0.640032	+	0.768348i	$0.278921\pi$
$348$	−659003.	−	2.02820e6i	−0.291702	−	0.897766i
$349$	−564544.			−0.248104			−0.124052	−	0.992276i	$-0.539589\pi$
$349$	−564544.			−0.248104			−0.124052	+	0.992276i	$0.539589\pi$
$350$	−1.48601e6	−	1.29189e6i	−0.648415	−	0.563712i
$351$	−274251.			−0.118817
$352$	29652.3	+	91260.3i	0.0127556	+	0.0392577i
$353$	1.68533e6	−	1.22447e6i	0.719862	−	0.523010i	−0.166478	−	0.986045i	$-0.553239\pi$
$353$	1.68533e6	−	1.22447e6i	0.719862	−	0.523010i	0.886340	+	0.463035i	$0.153239\pi$
$354$	2.29709e6	−	1.66894e6i	0.974250	−	0.707834i
$355$	995027.	−	1.25086e6i	0.419048	−	0.526791i
$356$	142218.	+	103328.i	0.0594744	+	0.0432107i
$357$	−3.80462e6			−1.57994
$358$	−1.09302e6	−	794127.i	−0.450735	−	0.327478i
$359$	−841102.	+	2.58865e6i	−0.344439	+	1.06007i	0.617444	+	0.786615i	$0.288168\pi$
$359$	−841102.	+	2.58865e6i	−0.344439	+	1.06007i	−0.961883	+	0.273460i	$0.911832\pi$
$360$	496361.	−	623981.i	0.201856	−	0.253755i
$361$	299488.	+	921730.i	0.120952	+	0.372251i
$362$	−518483.	+	1.59573e6i	−0.207952	+	0.640011i
$363$	1.01560e6	−	3.12570e6i	0.404536	−	1.24503i
$364$	−491355.	−	1.51223e6i	−0.194376	−	0.598226i
$365$	−2.58344e6	−	3.90335e6i	−1.01500	−	1.53358i
$366$	417527.	−	1.28502e6i	0.162923	−	0.501425i
$367$	3.99528e6	+	2.90274e6i	1.54840	+	1.12498i	0.944781	+	0.327702i	$0.106274\pi$
$367$	3.99528e6	+	2.90274e6i	1.54840	+	1.12498i	0.603616	+	0.797275i	$0.293726\pi$
$368$	−119664.			−0.0460622
$369$	−1.54042e6	−	1.11918e6i	−0.588944	−	0.427893i
$370$	3.52104e6	−	976381.i	1.33711	−	0.370779i
$371$	2.29291e6	−	1.66589e6i	0.864872	−	0.628366i
$372$	−1.94436e6	+	1.41266e6i	−0.728483	+	0.529274i
$373$	339585.	+	1.04513e6i	0.126379	+	0.388956i	0.994150	−	0.108009i	$-0.0344477\pi$
$373$	339585.	+	1.04513e6i	0.126379	+	0.388956i	−0.867771	+	0.496965i	$0.834448\pi$
$374$	419439.			0.155057
$375$	492415.	−	3.73824e6i	0.180823	−	1.37274i
$376$	959589.			0.350039
$377$	−1.20388e6	−	3.70515e6i	−0.436243	−	1.34262i
$378$	221602.	−	161003.i	0.0797709	−	0.0579570i
$379$	2.05417e6	−	1.49244e6i	0.734580	−	0.533703i	−0.156429	−	0.987689i	$-0.549998\pi$
$379$	2.05417e6	−	1.49244e6i	0.734580	−	0.533703i	0.891009	+	0.453986i	$0.149998\pi$
$380$	1.59981e6	−	443627.i	0.568343	−	0.157601i
$381$	−410816.	−	298475.i	−0.144989	−	0.105341i
$382$	644242.			0.225887
$383$	−1.72425e6	−	1.25274e6i	−0.600626	−	0.436381i	0.245475	−	0.969403i	$-0.421056\pi$
$383$	−1.72425e6	−	1.25274e6i	−0.600626	−	0.436381i	−0.846101	+	0.533022i	$0.821056\pi$
$384$	109277.	−	336321.i	0.0378183	−	0.116393i
$385$	−455434.	−	688121.i	−0.156594	−	0.236599i
$386$	893943.	+	2.75127e6i	0.305381	+	0.939865i
$387$	265748.	−	817887.i	0.0901969	−	0.277598i
$388$	241804.	−	744196.i	0.0815425	−	0.250962i
$389$	832105.	+	2.56096e6i	0.278807	+	0.858081i	0.988187	+	0.153254i	$0.0489753\pi$
$389$	832105.	+	2.56096e6i	0.278807	+	0.858081i	−0.709379	+	0.704827i	$0.751025\pi$
$390$	1.89547e6	−	2.38282e6i	0.631037	−	0.793284i
$391$	−161637.	+	497467.i	−0.0534685	+	0.164559i
$392$	414593.	+	301220.i	0.136272	+	0.0990075i
$393$	−3.69630e6			−1.20722
$394$	−2.39907e6	−	1.74302e6i	−0.778577	−	0.565669i
$395$	−3.08112e6	+	3.87332e6i	−0.993611	+	1.24908i
$396$	270323.	−	196402.i	0.0866255	−	0.0629371i
$397$	−2.53995e6	+	1.84538e6i	−0.808814	+	0.587638i	−0.913487	−	0.406869i	$-0.866621\pi$
$397$	−2.53995e6	+	1.84538e6i	−0.808814	+	0.587638i	0.104672	+	0.994507i	$0.466621\pi$
$398$	1.01351e6	+	3.11926e6i	0.320715	+	0.987061i
$399$	−6.31087e6			−1.98453
$400$	−179924.	−	779504.i	−0.0562264	−	0.243595i
$401$	−4.69345e6			−1.45757			−0.728787	−	0.684740i	$-0.759916\pi$
$401$	−4.69345e6			−1.45757			−0.728787	+	0.684740i	$0.759916\pi$
$402$	1.03323e6	+	3.17994e6i	0.318882	+	0.981418i
$403$	−3.55198e6	+	2.58067e6i	−1.08945	+	0.791534i
$404$	−1.56267e6	+	1.13535e6i	−0.476336	+	0.346078i
$405$	3.32690e6	+	1.24396e6i	1.00786	+	0.376852i
$406$	3.14794e6	+	2.28711e6i	0.947787	+	0.688608i
$407$	1.53126e6			0.458207
$408$	−1.25054e6	−	908572.i	−0.371919	−	0.270215i
$409$	−178840.	+	550412.i	−0.0528635	+	0.162697i	−0.974003	−	0.226536i	$-0.927260\pi$
$409$	−178840.	+	550412.i	−0.0528635	+	0.162697i	0.921139	+	0.389233i	$0.127260\pi$
$410$	−1.84098e6	+	510503.i	−0.540867	+	0.149982i
$411$	−687073.	−	2.11459e6i	−0.200631	−	0.617479i
$412$	965477.	−	2.97143e6i	0.280220	−	0.862428i
$413$	−1.60091e6	+	4.92709e6i	−0.461840	+	1.42140i
$414$	128765.	+	396297.i	0.0369229	+	0.113637i
$415$	3.46107e6	+	1.29414e6i	0.986486	+	0.368858i
$416$	199629.	−	614396.i	0.0565576	−	0.174066i
$417$	3.55400e6	+	2.58214e6i	1.00087	+	0.727175i
$418$	695740.			0.194763
$419$	881271.	+	640281.i	0.245231	+	0.178170i	0.703610	−	0.710586i	$-0.251570\pi$
$419$	881271.	+	640281.i	0.245231	+	0.178170i	−0.458380	+	0.888756i	$0.651570\pi$
$420$	−132720.	+	3.03815e6i	−0.0367123	+	0.840400i
$421$	2.44492e6	−	1.77634e6i	0.672293	−	0.488450i	−0.198499	−	0.980101i	$-0.563607\pi$
$421$	2.44492e6	−	1.77634e6i	0.672293	−	0.488450i	0.870792	+	0.491651i	$0.163607\pi$
$422$	678518.	−	492972.i	0.185473	−	0.134754i
$423$	−1.03257e6	−	3.17791e6i	−0.280587	−	0.863558i
$424$	1.15148e6			0.311059
$425$	−3.48358e6	−	304938.i	−0.935521	−	0.0818916i
$426$	−2.46851e6			−0.659039
$427$	761813.	+	2.34462e6i	0.202199	+	0.622304i
$428$	251530.	−	182747.i	0.0663713	−	0.0482216i
$429$	1.03229e6	−	750004.i	0.270807	−	0.196753i
$430$	−476229.	−	719540.i	−0.124207	−	0.187665i
$431$	1.75193e6	+	1.27285e6i	0.454280	+	0.330054i	0.791283	−	0.611450i	$-0.209413\pi$
$431$	1.75193e6	+	1.27285e6i	0.454280	+	0.330054i	−0.337003	+	0.941504i	$0.609413\pi$
$432$	111287.			0.0286904
$433$	5.34329e6	+	3.88213e6i	1.36959	+	0.995062i	0.997769	+	0.0667553i	$0.0212647\pi$
$433$	5.34329e6	+	3.88213e6i	1.36959	+	0.995062i	0.371816	+	0.928307i	$0.378735\pi$
$434$	1.35508e6	−	4.17051e6i	0.345335	−	1.06283i
$435$	−325179.	+	7.44382e6i	−0.0823946	+	1.88613i
$436$	1.10809e6	+	3.41036e6i	0.279165	+	0.859181i
$437$	−268113.	+	825167.i	−0.0671606	+	0.206699i
