LMFDB - Embedded newform 150.6.g.c.121.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.g (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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			121.5
Character	$\chi$	$=$	150.121
Dual form			150.6.g.c.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(43.0312 + 35.6835i) q^{5} +(29.1246 - 21.1603i) q^{6} +32.5493 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(43.0312 + 35.6835i) q^{5} +(29.1246 - 21.1603i) q^{6} +32.5493 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-188.938 + 119.593i) q^{10} +(-95.0205 + 292.443i) q^{11} +(44.4984 + 136.952i) q^{12} +(-262.489 - 807.859i) q^{13} +(-40.2331 + 123.825i) q^{14} +(-124.549 - 487.455i) q^{15} +(79.1084 + 243.470i) q^{16} +(870.731 - 632.623i) q^{17} -324.000 q^{18} +(2244.16 - 1630.48i) q^{19} +(-221.420 - 866.587i) q^{20} +(-236.996 - 172.188i) q^{21} +(-995.068 - 722.959i) q^{22} +(-1426.79 + 4391.21i) q^{23} -576.000 q^{24} +(578.374 + 3071.01i) q^{25} +3397.73 q^{26} +(225.273 - 693.320i) q^{27} +(-421.327 - 306.112i) q^{28} +(2748.44 + 1996.86i) q^{29} +(2008.34 + 128.716i) q^{30} +(-3658.54 + 2658.08i) q^{31} -1024.00 q^{32} +(2238.90 - 1626.66i) q^{33} +(1330.36 + 4094.42i) q^{34} +(1400.64 + 1161.47i) q^{35} +(400.486 - 1232.57i) q^{36} +(1120.42 + 3448.29i) q^{37} +(3428.78 + 10552.7i) q^{38} +(-2362.40 + 7270.73i) q^{39} +(3570.38 + 228.829i) q^{40} +(2022.72 + 6225.30i) q^{41} +(947.986 - 688.752i) q^{42} +14896.8 q^{43} +(3980.27 - 2891.84i) q^{44} +(-1671.81 + 4208.11i) q^{45} +(-14941.5 - 10855.7i) q^{46} +(20027.7 + 14551.0i) q^{47} +(711.975 - 2191.23i) q^{48} -15747.5 q^{49} +(-12397.7 - 1595.71i) q^{50} -9686.55 q^{51} +(-4199.83 + 12925.7i) q^{52} +(-2760.68 - 2005.75i) q^{53} +(2359.09 + 1713.98i) q^{54} +(-14524.2 + 9193.52i) q^{55} +(1685.31 - 1224.45i) q^{56} -24965.4 q^{57} +(-10993.7 + 7987.42i) q^{58} +(7018.96 + 21602.1i) q^{59} +(-2972.11 + 7481.08i) q^{60} +(-14773.0 + 45466.7i) q^{61} +(-5589.75 - 17203.5i) q^{62} +(814.721 + 2507.45i) q^{63} +(1265.73 - 3895.53i) q^{64} +(17532.0 - 44129.7i) q^{65} +(3420.74 + 10527.9i) q^{66} +(53639.8 - 38971.6i) q^{67} -17220.5 q^{68} +(33618.5 - 24425.3i) q^{69} +(-6149.79 + 3892.68i) q^{70} +(-11052.7 - 8030.22i) q^{71} +(4193.94 + 3047.08i) q^{72} +(-27248.2 + 83861.2i) q^{73} -14503.0 q^{74} +(12034.6 - 25420.1i) q^{75} -44383.0 q^{76} +(-3092.85 + 9518.81i) q^{77} +(-24739.4 - 17974.2i) q^{78} +(58246.9 + 42318.9i) q^{79} +(-5283.75 + 13299.7i) q^{80} +(-5307.96 + 3856.46i) q^{81} -26182.7 q^{82} +(59143.6 - 42970.3i) q^{83} +(1448.39 + 4457.70i) q^{84} +(60042.9 + 3848.19i) q^{85} +(-18413.5 + 56671.0i) q^{86} +(-9448.28 - 29078.8i) q^{87} +(6081.31 + 18716.4i) q^{88} +(24175.8 - 74405.5i) q^{89} +(-13942.1 - 11561.5i) q^{90} +(-8543.84 - 26295.2i) q^{91} +(59766.2 - 43422.7i) q^{92} +40699.8 q^{93} +(-80110.8 + 58203.9i) q^{94} +(154750. + 9918.07i) q^{95} +(7455.90 + 5417.03i) q^{96} +(-75373.6 - 54762.1i) q^{97} +(19465.0 - 59907.2i) q^{98} -24906.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−7.28115	−	5.29007i	−0.467086	−	0.339358i
$3$	−7.28115	−	5.29007i	−0.467086	−	0.339358i
$4$	−12.9443	−	9.40456i	−0.404508	−	0.293893i
$5$	43.0312	+	35.6835i	0.769766	+	0.638326i
$5$	43.0312	+	35.6835i	0.769766	+	0.638326i
$6$	29.1246	−	21.1603i	0.330280	−	0.239962i
$7$	32.5493			0.251071			0.125535	−	0.992089i	$-0.459935\pi$
$7$	32.5493			0.251071			0.125535	+	0.992089i	$0.459935\pi$
$8$	51.7771	−	37.6183i	0.286031	−	0.207813i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	−188.938	+	119.593i	−0.597473	+	0.378187i
$11$	−95.0205	+	292.443i	−0.236775	+	0.728718i	0.760106	+	0.649799i	$0.225147\pi$
$11$	−95.0205	+	292.443i	−0.236775	+	0.728718i	−0.996881	+	0.0789192i	$0.974853\pi$
$12$	44.4984	+	136.952i	0.0892055	+	0.274546i
$13$	−262.489	−	807.859i	−0.430778	−	1.32580i	−0.897352	−	0.441315i	$-0.854512\pi$
$13$	−262.489	−	807.859i	−0.430778	−	1.32580i	0.466574	−	0.884482i	$-0.345488\pi$
$14$	−40.2331	+	123.825i	−0.0548610	+	0.168845i
$15$	−124.549	−	487.455i	−0.142926	−	0.559380i
$16$	79.1084	+	243.470i	0.0772542	+	0.237764i
$17$	870.731	−	632.623i	0.730738	−	0.530912i	−0.159059	−	0.987269i	$-0.550846\pi$
$17$	870.731	−	632.623i	0.730738	−	0.530912i	0.889797	+	0.456357i	$0.150846\pi$
$18$	−324.000			−0.235702
$19$	2244.16	−	1630.48i	1.42617	−	1.03617i	0.435452	−	0.900212i	$-0.356588\pi$
$19$	2244.16	−	1630.48i	1.42617	−	1.03617i	0.990714	−	0.135959i	$-0.0434116\pi$
$20$	−221.420	−	866.587i	−0.123778	−	0.484437i
$21$	−236.996	−	172.188i	−0.117272	−	0.0852029i
$22$	−995.068	−	722.959i	−0.438325	−	0.318462i
$23$	−1426.79	+	4391.21i	−0.562394	+	1.73087i	0.113176	+	0.993575i	$0.463898\pi$
$23$	−1426.79	+	4391.21i	−0.562394	+	1.73087i	−0.675570	+	0.737296i	$0.736102\pi$
$24$	−576.000			−0.204124
$25$	578.374	+	3071.01i	0.185080	+	0.982724i
$26$	3397.73			0.985725
$27$	225.273	−	693.320i	0.0594703	−	0.183031i
$28$	−421.327	−	306.112i	−0.101560	−	0.0737879i
$29$	2748.44	+	1996.86i	0.606863	+	0.440912i	0.848308	−	0.529503i	$-0.177621\pi$
$29$	2748.44	+	1996.86i	0.606863	+	0.440912i	−0.241445	+	0.970414i	$0.577621\pi$
$30$	2008.34	+	128.716i	0.407412	+	0.0261114i
$31$	−3658.54	+	2658.08i	−0.683760	+	0.496781i	−0.874603	−	0.484840i	$-0.838878\pi$
$31$	−3658.54	+	2658.08i	−0.683760	+	0.496781i	0.190843	+	0.981621i	$0.438878\pi$
$32$	−1024.00			−0.176777
$33$	2238.90	−	1626.66i	0.357891	−	0.260023i
$34$	1330.36	+	4094.42i	0.197366	+	0.607429i
$35$	1400.64	+	1161.47i	0.193266	+	0.160265i
$36$	400.486	−	1232.57i	0.0515028	−	0.158509i
$37$	1120.42	+	3448.29i	0.134547	+	0.414094i	0.995519	−	0.0945582i	$-0.0301439\pi$
$37$	1120.42	+	3448.29i	0.134547	+	0.414094i	−0.860972	+	0.508652i	$0.830144\pi$
$38$	3428.78	+	10552.7i	0.385194	+	1.18551i
$39$	−2362.40	+	7270.73i	−0.248710	+	0.765449i
$40$	3570.38	+	228.829i	0.352829	+	0.0226131i
$41$	2022.72	+	6225.30i	0.187922	+	0.578363i	0.999986	−	0.00520397i	$-0.00165648\pi$
$41$	2022.72	+	6225.30i	0.187922	+	0.578363i	−0.812065	+	0.583567i	$0.801656\pi$
$42$	947.986	−	688.752i	0.0829237	−	0.0602476i
$43$	14896.8			1.22864			0.614318	−	0.789059i	$-0.289431\pi$
$43$	14896.8			1.22864			0.614318	+	0.789059i	$0.289431\pi$
$44$	3980.27	−	2891.84i	0.309942	−	0.225186i
$45$	−1671.81	+	4208.11i	−0.123071	+	0.309782i
$46$	−14941.5	−	10855.7i	−1.04112	−	0.756418i
$47$	20027.7	+	14551.0i	1.32247	+	0.960833i	0.999898	+	0.0142885i	$0.00454831\pi$
$47$	20027.7	+	14551.0i	1.32247	+	0.960833i	0.322575	+	0.946544i	$0.395452\pi$
$48$	711.975	−	2191.23i	0.0446028	−	0.137273i
$49$	−15747.5			−0.936963
$50$	−12397.7	−	1595.71i	−0.701321	−	0.0902673i
$51$	−9686.55			−0.521487
$52$	−4199.83	+	12925.7i	−0.215389	+	0.662899i
$53$	−2760.68	−	2005.75i	−0.134998	−	0.0980817i	0.518237	−	0.855237i	$-0.326589\pi$
$53$	−2760.68	−	2005.75i	−0.134998	−	0.0980817i	−0.653235	+	0.757155i	$0.726589\pi$
$54$	2359.09	+	1713.98i	0.110093	+	0.0799874i
$55$	−14524.2	+	9193.52i	−0.647421	+	0.409803i
$56$	1685.31	−	1224.45i	0.0718140	−	0.0521759i
$57$	−24965.4			−1.01778
$58$	−10993.7	+	7987.42i	−0.429117	+	0.311772i
$59$	7018.96	+	21602.1i	0.262508	+	0.807917i	0.992257	+	0.124202i	$0.0396369\pi$
$59$	7018.96	+	21602.1i	0.262508	+	0.807917i	−0.729749	+	0.683715i	$0.760363\pi$
$60$	−2972.11	+	7481.08i	−0.106583	+	0.268279i
$61$	−14773.0	+	45466.7i	−0.508329	+	1.56447i	0.286773	+	0.957999i	$0.407418\pi$
$61$	−14773.0	+	45466.7i	−0.508329	+	1.56447i	−0.795102	+	0.606476i	$0.792582\pi$
$62$	−5589.75	−	17203.5i	−0.184677	−	0.568378i
$63$	814.721	+	2507.45i	0.0258617	+	0.0795942i
$64$	1265.73	−	3895.53i	0.0386271	−	0.118882i
$65$	17532.0	−	44129.7i	0.514693	−	1.29553i
$66$	3420.74	+	10527.9i	0.0966629	+	0.297498i
$67$	53639.8	−	38971.6i	1.45982	−	1.06062i	0.476414	−	0.879221i	$-0.341936\pi$
$67$	53639.8	−	38971.6i	1.45982	−	1.06062i	0.983409	−	0.181402i	$-0.0580636\pi$
$68$	−17220.5			−0.451621
$69$	33618.5	−	24425.3i	0.850071	−	0.617613i
$70$	−6149.79	+	3892.68i	−0.150008	+	0.0949518i
$71$	−11052.7	−	8030.22i	−0.260208	−	0.189052i	0.450031	−	0.893013i	$-0.351413\pi$
$71$	−11052.7	−	8030.22i	−0.260208	−	0.189052i	−0.710239	+	0.703961i	$0.751413\pi$
$72$	4193.94	+	3047.08i	0.0953436	+	0.0692712i
$73$	−27248.2	+	83861.2i	−0.598453	+	1.84185i	−0.0617242	+	0.998093i	$0.519660\pi$
$73$	−27248.2	+	83861.2i	−0.598453	+	1.84185i	−0.536729	+	0.843755i	$0.680340\pi$
$74$	−14503.0			−0.307877
$75$	12034.6	−	25420.1i	0.247047	−	0.521825i
$76$	−44383.0			−0.881420
$77$	−3092.85	+	9518.81i	−0.0594473	+	0.182960i
$78$	−24739.4	−	17974.2i	−0.460419	−	0.334514i
$79$	58246.9	+	42318.9i	1.05004	+	0.762898i	0.972220	−	0.234070i	$-0.0752044\pi$
$79$	58246.9	+	42318.9i	1.05004	+	0.762898i	0.0778190	+	0.996968i	$0.475204\pi$
$80$	−5283.75	+	13299.7i	−0.0923034	+	0.232336i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	−26182.7			−0.430011
$83$	59143.6	−	42970.3i	0.942350	−	0.684657i	−0.00663518	−	0.999978i	$-0.502112\pi$
$83$	59143.6	−	42970.3i	0.942350	−	0.684657i	0.948985	+	0.315321i	$0.102112\pi$
$84$	1448.39	+	4457.70i	0.0223969	+	0.0689306i
$85$	60042.9	+	3848.19i	0.901393	+	0.0577710i
$86$	−18413.5	+	56671.0i	−0.268467	+	0.826256i
$87$	−9448.28	−	29078.8i	−0.133830	−	0.411888i
