LMFDB - Embedded newform 150.6.g.b.91.1

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			91.1
Character	$\chi$	$=$	150.91
Dual form			150.6.g.b.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-55.1199 - 9.31618i) q^{5} +(11.1246 - 34.2380i) q^{6} +58.3864 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})$	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-55.1199 - 9.31618i) q^{5} +(11.1246 - 34.2380i) q^{6} +58.3864 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(156.468 + 159.743i) q^{10} +(270.135 + 196.265i) q^{11} +(-116.498 + 84.6411i) q^{12} +(230.470 - 167.446i) q^{13} +(-188.942 - 137.275i) q^{14} +(-73.5551 - 497.709i) q^{15} +(-207.108 + 150.473i) q^{16} +(-147.333 + 453.443i) q^{17} +324.000 q^{18} +(-886.565 + 2728.57i) q^{19} +(-130.765 - 884.817i) q^{20} +(162.382 + 499.759i) q^{21} +(-412.730 - 1270.25i) q^{22} +(-2631.73 - 1912.07i) q^{23} +576.000 q^{24} +(2951.42 + 1027.01i) q^{25} -1139.51 q^{26} +(-589.773 - 428.495i) q^{27} +(288.678 + 888.461i) q^{28} +(-2560.39 - 7880.07i) q^{29} +(-932.156 + 1783.56i) q^{30} +(3216.11 - 9898.16i) q^{31} +1024.00 q^{32} +(-928.643 + 2858.07i) q^{33} +(1542.89 - 1120.97i) q^{34} +(-3218.26 - 543.938i) q^{35} +(-1048.49 - 761.770i) q^{36} +(-9568.07 + 6951.61i) q^{37} +(9284.22 - 6745.38i) q^{38} +(2074.23 + 1507.02i) q^{39} +(-1657.17 + 3170.77i) q^{40} +(-15536.8 + 11288.1i) q^{41} +(649.526 - 1999.04i) q^{42} -468.240 q^{43} +(-1650.92 + 5081.01i) q^{44} +(4055.58 - 2013.80i) q^{45} +(4020.93 + 12375.2i) q^{46} +(-8449.79 - 26005.8i) q^{47} +(-1863.98 - 1354.26i) q^{48} -13398.0 q^{49} +(-7136.33 - 10262.7i) q^{50} -4291.01 q^{51} +(3687.52 + 2679.14i) q^{52} +(3793.46 + 11675.1i) q^{53} +(901.094 + 2773.28i) q^{54} +(-13061.4 - 13334.7i) q^{55} +(1154.71 - 3553.84i) q^{56} -25820.8 q^{57} +(-10241.6 + 31520.3i) q^{58} +(-32708.5 + 23764.1i) q^{59} +(7209.92 - 3580.09i) q^{60} +(-19095.3 - 13873.6i) q^{61} +(-33679.5 + 24469.6i) q^{62} +(-3826.08 + 2779.81i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-14263.5 + 7082.53i) q^{65} +(9724.88 - 7065.54i) q^{66} +(2588.21 - 7965.70i) q^{67} -7628.46 q^{68} +(9047.10 - 27844.1i) q^{69} +(9135.62 + 9326.80i) q^{70} +(-21866.2 - 67297.1i) q^{71} +(1601.94 + 4930.28i) q^{72} +(27694.3 + 20121.1i) q^{73} +47307.1 q^{74} +(-582.397 + 28119.0i) q^{75} -45903.7 q^{76} +(15772.2 + 11459.2i) q^{77} +(-3169.14 - 9753.62i) q^{78} +(19342.0 + 59528.6i) q^{79} +(12817.6 - 6364.61i) q^{80} +(2027.46 - 6239.88i) q^{81} +76817.9 q^{82} +(7842.55 - 24136.9i) q^{83} +(-6801.93 + 4941.89i) q^{84} +(12345.3 - 23621.2i) q^{85} +(1515.26 + 1100.90i) q^{86} +(60328.7 - 43831.3i) q^{87} +(17288.7 - 12561.0i) q^{88} +(8729.51 + 6342.36i) q^{89} +(-17858.9 - 3018.44i) q^{90} +(13456.3 - 9776.59i) q^{91} +(16083.7 - 49500.6i) q^{92} +93667.8 q^{93} +(-33799.2 + 104023. i) q^{94} +(74287.2 - 142139. i) q^{95} +(2847.90 + 8764.94i) q^{96} +(17808.3 + 54808.4i) q^{97} +(43356.9 + 31500.6i) q^{98} -27046.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$3$	2.78115	+	8.55951i	0.178411	+	0.549093i
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−55.1199	−	9.31618i	−0.986016	−	0.166653i
$5$	−55.1199	−	9.31618i	−0.986016	−	0.166653i
$6$	11.1246	−	34.2380i	0.126156	−	0.388267i
$7$	58.3864			0.450367			0.225184	−	0.974316i	$-0.427702\pi$
$7$	58.3864			0.450367			0.225184	+	0.974316i	$0.427702\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−65.5304	+	47.6106i	−0.269672	+	0.195928i
$10$	156.468	+	159.743i	0.494796	+	0.505150i
$11$	270.135	+	196.265i	0.673131	+	0.489059i	0.871072	−	0.491155i	$-0.163425\pi$
$11$	270.135	+	196.265i	0.673131	+	0.489059i	−0.197941	+	0.980214i	$0.563425\pi$
$12$	−116.498	+	84.6411i	−0.233543	+	0.169679i
$13$	230.470	−	167.446i	0.378230	−	0.274800i	−0.382385	−	0.924003i	$-0.624897\pi$
$13$	230.470	−	167.446i	0.378230	−	0.274800i	0.760615	+	0.649203i	$0.224897\pi$
$14$	−188.942	−	137.275i	−0.257638	−	0.187185i
$15$	−73.5551	−	497.709i	−0.0844082	−	0.571147i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	−147.333	+	453.443i	−0.123645	+	0.380540i	−0.993652	−	0.112499i	$-0.964114\pi$
$17$	−147.333	+	453.443i	−0.123645	+	0.380540i	0.870007	+	0.493040i	$0.164114\pi$
$18$	324.000			0.235702
$19$	−886.565	+	2728.57i	−0.563412	+	1.73400i	0.109210	+	0.994019i	$0.465168\pi$
$19$	−886.565	+	2728.57i	−0.563412	+	1.73400i	−0.672622	+	0.739986i	$0.734832\pi$
$20$	−130.765	−	884.817i	−0.0730996	−	0.494628i
$21$	162.382	+	499.759i	0.0803505	+	0.247293i
$22$	−412.730	−	1270.25i	−0.181807	−	0.559543i
$23$	−2631.73	−	1912.07i	−1.03734	−	0.753674i	−0.0675779	−	0.997714i	$-0.521527\pi$
$23$	−2631.73	−	1912.07i	−1.03734	−	0.753674i	−0.969765	+	0.244040i	$0.921527\pi$
$24$	576.000			0.204124
$25$	2951.42	+	1027.01i	0.944454	+	0.328645i
$26$	−1139.51			−0.330585
$27$	−589.773	−	428.495i	−0.155695	−	0.113119i
$28$	288.678	+	888.461i	0.0695856	+	0.214162i
$29$	−2560.39	−	7880.07i	−0.565342	−	1.73994i	−0.666935	−	0.745116i	$-0.732394\pi$
$29$	−2560.39	−	7880.07i	−0.565342	−	1.73994i	0.101593	−	0.994826i	$-0.467606\pi$
$30$	−932.156	+	1783.56i	−0.189097	+	0.361813i
$31$	3216.11	−	9898.16i	0.601071	−	1.84991i	0.0792465	−	0.996855i	$-0.474749\pi$
$31$	3216.11	−	9898.16i	0.601071	−	1.84991i	0.521825	−	0.853053i	$-0.325251\pi$
$32$	1024.00			0.176777
$33$	−928.643	+	2858.07i	−0.148444	+	0.456865i
$34$	1542.89	−	1120.97i	0.228895	−	0.166302i
$35$	−3218.26	−	543.938i	−0.444069	−	0.0750550i
$36$	−1048.49	−	761.770i	−0.134836	−	0.0979642i
$37$	−9568.07	+	6951.61i	−1.14900	+	0.834797i	−0.988348	−	0.152214i	$-0.951360\pi$
$37$	−9568.07	+	6951.61i	−1.14900	+	0.834797i	−0.160652	+	0.987011i	$0.551360\pi$
$38$	9284.22	−	6745.38i	1.04301	−	0.757788i
$39$	2074.23	+	1507.02i	0.218371	+	0.158656i
$40$	−1657.17	+	3170.77i	−0.163763	+	0.313340i
$41$	−15536.8	+	11288.1i	−1.44345	+	1.04872i	−0.456138	+	0.889909i	$0.650768\pi$
$41$	−15536.8	+	11288.1i	−1.44345	+	1.04872i	−0.987308	+	0.158816i	$0.949232\pi$
$42$	649.526	−	1999.04i	0.0568164	−	0.174863i
$43$	−468.240			−0.0386186			−0.0193093	−	0.999814i	$-0.506147\pi$
$43$	−468.240			−0.0386186			−0.0193093	+	0.999814i	$0.506147\pi$
$44$	−1650.92	+	5081.01i	−0.128557	+	0.395657i
$45$	4055.58	−	2013.80i	0.298553	−	0.148247i
$46$	4020.93	+	12375.2i	0.280177	+	0.862295i
$47$	−8449.79	−	26005.8i	−0.557958	−	1.71722i	−0.688002	−	0.725709i	$-0.741512\pi$
$47$	−8449.79	−	26005.8i	−0.557958	−	1.71722i	0.130044	−	0.991508i	$-0.458488\pi$
$48$	−1863.98	−	1354.26i	−0.116772	−	0.0848395i
$49$	−13398.0			−0.797169
$50$	−7136.33	−	10262.7i	−0.403692	−	0.580545i
$51$	−4291.01			−0.231012
$52$	3687.52	+	2679.14i	0.189115	+	0.137400i
$53$	3793.46	+	11675.1i	0.185501	+	0.570912i	0.999957	−	0.00931311i	$-0.00296450\pi$
$53$	3793.46	+	11675.1i	0.185501	+	0.570912i	−0.814456	+	0.580225i	$0.802964\pi$
$54$	901.094	+	2773.28i	0.0420519	+	0.129422i
$55$	−13061.4	−	13334.7i	−0.582215	−	0.594399i
$56$	1154.71	−	3553.84i	0.0492044	−	0.151436i
$57$	−25820.8			−1.05265
$58$	−10241.6	+	31520.3i	−0.399757	+	1.23033i
$59$	−32708.5	+	23764.1i	−1.22329	+	0.888775i	−0.996369	−	0.0851370i	$-0.972867\pi$
$59$	−32708.5	+	23764.1i	−1.22329	+	0.888775i	−0.226925	+	0.973912i	$0.572867\pi$
$60$	7209.92	−	3580.09i	0.258555	−	0.128386i
$61$	−19095.3	−	13873.6i	−0.657056	−	0.477379i	0.208611	−	0.977999i	$-0.433106\pi$
$61$	−19095.3	−	13873.6i	−0.657056	−	0.477379i	−0.865668	+	0.500619i	$0.833106\pi$
$62$	−33679.5	+	24469.6i	−1.11272	+	0.808439i
$63$	−3826.08	+	2779.81i	−0.121452	+	0.0882397i
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−14263.5	+	7082.53i	−0.418737	+	0.207924i
$66$	9724.88	−	7065.54i	0.274805	−	0.199657i
$67$	2588.21	−	7965.70i	0.0704389	−	0.216789i	−0.909640	−	0.415398i	$-0.863642\pi$
$67$	2588.21	−	7965.70i	0.0704389	−	0.216789i	0.980079	+	0.198609i	$0.0636424\pi$
$68$	−7628.46			−0.200062
$69$	9047.10	−	27844.1i	0.228763	−	0.704061i
$70$	9135.62	+	9326.80i	0.222840	+	0.227503i
$71$	−21866.2	−	67297.1i	−0.514786	−	1.58435i	−0.783671	−	0.621176i	$-0.786655\pi$
$71$	−21866.2	−	67297.1i	−0.514786	−	1.58435i	0.268885	−	0.963172i	$-0.413345\pi$
$72$	1601.94	+	4930.28i	0.0364180	+	0.112083i
$73$	27694.3	+	20121.1i	0.608251	+	0.441920i	0.848798	−	0.528717i	$-0.177327\pi$
$73$	27694.3	+	20121.1i	0.608251	+	0.441920i	−0.240547	+	0.970638i	$0.577327\pi$
$74$	47307.1			1.00426
$75$	−582.397	+	28119.0i	−0.0119555	+	0.577226i
$76$	−45903.7			−0.911620
$77$	15772.2	+	11459.2i	0.303156	+	0.220256i
$78$	−3169.14	−	9753.62i	−0.0589801	−	0.181522i
$79$	19342.0	+	59528.6i	0.348686	+	1.07314i	0.959581	+	0.281433i	$0.0908096\pi$
$79$	19342.0	+	59528.6i	0.348686	+	1.07314i	−0.610895	+	0.791711i	$0.709190\pi$
$80$	12817.6	−	6364.61i	0.223915	−	0.111185i
$81$	2027.46	−	6239.88i	0.0343352	−	0.105673i
$82$	76817.9			1.26162
$83$	7842.55	−	24136.9i	0.124957	−	0.384579i	−0.868936	−	0.494925i	$-0.835196\pi$
$83$	7842.55	−	24136.9i	0.124957	−	0.384579i	0.993893	+	0.110345i	$0.0351957\pi$
$84$	−6801.93	+	4941.89i	−0.105180	+	0.0764179i
$85$	12345.3	−	23621.2i	0.185334	−	0.354613i
$86$	1515.26	+	1100.90i	0.0220922	+	0.0160509i
$87$	60328.7	−	43831.3i	0.854527	−	0.620850i
$88$	17288.7	−	12561.0i	0.237988	−	0.172908i