$438$	−2.23393e6	+	6.87532e6i	−0.556396	+	1.71241i
$439$	−1.11355e6	−	3.42716e6i	−0.275771	−	0.848737i	−0.989014	−	0.147820i	$-0.952774\pi$
$439$	−1.11355e6	−	3.42716e6i	−0.275771	−	0.848737i	0.713243	−	0.700917i	$-0.247226\pi$
$440$	14631.6	−	334940.i	0.00360298	−	0.0824774i
$441$	551439.	−	1.69715e6i	0.135021	−	0.415551i
$442$	−2.28451e6	−	1.65979e6i	−0.556208	−	0.404109i
$443$	2.58487e6			0.625790			0.312895	−	0.949788i	$-0.398701\pi$
$443$	2.58487e6			0.625790			0.312895	+	0.949788i	$0.398701\pi$
$444$	−4.56538e6	−	3.31694e6i	−1.09906	−	0.798510i
$445$	−338982.	−	512172.i	−0.0811478	−	0.122607i
$446$	919358.	−	667952.i	0.218850	−	0.159004i
$447$	4.82711e6	−	3.50710e6i	1.14266	−	0.830194i
$448$	199385.	+	613645.i	0.0469351	+	0.144451i
$449$	5.07221e6			1.18736			0.593679	−	0.804702i	$-0.297675\pi$
$449$	5.07221e6			1.18736			0.593679	+	0.804702i	$0.297675\pi$
$450$	−2.38791e6	+	1.43465e6i	−0.555888	+	0.333976i
$451$	−800622.			−0.185347
$452$	−754143.	−	2.32101e6i	−0.173623	−	0.534357i
$453$	4.66021e6	−	3.38584e6i	1.06699	−	0.775212i
$454$	1.24203e6	−	902384.i	0.282807	−	0.205472i
$455$	−242454.	+	5.55014e6i	−0.0549037	+	1.25683i
$456$	−2.07432e6	−	1.50708e6i	−0.467158	−	0.339410i
$457$	4.73519e6			1.06059			0.530294	−	0.847814i	$-0.322081\pi$
$457$	4.73519e6			1.06059			0.530294	+	0.847814i	$0.322081\pi$
$458$	−2.68791e6	−	1.95288e6i	−0.598757	−	0.435023i
$459$	150322.	−	462643.i	0.0333035	−	0.102498i
$460$	391609.	+	146427.i	0.0862896	+	0.0322647i
$461$	−228043.	−	701844.i	−0.0499763	−	0.153811i	0.922954	−	0.384911i	$-0.125768\pi$
$461$	−228043.	−	701844.i	−0.0499763	−	0.153811i	−0.972930	+	0.231099i	$0.925768\pi$
$462$	−393819.	+	1.21205e6i	−0.0858403	+	0.264189i
$463$	2.11373e6	−	6.50540e6i	0.458245	−	1.41033i	−0.409038	−	0.912517i	$-0.634136\pi$
$463$	2.11373e6	−	6.50540e6i	0.458245	−	1.41033i	0.867283	−	0.497815i	$-0.165864\pi$
$464$	488517.	+	1.50350e6i	0.105338	+	0.324197i
$465$	8.09165e6	−	2.24381e6i	1.73542	−	0.481231i
$466$	−1.73957e6	+	5.35385e6i	−0.371088	+	1.14209i
$467$	2.91812e6	+	2.12014e6i	0.619172	+	0.449855i	0.852632	−	0.522511i	$-0.175005\pi$
$467$	2.91812e6	+	2.12014e6i	0.619172	+	0.449855i	−0.233460	+	0.972366i	$0.575005\pi$
$468$	−2.24953e6			−0.474764
$469$	−4.93553e6	−	3.58587e6i	−1.03610	−	0.752771i
$470$	−3.14032e6	−	1.17420e6i	−0.655737	−	0.245187i
$471$	−4.90576e6	+	3.56424e6i	−1.01895	+	0.740313i
$472$	−1.70283e6	+	1.23718e6i	−0.351817	+	0.255610i
$473$	−111742.	−	343905.i	−0.0229647	−	0.0706782i
$474$	7.64379e6			1.56265
$475$	−5.77835e6	−	505812.i	−1.17509	−	0.102862i
$476$	2.82036e6			0.570541
$477$	−1.23906e6	−	3.81342e6i	−0.249342	−	0.767395i
$478$	−3.24664e6	+	2.35882e6i	−0.649926	+	0.472199i
$479$	4.37260e6	−	3.17688e6i	0.870765	−	0.632648i	−0.0600270	−	0.998197i	$-0.519119\pi$
$479$	4.37260e6	−	3.17688e6i	0.870765	−	0.632648i	0.930792	+	0.365549i	$0.119119\pi$
$480$	−769156.	+	966916.i	−0.152374	+	0.191551i
$481$	−8.34011e6	−	6.05944e6i	−1.64365	−	1.19418i
$482$	−1.25786e6			−0.246613
$483$	−1.28576e6	−	934160.i	−0.250780	−	0.182202i
$484$	−752864.	+	2.31708e6i	−0.146084	+	0.449601i
$485$	−1.70196e6	+	2.13955e6i	−0.328544	+	0.413017i
$486$	−1.56455e6	−	4.81518e6i	−0.300468	−	0.924744i
$487$	−3.08723e6	+	9.50152e6i	−0.589857	+	1.81539i	−0.0110357	+	0.999939i	$0.503513\pi$
$487$	−3.08723e6	+	9.50152e6i	−0.589857	+	1.81539i	−0.578821	+	0.815454i	$0.696487\pi$
$488$	−309512.	+	952580.i	−0.0588340	+	0.181072i
$489$	2.11583e6	+	6.51186e6i	0.400137	+	1.23149i
$490$	−988197.	−	1.49308e6i	−0.185932	−	0.280926i
$491$	−1.50345e6	+	4.62716e6i	−0.281441	+	0.866185i	0.706002	+	0.708209i	$0.250497\pi$
$491$	−1.50345e6	+	4.62716e6i	−0.281441	+	0.866185i	−0.987443	+	0.157976i	$0.949503\pi$
$492$	2.38702e6	+	1.73427e6i	0.444574	+	0.323002i
$493$	6.91021e6			1.28048
$494$	−3.78940e6	−	2.75316e6i	−0.698640	−	0.507592i
$495$	−1.12498e6	+	311956.i	−0.206363	+	0.0572243i
$496$	1.44135e6	−	1.04720e6i	0.263066	−	0.191129i
$497$	3.64381e6	−	2.64739e6i	0.661706	−	0.480758i
$498$	−1.76349e6	−	5.42745e6i	−0.318639	−	0.980669i
$499$	−1.59184e6			−0.286187			−0.143093	−	0.989709i	$-0.545705\pi$
$499$	−1.59184e6			−0.286187			−0.143093	+	0.989709i	$0.545705\pi$
$500$	−365026.	+	2.77115e6i	−0.0652979	+	0.495718i
$501$	−8.41935e6			−1.49860
$502$	−900957.	−	2.77286e6i	−0.159568	−	0.491099i
$503$	−5.10272e6	+	3.70734e6i	−0.899253	+	0.653345i	−0.938274	−	0.345893i	$-0.887576\pi$
$503$	−5.10272e6	+	3.70734e6i	−0.899253	+	0.653345i	0.0390213	+	0.999238i	$0.487576\pi$
$504$	1.81769e6	−	1.32063e6i	0.318744	−	0.231581i
$505$	6.50321e6	−	1.80333e6i	1.13475	−	0.314665i
$506$	141748.	+	102986.i	0.0246117	+	0.0178814i
$507$	−576451.			−0.0995962
$508$	304537.	+	221259.i	0.0523577	+	0.0380401i
$509$	1.83849e6	−	5.65829e6i	0.314534	−	0.968035i	−0.661412	−	0.750023i	$-0.730043\pi$
$509$	1.83849e6	−	5.65829e6i	0.314534	−	0.968035i	0.975946	−	0.218013i	$-0.0699574\pi$
$510$	2.98071e6	+	4.50359e6i	0.507452	+	0.766715i
$511$	−4.07599e6	−	1.25446e7i	−0.690527	−	2.12522i
$512$	−81007.0	+	249314.i	−0.0136568	+	0.0420312i
$513$	249344.	−	767403.i	0.0418317	−	0.128745i
$514$	509102.	+	1.56685e6i	0.0849957	+	0.261590i
$515$	−6.79559e6	+	8.54282e6i	−1.12904	+	1.41933i
$516$	−411800.	+	1.26739e6i	−0.0680866	+	0.209549i
$517$	−1.13668e6	−	825848.i	−0.187031	−	0.135886i
$518$	1.02963e7			1.68600
$519$	−793459.	−	576482.i	−0.129302	−	0.0939436i
$520$	−1.40511e6	+	1.76638e6i	−0.227877	+	0.286467i
$521$	−418035.	+	303720.i	−0.0674712	+	0.0490207i	−0.621010	−	0.783803i	$-0.713277\pi$
$521$	−418035.	+	303720.i	−0.0674712	+	0.0490207i	0.553538	+	0.832824i	$0.313277\pi$
$522$	4.45354e6	−	3.23569e6i	0.715368	−	0.519745i
$523$	−2.83678e6	−	8.73071e6i	−0.453494	−	1.39571i	−0.872894	−	0.487909i	$-0.837760\pi$
$523$	−2.83678e6	−	8.73071e6i	−0.453494	−	1.39571i	0.419401	−	0.907801i	$-0.362240\pi$
$524$	2.74006e6			0.435945
$525$	4.15197e6	−	9.78015e6i	0.657439	−	1.54863i
$526$	−7.76669e6			−1.22397