$88$	6081.31	+	18716.4i	0.0837126	+	0.257641i
$89$	24175.8	−	74405.5i	0.323524	−	0.995704i	−0.648579	−	0.761147i	$-0.724636\pi$
$89$	24175.8	−	74405.5i	0.323524	−	0.995704i	0.972103	−	0.234556i	$-0.0753637\pi$
$90$	−13942.1	−	11561.5i	−0.181436	−	0.150455i
$91$	−8543.84	−	26295.2i	−0.108156	−	0.332869i
$92$	59766.2	−	43422.7i	0.736183	−	0.534868i
$93$	40699.8			0.487961
$94$	−80110.8	+	58203.9i	−0.935129	+	0.679411i
$95$	154750.	+	9918.07i	1.75923	+	0.112750i
$96$	7455.90	+	5417.03i	0.0825700	+	0.0599906i
$97$	−75373.6	−	54762.1i	−0.813373	−	0.590950i	0.101433	−	0.994842i	$-0.467657\pi$
$97$	−75373.6	−	54762.1i	−0.813373	−	0.590950i	−0.914807	+	0.403892i	$0.867657\pi$
$98$	19465.0	−	59907.2i	0.204734	−	0.630106i
$99$	−24906.9			−0.255407
$100$	21394.9	−	45191.4i	0.213949	−	0.451914i
$101$	−71258.3			−0.695075			−0.347538	−	0.937666i	$-0.612982\pi$
$101$	−71258.3			−0.695075			−0.347538	+	0.937666i	$0.612982\pi$
$102$	11973.2	−	36849.8i	0.113949	−	0.350699i
$103$	−1158.13	−	841.433i	−0.0107564	−	0.00781495i	0.582394	−	0.812907i	$-0.302116\pi$
$103$	−1158.13	−	841.433i	−0.0107564	−	0.00781495i	−0.593150	+	0.805092i	$0.702116\pi$
$104$	−43981.2	−	31954.2i	−0.398734	−	0.289697i
$105$	−4053.97	−	15866.3i	−0.0358846	−	0.140444i
$106$	11042.7	−	8023.01i	0.0954579	−	0.0693542i
$107$	153712.			1.29792			0.648962	−	0.760820i	$-0.275203\pi$
$107$	153712.			1.29792			0.648962	+	0.760820i	$0.275203\pi$
$108$	−9436.37	+	6855.93i	−0.0778477	+	0.0565597i
$109$	−39145.0	−	120476.i	−0.315581	−	0.971258i	−0.975515	−	0.219934i	$-0.929416\pi$
$109$	−39145.0	−	120476.i	−0.315581	−	0.971258i	0.659934	−	0.751324i	$-0.270584\pi$
$110$	−17021.3	−	66617.3i	−0.134125	−	0.524935i
$111$	10083.7	−	31034.6i	0.0776809	−	0.239077i
$112$	2574.92	+	7924.79i	0.0193963	+	0.0596957i
$113$	−21894.6	−	67384.8i	−0.161303	−	0.496439i	0.837442	−	0.546526i	$-0.184050\pi$
$113$	−21894.6	−	67384.8i	−0.161303	−	0.496439i	−0.998745	+	0.0500872i	$0.984050\pi$
$114$	30859.0	−	94974.2i	0.222392	−	0.684453i
$115$	−218090.	+	138046.i	−1.53777	+	0.973375i
$116$	−16796.9	−	51695.7i	−0.115901	−	0.356705i
$117$	55663.7	−	40442.0i	0.375930	−	0.273129i
$118$	−90855.3			−0.600683
$119$	28341.7	−	20591.4i	0.183467	−	0.133297i
$120$	−24786.0	−	20553.7i	−0.157128	−	0.130298i
$121$	53799.0	+	39087.2i	0.334049	+	0.242701i
$122$	−154705.	−	112400.i	−0.941033	−	0.683701i
$123$	18204.5	−	56027.7i	0.108497	−	0.333918i
$124$	72355.3			0.422587
$125$	−84696.3	+	152788.i	−0.484830	+	0.874608i
$126$	−10546.0			−0.0591780
$127$	49001.0	−	150810.i	0.269585	−	0.829697i	−0.721017	−	0.692918i	$-0.756325\pi$
$127$	49001.0	−	150810.i	0.269585	−	0.829697i	0.990602	−	0.136779i	$-0.0436751\pi$
$128$	13254.9	+	9630.27i	0.0715077	+	0.0519534i
$129$	−108466.	−	78805.3i	−0.573879	−	0.416947i
$130$	146209.	+	121243.i	0.758778	+	0.629214i
$131$	−102803.	+	74691.0i	−0.523394	+	0.380268i	−0.817881	−	0.575388i	$-0.804851\pi$
$131$	−102803.	+	74691.0i	−0.523394	+	0.380268i	0.294487	+	0.955656i	$0.404851\pi$
$132$	−44279.0			−0.221189
$133$	73045.9	−	53071.0i	0.358069	−	0.260152i
$134$	81954.3	+	252229.i	0.394285	+	1.21348i
$135$	34433.9	−	21795.9i	0.162612	−	0.102930i
$136$	21285.7	−	65510.8i	0.0986828	−	0.303714i
$137$	−79486.2	−	244633.i	−0.361818	−	1.11356i	−0.951950	−	0.306254i	$-0.900924\pi$
$137$	−79486.2	−	244633.i	−0.361818	−	1.11356i	0.590132	−	0.807307i	$-0.299076\pi$
$138$	51364.5	+	158084.i	0.229596	+	0.706625i
$139$	−85370.0	+	262742.i	−0.374773	+	1.15343i	0.568858	+	0.822435i	$0.307385\pi$
$139$	−85370.0	+	262742.i	−0.374773	+	1.15343i	−0.943632	+	0.330998i	$0.892615\pi$
$140$	−7207.07	−	28206.8i	−0.0310770	−	0.121628i
$141$	−68849.1	−	211896.i	−0.291642	−	0.897583i
$142$	44210.6	−	32120.9i	0.183995	−	0.133680i
$143$	261195.			1.06813
$144$	−16775.8	+	12188.3i	−0.0674181	+	0.0489821i
$145$	47013.7	+	184001.i	0.185697	+	0.726775i
$146$	−285346.	−	207316.i	−1.10787	−	0.804917i
$147$	114660.	+	83305.6i	0.437643	+	0.317966i
$148$	17926.7	−	55172.6i	0.0672737	−	0.207047i
$149$	200303.			0.739130			0.369565	−	0.929205i	$-0.379507\pi$
$149$	200303.			0.739130			0.369565	+	0.929205i	$0.379507\pi$
$150$	81828.3	+	77203.5i	0.296945	+	0.280162i
$151$	−376540.			−1.34390			−0.671952	−	0.740595i	$-0.734544\pi$
$151$	−376540.			−1.34390			−0.671952	+	0.740595i	$0.734544\pi$
$152$	54860.4	−	168843.i	0.192597	−	0.592753i
$153$	70529.2	+	51242.5i	0.243579	+	0.176971i
$154$	−32388.7	−	23531.8i	−0.110051	−	0.0799564i
$155$	−252281.	−	16168.9i	−0.843443	−	0.0540569i
$156$	98957.6	−	71896.9i	0.325565	−	0.236537i
$157$	−191816.			−0.621065			−0.310532	−	0.950563i	$-0.600507\pi$
$157$	−191816.			−0.621065			−0.310532	+	0.950563i	$0.600507\pi$
$158$	−232988.	+	169276.i	−0.742490	+	0.539450i
$159$	9490.38	+	29208.4i	0.0297708	+	0.0916252i
$160$	−44064.0	−	36539.9i	−0.136077	−	0.112841i
$161$	−46441.0	+	142931.i	−0.141201	+	0.434571i
$162$	−8109.84	−	24959.5i	−0.0242787	−	0.0747221i
$163$	61011.6	+	187774.i	0.179864	+	0.553563i	0.999822	−	0.0188598i	$-0.00600362\pi$
$163$	61011.6	+	187774.i	0.179864	+	0.553563i	−0.819959	+	0.572423i	$0.806004\pi$
$164$	32363.6	−	99604.8i	0.0939608	−	0.289182i
$165$	154388.	+	9894.82i	0.441471	+	0.0282942i
$166$	90363.3	+	278110.i	0.254520	+	0.783332i
$167$	136038.	−	98837.3i	0.377458	−	0.274239i	−0.382839	−	0.923815i	$-0.625053\pi$
$167$	136038.	−	98837.3i	0.377458	−	0.274239i	0.760297	+	0.649576i	$0.225053\pi$
$168$	−18748.4			−0.0512496
$169$	−283353.	+	205868.i	−0.763152	+	0.554462i
$170$	−88856.4	+	223660.i	−0.235812	+	0.593562i
$171$	181777.	+	132069.i	0.475389	+	0.345390i
$172$	−192829.	−	140098.i	−0.496994	−	0.361087i
$173$	45204.0	−	139124.i	0.114832	−	0.353415i	−0.877080	−	0.480344i	$-0.840512\pi$
$173$	45204.0	−	139124.i	0.114832	−	0.353415i	0.991912	+	0.126928i	$0.0405119\pi$
$174$	122301.			0.306237
$175$	18825.6	+	99959.2i	0.0464681	+	0.246733i
$176$	−78718.2			−0.191555
$177$	63170.6	−	194419.i	0.151559	−	0.466451i
$178$	253172.	+	183941.i	0.598917	+	0.435138i
$179$	−235352.	−	170993.i	−0.549015	−	0.398883i	0.278407	−	0.960463i	$-0.410194\pi$
$179$	−235352.	−	170993.i	−0.549015	−	0.398883i	−0.827422	+	0.561580i	$0.810194\pi$
$180$	61215.8	−	38748.2i	0.140826	−	0.0891396i
$181$	−275827.	+	200400.i	−0.625807	+	0.454676i	−0.854945	−	0.518718i	$-0.826409\pi$
$181$	−275827.	+	200400.i	−0.625807	+	0.454676i	0.229138	+	0.973394i	$0.426409\pi$
$182$	110594.			0.247487
$183$	348086.	−	252900.i	0.768350	−	0.558239i
$184$	91314.6	+	281037.i	0.198836	+	0.611955i
$185$	−74834.1	+	188364.i	−0.160757	+	0.404641i
$186$	−50307.8	+	154831.i	−0.106623	+	0.328153i
$187$	102269.	+	314751.i	0.213865	+	0.658209i
$188$	−122398.	−	376704.i	−0.252570	−	0.777330i
$189$	7332.49	−	22567.1i	0.0149313	−	0.0459537i
$190$	−229013.	+	576446.i	−0.460230	+	1.15844i
$191$	−29484.9	−	90745.1i	−0.0584811	−	0.179986i	0.917549	−	0.397624i	$-0.130165\pi$
$191$	−29484.9	−	90745.1i	−0.0584811	−	0.179986i	−0.976030	+	0.217637i	$0.930165\pi$
$192$	−29823.6	+	21668.1i	−0.0583858	+	0.0424197i
$193$	617973.			1.19420			0.597099	−	0.802168i	$-0.296320\pi$
$193$	617973.			1.19420			0.597099	+	0.802168i	$0.296320\pi$
$194$	301494.	−	219048.i	0.575142	−	0.417865i
$195$	−361102.	+	228570.i	−0.680055	+	0.430459i
$196$	203840.	+	148099.i	0.379010	+	0.275367i
$197$	−33627.5	−	24431.8i	−0.0617347	−	0.0448529i	0.556490	−	0.830854i	$-0.312148\pi$
$197$	−33627.5	−	24431.8i	−0.0617347	−	0.0448529i	−0.618225	+	0.786001i	$0.712148\pi$
$198$	30786.6	−	94751.5i	0.0558084	−	0.171761i
$199$	415600.			0.743949			0.371975	−	0.928243i	$-0.378681\pi$
$199$	415600.			0.743949			0.371975	+	0.928243i	$0.378681\pi$
$200$	145473.	+	137251.i	0.257162	+	0.242627i
$201$	−596722.			−1.04179
$202$	88080.1	−	271083.i	0.151880	−	0.467437i
$203$	89459.6	+	64996.2i	0.152366	+	0.110700i
$204$	125385.	+	91097.7i	0.210946	+	0.153261i
$205$	−135100.	+	340060.i	−0.224529	+	0.565160i
$206$	4632.53	−	3365.73i	0.00760589	−	0.00552601i
$207$	−373992.			−0.606648
$208$	175925.	−	127817.i	0.281948	−	0.204847i
$209$	263581.	+	811219.i	0.417396	+	1.28461i
$210$	65370.1	+	4189.62i	0.102289	+	0.00655581i
$211$	251089.	−	772773.i	0.388259	−	1.19494i	−0.545829	−	0.837896i	$-0.683785\pi$
$211$	251089.	−	772773.i	0.388259	−	1.19494i	0.934088	−	0.357042i	$-0.116215\pi$
$212$	16871.8	+	51926.0i	0.0257823	+	0.0793497i
$213$	37995.6	+	116939.i	0.0573832	+	0.176607i
$214$	−189999.	+	584757.i	−0.283607	+	0.872853i
$215$	641030.	+	531572.i	0.945762	+	0.784270i
$216$	−14417.5	−	44372.5i	−0.0210259	−	0.0647112i
$217$	−119083.	+	86518.8i	−0.171672	+	0.124727i
$218$	506704.			0.722126
$219$	642029.	−	466462.i	0.904575	−	0.657212i
$220$	274467.	+	17590.8i	0.382325	+	0.0245035i
$221$	−739628.	−	537371.i	−1.01867	−	0.740105i
$222$	105598.	+	76721.7i	0.143805	+	0.104481i
$223$	−3203.10	+	9858.11i	−0.00431328	+	0.0132749i	−0.953190	−	0.302372i	$-0.902222\pi$
$223$	−3203.10	+	9858.11i	−0.00431328	+	0.0132749i	0.948877	+	0.315647i	$0.102222\pi$
$224$	−33330.5			−0.0443835
$225$	−222100.	+	121424.i	−0.292478	+	0.159900i
$226$	283410.			0.369100
$227$	−334545.	+	1.02962e6i	−0.430913	+	1.32621i	0.466304	+	0.884625i	$0.345585\pi$
$227$	−334545.	+	1.02962e6i	−0.430913	+	1.32621i	−0.897217	+	0.441590i	$0.854415\pi$