$89$	8729.51	+	6342.36i	0.116819	+	0.0848743i	0.644661	−	0.764469i	$-0.276999\pi$
$89$	8729.51	+	6342.36i	0.116819	+	0.0848743i	−0.527842	+	0.849343i	$0.676999\pi$
$90$	−17858.9	−	3018.44i	−0.232406	−	0.0392805i
$91$	13456.3	−	9776.59i	0.170342	−	0.123761i
$92$	16083.7	−	49500.6i	0.198115	−	0.609735i
$93$	93667.8			1.12301
$94$	−33799.2	+	104023.i	−0.394536	+	1.21426i
$95$	74287.2	−	142139.i	0.844510	−	1.61586i
$96$	2847.90	+	8764.94i	0.0315389	+	0.0970668i
$97$	17808.3	+	54808.4i	0.192174	+	0.591449i	0.999998	+	0.00202618i	$0.000644954\pi$
$97$	17808.3	+	54808.4i	0.192174	+	0.591449i	−0.807824	+	0.589423i	$0.799355\pi$
$98$	43356.9	+	31500.6i	0.456030	+	0.331325i
$99$	−27046.4			−0.277345
$100$	−1035.37	+	49989.3i	−0.0103537	+	0.499893i
$101$	−34449.5			−0.336031			−0.168015	−	0.985784i	$-0.553736\pi$
$101$	−34449.5			−0.336031			−0.168015	+	0.985784i	$0.553736\pi$
$102$	13886.0	+	10088.8i	0.132153	+	0.0960147i
$103$	7260.42	+	22345.3i	0.0674324	+	0.207536i	0.979095	−	0.203404i	$-0.0652006\pi$
$103$	7260.42	+	22345.3i	0.0674324	+	0.207536i	−0.911662	+	0.410940i	$0.865201\pi$
$104$	−5634.03	−	17339.8i	−0.0510782	−	0.157203i
$105$	−4294.62	−	29059.5i	−0.0380147	−	0.257226i
$106$	15173.8	−	46700.2i	0.131169	−	0.403696i
$107$	−105013.			−0.886718			−0.443359	−	0.896344i	$-0.646213\pi$
$107$	−105013.			−0.886718			−0.443359	+	0.896344i	$0.646213\pi$
$108$	3604.37	−	11093.1i	0.0297352	−	0.0915155i
$109$	−42148.1	+	30622.4i	−0.339791	+	0.246872i	−0.744574	−	0.667540i	$-0.767347\pi$
$109$	−42148.1	+	30622.4i	−0.339791	+	0.246872i	0.404783	+	0.914413i	$0.367347\pi$
$110$	10915.8	+	73861.3i	0.0860146	+	0.582017i
$111$	−86112.6	−	62564.5i	−0.663375	−	0.481970i
$112$	−12092.3	+	8785.58i	−0.0910887	+	0.0661798i
$113$	141125.	−	102534.i	1.03970	−	0.755388i	0.0694752	−	0.997584i	$-0.477868\pi$
$113$	141125.	−	102534.i	1.03970	−	0.755388i	0.970227	+	0.242195i	$0.0778675\pi$
$114$	83558.0	+	60708.5i	0.602180	+	0.437509i
$115$	127248.	+	129911.i	0.897234	+	0.916010i
$116$	107251.	−	77922.4i	0.740042	−	0.537672i
$117$	−7130.57	+	21945.6i	−0.0481570	+	0.148212i
$118$	161720.			1.06920
$119$	−8602.23	+	26474.9i	−0.0556857	+	0.171383i
$120$	−31749.1	−	5366.12i	−0.201270	−	0.0340179i
$121$	−15314.3	−	47132.4i	−0.0950894	−	0.292655i
$122$	29175.1	+	89791.6i	0.177465	+	0.546181i
$123$	−139831.	−	101593.i	−0.833374	−	0.605482i
$124$	166521.			0.972554
$125$	−153114.	−	84104.9i	−0.876476	−	0.481445i
$126$	18917.2			0.106153
$127$	44257.6	+	32155.1i	0.243489	+	0.176905i	0.702836	−	0.711352i	$-0.251917\pi$
$127$	44257.6	+	32155.1i	0.243489	+	0.176905i	−0.459347	+	0.888257i	$0.651917\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	−1302.25	−	4007.90i	−0.00688999	−	0.0212052i
$130$	62809.5	+	10615.8i	0.325962	+	0.0550930i
$131$	−18417.6	+	56683.5i	−0.0937680	+	0.288588i	−0.986931	−	0.161146i	$-0.948481\pi$
$131$	−18417.6	+	56683.5i	−0.0937680	+	0.288588i	0.893163	+	0.449734i	$0.148481\pi$
$132$	−48082.4			−0.240188
$133$	−51763.3	+	159311.i	−0.253742	+	0.780939i
$134$	−27104.1	+	19692.3i	−0.130399	+	0.0947401i
$135$	28516.3	+	29113.1i	0.134666	+	0.137485i
$136$	24686.2	+	17935.6i	0.114448	+	0.0831511i
$137$	315761.	−	229414.i	1.43733	−	1.04428i	0.448739	−	0.893663i	$-0.351873\pi$
$137$	315761.	−	229414.i	1.43733	−	1.04428i	0.988592	−	0.150619i	$-0.0481268\pi$
$138$	−94742.4	+	68834.4i	−0.423493	+	0.307686i
$139$	−3959.80	−	2876.96i	−0.0173835	−	0.0126298i	0.579060	−	0.815285i	$-0.303420\pi$
$139$	−3959.80	−	2876.96i	−0.0173835	−	0.0126298i	−0.596443	+	0.802655i	$0.703420\pi$
$140$	−7634.88	−	51661.3i	−0.0329217	−	0.222764i
$141$	199097.	−	144652.i	0.843366	−	0.612741i
$142$	−87464.6	+	269188.i	−0.364009	+	1.12030i
$143$	95122.0			0.388992
$144$	6407.78	−	19721.1i	0.0257514	−	0.0792547i
$145$	67716.4	+	458202.i	0.267469	+	1.80983i
$146$	−42313.1	−	130226.i	−0.164283	−	0.505611i
$147$	−37262.0	−	114681.i	−0.142224	−	0.437720i
$148$	−153089.	−	111226.i	−0.574500	−	0.417399i
$149$	−253007.			−0.933613			−0.466807	−	0.884359i	$-0.654596\pi$
$149$	−253007.			−0.933613			−0.466807	+	0.884359i	$0.654596\pi$
$150$	67996.3	−	89625.6i	0.246750	−	0.325240i
$151$	−407286.			−1.45364			−0.726821	−	0.686827i	$-0.759003\pi$
$151$	−407286.			−1.45364			−0.726821	+	0.686827i	$0.759003\pi$
$152$	148548.	+	107926.i	0.521503	+	0.378894i
$153$	−11933.9	−	36728.9i	−0.0412150	−	0.126847i
$154$	−24097.8	−	74165.5i	−0.0818797	−	0.252000i
$155$	−269485.	+	515624.i	−0.900958	+	1.72387i
$156$	−12676.6	+	39014.5i	−0.0417052	+	0.128355i
$157$	122193.			0.395639			0.197819	−	0.980239i	$-0.436614\pi$
$157$	122193.			0.395639			0.197819	+	0.980239i	$0.436614\pi$
$158$	77368.1	−	238114.i	0.246558	−	0.758827i
$159$	−89382.6	+	64940.2i	−0.280388	+	0.203714i
$160$	−56442.8	−	9539.77i	−0.174305	−	0.0294603i
$161$	−153658.	−	111639.i	−0.467185	−	0.339430i
$162$	−21231.8	+	15425.8i	−0.0635624	+	0.0461808i
$163$	398457.	−	289496.i	1.17466	−	0.853441i	0.183101	−	0.983094i	$-0.441386\pi$
$163$	398457.	−	289496.i	1.17466	−	0.853441i	0.991559	+	0.129653i	$0.0413864\pi$
$164$	−248588.	−	180610.i	−0.721723	−	0.524362i
$165$	77813.0	−	148885.i	0.222506	−	0.425737i
$166$	−82128.2	+	59669.6i	−0.231325	+	0.168067i
$167$	−187400.	+	576757.i	−0.519969	+	1.60030i	0.254085	+	0.967182i	$0.418226\pi$
$167$	−187400.	+	576757.i	−0.519969	+	1.60030i	−0.774054	+	0.633119i	$0.781774\pi$
$168$	33630.6			0.0919308
$169$	−89657.7	+	275938.i	−0.241474	+	0.743181i
$170$	−95487.1	+	47414.2i	−0.253409	+	0.125831i
$171$	−71811.7	−	221014.i	−0.187804	−	0.578002i
$172$	−2315.10	−	7125.16i	−0.00596691	−	0.0183643i
$173$	122742.	+	89177.4i	0.311802	+	0.226537i	0.732669	−	0.680585i	$-0.238274\pi$
$173$	122742.	+	89177.4i	0.311802	+	0.226537i	−0.420867	+	0.907122i	$0.638274\pi$
$174$	−298281.			−0.746884
$175$	172323.	+	59963.7i	0.425351	+	0.148011i
$176$	−85479.9			−0.208009
$177$	−294377.	−	213877.i	−0.706269	−	0.513135i
$178$	−13337.5	−	41048.6i	−0.0315518	−	0.0971066i
$179$	11594.0	+	35682.8i	0.0270460	+	0.0832389i	0.963668	−	0.267102i	$-0.0860659\pi$
$179$	11594.0	+	35682.8i	0.0270460	+	0.0832389i	−0.936622	+	0.350340i	$0.886066\pi$
$180$	50695.7	+	51756.6i	0.116625	+	0.119065i
$181$	100797.	−	310221.i	0.228692	−	0.703842i	−0.769204	−	0.639004i	$-0.779347\pi$
$181$	100797.	−	310221.i	0.228692	−	0.703842i	0.997896	−	0.0648383i	$-0.0206532\pi$
$182$	−66531.7			−0.148885
$183$	65643.9	−	202031.i	0.144899	−	0.445955i
$184$	−168431.	+	122372.i	−0.366756	+	0.266464i
$185$	592154.	−	294034.i	1.27205	−	0.631639i
$186$	−303115.	−	220226.i	−0.642430	−	0.466753i
$187$	−128795.	+	93574.9i	−0.269336	+	0.195684i
$188$	353949.	−	257159.i	0.730376	−	0.530649i
$189$	−34434.8	−	25018.3i	−0.0701201	−	0.0509452i
$190$	−574587.	+	285312.i	−1.15471	+	0.573371i
$191$	599.005	−	435.203i	0.00118808	−	0.000863193i	−0.587191	−	0.809448i	$-0.699766\pi$
$191$	599.005	−	435.203i	0.00118808	−	0.000863193i	0.588379	+	0.808585i	$0.299766\pi$
$192$	11391.6	−	35059.7i	0.0223014	−	0.0686366i
$193$	−843579.			−1.63017			−0.815085	−	0.579342i	$-0.803310\pi$
$193$	−843579.			−1.63017			−0.815085	+	0.579342i	$0.803310\pi$
$194$	71233.3	−	219234.i	0.135887	−	0.418218i
$195$	−100292.	−	102391.i	−0.188877	−	0.192830i
$196$	−66243.5	−	203876.i	−0.123169	−	0.379077i
$197$	148990.	+	458545.i	0.273522	+	0.841814i	0.989607	+	0.143801i	$0.0459324\pi$
$197$	148990.	+	458545.i	0.273522	+	0.841814i	−0.716085	+	0.698013i	$0.754068\pi$
$198$	87523.9	+	63589.8i	0.158659	+	0.115272i
$199$	−843276.			−1.50951			−0.754757	−	0.656004i	$-0.772245\pi$
$199$	−843276.			−1.50951			−0.754757	+	0.656004i	$0.772245\pi$
$200$	120882.	−	159334.i	0.213692	−	0.281666i
$201$	75380.6			0.131604
$202$	111481.	+	80995.6i	0.192230	+	0.139663i
$203$	−149492.	−	460089.i	−0.254611	−	0.783613i
$204$	−21215.9	−	65295.9i	−0.0356933	−	0.109853i
$205$	961547.	−	477457.i	1.59803	−	0.793505i
$206$	29041.7	−	89381.1i	0.0476819	−	0.146750i
$207$	263493.			0.427409
$208$	−22536.1	+	69359.1i	−0.0361178	+	0.111159i
$209$	−775014.	+	563081.i	−1.22728	+	0.891671i
$210$	−54425.2	+	104136.i	−0.0851632	+	0.162949i
$211$	218659.	+	158865.i	0.338113	+	0.245654i	0.743865	−	0.668330i	$-0.232990\pi$
$211$	218659.	+	158865.i	0.338113	+	0.245654i	−0.405752	+	0.913983i	$0.632990\pi$
$212$	−158902.	+	115449.i	−0.242823	+	0.176422i
$213$	515217.	−	374327.i	0.778110	−	0.565330i
$214$	339831.	+	246901.i	0.507257	+	0.368544i
$215$	25809.3	+	4362.20i	0.0380786	+	0.00643591i
$216$	−37745.5	+	27423.7i	−0.0550466	+	0.0399937i
$217$	187777.	−	577918.i	0.270703	−	0.833138i
$218$	208392.			0.296988
$219$	−95204.5	+	293009.i	−0.134137	+	0.412830i
$220$	138334.	−	264685.i	0.192696	−	0.368699i
$221$	41971.6	+	129175.i	0.0578063	+	0.177910i
$222$	131568.	+	404926.i	0.179172	+	0.551433i
$223$	766546.	+	556928.i	1.03223	+	0.749958i	0.968754	−	0.248025i	$-0.0797816\pi$
$223$	766546.	+	556928.i	1.03223	+	0.749958i	0.0634752	+	0.997983i	$0.479782\pi$
$224$	59787.7			0.0796144
$225$	−242304.	+	73218.1i	−0.319084	+	0.0964189i
$226$	−697762.			−0.908733
$227$	612258.	+	444832.i	0.788624	+	0.572969i	0.907555	−	0.419934i	$-0.137947\pi$
$227$	612258.	+	444832.i	0.788624	+	0.572969i	−0.118931	+	0.992903i	$0.537947\pi$
$228$	−127665.	−	392913.i	−0.162643	−	0.500564i