$527$	−2.40651e6	−	7.40647e6i	−0.377451	−	1.16168i
$528$	−418891.	+	304342.i	−0.0653907	+	0.0475091i
$529$	5.03034e6	−	3.65476e6i	0.781553	−	0.567831i
$530$	−3.76831e6	−	1.40901e6i	−0.582716	−	0.217884i
$531$	5.92955e6	+	4.30807e6i	0.912611	+	0.663050i
$532$	4.67823e6			0.716643
$533$	4.36065e6	+	3.16820e6i	0.664864	+	0.483052i
$534$	−293121.	+	902134.i	−0.0444830	+	0.136905i
$535$	−1.04677e6	+	290268.i	−0.158112	+	0.0438445i
$536$	−765928.	−	2.35728e6i	−0.115153	−	0.354405i
$537$	2.25279e6	−	6.93338e6i	0.337121	−	1.03755i
$538$	−167639.	+	515940.i	−0.0249701	+	0.0768499i
$539$	−231869.	−	713619.i	−0.0343772	−	0.105802i
$540$	−364195.	−	136177.i	−0.0537465	−	0.0200964i
$541$	−945783.	+	2.91082e6i	−0.138931	+	0.427585i	−0.996181	−	0.0873157i	$-0.972171\pi$
$541$	−945783.	+	2.91082e6i	−0.138931	+	0.427585i	0.857250	+	0.514900i	$0.172171\pi$
$542$	−1.84753e6	−	1.34231e6i	−0.270143	−	0.196271i
$543$	−9.05356e6			−1.31771
$544$	927024.	+	673523.i	0.134306	+	0.0975787i
$545$	546779.	−	1.25166e7i	0.0788534	−	1.80507i
$546$	6.94125e6	−	5.04311e6i	0.996451	−	0.723964i
$547$	4.79869e6	−	3.48646e6i	0.685732	−	0.498214i	−0.189522	−	0.981876i	$-0.560694\pi$
$547$	4.79869e6	−	3.48646e6i	0.685732	−	0.498214i	0.875254	+	0.483663i	$0.160694\pi$
$548$	509325.	+	1.56754e6i	0.0724509	+	0.222981i
$549$	3.48775e6			0.493873
$550$	−457732.	+	1.07821e6i	−0.0645216	+	0.151984i
$551$	1.14622e7			1.60838
$552$	−199533.	−	614098.i	−0.0278719	−	0.0857808i
$553$	−1.12831e7	+	8.19768e6i	−1.56898	+	1.13993i
$554$	−245008.	+	178009.i	−0.0339161	+	0.0246415i
$555$	1.08817e7	+	1.64414e7i	1.49957	+	2.26571i
$556$	−2.63458e6	−	1.91413e6i	−0.361430	−	0.262594i
$557$	−582569.			−0.0795627			−0.0397813	−	0.999208i	$-0.512666\pi$
$557$	−582569.			−0.0795627			−0.0397813	+	0.999208i	$0.512666\pi$
$558$	−5.01903e6	−	3.64654e6i	−0.682392	−	0.495787i
$559$	−752282.	+	2.31529e6i	−0.101824	+	0.313383i
$560$	98384.8	−	2.25217e6i	0.0132574	−	0.303481i
$561$	699389.	+	2.15250e6i	0.0938235	+	0.288759i
$562$	−1.64752e6	+	5.07056e6i	−0.220035	+	0.677197i
$563$	−2.68212e6	+	8.25471e6i	−0.356621	+	1.09757i	0.598443	+	0.801166i	$0.295786\pi$
$563$	−2.68212e6	+	8.25471e6i	−0.356621	+	1.09757i	−0.955064	+	0.296401i	$0.904214\pi$
$564$	1.60006e6	+	4.92447e6i	0.211806	+	0.651871i
$565$	−372125.	+	8.51849e6i	−0.0490419	+	1.12264i
$566$	−459339.	+	1.41370e6i	−0.0602688	+	0.185488i
$567$	8.09728e6	+	5.88302e6i	1.05775	+	0.768497i
$568$	1.82990e6			0.237989
$569$	−6.92879e6	−	5.03406e6i	−0.897174	−	0.651835i	0.0405646	−	0.999177i	$-0.487084\pi$
$569$	−6.92879e6	−	5.03406e6i	−0.897174	−	0.651835i	−0.937739	+	0.347342i	$0.887084\pi$
$570$	4.94422e6	+	7.47028e6i	0.637398	+	0.963052i
$571$	−2.55430e6	+	1.85581e6i	−0.327855	+	0.238201i	−0.739520	−	0.673135i	$-0.764947\pi$
$571$	−2.55430e6	+	1.85581e6i	−0.327855	+	0.238201i	0.411665	+	0.911335i	$0.364947\pi$
$572$	−765236.	+	555976.i	−0.0977924	+	0.0710503i
$573$	1.07423e6	+	3.30615e6i	0.136682	+	0.420664i
$574$	−5.38347e6			−0.681997
$575$	−1.10239e6	−	958386.i	−0.139049	−	0.120885i
$576$	912831.			0.114639
$577$	1.78645e6	+	5.49814e6i	0.223384	+	0.687505i	0.998452	+	0.0556270i	$0.0177158\pi$
$577$	1.78645e6	+	5.49814e6i	0.223384	+	0.687505i	−0.775068	+	0.631878i	$0.782284\pi$
$578$	−542611.	+	394230.i	−0.0675568	+	0.0490829i
$579$	−1.26285e7	+	9.17516e6i	−1.56551	+	1.13741i
$580$	241054.	−	5.51809e6i	0.0297540	−	0.681112i
$581$	8.42385e6	+	6.12028e6i	1.03531	+	0.752196i
$582$	4.22229e6			0.516703
$583$	−1.36399e6	−	990997.i	−0.166203	−	0.120754i
$584$	1.65601e6	−	5.09666e6i	0.200923	−	0.618378i
$585$	7.36175e6	+	2.75264e6i	0.889388	+	0.332552i
$586$	239633.	+	737513.i	0.0288272	+	0.0887208i
$587$	−1.00931e6	+	3.10633e6i	−0.120900	+	0.372093i	−0.993132	−	0.117000i	$-0.962672\pi$
$587$	−1.00931e6	+	3.10633e6i	−0.120900	+	0.372093i	0.872231	+	0.489093i	$0.162672\pi$
$588$	−854504.	+	2.62989e6i	−0.101923	+	0.313686i
$589$	−3.99177e6	−	1.22854e7i	−0.474108	−	1.45915i
$590$	7.08650e6	−	1.96508e6i	0.838112	−	0.232408i
$591$	4.94464e6	−	1.52180e7i	0.582325	−	1.79221i
$592$	3.38431e6	+	2.45884e6i	0.396886	+	0.288354i
$593$	−8.50067e6			−0.992696			−0.496348	−	0.868124i	$-0.665326\pi$
$593$	−8.50067e6			−0.992696			−0.496348	+	0.868124i	$0.665326\pi$
$594$	−131825.	−	95776.8i	−0.0153297	−	0.0111377i
$595$	−9.22982e6	−	3.45113e6i	−1.06881	−	0.399640i
$596$	−3.57833e6	+	2.59981e6i	−0.412634	+	0.299796i
$597$	−1.43176e7	+	1.04023e7i	−1.64412	+	1.19453i
$598$	−364509.	−	1.12184e6i	−0.0416827	−	0.128286i
$599$	8.96322e6			1.02070			0.510349	−	0.859967i	$-0.329516\pi$
$599$	8.96322e6			1.02070			0.510349	+	0.859967i	$0.329516\pi$
$600$	3.70028e6	−	2.22312e6i	0.419621	−	0.252107i
$601$	−2.75017e6			−0.310580			−0.155290	−	0.987869i	$-0.549631\pi$
$601$	−2.75017e6			−0.310580			−0.155290	+	0.987869i	$0.549631\pi$
$602$	−751363.	−	2.31246e6i	−0.0845003	−	0.260065i
$603$	−6.98254e6	+	5.07312e6i	−0.782025	+	0.568174i
$604$	−3.45460e6	+	2.50991e6i	−0.385306	+	0.279941i
$605$	5.29909e6	−	6.66155e6i	0.588590	−	0.739923i
$606$	−8.43207e6	−	6.12626e6i	−0.932723	−	0.677663i
$607$	−1.20631e7			−1.32888			−0.664441	−	0.747341i	$-0.731330\pi$
$607$	−1.20631e7			−1.32888			−0.664441	+	0.747341i	$0.731330\pi$
$608$	1.53769e6	+	1.11720e6i	0.168698	+	0.122566i
$609$	−6.48810e6	+	1.99683e7i	−0.708883	+	2.18172i
$610$	2.17853e6	−	2.73865e6i	0.237049	−	0.297997i
$611$	2.92301e6	+	8.99609e6i	0.316757	+	0.974879i
$612$	1.23301e6	−	3.79481e6i	0.133072	−	0.409555i
$613$	−1.50541e6	+	4.63316e6i	−0.161809	+	0.497997i	−0.998787	−	0.0492398i	$-0.984320\pi$
$613$	−1.50541e6	+	4.63316e6i	−0.161809	+	0.497997i	0.836978	+	0.547236i	$0.184320\pi$
$614$	1.14271e6	+	3.51690e6i	0.122325	+	0.376478i
$615$	−5.68955e6	−	8.59641e6i	−0.606583	−	0.916493i
$616$	291937.	−	898489.i	0.0309982	−	0.0954028i
$617$	−2.13536e6	−	1.55143e6i	−0.225818	−	0.164066i	0.469124	−	0.883132i	$-0.344570\pi$
$617$	−2.13536e6	−	1.55143e6i	−0.225818	−	0.164066i	−0.694941	+	0.719066i	$0.744570\pi$