$228$	323159.	+	234789.i	0.411699	+	0.299117i
$229$	93015.4	+	67579.6i	0.117210	+	0.0851583i	0.644846	−	0.764312i	$-0.276921\pi$
$229$	93015.4	+	67579.6i	0.117210	+	0.0851583i	−0.527636	+	0.849471i	$0.676921\pi$
$230$	−255585.	−	1.00030e6i	−0.318578	−	1.24684i
$231$	72874.7	−	52946.6i	0.0898559	−	0.0652842i
$232$	217424.			0.265209
$233$	1.04393e6	−	758459.i	1.25974	−	0.915255i	0.260996	−	0.965340i	$-0.415949\pi$
$233$	1.04393e6	−	758459.i	1.25974	−	0.915255i	0.998745	+	0.0500849i	$0.0159492\pi$
$234$	85046.5	+	261746.i	0.101535	+	0.312493i
$235$	342587.	+	1.34081e6i	0.404670	+	1.58378i
$236$	112303.	−	345634.i	0.131254	−	0.403958i
$237$	−200235.	−	616260.i	−0.231563	−	0.712678i
$238$	43302.2	+	133271.i	0.0495528	+	0.152508i
$239$	−329513.	+	1.01414e6i	−0.373145	+	1.14842i	0.571576	+	0.820549i	$0.306332\pi$
$239$	−329513.	+	1.01414e6i	−0.373145	+	1.14842i	−0.944721	+	0.327874i	$0.893668\pi$
$240$	108828.	−	68885.7i	0.121959	−	0.0771971i
$241$	28495.1	+	87699.1i	0.0316030	+	0.0972640i	0.965614	−	0.259981i	$-0.0837162\pi$
$241$	28495.1	+	87699.1i	0.0316030	+	0.0972640i	−0.934011	+	0.357245i	$0.883716\pi$
$242$	−215196.	+	156349.i	−0.236208	+	0.171615i
$243$	59049.0			0.0641500
$244$	618820.	−	449599.i	0.665411	−	0.483449i
$245$	−677636.	−	561928.i	−0.721243	−	0.598088i
$246$	190640.	+	138508.i	0.200852	+	0.145928i
$247$	−1.90627e6	−	1.38498e6i	−1.98811	−	1.44445i
$248$	−89436.0	+	275256.i	−0.0923386	+	0.284189i
$249$	−657949.			−0.672503
$250$	−476549.	−	511060.i	−0.482234	−	0.517156i
$251$	−484954.			−0.485866			−0.242933	−	0.970043i	$-0.578109\pi$
$251$	−484954.			−0.485866			−0.242933	+	0.970043i	$0.578109\pi$
$252$	13035.5	−	40119.3i	0.0129309	−	0.0397971i
$253$	−1.14860e6	−	834510.i	−1.12816	−	0.819653i
$254$	513145.	+	372822.i	0.499063	+	0.362591i
$255$	−416824.	−	345650.i	−0.401423	−	0.332879i
$256$	−53019.7	+	38521.1i	−0.0505636	+	0.0367366i
$257$	619441.			0.585016			0.292508	−	0.956263i	$-0.405510\pi$
$257$	619441.			0.585016			0.292508	+	0.956263i	$0.405510\pi$
$258$	433865.	−	315221.i	0.405794	−	0.294826i
$259$	36468.8	+	112239.i	0.0337809	+	0.103967i
$260$	−641960.	+	406346.i	−0.588944	+	0.372789i
$261$	−85034.5	+	261709.i	−0.0772670	+	0.237803i
$262$	−157069.	−	483410.i	−0.141364	−	0.435073i
$263$	230811.	+	710364.i	0.205763	+	0.633274i	0.999681	+	0.0252490i	$0.00803785\pi$
$263$	230811.	+	710364.i	0.205763	+	0.633274i	−0.793918	+	0.608025i	$0.791962\pi$
$264$	54731.8	−	168447.i	0.0483315	−	0.148749i
$265$	−47223.2	−	184821.i	−0.0413087	−	0.161673i
$266$	111604.	+	343482.i	0.0967111	+	0.297646i
$267$	−569638.	+	413866.i	−0.489013	+	0.355289i
$268$	−1.06084e6			−0.902220
$269$	142130.	−	103263.i	0.119758	−	0.0870092i	−0.526294	−	0.850303i	$-0.676419\pi$
$269$	142130.	−	103263.i	0.119758	−	0.0870092i	0.646052	+	0.763293i	$0.276419\pi$
$270$	40353.8	+	157935.i	0.0336880	+	0.131847i
$271$	−1.64268e6	−	1.19348e6i	−1.35872	−	0.987168i	−0.998525	−	0.0542908i	$-0.982710\pi$
$271$	−1.64268e6	−	1.19348e6i	−1.35872	−	0.987168i	−0.360195	−	0.932877i	$-0.617290\pi$
$272$	222907.	+	161952.i	0.182685	+	0.132728i
$273$	−76894.6	+	236657.i	−0.0624437	+	0.192182i
$274$	1.02889e6			0.827928
$275$	−953053.	−	122668.i	−0.759951	−	0.0978134i
$276$	−664876.			−0.525373
$277$	490210.	−	1.50871e6i	0.383869	−	1.18143i	−0.553428	−	0.832897i	$-0.686681\pi$
$277$	490210.	−	1.50871e6i	0.383869	−	1.18143i	0.937297	−	0.348531i	$-0.113319\pi$
$278$	−894007.	−	649534.i	−0.693791	−	0.504069i
$279$	−296342.	−	215305.i	−0.227920	−	0.165594i
$280$	116213.	+	7448.21i	0.0885852	+	0.00567750i
$281$	820736.	−	596300.i	0.620066	−	0.450504i	−0.232879	−	0.972506i	$-0.574815\pi$
$281$	820736.	−	596300.i	0.620066	−	0.450504i	0.852944	+	0.522002i	$0.174815\pi$
$282$	891202.			0.667350
$283$	1.91868e6	−	1.39400e6i	1.42409	−	1.03466i	0.433007	−	0.901391i	$-0.357453\pi$
$283$	1.91868e6	−	1.39400e6i	1.42409	−	1.03466i	0.991080	−	0.133269i	$-0.0425473\pi$
$284$	67547.8	+	207891.i	0.0496953	+	0.152946i
$285$	−1.07429e6	−	890855.i	−0.783449	−	0.649673i
$286$	−322854.	+	993643.i	−0.233395	+	0.718316i
$287$	65838.2	+	202629.i	0.0471817	+	0.145210i
$288$	−25631.1	−	78884.4i	−0.0182090	−	0.0560415i
$289$	−80799.3	+	248675.i	−0.0569066	+	0.175141i
$290$	−758094.	−	48586.8i	−0.529332	−	0.0339253i
$291$	259111.	+	797463.i	0.179372	+	0.552049i
$292$	1.14139e6	−	829265.i	0.783385	−	0.569162i
$293$	174921.			0.119035			0.0595173	−	0.998227i	$-0.481044\pi$
$293$	174921.			0.119035			0.0595173	+	0.998227i	$0.481044\pi$
$294$	−458641.	+	333222.i	−0.309460	+	0.224836i
$295$	−468806.	+	1.18003e6i	−0.313645	+	0.789473i
$296$	187730.	+	136394.i	0.124539	+	0.0904829i
$297$	181351.	+	131759.i	0.119297	+	0.0866742i
$298$	−247588.	+	761996.i	−0.161506	+	0.497064i
$299$	3.92199e6			2.53705
$300$	−394845.	+	215865.i	−0.253293	+	0.138477i
$301$	484882.			0.308475
$302$	465429.	−	1.43244e6i	0.293654	−	0.903773i
$303$	518842.	+	376961.i	0.324660	+	0.235879i
$304$	574506.	+	417403.i	0.356542	+	0.259043i
$305$	−2.25811e6	+	1.42933e6i	−1.38994	+	0.879800i
$306$	−282117.	+	204970.i	−0.172237	+	0.125137i
$307$	403867.			0.244564			0.122282	−	0.992495i	$-0.460979\pi$
$307$	403867.			0.244564			0.122282	+	0.992495i	$0.460979\pi$
$308$	129555.	−	94127.2i	0.0778175	−	0.0565377i
$309$	3981.31	+	12253.2i	0.00237208	+	0.00730051i
$310$	373347.	−	939749.i	0.220652	−	0.555402i
$311$	−79993.3	+	246194.i	−0.0468978	+	0.144337i	−0.971763	−	0.235958i	$-0.924177\pi$
$311$	−79993.3	+	246194.i	−0.0468978	+	0.144337i	0.924866	+	0.380294i	$0.124177\pi$
$312$	151194.	+	465327.i	0.0879321	+	0.270627i
$313$	−735668.	−	2.26415e6i	−0.424445	−	1.30631i	−0.903525	−	0.428536i	$-0.859030\pi$
$313$	−735668.	−	2.26415e6i	−0.424445	−	1.30631i	0.479080	−	0.877771i	$-0.340970\pi$
$314$	237098.	−	729713.i	0.135708	−	0.417665i
$315$	−54416.3	+	136971.i	−0.0308996	+	0.0777771i
$316$	−355974.	−	1.09557e6i	−0.200540	−	0.617197i
$317$	−2.17419e6	+	1.57964e6i	−1.21520	+	0.882898i	−0.995693	−	0.0927118i	$-0.970446\pi$
$317$	−2.17419e6	+	1.57964e6i	−1.21520	+	0.882898i	−0.219512	+	0.975610i	$0.570446\pi$
$318$	−122846.			−0.0681230
$319$	−845124.	+	614019.i	−0.464990	+	0.337835i
$320$	193472.	−	122464.i	0.105619	−	0.0668547i
$321$	−1.11920e6	−	813149.i	−0.606243	−	0.440461i
$322$	−486337.	−	353344.i	−0.261395	−	0.189915i
$323$	922583.	−	2.83942e6i	0.492039	−	1.51434i
$324$	104976.			0.0555556
$325$	2.32913e6	−	1.27335e6i	1.22316	−	0.668713i
$326$	−789750.			−0.411572
$327$	−352305.	+	1.08428e6i	−0.182201	+	0.560756i
$328$	338916.	+	246237.i	0.173943	+	0.126377i
$329$	651888.	+	473624.i	0.332034	+	0.241237i
$330$	−228476.	+	575095.i	−0.115493	+	0.290706i
$331$	758943.	−	551405.i	0.380749	−	0.276631i	−0.380905	−	0.924614i	$-0.624387\pi$
$331$	758943.	−	551405.i	0.380749	−	0.276631i	0.761654	+	0.647984i	$0.224387\pi$
$332$	−1.16969e6			−0.582404
$333$	−237596.	+	172624.i	−0.117416	+	0.0853081i
$334$	207847.	+	639689.i	0.101948	+	0.313764i
$335$	3.69883e6	+	237061.i	1.80075	+	0.115411i
$336$	23174.3	−	71323.1i	0.0111985	−	0.0344653i
$337$	−67490.1	−	207713.i	−0.0323717	−	0.0996299i	0.933565	−	0.358408i	$-0.116680\pi$
$337$	−67490.1	−	207713.i	−0.0323717	−	0.0996299i	−0.965937	+	0.258778i	$0.916680\pi$
$338$	−432925.	−	1.33241e6i	−0.206120	−	0.634373i
$339$	−197052.	+	606463.i	−0.0931282	+	0.286619i
$340$	−741020.	−	614489.i	−0.347643	−	0.288282i
$341$	−429702.	−	1.32249e6i	−0.200116	−	0.615893i
$342$	−727109.	+	528275.i	−0.336151	+	0.244228i
$343$	−1.05963e6			−0.486315
$344$	771315.	−	560393.i	0.351428	−	0.255327i
$345$	2.31822e6	+	148577.i	1.04859	+	0.0672052i
$346$	473382.	+	343932.i	0.212580	+	0.154448i
$347$	1.54171e6	+	1.12012e6i	0.687353	+	0.499391i	0.875789	−	0.482694i	$-0.160342\pi$
$347$	1.54171e6	+	1.12012e6i	0.687353	+	0.499391i	−0.188436	+	0.982086i	$0.560342\pi$
$348$	−151173.	+	465261.i	−0.0669152	+	0.205944i
$349$	−3.93959e6			−1.73136			−0.865680	−	0.500598i	$-0.833114\pi$
$349$	−3.93959e6			−1.73136			−0.865680	+	0.500598i	$0.833114\pi$
$350$	−403537.	−	51939.4i	−0.176081	−	0.0226635i
$351$	−619237.			−0.268280
$352$	97301.0	−	299462.i	0.0418563	−	0.128820i
$353$	1.08109e6	+	785457.i	0.461769	+	0.335495i	0.794225	−	0.607624i	$-0.207877\pi$
$353$	1.08109e6	+	785457.i	0.461769	+	0.335495i	−0.332456	+	0.943119i	$0.607877\pi$
$354$	661531.	+	480631.i	0.280571	+	0.203847i
$355$	−189063.	−	739948.i	−0.0796223	−	0.311623i
$356$	−1.01269e6	+	735762.i	−0.423498	+	0.307689i
$357$	−315290.			−0.130930
$358$	941406.	−	683972.i	0.388213	−	0.282053i
$359$	721428.	+	2.22033e6i	0.295432	+	0.909245i	0.983076	+	0.183197i	$0.0586447\pi$
$359$	721428.	+	2.22033e6i	0.295432	+	0.909245i	−0.687645	+	0.726047i	$0.741355\pi$
$360$	71740.1	+	280774.i	0.0291747	+	0.114183i
$361$	1.61265e6	−	4.96321e6i	0.651285	−	2.00445i
$362$	−421427.	−	1.29702e6i	−0.169025	−	0.520205i
$363$	−184944.	−	569200.i	−0.0736673	−	0.226725i
$364$	−136701.	+	420724.i	−0.0540779	+	0.166435i
$365$	−4.16498e6	+	2.63634e6i	−1.63637	+	1.03578i
$366$	531829.	+	1.63680e6i	0.207524	+	0.638694i
$367$	3.62498e6	−	2.63370e6i	1.40488	−	1.02071i	0.410843	−	0.911706i	$-0.365234\pi$
$367$	3.62498e6	−	2.63370e6i	1.40488	−	1.02071i	0.994042	−	0.109002i	$-0.0347655\pi$