$229$	−354094.	−	1.08979e6i	−0.446200	−	1.37326i	−0.881163	−	0.472813i	$-0.843238\pi$
$229$	−354094.	−	1.08979e6i	−0.446200	−	1.37326i	0.434963	−	0.900448i	$-0.356762\pi$
$230$	−106344.	−	719578.i	−0.132555	−	0.896929i
$231$	−54220.1	+	166872.i	−0.0668545	+	0.205757i
$232$	−530278.			−0.646820
$233$	141385.	−	435139.i	0.170614	−	0.525095i	−0.828792	−	0.559556i	$-0.810971\pi$
$233$	141385.	−	435139.i	0.170614	−	0.525095i	0.999406	+	0.0344611i	$0.0109715\pi$
$234$	74672.3	−	54252.6i	0.0891497	−	0.0647710i
$235$	223477.	+	1.51216e6i	0.263976	+	1.78619i
$236$	−523336.	−	380226.i	−0.611647	−	0.444388i
$237$	−455743.	+	331116.i	−0.527046	+	0.382922i
$238$	90083.7	−	65449.7i	0.103087	−	0.0748971i
$239$	−424003.	−	308057.i	−0.480147	−	0.348848i	0.321235	−	0.946999i	$-0.395902\pi$
$239$	−424003.	−	308057.i	−0.480147	−	0.348848i	−0.801383	+	0.598152i	$0.795902\pi$
$240$	90125.7	+	92011.7i	0.101000	+	0.103113i
$241$	−45565.6	+	33105.3i	−0.0505352	+	0.0367160i	−0.612766	−	0.790264i	$-0.709943\pi$
$241$	−45565.6	+	33105.3i	−0.0505352	+	0.0367160i	0.562231	+	0.826980i	$0.309943\pi$
$242$	−61257.0	+	188530.i	−0.0672384	+	0.206938i
$243$	59049.0			0.0641500
$244$	116700.	−	359167.i	0.125487	−	0.386208i
$245$	738498.	+	124818.i	0.786021	+	0.132851i
$246$	213642.	+	657524.i	0.225087	+	0.692745i
$247$	252562.	+	777305.i	0.263406	+	0.810679i
$248$	−538872.	−	391513.i	−0.556361	−	0.404220i
$249$	228411.			0.233463
$250$	297745.	+	632162.i	0.301297	+	0.639703i
$251$	−141369.			−0.141635			−0.0708174	−	0.997489i	$-0.522561\pi$
$251$	−141369.			−0.141635			−0.0708174	+	0.997489i	$0.522561\pi$
$252$	−61217.4	−	44477.0i	−0.0607258	−	0.0441199i
$253$	−335653.	−	1.03303e6i	−0.329677	−	1.01464i
$254$	−67619.6	−	208112.i	−0.0657641	−	0.202401i
$255$	236520.	+	39975.8i	0.227781	+	0.0384988i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−1.08157e6			−1.02146			−0.510731	−	0.859740i	$-0.670625\pi$
$257$	−1.08157e6			−1.02146			−0.510731	+	0.859740i	$0.670625\pi$
$258$	−5208.98	+	16031.6i	−0.00487196	+	0.0149944i
$259$	−558645.	+	405880.i	−0.517472	+	0.375965i
$260$	−178297.	−	182028.i	−0.163572	−	0.166995i
$261$	542958.	+	394482.i	0.493361	+	0.358448i
$262$	192872.	−	140129.i	0.173586	−	0.126118i
$263$	−791760.	+	575248.i	−0.705837	+	0.512820i	−0.881828	−	0.471571i	$-0.843687\pi$
$263$	−791760.	+	575248.i	−0.705837	+	0.512820i	0.175991	+	0.984392i	$0.443687\pi$
$264$	155598.	+	113049.i	0.137402	+	0.0998287i
$265$	−100328.	−	678869.i	−0.0877623	−	0.593843i
$266$	542073.	−	393839.i	0.469736	−	0.341283i
$267$	−30009.4	+	92359.4i	−0.0257620	+	0.0792872i
$268$	134010.			0.113973
$269$	−382968.	+	1.17866e6i	−0.322688	+	0.993130i	0.649786	+	0.760117i	$0.274858\pi$
$269$	−382968.	+	1.17866e6i	−0.322688	+	0.993130i	−0.972474	+	0.233013i	$0.925142\pi$
$270$	−23831.8	−	161258.i	−0.0198952	−	0.134621i
$271$	−198906.	−	612171.i	−0.164523	−	0.506348i	0.834478	−	0.551041i	$-0.185769\pi$
$271$	−198906.	−	612171.i	−0.164523	−	0.506348i	−0.999001	+	0.0446926i	$0.985769\pi$
$272$	−37717.2	−	116082.i	−0.0309113	−	0.0951351i
$273$	121107.	+	87989.3i	0.0983473	+	0.0714535i
$274$	−1.56121e6			−1.25627
$275$	595716.	+	856693.i	0.475015	+	0.683114i
$276$	468432.			0.370147
$277$	847265.	+	615574.i	0.663468	+	0.482038i	0.867832	−	0.496857i	$-0.165513\pi$
$277$	847265.	+	615574.i	0.663468	+	0.482038i	−0.204364	+	0.978895i	$0.565513\pi$
$278$	6050.03	+	18620.1i	0.00469511	+	0.0144501i
$279$	260505.	+	801751.i	0.200357	+	0.616636i
$280$	−96756.0	+	185130.i	−0.0737535	+	0.141118i
$281$	168990.	−	520097.i	0.127672	−	0.392933i	−0.866707	−	0.498818i	$-0.833768\pi$
$281$	168990.	−	520097.i	0.127672	−	0.392933i	0.994378	+	0.105885i	$0.0337676\pi$
$282$	−984387.			−0.737129
$283$	289442.	−	890810.i	0.214830	−	0.661179i	−0.784336	−	0.620337i	$-0.786996\pi$
$283$	289442.	−	890810.i	0.214830	−	0.661179i	0.999166	−	0.0408420i	$-0.0130040\pi$
$284$	915941.	−	665470.i	0.673863	−	0.489590i
$285$	1.42324e6	+	240552.i	1.03793	+	0.175427i
$286$	−307821.	−	223645.i	−0.222527	−	0.161676i
$287$	−907135.	+	659072.i	−0.650081	+	0.472311i
$288$	−67103.1	+	48753.3i	−0.0476718	+	0.0346356i
$289$	964784.	+	700957.i	0.679494	+	0.493681i
$290$	858162.	−	1.64198e6i	0.599204	−	1.14650i
$291$	−419605.	+	304861.i	−0.290475	+	0.211042i
$292$	−169252.	+	520905.i	−0.116166	+	0.357521i
$293$	967202.			0.658185			0.329093	−	0.944298i	$-0.393257\pi$
$293$	967202.			0.658185			0.329093	+	0.944298i	$0.393257\pi$
$294$	−149048.	+	458722.i	−0.100567	+	0.309515i
$295$	2.02428e6	−	1.00516e6i	1.35430	−	0.672481i
$296$	233899.	+	719868.i	0.155167	+	0.477555i
$297$	−75220.1	−	231504.i	−0.0494815	−	0.152288i
$298$	818748.	+	594855.i	0.534084	+	0.388035i
$299$	−926704.			−0.599464
$300$	−430763.	+	130166.i	−0.276335	+	0.0835012i
$301$	−27338.8			−0.0173926
$302$	1.31801e6	+	957587.i	0.831572	+	0.604173i
$303$	−95809.3	−	294871.i	−0.0599516	−	0.184512i
$304$	−226961.	−	698513.i	−0.140853	−	0.433501i
$305$	923285.	+	942606.i	0.568311	+	0.580204i
$306$	−47735.8	+	146916.i	−0.0291434	+	0.0896942i
$307$	−616665.			−0.373425			−0.186712	−	0.982415i	$-0.559783\pi$
$307$	−616665.			−0.373425			−0.186712	+	0.982415i	$0.559783\pi$
$308$	−96391.4	+	296662.i	−0.0578977	+	0.178191i
$309$	−171072.	+	124291.i	−0.101926	+	0.0740533i
$310$	2.08438e6	−	1.03500e6i	1.23189	−	0.611696i
$311$	1.25104e6	+	908937.i	0.733452	+	0.532884i	0.890654	−	0.454682i	$-0.150247\pi$
$311$	1.25104e6	+	908937.i	0.733452	+	0.532884i	−0.157202	+	0.987567i	$0.550247\pi$
$312$	132751.	−	96449.1i	0.0772059	−	0.0560934i
$313$	224326.	−	162982.i	0.129425	−	0.0940327i	−0.521189	−	0.853441i	$-0.674511\pi$
$313$	224326.	−	162982.i	0.129425	−	0.0940327i	0.650614	+	0.759408i	$0.274511\pi$
$314$	−395426.	−	287294.i	−0.226330	−	0.164438i
$315$	236791.	−	117579.i	0.134459	−	0.0667655i
$316$	−810209.	+	588651.i	−0.456435	+	0.331620i
$317$	−360469.	+	1.10941e6i	−0.201474	+	0.620074i	0.798366	+	0.602173i	$0.205698\pi$
$317$	−360469.	+	1.10941e6i	−0.201474	+	0.620074i	−0.999840	+	0.0179006i	$0.994302\pi$
$318$	441932.			0.245068
$319$	854928.	−	2.63120e6i	0.470385	−	1.44769i
$320$	160223.	+	163576.i	0.0874684	+	0.0892988i
$321$	−292058.	−	898863.i	−0.158200	−	0.486890i
$322$	234768.	+	722541.i	0.126182	+	0.388350i
$323$	−1.10663e6	−	804014.i	−0.590196	−	0.428802i
$324$	104976.			0.0555556
$325$	852183.	−	257508.i	0.447532	−	0.135233i
$326$	−1.97008e6			−1.02669
$327$	−379333.	−	275601.i	−0.196178	−	0.142532i
$328$	379809.	+	1.16893e6i	0.194931	+	0.599935i
$329$	−493353.	−	1.51838e6i	−0.251286	−	0.773378i
$330$	−601858.	+	298853.i	−0.304235	+	0.151068i
$331$	607464.	−	1.86958e6i	0.304755	−	0.937940i	−0.675013	−	0.737805i	$-0.735862\pi$
$331$	607464.	−	1.86958e6i	0.304755	−	0.937940i	0.979769	−	0.200134i	$-0.0641378\pi$
$332$	406064.			0.202185
$333$	296029.	−	911083.i	0.146293	−	0.450243i
$334$	1.96248e6	−	1.42582e6i	0.962583	−	0.699357i
$335$	−216872.	+	414956.i	−0.105582	+	0.202018i
$336$	−108831.	−	79070.2i	−0.0525901	−	0.0382089i
$337$	948931.	−	689438.i	0.455155	−	0.330690i	−0.336472	−	0.941693i	$-0.609234\pi$
$337$	948931.	−	689438.i	0.455155	−	0.330690i	0.791628	+	0.611004i	$0.209234\pi$
$338$	938907.	−	682156.i	0.447024	−	0.324782i
$339$	1.27013e6	+	922803.i	0.600273	+	0.436124i
$340$	420480.	+	71068.1i	0.197264	+	0.0333409i
$341$	2.81144e6	−	2.04263e6i	1.30931	−	0.951272i
$342$	−287247.	+	884055.i	−0.132798	+	0.408709i
$343$	−1.76356e6			−0.809386
$344$	−9260.42	+	28500.6i	−0.00421924	+	0.0129855i
$345$	−758076.	+	1.45048e6i	−0.342898	+	0.656091i
$346$	−187533.	−	577168.i	−0.0842148	−	0.259186i
$347$	1.03033e6	+	3.17104e6i	0.459361	+	1.41377i	0.865938	+	0.500151i	$0.166722\pi$
$347$	1.03033e6	+	3.17104e6i	0.459361	+	1.41377i	−0.406577	+	0.913616i	$0.633278\pi$
$348$	965259.	+	701301.i	0.427263	+	0.310425i
$349$	−52753.2			−0.0231838			−0.0115919	−	0.999933i	$-0.503690\pi$
$349$	−52753.2			−0.0231838			−0.0115919	+	0.999933i	$0.503690\pi$
$350$	−416665.	−	599202.i	−0.181810	−	0.261459i
$351$	−207675.			−0.0899739
$352$	276619.	+	200975.i	0.118994	+	0.0864542i
$353$	−46082.9	−	141829.i	−0.0196835	−	0.0605797i	0.940732	−	0.339150i	$-0.110139\pi$
$353$	−46082.9	−	141829.i	−0.0196835	−	0.0605797i	−0.960416	+	0.278570i	$0.910139\pi$
$354$	449768.	+	1.38424e6i	0.190757	+	0.587089i
$355$	578309.	+	3.91312e6i	0.243551	+	1.64798i
$356$	−53350.0	+	164195.i	−0.0223105	+	0.0686647i
$357$	−250537.			−0.104040
$358$	46376.2	−	142731.i	0.0191244	−	0.0588588i
$359$	−2.32342e6	+	1.68807e6i	−0.951464	+	0.691279i	−0.951153	−	0.308721i	$-0.900099\pi$
$359$	−2.32342e6	+	1.68807e6i	−0.951464	+	0.691279i	−0.000311451		1.00000i	$0.500099\pi$
$360$	−42367.7	−	286681.i	−0.0172297	−	0.116585i
$361$	−4.65586e6	−	3.38268e6i	−1.88032	−	1.36613i
$362$	−1.05556e6	+	766909.i	−0.423362	+	0.307590i
$363$	360839.	−	262165.i	0.143730	−	0.104426i
$364$	215301.	+	156425.i	0.0851712	+	0.0618805i
$365$	−1.33906e6	−	1.36708e6i	−0.526098	−	0.537107i
$366$	−687432.	+	499449.i	−0.268242	+	0.194889i
$367$	365278.	−	1.12421e6i	0.141566	−	0.435695i	−0.854988	−	0.518648i	$-0.826435\pi$
$367$	365278.	−	1.12421e6i	0.141566	−	0.435695i	0.996553	+	0.0829538i	$0.0264354\pi$
$368$	832768.			0.320557
$369$	480695.	−	1.47943e6i	0.183782	−	0.565624i