$618$	1.68588e7			1.77564
$619$	−222641.	−	161758.i	−0.0233549	−	0.0169684i	0.576047	−	0.817417i	$-0.304595\pi$
$619$	−222641.	−	161758.i	−0.0233549	−	0.0169684i	−0.599401	+	0.800449i	$0.704595\pi$
$620$	−5.99832e6	+	1.66333e6i	−0.626687	+	0.173780i
$621$	164395.	−	119440.i	0.0171064	−	0.0124285i
$622$	1.18376e6	−	860053.i	0.122684	−	0.0891352i
$623$	−534824.	−	1.64602e6i	−0.0552065	−	0.169908i
$624$	3.48585e6			0.358383
$625$	4.58549e6	−	8.62211e6i	0.469554	−	0.882904i
$626$	−2.52390e6			−0.257416
$627$	1.16010e6	+	3.57043e6i	0.117850	+	0.362704i
$628$	3.63663e6	−	2.64217e6i	0.367959	−	0.267338i
$629$	1.47932e7	−	1.07479e7i	1.49086	−	1.08317i
$630$	−7.56449e6	+	2.09763e6i	−0.759326	+	0.210561i
$631$	8.38907e6	+	6.09501e6i	0.838765	+	0.609398i	0.922025	−	0.387130i	$-0.126533\pi$
$631$	8.38907e6	+	6.09501e6i	0.838765	+	0.609398i	−0.0832605	+	0.996528i	$0.526533\pi$
$632$	−5.66633e6			−0.564299
$633$	3.66124e6	+	2.66005e6i	0.363178	+	0.263864i
$634$	−3.63300e6	+	1.11812e7i	−0.358957	+	1.10476i
$635$	−725874.	−	1.09673e6i	−0.0714376	−	0.107936i
$636$	1.92003e6	+	5.90924e6i	0.188220	+	0.579281i
$637$	−1.56102e6	+	4.80433e6i	−0.152426	+	0.469120i
$638$	715279.	−	2.20140e6i	0.0695703	−	0.214115i
$639$	−1.96907e6	−	6.06016e6i	−0.190769	−	0.587127i
$640$	570174.	−	716772.i	0.0550247	−	0.0691722i
$641$	−3.19519e6	+	9.83380e6i	−0.307151	+	0.945314i	0.671715	+	0.740810i	$0.265558\pi$
$641$	−3.19519e6	+	9.83380e6i	−0.307151	+	0.945314i	−0.978866	+	0.204504i	$0.934442\pi$
$642$	1.35724e6	+	986094.i	0.129963	+	0.0944236i
$643$	2.73673e6			0.261038			0.130519	−	0.991446i	$-0.458336\pi$
$643$	2.73673e6			0.261038			0.130519	+	0.991446i	$0.458336\pi$
$644$	953131.	+	692490.i	0.0905603	+	0.0657959i
$645$	2.89849e6	−	3.64372e6i	0.274329	−	0.344862i
$646$	6.72144e6	−	4.88341e6i	0.633696	−	0.460407i
$647$	−2.50024e6	+	1.81653e6i	−0.234813	+	0.170601i	−0.698969	−	0.715152i	$-0.746358\pi$
$647$	−2.50024e6	+	1.81653e6i	−0.234813	+	0.170601i	0.464157	+	0.885753i	$0.346358\pi$
$648$	1.25659e6	+	3.86738e6i	0.117559	+	0.361809i
$649$	3.08184e6			0.287209
$650$	6.75974e6	−	4.06123e6i	0.627547	−	0.377028i
$651$	2.36619e7			2.18825
$652$	−1.56846e6	−	4.82722e6i	−0.144496	−	0.444712i
$653$	−2.76151e6	+	2.00635e6i	−0.253433	+	0.184130i	−0.707247	−	0.706967i	$-0.750063\pi$
$653$	−2.76151e6	+	2.00635e6i	−0.253433	+	0.184130i	0.453814	+	0.891097i	$0.350063\pi$
$654$	−1.56538e7	+	1.13731e7i	−1.43112	+	1.03977i
$655$	−8.96704e6	−	3.35288e6i	−0.816669	−	0.305362i
$656$	−1.76949e6	−	1.28561e6i	−0.160542	−	0.116641i
$657$	−1.86608e7			−1.68662
$658$	−7.64318e6	−	5.55309e6i	−0.688191	−	0.500000i
$659$	6.17010e6	−	1.89896e7i	0.553450	−	1.70334i	−0.146551	−	0.989203i	$-0.546817\pi$
$659$	6.17010e6	−	1.89896e7i	0.553450	−	1.70334i	0.700001	−	0.714142i	$-0.253183\pi$
$660$	1.74326e6	−	483404.i	0.155776	−	0.0431967i
$661$	−5.21060e6	−	1.60366e7i	−0.463857	−	1.42760i	−0.860415	−	0.509595i	$-0.829795\pi$
$661$	−5.21060e6	−	1.60366e7i	−0.463857	−	1.42760i	0.396558	−	0.918010i	$-0.370205\pi$
$662$	1.66214e6	−	5.11553e6i	0.147408	−	0.453676i
$663$	4.70853e6	−	1.44914e7i	0.416008	−	1.28034i
$664$	1.30727e6	+	4.02336e6i	0.115065	+	0.354135i
$665$	−1.53098e7	−	5.72453e6i	−1.34251	−	0.501979i
$666$	4.50137e6	−	1.38538e7i	0.393241	−	1.21027i
$667$	2.33528e6	+	1.69668e6i	0.203247	+	0.147668i
$668$	6.24125e6			0.541166
$669$	4.96080e6	+	3.60423e6i	0.428535	+	0.311349i
$670$	−377940.	+	8.65161e6i	−0.0325264	+	0.744577i
$671$	1.18645e6	−	862005.i	0.101728	−	0.0739100i
$672$	−2.81667e6	+	2.04643e6i	−0.240609	+	0.174813i
$673$	−3.59100e6	−	1.10520e7i	−0.305617	−	0.940594i	−0.979446	−	0.201706i	$-0.935351\pi$
$673$	−3.59100e6	−	1.10520e7i	−0.305617	−	0.940594i	0.673829	−	0.738888i	$-0.264649\pi$
$674$	3.87145e6			0.328265
$675$	1.02522e6	+	891296.i	0.0866081	+	0.0752944i
$676$	427322.			0.0359657
$677$	−313953.	−	966248.i	−0.0263265	−	0.0810246i	0.937030	−	0.349249i	$-0.113563\pi$
$677$	−313953.	−	966248.i	−0.0263265	−	0.0810246i	−0.963357	+	0.268224i	$0.913563\pi$
$678$	1.06536e7	−	7.74029e6i	0.890066	−	0.646671i
$679$	−6.23260e6	+	4.52825e6i	−0.518794	+	0.376926i
$680$	−2.20959e6	−	3.33850e6i	−0.183248	−	0.276872i
$681$	6.70190e6	+	4.86921e6i	0.553771	+	0.402338i
$682$	−2.60860e6			−0.214757
$683$	9.32508e6	+	6.77507e6i	0.764893	+	0.555728i	0.900407	−	0.435048i	$-0.143269\pi$
$683$	9.32508e6	+	6.77507e6i	0.764893	+	0.555728i	−0.135514	+	0.990775i	$0.543269\pi$
$684$	2.04524e6	−	6.29460e6i	0.167149	−	0.514432i
$685$	251322.	−	5.75313e6i	0.0204646	−	0.468465i
$686$	1.71341e6	+	5.27335e6i	0.139012	+	0.427835i
$687$	5.53996e6	−	1.70502e7i	0.447832	−	1.37828i
$688$	305266.	−	939513.i	0.0245871	−	0.0756714i
$689$	3.50754e6	+	1.07951e7i	0.281484	+	0.866320i
$690$	−98457.5	+	2.25384e6i	−0.00787274	+	0.180219i
$691$	−3.71085e6	+	1.14208e7i	−0.295650	+	0.909918i	0.687352	+	0.726325i	$0.258773\pi$
$691$	−3.71085e6	+	1.14208e7i	−0.295650	+	0.909918i	−0.983002	+	0.183594i	$0.941227\pi$
$692$	588190.	+	427345.i	0.0466930	+	0.0339245i
$693$	−3.28970e6			−0.260210
$694$	−960618.	−	697930.i	−0.0757098	−	0.0550064i
$695$	6.27960e6	+	9.48793e6i	0.493140	+	0.745091i
$696$	−6.90116e6	+	5.01399e6i	−0.540007	+	0.392338i
$697$	−7.73469e6	+	5.61958e6i	−0.603060	+	0.438149i
$698$	697814.	+	2.14765e6i	0.0542127	+	0.166850i
$699$	−3.03758e7			−2.35144
$700$	−3.07784e6	+	7.25000e6i	−0.237411	+	0.559233i
$701$	1.51487e7			1.16434			0.582169	−	0.813068i	$-0.302204\pi$
$701$	1.51487e7			1.16434			0.582169	+	0.813068i	$0.302204\pi$
$702$	338992.	+	1.04331e6i	0.0259625	+	0.0799045i
$703$	2.45381e7	−	1.78280e7i	1.87263	−	1.36055i
$704$	310523.	−	225608.i	0.0236136	−	0.0171563i
$705$	789533.	−	1.80736e7i	0.0598270	−	1.36953i
$706$	−6.74134e6	−	4.89787e6i	−0.509019	−	0.369824i
$707$	1.90169e7			1.43084
$708$	−9.18837e6	−	6.67574e6i	−0.688899	−	0.500514i
$709$	−3.46036e6	+	1.06499e7i	−0.258527	+	0.795665i	0.734587	+	0.678514i	$0.237376\pi$