$368$	−1.18200e6			−0.454986
$369$	−428940.	+	311643.i	−0.163995	+	0.119149i
$370$	−624081.	−	517517.i	−0.236994	−	0.196526i
$371$	−89858.3	−	65285.8i	−0.0338940	−	0.0246255i
$372$	−526830.	−	382764.i	−0.197384	−	0.143408i
$373$	251238.	−	773232.i	0.0935004	−	0.287765i	−0.893360	−	0.449343i	$-0.851658\pi$
$373$	251238.	−	773232.i	0.0935004	−	0.287765i	0.986860	+	0.161578i	$0.0516583\pi$
$374$	−1.32380e6			−0.489376
$375$	1.42494e6	−	664422.i	0.523263	−	0.243986i
$376$	1.58436e6			0.577942
$377$	891742.	−	2.74450e6i	0.323137	−	0.994512i
$378$	76786.8	+	55788.9i	0.0276412	+	0.0200825i
$379$	−250782.	−	182204.i	−0.0896806	−	0.0651568i	0.542041	−	0.840352i	$-0.317652\pi$
$379$	−250782.	−	182204.i	−0.0896806	−	0.0651568i	−0.631722	+	0.775195i	$0.717652\pi$
$380$	−1.90986e6	−	1.58374e6i	−0.678487	−	0.562633i
$381$	−1.15458e6	+	838849.i	−0.407484	+	0.296054i
$382$	381660.			0.133819
$383$	−738746.	+	536730.i	−0.257334	+	0.186964i	−0.708971	−	0.705238i	$-0.750840\pi$
$383$	−738746.	+	536730.i	−0.257334	+	0.186964i	0.451637	+	0.892202i	$0.350840\pi$
$384$	−45566.4	−	140239.i	−0.0157695	−	0.0485334i
$385$	−472754.	+	299243.i	−0.162549	+	0.102890i
$386$	−763856.	+	2.35091e6i	−0.260942	+	0.803096i
$387$	372874.	+	1.14759e6i	0.126556	+	0.389501i
$388$	460642.	+	1.41771e6i	0.155340	+	0.478089i
$389$	832238.	−	2.56137e6i	0.278852	−	0.858218i	−0.709323	−	0.704884i	$-0.750999\pi$
$389$	832238.	−	2.56137e6i	0.278852	−	0.858218i	0.988174	−	0.153334i	$-0.0490010\pi$
$390$	−423183.	−	1.65624e6i	−0.140886	−	0.551394i
$391$	1.53563e6	+	4.72618e6i	0.507978	+	1.56340i
$392$	−815362.	+	592395.i	−0.268000	+	0.194714i
$393$	1.14365e6			0.373517
$394$	134510.	−	97727.3i	0.0436530	−	0.0317158i
$395$	996351.	+	3.89949e6i	0.321307	+	1.25752i
$396$	322402.	+	234239.i	0.103314	+	0.0750621i
$397$	−1.21838e6	−	885203.i	−0.387977	−	0.281882i	0.376649	−	0.926356i	$-0.377076\pi$
$397$	−1.21838e6	−	885203.i	−0.387977	−	0.281882i	−0.764626	+	0.644474i	$0.777076\pi$
$398$	−513710.	+	1.58104e6i	−0.162559	+	0.500305i
$399$	−812607.			−0.255534
$400$	−701946.	+	383759.i	−0.219358	+	0.119925i
$401$	1.79113e6			0.556244			0.278122	−	0.960546i	$-0.410288\pi$
$401$	1.79113e6			0.556244			0.278122	+	0.960546i	$0.410288\pi$
$402$	737589.	−	2.27007e6i	0.227640	−	0.700605i
$403$	3.10768e6	+	2.25787e6i	0.953179	+	0.692525i
$404$	922387.	+	670153.i	0.281164	+	0.204278i
$405$	−366020.	−	23458.5i	−0.110884	−	0.00710662i
$406$	−357839.	+	259985.i	−0.107739	+	0.0782768i
$407$	−1.11489e6			−0.333615
$408$	−501541.	+	364391.i	−0.149161	+	0.108372i
$409$	1.74045e6	+	5.35654e6i	0.514461	+	1.58335i	0.784261	+	0.620431i	$0.213042\pi$
$409$	1.74045e6	+	5.35654e6i	0.514461	+	1.58335i	−0.269800	+	0.962916i	$0.586958\pi$
$410$	−1.12667e6	−	934290.i	−0.331008	−	0.274487i
$411$	−715375.	+	2.20170e6i	−0.208896	+	0.642915i
$412$	7077.88	+	21783.5i	0.00205428	+	0.00632243i
$413$	228462.	+	703134.i	0.0659081	+	0.202844i
$414$	462280.	−	1.42275e6i	0.132558	−	0.407970i
$415$	4.07835e6	+	261385.i	1.16242	+	0.0745006i
$416$	268789.	+	827247.i	0.0761514	+	0.234370i
$417$	2.01151e6	−	1.46145e6i	0.566478	−	0.411570i
$418$	−3.41186e6			−0.955105
$419$	−699514.	+	508227.i	−0.194653	+	0.141424i	−0.680843	−	0.732429i	$-0.738386\pi$
$419$	−699514.	+	508227.i	−0.194653	+	0.141424i	0.486190	+	0.873853i	$0.338386\pi$
$420$	−96740.1	+	243504.i	−0.0267598	+	0.0673570i
$421$	153984.	+	111876.i	0.0423420	+	0.0307633i	0.608755	−	0.793358i	$-0.291669\pi$
$421$	153984.	+	111876.i	0.0423420	+	0.0307633i	−0.566413	+	0.824122i	$0.691669\pi$
$422$	2.62944e6	+	1.91040e6i	0.718757	+	0.522207i
$423$	−619642.	+	1.90706e6i	−0.168380	+	0.518220i
$424$	−218393.			−0.0589962
$425$	2.44640e6	+	2.30813e6i	0.656985	+	0.619853i
$426$	−491826.			−0.131307
$427$	−480851.	+	1.47991e6i	−0.127627	+	0.392794i
$428$	−1.98970e6	−	1.44560e6i	−0.525022	−	0.381451i
$429$	−1.90180e6	−	1.38174e6i	−0.498909	−	0.362478i
$430$	−2.81458e6	+	1.78156e6i	−0.734077	+	0.464654i
$431$	2.94316e6	−	2.13833e6i	0.763170	−	0.554475i	−0.136711	−	0.990611i	$-0.543653\pi$
$431$	2.94316e6	−	2.13833e6i	0.763170	−	0.554475i	0.899881	+	0.436136i	$0.143653\pi$
$432$	186624.			0.0481125
$433$	−2.34068e6	+	1.70061e6i	−0.599961	+	0.435897i	−0.845865	−	0.533397i	$-0.820915\pi$
$433$	−2.34068e6	+	1.70061e6i	−0.599961	+	0.435897i	0.245904	+	0.969294i	$0.420915\pi$
$434$	−181942.	−	559961.i	−0.0463671	−	0.142703i
$435$	631063.	−	1.58845e6i	0.159900	−	0.402484i
$436$	−626321.	+	1.92762e6i	−0.157790	+	0.485629i
$437$	3.95783e6	+	1.21809e7i	0.991410	+	3.05125i
$438$	980933.	+	3.01900e6i	0.244317	+	0.751931i
$439$	426111.	−	1.31143e6i	0.105526	−	0.324777i	−0.884327	−	0.466868i	$-0.845382\pi$
$439$	426111.	−	1.31143e6i	0.105526	−	0.324777i	0.989854	+	0.142091i	$0.0453824\pi$
$440$	−406179.	+	1.02239e6i	−0.100020	+	0.251759i
$441$	−394167.	−	1.21312e6i	−0.0965125	−	0.297035i
$442$	2.95851e6	−	2.14948e6i	0.720307	−	0.523334i
$443$	−1.14480e6			−0.277154			−0.138577	−	0.990352i	$-0.544253\pi$
$443$	−1.14480e6			−0.277154			−0.138577	+	0.990352i	$0.544253\pi$
$444$	−422393.	+	306887.i	−0.101686	+	0.0738790i
$445$	3.69537e6	−	2.33908e6i	0.884621	−	0.559945i
$446$	−33543.3	−	24370.6i	−0.00798487	−	0.00580135i
$447$	−1.45843e6	−	1.05961e6i	−0.345237	−	0.250830i
$448$	41198.7	−	126797.i	0.00969815	−	0.0298478i
$449$	−4.91013e6			−1.14942			−0.574708	−	0.818359i	$-0.694884\pi$
$449$	−4.91013e6			−1.14942			−0.574708	+	0.818359i	$0.694884\pi$
$450$	−187393.	−	995008.i	−0.0436237	−	0.231630i
$451$	−2.01275e6			−0.465959
$452$	−350314.	+	1.07816e6i	−0.0806514	+	0.248219i
$453$	2.74164e6	+	1.99192e6i	0.627719	+	0.456065i
$454$	−3.50340e6	−	2.54537e6i	−0.797719	−	0.579577i
$455$	570654.	−	1.43639e6i	0.129224	−	0.325270i
$456$	−1.29264e6	+	939156.i	−0.291115	+	0.211507i
$457$	−7.54756e6			−1.69050			−0.845251	−	0.534369i	$-0.820549\pi$
$457$	−7.54756e6			−1.69050			−0.845251	+	0.534369i	$0.820549\pi$
$458$	−372062.	+	270319.i	−0.0828803	+	0.0602160i
$459$	−242458.	−	746209.i	−0.0537161	−	0.165321i
$460$	4.12129e6	+	264136.i	0.908109	+	0.0582014i
$461$	1.52428e6	−	4.69126e6i	0.334051	−	1.02810i	−0.633136	−	0.774040i	$-0.718233\pi$
$461$	1.52428e6	−	4.69126e6i	0.334051	−	1.02810i	0.967188	−	0.254064i	$-0.0817672\pi$
$462$	111343.	+	342677.i	0.0242693	+	0.0746931i
$463$	190567.	+	586505.i	0.0413138	+	0.127151i	0.969586	−	0.244750i	$-0.0787060\pi$
$463$	190567.	+	586505.i	0.0413138	+	0.127151i	−0.928272	+	0.371901i	$0.878706\pi$
$464$	−268751.	+	827131.i	−0.0579503	+	0.178353i
$465$	1.75136e6	+	1.45231e6i	0.375616	+	0.311478i
$466$	1.59498e6	+	4.90885e6i	0.340244	+	1.04716i
$467$	−6.08751e6	+	4.42284e6i	−1.29166	+	0.938444i	−0.999837	−	0.0180286i	$-0.994261\pi$
$467$	−6.08751e6	+	4.42284e6i	−1.29166	+	0.938444i	−0.291821	+	0.956473i	$0.594261\pi$
$468$	−1.10087e6			−0.232338
$469$	1.74594e6	−	1.26850e6i	0.366519	−	0.266292i
$470$	−5.52419e6	−	354050.i	−1.15352	−	0.0739298i
$471$	1.39665e6	+	1.01472e6i	0.290091	+	0.210763i
$472$	1.17606e6	+	854455.i	0.242981	+	0.176536i
$473$	−1.41551e6	+	4.35648e6i	−0.290910	+	0.895329i
$474$	2.59190e6			0.529873
$475$	6.30519e6	+	5.94882e6i	1.28222	+	1.20975i
$476$	−560516.			−0.113389
$477$	85413.4	−	262876.i	0.0171882	−	0.0528998i
$478$	−3.45071e6	−	2.50709e6i	−0.690778	−	0.501879i
$479$	−6.35902e6	−	4.62010e6i	−1.26634	−	0.920052i	−0.267293	−	0.963615i	$-0.586129\pi$
$479$	−6.35902e6	−	4.62010e6i	−1.26634	−	0.920052i	−0.999051	+	0.0435630i	$0.986129\pi$
$480$	127538.	+	499154.i	0.0252660	+	0.0988853i
$481$	2.49163e6	−	1.81028e6i	0.491045	−	0.356765i
$482$	−368849.			−0.0723154
$483$	1.09426e6	−	795025.i	0.213428	−	0.155065i
$484$	−328790.	−	1.01191e6i	−0.0637977	−	0.196349i
$485$	−1.28931e6	−	5.04608e6i	−0.248888	−	0.974091i
$486$	−72988.6	+	224636.i	−0.0140173	+	0.0431408i
$487$	−1.39283e6	−	4.28669e6i	−0.266119	−	0.819029i	−0.991434	−	0.130612i	$-0.958306\pi$
$487$	−1.39283e6	−	4.28669e6i	−0.266119	−	0.819029i	0.725315	−	0.688417i	$-0.241694\pi$
$488$	945473.	+	2.90987e6i	0.179721	+	0.553125i
$489$	549104.	−	1.68997e6i	0.103844	−	0.319600i
$490$	2.97530e6	−	1.88330e6i	0.559811	−	0.354348i
$491$	−582598.	−	1.79305e6i	−0.109060	−	0.335652i	0.881602	−	0.471994i	$-0.156466\pi$
$491$	−582598.	−	1.79305e6i	−0.109060	−	0.335652i	−0.990662	+	0.136342i	$0.956466\pi$
$492$	−762560.	+	554032.i	−0.142024	+	0.103186i
$493$	3.65641e6			0.677543
$494$	7.62506e6	−	5.53993e6i	1.40581	−	1.02138i
$495$	−1.07178e6	−	888766.i	−0.196603	−	0.163033i
$496$	−936586.	−	680470.i	−0.170940	−	0.124195i
$497$	−359756.	−	261378.i	−0.0653307	−	0.0474655i
$498$	813270.	−	2.50299e6i	0.146947	−	0.452257i
$499$	−1.97115e6			−0.354380			−0.177190	−	0.984177i	$-0.556701\pi$
$499$	−1.97115e6			−0.354380			−0.177190	+	0.984177i	$0.556701\pi$
$500$	2.53324e6	−	1.18119e6i	0.453159	−	0.211298i
$501$	−1.51337e6			−0.269371
$502$	599436.	−	1.84487e6i	0.106166	−	0.326744i
$503$	−1.88707e6	−	1.37104e6i	−0.332559	−	0.241618i	0.408957	−	0.912554i	$-0.365893\pi$
$503$	−1.88707e6	−	1.37104e6i	−0.332559	−	0.241618i	−0.741515	+	0.670936i	$0.765893\pi$
$504$	136510.	+	99180.3i	0.0239380	+	0.0173920i
$505$	−3.06633e6	−	2.54275e6i	−0.535045	−	0.443685i
$506$	4.59442e6	−	3.33804e6i	0.797727	−	0.579582i
$507$	3.15219e6			0.544619