$370$	−2.60757e6	−	440722.i	−0.990219	−	0.167363i
$371$	221486.	+	681665.i	0.0835434	+	0.257120i
$372$	463119.	+	1.42533e6i	0.173514	+	0.534022i
$373$	−2.73332e6	−	1.98587e6i	−1.01723	−	0.739058i	−0.0515141	−	0.998672i	$-0.516405\pi$
$373$	−2.73332e6	−	1.98587e6i	−1.01723	−	0.739058i	−0.965713	+	0.259614i	$0.916405\pi$
$374$	636796.			0.235408
$375$	294063.	−	1.54449e6i	0.107985	−	0.567162i
$376$	−1.75002e6			−0.638372
$377$	−1.90958e6	−	1.38739e6i	−0.691966	−	0.502743i
$378$	52611.6	+	161922.i	0.0189388	+	0.0582876i
$379$	750405.	+	2.30951e6i	0.268347	+	0.825889i	0.990903	+	0.134576i	$0.0429672\pi$
$379$	750405.	+	2.30951e6i	0.268347	+	0.825889i	−0.722556	+	0.691313i	$0.757033\pi$
$380$	2.53021e6	+	427647.i	0.898872	+	0.151924i
$381$	−152144.	+	468252.i	−0.0536961	+	0.165260i
$382$	−2961.64			−0.00103842
$383$	−1.38278e6	+	4.25576e6i	−0.481677	+	1.48245i	0.355059	+	0.934844i	$0.384461\pi$
$383$	−1.38278e6	+	4.25576e6i	−0.481677	+	1.48245i	−0.836736	+	0.547606i	$0.815539\pi$
$384$	−119294.	+	86672.5i	−0.0412850	+	0.0299953i
$385$	−762609.	−	778568.i	−0.262211	−	0.267698i
$386$	2.72988e6	+	1.98337e6i	0.932557	+	0.677542i
$387$	30683.9	−	22293.2i	0.0104144	−	0.00756649i
$388$	−745965.	+	541975.i	−0.251558	+	0.182768i
$389$	1.55955e6	+	1.13308e6i	0.522547	+	0.379653i	0.817563	−	0.575840i	$-0.195325\pi$
$389$	1.55955e6	+	1.13308e6i	0.522547	+	0.379653i	−0.295016	+	0.955492i	$0.595325\pi$
$390$	83816.5	+	567143.i	0.0279041	+	0.188813i
$391$	1.25475e6	−	911632.i	0.415066	−	0.301563i
$392$	−264974.	+	815506.i	−0.0870939	+	0.268048i
$393$	−536405.			−0.175191
$394$	595961.	−	1.83418e6i	0.193409	−	0.595252i
$395$	−511552.	−	3.46141e6i	−0.164967	−	1.11625i
$396$	−133725.	−	411562.i	−0.0428522	−	0.131886i
$397$	−1.59273e6	−	4.90193e6i	−0.507186	−	1.56096i	−0.797065	−	0.603894i	$-0.793615\pi$
$397$	−1.59273e6	−	4.90193e6i	−0.507186	−	1.56096i	0.289879	−	0.957063i	$-0.406385\pi$
$398$	2.72890e6	+	1.98266e6i	0.863535	+	0.627395i
$399$	−1.50759e6			−0.474078
$400$	−765801.	+	231405.i	−0.239313	+	0.0723142i
$401$	1.49433e6			0.464071			0.232036	−	0.972707i	$-0.425461\pi$
$401$	1.49433e6			0.464071			0.232036	+	0.972707i	$0.425461\pi$
$402$	−243937.	−	177231.i	−0.0752857	−	0.0546982i
$403$	−916193.	−	2.81975e6i	−0.281012	−	0.864865i
$404$	−170328.	−	524214.i	−0.0519196	−	0.159792i
$405$	−169885.	+	325054.i	−0.0514658	+	0.0984731i
$406$	−597968.	+	1.84036e6i	−0.180037	+	0.554098i
$407$	−3.94903e6			−1.18169
$408$	−84863.6	+	261183.i	−0.0252389	+	0.0776775i
$409$	301181.	−	218821.i	0.0890264	−	0.0646815i	−0.542382	−	0.840132i	$-0.682477\pi$
$409$	301181.	−	218821.i	0.0890264	−	0.0646815i	0.631408	+	0.775451i	$0.282477\pi$
$410$	−4.23420e6	−	715650.i	−1.24398	−	0.210252i
$411$	2.84185e6	+	2.06472e6i	0.829843	+	0.602917i
$412$	−304128.	+	220962.i	−0.0882702	+	0.0641320i
$413$	−1.90973e6	+	1.38750e6i	−0.550932	+	0.400275i
$414$	−852682.	−	619510.i	−0.244504	−	0.177643i
$415$	−657144.	+	1.25736e6i	−0.187301	+	0.358377i
$416$	236001.	−	171465.i	0.0668623	−	0.0485783i
$417$	13612.6	−	41895.2i	0.00383354	−	0.0117984i
$418$	3.83188e6			1.07268
$419$	−1.15869e6	+	3.56607e6i	−0.322427	+	0.992328i	0.650162	+	0.759796i	$0.274701\pi$
$419$	−1.15869e6	+	3.56607e6i	−0.322427	+	0.992328i	−0.972589	+	0.232532i	$0.925299\pi$
$420$	420961.	−	209029.i	0.116445	−	0.0578206i
$421$	1.01016e6	+	3.10897e6i	0.277771	+	0.854891i	0.988473	+	0.151398i	$0.0483775\pi$
$421$	1.01016e6	+	3.10897e6i	0.277771	+	0.854891i	−0.710702	+	0.703493i	$0.751623\pi$
$422$	−334082.	−	1.02820e6i	−0.0913213	−	0.281058i
$423$	1.79187e6	+	1.30187e6i	0.486917	+	0.353766i
$424$	785656.			0.212235
$425$	−900533.	+	1.18699e6i	−0.241840	+	0.318767i
$426$	−2.54737e6			−0.680093
$427$	−1.11491e6	−	810028.i	−0.295917	−	0.214996i
$428$	−519215.	−	1.59798e6i	−0.137005	−	0.421659i
$429$	264549.	+	814197.i	0.0694005	+	0.213593i
$430$	−73264.6	−	74797.8i	−0.0191084	−	0.0195082i
$431$	2.23835e6	−	6.88893e6i	0.580410	−	1.78632i	−0.0365620	−	0.999331i	$-0.511641\pi$
$431$	2.23835e6	−	6.88893e6i	0.580410	−	1.78632i	0.616972	−	0.786985i	$-0.288359\pi$
$432$	186624.			0.0481125
$433$	784216.	−	2.41357e6i	0.201009	−	0.618643i	−0.798845	−	0.601538i	$-0.794555\pi$
$433$	784216.	−	2.41357e6i	0.201009	−	0.618643i	0.999854	−	0.0171050i	$-0.00544496\pi$
$434$	−1.96643e6	+	1.42869e6i	−0.501133	+	0.364095i
$435$	−3.73365e6	+	1.85395e6i	−0.946043	+	0.469758i
$436$	−674369.	−	489958.i	−0.169895	−	0.123436i
$437$	7.55040e6	−	5.48569e6i	1.89133	−	1.37413i
$438$	996994.	−	724359.i	0.248317	−	0.180413i
$439$	−3.19466e6	−	2.32106e6i	−0.791158	−	0.574810i	0.117149	−	0.993114i	$-0.462625\pi$
$439$	−3.19466e6	−	2.32106e6i	−0.791158	−	0.574810i	−0.908307	+	0.418304i	$0.862625\pi$
$440$	−1.06997e6	+	531295.i	−0.263475	+	0.130829i
$441$	877978.	−	637888.i	0.214975	−	0.156188i
$442$	167887.	−	516702.i	0.0408752	−	0.125801i
$443$	−5.49581e6			−1.33052			−0.665262	−	0.746610i	$-0.731680\pi$
$443$	−5.49581e6			−1.33052			−0.665262	+	0.746610i	$0.731680\pi$
$444$	526274.	−	1.61970e6i	0.126693	−	0.389922i
$445$	−422084.	−	430916.i	−0.101041	−	0.103156i
$446$	−1.17118e6	−	3.60451e6i	−0.278795	−	0.858044i
$447$	−703651.	−	2.16562e6i	−0.166567	−	0.512640i
$448$	−193477.	−	140569.i	−0.0455443	−	0.0330899i
$449$	−3.68524e6			−0.862681			−0.431340	−	0.902189i	$-0.641959\pi$
$449$	−3.68524e6			−0.862681			−0.431340	+	0.902189i	$0.641959\pi$
$450$	956259.	+	332753.i	0.222610	+	0.0774623i
$451$	−6.41249e6			−1.48452
$452$	2.25801e6	+	1.64054e6i	0.519851	+	0.377694i
$453$	−1.13273e6	−	3.48617e6i	−0.259346	−	0.798184i
$454$	−935447.	−	2.87901e6i	−0.213000	−	0.655547i
$455$	−832792.	+	413524.i	−0.188585	+	0.0936423i
$456$	−510661.	+	1.57165e6i	−0.115006	+	0.353952i
$457$	3.60911e6			0.808368			0.404184	−	0.914678i	$-0.367555\pi$
$457$	3.60911e6			0.808368			0.404184	+	0.914678i	$0.367555\pi$
$458$	−1.41637e6	+	4.35915e6i	−0.315511	+	0.971043i
$459$	281191.	−	204297.i	0.0622974	−	0.0452617i
$460$	−1.34769e6	+	2.57863e6i	−0.296958	+	0.568192i
$461$	4.55048e6	+	3.30611e6i	0.997251	+	0.724545i	0.961497	−	0.274815i	$-0.0886167\pi$
$461$	4.55048e6	+	3.30611e6i	0.997251	+	0.724545i	0.0357542	+	0.999361i	$0.488617\pi$
$462$	567801.	−	412531.i	0.123763	−	0.0899191i
$463$	−6.10811e6	+	4.43780e6i	−1.32420	+	0.962089i	−0.324332	+	0.945943i	$0.605139\pi$
$463$	−6.10811e6	+	4.43780e6i	−1.32420	+	0.962089i	−0.999870	+	0.0161453i	$0.994861\pi$
$464$	1.71602e6	+	1.24676e6i	0.370021	+	0.268836i
$465$	−5.16297e6	−	872626.i	−1.10730	−	0.187153i
$466$	−1.48061e6	+	1.07572e6i	−0.315845	+	0.229475i
$467$	−194217.	+	597737.i	−0.0412092	+	0.126829i	−0.969545	−	0.244915i	$-0.921240\pi$
$467$	−194217.	+	597737.i	−0.0412092	+	0.126829i	0.928335	+	0.371744i	$0.121240\pi$
$468$	−369200.			−0.0779197
$469$	151116.	−	465088.i	0.0317234	−	0.0976345i
$470$	2.83211e6	−	5.41887e6i	0.591378	−	1.13152i
$471$	339838.	+	1.04592e6i	0.0705863	+	0.217242i
$472$	799587.	+	2.46088e6i	0.165200	+	0.508434i
$473$	−126488.	−	91899.0i	−0.0259954	−	0.0188868i
$474$	2.25332e6			0.460655
$475$	−5.41890e6	+	7.14262e6i	−1.10199	+	1.45252i
$476$	−445398.			−0.0901014
$477$	−804443.	−	584462.i	−0.161882	−	0.117614i
$478$	647820.	+	1.99378e6i	0.129683	+	0.399124i
$479$	1.58739e6	+	4.88550e6i	0.316116	+	0.972904i	0.975293	+	0.220916i	$0.0709048\pi$
$479$	1.58739e6	+	4.88550e6i	0.316116	+	0.972904i	−0.659177	+	0.751988i	$0.729095\pi$
$480$	−75320.4	−	509654.i	−0.0149214	−	0.100965i
$481$	−1.04113e6	+	3.20428e6i	−0.205184	+	0.631491i
$482$	225288.			0.0441694
$483$	528228.	−	1.62572e6i	0.103028	−	0.317086i
$484$	641492.	−	466071.i	0.124474	−	0.0904354i
$485$	−470989.	−	3.18694e6i	−0.0909194	−	0.615205i
$486$	−191087.	−	138833.i	−0.0366978	−	0.0266625i
$487$	3.10773e6	−	2.25790e6i	0.593774	−	0.431402i	−0.249890	−	0.968274i	$-0.580394\pi$
$487$	3.10773e6	−	2.25790e6i	0.593774	−	0.431402i	0.843664	+	0.536872i	$0.180394\pi$
$488$	−1.22210e6	+	887909.i	−0.232305	+	0.168779i
$489$	3.58611e6	+	2.60546e6i	0.678191	+	0.492734i
$490$	−2.09637e6	−	2.14023e6i	−0.394436	−	0.402690i
$491$	−2.36818e6	+	1.72059e6i	−0.443314	+	0.322087i	−0.786950	−	0.617016i	$-0.788341\pi$
$491$	−2.36818e6	+	1.72059e6i	−0.443314	+	0.322087i	0.343636	+	0.939103i	$0.388341\pi$
$492$	854570.	−	2.63009e6i	0.159160	−	0.489845i
$493$	3.95039e6			0.732020
$494$	1.01025e6	−	3.10922e6i	0.186256	−	0.573236i
$495$	1.49079e6	+	251969.i	0.273467	+	0.0462204i
$496$	823323.	+	2.53393e6i	0.150268	+	0.462477i
$497$	−1.27669e6	−	3.92924e6i	−0.231843	−	0.713538i
$498$	−739154.	−	537027.i	−0.133555	−	0.0970337i
$499$	2.81056e6			0.505291			0.252645	−	0.967559i	$-0.418699\pi$
$499$	2.81056e6			0.505291			0.252645	+	0.967559i	$0.418699\pi$
$500$	522779.	−	2.74576e6i	0.0935175	−	0.491177i
$501$	−5.45794e6			−0.971482
$502$	457480.	+	332378.i	0.0810238	+	0.0588672i
$503$	−505917.	−	1.55705e6i	−0.0891577	−	0.274399i	0.896529	−	0.442984i	$-0.146080\pi$
$503$	−505917.	−	1.55705e6i	−0.0891577	−	0.274399i	−0.985687	+	0.168585i	$0.946080\pi$
$504$	93531.8	+	287861.i	0.0164015	+	0.0504786i
$505$	1.89885e6	+	320937.i	0.331332	+	0.0560005i
$506$	−1.34261e6	+	4.13214e6i	−0.233117	+	0.717461i
$507$	−2.61124e6			−0.451157
$508$	−270479.	+	832448.i	−0.0465022	+	0.143119i