$709$	−3.46036e6	+	1.06499e7i	−0.258527	+	0.795665i	−0.993114	+	0.117150i	$0.962624\pi$
$710$	−5.98848e6	−	2.23916e6i	−0.445831	−	0.166701i
$711$	6.09726e6	+	1.87654e7i	0.452335	+	1.39214i
$712$	217290.	−	668750.i	0.0160635	−	0.0494383i
$713$	1.00526e6	−	3.09387e6i	0.0740550	−	0.227918i
$714$	4.70277e6	+	1.44736e7i	0.345230	+	1.06251i
$715$	3.18461e6	−	883090.i	0.232965	−	0.0646011i
$716$	−1.66999e6	+	5.13970e6i	−0.121739	+	0.374675i
$717$	−1.75187e7	−	1.27280e7i	−1.27263	−	0.924621i
$718$	1.08875e7			0.788162
$719$	2.46353e6	+	1.78986e6i	0.177720	+	0.129121i	0.673089	−	0.739562i	$-0.264967\pi$
$719$	2.46353e6	+	1.78986e6i	0.177720	+	0.129121i	−0.495369	+	0.868683i	$0.664967\pi$
$720$	−2.98730e6	−	1.11699e6i	−0.214757	−	0.0803002i
$721$	−2.48856e7	+	1.80804e7i	−1.78283	+	1.29530i
$722$	3.13628e6	−	2.27864e6i	0.223909	−	0.162680i
$723$	−2.09741e6	−	6.45516e6i	−0.149224	−	0.459263i
$724$	6.71139e6			0.475845
$725$	−7.54108e6	+	1.77634e7i	−0.532830	+	1.25510i
$726$	−1.31462e7			−0.925677
$727$	−3.39214e6	−	1.04399e7i	−0.238033	−	0.732591i	−0.996705	−	0.0811175i	$-0.974151\pi$
$727$	−3.39214e6	−	1.04399e7i	−0.238033	−	0.732591i	0.758671	−	0.651474i	$-0.225849\pi$
$728$	−5.14553e6	+	3.73845e6i	−0.359834	+	0.261434i
$729$	9.61105e6	−	6.98283e6i	0.669810	−	0.486646i
$730$	−1.16559e7	+	1.46528e7i	−0.809543	+	1.01769i
$731$	−3.49339e6	−	2.53810e6i	−0.241799	−	0.175677i
$732$	−5.40459e6			−0.372808
$733$	1.69726e7	+	1.23314e7i	1.16678	+	0.847717i	0.990620	−	0.136645i	$-0.0436318\pi$
$733$	1.69726e7	+	1.23314e7i	1.16678	+	0.847717i	0.176162	+	0.984361i	$0.443632\pi$
$734$	6.10425e6	−	1.87870e7i	0.418208	−	1.28711i
$735$	6.01450e6	−	7.56089e6i	0.410659	−	0.516244i
$736$	147913.	+	455230.i	0.0100650	+	0.0309768i
$737$	−1.12146e6	+	3.45150e6i	−0.0760528	+	0.234066i
$738$	−2.35355e6	+	7.24350e6i	−0.159068	+	0.489562i
$739$	2.47546e6	+	7.61869e6i	0.166742	+	0.513179i	0.999160	−	0.0409683i	$-0.0130443\pi$
$739$	2.47546e6	+	7.61869e6i	0.166742	+	0.513179i	−0.832418	+	0.554148i	$0.813044\pi$
$740$	−8.06661e6	−	1.21879e7i	−0.541517	−	0.818184i
$741$	7.81021e6	−	2.40374e7i	0.522537	−	1.60820i
$742$	−9.17163e6	−	6.66358e6i	−0.611557	−	0.444322i
$743$	−1.81260e7			−1.20456			−0.602281	−	0.798284i	$-0.705741\pi$
$743$	−1.81260e7			−1.20456			−0.602281	+	0.798284i	$0.705741\pi$
$744$	7.77744e6	+	5.65064e6i	0.515115	+	0.374253i
$745$	1.48916e7	−	4.12943e6i	0.982992	−	0.272583i
$746$	3.55618e6	−	2.58371e6i	0.233957	−	0.169980i
$747$	1.19176e7	−	8.65867e6i	0.781428	−	0.567740i
$748$	−518456.	−	1.59564e6i	−0.0338811	−	0.104275i
$749$	−3.06100e6			−0.199369
$750$	−1.48298e7	+	2.74746e6i	−0.962678	+	0.178352i
$751$	−1.36900e7			−0.885734			−0.442867	−	0.896587i	$-0.646039\pi$
$751$	−1.36900e7			−0.885734			−0.442867	+	0.896587i	$0.646039\pi$
$752$	−1.18612e6	−	3.65050e6i	−0.0764862	−	0.235400i
$753$	1.27276e7	−	9.24715e6i	0.818012	−	0.594320i
$754$	−1.26072e7	+	9.15963e6i	−0.807586	+	0.586745i
$755$	1.43767e7	−	3.98664e6i	0.917891	−	0.254531i
$756$	−886409.	−	644014.i	−0.0564066	−	0.0409818i
$757$	2.33617e7			1.48172			0.740858	−	0.671661i	$-0.234419\pi$
$757$	2.33617e7			1.48172			0.740858	+	0.671661i	$0.234419\pi$
$758$	−8.21669e6	−	5.96978e6i	−0.519426	−	0.377385i
$759$	−292153.	+	899153.i	−0.0184079	+	0.0566538i
$760$	−3.66514e6	−	5.53770e6i	−0.230174	−	0.347773i
$761$	1.68403e6	+	5.18291e6i	0.105412	+	0.324423i	0.989827	−	0.142277i	$-0.0454425\pi$
$761$	1.68403e6	+	5.18291e6i	0.105412	+	0.324423i	−0.884415	+	0.466701i	$0.845443\pi$
$762$	−627671.	+	1.93177e6i	−0.0391602	+	0.120523i
$763$	1.09096e7	−	3.35762e7i	0.678416	−	2.08795i
$764$	−796326.	−	2.45084e6i	−0.0493580	−	0.151908i
$765$	−8.67863e6	+	1.09100e7i	−0.536164	+	0.674018i
$766$	−2.63443e6	+	8.10793e6i	−0.162224	+	0.499273i
$767$	−1.67855e7	−	1.21954e7i	−1.03026	−	0.748524i
$768$	−1.41451e6			−0.0865375
$769$	2.34298e7	+	1.70227e7i	1.42874	+	1.03804i	0.990250	+	0.139302i	$0.0444858\pi$
$769$	2.34298e7	+	1.70227e7i	1.42874	+	1.03804i	0.438488	+	0.898737i	$0.355514\pi$
$770$	−2.05482e6	+	2.58314e6i	−0.124896	+	0.157008i
$771$	−7.19196e6	+	5.22526e6i	−0.435724	+	0.316572i
$772$	9.36150e6	−	6.80153e6i	0.565330	−	0.410736i
$773$	7.73639e6	+	2.38102e7i	0.465682	+	1.43322i	0.858122	+	0.513445i	$0.171631\pi$
$773$	7.73639e6	+	2.38102e7i	0.465682	+	1.43322i	−0.392440	+	0.919778i	$0.628369\pi$
$774$	−3.43991e6			−0.206393
$775$	2.16653e7	+	1.89649e6i	1.29572	+	0.113422i
$776$	−3.12997e6			−0.186589
$777$	1.71685e7	+	5.28392e7i	1.02019	+	3.13981i
$778$	8.71392e6	−	6.33103e6i	0.516136	−	0.374995i
$779$	−1.28298e7	+	9.32141e6i	−0.757490	+	0.550349i
$780$	−1.14077e7	−	4.26547e6i	−0.671369	−	0.251033i
$781$	−2.16761e6	−	1.57486e6i	−0.127161	−	0.0923878i
$782$	2.09227e6			0.122349
$783$	−2.17180e6	−	1.57791e6i	−0.126595	−	0.0919766i
$784$	633442.	−	1.94953e6i	0.0368058	−	0.113277i
$785$	−1.51342e7	+	4.19671e6i	−0.876568	+	0.243072i
$786$	4.56888e6	+	1.40616e7i	0.263787	+	0.811853i
$787$	−7.50637e6	+	2.31022e7i	−0.432009	+	1.32959i	0.464111	+	0.885777i	$0.346374\pi$
$787$	−7.50637e6	+	2.31022e7i	−0.432009	+	1.32959i	−0.896120	+	0.443811i	$0.853626\pi$
$788$	−3.66545e6	+	1.12811e7i	−0.210287	+	0.647195i
$789$	−1.29505e7	−	3.98574e7i	−0.740616	−	2.27938i
$790$	1.85434e7	+	6.93361e6i	1.05712	+	0.395268i
$791$	−7.42480e6	+	2.28512e7i	−0.421933	+	1.29858i
$792$	−1.08129e6	−	785606.i	−0.0612535	−	0.0445033i
$793$	−9.87318e6			−0.557538
$794$	1.01598e7	+	7.38153e6i	0.571918	+	0.415523i
$795$	947420.	−	2.16878e7i	0.0531649	−	1.21702i
$796$	1.06136e7	−	7.71123e6i	0.593718	−	0.431361i
$797$	−2.34061e7	+	1.70056e7i	−1.30522	+	0.948298i	−0.999992	−	0.00398064i	$-0.998733\pi$
$797$	−2.34061e7	+	1.70056e7i	−1.30522	+	0.948298i	−0.305229	+	0.952279i	$0.598733\pi$
$798$	7.80067e6	+	2.40080e7i	0.433635	+	1.33459i
$799$	−1.67780e7			−0.929763
$800$	−2.74301e6	+	1.64799e6i	−0.151531	+	0.0910396i
$801$	−2.44854e6			−0.134842
$802$	5.80142e6	+	1.78549e7i	0.318492	+	0.980217i