$508$	−2.05258e6	+	1.49129e6i	−0.352891	+	0.256390i
$509$	−2.73252e6	−	8.40984e6i	−0.467487	−	1.43878i	−0.855828	−	0.517261i	$-0.826952\pi$
$509$	−2.73252e6	−	8.40984e6i	−0.467487	−	1.43878i	0.388341	−	0.921516i	$-0.373048\pi$
$510$	1.83015e6	−	1.15845e6i	0.311575	−	0.197220i
$511$	−886908.	+	2.72962e6i	−0.150254	+	0.462435i
$512$	−81007.0	−	249314.i	−0.0136568	−	0.0420312i
$513$	−624894.	−	1.92323e6i	−0.104837	−	0.322654i
$514$	−765672.	+	2.35649e6i	−0.127831	+	0.393422i
$515$	−19810.6	−	77534.1i	−0.00329139	−	0.0128817i
$516$	662887.	+	2.04015e6i	0.109601	+	0.337318i
$517$	−6.15838e6	+	4.47432e6i	−1.01330	+	0.736209i
$518$	−472061.			−0.0772991
$519$	−1.06511e6	+	773848.i	−0.173571	+	0.126106i
$520$	−752326.	−	2.94443e6i	−0.122011	−	0.477522i
$521$	−4.23197e6	−	3.07471e6i	−0.683044	−	0.496260i	0.191322	−	0.981527i	$-0.438722\pi$
$521$	−4.23197e6	−	3.07471e6i	−0.683044	−	0.496260i	−0.874366	+	0.485267i	$0.838722\pi$
$522$	−890493.	−	646981.i	−0.143039	−	0.103924i
$523$	−2.93316e6	+	9.02732e6i	−0.468901	+	1.44313i	0.385109	+	0.922871i	$0.374164\pi$
$523$	−2.93316e6	+	9.02732e6i	−0.468901	+	1.44313i	−0.854010	+	0.520257i	$0.825836\pi$
$524$	2.03315e6			0.323475
$525$	391719.	−	827407.i	0.0620263	−	0.131015i
$526$	−2.98768e6			−0.470836
$527$	−1.50404e6	+	4.62895e6i	−0.235902	+	0.726033i
$528$	573159.	+	416424.i	0.0894726	+	0.0650057i
$529$	−1.20399e7	−	8.74749e6i	−1.87061	−	1.35908i
$530$	761471.	+	48803.3i	0.117751	+	0.00754674i
$531$	−1.48845e6	+	1.08142e6i	−0.229085	+	0.166440i
$532$	−1.44464e6			−0.221299
$533$	4.49822e6	−	3.26815e6i	0.685840	−	0.498292i
$534$	−870329.	−	2.67860e6i	−0.132078	−	0.406494i
$535$	6.61443e6	+	5.48500e6i	0.999098	+	0.828499i
$536$	1.31127e6	−	4.03567e6i	0.197142	−	0.606742i
$537$	809067.	+	2.49005e6i	0.121073	+	0.372625i
$538$	217155.	+	668334.i	0.0323455	+	0.0995493i
$539$	1.49634e6	−	4.60526e6i	0.221849	−	0.682782i
$540$	−650702.	−	41704.0i	−0.0960280	−	0.00615451i
$541$	650408.	+	2.00175e6i	0.0955416	+	0.294047i	0.987394	−	0.158279i	$-0.0505945\pi$
$541$	650408.	+	2.00175e6i	0.0955416	+	0.294047i	−0.891853	+	0.452326i	$0.850594\pi$
$542$	6.57072e6	−	4.77391e6i	0.960760	−	0.698033i
$543$	3.06847e6			0.446604
$544$	−891629.	+	647806.i	−0.129177	+	0.0938529i
$545$	2.61455e6	−	6.58106e6i	0.377056	−	0.949084i
$546$	−805250.	−	585049.i	−0.115598	−	0.0839867i
$547$	1.06580e7	+	7.74353e6i	1.52303	+	1.10655i	0.959958	+	0.280142i	$0.0903817\pi$
$547$	1.06580e7	+	7.74353e6i	1.52303	+	1.10655i	0.563075	+	0.826406i	$0.309618\pi$
$548$	−1.27178e6	+	3.91413e6i	−0.180909	+	0.556781i
$549$	−3.87233e6			−0.548329
$550$	1.64469e6	−	3.47400e6i	0.231835	−	0.489693i
$551$	9.42377e6			1.32235
$552$	821831.	−	2.52934e6i	0.114798	−	0.353312i
$553$	1.89590e6	+	1.37745e6i	0.263634	+	0.191541i
$554$	5.13355e6	+	3.72974e6i	0.710630	+	0.516303i
$555$	1.54134e6	−	975633.i	0.212405	−	0.134448i
$556$	3.57603e6	−	2.59814e6i	0.490584	−	0.356430i
$557$	3.92327e6			0.535809			0.267905	−	0.963445i	$-0.413669\pi$
$557$	3.92327e6			0.535809			0.267905	+	0.963445i	$0.413669\pi$
$558$	1.18537e6	−	861219.i	0.161164	−	0.117092i
$559$	−3.91026e6	−	1.20345e7i	−0.529269	−	1.62892i
$560$	−171982.	+	432896.i	−0.0231747	+	0.0583329i
$561$	920421.	−	2.83276e6i	0.123475	−	0.380017i
$562$	1.25397e6	+	3.85933e6i	0.167474	+	0.515432i
$563$	−4.30842e6	−	1.32599e7i	−0.572858	−	1.76307i	−0.643361	−	0.765563i	$-0.722461\pi$
$563$	−4.30842e6	−	1.32599e7i	−0.572858	−	1.76307i	0.0705034	−	0.997512i	$-0.477539\pi$
$564$	−1.10159e6	+	3.39033e6i	−0.145821	+	0.448792i
$565$	1.46237e6	−	3.68093e6i	0.192724	−	0.485106i
$566$	2.93148e6	+	9.02217e6i	0.384633	+	1.18378i
$567$	−172770.	+	125525.i	−0.0225690	+	0.0163973i
$568$	−874357.			−0.113715
$569$	−429414.	+	311988.i	−0.0556027	+	0.0403977i	−0.615239	−	0.788340i	$-0.710941\pi$
$569$	−429414.	+	311988.i	−0.0556027	+	0.0403977i	0.559637	+	0.828738i	$0.310941\pi$
$570$	4.71691e6	−	2.98570e6i	0.608094	−	0.384910i
$571$	−2.68071e6	−	1.94765e6i	−0.344080	−	0.249989i	0.402301	−	0.915507i	$-0.368211\pi$
$571$	−2.68071e6	−	1.94765e6i	−0.344080	−	0.249989i	−0.746381	+	0.665518i	$0.768211\pi$
$572$	−3.38097e6	−	2.45642e6i	−0.432068	−	0.313915i
$573$	−265364.	+	816705.i	−0.0337641	+	0.103915i
$574$	−852227.			−0.107963
$575$	−1.43107e7	−	1.84193e6i	−1.80505	−	0.232329i
$576$	331776.			0.0416667
$577$	3.35075e6	−	1.03126e7i	0.418989	−	1.28952i	−0.489644	−	0.871922i	$-0.662873\pi$
$577$	3.35075e6	−	1.03126e7i	0.418989	−	1.28952i	0.908633	−	0.417595i	$-0.137127\pi$
$578$	−846141.	−	614758.i	−0.105347	−	0.0765393i
$579$	−4.49955e6	−	3.26912e6i	−0.557793	−	0.405260i
$580$	1.12189e6	−	2.82390e6i	0.138478	−	0.348562i
$581$	1.92508e6	−	1.39865e6i	0.236597	−	0.171898i
$582$	−3.35401e6			−0.410447
$583$	848890.	−	616755.i	0.103438	−	0.0751521i
$584$	1.74388e6	+	5.36712e6i	0.211585	+	0.651192i
$585$	3.83839e6	+	246005.i	0.463724	+	0.0297204i
$586$	−216214.	+	665439.i	−0.0260100	+	0.0800506i
$587$	2.71958e6	+	8.37000e6i	0.325766	+	1.00261i	0.971094	+	0.238699i	$0.0767210\pi$
$587$	2.71958e6	+	8.37000e6i	0.325766	+	1.00261i	−0.645327	+	0.763906i	$0.723279\pi$
$588$	−700741.	−	2.15666e6i	−0.0835823	−	0.257240i
$589$	−3.87641e6	+	1.19303e7i	−0.460406	+	1.41698i
$590$	−3.90962e6	−	3.24204e6i	−0.462385	−	0.383432i
$591$	115601.	+	355784.i	0.0136142	+	0.0419003i
$592$	−750922.	+	545577.i	−0.0880624	+	0.0639811i
$593$	−1.46632e7			−1.71235			−0.856177	−	0.516683i	$-0.827167\pi$
$593$	−1.46632e7			−1.71235			−0.856177	+	0.516683i	$0.827167\pi$
$594$	−725404.	+	527037.i	−0.0843556	+	0.0612879i
$595$	1.95435e6	+	125256.i	0.226314	+	0.0145046i
$596$	−2.59277e6	−	1.88376e6i	−0.298984	−	0.217225i
$597$	−3.02605e6	−	2.19855e6i	−0.347488	−	0.252465i
$598$	−4.84785e6	+	1.49202e7i	−0.554366	+	1.70616i
$599$	1.16846e7			1.33060			0.665300	−	0.746576i	$-0.268304\pi$
$599$	1.16846e7			1.33060			0.665300	+	0.746576i	$0.268304\pi$
$600$	−333143.	−	1.76890e6i	−0.0377792	−	0.200598i
$601$	−5.72955e6			−0.647045			−0.323523	−	0.946220i	$-0.604867\pi$
$601$	−5.72955e6			−0.647045			−0.323523	+	0.946220i	$0.604867\pi$
$602$	−599347.	+	1.84460e6i	−0.0674042	+	0.207449i
$603$	4.34482e6	+	3.15670e6i	0.486608	+	0.353541i
$604$	4.87403e6	+	3.54119e6i	0.543621	+	0.394963i
$605$	920266.	+	3.60171e6i	0.102217	+	0.400055i
$606$	−2.07537e6	+	1.50784e6i	−0.229569	+	0.166792i
$607$	−4.27779e6			−0.471247			−0.235623	−	0.971844i	$-0.575713\pi$
$607$	−4.27779e6			−0.471247			−0.235623	+	0.971844i	$0.575713\pi$
$608$	−2.29802e6	+	1.66961e6i	−0.252113	+	0.183171i
$609$	−307535.	−	946495.i	−0.0336009	−	0.103413i
$610$	−2.64633e6	−	1.03571e7i	−0.287951	−	1.12698i
$611$	6.49808e6	−	1.99990e7i	0.704177	−	2.16724i
$612$	−431036.	−	1.32659e6i	−0.0465195	−	0.143172i
$613$	−505480.	−	1.55571e6i	−0.0543317	−	0.167216i	0.920209	−	0.391428i	$-0.128019\pi$
$613$	−505480.	−	1.55571e6i	−0.0543317	−	0.167216i	−0.974540	+	0.224213i	$0.928019\pi$
$614$	−499207.	+	1.53640e6i	−0.0534392	+	0.164469i
$615$	2.78263e6	−	1.76134e6i	0.296666	−	0.187783i
$616$	197942.	+	609204.i	0.0210178	+	0.0646861i
$617$	−928954.	+	674925.i	−0.0982385	+	0.0713744i	−0.635820	−	0.771837i	$-0.719338\pi$
$617$	−928954.	+	674925.i	−0.0982385	+	0.0713744i	0.537582	+	0.843212i	$0.319338\pi$
$618$	−51535.1			−0.00542790
$619$	−1.88109e6	+	1.36669e6i	−0.197325	+	0.143365i	−0.682060	−	0.731296i	$-0.738916\pi$
$619$	−1.88109e6	+	1.36669e6i	−0.197325	+	0.143365i	0.484735	+	0.874661i	$0.338916\pi$
$620$	3.11354e6	+	2.58189e6i	0.325293	+	0.269748i
$621$	2.72310e6	+	1.97845e6i	0.283357	+	0.205871i
$622$	−837701.	−	608625.i	−0.0868186	−	0.0630774i
$623$	786906.	−	2.42185e6i	0.0812274	−	0.249992i
$624$	−1.95709e6			−0.201210
$625$	−9.09659e6	+	3.55238e6i	−0.931491	+	0.363764i
$626$	9.52269e6			0.971234
$627$	2.37223e6	−	7.30097e6i	0.240984	−	0.741672i
$628$	2.48292e6	+	1.80395e6i	0.251226	+	0.182526i
$629$	3.15705e6	+	2.29373e6i	0.318167	+	0.231162i
$630$	−453806.	−	376317.i	−0.0455532	−	0.0377749i
$631$	−2.98937e6	+	2.17191e6i	−0.298887	+	0.217154i	−0.727113	−	0.686517i	$-0.759139\pi$
$631$	−2.98937e6	+	2.17191e6i	−0.298887	+	0.217154i	0.428226	+	0.903671i	$0.359139\pi$
$632$	4.60782e6			0.458884
$633$	−5.91624e6	+	4.29840e6i	−0.586862	+	0.426380i
$634$	−3.32187e6	−	1.02237e7i	−0.328216	−	1.01014i
$635$	7.48999e6	−	4.74099e6i	0.737135	−	0.466589i
$636$	151846.	−	467334.i	0.0148854	−	0.0458126i
$637$	4.13356e6	+	1.27218e7i	0.403623	+	1.24222i
$638$	−1.29123e6	−	3.97401e6i	−0.125590	−	0.386525i
$639$	341961.	−	1.05245e6i	0.0331302	−	0.101964i
$640$	226734.	+	887385.i	0.0218810	+	0.0856372i
$641$	4.58950e6	+	1.41250e7i	0.441185	+	1.35783i	0.886614	+	0.462510i	$0.153051\pi$
$641$	4.58950e6	+	1.41250e7i	0.441185	+	1.35783i	−0.445429	+	0.895317i	$0.646949\pi$
$642$	4.47681e6	−	3.25260e6i	0.428678	−	0.311453i
$643$	−5.79495e6			−0.552742			−0.276371	−	0.961051i	$-0.589132\pi$
$643$	−5.79495e6			−0.552742			−0.276371	+	0.961051i	$0.589132\pi$
$644$	1.94535e6	−	1.41338e6i	0.184834	−	0.134290i
$645$	−1.85538e6	−	7.26155e6i	−0.175604	−	0.687274i
$646$	9.66142e6	+	7.01943e6i	0.910877	+	0.661791i
$647$	−2.93687e6	−	2.13376e6i	−0.275819	−	0.200394i	0.441273	−	0.897373i	$-0.354527\pi$
$647$	−2.93687e6	−	2.13376e6i	−0.275819	−	0.200394i	−0.717092	+	0.696979i	$0.754527\pi$