$509$	−435910.	+	316707.i	−0.0745766	+	0.0541831i	−0.624449	−	0.781066i	$-0.714676\pi$
$509$	−435910.	+	316707.i	−0.0745766	+	0.0541831i	0.549872	+	0.835249i	$0.314676\pi$
$510$	−671406.	−	685457.i	−0.114304	−	0.116696i
$511$	1.61697e6	+	1.17480e6i	0.273936	+	0.199026i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	1.69205e6	−	1.22935e6i	0.283870	−	0.206244i
$514$	3.50004e6	+	2.54293e6i	0.584339	+	0.424547i
$515$	−192021.	−	1.29931e6i	−0.0319030	−	0.215871i
$516$	54549.2	−	39632.3i	0.00901912	−	0.00655277i
$517$	2.82143e6	−	8.68348e6i	0.464241	−	1.42879i
$518$	2.76209e6			0.452287
$519$	−421950.	+	1.29863e6i	−0.0687611	+	0.211625i
$520$	149007.	+	1.00825e6i	0.0241657	+	0.163517i
$521$	2.83028e6	+	8.71069e6i	0.456809	+	1.40591i	0.868999	+	0.494815i	$0.164764\pi$
$521$	2.83028e6	+	8.71069e6i	0.456809	+	1.40591i	−0.412190	+	0.911098i	$0.635236\pi$
$522$	−829566.	−	2.55314e6i	−0.133252	−	0.410108i
$523$	6.94532e6	+	5.04607e6i	1.11029	+	0.806676i	0.982710	−	0.185152i	$-0.0592777\pi$
$523$	6.94532e6	+	5.04607e6i	1.11029	+	0.806676i	0.127584	+	0.991828i	$0.459278\pi$
$524$	−953609.			−0.151720
$525$	−34004.1	+	1.64177e6i	−0.00538435	+	0.259964i
$526$	3.91468e6			0.616924
$527$	4.01442e6	+	2.91664e6i	0.629645	+	0.457464i
$528$	−237733.	−	731666.i	−0.0371111	−	0.114216i
$529$	1.28109e6	+	3.94277e6i	0.199039	+	0.612580i
$530$	−1.27145e6	+	2.43275e6i	−0.196612	+	0.376191i
$531$	1.01198e6	−	3.11455e6i	0.155752	−	0.479356i
$532$	−2.68015e6			−0.410564
$533$	−1.69060e6	+	5.20314e6i	−0.257765	+	0.793319i
$534$	314262.	−	228325.i	0.0476913	−	0.0346498i
$535$	5.78833e6	+	978324.i	0.874318	+	0.147774i
$536$	−433666.	−	315077.i	−0.0651993	−	0.0473701i
$537$	−273182.	+	198479.i	−0.0408806	+	0.0297015i
$538$	4.01050e6	−	2.91380e6i	0.597369	−	0.434014i
$539$	−3.61928e6	−	2.62956e6i	−0.536600	−	0.389862i
$540$	−302018.	+	577873.i	−0.0445707	+	0.0852802i
$541$	4.93369e6	−	3.58454e6i	0.724734	−	0.526550i	−0.163159	−	0.986600i	$-0.552168\pi$
$541$	4.93369e6	−	3.58454e6i	0.724734	−	0.526550i	0.887893	+	0.460050i	$0.152168\pi$
$542$	−795625.	+	2.44868e6i	−0.116335	+	0.358042i
$543$	2.93567e6			0.427276
$544$	−150869.	+	464326.i	−0.0218576	+	0.0672707i
$545$	2.60848e6	−	1.29524e6i	0.376181	−	0.186793i
$546$	−185035.	−	569479.i	−0.0265627	−	0.0817516i
$547$	−2.97551e6	−	9.15767e6i	−0.425200	−	1.30863i	−0.902803	−	0.430054i	$-0.858494\pi$
$547$	−2.97551e6	−	9.15767e6i	−0.425200	−	1.30863i	0.477604	−	0.878575i	$-0.341506\pi$
$548$	5.05217e6	+	3.67062e6i	0.718666	+	0.522141i
$549$	1.91185e6			0.270722
$550$	86429.3	−	4.17293e6i	0.0121830	−	0.588212i
$551$	2.37712e7			3.33559
$552$	−1.51588e6	−	1.10135e6i	−0.211747	−	0.153843i
$553$	1.12931e6	+	3.47566e6i	0.157037	+	0.483309i
$554$	−1.29451e6	−	3.98408e6i	−0.179197	−	0.551510i
$555$	4.16366e6	+	4.25079e6i	0.573777	+	0.585784i
$556$	24200.1	−	74480.3i	0.00331994	−	0.0102177i
$557$	6.67560e6			0.911700			0.455850	−	0.890057i	$-0.349335\pi$
$557$	6.67560e6			0.911700			0.455850	+	0.890057i	$0.349335\pi$
$558$	1.04202e6	−	3.20700e6i	0.141674	−	0.436027i
$559$	−107915.	+	78405.0i	−0.0146067	+	0.0106124i
$560$	748376.	−	371607.i	0.100844	−	0.0500741i
$561$	−1.15915e6	−	842174.i	−0.155501	−	0.112978i
$562$	−1.76968e6	+	1.28575e6i	−0.236349	+	0.171718i
$563$	−749179.	+	544311.i	−0.0996127	+	0.0723729i	−0.636477	−	0.771296i	$-0.719609\pi$
$563$	−749179.	+	544311.i	−0.0996127	+	0.0723729i	0.536864	+	0.843669i	$0.319609\pi$
$564$	3.18554e6	+	2.31443e6i	0.421683	+	0.306371i
$565$	−8.73405e6	+	4.33690e6i	−1.15105	+	0.571555i
$566$	−3.03107e6	+	2.20220e6i	−0.397700	+	0.288946i
$567$	118376.	−	364324.i	0.0154635	−	0.0475916i
$568$	−4.52866e6			−0.588978
$569$	4.20349e6	−	1.29370e7i	0.544289	−	1.67515i	−0.178386	−	0.983961i	$-0.557088\pi$
$569$	4.20349e6	−	1.29370e7i	0.544289	−	1.67515i	0.722675	−	0.691188i	$-0.242912\pi$
$570$	−4.04014e6	−	4.12469e6i	−0.520846	−	0.531746i
$571$	3.30144e6	+	1.01608e7i	0.423753	+	1.30418i	0.904183	+	0.427146i	$0.140481\pi$
$571$	3.30144e6	+	1.01608e7i	0.423753	+	1.30418i	−0.480429	+	0.877033i	$0.659519\pi$
$572$	470309.	+	1.44746e6i	0.0601026	+	0.184977i
$573$	5391.04	+	3916.82i	0.000685940	+	0.000498365i
$574$	4.48512e6			0.568192
$575$	−5.80363e6	−	8.34614e6i	−0.732031	−	1.05273i
$576$	331776.			0.0416667
$577$	216767.	+	157490.i	0.0271053	+	0.0196931i	0.601255	−	0.799057i	$-0.294667\pi$
$577$	216767.	+	157490.i	0.0271053	+	0.0196931i	−0.574150	+	0.818750i	$0.694667\pi$
$578$	−1.47406e6	−	4.53669e6i	−0.183525	−	0.564832i
$579$	−2.34612e6	−	7.22062e6i	−0.290840	−	0.895114i
$580$	−6.63761e6	+	3.29591e6i	−0.819297	+	0.406823i
$581$	457898.	−	1.40927e6i	0.0562767	−	0.173202i
$582$	2.07464e6			0.253884
$583$	−1.26666e6	+	3.89837e6i	−0.154343	+	0.475020i
$584$	1.77243e6	−	1.28775e6i	0.215049	−	0.156242i
$585$	597486.	−	1.14321e6i	0.0721835	−	0.138114i
$586$	−3.12993e6	−	2.27403e6i	−0.376522	−	0.273560i
$587$	3.95407e6	−	2.87280e6i	0.473640	−	0.344120i	−0.325218	−	0.945639i	$-0.605438\pi$
$587$	3.95407e6	−	2.87280e6i	0.473640	−	0.344120i	0.798858	+	0.601519i	$0.205438\pi$
$588$	1.56085e6	−	1.13402e6i	0.186173	−	0.135263i
$589$	2.41565e7	+	1.75507e7i	2.86910	+	2.08452i
$590$	−8.91399e6	−	1.50661e6i	−1.05425	−	0.178185i
$591$	−3.51055e6	+	2.55057e6i	−0.413435	+	0.300378i
$592$	935597.	−	2.87947e6i	0.109720	−	0.337683i
$593$	−5.57503e6			−0.651044			−0.325522	−	0.945534i	$-0.605540\pi$
$593$	−5.57503e6			−0.651044			−0.325522	+	0.945534i	$0.605540\pi$
$594$	−300880.	+	926014.i	−0.0349887	+	0.107684i
$595$	720800.	−	1.37916e6i	0.0834684	−	0.159706i
$596$	−1.25094e6	−	3.84999e6i	−0.144251	−	0.443960i
$597$	−2.34528e6	−	7.21803e6i	−0.269314	−	0.828863i
$598$	2.99888e6	+	2.17881e6i	0.342930	+	0.249153i
$599$	−9.54969e6			−1.08748			−0.543741	−	0.839253i	$-0.682993\pi$
$599$	−9.54969e6			−1.08748			−0.543741	+	0.839253i	$0.682993\pi$
$600$	1.70002e6	+	591560.i	0.192786	+	0.0670843i
$601$	2.77784e6			0.313705			0.156852	−	0.987622i	$-0.449865\pi$
$601$	2.77784e6			0.313705			0.156852	+	0.987622i	$0.449865\pi$
$602$	88470.3	+	64277.5i	0.00994962	+	0.00722882i
$603$	209645.	+	645221.i	0.0234796	+	0.0722629i
$604$	−2.01373e6	−	6.19764e6i	−0.224600	−	0.691248i
$605$	405027.	+	2.74061e6i	0.0449878	+	0.304410i
$606$	−383237.	+	1.17948e6i	−0.0423922	+	0.130470i
$607$	4.90440e6			0.540275			0.270137	−	0.962822i	$-0.412931\pi$
$607$	4.90440e6			0.540275			0.270137	+	0.962822i	$0.412931\pi$
$608$	−907842.	+	2.79405e6i	−0.0995982	+	0.306532i
$609$	3.52238e6	−	2.55916e6i	0.384851	−	0.279610i
$610$	−771614.	−	5.22111e6i	−0.0839605	−	0.568118i
$611$	−6.30200e6	−	4.57867e6i	−0.682928	−	0.496176i
$612$	499896.	−	363196.i	0.0539512	−	0.0391978i
$613$	−1.25070e7	+	9.08684e6i	−1.34431	+	0.976701i	−0.345040	+	0.938588i	$0.612135\pi$
$613$	−1.25070e7	+	9.08684e6i	−1.34431	+	0.976701i	−0.999273	+	0.0381126i	$0.987865\pi$
$614$	1.99557e6	+	1.44987e6i	0.213622	+	0.155205i
$615$	6.76101e6	+	6.90249e6i	0.720815	+	0.735899i
$616$	1.00942e6	−	733389.i	0.107182	−	0.0778722i
$617$	−3562.58	+	10964.5i	−0.000376749	+	0.00115951i	−0.951245	−	0.308437i	$-0.900194\pi$
$617$	−3562.58	+	10964.5i	−0.000376749	+	0.00115951i	0.950868	+	0.309597i	$0.100194\pi$
$618$	845828.			0.0890863
$619$	−1.34646e6	+	4.14397e6i	−0.141243	+	0.434701i	−0.996509	−	0.0834887i	$-0.973394\pi$
$619$	−1.34646e6	+	4.14397e6i	−0.141243	+	0.434701i	0.855266	+	0.518189i	$0.173394\pi$
$620$	−9.17861e6	−	1.55134e6i	−0.958953	−	0.162079i
$621$	732815.	+	2.25537e6i	0.0762545	+	0.234687i
$622$	−1.91143e6	−	5.88276e6i	−0.198099	−	0.609685i
$623$	509685.	+	370308.i	0.0526116	+	0.0382246i
$624$	−656356.			−0.0674804
$625$	7.65611e6	+	6.06230e6i	0.783985	+	0.620779i
$626$	−1.10913e6			−0.113122
$627$	−6.97513e6	−	5.06773e6i	−0.708571	−	0.514807i
$628$	604157.	+	1.85941e6i	0.0611295	+	0.188137i
$629$	−1.74247e6	−	5.36278e6i	−0.175606	−	0.540459i
$630$	−1.04272e6	−	176236.i	−0.104668	−	0.0176906i
$631$	−2.90692e6	+	8.94659e6i	−0.290643	+	0.894508i	0.694007	+	0.719968i	$0.255844\pi$
$631$	−2.90692e6	+	8.94659e6i	−0.290643	+	0.894508i	−0.984650	+	0.174540i	$0.944156\pi$
$632$	4.00589e6			0.398939
$633$	−751684.	+	2.31345e6i	−0.0745635	+	0.229483i
$634$	3.77488e6	−	2.74261e6i	0.372975	−	0.270982i
$635$	−2.13992e6	−	2.18470e6i	−0.210602	−	0.215009i
$636$	−1.43012e6	−	1.03904e6i	−0.140194	−	0.101857i
$637$	−3.08784e6	+	2.24345e6i	−0.301513	+	0.219062i
$638$	−8.95293e6	+	6.50468e6i	−0.870790	+	0.632666i
$639$	4.63695e6	+	3.36894e6i	0.449242	+	0.326394i
$640$	−133903.	−	906052.i	−0.0129223	−	0.0874386i
$641$	1.38841e7	−	1.00874e7i	1.33467	−	0.969692i	0.335045	−	0.942202i	$-0.391249\pi$
$641$	1.38841e7	−	1.00874e7i	1.33467	−	0.969692i	0.999622	−	0.0274899i	$-0.00875142\pi$
$642$	−1.16823e6	+	3.59545e6i	−0.111864	+	0.344283i
$643$	1.14738e7			1.09441			0.547203	−	0.837000i	$-0.315693\pi$
$643$	1.14738e7			1.09441			0.547203	+	0.837000i	$0.315693\pi$
$644$	939071.	−	2.89016e6i	0.0892245	−	0.274605i
$645$	34441.4	+	233047.i	0.00325973	+	0.0220569i
$646$	1.69078e6	+	5.20369e6i	0.159406	+	0.490603i
$647$	−3.62423e6	−	1.11542e7i	−0.340373	−	1.04756i	−0.964015	−	0.265849i	$-0.914348\pi$
$647$	−3.62423e6	−	1.11542e7i	−0.340373	−	1.04756i	0.623642	−	0.781710i	$-0.285652\pi$