$803$	−6.34794e6	+	4.61205e6i	−0.347411	+	0.252409i
$804$	1.08201e7	−	7.86125e6i	0.590324	−	0.428896i
$805$	−2.27182e6	−	3.43252e6i	−0.123562	−	0.186691i
$806$	1.42079e7	+	1.03227e7i	0.770360	+	0.559699i
$807$	−2.92725e6			−0.158225
$808$	6.25067e6	+	4.54138e6i	0.336820	+	0.244714i
$809$	−6.01523e6	+	1.85130e7i	−0.323132	+	0.994499i	0.649144	+	0.760665i	$0.275127\pi$
$809$	−6.01523e6	+	1.85130e7i	−0.323132	+	0.994499i	−0.972277	+	0.233834i	$0.924873\pi$
$810$	620052.	−	1.41939e7i	0.0332059	−	0.760132i
$811$	−646394.	−	1.98940e6i	−0.0345100	−	0.106211i	0.932318	−	0.361640i	$-0.117783\pi$
$811$	−646394.	−	1.98940e6i	−0.0345100	−	0.106211i	−0.966828	+	0.255429i	$0.917783\pi$
$812$	4.80962e6	−	1.48025e7i	0.255989	−	0.787852i
$813$	3.80789e6	−	1.17195e7i	0.202050	−	0.621845i
$814$	−1.89274e6	−	5.82524e6i	−0.100122	−	0.308144i
$815$	−773942.	+	1.77167e7i	−0.0408145	+	0.934304i
$816$	−1.91066e6	+	5.88040e6i	−0.100452	+	0.309159i
$817$	−5.79463e6	−	4.21004e6i	−0.303718	−	0.220664i
$818$	2.31495e6			0.120965
$819$	1.79176e7	+	1.30179e7i	0.933407	+	0.678160i
$820$	4.21765e6	+	6.37250e6i	0.219046	+	0.330960i
$821$	2.39391e7	−	1.73928e7i	1.23951	−	0.900556i	0.241943	−	0.970290i	$-0.422215\pi$
$821$	2.39391e7	−	1.73928e7i	1.23951	−	0.900556i	0.997566	+	0.0697348i	$0.0222153\pi$
$822$	−7.19512e6	+	5.22756e6i	−0.371414	+	0.269848i
$823$	5.87736e6	+	1.80887e7i	0.302470	+	0.930908i	0.980609	+	0.195974i	$0.0627868\pi$
$823$	5.87736e6	+	1.80887e7i	0.302470	+	0.930908i	−0.678139	+	0.734934i	$0.737213\pi$
$824$	−1.24974e7			−0.641212
$825$	−6.29645e6	−	551165.i	−0.322078	−	0.0281933i
$826$	2.07226e7			1.05680
$827$	1.12296e6	+	3.45611e6i	0.0570952	+	0.175721i	0.975537	−	0.219835i	$-0.0705519\pi$
$827$	1.12296e6	+	3.45611e6i	0.0570952	+	0.175721i	−0.918442	+	0.395556i	$0.870552\pi$
$828$	1.34844e6	−	979701.i	0.0683528	−	0.0496612i
$829$	1.54548e6	−	1.12286e6i	0.0781047	−	0.0567464i	−0.548048	−	0.836447i	$-0.684629\pi$
$829$	1.54548e6	−	1.12286e6i	0.0781047	−	0.0567464i	0.626152	+	0.779701i	$0.284629\pi$
$830$	645059.	−	1.47664e7i	0.0325016	−	0.744009i
$831$	−1.32205e6	−	960526.i	−0.0664118	−	0.0482510i
$832$	−2.58406e6			−0.129418
$833$	−7.24896e6	−	5.26668e6i	−0.361962	−	0.262981i
$834$	5.43004e6	−	1.67119e7i	0.270326	−	0.831977i
$835$	−2.04249e7	−	7.63711e6i	−1.01378	−	0.379064i
$836$	−859982.	−	2.64675e6i	−0.0425573	−	0.130978i
$837$	−934888.	+	2.87729e6i	−0.0461260	+	0.141961i
$838$	1.34646e6	−	4.14399e6i	0.0662345	−	0.203849i
$839$	−6.93132e6	−	2.13324e7i	−0.339947	−	1.04625i	−0.964234	−	0.265054i	$-0.914610\pi$
$839$	−6.93132e6	−	2.13324e7i	−0.339947	−	1.04625i	0.624287	−	0.781195i	$-0.285390\pi$
$840$	1.17219e7	−	3.25046e6i	0.573189	−	0.158945i
$841$	5.44583e6	−	1.67605e7i	0.265506	−	0.817143i
$842$	−9.77967e6	−	7.10534e6i	−0.475383	−	0.345386i
$843$	−2.87685e7			−1.39427
$844$	−2.71407e6	−	1.97189e6i	−0.131149	−	0.0952854i
$845$	−1.39844e6	−	522893.i	−0.0673756	−	0.0251925i
$846$	−1.08132e7	+	7.85624e6i	−0.519431	+	0.377388i
$847$	1.94054e7	−	1.40988e7i	0.929424	−	0.675266i
$848$	−1.42331e6	−	4.38051e6i	−0.0679690	−	0.209187i
$849$	−8.02081e6			−0.381900
$850$	3.14589e6	+	1.36293e7i	0.149347	+	0.647031i
$851$	7.63829e6			0.361553
$852$	3.05125e6	+	9.39077e6i	0.144005	+	0.443203i
$853$	−1.24297e7	+	9.03068e6i	−0.584907	+	0.424960i	−0.840490	−	0.541827i	$-0.817733\pi$
$853$	−1.24297e7	+	9.03068e6i	−0.584907	+	0.424960i	0.255583	+	0.966787i	$0.417733\pi$
$854$	7.97781e6	−	5.79622e6i	0.374317	−	0.271957i
$855$	−1.43956e7	+	1.80968e7i	−0.673463	+	0.846618i
$856$	−1.00612e6	−	730989.i	−0.0469316	−	0.0340978i
$857$	1.95715e7			0.910275			0.455137	−	0.890421i	$-0.349590\pi$
$857$	1.95715e7			0.910275			0.455137	+	0.890421i	$0.349590\pi$
$858$	−4.12917e6	−	3.00002e6i	−0.191489	−	0.139125i
$859$	5.34529e6	−	1.64511e7i	0.247166	−	0.760698i	−0.748107	−	0.663578i	$-0.769037\pi$
$859$	5.34529e6	−	1.64511e7i	0.247166	−	0.760698i	0.995273	−	0.0971200i	$-0.0309631\pi$
$860$	−2.14864e6	+	2.70108e6i	−0.0990644	+	0.124535i
$861$	−8.97660e6	−	2.76271e7i	−0.412671	−	1.27007i
$862$	2.67671e6	−	8.23808e6i	0.122697	−	0.377622i
$863$	−4.75368e6	+	1.46303e7i	−0.217272	+	0.668693i	0.781713	+	0.623638i	$0.214346\pi$
$863$	−4.75368e6	+	1.46303e7i	−0.217272	+	0.668693i	−0.998985	+	0.0450546i	$0.985654\pi$
$864$	−137559.	−	423362.i	−0.00626908	−	0.0192942i
$865$	−1.40197e6	−	2.11825e6i	−0.0637087	−	0.0962582i
$866$	8.16382e6	−	2.51257e7i	0.369912	−	1.13847i
$867$	−2.92790e6	−	2.12724e6i	−0.132284	−	0.0961101i
$868$	−1.75405e7			−0.790211
$869$	6.71205e6	+	4.87659e6i	0.301513	+	0.219062i
$870$	2.87199e7	−	7.96401e6i	1.28643	−	0.356725i
$871$	1.97663e7	−	1.43611e7i	0.882836	−	0.641418i
$872$	1.16041e7	−	8.43088e6i	0.516798	−	0.375476i
$873$	3.36801e6	+	1.03657e7i	0.149568	+	0.460322i
$874$	3.47053e6			0.153680
$875$	1.89439e7	−	1.99599e7i	0.836469	−	0.881331i
$876$	2.89166e7			1.27317
$877$	1.45749e6	+	4.48568e6i	0.0639891	+	0.196938i	0.977940	−	0.208887i	$-0.0669841\pi$
$877$	1.45749e6	+	4.48568e6i	0.0639891	+	0.196938i	−0.913951	+	0.405825i	$0.866984\pi$
$878$	−1.16613e7	+	8.47240e6i	−0.510516	+	0.370912i
$879$	−3.38523e6	+	2.45951e6i	−0.147780	+	0.107369i
$880$	−1.29227e6	+	358346.i	−0.0562532	+	0.0155990i
$881$	−2.27093e7	−	1.64993e7i	−0.985746	−	0.716186i	−0.0267603	−	0.999642i	$-0.508519\pi$
$881$	−2.27093e7	−	1.64993e7i	−0.985746	−	0.716186i	−0.958985	+	0.283456i	$0.908519\pi$
$882$	−7.13797e6			−0.308961
$883$	−7.78859e6	−	5.65874e6i	−0.336168	−	0.244241i	0.406875	−	0.913484i	$-0.366618\pi$
$883$	−7.78859e6	−	5.65874e6i	−0.336168	−	0.244241i	−0.743043	+	0.669243i	$0.766618\pi$
$884$	−3.49042e6	+	1.07424e7i	−0.150227	+	0.462350i
$885$	2.19008e7	+	3.30902e7i	0.939944	+	1.42017i
$886$	−3.19507e6	−	9.83342e6i	−0.136740	−	0.420843i
$887$	1.35169e7	−	4.16009e7i	0.576859	−	1.77539i	−0.0529031	−	0.998600i	$-0.516847\pi$
$887$	1.35169e7	−	4.16009e7i	0.576859	−	1.77539i	0.629762	−	0.776788i	$-0.283153\pi$