$648$	−129757.	+	399352.i	−0.0121393	+	0.0373610i
$649$	−6.98434e6			−0.650899
$650$	1.96516e6	+	1.04345e7i	0.182438	+	0.968695i
$651$	1.32475e6			0.122513
$652$	976185.	−	3.00439e6i	0.0899318	−	0.276782i
$653$	−1.02549e6	−	745060.i	−0.0941125	−	0.0683768i	0.539734	−	0.841836i	$-0.318525\pi$
$653$	−1.02549e6	−	745060.i	−0.0941125	−	0.0683768i	−0.633846	+	0.773459i	$0.718525\pi$
$654$	−3.68939e6	−	2.68050e6i	−0.337295	−	0.245059i
$655$	−7.08899e6	−	454339.i	−0.645626	−	0.0413787i
$656$	−1.35566e6	+	984946.i	−0.122996	+	0.0893620i
$657$	−7.14233e6			−0.645545
$658$	−2.60755e6	+	1.89450e6i	−0.234784	+	0.170580i
$659$	2.06798e6	+	6.36458e6i	0.185495	+	0.570895i	0.999957	−	0.00932270i	$-0.00296755\pi$
$659$	2.06798e6	+	6.36458e6i	0.185495	+	0.570895i	−0.814462	+	0.580217i	$0.802968\pi$
$660$	−1.90538e6	−	1.58003e6i	−0.170263	−	0.141190i
$661$	−4.58839e6	+	1.41216e7i	−0.408466	+	1.25713i	0.509499	+	0.860471i	$0.329831\pi$
$661$	−4.58839e6	+	1.41216e7i	−0.408466	+	1.25713i	−0.917966	+	0.396659i	$0.870169\pi$
$662$	1.15956e6	+	3.56877e6i	0.102837	+	0.316499i
$663$	2.54261e6	+	7.82536e6i	0.224645	+	0.691386i
$664$	1.44581e6	−	4.44976e6i	0.127260	−	0.391666i
$665$	5.03701e6	+	322826.i	0.441691	+	0.0283083i
$666$	−363015.	−	1.11724e6i	−0.0317131	−	0.0976029i
$667$	−1.26901e7	+	9.21986e6i	−1.10446	+	0.802435i
$668$	−2.69043e6			−0.233282
$669$	75472.3	−	54833.8i	0.00651962	−	0.00473678i
$670$	−5.47384e6	+	1.37782e7i	−0.471091	+	1.18578i
$671$	−1.18927e7	−	8.64053e6i	−1.01970	−	0.740857i
$672$	242684.	+	176320.i	0.0207309	+	0.0150619i
$673$	2.77658e6	−	8.54542e6i	0.236304	−	0.727270i	−0.760641	−	0.649172i	$-0.775115\pi$
$673$	2.77658e6	−	8.54542e6i	0.236304	−	0.727270i	0.996946	−	0.0780978i	$-0.0248846\pi$
$674$	873611.			0.0740744
$675$	2.25949e6	+	290819.i	0.190876	+	0.0245676i
$676$	5.60390e6			0.471654
$677$	−4.59909e6	+	1.41545e7i	−0.385656	+	1.18693i	0.550347	+	0.834936i	$0.314496\pi$
$677$	−4.59909e6	+	1.41545e7i	−0.385656	+	1.18693i	−0.936003	+	0.351992i	$0.885504\pi$
$678$	−2.06355e6	−	1.49926e6i	−0.172402	−	0.125257i
$679$	−2.45336e6	−	1.78247e6i	−0.204214	−	0.148370i
$680$	3.25361e6	−	2.05946e6i	0.269832	−	0.170797i
$681$	7.88265e6	−	5.72708e6i	0.651335	−	0.473223i
$682$	5.56218e6			0.457914
$683$	−3.51842e6	+	2.55628e6i	−0.288599	+	0.209680i	−0.722660	−	0.691204i	$-0.757081\pi$
$683$	−3.51842e6	+	2.55628e6i	−0.288599	+	0.209680i	0.434060	+	0.900884i	$0.357081\pi$
$684$	−1.11092e6	−	3.41907e6i	−0.0907912	−	0.279427i
$685$	5.30899e6	−	1.33632e7i	0.432300	−	1.08814i
$686$	1.30977e6	−	4.03106e6i	0.106264	−	0.327046i
$687$	−319758.	−	984115.i	−0.0258482	−	0.0795526i
$688$	1.17846e6	+	3.62694e6i	0.0949173	+	0.292126i
$689$	−895716.	+	2.75673e6i	−0.0718823	+	0.221231i
$690$	−3.43070e6	+	8.63539e6i	−0.274322	+	0.690493i
$691$	6.22228e6	+	1.91502e7i	0.495740	+	1.52573i	0.815800	+	0.578335i	$0.196297\pi$
$691$	6.22228e6	+	1.91502e7i	0.495740	+	1.52573i	−0.320059	+	0.947398i	$0.603703\pi$
$692$	−1.89353e6	+	1.37573e6i	−0.150317	+	0.109211i
$693$	−810703.			−0.0641252
$694$	−6.16685e6	+	4.48048e6i	−0.486032	+	0.353123i
$695$	−1.30491e7	+	8.25981e6i	−1.02475	+	0.648646i
$696$	−1.58310e6	−	1.15019e6i	−0.123875	−	0.0900007i
$697$	5.69952e6	+	4.14094e6i	0.444382	+	0.322862i
$698$	4.86960e6	−	1.49871e7i	0.378316	−	1.16434i
$699$	−1.16133e7			−0.899007
$700$	696389.	−	1.47095e6i	0.0537164	−	0.113462i
$701$	384623.			0.0295624			0.0147812	−	0.999891i	$-0.495295\pi$
$701$	384623.			0.0295624			0.0147812	+	0.999891i	$0.495295\pi$
$702$	765419.	−	2.35572e6i	0.0586214	−	0.180418i
$703$	8.13676e6	+	5.91170e6i	0.620959	+	0.451153i
$704$	1.01895e6	+	740310.i	0.0774856	+	0.0562966i
$705$	4.59853e6	−	1.15749e7i	0.348454	−	0.877092i
$706$	−4.32435e6	+	3.14183e6i	−0.326520	+	0.237230i
$707$	−2.31941e6			−0.174513
$708$	−2.64613e6	+	1.92252e6i	−0.198393	+	0.144141i
$709$	264087.	+	812777.i	0.0197302	+	0.0607234i	0.960437	−	0.278498i	$-0.0898365\pi$
$709$	264087.	+	812777.i	0.0197302	+	0.0607234i	−0.940707	+	0.339221i	$0.889836\pi$
$710$	3.04862e6	+	195389.i	0.226964	+	0.0145463i
$711$	−1.80212e6	+	5.54634e6i	−0.133693	+	0.411465i
$712$	−1.54725e6	−	4.76195e6i	−0.114383	−	0.352034i
$713$	−6.45224e6	−	1.98579e7i	−0.475320	−	1.46289i
$714$	389720.	−	1.19944e6i	0.0286093	−	0.0880504i
$715$	1.12395e7	+	9.32034e6i	0.822210	+	0.681815i
$716$	1.43834e6	+	4.42676e6i	0.104853	+	0.322703i
$717$	7.76409e6	−	5.64094e6i	0.564018	−	0.409783i
$718$	−9.33836e6			−0.676020
$719$	1.23888e6	−	900096.i	0.0893729	−	0.0649332i	−0.542201	−	0.840249i	$-0.682409\pi$
$719$	1.23888e6	−	900096.i	0.0893729	−	0.0649332i	0.631574	+	0.775315i	$0.282409\pi$
$720$	−1.15680e6	−	74140.5i	−0.0831627	−	0.00532996i
$721$	−37696.4	−	27388.0i	−0.00270061	−	0.00196211i
$722$	1.68878e7	+	1.22697e7i	1.20568	+	0.875976i
$723$	256456.	−	789291.i	0.0182460	−	0.0561554i
$724$	5.45506e6			0.386770
$725$	−4.54274e6	+	9.59540e6i	−0.320976	+	0.677982i
$726$	2.39397e6			0.168569
$727$	−2.04144e6	+	6.28290e6i	−0.143252	+	0.440883i	−0.996782	−	0.0801597i	$-0.974457\pi$
$727$	−2.04144e6	+	6.28290e6i	−0.143252	+	0.440883i	0.853530	+	0.521043i	$0.174457\pi$
$728$	−1.43156e6	−	1.04009e6i	−0.100111	−	0.0727346i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	−4.88103e6	−	1.91032e7i	−0.339004	−	1.32678i
$731$	1.29711e7	−	9.42409e6i	0.897811	−	0.652298i
$732$	−6.88413e6			−0.474867
$733$	−656762.	+	477166.i	−0.0451490	+	0.0328027i	−0.610131	−	0.792301i	$-0.708883\pi$
$733$	−656762.	+	477166.i	−0.0451490	+	0.0328027i	0.564982	+	0.825103i	$0.308883\pi$
$734$	5.53848e6	+	1.70457e7i	0.379446	+	1.16782i
$735$	1.96134e6	+	7.67622e6i	0.133916	+	0.524118i
$736$	1.46103e6	−	4.49660e6i	0.0994181	−	0.305978i
$737$	6.30009e6	+	1.93897e7i	0.427246	+	1.31493i
$738$	−655362.	−	2.01700e6i	−0.0442935	−	0.136322i
$739$	−1.33366e6	+	4.10457e6i	−0.0898323	+	0.276475i	−0.985872	−	0.167498i	$-0.946431\pi$
$739$	−1.33366e6	+	4.10457e6i	−0.0898323	+	0.276475i	0.896040	+	0.443973i	$0.146431\pi$
$740$	2.74016e6	−	1.73446e6i	0.183949	−	0.116435i
$741$	6.55316e6	+	2.01686e7i	0.438435	+	1.34936i
$742$	359433.	−	261143.i	0.0239667	−	0.0174128i
$743$	−1.35521e7			−0.900604			−0.450302	−	0.892876i	$-0.648684\pi$
$743$	−1.35521e7			−0.900604			−0.450302	+	0.892876i	$0.648684\pi$
$744$	2.10732e6	−	1.53106e6i	0.139572	−	0.101405i
$745$	8.61926e6	+	7.14750e6i	0.568957	+	0.471806i
$746$	2.63100e6	+	1.91153e6i	0.173091	+	0.125758i
$747$	4.79063e6	+	3.48060e6i	0.314117	+	0.228219i
$748$	1.63630e6	−	5.03602e6i	0.106933	−	0.329104i
$749$	5.00323e6			0.325871
$750$	766283.	+	6.24208e6i	0.0497434	+	0.405206i
$751$	4.18586e6			0.270822			0.135411	−	0.990789i	$-0.456764\pi$
$751$	4.18586e6			0.270822			0.135411	+	0.990789i	$0.456764\pi$
$752$	−1.95838e6	+	6.02726e6i	−0.126285	+	0.388665i
$753$	3.53102e6	+	2.56544e6i	0.226941	+	0.164882i
$754$	9.33845e6	+	6.78478e6i	0.598200	+	0.434618i
$755$	−1.62030e7	−	1.34363e7i	−1.03449	−	0.857849i
$756$	−307147.	+	223156.i	−0.0195453	+	0.0142005i
$757$	−1.59159e7			−1.00946			−0.504732	−	0.863276i	$-0.668409\pi$
$757$	−1.59159e7			−1.00946			−0.504732	+	0.863276i	$0.668409\pi$
$758$	1.00313e6	−	728816.i	0.0634138	−	0.0460728i
$759$	3.94855e6	+	1.21524e7i	0.248790	+	0.765698i
$760$	8.38562e6	−	5.30791e6i	0.526625	−	0.333342i
$761$	7.50726e6	−	2.31050e7i	0.469915	−	1.44625i	−0.382779	−	0.923840i	$-0.625033\pi$
$761$	7.50726e6	−	2.31050e7i	0.469915	−	1.44625i	0.852694	−	0.522411i	$-0.174967\pi$
$762$	−1.76404e6	−	5.42914e6i	−0.110058	−	0.338722i
$763$	−1.27414e6	−	3.92141e6i	−0.0792331	−	0.243855i
$764$	−471758.	+	1.45192e6i	−0.0292406	+	0.0899932i
$765$	1.20645e6	+	4.72176e6i	0.0745341	+	0.291709i
$766$	−1.12870e6	−	3.47379e6i	−0.0695037	−	0.213910i
$767$	1.56091e7	−	1.13407e7i	0.958051	−	0.696065i
$768$	589824.			0.0360844
$769$	3.49410e6	−	2.53861e6i	0.213068	−	0.154803i	−0.476132	−	0.879374i	$-0.657962\pi$
$769$	3.49410e6	−	2.53861e6i	0.213068	−	0.154803i	0.689201	+	0.724570i	$0.257962\pi$
$770$	−554030.	−	2.16835e6i	−0.0336749	−	0.131796i
$771$	−4.51025e6	−	3.27689e6i	−0.273253	−	0.198530i
$772$	−7.99921e6	−	5.81176e6i	−0.483063	−	0.350966i
$773$	−4.60735e6	+	1.41800e7i	−0.277334	+	0.853545i	0.711259	+	0.702930i	$0.248125\pi$
$773$	−4.60735e6	+	1.41800e7i	−0.277334	+	0.853545i	−0.988593	+	0.150615i	$0.951875\pi$
$774$	−4.82658e6			−0.289592
$775$	−1.02790e7	−	9.69805e6i	−0.614748	−	0.580003i
$776$	−5.96268e6			−0.355457
$777$	328219.	−	1.01015e6i	0.0195034	−	0.0600254i
$778$	8.71531e6	+	6.33204e6i	0.516219	+	0.375055i
$779$	1.46895e7	+	1.06726e7i	0.867291	+	0.630124i
$780$	6.82380e6	+	437343.i	0.401597	+	0.0257386i
$781$	3.39861e6	−	2.46924e6i	0.199376	−	0.144855i
$782$	−1.98776e7			−1.16238
$783$	2.00361e6	−	1.45571e6i	0.116791	−	0.0848535i
$784$	−1.24576e6	−	3.83406e6i	−0.0723844	−	0.222776i
$785$	−8.25410e6	−	6.84469e6i	−0.478074	−	0.396442i
$786$	−1.41362e6	+	4.35069e6i	−0.0816165	+	0.251190i
$787$	−3.04192e6	−	9.36208e6i	−0.175070	−	0.538810i	0.824567	−	0.565765i	$-0.191419\pi$
$787$	−3.04192e6	−	9.36208e6i	−0.175070	−	0.538810i	−0.999637	+	0.0269548i	$0.991419\pi$
$788$	205513.	+	632504.i	0.0117903	+	0.0362867i
$789$	2.07730e6	−	6.39327e6i	0.118797	−	0.365621i