$648$	−339709.	−	246813.i	−0.0317812	−	0.0230904i
$649$	−1.34998e7			−1.25810
$650$	−3.36316e6	−	1.17029e6i	−0.312222	−	0.108645i
$651$	5.46893e6			0.505766
$652$	6.37531e6	+	4.63193e6i	0.587330	+	0.426720i
$653$	1.49820e6	+	4.61100e6i	0.137495	+	0.423167i	0.995970	−	0.0896893i	$-0.0285874\pi$
$653$	1.49820e6	+	4.61100e6i	0.137495	+	0.423167i	−0.858475	+	0.512856i	$0.828587\pi$
$654$	579569.	+	1.78373e6i	0.0529859	+	0.163074i
$655$	1.54325e6	−	2.95281e6i	0.140551	−	0.268926i
$656$	1.51923e6	−	4.67572e6i	0.137837	−	0.424218i
$657$	−2.77279e6			−0.250613
$658$	−1.97341e6	+	6.07354e6i	−0.177686	+	0.546861i
$659$	1.10458e6	−	802523.i	0.0990793	−	0.0719853i	−0.537143	−	0.843491i	$-0.680496\pi$
$659$	1.10458e6	−	802523.i	0.0990793	−	0.0719853i	0.636222	+	0.771506i	$0.280496\pi$
$660$	2.65030e6	+	447945.i	0.236829	+	0.0400280i
$661$	5.96189e6	+	4.33157e6i	0.530739	+	0.385604i	0.820634	−	0.571454i	$-0.193621\pi$
$661$	5.96189e6	+	4.33157e6i	0.530739	+	0.385604i	−0.289895	+	0.957058i	$0.593621\pi$
$662$	−6.36145e6	+	4.62186e6i	−0.564172	+	0.409895i
$663$	−988949.	+	718513.i	−0.0873756	+	0.0634821i
$664$	−1.31405e6	−	954714.i	−0.115662	−	0.0840336i
$665$	4.33736e6	−	8.29899e6i	0.380340	−	0.727731i
$666$	−3.10005e6	+	2.25232e6i	−0.270822	+	0.196764i
$667$	−8.32895e6	+	2.56339e7i	−0.724896	+	2.23100i
$668$	−9.70301e6			−0.841328
$669$	−2.63515e6	+	8.11016e6i	−0.227636	+	0.700590i
$670$	1.67743e6	−	832931.i	0.144364	−	0.0716840i
$671$	−2.43543e6	−	7.49549e6i	−0.208819	−	0.642678i
$672$	166279.	+	511753.i	0.0142041	+	0.0437157i
$673$	−3.48287e6	−	2.53045e6i	−0.296415	−	0.215358i	0.429631	−	0.903005i	$-0.358644\pi$
$673$	−3.48287e6	−	2.53045e6i	−0.296415	−	0.215358i	−0.726045	+	0.687647i	$0.758644\pi$
$674$	−4.69177e6			−0.397820
$675$	−1.30060e6	−	1.87037e6i	−0.109871	−	0.158004i
$676$	−4.64221e6			−0.390713
$677$	1.96644e6	+	1.42870e6i	0.164895	+	0.119803i	0.667173	−	0.744903i	$-0.267504\pi$
$677$	1.96644e6	+	1.42870e6i	0.164895	+	0.119803i	−0.502277	+	0.864707i	$0.667504\pi$
$678$	−1.94058e6	−	5.97250e6i	−0.162128	−	0.498979i
$679$	1.03976e6	+	3.20007e6i	0.0865487	+	0.266369i
$680$	−1.19361e6	−	1.21859e6i	−0.0989899	−	0.101061i
$681$	−2.10476e6	+	6.47777e6i	−0.173914	+	0.535252i
$682$	−1.39005e7			−1.14438
$683$	−3.07562e6	+	9.46580e6i	−0.252279	+	0.776436i	0.742074	+	0.670318i	$0.233842\pi$
$683$	−3.07562e6	+	9.46580e6i	−0.252279	+	0.776436i	−0.994354	+	0.106118i	$0.966158\pi$
$684$	3.00809e6	−	2.18550e6i	0.245839	−	0.178612i
$685$	−1.95420e7	+	9.70358e6i	−1.59126	+	0.790143i
$686$	5.70701e6	+	4.14639e6i	0.463019	+	0.336403i
$687$	8.34326e6	−	6.06173e6i	0.674441	−	0.490010i
$688$	96976.3	−	70457.4i	0.00781078	−	0.00567487i
$689$	2.82922e6	+	2.05555e6i	0.227049	+	0.164961i
$690$	5.86347e6	−	2.91151e6i	0.468848	−	0.232807i
$691$	−1.14357e7	+	8.30855e6i	−0.911106	+	0.661957i	−0.941294	−	0.337587i	$-0.890389\pi$
$691$	−1.14357e7	+	8.30855e6i	−0.911106	+	0.661957i	0.0301884	+	0.999544i	$0.490389\pi$
$692$	−750133.	+	2.30867e6i	−0.0595488	+	0.183272i
$693$	−1.57914e6			−0.124907
$694$	4.12133e6	−	1.26842e7i	0.324817	−	0.999684i
$695$	191462.	+	195468.i	0.0150356	+	0.0153502i
$696$	−1.47478e6	−	4.53892e6i	−0.115400	−	0.355164i
$697$	−2.82945e6	−	8.70815e6i	−0.220607	−	0.678959i
$698$	170713.	+	124030.i	0.0132626	+	0.00963583i
$699$	4.11779e6			0.318765
$700$	−60451.7	+	2.91870e6i	−0.00466298	+	0.225135i
$701$	−1.38250e7			−1.06260			−0.531300	−	0.847184i	$-0.678296\pi$
$701$	−1.38250e7			−1.06260			−0.531300	+	0.847184i	$0.678296\pi$
$702$	672051.	+	488273.i	0.0514706	+	0.0373956i
$703$	−1.04852e7	−	3.22701e7i	−0.800182	−	2.46271i
$704$	−422636.	−	1.30074e6i	−0.0321392	−	0.0989142i
$705$	−1.23218e7	+	6.11840e6i	−0.933687	+	0.463623i
$706$	−184332.	+	567314.i	−0.0139184	+	0.0428363i
$707$	−2.01138e6			−0.151337
$708$	1.79907e6	−	5.53697e6i	0.134885	−	0.415135i
$709$	−2.77941e6	+	2.01936e6i	−0.207652	+	0.150868i	−0.686751	−	0.726893i	$-0.740964\pi$
$709$	−2.77941e6	+	2.01936e6i	−0.207652	+	0.150868i	0.479099	+	0.877761i	$0.340964\pi$
$710$	7.32885e6	−	1.40228e7i	0.545620	−	1.04397i
$711$	−4.10168e6	−	2.98005e6i	−0.304290	−	0.221080i
$712$	558689.	−	405911.i	0.0413019	−	0.0300076i
$713$	−2.73899e7	+	1.98999e7i	−2.01774	+	1.46598i
$714$	810754.	+	589047.i	0.0595173	+	0.0432419i
$715$	−5.24312e6	−	886173.i	−0.383552	−	0.0648266i
$716$	−485658.	+	352851.i	−0.0354036	+	0.0257222i
$717$	1.45759e6	−	4.48601e6i	0.105886	−	0.325884i
$718$	1.14876e7			0.831610
$719$	3.68221e6	−	1.13327e7i	0.265636	−	0.817543i	−0.725910	−	0.687789i	$-0.758581\pi$
$719$	3.68221e6	−	1.13327e7i	0.265636	−	0.817543i	0.991546	−	0.129754i	$-0.0414187\pi$
$720$	−536922.	+	1.02733e6i	−0.0385993	+	0.0738548i
$721$	423910.	+	1.30466e6i	0.0303694	+	0.0934673i
$722$	7.11353e6	+	2.18932e7i	0.507858	+	1.56303i
$723$	−410090.	−	297948.i	−0.0291765	−	0.0211980i
$724$	5.21898e6			0.370032
$725$	536168.	−	2.58869e7i	0.0378840	−	1.82909i
$726$	−1.78409e6			−0.125624
$727$	−9.48129e6	−	6.88856e6i	−0.665321	−	0.483384i	0.203135	−	0.979151i	$-0.434887\pi$
$727$	−9.48129e6	−	6.88856e6i	−0.665321	−	0.483384i	−0.868456	+	0.495767i	$0.834887\pi$
$728$	−328951.	−	1.01241e6i	−0.0230040	−	0.0707989i
$729$	164224.	+	505430.i	0.0114451	+	0.0352243i
$730$	1.11908e6	+	7.57226e6i	0.0777241	+	0.525919i
$731$	68987.0	−	212320.i	0.00477501	−	0.0146960i
$732$	3.39885e6			0.234452
$733$	4.34358e6	−	1.33682e7i	0.298599	−	0.918993i	−0.683390	−	0.730054i	$-0.739495\pi$
$733$	4.34358e6	−	1.33682e7i	0.298599	−	0.918993i	0.981989	−	0.188939i	$-0.0605050\pi$
$734$	−3.82524e6	+	2.77920e6i	−0.262071	+	0.190406i
$735$	985493.	+	6.66832e6i	0.0672876	+	0.455301i
$736$	−2.69490e6	−	1.95796e6i	−0.183378	−	0.133232i
$737$	2.26255e6	−	1.64384e6i	0.153437	−	0.111479i
$738$	−5.03391e6	+	3.65735e6i	−0.340224	+	0.247187i
$739$	8.23902e6	+	5.98600e6i	0.554964	+	0.403205i	0.829612	−	0.558340i	$-0.188561\pi$
$739$	8.23902e6	+	5.98600e6i	0.554964	+	0.403205i	−0.274648	+	0.961545i	$0.588561\pi$
$740$	7.40206e6	+	7.55696e6i	0.496905	+	0.507304i
$741$	−5.95093e6	+	4.32361e6i	−0.398143	+	0.289268i
$742$	885945.	−	2.72666e6i	0.0590741	−	0.181811i
$743$	−7.29801e6			−0.484989			−0.242495	−	0.970153i	$-0.577966\pi$
$743$	−7.29801e6			−0.484989			−0.242495	+	0.970153i	$0.577966\pi$
$744$	1.85248e6	−	5.70134e6i	0.122693	−	0.377611i
$745$	1.39457e7	+	2.35706e6i	0.920557	+	0.155589i
$746$	4.17613e6	+	1.28528e7i	0.274744	+	0.845574i
$747$	635246.	+	1.95509e6i	0.0416525	+	0.128193i
$748$	−2.06072e6	−	1.49720e6i	−0.134668	−	0.0978420i
$749$	−6.13136e6			−0.399349
$750$	−4.58292e6	+	4.30669e6i	−0.297502	+	0.279570i
$751$	−1.18519e7			−0.766808			−0.383404	−	0.923581i	$-0.625248\pi$
$751$	−1.18519e7			−0.766808			−0.383404	+	0.923581i	$0.625248\pi$
$752$	5.66319e6	+	4.11455e6i	0.365188	+	0.265325i
$753$	−393169.	−	1.21005e6i	−0.0252692	−	0.0777706i
$754$	2.91758e6	+	8.97939e6i	0.186894	+	0.575199i
$755$	2.24496e7	+	3.79435e6i	1.43331	+	0.242254i
$756$	210447.	−	647688.i	0.0133917	−	0.0412156i
$757$	−2.01694e7			−1.27925			−0.639623	−	0.768689i	$-0.720909\pi$
$757$	−2.01694e7			−1.27925			−0.639623	+	0.768689i	$0.720909\pi$
$758$	3.00162e6	−	9.23803e6i	0.189750	−	0.583991i
$759$	7.90876e6	−	5.74605e6i	0.498315	−	0.362047i
$760$	−7.18248e6	−	7.33278e6i	−0.451066	−	0.460505i
$761$	1.08834e7	+	7.90727e6i	0.681246	+	0.494954i	0.873771	−	0.486338i	$-0.161668\pi$
$761$	1.08834e7	+	7.90727e6i	0.681246	+	0.494954i	−0.192525	+	0.981292i	$0.561668\pi$
$762$	1.59327e6	−	1.15758e6i	0.0994039	−	0.0722211i
$763$	−2.46088e6	+	1.78793e6i	−0.153031	+	0.111183i
$764$	9584.08	+	6963.24i	0.000594042	+	0.000431597i
$765$	315625.	+	2.13567e6i	0.0194993	+	0.131942i
$766$	1.44807e7	−	1.05208e7i	0.891695	−	0.647855i
$767$	−3.55912e6	+	1.09538e7i	−0.218451	+	0.672323i
$768$	589824.			0.0360844
$769$	−2.93351e6	+	9.02842e6i	−0.178884	+	0.550549i	−0.999790	−	0.0205153i	$-0.993469\pi$
$769$	−2.93351e6	+	9.02842e6i	−0.178884	+	0.550549i	0.820905	+	0.571064i	$0.193469\pi$
$770$	637332.	+	4.31250e6i	0.0387382	+	0.262121i
$771$	−3.00802e6	−	9.25772e6i	−0.182240	−	0.560878i
$772$	−4.17089e6	−	1.28367e7i	−0.251875	−	0.775192i
$773$	8.84149e6	+	6.42372e6i	0.532202	+	0.386667i	0.821181	−	0.570668i	$-0.193316\pi$
$773$	8.84149e6	+	6.42372e6i	0.532202	+	0.386667i	−0.288979	+	0.957336i	$0.593316\pi$
$774$	−151710.			−0.00910250
$775$	1.96576e7	−	2.59106e7i	1.17565	−	1.54961i
$776$	3.68825e6			0.219870
$777$	−5.02781e6	−	3.65292e6i	−0.298763	−	0.217064i
$778$	−2.38278e6	−	7.33345e6i	−0.141135	−	0.434369i
$779$	−1.70260e7	−	5.24007e7i	−1.00524	−	3.09381i
$780$	1.06220e6	−	2.03238e6i	0.0625128	−	0.119610i
$781$	7.30124e6	−	2.24709e7i	0.428320	−	1.31823i
$782$	−6.20385e6			−0.362781
$783$	−1.86652e6	+	5.74457e6i	−0.108800	+	0.334852i
$784$	2.77484e6	−	2.01604e6i	0.161231	−	0.117141i
$785$	−6.73529e6	−	1.13838e6i	−0.390106	−	0.0659343i
$786$	1.73584e6	+	1.26116e6i	0.100220	+	0.0728141i
$787$	1.00530e7	−	7.30394e6i	0.578574	−	0.420359i	−0.259635	−	0.965707i	$-0.583602\pi$
$787$	1.00530e7	−	7.30394e6i	0.578574	−	0.420359i	0.838210	+	0.545348i	$0.183602\pi$
$788$	−6.24098e6	+	4.53434e6i	−0.358045	+	0.260135i
$789$	−7.12584e6	−	5.17723e6i	−0.407515	−	0.296077i
$790$	−6.48284e6	+	1.24041e7i	−0.369571	+	0.707126i