$888$	−6.97528e6	+	2.14677e7i	−0.296845	+	0.913594i
$889$	−1.14524e6	−	3.52468e6i	−0.0486005	−	0.149577i
$890$	−1.52941e6	+	1.92264e6i	−0.0647217	+	0.0813624i
$891$	1.83988e6	−	5.66256e6i	0.0776416	−	0.238956i
$892$	−3.67743e6	−	2.67181e6i	−0.154751	−	0.112433i
$893$	−2.78302e7			−1.16785
$894$	−1.93085e7	−	1.40284e7i	−0.807986	−	0.587036i
$895$	1.17544e7	−	1.47765e7i	0.490502	−	0.616616i
$896$	2.08799e6	−	1.51701e6i	0.0868877	−	0.0631276i
$897$	5.14933e6	−	3.74121e6i	0.213683	−	0.155250i
$898$	−6.26960e6	−	1.92958e7i	−0.259447	−	0.798496i
$899$	−4.29763e7			−1.77349
$900$	8.40935e6	+	7.31083e6i	0.346064	+	0.300857i
$901$	−2.01331e7			−0.826228
$902$	989623.	+	3.04575e6i	0.0404998	+	0.124646i
$903$	1.06143e7	−	7.71175e6i	0.433184	−	0.314727i
$904$	−7.89749e6	+	5.73786e6i	−0.321416	+	0.233523i
$905$	−2.19635e7	−	8.21239e6i	−0.891414	−	0.333310i
$906$	−1.86408e7	−	1.35434e7i	−0.754475	−	0.548158i
$907$	−7.12349e6			−0.287524			−0.143762	−	0.989612i	$-0.545920\pi$
$907$	−7.12349e6			−0.287524			−0.143762	+	0.989612i	$0.545920\pi$
$908$	−4.96810e6	−	3.60954e6i	−0.199975	−	0.145290i
$909$	8.31385e6	−	2.55874e7i	0.333728	−	1.02711i
$910$	2.14137e7	−	5.93799e6i	0.857211	−	0.237704i
$911$	3.28249e6	+	1.01025e7i	0.131041	+	0.403303i	0.994953	−	0.100339i	$-0.0319929\pi$
$911$	3.28249e6	+	1.01025e7i	0.131041	+	0.403303i	−0.863912	+	0.503643i	$0.831993\pi$
$912$	−3.16928e6	+	9.75405e6i	−0.126175	+	0.388327i
$913$	1.91408e6	−	5.89093e6i	0.0759947	−	0.233888i
$914$	−5.85302e6	−	1.80137e7i	−0.231747	−	0.713244i
$915$	1.76869e7	+	6.61333e6i	0.698391	+	0.261136i
$916$	−4.10676e6	+	1.26393e7i	−0.161719	+	0.497719i
$917$	−2.18247e7	−	1.58566e7i	−0.857088	−	0.622711i
$918$	−1.94580e6			−0.0762066
$919$	3.38163e7	+	2.45690e7i	1.32080	+	0.959619i	0.999922	+	0.0124987i	$0.00397857\pi$
$919$	3.38163e7	+	2.45690e7i	1.32080	+	0.959619i	0.320880	+	0.947120i	$0.396021\pi$
$920$	72986.3	−	1.67076e6i	0.00284297	−	0.0650797i
$921$	−1.61428e7	+	1.17284e7i	−0.627090	+	0.455608i
$922$	−2.38810e6	+	1.73505e6i	−0.0925177	+	0.0672180i
$923$	5.57406e6	+	1.71552e7i	0.215361	+	0.662814i
$924$	5.09769e6			0.196424
$925$	1.14848e7	+	4.97566e7i	0.441334	+	1.91204i
$926$	−2.73607e7			−1.04858
$927$	1.34478e7	+	4.13882e7i	0.513988	+	1.58189i
$928$	5.11582e6	−	3.71686e6i	0.195005	−	0.141679i
$929$	536715.	−	389947.i	0.0204035	−	0.0148240i	−0.577537	−	0.816365i	$-0.695986\pi$
$929$	536715.	−	389947.i	0.0204035	−	0.0148240i	0.597940	+	0.801541i	$0.295986\pi$
$930$	−1.85378e7	−	2.80090e7i	−0.702831	−	1.06192i
$931$	−1.20241e7	−	8.73604e6i	−0.454652	−	0.330324i
$932$	2.25175e7			0.849141
$933$	6.38751e6	+	4.64080e6i	0.240230	+	0.174537i
$934$	4.45850e6	−	1.37218e7i	0.167233	−	0.514689i
$935$	−255827.	+	5.85626e6i	−0.00957012	+	0.219074i
$936$	2.78058e6	+	8.55773e6i	0.103740	+	0.319278i
$937$	681490.	−	2.09741e6i	0.0253577	−	0.0780431i	−0.937577	−	0.347778i	$-0.886936\pi$
$937$	681490.	−	2.09741e6i	0.0253577	−	0.0780431i	0.962935	+	0.269735i	$0.0869362\pi$
$938$	−7.54082e6	+	2.32083e7i	−0.279841	+	0.861263i
$939$	−4.20844e6	−	1.29523e7i	−0.155760	−	0.479382i
$940$	−585279.	+	1.33979e7i	−0.0216044	+	0.494558i
$941$	1.11730e6	−	3.43869e6i	0.0411334	−	0.126596i	−0.928381	−	0.371630i	$-0.878799\pi$
$941$	1.11730e6	−	3.43869e6i	0.0411334	−	0.126596i	0.969514	+	0.245034i	$0.0787991\pi$
$942$	1.96230e7	+	1.42570e7i	0.720508	+	0.523480i
$943$	−3.99370e6			−0.146250
$944$	6.81132e6	+	4.94871e6i	0.248772	+	0.180743i
$945$	2.11279e6	+	3.19223e6i	0.0769620	+	0.116283i
$946$	−1.17017e6	+	850180.i	−0.0425130	+	0.0308875i
$947$	3.17812e7	−	2.30904e7i	1.15158	−	0.836675i	0.162894	−	0.986644i	$-0.447917\pi$
$947$	3.17812e7	−	2.30904e7i	1.15158	−	0.836675i	0.988691	+	0.149968i	$0.0479172\pi$
$948$	−9.44825e6	−	2.90787e7i	−0.341453	−	1.05088i
$949$	5.28252e7			1.90404
$950$	5.21821e6	+	2.26074e7i	0.187591	+	0.812720i
$951$	−6.34382e7			−2.27457
$952$	−3.48615e6	−	1.07293e7i	−0.124668	−	0.383688i
$953$	−3.83183e7	+	2.78398e7i	−1.36670	+	0.992966i	−0.368714	+	0.929543i	$0.620202\pi$
$953$	−3.83183e7	+	2.78398e7i	−1.36670	+	0.992966i	−0.997987	+	0.0634237i	$0.979798\pi$
$954$	−1.29756e7	+	9.42730e6i	−0.461589	+	0.335364i
$955$	−392940.	+	8.99497e6i	−0.0139418	+	0.319147i
$956$	1.29865e7	+	9.43527e6i	0.459567	+	0.333895i
$957$	1.24899e7			0.440840
$958$	−1.74904e7	−	1.27075e7i	−0.615724	−	0.447350i
$959$	5.01448e6	−	1.54330e7i	0.176068	−	0.541880i
$960$	4.62909e6	+	1.73087e6i	0.162113	+	0.0606159i
$961$	6.11979e6	+	1.88348e7i	0.213761	+	0.657888i
$962$	−1.27425e7	+	3.92175e7i	−0.443934	+	1.36629i
$963$	−1.33821e6	+	4.11859e6i	−0.0465007	+	0.143114i
$964$	1.55480e6	+	4.78520e6i	0.0538869	+	0.165847i
$965$	−3.89588e7	+	1.08033e7i	−1.34675	+	0.373454i
$966$	−1.96447e6	+	6.04601e6i	−0.0677332	+	0.208462i
$967$	3.07813e6	+	2.23639e6i	0.105857	+	0.0769098i	0.639455	−	0.768829i	$-0.279160\pi$
$967$	3.07813e6	+	2.23639e6i	0.105857	+	0.0769098i	−0.533597	+	0.845739i	$0.679160\pi$
$968$	9.74527e6			0.334276
$969$	3.62685e7	+	2.63506e7i	1.24085	+	0.901532i
$970$	1.02431e7	+	3.83000e6i	0.349543	+	0.130698i
$971$	2.44551e7	−	1.77677e7i	0.832380	−	0.604760i	−0.0878513	−	0.996134i	$-0.528000\pi$
$971$	2.44551e7	−	1.77677e7i	0.832380	−	0.604760i	0.920232	+	0.391374i	$0.128000\pi$
$972$	−1.63841e7	+	1.19038e7i	−0.556235	+	0.404128i
$973$	9.90755e6	+	3.04923e7i	0.335493	+	1.03254i
$974$	3.99620e7			1.34974
$975$	3.21130e7	+	2.79181e7i	1.08186	+	0.940533i
$976$	4.00641e6			0.134627
$977$	−1.72166e7	−	5.29873e7i	−0.577047	−	1.77597i	−0.629100	−	0.777325i	$-0.716576\pi$
$977$	−1.72166e7	−	5.29873e7i	−0.577047	−	1.77597i	0.0520526	−	0.998644i	$-0.483424\pi$
$978$	2.21573e7	−	1.60982e7i	0.740745	−	0.538183i
$979$	−832934.	+	605162.i	−0.0277750	+	0.0201797i
$980$	−4.45853e6	+	5.60487e6i	−0.148295	+	0.186423i
$981$	−4.04076e7	−	2.93578e7i	−1.34057	−	0.973982i
$982$	1.94611e7			0.644005
$983$	3.96379e7	+	2.87986e7i	1.30836	+	0.950578i	1.00000		0.000692575i	$-0.000220454\pi$