$790$	−1.60661e7	−	1.02969e6i	−0.915888	−	0.0587000i
$791$	−712655.	−	2.19333e6i	−0.0404984	−	0.124641i
$792$	−1.28961e6	+	936955.i	−0.0730541	+	0.0530769i
$793$	4.06084e7			2.29315
$794$	4.87351e6	−	3.54081e6i	0.274341	−	0.199320i
$795$	−633875.	+	1.59552e6i	−0.0355702	+	0.0895334i
$796$	−5.37965e6	−	3.90854e6i	−0.300934	−	0.218641i
$797$	1.52870e7	+	1.11067e7i	0.852467	+	0.619354i	0.925825	−	0.377952i	$-0.123372\pi$
$797$	1.52870e7	+	1.11067e7i	0.852467	+	0.619354i	−0.0733581	+	0.997306i	$0.523372\pi$
$798$	1.00444e6	−	3.09134e6i	0.0558362	−	0.171846i
$799$	2.66440e7			1.47650
$800$	−592255.	−	3.14472e6i	−0.0327177	−	0.173723i
$801$	6.33700e6			0.348982
$802$	−2.21395e6	+	6.81385e6i	−0.121544	+	0.374073i
$803$	−2.19355e7	−	1.59371e7i	−1.20049	−	0.872207i
$804$	7.72413e6	+	5.61191e6i	0.421415	+	0.306176i
$805$	−7.09869e6	+	4.49331e6i	−0.386090	+	0.244386i
$806$	−1.24307e7	+	9.03146e6i	−0.673999	+	0.489689i
$807$	−1.58114e6			−0.0854646
$808$	−3.68955e6	+	2.68061e6i	−0.198813	+	0.144446i
$809$	3.38151e6	+	1.04072e7i	0.181652	+	0.559066i	0.999875	−	0.0158348i	$-0.00504058\pi$
$809$	3.38151e6	+	1.04072e7i	0.181652	+	0.559066i	−0.818223	+	0.574901i	$0.805041\pi$
$810$	541667.	−	1.36343e6i	0.0290081	−	0.0730162i
$811$	583642.	−	1.79627e6i	0.0311598	−	0.0958999i	−0.934267	−	0.356574i	$-0.883945\pi$
$811$	583642.	−	1.79627e6i	0.0311598	−	0.0958999i	0.965427	+	0.260674i	$0.0839448\pi$
$812$	−546729.	−	1.68266e6i	−0.0290992	−	0.0895583i
$813$	5.64703e6	+	1.73798e7i	0.299636	+	0.922185i
$814$	1.37808e6	−	4.24129e6i	0.0728976	−	0.224356i
$815$	−4.07504e6	+	1.02573e7i	−0.214901	+	0.540926i
$816$	−766287.	−	2.35839e6i	−0.0402871	−	0.123991i
$817$	3.34309e7	−	2.42890e7i	1.75224	−	1.27308i
$818$	−2.25288e7			−1.17721
$819$	1.81181e6	−	1.31636e6i	0.0943851	−	0.0685748i
$820$	4.94689e6	−	3.13127e6i	0.256920	−	0.162625i
$821$	2.25620e7	+	1.63923e7i	1.16821	+	0.848754i	0.990793	−	0.135382i	$-0.0432263\pi$
$821$	2.25620e7	+	1.63923e7i	1.16821	+	0.848754i	0.177416	+	0.984136i	$0.443226\pi$
$822$	−7.49151e6	−	5.44290e6i	−0.386714	−	0.280964i
$823$	5.08671e6	−	1.56553e7i	0.261781	−	0.805678i	−0.730637	−	0.682766i	$-0.760777\pi$
$823$	5.08671e6	−	1.56553e7i	0.261781	−	0.805678i	0.992418	−	0.122912i	$-0.0392232\pi$
$824$	−91618.0			−0.00470070
$825$	6.29041e6	+	5.93488e6i	0.321769	+	0.303583i
$826$	−2.95728e6			−0.150814
$827$	3.08394e6	−	9.49138e6i	0.156798	−	0.482576i	−0.841540	−	0.540194i	$-0.818351\pi$
$827$	3.08394e6	−	9.49138e6i	0.156798	−	0.482576i	0.998339	+	0.0576185i	$0.0183507\pi$
$828$	4.84106e6	+	3.51724e6i	0.245394	+	0.178289i
$829$	1.65923e7	+	1.20550e7i	0.838531	+	0.609228i	0.921960	−	0.387285i	$-0.126587\pi$
$829$	1.65923e7	+	1.20550e7i	0.838531	+	0.609228i	−0.0834291	+	0.996514i	$0.526587\pi$
$830$	−6.03549e6	+	1.51919e7i	−0.304100	+	0.765449i
$831$	−1.15505e7	+	8.39192e6i	−0.580227	+	0.421559i
$832$	−3.47928e6			−0.174253
$833$	−1.37119e7	+	9.96226e6i	−0.684675	+	0.497445i
$834$	3.07332e6	+	9.45871e6i	0.153000	+	0.470887i
$835$	9.38074e6	+	601219.i	0.465609	+	0.0298412i
$836$	4.21730e6	−	1.29795e7i	0.208698	−	0.642306i
$837$	1.01873e6	+	3.13534e6i	0.0502628	+	0.154693i
$838$	−1.06876e6	−	3.28931e6i	−0.0525740	−	0.161806i
$839$	6.12991e6	−	1.88659e7i	0.300642	−	0.925280i	−0.680626	−	0.732631i	$-0.738292\pi$
$839$	6.12991e6	−	1.88659e7i	0.300642	−	0.925280i	0.981268	−	0.192649i	$-0.0617079\pi$
$840$	−806766.	−	669009.i	−0.0394502	−	0.0327140i
$841$	−2.77183e6	−	8.53080e6i	−0.135138	−	0.415911i
$842$	−615937.	+	447505.i	−0.0299403	+	0.0217529i
$843$	−9.13037e6			−0.442506
$844$	−1.05178e7	+	7.64160e6i	−0.508238	+	0.369256i
$845$	−1.95391e7	−	1.25228e6i	−0.941376	−	0.0603335i
$846$	−6.48898e6	−	4.71452e6i	−0.311710	−	0.226470i
$847$	1.75112e6	+	1.27226e6i	0.0838700	+	0.0609352i
$848$	269949.	−	830816.i	0.0128911	−	0.0396749i
$849$	−2.13446e7			−1.01629
$850$	−1.18046e7	+	6.45365e6i	−0.560406	+	0.306379i
$851$	−1.67407e7			−0.792412
$852$	607930.	−	1.87102e6i	0.0286916	−	0.0883036i
$853$	1.74555e7	+	1.26822e7i	0.821409	+	0.596788i	0.917116	−	0.398621i	$-0.130511\pi$
$853$	1.74555e7	+	1.26822e7i	0.821409	+	0.596788i	−0.0957068	+	0.995410i	$0.530511\pi$
$854$	−5.03554e6	−	3.65853e6i	−0.236266	−	0.171657i
$855$	3.10941e6	+	1.21695e7i	0.145467	+	0.569323i
$856$	7.95878e6	−	5.78239e6i	0.371246	−	0.269726i
$857$	−2.85828e7			−1.32939			−0.664696	−	0.747114i	$-0.731439\pi$
$857$	−2.85828e7			−1.32939			−0.664696	+	0.747114i	$0.731439\pi$
$858$	7.60719e6	−	5.52695e6i	0.352782	−	0.256311i
$859$	−9.01666e6	−	2.77504e7i	−0.416930	−	1.28318i	−0.910513	−	0.413480i	$-0.864313\pi$
$859$	−9.01666e6	−	2.77504e7i	−0.416930	−	1.28318i	0.493584	−	0.869698i	$-0.335687\pi$
$860$	−3.29846e6	−	1.29094e7i	−0.152078	−	0.595197i
$861$	592544.	−	1.82366e6i	0.0272403	−	0.0838371i
$862$	4.49675e6	+	1.38396e7i	0.206125	+	0.634388i
$863$	−1.11909e7	−	3.44421e7i	−0.511492	−	1.57421i	−0.789576	−	0.613653i	$-0.789700\pi$
$863$	−1.11909e7	−	3.44421e7i	−0.511492	−	1.57421i	0.278084	−	0.960557i	$-0.410300\pi$
$864$	−230680.	+	709960.i	−0.0105130	+	0.0323556i
$865$	6.90960e6	−	4.37362e6i	0.313988	−	0.198747i
$866$	−3.57625e6	−	1.10066e7i	−0.162044	−	0.498720i
$867$	1.90382e6	−	1.38320e6i	0.0860157	−	0.0624941i
$868$	2.35511e6			0.106099
$869$	−1.79105e7	+	1.30128e7i	−0.804560	+	0.584547i
$870$	5.26277e6	+	4.36413e6i	0.235731	+	0.195479i
$871$	−4.55634e7	−	3.31038e7i	−2.03503	−	1.47854i
$872$	−6.55891e6	−	4.76533e6i	−0.292106	−	0.212228i
$873$	2.33200e6	−	7.17716e6i	0.103560	−	0.318726i
$874$	−5.12312e7			−2.26859
$875$	−2.75681e6	+	4.97313e6i	−0.121727	+	0.219589i
$876$	−1.26975e7			−0.559058
$877$	9.30060e6	−	2.86243e7i	0.408331	−	1.25671i	−0.509751	−	0.860322i	$-0.670263\pi$
$877$	9.30060e6	−	2.86243e7i	0.408331	−	1.25671i	0.918082	−	0.396391i	$-0.129737\pi$
$878$	4.46229e6	+	3.24204e6i	0.195354	+	0.141933i
$879$	−1.27363e6	−	925344.i	−0.0555994	−	0.0403953i
$880$	−3.38734e6	−	2.80894e6i	−0.147452	−	0.122274i
$881$	3.67321e6	−	2.66874e6i	0.159443	−	0.115842i	−0.505203	−	0.863001i	$-0.668582\pi$
$881$	3.67321e6	−	2.66874e6i	0.159443	−	0.115842i	0.664646	+	0.747158i	$0.268582\pi$
$882$	5.10220e6			0.220844
$883$	2.76416e7	−	2.00828e7i	1.19306	−	0.866807i	0.199473	−	0.979903i	$-0.436077\pi$
$883$	2.76416e7	−	2.00828e7i	1.19306	−	0.866807i	0.993584	+	0.113097i	$0.0360770\pi$
$884$	4.52020e6	+	1.39118e7i	0.194548	+	0.598758i
$885$	9.65587e6	−	6.11195e6i	0.414413	−	0.262314i
$886$	1.41505e6	−	4.35509e6i	0.0605604	−	0.186386i
$887$	3.04730e6	+	9.37862e6i	0.130049	+	0.400249i	0.994787	−	0.101974i	$-0.0325158\pi$
$887$	3.04730e6	+	9.37862e6i	0.130049	+	0.400249i	−0.864738	+	0.502223i	$0.832516\pi$
$888$	−645360.	−	1.98621e6i	−0.0274644	−	0.0845266i
$889$	1.59495e6	−	4.90874e6i	0.0676849	−	0.208313i
$890$	4.33068e6	+	1.69493e7i	0.183265	+	0.717259i
$891$	−623430.	−	1.91872e6i	−0.0263083	−	0.0809687i
$892$	134173.	−	97482.4i	0.00564616	−	0.00410217i
$893$	6.86705e7			2.88165
$894$	5.83373e6	−	4.23846e6i	0.244120	−	0.177363i
$895$	−4.02584e6	−	1.57562e7i	−0.167996	−	0.657497i
$896$	431439.	+	313459.i	0.0179535	+	0.0130440i
$897$	−2.85566e7	−	2.07476e7i	−1.18502	−	0.860968i
$898$	6.06925e6	−	1.86792e7i	0.251156	−	0.772980i
$899$	−1.53631e7			−0.633985
$900$	4.01686e6	+	517012.i	0.165303	+	0.0212762i
$901$	−3.67270e6			−0.150721
$902$	2.48789e6	−	7.65694e6i	0.101816	−	0.313357i
$903$	−3.53050e6	−	2.56506e6i	−0.144084	−	0.104683i
$904$	−3.66854e6	−	2.66535e6i	−0.149304	−	0.108476i
$905$	−1.90202e7	−	1.21902e6i	−0.771957	−	0.0494753i
$906$	−1.09666e7	+	7.96768e6i	−0.443864	+	0.322486i
$907$	−4.59080e7			−1.85298			−0.926489	−	0.376322i	$-0.877189\pi$
$907$	−4.59080e7			−1.85298			−0.926489	+	0.376322i	$0.877189\pi$
$908$	1.40136e7	−	1.01815e7i	0.564073	−	0.409823i
$909$	−1.78362e6	−	5.48942e6i	−0.0715967	−	0.220352i
$910$	4.75899e6	+	3.94637e6i	0.190507	+	0.157977i
$911$	1.70738e6	−	5.25479e6i	0.0681609	−	0.209778i	−0.911174	−	0.412021i	$-0.864823\pi$
$911$	1.70738e6	−	5.25479e6i	0.0681609	−	0.209778i	0.979335	+	0.202243i	$0.0648231\pi$
$912$	−1.97497e6	−	6.07835e6i	−0.0786275	−	0.241991i
$913$	6.94652e6	+	2.13792e7i	0.275797	+	0.848817i
$914$	9.32929e6	−	2.87126e7i	0.369388	−	1.13686i
$915$	2.40029e7	+	1.53837e6i	0.947789	+	0.0607445i
$916$	−568459.	−	1.74954e6i	−0.0223852	−	0.0688945i
$917$	−3.34617e6	+	2.43114e6i	−0.131409	+	0.0954742i
$918$	3.13844e6			0.122916
$919$	1.33079e7	−	9.66873e6i	0.519780	−	0.377642i	−0.296741	−	0.954958i	$-0.595900\pi$
$919$	1.33079e7	−	9.66873e6i	0.519780	−	0.377642i	0.816521	+	0.577316i	$0.195900\pi$
$920$	−6.09902e6	+	1.53518e7i	−0.237570	+	0.597985i
$921$	−2.94062e6	−	2.13648e6i	−0.114232	−	0.0829948i
$922$	1.59625e7	+	1.15974e7i	0.618405	+	0.449298i
$923$	−3.58608e6	+	1.10368e7i	−0.138553	+	0.426422i
$924$	−1.44125e6			−0.0555340
$925$	−9.94171e6	+	5.43521e6i	−0.382038	+	0.208863i
$926$	−2.46675e6			−0.0945362
$927$	35831.8	−	110279.i	0.00136952	−	0.00421495i
$928$	−2.81440e6	−	2.04478e6i	−0.107279	−	0.0779429i
$929$	3.74753e7	+	2.72274e7i	1.42464	+	1.03506i	0.990983	+	0.133987i	$0.0427780\pi$
$929$	3.74753e7	+	2.72274e7i	1.42464	+	1.03506i	0.433660	+	0.901077i	$0.357222\pi$
$930$	−7.68973e6	+	4.86743e6i	−0.291544	+	0.184541i
$931$	−3.53401e7	+	2.56760e7i	−1.33627	+	0.970854i