$791$	8.23981e6	−	5.98657e6i	0.468248	−	0.340202i
$792$	−534898.	+	1.64625e6i	−0.0303011	+	0.0932572i
$793$	−6.72398e6			−0.379703
$794$	−6.37093e6	+	1.96077e7i	−0.358634	+	1.10376i
$795$	5.53176e6	−	2.74680e6i	0.310417	−	0.154138i
$796$	−4.16939e6	−	1.28321e7i	−0.233233	−	0.717817i
$797$	1.05732e7	+	3.25410e7i	0.589605	+	1.81462i	0.579931	+	0.814665i	$0.303079\pi$
$797$	1.05732e7	+	3.25410e7i	0.589605	+	1.81462i	0.00967403	+	0.999953i	$0.496921\pi$
$798$	4.87865e6	+	3.54455e6i	0.271202	+	0.197040i
$799$	1.30371e7			0.722459
$800$	3.02225e6	+	1.05166e6i	0.166957	+	0.0580967i
$801$	−874012.			−0.0481322
$802$	−4.83575e6	−	3.51337e6i	−0.265477	−	0.192881i
$803$	3.53215e6	+	1.08708e7i	0.193308	+	0.594941i
$804$	372702.	+	1.14706e6i	0.0203340	+	0.0625815i
$805$	7.42955e6	+	7.58502e6i	0.404085	+	0.412541i
$806$	−3.66477e6	+	1.12790e7i	−0.198705	+	0.611552i
$807$	−1.11538e7			−0.602892
$808$	−681310.	+	2.09686e6i	−0.0367127	+	0.112990i
$809$	3.09215e6	−	2.24658e6i	0.166107	−	0.120684i	−0.501626	−	0.865085i	$-0.667265\pi$
$809$	3.09215e6	−	2.24658e6i	0.166107	−	0.120684i	0.667733	+	0.744401i	$0.267265\pi$
$810$	1.31401e6	−	652472.i	0.0703697	−	0.0349421i
$811$	1.57403e7	+	1.14360e7i	0.840353	+	0.610552i	0.922469	−	0.386071i	$-0.126168\pi$
$811$	1.57403e7	+	1.14360e7i	0.840353	+	0.610552i	−0.0821164	+	0.996623i	$0.526168\pi$
$812$	6.26200e6	−	4.54961e6i	0.333291	−	0.242150i
$813$	4.68669e6	−	3.40508e6i	0.248680	−	0.180676i
$814$	1.27793e7	+	9.28473e6i	0.676001	+	0.491143i
$815$	−2.46599e7	+	1.22449e7i	−1.30046	+	0.645745i
$816$	888704.	−	645681.i	0.0467231	−	0.0339463i
$817$	415125.	−	1.27762e6i	0.0217582	−	0.0669649i
$818$	−1.48912e6			−0.0778120
$819$	−416329.	+	1.28133e6i	−0.0216883	+	0.0667499i
$820$	1.20196e7	+	1.22711e7i	0.624244	+	0.637307i
$821$	2.25882e6	+	6.95193e6i	0.116956	+	0.359954i	0.992350	−	0.123456i	$-0.0393978\pi$
$821$	2.25882e6	+	6.95193e6i	0.116956	+	0.359954i	−0.875394	+	0.483411i	$0.839398\pi$
$822$	−4.34196e6	−	1.33632e7i	−0.224133	−	0.689811i
$823$	−5.40339e6	−	3.92579e6i	−0.278078	−	0.202035i	0.440001	−	0.897997i	$-0.354978\pi$
$823$	−5.40339e6	−	3.92579e6i	−0.278078	−	0.202035i	−0.718079	+	0.695962i	$0.754978\pi$
$824$	1.50369e6			0.0771510
$825$	−5.67609e6	+	7.48163e6i	−0.290345	+	0.382702i
$826$	9.44224e6			0.481532
$827$	2.12687e7	+	1.54526e7i	1.08138	+	0.785666i	0.977923	−	0.208968i	$-0.0670104\pi$
$827$	2.12687e7	+	1.54526e7i	1.08138	+	0.785666i	0.103454	+	0.994634i	$0.467010\pi$
$828$	1.30278e6	+	4.00955e6i	0.0660383	+	0.203245i
$829$	−7.52376e6	−	2.31558e7i	−0.380232	−	1.17023i	−0.939880	−	0.341504i	$-0.889064\pi$
$829$	−7.52376e6	−	2.31558e7i	−0.380232	−	1.17023i	0.559648	−	0.828730i	$-0.310936\pi$
$830$	5.08280e6	−	2.52387e6i	0.256099	−	0.127166i
$831$	−2.91264e6	+	8.96418e6i	−0.146313	+	0.450306i
$832$	−1.16685e6			−0.0584398
$833$	1.97397e6	−	6.07525e6i	0.0985661	−	0.303355i
$834$	−142553.	+	103571.i	−0.00709676	+	0.00515610i
$835$	1.57026e7	−	3.00450e7i	0.779393	−	1.49127i
$836$	−1.24002e7	−	9.00929e6i	−0.613640	−	0.445836i
$837$	−6.13809e6	+	4.45958e6i	−0.302844	+	0.220029i
$838$	1.21339e7	−	8.81582e6i	0.596886	−	0.433663i
$839$	9.85997e6	+	7.16369e6i	0.483583	+	0.351343i	0.802711	−	0.596368i	$-0.203390\pi$
$839$	9.85997e6	+	7.16369e6i	0.483583	+	0.351343i	−0.319128	+	0.947711i	$0.603390\pi$
$840$	−1.85372e6	−	313309.i	−0.0906452	−	0.0153205i
$841$	−3.89460e7	+	2.82959e7i	−1.89877	+	1.37954i
$842$	4.04066e6	−	1.24359e7i	0.196414	−	0.604499i
$843$	4.92176e6			0.238535
$844$	−1.33633e6	+	4.11279e6i	−0.0645739	+	0.198738i
$845$	7.51261e6	−	1.43744e7i	0.361951	−	0.692546i
$846$	−2.73773e6	−	8.42587e6i	−0.131512	−	0.404752i
$847$	−894144.	−	2.75189e6i	−0.0428252	−	0.131802i
$848$	−2.54244e6	−	1.84719e6i	−0.121412	−	0.0882108i
$849$	8.42987e6			0.401376
$850$	5.70496e6	−	1.72389e6i	0.270835	−	0.0818395i
$851$	3.84725e7			1.82107
$852$	8.24347e6	+	5.98923e6i	0.389055	+	0.282665i
$853$	−4.98495e6	−	1.53421e7i	−0.234578	−	0.721958i	−0.997177	−	0.0750860i	$-0.976077\pi$
$853$	−4.98495e6	−	1.53421e7i	−0.234578	−	0.721958i	0.762599	−	0.646872i	$-0.223923\pi$
$854$	1.70343e6	+	5.24261e6i	0.0799244	+	0.245982i
$855$	1.89925e6	+	1.28513e7i	0.0888522	+	0.601217i
$856$	−2.07686e6	+	6.39192e6i	−0.0968775	+	0.298158i
$857$	1.77133e7			0.823850			0.411925	−	0.911218i	$-0.364857\pi$
$857$	1.77133e7			0.823850			0.411925	+	0.911218i	$0.364857\pi$
$858$	1.05819e6	−	3.25679e6i	0.0490735	−	0.151033i
$859$	−6.81459e6	+	4.95109e6i	−0.315106	+	0.228938i	−0.734084	−	0.679058i	$-0.762388\pi$
$859$	−6.81459e6	+	4.95109e6i	−0.315106	+	0.228938i	0.418978	+	0.907996i	$0.362388\pi$
$860$	61229.2	+	414306.i	0.00282301	+	0.0191018i
$861$	−8.16422e6	−	5.93165e6i	−0.375324	−	0.272689i
$862$	−2.34403e7	+	1.70304e7i	−1.07447	+	0.780649i
$863$	4.24303e6	−	3.08274e6i	0.193932	−	0.140900i	−0.486582	−	0.873635i	$-0.661757\pi$
$863$	4.24303e6	−	3.08274e6i	0.193932	−	0.140900i	0.680514	+	0.732735i	$0.261757\pi$
$864$	−603928.	−	438779.i	−0.0275233	−	0.0199969i
$865$	−5.93475e6	−	6.05894e6i	−0.269688	−	0.275332i
$866$	−8.21241e6	+	5.96667e6i	−0.372114	+	0.270357i
$867$	−3.31663e6	+	1.02075e7i	−0.149848	+	0.461183i
$868$	9.72254e6			0.438006
$869$	−6.45841e6	+	1.98769e7i	−0.290119	+	0.892895i
$870$	1.64413e7	+	2.77884e6i	0.736439	+	0.124470i
$871$	−737321.	−	2.26924e6i	−0.0329315	−	0.101353i
$872$	1.03034e6	+	3.17107e6i	0.0458872	+	0.141226i
$873$	−3.77645e6	−	2.74375e6i	−0.167706	−	0.121845i
$874$	−3.73312e7			−1.65308
$875$	−8.93979e6	−	4.91059e6i	−0.394736	−	0.216827i
$876$	−4.92941e6			−0.217037
$877$	−7.33851e6	−	5.33174e6i	−0.322188	−	0.234083i	0.414921	−	0.909858i	$-0.363809\pi$
$877$	−7.33851e6	−	5.33174e6i	−0.322188	−	0.234083i	−0.737108	+	0.675775i	$0.763809\pi$
$878$	4.88101e6	+	1.50222e7i	0.213684	+	0.657653i
$879$	2.68994e6	+	8.27877e6i	0.117428	+	0.361405i
$880$	4.71165e6	+	796346.i	0.205100	+	0.0346653i
$881$	2.98115e6	−	9.17504e6i	0.129403	−	0.398261i	−0.865275	−	0.501298i	$-0.832856\pi$
$881$	2.98115e6	−	9.17504e6i	0.129403	−	0.398261i	0.994678	+	0.103037i	$0.0328560\pi$
$882$	−4.34096e6			−0.187895
$883$	8.57440e6	−	2.63893e7i	0.370085	−	1.13901i	−0.576649	−	0.816992i	$-0.695640\pi$
$883$	8.57440e6	−	2.63893e7i	0.370085	−	1.13901i	0.946735	−	0.322014i	$-0.104360\pi$
$884$	−1.75813e6	+	1.27736e6i	−0.0756695	+	0.0549771i
$885$	1.42335e7	+	1.45314e7i	0.610877	+	0.623661i
$886$	1.77848e7	+	1.29214e7i	0.761141	+	0.553002i
$887$	−2.64369e7	+	1.92075e7i	−1.12824	+	0.819713i	−0.985437	−	0.170038i	$-0.945611\pi$
$887$	−2.64369e7	+	1.92075e7i	−1.12824	+	0.819713i	−0.142801	+	0.989751i	$0.545611\pi$
$888$	−5.51121e6	+	4.00413e6i	−0.234539	+	0.170402i
$889$	2.58405e6	+	1.87742e6i	0.109659	+	0.0796722i
$890$	352746.	+	2.38685e6i	0.0149275	+	0.101007i
$891$	1.77236e6	−	1.28769e6i	0.0747924	−	0.0543398i
$892$	−4.68471e6	+	1.44181e7i	−0.197138	+	0.606729i
$893$	7.84498e7			3.29202
$894$	−2.81461e6	+	8.66247e6i	−0.117781	+	0.362491i
$895$	−306636.	−	2.07485e6i	−0.0127957	−	0.0865821i
$896$	295607.	+	909784.i	0.0123011	+	0.0378589i
$897$	−2.57731e6	−	7.93213e6i	−0.106951	−	0.329161i
$898$	1.19257e7	+	8.66452e6i	0.493506	+	0.358553i
$899$	−8.62326e7			−3.55854
$900$	−2.31217e6	−	3.32511e6i	−0.0951511	−	0.136836i
$901$	−5.85288e6			−0.240191
$902$	2.07512e7	+	1.50767e7i	0.849235	+	0.617005i
$903$	−76033.5	−	234007.i	−0.00310303	−	0.00955014i
$904$	−3.44993e6	−	1.06178e7i	−0.140407	−	0.432128i
$905$	−8.44600e6	+	1.61603e7i	−0.342791	+	0.655887i
$906$	−4.53090e6	+	1.39447e7i	−0.183385	+	0.564401i
$907$	3.52064e7			1.42103			0.710515	−	0.703682i	$-0.248462\pi$
$907$	3.52064e7			1.42103			0.710515	+	0.703682i	$0.248462\pi$
$908$	−3.74179e6	+	1.15160e7i	−0.150614	+	0.463542i
$909$	2.25749e6	−	1.64016e6i	0.0906182	−	0.0658380i
$910$	3.66723e6	+	619821.i	0.146803	+	0.0248121i
$911$	−1.43131e7	−	1.03991e7i	−0.571398	−	0.415145i	0.264215	−	0.964464i	$-0.414887\pi$
$911$	−1.43131e7	−	1.03991e7i	−0.571398	−	0.415145i	−0.835613	+	0.549319i	$0.814887\pi$
$912$	5.34771e6	−	3.88534e6i	0.212903	−	0.154683i
$913$	6.85577e6	−	4.98101e6i	0.272194	−	0.197761i
$914$	−1.16793e7	−	8.48552e6i	−0.462436	−	0.335980i
$915$	−5.50045e6	+	1.05244e7i	−0.217193	+	0.415570i
$916$	1.48325e7	−	1.07764e7i	0.584083	−	0.424361i
$917$	−1.07534e6	+	3.30955e6i	−0.0422300	+	0.129971i
$918$	−1.39029e6			−0.0544500
$919$	−5.92179e6	+	1.82254e7i	−0.231294	+	0.711850i	0.766297	+	0.642486i	$0.222097\pi$
$919$	−5.92179e6	+	1.82254e7i	−0.231294	+	0.711850i	−0.997591	+	0.0693639i	$0.977903\pi$
$920$	1.04239e7	−	5.17602e6i	0.406034	−	0.201617i
$921$	−1.71504e6	−	5.27835e6i	−0.0666231	−	0.205045i
$922$	−6.95251e6	−	2.13976e7i	−0.269348	−	0.828969i
$923$	−1.63081e7	−	1.18486e7i	−0.630087	−	0.457785i
$924$	−2.80736e6			−0.108173
$925$	−3.53788e7	+	1.06906e7i	−1.35953	+	0.410815i
$926$	3.02001e7			1.15739
$927$	−1.53965e6	−	1.11862e6i	−0.0588468	−	0.0427547i
$928$	−2.62184e6	−	8.06919e6i	−0.0999392	−	0.307581i
$929$	9.80818e6	+	3.01865e7i	0.372863	+	1.14755i	0.944909	+	0.327332i	$0.106150\pi$
$929$	9.80818e6	+	3.01865e7i	0.372863	+	1.14755i	−0.572046	+	0.820221i	$0.693850\pi$
$930$	1.46560e7	+	1.49627e7i	0.555660	+	0.567288i
$931$	1.18782e7	−	3.65574e7i	0.449135	−	1.38230i
$932$	7.32052e6			0.276059