$983$	3.96379e7	+	2.87986e7i	1.30836	+	0.950578i	0.308358	+	0.951270i	$0.400220\pi$
$984$	3.64705e6	−	1.12245e7i	0.120075	−	0.369554i
$985$	2.57995e7	−	3.24329e7i	0.847269	−	1.06511i
$986$	−8.54148e6	−	2.62880e7i	−0.279796	−	0.861123i
$987$	1.57531e7	−	4.84830e7i	0.514722	−	1.58415i
$988$	−5.78969e6	+	1.78188e7i	−0.188696	+	0.580747i
$989$	−557395.	−	1.71549e6i	−0.0181206	−	0.0557695i
$990$	2.57730e6	+	3.89408e6i	0.0835752	+	0.126275i
$991$	5.48845e6	−	1.68917e7i	0.177528	−	0.546374i	−0.822212	−	0.569181i	$-0.807260\pi$
$991$	5.48845e6	−	1.68917e7i	0.177528	−	0.546374i	0.999740	+	0.0228072i	$0.00726038\pi$
$992$	−5.76540e6	−	4.18881e6i	−0.186016	−	0.135148i
$993$	2.90236e7			0.934068
$994$	−1.45753e7	−	1.05895e7i	−0.467897	−	0.339947i
$995$	−4.41696e7	+	1.22482e7i	−1.41438	+	0.392206i
$996$	−1.84675e7	+	1.34174e7i	−0.589873	+	0.428568i
$997$	−1.30650e6	+	949229.i	−0.0416267	+	0.0302436i	−0.608404	−	0.793627i	$-0.708190\pi$
$997$	−1.30650e6	+	949229.i	−0.0416267	+	0.0302436i	0.566777	+	0.823871i	$0.308190\pi$
$998$	1.96763e6	+	6.05574e6i	0.0625340	+	0.192460i
$999$	−7.10359e6			−0.225198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.6.d.b.31.6	yes	28
25.21	even	5	inner	50.6.d.b.21.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.6.d.b.21.6	✓	28	25.21	even	5	inner
50.6.d.b.31.6	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 - 3.80423i) q^{2} +(17.4616 - 12.6866i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(53.8689 - 14.9378i) q^{5} +(-69.8465 - 50.7465i) q^{6} +157.525 q^{7} +(51.7771 + 37.6183i) q^{8} +(68.8673 - 211.952i) q^{9} +O(q^{10})\)	\(q+(-1.23607 - 3.80423i) q^{2} +(17.4616 - 12.6866i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(53.8689 - 14.9378i) q^{5} +(-69.8465 - 50.7465i) q^{6} +157.525 q^{7} +(51.7771 + 37.6183i) q^{8} +(68.8673 - 211.952i) q^{9} +(-123.412 - 186.465i) q^{10} +(-28.9573 - 89.1214i) q^{11} +(-106.716 + 328.438i) q^{12} +(-194.950 + 599.996i) q^{13} +(-194.712 - 599.262i) q^{14} +(751.129 - 944.253i) q^{15} +(79.1084 - 243.470i) q^{16} +(-905.297 - 657.737i) q^{17} -891.436 q^{18} +(-1501.65 - 1091.01i) q^{19} +(-556.810 + 699.973i) q^{20} +(2750.65 - 1998.47i) q^{21} +(-303.245 + 220.320i) q^{22} +(-144.446 - 444.560i) q^{23} +1381.36 q^{24} +(2678.72 - 1609.37i) q^{25} +2523.49 q^{26} +(134.335 + 413.440i) q^{27} +(-2039.05 + 1481.46i) q^{28} +(-4995.92 + 3629.75i) q^{29} +(-4520.60 - 1690.30i) q^{30} +(5630.27 + 4090.63i) q^{31} -1024.00 q^{32} +(-1636.29 - 1188.84i) q^{33} +(-1383.17 + 4256.96i) q^{34} +(8485.73 - 2353.09i) q^{35} +(1101.88 + 3391.23i) q^{36} +(-5049.57 + 15541.0i) q^{37} +(-2294.32 + 7061.18i) q^{38} +(4207.77 + 12950.2i) q^{39} +(3351.11 + 1253.02i) q^{40} +(2640.18 - 8125.65i) q^{41} +(-11002.6 - 7993.86i) q^{42} +3858.84 q^{43} +(1212.98 + 881.281i) q^{44} +(543.710 - 12446.3i) q^{45} +(-1512.66 + 1099.01i) q^{46} +(12130.1 - 8813.01i) q^{47} +(-1707.46 - 5255.01i) q^{48} +8007.27 q^{49} +(-9433.49 - 8201.18i) q^{50} -24152.4 q^{51} +(-3119.21 - 9599.93i) q^{52} +(14555.8 - 10575.4i) q^{53} +(1406.77 - 1022.08i) q^{54} +(-2891.18 - 4368.32i) q^{55} +(8156.21 + 5925.83i) q^{56} -40062.5 q^{57} +(19983.7 + 14519.0i) q^{58} +(-10162.9 + 31278.1i) q^{59} +(-842.528 + 19286.7i) q^{60} +(4836.13 + 14884.1i) q^{61} +(8602.29 - 26475.1i) q^{62} +(10848.3 - 33387.8i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-1539.14 + 35233.3i) q^{65} +(-2500.03 + 7694.30i) q^{66} +(-31331.7 - 22763.8i) q^{67} +17904.1 q^{68} +(-8162.24 - 5930.21i) q^{69} +(-19440.6 - 29373.1i) q^{70} +(23131.6 - 16806.1i) q^{71} +(11539.0 - 8383.57i) q^{72} +(-25875.1 - 79635.3i) q^{73} +65363.0 q^{74} +(26357.4 - 62086.2i) q^{75} +29698.3 q^{76} +(-4561.51 - 14038.9i) q^{77} +(44064.3 - 32014.6i) q^{78} +(-71627.4 + 52040.4i) q^{79} +(624.564 - 14297.2i) q^{80} +(51403.0 + 37346.5i) q^{81} -34175.2 q^{82} +(53476.1 + 38852.7i) q^{83} +(-16810.5 + 51737.4i) q^{84} +(-58592.5 - 21908.4i) q^{85} +(-4769.79 - 14679.9i) q^{86} +(-41187.7 + 126763. i) q^{87} +(1853.27 - 5703.77i) q^{88} +(-3395.16 - 10449.2i) q^{89} +(-48020.7 + 13316.1i) q^{90} +(-30709.7 + 94514.6i) q^{91} +(6050.65 + 4396.05i) q^{92} +150210. q^{93} +(-48520.3 - 35252.0i) q^{94} +(-97189.7 - 36340.3i) q^{95} +(-17880.7 + 12991.1i) q^{96} +(-39565.7 + 28746.1i) q^{97} +(-9897.53 - 30461.5i) q^{98} -20883.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9	\( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 7 * q^3 - 112 * q^4 - 145 * q^5 - 28 * q^6 - 236 * q^7 + 448 * q^8 - 446 * q^9 - 220 * q^10 - 389 * q^11 + 192 * q^12 + 1047 * q^13 + 164 * q^14 - 640 * q^15 - 1792 * q^16 + 909 * q^17 - 11576 * q^18 + 260 * q^19 - 1040 * q^20 - 1849 * q^21 + 556 * q^22 + 817 * q^23 + 2432 * q^24 + 16055 * q^25 - 4528 * q^26 + 1675 * q^27 + 2544 * q^28 - 2445 * q^29 - 5440 * q^30 + 16731 * q^31 - 28672 * q^32 + 29629 * q^33 - 7576 * q^34 - 825 * q^35 - 7136 * q^36 + 39819 * q^37 + 3100 * q^38 + 26008 * q^39 + 10231 * q^41 + 7396 * q^42 - 86148 * q^43 - 2224 * q^44 - 7870 * q^45 - 11708 * q^46 + 10019 * q^47 + 3072 * q^48 + 147076 * q^49 + 16520 * q^50 - 108074 * q^51 + 16752 * q^52 + 74512 * q^53 + 4260 * q^54 + 2735 * q^55 - 10176 * q^56 - 176840 * q^57 + 9780 * q^58 - 13430 * q^59 + 5760 * q^60 - 29774 * q^61 + 63956 * q^62 - 206818 * q^63 - 28672 * q^64 + 51235 * q^65 + 23264 * q^66 - 85061 * q^67 - 89696 * q^68 - 185227 * q^69 - 25260 * q^70 + 148501 * q^71 + 64064 * q^72 + 189082 * q^73 + 305304 * q^74 + 93630 * q^75 + 16480 * q^76 + 127243 * q^77 + 32028 * q^78 + 46930 * q^79 + 39680 * q^80 - 179812 * q^81 - 338864 * q^82 + 66807 * q^83 - 34464 * q^84 - 877380 * q^85 + 121332 * q^86 - 226000 * q^87 + 24896 * q^88 - 347190 * q^89 + 628660 * q^90 + 197001 * q^91 + 46832 * q^92 - 64906 * q^93 - 40076 * q^94 + 85970 * q^95 - 7168 * q^96 + 502364 * q^97 + 185056 * q^98 + 1151018 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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