$932$	−2.06459e7			−0.778562
$933$	1.88483e6	−	1.36941e6i	0.0708871	−	0.0515025i
$934$	−9.30089e6	−	2.86252e7i	−0.348865	−	1.07370i
$935$	−6.83068e6	+	1.71935e7i	−0.255526	+	0.643182i
$936$	1.36074e6	−	4.18794e6i	0.0507676	−	0.156247i
$937$	−2.40607e6	−	7.40512e6i	−0.0895281	−	0.275539i	0.896261	−	0.443527i	$-0.146273\pi$
$937$	−2.40607e6	−	7.40512e6i	−0.0895281	−	0.275539i	−0.985789	+	0.167988i	$0.946273\pi$
$938$	2.66756e6	+	8.20989e6i	0.0989934	+	0.304670i
$939$	−6.62101e6	+	2.03774e7i	−0.245053	+	0.754197i
$940$	8.17516e6	−	2.05776e7i	0.301770	−	0.759584i
$941$	−4.90793e6	−	1.51050e7i	−0.180686	−	0.556094i	0.819162	−	0.573563i	$-0.194439\pi$
$941$	−4.90793e6	−	1.51050e7i	−0.180686	−	0.556094i	−0.999847	+	0.0174691i	$0.994439\pi$
$942$	−5.58658e6	+	4.05889e6i	−0.205125	+	0.149032i
$943$	−3.02226e7			−1.10676
$944$	−4.70422e6	+	3.41782e6i	−0.171814	+	0.124830i
$945$	1.12080e6	−	709440.i	0.0408271	−	0.0258426i
$946$	−1.48234e7	−	1.07698e7i	−0.538541	−	0.391273i
$947$	−7.79146e6	−	5.66083e6i	−0.282322	−	0.205119i	0.437608	−	0.899166i	$-0.355826\pi$
$947$	−7.79146e6	−	5.66083e6i	−0.282322	−	0.205119i	−0.719929	+	0.694047i	$0.755826\pi$
$948$	−3.20376e6	+	9.86017e6i	−0.115782	+	0.356339i
$949$	7.49003e7			2.69972
$950$	−3.04243e7	+	1.66332e7i	−1.09373	+	0.597953i
$951$	2.41870e7			0.867224
$952$	692836.	−	2.13233e6i	0.0247764	−	0.0762539i
$953$	−3.26578e6	−	2.37273e6i	−0.116481	−	0.0846282i	0.528020	−	0.849232i	$-0.322935\pi$
$953$	−3.26578e6	−	2.37273e6i	−0.116481	−	0.0846282i	−0.644501	+	0.764604i	$0.722935\pi$
$954$	894461.	+	649864.i	0.0318193	+	0.0231181i
$955$	1.96933e6	−	4.95699e6i	0.0698732	−	0.175877i
$956$	1.38028e7	−	1.00283e7i	0.488454	−	0.354882i
$957$	9.40168e6			0.331838
$958$	2.54361e7	−	1.84804e7i	0.895440	−	0.650575i
$959$	−2.58722e6	−	7.96264e6i	−0.0908420	−	0.279583i
$960$	−2.05654e6	−	131805.i	−0.0720210	−	0.00461588i
$961$	−2.52740e6	+	7.77852e6i	−0.0882805	+	0.271699i
$962$	3.80687e6	+	1.17164e7i	0.132627	+	0.408183i
$963$	3.84748e6	+	1.18413e7i	0.133694	+	0.411467i
$964$	455922.	−	1.40318e6i	0.0158015	−	0.0486320i
$965$	2.65921e7	+	2.20514e7i	0.919252	+	0.762287i
$966$	1.67188e6	+	5.14551e6i	0.0576450	+	0.177413i
$967$	1.90122e7	−	1.38132e7i	0.653834	−	0.475038i	−0.210741	−	0.977542i	$-0.567588\pi$
$967$	1.90122e7	−	1.38132e7i	0.653834	−	0.475038i	0.864575	+	0.502504i	$0.167588\pi$
$968$	4.25595e6			0.145985
$969$	−2.17382e7	+	1.57937e7i	−0.743728	+	0.540350i
$970$	2.07901e7	+	1.33245e6i	0.709459	+	0.0454698i
$971$	−2.56932e7	−	1.86672e7i	−0.874521	−	0.635377i	0.0572754	−	0.998358i	$-0.481759\pi$
$971$	−2.56932e7	−	1.86672e7i	−0.874521	−	0.635377i	−0.931796	+	0.362982i	$0.881759\pi$
$972$	−764346.	−	555330.i	−0.0259492	−	0.0188532i
$973$	−2.77873e6	+	8.55206e6i	−0.0940946	+	0.289594i
$974$	1.80292e7			0.608945
$975$	−2.36948e7	−	3.04977e6i	−0.798256	−	0.102744i
$976$	−1.22385e7			−0.411247
$977$	1.63204e7	−	5.02292e7i	0.547010	−	1.68352i	−0.169151	−	0.985590i	$-0.554103\pi$
$977$	1.63204e7	−	5.02292e7i	0.547010	−	1.68352i	0.716161	−	0.697935i	$-0.245897\pi$
$978$	5.75029e6	+	4.17783e6i	0.192240	+	0.139670i
$979$	1.94622e7	+	1.41401e7i	0.648985	+	0.471515i
$980$	3.48682e6	+	1.36466e7i	0.115975	+	0.453900i
$981$	8.30113e6	−	6.03112e6i	0.275400	−	0.200090i
$982$	7.54131e6			0.249556
$983$	−2.01444e7	+	1.46358e7i	−0.664922	+	0.483094i	−0.868322	−	0.496002i	$-0.834801\pi$
$983$	−2.01444e7	+	1.46358e7i	−0.664922	+	0.483094i	0.203400	+	0.979096i	$0.434801\pi$
$984$	−1.16509e6	−	3.58577e6i	−0.0383593	−	0.118058i
$985$	−575220.	−	2.25128e6i	−0.0188905	−	0.0739331i
$986$	−4.51957e6	+	1.39098e7i	−0.148049	+	0.455647i
$987$	−2.24099e6	−	6.89706e6i	−0.0732229	−	0.225357i
$988$	1.16501e7	+	3.58552e7i	0.379696	+	1.16858i
$989$	−2.12547e7	+	6.54152e7i	−0.690977	+	2.12661i
$990$	4.70586e6	−	2.97870e6i	0.152599	−	0.0965915i
$991$	1.25308e7	+	3.85658e7i	0.405317	+	1.24744i	0.920630	+	0.390435i	$0.127675\pi$
$991$	1.25308e7	+	3.85658e7i	0.405317	+	1.24744i	−0.515314	+	0.857002i	$0.672325\pi$
$992$	3.74634e6	−	2.72188e6i	0.120873	−	0.0878192i
$993$	−8.44295e6			−0.271720
$994$	1.43902e6	−	1.04551e6i	0.0461957	−	0.0335632i
$995$	1.78838e7	+	1.48301e7i	0.572667	+	0.474882i
$996$	8.51667e6	+	6.18773e6i	0.272033	+	0.197644i
$997$	−3.65745e7	−	2.65730e7i	−1.16531	−	0.846646i	−0.174869	−	0.984592i	$-0.555950\pi$
$997$	−3.65745e7	−	2.65730e7i	−1.16531	−	0.846646i	−0.990440	+	0.137945i	$0.955950\pi$
$998$	2.43648e6	−	7.49871e6i	0.0774348	−	0.238320i
$999$	2.64317e6			0.0837936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.c.121.5	yes	24
25.6	even	5	inner	150.6.g.c.31.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.c.31.5	✓	24	25.6	even	5	inner
150.6.g.c.121.5	yes	24	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(43.0312 + 35.6835i) q^{5} +(29.1246 - 21.1603i) q^{6} +32.5493 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(-1.23607 + 3.80423i) q^{2} +(-7.28115 - 5.29007i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(43.0312 + 35.6835i) q^{5} +(29.1246 - 21.1603i) q^{6} +32.5493 q^{7} +(51.7771 - 37.6183i) q^{8} +(25.0304 + 77.0356i) q^{9} +(-188.938 + 119.593i) q^{10} +(-95.0205 + 292.443i) q^{11} +(44.4984 + 136.952i) q^{12} +(-262.489 - 807.859i) q^{13} +(-40.2331 + 123.825i) q^{14} +(-124.549 - 487.455i) q^{15} +(79.1084 + 243.470i) q^{16} +(870.731 - 632.623i) q^{17} -324.000 q^{18} +(2244.16 - 1630.48i) q^{19} +(-221.420 - 866.587i) q^{20} +(-236.996 - 172.188i) q^{21} +(-995.068 - 722.959i) q^{22} +(-1426.79 + 4391.21i) q^{23} -576.000 q^{24} +(578.374 + 3071.01i) q^{25} +3397.73 q^{26} +(225.273 - 693.320i) q^{27} +(-421.327 - 306.112i) q^{28} +(2748.44 + 1996.86i) q^{29} +(2008.34 + 128.716i) q^{30} +(-3658.54 + 2658.08i) q^{31} -1024.00 q^{32} +(2238.90 - 1626.66i) q^{33} +(1330.36 + 4094.42i) q^{34} +(1400.64 + 1161.47i) q^{35} +(400.486 - 1232.57i) q^{36} +(1120.42 + 3448.29i) q^{37} +(3428.78 + 10552.7i) q^{38} +(-2362.40 + 7270.73i) q^{39} +(3570.38 + 228.829i) q^{40} +(2022.72 + 6225.30i) q^{41} +(947.986 - 688.752i) q^{42} +14896.8 q^{43} +(3980.27 - 2891.84i) q^{44} +(-1671.81 + 4208.11i) q^{45} +(-14941.5 - 10855.7i) q^{46} +(20027.7 + 14551.0i) q^{47} +(711.975 - 2191.23i) q^{48} -15747.5 q^{49} +(-12397.7 - 1595.71i) q^{50} -9686.55 q^{51} +(-4199.83 + 12925.7i) q^{52} +(-2760.68 - 2005.75i) q^{53} +(2359.09 + 1713.98i) q^{54} +(-14524.2 + 9193.52i) q^{55} +(1685.31 - 1224.45i) q^{56} -24965.4 q^{57} +(-10993.7 + 7987.42i) q^{58} +(7018.96 + 21602.1i) q^{59} +(-2972.11 + 7481.08i) q^{60} +(-14773.0 + 45466.7i) q^{61} +(-5589.75 - 17203.5i) q^{62} +(814.721 + 2507.45i) q^{63} +(1265.73 - 3895.53i) q^{64} +(17532.0 - 44129.7i) q^{65} +(3420.74 + 10527.9i) q^{66} +(53639.8 - 38971.6i) q^{67} -17220.5 q^{68} +(33618.5 - 24425.3i) q^{69} +(-6149.79 + 3892.68i) q^{70} +(-11052.7 - 8030.22i) q^{71} +(4193.94 + 3047.08i) q^{72} +(-27248.2 + 83861.2i) q^{73} -14503.0 q^{74} +(12034.6 - 25420.1i) q^{75} -44383.0 q^{76} +(-3092.85 + 9518.81i) q^{77} +(-24739.4 - 17974.2i) q^{78} +(58246.9 + 42318.9i) q^{79} +(-5283.75 + 13299.7i) q^{80} +(-5307.96 + 3856.46i) q^{81} -26182.7 q^{82} +(59143.6 - 42970.3i) q^{83} +(1448.39 + 4457.70i) q^{84} +(60042.9 + 3848.19i) q^{85} +(-18413.5 + 56671.0i) q^{86} +(-9448.28 - 29078.8i) q^{87} +(6081.31 + 18716.4i) q^{88} +(24175.8 - 74405.5i) q^{89} +(-13942.1 - 11561.5i) q^{90} +(-8543.84 - 26295.2i) q^{91} +(59766.2 - 43422.7i) q^{92} +40699.8 q^{93} +(-80110.8 + 58203.9i) q^{94} +(154750. + 9918.07i) q^{95} +(7455.90 + 5417.03i) q^{96} +(-75373.6 - 54762.1i) q^{97} +(19465.0 - 59907.2i) q^{98} -24906.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9	\( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 - 54 * q^3 - 96 * q^4 + 80 * q^5 + 216 * q^6 - 454 * q^7 + 384 * q^8 - 486 * q^9 + 120 * q^10 + 125 * q^11 - 864 * q^12 - 578 * q^13 - 344 * q^14 + 855 * q^15 - 1536 * q^16 - 2664 * q^17 - 7776 * q^18 + 1424 * q^19 + 1520 * q^20 + 1269 * q^21 + 1280 * q^22 - 4810 * q^23 - 13824 * q^24 - 10880 * q^25 + 6392 * q^26 - 4374 * q^27 + 2256 * q^28 - 1554 * q^29 + 4320 * q^30 - 24513 * q^31 - 24576 * q^32 - 2880 * q^33 - 4004 * q^34 + 15310 * q^35 - 7776 * q^36 - 28123 * q^37 + 8384 * q^38 - 5202 * q^39 + 7680 * q^40 - 17914 * q^41 - 5076 * q^42 + 1256 * q^43 - 5120 * q^44 - 2025 * q^45 - 13040 * q^46 + 930 * q^47 - 13824 * q^48 + 24606 * q^49 - 7880 * q^50 + 29934 * q^51 - 9248 * q^52 - 49701 * q^53 + 17496 * q^54 - 99060 * q^55 - 9024 * q^56 + 12096 * q^57 + 6216 * q^58 - 14465 * q^59 - 3600 * q^60 - 52750 * q^61 - 72528 * q^62 + 6966 * q^63 - 24576 * q^64 - 34885 * q^65 - 4500 * q^66 + 199846 * q^67 + 53216 * q^68 + 29340 * q^69 + 116820 * q^70 - 42880 * q^71 + 31104 * q^72 + 35852 * q^73 + 21832 * q^74 - 28620 * q^75 + 21504 * q^76 - 114745 * q^77 - 49572 * q^78 - 236128 * q^79 - 6400 * q^80 - 39366 * q^81 + 46216 * q^82 - 97273 * q^83 + 12384 * q^84 + 372975 * q^85 - 232304 * q^86 + 21609 * q^87 - 8000 * q^88 + 278147 * q^89 - 25920 * q^90 - 103052 * q^91 + 52160 * q^92 + 114858 * q^93 - 3720 * q^94 + 79590 * q^95 + 55296 * q^96 - 249803 * q^97 - 28164 * q^98 + 31590 * q^99

Introduction

L-functions

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