$933$	−4.30071e6	+	1.32362e7i	−0.161747	+	0.497806i
$934$	2.03386e6	−	1.47769e6i	0.0762877	−	0.0554263i
$935$	7.97092e6	−	3.95797e6i	0.298181	−	0.148062i
$936$	1.19476e6	+	868042.i	0.0445748	+	0.0323855i
$937$	−6.18076e6	+	4.49059e6i	−0.229982	+	0.167091i	−0.696808	−	0.717257i	$-0.745397\pi$
$937$	−6.18076e6	+	4.49059e6i	−0.229982	+	0.167091i	0.466827	+	0.884349i	$0.345397\pi$
$938$	−1.58251e6	+	1.14976e6i	−0.0587273	+	0.0426679i
$939$	2.01893e6	+	1.46684e6i	0.0747235	+	0.0542898i
$940$	−2.19054e7	+	1.08772e7i	−0.808597	+	0.401509i
$941$	−2.16297e7	+	1.57149e7i	−0.796299	+	0.578545i	−0.909826	−	0.414990i	$-0.863785\pi$
$941$	−2.16297e7	+	1.57149e7i	−0.796299	+	0.578545i	0.113527	+	0.993535i	$0.463785\pi$
$942$	1.35935e6	−	4.18366e6i	0.0499120	−	0.153613i
$943$	6.24722e7			2.28775
$944$	3.19835e6	−	9.84350e6i	0.116814	−	0.359517i
$945$	1.66497e6	+	1.69981e6i	0.0606494	+	0.0619185i
$946$	193257.	+	594783.i	0.00702112	+	0.0216088i
$947$	−128801.	−	396409.i	−0.00466708	−	0.0143638i	0.948696	−	0.316190i	$-0.102404\pi$
$947$	−128801.	−	396409.i	−0.00466708	−	0.0143638i	−0.953363	+	0.301826i	$0.902404\pi$
$948$	−7.29188e6	−	5.29786e6i	−0.263523	−	0.191461i
$949$	9.75190e6			0.351499
$950$	3.43292e7	−	1.03734e7i	1.23411	−	0.372917i
$951$	−1.04985e7			−0.376423
$952$	1.44134e6	+	1.04719e6i	0.0515435	+	0.0374485i
$953$	−1.51988e7	−	4.67772e7i	−0.542099	−	1.66841i	−0.727790	−	0.685800i	$-0.759453\pi$
$953$	−1.51988e7	−	4.67772e7i	−0.542099	−	1.66841i	0.185692	−	0.982608i	$-0.440547\pi$
$954$	1.22908e6	+	3.78272e6i	0.0437229	+	0.134565i
$955$	−37071.5	+	18407.9i	−0.00131532	+	0.000653124i
$956$	2.59128e6	−	7.97514e6i	0.0917000	−	0.282224i
$957$	2.48995e7			0.878841
$958$	6.34958e6	−	1.95420e7i	0.223528	−	0.687947i
$959$	1.84361e7	−	1.33946e7i	0.647327	−	0.470311i
$960$	−954527.	+	1.82637e6i	−0.0334280	+	0.0639602i
$961$	−6.44687e7	−	4.68392e7i	−2.25185	−	1.63607i
$962$	1.09029e7	−	7.92140e6i	0.379842	−	0.275972i
$963$	6.88157e6	−	4.99975e6i	0.239123	−	0.173733i
$964$	−729049.	−	529685.i	−0.0252676	−	0.0183580i
$965$	4.64981e7	+	7.85894e6i	1.60737	+	0.271672i
$966$	−5.53167e6	+	4.01899e6i	−0.190728	+	0.138572i
$967$	−2.24750e6	+	6.91710e6i	−0.0772919	+	0.237880i	−0.982236	−	0.187651i	$-0.939913\pi$
$967$	−2.24750e6	+	6.91710e6i	−0.0772919	+	0.237880i	0.904944	+	0.425531i	$0.139913\pi$
$968$	−3.17171e6			−0.108794
$969$	3.80426e6	−	1.17083e7i	0.130155	−	0.400575i
$970$	−5.96879e6	+	1.14205e7i	−0.203684	+	0.389723i
$971$	−5.40003e6	−	1.66196e7i	−0.183801	−	0.565681i	0.816125	−	0.577876i	$-0.196118\pi$
$971$	−5.40003e6	−	1.66196e7i	−0.183801	−	0.565681i	−0.999926	+	0.0121947i	$0.996118\pi$
$972$	291954.	+	898543.i	0.00991172	+	0.0305052i
$973$	−231198.	−	167976.i	−0.00782894	−	0.00568806i
$974$	−1.53655e7			−0.518978
$975$	4.57419e6	+	6.57810e6i	0.154100	+	0.221610i
$976$	6.04240e6			0.203042
$977$	9.01937e6	+	6.55296e6i	0.302301	+	0.219635i	0.728586	−	0.684954i	$-0.240178\pi$
$977$	9.01937e6	+	6.55296e6i	0.302301	+	0.219635i	−0.426285	+	0.904589i	$0.640178\pi$
$978$	−5.47909e6	−	1.68629e7i	−0.183173	−	0.563749i
$979$	1.11337e6	+	3.42659e6i	0.0371263	+	0.114263i
$980$	1.75199e6	+	1.18548e7i	0.0582728	+	0.394302i
$981$	1.30403e6	−	4.01339e6i	0.0432628	−	0.133149i
$982$	1.17089e7			0.387471
$983$	−9.57890e6	+	2.94808e7i	−0.316178	+	0.973097i	0.659088	+	0.752065i	$0.270942\pi$
$983$	−9.57890e6	+	2.94808e7i	−0.316178	+	0.973097i	−0.975267	+	0.221031i	$0.929058\pi$
$984$	−8.94917e6	+	6.50195e6i	−0.294642	+	0.214070i
$985$	−3.94045e6	−	2.66630e7i	−0.129406	−	0.875625i
$986$	−1.27837e7	−	9.28793e6i	−0.418760	−	0.304247i
$987$	1.16245e7	−	8.44572e6i	0.379824	−	0.275959i
$988$	−1.05794e7	+	7.68641e6i	−0.344802	+	0.250514i
$989$	1.23228e6	+	895305.i	0.0400608	+	0.0291059i
$990$	−4.23190e6	−	4.32046e6i	−0.137229	−	0.140101i
$991$	2.74127e7	−	1.99165e7i	0.886681	−	0.644212i	−0.0483292	−	0.998831i	$-0.515390\pi$
$991$	2.74127e7	−	1.99165e7i	0.886681	−	0.644212i	0.935011	+	0.354620i	$0.115390\pi$
$992$	3.29329e6	−	1.01357e7i	0.106255	−	0.327021i
$993$	1.76922e7			0.569387
$994$	−5.10675e6	+	1.57170e7i	−0.163938	+	0.504548i
$995$	4.64813e7	+	7.85611e6i	1.48840	+	0.251565i
$996$	1.12933e6	+	3.47571e6i	0.0360721	+	0.111018i
$997$	1.50648e7	+	4.63646e7i	0.479981	+	1.47723i	0.839120	+	0.543946i	$0.183071\pi$
$997$	1.50648e7	+	4.63646e7i	0.479981	+	1.47723i	−0.359139	+	0.933284i	$0.616929\pi$
$998$	−9.09516e6	−	6.60802e6i	−0.289057	−	0.210012i
$999$	8.62173e6			0.273326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.g.b.91.1	yes	24
25.11	even	5	inner	150.6.g.b.61.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.6.g.b.61.1	✓	24	25.11	even	5	inner
150.6.g.b.91.1	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)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-55.1199 - 9.31618i) q^{5} +(11.1246 - 34.2380i) q^{6} +58.3864 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +O(q^{10})\)	\(q+(-3.23607 - 2.35114i) q^{2} +(2.78115 + 8.55951i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-55.1199 - 9.31618i) q^{5} +(11.1246 - 34.2380i) q^{6} +58.3864 q^{7} +(19.7771 - 60.8676i) q^{8} +(-65.5304 + 47.6106i) q^{9} +(156.468 + 159.743i) q^{10} +(270.135 + 196.265i) q^{11} +(-116.498 + 84.6411i) q^{12} +(230.470 - 167.446i) q^{13} +(-188.942 - 137.275i) q^{14} +(-73.5551 - 497.709i) q^{15} +(-207.108 + 150.473i) q^{16} +(-147.333 + 453.443i) q^{17} +324.000 q^{18} +(-886.565 + 2728.57i) q^{19} +(-130.765 - 884.817i) q^{20} +(162.382 + 499.759i) q^{21} +(-412.730 - 1270.25i) q^{22} +(-2631.73 - 1912.07i) q^{23} +576.000 q^{24} +(2951.42 + 1027.01i) q^{25} -1139.51 q^{26} +(-589.773 - 428.495i) q^{27} +(288.678 + 888.461i) q^{28} +(-2560.39 - 7880.07i) q^{29} +(-932.156 + 1783.56i) q^{30} +(3216.11 - 9898.16i) q^{31} +1024.00 q^{32} +(-928.643 + 2858.07i) q^{33} +(1542.89 - 1120.97i) q^{34} +(-3218.26 - 543.938i) q^{35} +(-1048.49 - 761.770i) q^{36} +(-9568.07 + 6951.61i) q^{37} +(9284.22 - 6745.38i) q^{38} +(2074.23 + 1507.02i) q^{39} +(-1657.17 + 3170.77i) q^{40} +(-15536.8 + 11288.1i) q^{41} +(649.526 - 1999.04i) q^{42} -468.240 q^{43} +(-1650.92 + 5081.01i) q^{44} +(4055.58 - 2013.80i) q^{45} +(4020.93 + 12375.2i) q^{46} +(-8449.79 - 26005.8i) q^{47} +(-1863.98 - 1354.26i) q^{48} -13398.0 q^{49} +(-7136.33 - 10262.7i) q^{50} -4291.01 q^{51} +(3687.52 + 2679.14i) q^{52} +(3793.46 + 11675.1i) q^{53} +(901.094 + 2773.28i) q^{54} +(-13061.4 - 13334.7i) q^{55} +(1154.71 - 3553.84i) q^{56} -25820.8 q^{57} +(-10241.6 + 31520.3i) q^{58} +(-32708.5 + 23764.1i) q^{59} +(7209.92 - 3580.09i) q^{60} +(-19095.3 - 13873.6i) q^{61} +(-33679.5 + 24469.6i) q^{62} +(-3826.08 + 2779.81i) q^{63} +(-3313.73 - 2407.57i) q^{64} +(-14263.5 + 7082.53i) q^{65} +(9724.88 - 7065.54i) q^{66} +(2588.21 - 7965.70i) q^{67} -7628.46 q^{68} +(9047.10 - 27844.1i) q^{69} +(9135.62 + 9326.80i) q^{70} +(-21866.2 - 67297.1i) q^{71} +(1601.94 + 4930.28i) q^{72} +(27694.3 + 20121.1i) q^{73} +47307.1 q^{74} +(-582.397 + 28119.0i) q^{75} -45903.7 q^{76} +(15772.2 + 11459.2i) q^{77} +(-3169.14 - 9753.62i) q^{78} +(19342.0 + 59528.6i) q^{79} +(12817.6 - 6364.61i) q^{80} +(2027.46 - 6239.88i) q^{81} +76817.9 q^{82} +(7842.55 - 24136.9i) q^{83} +(-6801.93 + 4941.89i) q^{84} +(12345.3 - 23621.2i) q^{85} +(1515.26 + 1100.90i) q^{86} +(60328.7 - 43831.3i) q^{87} +(17288.7 - 12561.0i) q^{88} +(8729.51 + 6342.36i) q^{89} +(-17858.9 - 3018.44i) q^{90} +(13456.3 - 9776.59i) q^{91} +(16083.7 - 49500.6i) q^{92} +93667.8 q^{93} +(-33799.2 + 104023. i) q^{94} +(74287.2 - 142139. i) q^{95} +(2847.90 + 8764.94i) q^{96} +(17808.3 + 54808.4i) q^{97} +(43356.9 + 31500.6i) q^{98} -27046.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9	\( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 54 * q^3 - 96 * q^4 + 30 * q^5 - 216 * q^6 - 212 * q^7 - 384 * q^8 - 486 * q^9 - 320 * q^10 + 578 * q^11 - 864 * q^12 + 964 * q^13 + 1312 * q^14 - 1350 * q^15 - 1536 * q^16 + 3318 * q^17 + 7776 * q^18 + 3240 * q^19 - 2400 * q^20 - 1998 * q^21 - 48 * q^22 - 2566 * q^23 + 13824 * q^24 + 16120 * q^25 - 2544 * q^26 - 4374 * q^27 - 3552 * q^28 + 2220 * q^29 + 4320 * q^30 + 12918 * q^31 + 24576 * q^32 - 108 * q^33 - 5968 * q^34 - 17190 * q^35 - 7776 * q^36 + 5738 * q^37 - 3600 * q^38 + 8676 * q^39 + 7680 * q^40 - 18732 * q^41 - 7992 * q^42 - 21176 * q^43 - 192 * q^44 + 6480 * q^45 + 20736 * q^46 + 37488 * q^47 - 13824 * q^48 + 62048 * q^49 + 7880 * q^50 - 32868 * q^51 + 15424 * q^52 + 49414 * q^53 - 17496 * q^54 - 83140 * q^55 - 14208 * q^56 - 42120 * q^57 + 8880 * q^58 - 37280 * q^59 + 11520 * q^60 + 65988 * q^61 - 20008 * q^62 + 26568 * q^63 - 24576 * q^64 - 62940 * q^65 + 20808 * q^66 + 38328 * q^67 - 58432 * q^68 + 46656 * q^69 + 33360 * q^70 + 199868 * q^71 - 31104 * q^72 - 50656 * q^73 + 2912 * q^74 - 82620 * q^75 - 74880 * q^76 - 83224 * q^77 - 23256 * q^78 + 132930 * q^79 + 20480 * q^80 - 39366 * q^81 + 15712 * q^82 - 304696 * q^83 + 47232 * q^84 + 12360 * q^85 + 9256 * q^86 + 93600 * q^87 + 36992 * q^88 - 343880 * q^89 + 9720 * q^90 + 453528 * q^91 + 82944 * q^92 - 142488 * q^93 + 149952 * q^94 + 321730 * q^95 - 55296 * q^96 + 153648 * q^97 + 125152 * q^98 - 91692 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more